What volume of hydrogen gas at STP would be liberated by action of 50 mL of $\mathrm{H}_2 \mathrm{SO}_4$ of $50 \%$ purity (density $=1.3 \mathrm{~g} \mathrm{~mL}^{-1}$ ) on 20 g of zinc?

Given : Molar mass of $\mathrm{H}, \mathrm{O}, \mathrm{S}, \mathrm{Zn}$ are 1, 16, 32, $65 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively.

Which of the following statement(s) is/are true ?

A. If two orbitals have the same value of ( $\mathrm{n}+l$ ), the orbital with lower value of n will have lower energy.

B. Energies of the orbitals in the same subshell increase with increase in atomic number.

C. The size of $2 \mathrm{p}_x$ orbital is less than the size of $3 \mathrm{p}_x$ orbital.

D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.

Choose the correct answer from the options given below :

The covalent radii of atoms $A$ and $B$ are $r_A$ and $r_B$, respectively. The covalent bond length and total length of AB molecule are respectively

Consider the following data for the reaction

$$ X_2(g)+Y_2(g) \rightleftharpoons 2 X Y(g) $$

at $600 \mathrm{~K}^{\circ}$. The $\Delta_{\mathrm{r}} \mathrm{G}^{\ominus}$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) for the reaction is :

$$ \begin{array}{|c|c|c|} \hline \text { Compound } & \Delta_f \mathrm{H}_{600 \mathrm{~K}}^{\ominus}\left(\mathrm{kJ} \mathrm{~mol}^{-1}\right) & \mathrm{S}^{\ominus}{ }_{600 \mathrm{~K}}\left(\mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) \\ \hline \mathrm{XY}(\mathrm{~g}) & 42 & 200 \\ \hline \mathrm{X}_2(\mathrm{~g}) & 8 & 140 \\ \hline \mathrm{Y}_2(\mathrm{~g}) & 80 & 250 \\ \hline \end{array} $$

The correct order of molar heat capacities measured at 298 K and 1 bar is :

The reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ was initiated with the amount ' a ' of $\mathrm{A}(\mathrm{g})$. At equilibrium it is found that the amount of $\mathrm{A}(\mathrm{g})$ remaining is ( $\mathrm{a}-x$ ) at a total pressure of p .

The equilibrium constant Kp of the reaction can be calculated from the expression :

One half cell in a voltaic cell is constructed by dipping silver rod in $\mathrm{AgNO}_3$ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of $\mathrm{ZnSO}_4$.

A voltage of 1.60 V is measured at 298 K for this cell. What is the concentration of $\mathrm{Ag}^{+}$ions used in terms of $\log x\left(x=\left[\mathrm{Ag}^{+}\right]\right)$?

$$ \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\ominus}=-0.76 \mathrm{~V}, \quad \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\ominus}=+0.80 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V} $$

Given below are two statements :

Statement I : The number of pairs among $\left[\mathrm{Al}_2 \mathrm{O}_3, \mathrm{Cr}_2 \mathrm{O}_3\right],\left[\mathrm{Cl}_2 \mathrm{O}_7, \mathrm{Mn}_2 \mathrm{O}_7\right],\left[\mathrm{Na}_2 \mathrm{O}, \mathrm{V}_2 \mathrm{O}_3\right]$ and $\left[\mathrm{CO}, \mathrm{N}_2 \mathrm{O}\right]$ that contain oxides of same nature (acidic, basic, neutral or amphoteric) is 4 .

Statement II : Among $\mathrm{Na}_2 \mathrm{O}, \mathrm{Al}_2 \mathrm{O}_3, \mathrm{CO}$ and $\mathrm{Cl}_2 \mathrm{O}_7$, the most basic and acidic oxides are $\mathrm{Na}_2 \mathrm{O}$ and $\mathrm{Cl}_2 \mathrm{O}_7$, respectively.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement I: Aluminium upon reaction with NaOH forms $\left[\mathrm{Al}(\mathrm{OH})_6\right]^{3-}$ ion.

Statement II : The geometry of $\mathrm{ICl}_4^{-}, \mathrm{ClO}_3^{-}$and $\mathrm{IBr}_2^{-}$is square planar, pyramidal and linear respectively.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.

Statement II : $\quad \mathrm{d}_{x y}=\mathrm{d}_{x z}=\mathrm{d}_{y z}<\mathrm{d}_{x^2-y^2}=\mathrm{d}_{z^2}$ and $\mathrm{d}_{x^2-y^2}=\mathrm{d}_{z^2}<\mathrm{d}_{x y}=\mathrm{d}_{x z}=\mathrm{d}_{y z}$ are the d-orbital splittings in $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ and $\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-}$ complex ions respectively.

In the light of the above statements, choose the correct answer from the options given below :

Identify the correct statements from the following

A. $\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ is the most stable complex among $\left[\mathrm{Fe}(\mathrm{OH})_6\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ and $\left[\mathrm{Fe}(\mathrm{SCN})_6\right]^{3-}$

B. The stability of $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ is greater than that of $\left[\mathrm{Cu}(\mathrm{en})_2\right]^{2+}$

C. The hybridization of Fe in $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ is $\mathrm{d}^2 \mathrm{sp}^3$

D. $\left[\mathrm{Fe}\left(\mathrm{NO}_2\right)_3 \mathrm{Cl}_3\right]^{3-}$ exhibits linkage isomerism

E. $ \mathrm{NO}_2^{-}$and $\mathrm{SCN}^{-}$ligands are NOT ambidentate ligands

Choose the correct answer from the options given below :

$$ \text { Match List - I with List - II. } $$

Choose the correct answer from the options given below :

IUPAC name of the some alkenes are given below.

Find out the correct stability order.

A. 2-Methylbut-2-ene

B. cis-But-2-ene

C. 2,3-Dimethylbut-2-ene

D. Prop-1-ene

Choose the correct answer from the options given below :

Identify the correct IUPAC name of hydrocarbon $(x)$ containing three primary carbon atoms and with molar mass $72 \mathrm{~g} \mathrm{~mol}^{-1}$.

$$ \text { Complete the following reaction sequence and give the name of major product ' } \mathrm{P} \text { '. } $$

Given below are two statements:

Statement I: The condensation reaction between $\mathrm{CH_3-CH=O}$ and
under optimum pH will produce

Statement II: The molecule, will generate $\mathrm{Ph-CH=O}$ in the presence of dilute acid.

In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements :

Statement I : Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will give benzylamine.

Statement II : Nitration of aniline with $\mathrm{HNO}_3 / \mathrm{H}_2 \mathrm{SO}_4$ at 288 K produces $m$-nitroaniline in higher amount than $o$-nitroaniline ( pH adjusted).

In the light of the above statements, choose the correct answer from the options given below :

Identify the incorrect statement about tertiary structure of proteins.

$$ \text { Given below are two statements : } $$

$$ \text { Statement I : } $$ and are two anomers of D-(+)-glucode.

Statement II : The open chain forms of D-glucose and D- fructose contain three similar chiral carbons at $\mathrm{C}_3, \mathrm{C}_4$ and $\mathrm{C}_5$.

In the light of the above statements, choose the correct answer from the options given below :

A paper dipped in a dil. $\mathrm{H}_2 \mathrm{SO}_4$ solution of ' $X$ ' upon treatment with $\mathrm{SO}_2$ gas turns into green. The compound ' $X$ ' is :

The total number of unpaired electrons present in the $d^3, d^4$ (low spin) $d^5$ (high spin), $\mathrm{d}^6$ (high spin) and $\mathrm{d}^7$ (low spin) octahedral complex systems is $\_\_\_\_$ .

RMgI when treated with ice cold water liberated a gas which occupied $1.4 \mathrm{dm}^3 / \mathrm{g}$ at STP. The gas produced is further reacted with iodine in presence of $\mathrm{HIO}_3$ to give compound $(\mathrm{X})$. Compound $(\mathrm{X})$ in presence of Na and dry ether produced compound $(\mathrm{Y})$. Molar mass of compound $(\mathrm{Y})$ is $\_\_\_\_$ $\mathrm{g} \mathrm{mol}^{-1}$. (Nearest integer)

20 g hemoglobin in a 1 L aqueous solution $(\mathrm{A})$ at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water.

The molar mass of hemoglobin is $\_\_\_\_$ $\mathrm{kg} \mathrm{mol}^{-1}$. (Nearest integer)

(Given : $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \mathrm{R}=8.3 \mathrm{kPa} \mathrm{dm} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$, density of solution $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )

At 298 K , the molar conductivity of $x \%(\mathrm{w} / \mathrm{w}) \mathrm{MX}$ solution (aqueous) is $123.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3} \mathrm{~S}$. The value of $x$ is $\_\_\_\_$ $\times 10^{-2}$.

(Given: cell constant $=1.3 \mathrm{~cm}^{-1}$; molar mass of MX is $75 \mathrm{~g} \mathrm{~mol}^{-1}$, density of aqueous solution of MX at 298 K is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$ )

For a reaction $\mathrm{A} \rightarrow \mathrm{P}$ at T K , the half life $\left(\mathrm{t}_{1 / 2}\right)$ is plotted as a function of initial concentration $[\mathrm{A}]_0$ of A as given below.

The value of $x$ in the given figure is $\_\_\_\_$ s (Nearest integer)

Let $\alpha, \beta$ be the roots of the equation $x^2-x+\mathrm{p}=0$ and $\gamma, \delta$ be the roots the equation $x^2-4 x+\mathrm{q}=0$; $p, q \in \mathbf{Z}$. If $\alpha, \beta, \gamma, \delta$ are in G.P., then $|p+q|$ equals :

Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2+4 z-(1+12 i)=0$.

Then $\left|z_1\right|^2+\left|z_2\right|^2$ is equal to :

If $f: \mathbf{N} \rightarrow \mathbf{Z}$ is defined by

$$ f(n)=\left|\begin{array}{ccc} n & -1 & -5 \\ -2 n^2 & 3(2 k+1) & 2 k+1 \\ -3 n^3 & 3 k(2 k+1) & 3 k(k+2)+1 \end{array}\right|, k \in N, $$

and $\sum\limits_{n=1}^k f(n)=98$, then $k$ is equal to :

Let M be a $3 \times 3$ matrix such that $\mathrm{M}\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right), \mathrm{M}\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)=\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)$ and $\mathrm{M}\left(\begin{array}{l}0 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{c}-1 \\ 1 \\ 1\end{array}\right)$. If $\mathrm{M}\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{c}1 \\ 7 \\ 11\end{array}\right)$, then $x+y+z$ equals :

If the sum of the first 10 terms of the series $\frac{1}{1+1^4 \times 4}+\frac{2}{1+2^4 \times 4}+\frac{3}{1+3^4 \times 4}+\frac{4}{1+4^4 \times 4}+\ldots \ldots$. is $\frac{m}{n}, \operatorname{gcd}(m, n)=1$, then $m+n$ is equal to :

Let $\mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_3, \ldots \ldots . ., \mathrm{A}_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $\mathrm{A}_{25}, \mathrm{~A}_{28}, \mathrm{~A}_{31}$ and $\mathrm{A}_{36}$ is equal to :

The coefficient of $x^2$ in the expansion of $\left(2 x^2+\frac{1}{x}\right)^{10}, x \neq 0$, is :

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If $A$ is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7 . Then the probability, that the team wins the tournament, is :

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :

A variable $X$ takes values $0,0,2,6,12,20, \ldots, n(n-1)$ with frequencies ${ }^n C_0,{ }^n C_1,{ }^n C_2,{ }^n C_3,{ }^n C_4,{ }^n C_5, \ldots,{ }^n C_n$, respectively. If the mean of this data is 60 , then its median is :

Let the point P be the vertex of the parabola $y=x^2-6 x+12$. If a line passing through the point P intersects the circle $x^2+y^2-2 x-4 y+3=0$ at the points R and S , then the maximum value of $(\mathrm{PR}+\mathrm{PS})^2$ is :

Let the directrix of the parabola $\mathrm{P}: y^2=8 x$, cut $x$-axis at the point A . Let $\mathrm{B}(\alpha, \beta), \alpha>1$, be a point on $P$ such that the slope of $A B$ is $3 / 5$. If $B C$ is a focal chord of $P$, then six times the area of $\triangle A B C$ is :

Let the eccentricity e of a hyperbola satisfy the equation $6 \mathrm{e}^2-11 \mathrm{e}+3=0$. If the foci of the hyperbola are $(3,5)$ and $(3,-4)$, then the length of its latus rectum is :

Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from $R(1,2,3)$. If $(\alpha, \beta, \gamma)$ is the centroid of $\Delta P Q R$, then $\alpha+\beta+\gamma$ is equal to :

If the distance of the point $(a, 2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is 4 , then the sum of all possible values of $a$ is equal to :

Let $O$ be the origin, $\overrightarrow{O P}=\vec{a}$ and $\overrightarrow{O Q}=\vec{b}$. If $R$ is the point on $\overrightarrow{O P}$ such that $\overrightarrow{O P}=5 \overrightarrow{O R}$, and $M$ is the point such that $\overrightarrow{O Q}=5 \overrightarrow{R M}$, then $\overrightarrow{P M}$ is equal to :

Let $f(x)=\lim \limits_{y \rightarrow 0} \frac{(1-\cos (x y)) \tan (x y)}{y^3}$. Then the number of solutions of the equation $f(x)=\sin x$, $x \in \mathbf{R}$ is :

Let $\left(2^{1-\mathrm{a}}+2^{1+\mathrm{a}}\right), f(\mathrm{a}),\left(3^{\mathrm{a}}+3^{-\mathrm{a}}\right)$ be in A.P. and $\alpha$ be the minimum value of $f(\mathrm{a})$. Then the value of the integral $\int\limits_{\log _e(\alpha-1)}^{\log _e(\alpha)} \frac{d x}{\left(e^{2 x}-e^{-2 x}\right)}$ is :

Let $f:[1, \infty) \rightarrow \mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(\mathrm{t}) \mathrm{dt}+(1-x)\left(\log _{\mathrm{e}} x-1\right)+\mathrm{e}$.

Then the value of $f(f(1))$ is :

Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f^{\prime \prime}(x)=g^{\prime \prime}(x)$ for all $x \in \mathbf{R}, f^{\prime}(1)=2 g^{\prime}(1)=4$ and $g(2)=3 f(2)=9$. Then $f(25)-g(25)$ is equal to :

Let $\mathrm{A}=\{1,4,7\}$ and $\mathrm{B}=\{2,3,8\}$. Then the number of elements, in the relation $R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in((A \times B) \times(A \times B)): a_1+b_2\right.$ divides $\left.a_2+b_1\right\}$ is $\_\_\_\_$ .

From the point $(-1,-1)$, two rays are sent making angles of $45^{\circ}$ with the line $x+y=0$. These rays get reflected from the mirror $x+2 y=1$. If the equations of the reflected rays are $\mathrm{a} x+\mathrm{b} y=9$ and $c x+d y=7, a, b, c, d \in \mathbf{Z}$, then the value of $a d+b c$ is $\_\_\_\_$ .

If $S=\left\{\theta \in[-\pi, \pi]: \cos \theta \cos \frac{5 \theta}{2}=\cos 7 \theta \cos \frac{7 \theta}{2}\right\}$, then $n(S)$ is equal to $\_\_\_\_$ .

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function such that $f(x)+3 f\left(\frac{\pi}{2}-x\right)=\sin x, x \in \mathbf{R}$. Let the maximum value of $f$ on $\mathbf{R}$ be $\alpha$. If the area of the region bounded by the curves $g(x)=x^2$ and $h(x)=\beta x^3, \beta>0$, is $\alpha^2$, then $30 \beta^3$ is equal to $\_\_\_\_$ .

Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1 / 2} \mathrm{~d} y=\left(\sec ^3 x-(\tan x)^{3 / 2} y\right) \mathrm{d} x, 0 < x <\frac{\pi}{2}, y\left(\frac{\pi}{4}\right)=\frac{6 \sqrt{2}}{5}$. If $y\left(\frac{\pi}{3}\right)=\frac{4}{5} \alpha$, then $\alpha^4$ equals

$\_\_\_\_$ .

$$ \text { Match List - I with List - II. } $$

where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units.

Choose the correct answer from the options given below :

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A , respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA , respectively. The estimated error in the resistance measurement is $\_\_\_\_$ $\Omega$

A mass of 1 kg is kept on a inclined plane with $30^{\circ}$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4 \mathrm{~m} / \mathrm{s}$. The work done by the frictional force in time 2 s is $\_\_\_\_$ J. (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40 s . The total distance travelled by the particle and the average velocity during this period are, respectively

$\_\_\_\_$.

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is $\_\_\_\_$ .

An object of uniform density rolls up the curved path with the initial velocity $v_{\mathrm{o}}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_0^2}{10 \mathrm{~g}}$ ( $\mathrm{g}=$ acceleration due to gravity), the object is a $\_\_\_\_$ .

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $\left(R_e\right)$. The increase in potential energy will be $\_\_\_\_$ .

( $g$ is acceleration due to gravity at the surface of earth)

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is $\_\_\_\_$ - ( $S$ is the surface tension of mercury).

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P T^3=$ constant. The coefficient of volume expansion of the gas is $\_\_\_\_$ .

$$ \text { Match List - I with List - II. } $$

Choose the correct answer from the options given below :

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(\mathrm{r})=B_{\mathrm{o}} \mathrm{e}^{-\lambda r} ; \lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

Under steady state condition the potential difference across the capacitor in the circuit is $\_\_\_\_$ V.

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}} \hat{x}+\frac{v_0}{\sqrt{2}} \hat{y}\right)$. There exists a uniform magnetic field $\vec{B}=B_0 \hat{z}$ and a space varying electric field $\vec{E}=E_{\mathrm{o}} \mathrm{e}^{-\lambda x} \hat{x}$ within the region $0 \leqslant x \leqslant L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is $\_\_\_\_$ .

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.

Reason (R) : There is no mass associated with the electromagnetic waves.

In the light of the above statements, choose the correct answer from the options given below :

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

An object $A B$ is placed 15 cm on the left of a convex lens $P$ of focal length 10 cm . Another convex lens $Q$ is now placed 15 cm right of lens $P$. If the focal length of lens $Q$ is 15 cm , the final image is $\_\_\_\_$ .

The maximum intensity in a Young's double slit experiment is $I_0$. Distance between the slits $(d)$ is $5 \lambda$, where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D=10 d$ is $\_\_\_\_$ .

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20 \%$. The de Broglie wavelength of electron in the medium is $\alpha \lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is $\_\_\_\_$ .

Assuming the experimental mass of ${ }_6^{12} C$ as $12 u$, the mass defect of ${ }_6^{12} C$ atom is $\_\_\_\_$ $\mathrm{MeV} / \mathrm{c}^2$.

(Mass of proton $=1.00727 \mathrm{u}$. mass of neutron $=1.00866 \mathrm{u}, 1 \mathrm{u}=931.5 \mathrm{MeV} / \mathrm{c}^2$ and c is the speed of the light in vacuum).

In a semiconductor $p$-n diode, the doping concentrations on $p$-side and $n$-side are $10^{15}$ atoms $/ \mathrm{cm}^3$ and $10^{18}$ atoms $/ \mathrm{cm}^3$, respectively. Which one of the following statements is true?

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6} \mathrm{~m}^3$. The elastic potential energy stored in the wire in stretched condition would be

$\_\_\_\_$ J.

(Given Young modulus of copper $=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

The heat extracted out of $x$ gram of water initially at $50^{\circ} \mathrm{C}$ to $\operatorname{cool}$ it down to $0^{\circ} \mathrm{C}$ is sufficient to evaporate $(1000-x)$ gram of water also initially at $50^{\circ} \mathrm{C}$. The value of $x$ (closest integer) is $\_\_\_\_$ .

(Take latent heat of water $2256 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}$, specific heat capacity of water $4200 \mathrm{~J} / \mathrm{kg} . \mathrm{K}$ )

A series LCR circuit with $R=20 \Omega, L=1.6 \mathrm{H}$ and $C=40 \mu \mathrm{~F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\_\_\_\_$ $\Omega$.

When an external resistance of $5 \Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5 \Omega$ resistor is replaced by a $2 \Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is $\_\_\_\_$ $\Omega$.

A circular loop of radius 20 cm and resistance $2 \Omega$ is placed in a time varying magnetic field $\vec{B}=\left(2 t^2+2 t+3\right) T$. At $t=0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t=3 \mathrm{~s}$ is $\frac{\alpha}{50} \mathrm{~A}$. The value of $\alpha$ is $\_\_\_\_$ . (Take $\pi=22 / 7$ )