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

`int ("d"x)/(2 + 3tanx)`

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

`int x^3tan^(-1)x  "d"x`

`int x sin2x cos5x  "d"x`

`int (x + sinx)/(1 - cosx)  "d"x`

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

`int ("d"x)/(x^3 - 1)`

Evaluate:

`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`

`int 1/(sinx(3 + 2cosx))  "d"x`

`int xcos^3x  "d"x`

`int (sin2x)/(3sin^4x - 4sin^2x + 1)  "d"x`

`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5)  "d"x`

`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`

Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings drawn.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

For X ~ B(n, p), if V(X) = 2.4 and p = 0.4, then n = ______.

Given that X ~ B(n = 10, p), E(X) = 8, then value of p = ______

A die is thrown. If X denotes the number of positive divisors of the outcomes, then find the range of random variable X

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Let the p.m.f. of r.v. X be P(x) = `""^4"C"_x (5/9)^x (4/9)^(4 - x)`, x = 0, 1, 2, 3, 4. Find E(X) and Var(X)