MikaStars39/nano-eval huggingface dataset:
The earth is just an approximate sphere . if the interior contained matter which is not of the same density everywhere , then on the surface of the earth, the acceleration due to gravity.

Options:
A. Will be the same value everywhere but will always be directed towards the center
B. Will have the same value everywhere but not directed towards the center
C. Will vary in both value and direction depending on the location on the surface
D. Cannot be zero at any point
E. Will be the same value everywhere but will always be directed away from the center
F. Will be same value everywhere but not directed towards the center.
G. Will vary in both value and direction but will always be directed towards the center
H. Will vary in value but will always be directed towards the center
I. Will be zero at some points
J. Will be focused on the center but not the same everywhere
Answer: D
A body is dropped from a height $h$ under acceleration due to gravity $g$. If $t_1$ and $t_2$ are time intervals for its fall for first half and the second half distance. The relation between them is

Options:
A. $$t_1 = 2_{t_2}$$
B. $$t_1 = 1.236_{t_2}$$
C. $$t_1 = 1.8_{t_2}$$
D. $$t_1 = 2.41_{t_2}$$
E. $$t_1 = 0.5_{t_2}$$
F. $$t_1 = 1.414_{t_2}$$
G. $$t_1 = 4_{t_2}$$
H. $$t_1 = 0.707_{t_2}$$
I. $$t_1 = 1.732_{t_2}$$
J. $$t_1 = 2.414_{t_2}$$
Answer: J
A particle with charge q moves inside a cyclotron, the electric, the electric and magnetic field are given by $ \bar E =E_0 $ $ [cos \omega t i-sin \omega t j] $ and $\bar B=B-o \hat k $ where $ \omega =qB_o / m $ the number of revolution in which its speed reaches 0.1c is

Options:
A. $$\frac { 0.1\quad B_{ o }C }{ 6 E_{ o } }$$
B. $$\frac { 0.1\quad B_{ o }C }{ 7 E_{ o } }$$
C. $$\frac { 0.1\quad B_{ o }C }{ 5 E_{ o } }$$
D. $$ \frac { 2 B_{ o }C }{ E_{ o } } $$
E. $$ \frac { B_{ o }C }{ 2 E_{ o } } $$
F. $$ \frac { 0.1\quad B_{ o }C }{ 2\pi E_{ o } } $$
G. $$\frac { 0.1\quad B_{ o }C }{ 8 E_{ o } }$$
H. $$ \frac { 0.1\quad B_{ o }C }{ E_{ o } } $$
I. $$\frac { 0.1\quad B_{ o }C }{ 4 E_{ o } }$$
J. $$\frac { 0.1\quad B_{ o }C }{ 3 E_{ o } }$$
Answer: H
What is the MP of benzene if $\Delta_{fusion} = 9.95 \,kJ/mol$ anel $\Delta S_{fusion} = 35.7 \,J/k-mol$

Options:
A. $$288.7^o C$$
B. $$283.7^o C$$
C. $$278.7^o C$$
D. $$283.7 \,K$$
E. $$300 \,K$$
F. $$288.7 \,K$$
G. $$273.7 \,K$$
H. $$298 \,K$$
Answer: C
The vapour density of a sample of hydrogen fluoride gas is measured by an experiment as $20$. It may represent that $(F=19)$

Options:
A. some molecules of hydrogen fluoride are in tetramer form
B. some hydrogen fluoride molecules are dissociated
C. all hydrogen fluoride molecules are in dimer form
D. some molecules of hydrogen fluorine are in monomer form
E. some molecules of hydrogen fluoride are dissociated
F. all hydrogen fluoride molecules are in trimer form
G. some hydrogen fluorine molecules are in dimer form
H. some hydrogen fluorine molecules are in trimer form
I. some molecules of hydrogen fluoride are in dimer form
J. all hydrogen fluoride molecules are in monomer form
Answer: H
A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ $(m_1>m_2)$. The masses are moving vertically. If the acceleration of the system is $g/8$, then:

Options:
A. tension in the string $=\displaystyle \frac{11}{8}(m_2 g)$
B. $$\displaystyle\frac{m_1}{m_2}=\frac{9}{7}$$
C. $$\displaystyle\frac{m_1}{m_2}=\frac{4}{3}$$
D. tension in the string $=\displaystyle \frac{9}{8}(m_1 g)$
E. tension in the string $=\displaystyle \frac{7}{8}(m_2 g)$
F. tension in the string $=\displaystyle \frac{5}{8}(m_1 g)$
G. $$\frac{7}{8}(m_1 g)$$
H. tension in the string $=\displaystyle \frac{3}{4}(m_1 g)$
I. tension in the string $=\displaystyle \frac{11}{8}(m_1 g)$
Answer: B
For the cell prepared from electrode $A$ and $B$, electrode $A$: $\dfrac{Cr_2O_7{^{2-}}}{Cr^{3+}}$ , $E^o{_{red}}$ = + 1.33 V and electrode $\dfrac{Fe^{3+}}{Fe^{2+}}$, $E^o{_{red}}$ = 0.77 V, which of the following statement is not correct?

Options:
A. $A$ will be positive electrode
B. The standard e.m.f. of the cell will 0.56 V
C. The electrons will flow $B$ to $A$ (in the outer circuit) when connections are made
D. None of the above
Answer: A
A particle with mass m and initial speed ${V_0}$ is subjected to a velocity-dependent damping force of the form $b{V^n}$ . The stopping time $\Delta t$ depends on m, ${V_0}$ and b. Begin with writing $\Delta t = A{m^lpha }{b^\beta {V_0}^\gamma $; powers $lpha ,\,\beta ,\,and\,\gamma $ will be

Options:
A. $$\alpha = 1,\,\beta = -1,\,\gamma = n + \frac{1}{2}$$
B. $$\alpha = 1,\,\beta = -1,\,\gamma = 1 - n/2$$
C. $$\alpha = 1,\,\beta = -1,\,\gamma = 1 + n$$
D. $$ \alpha = 1, \, \beta = -1, \, \gamma = 1 - n $$
E. $$ \alpha = 1, \, \beta = -1, \, \gamma = n - 1 $$
F. $$ \alpha = 1, \, \beta = 1, \, \gamma = 1 - n $$
G. $$\alpha = 1,\,\beta = -1,\,\gamma = 1 + n/2$$
H. $$\alpha = 1,\,\beta = -1,\,\gamma = n + 1$$
I. $$ \alpha = -1, \, \beta = -1, \, \gamma = 1 - n $$
J. $$ \alpha = 2 - n, \, \beta = -1, \, \gamma = 2 $$
Answer: F
The weight of silver (eq. wt. $= 108)$ displaced by that quantity of current which displaced $5600\ mL$ of hydrogen at STP is

Options:
A. $$54 g$$
B. $$108 g$$
C. $$216 g$$
D. None of these
E. $$10.8 g$$
F. $$21.6 g$$
G. $$540 g$$
H. $$5.4 g$$
Answer: B
The transverse displacement y(x, t) of a wave on a string is given by y(x, t) = $ e ^ { - \left( 2 x ^ { 2 } + b t ^ { 2 } + 2 \sqrt { a b } a \right) } $. This represents a

Options:
A. standing wave of frequency $ \frac { 1 } { \sqrt { b } } $
B. wave moving in -x-direction with speed $ \sqrt { ToWorld standards of \frac { b } { a } } $
C. wave moving in -x-direction with speed $ \sqrt { \frac { a } { b } } $
D. wave moving in + x-direction with speed $ \sqrt { \frac { 2b } { a } } $
E. standing wave of frequency $ \sqrt { b } $
F. wave moving in + x-direction with speed $ \sqrt { \frac { b } { 2a } } $
G. wave moving in + x-direction with speed $ \sqrt { \frac { b } { a } } $
H. wave moving in -x-direction with speed $ \sqrt { \frac { b } { a } } $
Answer: H
Electrolysis can be used to determine atomic masses. A current of $0.550$  A deposits $0.55 $ g of a certain metal in $100$ minutes. Calculate the atomic mass of the metal is $ n = 3$ :

Options:
A. $$47.75$$
B. $$100$$
C. 48.50
D. $$144.75$$
E. $$48.25$$
F. $$47.50$$
G. $$145.00$$
H. $$45.0$$
I. $$147.00$$
J. $$146.00$$
Answer: B
A  body of mass $10  kg$ lies on a rough inclined plane of inclination $\displaystyle \theta =\sin ^{-1}\left ( \frac{3}{5} \right )$ with the horizontal. When the force of $30 N$ is applied on the block parallel to an upward the plane, the total force by the plane on the block is nearly along:

Options:
A. $$OF$$
B. $$OD$$
C. $$OB$$
D. $$OX$$
E. $$OC$$
F. $$ON$$
G. $$OE$$
H. $$OA$$
I. $$OG$$
J. $$OH$$
Answer: B
Two blocks of $7kg$ and $5kg$ are connected by a heavy rope of mass $4kg$ and an upward force of $200N$ is applied on the upper block as shown in figure. Ratio of tension at the top P and mid-point Q of the heavy rope is ($g=10m{s}^{-2}$)

Options:
A. more than 1.5
B. less than 1
C. less than 3
D. more than 2.3
E. more than 2.5
F. less than 2
G. more than 2
H. more than 1
I. less than 1.5
J. more than 3
Answer: F
For the reaction: $N_2(g) +3H_2(g) \rightarrow 2NH_3(g)$, $\Delta H^\circ =-123.77 \: KJ\: mol^{-1}$ at $727^\circ C$. Given below is the data of $C_p$. The heat of formation of ammonia in $KJ\: mol^{-1}$ at $27^\circ C$ is
Substance     $N_2$     $H_2$     $NH_3$
     $C_p$           3.5R     3.5R     4R

Options:
A. +88.85
B. -44.44
C. -44.42
D. -44.43
E. -88.86
F. -88.85
G. -44.41
H. +44.42
I. -88.84
J. -88.83
Answer: C
For the standardization of $Ba(OH)_{2}$ solution, 0.204 g of potassium acid phthalate was weighed which was then titrated with $ Ba(OH)_{2}$ solution. The titration indicated equivalence at 25.0 ml of $Ba(OH)_{2} $ solution. The reaction involved is:$ KHC_{8} H_{4}O_{4} + Ba (OH)_{2} \rightarrow H_{2}O+K^{+} +Ba^{2+} +C_{8}H_{4} O_{4}^{2-}$The molarity of the base solution is (K = 39)

Options:
A. 0.0175M
B. 0.03M
C. 0.04M
D. 0.022M
E. 0.035M
F. 0.002M
G. 0.05M
H. 0.01M
I. 0.015M
J. 0.025M
Answer: F
The system shown in the figure is released from rest with the spring in the unstretched position. The spring is attached with the ground. The mass $2\ kg$ descends a distance of $1\ m$ on the inclined plane before it stops. The moment of inertia of the pulley is $2\ kg\ m^{2}$. There is no friction anywhere. The spring constant $k$ of the spring is nearly (Take $g = 10\ m/s^{2})$.

Options:
A. None of these
B. $$35\ N/m$$
C. 50\ N/m
D. $$45\ N/m$$
E. 65\ N/m
F. 40\ N/m
G. 30\ N/m
H. 55\ N/m
I. $$70\ N/m$$
J. 60\ N/m
Answer: B
pH of following buffer solution : $2\times 10^{-2}MCH_{3}COOH+3\times 10^{-2}M(CH_{3}COO)_{2}Ca.$  (pKa of $CH_{3}COOH= 4.75$

Options:
A. 5.23
B. 4.25
C. 4.24
D. 4.23
E. 4.27
F. 8.77
G. 4.73
H. 7.0
I. 4.29
J. 4.77
Answer: E
For a solution obtained by mixing equal volumes of $0.02\ M\ KOH$ solution & $0.2\ M\ B$ (weak diacidic base $K_{b_{1}}-10^{-7}$ & $K_{b_{2}}-10^{-14}$) solution:

Options:
A. pH=11.5
B. pH=10
C. $$[BH^{+}]=10^{-6}\ M$$
D. $$[BH^{2+}_{2}]=10^{-18}\ M$$
E. $$pH=12$$
F. pH=12.5
G. pH=11
H. $$All\ of\ these$$
I. pH=10.5
J. pH=10.8
Answer: E
M solution of three sodium salts NaX, NaY and NsZ have pH 7.0,9.0 and 11.0 respectively. Which of the following is correct order of increasing acidic strength for acids HX ,HY and HZ/

Options:
A. $$HY < HZ < HX$$
B. $$HX=HY=HZ$$
C. $$HZ < HX < HY$$
D. $$HY < HX < HZ$$
E. $$HZ < HX = HY$$
F. $$HX > HY > HZ$$
G. $$HX < HZ < HY$$
H. $$HX < HY = HZ$$
Answer: F
Consider the titration of 0.1000 M $NH_{3}(K_{b}=1.76\times 10^{-5})$ with 0.1000 M $HNO_{3}$. The pH at the equivalence point is

Options:
A. between 7.5 and 9.5
B. between 1.5 and 3.5
C. between 3.5 and 5.5
D. between 2.0 and 4.0
E. between 4.0 and 6.0
F. approximately 7.0
G. between 5.5 and 7.5
H. between 2.5 and 4.5
I. between 3.0 and 5.0
J. between 4.5 and 6.5
Answer: J
The reactions taking place in the dry cell are:Anode: $Zn\rightarrow Zn^{2+}+2e^{-} $Cathode: $ 2MnO_{2}+2NH_{4}^{+}+2e^{-}\rightarrow Mn_{2}O_{3}+2NH_{3}+H_{2}O $The minimum mass of reactants obtained, if a dry cell is to generate $0.25 A$ for $9.65\ h$, are:(Given: Molar mass of $Mn = 55 g/mol$ , $Zn = 65.4g/mol$) (neglect any other chemical reactions occurring in the cell)

Options:
A. 1.65\,g\,NH_{4}^{+}
B. 1.64\,g\,NH_{4}^{+}
C. 1.68\,g\,NH_{4}^{+}
D. $$ 2.943\,g\,Zn $$
E. $$ 3.915\,g\,MnO_{2} $$
F. $$ 1.62\,g\,NH_{4}^{+}$$
G. $$ 7.83\,g\,MnO_{2} $$
H. 1.61\,g\,NH_{4}^{+}
I. 1.63\,g\,NH_{4}^{+}
J. 1.60\,g\,NH_{4}^{+}
Answer: F
A quantity of $ 6.539\times 10^{-2}\,g $ of metallic zinc is added to 100 ml of saturated solution of AgCl. The value of $log \dfrac{[Zn^{2+}]}{[Ag^{+}]^{2}}$ is $(Zn = 65.39) $

Options:
A. 528.8
B. 52.24
C. 26.44
D. 52.84
E. 52.48
F. 5.288
G. 52.28
H. 264.4
I. 52.79
J. 52.44
Answer: I
$35$ drops of a liquid has density $1.2$ g/mL, mass $2.4$ g. Assuming molar mass of liquid $70$, select the correct statements.

Options:
A. Number of molecules in 35 drop of liquid = $2.10 \times 10^{22}$
B. Number of molecules in 35 drop of liquid = $2.25 \times 10^{22}$
C. Number of molecules in 35 drop of liquid =$1.95 \times 10^{23}$
D. Number of molecules in 35 drop of liquid =$1.95 \times 10^{22}$
E. Number of molecules in 35 drop of liquid =$2.05\times {10}^{22}$
F. Volume of one drop of liquid = $0.057$ mL
G. Number of molecules in 35 drop of liquid = $2.15 \times 10^{22}$
H. Mass of one drop of liquid = $0.068$ g
I. Number of molecules in one drop of liquid =$5.85\times {10}^{20}$
J. Number of molecules in 35 drop of liquid = $1.05 \times 10^{22}$
Answer: E
$50$% neutralisation of a solution of formic acid $\left( { K }_{ a }=2\times { 10 }^{ -4 } \right) $ with $NaOH$ would result in a solution having a hydrogen ion concentration of:

Options:
A. 4.20
B. 2.85
C. 3.39
D. $$4.0$$
E. 3.58
F. 3.72
G. $$3.69$$
H. 3.45
I. $$1.85$$
J. $$2\times { 10 }^{ -4 }$$
Answer: G
From the top of a tower of height 50 m, a ball is thrown vertically upwards with a certain velocity. It hits the ground 10 s after it is thrown up. How much time does it take to cover a distance AB where A and B are two points 20 m and 40 m below the edge of the tower? ( take, g = 10$ms^{-2}$)

Options:
A. 1.4 s
B. 2 s
C. 1.9 s
D. 2.0 s
E. 1.0 s
F. 1.5 s
G. 1.8 s
H. 0.4 s
I. 1.2 s
J. 0.5 s
Answer: H
A scientist proposed the following equation of state ${\text{P}} = \dfrac{{{\text{RT}}}}{{{{\text{V}}_{\text{m}}}}} - \dfrac{{\text{B}}}{{{\text{V}}_{\text{m}}^{\text{2}}}}{\text{ + }}\dfrac{{\text{C}}}{{{\text{V}}_{\text{m}}^{\text{3}}}}$. If this equation leads to the critical behaviour then critical temperature is:

Options:
A. None of these
B. $$\dfrac{{8B}}{{29RC}}$$
C. $$\dfrac{{3B}}{{27RC}}$$
D. $$\dfrac{{8B}}{{25RC}}$$
E. $$\dfrac{{{{\text{B}}^{\text{2}}}}}{{{\text{3RC}}}}$$
F. $$\dfrac{{\text{B}}}{{{\text{8RC}}}}$$
G. $$\dfrac{{{\text{8B}}}}{{{\text{27RC}}}}$$
H. $$\dfrac{{8B}}{{28RC}}$$
I. $$\dfrac{{8B}}{{26RC}}$$
J. $$\dfrac{{3B}}{{8RC}}$$
Answer: G
At $  100^{\circ} \mathrm{C}  $ the $  K_{w}  $ of water is 55 times its value at$  25^{\circ} \mathrm{C}  $ . What will be the pH of neutral solution?$  (\log 55=1.74)  $

Options:
A. 7.50
B. 5.13
C. 6.13
D. 7.00
E. 6.74
F. 5.25
G. 7.25
H. 6.25
I. 7.87
J. 6.87
Answer: D
The emf of a Daniel cell at 298 K is $ E_{1} $ .When the concentration of $ ZnSO_{4} $ is 0.01M and that $ CuSO_{4} $ is 1.0 M, the emf changed to $ E_{2} $. What is the relationship between $ E_{1} $ and $ E_{2} $?

Options:
A. $$E_{2} = \frac{1}{2}E_{1}$$
B. $$$E_{2}=0
eq E_{1}$$$
C. $$E_{1} < E_{2}$$
D. $$E_{1}> E_{2}$$
E. $$E_{2} = E_{1} - 0.059 \log \frac{1}{0.01}$$
F. $$E_{2} = E_{1} + 0.059 \log \frac{1}{0.01}$$
G. $$E_{2} > E_{1}$$
H. $$E_{1} = E_{2}$$
I. $$E_{2} = E_{1} + 0.059 \log 0.1$$
J. $$E_{2} = 2E_{1}$$
Answer: D
Find the distance $x_0$ to the point on the axis at which the value of $B$ differs by $\eta=1\%$ from that in the middle section of the solenoid.

Options:
A. $$\displaystyle x_0 \approx 3.5R$$
B. $$\displaystyle x_0 \approx 5R$$
C. $$\displaystyle x_0 \approx 4R$$
D. $$\displaystyle x_0 \approx 6R$$
E. $$\displaystyle x_0 \approx R$$
F. $$\displaystyle x_0 \approx 8R$$
G. $$\displaystyle x_0 \approx 3R$$
H. $$\displaystyle x_0 \approx 2.5R$$
I. $$\displaystyle x_0 \approx 2R$$
J. $$\displaystyle x_0 \approx 7R$$
Answer: G
A charged oil drop od mass $ 2.5\times { 10 }^{ -7 } kg$ is in space between the two plates, each of area $ 2\times { 10 }^{ -2 } { m }^{ 2 }$ of a parallel plate capacitor. When the upper plate has a charge of $ 5\times { 10 }^{ -7 } C$ and the lower plate has an equal negative charge then the oil remains stationery. The charge of the oil drop is (take, $g=10 { m/s }^{ 2 }$)

Options:
A. $$8.95 \times 10^{-6} C$$
B. $$8.95 \times 10^{-5} C$$
C. $$ 9\times { 10 }^{ -6 } C$$
D. $$ 1.8\times { 10 }^{ -14 } C$$
E. $$ 9\times { 10 }^{ -1 } C$$
F. $$8.9 \times 10^{-12} C$$
G. $$9 \times 10^{-11} C$$
H. $$9 \times 10^{-10} C$$
I. $$ 8.85\times { 10 }^{ -13 } C$$
J. $$8.9 \times 10^{-6} C$$
Answer: E
Select the correct order of $M-C$ bond order in the following molecule and ions.

Options:
A. $$[Ni(CO)_4] > [Co(CO)_4]^{\ominus} > [Fe(CO)_4]^{2-}$$
B. $$[Co(CO)_4]^{\ominus} < [Ni(CO)_4] < [Fe(CO)_4]^{2-}$$
C. $$[Ni(CO)_4] > [Fe(CO)_4]^{2-} > [Co(CO)_4]^{\ominus}$$
D. $$[Co(CO)_4]^{\ominus} > [Fe(CO)_4]^{2-} > [Ni(CO)_4]$$
E. $$[Fe(CO)_4]^{2-} < [Ni(CO)_4] < [Co(CO)_4]^{\ominus}$$
F. $$[Ni(CO)_4] < [Co(CO)_4]^{\ominus} < [Fe(CO)_4]^{2-}$$
G. $$[Ni(CO)_4] = [Co(CO)_4]^{\ominus} = [Fe(CO)_4]^{2-}$$
H. $$[Fe(CO)_4]^{2-} = [Co(CO)_4]^{\ominus} > [Ni(CO)_4]$$
I. $$[Fe(CO)_4]^{2-} < [Co(CO)_4]^{\ominus} = [Ni(CO)_4]$$
Answer: F
What will be sulphide concentration in $ 10^{-3} M HCI (aq) $ solution that has been saturated with $ 0.1 M H_2S $ ?
$$ [Given : for H_2S, K_{a_1} \times K_{a_1} = 1.3 \times 10^{-20} ] $$

Options:
A. $$ 1.30 \times 10^{-16} $$
B. $$1.35 \times 10^{-11}$$
C. $$1.35 \times 10^{-13}$$
D. $$1.4 \times 10^{-11}$$
E. $$ 1.45 \times 10^{-9} $$
F. $$ 1.25 \times 10^{-11} $$
G. $$ 1.3 \times 10^{-15} $$
H. $$1.35 \times 10^{-12}$$
I. $$1.20 \times 10^{-11}$$
J. $$1.15 \times 10^{-11}$$
Answer: G
The minimum volume of water required to dissolve 0.1 g lead(II) chloride to get a saturated solution (${ K }_{ sp }$ of ${ PbCl }_{ 2 }\quad =\quad 3.2\times { 10 }^{ -8 }$ ; atomic mass of Pb = 207 u) is :

Options:
A. 0.35 L
B. 17.98 L
C. 0.18 L
D. 0.72 L
E. 1.798 L
F. 3.596 L
G. 0.45 L
H. 0.359 L
I. 0.36 L
J. 0.54 L
Answer: I
A particle of mass 'm' original at rest, is subjected to a force whose direction is constant but whose magnitude varies with according to the relation $ F = F_ o t\left[ \dfrac { 2 }{ T } -\quad \dfrac { t }{ T^ 2 }  \right]$    Where  $F_0$  and  $T $ are constant. Then speed of the particle after a time 2T is

Options:
A. $$\dfrac { 5F_o }{ 6m }$$
B. $$\dfrac { 5F_o }{ 2m }$$
C. $$ \dfrac { 3F_o }{ 4m } $$
D. $$\dfrac { 3F_o }{ m }$$
E. $$ \dfrac { F_o }{ m } $$
F. $$ \dfrac { 4F_o }{ 3m } $$
G. $$\dfrac { 5F_o }{ 3m }$$
H. $$\dfrac { 3F_o }{ 2m }$$
I. $$ \dfrac { 2F_o }{ m } $$
J. $$\dfrac { 5F_o }{ 4m }$$
Answer: I
If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction 
$Zn(s)+{ Cu }^{ 2 }(aq)\rightleftharpoons { Zn }^{ 2 }(aq)+Cu(s)$ at 300 K is approximentely
$$(R=8\quad JK^{ -1 }{ mol }^{ -1 },F=96000\quad C\quad { mol }^{ -1 })$$

Options:
A. $${ e }^{ -80 }$$
B. $${ e }^{ -140 }$$
C. $${ e }^{ -120 }$$
D. $${ e }^{ -320 }$$
E. $${ e }^{ -180 }$$
F. $${ e }^{ 320 }$$
G. $${ e }^{ -170 }$$
H. $${ e }^{ -150 }$$
I. $${ e }^{ 160 }$$
J. $${ e }^{ -160 }$$
Answer: I
Which of the following statements are correct?

Options:
A. In an isocyanide, first an electrophile and then an electrophile add at the same C atom bearing positive charge.
B. In an isocyanide, first a nucleophile and then an electrophile add at the same C atom bearing positive charge.
C. In an isocyanide, first an electrophile and then a nucleophile add at the same C atom bearing positive charge.
D. In an isocyanide, first an electrophile and then an electrophile add at the same C atom bearing negative charge.
E. In an isocyanide, first a nucleophile and then an electrophile add at the same C atom bearing negative charge.
F. In an isocyanide, first an electrophile and then a nucleophile add at the same C atom bearing negative charge.
G. In an isocyanide, first a nucleophile and then a nucleophile add at the same C atom bearing positive charge.
Answer: F
Minimum temperature at which following reaction will be spontaneous is : 
$A\rightleftharpoons B,\triangle { H }^{ \circ  }=50$ kcal ${ mol }^{ -1 };$ $\triangle { S }^{ \circ  }=100$ cal ${ K }^{ -1 }$

Options:
A. 494 K
B. 490 K
C. 491 K
D. 500 K
E. 501 K
F. 499 K
G. 492 K
H. 495 K
I. 498 K
J. 500. 1 K
Answer: B
A motor cyclist moving with a velocity of $72\;km/hr$ on a flat road takes a turn on the road at a point where the radius of curvature of the road is $20$ meters. The acceleration due to gravity is $10\;m/s^2$. In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than

Options:
A. $$q=tan^{-1}\,5$$
B. $$q=tan^{-1}\,2$$
C. $$q=tan^{-1}\,7$$
D. $$q=tan^{-1}\,25.92$$
E. $$q=tan^{-1}\,7.5$$
F. $$q=tan^{-1}\,8$$
G. $$q=tan^{-1}\,10$$
H. $$q=tan^{-1}\,4$$
I. $$q=tan^{-1}\,3$$
J. $$q=tan^{-1}\,6$$
Answer: J
The ascending order of stability of the carboanion $(P)\ \overline {C}H_{3},$ $(Q)\ C_{6}H_{2}\overline {C}H_{2}$,$(R)\ (CH_{3})_{2} - \overline {C}H$ and $(S)\ H_{2}(\overline {C}) - CH = CH_{2}$ is:

Options:
A. $$R < P < S < Q$$
B. $$R < S < Q < P$$
C. R < S < P < Q
D. $$R < P < Q < S$$
E. P < R < S < Q
F. $$P < R < Q < S$$
G. P < Q < R < S
H. $$R < Q < P < S$$
Answer: A
The instantaneous value of current and potential difference in an alternating circuit are $i=sin\, \omega t$ and $E=100 \, cos\, \omega t$, respectively. The rms value of wattless current (in A) in the circuit is

Options:
A. 100
B. $$\frac{1}{2}$$
C. $$2/ \sqrt{2}$$
D. 1/2
E. $$1/ \sqrt{5}$$
F. $$1$$
G. 2
H. $$zero$$
I. $$1/ \sqrt{2}$$
J. $$1/ \sqrt{3}$$
Answer: F
Given that (at T=298 K)
$Cu(s)| Cu^{2+}(1.0M)|| Ag^{+}(1.0 m)| Ag(s)$          ${ E }_{ cell }^{ o }=0.46  V$
$Zn(s)| Zn^{2+}(1.0M)|| Cu^{2+}(1.0 m)| Cu(s)$      ${ E }_{ cell }^{ o }=1.10  V$ 
Then ${ E }_{ cell }$ for
       $Zn|Zn^{2+}(0.1  M)||  Ag^{+}(1.0  M)| Ag at 298  K $ will be

Options:
A. 1.58 V
B. $$1.59 V$$
C. 1.55 V
D. cannot be calculated due to insufficient data
E. $$2.53 V$$
F. 1.54 V
G. 1.56 V
H. 1.60 V
I. 1.57 V
J. $$1.53 V$$
Answer: J
A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown in figure. One end of the rope is held by Student $A$ of mass $70\ kg$, who is at rest on the floor. The opposite end of the rope is held by Student $B$ of mass $60\ kg$. Who is suspended at rest above the floor. The minimum acceleration $a_{0}$ with which the Students $B$ should climb up the rope to lift the Student $A$ upward off the floor. $(g=10\ m/s^{2})$

Options:
A. $$\dfrac{4}{3}\ m/s^{2}$$
B. $$\dfrac{10}{3}\ m/s^{2}$$
C. $$\dfrac{13}{3}\ m/s^{2}$$
D. $$\dfrac{5}{3}\ m/s^{2}$$
E. $$\dfrac{7}{3}\ m/s^{2}$$
F. $$\dfrac{1}{3}\ m/s^{2}$$
G. $$\dfrac{2}{3}\ m/s^{2}$$
H. $$\dfrac{11}{3}\ m/s^{2}$$
I. $$\dfrac{8}{3}\ m/s^{2}$$
Answer: F
$30\: mL$ of $CH_{3}OH (d = 0.8\: g/cm^{3})$ is mixed with $60\: mL$ of $C_{2}H_{5}OH (d= 0.92\: g/cm^{3})$ at $25 ^\circ C$ to form a solution of density $0.88\: g/cm^{ 3}$. Select the correct option.

Options:
A. The mole fraction of solute and molality are 0.385 and 13.59 respectively
B. Mole fraction of solute and molality are 0.385 and 14.59 respectively
C. Mole fraction of solvent and molality are 0.615 and 12.59 respectively
D. Mole fraction of solute and molality are 0.615 and 13.59 respectively
E. Molarity and $\%$ change in volume are 13.59 and zero respectively
F. Mole fraction of solute and molality are 0.385 and 12.59 respectively
G. Mole fraction of solvent and molality are 0.515 and 13.59 respectively
H. Mole fraction of solvent and molality are 0.615 and 13.59 respectively
I. Molarity and molality of resulting solution are 6.33 and 13.59 respectively
J. Mole fraction of solvent and molality are 0.615 and 14.59 respectively
Answer: H
An electron is at $P$ at $ t=0$ . It is circulating in anticlockwise direction with a constant angular speed $ \omega $ along the shown circular path. Magnetic field at $ Q(CQ = 2 R, $ where is $R$ radius of the circle $)$ will be recorded as zero at times.

Options:
A. $$ \dfrac {7 \pi }{3 \omega} $$
B. $$\dfrac {11 \pi }{3 \omega}$$
C. $$\dfrac {10 \pi }{3 \omega}$$
D. $$ \dfrac {5 \pi }{3 \omega} $$
E. $$ \dfrac {8 \pi }{3 \omega} $$
F. $$\dfrac {9 \pi }{3 \omega}$$
G. $$\dfrac {6 \pi }{3 \omega}$$
H. $$\dfrac {4 \pi }{3 \omega}$$
I. $$ \dfrac {\pi}{3 \omega} $$
J. $$\dfrac {13 \pi }{3 \omega}$$
Answer: A
Calculate ${ \Delta H }^{ \circ  }_{ combustion }$ of acetone if ${ \Delta H }^{ \circ  }_{ f }$ of acetone =${ -250kJ\Delta H }^{ \circ  }_{ combustion }$ of ${ C }_{ graphite }=-390kJ/mole$ and ${ \Delta H }^{ \circ  }_{ combustion }$ of ${ H }_{ 2\left( g \right)  }=-280kJ/mole$

Options:
A. -1310 kJ/mole
B. -1370 kJ/mole
C. -1430 kJ/mole
D. -1390 kJ/mole
E. -1410 kJ/mole
F. -1450 kJ/mole
G. -1330 kJ/mole
H. -1760 kJ/mole
I. -1230 kJ/mole
J. -1490 kJ/mole
Answer: I
A copper wire of length $Bm$ and steel wire of length $4m$ each of area of cross section $0.5{cm}^{2}$ are fastened end to end and stretched with a tension of $500N$. Given ${Y}_{copper}=10\times {10}^{10}Pa, {Y}_{steel}=20\times {10}^{10}Pa$. The energy stored in the composite wire is

Options:
A. 0.35J
B. 1.00J
C. $$0.25J$$
D. 0.65J
E. $$0.75J$$
F. 0.30J
G. 0.45J
H. $$0.50J$$
I. 0.55J
J. $$2.25J$$
Answer: C
$K_C$ for $PCl_3(g) + Cl_2(g) \rightleftharpoons PCl_5(g) $ is $15 M^{-1}$. The no. of moles of $PCl_5$ to be introduced in a 2.5 it vessel (initially evacuated) to obtain $[Cl_2] = 0.2 M$

Options:
A. 79/8
B. 75/8
C. None of these
D. 17/4
E. 77/8
F. 73/8
G. 2
H. 81/8
I. 39/4
J. 83/8
Answer: A
A $1$ litre solution containing $NH_4Cl$ and $NH_4OH$ has hydroxide ion concentration of $10^{-6}$ mol/litre. Which of the following hydroxides could be precipitated when the solution is added to $1$ litre solution of $0.1\space M$ metal ions?$(I)\quad Ba(OH)_2\space (K_{sp} = 5\times10^{-3})$$(II)\quad Ni(OH)_2\space (K_{sp} = 1.6\times10^{-16})$$(III)\quad Mn(OH)_2\space (K_{sp} = 2\times10^{-13})$$(IV)\quad Fe(OH)_2\space (K_{sp} = 8\times10^{-16})$

Options:
A. $$I, II, IV$$
B. $$IV$$
C. I, III, IV
D. II, IV
E. $$II, III, IV$$
F. I, II, III, IV
G. I, II, III
H. II, III
I. $II$ and $IV$
Answer: E
In a biprism experiment, interference bands are observed at a distance of one meter fromthe slit. A convex lens is put between the slit and the eyepiece gives two images of slit 0.7$\mathrm { cm }$ apart, the lens being 70$\mathrm { cm }$ from the eyepiece. The fringe width will be: $\left( \lambda = 6000 \mathrm { A } ^ { 9 } \right)$

Options:
A. $$0.4$\mathrm { mm }$$$
B. $$0.01$\mathrm { mm }$$$
C. $$0.6\mathrm { mm }$$
D. $$0.5\mathrm { mm }$$
E. $$0.05\mathrm { mm }$$
F. $$0.9\mathrm { mm }$$
G. $$0.3$\mathrm { mm }$$$
H. $$0.7\mathrm { mm }$$
I. $$0.2$\mathrm { mm }$$$
J. $$0.1$\mathrm { mm }$$$
Answer: B
The specific heat of substance veries with temperature according to equation $C=2T\times { 10 }^{ -3 }cal/gK$ (T is absolut temperature). The amount of heat raquired to raise the temperature of 100 g of substance from ${ 27 }^{ 0 }C$ to ${ 47 }^{ 0 }C$ is

Options:
A. 3400 cal
B. 4000 cal
C. 3600 cal
D. 1240 cal
E. 3200 cal
F. 3240 cal
G. 3800 cal
H. 3000 cal
I. 4200 cal
J. 2000 cal
Answer: B
The hybrid states of carbon atoms in ${(\overset{B}CN)_4}\overset{A}{C_2}$ are A and B and number of $\pi$ bonds in compound is C. Then?

Options:
A. $A=sp^3, B=sp$, and $C=9$
B. $A=sp, B=sp^2$ and $C=9$
C. $$A=sp^3, B=sp^2, and C=9$$
D. $$A=sp^2, B=sp^3, and C=9$$
E. $$A=sp, B=sp^3, and C=9$$
F. $A=sp^2, B=sp$, and $C=8$
G. $A=sp^2, B=sp^2$ and $C=9$
H. $A=sp, B=sp^2$, and $C=9$
Answer: A
A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x) = 20 + $(x - 2)^2$ where x is in meters. At x = 5.0 m, the particle has a kinetic energy of 20 J.The maximum and minimum values of x, respectively, are:

Options:
A. 7.38m, -3.38m
B. 6.38m, -4.38m
C. 6.38m, -3.38m
D. 7.38m, -4.38m
E. 7.38m, -2.38m
F. 6.38m, -2.38m
G. 7.38m, -1.38m
H. 8.38m, -2.38m
I. 6.38m, -1.38m
J. 8.38m, -1.38m
Answer: E
Mass of upper block and lower block kept over the table is $2\ kg$ and $1\ kg$ respectively and coefficient of friction between the blocks is $0.1$. Table surface is smooth. The maximum mass $M$ for which all the three blocks move with same acceleration is $(g={ 10\ m/s }^{ 2 })$

Options:
A. $$1\ kg$$
B. $$1/2\ kg$$
C. $$3/4\ kg$$
D. $$9/4\ kg$$
E. $$2/3\ kg$$
F. $$1/3\ kg$$
G. $$1/4\ kg$$
H. $$5/4\ kg$$
I. $$3/2\ kg$$
J. $$7/4\ kg$$
Answer: A
A metal plate of mass 250gm is balanced in air by throwing balls each of mass 25gm vertically up. if the ball rebound at the rate of 20 per second with the same velocity, the velocity with which the balls strike the plate is $ (g = 10ms^-2) $

Options:
A. $$ 5 ms^-1 $$
B. $$7.5 ms^-1$$
C. $$4 ms^-1$$
D. $$4.5 ms^-1$$
E. $$6 ms^-1$$
F. $$ 1.5 ms^-1$$
G. $$3 ms^-1$$
H. $$8 ms^-1$$
I. $$ 2.5 ms^-1$$
J. $$ 10 ms^-1$$
Answer: A
A wheel rotates around a stationary axis so that rotation angle $\theta$ varies with time  as $\theta = at^2$, where a = 1.5 $rad^{-2}$. Then the magnitude of net acceleration of the point A at the rim at the moment $t = \frac 2 3 s$ if the linear velocity of the point A at this moment $u = 2 ms^{-1}$

Options:
A. 7 m/s^2
B. $$3 m/s^2$$
C. 1 m/s^2
D. $$4 m/s^2$$
E. 9 m/s^2
F. 1.5 m/s^2
G. $$6 m/s^2$$
H. $$8 m/s^2$$
I. $$2 m/s^2$$
J. $$5 m/s^2$$
Answer: I
For the equilibrium,$LiCl\cdot { 3NH }_{ 3 }(s)\rightleftharpoons LiCl\cdot { NH }_{ 3 }(s)+2{ NH }_{ 3 }(g)\quad $ ${ K }_{ p }=9{ atm }^{ 2 }$ at ${ 37 }^{ o }C$. A $5$ litre vessel contains $0.1$ mole of $LiCl\cdot { 3NH }_{ 3 }$. How many moles of ${ NH }_{ 3 }$ should be added to the flask at this temperature to derive the backward reaction for completion?$R=0.082 \ atm.L/molK$

Options:
A. $$0.49$$
B. $$0.2$$
C. $$0.79$$
D. $$0.39$$
E. $$0.99$$
F. $$0.89$$
G. $$0.59$$
H. $$0.69$$
Answer: C
Which of the following conditions should be more favorable for increasing the  rate of forward reaction in the equilibrium ${H_2} \rightleftharpoons H + H\left( {\Delta H =  + ve} \right)$

Options:
A. all are wrong
B. 3500$^ \circ $C temperature and 500 mm of Hg pressure.
C. 3500^ \circ C temperature and 1 mm of Hg pressure.
D. 3500$^ \circ $C temperature and 100 cm of Hg pressure.
E. 2000$^ \circ $C temperature and 760 mm of Hg pressure
F. 3500$^ \circ $C tempreture and 1 mm of Hg pressure
G. 2000^ \circ C temperature and 100 cm of Hg pressure.
H. 3500$^ \circ $C temperature and 760 mm of Hg pressure.
I. 3500^ \circ C temperature and 50 cm of Hg pressure.
Answer: D
In the arrangement shown,the springs are light and have stiffness $ k_1 = 100 N/m and k_2 = 200 N/m $ and the pullcys are ideal.An 8.0 kg block suspended from the lower pulley is initially held at rest maintaining the strings straight and springs relaxed.Now the force supporting the block is gradually reduced to zero.How far does the block descend during the process of reduction of the force? Acceleration due to gravity is $ 10 m/s^2 $

Options:
A. 17 cm
B. 13 cm
C. 15 cm
D. 20 cm
E. 12 cm
F. 10 cm
G. 1.6 cm
H. None of these
I. 14 cm
J. 11 cm
Answer: C
A quantity of $25 g$ sample of $ baO_2 $ is heated to 954 K in clased and rigid evacuated vessel of $8.21 L$ capacity . what percentage of peroxide is converted into oxide?$ 2BaO_2 (s) \leftrightharpoons 2BaO(s) +O_2(g) ; K_P = 0.5 atm $

Options:
A. $$40 \%$$
B. $$30 \%$$
C. $$15 %$$
D. $$90 \%$$
E. $$60 \%$$
F. $$50 \%$$
G. $$75 \%$$
H. $$80 \%$$
I. $$10 \%$$
Answer: F
In the analysis of $0.50$ g sample of feldspar, a mixture of the chlorides of sodium and potassium is obtained, which weighs $0.1180$ g. Subsequent treatment of the mixed chlorides with silver nitrate gives $0.2451$ g of silver chloride. What is the percentage of sodium oxide and potassium oxide in feldspar?

Options:
A. $$Na_2O= 4.1\%, K_2O=9.1\%$$
B. $$Na_2O= 3.8\%, K_2O=10.1\%$$
C. $$None of the above$$
D. $$Na_2O= 3.7\%, K_2O=10.4\%$$
E. $$Na_2O= 3.4\%, K_2O=11.4\%$$
F. $$$Na_2O= 3.1\%$, $K_2O=11.1\%$$$
G. $$$Na_2O= 3.9\%$, $K_2O=9.9\%$$$
H. $$$Na_2O= 3.6\%$, $K_2O=10.6\%$$$
I. $$$Na_2O= 1.8\%$, $K_2O=5.3\%$$$
J. $$$Na_2O= 4.5\%$, $K_2O=6.6\%$$$
Answer: H
Charge -q and + q located at A and B, respectively, constitute an electric dipole.Distance AB=2a, O is mid point of the dipole and OP is perpendicular to AB.A charge q is lace at P where OP =y and Y >> 2a.The charge Q exprience an electrostatic force F.If Q is now moned along the equatorial line to P' such that OP'=$(\frac{y}{3})$, the force on Q will be close to :$(\frac{y}{3}>>2a$)

Options:
A. $$\frac{3F}{9}$$
B. 3 F
C. 27 F
D. $$\frac{F}{3}$$
E. $$\frac{F}{27}$$
F. $$\frac{F}{81}$$
G. \( \frac{F}{9} \)
H. 9 F
I. \(\frac{F}{27}\)
J. \(\frac{F}{243}\)
Answer: D
The pH of a solution containing $0.1\,M\,CH_3COONa$ and $0.1\,M\,(C_2H_5COO)_2Ba$ will be:
$$[K_a(CH_3COOH)=2 \times 10^{-5}, k_a (C_2H_5COOH)=8 \times 10^{-6}]$$

Options:
A. $$8.13$$
B. $$8.24$$
C. $$7.94$$
D. $$8.71$$
E. $$9.02$$
F. $$9.24$$
G. $$11.1$$
H. $$8.16$$
I. $$8.31$$
J. $$10.18$$
Answer: A
The emf of the cell ${ H }_{ 2 }(1atm)$ $Pt,\left| { H }^{ + }(a=x) \right| \left| { H }^{ + }(a=1) \right| { H }_{ 2 }(1atm)$ Pt at ${ 25 }^{ 0 }C$ is 0.59V. The pH of the solution is

Options:
A. 1
B. 2
C. 6
D. 4
E. 7
F. 5
G. 10
H. 9
I. 8
J. 3
Answer: A
A transverse wave propagating on the string can be described by the equation y = 2 sin (10x + 300t), where x and y are in metres and t in second. If the vibrating string has linear density of 0.6 x $10^{-3}$ g/cm, then the tension in the string is

Options:
A. 0.54 N
B. $$54 \times 10^{-3} \, \text{N}$$
C. $$5.4 \times 10^{-2} \, \text{N}$$
D. 540 N
E. 0.054 N
F. 54 N
G. $$54 \times 10^{-2} \, \text{N}$$
H. 0.0054 N
I. $$0.54 \times 10^{-2} \, \text{N}$$
Answer: C
Two blocks of mass $m_1$ and $m_2$ interconnected with a spring of stiffness $K$ are kept on a smooth horizontal surface. Which of the following ratios are correct when the spring is extended and released?Where  $X$ = displacement, $v$=speed, $P$=momentum, $a$=acceleration, all relative to the surface KE = kinetic energy, F= force.

Options:
A. $$\frac { { P }_{ 1 } }{ { P }_{ 2 } } = \frac { { m }_{ 2 } }{ { m }_{ 1 } } \& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } = \frac { { m }_{ 1 } }{ { m }_{ 2 } }$$
B. None of these
C. $$\frac { { P }_{ 1 } }{ { P }_{ 2 } } =1\& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } =\frac { { m }_{ 1 } }{ { m }_{ 2 } } $$
D. $$\frac { { F }_{ 1 } }{ { F }_{ 2 } } =1\& \frac { { X }_{ 1 } }{ { X }_{ 2 } } =1$$
E. $$\frac { { P }_{ 1 } }{ { P }_{ 2 } } =1\& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } = \frac { { m }_{ 1 } + 1 }{ { m }_{ 2 } }$$
F. \(\frac { { P }_{ 1 } }{ { P }_{ 2 } } =1\& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } = \frac { { m }_{ 1 } }{ { m }_{ 2 } + 1 } \)
G. $$\frac { { P }_{ 1 } }{ { P }_{ 2 } } = \frac { { m }_{ 2 } }{ { m }_{ 1 } } \& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } = \frac { { m }_{ 2 } }{ { m }_{ 1 } }$$
H. $$\frac { { P }_{ 1 } }{ { P }_{ 2 } } =1\& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } = \frac { { m }_{ 2 } }{ { m }_{ 1 } }$$
I. $$\frac { { V }_{ 1 } }{ { V }_{ 2 } } =\frac { { m }_{ 1 } }{ { m }_{ 2 } } \& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } =\frac { { m }_{ 2 } }{ { m }_{ 1 } } $$
J. $$\(\frac { { P }_{ 1 } }{ { P }_{ 2 } } =\frac { { m }_{ 1 } }{ { m }_{ 2 } } \& \frac { K{ E }_{ 1 } }{ K{ E }_{ 2 } } =1 \)$$
Answer: C
A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The force $F$ applied on the rod is such that the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu=KX$, where $K$ is a positive constant. Suppose friction is present only from $X=0$ to $X=L$. If the rod moves in the direction of application of force then the total heat generated in the time in which the rod crosses this region, is equal to

Options:
A. $$\dfrac { KMg{ L }^{ 2 } }{ g }$$
B. $$\dfrac { 2KMg{ L }^{ 2 } }{ 6 }$$
C. $$\dfrac { KMg{ L }^{ 2 } }{ 4 }$$
D. $$\dfrac { 2KMg{ L }^{ 2 } }{ 5 }$$
E. $$\dfrac { KMg{ L }^{ 2 } }{ 3 }$$
F. $$\dfrac { 2KMg{ L }^{ 2 } }{ 3 }$$
G. $$\dfrac { 3KMg{ L }^{ 2 } }{ 8 }$$
H. $$\dfrac { KMg{ L }^{ 2 } }{ 2 }$$
I. $$\dfrac { KMg{ L }^{ 2 } }{ 7 }$$
J. $$\dfrac { KMg{ L }^{ 2 } }{ 5 }$$
Answer: E
When $0.1$ mole of solid NaOH is added in $1$L of $0.1$M $NH_3$ (aq) then which statement is going to be wrong?
$$(K_b=2 \times 10^{-5}, log 2 = 0.3)$$

Options:
A. degree of dissociation of $NH_3$ decreases significantly.
B. Concentration of $[Na^+]=0.1M, [NH_3],=0.1M, [OH^-]=0.2M$
C. degree of dissociation of $NH_3$ remains unchanged
D. degree of dissociation of $NH_3$ increases slightly.
E. on addition of $OH^-,K_b$ of $NH_3$ does not changes
F. Change in pH would be $1.85$
G. degree of dissociation of $NH_3$ remains constant.
H. degree of dissociation of $NH_3$ approaches to zero.
I. degree of dissociation of $NH_3$ approaches to one.
Answer: H
The resultant amplitude due to superposition of two waves $y_{1} = 5\sin (wt - kx)$ and $y_{2} = -5\cos (wt - kx - 150^{\circ})$.

Options:
A. $$5\sqrt {2 - \sqrt {1}}$$
B. $$5\sqrt {3}$$
C. $$5\sqrt {2 + \sqrt {3}}$$
D. $$5\sqrt {2 - \sqrt {2}}$$
E. $$5\sqrt {2 + \sqrt {2}}$$
F. $$5\sqrt {2 + \sqrt {1}}$$
G. $$5\sqrt {2 - \sqrt {3}}$$
H. $$5\sqrt {1 - \sqrt {3}}$$
I. $$5$$
J. $$5\sqrt {3 - \sqrt {2}}$$
Answer: G
Two springs, each of spring constant $k=100N/m$, are attached to a block of mass $2\ kg$ as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass $5\ kg$. If the block is displaced by $x\ cm$ and released, the period of oscillation in seconds is :

Options:
A. $$T=2\pi \sqrt{\dfrac{1}{190}}$$
B. $$T=2\pi \sqrt{\dfrac{1}{160}}$$
C. $$T=2\pi \sqrt{\dfrac{1}{140}}$$
D. $$T=2\pi \dfrac{49}{100}$$
E. $$T=2\pi \sqrt{\dfrac{1}{20}}$$
F. $$T=2\pi \sqrt{\dfrac{1}{150}}$$
G. $$T=2\pi \sqrt{\dfrac{1}{170}}$$
H. $$T=2\pi \sqrt{\dfrac{1}{130}}$$
I. $$T=2\pi \sqrt{\dfrac{7}{1000}}$$
Answer: C
If ${CH}_{3}COOH$ (${K}_{a}={10}^{-5}$) reacts with $NaOH$ at $298K$, then find out the value of the maximum rate constant of the reverse reaction at $298K$ at the end point of the reaction. Given that the rate constant of the forward reaction is ${10}^{-11}$ ${mol}^{-1}$ $L$ ${sec}^{-1}$ at $298K$. Also calculate Arrhenius parameter for backward reaction, if $\Delta {H}_{298}=44kcal$ and ${E}_{{a}_{(f)}}=94kcal$:

Options:
A. ${K}_{b}={10}^{-21}$, ${A}_{b}=2.71 \times {10}^{15}$
B. ${K}_{b}={10}^{-20}$, ${A}_{b}=5.4 \times {10}^{16}$
C. ${K}_{b}={10}^{-20}$, ${A}_{b}=2.71 \times {10}^{14}$
D. ${K}_{b}={10}^{-20}$, ${A}_{b}=2.71 \times {10}^{15}$
E. ${K}_{b}={10}^{-19}$, ${A}_{b}=5.4\times {10}^{16}$
F. None of these
G. ${K}_{b}={10}^{-10}$, ${A}_{b}=5.4\times {10}^{14}$
H. ${K}_{b}={10}^{-19}$, ${A}_{b}=5.4 \times {10}^{14} $
I. ${K}_{b}={10}^{-20}$, ${A}_{b}=2.71\times {10}^{16}$
J. ${K}_{b}={10}^{-20}$, ${A}_{b}=5.4 \times {10}^{15}$
Answer: I
Steam is passed over hot carbon to attain the equilibrium at $400  K$,
                $C\left(s\right) + {H}_{2}O\left(g\right) \rightleftharpoons CO\left(g\right) + {H}_{2}\left(g\right)$
The equilibrium constant $K = 1.34$ (dimension less) and the total pressure of the equilibrium mixture is $200   kPa$. Which one is correct when equilibrium is attained?

Options:
A. Mole fraction of ${H}_{2}O = 0.224$
B. Mole fraction of ${H}_{2}O = 0.388$
C. $$Mole fraction of ${H}_{2}O = 0.575$$
D. Mole fraction of ${H}_{2}O = 0.85$
E. $$Mole fraction of ${H}_{2}O = 0.184$$
F. $$Mole fraction of ${H}_{2}O = 0.124$$
G. Mole fraction of $CO =$ mole fraction of ${H}_{2} = 0.075$
H. $$Mole fraction of ${H}_{2}O = 0.324$$
I. Mole fraction of ${H}_{2}O = 0.412$
Answer: A
A hollow sphere is filled with water through the small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will:

Options:
A. first increase and then decrease more slowly
B. first remain constant and then decrease
C. first increase and then increase more slowly
D. continuously increase
E. first increase and then remain constant
F. first remain constant and then increase
G. continuously decrease
H. first decrease and then remain constant
I. first decrease and then increase
J. first increase and then decrease
Answer: I
A block whose mass is $1$kg is fastened to a spring. The spring has a spring constant of $100Nm^{-1}$. The block is pulled to a distance $x = 10$cm from its equilibrium position at $x= 0$ on a frictionless surface from rest at $t = 0$. The kinetic energy and potential energy of the block when it is $5$cm away from the mean position is

Options:
A. $$0.125 J, 0.375 J$$
B. 0.125 J, 0.25 J
C. 0.25 J, 0.25 J
D. $$0.125 J, 0.125 J$$
E. 0.25 J, 0.125 J
F. $$0.375 J, 0.375 J$$
G. $$0.0375 J, 0.125 J$$
H. 0.125 J, 0.0625 J
I. 0.375 J, 0.125 J
Answer: D
If $0.1M\ H_2SO_4(aq)$ solution shows freezing point $-0.3906^oC$ then what is the $K_2$ for $H_2SO_4$?
(Assume $m=M$ and $K_{f(H_2O)} = 1.86\ K\ kg\ mol^{-1})$

Options:
A. 0.0212
B. 0.0112
C. $$0.122$$
D. None of these
E. 0.0222
F. 0.1212
G. 0.0221
H. $$1.11\times 10^{-3}$$
I. 0.1122
J. $$0.0122$$
Answer: J
A nonuniform ball of radius $R$ and radius of gyration about geometric centre $= R/2$, is kept on a frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck horizontally with a sharp impulse $= J$ The point of application of the impulse is at a height $h$ above the surface. Then

Options:
A. the ball with slip on surface tor all cases
B. there will be no rotation if $h= R$
C. the ball will roll purely if \( h = 9R/4 \)
D. the ball will roll purely if \( h = 7R/4 \)
E. the ball will roll purely if $h = 3R/4$
F. the ball will roll purely if \( h = R/4 \)
G. the ball will roll purely if \( h = 5R/2 \)
H. the ball will roll purely if $h = 3R/2$
I. the ball will roll purely if $h = R/2$
J. the ball will roll purely if $h = 5 R/4$
Answer: J
A cubical block of side 2m and mass 20 kg slides on an inclined plane lubricated with the oil of viscosity $\displaystyle \eta =10^{-1}$ poise, with a constant velocity of 10 m/sec (g = 10 m/$\displaystyle sec^{2}$). The thickness of the layer of liquid

Options:
A. 5 mm
B. 6 mm
C. 2 mm
D. 4 mm
E. 3 mm
F. 5.5 mm
G. 7 mm
H. 9 mm
I. 3.5 mm
J. 8 mm
Answer: D
A transverse wave travelling on a taut string is represented by $y =0.01\sin 2\pi (10t -x)$ where y and x are in metre and t is in second. Then

Options:
A. Maximum particle speed is $\frac{\pi}{6} m/s$
B. Maximum particle speed is $\frac{\pi}{4}$ m/s
C. Maximum particle speed is $\frac{\pi}{3}$ m/s
D. Maximum particle speed is $\frac{\pi}{5}$ m/s
E. Closest points on the string which differ in phase by $60^\circ$ are $(\frac{1}{6})$ m apart
F. The phase of a certain point on the string changes by $120^\circ$ is $(\frac{1}{20})$ seconds
G. Maximum particle speed is $\frac{\pi}{15}$ m/s
H. The speed of the wave is 10 m/s
Answer: D
A wedge of mass $M$ is free to move on smooth horizontal surface. Two blocks of mass $m_1$ and $m_2$, are free to move on smooth inclined surfaces of the wedge.
If $\dfrac{m_1}{m_2} = \dfrac{\sin 2 \theta_2}{\sin 2 \theta_1}$, the wedge

Options:
A. may remain stationary
B. remains stationary
C. may accelerate rightward
D. may accelerates leftward
E. may accelerate leftward
F. may accelerate right ward
G. None of these
Answer: F
Two blocks are connected by a massless string that passes over a frictionless peg as shown in fig. One end of the string is attached to a mass $m_1 = 3kg$, i.e. a distance $R = 1.20 m$ from the peg. The other end of the string is connected to a block of mass $m_2 = 6 kg$ resting on a table. When the 3 kg block be released at $\displaystyle \theta = \frac{\pi}{k}$, the 6 kg block just lift off the table? Find the value of k.

Options:
A. $$6$$
B. $$2$$
C. $$9$$
D. $$4$$
E. $$7$$
F. $$8$$
G. $$3$$
H. $$5$$
Answer: A
A body of mass $m$ attached to the spring experiences a drag force proportional to its velocity and an external force $F(t) = F_o \cos \omega _ot$. The position of the mass at any point in time can be given by:

Options:
A. $$x(t) = c_1 \cos (\omega t) + (\dfrac{F_o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$$
B. $$x(t) = c_1 \cos (\omega t) + (\dfrac{F_o}{\omega _o ^2 - 2\omega ^2}) \cos \omega _o t$$
C. $$x(t) = c_1 \sin (\omega t) + (\dfrac{F_o}{\omega ^2 + \omega _o ^2}) \cos \omega _o t$$
D. $$x(t) = c_1 \cos (\omega t) + (\dfrac{F_o}{\omega ^2 + \omega _o ^2}) \cos \omega _o t$$
E. $$x(t) = c_1 \sin (\omega t + \phi) + (\dfrac{F_o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$$
F. $$x(t) = c_1 \cos (\omega t) + (\dfrac{F_o}{2\omega ^2 - \omega _o ^2}) \cos \omega _o t$$
G. $$x(t) = c_1 \cos (\omega t) + (\dfrac{F_o}{\omega _o ^2 + \omega ^2}) \cos \omega _o t$$
Answer: A
Oxygen diffuses two different vessels 'A' and 'B' under identical conditions but 'A' has circular orifice while 'B' has square orifice. The ratio of rate of diffusion in the two vessel will be: (Given : Diagonal of square=Diameter of circle)

Options:
A. $$\pi :3$$
B. $$\pi : 8$$
C. $$\pi :6$$
D. $$\pi :7$$
E. $$\pi :4$$
F. $$\pi :2$$
G. $$4: \pi$$
H. $$2: \pi$$
I. $$\pi : 5$$
Answer: E
One gram of radium is reduced by $2 mg$ in $5$ years by $\alpha $- decay. The half life of radium is:(log$_{10}998=$ $2.9991$ )

Options:
A. $1617.5$ years
B. 1632.86 years
C. 1732.84 years
D. $1671.7$ years
E. 1732.85 years
F. 1732.85
G. $1520.4$ years
H. $1732.86$ years
I. 1617.85 years
J. 1732.87 years
Answer: H
In an acidic indicator 'Hln' has ionization constant is $10^{-8}$. The acid form of indicator is yellow and alkaline from is red. Which is correct statement?
(Given: $log2=0.3,log3=0.48$)

Options:
A. Change in pH is 0.96 when $75\%$ yellow colour cahnge to $75\%$ red colour.
B. pH of indicator is 8.3 when ratio of acid form to alkaline form is 0.5
C. pH of indicator is 7.3 when ratio of acid form to alkaline form is 1
D. This indicator is suitable for the litration of strong acid Vs strong base.
E. pH of indicator is 8.3 when ratio of acid form to alkaline form is 2
F. pH of indicator is 8.3 when ratio of acid form to alkaline form is 0.25
G. pH of indicator is 8.3 when ratio of acid form to alkaline form is 1
H. pH of indicator is 7.3 when ratio of acid form to alkaline form is 2
I. the pH range of indicator is 7 to 9.
Answer: E
50 ml of 20.8% (w/V) $BaCl_2$ (aq) and 100 ml of 9.8% (w/V) $H_2SO_4$ (aq) solutions are mixed. Molarity of $Cl^-$ ions in the resulting solution is : (At mass of Ba =137)

Options:
A. 0.444 M
B. 0.222 M
C. 0.666 M
D. 0.555 M
E. 0.267 M
F. 0.1 M
G. 1.33 M
H. 0.167 M
I. 0.133 M
J. 0.333 M
Answer: J
Given
$C + 2S \longrightarrow CS_2$, $\Delta { Hf }^{ \circ  }$ = + $117.0 KJ  mol^{-1}$
$C + O_2 \longrightarrow$, $CO_2,\Delta {Hf}^{\circ }$ = $-393.0 KJmol^{-1}$
$S + O_2 \longrightarrow$, $SO_2,\Delta {Hf}^{\circ }$ = $-297.0 KJmol^{-1}$
The heat of combustion of
$$CS_2 + 3O_2 \longrightarrow CO_2+2SO_2 is $$

Options:
A. $$ +807 KJ MOl^{-1}$$
B. $$-803 KJ mol^{-1}$$
C. $$-804 KJ MOl^{-1}$$
D. $$-807 KJ MOl^{-1}$$
E. $$-806 KJ MOl^{-1}$$
F. $$-802 KJ mol^{-1}$$
G. $$-1104KJ mol^{-1}$$
H. $$+1104KJ mol^{-1}$$
I. $$-808 KJ mol^{-1}$$
J. $$-805 KJ mol^{-1}$$
Answer: D
A block slides down a slope of angle $\theta$ with constant velocity. It is then projected up with a velocity of $10{ms}^{-1}$, $g=10{ms}^{-2}$ and $q={30}^{o}$. The maximum distance it can go up the plane before coming to stop is

Options:
A. $$10m$$
B. $$12m$$
C. $$5m$$
D. $$4m$$
E. $$6m$$
F. $$9m$$
G. $$14m$$
H. $$8m$$
I. $$15m$$
J. $$11m$$
Answer: A
Calculate the enthalpy of the following homoheneous gaseous reaction:
$$CH_{2}COCH_{3}+2O_{2}\rightarrow CH_{3}COOH+CO_{2}+H_{2}O$$
from hte following data:
Bond energies $(kJ/mol): C-H=414; C-C=348; C=O=580; C-O=354; O=O=610; O-H=462$;
Magnitude of resonance energies $(kJ/mol): COOH=118; CO_{2}=140$

Options:
A. $$-168\ kJ$$
B. $$348= kJ$$
C. $$168\ kJ$$
D. $$-448\ kJ$$
E. $$-348\ kJ$$
F. $$-388\ kJ$$
G. $$-358\ kJ$$
H. $$-338\ kJ$$
I. $$-318\ kJ$$
J. $$-378\ kJ$$
Answer: E
Calculate relative rates of effusion of $SO_2$ to $CH_4$, in the mixture obtained by effusing out a mixture with initial molar ratio $\dfrac{n_{SO_2}}{n_{CH_4}}=\dfrac{8}{1}$ for three effusing steps.

Options:
A. $$1:3$$
B. $$4:1$$
C. $$2:1$$
D. $$1:5$$
E. $$1:4$$
F. $$1:2$$
G. $$3:1$$
H. $$1:1$$
I. 3:2
J. None of these
Answer: F
$$AgBr(s) + 2S_2O_3^{2-}(aq.) \rightleftharpoons Ag(S_2O_3)_2^{3-}(aq.) + Br^-(aq.)$$
[Using: $K_{sp} (AgBr) = 5\times10^{-13}, \space K_f (Ag(S_2O_3)_2^{3-}) = 5\times10^{13}$]
What is the molar solubility of $AgBr$ in $0.1\space M\space Na_2S_2O_3$?

Options:
A. $$0.405\space M$$
B. $$0.045\space M$$
C. $$0.4\space M$$
D. $$0.45\space M$$
E. $$0.5\space M$$
F. $$0.05\space M$$
G. $$0.055\space M$$
H. $$0.55\space M$$
I. $$0.505\space M$$
J. None of these
Answer: E
In a certain gaseous reaction between $X$ and $Y$, $X+3Y\rightarrow X{Y}_{3}$. The initial rates are reported as follows-$[X]$$[Y]$Rate$0.1\ M$$0.1\ M$$0.002\ M{s}^{-1}$$0.2\ M$$0.1\ M$$0.002\ M{s}^{-1}$$0.3\ M$$0.2\ M$$0.008\ M{s}^{-1}$$0.4\ M$$0.3\ M$$0.018\ M{s}^{-1}$The rate law is:

Options:
A. $$r=K[X][Y]$$
B. $$r=K[X]{[Y]}^{3}$$
C. $$r=K{[X]}^{o}{[Y]}^{2}$$
D. $$r=K{[X]}^{1}{[Y]}^{3}$$
E. $$r=K{[X]}^{2}[Y]$$
F. $$r=K{[X]}^{1}{[Y]}^{2}$$
G. $$r=K{[X]}^{3}[Y]$$
H. $$r=K{[X]}^{2}{[Y]}^{2}$$
I. $$r={[X]}^{o}{[Y]}^{3}$$
J. $$r=K{[X]}^{2}{[Y]}^{3}$$
Answer: I
A body of mass $5$ kg falls from a height of $20$ meters on the ground and it rebounds to a height of $0.2$ m. If the loss in potential energy is used up by the body, then what will be the temperature rise? (specific heat of material=$0.09\ cal\ gm^{-1}\ {^{o}C^{-1}}$)

Options:
A. $$5^0C$$
B. $$0.52^0C$$
C. $$4^0C$$
D. $$10^0C$$
E. $$9^0C$$
F. $$11^0C$$
G. $$6^0C$$
H. $$12^0C$$
I. $$7^0C$$
Answer: B