MikaStars39/nano-eval huggingface dataset:
A particle moves in a circle of radius $20 \mathrm { cm }$ .Its linear speed is given by $v = 2 t$ where $t$ is  in $s$ and $v$ in$\mathrm { m } /s$. Then 
A) the radial acceleration at $t = 2 s \text { is } 80 m s ^ { - 2 }$
B) tangential acceleration at $t = 2 s \text { is } 2 m s ^ { - 2 }$
C) net acceleration at $t = 2 s$ greater than  $80 \mathrm { ms } ^ { - 2 }$
D) tangential acceleration remains constant in  magnitude.

Options:
A. only b, c, d are correct
B. only a, b, c are correct
C. only b, c, a are correct
D. all a, b,c,d are correct
E. only a, b, d are correct
F. only a, b, c, d are correct
G. only a,c, d are correct
H. only a, c are correct
I. only b, d, a are correct
Answer: G
${ NO }_{ 2 }$ is involved in the formation of smog and acid rain. It is formed importantly as 
${ NO }(g)+{ O }_{ 3 }(g)\rightleftharpoons { NO }_{ 2 }(g)+{ O }_{ 2 }(g)$ ${ K }_{ C }=6.0\times 1{ 0 }^{ 34 }$ The air over a metropolitan city contained $1.01\times { 0 }^{ -5 }M-NO$, $1.0\times 1{ 0 }^{ -6 }M-{ O }_{ 3 }$, $2.5\times 10^{ -4 }M-N{ O }_{ 2 }$, $8.2\times 10^{ -3 }M-{ O }_{ 2 }$ These data suggest that

Options:
A. More of ${ NO }$ and ${ O }_{ 2 }$ tend to be formed
B. More of NO and ${ O }_{ 2 }$ tend to be formed
C. More of NO and ${ O }_{ 3 }$ tend to be formed
D. More of ${ O }_{ 3 }$ and ${ O }_{ 2 }$ tend to be formed
E. More of ${ NO }_{ 2 }$ and ${ O }_{ 3 }$ tend to be formed
F. More of ${ NO }_{ 2 }$ and ${ O }_{ 2 }$ tend to be formed
G. No tendency to change because the reaction is at equilibrium
H. More of ${ O }_{ 2 }$ and ${ O }_{ 3 }$ tend to be formed
Answer: C
A particle of charge per unit mass $\alpha $ is released from origin with a velocity $\overrightarrow v  = {v_0}i$ in a uniform magnetic field $\overrightarrow B  =  - {B_0}K$ If the particle through $\left( {0,y,0} \right)$ then $y$ is equal to

Options:
A. $$\dfrac{{ - 2{v_0}}}{{{B_0}\alpha }}$$
B. $$\dfrac{{3{v_0}}}{{{B_0}\alpha}}$$
C. $$\dfrac{{4{v_0}}}{{2{B_0}\alpha}}$$
D. $$\dfrac{{ - {v_0}}}{{{B_0}\alpha }}$$
E. $$\dfrac{{2{v_0}}}{{3{B_0}\alpha}}$$
F. $$\dfrac{{ - 3{v_0}}}{{2{B_0}\alpha}}$$
G. $$\dfrac{{5{v_0}}}{{2{B_0}\alpha}}$$
H. $$\dfrac{{3{v_0}}}{{2{B_0}\alpha}}$$
I. $$\dfrac{{2{v_0}}}{{{B_0}\alpha }}$$
J. $$\dfrac{{{v_0}}}{{{B_0}\alpha }}$$
Answer: D
What molar concentration of $NH_3$ provides a $[OH^-]$ of $1.5 \times 10^{-3}$ ?
$$(K_b = 1.8 \times 10^{-5})$$

Options:
A. $$(0.125 + 1.8 \times 10^{-3})$$
B. $$(0.125 + 1.8 \times 10^{-5})$$
C. $$0.125$$
D. $$(1.5 \times 10^{-3})$$
E. $$(0.125 +1.5 \times 10^{-3})$$
F. $$(0.125 - 1.8 \times 10^{-5})$$
G. $$(0.125 - 1.5 \times 10^{-3})$$
H. $$(0.125 - 1.8 \times 10^{-4})$$
I. $$(0.125 - 1.5 \times 10^{-5})$$
J. $$(0.125 - 1.5 \times 10^{-4})$$
Answer: D
A heavy chain of length $1  \ m$ and weighing $10  \ kg$ per metre hangs vertically with one end attached to a peg and carries a weight of $10  \ kg$ at the other end. Then in winding $50  cm$ of chain round the peg$($Take $\mathrm{g}=10 \ \mathrm{m}/\mathrm{s}^{2})$

Options:
A. the centre of gravity of the chain is lifted vertically through $0.375 m$
B. total work done is $72.5 J$
C. total work done is $37.5 J$
D. the centre of gravity (C.G.) of the chain is lifted vertically through $0.25 m$
E. total work done is $85 J$
F. total work done is $62.5 J$
G. total work done is $87.5 J$
H. total work done is $82.5 J$
I. total work done is $112.5 J$
J. total work done is $75 J$
Answer: G
Two particles $A$ and $B$ are connected by a rigid rod $AB$. The rod slides along perpendicular rails as shown here. The velocity of $A$ to the left is $10m/s$. What is the velocity of $B$ when angle $\alpha={30}^{o}$?

Options:
A. $$5.8m/s$$
B. $$4.3m/s$$
C. $$4.8m/s$$
D. $$10m/s$$
E. $$6.8m/s$$
F. $$3.8m/s$$
G. $$17.3m/s$$
H. $$7.6m/s$$
I. $$6.0m/s$$
J. $$5.5m/s$$
Answer: F
A sample consisting of 1mol of a monoatomic perfect  gas $\begin{pmatrix} C_{ v }=\frac { 3 }{ 2 } R \end{pmatrix} $ is taken through the cycle as shown :$\Delta U$ for the process $(1 \longrightarrow 2)$ is :

Options:
A. $$3.40 \times 10^{ 2 } J$$
B. $$3.40 \times 10^{ 1 } J$$
C. $$0.00 J$$
D. $$-3.40 \times 10^{ 3 } J$$
E. $$-3.40 J$$
F. $$3.40 \times 10^{ 0 } J$$
G. $$-3.40 \times 10^{ 2 } J$$
H. $$3.40\times 10^{ 3 } J$$
I. $$3.40 \times 10^{ 4 } J$$
Answer: H
A ring of a radius 0.1 m is made of thin metallic wire of cross section $10^{-6}m^2$. The ring has a uniform charge of $\pi$ coulomb. Young's modulus of metal of wire in $2\times 10^{11}N/m^2$ and ${ { arepsilon  }_{ 0 } }^{ -1 }=36\pi \times 10^9 Vm/As$. When a charge of $10^8 C$ is placed at the centre of the ring, then

Options:
A. tension in the wire is $4.5\times 10^3$ N
B. change in radius is $2.25\times10^{-3}$
C. tension in the wire is $4.5 \times 10^2$ N
D. tension in the wire is $4.5\times 10^5$ N
E. tension in the wire is $4.5 \times 10^1$ N
F. change in radius is $2.25\times10^{-5}$
G. tension in the wire is $4.5 \times 10^6$ N
H. tension in the wire is $4.5 \times 10^{-3}$ N
I. tension in the wire is $4.5\times 10^7$ N
J. tension in the wire is $4.5 \times 10^4$ N
Answer: A
A gas obey $P(V-b)=RT$. Which of the following is correct about this gas :

Options:
A. Compressibility factor for the gas is $Z=1+\cfrac{Pb}{2RT}$ only in low pressure region
B. Compressibility factor for the gas is \( Z=1+\cfrac{Pb}{RT} \) only in low pressure region
C. Compressibility factor for the gas is $Z=1+\cfrac{Pb}{2RT}$ only in high pressure region
D. Compressibility factor for the gas is $Z=I+\cfrac{Pb}{RT}$ only in high pressure region
E. Compressibility factor for the gas is $Z=1-\cfrac{Pb}{2RT}$ only in low pressure region
F. The same expression is followed by $CO_{2}$ gas at low pressure
G. Compressibility factor for the gas is $Z=1-\cfrac{Pb}{RT}$ only in low pressure region
H. At high pressure and high temperature the gas will behave as an ideal gas
I. Compressibility factor for the gas is $Z=1-\cfrac{Pb}{RT}$ only in high pressure region
J. Repulsive forces are dominant over attraction force
Answer: D
At a certain temperature 
$S_{(s)} + O_{2(g)} \rightleftharpoons SO_{2(g)}$  $K_C = 5 \times 10^{52}$
$2S_{(s)} + 3O_{2(g)} \rightleftharpoons 2SO_{3(g)}$  $K_C = 10^{29}$
$K_C$ (at same temperature) for the reaction below is 
$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$

Options:
A. $$2.5 \times 10^{81}$$
B. $$5 \times 10^{76}$$
C. $$4 \times 10^{-77}$$
D. $$5 \times 10^{23}$$
E. $$5 \times 10^{81}$$
F. $$4 \times 10^{81}$$
G. $$2.5 \times 10^{76}$$
H. $$5 \times 10^{82}$$
I. $$5 \times 10^{80}$$
J. $$5 \times 10^{79}$$
Answer: E
A string fixed at both the ends of length 2 m, vibrating in its 7th overtone. Equation of the standing wave is given by $y=A\sin kx \cos (\omega t+ \pi /3)$. All the symbols have their usual meaning. Mass per unit length of the string is 0.5 gm/cm. Given that A=1 cm and $\omega=100\pi rad/sec$. After what time starting from t=0 sec, energy of the vibration is completely potential for the second time.

Options:
A. $$\cfrac{13}{600}sec$$
B. $$\cfrac{11}{500}sec$$
C. $$\cfrac{7}{500}sec$$
D. $$\cfrac{1}{150}sec$$
E. $$\cfrac{1}{60}sec$$
F. $$\cfrac{11}{600}sec$$
G. $$\cfrac{13}{500}sec$$
H. $$\cfrac{9}{500}sec$$
I. $$\cfrac{7}{600}sec$$
J. $$\cfrac{3}{250}sec$$
Answer: H
The height of a solid cylinder is four times its radius. It is kept vertically at time $t=0$ on a belt which is moving in the horizontal direction with a velocity $v=2.45t^{2}$,where $v$ is in $ms^{-1}$ and $t$ is in seconds. If the cylinder does not slip, it will topple over at time $t$ equal to:

Options:
A. 3 s
B. 1.5 s
C. 3.5 s
D. $$4  s$$
E. $$1  s$$
F. $$2  s$$
G. 2.5 s
H. $$1.5 \ s$$
Answer: E
In an uniform field the magnetic needle completes 10 oscillations in 92seconds. When a small magnet is placed in the magnetic meridian 10cm due north of needle with north pole towards south completes 15 oscillations in 69seconds. The magnetic moment of magnet ($B_H =0.3 \ G$) is

Options:
A. $$0.55 \ A m^2$$
B. $$0.75 \ A m^2$$
C. $$0.85 \ A m^2$$
D. $$0.225 \ A m^2$$
E. $$0.45 \ A m^2$$
F. $$3.5 \ A m^2$$
G. $$5.5 \ A m^2$$
H. $$4.05 \ A m^2$$
I. $$4.00 \ A m^2$$
J. $$4.5 \ A m^2$$
Answer: E
Assuming complete dissociation, which of the following solutions will have $pH=13 $?

Options:
A. $4g$ of $NaOH$ in $500\: ml$ solution
B. $100 \:ml$ of solution of $0.1N \: Ca(OH)_{2}$
C. $100 \:ml$ of solution of $0.15N \: Ca(OH)_{2}$
D. 100 \:ml \: of \: solution \: of \: 0.2N \: NaOH
E. $100 \:ml$ of solution of $0.01N \: Ca(OH)_{2}$
F. $100 \:ml$ of solution of $0.2N \: Ca(OH)_{2}$
G. 100 \:ml \: of \: solution \: of \: 0.15N \: Ca(OH)_{2}
H. 2g of $NaOH$ in $500\: ml$ solution
I. $100 \:ml$ of solution of $0.05N \: Ca(OH)_{2}$
Answer: B
0.1 mole of $ \mathrm { N } _ { 2 } \mathrm { O } _ { 4 } ( \mathrm { g } ) $ was sealed in a tube under one atmospheric conditions at 25$ ^{\circ}C$. Calculate the number of moles of $ \mathrm { NO } _ { 2 } ( \mathrm { g } ) $ present, if the equilibrium $ \mathrm { N } _ { 2 } \mathrm { O } _ { 4 } ( \mathrm { g } ) \rightleftharpoons 2 \mathrm { NO } _ { 2 } ( \mathrm { g } ) \left( \mathrm { K } _ { \mathrm { p } } = 0.14 \right) $ is reached after some time:-

Options:
A. $$2.8 \times 10 ^ { - 1 }$$
B. $$1.8 \times 10 ^ { - 2 }$$
C. $$ 1.8 \times 10 ^ { 2 } $$
D. $$ 2.8 \times 10 ^ { - 2 } $$
E. $$3.8 \times 10 ^ { - 2 }$$
F. $$3.8 \times 10 ^ { - 3 }$$
G. $$ 2.8 \times 10 ^ { 2 } $$
H. $$1.8 \times 10 ^ { - 1 }$$
I. $$0.034$$
J. $$1.8 \times 10 ^ { - 3 }$$
Answer: I
Two conductors carrying equal and opposite charges create a non-uniform field as shown in fig. What is the capacity of this capacitor if the field along $ y-a x i s  $ varies as $  E= $ $ \frac{Q}{\varepsilon_{0} A}\left(1+B y^{2}\right)  $ with $ B= $ constant

Options:
A. $$ \mathrm{C}=\frac{\varepsilon_{0} \mathrm{A}}{\mathrm{d}\left[1+\frac{1}{3} \mathrm{Bd}^{2}\right]} $$
B. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{2}{5} B d^{2}\right]}$$
C. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{1}{5} B d^{2}\right]}$$
D. $$ C=\frac{\varepsilon_{0} A}{d\left[1+\frac{1}{2} B d^{2}\right]} $$
E. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{3}{5} B d^{2}\right]}$$
F. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{1}{4} B d^{2}\right]}$$
G. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{3}{4} B d^{2}\right]}$$
H. $$ C=\frac{\varepsilon_{0} A B}{2 d} $$
I. $$C=\frac{\varepsilon_{0} A}{d\left[1+\frac{1}{6} B d^{2}\right]}$$
J. $$ C=\frac{\varepsilon_{0} A}{d} $$
Answer: A
Calculate the solubility of silver phosphate $({Ag}_{3} PO4)$ in $0.10 M Ag{NO}_{3}$? ${K}_{sp}=1.1\times {10}^{-6}$

Options:
A. $$4.4 \times 10^{-5}M$$
B. $$1.1 \times 10^{-17}M$$
C. $$1.1 \times 10^{-14}M$$
D. $$1.1 \times 10^{-15}M$$
E. $$1.1\times {10}^{-5}M$$
F. $$4.1 \times {10}^{-5}M$$
G. $$1.1 \times 10^{-16}M$$
H. $$1.1\times {10}^{-13}M$$
I. $$0.10 M$$
J. $$1.1 \times 10^{-18}M$$
Answer: I
The standard reduction potential of the $Ag^+|Ag$ electrode at 298 K is 0.80 V. The solubility product of AgI is $6.4 \times  10^{-17}$ at 298 K. (2.303RT/F = 0.06). The potential of $ I^{-} (0.04 \, M)|AgI|Ag $ electrode at 198 K is

Options:
A. $$+0.102\,V$$
B. $$+0.068\,V$$
C. $$+0.062\,V$$
D. $$ +0.172\,V $$
E. $$+0.124\,V$$
F. $$+0.078\,V$$
G. $$+0.098\,V$$
H. $$ -0.088\,V $$
I. $$ +0.088\,V $$
J. $$ -0.172\,V $$
Answer: I
The cubical container $ABCDEFGH$ which is completely filled with an ideal (nonviscous and incompressible) fluid, moves in a gravity free space with a accelaration of $a={ a }_{ 0 }\left( \hat { i } -\hat { j } +\hat { k }  \right)$ where ${ a }_{ 0 }$ is a positive constant. Then the only point in the container shown in the figure where pressure is maximum, is

Options:
A. $$B$$
B. $$G$$
C. $$F$$
D. $$E$$
E. $$C$$
F. $$D$$
G. $$A$$
H. $$H$$
Answer: A
What is $ [H^+] $ in mol/L of a solution that is 0.20 M $ CH_3CCONa $ and 0.10 M in $ CH_3COOH $? $( K_a\ for\ CH_3COOH = 1.8 \times 10^{-5} ) $

Options:
A. $$ 3.5 \times 10^{-4} $$
B. $$8.0 \times 10^{-6}$$
C. $$ 9.0 \times 10^{-6} $$
D. $$3.5 \times 10^{-5}$$
E. $$3.5 \times 10^{-6}$$
F. $$7.0 \times 10^{-5}$$
G. $$ 1.8 \times 10^{-5} $$
H. $$2.1 \times 10^{-5}$$
I. $$ 1.1 \times 10^{-5} $$
J. $$4.5 \times 10^{-4}$$
Answer: A
A wire of resistance $R$ in the form of semicircle lies on the top of smooth table . A uniform magnetic field $B$ is confined to the region as shown. The ends of the semicircle are attached to springs C and D, whose other ends are fixed . If $r$ is the radius of the semicircle and $k$ is the force constant for each springs , then the extension $x$ in each springs is :

Options:
A. $$x=\dfrac { 5EBr }{ 2kR }$$
B. $$x=\dfrac { 3EBr }{ 4kR }$$
C. $$x=\dfrac { 4EBr }{ kR }$$
D. $$x=\dfrac { EBr }{ kR } $$
E. $$x=\dfrac { 2EBR }{ kR } $$
F. $$x=\dfrac { EBr }{ 2kR } $$
G. $$x=\dfrac { 3EBr }{ 2kR }$$
H. $$x=\dfrac { 3EBr }{ kR }$$
I. $$x=\dfrac { 2EBr }{ kR } $$
Answer: I
In the arrangement shown in Fig. mass of blocks A, B and C is 18.5 kg , 8 kg and 1.5 kg, respectively.
The bottom surface of A si smooth, while coefficient of friction that between block A and C is $\mu_1$ = 1/3 between B and floor is $\mu_2$= 1/5. System is released from rest at t=0 and pulleys are light and frictionless. Calculate accelerations of blocks A, B and C.

Options:
A. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 2 $ms^{-2}$
B. a = 2 $ms^{-2}$, b = 0.5 $ms^{_2}$; c = 6 $ms^{-2}$
C. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 3.5 $ms^{-2}$
D. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 5.5 $ms^{-2}$
E. a = 1 $ms^{-2}$, b = 0.5 $ms^{_2}$; c = 3 $ms^{-2}$
F. a = 1 $ms^{-2}$, b = 0.5 $ms^{_2}$; c = 5 $ms^{-2}$
G. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 3.2 $ms^{-2}$
H. a = 1 $ms^{-2}$, b = 0.5 $ms^{_2}$; c = 4 $ms^{-2}$
I. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 2.5 $ms^{-2}$
J. a = 1 $ms^{-2}$, b = 0.5 $ms^{-2}$; c = 4.5 $ms^{-2}$
Answer: E
There is an electric field $\overrightarrow {\rm{E}}  = {{a{x^3}\widehat i + b{y^4}\widehat j + c{z^2}\widehat k} \over {a{x^4} + b{y^5} + c{z^3}}}$ at any (x,y,z) coordinates in the space except origin, Where a,b & c are constant. Find the electrostatic flux passing through a sphere of radius R whose center is at the origin.

Options:
A. Zero
B. $$4\pi R^2$$
C. $$2\pi R$$
D. $$2\pi R^3$$
E. $$3\pi R^2$$
F. $$2\pi R^2$$
G. $$\pi R^2$$
H. $$4\pi R$$
I. $$\pi R$$
Answer: I
The figure shows the top view of a uniform solid prism. The sides of the prism are $AB= 4 cm, BC=3cm$ and $AC=5 cm$ the thickness of the prism (perpendicular to the plane of the paper) is $t=1 cm$. The prism is mounted on a frictionless axis passing through $D$ (which is the mid point of $AC$) and perpendicular to the plane of the paper. An impulse $J=1 Ns$ is imparted at point $A$ of the prism, perpendicular to edge $AB$ of the prism. (The impulse vector line in the plane of the paper). It was found that after the impulse was imparted,  the prism took $1$  second to undergo one complete rotation about the axis.The moment of inertia of the prism about the given axis is:

Options:
A. $$\frac{{{{10}^{ - 2}}}}{2\pi }kg{m^2}$$
B. $$\frac{{{{10}^{ - 2}}}}{\pi }kg{m^2}$$
C. $$\frac{{2 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
D. $$\frac{{\sqrt 3 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
E. $$\frac{{5 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
F. $$\frac{{4 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
G. $$\frac{{6 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
H. $$\frac{{3 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
I. $$\frac{{\sqrt 2 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
J. $$\frac{{\sqrt 5 \times {{10}^{ - 2}}}}{\pi }kg{m^2}$$
Answer: I
Rate law expression of a reaction is:            Rate $=k{ \left[ A \right]  }^{ { 2 }/{ 3 } }\left[ B \right] $Which of the following are correct about the corresponding reaction?

Options:
A. Unit of rate constant $=mol$ ${ L }^{ -1 }{ sec }^{ -1 }$
B. Unit of rate constant $={ atm }^{ { -1 }/{ 2 } }{ sec }^{ -1 }$
C. Unit of rate constant $={ atm }^{ { -1 }/{ 3 } }{ sec }^{ -2 }$
D. Unit of rate constant $={ L }^{ { 2 }/{ 3 } }{ mol }^{ { -2 }/{ 3 } }{ sec }^{ -1 }$
E. Unit of rate constant $={ atm }^{ { -1 }/{ 3 } }{ sec }^{ -1 }$
F. Unit of rate constant $={ atm }^{ { -2 }/{ 3 } }{ sec }^{ -1 }$
G. Unit of rate constant $={ atm }^{ { -1 } }{ sec }^{ -1 }$
Answer: F
$0.80\ g$ of choloplatinate of a monoacid organic base on ignition gave $0.25\ g$ of Pt. The molecular weight of the base is $(Pt=195)$

Options:
A. $$214$$
B. $$624$$
C. $$109$$
D. $$107$$
E. $$312$$
F. $$106$$
G. $$124$$
H. $$108$$
I. $$105$$
Answer: D
Two moles of a monatomic gas is taken through a mass $PT^2=$ constant. ITs temperature is increased from $2T_0\ K$ to $3T_0\ K$. Work done in proportional to $T_0^k,k=?$

Options:
A. $$1$$
B. $$-2$$
C. $$1/2$$
D. $$0$$
E. $$4$$
F. $$3$$
G. $$-\frac{1}{2}$$
H. $$2$$
I. $$-3$$
J. $$-1$$
Answer: J
The (approx.) $pH$ of solution when $HCL (0.002 M)$ and a weak acid $(0.002 M)$ was mixed in equal volume $\left( {{\rm{given}}\,{{\rm{k}}_{\rm{a}}}\,{\rm{of}}\,{\rm{weak}}\,{\rm{acid}} = 2 \times {{10}^{ - 6}}} \right)$

Options:
A. $$3.3$$
B. $$1$$
C. $$4.5$$
D. $$4$$
E. $$5$$
F. $$2$$
G. $$3.8$$
H. $$3$$
I. $$6$$
Answer: F
A proton has kinetic energy E = 100 KeV which  is equal to that of a photon. The wavelength photon is $\gamma_2$ and that of proton is $\gamma_1$. The ratio of $\gamma_1/\gamma_2$ is proportional to

Options:
A. $$E^{-1}$$
B. $$E^{-1/2}$$
C. $$E^{-3/2}$$
D. $$E^{-2}$$
E. $$E^{1/2}$$
F. $$E^{3/2}$$
G. $$E^2$$
H. $$E^{-2/3}$$
Answer: B
In the arrangement shown in figure, three concentric conducting shells are shown. The charge on the shell of radius $b$ is $q_0$. If the innermost and outermost shells are connected to the earth, find their charge densities and the potentials on the shell of radius $b$ in terms of $a$ and $q_0$. Given that $a:b:c = 1: 2: 4$.

Options:
A. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{36\pi a^2}, V_0 = \dfrac{q_0}{12\pi \varepsilon_0 a}$$
B. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{96\pi a^2}, V_0 = \dfrac{q_0}{24\pi \varepsilon_0 a}$$
C. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{84\pi a^2}, V_0 = \dfrac{q_0}{24\pi \varepsilon_0 a}$$
D. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{48\pi a^2}, V_0 = \dfrac{q_0}{18\pi \varepsilon_0 a}$$
E. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{36\pi a^2}, V_0 = \dfrac{q_0}{24\pi \varepsilon_0 a}$$
F. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{72\pi a^2}, V_0 = \dfrac{q_0}{24\pi \varepsilon_0 a}$$
G. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{64\pi a^2}, V_0 = \dfrac{q_0}{20\pi \varepsilon_0 a}$$
H. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{108\pi a^2}, V_0 = \dfrac{q_0}{24\pi \varepsilon_0 a}$$
I. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{16\pi a^2}, V_0 = \dfrac{q_0}{36\pi \varepsilon_0 a}$$
J. $$\sigma_{inner} = \dfrac{q_0}{12\pi a^2}, \sigma_{outer} = \dfrac{q_0}{72\pi a^2}, V_0 = \dfrac{q_0}{28\pi \varepsilon_0 a}$$
Answer: B
(a) Find the time period of oscillations of a torsional pendulum,if the torsional constant of the wire is ${K=10\pi^2}{J/rad}$.The moment of inertia of rigid  body is ${10  kg  m^2}$ about the axis of rotation.
(b) A simple pendulum of length l=0.5 m is hanging from ceiling of a car. The car is kept on a horizontal plane.The car starts accelerating on the horizontal road with acceleration of $ {5 m}/{s^2}$.Find the time period of oscillations of the pendulum for small amplitudes about the mean position

Options:
A. (a) 2sec, (b) $\displaystyle T = \frac{2}{5^{1/6}}sec$
B. (a) 4sec, (b) $\displaystyle T = \frac {2}{5^{1/4}}sec$
C. (a) 2sec, (b) $\displaystyle T = \frac{2}{5^{1/5}}sec$
D. (a) 3sec, (b) $T=\frac{3}{5^{1/4}}sec$
E. (a) 2sec, (b) $T=0.628sec$
F. (a) 3sec, (b) $\displaystyle T = \frac {2}{5^{1/4}}sec$
G. (a) 2sec, (b) $\displaystyle T = \frac {2}{5^{1/3}}sec$
H. (a) 2sec, (b) $\displaystyle T = \frac{2}{5^{1/7}}sec$
I. (a) 3sec, (b) $\displaystyle T = \frac{2}{5^{1/5}}sec$
J. (a) 2sec, (b) $\displaystyle T = \frac{2}{5^{1/8}}sec$
Answer: E
A body slides without friction form a height $H=60\ cm$ and then loops the loop of radius $R=20\ cm$ at the bottom of incline. The ratio of forces exerted on the body by the track at $A,\ B$ and $C$ are $(g=10\ ms^{-2})$

Options:
A. $$4:2:7$$
B. $$7:4:2$$
C. $$1:4:7$$
D. $$7:1:4$$
E. $$7:4:1$$
F. $$4:1:7$$
G. $$1:7:4$$
H. $$7:2:1$$
I. $$4:7:1$$
Answer: C
A particle of mass m is attached to one end of a massless spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5 u_0$. It collides elastically with a rigid wall. After this collision.

Options:
A. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{5\pi}{3}\sqrt{\dfrac{m}{k}}$
B. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{11\pi}{3}\sqrt{\dfrac{m}{k}}$
C. $$t=\dfrac{6\pi}{3}\sqrt{\dfrac{m}{k}}$$
D. The time at which the particle passes through the equilibrium position for the first time is $t=\pi\sqrt{\dfrac{m}{k}}$
E. $$t=\dfrac{7\pi}{3}\sqrt{\dfrac{m}{k}}$$
F. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{10\pi}{3}\sqrt{\dfrac{m}{k}}$
G. The time at which the maximum compression of the spring occurs is $t=\dfrac{4\pi}{3}\sqrt{\dfrac{m}{k}}$
H. The speed of the particle when it returns to its equilibrium position is $2u_0$
I. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{8\pi}{3}\sqrt{\dfrac{m}{k}}$
J. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{7\pi}{3}\sqrt{\dfrac{m}{k}}$
Answer: A
Ammonia is manufactured from $N_2(g)$ and $H_2(g)$ in Haber's process , which is governed by following  equilibrium reaction:
$$N_2(g)+3H_2(g) \rightleftharpoons 2NH_3(g); \Delta H=-92 KJ/mol$$
Which of the following will decrease the concentration of ammonia$(NH_3)$?

Options:
A. Increase in pressure by increasing the volume of the container.
B. Increasing the amount of catalyst.
C. Decreasing pressure by increasing volume of container.
D. Increasing the amount of $N_2(g)$.
E. Increase in pressure by decreasing the volume of the container.
F. Increase in temperature.
G. Increasing the amount of $NH_3(g)$.
H. Decrease in temperature.
I. Increaseing amount of catalllyst.
J. Addition of $NH_3(g)$
Answer: I
a) Calculate heat of dissociation for Acetic acid from the following data:$CH_3COOH + NaOH\longrightarrow CH_3COONa + H_2O .... \Delta H = -13.2  Kcal$$H^{ \oplus } + \overset { \ominus }{ O }H\longrightarrow H_2O; .... \Delta H = -13.7  Kcal$.b) calculate heat of dissociation for $NH_4OH$ if $HCl + NH_4OH\longrightarrow NH_4Cl + H_2O; \Delta H = -12.27  Kcal$.

Options:
A. a) $ -1.5\ kcal$ , b)$ -2.43\ cal$
B. a) $ 0.7\ kcal$ , b)$ -1.76\ cal$
C. a) $ 1.2\ kcal$ , b)$ -0.72\ cal$
D. a) $ 1.5\ kcal$ , b)$ -2.43\ cal$
E. a) $ -0.5\ kcal$ , b)$ -1.43\ cal$
F. a) $ -0.7\ kcal$ , b)$ -1.56\ cal$
G. a) $ 0.0\ kcal$ , b)$ 2.86\ cal$
H. None of these
I. a) $ 0.5\ kcal$ , b)$ 1.43\ cal$
J. a) $ -1.2\ kcal$ , b)$ -2.43\ cal$
Answer: I
A simple pendulum of length 1mhas a bob of mass 200 kg It is displaced ${ 60 }^{ * }$ and then relessed. Find the kinetic energy of the bob when 
i) It passes through the mean position 
ii) The string makes an angle of ${ 30 }^{ \circ  }$ with the vertical (g=10${ m/s }^{ 2 }$)

Options:
A. $$2J_{ ' }1.732J$$
B. $${ 2J }_{ ' }1.732J$$
C. ${ 1J }_{ ' }1.632J$
D. ${ 2J }_{ ' }2.732J$
E. $$1J_{ ' }0.732J$$
F. $${ 2J }_{ ' }0.732J$$
G. $$1J_{ ' }0.832J$$
H. $${ 1J }_{ ' }0.732J$$
I. ${ 1J }_{ ' }2.732J$
J. $${ 1J }_{ ' }1.732J$$
Answer: J
The final product formed when acetylene reacts with $HCN$ and $CH_3COOH$ separately, respectively are

Options:
A. $C{H_3} - CH{(CN)_2}$ and $C{H_3} - CH(OCOC{H_3})_2$
B. $C{H_2} = CH{(CN)_2} and C{H_3} - CH(OCOC{H_3})_2$
C. $C{H_2} = CH{(CN)}$ and $C{H_3} - CH(OCOC{H_3})_2$
D. $C{H_3} - CH{(CN)_2}$ and $C{H_2} = CH(OCOC{H_3})$
E. $C{H_3} - CH{(CN)_2}$ and $C{H_2} = CH(OCOC{H_3})_2$
F. $C{H_2} = CH{(CN)}$ and $C{H_2} = CH(OCOC{H_3})_2$
G. $C{H_2} = CH{(CN)_2}$ and $C{H_2} = CH(OCOC{H_3})_2$
Answer: A
If 10 g of ice is added to 40 g of water at ${ 15 }^{ 0 }$C, then the temperature of the mixture is (Specific heat of water =$4.2\times { 10 }^{ 3 }\quad J\quad { kg }^{ -1 }{ K }^{ -1 }$, latent heat of fusion of ice =$3.36\times { 10 }^{ 5 }\quad { kg }^{ -1 }$)

Options:
A. $${ 14 }^{ 0 }C$$
B. $${ 12 }^{ 0 }C$$
C. $${ 0 }^{ 0 }C$$
D. $${ 8 }^{ 0 }C$$
E. $${ 7 }^{ 0 }C$$
F. $${ 11 }^{ 0 }C$$
G. $${ 15 }^{ 0 }C$$
H. $${ 10 }^{ 0 }C$$
I. $${ 13 }^{ 0 }C$$
J. $${ 9 }^{ 0 }C$$
Answer: H
A police man is running towards a thief with a constant acceleration of $0.1m/{s}^{2}$. At a particular instant $t=0$, the policeman is $20m$ behind the thief and at that instant the velocity of policman is $4m/s$. At this instant the thief observes, the policeman coming towards him. So, he starts running away from the policemen in the same direction with a constant acceleration. Then what is the minimum constant acceleration with which the thief should run so that he is not caught?

Options:
A. $$0.5m/{s}^{2}$$
B. $$0.3m/{s}^{2}$$
C. $$0.1m/{s}^{2}$$
D. $$0.2m/{s}^{2}$$
E. $$0.4m/{s}^{2}$$
F. $$0.8m/{s}^{2}$$
G. $$0.9m/{s}^{2}$$
H. $$0.15m/{s}^{2}$$
I. $$0.6m/{s}^{2}$$
J. $$0.7m/{s}^{2}$$
Answer: D
In a certain process on one mole of diatomic ideal gas, pressure increases linearly with volume from $P_1=1\times 10^3N/m^2$ at $V_1=1m^3$ to $P_2=2\times 10^3N/m^3$ at $V_2=2m^3$. Heat supplied to the gas in above interval is.

Options:
A. $$9KJ$$
B. $$8KJ$$
C. $$7.5KJ$$
D. $$6KJ$$
E. $$1.5KJ$$
F. $$8.0KJ$$
G. $$8.5KJ$$
H. $$6.5KJ$$
I. $$7.0KJ$$
Answer: C
One mole of an ideal gas $\left( \frac { C _ { \mathrm { p} } } { \mathrm { C } _ { \mathrm { v } } } = \gamma \right)$ heated by law $\mathrm { P } = \alpha \mathrm { V }$ where $\mathrm { P }$ is pressure of gas, V is volume; $\alpha$ is a constant what is the heat capacity of gas in the process-

Options:
A. $$C = \frac { R } { \gamma - 1 }$$
B. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 2 ) }$$
C. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 3 ) }$$
D. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 6 ) }$$
E. $$C = \frac { \gamma R } { \gamma - 1 }$$
F. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 4 ) }$$
G. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 1 ) }$$
H. $$C = \frac { R } { 2 } \frac { ( \gamma - 1 ) } { ( \gamma - 2 ) }$$
I. $$C = \frac { R } { 2 } \frac { ( \gamma + 1 ) } { ( \gamma - 5 ) }$$
J. $$C = \frac { R } { 2 } \frac { ( \gamma - 1 ) } { ( \gamma + 1 ) }$$
Answer: A
A string of length $ \ell $ has one end fixed and a particle of mass m is attached to the other end. If the particle describe a horizontal circle at an angular speed $ \omega $, in gravity free space.

Options:
A. The tension in the string = \(m\omega^2\ell^2\)
B. None of these
C. The tension in the string = \( m\omega^2 \ell \sqrt{4} \)
D. The tension in the string = \( m\omega^2 \ell \sqrt{1} \)
E. The speed of the particle is $ \ell \omega $
F. The tension in the string = \( m\omega^2 \ell \sqrt{5} \)
G. The tension in the string = \( m\omega^2 \ell \sqrt{2} \)
H. The tension in the string = $m\omega^2\ell $
I. The tension in the string = \( m\omega^2 \ell \sqrt{3} \)
J. The resultant force acting on the particle has no vertical component
Answer: J
An ideal diatomic gas undergoes a process in which internal energy relates to its volume as $ U= k\sqrt V$, where k is a positive constant. Based on the given information, answer the following question.
The molar heat capacity of gas for this process is :

Options:
A. $$6.5 R$$
B. $$2 R$$
C. $$4.5 R$$
D. $$3 R$$
E. $$4.25 R$$
F. $$3.5 R$$
G. $$5.5 R$$
H. $$2.5 R$$
Answer: C
A positively charged small disc is released on the top of fixed hemispherical frictionless dome in presence of a uniform horizontal electric field. If the disc leaves the dome after an angular displacement $ \theta  = sin^{-1} (3 / 5) $, find ratio of gravitational and electrostatic forces on the disc. Assume that the dome does not exhibit any electrical property.

Options:
A. 3/4
B. 7/3
C. 8/3
D. 8/5
E. 9/2
F. 6/5
G. 4/3
H. 3/2
I. 12
J. 7/2
Answer: E
The normal boiling point of water is 373$\mathrm { K }$ . Vapour pressure of water at temperature $T$ is 19 $\mathrm { mm }$ Hg. If enthalpy of vaporisation is $40.67 \mathrm { kJ } / \mathrm { mol } ,$ then temperature $T$ would be (Use $: \log 2 = 0.3 , R : 8.3 \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } )$

Options:
A. 280$\mathrm { K }$
B. 240$\mathrm { K}$
C. 290$\mathrm { K }$
D. 245$\mathrm { K }$
E. 265$\mathrm { K }$
F. 260$\mathrm { K }$
G. 250$\mathrm { K }$
H. 230$\mathrm { K }$
I. 291.4$\mathrm { K }$
J. 255$\mathrm { K }$
Answer: G
When $CO_2$ dissolve in water, the following equilibrium is established 
$CO_2+2H_2O \rightleftharpoons H_3O^+ + HCO_3^-$ for which the equilibrium constant is $3.8 \times 10^{-7}$ and pH=6. The ratio of $HCO_3^- $ to $CO_2$ would be:

Options:
A. $$3.8$$
B. 6
C. 2.6
D. 7.6
E. 13.4
F. 1.9
G. 0.38
H. 5.7
I. 1.52
Answer: A
The denisity of water vapour at 240 atm and $527^{\circ}C$ is $90gm/dm^{3}$. Determine the molar volume$(v_{m})$ of water and the compression factor.[Use :R=0.08 atmL/molK]

Options:
A. Molar vol=0.6 L/mol; Z=0.4
B. Molar vol=0.9 L/mol; Z=0.3
C. Molar vol=0.8 L/mol; Z=0.4
D. Molar vol=0.2 L/mol; Z=0.75
E. None of these
F. Molar vol=0.7 L/mol; Z=0.5
G. Molar vol=0.3 L/mol; Z=0.8
H. Molar vol=0.1 L/mol; Z=0.8
I. Molar vol=0.4 L/mol; Z=0.75
J. Molar vol=0.5 L/mol; Z=0.6
Answer: E
Rain is falling vertically with a speed of 1.7 m/s. A girl is walking with speed of 1.0 m/s in the N - E (north-east) direction. To shield herself she holds her umbrella making an approximate angle $\theta $ with the vertical in a certain direction. Then

Options:
A. $$\theta=30^0 \:in \:N - E \:direction$$
B. $$\theta=60^0 \:in \:N - E \:direction$$
C. $$\theta=25^0 \:in \:S - W \:direction$$
D. $$\theta=30^0 \:in \:S - W \:direction$$
E. $$\theta=45^0 \:in \:S - W \:direction$$
F. $$\theta=50^0 \:in \:N - E \:direction$$
G. $$\theta=40^0 \:in \:N - E \:direction$$
H. $$\theta=45^0 \:in \:N - E \:direction$$
I. $$\theta=60^0 \:in \:S - W \:direction$$
J. $$\theta=35^0 \:in \:N - E \:direction$$
Answer: A
Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be ${ P }_{ 1 }$ and that by the second wave be ${ P }_{ 2 }.$  Then

Options:
A. $${ P }_{ 2 }={ 2P }_{ 1 }$$
B. $${ P }_{ 2 }={ 4P }_{ 1 }$$
C. $${ P }_{ 1 }={ \frac{1}{2}P }_{ 2 }$$
D. $${ P }_{ 1 }={ \frac{3}{4}P }_{ 2 }$$
E. $${ P }_{ 1 }={ 3P }_{ 2 }$$
F. $${ P }_{ 1 }={ P }_{ 2 }$$
G. $${ P }_{ 1 }={ 2P }_{ 2 }$$
H. $${ P }_{ 1 }={ \frac{1}{4}P }_{ 2 }$$
I. $${ P }_{ 1 }={ 4P }_{ 2 }$$
J. $${ P }_{ 2 }={ 3P }_{ 1 }$$
Answer: H
The acceleration of a particle is given by  $\vec a = \lfloor 2 \hat{i} + 6 t \hat{j} + \dfrac{2 \pi^2}{9} \cos \dfrac{\pi t}{3} \hat{k} \rfloor m/s^2$. At $t = 0, \vec{r} = 0$ and $\vec{v} = (2 \vec{i} + \hat{j}) ms^1$. The position vector at $t =2 s$ is

Options:
A. $$(8 \hat{i} + 10 \hat{j} + 4\hat{k}) m$$
B. $$(8 \hat{i} + 10 \hat{j} + 3\hat{k}) m$$
C. $$(8 \hat{i} + 10 \hat{j} - 2\hat{k}) m$$
D. $$(8 \hat{i} + 10 \hat{j} - 1\hat{k}) m$$
E. $$(10 \hat{i} + 3 \hat{j} + 8\hat{k}) m$$
F. $$(8 \hat{i} + 10 \hat{j} - \hat{k}) m$$
G. $$(8 \hat{i} + 10 \hat{j} + 2\hat{k}) m$$
H. $$(8 \hat{i} + 10 \hat{j} + \hat{k}) m$$
I. $$(3 \hat{i} + 8 \hat{j} + 10\hat{k}) m$$
J. $$(8 \hat{i} + 10 \hat{j} + 5\hat{k}) m$$
Answer: H
Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B={B}_{0}k$

Options:
A. They must have equal charges
B. They have equal z-components of velocities
C. They have unequal z-components of velocities
D. They have equal charges but opposite signs
E. They necessarily represent a particle-anti particle pair
F. They have unequal charges
G. They have unequal z-components of moments
H. The charge to mass ratio satisfy: ${ \left( \cfrac { e }{ { m }_{ } } \right) }_{ 1 }+{ \left( \cfrac { e }{ { m }_{ } } \right) }_{ 2 }=0$
I. They have equal charges
J. They have equal z-components of moments
Answer: J
Freshly precipitated $Al$ and $Mg$ hydroxides are stirred vigorously in a buffer solution containing $0.25M$ of ${NH}_{4}Cl$ and $0.05M$ of ${NH}_{4}OH$. $[{Al}^{3+}]$ and $[{Mg}^{2+}]$ in solution are:Given: ${K}_{b}$ for ${NH}_{4}OH=1.8\times {10}^{-5}$$ { K }_{ { sp }_{ Al{ \left( OH \right)  }_{ 3 } } }=6\times {10}^{-32}$${ K }_{ { sp }_{ Mg{ \left( OH \right)  }_{ 2 } } }=8.9\times {10}^{-12}$

Options:
A. 0.674M
B. $$0.698M$$
C. 0.668M
D. 0.672M
E. none of these
F. $$0.656M$$
G. 0.678M
H. 0.664M
I. $$0.686M$$
J. 0.676M
Answer: I
Hail storms are observed to strike the surface of the frozen lake at $30^{\circ}$ with the vertical and rebound at $60^{\circ}$ with the vertical. Assume contact to be smooth, the coefficient of restitution is :

Options:
A. \displaystyle e=\dfrac{2}{5}
B. $$\displaystyle e=\sqrt{3}$$
C. $$\displaystyle e=\dfrac{1}{\sqrt{3}}$$
D. $$\displaystyle e=3$$
E. $$\displaystyle e=\dfrac{1}{3}$$
F. \displaystyle e=\dfrac{1}{4}
G. \displaystyle e=\dfrac{2}{3}
H. e=\dfrac{1}{2}
I. e=\dfrac{2}{3}
J. e=\dfrac{1}{\sqrt{2}}
Answer: E
The coefficient of static and kinetic friction between the two blocks and also between the lower block and the ground are $\mu_s= 0.6$ and $\mu_k= 0.4$. Find the value of tension $T$ applied on the lower block at which the upper block begins to slip relative to lower block.

Options:
A. $$50 N$$
B. $$55 N$$
C. $$70 N$$
D. $$60 N$$
E. $$45 N$$
F. $$42 N$$
G. $$20 N$$
H. $$30 N$$
I. $$80 N$$
J. $$40 N$$
Answer: J
How many gm of solid NaOH must be added to 100 ml of a buffer solution which is 0.1 M each w.r.t.Acid HA and salt $Na^{+} A^{-}$ to make the pH of solution 5.5.Given $pk_{a}$(HA)=5.(use antilog(0.5)=3.16)

Options:
A. $$3.5 \times 10^{-1}$$
B. $$None of these$$
C. $$3.16 \times 10^{-3}$$
D. $$2.01\times10^{-2}$$
E. $$3.16 \times 10^{-2}$$
F. $$3.5\times10^{-3}$$
G. $$3.5 \times 10^{-5}$$
H. $$3.5 \times 10^{-4}$$
I. $$2.08\times10^{-1}$$
J. $$3.5 \times 10^{-2}$$
Answer: I
Given that,
$$Ni^{2+}/ Ni = 0.25\ V, Cu^{2+} / Cu = 0.34\ V$$
$Ag^{+} / Ag =0.80\ V$ and $Zn^{2+}/ Zn = -0.76\ V$
Which of the following reactions under standard condition will not take place in the specified direction?

Options:
A. Zn(s) + 2H^{+}(aq.) \rightarrow Zn^{2+}(aq.) + 2H_{2}(g)
B. $$Cu(s) + 2Ag^{+}(aq.) \rightarrow Cu^{2+}(aq.) + 2Ag(s)$$
C. Zn(s) + 2H^{+}(aq.) \rightarrow Zn^{2+}(aq.) + H_{2}(g)
D. $$Ni^{2+}(aq.) + Cu(s) \rightarrow Ni(s) + Cu^{2+}(aq.)$$
E. Cu(s) + 2H^{+}(aq.) \rightarrow Cu^{2+}(aq.) + 3H_{2}(g)
F. Cu(s) + 2H^{+}(aq.) \rightarrow Cu^{2+}(aq.) + 2H_{2}(g)
G. Cu(s) + 2Ag^{+}(aq.) \rightarrow Cu^{2+}(aq.) + Ag(s)
H. $$Cu(s) + 2H^{+}(aq.) \rightarrow Cu^{2+}(aq.) + H_{2}(g)$$
I. $$Zn(s) + 2H^{+}(aq.) \rightarrow Zn^{2+}(aq.) + 3H_{2}(g)$$
Answer: H
A vessel has a liquid of density $ \rho  = \alpha x +\beta $ , Where x is the depth from the free surface $ \alpha = 4 \times 10^3 gm^{-4} $ and $ \beta = 10^3 Kgm^{-3} $. A solid cylindrical shape, length (3/4)m and density $ 0.5 \times 10^3 Kgm^{-3} $ floats vertically. Find the length of the cylinder, beneath the free surface of liquid.

Options:
A. 0. 17 m
B. 0. 24 m
C. 0. 20 m
D. 0. 50 m
E. 0 . 25 m
F. 0 . 14 m
G. 0. 22 m
H. 0. 21 m
I. 0. 23 m
J. 0. 19 m
Answer: H
At what relative humidity will $Na_2SO_4$ be deliquescent (absorb moisture) when exposed to the air at $0^o$C? Given: $Na_2SO_4\cdot 10H_2O(s)\rightleftharpoons Na_2SO_4(s)+10H_2O(g); K_p=4.08\times 10^{-25}$ and vapour pressure of water $0^o$C $=4.58$ Torr.

Options:
A. Below $50.5\%$ but Above $30.5\%$
B. Below $50.5\%$ but Above $40.5\%
C. Above $30.5\%$
D. Below $30.5\%$
E. Above $40.5\%$ but Below $60.5\%$
F. Below $40.5\%$ but Above $20.5\%$
G. Above $50.5\%$
H. Below $40.5\%$ but Above $30.5\%
I. Below $60.5\%$ but Above $50.5\%
Answer: A
A solid ball of radius $R$ has a charge density $\rho$ given by $\rho = \rho _o \left( {1 - \frac{r}{R}} \right)$ for $0 \le r \le R$. The electric field outside the ball is:

Options:
A. $$\frac{{3{\rho _0}{R^3}}}{{5{\varepsilon _0}{r^2}}}$$
B. $$\frac{{8{\rho _0}{R^3}}}{{15{\varepsilon _0}{r^2}}}$$
C. $$\frac{{3{\rho _0}{R^3}}}{{4{\varepsilon _0}{r^2}}}$$
D. $$\frac{{4{\rho _0}{R^3}}}{{3{\varepsilon _0}{r^2}}}$$
E. $$\frac{{5{\rho _0}{R^3}}}{{12{\varepsilon _0}{r^2}}}$$
F. $$\frac{{{\rho _0}{R^3}}}{{12{\varepsilon _0}{r^2}}}$$
G. $$\frac{{{\rho _0}{R^3}}}{{{\varepsilon _0}{r^2}}}$$
H. $$\frac{{2{\rho _0}{R^3}}}{{3{\varepsilon _0}{r^2}}}$$
I. $$\frac{{7{\rho _0}{R^3}}}{{12{\varepsilon _0}{r^2}}}$$
J. $$\frac{{6{\rho _0}{R^3}}}{{13{\varepsilon _0}{r^2}}}$$
Answer: F
A force $F=10\sqrt {2}N$ acts an angle of $45^{o}$ above the horizontal on a $2kg$ block placed on a rough horizontal surface. The coefficient of friction between the block  and surface is $0.2$ Find the work done by the force $F$ on the block in $5s$ initially the block is at rest. [Take $g=10/s^{2}$]

Options:
A. $$125\ J$$
B. $$50\ J$$
C. $$150\ J$$
D. $$2500\ J$$
E. $$500\ J$$
F. $$750\ J$$
G. $$250\ J$$
H. $$100\ J$$
Answer: E
The standard enthalpies of formation of 1,3- butadiene (g), $CO_{2}(g)$ and $H_{2}O(g)$ at 298 K are -30. -94 and -68 kcal/mol, respectively. If the magnitude of resonance enthalpies of 1,3-butadiene and $CO_{2}$ are 10 and 20 kcal/mol, respectively, the enthalpy of combustion of 1.3-butadiene (g) at 298K, is (enthalpy of vaporisation of $H_{2}O(I)$ at 298K = 10 kcal/mol)

Options:
A. -660 kcal/mol
B. -680 kcal/mol
C. -645 kcal/mol
D. -670 kcal/mol
E. -650 kcal/mol
F. -640 kcal/mol
G. -610 kcal/mol
H. +650 kcal/mol
I. -620 kcal/mol
J. -630 kcal/mol
Answer: E
What is the change $pH$ that result from the addition of $20ml$ of $0.1M$ $NaOH$ to a buffer made by combining $200ml$ of $0.07M$ benzoic acid with $100ml$ of $0.07M$ sodium benzoate ($K_a$ of benzoic acid =$6.4\times10^{-5}$)

Options:
A. $$-0.19$$
B. $$+0.17$$
C. $$+0.16$$
D. $$+0.21$$
E. $$-0.20$$
F. $$+0.18$$
G. $$+0.23$$
H. $$+0.19$$
I. $$+0.22$$
J. $$+0.20$$
Answer: D
Ata given instant , say t=0 , two radioactive substances A and B have qeual activities . 
the ratio $\frac { { R }_{ 8 } }{ { R }_{ A } } $ of their activities after time 1 itself decays with time t as ${ e }^{ - }3r$ if the half-life of A is In 20, the half - life of B is :

Options:
A. $$\dfrac{3 \ln2}{2}$$
B. $$4ln2$$
C. $$2ln2$$
D. $$\dfrac { \ln2 }{ 2 }$$
E. $$\dfrac { In2 }{ 4 } $$
F. $$\dfrac{3 \ln 2}{4}$$
G. $$\dfrac { \ln2 }{ 3 }$$
H. $$\dfrac{\ln2}{4}$$
I. $$\dfrac{\ln2}{12}$$
Answer: B
Two blocks of masses $m_{1}=5kg$ and $m_{2}=6kg$ are connected by a light string passing over a light frictionless pulley as shown. The mass $m_{1}$ is at rest on the inclined plane and mass $m_{2}$ hangs vertically. If the angle of incline $\theta =30^{0}$ what is magnitude and direction of force of friction on the 5kg block$(g=10ms^{-2})$

Options:
A. 40 N down the plane
B. 45 N down the plane
C. 35 N up the plane
D. 35 N down the plane
E. 85 N up the plane
F. 85 N down the plane
G. 25 N up the plane
H. 40 N up the plane
I. 25 N down the plane
J. 45 N up the plane
Answer: D
Calcium Lactate is a salt of weak acid and represented as $Ca(Lac)_{2}$. A saturated solution of $Ca(Lac)_{2}$ contains $0.125$ mole of salt in $0.50 L$ solution. The $pOH$ of this is $5.60$. Assuming complete dissociation of salt, calculate $K_{a}$ of lactate acid. ($log 2.5 = 0.4$)

Options:
A. $$6.34 \times 10^{-19}$$
B. $$8.0 \times 10^{-4}$$
C. $$6.34 \times 10^{-14}$$
D. $$6.34 \times 10^{-15}$$
E. $$6.34 \times 10^{-16}$$
F. $$1.25 \times 10^{-11}$$
G. $$4 \times 10^{-5}$$
H. $$6.34 \times 10^{-12}$$
I. $$6.34 \times 10^{-18}$$
J. $$6.34 \times 10^{-17}$$
Answer: J
A and B are two points on a uniform metal ring whose centre is O. The angle AOB = $\theta$. A angle B are maintained at two different constant temperatures. When $\theta = 180^o$, the rate of total heat flow from A to B is $1.2 W$. When $\theta = 90^o$ then this rate will be

Options:
A. $$0.8 watt$$
B. $$0.6 watt$$
C. $$1.6 watt$$
D. $$1.4 watt$$
E. $$0.9 watt$$
F. $$1.8 watt$$
G. $$1.2 watt$$
H. $$1.5 watt$$
I. $$1.1 watt$$
J. $$2.0 watt$$
Answer: C
$ 5.1\ g$ of $NH_{4} SH $ is introduced in a $ 3.0\ L $ evacuated flask at $ 327 ^{\circ}C$. $30\ %$  of the solid $ NH_{4} SH $ is decomposed to $ NH_{4} and $ $H_{2} S $ as gases. The $ K_{p} $ of the reaction at $ 327 ^{\circ}  C $ is $( R = 0.082\ L\  atm\ mol ^{-1}\  K^{-1})$ Molar mass of $S = 32\ g\ mol^ {-1} $ Molar mass of $ N = 14\ g\ mol ^{-1} $

Options:
A. $$0.242 \times 10^{-3}\ atm^{2}$$
B. $$ 0.242\ atm^{2}$$
C. $$4.9 \times 10^{-4}\ atm^{2}$$
D. $$4.8 \times 10^{-3}\ atm^{2}$$
E. $$4.9 \times 10^{-2}\ atm^{2}$$
F. $$5.1 \times 10^{-3}\ atm^{2}$$
G. $$0.242 \times 10^{-4}\ atm^{2}$$
H. $$ 1 \times 10^{-4}\ atm^{2}$$
I. $$ 4.9 \times 10^{-3}\ atm^{2}$$
J. $$5.9 \times 10^{-3}\ atm^{2}$$
Answer: I
Choose the correct statement (s) for hydrogen and deuterium atoms considering motion of reaction

Options:
A. The radius of first Bohr orbit of deuterium is less than that of hydrogen
B. The angular momentum of electron in the first Bohr orbit of deuterium is half that of hydrogen
C. The wave length of first Balmer line of deuterium is more than that of hydrogen
D. The angular momentum of electron in the first Bohr orbit of deuterium is more than that of hydrogen
E. The speed of electron in the first Bohr orbit of deuterium is more that that of hydrogen
F. The angular momentum of electron in the first Bohr orbit of deuterium is less than that of hydrogen
G. The angular momentum of electron in the first Bohr orbit of deuterium is twice that of hydrogen
Answer: A
One mole of argon is expanded according to process equation  $P V ^ { 1.5 } =$  constant and its temperature falls by  $26 { K } ,$  then

Options:
A. Heat exchanged is zero
B. Heat exchanged is $132 J$
C. Work done by gas is $432 J$
D. Heat exchanged is 96 J
E. Heat exchanged is 114 J
F. Heat exchanged is 120 J
G. Work done by gas is $132 J$
H. Heat exchanged is $72 J$
I. Heat exchanged is $108 J$
J. Work done by gas is $39 J$
Answer: I
A force $\vec { F } =\left( { 3x }^{ 2 }+2x-7 \right) $ N acts on a 2 kg body as a result of which the body gest displaced x=0 to x=5 cm. The work done by the force will be-

Options:
A. 125 Joule
B. 215 Joule
C. 175 Joule
D. 145 Joule
E. 270 Joule
F. 245 Joule
G. 135 Joule
H. 35 Joule
I. 70 Joule
J. 115 Joule
Answer: J
A monomeric complex of cobalt gave the following results on analysis :$Co^{3+} =$ 21.24%,  $NH_3 =$ 24.77%, $Cl^- =$ 12.81% and $SO^{2-}_4 =$ 34.65%   The compound is diamagnetic and contains no other groups or elements, except water which might be present. What is probable formula of the compound ? $(M_{Co}=59)$

Options:
A. $$[Co(NH_3)_4SO_4]Cl.H_2O$$
B. $$[Co(NH_3)_4SO_4]Cl.2H_2O$$
C. $$[Co(NH_3)_4ClSO_4].3H_2O$$
D. $$[Co(NH_3)_5Cl]SO_4$$
E. $$[Co(NH_3)_4SO_4]Cl.3H_2O$$
F. $$[Co(NH_3)_4ClH_2O]Cl$$
G. $$[Co(NH_3)_4ClH_2O]SO_4.$$
H. $$[Co(NH_3)_4ClSO_4].2H_2O$$
I. $$[Co(NH_3)_4ClSO_4].H_2O$$
Answer: G
$N$ turns are tightly wound to form a spiral plane of outer radius $a$. If the magnetic induction $B= B_0   \sin  \omega t$ varies perpendicular to the plane of spiral then find the emf induced in the spiral.

Options:
A. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{12}$$
B. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{5}$$
C. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{6}$$
D. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{4}$$
E. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{3}$$
F. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{7}$$
G. $$\displaystyle \frac{\pi a^2 B_0 \omega N \cos \omega t}{2}$$
H. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{8}$$
I. $$\displaystyle \pi a^2 B_0 N \omega \cos \omega t$$
J. $$\displaystyle \frac{\pi a^2 B_0 N \omega \cos \omega t}{9}$$
Answer: E
The data for the reaction $A + B \rightarrow C $ is:
Exp.$[A]_0$$[B]_0$initial rate1.0.0120.0350.102.0.0240.0350.0803.0.0120.0700.104.0.0240.0700.80The rate law corresponding on above data is :

Options:
A. $$r = k[A][B]^2$$
B. $$r = k[A]^2[B]^3$$
C. $$r = k[A]^2$$
D. $$r = k[A]^3$$
E. $$r = k[A][B]^3$$
F. $$r = k[A]^2[B]$$
G. $$r = k[A][B]$$
H. $$r = k[B]^2$$
I. $$r = k[A]^2[B]^2$$
Answer: D
The decomposition reaction, $4HNO_{3} \rightleftarrows  4NO_{2} (g)+2H_{2}O (g)+O_{2} (g)$ is started with pure $HNO_{3} (g)$. If $p$ is the total pressure at equilibrium, then

Options:
A. $$K_{p}=(Po_{2})^{7} /(p-7po_{2})^{4}$$
B. $$K_{p}=(Po_{2})^{7} /(p-3Po_{2})^{4}$$
C. $$K_{p}=7Po_{2}/(p-4Po_{2})$$
D. $$K_{p}=(Po_{2})^{7} /(p-9Po_{2})^{4}$$
E. $$K_{p}=(p-Po_{2})^{7}/(-7Po_{2})^{4}$$
F. $$K_{p}=(Po_{2})^{7} /(p-5Po_{2})^{4}$$
G. $$K_{p}=1024(Po_{2})^{7}/(p-7Po_{2})^{4}$$
H. $$K_{p}=(Po_{2})^{7} /(p-6Po_{2})^{4}$$
I. $$K_{p}=(Po_{2})^{7} /(p-8Po_{2})^{4}$$
J. $$K_{p}=(Po_{2})^{7} /(p-4Po_{2})^{4}$$
Answer: A
Ig $^{210}_{84}Po (t_{1/2} = 138. 4 \,days)$ is disintegrated in a sealed tube at NTP. How much helium will be accumulated after $69.2$ days?

Options:
A. $$96 \,ml$$
B. $$68 \,ml$$
C. $$320 \,ml$$
D. $$64 \,ml$$
E. $$680 \,ml$$
F. $$32 \,ml$$
G. $$16 \,ml$$
H. $$160 \,ml$$
I. $$128 \,ml$$
Answer: F
Find the enthalpy of reaction,$2HC\equiv CH+5O_2\rightarrow 4CO_2+2H_2O$If the bond energies of $C-H,\ C\equiv C,\ O=O,\ C=O$ and $O-H$ bonds are $p,\ q,\ r,\ s,\ t$ respectively

Options:
A. $$[4p+2q+5r]-[7s+4t]$$
B. $$[4p+2q+5r]-[8s+5t]$$
C. $$[6s+4t]-[4p+2q+5r]$$
D. $$[4p+2q+5r]-[9s+4t]$$
E. $$[4p+2q+5r]-[6s+3t]$$
F. $$[4p+2q+5r-8s+4t]$$
G. $$[2p+q+5r]-[8s+4t]$$
H. $$[4p+2q+5r]-[8s+4t]$$
I. $$[4p+2q+5r]-[8s+3t]$$
J. $$[8s+4t]-[4p+2q+5r]$$
Answer: J
What is the EMF of the cell: $Pt, H_{2}\ (1\ atm) |CH_{3}COOH\ (0.1\ M) \parallel (0.01\, M) NH_{4}OH | H_{2}\ (1\ atm), Pt$? Given: $ K_{a} $ for $ CH_{3}COOH = 1.8 \times 10^{-5}$             $K_{b}$ for $ NH_{4}OH = 1.8 \times 10^{-5}$           $(2.303 RT)/F = 0.06$            $ log\ 1.8 = 0.25 $

Options:
A. $$-0.93\ V$$
B. $$-0.30375\ V$$
C. $$-0.34875\ V$$
D. $$-0.585\ V$$
E. $$-0.52125\ V$$
F. $$0.465\ V$$
G. $$-0.11625\ V$$
H. $$-0.465\ V$$
I. $$-0.2325\ V$$
Answer: H
Two moles of helium are mixed with n moles of hydrogen.If $\frac{Cp}{Cv}$$=\frac{3}{2}$ for the mixture , then the value of n is

Options:
A. 3/4
B. 5/2
C. 1
D. 3
E. 1/4
F. 5/4
G. 1/2
H. 3/2
I. 2
J. 4/3
Answer: C
The length of the carbon-carbon single bond of the
compounds
$(I)$ $\mathrm { CH } _ { 2 } = \mathrm { CH } - \mathrm { C } \equiv \mathrm { CH }$ $(II)$ $\mathrm { CH } \equiv \mathrm { C } - \mathrm { C } \equiv \mathrm { CH }$ $(III)$ $\mathrm { CH } _ { 3 } - \mathrm { CH } = \mathrm { CH } _ { 2 }$ $(IV)$ $\mathrm { CH } _ { 2 } = \mathrm { CH } - \mathrm { CH } = \mathrm { CH } _ { 2 }$ 
is expected to decrease in the
order :

Options:
A. $$ II > IV > I > III $$
B. $$ III > I > IV > II $$
C. $$III > I > II > IV$$
D. $$III > II > IV > I$$
E. $$III > II > I > IV$$
F. $$III > IV > I > II$$
G. $$III > IV > II > I$$
H. $$I > III > II > IV$$
Answer: E
The maximum speed with which a car can be driven safely along a  curved road of radius 17.32 m and banked at $30^{\circ}$ with the horizontal is $ [ g = 10 m /s ^{2} ] $

Options:
A. 6 m /s
B. 20 m /s
C. 7.5 m /s
D. 12.5 m /s
E. 8.5 m /s
F. 4.5 m /s
G. 10 m /s
H. 5 m /s
I. 6.5 m /s
J. 15 m /s
Answer: H
Dimer of acetic acid in liquid benzene is in equilibrium with acetic acid monomer at certain temperature and pressure. If 25% of the dimer molecules are separated out then

Options:
A. Freezing point of the solution increases
B. Average molar mass of solute decreases
C. Average molar mass of solute increases
D. Freezing point of the solution remains unchanged
E. Boiling point of solution increases
F. Freezing point of the solution reduces
G. Boiling point of the solution decreases
H. Boiling point of the solution remains unchanged
I. Boiling point of the solution increases
J. Molar mass of solute decreases
Answer: F