English Medium इयत्ता १० - CBSE Important Questions

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.

Solve for x: 9x² – 6px + (p² – q²) = 0

Let p be a prime number. The quadratic equation having its roots as factors of p is ______.

Find the value of ‘k’ for which the quadratic equation 2kx² – 40x + 25 = 0 has real and equal roots.

Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.

Solve the equation: 3x² – 8x – 1 = 0 for x.

Find the value(s) of 'a' for which the quadratic equation x² – ax + 1 = 0 has real and equal roots.

If 'p' is a root of the quadratic equation x² – (p + q) x + k = 0, then the value of 'k' is ______.

If one root of the quadratic equation x² + 12x – k = 0 is thrice the other root, then find the value of k.

If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is ______.

The nature of roots of the quadratic equation 9x² – 6x – 2 = 0 is ______.

If the discriminant of the quadratic equation 3x² - 2x + c = 0 is 16, then the value of c is ______.

Find the value of ‘c’ for which the quadratic equation 

(c + 1) x² - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1

has real and equal roots.

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.

The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?

How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?