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In Fraunhofer diffraction experiment at a single slit using a light of wavelength $400\text{nm}$, the first minimum is formed at an angle of ${30}^{\circ }$. The direction $\theta$ of the first secondary maximum is given by

The angle of a prism is ${}^{\prime }{A}^{\prime }$. One of its refracting surface is silvered. Light rays falling at an angle of incident $2A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$, of the prism is

A thin, rectangular film of liquid is extended from $(2\text{cm}\times 3\text{cm})$ to $(4\text{cm}\times 6\text{cm})$. If the work done in the process is $6\times {10}^{-4}\text{J}$, the value of surface tension of the liquid is

The wire loop $\text{PQRSP}$ formed by joining two semicircular wires of radii $R_1$ and $R_2$ carries a current $I$, as shown in the figure. The magnetic moment of the loop is

A point moves along a circle with a velocity $v=kt$, where $k=0.5\text{m}/{\text{s}}^2$. Find the acceleration of the point at the moment when it has covered the $n^{th}$ fraction of the circle after the beginning of motion, where $n=\frac{1}{10}$.

A block of mass $m$ is placed on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the inclined plane. The direction of force pointing up the plane is taken to be positive. As force $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, then the graph of frictional force $f$ versus $P$ graph will look like:

An uniform rod of mass $3\text{kg}$ is hinged at the wall and connected through a light string as shown in the figure. Find the tension in the string.(Take $g=10{\text{m/s}}^2$).

How there will be no change in angle of revolution when an electron moves in a circular motion in a atom

A small creatures moves with constant speed in a small vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a simple harmonic motion?

The frequency and intensity of a light source are both doubled. Consider the following statements.

A. The saturation photocurrent remains almost the same

B. The maximum kinetic energy of the photoelectrons is doubled

The range of a particle when thrown at angle of ${15}^{\circ }$ with the horizontal is 1.5 km. What maximum range can the particle achieve if speed of projection is kept constant?

Mass $m$ of a liquid $\text{A}$ is kept in a cup at a temperature of ${90}^{\circ }\text{C}$. When placed in a room having temperature of ${20}^{\circ }\text{C}$, it takes $5\text{min}$ for the temperature of the liquid to drop to ${30}^{\circ }\text{C}$. Another liquid $\text{B}$ having nearly the same density as $\text{A}$ and of mass $m$, kept in another identical cup at ${50}^{\circ }\text{C}$ takes $5\text{min}$ for its temperature to fall to ${30}^{\circ }\text{C}$ when placed in a room having temperature ${20}^{\circ }\text{C}$. If the two liquids at ${90}^{\circ }\text{C}$ and ${50}^{\circ }\text{C}$ are mixed in a calorimeter where no heat is allowed to leak, find the final temperature of the mixture. Assume that Newton's law of cooling is applicable for the given temperature ranges.

Two masses are connected by a string which passes over a pulley accelerating upwards at a rate A as shown. If $a_{1}and{a}_2$ be the accelerations of bodies 1 and 2 respectively, then:

A ball of density $\rho$ is dropped from a height $h$ into a container filled with a liquid of density $2\rho$ as shown in the figure. The maximum depth up to which the ball reaches is

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_p}{C_v}=\gamma$ for the gas is

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta \left(t\right)=3t^3-9t^2$ (Here $t$ is in seconds). The angular acceleration of the wheel becomes zero at

In a potentiometer circuit, a cell of EMF $1.5\text{V}$ gives the balance point at $36\text{cm}$ length of wire. If another cell of EMF $2.5\text{V}$ replaces the first cell, then at what length of the wire, the balance point occurs?

A projectile of mass $2\text{m}$ explodes at the highest point of its path. It breaks into two equal parts. One part retraces its path. Find the distance of the second part from the point of projection when it finally lands on the ground. Given that range of the projectile would be $200\text{m}$ if no explosion had taken place.

A current of $2\text{A}$ flows through a $2\Omega$ resistor when connected across a battery. The same battery supplies a current of $0.5\text{A}$, when connected across a $9\Omega$ resistor. The internal resistance of the battery is:



​​​​​​​$[$1 Mark$]$

A plane mirror is moving with velocity $(4\hat{i}+5\hat{j}+7\hat{k})\text{m/s}$. A point object in front of the mirror moves with a velocity $(3\hat{i}+4\hat{j}+5\hat{k})\text{m/s}$. Here $\hat{k}$ is along the normal to plane mirror and facing towards the object. The velocity of image w.r.t ground is (in SI units)

A body of mass 10kg is hanging from another body of mass 15kg. The combination is pulled up by a string with an acceleration of . $1.2m^{-2}$ Find the tensions (in N) at A and B points as shown in figure $(Takeg=9.8m/s^2)$.

Which of the following waves have the maximum wavelength ?

Figure shows a block of mass $m=2.5\text{kg}$ moving towards a spring of spring constant $k=10{\text{Nm}}^{-1}$ with a constant velocity $u=1{\text{ms}}^{-1}$. $A$ and $B$ are two rigid vertical walls. The block starts moving from $A$ and strikes the end $C$ of the spring at a distance $x=50\text{cm}$. If the collision between the block and wall $A$ is perfectly elastic, the time period $T$ (in seconds) of the motion of the block will be

A plate of mass 10 gm is in equilibrium in air due to the force exerted by light beam on plate. Calculate power of the beam. Assume plate is perfectly absorbing.

Calculate the focal length of the thin lens shown in figure. The points $C_1$ and $C_2$ denote the centres of curvature. Refractive index of lens is $1.5$.

A cuboid ABCDEFGH is anisotropic with ${\alpha }_x=1\times {10}^{-5}{\left(°C\right)}^{-1}$

, ${\alpha }_y=2\times {10}^{-5}{\left(°C\right)}^{-1}$

and ${\alpha }_z=3\times {10}^{-5}{\left(°C\right)}^{-1}$

. Coefficient of superficial expansion of faces can be

In the metre bridge arrangement, an unknown resistance $R_1$ is connected in series with resistance of $10\Omega$. When the combination is connecetd to left gap of the meter bridge and $R_2$ is connected to right gap, balance point from left end is at $50\text{cm}$. When $10\Omega$ resistor is removed, the balance point shifts to $40\text{cm}$. The value of $R_1$ is

When a forward bias is applied to a p-n junction, it

(a) raises the potential barrier.

(b) reduces the majority carrier current to zero.

(c) lowers the potential barrier.

(d) None of the above.

An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR The magnetic field due to this current at the point M is $H_1$. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, The current in PQ remaining unchanged. The magnetic field at M is now $H_2$ The ratio $\frac{H_1}{H_2}$ is given by

A photon has kinetic energy E = 100 keV which is equal to that of a proton. The wavelength of photon is ${\lambda }_2$ and that of proton is ${\lambda }_1.$ The ratio of ${\lambda }_2/{\lambda }_1$ is proportional to

There is a box of 70 kg on a rough surface and Ram is just able to pull the box by applying a force of $F_1$ (Figure1) Avinash tries to pull the same box but in different orientation (figure (ii)). He had to apply force $F_2$ is order to just move the box. Who had to apply a lesser force in order to just move the box?