Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to ______.

For all sets A, B and C, show that (A – B) ∩ (A – C) = A – (B ∪ C)

For the hyperbola 9x² – 16y² = 144, find the vertices, foci and eccentricity

Find the equation of the ellipse which passes through the point (–3, 1) and has eccentricity `sqrt(2)/5`, with x-axis as its major axis and centre at the origin.

If e is the eccentricity of the ellipse `x^2/a^2 + y^2/b^2` = 1 (a < b), then ______.

Find the derivative of f(x) = ax + b, where a and b are non-zero constants, by first principle

Find the derivative of f(x) = ax² + bx + c, where a, b and c are none-zero constant, by first principle.

Find the derivative of f(x) = x³, by first principle.

Find the derivative of f(x) = `1/x` by first principle.

Find the derivative of f(x) = sin x, by first principle.

Find the derivative of `cosx/(1 + sinx)`

`(x^4 + x^3 + x^2 + 1)/x`

`(x + 1/x)^3`

`(3x + 4)/(5x^2 - 7x + 9)`

`(x^5 - cosx)/sinx`

`(x^2 cos  pi/4)/sinx`

(sin x + cos x)²

(2x – 7)² (3x + 5)³ 

x² sin x + cos 2x

sin³x cos³x