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

`int sqrt(x^2 - 8x + 7) dx` is equal to ______.

Consider `f:R - {-4/3} -> R - {4/3}` given by f(x) = `(4x + 3)/(3x + 4)`. Show that f is bijective. Find the inverse of f and hence find `f^(-1) (0)` and X such that `f^(-1) (x) = 2`

Find `int dx/(5 - 8x - x^2)`

Evaluate : `int_2^3 3^x dx`

Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`

Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`

Prove that :

x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3

2x − 3z + w = 1
x − y + 2w = 1
− 3y + z + w = 1
x + y + z = 1

2x − y = 5
4x − 2y = 7

Differentiate the following functions from first principles e^−x.

Differentiate the following functions from first principles e^3x.

Differentiate the following functions from first principles e^ax+b.

Differentiate the following functions from first principles e^cos x.

Differentiate the following functions from first principles  \[e^\sqrt{2x}\].

Differentiate the following functions from first principles log cos x ?

​Differentiate the following function from first principles \[e^\sqrt{\cot x}\] .

Differentiate the following functions from first principles x²e^x ?