MikaStars39/nano-eval huggingface dataset:
The displacement of a particle ( in meters ) from its mean position is given by the equation $y = 0.2\left( {{{\cos }^2}\dfrac{{\pi t}}{2} - {{\sin }^2}\dfrac{{\pi t}}{2}} \right)$. The motion of the above particle is.

Options:
A. Simple harmonic with a period equal double that of a second's pendulum
B. Simple harmonic with an amplitude of 0.15 m
C. Simple harmonic with amplitude of 0.2 m
D. Simple harmonic with a period equal to that of a second's pendulum
E. Simple harmonic with an amplitude of 0.35 m
F. not simple harmonic
G. Simple harmonic with an amplitude of 0.3 m
H. Simple harmonic with an amplitude of 0.25 m
I. Simple harmonic with an amplitude of 0.1 m
J. Simple harmonic with an amplitude of 0.4 m
Answer: F
Two spheres are moving towards each other. Both have the same radius but their masses are $2\ kg$ and $4\ kg$. If the velocities are $4$ m/s and $2$ m/s respectively and coefficient of restitution is e = 1/3, find the impulse of deformation?

Options:
A. $$-4\sqrt{3} Ns$$
B. $$-1\sqrt{3} Ns$$
C. $$4\sqrt{3} Ns$$
D. $$-3\sqrt{3} Ns$$
E. $$-2\sqrt{3} Ns$$
F. $$-5\sqrt{3} Ns$$
G. $$2\sqrt{3} Ns$$
H. $$-6\sqrt{3} Ns$$
I. $$3\sqrt{3} Ns$$
Answer: A
Select the correct statements regarding the final product (Y) :

Options:
A. It undergoes coupling reaction with benzene diazonium chloride at high temperature (75 - $\displaystyle 85^{\circ}C$) in slightly acidic medium
B. On treatment with Zn-dust it yields a product having degree of unsaturation = 4
C. It liberates $\displaystyle H_{2}$ gas with Na
D. It liberates $\displaystyle H_{2}$ gas with $\displaystyle K$
E. It liberates $\displaystyle H_{2}$ gas with $\displaystyle Li$
F. It reacts with Zn-dust to form a product having degree of unsaturation = 2
G. It liberates $\displaystyle H_{2}$ gas with $\displaystyle Mg$
H. It reacts with Zn-dust to form a product having degree of unsaturation = 3
I. It can be identified with neutral $\displaystyle FeCl_{3}$ solution
J. It undergoes coupling reaction with benzene diazonium chloride at low temperature (0 - $\displaystyle 5^{\circ}C$) in slightly basic medium
Answer: C
A closed rectangular vessel completely filled with a liquid of density  $\rho$  moves with an acceleration  $a=g$  The value of the pressure difference  $\left( P _ { 1 } - P _ { 2 } \right)$  is:

Options:
A. $$\rho g \left( b + \frac{h}{5} \right)$$
B. $$\rho ( a b - g h )$$
C. $$\rho g \left( b + \frac{h}{2} \right)$$
D. $$\rho g b$$
E. $$\rho g \left( b + \frac{h}{3} \right)$$
F. $$\dfrac { \rho g ( b + h ) } { 2 }$$
G. $$\rho g \left( b + \frac{h}{4} \right)$$
H. $$\rho g \left( b - \frac{h}{2} \right)$$
I. $$\rho gh$$
J. $$\rho g \left( b + \frac{h}{6} \right)$$
Answer: I
Second overtone frequency of a closed pipe and fourth harmonic frequency of an open pipe are same. Which of the following is correct?

Options:
A. Ninth harmonic frequency of closed pipe is equal to eighth harmonic frequency of open pipe
B. Ninth harmonic frequency of closed pipe is equal to seventh harmonic frequency of open pipe
C. Thirteenth harmonic frequency of closed pipe is equal to tenth harmonic frequency of open pipe
D. Ninth harmonic frequency of closed pipe is equal to ninth harmonic frequency of open pipe
E. Fifteenth harmonic frequency of closed pipe is equal to tenth harmonic frequency of open pipe
F. Eighth harmonic frequency of closed pipe is equal to tenth harmonic frequency of open pipe
G. Fundamental frequency of closed pipe is more than the fundamental frequency of open pipe
H. Tenth harmonic frequency of closed pipe is equal to eighth harmonic frequency of open pipe
Answer: H
An equal volumes of 1.0 M $KCl$ and 1.0 M $AgNO_3$ are mixed. The elevation of the boiling point of the resulting solution will be:$(K_b = 0.52\ K/ molal$ and van't Hoff factor for $KNO_3$ is 2)

Options:
A. 2.08
B. 1.06
C. 2.10
D. 0.026
E. 2.60
F. 0.26
G. 1.02
H. 1.56
I. 0.52
J. 1.04
Answer: I
A certain mirror placed at the origin has $\hat{j}$ as the normal vector to its reflecting surface. The mirror begins to translate with a velocity $\hat{i}+\hat{j}+\hat{k}$ at $t=0$. At the same time an object which was initially at $\hat{i}+\hat{j}$ starts moving with a velocity $(\hat{i}+\hat{j})m/ s$ , then which of the following is/are correct ?

Options:
A. The velocity of image relative to the mirror will be $\hat{i} + 2\hat{k}$
B. The velocity of the image will be $\hat{i}+\hat{j} + 2\hat{k}$
C. The velocity of image relative to the mirror will be $\hat{k}$
D. The velocity of image relative to the mirror will be $\hat{i} + \hat{k}$
E. The velocity of image relative to the mirror will be $2\hat{k}$
F. The velocity of image relative to the mirror will be $\hat{i} - \hat{k}$
G. The velocity of the image will be $\hat{i}+\hat{j} + \hat{k}$
H. The velocity of the image will be $\hat{i}+\hat{j} - \hat{k}$
Answer: C
A parallel combination of $0.1 M \;\Omega $ resistor and a $10\; \mu F$ capacitor is connected across a battery of emf, $E=1.5 \;V$ source of negligible resistance. The time required for the capacitor to get charged upto $0.75 \;V$ is approximately (in seconds)

Options:
A. $$log_e 8$$
B. $$log_e 6$$
C. $$log_e 2$$
D. $$log_e 3$$
E. $$log_e 5$$
F. $$log_e 4$$
G. $$log_{10} 2$$
H. $$log_e 7$$
I. $$\infty$$
J. $$zero$$
Answer: J
An electron gun G emits electrons of energy $2$ keV travelling in the positive x-direction. The electrons are required to hit the spot S where GS$=0.1$m, and the line GS makes an angle $60^o$ with the x-axis, as shown. A uniform magnetic field B parallel to GS exists in the region outside the electron gun. Find the minimum value of B needed to make the electrons hit S.

Options:
A. $$3.2 \times 10^{-3}T$$
B. $$5.2 \times 10^{-3}T$$
C. $$4.7\times 10^{-3}T$$
D. $$6.7 \times 10^{-3}T$$
E. $$1.7\times 10^{-3}T$$
F. $$7.7 \times 10^{-3}T$$
G. $$8.7 \times 10^{-3}T$$
H. $$5.7\times 10^{-3}T$$
I. $$3.7\times 10^{-3}T$$
Answer: C
An ideal gas is expanding such that $\dfrac{V}{T^{3}}= constant$. The Molar Specific heat of the gas is

Options:
A. $$\displaystyle \dfrac{9R}{2}$$
B. $$\dfrac{12R}{2}$$
C. $$\displaystyle \dfrac{5R}{2}$$
D. $$\displaystyle \dfrac{11R}{2}$$
E. $$\dfrac{10R}{2}$$
F. $$\dfrac{8R}{2}$$
G. $$\dfrac{13R}{2}$$
H. $$\dfrac{15R}{2}$$
I. $$\dfrac{14R}{2}$$
J. $$\displaystyle \dfrac{7R}{2}$$
Answer: A
$H_2C_2O_4.2H_2O$ (Mol.wt=126) can be oxidised into $CO_2$ by acidified $KMnO_4$.  6.3 gms of oxalic acid can be oxidised by

Options:
A. 0.15 mole of $KMnO_4$
B. 3.16 gms of $KMnO_4$
C. 0.2 mole of $KMnO_4$
D. 0.05 mole of $KMnO_4$
E. 0.02 moles of $KMnO_4$
F. 200 ml of 0.1 M $KMnO_4$
G. 0.09 mole of $KMnO_4$
H. 0.08 mole of $KMnO_4$
I. 0.1 mole of $KMnO_4$
J. 0.06 mole of $KMnO_4$
Answer: I
Benzene burns according to the following equation at $300$ $K$ $(R = 8.314Jmole^{-1}K^{-1})$
       $2C_6H_6(l) + 15 O_2(g) \to 12 CO_2(g) + 6 H_2O(l)$  $\Delta H^{0} =  -6542 kJ/mol$
What is the $\Delta E^{0}$ for the combustion of $1.5$ mol of benzene

Options:
A. $$-9813 kJ$$
B. $$-9810 kJ$$
C. $$-3271 kJ$$
D. $$-4906.5 kJ$$
E. $$-4360.5 kJ$$
F. $$-6542 kJ$$
G. $$-4731 kJ$$
H. $$-3456 kJ$$
I. None of these
Answer: A
A wedge is moving rightwards on which a block of mass $10kg$ is place on it. Friction coefficient between the wedge and the block is $0.8$. [take $g = 10\ m/s^{2}]$. Select correct alternative(s) among the following options.

Options:
A. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $42N$
B. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $44N$
C. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $40N$
D. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $46N$
E. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $38N$
F. If wedge is moving with constant velocity then friction acting on block is $64N$
G. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $54N$
H. If wedge is moving with $ a = 2(\hat {i})m/s^{2}$ then friction acting on block is $34N$
Answer: B
An electric dipole is placed in an electric field generated by a point charge.

Options:
A. The torque on the dipole due to the field may not be zero.
B. The net electric force on the dipole due to the field may be zero.
C. The net electric force on the dipole must be zero.
D. The torque on the dipole due to the field must not be zero.
E. The net electric force on the dipole due to the field must be zero.
F. The net eiectric force on the dipole may be zero.
G. The net electric force on the dipole due to the field may not be zero.
H. The torque on the dipole due to the field must be zero.
I. The torque on the dipole due to the field may be zero.
J. The net electric force on the dipole due to the field must not be zero.
Answer: I
Two particles of equal mass go around a circle of radius $R$ under the action of their mutual gravitational attraction.The speed of each particle is

Options:
A. $$v = \sqrt { \left( \dfrac { 4 G m } { R } \right) }$$
B. $$v = \sqrt { \left( \dfrac { 3 G m } { 2 R } \right) }$$
C. $$v =  \sqrt { \left( \dfrac { G m } { R } \right) }$$
D. $$v = \sqrt { \left( \dfrac { G m } { 5 R } \right) }$$
E. $$v = \sqrt { \left( \dfrac { G m } { 3 R } \right) }$$
F. $$v = \sqrt { \left( \dfrac { G m } { 2 R } \right) }$$
G. $$v = \sqrt { \left( \dfrac { G m } { 2.5 R } \right) }$$
H. $$v = \sqrt { \left( \dfrac { G m } { 4 R } \right) }$$
I. $$v = \sqrt { \left( \dfrac { 2 G m } { R } \right) }$$
J. $$v = \dfrac { 1 } { 2 R } \sqrt { \left( \dfrac { 1 } { G m } \right) }$$
Answer: H
the enthalpy changes for the following processes are lised below
$${ CI }_{ 2 }\left( g \right) =2CI(g)\quad ;\quad 242.3\quad { kJmol }^{ -1 }$$
$${ I }_{ 2 }(g)=2I(g)\quad ;\quad 151.{ OKJmol }^{ -1 }$$
$$ICI(g)=I(g)+CI(g)\quad ;\quad 211.3{ KJmol }^{ -1 }$$
$${ I }_{ 2 }(s)={ I }_{ 2 }(g)\quad ;\quad 62.76{ KJmol }^{ -1 }$$
Given that the standard states for iodine and chlorine are ${ I }_{ 2 }(s)\quad and\quad { CI }_{ 2 }(g)$, the standard enthalpy of formation of ICI(g) is:

Options:
A. $$-\quad 14.6{ kJmol }^{ -1 }$$
B. $$+\quad 16.8{ kJmol }^{ -1 }$$
C. $$-\quad 15.2{ kJmol }^{ -1 }$$
D. $$-13.2{ kJmol }^{ -1 }$$
E. $$-\quad 15.4{ kJmol }^{ -1 }$$
F. $$-\quad 13.8{ kJmol }^{ -1 }$$
G. $$+\quad 244.8{ kJmol }^{ -1 }$$
H. $$-\quad 16.8{ kJmol }^{ -1 }$$
I. $$-\quad 12.8{ kJmol }^{ -1 }$$
J. $$-\quad 17.2{ kJmol }^{ -1 }$$
Answer: A
An electron revolves along a circular path of radius $20 cm$ with constant angular velocity $120 rad { s }^{ -1 }$ about an axis passing through the centre and perpendicular to the plane of the circle. If the external magnetic field is absent, then the potential difference between the centre of the circle and a point on the circumference of the circle is (Mass of the electron $= 9.1 \times { 10 }^{ -31 }kg$)

Options:
A. $$3.691\times { 10 }^{ -9 }V$$
B. $$1.728 \times { 10 }^{ -9 }V$$
C. $$2.156 \times { 10 }^{ -9 }V$$
D. $$4.278\times { 10 }^{ -9 }V$$
E. $$1.892 \times { 10 }^{ -9 }V$$
F. $$1.921 \times { 10 }^{ -9 }V$$
G. $$1.738 \times { 10 }^{ -9 }V$$
H. $$1.638\times { 10 }^{ -9 }V$$
I. $$1.598 \times { 10 }^{ -9 }V$$
J. $$2.347\times { 10 }^{ -9 }V$$
Answer: H
The potential energy of a 1$\mathrm { kg }$ particle free to move alongthe $x$ -axis is given by$V ( x ) = \left( \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 2 } } { 2 } \right) J$
The total mechanical energy of the particle is $21 .$ Then, the maximum speed (in ms $^ { 1 }$ ) is

Options:
A. $$\dfrac{4}{\sqrt{2}}$$
B. $$\dfrac{6}{\sqrt{2}}$$
C. $$\dfrac { 1 } { \sqrt { 2 } }$$
D. $$\sqrt { 2 }$$
E. 2
F. 3
G. $$\dfrac{8}{\sqrt{2}}$$
H. $$\dfrac{7}{\sqrt{2}}$$
I. $$\dfrac{5}{\sqrt{2}}$$
J. $$\dfrac { 3 } { \sqrt { 2 } }$$
Answer: E
A cubical box with dimension \( L = \frac{5}{4} \, \text{m} \) starts moving with an acceleration \( \mathbf{a} = 0.5 \, \text{m/s}^2 \, \hat{\mathbf{i}} \) from rest. At the same time, a stone is thrown from the origin with velocity \( \overrightarrow{\mathbf{V}} = v_1 \hat{\mathbf{i}} + v_2 \hat{\mathbf{j}} - v_3 \hat{\mathbf{k}} \) with respect to the earth. The acceleration due to gravity is \( \mathbf{g} = 10 \, \text{m/s}^2 \, (-\hat{\mathbf{j}}) \). The stone just touches the roof of the box and finally falls at the diagonally opposite point. Then:

Options:
A. $${ v }_{ 3 }=\dfrac { 5 }{ 4 }$$
B. $${ v }_{ 3 }=\dfrac { 9 }{ 4 }$$
C. $${ v }_{ 3 }=\dfrac { 11 }{ 8 }$$
D. $${ v }_{ 3 }=\dfrac { 15 }{ 4 }$$
E. $${ v }_{ 3 }=\dfrac { 5 }{ 2 }$$
F. $${ v }_{ 3 }=\dfrac { 7 }{ 8 }$$
G. $${ v }_{ 2 }=5$$
H. $${ v }_{ 1 }=\dfrac { 3 }{ 2 }$$
Answer: A
A plane light wave of intensity $I = 0.20 \,W \,cm^{-2}$ falls on a plane mirror surface with reflection coefficient $\rho = 0.8$. The angle of incidence is $45^o$. In terms of corpuscular theory, find the magnitude of the normal pressure exerted on that surface.

Options:
A. $$0.5 \,N \,cm^{-2}$$
B. $$0.2 \,N \,cm^{-2}$$
C. $$0.8 \,N \,cm^{-2}$$
D. $$1.4 \,N \,cm^{-2}$$
E. $$0.3 \,N \,cm^{-2}$$
F. $$1.2 \,N \,cm^{-2}$$
G. $$2.6 \,N \,cm^{-2}$$
H. $$0.4 \,N \,cm^{-2}$$
I. $$1.6 \,N \,cm^{-2}$$
J. $$1.0 \,N \,cm^{-2}$$
Answer: F
In the figure shown, a source of sound of frequency 510 Hz moves with constant velocity $v_{S} =$ 20 m/s in the direction shown. The wind is blowing at a constant velocity $v_{w} = $ 20 m/s towards an observer who is at rest at point $B$. Corresponding to the sound emitted by the source at initial position $A$, the frequency detected by the observer is equal to :(speed relative to air is 330 m/s)

Options:
A. 545 Hz
B. 510 Hz
C. 530 Hz
D. 525 Hz
E. 500 Hz
F. 540 Hz
G. 515 Hz
H. 520 Hz
I. 535 Hz
J. 550 Hz
Answer: D
Given the listed standard electrode potentials, What is $E^{o}$ for the cell?$4BiO + 3N_{2}H_{5} (aq)\rightarrow 4Bi(s)+3N_{2}(g)+4H_{2}O(l)+7H^{+}(aq)$$N_{2}(g)+5H^{+}(aq)+4e^{-}\rightarrow N_{2}H_{5}^{+}(aq),\ E^{o}=-0.23\ V$$BiO^{+}(aq)+2H^{+}(aq)+3e^{-}\rightarrow Bi(s)+H_{2}O(l),\ E^{o}=+0.32\ V$

Options:
A. +0.42
B. $$+0.55$$
C. $$+0.39$$
D. $$+0.09$$
E. +0.67
F. $$+.34$$
G. $$+1.88$$
H. +0.38
I. +0.53
J. +0.59
Answer: F
A sonometer string AB of length 1 m is stretched by a load and the tension T is adjusted sothat the string resonates to a frequency of 1kHz. Any point P of the wire may be held fixed by use of a movable bridge that can slide alomg the base of sonometer.

Options:
A. The fundamental frequency of the sonometer wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio 4a : 3b.
B. The fundamental frequency of the sonometer wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio a : 2b.
C. The fundamental frequency of the sonometer wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio 3a : 2b.
D. If the fixed point P divides AB in the ratio 1 : 2, then the tension needed to make the string vibrate at 1kHz will be 3 T. (neglecting the terminal effects)
E. The fundamental frequency of the sonomter wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio 2a : 2b.
F. If point P is fixed so that AP : PB :: 1 : 4, then the smallest frequency for which the sonometer wire resonates is 5 kHz/.
G. The fundamental frequency of the sonomter wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio 2a : b.
H. If P be taken at mid point of AB and fixed, then when the wire vibrates in the third harmonic of its fundamental, the number of nodes in the wire (including A and B) will be totally seven.
I. The fundamental frequency of the sonometer wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio a : 3b.
J. The fundamental frequency of the sonomter wire when P divides AB in the ratio a : b will be the same as the fundamental frequency when P divides AB in the ratio b : a.
Answer: J
A particle of mass $m$ can move in a force field. Potential energy $U$ varies on location of the particle according to the following equation.
$U=-k(x-a)^2(x-b)^2$ 
Here, $k, a$ and $b$ are positive constants.
What can you conclude about small amplitude oscillations of the particle?

Options:
A. It can oscillate about a specific location with angular frequency $(a-b)\sqrt{2k/m}$.
B. It can oscillate about two separate locations with angular frequency $(b-a)\sqrt{k/m}$.
C. It can oscillate about two separate locations with angular frequency $(b-a)\sqrt{2k/m}$.
D. It can oscillate about a specific location with angular frequency $(b-a)\sqrt{k/m}$.
E. It can oscillate about a specific location with angular frequency $(b-a)\sqrt{3k/m}$.
F. It can oscillate about a specific location with angular frequency $(b+a)\sqrt{k/m}$.
G. It can oscillate about a specific location with angular frequency $(b-a)\sqrt{2k/m}$.
H. It can oscillate about a specific location with angular frequency $(b-a)\sqrt{4k/m}$.
I. It can oscillate about two separate locations with angular frequency $(b+a)\sqrt{k/m}$.
J. It can oscillate about a specific location with angular frequency $(a+b)\sqrt{k/m}$.
Answer: D
A bar magnet $M$ is allowed to fall towards a fixed conducting ring $C$ with its plane horizontal. If $g$ is the acceleration due to gravity, $v$ is the velocity of the magnet at $t=2s$ and $s$ is the distance travelled by it in the same time then

Options:
A. $$v > 2.5g$$
B. $$v > 2g$$
C. $$v > 4g$$
D. $$v > 3.5g$$
E. $$v > 1.5g$$
F. $$v > 2.75g$$
G. $$v > 3g$$
H. $$s < 2g$$
I. $$v > 2.25g$$
J. $$s > 2g$$
Answer: B
When $1\ mole$ of $A\ (g)$ is introduced in a closed rigid $1\ liter $ vessel maintained at a constant temperature the following equilibria are established.$A (g) \rightleftharpoons B(g) + C(g) : K_{C_1}$$C (g) \rightleftharpoons D(g) + B(g) : K_{C_2}$The pressure at equilibrium is twice the initial pressure. Calculate the value of $\dfrac {K_{C_2}}{K_{C_1}}$ if $\dfrac {[C]_{q}}{[B]_{eq}}=\dfrac {1}{5}$

Options:
A. 0.48
B. $$0.5$$
C. $$0.16$$
D. 0.8
E. 0.32
F. $$4$$
G. 0.24
H. $$2$$
I. 0.64
J. 0.25
Answer: C
The acid catalysed hydrolysis of an organic compound $A$ at $30^{\circ}C$ has a time for half change of $100$ minutes, when carried out in a buffer solution at $pH\ 5$ and of $10$ minutes, wen carried out at $pH\ 4$. Both times of half change are independent of the initial concentration of $A$. If the rate of reaction is given by $\dfrac {-d[A]}{dt} = k[A]^{a} [H^{+}]^{b}$, what are the values of $a$ and $b$?

Options:
A. $$a=0,\ b=1$$
B. $$a=2,\ b=0$$
C. $$a=0,\ b=0$$
D. $$a=1,\ b=2$$
E. $$a=1,\ b=0$$
F. $$a=1,\ b=1$$
G. $$a=0,\ b=2$$
H. $$a=1,\ c=0$$
Answer: F
An ideal gaseous sample at initial state $({P}_{0},{V}_{0},{T}_{0})$ is allowed to expand to volume $2{V}_{0}$ using two different processes. For the first process, the equation of process is $2P{V}^{2}={K}_{1}$ and for the second process, the equation of the process is $PV={K}_{2}$. Then:

Options:
A. The magnitude of work done in the second process will be equal to that in the first process
B. The magnitude of work done in the first process will be greater than that in the second process
C. The magnitude of work done in the first process will be less than that in the second process
D. The magnitude of work done in the second process will be greater than that in the first process
E. The magnitude of work done in the second process will be less than that in the first process
F. Work done in both the processes cannot be compared without knowing the relation between ${K}_{1}$ and ${K}_{2}$
G. The magnitude of work done in the first process will be twice that in the second process
H. The magnitude of work done in the second process will be half that in the first process
I. The magnitude of work done in the first process will be equal to that in the second process
J. The first process is impossible
Answer: D
A lift of mass $10^{3}\ kg$ is tied with thick iron wires. If the maximum acceleration of the lift is $1.2\ ms^{-2}$ and the maximum safe stress is $1.4 \times 10^{8}\ Nm^{-2}$, the minimum diameter of wire is ($g=9.8\ ms^{-2}$)

Options:
A. $$0.0017\ m$$
B. $$0.002\ m$$
C. $$0.00141\ m$$
D. $$0.001\ m$$
E. $$0.00175\ m$$
F. $$0.0018\ m$$
G. 0.0015\ m
H. $$0.0012\ m$$
I. $$0.00282\ m$$
J. $$0.005\ m$$
Answer: D
Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of gas $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The change in the pressure in $A$ and $B$ are found to be $\triangle P$ and $1.5\triangle P$ respectively. Then

Options:
A. $$5m_{A} = 4m_{B}$$
B. $$3m_{A} = 2m_{B}$$
C. $$3m_{A} = 5m_{B}$$
D. $$2m_{A} = 3m_{B}$$
E. $$5m_{A} = 6m_{B}$$
F. $$9m_{A} = 4m_{B}$$
G. $$5m_{A} = 2m_{B}$$
H. $$4m_{A} = 9m_{B}$$
I. $$3m_{A} = 4m_{B}$$
Answer: B
Among the following compounds, which one of the following will react with acetone to give a product containing $> C=N $ ?

Options:
A. $$C_6H_5NHNHCH_3$$
B. $$C_6H_5NH_2$$
C. $$ C_6H_5NHNH_2 $$
D. $$C_6H_5NHC_6H_4$$
E. $$C_6H_5NHC_2H_5$$
F. $$ (CH_3)_3N $$
G. $$C_6H_5NHCH_3$$
H. $$ C_6H_5NHC_6H_5 $$
Answer: C
The correct statement(s) about the compound $H_{3}C(HO)HCCH=CHCH(OH)CH_{3} (X)$ are:

Options:
A. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $3.$
B. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $6.$
C. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $4.$
D. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $5.$
E. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $1.$
F. The total number of diastereomers possible for X is $3$.
G. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $8.$
H. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is $2.$
Answer: H
A nuclear explosion has taken place leading to increase in the concentration of $\mathrm{C}^{14}$ in nearby areas. $\mathrm{C}^{14}$ concentration is $\mathrm{C}_{1}$ in nearby areas and $\mathrm{C}_{2}$ in areas far away. If the age of the fossil is determined to be $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ at the places respectively then :

Options:
A. The age of fossil will be determined to be same.
B. The age of the fossil will increase at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}\).
C. The age of the fossil will increase at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{1}^2}{\mathrm{C}_{2}^2}\).
D. The age of the fossil will decrease at the place where explosion has taken place and $\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{1}}{\mathrm{C}_{2}}$.
E. The age of the fossil will decrease at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}\).
F. $$\displaystyle \frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=\frac{\mathrm{C}_{1}}{\mathrm{C}_{2}}$$
G. The age of the fossil will increase at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{2\lambda}\ln\frac{\mathrm{C}_{1}}{\mathrm{C}_{2}}\).
H. The age of the fossil will increase at the place where explosion has taken place and $\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{1}}{\mathrm{C}_{2}}$.
I. The age of the fossil will increase at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{3\lambda}\ln\frac{\mathrm{C}_{1}}{\mathrm{C}_{2}}\)
J. The age of the fossil will increase at the place where explosion has taken place and \(\displaystyle \mathrm{T}_{1}-\mathrm{T}_{2}=\frac{1}{\lambda}\ln\frac{\mathrm{C}_{2}^2}{\mathrm{C}_{1}^2}\).
Answer: H
A composite wire is mad eby joining two uniforms wires. if $ l_1= l_2=l $ and $ \mu_1= \dfrac { \mu_2}{9} = \mu $ Tension in the string is T, $ \mu $ is mass per unit length. then lowest frequency such that the junction is antinode.

Options:
A. $$\dfrac {2}{l} \sqrt{ \dfrac {l}{ \mu }}$$
B. $$ \dfrac {7}{4l} \sqrt {\dfrac {l}{ \mu } }$$
C. $$ \dfrac {5}{4l} \sqrt {\dfrac {l}{ \mu } }$$
D. $$ \dfrac {3}{4l} \sqrt { \dfrac {l}{ \mu } }$$
E. $$\dfrac {1}{2l} \sqrt{ \dfrac {l}{ \mu }}$$
F. $$\dfrac {9}{4l} \sqrt{ \dfrac {l}{ \mu }}$$
G. $$\dfrac {3}{2l} \sqrt{ \dfrac {l}{ \mu }}$$
H. $$\dfrac {1}{l} \sqrt{ \dfrac {l}{ \mu }}$$
I. $$ \dfrac {1}{4l} \sqrt{ \dfrac {l}{ \mu }} $$
J. $$\dfrac {1}{8l} \sqrt{ \dfrac {l}{ \mu }}$$
Answer: I
At what temperature the mean kinetic energy of hydrogen molecules increases to such that they will escape out of the gravitational filed of earth for ever?(take $v_1=11.2 km/sec$)

Options:
A. $$20000 K$$
B. $$10075 K$$
C. $$10375 K$$
D. $$11150 K$$
E. $$12075 K$$
F. $$10150 K$$
G. $$10275 K$$
H. $$9975 K$$
I. $$11075 K$$
J. $$10025 K$$
Answer: B
A body of mass $M\ kg$ is on the top of a smooth hemisphere of radius $5\ m.$ It is released to slide down the surface of the hemisphere.It leaves the surface when its velocity is $5\ m/s.$ At this instant the angle made by the radius vector of the body with the vertical is : ($g = 10\ m/s^2$)

Options:
A. Given condition is not possible
B. $$45^\circ$$
C. $$30^\circ$$
D. $$65^\circ$$
E. $$70^\circ$$
F. $$60^\circ$$
G. $$75^\circ$$
H. $$50^\circ$$
I. $$55^\circ$$
Answer: B
Kinetic energy of a particle executing SHM changes with time according to following graph mass of the particle is $2\ kg$. Then

Options:
A. time period of oscillation is $0.15\ s$
B. time period of oscillation is $0.14\ s$
C. amplitude of oscillation is $0.6\ m$
D. time period of oscillation is $0.12\ s$
E. acceleration of the particle is zero at $t=0.1\ s$
F. time period of oscillation is $0.1\ s$
G. time period of oscillation is $0.2\ s$
H. frequency of oscillation is $5\ Hz$
I. time period of oscillation is $0.05\ s$
J. time period of oscillation is $0.08\ s$
Answer: F
Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area $A$, separated by a distance $d$. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $K_1, K_2$ and $K_3$. The first capacitor is filled as shown in fig.-I, and the second one is filled as shown in fig.-II.
If these two modified capacitors are charged by the same potential $V$, the ratio of the energy stored in the two, would be ($E_1$ refers to capacitor (I) and $E_2$ to capacitor (II)) :

Options:
A. $$\dfrac{E_1}{E_2} = \dfrac{4K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
B. $$\dfrac{E_1}{E_2} = \dfrac{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}{9K_1K_2K_3}$$
C. $$\dfrac{E_1}{E_2} = \dfrac{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}{K_1K_2K_3}$$
D. $$\dfrac{E_1}{E_2} = \dfrac{9K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
E. $$\dfrac{E_1}{E_2} = \dfrac{5K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
F. $$\dfrac{E_1}{E_2} = \dfrac{8K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
G. $$\dfrac{E_1}{E_2} = \dfrac{7K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
H. $$\dfrac{E_1}{E_2} = \dfrac{K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
I. $$\dfrac{E_1}{E_2} = \dfrac{3K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
J. $$\dfrac{E_1}{E_2} = \dfrac{6K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3 + K_3K_1+K_1K_2)}$$
Answer: D
$y(x, t)=\dfrac{0.8}{(4x+5t)^2+5}$ represents a moving pulse where x and y are in meter and t in seconds. Then.

Options:
A. Pulse is moving in $+$x direction
B. It's a symmetric pulse with a maximum displacement of $0.12$ m
C. It's a symmetric pulse with a maximum displacement of $0.17$ m
D. It's a symmetric pulse with a maximum displacement of $0.14$ m
E. In two seconds it will travel a distance of $2.5$ m
F. It's a symmetric pulse with a maximum displacement of $0.15$ m
G. It's a symmetric pulse
H. It's a symmetric pulse with a maximum displacement of $0.13$ m
I. It's a symmetric pulse with a maximum displacement of $0.18$ m
Answer: G
What % of the carbon in the $H_2CO_3\,-\,HCO_3^-$ buffer should be in the form of $HCO_3^-$ so as to have a neutral solution? $(K_a\, =\, 4\,\times\, 10^{-7})$

Options:
A. 20 %
B. 75%
C. 60 %
D. 40 %6
E. 70 %
F. 55%
G. 45 %
H. 30 %
I. 50 %
J. 80 %
Answer: C
How much water should be filled in a container $21 cm$ in height, so that it appears half filled when viewed from the top of the container? (given that $a \mu_\omega$ = 4/3)

Options:
A. $$12.0 cm$$
B. 11.5 cm
C. 11.0 cm
D. 12.5 cm
E. $$8.0 cm$$
F. None of the above
G. 13.0 cm
H. $$10.5 cm$$
I. 9.5 cm
J. 10.0 cm
Answer: A
The electric potential varies in space according to relation V=(2x + 4y). a particle of mass 0.1 kg starts from rest from point (2, 2) under the influence of the flied. If charge on the particle is $1\mu C$, then speed of the particle when it crosses the x-axis will be (assume V and (x, y) are in S.I. unit)

Options:
A. $\sqrt{2}\times 10^{-2}$m/s
B. $2\times 10^{-2}$m/s
C. \dfrac{1}{\sqrt{3}} \times 10^{-2} m/s
D. $\dfrac{1}{\sqrt{5}} \times 10^{-2}$ m/s
E. $\dfrac{1}{2}\times 10^{-2}$ m/s
F. \dfrac{1}{\sqrt{8}} \times 10^{-2} m/s
G. 3 \times 10^{-2}
H. $\dfrac{1}{\sqrt{2}}\times 10^{-2}$ m/s
I. \dfrac{1}{\sqrt{6}} \times 10^{-2} m/s
J. $\dfrac{1}{\sqrt{4}} \times 10^{-2}$ m/s
Answer: H
The ionization constant of benzoic acid is $6.46 \times 10^{-5}$ and $K_{sp}$ for silver benzoate is $2.5\times 10^{-13}$. How many times is silver benzoate more soluble in a buffer of $pH = 3.19$ compared to its solubility in pure water?

Options:
A. $$4$$
B. $$3.28$$
C. $$3.02$$
D. $$3.01$$
E. $$2.5$$
F. $$3.18$$
G. $$3.45$$
H. $$3.25$$
I. $$3.22$$
J. $$3.32$$
Answer: J
A massless piston, which can move without friction, closes a sample of helium in a vertical, thermally insulated cylinder, which is closed at its bottom, and the cross-section of which is $A= 2dm^2$.Above the piston there is a fixed stand to which an unstretched spring of spring constant $2000 N/m$ is attached, whose bottom end is at a distance of 2 dm from the piston when the volume of the gas is $V_0=8 dm^2$. The external pressure is $p_0=10^5 Pa$, $g= 10 m/S^2$. The gas confined in the cylinder is heated with an electric heating element.(1dm=$10^{-1}$)
How much heat is supplied by the element till it reaches spring

Options:
A. 8000 J
B. 1000 J
C. 4000 J
D. 1600 J
E. zero
F. 1800 J
G. 1200 J
H. 2000 J
I. 1400 J
J. 600 J
Answer: B
A block of mass $0.2\ kg$ is thrust up along a fixed inclined plane of inclination $30^\circ$ with an initial velocity of $5 m/s$. It moves $2$ metre up along the incline a then slides back to the bottom. The speed with which it return to the bottom the incline is $(g = 10ms^{-1})$

Options:
A. $$\sqrt{50} ms^{-1}$$
B. $$5m/s$$
C. $$\sqrt{15} ms^{-1}$$
D. $$\sqrt{35} ms^{-1}$$
E. $$\sqrt{20} ms^{-1}$$
F. $$\sqrt{10} ms^{-1}$$
G. $$\sqrt{40} ms^{-1}$$
H. $$\sqrt{45} ms^{-1}$$
I. $$\sqrt{25} ms^{-1}$$
J. $$\sqrt{30} ms^{-1}$$
Answer: G
Let current $i=2\ A$ be flowing in each part of a wire frame as shown in fig. The frame is a combination of two equilateral triangles $ACD$ and $CDE$ of side $1\  m$. It is placed in uniform magnetic field $B=4\ T$  acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is

Options:
A. 18 N
B. 28 N
C. 20 N
D. 24 N
E. 16 N
F. 26 N
G. 8 N
H. zero
I. 12 N
J. 22 N
Answer: D
A bomb at rest at the summit of a cliff breaks into two equal fragments. One of the fragments attains a horizontal velocity of $20\sqrt{3}\,m/s$. The horizontal distance between the two fragments, when their displacement vectors is inclined at $60^0$ relative to each other is (g=10\,m/s^2$

Options:
A. 240\sqrt3\,m
B. 640\sqrt3\,m
C. 560\sqrt3\,m
D. $$120\sqrt3\,m$$
E. 160\sqrt3\,m
F. $$80\sqrt3\,m$$
G. 320\sqrt3\,m
H. $$40\sqrt3\,m$$
I. $$480\sqrt3\,m$$
Answer: I
Newton's laws of motion can be applied to a block in liquid also. Force due to liquid (e.g., upthrust) are also considered in addition to other forces. A small block of weight $W$ is kept inside. The block is attached with a string connected to the bottom of the vessel. Tension in the string is $\dfrac {W}{2}$If weight of the block is doubled (keeping the density constant), then tension in the string becomes $x$ times and the time calculated above becomes $y$ times. Then

Options:
A. x = \dfrac{7}{2}
B. both (a) and (b) are incorrect
C. $$y = \sqrt 2$$
D. both (a) and (b) are correct
E. x = \dfrac{3}{2}
F. x = \dfrac{4}{2}
G. x = \dfrac{6}{2}
H. x = \dfrac{8}{2}
I. x = \dfrac{5}{2}
J. $$x = 2$$
Answer: J
At what temperature, hydrogen molecules will escape from the earth's surface? (TAke mass of hydrogen molecule $=0.34\times{10}^{-6}kg$, Boltzmann constant $=1.38\times{10}^{-23}K{J}^{-1}$, Radius of earth $=6.4\times{10}^{6}m$ and acceleration due to gravity $=9.8m{s}^{-2}$)

Options:
A. 1000K
B. $${10}^{4}K$$
C. $${10}^{2}K$$
D. 10000K
E. 20K
F. 50K
G. 100K
H. 500K
I. $$10K$$
Answer: I
A simple harmonic oscillator consist of a block attached to a spring with k = 100 N/m. The block slides on a frictionless horizontal surface, with equilibrium point x = 0. A graph of block's velocity as a function of time is shown. correctly match the two column:- ($\pi^2 = 10)$
          List - I                                                                                    List - II   
(P) The block's mass in Kg                                                   (1) -0.20
(Q) The block's displacement at t = 0 in meters                   (2) -200   
(R) The block's acceleration at t =  0.1 s in $m/s^2$                (3) 0.20
(S) The block's maximum kinetic energy in joules                (4) 4.0

Options:
A. P-1 Q-3 R-2 S-4
B. P-3 Q-4 R-2 S-1
C. P-1 Q-4 R-3 S-2
D. P-2 Q-1 R-4 S-3
E. P-2 Q-3 R-1 S-4
F. P-3 Q-4 R-1 S-2
G. P-1 Q-3 R-1 S-4
H. P-2 Q-3 R-2 S-4
I. P-4 Q-2 R-3 S-1
J. P-4 Q-3 R-1 S-2
Answer: A
A simple pendulum of length L and mass M is oscillating in a plane about a vertical line between angular limits -$\phi$ and +$\phi$. For an angular displacement, $\theta$(|$\theta$| < $\phi$) the tension in the string and velocity of the bob are T and v respectively. The following relations hold good under the above condition.

Options:
A. T + Mg cos $\theta$ = $Mv^{2}$/L
B. T = Mg (2 cos $\theta$ - 3 cos $\phi$)
C. T = Mg (3 cos \phi - 2 cos \theta)
D. The magnitude of tangential acceleration of the bob $|a_{T}|$ = g sin $\theta$
E. T = Mg (3 cos $\theta$ - 2 cos $\phi$)
F. T = Mg (2 cos $\phi$ - 3 cos $\theta$)
G. T = Mg (3 cos $\phi$ - 2 cos $2\theta$)
H. T cos $\theta$ cos $\theta$ = Mg
Answer: E
Fixed mass of an ideal gas contained in a $24.63L$ sealed rigid vessel at $1$ atm is heated from $-{ 73 }^{ o }C$ to ${ 27 }^{ o }C$. Calculate change in Gibb's energy if entropy of gas is a function of temperature as $S=2+{ 10 }^{ -2 }T(J/K)$: (Use $1$ atm $L=0.1kJ$)

Options:
A. $$0$$
B. $$1281.5J$$
C. 881.5J
D. 831.5J
E. $$781.5J$$
F. 1331.5J
G. $$1231.5J$$
H. 731.5J
I. 681.5J
Answer: E
The hydrolysis of an ester was carried out with 0.1 M $H_2SO_4$ and 0.1 M HCl separately. Which of the following expressions between the rate consists is expected? The rate expression being rate = $k[H^{\oplus}][ester]$

Options:
A. $$k_{H_2SO_4} \, = \, 2k_{HCl}$$
B. $$k_{H_2SO_4} = 2k_{HCl}$$
C. $$k_{H_2SO_4}\, \leq\, k_{HCl}$$
D. $$k_{HCl}\, >\, k_{H_2SO_4}$$
E. $$k_{H_2SO_4}\, <\, k_{HCl}$$
F. $$k_{HCl}\, =\, k_{H_2SO_4}$$
G. $$k_{H_2SO_4}\, >\, k_{HCl}$$
H. $$k_{ H_2SO_4}\, =\, k_{HCl}$$
I. $$k_{HCl}\, \geq\, k_{H_2SO_4}$$
J. $$k_{HCl}\, <\, k_{H_2SO_4}$$
Answer: D
A uniform bar with mass m lies symmetrically across two rapidly rotating fixed rollers, A and B with distance $L = 2.0 cm$ between the bar's centre of mass and each roller. The rollers, whose directions of rotation are shown in figures slip against the bar with coefficient of kinetic friction $\mu_{k} = 0.40$. Suppose the bar is displaced horizontally by a distance x as shown in figure and then released. The angular frequency $\omega$ of the resulting horizontal simple harmonic motion of the bar is(in rad $s^{-1})$

Options:
A. 21
B. $$17$$
C. 18
D. $$15$$
E. $$16$$
F. 22
G. 19
H. $$20$$
I. 14
Answer: H
A particle of mass $m$ and charge $q$ is placed in an electric field $E$ which varies with time $t$ as $E=E_o \sin \omega t$. It will undergo SHM of amplitude

Options:
A. $$\dfrac{Q{E_o}^2}{m\omega}$$
B. $$\dfrac{Q{E_o}}{m\omega}$$
C. $$\dfrac{Q{E_o}^2}{m\omega^2}$$
D. $$\dfrac{Q{E_o}^2}{m\omega^4}$$
E. $$\dfrac{Q{E_o}}{m\omega^3}$$
F. $$\dfrac{Q{E_o}^2}{m\omega^3}$$
G. $$\sqrt{\dfrac{Q{E_o}^2}{m\omega^2}}$$
H. $$\dfrac{QE_o}{m\omega^2}$$
Answer: H
One mole ideal gas is compressed adiabatically at $27^{\circ}C$, Its temperature becomes $102^{\circ}C$. The work done in this process will be - (y=1.5)

Options:
A. -1245 J
B. -1255 J
C. 1255 J
D. 625 J
E. 1250 J
F. -1250 J
G. -625 J
H. -630 J
I. -635 J
J. 1245 J
Answer: J
The rate constant of a reaction increased by $5%$ when temperature is raised from $27^{o}$ to $28^{o}\ C$. The activation energy of the reaction is $(\log\ 7=0.8450)$

Options:
A. $$38.5\ KJ$$
B. $$34.5\ KJ$$
C. $$35.5\ KJ$$
D. $$46.5\ KJ$$
E. $$36.5\ KJ$$
F. $$39.5\ KJ$$
G. $$47.5\ KJ$$
H. $$16.5\ KJ$$
I. $$37.5\ KJ$$
J. $$27.5\ KJ$$
Answer: E
A particle is projected with speed 100 m/s at angle $\theta ={ 60 }^{ \circ  }$ with the horizontal at time t = 0. At time t the velocity vector of the particle becomes perpendicular to the direction of velocity of projection
Its tangential acceleration at time t is :

Options:
A. $$5\sqrt{3} m/s^{2}$$
B. $$10m/s^{ 2 }$$
C. $$15m/s^{2}$$
D. $$10\sqrt{3} m/s^{2}$$
E. $$1cm/s^{ 2 }$$
F. zero
G. $$5m/s^{ 2 }$$
H. $$5\sqrt{2} m/s^{2}$$
Answer: G
1.0 mole of $\displaystyle { Fe }_{ 2 }{ O }_{ 3 }$ and 2 moles of $\displaystyle Al$ are mixed at temperature $\displaystyle { 25 }^{ o }C$ and the reaction is completed to give:$\displaystyle { Fe }_{ 2 }{ O }_{ 3 }(s)+2Al(s)\longrightarrow { Al }_{ 2 }{ O }_{ 3 }(s)+2Fe(l);\Delta H=-850kJ$The liberated heat is retained within the products, whose combined specific heat over a broad temperature range is about $\displaystyle 0.8{ Jg }^{ -1 }{ K }^{ -1 }$. The melting point of iron is $\displaystyle { 1530 }^{ o }C$. Calculate the temperature required to heat liberated of the product to the melting point of iron in order to get it welded.

Options:
A. $$1928K$$
B. 1830K
C. $$4990K$$
D. 1835K
E. $$1257K$$
F. 1900K
G. $$1800K$$
H. 1850K
I. 1925K
J. 1930K
Answer: C
Successive acid dissociation consists for a tribasic acid, $H_3XO_3,$ are $k_1=7.5\times 10^{-10}, k_2=2\times 10^{-13}, k_3= 1.6\times 10^{-14}$. Decimolar aqueous solutions of which of the following are expected to be basic?

Options:
A. $$Na_3XO_3$$
B. Na_3XO_4
C. NaHXO_3
D. Na_2H_2XO_3
E. $$H_3XO_3$$
F. $$NaH_2XO_3$$
G. Na_3H_2XO_3
H. $$Na_2HXO_3$$
Answer: H
A metallic square wire loop of side $10cm$ and resistance $1\Omega$ is moved with a constant velocity ${ v }_{ 0 }$ in a uniform magnetic field of induction $B=2T$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors each of value $3 \Omega $. The resistance of the lead wires OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of $1mA$ in it ? Give the direction of current in the loop.

Options:
A. $2\times { 10 }^{ -2 }$, anticlockwise direction
B. $4\times { 10 }^{ -2 }$, clockwise direction
C. $2\times { 10 }^{ -2 }$, clockwise direction
D. $8 \times { 10 }^{ -2 }$, anticlockwise direction
E. 3 \times { 10 }^{ -2 }, clockwise direction
F. 6 \times { 10 }^{ -2 }, clockwise direction
G. $4\times { 10 }^{ -2 }$, anticlockwise direction
H. 3 \times { 10 }^{ -2 } , anticlockwise direction
I. 6 \times { 10 }^{ -2 }, anticlockwise direction
Answer: C
Point charge $+4q$, $-q$ and $+4q$ are kept on the x-axis at points $x=0, x=a$ and $x=4a$ respectively. Then:

Options:
A. Only the charge at \( x=a \) is in unstable equilibrium.
B. Only the charges at \( x=0 \) and \( x=4a \) are in stable equilibrium.
C. Only the charge at \( x=a \) is in stable equilibrium.
D. Only -q is in stable equilibrium
E. None of the charges are in equilibrium.
F. All the charges are in stable equilibrium.
G. Only the charges at \( x=a \) and \( x=4a \) are in unstable equilibrium.
H. Only the charges at \( x=0 \) and \( x=4a \) are in unstable equilibrium.
I. Only the charges at \( x=0 \) and \( x=a \) are in unstable equilibrium.
J. All the charges are in unstable equilibrium.
Answer: J
A straight rod is partially immersed in water $(\mu = 1.33)$. Its submerged portion appears to be inclined at $45^o$ with the surface when viewed vertically from air. The actual inclination of the rod is?

Options:
A. $$53.9^o$$
B. $$54.9^o$$
C. $$32.14^o$$
D. $$59.9^o$$
E. $$57.9^o$$
F. $$51.9^o$$
G. $$45^o$$
H. $$62^o$$
I. $$52.9^o$$
J. $$60.3^o$$
Answer: E
A gas park in two processes in which it is hcated from the same initial state 1 to the same final temperature. The processes are shown on the P - V diagram by the straight lines $1-3$ and $1-2$. $2$ and $3$ are the points on the same isothermal curve. $Q_1$ and $Q_2$ are the heat transfer along the two processes. Then

Options:
A. $$Insufficient data$$
B. $$Q_1\, =\, 2Q_2$$
C. $$Q_1\, <\, Q_2$$
D. $$Q_1\, =\, \frac{4}{3}Q_2$$
E. $$Q_1\, >\, Q_2$$
F. $$Q_1\, <\, 2Q_2$$
G. $$Q_1\, =\, Q_2$$
H. $$Q_1\, =\, \frac{3}{2}Q_2$$
Answer: E
To beaker containing $ 0.1 M \ HCl,$ a little pure solid AgCl is added. Both a silver and a hydrogen electrode $ (P_{H_{2}} = 1.0 $ bar) are then placed in the solution. What is the approximate value of EMF measured between the electrodes at $ 25^{\circ}C?$ (Given: $ E_{Ag^{+}|Ag}^{0} = 0.80 V$ and $K_{sp} (AgCl) = 10^{-10})$

Options:
A. 0.34 V
B. 0.32 V
C. 0.26 V
D. 0.76 V
E. 1.28 V
F. 0.38 V
G. 0.92 V
H. 0.56 V
I. 0.82 V
J. 0.42 V
Answer: B
The reaction $v_{1}A + v_{2}B \rightarrow Products$ is first order w.r.t  $A$ and zero order w.r.t $B$. If the reaction is started with $[A_{0}]$ and $[B_{0}]$ the integral rate equation for the reaction would be:

Options:
A. $$ln \dfrac {[A_{0}]}{[A_{0}] - v_{1}x} = k_{1}t$$
B. $$ln \dfrac {[A_{0}]}{[A_{0}] - 4x} = k_{1}t$$
C. $$ln \dfrac {[A_{0}]}{[A_{0}] - 2x} = k_{1}t$$
D. $$ln \dfrac {[A_{0}]}{[A_{0}] - x} = k_{1}t$$
E. $$ln \dfrac {[A_{0}]}{[A_{0}] - 5x} = k_{1}t$$
F. $$ln \dfrac {[A_{0}]}{[A_{0}] - 3x} = k_{1}t$$
G. $$ln \dfrac {[A_{0}]}{[A_{0}] - x} = v_{1}k_{1}t$$
H. $$ln \dfrac {[A_{0}]}{[A_{0}] - 2x} = v_{1}k_{1}t$$
I. $$ln \dfrac {[A_{0}]}{[A_{0}] - v_{1}x} = v_{1}k_{1}t$$
J. $$ln \dfrac {[A_{0}]}{[A_{0}] - 6x} = k_{1}t$$
Answer: D
A small ball of mass m is placed in a circular tube of mass /m and radius R in gravity free space. Friction is absent between tube and ball. Ball is given a velocity $V_0$ as shown. Then,

Options:
A. Path of ball from centre of mass of system will be straight.
B. Path of ball from centre of mass of system will be circular.
C. Path of ball from centre of mass of system will be elliptical.
D. Path of ball from centre of mass of system will be spiral.
E. Radius of curvature of ball at the time of projection of ball is $\dfrac{MR}{m + M}$
F. Path of ball from centre of mass of system will be elliptical
G. Path of ball from centre of mass of system will be linear.
H. Normal force between tube and ball if M = 2m, at the time of projection of ball is $\dfrac{2mV_0^2}{3R}$
I. Path of ball from centre of mass of system will be hyperbolic.
J. Path of ball from centre of mass of system will be parabolic.
Answer: B
Ball of mass 1 kg falls from a height of $5m$ above the free surface of water. The relative density of the solid ball is $s=\frac{2}{3}.$ The ball travels a distance of 2 m under water and becomes stationary. The work done by the resistive forces of water is

Options:
A. $$ - 50J$$
B. $$ \sqrt {20} J$$
C. - 60J
D. - 25J
E. - 10J
F. $$ - 40J$$
G. - 70J
H. $$ - 30J$$
I. - 20J
J. - 35J
Answer: B
A straight rod of length L extends from $x=0$ to $x=L$. the linear mass density of the rod varies with x co-ordinate is $ \gamma=a_0+b_0x^2 $. the gravitational force experienced by a point mass $m$ at $x=-a$,is

Options:
A. Gm\left( \dfrac { a_{ 0 } }{ a } +2b_0L \right)
B. Gm\left( \dfrac { a_{ 0 } }{ a+L } +b_0a \right)
C. $$ Gm\left( \dfrac { a_{ 0 } }{ a } +b_0L \right) $$
D. $$ Gm\left(b_0L \dfrac { a_0 }{ a } \right) $$
E. Gm\left( \dfrac { a_{ 0 } }{ a+2L } +b_0L \right)
F. Gm\left( \dfrac { a_{ 0 } }{ a+L } +b_0a^2 \right)
G. Gm\left( \dfrac { a_{ 0 } }{ a } +b_0a \right)
H. $$ Gm\left(b_0L \dfrac { a_0 }{ a+L } \right) $$
I. Gm\left( \dfrac { a_{ 0 } }{ a+L } +b_0L \right)
J. $$ Gm\left[ a_{ 0 }(\dfrac { 1 }{ a } -\dfrac { 1 }{ a+L } )+b_{ 0 }L+b_{ 0 }a^{ 2 }\left( \frac { 1 }{ a } -\frac { a }{ a+L } \right) +2a{ b }_{ 0 }in\quad \left( \frac { a+L }{ a } \right) \right] $$
Answer: C
An aluminium container of mass $100\: gm$ contains $200\: gm$ of ice at $-20 ^\circ C$. Heat is added to the system at the rate of $100\: cal/s$. Find the temperature of the system after 4 minutes (specific heat of ice $+0.5$ and $L = 80\: cal/gm$, specific heat of Al$ = 0.2\: cal/gm/^\circ C$)

Options:
A. 24.36 ^\circ C
B. $$37.36 ^\circ C$$
C. 28.36 ^\circ C
D. 29.36 ^\circ C
E. $$26.36 ^\circ C$$
F. 25.36 ^\circ C
G. 23.36 ^\circ C
H. $$27.36 ^\circ C$$
I. $$36.36 ^\circ C$$
J. 34.36 ^\circ C
Answer: E
According to Maxwell's distribution law,the fraction of molecules per unit change to speed [velocity distribution function f(c)],travelling with the speed from C to C $+$ dC is given as:
$$f\left( c \right) = \frac{1}{{dC}}.\left( {\frac{{dN}}{N}} \right) = 4\pi .\left( {\frac{M}{{2\pi RT}}} \right).{C^2}.{e^{ - M{C^2}12RT}}.\left( {R = 8.0J/K - mol,ln2 = 0.7} \right)$$
 At what temperature ,the velocity distribution function for the oxygen molecules will have maximum value at the speed $400 m/s$

Options:
A. $$315^{o}C$$
B. $$-31.3^{o}C$$
C. $$340^{o}C$$
D. $$327^{o}C$$
E. $$47^{o}C$$
F. $$34.9^{o}C$$
G. $$310^{o}C$$
H. $$330^{o}C$$
I. $$320^{o}C$$
J. $$325^{o}C$$
Answer: I
A charged particle $(Q = 10^{-4}C)$ is released from rest at $z=0$ in magnetic field given as $\vec{B}=B_0\cos(\omega t - kz)\hat{i} + B_1 \cos(\omega t + kz)\hat{j}$ where $B_0 = 3\times 10^{-5}T$ and $B_1 = 2 \times 10^{-6}T$. Then the rms value of force acting on particle is?

Options:
A. $$3\times 10^{-2}$$
B. $$0.9$$
C. $$0.6$$
D. 0.5
E. 0.3
F. 0.2
G. 0.8
H. 0.4
I. $$0.1$$
J. 0.7
Answer: C
The successive ionization energies for an unkonown element are.
$$IP_{1}=899kJ/mole$$
$$IP_{2}=1757kJ/mole$$
$$IP_{3}=14847kJ/mole$$
$$IP_{4}=17948kJ/mole$$
To which group in the periodic table does the unknown element most likely belong

Options:
A. $$VIA$$
B. $$IA$$
C. $$VIIA$$
D. IIIA
E. IIA
F. $$IVA$$
Answer: B
Two point charges $+8q$ and $-2q$ are located at $x\,=\,0$ and $x\,=\,L$ respectively. The location of a point on the $X-axis$ at  which the net electric field due to these two point charges is zero, is

Options:
A. $$\frac{L}{6}$$
B. $$\frac{L}{9}$$
C. $$2L$$
D. $$\frac{L}{4}$$
E. $$\frac{L}{2}$$
F. $$\frac{L}{5}$$
G. $$\frac{L}{7}$$
H. $$4L$$
I. $$8L$$
J. $$\frac{L}{3}$$
Answer: I
A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be ${ 75 }^{ 0 }$C. T is given by : (Given : room temperature = ${ 30 }^{ 0 }$C, specific heat of copper = 0.1 cal/${ gm }^{ 0 }$C)

Options:
A. $775^{ 0 }$C
B. $$825^{ 0 }C$$
C. 850^{ 0 }C
D. $800^{ 0 }$C
E. $790^{ 0 }$C
F. $$820^{ 0 }$C
G. 900^{ 0 }C
H. $885^{ 0 }$C
I. 810^{ 0 }C
J. $$1250^{ 0 }C$$
Answer: D
Copper reduces $NO_3^-$ into $NO $ and $NO_2$ depending upon concentration of $HNO_3$ in solution. Assuming $[Cu^{2+}] = 0.1\space M$, and $P_{NO} = P_{NO_2} = 10^{-3}$ bar. At which concentration of $HNO_3$, thermodynamic tendency for reduction of $NO_3^-$ into $NO$ and $NO_2$ by copper is same?
[Given: $ E^{\small\circ}_{Cu^{2+}|Cu} = +0.34\ V, \ E^{\small\circ}_{NO_3^-|NO} = +0.96\ V, \ E^{\small\circ}_{NO_3^-|NO_2} = +.79\ V$].

Options:
A. $$10^{0.72}\space M$$
B. $$10^{0.68}\space M$$
C. $$10^{0.56}\space M$$
D. $$10^{0.86}\space M$$
E. $$10^{0.76}\space M$$
F. $$10^{0.78}\space M$$
G. $$10^{0.66}\space M$$
H. $$10^{0.12}\space M$$
I. $$10^{0.58}\space M$$
J. $$10^{1.23}\space M$$
Answer: G