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## Q1. Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

(d) 0, 8

## Q2. Find the two consecutive odd positive integers, sum of whose square is 290

(a) 15, 17

(b) 9, 11

(c) 13, 15

(d) 11, 13

(d) 11, 13

## Q3. Which of the following are the roots of the quadratic equation, x^{2} – 9x + 20 = 0 by factorisation?

(a) 3,4

(b) 4, 5

(c) 5, 6

(d) 6, 7

(b) 4, 5

## Q4. Reduction of a rupee in the price of onion makes the possibility of buying one more kg of onion for Rs.56. Find the original price of the onion per kg?

(a) 7

(b) 1

(c) 7, -8

(d) 8

(d) 8

## Q5. The equation (x – 2)^{2} + 1 = 2x – 3 is a

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

(b) quadratic equation

## Q6. Two candidates attempt to solve a quadratic equation of the form x^{2} + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :

(a) 3, 4

(b) – 3, – 4

(c) 3, – 4

(d) – 3, 4

(b) – 3, – 4

## Q7. The quadratic equation has degree

(a) 0

(b) 1

(c) 2

(d) 3

(c) 2

## Q8. The polynomial equation x (x + 1) + 8 = (x + 2) (x – 2) is

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

(a) linear equation

## Q9. If (x – a) is one of the factors of the polynomial ax^{2} + bx + c, then one of the roots of ax^{2 }+ bx + c = 0 is

(a) 1

(b) c

(c) a

(d) none of these

(c) a

## Q10. The equation x^{2 }– px + q = 0 p, q e R has no real roots if :

(a) p^{2} > 4q

(b) p^{2} < 4q

(c) p^{2 }= 4q

(d) None of these

(b) p2 = 4q

## Q11. The roots of the equation (b – c) x^{2} + (c – a) x + (a – b) = 0 are equal, then

(a) 2a = b + c

(b) 2c = a + b

(c) b = a + c

(d) 2b = a + c

(d) 2b = a + c

## Q12. If the roots of px^{2} + qx + 2 = 0 are reciprocal of each other, then

(a) P = 0

(b) p = -2

(c) p = ±2

(d) p = 2

(d) p = 2

## Q13. If a, p are the roots of the equation (x – a) (x – b) + c = 0, then the roots of the equation (x – a) (x – P) = c are

(a) a, b

(b) a, c

(c) b, c

(d) none of these

(a) a, b

## Q14. The sum of the roots of the quadratic equation 3x^{2} – 9x + 5 = 0 is

(a) 3

(b) 6

(c) -3

(d) 2

(c) -3

## Q15. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

(c) 3

## Q16. The equation 2x^{2} + kx + 3 = 0 has two equal roots, then the value of k is

(a) ±v6

(b) ± 4

(c) ±3v2

(d) ±2v6

(d) ±2v6

## Q17. The quadratic equation whose one rational root is 3 + v^{2} is

(a) x^{2} – 7x + 5 = 0

(b) x^{2} + 7x + 6 = 0

(c) x^{2} – 7x + 6 = 0

(d) x^{2 }– 6x + 7 = 0

(d) x2 – 6x + 7 = 0

## Q18. A bi-quadratic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

(d) 4

## Q19. If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

(a) 87

(b) 88

(c) 89

(d) 90

(c) 89

## Q20. The quadratic equation 2x^{2} – 3x + 5 = 0 has?

(a) Real and distinct roots

(b) Real and equal roots

(c) Imaginary roots

(d) All of the above

(c) Imaginary roots

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