English Medium Class 10 - CBSE Important Questions

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

If the sum of the roots of the quadratic equation ky² – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.

If x = –2 is the common solution of quadratic equations ax² + x – 3a = 0 and x² + bx + b = 0, then find the value of a²b.

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

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

Assertion (A): If one root of the quadratic equation 4x² – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x² – x + 1 = 0 are real.

Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.

Find the roots of the quadratic equation x² – x – 2 = 0.

Find the value of k for which the roots of the quadratic equation 5x² – 10x + k = 0 are real and equal.

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.

In an A.P., if S5 + S7 = 167 and S₁₀₌235, then find the A.P., where Sn denotes the sum of its first n terms.

Find the 9^th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185

Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

What value is generated in the above situation?

Find the sum of first 15 multiples of 8.

Find how many integers between 200 and 500 are divisible by 8.

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^th terms.

Find the sum of first 8 multiples of 3