A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $v$ in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)?

If $c$ is the velocity of light in free space, the correct statements about photon among the following are:$\newline$A. The energy of a photon is $E = h\nu. \newline$B. The velocity of a photon is $c. \newline$C. The momentum of a photon $p = \frac{h\nu}{c} \newline$D. In a photon-electron collision, both total energy and total momentum are conserved.$\newline$E. Photon possesses positive charge.

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are $8 \times 10^8$ N/m$^2$ and $2 \times 10^{11}$

A logic circuit provides the output $Y$ as per the following truth table:

The moment of inertia of a thin rod about an axis passing through its mid-point and perpendicular to the rod is $2400$ g cm$^2.$ The length of the 400 g rod is nearly:

In a vernier calipers, (N + 1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

Match List I with List II.

If the monochromatic source in Young’s double slit experiment is replaced by white light, then:

The graph which shows the variation of $\frac{1}{\lambda^2}$ and its kinetic energy, $E$ (where $\lambda$

Match List I with List II.

An unpolarised light beam strikes a glass surface at Brewster’s angle. Then:

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

A particle moving with uniform speed in a circular path maintains:

The quantities which have the same dimensions as those of solid angle are:

A bob is whirled in a horizontal plane by means of a string with an initial speed of $v$ rpm. The tension in the string is $T.$ If speed becomes $2v$ while keeping the same radius, the tension in the string becomes:

If $x = 5 \sin\left(\pi t + \frac{\pi}{3}\right)$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are:

A thermodynamic system is taken through the cycle abda. The work done by the gas along the path bc is:

Given below are two statements:$\\ \textbf{Statement I:}$ Atoms are electrically neutral as they contain equal number of positive and negative charges.$\\ \textbf{Statement II:}$ Atoms of each element are stable and emit their characteristic spectrum.$\\$In the light of the above statements, choose the most appropriate answer from the options given below:

In an ideal transformer, the turns ratio is $\frac{N_p}{N_s} = \frac{1}{2}.$

Two bodies A and B of same mass undergo completely inelastic one-dimensional collision. The body A moves with velocity $v_1$ while body B is at rest before collision. The velocity of the system after collision is $v_2.$ The ratio $v_1: v_2$

In the nuclear emission stated below, the mass number and atomic number of the product Q respectively, are:$\\ ^{200}_{82}X \xrightarrow{\alpha} Y \xrightarrow{e^+} Z \xrightarrow{\beta^-} P \xrightarrow{e^-} Q$

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.$\newline \textbf{Assertion A:}$ The potential (V) at any axial point, at $2m$ distance $(r)$ from the centre of the dipole of dipole moment vector $\vec{P}$

Consider the following statements A and B and identify the correct answer:$\\ A.$For a solar-cell, the I-V characteristics lies in the IV quadrant of the given graph.$\\ B.$In a reverse biased pn junction diode, the current measured in (\mu A), is due to majority charge carriers.

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is:$\\ ( \frac{1}{4\pi \varepsilon_0} = 9 \times 10^9$

A thin flat circular disc of radius $4.5m$ is placed gently over the surface of water. If surface tension of water is $0.07$ N/m$,$ then the excess force required to take it away from the surface is:

A light ray enters through a right-angled prism at point P with the angle of incidence $30^\circ$ as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is:

At any instant of time $t,$ the displacement of any particle is given by $2t - 1$ (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):

A tightly wound 100 turns coil of radius 10 cm carries a current of 7A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4\pi \times 10^{-7}$ SI units):

A horizontal force 10N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg, respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is:

A small telescope has an objective of focal length 120 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is:

Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:

A wire of length $l$ and resistance $100\Omega$ is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

A metallic bar of Young’s modulus, $0.5 \times 10^{11}$ N/m$^2$ and coefficient of linear thermal expansion $10^{-5}$

The velocity (v) - time (t) plot of the motion of a body is shown below. The acceleration (a) - time (t) graph that best suits this motion is:

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures $P_1, P_2, P_3$ compared with those of Charles’s law represented as dotted lines. Then the correct relation is:

A $10 \mu F$ capacitor is connected to a $210 V, 50 Hz$ source as shown in figure. The peak current in the circuit is nearly ( $\pi = 3.14$):

Choose the correct circuit which can achieve the bridge balance.

The property which is NOT of an electromagnetic wave travelling in free space is that:

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then:$\\ A.$ The charge stored in it, increases.$\\ B.$ The energy stored in it, decreases.$\\ C.$ Its capacitance increases.$\\ D.$ The ratio of charge to its potential remains the same.$\\ E.$

A force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t.$ The factor which is dimensionless, if $\alpha$ and $\beta$

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to:$\\ A.$ Hold the sheet there if it is magnetic.$\\ B.$ Hold the sheet there if it is non-magnetic.$\\ C.$ Move the sheet away from the pole with uniform velocity if it is conducting.$\\ D.$ Move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar.

In the following circuit, the equivalent capacitance between terminal A and terminal B is:

An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle $60^\circ$ with each other. The magnetic moment of this new magnet is:

The output (Y) of the given logic gate is similar to the output of an:

The terminal voltage of the battery, whose emf is $10V$ and internal resistance $1\Omega,$ when connected through an external resistance of $4\Omega$ as shown in the figure is:

The mass of a planet is $\frac{1}{10}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

In a uniform magnetic field of $0.049T,$ a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6}$ kg m$^2.$