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.

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…
Q14 2025

The quadratic equation whose roots are 7 and $\frac{1}{7}$ is…
Q15 2025

The sum of the areas of two squares is 52 cm² and difference of their perimeters is 8 cm. Find the lengths of…
Q16 2025

If $\frac{x}{12} - \frac{3}{x} = 0$, then the values of x are…
Q17 2025

The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides…
Q18 2025 (Basic)

The discriminant of the quadratic equation $x^2-3x-2=0$ is…
Q19 2025 (Basic)

The equation $x + \frac{1}{x} = 3$ ($x \neq 0$) is expressed as a quadratic equation in the form of…
Q20 2025 (Basic)

The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the…
Q21 2024

In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100…
Q22 2024

The quadratic equation $x^2 + x + 1 = 0$ has ______ roots.
Q23 2024

In a 2-digit number, the digit at the unit's place is 5 less than the digit at the ten's place. The product…
Q24 2024

If the roots of equation $ax^2 + bx + c = 0$, $a \neq 0$ are real and equal, then which of the following…
Q25 2024 (Basic)

If the roots of quadratic equation $4x^2-5x+k=0$ are real and equal, then value of $k$ is…
Q26 2023

Which of the following quadratic equations has sum of its roots as 4 ?
Q27 2023

The roots of the equation $x^2 + 3x - 10 = 0$ are…
Q28 2023

Find the sum and product of the roots of the quadratic equation $2x^2 - 9x + 4 = 0$.
Q29 2023

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Q30 2023

The least positive value of k, for which the quadratic equation $2x^2 + kx - 4 = 0$ has rational roots, is
Q31 2023 (Basic)

The discriminant of the quadratic equation $2x^2 - 5x - 3 = 0$ is
Q32 2022

Find the value of m for which the quadratic equation…
Q33 2022

The product of Rehan’s age (in years) 5 years ago and his age 7 years from now, is one more than twice his…
Q34 2022 (Basic)

Find the nature of the roots of the quadratic equation $x^2 – 5x + 9 = 0$.
Q35 2022 (Basic)

Solve the quadratic equation $2x^2 - 5x - 1 = 0$ for x.