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

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

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) x^{2} + 3x = ( -1) (1 – 3x)

(c) (x + 2) (x – 1) = x^{2} – 2x – 3

(d) x^{3} – x^{2} + 2x + 1 = (x + 1)^{3}

Solution:

Question 2.

Which of the following is a quadratic equation ?

(a) (x – 2) (x + 1) = (x – 1) (x – 3)

(b) (x + 2)^{3} = 2x(x^{2} – 1)

(c) x^{2} + 3x + 1 = (x – 2)^{2}

(d) 8(x – 2)^{3} = (2x – 1)^{3} + 3

Solution:

Question 3.

Which of the following equations has 2 as a root ?

(a) x^{2} – 4x + 5 = 0

(b) x^{2} + 3x – 12 = 0

(c) 2x^{2} – 7x + 6 = 0

(d) 3x^{2} – 6x – 2 = 0

Solution:

Question 4.

If \(\\ \frac { 1 }{ 2 } \) is a root of the equation x^{2} + kx – \(\\ \frac { 5 }{ 4 } \) = 0, then the value of k is

(a) 2

(b) -2

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

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

Solution:

Question 5.

If \(\\ \frac { 1 }{ 2 } \) is a root of the quadratic equation 4x^{2} – 4kx + k + 5 = 0, then the value of k is

(a) -6

(b) -3

(c) 3

(d) 6

Solution:

Question 6.

The roots of the equation x^{2} – 3x – 10 = 0 are

(a) 2, -5

(b) -2, 5

(c) 2, 5

(d) -2, – 5

Solution:

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:

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:

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:

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:

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:

Question 12.

If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by

(a) p < \(\\ \frac { 9 }{ 2 } \)

(b) p ≤ \(\\ \frac { 9 }{ 2 } \)

(c) p > \(\\ \frac { 9 }{ 2 } \)

(d) p ≥ \(\\ \frac { 9 }{ 2 } \)

Solution:

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:

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:

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: