MHT CET 2026 Physics Paper: 19 Apr, Shift 1

An alternating voltage $e = 150\sqrt{2} \sin 100t$ volt is applied to a capacitor of capacity $2\ \mu$F. The root mean square value of current in the circuit is

In an LCR circuit at resonance, the a.c. source current is

A) maximum in a series LCR circuit only.

B) maximum in a parallel LCR circuit only.

C) maximum in both series and parallel LCR circuits.

D) minimum in both series and parallel LCR circuits.

The correct answer is

For a series LCR circuit inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage V and current i are respectively

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number 'Z'. The value of 'Z' is

A parallel plate capacitor of capacitance 'C' is connected to a battery and charged to a potential 'V'. Another capacitor of capacitance '$3C$' is charged to a potential '$3V$'. The charging battery is then disconnected and both the capacitors are connected in parallel to each other such that positive terminal of one is connected to negative terminal of the other. The final energy of the configuration is

A slab of material of dielectric constant $K$ has the same area as the plates of a parallel plate capacitor but has a thickness $(4/5)d$, where $d$ is the separation of the plates. The capacitance in the presence and absence of dielectric are $C$ and $C_0$ respectively. The ratio $(C/C_0)$ is

Two particles having mass 'M' and 'm' are moving in a circular path with radius 'R' and 'r' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be

Two stones of masses $m$ and $3m$ are whirled in horizontal circles, the heavier one in a radius $\frac{r}{3}$ and the lighter one in radius $r$. When both the stones experience same centripetal forces, the tangential speed of lighter stone is '$n$' times that of the value of heavier stone. The value of '$n$' is

In a potentiometer circuit when two cells of e.m.f. $1.5$ volt and $1.2$ volt are connected to assist each other, balancing length is $270$ cm. What will be the balancing length in cm when these two cells are connected in opposition?

In a meter bridge experiment, the balance point is obtained at length '$l_1$ ' cm from left hand when resistances in the left gap and right gap are $15\ \Omega$ and $R\ \Omega$ respectively. When the resistance $R$ is shunted with equal resistance the new balance point is at $(1.6\, l_1)$. The resistance $R$ in ohm is

A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $(\lambda/3)$. If the maximum kinetic energy of the emitted photo electrons in the second case is $4$ times that in the first case, the work function of the surface of the material is ($h$ = Planck's constant, $c$ = speed of light)

According to Einstein's photoelectric equation, the graph of the kinetic energy of the emitted photoelectrons versus the frequency of incident radiation gives a straight line whose slope

Magnetic flux linked with the coil in weber is given by the equation $\Phi = 5t^{2} + 6t + 11$. The e.m.f. induced in the coil in the $5$th second will be

Consider two coils in which a current in one coil carrying $6$ A causes the change in the flux in the second coil $12 \times 10^{-4}$ weber/turn. The second coil has $2000$ turns. The mutual inductance between the coils is

Two different coils have self-inductance $3L$ and $L$. The current in both the coils is increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time there was current and voltage induced in the two coils. At the same instant, the ratio of energy stored in the first coil to that in the second coil is

Two electric dipoles of moment $P$ and $8P$ are placed in opposite directions on a line at a distance of $24$ cm. The electric field will be zero at the point between the dipoles whose distance from the dipole of moment $P$ will be $x_1$. When $8P$ is replaced by $27P$ keeping all other quantities the same, the distance $x_1$ now becomes $x_2$. The difference $|x_2 - x_1|$ is ( All the distances are measured from the centers of the dipole.)

'$n$' small spherical drops of the same size which are charged to 'V' volt each coalesce to form a single big drop. The potential of a big drop is

An in-compressible fluid flows steadily through a horizontal cylindrical pipe. The pipe has radius '$3R$' at point A and '$1.5R$' at point B, further along the flow direction at the same level. If the velocity at point A is '$v$', then that at point B is

A geostationary satellite is orbiting the earth at a height of $4R$ above the surface of the earth, where $R$ is the radius of the earth. Another satellite is orbiting the earth at a height $1.5R$ from the surface of the earth with periodic time 'T' in hour. The value of 'T' in hour is

When $170$ J of energy is incident on a surface of a body, $17$ J of energy is reflected by it. If the coefficient of absorption is $0.7$, then the amount of energy transmitted will be

A black body is at temperature $827^\circ$C. The rate at which it emits energy is proportional to

The kinetic energy of an ideal gas is $E_0$ at $27^\circ$C. When the temperature is increased to $177^\circ$C, then kinetic energy will be

Which of the following person is in an inertial frame of reference?

A diamagnetic liquid is filled in a U-tube. One arm of a U-tube is placed in an external magnetic field with the meniscus in line with the field. The level of the liquid in that arm will

The frequency of oscillation of a small magnet in a magnetic field of induction 'B' is '$n$'. If the frequency of oscillations of the same magnet in a field of induction 'X' falls to $\left(\frac{n}{3}\right)$, the value of 'X' is

Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are $d$ and $\left(\frac{d}{2}\right)$ for coil Y and X respectively. The radii of coils Y and X are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point 'O' is $B_y$ and that due to smaller coil X at point 'O' is $B_x$. ($d \gg r$) The relation between $B_x$ and $B_y$ is

Two thin long parallel wires, $W_1$ and $W_2$ separated by distance '$a$', carry currents $i$ and $3i$ respectively in the same direction. The magnitude of the force per unit length exerted by wire $W_1$ on wire $W_2$ is

A radioactive sample has half-life of $5$ years. The percentage of fraction decayed in $10$ years will be

A particle executes a simple harmonic motion with a periodic time $8$ second. At time $t = 0$, it is at a mean position. The ratio of the distance traveled by a particle in the 2nd and that in the 1st second of its motion is

($\sin 45^\circ = \cos 45^\circ = \frac{1}{\sqrt{2}},\ \sin 90^\circ = \cos 0^\circ = 1$)

A glass slab of thickness $6.0$ cm is placed on the piece of paper on which an inkdot is marked. By how much distance would an inkdot appear to be raised? The velocity of light in glass is $2 \times 10^{8}$ ms$-1$ and that in air is $3 \times 10^{8}$ ms$-1$.

The radius of gyration of a solid sphere of radius 'R' and mass 'M' about its diameter is $K_d$ and that about a tangent of a solid sphere is $K_t$. The ratio of $K_d$ to $K_t$ is

A thin uniform rod AB of mass '$m$' and length '$l$' is hinged at one end A to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its B end strikes the ground is

($g$ = acceleration due to gravity)

In n-type semiconductor

A) pentavalent impurity are dopants and holes are majority carriers.

B) trivalent impurity are dopants and electrons are minority carriers.

C) pentavalent impurity are dopants and electrons are majority carriers.

D) trivalent impurity are dopants and holes are majority carriers.

For a two input logic gate, when the inputs are 'zero' and 'zero' the output is 'one'. When the inputs are 'one' and 'zero' the output is 'zero'. The type of logic gate is

The material used for solar cell should have band gap

(A) equal to zero.

(B) equal to $0.08$ eV.

(C) between $1.0$ eV to $1.8$ eV.

(D) equal to $2$ eV.

The pressures inside two soap bubbles A and B are $1.02$ atmosphere and $1.04$ atmosphere respectively. The ratio of volume of bubble A to that of bubble B is (outside pressure $= 1$ atmosphere)

One large soap bubble of diameter 'D' breaks into $64$ bubbles having surface tension 'T'. The change in surface energy is

The thermodynamic process in which no work is done by the gas or on the gas is

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$, then the increase in the temperature of the gas in Kelvin is ($\gamma$ is the ratio of specific heats)

If the two temperatures on Fahrenheit scale differ by $54^\circ$F, then the difference in temperature on the Celsius scale is

The voltage across a lamp is $(6.0 \pm 0.3)$ volt and the current passing through it is $(4.0 \pm 0.1)$ ampere. The power consumed in watt will be (using percentage error)

For two vectors $\vec{P}$ and $\vec{Q} \quad \vec{P} \cdot \vec{Q} = |\vec{P} \times \vec{Q}|$

The magnitude of $\vec{R} = \vec{P} + \vec{Q}$ is ($\cos 45^\circ = \frac{1}{\sqrt{2}}$)?

A set of $14$ tuning forks is arranged in a series of increasing frequencies. Each fork produces '$x$' beats per second with the preceding fork and the last fork is an octave of the first fork. If the seventh fork has the frequency of $114$ Hz, the value of $x$ is

A tuning fork gives $5$ beats per second with a $33$ cm length of sonometer wire. If the length of the wire is shortened by $1$ cm, the number of beats is still the same. The frequency of the fork is

The third overtone of a closed pipe of length '$L_c$' has the same frequency as the third overtone of the open pipe of length '$L_0$'. Both the pipes have same diameters. The ratio $L_c : L_0$ is equal to

Which one of the following statements regarding pitch of sound is 'WRONG'?

(A) Pitch refers to sharpness of sound.

(B) Tone refers to the single frequency of that wave.

(C) High pitch sound need not be louder.

(D) In general male sound is sharper than that of a female.

In a single slit diffraction pattern, the distance between the plane of the slit and the screen is $1.4$ m. The width of the slit is $0.66$ mm. The second maximum is formed at the distance of $2.8$ mm from the center of the screen. The wavelength of light used is

In Young's double slit experiment, for the $n$th dark fringe ($n = 1, 2, 3, \ldots$) the phase difference of the interfering waves in radian will be

In Young's double slit experiment, the wavelength of light used is $\lambda$. The intensity on the screen at a point for path difference '$\lambda$' is 'X'. The intensity at the point for path difference $\left(\frac{\lambda}{6}\right)$ is ($\cos 180^\circ = -1,\ \cos 30^\circ = \frac{\sqrt{3}}{2}$)

The spring is initially in unstretched condition. It is first stretched by a length '$x$' and the work done is $W_1$. Then again it is stretched by further length '$x$' when the work done is $W_2$. The value of $W_2$ is given by