Category: MCQ 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.

Integrals Class 12 MCQs Questions with Answers

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

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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

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

Answer

Answer: (b) 2√x + k

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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

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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

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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

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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

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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

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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) \(\frac{π^2}{192}\)

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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

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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

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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

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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

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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)

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MCQ Integration Class 12 Chapter 7 Question 15.
∫\(\frac{xdx}{(x-1)(x-2)}\) equals

(d) log |(x – 1)(x – 2) + c

Answer

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

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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) \(\frac{π}{4}\)

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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

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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

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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

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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) \(\frac{3}{2}\)

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

Answer

Answer: (b) 0

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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

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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

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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) \(\frac{1}{10100}\)

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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) \(\frac{π}{2}\)

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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

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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

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

Answer

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

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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

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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

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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

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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

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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

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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

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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

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Question 36.
∫e^x(\(\frac{1-x}{1+x^2}\))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

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Question 37.
∫\(\frac{x^9}{(4x^2+1)^6}\) dx is equal to

Answer

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

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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 = \(\frac{2}{5}\)

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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

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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

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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

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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

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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

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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

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

Answer

Answer: (d) log_e(10^x + x¹⁰) + C

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Question 46.
Evaluate: ∫ sec^4/3 x cosec^8/3 xdx
(a) \(\frac{3}{5}\) tan^-5/3 x – 3 tan^1/3 x + C
(b) –\(\frac{3}{5}\) tan^-5/3 x + 3 tan^1/3 + C
(c) –\(\frac{3}{5}\) tan^-05/3 x – 3 tan^1/3 + C
(d) None of these

Answer

Answer: (b) –\(\frac{3}{5}\) tan^-5/3 x + 3 tan^1/3 + C

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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

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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

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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

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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

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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

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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

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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

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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

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

Answer

Answer: (b) –\(\frac{3}{5}\) tan^-5/3 x + 3 tan^1/3 + C

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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

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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

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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

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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.

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.

Linear Programming Class 12 MCQs Questions with Answers

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

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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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)

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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 (\(\frac{9}{2}\), \(\frac{5}{2}\))

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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)

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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)

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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) (\(\frac{7}{2}\), \(\frac{9}{4}\))

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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, \(\frac{7}{2}\))

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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

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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

(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)

Answer

Answer: (b) (0, 8)

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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)

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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.

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.

Probability Class 12 MCQs Questions with Answers

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)

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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

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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) \(\frac{1}{36}\)

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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) \(\frac{13}{24}\)

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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) \(\frac{5}{6}\)

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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

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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) \(\frac{1}{3}\)

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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

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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

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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) \(\frac{5}{8}\)

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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) \(\frac{1}{13}\)

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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) \(\frac{1}{6}\)

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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) \(\frac{1}{15}\)

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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) \(\frac{1}{5}\)

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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) \(\frac{1}{4}\)

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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) \(\frac{4}{1155}\)

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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) \(\frac{4}{5}\)

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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) \(\frac{5}{9}\)

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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) \(\frac{7}{64}\)

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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) \(\frac{1}{36}\)

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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

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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) \(\frac{2}{3}\)

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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) \(\frac{2}{7}\)

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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

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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) \(\frac{17}{20}\)

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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) \(\frac{14}{17}\)

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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) \(\frac{7}{12}\)

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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) \(\frac{25}{42}\)

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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

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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) = \(\frac{P(A∩B)}{P(B)}\)

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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) \(\frac{1}{5}\)

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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) \(\frac{3}{5}\)

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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) \(\frac{1-P(A∪B)}{P(B’)}\)

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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

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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) \(\frac{2}{9}\)

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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) \(\frac{6}{25}\)

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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)

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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.

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.

Differential Equations Class 12 MCQs Questions with Answers

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) ∫e^pdx
(b) \(_{e}\)∫pdx
(c) \(_{e}\)-∫pdx
(d) None of these

Answer

Answer: (d) None of these

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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

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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

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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

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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

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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

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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

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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

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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

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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 = -e^x
(b) xy = -e^-x
(c) xy = -1
(d) y = 2e^x – 1

Answer

Answer: (d) y = 2e^x – 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 e^x cos y dx – e^x sin y dy = 0 is
(a) e^x cos y = k
(b) e^x sin y = k
(c) e^x = k cos y
(d) e^x = k sin y

Answer

Answer: (a) e^x 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 = e^x(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) e^{cos x}
(d) e^{sec 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) xe^x
(d) e^x

Answer

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

---

Question 26.
y = ae^mx + 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 = e^x is
(a) y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)
(b) y = xe^x + cx
(c) y = xe^x + 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 e^x2-y is
(a) e^x2-y = c
(b) e^-y + e^x2 = c
(c) e^y = e^x2 + c
(d) e^x2+y = c

Answer

Answer: (c) e^y = e^x2 + 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 = xe^x
(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)e^x
(b) y = (Ax + B)e^-x
(c) y = Ae^x + Be^-x
(d) y = A cos x + B sin x

Answer

Answer: (a) y = (Ax + B)e^x

---

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.

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.

Application of Integrals Class 12 MCQs Questions with Answers

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

---

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers Pdf free download will help you. If you have any queries regarding Application of Integrals CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Determinants Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Determinants Class 12 MCQs Questions with Answers

Determinants Class 12 MCQ Questions Question 1.
\(\left[\begin{array}{ccc}
1 & x & x^{2} \\
1 & y & y^{2} \\
1 & z & z^{2}
\end{array}\right]\)
(a) (x – y) (y + z)(z + x)
(b) (x + y) (y – z)(z – x)
(c) (x – y) (y – z)(z + x)
(d) (x – y) (y – z) (z – x)

Answer

Answer: (d) (x – y) (y – z) (z – x)

---

Determinants Class 12 MCQ Question 2.
The value of the determinant
\(\left[\begin{array}{ccc}
3 & 1 & 7 \\
5 & 0 & 2 \\
2 & 5 & 3
\end{array}\right]\)
(a) 124
(b) 125
(c) 134
(d) 144

Answer

Answer: (c) 134

---

MCQ Of Determinants Class 12 Question 3.
If a, b, c are in A.P. then the determinant
\(\left[\begin{array}{ccc}
x+2 & x+3 & x+2a \\
x+3 & x+4 & x+2b \\
x+4 & x+5 & x+2c
\end{array}\right]\)
(a) 1
(b) x
(c) 0
(d) 2x

Answer

Answer: (c) 0

---

Class 12 Maths Chapter 4 MCQ Question 4.
If w is a non-real root of the equation x² – 1 = 0. then
\(\left[\begin{array}{ccc}
1 & ω & ω^{2} \\
ω & ω^{2} & 1 \\
ω^{2} & 1 & ω
\end{array}\right]\) =
(a) 0
(b) 1
(c) ω
(d) ω²

Answer

Answer: (a) 0

---

Determinants MCQ Class 12 Question 5.
If Δ = \(\left[\begin{array}{cc}
10 & 2 \\
30 & 6
\end{array}\right]\) then A =
(a) 0
(b) 10
(c) 12
(d) 60

Answer

Answer: (a) 0

---

MCQ On Determinants Class 12 Question 6.
If 7 and 2 are two roots of the equation \(\left[\begin{array}{ccc}
x & 3 & 7 \\
2 & x & 2 \\
7 & 6 & x
\end{array}\right]\) then the third root is
(a) -9
(b) 14
(c) \(\frac{1}{2}\)
(d) None of these

Answer

Answer: (a) -9

---

Determinants MCQs Class 12 Question 7.
If \(\left[\begin{array}{cc}
x & 2 \\
18 & x
\end{array}\right]\) = \(\left[\begin{array}{cc}
6 & 2 \\
18 & 6
\end{array}\right]\) x is equal to
(a) 6
(b) ±6
(c) -1
(d) -6

Answer

Answer: (b) ±6

---

Determinants MCQs With Answers Class 12 Question 8.
\(\left[\begin{array}{ccc}
1 & a & a^{2}-bc \\
1 & b & b^{2}-ca \\
1 & c & c^{2}-ab
\end{array}\right]\) is equal to
(a) abc
(b) ab + bc + ca
(c) 0
(d) (a – b)(b – c)(c – a)

Answer

Answer: (c) 0

---

Determinant MCQ Class 12 Question 9.
A = \(\left[\begin{array}{ll}
\alpha & q \\
q & \alpha
\end{array}\right]\) |A³| = 125 then α =
(a) ±3
(b) ±2
(c) ±5
(d) 0

Answer

Answer: (a) ±3

---

Class 12 Determinants MCQ Question 10.
If a ≠ 0 and \(\left[\begin{array}{ccc}
1+a & 1 & 1 \\
1 & 1+a & 1 \\
1 & 1 & 1+a
\end{array}\right]\) = 0 then a =
(a) a = -3
(b) a = 0
(c) a = 1
(d) a = 3

Answer

Answer: (a) a = -3

---

MCQ Questions On Determinants Class 12 Question 11.
If x > 0 and x ≠ 1. y > 0. and y ≠ 1, z > 0 and z ≠ 1 then
\(\left[\begin{array}{ccc}
1 & log_{x}y & log_{x}z \\
log_{y}x & 1 & log_{y}z \\
log_{z}x & log_{z}y & 1
\end{array}\right]\) is equal to
(a) 1
(b) -1
(c) 0
(d) None of these

Answer

Answer: (c) 0

---

Determinants MCQs Class 12 Question 12.
\(\left[\begin{array}{ccc}
y+z & z & x \\
y & z+x & y \\
z & z & x+y
\end{array}\right]\) is equal to
(a) 6xyz
(b) xyz
(c) 4xyz
(d) xy + yz + zx

Answer

Answer: (c) 4xyz

---

MCQ Of Chapter 4 Maths Class 12 Question 13.
If \(\left[\begin{array}{cc}
2 & 4 \\
5 & 1
\end{array}\right]\) = \(\left[\begin{array}{cc}
2x & 4 \\
6 & x
\end{array}\right]\) then the value of x is
(a) ±2
(b) ±\(\frac{1}{3}\)
(c) ±√3
(d) ± (0.5)

Answer

Answer: (c) ±√3

---

MCQs On Determinants Class 12 Question 14.
If \(\left[\begin{array}{cc}
2x & 5 \\
8 & x
\end{array}\right]\) = \(\left[\begin{array}{cc}
6 & -2 \\
7 & 3
\end{array}\right]\) then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Answer

Answer: (c) ±6

---

MCQ Determinants Class 12 Question 15.
The value of determinant \(\left[\begin{array}{ccc}
a-b & b+c & a \\
b-c & c+a & b \\
c-a & a+b & c
\end{array}\right]\)
(a) a³ + b³ + c ³
(b) 3bc
(c) a³ + b³ + c³ – 3abc
(d) None of these

Answer

Answer: (c) a³ + b³ + c³ – 3abc

---

MCQ On Determinants Class 12 With Solutions Question 16.
The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be
(a) 9
(b) 3
(c) -9
(d) 6

Answer

Answer: (b) 3

---

Class 12 Maths Ch 4 MCQ Question 17.
The determinant \(\left[\begin{array}{ccc}
b^{2}-ab & b-c & bc-ac \\
ab-a^{2} & a-b & b^{2}-ab \\
bc-ac & c-a & ab-a^{2}
\end{array}\right]\) equals
(a) abc(b – c)(c -a)(a – b)
(b) (b – c)(c – a)(a – b)
(c) (a + b + c)(b – c)(c – a)(a – b)
(d) None of these

Answer

Answer: (d) None of these

---

Ch 4 Maths Class 12 MCQ Question 18.
The number of distinct real roots of \(\left[\begin{array}{ccc}
sin x & cos x & cos x \\
cos x & sin x & cos x \\
cos x & cos x & sin x
\end{array}\right]\) = 0 in the interval –\(\frac{π}{4}\) ≤ x ≤ \(\frac{π}{4}\) is
(a) 0
(b) 2
(c) 1
(d) 3

Answer

Answer: (c) 1

---

Chapter 4 Maths Class 12 MCQ Question 19.
If A, B and C are angles of a triangle, then the determinant
\(\left[\begin{array}{ccc}
-1 & cos C & cos B \\
cos C & -1 & cos A \\
cos B & cos A & -1
\end{array}\right]\)
(a) 0
(b) -1
(c) 1
(d) None of these

Answer

Answer: (a) 0

---

MCQ On Matrices And Determinants Class 12 Question 20.
Let f(t) = \(\left[\begin{array}{ccc}
cot t & t & 1 \\
2 sin t & t & 2t \\
sin t & t & t
\end{array}\right]\) then \(_{t→0}^{lim}\) \(\frac{f(t)}{t^2}\) is equal to
(a) 0
(b) -1
(c) 2
(d) 3

Answer

Answer: (a) 0

---

Question 21.
The maximum value of \(\left[\begin{array}{ccc}
1 & 1 & 1 \\
1 & 1+sin θ & 1 \\
1+cos θ & 1 & 1
\end{array}\right]\) is (θ is real number)
(a) \(\frac{1}{2}\)
(b) \(\frac{√3}{2}\)
(c) \(\frac{2√3}{4}\)
(d) √2

Answer

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

---

Question 22.
If f(x) = \(\left[\begin{array}{ccc}
0 & x-a & x-b \\
x+a & 0 & x-c \\
x+b & x+c & 0
\end{array}\right]\) then
(a) f(a) = 0
(b) f(b) = 0
(c) f(0) = 0
(d) f(1) = 0

Answer

Answer: (c) f(0) = 0

---

Question 23.
If A = \(\left[\begin{array}{ccc}
2 & \lambda & -3 \\
0 & 2 & 5 \\
1 & 1 & 3
\end{array}\right]\) then A^-1 exists if
(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) None of these

Answer

Answer: (d) None of these

---

Question 24.
If A and B are invertible matrices, then which of the following is not correct?
(a) adj A = |A|.A^-1
(b) det (a)^-1 = [det (a)]^-1
(c) (AB)^-1 = B^-1A^-1
(d) (A + B)^-1 = B^-1 + A^-1

Answer

Answer: (d) (A + B)^-1 = B^-1 + A^-1

---

Question 25.
If x, y, z are all different from zero and
\(\left[\begin{array}{ccc}
1+x & 1 & 1 \\
1 & 1+y & 1 \\
1 & 1 & 1+z
\end{array}\right]\) = 0, then value of x^-1 + y^-1 + z^-1 is
(a) xyz
(b) x^-1y^-1z^-1
(c) -x – y – z
(d) -1

Answer

Answer: (d) -1

---

Question 26.
The value of the determinant \(\left[\begin{array}{ccc}
x & x+y & x+2y \\
x+2y & x & x+y \\
x+y & x+2y & x
\end{array}\right]\) is
(a) 9x² (x + y)
(b) 9y² (x + y)
(c) 3y² (x + y)
(d) 7x² (x + y)

Answer

Answer: (b) 9y² (x + y)

---

Question 27.
There are two values of a which makes determinant
Δ = \(\left[\begin{array}{ccc}
1 & -2 & 5 \\
2 & a & -1 \\
0 & 4 & 2a
\end{array}\right]\) = 86, then sum of these number is
(a) 4
(b) 5
(c) -4
(d) 9

Answer

Answer: (c) -4

---

Question 28.
Evaluate the determinant Δ = \(\left|\begin{array}{cc}
log_{3}512 & log_{4}3 \\
log_{3}8 & log_{4}9
\end{array}\right|\)
(a) \(\frac{15}{2}\)
(b) 12
(c) \(\frac{14}{3}\)
(d) 6

Answer

Answer: (a) \(\frac{15}{2}\)

---

Question 29.
\(\left|\begin{array}{cc}
x & -7 \\
x & 5 x+1
\end{array}\right|\)
(a) 3x² + 4
(b) x(5x + 8)
(c) 3x + 4x²
(d) x(3x + 4)

Answer

Answer: (b) x(5x + 8)

---

Question 30.
\( \left|\begin{array}{cc}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \alpha
\end{array}\right|\)
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (b) 1

---

Question 31.
\( \left|\begin{array}{ll}
\cos 15^{\circ} & \sin 15^{\circ} \\
\sin 75^{\circ} & \cos 75^{\circ}
\end{array}\right|\)
(a) 0
(b) 5
(c) 3
(d) 7

Answer

Answer: (a) 0

---

Question 32.
\(\left|\begin{array}{cc}
a+i b & c+i d \\
-c+i d & a-i b
\end{array}\right|\)
(a) (a + b)²
(b) (a + b + c + d)²
(c) (a² + b² – c² – d²)
(d) a² + b² + c² + a²

Answer

Answer: (d) a² + b² + c² + a²

---

Question 33.
If \(\left|\begin{array}{lll}
b+c & c+a & a+b \\
c+a & a+b & b+c \\
a+b & b+c & c+a
\end{array}\right|\) = \(k\left|\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right|\) then k =
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (c) 2

---

Question 34.
If \(\left|\begin{array}{ccc}
a-b-c & 2 a & 2 a \\
2 b & b-c-a & 2 b \\
2 c & 2 c & c-a-b
\end{array}\right|\) = k (a + b + c)³ then k is
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (b) 1

---

Question 35.
\(\left|\begin{array}{lll}
a+1 & a+2 & a+4 \\
a+3 & a+5 & a+8 \\
a+7 & a+10 & a+14
\end{array}\right|\) =
(a) 2
(b) -2
(c) 4
(d) -4

Answer

Answer: (b) -2

---

Question 36.
If abc ≠ 0 and \(\left|\begin{array}{ccc}
1+a & 1 & 1 \\
1 & 1+b & 1 \\
1 & 1 & 1+c
\end{array}\right|\) = 0 then \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\) =
(a) 1
(b) 2
(c) -1
(d) -3

Answer

Answer: (c) -1

---

Question 37.
\(\left|\begin{array}{ccc}
2 x y & x^{2} & y^{2} \\
x^{2} & y^{2} & 2 x y \\
y^{2} & 2 x y & x^{2}
\end{array}\right|\) =
(a) (x³ + y³)²
(b) (x² + y²)³
(c) -(x² + y²)³
(d) -(x³ + y³)²

Answer

Answer: (d) -(x³ + y³)²

---

Question 38.
\(\left|\begin{array}{ccc}
b^{2} c^{2} & b c & b+c \\
c^{2} a^{2} & c a & c+a \\
a^{2} b^{2} & a b & a+b
\end{array}\right|\) =
(a) a⁷ + b⁷ + c⁷
(b) (a + b + c)⁷
(c) (a² + b² + c²) (a⁵ + b⁵ + c⁵)
(d) 0

Answer

Answer: (d) 0

---

Question 39.
If a, b, c are cube roots of unity, then
\(\left|\begin{array}{lll}
e^{a} & e^{2 a} & e^{3 a}-1 \\
e^{b} & e^{2 b} & e^{3 b}-1 \\
e^{c} & e^{2 c} & e^{3 c}-1
\end{array}\right|\) =
(a) 0
(b) e
(c) e²
(d) e³

Answer

Answer: (a) 0

---

Question 40.
The value of
\(\left|\begin{array}{ccc}
\cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\
\sin \alpha & \cos \alpha & \sin \beta \\
-\cos \alpha & \sin \alpha & \cos \beta
\end{array}\right|\)
is independent of
(a) α
(b) β
(c) α.β
(d) None of these

Answer

Answer: (a) α

---

Question 41.
If x is a complex root of the equation
\(\left|\begin{array}{lll}
1 & x & x \\
x & 1 & x \\
x & x & 1
\end{array}\right|\) + \(\left|\begin{array}{ccc}
1-x & 1 & 1 \\
1 & 1-x & 1 \\
1 & 1 & 1-x
\end{array}\right|\) = 0
then x²⁰⁰⁷ + x^-2007 =
(a) 1
(b) -1
(c) -2
(d) 2

Answer

Answer: (c) -2

---

Question 42.
\(\left|\begin{array}{lll}
b-c & c-a & a-b \\
c-a & a-b & b-c \\
a-b & b-c & c-a
\end{array}\right|\) =
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: (a) 0

---

Question 43.
Let Δ = \(\left|\begin{array}{ccc}
x & y & z \\
x^{2} & y^{2} & z^{2} \\
x^{3} & y^{3} & z^{3}
\end{array}\right|\) then the value of Δ is
(a) (x – y) (y- z)(z – x)
(b) xyz
(c) x² + y² + z²)²
(d) xyz (x – y)(y – z) (z – x)

Answer

Answer: (d) xyz (x – y)(y – z) (z – x)

---

Question 44.
The value of the determinant \(\left|\begin{array}{ccc}
\alpha & \beta & \gamma \\
\alpha^{2} & \beta^{2} & \gamma^{2} \\
\beta+\gamma & \gamma+\alpha & \alpha+\beta
\end{array}\right|\)
(a) (α + β)(β + γ)(γ + α)
(b) (α – β)(β – γ) (γ – α) (α + β + γ)
(c) (α + β + γ)² (α – β – γ)²
(d) αβγ (α + β + γ)

Answer

Answer: (b) (α – β)(β – γ) (γ – α) (α + β + γ)

---

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download will help you. If you have any queries regarding Determinants CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Inverse Trigonometric Functions Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Inverse Trigonometric Functions Class 12 MCQs Questions with Answers

Inverse Trigonometric Functions Class 12 MCQ Question 1.
sin^-1 (sin\(\frac{2π}{3}\)) =
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{4π}{3}\)
(d) \(\frac{π}{3}\)

Answer

Answer: (d) \(\frac{π}{3}\)

---

Inverse Trigonometry Class 12 MCQ Question 2.
sin^-1 (1 – x) – 2 sin^-1 x = \(\frac{π}{2}\) then x = ?
(a) 0, \(\frac{1}{2}\)
(b) 1, \(\frac{1}{2}\)
(c) \(\frac{1}{2}\)
(d) 0

Answer

Answer: (d) 0

---

MCQ Of Inverse Trigonometry Class 12 Question 3.
tan^-1 √3 – sec^-1(-2)
(a) π
(b) –\(\frac{π}{3}\), 0
(c) \(\frac{π}{3}\)
(d) \(\frac{2π}{3}\)

Answer

Answer: (b) –\(\frac{π}{3}\), 0

---

Inverse Trigonometric Functions MCQ Question 4.
sin(sec^-1 x + cosec^-1x) =
(a) 1
(b) -1
(c) \(\frac{π}{2}\)
(d) \(\frac{π}{3}\)

Answer

Answer: (a) 1

---

Class 12 Maths Chapter 2 MCQ Question 5.
2 tan^-1 \(\frac{1}{3}\) + tan^-1 \(\frac{1}{7}\) =
(a) tan^-1 \(\frac{44}{29}\)
(b) \(\frac{π}{2}\)
(c) 0
(d) \(\frac{π}{4}\)

Answer

Answer: (d) \(\frac{π}{4}\)

---

MCQ On Inverse Trigonometric Functions Question 6.
The principle value of sin^-1 \(\frac{√3}{2}\) is
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{π}{4}\)
(d) \(\frac{π}{3}\)

Answer

Answer: (d) \(\frac{π}{3}\)

---

MCQ Inverse Trigonometry Class 12 Question 7.
The value of the expression tan^-1(\(\frac{1}{2}\)cos^-1\(\frac{2}{√5}\)) is
(a) 2 + √5
(b) √5 – 2
(c) \(\frac{√5+2}{4}\)
(d) √5 + 2

Answer

Answer: (d) √5 + 2

---

Class 12 Inverse Trigonometry MCQ Question 8.
Simplified form of cos^-1 (4x³ – 3x)
(a) 3 sin^-1x
(b) 3 cos^-1x
(c) π – 3 sin^-1x
(d) None of these

Answer

Answer: (b) 3 cos^-1x

---

Inverse Trigonometric Functions Class 12 MCQ With Solutions Question 9.
The value of tan(tan^-1 \(\frac{4}{5}\) + tan^-1 \(\frac{2}{3}\)) is
(a) \(\frac{6}{17}\)
(b) \(\frac{7}{16}\)
(c) \(\frac{17}{6}\)
(d) None of these

Answer

Answer: (d) None of these

---

MCQ On Inverse Trigonometric Functions Class 12 Question 10.
tan^-1(\(\frac{x}{y}\)) – tan^-1(\(\frac{x-y}{x+y}\)) is equal to
(a) \(\frac{π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{-3π}{4}\)

Answer

Answer: (b) \(\frac{π}{4}\)

---

Inverse Trigonometry MCQ Question 11.
The value of x for which sin |cot^-1(1 – x)| = cos (tan^-1 x) is
(a) \(\frac{2}{1}\)
(b) 1
(c) 0
(d) \(\frac{1}{2}\)

Answer

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

---

Class 12 Maths Chapter 2 MCQ Questions Question 12.
Princal value of cos^-1(\(\frac{-1}{√2}\))
(a) \(\frac{3π}{4}\)
(b) \(\frac{5π}{4}\)
(c) –\(\frac{π}{4}\)
(d) None of these

Answer

Answer: (a) \(\frac{3π}{4}\)

---

MCQ Questions For Inverse Trigonometry Class 12 With Solutions Question 13.
tan^-1 √3 – sec^-1 (-2) is equal to
(a) π
(b) –\(\frac{π}{3}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{2π}{3}\)

Answer

Answer: (b) –\(\frac{π}{3}\)

---

Class 12 Maths Ch 2 MCQ Question 14.
If y = sec^-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ \(\frac{π}{2}\)
(c) –\(\frac{π}{2}\) < y < \(\frac{π}{2}\)
(d) None of these

Answer

Answer: (d) None of these

---

Ch 2 Maths Class 12 MCQ Question 15.
If x + \(\frac{1}{x}\) = 2 then the principal value of sin^-1 x is x
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{2}\)
(c) π
(d) \(\frac{3π}{2}\)

Answer

Answer: (d) \(\frac{3π}{2}\)

---

Inverse Trigonometry MCQ Class 12 Question 16.
4 tan^-1 \(\frac{1}{5}\) – tan^-1 \(\frac{1}{239}\)
(a) π
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{4}\)

Answer

Answer: (d) \(\frac{π}{4}\)

---

Inverse Trigonometric Functions MCQ Pdf Question 17.
The principle value of sin^-1(sin\(\frac{2π}{3}\)) is
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{-π}{6}\)
(d) \(\frac{π}{6}\)

Answer

Answer: (b) \(\frac{π}{3}\)

---

MCQ Questions For Inverse Trigonometry Class 12 Question 18.
The value of cos^-1(\(\frac{1}{2}\)) + 2sin^-1(\(\frac{1}{2}\)) is equal to
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)

Answer

Answer: (b) \(\frac{π}{6}\)

---

Chapter 2 Maths Class 12 MCQ Question 19.
Algebraic expression for sin (cot^-1 x) is
(a) \(\frac{1}{1+x^2}\)
(b) \(\frac{1}{\sqrt{1+x^2}}\)
(c) \(\frac{x}{\sqrt{1+x^2}}\)
(d) None of these

Answer

Answer: (b) \(\frac{1}{\sqrt{1+x^2}}\)

---

Inverse Trigonometry MCQs Question 20.
If sin^-1(\(\frac{2x}{1+x^2}\)) + sin^-1\(\frac{2y}{1+y^2}\) = 2 tan^-1 a then a is equal to
(a) \(\frac{x-y}{1+xy}\)
(b) \(\frac{y}{1+xy}\)
(c) \(\frac{y}{1-xy}\)
(d) \(\frac{x+y}{1-xy}\)

Answer

Answer: (d) \(\frac{x+y}{1-xy}\)

---

Question 21.
Princal value of tan^-1 (-1) is
(a) \(\frac{π}{4}\)
(b) \(\frac{-π}{2}\)
(c) \(\frac{5π}{4}\)
(d) \(\frac{-π}{4}\)

Answer

Answer: (d) \(\frac{-π}{4}\)

---

Question 22.
tan^-1(\(\frac{1}{4}\)) + tan^-1(\(\frac{2}{9}\)) equal to

Answer

Answer: (d) tan^-1(\(\frac{1}{2}\))

---

Question 23.
Principal value of sin^-1(\(\frac{1}{√2}\))
(a) \(\frac{π}{4}\)
(b) \(\frac{3π}{4}\)
(c) \(\frac{5π}{4}\)
(d) None of these

Answer

Answer: (a) \(\frac{π}{4}\)

---

Question 24.
sin^-1 x = y Then
(a) 0 ≤ y ≤ π
(b) –\(\frac{π}{2}\) ≤ y ≤ \(\frac{π}{2}\)
(c) 0 < y < π
(d) –\(\frac{π}{2}\) < y < –\(\frac{π}{2}\)

Answer

Answer: (b) –\(\frac{π}{2}\) ≤ y ≤ \(\frac{π}{2}\)

---

Question 25.
cos^-1(cos\(\frac{7π}{6}\)) is equal to
(a) \(\frac{7π}{6}\)
(b) \(\frac{5π}{6}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{6}\)

Answer

Answer: (b) \(\frac{5π}{6}\)

---

Question 26.
sin[\(\frac{π}{3}\) – sin^-1(-\(\frac{1}{2}\))] is equal to
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{4}\)
(d) 1

Answer

Answer: (d) 1

---

Question 27.
tan^-1\(\frac{1}{2}\) + tan^-1\(\frac{2}{11}\) = tan^-1 a then a = ?
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{3}{4}\)
(d) 1

Answer

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

---

Question 28.
tan^-1\(\frac{1}{2}\) + tan^-1\(\frac{1}{3}\) =
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{3}\)
(d) π

Answer

Answer: (a) \(\frac{π}{4}\)

---

Question 29.
If sin^-1 x + sin^-1 y = \(\frac{2π}{3}\) then cos^-1 x + cos^-1 y =
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)

Answer

Answer: (c) \(\frac{π}{3}\)

---

Question 30.
The principal value of cosec^-1 (-2) is
(a) –\(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{2π}{3}\)
(d) –\(\frac{π}{6}\)

Answer

Answer: (d) –\(\frac{π}{6}\)

---

Question 31.
The domain of the following f(x) = \(\sqrt{sin^{-1}x}\) is
(a) [0, 1]
(b) [-1, 1]
(c) [-, 0]
(d) [0, 1]

Answer

Answer: (a) [0, 1]

---

Question 32.
Which of the following is the principal value branch of cos^-1 x?
(a) [\(\frac{-π}{2}\), \(\frac{π}{2}\)]
(b) (0, π)
(c) (0, π)
(d) (0, π) – {\(\frac{π}{2}\)}

Answer

Answer: (c) (0, π)

---

Question 33.
Which of the following is the principal value branch of cosec^-1 x?
(a) (\(\frac{-π}{2}\), \(\frac{π}{2}\))
(b) (0, π) – {\(\frac{π}{2}\)}
(c) [\(\frac{-π}{2}\), \(\frac{π}{2}\)]
(d) [\(\frac{-π}{2}\), \(\frac{π}{2}\)] – [0]

Answer

Answer: (d) [\(\frac{-π}{2}\), \(\frac{π}{2}\)] – [0]

---

Question 34.
If 3 tan^-1 x + cot^-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) \(\frac{1}{2}\)

Answer

Answer: (b) 1

---

Question 35.
The value of cos^-1[cos(\(\frac{33π}{5}\))] is
(a) \(\frac{3π}{5}\)
(b) \(\frac{-3π}{5}\)
(c) \(\frac{π}{10}\)
(d) –\(\frac{-π}{10}\)

Answer

Answer: (a) \(\frac{3π}{5}\)

---

Question 36.
The domain of the function cos^-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]

Answer

Answer: (a) [0, 1]

---

Question 37.
The domain of the function defined by f (x) = sin^-1 \(\sqrt{x-1}\) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) None of these

Answer

Answer: (a) [1, 2]

---

Question 38.
If cos(sin^-1\(\frac{2}{5}\) + cos^-1 x) = 0 then x is equal to
(a) \(\frac{1}{5}\)
(b) \(\frac{2}{5}\)
(c) 0
(d) 1

Answer

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

---

Question 39.
The value of sin (2 tan^-1 (.75)) is equal to
(a) .75
(b) 1.5
(c) .96
(d) sin 1.5

Answer

Answer: (c) .96

---

Question 40.
The value of cos^-1 (cos\(\frac{3π}{2}\)) is equal to
(a) \(\frac{π}{2}\)
(b) \(\frac{3π}{2}\)
(c) \(\frac{5π}{2}\)
(d) –\(\frac{7π}{2}\)

Answer

Answer: (a) \(\frac{π}{2}\)

---

Question 41.
The value of expression 2 sec^-1 2 + sin^-1 (\(\frac{1}{2}\)) is
(a) \(\frac{π}{6}\)
(b) \(\frac{5π}{6}\)
(c) \(\frac{7π}{6}\)
(d) 1

Answer

Answer: (b) \(\frac{5π}{6}\)

---

Question 42.
If tan^-1 x + tan^-1 y = \(\frac{4π}{5}\) then cot^-1 x + cot^-1 y equals
(a) \(\frac{π}{5}\)
(b) \(\frac{2π}{5}\)
(c) \(\frac{3π}{5}\)
(d) π

Answer

Answer: (a) \(\frac{π}{5}\)

---

Question 43.
If sin^-1(\(\frac{2a}{1+a^2}\)) + cos^-1(\(\frac{1-a^2}{1+a^2}\)) = tan^-1(\(\frac{2x}{1-x^2}\)) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) \(\frac{a}{2}\)
(c) a
(d) \(\frac{2a}{1-a^2}\)

Answer

Answer: (d) \(\frac{2a}{1-a^2}\)

---

Question 44.
The value of sin [cos^-1(\(\frac{7}{25}\))] is
(a) \(\frac{25}{24}\)
(b) \(\frac{25}{7}\)
(c) \(\frac{24}{25}\)
(d) \(\frac{7}{24}\)

Answer

Answer: (c) \(\frac{24}{25}\)

---

Question 45.
If |x| ≤ 1, then 2 tan^-1 x + sin^-1(\(\frac{2x}{1+x^2}\)) is equal to
(a) 4 tan^-1 x
(b) \(\frac{π}{2}\)
(c) 0
(d) π

Answer

Answer: (a) 4 tan^-1 x

---

Question 46.
If cos^-1 α + cos^-1 β + cos^-1 γ = 3π, then α(β + γ) + β (γ + α) + γ(α + β) equals
(a) 0
(b) 1
(c) 6
(d) 12

Answer

Answer: (c) 6

---

Question 47.
The number of real solution of the equation is
\(\sqrt{1+cos 2x}\) = √2 cos^-1(cos x) in [\(\frac{π}{2}\), π] is
(a) 0
(b) 1
(c) 2
(d) None of these

Answer

Answer: (c) 2

---

Question 48.
If cos^-1 x > sin^-1 x, then
(a) \(\frac{1}{√2}\) < x ≤ 1
(b) 0 ≤ x < \(\frac{1}{√2}\)
(c) -1 ≤ x < \(\frac{1}{√2}\) (d) x > 0

Answer

Answer: (b) 0 ≤ x < \(\frac{1}{√2}\)

---

Question 49.
sin^-1(\(\frac{-1}{2}\))
(a) \(\frac{π}{3}\)
(b) –\(\frac{π}{3}\)
(c) \(\frac{π}{6}\)
(d) –\(\frac{π}{6}\)

Answer

Answer: (d) –\(\frac{π}{6}\)

---

Question 50.
sec^-1(\(\frac{-2}{√3}\))
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{5π}{6}\)
(d) –\(\frac{2π}{3}\)

Answer

Answer: (c) \(\frac{5π}{6}\)

---

Question 51.
cos^-1(\(\frac{1}{2}\))
(a) –\(\frac{π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{2π}{3}\)

Answer

Answer: (b) \(\frac{π}{3}\)

---

Question 52.
cosec^-1(\(\frac{-2}{√3}\))
(a) –\(\frac{π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) –\(\frac{π}{2}\)

Answer

Answer: (a) –\(\frac{π}{3}\)

---

Question 53.
cot^-1(1)
(a) \(\frac{π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{2}\)
(d) 0

Answer

Answer: (b) \(\frac{π}{4}\)

---

Question 54.
cos^-1(\(\frac{√3}{2}\))
(a) \(\frac{5π}{6}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{4π}{9}\)
(d) \(\frac{2π}{3}\)

Answer

Answer: (a) \(\frac{5π}{6}\)

---

Question 55.
cosec^-1(2)
(a) \(\frac{π}{6}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{5π}{6}\)
(d) 0

Answer

Answer: (a) \(\frac{π}{6}\)

---

Question 56.
sec^-1(2)
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)

Answer

Answer: (b) \(\frac{π}{3}\)

---

Question 57.
tan^-1(√3)
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)

Answer

Answer: (b) \(\frac{π}{3}\)

---

Question 58.
cot^-1(-√3)
(a) \(\frac{5π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{π}{4}\)

Answer

Answer: (a) \(\frac{5π}{6}\)

---

Question 59.
tan^-1 + cos^-1 (\(\frac{-1}{2}\)) + sin^-1 (\(\frac{-1}{2}\))
(a) \(\frac{2π}{3}\)
(b) \(\frac{3π}{4}\)
(c) \(\frac{π}{2}\)
(d) 6π

Answer

Answer: (b) \(\frac{3π}{4}\)

---

Question 60.
tan^-1 (√3) + sec^-1 (-2) – cosec^-1 (\(\frac{2}{√3}\))
(a) \(\frac{5π}{6}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{π}{3}\)
(d) 0

Answer

Answer: (d) 0

---

Question 61.
cos^-1 (\(\frac{-1}{2}\)) + 2sin^-1 (\(\frac{-1}{2}\))
(a) \(\frac{π}{3}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{3π}{4}\)
(d) \(\frac{5π}{8}\)

Answer

Answer: (a) \(\frac{π}{3}\)

---

Question 62.
If cot^-1 (\(\sqrt{cosα}\)) – tan^-1 (\(\sqrt{cosα}\)) = x then sin x is equal to
(a) tan² (\(\frac{α}{2}\))
(b) cot² (\(\frac{α}{2}\))
(c) tan α
(d) cot (\(\frac{α}{2}\))

Answer

Answer: (a) tan² (\(\frac{α}{2}\))

---

Question 63.
4 tan^-1 \(\frac{1}{5}\) – tan^-1 \(\frac{1}{70}\) + tan^-1 \(\frac{1}{99}\) is equal to
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)

Answer

Answer: (b) \(\frac{π}{4}\)

---

Question 64.
If 6 sin^-1 (x² – 6x + 8.5) = π, then x is equal to
(a) 1
(b) 2
(c) 3
(d) 8

Answer

Answer: (b) 2

---

Question 65.
Number of solutions of the equation
tan^-1 (\(\frac{1}{2x+1}\)) + tan^-1 (\(\frac{1}{4x+1}\)) = tan^-1 (\(\frac{2}{x^2}\))
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (b) 2

---

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download will help you. If you have any queries regarding Inverse Trigonometric Functions CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

Check the below NCERT MCQ Questions for Class 11 Physics Chapter 1 Physical World with Answers Pdf free download. MCQ Questions for Class 11 Physics with Answers were prepared based on the latest exam pattern. We have provided Physical World Class 11 Physics MCQs Questions with Answers to help students understand the concept very well. https://ncertmcq.com/mcq-questions-for-class-11-physics-with-answers/

Physical World Class 11 MCQs Questions with Answers

MCQ Questions For Class 11 Physics Chapter 1 Question 1.
The word Science originates from the Latin verb Scientia meaning
(a) to know
(b) to see
(c) to experience
(d) to observe

Answer

Answer: (a) to know

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Class 11 Physics Chapter 1 MCQ Question 2.
Atomic and molecular phenomena are dealt with by
(a) Newtonian Mechanics
(b) fluid Mechanics
(c) applied Mechanics
(d) Quantum Mechanics

Answer

Answer: (d) Quantum Mechanics

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Physical World Class 11 MCQ Questions Question 3.
Wave picture of light failed to explain.
(a) the photoelectric effect
(b) polarization of light
(c) diffraction of light
(d) interference of light

Answer

Answer: (a) the photoelectric effect

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Class 11 Physics Chapter 1 MCQ With Answers Question 4.
Heliocentric theory proposed by Nicolas Copernicus was
(a) replaced by circular orbits to fit the data better
(b) replaced by elliptical orbits to fit the data better
(c) replaced by elliptical orbits to fit the taste of new rulers of Italy
(d) replaced by parabolic orbits to fit the data better

Answer

Answer: (b) replaced by elliptical orbits to fit the data better

---

Physical World Class 11 MCQ Question 5.
Just as a new experiment may suggest an alternative theoretical model, a theoretical advance may suggest what to look for in some for in some experiments. Which of the following experiments can be considered to support this claim?
(a) Davisson and Germer Experiment
(b) experimental discovery of positron
(c) scattering of alpha particle or the gold foil experiment
(d) Michelson Morley experiment

Answer

Answer: (b) experimental discovery of positron

---

Physics Class 11 Chapter 1 MCQ Questions Question 6.
The scientific method is
(a) a prescribed method for investigating phenomena, acquiring new knowledge…
(b) A procedure for proposing new hypothesis
(c) a body of techniques for investigating phenomena, acquiring new knowledge…
(d) A method for proposing new theories.

Answer

Answer: (c) a body of techniques for investigating phenomena, acquiring new knowledge…

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MCQ On Physical World Class 11 Question 7.
A scientific theory
(a) cannot be changed but can be reformulated
(b) is fixed once and for all because it is logical
(c) is changed to suit new fashion among scientists
(d) can be revised if required to fit new phenomenon or data

Answer

Answer: (d) can be revised if required to fit new phenomenon or data

---

Ch 1 Physics Class 11 MCQ Question 8.
Which of the following is a possible first step in applying the scientific method
(a) Conducting tests
(b) Formulating a hypothesis
(c) Formulation of a question
(d) Building a theory

Answer

Answer: (c) Formulation of a question

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Class 11 Physics Ch 1 MCQ Question 9.
Which of the following is a possible final step in applying the scientific method
(a) Formulating a hypothesis
(b) Building a theory
(c) Analysis of test results
(d) Formulation of a question

Answer

Answer: (c) Analysis of test results

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MCQs Of Physics Class 11 Chapter 1 With Answers Question 10.
Physics is a
(a) Applied Science
(b) Mathematical Science
(c) Engineering Science
(d) Natural Science

Answer

Answer: (d) Natural Science

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Physics Class 11 Chapter 1 MCQ Question 11.
Newtonian mechanics could not explain
(a) fall of bodies on earth
(b) Some of the most basic features of atomic phenomena.
(c) movement of planets
(d) flight of rockets

Answer

Answer: (b) Some of the most basic features of atomic phenomena.

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We hope the given NCERT MCQ Questions for Class 11 Physics Chapter 1 Physical World with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 11 Physics Physical World MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

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Students can also read NCERT Solutions for Class 6 Sanskrit Chapter 12 Questions and Answers at LearnInsta. Here all questions are solved with a detailed explanation, It will help to score more marks in your examinations.

संस्कृतपर्यायं लिखत- (संस्कृत पर्याय लिखिए)
Give the Sanskrit equivalent.

1. (i) एक छात्र – ………………..
(ii) दो कबूतर – ………………
(iii) तीन शेर – ……………….
(iv) चार घोड़े – ……………….
(v) पाँच बकरियाँ – ………………
(vi) छः हाथी – ……………….
(vii) सात लड़कियाँ – ………………
(vii) आठ पुस्तकें – …………………
(xi) नौ घर – ………………….
(x) दस पेड़ – ……………….

Answer

Answer:
(i) एक: छात्रः
(ii) द्वौ कपोतौ
(iii) त्रयः सिंहाः
(iv) चत्वारः अश्वाः
(v) पञ्च अजाः
(vi) षट् गजाः
(vii) सप्त बालिकाः
(viii) अष्ट पुस्तकानि
(ix) नव गृहाणि
(x) दश वृक्षाः

---

2.

Answer

Answer:
(i) सः बालकम् अकथयत्।
(ii) नायकः बालकान् अगणयत्।
(iii) ते सर्वे गृहम् अगच्छन्।
(iv) बालकः स्नानाय अगच्छत्।

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परस्परं मेलयत- (परस्परं मेलयत)
Match the following.

क्त्वा प्रत्ययान्तानि – हिन्दी-पर्यायाः
(i) दृष्ट्वा – सुनकर
(ii) स्नात्वा – गिनती करके
(iii) कृत्वा – लिखकर
(iv) श्रुत्वा – तैरकर
(v) गणयित्वा – देखकर
(vi) लिखित्वा – करके
(vii) तीर्वा – स्नान करके

Answer

Answer:
(i) दृष्ट्वा – देखकर
(ii) स्नात्वा – स्नान करके
(iii) कृत्वा – करके
(iv) श्रुत्वा – सुनकर
(v) गणयित्वा – गिनकर
(vi) लिखित्वा – लिखकर
(vii) तीर्खा – तैरकर।

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‘क’ खण्डात् उचितम् क्त्वा-प्रत्ययान्तं पदं चित्वा अधोदत्तानि वाक्यानि पूरयत- (खण्ड ‘क’ के अंतर्गत ‘क्त्वा’ प्रत्ययांत पदों में से उचित पद चुनकर वाक्य पूरे कीजिए।)
Pick out the appropriate word ending in suffix*fall’ from section ‘o’ and complete the sentences given below.

(i) सा …………….. भोजनं करोति।
(ii) चलचित्रं …………… सर्वे प्रसन्नः सन्ति।
(iii) समाचारं ………………. सः दुःखितः आसीत्।
(iv) तान् बालकान् ………………. पथिकः अवदत्।
(v) अहं विद्यालयकार्य ………………. क्रीडामि।
(vi) बालकाः नदी ……………. पारं गताः।
(vii) निबंध ……………… छात्रा अध्यापिकाम् अवदत्।

Answer

Answer:
(i) स्नात्वा
(ii) दृष्ट्वा
(iii) श्रुत्वा
(iv) गणयित्वा,
(v) कृत्वा
(vi) तीा
(vii) लिखित्वा।

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मञ्जूषायाः उचितम् अव्ययं चित्वा वाक्यपूर्ति कुरुत। (मञ्जूषा से उचित अव्यय पद चुनकर वाक्य पूरे कीजिए।)
Pick out the appropriate indeclinable from the box and complete the sentences.

अपि, न, अतः, तूष्णीम्, एव, पुनः
सः अवदत्-‘नव ……………… सन्ति। दशमः ……………… अस्ति।’ अपरः अपि बालकः ………………. अन्यान् बालकान् अगणयत्। तदा ……………….. नव एव आसन्। …………….. ते निश्चयम् अकुर्वन् यत् दशमः नद्यां मग्नः। ते दुःखिताः ………………… अतिष्ठिन।

Answer

Answer:
(क) एव
(ख) न
(ग) पुनः
(घ) अपि
(ङ) अतः
(च) तूष्णीम्।

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प्रदत्तविकल्पेभ्य उचितं पदं चित्वा वाक्यानि पूरयत। (दिए गए विकल्पों में से उचित विकल्प चुनकर वाक्य पूरे कीजिए।)
Pick out the correct word from the options given and complete the sentences.

1. (i) ……………… बालकाः नदीम् अगच्छन्। (अष्ट, नव, दश)
(ii) कश्चित् ……………. तत्र आगच्छत्। (बालकः, यात्रिकः, पथिकः)
(iii) एकः नद्यां …………..। (भग्नः, संलग्नः, मग्नः)
(iv) युष्माकं ……………….. कारणं किम्? (हर्षस्य, दुःखस्य, बालकस्य)
(v) ते …………… पारं गताः। (दृष्ट्वा, श्रुत्वा, तीर्वा)

Answer

Answer:
(i) दश
(ii) पथिकः
(iii) मग्नः
(iv) दु:खस्य
(v) तीा।

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2. (i) बालकाः …………….. अगच्छन्। (स्नानम्, स्नानाय, स्नानेन)
(ii) पथिकः तान् ………………. (अगणयन्, अगणयत्, अगणयत्)
(iii) ……………… बालकाः गृहम् अगच्छन्। (सर्वाः, सर्वे, सर्वः)
(iv) ते ……………… स्नानम् अकुर्वन्। (नदीजलम्, नदीजलात्, नदीजले)
(v) तत्र ……………… बालकाः आसन्। (दशाः, दश, दशः)

Answer

Answer:
(i) स्नानाय
(ii) अगणयत्
(iii) सर्वे
(iv) नदीजले
(v) दश।

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3. (i) ……………… उपवनम्। (एक, एकः, एकम्)
(ii) …………… वृक्षौ। (द्वे, द्वौ, त्रयः)
(iii) ……………… छात्रा। (एक, एका, एका:)
(iv) ……………….. मित्राणि। (चत्वारः, चतस्त्रः, चत्वारि) .
(v) …………………. लते। (द्वौ, द्वे, एकम्)
(vi) ………………… पादपाः। (त्रयः, त्रीणि, तिस्त्र)
(vii) ………………… बालकाः। (सर्वे, सर्वाः, सर्वम्)

Answer

Answer:
(i) एकम्
(ii) द्वौ।
(iii) एका
(iv) चत्वारि
(v) द्वे
(vi) त्रयः
(vii) सर्वे।

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4. (i) एकः एकः च ……………. भवतः। (द्वि, द्वे, द्वौ)
(ii) त्रयः षट् च ………………. भवन्ति। (अष्ट, नव, दश)
(iii) पञ्च द्वौ च ……………….. भवन्ति। (सप्त, अष्ट, षट्)
(iv) चत्वारः चत्वारः च ………………. भवन्ति। (अष्टः, अष्ट, अष्टा)
(v) द्वौ त्रयः च ………………… भवन्ति। (पञ्चः, पञ्च, पञ्चम)

Answer

Answer:
(i) द्वौ
(ii) नव
(iii) सप्त
(iv) अष्ट
(v) पञ्च।

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Check the below NCERT MCQ Questions for Class 6 Sanskrit Chapter 15 मातुलचन्द्र with Answers Pdf free download. MCQ Questions for Class 6 Sanskrit with Answers were prepared based on the latest exam pattern. We have provided मातुलचन्द्र Class 6 Sanskrit MCQs Questions with Answers to help students understand the concept very well.

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मञ्जूषायाः सहायतया रिक्तस्थानानि पूरयत। (मञ्जूषा की सहायता से रिक्त स्थान भरिए।)
Fill in the blanks with help from the box.

दास्यसि, कुत्र, मातुल, गीतिम्, कुतः
(क) त्वरितमेहि मां श्रावय …………….. ।
ख) ……………… आगच्छसि मातुलचन्द्र?
(ग) ……………. गमिष्यसि मातुलचन्द्र?
(घ) ………….. ! किरसि कथं न स्नेहम्?
(ङ) मह्यम् ……………… मातुलचन्द्र?

Answer

Answer:
(क) गीतिम्
(ख) कुतः
(ग) कुत्र
(घ) मातुल
(ङ) दास्यसि।

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मञ्जूषात् समानार्थकं पदं चित्वा रिक्तस्थाने लिखत। (मञ्जूषा से समानार्थक शब्द चुनकर सामने रिक्त स्थान में लिखिए।)
Pick out the word having similar meanings and write down in the blank space.

त्वरितम्, आयासि, एहि, आकाशः, प्रीतिम्, गेहम्
(क) आगच्छसि …………….
(ख) आगच्छ ……………..
(ग) गगनम् ……………..
(घ) शीघ्रम् …………..
(ङ) गृहम् ……………
(च) स्नेहम्। …………..

Answer

Answer:
(क) आयासि
(ख) एहि
(ग) आकाशः
(घ) त्वरितम्
(ङ) गेहम्
(च) प्रीतिम्।

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भिन्नप्रकृतिकम् पदं चिनुत। (भिन्न प्रकृति वाला पद चुनिए।)
Pick out the word that is different from the rest.

(क) बालिका, बालकः, बालकौ, गृहम्।
(ख) आगमिष्यति, आनयति, आगच्छति, आगच्छ।
(ग) कदा, कः, कुत्र, कुतः।
(घ) छात्रान्, छात्रेभ्यः, छात्राणाम्, छात्रस्य।

Answer

Answer:
(क) बालको
(ख) आगच्छ
(ग) कः
(घ) छात्रस्य।

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मञ्जूषात् उचितम् अव्ययपदं चित्वा अधोदत्तान् प्रश्नान् पूरयत- (मञ्जूषा से उचित अव्ययपद चुनकर निम्नलिखित प्रश्न पूरे कीजिए)
Pickout the appropriate indeclinable from the box and complete the questions given below.

किम्, कदा, कुतः, कथम्, कुत्र
(क) बालक! त्वम् इदानीं ……………. गच्छसि?
(ख) बालिके! त्वम् इदानीं ……………. आगच्छसि?
(ग) ……………….. त्वम इदानीं आपणम गच्छसि?
(घ) …………… प्रयास्यसि मातुलचन्द्र?
(ङ) छात्राः विद्यालयात् ……………….. आगच्छन्ति?

Answer

Answer:
(क) कुत्र
(ख) कुतः
(ग) किम्
(घ) कथम्
(ङ) कदा।

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उचितेन विकल्पस्य प्रयोगे वाक्यपूर्तिं कुरुत। (उचित विकल्प चुनकर वाक्य पूर्ति कीजिए।
Complete the sentences by using the correct option.

1. (i) कथमायासि न भो! मम ……………. (स्नेहम्, गेहम्, मातुलम्)
(ii) त्वरितमेहि मां श्रावय …………… । (नीतिम्, प्रीतिम्, गीतिम्)
(ii) नैव दश्यते क्वचिद ………………… । (अवकाशः. नीलाकाशः, चन्द्रः)
(iv) …………….. तव चन्द्रिकावितानम्। (तारकखचितम्, धवलम्, सितपरिधानम्)
(v) मातुल! किरसि ………………… न स्नेहम्? (किम्, मम, कथम्)

Answer

Answer:
(i) गेहम्
(ii) गीतिम्
(iii) अवकाशः
(iv) धवलम्
(v) कथम्।

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2. (i) कुत्र …………….. मातुलचन्द्र? (गमिष्यति, गमिष्यन्ति, गमिष्यसि)
(ii) किं त्वं ……………… उपहारं दास्यसि? (माम्, मम्, मह्यम्)
(iii) कुतः आगच्छसि (मातुलचन्द्रः, मातुलः, मातुलचन्द्र)
(iv) ……………… ! वर्धय मे प्रीतिम्। (प्रिय मातुलः, प्रिय मातुल, प्रियः मातुलः)
(v) मातुलचन्द्रः कुत्र ……………….? (गमिष्यसि, गमिष्यति, गमिष्यामि)

Answer

Answer:
(i) गमिष्यसि
(ii) मह्यम्
(iii) मातुलचन्द्र
(iv) प्रिय मातुल
(v) गमिष्यसि।

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उचितं विकल्पं चित्वा प्रश्नान् उत्तरत- (उचित विकल्प चुनकर प्रश्नों के उत्तर दीजिए)
Pick out the correct option and answer the questions.

(क) अस्मिन् बालगीते मातुलः कः अस्ति? (सूर्यः, चन्द्रः, बालकः)
(ख) बालकः कं सम्बोधयति? (आकाशम्, चन्द्रिकावितानम्, मातुलचन्द्रम्)
(ग) नीलाकाशः कीदृशः वर्तते? (विस्तृतः, धवलः, प्रियः)
(घ) सितपरिधानम् कथं खचितम्? (स्नेहेन, चन्द्रिकया, तारकै:)
(ङ) मातुलचन्द्रः कुत्र न आयाति/आगच्छति। (गेहम्, आकाशम्, स्नेहम्)

Answer

Answer:
(क) अस्मिन् बालगीते चन्द्रः मातुलः वर्तते।
(ख) बालकः मातुलचन्द्रम् सम्बोधयति।
(ग) नीलाकाशः विस्तृतः वर्तते।
(घ) सितपरिधानम् तारकैः खचितम्।
(ङ) मातुलचन्द्रः गेहम् न आयाति।

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Check the below NCERT MCQ Questions for Class 6 Sanskrit Chapter 13 विमानयानं रचयाम with Answers Pdf free download. MCQ Questions for Class 6 Sanskrit with Answers were prepared based on the latest exam pattern. We have provided विमानयानं रचयाम Class 6 Sanskrit MCQs Questions with Answers to help students understand the concept very well.

Students can also read NCERT Solutions for Class 6 Sanskrit Chapter 13 Questions and Answers at LearnInsta. Here all questions are solved with a detailed explanation, It will help to score more marks in your examinations.

निम्न पङ्क्तीन् पठित्वा तदाधारितानां प्रश्नानाम् उत्तराणि लिखत (निम्न पंक्तियों को पढ़कर उसपर आधारित प्रश्नों के उत्तर लिखिए)

उन्नतवृक्षं तुझं भवनं
क्रान्त्वाकाशं खलु याम।
कृत्वा हिमवन्तं सोपानं
चन्दिरलोकं प्रविशाम ।।

Question 1.
‘क्रान्त्वाकाशं खलु याम’। अत्र क्रियापदं किम्?
(क) आकाशम्
(ख) खलु
(ग) याम
(घ) आकाशे

Answer

Answer: (ग) याम

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Question 2.
‘हिमवन्तं सोपानम्’ अनयोः पदयोः विशेषणं किम् अस्ति?
(क) हिमवन्तम्
(ख) हिमवतः
(ग) सोपानः
(घ) सोपानम्

Answer

Answer: (क) हिमवन्तम्

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Question 3.
वयं कीदृशं भवनं क्रान्त्वा आकाशं याम?

Answer

Answer: तुङ्गम्

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Question 4.
वयं उन्नतवृक्षं क्रान्त्वा कुत्र याम?

Answer

Answer: आकाशम्

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Question 5.
वयं किं कृत्वा चन्दिरलोकं प्रविशाम?

Answer

Answer: वयं हिमवन्तं सोपानं कृत्वा चन्दिरलोकं प्रविशाम।

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निम्नश्लोकं पठित्वा रिक्तस्थानानि पूरयत (नीचे लिखे श्लोक को पढ़कर खाली स्थानों को भरिए)

शुक्रश्चन्द्रः सूर्यो गुरुरिति
ग्रहान् हि सर्वान गणयाम।
विविधाः सुन्दरताराश्चित्वा
मौक्तिकहारं रचयाम।।

अन्वयः- (वयं) शुक्र: चन्द्रः (i) ……………. गुरुः इति सर्वान् (ii) …………… हि गणयाम। विविधाः (iii) …………….. चित्वा ……………… रचयाम।

Answer

Answer:
(i) सूर्यः
(ii) ग्रहान्
(iii) सुन्दरताराः
(iv) मौक्तिकहारं।

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उचितानि पदानि सम्मेलयत (उचित शब्दों को मिलाइए)

(क) – (ख)
(i) शुक्रचन्द्रः – कृषिकजनानाम्
(ii) नीले गगने – चन्दिरलोकं प्रविशाम
(iii) दुःखित-पीड़ित – मौक्तिकहारं रचयाम
(iv) कृत्वा हिमवन्तं सोपानं – सीते! ललिते!
(v) राघव! माधव! – सूर्यो गुरुरिति
(vi) विविधाः सुन्दरताराश्चित्वा – विपुले विमले

Answer

Answer:
(i) सूर्यो गुरुरिति
(ii) विपुले विमले
(iii) कृषिकजनानाम्
(iv) चन्द्रिरलोकं प्रविशाम,
(v) सीते! ललिते!
(vi) मौक्तिकहारं रचयाम।

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निम्न पदानि पठित्वा प्रश्नवाचकानि पदानि लिखत (नीचे लिखे पदों को पढ़कर प्रश्नवाचक पदों को लिखिए)

यथा- सूर्यः – कः
(i) अम्बुदमालाम् – ………………..
(ii) हर्षम् – ………………..
(iii) उन्नतवृक्षम् – …………………
(iv) सर्वान् – ………………….
(v) सुन्दरताराः – ………………..
(vi) चन्दिरलोकम् – ………………..

Answer

Answer:
(i) काम्
(ii) किम्
(iii) कम्
(iv) कान्
(v) काः
(vi) कुत्र।

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पर्यायपदानि चित्वा लिखत (पर्यायवाची पदों को चुनकर लिखिए)

पदानि – पर्यायाः
(i) आकाशे – सूर्यः
(ii) स्वच्छे – हर्षम्
(iii) चन्द्रः – गगने
(iv) दिनकरः – चन्दिरः
(v) प्रसन्नताम् – विमले

Answer

Answer:
(i) गगने
(ii) विमले
(iii) चन्दिर
(iv) सूर्यः
(v) हर्षम्।

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We hope the given NCERT MCQ Questions for Class 6 Sanskrit Chapter 13 विमानयानं रचयाम with Answers Pdf free download will help you. If you have any queries regarding CBSE Class 6 Sanskrit विमानयानं रचयाम MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.