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

Using the method of integration find the area of the region bounded by lines: 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0

Area bounded by the curve y = x³, the x-axis and the ordinates x = –2 and x = 1 is ______.

The area bounded by the curve y = x | x|, x-axis and the ordinates x = –1 and x = 1 is given by ______.

[Hint: y = x² if x > 0 and y = –x² if x < 0]

Determine the value of the constant 'k' so that function f(x) `{((kx)/|x|, ","if  x < 0),(3"," , if x >= 0):}` is continuous at x = 0

`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)`