Quadratic Equations: Class 10 Previous Year Questions

Quadratic Equations 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. If the roots of quadratic equation 4x2 -5x+ k = 0 are real and equal, then value of k is : 25 (a) (b) (c) (d) 16 16
   Board 20241 markMCQRepeated: 2023,2024
2. If the quadratic equation 9x2 + bx + 4 1 = 0 has equal roots, then the value of b is : (a) 0 (b) 3 only (c) 3 only (d) ±
   Board 20231 markMCQRepeated: 2023,2024
3. | P a g e 3. The discriminant of the quadratic equation x2 3x 2 = 0 is : (A) 1 (B) 17 (C) (D) 4| P a g e 4. x + = 3 (x 0) ax2 + bx + c = 0 a b + c (A) 5 (B) 2 (C) 1 (D) 1 5. (3, 5) (A) 8 (B) 2 (C) 2 (D) 8 6. - , (A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) : 2 7. - ? (A)…
   Board 20251 markMCQ
4. The equation x + = 3 (x 0) is expressed as a quadratic equation in the form of ax2 + bx + c = 0. The value of a b + c is : (A) 5 (B) 2 (C) 1 (D)
   Board 20251 markMCQ
5. | P a g e 3. If (0, 0) is the solution of the equation x + y = c 1, then the value of c is : (A) 0 (B) 1 (C) 1 (D) any real number 4| P a g e 4. ax2 + 3x + 1 = 0 (A) (B) (C) (D) 5. - ? (A) x2 = (x + 1)2 (B) (x 1) (x + 2) = 2x + 1 (C) (x + 2)3 = 2x (x2 1) (D) =…
   Board 20251 markMCQ
6. (a) The sum of areas of two squares is 2650 cm2. If the sum of their perimeters is 280 cm, find the sides of the two given squares. OR (b) Express the equation (x 0, 2) as a quadratic equation in standard form. Hence, find the roots of the quadratic equation s…
   Board 20255 markslong answer
7. | P a g e 32. (a) The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers. OR (b) Find the value(s) of k for which the equation 2x2 + kx + 3 = 0 has real and equal roots…
   Board 20255 markslong answer
8. To keep the lawn green and cool, Sadhna uses water sprinklers which rotate in circular shape and cover a particular area. The diagram below shows the circular areas covered by two sprinklers : (R>r) Two circles touch externally. The sum of their areas is 130 ·…
   Board 20244 marksshort answer
9. (a) Find the nature of the roots of the quadratic equation x2 5x + 9 = 0. 2 OR (b) Write a quadratic equation with roots 3 and 5.
   Board 20221 markvery short
10. Find the nature of the roots of the quadratic equation : 4x2 - 5x - 1 =
    Board 20221 markvery short
11. (H$) 4 go_r {ÌÁ`m H$m EH$ d¥Îm It{ME & Ho$ÝÐ go 6 go_r Xÿa pñWV EH$ {~ÝXþ go d¥Îm na EH$ ñne©-aoIm `w½_ H$s aMZm H$s{OE & 3 AWdm (I) EH$ aoImIÊS> PQ = 7·5 go_r It{ME & Bg aoImIÊS> H$mo 3 : 1 Ho$ AZwnmV _| {d^m{OV H$s{OE & 3 5. Solve the quadratic equation 2x2 …
    Board 20221 markvery short
12. is increased by 1, the fraction becomes 1 2 , then the fraction is (A) 2 9 (B) 3 8 (C) 4 7 (D) 5 6 1 If one root of the quadratic equation 𝑎𝑥2 + 𝑏𝑥+ 𝑐= 0 is the reciprocal of the
    Sample paper 2026-271 markMCQ

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