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

A random variable X has the following probability distribution

Then the variance of this distribution is

For the random variable X, if V(X) = 4, E(X) = 3, then E(x²) is ______

Find the probability distribution of the number of doublets in three throws of a pair of dice

Find the mean and variance of the number randomly selected from 1 to 15

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X and variance of X

If the p.m.f of a r. v. X is

P(x) = `c/x^3`, for x = 1, 2, 3

        = 0, otherwise

then E(X) = ______.

Solve the differential equation

`y (dy)/(dx) + x` = 0

Find the mean of number randomly selected from 1 to 15.

If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.

Solve the differential equation

`x + y dy/dx` = x² + y²

If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A^–1

Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.

Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.

If p ˄ q = F, p → q = F, then the truth value of p and q is ______.

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.

Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n² + n is an even number and n² - n is an odd number.