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

Verify which of the following is p.d.f. of r.v. X:

 f(x) = sin x, for 0 ≤ x ≤ `π/2`

Evaluate the following:

`int_0^a (1)/(x + sqrt(a^2 - x^2)).dx`

Choose the correct option from the given alternatives : 

`int_0^(pi/2) (sin^2x*dx)/(1 + cosx)^2` = ______.

Verify which of the following is p.d.f. of r.v. X:

f(x) = x, for 0 ≤ x ≤ 1 and 2 - x for 1 < x < 2

Verify which of the following is p.d.f. of r.v. X:

 f(x) = 2, for 0 ≤ x ≤ 1.

It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is non-negative

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

Evaluate the following.

`int e^x (1/x - 1/x^2)`dx

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`