Polynomials: Class 10 Previous Year Questions

Polynomials questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Assertion (A) : The polynomial p(y) = y2 + 4y + 3 has two zeroes. Reason (R) : A quadratic polynomial can have at most two zeroes.
   Board 20261 markAssertion-ReasonRepeated: 2023,2026
2. JJJJ Page 11 20. Assertion (A) : The polynomial p(x) = x2 + 3x + 3 has two real zeroes. Reason (R): A quadratic polynomial can have at most two real zeroes. IÊS> I (VSA)
   Board 20231 markAssertion-ReasonRepeated: 2023,2026
3. If ·, · are the zeroes of the polynomial p(x) = x2 -3x-1, then find the
   Board 20262 marksshort answer
4. If ·, · are the zeroes of the quadratic polynomial px2 + qx + r, then find the value of · + ·3·.
   Board 20262 marksshort answer
5. If and · are two zeroes of a polynomial f(x)= px2-2x+ 3p and · + · = ··, then value of p is : 2- (A) 2- (B) (C) -3 (D) : ax+ biy+ c =0 ax + by + C2 = 0 6. b1 (A) a2 b2 b1 (B) b2 a2 C2 b1 (C) a2 b2 C2 b1 (D) a2 b2 C2 7. - (A.P)· (A) 2, (B) 1·2, - 3·2, - 5·2, - …
   Board 20261 markMCQ
6. The total surface area of a solid hemisphere of diameter ·2d' is : 3· (b) 2 · d (d) (a) (c) Page 5 of 16 17. (a) 6 (b)13.5 (c) 15 (d) 14 18. (a) (b) (c) (d) 1 19 20 (a), (b), (c) (): (a)(A) (R(R),(A) (b) 3(A)(R)(R),(A (c) (A),(R)I (d) (A),(R)1 (A) : (leap year…
   Board 20261 markMCQ
7. If p and q are zeroes of the polynomial p(y) = 21y2 y 2, then find the value of (1 p) . (1 q).
   Board 20252 marksshort answer
8. | P a g e 10. Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is : (A) 3 (B) 5 (C) 2 (D) 4 8| P a g e 11. m 2m2 + 3m (A) 10 (B) 9 (C) 12 (D) 4 12. 15x 18x (A) x (B) 11x (C) 17x (D) 34x 13. 52 (A) (B) (C) (D) …
   Board 20251 markMCQ
9. The zeroes of a polynomial x? + px + q are twice the zeroes of the polynomial 4x? - 5x - 6. The value of p is : (a) (b) (c) -5 (d) 10
   Board 20241 markMCQ
10. Page 7 9. If a and b are zeroes of the polynomial 5x2 + 3x – 7, the value of 1 a + 1 b is 1 (A) –3 7 (B) 3 5 (C) 3 7 (D) –5 7 Page 8 10.    ABC  PQR   : 56 cm  48 cm   PQ/AB   : 1 (A) 7 8 (B) 6 7 (C) 7 6 (D) 8 7 11. AB …
    Board 20241 markMCQ
11. Assertion (A) : If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial. Reason (R) : A polynomial of degree n(n >1) can have at most n zeroes. C3ABD/1 / 31 Page 7 21. 2=58=15 22. h 23. · 2~2 cos 45°s…
    Board 20241 markAssertion-Reason
12. This section consists of 3 case based questions of 4 marks each. 36. A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t – 5t2. Observe the graph of the polynomial and…
    Board 20244 markscase-based
13. The graph of y = p(·) is given, for a polynomial p(x). The number of zeroes of p(·x) from the graph is y= p(·) (A) (B) (C) ()
    Board 20231 markMCQ
14. 2- Which of the following is a quadratic polynomial having zeroes 14. and 4x2 - 9 (A) (B) (9x2 + 4) (C) ·2+ 9 (D) 5(9x2 - 4)
    Board 20231 markMCQ
15. If one zero of the polynomial 6x2 + 37x (k 2) is reciprocal of the other, then what is the value of k ? (a) 4 (b) 6 (c) 6 (d)
    Board 20231 markMCQ
16. If and are the zeroes of the quadratic polynomial p(x) = x2 ax b, then the value of 2 + 2 is : (a) a2 2b (b) a2 + 2b (c) b2 2a (d) b2 + 2a
    Board 20231 markMCQ
17. Assertion (A): If zeroes of the polynomial (2k – 1) x2 + 4x – 3 are reciprocal of each other, then k = –1. Reason (R): If a = c, then zeroes of the polynomial ax2 + bx + c, a ≠ 0 are reciprocal of each other.
    Sample paper 2026-271 markAssertion-Reason
18. If m and n are zeroes of the polynomial (3x2 - x – 2), find the values of the following without factorising the polynomial. (i) 1 𝑚+ 1 𝑛 (ii) m2 + n2 Show your steps
    CBSE practice 2022-233 marksshort answer
19. Which of the following could be the graph of the polynomial? (x - 1)2(x + 2)? 1 (a) (b) (c) (d)
    CBSE practice 2023-241 markMCQ
20. The graph of a polynomial p(x) passes through the points (-5, 0), (0, -40), (8, 0) and (5, -30). Which among the following is a factor of p(x)? A) (x - 5) B) (x - 8) C) (x + 30) D) (x + 40)
    CBSE practice 2022-231 markvery short

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