Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the angle between the lines whose direction ratios are a, b, c and b − c, c − a, a − b.

Differentiate the function with respect to x.

sin (x² + 5)

Differentiate the function with respect to x.

cos (sin x)

Differentiate the function with respect to x.

sin (ax + b)

Differentiate the function with respect to x.

`sec(tan (sqrtx))`

Differentiate the function with respect to x.

`(sin (ax + b))/cos (cx + d)`

Differentiate the function with respect to x. 

cos x³ . sin² (x⁵)

Differentiate the function with respect to x. 

`2sqrt(cot(x^2))`

Differentiate the function with respect to x.

`cos (sqrtx)`

Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.

Differentiate the function with respect to x:

(3x² – 9x + 5)⁹

Differentiate the function with respect to x:

sin³ x + cos⁶ x

Differentiate the function with respect to x:

`(5x)^(3cos 2x)`

Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`

Differentiate the function with respect to x:

`(cos^(-1)  x/2)/sqrt(2x+7)`, −2 < x < 2

Differentiate the function with respect to x:

`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3

Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.

If (x – a)² + (y – b)² = c², for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.

If f(x) = |x|³, show that f"(x) exists for all real x and find it.

Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?