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If Young’s modulus ‘Y’, surface tension ‘S’ and time ‘T’ are fundamental quantities, then the dimensional formula for density is

A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

An $\alpha$ -particle of energy 5 MeV is scattered through ${180}^{\circ }$ by gold nucleus. The instance of closest approach is of the order of

Consider the spectral line resulting from the transition n = 2 $\Rightarrow$ n = 1 in the atoms and ions given below. The shortest wavelength is produce by

If power factor is $\frac{1}{2}$ in a series RL circuit , $R=200\Omega ,50Hz$ ac mains is used then L is

A coil having an area $A_0$ is placed in a magnetic field which changes from $B_0$ to $3B_0$ in a time interval t. The e.m.f. induced in the coil will be

Three concentric conducting spherical shells A, B and C of radius $R$, $2R$ and $4R$ carry charges $Q$, $-2Q$ and $4Q$ respectively. Then the energy stored between shells B and C is

The vernier of a vernier scale is divided into 10 divisions which coincide with 9 divisions of the main scale, each main scale division being 0.5 mm. When the two jaws of the instrument are in contact with each other, the 4th division of the vernier scale coincides with a main scale division and the zero of the vernier lies to the right of the zero of the main scale. When a sphere is inserted between the jaws, the zero of vernier scale lies slightly to the right of 1.8 cm and the sixth vernier division coincides with a main division. The diameter of sphere will be

Two conducting plates of parallel plate capacitor are placed at a small distance from each other as shown in figure. a, b, c and d are charges on different surfaces.

Then, potential difference between plates ($V_H-V_L$ ) is

What should be the minimum length of an antenna for good transmission?

If the container filled with liquid gets accelerated horizontally, find the value of acceleration $a$ for which point $x$ is exposed to air as shown in the figure.

Two resistors each $4\Omega$ are connected in the left and right gaps of a meter bridge and balance point is obtained. Now a $4\Omega$ resistor is connected is series with that in the left gap and another $4\Omega$ resistor is connected in parallel with that in the right gap. The shift in the balance point is

A syringe of diameter D = 8 mm and having a nozzle of diameter d = 2 mm is placed horizontally at a height of 1.25 m as shown in the figure. An incompressible and non - viscous liquid is filled in syringe and the piston is moved at speed of 0.25 m/s. Find the range of liquid jet on the ground.

A cubical vessel has opaque walls. An observer (dark circle in figure below) is located such that she can see only the wall CD but not the bottom. Nearly to what height should water be poured so that she can see an object placed at the bottom at a distance of 10cm from the corner C ? (Refractive index of water is 1.33.

In a thin spherical bowl of radius 10 cm filled with water of refractive index $\frac{4}{3}$ there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E

A body of mass M moving with velocity v ms^-1 suddenly breaks into two pieces. One part having mass M/4 remains stationary, then the velocity of the other part will be

A hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of the same material of thermal conductivity $K$. The inside of the smaller sphere is maintained at $0^{\circ }\text{C}$ and the outside of the bigger sphere is at ${100}^{\circ }\text{C}$. The system is in steady state. Find the temperature of the interface.

When two tuning forks, fork $A$ and fork $B$ are sounded together, $4$ beats per second are heard. When the tuning fork $B$ is loaded with wax then $6$ beats per second are heard. If the frequency of fork $A$ is $200\text{Hz}$ then what was the original frequency of fork $B$?

Two bodies are in equilibrium when suspended in water from the arms (equal length) of a balance (in balanced condition). The mass of one body is $36\text{g}$ and its density is $9\frac{g}{c{m}^3}$. If the mass of the other body is $48\text{g}$, its density in $\frac{g}{c{m}^3}$ is

Two short magnets of equal dipole moments M are fastened perpendicularly at their centre (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is

A square coil of N turns (with length of each side equal L) carrying current i is placed in a uniform magnetic field $\overrightarrow{B}=B_0\hat{j}$ as shown in figure. What is the torque acting on the coil

Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density $\sigma$ as shown in figure (30-E6). Find the electric field (a) at the left of the plates,(b) in between the plates and (c) at the right of the plates.

Take the potential of the point B in figure (31-E7) to be zero. (a) Find the potentials at the points C and D. (b) If a capacitor is connected between C and D, what charge will appear on this capacitor ?

A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

A block placed on a rough horizontal table is acted upon by an external horizontal force $P$. The graph of frictional force $F$ against external force $P$ is

Two unequal masses of $1\text{kg}$ and $2\text{kg}$ are connected by an inextensible light string passing over a smooth pulley as shown in figure. A force $F=20\text{N}$ is applied on $1\text{kg}$ block. Find the magnitude of acceleration of either block. ($g=10{\text{m/s}}^2$)

If a current I given by $I_{0}sin(\omega t-\frac{\pi }{2})$ flows in an ac circuit across which an ac potential of $E=E_{0}sin\omega t$ has been applied, then the power consumption P in the circuit will be

In the photoelectric effect, the strength of the photoelectric current is proportional to

The radius of gyration of uniform disc of radius $R$ about an axis passing through a point $\frac{R}{2}$ from center and perpendicular to plane is

The surface tension of water in contact with air at ${18}^{\circ }\text{C}$ is $0.073\text{N/m}$. The pressure inside a droplet of water is to be $0.02{\text{N/cm}}^2$ greater than the outside pressure. Calculate the diameter of the droplet of water.

An empty plastic box of mass m is found to acclerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6 ?

The acceleration due to gravity at a height $1km$ above the earth is the same as at a depth $d$ below the surface of earth. Then

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two times of flights is proportional to

A circular conducting loop is connected with a battery as shown in the figure. The length of $ABC$ and $ADC$ is $l_1$ and $l_2$ respectively, then which one is correct :-

A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time of flight of the projectile is

A parallel plate condenser initially has air as a medium between the plates. If a slab of dielectric constant 5 having thickness half the distance of separation between the plates is introduced, the percentage increase in its capacity will be ___

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of $2\%$, the relative percentage error in the density is

A disc of mass $2\text{kg}$ and radius $0.5\text{m}$ is doing translational and rolling motion on a surface as shown in the figure. If $v_{com}=4\text{m/s}$ and $\omega =1{\text{rad/s}}^2$ then, find the total kinetic energy of the disc.

A rectangular loop of sides ‘a’ and ‘b’ is placed in XY plane. A very long wire is also placed in XY plane such that side of length ‘a’ of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is ‘d’. The mutual inductance of this system is proportional to :

A mass m is attached to a string of length $l_0$ ,Young’s modulus Y and area of cross section A. It is pushed with a velocity v as shown. Find the time in which the block comes to an instantaneous rest.

According to Boyle’s law PV = C, the value of C depends on
(i) mass of the gas
(ii) type of gas
(iii) temperature of gas

A detector is released from rest under gravity over a source of sound of frequency $f_0={10}^{3}Hz$. The frequency observed by the detector at time t is plotted in the graph. The speed of sound in air is $(g=10m/se{c}^2)$ (solve the problem by using apparent frequency relation, when the observer is moving with constant velocity)