MikaStars39/nano-eval huggingface dataset:
Chemical equilibrium:The two containers contain liquid X (in A) and Y (in B). X is similar to water and Y is similar to $\mathrm CCl_{4}$. 20 moles of each are taken in A and B. How many of the following statement(s) is/are correct?$\mathrm P_{X}^{0}=200 \  torr$$\mathrm P_{Y}^{0}=50 \ torr$(i) If $\mathrm NaCl$ is added to vessel B, the lowering of vapour pressure takes place.(ii) If glucose is added to vessel A, the boiling point of the solution increases.(iii) If the valve connecting A and B is opened, then $\mathrm P_{T}$ in both the vessel becomes equal and is given by Raoult's law. (iv) After opening the valve, the level of liquid in both the container decreases (even a slight decrease is to be considered).(v) After opening the valve, the final pressure in vessel B is more than 50 torr. (vi) After opening the valve, the final pressure in vessel A is more than 200 torr.

Options:
A. $$6$$
B. $$2$$
C. $$4$$
D. $$3$$
E. $$1$$
F. $$5$$
Answer: B
In an LR circuit current at $t=0$ is $20A$. After $2s$ it reduces to $18A$. The time constant of the circuit is (in second)

Options:
A. $$2\ln { \cfrac { 10 }{ 9 } } $$
B. $$\cfrac { 4 }{ \ln { \cfrac { 10 }{ 9 } } }$$
C. $$\cfrac { 2 }{ \ln { \cfrac { 12 }{ 11 } } }$$
D. $$\cfrac { 2 }{ \ln { \cfrac { 9 }{ 10 } } }$$
E. $$\cfrac { 2 }{ \ln { \cfrac { 10 }{ 9 } } } $$
F. $$\ln { \cfrac { 10 }{ 9 } } $$
G. $$2$$
H. $$\cfrac { 4 }{ \ln { \cfrac { 11 }{ 10 } } }$$
I. $$\cfrac { 4 }{ \ln { \cfrac { 9 }{ 10 } } }$$
J. $$\cfrac { 2 }{ \ln { \cfrac { 11 }{ 10 } } }$$
Answer: A
$M_{(g)}+e^- \rightarrow M^{-}_{(g)}$ ; $\Delta H=-354\ kJ/mole $ at $300\ K$, then the electron affinity value at $0\ K$ is:

Options:
A. $$-348\ kJ/mol$$
B. $$-298\ kJ/mol$$
C. $$+348\ kJ/mol$$
D. $$-308\ kJ/mol$$
E. $$-344\ kJ/mol$$
F. $$-304\ kJ/mol$$
G. $$-364\ kJ/mol$$
H. $$-358\ kJ/mol$$
I. $$+298\ kJ/mol$$
J. $$-354\ kJ/mol$$
Answer: B
With two fingers, you hold a cone motionless upside down. The mass of the cone is $2 kg$, and the coefficient of static friction between you fingers and the cone is $\mu = 1$. Find the minimum normal force (in Newton) that must be applied with each finger in order to hold up the cone.

Options:
A. 25 N
B. 23 N
C. 20 N
D. 22 N
E. 100 N
F. 50 N
G. 27 N
H. 75 N
I. 26 N
J. 30 N
Answer: A
${ Cu }^{ + }$ ion is not stable aqueous solution because of disproportionation reaction ${ E }^{ 0}$ value for disproportionation  of ${ Cu }^{ + }$ is :
(given $E\cdot { Cu }^{ 2+ }/{ Cu }^{ + }=0.15V$; ${ E }^{ \circ  }{ Cu }^{ 2+ }/{ Cu }^{ + }=0.34 V$)

Options:
A. -0.29 V
B. 0.19 V
C. -0.19 V
D. 0.49 V
E. 0.09 V
F. 0.15 V
G. 0.38 V
H. 0.29 V
I. -0.38 V
J. -0.09 V
Answer: C
On increasing temperature from 200 K o 220 K rate of reaction A increase by 3 times and rate of reaction B increases by 9 times hen correct relationship between activation energy of A and B is

Options:
A. $$3{ E }_{ A }={ E }_{ B }$$
B. $${ E }_{ A }={ 4E }_{ B }$$
C. $${ E }_{ A }={ 3E }_{ B }$$
D. $${ E }_{ A }={ \frac{9}{2}E }_{ B }$$
E. $${ E }_{ B }={ 2E }_{ A }$$
F. $${ E }_{ A }={ \frac{3}{2}E }_{ B }$$
G. $${ E }_{ A }={ 2E }_{ B }$$
H. $${ E }_{ B }={ 4E }_{ A }$$
I. $${ E }_{ A }={ \frac{9}{4}E }_{ B }$$
J. $${ E }_{ B }={ 3E }_{ A }$$
Answer: E
An ideal gas undergoes a cyclic process as shown in figure.
$$\Delta U_{BC} = -5 \ kJ \ mol^{-1}, q_{AB}  = 2 \ kJ \ mol^{-1}$$
$$\Delta W_{AB} = -5 \ kJ \ mol^{-1}, W_{CA}  = 3 \ kJ \ mol^{-1}$$
Heat absorbed by the system during process CA is

Options:
A. $$18 \ kJ \ mol^{-1}$$
B. $$+5 \ kJ \ mol^{-1}$$
C. $$-15 \ kJ \ mol^{-1}$$
D. $$-8 \ kJ \ mol^{-1}$$
E. $$-10 \ kJ \ mol^{-1}$$
F. $$-18 \ kJ \ mol^{-1}$$
G. $$+10 \ kJ \ mol^{-1}$$
H. $$-6 \ kJ \ mol^{-1}$$
I. $$-5 \ kJ \ mol^{-1}$$
J. $$-12 \ kJ \ mol^{-1}$$
Answer: I
A body with zero initial velocity slips from the top of an inclined plane forming an angle $a$ with the horizontal. The coefficient of friction $\mu$ between the body and the plane increase with the distance $'s'$ from the top according to relation $\mu=bs$. After what distance the body will stops.

Options:
A. $$\dfrac {9 \tan \alpha}{b}$$
B. $$\dfrac {\tan \alpha}{b}$$
C. $$\dfrac {8 \tan \alpha}{b}$$
D. $$\dfrac {4\tan \alpha}{b}$$
E. $$\dfrac {2 \tan \alpha}{b}$$
F. $$\dfrac {7 \tan \alpha}{b}$$
G. $$\dfrac {5 \tan \alpha}{b}$$
H. $$\dfrac {6 \tan \alpha}{b}$$
I. $$\dfrac {3\tan \alpha}{b}$$
J. $$\dfrac {2\tan \alpha}{b}$$
Answer: J
Two small spheres with masses ${m_1}$ and ${m_2}$ hang on weightless, insulating threads of length ${l_1}$ and ${l_2}$. The two spheres carry charges of ${q_1}$ and ${q_2}$ respectively. The spheres hang such that they are at the same level with one another the threads are inclined at angle ${\theta _1}$ and ${\theta _2}$ with the vertical. The angle ${\theta _1}$ will be equal to ${\theta _2}$ when

Options:
A. ${m_1} \neq {m_2}$, ${q_1} \neq {q_2}$, ${l_1} = {l_2}$
B. None of these
C. ${m_1} \neq {m_2}$, ${l_1} = {l_2}$
D. ${m_1} \neq {m_2}$, ${q_1} = {q_2}$
E. ${m_1} = {m_2}$, ${l_1} \neq {l_2}$
F. ${m_1} = {m_2}$, ${q_1} = {q_2}$
G. ${m_1} \neq {m_2}$, ${q_1} = {q_2}$, ${l_1} = {l_2}$
H. ${m_1} = {m_2}$, ${q_1} \neq {q_2}$
I. ${m_1} = {m_2}$, ${l_1} = {l_2}$
J. ${q_1} = {q_2}$, ${l_1} = {l_2}$
Answer: F
Nickel (z = 28) combines with a negative monodenate ligand X- to form a paramagnetic complex $\left[ { NiX }_{ 4 } \right] ^{ 2- }$. The number of unpaired electron (s) in the nickel and geometry of this complex ion are, respectively

Options:
A. One , tetrahedral
B. One, octahedral
C. Two, octahedral
D. One, square planar
E. Two, tetrahedral
F. Two, square planar
G. Three, tetrahedral
H. two, tetrahedral
I. Three, octahedral
Answer: D
For the following three reactions 1,2 and 3, equilibrium constant are given :
(1) $CO(g)+H_2O(g)\rightleftharpoons CO_2(g)+H_2(g)$                     ;$K_1$
(2) $CH_4(g)+H_2O(g)\rightleftharpoons CO(g)+3H_2(g)$                       ;$K_2$
(3) $CH_4(g)+2H_2O(g)\rightleftharpoons CO_2(g)+4H_2(g)                       ;$K_3$
Which of the following reaction is correct?

Options:
A. $${ K }_{ 3 }.{ K }_{ 2 }^{ 3 }{ K }_{ 1 }^{ 2 }$$
B. $$K_2K_3=K_1$$
C. $$K_1\sqrt[4]{K_2}=K_3$$
D. $$K_1\sqrt {K_2}=K_3$$
E. $$K_1\sqrt[3]{K_2}=K_3$$
F. $$K_1\sqrt[6]{K_2}=K_3$$
G. $$ K_1 \sqrt[3]{K_2} = K_3 $$
H. $$K_3=K_1K_2$$
I. $$K_1\sqrt[5]{K_2}=K_3$$
J. $$ K_1 \sqrt[4]{K_2} = K_3 $$
Answer: H
$0.5$  mole each of two ideal gas  $A \left( C _ { v , m } = \dfrac { 5 } { 2 } R \right)$  and  $B \left( C _ { v , m } = 3 R \right)$  are taken in a container and expanded reversibly and adiabatically, during this process temperature of gaseous mixture decreased from  $350 \mathrm { K }$  to  $250 \mathrm { K }.$  Find  $\Delta H$  (in  $cal/mol$) for the process:

Options:
A. $$None of these$$
B. $$-150R$$
C. $$-100R$$
D. $$-125R$$
E. $$-137.5R$$
F. $$-135R$$
G. $$-375R$$
H. $$-122.5R$$
I. $$-140R$$
J. $$-120R$$
Answer: G
In the reaction $4NO_{2_{(g)}}+O_2{_{(g)}}\rightarrow 2N_2O_{5_{(g)}}, \Delta H =-111$kJ if $N_2O_{5_{(s)}}$ is formed instead of $N_2O_{5_{(g)}}$, the $\Delta$H value in kJ is: $[\Delta H_{sublimation}$ for $N_2O_5=54$ kJ $mol^{-1}]$

Options:
A. $$-57$$
B. $$-111$$
C. $$-219$$
D. $$-273$$
E. $$-165$$
F. $$-225$$
G. $$-171$$
H. $$-177$$
I. $$+219$$
Answer: E
A reaction $S_8(g)\rightleftharpoons 4S_2(g)$ is carried out by taking 2 mol of $S_8(g)$ and 0.2 mol of $S_2(g)$ is a reaction vessel of 1 L. Which one is not correct if $K_c=6.30\times 10^{-6}$?

Options:
A. $$K_p=2.55 atm^3$$
B. $$K_p=4.55 atm^3$$
C. $$K_p=7.55 atm^3$$
D. $$K_p=3.55 atm^3$$
E. $$K_p=5.55 atm^3$$
F. $$K_p=6.55 atm^3$$
G. $$K_p=1.55 atm^3$$
Answer: A
1 molal aqueous solution of an electrolyte $AB_{2}$  is 80% ionized into  $A^{+2}$  and $B^{-}$  ions.  The boiling point of the solution at 1 atm is: 
$[K_{b(H_{2}O)}= 0.5Kg mol^{-1}]$

Options:
A. 274.3 K
B. 374.3 K
C. 273.5 K
D. 273.3 K
E. 273.8 K
F. 375.3 K
G. 275.3 K
H. 374.5 K
I. 100.5 K
J. 373.5 K
Answer: B
Given that:
$2SO_3(g) \rightarrow 2SO_2(g)+O_2(g)$; $\triangle H^o=+197.8 kj/mol-RXN$
$S(s)+ (\frac { 1 }{ 3 } )O_2(g) \rightarrow SO_3(g)$; $\triangle H^o=-395.7 kj/mol-RXN$
Determine the heat of formation for $SO_2$

Options:
A. $$-296.8 kj/mol$$
B. $$+395.7 kj/mol$$
C. $$+98.9 kj/mol$$
D. $$+49.5 kj/mol$$
E. $$-492.6 kj/mol$$
F. $$+394.2 kj/mol$$
G. $$+691.8 kj/mol$$
H. $$+593.6 kj/mol$$
I. $$+296.8 kj/mol$$
J. $$+197.8 kj/mol$$
Answer: C
The precipitate of $Ag_2CrO_4(K_{sp}=1.1\times 10^{-12})$ is obtained when equal volumes of the following are mixed:

Options:
A. $10^{-4}M\ Ag^{-}$ and $10^{-2}M\ CrO^{2-}_{4}$
B. $10^{-5}M\ Ag^{-}$ and $10^{-4}M\ CrO^{2-}_{4}$
C. $10^{-6}M\ Ag^{-}$ and $10^{-2}M\ CrO^{2-}_{4}$
D. $10^{-5}M\ Ag^{-}$ and $10^{-3}M\ CrO^{2-}_{4}$
E. $10^{-7}M\ Ag^{-}$ and $10^{-3}M\ CrO^{2-}_{4}$
F. $$10^{-5}M\ Ag^{-} and 10^{-2}M\ CrO^{2-}_{4}$$
G. $$10^{-6}M\ Ag^{-} and 10^{-3}M\ CrO^{2-}_{4}$$
Answer: D
A thin uniform metallic triangle sheet of mass $M$ has side's $AB=BC=L$. What is its moment, of inertia about axis $AC$ lying in plane of sheet?

Options:
A. $$\dfrac{ML^{}}{6}$$
B. $$\dfrac{ML^{2}}{20}$$
C. $$\dfrac{2ML^{}}{3}$$
D. $$\dfrac{ML^{2}}{24}$$
E. $$\dfrac{ML^{2}}{12}$$
F. $$\dfrac{ML^{2}}{16}$$
G. $$\dfrac{ML^{}}{3}$$
H. $$\dfrac{ML^{2}}{10}$$
I. $$\dfrac{ML^{2}}{14}$$
J. $$\dfrac{ML^{2}}{18}$$
Answer: E
The motion represented by equation $x=2\sin \omega t+3\sin^{2}\omega t$ is

Options:
A. Periodic but not SHM
B. Periodic and SHM
C. Oscillatory
D. Periodic
E. Periodic and Non-Oscillatory
F. Periodic and Oscillatory
G. SHM
H. Periodic but not Oscillatory
Answer: C
A rod of length L with linear mass density $\lambda = kx$ is placed along x-axis with one end at origin. The distance of CM of rod form origin is

Options:
A. L/2
B. 4L/5
C. 2L/5
D. L/3
E. 3L/10
F. 2L/3
G. 4L/3
H. 5L/12
I. 3L/5
J. 5L/6
Answer: F
What is the molarity of ${ F }^{ - }$ ions in a saturated solution of $Ba{ F }_{ 2 }$?
$$({ K }_{ sp } = 1.0\ \times \ { 10 }^{ -6 })$$

Options:
A. $$1.4 \times 10^{-2}$$
B. $$1.0\ \times \ { 10 }^{ -4 }$$
C. $$1.5\ \times \ { 10 }^{ -2 }$$
D. $$1.0\ \times \ { 10 }^{ -5 }$$
E. $$1.26\ \times \ { 10 }^{ -2 }$$
F. $$1.0\ \times \ { 10 }^{ -2 }$$
G. $$1.5\ \times \ { 10 }^{ -3 }$$
H. $$1.0\ \times \ { 10 }^{ -3 }$$
I. $$6.3\ \times \ { 10 }^{ -3 }$$
Answer: F
For a triode $\mu =64$ and $g_m =1600\ \mu$ mho. It is used as an amplifier and an input signal of $1V$ (rms) is applied. The signal power in the load of $40\ k\Omega $ will be

Options:
A. 26.5\ mW
B. $$None\ of\ these$$
C. 27.5\ mW
D. $$25.6\ mW$$
E. 24.6\ mW
F. 27.4\ mW
G. 25.7\ mW
H. $$23.5\ mW$$
I. 24.5\ mW
J. $$48.7\ mW$$
Answer: D
In a certain circuit current changes with time according to $i=2\sqrt{t}$.  RMS value of current between $t=2$ to $t=4s$ will be

Options:
A. $$2\sqrt{2}A$$
B. $$3\sqrt{3}A$$
C. $$(2+\sqrt{2})A$$
D. $$3\sqrt{2}A$$
E. $$4A$$
F. $$(2-\sqrt{2})A$$
G. $$3A$$
H. $$4\sqrt{2}A$$
I. $$2A$$
J. $$2\sqrt{3}A$$
Answer: G
A steel rod of cross-sectional area $16 cm^2$ and two brass rods of cross section area $10 cm^2$ together support a load of 5000 kg. The stress in steel rod will be : (Take Y for steel $= 2.0 \times 10^6 N/cm^2$ and for brass $= 1.0 \times 10^6 N/cm^2$)

Options:
A. $$151.2 N/cm^2$$
B. $$161.2 N/cm^2$$
C. $$None of these$$
D. $$151.4 N/cm^2$$
E. $$131.4 N/cm^2$$
F. $$152.4 N/cm^2$$
G. $$171.2 N/cm^2$$
H. $$171.4 N/cm^2$$
I. $$162.4 N/cm^2$$
J. $$141.4 N/cm^2$$
Answer: B
The Gibbs energy for the decomposition of ${ AI }_{ 2 }{ O }_{ 3 }$ at ${ 500 }^{ 0 }C$ is as fellow:$\frac { 2 }{ 3 } { AI }_{ 2 }{ O }_{ 3 }\longrightarrow \frac { 4 }{ 3 } AI+{ O }_{ 2 };\quad \triangle _{ r }G=+966kJ\quad { mol }^{ -1 }$.The potential difference needed for the electrolytic reduction of ${ AI }_{ 2 }{ O }_{ 3 }$ at ${ 500 }^{ 0 }C$ is at least:

Options:
A. 3.5 V
B. 6.0 V
C. 2.5 V
D. 3.0 V
E. 5.2 V
F. 4.5 V
G. 5.5 V
H. 5.0 V
I. 4.0 V
J. 4.8 V
Answer: H
If nuclei of a radioactive element X are product at a constant rate $\delta $ and the element has a decay constant $\eta $ then (assume that $N_{ o }$ nuclei of  the element were present at t=0 and $\delta =3\eta { N }_{ o }$)

Options:
A. Number of nuclei of X after very long time is $3{ N }_{ o }$
B. Number of nuclei of X after very long time ${ N }_{ o }$
C. Number of nuclei of X after two half lives is $2.25{ N }_{ o }$
D. Number of nuclei of X after two half lives is $2.5{ N }_{ o }$
E. Number of nuclei of X after two half lives is $1.75{ N }_{ o }$
F. Number of nuclei of X after two half lives is $1.25{ N }_{ o }$
G. Number of nuclei of X after two half lives is $1.875{ N }_{ o }$
H. Number of nuclei of X after two half lives is $2.0{ N }_{ o }$
I. Number of nuclei of X after two half lives is $1.5{ N }_{ o }$
J. Number of nuclei of X after-lives is $2.5{ N }_{ o }$
Answer: I
On a planet where ${ g }_{ planet }=0.2{ g }_{ earth }$. What will be the difference in the height of column filled with mercury in a closed end manometer when the gas is filled withe pressure of $2atm$ on earth (Assuming:outside pressure to be $1atm$ on both planet; Volume of gas remain constant)

Options:
A. $$76cm$$
B. $$760cm$$
C. $$304cm$$
D. $$38cm$$
E. $$380cm$$
F. $$152cm$$
G. $$30.4cm$$
H. $$190cm$$
I. $$1520cm$$
Answer: B
One end of a glass capillary tube with a radius $r=0.05$ $cm$ is immersed into water to a depth of $h = 2cm$. What pressure is required to blow an air bubble out of the lower end of the tube:
$T=7\times { 10 }^{ -2 }N/m$ and $\rho ={ 10 }^{ 3 }$ kg/ ${ m }^{ 3 }$)

Options:
A. 2080 N/ ${ m }^{ 2 }$
B. 480 N/ ${ m }^{ 2 }$
C. 2003 N/ ${ m }^{ 2 }$
D. 2030 N/ ${ m }^{ 2 }$
E. 820 N/ ${ m }^{ 2 }$
F. 2083 N/ ${ m }^{ 2 }$
G. 780 N/ ${ m }^{ 2 }$
H. 800 N/ ${ m }^{ 2 }$
I. 2033 N/ ${ m }^{ 2 }$
J. 680 N/ ${ m }^{ 2 }$
Answer: B
Two point particles $A$ and $B$ are placed in line on a frictionless horizontal plane. If particle $A$ (mass $1 kg$) is moved with velocity $10 m/s$ towards stationary particle $B$ (mass = $2 kg$) and after collision the two move at an angle of $45$ degrees with the initial direction of motion then find coefficient of restitution.

Options:
A. $$\cfrac{3}{5}$$
B. $$\cfrac{2}{3}$$
C. $$\cfrac{1}{4}$$
D. $$\cfrac{3}{4}$$
E. $$0$$
F. $$\cfrac{1}{6}$$
G. $$\cfrac{1}{2}$$
H. $$1$$
I. $$\cfrac{1}{5}$$
J. $$\cfrac{1}{3}$$
Answer: G
For an ideal solution of $A$ and $B$ liquid, when $x _ { A } = 0.2 ,$ total vapor pressure over solution was $560 torr$ and partial pressure of $A$ was $80 torr.$ What will be the composition of vapor when $x _ { A } = 0.8 ?$

Options:
A. $$y _ { B } = \cfrac { 3 } { 7 }$$
B. $$y _ { B } = \cfrac { 2 } { 5 }$$
C. $$y _ { B } = \cfrac { 2 } { 7 }$$
D. $$v _ { A } = \cfrac { 1 } { 7 }$$
E. $$y _ { A } = \cfrac { 8 } { 11 }$$
F. $$y _ { B } = \cfrac { 5 } { 7 }$$
G. $$y _ { B } = \cfrac { 6 } { 7 }$$
H. $$y _ { B } = \cfrac { 4 } { 7 }$$
I. $$y _ { B } = \cfrac { 9 } { 11 }$$
J. $$y _ { B } = \cfrac { 1 } { 7 }$$
Answer: A
A train moves from rest with acceleration $\alpha$ and in time ${t}_{1}$ covers a distance $x$. It then decelerates to rest at constant retardation $\beta$ for distance $y$ in time ${t}_{2}$. Then

Options:
A. $$\cfrac { \alpha }{ \beta } =\cfrac { t_{ 1 } }{ t_{ 2 }+1 }$$
B. $$\cfrac { \beta }{ \alpha } = \cfrac { t_{ 2 } + 1 }{ t_{ 1 } + 1 }$$
C. $$\cfrac { \beta }{ \alpha } = \cfrac { t_{ 1 } }{ t_{ 2 } + 1 }$$
D. $$\cfrac { x }{ y } =\cfrac { \beta }{\alpha } $$
E. $$\cfrac { \beta }{\alpha } =\cfrac { { t }_{ 1 } }{ { t }_{ 2 } } $$
F. $$\cfrac { \beta }{ \alpha } = \cfrac { t_{ 1 } + 1 }{ t_{ 2 } }$$
G. $$\cfrac { x }{ y } =\cfrac { \beta { t }_{ 1 } }{\alpha { t }_{ 2 } } $$
H. $$\cfrac { \beta }{\alpha } =\cfrac { { t }_{ 2 } }{ { t }_{ 1 } }$$
I. $$\cfrac { \beta }{ \alpha } =\cfrac { t_{ 2 }-1 }{ t_{ 1 } }$$
J. $$x=y$$
Answer: E
The degree of dissociation is $0.4$ at $400$K and $1.0$ atm for the gaseous reaction $PCl_5\rightleftharpoons PCl_3+Cl_2$. Assuming ideal behaviour of all the gases, calculate the density of equilibrium mixture at $400$K and $1.0$ atm. (Relative atomic mass of $P=31.0$ and $Cl=35.5$) unit: g/litre.

Options:
A. 1.3
B. 3.55
C. 3.53
D. 3.58
E. 67
F. 4.53
G. None of the above
H. 3.54
I. 3.45
J. 3.63
Answer: F
Ten charges having charge $1\mu C,\,8\mu C,\,27\mu C,.......1000\mu C$ are placed on the x-axis with co-ordinates $x = 1\,m,\,2\,m,\,3\,m,\,4\,m,\,.....\,10\,m.$ The net electric field intensity at the origin is:

Options:
A. $$4.5 \times {10^4}\,N/C$$
B. $$4.95 \times {10^4}\,N/C$$
C. $$9 \times {10^4}\,N/C$$
D. $$4.95 \times {10^5}\,N/C$$
E. $$4.95 \times {10^{ - 5}}\,N/C$$
F. $$9.45 \times {10^5}\,N/C$$
G. $$4.95 \times {10^{5}}\,N/C$$
H. $$9 \times {10^5}\,N/C$$
I. $$4.5 \times {10^5}\,N/C$$
Answer: D
A certain reaction obeys the rate equation (in the integrated form) $[C^{(1-n)} - C_0^{(1-n)}] = (n-1)$ kt where C$_o$ is the initial concentration of C is the concentration after time, t. Then:

Options:
A. the unit of k for n = 3 is mol litre$^{-1}$ sec$^{-1}$
B. the unit of k for n = 3 is litre$^{-1}$ mol$^{-2}$ sec$^{-1}$
C. the unit of k for n = 3 is litre$^{-1}$ mol$^{-3}$ sec$^{-1}$
D. the unit of k for n = 3 is litre$^{-2}$ mol$^{-2}$ sec$^{-1}$
E. the unit of k for n = 3 is litre$^2$ mol$^{-2}$ sec$^{-1}$
F. the unit of k for n = 3 is litre$^2$ mol$^{-1}$ sec$^{-1}$
G. the unit of k for n = 3 is litre$^{-2}$ mol$^{-1}$ sec$^{-1}$
H. the unit of k for n = 3 is litre$^{-1}$ mol$^{-1}$ sec$^{-1}
Answer: F
The kinetic energy $T$ of a particle moving along a circle of radius $R$ depends on the distance covered as $T=as^{2}$. The force acting on the particle is:

Options:
A. $$\dfrac{2as^{3}}{R^2}$$
B. $$\dfrac{2as^{2}}{R}$$
C. $$2as\left ( 1+\dfrac{s}{R^2} \right )^{\dfrac{1}{2}}$$
D. $$2a\dfrac{R^{2}}{s}$$
E. $$2as$$
F. $$\dfrac{2as^{3}}{R}$$
G. $$2as\left ( 1+\dfrac{s^{2}}{R} \right )^{\dfrac{1}{2}}$$
H. $$2as\left ( 1-\dfrac{s^{2}}{R^2} \right )^{\dfrac{1}{2}}$$
I. $$2as\left ( 1+\dfrac{s^{2}}{R^2} \right )^{\dfrac{1}{2}}$$
J. $$2as\left ( 1-\dfrac{s^{2}}{R} \right )^{\dfrac{1}{2}}$$
Answer: G
20 ml of 0.2 M HCN is titrated with 0.2 M NaOH. The pH at 20% neutralization and at the equivalence point will be respectively ($k_{a}$ for HCN= $4\times 10^{-10})$ (Neglect $H^{+}$ from water)

Options:
A. 8.80 and 9.4
B. 8.80 and 10.60
C. 9.4 and 11.2
D. 9.4 and 10.60
E. 8.80 and 11.60
F. 8.80 and 12.05
G. 8.80 and 11.40
H. 9.4 and 12.05
I. 8.80 and 11.2
J. 11.2 and 8.80
Answer: J
For a homogenous gaseous reaction $A \rightarrow 2B$, the initial pressure was $P_0$ while pressure after time $t$ was $P$ and $ P > P_0$. The expression for the rate constant K is

Options:
A. $$k=\dfrac{2.303}{t}log\dfrac{2P_0}{2P_0-2P}$$
B. $$k=\dfrac{2.303}{t}log\dfrac{2P_0}{2P_0-4P}$$
C. $$k=\dfrac{2.303}{t}log\dfrac{P_0}{2P_0-P/2}$$
D. $$k=\dfrac{2.303}{t}log\dfrac{2P_0}{2P_0-P/2}$$
E. $$k=\dfrac{2.303}{t}log\dfrac{P_0}{P_0-P}$$
F. $$k=\dfrac{2.303}{t}log\dfrac{P_0}{2P_0-P}$$
G. $$k=\dfrac{2.303}{t}log\dfrac{2P_0}{2P_0-3P}$$
H. $$k=\dfrac{2.303}{t}log\dfrac{P_0}{2P_0-2P}$$
I. $$k=\dfrac{2.303}{t}log\dfrac{2P_0}{2P_0-P}$$
J. $$k=\dfrac{2.303}{t}log\dfrac{P_0}{2P}$$
Answer: I
Which of the following statements is(are) correct?

Options:
A. The number of moles of $Na_2CO_3=CaCO_3=0.15$ mol.
B. The number of moles of $Na_2CO_3=CaCO_3=0.05$ mol.
C. The percentage purity of $Na_2CO_3$ is $60\%$.
D. The number of moles of $NaCl$ formed is $0.1$ mol.
E. The number of moles of $Na_2CO_3=CaCO_3=0.1$ mol.
F. The number of moles of $Na_2CO_3=CaCO_3=0.13$ mol.
G. The number of moles of $Na_2CO_3=CaCO_3=0.12$ mol.
H. The number of moles of $Na_2CO_3=CaCO_3=0.25$ mol.
Answer: E
Calculate the current through each resistance in the given circuit. Also, calculate the potential difference between points a and b. $E_1= 6 \ V,$            $E_2= 8 \ V,$                  $E_3= 10 \ V,$ $R_1=5 \Omega,$              $R_2=10 \Omega,$             $R_3=4\Omega,$Assuming that all the cells have no internal resistance.

Options:
A. $$\frac{130}{11} \ V$$
B. $$ \frac{120}{11} \ V $$
C. $$\frac{110}{11} \ V$$
D. $$\frac{80}{11} \ V$$
E. $$\frac{70}{11} \ V$$
F. $$ \frac{90}{11} \ V $$
G. $$\frac{140}{11} \ V$$
H. $$ \frac{60}{11} \ V $$
I. $$\frac{100}{11} \ V$$
J. $$ \frac{150}{11} \ V $$
Answer: F
Calculate the cell emf for the following reaction
$2 Ag^{+} (0.010 M)+H_{2}(1atm)$$\longrightarrow$$2Ag(s)+2H^{+}(pH=10.0).$

Options:
A. 1.04 V
B. 1.06 V
C. 0.92 V
D. 1.10 V
E. 1.08 V
F. 1.27 V
G. 0.56 V
H. 1.07 V
I. 1.12 V
J. 1.15 V
Answer: A
A ring of radius $R$ is having two charges $q$ and $2q$ distributed on its two half parts. The electric potential at a point on its axis at a distance of $2\sqrt {2}R$ from its centre is $\left (k = \dfrac {1}{4\pi \epsilon_{0}}\right )$

Options:
A. $$\dfrac{kq}{R}$$
B. $$\dfrac {3kq}{\sqrt {2}R}$$
C. $$\dfrac {3kq}{\sqrt {6}R}$$
D. $$\dfrac {3kq}{2R}$$
E. $$\dfrac {kq}{3R}$$
F. $$\dfrac{3kq}{2\sqrt{5}R}$$
G. $$\dfrac {3kq}{R}$$
H. $$\dfrac {3kq}{2\sqrt {3}R}$$
I. $$\dfrac {3kq}{2\sqrt {2}R}$$
J. $$\dfrac {3kq}{\sqrt {3}R}$$
Answer: A
A block of mass 6 kg is kept over a rough horizontal surface. The coeffcient of friction between the block and the surface is 0.1. At t=0.3, $(3\hat {i})$ m/s velocity is imparted to the block and simultaneously 2N $\left( \hat { -i }  \right) $ force starts acting on it. It's displacement first 5 second is

Options:
A. $$8\hat { i } $$
B. $$-12\hat { i }$$
C. $$9\hat { i }$$
D. $$-3\hat { i } $$
E. $$6\hat { i }$$
F. $$-8\hat { i } $$
G. $$-4\hat { i }$$
H. $$5\hat { i }$$
I. $$3\hat { i } $$
J. $$-6\hat { i }$$
Answer: I
The degree of  dissociation $\alpha$ of the reaction $N_2O_4(g) \rightleftharpoons 2NO_2 (g) O $ can be related to $K_p$ as

Options:
A. $$\alpha = \frac{\frac{K_p}{2P}}{3 + \frac{K_p}{2P}}$$
B. $$\alpha = \frac{\frac{K_p}{2P}}{4 + \frac{K_p}{2P}}$$
C. $$\alpha = \frac{\frac{K_p}{P}}{5 + \frac{K_p}{P}}$$
D. $$\alpha = \frac{K_p}{4 + K_p}$$
E. $$\alpha = \frac{K_p}{2 + K_p}$$
F. $$\alpha = \frac{\frac{K_p}{3P}}{4 + \frac{K_p}{3P}}$$
G. $$\alpha =\Bigg[ \frac{K_p}{4 + K_p} \Bigg]^{1/2}$$
H. $$\alpha = \frac{\frac{K_p}{P}}{3 + \frac{K_p}{P}}$$
I. $$\alpha = \Bigg[ \frac{K_p/P}{4 + K_p/P} \Bigg]^{1/2}$$
J. $$\alpha = \frac{\frac{K_p}{P}}{4 + \frac{K_p}{P}}$$
Answer: G
Two point masses \( m \) and \( 2m \), moving in the same horizontal plane with speeds \( 2v \) and \( v \), respectively, strike a uniform bar of length \( 8m \) and mass \( M \), initially at rest; the mass \( m \) strikes at a point \( 2a \) to the left of the bar's center \( C \), and the mass \( 2m \) strikes at a point \( a \) to the right of \( C \); after sticking to the bar, determine the angular velocity (\( \omega \)) about the new center of mass, the total energy (\( E \)), and the velocity of the center of mass (\( v_c \)).

Options:
A. $$E=\dfrac{3}{5}mv^{2}$$ and $$v_{c}=0$$ and $$\omega =\dfrac{v}{5a}$$
B. $$E=\dfrac{3}{9}mv^{2}$$
C. $$E=\dfrac{3}{6}mv^{2}$$
D. $$E=\dfrac{3}{8}mv^{2}$$
E. $$E=\dfrac{3}{11}mv^{2}$$
F. $$E=\dfrac{3}{10}mv^{2}$$
G. $$\omega =\dfrac{3v}{5a}$$
H. $$E=\dfrac{3}{7}mv^{2}$$
Answer: A
A particle having a charge of $20\mu C$ and mass $20\mu g$ moves along a circle of radius 5 cm under the action of a magnetic field B=0.1 tesla. When the particle is at P, uniform transverse electric field is switched on and it is found that the particle continues along the tangent with a uniform velocity. Find the electric field :

Options:
A. 0.6 V/m
B. 0.4 V/m
C. 5 V/m
D. 2 V/m
E. 1.0 V/m
F. 0.8 V/m
G. 0.7 V/m
H. 1.2 V/m
I. 1.5 V/m
J. 0.5 V/m
Answer: J
The degree of association can be defined as the number of moles of a particular substance associated per more of the substance taken.For example: If out of 10 mole of N$_2$, 3 mole of N$_2$ combine with H$_2$ to form NH$_3$, then degree of association of $N_2 = 0.3$Consider the equilibrium situation:  $N_2 (g) + 2H_2 (g)\rightleftharpoons  2 NH_3 (g)$ initially $N_2$ & $H_2$ were mixed in 1 : 3 molar ratio and after long time the mean molar mass of the mixture was found to be $\frac{34}{3}$ g. The degree of association of $N_2$ is________.

Options:
A. 0.55
B. 0.25
C. 0.35
D. 0.3
E. 0.45
F. 0.9
G. 0.5
H. 0.6
I. 0.4
J. 0.7
Answer: G
The standard heat of combustion of ethene gas is $-330 \ Kcalmol^{-1} $. Calculate $ {C = C} $ bond energy (in kcal/mol) assuming that bond energy of $C -H$ bond is $93.6 \ Kcalmol^{-1} $Given : $ \Delta H_{f}^{0}  $ for $ CO_2(g) $ and $ H_2O (l) $ are $-94.2$ and $-61\ Kcalmol^{-1} $ respectively. Heat of atomisation of carbon and hydrogen are $150$ and $51.5 \ Kcalmol^{-1} $ respectively.

Options:
A. 115 Kcal/mol
B. 117 Kcal/mol
C. 112 Kcal/mol
D. 95 Kcal/mol
E. 82 Kcal/mol
F. 97 Kcal/mol
G. 107 Kcal/mol
H. 102 Kcal/mol
I. 92 Kcal/mol
J. 105 Kcal/mol
Answer: C
10 litres of a mono-atomic ideal gas atomic ideal gas at $0^oC$ and 10 atm pressure is suddenly released to 1atm pressure and the gas expands adiabatically against this constant pressure. The final temperature and volume of the gas respectively are:

Options:
A. $$T=174.9 K, V=78.8 \quad litres$$
B. $$T=164.4 K,V=79.8 \quad litres$$
C. $$T=163.6 K,V=73.1 \quad litres$$
D. $$T=167.8 K,V=76.5 \quad litres$$
E. $$T=153 K,V=57 \quad litres$$
F. $$T=161.2 K,V=68.3 \quad litres$$
G. $$T=166.2 K,V=77.4 \quad litres$$
H. $$T=169.2 K,V=73.1 \quad litres$$
I. $$T=165.4 K,V=64.04 \quad litres $$
J. $$T=168.6 K, V=75.4 litres$$
Answer: I
A particle of charge $q$ and mass $m$ starts moving from the origin under the action of an electric field $E = E_oi$ and $B = B_oi$ with a velocity $V = V_oi$.The speed of the article will become $\frac {\sqrt 5}{2} v_o$ after a time

Options:
A. $$\frac{{\sqrt 5 - m{v_0}}}{{qE}}$$
B. $$\frac{{\sqrt 3 m{v_0}}}{{qE}}$$
C. $$\frac{{m{v_0}}}{{qE}}$$
D. $$\frac{{\sqrt 7 m{v_0}}}{{2qE}}$$
E. $$\frac{{\sqrt 4 m{v_0}}}{{qE}}$$
F. $$\frac{{m{v_0}}}{{2qE}}$$
G. $$\frac{{\sqrt 2 m{v_0}}}{{2qE}}$$
H. $$\frac{{\sqrt 6 m{v_0}}}{{2qE}}$$
I. $$\frac{{2\sqrt 3 m{v_0}}}{{qE}}$$
J. $$\frac{{\sqrt 2 m{v_0}}}{{qE}}$$
Answer: C
A cylinder filled with hydrogen at $500\ K$ exerts a pressure of $4$ atmospheres. If hydrogen is replaced by equal mass of Helium at the same temperature, what will be i) the pressure exerted by helium ii) the relative number of molecules of hydrogen and helium? (Molecular weight of hydrogen $= 2$ and molecular weight of helium $= 4$).

Options:
A. $$4\ atm, 0.5$$
B. $$2\ atm, 2$$
C. $$4\ atm, 1$$
D. $$2\ atm, 1$$
E. $$2\ atm, 4$$
F. $$2\ atm, 0.5$$
G. $$8\ atm, 1$$
H. $$4\ atm, 2$$
I. $$2\ atm, 0.25$$
Answer: F
The energy change for the alternating reaction that yields chlorine sodium $(Cl^{+}Na^{-})$ will be:$2Na(s)\, +\, Cl_2(g)\,\rightarrow\, 2Cl^{+}Na^{-}(s)$Given that:Lattice energy of $NaCl\,=\,-787\, kJ\,mol^{-1}$Electron affinity of $Na\,=\,-52.9\, kJ\, mol^{-1}$Ionisation energy of $Cl\, =\, +\,1251\, kJ\, mol^{-1}$BE of $Cl_2\,=\,244\, kJ\, mol^{-1}$Heat of sublimation of $Na(s)\, =\,107.3\, kJ\, mol^{-1}$$\Delta H_f(NaCl)\, =\,-411\, kJ\, mol^{-1}$.

Options:
A. +1240 kJ
B. +840 kJ
C. +650 kJ
D. +630 kJ
E. -410 kJ
F. +640 kJ
G. +635 kJ
H. +410 kJ
I. +1280 kJ
J. +660 kJ
Answer: F
Magnetic flux linked with a stationary loop of resistance $4W$ varies with respect to time during the time period $2$ second, as $f=3t(2-t)$ the amount of heat generated (in joules) during that time is

Options:
A. 8
B. 3
C. 10
D. 4
E. 16
F. 12
G. 18
H. 6
I. 2
J. 14
Answer: I
Three rods of equal lengths are joined to form an equilateral triangle $ABC,\ D$ is the mid-point of $AB$ The coefficient of linear expansion is $\alpha _{1}$ for material of rod $AB$ and $BC$, $\alpha _{2}$ for material of rod $AC$. If the distance $DC$ remains constant for small changes in temperature. then:

Options:
A. $$\alpha_{1}=\alpha_{2}$$
B. $$\alpha_{1}= 9\alpha_{2}$$
C. $$\alpha_{1}= 3\alpha_{2}$$
D. $$\alpha_{1}= 4\alpha_{2}$$
E. $$\alpha_{1}= 2\alpha_{2}$$
F. $$\alpha_{1}= 6\alpha_{2}$$
G. $$\alpha_{1}= 8\alpha_{2}$$
H. $$\alpha_{1}= 5\alpha_{2}$$
I. $$\alpha_{1}= 7\alpha_{2}$$
Answer: D
Which of the following species represents the given mode of hybridisation, $sp^{2}-sp^{2}-sp^{2}-sp$ for the carbon atom as we move from left to right?

Options:
A. $$\overset { \ominus }{ C } H_{2}-CH=CH-CH \equiv CH$$
B. $$\overset { \ominus }{ C } H_{2}-CH_{2}-CH=CH_{2}$$
C. $$\overset { \ominus }{ C } H_{2}-CH=CH-CH \equiv N$$
D. $$\overset { \ominus }{ C } H_{2}-CH=CH-C \equiv CH$$
E. $$\overset { \ominus }{ C } H_{2}-CH=CH-CH_{2}$$
F. $${ C } H_{3}-CH=CH-C \equiv N$$
G. $$\overset { \ominus }{ C } H_{2}-CH=CH-C \equiv N$$
H. $$\overset { \ominus }{ C } H_{2}-CH=CH-CH_{3}$$
I. $$\overset { \ominus }{ C } H_{2}-CH=CH-CH \equiv C \overset { \ominus }{ H }$$
J. $${ C } H_{2}=CH=CH_{2}-C \equiv N$$
Answer: G
${l_2}(aq)\rightleftharpoons {l_2}(oil)$ Equilibrium constant is ${K_1}$
${l_2}(oil)\rightleftharpoons {l_2}(ether)$ Equilibrium constant is ${K_2}$
for the reaction
${l_2}(aq)\rightleftharpoons {l_2}(ether)$ Equilibrium constant is ${K_3}$
The reaction between ${K_1},{K_2},{K_3}$ is

Options:
A. ${K_3} = {K_2} + {K_1}$
B. ${K_3} = {K_1} \times \frac{1}{K_2}$
C. $${K_3} = {K_2} /{K_1}$$
D. $${K_3} = {K_1} {K_2}$$
E. ${K_3} = {K_1} + {K_2}$
F. ${K_3} = {K_2} - {K_1}$
G. ${K_3} = {K_1} - {K_2}$
H. $${K_3} = {K_1} /{K_2}$$
Answer: H
Three observers $A,B$ and $C$ measure the speed of light coming from a source as $v_A,v_B$ and $v_C$. Observer $A$ moves towards the source, $C$ moves away from source and $B$ stays stationary. The surrounding medium is water. If A and C are moving at the same speed, then

Options:
A. $$\displaystyle v_B=\frac{1}{2}(v_C+v_A)$$
B. $$\displaystyle v_A < v_B < v_C $$
C. $$\displaystyle v_A>v_B>v_C$$
D. $$\displaystyle v_B = \frac{1}{3}(v_C + 2v_A)$$
E. $$\displaystyle v_B = \frac{1}{3}(v_C + v_A)$$
F. $$\displaystyle v_A=v_B=v_C$$
G. $$\displaystyle v_B = \frac{1}{2}(v_C + v_A + 1)$$
H. $$\displaystyle v_B = \frac{1}{2}(v_C + 3v_A)$$
I. $$\displaystyle v_B = \frac{1}{2}(v_C + 2v_A)$$
J. $$\displaystyle v_B = \frac{1}{4}(v_C + 3v_A)$$
Answer: A
1 L concentrated NACL solution is electrolysed using Hg cathode. Calculate the pH of solution after passing 0.005 F change to this solution. Assume volume of electrolyte remains constant the electrolysis

Options:
A. 12.3
B. 5.3
C. 13.3
D. 12.1
E. 11.3
F. 12.7
G. 11.7
H. 13.7
I. 12.9
J. Will remain unchanged, i.e solution will have pH = 7
Answer: F
A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L_0$ the particle speed is $v = v_0$. The piston is moved inward at  a very low speed V such that $V << \dfrac{dL}{L} v_0$. Where dL is the infinitesimal displacement of the piston. 
Which of the following statement (s) is/are correct ?

Options:
A. The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
B. The particle's kinetic energy increases by a factor of 2 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
C. The particle's kinetic energy increases by a factor of 8 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
D. The particle's kinetic energy increases by a factor of 3 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
E. The particle's kinetic energy increases by a factor of 6 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
F. The particle's kinetic energy increases by a factor of 5 when the piston is moved inward from $L_0$ to $\dfrac{1}{2} L_0$
Answer: A
An ideal gas is trapped between Hg thread of $12\ cm$ and the closed lower end of a narrow vertical tube of uniform cross section. Length of the air column is $20.5\ cm$, when the open end is kept upward. If the tube is making $30^{0}$with the horizontal then the length of the air column is (assuming temperature to be constant and atmospheric pressure = $76\ cm$ of $Hg$)

Options:
A. $$20.2\ cm$$
B. 20.8\ cm
C. 23.0\ cm
D. 21.5\ cm
E. 19.5\ cm
F. 21.0\ cm
G. $$24\ cm$$
H. $18\ cm
I. $$22\ cm$$
J. 21.8\ cm
Answer: I
The solubility product of $Pb_3(AsO_4)_2$ is $4.1\, \times\, 10^{-36}.\, E^{\ominus}$ for the reaction:
$$Pb_3(AsO_4)_2(s)\, +\, 6e^-\, \rightleftharpoons\, 3Pb(s)\, +\, 2AsO_4^{2-}\, if\, E^{\ominus}_{Pb^{2+}\, |\, Pb}\, =\, -0.13\, V$$

Options:
A. $$-0.13 V$$
B. $$+0.13 V$$
C. $$-0.478 V$$
D. $$-0.378 V$$
E. $$-0.438 V$$
F. $$-0.578 V$$
G. $$-0.138 V$$
H. $$+0.478 V$$
I. $$-0.278 V$$
Answer: C
A bob B of mass 1 kg is suspended from the ceiling of a toy train. The train oscillates simple harmonically in horizontal direction with angular frequency $\Theta =5rad/s$ and amplitude a =0.1 m. What is the ratio of maximum and minimum tensions in the string AB during the motion $(g=10{ ms }^{ -2 }\quad $&$ \quad tan\quad { 37 }^{ \circ  }=3/4)$

Options:
A. 1.75
B. 1
C. 2.25
D. 2.5
E. 1.5
F. 1.25
G. 3
H. 5
I. 4
J. 2
Answer: J
From the following reactions at $298\ K$.(A) $CaC_{2}(s) + 2H_{2}O(l) \rightarrow Ca(OH)_{2}(s) + C_{2}H_{2} (g);\ \Delta H^{\circ}= - 127.9\ kJ\ mol^{-1}$(B) $Ca(s) + \dfrac {1}{2} O_{2}(g) \rightarrow CaO(s) ;\ \Delta H=- 635.1kJ\ mol^{-1}$(C) $CaO(s) + H_{2}O(l) \rightarrow Ca(OH)_{2}(s);\ \Delta H=- 65.2\ kJ\ mol^{-1}$(D) $C(s) + O_{2}(s) \rightarrow CO_{2}(s) ;\ \Delta H=- 393.5\ kJ\ mol^{-1}$(E) $C_{2}H_{2}(g) + \dfrac {5}{2}O_{2}(g) \rightarrow 2CO_{2}(g) + H_{2}O(l);\ \Delta H= - 1299.58\ kJ\ mol^{-1}$Calculate the heat of formation of $CaC_{2}(s)$ at $298\ K$.

Options:
A. -190.82\ kJ\ mol^{-1}
B. $$-190.22\ kJ\ mol^{-1}$$
C. -127.90\ kJ\ mol^{-1}
D. -127.92\ kJ\ mol^{-1}
E. $$+59.82\ kJ\ mol^{-1}$$
F. -58.82\ kJ\ mol^{-1}
G. $$+190.22\ kJ\ mol^{-1}$$
H. -59.92\ kJ\ mol^{-1}
I. $$-59.82\ kJ\ mol^{-1}$$
J. -60.82\ kJ\ mol^{-1}
Answer: I
If lattice energy of a compound $MX_3$ is $5000$ Kj/mole, $\Delta H_{hydration}$ of $M^{+3}=-4000$ KJ/mole and it is completely soluble in water then find $\Delta H_{hydration}$ of $X^-$.

Options:
A. $305$ KJ/mole
B. $290$ KJ/mole
C. $310$ KJ/mole
D. 330 KJ/mole
E. 320 KJ/mole
F. $295$ KJ/mole
G. 300 KJ/mole
H. $271$ KJ/mole
I. 281 KJ/mole
J. $380$ KJ/mole
Answer: I
A wire shaped as a semicircle of radius \( a \) rotates about an axis \( PQ \) with a constant angular velocity \( \omega = \frac{1}{\sqrt{LC}} \), driven by an external agent. A uniform magnetic field \( B \) exists in space and is directed into the plane of the circuit. The left part of the circuit, containing a resistor \( R \), an inductor \( L \), and a capacitor \( C \), remains at rest, while the rotating semicircular wire interacts with the magnetic field. Analyze the behavior of the system based on these conditions.

Options:
A. The maximum power delivered by the external agent is$$\frac{\pi^2B^2a^4}{3LCR}$$
B. The maximum power delivered by the external agent is $$\frac{\pi^2B^2a^4}{6LCR}$$
C. The rms value of current in the circuit is $\displaystyle\frac{\pi Ba^2}{R\sqrt{2LC}}$
D. The maximum power delivered by the external agent is $\displaystyle\frac{\pi^2B^2a^4}{4LCR}$
Answer: D
Which is correct stability order of the given species?
$Ph\overset{\oplus}{C}H_2, Ph_2\overset{\oplus}{C}H, Ph_3\overset{\oplus}{C}$ and $\overset{\oplus}{C}H_3$[Ph$=$ Phenyl group]

Options:
A. $$Ph\overset{\oplus}{C}H_2 > \overset{\oplus}{C}H_3 > Ph_2\overset{\oplus}{C}H > Ph_3\overset{\oplus}{C}$$
B. $$\overset{\oplus}{C}H_3 > Ph_3\overset{\oplus}{C} > Ph_2\overset{\oplus}{C}H > Ph\overset{\oplus}{C}H_2$$
C. $$Ph_3\overset{\oplus}{C} > Ph\overset{\oplus}{C}H_2 > \overset{\oplus}{C}H_3 > Ph_2\overset{\oplus}{C}H$$
D. $$Ph\overset{\oplus}{C}H_2 > Ph_2\overset{\oplus}{C}H > \overset{\oplus}{C}H_3 > Ph_3\overset{\oplus}{C}$$
E. $$Ph_3\overset{\oplus}{C} > \overset{\oplus}{C}H_3 > Ph_2\overset{\oplus}{C}H > Ph\overset{\oplus}{C}H_2$$
F. $$Ph_3\overset{\oplus}{C} > \overset{\oplus}{C}H_3 > Ph\overset{\oplus}{C}H_2 > Ph_2\overset{\oplus}{C}H$$
G. $$Ph_3\overset{\oplus} > \overset{\oplus}{C}H_3 > Ph_2\overset{\oplus}{C}H > Ph\overset{\oplus}{C}H_2$$
H. $$Ph_3\overset{\oplus}{C} > Ph\overset{\oplus}{C}H_2 > Ph_2\overset{\oplus}{C}H > \overset{\oplus}{C}H_3$$
I. $$Ph_3\overset{\oplus}{C} > Ph_2\overset{\oplus}{C}H > Ph\overset{\oplus}{C}H_2 > \overset{\oplus}{C}H_3$$
J. $$Ph_3\overset{\oplus}{C} > Ph_2\overset{\oplus}{C}H > \overset{\oplus}{C}H_3 > Ph\overset{\oplus}{C}H_2$$
Answer: D
If $0.2\ mol$ of $H_{2}(g)$ and $2\ mol$ of $S(s)$ are mixed in a $1\ dm^{3}$ vessel at $90^{\circ}C$, the partial pressure of $H_{2}S(g)$ formed according to the reaction, $H_{2}(g) + S(s)\rightleftharpoons H_{2}S, K_{P} = 6.8\times 10^{-2}$ would be:

Options:
A. $$0.24\ atm$$
B. $$0.18\ atm$$
C. $$0.36\ atm$$
D. $$0.38\ atm$$
E. $$0.19\ atm$$
F. $$0.20\ atm$$
G. $$0.072\ atm$$
H. $$0.17\ atm$$
I. $$0.6\ atm$$
J. $$0.23\ atm$$
Answer: E
Two plates of masses $m_{1}$ and $m_{2}$ are connected by a spring of force constant K. What force should be applied to the upper plate so that $m_{2}$ plate leaves the contact after the force is removed?

Options:
A. $$F= m_{1}.m_{2}\left(\frac{K}{m_{1} + m_{2} - m_{1}}\right)g$$
B. $$F = m_{1}g + m_{2}g$$
C. $$F = m_{1}.m_{2}\left(\frac{K}{m_{1} + m_{2} + m_{2}}\right)g$$
D. $$F= m_{1}.m_{2}(\frac{K}{m_{1} + m_{2} + m_{1}})g$$
E. $$F = m_{1}.m_{2}(\frac{K}{m_{1} + m_{2} - m_{2}})g$$
F. $$F= (\frac{m_{1}.m_{2}}{m_{1} + m_{2}})g$$
G. $$F= m_{1}.m_{2}(\frac{K}{m_{1} - m_{2}})g$$
H. $$F= m_{1}.m_{2}(\frac{K}{m_{1} + m_{2} + m_{1} + m_{2}})g$$
I. $$F= m_{1}.m_{2}(\frac{K}{m_{1} + m_{2}})g$$
J. $$F = m_{1}g$$
Answer: B
A cone of radius r and height h rests on a rough horizontal surface, the coefficient of friction between the cone and the surface being $\mu$. A gradually increasing horizontal force F is applied to the vertex of the cone. The largest value of $\mu$ for which the cone will slide before it topples is:

Options:
A. $$\mu = \dfrac{2r}{5h}$$
B. $$\mu = \dfrac{r}{3h}$$
C. $$\mu = \dfrac{2r}{3h}$$
D. $$\mu = \dfrac{r}{h}$$
E. $$\mu = \dfrac{4r}{5h}$$
F. $$\mu = \dfrac{r}{2h}$$
G. $$\mu = \dfrac{3r}{4h}$$
H. $$\mu = \dfrac{r}{4h}$$
I. $$\mu = \sqrt{\dfrac{r}{2h}}$$
J. $$\mu = \dfrac{3r}{5h}$$
Answer: D
In a flexible balloon, 2 moles of $SO_{2}$ having initial volume of 1kl at a temperature of $27^{o}C$ is filled. ($SO_{2}$ is a linear triatomic gas). The gas is first expanded to thrice its initial volume  isobarically and then expanded adiabatically so as to attain its initial temperature. Assuming gas is ideal, $\gamma = \dfrac{4}{3}$ and $R=\dfrac{25}{3}Jmol^{-1}K^{-1}$. Work done by the gas in the whole process is:

Options:
A. $$3.2kJ$$
B. $$15kJ$$
C. $$18kJ$$
D. $$2kJ$$
E. $$30kJ$$
F. $$40kJ$$
G. $$12kJ$$
H. $$20kJ$$
I. $$16kJ$$
J. $$10kJ$$
Answer: B
The voltage and the current of an $a.c$ circuit are $V=100\sin(100t)$ volt and $i=100\sin(100t+\pi/3)mA$ receptively. The power dissipated in the circuit is:

Options:
A. $$5.0W$$
B. $$5.5W$$
C. $$3.75W$$
D. $$7.5W$$
E. $$10W$$
F. $$2.5W$$
G. $$12.5W$$
H. $$6.25W$$
I. $$4.5W$$
J. $${10}^{4}W$$
Answer: A
At what temperature does a lamp (100 W, 200 V) work, if it is given that resistance of cold tungsten filament is $40\Omega $. Take $\alpha =3\times 10^{ -3 }/^{ o }C$ and $25^{ o }C$ as normal room temperature.

Options:
A. $$3020^{ o }C$$
B. $$325^{ o }C$$
C. $$3055^{ o }C$$
D. $$300^{ o }C$$
E. $$3000^{ o }C$$
F. $$3200^{ o }C$$
G. $$3075^{ o }C$$
H. $$3070^{ o }C$$
I. $$3050^{ o }C$$
J. $$3025^{ o }C$$
Answer: E
If radius vector of a point varies with time $t$ as $\vec { r } =\vec { b } t\left( 1-\alpha t \right) $ where $\vec { b } $ is a constant vector and a is a positive constant, then its

Options:
A. Magnitude of acceleration is changing but direction of acceleration is constant
B. Magnitude of velocity is constant but its direction is changing
C. Magnitude of acceleration is changing but its direction is constant
D. Magnitude of velocity is constant but its direction is unchanged
E. Magnitude of acceleration is changing but its direction is unchanged
F. Magnitude of acceleration is constant but direction of acceleration is changing
G. Acceleration is constant
H. Velocity is constant
I. Magnitude of velocity is changing but its direction is unchanged
Answer: F
Calculate $\Delta G^0$ (in kcal/mole) for decomposition of $Cl_2 (g) \rightleftharpoons 2Cl(g)$, if chlorine molecules are 50% dissociated at 1000 k at a pressure of 15 atm at equilibrium (In 20= 2.99)

Options:
A. -2.56
B. -2.99
C. -4.13
D. -3.25
E. -5.99
F. -3.52
G. -4.56
H. -3.14
I. -2.01
J. -2.6
Answer: J
A projectile is fired horizontally from the top of an inclined plane (of inclination $45^{\circ}$ with horizontally ) with speed $=50m/s$. If $g=10m/s^{2}$ the range measured along the incline is

Options:
A. $$750\sqrt{2}m$$
B. $$250\sqrt{2}m$$
C. $$200\sqrt{2}m$$
D. $$none of these$$
E. $$600\sqrt{2}m$$
F. $$550\sqrt{2}m$$
G. $$400\sqrt{2}m$$
H. $$500\sqrt{2}m$$
I. $$450\sqrt{2}m$$
J. $$500m$$
Answer: H
An inclined plane makes an angle of \( 30^\circ \) with the horizontal. A groove \( OA \) of length 5 m is cut in the plane, making an angle of \( 30^\circ \) with the \( OX \)-axis, where \( OX \) lies on the horizontal ground. A short smooth cylinder is free to slide down under the influence of gravity. The time taken by the cylinder to slide from point \( A \) to point \( O \) is to be determined, with \( g = 10 \, \text{m/s}^2 \).

Options:
A. $$1s$$
B. $$3s$$
C. $$2.25s$$
D. $$3.5s$$
E. $$2.5s$$
F. $$1.5s$$
G. $$4s$$
H. $$2s$$
Answer: H
10 mole of $N{H}_{3}$ is heated at 15 atm from $27$ to $347$ assuming volume constant. The pressure at equilibrium is found to be 50 atm. The equilibrium constant for dissociation of                $N{H}_{3} : 2N{H}_{3} \rightleftharpoons {N}_{2} + 3{H}_{2}$; $\Delta H = 91.94   kJ$ can be written as;                   ${K}_{p} = \displaystyle\frac{{P}_{{N}_{2}} \times {\left({P}_{{H}_{2}}\right)}^{3}}{{\left({P}_{N{H}_{3}}\right)}^{2}} {\left(atm\right)}^{2}$The degree of dissociation of $N{H}_{3}$ is :

Options:
A. 20%
B. 46%
C. 58.3%
D. 55%
E. 59.3%
F. 56.3%
G. 63.3%
H. 61.3%
I. 48%
J. none of these
Answer: H
The time period of a particle executing SHM is $8$s. At $t=0$, it is at mean position. If A is the amplitude of particle, then the distance travelled by particle (in second) is?

Options:
A. $$\left(\displaystyle 1 - \frac{1}{2\sqrt{2}} \right)A$$
B. $$2A$$
C. $$\left(\displaystyle 1 - \frac{2}{\sqrt{2}} \right)A$$
D. $$\left(\displaystyle 1-\frac{1}{\sqrt 2}\right)A$$
E. $$\left(\displaystyle \frac{3}{2} - \frac{1}{\sqrt{2}} \right)A$$
F. $$\left(\displaystyle \frac{1}{2} - \frac{1}{\sqrt{2}} \right)A$$
G. $$\displaystyle\frac{A}{\sqrt{2}}$$
H. $$\sqrt{2}A$$
I. $$\left(\displaystyle 1 + \frac{1}{\sqrt 2} \right)A$$
J. $$\left(\displaystyle \frac{3}{2} + \frac{1}{\sqrt{2}} \right)A$$
Answer: D
Consider the following half-cell reactions and associated standard half-cell potentials and determine the maximum voltage that obtained by combination resulting in spontaneous process :
$AuBr_{4}^{-}$(aq) + $3e^{-}$ $\rightarrow$ Au(s) + $4Br^{-}$(aq) ; $E^o$ = -0.86 V
$Eu^{3+}$(aq) + $e^{-}$ $\rightarrow$ $Eu^{2+}$(aq) ;    $E^o$ = - 0.43 V
${Sn}^{2+}$(aq) + ${2e}^{-}$ $\rightarrow$ Sn(s) ;   ${E}^{o}$ = - 0.14 V
${IO}^{-}$(aq) +${H_2}O$(l) + ${2e}^{-}$ $\rightarrow$ ${I}^{-}$(aq) + ${2OH}^{-}$ (aq) ;   ${E}^{o}$ = + 0.49 V

Options:
A. + 0.82
B. + 1.54
C. + 0.72
D. + 0.90
E. 0.80
F. + 1.35
G. + 0.80
H. + 1.00
I. + 1.10
J. + 1.23
Answer: C
Three ball A, B and C of masses 2 kg, 4 kg and 8 kg, respectively, move along the same straight line and in the same direction, with velocities $4 m/s, 1 m/s$ and $3/4 m/s$. If $A$ collides with $B$ and subsequently $B$ collides with $C$, find the velocity of ball $A$ and ball $B$ after collision, taking the coefficient of restitution as unity.

Options:
A. $$V_A = 3, V_B = 0$$
B. $$V_A = 0, V_B = 0$$
C. $$V_A = 3, V_B = 9/4$$
D. $$V_A = 1, V_B = 0$$
E. $$V_A = 0, V_B = 4$$
F. $$V_A = 0, V_B = 3$$
G. $$V_A = 2, V_B = 3$$
H. $$V_A = 1, V_B = 3$$
I. $$V_A = 2, V_B = 2$$
J. $$V_A = 1, V_B = 2$$
Answer: B
An inductor of inductance L = 8 H and resistor of resistance $ R = 2 \Omega $ are connected in series with a battery of emf E = 10 V.If the switch is closed at t = 0,then the voltage drop across the inductor at t = 1 s will be (in volts)

Options:
A. $$ 5e \theta^{1/2} $$
B. $$\frac{5}{6} \theta^{1/2}$$
C. $$\frac{5}{9} \theta^{1/2}$$
D. $$\frac{5}{7} \theta^{1/2}$$
E. $$\frac{5}{3} \theta^{1/2}$$
F. $$ \frac {5}{8} \theta^{1/2} $$
G. $$ 10 \theta^{1/2} $$
H. $$ \frac {5}{2} \theta^{1/2} $$
I. $$\frac{5}{4} \theta^{1/2}$$
Answer: H
$\Delta_fG^o$ at $500 \ K$  for substance 'S' in liquid state and gaseous state are $+100.7 \ kcal \ mol^{-1}$ and $+103 \ kcal \ mol^{-1}$, respectively. Vapour pressure of liquid 'S' at $500 \ K$  is approximately equal to: $(R=2 \  cal  \ K^{-1}mol^{-1})$.

Options:
A. 0.01 \ atm
B. 5 \ atm
C. 0.1 \ atm
D. $10$ atm
E. 1 \ atm
F. 100 \ atm
G. $1$ atm
H. $100$ atm
I. $1000$ atm
J. $0.1$ atm
Answer: D
The average pressure exerted on the walls of a container filled with a certain gas will be doubled if:

Options:
A. the average speed of molecules gets double.
B. The root means square velocity of molecules gets double.
C. The root means square velocity of molecules gets increased by a factor of 2.5.
D. The average velocity of molecules gets double.
E. The root means square velocity of molecules gets increased by a factor of 1.5.
F. The average kinetic energy of molecules gets double.
G. The root means square velocity of molecules gets tripled.
H. The root means square velocity of molecules gets increased by a factor of 1.2.
I. The root means square velocity of molecules gets quadrupled.
J. the mean square velocity of molecules gets double.
Answer: B
A body of mass m is moving along x-axis under the influence of conservative force with a potential energy given by $U(x)=\dfrac { -\quad cx }{ { x }^{ 2 }+{ a }^{ 2 } } $ Where c and a are positive constant, When displaced slightly from stable equilibrium position x=${ x }_{ 0 }$. It will experience restoring force proportional to its displacement, the force constant being $\left[ \dfrac { { d }^{ 2 }U }{ { dx }^{ 2 } }  \right] _{ x={ x }_{ 0 } }$ The body is in equilibrium  at (Moderate)

Options:
A. x= 0
B. $x= \pm a$
C. No value of x
D. $x= -a, x\neq +a$
E. x= -0.5a
F. $x= +a, x \neq -a$
G. x= 0.3a
H. x= 0.25a
I. x= 0.1a
J. x= 0.5a
Answer: B
A particular water sample has $136$ ppm $CaS{O_4}$,what fraction of the water must be evaporated from the sample before solid $CaS{O_4}$ begins to deposit $\left( {KspofCaS{O_4} = 9 \times {{10}^{ - 6}}} \right)$

Options:
A. $46$%
B. $67$%
C. $18$%
D. $23$%
E. $20$%
F. 17%
G. 16%
H. 19%
I. $92$%
Answer: B
At time t = 0, one particle is at maximum positive amplitude and the other particle is at $\cfrac{1}{\sqrt{2}}$ of the positive amplitude. Their amplitudes and time periods T are same. If they are approaching, find the time by which they cross each other :

Options:
A. $$\cfrac{T}{8}$$
B. $$\cfrac{T}{15}$$
C. $$\cfrac{T}{10}$$
D. $$\cfrac{T}{18}$$
E. $$\cfrac {T}{6}$$
F. $$\cfrac{T}{14}$$
G. $$\cfrac {T}{16}$$
H. $$\cfrac{T}{20}$$
I. $$\cfrac {T}{24}$$
J. $$\cfrac {T}{12}$$
Answer: J
Mass density of a rod of length L change with respect to distance x from one end is accordind to equation $\lambda  = \beta \,x$ , where $\beta $= constant. Then the distance of centre of mass from x=0 is...........

Options:
A. $$\dfrac{L}{3}$$
B. $$\dfrac{3L}{2}$$
C. $$\dfrac{3L}{5}$$
D. $$\dfrac{L}{5}$$
E. $$\dfrac{L}{4}$$
F. $$\dfrac{2L}{5}$$
G. $$\dfrac{4L}{5}$$
H. $$\dfrac{2L}{3}$$
I. $$\dfrac{L}{6}$$
J. $$\dfrac{L}{2}$$
Answer: A
The vapour pressure of two pure liquids A and B which form an ideal solution are 1000 and 1600 torr respectively at 400 K. A liquid solution of A and B for which the mole fraction of A is 0.60 is contained in a cylinder by a piston on which the pressure can be varied. The solution use slowly vapourised at 400 K by decreasing the applied pressure. What is the composition of last droplet of liquid remaining in equilibrium with vapour?

Options:
A. $$X_A= 0.35, X_B= 0.65$$
B. $$X_A= 0.50, X_B= 0.50$$
C. $$X_A= 0.20, X_B= 0.80$$
D. $$X_A= 0.80, X_B= 0.20$$
E. $$X_A= 0.70, X_B= 0.30$$
F. $$X_A= 0.40, X_B= 0.60$$
G. $$X_A= 0.30, X_B= 0.70$$
H. $$X_A= 0.90, X_B= 0.10$$
I. $$X_A= 0.60, X_B= 0.40$$
Answer: E