HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Important Questions

Evaluate: `int_0^(pi/2) sqrt(1 - cos 4x)  "d"x`

Evaluate:

`int_0^(pi/2) cos^3x  dx`

Evaluate: `int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x`

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 `y - x dy/dx = 0`

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

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below: 

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.

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

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.

Obtain an expression for torque acting on a body rotating with uniform angular acceleration.

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?