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

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is odd

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is even

The acute angle between the lines represented by x² + xy = 0 is ______.

Find the measure of the acute angle between the lines given by x² − 4xy + y² = 0 

Find the value of h, if the measure of the angle between the lines 3x² + 2hxy + 2y² = 0 is 45°. 

If θ is the acute angle between the lines given by ax² + 2hxy + by² = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x² + 7xy + 3y² = 0 

If the angle between the lines represented by ax² + 2hxy + by² = 0 is equal to the angle between the lines 2x² − 5xy + 3y² = 0, then show that 100(h² − ab) = (a + b)²

`int (sinx)/(1 + sin x)  "d"x`

`int 1/(4x + 5x^(-11))  "d"x`

`int (sin(x - "a"))/(cos (x + "b"))  "d"x`

`int 1/sqrt(2x^2 - 5)  "d"x`

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

`int (cos2x)/(sin^2x cos^2x)  "d"x`

`int sin4x cos3x  "d"x`

`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`

`int sqrt(tanx) + sqrt(cotx)  "d"x`

`int_0^(x/4) sqrt(1 + sin 2x)  "d"x` =

If `int_0^1 ("d"x)/(sqrt(1 + x) - sqrt(x)) = "k"/3`, then k is equal to ______.

`int_(pi/5)^((3pi)/10)  sinx/(sinx + cosx)  "d"x` =

`int_0^1 (x^2 - 2)/(x^2 + 1)  "d"x` =