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

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.

Find the probability that the visitor obtains answer yes from at least 2 pupils:

1. when the number of pupils questioned remains at 4.
2. when the number of pupils questioned is increased to 8.

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of a given week.

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

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)

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).