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A magnet with a mass of $0.25\text{kg}$ moving with a velocity of $10\text{m/s}$ strikes a metal block of mass $20\text{kg}$ moving with a velocity of $5\text{m/s}$. Both magnet and block are moving in the same direction initially. The magnet sticks to the metal block after the collision. What is the final velocity of the system ?

A perfectly elastic ball falls freely from a height h = 2.5 m onto an inclined plane of inclination $\alpha ={37}^{\circ }$. Find the range S of the ball on the inclined plane. (See figure) (Take $g=10m{s}^{-2}$)

Two waves each having a frequency of 100 Hz and a wavelength of 2 cm are travelling in the same direction on a string. Both the waves were produced at the same instant but the first one was produced at a distance 4 cm behind the second one. If both waves have an amplitude of 2 mm what would be the amplitude of the resultant wave?

In the given circuit the steady state current through the $2\Omega$ resistor is

A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2m$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m,$ which move at angle ${45}^{\circ }$ with respect to the original direction.

The speed of each of the moving particle will be-

A double slit interference pattern is produced on a screen, as shown in the figure, using monochromatic light of wavelength $500nm$. Point $P$ is the location of the central bright fringe, that is produced when light waves arrive in phase without any path difference. A choice of three strips A, B and C of transparent materials with different thickness and refractive indices is available, as shown in the table. These are placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be shifted across the screen from the original pattern. In the column - I, how the strips have been placed , is mentioned whereas in the column -II, order of the fringe at point P on the screen that will be produced due to the placement of the strip (s), is shown. Correctly match both the columns.

Two point charge
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$\text{A}$ and $\text{B}$ having charges $+Q$ and $-Q$ respectively, are placed at certain distance apart and force acting between them is $F$. If $25\%$ charge of
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$\text{A}$ is transfered to $\text{B}$, then force between the charges becomes

In the displacement ($d$) - time ($t$) graph given below, the value of average velocity in the time interval $0$ to $20\text{s}$ is (in $\text{m/s}$)

Let $\overline{v}$ be a unit vector which follows the equation, $\overline{v}\times \overline{b}=\overline{c}$. Also, $\left|\overline{b}\right|=2$ and $\left|\overline{c}\right|=\sqrt{3}$ then

Two metallic spheres $S_1$ and $S_2$ are made of the same material and have identical surface finish. The mass of $S_1$ is three times that of $S_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature, but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_1$ to that of $S_2$ is

A sample of metal weighs 210 gm in air, 180 gm in water and 120 gm in liquid. Then relative density (RD) of

A physical quantity $Z$ as a function of time is given as $Z\left(t\right)=A^{\frac{3}{2}}{e}^{–kt},$ where $k=0.1s^{–1}$. The measurement of A has an error of $2.00\%.$ If the error in the measurement of time is $1.25\%,$ then the percentage error in the value of $Z\left(t\right)$ at $t=10s$ would be

A capacitor of capacitance $C$ has charge $Q$. It is joined in parallel across an identical uncharged capacitor through a resistor. The heat produced in the resistor is,

A pin-ended column of length L, modulus of elasticity E and second moment of the cross sectional area is $I$ loaded concentrically by a compressive load P. The critical bucking load $P_{cr}$ is given by

Find the direction of friction on A and B at the surfaces of contact between them (for the figure shown).

The potential energy of a $4\text{kg}$ particle free to move along the $x-$ axis is given by $U\left(x\right)=\frac{x^3}{3}-\frac{5x^2}{2}+6x+3$. Total mechanical energy of the particle is $17\text{J}$. Then the maximum kinetic energy is

A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects, each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity

A charge +q is placed at the middle of a closed cylinder of radius r and height h. A spherical shell of radius r with its centre at the point at which charge is placed, is so oriented so that h > 2 r. what is the ratio of flux passing thorugh cylinder and sphere?

Escape velocity from the center of imaginary planet of the shape of hemispherical shell of mass M and radius R as shown in figure in given direction is $\sqrt{\frac{nGM}{R}}$ then n is

1. 700

A particle is projected vertically upwards with speed $20\text{m/s}$ from top of a tower of height $20\text{m}$ as shown in figure. Given $B$ is top most point of trajectory and $C$ is at same height as $A$ :
$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ \left(A\right)& \text{ratio of maximum height from ground (BD)}& \left(P\right)& \frac{1}{\sqrt{2}}\\ & \text{to the initial height from ground (AD)is}& & \\ \left(B\right)& \text{ratio of distance travelled in 1st second to}& \left(Q\right)& \frac{1}{\sqrt{3}}\\ & \text{the distance travelled in 2nd second is}& & \\ \left(C\right)& \text{ratio of initial speed at A to the final}& \left(R\right)& 1\\ & \text{just before reaching to ground (D) is}& & \\ \left(D\right)& \text{ratio of time taken from A to C and time}& \left(S\right)& 2\\ & \text{taken from A to B is}& & \\ & & \left(T\right)& 4\\ & & \left(U\right)& 3\end{array}$
Which of the following option has the incorrect combination considering column-I and column-II

A laser beam has intensity $2.5\times {10}^{14}$${\text{Wm}}^{-2}$. The amplitudes of electric and magnetic fields in the beam are :

A glass flask of volume $200{\text{cm}}^3$ is just filled with mercury at ${20}^{\circ }\text{C}$. The amount of mercury that will overflow when the temperature of the system is raised to ${100}^{\circ }\text{C}$ is



$({\gamma }_{\text{glass}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1},{\gamma }_{\text{mercury}}=1.8\times {10}^{-4}{}^{\circ }{\text{C}}^{-1})$

If A vector = Axi, B vector = Byj, C vector = A vector + B vector and D vector = A vector × B vector, then C vector • D vector is equal to what

Two point charges $100\mu \text{C}$ and $5\mu \text{C}$ are placed at points $\text{A}$ and $\text{B}$ respectively with $AB=40\text{cm}$.The workdone by external force in displacing the charge $5\mu \text{C}$ from $\text{B}$ to $\text{C}$ is

$\text{Here}BC=30\text{cm},$ $\angle ABC=\frac{\pi }{2}$

The temperature of equal masses of three different liquids $\text{A, B}$ and $\text{C}$ are $10{}^{\circ }\text{C},15{}^{\circ }\text{C}$ and $20{}^{\circ }\text{C}$ respectively. The temperature when $\text{A}$ and $\text{B}$ are mixed is $13{}^{\circ }\text{C}$ and when $\text{B}$ and $\text{C}$ are mixed is $16{}^{\circ }\text{C}$. What will be the temperature when $\text{A}$ and $\text{C}$ are mixed ?

By a surface of a liquid, we mean?

Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

A resistor and an inductor are connected to an $\text{AC}$ supply of $120\text{V}$ and $50\text{Hz}$. The current in the circuit is $3\text{A}$. If the power consumed in the circuit is $108W$, then the resistance in the circuit is