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

Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`

Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`

Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`

Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`

Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.

Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`

Integrate the following functions w.r.t. x : [2 + cot x – cosec²x]e^x  

Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`

Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`

Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`

Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`

Integrate the following functions w.r.t.x:

`e^(5x).[(5x.logx + 1)/x]`

Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`

Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`

Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)] 

Given X ~ B(n, P) if n = 10 and p = 0.4, find E(x) and Var(X).

Given X ~ B(n, p) if p = 0.6 and E(X) = 6, find n and Var(X). 

Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X).

Given X ~ B(n, P) if n = 10, E(X) = 8, find Var(X).

If a fair coin is tossed 10 times and the probability that it shows heads in the first four tosses and tail in last six tosses.