MHT CET 2026 Physics Paper: 19 May, Shift 1

An alternating voltage is given by $V = V_0 \sin\left(\omega t + \frac{\pi}{4}\right)$. The time when the voltage is maximum for the first time is

($T$ = periodic time of the alternating voltage, $\cos 0^\circ = \sin 90^\circ = 1$)

A transformer having an efficiency 80% is working on $200$ V and $4$ kW power supply. If the current in the secondary coil is $5$ A, the voltage across the secondary coil and the current in the primary coil, respectively, are

An inductor of inductance $L$ and a resistor of resistance $R$ are joined in series and connected to an a.c. source of frequency $\omega$. The power dissipated in the circuit is

In a discharging series L-C-R circuit, $C = 2\ \mu$F, $L = 1$ mH and $R = 10\ \Omega$. The ratio of the energies stored in the inductor and in the capacitor, when the maximum current flows in the circuit, is

The de Broglie wavelength of an electron moving in the $n^{th}$ Bohr orbit of radius '$r$' is

The moment of inertia of the electron moving in the second Bohr orbit of a hydrogen atom is [$m$ = mass of electron, $h$ = Planck's constant, $e$ = charge on electron, $\varepsilon_0$ = permittivity of free space]

Consider the earth to be a sphere, having charge $Q$. Let $R, V$ and $A$ be its radius, volume and area respectively. The capacitance of the earth is [$\varepsilon_0$ = permittivity of free space]

Two parallel plate air capacitors of same capacity '$C$' are connected in series to a battery of emf '$E$'. Then one of the capacitors is completely filled with dielectric material of constant '$K$'. The change in the effective capacity of the series combination is

A particle moves along a circular path of radius '$r$' with uniform speed '$v$'. The angle described by the particle in two seconds in radians is

On a dry curved (banked) road, with banking angle of zero, the maximum safe speed for a moving vehicle is '$v$'. After heavy rain, the maximum safe speed for the same road was reduced by 60%. The ratio of the coefficient of friction for the dry road to that of the wet road is

In the following circuit, the current in the $4\ \Omega$ resistance is $1.2$ A. The total current ($I$) flowing in the circuit is

The potential gradient along the length of 1 metre wire of uniform cross section is $6$ V/m. Let '$B$' and '$C$' be the two points at $40$ cm and $60$ cm marks respectively from one end. The potential difference between points B and C is

In an experiment on photoelectric effect, the stopping potential $V_0$ is plotted against the frequency $\nu$ of the incident light. Considering $e$ as the electronic charge, the work function of the photoelectric surface is given by

Whenever a magnet is moved either towards or away from a conducting coil, magnetic flux linked with the coil changes. This change is dependent on

(a) the strength of the magnetic field.

(b) the area of cross-section of the coil.

(c) the resistance of the coil.

(d) the number of turns in the coil.

The magnetic flux through a coil of resistance '$R$' changes by an amount $\Delta\phi$ in the time $\Delta t$. The total quantity of induced current and charge is respectively

Two charged particles each having a charge '$+q$' and mass 'm' are kept at a distance 'd'. If they are in equilibrium under the gravitational force and the electric force between them, then the ratio $\frac{q}{m}$ (specific charge) of each particle is ($G$- Universal gravitation constant, $\varepsilon_0$ = permittivity of free space)

A semicircular arc of radius '$R$' is charged uniformly and has charge per unit length as $\lambda$. The electric potential $V$ at the centre of curvature is [$\varepsilon_0$ = permittivity of vacuum]

A body of mass 'm' is raised to a height '$10R$' from the surface of the earth, where 'R' is the radius of the earth. Suppose it is released now. The speed with which it will strike the surface of the earth is nearly

[$g$ = acceleration due to gravity]

A perfectly black body radiates power at temperature $T_1$ K. If it is to radiate 16 times this power, its temperature should be increased by

If '$m$' represents the mass of each molecule of a gas and '$T$' its absolute temperature respectively, then the root mean square velocity of the gaseous molecule is proportional to

A cricket ball of mass $120$ g is moving with a velocity of $8$ m/s and is hit by a bat so that the ball gets turned back with a velocity of $12$ m/s. If the duration of contact between the ball and bat is $0.02$ s, the impulse (in Ns) given to the ball by the bat is

A magnetic dipole lying parallel to a magnetic field requires '$W$' units of work to turn it through $30^\circ$. The torque required to keep this needle in this position is

$\left[\sin 30^\circ = \cos 60^\circ = 0.5, \sin 60^\circ = \cos 30^\circ = \frac{\sqrt{3}}{2}, \sin 90^\circ = \cos 0^\circ = 1\right]$

A juggler throws balls into air. He throws one ball whenever the previous one is at its highest point. If he throws 4 balls in one second, the height from which each ball returns is nearly [acceleration due to gravity is $9.8$ m/s${}^{2}$]

Two particles X and Y of masses '$m_1$' and '$m_2$' respectively, having equal charges after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii '$r_1$ ' and '$r_2$' respectively. The ratio of '$r_1$' and '$r_2$' is

A rectangular coil of effective area $0.04$ m$^{2}$ is suspended freely in a radial magnetic field of $0.02$ Wb/m$^{2}$. The torsional constant of the suspension fibre is $5 \times 10^{-9}$ Nm/degree. If a current of $250\ \mu$A is passed through it, then the angle through which it rotates is

Initially $8 \times 10^{10}$ atoms are present in a radioactive sample. The half-life of the sample is 1 hour. The number of atoms that will decay in the time interval $t = 2$ hour to $t = 5$ hour, is

The differential equation of a particle performing S.H.M. is $\frac{d^2x}{dt^2} + 64x = 0$, where $x$ is in meter. The period of oscillation of the particle is (in second)

Two simple harmonic motions are represented as $y_1 = 10\sin \omega t$ and $y_2 = 5\sin \omega t + 5\cos \omega t$, both in cm. The ratio of the amplitudes of $y_2$ ($A_2$) to that of $y_1$ ($A_1$ ), is

The radii of curvature of both the surfaces of a convex lens are equal. One of the surfaces is made plane by grinding. The new focal length and power of the lens, respectively, are

A ray of light takes time '$t$' to travel a distance '$d$' in air and it travels a distance '$4d$', in time '$T$' in a certain medium. If $T = 8t$, the critical angle for the pair of media is

$\left[\sin\left(\frac{\pi}{6}\right) = 0.5, \sin\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}, \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}, \sin\left(\frac{\pi}{2}\right) = 1\right]$

The band diagrams of three semiconductors p, n and intrinsic are given in the figures (1), (2) and (3). C and V are the conduction and valence bands and $E_F$ is the Fermi level. Figures, from (2),(1) and (3) respectively represent the type of semiconductors as

If two inputs of a NOR gate are shorted, the resulting gate is

In the following circuit, the current through the Zener diode is

Under isothermal conditions, a single drop of radius $R$ is formed from two mercury drops of radii $R_1$ and $R_2$. After combination, the relation between $R, R_1$ and $R_2$ is

A metal wire of length '$L$' and density '$d$' rests horizontally on the free surface of water. The maximum radius of the wire so that the wire does not sink in water is

[$T$ = surface tension of water, $g$ = gravitational acceleration]

There is an expansion of a gas in a thermodynamic system. But this change cannot be plotted on a P-V diagram. Then it is

The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2}R$. The gas is made up of molecules which are

When the temperature of 4 moles of a gas was increased from $70^\circ$C to $90^\circ$C, at constant volume, the change in internal energy was $60$ J. The total heat capacity of the gas at constant volume is

The length of mercury column in a mercury-in-glass thermometer is $H_1$ mm at the ice point and $H_2$ mm at the steam point. When the length is $H$ mm, the temperature $T$ is given in $^\circ$C by ($H_1 < H_2$)

In a certain system, the quantities A and B are measured as $8 \pm 0.08$ and $6 \pm 0.06$ respectively. Let $x = AB,\ y = A + B$ and $z = A - B$. The correct order of % error in $x,\ y$ and $z$ is

In a vector $\vec{p}$, 'x' and 'y' components have magnitudes 2 units and 5 units respectively. A vector $\vec{q}$, along negative Y axis has magnitude of 3 units. Then $\vec{p} \cdot \vec{q}$ is

'$n$' identical small drops of water are falling down vertically through a medium each with a terminal velocity '$v$'. If they combine to form a single drop, then its terminal velocity is $xv$. The value of $x$ is

Two simple harmonic sound waves travelling in the same direction are given by $y_1(x,t) = A\sin(0.5\pi x - 100\pi t)$ and $y_2(x,t) = A\sin(0.46\pi x - 92\pi t)$

The number of times, a stationary listener can hear sound of maximum intensity in one second is

For a stationary wave, $y = 10\cos(\pi x/15)\sin(48\pi t)$ cm, the distance between a node and the successive antinode is

A stretched string of length '$L$' is fixed at both the ends, has '$n$' nodes ($n > 2$). The length of the string in terms of $n$ and wavelength $\lambda$ is

The amplitude of a sound wave at a distance $r$ from a point source is $A$. The amplitude at a distance $2r$ from the point source is

In a biprism experiment, using a light of wavelength $4800$ Å, a steady interference pattern was obtained on a screen $1$ m away from the source. Now the source is replaced by another of wavelength $6400$ Å and the screen is moved away from it by $20$ cm. The fringewidth will

In the diffraction pattern due to a single slit of width '$a$' with incident light of wavelength '$\lambda$', at an angle of diffraction '$\theta$', the condition for the second maximum is

The bob of a simple pendulum of length 2m is kept at P. It is released and when it reaches Q, it losses 20% of its total energy due to air resistance. Its velocity at Q is [Take $g = 9.8$ m/s${}^{2}$ ]

A $6$ kg mass and $1.5$ kg mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is