HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove that:

tan^–1x + tan^–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1

If the straight lines `(x - 1)/k = (y - 2)/2 = (z - 3)/3` and `(x - 2)/3 = (y - 3)/k = (z - 1)/2` intersect at a point, then the integer k is equal to ______.

Find k, if the following function is p.d.f. of r.v.X:

f(x) = `{:(kx^2(1 - x)",", "for"  0 < x < 1),(0",", "otherwise"):}`

Evaluate:

`int((1 + sinx)/(1 + cosx))e^x dx`

The value of `tan(cos^-1  4/5 + tan^-1  2/3)` is ______.

The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then P(X = 1) is ______.

Evaluate:

`int_0^(π/2) sin^8x  dx`

Evaluate:

`int_(-π/2)^(π/2) |sinx|dx`

Find the value of `sin(2cos^-1  sqrt(5)/3)`.

Find the combined equation of the pair of lines through the origin and making an angle of 30° with the line 2x – y = 5

Evaluate:

`int e^(ax)*cos(bx + c)dx`

Evaluate `int_(π/6)^(π/3) cos^2x  dx`

Find the area enclosed between 3y = x², X-axis and x = 2 to x = 3.

Evaluate:

`int_-4^5 |x + 3|dx`

The value of `int_2^(π/2) sin^3x  dx` = ______.

Evaluate:

`int_(π/6)^(π/3) (root(3)(sinx))/(root(3)(sinx) + root(3)(cosx))dx`

Evaluate:

`int_0^(π/2) (sin 2x)/(1 + sin^4x)dx`

Evaluate:

`inte^x sinx  dx`

`int_0^1 x^2/(1 + x^2)dx` = ______.

Evaluate:

`int e^(logcosx)dx`