List of top Questions asked in MHT CET

A plano-convex lens fits exactly in to a plano-concave lens. Their plane surfaces are parallel to each other. Lenses are made up of different materials of refractive indices \( n_1 \) and \( n_2 \) and \( R \) is the radius of curvature of the curved surface of lenses. Focal length of the combination is
The length of the simple pendulum is made 3 times the original length. If \( T \) is its original time period, then the new time period will be
Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \( I \). If the same rod is bent in the form of a ring, its moment of inertia about the diameter is \( I' \). If \( I_1 = I_2 \), then the value of \( x \) is
A parallel plate capacitor having plate area \( A' \) and separation \( d' \) is charged to a potential difference \( V \). The charging battery is disconnected and the plates are pulled apart to four times the initial separation. The work required to increase the distance between the plates is
If an ammeter is to be used in place of a galvanometer, then we must connect
The temperature of an ideal gas is increased from 100 K to 400 K. If \( v \) is the R.M.S. velocity of its molecules at 100 K, it becomes
If the internal resistance of the cell is negligible, then the current flowing through the circuit is
A transverse displacement of vibrating string is \( y = 0.06 \sin\left(\frac{2 \pi}{3} x\right) \cos(120 \pi t) \). If the mass per unit length of a string is \( 4 \times 10^{-2} \) kg/m, then the tension in the string will be
Water flows through a horizontal pipe of varying cross-section at the rate of \( \pi \times 10^{-1} \, \text{m}^3/\text{s} \). The velocity of water at a point where the radius of the pipe is 10 cm is \( (\pi = 3.14) \)
In an electrical circuit \( R, L, C \) and an a.c. voltage source are all connected in series. When \( L' \) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{3}{4} \). If instead \( C' \) is removed from the circuit, the phase difference is again \( \frac{3}{4} \). The power factor of the circuit is
In common emitter mode of a transistor, the current gain is 8. The input impedance is 25kΩ and load resistance is 75kΩ. The power gain is
If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling \( \propto T^4 \), the same body at 900 K, surrounded by same atmosphere, will have rate of cooling nearly
A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then
The electric field intensity on the surface of a solid charged sphere of radius \( r \) and volume charge density \( \sigma \) is \( (\varepsilon_0 = \text{permittivity of free space}) \)
Two strings 'X' and 'Y' of a guitar produces a beat frequency of 6 Hz. When the tension of the string 'Y' is increased, the beat frequency is found to be 4 Hz. If the frequency of string 'X' is 300 Hz, then the original frequency of string 'Y' is
In the following combination of logic gates, the output \( Y \) can be written in terms of inputs \( A \) and \( B \) as
A Carnot engine has efficiency \( \frac{1}{3} \). It becomes \( \frac{1}{3} \), when the temperature of sink is lowered by 57 K. The temperature of the source is
If the charge on the capacitor is increased by 3C, the energy stored in it increases by 21%. The original charge on the capacitor is
An electron moves in Bohr orbit. The magnetic field at the centre is proportional to
An alternating e.m.f. having voltage \( V = V_0 \sin \omega t \) is applied to a series L-C-R circuit. Given \( X_L - X_C = R \), the r.m.s. value of the potential difference across the capacitor will be
A simple pendulum oscillates with an angular amplitude \( \theta \). If the maximum tension in the string is 4 times the minimum tension then the value of \( \theta \) is
A coil having 9 turns carrying current produces magnetic field \( B_1 \) at the centre. Now that coil is rewound into 3 turns carrying same current. Then magnetic field at the centre \( B_2 \) is
A conveyor belt is moving with constant velocity \( V \). Sand is being dropped on the belt at the rate of \( M \, \text{kg/s} \). The force necessary to keep the belt moving with a constant velocity \( V \, \text{m/s} \) will be
Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio \( 4:3 \). If their surface tensions are in the ratio \( 6:5 \), the ratio of heights \( \left( \frac{h_1}{h_2} \right) \) of liquids in the two capillary tubes is (Their angle of contacts are same)
An ideal inductor of \( \frac{1}{2} \, \text{H} \) is connected in series with a \( 300 \, \Omega \) resistor. If a 20 V, 200 Hz alternating source is connected across the combination, the phase difference between the voltage and current is