MCQ Questions for Class 11 Maths Chapter 14 Mathematical Reasoning with Answers

Mathematical Reasoning Class 11 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 11 Maths Chapter 14 Mathematical Reasoning with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have provided Mathematical Reasoning Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 11 Maths Chapter 14 MCQ With Answers

Maths Class 11 Chapter 14 MCQs On Mathematical Reasoning

Mathematical Reasoning MCQ Question 1.
The connective in the statement 2 + 7 > 9 or 2 + 7 < 9 is
(a) and
(b) or
(c) >
(d) <

Answer

Answer: (b) or
Hint:
Given, statement is 2 + 7 > 9 or 2 + 7 < 9 Here, connective is or. It connects two statement 2 + 7 > 9, 2 + 7 < 9

MCQ On Mathematical Reasoning Class 11 Question 2.
Which of the following is not a negation of the statement A natural number is greater than zero
(a) A natural number is not greater than zero
(b) It is false that a natural number is greater than zero
(c) It is false that a natural number is not greater than zero
(d) None of these

Answer

Answer: (c) It is false that a natural number is not greater than zero
Hint:
Gievn statement is:
A natural number is greater than zero
Negation of the statement:
A natural number is not greater than zero
It is false that a natural number is greater than zero
So, option 3 is not true.

Mathematical Reasoning Class 11 MCQ Question 3.
Which of the following is a statement
(a) x is a real number
(b) Switch of the fan
(c) 6 is a natural number
(d) Let me go

Answer

Answer: (c) 6 is a natural number
Hint:
The statement 6 is a natural number is true.
So, it is a statement.

Mathematical Reasoning Questions With Answers For Class 11 Question 4.
The contra-positive of the statement If a triangle is not equilateral, it is not isosceles is
(a) If a triangle is not equilateral, it is not isosceles
(b) If a triangle is equilateral, it is not isosceles
(c) If a triangle is not equilateral, it is isosceles
(d) If a triangle is equilateral, it is isosceles

Answer

Answer: (d) If a triangle is equilateral, it is isosceles
Hint:
Given, statement is:
If a triangle is not equilateral, it is not isosceles.
Now, contra-positive is:
If a triangle is equilateral, it is isosceles.

MCQ On Mathematical Reasoning Question 5.
Which of the following is a statement
(a) I will go tomorrow
(b) She will come today
(c) 3 is a prime number
(d) Tomorrow is Friday

Answer

Answer: (c) 3 is a prime number
Hint:
The statement 3 is a prime number is true.
So, it is a statement.

Mathematical Reasoning Questions With Answers Pdf Question 6.
The contra-positive of the statement if p then q is
(a) if ~p then q
(b) if p then ~q
(c) if q then p
(d) if ~q then ~p

Answer

Answer: (d) if ~q then ~p
Hint:
Given statement is if p then q
Now, contra-positive of the statement is:
if ~q then ~p

Mathematical Reasoning MCQs Question 7.
Which of the following is not a statement
(a) The product of (-1) and 8 is 8
(b) All complex number are real number
(c) Today is windy day
(d) All of the above

Answer

Answer: (d) All of the above
Hint:
A sentence is a statement if it is true.
None of the above sentence is true.
So, option 4 is the correct answer.

Mathematical Reasoning Questions Class 11 Question 8.
If (p or q) is true, then
(a) p is true and q is false
(b) p is true and q is true
(c) p is false and q is true
(d) All of the above

Answer

Answer: (d) All of the above
Hint:
(p or q) is false when both p and q are false otherwise it is true.

Mathematical Reasoning Class 11 Questions Question 9.
Which of the following statement is a conjunction
(a) Ram and Shyam are friends
(b) Both Ram and Shyam are friends
(c) Both Ram and Shyam are enemies
(d) None of these

Answer

Answer: (d) None of these
Hint:
All the statements are conjunction. So, option 4 is the correct answer.

MCQ Questions For Class 11th Maths Question 10.
Which of the following is a compound statement
(a) Sun is a star
(b) I am a very strong boy
(c) There is something wrong in the room
(d) 7 is both odd and prime number.

Answer

Answer: (d) 7 is both odd and prime number.
Hint:
A compound statement is connected with And , or , etc.
So, the statement 7 is both odd and prime number is a compound statement.

Reasoning Questions For Class 11 Question 11.
Which of the following is a statement
(a) x is a real number
(b) Switch of the fan
(c) 6 is a natural number
(d) Let me go

Answer

Answer: (c) 6 is a natural number
Hint:
The statement 6 is a natural number is true.
So, it is a statement.

Mathematical Reasoning Questions Question 12.
Which of the following is not a statement
(a) 8 is less than 6.
(b) Every set is finite set.
(c) The sun is a star.
(d) Mathematics is fun.

Answer

Answer: (d) Mathematics is fun.
Hint:
8 is less than 6 if false. So it is a statement.
Every set is finite set is false. So it is a statement.
The sun is a star is true. So it is a statement.
Mathematics is fun. This sentence is not always true. Hence, it is not a statement.

Maths MCQs For Class 11 With Answers Pdf Question 13.
Which of the following is true
(a) A prime number is either even or odd
(b) √3 is irrational number.
(c) 24 is a multiple of 2, 4 and 8
(d) Everyone in India speaks Hindi.

Answer

Answer: (d) Everyone in India speaks Hindi.
Hint:
The statement Everyone in India speaks Hindi is not true.
This is because, there are some states like Tamilnadu, Kerala, etc. where the person does not speak Hindi.

MCQ Questions For Class 11 Maths With Answers Pdf Download Question 14.
If (p and q) is false then
(a) p is true and q is false
(b) p is false and q is false
(c) p is false and q is true
(d) all of the above

Answer

Answer: (d) all of the above
Hint:
(p and q) is true when both p and q are true otherwise it is false.

Mathematical Reasoning Class 11 Question 15.
The converse of the statement p ⇒ q is
(a) p ⇒ q
(b) q ⇒ p
(c) ~p ⇒ q
(d) ~q ⇒ p

Answer

Answer: (b) q ⇒ p
Hint:
The converse of the statement p ⇒ q is
q ⇒ p

Mathematical Reasoning Questions Pdf Question 16.
The negation of the statement The product of 3 and 4 is 9 is
(a) It is false that the product of 3 and 4 is 9
(b) The product of 3 and 4 is 12
(c) The product of 3 and 4 is not 12
(d) It is false that the product of 3 and 4 is not 9

Answer

Answer: (a) It is false that the product of 3 and 4 is 9
Hint:
Given, statement is The product of 3 and 4 is 9
The negation of the statement is:
It is false that the product of 3 and 4 is 9

MCQ Questions For Class 11 Maths With Answers Pdf Question 17.
Sentence involving variable time such as today, tomorrow, or yesterday are
(a) Statements
(b) Not statements
(c) may or may not be statements
(d) None of these

Answer

Answer: (b) Not statements
Hint:
Sentence involving variable time such as today, tomorrow, or yesterday are not statements. This is because it is not known what time is referred here.

Question 18.
The converse of the statement if a number is divisible by 10, then it is divisible by 5 is
(a) if a number is not divisible by 5, then it is not divisible by 10
(b) if a number is divisible by 5, then it is not divisible by 10
(c) if a number is not divisible by 5, then it is divisible by 10
(d) if a number is divisible by 5, then it is divisible by 10

Answer

Answer: (d) if a number is divisible by 5, then it is divisible by 10
Hint:
Given, statement is if a number is divisible by 10, then it is divisible by 5
Now, converse of the statement is:
if a number is divisible by 5, then it is divisible by 10

Question 19.
Which of the following is the conditional p → q
(a) q is sufficient for p
(b) p is necessary for q
(c) p only if q
(d) if q then p

Answer

Answer: (c) 6 is a natural number
Hint:
Given, p → q
Now, conditional of the statement is
p only if q

Question 20.
Which of the following is not a negation of the statement A natural number is greater than zero
(a) A natural number is not greater than zero
(b) It is false that a natural number is greater than zero
(c) It is false that a natural number is not greater than zero
(d) None of these

Answer

Answer: (c) It is false that a natural number is not greater than zero
Hint:
Given statement is:
A natural number is greater than zero
Negation of the statement:
A natural number is not greater than zero
It is false that a natural number is greater than zero
So, option 3 is not true.

We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 14 Mathematical Reasoning with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 11 Maths Mathematical Reasoning MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 11 Maths MCQ:

MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions with Answers

Relations and Functions Class 11 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have provided Relations and Functions Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 11 Maths Chapter 2 MCQ With Answers

Maths Class 11 Chapter 2 MCQs On Relations and Functions

Relation And Function Class 11 MCQ Question 1.
If f(x) = (a – x)1/n, a > 0 and n ∈ N, then the value of f(f(x)) is
(a) 1/x
(b) x
(c) x²
(d) x1/2

Answer

Answer: (b) x
Hint:
Given, f(x) = (a – x)1/n
Now, f(f(x)) = [(a – f(x))n]1/n
⇒ f(f(x)) = [(a – {(a – xn)1/n }n ]1/n
⇒ f(f(x)) = [a – (a – xn)]1/n
⇒ f(f(x)) = [a – a + xn)]1/n
⇒ f(f(x)) = (xn)1/n
⇒ f(f(x)) = x

MCQ On Relation And Function Class 11 Question 2.
The domain of the definition of the real function f(x) = √(log12 x² ) of the real variable x is
(a) x > 0
(b) |x| ≥ 1
(c) |x| > 4
(d) x ≥ 4

Answer

Answer: (b) |x| ≥ 1
Hint:
We have f(x) = √(log12 x²)
Since, loga k ≥ 0 if a > 1, k ≥ 1
or 0 < a < 1 and 0 < k ≤ 1
So, the function f(x) exists if
log12 x² ≥ 0
⇒ x² ≥ 1
⇒ |x| ≥ 1

Relations And Functions Class 11 MCQ Question 3.
If f(x) = ex and g(x) = loge x then the value of fog(1) is
(a) 0
(b) 1
(c) -1
(d) None of these

Answer

Answer: (b) 1
Hint:
Given, f(x) = ex
and g(x) = log x
fog(x) = f(g(x))
= f (log x)
= elog x
= x
So, fog(1) = 1

Class 11 Maths Chapter 2 MCQ With Answers Question 4.
Two functions f and g are said to be equal if f
(a) the domain of f = the domain of g
(b) the co-domain of f = the co-domain of g
(c) f(x) = g(x) for all x
(d) all of above

Answer

Answer: (d) all of above
Hint:
Two functions f and g are said to be equal if f
1. the domain of f = the domain of g
2. the co-domain of f = the co-domain of g
3. f(x) = g(x) for all x

Relations And Functions Class 11 MCQ Questions Question 5.
A function f(x) is said to be an odd function if
(a) f(-x) = f(x)
(b) f(-x) = -f(x)
(c) f(-x) = k * f(x) where k is a constant
(d) None of these

Answer

Answer: (b) f(-x) = -f(x)
Hint:
A function f(x) is said to be an odd function if
f(-x) = -f(x) for all x

Class 11 Maths Chapter 2 MCQ Question 6.
If f(x) is an odd differentiable function on R, then df(x)/dx is a/an
(a) Even function
(b) Odd function
(c) Either even or odd function
(d) Neither even nor odd function

Answer

Answer: (a) Even function
Hint:
Given, f(x) is an odd differentiable function on R
⇒ f(-x) = -f(x) for all x ∈ R
differentiate on both side, we get
⇒ -df(-x)/dx = -df(x)/dx for all x ∈ R
⇒ df(-x)/dx = df(x)/dx for all x ∈ R
⇒ df(x)/dx is an even function on R.

MCQ Of Relation And Function Class 11 Question 7.
The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period
(a) 4
(b) 6
(c) 12
(d) 24

Answer

Answer: (a) 4
Hint:
Period of sin (‎πx/2) = 2π/(π/2) = 4
Period of cos (πx/2) = 2π/(π/2) = 4
So, period of f(x) = LCM (4, 4) = 4

Relations And Functions MCQ Class 11 Question 8.
If f(x) = log3 x and A = (3, 27) then f(A) =
(a) (1, 1)
(b) (3, 3)
(c) (1, 3)
(d) (2, 3)

Answer

Answer: (c) (1, 3)
Hint:
Since f(x) = log3 x is an increasing function
So, f(A) = (log3 3, log3 27) = (1, 3)

Relation And Function MCQ Class 11 Question 9.
The domain of tan-1 (2x + 1) is
(a) R
(b) R -{1/2}
(c) R -{-1/2}
(d) None of these

Answer

Answer: (a) R
Hint:
Since tan-1 x exists if x ∈ (-∞, ∞)
So, tan-1 (2x + 1) is defined if
-∞ < 2x + 1 < ∞
⇒ -∞ < x < ∞
⇒ x ∈ (-∞, ∞)
⇒ x ∈ R
So, domain of tan-1 (2x + 1) is R.

Class 11 Maths Ch 2 MCQ Question 10.
the function f(x) = x – [x] has period of
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (b) 1
Hint:
Let T is a positive real number.
Let f(x) is periodic with period T.
Now, f(x + T) = f(x), for all x ∈ R
⇒ x + T – [x + T] = x – [x], for all x ∈ R
⇒ [x + T] – [x] = T, for all x ∈ R
Thus, there exist T > 0 such that f(x + T) = f(x) for all x ∈ R
Now, the smallest value of T satisfying f(x + T) = f(x) for all x ∈ R is 1
So, f(x) = x – [x] has period 1

MCQ Questions On Relations And Functions Class 11 Question 11.
If f(x) =(3x – 2)/(2x – 3) then the value of f(f(x)) is
(a) x
(b) x²
(c) x³
(d) None of these

Answer

Answer: (a) x
Hint:
Given, f(x) = (3x – 2)/(2x – 3)
Now, f(f(x)) = f{(3x – 2)/(2x – 3)}
= {(3×(3x – 2)/(2x – 3) – 2)}/{(2(3x – 2)/(2x – 3) – 3)}
= {(9x – 6)/(2x – 3) – 2)}/{((6x – 4)/(2x – 3) – 3)}
= [{(9x – 6) – 2(2x – 3)}/(2x – 3)]/[{(6x – 4) – 3(2x – 3)}/(2x – 3)]
= {(9x – 6) – 2(2x – 3)}/{(6x – 4) – 3(2x – 3)}
= (9x – 6 – 4x + 6)/(6x – 4 – 6x + 9)
= 5x/5
= x
So, f(f(x)) = x

Ch 2 Maths Class 11 MCQ Question 12.
Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to
(a) 2x + 1
(b) 2x² + 1
(c) (2x + 1)²
(d) None of these

Answer

Answer: (b) 2x² + 1
Hint:
Given, f(x) = x² and g(x) = 2x + 1
Now gof(x) = g(f(x)) = f(x²) = 2x² + 1

MCQ Questions For Class 11 Maths Chapter 2 Question 13.
A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is
(a) (0, 4, 4)
(b) (0, -4, 4)
(c) (0, -4, -4)
(d) None of these

Answer

Answer: (b) (0, -4, 4)
Hint:
Given that:
(x, y) ∈ R ⇔ x² + y² = 16
⇔ y = ±√(16 – x² )
when x = 0 ⇒ y = ±4
(0, 4) ∈ R and (0, -4) ∈ R
when x = ±4 ⇒ y = 0
(4, 0) ∈ R and (-4, 0) ∈ R
Now for other integral values of x, y is not an integer.
Hence R = {(0, 4), (0, -4), (4, 0), (-4, 0)}
So, Domain(R) = {0, -4, 4}

MCQ Questions For Class 11 Maths With Answers Chapter 2 Question 14.
The number of binary operations on the set {a, b} are
(a) 2
(b) 4
(c) 8
(d) 16

Answer

Answer: (d) 16
Hint:
Let S is a finite set containing n elements.
Since binary operation on S is a function from S×S to S, therefore total number of
binary operations on S is the
total number of functions from S×S to S = (nn)²
Given Set = {a, b}
Total number of elements = 2
Total number of binary operations = (2²)² = 24 = 16

Class 11 Relations And Functions MCQ Questions Question 15.
If f is an even function and g is an odd function the fog is a/an
(a) Even function
(b) Odd function
(c) Either even or odd function
(d) Neither even nor odd function

Answer

Answer: (a) Even function
Hint:
Given, f is an even function and g is an odd function.
Now, fog(-x) = f{g(-x)}
= f{-g(x)} {since g is an odd function}
= f{g(x)} for all x {since f is an even function}
So, fog is an even function.

Question 16.
The domain of the function f(x) = 1/(x² – 3x + 2) is
(a) {1, 2}
(b) R
(c) R – {1, 2}
(d) R – {1, -2}

Answer

Answer: (c) R – {1, 2}
Hint:
Given, function is f(x) = 1/(x² – 3x + 2)
Clearly, f(x) is not defined when x² – 3x + 2 = 0
⇒ (x – 1)×(x – 1) = 0
⇒ x = 1, 2
So, f(x) is not defined when x = 1, 2
So, domain of function is R – {1, 2}

Question 17.
The domain of the function f(x) = sin-1 (tan x) is
(a) -π/4 ≤ x ≤ π/4
(b) nπ – π/4 ≤ x ≤ nπ + π/4
(c) nπ – π/3 ≤ x ≤ nπ + π/3
(d) -π/3 ≤ x ≤ π/3

Answer

Answer: (b) nπ – π/4 ≤ x ≤ nπ + π/4
Hint:
sin-1 (tan x) is defined for -1 ≤ tan x ≤ 1
= -π/4 ≤ x ≤ π/4
The general solution of the above inequality is
nπ -π/4 ≤ x ≤ nπ + π/4

Question 18.
Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is
(a) {7, -5, -3}
(b) {-7, 5, -3}
(c) {-7, -5, 3}
(d) {-7, -5, -3}

Answer

Answer: (d) {-7, -5, -3}
Hint:
Given, A = {-2, -1, 0}
and f(x) = 2x – 3
Now, f(-2) = 2 × (-2) – 3 = -4 – 3 = -7
f(-1) = 2 × (-1) – 3 = -2 – 3 = -5
f(0) = 2 × 0 – 3 = -3
So, range of f = {-7, -5, -3}

Question 19.
The range of the function 7-xPx-3 is
(a) {1, 2, 3, 4, 5}
(b) {3, 4, 5}
(c) None of these
(d) {1, 2, 3}

Answer

Answer: (d) {1, 2, 3}
Hint:
The function f(x) = 7-xPx-3 is defined only if x is an integer satisfying the following inequalities:
1. 7 – x ≥ 0
2. x – 3 ≥ 0
3. 7 – x ≥ x – 3
Now, from 1, we get x ≤ 7 ……… 4
from 2, we get x ≥ 3 ……………. 5
and from 2, we get x ≤ 5 ………. 6
From 4, 5 and 6, we get
3 ≤ x ≤ 5
So, the domain is {3, 4, 5}
Now, f(3) = 7-3P3-3 = 4P0 = 1
⇒ f(4) = 7-4P4-3 = 3P1 = 3
⇒ f(5) = 7-5P5-3 = 2P2 = 2
So, the range of the function is {1, 2, 3}

Question 20.
The period of the function f(x) = sin4 3x + cos4 3x is
(a) π/2
(b) π/3
(c) π/4
(d) π/6

Answer

Answer: (d) π/6
Hint:
Since g(x) = sin4 x + cos4 x is periodic with period π/2
So, f(x) = sin4 3x + cos4 3x is periodic with period (π/2)/3 = π/6

We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 2 Relations and Functions with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 11 Maths Relations and Functions MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 11 Maths MCQ:

MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers

Linear Inequalities Class 11 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have provided Linear Inequalities Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 11 Maths Chapter 6 MCQ With Answers

Maths Class 11 Chapter 6 MCQs On Linear Inequalities

Linear Inequalities Class 11 MCQ Question 1.
Sum of two rational numbers is ______ number.
(a) rational
(b) irrational
(c) Integer
(d) Both 1, 2 and 3

Answer

Answer: (a) rational
Hint:
The sum of two rational numbers is a rational number.
Ex: Let two rational numbers are 1/2 and 1/3
Now, 1/2 + 1/3 = 5/6 which is a rational number.

MCQ On Linear Inequalities Class 11 Question 2.
If x² = -4 then the value of x is
(a) (-2, 2)
(b) (-2, ∞)
(c) (2, ∞)
(d) No solution

Answer

Answer: (d) No solution
Hint:
Given, x² = -4
Since LHS ≥ 0 and RHS < 0
So, No solution is possible.

Class 11 Maths Chapter 6 MCQ With Answers Question 3.
Solve: (x + 1)² + (x² + 3x + 2)² = 0
(a) x = -1, -2
(b) x = -1
(c) x = -2
(d) None of these

Answer

Answer: (b) x = -1
Hint:
Given, (x + 1)² + (x² + 3x + 2)² = 0
This is true when each term is equal to zero simultaneously,
So, (x + 1)² = 0 and (x² + 3x + 2)² = 0
⇒ x + 1 = 0 and x² + 3x + 2 = 0
⇒ x = -1, and x = -1, -2
Now, the common solution is x = -1
So, solution of the equation is x = -1

Linear Inequalities Objective Questions Class 11 Question 4.
If (x + 3)/(x – 2) > 1/2 then x lies in the interval
(a) (-8, ∞)
(b) (8, ∞)
(c) (∞, -8)
(d) (∞, 8)

Answer

Answer: (a) (-8, ∞)
Hint:
Given,
(x + 3)/(x – 2) > 1/2
⇒ 2(x + 3) > x – 2
⇒ 2x + 6 > x – 2
⇒ 2x – x > -2 – 6
⇒ x > -8
⇒ x ∈ (-8, ∞)

Linear Inequalities MCQ Questions Question 5.
The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is
(a) unbounded
(b) a polygon
(c) none of these
(d) exterior of a triangle

Answer

Answer: (c) none of these
Hint:
Given inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10
Now take x = 6, y = 2 and 2x + y = 10
when x = 0, y = 10
when y = 0, x = 5
So, the points are A(6, 2), B(0, 10) and C(5, 0)
MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers 1
So, the region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is not defined.

MCQ Of Chapter 6 Maths Class 11 Question 6.
The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is
(a) x > 2
(b) 2 < x and x < 1
(c) 2 < x < 1 and x < 3
(d) 2 < x < 3 and x < 1

Answer

Answer: (d) 2 < x < 3 and x < 1
Hint:
Given, f(x) = (x – 1) × (x – 2) × (x – 3) has all factors with odd powers.
So, put them zero
i.e. x – 1 = 0, x – 2 = 0, x – 3 = 0
⇒ x = 1, 2, 3
Now, f(x) < 0 when 2 < x < 3 and x < 1

MCQ Of Linear Inequalities Class 11 Question 7.
If -2 < 2x – 1 < 2 then the value of x lies in the interval
(a) (1/2, 3/2)
(b) (-1/2, 3/2)
(c) (3/2, 1/2)
(d) (3/2, -1/2)

Answer

Answer: (b) (-1/2, 3/2)
Hint:
Given, -2 < 2x – 1 < 2
⇒ -2 + 1 < 2x < 2 + 1
⇒ -1 < 2x < 3
⇒ -1/2 < x < 3/2
⇒ x ∈(-1/2, 3/2)

Linear Inequalities Class 11 MCQ Questions Question 8.
The solution of the inequality |x – 1| < 2 is
(a) (1, ∞)
(b) (-1, 3)
(c) (1, -3)
(d) (∞, 1)

Answer

Answer: (b) (-1, 3)
Hint:
Given, |x – 1| < 2
⇒ -2 < x – 1 < 2
⇒ -2 + 1 < x < 2 + 1
⇒ -1 < x < 3
⇒ x ∈ (-1, 3)

Linear Inequalities Class 11 MCQ Pdf Question 9.
If | x − 1| > 5, then
(a) x∈(−∞, −4)∪(6, ∞]
(b) x∈[6, ∞)
(c) x∈(6, ∞)
(d) x∈(−∞, −4)∪(6, ∞)

Answer

Answer: (d) x∈(−∞, −4)∪(6, ∞)
Hint:
Given |x−1| >5
Case 1:
(x – 1) > 5
⇒ x > 6
⇒ x ∈ (6,∞)
Case 2:
-(x – 1) > 5
⇒ -x + 1 > 5
⇒ -x > 4
⇒ x < -4
⇒ x ∈ (−∞, −4)
So the range of x is (−∞, −4)∪(6, ∞)

MCQ Questions On Linear Inequalities Class 11 Question 10.
The solution of |2/(x – 4)| > 1 where x ≠ 4 is
(a) (2, 6)
(b) (2, 4) ∪ (4, 6)
(c) (2, 4) ∪ (4, ∞)
(d) (-∞, 4) ∪ (4, 6)

Answer

Answer: (b) (2, 4) ∪ (4, 6)
Hint:
Given, |2/(x – 4)| > 1
⇒ 2/|x – 4| > 1
⇒ 2 > |x – 4|
⇒ |x – 4| < 2
⇒ -2 < x – 4 < 2
⇒ -2 + 4 < x < 2 + 4
⇒ 2 < x < 6
⇒ x ∈ (2, 6) , where x ≠ 4
⇒ x ∈ (2, 4) ∪ (4, 6)

Linear Inequalities MCQs Pdf Question 11.
If (|x| – 1)/(|x| – 2) ‎≥ 0, x ∈ R, x ‎± 2 then the interval of x is
(a) (-∞, -2) ∪ [-1, 1]
(b) [-1, 1] ∪ (2, ∞)
(c) (-∞, -2) ∪ (2, ∞)
(d) (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Answer

Answer: (d) (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)
Hint:
Given, (|x| – 1)/(|x| – 2) ‎≥ 0
Let y = |x|
So, (y – 1)/(y – 2) ‎≥ 0
⇒ y ≤ 1 or y > 2
⇒ |x| ≤ 1 or |x| > 2
⇒ (-1 ≤ x ≤ 1) or (x < -2 or x > 2)
⇒ x ∈ [-1, 1] ∪ (-∞, -2) ∪ (2, ∞)
Hence the solution set is:
x ∈ (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Class 11 Linear Inequalities MCQ Question 12.
The solution of the -12 < (4 -3x)/(-5) < 2 is
(a) 56/3 < x < 14/3
(b) -56/3 < x < -14/3
(c) 56/3 < x < -14/3
(d) -56/3 < x < 14/3

Answer

Answer: (d) -56/3 < x < 14/3
Hint:
Given inequality is :
-12 < (4 -3x)/(-5) < 2
⇒ -2 < (4-3x)/5 < 12
⇒ -2 × 5 < 4 – 3x < 12 × 5
⇒ -10 < 4 – 3x < 60
⇒ -10 – 4 < -3x < 60-4
⇒ -14 < -3x < 56
⇒ -56 < 3x < 14
⇒ -56/3 < x < 14/3

Inequalities MCQ Questions Question 13.
If x² = -4 then the value of x is
(a) (-2, 2)
(b) (-2, ∞)
(c) (2, ∞)
(d) No solution

Answer

Answer: (d) No solution
Hint:
Given, x² = -4
Since LHS ≥ 0 and RHS < 0
So, No solution is possible.

Question 14.
Solve: |x – 3| < 5
(a) (2, 8)
(b) (-2, 8)
(c) (8, 2)
(d) (8, -2)

Answer

Answer: (b) (-2, 8)
Hint:
Given, |x – 3| < 5
⇒ -5 < (x – 3) < 5
⇒ -5 + 3 < x < 5 + 3
⇒ -2 < x < 8
⇒ x ∈ (-2, 8)

Question 15.
The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is
(a) none of these
(b) interior of a triangle including the points on the sides
(c) in the 2nd quadrant
(d) exterior of a triangle

Answer

Answer: (b) interior of a triangle including the points on the sides
Hint:
Given inequalities x ≥ 0, y ≥ 0, 3x + 4y ≤ 12
Now take x = 0, y = 0 and 3x + 4y = 12
when x = 0, y = 3
when y = 0, x = 4
So, the points are A(0, 0), B(0, 3) and C(4, 0)
MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers 2
So, the graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is interior of a triangle including the points on the sides.

Question 16.
If |x| < 5 then the value of x lies in the interval
(a) (-∞, -5)
(b) (∞, 5)
(c) (-5, ∞)
(d) (-5, 5)

Answer

Answer: (d) (-5, 5)
Hint:
Given, |x| < 5
It means that x is the number which is at distance less than 5 from 0
Hence, -5 < x < 5
⇒ x ∈ (-5, 5)

Question 17.
Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0
(a) (-∞, 1] ∪ (2, ∞)
(b) (-∞, 1] ∪ (2, 3)
(c) (-∞, 1] ∪ (3, ∞)
(d) None of these

Answer

Answer: (b) (-∞, 1] ∪ (2, 3)
Hint:
Given, f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0
or f(x) = -{(x – 1)×(2 – x)}/(x – 3)
which gives x – 3 ≠ 0
⇒ x ≠ 3
MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers 3
Using number line rule as shown in the figure,
which gives f(x) ≥ 0 when x ≤ 1 or 2 ≤ x < 3
i.e. x ∈ (-∞, 1] ∪ (2, 3)

Question 18.
If x² = 4 then the value of x is
(a) -2
(b) 2
(c) -2, 2
(d) None of these

Answer

Answer: (c) -2, 2
Hint:
Given, x² = 4
⇒ x² – 4 = 0
⇒ (x – 2)×(x + 2) = 0
⇒ x = -2, 2

Question 19.
The solution of the 15 < 3(x – 2)/5 < 0 is
(a) 27 < x < 2
(b) 27 < x < -2
(c) -27 < x < 2
(d) -27 < x < -2

Answer

Answer: (a) 27 < x < 2
Hint:
Given inequality is:
15 < 3(x-2)/5 < 0
⇒ 15 × 5 < 3(x-2) < 0 × 5
⇒ 75 < 3(x-2) < 0
⇒ 75/3 < x-2 < 0
⇒ 25 < x-2 < 0
⇒ 25 +2 < x <0+2
⇒ 27 < x < 2

Question 20.
Solve: 1 ≤ |x – 1| ≤ 3
(a) [-2, 0]
(b) [2, 4]
(c) [-2, 0] ∪ [2, 4]
(d) None of these

Answer

Answer: (c) [-2, 0] ∪ [2, 4]
Hint:
Given, 1 ≤ |x – 1| ≤ 3
⇒ -3 ≤ (x – 1) ≤ -1 or 1 ≤ (x – 1) ≤ 3
i.e. the distance covered is between 1 unit to 3 units
⇒ -2 ≤ x ≤ 0 or 2 ≤ x ≤ 4
Hence, the solution set of the given inequality is
x ∈ [-2, 0] ∪ [2, 4]

We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 11 Maths Linear Inequalities MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 11 Maths MCQ:

MCQ Questions for Class 11 Business Studies Chapter 10 Internal Trade with Answers

Internal Trade Class 11 MCQ Online Test With Answers Questions

Check the below Online Education NCERT MCQ Questions for Class 11 Business Studies Chapter 10 Internal Trade with Answers Pdf free download. MCQ Questions for Class 11 Business Studies with Answers were prepared based on the latest exam pattern. We have provided Internal Trade Class 11 Business Studies MCQs Questions with Answers to help students understand the concept very well.

Class 11 Business Studies Chapter 10 Internal Trade MCQ With Answers

Business Studies Class 11 Chapter 10 MCQs On Internal Trade

Internal Trade Class 11 MCQ Question 1.
It helps disabled and elderly people.
(a) Tele-shopping
(b) E-commerce
(c) multiple shop
(d) installment system

Answer

Answer: (a) Tele-shopping

MCQ On Internal Trade Class 11 Question 2.
The aim is to economies by buying in common and to retain their profits by selling in common.
(a) multiple shop
(b) web marketing
(c) teleshopping
(d) consumer?s co-operative store

Answer

Answer: (d) consumer?s co-operative store

MCQ Questions For Class 11 Business Studies Chapter 10 Question 3.
This retail business acts as a universal supplier of a wide variety of products.
(a) Departmental store
(b) Multiple shop
(c) Mail order Business.
(d) Tele-shopping

Answer

Answer: (a) Departmental store

MCQ Of Internal Trade Class 11 Question 4.
____ are mobile traders who deal in low priced articles with no fixed place of business.
(a) Street stalls
(b) Retailers
(c) Itinerant traders
(d) Agents

Answer

Answer: (c) Itinerant traders

Question 5.
____________ can check the price fluctuations in the market by holding back the goods when prices fall and releasing the goods when prices raise.
(a) Wholesaler
(b) Agent
(c) Retailer
(d) Mercantile agent

Answer

Answer: (a) Wholesaler

Question 6.
A warehouse keeper accepts goods for the purpose of ____________
(a) Selling
(b) Packaging
(c) Export
(d) Storage

Answer

Answer: (d) Storage

Question 7.
When goods are imported for the purpose of export is called as _________
(a) Foreign trade
(b) Entrepot
(c) Home trade
(d) Trade

Answer

Answer: (b) Entrepot

Question 8.
The purchase of goods from a foreign country is called ____________
(a) Entreport
(b) Import
(c) Re-Export
(d) Export

Answer

Answer: (b) Import

Question 9.
The risk of bad debts in this business is eliminated particularly when payment is received through V.P.P.
(a) Tele-shopping
(b) mail order trading house
(c) Departmental store
(d) co-operative store

Answer

Answer: (b) mail order trading house

Question 10.
It is a network of a number of branches situated at different localities in the city or in the different parts of the country.
(a) Multiple shop
(b) Consumers? co-operative store
(c) Hire purchase system
(d) Internet marketing

Answer

Answer: (a) Multiple shop

Question 11.
Small scale Fixed retailers includes ____________
(a) Hawkers
(b) Pedlars
(c) Cheap Jacks
(d) General stores

Answer

Answer: (d) General stores

Question 12.
____________ are agents who merely bring the buyer and the seller into contact.
(a) Selling agent
(b) Commission agent
(c) Stockist
(d) Broker

Answer

Answer: (d) Broker

Question 13.
Wholesaler?s deals in ____________ quantity of goods
(a) Small
(b) Limited
(c) Large
(d) Medium

Answer

Answer: (c) Large

Question 14.
An agent is appointed by the ____________
(a) Principal
(b) Manufacturer
(c) Wholesaler
(d) Retailer

Answer

Answer: (a) Principal

Question 15.
The persons who come in between the primary producer and the final consumer to promote trade is called as ____________
(a) Trader
(b) Middleman
(c) Auctioneer
(d) Agent

Answer

Answer: (b) Middleman

One Mark Questions

1. What is internal trade?

Answer

Answer: Buying and selling of goods and services within the boundaries of a nation is referred as internal trade.

2. What is wholesale trade?

Answer

Answer: Wholesale trade refers to buying and selling of goods and services in large quantities for the purpose of resale or intermediate use.

3. Who is a wholesaler?

Answer

Answer: Wholesaler is a person who buys goods from the producers in bulk quantities and sells them in small quantities to a retailer.

4. What is retail trade?

Answer

Answer: Retail trade refers to sale of goods in small quantities for the final consumptions.

5. Who is a retailer?

Answer

Answer: Retailer is a person who buys the goods in large quantities from the wholesalers and sells ‘them in small quantities to the ultimate consumers.

6. Expand AVM.

Answer

Answer: Automatic Vending Machine

7. Expand FOB

Answer

Answer: Free on Board

8. Expand CIF

Answer

Answer: Cost, Insurance and Freight Price

9. Expand E&OE

Answer

Answer: Errors and Omissions excepted

10. Expand COD

Answer

Answer: Cash on Delivery

11. Name any one type of internal trade.

Answer

Answer: Wholesale Trade

12. State one type of Itinerant retailers.

Answer

Answer: Street Traders

13. Give an example for small scale fixed retail shop.

Answer

Answer: Soaps, Hair oil and Tooth Paste

14. Give an example for large scale fixed retail shop.

Answer

Answer: Spencer, Food world and reliance fresh

15. Give an example for departmental stores.

Answer

Answer: Spencer

16. Give an example for multiple shops.

Answer

Answer: Pizza Hut and Me. Donald

17. Give an example for Super markets.

Answer

Answer: Reliance Fresh and Food world

18. Give an example for malls.

Answer

Answer: Garuda Mall and Orion Mall

19. Who are peddlers?

Answer

Answer: Peddlers are those who carry their goods on their heads and backs from one door to another in the streets for selling the goods.

20. Who are Hawkers?

Answer

Answer: Hawkers are those who carry their goods on back of animals or by using wheeled carts from one door to another for selling the articles.

21. Who are cheap jacks?

Answer

Answer: Cheap jacks are petty retailers who have independent shops of a temporary nature in the business locality.

We hope the given NCERT MCQ Questions for Class 11 Business Studies Chapter 10 Internal Trade with Answers Pdf free download will help you. If you have any queries regarding Internal Trade CBSE Class 11 Business Studies MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 11 Business Studies MCQ:

MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers

Vector Algebra Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Vector Algebra Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 10 MCQ With Answers

Maths Class 12 Chapter 10 MCQs On Vector Algebra

Vector MCQ Chapter 10 Class 12 Question 1.
The position vector of the point (1, 0, 2) is
(a) \(\vec{i}\) +\(\vec{j}\) + 2\(\vec{k}\)
(b) \(\vec{i}\) + 2\(\vec{j}\)
(c) \(\vec{2}\) + 3\(\vec{k}\)
(d) \(\vec{i}\) + 2\(\vec{K}\)

Answer

Answer: (d) \(\vec{i}\) + 2\(\vec{K}\)

Vector MCQ Questions Chapter 10 Class 12 Question 2.
The modulus of 7\(\vec{i}\) – 2\(\vec{J}\) + \(\vec{K}\)
(a) \(\sqrt{10}\)
(b) \(\sqrt{55}\)
(c) 3\(\sqrt{6}\)
(d) 6

Answer

Answer: (c) 3\(\sqrt{6}\)

MCQ On Vectors Chapter 10 Class 12 Question 3.
If O be the origin and \(\vec{OP}\) = 2\(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) and \(\vec{OQ}\) = 5\(\hat{i}\) + 4\(\hat{j}\) -3\(\hat{k}\), then \(\vec{PQ}\) is equal to
(a) 7\(\hat{i}\) + 7\(\hat{j}\) – 7\(\hat{k}\)
(b) -3\(\hat{i}\) + \(\hat{j}\) – \(\hat{k}\)
(c) -7\(\hat{i}\) – 7\(\hat{j}\) + 7\(\hat{k}\)
(d) 3\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

Answer

Answer: (d) 3\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

MCQs On Vectors Chapter 10 Class 12 Question 4.
The scalar product of 5\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and 3\(\hat{i}\) – 4\(\hat{j}\) + 7\(\hat{k}\) is
(a) 10
(b) -10
(c) 15
(d) -15

Answer

Answer: (b) -10

MCQ On Vector Chapter 10 Class 12 Question 5.
If \(\vec{a}\).\(\vec{b}\) = 0, then
(a) a ⊥ b
(b) \(\vec{a}\) || \(\vec{b}\)
(c) \(\vec{a}\) + \(\vec{b}\) = 0
(d) \(\vec{a}\) – \(\vec{b}\) = 0

Answer

Answer: (a) a ⊥ b

Vectors MCQs Chapter 10 Class 12 Question 6.
\(\vec{i}\) – \(\vec{j}\) =
(a) 0
(b) 1
(c) \(\vec{k}\)
(d) –\(\vec{k}\)

Answer

Answer: (a) 0

MCQ On Vectors Class 12 Chapter 10 Question 7.
\(\vec{k}\) × \(\vec{j}\) =
(a) 0
(b) 1
(c) \(\vec{i}\)
(d) –\(\vec{i}\)

Answer

Answer: (d) –\(\vec{i}\)

Vectors MCQ Chapter 10 Class 12 Question 8.
\(\vec{a}\). \(\vec{a}\) =
(a) 0
(b) 1
(c) |\(\vec{a}\)|²
(d) |\(\vec{a}\)|

Answer

Answer: (c) |\(\vec{a}\)|²

Vector MCQ Questions Class 12 Chapter 10 Question 9.
The projection of the vector 2\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\) on the vector \(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\) is
(a) \(\frac{4}{√6}\)
(b) \(\frac{5}{√6}\)
(c) \(\frac{4}{√3}\)
(d) \(\frac{7}{√6}\)

Answer

Answer: (b) \(\frac{5}{√6}\)

Vectors Are MCQ Chapter 10 Class 12 Question 10.
If \(\vec{a}\) = \(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and b = 3\(\vec{i}\) + 2\(\vec{j}\) – \(\vec{k}\) then the value of (\(\vec{a}\) + 3\(\vec{b}\))(2\(\vec{a}\) – \(\vec{b}\))=.
(a) 15
(b) -15
(c) 18
(d) -18

Answer

Answer: (b) -15

MCQ On Vector Algebra Chapter 10 Class 12 Question 11.
If |\(\vec{a}\)|= \(\sqrt{26}\), |b| = 7 and |\(\vec{a}\) × \(\vec{b}\)| = 35, then \(\vec{a}\).\(\vec{b}\) =
(a) 8
(b) 7
(c) 9
(d) 12

Answer

Answer: (b) 7

Vector Algebra MCQ Chapter 10 Class 12 Question 12.
If \(\vec{a}\) = 2\(\vec{i}\) – 3\(\vec{j}\) + 4\(\vec{k}\) and \(\vec{b}\) = \(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\) + \(\vec{b}\) =
(a) \(\vec{i}\) + \(\vec{j}\) + 3\(\vec{k}\)
(b) 3\(\vec{i}\) – \(\vec{j}\) + 5\(\vec{k}\)
(c) \(\vec{i}\) – \(\vec{j}\) – 3\(\vec{k}\)
(d) 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\)

Answer

Answer: (b) 3\(\vec{i}\) – \(\vec{j}\) + 5\(\vec{k}\)

Vector MCQs Chapter 10 Class 12 Question 13.
If \(\vec{a}\) = \(\vec{i}\) + 2\(\vec{j}\) + 3\(\vec{k}\) and \(\vec{b}\) = 3\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\), then cos θ =
(a) \(\frac{6}{7}\)
(b) \(\frac{5}{7}\)
(c) \(\frac{4}{7}\)
(d) \(\frac{1}{2}\)

Answer

Answer: (b) \(\frac{5}{7}\)

Vectors MCQs With Solutions Chapter 10 Class 12 Question 14.
If |\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)|, then
(a) \(\vec{a}\) || \(\vec{a}\)
(b) \(\vec{a}\) ⊥ \(\vec{b}\)
(c) |\(\vec{a}\)| = |\(\vec{b}\)|
(d) None of these

Answer

Answer: (b) \(\vec{a}\) ⊥ \(\vec{b}\)

MCQ Questions On Vectors Chapter 10 Class 12 Question 15.
The projection of the vector 2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\) on the line joining the points (3, 4, 2) and (5, 6,3) is
(a) \(\frac{2}{3}\)
(b) \(\frac{4}{3}\)
(c) –\(\frac{4}{3}\)
(d) \(\frac{5}{3}\)

Answer

Answer: (b) \(\frac{4}{3}\)

Question 16.
If |\(\vec{a}\) × \(\vec{b}\)| – |\(\vec{a}\).\(\vec{b}\)|, then the angle between \(\vec{a}\) and \(\vec{b}\), is
(a) 0
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{4}\)
(d) π

Answer

Answer: (c) \(\frac{π}{4}\)

Question 17.
The angle between two vector \(\vec{a}\) and \(\vec{b}\) with magnitude √3 and 4, respectively and \(\vec{a}\).\(\vec{b}\) = 2√3 is
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{5π}{2}\)

Answer

Answer: (b) \(\frac{π}{3}\)

Question 18.
Unit vector perpendicular to each of the vector 3\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\) and 2\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) is
(a) \(\frac{\hat{i}+\hat{j}+\hat{k}}{√3}\)
(b) \(\frac{\hat{i}-\hat{j}+\hat{k}}{√3}\)
(c) \(\frac{\hat{i}-\hat{j}-\hat{k}}{√3}\)
(d) \(\frac{\hat{i}+\hat{j}-\hat{k}}{√3}\)

Answer

Answer: (c) \(\frac{\hat{i}-\hat{j}-\hat{k}}{√3}\)

Question 19.
If \(\vec{a}\) = 2\(\vec{i}\) – 5\(\vec{j}\) + k and \(\vec{b}\) = 4\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\).\(\vec{b}\) =
(a) 0
(b) -1
(c) 1
(d) 2

Answer

Answer: (b) -1

Question 20.
If 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\), 6\(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and 14\(\vec{i}\) – 5\(\vec{j}\) + 4\(\vec{k}\) be the position vector of the points A, B and C respectively, then
(a) The A, B and C are collinear
(b) A, B and C are not colinear
(c) \(\vec{AB}\) ⊥ \(\vec{BC}\)
(d) None of these

Answer

Answer: (a) The A, B and C are collinear

Question 21.
According to the associative lass of addition of addition of s ector
(\(\vec{a}\) + …….) + \(\vec{c}\) = …… + (\(\vec{b}\) + \(\vec{c}\))
(a) \(\vec{b}\), \(\vec{a}\)
(b) \(\vec{a}\), \(\vec{b}\)
(c) \(\vec{a}\), 0
(d) \(\vec{b}\), 0

Answer

Answer: (a) \(\vec{b}\), \(\vec{a}\)

Question 22.
Which one of the following can be written for (\(\vec{a}\) – \(\vec{b}\)) × (\(\vec{a}\) + \(\vec{b}\))
(a) \(\vec{a}\) × \(\vec{b}\)
(b) 2\(\vec{a}\) × \(\vec{b}\)
(c) \(\vec{a}\)² – \(\vec{b}\)
(d) 2\(\vec{b}\) × \(\vec{b}\)

Answer

Answer: (b) 2\(\vec{a}\) × \(\vec{b}\)

Question 23.
The points with position vectors (2. 6), (1, 2) and (a, 10) are collinear if the of a is
(a) -8
(b) 4
(c) 3
(d) 12

Answer

Answer: (c) 3

Question 24.
|\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
(a) \(\frac{π}{2}\)
(b) 0
(c) \(\frac{π}{4}\)
(d) \(\frac{π}{6}\)

Answer

Answer: (a) \(\frac{π}{2}\)

Question 25.
|\(\vec{a}\) × \(\vec{b}\)| = |\(\vec{a}\).\(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
(a) 0
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{4}\)
(d) π

Answer

Answer: (a) 0

Question 26.
If ABCDEF is a regular hexagon then \(\vec{AB}\) + \(\vec{EB}\) + \(\vec{FC}\) equals
(a) zero
(b) 2\(\vec{AB}\)
(c) 4\(\vec{AB}\)
(d) 3\(\vec{AB}\)

Answer

Answer: (d) 3\(\vec{AB}\)

Question 27.
Which one of the following is the modulus of x\(\hat{i}\) + y\(\hat{j}\) + z\(\hat{k}\)?
(a) \(\sqrt{x^2+y^2+z^2}\)
(b) \(\frac{1}{\sqrt{x^2+y^2+z^2}}\)
(c) x² + y² + z²
(d) none of these

Answer

Answer: (a) \(\sqrt{x^2+y^2+z^2}\)

Question 28.
If C is the mid point of AB and P is any point outside AB then,
(a) \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\)
(b) \(\vec{PA}\) + \(\vec{PB}\) = \(\vec{PC}\)
(c) \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\) = 0
(d) None of these

Answer

Answer: (a) \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\)

Question 29.
If \(\vec{OA}\) = 2\(\vec{i}\) – \(\vec{j}\) + \(\vec{k}\), \(\vec{OB}\) = \(\vec{i}\) – 3\(\vec{j}\) – 5\(\vec{k}\) then |\(\vec{OA}\) × \(\vec{OB}\)| =
(a) 8\(\vec{i}\) + 11\(\vec{j}\) – 5\(\vec{k}\)
(b) \(\sqrt{210}\)
(c) sin θ
(d) \(\sqrt{40}\)

Answer

Answer: (b) \(\sqrt{210}\)

Question 30.
If |a| = |b| = |\(\vec{a}\) + \(\vec{b}\)| = 1 then |\(\vec{a}\) – \(\vec{b}\)| is equal to
(a) 1
(b) √3
(c) 0
(d) None of these

Answer

Answer: (b) √3

Question 31.
If \(\vec{a}\) and \(\vec{b}\) are any two vector then (\(\vec{a}\) × \(\vec{b}\))² is equal to
(a) (\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))²
(b) (\(\vec{a}\))² (\(\vec{b}\))² + (\(\vec{a}\).\(\vec{b}\))²
(c) (\(\vec{a}\).\(\vec{b}\))²
(d) (\(\vec{a}\))²(\(\vec{b}\))²

Answer

Answer: (a) (\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))²

Question 32.
If \(\hat{a}\) and \(\hat{b}\) be two unit vectors and 0 is the angle between them, then |\(\hat{a}\) – \(\hat{b}\)| is equal to
(a) sin \(\frac{θ}{2}\)
(b) 2 sin \(\frac{θ}{2}\)
(c) cos \(\frac{θ}{2}\)
(d) 2 cos \(\frac{θ}{2}\)

Answer

Answer: (b) 2 sin \(\frac{θ}{2}\)

Question 33.
The angle between the vector 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) – \(\hat{k}\) is
(a) \(\frac{π}{2}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{3}\)
(d) 0

Answer

Answer: (a) \(\frac{π}{2}\)

Question 34.
If \(\vec{a}\) = \(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) – \(\hat{k}\), \(\vec{c}\) = 3\(\hat{i}\) – p\(\hat{j}\) – 5\(\hat{k}\) are coplanar then P =
(a) 6
(b) -6
(c) 2
(d) -2

Answer

Answer: (a) 6

Question 35.
The distance of the point (- 3, 4, 5) from the origin
(a) 50
(b) 5√2
(c) 6
(d) None of these

Answer

Answer: (b) 5√2

Question 36.
If \(\vec{AB}\) = 2\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and the co-ordinates of A are (1, 2, -1) then coordinate of B are
(a) (2, 2, -3)
(b) (3, 2, -4)
(c) (4, 2, -1)
(d) (3, 3, -4)

Answer

Answer: (d) (3, 3, -4)

Question 37.
If \(\vec{b}\) is a unit vector in xy-plane making an angle of \(\frac{π}{4}\) with x-axis. then \(\vec{b}\) is equal to
(a) \(\hat{i}\) + \(\hat{j}\)
(b) \(\vec{i}\) – \(\vec{j}\)
(c) \(\frac{\vec{i}+\vec{j}}{√2}\)
(d) \(\frac{\vec{i}-\vec{j}}{√2}\)

Answer

Answer: (c) \(\frac{\vec{i}+\vec{j}}{√2}\)

Question 38.
\(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) – 8\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) then the magnitude of \(\vec{a}\) + \(\vec{b}\) is equal to
(a) 13
(b) \(\frac{13}{4}\)
(c) \(\frac{3}{13}\)
(d) \(\frac{4}{13}\)

Answer

Answer: (a) 13

Question 39.
The vector in the direction of the vector \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\) that has magnitude 9 is
(a) \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\)
(b) \(\frac{\hat{i}-2\hat{j}+2\hat{k}}{3}\)
(c) 3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))
(d) 9(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))

Answer

Answer: (c) 3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))

Question 40.
The position vector of the point which divides the join of points 2\(\vec{a}\) – 3\(\vec{b}\) and \(\vec{a}\) + \(\vec{b}\) in the ratio 3 : 1 is
(a) \(\frac{3\vec{a}-2\vec{b}}{2}\)
(b) \(\frac{7\vec{a}-8\vec{b}}{2}\)
(c) \(\frac{3\vec{a}}{2}\)
(d) \(\frac{5\vec{a}}{4}\)

Answer

Answer: (d) \(\frac{5\vec{a}}{4}\)

Question 41.
The vector having, initial and terminal points as (2, 5, 0) and (- 3, 7, 4) respectively is
(a) –\(\hat{i}\) + 12\(\hat{j}\) + 4\(\hat{k}\)
(b) 5\(\hat{i}\) + 2\(\hat{j}\) – 4\(\hat{k}\)
(c) -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)
(d) \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

Answer

Answer: (c) -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)

Question 42.
Find the value of λ such that the vectors \(\vec{a}\) = 2\(\hat{i}\) + λ\(\hat{j}\) + \(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) + 3\(\hat{k}\) are orthogonal
(a) 0
(b) 1
(c) \(\frac{3}{2}\)
(d) –\(\frac{5}{2}\)

Answer

Answer: (d) –\(\frac{5}{2}\)

Question 43.
The value of λ for which the vectors 3\(\hat{i}\) – 6\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – 4\(\hat{j}\) + λ\(\hat{k}\) are parallel is
(a) \(\frac{2}{3}\)
(b) \(\frac{3}{2}\)
(c) \(\frac{5}{2}\)
(d) –\(\frac{2}{5}\)

Answer

Answer: (a) \(\frac{2}{3}\)

Question 44.
The vectors from origin to the points A and B are \(\vec{a}\) = 2\(\hat{i}\) – 3\(\hat{j}\) +2\(\hat{k}\) and \(\vec{b}\) = 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) respectively, then the area of triangle OAB is
(a) 340
(b) \(\sqrt{25}\)
(c) \(\sqrt{229}\)
(d) \(\frac{1}{2}\) \(\sqrt{229}\)

Answer

Answer: (d) \(\frac{1}{2}\) \(\sqrt{229}\)

Question 45.
For any vector \(\vec{a}\) the value of (\(\vec{a}\) × \(\vec{i}\))² + (\(\vec{a}\) × \(\hat{j}\))² + (\(\vec{a}\) × \(\hat{k}\))² is equal to
(a) \(\vec{a}\)²
(b) 3\(\vec{a}\)²
(c) 4\(\vec{a}\)²
(d) 2\(\vec{a}\)²

Answer

Answer: (d) 2\(\vec{a}\)²

Question 46.
If |\(\vec{a}\)| = 10, |\(\vec{b}\)| = 2 and \(\vec{a}\).\(\vec{b}\) = 12, then the value of |\(\vec{a}\) × \(\vec{b}\)| is
(a) 5
(b) 10
(c) 14
(d) 16

Answer

Answer: (d) 16

Question 47.
The vectors λ\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\), \(\hat{i}\) + λ\(\hat{j}\) – \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) + λ\(\hat{k}\) are coplanar if
(a) λ = -2
(b) λ = 0
(c) λ = 1
(d) λ = -1

Answer

Answer: (a) λ = -2

Question 48.
If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are unit vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = \(\vec{0}\), then the value of \(\vec{a}\).\(\vec{b}\) + \(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\)
(a) 1
(b) 3
(c) –\(\frac{3}{2}\)
(d) None of these

Answer

Answer: (c) –\(\frac{3}{2}\)

Question 49.
Projection vector of \(\vec{a}\) on \(\vec{b}\) is
(a) (\(\frac{\vec{a}.\vec{b}}{|\vec{b}|^2}\))\(\vec{b}\)
(b) \(\frac{\vec{a}.\vec{b}}{|\vec{b}|}\)
(c) \(\frac{\vec{a}.\vec{b}}{|\vec{a}|}\)
(d) (\(\frac{\vec{a}.\vec{b}}{|\vec{a}|^2}\))\(\hat{b}\)

Answer

Answer: (b) \(\frac{\vec{a}.\vec{b}}{|\vec{b}|}\)

Question 50.
If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = 5 and |\(\vec{a}\)| = 2, |\(\vec{b}\)| = 3, |\(\vec{c}\)| = 5, then the value of \(\vec{a}\).\(\vec{b}\) +\(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\) is
(a) 0
(b) 1
(c) -19
(d) 38

Answer

Answer: (c) -19

Question 51.
If |\(\vec{a}\)| 4 and – 3 ≤ λ ≤ 2, then the range of |λ\(\vec{a}\)| is
(a) [0, 8]
(b) [-12, 8]
(c) [0, 12]
(d) [8, 12]

Answer

Answer: (b) [-12, 8]

Question 52.
The number of vectors of unit length perpendicular to the vectors \(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\) and \(\vec{b}\) = \(\hat{j}\) + \(\hat{k}\) is
(a) one
(b) two
(c) three
(d) infinite

Answer

Answer: (b) two

Question 53.
If (\(\frac{1}{2}\), \(\frac{1}{3}\), n) are the direction cosines of a line, then the value of n is
(a) \(\frac{\sqrt{23}}{6}\)
(b) \(\frac{23}{6}\)
(c) \(\frac{2}{3}\)
(d) –\(\frac{3}{2}\)

Answer

Answer: (a) \(\frac{\sqrt{23}}{6}\)

Question 54.
Find the magnitude of vector 3\(\hat{i}\) + 2\(\hat{j}\) + 12\(\hat{k}\)
(a) \(\sqrt{157}\)
(b) 4\(\sqrt{11}\)
(c) \(\sqrt{213}\)
(d) 9√3

Answer

Answer: (a) \(\sqrt{157}\)

Question 55.
Three points (2, -1, 3), (3, – 5, 1) and (-1, 11, 9) are
(a) Non-collinear
(b) Non-coplanar
(c) Collinear
(d) None of these

Answer

Answer: (c) Collinear

Question 56.
The vectors 3\(\hat{i}\) + 5\(\hat{j}\) + 2\(\hat{k}\), 2\(\hat{i}\) – 3\(\hat{j}\) – 5\(\hat{k}\) and 5\(\hat{i}\) + 2\(\hat{j}\) – 3\(\hat{k}\) form the sides of
(a) Isosceles triangle
(b) Right triangle
(c) Scalene triangle
(d) Equilateral triangle

Answer

Answer: (a) Isosceles triangle

Question 57.
The points with position vectors 60\(\hat{i}\) + 3\(\hat{j}\), 40\(\hat{i}\) – 8\(\hat{j}\) and a\(\hat{i}\) – 52\(\hat{j}\) are collinear if
(a) a = -40
(b) a = 40
(c) a = 20
(d) None of these

Answer

Answer: (a) a = -40

Question 58.
The ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1, -5, 7) is
(a) 5 : 3
(b) 3 : 2
(c) 2 : 1
(d) 1 : 3

Answer

Answer: (a) 5 : 3

Question 59.
If O is origin and C is the mid point of A (2, -1) and B (-4, 3) then the value of \(\bar{OC}\) is
(a) \(\hat{i}\) + \(\hat{j}\)
(b) \(\hat{i}\) – \(\hat{j}\)
(c) –\(\hat{i}\) + \(\hat{j}\)
(d) –\(\hat{i}\) – \(\hat{j}\)

Answer

Answer: (c) –\(\hat{i}\) + \(\hat{j}\)

Question 60.
If ABCDEF is regular hexagon, then \(\vec{AD}\) + \(\vec{EB}\) + \(\vec{FC}\) is equal
(a) 0
(b) 2\(\vec{AB}\)
(c) 3\(\vec{AB}\)
(d) 4\(\vec{AB}\)

Answer

Answer: (d) 4\(\vec{AB}\)

Question 61.
If \(\vec{a}\) = \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = 2\(\hat{i}\) – 4\(\hat{k}\), \(\vec{c}\) = \(\hat{i}\) + λ\(\hat{j}\) + 3\(\hat{j}\) are coplanar, then the value of λ is
(a) \(\frac{5}{2}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{7}{3}\)
(d) –\(\frac{5}{3}\)

Answer

Answer: (d) –\(\frac{5}{3}\)

Question 62.
The vectors \(\vec{a}\) = x\(\hat{i}\) – 2\(\hat{j}\) + 5\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + y\(\hat{j}\) – z\(\hat{k}\) are collinear, if
(a) x = 1, y = -2, z = -5
(b) x = \(\frac{3}{2}\), y = -4, z = -10
(c) x = \(\frac{3}{2}\), y = 4, z = 10
(d) All of these

Answer

Answer: (d) All of these

Question 63.
The vectors (x, x + 1, x + 2), (x + 3, x + 4, x + 5) and (x + 6, x + 7, x + 8) are coplanar for
(a) all values of x
(b) x < 0
(c) x ≤ 0
(d) None of these

Answer

Answer: (a) all values of x

Question 64.
The vectors \(\vec{AB}\) = 3\(\hat{i}\) +4\(\hat{k}\) and \(\vec{AC}\) = 5\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) are the sides of ΔABC. The length of the median through A is
(a) \(\sqrt{18}\)
(b) \(\sqrt{72}\)
(c) \(\sqrt{33}\)
(d) \(\sqrt{288}\)

Answer

Answer: (c) \(\sqrt{33}\)

Question 65.
The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is
(a) √3
(b) 1 – √3
(c) 1 + √3
(d) -√3

Answer

Answer: (a) √3

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MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry with Answers

Three Dimensional Geometry Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Three Dimensional Geometry Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 11 MCQ With Answers

Maths Class 12 Chapter 11 MCQs On Three Dimensional Geometry

Three Dimensional Geometry Class 12 MCQ Questions Chapter 11 Question 1.
The direction cosines of the y-axis are
(a) (6, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)

Answer

Answer: (c) (0, 1, 0)

MCQ On Three Dimensional Geometry Class 12 Chapter 11 Question 2.
The direction ratios of the line joining the points (x, y, z) and (x2, y2, z1) are
(a) x1 + x2, y1 + y2, z1 + z2
(b) \(\sqrt{(x_1 – x_2)^2 + (y_1 – y_2)^2 + (z_1 + z_2)^2}\)
(c) \(\frac{x_1+x_2}{2}\), \(\frac{y_1+y_2}{2}\), \(\frac{z_1+z_2}{2}\)
(d) x2 – x1, y2 – y1, z2 – z1

Answer

Answer: (d) x2 – x1, y2 – y1, z2 – z1

3d Geometry Deals With MCQ Class 12 Chapter 11 Question 3.
The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
(a) (10, 0, 12)
(b) (5, 6, 0)
(c) (6, 5, 0)
(d) (5, 0, 6)

Answer

Answer: (d) (5, 0, 6)

MCQ On 3d Geometry Class 12 Chapter 11 Question 4.
If the planes a1x + b, y + c, z + d1 = 0 and a2x + b, y + c2z + d2 = 0 are perpendicular to each other then
(a) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\)
(b) \(\frac{a_1}{a_2}\) + \(\frac{b_1}{b_2}\), \(\frac{c_1}{c_2}\)
(c) a1a2 + b1b2 + c1c2 = 0
(d) a\(_{1}^{2}\)a\(_{2}^{2}\) + b\(_{1}^{2}\)b\(_{2}^{2}\) + c\(_{1}^{2}\)c\(_{2}^{2}\) = 0

Answer

Answer: (c) a1a2 + b1b2 + c1c2 = 0

3d Geometry Class 12 MCQ Chapter 11 Question 5.
The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is
(a) 4
(b) 3
(c) 2
(d) \(\frac{1}{5}\)

Answer

Answer: (c) 2

MCQ Questions For Class 12 Maths With Answers Chapter 11 Question 6.
The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are
(a) \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
(b) \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{6}{7}\)
(c) \(\frac{-2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
(d) None of these

Answer

Answer: (a) \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)

MCQ Questions For Class 12 Maths With Answers Pdf Download Question 7.
If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
(a) 3x + 5y – 6z + 3 = 0
(b) 2x – 5y – 6z + 3 = 0
(c) 2x + 5y – 6z + k = 0
(d) None of these

Answer

Answer: (c) 2x + 5y – 6z + k = 0

Class 12 Maths MCQ Pdf Chapter 11 Question 8.
(2, – 3, – 1) 2x – 3y + 6z + 7 = 0
(a) 4
(b) 3
(c) 2
(d) \(\frac{1}{5}\)

Answer

Answer: (c) 2

Class 12 Maths Chapter 11 Important Questions Question 9.
The length of the ⊥er from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is
(a) 0
(b) 2√3
(c) \(\frac{2}{3}\)
(d) 2

Answer

Answer: (d) 2

3d Geometry Class 12 Important Questions Chapter 11 Question 10.
The shortest distance between the lines \(\vec{r}\) = \(\vec{a}\) + k\(\vec{b}\) and r = \(\vec{a}\) + l\(\vec{c}\) is (\(\vec{b}\) and \(\vec{c}\) are non-collinear)
(a) 0
(b) |\(\vec{b}\).\(\vec{c}\)|
(c) \(\frac{|\vec{b}×\vec{c}|}{|\vec {a}|}\)
(d) \(\frac{|\vec{b}.\vec{c}|}{|\vec {a}|}\)

Answer

Answer: (a) 0

Class 12 Maths MCQ Pdf Free Download Chapter 11 Question 11.
The equation xy = 0 in three dimensional space is represented by
(a) a plane
(b) two plane are right angles
(c) a pair of parallel planes
(d) a pair of st. line

Answer

Answer: (b) two plane are right angles

Maths MCQ Questions Class 12 Chapter 11 Question 12.
The direction cosines of any normal to the xy plane are
(a) 1, 0 ,0
(b) 0, 1, 0
(c) 1, 1, 0
(d) 1, 1, 0

Answer

Answer: (d) 1, 1, 0

Class 12 Maths MCQs Chapter Wise Chapter 11 Question 13.
How many lines through the origin in make equal angles with the coordinate axis?
(a) 1
(b) 4
(c) 8
(d) 2

Answer

Answer: (c) 8

Class 12 Maths MCQ Pdf Download Chapter 11 Question 14.
The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are
(a) 2, -2, 0
(b) 1, -1, 0
(c) \(\frac{1}{√2}\), – \(\frac{1}{√2}\)
(d) None of these

Answer

Answer: (c) \(\frac{1}{√2}\), – \(\frac{1}{√2}\)

MCQ Questions For Class 12 Maths With Solutions Chapter 11 Question 15.
The equation x² – x – 2 = 0 in three dimensional space is represented by
(a) A pair of parallel planes
(b) A pair of straight lines
(c) A pair of perpendicular plane
(d) None of these

Answer

Answer: (a) A pair of parallel planes

Maths MCQs For Class 12 With Answers Pdf Chapter 11 Question 16.
The distance of the point (-3, 4, 5) from the origin
(a) 50
(b) 5√2
(c) 6
(d) None of these

Answer

Answer: (b) 5√2

Three Dimensional Element Is MCQ Class 12 Chapter 11 Question 17.
If a line makes angles Q1, Q21 and Q3 respectively with the coordinate axis then the value of cos² Q1 + cos² Q2 + cos² Q3
(a) 2
(b) 1
(c) 4
(d) \(\frac{3}{2}\)

Answer

Answer: (b) 1

Ncert Solutions For Class 12 Maths Chapter 11 Question 18.
The direction ratios of a line are 1,3,5 then its direction cosines are
(a) \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)
(b) \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\)
(c) \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\)
(d) None of these

Answer

Answer: (a) \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)

Class 12 Maths MCQs Chapter 11 Question 19.
The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are
(a) 7, 4,-2
(b)7, 4, 5
(c) 7, 4, 2
(d) 4, -2, 5

Answer

Answer: (a) 7, 4,-2

MCQ Questions For Class 12th Maths Chapter 11 Question 20.
The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
(a) 3, 2, -1
(b) -3, 7, 5
(c) 1, -1, 2
(d) – 11, 4, -5

Answer

Answer: (b) -3, 7, 5

Question 21.
The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector
(a) 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
(b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
(c) 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)
(b) -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\)

Answer

Answer: (b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)

Question 22.
The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
(a) 3x – 4y – 5z – 6 = 0
(b) 3x – 4y + 5z + 6 = 0
(c) 3x – 4y + 5z = 0
(d) 3x + 4y – 5z + 6 = 0

Answer

Answer: (c) 3x – 4y + 5z = 0

Question 23.
The locus of xy + yz = 0 is
(a) A pair of st. lines
(b) A pair of parallel lines
(c) A pair of parallel planes
(d) A pair of perpendicular planes

Answer

Answer: (d) A pair of perpendicular planes

Question 24.
The plane x + y = 0
(a) is parallel to z-axis
(b) is perpendicular to z-axis
(c) passes through z-axis
(d) None of these

Answer

Answer: (c) passes through z-axis

Question 25.
If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =
(a) 1
(b) 2
(c) 0
(d) -1

Answer

Answer: (b) 2

Question 26.
If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
(a) -2
(b) -1
(c) 1
(d) 2

Answer

Answer: (b) -1

Question 27.
The line x = 1, y = 2 is
(a) parallel to x-axis
(b) parallel to y-axis
(c) parallel to z-axis
(d) None of these

Answer

Answer: (c) parallel to z-axis

Question 28.
The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(\(\frac{2}{3}\), \(\frac{2}{3}\), \(\frac{2}{3}\))
(a) Coplanar
(b) Non-coplanar
(c) Vertices of a parallelogram
(d) None of these

Answer

Answer: (a) Coplanar

Question 29.
The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)

Answer

Answer: (c) \(\frac{π}{3}\)

Question 30.
The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is
(a) \(\frac{\sqrt{31}}{21}\)
(b) \(\frac{13}{21}\)
(c) \(\frac{13}{\sqrt{21}}\)
(d) \(\sqrt{\frac{π}{2}}\)

Answer

Answer: (c) \(\frac{13}{\sqrt{21}}\)

Question 31.
The planes \(\vec{r}\)(2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\)) = 7 and
\(\vec{r}\)(\(\frac{-2}{7}\)\(\vec{i}\) – \(\frac{3}{j}\)\(\vec{j}\) + \(\frac{6}{7}\)\(\vec{k}\)) = 0 are
(a) parallel
(b) at right angles
(c) equidistant front origin
(d) None of these

Answer

Answer: (a) parallel

Question 32.
The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
(a) 3x – 5y + 2z – 13 = 0
(b) 5x – 3y + 2z + 13 = 0
(c) 3x – 2y + 5z + 13 = 0
(d) 3x – 5y + 2z + 13 = 0

Answer

Answer: (d) 3x – 5y + 2z + 13 = 0

Question 33.
Distance of the point (a, β, γ) from y-axis is
(a) β
(b) |β|
(c) |β + γ|
(d) \(\sqrt{α^2+γ^2}\)

Answer

Answer: (d) \(\sqrt{α^2+γ^2}\)

Question 34.
If the directions cosines of a line are A, k, k, then
(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)

Answer

Answer: (d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)

Question 35.
The distance of the plane \(\vec{r}\)(\(\frac{-2}{7}\)\(\hat{i}\) – \(\frac{3}{7}\)\(\hat{j}\) + \(\frac{6}{7}\)\(\hat{k}\)) = 0 from the orgin is
(a) 1
(b) 7
(c) \(\frac{1}{7}\)
(d) None of these

Answer

Answer: (a) 1

Question 36.
The sine of the angle between the straight line \(\frac{x-2}{3}\) = \(\frac{y-3}{4}\) = \(\frac{z-4}{5}\) and the plane 2x – 2y + z = 5 is
(a) \(\frac{10}{6√5}\)
(b) \(\frac{4}{5√2}\)
(c) \(\frac{2√3}{5}\)
(d) \(\sqrt{\frac{√2}{10}}\)

Answer

Answer: (c) \(\frac{2√3}{5}\)

Question 37.
The reflection of the point (a, β, γ) in the xy-plane is
(a) (α, β, 0)
(b) (0, 0, γ)
(c) (- α, – β, γ)
(d) (α, β, γ)

Answer

Answer: (d) (α, β, γ)

Question 38.
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
(a) 9 sq. units
(b) 18 sq. units
(c) 27 sq. units
(d) 81 sq. units

Answer

Answer: (a) 9 sq. units

Question 39.
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin-1 (α) with .e-axis. The value of a is equal to
(a) \(\frac{√3}{2}\)
(b) \(\frac{√2}{3}\)
(c) \(\frac{2}{7}\)
(d) \(\frac{3}{7}\)

Answer

Answer: (c) \(\frac{2}{7}\)

Question 40.
The cosines of the angle between any two diagonals of a cube is
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{√3}\)

Answer

Answer: (a) \(\frac{1}{3}\)

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MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers

Integrals Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Integrals Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 7 MCQ With Answers

Maths Class 12 Chapter 7 MCQs On Integrals

Integration MCQ Class 12 Chapter 7 Question 1.
\(\int \frac{x+\sin x}{1+\cos x}\) dx is equal to
(a) log |1 + cos x | + c
(b) log | x + sin x | + c
(c) x – tan + c
(d) x. tan \(\frac{x}{2}\) + c

Answer

Answer: (d) x. tan \(\frac{x}{2}\) + c

MCQ On Integration Class 12 Chapter 7 Question 2.
∫1.dx =
(a) x + k
(b) 1 + k
(c) \(\frac{x^2}{2}\) + k
(d) log x + k

Answer

Answer: (a) x + k

Integration MCQ Questions Class 12 Chapter 7 Question 3.
∫\(\frac{dx}{√x}\) =
(a) √x + k
(b) 2√x + k
(c) x + k
(d) \(\frac{2}{3}\)x3/2 + k

Answer

Answer: (b) 2√x + k

MCQ On Integration Class 12 Chapter 7 Question 4.
∫\(\frac{dx}{1+cos x}\) =
(a) tan \(\frac{x}{2}\) + k
(b) \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
(c) 2 tan \(\frac{x}{2}\) + k
(d) tan² \(\frac{x}{2}\) + k

Answer

Answer: (a) tan \(\frac{x}{2}\) + k

Integration MCQs With Answers Pdf Class 12 Chapter 7 Question 5.
\(\int_{a}^{b}\) x5 dx =
(a) tan \(\frac{x}{2}\) + k
(b) \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
(c) 2 tan \(\frac{x}{2}\) + k
(d) tan² \(\frac{x}{2}\) + k

Answer

Answer: (a) tan \(\frac{x}{2}\) + k

Integration MCQ With Answers Class 12 Chapter 7 Question 6.
If x > a, ∫\(\frac{dx}{x^2-a^2}\) =
(a) \(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k
(b) \(\frac{2}{2a}\) log \(\frac{x+a}{x-a}\) + k
(c) \(\frac{1}{a}\) log(x² – a²) + k
(d) log(x + \(\sqrt{x^2-a^2}\) + k)

Answer

Answer: (a) \(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k

Integration Objective Questions Class 12 Chapter 7 Question 7.
∫\(\frac{cos 2x dx}{(sinx+cosx)^2}\) =
(a) –\(\frac{1}{sinx+cosx}\) + c
(b) log | sin x + cos x | + c
(c) log | sin x – cos x | + c
(d) \(\frac{1}{(sinx+cosx)^2}\)

Answer

Answer: (b) log | sin x + cos x | + c

MCQ On Integration With Answers Class 12 Chapter 7  Question 8.
∫\(\frac{(1+logx)^2}{1+x^2}\) dx =
(a) \(\frac{1}{3}\)(1+log)³ + c
(b) \(\frac{1}{2}\)(1+log)² + c
(c) log (log 1 + x) + 2
(d) None of these

Answer

Answer: (a) \(\frac{1}{3}\)(1+log)³ + c

Integration MCQs Class 12 Chapter 7  Question 9.
\(\int_{0}^{1}\frac{(tan^{-1}x)^2}{1+x^2}\) dx =
(a) 1
(b) \(\frac{π^2}{64}\)
(c) \(\frac{π^2}{192}\)
(d) None of these

Answer

Answer: (c) \(\frac{π^2}{192}\)

MCQ Of Integration Class 12 Chapter 7 Question 10.
\(\int_{-2}^{2}\) |x|dx =
(a) 0
(b) 2
(c) 1
(d) 4

Answer

Answer: (d) 4

MCQs On Integration Class 12 Chapter 7 Question 11.
∫\(\frac{x^4+1}{x^2+1}\) dx is equal to
(a) \(\frac{x^3}{3}\) + x + tan-1 x + c
(b) \(\frac{x^3}{3}\) – x + tan x + c
(c) \(\frac{x^3}{3}\) + x + 2tan-1 x + c
(d) \(\frac{x^3}{3}\) – x + 2tan-1 x + c

Answer

Answer: (d) \(\frac{x^3}{3}\) – x + 2tan-1 x + c

Integration MCQ With Answers Pdf Class 12 Chapter 7 Question 12.
∫(√x + \(\frac{1}{√x}\)) dx =
(a) \(\frac{1}{x}\) x\(\frac{1}{3}\) + 2x\(\frac{1}{2}\) + c
(b) \(\frac{2}{3}\) x\(\frac{2}{3}\) + \(\frac{1}{2}\)x2 + c
(c) \(\frac{2}{3}\) x\(\frac{3}{2}\) + 2x\(\frac{1}{2}\) + c
(d) \(\frac{3}{2}\) x\(\frac{3}{2}\) + \(\frac{1}{2}\)x\(\frac{1}{2}\) + c

Answer

Answer: (c) \(\frac{2}{3}\) x\(\frac{3}{2}\) + 2x\(\frac{1}{2}\) + c

Integration MCQ Questions And Answers Class 12 Chapter 7  Question 13.
∫\(\frac{sin^2x-cos^2x}{sin^2xcos^2x}\) dx is equal to
(a) tan x + cos x + c
(b) tan x + cosec x + c
(c) tan x + cot x + c
(d) tan x+ sec x + c

Answer

Answer: (c) tan x + cot x + c

Integral MCQ Questions Class 12 Chapter 7 Question 14.
\(\frac{d}{dx}\)∫f(x)dx is equal to
(a) f'(x)
(b) f(x)
(c) f'(x’)
(d) f(x) + c

Answer

Answer: (b) f(x)

MCQ Integration Class 12 Chapter 7 Question 15.
∫\(\frac{xdx}{(x-1)(x-2)}\) equals
MCQ Integration Class 12 Chapter 7
(d) log |(x – 1)(x – 2) + c

Answer

Answer: (b) log|\(\frac{(x-2)^2}{x-2}\)| + c

Integration MCQs With Answers Chapter 7  Question 16.
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{\sqrt{tan x}}{\sqrt{tan x}+\sqrt{cot x}}\) dx?
(a) \(\frac{π}{2}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{8}\)
(d) None of these

Answer

Answer: (b) \(\frac{π}{4}\)

Integrals MCQs Class 12 Chapter 7 Question 17.
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{sinx – cos x}{1+sin xcos x}\) dx?
(a) 1
(b) \(\frac{π}{2}\)
(c) 0
(d) –\(\frac{π}{2}\)

Answer

Answer: (c) 0

Integration MCQs Class 12 Chapter 7 Question 18.
What is the value of \(\int_{\pi / 6}^{\pi / 3}\) \(\frac{dx}{sin2x}\)?
(a) \(\frac{1}{2}\) log(-l)
(b) log(- 1)
(c) log 3
(d) log √3

Answer

Answer: (c) log 3

Integration MCQ Class 12 Question 19.
What is the value of \(\int_{-1}^{1}\) sin³ x cos² xdx?
(a) 0
(b) 1
(c) \(\frac{1}{2}\)
(d) 2

Answer

Answer: (a) 0

MCQ Questions On Integration Question 20.
What is the value of \(\int_{1}^{e} \frac{1+\log x}{x}\) dx?
(a) \(\frac{3}{2}\)
(b) \(\frac{1}{2}\)
(c) e
(d) \(\frac{1}{e}\)

Answer

Answer: (a) \(\frac{3}{2}\)

Question 21.
\(\int_{-\pi / 2}^{\pi / 2}\) sin9 xdx =
(a) -1
(b) 0
(c) 1
(d) None of these

Answer

Answer: (b) 0

Question 22.
\(\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}\)
(a) 1
(b) 2
(c) \(\frac{π}{4}\)
(d) \(\frac{π^2}{8}\)

Answer

Answer: (b) 2

Question 23.
\(\int_{0}^{\infty} \frac{1}{1+e^{x}}\) dx =
(a) log 2
(b) -log 2
(c) log 2 – 1
(d) log 4 – 1

Answer

Answer: (a) log 2

Question 24.
\(\int_{0}^{1}\) x(1 – x)99 is equal to
(a) \(\frac{1}{10010}\)
(b) \(\frac{1}{10100}\)
(c) \(\frac{1}{1010}\)
(d) \(\frac{11}{10100}\)

Answer

Answer: (b) \(\frac{1}{10100}\)

Question 25.
What is the value of \(\int_{0}^{1}\) \(\frac{d}{dx}\){sin-1(\(\frac{2x}{1+x^2}\))}dx?
(a) 0
(b) π
(c) -π
(d) \(\frac{π}{2}\)

Answer

Answer: (d) \(\frac{π}{2}\)

Question 26.
\(\int_{0}^{1}\) \(\frac{x}{1+x}\) dx =
(a) 1 – log 2
(b) 2
(c) 1 + log 2
(d) log 2

Answer

Answer: (a) 1 – log 2

Question 27.
∫\(\frac{sin x + cos x}{\sqrt{1+2sin x}}\) dx =
(a) log(sin x – cos x)
(b) x
(c) log x
(d) log sin (cos x)

Answer

Answer: (b) x

Question 28.
∫log10 xdx =
(a) loge 10.x loge (\(\frac{x}{e}\)) + c
(b) log10 e.x loge (\(\frac{x}{e}\)) + c
(c) (x – 1) loge x + c
(d) \(\frac{1}{x}\) + c

Answer

Answer: (b) log10 e.x loge (\(\frac{x}{e}\)) + c

Question 29.
∫(\(\frac{cos 2θ – 1}{cos 2θ + 1}\)) dθ =
(a) tan θ – θ + c
(b) θ + tan θ + c
(c) θ – tan θ + c
(d) -θ – cot θ + c

Answer

Answer: (c) θ – tan θ + c

Question 30.
∫\(\frac{2dx}{\sqrt{1-4x^2}}\) =
(a) tan-1 (2x) + c
(b) cot-1 (2x) + c
(c) cos-1 (2x) + c
(d) sin-1 (2x) + c

Answer

Answer: (d) sin-1 (2x) + c

Question 31.
Value of ∫\(\frac{dx}{\sqrt{2x – x^2}}\)
(a) sin-1 (x – 1) + c
(b) sin-1 (1 + x) + c
(c) sin-1 (1 + x²) + c
(d) –\(\sqrt{2x-x^2}\) + c

Answer

Answer: (a) sin-1 (x – 1) + c

Question 32.
∫x² sin x³ dx =
(a) \(\frac{1}{3}\) cos x³ + c
(b) –\(\frac{1}{3}\) cos x + c
(c) \(\frac{-1}{3}\) cos x³ + c
(d) \(\frac{1}{2}\) sin² x³ + c

Answer

Answer: (c) \(\frac{-1}{3}\) cos x³ + c

Question 33.
∫\(\frac{cos 2x- cos 2θ}{cos x – cos θ}\)dx is equal to
(a) 2 (sin x + x cos θ) + C
(b) 2 (sin x – x cos θ) + C
(c) 2 (sin x + 2x cos θ) + C
(d) 2 (sin x – 2x cos θ) + C

Answer

Answer: (a) 2 (sin x + x cos θ) + C

Question 34.
∫\(\frac{dx}{sin(x-a)sin(x-b)}\) is equal to
(a) sin(b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
(b) cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-b)}\)| + C
(c) cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
(d) sin (b – a) log |\(\frac{sin (x-a)}{sin(x-b)}\)| + C

Answer

Answer: (c) cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C

Question 35.
∫tan-1 √xdx is equal to
(a) (x + 1)tan-1 √x – √x + C
(b) x tan-1 √x – √x + C
(c) √x – x tan-1 √x + C
(d) √x – (x + 1)tan-1 √x + C

Answer

Answer: (a) (x + 1)tan-1 √x – √x + C

Question 36.
∫ex(\(\frac{1-x}{1+x^2}\))² dx is equal to
(a) \(\frac{e^x}{1+x^2}\) + C
(b) –\(\frac{-e^x}{1+x^2}\) + C
(c) \(\frac{e^x}{(1+x^2)^2}\) + C
(d) \(\frac{-e^x}{(1+x^2)^2}\) + C

Answer

Answer: (a) \(\frac{e^x}{1+x^2}\) + C

Question 37.
∫\(\frac{x^9}{(4x^2+1)^6}\) dx is equal to
MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers

Answer

Answer: (d) \(\frac{1}{10}\) (\(\frac{1}{x^2}\) + 4)-5 + C

Question 38.
If ∫\(\frac{dx}{(x+2)(x^2+1)}\) = a log |1 + x²| + b tan-1 x + \(\frac{1}{5}\) log |x + 2| + C, then
(a) a = \(\frac{-1}{10}\), b = \(\frac{-2}{5}\)
(b) a = \(\frac{1}{10}\), b = \(\frac{-2}{5}\)
(c) a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\)
(d) a = \(\frac{1}{10}\), b = \(\frac{2}{5}\)

Answer

Answer: (c) a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\)

Question 39.
∫ \(\frac{x^3}{x+1}\) is equal to
(a) x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 – x| + C
(b) x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 – x| + C
(c) x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 + x| + C
(d) x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C

Answer

Answer: (d) x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C

Question 40.
If ∫\(\frac{x^3dx}{\sqrt{1+x^2}}\) = a(1 + x²)3/2 + b\(\sqrt{1 + x^2}\) + C, then
(a) a = \(\frac{1}{3}\), b = 1
(b) a = \(\frac{-1}{3}\), b = 1
(c) a = \(\frac{-1}{3}\), b = -1
(d) a = \(\frac{1}{3}\), b = -1

Answer

Answer: (d) a = \(\frac{1}{3}\), b = -1

Question 41.
\(\int_{-\pi / 4}^{\pi / 4}\) \(\frac{dx}{1+cos 2x}\) dx is equal to
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (a) 1

Question 42.
\(\int_{0}^{\pi / 2}\) \(\sqrt{1+sin 2x}\) dx is equal to
(a) 2√2
(b) 2(√2 + 1)
(c) 0
(d) 2(√2 – 1)

Answer

Answer: (c) 0

Question 43.
Evaluate: ∫(2 tan x – 3 cot x)² dx
(a) -4tan x – cot x – 25x + C
(b) 4 tan x – 9 cot x – 25x + C
(c) – 4 tan x + 9 cot x + 25x + C
(d) 4 tan x + 9 cot x + 25x + C

Answer

Answer: (b) 4 tan x – 9 cot x – 25x + C

Question 44.
Evaluate: ∫ sec²(7 – 4x)dx
(a) –\(\frac{1}{4}\) tan(7 – 4x) + C
(b) \(\frac{1}{4}\) tan(7 – 4x) + C
(c) \(\frac{1}{4}\) tan(7 + 4x) + C
(d) –\(\frac{1}{4}\) tan(7x – 4) + C

Answer

Answer: (a) –\(\frac{1}{4}\) tan(7 – 4x) + C

Question 45.
∫ \(\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}\) dx is equal to
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10)-1 + C
(d) loge(10x + x10) + C

Answer

Answer: (d) loge(10x + x10) + C

Question 46.
Evaluate: ∫ sec4/3 x cosec8/3 xdx
(a) \(\frac{3}{5}\) tan-5/3 x – 3 tan1/3 x + C
(b) –\(\frac{3}{5}\) tan-5/3 x + 3 tan1/3 + C
(c) –\(\frac{3}{5}\) tan-05/3 x – 3 tan1/3 + C
(d) None of these

Answer

Answer: (b) –\(\frac{3}{5}\) tan-5/3 x + 3 tan1/3 + C

Question 47.
∫ \(\frac{a}{(1+x^2)tan^{-1}x}\) dx =
(a) a log |tan-1 x| + C
(b) \(\frac{1}{2}\)(tan-1 x)² + C
(c) a log (1 + x2) + C
(d) None of these

Answer

Answer: (a) a log |tan-1 x| + C

Question 48.
∫ \(\frac{cot x}{\sqrt[3]{sin x}}\) dx =
(a) \(\frac{-3}{\sqrt[3]{sin x}}\) + C
(b) \(\frac{-2}{sin^3 x}\) + C
(c) \(\frac{3}{sin^{1/3}x}\) + C
(d) None of these

Answer

Answer: (a) \(\frac{-3}{\sqrt[3]{sin x}}\) + C

Question 49.
Evaluate: ∫ \(\frac{1}{1+3sin^2x+8cos^2x}\) dx
(a) \(\frac{1}{6}\) tan-1 (2 tan x) + C
(b) tan-1 (2 tan x) + C
(c) \(\frac{1}{6}\) tan-1(\(\frac{2 tan x}{3}\)) + C
(d) None of these

Answer

Answer: (c) \(\frac{1}{6}\) tan-1(\(\frac{2 tan x}{3}\)) + C

Question 50.
Evaluate: ∫ \(\frac{1}{\sqrt{9+8x-x^2}}\) dx
(a) -sin-1 (\(\frac{x-4}{5}\)) + C
(b) sin-1 (\(\frac{x+4}{5}\)) + C
(c) sin-1 (\(\frac{x-4}{5}\)) + C
(d) None of these

Answer

Answer: (c) sin-1 (\(\frac{x-4}{5}\)) + C

Question 51.
∫ \(\frac{dx}{1-cosx-sinx}\) is equal to
(a) log |1 + cot\(\frac{x}{2}\)| + C
(b) log |1 – tan\(\frac{x}{2}\)| + C
(c) log |1 – cot\(\frac{x}{2}\)| + C
(d) log |1 + tan\(\frac{x}{2}\)| + C

Answer

Answer: (c) log |1 – cot\(\frac{x}{2}\)| + C

Question 52.
Evaluate: ∫ \(\frac{1}{\sqrt{1-e^{2x}}}\) dx
(a) log |e-x + \(\sqrt{e^{-2x} – 1}\)| + C
(b) -log |e-x + \(\sqrt{e^{-2x} – 1}\)| + C
(c) -log |e-x – \(\sqrt{e^{-2x} – 1}\)| + C
(d) None of these

Answer

Answer: (b) -log |e-x + \(\sqrt{e^{-2x} – 1\)| + C

Question 53.
If ∫ \(\frac{3x+4}{x^3-2x-4}\) dx = log |x – 2| + k log f(x) + c, then
(a) f(x) = |x² + 2x + 2|
(b) f(x) = x² + 2x + 2
(c) k = –\(\frac{1}{2}\)
(d) All of these

Answer

Answer: (d) All of these

Question 54.
Evaluate: ∫ \(\frac{1-cosx}{cosx(1+cosx)}\) dx
(a) log|sec x + tan x| – 2 tan(x/2) + C
(b) log|sec x – tan x| – 2 tan(x/2) + C
(c) log|sec x + tan x| + 2 tan(x/2) + C
(d) None of these

Answer

Answer: (a) log|sec x + tan x| – 2 tan(x/2) + C

Question 55.
∫ cos(loge.x)dx is equal to
(a) \(\frac{1}{2}\) x[cos (logex) + sin(logex)]
(b) x[cos (logex) + sin(logex)]
(c) \(\frac{1}{2}\) x[cos (logex) – sin(logex)]
(d) x[cos (logex) – sin(logex)]

Answer

Answer: (b) –\(\frac{3}{5}\) tan-5/3 x + 3 tan1/3 + C

Question 56.
∫ |x| dx is equal to
(a) \(\frac{1}{2}\) x² + C
(b) –\(\frac{x^2}{2}\) + C
(c) x|x| + C
(d) \(\frac{1}{2}\) x|x| + C

Answer

Answer: (d) \(\frac{1}{2}\) x|x| + C

Question 57.
∫ sin-1 xdx is equal to
(a) cos-1 x + C
(b) x sin-1x + \(\sqrt{1-x^2}\) + C
(c) \(\frac{1}{\sqrt{1-x^2}}\) + C
(d) x sin-1x – \(\sqrt{1-x^2}\) + C

Answer

Answer: (b) x sin-1x + \(\sqrt{1-x^2}\) + C

Question 58.
∫ cos-1(\(\frac{1}{x}\))dx equals
(a) x sec-1 x + log |x + \(\sqrt{x^2-1}\)| + C
(b) x sec-1 x – log |x + \(\sqrt{x^2-1}\)| + C
(c) -x sec-1 x – log |x + \(\sqrt{x^2-1}\)| + C
(d) None of these

Answer

Answer: (b) x sec-1 x – log |x + \(\sqrt{x^2-1}\)| + C

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download will help you. If you have any queries regarding Integrals CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 12 Maths MCQ:

MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers

Linear Programming Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Linear Programming Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 12 MCQ With Answers

Maths Class 12 Chapter 12 MCQs On Linear Programming

Linear Programming Class 12 MCQ Question 1.
Feasible region in the set of points which satisfy
(a) The objective functions
(b) Some the given constraints
(c) All of the given constraints
(d) None of these

Answer

Answer: (c) All of the given constraints

MCQ Questions On Linear Programming Class 12 Question 2.
Of all the points of the feasible region for maximum or minimum of objective function the points
(a) Inside the feasible region
(b) At the boundary line of the feasible region
(c) Vertex point of the boundary of the feasible region
(d) None of these

Answer

Answer: (c) Vertex point of the boundary of the feasible region

Linear Programming MCQ With Answers Pdf Question 3.
Objective function of a linear programming problem is
(a) a constraint
(b) function to be obtimized
(c) A relation between the variables
(d) None of these

Answer

Answer: (b) function to be obtimized

Linear Programming MCQ Class 12 Question 4.
A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of a L.P.P. is called its
(a) Unbounded solution
(b) Optimum solution
(c) Feasible solution
(d) None of these

Answer

Answer: (c) Feasible solution

Lpp MCQ Class 12 Question 5.
The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is
(a) 300
(b) 600
(c) 400
(d) 800

Answer

Answer: (b) 600

Lpp MCQ Questions Class 12 Question 6.
The maximum value of Z = 4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10, x, y ≤ 0 is
(a) 36
(b) 40
(c) 30
(d) None of these

Answer

Answer: (d) None of these

Lpp Class 12 MCQ Question 7.
In equation 3x – y ≥ 3 and 4x – 4y > 4
(a) Have solution for positive x and y
(b) Have no solution for positive x and y
(c) Have solution for all x
(d) Have solution for all y

Answer

Answer: (a) Have solution for positive x and y

Linear Programming Is A MCQ Question 8.
The maximum value of Z = 3x + 4y subjected to contraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is
(a) 120
(b) 140
(c) 100
(d) 160

Answer

Answer: (b) 140

MCQ On Lpp Class 12 Question 9.
Maximize Z = 11 x + 8y subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0.
(a) 44 at (4, 2)
(b) 60 at (4, 2)
(c) 62 at (4, 0)
(d) 48 at (4, 2)

Answer

Answer: (b) 60 at (4, 2)

MCQ Of Linear Programming Class 12 Question 10.
Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0
(a) 20 at (1, 0)
(b) 30 at (0, 6)
(c) 37 at (4, 5)
(d) 33 at (6, 3)

Answer

Answer: (c) 37 at (4, 5)

MCQ On Linear Programming Question 11.
Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0
(a) 16 at (4, 0)
(b) 24 at (0, 4)
(c) 24 at (6, 0)
(d) 36 at (0, 6)

Answer

Answer: (d) 36 at (0, 6)

MCQ On Linear Programming Class 12 Question 12.
Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
(a) 59 at (\(\frac{9}{2}\), \(\frac{5}{2}\))
(b) 42 at (6, 0)
(c) 49 at (7, 0)
(d) 57.2 at (0, 5.2)

Answer

Answer: (a) 59 at (\(\frac{9}{2}\), \(\frac{5}{2}\))

MCQ Of Lpp Class 12 Question 13.
Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0
(a) 12 at (2, 0)
(b) \(\frac{140}{3}\) at (\(\frac{2}{3}\), \(\frac{1}{3}\))
(c) 16 at (2, 1)
(d) 4 at (0, 1)

Answer

Answer: (c) 16 at (2, 1)

Class 12 Maths Chapter 12 MCQ Question 14.
Maximize Z = 10 x1 + 25 x2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5
(a) 80 at (3, 2)
(b) 75 at (0, 3)
(c) 30 at (3, 0)
(d) 95 at (2, 3)

Answer

Answer: (d) 95 at (2, 3)

Linear Programming MCQs  Question 15.
Z = 20x1 + 202, subject to x1 ≥ 0, x2 ≥ 0, x1 + 2x2 ≥ 8, 3x1 + 2x2 ≥ 15, 5x1 + 2x2 ≥ 20. The minimum value of Z occurs at
(a) (8, 0)
(b) (\(\frac{5}{2}\), \(\frac{15}{4}\))
(c) (\(\frac{7}{2}\), \(\frac{9}{4}\))
(d) (0, 10)

Answer

Answer: (c) (\(\frac{7}{2}\), \(\frac{9}{4}\))

Linear Programming MCQ Class 12 Question 16.
Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(a) (4, 0)
(b) (28, 8)
(c) (2, \(\frac{7}{2}\))
(d) (0, 3)

Answer

Answer: (c) (2, \(\frac{7}{2}\))

Linear Programming Class 12 MCQ Questions Question 17.
The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.
Compare the quantity in Column A and Column B

Column A Column B
Maximum of Z 325

(a) The quantity in column A is greater
(b) The quantity in column B is greater
(c) The two quantities are equal
(d) The relationship cannot be determined On the basis of the information supplied

Answer

Answer: (b) The quantity in column B is greater

Question 18.
The feasible region for a LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at
MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers
(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)

Answer

Answer: (b) (0, 8)

Question 19.
Refer to Question 18 maximum of Z occurs at
(a) (5, 0)
(b) (6, 5)
(c) (6, 8)
(d) (4, 10)

Answer

Answer: (a) (5, 0)

Question 20.
Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to
(a) 13
(b) 1
(c) -13
(d) -17

Answer

Answer: (d) -17

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers Pdf free download will help you. If you have any queries regarding Linear Programming CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 12 Maths MCQ:

MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers

Probability Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Probability Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 13 MCQ With Answers

Maths Class 12 Chapter 13 MCQs On Probability

MCQ On Probability Class 12 Question 1.
If A and B are two independent events, then
(a) P(A∩B) = P(a) × P(b)
(b) P(AB) = 1 – P(A’) P(B’)
(c) P(AB) = 1 + P (A’) P(B’) P(A’)
(d) P (AB) = \(\frac{P(A’)}{P(B’)}\)

Answer

Answer: (a) P(A∩B) = P(a) × P(b)

Probability MCQ Class 12 Question 2.
The probability of an event is \(\frac{3}{7}\). Then odd against the event is
(a) 4 : 3
(b) 7 : 3
(c) 3 : 7
(d) 3 : 4

Answer

Answer: (a) 4 : 3

MCQ On Probability Class 12 Pdf Question 3.
A pair of dice are rolled. The probability of obtaining an even prime number on each die is
(a) \(\frac{1}{36}\)
(b) \(\frac{1}{12}\)
(c) \(\frac{1}{6}\)
(d) 0

Answer

Answer: (a) \(\frac{1}{36}\)

Probability Class 12 MCQ Question 4
If P(a) = \(\frac{3}{8}\), P(b) = \(\frac{1}{3}\) and P(A∩B) = — then P (A’ ∩B’)
(a) \(\frac{13}{24}\)
(b) \(\frac{13}{8}\)
(c) \(\frac{13}{9}\)
(d) \(\frac{13}{4}\)

Answer

Answer: (a) \(\frac{13}{24}\)

MCQ Of Probability Class 12 Question 5.
P(A∩B) = \(\frac{3}{8}\), P(b) = \(\frac{1}{2}\) and P(a) = \(\frac{1}{4}\) then P(\(\frac{B’}{A’}\)) =
(a) \(\frac{3}{5}\)
(b) \(\frac{5}{8}\)
(c) \(\frac{3}{8}\)
(d) \(\frac{5}{6}\)

Answer

Answer: (d) \(\frac{5}{6}\)

Probability MCQs With Answers Pdf Class 12 Question 6.
If A and B are two events such that P(a) ≠ 0 and P(\(\frac{B}{A}\)) = 1 then
(a) P(\(\frac{A}{B}\)) = 1
(b) P(\(\frac{B}{A}\)) = 1
(c) P(\(\frac{A}{B}\)) = 0
(d) P(\(\frac{B}{A}\)) = 0

Answer

Answer: (b) P(\(\frac{B}{A}\)) = 1

Probability Class 12 MCQ Questions Question 7.
If P (a) = \(\frac{3}{8}\), P(b) = \(\frac{1}{2}\) and P(A∩B) = \(\frac{1}{4}\) then P(\(\frac{A’}{B’}\)) =
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{3}{4}\)
(d) \(\frac{3}{8}\)

Answer

Answer: (b) \(\frac{1}{3}\)

Probability Questions And Answers Pdf Class 12 Question 8.
If A and B are two events such that P(a) ≠ 0 and P(\(\frac{B}{A}\)) = 1, then
(a) B ⊂ A
(b) B = φ
(c) A ⊂ B
(d) A ∩ B = φ

Answer

Answer: (c) A ⊂ B

Probability Class 12 Applied Mathematics MCQ Question 9.
If A and B are any two events such that P(a) + P(b) – P(A∩B) = P(a) then
(a) P(\(\frac{B}{A}\)) = 1
(b) P(\(\frac{B}{A}\)) = 0
(c) P(\(\frac{A}{B}\)) = 1
(d) P(\(\frac{A}{B}\)) = 0

Answer

Answer: (c) P(\(\frac{A}{B}\)) = 1

Class 12 Probability MCQ Question 10.
If A and B are events such that P (A∪B) = \(\frac{3}{4}\). P(A∩B) = \(\frac{1}{4}\), P(a) = \(\frac{2}{3}\) then P(AB) is
(a) \(\frac{3}{8}\)
(b) \(\frac{5}{8}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (b) \(\frac{5}{8}\)

Probability Class 12 Questions And Answers Question 11.
If one card is drawn out of 52 playing cards, the probability that it is an dice is
(a) \(\frac{1}{26}\)
(b) \(\frac{1}{13}\)
(c) \(\frac{1}{52}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (b) \(\frac{1}{13}\)

Probability Class 12 Important Questions Question 12.
The chance of getting a doublet with 2 dice is
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{6}\)
(c) \(\frac{5}{6}\)
(d) \(\frac{5}{36}\)

Answer

Answer: (b) \(\frac{1}{6}\)

Question 13.
Two number are chosen, one by one without replacement from the set of number A = {1, 2, 3, 4, 5, 6} then the probability that minimum value of two number chosen is less than 4 is
(a) \(\frac{14}{15}\)
(b) \(\frac{1}{15}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{8}{5}\)

Answer

Answer: (b) \(\frac{1}{15}\)

Question 14.
If P(x) = \(\frac{2}{15}\); y = 1, 2, 3, 4, 5, 0 otherwise then P|x = 1 or 2| is
(a) \(\frac{1}{15}\)
(b) \(\frac{2}{15}\)
(c) \(\frac{1}{5}\)
(d) None of these

Answer

Answer: (c) \(\frac{1}{5}\)

Question 15.
Five horse are in a race. Mr. A select two of the horses at random and best on them. The probability that Mr. A select the winning horses is
(a) \(\frac{4}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{2}{5}\)

Answer

Answer: (d) \(\frac{2}{5}\)

Question 16.
The probability of India w inning a test match against. West Indies is \(\frac{1}{2}\). Assuming independence from match to match the probability that in a match series India second win occurs at the third test is
(a) \(\frac{1}{6}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{2}{3}\)

Answer

Answer: (b) \(\frac{1}{4}\)

Question 17.
Three distinct numbers.are selected from First 100 natural numbers. The probability divisible by 2 and 3 is
(a) \(\frac{9}{25}\)
(b) \(\frac{4}{35}\)
(c) \(\frac{4}{55}\)
(d) \(\frac{4}{1155}\)

Answer

Answer: (d) \(\frac{4}{1155}\)

Question 18.
The probability that A speaks truth is \(\frac{4}{5}\) while this probability for B is \(\frac{3}{4}\). The probability that they contradict each others when asked to speak ana fact is
(a) \(\frac{7}{20}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{3}{20}\)
(d) \(\frac{4}{5}\)

Answer

Answer: (d) \(\frac{4}{5}\)

Question 19.
Two dice are tossed once. The probability of getting an even number at the first dice ora total of 8 is
(a) \(\frac{1}{36}\)
(b) \(\frac{3}{36}\)
(c) \(\frac{11}{36}\)
(d) \(\frac{5}{9}\)

Answer

Answer: (d) \(\frac{5}{9}\)

Question 20.
The mean and the variance of binomial distribution are 4 and 2, respectively. Then the probability of 2 success
(a) \(\frac{128}{256}\)
(b) \(\frac{219}{256}\)
(c) \(\frac{7}{64}\)
(d) \(\frac{28}{256}\)

Answer

Answer: (c) \(\frac{7}{64}\)

Question 21.
A pair of dice are rolled. The probability of obtaining an even prime number on each dice is
(a) \(\frac{1}{36}\)
(b) \(\frac{1}{12}\)
(c) \(\frac{1}{6}\)
(d) 0

Answer

Answer: (a) \(\frac{1}{36}\)

Question 22.
If A, B are two events associated with same random experiment such that P(a) = 0.4, P(b) = 0.8 and P(B/A) = 0.6 then P(A/B) is
(a) 0.3
(b) 0.4
(c) 0.5
(d) 0.6

Answer

Answer: (a) 0.3

Question 23.
If P(a) = \(\frac{3}{8}\), P(b) = \(\frac{5}{8}\), P(A∪B) = \(\frac{3}{4}\) then p(\(\frac{B}{A}\)) is
(a) \(\frac{3}{47}\)
(b) \(\frac{5}{49}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{4}\)

Answer

Answer: (c) \(\frac{2}{3}\)

Question 24.
An urn contain’s balls of which 3 are red, 4 are blue and 2 are green, 3 balls are drawn at random without replacement from the urn. The probability that the 3 balls haye different colours is
(a) \(\frac{1}{3}\)
(b) \(\frac{2}{7}\)
(c) \(\frac{1}{21}\)
(d) \(\frac{2}{23}\)

Answer

Answer: (b) \(\frac{2}{7}\)

Question 25.
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. A consists 4 outcomes, the number of outcomes that B must have so that A and B are independent is
(a) 2, 4 or 8
(b) 36 or 9
(c) 4 or 8
(d) 5 or 10

Answer

Answer: (d) 5 or 10

Question 28.
If P(a) = \(\frac{4}{5}\) and P(A∩B) = \(\frac{7}{10}\), then P(B/A) is equal
(a) \(\frac{1}{10}\)
(b) \(\frac{1}{8}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{17}{20}\)

Answer

Answer: (d) \(\frac{17}{20}\)

Question 29.
If P(A∩B) = \(\frac{7}{10}\) and P(b) = \(\frac{17}{20}\), then P(A|B) equals
(a) \(\frac{14}{17}\)
(b) \(\frac{17}{20}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{1}{8}\)

Answer

Answer: (a) \(\frac{14}{17}\)

Question 30.
If P(a) = \(\frac{7}{10}\) P(b) = \(\frac{7}{10}\) and P(A∪B) = \(\frac{7}{10}\) then P (B|A) + P(A|B) equals
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{7}{12}\)

Answer

Answer: (d) \(\frac{7}{12}\)

Question 31.
If P(a) = \(\frac{2}{5}\), P(b) = \(\frac{3}{10}\) and P (A∩B) = \(\frac{1}{5}\), then P (A’|B’). P(B’|A’) is equal to
(a) \(\frac{5}{6}\)
(b) \(\frac{5}{7}\)
(c) \(\frac{25}{42}\)
(d) 1

Answer

Answer: (c) \(\frac{25}{42}\)

Question 32.
If P(a) = 0,4, P(b) = 0.8 and P(B|A) = 0.6 then P(A∪B) is equal to
(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96

Answer

Answer: (d) 0.96

Question 33.
If A and B are two events and A ≠ Φ, B ≠ Φ, then
(a) P (A|B) = P (a). P (b)
(b) P (A|B) = \(\frac{P(A∩B)}{P(B)}\)
(c) P (A + B). P (B|A) = 1
(d) P (A|B) = P (a) | P (b)

Answer

Answer: (b) P (A|B) = \(\frac{P(A∩B)}{P(B)}\)

Question 34.
A and B are events such that P(a) = 0.4, P(b) = 0.3 and P(A∪B) = 0.5. Then P(B∩A) equals
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{3}{10}\)
(d) \(\frac{1}{5}\)

Answer

Answer: (d) \(\frac{1}{5}\)

Question 35.
You are given that A and B are two events such that P(b) = \(\frac{3}{5}\), P(A|B) = \(\frac{1}{2}\) and P (A∪B) = \(\frac{4}{5}\), then P(a) equals
(a) \(\frac{3}{10}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (c) \(\frac{1}{2}\)

Question 36.
You are given that A and B are two events such that P(b) = \(\frac{3}{5}\), P(A|B) = \(\frac{1}{2}\) and P (A∪B) = then P(B|A’) equals
(a) \(\frac{1}{5}\)
(b) \(\frac{3}{10}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (d) \(\frac{3}{5}\)

Question 37.
If P(b) = \(\frac{1}{5}\), P(A|B) = \(\frac{1}{2}\) and P(A∪B) = \(\frac{4}{5}\) then P (A∪B)’ + P (A’∪B) =
(a) \(\frac{1}{5}\)
(b) \(\frac{4}{5}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)

Answer

Answer: (d) \(\frac{3}{5}\)

Question 38.
Let P (a) = \(\frac{7}{13}\), P(b) = \(\frac{9}{13}\) and P (A∪B) = \(\frac{9}{13}\), Then P(A’|B) is equal to
(a) \(\frac{6}{13}\)
(b) \(\frac{4}{13}\)
(c) \(\frac{4}{9}\)
(d) \(\frac{5}{9}\)

Answer

Answer: (d) \(\frac{5}{9}\)

Question 39.
If A and B are such that events that P(a) > 0 and P(b) ≠ 1, then P (A’|B’) equal
(a) 1 – P (A|B)
(b) 1 – P(A’|B)
(c) \(\frac{1-P(A∪B)}{P(B’)}\)
(d) p(A’) | P(B’)

Answer

Answer: (c) \(\frac{1-P(A∪B)}{P(B’)}\)

Question 40.
If two events are independent, then
(a) they must be mutually exclusive
(b) the sum of their probabilities must be equal to 1
(c) (a) and (b) both are correct
(d) None of the above is correct

Answer

Answer: (d) None of the above is correct

Question 41.
If A and B are two independent events with P(a) = \(\frac{3}{5}\) and P (b) = \(\frac{4}{9}\), then P (A’∩B’) equals
(a) \(\frac{4}{15}\)
(b) \(\frac{8}{15}\)
(c) \(\frac{1}{3}\)
(d) \(\frac{2}{9}\)

Answer

Answer: (d) \(\frac{2}{9}\)

Question 42.
Let A and B two event such that P(a) = \(\frac{3}{8}\), P(b) = \(\frac{5}{8}\) and P(A∪B) = \(\frac{3}{4}\). Then P(A|B).P(A’|B) is equal to
(a) \(\frac{2}{5}\)
(b) \(\frac{3}{8}\)
(c) \(\frac{3}{20}\)
(d) \(\frac{6}{25}\)
Ans. (d)

Answer

Answer: (d) \(\frac{6}{25}\)

Question 43.
If the event A and B are independent, then P(A∩B) is equal to
(a) P(a) + P(b)
(b) P(a) – P(b)
(c) P(a). P(b)
(d) P(a) | P(b)

Answer

Answer: (c) P(a). P(b)

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers Pdf free download will help you. If you have any queries regarding Probability CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 12 Maths MCQ:

MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers

Differential Equations Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Differential Equations Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 9 MCQ With Answers

Maths Class 12 Chapter 9 MCQs On Differential Equations

MCQ On Differential Equations Class 12 Chapter 9 Question 1.
Integration factor of differential equation \(\frac{dy}{dx}\) + py = Q, where P and IQ are functions of x is
(a) ∫epdx
(b) \(_{e}\)∫pdx
(c) \(_{e}\)-∫pdx
(d) None of these

Answer

Answer: (d) None of these

Differential Equations Class 12 MCQ Chapter 9 Question 2.
The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is
(a) 0.4 π cm/s
(b) 0.8 π cm/s
(c) 0.8 cm/s
(d) None of these

Answer

Answer: (b) 0.8 π cm/s

Differential Equations MCQ Class 12 Chapter 9 Question 3.
The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is
(a) x – y = k(1 + xy)
(b) log (1 + y) = x + \(\frac{x^2}{2}\) + k
(c) log (1 + x) + y + \(\frac{y^2}{2}\) = k
(d) None of these

Answer

Answer: (b) log (1 + y) = x + \(\frac{x^2}{2}\) + k

MCQ On Differential Equations Class 12 Chapter 9 Question 4.
The degree of the differential equation
(\(\frac{d^2y}{dx}\))² + (\(\frac{dy}{dx}\))² = x sin \(\frac{dy}{dx}\) is
(a) 1
(b) 2
(c) 3
(d) not defined

Answer

Answer: (d) not defined

Differential Equations MCQ Questions And Answers Class 12 Chapter 9 Question 5.
The degree of differential equation
[1 + (\(\frac{dy}{dx}\))²]\(\frac{3}{2}\) = \(\frac{d^2y}{dx^2}\) is
(a) 4
(b) \(\frac{3}{2}\)
(c) 2
(d) not defined

Answer

Answer: (c) 2

Differential Equation MCQ Class 12 Chapter 9 Question 6.
The order and degree of the differential equation
\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))\(\frac{1}{4}\) + x\(\frac{1}{3}\) = 0 respectvely, are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3

Answer

Answer: (a) 2 and not defined

Differential Equations MCQ With Answers Class 12 Chapter 9 Question 7.
If y = e-x (A cos x + B sin x), then y is a solution of
(a) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) = 0
(b) \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + 2y = 0
(c) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
(d) \(\frac{d^2y}{dx^2}\) + 2y = 0

Answer

Answer: (c) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0

Differential Equations MCQ Questions Class 12 Chapter 9 Question 8.
The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is
(a) \(\frac{d^2y}{dx^2}\) – α²y = 0
(b) \(\frac{d^2y}{dx^2}\) + α²y = 0
(c) \(\frac{d^2y}{dx^2}\) + αy = 0
(d) \(\frac{d^2y}{dx^2}\) – αy = 0

Answer

Answer: (b) \(\frac{d^2y}{dx^2}\) + α²y = 0

MCQ Differential Equations Class 12 Chapter 9 Question 9.
Solution of differential equation xdy – ydx = Q represents
(a) a rectangular hyperbola
(b) parabola whose vertex is at origin
(c) straight line passing through origin
(d) a circle whose centre is at origin

Answer

Answer: (c) straight line passing through origin

Integrating Factor MCQ Class 12 Chapter 9 Question 10.
Integrating factor of the differential equation cos x \(\frac{dy}{dx}\) + y sin x = 1 is
(a) cos x
(b) tan x
(c) sec x
(d) sin x

Answer

Answer: (c) sec x

Differential Equations MCQ With Solution Pdf Class 12 Chapter 9 Question 11.
Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is .
(a) tan x + tan y = k
(b) tan x – tan y = k
(c) \(\frac{tan x}{tan y}\) = k
(d) tan x.tan y = k

Answer

Answer: (d) tan x.tan y = k

Differential Equation MCQs Class 12 Chapter 9 Question 12.
Family r = Ax + A³ of curves is represented by the differential equation of degree
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (b) 2

MCQ Of Differential Equation Class 12 Chapter 9 Question 13.
Integrating factor of \(\frac{xdy}{dx}\) – y = x4 – 3x is
(a) x
(b) log x
(c) \(\frac{1}{2}\)
(d) -x

Answer

Answer: (c) \(\frac{1}{2}\)

Linear Differential Equations MCQs With Answers Class 12 Chapter 9 Question 14.
Solution of \(\frac{dy}{dx}\) – y = 1 y(0) = 1 is given by
(a) xy = -ex
(b) xy = -e-x
(c) xy = -1
(d) y = 2ex – 1

Answer

Answer: (d) y = 2ex – 1

MCQs On Differential Equations Class 12 Chapter 9 Question 15.
The number of solutions of \(\frac{dy}{dx}\) = \(\frac{y+1}{x-1}\) when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite

Answer

Answer: (b) one

Differential Equations MCQs Class 12 Chapter 9 Question 16.
Which of the following is a second order differential equation?
(a) (y’)² + x = y²
(b) y’y” + y = sin x
(c) y” + (y”)² + y = 0
(d) y’ = y²

Answer

Answer: (b) y’y” + y = sin x

MCQ Questions On Differential Equations Class 12 Chapter 9 Question 17.
Integrating factor of the differential equation
(1 – x²) \(\frac{dy}{dx}\) – xy = 1 is
(a) -x
(b) \(\frac{x}{1+x^2}\)
(c) \(\sqrt{1-x^2}\)
(d) \(\frac{1}{2}\) log(1 – x²)

Answer

Answer: (c) \(\sqrt{1-x^2}\)

MCQ On Differential Calculus Class 12 Chapter 9 Question 18.
tan-1 x + tan-1 y = c is the general solution of the differential equation
(a) \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
(b) \(\frac{dy}{dx}\) = \(\frac{1+x^2}{1+y^2}\)
(c) (1 + x²)dy + (1 + y²)dx = 0
(d) (1 +x²2)dx+(1 + y²)dy = 0

Answer

Answer: (c) (1 + x²)dy + (1 + y²)dx = 0

Maths MCQ Questions Class 12 Chapter 9 Question 19.
The differential equation y \(\frac{dy}{dx}\) + x = c represents
(a) Family of hyperbolas
(b) Family of parabolas
(c) Family of ellipses
(d) Family of circles

Answer

Answer: (d) Family of circles

MCQ Questions For Class 12 Maths With Answers Chapter 9 Question 20.
The general solution of ex cos y dx – ex sin y dy = 0 is
(a) ex cos y = k
(b) ex sin y = k
(c) ex = k cos y
(d) ex = k sin y

Answer

Answer: (a) ex cos y = k

Question 21.
The degree of the differential equation
\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))³ + 6y5 = 0 is
(a) 1
(b) 2
(c) 3
(d) 5

Answer

Answer: (a) 1

Question 22.
The solution of \(\frac{dy}{dx}\) + y = e-x, y (0) = 0 is
(a) y = ex(x – 1)
(b) y = xe-x
(c) y = xe-x + 1
(d) y = (x + 1 )e-x

Answer

Answer: (b) y = xe-x

Question 23.
Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is
(a) cos x
(b) sec x
(c) ecos x
(d) esec x

Answer

Answer: (b) sec x

Question 24.
The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
(a) y = tan-1 x
(b) y – x = k(1 + xy)
(c) x = tan-1 y
(d) tan (xy) = k

Answer

Answer: (b) y – x = k(1 + xy)

Question 25.
The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is
(a) \(\frac{x}{e^x}\)
(b) \(\frac{e^x}{x}\)
(c) xex
(d) ex

Answer

Answer: (b) \(\frac{e^x}{x}\)

Question 26.
y = aemx + be-mx satisfies which of the following differential equation?
(a) \(\frac{dy}{dx}\) + my = 0
(b) \(\frac{dy}{dx}\) – my = 0
(c) \(\frac{d^2y}{dx^2}\) – m²y = 0
(d) \(\frac{d^2y}{dx^2}\) +m²y = 0

Answer

Answer: (c) \(\frac{d^2y}{dx^2}\) – m²y = 0

Question 27.
The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
(a) \(\frac{sin x}{sin y}\) = c
(b) sin x sin y = c
(c) sin x + sin y = z
(d) cos x cos y = c

Answer

Answer: (b) sin x sin y = c

Question 28.
The solution of x \(\frac{dy}{dx}\) + y = ex is
(a) y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)
(b) y = xex + cx
(c) y = xex + k
(d) x = \(\frac{e^vy}{y}\) + \(\frac{k}{y}\)

Answer

Answer: (a) y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)

Question 29.
The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is
(a) (x² – y²)\(\frac{dy}{dx}\) = 2xy
(b) 2 (x² + y²)\(\frac{dy}{dx}\) = xy
(c) 2(x² – y²)\(\frac{dy}{dx}\) = xy
(d) (x² + y²) \(\frac{dy}{dx}\) = 2xy

Answer

Answer: (a) (x² – y²)\(\frac{dy}{dx}\) = 2xy

Question 30.
Family y = Ax + A³ of curves will correspond to a differential equation of order
(a) 3
(b) 2
(c) 1
(d) not finite

Answer

Answer: (b) 2

Question 31.
The general solution of \(\frac{dy}{dx}\) = 2x ex2-y is
(a) ex2-y = c
(b) e-y + ex2 = c
(c) ey = ex2 + c
(d) ex2+y = c

Answer

Answer: (c) ey = ex2 + c

Question 32.
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is
(a) an ellipse
(b) parabola
(c) circle
(d) rectangular hyperbola

Answer

Answer: (d) rectangular hyperbola

Question 33.
The general solution of the differential equation \(\frac{dy}{dx}\) = e\(\frac{x^2}{2}\) + xy is
(a) y = ce\(\frac{-x^2}{2}\)
(b) y = ce\(\frac{x^2}{2}\)
(c) y = (x + c)e\(\frac{x^2}{2}\)
(d) y = (c – x)e\(\frac{x^2}{2}\)

Answer

Answer: (c) y = (x + c)e\(\frac{x^2}{2}\)

Question 34.
The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is
(a) \(\frac{2x-1}{2y+3}\) = k
(b) \(\frac{2y+1}{2x-3}\) = k
(c) \(\frac{2x+3}{2y-1}\) = k
(d) \(\frac{2x-1}{2y-1}\) = k

Answer

Answer: (c) \(\frac{2x+3}{2y-1}\) = k

Question 35.
The differential equation for which y = a cos x + b sin x is a solution is
(a) \(\frac{d^2y}{dx^2}\) + y = 0
(b) \(\frac{d^2y}{dx^2}\) – y = 0
(c) \(\frac{d^2y}{dx^2}\) + (a + b)y = 0
(d) \(\frac{d^2y}{dx^2}\) + (a – b)y = 0

Answer

Answer: (a) \(\frac{d^2y}{dx^2}\) + y = 0

Question 36.
The solution of \(\frac{dy}{dx}\) + y = e-x, y (0) = 0 is
(a) y = e-x (x – 1)
(b) y = xex
(c) y = xe-x + 1
(d) y = xe-x

Answer

Answer: (d) y = xe-x

Question 37.
The order and degree of the differential equation
(\(\frac{d^2y}{dx^3}\))² – 3\(\frac{d^2y}{dx^2}\) + 2(\(\frac{dy}{dx}\))4 = y4 are
(a) 1, 4
(b) 3, 4
(c) 2, 4
(d) 3, 2

Answer

Answer: (d) 3, 2

Question 38.
The order and degree of the differential equation
[1 + (\(\frac{dy}{dx}\))²] = \(\frac{d^2y}{dx^2}\) are
(a) 1, \(\frac{3}{2}\)
(b) 2, 3
(c) 2, 1
(d) 3, 4

Answer

Answer: (c) 2, 1

Question 39.
The differential equation of the family of curves y² = 4a (x + a) is
(a) y² = 4\(\frac{dy}{dx}\) (x + \(\frac{dy}{dx}\))
(b) 2y\(\frac{dy}{dx}\) = 4a
(c) y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
(d) 2x\(\frac{dy}{dx}\) + y(\(\frac{dy}{dx}\))² – y

Answer

Answer: (c) y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0

Question 40.
Which of the following is the general solution of \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + y = 0
(a) y = (Ax + B)ex
(b) y = (Ax + B)e-x
(c) y = Aex + Be-x
(d) y = A cos x + B sin x

Answer

Answer: (a) y = (Ax + B)ex

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Pdf free download will help you. If you have any queries regarding Differential Equations CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Class 12 Maths MCQ:

MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers

Application of Integrals Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Application of Integrals Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 8 MCQ With Answers

Maths Class 12 Chapter 8 MCQs On Application of Integrals

MCQ On Application Of Integration Chapter 8 Question 1.
The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ \(\frac{π}{2}\) is
(a) √2 sq.units
(b) (√2 + 1) sq. units
(c) (√2 – 1) sq. units
(d) (2√2 – 1) sq.units

Answer

Answer: (c) (√2 – 1) sq. units

Application Of Integration MCQ Chapter 8 Question 2.
The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
(a) \(\frac{3}{8}\) sq.units
(b) \(\frac{5}{8}\) sq.units
(c) \(\frac{7}{8}\) sq.units
(d) \(\frac{9}{8}\) sq. units

Answer

Answer: (d) \(\frac{9}{8}\) sq. units

Application Of Integrals MCQ Chapter 8 Question 3.
The area of the region bounded by the curve y = \(\sqrt{16-x^2}\) and x-axis is
(a) 8π sq.units
(b) 20π sq. units
(c) 16π sq. units
(d) 256π sq. units

Answer

Answer: (a) 8π sq.units

Application Of Integration Important Questions Chapter 8 Question 4.
Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is
(a) 16π sq.units
(b) 4π sq. units
(c) 32π sq. units
(d) 24π sq. units

Answer

Answer: (b) 4π sq. units

Application Of Integrals Class 12 Chapter 8 Question 5.
Area of the region bounded by the curve y = cos x between x = 0 and x = π is
(a) 2 sq. units
(b) 4 sq, units
(c) 3 sq.units
(d) 1 sq. units

Answer

Answer: (a) 2 sq. units

MCQ On Line Integral Chapter 8 Question 6.
The area of the region bounded by parabola y² = x and the straight line 2y = x is
(a) \(\frac{4}{3}\) sq. unit
(b) 1 sq. unit
(c) \(\frac{2}{3}\) sq. units
(d) \(\frac{1}{3}\) sq. units

Answer

Answer: (a) \(\frac{4}{3}\) sq. unit

Question 7.
The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = \(\frac{π}{2}\) and the x-axis is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq, unit

Answer

Answer: (d) 1 sq, unit

Question 8.
The area of the region bounded by the ellipse \(\frac{x²}{25}\) + \(\frac{y²}{16}\) = 1 is
(a) 20π sq. units
(b) 20π² sq. units
(c) 16π² sq. units
(d) 25π sq. units

Answer

Answer: (a) 20π sq. units

Question 9.
The area of the region bounded by the circle x² + y² = 1 is
(a) 2π sq. units
(b) 7π sq. units
(c) 3π sq. units
(d) 4π sq. units

Answer

Answer: (b) 7π sq. units

Question 10.
The area of the region bounded by the and the lines x = 2 and x = 3
(a) \(\frac{7}{2}\) sq. unit
(b) \(\frac{9}{2}\) sq. unit
(c) \(\frac{11}{2}\) sq. units
(d) \(\frac{13}{2}\) sq. units

Answer

Answer: (a) \(\frac{7}{2}\) sq. unit

Question 11.
The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is
(a) 4 sq. units
(b) \(\frac{3}{2}\) sq. units
(c) 6 sq. units
(d) 8 sq, units

Answer

Answer: (c) 6 sq. units

Question 12.
If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
(a) \(\frac{9}{2}\) sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. unjts

Answer

Answer: (c) 12 sq. units

Question 13.
Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
(a) \(\frac{9}{2}\) sq. units
(b) 4 sq. units
(c) \(\frac{7\sqrt{17}}{6}\) sq. units
(d) \(\frac{17\sqrt{17}}{6}\) sq. unjts

Answer

Answer: (d) \(\frac{17\sqrt{17}}{6}\) sq. unjts

Question 14.
Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to
(a) 4 sq. units
(b) 6 sq. units
(c) 2 sq. units
(d) 8 sq. units

Answer

Answer: (a) 4 sq. units

Question 15.
The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is
(a) 1 sq. unit
(b) 2 sq. unit
(c) 2√2 sq. units
(d) 4 sq. units

Answer

Answer: (b) 2 sq. unit

Question 16.
The area of the region bounded by the line y = | x – 2 |, x = 1, x = 3 and x-axis is
(a) 4 sq. units
(b) 2 sq, units
(c) 3 sq. units
(d) 1 sq. unit

Answer

Answer: (d) 1 sq. unit

Question 17.
Area bounded by the ellipse \(\frac{x^2}{4}\) + \(\frac{y^2}{9}\) = 1 is
(a) 6π sq. units
(b) 3π sq. units
(c) 12π sq. units
(d) None of these

Answer

Answer: (a) 6π sq. units

Question 18.
Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
(a) 9 sq. units
(b) \(\frac{3}{2}\) sq. units
(c) 3 sq. units
(d) None of these

Answer

Answer: (d) None of these

Question 19.
The area of ellipse \(\frac{x^2}{4^2}\) + \(\frac{y^2}{9^2}\) = 1 is
(a) 6π sq. units
(b) \(\frac{π(a^2+b^2)}{4}\) sq. units
(c) π(a + b) sq. units
(d) None of these

Answer

Answer: (d) None of these

Question 20.
The area bounded by the lines |x| + |y| = 1 is
(a) 1 sq. unit
(b) 2 sq. units
(c) 2√2 sq. units
(d) 4 sq. units

Answer

Answer: (b) 2 sq. units

Question 21.
The area bounded by the curve 2x² + y² = 2 is
(a) π sq. units
(b) √2π sq. units
(c) \(\frac{π}{2}\) sq. units
(d) 2π sq. units

Answer

Answer: (b) √2π sq. units

Question 22.
The area bounded by the curve x² = 4y + 4 and line 3x + 4y = 0 is
(a) \(\frac{25}{4}\) sq. units
(b) \(\frac{125}{8}\) sq. units
(c) \(\frac{125}{16}\) sq. units
(d) \(\frac{124}{4}\) sq. units

Answer

Answer: (d) \(\frac{124}{4}\) sq. units

Question 23.
Area of the ellipse \(\frac{x^2}{a^2}\) + \(\frac{y^2}{b^2}\) = 1 is
(a) 4π ab sq. units
(b) 2π ab sq. units
(c) π ab sq. units.
(d) \(\frac{π ab}{2}\) sq. units

Answer

Answer: (c) π ab sq. units.

Question 24.
Area bounded between the parabola y² = 4ax and its latus rectum is
(a) \(\frac{1}{3}\) a sq. units
(b) \(\frac{1}{3}\) a² sq. units
(c) \(\frac{8}{3}\) a sq. units
(d) \(\frac{8}{3}\) a² sq. units

Answer

Answer: (d) \(\frac{8}{3}\) a² sq. units

Question 25.
The area bounded by the line y = 2x – 2, y = -x and x-axis is given by
(a) \(\frac{9}{2}\) sq. units
(b) \(\frac{43}{6}\) sq. units
(c) \(\frac{35}{6}\) sq. units
(d) None pf these

Answer

Answer: (d) None pf these

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