Quadratic Equations

CBSE Class 10 · Mathematics · 35 past questions

These are the board's own papers. 123 more board questions reprinted in the books we use in class are for signed-in students: sign in.

13 of 35 · show all

Q1 2026

The roots of the quadratic equation $(x-1)^2 = 16$ are…
Q2 2026

If the roots of the quadratic equation $\sqrt{3}x^2 - kx + 2\sqrt{3} = 0$ are real and equal, then the…
Q3 2026

Find two consecutive negative integers, sum of whose squares is 481.
Q4 2026

The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, is
Q5 2026

The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is
Q6 2026

Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km…
Q7 2026

If the quadratic equation $9x^2 + 8kx + 16 = 0$ has real and equal roots, then the value of k is
Q8 2026

Verify that roots of the quadratic equation $(p - q)x^2 + (q - r)x + (r - p) = 0$ are equal when $q + r = 2p$.
Q9 2026

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily…
Q10 2026 (Basic)

The value of k for which the equation $2kx^2 - 6x + 3 = 0$ has real and equal roots, is…
Q11 2026 (Basic)

Observe the figure given above. It shows six identical rectangular enclosures made by using fencing wire… (with a figure)
Q12 Sample paper 2026-27

If $(1 - p)$ is a root of the quadratic equation $x^2 + px + 1 - p = 0$, then its roots are…
Q13 Sample paper 2026-27

In a rectangular park measuring 50 m $\times$ 40 m, the gram panchayat plans to construct a rectangular…