MikaStars39/nano-eval huggingface dataset:
A transverse sinusoidal wave of a amplitude a,  wavelength $\lambda$ and frequency n is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If $a = 10^{-3} m $ and $v = 10 ms^{-1} m $, then $\lambda$ and n are given by ()

Options:
A. $\lambda = \frac{10^{4}}{2\pi}$ Hz
B. $$\lambda = \frac{10^{2}}{3\pi} \text{ Hz}$$
C. $\lambda = \frac{10^{3}} {2\pi} $ Hz
D. $$\lambda = \frac{10^{2}}{2\pi} \text{ m}$$
E. $$\lambda = \frac{10^{3}}{3\pi} \text{ Hz}$$
F. $\lambda = 10^{-3}$ m
G. $ n = 10^{4}$ Hz
H. $$\lambda = \frac{10^{2}}{4\pi} \text{ Hz}$$
I. $$\lambda = \frac{10^{4}}{2\pi} \text{ Hz}$$
J. $\lambda = 2\pi \times 10^{-2}$ m
Answer: C
$$ For a reaction, {X}_{2(g)} + {Y}_{2(g)} \rightleftarpoons {2xy)_{(g)}. If \delta {G}_{r}^{0} = 20 kJ/mol and \delta {S}_{r}^{0} = -20 {JK}^{-1} {mol}^{-1} at 200 K. Calculate \delta {H}_{r}^{0} at 400 K. (Given \delta _{r}{C}_{p} = 20 {JK}^{-1} {mol}^{-1} $$

Options:
A. $$27\dfrac{kJ}{mol}$$
B. $$24\dfrac{kJ}{mol}$$
C. $$30\dfrac{kJ}{mol}$$
D. $$22\dfrac{kJ}{mol}$$
E. $$25\dfrac{kJ}{mol}$$
F. $$ 28\dfrac{kJ}{mol} $$
G. $$32\dfrac{kJ}{mol}$$
H. $$ 20\dfrac{kJ}{mol} $$
I. $$ 7.98\dfrac{kJ}{mol} $$
J. $$None of these$$
Answer: F
A block $'A'$ of mass $m$ is placed on a smooth horizontal platform $P$ and between two elastic massless springs $S_1$ and $S_2$ fixed horizontally to two fixed vertical walls. The elastic constants of the two springs are equal to $k$ and the equilibrium distance between the two springs both in relaxed states is $d$. The block is given a velocity $v_0$ initially towards one of the springs and it then oscillates between the springs. The time period $T$ of oscillations and the minimum separation $d_m$ of the springs will be

Options:
A. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}} \right), d_m=d-2v\sqrt{\dfrac{m}{k}}$$
B. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}} \right), d_m=d-v\sqrt{\dfrac{m}{k}}$$
C. $$T=2\pi \sqrt{\dfrac{m}{k}}, d_m=d$$
D. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}} \right), d_m=d+v\sqrt{\dfrac{m}{k}}$$
E. $$T=2\left( \dfrac{d}{v}+2\pi \sqrt{\dfrac{m}{k}}\right), d_m=d-v\sqrt{\dfrac{m}{k}}$$
F. $$T=2\left( \dfrac{d}{v}+2\pi \sqrt{\dfrac{m}{k}} \right), d_m=d$$
G. $$T=2\left( \dfrac{d}{v}+2\pi \sqrt{\dfrac{m}{k}}\right), d_m=d-2v\sqrt{\dfrac{m}{k}}$$
H. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}} \right), d_m=d-3v\sqrt{\dfrac{m}{k}}$$
I. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}}\right), d_m=d$$
J. $$T=2\left( \dfrac{d}{v}+\pi \sqrt{\dfrac{m}{k}} \right), d_m=d+2v\sqrt{\dfrac{m}{k}}$$
Answer: I
The density of KBr is $2.75$ g cm$^{-3}$. The length of the unit cell is $654$ pm. Atomic mass of K $= 39$ amu, Br $= 80$ amu.  What is true about the predicted nature of the solid?

Options:
A. There are $8$ ions at the corners and $9$ at the centres of the faces.
B. There are $8$ ions at the corners and $6$ at the centres of the faces.
C. There are four constituents per unit cell.
D. There are $8$ ions at the corners and $2$ at the centres of the faces.
E. There are $8$ ions at the corners and $5$ at the centres of the faces.
F. The unit cell is fcc.
G. There are $8$ ions at the corners and $3$ at the centres of the faces.
H. There are $8$ ions at the corners and $4$ at the centres of the faces.
I. The number of atoms per unit cell is $4$.
J. There are $8$ ions at the corners and $7$ at the centres of the faces.
Answer: B
Given that $\displaystyle E^o_{Fe^{2+}/Fe} = -0.44, E^o_{Cu^{2+}/Cu} = 0.34V, E^o_{Ag+/Ag} = 0.80V$Which of the following statements are true :

Options:
A. Cu displace Fe from $Fe_2(SO_4)_3$ solution
B. Cu displace Ag from $CuSo_4$ solution
C. Ag displace Fe from $FeSO_4$ solution
D. Cu displace Fe from $FeSO_4$ solution
E. Cu displace Ag from $AgNO_3$ solution
F. Ag displace Cu from $CuSO_4$ solution
Answer: E
A balloon starts from rest, moves vertically upwards with an acceleration $\dfrac{g}{8}\ \text{ms}^{-2}$. A stone falls from the balloon after $8\ \text{s}$ from the start. The time taken by the stone to reach the ground  is $\left(g=9.8\ \text{ms}^{-2}\right)$:

Options:
A. $$10\sqrt{2}\; s$$
B. $$6 s$$
C. $$8\; s$$
D. $$$2$$\sqrt{2}$ s$$
E. $$4\sqrt{2}\; s$$
F. $$6\sqrt{2}\; s$$
G. $$4\; s$$
H. $$12\; s$$
I. $$3\sqrt{2}\; s$$
J. $$2\sqrt{3}\; s$$
Answer: D
The $pH$ of the solution when $0.2$ mole of $HCl$ is added to one litre of a solution containing $0.1\ M\ CH_3COOH$ and $0.1\ M\ CH_3COO^-$ isAssume $K_a$ for $CH_3COOH = 1.8 \times 10^{-5}$

Options:
A. $$4.65$$
B. $$3.8$$
C. $$4.67$$
D. $$4.57$$
E. $$4.45$$
F. $$4.59$$
G. $$4.55$$
H. $$0.7$$
I. $$4.75$$
J. $$1.0$$
Answer: D
For the equilibrium : $NH_2COONH_4(s) \rightleftharpoons N_2(g)+H_2(g)+CO(g)+O_2(g)$ If the equilibrium pressure is 22 bar. Then the value of $K^0_p$ will be [1 atm =1.01325 bar]

Options:
A. $$\dfrac{11^4}{8} \times (1.01325)^{-2}$$
B. $$\dfrac{11^4}{8}$$
C. $$\dfrac{11^4}{8} \times (1.01325)^{-5}$$
D. $$\dfrac{11^3}{8} \times (1.01325)^{-3}$$
E. $$\dfrac{11^4}{8} \times (1.01325)^{-6}$$
F. $$\dfrac{11^4}{8} \times (1.01325)^{-4}$$
G. $$64$$
H. $$4^5 3^3\sqrt{2}$$
I. $$\dfrac{11^3}{8} \times (1.01325)^{-4}$$
J. $$\dfrac{11^4}{8} \times (1.01325)^{-3}$$
Answer: B
A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of $227^{\circ}$C and suspended inside a box whose walls are at a temperature of $27^{\circ}$C. The maximum rate at which its temperature will fall is :(Take e = 1, Stefan's constant; and specific heat of the metal s = 90 cal/kg/deg J = 4.2 Joules/Calorie)

Options:
A. $0.276^{\circ}$ C/sec
B. $0.055^{\circ}$C/sec
C. $0.044^{\circ}$ C/sec
D. $0.03^{\circ}$ C/sec
E. $0.367^{\circ}$ C/sec
F. $0.286^{\circ}$ C/sec
G. 0.267^{\circ} C/sec
H. 0.287^{\circ} C/sec
Answer: A
If the given two identical charged rings lie in $xy$ plane both having linear charge density $\lambda$ varies as per $\lambda = \lambda_0 \cos \theta$ ($\lambda_0$ = constant) where $\theta$ is measured from +x-axis. Radius for both the rings is $R$. Electric force between the two rings is $\dfrac{x K \lambda_{0}^{2} \pi^{2} R^{4}}{d^4}$ then $x$ is.

Options:
A. $$5$$
B. $$7$$
C. $$2$$
D. $$1$$
E. $$8$$
F. $$6$$
G. $$3$$
H. $$9$$
I. $$4$$
Answer: F
An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_i$ is the initial temperature and $T_f$ is the final temperature , which of the following is correct?

Options:
A. $$(T_i)irrev>(T_f)rev$$
B. $$(T_i)rev > (T_f)irrev$$
C. $$(T_f)rev=(T_i)irrev$$
D. $$(T_i)rev < (T_f)irrev$$
E. $$(T_f)rev=(T_f)irrev$$
F. $$(T_f)rev > (T_i)irrev$$
G. $$(T_i)irrev < (T_f)rev$$
H. $T_f>T_i$ for reversible process but $T_f=T_i$ for irreversible process
I. $$(T_i)irrev = (T_f)rev$$
Answer: A
$pH$ of a solution obtained by mixing equal volumes of $0.1M$ Triethyl amine $(K_b=6.4\times10^{-5})$ & $\dfrac{4}{45}M$ $NH_4OH(K_b=1.8\times10^{-5})$ will be :

Options:
A. $$11.3$$
B. $$10.4$$
C. $$12.3$$
D. $$11.45$$
E. $$10.45$$
F. $$10.35$$
G. $$11.25$$
H. $$10.3$$
I. $$10.95$$
J. $$11.2$$
Answer: A
Four parallel conductors, carrying equal currents, pass vertically through the four corners of a square WXYZ. In two conductors, the current is flowing into the page, and in the other two out of the page. In what directions must the current flow to produce a resultant magnetic field in the direction shown at $O$, the center of the square?

Options:
A. Into the page= W and Y; Out of the page =X and Z
B. Into the page= W and Z; Out of the page =X and Y
C. Into the page= X and W; Out of the page =Z and Y
D. Into the page= Y and X; Out of the page =W and Z
E. Into the page= Y and W; Out of the page =X and Z
F. Into the page= X and W; Out of the page =Y and Z
G. Into the page= W and X; Out of the page =Y and Z
H. Into the page= X and Z; Out of the page =W and Y
I. Into the page= Y and Z; Out of the page =W and X
J. Into the page= X and Y; Out of the page =W and Z
Answer: G
A point charge $50\mu C$ is located in the $x{\text{ - }}y$ plane at the position vector ${/vec r_0} = \left( {2\hat i + 3\hat j} \right)m.$ The electric field at the point of position vector $/vec r = \left( {8\hat i - 5\hat j} \right)m,$ in vector from is equal to:

Options:
A. $$90\left( {3\hat i + 4\hat j} \right)V/m$$
B. $$900\left( { - 3\hat i + 4\hat j} \right)V/m$$
C. $$9\left( { - 3\hat i + 4\hat j} \right)V/m$$
D. $$900\left( {3\hat i - 4\hat j} \right)V/m$$
E. $$900\left( {3\hat i + 4\hat j} \right)V/m$$
F. $$90\left( { - 3\hat i - 4\hat j} \right)V/m$$
G. $$90\left( { - 3\hat i + 4\hat j} \right)V/m$$
H. $$90\left( {3\hat i - 4\hat j} \right)V/m$$
Answer: B
The number of photons $(\lambda =6630 \overset{o}{A})$ that strike per second on a totally reflecting screen (as shown in figure), so that a force of $1\ N$ is exerted on the screen, is approximately:

Options:
A. $$10^{27}$$
B. $$10^{23}$$
C. $$10^{26}$$
D. $$10^{28}$$
E. $$10^{25}$$
F. $$10^{29}$$
G. $$10^{24}$$
H. $$10^{22}$$
Answer: A
Following transverse waves, $y_{1}=2 \sin (100 \pi t-5.3x), $ $y_{2}=2\sqrt {2} \sin \left (100 \pi -5.3x+\dfrac {\pi}{4}\right)$ and $y_{3}=\cos(100\pi t-5.3\ x)$ superpose in a homogeneous medium. Find the resultant amplitude at $x=0$.

Options:
A. $$3\sqrt{2}\ unit$$
B. $$4\ unit$$
C. $$6\ unit$$
D. $$2\ unit$$
E. $$1\ unit$$
F. $$3\ unit$$
G. $$5\ unit$$
H. $$2\sqrt{2}\ unit$$
Answer: B
In a galvanic cell the following reaction takes place at $298^o K$
$Cr_2O_7^{-2} + 14 H^+ + 6 Fe^{2+} \rightarrow 2 Cr^{3+} + 6 Fe^{3+} + 7 H_2O$ 
given that : $E^0 (Cr_2O_7^{-2}, H^+, Cr^{3+} /Pt) = 1.33 V$
$E^0 (Fe^{3+}, Fe^{2+} / Pt) = 0.77 V$. The standard e.m.f. of the cell is

Options:
A. $$(1.33 + 2 \times 0.77) V$$
B. $$(1.33 + 0.77) V$$
C. $$- (1.33 + 0.77) V$$
D. $$(1.33 + 0.77) \times 2 V$$
E. $$(1.33 - 0.77) V$$
F. $$(1.33 + 0.77) \times 3 V$$
G. $$(1.33 - 2 \times 0.77) V$$
H. $$(-1.33 + 0.77) V$$
I. $$(1.33 - 0.77) \times 2 V$$
Answer: B
Molar conductivity of $0.1 M\ HBr $ at certain temperature is $256.62\ S\ cm^2 mol^{-1}$. What is its $pH$? [$\lambda^0_{H^+}= 349.6 S cm^2 mol^{-1}, \lambda^0_{Br^-}= 78.1\ S\ cm^2 mol^{-1}$]

Options:
A. $$4.35$$
B. $$3.95$$
C. $$4.15$$
D. $$2.5$$
E. $$3.65$$
F. $$3.85$$
G. $$3.75$$
H. $$1.22$$
I. $$4.05$$
J. $$4.2$$
Answer: J
What s-character is used by the carbon atom in the orbital directed to hydrogen atom in $CH_{2}F_{2}$ molecule?[$H-C-H$ bond angle in $CH_{2}F_{2}$ is $111.9^{\circ}$ (cos $111.9^{\circ}$ = $-0.3729$)]

Options:
A. 26.1%
B. 27.2%
C. $27.1$%
D. 28.1%
E. 37.19%
F. $37.29$%
G. $29$%
H. 28.2%
I. 26.2%
J. $29.99$%
Answer: C
The dissociation constant $(K_a)$ and percent of degree of dissociation $(lpha)$ of a weak monobasic acid solution of $0.1\ M$ with a $pH = 5$ are respectively :

Options:
A. $$10^{-8}, \ \ 10^{-4}$$
B. $$10^{-9}, \ \ 10^{-3}$$
C. $$10^{-8}, \ \ 10^{-1}$$
D. $$10^{-5}, \ \ 10^{-2}$$
E. $$10^{-9} ,\ \  1$$
F. $$10^{-9}, \ \ 10^{-2}$$
G. $$10^{-8}, \ \ 10^{-3}$$
H. $$10^{-9}, \ \ 10^{-4}$$
I. $$10^{-8}, \ \ 10^{-2}$$
J. $$10^{-9}, \ \ 10^{-1}$$
Answer: H
Consider a uniform spherical charge distribution of radius $R_1$ centered at the origin $O$. In this distribution, a spherical cavity of radius ${R}_{2}$, centre at $P$ with distance $OP=\alpha=R_1-R_2$ is made. If the electric field inside the cavity at position $r$ is $E(r)$, then the  correct statement(s) is (are)  ?

Options:
A. $E$ is uniform, its magnitude is depends of ${R}_{2}$ and its direction depends on $r$
B. $E$ is uniform, its magnitude is independent of ${R}_{2}$ and its direction depends on $r$
C. E is uniform, its magnitude depends on $R_2$ but its direction is independent of $r$
D. $E$ is uniform, its magnitude is independent of ${R}_{2}$ but its direction depends on $r$
E. $E$ is uniform and both its magnitude and direction depend on $ {a}$
F. $E$ is uniform, its magnitude is independent of $a$ but its direction depends on $ {a}$
G. $E$ is uniform, its magnitude is independent of $a$ but its direction is independent of $r$
H. E is uniform, its magnitude is independent of ${R}_{2}$ but its direction depends on ${a}$
I. E is uniform, its magnitude is independent of $a$ but its direction depends on $r$
Answer: E
A large block of ice $4 m$ thick has a vertical hole drilled through it and is floating in the middle of water in a lake. The minimum length of rope required to scoop up a bucket full of water through the hole is: (density of ice $= 0.8 $ g/cc, density of water: $= 1$ g/cc)

Options:
A. $$400 m$$
B. $$90 cm$$
C. 300 m
D. $$130 cm$$
E. $$100 m$$
F. $$140 cm$$
G. $$80 cm$$
H. $$120 cm$$
I. $$350 m$$
J. $$110 cm$$
Answer: A
A spherical ball of mass $m$ is kept at the highest point in the space between two fixed, concentric spheres $A$ and $B$ (see figure). The smaller sphere $A$ has a radius $R$ and the space between the two spheres has a width $d$. The ball has a diameter very slightly less than $d$. All surfaces are frictionless. The ball is given a gentle push (towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by $\theta$ (shown in figure).Express the total normal reaction force exerted by the sphere on the ball as a function angle $\theta$.

Options:
A. $N = (3\cos \theta - 2)$ radially outwards.
B. N = mg(3\cos \theta + 2) radially inwards.
C. $N = mg(3\cos \theta - 2)$ radially inwards.
D. N = mg(3\cos \theta - 1) radially outwards.
E. N = mg(3\cos \theta - 1) radially inwards.
F. N = mg(3\cos \theta + 1) radially outwards.
G. $N = mg(3\cos \theta - 2)$ radially outwards.
H. $N = (3\cos \theta - 2)$ radially inwards.
I. N = mg(3\cos \theta - 3) radially outwards.
J. N = mg(3\cos \theta + 1) radially inwards.
Answer: G
A mass of 0.98 kg attached to a spring of constant K = 100 $Nm^{-1}$ is hit by bullet of 20 gm moving with a velocity 30 $ms^{-1}$ horizontally. The bullet gets embedded and the system oscillates with the mass on horizontal friction less surface. The amplitude of oscillations will be:

Options:
A. 0.6 cm
B. 0.5 cm
C. 1.8 cm
D. 0.9 cm
E. 6 cm
F. 12 cm
G. 0.4 cm
H. 0.7 cm
I. 1.2 cm
J. 0.8 cm
Answer: A
A load of mass $M$ is on horizontal rails. A pendulum made of a ball of mass $m$ tied to a weightless inextensible thread is suspended from the load vertically. The load can move only along the rails. Find the ratio of the period $\dfrac{T_{2}}{T_{1}}$where $T_{2}$ is the period in the vertical plane parallel to rails and $T_{1}$ is the period in vertical plane perpendicular to rails.

Options:
A. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{m+M}{M} }$$
B. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{m}{M+m} }$$
C. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{m}{M+2m} }$$
D. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{M}{M-m} }$$
E. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{M+m}{m}}$$
F. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{M}{m}} $$
G. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{m}{M}} $$
H. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{m}{M-m}}$$
I. $$\dfrac{T_{2}}{T_{1}}=\sqrt{\dfrac{M}{m-M}}$$
Answer: B
In an AC circuit, the instantanceous emf and current are given by
e=100 sin 30 t, i=sin(30 t $\frac{\pi}{4}$)
In one cycle of AC, the average power consumed by the circuit and the wattles current are, respectively

Options:
A. $\frac{500}{\sqrt2}$,0
B. 50,0
C. $\frac{1000}{\sqrt2}$,10
D. $\frac{500}{2}$,10
E. $\frac{1000}{2}$,10
F. $\frac{500}{\sqrt2}$,10
G. $\frac{50}{\sqrt2}$,0
H. 50,10
Answer: C
At a given temperature if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ be the velocity of sound in it, then these are related as $\left(\gamma = \dfrac{C_p}{C_v} \right)$

Options:
A. $$v_{rms} = \sqrt{\dfrac{\gamma}{1.5}} \times v_s$$
B. $$v_{rms} = \sqrt{\dfrac{\gamma}{4}} \times v_s$$
C. $$v_{rms} = \sqrt{\dfrac{\gamma}{5}} \times v_s$$
D. $$v_{rms} = \sqrt{\dfrac{3}{\gamma}} \times v_s$$
E. $$v_{rms} = \left(\dfrac{3}{\gamma} \right) \times v_s$$
F. $$v_{rms} = v_s$$
G. $$v_{rms} = \sqrt{\dfrac{\gamma}{6}} \times v_s$$
H. $$v_{rms} = \sqrt{\dfrac{\gamma}{7}} \times v_s$$
I. $$v_{rms} = \sqrt{\dfrac{\gamma}{3}} \times v_s$$
J. $$v_{rms} = \sqrt{\dfrac{\gamma}{2}} \times v_s$$
Answer: E
A mixture of 250 gm of water and 200 gm of ice at $ 0^o C $ is kept is coalorimeter of water equation 50 gm. If 200 gm of steam at $ 100^oC $ is passed through the mixture then the final amount of water in the mixture will be (Latent heat of ice = 80 cal/gm, latent Heat of vaporisation of water = 540 cal/gm and specific heat of $ water = 1 cal/gm^oC) $

Options:
A. 570 gm
B. 572 gm
C. 562 gm
D. 650 gm
E. 450 gm
F. 620 gm
G. 622 gm
H. 560 gm
I. 575 gm
J. 582 gm
Answer: B
A wire of length '2m' is clamped horizontally between two fixed support . A mass m =5 kg is hanged from middle of wire. The vertical depression in wire in equailibrium is (young modulus of wire $\quad =2.4\times { 10 }^{ 9 }N/{ m }^{ 2 }$, cross- sectional area $=1{ cm }^{ 2 }\quad $)

Options:
A. 4.72 cm
B. 1.52 cm
C. 4.14 cm
D. 3.14 cm
E. 3.68 cm
F. 1.12 cm
G. 4.18 cm
H. 0.58 cm
I. 4.68 cm
J. 4.64 cm
Answer: I
The following deuterium reactions and corresponding reaction energies are found to occur
$$^{14}N(d, p)^{15}N, Q=8.53 MeV$$
$$^{15}N(d,\alpha)^{13}C, Q=7.58 MeV$$
$$^{13}C(d,\alpha)^{11}B, Q=5.16 MeV$$
The rotation $^{14}N(d, p)^{15}N$ represents the reaction $^{14}N+d\rightarrow ^{15}N+p$
$$_2^4He=4.0026 amu, _1^2He=2.014 amu, _1^1H=1.0078 amu, n=1.0087 amu (1 amu=931 MeV)$$
The Q values of the reaction $^{11}B(\alpha, n)^{14}N$ is

Options:
A. $$0.55 MeV$$
B. $$0.5 eV$$
C. $$0.04 MeV$$
D. $$0.05 eV$$
E. $$0.4 MeV$$
F. $$0.65 MeV$$
G. $$0.45 MeV$$
H. $$0.05 MeV$$
I. $$0.5 MeV$$
J. $$0.06 MeV$$
Answer: H
The equilibrium constant for the reaction will be:$Cu(s) + Cu^{2+} (aq.)\rightleftharpoons 2Cu^{+}(aq.)$$E_{Cu^{2+}/Cu}^{\circ} = 0.34\ V \ E_{Cu^{2+}/ Cu^+}^{\circ} = 0.15\ V$(Given: $\log 3.72 = 0.571$)

Options:
A. $$3.72\times 10^{-6}$$
B. $$3.72 \times 10^{-12}$$
C. $$3.72 \times 10^{-11}$$
D. $$3.72\times 10^{-8}$$
E. $$3.72 \times 10^{-13}$$
F. $$3.72 \times 10^{-4}$$
G. $$3.72 \times 10^{-10}$$
H. $$3.72\times 10^{-5}$$
I. $$3.72\times 10^{-7}$$
J. $$3.72 \times 10^{-9}$$
Answer: A
For a gaseous reaction.
$$A\left( g \right) + 3B\left( g \right) \to 3C\left( g \right) + 3D\left( g \right)$$
$\Delta \,E$ is $17 Kcal $ at ${27^ \circ }C$ cassuming $R = 2\,cal\,{K^{ - 1}}mo{l^{ - 1}}.$ the value of $\Delta \,H$ for the above reaction is:

Options:
A. 17.0 Kcal
B. 21.2 Kcal
C. 21.0 Kcal
D. $18.2$ Kcal
E. $16.4$Kcal
F. 19.2 Kcal
G. 19.8 Kcal
H. 18.4 Kcal
I. $15.8 $ Kcal
J. $20$ Kcal
Answer: J
A $3$ cm cube of iron one face at $100^o$ C and the other in a blocks of ice at $0^o$ C. If K of iron $= 0)2$ CGS units and L for ice is $80$ cal/gm, then the amount of ice that melts in $10$ minutes is (assume steady state heat transfer)

Options:
A. 550g
B. 300g
C. $350$g
D. $500$g
E. 600g
F. $900$g
G. 450g
H. $400$g
Answer: C
A $2.5 g$ impure sample containing weak monoacidic base (Molecular weight = $45$) is dissolved in $100 ml$ water and titrated with $0.5 - M - HCl$ at $25^{\circ}C$. When $1/5^{th}$ of the base was neutralized, the $pH$ was found to be $9$ and at equivalent point, $pH$ of solution is $4.5$.Which of the following statements is true?

Options:
A. Concentration of salt at equivalent point is $0.25 M$.
B. Volume of $HCl$ used at equivalent point is $150 ml$.
C. Volume of $HCl$ used at equivalent point is $110 ml$
D. Volume of $HCl$ used at equivalent point is $95 ml$.
E. Volume of $HCl$ used at equivalent point is $105 ml$
F. Volume of $HCl$ used at equivalent point is $130 ml$
G. Mass percentage of base in given sample is $80$%.
H. Volume of $HCl$ used at equivalent point is $100 ml$.
I. Volume of $HCl$ used at equivalent point is $125 ml$.
J. $K_{b}$ of base is less than $10^{-6}$.
Answer: H
A neutron of kinetic energy $65\ eV$ collides inelastically with a singly ionized helium atom at rest. It is scattered at an angle of $90^{\circ}$ with respect to its original direction.
Find the allowed values of the energy of the neutron and that of the atom after the collision.
[Given : Mass of $He\ atom = 4\times$ (mass of neutron) Ionization energy of $H$ atom $= 13. 6\ eV$]

Options:
A. 7.36\ eV, 0.312, 17.8\ eV; 27.328\ eV
B. 7.36\ eV, 0.312, 17.8\ eV; 15.328\ eV
C. $6.36\ eV, 0.312, 87.8\ eV; 16.328\ eV$.
D. 6.36\ eV, 0.312, 17.8\ eV; 28.328\ eV
E. $6.36\ eV, 0.312, 17.8\ eV; 26.328\ eV$.
F. 7.36\ eV, 0.312, 17.8\ eV; 14.328\ eV
G. $6.36\ eV, 0.312, 17.8\ eV; 16.328\ eV$.
H. $7.36\ eV, 0.312, 17.8\ eV; 16.328\ eV$.
I. 6.36\ eV, 0.312, 17.8\ eV; 27.328\ eV
J. 7.36\ eV, 0.312, 17.8\ eV; 26.328\ eV
Answer: H
We have an oxidation - reduction system: $ [Fe(CN)_{6}]^{3-}+e^{-}\rightleftharpoons [Fe(CN)_{6}]^{4-};E^{0}= +0.36 V.$ The ratio of concentrations of oxidized and reduced from at which the potential of the system becomes 0.24 V, is [Given : 2.303 RT/F = 0.06)

Options:
A. 1:100
B. 2:1
C. 5:1
D. 20:1
E. 10:1
F. 1:50
G. 1:20
H. 1:10
I. 1:2
J. 1:5
Answer: G
A dielectric slab of thickness $d$ inserted in a parallel plate capacitor whose negative plate is at $x=0$ and   positive plate is at $x=3d$.  The slab is equidistant from the plates. The capacitor is given some charge .As $x$ goes from $0$ to $3d$:

Options:
A. The electric potential decreases at first, then remains constant, and then increases.
B. $$The\ direction\ of\ the\ electric\ field\ remains\ the\ same.$$
C. $$The\ electric\ potential\ increases\ continuously.$$
D. The electric potential decreases at first, then increases, and then remains constant.
E. $$The\ magnitude\ of\ the\ elecrtric\ field\ remains\ the\ same.$$
F. $$The\ electric\ potential\ increase\ at\ first\, then\ decreases\ and\ again\ increases.$$
G. The\ electric\ potential\ decreases\ at\ first,\ then\ remains\ constant,\ and\ then\ decreases\ continuously.
H. The electric potential decreases at first, then increases, and again decreases.
Answer: C
Which of the following is a correct thermodynamic relation for ideal gases?

Options:
A. $${\left( {\frac{{\partial G}}{{\partial T}}} \right)_P} = 0$$
B. $${\left( {\frac{{\partial H}}{{\partial T}}} \right)_P} = 0$$
C. $${\left( {\frac{{\partial S}}{{\partial V}}} \right)_T} = 0$$
D. $${\left( {\frac{{\partial S}}{{\partial T}}} \right)_V} = 0$$
E. $${\left( {\frac{{\partial S}}{{\partial T}}} \right)_P} = 0$$
F. $${\left( {\frac{{\partial G}}{{\partial T}}} \right)_V} = 0$$
G. $${\left( {\frac{{\partial G}}{{\partial V}}} \right)_T} = 0$$
Answer: E
Which of the following complexes exhibits the highest paramagnetic behaviour ? Where gly = glycine, en = ethylenediamine and bipy = bipyridyl
(At. nos. Ti = 22, V = 23, Fe = 26, Co = 27)

Options:
A. $$[Co(OX)_3]^{-4}$$
B. $$[Cr(NH_3)_6]^{-3}$$
C. $$[Co(OX)_3]^{-2}$$
D. $$[Co(OX)_3]^{-1}$$
E. $$[Co(OX)_3]^{-5}$$
F. $$[Fe(OX)_3]^{-2}$$
G. $$[Cr(NH_3)_6]^{+3}$$
H. $$[V (gly)_2(OH)_2(NH_3)_2]^+$$
I. $$[Fe(en) (bipy) (NH_3)_2]^{2+}$$
J. $$[Co(OX)_3]^{-3}$$
Answer: J
Which will be the least stable resonating structure?

Options:
A. $$CH_2=CH-\overset{\oplus}{C}H-\overset{\ominus}{N}H_2$$
B. $$CH_2=CH-\overset{\ominus}{C}H-\overset{\oplus}{N}H_2$$
C. $$\overset{\ominus}{C}H_2-CH=CH-CH=\overset{\oplus}{N}H_2$$
D. $$CH_2=CH-\overset{\oplus}{C}H-\overset{\ominus}{C}H-NH_2$$
E. $$CH_2=CH-\overset{\ominus}{C}H-CH-\overset{\oplus}{N}H_2$$
F. $$\overset{\ominus}{C}H_2-\overset{\oplus}{C}H-CH=CH-NH_2$$
G. $$CH_2=CH-\overset{\ominus}{C}H-CH=\overset{\oplus}{N}H_2$$
H. $$CH_2=CH-\overset{\ominus}{C}H-\overset{\oplus}{C}H-NH_2$$
I. $$\overset{\ominus}{C}H_2-CH=CH-\overset{\oplus}{C}H-NH_2$$
Answer: D
A man can swim with velocity v relative to water.He has to cross a river of width d flowing with a velocity $u(u > v)$. The distance through which he is carried down stream by the river is x.Which of the following statement is correct.

Options:
A. x can not be less than $\dfrac{du}{v}$
B. For x to be minimum he has to swim in a direction making an angle of \(\dfrac{\pi}{2}+cos^{-1}(\dfrac{v}{u})\) with the direction of the flow of water
C. For x to be minimum he has to swim in a direction making an angle of \(\dfrac{\pi}{2}-sin^{-1}(\dfrac{u}{v})\) with the direction of the flow of water
D. For x to be minimum he has to swim in a direction making an angle of $\dfrac{\pi}{2}-sin^{-1}(\dfrac{v}{u})$ with the direction of the flow of water
E. For x to be minimum he has to swim in a direction making an angle of $\dfrac{\pi}{2}+tan^{-1}(\dfrac{v}{u})$ with the direction of the flow of water
F. If he crosses the river in minimum time $x=\dfrac{du}{v}$
G. For x to be minimum he has to swim in a direction making an angle of \(\dfrac{\pi}{2}+tan^{-1}(\dfrac{v}{u})\) with the direction of the flow of water
H. x will be max, if he swims in a direction making an angle of $\dfrac{\pi}{2}+sin^{-1}\dfrac{v}{u}$ with direction of the flow of water
I. For x to be minimum he has to swim in a direction making an angle of \(\dfrac{\pi}{2}-cos^{-1}(\dfrac{v}{u})\) with the direction of the flow of water
J. For x to be minimum he has to swim in a direction making an angle of $\dfrac{\pi}{2}+sin^{-1}(\dfrac{v}{u})$ with the direction of the flow of water
Answer: J
Calculate the pH of a buffer solution prepared by dissolving 10.6 g of $Na_2CO_3$ in 500 ml of an aqueous solution containing 80 ml of 1 M HCl. ($K_a$ for $HCO_3^-=6\times 10^{-11}$)

Options:
A. 9.4
B. 10.3
C. 10.6
D. 8.6
E. 11.6
F. 12.6
G. 9.3
H. 9.6
I. 7.6
J. 7.3
Answer: D
A copper wire $(Y = 1\times 10^{11} N/m^{2})$ of length $8\ m$, and a steel wire $(Y =2\times 10^{11} N/m^{2})$ of the length $4m$, each of cross-section $0.5\ cm^{2}$ are fastened end to end and stretched with a tension of $500\ N$. The elastic potential energy of the system is

Options:
A. $$0.15\ J$$
B. $$0.375\ J$$
C. $$0.5\ J$$
D. $$0.35\ J$$
E. $$0.125\ J$$
F. $$0.175\ J$$
G. $$0.2\ J$$
H. $$0.25\ J$$
Answer: H
Two narrow organ pipes, one open ($l_{1}$) and the other closed (length $l_{2}$) are sounded in their respectively fundamental modes. The beat frequency heard is 5 Hz. If now the pipes are sounded in their first overtones, then also the beat frequency heard is 5 Hz. then:

Options:
A. $$\dfrac{l_{1}}{l_{2}}=\dfrac{5}{4}$$
B. $$\dfrac{l_{1}}{l_{2}}=\dfrac{1}{1}$$
C. $$\dfrac{l_{1}}{l_{2}}=\dfrac{2}{1}$$
D. $$\dfrac{l_{1}}{l_{2}}=\dfrac{4}{3}$$
E. $$\dfrac{l_{1}}{l_{2}}=\dfrac{3}{2}$$
F. $$\dfrac{l_{1}}{l_{2}}=\dfrac{7}{5}$$
G. $$\dfrac{l_{1}}{l_{2}}=\dfrac{1}{2}$$
H. $$\dfrac{l_{1}}{l_{2}}=\dfrac{3}{4}$$
I. $$\dfrac{l_{1}}{l_{2}}=\dfrac{5}{3}$$
J. $$\dfrac{l_{1}}{l_{2}}=\dfrac{2}{3}$$
Answer: B
Given the following information
$${ A }^{ - }(g)\rightarrow { A }^{ 2+ }(g)+{ 3e }^{ - }\quad \quad \triangle { H }_{ 1 }=\quad 1400\quad kJ{ mol }^{ -1 }$$
$${ A }(g)\rightarrow { A }^{ 2+ }(aq)+{ 2e }^{ - }\quad \quad \triangle { H }_{ 2 }=\quad 700\quad kJ{ mol }^{ -1 }$$
$$\quad \quad \triangle { H }_{ e.g }\left[ { A }^{ + }(g) \right] =\quad -350\quad kJ{ mol }^{ -1 }$$
where $\quad \quad \triangle { H }_{ e.g. }$ is electron gain enthalpy.
$\left( { I.E }_{ 1 }+{ I.E }_{ 2 } \right) $ for A(g) = 950 kJ ${ mol }^{ -1 }$ 
The value of ${ \triangle H }_{ e.g }$ of ${ A }^{ 2+ }$ (g) in kJ ${ mol }^{ -1 }$ is

Options:
A. +600
B. +500
C. +700
D. -650
E. +650
F. +550
G. -500
H. -700
I. +750
J. -600
Answer: A
1 mole of argon is expanded isothermally and irreversibly (not against vaccum) from 10L to 100 L.Which of the following is incorrect of the process?

Options:
A. Heat supplied (q)=20
B. $$\Delta H=0$$
C. Heat supplied (q)=5
D. $$\Delta H=5$$
E. Heat supplied (q)=10
F. $$\Delta T=5$$
G. Heat supplied (q)=0
H. $$\Delta T=0$$
I. $$\Delta U=0$$
J. Heat supplied (q)=15
Answer: B
A heavy plank of mass $102.5\ kg$ is placed over two cylindrical rollers of radii $R = 10\ cm$ and $r = 5\ cm$. Mass of rollers is $40\ kg$ and $20\ kg$, respectively. Plank is pulled towards right by applying a horizontal force $F = 35\ N$ as shown in figure. During the first second of motion the plank gets displaced by $10\ cm$. If the plank remains horizontal and slipping does not takes place, calculate the magnitude and direction of force of friction acting between
 Plank and bigger roller

Options:
A. $4N$ towards left
B. $1N$ towards left
C. $2N$ towards right
D. $4N$ towards right
E. $3N$ towards left
F. $3N$ towards right
G. $1N$ towards right
H. $5N$ towards left
I. $2N$ towards left
Answer: F
There is a small black dot at the centre $C$ of a solid glass sphere of refractive index $\mu$. When seen from outside, comment on the location of the dot.

Options:
A. at $C$ for $\mu = \sqrt{2}$, but away from $C$ for $\mu \neq \sqrt{2}$
B. away from $C$ for $\mu < 1.5$, but at $C$ for $\mu \geq 1.5$
C. at $C$ only for $\sqrt {2} \leq \mu \leq 1.5$
D. away from $C$ for all values of $\mu$
E. at $C$ for $\mu \leq 1.5$, but away from $C$ for $\mu > 1.5$
F. at $C$ for $\mu = 1.5$, but away from $C$ for $\mu
eq 1.5$
G. away from $C$ for $\mu \geq \sqrt{2}$, but at $C$ for $\mu < \sqrt{2}$
Answer: D
A charged particle of radius $5 \times 10^{-7}$ m is loacted in a horizontal electric field of intensity $6.28 \times 10^5 Vm^{-1}$. The surrounding medium has the coefficient of viscosity $\eta = 1.6 \times 10^5 Nsm^{-2}$. The particle starts moving under the effect of electric field and finally attains a uniform horizontal speed of $0.02 \ ms^{-1}$. Find the number of electrons on it :(Assume gravity free space)

Options:
A. 2 \times 10^{11}
B. $$1 \times 10^{11}$$
C. 5 \times 10^{11}
D. 8 \times 10^{11}
E. 4 \times 10^{10}
F. $$9 \times 10^{11}$$
G. 4 \times 10^{11}
H. $$6 \times 10^{11}$$
I. $$3 \times 10^{11}$$
J. 7 \times 10^{11}
Answer: I
A projectile projected tangentially from the surface of a planet of radius R from a point A, follows the indicated trajectory during its motion. If it is at height of 3R at the farthest point of its trajectory, then the velocity of projection at A, $v_0$ is given by (acceleration due to gravity on surface = g)

Options:
A. $$v_0 =\sqrt{1.5gR}$$
B. $$v_0 =\sqrt{1.9gR}$$
C. $$v_0 =\sqrt{1.8gR}$$
D. $$v_0 =\sqrt{1.7gR}$$
E. $$v_0 =\sqrt{0.5gR}$$
F. $$v_0 =\sqrt{1.4gR}$$
G. $$v_0 =\sqrt{1.55gR}$$
H. $$v_0 =\sqrt{1.6gR}$$
I. $$v_0 =\sqrt{2gR/3}$$
Answer: A
An aluminum foil of relative emittance $0.1$ is placed in between two concentric spheres at temperatures $300$K and $200$K respectively. Assume that the spheres are perfect black body radiators. The rate of energy transfer between one of the spheres and the foil is :($\sigma = 5.672 \times 10^{-8}$ M.K.S.units)

Options:
A. 19.5 watt
B. 18.8 watt
C. 12.3 watt
D. 19.0 watt
E. 17.8 watt
F. 18.5 watt
G. 20.2 watt
H. 17.5 watt
I. 15.6 watt
J. 17.9 watt
Answer: F
An ideal gas is subjected to a cyclic process involving four thermodynamic states; the amounts of heat (Q) and work (W) involved in each of these states are $Q_1 = 6000 \,J, Q_2 = 5500 \,J, Q_3 = -3000 \,J, Q_4  = 3500 \,J \,W_1 = 2500 \,J, W_2 = -1000 \,J, W_3 = -1200 \,J, W_4 = xJ$. The ratio of the net work done by the gas to the total heat absorbed by the gas in '$\eta$'. What are he values of $x$ and $\eta$ respectively?

Options:
A. $$1500, 7.5 \%$$
B. $$1000, 7.5 \%$$
C. $$1000, 10.5 \%$$
D. $$1000, 5 \%$$
E. $$1000, 21 \%$$
F. $$500, 15 \%$$
G. $$500, 7.5 \%$$
H. $$1500, 15 \%$$
I. $$1500, 10.5 \%$$
J. $$1000, 15 \%$$
Answer: C
The rate of change of pressure (p) of a gas at constant temperature and constant external pressure due to effusion of gas from a vessel of constant volume is related to rate of change of number of molecules present by $ {\frac{dp}{dt}}$=${\frac{kT}{V}}$ ${\frac{dN}{dt}}$ where k=Boltzmann constant,T=temperature,V=volume of vessel and N =No of molecules and ${\frac{dN}{dt}}$=${\frac{-pA_0}{(2\pi mkT)^{1/2}}}$, where ${A_0}$= area of office and m =mass of molecule.The time required for pressure inside vessel to reduce to 1/e of its initial value in (In e=1)

Options:
A. $$\left ( \dfrac{kT}{2\pi m} \right )^{3/2} \dfrac{V}{pA_0}$$
B. $$\left ( \dfrac{2 \pi m}{kT} \right )^{1/4} \dfrac{V}{pA_0}$$
C. $${\left ( \dfrac{2 \pi m k T}{pA^0} \right )^{1/2}}$$
D. ${\dfrac{2\pi m}{kT}}$ ${\dfrac{V}{pA_0}}$
E. ${\left ( \dfrac{kT}{2\pi m} \right )^{1/2}}$ ${\dfrac{V}{pA_0}}$
F. $$\left ( \dfrac{2 \pi m}{kT} \right )^{1/3} \dfrac{V}{pA_0}$$
G. $$\left ( \dfrac{2 \pi m}{kT} \right )^{1/2} \dfrac{V}{pA_0}$$
H. ${\binom{2\pi m}{kT}^{1/2}}$ ${\dfrac{V}{pA_0}}$
I. ${\left ( \dfrac{kT}{2\pi m} \right )^{1/3}} \dfrac{V}{pA_0}$
Answer: H
Calculate the pH of a 0.033 M ammonia solution, if 0.33 M $NH_4Cl$ is introduced in this solution at the same temperature. $ (k_b\, for \, NH_3=1.77 \times 10^{-5})$

Options:
A. 9.50
B. 4.75
C. None of these
D. 8.75
E. 9.05
F. 9.15
G. 9.75
H. 9.10
I. 10
J. 9.25
Answer: J
What will be density ( in $g\ { mL }^{ -1 }$) of 3.60 molar sulphuric acid having 29% by mass?$(Molar\ mass\ =\ 98\ g\ { mL }^{ -1 })$

Options:
A. 1.76
B. 1.72
C. 1.53
D. 1.92
E. 1.84
F. 1.69
G. 1.64
H. 1.45
I. 1.22
J. 1.88
Answer: J
In a region of uniform magnetic induction  $B = 10 ^ { 2 } T ,$  a circular coil of radius  $30\mathrm { cm }$  and resistance  $\pi ^ { 2 } ohm$  is rotated about an axis which is perpendicular to the direction of  $\mathrm { B }$  and which forms a diameter of the coil, If the coil rotates at  $200 rpm,$  the amplitude of the alternating current induced in the coil is:

Options:
A. $$6\mathrm { m }A$$
B. $$14\mathrm { m }A$$
C. $$12\mathrm { m }A$$
D. $$8\mathrm { m }A$$
E. $$30\mathrm { m }A$$
F. $$4\mathrm { m }A$$
G. $$10\mathrm { m }A$$
H. $$$4\pi ^ { 2 } \mathrm { m } A$$$
I. $$$200\mathrm { m }A$$$
J. $$18\mathrm { m }A$$
Answer: A
A particle of mass $2\ kg$ is moving in a circular path of radius $1\ m$ such that its centripetal acceleration is varying with time $a_{c}=4t^{2}$. The power delivered to the particle is

Options:
A. $$16t$$
B. $$2t^2$$
C. $$14t$$
D. $$8t$$
E. $$4t$$
F. $$2t$$
G. $$10t$$
H. $$6t$$
I. $$12t$$
J. $$18t$$
Answer: E
$1$ mole of an ideal gas $\left( { C }_{ V }=12.55J{ K }^{ -1 }{ mol }^{ -1 } \right) $ at $300K$ compressed adiabatically and reversibly to one-fourth of its original volume. What is the final temperature of the gas?

Options:
A. $$757 K$$
B. $$751 K$$
C. $$758 K$$
D. $$753 K$$
E. $$756 K$$
F. $$752 K$$
G. $$750 K$$
H. $$755 K$$
I. $$754 K$$
Answer: G
Two monochromatic coherent point sources $S_{1}$ and $S_{2}$ are separated by a distance $L$. Each source emits light of wavelength $\lambda$, where $L > > \lambda$. The line $S_{1} S_{2}$ when extended meets a screen perpendicular to it at a point $A$.

Options:
A. The interference fringes on the screen are elliptical in shape
B. The interference fringes on the screen are parabolic in shape
C. Point $A$ is always an intensity maxima for any separation $L$
D. The interference fringes on the screen are straight lines perpendicular to the line \( S_{1}S_{2}A \)
E. The interference fringes on the screen are hyperbolic in shape
F. The interference fringes on the screen are circular in shape
G. The interference fringes on the screen are straight lines perpendicular to the line $S_{1}S_{2}A$
H. The interference fringes on the screen are concentric in shape
I. The interference fringes on the screen are straight lines parallel to the line $S_{1}S_{2}A$
J. Point $A$ is an intensity maxima if $L = n\lambda$
Answer: F
A small object is placed $50\ cm$ to the left of a thin convex lens of focal length $30\ cm.$ A convex spherical mirror of radius of curvature $100\ cm$ is placed to the right of the lens at a distance of $50\ cm.$ The mirror is tilted such that the axis of the mirror is at an angle $\theta = 30^{o}$ to the axis of the lens.
If the origin of the coordinates system is taken to be at the centre of the lens, the coordinates (in $cm$) of the point $(x,y)$ at which the image is formed are

Options:
A. $$(30 cm, 40 cm)$$
B. $$(25, 25\sqrt{3})$$
C. $$(125/3, 25/\sqrt{3})$$
D. $$0,\ 0$$
E. $$(125/4, 25/\sqrt{3})$$
F. $$(27 cm, 37 cm)$$
G. $$(30 cm, 38 cm)$$
H. $$(50-25\sqrt {3},\ 25)$$
I. $$(150/5, 50/\sqrt{3})$$
Answer: B
$0.5\ mol\ NaCl$ is dissolved in $500\ g\ H_{2}O$. Then determine freezing point and boiling point of solution :
Given ($K_{f})_{H_{2}O}=1.8\ K\ kg/mol$
           ($K_{b})_{H_{2}O}=0.5\ K\ kg/mol$

Options:
A. $$-3.6^{o}C,\ 100^{o}C$$
B. $$-1.8^{o}C,\ 100^{o}C$$
C. $$-1.8^{o}C,\ 100.5^{o}C$$
D. $$-1.8^{o}C,\ 99.5^{o}C$$
E. $$-3.6^{o}C,\ 99^{o}C$$
F. $$-1.8^{o}C,\ 98.5^{o}C$$
G. $$-1.8^{o}C,\ 101^{o}C$$
H. $$-3.6^{o}C,\ 101^{o}C$$
I. $$-1.8^{o}C,\ 99^{o}C$$
J. $$0^{o}C,\ 100^{o}C$$
Answer: C
Object PinConvex Lens Convex Mirror Image Pin  22.2 cm32.2  cm45.8 cm71.2 cm To find the focal length of a convex mirror, a student records the following data:The focal length of the convex lens is ${f}_{1}$ and that of mirror is ${f}_{2}$. Then taking index correction to be negligibly small, ${f}_{1}$ and ${f}_{2}$ are close to :

Options:
A. $${ f }_{ 1 }=7.8cm\quad \quad { f }_{ 2 }=12.7cm$$
B. ${ f }_{ 1 }=7.8cm\quad \quad { f }_{ 2 }=38.1cm$
C. $${ f }_{ 1 }=12.7cm\quad \quad { f }_{ 2 }=7.8cm$$
D. $${ f }_{ 1 }=7.8cm\quad \quad { f }_{ 2 }=25.4cm$$
E. ${ f }_{ 1 }=15.6cm\quad \quad { f }_{ 2 }=12.7cm$
F. ${ f }_{ 1 }=12.7cm\quad \quad { f }_{ 2 }=25.4cm$
G. $${ f }_{ 1 }=15.6cm\quad \quad { f }_{ 2 }=25.4cm$$
H. ${ f }_{ 1 }=7.8cm\quad \quad { f }_{ 2 }=15.6cm$
I. ${ f }_{ 1 }=12.7cm\quad \quad { f }_{ 2 }=15.6cm$
Answer: A
A block of mass $4kg$ is kept over a rough horizontal surface. The coefficient of friction between the block and the surface is $0.1$. At $t=0,\left( 3\hat { i }  \right) \cfrac { m }{ s } $ velocity is imparted to the block and simultaneously $\left( -2\hat { i }  \right) N$ force starts acting on it. Its displacment in first $5s$ is

Options:
A. 4\hat { i }
B. 6\hat { i }
C. $$3\hat { i } $$
D. $$8\hat { i } $$
E. 7\hat { i }
F. $$-8\hat { i } $$
G. 2\hat { i }
H. $$-3\hat { i } $$
I. 5\hat { i }
Answer: H
The standard cell potential for the cell $Pt| Hg(l) | Hg_2Cl_2(s) KCl_{(0.1M)} || Zn Cl_2(0.1 M) | Zn (s)$
[Given $E^0_{Zn^{2+/Zn}}= -0.76 V$ and $E^0_{Cr^-|Hg_2Cl_2|Hg} = 0.34 V]$ is

Options:
A. $$-1.11 V$$
B. $$-0.89 V$$
C. $$-1.15 V$$
D. $$-0.85 V$$
E. $$-1.10 V$$
F. $$-1.12 V$$
G. $$-1.09 V$$
H. $$-0.99 V$$
I. $$1.10 V$$
J. $$0.99 V$$
Answer: E
A capacitor of capacitance $ C= \frac {18}{ \pi } mF $ having initial charge $ Q_0 $ connected to an inductor of inductance $ L= \frac {18}{ \pi } mH $ at t=0 . find the time (in mili second) after energy stored in electric field is three times energy stored in magnetic field.

Options:
A. 7
B. 5.8
C. 4
D. 6
E. 4.5
F. 5.5
G. 2
H. 3
I. 5
J. 7.5
Answer: D
For the reaction, 2AB(s) $\rightleftharpoons A_{2}(g)+B_{2}(g),\Delta H=1.38$ KCal, the equilibrium pressure is 2 atm at 500 K. Assuming the enthalpy change to be independent of temperature, the equilibrium pressure at 1000 K will be : [Take log2=0.3]

Options:
A. 0.707 atm
B. 1.417 atm
C. 2.828 atm
D. 3.414 atm
E. 2 atm
F. 1.415 atm
G. 1.828 atm
H. 4 atm
I. 1.414 atm
J. 1.707 atm
Answer: I
Consider the following reactions at $1000^0C$
A) $Zn_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow ZnO_{(s)}; \ \Delta G^0$ = -360 KJ/mol
B) $C_{(gra)} + \frac{1}{2}O_{2(g)} \rightarrow CO_{(g)}; \ \Delta G^0$ = -460 KJ / mol
Correct statement at $1000^0C$ is

Options:
A. ZnO can be reduced by "C"
B. ZnO can be reduced by CO
C. Both (1) & (2) true
D. Zn can be oxidised by C
E. ZnO can be reduced by "CO"
F. CO can be reduced by "C"
G. Zn can be reduced by CO
H. Zn can be oxidised by CO
I. CO can be reduced by "Zn"
J. ZnO can be oxidised by CO
Answer: H
A point mass $m=20kg$, is suspended by a massless spring of constant $2000 N/m$. The point mass is released when elongation in the spring is $15cm$. The equation of displacement of particle as function of time is: (Take $g=10 m/s^2$)

Options:
A. $$y=10\sin 10t$$
B. $$y=10\cos\left(10t+\dfrac{\pi}{6}\right)$$
C. $$y=10\cos 10t$$
D. $$y=10\sin\left(10t-\dfrac{\pi}{6}\right)$$
E. $$y=10\sin\left(10t+\dfrac{\pi}{4}\right)$$
F. $$y=10\sin\left(10t+\dfrac{\pi}{3}\right)$$
G. $$y=10\cos\left(10t-\dfrac{\pi}{6}\right)$$
H. None of these.
I. $$y=10\sin\left(10t-\dfrac{\pi}{3}\right)$$
J. $$y=10\sin\left(10t+\dfrac{\pi}{6}\right)$$
Answer: J
A uniform thin rod of weight W is supported horizontally by two vertical props at its ends. At $t = 0,$ one of these supports is kicked out. The force on the other support immediately thereafter is

Options:
A. \dfrac{W}{6}
B. \dfrac{W}{5}
C. $$\dfrac{W}{4}$$
D. $$4W$$
E. \dfrac{3W}{4}
F. $$\dfrac{W}{2}$$
G. $$2W$$
H. \dfrac{W}{7}
I. \dfrac{W}{8}
J. \dfrac{W}{3}
Answer: C
At $30^oC$, the solubility of $Ag_2CO_3(K_{sp} = 8\times 10^{-12})$ would be maximum in 1 litre of:

Options:
A. $$0.05\ M \ NH_4NO_3$$
B. $$0.05\ M \ AgNO_3$$
C. $$0.05\ M \ Na_2CO_3$$
D. $$0.05\ M \ NH_3$$
E. $$0.05\ M \ Na_2SO_4$$
F. $$0.05\ M \ NaNO_3$$
G. $$0.05\ M \ KNO_3$$
H. Pure water
Answer: H
We have a thin spherical shell of radius $R$. Half of the sphere carrying surface change density $\sigma_{1}$ and rest half carrying $\sigma_{2}$. Magnitude of force of electromagnetic interaction between hemispherical parts carrying surface charge density $\sigma_{1}$ and rest of the hemispherical portion is $f_{0} = \alpha \times 10^{4}$ Newton. Here $\alpha$ is an integer. Value of $\alpha$ will be.
(Given $\sigma_{1} = \sqrt {\epsilon_{0}} \times 10^{2} cm/m^{2}, \sigma_{2} = 4\sigma_{1}, R = \sqrt {\dfrac {3}{\pi}m})$

Options:
A. $$4$$
B. $$5$$
C. $$8$$
D. $$7$$
E. $$6$$
F. $$2$$
G. $$3$$
H. $$1$$
Answer: E
A particle of mass 1 kg is moving in the $x- y$ plane and its potential energy $U$ in joule obeys the law $U = 6x + 8y$, where ($x,y$) are the coordinates of the particle in meter. If the particle starts from rest at (9,3) at time $t = 0$, then

Options:
A. The speed of the particle when it crosses the y axis is \( 5 \sqrt{3}\ m/s \)
B. The speed of the particle when it crosses y axes is $7 \sqrt{3}\ m/s$
C. Magnitude of acceleration of particle is $10\ m/s^{2}$
D. The speed of the particle when it crosses y axes is \( 11 \sqrt{3}\ m/s \)
E. Acceleration of particle is zero
F. The speed of the particle when it crosses y axes is \( 8 \sqrt{3}\ m/s \)
G. The speed of the particle when it crosses y axes is \( 9 \sqrt{3}\ m/s \)
H. The speed of the particle when it crosses y axes is \( 12 \sqrt{3}\ m/s \)
I. The speed of the particle when it crosses y axes is $10 \sqrt{3}\ m/s$
Answer: I
How much energy must be supplied to charge $36$g of ice at ${0^0}C$ to water at room temperature,${25^0}C$?
$\eqalign{  & \Delta {H^0}{^{}_{fussion}} = 6.01\,KJ\,mo{l^{ - 1}}  \cr   & {C_{p,liquid}} = 4.18K{J^{ - 1}}\,mo{l^{ - 1}}  \cr   &  \cr} $

Options:
A. 14 KJ
B. 18 KJ
C. $22$KJ
D. $1256.09$KJ
E. 17 KJ
F. 21 KJ
G. $16$KJ
H. $19$KJ
I. 14.5 KJ
J. 15 KJ
Answer: G
A uniform glass tube is bent into a U - tube such as shown in the figure. water is poured into the tube until it stands 10cm high in each limb. Benzene (specific gravity = 0.879) is the added slowly in the left limb until the water rises 4 cm higher in the right limb. What length is the colimn of benzene of when the situation is reached? Water and benzene do not mix.

Options:
A. 9.1 cm
B. 17.1 cm
C. 19.1 cm
D. 22.1 cm
E. 21.1 cm
F. 10.1 cm
G. 16.1 cm
H. 20.1 cm
I. 15.1 cm
J. 18.1 cm
Answer: H
The magnetic flux associated with a metal ring varies with time according  to $\phi =3(at^3-bt^2)T-m^2,a=2\sec^{-3},b=6\sec^{-2}$. If the resistance of ring is $3\Omega$,the current induced in the ring during the time $t=2$ sec is :

Options:
A. $$5\ amp$$
B. $$4\ amp$$
C. $$6\ amp$$
D. $$12\ amp$$
E. $$10\ amp$$
F. $$3\ amp$$
G. $$0$$
H. $$7\ amp$$
I. $$8\ amp$$
J. $$2\ amp$$
Answer: C
For reaction, at $1000^{o}C$
$$CaCO_{3}(s)\longrightarrow CaO(s)+CO_{2}(g)$$
$$\Delta G^{o}=-24\ kJ\ mol^{-1},pco_{2}=0.0030\ atm$$
Hence, $\Delta G$ at the is temperature is

Options:
A. $$-85.5\ kJ\ mol^{-1}$$
B. $$-61.0\ kJ\ mol^{-1}$$
C. $$-87.5\ kJ\ mol^{-1}$$
D. $$-63.5\ kJ\ mol^{-1}$$
E. $$-62.5\ kJ\ mol^{-1}$$
F. $$-60.5\ kJ\ mol^{-1}$$
G. $$-61.5\ kJ\ mol^{-1}$$
H. $$-61.7\ kJ\ mol^{-1}$$
I. $$-84.9\ kJ\ mol^{-1}$$
J. $$+33.5\ kJ\ mol^{-1}$$
Answer: F
One end of a taut string of length $3m$ along the $x$ axis is fixed at $x=0$. The speed 8of the waves in the string is $100\ ms^{-1}$. The other end of the string is vibrating in the $y$ direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

Options:
A. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { 125\pi t } }$$
B. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { \dfrac { 250\pi t }{ 4 } } }$$
C. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { 225\pi t } }$$
D. $$y(t)=A\sin { \dfrac { \pi }{ 6 } \cos { \dfrac { 50\pi }{ 3 } } } $$
E. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { 200\pi t } }$$
F. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { \dfrac { 200\pi t }{ 3 } } }$$
G. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { \dfrac { 250\pi }{ 3 } } } $$
H. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { \dfrac { 250\pi t }{ 2 } } }$$
I. $$y(t)=A\sin { \dfrac { 5\pi X }{ 6 } \cos { 250\pi t } } $$
Answer: I
The ratio of adiabatic bulk modulus and isothermal  bulk modulus of gas is $(\quad \gamma ={ C }_{ p }/{ C }_{ V })\quad $

Options:
A. 1
B. $$\dfrac { \gamma - 1 }{ 2 }$$
C. $$\dfrac { \gamma + 1 }{ \gamma }$$
D. $$\dfrac { (\gamma -1) }{ \gamma } $$
E. $$\gamma $$
F. $$\dfrac { \gamma }{ (\gamma -1) } $$
G. $$\dfrac { \gamma + 1 }{ 2}$$
H. $$\dfrac { \gamma }{ (\gamma + 1) }$$
I. $$\dfrac { \gamma + 2 }{ \gamma }$$
J. $$\dfrac { \gamma - 1 }{ \gamma + 1 }$$
Answer: A
A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass $\cfrac{M}{2}$ each. Speed of light is $c$. The binding energy per nucleon for the parent nucleus is ${E}_{1}$ and that for the daughter nuclei is ${E}_{2}$. Then :

Options:
A. $${ E }_{ 1 }=2{ E }_{ 2 }$$
B. $${ E }_{ 1 }=\frac{3}{2}{ E }_{ 2 }$$
C. $${ E }_{ 1 }>{ E }_{ 2 }$$
D. $${ E }_{ 1 }=3{ E }_{ 2 }$$
E. $${ E }_{ 2 }>2{ E }_{ 1 }$$
F. $${ E }_{ 2 }>{ E }_{ 1 }$$
G. $${ E }_{ 2 }>3{ E }_{ 1 }$$
H. $${ E }_{ 1 }<{ E }_{ 2 }$$
I. $${ E }_{ 2 }>\frac{3}{2}{ E }_{ 1 }$$
J. $${ E }_{ 1 }=\frac{1}{2}{ E }_{ 2 }$$
Answer: C
Rate of change of speed of a particle in motion is nothing but the component of acceleration along velocity $v$.
Velocity and acceleration of a particle at some instant of time are $\vec {v} = (2\hat {i} + \hat {j} + 2\hat {k})m/s^{2}$ and acceleration $-(\hat {i} + 2\hat {j} + \hat {k})m/s^{2}$. Then, the speed of the particle is _________ at a rate of ________ $m/s^{2}$.

Options:
A. Decreasing, $\sqrt{7}$
B. Decreasing, $\sqrt6$
C. Increasing, $6$
D. Decreasing, $3$
E. Decreasing, $\sqrt{3}$
F. Decreasing, $\sqrt{5}$
G. Decreasing, $\sqrt{2}$
H. Decreasing, $2$
I. Increasing, $2$
J. Increasing, $\sqrt{6}$
Answer: B
A  solid cylinder of radius $r$ and a hollow cylinder with inner and outer radius $r$ and $2r$ respectively of the same masses are placed on a horizontal table top.
If $P_{1}$ and $P_{2}$ are the pressure exerted due to solid and hollow cylinder respectively, then

Options:
A. $$P_{2}=2P_{1}$$
B. $$P_{1} = \frac{P_{2}}{2}$$
C. P_{1}=4P_{2}
D. $$P_{1}=2P_{2}$$
E. $$P_{1} = \frac{P_{2}}{3}$$
F. $$P_{1}=P_{2}$$
G. $$P_{2}=4P_{1}$$
H. $$P_{1} = \frac{P_{2}}{4}$$
I. $$P_{2}=3P_{1}$$
J. $$P_{1}=3P_{2}$$
Answer: F
A small block of mass $m =1$ is placed to a plank which moves on a horizontal frictionless surface. The mass of the plank is $M = 4\ kg$, and its length is $L = 0.8\ m$. The coefficient of friction between the plank and the block is $0.4. [g = 10\ m/s^{2}]$.
What is the least constant force $F_{0}$ (in $N$) with which the plank must be pulled in order to make the block slide down from it?

Options:
A. $$28$$
B. $$16$$
C. $$20$$
D. $$25$$
E. $$10$$
F. $$15$$
G. $$30$$
H. $$24$$
I. $$18$$
J. $$22$$
Answer: F
Given:$NaCl(s) + aq\longrightarrow Na^{ \oplus } (aq) + Cl^{ \ominus }$     $\Delta H = 3.9 kJ$$Na^{ \oplus } (g) + Cl^{ \ominus } (g)\longrightarrow NaCl(s)\,\,\,\,\Delta H = -788 kJ$$Cl^{ \ominus } (g) +aq\longrightarrow Cl^{ \ominus } (aq)\,\,\,\,\Delta H = -394.1 kJ$Then the enthalpy of hydration of $Na^{ \oplus }$ ions is :

Options:
A. -630.0 kJ
B. -395.0 kJ
C. -634.1 kJ
D. -393.1 kJ
E. -780.0 kJ
F. -635.0 kJ
G. -960.0 kJ
H. -620.0 kJ
I. -390.0 kJ
J. -629.1 kJ
Answer: I
Figure shows an end view of two long, parallel wires perpendicular to the xy plane, each carrying a current $I$, but in opposite directions. At what value of $x$, the magnitude of $ec { B } $ is maximum?

Options:
A. $$x=0$$
B. $$x=a$$
C. $$x = 3a$$
D. $$x=3a/2$$
E. $$x=a/2$$
F. $$x=2a$$
G. $$x=1/ \sqrt{2} a$$
H. $$x=\sqrt{2} a$$
I. $$x=1/2 a$$
Answer: A
The transverse displacement of a string (clamped at its both ends) is given by
$$y(x,t)=0.06 sin \bigg( \dfrac{2 \pi}{3}x \bigg) cos (120 \pi t)$$
All the points on the string between two consecutive nodes vibrate with

Options:
A. same energy
B. different energy
C. same amplitude
D. different wavelength
E. different phase
F. different amplitude
G. different frequency
H. same frequency
Answer: F