MHT CET 2026 Physics Paper: 18 Apr, Shift 1

In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

An a.c. source is applied to a series LR circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to LR circuit and power factor is $X_2$. The ratio $X_1$ to $X_2$ is

In an a.c. circuit, a resistance R is connected in series with an inductance 'L'. If phase angle between voltage and current is $45^\circ$, the value of inductive reactance will be

($\sin 45^\circ = \frac{1}{\sqrt{2}} = \cos 45^\circ$)

The angular momentum of the electron in the third Bohr orbit of a hydrogen atom is '$l$' so its angular momentum in the fourth Bohr orbit is

The triply ionized beryllium (Be$^{+++}$) has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given $Z = 4$ for beryllium)

A capacitor of capacitance C has charge Q and energy stored in it is W. If the charge is increased to 3Q, the energy stored in the capacitor W' will be

Two circular plates each of radius '$r$' are kept parallel to each other distance '$d$' apart. The capacitance of the capacitor formed is '$C_1$ '. If the radius of each of the plates is increased to $\sqrt{3}$ times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes '$C_2$'. The ratio $C_1 : C_2$ is

A body moves along a circular path of diameter $30$ cm. It starts from one end of diameter, moves along the circular path and reaches the other end of diameter in 3 second. The angular speed of the body in radian per second is

By connecting a resistance of $980\ \Omega$ in series with a galvanometer, it is converted into a voltmeter of a certain range. When the resistance of $470\ \Omega$ is connected in series, the range is halved. The resistance of the galvanometer is

A potentiometer wire of length $4$ m and resistance $5\ \Omega$ is connected in series with a resistance of $992\ \Omega$ and a cell of e.m.f. $4$ V with internal resistance $3\ \Omega$. The length of $0.75$ m on potentiometer wire balances the e.m.f. of

If the kinetic energy of a particle is increased to 16 times, the percentage change in the de Broglie wavelength of a particle is

In case of photoelectric emission from certain metal, the cutoff frequency is $\nu$. If the radiation of frequency $3\nu$ is incident on the metal plate, the maximum possible velocity of the emitted electrons will be ($m$ = mass of electron, $h$ = Planck's constant)

In the circuit shown, when the current '$i$' is $3$A and increasing at the rate of $1$A/s the measurement of the potential difference between A and B is $12$ V. But when the same current $3$A is decreasing at the rate of $1$A/s, the measured potential difference $V_{AB}$ between A and B is $6$V. The value of 'R' in the circuit is

Two coils have a mutual inductance of $0.005$ H. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10$ A and $\omega = 60\pi$ rad s${}^{-1}$. The maximum values of e.m.f. in the second coil in volt will be

The magnetic potential energy stored in a certain inductor is $49$ mJ when the current in the inductor is $70$ mA. The inductance of the inductor is

When a dipole placed parallel to electric field is rotating through $\pi^c$, the work done is W. The work done in rotating the dipole through $\left(\frac{\pi}{3}\right)^c$ is

($\cos 0^\circ = 1,\ \cos 60^\circ = \frac{1}{2},\ \cos 180^\circ = -1$)

The point charges $+q, -q, -q, +q, +Q$ and $-q$ are placed at the vertices of a regular hexagon ABCDEF as shown in the figure.

The electric field at the centre of the hexagon 'O' due to the five charges at A, B, C, D and F is thrice the electric field at centre 'O' due to charge $+Q$ at E alone. The value of Q is

A piston of cross-sectional area $2.5 \times 10^{-2}$ m$^{2}$ is used in a hydraulic lift to exert a force of $250$ N on water. The cross-sectional area of the other piston which supports a car of mass $3000$ kg is ($g = 9.8$ m/s$^{2}$)

The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth 'h' of the lake is ($\rho$ = density of water in the lake, $g$ = acceleration due to gravity, $P_0$ = atmospheric pressure).

Time period of a simple pendulum is $T_1$ when on the earth's surface and $T_2$ when taken to a height '2R' above the earth's surface, where 'R' is the radius of the earth. The ratio $T_1 : T_2$ is

The lengths of seconds pendulums on the surface of the earth and at an altitude '$h$' from the surface of the earth are $l_s$ and $l_h$ respectively. The radius of the earth is

The ratio of thermal conductivity of two rods of different materials is $4 : 3$. The two rods have same area of cross-section and same thermal resistance. The lengths of rods are in the ratio

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperature $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be

A block of mass M is lying on a horizontal frictionless surface. One end of the uniform rope of half the mass of the block is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. The tension in the middle of the rope will be

The region inside a current carrying toroid is filled with a material (Niobium) having susceptibility $\chi = 2.6 \times 10^{-5}$. The percentage increase in the magnetic field in the presence of Niobium over that without it, is

The ratio of magnetic field at the centre of the current carrying circular loop and its magnetic moment is '$x$'. When both the current and radius are tripled, then the ratio will be

In the following figure, the magnitude of the magnetic field at point 'O' will be

All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If $T_a, T_b$ and $T_c$ are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

A particle is performing simple harmonic motion about $x = 0$ with an amplitude '$a$' and periodic time T. The speed of the particle at $x = \frac{a}{3}$ will be

A simple microscope is a combination of two lenses in contact. Their powers are $+20$D and $-4$D. The distance of distinct vision is $25$ cm. When seen through the microscope, the size of the image of an object $3$ mm high is

The radius of gyration K of a hollow sphere of mass M and radius R about an axis XY is equal to R as shown in figure. The distance of that axis from the center of the sphere is h. The value of h is

A solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder $(a_c)$ to that of the sphere $(a_s)$ is

The angular momentum of a rotating body is 'L'. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

Which of the following logic gates will have an output of '1' (one) for the given inputs?

A diode and resistance are connected as shown in figures.

Out of the following statements, which one is true?

Diode in

A) fig (1) and fig (2) are both forward biased.

B) fig (1) and fig (2) are both reverse biased.

C) fig (1) is forward biased and in fig (2) is reverse biased.

D) fig (1) is reverse biased and in fig (2) is forward biased.

Which one of the following statements is 'WRONG' regarding LED?

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

Which of the following graphs between pressure and volume of a gas correctly shows isochoric process in thermodynamics?

In thermodynamic process for free expansion, select the 'WRONG' statement out of the following options.

The r.m.s. speed of hydrogen at S.T.P. is '$u$' m/s. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively

If two resistors of resistances have values $R_1 = (350 \pm 3)\ \Omega$ and $R_2 = (140 \pm 4)\ \Omega$. The percentage error for the sum and difference of $R_1$ and $R_2$ are respectively

The angle made by vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with x-axis and that with y-axis are respectively.

A spherical object is falling under gravity through a viscous fluid. The sphere attains the terminal velocity when

Two sources of sound are emitting progressive waves $y_1 = 4\sin 708\pi t$ and $y_2 = 3\sin 700\pi t$. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and wanning are respectively

The lengths of the two pipes open at both ends are L and $(L + L_1)$. If they are sounded together, the beat frequency will be

($v$ = velocity of sound in air)

Fifth overtone of an open pipe of length $L_0$ is in unison with the fifth overtone of the pipe closed at one end of length $L_c$.

The ratio $L_0$ to $L_c$ is

The number of waves counted by an observer on the sea-coast in one minute is 54. If the wavelength of the waves is $5$ m then the velocity of the waves in m/s will be

In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength $6480$ Å, angular width of central maximum is measured. When the slit is illuminated by light of another wavelength '$\lambda$' the angular width decreases by $25\%$. The value of $\lambda$ in Å units is

When a glass plate of refractive index $1.44$ is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$y$'. If this plate is replaced by another plate of same thickness but of refractive index $1.66$, the fringes will be displaced by a distance

In a certain region of the screen, number of fringes formed is observed to be 8 in Young's double slit experiment when light of wavelength $6600$ Å is used. If the light of wavelength $4400$ Å is used, the number of fringes observed in the same region of the screen will be