List of top Questions asked in MHT CET

A particle performs S.H.M. Its potential energies are \( U_1 \) and \( U_2 \) at displacements \( x_1 \) and \( x_2 \) respectively. At displacement \( x_1 + x_2 \), its potential energy \( U \) is

The equation of vibration of a stretched string fixed at both ends and vibrating in 5th harmonic is \( Y = 3 \sin(0.4x) \cos(200\pi t) \), where \( x \) and \( Y \) are in cm and \( t \) in seconds. The length of the string is

The acceleration due to gravity on moon is \( \frac{1}{6} \)th times the acceleration due to gravity on earth. If the ratio of the density of earth \( \rho_e \) to the density of moon \( \rho_m \) is \( \frac{5}{3} \), then the radius of moon \( R_m \) in terms of the radius of earth \( R_e \) is

The electron in hydrogen atom is moving in an orbit of radius 0.53 Å. It takes \( 1.571 \times 10^{-16} \, \text{s} \) to complete one revolution. The velocity of electron will be

A resonance tube completely filled with water has a small hole at the bottom. Length of the tube is 80 cm. A vibrating tuning fork of frequency 500 Hz is held near the open end of the tube. Water is slowly removed from the bottom. The maximum number of resonances heard will be (neglect end correction). Speed of sound in air is 340 m/s

If \( \Delta Q \) is the amount of heat supplied to \( n \) moles of a diatomic gas at constant pressure, \( \Delta U \) is the change in internal energy and \( \Delta W \) is the work done, then \( \Delta W : \Delta U : \Delta Q \) is

The width of the depletion layer of a p-n junction diode, when it is (i) forward biased and (ii) reverse biased respectively

The relative angular speed of hour hand and second hand of a clock is

Water rises to height 2.2 cm in glass capillary tube. The height to which same water rises in another capillary having \( \frac{1}{4} \)th area of cross-section is

Solution of the differential equation \[ \frac{dy}{dx} + 2y = e^{-x} \text{ is:} \]

The function \( f(x) = \log x - \frac{2x}{x+2} \) is increasing for all:

A thin, uniform metal rod of mass \( M \) and length \( L \) is swinging about a horizontal axis passing through its end. Its maximum angular velocity is \( \omega \). Its centre of mass rises to a maximum height of \( \frac{L^2 \omega^2}{6g} \). (where \( g \) is the acceleration due to gravity)

A series LCR circuit has \( R = 200 \, \Omega \), \( L = 663 \, \text{mH} \), and \( C = 265 \, \mu\text{F} \). The applied alternating voltage has an amplitude of 50 V and a frequency of 60 Hz so that \( X_L = 250 \, \Omega \) and \( X_C = 100 \, \Omega \). The peak current is

Two masses of 1 gram and 4 gram are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is

If the frequency of incident radiation is kept constant and the experiment is repeated by using incident light of different intensities, then stopping potential (\( V_s \))

If \( X \sim B(4, p) \) and \( 2 P(X = 3) = 3 P(X = 2) \), then the value of \( p \) is:

If \( \tan \theta + \sin \theta = a \) and \( \tan \theta - \sin \theta = b \), then the values of \( \cot \theta \) and \( \csc \theta \) are respectively:

If \( P(\theta) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and \( S \) and \( S' \) are foci of the hyperbola, then \( SP \cdot SP' = \)

Evaluate: \[ \frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} \]

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

If one of the lines given by \( kx^2 + xy - y^2 = 0 \) bisects the angle between the co-ordinate axes, then values of \( k \) are:

The particular solution of the differential equation \[ \left( y + x \frac{dy}{dx} \right) \sin y = \cos x \quad \text{at} \quad x = 0 \, \text{is:} \]

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if: