1. Which of the following is not irrational?
(a) (2 – √3)2
(b) (√2 + √3)2
(c) (√2 -√3)(√2 + √3)
(d)Non of these
2. sin (90° – A) and cos A are:
(a) Different
(b) Same
(c) Not related
(d) None of the above
3. The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 0
(b) 1
(c) 2
(d) 4
4. The value of the expression sin6θ + cos6θ + 3 sin2θ cos2θ is
(a) 0
(b) 3
(c) 2
(d) 1
5. The value of the expression sin6θ + cos6θ + 3 sin2θ cos2θ is
(a) 0
(b) 3
(c) 2
(d) 1
6. If ∆ABC is right angled at C, then the value of cos(A+B) is
(a) 0
(b) 1
(c) 1/2
(d) √3/2
7. If cos X = a/b, then sin X is equal to:
(a) (b2-a2)/b
(b) (b-a)/b
(c) √(b2-a2)/b
(d) √(b-a)/b
8. The value of (tan 1° tan 2° tan 3° … tan 89°) is
(a) 0
(b) 1
(c) 2
(d) 1/2
9. If sin A + sin2A = 1, then the value of the expression (cos2A + cos4A) is
(a) 1
(b) 1/2
(c) 2
(d) 3
10. The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is
(a) -1
(b) 0
(c) 1
(d) 3/2
11. If cos(α + β) = 0, then sin(α – β) can be reduced to
(a) cos β
(b) cos 2β
(c) sin α
12. If b = 3, then any integer can be expressed as a =
(a) 3q, 3q+ 1, 3q + 2
(b) 3q
(c) none of the above
13. The product of three consecutive positive integers is divisible by
(a) 4
(b) 6
(c) no common factor
(d) only 1
14. The set A = {0,1, 2, 3, 4, …} represents the set of
(a) whole numbers
(b) integers
(c) natural numbers
(d) even numbers
15. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(d) https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/fonts/HTML-CSS/TeX/png/Math/Italic/283/0078.png?V=2.7.5
16. The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is
(a) 17
(b) 11
(c) 34
(d) 45
17. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students
(a) 52
(b) 56
(c) 48
(d) 63
18. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet ?
(a) 36 minutes
(b) 18 minutes
(c) 6 minutes
(d) They will not meet
19. Express 98 as a product of its primes
(a) 2² × 7
(b) 2² × 7²
(c) 2 × 7²
(d) 23 × 7
20. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 kg
(b) 290 kg
(c) 200 kg
(d) 350 kg
21. For some integer p, every even integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
22. For some integer p, every odd integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
23. m² – 1 is divisible by 8, if m is
(a) an even integer
(b) an odd integer
(c) a natural number
(d) a whole number
24. If two positive integers A and B can be ex-pressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
25. The product of a non-zero rational and an irrational number is
(a) always rational
(b) rational or irrational
(c) always irrational
(d) zero
26. If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
27. The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is
(a) 260
(b) 75
(c) 65
(d) 13
28. The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is
(a) 5
(b) 60
(c) 20
(d) 100
29. (6 + 5 √3) – (4 – 3 √3) is
(a) a rational number
(b) an irrational number
(c) a natural number
(d) an integer
30. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is
(a) 24
(b) 16
(c) 8
(d) 48 8. If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the
other two zeroes is
(a) b – a + 1
(b) b – a – 1
(c) a – b + 1
(d) a – b – 1
31 The zeroes of the quadratic polynomial x2 + 99x + 127 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal
32. The zeroes of the quadratic polynomial x² + kx + k, k? 0,
(a) cannot both be positive
(b) cannot both be negative
(c) are always unequal
(d) are always equal
33. If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then
(a) c and a have opposite signs
(b) c and b have opposite signs
(c) c and a have the same sign
(d) c and b have the same sign
34. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it
(a) has no linear term and the constant term is negative.
(b) has no linear term and the constant term is positive.
(c) can have a linear term but the constant term is negative.
(d) can have a linear term but the constant term is positive.
35. The number of polynomials having zeroes as 4 and 7 is
(a) 2
(b) 3
(c) 4
(d) more than 4
36. A quadratic polynomial, whose zeores are -4 and -5, is
(a) x²-9x + 20
(b) x² + 9x + 20
(c) x²-9x- 20
(d) x² + 9x- 20
37. The zeroes of the quadratic polynomial x² + 1750x + 175000 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal
38. The zeroes of the quadratic polynomial x² – 15x + 50 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal
39. The zeroes of the quadratic polynomial 3x² – 48 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal
40 The zeroes of the quadratic polynomial x² – 18x + 81 are
(a) both negative
(b) one positive and one negative
(c) both positive and unequal
(d) both equal and positive
41. The zeroes of the quadratic polynomial x² + px + p, p ≠ 0 are
(a) both equal
(b) both cannot be positive
(c) both unequal
(d) both cannot be negative
42. If one of the zeroes of the quadratic polynomial (p – l)x² + px + 1 is -3, then the value of p isMCQ Questions for Class 10 Maths Polynomials with Solutions 5
43. If the zeroes of the quadratic polynomial Ax² + Bx + C, C # 0 are equal, then
(a) A and B have the same sign
(b) A and C have the same sign
(c) B and C have the same sign
(d) A and C have opposite signs
44. If 1 is one of the zeroes of the polynomial x² + x + k, then the value of k is:
(a) 2
(b) -2
(c) 4
(d) -4
Question 45.
If the zeroes of the polynomial x³ – 3x² + x – 1 are st, s and st then value of s is
(a) 1
(b) -1
(c) 2
(d) -3
Question 46.
If a polynomial of degree 4 is divided by quadratic polynomial, the degree of the remainder is
(a) ≤ 1
(b) ≥ 1
(c) 2
(d) 4
Question 47.
If a – b, a and a + b are zeroes of the polynomial fix) = 2x³ – 6x² + 5x – 7, then value of a is
(a) 1
(b) 2
(c) -5
(d) 7
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Question 48.
A quadratic polynomial whose sum of the zeroes is 2 and product is 1 is given by
(a) x² – 2x + 1
(b) x² + 2x + 1
(c) x² + 2x – 1
(d) x² – 2x – 1
Question 49.
If one of the zeroes of a quadratic polynomial ax² + bx + c is 0, then the other zero is
(a) −ba
(b) 0
(c) ba
(d) –ca
Question 50.
The sum and the product of the zeroes of polynomial 6x² – 5 respectively are
(a) 0, −65
(b) 0, 65
(c) 0, 5
