The document contains a series of mathematics questions related to polynomials, zeroes, factors, and assertions with reasons. Each question provides multiple-choice options, focusing on algebraic concepts such as the relationship between roots and coefficients, properties of polynomials, and basic number theory. The content is structured for a class 10 mathematics curriculum, possibly for examination practice.

1. * Choose the right answer from the given options. [1 Marks Each] [34]
1. In the figure, graph of a polynomial is given. Find the zeroes of .
(A) (B) 3, 5 (C) (D) 3, 4
2. The zeroes of the quadratic polynomial are
(A) both positive (B) both negative
(C) one positive and one negative (D) can't be determined
3. If one root of the polynomial is reciprocal of the other, then the
value of is
(A) 0 (B) 3 (C) (D) -3
4. The zeroes of the quadratic polynomial , where
(A) are both positive (B) are both negative (C) are always equal (D) are always
unequal
5. If are the zeroes of , then
(A) (B) (C) (D)
6. If one of the zeroes of the quadratic polynomial is 0 , then the other zero is
(A) (B) (C) (D)
7. The zeroes of the polynomial are
(A) (B) (C) (D)
8. If one zero of the quadratic polynomial is , then find the other zero.
(A) (B) (C) (D)
9. If one of the zeroes of a quadratic polynomial of the form is 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.
10. Is a zero of the polynomial ?
BSS EDUCATION CENTRE
Class 10 Maths Total Marks : 49
p(x) p(x)
−3, 4 −3, 5
+ 25x + 156
x
2
f(x) = 3 + 11x + p
x
2
p
1
3
+ kx + k
x
2
k > 0
α, β f(x) = 2 + 8x − 8
x
2
α + β = αβ α + β > αβ α + β < αβ α + β + αβ = 0
b + cx + d
x
2
−
b
d
−
c
b
b
d
c
b
f(x) = + x −
x
2 3
4
− ,
1
2
3
2
, −
1
2
3
2
1, −
3
2 1,
3
√
2
2 − 8x − m
x
2
5/2
1
2
3
2
−3
2
−1
2
+ ax + b
x
2
x = −2 p(x) = − 2x + 8
x
2
[1]

2. (A) Yes (B) No
(C) May or may not be (D) Can't be determined
11. If 1 is a zero of the polynomial , then find the value of .
(A) 1 (B) 2 (C) -1 (D) -2
12. If one zero of the polynomial is , then the other zero is
(A) (B) (C) (D)
13. If the product of zeroes of the polynomial is 4 , then the value of ' ' is
(A) (B) (C) (D)
14. If one zero of the polynomial is reciprocal of the other,
then is equal to
(A) 2 (B) -2 (C) 1 (D) -1
15. The graph of is given below. Find the number of zeroes of .
(A) 1 (B) 2
(C) 3 (D) All of these
16. It the sum of the zeroes of a polynomial is and product of the zeroes of the
polynomial is -2 , then the polynomial is
(A) (B)
(C) (D) None of these
17. If is the factor of quadratic polynomial and 2 is a zero of , then find the
polynomial .
(A) (B)
(C) (D)
18.
If and be the zeroes of the polynomial , then the value of
is
(A) (B)
(C) (D)
19. Twice the product of the zeroes of the polynomial is . Find .
(A) 1 (B) 2 (C) 4 (D) 3
20. Zeroes of a quadratic polynomial are in the ratio and their sum is 15 . The product of
zeroes of this polynomial is
p(x) = a − 3(a − 1)x − 1
x
2
a
− 5x + 3 +
x
2
3
–
√ 2 + 3
–
√
1 − 3
–
√ 2 − 3
–
√ 3 − 3
–
√ 2 + 3
–
√
a − 6x − 6
x
2
a
2
3
3
2
−3
2
−
2
3
f(x) = ( + 4) + 13x + 4k
k
2
x
2
k
y = p(x) p(x)
−
1
6
− x − 2
x
2 1
6
+ x + 2
x
2 1
6
+ x − 2
x
2 1
6
(x − 4) p(x) p(x)
p(x)
+ 6x + 8
x
2
− 6x + 8
x
2
+ x + 8
x
2
− x + 8
x
2
α β a + bx + c
x
2
+
α
β
−
−
√
β
α
−
−
√
b −b
ac
√
−
b
√
ac
1
ac
23 − 26x + 161
x
2
14p p
2 : 3
[2]

3. (A) 36 (B) 48 (C) 54 (D) 60
21. If and are primes, then will be
(A) (B) (C) 1 (D)
22. If , then equal to
(A) 26 (B) 52 (C) 338 (D) 13
23. The HCF and the LCM of 12,21 and 15 respectively, are
(A) 3,140 (B) 12,420 (C) 3,420 (D) 420,3
24. The exponent of 2 in the prime factorisation of 144 , is
(A) 2 (B) 1 (C) 3 (D) 4
25. The HCF of and is
(A) 35 (B) 21 (C) 15 (D) 105
26. A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with
square tiles, all of the same size. Then the largest size of the tile which could be used for
the purpose is equal to
(A) 25 (B) 21 (C) 15 (D) 35
27. If the HCF of 45 and 105 is 15 , then their LCM is
(A) 735 (B) 753 (C) 315 (D) 351
28. If is prime, then HCF and LCM of and would be
(A) (B)
(C) (D) None of these
29. Which of the following is a pair of co-primes?
(A) (B) (C) (D)
30. Two numbers are in the ratio of . If their HCF is 13 , then numbers will be
(A) 195 and 143 (B) 190 and 140 (C) 185 and 163 (D) 185 and 143
31. The product of two numbers is 4107 . If the HCF of these numbers is 37 , then find the
greater number.
(A) 111 (B) 37 (C) 3 (D) 1
32. Three numbers are in the ratio and their HCF is 12. Then the positive square root
of largest number is
(A) 3 (B) 2 (C) 6 (D) 4
33. Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of
pack of each type that one should buy so that there are equal number of pens and
notepads.
(A) 3 and 2 (B) 2 and 5 (C) 3 and 4 (D) 4 and 5
34. If and are co-prime numbers, then and are
(A) co-prime (B) not co-prime (C) even (D) odd
* A statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option.
[15]
p q HCF(p, q)
p q pq
HCF(26, 169) = 13 LCM(26, 169)
× × × 7, × × ×
2
2
3
2
5
3
2
3
3
3
5
2
7
2
3 × 5 × 7 × 11
p p p + 1
HCF = p, LCM = p + 1 HCF = p(p + 1), LCM = 1
HCF = 1, LCM = p(p + 1)
(14, 35) (18, 25) (31, 93) (32, 62)
15 : 11
1 : 2 : 3
p q p
2
q
2
[3]

4. 35. Statement A (Assertion): If -1 is the zero of the polynomial ,
then value of is 3 .
Statement R (Reason): The zeroes of polynomial are the -
coordinate of the points where the parabola representing intersects
the -axis.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion .
(B) Both assertion (A) and reason ( ) are true and reason is not the correct explanation of
assertion (A).
(C) Assertion is true but reason is false.
(D) Assertion (A) is false but reason is true.
36. Statement A (Assertion) : is a linear polynomial.
Statement R (Reason): A polynomial of degree 1 is a linear polynomial.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion .
(B) Both assertion (A) and reason ( ) are true and reason is not the correct explanation of
assertion (A).
(C) Assertion is true but reason is false.
(D) Assertion (A) is false but reason is true.
37. Statement A (Assertion): The polynomial has one real zero.
Statement R (Reason) : A polynomial of degree has at most zeroes.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion .
(B) Both assertion (A) and reason ( ) are true and reason is not the correct explanation of
assertion (A).
(C) Assertion is true but reason is false.
(D) Assertion (A) is false but reason is true.
38. Statement A (Assertion) : A quadratic polynomial having 5 and -3 as zeroes is -15
.
Statement R (Reason): The quadratic polynomial having and as zeroes is given by
.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion .
(B) Both assertion (A) and reason ( ) are true and reason is not the correct explanation of
assertion (A).
(C) Assertion is true but reason is false.
(D) Assertion (A) is false but reason is true.
39. Statement A (Assertion): If the sum and product of zeroes of a quadratic polynomial is 3
and -2 respectively, then the quadratic polynomial is .
Statement R (Reason) : If is the sum of zeroes and is the product of zeroes of a
quadratic polynomial, then the quadratic polynomial is given by .
p(x) = − 3ax + 3a − 7
x
2
a
a + bx + c, a ≠ 0
x
2
x
y = a + bx + c
x
2
x
R (R)
(A)
R (R)
(A) (R)
(R)
4x + 1
R (R)
(A)
R (R)
(A) (R)
(R)
p(x) = + x
x
3
n
th
n − 1
R (R)
(A)
R (R)
(A) (R)
(R)
− 2x
x
2
α β
p(x) = − (α + β)x + αβ
x
2
R (R)
(A)
R (R)
(A) (R)
(R)
− 3x − 2
x
2
S P
− Sx + P
x
2
[4]

5. (A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion .
(B) Both assertion (A) and reason ( ) are true and reason is not the correct explanation of
assertion (A).
(C) Assertion is true but reason is false.
(D) Assertion (A) is false but reason is true.
40. Statement A (Assertion) : The greatest number which on dividing 1657 and 2037 leaves
remainders 6 and 5 respectively is 127 .
Statement R (Reason) : HCF = Product of the smallest power of each common prime factor
in the numbers.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
41. Statement A (Assertion) : is a composite number.
Statement R (Reason) : Every composite number can be expressed as product of primes.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
42. Statement A (Assertion) : For no value of , where is a natural number, the number
ends with the digit zero.
Statement R (Reason) : The prime factorisation of a natural number is unique, except for
the order of its factors.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
43. Statement A (Assertion): If LCM of two numbers and their product is , then
their .
Statement R (Reason) : LCM Product of numbers .
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
R (R)
(A)
R (R)
(A) (R)
(R)
R (R)
(A) (R) (R)
R
(R)
11 × 4 × 3 × 2 + 4
R (R)
(A) (R) (R)
R
(R)
n n 8
n
R (R)
(A) (R) (R)
R
(R)
= 350 25 × 70
HCF = 5
× = HCF
R (R)
(A) (R) (R)
[5]

6. (C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
44. Statement A (Assertion): HCF of is 1 .
Statement (Reason) : If and are distinct primes, then .
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
45. Statement A (Assertion): If and , then
the value of is 68 .
Statement R (Reason) : For any two positive numbers and , HCF
.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
46. Statement A (Assertion) : is an irrational number.
Statement (Reason) : If be a prime, then is an irrational number.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
47. Statement A (Assertion) : If L.C.M. = 182, product of integers is , then H.C.F. .
Statement R (Reason) : L.C.M. Product of integers H.C.F.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
48. Statement A (Assertion) : If product of two numbers is 5780 and their HCF is 17, then their
LCM is 340.
Statement R (Reason) : HCF is always a factor of LCM.
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
R
(R)
(23, 53)
R p q HCF(p, q) = 1
R (R)
(A) (R) (R)
R
(R)
HCF(209, 737) = 11 LCM(209, 737) = 209 × R
R
a b
(a, b) × LCM(a, b) = a × b
R (R)
(A) (R) (R)
R
(R)
2
–
√
R p p
–
√
R (R)
(A) (R) (R)
R
(R)
26 × 91 = 13
× =
R (R)
(A) (R) (R)
R
(R)
R (R)
[6]

7. (B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
49. Statement A (Assertion) : If HCF of two numbers is 13 and their product is , then
their LCM is 273.
Statement R (Reason) : HCF of two coprime numbers is always .
(A) Both assertion (A) and reason ( ) are true and reason is the correct explanation of
assertion (A).
(B) Both assertion and reason are true and reason is not the correct explanation of
assertion (A).
(C) Assertion (A) is true but reason ( ) is false.
(D) Assertion (A) is false but reason is true.
----- -----
(A) (R) (R)
R
(R)
39 × 91
> 1
R (R)
(A) (R) (R)
R
(R)