HSC Science (General) 12th Standard Board Exam - 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.

The cost of 4 pencils, 3 pens and 2 erasers is Rs. 60. The cost of 2 pencils, 4 pens and 6 erasers is Rs. 90 whereas the cost of 6 pencils, 2 pens and 3 erasers is Rs. 70. Find the cost of each item by using matrices.

The equation of tangent to the curve y=`y=x^2+4x+1` at

(-1,-2) is...............

(a)  2x -y = 0                        (b)  2x+y-5 = 0

(c)  2x-y-1=0                        (d)  x+y-1=0

Given that X ~ B(n= 10, p). If E(X) = 8 then the value of

p is ...........

(a) 0.6

(b) 0.7

(c) 0.8

(d) 0.4

Find the area bounded by the curve y² = 4ax, x-axis and the lines x = 0 and x = a.

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`