objective
doyletaft
objective50questions.pdf
Class - X
Polynomials
1. Find the zeroes of the quadratic polynomial x 2 +7x + 12
(1) -2, -5
(2) -3, -4
(3) 2, 5
(4) 3, 4
Ans : (2)
2. Find the zeroes of the polynomial x 2 - 17
(1)
(2)
(3)
(4) none of these
Ans : (1)
3. Find a quadratic polynomial, the sum and product of whose zeroes are -7 and -2
(1) x 2 -7x -2
(2) x 2 -7 x + 2
(3) x 2 + 7x -2
(4) x 2 + 2x -7
Ans : (3)
4. Find a cubic polynomial when the zeroes are 3, -1,
(1) 3x 3 - 5x
2 - 11x -3
(2) 3x 3 + 5x
2 + 11x -3
(3) 3x 3 -5x
2 + 11x + 3
(4) none of these
Ans : (1)
5. Find a quadratic polynomial, the sum and product of whose zeroes are
(1) 4x 2 - x + 1
(2) 4x 2
+ x - 1
(3) 4x 2
+ x + 1
(4) none of these
Ans : (3)
6. Find all the zeroes of 2x 4 - 3x
3 - 3x
2 + 6x - 2 if two of its zeroes are and
(1)
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(2)
(3)
(4)
Ans : (4)
7. Find the quotient and remainder when the polynomial x 4 - 3x
2 + 4x + 5 is divided by x
2 - x + 1
(1) x 2 + x - 3, 8
(2) x 2 - x + 3, 7
(3) x 2 - x -3, 4
(4) x 2
+ 2x + 3, 6
Ans : (1)
8. The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x 3 - 3x
2 + x + 2
is divided by g(x). Find g(x)
(1) x 2
+ x + 1
(2) x 2
- x - 1
(3) x 2
- x + 1
(4) none of these
Ans : (3)
9. Find P and q, if the zeroes of the polynomial x 3 - 3x
2 + x + 1 are p-q, p, p + q
(1)
(2)
(3)
(4)
Ans : (4)
10. Find a quadratic polynomial whose zeroes are and
(1) x 2 - 7x + 10
(2) x 2 + 7x + 10
(3) x 2 - 7x - 10
(4) x 2
+ 7x - 10
Ans : (1)
11. If the quotient and remainder were 3y - 5 and 9y + 10, on dividing 3y 3 + y
2 + 2y + 5 by g (y).
Find g (y)
(1) y 2
- 2y + 1
(2) y 2
+ 2y + 1
(3) y 2 -2y - 1
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(4) 2y 2 - 2y - 1
Ans : (2)
12. Obtain the zeroes of the quadratic polynomial pqx 2 + (q
2 - Pr) x - qr
(1)
(2)
(3)
(4)
Ans : (1)
13. If two of the zeroes are and . Find the other zeroes of t 4 - 6t
3 - 26t
2 + 138t - 35
(1) 7 and 5
(2) 7 and - 5
(3) (-6, 7)
(4) (-5 and -7)
Ans : (2)
14. If p and q are the zeroes of the quadratic polynomial 4x 2 - 1 = 0. Find the value of p
2 + q
2
(1) 3/2
(2)
(3)
(4) 1
Ans : (3)
15. Find the zeroes of the quadratic polynomial x 2 + 19 x + 90
(1) -9, -10
(2) 9, 10
(3) 4, 5
(4) -4, -5
Ans : (1)
16. Find the sum and product of zeroes of the polynomial
(1)
(2)
(3)
(4)
Ans : (2)
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17. Find the zeroes of the polynomial x 2
- 21
(1)
(2) -3, 3
(3)
(4) none of these
Ans : (1)
18. Find the sum and product of the zeroes of polynomial x 2 - 51
(1) 0, 51
(2) 0, -51
(3) 2, 51
(4) -2, 51
Ans : (2)
19. Find the sum and product of the zeroes of quadratic polynomial 19x 2 - 16x - 21
(1)
(2)
(3)
(4)
Ans : (4)
20. If p and q are the zeroes of the polynomial x 2 - 5x - k. Such that p - q = 1, find the value of K
(1) 6
(2) 7
(3) 8
(4) 9
Ans : (1)
21. Find the sum and product of the zeroes of cubic polynomial 2x 3 - 5x
2 - 14x + 8.
(1) 5/2, 7, -4
(2) -5/2, 7, -4
(3) -5/2, -7, 4
(4) 5/2, -7, 4
Ans : (1)
22. Find the zeroes of the polynomial 4x 2 - 4x + 1
(1)
(2)
(3) 1
(4)
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Ans : (2)
23. Find the quotient and remainder, when the polynomial x 4 - 5x + 6 is divided by 2 - x
2
(1) - x 2 + 2, 5x - 10
(2) -x 2 - 2, - 5x + 10
(3) x 2 + 2, 5x - 10
(4) x 2 -2, - 5x + 10
Ans : (2)
24. Form a quadratic polynomial of which one zero is and the sum of the zeroes is 12
(1) x 2 - 4x + 30
(2) x 2
+ 4x - 31
(3) x 2
- 12x + 31
(4) none of these
Ans : (3)
25. Find the value of a so that -2 is a root of 2x 2 - x + a = 0
(1) 10
(2) - 10
(3) 9
(4) -9
Ans : (2)
26. If p and q are the zeroes of the quadratic polynomial 2x 3 + 3x + 5. Find the value of
(1) 3/5
(2) 5/3
(3) -3/5
(4) - 5/3
Ans : (3)
27. Find the quadratic polynomial whose sum and product of its zeroes are and respectively
(1)
(2)
(3)
(4) none of these
Ans : (1)
28. If P and q are the zeroes of the quadratic polynomial x 2 + mx + n
2 + a, then the value of p
2 +
q 2 + pq is
(1) 0
(2) a
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(3) -a
(4)
Ans : (3)
29. If , are the zeroes of the equation ax 2 + bx + c = 0, them form the quadratic polynomial
whose zeroes are 2 + 3 , 3 + 2
(1)
(2) a 2 x
2 + 5abx + 6b
2 + ac
(3) ax 2 + abx + 6b
2 + ac
(4) a 2 x
2 + abx + b
2 + ac
Ans : (1)
30. If p and q are the zeroes of the polynomial x 2 + px + q = 0, then
(1) p = 1
(2) p = 1 or 0
(3) p = -2
(4) p = -2 or 0
Ans : (2)
31. If one zero of quadratic polynomial x 2 - x - k is the square of other, then find k
(1)
(2)
(3)
(4)
Ans : (3)
32. If and are the zeroes of quadratic polynomial ax 2 + bx + c = 0, then find the value of
(1)
(2)
(3)
(4)
Ans : (1)
33. If the product of zeroes of the quadratic polynomial mx 2 + 6x + (2m-1) is -1, then find the
value of m
(1)
(2) 3
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(3)
(4) - 3
Ans : (1)
34. If the zeroes of the quadratic polynomial ax 2 + bx +c are of the form and , then find
the value of (a + b + c) 2
(1) b 2 + 4ac
(2) b 2 - 4ac
(3) a 2 + 4ac
(4) c 2
+ 4ab
Ans : (2)
35. If , are the zeroes of the quadratic polynomial ax 2 + bx +c , then form the quadratic
polynomial whose zeroes are and is
(1)
(2)
(3)
(4)
Ans : (1)
36. If the difference of the zeroes of the quadratic polynomial x 2 - bx + c be 1, then
(1)
(2)
(3)
(4)
Ans : (1)
37. If , are the zeroes of the quadratic polynomial ax 2 + bx + c, then is
(1) 2 / a
(2) 2 / b
(3) 2 / c
(4) - 2 / a
Ans : (4)
38. Find the zeroes of the polynomial x 2 + 2x + 1 = 0
(1) - 1, -1
(2) 1, 1
(3) - 1, 1
(4) -2, 1
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Ans : (1)
39. Find the zeroes of the quadratic polynomial 6x 2 - 7x - 3
(1) 3/2
(2) - 3/2 , 1/3
(3) , - 1/3
(4) 3/2 , - 1/3
Ans : (4)
40. Find the zeroes of the quadratic polynomial 5x 2 - 4 - 8x
(1) 2/5, -2
(2) , -2
(3) 2, -2/5
(4) 2/5, 2
Ans : (3)
41. Find the quadratic polynomial whose zeroes are and respectively
(1)
(2)
(3)
(4) None of these
Ans : (2)
42. Find the sum and product of zeroes of the cubic polynomial p (x) = 5x 3 - 10x
2 + 7x + 15
(1) 2, 7/5, -3
(2) -2 , -7/5, 3
(3) 2, -7/5, 3
(4) -2, - 7/5, -3
Ans : (1)
43. Find the remainder when y 3 + 4y
2 - 3y + 10 is divided by y + 4
(1) 22
(2) -22
(3) 21
(4) 20
Ans : (1)
44. Find the quotient and remainder when 2t 4 - 6t
3 + 2t
2 - t + 2 is divided by t + 2
(1) 2t 3 + 10t
2 -22t + 45, 91
(2) 2t 2 -20t + 45, 90
(3) 2t 3 - 10t
2 + 22t - 45, 92
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(4) 2t 3 -22t + 45, 91
Ans : (3)
45. Find the quotient and remainder when 4y 3 -12y
2 + 14y -13 is divided by t -
(1) 4t 2 -10t + 9 , -17/2
(2) 4t 2
+ 10t -9 , 17/2
(3) 4t 2 -10t - 9, 19/2
(4) 4t 2 + 4t + 5, 17/2
Ans : (1)
46. If p and q are the zeroes of x 2 - 5x + 4 = 0, find the value of p
2 q + q
2 p
(1) 19
(2) 16
(3) 17
(4) 20
Ans : (4)
47. Find the quotient and remainder when t 4 + 1 is divided by t - 1
(1) t 3 - t
2 - t - 1, 3
(2) t 3 - t
2 + t - 1, 4
(3) t 3 + t
2 + t + 1, 2
(4) t 3 - t
2 - t + 1, 2
Ans : (3)
48. Find the quotient and remainder when y 4 + y
2 +1 is t
3 divided by y
2 + y + 1
(1) y 2 - y + 1, 0
(2) y 2
+ y + 1, 1
(3) y 2 - y - 1, 0
(4) y 2 + y -1, 2
Ans : (1)
49. Form the quadratic polynomial in t when zeroes are and
(1) t 2 - 2t - 1
(2) t 2 - 4t - 1
(3) t 2 + t + 1
(4) t 2 - t - 1
Ans : (2)
50. If and are the zeroes of x 2
- 6x + 4 = 0, Find the value of 2 2
+ 2 3
(1) 92
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(2) 94
(3) 96
(4) 90
Ans : (3)
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