MikaStars39/nano-eval huggingface dataset:
A car is moving with uniform acceleration along a straight line between two stops X and Y, Its speed at X and Y are $\displaystyle 2\ ms^{-1}$ and $\displaystyle 14\ ms^{-1}$. Which of the following statements is(are) correct.

Options:
A. the time to go from X to the mid-point of XY is 1.5 times that to go from mid-point to Y
B. its speed at a point A such that XA : AY = 1 : 3 is 5 $\displaystyle ms^{-1}$
C. the time to go from X to the mid-point of XY is triple of that to go from mid-point to Y
D. the time to go from X to the mid-point of XY is 2.5 times that to go from mid-point to Y
E. the time to go from X to the mid-point of XY is half of that to go from mid-point to Y
F. the time to go from X to the mid-point of XY is four times that to go from mid-point to Y
G. the time to go from X to the mid-point of XY is double of that to go from mid-point to Y
H. the time to go from X to the mid-point of XY is three times that to go from mid-point to Y
I. the distance travelled in first half of the total time is half of the distance travelled in the second half of the time
Answer: G
At what $pH$, is the solubility of $Zn(OH)_{2}$, minimum? What is the minimum solubility?
$$Zn(OH)_{2}(s) \leftrightharpoons Zn^{2+}(aq) + 2OH^{-}(aq); K_{sp} = 1.2\times 10^{-17}$$
$$Zn(OH)_{2}(s) +2OH^{-}(aq) \leftrightharpoons Zn(OH)_{4}^{2-}(aq); K_{f} = 0.12$$

Options:
A. $$10.0, 2.3 \times 10^{-9}M$$
B. $$10.0, 1.5 \times 10^{-9}M$$
C. $$10.0, 1.32 \times 10^{-9}M$$
D. $$10.0, 1.2 \times 10^{-9}M$$
E. $$10.0, 2.5 \times 10^{-9}M$$
F. $$10.0, 2.4 \times 10^{-9}M$$
G. $$10.0, 1.4 \times 10^{-9}M$$
H. $$10.0, 1.44 \times 10^{-9}M$$
I. $$10.0, 1.6 \times 10^{-9}M$$
J. $$4.0, 2.4 \times 10^{-9}M$$
Answer: F
Two identical vessel contain helium and hydrogen at same temperature, then :

Options:
A. average kinetic energy per mole of hydrogen = $\dfrac{7}{5}$ average kinetic energy per mole of helium
B. average kinetic energy per mole of hydrogen = $\dfrac{5}{2}$ average kinetic energy per mole of helium
C. average kinetic energy per mole of hydrogen = $\dfrac{5}{4}$ average kinetic energy per mole of helium
D. average kinetic energy per mole of hydrogen = $\dfrac{3}{4}$ average kinetic energy per mole of helium
E. average kinetic energy per mole of hydrogen = $\dfrac{5}{3}$ average kinetic energy per mole of helium
F. average kinetic energy per mole of hydrogen $=\dfrac{3}{5}$ average kinetic energy per mole of helium
G. average kinetic energy per mole of hydrogen = \dfrac{4}{5} average kinetic energy per mole of helium
H. average kinetic energy per mole of hydrogen = $\dfrac{4}{3}$ average kinetic energy per mole of helium
I. average translation kinetic energy per mole of hydrogen = average translation kinetic energy per mole of helium
Answer: E
A solution is prepared in which $0.1$ mole each of $HCl$, $CH_{3}COOH$ and $CHCl_{2}COOH$ is present in a litre. If the ionization Constant of $CH_{3}COOH$ is $10^{-5}$ and that of $Cl_{2}CHCOOH$ is $0.15$, the $pH$ of solution is ($log 2 = 0.3$, $log 3 = 0.48$)

Options:
A. $$5.12$$
B. $$3.79$$
C. $$4.88$$
D. $$3.92$$
E. $$1.0$$
F. $$3.80$$
G. $$4.91$$
H. $$0.95$$
I. $$3.85$$
J. $$3.82$$
Answer: G
A circular smooth road of radius $r=20m$ is banked for vehicles moving at a speed of $v=36kmph$. If the friction coefficient between the road and the road and the Tyre is $0.3$, find the maximum speed of a vehicle going around this curved road.

Options:
A. $$38.39kmph$$
B. $$37.39kmph$$
C. None of these
D. $$41.39kmph$$
E. $$36.39kmph$$
F. $$39.29kmph$$
G. $$29.39kmph$$
H. $$39.39kmph$$
I. $$40.39kmph$$
J. $$35.39kmph$$
Answer: I
A point traversed half a circle of radius $R=160\:cm$ during time interval $\tau=10.0\:s$. Calculate the modulus of the mean vector of the total acceleration $|\left<w\right>|$ if the point moved with constant tangential acceleration averaged over that time.

Options:
A. $$15\:cm/s^2$$
B. $$12\:cm/s^2$$
C. $$16\:cm/s^2$$
D. $$14\:cm/s^2$$
E. $$10\:cm/s^2$$
F. $$13\:cm/s^2$$
G. $$20\:cm/s^2$$
H. $$9\:cm/s^2$$
I. $$8\:cm/s^2$$
J. $$11\:cm/s^2$$
Answer: E
A bulb is placed at a depth of $2\sqrt{7}m$ in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. The radius of the disc should be at least $(\mu_{water} = 4/3)$ (Note, centre of disc is on the vertical line above the bulb) :

Options:
A. $$2\sqrt{14} \,m$$
B. $$42 \,m$$
C. $$4\sqrt{7} \,m$$
D. $$12 \,m$$
E. $$2\sqrt{21} \,m$$
F. $$2\sqrt{15} \,m$$
G. $$3\sqrt{21} \,m$$
H. $$6 \,m$$
I. $$2\sqrt{28} \,m$$
J. $$3\sqrt{7} \,m$$
Answer: E
Endothermic reactions, having $\Delta S = +ve$ may be spontaneous if:

Options:
A. \( T \) is moderately low
B. $$\Delta H = T\Delta S$$
C. \( T \) is moderate
D. $T$ is moderately low
E. T is moderately high
F. $$\Delta H > T\Delta S$$
G. $T$ is very low
H. \( T \) is moderately high
I. $T$ is very high
Answer: I
Two metallic spheres of radii ${ R }_{ 1 }$ and ${ R }_{ 2 }$, are I connected by a thin wire. If $+{ q }_{ 1 }$ and $+ { q }_{ 2 }$ are the charges on the two spheres then :

Options:
A. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 0.8 } }{ { R }_{ 2 }^{ 0.8 } }$$
B. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 1.8 } }{ { R }_{ 2 }^{ 1.8 } }$$
C. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 2.2 } }{ { R }_{ 2 }^{ 2.2 } }$$
D. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } \left( \frac { { R }_{ 1 }^{ 2 }-{ R }_{ 2 }^{ 2 } }{ { R }_{ 1 }^{ 2 }+{ R }_{ 2 }^{ 2 } } \right) $$
E. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } =\frac { { R }_{ 1 } }{ { R }_{ 2 } } $$
F. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } =\frac { { { R }_{ 1 }^{ 2 } } }{ { R }_{ 2 }^{ 2 } } $$
G. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 1 } }{ { R }_{ 2 }^{ 1 } }$$
H. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } =\frac { { { R }_{ 1 }^{ 3 } } }{ { R }_{ 2 }^{ 3 } } $$
I. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 1.5 } }{ { R }_{ 2 }^{ 1.5 } }$$
J. $$\frac { { q }_{ 1 } }{ { q }_{ 2 } } = \frac { { R }_{ 1 }^{ 1.2 } }{ { R }_{ 2 }^{ 1.2 } }$$
Answer: F
For the reaction, If $\Delta { H }_{ f }^{ o }\left[ { NH }_{ 3 }(g) \right] =-45.9kJ{ mol }^{ -1 }$ and $\Delta { H }_{ f }^{ o }\left[ { H }_{ 2 }O(g) \right] =-241.8kJ{ mol }^{ -1 } $, then $\Delta { H }_{ f }^{ o }\left[ { N }_{ 2 }O(g) \right] $ will be:$3{ N }_{ 2 }O(g)+2{ NH }_{ 3 }(g)\longrightarrow 4{ N }_{ 2 }(g)+3{ H }_{ 2 }O(g);\Delta { H }^{ o }=-879.6kJ$

Options:
A. $$-246kJ$$
B. $$+246kJ$$
C. $$+82kJ$$
D. $$-87.9kJ$$
E. $$-241.8kJ$$
F. $$-82kJ$$
G. $$-83kJ$$
H. $$-879.6kJ$$
I. $$-242kJ$$
Answer: C
A uniform slender rod of mass $m$ and length $L $ is released from rest, with its lower end touching a frictionless horizontal floor. At the initial moment, the rod is inclined at an angle $\theta=30^{\circ}$ with the vertical. Then the value of normal reaction from the floor just after release will be

Options:
A. $$3 g/8$$
B. $$3 g/7$$
C. $$3 g/5$$
D. $$ 5 g/9$$
E. $$5 g/8$$
F. None of these
G. $$2 mg/5$$
H. $$3\sqrt{3} g/7$$
I. $$4 g/9$$
Answer: H
$\displaystyle I_{2}(s)/I(aq)(1.0M)$ half cell is connected to $\displaystyle H^{+}(aq)/H_{2}(g)(1\, atm)$ Pt half cell and its cell potential is found to be 0.7714 V if $\displaystyle E_{I_{2}\Delta }^{0}=0.535V,$ the pH of $\displaystyle H^{+}/H_{2}$ half cell will be .........

Options:
A. 6
B. 2
C. 4.23
D. 7
E. 3
F. 9
G. 8
H. 5
I. 4
J. 1
Answer: E
A particle is hanging from a rigid support by a starting of length 1 m. It is struck inelastically by an identical particle moving horizontally velocity with $v=\sqrt {20}$ m/s. The tension in the string just after strike is [mass of each particle-1 kg]

Options:
A. 19 N
B. 20 N
C. 22 N
D. 18 N
E. 25 N
F. 17 N
G. 21 N
H. 10 N
I. 30 N
J. 15 N
Answer: B
A certain mass of gas is expanded from ($1$L. $10$ atm) to ($4$L.$5$atm) against a constant external pressure of $1$ atm. If initial temperature of gas is $300$K and the heat capacity of process is $50$ J$/^o$C. Then the enthalpy change during the process is: ($-1$ L atm $100$J).

Options:
A. $\Delta H=16.4$ kJ
B. $\Delta H=14.4$ kJ
C. $$\Delta H=14.8 \text{ kJ}$$
D. $$\Delta H=14.5 \text{ kJ}$$
E. $$\Delta H=14.9 \text{ kJ}$$
F. $\Delta H=14.7$ kJ
G. $\Delta H=15$ kJ
H. $\Delta H=15.7$ kJ
I. $$\Delta H=14.75 \text{ kJ}$$
J. $$\Delta H=15.3 \text{ kJ}$$
Answer: G
If $\triangle E$ is the heat of reaction for ${ C }_{ 2 }{ H }_{ 3 }{ OH }_{ \left( 1 \right)  }+{ 3O }_{ 2\left( g \right)  }\rightarrow { 2CO }_{ 2\left( s \right)  }+3{ H }_{ 2 }{ 0 }_{ \left( 1 \right)  }$ at constant volume, the $\triangle H$ ( Heat of reaction at constant pressure) at constant temperature is:

Options:
A. $$\triangle H= \triangle E + 1RT$$
B. $$\triangle H=\triangle E-2RT$$
C. $$\triangle H= \triangle E + 4RT$$
D. $$\triangle H= \triangle E - 3RT$$
E. $$\triangle H= \triangle E + 5RT$$
F. $$\triangle H=\triangle E+RT$$
G. $$\triangle H=\triangle E-RT$$
H. $$\triangle H=\triangle E+2RT$$
I. $$\triangle H= \triangle E + 3RT$$
J. $$\triangle H= \triangle E + 6RT$$
Answer: H
When Cu plate is dipped in a solution of $CuSO_4$ its electrode potential was found to be zero volt at $25^0C$ conc. of $CuSO_4$ solution ( Given $E^0_{Cu^{2+}/cu}= 0.32 V$)

Options:
A. $0.001$ M
B. 0.1 M
C. 0.2 M
D. 0.05 M
E. $1$ M
F. None of these
G. 0.5 M
H. 0.01 M
I. 0.005 M
Answer: E
A lead bullet at $27^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25$% of its heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking is
(Melting point of lead $= 327^{\circ}C$ specific heat of lead $= 0.03\ cal/gm^{\circ}C$, latent heat of fusion of lead$\ = 6\ cal/gm$ and $J = 4.2\ Joule/ cal)$.

Options:
A. $$410\ m/sec$$
B. $$400\ m/sec$$
C. $$360\ m/sec$$
D. $$320\ m/sec$$
E. $$390\ m/sec$$
F. $$307.5\ m/sec$$
G. $$330\ m/sec$$
H. $$1230\ m/sec$$
I. $$380\ m/sec$$
J. $$None of these$$
Answer: A
$\log { \cfrac { { K }_{ C } }{ { K }_{ P } }  } +\log { RT } =0$ is the relationship for the following gaseous phase reaction:

Options:
A. $$2{SO}_{2}+2{O}_{2} \rightleftharpoons 2{SO}_{3}$$
B. $$2{SO}_{2}+2{O}_{2} \rightleftharpoons 4{SO}_{3}$$
C. $${N}_{2}+3{H}_{2}\rightleftharpoons 2{NH}_{3}$$
D. $$2{SO}_{2}+{O}_{2} \rightleftharpoons 3{SO}_{3}$$
E. $$2{SO}_{2}+{O}_{2}\rightleftharpoons 2{SO}_{3}$$
F. $${H}_{2}+{I}_{2}\rightleftharpoons 2HI$$
G. $$2{SO}_{2}+2{O}_{2} \rightleftharpoons 3{SO}_{3}$$
H. $$P{Cl}_{5}\rightleftharpoons P{Cl}_{3}+{Cl}_{2}$$
Answer: E
In a thermodynamic process two moles of monatomic ideal gas obeys P $ \propto {v^{ - 2}}.$ If temperature of the gas increases from 300 K to 400 K, then find work done by the gas(where R = universal gas  constant)

Options:
A. $\frac{200R}{3}$
B. -150 R
C. 50 R
D. -400 R
E. 100 R
F. 150 R
G. 200 R
H. -300 R
I. -50 R
J. -200 R
Answer: A
At constant temperature, the equilibrium constant $(K_P)$ for the decomposition reaction $N_2O_4\leftrightharpoons 2NO_2$ Is expressed by $K_P=\dfrac {4x^2P}{(1-x^2)}$
Where P = pressure, x = extent of decomposition. Which one of the following statements are false?

Options:
A. $K_P$ increases with increase of P.
B. $K_P$ increases with increase of P and x.
C. $K_P$ decreases with decrease of x.
D. $K_P$ increases with increase of x.
E. $K_P$ remains constant with change in P and x.
Answer: E
A parallel plate capacitor of plate area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constants $K_1, K_2$ and $K_3$. If a single dielectric material is to be used to having the same capacitance C in this capacitor then its dielectric constant $K$ is given by :

Options:
A. $$\dfrac {1}{K}=\dfrac {1}{K_1+K_2}+\dfrac {1}{2K_3}$$
B. $$\dfrac {1}{K}=\dfrac {K_1K_2}{K_1+K_2}+\dfrac{K_{1}K_{3}}{K_{1}+K_{3}}$$
C. $$\dfrac {1}{K}=\dfrac {K_1K_2}{K_1+K_2}+\dfrac{K_{3}K_{1}}{K_{3}+K_{1}}$$
D. $$\dfrac {1}{K}=\dfrac {K_1K_3}{K_1+K_3}+\dfrac{K_{2}K_{3}}{K_{2}+K_{3}}$$
E. $$\dfrac {1}{K}=\dfrac {K_1K_3}{K_1+K_3}+\dfrac{K_{1}K_{2}}{K_{1}+K_{2}}$$
F. $$\dfrac {1}{K}=\dfrac {K_1K_3}{K_1+K_3}+\dfrac {K_2K_3}{K_2+K_3}+\dfrac {1}{2K_1}$$
G. $$\dfrac {1}{K}=\dfrac {K_1K_2}{K_1+K_2}+2K_3$$
H. $$\dfrac {1}{K}=\dfrac {K_1K_2}{K_1+K_2}+\dfrac{K_{2}K_{3}}{K_{2}+K_{3}}$$
I. $$\dfrac {1}{K}=\dfrac {1}{K_1}+\dfrac {1}{K_2}+\dfrac {1}{2K_3}$$
J. $$\dfrac {1}{K}=\dfrac {K_1K_3}{K_1+K_3}+\dfrac {K_1K_2}{K_1+K_2}$$
Answer: D
Solution A contains a buffer formed of 2.0 M acetic acid and 0.8 M potassium acetate. Solution B contains a buffer formed of 0.2 M acetic acid and 0.08 M potassium acetate. How do the solutions compare?

Options:
A. The pH of solution A is lower than that of solution B, and solution B has a greater buffer capacity than solution A.
B. The pH of solution A is lower than that of solution of B, and solution A has a greater buffer capacity than solution B
C. The pH of solution A is the same as that of solution B, and solution B has a greater buffer capacity than solution A.
D. The pH of solution A is higher than that of solution B, but the buffer capacity of solution A is the same as solution B.
E. The pH of solution A is higher than that of solution B, and solution A has a greater buffer capacity than solution B
F. The pH of solution A is higher than that of solution B, but the buffer capacity is the same.
G. The pH of solution A is lower than that of solution of B, but the buffer capacity is the same.
H. The pH of solution A is higher than that of solution B, and solution B has a greater buffer capacity than solution A.
I. The pH of solution A is the same than that of solution of B, but solution A has a greater buffer capacity
J. The pH and buffer capacity of both solutions are the same.
Answer: J
A solid sphere moves at a terminal velocity of $20ms^{-1}$ in air at a place where $g = 9.8ms^{-2}$. The sphere is taken in agravity=free hall having air at the same pressure and pushed down at a speed of $20ms^{-1}$.

Options:
A. Its initial acceleration will be $0ms^{-1}$
B. Its initial acceleration will be $4.9ms^{-2}$ downward
C. Its initial acceleration will be $9.8ms^{-1}$ downward
D. Its initial acceleration will be $29.4ms^{-2}$ downward
E. Its initial acceleration will be $19.6ms^{-2}$ downward
F. Its initial acceleration will be $9.8ms^{-2}$ upward
G. Its initial acceleration will be $14.7ms^{-2}$ downward
H. It will eventually stop
Answer: H
A heavy sphere of mass m is suspended by a string of length l. The sphere is made to revolve about a vertical line passing through the point of suspension, in a horizontal circle such that the string always remains inclined to the vertical making an angle $\theta $. What is the period of revolution ?

Options:
A. $$T=2\pi \sqrt { \dfrac { l - l\cos{2\theta} }{ g } }$$
B. $$T=2\pi \sqrt { \dfrac { l - l\sin{\theta} }{ g } }$$
C. $$T=2\pi \sqrt { \dfrac { l\cos { \theta } }{ g } } $$
D. $$T=2\pi \sqrt { \dfrac { l }{ g } } $$
E. $$T=2\pi \sqrt { \dfrac { l\sin { \theta } }{ g } } $$
F. $$T=2\pi \sqrt { \dfrac { l + l\sin{\theta} }{ g } }$$
G. $$T=2\pi \sqrt { \dfrac { l\tan { \theta } }{ g } } $$
H. $$T=2\pi \sqrt { \dfrac { l - l\cos{\theta} }{ g } }$$
I. $$T=2\pi \sqrt { \dfrac { l + l\cos{\theta} }{ g } }$$
J. $$T=2\pi \sqrt { \dfrac { l\sin^2{\theta} }{ g } }$$
Answer: C
A trolley T of mass $5 kg$ on a horizontal smooth surface is pulled by a load of $2 kg$ through a uniform rope ABC of length $2 m$ and mass $1 kg$. As the load falls from $BC=0$ to $BC=2 m$, its acceleration (in $m{ s }^{ -2 }$) changes from

Options:
A. $$\frac{20}{7} to \frac{30}{6}$$
B. $$\frac{20}{6} to \frac{30}{5}$$
C. $$\frac { 20 }{ 8 } to \frac { 30 }{ 8 } $$
D. $$\frac{20}{5} to \frac{30}{8}$$
E. $$\frac { 20 }{ 6 } to \frac { 30 }{ 6 } $$
F. $$\frac{20}{5} to \frac{30}{5}$$
G. $$\frac{20}{5} to \frac{30}{7}$$
H. $$\frac{20}{7} to \frac{30}{7}$$
I. None of these
J. $$\frac { 20 }{ 5 } to \frac { 30 }{ 6 } $$
Answer: C
One mole of a diatomic gas is compressed-to one fourth its original volume  $ V_o $ according to law- VT = Constant. The inital pressure is $ p_o $.Then which of the following is not true.

Options:
A. $$ \triangle Q = p_o v_o / 2 $$
B. \(\triangle U = 2.0 p_o v_o \)
C. \(\triangle U = 2.75 p_o v_o \)
D. $$ \triangle U = 2.5 p_o v_o $$
E. $$ \triangle P = 7 p_o $$
F. \(\triangle U = 3.5 p_o v_o \)
G. \(\triangle U = 3.0 p_o v_o\)
H. $$ W = - p_o v_o $$
I. \(\triangle U = 2.25 p_o v_o\)
Answer: D
A particle of mass $m=0.1 kg$ is released from rest from a point A of a wedge of mass $M=2.4 kg$ free to slide on a frictionless horizontal plane. The particle slides down the smooth face AB of the wedge. When the velocity of the wedge is 0.2 m/s what is the velocity of the particle in m/s relative to the wedge.

Options:
A. 4.5
B. 5.2
C. 5.5
D. 5.3
E. 4.8
F. 7.5
G. 10
H. 5.8
I. 6.5
J. 5
Answer: G
The density of a liquid is 1.2 g/mL. That are 35 drops in 2 mL. The number of molecules in 1 drop is (molecular weight of liquid = 70):

Options:
A. $$\frac{1.2}{(35)^2} N_A$$
B. $$\frac{1.2 \cdot 70}{(35)^2} N_A$$
C. $$\frac{1.2}{35} N_A$$
D. $$\frac{1.2 \cdot 35}{70} N_A$$
E. $$\frac{1.2 \cdot 2}{35} N_A$$
F. $$\frac{1.2 \cdot 70}{35} N_A$$
G. $$1.2 N_A$$
H. $$\frac{1.2 \cdot 35}{2} N_A$$
I. $$\left (\frac{1}{35} N_A \right )^2$$
J. $$\frac{1.2 \cdot 70}{70} N_A$$
Answer: A
If the total charge stored in the $LC$ circuit is $Q_{0},$ then for $t \ge 0$

Options:
A. the charge on the capacitor is $Q=-\dfrac{1}{LC}\dfrac{d^2Q}{dt^2}$
B. the charge on the capacitor is \( Q=-\dfrac{1}{\sqrt{LC}}\dfrac{dQ}{dt} \)
C. the charge on the capacitor is $Q=-LC\dfrac { { d }^{ 2 }Q }{ d{ t }^{ 2 } } $
D. the charge on the capacitor is \( Q={ Q }_{ 0 }\cos { \left( \dfrac { \pi }{ 2 } -\dfrac { 2t }{ \sqrt { LC } } \right) } \)
E. the charge on the capacitor is $Q={ Q }_{ 0 }\cos { \left( \dfrac { \pi }{ 2 } +\dfrac { t }{ \sqrt { LC } } \right) } $
F. the charge on the capacitor is \( Q=-\dfrac{1}{2LC}\dfrac{d^2Q}{dt^2} \)
G. the charge on the capacitor is $Q={ Q }_{ 0 }\cos { \left( \dfrac { \pi }{ 2 } -\dfrac { t }{ \sqrt { LC } } \right) } $
H. the charge on the capacitor is \( Q=-\dfrac{1}{LC}\dfrac{dQ}{dt} \)
I. the charge on the capacitor is $Q=-\dfrac { 1 }{ \sqrt { qc } } \dfrac { { d } Q }{ d{ t }^{ 2 } }$
J. the charge on the capacitor is \( Q=-\dfrac{1}{\sqrt{LC}}\dfrac{d^2Q}{dt^2} \)
Answer: C
The following reaction has $\Delta H$ as $-25\ kcal$.$CH_4(g)+Cl_2(g) \to CH_3Cl(g) + HCl(g)$ BondBond Energy kCal$arepsilon_{C-Cl}$84$arepsilon_{H-Cl}$109$arepsilon_{C-H}$$x$$arepsilon_{Cl-Cl}$$y$$x : y = 9: 5$From the given data, what is the bond enthalpy of $Cl - Cl$ bond?

Options:
A. 73.5\ kcal
B. 79.25\ kcal
C. 65.25\ kcal
D. 76.5\ kcal
E. 71.5\ kcal
F. 69.5\ kcal
G. $$108\ kcal$$
H. $$67.75\ kcal$$
I. $$70\ kcal$$
J. $$80\ kcal$$
Answer: G
Consider the following half cell reduction reaction 
$$Mn^{+2}+2e^-\rightarrow Mn, E^=-1.18V$$
$$Mn^{+2}\rightarrow Mn^{+3}+e^-, E^=-1.51V$$
The E^ for the reaction $3Mn^{+2}\rightarrow Mn+2Mn^{+3}$ and the possibility of the forward reaction are respectively

Options:
A. -4.18V and no
B. +4.18V and yes
C. -0.33V and yes
D. +2.69V and no
E. -2.69V and no
F. +4.18V and no
G. -0.33V and no
H. -2.69V and yes
I. -4.18V and yes
J. +0.33V and yes
Answer: I
The variation of rate constant 'K' of a chemical reaction with temperature T is observed to follow the expansion:
$\ln{K} = \alpha + \beta \ln{\left( T - \frac{\gamma}{T} \right)}$
where $\alpha, \beta, \gamma$ are constants, The Arrhenius activation energy for the reaction can be give by:

Options:
A. $$\gamma R$$
B. $$\alpha + \beta R$$
C. $$\alpha + \beta R T - \gamma R$$
D. $$\alpha RT+\gamma R$$
E. $$\alpha + \beta R T$$
F. $$\beta+\gamma R$$
G. $$\beta RT - \gamma R$$
H. $$\alpha + \gamma R$$
I. $$\alpha R T - \gamma R$$
J. $$\beta RT+\gamma R$$
Answer: J
A mixture of $NaHCO_3$  and $Na_2CO_3$ weighs 950 gm. When the mixture is heated strongly in an open vessel, till constant weight, the mass of sample reduced by 155 gm. The correct information(s) is/ are ?

Options:
A. The mass percent of $NaHCO_3$ in initial mixture = 50%
B. The mass percent of $NaHCO_3$ in initial mixture = 45%
C. Final sample contains only $Na_2O$
D. The mole percent of $Na_2CO_3$ in initial mixture = 50%
E. The mass percent of $NaHCO_3$ in initial mixture = 48%
F. The mass percent of $NaHCO_3$ in initial mixture = 40%
G. The mass percent of $NaHCO_3$ in initial mixture = 42%
H. The mass percent of $NaHCO_3$ in initial mixture = 55%
I. The loss in mass is only due to $CO_2$ gas evolved
J. The mass percent of $NaHCO_3$ in initial mixture = 57%
Answer: A
I mol of an ideal gas, initially present in an insulated piston fitted cylinder at 400 K and 10 atm. ia allowed to expand against a constant 2.0 atm pressure till the mechanical equilibrium is established.Given ${ C }_{ v.\quad m }=\dfrac { 5 }{ 2 } R$ determine final temperature of the gas-

Options:
A. 500 K
B. 398.6 K
C. 350 K
D. 550 K
E. 498.6 K
F. 408.6 K
G. 300 K
H. 308.6 K
I. 505 K
J. 450 K
Answer: H
In $20\ ml\ 0.4\ M-HA$ solution, $80\ ml$ water is added. Assuming volume to be additive, the $pH$ off final solution is (${K }_{  a} of HA=4\times 1{ 0 }^{ -7 }, log2=0.3  $)

Options:
A. $$3.89$$
B. $$4.30$$
C. $$4.50$$
D. $$4.20$$
E. $$5.30$$
F. $$3.70$$
G. $$4.00$$
H. $$4.40$$
I. $$4.10$$
J. $$4.09$$
Answer: B
Consider the following two reactions:(i) Propene + $H_2\rightarrow$ Propane; $\Delta H_1$(ii) Cyclopropane + $H_2\rightarrow$ Propane; $\Delta H_2$Then, $|\Delta H_2$ - $\Delta H_1|$ will be:

Options:
A. $$|3BE_{C-C} - 2BE_{C=C}|$$
B. $$|2BE_{C=C}-BE_{C-C}|$$
C. $$BE_{C=C}$$
D. $$0$$
E. $$|BE_{C-C}-2BE_{C-C}|$$
F. $$|3BE_{C=C}-2BE_{C-C}|$$
G. $$|2BE_{C-C}-BE_{C=C}|$$
H. $$|BE_{C-C}-2BE_{C=C}|$$
I. $$|BE_{C-C}+2BE_{C=C}|$$
J. $$|3BE_{C-C}-BE_{C=C}|$$
Answer: G
${ (IE) }_{ 1 }$ and $(IE)_{ 2 }$ of ${ Mg }_{ g }$ are 740, 1540kJ ${ mol }^{ -1 }$. Calculate percentage of ${ Mg }_{ (g) }^{ + }$ and ${ Mg }_{ (g) }^{ 2+ }$ if 1 g  of ${ Mg }_{ (g) }$ absorbs 50.0 kJ of energy.

Options:
A. %${ Mg }^{ + }=75$% %${ Mg }^{ 2+ }=25$%
B. %${ Mg }^{ + }=30$% %${ Mg }^{ 2+ }=70$%
C. %${ Mg }^{ + }=65$% %${ Mg }^{ 2+ }=35$%
D. %${ Mg }^{ + }=70.13$% %${ Mg }^{ 2+ }=29.87$%
E. %${ Mg }^{ + }=80$% %${ Mg }^{ 2+ }=20$%
F. %${ Mg }^{ + }=40$% %${ Mg }^{ 2+ }=60$%
G. %${ Mg }^{ + }=45$% %${ Mg }^{ 2+ }=55$%
H. %${ Mg }^{ + }=60$% %${ Mg }^{ 2+ }=40$%
I. %${ Mg }^{ + }=68.65$% %${ Mg }^{ 2+ }=31.65$%
J. %${ Mg }^{ + }=55$% %${ Mg }^{ 2+ }=45$%
Answer: I
Calculate EMF of the cell
$$A|A^{-3}(0.1m)||B^{+2}(0.01m)|B$$
$$Given \quad E^oA|A^{+3}=0.75V$$
           $E^oB|B^{+2}=0.45 V$

Options:
A. $$0.80 V$$
B. $$0.32 V$$
C. $$0.29 V$$
D. $$0.31 V$$
E. $$1.21 V$$
F. $$0.28 V$$
G. $$0.26 V$$
H. $$0.30 V$$
I. $$0.33 V$$
J. $$0.34 V$$
Answer: G
The conducting loop in the form of a circle is placed in a uniform magnetic field with its plane perpendicular to the direction of the field. An emf will be induced in the loop if :

Options:
A. it is rotated about an axis perpendicular to the field and the loop's plane
B. the loop is translated parallel to itself
C. the loop is translated perpendicular to the field
D. the loop is rotated about one of its diameters
E. the loop is translated parallel to the field
F. it is rotated about its own axis which is parallel to the field
G. the loop is deformed from the original shape
H. the loop is deformed to a different geometric shape
I. it is translated parallel to itself
Answer: G
A mixture of three proteins $(A)$ (pepsin), $(B)$ (haemoglobin) and $(C)$ (lysozyme) was separated by eletrophoresis method at $pH=7$. The $pH$ at isoelectric point $(pI)$ of the proteins are $pI$ of $(A), (B)$ and $(C)$ which are $1.1,6.7$ and $11.0$ respectively. Which of the statement are correct?

Options:
A. Haemoglobin will not migrate
B. Lysozyme $(C)$ will migrate to the anode
C. At $pH=7$, $(B)$ and $(C)$ would remain in the solution while $(A)$ would precipitate out.
D. At $pH=7$, $(A)$ and $(C)$ would precipitate out while $(B)$ would remain in the solution.
E. Pepsin $(A)$ will migrate to the cathode
F. At $pH=7$, $(B)$ and $(C)$ would precipitate out while $(A)$ would remain in the solution.
G. At $pH=7$, $(A)$ and $(B)$ would precipitate out while $(C)$ would remain in the solution.
H. At pH=7, (A) and (B) would migrate to the anode while (C) would remain in the solution.
Answer: A
In the arrangement shown, the 2 kg block is held to keep the system at rest. The string and pulley are ideal. When the 2 kg block is set free, by what amount the tension in the string changes? [ g = 10 $m/s^2$]

Options:
A. decrease of 16 N
B. Decrease of 14 N
C. Increase of 12 N
D. decrease of 12 N
E. Decrease of 18 N
F. decrease of 14 N
G. Decrease of 10 N
H. Increase of 18 N
I. decrease of 13 N
J. decrease of 15 N
Answer: D
The 10 kg block is moving to the left with a speed of $1.2 m/s$ at time $t =0.$ A force F is applied as shown in the graph. After $0.2$ s the force continues at the $10 N$ level. If the coefficient of kinetic friction is $\displaystyle \mu _{k}=0.2.$ Determine the time t at which the block comes to a stop. (g= $\displaystyle 10m/s^{2}$)

Options:
A. $$0.400s$$
B. $$0.415s$$
C. $$0.295s$$
D. $$0.333s$$
E. $$0.526 s$$
F. $$0.395s$$
G. $$0.165 s$$
H. $$0.367s$$
I. None of  the above.
J. $$0.375s$$
Answer: D
A body of mass $m$ is hauled from the earth's surface by applying a force
$$f = 2 (ah - 1)m \vec{g}$$
where $a$ is positive constant and $h$ is height from the earth's surface.

Options:
A. At height \( h = \frac{1}{6a} \), the velocity of the body is maximum
B. At height \( h = \frac{1}{5a} \), the velocity of the body is maximum
C. At height \( h = \frac{1}{3a} \), the velocity of the body is maximum
D. At height \( h = \frac{1}{2a} \), the velocity of the body is zero
E. At height \( h = \frac{1}{4a} \), the velocity of the body is maximum
F. All the above are correct
G. At height \( h = \frac{1}{a} \), the velocity of the body is maximum
H. At height $h = \dfrac {1}{2a}$, the velocity of the body is maximum
Answer: F
A radioactive species decay for time t, where t = $4 \times t_{1/2}$. The average life of species can therefore be:

Options:
A. $$2t \ ln \ 2$$
B. $$\frac{t}{6 \ ln \ 2}$$
C. $$\frac{t}{5 \ ln \ 2}$$
D. $$\frac{t}{7 \ ln \ 2}$$
E. $$4t \ ln \ 2$$
F. $$\frac{t}{2 \ ln \ 2}$$
G. $$\frac{t}{8 \ ln \ 2}$$
H. $$( 3t \ ln \ 2 )$$
I. $$\frac{t}{3 \ ln \ 2}$$
J. $$\frac{t}{4 \ ln \ 2}$$
Answer: A
A very broad elevator is going up vertically with a constant acceleration of $2m/{s}^{2}$. At the instant when its velocity is $4m/s$ a ball is projected from the floor of the lift with a speed of $4m/s$, relative to the floor at an elevation of ${30}^{o}$. The time taken by the ball to return the floor is 
($g=10m/{s}^{2}$)

Options:
A. $$1s$$
B. $$\cfrac{2}{3}s$$
C. $$\cfrac{2}{5}s$$
D. $$\cfrac{1}{2}s$$
E. $$\cfrac{1}{6}s$$
F. $$\cfrac{1}{3}s$$
G. $$\cfrac{1}{5}s$$
H. $$\cfrac{3}{4}s$$
I. $$\cfrac{1}{4}s$$
Answer: F
A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\dfrac{81\pi}{7}\times 10^{5} Vm^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity $2\times 10^{-3} ms^{-1}$. Given $g=9.8 ms^{-2}$, viscosity of the air$=1.8\times 10^{-5} Ns\ m^{-2}$ and the density of oil $=900\ kg\ m^{-3}$, the magnitude of $q$ is:

Options:
A. 5.6 \times 10^{-19}C
B. 7.2 \times 10^{-19}C
C. 1.2 \times 10^{-19}C
D. $$8.0\times 10^{-19}C$$
E. 9.6 \times 10^{-19}C
F. 6.4 \times 10^{-19}C
G. $$1.6\times 10^{-19}C$$
H. $$4.8\times 10^{-19}C$$
I. $$3.2\times 10^{-19}C$$
J. 2.4 \times 10^{-19}C
Answer: D
What is the molarity and normality of a $13\%$ solution (by weight) of sulphuric acid with a density of $1.02$ g/mL and also calculate the volume (in mL) that is required to prepare  1.5 $N$ of  this acid to make it upto 100$ml$?

Options:
A. Molarity$=2 $, Normality$=4$, Volume$=200\ mL$
B. Molarity$=1.30$, Normality$=2.60$, Volume$=180\ mL$
C. Molarity$=1.35$, Normality$=2.70$, Volume$=180\ mL$
D. Molarity$=1.5 $, Normality$=3$, Volume$=150\ mL$
E. Molarity$=1.35$, Normality$=2.70$, Volume$=190\ mL$
F. None of these
G. Molarity$=1.40$, Normality$=2.80$, Volume$=180\ mL$
H. Molarity$=1.35$, Normality$=2.70$, Volume$=185\ mL$
I. Molarity$=1.35$, Normality$=2.70$, Volume$=182\ mL$
J. Molarity$=1.35$, Normality$=2.70$, Volume$=175\ mL$
Answer: C
A spherical of iron of radius 2 mm is falling through a column of glycerine. If denesities of glycerine and iron are respectively : $1.3*10^3 kg/m^3$ and $8*10^3 kg/m^3$ n for glycerine =0.83 kg/m-s, then the terminal velocity is:

Options:
A. 0.077 m/s
B. 0.6 m/s
C. 0.07 m/s
D. 0.007 m/s
E. 0.7 m/s
F. 0.77 m/s
G. 0.0007 m/s
H. 0.00077 m/s
I. 0.67 m/s
J. 0.0077 m/s
Answer: E
Two identical pendulums $A$ and $B$ are suspended from the same point. Both are given a positive charge, with $A$ having more charge than $B$. They diverge and reach equilibrium with the strings of pendulums $A$ and $B$ making angles $\theta_1$ and $\theta_2$ with the vertical respectively. Then:

Options:
A. $\theta_1$ > $\theta_2$
B. $$\theta_1 = \frac{3}{2}\theta_2$$
C. the tension in A is greater than that in B
D. $$\theta_1= \theta_2$$
E. $$\theta_1 = \frac{1}{2}\theta_2$$
F. $$\theta_1 = 4\theta_2$$
G. $$\theta_1 = 3\theta_2$$
H. $\theta_1$ < $\theta_2$
I. $$\theta_1 = \frac{4}{3}\theta_2$$
J. $$\theta_1 = 2\theta_2$$
Answer: D
A source of sound with natural frequency $ f_0 = 1800\,Hz $ moves uniformly along a straight line separated from a stationary observer  by a distance $ l = 250\,m $ . The velocity of the source is equal to $ \eta = 0.80 $ fraction of the velocity of the sound. The distance between the source and the observer at the moment when the observer receives a frequency $ f = f_0 $ is

Options:
A. $$ 250\,m $$
B. $$360\,m$$
C. $$400\,m$$
D. $$300\,m$$
E. $$380\,m$$
F. $$ 640\,m $$
G. $$350\,m$$
H. 500\,m
I. $$ 620\,m $$
J. $$ 420\,m $$
Answer: F
A charged particle enters a uniform magnetic field with velocity ${v_o}$. Perpendicular to if the length of the magnetic field is $x = \dfrac{{\sqrt 3 }}{2}R$ . Where R is the radius of the circular path of a particle in the field. Find the magnitude of charge in velocity when particle comes out of the field.

Options:
A. $$\dfrac{{\sqrt 3 {v_o}}}{2}$$
B. $$\dfrac{{\sqrt 2 {v_o}}}{2}$$
C. $$\dfrac{{4{v_o}}}{3}$$
D. $$\dfrac{{3{v_o}}}{4}$$
E. $$\dfrac{{\sqrt 2 {v_o}}}{3}$$
F. $$\dfrac{{{v_o}}}{2}$$
G. $$\dfrac{{\sqrt 3 {v_o}}}{3}$$
H. $$\dfrac{{3{v_o}}}{2}$$
I. $$2{v_o}$$
J. $${v_o}$$
Answer: I
The given figure shows a heavy block of mass $M$ kept on a frictionless surface and being pulled by two ropes of equal mass $m$. At $t=5s$ the force on the left rope is withdrawn but the force on the right end continues to act. Find the magnitude of the force by the right rope on the block.

Options:
A. $$\cfrac{mF}{(M+2m)}$$
B. $$\cfrac{2mF}{(M+2m)}$$
C. $$\cfrac{mF}{(M+m)}$$
D. $$\cfrac{(M+m)F}{(M+2m)}$$
E. $$\cfrac{2MF}{(M+m)}$$
F. $$\cfrac{(M+2m)F}{(M+m)}$$
G. $$\cfrac{2MF}{(M+2m)}$$
H. $$\cfrac{(M+2m)F}{(M+2m)}$$
I. $$\cfrac{(M+m)F}{(2M+2m)}$$
J. $$\cfrac{MF}{(M+2m)}$$
Answer: A
Molecules of benzoic acid $(C_{ 6 }{ H }_{ 5 }COOH)\quad $ dimerise  in  benzene . 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is : 
(Given that ${ K }_{ f }=5\quad K\quad kg\quad mol^{ -1 }$, Molar mass of benzoic acid = 122 g $mol^{ -1 }$)

Options:
A. 1.5 g
B. 1.7 g
C. 1.1 g
D. 1.8 g
E. 1.0 g
F. 1.2 g
G. 1.3 g
H. 1.6 g
I. 2.4 g
J. 1.4 g
Answer: E
Calcium lactate is a salt of weak acid and represented as $Ca(Lac)_{2}$. A saturated solution of $Ca(Lac)_{2}$ contains 0.13 mol of salt in 0.5 It solution and pOH=5.6. Assuming complete dissociation of salt, the $K_{a}$ for lactic acid is

Options:
A. $$2.4\times 10^{-5}$$
B. $$4.125 \times 10^{-5}$$
C. $$8.25\times 10^{-2}$$
D. $$5\times 10^{-5}$$
E. $$4.125 \times 10^{-2}$$
F. $$4.125 \times 10^{-4}$$
G. $$4.125 \times 10^{-1}$$
H. $$4.125 \times 10^{-3}$$
I. $$4.125 \times 10^{-6}$$
J. $$8.25\times 10^{-4}$$
Answer: C
Equation of a wave travelling in a medium is : $y = a \,sin \,(bt - cx).$ Which of the following are correct ?

Options:
A. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to ac / 3.
B. None of the above
C. Ratio of the displacement amplitude, with which the particles of the medium oscillate, to the wavelength is equal to \( ac / 4 \pi. \)
D. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to 2ac / 3.
E. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to 3ac / 4.
F. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to ac / 2.
G. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to 3ac / 5.
H. Oscillation amplitude of relative deformation of the medium is directly proportional to velocity oscillation amplitude of medium particles.
Answer: H
For the reaction at 300 K
$$A(g)\rightleftharpoons V(g)+S(g)$$
$$\Delta ,H^{0}=-30kJ/mol,\Delta ,S^{0}=-0.1kJ.K^{-1}mol^{-1}$$
What is the value of equilibrium constant?

Options:
A. -1
B. 10
C. -10
D. 0.1
E. 1
F. 0.01
G. -0.1
H. 100
I. +RT
J. 0
Answer: J
A wave represented by the equation $y=A \sin  (kx-\omega t) $ is superimposed with another wave to form a stationary wave such that the point $x=0$ is a node. The equation of the other wave is :

Options:
A. $$A \cos (kx + \omega t)$$
B. $$A \cos (kx - \omega t + \pi)$$
C. $$A \sin (kx + \omega t)$$
D. $$-A \cos (kx - \omega t)$$
E. $$A \cos (kx - \omega t)$$
F. $$A \cos (kx + \omega t + \pi)$$
G. $$A \sin (kx - \omega t)$$
H. $$A \sin (kx - \omega t + \pi)$$
I. $$-A \sin (kx + \omega t)$$
Answer: E
Which of the following is/are correct statement(s) regarding solubility of $AgCl(s)$?
$$[K_{sol(AgCl)}=10^{-10}\ M^{2}; K,[Ag(NH_{3})_{2}^{+}]=10^{8}]$$

Options:
A. Solubility of $AgCl$ in pure water is $10^{-5}\ gm/litre$
B. Solubility of $AgCl$ in pure water is $10^{-6}\ gm/litre$
C. Solubility of $AgCl$ in pure water is $10^{-3}\ gm/litre$
D. Solubility of $AgCl$ in pure water is $10^{-4}\ gm/litre$
E. Solubility of $AgCl$ in pure water is $10^{-7}\ gm/litre$
F. Solubility of $AgCl$ in $2\ M\ AgNO_{3}$ is $5\ \times\ 10^{-11}\ gm/litre$
G. Solubility of $AgCl$ in pure water is $10^{-8}\ gm/litre$
Answer: F
A particle slides along a track with elevated ends and a flat central part as shown in the Figure below. The flat portion BC has a length $l=3.0 m$. The curved portions of the track are frictionless. For the flat part the coefficient of kinetic friction is $\displaystyle \mu _{k}= 0.20,$ the particle is released at point A which is at height $h=1.5 m$ above the flat part of the track. Where does the particle finally comes to rest?

Options:
A. The particle comes to rest at $\frac{1}{3}$rd distance from the point B of the flat part.
B. The particle comes to rest at point B
C. The particle comes to rest at $\frac{3}{5}$ distance from the point B of the flat part.
D. The particle comes to rest at $\frac{1}{5}$ distance from the point B of the flat part.
E. The particle comes to rest at the center. of the flat part.
F. The particle comes to rest at $\frac{3}{4}$th distance from the point B of the flat part.
G. The particle comes to rest at $\frac{2}{3}$ distance from the point B of the flat part.
H. The particle comes to rest at $\frac{1}{6}$th distance from the point B of the flat part.
I. The particle comes to rest at $\frac{1}{4}$th distance from the point B of the flat part.
J. The particle comes to rest at $\frac{1}{2}$ distance from the point B of the flat part.
Answer: E
A  thin disc  of radius b  =  2a has a concentric hole of radius 'a' init  It carries uniform surface  charge  density $ \sigma  $ on it . If the electric field on its axis at height 'h' ( h < < a) from its center is given as 'Ch' then value of 'C' is

Options:
A. $$ \dfrac{\sigma}{4 a \varepsilon_0} $$
B. $$ \dfrac{\sigma}{8 a \varepsilon _{0}} $$
C. $$ \dfrac{\sigma}{a \varepsilon_0} $$
D. $$\dfrac{\sigma}{6 a\varepsilon _{0}}$$
E. $$\dfrac{\sigma}{10a\varepsilon _{0}}$$
F. \dfrac{\sigma}{3a\varepsilon _{0}}
G. $$\dfrac{\sigma}{5a\varepsilon_{0}}$$
H. $$ \dfrac{\sigma}{2 a \varepsilon_0} $$
I. $$\dfrac{\sigma}{9a\varepsilon _{0}}$$
J. $$\dfrac{\sigma}{7a\varepsilon_{0}}$$
Answer: A
Select the complex in which metal have primary valency=2, secondary valency=4 and shows stereo-isomerism:

Options:
A. $$PtCl_3.2NH_3$$
B. $$PtCl_4.3NH_3$$
C. $$PtCl_4.2NH_3$$
D. $$PtCl_3.4NH_3$$
E. $$PtCl_2.2NH_3$$
F. $$PtCl_3.3NH_3$$
G. $$PtCl_2.3NH_3$$
H. $$PtCl_2.4NH_3$$
Answer: C
$ C u S O_{4} .5 H_{2} O(s) \rightleftharpoons C u S O_{4} \cdot 3 H_{2} O(s)+2 H_{2} O(g) \quad K_{p}=4 \times 10^{-4} a t m^{2} $ If the vapour pressure of water is 38 torr then percentage of relative humidity is (Assume all data at constant temperature)

Options:
A. 6
B. 12
C. 40
D. 10
E. 4
F. 8
G. None of these
H. 16
I. 2
J. 14
Answer: E
A uniform wooden stick of mass $1.6$ kg and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h(<l)$ such that a  small portion of the stick extends beyond the wall. The reaction force of  the wall on the stick is perpendicular to  the stick. The stick makes an angle of ${ 30 }^{ \circ  }$ with the wall and  the bottom of the stick is on  a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio of $h/l$ and the frictional force $f$ at the bottom of the stick are(g = 10 m${ s }^{ -2 }$):

Options:
A. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 8\sqrt { 3 } }{ 3 } N$$
B. $$\dfrac { h }{ l } = \dfrac { \sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 16\sqrt { 3 } }{ 3 } N$$
C. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 4\sqrt { 3 } }{ 3 } N$$
D. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 14\sqrt { 3 } }{ 3 } N$$
E. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 5\sqrt { 3 } }{ 3 } N$$
F. $$\dfrac { h }{ l } = \dfrac { 3 }{ 16 } ,\quad f= \dfrac { 16\sqrt { 3 } }{ 3 } N$$
G. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 16\sqrt { 3 } }{ 3 } N$$
H. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 10\sqrt { 3 } }{ 3 } N$$
I. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 2\sqrt { 3 } }{ 3 } N$$
J. $$\dfrac { h }{ l } = \dfrac { 3\sqrt { 3 } }{ 16 } ,\quad f= \dfrac { 7\sqrt { 3 } }{ 3 } N$$
Answer: G
One gram hydrogen has $6\times 10^{23}$ atoms. Imagine that all the nuclei are put at the north pole of the earth and the electrons at the south pole of the earth (radius=6400 km). The force between the charges is

Options:
A. $$2.5\times 10^{5}N$$
B. $$10\times 10^{5}N$$
C. $$7.5 \times 10^{5}N$$
D. $$5\times 10^{5}N$$
E. $$12.5 \times 10^{5}N$$
F. $$7.5 \times 10^{4}N$$
G. $$15 \times 10^{5}N$$
H. $$5 \times 10^{6}N$$
I. $$2\times 10^{5}N$$
J. $$15 \times 10^{4}N$$
Answer: B
EMF of the cell $Zn\left | ZnSO_{4}(a=0.2) \right |\left | ZnSO_{4}(a_{2}) \right | Zn$ is $-0.0088$ V at $25^{\circ}C$. Calculate the value of $a_{2}$.

Options:
A. None of these
B. $$a_{2}=0.3018\:M$$
C. $$a_{2}=0.2512\:M$$
D. $$a_{2}=0.1509\:M$$
E. $$a_{2}=0.1003\:M$$
F. $$a_{2}=0.2012\:M$$
G. $$a_{2}=0.1012\:M$$
H. $$a_{2}=0.1009\:M$$
I. $$a_{2}=0.1006\:M$$
J. $$a_{2}=0.2004\:M$$
Answer: I
A block of mass of 10 kg is kept on rough inclined plane.The inclined plane is kept inside a lift.At t=0, the system is set in motion, the lift accelerates upwards with 10 $m/{s^2}.$
The work done by normal reaction on the block in one second w.r.t. lift is.

Options:
A. 10 j
B. 20 j
C. 40 j
D. 5j
E. zero
F. 30 j
G. 25 j
H. 15 j
I. none of these
J. 50 j
Answer: I
The figure shows an $L$ shaped body of mass $M$ placed on smooth horizontal surface. The block $A$ is connected to the body by means of an inextensible string, which is passing over a smooth pulley of negligible mass. Another block $B$ of mass $m$ is placed against a vertical wall of the body. Find the minimum value of the mass of block $A$ so that block $B$ remains stationary relative to the wall. Coefficient of friction between the block $B$ and the vertical wall is $\displaystyle \mu=2.(Take\ g=10\ m/s^{2})$

Options:
A. $$\displaystyle m_{A}=\frac{M}{\mu - 1}\:but\:\mu > 1$$
B. $$\displaystyle m_{A}=\frac{M+m}{\mu - 1}\:but\:\mu > 1$$
C. $$\displaystyle m_{A}=\frac{M+m}{\mu + 1}\:but\:\mu > 1$$
D. $$\displaystyle m_{A}=\frac{M+m}{\mu + 2}\:but\:\mu > 1$$
E. $$\displaystyle m_{A}=\frac{M-m}{\mu + 1}\:but\:\mu > 1$$
F. $$\displaystyle m_{A}=\frac{M-m}{\mu - 2}\:but\:\mu > 1$$
G. $$\displaystyle m_{A}=\frac{M+m}{\mu - 2} \:but\:\mu > 1$$
H. $$m_{A} = \dfrac{M - m}{\mu - 1} \quad \text{but} \quad \mu > 1$$
I. $$\displaystyle m_{A}=\frac{m}{\mu - 1}\:but\:\mu > 1$$
J. $$\displaystyle m_{A}=\frac{M+m}{\mu + 1}$$
Answer: B
A silver wire dipped in 0.1 M HCl  solution saturated with AgCl develops oxidation potential of -0.25v. If ${{\text{E}}^{\text{o}}}_{{\text{Ag/A}}{{\text{g}}^{\text{ + }}}}{\text{ = }}\, - {\text{0}}{\text{.799V}}\,$, the ${{\text{K}}_{{\text{sp}}}}$ of AgCl in pure water will be

Options:
A. $$3.45 \times 10^{ - 11}$$
B. $$4.95 \times {10^{ - 11}}$$
C. $$2.95 \times {10^{ - 11}}$$
D. $$3.95 \times {10^{ - 11}}$$
E. $$4.45 \times {10^{ - 11}}$$
F. $$5.1 \times {10^{ - 11}}$$
G. $$1.95 \times {10^{ - 11}}$$
H. $$4.45 \times 10^{-11}$$
Answer: C
The temperature dependence of the rate of a chemical reaction is given by Arrhenius equation, $k = Ae^{-E_a/RT}$.
Which of the following graphs will be a straight line?

Options:
A. $\ln k $ versus $1/RT$
B. $\ln k $ versus $1/T$
C. $\ln A $ versus $1/T$
D. $\ln k $ versus $E_a /R$
E. $\ln A$ versus $T$
F. $\ln k$ versus $E_a$
G. $\ln A $ versus $E_a$
Answer: C
Two monochromatic sources of electromagnetic wave, P and Q  emit waves of wavelength $\lambda = 20 m$ and separated by $5m$ as shown. A, B and C are three points where interference of these waves is observed. If phase of a wave generated by P is ahead of wave generated by Q y $\dfrac{\pi}{2}$ then (given intensity of both waves is I):

Options:
A. intensities at A, B and C are in the ratio 0 : 1 : 2 respectively.
B. intensities at A, B and C are in the ratio 1 : 0 : 2 respectively.
C. intensities at A, B and C are in the ratio 0 : 2 : 1 respectively.
D. intensities at A, B and C are in the ratio 2 : 1 : 0 respectively.
E. phase difference of these waves at B is $180^\circ $
F. intensities at A, B and C are in the ratio 1 : 1 : 1 respectively.
G. phase difference at A is $0^\circ$
H. intensities at A, B and C are in the ratio 2 : 1 : 1 respectively.
I. intensities at A, B and C are in the ratio 2 : 0 : 1 respectively.
J. intensities at A, B and C are in the ratio 1 : 2 : 0 respectively.
Answer: J
If the rate of reaction, $ 2 \mathrm { SO } _ { 2 } ( g ) + \mathrm { O } _ { 2 } ( \mathrm { g } ) \stackrel { \mathrm { Pt } } { \longrightarrow } 2 \mathrm { SO } _ { 3 } ( \mathrm { g } ) $ is given by: 
Rate $ = K \frac { \left[ \mathrm { SO } _ { 2 } \right] } { \left[ \mathrm { SO } _ { 3 } \right] ^ { 1 / 2 } } $
which statements are correct:

Options:
A. The rate of reaction does not depend upon concentration of $ \mathrm { SO } _ { 3 } $ formed
B. The overall order of reaction is $ - 1 / 3 $
C. The overall order of reaction is $ - 3 / 4 $
D. The overall order of reaction is $ - 1 / 2 $
E. The overall order of reaction is $ - 1 / 4 $
F. The overall order of reaction is $ + 1 / 2 $
G. The overall order of reaction is $ 0 $
H. The overall order of reaction is $ - 1 / 6 $
I. The overall order of reaction is $ 1 / 4 $
Answer: D
A block of mass $2.5\ kg$ is kept on a rough horizontal surface. It is found that the block does not slide if a horizontal force less than $15\ N$ is applied to it. Also it is found that it takes $5\ s$ to slide throughout the first $10\ m$ if a horizontal force of $15\ N$ is applied and the block is gently pushed to start the motion. Taking $g=10\ m/{s}^{2}$, then

Options:
A. $${ \mu }_{ k }=0.62$$
B. $${ \mu }_{ k }=0.61$$
C. $${ \mu }_{ s }=0.60$$
D. $${ \mu }_{ k }=0.55$$
E. $${ \mu }_{ k }=0.58$$
F. $${ \mu }_{ k }=0.57$$
G. $${ \mu }_{ s }=0.52$$
H. $${ \mu }_{ k }=0.52$$
I. $${ \mu }_{ k }=0.59$$
J. $${ \mu }_{ k }=0.60$$
Answer: J
The energy stored in magnetic field produced by a metal sphere is $4.5\ J$. If the sphere contains $4 \mu  C$ charge, its radius will be : 
[Take : $\dfrac{1} {4 \pi \epsilon_0} = 9 \times 10^9 N - m^2/C^2$ ]

Options:
A. $$32\ mm$$
B. $$21\ mm$$
C. $$22\ mm$$
D. $$24\ mm$$
E. $$25\ mm$$
F. $$18\ mm$$
G. $$28\ mm$$
H. $$19\ mm$$
I. $$20\ mm$$
J. $$16\ mm$$
Answer: I
A rough and inelastic sphere of radius 'R' rolling without sliding with an angular velocity $\omega_0$ on a horizontal plane meets a fixed obstacle of height $h=R/2$ as shown. If the sphere does not slide after collision,its angular velocity is

Options:
A. $$15\omega_0/14$$
B. $$7\omega_0/14$$
C. $$13\omega_0/14$$
D. $$12\omega_0/14$$
E. $$5\omega_0/14$$
F. $$3\omega_0/14$$
G. $$\omega_0/14$$
H. $$9\omega_0/14$$
I. $$11\omega_0/14$$
J. $$17\omega_0/14$$
Answer: H
An electric field prevailing in a region depends only on X and Y coordinates according to an equation, $\overrightarrow E  = b{{X\widehat i + Y\widehat j} \over {{X^2} + {Y^2}}}$ where b is a constant. Find the flux passing through a sphere of radius r whose center is on the origin of the coordinate system.

Options:
A. $$9\pi br$$
B. $$7\pi br$$
C. $$\pi rb$$
D. $$2\pi br$$
E. $$6\pi rb$$
F. $$3\pi br$$
G. $$5\pi br$$
H. $$4\pi br$$
I. $$8\pi br$$
Answer: H
In the given circuit diagram capacity $C_{1}=3C$ and capacity $C_{2}=6C$. When switches $S_{1}, S_{2}$ and $ S_{2} $ are open and switch $S_{4}$ is closed total energy stored in both the capacitors is $U$. When the switches $S_{1}, S_{2}$ and $S_{3}$ are closed and switch $S_{4}$ is open, total energy stored in both the capacitors is $U$. The relation between $U$ and $U'$ is:

Options:
A. $$U'=0.6U$$
B. $$U'=0.5U$$
C. $$U'=1.25U$$
D. $$U'=0.75U$$
E. $$U'=3U$$
F. $$U'=U$$
G. $$U'=2.5U$$
H. $$U'=4.5U$$
I. $$U'=1.5U$$
J. $$U'=2U$$
Answer: B
A cylindrical vessel of a very large cross-sectional area is containing two immiscible liquids of density $\rho_1=600 kg/m^3$ and $\rho_2=1200 kg/m^3$ as shown in the figure.A small hole having cross-sectional area $5 cm^2$ is made in right side vertical wall as shown. Take atmospheric pressure as $p_0=10^5 N/m^2, g=9.8m/s^2$. For this situation, which of following is correct? (Take cross-sectional area of the cylindrical vessel as $1000 cm^2$. Neglect the mass of the vessel)

Options:
A. If the surface on which the vessel is placed is smooth, then no force is needed to maintain its static equilibrium.
B. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 20.2 N.
C. If the surface on which the vessel is placed is rough $(\mu=0.04)$, then the minimum force (horizontal) needed to be applied on the vessel to maintains its static equilibrium is zero.
D. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 18.2 N.
E. If the surface on which the vessel is placed is smooth, then a rightward force of magnitude 2N is to be applied on the vessel to maintain its static equilibrium.
F. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 20.5 N.
G. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 19.8 N.
H. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 21.0 N.
I. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 18.9 N.
J. If the surface on which the vessel is placed is rough ($\mu=0.04$), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 19.0 N.
Answer: G