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

Solve the following differential equation:

`x^2 dy/dx = x^2 + xy + y^2`

Solve the following differential equation:

(9x + 5y) dy + (15x + 11y)dx = 0

Solve the following differential equation:

(x² + 3xy + y2)dx - x² dy = 0

Evaluate: `int_0^(pi/2) x sin x.dx`

Solve the following differential equation:

(x² – y²)dx + 2xy dy = 0

Evaluate: `int_0^oo xe^-x.dx`

Evaluate: `int_0^π sin^3x (1 + 2cosx)(1 + cosx)^2.dx`

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 :

Find the area of the region lying between the parabolas y² = 4x and x² = 4y.

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

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(p ∧ ~ q) → (~ p ∧ ~ q)

Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.

Find the principal solutions of the following equation:

sin 2θ = `− 1/(sqrt2)`