MikaStars39/nano-eval huggingface dataset:
The displacement Y (in cm) produced by a simple harmonic wave is given by $Y = \frac{10}{\pi} sin (2000 \pi t - \frac{\pi x}{17})$
then the period and the maximum velocity of the particle in the medium respectively will be

Options:
A. $10^{-3}$ sec and 330 metre per sec
B. $10^{-4}$ sec and 230 metre per sec
C. $10^{-3}$ sec and 200 metre per sec
D. $10^{-3}$ sec and 300 metre per sec
E. $10^{-4}$ sec and 330 metre per sec
F. $10^{-4}$ sec and 180 metre per sec
G. $10^{-4}$ sec and 300 metre per sec
H. $10^{-4}$ sec and 200 metre per sec
I. $10^{-4}$ sec and 210 metre per sec
J. $10^{-4}$ sec and 220 metre per sec
Answer: C
Which of these ions $Cu^+, Co^{3+}, Fe^{2+}$ is stable in the aqueous medium?Given: $E_{Cu^{2+}/Cu^+}^0 = 0.15 V;\   E_{Cu^+/Cu}^0 = 0.53 V\      E_{Co^{3+}/Co^{2+}}^0 = 1.82 V;  \     E_{Fe^{3+}/Fe^{2+}}^0 = 0.77 V \       E_{Fe^{2+}/Fe}^0 = - 0.44  V;    \    E_{O_2, H^+/H_2O}^0 = 1.23 V$

Options:
A. $$Fe^{3+}$$
B. $$Co^{2+}, Fe^{3+}$$
C. $$Cu^+, Co^{3+}$$
D. $$Co^{3+}, Cu^+$$
E. $$Co^{3+}, Cu^+, Fe^{2+}$$
F. $$Fe^{3+}, Co^{3+}$$
G. $$Co^{2+}, Fe^{2+}$$
H. $$Co^{2+}$$
I. $$Co^{3+}$$
J. $$Cu^{2+}$$
Answer: I
Pressure $P$, volume $V$ and temperature $T$ of a certain material are related by $P = \dfrac{\alpha T^2}{V}$. Here, $\alpha$ is a constant. The work done by the material when temperature changes from $T_0$ to $2T_0$ while pressure remains constant is:

Options:
A. $$\dfrac{3}{2} \alpha T_{0}^{2}$$
B. \(\dfrac{1}{2} \alpha T_{0}^{2}\)
C. $$2 \alpha T_{0}^{2}$$
D. $$\dfrac{5}{2} \alpha T_{0}^{2}$$
E. \(\dfrac{7}{2} \alpha T_{0}^{2}\)
F. $$4 lpha T_{0}^{2}$$
G. $$4 \alpha T_{0}^{2}$$
H. $$3 lpha T_{0}^{2}$$
I. $$6 \alpha T_{0}^{3}$$
Answer: A
An object is placed at 15 cm in front of convex lens of focal length 10 cm. Where shall we place a convex mirror of focal length 13 cm so that real image and object coincide?

Options:
A. 6 cm from lens
B. 1 cm from lens
C. 8 cm from lens
D. 5 cm from lens
E. 9 cm from lens
F. 3 cm from lens
G. 4 cm from lens
H. 7 cm from lens
I. 10 cm from lens
J. 2 cm from lens
Answer: G
A solid sphere of radius $R$ is placed on smooth horizontal surface. A horizontal force $'F'$ is applied at height $'h'$ from the lowest point. For the maximum acceleration of centre of mass, which is correct ?

Options:
A. $$h = \frac{3R}{2}$$
B. $$h = R$$
C. $$h = \frac{R}{2}$$
D. $$h = \frac{R}{4}$$
E. $$h = \frac{3R}{4}$$
F. $$h = 0$$
G. No relation between $h$ and $R$.
H. $$h = \frac{2R}{3}$$
I. $$h = 2R$$
J. $$h = \frac{R}{3}$$
Answer: G
One ens of uniform glass capillary tube of radius r = 0.025 cm is immersed vertically in water if a depth h = 1 cm. The excess pressure in N/m$^{2}$ requrired to blow an air bubble out of the tube is [Surface tension of water = $7\times 10^{-2}$Nm. Densitty = $ 10^{3}$ kgm$ ^{-3}$. Acceleration due yto gravity =$ 10ms^{-2}$]

Options:
A. $$1.0018\times 10^{5}$$
B. $$0.0072 \times 10^{5}$$
C. $$0.0060 \times 10^{5}$$
D. $$0.0048\times 10^{5}$$
E. $$0.0056 \times 10^{5}$$
F. $$1.0033\times 10^{5}$$
G. $$0.0064 \times 10^{5}$$
H. $$0.0054 \times 10^{5}$$
I. $$0.0050 \times 10^{5}$$
J. $$0.0066\times 10^{5}$$
Answer: D
A rectangular loop has a sliding connector $PQ$ of length $1$ and resistance $R\Omega$ and it is moving with a speed $v$ as shown. The set-up is paced in a uniform magnetic field going into the plane of the paper. The three currents $I_1,I_2$ and $I$are

Options:
A. $$I_1=-I_2=\dfrac {B1v}{R},I=\dfrac {3\ B1v}{2R}$$
B. $$I_1=-I_2=\dfrac {B1v}{4R},I=\dfrac {B1v}{2R}$$
C. $$I_1=-I_2=\dfrac {B1v}{R},I=\dfrac {2\ B1v}{R}$$
D. $$I_1=-I_2=\dfrac {B1v}{3R},I=\dfrac {4B1v}{3R}$$
E. $$I_1=-I_2=\dfrac {B1v}{2R},I=\dfrac {3B1v}{R}$$
F. $$I_1=-I_2=\dfrac {B1v}{5R},I=\dfrac {2\ B1v}{5R}$$
G. $$I_1=-I_2=\dfrac {B1v}{3R},I=\dfrac {2\ B1v}{3R}$$
H. $$I_1=-I_2=\dfrac {B1v}{4R},I=\dfrac {B1v}{R}$$
I. $$I_1=-I_2=\dfrac {B1v}{6R},I=\dfrac {2\ B1v}{3R}$$
J. $$I_1=-I_2=I=\dfrac {B1v}{R}$$
Answer: C
What would be the pH of a solution obtained by mixing $5g$ of acetic acid and $7.5g$ of sodium acetate and making the volume equal to :$500mL$?($K_a=1.75\times 10^{-5},pK_a=4.76$)

Options:
A. $$pH=4.8$$
B. $$pH=4.56$$
C. $$pH<4.70$$
D. $$pH=4.61$$
E. $$pH=4.52$$
F. $$pH=4.49$$
G. $$pH=4.51$$
H. $$pH=4.54$$
I. $pH$ of solution will be equation to $pH$ of acetic acid
J. $$pH=4.59$$
Answer: F
Two rods of length $ L_1$ and $L_2 $ are made of material whose coefficient of linear expansion are $ \alpha_1$ and $\alpha_2 $ if the difference between  the two lengths is independent of temperature

Options:
A. $$( L_1 / L_2 ) = ( \alpha_2 / \alpha_1 )$$
B. $$( L_1 / L_2 ) = ( \alpha_1 / \alpha_2 )^{1/2}$$
C. $$( L_1 / L_2 ) = ( \alpha_1 / \alpha_2 )^2$$
D. $$( L_1 /L_2 ) = ( \alpha_2 / \alpha_1 )^{1/2}$$
E. $$( L_1 /L_2 ) = ( \alpha_1 / \alpha_2 )^{3/2}$$
F. $$ \alpha^2_1L_1 = \alpha^2_2L_2 $$
G. $$ ( L_1 /L_2 ) = ( \alpha_1 / \alpha_2 ) $$
H. $$ ( L_1 /L_2 ) = ( \alpha_2 / \alpha_1 ) $$
I. $$ L^2_1 \alpha_1 = L^2_2 \alpha_2 $$
Answer: A
How much $NH_{3}$ should be added to a 0.004 M $Ag^{+}$ solution to prevent the precipitation of AgCl when $Cl^{-}$ ion reaches 0.001 M? $K_{sp} (AgCl) = 1.8\times 10^{-10},K_{d} (Ag(NH_{3})_{2}^{+}) = 6\times 10^{-8}$

Options:
A. 1.6 molar/litre
B. 0.0016 molar/litre
C. 0.0015 molar/litre
D. 0.36 molar/litre
E. 0.0013 molar/litre
F. 0.0024 molar/litre
G. 0.0022 molar/litre
H. 0.0036 molar/litre
I. 0.0012 molar/litre
J. 0.044 molar/litre
Answer: J
For a chemical reaction of the type
$A \rightleftharpoons  B,K=2.0$ and $B \rightleftharpoons C,K=0.01$ Equilibrium constant for the reaction $2C \rightleftharpoons  2A$ is

Options:
A. $$500$$
B. $$25$$
C. $$2500$$
D. $$200$$
E. $$100$$
F. $$400$$
G. $$2000$$
H. $$50$$
I. $$4\ \times 10^{-4}$$
Answer: H
A process $ 1 \rightarrow 2 $ using diatomic gas is: $ P_2 = 2P_1 = 10^6 N /m^2 , V_2 = 4V_1 = 0.4m^3 $ the molar heat capacity of the gas in this process will be :

Options:
A. $$ 35 R / 11 $$
B. $$ 25 R / 13 $$
C. $$ 22 R / 7 $$
D. $$32 R / 7$$
E. $$35 R / 7$$
F. $$25 R / 11$$
G. $$25 R / 12$$
H. $$32 R / 13$$
I. $$ 35 R / 12 $$
J. $$32 R / 11$$
Answer: C
Potassium permanganate acts as an oxidising agent in acidic, alkaline as well as neutral media. Which among the following statements is incorrect?

Options:
A. $N = M/3$ (in neutral medium)
B. $N = M$ (in alkaline medium)
C. N = M/4 (in neutral medium)
D. $N = M/5$ (in acid medium)
Answer: D
A uniform rope of mass $0.1\ kg$ and length $2.45\ m$ hangs from a ceiling. The time taken by a transverse wave to travel the full length of the rope is $(g=9.8\ m/s^{2})$

Options:
A. $$2\ s$$
B. $$3\ s$$
C. $$1\ s$$
D. $$6\ s$$
E. $$4\ s$$
F. $$10\ s$$
G. $$5\ s$$
H. $$7\ s$$
I. $$8\ s$$
Answer: E
Two particles of masses $m_1$ and $m_2$ and velocities $u_1$ and $\alpha u_1 (\alpha \neq 0)$ make an elastic bead on collision. If the initial kinetic energies of the two particles are equal and $m_1$ comes to rest after collision. Then

Options:
A. $\dfrac{m_2}{m_1} = 3 + 2 \sqrt{2}$ and $\dfrac{u_1}{u_2} = \sqrt{2} + 1$
B. $$\dfrac{m_2}{m_1} = 3 - 2 \sqrt{2}$$
C. $$\dfrac{m_2}{m_1} = 3 + 2 \sqrt{3}$$
D. $$\dfrac{u_1}{u_2} = \sqrt{2} - 1$$
E. $$\dfrac{m_2}{m_1} = 3 - 2 \sqrt{1}$$
F. $$\dfrac{m_2}{m_1} = 3 + 2 \sqrt{1}$$
G. $$\dfrac{m_2}{m_1} = 3 - 2 \sqrt{3}$$
H. $$\dfrac{m_2}{m_1} = 3 - 2 \sqrt{4}$$
Answer: A
Which of the following statements is/are correct with respect to the equilibrium for equation $PCl_5(g)\rightleftharpoons PCl_3(g)+Cl_2(g)$?

Options:
A. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.4.
B. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.2.
C. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.3.
D. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.22.
E. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.18.
F. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.25.
G. The value of $K_P=0.041$ atm at one atmospheric pressure when the degree of dissociation is 0.1.
Answer: B
In a competing first-order reaction where \( A \xrightarrow{k_1} C \) and \( A \xrightarrow{k_2} D \), with \( [C] = [D] \) at all times, determine the time at which \( [A] = [C] = [D] \).

Options:
A. $$\displaystyle t = \frac{1}{3k_2} ln 2$$
B. $$\displaystyle t = \frac{1}{3k_2} \ln 4$$
C. $$\displaystyle t = \frac{1}{3k_1} ln 2$$
D. $$t = \frac{1}{3k_2} \ln 3$$.
E. $$\displaystyle t = \frac{1}{3k_1} ln 3$$
F. $$\displaystyle t = \frac{1}{2k_2} ln 3$$ and $$\displaystyle t = \frac{1}{2k_1} \ln 3$$
G. $$\displaystyle t = \frac{1}{2k_1} \ln 2$$
H. $$\displaystyle t = \frac{1}{4k_1} \ln 3$$
I. $$\displaystyle t = \frac{1}{4k_2} \ln 4$$
Answer: F
As a gas (insolube in liquid ) is bubbled through a liquid , a part of the liquid vaporises and these vapour are carried off by the gas. As a sample of dry air is bubbled through a liquid (A). it is found that same mass of 'wet'' air , at same pressure and temperature in identical vessels weigh more than the correspondibg dry air sample. If average molecular mass of air is $29\,g\,mo{l^{ - 1}}$ , (A) could be which one? (H=1, D=2, C=12)

Options:
A. $$butane$$
B. $$benzene$$
C. $$butanol$$
D. $$water$$
E. $$methanol$$
F. $$propane$$
G. $\text{Heavy water} \left( \text{D}_2\text{O} \right)$
H. $$ethanol$$
Answer: H
Ammonia is produced by $H_2$ & $N_2$ by Haber process according to given reaction :
$$N_2(g)+H_2(g) \rightarrow NH_3(g)$$
Find $\triangle H_f\quad of\quad NH_3 (g)$
Given: $BE_{N-H} = 350 kj/mol$
$BE_{N \equiv N} =700kj/mol$, $BE_{H-H} = 430 kj/mol$

Options:
A. $$+115kj/mol$$
B. $$+110kj/mol$$
C. $$-110kj/mol$$
D. $$-115kj/mol$$
E. $$110kj/mol$$
F. $$+55kj/mol$$
G. $$-55kj/mol$$
H. $$-105kj/mol$$
I. $$-50kj/mol$$
Answer: E
A coin is dropped in a lift, it takes time ${ t }_{ 1 }$ to reach the floor when lift is stationary. It takes time ${ t }_{ 2 }$ when the lift is moving up with costant acceleration. Then

Options:
A. $$t _ { 1 } < t _ { 2 }$$
B. $$t _ { 1 } = t _ { 2 }$$
C. \( t _ { 1 } = \frac{4}{3} t _ { 2 } \)
D. \( t _ { 1 } = \frac{1}{2} t _ { 2 } \)
E. $$t _ { 1 } > t _ { 2 }$$
F. $$ t _ { 1 } = \sqrt{2} t _ { 2 } $$
G. $$t _ { 1 } = \frac{5}{3} t _ { 2 }$$
H. $$t _ { 1 } = \frac{3}{2} t _ { 2 }$$
I. \( t _ { 1 } = 2 t _ { 2 } \)
J. none of these
Answer: B
A spinning ball (uniform solid sphere) of radius $R$ fall vertically on a rough horizontal floor (co-efficient of friction $\mu=0.5$ with velocity $u$. The ball is also rotating about a horizontal axis with angular velocity $\dfrac{5u}{R}$. The co-efficient of restitution of ball with the floor is $0.5$. If the ball still rotates in same direction after collision, what is the new angular velocity of ball?

Options:
A. $$\dfrac{3u}{R}$$
B. $$\dfrac{35u}{8R}$$
C. $$\dfrac{5u}{2R}$$
D. $$\dfrac{4u}{R}$$
E. $$\dfrac{2u}{R}$$
F. $$\dfrac{3u}{4R}$$
G. $$\dfrac{u}{2R}$$
H. $$\dfrac{3u}{2R}$$
I. $$27u8R27u8R$$
J. $$\dfrac{u}{R}$$
Answer: A
Two particles $A$ and $B$ each of mass $m$ are attached by a light in-extensible string of length $2l$. The whole system lies on a smooth horizontal table with $B$ initially at a distance $l$ from $A$. The particle at end $B$ is projected across the table with speed $u$ perpendicular to $AB$. Velocity of ball $A$ just after the jerk, is :

Options:
A. component of $v_{B}$ perpendicular to $AB=\dfrac{u \sqrt{3}}{5}$
B. $$v_{B}=\dfrac{u\sqrt{3}}{4}$$
C. component of \( v_{B} \) perpendicular to \( AB = \dfrac{u \sqrt{3}}{6} \)
D. component of $v_{B}$ perpendicular to $AB=\dfrac{u \sqrt{3}}{7}$
E. component of $v_{B}$ along $AB$ is $\dfrac{u\sqrt{3}}{4}$
F. component of $v_{B}$ perpendicular to $AB=\dfrac{u}{2}$
G. component of $v_{B}$ perpendicular to $AB=\dfrac{u\sqrt{3}}{3} $
H. component of \( v_{B} \) perpendicular to \( AB = \dfrac{u \sqrt{3}}{2} \)
I. $$v_{A}=\displaystyle \frac{u \sqrt 3}{4}$$
J. component of \( v_{B} \) perpendicular to \( AB = \dfrac{u \sqrt{3}}{8} \)
Answer: I
For the gaseous phase reaction $2A +B\rightleftharpoons 2C +D$, identically there are 2 mole each of A and B. If 0.4 mol of D is present at equilibrium at a given T and P, in-correct relationship  is?

Options:
A. $P_A > P_D$ & $P_A > P_C $
B. $P_A < P_B$ & $P_D < P_C$
C. $ P_C = 2P_D$ & $P_A = 3P_B/4 $
D. $P_C = P_D$ & $P_A = 3P_B/4$
Answer: C
Autoionisation of liquid $NH_3$ is $2NH_3 \rightleftharpoons NH_4^++NH^-_2$ with $K_{NH_3}=[NH_4^+][NH_2^-]=10^{-30}$ at $-50^0C$. Number of amide ions $NH_2^-$, present per $mm^3$ of pure liquid $NH_3$ is :

Options:
A. 100
B. 180
C. 450
D. 500
E. 250
F. 400
G. 150
H. 600
I. 300
J. 602
Answer: J
Three uniformly charged wires with linear charge density 1 are placed along x, y and z axis respectively. What is flux of electric field through Gaussian surface given by $x^2 + y^2 + z^2 =1 ; x > 0 ; y > 0 ; z > 0$

Options:
A. \(\frac{5\lambda }{2\varepsilon _0} \)
B. \(\frac{4\lambda }{2\varepsilon _0} \)
C. \(\frac{3\lambda }{5\varepsilon _0} \)
D. $$\frac{3\lambda }{\varepsilon _0}$$
E. \(\frac{3\lambda }{6\varepsilon _0}\)
F. $$\frac{6\lambda }{\varepsilon _0}$$
G. $$\frac{3\lambda }{4\varepsilon _0}$$
H. $$\frac{3\lambda }{2\varepsilon _0}$$
I. \(\frac{3\lambda }{3\varepsilon _0}\)
J. \(\frac{2\lambda }{\varepsilon _0} \)
Answer: H
Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = $[position]=[X^{\alpha}];[speed]=[X^{\beta}];[acceleration]=[X^{p}];[liner\,\, momentum]=[X^{q}];[force]=[X^r]$. Then

Options:
A. $$p-q+r=\beta$$
B. $p+q-r=\beta$ and $\alpha+p=2\beta$
C. $$p+q+r=\beta$$
D. $$p-q+r=\alpha$$
E. $$p+q+r=\alpha$$
F. $$p-q-r=\alpha$$
G. $$p+q-r=\alpha$$
H. $$p-q-r=\beta$$
Answer: B
Three dense point size bodies of same mass are attached at three vertices of a light equilateral triangular frame. Identify the increasing order of their moments of inertia about following axes:I) about an axis perpendicular to plane and passing through a cornerII) about an axis perpendicular to plane and passing through centreIII) about an axis passing through any side in the plane of the triangleIV) about perpendicular bisector of any side

Options:
A. III, I, IV, II
B. III, II, I, IV
C. III, II, IV, I
D. II, III, I, IV
E. II, III, IV, I
F. II, IV, III, I
G. II, IV, I, III
H. III, IV, I, II
I. III, IV, II, I
J. III, I, II, IV
Answer: C
Two metallic shells with charges q each are kept in air with their centre distance r. The magnitude of electrostatic force between them is:$\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

Options:
A. less than $K\frac{{q^2}}{{r^2}}$
B. cant be predicted
C. more than $K\frac{{4q^2}}{{r^2}}$
D. more than $K\frac{{5q^2}}{{r^2}}$
E. more than $K\frac{{2q^2}}{{r^2}}$
F. less than $K\frac{{{q^2}}}{{{r^2}}}$
G. more than $K\frac{{3q^2}}{{r^2}}$
H. equal to $K\frac{{{q^2}}}{{{r^2}}}$
I. less than $K\frac{{q^2}}{{2r^2}}$
J. more than $K\frac{{{q^2}}}{{{r^2}}}$
Answer: J
A body moves in a circular path of radius $R$ with deceleration such that, at any moment of time, its tangential acceleration and normal acceleration are equal in magnitude. At the initial moment $t = 0$, the velocity of the body is $v_0$. Determine the velocity of the body at any later time.

Options:
A. $$v = v _ { 0 } e ^ { - S / (R + 1) }$$
B. $$v = v _ { 0 } e ^ { - 2S / R }$$
C. $$v = v _ { 0 } e ^ { - S / (R - 1) }$$
D. $$v = \dfrac { v _ { 0 } } { 1 + \left( \frac { v _ { 0 } t } { R } \right) } \text { at time } t$$
E. $$v = v _ { 0 } e ^ { - S / (3R) }$$
F. None of these.
G. $$v = v _ { 0 } e ^ { - S / (2R) }$$
H. $$v = v _ { 0 } e ^ { - S R } \text { after it has moved S meter }$$
I. $$v = v _ { 0 } e ^ { - S / (R + 2) }$$
Answer: F
Enthalpy change for the following reaction has been given as follows:
$$\mathrm { M } _ { ( \mathrm { g } ) } \longrightarrow \mathrm { M } _ { ( \mathrm { g } ) } ^ { 2 + } + 2 \mathrm { e } ^ { - } \quad \Delta \mathrm { H } = 280 \mathrm { KJ } / \mathrm { mole }$$
$\mathrm { M } _ { ( \mathrm { g } ) } \longrightarrow \mathrm { M } _ { ( \mathrm { g } ) } ^ { \mathrm { S } + }$ $+ 3 \mathrm { e } ^ { - } \quad \Delta \mathrm { H } = 500 \mathrm { KJ } / \mathrm { mole }$
then choose the correct statement :-

Options:
A. \mathrm { IP } _ { 2 } of \mathrm { M } _ { ( \mathrm { g } ) } is 480\mathrm { KJ } / \mathrm { mole }
B. $\mathrm { IP } _ { 2 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 420$\mathrm { KJ } / \mathrm { mole }$
C. $\mathrm { IP } _ { 2 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 380$\mathrm { KJ } / \mathrm { mole }$
D. $\mathrm { IP } _ { 2 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 500$\mathrm { KJ } / \mathrm { mole }$
E. $\mathrm { IP } _ { 3 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 320$\mathrm { KJ } / \mathrm { mole }$
F. $\mathrm { IP } _ { 2 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 280$\mathrm { KJ } / \mathrm { mole }$
G. \mathrm { IP } _ { 2 } of \mathrm { M } _ { ( \mathrm { g } ) } is 220\mathrm { KJ } / \mathrm { mole }
H. $\mathrm { IP } _ { 3 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 500$\mathrm { KJ } / \mathrm { mole }$
I. $\mathrm { IP } _ { 3 }$ of $\mathrm { M } _ { ( \mathrm { g } ) }$ is 220$\mathrm { KJ } / \mathrm { mole }$
J. (1) and (3) both are correct
Answer: F
An infinitely long wire is kept along z-axis from $z = - \infty \text { to } z = + \infty$ having uniform linear charge density $\frac { 10 } { 9 } n \mathrm { C } / \mathrm { m }$. The electric field $\vec { \mathrm { E } }$ at point $( 6 \mathrm { cm } , 8 \mathrm { cm } , 10 \mathrm { cm } )$ will be

Options:
A. $$( 160 i + 120 j + 140 k ) N / C$$
B. $$( 200 k ) N / C$$
C. $$( 160 i + 120 j + 180 k ) N / C$$
D. $$( 160 i + 120 j + 190 k ) N / C$$
E. $$( 160 i + 120 j ) N / C$$
F. $$( 160 i + 120 j + 170 k ) N / C$$
G. $$( 160 i + 120 j + 150 k ) N / C$$
H. $$( 160 i + 120 j + 200 k ) N / C$$
I. $$( 120 i + 160j ) N / C$$
J. $$( 160 i + 120 j + 160 k ) N / C$$
Answer: I
A homogeneous rod \( AB \) of length \( 1.8 \, \text{m} \) and mass \( M \) pivots at its center \( O \) and rotates freely in the vertical plane; initially horizontal, an insect of mass \( M \) falls vertically with speed \( V \) onto the midpoint \( C \) (located at \( L/4 \) from \( O \) and \( B \)) of the rod, then moves towards end \( B \) such that the rod rotates at constant angular velocity \( \omega \), reaching \( B \) when the rod rotates by \( 90^\circ \); determine \( V \).

Options:
A. $$3.7$$
B. $$6$$
C. $$4.2$$
D. $$3.8$$
E. $$4$$
F. $$3.5$$
G. $$5$$
H. $$4.1$$
I. $$4.5$$
J. $$4.3$$
Answer: F
$$Cl_{2}\Leftrightarrow 2Cl$$
$$CH_{4} + Cl\rightarrow CH_{3} + HCl (slow)$$
$$CH_{3} + Cl_{2} \rightarrow CH_{2} Cl + Cl$$
$$CH_{3}Cl + Cl \rightarrow CH_{2}Cl_{2} + H$$
$$H + Cl\rightarrow HCl$$
The above mechanism shows the overall reaction between chlorine gas and methane gas to form dichloromethane gas and hydrogen monochloride gas. The reaction is carried out in the gas state with no ions being formed during the reaction.
Which of the following statements is not supported by the mechanism?

Options:
A. The order of the reaction with respect to $CH_{4}$ is one since step $2$ is the slowest step, making the rate law for step $2: rate = k[CH_{4}][Cl]$
B. The first step is the only equilibrium step in the reaction
C. $CH_{3}Cl$ is an intermediate because it is made in step $3$ and used in step $4$
D. The order of the reaction with respect to $CH_{4}$ is zero since step $2$ is the slowest step, making the rate law for step $2: rate = k[Cl]$
E. The order of the reaction with respect to $CH_{4}$ is zero since step $2$ is the slowest step, making the rate law for step $2: rate = k[Cl]^{2}$
F. $CH_{3}Cl$ is a product because it is formed in step $3$ and does not appear in the reactants
G. The order of the reaction with respect to $CH_{4}$ is one since step $2$ is the slowest step, making the rate law for step $2: rate = k[CH_{4}][Cl]^{2}$
H. The first step is an equilibrium step and all other steps are irreversible
I. The overall rate law for the reaction is: $rate = k[CH_{4}][Cl_{2}]$
Answer: C
Under standard condition $\Delta G^{0}$ for the reaction $2Cr(s)+3Cd^{2+}(aq) \rightarrow 2Cr_{(aa)}^{3+}+Cd(s)$ is
$$(E^{o}(Cr^{3+}/Cr)=-0.74V, E^{o}(Cd^{2+}/Cd)=-0.4V)$$

Options:
A. $$-196.86\ kJ/mole$$
B. $$-19.686\ kJ/mole$$
C. $$-66.62\ J/mole$$
D. $$-67.62\ J/mole$$
E. $$-96.86\ J/mole$$
F. $$-65.62\ J/mole$$
G. $$-64.52\ J/mole$$
H. $$-66.12\ J/mole$$
I. $$-98.43\ kJ/mole$$
J. $$-64.62\ J/mole$$
Answer: F
A uniform disc of radius $R$ is spinned to the angular velocity $\omega$ and then carefully placed on a horizontal surface. How long will the disc be rotating on the surface if the friction coefficient is equal to $k$ ? The pressure exerted by the disc on the surface can be regarded as uniform.

Options:
A. $$\displaystyle t= \frac{3R\omega_0}{6kg}$$
B. $$\displaystyle t= \frac{5R\omega_0}{7kg}$$
C. $$\displaystyle t= \frac{5R\omega_0}{8kg}$$
D. $$\displaystyle t= \frac{3R\omega_0}{5kg}$$
E. None of these
F. $$\displaystyle t=\frac{5R\omega_0}{4kg}$$
G. $$\displaystyle t=\frac{3R\omega_0}{4 \mu g}$$
H. $$\displaystyle t= \frac{5R\omega_0}{6kg}$$
I. $$\displaystyle t= \frac{3R\omega_0}{7kg}$$
J. $$\displaystyle t=\frac{3R\omega_0}{8kg}$$
Answer: G
A hill is $500\ m$ high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of $125\ m/s$ over the hill. The canon is located at a distance of $800\ m$ from the foot of a hill and can be moved on the ground at a speed of $2\ m/s$; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take $ g=10{ m }/{ { s }^{ 2 } } $.

Options:
A. None of these
B. $$45 s$$
C. $$40 s$$
D. $$50 s$$
E. $$60 s$$
F. $$55 s$$
G. $$30 s$$
H. $$48 s$$
I. $$42 s$$
Answer: B
Given that the data for neutralization of a weak acid $(HA)$ and strong acid with a strong base is:
$$HA + OH^{-}\rightarrow A^{-} + H_{2}O;\ \triangle H = -41.80\ kJ$$
$$H^{+} + OH^{-}\rightarrow H_{2}O;\ \triangle H = -55.90\ kJ$$
The enthalpy of dissociation of weak and would be:

Options:
A. $$+97.70\ KJ$$
B. $$-14.10\ KJ$$
C. $$-55.90\ KJ$$
D. $$-56.10\ KJ$$
E. $$-55.80\ KJ$$
F. $$-97.20\ KJ$$
G. $$-14.20\ KJ$$
H. $$14.10\ KJ$$
I. $$+97.20\ KJ$$
Answer: F
The intensity of an electric field depends on the co-ordinates x , y and z as follows $\displaystyle E=\frac{a\left ( xi+yj+zk \right )}{(x^{2}+y^{2}+z^{2})^{3/2}}$ unit The electrostatic energy stored between two imaginary concentric spherical shells of radii r and 2 R with center at origin is

Options:
A. $$\dfrac{a^2 R}{k}$$
B. $$\dfrac{aR^2}{k}$$
C. $$\dfrac{aR}{k}$$
D. $$\displaystyle \frac{4\pi\varepsilon _{0}a^{2}}{R}$$
E. $$\dfrac{aR^2}{2k}$$
F. $$\dfrac{2aR}{k}$$
G. $$\dfrac{a^2 R^2}{k}$$
H. $$\displaystyle \frac{2\pi\varepsilon _{0}a^{2}}{R}$$
I. $$\displaystyle \frac{\pi\varepsilon _{0}a^{2}}{R}$$
J. $$\dfrac{a^2 k}{R}$$
Answer: I
An oscillator of mass $M$ is at rest in the equilibrium position in a potential $V = \dfrac {1}{2}k(x - X)^{2}$. A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after $13$ collisions is : $(M = 10, m = 5, u = 1, k = 1)$.

Options:
A. $$\dfrac {1}{3}$$
B. $$\sqrt {\dfrac {3}{5}}$$
C. $$\dfrac {1}{\sqrt {3}}$$
D. $$\dfrac{1}{\sqrt{6}}$$
E. $$\dfrac {1}{\sqrt {5}}$$
F. $$\dfrac {1}{2}$$
G. $$\dfrac {2}{3}$$
H. $$\dfrac {3}{5}$$
I. $$\dfrac{4}{5}$$
J. $$\dfrac {3}{4}$$
Answer: C
Many lead salts are often used as pigments. If $PbSO_4$ $( {K_{sp}} = {1.6 \times 10^{-8}})$ were used in an unglazed ceramic bowl, how many milligrams of lead (II) could dissolve per liter of water?

Options:
A. 35
B. 39
C. 11
D. 37
E. 42
F. 40
G. 38
H. 36
I. 43
J. 41
Answer: G
Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^{o}$ and $60^{o}$ with field. Let a, b and c be the ratio of their time periods, radii and pitches of the helical paths then:

Options:
A. $$abc<1$$
B. $$a = b/c$$
C. $$a = c/b$$
D. $$a = b + c$$
E. $$a = b - c$$
F. $$a = b + 2c$$
G. $$abc>1$$
H. $$a =bc$$
Answer: H
An organic compound $(X)$ with molecular formula $C_{3}H_{7}NO$ reacts with bromine and caustic soda to give another compound $(Y)$. It reacts with $HNO_{2}$ to form alcohol and nitrogen gas. Compound $(X)$ and $(Y)$ respectively are

Options:
A. $$X = CH_{3}CONHCH_{3}; Y = CH_{3}CH_{2}OH$$
B. $$X = CH_{3}CONHCH_{3}; Y = CH_{3}COOH$$
C. $$X = CH_{3}CH_{2}CONH_{2}, Y = CH_{3}CH_{2}NH_{2}$$
D. $$X = CH_{3}CONHCH_{3}; Y = CH_{3}CH_{2}CHO$$
E. $$X = CH_{3}CONH_{2}; Y = CH_{3}CH_{2}OH$$
F. $$X = CH_{3}CH_{2}NHCHO, Y = BrCH_{2}CH_{2}NH_{2}$$
G. $$X = CH_{3}CH_{2}CONH_{2}, Y = CH_{3}CH_{2}COBr$$
H. $$X = CH_{3}CH_{2}CONHCH_{3}; Y = CH_{3}CH_{2}COOH$$
I. $$X = CH_{3}CH_{2}CONHCH_{3}; Y = CH_{3}CH_{2}OH$$
J. $$X = CH_{3}CONHCH_{2}CH_{3}; Y = CH_{3}CH_{2}OH$$
Answer: A
What would be the equivalent weight of the reductant in the given reaction?${ \left[ Fe{ \left( CN \right)  }_{ 6 } \right]  }^{ -3 }+{ H }_{ 2 }{ O }_{ 2 }+2{ Oh }^{ - }\rightarrow 2{ \left[ Fe{ CN }_{ 6 } \right]  }^{ 4- }+{ 2H }_{ 2 }O+{ O }_{ 2 }$$\left[ Given:\quad Fe=56,\quad C=12,\quad N=14,\quad O=16,\quad H=1 \right] $

Options:
A. $$17$$
B. $$38$$
C. $$33$$
D. $$34$$
E. $$30$$
F. $$32$$
G. $$212$$
H. $$31$$
I. $$36$$
J. $$35$$
Answer: D
The approach to the following equilibrium was observed kinetically from both directions:$ Pt{ Cl }_{ 4 }^{ -2 }+H_{ 2 }O\rightleftharpoons Pt(H_{ 2 }O)Cl_{ 3 }+Cl^{ - } $At $ 25^o C,$  it was found that  $ -\dfrac { d[PtC{ l }_{ 4 }^{ 2- }] }{ dt } =(3.9  \times 10^{ -5 } s^{ -1 }) [PtC{ l }_{ 4 }^{ 2- }]-(2.1  \times 10^{ -3 } L mol^{ -1 }s^{ -1 }) [Pt(H_{ 2 }O)C{ l }_{ 3 }^{ - }][Cl^{ - }] $The value of $ K_{eq} $ (equilibrium constant) for the complexation of the fourth $ cl^- $ by $ Pt( II ) $ is

Options:
A. $$5.38 mol L^{-1}$$
B. $$ 0.538 L mol^{-1} $$
C. $$53.8 mol^{-1} L$$
D. $$ 53.8 mol L^{-1} $$
E. $$ 0.018 mol L^{-1} $$
F. $$538 L mol^{-1}$$
G. $$5.38 L mol^{-1}$$
H. $$ 53.8 L mol^{-1} $$
I. $$ 0.018 L mol^{-1} $$
Answer: D
Arrange ein increasing order of solubility of $AgBr$ in following
i) 0.1 M ${ NH }_{ 3 }$
ii) 0.1 M $AgNO_{ 3 }$
iii) 0.2 M NaBr
iv) pure water

Options:
A. $$(iii)<(iv)<(ii)<(i)$$
B. $$(iii)<(ii)<(i)<(iv)$$
C. $$(ii)<(iii)<(iv)<(i)$$
D. $$(iii)<(i)<(ii)<(iv)$$
E. $$(iii)<(ii)=(i)<(iv)$$
F. $$(iii)<(ii)<(iv)<(i)$$
G. $$(iii)<(i)<(iv)<(ii)$$
Answer: F
For an adiabatic irreversible process involving an ideal gas:

Options:
A. $$\Delta W=nC_{v}\Delta T$$
B. $$\Delta U=P_{ext.}(V_{1}+V_{2})$$
C. $$\Delta U=P_{ext.}(V_{1}-V_{2})$$
D. $$\Delta U=nC_{v}\Delta T$$
E. $$\Delta U=-nC_{v}\Delta T$$
F. $$\Delta U=-P_{ext.}(V_{2}-V_{1})$$
Answer: D
First overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further nth harmonic of closed organ pipe is also equal to the mth harmonic of open pipe, where n and m are :

Options:
A. 8, 6
B. 7, 4
C. 5, 4
D. 8, 5
E. 9, 4
F. 7, 5
G. 9, 6
H. 9, 5
I. 8, 3
J. 7, 3
Answer: G
A ring, a disc , a hollow sphere and a solid sphere take part in a  race on an inclined plane. If all of them have the same radius and the same mass, which of them will win the race?

Options:
A. Cylinder
B. cylinder
C. hollow sphere
D. Solid sphere
E. Disc
F. Hollow cylinder
G. Solid cylinder
H. hollow cylinder
I. Hollow sphere
J. ring
Answer: J
Work done in an isothermal reversible expansion of $1$ mole $Cl_2$ from $1$ litre to $50$ litre at $273\ K$ (for $Cl_2$, $a = 0.655\ litre^2\ MPa\ mol^{-2}, b = 0.055\ litre\ mol^{-1}$)

Options:
A. $$83.65 kJ/mol$$
B. $$-8.365 kJ/mol$$
C. $$32.65 kJ/mol$$
D. $$8.365 kJ/mol$$
E. $$325.5 kJ/mol$$
F. $$325.6 kJ/mol$$
G. $$83.55 kJ/mol$$
H. $$32.55 kJ/mol$$
I. $$32.56 kJ/mol$$
J. $$8.355 kJ/mol$$
Answer: H
For the reaction :
$$CH_4(g) + 2 O_2 (g) \rightarrow CO_2(g) + 2 H_2O (g)$$

Options:
A. $$\Delta H > \Delta E$$
B. $$\Delta H = \Delta E$$
C. $$\Delta H < \Delta E$$
D. $\Delta H$ is independent of the physical state of products but depends on reactants
E. $\Delta H$ depends on the physical state of reactants but not on products
F. $\Delta H \leq \Delta E$
G. $\Delta H$ depends on the physical state of both reactants and products
H. $\Delta H$ depends on the physical state of reactants but not products
I. $\Delta H$ is always equal to $\Delta E$ for all reactions
J. $\Delta H$ is independent of physical state of reactant and product
Answer: J
What is the pH of 0.01M glycine solution ? For glycine, $Ka_1 = 4.5\times 10^{-3}. and.   Ka_2 = 1.7 \times 10^{-10}$ at 298 K.

Options:
A. 3.1
B. 6.1
C. 3.2
D. 9.0
E. 7.2
F. 3.0
G. 10.0
H. 3.4
I. 3.3
J. 3.5
Answer: B
A monoatomic ideal gas undergoes a thermodynamic process according to the relation $PV^2$= constant. If the molar heat capacity of this gas at constant volume is C, then its molar heat capacity for the given process will be

Options:
A. $$\frac{4C}{3}$$
B. $$\frac{3C}{4}$$
C. $$\frac{C}{6}$$
D. $$\frac{C}{7}$$
E. C
F. $$\frac{C}{3}$$
G. $$\frac{C}{2}$$
H. $$\frac{C}{4}$$
I. $$\frac{2C}{3}$$
J. $$\frac{C}{5}$$
Answer: E
$18$ mL of $1.0$M $Br_2$ solution undergoes complete disproportionation in basic medium to $Br^{\circleddash}$ and $BrO^{\circleddash}_3$. Then, the resulting solution requires $45$ mL of $As^{3+}$ solution to reduce $BrO^{\circleddash}_3$ to $Br^{\circleddash}$. $As^{3+}$ is oxidized to $As^{5+}$. Which statements are correct?

Options:
A. Molarity of $As^{3+}=0.6M$
B. Molarity of $As^{3+}=0.3M$
C. Molarity of $As^{3+}=0.45M$
D. Molarity of $As^{3+}=0.2M$
E. Molarity of $As^{3+}=0.7M$
F. Equivalent weight of $Br_2=\displaystyle\frac{5M}{3}$
G. Molarity of $As^{3+}=0.4M$
H. Molarity of $As^{3+}=0.8M$
Answer: G
The freezing point of a solution containing $50 \ cm^3$ of ethylene glycol in 50 g of water is found to be $-4^oC$. Assuming ideal behaviour, the density of ethylene glycol $(K_f$ for water $=1.86 K kg mol^{-1}$) is:

Options:
A. 1.033\ g/cm^3
B. None of these
C. 1.233\ g/cm^3
D. $$1.133\ g/cm^3$$
E. 1.433\ g/cm^3
F. 1.235\ g/cm^3
G. 1.035\ g/cm^3
H. $$4.433\ g/cm^3$$
I. $$3.235\ g/cm^3$$
J. 1.333\ g/cm^3
Answer: D
A 1.85 g sample of an arsenic-containing pesticide was chemically converted to $AsO_4^{3-}$ (atomic mass of As = 74.9) and titrated with $Pb^{2+}$ to form $Pb_3(AsO_4)_2$. If 20 mL of 0.1 M $PB^{2+}$ is required to reach the equivalence point, the mass percentages of arsenic in the pesticide sample is closest to

Options:
A. 3.1
B. 3.6
C. 2.7
D. 8.1
E. 4.8
F. 2.9
G. 7.2
H. 5.4
I. 2.3
J. 6.9
Answer: I
(Thermochemistry, Enthalpy of reaction) 
For the reaction ${\text{PC}}{{\text{l}}_{\text{5}}}\left( g \right) \rightleftharpoons {\text{PC}}{{\text{l}}_{\text{3}}}\left( {\text{g}} \right) + {\text{C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right)$

Options:
A. $$\Delta {\text{H}} \neq 2\Delta {\text{E}}$$
B. $$\Delta {\text{H}} \neq \Delta {\text{E}}$$
C. $$\Delta {\text{H}} \approx \Delta {\text{E}}$$
D. $$\Delta {\text{H}} < \Delta {\text{E}}$$
E. $$\Delta {\text{H}} = \Delta {\text{E}}$$
F. Can't predicted.
G. $$\Delta {\text{H}} > \Delta {\text{E}}$$
H. $$\Delta {H} \neq \Delta {E}$$
Answer: E
Two bar magnets with magnetic moments 2M and M are fastened together at right angles to each other at their center to form a crossed system, which can rotate freely about a vertical axis through the center. The crossed system sets in earth's magnetic field with magnet having magnetic moment making an angle $\Theta $ with the magnetic meridian such that

Options:
A. $\Theta=tan^{-1}(\frac{1}{3}) $
B. $$\Theta=tan^{-1}(\frac{2}{\sqrt{3}})$$
C. \(\Theta=tan^{-1}(\sqrt{3})\)
D. $\Theta=tan^{-1}(\frac{1}{2\sqrt{3}})$
E. \(\Theta=tan^{-1}(\frac{1}{\sqrt{5}}) \)
F. $$\Theta=tan^{-1}(\frac{1}{2}) $$
G. $$\Theta=tan^{-1}(\frac{1}{\sqrt{3}}) $$
H. $$\Theta=tan^{-1} \sqrt{3} $$
I. $\Theta=tan^{-1}(\frac{\sqrt{3}}{2})$
J. $$\Theta=tan^{-1}(\frac{3}{4}) $$
Answer: G
Molar heat capacity of ${CD}_{2}O$ (deuterated form of formaldehyde) vapour at constant pressure is vapour $14cal/K-mol$. The entropy change associated with the cooling of $3.2g$ of ${CD}_{2}O$ vapour from $1000K$ to $900K$ at constant pressure is (assume ideal gas behaviour for ${CD}_{2}O$)
$$\left[ \ln { 0.9 } =-0.1 \right] $$

Options:
A. $$+0.56cal/K$$
B. $$+0.42cal/K$$
C. $$+1.4cal/K$$
D. $$+0.28cal/K$$
E. $$-0.28cal/K$$
F. $$-1.4cal/K$$
G. $$+0.14cal/K$$
H. $$-0.42cal/K$$
I. $$-0.14cal/K$$
Answer: G
Let the solubilities of AgCl in pure water, 0.01 M $CaCl_2$, 0.01 M NaCl & 0.04 M $AgNO_3$ be $S_1, S_2, S_3 , S_4$ respectively. What is the correct order?

Options:
A. $$S_1 > S_2 =S_3 > S_4$$
B. $$S_1 > S_4 > S_2 > S_3$$
C. $$S_1 > S_3 > S_2 > S_4$$
D. $$S_4 > S_3 > S_2 > S_1$$
E. $$S_4 > S_1 > S_3 > S_2$$
F. $$S_4 > S_1 > S_2 = S_3$$
G. $$S_1 > S_2 > S_3 > S_4$$
H. $$S_1 > S_4 > S_3 > S_2$$
I. $$S_4 > S_2 > S_3 > S_1$$
Answer: G
How many grams of $MnO_2 (M = 87)$ are needed to react with an excess of HCl to prepare $5$L of $Cl_2$ at $750$mm Hg pressure and $27^0$C? ($MnCl_2$ and water are also formed in this reaction)

Options:
A. 22.8g
B. 17.4g
C. 34.8g
D. $8.7$g
E. $26.1$g
F. 13.5g
G. 4.35g
Answer: D
${ CH }_{ 3 }{ COOH }(g)$ can be prepared using equationCO(g) + ${ 2H }_{ 2 }(g)\rightleftharpoons{ CH }_{ 3 }{ COOH }(g)$, ${ K }_{ C }={ 4\times 10 }^{ 2 }$.At equilibrium, a 5L flask contains equal moles of CO(g) and ${ CH }_{ 3 }{ COOH }(g)$. Hence, number of moles of hydrogen at equilibrium:

Options:
A. 0.200mole
B. 0.175mole
C. 0.125mole
D. 0.225mole
E. 0.10mole
F. 0.100mole
G. 0.375mole
H. 0.150mole
I. 0.50mole
J. 0.25mole
Answer: C
The density of an equilibrium mixture of $N_2O_4$ and $NO_2$ at 101.32 $KP_a$ is 3.62 g $dm^{3}$ at 288 K and 1.84 g $dm^{3}$ at 348 K. What is the heat of the reaction for the following reaction?$N_2O_4\rightleftharpoons 2NO_2(g)$

Options:
A. $\Delta_rH = 75.68 $  kJ mol$^{ -1 }$.
B. \Delta_rH = 37.89 \text{ kJ mol}^{-1}
C. \Delta_rH = 73.42 \text{ kJ mol}^{-1}
D. $\Delta_rH = 85.56 $  kJ mol$^{ -1 }$
E. $\Delta_rH = 95.7$  kJ mol$^{ -1 }$.
F. $\Delta_rH = 151.3 $  kJ mol$^{ -1 }$.
G. $\Delta_rH = 37.29 $  kJ mol$^{ -1 }$.
H. \Delta_rH = 45.97 \text{ kJ mol}^{-1}
I. \Delta_rH = 79.46 \text{ kJ mol}^{-1}
J. $\Delta_rH = 87.43 $  kJ mol$^{ -1 }$
Answer: A
For one mole of an ideal gas which of the following relation is correct?

Options:
A. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, V }{ \partial \, P } \right)_{ T }=-1$$
B. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, P }{ \partial \, V } \right)_{ T }=1$$
C. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, T }{ \partial \, V } \right)_{ P }\, \left(\dfrac { \partial \, V }{ \partial \, P } \right)_{ T }=1$$
D. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, T }{ \partial \, V } \right)_{ P }=-1$$
E. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, T }{ \partial \, V } \right)_{ P }\, \left(\dfrac { \partial \, V }{ \partial \, P } \right)_{ T }=2$$
F. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, P }{ \partial \, V } \right)_{ T }=-1$$
G. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, P }{ \partial \, V } \right)_{ T }=2$$
H. $$None\ of\ these$$
I. $$\left(\dfrac { \partial \, P }{ \partial \, T } \right)_{ v }\, \left(\dfrac { \partial \, V }{ \partial \, T } \right)_{ P }\, \left(\dfrac { \partial \, T }{ \partial \, V } \right)_{ P }=1$$
Answer: F
Figure shows a plastic rod having a uniformly distributed charge $Q$. The rod has been bent in a $120^o$ circular arc of radius $r$. In terms of $Q$ and $r$, what is the electric field $ec E$ due to the rod at point $P$?

Options:
A. $$\vec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i \text{ where } \lambda = \dfrac{Q}{3\pi r}$$
B. $$\vec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i \text{ where } \lambda = \dfrac{5Q}{3\pi r}$$
C. $$\vec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i \text{ where } \lambda = \dfrac{3Q}{4\pi r}$$
D. $ec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat j$ where $\lambda = \dfrac{2Q}{3\pi r}$
E. $$\dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i \text{ where } \lambda = \dfrac{Q}{2\pi r}$$
F. $ec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat j$ where $\lambda = \dfrac{3Q}{2\pi r}$
G. $$\vec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i \text{ where } \lambda = \dfrac{4Q}{3\pi r}$$
H. $$\vec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat j \text{ where } \lambda = \dfrac{4Q}{3\pi r}$$
I. $ec E = \dfrac{3\sqrt3 \lambda}{8 \pi^2 \epsilon_0 r^2} \hat i$ where $\lambda = \dfrac{2Q}{3\pi r}$
Answer: I
The equation for the combustion of methane is shown.                      $CH_{ 4 }+2{ O }_{ 2 }\longrightarrow C{ O }_{ 2 }+2H_{ 2 }O$   The energy change for the combustion of methane is -890kJ/mol.   The bond energies are shown in the table.
What is the energy of the C=o bond ?

Options:
A. +1330kJ/mol
B. +1301kJ/mol
C. +1320kJ/mol
D. +1355kJ/mol
E. +841kJ/mol
F. +1325kJ/mol
G. +1335kJ/mol
H. +1340kJ/mol
I. +1345kJ/mol
J. +49kJ/mol
Answer: G
Let $P(r)=\frac{Q}{\pi R^4}r$ be the charge density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

Options:
A. $$\frac{Q \eta ^2}{4 \pi \epsilon_0 R^5}$$
B. $$\frac{Q \eta ^3}{4 \pi \epsilon_0 R^4}$$
C. $$\frac{Q \eta ^2}{5 \pi \epsilon_0 R^4}$$
D. 0
E. $$\frac{Q \eta ^2}{2 \pi \epsilon_0 R^4}$$
F. $$\frac{Q \eta ^2}{4 \pi \epsilon_0 R^3}$$
G. $$\frac{Q \eta ^2}{6 \pi \epsilon_0 R^4}$$
H. $$\frac{Q \eta ^2}{3 \pi \epsilon_0 R^4}$$
I. $$\frac{Q \eta ^2}{4 \pi \epsilon_0 R^4}$$
J. $$\frac{Q}{4 \pi \epsilon_0 \eta ^2}$$
Answer: J
A radioactive element A of decay constant $ \lambda _A $ decays into another radioactive element B of decay constant  $ \lambda _B $ Initially the number of active nuclei of A was $ N_0 $ and B was absent in the sample. The maximum number of active nuclie of B is found at $ t = 2 in 2 / \lambda _A $ The maximum number of active nuclie of B is

Options:
A. None of these
B. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 8 }$$
C. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 3 }$$
D. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 6 }$$
E. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 2 }$$
F. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 7 }$$
G. $$ \frac { \lambda _{ A } }{ \lambda _{ B } } N_{ 0 }e^{ -\lambda _{ B }t } $$
H. $$ \frac { { N }_{ 0 } }{ 4 } $$
I. $$\frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 5 }$$
J. $$ \frac { \lambda _{ A } }{ \lambda _{ B } } \frac { { N }_{ 0 } }{ 4 } $$
Answer: H
An ammeter and a voltmeter are connected in series to an ideal battery of emf $E$. If the ammeter reads $I$ and voltmeter reads $V$, then.

Options:
A. Ammeter and voltmeter have equivalent resistance $=I/E$
B. Ammeter and voltmeter have equivalent resistance $=\frac{E}{V}$
C. Ammeter and voltmeter have equivalent resistance $=E + I$
D. Ammeter and voltmeter have equivalent resistance $=E/(V+I)$
E. Ammeter and voltmeter have equivalent resistance $=E - V/I$
F. Ammeter and voltmeter have equivalent resistance $=E/I$
G. Ammeter and voltmeter have equivalent resistance $=I/E + 1$
Answer: F
Arrange the following in the order of rate of oxidation with periodic acidI. $HOCH_{2}CH_{2}OH$II. $CH_{3}CHOHCHOHCH_{3}$III. $(CH_{3})_{2} C(OH)C(OH) (CH_{3})_{2}$

Options:
A. $$II > III > I$$
B. $$III > I > II$$
C. $$II > I > III$$
D. $$I > II > III$$
E. $$I > III > II$$
F. $$I > III = II$$
Answer: D
The solubility of $Ca{F}_{2}$ in a solution buffered at $pH=3.0$ is ${K}_{a}$ for $HF$ is $6.3\times {10}^{-4}$ and ${K}_{sp}$ of $Ca{F}_{2}=3.45\times {10}^{-11}M$

Options:
A. none of these
B. 3.96 \times 10^{-4}M
C. $$3.86\times {10}^{-4}M$$
D. 4.06 \times 10^{-4}M
E. 3.66 \times {10}^{-4}M
F. $$4.16\times {10}^{-4}M$$
G. 3.76 \times 10^{-4}M
H. $$3.56\times {10}^{-4}M$$
I. 4.26 \times 10^{-4}M
Answer: C
A $3.0$ g sample containing $Fe_{3}O_{4}$, $Fe_{2}O_{3}$ and an inert impure substance is treated with excess of $KI$ solution in the presence of dilute $H_{2}SO_{4}$. The entire iron is converted into $Fe^{2+}$ along with the liberation of iodine. The resulting solution is diluted to $100$ mL. A $20$ mL of the diluted solution require $11.0$ mL of $0.5\ M$ $Na_{2}S_{2}O_{3}$ solution to reduce the iodine present. A $50$ mL of the dilute solution after complete extraction of the iodine requires $12.80$ mL of $0.25\ M$ $KMnO_{4}$ solution in dilute $H_{2}SO_{4}$ medium for the oxidation of $Fe^{2+}$. Calculate the percentage of $Fe_{2}O_{3}$ and $Fe_{3}O_{4}$ in the original sample.

Options:
A. $$$Fe_{2}O_{3}=50.67\%$, $Fe_{3}O_{4}=65.2\%$$$
B. $$Fe_{2}O_{3}=59.33\%, Fe_{3}O_{4}=33.8\%$$
C. $$Fe_{2}O_{3}=48.33\%, Fe_{3}O_{4}=33.8\%$$
D. $$$Fe_{2}O_{3}=47.83\%$, $Fe_{3}O_{4}=35.2\%$$$
E. $$Fe_{2}O_{3}=48.33\%, Fe_{3}O_{4}=35.8\%$$
F. $$$Fe_{2}O_{3}=38.87\%$, $Fe_{3}O_{4}=24.58\%$$$
G. $$$Fe_{2}O_{3}=61.13\%$, $Fe_{3}O_{4}=75.42\%$$$
H. $$$Fe_{2}O_{3}=52.33\%$, $Fe_{3}O_{4}=37.8\%$$$
I. $$$Fe_{2}O_{3}=49.33\%$, $Fe_{3}O_{4}=34.8\%$$$
J. $$Fe_{2}O_{3}=47.33\%, Fe_{3}O_{4}=32.8\%$$
Answer: I
The coefficient of friction between 12 kg block and 3 kg platform BD are $\mu _ { S } = 0.60$  and $\mu _ { k } = 0.40$ respectively. Determine the magnitude of acceleration of the block immediately after the wire AB is cut

Options:
A. $$4.5 \mathrm { m } / \mathrm { s } ^ { 2 }$$
B. 2 .5 $\mathrm { m } / \mathrm { s } ^ { 2 }$
C. $$6 \mathrm { m } / \mathrm { s } ^ { 2 }$$
D. $$3.5 \mathrm { m } / \mathrm { s } ^ { 2 }$$
E. $$4 \mathrm { m } / \mathrm { s } ^ { 2 }$$
F. 8 $\mathrm { m } / \mathrm { s } ^ { 2 }$
G. none of these
H. $$3 \mathrm { m } / \mathrm { s } ^ { 2 }$$
I. $$4.75 \mathrm { m } / \mathrm { s } ^ { 2 }$$
J. 5.89 $\mathrm { m } / \mathrm { s } ^ { 2 }$
Answer: J
Two blocks of masses $8\ kg$ and $6\ kg$ are connected with a string & placed on a rough horizontal surface. Surface itself is accelerating up with $ 2\ m/s^2$. Two forces $60\ N$ each are acting on the two blocks as shown. Friction coefficient for $8\ kg$ is $0.5$ and that for $6\ kg$ is $0.6$. Tension in the string is : ($g=10\ m/s^2$)

Options:
A. $$60\ N$$
B. $$32.0\ N$$
C. $$43.2\ N$$
D. $$33.6\ N$$
E. $$36.0\ N$$
F. $$28.8\ N$$
G. $$34.4\ N$$
H. $$12\ N$$
I. $$38.4\ N$$
J. $$41.6\ N$$
Answer: F
A mixture weighing 228 g contain ${\text{CaC}}{{\text{l}}_{\text{2}}}$ and $\text{NaCl}$ if this mixture is dissolved in 10 kg of water and form ideal solution that boil at 100.364$^\circ {\text{C}}$. The mol % of $\text{NaCl}$ in mixture is: [${K_b}$ of water = 0.52 K mol$^{ - 1}$ Kg]

Options:
A. 66.67%
B. 33.37%
C. 66.66%
D. 33.33%
E. 33.3%
F. 66.6%
G. 50%
H. 50.0%
I. 75%
Answer: A
Two metal rods are fixed end to end between two rigid supports, as shown in figure. Each rod is of length $'l'$ and area of cross-section is $A$. When the system is heated up, determine the condition when the junction between rods does not shift ?
[ Given : $Y_1$ and $Y_2$ are Young's modulus of materials of the rods, $lpha_1$ and $lpha_2$ are coefficients of linear expansion.]

Options:
A. $$lpha_1Y_2=lpha_2Y_1$$
B. $$\alpha_1 Y_2 = \alpha_1 Y_1$$
C. \(\alpha_1 Y_2 = \alpha_2 Y_1 \)
D. $lpha_1Y_1=lpha_2Y_2$
E. \(\alpha_1 Y_1 = \alpha_1 Y_2 \)
F. $$lpha_1=lpha_2$$
G. \(\alpha_1 Y_2 = \alpha_2 Y_2 \)
H. $$Y_1=Y_2$$
I. $$\alpha_1 Y_1 = \alpha_2 Y_1$$
J. \(\alpha_1 Y_1 = \alpha_2 Y_2\)
Answer: D
A particle is moving in a plane and whose acceleration and velocity given by $ec { a } = (\hat { i } + \hat { j } )m/s^2$ and $ec{ v } = (\hat { 4i } + \hat { 3j } )m/s$ respectively.the tangential acceleration of the particle is

Options:
A. $$\dfrac{7}{25} (\hat{4i}+\hat{3j})$$
B. $$\dfrac{1}{2} (\hat{i} + \hat{j})$$
C. $$ \dfrac{\hat{i}+\hat{j}}{\sqrt{2}}$$
D. $$\dfrac{1}{5} (\hat{i} + \hat{j})$$
E. $$\dfrac{1}{\sqrt{2}} (\hat{4i} + \hat{3j})$$
F. $$\dfrac{1}{5} (\hat{4i} + \hat{3j})$$
G. $$\dfrac{7}{25} (\hat{i} + \hat{j})$$
H. $$\dfrac{1}{25} (\hat{4i} + \hat{3j})$$
I. $$0$$
Answer: I
Force acting on a particle of mass $m = 1\ kg$ with time as shown in the graph. Initially particle is at rest. Kinetic energy of particle at $t = 3\ s$ is:

Options:
A. $$225\ J$$
B. $$150\ J$$
C. $$625/2\ J$$
D. $$300\ J$$
E. $$750\ J$$
F. $$375\ J$$
G. $$720\ J$$
H. $$900\ J$$
I. $$450\ J$$
Answer: H
For the real gases reaction  $200 ( g ) + O _ { 2 } ( g ) \longrightarrow 2 C O , ( g ) : \Delta H = - 560 kJ$. In  $10 litre$  rigid vessel at  $500\mathrm { K }$  the initial pressure is  $70 bar$  and after the reaction it becomes  $40 bar.$  The change in internal energy is

Options:
A. $$-559 kJ$$
B. $$- 563 k J$$
C. $$- 553 k J$$
D. $$- 557 k J$$
E. $$- 550 k J$$
F. $$-555 kJ$$
G. $$-560 kJ$$
H. $$None of these$$
I. $$- 561 kJ$$
J. $$- 530 k J$$
Answer: D
A ball rolls off the top of a stairway with horizontal velocity ${v}_{0}m{S}^{-1}$. If the steps are $h$ metre high and $w$ metre wide, the ball will hit the edge of $n$th step if

Options:
A. $$n=\cfrac{2h{v}_{0}^{2}}{g{w}^{2}}$$
B. $$n=\cfrac{2h{v}_{0}^{2}}{5g{w}^{2}}$$
C. n=\cfrac{2h{v}_{0}^{2}}{3g{w}^{2}}
D. $$n=\cfrac{2h{v}_{0}^{2}}{g{w}^{}}$$
E. $$n=\cfrac{h{v}_{0}^{}}{g{w}^{2}}$$
F. $$n=\cfrac{2h{v}_{0}^{}}{g{w}^{2}}$$
G. $$n=\cfrac{2h{v}_{0}^{2}}{4g{w}^{2}}$$
H. n=\cfrac{2h{v}_{0}^{2}}{2g{w}^{2}}
I. $$n=\cfrac{h{v}_{0}^{2}}{g{w}^{2}}$$
J. $$n=\cfrac{h{v}_{0}^{2}}{2g{w}^{2}}$$
Answer: F
A stretched string is vibrating according to the equation $y = 5 \sin \left( \frac { \pi x } { 3 } \right) \cos 400 \pi t$ , where $y$ and a are in cm and $t$ is second. Potential energy will be zero at time t:-

Options:
A. 8 s
B. 18 s
C. 2 s
D. 4 s
E. 10 s
F. 14 s
G. 6 s
H. 16 s
I. 9 s
J. 12 s
Answer: A
A solid cylinder of mass $m$ is kept in balance on fixed incline of angle $lpha  = 37^\circ $ with the help of a thread fastened to its jacket. The cylinder does not slip.
In what direction should the thread be pulled to minimize the force required to hold the cylinder ? What is the magnitude of this force ?

Options:
A. $$vertical \frac{{3mg}}{{6}}$$
B. vertical $\frac{{3mg}}{{7}}$
C. $$vertical \frac{{3mg}}{{11}}$$
D. $$vertical \frac{{3mg}}{{12}}$$
E. $$vertical \frac{{3mg}}{{9}}$$
F. $$vertical \frac{{3mg}}{{10}}$$
G. horizontal $\frac{{mg}}{{5}}$
H. None of these
I. vertical $\frac{{3mg}}{{8}}$
J. $\frac{{3mg}}{{10}}$ parallel to incline
Answer: I
A rod of length $1\ m$ and mass $0.5\ kg$ hinged at one end, is initially hanging vertical. The other end is now raised slowly until it makes an angle $60^o$ with the vertical. The required work is (use $g=10$ $m/s^2$).

Options:
A. $$\displaystyle\frac{17}{8}\ J$$
B. $$\frac{5\sqrt{3}}{12}\ J$$
C. $$\displaystyle \frac{5\sqrt{3}}{8}\ J$$
D. \frac{5\sqrt{3}}{8}\ J
E. $$\frac{5\sqrt{3}}{6}\ J$$
F. $$\displaystyle\frac{5}{4}\ J$$
G. $$\displaystyle\frac{5\sqrt{3}}{4}\ J$$
H. $$\frac{5\sqrt{2}}{4}\ J$$
I. $$\frac{5\sqrt{3}}{16}\ J$$
Answer: F
The half cell reactions for the corrosion are
$$2{H}^{+}+1/2{O}_{2}+2{e}^{-}\rightarrow {H}_{2}O;{E}^{o}=1.23V$$
${Fe}^{2+}+2{e}^{-}\rightarrow {Fe}_{(s)};{E}^{o}=-0.44V$. Find teh $\Delta {G}^{o}$ (in kJ) for the overall reaction:

Options:
A. $$-161$$
B. $$-322$$
C. -304
D. -344
E. -310
F. $$-152$$
G. -176
H. $$-76$$
Answer: F