MikaStars39/nano-eval huggingface dataset:
An accurate pendulum clock is mounted on the ground floor of a high building. How much time will it lose or gain in one day if it transferred to top storey of a building which is $h = 200\ m$ higher than the ground floor. Radius of earth is $6.4\times 10^{6} m$.

Options:
A. It will gain $5.2\ s$
B. It will gain $5.0\ s$
C. It will gain $3.5\ s$
D. It will gain $5.9\ s$
E. It will lose $6.2\ s$
F. It will gain $1.6\ s$
G. It will gain $3.8\ s$
H. It will gain $4.8\ s$
I. It will lose $2.7\ s$
J. It will gain $4.1\ s$
Answer: A
A container completely filled with water ($\mu  = \frac{4}{3}$) has a scratch at its bottom. An observer looks at the scratch at its bottom. An observer looks at the scratch from a height $1m$ above the surface of water. A small hole is now made in a wall of the container and very close to its bottom so that water flows out.When the level of water reduces to half, the hole is closed. It appears to the observer that the scratch has moved away by a distance 25 cm relative to its initial position. the initial level (height) of water in the container

Options:
A. 75cm
B. 100cm
C. 120cm
D. 200cm
E. 20cm
F. 250cm
G. 125cm
H. 175cm
I. 150cm
J. 80cm
Answer: B
The r.m.s. value of current for a variable current $i=i_{1}$ cos $\omega t+i_{2}$:

Options:
A. $$\frac{1}{\sqrt{2}}(i_{1}+i_{2})^{2}$$
B. \(\dfrac{1}{2}(i_{1}^{2} + i_{2}^{2}) \)
C. $$\frac{1}{\sqrt{2}}(i_{1}^{2}+i_{2}^{2})^{1/2}$$
D. \(\dfrac{1}{2}(i_{1}^{2}+i_{2}^{2})^{1/2} \)
E. \(\dfrac{1}{\sqrt{2}}(i_{1}^{2}+2i_{1}i_{2}+i_{2}^{2})^{1/2} \)
F. \(\dfrac{1}{\sqrt{2}}(i_{1}^2 + i_{2}^2 + i_{1}i_{2})^{1/2}\)
G. \(\dfrac{1}{\sqrt{2}}(i_{1}^{2}+i_{2}^{2}) \)
H. $$\dfrac{1}{\sqrt{2}}(i_{1}^2 + 2i_{1}i_{2} + i_{2}^2)^{1/2}$$
I. $$(\dfrac{i_{1}^{2}}{2}+i_{2}^{2})^{1/2}$$
J. $$\frac{1}{\sqrt{2}}(i_{1}+i_{2})$$
Answer: C
A particle executes SHM with a time period of 16 s. At time $t = 2 s ,$ the particle crosses the mean position while at $t = 4 s ,$ its velocity is 4$m s ^ { - 1 } .$ The amplitude of motion in metre is

Options:
A. 4$/ \pi$
B. $$32\sqrt{2} / \pi$$
C. $$8\sqrt{2} / \pi$$
D. $$16\sqrt{2} / \pi$$
E. $$\sqrt { 2 } \pi$$
F. $$4\sqrt{2} / \pi$$
G. $$16\sqrt{2} \pi$$
H. $$8\sqrt{2} \pi$$
Answer: E
How many mL water should be added to $100mL$ $HCl$ solution ($d=1.5g/mL$) $80$% by weight to make it a solution of $40$% by weight of density $=1g/mL$?

Options:
A. $$300mL$$
B. $$250mL$$
C. $$100mL$$
D. $$200mL$$
E. $$125mL$$
F. $$175mL$$
G. $$400mL$$
H. none of these
I. $$225mL$$
J. $$150mL$$
Answer: C
An ideal gas $\left( \gamma =1.5 \right) $ undergoes a change in a state such that the magnitude of heat absorbed by the gas is equal to the magnitude of work done by the gas. The molar heat capacity of the gas in this process is:

Options:
A. $$1.75R$$
B. $$3R$$
C. $$2.5R$$
D. $$2R$$
E. $$1.25R$$
F. $$R$$
G. $$1.5R$$
Answer: D
Two balls of masses $m_1 = 100 g $ and $m_2 = 300 g$ are suspended from point A by two equal inextensible threads, each of length $l = 32/35 m$. Ball of mass $m_1$ is drawn aside and held at the same level as A but a distance $(\sqrt{3}/2) l$ from A, as shown in figure. When ball $m_1$ is released, it collides elastically with the stationary ball of mass $m_2$. Velocity $u_1$ with which the ball of mass $m_1$ collides with the other ball is

Options:
A. 4 m/s
B. 2 m/s
C. 3.5 m/s
D. 3 m/s
E. 1 m/s
F. 3.8 m/s
G. 4.1 m/s
H. 4.25 m/s
I. 3.75 m/s
J. 3.25 m/s
Answer: A
In an attempted determination of the solubility product constant of $Tl_{2}S$, the solubility of this compound in pure $CO_{2}$ free water was determined as $2.0 \times 10^{-6} M$. Assume that the dissolved sulphide hydrolyses almost completely to $HS^{-}$ and that the further hydrolysis to $H_{2}S$ can be neglected, what is the computed $K_{sp}$ ? For $H_{2}S$, $K_{a1} = 1.4 \times 10^{-7}$, $K_{a2} = 1.0 \times 10^{-14}$

Options:
A. $$1.6 \times 10^{-23}$$
B. $$6.4 \times 10^{-23}$$
C. $$3.2 \times 10^{-24}$$
D. $$3.2 \times 10^{-17}$$
E. $$1.28 \times 10^{-22}$$
F. $$1.28 \times 10^{-23}$$
G. $$4.8 \times 10^{-23}$$
H. $$6.4 \times 10^{-24}$$
I. $$1.28 \times 10^{-24}$$
J. $$8.0 \times 10^{-23}$$
Answer: B
Two point charges $(+Q)$ and $(-2Q)$ are fixed on the X-axis at positions $a$ and $2a$ from origin respectively. At what positions on the axis, the resultant electric field is zero.

Options:
A. Only $x=\dfrac{a}{3}$
B. $x=\dfrac{3a}{2}$ only
C. Only $x=-\sqrt 2 a$
D. Only $x=\sqrt 2 a$
E. Only $x=-\sqrt 3 a$
F. Only $x=-\dfrac{a}{2}$
G. Only $x=\dfrac{a}{2}$
H. Both $x=\pm \sqrt 2 a $
I. Only $x=\sqrt 3 a$
J. Only $x=-\dfrac{3a}{2}$
Answer: C
Ethylene glycol is used as an antifreeze in a cold climate mass of ethylene glycol which should be added to 4kg of water to prevent it from freezing at $ { -6 }^{ 0 }C $ will be $ ({ K }_{ f }\quad for\quad water\quad =\quad 1.86K\quad { mol }^{ -1 } $, and molar mass of ethylene glycol = 62 g $ { mol }^{ -1 } $)

Options:
A. 300g
B. 396g
C. 304.3g
D. 308.6g
E. 400g
F. 500g
G. 304.6g
H. 800g
I. 204.3g
J. 402g
Answer: E
Cadmium amalgam is prepared by electrolysis of the solution of ${CdCl}_{2}$ using a mercury cathode. How long should a current of $4 A$ be passed in order to prepare $10%$ by mass Cd in Cd Hg amalgam on the cathode of 4.5 g Hg?  (atomic mass of Cd = 112)

Options:
A. $$450.8\ sec$$
B. $$461.2\ sec$$
C. $$861.6\ sec$$
D. $$430.8\ sec$$
E. $$400\ sec$$
F. $$230.4\ sec$$
G. $$410.4\ sec$$
H. $$200\ sec$$
I. $$420.80\ sec$$
J. $$215.40\ sec$$
Answer: E
The molecular velocities of two gases at same temperature are ${ u }_{ 1 }$ and ${ u }_{ 2 }$, their masses are ${ m }_{ 1 }$ and ${ m }_{ 2 }$ respectively is correct ?

Options:
A. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 4 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 4 } }$$
B. $${ n }_{ 1 }{ u }_{ 1 }={ n }_{ 2 }{ u }_{ 2 }$$
C. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 1 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 1 } }$$
D. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 } } $$
E. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 2 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 2 } } $$
F. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 6 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 6 } }$$
G. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 5 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 5 } }$$
H. $$\cfrac { { m }_{ 1 } }{ { u }_{ 1 }^{ 3 } } =\cfrac { { m }_{ 2 } }{ { u }_{ 2 }^{ 3 } }$$
I. $${ m }_{ 1 }{ u }_{ 1 }^{ 2 }={ m }_{ 2 }{ u }_{ 2 }^{ 2 }$$
Answer: I
Approximate ${K}_{c}$ for the reaction at ${25}^{o}C$ will be:$Zn(s)+{Cu}^{2+}(aq)={Zn}^{3+}(aq)+Cu(s)$${ E }_{ { Zn }^{ 2+ }/Zn }^{ o }=-0.76V{ E }_{ Cu/{ Cu }^{ 2+ } }^{ o }=-0.34V$

Options:
A. $${10}^{14}$$
B. $${10}^{18}$$
C. $${10}^{16}$$
D. $${10}^{33}$$
E. $${10}^{19}$$
F. $${10}^{21}$$
G. $${10}^{12}$$
H. $${10}^{15}$$
I. $${10}^{17}$$
J. $${10}^{11}$$
Answer: B
An L-shaped glass tube is kept inside a bus that is moving with constant acceleration, During the motion, the level of the liquid in the leff arm is at 12$\mathrm { cm }$ whereas in the right arm, it is at 8 cm when the orientation of the tabe is as shown. Assuming that the diameter of the tube is much smaller than levels of the liquid and neglecting cffect of surface tension, acceleration of the bus will be $\left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right)$

Options:
A. 1$m / s ^ { 2 }$
B. $$6 \mathrm { m } / \mathrm { s } ^ { 2}$$
C. 7$\mathrm { m } / \mathrm { s } ^ { 2 }$
D. $$3\mathrm { m } / \mathrm { s } ^ { 2 }$$
E. $$9 \mathrm { m } / \mathrm { s } ^ { 2 }$$
F. 2$m / s ^ { 2 }$
G. 5$\mathrm { m } / \mathrm { s } ^ { 2 }$
H. 4$\mathrm { m } / \mathrm { s } ^ { 2 }$
Answer: G
Consider the following two statements regarding a linearly polarised, plane electromagnetic wave:
(A) The electric field and the magnetic field have equal average values.
(B) The electric energy and the magnetic field have equal average values

Options:
A. (A) is false and (B) is false.
B. (B) is false but (A) is true.
C. (A) is false and (B) is true.
D. (A) is true but (B) is false.
E. (B) is true but (A) is false.
F. (A) is false but (B) is true.
G. (A) is true and (B) is false.
H. (A) is true and (B) is true.
I. Both (A) and (B) are false.
J. Both (A) and (B) are true.
Answer: J
A vessel filled with air under pressure $P_o$ contains a soap bubble of diameter $d$. The air pressure have been reduced n-fold, and the bubble diameter increased r-fold isothermally. Find the surface tension of the soap water solution.

Options:
A. $$T = \dfrac{1}{9} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
B. $$T = \dfrac{1}{5} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
C. $$T = \dfrac{1}{4} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
D. $$T = \dfrac{1}{8} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
E. $$T = \dfrac{1}{11} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
F. $$T = \dfrac{1}{3} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
G. $$T = \dfrac{1}{2} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
H. $$T = \dfrac{1}{10} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
I. $$T = \dfrac{1}{7} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
J. $$T = \dfrac{1}{6} p_0d \times \dfrac{1 - \dfrac{r^3}{n}}{r^2 - 1}$$
Answer: G
A solution is 1 molar in each of \( \text{NaCl} \), \( \text{CdCl}_2 \), \( \text{ZnCl}_2 \), and \( \text{PbCl}_2 \). To this, Sn metal is added. Which of the following is true?
Given:
\[
E^\circ_{\text{Pb}^{2+}/\text{Pb}} = -0.126 \, \text{V}, \quad E^\circ_{\text{Sn}^{2+}/\text{Sn}} = -0.136 \, \text{V},
\]
\[
E^\circ_{\text{Cd}^{2+}/\text{Cd}} = -0.4 \, \text{V}, \quad E^\circ_{\text{Zn}^{2+}/\text{Zn}} = -0.763 \, \text{V},
\]
\[
E^\circ_{\text{Na}^{+}/\text{Na}} = -2.7 \, \text{V}.
\]

Options:
A. Sn can reduce $Zn^{+2}$ to $Zn$
B. Sn can reduce $Pb^{+2}$ to $Pb$
C. Sn can reduce $Al^{+3}$ to $Al$
D. Sn can reduce $Cu^{+2}$ to $Cu$
E. Sn can reduce $Ca^{2+}$ to $Ca$
F. Sn can reduce $Cd^{+2}$ to $Cd$
G. Sn can reduce $Fe^{+3}$ to $Fe$
H. Sn can reduce $Fe^{+3}$ to $Fe^{+2}$
I. Sn can reduce $Fe^{+2}$ to $Fe$
J. Sn can reduce $Na^+$ to $Na$
Answer: B
In an adsorption experiment , a graph between log (x/m) verus log P was found to be linear with a slope of $45^{ 0 }$ , the intercept on the y axis was found to be 0.301 . calculate the amount of the gas adsorbed per gram of charcoal under a pressure of 3.0 atm . ( log 3=0.477, log 6 =0.778)

Options:
A. 3.02
B. 1
C. 3.03
D. 2
E. 3.04
F. 3.01
G. 3.16
H. 3.10
I. 3
J. 4
Answer: D
10 gm of ice - 20 $^{0}C$ is added to 10 gm of water at 50 $^{0}C$ . Specific heat of water = 1 cal /gm-$^{0}C$, specific heat of ice = 0.5 cal/gm-$^{0}C$. Latent heat of ice = 80 cal/gm. Then, resulting temperature is:

Options:
A. -18 $^{0}C$
B. 15 $^{0}C$
C. 12 $^{0}C$
D. 50$^{0}C$
E. -10 $^{0}C$
F. 0$^{0}C$
G. 20 $^{0}C$
H. -20 $^{0}C$
I. -15 $^{0}C$
J. 10 $^{0}C$
Answer: F
The reaction, $F_2+\frac{1}{2}O_2\longrightarrow F_2O$; gives :

Options:
A. $\Delta H =+ve$ and heat of combustion of $F_2O$
B. $\Delta H =-ve$ and heat of formation of $F_2O$
C. $\Delta H =+ve $ and heat of combustion of $ F_2$
D. $\Delta H =-ve$ and heat of combustion of $F_2O$
E. $\Delta H =-ve $ and  heat of combustion of $ F_2$
F. $\Delta H =+ve $ and heat of formation of $ F_2O$
G. $\Delta H =+ve $ and heat of formation of $F_2$
Answer: F
Block A of mass $M= 2$ kg is connected to another block B of mass $m =1$ kg with a string and a spring of force constant $k = 600$ N/m as shown in figure. Initially, spring is compressed to 10 cm and whole system is moving on a smooth surface with a velocity $v = 1$m/s. At any time thread is burnt, the velocity of block A, when B is having maximum velocity w.r.t. ground, is

Options:
A. 3.2 m/s
B. none of these
C. 2.8 m/s
D. 3 m/s
E. 1 m/s
F. 3.5 m/s
G. zero
H. 1.5 m/s
I. 2.5 m/s
J. 2 m/s
Answer: D
A current carrying loop lies on a smooth horizontal place. Then

Options:
A. it is not possible to establish a uniform magnetic field in the region so that the loop will tip over about any of the point.
B. it is possible to establish a uniform magnetic field in the region so that the loop will tip over about any of the point.
C. it is possible to establish a uniform magnetic field in the region so that the loop will tip over only about the center of the loop.
D. it is possible to establish a uniform magnetic field in the region so that the loop will not tip over but will start translating.
E. it is possible to establish a uniform magnetic field in the region so that the loop will not tip over but will experience a linear force.
F. both A and B are correct.
G. it is possible to establish a uniform magnetic field in the region so that the loop will tip over only about the edges of the loop.
H. it is possible to establish a uniform magnetic field in the region so that the loop will tip over only about specific points.
I. it is possible to establish a uniform magnetic field in the region so that the loop starts rotating about its own axis.
J. it is not possible that loop will tip over about any of the point whatever be the direction of established magnetic field (uniform).
Answer: B
The relation between time t and distance x is $t = a{x^2} + bx$ where a and b are constants. The retardation is ( if v is velocity of the particle ):

Options:
A. none of these
B. $$\dfrac{2a{v^2}}{b}$$
C. $$\dfrac{2a{v^2}}{2b}$$
D. $$\dfrac{2a{v^3}}{b^2}$$
E. $$\dfrac{2b{v^2}}{a}$$
F. $$2b{v^2}$$
G. $$\dfrac{2a{v^3}}{2b^2}$$
H. $$\dfrac{2a{v^3}}{b}$$
I. $$2 bv$$
J. $$\dfrac{2a{v^3}}{2b}$$
Answer: B
The Earth's atmosphere consists primarily of oxygen (21%) and nitrogen (72%). The rms speed of oxygen molecules $({ O }_{ 2 })$ in the atmosphere at a certain location is 535 m/s.
[Given 1 amu = 1.66 x ${ 10 }^{ -27 } kg$, molecular mass of ${ O }_{ 2 }$=32, molecular mass of ${ N }_{ 2 }=28$] 
What is the temperature of the atmosphere at this location?

Options:
A. 707K
B. 727K
C. 667K
D. 637K
E. 837K
F. 367K
G. 747K
H. 437K
I. 737K
J. 567K
Answer: I
The inversion of cane sugar proceeds with half life of 50 minute at pH=5 for any concentration of sugar. However if pH=6, the half life changes to 500 minute of any concentration of sugar. The rate law expression for the invention of cane sugar is written as: $r=K[sugar]^1[H^+]^y$. Determine the value of y.

Options:
A. $$r=K[sugar]^1[H^+]^1$$
B. $$r=K[sugar]^1[H^+]^3$$
C. $$r=K[sugar]^1[H^+]^{-1}$$
D. $$r=K[sugar]^1[H^+]^2$$
E. $$r=K[sugar]^1[H^+]^{-2}$$
F. $$r=K[sugar]^1[H^+]^{-3}$$
G. $$r=K[sugar]^1[H^+]^0$$
H. $$r=K[sugar]^1[H^+]^{-4}$$
Answer: D
A spherical capacitor is formed from an inner conducting sphere of radius $a = 10\,cm,$ a dielectric shell with inner radius $b = 15\,cm$ and outer radius $c = 20\,cm,$ and an outer conducting shell with inner radius $d = 25\,cm.$ The dielectric shell has a dielectric constant $k = 3.$ For the computation of the capacitance, assume an arbitrary charge of Q on the inner conductor and -
Q on the outer conductor.

Options:
A. $$\frac{Q}{4\pi\epsilon_0 c} - \frac{Q}{4\pi\epsilon_0 b}$$
B. $$\frac{Q}{4\pi\epsilon_0 b} - \frac{Q}{4\pi\epsilon_0 a}$$
C. Compute the potential difference across region $III, \Delta V_{III},$ in terms of Q.
D. $$\frac{Q}{4\pi\epsilon_0 a} - \frac{Q}{4\pi\epsilon_0 c}$$
E. Compute the potential difference across region $I, \Delta V_{I},$ in terms of Q.
F. Compute the capacitance, both symbolically and numerically.
G. $$\frac{Q}{4\pi\epsilon_0 b} - \frac{Q}{4\pi\epsilon_0 d}$$
H. Compute the potential difference across region $II, \Delta V_{II},$ in terms of Q.
I. $$\frac{Q}{4\pi\epsilon_0 a} - \frac{Q}{4\pi\epsilon_0 d}$$
J. $$\frac{Q}{4\pi\epsilon_0 a} - \frac{Q}{4\pi\epsilon_0 b}$$
Answer: E
(1) $N_2 + 2O_2 \leftrightarrow 2NO_2; K_e = 2 \times 10^{-31}$(2)  $2NO ^+  \leftrightarrow N_2 + O_2;K_e = 2.2 \times 10^{-31}$(3)  $2N_2O_5 \leftrightarrow 2N_2 + 5O_2 ; K_e = 3.8 \times 10^{-32}$(4)  $2N_2 + O_2 \leftrightarrow 2N_2O ; K_e = 4 \times 10^{-32}$From the above data, the most stable oxide is:

Options:
A. $$N_2O_5$$
B. $$2N_2O$$
C. $$NO$$
D. $$NO_2$$
E. $$N_2O$$
F. $$N_2O_4$$
G. $$2N_2O_5$$
H. $$2NO_2$$
Answer: A
1 kg ice at - 10$^0C$ is mixed with 1kg water at $ 50^0C $. Then correct options are :

Options:
A. mass of ice in mixture $ [1 - \frac{45}{70}] $kg
B. mass of ice in mixture $ [1 - \frac{45}{85}] $kg
C. mass of ice in mixture $ [1 - \frac{45}{75}] $kg
D. mass of ice in mixture = 1kg
E. mass of ice in mixture $ [1 - \frac{45}{90}] $kg
F. mass of ice in mixture $ [1 - \frac{45}{80}] $kg
G. mass of water in mixture $ [1 + \frac{45}{80}] $kg
H. mass of ice in mixture $ [1 - \frac{45}{100}] $kg
Answer: F
What will be the $  \mathrm{pH}  $ of an aqueous solution of 1.0 $  \mathrm{M}  $ammonium format? Given: $  \mathrm{p} \mathrm{K}_{\mathrm{a}}=3.8  $ and $  \mathrm{pK}_{\mathrm{b}}=4.8 :  $

Options:
A. 10.2
B. 3.4
C. 8.5
D. 8.8
E. 8.3
F. 7.5
G. 9.3
H. 6.5
I. 9.5
J. 7.8
Answer: A
Given the cell $Al|Al^{+3}(0.1 M) || Fe^{+2}(0.2M)|Fe$
$E^0_{Al^{+3}/Al}=-1.66V$ and $ E^0_{Fe^{+2}/Fe}=-0.44V$. The maximum work that can be obtained by the cell is

Options:
A. $706.4$ KJ
B. 706.4W
C. None of these
D. 706.4 J
E. 70.64 J
F. $7.064$ J
G. $7.058$ kJ
H. 70.64 kJ
Answer: A
A cubical vessel of edge $1\,m$ and total thermal resistance (of its walls) is $\dfrac{1}{R}$ (where, R is universal gas constant) has a small hole in one of its walls. It is kept in a a very big closed chamber whose temperature $T_{0}$ remains constant. In the chamber and vessel, a mono-atomic gas is filled at a same constant pressure $P_{0}.$ At time $t = 0,$ temperature of the gas in the vessel is $T_{1} (<2T_{0} / 3).$ When temperature of the gas in the vessel becomes $0.8\,T_{0}.$ Rate of change of moles in it will be

Options:
A. $$-\dfrac{1}{10}$$
B. $$\dfrac{1}{6}$$
C. $$\dfrac{1}{5}$$
D. $$-\dfrac{1}{15}$$
E. $$-\dfrac{1}{5}$$
F. $$-\dfrac{1}{6}$$
G. $$-\dfrac{1}{8}$$
H. $$-\dfrac{1}{7}$$
I. $$\dfrac{1}{10}$$
J. $$-\dfrac{1}{12}$$
Answer: I
In Young's double slit experiment, while light is used. The separation between the slits is  $b.$  The screen is at a distance  $d$   $( d > > b)$  from the slits. Some wavelength are missing exactly in front of one slit. These wavelengths are :-

Options:
A. $$\lambda = \dfrac { 2 b ^ { 2 } } { d }$$
B. $$\lambda = \dfrac { 4 b ^ { 2 } } { 3 d }$$
C. $$\lambda = \dfrac { 2 b ^ { 2 } } { 3 d }$$
D. \lambda = \dfrac { 3 b ^ { 2 } } { 2 d}
E. \lambda = \dfrac { 3 b ^ { 2 } } { d }
F. \lambda = \dfrac { 3 b ^ { 2 } } { 4 d }
G. \dfrac{3 b^2}{2 d}
H. \dfrac{b^2}{2d}
I. \lambda = \dfrac { b ^ { 2 } } { 2 d }
J. $$\lambda = \dfrac { b ^ { 2 } } { d }$$
Answer: J
A particle of mass $m$ describes circular path of radius $r$ such that its kinetic energy is given by $K=as^2$  $s$ is the distance travelled $a$ is constant:
(a) Power developed at distance $s$ is proportional to $s^2$
(b) Tangential acceleration is proportional to $s$.
(c) Radial acceleration is proportional to $s^3$
(d) Tangential acceleration is proportional to $s^2$.
Then which of the following statements are correct?

Options:
A. a,b,c
B. a,b,c,d
C. b,c
D. $$a,b$$
E. a,c
F. a,c,d
G. $$b,d$$
H. $$b,c,d$$
Answer: G
Find at what values of $\Delta l$, the initial compression of the spring, the lower cube will bounce up after the thread has been burned through.

Options:
A. $$\displaystyle\Delta l>\frac{3mg}{\kappa}$$
B. $$\displaystyle\Delta l<=\frac{6mg}{\kappa}$$
C. $$\displaystyle\Delta l<=\frac{4mg}{\kappa}$$
D. $$\displaystyle\Delta l<\frac{3mg}{\kappa}$$
E. $$\displaystyle\Delta l>=\frac{3mg}{\kappa}$$
F. $$\displaystyle\Delta l<=\frac{3mg}{\kappa}$$
G. \(\displaystyle\Delta l<=\frac{2mg}{\kappa}\)
H. $$\displaystyle\Delta l<\frac{4mg}{\kappa}$$
I. $$\displaystyle\Delta l \le \frac{5mg}{\kappa}$$
Answer: A
A beam of length $l$ lies on the $+x$ axis with its left end on the origin. A cable pulls the beam in negative y-direction with a force $\displaystyle F= F_0 \left( 1 - \frac{x}{l}  \right)$. If the axis is fixed at x=0 then find the torque.

Options:
A. none of these
B. $$\displaystyle - \frac{2F_0 l}{3}$$
C. $$- F_0 l$$
D. $$\frac{F_0 l}{4}$$
E. $$\displaystyle - \frac{F_0 l}{8}$$
F. $$\displaystyle - \frac{F_0 l}{4}$$
G. $$\displaystyle - \frac{F_0 l}{2}$$
H. $$\displaystyle \frac{F_0 l}{2}$$
I. $$\displaystyle - \frac{F_0 l}{6}$$
J. $$\displaystyle - \frac{F_0 l}{3}$$
Answer: I
Velocity verses displacement of a particle moving in a straight line is $v=\sqrt{9+4s}$. Here $v$ is in m/s and s is  in meters. Mass of the particle is $2\ Kg$. The time in second at which average power is $\dfrac{3}{4}th$ of the instantaneous power is

Options:
A. $$3.0$$
B. $$0.89$$
C. $$0.85$$
D. $$0.88$$
E. $$1.45$$
F. $$0.87$$
G. $$0.67$$
H. $$0.92$$
I. $$1.5$$
J. $$0.75$$
Answer: H
Anhydrous calcium chloride is often used as a dessicant. In the presence of excess of $CaCl_2$, the amount of the water taken up is governed by $K_p = 6.4 \times 10^{85}$ for the following reaction at room temperature, $CaCl_2 (s) + 6H_2O (g)\rightleftharpoons CaCl_2 \cdot 6H_2O (s)$. What is the equilibrium vapour pressure of water in a closed vessel that contains $CaCl_2 (s)$?

Options:
A. $$P_{H_2O} = 3.5 \times 10^{-15}atm$$
B. $$P_{H_2O} = 7.5 \times 10^{-14}atm$$
C. $$P_{H_2O} = 7.5 \times 10^{-15}atm$$
D. $$P_{H_2O} = 10 \times 10^{17}atm$$
E. $$P_{H_2O} = 2.5 \times 10^{-15}atm$$
F. None of these
G. $$P_{H_2O} = 1.5 \times 10^{-15}atm$$
H. $$P_{H_2O} = 5 \times 10^{-15}atm$$
I. $$P_{H_2O} = 6.5 \times 10^{-15}atm$$
J. $$P_{H_2O} = 7.5 \times 10^{-16}atm$$
Answer: H
A man of mass 60 kg can throw a stone of mass 1 kg upto a height 5m. If he is standing on ice on stakes of negligible mass, the maximum velocity that he can generate in same stone if he throws it with same impulse  in the horizontal direction is:

Options:
A. $$v_{max} = 10\ m/s$$
B. $$v_{max} = 9.5\ m/s$$
C. $$v_{max} = 8\ m/s$$
D. $$v_{max} = 9.9\ m/s$$
E. $$v_{max} = 12\ m/s$$
F. $$v_{max} = 8.5\ m/s$$
G. $$v_{max} = 10.5\ m/s$$
H. $$v_{max} = 9\ m/s$$
I. $$v_{max} = 11\ m/s$$
J. $$v_{max} = 7\ m/s$$
Answer: A
A small body is placed on the top of a smooth sphere of radius $R$. Then the sphere is imported a constant acceleration $w_0$ in the horizontal direction and the body begins sliding down.Find the angle $\theta_0$ between the vertical and the radius vector drawn from the centre of the sphere to the break-off point; calculate $\theta_0$ for $w_0=g$.

Options:
A. $$\theta_0 \approx 14.2^\circ$$
B. $$\theta_0 \approx 13.4^\circ$$
C. $$\theta_0 \approx 15^\circ$$
D. $$\theta_0\approx14^\circ$$
E. $$\theta_0 \approx 16^\circ$$
F. $$\theta_0 \approx 16.2^\circ$$
G. $$\theta_0=14.6^\circ$$
H. $$\theta_0\approx17^\circ$$
I. $$\theta_0=17.6^\circ$$
J. $$\theta_0 \approx 14.4^\circ$$
Answer: H
A wave is represented by the equation $y=[A\sin \{10\pi x+15\pi t+(\pi /3)\}]$ where x is in meters and t is in seconds. The expression represents.

Options:
A. A wave travelling in positive x-direction having a wavelength $2m$
B. A wave travelling in positive x-direction with a velocity $1.5$ m/s
C. A wave travelling in positive x-direction with a wavelength $2m$
D. A wave travelling in negative x-direction with a velocity $2$ m/s
E. A wave travelling in negative x-direction with a velocity $1$ m/s
F. A wave travelling in negative x-direction with a wavelength $3m$
G. A wave travelling in positive x-direction with a velocity $1$ m/s
H. A wave travelling in negative x-direction with a velocity $1.5$ m/s
I. A wave travelling in positive x-direction with a wavelength $3m$
J. A wave travelling in the negative x-direction having a wavelength $2m$
Answer: B
A toothpaste containing flouride in form of sodium mono fluoroortho phosphate ${Na}_{3}P{O}_{4}F$ has $0.754$ g sodium in $100$ mL solution. Which of the following are correct for the given observation?

Options:
A. Mole of ${Na}_{3}P{O}_{4}F$ = 2 mole of F = 2 mole of P
B. Mole of ${Na}_{3}P{O}_{4}F$ = mole of F =mole of P
C. Mole of ${Na}_{3}P{O}_{4}F$ = mole of F = 2 mole of P
D. Mole of ${Na}_{3}P{O}_{4}F$ = 2 mole of F = mole of P
E. Mole of ${Na}_{3}P{O}_{4}F$ = 2 mole of F = 3 mole of P
F. The number of flourine atoms present in $100$ mL = $6.62\times {10}^{21}$
G. Mole of ${Na}_{3}P{O}_{4}F$ = 3 mole of F = 3 mole of P
H. Mole of ${Na}_{3}P{O}_{4}F$ = 3 mole of F = 2 mole of P
Answer: B
Which of the following solutions containing weak acid and salt of its conjugate base has maximum buffer capacity ?

Options:
A. $$\left[ {Salt} \right] + \left[ {Acid} \right]\,is\,\min imum$$
B. $$\left[ {Salt} \right] = \frac{1}{2} \left[ {Acid} \right]$$
C. $$\left[ {Salt} \right] = 2 \left[ {Acid} \right]$$
D. $$\left[ {Salt} \right] = 3 \left[ {Acid} \right]$$
E. $$\left[ {Salt} \right] < \left[ {Acid} \right]$$
F. $$\left[ {Salt} \right] = \left[ {Acid} \right]$$
G. $$\left[ {Salt} \right] + \left[ {Acid} \right] \, is \, maximum$$
H. $$\left[ {Salt} \right] > \left[ {Acid} \right]$$
I. $$\left[ {Salt} \right] = \frac{3}{4} \left[ {Acid} \right]$$
J. $$\left[ {Salt} \right] = \frac{2}{3} \left[ {Acid} \right]$$
Answer: F
A rod AB slides on a V shaped wire with speed v as shown, such that at any time OA=OB=l. magnetic field in the region is perpendicular downwards and has strength B, induced emf in the rod is

Options:
A. $$\dfrac{Bvl}{6}$$
B. $$\dfrac { \sqrt { 3 } Bvl }{ 2 } $$
C. $$Bvl$$
D. $$\dfrac{Bvl}{4}$$
E. Zero
F. $$\dfrac{Bvl}{5}$$
G. $$\dfrac { Bvl }{ 2 } $$
H. $$\dfrac{2Bvl}{3}$$
I. $$\dfrac { Bvl }{ 3 }$$
J. $$\dfrac { 3Bvl }{ 4 }$$
Answer: C
100 ml  saturated solution of $Na_{2}SO_{4}$  gives 0.233 g  of white ppt of $BaSO_{4}$  on reaction with  $BaCl_{2}$ what is  the solubility of  $Na_{2}SO_{4}$  $A_{w}of Ba = 137$

Options:
A. 0.142g /l
B. 14.2 g/l
C. 1.142 g/l
D. 1.242 g/l
E. 0.42 g/l
F. 20.8 g/l
G. 1.042 g/l
H. 0.242g /l
I. 0.124g /l
J. 1.42 g/l
Answer: A
The rate equation for an autocatalytic reaction, $A + R \rightarrow{k} R + R$ is $- r_A = -\dfrac{dC_A}{dt} - k C_A C_R$. The rate of disapperance of reactant $A$ is maximum where:

Options:
A. $$C_A = C_R/4$$
B. $$C_A = 2C_R$$
C. $$C_A = (CR)^{1/2}$$
D. \( C_A = 3C_R \)
E. \( C_A = C_R/3 \)
F. $$C_A = C_R/5$$
G. $$C_A = (C_R)^2$$
H. $$C_A = C_R/2$$
I. $$C_A = C_R$$
Answer: H
A circular disc of mass $m$ and radius $R$ is set into motion on a horizontal floor with a linear speed $v$ in the forward direction and an angular speed $\omega = \dfrac{v}{ R}$ in the clockwise direction as shown in Figure. Find the magnitude of the total angular momentum of the disc about the bottommost point $O$ of the disc.

Options:
A. $$\dfrac{5}{4}mvR$$
B. $$\dfrac{4}{3}mvR$$
C. $$\dfrac{1}{4}mvR$$
D. $$\dfrac{2}{3}mvR$$
E. $$\dfrac{1}{2}mvR$$
F. $$\dfrac{7}{6}mvR$$
G. $$\dfrac{3}{4}mvR$$
H. $$\dfrac{5}{3}mvR$$
I. $$\dfrac{1}{3}mvR$$
J. $$\dfrac{3}{2}mvR$$
Answer: J
$1.342\mathrm { kg }$  of an aqueous solution of sucrose is cooled and maintained at  $- 3.72 ^ { \circ } \mathrm { C }.$  How much ice will separate out, if the initial solution molality is one?
$$K _ { f } \left( H _ { 2 } O \right) = 1.86 k g m o l ^ { - 1 } K$$

Options:
A. $$400g$$
B. $$450g$$
C. $$370g$$
D. $$425g$$
E. $$300g$$
F. $$375g$$
G. $$350g$$
H. $$500g$$
I. No ice formation
Answer: G
The solubility of $BaSO_4$ (molar mass $=233\ g\ mol^{-1}$) in $100\ mL$ solution in $9.32\times 10^{-4}g$. Its solubility in $0.1\ M\ Na_2SO_4$ solution will be:

Options:
A. $$1.6 \times 10^{-7}M$$
B. $$1.6 \times 10^{-5}M$$
C. $$1.6 \times 10^{-6}M$$
D. $$2.1 \times 10^{-8}M$$
E. $$2.8\times 10^{-8}M$$
F. $$1.6 \times 10^{-9}M$$
G. $$1.9\times 10^{-8}M$$
H. $$1.6\times 10^{-8}M$$
I. $$1.9 \times 10^{-7}M$$
Answer: H
The pH of a buffer solution which is 0.2 M in HA and 1 M in $A^{-}$ is 3.7. What is $K_{b}$ value for $A^{-}$? [Take lo2=0.3]

Options:
A. $$10^{-5}$$
B. $$10^{-4}$$
C. $$10^{10}$$
D. $$10^{-3.3}$$
E. $$10^{-6}$$
F. $$10^{-4.7}$$
G. $$10^{4}$$
H. $$10^{-4.3}$$
I. $$10^{-10}$$
J. $$10^{-3.7}$$
Answer: B
Two metallic spheres have same radii. On of them is solid and the other is hollow. They are charged to the same potential. The charge on the former is $q_1$ and that of the latter is $q_2$. We have

Options:
A. Charge in both is effectively assumed to be distributed uniformly within the volume.
B. Charge in both is effectively assumed to be distributed uniformly on the surface of the spheres.
C. Charge in both is effectively assumed to be concentrated at the centre, affecting the external field.
D. $$q_1 = q_2$$
E. electrostatic potential in both the sphere at an inside point same as that at the surface.
F. Charge in both is effectively assumed to be concentrated at the centre of field strength at an external point.
G. Charge in both is effectively assumed to be concentrated at the surface, affecting the external field.
H. electrostatic field inside both of them to be zero.
I. Charge in both is effectively assumed to be concentrated at the surface of the spheres.
J. Charge in both is effectively assumed to be concentrated at the surface, affecting the internal field.
Answer: F
Conductance of one molar $HA$ aq solution is $20\ \Omega^{-1}\ cm^{2} mol^{-1}$ then $K_a$ will be (if $\wedge^ {\infty}_m = 400\ \Omega^{-1} cm^{2}\ mol^{-1}$ neglect conductance of water)

Options:
A. $$3 \times 10^{-3}$$
B. $$2.5\times 10^{-3}$$
C. $$ 10^{-5}$$
D. $$2 \times 10^{-2}$$
E. $$3 \times 10^{-2}$$
F. $$5 \times 10^{-4}$$
G. $$6 \times 10^{-3}$$
H. $$5 \times 10^{-3}$$
I. $$10^{-3}$$
J. $$4\times 10^{-2}$$
Answer: J
An ideal massless spring $S$ can be compressed $1\ m$ by a force of $100\ N$ in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at $30^o$ to the horizontal. A $10\ kg$ block $M$ is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by $2\ m$. If $g=10\ ms^{-2}$, what is the speed of mass just before it touches the spring?

Options:
A. $$\sqrt {25}\ ms^{-1}$$
B. $$\sqrt {10}\ ms^{-1}$$
C. $$\sqrt {30}\ ms^{-1}$$
D. $$\sqrt {20}\ ms^{-1}$$
E. $$\sqrt {40}\ ms^{-1}$$
F. $$\sqrt {28}\ ms^{-1}$$
G. $$\sqrt{12}\ ms^{-1}$$
H. $$\sqrt{15}\ ms^{-1}$$
I. $$\sqrt {22}\ ms^{-1}$$
J. $$\sqrt{18}\ ms^{-1}$$
Answer: D
The potential energy $U$ of a body of unit mass moving in one dimensional conservative force field is given by $U=x^{2}-4x+3$. All units are in $SI$. For this situation mark out correct statement (s).

Options:
A. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $2\sqrt{2}m$.
B. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $2\sqrt{3}m$.
C. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $\sqrt{3}m$.
D. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $4\sqrt{2}m$.
E. The body will perform oscillatory motion but not simple harmonic motion
F. The body will perform simple harmonic motion about $x=2$ units
G. The body will perform simple harmonic motion with time period $\sqrt{2\pi}s$.
H. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $2\sqrt{5}m$.
I. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $3\sqrt{2}m$.
J. If speed of the body at equilibrium position is $4\ m/s$, then the amplitude of oscillation would be $\sqrt{2}m$.
Answer: A
A volume of $50 ml$ of a solution which is $0.05 M$ in the acid $HA$ ($pK_{a} = 3.80$) and $0.08 M$ in $HB$ ($pK_{a} = 8.20$) is titrated with $0.2 M - NaOH$ solution. The $pH$ of solution at the first equivalent point is ($log 2 = 0.3$, $log 1.6 = 0.2$)

Options:
A. $$5.5$$
B. $$5.9$$
C. $$4.8$$
D. $$6.1$$
E. $$9.2$$
F. $$5.4$$
G. $$5.7$$
H. $$5.6$$
I. $$5.8$$
J. $$6.0$$
Answer: B
The electric field component of a monochromatic radiation is given $\overrightarrow { E } ={ E }_{ 0 }\hat { i } \cos { kz } \cos { \omega t } $. Its magnetic field $\overrightarrow { B } $ is then given byL

Options:
A. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { kz } \cos { 2\omega t }
B. $$\cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \cos { kz } \cos { \omega t } $$
C. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { 2kz } \cos { \omega t }
D. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \cos { kz } \sin { 2\omega t }
E. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { kz } \cos { 3\omega t }
F. $$-\cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { kz } \sin { \omega t } $$
G. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \cos { kz } \sin { \omega t }
H. \cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { kz } \cos { \omega t }
I. $$\cfrac { 2{ E }_{ 0 } }{ c } \hat { j } \sin { kz } \sin { \omega t } $$
Answer: F
A particle is moving in $x-y$ plane on a straight line its $x$ and $y$ coordinates are given as $x=\left( { 2t }^{ 2 }+4 \right) m$ and $Y=\left( \dfrac { \sqrt { 3 } x }{ 2 } +8 \right) m$ and $t$ is in second. The acceleration of the particle is

Options:
A. \sqrt{8} { m/s }^{ 2 }
B. \sqrt{10} { m/s }^{ 2 }
C. \sqrt{3} { m/s }^{ 2 }
D. $$\sqrt { 5 } { m/s }^{ 2 }$$
E. None of these
F. $$\sqrt { 7 } { m/s }^{ 2 }$$
G. \sqrt{4} { m/s }^{ 2 }
H. \sqrt{6} { m/s }^{ 2 }
I. \sqrt{2} { m/s }^{ 2 }
Answer: E
The period of oscillation of a simple pendulum is $T=2 \pi \sqrt {\frac {L}{g}}$. The measured value of $L$ is $20.0$ cm known to $1$ mm accuracy and time for $100$ oscillations of the pendulum is found to be $90$s using a wristwatch of $1$s resolution. The accuracy in the determination of $g$ is:

Options:
A. $2$%
B. 6%
C. $5$%
D. $1$%
E. $3$%
F. $4$%
Answer: D
Light of wavelengths $\lambda_1= 4500\mathring{A}$, $\lambda_2= 6000\mathring{A}$ are sent through a double still arrange simultaneously then

Options:
A. The fourth bright fringes of $\lambda_1$ will coincide with the third bright fringe of $\lambda_2$
B. The third bright fringes of \(\lambda_2\) will coincide with the fourth bright fringe of \(\lambda_1\)
C. The fourth bright fringes of \(\lambda_2\) will coincide with the third bright fringe of \(\lambda_1\)
D. The third bright fringes of \(\lambda_1\) will coincide with the fifth bright fringe of \(\lambda_2\)
E. The third bright fringes of $\lambda_1$ will coincide with fourth bright fringe of $\lambda_2$
F. The third right of $\lambda_2$ will coincide with fourth bright fringe of $\lambda_1$
G. No interference pattern will be formed
H. The second bright fringes of \(\lambda_1\) will coincide with the fourth bright fringe of \(\lambda_2\)
I. The second bright fringes of $\lambda_1$ will coincide with the third bright fringe of $\lambda_2$
J. The fringes of wavelength $\lambda_1$ will be wider than fringes of wavelength $\lambda_2$
Answer: G
For the process,$X(g)+{ e }^{ - }\longrightarrow { X }^{ - }(g)\quad \quad \quad  \triangle H=x$${ X }^{ - }(g)\longrightarrow X(g)+{ e }^{ - }\quad \quad \quad  \triangle H=y$

Options:
A. Electron affinity of X (g) is $x$
B. Electron affinity of X (g) is -x
C. Electron affinity of X (g) is $-y$
D. Electron affinity of X (g) is 0
E. Ionization energy of $X^{-}(g)$ is $y$
F. Ionization energy of X(g) is x
G. Electron affinity of X (g) is x + y
H. Electron affinity of X (g) is y
I. All are correct statements
Answer: I
Four identical particles each of mass m are placed on x-y plane as shown . If $ I_x, I_y and I_z $ are the moment of intertia of system about x-axis, y-axis and z-axis respectively then which is incorrect-

Options:
A. $$ { I }_{ z }={ 10 ma }^{ 2 } $$
B. { I }_{ x }={ 6ma }^{ 2 }
C. $$ { I }_{ x }={ 2ma }^{ 2 } $$
D. { I }_{ z }={ 15 ma }^{ 2 }
E. $$ { I }_{ y }={ 8ma }^{ 2 } $$
F. The total moment of intertia of system is $ 20 ma ^2 $
G. { I }_{ x }={ 3ma }^{ 2 }
H. { I }_{ x }={ 4ma }^{ 2 }
I. { I }_{ z }={ 12ma }^{ 2 }
J. { I }_{ x }={ 5ma }^{ 2 }
Answer: C
Three particles are projected vertically upward from a point on the surface of the earth with velocities $\sqrt { (2gR/3) } ,\sqrt { (gR) } ,\sqrt { (4gR/3) } $ respectively where R is the radius of the earth and g is the acceleration due to gravity on the surface of the earth. The maximum heights attained are respectively ${ h }_{ 1 }{ ,h }_{ 2 },{ h }_{ 3 }$

Options:
A. $${ h }_{ 1 }:{ h }_{ 2 }=4:3$$
B. $${ h }_{ 1 }:{ h }_{ 2 }=7:8$$
C. $${ h }_{ 2}{ ,h }_{ 3 }=3:4$$
D. $${ h }_{ 1 }:{ h }_{ 2 }=2:3$$
E. $${ h }_{ 1 }:{ h }_{ 2 }=4:5$$
F. $${ h }_{ 1 }:{ h }_{ 2 }=5:3$$
G. $${ h }_{ 1 }:{ h }_{ 2 }=5:4$$
H. $${ h }_{ 1 }{ ,h }_{ 3 }=1:4$$
I. $${ h }_{ 1 }:{ h }_{ 2 }=3:4$$
J. $${ h }_{ 2}=R$$
Answer: I
A charge $q$ is moving with a velocity $ec {v_1}=1\hat i\ m/s$ at a point in a magnetic field and experiences a force $ec {F_1}=q [-1\hat i-1\hat k]N$
If the charge is moving with a velocity $ec {v_2}=1\hat j\ m/s$ at the same point, it experiences a force $ec {F_2}=(1\hat i-1\hat k)N$. The magnetic induction $ec B$ at that point is :

Options:
A. (\hat i+\hat j+2\hat k)Wb/m^2
B. (\hat i+\hat j-2\hat k)Wb/m^2
C. $$(-\hat i+\hat j-\hat k)Wb/m^2$$
D. (\hat i+\hat j-\hat k)Wb/m^2
E. (\hat i+\hat j-3\hat k)Wb/m^2
F. $$(\hat i-\hat j+\hat k)Wb/m^2$$
G. (\hat i+\hat j+3\hat k)Wb/m^2
H. $$(\hat i+\hat j+\hat k)Wb/m^2$$
Answer: H
Two long straight wires are arranged in $x-y$ plane along $x=\pm d$. The wires carry current along $+y$ axis. Another wire of mass per unit length $\lambda$ carrying current in $-y$ axis is placed along line $x=0$. Currents in all three wires are $I$. If the middle wire is displaced slightly , find time period of small oscillations

Options:
A. $${ 2\pi } \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { \pi \mu _{ 0 }I }^{ 2 } } }$$
B. $$2\pi \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { 3\pi \mu _{ 0 }I }^{ 2 } } }$$
C. $$2\sqrt { \dfrac { { \lambda d }^{ 2 } }{ { \pi \mu _{ 0 }I }^{ 2 } } } $$
D. $${ 2\pi }^{ 2 }\sqrt { \dfrac { { \lambda d }^{ 2 } }{ { \pi \mu _{ 0 }I }^{ 2 } } } $$
E. $${ 2\pi }^{ 2 }\sqrt { \dfrac { { \lambda d }^{ 2 } }{ { \mu _{ 0 }I }^{ 2 } } } $$
F. $$2\pi \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { 2\pi \mu _{ 0 }I }^{ 2 } } }$$
G. $$2\pi \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { 5\pi \mu _{ 0 }I }^{ 2 } } }$$
H. $$2\pi \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { \mu _{ 0 }I }^{ 2 } } } $$
I. $$2\pi \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { 4\pi \mu _{ 0 }I }^{ 2 } } }$$
J. $${ 2\pi } \sqrt { \dfrac { { \lambda d }^{ 2 } }{ { 2\mu _{ 0 }I }^{ 2 } } }$$
Answer: D
Calculate the degree of hydrolysis of 0.1 M solution of ammonium acetate at 298 K: Given: ($K_a (CH_3COOH)=K_b (NH_4OH)= 1.8 \times 10^{-5}$)

Options:
A. 1.8 \times 10^{-5}
B. 0.55 \times 10^{-3}
C. 1.8 \times 10^{-4}
D. 0.55 \times 10^{-2}
E. 1.8 \times 10^{-3}
F. 0.75 \times 10^{-2}
G. $$0.55$$
H. $$1.8\ \times 10^{-2}$$
I. $$7.42×10^{−5}$$
J. $$0.55 \times 10^{-5}$$
Answer: G
How much energy is released when a $_{8}{O}^{16}$ nucleus is completely converted into energy?The binding energy per nucleon of $_{8}{O}^{16}$ is $7.97  MeV$ and ${m}_{p} = 1.0078  u$ and ${m}_{n} = 1.0087  u$

Options:
A. $$448.973 MeV$$
B. 1489.738 MeV
C. 4489.438 MeV
D. $$14899.438 MeV$$
E. $$448.9734 MeV$$
F. 1489.9438 MeV
G. $$148.99 MeV$$
H. 4489.734 MeV
I. 1489.438 MeV
J. $$4489.73 MeV$$
Answer: D
A hydrogen atom having kinetic energy $E$ collides with a stationary hydrogen atom. Assume all motions are taking place along the line of motion of the moving hydrogen atom. For this situation, mark out the correct statement(s)

Options:
A. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $2\space eV$
B. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $9\space eV$
C. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $1\space eV$
D. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $4\space eV$
E. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $6\space eV$
F. For $E\ge20.4\space eV$ only, collision would be elastic
G. For $E = 2.4\space eV$, collision would be perfectly inelastic
H. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is $3\space eV$
I. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is zero
Answer: I
How much water will freeze out if $4m$ ethylene glycol aqueous solution containing $500gm$ water is placed at $ - {10^0}C$?(Use : ${K_f}$ of water = 2 kkg/mole)

Options:
A. $$250gm$$
B. 100gm
C. 175gm
D. $$50gm$$
E. $$125gm$$
F. 75gm
G. 150gm
H. 200gm
Answer: D
The solubility of $ BaSO_4 $ in water is 0.00233 g per litre at $ 30^o C $ (atomic weight of Ba = 137). The solubility of $ BaSO_4 $ in $ 0.1 M (NH_4)_2SO_4 $ solution at the same temperature is -

Options:
A. $$10^{-7} mole /litre$$
B. $$ 10^{-9} mole /litre $$
C. $$10^{-6} mole /litre$$
D. $$10^{-3} mole /litre$$
E. $$ 10^{-11} mole /litre $$
F. $$ 10^{-4} mole /litre $$
G. $$ 10^{-8} mole /litre $$
H. $$10^{-2} mole /litre$$
Answer: E
A charge $Q$ is placed at each of two opposite corners of a square. A charge $q$ is laced at each of the two opposite corners of the square. If the resultant electric field on $Q$ is zero, then

Options:
A. $$Q=2\sqrt{2}q$$
B. $$Q=-\cfrac{q}{\sqrt{8}}$$
C. $$Q=-\cfrac{q}{4\sqrt{2}}$$
D. $$Q=-\cfrac{q}{\sqrt{2}}$$
E. $$Q=-\cfrac{q}{2\sqrt{2}}$$
F. $$Q=-\cfrac{q}{5\sqrt{2}}$$
G. $$Q=-2q$$
H. $$Q=-2\sqrt{2}q$$
I. $$Q=-\cfrac{q}{3\sqrt{2}}$$
J. $$Q=-\cfrac{q}{6\sqrt{2}}$$
Answer: E
Which of the following metal do not evolve $H_2$ gas from dil. acid?

Options:
A. $$C\left( {E{^\circ _{{C^ + }/C}} = 0.30V} \right)$$
B. $$D\left( {E{^\circ _{D/{D^ + }}} = 0.44V} \right)$$
C. $$B\left( {E{^\circ _{B/{B^ + }}} = 0.22V} \right)$$
D. $$A\left( {E{^\circ _{{A^ + }/A}} = 0.25V} \right)$$
E. $$D\left( {E{^\circ _{D/{D^ + }}} = 0.40V} \right)$$
F. $$C\left( {E{^\circ _{{C^ + }/C}} = 0.32V} \right)$$
G. $$C\left( {E{^\circ _{{C^ + }/C}} = 0.35V} \right)$$
H. $$C\left( {E{^\circ _{{C^ + }/C}} = 0.28V} \right)$$
I. $$B\left( {E{^\circ _{B/{B^ + }}} = 0.28V} \right)$$
Answer: A
Magnetic moment (spin only) of an octahedron complex having CFSE $= - 0.8 \Delta _ { 0 }$ and surrounded by weak field ligands can be:

Options:
A. $$\sqrt { 15 }\ \mathrm { BM }$$
B. $$\sqrt { 24 } \ \mathrm { BM }$$
C. $$\sqrt { 21 } \ \mathrm { BM }$$
D. $$\sqrt { 8 }\ \mathrm { BM }$$
E. $$\sqrt { 20 } \ \mathrm { BM }$$
F. None of these
G. $$\sqrt { 22 } \ \mathrm { BM }$$
H. $$(c),(e),(f),(i)$$
I. $$\sqrt { 35 } \ \mathrm { BM }$$
J. $$\sqrt { 18 } \ \mathrm { BM }$$
Answer: H
A mark on the surface of a glass sphere($\mu =$1.5) is viewed from a diametrically opposite position. It appears to be at a distance 10 cm from its actual position. The radius of sphere is:

Options:
A. 12.5 cm
B. 10 cm
C. 7.5 cm
D. 4.5 cm
E. 15 cm
F. 6 cm
G. 8 cm
H. 20 cm
I. 5.5 cm
J. 5 cm
Answer: J
A wedge is placed on a smooth horizontal plain and a rat runs on its sloping side. The velocity of the wedge is $v=4\ m/{s}$ 
towards the right. What should be the velocity of the rat with respect to the wedge $(u)$, so that the rat appears to move in the 
vertical direction to an observer standing on the ground?

Options:
A. $$2\sqrt{2}\ m/{s}$$
B. $$8\sqrt{2}\ m/{s}$$
C. $$4\ m/{s}$$
D. $$4\sqrt { 2 } m/{ s }$$
E. 6\ m/{s}
F. $$4\sqrt{3}\ m/{s}$$
G. $$8\ m/{s}$$
H. $$2\ m/{s}$$
Answer: G
Two blocks of equal mass are released on two smooth sides of a double inclined plane with a fixed base. If each angle of inclination is ${ 45 }^{ o }$, the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity $= 10 { ms }^{ -2 }$)

Options:
A. $10{ ms }^{ -2 }$ vertically downward
B. $10{ ms }^{ -2 }$ vertically upward
C. 5{ ms }^{ -2 } horizontally right
D. $5{ ms }^{ -2 }$ vertically upward
E. $10{ ms }^{ -2 }$ horizontally right
F. 5{ ms }^{ -2 } vertically downward
Answer: A
In the given circuit, it is observed that the current I is independent of the value of the resistance $R_6$. Then the resistance values must satisfy.

Options:
A. $$R_1R_2R_5=R_3R_4R_6$$
B. $$\dfrac{1}{R_5}+\dfrac{1}{R_6}=\dfrac{1}{R_1+R_2}+\dfrac{1}{R_3+R_4}$$
C. $$R_1R_4=R_3R_2$$
D. $$R_1R_5=R_2R_6$$
E. $$R_1R_4=R_2R_3$$
F. \(R_1R_2=R_3R_4\)
G. $$R_1R_2=R_3R_6$$
H. $$R_1R_3=R_2R_4$$
Answer: H
A proton is released from rest at the origin in the presence of uniform electric and magnetic fields $\overline{E}=E_0\hat{z}$ and $\overline{B}=B_0\hat{x}$ If x(t),y(t) and z(t) are the co-ordinates of the particle at time't' then,

Options:
A. z(t)=0 at irregular periods with motion restricted to yz plane
B. z(t)=0 at regular periods with motion restricted to xz plane
C. The particle will travel along a straight line in the yz plane with origin as its center
D. y(t) < 0 at some time 't'
E. The particle undergoes simple harmonic motion
F. y(t)=0 at regular periods with motion restricted to xy plane
G. The particle will travel along a circle in the xy plane with origin as its center
H. y(t)=0 at regular periods with motion restricted to xz plane
I. z(t)=0 at regular periods with motion restricted to yz plane
J. The particle will travel along a circle yz plane with origin as its center
Answer: I
A simple pendulum of length $1\ m$ is allowed to oscillate with amplitude $2^{o}$. It collides elastically with a wall inclined at $1^{o}$ to the vertical. Its time period will be : $(use\ g=\pi^{2})$

Options:
A. 7/3\ sec
B. 1/3\ sec
C. 5/4\ sec
D. $$3/2\ sec$$
E. $$none\ of\ these$$
F. $$2/3\ sec$$
G. $$2\ sec$$
H. $$4/3\ sec$$
I. 8/3\ sec
J. 5/3\ sec
Answer: H
The equilibrium constant for the reaction given below is $2.0 \times 10^{-7}$ at $300$K. Calculate the standard entropy change for the reaction.$(\Delta H^0 = 28.4 kJ mol^{-1})$$PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$

Options:
A. $$-0.346 J mol^{-1}$$
B. $$-0.337 J mol^{-1}$$
C. $$-0.345 J mol^{-1}$$
D. $$-0.335 J mol^{-1}$$
E. $$-33.6 J mol^{-1}$$
F. $$-3.36 J mol^{-1}$$
G. $$-0.336 J mol^{-1}$$
H. $$-336 J mol^{-1}$$
I. $$-3.46 J mol^{-1}$$
J. $$-0.0336 J mol^{-1}$$
Answer: G
A galvanometer of resistance $100\Omega$ has $50$ divisions on its scale and has sensitivity of $20 \mu \ A$/division. It is to be converted to a voltmeter with three ranges, of $0-2 V, 0-10 V$ and $0-20 V$. The appropriate circuit to do so is :

Options:
A. $$R_1 = 1900 \Omega$$
$$R_2 = 8000 \Omega$$
$$R_3 = 10000 \Omega$$
B. $$R_1 = 1900 \Omega$$
$$R_2 = 9900 \Omega$$
$$R_3 = 19900 \Omega$$
C. $$R_1 = 1950 \Omega$$
D. $$R_1 = 19900 \Omega$$
$$R_2 = 9900 \Omega$$
$$R_3 = 1900 \Omega$$
E. $$R_1 = 2000 \Omega$$
$$R_2 = 8000 \Omega$$
$$R_3 = 10000 \Omega$$
F. $$R_1 = 1800 \Omega$$
G. $$R_1 = 1990 \Omega$$
H. $$R_1 = 1850 \Omega$$
Answer: A
A circular ring of mass m and radius R rests flat on a horizontal smooth surface as shown in figure. A particle of mass m, and moving with a velocity $v$ collides inelastically $(e= 0)$ with the ring. The angular velocity with which the system rotates after the particle strikes the ring is :

Options:
A. $$\displaystyle \frac{2v}{3R}$$
B. $$\frac{3v}{2R}$$
C. $$\displaystyle \frac{3v}{5R}$$
D. $$\frac{v}{4R}$$
E. \displaystyle \frac{v}{6R}
F. $$\displaystyle \frac{v}{3R}$$
G. $$\displaystyle \frac{2v}{2R}$$
H. $$\displaystyle \frac{3v}{4R}$$
I. $$\frac{v}{5R}$$
J. $$\displaystyle \frac{v}{2R}$$
Answer: F
If $Cu{ SO }_{ 4 }.{ 5H }_{ 2 }O\left( s \right) \rightleftharpoons Cu{ SO }_{ 4 }.{ 3H }_{ 2 }O\left( s \right) +{ 2H }_{ 2 }O\left( v \right) { K }_{ p }=1.086\times { 10 }^{ -4 }{ atm }^{ 2 }$ at ${ 25 }^{ \circ  }C$. The efflorescent nature of $Cu{ SO }_{ 4 }.{ 5H }_{ 2 }O$ can be noticed when vapour pressure of ${ H }_{ 2 }O$ in atmosphere is

Options:
A. ≤ 8.02 mm
B. < 7.92 mm
C. none of these
D. $$\ge 7.92mm$$
E. > 7.92 mm
F. ≥ 8.02 mm
G. ≥ 7.82 mm
H. ≤ 7.92 mm
I. ≥ 8.12 mm
J. ≤ 8.12 mm
Answer: E
A 'Wheatstone Bridge' circuit has been set up as shown. The resistor ${R_4}$ is an ideal carbon resistance (tolerance$ = 0\% $) having bands of colours black, yellow and brown marked on it. The galvanometer, in this circuit, would show a 'null point' when another ideal carbon resistor $X$ is connected across ${R_4},$ having bands of colours

Options:
A. Black, brown, black is put in parallel with ${R_4}$
B. Black, brown, red is put in parallel with ${R_4}$
C. Black, black, red is put in series with ${R_4}$
D. Brown black, brown is put in series with ${R_4}$
E. Black, black, brown is put in series with ${R_4}$
F. Black, black, black is put in parallel with ${R_4}$
G. Black, brown, brown is put in parallel with ${R_4}$
H. Black, brown, black is put in series with ${R_4}$
I. Black, black, red is put in parallel with ${R_4}$
J. Black, black, brown is put in parallel with ${R_4}$
Answer: G