MHT CET (PCB) 2024 22th April Evening Shift

An alternating current is given by $\mathrm{I}=100 \sin (50 \pi t)$. How many times will the current become zero in one second?

A resistor of $400 \Omega$, an inductance of 0.4 H are in series with an a.c. source of e.m.f. $\mathrm{E}=200 \sqrt{2} \sin (1000 \mathrm{t})$. The power factor of the circuit is

In the series LCR circuit shown in figure, the impedance is

If $R_1$ and $R_2$ are the radii of the atomic nuclei of mass numbers 27 and 125 respectively, then the ratio $R_2: R_1$ is

Radioactive materials A and B have decay constants ' $9 \lambda$ ' and ' $\lambda$ ' respectively. Initially they have same number of nuclei. The ratio of number of nuclei of material ' $A$ ' to that of ' $B$ ' will be $\left(\frac{1}{\math...

The centre of mass of a system of particles does NOT depend on

Which one of the following statements is false for a particle moving in a circle with constant angular speed?

A galvanometer of resistance ' $G$ ' is converted into an ammeter of resistance $\frac{\mathrm{G}}{40}$, by connecting a shunt ' $S$ ' to it. The part of main current passing through the galvanometer is

\(\text { In the following figure, the current } \mathrm{I} \text { is equal to }\)

The work function of a photosensitive metallic surface is $h v_0$. If photons of energy (2.5) $h v_0$ fall on this surface, the electrons come out with maximum velocity ' v '. When the photon energy is increased to $7 \mathrm{~h} v_0$, the ...

In the Davisson Germer experiment, the velocity of electrons emitted from the electron gun can be increased by

A spring has length ' $L$ ' and force constant ' $K$ '. It is cut into two springs of length ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' such that $\mathrm{L}_1=\mathrm{nL}_2$ ( n is an integer). The force constant of the spring of length ' $...

The flux linked with the coil at any instant ' t ' is given by $\phi=12 t^2-60 t+275$. The magnitude of induced e.m.f. at $\mathrm{t}=3 \mathrm{~second}$ is

A coil of area $12 \mathrm{~cm}^2$ has 250 turns. Magnetic field of $0.2 \mathrm{~Wb} / \mathrm{m}^2$ is perpendicular to the plane of the coil. The field is reduced to $0.1 \mathrm{~Wb} / \mathrm{m}^2$ in 0.1 second. The magnitude of induc...

A large insulated sphere of radius ' $r$ ', charged with ' $Q$ ' units of electricity, is placed in contact with a small insulated uncharged sphere of radius ' R ' and is then separated. The charge on the smaller sphere will now be

The wrong statement out of the following statements is

The potentials at points A and B are $\mathrm{V}_{\mathrm{A}}$ and $\mathrm{V}_{\mathrm{B}}$ respectively for the charges $+q$ and $-q$ placed at distances ' $x$ ' each from points $A$ and $B$ as shown in figure. The distance between points...

Three charges $Q,-2 q$ and $-2 q$ are placed at the vertices of an isosceles right-angled triangle as shown in figure. The net electrostatic potential energy is zero if $Q$ is equal to

Water rises up to height ' $x$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth 'd' in a mine, the water level rises height ' $Y$ '. If ' $R$ ' is the radius of earth then the ratio $(\mathr...

At two points on a horizontal tube of varying cross-section the radii are 1 cm and $\mathbf{0 . 4 ~ c m}$, velocities of fluid are $\mathrm{V}_1, \mathrm{~V}_2$ and pressure difference ( $P_1-P_2$ ) between these points is 4.9 cm of water. ...

A soap bubble of radius $R$ is surrounded by another soap bubble of radius $2 R$ as shown in figure. The excess pressure inside the smaller soap bubble will be ( $T=$ surface tension of soap solution)

The period of revolution of planet A around the sun is 8 times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun?

A satellite of mass ' $m$ ' is orbiting the earth of radius ' $R$ ' at height ' $h$ ' from the surface of earth. The total energy of the satellite is ( $\mathrm{g}=$ acceleration due to gravity at the earth's surface)

A blackbody at $1227^{\circ} \mathrm{C}$ emits radiation with maximum intensity at a wavelength of $5600 $$\mathop {\rm{A}}\limits^{\rm{o}} $. If the temperature of the body is increased by $1000^{\circ} \mathrm{C}$, the maximum intensity w...

For which of the following combinations of working temperatures, the efficiency of Carnot's engine is maximum?

Pressure of the gas remaining same, the temperature at which r. m. s. speed of the gas molecules is double its value at $27^{\circ} \mathrm{C}$ is

Rate of flow of heat through a cylindrical rod is $\mathrm{H}_1$. The temperature of the ends of the rod are ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ '. If all the dimensions of the rod become double and the temperature difference remains th...

An ideal gas is heated from $27^{\circ} \mathrm{C}$ to $627^{\circ} \mathrm{C}$ at constant pressure. If initial volume of gas is $4 \mathrm{~m}^3$, then the final volume of the gas will be

An ideal gas of mass ' $M$ ' is in the state ' $A$ ' goes to another state B via three different processes. If $Q_1, Q_2$ and $Q_3$ denote the heat absorbed by the gas along the paths 1,2 and 3 respectively, then

A magnet having a magnetic dipole moment ' M is placed in two magnetic fields ' $\mathrm{B}_1$ ' and ' $\mathrm{B}_2$ ' respectively. If it is displaced slightly from the equilibrium position, it oscillates 60 times in 20 second in field ' ...

Rods ' $A$ ', ' $B$ ' and ' $C$ ' are made of a paramagnetic, a ferromagnetic and a diamagnetic substance respectively. A magnet is brought close to them, it will

Two objects A and B are separated horizontally by distance ' a '. Object B moves in a direction perpendicular to distance ' $a$ ' with velocity ' $V_1$ '. Simultaneously object A covers shortest distance with velocity ' $V$ ' and meets obje...

To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (cross - sectional diameter of a solenoid is considerably less than length, $\mu_0=$ permeability of free space)

A circular coil carrying current ' $I$ ' has radius ' $R$ ' and magnetic field at the centre is ' $B$ '. At what distance from the centre along the axis of the same coil, the magnetic field will be $\frac{\mathrm{B}}{8}$ ?

The magnitude of magnetic induction at a point on the axis at a large distance ' $r$ ' from the centre of a circular coil of ' $n$ ' turns and area ' $A$ ' carrying current ' I ' is ( $\mu_0=$ permeabilty of free space)

The intermediate image formed by an objective lens of a compound microscope is

A thin concavo-convex lens with convex face receiving incident rays has radii of curvatures 12 cm and 24 cm respectively. If refractive index of material of lens is 1.5 , then the focal length of the lens is

A plane wavefront of width ' $x$ ' is incident on an air-water interface and the corresponding refracted wavefront has a width ' y ' as shown in figure. The refractive index of air with respect to water in terms of distances ' $w$ ' and ' $...

A solid sphere and a ring have equal mass and equal radius of gyration. If sphere is rotating about its diameter and ring about an axis passing through centre and perpendicular to its plane, then the ratio of radius of sphere to that of rin...

Two bodies A and B have their moments of inertia ' I ' and ' 2 I ' respectively about their axis of rotation. If their kinetic energy of rotation are equal then angular momentum of body A to that of body $B$ will be in the ratio

By increasing the temperature, the electrical conductivity of a conductor and a semiconductor,

For a transistor, the current amplification factor ' $\alpha$ ' is 0.8 . The transistor is then connected in common emitter configuration. The change in the collector current when the base current changes by 6 mA is

To get an output $\mathrm{Y}=1$ in the given logic circuit, the correct choice for the input is

A particle starts from mean position and performs S.H.M. with period 6 second. At what time its kinetic energy is $50 \%$ of total energy?
\(\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)\)

In Young's double slit experiment, fringe width is 1.4 mm with light of wavelength $6000 \(\mathop {\rm{A}}\limits^{\rm{o}} $. If the light of wavelength $5400\)\mathop {\rm{A}}\limits^{\rm{o}} $ is used, with no other change in the experi...

In a single slit diffraction experiment, slit of width ' a ' and incident light of wavelength $5600 $$\mathop {\rm{A}}\limits^{\rm{o}} $, the first minimum is observed at angle $30^{\circ}$. The first secondary maximum is observed at angle ...

The third overtone of a closed pipe of length ' $\mathrm{L}_{\mathrm{c}}$ ' has the same frequency as the third overtone of an open pipe of length ' $L_0$ '. The ratio ' $\mathrm{L}_{\mathrm{c}}$ ': ' $\mathrm{L}_0$ ' is equal to (Neglectin...

Three tuning forks $\mathrm{A}, \mathrm{B}$ and C have respective frequencies $\mathrm{n}_1, \mathrm{n}_2$ and $\mathrm{n}_3$ related as $\mathrm{n}_1=1.03 \mathrm{n}_2$ and $n_3=0.99 n_2$. When $A$ and $C$ are sounded together 4 beats are ...

Two sounding sources send waves at certain temperature in air of wavelength 60 cm and 60.6 cm respectively. The frequency of sources differ by 5 Hz . The velocity of sound in air at same temperature is

A simple harmonic progressive wave is given by equation $y=\operatorname{asin} 2 \pi\left(n t-\frac{x}{\lambda}\right)$. If the wave velocity is equal to $\frac{1}{4} \times$ (maximum particle velocity), then the wavelength ' $\lambda$ ' is...