MikaStars39/nano-eval huggingface dataset:
ABCDE is a frictionless circular track of radius R. A body slides down the track from point A which is at a height h=5 cm. Maximum value of R for the body to successfully complete the loop is :

Options:
A. 5 cm
B. $$\frac{25}{3}cm$$
C. $$\frac{20}{4}cm$$
D. $$\frac{10}{3}cm$$
E. $$\frac{10}{2}cm$$
F. 2 cm
G. $$\frac{15}{4}cm$$
H. $$\frac{20}{3}cm$$
I. $$\frac{15}{3}cm$$
Answer: A
One mole of solid Zn is placed in excess of dilute $H_2SO_4$ at $27^oC$ in a cylinder fitted with a piston. Find the value of $\Delta E$, q and w for the process if the area of piston is 500 cm2 and it moves out by 50 cm against a pressure of 1 atm during the reaction. The heat given to surrounding is 36.5 kJ
$$Zn(s)+2H^+(aq)\rightleftharpoons Zn^{2+}(aq)+H_2(g)$$

Options:
A. $$\Delta E = -39.03 kJ mol^{1}, q = -36.5 kJ, w = -2.53 J$$
B. $$\(\Delta E = -39.03 kJ mol^{1}, q = 36.5 kJ, w = 2.53 J\)$$
C. \(\Delta E = 39.03 kJ mol^{1}, q = -36.5 kJ, w = 2.53 J\)
D. $$\(\Delta E = 39.03 kJ mol^{1}, q = 36.5 kJ, w = -2.53 J\)$$
E. None of these
F. $$\Delta E = 39.03 kJ mol^{1}, q = 36.5 kJ, w = 2.53 J$$
G. $$\(\Delta E = -39.03 kJ mol^{1}, q = 36.5 kJ, w = -2.53 J\)$$
H. $$\(\Delta E = -39.03 kJ mol^{1}, q = 36.5 kJ, w = 5.06 J\)$$
I. $$\Delta E = -39.03 kJ mol^{1}, q = -36.5 kJ, w = 2.53 J$$
J. \(\Delta E = 39.03 kJ mol^{1}, q = -36.5 kJ, w = -2.53 J\)
Answer: F
Calculate the heat of combustion (in kJ/mol) of benzene $(C_6H_6)$.
[Given : $\Delta_fH^0$ of $CO_2=x \quad kJ/mol$
              $\Delta_fH^0$ of $H_2O=y\quad  kJ/mol$
              $\Delta_fH^0$ of $C_6H_6=z \quad kJ/mol$ sign inclusive]

Options:
A. 3x+6y+z
B. 3x+6y-z
C. 6x+3y+z
D. 6x+3y-z
E. 3x+3y+z
F. x+y-z
G. 6x+6y-z
H. 3x+3y-z
I. 6x+6y+z
J. -x+y-z
Answer: F
Three concentric spherical shells have radii a, b and $(a < b < c)$ and have surface charge densities $\sigma, -\sigma$ respectively. If $V_A, V_B$ and $V_C$ denote the potentials of the three shells, then, for $c = a +b$, we have:

Options:
A. $$V_C = V_A \neq V_B$$
B. $$V_C = V_B \neq V_A$$
C. $$V_C \neq V_B \neq V_A$$
D. $V_C
eq V_B
eq V_A$
E. $$$V_C=V_A$$
F. $$V_C = V_B = V_A$$
G. $$$V_C \neq V_B = V_A$$$
Answer: G
A truck is carry a box of mass $m = 50 \,kg$ on its flat horizontal rough surface with coefficient of friction $p = 0.3$. It is crossing a circular track of radius $27 \,m$. What is the maximum speed of the truck to that the box does not slide from the muck while moving on the circular path?

Options:
A. $$2.5\,km/hr$$
B. 3.5\,km/hr
C. $$32.4 \,km/hr$$
D. 3.6 \,km/hr
E. $$18 \,km/hr$$
F. 3.2 \,km/hr
G. 3.0 \,km/hr
H. 4.5\,km/hr
I. 4.8 \,km/hr
J. $$36 \,km/hr$$
Answer: A
A train $A$ runs from east to west and another train $B$ of the same mass runs from west to east at the same speed along the equator. A presses the track with a force $F_1$ and B presses the track with a force $F_2$. Then:

Options:
A. $$incomplete information to find the relation between $F_1$ and $F_2$$$
B. $$F_1 = \frac{1}{3}F_2$$
C. $$F_1 = F_2$$
D. $$F_1 = \frac{3}{2}F_2$$
E. $$F_1 = \frac{2}{3}F_2$$
F. $$F_1 = \frac{1}{2}F_2$$
G. $$F_1 < F_2$$
H. $$F_1 > F_2$$
I. $$\( F_1 = 2F_2 \)$$
Answer: H
The vapour pressure of water at T(K) is 20 mm Hg. The following solutions are prepared at T(K) :

Options:
A. 5.3 g of \(N{a_2}C{O_3}\) (mol. wt. =108) is dissolved in 179.1 g of water.
B. 5.3 g of $N{a_2}C{O_3}$ (mol. wt. =107) is dissolved in 179.1 g of water.
C. non of these
D. 5.3 g of \(N{a_2}C{O_3}\) (mol. wt. =105) is dissolved in 179.1 g of water.
E. 5.3 g of $N{a_2}C{O_3}$ (mol. wt. =104) is dissolved in 179.1 g of water.
F. 5.3 g of \(N{a_2}C{O_3}\) (mol. wt. =109) is dissolved in 179.1 g of water.
G. 5.3 g of $N{a_2}C{O_3}$ (mol. wt. =106) is dissolved in 179.1 g of water.
H. 5.3 g of \(N{a_2}C{O_3}\) (mol. wt. =106.5) is dissolved in 179.1 g of water.
Answer: G
A mixture of iron (II) and lead (II) carbonates was calcined. As a result of this, an amount of $0.9$ mol of $CO_2$ was evolved. The mixture of metal oxides obtained by decomposing the above carbonates was treated with sulphuric acid which resulted in a mass of $151.6$ g of a sulphate as precipitate. Determine the composition of the starting mixture of carbonates in mass percentage.

Options:
A. Mass of $FeCO_3=45.79\%$ , Mass of $PbCO_3 =54.21\%$
B. Mass of $FeCO_3=30.79\%$ , Mass of $PbCO_3 =69.21\%$
C. Mass of $FeCO_3=15.79\%$ , Mass of $PbCO_3 =84.21\%$
D. Mass of $FeCO_3=35.79\%$ , Mass of $PbCO_3 =64.21\%$
E. Mass of $FeCO_3=20.79\%$ , Mass of $PbCO_3 =79.21\%$
F. Mass of $FeCO_3=25.79\%$ , Mass of $PbCO_3 =75.21\%$
G. Mass of $FeCO_3=27.79\%$ , Mass of $PbCO_3 =72.21\%$
H. None of these
I. Mass of $FeCO_3=25.79\%$ , Mass of $PbCO_3 =74.21\%$
J. Mass of $FeCO_3=25.79\%$ , Mass of $PbCO_3 =64.21\%$
Answer: I
In the figure, an air lens of radii of curvature 10 $ \mathrm{cm}\left(R_{1}=R_{2}=10 \mathrm{cm}\right)  $ is cut in a cylinder of
glass $ (\mu=1.5)  $. The focal length and the nature of the lens is

Options:
A. $ 15 \mathrm{cm}, $ concave
B. 20 \mathrm{cm}, concave
C. 15 \mathrm{cm}, convex
D. 10 \mathrm{cm}, convex
E. $ 0, $ concave
F. $ \infty, $ neither concave nor convex
G. 10 \mathrm{cm}, concave
H. 20 \mathrm{cm}, convex
Answer: A
Two smooth blocks are placed at a smooth corner as shown in $Fig. 6.380$. Both the blocks are having mass m. We apply a force F on the small block m. Block a presses blocks B in the normal direction, due to which pressing force on vertical wall will increase, and pressing force on the horizontal wall decreases, as we increases F ($\theta =37^0$ with horizontal.)As soon as the pressing force on the horizontal wall by block B becomes zero, it will lose contact with ground. If the value of F further increases, block B will accelerate in the upward direction and simultaneously block A will move towards right.If both the blocks are stationary, the force exerted by ground on block A is:

Options:
A. $$mg-\dfrac { 5F }{ 4 }$$
B. $$mg-\dfrac { 4F }{ 3 } $$
C. $$mg-\dfrac { 3F }{ 4 } $$
D. $$mg+\dfrac { 4F }{ 3 } $$
E. $$mg+\dfrac { 3F }{ 4 }$$
F. $$mg+\dfrac { 5F }{ 4}$$
G. $$mg+\dfrac { 5F }{ 3 }$$
H. $$mg+\dfrac { 3F }{ 5 }$$
Answer: D
Which of the following properties is/are common amongst the oxy acids $ H_2S_2O_7 , H_4P_2O_5 and H_3P_3O_9 $

Options:
A. all have a cyclic structure
B. all have a planar structure
C. atleast one X=0 bond is is present (X=central atom)
D. all have cyclic structure
E. all have chain type open structure
F. all have a linear structure
G. all have linear structure
H. central atoms have it's highest oxidation state
I. all have X-O-X type linkage (X= central atom)
Answer: E
a wire of length l meters, made of a material of specific gravity 8 is floating horizontally on the surface of water. if it is not wet by water, the maximum diameter of the wire up to which it can continue to float is (surface tension of water is T=70*10^-3 Nm^-1)

Options:
A. 1.25
B. 0.55
C. 1.1
D. 1.5
E. 1.2
F. 1.7
G. 1.6
H. 1.4
I. 1.3
J. 0.75
Answer: D
$SnO_{2}(s)$+$2H_{2}(g)$$\rightleftharpoons $ $2H_{2}O(steam)+Sn(s)$ For the above reaction find $K_{p}$ if at $900\ K$, the equilibrium mixture contains $45\%$ $H_{2}$ by volume.

Options:
A. $$K_{p}=6.5$$
B. $$K_{p}=7.75$$
C. $$K_{p}=2.5$$
D. $$K_{p}=5.5$$
E. $$K_{p}=3.25$$
F. $$K_{p}=2.25$$
G. $$K_{p}=1.5$$
H. $$K_{p}=4.5$$
I. $$K_{p}=3.5$$
J. $$K_{p}=10$$
Answer: F
In thermodynamics, the work done is given by
$$\displaystyle w=-\int dVP_{ext}$$
For a system undergoing a particular process, the work done is,
$$\displaystyle w=-\int dV\left(\dfrac{RT}{V-b}-\dfrac{a}{V^2}\right)$$
This equation is applicable to a

Options:
A. process that is irreversible and isochoric
B. process that is irreversible and isobaric
C. process that is reversible and adiabatic
D. process that is reversible and isobaric
E. process that is irreversible and adiabatic
F. process that is irreversible and at constant pressure.
G. process that is irreversible and isothermal
H. process that is reversible and isochoric
Answer: C
Two identical current carrying coaxial loops, carry current I in opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C, then which statement is correct?

Options:
A. the value of $\oint\bar H. \bar {dl} $ is dependent on the current I.
B. none of these
C. the value of $\oint\bar H. \bar {dl} $ is dependent on the orientation of C.
D. $$\oint\bar H. \bar {dl} =\mp 2\mu_0 I$$
E. the value of $\oint\bar H. \bar {dl} $ is dependent on the sense of C.
F. there may be a point on C where B and $dl$ are parallel.
G. the value of $\oint\bar H. \bar {dl} $ is dependent on the shape of C.
H. the value of $\oint\bar H. \bar {dl} $ is dependent on the radius of C.
I. the value of $\oint\bar H. \bar {dl} $ is independent of sense of C.
Answer: F
Consider the motion of a positive point Charge in a region where there are simultaneous uniform electric and magnetic fields $\overrightarrow{E} =  E_{0}\hat{j}$ and $\overrightarrow{B} = B_{0}\hat{j}$. At time t = 0, this charge has velocity $\overrightarrow{v}$ in the x-y piane, making an angle $\theta$ with thexaxis.
Which of the following option(s) is(are) correct for time t > 0

Options:
A. If $\theta = 0^{\circ}$ , the charge undergoes helical motion with constant pitch along the y-axis.
B. If \( \theta = 90^{\circ} \), the charge undergoes linear but decelerated motion along the z-axis.
C. If $\theta = 90^{\circ}$, the charge undergoes linear but accelerated motion along the y-axis.
D. If \( \theta = 90^{\circ} \), the charge undergoes linear but decelerated motion along the y-axis.
E. If \( \theta = 90^{\circ} \), the charge undergoes linear but decelerated motion along the x-axis.
F. If $\theta = 90^{\circ}$, the charge undergoes linear but decelerated motion along the y-axis.
G. If \( \theta = 90^{\circ} \), the charge undergoes linear but accelerated motion along the z-axis.
Answer: C
$1$ mole of $CaCO_3$ is heated in 1 liter flask at $25^oC$ to achieve the equilibrium
$$CaCO_3(s) \rightleftharpoons CaO(s) +CO_2(g)$$
If $K_c=0.2$ mole/liter. Find degree of dissociation for $CaCO_3$ at $25^oC$

Options:
A. $$0.02$$
B. $$0.65$$
C. $$0.55$$
D. $$0.8$$
E. $$0.15$$
F. 0.70
G. $$0.75$$
H. $$0.25$$
I. $$0.45$$
J. $$0.2$$
Answer: G
A point object moves along an arc of a circle of radius R. Its velocity depends upon the distance covered 'S' as V=$K\sqrt S $ where 'K' is a constant. If $\theta$ is the angle between the total acceleration and tangential acceleration, then

Options:
A. $$tan \theta =\dfrac{3S}{4R}$$
B. $$tan \theta = \dfrac{3S}{8R}$$
C. $$tan \theta =\sqrt {\dfrac{S}{R}}$$
D. $$tan \theta = \dfrac{3S}{2R}$$
E. \( tan \theta = \sqrt{\dfrac{2S}{R}} \)
F. $$tan \theta = \dfrac{S}{4R}$$
G. $$tan \theta = \dfrac{S}{R}$$
H. $$tan \theta =\dfrac{2S}{R}$$
I. $$tan \theta =\sqrt {\dfrac{S}{2R}}$$
J. $$tan \theta =\dfrac{S}{2R}$$
Answer: J
An open organ pipe resonated with frequency ` $\mathrm{f}_{1}$' and $2^{\mathrm{n}\mathrm{d}}$ harmonic. Now one end is closed and the frequency is slowly increased then it resonates with frequency $\mathrm{f}_{2}$ and nth harmonic then

Options:
A. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{10}{4}\mathrm{f}_{1}$$
B. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{4}{4}\mathrm{f}_{1}$$
C. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{3}{4}\mathrm{f}_{1}$$
D. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{6}{4}\mathrm{f}_{1}$$
E. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{9}{4}\mathrm{f}_{1}$$
F. $$\mathrm{n}=3,\ \displaystyle \mathrm{f}_{2}=\frac{5}{4}\mathrm{f}_{1}$$
G. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{5}{4}\mathrm{f}_{1}$$
H. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=‌\frac{7}{4}\mathrm{f}_{1}$$
I. $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{8}{4}\mathrm{f}_{1}$$
J. $$\mathrm{n}=3,\ \displaystyle \mathrm{f}_{2}=\frac{3}{4}\mathrm{f}_{1}$$
Answer: G
If two gases 'A' & 'B' at temperatures $T_{A}\,\&\, T_{B}$ respectively have identical Maxwellian plots, then which of the following statements are true?

Options:
A. Gases A and B may be $O_2$ and $Cl_2$ at $27^o C$ and $327^o C$ respectively.
B. Gases A and B may be $O_2$ and $Ar$ at $27^o C$ and $327^o C$ respectively.
C. Gases A and B may be $O_2$ and $N_2$ at $27^o C$ and $327^o C$ respectively.
D. Gases A and B may be $O_2$ and $SO_2$ at $27^o C$ and $327^o C$ respectively.
E. $$T_B=T_A$$
F. Gases A and B may be $O_2$ and $H_2$ at $27^o C$ and $327^o C$ respectively.
G. Gases A and B may be $O_2$ and $He$ at $27^o C$ and $327^o C$ respectively.
H. Gases A and B may be $O_2$ and $CO_2$ at $27^o C$ and $327^o C$ respectively.
Answer: D
A block is moving on horizontal rough surface. It has velocity ${v}_{0}\hat{i}$ at $x=0.1m$. The coefficient of friction varies with distance ($x$) from origin as $\mu=\cfrac{1}{2{x}^{2}}$. The minimum value of ${v}_{0}$ so that it never stops is

Options:
A. $$6m/s$$
B. $$4m/s$$
C. $$10m/s$$
D. $$5m/s$$
E. $$7m/s$$
F. $$8.5m/s$$
G. $$6.5m/s$$
H. $$9m/s$$
Answer: D
A broad source of light $( 1 = 680 \mathrm { nm } )$ illuminates normally two glass plates 120$\mathrm { mm }$ long that touch at one endand are separated by a wire 0.034$\mathrm { mm }$ in diameter at the other end. The total number of bright fringes thatappear over the 120$\mathrm { mm }$ distance is:

Options:
A. 50
B. 125
C. 25
D. 400
E. 45
F. 150
G. 300
H. 75
I. 100
J. 200
Answer: A
The energy stored in the in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $4\, \mu C$ charge, its radius will be:
[Take$ = \frac{1}{{4\pi {arepsilon _o}}} = 9 \times {10^9}{\rm{N}} - {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}$]

Options:
A. $$24\, mm$$
B. $$26\, mm$$
C. $$28\, mm$$
D. $$20\, mm$$
E. $$30\, mm$$
F. $$36\, mm$$
G. $$34\, mm$$
H. $$16\, mm$$
I. $$32\, mm$$
Answer: I
One mole of monoatomic ideal gas expands adiabatically at initial temp.T aginst a constant external pressure of 1 atm from ane litre to two litre.Find out the final temperature.
(R=0.0821 litre.atm $K^{-1} mol^{-1}$)

Options:
A. $$( T \cdot \left( \frac{1}{2} \right)^{\frac{2}{5}} )$$
B. $$T \cdot \left( \frac{1}{2} \right)^{\frac{4}{5}}$$
C. $$\frac { T }{ (2)^{ \frac { 5 }{ 3 } -1 } } $$
D. $$T-\frac { 2 }{ 3\times 0.0821 } $$
E. $$T$$
F. $$( T \cdot \left( \frac{1}{2} \right)^{\frac{1}{5}} )$$
G. $$T+\frac { 2 }{ 3\times 0.0821 } $$
H. $$(\frac{T}{(2)^{\frac{3}{5} - 1}} )$$
I. $$( T \cdot \left( \frac{1}{2} \right)^{\frac{3}{5}} )$$
J. $$T \cdot \left( \frac{1}{2} \right)^{\frac{2}{3}}$$
Answer: E
For a gas, molar specific heat in process is greater than $C_v$, which of the following relation is possible?

Options:
A. $$P^2V^{\frac{10}{3}} = C$$
B. $$P^2V^3 = C$$
C. $$P^2V^{\frac{7}{3}} = C$$
D. P^2V^{2} = C
E. $$PV^2 = C$$
F. $$PV^3 = C$$
G. $$P^2V^{\frac{11}{3}} = C$$
Answer: B
A capacitor ${ C }_{ 1 }=1\mu F$ is charged to a potential of $100 V$ . The charging battery is taken removed and it is connected to another capacitor of capacity ${ C }_{ 2 }=2\mu F$. One plate of ${ C }_{ 2 }$ is earthed as shown in figure. The charges on ${ C }_{ 1 }$and ${ C }_{ 2 }$ in steady state will be :

Options:
A. $$50\mu C, 25\mu C$$
B. $$100\mu C, zero$$
C. $$50\mu C,50\mu C$$
D. $$100\mu C, 25\mu C$$
E. $$100\mu C, 75\mu C$$
F. $$zero, zero$$
G. $$\dfrac { 100 }{ 3 } \mu C, \dfrac { 200 }{ 3 } \mu C$$
H. $$100\mu C, 50\mu C$$
I. $$\dfrac { 200 }{ 3 } \mu C, \dfrac { 100 }{ 3 } \mu C$$
Answer: B
Magnitude of magnetic field at point $A$ due to infinitely long current carrying wire is 
[Given, $PA = AR = 2a, PR = 2\sqrt{3a}, PQ = QR = 2 \sqrt{3a}$]

Options:
A. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{4})$$
B. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{6})$$
C. $$\dfrac{\mu_0 i}{2\pi a}(3 - \sqrt{2})$$
D. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{7})$$
E. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{5})$$
F. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{2})$$
G. $$\dfrac{\mu_0 i}{4\pi a}(\sqrt{3} - \sqrt{2})$$
H. $$\dfrac{\mu_0 i}{8\pi a}(4 - 2)$$
I. $$\dfrac{\mu_0 i}{2\pi a}(1 - \sqrt{3})$$
J. $$\dfrac{\mu_0 i}{8\pi a}(4 - \sqrt{3})$$
Answer: J
Molar solubility of $M(OH)_2$ at pH = $13$ is-
($K_{sp}$  of  $M(OH)_2$  is  $8 \times 10^{-16}$)

Options:
A. $$8 \times 10^{-18} M$$
B. $$8 \times 10^{-13} M$$
C. $$8 \times 10^{-12} M$$
D. $$8 \times 10^{-15} M$$
E. $$8 \times 10^{-16}M$$
F. $$8 \times 10^{-14} M$$
G. $$8 \times 10^{-17} M$$
H. $$8 \times 10^{-19} M$$
Answer: A
If for hydrogen $S_p - S_v = a$ and for oxygen,  $S_p - S_v = b$ where $S_p$ and $S_v$ are specific heat at constant pressure and at constant volume, then

Options:
A. $a$ and $b$ are not pressures
B. $$a = 2b$$
C. $$a = 16b$$
D. $$a = 6b$$
E. $$a = 3b$$
F. $$a = 12b$$
G. $$a = b$$
H. $$a = 4b$$
I. $$a = 8b$$
J. $$b = 16a$$
Answer: G
A 1 litre solution containing $NH_{4}Cl$ and $NH_{4}OH$ has hydroxide ions concentration of $10^{-6}$ mol/litre.Which of the following hydroxides could be precipitated when the solution is added to 1 litre solution of 0.1 M metal ions?
(I)$ Ba(OH)_{2}(K_{sp}=5\times10^{--3}$
(II)$Ni(OH)_{2}(K_{sp}=1.6\times10^{-16}$
(III)$ Mn(OH)_{2}(K_{sp}=2\times10^{-13}$
(IV)$ Fe(OH)_{2}(K_{sp}=8\times10^{-16}$

Options:
A. II, IV
B. I, II, III
C. I, III, IV
D. II, III, IV
E. I II, IV
F. II, III
G. IV
H. II and IV
I. II and III
Answer: G
A source which is emitting sound of frequency f is initially at $(-r, 0)$ and an observer is situated initially at $(2r, 0)$. If observer and source both are moving with velocities \[ \vec{v}_{\text{observer}} = -\sqrt{2}V \hat{i} - \sqrt{2}V \hat{j} \] and \[ \vec{v}_{\text{source}} = \frac{V}{\sqrt{2}} \hat{i} + \frac{V}{\sqrt{2}} \hat{j} \], then which of the following is correct option?

Options:
A. Apparent frequency first increases, then decreases and observer observes the original frequency twice during the motion
B. Apparent frequency continuously increases and observer never observes the original frequency
C. Apparent frequency continuously increases and observer observes the original frequency twice during the motion
D. Apparent frequency continuously increases and once during the motion, observer hears the original frequency
E. Apparent frequency continuously increases and once during the motion, observer hears the original frequency twice
F. Apparent frequency continuously decreases and once during the motion, observer hears the original frequency
G. Apparent frequency first increases, then decreases and observer observes the original frequency once during the motion
H. Apparent frequency first decreases, then increases and observer observes the original frequency twice during the motion
I. Apparent frequency first decreases, then increases and observer observes the original frequency once during the motion
J. Apparent frequency first increases, the decreases during the motion and observer never observes the initial frequency
Answer: G
$CH_3 O - CH = CH - NO_2$  $I$$CH_2 = CH - NO_2$$II$$CH_2 = CH - Cl$$III$$CH_2 = CH_2$$IV$Which of the following is the correct order of $C = C$ bond lengths among these compounds?

Options:
A. $$III > I > II > IV$$
B. I > III > IV > II
C. $$IV > II > III > I$$
D. $$IV > III > II > I$$
E. $$I > III > II > IV$$
F. $$II > I > IV > III$$
G. $$IV > III > I > II$$
H. $$II > III > I > IV$$
I. III > II > I > IV
J. $$I > II > III > IV$$
Answer: J
A point charge $q=100 \mu C$ is located in the x-y plane at the point with position vector \[ \vec{r_0} = 2 \hat{i} + 3 \hat{j} + \hat{k} \] What is the electric field vector(in kV/m) at the point with position vector \[ \vec{r} = 8 \hat{i} - 5 \hat{j} + \hat{k} \]?

Options:
A. $$55 \hat{i} - 73 \hat{j}$$
B. $$4.2 \hat{i} - 5.6 \hat{j}$$
C. $$54 \hat{i} - 71 \hat{j}$$
D. $$54 \hat{i} - 70 \hat{j}$$
E. $$54.4 \hat{i} - 72.4 \hat{j}$$
F. $$54.1 \hat{i} - 72.1 \hat{j}$$
G. $$5.4 \hat{i} - 7.2 \hat{j}$$
H. $$54.5 \hat{i} - 71.5 \hat{j}$$
I. $$54 \hat{i} - 72 \hat{j}$$
J. $$6 \hat{i} - 8 \hat{j}$$
Answer: I
$P_i,V_i$ and $P_f,V_f$ are initial and final pressures and volumes of a gas in a thermodynamic process respectively. If $PV^n=constant$, then the amount of work done is:-

Options:
A. minimum for $n=0$
B. minimum for $n=\frac{3}{2}$
C. minimum for $n=\gamma$
D. minimum for $n=1.5$
E. minimum for $n=\infty$
F. minimum for $n=2$
G. minimum for $n=1$
H. minimum for $n=\frac{4}{3}$
I. minimum for $n=\frac{5}{2}$
J. minimum for $n=\frac{7}{3}$
Answer: C
$H_{2}CO_{3}$ ionizes as:
$$H_{2}CO_{3} \leftrightharpoons H^{+} + HCO_{3}^{-}; K_{1} = 4.0 \times 10^{-6}$$
$$HCO_{3}^{-} \leftrightharpoons H^{+} + CO_{3}^{2-}; K_{2} = 5.0 \times 10^{-11}$$
The correct information(s) related with $0.5 M - Na_{2}CO_{3}$ solution is/are

Options:
A. $pH$ of solution is $2.0$.
B. [H_{2}CO_{3}] = 7.5 \times 10^{-9} M
C. [H_{2}CO_{3}] = 3.5 \times 10^{-9} M
D. [H_{2}CO_{3}] = 3.0 \times 10^{-9} M
E. [H_{2}CO_{3}] = 4.5 \times 10^{-9} M
F. [H_{2}CO_{3}] = 5.0 \times 10^{-10} M
G. $$[H_{2}CO_{3}] = 2.5 \times 10^{-9} M$$
H. [H_{2}CO_{3}] = 7.5 \times 10^{-10} M
Answer: G
An electric field $\overline E  = 50\widehat i + 75\widehat jN/C$ exists in a certain region of space. Presuming the potential at the origin to be zero, the potential at point P(1m,2m) will be

Options:
A. 50 V
B. -50 V
C. -150 V
D. 100 V
E. 175 V
F. -200 V
G. 150 V
H. -100 V
I. 125 V
J. 200 V
Answer: D
The complex $[Co(NH_{3})_5F]^{2+}$ reacts with water according to equation. $[Co(NH_{3})_5F]^{2+}+H_2O\rightarrow [Co(NH_{3})_5(H_{2}O)]^{3+}+F^{-}$The rate of the reaction = rate const. x $[complex]^{ax}[H^{+}]^{b}$. The reaction is acid catalysed i.e. $[H^{+}]$ does not change during the reaction. Thus $rate=k^{1}[Complex]^a\:where\:k^{1}=k[H^{+}]^{b}$, calculate 'a' and 'b' given the following data at $25^{\circ}C$.[Complex]M    $[H^{+}]M$    $T_{1/2}hr$    $T_{3/4}hr$        0.1              0.01             1            2        0.2             0.02           0.5            1

Options:
A. $$a=b=0.25$$
B. $$a=b=0.5$$
C. $$a=b=1.75$$
D. $$a=b=0.75$$
E. $$a=b=1.5$$
F. $$a=b=2$$
G. $$a=b=3$$
H. $$a=b=1$$
I. $$a=b=1.25$$
J. $$a=b=1.1$$
Answer: B
A cubical block of wood of edge $3 cm$ floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. The maximum weight that can be put on the block without wetting it is :(Density of wood$= 800 kg/m^{3}$ and spring constant of the spring $=50 N/m$. Take g$=10 m/s^{2}$ )

Options:
A. $$0.55 N$$
B. $$0.45 N$$
C. $$0.75 N$$
D. $$0.354 N$$
E. $$0.25 N$$
F. $$0.65 N$$
G. $$0.40 N$$
H. $$0.85 N$$
Answer: D
The temperature of a definite amount of an ideal monoatomic gas becomes four times in an isoentropic process. Which of following is correct relation between the final and initial parameters of gas?

Options:
A. $$p_{f}= 32p_{i}$$
B. $$V_{f}= 32V_{i}$$
C. $$P_{f}= \frac{1}{16}P_{i}$$
D. $$V_{f}= 12V_{i}$$
E. $$V_{f}= 16V_{i}$$
F. $$V_{f}= 4V_{i}$$
G. $$V_{f}= 8V_{i}$$
H. $$V_{f}= 6V_{i}$$
I. $$V_{f}= 2V_{i}$$
Answer: G
Two non-conducting plates $A$ and $B$ of radii $2R$ and $4R$
respectively are kept at distances $x$ and $2x$ from the point
charge $q$. A surface cutout of a non conducting shell $C$ is kept
such that its centre coincides with the point charge. Each plate and the
spherical surface carries a surface charge density $\sigma$. If $\phi_{1}$ is flux through surface of $(B)$ due to electric field of $(A)$ and $\phi_{2}$ be the flux through $(A)$ due to electric field of $(B)$ then:

Options:
A. $$(\phi_{1} < \phi_{2} )$$
B. $$\phi_{1} = \phi_{2}$$
C. $$\phi_{1} > \phi_{2}$$
D. $$(\phi_{1} = 5\phi_{2} )$$
E. It depend and on $x$ and $R$
F. $$(\phi_{1} = \phi_{2})$$
G. $$\phi_{1} < \phi_{2}$$
H. $$(\phi_{1} = 3\phi_{2} )$$
I. $$(\phi_{1} = 4\phi_{2} )$$
J. \phi_{1} = 2\phi_{2}
Answer: C
Equivalent mass of $H_{3}PO_{2}$ when it disproportionates into $PH_{3}$ and $H_{2}PO_{3}$ is: (Molecular mass $= M$)

Options:
A. $$\dfrac {M}{4}$$
B. $$\dfrac{5M}{6}$$
C. $$\dfrac{2M}{3}$$
D. $$M$$
E. $$\dfrac{M}{3}$$
F. $$\dfrac{4M}{3}$$
G. $$\dfrac {M}{2}$$
H. $$\dfrac{M}{6}$$
I. $$\dfrac{3M}{8}$$
J. $$\dfrac {3M}{4}$$
Answer: J
A uniform electric field of $100\ Vm^{-1}$ is directed at $30^{\circ}$ with the positive x-axis as shown in Fig. $OA =2m$ and $OB =4m$. The potential difference $V_B-V_A$ is :

Options:
A. $$\displaystyle -100 \left[2-\sqrt3\right]V$$
B. $$-100 \left[1+\sqrt3\right]V$$
C. $$\displaystyle 100 \left[2-\sqrt3\right]V$$
D. $$\displaystyle 100 \left[2+\sqrt3\right]V$$
E. $$\displaystyle -100 \left[1+\sqrt3\right]V$$
F. $$-100 \left[1+2\sqrt3\right]V$$
G. $$-100 \left[1-\sqrt3\right]V$$
H. $$-100 \left[1-2\sqrt3\right]V$$
I. $$\displaystyle -100 \left[2+\sqrt3\right]V$$
J. $$-100 \left[2+2\sqrt3\right]V$$
Answer: I
A particle executes simple harmonic motion along a straight line with mean position at $x = 0$ and  period of $20\ s$ and amplitude of $5\ cm$. The shortest time taken by the particle to go from $x= 4$cm to $x=-3$cm is

Options:
A. $$8\ s$$
B. $$6\ s$$
C. $$5\ s$$
D. $$3\ s$$
E. $$7\ s$$
F. $$9\ s$$
G. $$10\ s$$
H. $$4\ s$$
I. $$2\ s$$
Answer: C
An amount of $0.10$ moles of $AgCl(s)$ is added to one litre of water. Next, the crystals of $NaBr$ are added until $75$% of the $AgCl$ is converted to $AgBr(s)$, the less soluble silver halide. What is $Br^{-}$ at this point? $K_{sp}$ of $AgCl = 2 \times 10^{-10}$ and $K_{sp}$ of $AgBr = 4 \times 10^{-13}$.

Options:
A. $$1.6 \times 10^{-4}M$$
B. $$1.3 \times 10^{-4}M$$
C. $$1.7 \times 10^{-4}M$$
D. $$0.027\ M$$
E. $$1.4 \times 10^{-4}M$$
F. $$0.075\ M$$
G. $$1.5 \times 10^{-4}M$$
H. $$1.8 \times 10^{-4}M$$
I. $$1.2 \times 10^{-4}M$$
J. $$0.025\ M$$
Answer: G
Equal volume of $0.02$M $NH_4OH$ is mixed with $0.02$M HCl. Calculate $[NH_4OH]$ at equivalence point:$K_b[NH_4OH]=10^{-5}$.

Options:
A. $$3.16 \times 10^{-4.5}$$
B. $$1.414 \times 10^{-4}$$
C. $$\dfrac{1.414}{3.16}\times 10^{-5}$$
D. $$3.16\times 10^{-5}$$
E. $$3.16\times 10^{-6}$$
F. $$1.414 \times 10^{-5}$$
G. $$1.414\times 10^{-3.5}$$
H. $$1.414 \times 10^{-6.5}$$
I. $$3.16 \times 10^{-3.5}$$
J. $$1.414 \times 10^{-4.5}$$
Answer: E
Arrange the following compounds in increasing order of reactivity  towards the addition of  HBr,RCH = CHR ,$CH_{ 2 }$  =  $CH_{ 2 }$,$ R_{ 2 }C$  =  CHR, $ R_{ 2 }C$ = $CR_{ 2 }$

Options:
A. $RCH$ = $CHR$ < $ { R }_{ 2 }C$ = $ { CR }_{ 2 }$ < $ { R }_{ 2 }C$ = $CHR$ < ${ CH }_{ 2 }$ = ${ CH }_{ 2 }$
B. ${ R }_{ 2 }C$=$CHR$<${ CH }_{ 2 }$=${ CH }_{ 2 }$<${ R }_{ 2 }C$=${ CR }_{ 2 }$<$RCH$=$CHR$
C. ${ R }_{ 2 }C$=$CHR$<$RCH$=$CHR$<${ R }_{ 2 }C$=${ CR }_{ 2 }$<${ CH }_{ 2 }$=${ CH }_{ 2 }$
D. ${ R }_{ 2 }C$=$CHR$<${ CH }_{ 2 }$ = ${ CH }_{ 2 }$<$RCH$=$CHR$<${ R }_{ 2 }C$ =$ { CR }_{ 2 }$
E. ${ R }_{ 2 }C$ = $ { CR }_{ 2 }$ < ${ R }_{ 2 }C$ = $CHR$ < $RCH$ = $CHR$ < ${ CH }_{ 2 }$ = ${ CH }_{ 2 }$
F. ${ CH }_{ 2 }\quad$ =${ CH }_{ 2 }$<$RCH$=$CHR$<${ R }_{ 2 }C$=$CHR$<${ R }_{ 2 }C$=${ CR }_{ 2 }$
G. ${ R }_{ 2 }C$=$CHR$<$RCH$=$CHR$<${ CH }_{ 2 }$ = ${ CH }_{ 2 }$<${ R }_{ 2 }C$ =$ { CR }_{ 2 }$
Answer: G
Two liquids X and Y are perfectly immiscible. If X and Y have molecular masses in ratio 1 : 2, the total vapour pressure of a mixture of X and Y prepared in weight ratio 2 : 3 should be ($Px^0 = 400 torr, Py^0 = 200 torr$)

Options:
A. 314 torr
B. 500 torr
C. 550 torr
D. 466.7 torr
E. 533.3 torr
F. 666.7 torr
G. 566.7 torr
H. 433.3 torr
I. 600 torr
J. 700 torr
Answer: I
For the reaction ${ N }_{ 2 }{ O }_{ 4 }(g)\rightleftharpoons 2N{ O }_{ 2 }(g)$ the reaction connecting the degree of dissociation(A) of ${ N }_{ 2 }{ O }_{ 4 }(g)$  with its equilibrium constant ${ K }_{ P }$ and total pressure P is

Options:
A. $$\alpha =\dfrac { { K }_{ P }/P }{ 4+K_{ P } }$$
B. $$\alpha =\dfrac { { K }_{ P }/p }{ 4+K_{ P }/p }$$
C. $$\alpha =\dfrac { { K }_{ P }/P }{ 4+K_{ P }/P }$$
D. $$\alpha =\left[ \dfrac { { K }_{ P } }{ 4+K_{ P } } \right] ^{ 1/2 }$$
E. $$\alpha =\left[ \frac { { K }_{ P } }{ 4+\frac{K_{ P }}{P} } \right] ^{ 1/2 }$$
F. $$\alpha =\dfrac { { K }_{ P } }{ 4+K_{ P } } $$
G. $$\alpha =\dfrac { { K }_{ P }/p }{ 4+K_{ P } }$$
Answer: E
The enthalpy change on freezing $1$ mol of water at ${5}^{o}C$ to ice at $-{5}^{o}C$ is:(Given: ${\Delta}_{fus}H=6kJ{mol}^{-1}$ at ${0}^{o}C$${C}_{P}({H}_{2}O,l)=75.3J{mol}^{-1}$ ${K}^{-1}$,${C}_{P}({H}_{2}O,s)=36.8J{mol}^{-1}$ ${K}^{-1}$)

Options:
A. $$-5.81\ kJ{mol}^{-1}$$
B. $$6.0\ kJ{mol}^{-1}$$
C. -5.93\ kJ{mol}^{-1}
D. $$-5.19\ kJ{mol}^{-1}$$
E. $$-5.75\ kJ{mol}^{-1}$$
F. $$-5.62\ kJ{mol}^{-1}$$
G. $$-6.56\ kJ{mol}^{-1}$$
H. $$5.44\ kJ{mol}^{-1}$$
I. $$-5.87\ kJ{mol}^{-1}$$
J. $$-5.49\ kJ{mol}^{-1}$$
Answer: G
The power emitted per unit area of a black body is $R\ watt/m^2$. At what wavelength will the power radiated by the black body be maximum.  If the Stefan's constant is $\sigma$ and Wien's constant is $b$, then :

Options:
A. $$\lambda =\left( \dfrac{b^2 }{R} \right)^{1/4}$$
B. $$\lambda =\left( \dfrac{b^2 \sigma}{R} \right)^{1/4}$$
C. $$\lambda =\left( \dfrac{b R}{\sigma^2} \right)^{1/4}$$
D. $$\lambda =\left( \dfrac{b \sigma^2 }{R} \right)^{1/4}$$
E. $$\lambda =\left( \dfrac{b }{R}\right)^{1/4}$$
F. $$\lambda =\left( \dfrac{b R}{\sigma}\right)^{1/4}$$
G. $$\lambda =\left( \dfrac{b^2 R}{\sigma} \right)^{1/4}$$
H. $$\lambda =\left( \dfrac{\sigma }{R}\right)^{1/4}$$
I. $$\lambda =\left( \dfrac{b R^2}{\sigma^2} \right)^{1/4}$$
J. $$\lambda =\left( \dfrac{b\sigma }{R}\right)^{1/4}$$
Answer: E
A piece of wire is bent in the shape of a parabola $y = kx^2$ (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

Options:
A. $$(\frac{a}{8gk})$$
B. $$(\frac{a}{6gk} )$$
C. $$(\frac{a}{5gk} )$$
D. $$\frac{a}{gk}$$
E. $$\frac{a}{4gk}$$
F. $$(\frac{a}{7gk} )$$
G. $$\frac{a}{3gk}$$
H. $$\frac{a}{2gk}$$
I. $$(\frac{3a}{4gk} )$$
J. $$\frac{2a}{gk}$$
Answer: H
A plank is moving in a horizontal direction with a constant acceleration $a \hat{l}$. A uniform rough cubical block of side $l$ rests on the plank, and is at rest relative to the plank.
Let the center of mass of the block be at $(0,l/2)$ at a given instant.If $a=\dfrac{g}{10}$,then the normal reaction exerted by the plank on the block at that instant acts at

Options:
A. $$(\dfrac{l}{20},0)$$
B. $$(\dfrac{l}{15},0)$$
C. $$(0,0)$$
D. $$(\dfrac{l}{10},0)$$
E. $$(\dfrac{-l}{20},0)$$
F. $$(\dfrac{l}{30},0)$$
G. $$(\dfrac{l}{25},0)$$
H. $$(\dfrac{l}{5},0)$$
I. $$(\dfrac{-l}{10},0)$$
Answer: E
the equations of S.H.M. of the medium particle due to sound waves propagating in a medium are giving by ${s}^{1} = 2 \sin (200 \pi t)$ and ${s}^{2} = 2 \sin (150 \pi t)$. The ratio of average intensities of sound at there point is

Options:
A. $$9 : 100$$
B. $$16 : 100$$
C. $$64 : 225$$
D. $$16 : 49$$
E. $$4 : 25$$
F. $$4 : 9$$
G. $$16 : 25$$
H. $$8 : 25$$
I. $$8 : 15$$
Answer: E
Three samples A, B and C of the same ideal gas ($\gamma = 1.5$) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, then the ratio of their initial pressures is

Options:
A. $$1:2:2$$
B. $$2:2:2$$
C. $$1:2\sqrt{2}:2$$
D. $$1:1:1$$
E. $$2:2:1$$
F. $$2:2\sqrt{2}:1$$
G. $$1:2:1$$
H. $$2:2\sqrt{3}:2$$
I. $$2:2\sqrt{3}:1$$
Answer: C
Degree of dissociation of $0.1$ $N     CH_3COOH$ is
$$(K_a=1.0 \times 10^{-5})$$

Options:
A. $$10^{-1}$$
B. $$10^{-2}$$
C. $$10^{-5}$$
D. $$10^{-3}$$
E. $$10^{-4}$$
F. $$10^{-6}$$
G. $$10^{-7}$$
Answer: B
An organic compound contains $C, H$ and $O$. If $C$ (%) $:$ $H$(%) = $6:1$, what is the simplest formula of the compound, given that one mole of the compound contains half as much oxygen as would be required to burn all the $C$ and $H$ atoms in it to $CO_2$ and $H_2O$?

Options:
A. $$C_3H_6O_2$$
B. $$C_2H_4O_4$$
C. $$C_3H_6O$$
D. $$CH_2O$$
E. $$C_2H_4O$$
F. $$C_2H_4O_2$$
G. $$C_2H_4O_3$$
H. $$C_3H_6O_3$$
Answer: D
Let the solubilities of AgCI in ${H_2}O.{\rm{ }}$ 0.01 M $CaC{I_2}:$ 0.01 M NaCI and 0.05 M $AgN{O_3}$ be ${S_1},{S_2},{S_3}$ and ${S_4},$ respectively. What is the correct relationship between these quantities ?

Options:
A. $${S_1} > {S_4} > {S_3} > {S_2}$$
B. $${S_1} > {S_4} > {S_2} > {S_3}$$
C. $${S_1} > {S_4} > {S_2} = {S_3}$$
D. $${S_4} > {S_2} > {S_3} > {S_1}$$
E. $${S_1} > {S_3} > {S_4} > {S_2}$$
F. $${S_1} > {S_2} = {S_3} > {S_4}$$
G. $${S_1} > {S_3} > {S_2} > {S_4}$$
H. $${S_1} > {S_2} > {S_3} > {S_4}$$
I. $${S_1} > {S_2} > {S_4} > {S_3}$$
Answer: G
A practical of mass $m$ is moving in $X-Y$ plane under the action of a central force $\overrightarrow { F }$ in such a manner that at any instant $t$, the components of the velocity of the particle are-${ v }_{ x }=4\cos { t,{ v }_{ y }=4sint} $Then the amount of the work done by the force in a time interval $t=0$ to $t$ is-

Options:
A. $$\frac{4F}{t^2}$$
B. $$\frac{4Ft}{2}$$
C. $$\frac{4Ft}{3}$$
D. $$zero$$
E. $$\frac{4Ft}{4}$$
F. $$\frac{4Ft}{5}$$
G. $$\frac{4F}{t}$$
H. $$4Ft$$
I. None of the above
Answer: H
A mixture of ethane and ethene occupies $41L$ at 1 atm and $500K$. The mixture reacts completely with $\cfrac{10}{3}$mol of $O_{2}$ to produce $CO_{2}$ and $H_{2}O$. The mole fractions of ethane and ethene in the mixture are respectively ($R=0.082 L atm K^{-1} mol^{-1})$

Options:
A. 0.40 and 0.60
B. 0.25 and 0.75
C. 0.33 and 0.67
D. 0.30 and 0.70
E. 0.45 and 0.55
F. 0.67 and 0.33
G. 0.60 and 0.40
H. 0.50 and 0.50
I. 0.75 and 0.25
J. 0.55 and 0.45
Answer: H
At $320K$, a gas ${A}_{2}$ is $20$% dissociated at $A(g)$. The standard free energy change at $320K$ and $1$ atm in $J$ ${mol}^{-1}$ is approximately:
($R=8.314J{K}^{-1}$ ${mol}^{-1};\ln{2}=0.693;\ln{3}=1.098$)

Options:
A. 4361
B. 4281
C. 4261
D. 4461
E. 4291
F. 4381
G. 4763
H. 2068
I. 1844
J. 4481
Answer: B
Five moles of helium is mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $ M_1 = 4g $ and that of hydrogen $M_2=2g$.
The equivalent value of $\gamma$ is:

Options:
A. None of the above
B. 1.57
C. 1.61
D. 1.62
E. 1.58
F. 1.55
G. 1.60
H. 1.59
I. 1.53
J. 1.56
Answer: A
The boiling point of $0.1$ molal $K_{4}[Fe(CN)_{6}]$ solution will be $($Given $K_{b}$ for water $=0.52\ K\ kg\ mol^{-1}$)

Options:
A. $$100.13 ^{o}C$$
B. $$100.48 ^{o}C$$
C. $$100.24 ^{o}C$$
D. $$100.65 ^{o}C$$
E. $$100.10 4^{o}C$$
F. $$102.6 ^{o}C$$
G. $$101.04 ^{o}C$$
H. $$100.52 ^{o}C$$
I. $$100.26 ^{o}C$$
J. $$100.39 ^{o}C$$
Answer: H
${\text{Fe}}{\left( {{\text{OH}}} \right)_{\text{2}}}$ is diacidic base has ${{\text{K}}_{{{\text{b}}_{\text{1}}}}}{\text{ = 1}}{{\text{0}}^{{\text{ - 4}}}}$ and ${{\text{K}}_{{{\text{b}}_{\text{2}}}}}{\text{ = }}\,{\text{2}}{\text{.5}} \times {\text{1}}{{\text{0}}^{{\text{ - 6}}}}$. What is diacidic base concentration of ${\text{Fe}}{\left( {{\text{OH}}} \right)_{\text{2}}}$ in 0.01 M ${\text{Fe}}{\left( {{\text{N}}{{\text{O}}_3}} \right)_{\text{2}}}$?

Options:
A. $${\text{1}}{{\text{0}}^{{\text{ - 10}}}}\,$$
B. $$5 \times 10^{-10}$$
C. $$2.5 \times {\text{1}}{{\text{0}}^{{\text{ - 6}}}}$$
D. $$3 \times 10^{-10}$$
E. $$7 \times 10^{-10}$$
F. $${\text{1}}{{\text{0}}^{{\text{ - 14}}}}\,$$
G. $$6 \times 10^{-10}$$
H. $$1.5 \times 10^{-10}$$
I. $$4 \times {\text{1}}{{\text{0}}^{{\text{ - 9}}}}$$
J. $$2 \times 10^{-10}$$
Answer: A
A particle is attached to end of a massless spring whose other end are fixed to supports. The particle is at rest when the spring is in its relaxed state. All the spring have spring constant $k$. $\angle BOA = \angle COA = 135^\circ$.. The particle is slightly displaced towards $A$ and then released. Find the time period of oscillations.

Options:
A. $$ 2 \pi \sqrt {\dfrac{m}{k}}$$
B. $$ 2 \pi \sqrt {\dfrac{m}{3k}}$$
C. $$2 \pi \sqrt {\dfrac{m}{5k}}$$
D. $$2 \pi \sqrt {\dfrac{m}{9k}}$$
E. $$2 \pi \sqrt {\dfrac{m}{10k}}$$
F. $$2 \pi \sqrt {\dfrac{m}{6k}}$$
G. $$2 \pi \sqrt {\dfrac{m}{8k}}$$
H. $$ 2 \pi \sqrt {\dfrac{m}{2k}}$$
I. $$2 \pi \sqrt {\dfrac{m}{4k}}$$
J. $$2 \pi \sqrt {\dfrac{m}{7k}}$$
Answer: H
Determine the volume of the dilute nitric acid ($d=1.11 g/ml, 19% HNO_3$ by mass) that can be prepared by diluting 50 ml of conc. $HNO_3(d=1.42 g/ml, 69.8% HNO_3$ by mass) with water.

Options:
A. 250 ml
B. 300 ml
C. 180 ml
D. 210 ml
E. 225 ml
F. 200 ml
G. 235 ml
H. 400 ml
I. 215 ml
J. 240 ml
Answer: F
A bus is moving with a constant acceleration $a = \dfrac{3g}{4}$ towards right. In the bus, a ball is tied with a rope and is rotated in a vertical circle at constant speed $v_0$ as shown. The tension in the rope will be minimum, when the rope makes an angle $\theta$ =?

Options:
A. $$90^o < \theta < 180^o$$
B. $$0^o < \theta < 90^o$$
C. $$0^o < \theta < 180^o$$
D. $$180^o < \theta < 270^o$$
E. $$270^o < \theta < 360^o$$
F. $$180^o < \theta < 360^o$$
Answer: B
For the reversible reaction, $N_2(g)+3H_2(g)=2NH_3(g)$ at $500^o$C, the value of $K_p$ is $1.44\times 10^{-5}$ when partial pressure is measured in the atmosphere. The corresponding value of $K_c$, with concentration in $mol \ litre^{-1}$ is:

Options:
A. $$1.44\times 10^{-5}/(0.082\times 773)^{-2}$$
B. $$1.44 \times 10^{-5}/(0.082 \times 500)^{-2}$$
C. $$1.44\times 10^{-5}/(8.314\times 773)^{-2}$$
D. $$1.44\times 10^5/(0.082\times 500)^{-2}$$
E. $$1.44 \times 10^{-5}/(0.082 \times 500)^2$$
F. $$1.44 \times 10^{-5}/(8.314 \times 500)^{-2}$$
G. $$1.44 \times 10^{-5}/(0.082 \times 773)^3$$
H. $$1.44\times 10^{-5}/(0.082\times 773)^2$$
I. $$1.44 \times 10^{-5}/(0.082 \times 500)^3$$
J. $$1.44 \times 10^{-5}/(8.314 \times 773)^{-1}$$
Answer: D
A plank of mass M is placed on a rough horizontal surface. A man of mass m  walks on the plank with an acceleration 'a' while the plank is also acted upon by a horizontal force F whose magnitude and direction can be adjusted to keep the plank at rest. he coefficient of friction between plank and surface is $\mu$. Choose the correct options.

Options:
A. If $F=ma$ then friction on man due to plank is also F and friction between plank and ground will be zero
B. If $F=ma$ then friction on man due to plank is also $\mu mg$ and friction between plank and ground will be F
C. The direction of friction on ground due to plank will always be forward
D. If $F=ma$ then friction on man due to plank is also $\mu mg$ and friction between plank and ground will be zero
E. If $F=ma$ then friction on man due to plank is also $\mu Mg$ and friction between plank and ground will be F
F. If $F=ma$ then friction on man due to plank is also $\mu Mg$ and friction between plank and ground will be zero
G. If $F=ma$ then friction on man due to plank is zero and friction between plank and ground is F
H. If $F=ma$ then friction on man due to plank is also $\mu mg$ and friction between plank and ground is F
Answer: A
A prism of angle $\angle BAC=45^{0}$ and refractive index $\sqrt{6}$ is surrounded by medium of refractive index n. A ray of light PQ is incident on side AB of prism. The refracted ray QR is incident on side AC. The angle of incidence of ray PQ is i such that $0\leq i\leq 90^{0}.$ Then the possible value of n such that the ray suffers no deviation by face AC of prism is :

Options:
A. $$1.5$$
B. $$\dfrac{\sqrt{13}}{3}$$
C. $$\dfrac{\sqrt{12}}{2}$$
D. $$2.5$$
E. $$\dfrac{\sqrt{18}}{3}$$
F. 1.732
G. $$\dfrac{\sqrt3}{2}$$
H. $$\sqrt{2}$$
I. $$\dfrac{\sqrt{15}}{3}$$
J. $$\dfrac{\sqrt{14}}{3}$$
Answer: D
A pendulum of a uniform wire of cross-sectional area $A$ has time period $T.$ When an additional mass $M$ is added to its bob, the time period changes to $T_M$ . If the Young's modulus of the material of the wire is $Y$ then $\displaystyle \frac {1} {Y} $ is equal to :
($g$ = gravitational acceleration)

Options:
A. $$\left[1- \left( \frac{T} {T_M} \right)^2 \right] \frac{A} {Mg}$$
B. $$\frac {A} {Mg}+ \left[ \left( \frac {T_M} {T} \right)^2 -1\right]$$
C. $$\displaystyle \left[ \left( \frac {T_M} {T} \right)^2 -1\right] \frac {A} {Mg} $$
D. $$\displaystyle \left[1- \left( \frac {T_M} {T} \right)^2 \right] \frac {Mg} {A} $$
E. $$\displaystyle \left[ \left( \frac{T} {T_M} \right)^2 - 1 \right] \frac{A} {Mg}$$
F. $$\displaystyle \left[\left( \frac{T} {T_M} \right)^2 + 1 \right] \frac{Mg} {A}$$
G. $$\displaystyle \left[\left( \frac {T} {T_M} \right)^2 -1\right] \frac {Mg} {A} $$
H. $$\displaystyle \left[ \left( \frac{T_M} {T} \right)^2 + 1 \right] \frac{A} {Mg}$$
I. $$\left[ \left( \frac{T} {T_M} \right)^2 - 1 \right] \frac{A} {Mg}$$
Answer: B
The rate of a reaction triples when temperature changes from $  20^{\circ} \mathrm{C}  $ to $  50^{\circ} \mathrm{C}  $ . Energy of activation for the reaction is $ \left(R=8.314 J K^{-1} m o l^{-1}\right) $

Options:
A. $$34.81 \mathrm{KJ} \mathrm{mol}^{-1}$$
B. $$31.81 \mathrm{KJ} \mathrm{mol}^{-1}$$
C. 30 $ \mathrm{KJ} \mathrm{mol}^{-1} $
D. $$33.81 \mathrm{KJ} \mathrm{mol}^{-1}$$
E. 31 $ \mathrm{KJ} \mathrm{mol}^{-1} $
F. 28.81 $ \mathrm{KJ} \mathrm{mol}^{-1} $
G. 25.81 $ \mathrm{KJ} \mathrm{mol}^{-1} $
H. $$29.81 \mathrm{KJ} \mathrm{mol}^{-1}$$
I. $$32.81 \mathrm{KJ} \mathrm{mol}^{-1}$$
J. $$40 \mathrm{KJ} \mathrm{mol}^{-1} $$
Answer: C
Which of the following resonating strictures of l-methoxy 1, 3 -butadiene is least stable?

Options:
A. $$ \overset { \ominus} CH_2-CH- \overset { \oplus} CH-CH=O-CH_3 $$
B. $$ \overset { \ominus} CH_2-CH- \overset { \oplus} CH-CH-O-CH_3 $$
C. $$ CH_2=CH- \overset { \ominus} CH- \overset { \oplus} CH-O-CH_3 $$
D. $$ \overset { \ominus} CH_2- \overset { \oplus} CH-CH=CH-CH_3 $$
E. $$ \overset { \ominus} CH_2- \overset { \oplus} CH-CH=CH-O-CH_3 $$
F. $$ \overset { \oplus} CH_2 -CH=CH-CH = \overset { \oplus} O -CH_3 $$
G. $$ CH_2=CH- \overset { \ominus} CH-CH = \overset { \oplus}O-CH_3 $$
H. $$ \overset { \ominus} CH_2- \overset { \oplus} CH-CH=CH-CH_2-O-CH_3 $$
Answer: E
A block of mass m is sliding on a fixed smooth inclined plane of angle $\theta=30^0$ in case (I). In case (II) inclined plane is accelerated horizontally so that the block does not slide with respect to it. The ratio of acceleration($a_{1}$:$a_{2}$) of the blocks along inclined direction in two cases is

Options:
A. $$\dfrac{\sqrt{2}}{4}$$
B. $$\dfrac{2\sqrt{3}}{3}$$
C. $$\dfrac{1}{4}$$
D. $$\dfrac{1}{2}$$
E. $$\dfrac{\sqrt{2}}{2}$$
F. $$\dfrac{3}{2}$$
G. $$\dfrac{3}{4}$$
H. $$\dfrac{2\sqrt{3}}{4}$$
I. $$\dfrac{\sqrt{3}}{2}$$
J. $$\dfrac{\sqrt{3}}{4}$$
Answer: I
What is the pH OF $0.1$ M $NaHCO_3$? $K_1$ = $ 5 $ $\times$ ${ 10 } ^{ -7 }$,$K_2$ = $ 5 $ $\times$ ${ 10 }^{ -11 }$ for carbonic acids.

Options:
A. 9.78
B. 9.88
C. 8.78
D. 7.58
E. 7.68
F. 9.58
G. 5.58
H. 8.58
I. 9.68
J. 8.68
Answer: I
In an experiment to measure the absorption coefficient by stationary method, $i_{1}$ is the current measured due to maximum amplitude of sound and $i_{2}$ is the current due to minimum amplitude of sound, then:

Options:
A. $$a=\dfrac{4i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
B. $$a=\dfrac{7i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
C. $$a= \dfrac{(i_{1}-i_{2})^{2}}{(i_{1}+i_{2})^{2}}$$
D. $$a= \dfrac{i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
E. $$a=\dfrac{2i_{1}i_{2}}{(i_{1}-i_{2})^{2}}$$
F. $$a= \dfrac{3i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
G. $$a= \dfrac{(i_{1}-i_{2})}{(i_{1}+i_{2})}$$
H. $$a=\dfrac{5i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
I. $$a=\dfrac{2i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
J. $$a=\dfrac{6i_{1}i_{2}}{(i_{1}+i_{2})^{2}}$$
Answer: A
At given temperature, density of gas x is twice as that of gas y and moral mass of x is one third of gas y. The ratio of their pressure will be

Options:
A. $$\dfrac{P_(x)}{P_(y)} = \dfrac{8}{3}$$
B. $$\dfrac{P_(x)}{P_(y)} = 3$$
C. $\dfrac{P_(x)}{P_(y)}$ =$\dfrac{1}{6}$
D. $$\dfrac{P_(x)}{P_(y)} = \dfrac{3}{2}$$
E. $\dfrac{P_(x)}{P_(y)}$ = $6$
F. $\dfrac{P_(x)}{P_(y)}$ = $4$
G. $\dfrac{P_(x)}{P_(y)}$ =$\dfrac{1}{4}$
H. $$\dfrac{P_(x)}{P_(y)} = \dfrac{2}{3}$$
I. $\dfrac{P_(x)}{P_(y)}$ = $8$
J. $$\dfrac{P_(x)}{P_(y)} = 2$$
Answer: F
Consider the two first order reactions $X\rightarrow Y$ and $Y \rightarrow X$ for which the rate constants $k_{1}$ and $k_{2}$ are $4.0 \times 10^{3}s^{-1}$ and $2.0 \times 10^{3}s^{-1}$ respectively. One mole of $X$ and three moles of $Y$ are allowed to react and the concentrations of $X$ and $Y$ are measured as a function of time and plotted.The correct figure showing the variation of the concentrations $[X]$ and $[Y]$ with time and the correct equilibrium concentration $[X]_{eq}$ and $[Y]_{eq}$ of $X$ and $Y$ are: (Figures are not drawn to scale.)

Options:
A. $Fig. 1$ and $[X]_{eq} = \dfrac {4}{3}, [Y]_{eq} = \dfrac {8}{3}$
B. Fig. 2 and $[X]_{eq} = \dfrac {8}{3}, [Y]_{eq} = \dfrac {4}{3}$
C. Fig. 1 and [X]_{eq} = \dfrac{3}{4}, [Y]_{eq} = \dfrac{9}{4}
D. $Fig. 4$ and $[X]_{eq} = \dfrac {3}{4}, [Y]_{eq} = \dfrac {3}{2}$
E. $Fig. 3$ and $[X]_{eq} = \dfrac {8}{3}, [Y]_{eq} = \dfrac {4}{3}$
F. Fig. 3 and [X]_{eq} = \dfrac{4}{3}, [Y]_{eq} = \dfrac{8}{3}
G. Fig. 1 and [X]_{eq} = \dfrac{8}{3}, [Y]_{eq} = \dfrac{4}{3}
H. Fig. 2 and [X]_{eq} = \dfrac{3}{4}, [Y]_{eq} = \dfrac{9}{4}
I. $Fig. 2$ and $[X]_{eq} = \dfrac {4}{3}, [Y]_{eq} = \dfrac {8}{3}$
J. Fig. 3 and $[X]_{eq} = \dfrac{3}{4}, [Y]_{eq} = \dfrac{9}{4}$
Answer: I
If $r=5\times 10^{-4}m\quad \rho=10^3Kgm^{-3},g=10m/s^{2},T=0.11Nm^{-1}$ the radius of the drop when it detached from the dropper is approximately:

Options:
A. $$2.0\times 10^{-3}m$$
B. $$1.4\times 10^{-3}m$$
C. $$2.5 \times 10^{-3}m$$
D. $$1.5 \times 10^{-3}m$$
E. $$4.1\times 10^{-3}m$$
F. $$3.3\times 10^{-3}m$$
G. $$1.7 \times 10^{-3}m$$
H. $$2.2 \times 10^{-3}m$$
I. $$3.0 \times 10^{-3}m$$
J. $$1.6 \times 10^{-3}m$$
Answer: B
A bike moves with uniform acceleration such that it crosses point $P$ & $R$ at $10\ m/s$ & $50\ m/s$ respectively. If $QR=2PQ$ and time taken in $P-Q$ is $t_{1}$ & $Q-R$ is $t_{2}$ then :-

Options:
A. $$t_{1} = \frac{3}{2}t_{2}$$
B. $$t_{1} = 2t_{2}$$
C. $$t_{1}=t_{2}$$
D. $$t_{1} = \frac{4}{3}t_{2}$$
E. Information insufficient
F. $$t_2=t_1$$
G. $$t_{1} \neq t_{2}$$
H. $$t_{1} = \frac{5}{4}t_{2}$$
I. $$t_{1} < t_{2}$$
J. $$t_{1}>t_{2}$$
Answer: I
Under what pressure must an equimolar mixture of $ Cl_2 $ and $ PCl_3 $ be placed at $ 250^o $ in order to obtain 75% conversion of $ PCl_3 $ into $PCl_5$? $  Given: $ $ PCl_3 (g) + Cl_2(g) \leftrightharpoons  PCl_5(g); \quad  K_P= 2 atm^{-1} $

Options:
A. 10 atm
B. 12 atm
C. 6 atm
D. 7 atm
E. 9 atm
F. 8 atm
G. 30 atm
H. 18 atm
I. 15 atm
J. 24 atm
Answer: B
If a ball of steel ( density $ p= 7.8 g cm^{-3} ) $ attains a terminal velocity $ 10 ms^{-1} $ when falling in a tank of water ( coefficient of viscosity $ n_{water}= 8.5 \times 10^{-4} Pa-s $ ) then its terminal velocity in glycerine would be nearly $ ( p_{glyerine}= 1.2 gcm^{-3} , n_{glyerine}=13.2 Pa-s) $

Options:
A. $$1.5 \times 10^{-4} cms^{-1}$$
B. $$ 1.6 \times 10^{-5} cms^{-1} $$
C. $$1.75 \times 10^{-5} cms^{-1}$$
D. $$ 6.25 \times 10^{-4} cms^{-1} $$
E. $$1.65 \times 10^{-5} cms^{-1}$$
F. $$1.7 \times 10^{-5} cms^{-1}$$
G. $$ 6.45 \times 10^{-4} cms^{-1} $$
H. $$1.8 \times 10^{-5} cms^{-1}$$
I. $$1.55 \times 10^{-4} cms^{-1}$$
J. $$ 1.5 \times 10^{-5} cms^{-1} $$
Answer: E
Calculate the resonance enthalpy of $CO_{2}(g)$ from following date :
$$\Delta H_{combustaion}^{0}[C(graphite)]=-390 kJ/mol$$
$$\Delta H_{atomisation}^{0}[C(graphite)]=715 kJ/mol$$
$$\Delta H_{BE}^{0}[O=O]=500 kJ/mol$$
$$\Delta H_{BE}^{0}[C=O]=875 kJ/mol$$

Options:
A. -215 kJ/mol
B. -175 kJ/mol
C. -235 kJ/mol
D. -165 kJ/mol
E. -180 kJ/mol
F. $-245$ kJ/mol
G. $-145$ kJ/ mol
H. $-200$ kJ/ mol
I. $-195$ kJ/mol
J. -185 kJ/mol
Answer: G
A uniform electric field, $\vec{E} = -400\sqrt{3}y \, \text{N/C}$is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of $2\sqrt{10}\times 10^6ms^{-1}$. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure.
Take $\dfrac{q}{m}=10^{10}Ckg^{-1}$. Then

Options:
A. the particle will hit T if projected at an angle $45^0$ from the horizontal
B. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{9}}\mu s$ us as well as $\sqrt{\dfrac{5}{9}}\mu s
C. time taken by the particle to hit T is $\sqrt{\dfrac{5}{3}}\mu s$
D. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{6}}\mu s$ us as well as $\sqrt{\dfrac{5}{6}}\mu s$
E. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{10}}\mu s$ us as well as $\sqrt{\dfrac{5}{10}}\mu s
F. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{11}}\mu s$ us as well as $\sqrt{\dfrac{5}{11}}\mu s
G. the particle will hit T if projected either at an angle $30^o$ or $60^o$ from the horizontal
H. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{7}}\mu s$ us as well as $\sqrt{\dfrac{5}{7}}\mu s
I. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{4}}\mu s$ us as well as $\sqrt{\dfrac{5}{4}}\mu s$
J. time taken by the particle to hit T could be $\sqrt{\dfrac{5}{8}}\mu s$ us as well as $\sqrt{\dfrac{5}{8}}\mu s
Answer: D