MikaStars39/nano-eval huggingface dataset:
A radioactive substance X decays into another radioactive substance Y and Y into another product Z initially. only X was present and $\lambda_x$ and $\lambda_y$ are the disintegration constant of X and Y. $N_y$ will be maximum when

Options:
A. $$\frac{N_y}{N_x + N_y} = \frac{\lambda_y}{\lambda_x - \lambda_y}$$
B. $$\lambda_x N_y = \lambda_x N_x$$
C. $$\lambda_y N_x = \lambda_x N_y$$
D. $$\lambda_y N_y = \lambda_x N_x$$
E. $$\frac{N_y}{N_x -N_y} = \frac{\lambda_y}{\lambda_x -\lambda_y}$$
F. $$\frac{N_x}{N_x -N_y} = \frac{\lambda_x}{\lambda_x -\lambda_y}$$
G. $$\lambda_x N_y = \lambda_y N_x$$
H. $$\lambda_x N_x = \lambda_x N_y$$
I. \lambda_x N_x = \lambda_y N_y
Answer: G
Two uniform non conducting balls A and B having radius R but made of different density material (density of A=2 density of B). Ball A is positively charged & ball B is negatively charged. The balls are released on the horizontal smooth surface at the separation 10R as shown in figure. Because of mutual attraction, the balls start moving towards each other. They will collide at a point.

Options:
A. $$x=\cfrac { 7R }{ 3 } $$
B. $$x=5R $$
C. $$x=\cfrac { 16R }{ 3 }$$
D. $$x=\cfrac { 12R }{ 3 }$$
E. $$x=\cfrac { 14R }{ 3 }$$
F. $$x=\cfrac { 8R }{ 3 }$$
G. $$x=\cfrac { 9R }{ 3 }$$
H. $$x=\cfrac { 13R }{ 3 }$$
I. $$x=\cfrac { 11R }{ 3 } $$
J. $$x=\cfrac { 10R }{ 3 } $$
Answer: J
$${ H }_{ 2\left( g \right)  }+\frac { 1 }{ 2 } { O }_{ 2\left( g \right)  }\longrightarrow { H }_{ 2 }{ O }_{ \left( 1 \right)  }$$
$$B.E\left( H-H \right) ={ X }_{ 1 };B.E\left( O=O \right) ={ X }_{ 2 },B.E\left( O-H \right) ={ X }_{ 3 }$$
Latent heat of vaporization of water vapor is ${X}_{4}$. then ${ \Delta  }_{ f }H$ for liquid water is

Options:
A. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 3 }+2{ X }_{ 4 }$$
B. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -2{ X }_{ 3 }+2{ X }_{ 4 }$$
C. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 3 }+{ X }_{ 4 }$$
D. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -2{ X }_{ 3 }-{ X }_{ 4 }$$
E. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -2{ X }_{ 3 }+{ X }_{ 4 }$$
F. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 3 }-{ X }_{ 4 }$$
G. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 3 }-{ 2X }_{ 4 }$$
H. $${ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 3 }+{ 2X }_{ 4 }$$
I. $$2{ X }_{ 3 }-{ X }_{ 1 }+\dfrac { { X }_{ 2 } }{ 2 } -{ X }_{ 4 }$$
Answer: C
For $Mn^{+3}$ pairing energy is $28000\ cm^{-1},\ \Delta _{0}$ for $\left [ Mn\left ( CN \right )_{6} \right ]^{3-}$ is $38500\ cm^{-1}$ then which of the following is/are correct.

Options:
A. Complex will be colourless
B. Net CFSE = -32200 $cm^{-1}$
C. Net CFSE = -31500 $cm^{-1}$
D. Net CFSE = -28000 $cm^{-1}$
E. Net CFSE = -34300 $cm^{-1}$
F. Net CFSE = -33600 $cm^{-1}$
Answer: F
A $50kg$ boy stands on a plateform spring scale in a lift that is going down with a constant speed $3 m/s$ . If the lift is brought to rest by a constant deceleration in a distance of $9m$ what does the scale read during this period ?$(g=9.8m/s^2)$

Options:
A. $$525N$$
B. $$495N$$
C. $$505N$$
D. $$zero$$
E. $$465N$$
F. $$515N$$
G. $$500N$$
H. $$520N$$
I. $$535N$$
J. $$508N$$
Answer: F
Select the rate law that corresponds to the data shown for the following reaction:$A+B\rightarrow C$Expt No.$[A]_0 mole L^{-1}$$[B]_0 mole L^{-1}$Initital rate1.0.0120.0350.102.0.0240.0700.803.0.0240.0350.104.0.0120.0700.80

Options:
A. The rate law expression for the given reaction is Rate $=k[A][B]^3$
B. The rate law expression for the given reaction is Rate $=k[A]^2[B]^3$
C. The order with respect to [A] is one.
D. The order with respect to [A] is two.
E. The order with respect to [A] is five.
F. The rate law expression for the given reaction is Rate $=k[A]^0[B]^3$
G. The order with respect to [A] is zero.
H. The rate law expression for the given reaction is Rate $=k[B]^3$
I. The order with respect to [A] is four.
J. The order with respect to [A] is three.
Answer: G
$1.4275\ g$ sample of $[Cr(NH_3)_6]SO_4Cl$ (mol. wt $= 285.5$) is dissolved to prepare $250\ mL$ solution showing an osmotic pressure of $1.478\ atm$ at $27^{\circ}C$.Which of the following statements are correct about this solution?I.Each molecule furnishes three ions in the solution.II.The Van't Hoff factor is $= 3$.III.The equilibrium molarity of $[Cr(NH_3)_6]SO_4Cl=0$ IV.The equilibrium molarity of $[Cr(NH_3)_6]^{3+}=0.02M$

Options:
A. $I$ and $III$ only
B. $II$ and $IV$ only
C. I, II, and IV only
D. I and II only
E. $I$ and $IV$ only
F. $I$, $II$ and $IV$ only
G. I, II, and III only
H. All of the these
Answer: H
If an electron enters with a velocity $\bar{v}$ = $v_0 \hat{j}$ into a cubical region in a uniform electromagnetic field and the orbit of the electron is found to spiral down inside the cube in plane parallel to x-y plane then the configuration of electric field and magnetic field is then

Options:
A. \(\bar{E} = E_0\hat{k}\), \(\bar{B} = B_0\hat{j}\)
B. \(\bar{E} = E_0\hat{j}\), \(\bar{B} = B_0\hat{i}\)
C. \(\bar{E} = E_0\hat{k}\), \(\bar{B} = B_0\hat{i}\)
D. $\bar{E} = E_0\hat{j}$, $\bar{B} = B_0\hat{j}$
E. \(\bar{E} = E_0\hat{i}\), \(\bar{B} = B_0\hat{i}\)
F. $\bar{E} = E_0\hat{j}$, $\bar{B} = B_0\hat{k}$
G. \(\bar{E} = E_0\hat{j}\), \(\bar{B} = B_0\hat{k}\)
H. $\bar{E} = E_0\hat{i}$, $\bar{B} = B_0\hat{k}$
I. \(\bar{E} = E_0\hat{i}\), \(\bar{B} = B_0\hat{j}\)
J. $\bar{E} = E_0\hat{i}$, $\bar{B} = B_0\hat{j}$
Answer: H
Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation $lpha =30^{o}$, $\beta=60^{o}$, respectively (Fig. A.15). The shots strike an object simultaneously at the same point. If $a=30\sqrt { 3 }\ m$ is the horizontal distance of the object from the cliff, then the height $h$ of the cliff is

Options:
A. $$80\ m$$
B. $$30\ m$$
C. $$70\ m$$
D. $$60\ m$$
E. $$75\ m$$
F. $$50\ m$$
G. $$55\ m$$
H. $$45\ m$$
I. $$90\ m$$
Answer: D
A man is raising himself and the crate on which he stands with an acceleration of $5m{ s }^{ -2 }$ by a massless rope-and-pulley arrangement. Mass of the man is $100 kg$. If $g=10m{ s }^{ -2 }$,, the contact force between the man and the crate is:

Options:
A. $$425N$$
B. $$300N$$
C. $$500N$$
D. $$2250N$$
E. $$625N$$
F. $$750N$$
G. $$375N$$
H. $$450N$$
I. $$1125N$$
J. $$1875N$$
Answer: G
In certain areas where coal is cheap, artificial gas is produced for house hold use by the 'water gas' reaction:
$$C(s)+H_2O(g)\to H_2(g)+CO(g)$$
Assume that coke is $100\%$ carbon. Given $\Delta H_c (kcal /mol)$ at $25^oC: H_2(g)=-68.0; CO(g)=-68.0; C(s)=-94.0$. Select the correct option(s):

Options:
A. The maximum heat obtained at $25^oC$ from burning water gas produced from $1.2\ kg$ of coke is $13,600\ lcal$
B. The maximum heat obtainable at $25^oC$ from burning water gas or burning the same mass of coke will be same
C. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $5440\ kcal$
D. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $5640\ kcal$
E. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $5740\ kcal$
F. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $5540\ kcal$
G. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $5340\ kcal$
H. The maximum heat obtainable at $25^oC$ from burning $1.2\ kg$ of water gas is $4840\ kcal$
Answer: C
The electrical resistance of a column $0.07\ mol^{-1}\ NaOH$ solution of diameter $1\ cm$ and length $55\ cm$ is $5\times 10^{3}ohm$. What will be its molar conductivity $(\pi =\dfrac {22}{7})$.

Options:
A. $$25\ Scm^{2}mol^{-1}$$
B. $$200\ Scm^{2}mol^{-1}$$
C. $$350\ Scm^{2}mol^{-1}$$
D. $$100\ Scm^{2}mol^{-1}$$
E. $$75\ Scm^{2}mol^{-1}$$
F. $$175\ Scm^{2}mol^{-1}$$
G. $$50\ Scm^{2}mol^{-1}$$
H. $$60\ Scm^{2}mol^{-1}$$
I. $$125\ Scm^{2}mol^{-1}$$
J. $$150\ Scm^{2}mol^{-1}$$
Answer: G
A body of mass 10 kg falls from a height of 5 m ($\left( {g = 10\;m/{s^2}} \right)$) and is stopped within (1/10) sec. on the  ground the force of interaction is

Options:
A. 100 N
B. 1000 N
C. 250 N
D. 150 N
E. 200 N
F. 10 N
G. 500 N
H. zero
I. 50 N
J. 30 N
Answer: F
The angular velocity of a body changes from one revolution per 9 second to 1 revolution per second without applying any torque. the ratio of its radius of gyration in the two cases is,

Options:
A. 1 : 27
B. 9 : 1
C. 1 : 2
D. 1 : 8
E. 3 : 1
F. 1 : 4
G. 1 : 6
H. 1 : 9
I. 1 : 3
J. 3 : 27
Answer: I
An ideal gas is expanded adiabatically. If root mean square speed becomes  $\dfrac { 1 } { \sqrt { 2 } }$  times then the percentage change in volume of gas is  $( \gamma = 1.5 ).$

Options:
A. $$300 \%$$
B. $$100 \%$$
C. $$250 \%$$
D. $$60 \%$$
E. $$50 \%$$
F. $$200 \%$$
G. $$150 \%$$
H. $$75 \%$$
I. $$125 \%$$
Answer: E
For a reaction , $ Ag_2O(s) \rightarrow 2Ag(s) + O(g) , $ the value of $ \Delta H = 132.6 KJ, \Delta S= 66 JK^{-1}mol^{-1} $ the free energy change for the reaction will be zero at which of the temperature:-

Options:
A. 2023 K
B. 2015 K
C. 2018 K
D. 2009 K
E. 2030 K
F. 2000 K
G. 2010 K
H. 2005 K
I. 2001 K
J. 2029 K
Answer: F
A body of mass $m$ at rest is applied with a force $F=(2+4i)N$. The change in momentum of the interval once second to two second is

Options:
A. $$4\ kg-ms^{-1}$$
B. $$7\ kg\ ms^{-1}$$
C. $$8\ kg\ ms^{-1}$$
D. $$5\ kg\ ms^{-1}$$
E. $$3\ kg-ms^{-1}$$
F. $$12\ kg\ ms^{-1}$$
G. $$6\ kg\ ms^{-1}$$
H. $$2\ kg\ ms^{-1}$$
I. $$9\ kg\ ms^{-1}$$
J. $$10\ kg\ ms^{-1}$$
Answer: G
The composition of nickel oxide is $Ni_{0.98}O$. What fraction of Ni exists as $Ni^{+2}$ and $Ni^{+3}$ ions?

Options:
A. $Ni^{2+}=0.84, Ni^{+3}=0.16$
B. $Ni^{2+}=0.16$, $Ni^{+3}=0.84$
C. $Ni^{2+}=0.12$, $Ni^{+3}=0.88$
D. $Ni^{2+}=0.08$, $Ni^{+3}=0.92$
E. $Ni^{2+}=0.86$, $Ni^{+3}=0.12$
F. $Ni^{2+}=0.94$, $Ni^{+3}=0.06$
G. $Ni^{2+}=0.92$, $Ni^{+3}=0.08$
H. $Ni^{2+}=0.06$, $Ni^{+3}=0.94$
Answer: H
${ H }_{ 2 }A$ is a diprotic acid for which ${ K }_{ { a }_{ 1 } }={ 10 }^{ -7 }\ and\ { K }_{ { a }_{ 2 } }={ 10 }^{ -11 }$. The  solution which will have a pH closest to 9 is:

Options:
A. 0.1 M ${ H }_{ 2 }A + 0.01 M { Na }_{ 2 }A$
B. 0.1 M ${ H }_{ 2 }A + 0.1 M { Na }_{ 2 }A$
C. 0.1 M NaHA + 0.001 M ${ Na }_{ 2 }A$
D. 0.1 M ${ Na }_{ 2 }A + 0.01 M NaHA$
E. 0.1 M ${ Na }_{ 2 }A$
F. 0.1 M NaHA
G. 0.1 M NaHA + 0.1 M ${ Na }_{ 2 }A$
H. 0.01 M NaHA + 0.1 M ${ Na }_{ 2 }A$
I. 0.1 M ${ H }_{ 2 }A$
J. 0.1 M NaHA + 0.01 M ${ Na }_{ 2 }A$
Answer: I
To produce characteristic X-rays using a Tungsten target in an X-rays generator, the accelerating voltage should be greater than _________ volts and the energy of the characteristic radiation is _________ eV. Binding energy of the inner most electron in Tungsten $=40\ KeV$.

Options:
A. $$40000 \,\, , 40000$$
B. $$30000 \,\, , 30000$$
C. $$50000 \,\, , 35000$$
D. $$30000 \,\, , 35000$$
E. $$50000 \,\, , 30000$$
F. $$40000 \,\, , 35000$$
G. $$60000 \,\, , 40000$$
H. $$40000 \,\, , 30000$$
I. $$50000 \,\, , 40000$$
Answer: B
If the first minima in a Young's double-slit experiment occurs directly in front of one of the slits (distance between slit and screen D=$12cm$ and distance between slits $d=5cm$), then wavelength of the radiation used can be

Options:
A. $$\dfrac{1}{3}cm$$
B. $$\dfrac{2}{3}cm$$
C. $$\dfrac{3}{2}cm$$
D. $$2cm$$
E. $$\dfrac{5}{3}cm$$
F. $$\dfrac{1}{4}cm$$
G. $$\dfrac{4}{3}cm$$
H. $$\dfrac{3}{4}cm$$
I. $$4cm$$
J. $$\dfrac{1}{2}cm$$
Answer: B
For a particular reversible reaction at temperature T, $\Delta$H and $\Delta$S were found to be both $+$ve. If $T_e$ is the temperature at equilibrium, the reaction would be spontaneous when?

Options:
A. T_e = 2T
B. $$T > T_e$$
C. $$T_e = 4T$$
D. T_e = 3T
E. T_e < T
F. $T_e$ is $5$ times T
G. $$T = T_e$$
H. $$T_e > T$$
I. T_e = T + 1
J. $T_e = \frac{T}{2}$
Answer: H
At ${!00}^{o}C$, the following equilibrium is established.
${H}_{2}(g)+S(s)\rightleftharpoons  {H}_{2}S(g);{K}_{c}=0.08$. If $0.3$ mol hydrogen and $2$ mol sulphur are heated to ${100}^{o}C$ in a $2L$ vessel, what will be the amount of $S(s)$ at equilibrium?

Options:
A. $$1.905mol$$
B. $$0.045mol$$
C. $$0.268mol$$
D. $$0.276mol$$
E. $$1.923mol$$
F. none of the above
G. $$1.978mol$$
H. $$1.955mol$$
I. $$0.022mol$$
J. $$0.285mol$$
Answer: D
A stretched wire carries a body of density $\sigma =8000\ kg/m^3$ at its end. The fundamental frequency of vibration of wire is $260\ Hz$. The body is dipped completely in a vessel of water. The new frequency of fundamental mode of vibrations is : ( The density of water is $\rho =1000 \ kg/m^3$)

Options:
A. $$264.5\ Hz$$
B. $$260\ Hz$$
C. $$250.4\ Hz$$
D. $$262\ Hz$$
E. $$243.2\ Hz$$
F. $$263.5\ Hz$$
G. $$247.5\ Hz$$
H. $$240.5\ Hz$$
I. $$265\ Hz$$
J. $$255.5\ Hz$$
Answer: D
A glass sphere has a cavity inside it , When placed in water it floats with $20\%$ of volume above water surface. Volume of cavity as a fraction of total volume enclosed by glass surface is (density of glass $= 2.5\ g/cc$)

Options:
A. $$\dfrac {17} {25}$$
B. $$\dfrac {8} {25}$$
C. $$\dfrac{10}{25}$$
D. $$\dfrac {13} {25}$$
E. $$\dfrac{19}{25}$$
F. $$\dfrac{16}{25}$$
G. $$\dfrac{9}{25}$$
H. $$\dfrac{12}{25}$$
I. $$\dfrac{14}{25}$$
J. $$\dfrac {11} {25}$$
Answer: J
A cylinder, released from the top of an 95 inclined plane, rolls without sliding and reaches the bottom with speed ${ v }_{ r }$ .Another identical cylinder, released from the top of the same inclined plane, slides without rolling and reaches the bottom with speed ${ v }_{ s }$Then

Options:
A. ${ v }_{ r }$=${ v }_{ s }$>0
B. ${ v }_{ r }$=${ v }_{ s }$+1
C. ${ v }_{ r } = 2{ v }_{ s }$
D. { v }_{ r } = 0.75{ v }_{ s }
E. ${ v }_{ r }$>${ v }_{ s }$
F. ${ v }_{ r } < { v }_{ s }$
G. ${ v }_{ r } = 0.5{ v }_{ s }$
H. ${ v }_{ r }$=${ v }_{ s }$
I. ${ v }_{ r }$=${ v }_{ s }$=$0$
Answer: E
When 0.4 mole of HCL added to one litre of solution contaning 0.2 M each of HCN and CN-ion . ph of solution become$(K_{ a } = 1.8 *{ 10 }^{ -5 })$

Options:
A. 4
B. 3.7
C. 3.9
D. 3.4
E. 3.8
F. 3.6
G. 1
H. 0.7
I. 3.5
J. 3.3
Answer: I
What is the molar solubility of $Mn(OH)_2$ ($k_{sp}$ = 4.5 $\times 10^{-14}$) in a buffer solution containing equal amounts of ${NH}_{4}^{+}$ and $NH_3$ ($k_b = 1.8 \times 10^{-5}$)?

Options:
A. 1.38 $\times 10^{-4}$
B. 1.5 $\times 10^{-4}$
C. 1.3 $\times 10^{-4}$
D. 1.38 $\times 10^{-3}$
E. 2.0 $\times 10^{-4}$
F. 1.0 $\times 10^{-4}$
G. 2.5 $\times 10^{-4}$
H. 3.0 $\times 10^{-4}$
I. 1.3 $\times 10^{-3}$
Answer: A
A car moves along a circular road of radius $\dfrac{200}{\pi}m$ with a constant speed of $36$ kmph start $t = 0$. The minimum time after which the magnitude of change in velocity is half of the maximum change in velocity is:

Options:
A. $$\dfrac{30}{3} sec$$
B. $$\dfrac{10}{3} sec$$
C. $${20} sec$$
D. $$\dfrac{20}{3} sec$$
E. $$\dfrac{60}{3} sec$$
F. $$\dfrac{80}{3} sec$$
G. $$\dfrac{50}{3} sec$$
H. $$\dfrac{70}{3} sec$$
I. $$\dfrac{40}{3} sec$$
J. $$\dfrac{100}{3} sec$$
Answer: D
If a fish moving in upward direction in water with a speed of 9 m/s is observing a bird which is diving straight downwards in air with a speed of 12 m/s. then calculate speed of the bird as seen by the fish-
$({\mu _{water}} = 4/3)$

Options:
A. 26 m/s
B. 7 m/s
C. 25 m/s
D. 23 m/s
E. 27 m/s
F. 3 m/s
G. 21 m/s
H. 24 m/s
I. 19 m/s
J. 29 m/s
Answer: C
Infite springs with force constant $k,2k,4k,8k,...$ respectively are connected in series to which mass $'m'$ is attached. The frequency of small oscillations is:

Options:
A. $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{768K}{m}}$$
B. $$f=\dfrac {1}{2\pi}\sqrt {\dfrac {2048K}{m}}$$
C. $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{1536K}{m}}$$
D. $$f=\dfrac {1}{2\pi}\sqrt {\dfrac {K}{4m}}$$
E. $$f=\dfrac {1}{2\pi}\sqrt {\dfrac {1024K}{3m}}$$
F. $$f=\dfrac {1}{2\pi}\sqrt {\dfrac {K}{m}}$$
G. $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{512K}{m}}$$
H. $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{1024K}{m}}$$
I. $$f=\dfrac {1}{2\pi}\sqrt {\dfrac {2K}{m}}$$
J. $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{1024K}{2m}}$$
Answer: B
The Ksp of $CaCO_3$ is $4.9\times 10^{-9}$. The volume required to dissolve 1 g $CaCO_3$ is (Molecular weight of $CaCO_3=100$):

Options:
A. 102.40 liter
B. $10.24$ liter
C. $142.85$ liter
D. $104.20$ liter
E. $14.28$ liter
F. 14.25 liter
G. $10.42$ liter
H. 142.58
I. 102.42 liter
J. $208.52$ liter
Answer: G
A string of length 1 m and linear mass density 0.01 kg/m is stretched to a tension of 100 N. When both ends of the string are fixed, the three lowest frequencies for standing wave are $n_1,\,n_2\,and\,n_3$. Then

Options:
A. $$\displaystyle \,n_2\,=\,\frac{f_1\,+\,f_2}{2}\,=\,75\,Hz$$
B. $$n_3\,=\,5n_1\,=\,f_3\,=\,125\,Hz$$
C. $$\,n_2\,=\,\frac{f_1\,+\,f_3}{2}\,=\,100\,Hz$$
D. $$\,n_2\,=\,\frac{f_1\,+\,f_2}{2}\,=\,100\,Hz$$
E. $$\,n_2\,=\,\frac{f_1\,+\,f_2}{2}\,=\,25\,Hz$$
F. $$\displaystyle \,n_2\,=\,\frac{f_1\,+\,f_2}{2}\,=\,50\,Hz$$
G. $$f_3\,=\,n_2\,=\,3\,f_1\,=\,150\,Hz$$
H. $$f_3\,=\,5f_1\,=\,n_2\,=\,125\,Hz$$
I. $$\,n_2\,=\,\frac{f_1\,+\,f_2}{2}\,=\,150\,Hz$$
J. $$\,n_2\,=\,\frac{f_1\,+\,f_3}{2}\,=\,125\,Hz$$
Answer: A
The e.m.f. of a cell corresponding to the reaction : $Zn+2H^{+} (aq)\rightarrow Zn^{2+}(0.1M)+H_{2}(g)(1 bar)$ is 0.169 volt at $25^{\circ}C$. Calculate the pH of the solution at the hydrogen electrode. $E^{\circ}_{zn^{2+}/Zn}=-0.76$ volt and $E^{\circ}_{H^{+}/H_{2}}=-0$

Options:
A. 8.7
B. 8.5
C. 9.2
D. 10.5
E. 9.5
F. 7.5
G. 8.8
H. 9
I. 8.9
J. 11.5
Answer: H
For given cell reaction$O_{2}(g)+4\ H^{+} (aq)+4e^{-} \rightarrow 2\ H_{2}O (l)$$E^{o}=1.23\ V$ and $\Delta_{r}\ S^{O}_{298\ K}=-0.32\ kJ\ K^{-1}$What is the value of $\Delta_{r}H^{o}(H_{2}O)$?

Options:
A. $$-285.07\ kJ\ mol^{-1}$$
B. $$-570.18\ kJ\ mol^{-1}$$
C. $$-285.08\ kJ\ mol^{-1}$$
D. $$-379.42\ kJ\ mol^{-1}$$
E. $$-189.71\ kJ\ mol^{-1}$$
F. $$-285.09\ kJ\ mol^{-1}$$
G. $$-570.16\ kJ\ mol^{-1}$$
H. $$-285.10\ kJ\ mol^{-1}$$
I. $$-570.17\ kJ\ mol^{-1}$$
Answer: C
For a gaseous reaction involving the complete combustion of isobutane:

Options:
A. $\triangle H = \triangle E$
B. \(\triangle H = \triangle E\)
C. \(\triangle H > \triangle E\)
D. \(\triangle H \neq \triangle E\)
E. none of these
F. $\triangle H < \triangle E$
G. \(\triangle H \geq \triangle E\)
H. $\triangle H > \triangle E$
I. \(\triangle H < \triangle E\)
J. \(\triangle H \leq \triangle E\)
Answer: F
In the system shown in figure $m_A=4m,m_B=3m$ and $m_C=8m$. Friction is absent everywhere. String is light and in-extensible. If the system is released from rest find the acceleration of block $B$

Options:
A. $\frac{g}{2}$ (left ward)
B. $\frac{g}{8}$ (leftward)
C. $\frac{g}{5}$ (rightward)
D. $\frac{g}{5}$ (leftward)
E. $\frac{g}{6}$ (rightward)
F. $\frac{g}{7}$ (leftward)
G. $\frac{g}{7}$ (rightward)
H. $\frac{g}{3}$ (rightward)
I. $\frac{g}{4}$ (rightward)
Answer: I
The free end of the open-link chain of total L and mass per unit $\lambda$ is released from rest at x = 0. The thrust force at the lower end of non-moving part due to relative motion of other part as a function of x is :

Options:
A. $$\lambda g \sqrt{x}$$
B. $$\sqrt {2\lambda} gx$$
C. $$\lambda g x^2$$
D. $$\lambda g x$$
E. Zero
F. $$2\lambda gx$$
G. $$\lambda gx^3$$
Answer: F
Power of the only force acting on a particle of mass $m=1$kg moving in straight line depends on its velocity as $P=v^2$ where v is m/s and P is in watt. If initial velocity of the particle is $1m/s,$ then the displacement of the particle in $2$  second will be:

Options:
A. $$(\ell n2)^2m$$
B. $$(ln2-3)m$$
C. $$(\ell n2-1)m$$
D. $$(\ell n2+2)m$$
E. $$(\ell n2-2)m$$
F. $$(\ell n2+1)m$$
G. $$2m$$
H. $$(\ell n2+3)m$$
I. $$(ln2+1)m$$
J. $$1m$$
Answer: J
$pK_a (CH_3 COOH)$ is 4.74 . $x$ mol of lead acetate and 0.1 mol of acetic acid in one L solution make a solution of  $p^H = 5.04$ . Hence, $x$ is -

Options:
A. 0.15
B. 0.2
C. 0.06
D. 0.04
E. 0.03
F. 0.07
G. 0.08
H. 0.1
I. 0.05
J. 0.02
Answer: I
A wire, of length $L(=20 cm)$, is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges $\pm Q, [|Q|=10^3 \epsilon_0$ Coulomb where $\epsilon_0$ is the permittivity (in SI units) of free space] the net electric field at the centre O of the semi-circular arc would be :

Options:
A. $$(50 \times 10^3 N/C)\hat k$$
B. $$(25 \times 10^3 N/C)\hat k$$
C. $$(75 \times 10^3 N/C)\hat i$$
D. $$(50\times 10^3 N/C)\hat j$$
E. $$(75 \times 10^3 N/C)\hat k$$
F. $$(50 \times 10^3 N/C)\hat i$$
G. $$(25\times 10^3 N/C)\hat i$$
H. $$(25\times 10^3 N/C)\hat j$$
Answer: G
A pivoted beam of negligible mass has a mass suspended from one end and an Atwood's machine suspended from the other. The frictionless pulley has negligible mass and dimension. Gravity is directed downward and $\displaystyle M_{2}=3M_{3},l_{2}=3l_{1}.$ Find the ratio  $\displaystyle \frac{M_{1}}{M_{2}}$ which will ensure that the beam has no tendency to rotate just after the masses are released

Options:
A. $$\displaystyle \frac{M_{1}}{M_{2}}= 2.75$$
B. $$\displaystyle \frac{M_{1}}{M_{2}}=4$$
C. $$\displaystyle \frac{M_{1}}{M_{2}}= 3$$
D. $$\frac{M_{1}}{M_{2}}= 2.5$$
E. $$\displaystyle \frac{M_{1}}{M_{2}}= 2.25$$
F. $$\frac{M_{1}}{M_{2}}= 3.5$$
G. None of these
H. $$\displaystyle \frac{M_{1}}{M_{2}}= 1.75$$
I. $$\displaystyle \frac{M_{1}}{M_{2}}= 2$$
J. $$\displaystyle \frac{M_{1}}{M_{2}}= 1.5$$
Answer: C
An object of mass m is attached to a spring.The restoring force of the spring is F=$ - \lambda {x^3},$ where x is the displacement. the oscillation period  depends on the mass, $\lambda $ and oscillation amplitude.suppose the object is initially at rest.If the initial displacement is D then its period is $\tau $ .If the initial displacement is 2D, find the period.(Hint: Use dimension analysis.)

Options:
A. $\tau $
B. 16$\tau $
C. 4$\tau $
D. 10$\tau $
E. 32$\tau $
F. 8$\tau $
G. 12$\tau $
H. $\tau $/2
I. 6$\tau $
J. 2$\tau $
Answer: F
The standard reduction potentials for two reactions are given below:
$$AgCl(s)+e^- \rightarrow Ag_(s)+Cl^- , E^o=0.22V$$
$$Ag_(aq)+e^- \rightarrow Ag_(s)+Cl^- , E^o=0.80 V$$
The solubility product of $AgCl$ under standard conditions of temperature (298 K) is given by

Options:
A. $$1.5 \times 10^{-9}$$
B. $$3.2 \times 10^{-8}$$
C. $$3.2 \times 10^{-11}$$
D. $$1.5 \times 10^{-11}$$
E. $$3.2 \times 10^{-9}$$
F. $$1.5 \times 10^{-10}$$
G. $$3.2 \times 10^{-10}$$
H. $$3.2 \times 10^{-12}$$
I. $$1.5 \times 10^{-8}$$
Answer: G
${ XeF }_{ 6 }+{ H }_{ 2 }O\rightleftharpoons { XeOF }_{ 4 }+2HF;$ equilibrium constant=${ K }_{ 1 }$
${ XeO }_{ 4 }+{ XeF }_{ 6 }\rightleftharpoons { XeOF }_{ 4 }+{ XeO }_{ 3 }{ F }_{ 2 };$ equilibrium constant = ${ K }_{ 2 }$
Then equilibrium constant for the following reaction will be :
$${ XeO }_{ 4 }+2HF\rightleftharpoons { XeO }_{ 3 }{ F }_{ 2 }+{ H }_{ 2 }O$$

Options:
A. $$\dfrac { { K }_{ 1 } + { K }_{ 2 } }{ { K }_{ 1 } - { K }_{ 2 } }$$
B. $${ K }_{ 2 }-{ K }_{ 1 }$$
C. $${ K }_{ 1 }+{ K }_{ 2 }$$
D. $$\dfrac { { K }_{ 2 } }{ { K }_{ 1 } + { K }_{ 2 } }$$
E. $$\dfrac { { K }_{ 2 } }{ { K }_{ 1 } }$$
F. $$\dfrac { { K }_{ 1 } - { K }_{ 2 } }{ { K }_{ 1 } + { K }_{ 2 } }$$
G. $$\dfrac { { K }_{ 1 } \cdot { K }_{ 2 } }{ { K }_{ 1 } + { K }_{ 2 } }$$
H. $$\dfrac { { K }_{ 2 } \cdot { K }_{ 1 } }{ { K }_{ 2 } + { K }_{ 1 } }$$
I. $$\dfrac { { K }_{ 1 } }{ { K }_{ 2 } } $$
Answer: I
What will be the volume of  Cl$_{2}$ at  STP produced during electrolysis of MgCl$_{2}$ which produce 6.5 g Mg (At wt. of Mg =24.3 g ,Cl=35.5 g)

Options:
A. 12.02 Litre
B. 6.099 litre
C. 5.199 litre
D. 5.099 litre
E. 4.999 litre
F. 4.099 litre
G. 3.099 litre
H. 5.99litre
I. 4.599 litre
J. 5.699 litre
Answer: D
A 2 cm diameter coin rests flat on the bottom of a bowl in which the water is which the water is 20 cm deep $\left( { \mu  }_{ w }=4/3 \right) $. if the coin is viewed directly from above, what is the apparent diameter:

Options:
A. 1.5 cm
B. 2.5 cm
C. 2.17 cm
D. 2.33 cm
E. 2.4 cm
F. 2 cm
G. 2.2 cm
H. 1.67 cm
I. 2.67 cm
J. 1.87 cm
Answer: F
Two circular coils made up of identical wires of length 40 cm have respectively 18 and 9 turns and the current flowing through the second coil is 4 times the current through the first coil. The ratio of magnetic induction at their centres is :

Options:
A. 3:2
B. 4:1
C. 1:3
D. 1:4
E. 3:4
F. 1:1
G. 3:1
H. 1:2
I. 2:1
J. 2:3
Answer: H
A 3 Kg sphere dropped through air has a terminal speed of 25 m/s. (Assume that the drag force is -bV) Now suppose the sphere is attached to a spring of force constant $ K = 300 N/m_1 $ and that it ocillates with an initial amplitude of 20 cm. What is the angular frequency of its damped SHM $ (g = 10 m/s^2)? $

Options:
A. 10.01 rad/s
B. 9.998 rad/s
C. 8.995 rad/s
D. 9.001 rad/s
E. 10.00 rad/s
F. 9.005 rad/s
G. 8.990 rad/s
H. 9.000 rad/s
I. 9.010 rad/s
J. 9.008 rad/s
Answer: B
In the given figure two concentric cylindrical region in which time varying magnetic filed is present as shown. From the center to radius $R$ magnetic field is perpendicular into the plane varying as $dB/dt-2k_0$ and in a region from $R$to $2R$ magnetic field is perpendicular out of the plane varying as $dB/dt=4k_0$. Find the induced emf across an area $AB$ of radius $3R$.

Options:
A. $$10R^2k\theta$$
B. $$9R^2k\theta$$
C. None of them
D. $$3R^2k\theta$$
E. $$6R^2k \theta$$
F. $$4R^2k\theta$$
G. $$2R^2k\theta$$
H. $$8R^2k \theta$$
I. $$7R^2k \theta$$
J. $$5R^2k \theta$$
Answer: J
For a saturated solution of $AgCl\quad at{ 25 }^{ \circ  }C.$ specific conductance is $3.41\times { 10 }^{ -6 }{ \Omega  }^{ -1 }{ cm }^{ -1 }$ and that of water used for preparing the solution was$1.60\times { 10 }^{ -6 }{ \Omega  }^{ -1 }{ cm }^{ -1 }.$ The solubility product of AgCl is is $\left[ { \wedge  }^{ \infty  }_{ eq }\left( AgCl \right) =138.30{ \Omega  }^{ -1 }{ cm }^{ -1 }{ equiv }^{ -1 } \right] $

Options:
A. $$1.31 \times 10^{-9}$$
B. $$1.31 \times 10^{-4}$$
C. $$1.74 \times { 10 }^{ -7 }$$
D. $$1.71\times { 10 }^{ -10 }$$
E. $$1.74\times { 10 }^{ -8 }$$
F. $$1.31 \times 10^{-6}$$
G. $$1.31 \times { 10 }^{ -7 }$$
H. $$3.24\times { 10 }^{ -4 }$$
I. $$1.31 \times 10^{-3}$$
J. $$1.31\times { 10 }^{ -5 }$$
Answer: J
A spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same small time t. If the coefficients of friction $\mu$ between the ground and the toy carts are equal, then the magnitude of displacements of the toy carts are in the ratio

Options:
A. $$\frac{S_1}{S_2} = \left( \frac{m_1}{m_2} \right)^{2}$$
B. $$\frac{S_1}{S_2} = \left( \frac{m_1}{m_2} \right)^{5}$$
C. $$\frac{S_1}{S_2} =\lgroup \frac{m_2}{m_1} \rgroup^2$$
D. $$\frac{S_1}{S_2} = \left( \frac{m_2}{m_1} \right)^{4}$$
E. $$\frac{S_1}{S_2} = \left( \frac{m_2}{m_1} \right)^{3}$$
F. $$\frac{S_1}{S_2} = \frac{m_1}{m_2}$$
G. $$\frac{S_1}{S_2} = \left( \frac{m_1}{m_2} \right)^{3}$$
H. $$\frac{S_1}{S_2} =\lgroup \frac{m_1}{m_2} \rgroup^2$$
I. $$\frac{S_1}{S_2} = \left( \frac{m_1}{m_2} \right)^{4}$$
J. $$\frac{S_1}{S_2} = \frac{m_2}{m_1}$$
Answer: C
A man watches a steam boat starting from a point directly in front of him on the opposite bank of river flowing at a speed of $18\ km\ hr^{-1}$. The boat has a velocity $v_{0}$ with respect to river at an angle $\theta_{0}$ with the bank. If the steam boat blows a whistle of frequency $f_{0}$, then for which of the following combinations of $v_{0}$ and $\theta_{0}$ the frequency registered by the man will be highest?

Options:
A. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 70^{\circ}$$
B. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 45^{\circ}$$
C. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 60^{\circ}$$
D. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 40^{\circ}$$
E. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 55^{\circ}$$
F. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 80^{\circ}$$
G. Same for all the above
H. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 30^{\circ}$$
I. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 50^{\circ}$$
J. $$v_{0} = 10\ ms^{-1}, \theta_{0} = 65^{\circ}$$
Answer: C
The standard electrode potential of a metal ion $(Ag | Ag^{\oplus}$ and metal insoluble salt anion $(Ag | AgCl | Cl^{\ominus})$ are related as:

Options:
A. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} + \displaystyle \frac{RT}{F}\, ln \frac{K_{sp}}{[AgCl]}$$
B. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} + \displaystyle \frac{RT}{F}\, ln \frac{K_{sp}}{[Ag^{\oplus}]}$$
C. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} |Ag} +\displaystyle \frac{RT}{F}\, ln \frac{K_{sp}}{[Cl^{\ominus}]}$$
D. $$E^{\ominus}_{Ag^{\oplus} | Ag} = E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} + \displaystyle \frac{RT}{F}\, ln\, \frac{[Cl^{\ominus}]}{K_{sp}}$$
E. $$E^{\ominus}_{Ag^{\oplus} | Ag} | = E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} + \displaystyle \frac{RT}{F}\, ln\, K_{sp}$$
F. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} - \displaystyle \frac{RT}{F}\, ln \frac{K_{sp}}{[Cl^{\ominus}]}$$
G. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} - \displaystyle \frac{RT}{F}\, ln K_{sp}$$
H. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} + \displaystyle \frac{RT}{F}\, ln \frac{K_{sp}}{2}$$
I. $$E^{\ominus}_{Cl^{\ominus} | AgCl | Ag} = E^{\ominus}_{Ag^{\oplus} | Ag} + \displaystyle \frac{RT}{F}\, ln K_{sp}$$
Answer: I
If four identical samples of an ideal gas initially at same state $\left( { P }_{ 0 },{ V }_{ 0 },{ T }_{ 0 } \right) $ are allowed to expand to double their volumes by the following processes:Process I: Isothermal reversible processProcess II: Reversible process ${P}^{2}V=$ constantProcess III: Reversible adiabatic processProcess IV: Irreversible adiabatic expansion against constant external pressure.If the final states of gases are shown by different points in the graph represented, then match each point with the correct process:

Options:
A. $$I-2,II-1,III-4,IV-3$$
B. $$I-4,II-2,III-1,IV-3$$
C. $$I-2,II-1,III-3,IV-4$$
D. $$I-4,II-3,III-2,IV-1$$
E. $$I-3,II-4,III-1,IV-2$$
F. $$I-1,II-3,III-4,IV-2$$
G. $$I-1,II-3,III-2,IV-4$$
H. $$I-3,II-2,III-1,IV-4$$
I. $$I-1,II-2,III-3,IV-4$$
Answer: A
If $K_1$ for a reaction at $25^oC$ is 10 atm, then $K_c$ for the reaction at $40^oC$ will be: (Given: $\Delta H=-8\ kJ$ and anti log (0.067) = 0.1167 and $\Delta n=1$)

Options:
A. $$3.75 \times 10^{-1}M$$
B. $$4.33\times 10^{-1}M$$
C. $$3.95 \times 10^{-1}M$$
D. $$3.5 \times 10^{-1}M$$
E. $$3.3\times 10^{-2}M$$
F. $$4.05 \times 10^{-1}M$$
G. $$3.65 \times 10^{-1}M$$
H. $$4.5\times 10^{-1}M$$
I. $$3.89\times 10^{-1}M$$
J. $$3.45 \times 10^{-1}M$$
Answer: H
A uniform solid cylinder of mass $2kg$ and radius $0.2m$ is released from the rest at the top of a semicircular track of radius $0.7m$ cut in block of mass $M=3kg$ as shown. The block is resting on a smooth horizontal surface and the cylinder rolls down without slipping. The distance moved by the block when the cylinder reaches the bottom of the track is:

Options:
A. $$0.5 \ m$$
B. $$0.6 \ m$$
C. $$0.15 \ m$$
D. $$0.1 \ m$$
E. $$0.4 \ m$$
F. $$0.35 \ m$$
G. $$0.3 \ m$$
H. $$0.7 \ m$$
I. $$0.25 \ m$$
J. $$0.2 \ m$$
Answer: J
An insect of mass m is initially at rest at the one end of a stick length L and mass M, which rests on a smooth horizontal floor. The coefficient of friction between the insect and stick is k. The insect starts moving to reach the other end in shortest possible time. Choose the incorrect statement.

Options:
A. Time taken by the insect to reach the other end is \( t=\sqrt { \dfrac { 2LM }{ k(2M-3m)g } } \)
B. Time taken by the insect to reach the other end is \( t=\sqrt { \dfrac { 2LM }{ k(M+2m)g } } \)
C. The maximum speed acquired by the stick is ${ v }_{ max }=\sqrt { \dfrac { 2kLM{ m }^{ 2 }g }{ (M+m)m } } $
D. The centre of mass of the stick has speed $v=\left[ \dfrac { kmg }{ 3M } \right] t$ w.r.t. horizontal floor at time t
E. Time taken by the insect to reach the other end is \( t=\sqrt { \dfrac { 2LM }{ k(2M-2m)g } } \)
F. Time taken by the insect to reach the other end is \( t=\sqrt { \dfrac { 2LM }{ k(3M+m)g } } \)
G. Time taken by the insect to reach the other end is $t=\sqrt { \dfrac { 2LM }{ k(2M+m)g } } $
H. Time taken by the insect to reach the other end is \( t=\sqrt { \dfrac { 2LM }{ k(M-m)g } } \)
I. The magnitude of the linear momentum of the insect at time 't' is equal to kmgt
J. Time taken by the insect to reach the other end is $t=\sqrt { \dfrac { 2LM }{ k(M+m)g } } $
Answer: J
Two particles each of mass $m$ are revolving is circular orbits of radius $r=5R$ in opposite directions with orbital speed ${v_0}.$ They collide perfectly inelastically and fall to the ground$.$ The speed of combined mass on striking the ground will be

Options:
A. $$2\sqrt{3{v_0}}$$
B. $$2\sqrt {2{v_0}} $$
C. $$2{v_0}$$
D. $$\sqrt{3v_0}$$
E. $$3\sqrt{2{v_0}}$$
F. $${v_0}$$
G. $$\sqrt{5v_0}$$
H. $$\sqrt {2{v_0}}$$
I. $$\sqrt{6v_0}$$
Answer: B
$ H_2 O (l) \longrightarrow H_2 O (vapour) $$ \begin{matrix} 1\quad atm & 0.1\ atm \ 373\quad K & 373\  K \end{matrix} $$ \Delta S $ for above process is:(Given  $ : \Delta_{vap} H = 40.668 kJ / mol ) $

Options:
A. $$11.818\ J / Kmol$$
B. $$ 12.818\ J / Kmol $$
C. $$ 128.18\ J /Kmol $$
D. $$ 109.03\  J / Kmol $$
E. $$108.03\ J / Kmol$$
F. $$112.818\ J / Kmol$$
G. $$118.03\ J / Kmol$$
H. $$13.818\ J / Kmol$$
I. $$ 10.903\ J / Kmol $$
Answer: B
Find the amount of work done to increase the temperature of one mole of ideal gas by $30^0C$ it is expanding under the condition $V\propto T^{1/3}(R=8.31J/mol-k)$

Options:
A. $$16.62J$$
B. $$16.620J$$
C. $$1662J$$
D. $$166.20J$$
E. $$16620J$$
F. $$1.662J$$
G. $$166.2J$$
Answer: G
Two jars $A$ and $B$ contain helium gas at pressure of $1 \,atm$ and $2 \,atm$ respectively at room temperature. They are mixed. If $v_1$ is the r.m.s. velocity of molecules in $A, v_2$ of those in $B$ and $v$ that of mixture, then correct statement is:

Options:
A. $v > v_1$ and $v_2$
B. $$v < v_1 \, \text{and} \, v > v_2$$
C. $v$ is between $v_1 \& v_2$
D. $v > v_1$ and $v < v_2$
E. $$v > v_1 \, \text{and} \, v_2$$
F. $$v > v_1 \, \text{and} \, v < v_2$$
G. $$v < v_1 \, \text{and} \, v < v_2$$
H. $v > v_1$ and $v > v_2$
I. $$v < v_1 and v_2$$
J. $$v_1 = v_2 = v$$
Answer: I
Let the solubilities of $AgCl$ in water, in $0.01M CaCl_2$,in $0.01M NaCl$ and $0.05M AgNo_3$ be $S_1,S_2,S_3$ and $S_4$ respectively. Which of the following relationship between these quantities is correct?

Options:
A. $$S_4 > S_2, > S_3 > S_1$$
B. $$S_1 > S_2, = S_3 > S_4$$
C. $$S_1 > S_4, > S_2 > S_3$$
D. $$S_1 > S_3, > S_2 > S_4$$
E. $$S_1 > S_3, > S_4 > S_2$$
F. $$S_1 > S_2, > S_3 > S_4$$
G. $$S_1 > S_4, > S_3 > S_2$$
Answer: F
An aqueous solution of $CH_3COOH$ has a pH = $3$ and acid dissociation constant of $CH_3COOH$ is $10^{-5}$. What will be the concentration of acid taken initially?

Options:
A. $0.11$M
B. 0.092 M
C. 0.098 M
D. $0.101$M
E. 0.099 M
F. $0.1$M
G. 0.102 M
H. 0.097 M
I. $0.09$M
J. 0.095 M
Answer: F
Which pair of reagents,mixed in the appropriate proportion, could make buffer of pH range is $7-8$ ?

Options:
A. $$N{H_3}\,\,and\,\,NaN{O_2}\left( {{K_a}\,\,for\,\,\,HN{O_2} = 4.6 \times {{10}^{ - 4}}} \right)$$
B. $$HClO\,\,and\,NaClO\left( {{K_a}\,\,for\,\,\,HClO = 3.0 \times {{10}^{ - 8}}} \right)$$
C. $$N{H_3}\,\,and\,\,N{H_4}Cl\left( {{K_6}\,\,for\,\,\,N{H_3} = 1.8 \times {{10}^{ - 5}}} \right)$$
D. $${C_2}{H_5}N\,\,and\,\,HCl\left( {{K_b}\,\,for\,\,\,{C_2}{H_5}N = 1.8 \times {{10}^{ - 9}}} \right)$$
E. $$HClO\,\,and\,\,NaClO\left( {{K_a}\,\,for\,\,\,HClO = 3.0 \times {{10}^{ - 7}}} \right)$$
F. $$N{H_3}\,\,and\,\,N{H_4}Cl\left( {{K_b}\,\,for\,\,\,N{H_3} = 1.8 \times {{10}^{ - 3}}} \right)$$
G. $$N{H_3}\,\,and\,\,N{H_4}Cl\left( {{K_b}\,\,for\,\,\,N{H_3} = 1.8 \times {{10}^{ - 6}}} \right)$$
H. $$HClO\,\,and\,\,NaClO\left( {{K_a}\,\,for\,\,\,HClO = 3.0 \times {{10}^{ - 6}}} \right)$$
I. $$N{H_3}\,\,and\,\,N{H_4}Cl\left( {{K_b}\,\,for\,\,\,N{H_3} = 1.8 \times {{10}^{ - 4}}} \right)$$
Answer: C
Assertion: In the purely resistive element of a series LCR, AC circuit the maximum value of rms current increases with increase in the angular frequency of the applied e.m.f.
Reason: $\displaystyle { I }_{ max }=\frac { { \varepsilon  }_{ max } }{ z } ,z=\sqrt { { R }^{ 2 }+{ \left( \omega L-\frac { I }{ \omega C }  \right)  }^{ 2 } } $
where $\displaystyle { I }_{ max }$ is the peak current in a cycle.

Options:
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If Assertion is correct but Reason is not the correct explanation of Assertion.
C. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
D. If both Assertion and Reason are correct and Reason is not the correct explanation of Assertion.
E. If both Assertion and Reason are incorrect.
F. If Assertion is correct but Reason is incorrect.
G. If Assertion is incorrect but Reason is correct.
H. If both Assertion and Reason are correct, but Reason is the correct explanation of Assertion.
I. If Assertion is correct but Reason is the correct explanation of Assertion.
J. If Assertion is correct but Reason is correct.
Answer: F
Two communicating vessels contain mercury. The diameter of one vessel is four times larger than the diameter of the other. A column of water of height $h_0=70$ cm is poured into the left hand vessel (the narrower one). How much will be mercury level rise in the right hand vessel? ( Specific density of mercury= $13.6$)

Options:
A. 1.2 cm
B. $0.9$ cm
C. $0.3$ cm
D. $0.8$ cm
E. $0.1$ cm
F. 0.6 cm
G. 1.1 cm
H. 0.5 cm
I. $1.0$ cm
J. $0.7$ cm
Answer: I
A boy of mass 50 kg is standing at one end of a 9.0 m long boat of mass 100 kg that is floating motionless on a calm lake. The boy walks to the other end of the boat and stops there. The boat also moves and finally stops due to water resistance. If force of water resistance is proportional to velocity of the boat relative to water. what is the magnitude of the net displacement s of the boat?

Options:
A. s = 1.5 m
B. s = 0.0 m
C. s = 0.75 m
D. s = 0.5 m
E. s = 3.0 m
F. s < 3.0 m
G. s = 1.0 m
H. s = 2.0 m
I. s > 3.0 m
J. s = 2.5 m
Answer: B
A metal ball immersed in alcohol weight $W_1$ at $0^{\circ}C$ and $W_2$ at $59^{\circ}C$. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

Options:
A. $$W_1 = (W_2/4)$$
B. $$W_1 = W_2 + 1$$
C. $$W_1 = W_2 - 2$$
D. $$W_1 = W_2 + 2$$
E. $$W_1 = W_2$$
F. $$W_1 < W_2$$
G. $$W_1 > W_2$$
H. $$W_1 = W_2 - 1$$
I. $$W_1 = (W_2/2)$$
J. $$W_1 = (W_2/3)$$
Answer: F
A sound wave starting from source S, follows two paths SEFD and SEABFD. If AB = l, AE = BF = 0.6 l and wavelength of wave is $\lambda = 11$ m. If maximum sound heard at D, then minimum value of length l is

Options:
A. 7 m
B. 12 m
C. 2.5 m
D. 4 m
E. 5 m
F. 8 m
G. 11 m
H. 9 m
I. 10 m
J. 6 m
Answer: H
The following two reactions are known :$fe_2O_3(s)+3CO(g)\rightarrow 2Fe(s)+3CO_2(g); \Delta H=-26.8 kJ$$FeO(s)+CO(g)\rightarrow Fe(s)+CO_2(g);\Delta H=-16.5 kJ$Correct target equation is $Fe_2O_3(s) + CO(g) \rightarrow 2FeO(s)+CO_2(),\Delta H=?$

Options:
A. -13.3 kJ
B. +6.2 kJ
C. -33.3 kJ
D. -40.3 kJ
E. +10.3 kJ
F. -43.3 kJ
G. -36.6 kJ
H. -10.3 kJ
I. +43.3 kJ
J. -40.1 kJ
Answer: F
A sample of $50.0$ mL of $0.10$ M $NH_3$
$(K=1.8 \times 10^{-5})$ is titrated with $0.10$ M HCl. Calculate the pH at
the equivalence point.

Options:
A. $$2.87$$
B. 6.88
C. $$6.98$$
D. 5.98
E. 5.68
F. 6.78
G. 7.58
H. $$5.28$$
I. $$7.78$$
J. 7.28
Answer: H
The number of geometric isomers possible for the complex $[CoL_2Cl_2]^-$ (unsymmetrical didentate ligand $L = H_2NCH_2CH_2O^-$)  is:

Options:
A. 9
B. 5
C. 7
D. 8
E. 4
F. 2
G. 10
H. 3
I. 6
J. 12
Answer: B
An ideal gas can be expanded from an initial state to a certain volume through two different processes (i) $PV^2 = constant\:and\:(ii)P = KV^2$ where K is a positive constant. Based on the given situation, choose the correct statements

Options:
A. Total heat given to the gas in case (ii) is equal to in (i)
B. Final temperature in (ii) will be less than in (i)
C. Total heat given to the gas in case (ii) is less than in (i)
D. Total heat given to the gas in case (ii) is greater than in (i)
E. Total heat given to the gas in case (i) is less than in (ii)
F. Total heat given to the gas in case (i) is equal to in (ii)
G. Total heat given to the gas in case (i) is greater than in (ii)
H. Final temperature in (ii) will be greater than in (i)
I. Final temperature in (ii) will be equal to in (i)
Answer: D
The Bohr radius of the fifth electron of phosphorous atom (atomic number $= 15)$ acting as a dopant in silicon (relative dielectric constant $= 12)$ is __________ $A^{\circ}$.

Options:
A. 1.8\ A^{0}
B. $4.8\ A^{0}$.
C. 2.8\ A^{0}
D. 5.8\ A^{0}
E. 7.8\ A^{0}
F. 9.8\ A^{0}
G. $3.8\ A^{0}$.
H. 4.2\ A^{0}
I. $6.8\ A^{0}$.
J. $8.8\ A^{0}$.
Answer: G
Calculate the work done during combustion of $0.138$kg of ethanol, $C_2H_5OH_{(l)}$ at $300$K. [Given: $R=8.314$ $Jk^{-1}$ $mol^{-1}$; molar mass of ethanol $=46$ g $mol^{-1}$.]

Options:
A. $$37410\ J$$
B. $$3741\ J$$
C. $$2494\ J$$
D. $$-7482\ J$$
E. $$74820\ J$$
F. $$7482\ J$$
G. $$-3741\ J$$
H. $$-748.2\ J$$
I. $$-2494\ J$$
J. $$748.2\ J$$
Answer: F
The standard reduction potentials for two half -cell reaction are given below ,${ Cd }^{ 2+ }(aq)+{ 2e }^{ - }\longrightarrow Cd(s)$,  ${ E }^{ o }=-0.40V$  
${ Ag }^{ + }(aq)+{ e }^{ - }\longrightarrow Ag(s)$  ${ E }^{ o }=-0.80V$
The standard free energy change for the reaction 
$${ 2Ag }^{ + }(aq)+Cd(s)\longrightarrow 2Ag(s)+{ Cd }^{ 2+ }(q)$$

Options:
A. -231.6 KJ
B. 113.8 KJ
C. 110.8 KJ
D. -111.8 KJ
E. -115.5 KJ
F. 231.6 KJ
G. 115.5 KJ
H. 111.8 KJ
I. 112.8 KJ
J. 111.6 KJ
Answer: H
A sound source is moving with uniform speed along a curve $y=A\sin kx$ in $x-y$ plane. Three detectors are placed at $\left(\dfrac{\pi}{2k},10A\right),\left(\dfrac{\pi}{2k},0\right)$ and $\left(\dfrac{\pi}{2k},-10A\right)$, When the sound source crosses the point $\left(\dfrac{\pi}{2k},A\right)$, the frequency registered by the detectors are $f_{1}, f_{2}$ and $f_{3}$ respectively. If the waves $(f_{1}, f_{2}, f_{3})$ detected are emitted at $x$ co-ordinates $x$, such that $0<x<\pi/2k$ then:

Options:
A. $$f_{1}<f_{3}<f_{2}$$
B. $$f_{1}<f_{2}>f_{3}$$
C. $$f_{1}>f_{3}>f_{2}$$
D. $$f_{2}=\dfrac{f_{1}+f_{3}}{3}$$
E. $$f_{1}>f_{2}>f_{3}$$
F. $$f_{1}<f_{2}<f_{3}$$
G. $$f_1<f_2<f_3$$
H. $$f_{2}=\dfrac{f_{1}+f_{3}}{2}$$
I. $$f_{1}=f_{2}=f_{3}$$
J. $$f_{2}=\dfrac{f_{1}+f_{3}}{4}$$
Answer: E
The displacement of a particle executing periodic motion is given by $y=4 cos^2(0.5t) \sin(1000 t)$. The given expresion is composed by minimum:

Options:
A. Nine $SHMs$
B. Six $SHMs$
C. One $SHM$
D. Seven $SHMs$
E. Eight $SHMs$
F. Two $SHMs$
G. Five $SHMs$
H. No $SHM$
I. Four $SHMs$
J. Three $SHMs$
Answer: C
Two blocks of masses 3kg and 2kg are placed beside each other in contact with each other on a rough horizontal surface. A horizontal force of 20 N is applied on 3 kg the coefficient of friction between blocks and the surface is 0.1 and $g = 10ms^{2}$ The force of contact between the two blocks is

Options:
A. $$12N$$
B. $$11N$$
C. $$6N$$
D. $$7N$$
E. $$14N$$
F. $$5N$$
G. $$9N$$
H. $$8N$$
I. $$10N$$
J. $$4N$$
Answer: C
25 mL of an aqueous solution of KCI was found to require 20 mL of 1 M $AgNO_{3}$ solution when titrated using a $K_{2}CrO_{4}$ as indicator. Depression in freezing point of KCI solution with 100% ionisation will be :
$(K_{f}=2.0 mol^{-1}kg$ and molarity=molality)

Options:
A. 4.0
B. 5.0
C. 4.8
D. 0.8
E. 5.4
F. 3.2
G. 1.6
H. 6.4
I. 4.6
J. 5.2
Answer: B
A metal rod $AB$ of length $l$ is rotated with a constant angular velocity $\omega$ about an axis passing through $O$ and normal to its length. Potential difference between ends of rod in absence of external magnetic field is: (where $e=$ electric charge)

Options:
A. $$\dfrac{m\omega^{2}l^{2}}{10e}$$
B. $$\dfrac{m\omega^{2}l^{2}}{5e}$$
C. $$\dfrac{m\omega^{2}l^{2}}{12e}$$
D. $$\dfrac{m\omega^{2}l^{2}}{4e}$$
E. $$\dfrac{m\omega^{2}l^{2}}{6e}$$
F. $$\dfrac{m\omega^{2}l^{2}}{16e}$$
G. zero
H. $$\dfrac{m\omega^{2}l^{2}}{2e}$$
I. $$\dfrac{m\omega^{2}l^{2}}{8e}$$
J. $$\dfrac{m\omega^{2}l^{2}}{3e}$$
Answer: D
Which of the following does not represent radius of the atom correctly?
(i) Simple cubic cell: Radius $=\dfrac{a}{2}$
(ii) Face centred cubic cell: Radius $=\dfrac{a}{3\sqrt{3}}$
(iii) Body centred cubic cell : Radius $=\dfrac{\sqrt{3}}{4}a$

Options:
A. $$(i)$$
B. $(i)$ and $(ii)$
C. $(i)$ and $(iii)$
D. $(i)$ and $(ii)$ and $(iv)$
E. $(ii)$ and $(iv)$
F. $(ii)$ and $(iii)$
G. $$(iii)$$
H. $$(ii)$$
I. $(i)$ and $(ii)$ and $(iii)$
J. $(i)$ and $(iv)$
Answer: B
Two moles of an ideal monatomic gas is taken through a cycle  $A B C A$  as shown in the  $P - T$  diagram. During the process  $A B ,$  pressure and temperature of the gas vary such that  $P T =constant,$  If  $T _ { 1 } = 300 \mathrm { K } ,$  calculate the work done on the gas is the process  $A B$

Options:
A. 1000 R
B. $$1200 R$$
C. 1400 R
D. 900 R
E. $$200 R$$
F. $$700 R$$
G. 1500 R
H. None of these
I. 1100 R
J. 1300 R
Answer: B
A 1 litre solution of $pH=1$ is diluted upto 10 times. What volume of a solution with $pH=2$ needs to be added in diluted solution so that the final pH remains '2'?

Options:
A. 30 litre
B. 15 litre
C. 100 litre
D. 5 litre
E. 10 litre
F. 25 litre
G. 50 litre
H. 75 litre
I. 1 litre
J. 20 litre
Answer: F
Rain drops are falling with velocity $ec v = (4\hat i - 4\hat j)\,m/s$, where $\hat i\,and\,\hat j$ are unit vectors along the horizontal and vertically direction. If a man is walking on the horizontal road with the velocity of $\hat i\,m/s$ along with the umbrella then the direction in which man should hold his umbrella to save himself from the rain drops is

Options:
A. Vertically upward
B. ${47^ \circ }$ with vertical
C. ${54^ \circ }$ with vertical
D. ${45^ \circ }$ with vertical
E. ${52^ \circ }$ with vertical
F. ${53^ \circ }$ with vertical
G. ${60^ \circ }$ with horizontal
H. ${48^ \circ }$ with vertical
I. ${51^ \circ }$ with vertical
J. ${37^ \circ }$ with vertical
Answer: F
The compressibility factor $z=\dfrac{PV}{nRT}$ of a gas above $T=\dfrac{a}{Rb}$ will be:

Options:
A. Always equal to 0.95
B. Always equal to 1.05
C. Always equal to unity
D. Always equal to 0.98
E. Depends on pressure
F. Always equal to 0
G. Always greater than Unity
H. Always equal to 1
I. Always equal to 1.02
J. Always less than Unity
Answer: G
Determine resonance energy of benzene $[{C}_{6}{H}_{6}(l)]$ from the following information:$\Delta {H}_{f}^{o}$ of ${C}_{6}{H}_{6}(l)=+49kJ$;$\Delta {H}_{f}^{o}$ of ${C}_{2}{H}_{2}(g)=+75kJ;$   $\Delta {H}_{v}^{o}$ of ${C}_{6}{H}_{6}(l)=+45kJ$$B.E$ of $C\equiv C=930kJ/mol$;  $C=C=615kJ/mol$;    $C-C=348kJ/mol$

Options:
A. $$R.E=-32kJ/mol$$
B. R.E=+160kJ/mol
C. $$R.E=-230kJ/mol$$
D. R.E=+230kJ/mol
E. None of these
F. $$R.E=+130kJ/mol$$
G. $$R.E=+32kJ/mol$$
H. $$R.E=+150kJ/mol$$
I. R.E=-130kJ/mol
Answer: A
A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle ${ 30 }^{ \circ  }$) where it runs into a spring if negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force of the spring is 400 $Nm^{ -1 }$ the value of d is (take g=$10ms^{ -2 }$)

Options:
A. 37.5 cm
B. 52.5 cm
C. 25 cm
D. 27.5 cm
E. 62.5 cm
F. None of above
G. 75 cm
H. 30 cm
I. 32.5 cm
J. 50 cm
Answer: C
A uniform bar of length $6a$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane with speed $2v$ and $v$ respectively, strike the bar (as shown in figure) and stick to the bar after collision. C represents centre of mass of bar. Denoting angular velocity (about the centre of mass), total energy and centre of mass by $\omega$, E and $v_c$ respectively, then after collision we have

Options:
A. $$\omega = \displaystyle\frac{3v}{5a}$$
B. $$E = \displaystyle\frac{7mv^2}{5}$$
C. $$E = \displaystyle\frac{4mv^2}{5}$$
D. $$E = \displaystyle\frac{3mv^2}{5}$$
E. $$E = \displaystyle\frac{mv^2}{5}$$
F. $$E = \displaystyle\frac{2mv^2}{5}$$
G. $$E = \displaystyle\frac{5mv^2}{6}$$
H. $$E = \displaystyle\frac{4mv^2}{6}$$
Answer: D
Multiple Correct Answers Type
Consider the quantities : $x = \dfrac{E}{b}, y = \dfrac{1}{\mu_0\epsilon_0}$, and $z =\dfrac{l}{CR}$.
Here , l is the length of a wire, C is the capacitance, and R is a resistance. All other symbols have usual meanings. Then

Options:
A. x and z have the same dimensions.
B. y and z have different dimensions
C. None of the above three pairs have the same dimensions.
D. y and z have the same dimensions.
E. y and z have different dimensions.
F. x and y have the same dimensions.
G. y and z have the same dimensions, but with a typo in the variable (e.g., y and z have the sme dimensions).
Answer: D