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A horizontal disc rotating freely about a vertical axis makes $200\text{rpm}$. A piece of wax of mass $20\text{g}$ falls verticaly on the disc and adheres to it at a distance of $8\text{cm}$ from the axis. If the number of revolutions per minute is thereby reduced to $120\text{rpm}$, then calculate the moment of inertia of disc.

Two balls $A$ and $B$ are thrown with speed $u$ and $\frac{u}{2}$ respectively. Both the balls cover the same horizontal distance before returning to the horizontal plane of projection. If the angle of projection of ball $B$ is ${15}^{\circ }$ with the horizontal, then the angle of projection of $A$ is

The refractive index of a certain glass is 1.5 for light whose wavelength in vacuum is 6000 Å. The wavelength of this light when it passes through glass is

[NCERT 1979; CBSE PMT 1993; MP PET 1985, 89]

When a mica sheet of thickness 7 microns and $\mu =1.6$ is placed in the path of one of interfering beams in the $YDSE$, then the central fringe gets at the position of the seventh bright fringe. What is the wavelength of light used ?

A Vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier caliper, the least count is:

Two bodies of masses $3\text{kg}$ and $2\text{kg}$ are located at $x=0\text{m}$ and $x=4\text{m}$ respectively. Find the position of the centre of mass of the system (with respect to mass $2\text{kg}$) .

If $M$ is the mass of water that rises in a capillary tube of radius $r$, then mass of water which will rise in a capillary tube (of same material) of radius $2r$ is

An object moves along the grid through points A, B, C, D, E and F as shown in the figure. Find the magnitude of displacement covered by the moving object.

Following figure shows a network of capacitors where the numbers indicate capacitance in $\mu F.$ The equivalent capacitance between points A and B is

A body of mass $1\text{kg}$ is subjected to a force of $20\text{N}$ for $10$ seconds after which the force ceases to act. What distance would it travel in the next $10$ seconds?

When wavelength of incident photon is decreased then

A signal of frequency $10\text{kHz}$ and peak voltage of $10\text{V}$ is used to modulate a carrier of frequency $800\text{kHz}$ and peak voltage of $20\text{V}$. What is the amplitude modulation index?

The above picture depicts the possible transitions of electron in Bohr's atomic model.

Match the transition lines to corresponding series.

$\begin{array}{cc}\text{p.}{L}_1& \text{i. Lyman}\\ \text{q.}{L}_2& \text{ii. Blamer}\\ \text{r.}{L}_3& \text{iii. Paschen}\\ \text{s.}{L}_4& \text{iv. None of these}\end{array}$

A force of magnitude $18\text{N}$ acts on a particle in the direction of a vector $\overrightarrow{A}=2\hat{i}-4\hat{j}+4\hat{k}$, which results in the change of position of the particle from $(3,3,5)\text{m}$ to $(2,-1,4)\text{m}$. The work done by the force is (in Joule )

A body covers the first $1/3$ of the distance with a velocity of $2\text{m/s}$, the next $1/3$ with $3\text{m/s}$ and the rest of the distance with $6\text{m/s}$. The average velocity in $\text{m/s}$ for covering the whole distance is (assume that the body travels with constant velocity in all the parts in a straight line)

A river is flowing with a speed of $1\text{km/hr}$ as shown in figure. A swimmer wants to go to the point C starting from point A. He swims with a speed of $5\text{km/hr}$ with respect to the flowing river at an angle $\theta$ as shown. If $AB=BC=400\text{m}$, then value of $\theta$ is:

Find $\frac{dy}{dx}$ of $y=\tan x^2$.

A block rests on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in $\text{kg}$) is (take $g=10{\text{m/s}}^2$)

Find the ratio of radii of gyration of a circular disc and a circular ring of same mass and radius, about an axis passing through their centre and perpendicular to their planes.

When a bimetallic strip is heated, it

Find the weight of the air at 20⁰C contained in a room with $4.0m\times 5.0m$ floor and a ceiling 3.0 m high. (Density of air at 20⁰C is 1.20 kg/m³).

What is the angle between two forces of equal magnitude such that the resultant is one-third as much as either of the original forces?

A particle is suspended from a fixed point by a string of length $3\text{m}$. It is projected from equilibrium position with such a velocity that the string slackens after the particle has reached a height of $5\text{m}$ above the lowest point. Find the velocity of the particle, just before the string slackens. Take $g=9.81{\text{m/s}}^2$.

In the arrangement shown in figure $m_A=4.0\text{kg}$ and $m_B=1.0\text{kg}.$ The system is released from rest and block $B$ is found to have a speed $0.3\text{m/s}$ after it has descended through a distance of $1\text{m}$. Find the coefficient of friction between the block $A$ and the table. Neglect friction elsewhere. (Take $g=10m/s^2$)

Evaluate:

i. $\int (\sin x+\cos x)dx$

ii. $\int (3x^2+4)dx$

A Carnot engine, having an efficiency of $\eta =1/10$ as heat engine, is used as a refrigerator. If the work done on the system is $10J$, the amount of energy absorbed from the reservoir at lower temperature is

A simple microscope is rated $5X$ for a normal relaxed eye. What will be its magnifying power for a relaxed farsighted eye whose near point is $40cm$?

The x and y coordinates of a particle is given by

x(t)=5t+1

y(t)=t

The velocity of the body at t = 1 s is

The intensity level $1\text{m}$ away from a point source is $40\text{dB}$. Threshold intensity of hearing is ${10}^{-12}{\text{W/m}}^2$. If there is no loss of power in air, then intensity level at $10\text{m}$ from the source is

In List - I condition on initial velocity $\overrightarrow{u}$, force $\overrightarrow{F}$ and acceleration $\overrightarrow{a}$ of a particle is given.

Resultant motion is described in List-II.

Match List-I with List-II

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \overrightarrow{u}\times \overrightarrow{F}=0\text{and}& \text{(P)}& \text{Path will be}\\ & \overrightarrow{F}=\text{constant}& & \text{circular path}\\ \text{(II)}& \overrightarrow{u}.\overrightarrow{F}=0\text{and}& \text{(Q)}& \text{Speed will increase}\\ & \overrightarrow{F}=\text{constant}& & \\ \text{(III)}& \overrightarrow{v}.\overrightarrow{F}=0\text{all the time}& \text{(R)}& \text{Path will be}\\ & \text{and}|\overrightarrow{F}|=\text{constant}& & \text{straight line}\\ & \text{and the particle}& & \\ & \text{always remains in}& & \\ & \text{one plane}\left(\overrightarrow{v}\text{is instantaneous velocity}\right)& & \\ \text{(IV)}& \overrightarrow{u}=2\hat{i}-3\hat{j}\text{and}& \text{(S)}& \text{Path will be}\\ & \text{acceleration at all time}& & \text{parabolic}\\ & \overrightarrow{a}=6\hat{i}-9\hat{j}& & \end{array}$

Two non-conducting concentric spherical shells having uniform charge distribution +Q and –Q over their surface are shown in figure. A point charge q is taken slowly from point P to infinity. The work done by external agent in this process is equal to $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$



दो अचालक संकेन्द्रीय गोलीय कोशों के पृष्ठ पर एकसमान आवेश वितरण चित्रानुसार +Q तथा –Q हैं। एक बिंदु आवेश q को धीरे-धीरे बिंदु P से अनन्त तक लाया जाता है। इस प्रक्रिया में बाह्य कारक द्वारा किया गया कार्य है $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\omega }_1$ and ${\omega }_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss in coinciding of energy during this process is

A body of mass $m$ hangs by as inextensible light string that passes over a smooth massless pulley that is fitted with a light spring of stiffness $k$ as shown in the figure. If the body is released from rest, calculate the maximum elongation of the spring. Take $g=10{\text{m/s}}^2$.

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3}{\text{m/s}}^2$, in the third second is

A force of $5kg-wt$ is acting on a body of mass $5kg$ kept on a smooth horizontal surface at rest. If it acts for $10$ seconds at an angle of ${60}^{\circ }$ with the horizontal, find the distance travelled by the body. (Take $g=10m/s^2)$

A tangential force $10\text{N}$ acts at the top of a thin spherical shell of mass $m\left(5\text{kg}\right)$ and radius $R\left(20\text{cm}\right)$. Find the acceleration of the shell if it rolls without slipping.

A toy car travels in a horizontal circle of radius $2a$. It is kept on the track by a radial elastic string of unstretched length $a$. The period of rotation of the toy car is $T_0$. Now, the toy car is speeded up until it is moving in a circle of radius $3a$. Assuming that the string obeys Hooke's law, find the new period $T$ in terms of $T_0$.

A circuit of resistance $5\Omega$ and inductance $0.6H$ is in series with a capacitance of $10\mu F$. If a voltage of $200\text{V}$ is applied and the frequency is adjusted to resonance. The current in the circuit is $I_0$ and voltage across the inductor and capacitor are $V_0$, and $V_1$ respectively. We have

The total acceleration of a particle in circular motion is $25m{s}^{-2}.$ If the speed of the particle decreases at a rate of $15m{s}^{-2}.$ If radius of the path of the particle is $r=2m$, the angular speed $\omega$ of the particle relative to the centre of the circle is

A force is inclined at ${60}^{\circ }$ to the horizontal produces a displacement of $\overrightarrow{s}=(\hat{i}+\hat{j})\text{m}$. If the component of force in horizontal direction is $50\text{N}$, the net work done by the force on the body is

A particle is projected making an angle of ${45}^{\circ }$ with horizontal, with kinetic energy $K$. The kinetic energy at highest point will be

A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes $10$ minutes with a drift of $120m$. If he crosses the river taking shortest route, he takes $12.5$ minutes, find the velocity of the boat with respect to water.

The length of a sonometer wire is $0.75\text{m}$ and density is $9\times {10}^3{\text{kg/m}}^3$. It can bear a stress of $8.1\times {10}^8{\text{N/m}}^2$ without exceeding elastic limit. The fundamental frequency that can be produced in the wire is

The input signal given to a a CE amplifier having a voltage gain of $150$ is $V_i=2\cos (15t+\frac{\pi }{3})$. The corresponding output signal will be