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

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.

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?

Derive an expression for maximum safety speed with which a vehicle should move along a curved horizontal road. State the significance of it.

The moment of inertia of a body about a given axis is 1.2 kgm². initially, the body is at rest. For what duration on the angular acceleration of 25 radian/sec² must be applied about that axis in order to produce rotational kinetic energy of 1500 joule?  

Derive an expression for the difference in tensions at the highest and lowest point for a particle performing the vertical circular motion. 

Derive an expression for critical velocity of a satellite revolving around the earth in a circular orbit.

Explain why an astronaut in an orbiting satellite has a feeling of weightlessness.

State Kepler's law of orbit and law of equal areas.

Why two or more mercury drops form a single drop when brought in contact with each other?

Two capillary tubes of radii 0.6 cm and 0.3 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is ______.