HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :

Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :

Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :

Find the expected value, variance, and standard deviation of the random variable whose p.m.f.’s are given below :

Examine whether the statement pattern

[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground, away from the wall at the rate of 1.5 m /sec. The length of the higher point of the when foot of the ladder is 4 m away from the wall decreases at the rate of ______

`int (2x - 7)/sqrt(4x- 1) dx`

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

`int x^7/(1 + x^4)^2  "d"x`

`int x^2sqrt("a"^2 - x^6)  "d"x`

`int sqrt(4^x(4^x + 4))  "d"x`

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

If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)

`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`

`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`

`int sqrt((9 + x)/(9 - x))  "d"x`

`int 1/(4x^2 - 20x + 17)  "d"x`

`int (sinx)/(sin3x)  "d"x`