Science (English Medium) Class 12 - CBSE Question Bank Solutions

Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`

Two vectors `veca = a_1 hati + a_2 hatj + a_3 hatk` and `vecb = b_1 hati + b_2 hatj + b_3 hatk` are collinear if ______.

Find: `int x^4/((x - 1)(x^2 + 1))dx`.

If `veca = 4hati + 6hatj` and `vecb = 3hatj + 4hatk`, then the vector form of the component of `veca` along `vecb` is ______.

Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.

Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`

If A= `[(cos α, -sin α), (sin α, cos α)]` then A + A' = I then the value of α is  ______.

Differentiate the following w.r.t. x:

`e^x/sinx`

Differentiate the following w.r.t. x: 

`e^(sin^(-1) x)`

Differentiate the following w.r.t. x:

`e^(x^3)`

Differentiate the following w.r.t. x: 

sin (tan^–1 e^–x)

Differentiate the following w.r.t. x:

log (cos e^x)

Differentiate the following w.r.t. x:

`e^x + e^(x^2) + "..." + e^(x^5)`

Differentiate the following w.r.t. x:

`sqrt(e^(sqrtx))`, x > 0

Differentiate the following w.r.t. x:

log (log x), x > 1

Differentiate the following w.r.t. x: 

`cos x/log x`, x > 0

Differentiate the following w.r.t. x:

cos (log x + e^x), x > 0

Differentiate the function with respect to x:

(log x)^{log x}, x > 1

Differentiate the function with respect to x:

cos (a cos x + b sin x), for some constant a and b.

Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.