MikaStars39/nano-eval huggingface dataset:
Two small rings $O$ and $O'$ are put on two vertical stationary rods $AB$ and $A'B'$, respectively. One end of an inextensible thread is tied at point $A'$. The thread passes through ring $O$' and its other end is tied to ring $O$. Assuming that ring $O$' moves downwards at a constant velocity ${ v }_{ 1 }$, then velocity ${ v }_{ 2 }$ of the ring $O$, when $ngleAOO'=lpha$, is

Options:
A. None of these
B. $$v_1 \left[ \frac{2 \cos^2 \left( \frac{\alpha}{2} \right)}{\cos \alpha} \right]
$$
C. $$v_1 \left[ \frac{2 \sin^2 \left( \frac{\alpha}{2} \right)}{\cos \alpha} \right]
$$
D. $$v_1 \left[ \frac{3 \cos^2 \left( \frac{\alpha}{2} \right)}{\sin \alpha} \right]
$$
E. $$v_1 \left[ \frac{3 \cos^2 \left( \frac{\alpha}{2} \right)}{\cos \alpha} \right]
$$
F. $v_1 \left[ \frac{2 \sin^2 \left( \frac{\alpha}{2} \right)}{\sin \alpha} \right]
$
G. $$v_1 \left[ \frac{2 \cos^2 \left( \frac{\alpha}{2} \right)}{\sin \alpha} \right]
$$
H. $$v_1 \left[ \frac{3 \sin^2 \left( \frac{\alpha}{2} \right)}{2 \cos \alpha} \right]$$
I. $$v_1 \left[ \frac{3 \sin^2 \left( \frac{\alpha}{2} \right)}{\cos \alpha} \right]
$$
J. { v }_{ 1 }\left[ \frac { 2{ \sin { } }^{ 2 }lpha /2 }{ 2\cos { lpha } } \right]
Answer: C
For the reaction equilibrium, $2NOBr \rightleftharpoons 2NO(g)+Br_{2}(g)$
If $P_{Br_{2}}=\dfrac {P}{6}$ equilibrium and $P$ is total pressure, the ratio of $\dfrac {K_{p}}{P}$ is equal to

Options:
A. \dfrac{1}{108}
B. \dfrac{1}{405}
C. $$\dfrac {1}{3}$$
D. $$\dfrac {1}{9}$$
E. \dfrac{1}{54}
F. \dfrac{1}{162}
G. $$\dfrac {1}{81}$$
H. $$\dfrac {1}{27}$$
I. \dfrac{1}{135}
J. \dfrac{1}{243}
Answer: G
A cycle starts from rest with acceleration $2m/{s}^{2}$ for time ${t}_{0}$ sec after which brakes are applied. Cycle decelerates at a constant rate $10m/{sec}^{2}$ and comes to rest at $C$. If total time taken is $12sec$ thenThen choose the correct statement:

Options:
A. distance AC covered by cycle is $120m$ and ${t}_{0}=5sec$
B. distance AC covered by cycle is $110m$ and ${t}_{0}=6sec$
C. distance AC covered by cycle is $100m$
D. distance AC covered by cycle is $110m$ and ${t}_{0}=4.5sec$
E. distance AC covered by cycle is $100m$ and ${t}_{0}=6sec$
F. $${t}_{0}=6sec$$
G. distance AC covered by cycle is $115m$ and ${t}_{0}=5.5sec$
H. distance AC covered by cycle is $110m$ and ${t}_{0}=4sec$
I. maximum velocity of cycle is $20m/sec$ and ${t}_{0}=10sec$
J. distance AC covered by cycle is $110m$ and ${t}_{0}=5sec$
Answer: A
If an iodized salt contains $1\%$ of $KI$ and a person takes $2\ g$ of the salt every day, the iodine ions going into his body every day would be approximately $(K=39, I=127)$

Options:
A. $$9.2 \times 10^{21}$$
B. $$7.2 \times 10^{18}$$
C. $$9.5 \times 10^{19}$$
D. $$9.5 \times 10^{21}$$
E. $$7.2 \times 10^{23}$$
F. $$9.2 \times 10^{19}$$
G. $$7.2 \times 10^{19}$$
H. $$7.2 \times 10^{22}$$
I. $$7.2 \times 10^{20}$$
Answer: G
Given the data $25^0C$$Ag+I^+\longrightarrow AgI+e^-$         $E=0.152 V$$Ag\longrightarrow Ag^+ + e^-$           $E=-0.800 V$What is the value of $LogK_{sp}$ for $AgI\left[ 2.303\cfrac { RT }{ F } =0.059V \right] $

Options:
A. +8.10
B. -8.10
C. +8.610
D. -8.610
E. -8.12
F. -8.612
G. -37.83
H. -16.10
I. +8.12
J. +8.612
Answer: J
A cylinder, fitted with piston, contains a diatomic gas at temperature $T_{1} = 27^{\circ}C$. Initially, the height of the piston from the base of the cylinder is $h_{1} = 20 cm$ as shown in the figure. When the temperature is raised to $T_{2} = 177^{\circ}C$, the new height of the piston above the base becomes $h_{2}$. The system is then insulated from the surroundings and the piston is brought back to its original height. The new equilibrium temperature becomes $T_{3}$. Then :[Given $(1.5)^{0.4} = 1.18$]

Options:
A. h_{2} = 31 cm
B. h_{2} = 29 cm
C. h_{2} = 27 cm
D. $$h_{2} = 32 cm$$
E. $$T_{3} = 81^{\circ}C$$
F. $$h_{2} = 30 cm$$
G. h_{2} = 28.5 cm
H. $$h_{2} = 24.5 cm$$
I. $$T_{3} = 258^{\circ}C$$
J. h_{2} = 26 cm
Answer: F
A partcle is subjected to two simple harmonic motions (both along x-axis) ${x_1} = A\sin \left( {\omega t - \frac{\pi }{6}} \right)$ and ${x_2} = 2A\cos \omega t$. Find the resultant amplitude of the oscillation

Options:
A. $$A\sqrt{8}$$
B. $$A\sqrt{3}$$
C. $$A$$
D. $$A\sqrt{4}$$
E. $$A\sqrt 5 $$
F. $$A\sqrt 2 $$
G. $$A\sqrt 6 $$
H. $$A\sqrt{6}$$
I. $$A\sqrt 3 $$
J. $$A\sqrt{7}$$
Answer: E
An electric line of force in the xy plane is given by equation $x^2 + y^2 = 1$. A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the xy plane

Options:
A. will move along an elliptical line of force
B. will move along the circular line of force
C. will move along a hyperbolic line of force
D. will move along a parabolic line of force
E. will move along a circular line of force
F. information is insufficient to draw any conclusion
G. will move along the hyperbolic line of force
H. will move along straight line
I. will move along the parabolic line of force
J. not move at all
Answer: H
A circular road of radius $r$ is banked for a speed $v=40$ km/hr. A car of mass $m$ attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible. Find the correct option(s).

Options:
A. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is greater than mg as well as greater than $\displaystyle \frac{mv^2}{r}$
B. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is equal to $\displaystyle \frac{mg}{2} + \frac{mv^2}{r}$
C. If the car turns at a correct speed of 40 km/hr, the force by the road on the car is equal to \(\frac{mg}{2} + \frac{mv^2}{4r}\)
D. If the car turns at a speed less than $40$ km/hr, it will slip down
E. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is equal to $\displaystyle \frac{mg}{2} + \frac{2mv^2}{r}$
F. The car cannot make a turn without skidding
G. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is equal to $\displaystyle \frac{mg}{2} - \frac{mv^2}{r}$
H. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is equal to $\displaystyle \frac{mg}{2} + \frac{mv^2}{2r}$
I. If the car turns at a correct speed of $40$ km/hr, the force by the road on the car is equal to $\displaystyle \frac{mv^2}{r}$
Answer: A
For the following cell,$Zn(s)|{ ZnSO }_{ 4 }(aq)\parallel { CuSO }_{ 4 }(aq)|Cu(s)$When the concentration of ${ Zn }^{ 2+ }$ is $10$ times the concentration of ${ Cu }^{ 2+ }$, the expression for the $\triangle G$ (in $J\quad { mol }^{ -1 }$) is: [$F$ is Faraday constant; $R$ is gas constant; $T$ is temperature; ${ E }^{ }$(cell)$=1.1V$]

Options:
A. $$-2.2F$$
B. $$2.303R-2.2F$$
C. $$2.303RT-1.1F$$
D. $$2.303RT+1.1F$$
E. $$2.303R-1.1F$$
F. $$2.303RT-2.2F$$
G. $$2.303R+2.2F$$
H. $$2.303RT+2.2F$$
I. $$1.1F$$
Answer: B
One mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{o}C$. If the work done by the gas in the process is $3$ KJ, then the final temperature will be equal to :Given : $(C_v= 20 \:J/K mol)$

Options:
A. $$375\ K$$
B. $$400\ K$$
C. $$300\ K$$
D. $$450\ K$$
E. $$150\ K$$
F. $$350\ K$$
G. $$500\ K$$
H. $$550\ K$$
I. $$100\ K$$
Answer: D
The sound waves each of amplitude $\alpha$ and of frequency $500Hz$ and $512Hz$ superpose. Then the resultant of the amplitude of the resultant wave at $t=\frac {5}{48}s$ is

Options:
A. $$\frac{a}{\sqrt{2}}$$
B. $$\frac{a\sqrt{3}}{\sqrt{2}}$$
C. $$\frac{a\sqrt{2}}{2}$$
D. $$2a$$
E. $$\frac{a\sqrt{3}}{2}$$
F. $$\frac{a}{2}$$
G. $$\frac{a}{\sqrt{3}}$$
H. $$\frac{2a}{\sqrt{2}}$$
I. $$2\sqrt{2}$$
J. $$0$$
Answer: A
A body is given a velocity $\sqrt{2g r}$ at the highest point of a half circular smooth track which is joined by a rough horizontal track whose co-efficient of friction is $\mu = 0.5.$ Then the distance traveled by the particle before it stops on horizontal track is (Given acceleration due to gravity$=g$)

Options:
A. $$5 m$$
B. $$9 m$$
C. $$none of these$$
D. $$8 m$$
E. $$10 m$$
F. $$4 m$$
G. $$7 m$$
H. $$3 m$$
I. $$6 m$$
J. $$1 m$$
Answer: I
A liquid flow through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross section ${ A }_{ 1 }$ and ${ A }_{ 2 }$ are ${ v }_{ 1 }$ and ${ v }_{ 2 }$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$. Then

Options:
A. $$${ v }_{ 2 }^{ 2 }-{ v }_{ 1 }^{ 2 }=gh/4$$$
B. $$${ v }_{ 2 }^{ 2 }-{ v }_{ 1 }^{ 2 }=gh/2$$$
C. The energy per unit mass of the liquid is different in the two sections of the tube
D. $${ v }_{ 2 }\ -\ { v }_{ 1 }\ =\ \sqrt { 2gh }$$
E. $$${ v }_{ 2 }^{ 2 } - { v }_{ 1 }^{ 2 } = \frac{gh}{5} $$$
F. The energy per unit mass of the liquid is the same in both section of the tube
G. $$${ v }_{ 2 }^{ 2 }-{ v }_{ 1 }^{ 2 }=gh/3$$$
H. The energy per unit mass of the liquid is different in the two sections of the tube \({ v }_{ 2 }^{ 2 } - { v }_{ 1 }^{ 2 } = gh \)
Answer: F
In the potentiometer arrangement (Fig.), the driving cell $ A $ has e.m.f. $\varepsilon $ and internal resistance $ r $. The e.m.f. of the cell $ B $ is to be rechecked has e.m.f. $\varepsilon / 2 $ and internal resistance $ 2 r . $ The potentiometer wire $ C D $ is $ 100 \mathrm{cm} $ long. If balance is obtained, the length $ C J=l $ is

Options:
A. l = 65 \mathrm{cm}
B. l = 75 \mathrm{cm}
C. l = 45 \mathrm{cm}
D. l = 60 \mathrm{cm}
E. Balance cannot be obtained
F. l = 55 \mathrm{cm}
G. l<50 \mathrm{cm}
H. $$ l=50 \mathrm{cm} $$
I. $$ l>50 \mathrm{cm} $$
Answer: I
The pH of a solution obtained by mixing 100 ml of 0.2 M ${ CH }_{ 3 }COOH$ with 100 ml of 0.1 M $NaOH$ will be: ($p{ K }_{ a }$ for ${ CH }_{ 3 }COOH$ = 4.74 )

Options:
A. 8.87
B. 8.77
C. 8.47
D. 8.54
E. 8.27
F. 4.74
G. 9.1
H. 8.37
I. 8.67
J. 8.57
Answer: A
Two equal charges of $2C$ each are fixed at $x = -5 m$ and $x = +5 m$ on the x-axis. Another point charge $Q = 4C$ is placed at the origin. The change in the electric potential energy of Q, when it is displaced by a distance of $2 m $along x-axis, is

Options:
A. $3.9 \times 10^{20}$
B. $2.87 \times 10^{20}$J
C. $$4.9 \times 10^{20} \text{ J}$$
D. $$3.7 \times 10^{20} \text{ J}$$
E. $$5.19 \times 10^{20} \text{ J}$$
F. $5.86 \times 10^{20}$J
G. $6.77 \times 10^{20}$J
H. $$4.96 \times 10^{20} \text{ J}$$
I. $$3.79 \times 10^{20} \text{ J}$$
J. $$3.19 \times 10^{20} \text{ J}$$
Answer: A
Rear window of a car has a size of $ 120 \times 45 \,cm^2 $. The driver sits at a distance $ L = 2\,m $ from the rear window. What should be the minimum size of flat mirror, hanging at a distance of $ 0.5\,m $ in front of the driver so that he has best view of road situation behind the car?

Options:
A. $$( 25 \times 8.75\,cm)$$
B. $$ ( 24 \times 9\,cm) $$
C. $$( 21 \times 7.75\,cm)$$
D. $$ ( 30 \times 11.25\,cm) $$
E. $$( 18 \times 6.75\,cm)$$
F. $$ ( 40 \times 15\,cm) $$
G. $$ ( 20 \times 7.5\,cm) $$
H. $$( 16 \times 6\,cm)$$
I. $$( 22 \times 8.25\,cm)$$
J. $$( 19 \times 7\,cm)$$
Answer: G
For a given amount of ideal gas , if $A$ be the slope of $P-V$ curve for its isothermal process and $B$ be the slope of $P-V$ curve for its adiabatic process then $\gamma \left( { = \frac{{{C_p}}}{{{C_v}}}} \right)$

Options:
A. $$\frac{A^2}{B^2}$$
B. $$\frac{A}{B^2}$$
C. $$\frac{B^2}{A^2}$$
D. $${\frac{-B}{A}}$$
E. $${\frac{A}{B}}$$
F. $$\frac{A^2}{B}$$
G. $$\frac{B}{A^2}$$
H. $${\frac{B}{A}}$$
I. $$AB$$
J. $$\frac{B^2}{A}$$
Answer: E
A particle starting from rest moves along the circumference of a circle of radius r =$\sqrt{2}$ m and angular acceleration $\alpha$ = $\dfrac{\pi}{4}$ rad /s$^{2}$ .What is the magnitude of its average velocity in the times it completes a quarter rotation ?

Options:
A. $\dfrac {2\sqrt{2}}{\pi}$ m/ s
B. $\dfrac{\pi} {\sqrt{2}}$ m /s
C. $$\dfrac{\pi} {2\sqrt{3}}$$
D. $\dfrac{\pi} {2\sqrt{2}}$ m/s
E. $\dfrac{\pi} {3\sqrt{2}}$ m/s
F. $\dfrac{\pi} {3}$ m/s
G. $$\dfrac{\pi} {4} m/s$$
H. $\dfrac{\pi} {2}$ m/s
I. $$\dfrac{2\sqrt{2}}{\pi}$$
J. $\dfrac{\pi} {4\sqrt{2}}$ m/s
Answer: H
In the figure shown below the conducting shell $A$ having radius $R$ is given charge $Q$ initially. The shell $A$ is connected to shell $B$ of radius $2R$ via switch $S$ and a conducting wire. The switch $S$ is closed at $t = 0,$ then charge density on the shell $B$ is
(Assuming separation between $A$ and $B$ is very very large)

Options:
A. $$\dfrac{Q}{{48\pi {R^2}}}$$
B. $$\dfrac{Q}{{12\pi {R^2}}}$$
C. $$\dfrac{Q}{{36\pi {R^2}}}$$
D. $$\dfrac{Q}{{16\pi {R^2}}}$$
E. $$\dfrac{Q}{{6\pi {R^2}}}$$
F. $$\dfrac{Q}{{24\pi {R^2}}}$$
G. $$\dfrac{Q}{{32\pi {R^2}}}$$
H. $$\dfrac{Q}{{44\pi {R^2}}}$$
I. $$\dfrac{Q}{{56\pi {R^2}}}$$
J. $$\dfrac{Q}{{52\pi {R^2}}}$$
Answer: A
A body of mass $1$ kg is dropped from a height of $5$ m on to the ground. If the body penetrates $2$ cm in to the ground, the average resistance offered by the ground on to the body is $ (g= 10 ms^{-2})$

Options:
A. 2512 N
B. 2511 N
C. 2515 N
D. $35$ N
E. $2500$ N
F. 2530 N
G. $52.2$ N
H. 2520 N
I. $2510$ N
Answer: I
A block is placed at distance of $2\, m$ from the rear on the floor of a truck $(g = 10\, ms^{-2})$. When the truck moves with an acceleration of $8\, ms^{-2}$, the block takes $2\, \sec$ to fall off from the rear of the truck. The coefficient of sliding friction between the truck and the block is

Options:
A. $$0.3$$
B. $$0.4$$
C. $$0.6$$
D. $$0.8$$
E. $$0.9$$
F. $$0.75$$
G. $$0.5$$
H. $$0.95$$
I. $$0.7$$
J. $$0.1$$
Answer: D
How many moles of a monoatomic gas ($\gamma = \frac{5}{3}$) is mixed with 2 moles of a poly atomic gas ($\gamma = \frac{4}{3}$) at constant temperature such that the mixture be haves like a diatomic gas ($\gamma = \frac{7}{5}$)

Options:
A. None of these
B. 3.5
C. 1
D. 1.5
E. 2.25
F. 2.75
G. 2
H. 4
I. 3
J. 2.5
Answer: G
A tube of 1 mm bore is dipped into a vessel containing a liquid of density p = 800 kg ${ m }^{ -3 }$ and of surface tension, $S=49\times { 10 }^{ -3 }{ Nm }^{ -1 }$ and angle of contact, $\theta ={ 0 }^{ \circ  }$. The tube is held inclined to the vertical at an angle of ${ 60 }^{ \circ  }$, find the height to which the liquid can rise and the length which the liquid will occupy in the tube.

Options:
A. 2.5 cm, 3 cm
B. 3.5 cm, 4 cm
C. 1.5 cm, 5 cm
D. 2.5 cm, 4 cm
E. 1 cm, 5 cm
F. 2.5 cm, 5 cm
G. 2 cm, 5 cm
H. 4 cm, 2.5 cm
I. 3 cm, 5 cm
J. 3.5 cm, 5 cm
Answer: C
A piece of copper metal weighing 7 g requires 5.4 J of heat to raise the temperature from 300 K to 302 K. What is the value of heat capacity and molar heat capacity of copper metal respectively ? (Atomic mass of Cu = 63.5)

Options:
A. $$27{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.5\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
B. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },25.5\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
C. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },244.5\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
D. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.51\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
E. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.6\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
F. $$0.27{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },2.45\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
G. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },245\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
H. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.49\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
I. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.45\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
J. $$2.7{ JK }^{ -1 },0.385{ Jg }^{ -1 }{ K }^{ -1 },24.55\quad J\quad { mol }^{ -1 }{ K }^{ -1 }$$
Answer: G
A very thin uniform rod, $2.40m$ long and of weight $135\, N$, has a frictionless hinge at its lower end. It starts out vertically from rest and falls, pivoting about the hinge, just as it has rotated through an angle of $55.0^0$, what is the downward acceleration of the end farthest from the hinge ?$(\sin 55^0 = 0.582)$

Options:
A. $$8.03\, m/s^2$$
B. $$9.80\, m/s^2$$
C. $$7.83\, m/s^2$$
D. $$6.20\, m/s^2$$
E. $$12.0\, m/s^2$$
F. $$5.82\, m/s^2$$
G. $$7.05\, m/s^2$$
H. $$8.53\, m/s^2$$
I. $$5.02\, m/s^2$$
J. $$7.30\, m/s^2$$
Answer: A
Two volatile liquids $A$ and $B$ an mixed in mole ratio $1 : 3$, to form an ideal liquid solution. Vapour pressure of pure $A$ and $B$ are $600\ torr$ and $200\ torr$. Volume of container for vapour is $76$ litre. $(R = 1/12$ litre atm/K/mole).Calculate the mole of $\wedge$ in vapour phase at $300\ K$, assuming negligible amount of vapour is present compared to liquid in container.

Options:
A. $$0.4\ mole$$
B. $$0.3\ mole$$
C. $$1.2\ mole$$
D. $$0.7\ mole$$
E. $$0.9\ mole$$
F. $$0.8\ mole$$
G. $$0.6\ mole$$
H. $$2\ mole$$
I. $$0.5\ mole$$
J. $$0.2\ mole$$
Answer: B
An object is projected from ground with speed $20\ m/s$ at angle $30^{o}$ with horizontal. Its centripetal acceleration one second after the projection is [Take $g=10\ m/s^{2}$]

Options:
A. $$zero$$
B. $$10\ m/s^{2}$$
C. $$5\ m/s^{2}$$
D. $$11\ m/s^{2}$$
E. $$12 \ m/s^{2}$$
F. $$9\ m/s^{2}$$
G. $$6\ m/s^{2}$$
H. $$15\ m/s^{2}$$
I. $$7\ m/s^{2}$$
J. $$8\ m/s^{2}$$
Answer: B
Two loudspeakers M and N are located $20$ m apart and emit sound at frequencies $118$ Hz and $121$ Hz respectively. A car is initially at a point P, $1800$ m away from the midpoint Q of the line MN and moves towards Q constantly at $60$ km/hr along perpendicular bisector of MN. It crosses Q and eventually reaches a point R, $1800$ m away from Q. Let $
u(t)$ represent the beat frequency measured by a person sitting in the car at time $t$. Let ${
u }_{ p }$, ${
u}_{ Q }$ and ${
u}_{ R }$ be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is $330$ ${ ms }^{ -1 }$. Which of the following statement (s) is (are) true regarding the sound heard by the person?

Options:
A. A plot below represents schematically the variation of beat frequency with time
B. The plot below represents schematically the variation of beat frequency with time
C. The plot below represents the variation of beat frequency with time, but shows a linear increase as the car moves from P to R
D. The rate of change in beat frequency is zero when the car is halfway between P and R
E. The rate of change in beat frequency is maximum when the car is halfway between P and R
F. The plot below represents the variation of beat frequency with time, but shows a constant beat frequency as the car moves from P to R
G. ${
u}_{ P }+{
u }_{ R }=2{
u }_{ Q }$
H. The plot below represents the variation of beat frequency with time, but shows a quadratic increase as the car moves from P to R
I. The rate of change in beat frequency is zero when the car passes through Q
Answer: B
If $\text{a}$ g of $KHC_2O_4$ is used to neutralize $100$ mL of $0.02\:M\;KMnO_4$ in acid medium whereas, $\text{b}$ g of $KHC_2O_4$ is used to neutralize $100$ mL of $0.02\:M\:Ca{(OH)}_2$, then:

Options:
A. $$5a=4b$$
B. $$3a=5b$$
C. $$a=b$$
D. $$2a=b$$
E. $$3a=2b$$
F. $$3a=4b$$
G. $$5a=2b$$
H. $$4a=3b$$
I. $$4a=5b$$
Answer: I
Plane figures made of thin wires of resistance $R = 50$ milli ohm/metre are located in a uniform magnetic field perpendicular into the plane of the figures and which decrease at the rate $dB/dt =0.1\, m \,T/s.$ Then currents in the inner and outer boundary are. (The inner radius $a = 10\, cm$ and outer radius $b = 20\, cm$)

Options:
A. $2 \times 10^{-4} \,A$ (Clockwise), $10^{-4} \,A$ (Clockwise)
B. $2 \times 10^{-4} \,A$ (Clockwise), $10^{-4} \,A$ (Anticlockwise)
C. $2 \times 10^{-4} \,A$ (Anticlockwise), $10^{-4} \,A$ (Anticlockwise)
D. $10^{-4} \,A$ (Anticlockwise), $2 \times 10^{-4} \,A$ (Anticlockwise)
E. $10^{-4} \,A$ (Clockwise), $10^{-4} \,A$ (Clockwise)
F. $2 \times 10^{-4} \,A$ (Anticlockwise), $10^{-4} \,A$ (Clockwise)
G. $10^{-4} \,A$ (Clockwise), $10^{-4} \,A$ (Anticlockwise)
H. $10^{-4} \,A$ (Clockwise), $2 \times 10^{-4} \,A$ (Anticlockwise)
I. $$$10^{-4} \,A$ (Anticlockwise), $2 \times 10^{-4} \,A$ (Clockwise)$$
J. $10^{-4} \,A$ (Clockwise), $2 \times 10^{-4} \,A$ (Clockwise)
Answer: J
Liquid A and B from an ideal solution and the former has strong intermolecular forces. If ${ X }_{ A }$ and ${ X' }_{ A }$ are the mole fraction A in the solution and vapour in equilibrium then

Options:
A. $$\frac { { X' }_{ A } }{ { X }_{ A } } < 1.5$$
B. $${ X' }_{ A }+{ X }_{ A }=1$$
C. $$\frac { { X' }_{ A } }{ { X }_{ A } } = 0.85$$
D. $$\frac { { X' }_{ A } }{ { X }_{ A } } = 0.75$$
E. $$\frac { { X' }_{ A } }{ { X }_{ A } } = 0.5$$
F. $$\frac { { X' }_{ A } }{ { X }_{ A } } =1$$
G. $$\frac { { X' }_{ A } }{ { X }_{ A } } <1$$
H. $$\frac { { X' }_{ A } }{ { X }_{ A } } >1$$
I. $$\frac { { X' }_{ A } }{ { X }_{ A } } = 0.95$$
Answer: F
A nylon guitar string has a linear density of $7.20\ g/m$ and is under tension of $150\ N$. The fixed supports are distance $D= 90.0\ cm$ apart. The string is oscillating in the standing wave pattern shown in figure.Calculate the speed of the traveling waves whose superposition gives this standing wave

Options:
A. $$\dfrac{250}{\sqrt{3}}m/s$$
B. $$\dfrac{375}{\sqrt{3}}m/s$$
C. $$\dfrac{100}{\sqrt{3}}m/s$$
D. $$\dfrac{150}{\sqrt{3}}m/s$$
E. $$\dfrac{175}{\sqrt{3}}m/s$$
F. $$100\sqrt{3}\ m/s$$
G. $$\dfrac{125}{\sqrt{3}}m/s$$
H. $$\dfrac{300}{\sqrt{3}}m/s$$
I. $$\dfrac{225}{\sqrt{3}}m/s$$
J. $$\dfrac{500}{\sqrt{3}}m/s$$
Answer: G
A $30kg$ box has to move up an inclined slope of $30^{o}$ to the horizontal at a uniform velocity of $5ms^{-1}$. If the frictional force retarding the motion is $150N$, the horizontal force required to move up is $(g=10\ ms^{-2})$

Options:
A. $$300 \times \dfrac{\sqrt{3}}{4}\ N$$
B. $$150\ N$$
C. $$300 \times \dfrac{1}{\sqrt{3}}\ N$$
D. $$300\ N$$
E. $$300 \times \dfrac {2}{\sqrt {3}}\ N$$
F. $$300 \times \dfrac {\sqrt {3}}{2}\ N$$
G. $$300 \times \dfrac{\sqrt{3}}{5}\ N$$
H. $$300 \times \dfrac{\sqrt{3}}{3}\ N$$
I. $$300 \times \dfrac{3}{\sqrt{3}}\ N$$
J. $$300 \times \dfrac{\sqrt{3}}{6}\ N$$
Answer: D
Two magnetic poles one of which is 4 time as strong as the other exert a force of $64\ mg.wt$. When placed 10cm apart in air, strength of the poles are $(g=10m{ s }^{ 2 })$

Options:
A. 7A-m and 21Am
B. 5A-m and 20Am
C. 6A-m and 10Am
D. 3A-m and 12Am
E. 7A-m and 14Am
F. 7A-m and 28Am
G. 9A-m and 36Am
H. 8A-m and 32Am
I. 8A-m and 20Am
J. 4A-m and 16Am
Answer: C
What is the emf at $25\ C$ for the cell, $Ag\begin{vmatrix} AgBr\left( s \right) , & { Br }^{ - } \  & a=0.34 \end{vmatrix}.\begin{vmatrix} F{ e }^{ 3+ }, & F{ e }^{ 2+ } \ a=0.1 & a=0.02 \end{vmatrix}Pt$
The standard reduction potentials for the half-reactions $AgBr+{ e }^{ - }\longrightarrow Ag+B{ r }^{ - }$ and $F{ e }^{ 3+ }+{ e }^{ - }\longrightarrow F{ e }^{ 2+ }$ are $+\ 0.0713\ V$ and $+\ 0.770\ V$ respectively.

Options:
A. $$0.574\ volt$$
B. $$0.594\ volt$$
C. $$0.604\ volt$$
D. $$0.713\ volt$$
E. $$0.514\ volt$$
F. $$0.356\ volt$$
G. $$0.464\ volt$$
H. $$0.529\ volt$$
I. $$0.674\ volt$$
J. $$0.474\ volt$$
Answer: J
A glass tube of circular cross-section is closed at one end. This end is weighted and the tube floats vertically in water heavy end down. How far below the water surface is the end of the tube? Given Outer radius of the tube 0.14 cm, mass of weighted tube 0.2 gm, surface tension of water 73 dyne/cm and g = 980 cm/$\displaystyle sec^{2}$

Options:
A. 4.31 cm
B. 4.51 cm
C. 4.21 cm
D. 2.31 cm
E. 4.71 cm
F. 2.15 cm
G. 4.61 cm
H. 8.62 cm
I. 4.62 cm
J. 4.41 cm
Answer: A
A cube of coefficient of linear expansion $a_s$ is floating in a bath containing a liquid of coefficient of volume exertion $y_1$. When the temperature is raised by $\Delta T$, the depth d upto which the cube is submerged in the liquid remains the same. Then the relation between $a_s$ and $y _1$ is

Options:
A. $$y_1 = 5 a_s / 2$$
B. $$y_1 = a_s /2$$
C. $$y_1 = 2 a_s$$
D. $$y_1 = 3 a_s / 4$$
E. $$y_1 = 3 a_s$$
F. $$y_1 = 3 a_s /2$$
G. $$y_1 = \frac{5 a_s}{3}$$
H. $$y_1 = 7 a_s / 3$$
I. $$y_1 = 4 a_s / 3$$
J. $$y_1 = \frac{3 a_s}{4}$$
Answer: C
The ratio of temperatures at which the average velocities of hydrogen molecules be equal to the escape velocity from the surface of earth is : (Given that escape velocity from earth's surface = 11.2 km/s, Boltzmann constant $ k = 1.33 \times 10^{23} J/K $ and Avogadros number $ N = 6.02 \times 10^{23} $ molecules/mole)

Options:
A. 1/32
B. 1/12
C. 1/8
D. 1/36
E. 1/64
F. 1/4
G. 1
H. 1/2
I. 1/16
J. 2/1
Answer: I
The half-life of $^{32}{P}$ is 14.3 days. Calculate the specific activity of a specimen of phosphorus containing 1.00 part per million $^{32}{P}$. (atomic wt. of $P=31$)?

Options:
A. $$284.32 Ci\quad kg^{-1}$$
B. $$284.30 Ci\quad kg^{-1}$$
C. None of these
D. $$274.52 Ci\quad kg^{-1}$$
E. $$284.10 Ci\quad kg^{-1}$$
F. $$274.30 Ci\quad kg^{-1}$$
G. $$294.32 Ci\quad kg^{-1}$$
H. $$284.52 Ci\quad kg^{-1}$$
I. $$294.12 Ci\quad kg^{-1}$$
J. $$274.12 Ci\quad kg^{-1}$$
Answer: G
A disc of mass $5\ kg$ is kept floating horizontally in mid air by firing $10$ bullets per second vertically up. If the mass of each bullet is $50\ gm$ and bullets rebound with same speed, the speed of each bullets is $(g=10{ms}^{2})$

Options:
A. $$75\ {ms}^{-1}$$
B. $$10\ {ms}^{-1}$$
C. $$50\ {ms}^{-1}$$
D. $$200\ {ms}^{-1}$$
E. $$100\ {ms}^{-1}$$
F. $$175\ {ms}^{-1}$$
G. $$150\ {ms}^{-1}$$
H. $$120\ {ms}^{-1}$$
I. $$125\ {ms}^{-1}$$
J. $$250\ {ms}^{-1}$$
Answer: E
The hyperconjugative effect in the compoundsI) $CH_3CH=CH_2$II) $(CH_3)_2CH-CH= CH_2$III) $(CH_3)_3C-CH = CH_2$ is of the order

Options:
A. II > III > I
B. III > II > I
C. III > I > II
D. $$II > I > III $$
E. $$I > III > II$$
F. $$I > II > III $$
Answer: F
In a photocell bichromatic light of wavelengths  $2475 \mathring { A } $  and  $6000 \mathring { A } $  are incident on cathode whose work function is  $4.8 e V.$  If a uniform magnetic field of  $3 \times 10 ^ { - 5 }$  Tesla exists parallel to the plate, the radius of the path describe by the photoelectron will be (mass of electron  $=9\times 10^{ { -31 } }{ kg }$ )

Options:
A. 3 cm
B. 6 cm
C. 15 cm
D. $$10 cm$$
E. 7 cm
F. $$25 cm$$
G. $$1 cm$$
H. $$5 cm$$
I. 2 cm
Answer: H
The potential in an electric field has the form $V = a({x^2} + {y^2} + {z^2})$. The modulus of the electric field at a point (z,y,x) is

Options:
A. $$a\sqrt {{x^2} + {y^2} + {z^2} - 1}$$
B. $${{2a} \over {\sqrt {{x^2} + {y^2} + {z^2}} }}$$
C. $$a\sqrt {{x^2} + {y^2} + {z^2} + 1}$$
D. $$2a{({x^2} + {y^2} + {z^2})^{{3 \over 2}}}$$
E. $$2a\sqrt {{x^2} + {y^2} + {z^2}} $$
F. $$a\sqrt {{x^2} + {y^2} + {z^2}} $$
G. $${{3a} \over {\sqrt {{x^2} + {y^2} + {z^2}} }}$$
H. $${{a} \over {\sqrt {{x^2} + {y^2} + {z^2}} }}$$
I. $${{2a} \over {\sqrt {{x^2} + {y^2} + {z^2} + 1}}}$$
J. $${{3a} \over {\sqrt {{x^2} + {y^2} + {z^2} + 1}}}$$
Answer: F
Solubility of $CO_{2}(g)$ in water at $1\ bar$ and $25^{\circ}C$ involves the following equilibria:$CO_{2}(g) \rightleftharpoons CO_{2}(aq); K_{1}^{\circ} = 0.04$$CO_{2}(aq.) + H_{2}O(l) \rightleftharpoons H^{+}(aq.) + HCO_{3}^{-}(aq); K_{2}^{\circ} = 4\times 10^{-6}$$HCO_{3}^{-}(aq.) \rightleftharpoons H^{+}(aq.) + CO_{3}^{2-}(aq); K_{3}^{\circ} = 5\times 10^{-11}$$[H^{+}]$ in saturated solution of $CO_{2}(g)$ water is ?

Options:
A. $$4\times 10^{-4}M$$
B. $$2 \times 10^{-4}M$$
C. $$3 \times 10^{-3}M$$
D. $$4\times 10^{-3}M$$
E. $$5 \times 10^{-3}M$$
F. $$5 \times 10^{-4}M$$
G. $$0.04\ M$$
H. $$3 \times 10^{-4}M$$
I. $$2\times 10^{-3}M$$
J. $$6 \times 10^{-3}M$$
Answer: D
$100$ ml of $0.1$ M aqueous solution of $HNO_{2}\:(K_{a}=10^{-5})$ is titrated using $0.1$ M barium hydroxide solution, then :(Given that, $log\: 3 = 0.48,\: log\: 2 = 0.30$)

Options:
A. pH of solution at equivalent point of titration is $8.91$
B. pH of solution at equivalent point of titration is $8.70$
C. pH of solution after adding $100$ ml of $Ba(OH)_{2}$ solution is $12.7$
D. pH of solution after adding $20$ ml of $Ba(OH)_{2}$ solution is $4.82$
E. pH of solution at equivalent point of titration is $8.88$
F. pH of solution at equivalent point of titration is $8.95$
G. pH of solution at equivalent point of titration is $8.75$
H. pH of solution at equivalent point of titration is $8.85$
I. pH of solution at equivalent point of titration is $8.80$
J. pH of solution at equivalent point of titration is $8.65$
Answer: H
A small body slides from rest along two equally rough circular surfaces from A to B through path 1 and 2 of equal radius if ${v}_{1}$ and ${v}_{2}$ are the speed of the block at point B via path (1) and (2) then

Options:
A. $${ v }_{ 1 }< { v }_{ 2 }$$
B. $${ v }_{ 1 }={ v }_{ 2 } - 1$$
C. can't be predicted
D. $${ v }_{ 1 }>{ v }_{ 2 }$$
E. $${ v }_{ 1 }= { v }_{ 2 } + 0.25$$
F. $${ v }_{ 1 }={ v }_{ 2 }$$
G. $${ v }_{ 1 }= { v }_{ 2 } + 1$$
H. $${ v }_{ 1 }= { v }_{ 2 } + 0.5$$
I. $${ v }_{ 1 }>{ v }_{ 2 } + 1$$
Answer: D
${ K }_{ p }$ for the reaction ${ NH }_{ 4 }I(s)\rightleftharpoons { NH }_{ 3 }(g)+HI(g)$ is $\dfrac{1}{4}$ at a particular temperature . Above equilibrium is established by taking $4$ moles of ${ NH }_{ 4 }$ in $100$ litre container, then moles of ${ NH }_{ 4 }I_{(s)}$ left in the container at equilibrium is? [Take $ R=\dfrac{1}{12} Litre \quad atm\quad { mol }^{ -1 }\quad { K }^{ -1 }]$

Options:
A. 2 moles
B. 3.2 moles
C. 3.5 moles
D. 3.4 moles
E. 3.8 moles
F. 4.2 moles
G. 2.5 moles
H. 3.6 moles
I. 5 moles
J. 4.5 moles
Answer: H
The particle of charge $q$ and mass $m$ starts moving from origin under the action of an electric field $E=E_0i$ and magnetic field $V=V_0i$ . Its velocity at $( x , 3,0 )$ is $( 4 i + 3 \hat { i } )$ . The value of $x$ is :

Options:
A. $$\dfrac{25 m}{4 q E_0}$$
B. \dfrac{{\sqrt 2 m{v_0}}}{{qE}}
C. $$\dfrac{{\sqrt 3 m{v_0}}}{{qE}}$$
D. $$\dfrac { 10 m } { q E _ { o } }$$
E. $$\dfrac { 25 E _ { 0 } B _ { 0 } } { m }$$
F. $$\dfrac{20 m}{q E_0}$$
G. \dfrac{15 m}{q E_0}
H. $$\dfrac { 25 m } { 2 q E _ { o } }$$
I. $$\dfrac{{\sqrt 5 m{v_0}}}{{qE}}$$
Answer: C
In the Rutherford scattering experiment, the number of alpha particles scattered at an angle $\theta = 60^0$ is 36 per minute. The number of alpha particles per minute scattered at angles $\theta = 90^0$ is (Assume all other conditions to be identical).

Options:
A. 1296
B. 16
C. 216
D. 81
E. 108
F. 432
G. 36
H. 72
I. 9
J. 144
Answer: J
17.4% (mass/volume) $K_2SO_4$ solution at $27^oC$ is isotonic to 5.85% (mass/volume)  NaCl solution at $27^o C$ If NaCl is 100% ionised, what is % ionisation of $K_2SO_4$ in aq. Solution ? [At wt. of K = 39 , Na = 23]

Options:
A. 35%
B. 50%
C. 75%
D. 70%
E. 60%
F. 90%
G. 80%
H. none of these
I. 30%
J. 25%
Answer: J
100 ml of 5 M NaOH solution (d=1.2 g/ml) was added in 200 ml of another NaOH solution which has a density of 1.5 g/ml and contains $20%\dfrac{w}{W}$ of NaOH.What will be the volume of the gas liberated at 1 atm and 273 K when aluminium reacts with this final solution.The reaction is $Al+NaOH+H_2O\rightarrow NaAlO_2+H_2$

Options:
A. 55.2 L
B. 29.3 L
C. None of these
D. 681 L
E. 53.2 L
F. 44.8 L
G. 22.4 L
H. 48.6 L
I. 33.4 L
J. 44.6 L
Answer: D
$N_2(g)$ and $H_2(g)$ are taken in a vessel in mass ratio of $7:1$. The only reaction $N_2(g)+2H_2(g)\rightleftharpoons N_2H_4(g)$ occurs. Pressure due to $N_2H_4$ at equilibrium is $0.2$ times of total pressure $P$. Then at equilibrium:

Options:
A. Partial pressure of \( H_2 \) is one time of partial pressure of \( N_2 \) at equilibrium.
B. Partial pressure of $N_2$ is four times of partial pressure of $N_2H_4$ at equilibrium.
C. Degree of dissociation of $N_2$ is $0.428$
D. Partial pressure of $N_2=4P/15$
E. Partial pressure of $N_2$ is three times of partial pressure of $N_2H_4$ at equilibrium.
F. Partial pressure of $H_2$ is three times of partial pressure of $N_2$ at equilibrium.
G. Partial pressure of \( H_2 \) is two and a half times of partial pressure of \( N_2 \) at equilibrium.
H. Partial pressure of $H_2$ is one and a half times of partial pressure of $N_2$ at equilibrium.
I. Partial pressure of $H_2$ is two times of partial pressure of $N_2$ at equilibrium.
J. Partial pressure of \( H_2 \) is one and a half times of partial pressure of \( N_2H_4 \) at equilibrium.
Answer: I
At $25^{\circ}C$, the solubility product of $CuCl$ is $2.0\times 10^{-7}$ and $E_{Cl^{-}|CuCl|Cu}^{^{\circ}}$ is 0.128 V. The value of $E_{Cu^{+}|Cu}^{^{\circ}}$ is (log 2 = 0.3; 2.303 RT/F = 0.06)

Options:
A. $$-0.474 V$$
B. $$-0.274 V$$
C. $$-0.374 V$$
D. $$+1.682 V$$
E. $$+0.402 V$$
F. $$-0.53 V$$
G. $$-0.402 V$$
H. $$+0.474 V$$
I. $$+0.434 V$$
J. $$+0.594 V$$
Answer: D
A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the center of the ring figure. Then which statement is incorrect:

Options:
A. If q>0 and is displaced away from the centre in the plane of the ring,it will be pushed back towards the centr
B. if q<0 and is displaced away from the centre in the plane of the ring,it will never return towards the centre and will continue moving till it hits the ring
C. q at the centre of the ring is in an unstable equilibrium within the plane of the ring q>0
D. if q<0, it will perform SHM for small displacement along the axis
E. ifif q>0, it will perform SHM for small displacement along the axis
F. if q>0 and is displaced away from the centre in the plane of the ring, it will perform SHM for small displacement
G. if q>0, it will perform SHM for small displacement along the plane of the ring
H. if q<0 and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
I. if q<0, it will perform SHM for small displacement along the plane of the ring
J. if q<0, it will perform SHM for small displacement in the plane of the ring
Answer: E
A block of mass $5 kg$ is pressed against a wall (in YZ-plane) with a force $F=40\hat{i} + 30\hat{j} + 10\hat{k}$. The vetical upword direction is taken as positive $z-axis$. The coefficient of friction is $0.5$. The acceleration of the block is

Options:
A. $$\left(3.6\hat{i} + 2.4\hat{k}\right) m/s^2$$
B. Zero
C. $$\left(- 4\hat{k}\right) m/s^2$$
D. $$\left(3.6\hat{i} - 4.8\hat{k} \right) m/s^2$$
E. $$\left(3.6\hat{i} - 2.4\hat{k}\right) m/s^2$$
F. $$\left(3.6\hat{i} - 6.0\hat{k} \right) m/s^2$$
G. $$\left(3.6\hat{j} + 4.8\hat{k}\right) m/s^2$$
H. $$\left(3.6\hat{i} + 1.2\hat{k} \right) m/s^2$$
I. $$\left(3.6\hat{i} + 4.8\hat{k} \right) m/s^2$$
J. $$\left(3.6\hat{j} - 4.8\hat{k}\right) m/s^2$$
Answer: B
Two men of masses $m_1\ and\ m_2$ hold on the opposite ends of a rope passing over a frictionless pulley. The mass $m_1$ climbs up the rope with an acceleration of $1.2m/s^2$ relative to the rope. The man $m_2$ climbs up the rope with an acceleration of $2.0m/s^2$ relative to the rope. They start from rest and are initially separated by $5 m$. (Given $m_1= 40 kg$ and $m_2=60 kg$)

Options:
A. Time after which they will be at same horizontal level is $1.47 sec$
B. Time after which they will be at same horizontal level is $2.45 sec$
C. Tension in the rope is $556.8 N$
D. Time after which they will be at same horizontal level is $1.72 sec$
E. Time after which they will be at same horizontal level is $1.96 sec$
F. Time after which they will be at same horizontal level is $2.00 sec$
G. Time after which they will be at same horizontal level is $1.55 sec$
H. Tension in the rope is $555.68 N$
I. Time after which they will be at same horizontal level is $1.64 sec$
J. Time after which they will be at same horizontal level is $2.94 sec$
Answer: A
The minimum work done by external agent in moving a particle from a point $(1, 1)$ to $(2, 3)$ in a plane and in a force field with potential energy $U = \lambda (x + y)$ is

Options:
A. $$3\lambda$$
B. $$6\lambda$$
C. $$-3\lambda$$
D. $$0$$
E. $$-\lambda$$
F. $$\lambda$$
G. $$4\lambda$$
H. $$2\lambda$$
I. $$5\lambda$$
J. $$-2\lambda$$
Answer: F
$105$ calories of heat is required to raise the temperature of $3$ moles of an ideal gas at constant pressure from $30^\circ C$ to $35^\circ C$. The amount of heat required in calories to raise the temperature of the gas through the range($60^\circ C$ to $65^\circ C$) at constant volume is $\left( {\gamma  = \frac{{{C_p}}}{{{C_v}}} = 1.4} \right)$

Options:
A. $70$ cal
B. $50$ cal
C. 80 cal
D. 65 cal
E. $75$ cal
F. 85 cal
G. 60 cal
H. $90$ cal
I. 45 cal
Answer: B
A source of frequency $340\ Hz$ is kept above a certical cylindrical tube closed at lower end. The length of the tube is $120\ cm$. Water is slowly poured in just enough to produce resonance. Then the minimum height (velocity of sound $= 340\ m/s$) of the water level in the tube for the resonance is

Options:
A. $$0.25\ m$$
B. $$0.75\ m$$
C. $$0.35\ m$$
D. $$0.45\ m$$
E. $$0.50\ m$$
F. $$0.95\ m$$
G. $$0.30\ m$$
H. $$0.55\ m$$
I. $$0.65\ m$$
J. $$0.85\ m$$
Answer: D
Which of the following statements are correct about the following reaction:

Options:
A. Slow and rate-determining step (R.D.S) is the addition of the protonated alcohol to the acid
B. Slow and rate-determining step (R.D.S) is the addition of acid to the protonated alcohol
C. Slow and rate-determining step (R.D.S) is the addition of alcohol to the protonated acid
D. Slow and rate-determining step (R.D.S) is the addition of the protonated acid to the alcohol
E. Slow and rate-determining step (R.D.S) is the protonation of the acid by ${ H }^{ \oplus }$
F. Slow and rate-determining step (R.D.S) is the protonation of the alcohol by ${ H }^{ \oplus }
G. Rate $=K[RCOOH][R'OH]$. First order in acid and alcohol; second order overall
H. Slow and rate-determining step (R.D.S) is the addition of the protonated alcohol to the protonated acid
I. Rate $=K[RCOOH][R'OH][{H}^{+}]$. First order in acid, alcohol, and ${ H }^{ \oplus }$, third order overall
J. Slow and rate-determining step (R.D.S) is the protonation of the protonated acid by ${ H }^{ \oplus }
Answer: C
Select the correct statement(s):

Options:
A. $ CH_3-C-CH_3 $ angle in $ (CH_3)_2C = CH_2 $is smaller and the $ CH_3-C =CH_2 $ angle is larger than the trigonal $ 120^0 $
B. $ POCl_3 $ is trigonal pyramidal with a double bond between $P$ and $O$. There is one lone pair on the central atom.
C. $ POCl_3 $ is tetrahedral with a single bond between $P$ and $O$. There is no lone pair on the central atom.
D. $ POCl_3 $ is trigonal bipyramidal with a single bond between $P$ and $O$. There is one lone pair on the central atom.
E. $ POCl_3 $is tetrahedral with a double bond between $P$ and $O$. There is no lone pair on the central atom.
F. $ POCl_3 $ is tetrahedral with a single bond between $P$ and $O$. There is one lone pair on the central atom.
G. $ POCl_3 $is tetrahedral with a double bond between $P$ and $O$. There is one lone pair on the central atom.
Answer: E
Anhydrous $AlCl_3$ is covalent. from the data given below
Lattice Energy $= 5137 \, KJ \, mol^{-1}$
 $\triangle H\ hydration\ Al^{3+} = - 4665 \ KJ / mol^{-1}$
 $\triangle H\ hydration\ Cl^- = -381\, KJ / mol^{-1}$
Identify the correct statement-

Options:
A. The solution will consists of hydrate $AI^{3+}$ and $CI^{-}$
B. The solution will consist of hydrated $Al^{3+}$ and unhydrated $Cl^-$ ions
C. The solution will consist of unhydrated $Al^{3+}$ and $Cl^-$ ions
D. It will remain covalent in aqueous solution
E. The solution will consist of hydrated $Al^{3+}$ and partially hydrated $Cl^-$ ions
F. None of these
G. The solution will consists of $AI^{3+}$ and $CI^{-}$
H. The solution will consist of hydrated $Cl^-$ and $Al^{3+}$ ions
I. The solution will consist of hydrated $AI^{3+}$ and $CI^{-}$ ions
J. The solution will consists of hydrated $AI^{3+}$ and $CI^{-}$
Answer: G
The root mean square speeds at STP for the gases $ H_2 , N_2, O_2 $ and $HBr$ are in the order:

Options:
A. $$ H_2 < HBr < N_2 < O_2 $$
B. $$HBr < H_2 < N_2 < O_2$$
C. $$ HBr < O_2 < H_2 < N_2 $$
D. $$ H_2 < N_2 < O_2 < HBr $$
E. $$HBr < N_2 < O_2 < H_2$$
F. $$ HBr < O_2 < N_2 < H_2 $$
G. $$H_2 < O_2 < N_2 < HBr$$
H. $$ H_2 < N_2 = O_2 < HBr $$
I. $$HBr < H_2 < O_2 < N_2$$
J. $$HBr < O_2 = N_2 < H_2$$
Answer: D
The wave function for the wave pulse is $ Y (X,t) = \frac {0.1a^3}{a^2 +(X-Vt)^2}  with a = 4 cm. At X = 0 $ The displacement y (x,t) is observed to decreases from its maximum value to half of that value in time $ t = 2 \times 10^{-3} s $ choose the correct statement

Options:
A. The wave pulse is moving is negative X direction with speed 10 m/s
B. The wave pulse is moving is negative X direction with speed 20 m/s
C. The wave pulse is moving is negative X direction with speed 15 m/s
D. The wave pulse is moving is positive X direction with speed 20 m/s
E. The wave pulse is moving in the positive X direction with speed 18 m/s
F. The wave pulse is moving in the positive X direction with speed 15 m/s
G. The wave pulse is moving is positive X direction with speed 10 m/s
H. The wave pulse is moving in the positive X direction with speed 10 m/s
I. The wave pulse is moving in the positive X direction with speed 14 m/s
J. The wave pulse is moving in the positive X direction with speed 12 m/s
Answer: A
a hypothetical reaction,$A \longrightarrow$ 2B, proceed through following sequence of steps-
$A\longrightarrow$C;$\triangle$H=$q_{1}$
$C\longrightarrow$D;$\triangle$H=$q_{2}$
$$\frac { 1 }{ 2 } D\longrightarrow B;\Delta H={ q }_{ 3 }$$
The heat of reaction is

Options:
A. $$q_{1}-q_{2}+q_{3}$$
B. $$q_{1}+q_{2}+2q_{3}$$
C. $$q_{1}-q_{2}-2q_{3}$$
D. $$q_{1}+2q_{2}-2q_{3}$$
E. $$q_{1}+q_{2}-2q_{3}$$
F. $$q_{1}+q_{2}+q_{3}$$
G. $$q_{1}-q_{2}+2q_{3}$$
H. $$q_{1}-q_{2}-q_{3}$$
I. $$q_{1}+q_{2}-q_{3}$$
Answer: G
$1.5$ gram fuming $H_{2}SO_{4}$ (Oleum) is diluted, the resulting solution requires $0.2 N, 160 ml NaOH$ for complete neutralization. {Take $mol.wt.$ of $H_{2}SO_{4}=100$ & $mol.wt$ of $SO_{3}=80$}.Which of the following options is/are correct?

Options:
A. Oleum percentage labelling is $106$
B. Mass fraction of $SO_{3} $ is $1/2$
C. Mass fraction of $SO_{3} $ is $3/10$
D. Mass fraction of $SO_{3} $ is $2/5$
E. Mass fraction of $SO_{3} $ is $3/5$
F. Mass fraction of $SO_{3} $ is $4/9$
G. Mass fraction of $SO_{3} $ is $1/3$
H. Oleum percentage labelling is $112$
I. Mass fraction of $SO_{3} $ is $1/4$
Answer: D
A bulb of constant volume is attached to a very thin manometer tube as shown in figure. Gas leaking through a small hole in the bulb causing a change in pressure as $\displaystyle\frac{dP}{dt}=-kP^2$. Where $k$ is constant and $P$ is pressure at any instant. Initial height difference $'h'$ was $76$cm and after $10$min $'h'$ was $38$cm. Calculate the value of $k$ in unit of $atm^{-1}hr^{-1}$.

Options:
A. $$5.00$$
B. $$0.25$$
C. $$0.5$$
D. $$1.00$$
E. $$2.00$$
F. $$0.75$$
G. $$0.15$$
H. $$0.10$$
Answer: D
If 0.50 Litre of a 0.60M $SnSO^{-2}_4$ is electrolyzed for a period of 30.0 min using a current of 4.60

Options:
A. 0.358 M
B. 0.352 M
C. 0.514 M
D. 0.362 M
E. 0.444 M
F. 0.389 M
G. 0.488 M
H. 0.544 M
I. 0.375 M
J. 0.342 M
Answer: J
The two plate X and Y of a parallel-plates capacitor of capacitance C are given a charge of amount Q each. X is now joined to the positive terminal and y to the negative terminal of a cell of emf \[ \varepsilon = \frac{Q}{C} \]

Options:
A. The total charge on the plate Y will be \( -Q/2 \).
B. The total charge on the plate Y will be \( -2Q \).
C. The total charge on the plate Y will be zero.
D. The total charge on the plate Y will be \( -Q/3 \)
E. The total charge on the plate Y will be \( -Q/4 \)
F. The total charge on the plate Y will be \( -Q \).
G. The total charge on the plate Y will be \( Q \)
Answer: C
$50\ mL$ of a solution containing $10^{-3}$ mole of $Ag^+$ is mixed with $50\ mL$ of a $0.1M$ $HCI$ solution. How much $Ag^+$ remains in solution ?$K_{sp}$ of $AgCl = 1.0 \times 10^{-10} )$

Options:
A. $$2.5\times 10^{-10}$$
B. $$2.5 \times 10^{-12}$$
C. $$2.5\times 10^{-8}$$
D. $$2.5 \times 10^{-11}$$
E. $$2.5\times 10^{-9}$$
F. $$2.5 \times 10^{-13}$$
G. $$2.5 \times 10^{-6}$$
H. $$2.5\times 10^{-7}$$
Answer: C
A dihybrid plant with genotype PpNn. It produces four types of gametes in following number PN=200, pn=200, Pn=800, pN = 800 then what is the distance between linked genes?

Options:
A. 15 cM
B. 22 cM
C. 10 cM
D. 25 cM
E. 30 cM
F. 27 cM
G. 14 cM
H. 18 cM
I. 20 cM
J. 28 cM
Answer: E
A heavy block of mass $150\ kg$ hangs with the help of three vertical wires of equal length and equal cross-sectional area as shown in the figure.
Wire is attached to the mid-point (centre of mass) of block. Take $Y_{2} = 2Y_{1}$. For this arrangement mark out the correct statement(s).

Options:
A. Tension in $II$ is $150g/2$.
B. Tension in $II$ is $150g/3$
C. Tension in $I$ and $III$ would be $75g$
D. The wire $I$ and $III$ should have same Young's modulus
E. Tension in $II$ is $150g/4$.
F. Tension in $I$ and $III$ would be different.
G. Tension in $II$ is $150g$
H. Tension in $II$ is $75g$.
Answer: H
At  $30 ^ { \circ } \mathrm { C } ,$  the solubility of  $\mathrm { Ag } _ { 2 } \mathrm { CO } _ { 3 }$  ( $\mathrm { K } _ { sp } = 8 \times 10 ^ { - 2 }$ ) will be maximum in -

Options:
A. $$0.05 \mathrm { M } \mathrm { Na } _ { 3 } \mathrm { PO } _ { 4 }$$
B. $$0.05 \mathrm { M } \mathrm { Na } _ { 2 } \mathrm { SO } _ { 4 }$$
C. $0.05 \mathrm { M }$ $\mathrm { Na } _ { 2 } \mathrm { CO } _ { 3 }$
D. $$0.05 \mathrm { M } \mathrm { K } _ { 2 } \mathrm { CO } _ { 3 }$$
E. $$0.05 \mathrm { M } \mathrm { Na } _ { 3 } \mathrm { CO } _ { 3 }$$
F. $$0.05 \mathrm { NH } _ { 3 }$$
G. Pure water
H. $0.05 \mathrm { M }$ $\mathrm { AgNO } _ { 3 }$
I. $$0.05 \mathrm { M } \mathrm { K } _ { 2 } \mathrm { SO } _ { 4 }$$
J. $$0.05 \mathrm { M } \mathrm { Na } _ { 3 } \mathrm { CO } _ { 4 }$$
Answer: C
The weight of ${ KMnO }_{ 4 }$ that can oxidise $100ml$ of  $0.2M$ oxalic acid in acidic medium is (Mo.wt of ${ KMnO }_{ 4 }$ = 158.1]

Options:
A. $$1.264g$$
B. $$1.85g$$
C. $$1.564g$$
D. $$12.64g$$
E. $$1.58g$$
F. $$3.16g$$
G. $$15.6g$$
H. $$15.8g$$
I. $$1.581g$$
Answer: H
Select the correct statement(s):

Options:
A. $ POCl_3 $ is tetrahedral with a single bond between $P$ and $O$. There is one lone pair on the central atom.
B. $ POCl_3 $ is trigonal bipyramidal with a single bond between $P$ and $O$. There is one lone pair on the central atom.
C. $ POCl_3 $is tetrahedral with a double bond between $P$ and $O$. There is no lone pair on the central atom.
D. $ CH_3-C-CH_3 $ angle in $ (CH_3)_2C = CH_2 $is smaller and the $ CH_3-C =CH_2 $ angle is larger than the trigonal $ 120^0 $
E. $ POCl_3 $ is trigonal pyramidal with a double bond between $P$ and $O$. There is one lone pair on the central atom.
F. $ POCl_3 $ is tetrahedral with a single bond between $P$ and $O$. There is no lone pair on the central atom.
G. $ POCl_3 $is tetrahedral with a double bond between $P$ and $O$. There is one lone pair on the central atom.
H. $ POCl_3 $ is trigonal bipyramidal with a double bond between $P$ and $O$. There is one lone pair on the central atom.
Answer: C
Two guns situated at the top of a hill off height $10\ m$, fire one shot each with the same speed of $\sqrt { 3 } { ms }^{ -1 }$ at same interval of time. One gun fires horizontally and other fires upwards at an angle of $60^o$ to with the horizontal. The shots collide in mid air at the point $P$. Taking the origin of the coordinate system at the four of the hill right below the muzzle, trajectories to be in $x-y$ plane and $g=10\ {ms}^{-2}$

Options:
A. one shell is fired $1\ s$ after the firing of the other shell.
B. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,10 \right) m$
C. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,7.5 \right) m$
D. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,0 \right) m$
E. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,2.5 \right) m$
F. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,15 \right) m$
G. one shell reaches the point $P$   at  $1\ s$ from the start of its firing
H. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,12.5 \right) m$
I. one shell reaches the point $P$ at  $2\ s$ from the start of its firing
J. they collide at $P$ whose coordinates are given by $\left( 5\sqrt { 3 } ,5 \right) m$
Answer: J
An object is placed 20 cm in front of a plano convex lens of focal length 15 cm. The plane surface of the lens is silvered. The image will be formed at a distance

Options:
A. 12 cm to the right of the lens
B. 60 cm to the left of the lens
C. 12 cm to the left of the lens
D. 12 cm to the right of the lens.
E. 24 cm to the right of the lens
F. 20 cm to the right of the lens
G. 30 cm to the left of the lens
H. 15 cm to the left of the lens
I. 60 cm to the right of the lens
J. 15 cm to the right of the lens
Answer: C