English Medium Class 10 - CBSE Question Bank Solutions

Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.

The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.

If cos (α + β) = 0, then sin (α – β) can be reduced to ______.

If cos 9α = sin α and 9α < 90°, then the value of tan 5α is ______.

If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ______.

`sqrt((1 - cos^2theta) sec^2 theta) = tan theta` 

Prove the following:

`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ

Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A

Prove the following:

`1 + (cot^2 alpha)/(1 + "cosec"  alpha)` = cosec α

If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`

Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`

If 1 + sin²θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.

Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

The zeroes of the quadratic polynomial x² + 99x + 127 are ______.

If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.

The only value of k for which the quadratic polynomial kx² + x + k has equal zeros is `1/2`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`v^2 + 4sqrt(3)v - 15`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`y^2 + 3/2 sqrt(5)y - 5`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`7y^2 - 11/3 y - 2/3`

The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.