MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

Soap solution is used for cleaning dirty clothes because ______.

The maximum kinetic energy of a simple pendulum is 'K'. Its displacement in terms of amplitude 'a', when kinetic energy becomes `(K/2)` is ______.

The coefficient of mutual inductance is 2H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A and 3A. The time required for the change of current is ____________.

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ > > R₂, the mutual inductance M between them will be directly proportional to ______.

The radioactivity of a sample is R₁ at a time T₁ and R₂ at a time T₂. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T₁ - T₂) is proportional to ______.

A soap film of surface tension 3 × 10^-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms^-12, the mass of the straw is ______.

A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it become 2500 disintegrations per minute. The decay constant per minute is ______.

When one end of the capillary is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of capillary is ______.

(Surface tension of water = 7 × 10^-2 N/m)

The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is ______.

(N = maximum electron density of lonosphere, g = acceleration due to gravity)

The bob of a simple pendulum performs SHM with period T in air and with period T₁ in water Relation between T and T₁ is ______.

(neglect friction due to water, density of the material of the bob is = `9/8xx10^3` kgm³, density of water = 1 gcc^-1) 

The surface tension of a soap solution is T. The work done in blowing a soap bubble of diameter d to that of a diameter 2d is ______.

For radioactive substances, the fraction of its initial quantity (N₀) which will disintegrate in its average lifetime is about ______.

(e = 2.71)

The ratio of frequencies of two oscillating pendulums is 3 : 2. Their lengths are in the ratio.

A liquid drop of density ρ is floating half immersed in a liquid of density d. The diameter of the liquid drop is ______.

(ρ > d, g = acceleration due to gravity, T = surface tension)

A pendulum bob is swinging in a vertical plane, such that its angular amplitude is less than 90°. At its highest point, the string is cut. Which trajectory is possible for bob afterwards?

The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is ______.

Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pully as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is ______.

A radioactive sample S₁​ having the activity A₁​ has twice the number of nuclei as another sample S_2​ of activity A₂​ If A₂​ = 2A_1​ then the ratio of half-life of S_1​ to the half-life of S₂​ is ______.

Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be ______.

A toroid is a long coil of wire wound over a circular core. The major radius and cross-sectional radius of the toroid are R and r, respectively. The coefficient of mutual induction of the toroid is ______.

(The magnetic field in it is uniform, N = number of turns, R >> r, μ₀ = permeability of free space)