List of top Questions asked in MHT CET

A glass convex lens is of refractive index 1.55 with both faces of same radius of curvature. What will be the radius of curvature if focal length is to be 20 cm?

In communication system, the range for line of sight propagation in case of earth is \( d \), for the height of antenna \( h \). If \( h \) is doubled then the new range is

A uniform metal wire of length \( L \), mass \( M \) and density \( \rho \) is under a tension \( T \). If the speed of transverse wave along the wire is \( V \), then area of cross-section of the wire is

The polarising angle for a transparent medium is \( \theta \) and \( v \) is the speed of light in that medium, then relation between \( \theta \) and \( v \) is (c = velocity of light)

In energy band diagram of insulators, a band gap and the conduction band is respectively

An alternating e.m.f. is given by \( e = e_0 \sin \omega t \). In what time the e.m.f. will have half its maximum value, if \( e_0 \) starts from zero? (T = Time period)

Due to surface tension, the excess pressure inside a smaller drop is 9 units. If 27 smaller drops combine, then the excess pressure inside the bigger drop is

The 3rd overtone of a closed organ pipe is in unison with 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of open pipe is

What should be the velocity of earth due to rotation about its own axis so that the weight at equator becomes \( \frac{1}{25} \) of initial value?
(Radius of Earth on equator = 6400 km, \( g = 10 \, \text{m/s}^2 \), \( \cos 0^\circ = 1 \))

When a photosensitive surface is irradiated by lights of wavelengths \( \lambda_1 \) and \( \lambda_2 \), kinetic energies of emitted photoelectrons are \( E_1 \) and \( E_2 \) respectively. The work function of the photosensitive surface is

The unknown resistances are connected in two gaps of a metre bridge. The null point is at 20 cm from zero end. A resistance of 15 \( \Omega \) is connected in series with the smaller of the two. The null point shifts to 40 cm. The smaller resistance is

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

A circular and a square coil is prepared from two identical metal wires and a current is passed through them. Ratio of magnetic dipole moment associated with circular coil to that with square coil is

Light of incident frequency 2 times the threshold frequency is incident on a photosensitive material. If the incident frequency is made \( \frac{1}{3} \)rd and intensity is doubled then the photoelectric current will

Evaluate the integral \( \int_0^1 \frac{x^2}{1 + x^2} dx \)

The general solution of the differential equation \( (1 - x^2) \frac{dy{dx} + 2xy = x(1 - x^2)^{\frac{1}{2}} \) is}

Simplify the expression \( \sin \left( \frac{\pi}{3} + x \right) - \cos \left( \frac{\pi}{6} + x \right) \)

If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots \), then \[ \frac{dy}{dx} = \]

Evaluate the integral \( \int \frac{4e^x + 6e^{-x}}{9e^x - 4e^{-x}} dx = Ax + B \log |9e^{2x} - 4| + c \), then (where \( c \) is the constant of integration)

Two galvanometers 'G1' and 'G2' require 2 mA and 3 mA respectively to produce the same deflection. Then

The shortest distance between the lines \( 1 + x = 2y = -12z \) and \( x = y + 2 = 6z - 6 \) is

The particular solution of the differential equation \( \cos \left( \frac{dy}{dx} \right) = a \), under the conditions \( a \in \mathbb{R} \) and \( y(0) = 2 \) is

If \( \sqrt{x + y} + \sqrt{y - x} = 5 \), then \( \frac{d^2y}{dx^2} = \)

The domain of the function \( f(y) = \frac{\cos^{-1(y - 5)}{\sqrt{25 - y^2}} \) is}

In a box containing 100 bulbs, 10 are defective. The probability that out of 20 bulbs selected at random, none is defective is