HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`

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

`int (x^2 + x -1)/(x^2 + x - 6)  "d"x`

`int (6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)  "d"x`

`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).