HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Important Questions

Solve the following:

Find the area enclosed between the circle x² + y² = 1 and the line x + y = 1, lying in the first quadrant.

Find the area of the region lying between the parabolas 4y² = 9x and 3x² = 16y

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

Prove that:

`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`

Solve the differential equation sec²y tan x dy + sec²x tan y dx = 0

Find the differential equation of family of all ellipse whose major axis is twice the minor axis

Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

A fair coin is tossed 8 times. Find the probability that it shows heads at least once

Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).

The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is 

Find the expected value and variance of X.

Given X ~ B(n, p) if p = 0.6 and E(X) = 6, find n and Var(X). 

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

If X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2, then find n and p.

Prove the theorem of parallel axes about moment of inertia

Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.

Define moment of inertia. State its SI unit and dimensions.

The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of the loop is ______

A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity?