Q. A box is moved along a straight line by machine delivering constant power. The distance moved by the body in time $t$ is proportional to:

1. $t^2$
2. $t^{\frac{3}{2}}$
3. $t^{\frac{3}{4}}$
4. $t^{\frac{1}{2}}$

Q. A cubical vessel of height $1m$ is full of water. What is the amount of work done in pumping water out of the vessel?
(Take $g=10m/s^2$)

1. $1250J$
2. $5000J$
3. $1000J$
4. $2500J$

Q. An object weights $m_1$ in a liquid of density $d_1$ and that in liquid of density $d_2$ is $m_2$. The density $d$ of the object is

1. $\frac{m_2{d}_2-m_1{d}_1}{m_2-m_1}$
2. $\frac{m_1{d}_1-m_2{d}_2}{m_2-m_1}$
3. $\frac{m_2{d}_1-m_1{d}_2}{m_1-m_2}$
4. $\frac{m_1{d}_2-m_2{d}_1}{m_1-m_2}$

Q. A stone of relative density $K$ is released from rest on the surface of a lake. If viscous effect are ignored, the stone sinks in water with an acceleration of:

1. $g(1-K)$
2. $g(1+\frac{1}{K})$
3. $g(1+K)$
4. $g(1-\frac{1}{K})$

Q. A material has Poisson's ratio $0.50$. If a uniform rod of it suffers a longitudinal strain of $2\times {10}^{-3}$, then the percentage change in volume is

1. $0.6$
2. $0.4$
3. zero
4. $0.2$

Q. The resistance across $A$ and $B$ in the given figure will be:

1. None of the above
2. $3R$
3. $\frac{R}{3}$
4. $R$

Q. Two identical cylindrical vessels, with their bases at the same level, each contain a liquid of density $\rho$. The height of liquid in one vessel in $h_1$ and that in the other is $h_2$. The area of either base is $A$. What is the work done by gravity in equalising the levels when the vessels are interconnected?

1. $A\rho g{\left(\frac{h_1-h_2}{2}\right)}^2$
2. $A\rho g{\left(\frac{h_1+h_2}{2}\right)}^2$
3. $\frac{1}{2}A\rho g{(h_1-h_2)}^2$
4. None of these

Q. Tow identical springs are connected to mass $m$ as shown ($k=$ spring constant). IF the period of the configuration in (a) is $2s$, the period of the configuration in (b) is

1. $\sqrt{2}s$
2. $2\sqrt{2}s$
3. $\frac{1}{\sqrt{2}}s$
4. $1s$

Q. Two cells with the same emf $E$ and different internal resistances $r_1$ and $r_2$ are connected in series to an external resistance $R$. The value of $R$ so that the potential difference across the first cell be zero, is

1. $\sqrt{r_1{r}_2}$
2. $r_1-r_2$
3. $r_1+r_2$
4. $\frac{r_1+r_2}{2}$

Q. If $g$ is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass $m$ raised from the earth's surface to a height equal to the radius $R$ of the earth is

1. $\frac{mgR}{4}$
2. $\frac{mgR}{2}$
3. $mgR$
4. $2mgR$

Q. The charge on the capacitor of capacitance $C$ shown in the figure will be :

1. $\frac{CE{R}_1}{R_2+r}$
2. $\frac{CE{R}_1}{R_1+r}$
3. $CE$
4. $\frac{CE{R}_2}{R_2+r}$

Q. A shell of mass $m$ is at rest initially. It explodes into three fragments having masses in the ratio $2:2:1$. The fragments having equal masses fly off along mutually perpendicular direction with speed $v$. What will be the speed of the third (lighter) fragment?

Q. If a person can throw a stone to maximum height of $h$ metre vertically, then the maximum distance through which it can be thrown horizontally by the same person is

1. $h$
2. $3h$
3. $2h$
4. $\frac{h}{2}$

Q. A small spherical ball of mass $m$ slides without friction from the top of a hemisphere of radius $R$. At what height will the ball lose contact with surface of the sphere?

Q. Which type of gate the following truth table represents?

Input	Input	Output
$A$	$B$	$Q$
$0$	$0$	$1$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$0$

1. NOT
2. OR
3. AND
4. NAND

Q. A body of mass $6kg$ is acted upon by a force which causes a displacement in it given by $x=\frac{t^2}{4}$ metre, where $t$ is the time in second. The work done by the force in $2s$ is

1. $12J$
2. $9J$
3. $6J$
4. $3J$

Q. In the nuclear reaction, ${}_7^{14}N+X{⟶}_6^{14}C{+}_1^{1}H$, the $X$ will be

1. ${}_{-1}^{0}e$
2. ${}_0^{1}n$
3. ${}_1^{1}H$
4. ${}_1^{2}H$

Q. Current through $ABC$ and $A^{\prime }{B}^{\prime }{C}^{\prime }$ is $I$. What is the magnetic field at $P$?

1. $B=\frac{1}{4\pi }\left(\frac{2I}{r}\right)$
2. $B=\frac{{\mu }_0}{4\pi }\left(\frac{2I}{r}\right)$
3. $B=\frac{{\mu }_0}{4\pi }\left(\frac{I}{r}\right)$
4. Zero

Q. A body floats in water with $40$% of its volume outside water. When the same body floats in an oil $60$% of its volume remains outside oil. The relative density of oil is:

1. $0.9$
2. $1.2$
3. $1.0$
4. $1.5$

Q. The magnetic field at the point of intersection of diagonals of a square wire loop side $L$ carrying a current $I$ is

1. $\frac{{\mu }_{0}I}{\pi L}$
2. $\frac{{2\mu }_{0}I}{\pi L}$
3. $\frac{\sqrt{2}{\mu }_{0}I}{\pi L}$
4. $\frac{2\sqrt{2}{\mu }_{0}I}{\pi L}$

Q. Given $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+\hat{j}$. The component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ is:

1. $\frac{1}{\sqrt{2}}$
2. $\frac{5}{\sqrt{2}}$
3. $\frac{7}{\sqrt{2}}$
4. $\frac{3}{\sqrt{2}}$

Q. A particle is moving with constant speed $v$ in circle. What is the magnitude of average velocity after half rotation?

1. $2\frac{v}{\pi }$
2. $2v$
3. $\frac{v}{2}$
4. $\frac{v}{2\pi }$

Q. A radioactive nucleus of mass number $A$, initially at rest, emits an $\alpha$-particle with a speed $v$. The recoil speed of the daughter nucleus will be

1. $\frac{2v}{A+4}$
2. $\frac{2v}{A-4}$
3. $\frac{4v}{A-4}$
4. $\frac{4v}{A+4}$

Q. A battery of emf $E$ and identical resistance $r$ is connected across a pure resistive device (such as an electric heater) of resistance $R$. Prove that the power output of the device will be maximum if $R=r$.

Q. Two soap bubbles of radii $x$ and $y$ coalesce to constitute a bubble of radius $z$. Then $z$ is equal to:

1. $\sqrt{x^2+y^2}$
2. $\sqrt{x+y}$
3. $\frac{x+y}{2}$
4. $x+y$

Q. A cricket ball of mass $0.25kg$ with speed $10m/s$ collides with a bat and returns with same speed within $0.01s$. The force acted on bat is

1. $25N$
2. $250N$
3. $50N$
4. $500N$

Q. Five equal resistance, each of resistance $R$ are connected as shown in figure. A battery of $V$ volt is connected between $A$ and $B$. The current flowing in $FC$ will be

1. $\frac{3V}{R}$
2. $\frac{V}{2R}$
3. $\frac{2V}{R}$
4. $\frac{V}{R}$

Q. In an inelastic collision an electron excites a hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-shell state and ionizes it. At least how much energy the second electron transfers to the atom in the M-shell state?

1. $+3.4eV$
2. $+1.51eV$
3. $-3.4eV$
4. $-1.51eV$

Q. A radioactive isotope $X$ with half life $1.5\times {10}^9$yr decays into a stable nucleus $Y$. A rock sample contains both elements $X$ and $Y$ in ratio $1:15$. Find the age of the rock

Q. If the earth were to suddenly contract to $\frac{1}{n}th$ if its present radius without any change in its mass, the duration of the new day will be nearly

1. $\frac{24}{n}$ $hr$
2. $\frac{24}{n^2}hr$
3. $24n^{2}hr$
4. $24nhr$