MikaStars39/nano-eval huggingface dataset:
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left(x\right)=\dfrac{a}{{x}^{12}}-\dfrac{b}{{x}^{6}}$, where $a$ and $b$ constants and $x$ is the distance between the atoms. Find $x$ such that particle is in equilibrium.

Options:
A. \left(\dfrac{a}{4b}\right)^{1/6}
B. $$\left(\dfrac{b}{a}\right)^{1/6}$$
C. \left(\dfrac{2b}{a}\right)^{1/2}
D. \left(\dfrac{3a}{2b}\right)^{1/6}
E. $$\left(\dfrac{b}{2a}\right)^{1/6}$$
F. $$\left(\dfrac{2a}{b}\right)^{1/2}$$
G. $$\left(\dfrac{2a}{b}\right)^{1/6}$$
H. \left(\dfrac{a}{2b}\right)^{1/6}
I. \left(\dfrac{a}{b}\right)^{1/2}
J. \left(\dfrac{2b}{a}\right)^{1/6}
Answer: F
The coefficient of linear expansion of a rod of length 1 m, at $ 27^o $ C is, varying with temperature as $ lpha = 2/T\  unit (300 K \le  T \le  600 K) $ where T is the temperature of rod in Kelvin. The increment in the length of rod if its temperature increases from $ 27^o C\  to\ 327^o C $ is

Options:
A. $$0.4 m$$
B. 0.5 m
C. 1.5 m
D. 0.6 m
E. $$3 m$$
F. 2 m
G. 0.7 m
H. $$0.3 m$$
I. 0.9 m
J. $$4 m$$
Answer: E
A ray emanating from the point (0, 6) is incident on the ellipse$25x^{2}+16y^{2} = 1600$  at the point P with ordinate S. After reflection, ray cuts the Y- axis at B.  The length of PB is

Options:
A. 4
B. 9
C. 14
D. 12
E. 13
F. 8
G. 5
H. 11
I. 7
J. 6
Answer: G
A monochromatic radiation wavelength ${ \lambda  }_{ 1 }$ is the incidenct on the stationary atom as a result of which wavelength of photon after collision becomes ${ \lambda  }_{ 2 }$ and recoiled atom has De-Broglie's  wavelength ${ \lambda  }_{ 3 }$. then

Options:
A. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } - { \lambda }_{ 1 } }
B. $${ \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } }$$
C. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } + { \lambda }_{ 2 }^{ 2 } }
D. $${ \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }^{ 2 }+{ \lambda }_{ 2 }^{ 2 } }$$
E. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } + { \lambda }_{ 1 }^{ 2 } }
F. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } - { \lambda }_{ 2 }^{ 2 } }
G. $${ \lambda }_{ 1 }=\sqrt { { \lambda }_{ 1 }^{ 2 }+{ \lambda }_{ 2 }^{ 2 } }$$
H. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } + { \lambda }_{ 1 } }
I. { \lambda }_{ 3 }=\sqrt { { \lambda }_{ 1 }{ \lambda }_{ 2 } + { \lambda }_{ 1 }^{ 3 } }
J. $${ \lambda }_{ 1 }=\frac { { \lambda }_{ 2\quad }{ \lambda }_{ 3 } }{ { \lambda }_{ 2 } +{ \lambda }_{ 3 }}$$
Answer: D
Photon and electron are given energy $\left( {{{10}^{ - 2}}J} \right).$ Wavelengths associated with photon and electeon are ${\lambda _{ph}}$ and ${\lambda _{el}},$ then correct statement will be

Options:
A. {\lambda _{ph}} \gg {\lambda _{el}}
B. {\lambda _{ph}} \neq {\lambda _{el}}
C. {\lambda _{el}} = 10{\lambda _{ph}}
D. {\lambda _{ph}} = 2{\lambda _{el}}
E. {\lambda _{ph}} < {\lambda _{el}}
F. $$\dfrac{{{\lambda _{el}}}}{{{\lambda _{ph}}}} = c$$
G. $${\lambda _{ph}} = {\lambda _{el}}$$
H. {\lambda _{el}} > {\lambda _{ph}}
I. $${\lambda _{ph}} > {\lambda _{el}}$$
Answer: I
In a double slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen D = 100 cm from the slits, If the wavelength of light used is $\lambda  = 6000\mathop {\text{A}}\limits^{\text{o}} \,{\text{and}}\,{{\text{I}}_{\text{0}}}$ is the intensity of the central bright fringe, the intensity at a distance $y = 4 \times {10^{ - 5}}$ m from the central maximum is

Options:
A. $${I_0}$$
B. 3${I_0}$/4
C. ${I_0}$/4
D. 2{I_0}/3
E. 5{I_0}/6
F. ${I_0}$/3
G. 7{I_0}/8
H. ${I_0}/5 $
I. ${I_0}/6 $
J. ${I_0}$/2
Answer: A
A particle move along x-axis and displacement varies with time $t$ as $x=(t^3-3t^2-9t+5)$. Then

Options:
A. in the interval $5\le t \le 6$ seconds, the distance travelled is equal to the magnitude of the displacement.
B. in the interval $5\le t \le 6$ seconds, the distance travelled is not equal to the magnitude of the displacement.
C. in the interval $3< t <5$, the particle is moving in +x direction
D. in the interval $5\le t \le 6$ seconds, the distance travelled is equal to the displacement.
E. in the interval $5\le t \le 6$ seconds, the distance travelled is greater than the displacement.
F. the particle reverses its direction of motion twice in entire motion if it starts at $t=0$
G. the average acceleration from $ 1\le t\le 2$ seconds is $6 \,m/s^2$
H. in the interval $5\le t \le 6$ seconds, the distance travelled is greater than the magnitude of the displacement.
I. in the interval $5\le t \le 6$ seconds, the distance travelled is not equal to the displacement.
J. in the interval $5\le t \le 6$ seconds, the distance travelled is less than the displacement.
Answer: D
The given figure shows a part of a bigger circuit. The rate of change of the capacitor is $6$ $mF$ and is decreasing at the constant rate $0.5$ $mF  s^{-1}$. The potential difference across the capacitor at the shown moment is changing as follows $\dfrac {dV}{dt}=2 Vs^{-1}$, $\dfrac {d^2V}{dt^2}=\dfrac {1}{2}Vs^{-2}$ and the current in the $4\Omega$ resistor is decreasing at the rate of $1 mA s^{-1}$. What is the potential difference (in $mV$) across the inductor at this moment?

Options:
A. 9
B. $$5$$
C. $$8$$
D. $$4$$
E. $$3$$
F. $$6$$
G. 7
Answer: D
The relation between an alternative current voltage source and time in international system units is:
$V = 120 \ \sin (100 \ \pi t) \ \cos (100 \ \pi t)$ volt value of peak velocity and frequency will be respectively:-

Options:
A. 60volt and 50 \ Hz
B. 60 \ \text{volt} \ \text{and} \ 150 \ \text{Hz}
C. 60 \ \text{volt} \ \text{and} \ 100 \ \text{Hz}
D. 120 \ \text{volt} \ \text{and} \ 200 \ \text{Hz}
E. $\dfrac{120}{\sqrt 2}$volt and $100 \ Hz$
F. $120$volt and $200 \ Hz$
G. $60$volt and $100 \ Hz$
H. $60$volt and $200 \ Hz$
I. $120$volt and $100 \ Hz$
J. 120 \ \text{volt} \ \text{and} \ 50 \ \text{Hz}
Answer: H
Ratio of n$^{th}$ to m$^{th}$ wavelength of Lyman series in $H$ - atom is equal to:

Options:
A. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-2}{(n+1)^2-2}\right\}
B. $$\displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\displaystyle\left\{\frac{(m+1)^2-1}{(n+1)^2-1}\right\}$$
C. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+1}{(n+1)^2-1}\right\}
D. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-1}{(n+1)^2+1}\right\}
E. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-3}{(n+1)^2-3}\right\}
F. $$\displaystyle\frac{\lambda_n}{\lambda_m}=\frac{(m^2-1)\times n^2}{(n^2-1)\times m^2}$$
G. $$\displaystyle\frac{\lambda_n}{\lambda_m}=\frac{(n^2-1)\times m^2}{(m^2-1)\times n^2}$$
H. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+2}{(n+1)^2+2}\right\}
I. \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+1}{(n+1)^2+1}\right\}
J. $$\displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(m+1)}{(n+1)}\right\}^2\displaystyle\left\{\frac{(n+1)^2-1}{(m+1)^2-1}\right\}$$
Answer: B
The eccentricity of the conic $\frac{7}{r}=2+3cos{\theta}$

Options:
A. \frac{7}{3}
B. \frac{4}{3}
C. \frac{5}{3}
D. $$\frac{3}{2}$$
E. \frac{5}{4}
F. $$-3$$
G. \frac{3}{4}
H. \frac{3}{5}
I. $$3$$
J. $$\frac{2}{3}$$
Answer: F
Water is filled in a container up to a height of $3m$. A small hole of area $'a'$ is punched in the wall of the container at a height of $52.5 \  cm$ from the bottom. The cross-sectional area of the container is $A$. If $\dfrac{a}{A}=0.1$ then $v^2$ (in $m^2s^{-2}$) is (where v is the velocity of water coming out of the hole)

Options:
A. 49
B. 47
C. $$ 48 $$
D. 49.5
E. 51
F. $$ 52 $$
G. 48.5
H. $$ 50 $$
Answer: H
Hard X-rays for the study of fractures in bones should have a minimum wavelength of $10^{11} m$. The accelerating voltage for electrons in X-ray machine should be

Options:
A. < 144.2\ kV
B. $$< 124. 2\ kV$$
C. $$< 114.2\ kV$$
D. Between $60\ kV$ and $70\ kV$
E. $$> 124.2\ kV$$
F. < 134.2\ kV
G. $$= 100\ kV$$
H. > 154.2\ kV
I. > 134.2\ kV
Answer: B
An oxyacid of phosphorus has the following properties: The complex neutralisation of the acid with sodium hydroxide solution given an aqueous solution of sodium ions and oxy-acid anions in the ratio 2:1. When a solution of the acid is warmed with silver nitrate solution, metallic silver is deposited.$pH$ 0.01 M solution of the sodium salt of this acid formed (assume $pK_{a_1} = 2x$) is___________.

Options:
A. 6+3x
B. 6-3x
C. 6+5x
D. 6+x
E. 6-2x
F. 6-x
G. 6+6x
H. 6+4x
I. 6+2x
J. 6-4x
Answer: D
A particle having charges $Q$ and mass $m$ starts moving from the origin under the action of an electric field. $ec E=E_{0}\hat i$ and the magnetic field $ec B=B_{0}\hat k$. Its velocity at $(x,\ 3,\ 0)$ is $4\hat i+3\hat j$. The value of $x$ is

Options:
A. $$\dfrac {3m}{2qE_{0}}$$
B. \dfrac {24m}{2qE_{0}}
C. $$\dfrac {4m}{2qE_{0}}$$
D. $$\dfrac {25m}{2qE_{0}}$$
E. \dfrac {22m}{2qE_{0}}
F. \dfrac {15m}{2qE_{0}}
G. \dfrac {16m}{2qE_{0}}
H. \dfrac {32m}{2qE_{0}}
I. $$\dfrac {9m}{2qE_{0}}$$
J. \dfrac {20m}{2qE_{0}}
Answer: D
Eight charges (each $q$) are placed at the vertices of a regular cube of side $a$. The electric potential energy of the configuration will be $ U=12\times \dfrac { 1 }{ 4\pi arepsilon _{ 0 } } ,\dfrac { q^{ 2 } }{ a } \times \quad x $ then x.

Options:
A. $$ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $$
B. $$ \left[ 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ 3\sqrt { 3 } } \right] $$
C. $$ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 2 }{ \sqrt { 3 } } $$
D. 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ 2\sqrt { 3 } }
E. 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 1 }{ 2\sqrt { 3 } }
F. 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 2 }{ 3\sqrt { 3 } }
G. 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 1 }{ 4\sqrt { 3 } }
H. $$ 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $$
I. 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ 4\sqrt { 3 } }
J. 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 2 }{ \sqrt { 3 } }
Answer: B
A light of wavelength $ \lambda$ is incident on a metal sheet of work function $ \phi$ = 2eV. The wavelength $ \lambda$ varies with time as$ \lambda = 3000 + 40t,  $ where   $\lambda$ is in $\mathring{A}$  and t is in second. The power incident on metal  sheet is constant at $100 W$. This signal is switched on and off for time intervals of $2 mins$ and $1 min$ respectively. Each time the signal is switched on, the $ \lambda$ start from initial value of $3000$. The metal plate is grounded and electron clouding is negligible. The efficiency of photo-emission is $1  \%$.  $(hc = 12400 eV)$The total number of photoelectrons ejected in one hour is

Options:
A. 3.71 \times 10^{20}
B. 3.71 \times 10^{24}
C. 3.71 \times 10^{25}
D. 3.71 \times 10^{22}
E. $$ 3.71 \times 10^{23}$$
F. $$ 3.71 \times 10^{21}$$
Answer: F
The magnetic field in a plane electromagnetic wave is given by 
$B=(200\mu T)\sin \left[4\times 10^{15}\left(t-\dfrac {x}{c}\right)\right]$. The average energy density is

Options:
A. 0.032\ J/m^{3}
B. 0.16\ J/m^{3}
C. 0.02\ J/m^{3}
D. $$16\ J/m^{3}$$
E. $$0.016\ J/m^{3}$$
F. 0.0016\ J/m^{3}
G. $$160\ J/m^{3}$$
H. 0.024\ J/m^{3}
I. 0.012\ J/m^{3}
Answer: E
A cylinder of mass 1 kg is given heat of 20000 J at atmospheric pressure. If initially temperature of cylinder is ${\text{2}}{{\text{0}}^{\text{o}}}{\text{C,}}$ then work done by the cylinder will be (given that specific heat of cylinder ${\text{ = 400}}\;{\text{J}}\;{\text{K}}{{\text{g}}^{{\text{ - 1}}}}{\text{,}}$ coefficient of volume expansion $ = 9 \times {10^{ - 5}}{\;^{\text{o}}}{{\text{C}}^{{\text{ - 1}}}}{\text{.}}$ atmospheric pressure ${\text{ = }}\;{\text{1}}{{\text{0}}^{\text{5}}}\;{\text{N/}}{{\text{m}}^{\text{2}}}$ and density of cylinder ${\text{9000}}\;{\text{Kg/}}{{\text{m}}^{\text{3}}}$)

Options:
A. 0.01\;J
B. $${\text{0}}{\text{.08}}\;{\text{J}}$$
C. 0.06\;J
D. 0.09\;J
E. 0.03\;J
F. $${\text{0}}{\text{.1}}\;{\text{J}}$$
G. $${\text{0}}{\text{.05}}\;{\text{J}}$$
H. 0.04\;J
I. $${\text{0}}{\text{.02}}\;{\text{J}}$$
J. 0.07\;J
Answer: I
A train of mass  $100$  tons ( $1$  ton  $= 1000 { kg }$ ) runs on a meter gauge track (distance between the two rails is  $1{ m } .$  The coefficient of friction between the rails and the train is  $0.045 .$  The train is powered by an electric engine of  $90 \%$  efficiency. The train is moving with uniform speed of  $72$ Kmph  at its highest speed limit. Horizontal and vertical component of earth's magnetic field are  $B _ { H } = 10 ^ { - 5 } T$  and  $B _ { V } = 2 \times 10 ^ { - 5 } T.$  Assume the body of the train and rails to be perfectly conducting.
The potential difference between the two rails is -

Options:
A. 600 \mu V
B. 700 \mu V
C. $$800 \mu V$$
D. 200 \mu V
E. $$400 \mu V$$
F. 150 \mu V
G. 500 \mu V
H. $$100 \mu V$$
I. 300 \mu V
Answer: H
In hydrogen atom, an electron makes transition from $n=3$ to $n=2$ state in time interval of $1.2\times{10}^{-8}s$. Calculate the average torque (in Nm) acting on the electron during this transition.

Options:
A. $$4.40\times{10}^{-27}$$
B. 4.10 \times{10}^{-27}
C. 1.355 \times{10}^{-26}
D. 1.655 \times{10}^{-26}
E. $$1.055\times{10}^{-26}$$
F. $$8.79\times{10}^{-27}$$
G. 1.455 \times{10}^{-26}
H. $$1.7\times{10}^{-26}$$
I. 1.255 \times{10}^{-26}
J. 1.555 \times{10}^{-26}
Answer: E
Charge over a non-conducting ring is distributed so that the linear charge density varies as $\lambda=\lambda_0 sin\theta$. What is direction of force on a charge $q_0$ placed at the center?

Options:
A. Positive Y-axis if $q_0$ is negative
B. Negative X-axis if \( q_0 \) is negative
C. Positive Y-axis if \( q_0 \) is positive
D. Negative Y-axis if $q_0$ is positive
E. Negative Y-axis if $q_0$ is negative
F. Positive Y-axis if $q_0$ is positive
G. Positive X-axis if \( q_0 \) is positive
H. Positive X-axis if \( q_0 \) is negative
I. Positive Y-axis if \( q_0 \) is negative
J. Negative X-axis if \( q_0 \) is positive
Answer: D
Infinite number of masses, each  $1 \mathrm { kg } ,$  are placed along the  $x$-axis at  $x = \pm 1 m , \pm 4 m , \pm 8 m , \pm 16 \mathrm { m } , \ldots$  The magnitude of the resultant gravitational potential in terms of gravitational constant  $G$ at the origin  $( x = 0 )$  is

Options:
A. 9G
B. $$3G$$
C. 8G
D. $$4G$$
E. 6G
F. $$2G$$
G. $$G$$
H. 7G
I. $$5G$$
Answer: D
In the  given circuit the capacitor has capacitance and it is filled with a resistance material of effective resistance r. The switch is closed at time $\tau=0$. The charge on capacitor as a function of time t is

Options:
A. \dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-t}{2\tau}}\right), \tau=\dfrac{C(R+r)}{R}
B. \dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-3t}{\tau}}\right), \tau=\dfrac{CRr}{(R+r)}
C. \dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-t}{2\tau}}\right), \tau=\dfrac{CRr}{(R+r)}
D. $$ \dfrac {CEr}{(R+r)} \left (1-e^{\dfrac {-t}{\tau}}\right), \tau=\dfrac{CRr}{(R+r)} $$
E. $$CE \left(1-e^{\dfrac{-t}{\tau}}\right), \tau=(R+r)C$$
F. \dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-t}{\tau}}\right), \tau=\dfrac{CrR}{(R+r)}
G. $$\dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-2t}{\tau}}\right), \tau=\dfrac{CRr}{(R+r)}$$
H. $$EC \left(1-e ^\dfrac {-t}{\tau}\right),\tau= \dfrac {CrR}{(R+r) }$$
I. $$\dfrac{CEr}{(R+r}\left(1-e^{\dfrac{-t}{\tau}}\right),\tau=(R+r)c$$
J. \dfrac{CEr}{(R+r)} \left(1-e^{\dfrac{-t}{\tau}}\right), \tau=\dfrac{C(R+r)}{2}
Answer: E
Consider the following orbitals given by quantum numbers $n$ and $l$ for $He^{+}$ ion:I. $n = 3, l = 2$II. $n = 4, l = 0$III. $n = 4, l = 1$IV. $n = 5, l = 0$The correct relation of energy is given in:

Options:
A. II < I < III < IV
B. I < II = III < IV
C. II < I < IV < III
D. II < I = IV = III
E. I < II = III = IV
F. II < III < I < IV
G. II < III < I = IV
H. II < I = III < IV
I. I < II < IV < III
J. II < IV < III < I
Answer: A
A cubical vessel of side $10\ cm$ is filled with ice at $0^{o}\ C$ and is immersed in water bath as $100^{o}\ C$. If thickness of walls of vessel is $0.2\ cm$ and conductivity is $0.02\ CGS\ units$, then time in which all the ice melts is (Density of ice=$0.9\ gm/cc$)

Options:
A. 4\ sec
B. $$15\ sec$$
C. 3\ sec
D. $$12\ sec$$
E. 5\ sec
F. 7\ sec
G. 10\ sec
H. $$9\ sec$$
I. 8\ sec
J. $$6\ sec$$
Answer: J
A simple harmonic progressive wave, in a gas, has a particle displacement of $y=a$ at a time $t=\dfrac{T}{4}$ at the origin of the wave and a particle velocity of $y=v$ at the same instant but at a distance $x=\dfrac{\lambda}{4}$ from the origin where $T$ and $\lambda$ are the periodic time and wavelength of the wave respectively. Then for this wave:

Options:
A. the amplitude $A$ of the wave is $A=a$
B. the equation of the wave can be represented by \( y=a\sin \dfrac{v}{2a}\left[ t-\dfrac{x}{v} \right] \)
C. the equation of the wave can be represented by $y=a\sin \dfrac{v}{a}\left[ t-\dfrac{x}{v}\right]$
D. the equation of the wave can be represented by $y=a\sin \dfrac{v}{a}\left[ t-\dfrac{x}{4v} \right]$
E. the equation of the wave can be represented by \( y=a\sin \dfrac{v}{a}\left[ t-\dfrac{x}{2v} \right] \)
F. the equation of the wave can be represented by $y=2a\cos \dfrac{v}{a}\left[ t-\dfrac{x}{v}\right]$
G. the amplitude $A$ of the wave is $A=2a$
H. the equation of the wave can be represented by \( y=a\cos \dfrac{v}{a}\left[ t-\dfrac{x}{v} \right] \)
I. the equation of the wave can be represented by \( y=a\cos \dfrac{v}{2a}\left[ t-\dfrac{x}{2v} \right] \)
J. the equation of the wave can be represented by \( y=a\cos \dfrac{2v}{a}\left[ t-\dfrac{x}{v} \right] \)
Answer: C
In the circuit shown, the cell is ideal. The coil has an inductance of $4H$ and zero resistance. $F$ is a fuse of zero resistance and will blow when the current through it reaches $5A$. The switch is closed at $t = 0$. The fuse will blow.

Options:
A. After $5s$
B. After $8s$
C. After $2s$
D. After $3s$
E. After $6s$
F. Just after $t = 0$
G. After $9s$
H. After $4s$
I. After $12s$
J. After $10s$
Answer: J
Which of the following electronic transitions requires that the greatest quantity energy be absorbed by the hydrogen atom?

Options:
A. $$n=2 \ to \ n=3$$
B. $$n=2 \ to \ n=4$$
C. $$n=1 \ to \ n=4$$
D. n=1 \ to \ n=3
E. n=2 \ to \ n=5
F. $$n=3 \ to \ n=1$$
G. $n=1 \ to \ n=$$ \infty$
H. $$n=1 \ to \ n=2$$
I. n=2 \ to \ n=1
Answer: H
A plane light wave of intensity $I=0.20 W cm^{-2}$ falls on a plane mirror surface with reflection coefficient $\rho=0.8$. The angle of incident is $45^o$. In terms of corpuscular theory, find the magnitude of the normal pressure exerted on that surface:

Options:
A. 0.53 \times 10^{-13} N m^{-2}
B. $$2.6 N cm^{-2}$$
C. 0.53 \times 10^{-12} N m^{-2}
D. 0.53 \times 10^{-10} N m^{-2}
E. $$0.2 N cm^{-2}$$
F. $$1.2 N cm^{-2}$$
G. 0.53 \times 10^{-8} N m^{-2}
H. 0.53 \times 10^{-7} N m^{-2}
I. $$0.53 \times 10^{-9} N m^{-2}$$
J. 0.53 \times 10^{-11} N m^{-2}
Answer: I
On adding $100\ mL$ of $10^{-2} M\ NaOH$ solution to $100\ mL$ of $0.01\ M$ triethylamine solution $(K_{b} = 6.4\times 10^{-5})$, change in $pH$ of solution with respect to triethylamine solution will be_________.

Options:
A. +1.0
B. $$+1.1$$
C. +1.2
D. +0.9
E. $$-0.8$$
F. +0.7
G. $$-1.1$$
H. +1.3
I. $$+0.8$$
J. +1.4
Answer: B
A vessel containing water is suspended from a spring balance. The spring balance reads $15kg$. When a piece of iron of mass $1.8kg$, suspended by a string is immersed with half of its volume inside the water the reading of the  spring balance is (relative density of iron$=7.8$)

Options:
A. 15.135kg
B. 15.116kg
C. $$16.756kg$$
D. 15.126kg
E. 15.120kg
F. $$16.8kg$$
G. $$15.115kg$$
H. 15.125kg
I. 15.118kg
J. $$15kg$$
Answer: G
Through the point $P(4,6)$ secants are drawn to the circle $x^{2}+y^{2}=50$. The locus of the middle points of the portion intercepts is a

Options:
A. Circle through the point (3,2)
B. Straight line through is a
C. Circle through the point (1,1)
D. Circle through the point (2,3)
E. Circle through the point (4,6)
F. Circle through the point (3,4)
G. Straight line not through the origin
H. Circle through the point (2,2)
I. Circle through the origin
J. Circle not through the origin
Answer: B
A circular disc $A$ of radius $r$ is made from Iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from Iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is

Options:
A. $$I_A > I_B$$
B. I_A = 2I_B
C. I_A = 4I_B
D. $$I_A = I_B$$
E. I_A = I_B/2
F. I_A = I_B/8
G. I_A = I_B/4
H. $$I_A < I_B$$
I. The condition are insufficient to predict the relation between $I_A$ and $I_B$.
Answer: A
In a car race, car $A$ take time `$t$' less than the car $B$ and passes the finishing point with a velocity `$v$' more than the velocity with which the car $B$ passes the point. Assuming that the cars starts from rest travels with constant acceleration $a_1$ and $a_2$, then:

Options:
A. v=\frac{3t_0\sqrt{a_1a_2}}{2}
B. v=\frac{t_0\sqrt{a_1a_2}}{3}
C. $$v=t_0\sqrt{a_1a_2}$$
D. v=(t_0\sqrt{a_1a_2})/2
E. v=\sqrt{t_0a_1a_2}
F. v=\frac{t_0\sqrt{a_1a_2}}{4}
G. $$a_1\;{>}\;a_2$$
H. v=(2t_0\sqrt{a_1a_2})
I. $$v=(a_1+a_2)t_0$$
J. $$a_1\;{<}\;a_2$$
Answer: C
It can be assumed that orbits of earth and mars are nearly circular around the sun, It is proposed to launch an artificial planet around the sun such that its apogee is at the orbit of mars, while its perigee is at the orbit of earth. Let $T_e$ and $T _ m$ be periods of revolution of earth and mars . Further the variables are assigned the meaning as follows $M _ { e } , M _ m$ are masses of earth and mars $L _ { e } , L _ { m }$ a arengular momenta of earth and mars (each about the sun) $a _ { r + } a _ { m } $ are semi $-$ major axes of earth and mars orbits, $M =$ mass of the artificial planet $E _ { e } , E _ { m } =$ total energies of earth and mars. Time period of revolution of the artificial planet about the sun will be (neglect gravitational effects of earth and mars)

Options:
A. \dfrac { T _ { e } + T _ { m } } { 3 }
B. \dfrac { T _ { e } T _ { m } } { \sqrt { T _ { e } + T _ { m } } }
C. \dfrac { T _ { e } T _ { m } } { 2 \sqrt { T _ { e } T _ { m } } }
D. $$\dfrac { 2 T _ { e } T _ { m } } { T _ { e } + T _ { m } }$$
E. \dfrac { 3 T _ { e } T _ { m } } { T _ { e } + T _ { m } }
F. $$\dfrac { T _ { e } + T _ { m } } { 2 }$$
G. \dfrac { T _ { e } T _ { m } } { T _ { e } - T _ { m } }
H. $$\sqrt { T _ { e } T _ { m } }$$
I. None of these
J. \dfrac { T _ { e } T _ { m } } { \sqrt { 2 ( T _ { e } + T _ { m } ) } }
Answer: F
The figure shows a double-slit experiment in which coherent monochromatic light of wavelength $\lambda$ from a distant source is incident upon the two slits, each of width $w(w > > \lambda)$ and the interference pattern is viewed on a distant screen. A thin piece of glass of thickness $t$ and refractive index $n$ is placed between one of the slit and the screen; perpendicular to the light path. Intensity at $P$ for $t = 0$ is given is $I_{0}$.
If the width $w$ of one of the lists is increased to $2w$, the maximum intensity at $P$ for $t_{0}$ is

Options:
A. $$(9/2)I_{0}$$
B. $$(9/4)I_{0}$$
C. \left (\dfrac {5}{4} + \dfrac {1}{\sqrt {3}} \right )I_{0}
D. \left (\dfrac {5}{4} + \dfrac {1}{\sqrt {5}} \right )I_{0}
E. \left (\dfrac {5}{4} + \dfrac {1}{\sqrt {4}} \right )I_{0}
F. \left (\dfrac {7}{4} + \dfrac {1}{\sqrt {2}} \right )I_{0}
G. $$\left (\dfrac {3}{4} + \dfrac {1}{\sqrt {2}}\right )I_{0}$$
H. $$(3/2)I_{0}$$
I. \left (\dfrac {3}{4} + \dfrac {1}{\sqrt {3}} \right )I_{0}
J. \left (\dfrac {5}{4} + \dfrac {1}{\sqrt {2}} \right )I_{0}
Answer: G
Two massless ring slide on a smooth circular loop of the wire whose axis lies in a horizontal plane. A smooth massless inextensible string passes through the rings which carries masses $m_1$ & $m_2$ at the two ends and mass $m_3$ between the rings. If there is equilibrium when the line connecting each ring with centre subtends an angle $30^{o}$ with vertical as shown in figure. Then the ratio of masses are :

Options:
A. \(m_1=3m_2=2m_3\)
B. $$2m_1=m_2=2m_3$$
C. m_1=m_2=3m_3
D. $$m_1=2m_2=m_3$$
E. \(m_1=2m_2=2m_3\)
F. $$None\ of\ these$$
G. $$m_1=m_2=m_3$$
H. \(m_1=2m_2=3m_3\)
I. \(m_1=3m_2=3m_3\)
J. \(2m_1=m_2=3m_3\)
Answer: D
$20$ mL of $0.1\space M$ weak acid $HA\space (K_a = 10^{-5})$ is mixed with the solution of $10$ mL of $0.3\space M\space HCl$ and $10$ mL of $0.1\space M\space NaOH$. Find the value of $\dfrac{[A^-]}{([HA]+ [A^-])}$ in the resulting solution?

Options:
A. 2 \times 10^{-2}
B. 2 \times 10^{-6}
C. 2 \times 10^{-3}
D. $$2\times10^{-4}$$
E. $$2\times10^{-5}$$
F. 2 \times 10^{-7}
G. $$0.05$$
Answer: D
Which of the following aqueous solutions are isotonic $(R = 0.082 \,atm \,K^{-1} \,mol^{-1})$

Options:
A. $500 \,ml$ solution containing $0.2 \,g$ urea
B. 500 \,ml solution containing 0.4 \,g urea
C. 500 \,ml solution containing 0.27 \,g urea
D. 500 \,ml \,solution \,containing \,0.32 \,g \,urea
E. $500 \,ml$ solution containing $0.3 \,g$ urea
F. 500 \,ml solution containing 0.25 \,g urea
G. $500 \,ml$ solution containing $0.35 \,g$ urea
H. $$0.04 \,N \,HCl$$
I. $$0.01 \,M \,NaNO_3$$
Answer: E
The $k_{lpha}$ wavelength of an element with atomic number $z = 17$ is given by $\lambda$. What is the atomic number of an element with a $k_{lpha}$ wavelength of $\lambda/4$? (Ignore screening effect).

Options:
A. $$34$$
B. 36
C. 65
D. 35
E. $$63$$
F. $$33$$
G. $$64$$
H. 31
I. 37
J. 32
Answer: F
Two long thin parallel conductor are kept very close to each other without  touching. One carries a current $i$ and the other has charge $\lambda$ per unit length. An electron moving parallel to the conductor is undeflected. lf  $c$ is the velocity of light. then :

Options:
A. the electron may be at any distance from the conductor
B. v=\dfrac{\lambda c}{i}
C. v=\dfrac{\lambda c^{3}}{i}
D. $$c=\dfrac{i}{\lambda }$$
E. $$v=\dfrac{\lambda c^{2}}{i}$$
F. $$v=\dfrac{i}{\lambda }$$
G. v=\dfrac{\lambda c^{5}}{i}
H. v=\dfrac{\lambda c^{4}}{i}
I. v=\dfrac{\lambda c^{6}}{i}
Answer: A
The density of solid argon (Ar = 40 g / mol) is 1.68 g/mL at 40 K. If the argon atom is assumed to be a sphere of radius 1.50 x $10^{-8}$ cm, what % of solid Ar is apparently empty space? (use $N_A = 6 \times10^{23}$)

Options:
A. 65.36
B. 64.37
C. 35.65
D. 35.64
E. 64.36
F. 64.35
G. 65.64
H. 64.34
I. none of these
J. 74%
Answer: I
A solid sphere, a hollow sphere and a ring, all having equal mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are equal but not sufficient to allow pure rolling. The greatest kinetic energy at the bottom of the incline will be achieved by:

Options:
A. The solid sphere will achieve the greatest kinetic energy, but only slightly more than the hollow sphere.
B. The hollow sphere
C. The solid sphere
D. The ring
E. All will achieve same kinetic energy.
F. The ring will achieve the greatest kinetic energy, but only slightly more than the solid sphere.
G. The solid sphere will achieve the greatest kinetic energy, but not significantly more than the ring.
H. The ring will achieve the greatest kinetic energy, but not significantly more than the hollow sphere.
I. The ring will achieve the greatest kinetic energy.
J. The solid sphere will achieve the greatest kinetic energy.
Answer: B
A bulb of 40 W is producing a light of wavelength 620 nm with 80% of efficiency, then the number of photons emitted by the bulb in 20 seconds are ($1eV = 1.6 \times 10^{-19} $ J, $ hc = 12400 eV  $) :

Options:
A. 2 \times 10^{12}
B. 4 \times 10^{11}
C. 2 \times 10^{17}
D. $$2\, \times\, 10^{18}$$
E. 5 \times 10^{11}
F. 2 \times 10^{21}
G. $$10^{21}$$
H. $$2\, \times\, 10^{11}$$
I. $$10^{18}$$
J. 5 \times 10^{17}
Answer: H
Which sequence of steps describes the best synthesis of $2$-phenylpropene?

Options:
A. Benzene $+$ $2$-chloropropene, $FeCl_3$
B. $1$. Benzaldehyde $(C_6H_5CH=O) +CH_3CH_2MgBr$, diethyl ether
$2$. $H_3O^+$
$3$ $H_2SO_4$, heat
C. Benzene + 1-chloropropane, AlCl_3
D. $1$. Bromobenzene $+$Mg, diethyl ether
E. Benzene $+$ $2$-chloropropene, $FeBr_3$
F. Benzene + 1-chloropropane, FeCl_3
G. Benzene $+$ $1$-chloropropene, $FeCl_3$
H. Benzene + 2-chloropropane, FeCl_3
I. $1$. Bromobenzene $+$ Mg, diethyl ether
$2$. Propanal $(CH_3CH_2CH=O)$
$3$. $H_3O^+$
$4$. $H_2SO_4$, heat
J. Benzene $+$ $2$-chloropropene, $AlCl_3$
Answer: J
In free space, a particle A of charge $1 \, \mu C$ is held fixed at a point P. Another particle B of the same charge and mass $4 \mu g$ is kept at a distance of $1 \, mm$ from P. if B is released, then its velocity at a distance of $9 mm$ from P is :
[Take $\dfrac{1}{4 \pi arepsilon_0} = 9 \times 10^9 Nm^2 C^{-2}$]

Options:
A. 1.7 \times 10^3 m/s
B. $$1.0 m/s $$
C. $$3.0 \times 10^4 m/s$$
D. $$1.5 \times 10^2 m/s$$
E. 1.8 \times 10^3 m/s
F. 1.9 \times 10^3 m/s
G. 1.0 \times 10^3 m/s
H. $$2.0 \times 10^3 m/s$$
I. 2.5 \times 10^3 m/s
J. 1.5 \times 10^3 m/s
Answer: H
Two moles of a monoatomic gas follows the process $PV^{\frac 4/3}$= const. If the initial temperature of the system is $T_0$ and it is compressed to $\eta$ times its initial volume then work done by the system is:

Options:
A. $$6RT_{ 0 }(1-(\frac { 1 }{ \eta } )^{-1/3})$$
B. 6RT_{ 0 }(1-(\eta)^{-1/4})
C. 6RT_{0}(1-(\frac{1}{\eta})^{-2/3})
D. 3RT_{0}(1-(\eta)^{-2/3})
E. $$3RT_{ 0 }(1-(\frac { 1 }{ \eta } )^{-1/3})$$
F. 6RT_{0}(1-(\frac{1}{\eta})^{1/3})
G. $$6RT_{ 0 }(1-\eta ^{ -1/3 })$$
H. $$3RT_{ 0 }(1-(\eta )^{ -1/3 })$$
Answer: G
The direction rations of the normal to the plane passing through the points $(1,-2,3) ,(-1,2,-4)$ and parallel to $\dfrac {x-2}{2}=\dfrac {y+1}{3}=\dfrac {z}{4}$ is

Options:
A. (2,3,3)
B. (2,3,7)
C. $$(2,0,-1)$$
D. $$(2,3,4)$$
E. (2,3,5)
F. (2,0,4)
G. $$(-2,0,-1)$$
H. (2,3,6)
I. (2,0,3)
J. $$(4,0,7)$$
Answer: D
Two electric bulbs rated 25 W, 220 V and 100 W, 220 V are connected in series across a 220 V voltage source. The 25 W and 100 W bulbs now draw $P_1$ and $P_2$ powers, respectively.

Options:
A. $$P_1\, = \, 4 W$$
B. $$P_2 \, = \, 4 W$$
C. P_2 \, = \, 10 W
D. P_2 \, = \, 6 W
E. P_2 \, = \, 12 W
F. P_2 \, = \, 8 W
G. P_2 \, = \, 2 W
H. $$P_2\, = \, 16 W$$
I. $$P_2 \, = \, 20 W$$
J. $$P_1\, = \, 16 W$$
Answer: B
A current of $2.68$ A is passed for $1.0$ hour through an aqueous solution of $CuSO_{4}$ using copper electrodes. Which ofthe following statements is/are correct ?

Options:
A. Increase in the mass of cathode = 6.348 g
B. Decrease in the mass of anode = $4.761 g$
C. Decrease in the mass of anode = $3.174 g$
D. The ratio between the change in the mass of cathode to anode is $1 : 2$
E. Decrease in the mass of anode = 6.348 g
F. Increase in the mass of cathode = 1.587 g
G. No change in the mass of electrodes
H. Decrease in the mass of anode = 1.058 g
I. Decrease in the mass of anode = $1.587 g$
Answer: C
Given a balanced redox reaction:$2MnO^{\circleddash}_4+8H^{\bigoplus}+Br_2\rightarrow 2Mn^{2+}+2BrO^{\circleddash}_3+2H_2O$If the molecular weights of $MnO^{\circleddash}_4$ and $Br_2$ be $M_1$ and $M_2$ respectively, then:

Options:
A. equivalent weight of $Br_2$ = $\dfrac{M_2}{12}$
B. equivalent weight of $Br_2$ = $\dfrac{M_2}{8}$
C. none of the above
D. equivalent weight of $Br_2$ = $\dfrac{M_2}{9}$
E. equivalent weight of $Br_2$ = $\dfrac{M_2}{5}$
F. equivalent weight of $Br_2$ = $\dfrac{M_2}{7}$
G. the $n$-factor ratio of $MnO^{\circleddash}_4:Br_2$ is $1:1$
H. equivalent weight of $Br_2$ = $\dfrac{M_2}{15}$
I. equivalent weight of $Br_2$ = $\dfrac{M_2}{10}$
Answer: I
A silver sphere (work function 4.6eV) is suspended in a vacuum chamber by an insulating thread Ultraviolet light of wavelength $0.2  \mu m$ strike.The maximum electric potential of the sphere will be $(hc=12400eV \AA $ )

Options:
A. 3.6 V
B. 1.6 V
C. 5.8 V
D. 6.0 V
E. 6.2 V
F. 5.2 V
G. 3.2 V
H. 4.2 V
I. 4.6 V
J. 5.6 V
Answer: I
Maximum magnetic moments of $ Cr (Z = 24), Mn^{+} (Z=25),$ and $Fe^{2+} (Z=26), $ are x, y, and z. They are in order:

Options:
A. z < y < x
B. x = z <y
C. z = y < x
D. x < z = y
E. z < x = y
F. x < y < z
G. x < y = z
H. x = y = z
I. z < x < y
J. x = y < z
Answer: B
X-ray from a tube with a target $A$ of atomic number $Z$ shows strong $K$ lines for target $A$ and weak $K$ lines for impurities. The wavelength of $K_lpha$ lines is $\lambda_z$ for target $A$ and $\lambda_1$ and $\lambda_2$ for two impurities.
$$\quad \displaystyle\frac{\lambda_z}{\lambda_1} = 4 \quad and \quad \displaystyle\frac{\lambda_z}{\lambda_2} = \displaystyle\frac{1}{4}$$
Assuming the screening constant of $K_lpha$ lines to be unity, select the correct statement(s)

Options:
A. The atomic number of second impurity is \displaystyle\frac{(z-3)}{2}
B. The atomic number of second impurity is \displaystyle\frac{z-1}{2}
C. \displaystyle\frac{(z+3)}{2}
D. The atomic number of second impurity is \displaystyle\frac{(z+7)}{2}
E. \displaystyle\frac{(z+9)}{2}
F. The atomic number of first impurity is $2z+1$
G. The atomic number of second impurity is $\displaystyle\frac{(z+1)}{2}$
H. The atomic number of second impurity is \displaystyle\frac{(z+5)}{2}
I. The atomic number of second impurity is $\displaystyle\frac{z}{2}+1$
Answer: G
The electric flux through a certain area of dielectric is $8.76 \times 10^3 t^4$. The displacement current through the area is $12.9 pA$ at $t = 26.1 ms$ . Find the dielectric constant of the material.

Options:
A. 5 \times 10^{-8}
B. 1 \times 10^{-8}
C. 3 \times 10^{-8}
D. $$2 \times 10^{-7}$$
E. 7 \times 10^{-8}
F. 6 \times 10^{-8}
G. $$8 \times 10^{-8}$$
H. 6 \times 10^{-7}
I. $$2 \times 10^{-8}$$
J. $$4 \times 10^{-8}$$
Answer: I
A long string having a cross-sectional area $0.80 \,mm^2$and density, $12.5 \,g / cm^3$ is subjected to a tension of $64 \,N$ along the  x-axis. One end (at x = 0) of this string is attached to a vibrator moving in transverse direction at a frequency of $20 \,Hz.$ At $t = 0$, the source is at a maximum displacement $y = 1.0 \,cm.$What is the velocity of this particle at this instant?

Options:
A. 30 \pi/\sqrt {2} \,cm/s
B. $$50 \pi/\sqrt{2} \,cm/s$$
C. 25 \pi/\sqrt{2} \,cm/s
D. $$20 \sqrt {2} \pi \,cm/s$$
E. $$40 \pi/\sqrt {2}  \,cm/s$$
F. 60 \pi/\sqrt{2} \,cm/s
G. 35 \pi/\sqrt{2} \,cm/s
H. $$30 \sqrt {2} \pi \,cm/s$$
I. $$10 \sqrt {2} \pi \,cm/s$$
Answer: E
A beam of light having $\lambda$ between $5\times {10}^{-7}m$ and $6\times {10}^{-7}m$ is incident on a sample of atomic hydrogen. If the atoms are in first excited state, the wavelength which will have low intensity in the transmitted beam is
(Take $R={10}^{7}{m}^{-1}$)

Options:
A. 5.21 \times {10}^{-7}m
B. $$5.44\times {10}^{-7}m$$
C. $$5.11\times {10}^{7}m$$
D. 5.31 \times {10}^{-7}m
E. 5.22 \times {10}^{-7}m
F. 5.33 \times {10}^{-7}m
G. $$5.33\times {10}^{7}m$$
H. 5.11 \times {10}^{-7}m
I. $$5.22\times {10}^{7}m$$
J. 5.55 \times {10}^{-7}m
Answer: C
In a standard YDSE setup, the fringe width on the screen is 1.5 mm. When a thin glass film is pasted in front of the upper slit, the fringe pattern shifts up. But it is seen that at a point P above central maxima where intensity was one fourth the intensity at central maxima, intensity remains the same. There were no maxima between central maxima and point P before film was introduced. What can be the thickness of the film? Take $\mu$ = 1.5, $\lambda$ = 450 nm :-

Options:
A. 5 x $10^{-7}$m
B. 1.5 x $10^{-6}$m
C. 1.7 x $10^{-6}$m
D. 9 x $10^{-7}$m
E. 1.8 x $10^{-6}$m
F. 1.2 x $10^{-6}$m
G. 1.3 x $10^{-6}$m
H. 1.6 x $10^{-6}$m
I. 1.4 x $10^{-6}$m
J. 3 x $10^{-7}$m
Answer: I
A brass wire of cross-sectional area $2\ mm^{2}$ is suspended from rigid support and a body of volume $100cm^{3}$ is attached to its other end. If the decrease in the length of the wire is $0.11\ mm$, when the body is completely immersed in water, find the natural length of the wire ($Y_{brass}=0.91\times10^{11}N/m^{2}$,$\rho_{water}=10^{3}kgm^{-3}$)

Options:
A. $$2.043m$$
B. 30.43m
C. $$31.9 m$$
D. $$10.43m$$
E. 21.9 m
F. 30.9 m
G. 31.4 m
H. 31.43 m
I. 32.9 m
J. $$40.43m$$
Answer: C
A liquid mixture of A and B (assume ideal solution ) is placed in a cylinder and piston arrangement . The piston is slowly pulled out isothermally so that the volume of liquid decreases and that of vapour increases. at the instant when the quantity of the liquid still remaining is negligibly small, the mole fraction of 'A' in the vapour is 0.4 .If $ P^0_A = 0.4 atm , P^0_B = 1.2 atm $ at this temperature, the total pressure at which the liquid has almost evaporated is ?

Options:
A. 0.657 atm
B. 0.545 atm
C. 0.687 atm
D. 0.675 atm
E. 0.8 atm
F. 1.5 atm
G. 1.2 atm
H. 0.567 atm
I. 0.667 atm
J. 0.677 atm
Answer: I
Which of the following set orbitals are arranged in correct energy order ?

Options:
A. 3px > 3s = 2pz (in H)
B. 3px = 3s > 2pz(in H)
C. $${\text{3px}} = {\text{3s}} = 2{\text{pz(in}}\;{\text{H)}}$$
D. $${\text{4px}}\;{\text{ = }}\;4{\text{py}}\;{\text{ = }}\;4{\text{pz}}\;{\text{ = }}\;{\text{4s}}\;{\text{ = }}\;{\text{4dxy(in}}\;{\text{H)}}\;\;\;$$
E. $${\text{4px}}\;{\text{ = }}\;4{\text{py}}\;{\text{ = }}\;4{\text{pz}}\;{\text{(in}}\;{\text{H}}{{\text{e}}^ + }{\text{)}}\;\;\;$$
F. 3px = 2pz = 3s (in H)
G. 3px = 3s > 2pz (in He)
H. ${\text{3px}} = {\text{3s}} > 2{\text{pz(in}}\;{\text{H)}}$
I. $${\text{3px}} > {\text{3s}} > 2{\text{pz(in}}\;{\text{He)}}$$
Answer: C
Two identical coils each of radius $R$ and each carrying a current $I$ in the same direction are placed along a common axis and separated by distance $R$. At the midpoint between the two coils the

Options:
A. First derivative of magnetic field $dB/ dx = 0$
B. Magnetic field is $0.7\sqrt {0.9}\mu_{0}I/R$
C. Magnetic field is zero
D. Magnetic field is $0.9\sqrt {0.8}\mu_{0}I/R$
E. Magnetic field is $0.8\sqrt {0.8}\mu_{0}I/R$
F. Magnetic field is $0.8\sqrt {0.7}\mu_{0}I/R$
G. Magnetic field is $0.9\sqrt {0.7}\mu_{0}I/R$
H. Second derivative of magnetic field $d^{2}B/ dx^{2} = 0$
Answer: E
The third line of the Balmer series spectrum of a hydrogen-like ion of atomic number $Z$ equals to $108.5\space nm$. The binding energy of the electron in the ground state of these ions is $E_B$. Then

Options:
A. E_B = 108.8\space eV
B. E_B = 85.4\space eV
C. $$Z = 2$$
D. E_B = 73.2\space eV
E. E_B = 59.4\space eV
F. E_B = 48.8\space eV
G. E_B = 67.6\space eV
H. $$E_B = 122.4\space eV$$
I. $$E_B = 54.4\space eV$$
J. $$Z = 3$$
Answer: I
A particle is executing $SHM$ with amplitude $A$. At displacement $x=\dfrac {-A}{4}$, magnitude of force acting on the particle is $F$, potential energy of the particle is $U$, speed of particle is $v$ and kinetic energy is $K$. Assuming potential energy to be zero at mean position.
At displacement $x=\dfrac {A}{2}$

Options:
A. potential energy of particle will be $6U$
B. potential energy of particle will be $2U$
C. potential energy of particle will be $8U$
D. potential energy of particle will be $4U$
E. kinetic energy of particle will be $0.8\ K$
F. potential energy of particle will be $3U$
G. potential energy of particle will be $2.5U$
H. potential energy of particle will be $0.5U$
Answer: D
What is the relation between $T$ and $V$ of gas in this process?

Options:
A. ${ T.V }^{ \left( \gamma +1 \right) /4 }=$constant
B. $T{ V }^{ \left( \gamma -2 \right) }=$constant
C. $TV^{2(\gamma -1)}=$ constant
D. ${ T.V }^{ \left( \gamma -1 \right) /2 }=$constant
E. $T{ V }^{ \gamma }=$constant
F. $T{ V }^{ \gamma -1 }=$constant
G. $T{ V }^{ \left( \gamma -1 \right) }=$constant
H. ${ T.V }^{ \left( \gamma +1 \right) /2 }=$constant
I. T{ V }^{ \left( \gamma -3 \right) /2 }=constant
Answer: D
Two parallel discs are connected by a rigid rod of length $L=0.5$m centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms are incident on one of the discs axially at different velocities v, while the system is rotated at angular speed of $600$ rev/second so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds(in meter/second) of the atoms that will emerge at the other end.

Options:
A. 600, 125
B. 600, 150
C. 600, 100
D. 600, 175
E. $$100, 50$$
F. $$300, 100$$
G. $$600, 200$$
H. 600, 225
I. 550, 150
J. $$75, 25$$
Answer: G
Two soap bubbles combine to from a single bubble. In this process, the change in volume and surface are respectively V and

Options:
A. $$4PV +3TA =0$$
B. $$3PV+6TS=0$$
C. 3PV + 5TS = 0
D. 3PV + 4AS = 0
E. $$3PV-4TA =0$$
F. $$5PV+6TS=0$$
G. 4PV + 3TS = 0
H. $$3PV+4TS=0$$
I. 3PV - 4TS = 0
Answer: H
Tangents are drawn from a point P to the parabola ${ y }^{ 2 }=8x$ such that the slope of one tangent is twice the slope of other. The locus of P is

Options:
A. a hyperbola
B. a straight line
C. an ellipse
D. a circle
E. a parabola
Answer: D
A particle is subjected to two simple harmonic motions along $x$ and $y$ directions according to $x =6 sin 100 \pi t$ and $y=8 cos (100 \pi t- \dfrac{ \pi}{2})$

Options:
A. Motion of particle is straight line
B. Motion of particle is circle
C. Motion of particle is parabola
D. Can't say
E. Motion of particle is hyperbola
F. Motion of particle is ellipse
Answer: F
Position vector of a particle is given by $ec{r}=a cos\omega t\hat {i}+a sin\omega t\hat {j}$. Which of the following is/are true?

Options:
A. velocity vector is parallel to position vector
B. acceleration vector is parallel to the position vector
C. acceleration vector is directed towards the origin
D. acceleration vector is directed away from the origin
Answer: C
An equilibrium reaction $X+Y \rightleftharpoons W+Z, \triangle H=+ve $ is spontaneous in the forward direction. Then corresponding sign of $\triangle G$ and $\triangle S $ should be respectively:

Options:
A. +ve, +ve
B. +ve, -ve
C. -ve, -ve
D. -ve , +ve
Answer: A
Which harmonic major or minor mode could the following diminished triad possibly belong to?
L:1/4
M:4/4
K:C
[F_A_c]4 |] %1

Options:
A. ♭E harmonic major and ♭e harmonic minor
B. ♭g harmonic minor
C. ♭G harmonic major
D. All of the above
Answer: D
A cylindrical container with a diameter of 1m holds water at a temperature of 27°C and a depth of $0.5 \mathrm{m}$. Water is added at a flow rate of $1 \mathrm{kg/s}$ until the water depth reaches 2m. It is assumed that the added water is thoroughly mixed, the outer wall of the container is insulated, and the average specific heat capacity and density of the water are: $c_{p}=4183 \mathrm{J/(kg \cdot °C)}, \ \rho=1000 \mathrm{kg/m}^{3}$.
If the water added has a temperature of 27°C and a steam heating coil is installed in the container, the heat transfer rate from the heater to the water is:
$$
q=h A ( t_{\mathrm{v}}-t )
$$
where $h=300 \mathrm{W/(m^{2} \cdot °C)}; \ A=3 \ \mathrm{m^{2}}$; $t_{\mathrm{v}}=110°C$, and $t$ is the instantaneous temperature of the water in the container at any given moment. Determine the final temperature reached by the water.

Options:
A. $$
t_{2}=37 \mathrm{~} \mathrm{~^{\circ} C}
$$
B. $$
t_{2}=3 3 \mathrm{~} \mathrm{~^{\circ} C}
$$
C. $$
t_{2}=3 9 \mathrm{~} \mathrm{~^{\circ} C}
$$
D. $$
t_{2}=3 1 \mathrm{~} \mathrm{~^{\circ} C}
$$
E. $$
t_{2}=4 5 \mathrm{~} \mathrm{~^{\circ} C}
$$
F. $$
t_{2}=4 7 \mathrm{~} \mathrm{~^{\circ} C}
$$
G. $$
t_{2}=3 5 \mathrm{~} \mathrm{~^{\circ} C}
$$
H. $$
t_{2}=4 1 \mathrm{~} \mathrm{~^{\circ} C}
$$
I. $$
t_{2}=4 3 \mathrm{~} \mathrm{~^{\circ} C}
$$
Answer: C
The development of the primary phloem in roots is of the _______ type. In this development, _________ is positioned on the outer side, while________ is located towards the inner side.

Options:
A. Homoxylary; The secondary xylem; The primary xylem
B. Pseudoxylary; The meta-xylem; The proto-xylem
C. Acropetal; The phloem; The xylem
D. Exogenous; The primary phloem; The secondary phloem
E. Protocambial; The primary phloem; The vascular cambium
F. Basal; The cortical cells; The stele
G. Endogenous; The secondary phloem; The primary phloem
H. Amphivasal; The pericycle; The endodermis
I. Symplastic; The primary phloem; The secondary phloem
J. Centrifugal; The proto-phloem; The meta-phloem
Answer: D
Which of the following descriptions about narrow-leaved senna leaves and pointed-leaved senna leaves is accurate?

Options:
A. Senna Alexandrina leaves are graded and packaged according to size.
B. The basal leaves of the sharp-leaved senna are conspicuously asymmetrical.
C. Cassia angustifolia leaves have overlapping striae.
D. Cassia angustifolia's basal leaves display symmetric growth patterns.
E. Senna Alexandrina leaves are often mixed with other herbs during packaging.
F. The narrow-leaf senna leaves have a perfectly balanced shape.
G. Sharp-leaved senna leaves are packaged together irrespective of condition.
H. Narrow-leaf senna leaves are packaged separately as whole leaves and crushed leaves.
I. The narrow-leaf senna leaves are relatively thin and brittle.
J. The basal leaves of the narrow-leaved senna are rigorously symmetrical.
Answer: B
What is the formula for computing the Azimuth angle?

Options:
A. $\tan\beta={\frac{V_E}{V_N}}$
B. $\tan\beta={\frac{V_N}{V_E}}$
C. $\tan\beta={\frac{-V_S}{V_N}}$
D. $\tan\beta={\frac{-V_E}{V_S}}$
E. $\tan\beta={\frac{V_S}{V_E}}$
F. $\tan\beta={\frac{V_N}{V_S}}$
G. $\tan\beta={\frac{-V_S}{V_E}}$
H. $\tan\beta={\frac{-V_E}{V_N}}$
I. $\tan\beta={\frac{V_E}{V_S}}$
J. $\tan\beta={\frac{-V_N}{V_E}}$
Answer: D
In Elgamal cryptosystem, given the prime p=31.
Choose $e1=$ first primitive root of p and $\mathrm{d=1 0}$. What is e2?

Options:
A. 25
B. 29
C. 32
D. 40
E. 15
F. 24
G. 18
H. 36
I. 62
J. 23
Answer: A
What is the block size of the blowfish block cipher?

Options:
A. 256 bits
B. 32 bits
C. 48 bits
D. 1043 bits
E. 64 bits
F. 128 bits
G. 512 bits
H. 10 bits
I. 1024 bits
Answer: E
In asymmetric key cryptography, the private key is kept by ______.

Options:
A. every user
B. sender and receiver
C. sender
D. cryptographic software
E. external server
F. receiver
G. all the connected devices to the network
H. encryption algorithm
I. network administrator
J. network firewall
Answer: F
Pilley and Reid (2011) claim that a border collie, Chaser, has learned more than one thousand worTheir claim is based on the finding that Chaser was().

Options:
A. not only reacting to hand signals (raised arm); she could differentiate between textures (e.g. 'smooth toy' versus 'rough toy')
B. not simply responding to emotional cues (happy tone); she could separate emotional commands (e.g. 'bring joyfully' versus 'take sadly')
C. not only recognizing ball locations (in the room); she could differentiate between toys by category (e.g. 'soft toy' versus 'hard toy')
D. not just responding to a global situation (fetch the ball); she could distinguish between different commands (e.g. 'take the ball' versus 'paw the ball")
E. not merely recognizing sound volumes (quiet voice); she could separate commands by length (e.g. 'long fetch' versus 'short fetch')
F. not just responding to vocal tones (loud voice); she could differentiate between colors in requests (e.g. 'red ball' versus 'blue ball')
G. not merely reacting to visual gestures (pointing hand); she could identify objects by shape (e.g. 'round object' versus 'square object')
H. not simply associating commands with actions (sit down); she could distinguish similar actions (e.g. 'roll over' versus 'lay down')
I. not solely reacting to environmental changes (light on); she could identify commands based on timing (e.g. 'fetch quickly' versus 'fetch slowly')
J. not just responding to spatial cues (near the box); she could distinguish between locations (e.g. 'behind the table' versus 'under the chair')
Answer: D
Arrange the following indicator digits/connecting symbols used in Colon Classification (6th edition) according to their descending order :
(a).(dot)
(b)'(inverted comma)
(c):(colon)
(d);(semi-colon)

Options:
A. (a),(d),(c) and (b)
B. (b),(a),(d) and (c)
C. (c),(a),(b) and (d)
D. (c),(b),(a) and (d)
E. (a),(b),(d) and (c)
F. (c),(d),(b) and (a)
G. (d),(c),(a) and (b)
H. (b),(c),(d) and (a)
I. (b),(d),(a) and (c)
J. (d),(b),(c) and (a)
Answer: G
The word "________________" means the Code is the same for all of the armed services.

Options:
A. Generic
B. Homogeneous
C. Uniform
D. Unified
E. Identical
F. Consistent
G. Regular
H. Equal
I. Common
J. Standard
Answer: C
According to most sources, what is the main source of news for Americans?

Options:
A. Public Radio
B. Video Streaming
C. Social Media Feeds
D. Cable Television
E. News Applications
F. Local Magazines
G. Professional Journals
H. Educational TV
I. National Podcasts
J. Community Forums
Answer: H
The thermogenic coefficients of the energy-producing nutrients: proteins, fats, and carbohydrates are respectively ().

Options:
A. 4kcal/g,9kcal/g,4kcal/g
B. 4kJ/g,9 kJ/g,4 kJ/g
C. 4.2kcal/g,8.8kcal/g,4.2kcal/g
D. 9kcal/ $\mathbf{g}$ ,4kcal/g,4kcal/ $\mathbf{g}$
E. 4.5kcal/g,9kcal/g,3.5kcal/g
F. 3.9kcal/g,9.2kcal/g,3.9kcal/g
G. 5kcal/g,10kcal/g,5kcal/g
H. 37.56 kJ/g,16.81 kJ/g,16.74 kJ/g
I. 16.81kcal/g,37.56kcal/ $\mathbf{g}$ ,16.74kcal/g
Answer: A