HSC Science (Electronics) इयत्ता १२ वी - Maharashtra State Board Important Questions for Mathematics and Statistics

`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`

`int sec^2x sqrt(tan^2x + tanx - 7)  "d"x`

`int (3x + 4)/sqrt(2x^2 + 2x + 1)  "d"x`

Prove that:

`int 1/(a^2 - x^2) dx = 1/2 a log ((a +x)/(a-x)) + c`

Evaluate: `int_0^(pi/2) sqrt(1 - cos 4x)  "d"x`

Evaluate: `int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x`

Find the area of the region lying between the parabolas y² = 4ax and x² = 4ay.

Find the area of the region lying between the parabolas 4y² = 9x and 3x² = 16y

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7

Prove that:

`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`

Solve the differential equation sec²y tan x dy + sec²x tan y dx = 0

Find the differential equation of family of all ellipse whose major axis is twice the minor axis

Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

A fair coin is tossed 8 times. Find the probability that it shows heads at least once

Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).

The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is 

Find the expected value and variance of X.

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

Show that:

`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`