ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS

More Exercises

Choose the correct answer from the given four options (1 to 15) :

Question 1.
Which of the following is not a quadratic equation ?
(a) (x + 2)2 = 2(x + 3)
(b) x2 + 3x = ( – 1) (1 – 3x)
(c) (x + 2) (x – 1) = x2 – 2x – 3
(d) x3 – x2 + 2x + 1 = (x + 1)3
Solution:
(a) (x + 2)2 = 2(x + 3)
⇒ x2 + 4x + 4 = 2x + 6
⇒ x2 + 4x – 2x + 4 – 6 = 0
⇒ x2 + 2x – 2
It is a quadratic equation.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q1.1

Question 2.
Which of the following is a quadratic equation ?
(a) (x – 2) (x + 1) = (x – 1) (x – 3)
(b) (x + 2)3 = 2x(x2 – 1)
(c) x2 + 3x + 1 = (x – 2)2
(d) 8(x – 2)3 = (2x – 1)3 + 3
Solution:
(a) (x – 2) (x + 1) = (x – 1) (x – 3)
⇒ x2 + x – 2x – 2 = x2 – 3x – x + 3
⇒ 3x + x – 2x + x = 3 + 2
⇒ 3x = 5
It is not a quadratic equation.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q2.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q2.2

Question 3.
Which of the following equations has 2 as a root ?
(a) x2 – 4x + 5 = 0
(b) x2 + 3x – 12 = 0
(c) 2x2 – 7x + 6 = 0
(d) 3x2 – 6x – 2 = 0
Solution:
(a) x2 – 4x + 5 = 0
⇒ (2)2 – 4x2 + 5 = 0
⇒ 4 – 8 + 5 = 0
⇒ 9 – 8 ≠ 0
2 is not its root.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q3.1

Question 4.
If \(\\ \frac { 1 }{ 2 } \) is a root of the equation x2 + kx – \(\\ \frac { 5 }{ 4 } \) = 0, then the value of k is
(a) 2
(b) – 2
(c) \(\\ \frac { 1 }{ 4 } \)
(d) \(\\ \frac { 1 }{ 2 } \)
Solution:
\(\\ \frac { 1 }{ 2 } \) is a root of the equation
x2 + kx – \(\\ \frac { 5 }{ 4 } \) = 0
Substituting the value of x = \(\\ \frac { 1 }{ 2 } \) in the
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q4.1

Question 5.
If \(\\ \frac { 1 }{ 2 } \) is a root of the quadratic equation 4x2 – 4kx + k + 5 = 0, then the value of k is
(a) – 6
(b) – 3
(c) 3
(d) 6
Solution:
\(\\ \frac { 1 }{ 2 } \) is a root of the equation
4x2 – 4kx + k + 5 = 0
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q5.1

Question 6.
The roots of the equation x2 – 3x – 10 = 0 are
(a) 2,- 5
(b) – 2, 5
(c) 2, 5
(d) – 2, – 5
Solution:
x2 – 3x – 10 = 0
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q6.1
x = 5, – 2 or – 2, 5 (b)

Question 7.
If one root of a quadratic equation with rational coefficients is \(\frac { 3-\sqrt { 5 } }{ 2 } \), then the other
(a)\(\frac { -3-\sqrt { 5 } }{ 2 } \)
(b)\(\frac { -3+\sqrt { 5 } }{ 2 } \)
(c)\(\frac { 3+\sqrt { 5 } }{ 2 } \)
(d)\(\frac { \sqrt { 3 } +5 }{ 2 } \)
Solution:
One root of a quadratic equation is \(\frac { 3-\sqrt { 5 } }{ 2 } \)
then other root will be \(\frac { 3+\sqrt { 5 } }{ 2 } \) (c)

Question 8.
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
(a)\(\\ \frac { 9 }{ 8 } \)
(b)\(– \frac { 9 }{ 8 } \)
(c)\(\\ \frac { 1 }{ 8 } \)
(d)\(– \frac { 1 }{ 8 } \)
Solution:
2x² – 5x + (k + 3) = 0
a = 2, b = -5, c = k + 3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q8.1

Question 9.
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
(a) 0 only
(b) 4
(c) 8 only
(d) 0, 8
Solution:
2x² – kx + k = 0
a = 2, b = -k, c = k
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q9.1

Question 10.
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
(a) 6
(b) 0 Only
(c) 24 only
(d) 0
Solution:
3x² – kx + 2k = 0
Here, a = 3, b = -k, c = 2k
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q10.1

Question 11.
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
(a) 1, 3
(b) 0, 3
(c) 0, 1
(d) 0, 1
Solution:
(k + 1)x² – 2(k – 1)x + 1 = 0
Here, a = k + 1, b = -2(k – 1), c = 1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q11.1
k = 0, 3 (b)

Question 12.
If the equation 2x² – 6x + p = 0 has real and different roots, then the values ofp are given by
(a)p < \(\\ \frac { 9 }{ 2 } \)
(b)p ≤ \(\\ \frac { 9 }{ 2 } \)
(c)p > \(\\ \frac { 9 }{ 2 } \)

(d)p ≥ \(\\ \frac { 9 }{ 2 } \)
Solution:
2x² – 6x + p = 0
Here, a = 2, b = -6, c = p
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q12.1

Question 13.
The quadratic equation 2x² – √5x + 1 = 0 has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than two real roots
Solution:
2x² – √5x + 1 = 0
Here, a = 2, b = -√5, c = 1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q13.1

Question 14.
Which of the following equations has two distinct real roots ?
(a) 2x² – 3√2x + \(\\ \frac { 9 }{ 4 } \) = 0
(b) x² + x – 5 = 0
(c) x² + 3x + 2√2 = 0
(d) 5x² – 3x + 1 = 0
Solution:
(a) 2x² – 3√2x + \(\\ \frac { 9 }{ 4 } \) = 0
b² – 4ac = ( -3√2)² – 4 x 2 x \(\\ \frac { 9 }{ 4 } \) = 18 – 18 = 0
.’. Roots are real and equal.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable MCQS Q14.1

Question 15.
Which of the following equations has no real roots ?
(a) x² – 4x + 3√2 = 0
(b) x² + 4x – 3√2 = 0
(c) x² – 4x – 3√2 = 0
(d) 3x² + 4√3x + 4 = 0
Solution:
(a) x² – 4x + 3√2 = 0
b² – 4ac = ( -4)² – 4 × 1 × 3√2
= 16 – 12√2
= 16 – 12(1.4)
= 16 – 16.8
= -0.8
b² – 4ac < 0
Roots are not real. (a)

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