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. (a) A person on a tour has 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by 70. Find the original duration of the tour. OR (b) The area of a right-angled triangle is 600 cm2. If the base of the triangle exceeds th…
   Board 20265 markslong answer
2. | P a g e 33. (a) The sum of the areas of two squares is 52 cm2 and difference of their perimeters is 8 cm. Find the lengths of the sides of the two squares. OR 20| P a g e ( ) 150 km 2 10 km/h , 34. - , = LM || CB LN || CD 35. 0 10 8 10 20 7 20 30 15 30 40 20…
   Board 20255 markslong answer
3. A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor. (i) Assuming the original length of each side of a tile be x units, make a quadrati…
   Board 20244 marksshort answer
4. For some data xi, X2, ... Xn with respective frequencies fi, 2,. . fn . the value of Zfi is equal to : Xi-x nx (b) 1 (c) Zfi (a) (d)
   Board 20241 markMCQ
5. The least positive value of k, for which the quadratic equation 2x2 + kx - 4 = 0 has rational roots, is (A) ±2/2 (B) (C) (D) ±2 [3
   Board 20231 markMCQ
6. JJJJ Page 7 12. In the given figure, DE BC. If AD = 2 units, DB = AE = 3 units and EC = x units, then the value of x is : (a) 2 (b) 3 (c) 5 (d) 2 9 JJJJ Page 8 13. 6 cm b§~r h¡ & Bg gwB© Ûmam 7:20 a.m. Am¡a 7:55 a.m. Ho$ ~rM Omo H$moU a{MV hmoJm, dh h¡ : (a) 4…
   Board 20231 markMCQ
7. Which of the following quadratic equations has sum of its roots as 4 ? (a) 2x2 4x + 8 = 0 (b) x2 + 4x + 4 = 0 (c) 2 x2 2 4 x + 1 = 0 (d) 4x2 4x + 4 =
   Board 20231 markMCQ
8. Case Study 36. While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide. Based on the above i…
   Board 20234 markscase-based
9. (a) Find the value of m for which the quadratic equation (m 1) x2 + 2 (m 1) x + 1 = 0 has two real and equal roots. 2 OR (b) Solve the following quadratic equation for x : 2 3 x2 + 10x + 7 3 =
   Board 20221 markvery short
10. What is/are the roots of 3x2 = 6x? (a) only 2 (b) only 3 (c) 0 and 6 (d) 0 and 2
    CBSE practice 2023-241 markMCQ
11. If (1 – p) is a root of the quadratic equation x2 + px + 1 – p = 0, then its roots are: (A) 0, 1 (B) – 1, 1 (C) 0, – 1 (D) – 1, 2 1 *There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27
    Sample paper 2026-271 markMCQ
12. q 21. A forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal rows (in terms of number of trees). Also, he wants to make distinct roots of the trees (only one type of tree in one row). Find the minimum number of rows required.
    CBSE practice 2023-242 marksshort answer
13. A teacher asks three students to complete the following statement about the nature of the roots of a quadratic equation. If q2 – 4pr > 0, the roots of the quadratic equation px2 + qx + r = 0 will be... Zain answers, "always positive". Vipul answers, "positive,…
    CBSE practice 2022-231 markvery short

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