HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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.

Choose the correct options from the given alternatives :

`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =

Choose the correct options from the given alternatives :

`int (log (3x))/(xlog (9x))*dx` =

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

Choose the correct options from the given alternatives :

`int tan(sin^-1 x)*dx` =

Choose the correct options from the given alternatives :

`int (x- sinx)/(1 - cosx)*dx` =

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.

Choose the correct options from the given alternatives :

`int (1)/(cosx - cos^2x)*dx` =

Choose the correct options from the given alternatives :

`int sin (log x)*dx` =

Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =

Choose the correct options from the given alternatives :

`int [sin (log x) + cos (log x)]*dx` =

Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`

Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`

Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`