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

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`

Two parallel plates separated by distance d are kept at potential difference V volt. A charge q of mass m enters in parallel plates with some velocity. The acceleration of the charged particle will be_____________________________ .

1. q V/d m
2. d m/ q V
3. q m/d V
4. d V/q m

A car of mass 1500Kg rounds a curve of radius 250m at 90 Km/hour. Calculate the centripetal force acting on it.

A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points.

The Earth is rotating with angular velocity ω about its own axis. R is the radius of the Earth. If Rω² = 0 · 03386 m/ s² , calculate the weight of a body of mass 100 gram at latitude 25°.   (g=9·8m/s²).

Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere.

For a particle performing uniform circular motion `vecv=vecomegaxxvecr`obtain an expression for linear acceleration of the particle performing non-uniform circular motion.

A stone of mass 1 kg is whirled in horizontal circle attached at the end of a 1 m long string. If the string makes an angle of 30^º with vertical, calculate the centripetal force acting on the stone.(g=9.8m/s²).