HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Important Questions

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

Bernoulli distribution is a particular case of binomial distribution if n = ______

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Let the p.m.f. of r.v. X be P(x) = `""^4"C"_x (5/9)^x (4/9)^(4 - x)`, x = 0, 1, 2, 3, 4. Find E(X) and Var(X)

A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation none will recover

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation half of them recover.

If a fair coin is tossed 10 times. Find the probability of getting at most six heads.

Let the probability mass function (p.m.f.) of a random variable X be P(X = x) = `""^4C_x (5/9)^x xx (4/9)^(4 - x)`, for x = 0, 1, 2, 3, 4 then E(X) is equal to ______.

In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.

A coin kept at a distance of 5cm from the centre of a turntable of radius 1.5m just begins to slip when the turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable.

[g = 9.8 m/s²]

A particle rotates in U.C.M. with tangential velocity V along a horizontal circle of diameter ‘D' . Total angular displacement of the particle in time 't' is..........

In circular motion, assuming `bar v = bar w xx bar r` , obtain an expression for the resultant acceleration of a particle in terms of tangential and radial component.

State the theorem of perpendicular axes about moment of inertia.

The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration.

State an expression for the moment of intertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration:

i. about a tangent in the plane of the disc, and

ii. about a tangent perpendicular to the plane of the disc.

Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length.

State the law of conservation of angular momentum and explain with a suitable example.

A stone of mass 5 kg. tied to one end of a rope of length 0.8 m, is whirled in a vertical circle. Find the minimum velocity at the highest point and at the midway point.

[g = 9.8 m/s²]

Let velocity of a sound wave be 'v' and 'ω' be angular velocity. The propagation constant of the wave is .................................

1. `sqrt(omega/v)`
2. `sqrt(v/omega)`
3. `omega/v`
4. `v/omega`