Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Find the shortest distance between lines `vecr = 6hati + 2hatj + 2hatk + lambda(hati - 2hatj + 2hatk)` and `vecr =-4hati - hatk + mu(3hati - 2hatj - 2hatk)`.

Find `bb(dy/dx)` in the following:

`y = tan^(-1) ((3x -x^3)/(1 - 3x^2)), - 1/sqrt3 < x < 1/sqrt3`

Find `bb(dy/dx)` in the following:

y = `cos^(-1) ((1-x^2)/(1+x^2))`, 0 < x < 1

Find `bb(dy/dx)` in the following:

y = `sin^(-1) ((1-x^2)/(1+x^2))`, 0 < x < 1

Find `bb(dy/dx)` in the following:

y = `cos^(-1) ((2x)/(1+x^2))`, −1 < x < 1

Find `bb(dy/dx)` in the following:

y = `sin^(-1)(2xsqrt(1-x^2)), -1/sqrt2 < x < 1/sqrt2`

Find `bb(dy/dx)` in the following:

y = `sec^(-1) (1/(2x^2 - 1)), 0 < x < 1/sqrt2`

Differentiate the function with respect to x:

`cot^(-1) [(sqrt(1+sinx) + sqrt(1-sinx))/(sqrt(1+sinx) - sqrt(1-sinx))], 0 < x < pi/2`

Differentiate the function with respect to x:

`(sin x - cos x)^((sin x - cos x)), pi/4 < x < (3pi)/4`

Find `dy/dx`, if y = `sin^-1 x + sin^-1 sqrt (1 - x^2)`, 0 < x < 1.

If `xsqrt(1+y) + y  sqrt(1+x) = 0`, for, −1 < x < 1, prove that `dy/dx = -1/(1+ x)^2`.

Find the unit vector in the direction of the vector `veca = hati + hatj + 2hatk`.

Find the unit vector in the direction of vector `vec(PQ)`, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Integrate the function `(3x^2)/(x^6 + 1)`

Integrate the function `1/sqrt(1+4x^2)`

Integrate the function `1/sqrt((2-x)^2 + 1)`

Integrate the function `1/sqrt(9 - 25x^2)`

Integrate the function `(3x)/(1+ 2x^4)`

Integrate the function `x^2/(1 - x^6)`

Integrate the function `(x - 1)/sqrt(x^2 - 1)`