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

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.

Compute the magnitude of the following vector:

`veca = hati + hatj + hatk;` `vecb = 2hati - 7hatj - 3hatk`;  `vecc = 1/sqrt3 hati + 1/sqrt3 hatj - 1/sqrt3 hatk`

The value of is `hati.(hatj xx hatk)+hatj.(hatixxhatk)+hatk.(hatixxhatj)` is ______.

If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to ______.

Integrate the rational function:

`x/((x + 1)(x+ 2))`

Integrate the rational function:

`1/(x^2 - 9)`

Integrate the rational function:

`(3x - 1)/((x - 1)(x - 2)(x - 3))`

Integrate the rational function:

`x/((x-1)(x- 2)(x - 3))`

Integrate the rational function:

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

Integrate the rational function:

`(1 - x^2)/(x(1-2x))`

Integrate the rational function:

`x/((x^2+1)(x - 1))`

Integrate the rational function:

`x/((x -1)^2 (x+ 2))`

Integrate the rational function:

`(3x + 5)/(x^3 - x^2 - x + 1)`

Integrate the rational function:

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

Integrate the rational function:

`(5x)/((x + 1)(x^2 - 4))`

Integrate the rational function:

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

Integrate the rational function:

`2/((1-x)(1+x^2))`