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

Choose the correct answer.

If a, b, c, are in A.P., then the determinant

`|(x+2, x+3,x +2a),(x+3,x+4,x+2b),(x+4,x+5,x+2c)|`

A. 0

B. 1

C. x

D. 2x

`sin^-1  1/2-2sin^-1  1/sqrt2`

`sin^-1{cos(sin^-1  sqrt3/2)}`

Find the domain of the following function:

`f(x)=sin^-1x^2`

Find the domain of the following function:

`f(x) = sin^-1x + sinx`

Find the domain of the following function:

`f(x)sin^-1sqrt(x^2-1)`

Find the domain of the following function:

`f(x)=sin^-1x+sin^-1 2x`

If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x² + y² + z² + t² 

Evaluate the following:

`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`

Evaluate the following:

`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`

Evaluate the following:

`tan^-1(tan  (5pi)/6)+cos^-1{cos((13pi)/6)}`

Find the set of values of `cosec^-1(sqrt3/2)`

Find the domain of `f(x)=cotx+cot^-1x`

Evaluate the following:

`cot^-1  1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`

Evaluate the following:

`cot^-1{2cos(sin^-1  sqrt3/2)}`

Evaluate the following:

`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`

Evaluate the following:

`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`