HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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`

If θ is the acute angle between the lines given by 3x² – 4xy + by² = 0 and tan θ = `1/2`, find b.

Find the value of ‘a’ if `int_2^a (x + 1)dx = 7/2`

Evaluate:

`int (logx)^2 dx`

Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.

Evaluate:

`int_0^(π/2) sinx/(1 + cosx)^3 dx`