MikaStars39/nano-eval huggingface dataset:
pH of a sample of KOH and another of $NaOH$ are 10 and 12 respectively. Their normalities are related as $N_{NaOH}=X N_{KOH^+}.$ What is the value of X?

Options:
A. $$10^{-2}$$
B. 3/5
C. 6/4
D. 5/6
E. 6/5
F. 5/3
G. 3/6
H. 4/5
I. $$10^{2}$$
J. 5/4
Answer: D
Barometers are made of two capillary tubes of radii $1.44\times 10^{-3}m$ and $7.2\times 10^{-4}$ respectively. If the height of a liquid in narrow tube is $0.2\ m$ more than the height of it in broad tube, then what will be the exact pressure difference? (Density of liquid $= 10^{3} kgm^{-3}$, surface tension $= 72\times 10^{-3}N/m$ and $g = 9.8 ms^{-2}$).

Options:
A. $$1840\ Nm^{-2}$$
B. $$1680\ Nm^{-2}$$
C. $$1600\ Nm^{-2}$$
D. $$1880\ Nm^{-2}$$
E. $$1770\ Nm^{-2}$$
F. $$1900\ Nm^{-2}$$
G. $$1750\ Nm^{-2}$$
H. $$1860\ Nm^{-2}$$
I. $$1650\ Nm^{-2}$$
J. $$1570\ Nm^{-2}$$
Answer: H
For an isobaric process. The ratio of $\triangle Q$ (amount of heat supplied) to the $\triangle W$ (work done by the gas) is $\left( \gamma=\dfrac{{C}_{p}}{{C}_{v}} \right )$

Options:
A. $$\dfrac{\gamma + 1}{\gamma}$$
B. $$\gamma$$
C. $$\dfrac{\gamma}{\gamma -1}$$
D. $$\dfrac{\gamma - 1}{\gamma}$$
E. $$\gamma -1$$
F. $$\dfrac{\gamma + 2}{\gamma}$$
G. $$\dfrac{\gamma - 3}{\gamma}$$
H. $$\dfrac{\gamma - 2}{\gamma}$$
I. $$\dfrac{\gamma}{\gamma +1}$$
J. $$\dfrac{\gamma - 1}{2}$$
Answer: E
For elementary gaseous phase reaction 
2NO + $O_2$ $\rightleftharpoons$ $2NO_2$ at $27^o$C 
Rate of the foroward reaction is given by rate = 2 $\times10^3 [NO]^2[O_2]$ and
Rate of reverse reaction at $27^o$C is given by rate = 20 $[NO_2]^2$ 
Hence equilibrium constant for reaction is :
$NO_2$ $\rightleftharpoons$ NO + $\frac 1 2  O_2$ at $27^o$C

Options:
A. 0.005
B. 10
C. 100
D. 0.001
E. 0.01
F. 0.1
G. 500
H. 1000
I. 0.0001
J. 50
Answer: C
For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression $w=-n R T I n \dfrac{V_{f}}{V_{l}} .$ A sample containing $1.0 \mathrm{mol}$ of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at $300 \mathrm{K}$ and at $600 \mathrm{K}$ respectively. Choose the correct option.
Note: Two or more options may be correct.

Options:
A. Work done at $600 \mathrm{K}$ is 20 times the work done at $300 \mathrm{K}$
B. Work done at $300 \mathrm{K}$ is twice the work done at $600 \mathrm{K}$
C. Work done at $300 \mathrm{K}$ is one-fifth the work done at $600 \mathrm{K}$
D. Work done at $600 \mathrm{K}$ is 10 times the work done at $300 \mathrm{K}$
E. Work done at 300 K is the same as the work done at 600 K
F. $\Delta U=0$ in both cases.
G. Work done at $600 \mathrm{K}$ is five times the work done at $300 \mathrm{K}$
H. Work done at $300 \mathrm{K}$ is 10 times the work done at $600 \mathrm{K}$
Answer: F
$2.5ml$ of  $\dfrac { 2 }{ 5 }\ M$ weak monoacidic base $({ K }_{ b }={ 1\times 10 }^{ -12 }$ at ${ 25 }^{ 0 }C)$ is titrated with $\dfrac{2}{5}M$ HCl in water at ${25}^{0}C$. The concentration of ${H}^{+}$ at equivalence point is:      (${K_w=10}^{-14}$ at ${25}^{0}C$)

Options:
A. $${2.9 \times 10^{-2}}M$$
B. $${3.2\times10}^{-7}M$$
C. $${2.3 \times 10^{-2}}M$$
D. $${3.2 \times 10^{-1}}M$$
E. $${3.2 \times10}^{-2}M$$
F. $${2.2 \times10}^{-2}M$$
G. $${3.7\times10}^{-13}M$$
H. $${2.5 \times 10^{-2}}M$$
I. $${2.7\times10}^{-2}M$$
Answer: I
To prepare a buffer solution of $pH = 4.04$, amount of Barium acetate to be added to $100 mL$ of $0.1$ M acetic acid solution [ $pK_0(CH_3COO^-) =9.26$] is:

Options:
A. $0.005$ mole
B. 0.0175 mole
C. $0.075$ mole
D. $0.1$ mole
E. 0.035
F. 0.0125 mole
G. $0.05$ mole
H. $0.025$ mole
I. 0.035 mole
Answer: H
Acid rain is an environmental concern all of the world. In assessing the acidity of rainfall, it is important to have an idea of the acidity of natural rainwater. Assuming that natural rain water (that is, rainwater uncontaminated with nitric acid or sulphuric acid) is in equilibrium with 3.6 x $10^{-4}$ atm $CO_2$.
What is the pH of natural rainwater? 
(Given : The Henry's law constant is 1.25 x $10^6$ Torr, $Ka_1 (H_2CO_3)$ = 4.3 x $10^{-7}$)

Options:
A. 5.70
B. None of these
C. 5.85
D. 5.60
E. 7.00
F. 6.75
G. 6.64
H. 6.68
I. 6.55
J. 6.74
Answer: G
A tiny ball of mass \( m \) is projected horizontally with velocity \( u = \sqrt{5} \, \text{m/s} \). The ball is attached to an inextensible string that passes over a smooth fixed peg \( P \). The ball moves in a circular path in a vertical plane under the influence of gravity (\( g = 10 \, \text{m/s}^2 \)). The initial length of the string from the ball to the peg is \( 1 \, \text{m} \), and after passing over the peg, the string extends an additional \( 1/2 \, \text{m} \) on the left side. Determine the maximum angle \( \theta \) that the ball swings to on the left-hand side from the vertical.

Options:
A. $$cos\, \theta =\dfrac{4}{6}$$
B. $$cos \, \theta =\dfrac{7}{6}$$
C. $$ cos\, \theta=\dfrac{5}{6}$$
D. $$cos \, \theta =\dfrac{1}{5}$$
E. $$cos \, \theta =\dfrac{3}{6}$$
F. $$ sin \theta =\dfrac{5}{6}$$
G. $$cos \, \theta =\dfrac{3}{5}$$
H. $$sin \, \theta =\dfrac{1}{6}$$
I. $$ cos \, \theta =\dfrac{1}{6}$$
J. $$cos \, \theta =\dfrac{2}{6}$$
Answer: I
$PC{l_5}$ decomposes as $PC{l_5} \Leftrightarrow PC{l_3} + C{l_2}$ if at equilibrium, total pressure is p and density of the gaseous mixture be $\rho$ at temperature T, then degree of dissociation $\left( \alpha  \right)$ would be

Options:
A. $$\alpha = \frac{{pM}}{{\rho RT}} - 1$$
B. \(\alpha = 1 - \frac{2pM}{\rho RT} \)
C. $$\alpha = \frac{{\rho RT}}{{PM}}$$
D. $$\alpha = 1 + \frac{\rho RT}{pM}$$
E. $$\alpha = 1 - \frac{{pM}}{{\rho RT}}$$
F. \(\alpha = 1 + \frac{\rho RT}{PM} \)
G. $$\alpha = 1 - \frac{\rho RT}{pM}$$
H. \(\alpha = 1 - \frac{\rho RT}{2pM} \)
I. \(\alpha = 1 + \frac{pM}{\rho RT}\)
J. $$\alpha = 1 - \frac{{\rho RT}}{{PM}}$$
Answer: A
A system consists of two blocks, \( A \) with mass \( m \) and \( B \) with mass \( 2m \), connected by a spring with spring constant \( k \). The spring is unstretched at the beginning. The blocks are initially released from a height \( h \). After a perfectly inelastic collision (\( e = 0 \)) with the ground, block \( B \) must be lifted off the ground. Determine the minimum height \( h \) from which the system must be released for this condition to be satisfied.

Options:
A. $$\dfrac{3mg}{2k}$$
B. $$\dfrac{2mg}{k}$$
C. $$\dfrac{7mg}{k}$$
D. $$\dfrac{5mg}{k}$$
E. $$\dfrac{mg}{2k}$$
F. $$\dfrac{5mg}{2k}$$
G. $$\dfrac{4mg}{k}$$
H. $$\dfrac{mg}{4k}$$
I. $$\dfrac{6mg}{k}$$
J. $$\dfrac{3mg}{k}$$
Answer: G
A neutral water molecule is placed in electic field $E= 1.25 \times { 10 }^{ 4 } N/C.$ The work done to rotate it by ${ 180 }^{ \circ   }\ is \ 2.5 \times { 10 }^{ -25 }J.$ Find aproximate separation of center of charges.

Options:
A. $$0.725 \times { 10 }^{ -10 }m$$
B. $$0.655 \times { 10 }^{ -10 }m$$
C. $$0.675 \times { 10 }^{ -9 }m$$
D. $$0.75\times { 10 }^{ -10}m$$
E. $$0.675 \times { 10 }^{ -10 }m$$
F. $$0.625\times { 10 }^{ -9 }m$$
G. $$0.65\times { 10 }^{ -10 }m$$
H. $$0.700 \times { 10 }^{ -10 }m$$
I. $$0.625 \times { 10 }^{ -10 }m$$
Answer: F
A sphere of mass m and radius r rolls without slipping over a tunnel of width $ d= \frac {8r}{5} $ (the sphere rolls perpendicular to the plane of the page). The velocity of centre of mass of sphere is v directed into the plane of the page. The maximum speed of a point on the sphere is

Options:
A. $$\frac{5v}{3}$$
B. $$\frac{7v}{3}$$
C. $$\frac{9v}{4}$$
D. $$ \frac {6v}{3} $$
E. $$ \frac {4v}{3} $$
F. $$\frac{7v}{4}$$
G. $$ \frac {3v}{2} $$
H. $$\frac{9v}{3}$$
I. $$ \frac {8v}{3} $$
J. $$\frac{5v}{2}$$
Answer: I
A one litre solution is prepared by dissolving some solid lead-nitrate in water. The solution was found to boil at $100.15^{\circ}C$. To the resulting solution $0.2\:mole\:NaCl$ was added. The resulting solution was found to freeze at $-0.83^{\circ}C$. Determine solubility product of $PbCl_2$. Given $K_b\,=\,0.5$ and $K_f\,=\,1.86$. Assume molality to be equal to molarity in all case.

Options:
A. $$\;1.2 \times10^{-5}$$
B. $$\;1.7 \times10^{-5}$$
C. $$\;9.0\times10^{-5}$$
D. $$\;1.9 \times10^{-5}$$
E. $$\;1.5\times10^{-5}$$
F. $$\;1.6 \times10^{-5}$$
G. $$\;1.4 \times10^{-5}$$
H. $$\;3\times10^{-5}$$
I. $$\;2.3\times10^{-5}$$
J. $$\;1.8 \times10^{-5}$$
Answer: E
Select the correct statement(s)

Options:
A. Bromothymol blue (6.0 to 7.6) is a suitable indicator for titration of $0.1\space M\space NH_4OH\space (pK_b = 4.74)$ and $0.1\space M\space HCl$
B. Thymol blue (1.2 to 2.8) is a very good indicator for tittation of $100\space mL$ of $0.1\space M\space NH_4OH\space (pK_b = 4.74)$ and $0.1\space M\space HCl$
C. Methyl orange (3.1 to 4.4) is a good indicator for titration of $HCl$ and $NaOH$
D. Methyl orange (3.1 to 4.4) is a suitable indicator for titration of weak acid and strong base
E. Methyl orange (3.1 to 4.4) is a very good indicator for titration of $100\space mL$ of $0.1\space M\space NH_4OH\space (pK_b = 4.74)$ and $0.1\space M\space HCl$
F. Thymol blue (1.2 to 2.8) is a good indicator for titration of $HCl$ and $NaOH$
G. Bromothymol blue (6.0 to 7.6) is a good indicator for titration of $HCl$ and $NaOH$
Answer: G
Two moles of a monoatomic gas follows the process $PV^{\frac{4}{3}}$= const
Which of the following statement is correct about this process?

Options:
A. It is a process in which $\Delta Q=-\frac{1}{5} \Delta U$
B. It is a process in which $dQ= 2dU$ (always)
C. It is a process in which $dQ= dU$ (always)
D. It is a process in which $dQ= \frac{1}{2}dU$ (always)
E. It is a process in which $dQ= \frac{5}{2}dU$ (always)
F. It is a process in which $dQ= \frac{3}{2}dU$ (always)
G. It is a process in which $dQ= \frac{2}{3}dU$ (always)
H. It is an adiabatic process
I. It is a process in which $dQ= -dU$ (always)
J. It is a process in which $dQ= 3dU$ (always)
Answer: C
How much ethyl alcohol much be added to $1.0 L$ of water so that solution will not freeze at $-4^{\circ }F?(K_f = 1.86^{\circ }C/m)$

Options:
A. $$495.0 g$$
B. $$ > 494.5 g$$
C. $$496.0 g$$
D. $$< 20 g$$
E. $$< 493.5 g$$
F. $$496.5 g$$
G. $$493.5 g$$
H. $$< 10.75 g$$
I. $$495.5 g$$
J. $$< 494.5 g$$
Answer: B
$K_{sp} (AgCl) = 2 \times 10^{-10}, \, K_{sp} (AgCNS) = 2.5 \times 10^{-11}$. When water is saturated with both solids, then :

Options:
A. None of these
B. Solubility of $AgCl $ is $1.7 \times 10^{-5}$
C. Solubility of $AgCNS$ is $1.67 \times 10^{-5}M$
D. Solubility of $AgCl $ is $1.3 \times 10^{-5}$
E. Solubility of $AgCl $ is $1.6 \times 10^{-5}$
F. Solubility of $AgCl $ is $1.5 \times 10^{-5}$
G. Solubility of $AgCl$ is $1.42 \times 10^{-5}$
H. Silver ion conc. = $15 \times 10^{-6} M$
I. Solubility of $AgCl$ is $1.4 \times 10^{-5}$
J. Solubility of $AgCl$ is $1.45 \times 10^{-5}$
Answer: F
A wire in the form of a square of side a caries a current i. Then the magnetic induction at the centre of the square wire is( Magnetic permeability of free space=${ \mu  }_{ \circ  }$)

Options:
A. $$\cfrac { \mu _ { 0 } i \sqrt { 2 } } { 2 \pi a }$$
B. $$\cfrac { \mu _ { 0 } i \sqrt { 2 } } { \pi a }$$
C. $$\cfrac { 2 \mu _ { 0 } i \sqrt { 2 } } { 3 \pi a }$$
D. $$\cfrac { 2 \sqrt { 2 } \mu _ { 0 } t } { \pi a }$$
E. $$\cfrac { 2 \mu _ { 0 } i } { \pi a }$$
F. $$\cfrac { 2 \mu _ { 0 } i \sqrt { 2 } } { 4 \pi a }$$
G. $$\cfrac { 2 \mu _ { 0 } i \sqrt { 3 } } { \pi a }$$
H. $$\cfrac { \mu _ { 0 } t } { \sqrt { 2 } \pi \mathrm { a } }$$
I. None of these
J. $$\cfrac { 2 \mu _ { 0 } i \sqrt { 2 } } { \pi a }$$
Answer: J
The oxidation potential of ${H}_{2}$ electrode ${H}_{2}/{H}_{3}{O}^{+}(aq)$ will be more than zero, if:(keeping all other terms unity)

Options:
A. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =0.1M$$
B. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =0.5M$$
C. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =0.8M$$
D. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =2M$$
E. pressure ${H}_2=2$ bar
F. $$${E}_{ox}$ can never be +ve$$
G. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =1.2M$$
H. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =1.5M$$
I. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =1M$$
J. $$\left[ { H }_{ 3 }{ O }^{ + } \right] =1.1M$$
Answer: I
If a hollow sphere (mass=$m$ and radius=$r$) is filled with non viscous fluid and is allowed to rolled on horizontal plane with velocity $v$,then

Options:
A. Angular momentum about a fixed point on ground is $\dfrac{13mvr}{3}$
B. Angular momentum about a fixed point on ground is $\dfrac{8mvr}{3}$
C. Angular momentum about a fixed point on ground is $\dfrac{11mvr}{3}$
D. Angular momentum about a fixed point on ground is $\dfrac{12mvr}{3}$
E. Kinetic energy of sphere is $\dfrac{5mv^{2}}{3}$
F. Angular momentum about a fixed point on ground is $\dfrac{7mvr}{3}$
G. Angular momentum about a fixed point on ground is $\dfrac{10mvr}{3}$
H. Kinetic energy of sphere is $\dfrac{5mv^{2}}{6}$
I. none of the above
J. $$Angular momentum about a fixed point on ground is \dfrac{9mvr}{3}$$
Answer: B
Angular velocity is varying to $  w=a t $,find the angular displacement of particle from $  t_{1} $ to $  t_{2} $ seconds, if $ t_{2}=2 t_{1} $

Options:
A. lpha t_{1}^{2}
B. $$\frac{6}{2} \alpha t_{1}^{2}$$
C. $$\frac{7}{2} \alpha t_{1}^{2}$$
D. 2$ lpha t_{1}^{2} $
E. $$\frac{3}{2} \alpha t_{1}^{2}$$
F. \( \frac{5}{2} \alpha t_{1}^{2} \)
G. $$\frac{9}{2} \alpha t_{1}^{2}$$
H. frac{3}{2}lpha t_{1}^{2}
I. 3$ a t_{1}^{2} $
J. $$\frac{4}{2} \alpha t_{1}^{2}$$
Answer: A
In a compound of molecular formula $A_mB_n$:

Options:
A. $n \times moles$ of $A = n \times moles$ of $B = (m - n) \times moles$ of $A_mB_n$
B. $n \times moles$ of $A = m \times moles$ of $B = (m - n) \times moles$ of $A_mB_n$
C. number of moles of A, B and $A_mB_n$ are same
D. $n \times moles$ of $A = n \times moles$ of $B = (n - m) \times moles$ of $A_mB_n$
E. $m \times moles$ of $A = n \times moles$ of $B = (n - m) \times moles$ of $A_mB_n$
F. $n \times moles$ of $A = m \times moles$ of $B = (m+ n) \times moles$ of $A_mB_n$
G. $m \times moles$ of $A = m \times moles$ of $B = (m+ n) \times moles$ of $A_mB_n$
H. number of equivalents of A, B and $A_mB_n$ are same
Answer: H
As shown in figure a horizontal platform with a mass $m$ placed on it is executing SHM along y-axis. If the amplitude of oscillation is $2.5cm$, the minimum period of the motion for the mass not to be detached from the platform is 
($g=10m/{sec}^{2}={\pi}^{2}$)

Options:
A. $$\cfrac{2}{\sqrt{10}}s$$
B. $$\cfrac{1}{\sqrt{10}}s$$
C. $$\cfrac{10}{\pi}s$$
D. $$\cfrac{\pi}{\sqrt{10}}s$$
E. $$\cfrac{5}{\sqrt{10}}s$$
F. $$\cfrac{\pi}{10\sqrt{10}}s$$
G. $$\cfrac{\pi}{10}s$$
H. $$\cfrac{\pi}{5\sqrt{10}}s$$
I. $$\cfrac{10}{\sqrt{10}}s$$
J. $$\cfrac{\pi}{2\sqrt{10}}s$$
Answer: B
Using the following thermochemical Data .
$$ C(S)+O_{ 2 }(g)\rightarrow CO_{ 2 }(g),\quad \Delta H=94.0\quad Kcal $$
$$ H_{ 2 }(g)+1/2O_{ 2 }(g)\rightarrow H_{ 2 }O(\ell ),\Delta H=68.0Kcal $$
$$ CH_{ 3 }COOH(\ell )+2O_{ 2 }(g)\rightarrow 2CO_{ 2 }(g)+2H_{ 2 }O(\ell ),\Delta H $$
$$ = -210.0 Kcal $$
The heat of formation of acetic acid is :-

Options:
A. +118.0 K cal
B. -116.0 K cal
C. +116.0 K cal
D. 118.0 K cal
E. 114.0 K cal
F. 116.0 K cal
G. -114.0 K cal
H. +112.0 K cal
I. -118.0 K cal
J. +114.0 K cal
Answer: F
Solubility of $Ag_2 CrO_4$ ($K_{sp}$ = 4 $\times 10^{-13}$) im 0.1 M $K_2 CrO_4$ solution will be :-

Options:
A. $$2 \times 10^{-6} M$$
B. 5 $\times 10^{-7}$ M
C. $10^{-6}$ M
D. $$2 \times 10^{-8} M$$
E. $10^{-5}$ M
F. 4 $\times 10^{-6}$ M
G. $$5 \times 10^{-6} M$$
H. $$3 \times 10^{-7} M$$
I. $$3 \times 10^{-6} M$$
J. $$2 \times 10^{-7} M$$
Answer: E
Find the minimum load resistance which can be used for the zener diode as shown in figure. Given, $V_Z=10 V, R_Z=0 \Omega,  R=450 \Omega, I_Z(min)=2 mA $ and $I_Z(max)=60 mA$

Options:
A. $$333.3 \Omega$$
B. $$318.0 \Omega$$
C. $$0 \Omega$$
D. $$322.5 \Omega$$
E. $$319.5 \Omega$$
F. $$321.5 \Omega$$
G. $$31.95 \Omega$$
H. $$320.5 \Omega$$
I. $$318.5 \Omega$$
Answer: E
A wagon filled with sand has a hole so that sand leaks through the bottom at a constant rate $\lambda$. An external force $ec{F}$ acts on the wagon in the direction of motion. Assuming instantaneous velocity of the wagon to be $ec{v}$ and initial mass of system to be $m_0$, the force equation governing the motion of the wagon is

Options:
A. $$\vec{F}\, =\, (m_0-\lambda t) \frac{d\vec{v}}{dt} + \lambda v^2$$
B. $$\vec{F}\, =\, (m_0-\lambda t) \frac{d\vec{v}}{dt}\, +\, 2\lambda\, \vec{v}$$
C. $$ \mathbf{F} = m_0 \frac{d \mathbf{v}}{dt} + \lambda \mathbf{v} $$
D. $$\mathbf{F} = m_0 \frac{d \mathbf{v}}{dt} - \lambda \mathbf{v}$$
E. $$\vec{F}\, =\, (m_0-\lambda t) \frac{d\vec{v}}{dt}\, +\, \lambda\, t \vec{v}$$
F. $$ec{F}\, =\, (m_0-\lambda t) \displaystyle \frac {dec{v}}{dt}\,+\, \lambda\, ec{v}$$
G. $$\vec{F} = (m_0 - \lambda t) \frac{d\vec{v}}{dt} + \lambda v$$
H. $$\vec{F}\, =\, (m_0-\lambda t) \displaystyle \frac {d\vec{v}}{dt}\, -\, \lambda\, \vec{v}$$
I. $$\vec{F}\, =\, (m_0-\lambda t) \frac{d\vec{v}}{dt}\, +\, \lambda\, \vec{v}\, -\, \lambda\, t$$
J. $$\mathbf{F} = (m_0 - \lambda t) \frac{d \mathbf{v}}{dt}$$
Answer: J
The table below shows recorded concentration data for the following chemical reaction:$Rate = k[Fe(NO_{3})_{3}]^{x} [NaOH]^{y}$Use the data to determine the exponents $x$ and $y$ in the rate law:$Rate = k[Fe(NO_{3})_{3}]^{x} [NaOH]^{y}$$[Fe(NO_{3})_{3}]M$$[NaOH]M$Rate M/s$0.100$$0.250$$1.3\times 10^{-6}$$0.100$$0.500$$5.2\times 10^{-6}$$0.200$$0.250$$2.6\times 10^{-6}$$0.300$$0.500$$3.9\times 10^{-6}$

Options:
A. $$x = 2, y = 3$$
B. $$x = 2, y = 4$$
C. $$x = 1, y = 1$$
D. $$x = 1, y = 2$$
E. $$x = 2, y = 1$$
F. $$x = 2, y = 2$$
G. $$\(x = 1, y = 4\)$$
H. $$x = 1, y = 3$$
I. $$x = 1, y = 0$$
Answer: C
For the decomposition of the compound represented as
${NH}_{2}COO{NH}_{4}(s)\rightleftharpoons 2{NH}_{3}(g)+{CO}_{2}(g)$ the ${K}_{p}=2.9\times {10}^{-5}{atm}^{3}$
IF the reaction is started with $1$ mol of the compound, the total pressure at equilibrium would be:

Options:
A. $$3.88 \times 10^{-2}atm$$
B. $$7.66\times {10}^{-2}atm$$
C. $$38.8\times {10}^{-2}atm$$
D. $$2.92 \times 10^{-2}atm$$
E. $$5.82\times {10}^{-2}atm$$
F. $$2.94 \times 10^{-2}atm$$
G. $$3.88 \times 10^{-3}atm$$
H. $$3.88 \times {10}^{-3}atm$$
I. $$5.88 \times 10^{-2}atm$$
J. $$1.94\times {10}^{-2}atm$$
Answer: J
A voltaic cell consist of an electrode of a solid metal 'A' immersed in  a $0.1 \ M \ ANO_3$ solution and an electrode of a solid metal 'B' immersed in a $0.1 \ M \ B(NO_3)_2$ solution. A porous barrier separates the two half cells. Current flows from electrode 'A' to 'B' in the outer circuit. Both electrodes are participating electrodes. 
Given: $E^o_{A^+/A}=0.4 \ V; \ E^o_{cell}=0.7 \ V$
What will be the cell emf if in the above cell electrode 'A' is replaced by hydrogen electrode having $pH=1?$ $\left [\cfrac {2.303RT}F=0.06 \ V \right]$, $(P_{H_2}=1 \ bar)$

Options:
A. $$0.36 \ V$$
B. $$0.33 \ V$$
C. $$0.24 \ V$$
D. $$0.31 \ V$$
E. $$-0.30 \ V$$
F. $$0.39 \ V$$
G. $$None \ of \ these$$
H. $$0.27 \ V$$
I. $$0.34 \ V$$
J. $$0.30 \ V$$
Answer: J
In a 0.2 molal aqueous solution of a weak add FIX the degree of ionisation is 0.25. The freezing point of the solution will be nearest to $(K_f = 1.86 K kg mol^{-1}$

Options:
A. $$ -0.465C$$
B. $$0.475C$$
C. $$-0.45C$$
D. $$0.485C$$
E. $$-0.26C$$
F. $$0.465C$$
G. $$0.48C$$
H. $$0.455C$$
I. $$0.470C$$
J. $$-0.48C$$
Answer: F
For hydrogen, $c_{p}=3400$ cal/kg.K, $c_{v}=2400$ cal/Kg/K$, R=8400 J/k mole. K. If the molecular weight of $H_{2}$ is 2, the value of J is

Options:
A. $$4.0 J/cal$$
B. $$4.12 J/cal$$
C. $$4.2 J/cal$$
D. $$4.3 J/cal$$
E. $$4.13 J/cal$$
F. $$4.17 J/cal$$
G. $$4.25 J/cal$$
H. $$4.15 J/cal$$
I. $$4.1 J/cal$$
J. $$4.18 J/cal$$
Answer: I
Find to what height $h$ the centre of gravity of this system will rise if the initial compression of the spring $\displaystyle\Delta l=\frac{7mg}{\kappa}$.

Options:
A. $$\dfrac{10mg}{\kappa}$$
B. $$\dfrac{9mg}{\kappa}$$
C. $$\dfrac{6mg}{\kappa}$$
D. $$\dfrac{7mg}{\kappa}$$
E. $$\dfrac{3mg}{\kappa}$$
F. $$\dfrac{2mg}{\kappa}$$
G. $$\dfrac{5mg}{\kappa}$$
H. $$\dfrac{4mg}{\kappa}$$
I. $$\dfrac{mg}{\kappa}$$
J. $$\dfrac{8mg}{\kappa}$$
Answer: J
In an organ pipe whose one end is at $X=0$, the pressure is expressed by
$\displaystyle p=p_{0}\cos{ \dfrac {3 \pi X}{2}} \sin { 300 \pi t}$ where $X$ is in meter and $t$ in sec. The organ pipe can be

Options:
A. open at both ends, length $ = 1\ m$
B. closed at both ends, length $ = 0.5\ m$
C. closed at one end, open at another with length $0.5\ m$
D. closed at both ends, length $ = 2\ m$
E. closed at both ends, length $ = 1\ m$
F. closed at one end, open at another with length $\displaystyle= \dfrac {2}{3}\ m$
G. closed at one end, open at another with length $\displaystyle= \dfrac {5}{3}\ m$
H. closed at both ends, length $ = 3\ m$
I. closed at one end, open at another with length $\displaystyle= \dfrac {4}{3}\ m$
J. closed at one end, open at another with length $\displaystyle= \dfrac{8}{3}\ m$
Answer: D
Equilibrium concentration of $B$ if initial moles of $'A','B'$ and $'C'$ are $8,16$ and $16$ respectively in $1$ litre container is Given :$A(g)+3B(g)\rightarrowC(g)$   ; $K_C=10^9M^{-3}$

Options:
A. $$\left(\dfrac{12}{27}\right) \times 10^{-3}M$$
B. $$\left(\dfrac{2}{27}\right) \times 10^{-3}M$$
C. $$\left(\dfrac{6}{27}\right) \times 10^{-3}M$$
D. $$2\times 10^{-3}M$$
E. \left(\dfrac{10}{27}\right) \times 10^{-3}M
F. $$\left(\dfrac{8}{27}\right) \times 10^{-3}M$$
G. $$\left(\dfrac{4}{27}\right) \times 10^{-3}M$$
H. $$\left(\dfrac{16}{27}\right) \times 10^{-3}M$$
I. $$2\times 10^3 M$$
J. $$\left(\dfrac{14}{27}\right) \times 10^{-3}M$$
Answer: F
The total number of configurational isomers of the given compound are: 
$$\mathrm { CH } _ { 3 } - \mathrm { CH } = \mathrm { CHCHOHCHOHCH } _ { 3 }$$

Options:
A. $$2$$
B. $$8$$
C. $$16$$
D. $$4$$
E. $$3$$
F. $$10$$
G. $$18$$
H. $$6$$
I. $$12$$
J. $$14$$
Answer: A
A drop of water of mass m and density p is placed between two well cleaned glass plates, the distance between which is d. What is the force of attraction between the plates? ( T= surface Tension)

Options:
A. $$\frac{Tm}{p d^2}$$
B. $$\frac{Tm}{4 p d^2}$$
C. $$\frac{2Tm}{ p d^2}$$
D. $$\frac{Tm}{5 p d^2}$$
E. $$\frac{Tm}{3 p d^2}$$
F. $$\frac{Tm}{7 p d^2}$$
G. $$\frac{Tm}{2 p d^2}$$
H. $$\frac{4Tm}{ p d^2}$$
I. $$\frac{3Tm}{2 p d^2}$$
J. $$\frac{Tm}{6 p d^2}$$
Answer: G
At a certain temperature,the following reactions have the equilibrium constant as shown below:
$$\begin{array}{l}S\left( s \right) + {O_2}S \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over{\smash{\leftarrow}phantom{_{box to.5ex{ss}}}}$}} {O_2}\left( g \right);{K_c} = 5 \times {10^{52}}\2S\left( s \right) + 3{O_2}\left( g \right) \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over{\smash{\leftarrow}phantom{_{box to.5ex{ss}}}}$}} 2S{O_3}\left( g \right);{K_c} = {10^{29}}\end{array}$$
What is the equilibrium constant ${K_c}$ for the reaction at the same temperature ?
$2S\left( s \right) + {O_2} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over
{\smash{\leftarrow}phantom{_{box to.5ex{ss}}}}$}} 2S{O_3}\left( g \right)$

Options:
A. $$5 \times {10^{29}}$$
B. $$3 \times 10^{25}$$
C. $$4 \times {10^{23}}$$
D. $$None of these$$
E. $$5 \times 10^{31}$$
F. $$3 \times 10^{28}$$
G. $$4 \times {10^{-77}}$$
H. $$3 \times 10^{27}$$
I. $$2 \times 10^{25}$$
J. $$2.5 \times {10^{76}}$$
Answer: C
EMF of the cell: $ Cd(s)|CdCl_{2}.5H_{2}O $ (sat.)$ |AgCl(s)|Ag(s)$  is $+0.70 V $ at $0^{\circ}C $ and +0.60 V at $ 50^{\circ}C. $ If $ \Delta H^{\circ} $ are $ \triangle S^{\circ} $ are temperature independent, then the correct information(s) regarding the cell reaction is/are:

Options:
A. $$\Delta H^{\circ} = -221.177\,kJ$$
B. $$\Delta H^{\circ} = -224.178\,kJ$$
C. $$\Delta H^{\circ} = -222.178\,kJ$$
D. $$\Delta H^{\circ} = -219.178\,kJ$$
E. $$$\Delta G^{\circ} = -115.8\,kJ $ at $ 50^{\circ}C $$$
F. $$\Delta H^{\circ} = -220.178\,kJ$$
G. $$ \Delta H^{\circ} = -221.178\,kJ $$
H. $$ \Delta S^{\circ} = -386J/K $$
I. $$$\Delta G^{\circ} = -135.1\,KJ $ at $ 0^{\circ}C $$$
J. $$\Delta H^{\circ} = -223.178\,kJ$$
Answer: G
In the potentiometer arrangement shown, the driving cell D has emf E and internal resistance r. The cell C, whose emf is to be measured, has emf E/2 and internal resistance 2r. The potentiometer wire is 100 cm long. If balance is obtained, the length $AJ=l$

Options:
A. balance will be obtained only if resistance of AB is < r
B. balance will be obtained only if resistance of AB is < 1.5r
C. balance will be obtained only if resistance of AB is < 2r
D. balance will be obtained only if resistance of AB is < 1.8r
E. $$l=50 cm$$
F. l < 50 cm
G. balance cannot be obtained
H. l > 50 cm
I. balance will be obtained only if resistance of AB is > 2r
J. balance will be obtained only if resistance of AB is > r
Answer: J
The equivalent weight of $Cr_2(SO_4)_3 \,\, [mot wt. = M]$ in the following reaction is
$$Cr_2(SO_4)_3 + H_2O_2 + NaOH \rightarrow Na_2CrO_4 + Na_2SO_4 + H_2O$$

Options:
A. $$\displaystyle \frac{M}{4}$$
B. $$\displaystyle \frac{M}{3}$$
C. $$\displaystyle \frac{M}{2}$$
D. $$\frac{M}{5}$$
E. $$\displaystyle \frac{M}{10}$$
F. $$\displaystyle \frac{M}{7}$$
G. $$\displaystyle \frac{M}{6}$$
H. $$\displaystyle \frac{M}{9}$$
I. $$\frac{M}{8}$$
J. M
Answer: B
If volume occupied by $CO_{2}$ molecules is negligible, then what will be the pressure $\left (\dfrac {P}{5.277}\right )$ exerted by one mole of $CO_{2}$ gas at $300\ K? (a = 3.592\ atm\ L^{2} mol^{-2})$.

Options:
A. $$9$$
B. $$7.25$$
C. $$7$$
D. $$7.75$$
E. $$6.5$$
F. $$3$$
G. $$7.5$$
H. $$8.25$$
I. $$8$$
J. $$8.5$$
Answer: I
A particle of mass $m$ and charge $q$ starts moving from rest along a straight line in an electric field $E=E_0-ax$ where $a$ is a positive constant and $x$ is the distance from starting point. Find the distance travelled by the article till the moment it came to instantaneous rest

Options:
A. $$\frac {E_0}{q}$$
B. $$\frac {2E_0}{a}$$
C. $$\frac {E_0q}{m}$$
D. $$\frac{E_0}{6a}$$
E. $$\frac{E_0}{2a}$$
F. $$\frac{E_0}{3a}$$
G. $$\frac{E_0}{5a}$$
H. $$\frac{3E_0}{2a}$$
I. $$\frac{E_0}{4a}$$
J. $$\frac {E_0}{a}$$
Answer: J
During the kinetic study of the reaction, 2A+B$\longrightarrow $C+D, following results were obtained
$$Run\quad \quad [A]/mol\quad { L }^{ -1 }\quad \quad [B]/mol\quad { L }^{ -1 }\quad \quad Initial\quad rate\quad of\quad formation\quad of\quad D/mol\quad { L }^{ -1 }{ min }^{ -1 }\ I.\quad \quad \quad \quad 0.1\quad \quad \quad \quad \quad \quad \quad \quad 0.1\quad \quad \quad \quad \quad \quad \quad 6.0\times { 10 }^{ -3 }\ II\quad \quad \quad \quad 0.3\quad \quad \quad \quad \quad \quad \quad \quad 0.2\quad \quad \quad \quad \quad \quad \quad 7.2\times { 10 }^{ -2 }\ III\quad \quad \quad 0.3\quad \quad \quad \quad \quad \quad \quad \quad 0.4\quad \quad \quad \quad \quad \quad \quad 2.88\times { 10 }^{ -1 }\ IV\quad \quad \quad 0.4\quad \quad \quad \quad \quad \quad \quad \quad 0.1\quad \quad \quad \quad \quad \quad \quad 2.44\times { 10 }^{ -2 }\ Based\quad on\quad the\quad above\quad data\quad which\quad one\quad of\quad the\quad following\quad is\quad correct\quad ?\ \quad \ \ $$

Options:
A. $$Rate=K[A][B{ ] }^{ 2 }$$
B. $$Rate=K[A][B]$$
C. $$Rate=K{[A]}[B]^{2}$$
D. $$Rate=K[A][B]^{2}$$
E. $$Rate=K{ [A] }^{ 2 }[B{ ] }^{ 3 }$$
F. $$Rate=K{ [A] }^{ 2 }[B]$$
G. $$Rate=K[A][B]^{3}$$
H. $$Rate=K[A]^{2}[B]^{2}$$
I. $$Rate=K[{ A }]^{ 2 }[B{ ] }^{ 2 }$$
J. $$Rate=K{ [A] }^{ 3 }[B]$$
Answer: F
Two blocks of mass $3kg$ and $6kg$ respectively are placed smooth horizontal surface. They are connected by a light spring of force constant $K=100N/m$. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be

Options:
A. $$40cm$$
B. $$25cm$$
C. $$32cm$$
D. $$33cm$$
E. $$15cm$$
F. $$20cm$$
G. $$30cm$$
H. $$35cm$$
I. $$50cm$$
J. $$45cm$$
Answer: G
The structures of two compounds $(I)$ and $(II)$ are given below. Which statement is correct ?$F_2C = C =  CF_2\ (I)$ and $F_2C = C = C = CF_2\ (II)$

Options:
A. Reductive ozonolysis of both gave different products.
B. Reductive and oxidative ozonolysis of $(I)$ gave the same product but of $(II)$ gave different products.
C. Reductive ozonolysis of both gave the same product.
D. Reductive and oxidative ozonolysis of both gave different products.
E. Reductive and oxidative ozonolysis of $(I)$ gave the same product, but of $(II)$ gave different products.
F. Reductive ozonolysis of $(I)$ gave a different product than $(II)$
G. Reductive ozonolysis of $(I)$ gave a different product than $(II)$.
H. Reductive and oxidative ozonolysis of $(I)$ gave the same product, but of $(II)$ gave a different product.
I. Reductive and oxidative ozonolysis of both gave the same product.
J. Reductive and oxidative ozonolysis of $(I)$ gave different products, but of $(II)$ gave the same product.
Answer: C
If $E_0 = 200$ volt, $R = 25 $ ohm, $L = 0.1 \,H$ and $C = 10^{- 5} F$ and the frequency is variable, then the current at $f = 0$ and $f = \infty $ will be respectively.

Options:
A. $0A$ and $0A$
B. 0A and 8A
C. $8A$ and $8A$
D. $8A$ and $4A$
E. 4A and 0A
F. $4A$ and $4A$
G. 8A and 0A
H. $0A$ and $4A$
Answer: A
The pressure exerted by 12 gm of an ideal gas at temperature $t^oC$ in a vessel of volume V is 1 atm. When the temperature is increased by $10^oC$ at the same volume, the pressure increases by 10%. If molecular weight of the gas is 120. The temperature, $t^oC$ and volume (V) are :

Options:
A. $$t = -253^oC, V = 0.082 L$$
B. $$t = -263^oC, V = 0.082 L$$
C. $$t = -273^oC, V = 0.82 L$$
D. $$t = -283^oC, V = 0.082 L$$
E. $$t = -263^oC, V = 0.82 L$$
F. $$t = 27^o C, V = 22.4 L$$
G. $$t = 0^o C, \, V = 22.4L$$
H. $$t = -173^oC, V = 0.082 L$$
I. $$t = -173^oC, V = 0.0821 L$$
J. $$t = -173^o C, V = 0.82 L$$
Answer: I
The time period of oscillation of an object whose displacement varies with time $y= sin \ w t + sin \ 3 w t$ is:

Options:
A. $$\cfrac {3\pi}{w}$$
B. $$\cfrac {\pi}{w}$$
C. $$\cfrac {5\pi}{w}$$
D. $$\cfrac {4\pi}{3w}$$
E. $$\cfrac {5\pi}{2w}$$
F. $$\cfrac {\pi}{2w}$$
G. $$\cfrac {2\pi}{3w}$$
H. $$\cfrac {2\pi}{w}$$
I. $$\cfrac {3\pi}{2w}$$
J. $$\cfrac {4\pi}{w}$$
Answer: H
At $ 25^{o}C $ the equilibrium constant for the reaction $ NH_{4}HS(S) \rightleftharpoons  NH_{3}(g) + H_{2}S(g) $ is $ K_{p} =  12 . A 8.21 $ liter flask is charged with 1 atm of pure $NH_{3}(g) $ at $ 27^{o}C$ what is the minimum mass  in gram of $ NH_{4}HS $ that must be added to the flask in order to achieve equilibrium

Options:
A. 55 g
B. 53 g
C. 50 g
D. 51 g
E. 54 g
F. 81 g
G. 52 g
H. 62 g
I. 57 g
J. 59 g
Answer: F
The bond enthalpies of $C-C, C=C$ and $C\equiv C$ bonds are $348, 610$ and $835\ kJ/mol$, respectively, at $298\ K$ and $1\ bar$. The enthalpy of polymerization per mole of $2$ -Butyne at $298\ K$ and $1\ bar$ as shown below is $nCH_{3}-C\equiv C-CH_{3}(g)\rightarrow -(CH_{2}-CH=CH-CH_{2})_{n}-(g)$

Options:
A. $$-123\ kJ$$
B. $$-128\ kJ$$
C. $$-231\ kJ$$
D. $$-37\ kJ$$
E. $$-131\ kJ$$
F. $$-139\ kJ$$
G. $$-133\ kJ$$
H. -113\ kJ
I. $$-118\ kJ$$
J. $$-213\ kJ$$
Answer: A
At 298 K, the conductivity of a saturated solution of $AgCl$ in water is $2.6\times 10^{-6}S cm^{-1}$. What is its solubility product at 298K?$[{Given:\ \lambda ^{\infty }(Ag^{+})=63.0 \ Scm^{2}mol^{-1},}\quad {\lambda ^{\infty }(Ci^{-})=67.0\ Scm^{2}mol^{-1}}]$

Options:
A. $$4.0 \times 10^{-17}\ M^{2}$$
B. $$4.0\times 10^{-10}\ M^{2}$$
C. $$2.0 \times 10^{-21}\ M^{2}$$
D. $$4.0 \times 10^{-21}\ M^{2}$$
E. $$4.0\times 10^{-16}\ M^{2}$$
F. $$4.0 \times 10^{-18}\ M^{2}$$
G. $$2.0\times 10^{-5}\ M^{2}$$
H. $$2\times 10^{-8}\ M^{2}$$
I. $$2.0 \times 10^{-19}\ M^{2}$$
J. $$4.0 \times 10^{-19}\ M^{2}$$
Answer: B
In each of the following total pressure set-up at equilibrium is assumed to be equal and is one atm with equilibrium constants $K_p$ given:
1. $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g), K_1$
2. $NH_4HS(s) \rightleftharpoons NH_3(g) + H_2S(g), K_2$
3. $NH_2COONH_4(s) \rightleftharpoons 2NH_3(g) + CO_2(g), K_3$
In the increasing order:

Options:
A. $$K_2 = K_1 = K_3$$
B. None of these
C. $$K_2 < K_3 < K_1$$
D. $$K_2 < K_1 < K_3$$
E. $$K_1 = K_2 = K_3$$
F. $$K_1 = K_3 < K_2$$
G. $$K_3 < K_2 < K_1$$
H. $$K_1 < K_3 < K_2$$
I. $$K_2 < K_1 = K_3$$
J. $$K_1 < K_2 < K_3$$
Answer: G
The filament of a light bulb has surface area $64 mm^2$. The filament can be considered as a black body at temperature $2500 K$ emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then
(Take Stefan-Boltzmann constant $=5.67\times 10^{-8}Wm^{-2}K^{-4}$, Wien' displacement constant= $2.90\times 10^{-3}m-K$, Planck's constant $=6.63\times 10^{-34}Js$ speed of light in vaccum $=3.00\times 10^8ms^{-1}$)

Options:
A. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.75\times 10^{11}$ to $2.85\times 10^{11}$
B. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.60\times 10^{11}$ to $2.70\times 10^{11}
C. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.55 \times 10^{11}$ to $2.65 \times 10^{11}$
D. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.50 \times 10^{11}$ to $2.60 \times 10^{11}$
E. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.90 \times 10^{11}$ to $3.00 \times 10^{11}
F. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.85\times 10^{11}$ to $2.95\times 10^{11}
G. taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range $2.65 \times 10^{11}$ to $2.75 \times 10^{11}$
Answer: A
In the process:
$$H_2O(s, -10^{ \circ }C, 1  atm)\longrightarrow H_2O(l, 10^{ \circ }C,  1  atm)$$
$C_P  for  ice = 9  cal  deg^{ -1 }  mol^{ -1 }, C_P  for  H_2O = 18  cal  deg^{ -1 }  mol^{ -1 }$.
Latent heat of fusion of ice $=1440  cal  mol^{ -1 } at  0^{ \circ }C$.
The entropy change for the above process is $6.258  cal  deg^{ -1 }  mol^{ -1 }$.
Give the total number of steps in which the third law of thermodynamics is used.

Options:
A. 3rd Law is not used at all
B. 3
C. 1
D. 2
E. 4
F. 6
G. 5
H. 8
I. 9
J. 7
Answer: D
A particle located at x=0 at time t=0 starts moving along the positive x-direction with a velocity v that varies as $ v= \alpha \sqrt x $ . the displacement of the particles varies with time as

Options:
A. $$t$$
B. $$t^{1/3}$$
C. $$ t^2 $$
D. $$t^{3/2}$$
E. $$t^{2/3}$$
F. $$ t^3 $$
G. $$t^{1/4}$$
H. $$ t^{3/4} $$
I. $$t^{5/2}$$
J. $$ t^{1/2} $$
Answer: J
A plank of mass $ 5 kg $ is resting on a smooth horizontal surface with a block of mass $ 4kg $ placed on it as shown. The coefficient of friction between the block and the plank is $ 0.25 $. At time $  t = 0 $ a horizontal force $  F = 6N $ is applied on the block.  The work done by the frictional force on the plank during the time interval $ t = 2sec $ to $ t = 3 sec $ will be

Options:
A. $$\dfrac{ 60 }{ 9 }$$
B. $$ \dfrac{ 50 }{ 9 } $$
C. $$\dfrac{ 45 }{ 9 }$$
D. $$\dfrac{ 70 }{ 9 }$$
E. $$ \dfrac{ 40 }{ 9 } $$
F. $$ \dfrac{ 50 }{ 3 } $$
G. $$\dfrac{ 55 }{ 9 }$$
H. $$ \dfrac{ 40 }{ 3 } $$
I. $$\dfrac{ 65 }{ 9 }$$
Answer: B
Which of the following when  added to $1.0L$ of$0.5M$ HBr would result in maximum increase in pH:-$\left[ {PKa\left( {C{H_3}COOH} \right) = 4.74} \right]$

Options:
A. $$0.7\,mol\,C{H_3}COOH$$
B. $$0.45\,mol\,C{H_3}COOH$$
C. $$0.55\,mol\,C{H_3}COONa$$
D. $$0.6\,mol\,C{H_3}COOH$$
E. $$01.0\,mol\,NaCl$$
F. $$0.5\,mol\,C{H_3}COOH$$
G. $$0.6\,mol\,C{H_3}COONa$$
H. $$0.4\,mol\,NaOH$$
I. $$0.55\,mol\,C{H_3}COOH$$
J. $$0.65\,mol\,C{H_3}COOH$$
Answer: F
The equivalent weight of ${Cu}_{2}S$ $\left(mol. wt. = M\right)$ in the following reaction is:${Cu}_{2}S + 4 {MnO}_{4} \longrightarrow {Cu}^{2} + {SO}_{2} + {Mn}^{2+}$

Options:
A. $$M/3$$
B. $$M/6$$
C. $$M/9$$
D. $$M/4$$
E. $$M/7$$
F. $$M/11$$
G. $$M/2$$
H. $$M/8$$
I. $$M/10$$
J. $$M/5$$
Answer: H
An intimate mixture of ferric oxide and aluminium is used as solid fuel in rockets. Find the  fuel value per $cm^3$ of the mixture. Heat of formation and densities are as follows.
$$\Delta _f H \,Al_2O_3=-399\,Kcal\,mole^{-1},\Delta_fh Fe_2O_3=-199\,Kcal\,mole^{-1}$$
density of $Al=2.7gm/cm^3$, density of $Fe_2O_3=5.2gr/CC$

Options:
A. $$4\,Kcal$$
B. $$4.4\,Kcal$$
C. $$3.6\,Kcal$$
D. $$4.8\,Kcal$$
E. $$3.92\,Kcal$$
F. $$5.1\,Kcal$$
G. $$7\,Kcal$$
H. $$4.9\,Kcal$$
I. $$4.2\,Kcal$$
J. $$4.6\,Kcal$$
Answer: A
A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure.  A string is wrapped over its rim and a mass of 4 kg is hung.  An angular acceleration of 8 rad $-s^{-2}$  is produced in it due to the torque.  Then, moment of inertia of the wheel is $(g = 10 ms^{-2})$ :

Options:
A. $$4 kg -m^{2}$$
B. $$1.60 kg -m^{2}$$
C. $$1.44 kg -m^{2}$$
D. $$1.40 kg -m^{2}$$
E. $$1.36 kg -m^{2}$$
F. $$1.63 kg -m^{2}$$
G. $$1.52 kg -m^{2}$$
H. $$2 kg -m^{2}$$
I. $$1.48 kg -m^{2}$$
J. $$8 kg -m^{2}$$
Answer: H
\textbf{Statement 1:} A charge is outside the Gaussian sphere of radius \( R \). Then the electric field on the surface of the sphere is zero.
\textbf{Statement 2:} As
\[
\oint \vec{E} \cdot \vec{ds} = \frac{q_{\text{in}}}{\epsilon_0},
\]
for the sphere, \( q_{\text{in}} = 0 \), so
\[
\oint \vec{E} \cdot \vec{ds} = 0.
\]

Options:
A. Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1
B. Statement 1 is true, statement 2 is false and statement 2 is NOT the correct explanation for statement 1
C. Statement 1 is false, statement 2 is false
D. Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement 1
E. Statement 1 is false, statement 2 is true
F. Statement 1 is true, statement 2 is false
G. Statement 1 is true, statement 2 is false and statement 2 is the correct explanation for statement 1
H. Statement 1 is false, statement 2 is true and statement 2 is NOT the correct explanation for statement 1
I. Statement 1 is false, statement 2 is true and statement 2 is the correct explanation for statement 1
J. Statement 1 is false, statement 2 is false and statement 2 is NOT the correct explanation for statement 1
Answer: A
The figure shows two point sources which emit light of wavelength $\lambda$ in phase with each other and are at a distance $d = 5.5\ \lambda$ apart along a line which is perpendicular to a large screen at a distance $L$ from the center of the source. Assume that $d$ is much less than $L.$
Which of the following statement is (are) correct?

Options:
A. Point $y = 0$ corresponds to bright fringe
B. Point $y = 0$ corresponds to a dark bright fringe
C. Point $y = 0$ corresponds to a bright fringe
D. Only six bright fringes appear on the screen
E. Point \( y = 0 \) corresponds to a dark bright fringe
F. Point $y = 0$ corresponds to dark fringe
G. Only five bright fringes appear on the screen
H. Only four bright fringes appear on the screen
Answer: F
There are two current carrying planar coils each made from identical wires of length L. $C_1$ is circular (radius R) and $C_2$ is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform magnetic field $\bar{B}$ and carry the same current. Find a in terms of R:

Options:
A. $$2a = 5R$$
B. $$a = \frac{5R}{3}$$
C. $$a = \frac{7R}{2}$$
D. $$a = 3R$$
E. a = 4R
F. $$a = R$$
G. $$a = 2R$$
H. $$a = \frac{4R}{3}$$
I. $$a = \frac{3R}{2}$$
J. $$a = \frac{5R}{2}$$
Answer: D
A cylinder contains 20n kg of ${ N }_{ 2 }$ gas $\left( M=28kg{ k }^{ -1 }{ mol }^{ -1 } \right) $ at a pressure of 5 atm. The mass of hydrogen $\left( M=2kg{ k }^{ -1 }{ mol }^{ -1 } \right) $ at a pressure of 3 atm contained in the same cylinder at same temperature is

Options:
A. 0.68 kg
B. 1.16 kg
C. 1.08 kg
D. 1.28 kg
E. 1.48 kg
F. 1.26 kg
G. 1.68 kg
H. 0.86 kg
I. 1.18 kg
J. 1.36 kg
Answer: C
A glass capillary tube of inner diameter $0.28mm$ is lowered vertically into water in a vessel.The pressure to be applied on the water in the capillary tube so that water level in the tube is same as the vessel in $N /m ^{2}$ is(surface tension of water $= 0.07 N/m$ atmospheric pressure $=10^{5} N /m ^{2}$ )

Options:
A. $$10^{3}$$
B. $$95 \times 10^{3}$$
C. $$102 \times 10^{3}$$
D. $$103 \times 10^{3}$$
E. $$101 \times 10^{3}$$
F. $$97 \times 10^{3}$$
G. $$100 \times 10^{3}$$
H. $$99 \times 10^{3}$$
I. $$98 \times 10^{3}$$
J. $$96 \times 10^{3}$$
Answer: A
A small block slides down from rest at point A on the surface of a smooth circular cylinder, as shown. At point B, the block falls off(leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by?

Options:
A. $$\sin\theta_2=\dfrac{2}{3}\cos\theta_1$$
B. $$\cos\theta_2=\dfrac{3}{2}\sin\theta_1$$
C. $$\sin\theta_2=\dfrac{2}{3}\sin\theta_1$$
D. $$\cos\theta_2=\dfrac{2}{3}\cos\theta_1$$
E. $$\sin\theta_2=\dfrac{3}{2}\cos\theta_1$$
F. $$\cos\theta_2=\dfrac{3}{2}\cos\theta_1$$
G. $$\cos\theta_2=\dfrac{2}{3}\sin\theta_1$$
H. $$\sin\theta_2=\dfrac{3}{4}\cos\theta_1$$
I. $$\sin\theta_2=\dfrac{3}{2}\sin\theta_1$$
Answer: A
A plane wave $y=a sin(bx+ct)$ is incident on a surface. Equation of the reflected wave is $y'=a'sin(ct-bx)$ Which of the following statement is not correct?

Options:
A. Reflecting surface is y-z plane.
B. a' can be equal to a.
C. The wave is incident on the surface normally.
D. a' can be greater than a.
E. a' can be less than a.
F. a' cannot be greater than a.
Answer: F
A progressive wave is represented as $y=0.2\cos \pi (0.04 t+0.2x-\dfrac{\pi}{6})$ where distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $\dfrac{\pi}{2}$?

Options:
A. 8 cm
B. 12.5 cm
C. 50 cm
D. 20 cm
E. 25 cm
F. 15 cm
G. 37.5 cm
H. 4 cm
I. 10 cm
J. 30 cm
Answer: E
Two positive point charges $q_{1}$ and $q_{2}$ are kept at a distance of $3m$ in air. If $q_{1} + q_{2} = 16\mu C$ and the coulomb force between them is $48\times 10^{-3} N$, then the two charges are

Options:
A. $$9\mu C, 7\mu C$$
B. $$7\mu C, 9\mu C$$
C. $$15\mu C, 1\mu C$$
D. $$8\mu C, 8\mu C$$
E. $$6\mu C, 10\mu C$$
F. $$12\mu C, 4\mu C$$
G. $$10\mu C, 6\mu C$$
H. $$14\mu C, 2\mu C$$
I. $$11\mu C, 5\mu C$$
J. $$13\mu C, 3\mu C$$
Answer: D
A particle is moving in a plane on curve $y= \cfrac {x^3} {\sqrt 3}$. Its $x-$ component of velocity is constant and is equal to $2ms^{-1}$. Angle between its velocity and acceleration at $x= 1$ m is

Options:
A. $$75^o$$
B. $$55^o$$
C. $$30^o$$
D. $$15^o$$
E. $$45^o$$
F. $$85^o$$
G. $$90^o$$
H. $$60^o$$
Answer: E
For reaction $A(g)+3B(g)\rightarrow 2C(g);\Delta H^{\circ}=-24kJ$ The value of $\Delta G^{\circ}$ is -9 kJ. The standard entropy change of reaction is:

Options:
A. $$-10 JK^{-1}$$
B. $$-5 JK^{-1}$$
C. $$50 JK^{-1}$$
D. $$-500 JK^{-1}$$
E. $$0.5 JK^{-1}$$
F. $$5 JK^{-1}$$
G. $$15 JK^{-1}$$
H. $$10 JK^{-1}$$
I. $$-50 JK^{-1}$$
J. $$500 JK^{-1}$$
Answer: F
Two coaxial hollow conducting cylinder shells carry equal and opposite currents. Magnetic field due to a point outside both the shells is $\bar{B}$ due to one shell and $\bar{B}_{2}$ due two the other shell then:

Options:
A. Depend on the length of the shells
B. $$\bar{B}_{1}=-\bar{B}_{2}$$
C. Depend on the material of the shells
D. Depend on the thickness of the shells
E. Depend on the current in the shells
F. $$\bar{B}_{1}=\bar{B}_{2}$$
G. Depend on distance from conductor
H. Depend on the radius of the shells
I. Depend on radius of cylinders
J. Depend on the electric field in the region
Answer: G
Benzene $\left( l \right) \rightleftharpoons$ Benzene $(g)$ : ${ K }_{ p } = 60\ mm\ Hg$ at $300\ K$Toluene $\left( l \right) \rightleftharpoons$ Toluene $(l)$ : ${ K }_{ p } = 40\ mm\ Hg$ at $300\ K$The mole fraction of benzene in vapors of benzene toluene mixture is $0.6$ at $300\ K$ temperature. The mole fraction of toluene in the liquid phase of solution at $300\ K$ is:

Options:
A. $$0.60$$
B. 0.58
C. 0.45
D. 0.5
E. 0.48
F. 0.65
G. 0.40
H. 0.52
I. $$0.55$$
Answer: D
A ray of light enters a spherical liquid drop at angle of incidence $i$ and suffers one internal reflection inside the drop. If angle $i$ is adjusted such that ray suffers minimum deviation as it comes out of drop, then value of $i$ is $\left( \mu _ { liquid } = \sqrt { 2 } \right)$

Options:
A. $$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 2 } } \right)$$
B. $$\sin ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$$
C. $$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 2.2 } } \right)$$
D. $$\sin ^ { - 1 } \left( \sqrt { \frac { 2 } { 3 } } \right)$$
E. $$30 ^ { \circ }$$
F. $$\sin ^ { - 1 } \left( \frac { 1 } { 2 } \right)$$
G. $$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 2.1 } } \right)$$
H. $$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 3 } } \right)$$
I. $$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 2.5 } } \right)$$
J. $$45 ^ { \circ }$$
Answer: J
A block of base $10cm\ \times  10cm$ and height 15cm is kept on an inclined plane. The coefficient of friction between them is $\sqrt { 3 } $ . The inclination $\theta $ of this inclined plane from the horizontal plane is gradually increased from ${ 0 }^{ \circ  }$. Then :

Options:
A. at $\theta = {65}^{\circ}$, the block will start sliding down the plane and continue to do so at higher angle
B. at $\theta = {45}^{\circ}$, the block will start sliding down the plane and continue to do so at higher angle
C. at $\theta ={ 60 }^{ \circ }$, the block will start sliding down the plane and continue to do so at higher angle
D. the block will remain at rest on the plane up to certain $\theta $ and then it will topple
E. at $\theta ={ 30 }^{ \circ }$ the block will start sliding down the plane
F. at $\theta = {45}^{\circ}$, the block will start sliding down the plane and then topple at a higher angle
G. at $\theta = {50}^{\circ}$, the block will start sliding down the plane and continue to do so at higher angle
H. the block will remain at rest on the plane up to a certain \(\theta\) and then it will slide down
I. at $\theta = {55}^{\circ}$, the block will start sliding down the plane and continue to do so at higher angle
J. at $\theta ={ 60 }^{ \circ }$, the block will start sliding down the plane and on further increasing $\theta $ , it will topple at certain $\theta $
Answer: D
At $25^{o}C$, consider following reactions 
$$NO+SO_{3}\rightleftharpoons NO_{2}+SO_{2};K_{c}=3$$
$$2SO_{2}+O_{2}\rightleftharpoons 2SO_{3};K_{c}=16(mol/L)^{-1}$$
The value of equilibrium constant $(K_{c})$ for the reaction $2NO_{2}\rightleftharpoons 2NO+O_{2}$ will be

Options:
A. $$\dfrac{1}{48}\ mol/L$$
B. $$\dfrac{1}{3} \ mol/L$$
C. $$\dfrac{1}{144}\ mol/L$$
D. $$\dfrac{1}{12}\ mol/L$$
E. $$144\ mol/L$$
F. $$\dfrac{1}{9}\ mol/L$$
G. $$9\ mol/L$$
H. $$12\ mol/L$$
I. $$\dfrac{1}{36}\ mol/L$$
Answer: H
Solubility of $CuCl$ in $0.02\,M\,KCl$ solution at $25^oC$ is ($K_{sp}$ of $CuCl=1.7\times10^{-6}$)

Options:
A. $$8.5 \times 10^{-4}$$
B. $$1.7 \times 10^{-5}$$
C. $$8.5 \times 10^{-3}$$
D. $$1.7 \times 10^{-4}$$
E. $$8.5\times10^{-5}$$
F. $$1.7 \times 10^{-2}$$
G. $$8.5 \times 10^{-2}$$
H. $$1.7\times10^{-3}$$
Answer: H
Half-life of radioactive $_6C^{14}$ is $8000$ years. What will be the age of wooden article if its $_6C^{14}$ activity is $1/3$ of that of newly cut wood? ( Take $\log_{10}3=0.477$)

Options:
A. 6788
B. 6748
C. $$8788$$
D. $$8748$$
E. $$None\ of\ these$$
F. 8888
G. $$8878$$
Answer: C
Argon gas adiabatically compressed to half of its volume if then the correct equation of process is

Options:
A. $$T.P^{-1/3} = constant$$
B. $$T.P^{-3/7} = constant$$
C. $$T.P^{-3/5} = constant$$
D. $$ P.T^{2/5} = constant $$
E. $$T.P^{-1/4} = constant$$
F. $$ VP^{5/3} = constant $$
G. $$ TV^{2/5} = constant $$
H. $$ T.P^{-2/5} = constant $$
I. $$T.P^{-1/5} = constant$$
Answer: H
The equation of SHM of a particle is $\dfrac{d^2x}{dt^2} + 0.2 \dfrac{dx}{dt} + 36x=0$. Its time period is

Options:
A. $$\dfrac{\pi}{3}S$$
B. $$\dfrac{\pi}{10}S$$
C. $$\dfrac{\pi}{8}S$$
D. $$\dfrac{\pi}{5}S$$
E. $$none of these$$
F. $$\dfrac{\pi}{4}S$$
G. \dfrac{\pi}{9}S
H. $$\dfrac{\pi}{6}S$$
I. $$both a and b$$
J. $$\dfrac{\pi}{7}S$$
Answer: H