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PN is the ordinate of any point P on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If Q divides AP in the ratio $a^2:b^2$ then NQ is

A block of mass $5.0\text{kg}$ slides down from the top of an inclined plane of length $3\text{m}$. The first $1\text{m}$ of the plane is smooth and the next $2\text{m}$ is rough. The block is released from rest and again comes to rest at the bottom of the plane. If the plane is inclined at ${30}^{\circ }$ with the horizontal, find the coefficient of friction on the rough portion.

Two equal negative point charges $-q$ are fixed at points $(0,a)$ and $(0,-a)$ on the $\text{y-}$axis. A positive point charge $Q$ is in rest at point $(2a,0)$ on the $\text{x-}$axis. The net electric field on $Q$ due to both $-q$ charges will be $(\frac{1}{4\pi {ϵ}_0}=k)$

The echo of a gunshot is heard $8\text{s}$ after the gun is fired. How far from him is the surface that reflects the sound?



Velocity of sound in air $=350\text{m/s}$

A block of mass $10kg$ is connected to another block of mass $20kg$ by a massless spring of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force $200N$ starts acting on the block of mass $20kg$ to pull it. Find the force on the block of mass $10kg$ in $N$, if the acceleration of both blocks are same.

Radiation of wavelength $\lambda$ is incident on a photocell. The fastest emitted electron has a speed $v$. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be :

Two bodies of masses $2\text{kg}$ and $4\text{kg}$ have position vector $(\hat{i}+2\hat{j})$ and $\left(2\hat{i}\right)$ respectively. Find the position vector for the centre of mass of the system.

Consider the nuclear reaction $X^{200}\to A^{110}+B^{80}.$ If the binding energy per nucleon for $X,A$ and $B$ are $7.4\text{MeV},8.2\text{MeV}$ and $8.1\text{MeV}$ respectively, then the energy released in the reaction is

A virtual erect image in a concave mirror is represented, in the given figure, by

If a body of mass $m$ is sent to a height of $R/5$ from the earth surface, the potential energy increases by $(R\to$ radius of earth):-

A ball of mass $0.25\text{kg}$ attached to the string of length $1.96\text{m}$ is moving in a horizontal circle. The string will break if the tension in the string is more than $25\text{N}$. What is the maximum angular velocity with which the ball can be moved?

A disc of radius 'r' is removed from the disc of radius 'R' then

a. the minimum shift in centre of mass is zero

b. the maximum shift in centre of cannot be greater than $\frac{r^2}{(R+r)}$

c. Centre of mass must be lie where mass exists

d. the shift in centre of mass is $\frac{r^2}{(R+r)}$

A man is swimming at a depth $d$ in the sea at a distance $(L>>d)$ from a ship $\left(S\right)$. An explosion occurs in the ship and after hearing the sound, the man immediately moves to the surface. It takes $0.8\text{s}$ for the man to rise to the surface after he hears the sound of explosion. $0.2\text{s}$ after reaching the surface, he once again hears the sound of explosion. Then, calculate $L$.





Given: Speed of sound in air = $340{\text{ms}}^{-1}$; Bulk modulus of water $2\times {10}^9\text{Pa}$

After perfectly inelastic collision between two identical particles, moving with the same initial speed in different directions, the speed of the composite particle becomes half the initial speed of an individual particle. Find the angle made by velocity of both the particles with $x-$axis before collision.

The following arrangement consists of five identical metal plates parallel to each other. Area of each plate is $A$ and separation between the successive plates is $d$. The capacitance between $\text{P}$ and $\text{Q}$ is

A uniform rectangular lamina is shown in figure. Find the moment of inertia $I_{\text{com}}$ about $z$ axis which passes through its centre and perpendicular to its plane. Here $b=10\text{m}$, $l=20\text{m}\&M=12\text{kg}$.

If $|\overrightarrow{a}|=5,|\overrightarrow{a}-\overrightarrow{b}|=8$ and $|\overrightarrow{a}+\overrightarrow{b}|=10$, then $|\overrightarrow{b}|$ is equal to:

Two vessels $A$ and $B$ of different shapes have the same base area and are filled with water upto the same height $h$ (as shown). The force exerted by water on the base is $F_A$ for vessel $A$ and $F_B$ for vessel $B$. The respective weights of water in the vessels are $W_A$ and $W_B$. Then

Two objects that are moving in the $xy$ plane on a frictionless floor collide head on. Assume that they form a closed isolated system. The following table gives the momentum components in $\text{kg m/s}$ before and after the collision. What are the missing values $(a,b)$ (in $\text{kg m/s}$)?

$$\begin{array}{ccccc}& \text{Before collision along X-axis}& \text{Before collision along Y-axis}& \text{After collision along X-axis}& \text{After collision along Y-axis}\\ \text{Object}& P_{xi}& P_{yi}& P_{xf}& P_{yf}\\ A& -4& 5& 3& a\\ B& b& -2& 4& 2\end{array}$$

A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius $\frac{100}{\pi }$ cm at a constant angular speed of 5.0 revolutions per second. A listener situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air $=332m{s}^{-1}$.

In the shown circuit, all three capacitors are identical and have capacitance $C\mu \text{F}$ each. Each resistor has resistance of $R\Omega$. An ideal cell of emf $V$ volts is connected as shown. Then the magnitude of potential difference across capacitor $C_3$ in steady state is:

Two small balls of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ are placed in a fixed smooth horizontal circular hollow tube of mean radius ${}^{\prime }{r}^{\prime }$ as shown. The ball of mass ${}^{\prime }{m}^{\prime }$ is moving with speed ${}^{\prime }{u}^{\prime }$ and the ball of mass ${}^{\prime }2m^{\prime }$ is stationary. After their first collision, the time elapsed for next collision is: (coefficient of restitution $e$ = $\frac{1}{2}$)

Calculate the smallest thickness of the soap bubble which produces a constructive interference for a red light of the wavelength $650\text{nm}$.



Take refractive index to be $1.33$.

When a semiconductor is heated, its resistance

[KCET 1992; MP PMT 1994; MP PET 1992, 2002;RPMT 2001; DCE 2001]

An electric dipole of length $4\text{cm}$ , when placed with its axis making an angle of ${60}^{\circ }$ with a uniform electric field , experiences a torque of $4\sqrt{3}\text{Nm}$. Find the potential energy of the dipole, if the dipole has charges of $\pm 8\text{nC}$ (in $\text{J}$)

Which of the following case shows work done is not zero?