The magnetic field in a plane electromagnetic wave is $B_{y} =(3.5 \times 10^{-7})sin(1.5 \times 10^{3}x+ 0.5 \times 10^{11}t)T$ .
The corresponding electric field will be :
A force $(3x^{2} + 2x-5)N$ displaces a body from $x= 2\,m$ to $x= 4\,m$ . Work done by this force is ________ $J$ .
✓ Accepted Answer:58
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Q3nat
The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$ . The angle
between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$ .
✓ Accepted Answer:150
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Q4mcq
UV light of $4.13eV$ is incident on a photosensitive metal surface having work function $3.13eV$ . The maximum
kinetic energy of ejected photoelectrons will be:
a.
$4.13eV$
b.
$3.13eV$
c.
$1eV$
Correct Answer
d.
$7.26eV$
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Q5mcq
A $1\,kg$ mass is suspended from the ceiling by a rope of length $4\,m$ . A horizontal force ' $F$ ' is applied at the mid
point of the rope so that the rope makes an angle of $45^{\circ }$ with respect to the vertical axis as shown in figure. The
magnitude of $F$ is : (Assume that the system is in equilibrium and $g= 10\,m/s^{2}$ )
a.
$10\,N$
Correct Answer
b.
$\frac{10}{\sqrt{2}}\,N$
c.
$1\,N$
d.
$\frac{1}{10\times \sqrt{2}}N$
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Q6mcq
The $I- V$ characteristics of an electronic device shown in the figure. The device is:
a.
a diode which can be used as a rectifier
b.
a zener diode which can be used as a voltage
regulator
Correct Answer
c.
a transistor which can be used as an amplifier
d.
a solar cell
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Q7mcq
A proton and a deutron ( $q= +e,\vec{m}= 2.0u)$ having same kinetic energies enter a region of uniform magnetic
field $\vec{B}$ , moving perpendicular to $B$ . The ratio of the radius $r_{d}$ of deutron path to the radius $r_{p}$ of the proton
path is:
a.
$\sqrt{2}: 1$
Correct Answer
b.
$1 : 1$
c.
$1 : \sqrt{2}$
d.
$1 : 2$
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Q8mcq
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2 : 1$ . After
disintegration they will move :
a.
in the same direction with same speed.
b.
in opposite directions with the same speed.
c.
in opposite directions with speed in the ratio of
$2 : 1$ respectively.
d.
in opposite directions with speed in the ratio of
$1 : 2$ respectively.
Correct Answer
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Q9mcq
In the truth table of the above circuit the value of $X$ and $Y$ are :
a.
0,0
b.
1,1
Correct Answer
c.
1,0
d.
0,1
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Q10mcq
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/ 2mE$ . The dimensional
formula for Planck's constant is :
a.
$[ML^{2}\,T^{-1}]$
Correct Answer
b.
$[ML^{-1}\,T^{-2}]$
c.
$[MLT^{-2}]$
d.
$[M^{2}\,L^{2}\,T^{-2}]$
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A real gas within a closed chamber at $27^{\circ }C$ undergoes the cyclic process as shown in figure. The gas obeys
$PV^{3} =RT$ equation for the path $A$ to $B$ . The net work done in the complete cycle is (assuming $R= 8\,J/molK$
):
a.
$20\,J$
b.
$205\,J$
c.
$-20\,J$
d.
$225\,J$
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The energy released in the fusion of $2\,kg$ of hydrogen deep in the sun is $E_{H}$ and the energy released in the
fission of $2\,kg$ of $^{235}U$ is $E_{U}$ . The ratio $\frac{E_{H}}{E_{U}}$ is approximately: (Consider the fusion reaction as
$4 | H+ 2e^{-} \rightarrow \rightarrow^{4}_{2}He + 2v+ 6\gamma + 26.7MeV$ , energy released in the fission reaction of $^{235}U$ is $200MeV$ per
fission nucleus and $N_{A} = 6.023 \times 10^{23})$
a.
7.62
b.
25.6
c.
15.04
d.
9.13
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Two cars are travelling towards each other at speed of $20\,m\,s^{-1}$ each. When the cars are $300\,m$ apart, both the
drivers apply brakes and the cars retard at the rate of $2\,m\,s^{-2}$ . The distance between them when they come to
rest is :
a.
$200\,m$
b.
$100\,m$
c.
$50\,m$
d.
$25\,m$
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The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio
between the volume of the first and the second bubble is:
a.
$1 : 9$
b.
$1 : 3$
c.
$1 : 27$
d.
$1 : 81$
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A spherical ball of radius $1 \times 10^{-4}\,m$ and density $10^{5}\,kg/m^{3}$ falls freely under gravity through a distance $h$
before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value
of $h$ is approximately: (The coefficient of viscosity of water is $9.8 \times 10^{-6}\,N\,s/m^{2}$ )
a.
$2296\,m$
b.
$2518\,m$
c.
$2249\,m$
d.
$2396\,m$
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The temperature of a gas is $-78^{\circ }C$ and the average translational kinetic energy of its molecules is $K$ . The
temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2\,K$ is :
a.
$127^{\circ }C$
b.
$117^{\circ }C$
c.
$-39^{\circ }C$
d.
$-78^{\circ }C$
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At room temperature $(27^{\circ }C)$ , the resistance of a heating element is $50\Omega$ . The temperature coefficient of the
material is $2.4 \times 10^{-4^{\circ} }C^{-1}$ . The temperature of the element, when its resistance is $62\Omega$ , is _____ $^{\circ }C$ .
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The following figure represents two biconvex lenses $L_{1}$ and $L_{2}$ having focal length $10\,cm$ and $15\,cm$
respectively. The distance between $L_{1}&L_{2}$ is :
a.
$10\,cm$
b.
$35\,cm$
c.
$25\,cm$
d.
$15\,cm$
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A capacitor of reactance $4\sqrt{3}\Omega$ and a resistor of resistance $4\Omega$ are connected in series with an ac source of
peak value $8\sqrt{2}\,V$ . The power dissipation in the circuit is ________ W.
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A straight magnetic strip has a magnetic moment of $44Am^{2}$ . If the strip is bent in a semicircular shape, its
magnetic moment will be _______ $Am^{2}$ . (given $\pi = \frac{22}{7}$ )
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An electric field $E = (2x\hat{i})NC^{-1}$ exists in space. A cube of side $2\,m$ is placed in the space as per figure given
below. The electric flux through the cube is ______ $Nm^{2}/C$ .
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Five charges $+q, +5q, -2q, +3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this
configuration through the surface $S$ is :
a.
$\frac{4q}{\epsilon _{0}}$
b.
$\frac{5q}{\epsilon _{0}}$
c.
$\frac{q}{\epsilon _{0}}$
d.
$\frac{3q}{\epsilon _{0}}$
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To determine the resistance $(R)$ of a wire, a circuit is designed below. The $V - I$ characteristic curve for this
circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is ______ $\Omega$ .
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A satellite of $10^{3}\,kg$ mass is revolving in circular orbit of radius $2R$ . If $\frac{10^{4}R}{6}J$ energy is supplied to the satellite,
it would revolve in a new circular orbit of radius (use $g= 10\,m/s^{2},R=$ radius of earth)
a.
$2.5R$
b.
$3R$
c.
$4R$
d.
$6R$
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A square loop of side $15\,cm$ being moved towards right at a constant speed of 2 $cm/s$ as shown in figure. The
front edge enters the $50\,cm$ wide magnetic field at $t=$ 0 . The value of induced emf in the loop at $t= 10\,s$ will
be :
a.
$0.3mV$
b.
zero
c.
$4.5mV$
d.
$3mV$
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A particle of mass $0.50\,kg$ executes simple harmonic motion under force $F = -50(Nm^{-1})x$ . The time period
of oscillation is $\frac{\vec{x}}{35}\,s$ . The value of $x$ is _______ (Given $\pi = \frac{22}{7}$ )
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A circular disc reaches from top to bottom of an inclined plane of length $l$ . When it slips down the plane, if
takes $t\,s$ . When it rolls down the plane then it takes $(\frac{\alpha}{2})^{1/2}t\,s$ , where $\alpha$ is _________
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Monochromatic light of wavelength $500\,nm$ is used in Young's double slit experiment. An interference pattern
is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$ ),
the central maximum is shifted to a position previously occupied by the $4^{th\,}$ bright fringe. The thickness of the
glass-plate is ______ $\mu m$ .
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The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of
frequency ' $A$ ' $\times 10^{12}$ hertz and that has a radiant intensity in that direction of $\frac{1}{^{'}\,B^{'}}$ watt per steradian. 'A' and
'B' are respectively
a.
540 and 683
b.
450 and 683
c.
450 and $\frac{1}{683}$
d.
540 and $\frac{1}{683}$
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$M^{2+} + H_{2}\,S A\,(Black precipitate)\, + \,by product\,$
Consider the following test for a group-IV cation. $A + \,aqua re\vec{g}ia\, \rightarrow B + NOCl + S + H\rightarrow_{2}O$ The
$B + KNO_{2}+ CH_{3}COOH C + \,by product\,$
spin-only magnetic moment value of the metal complex $C$ is ______ BM (Nearest integer)
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Which out of the following is a correct equation to show change in molar conductivity with respect to
concentration for a weak electrolyte, if the symbols carry their usual meaning :
For a sparingly soluble salt $AB_{2}$ , the equilibrium concentrations of $A^{2+}$ ions and $B^{-}$ ions are $1.2 \times 10^{-4}M$ and
$0.24 \times 10^{-3}M$ , respectively. The solubility product of $AB_{2}$ is :
a.
$6.91 \times 10^{-12}$
b.
$0.276 \times 10^{-12}$
c.
$27.65 \times 10^{-12}$
d.
$0.069 \times 10^{-12}$
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Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within
an atomic nucleus of diameter $10^{-15}\,m$ is ________. $10^{9}\,ms^{-1}$ (nearest integer) [Given : mass of electron
$= 9.1 \times 10^{-31}\,kg$ , Plank's constant $(h) = 6.626 \times 10^{-34}Js$ ] (Value of $\pi = 3.14$ )
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Match List I with List II
$\,List - I (Test)\, List - II (Observation)$
$\frac{\,A.\,}{\,B.\,} Br_{2}\,water test\, \frac{\,I.\,}{\,II.\,} \,Yellow orange or orange red precipitate formed\,$
$\,Ceric ammonium nitrate test\, \,Reddish orange colour disappears\,$ Choose
$\frac{\,C.\,}{\,D.\,} \,Ferric chloride test\, \frac{\,III.\,}{\,IV.\,} \,Red colour appears\,$
$2, 4\,- DNP test\, \,Blue, Green, Violet or Red colour appear\,$
the correct answer from the options given below:
a.
A-III, B-IV, C-I, D-II
b.
A-I, B-II, C-III, D-IV
c.
A-IV, B-I, C-II, D-III
d.
A-II, B-III, C-IV, D-I
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Consider the following first order gas phase reaction at constant temperature $A(g) \rightarrow 2\,B(\,g) + C(g)\rightarrow$ If the
total pressure of the gases is found to be 200 torr after $23sec$ . and 300 torr upon the complete decomposition of
A after a very long time, then the rate constant of the given reaction is ______ $\times 10^{-2}\,s^{-1}$ (nearest integer)
[Given : $log_{10}(2) = 0.301$ ]
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In the given TLC, the distance of spot A & B are $5\,cm\,&\,7\,cm$ , from the bottom of TLC plate, respectively. $R_{f}$
value of $B$ is $x\times 10^{-1}$ times more than $A$ . The value of $x$ is ______.
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$\,List - I (Element)\, List - II (Electronic configuration)$
$\frac{\,A.\,}{\,B.\,}\frac{N}{S}\frac{\,I.\,}{\,II.\,} [Ar]3\,d^{10}4\,s^{2}4p^{5}AR$
Match List I with List II $[Ne]3\,s^{2}3p^{4}$ Choose
$\,C.\, Br \,III.\, [He]2\,s^{2}2p^{3}$
$\,D.\, Kr \,IV.\, [Ar]3\,d^{10}4\,s^{2}4p^{6}$
the correct answer from the options given below:
a.
A-III, B-II, C-I, D-IV
b.
A-II, B-I, C-IV, D-III
c.
A-I, B-IV, C-III, D-II
d.
A-IV, B-III, C-II, D-I
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A transition metal ' $M$ ' among $Sc, Ti, V, Cr, Mn$ and $Fe$ has the highest second ionisation enthalpy. The spin-
only magnetic moment value of $M^{+}$ ion is _______. $BM$ (Near integer) (Given atomic number
$Sc : 21, Ti : 22, \,V : 23, Cr : 24, Mn : 25, Fe : 26$ )
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Which of the following compounds will give silver mirror with ammoniacal silver nitrate? A. Formic acid B.
Formaldehyde C. Benzaldehyde D. Acetone Choose the correct answer from the options given below :
a.
A, B and C only
b.
C and D only
c.
B and C only
d.
A only
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$\frac{\,List - I\,}{\,Melting Point\,[K]} List - II$
$\frac{\,A.\,}{\,B.\,} \frac{\,I.\,}{\,II.\,} T1 > In > Ga > A1 > B$
Match List I with List II $\,Ionic Radius\,[M^{+3}/pm] B > T1 > A1 ≈Ga > In$ Choose the
$^{-1} T1 > In > A1 > Ga > B$
$\frac{\,C.\,}{\,D.\,}\frac{\Delta _{i}H_{1}[\,kJ\,mol]}{\,Atomic Radius\,[pm]}\frac{\,III.\,}{\,IV.\,}$
$B > A1 > T1 > In > Ga$
correct answer from the options given below:
a.
A-II, B-III, C-IV, D-I
b.
A-IV, B-I, C-II, D-III
c.
A-I, B-II, C-III, D-IV
d.
A-III, B-IV, C-I, D-II
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$\frac{Match List I with List II}{\,List - I (Cell)\,}$
$List - II (Use/Property/Reaction)$
$\,Converts energy of combustion into electrical\,$
$\,A.\, \,Leclanche cell\, \,I.\,$
$\,energy\,$
$\,Does not involve any ion in solution and is used\,$ Choose the correct
$\,B.\, Ni -Cd\,cell\, \,II.\,$
$\,in hearing aids\,$
$\,C.\, \,Fuel cell\, \,III.\, \,Rechargeable\,$
$\,D.\, \,Mercury cell\, \,IV.\, \,Reaction at anode\,Zn \rightarrow Zn\rightarrow^{2+} + 2e^{-}$
answer from the options given below:
a.
A-II, B-III, C-IV, D-I
b.
A-I, B-II, C-III, D-IV
c.
A-III, B-I, C-IV, D-II
d.
A-IV, B-III, C-I, D-II
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Number of compounds from the following which cannot undergo Friedel-Crafts reactions is: ________.
toluene, nitrobenzene, xylene, cumene, aniline, chlorobenzene, $m$ -nitroaniline, $m$ -dinitrobenzene
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$\frac{\,List - I\,}{K]} \frac{List - II}{sp^{3}}$
$\,A.\,_{2}[Ni(CN)_{4} \,I.\,$
Match List I with List II $\,B.\, [Ni(CO)_{4}] \,II.\, \frac{sp\,d}{2}^{3}^{2}$ Choose the correct answer from the
$\,C.\, [Co(NH_{3})_{6}]Cl_{3} \,III.\, \frac{dsp}{23}$
$\,D.\, Na_{3}[CoF_{6}] \,IV.\, d sp$
options given below:
a.
A-III, B-I, C-IV, D-II
b.
A-III, B-I, C-II, D-IV
c.
A-I, B-III, C-II, D-IV
d.
A-III, B-II, C-IV, D-I
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The vapour pressure of pure benzene and methyl benzene at $27^{\circ }C$ is given as 80 Torr and 24 Torr, respectively.
The mole fraction of methyl benzene in vapour phase, in equilibrium with an equimolar mixture of those two
liquids (ideal solution) at the same temperature is _______ $\times 10^{-2}$ (nearest integer)
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Give below are two statements: Statement I : The higher oxidation states are more stable down the group
among transition elements unlike p-block elements. Statement II : Copper can not liberate hydrogen from weak
acids. In the light of the above statements, choose the correct answer from the options given below :
a.
Both Statement I and Statement II are true
b.
Statement I is false but Statement II is true
c.
Both Statement I and Statement II are false
d.
Statement I is true but Statement II is false
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Let the inverse trigonometric functions take principal values. The number of real solutions of the equation
$2 sin^{-1} x+ 3 cos^{-1} x= \frac{2\pi}{5}$ , is _______
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Let $\vec{a}= 2\hat{i}+\alpha \hat{j}+ \hat{k}, \vec{b}= -\hat{i}+ \hat{k}, \vec{c}=\beta \hat{j}- \hat{k}$ , where $\alpha$ and $\beta$ are integers and $\alpha \beta = -6$ . Let the values of the
ordered pair $(\alpha ,\beta )$ , for which the area of the parallelogram of diagonals $\vec{a}+ \vec{b}$ and $\vec{b}+ \vec{c}$ is $\frac{\sqrt{21}}{2}$ , be $(\alpha _{1},\beta _{1})$
and $(\alpha _{2},\beta _{2})$ . Then $\alpha ^{2}_{1} +\beta ^{2}_{1} - \alpha _{2}\beta _{2}$ is equal to
a.
19
b.
17
c.
24
d.
21
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Consider the circle $C :x^{2} +y^{2} = 4$ and the parabola $P :y^{2} = 8x$ . If the set of all values of $\alpha$ , for which three
chords of the circle $C$ on three distinct lines passing through the point $(\alpha , 0)$ are bisected by the parabola $P$ is
the interval $(p,q)$ , then $(2q- p)^{2}$ is equal to ________
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Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point $( \frac{11}{3}, \frac{11}{3}, \frac{19}{3} )$
from the line $L$ along the line $\frac{3x-11}{2} = \frac{3y-11}{1} = \frac{3z-19}{2}$ is equal to
a.
6
b.
5
c.
4
d.
3
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Between the following two statements: Statement I : Let $\vec{a}= \hat{i}+ 2\hat{j}-3\hat{k}$ and $\vec{b}= 2\hat{i}+ \hat{j}- \hat{k}$ . Then the vector
$\vec{r}$ satisfying $\vec{a}\times \vec{r}= \vec{a}\times \vec{b}$ and $\vec{a}\cdot \vec{r}= 0$ is of magnitude $\sqrt{10}$ .
Statement II : In a triangle $ABC, cos 2A+ cos 2B+ cos 2C \geq -\frac{3}{2}$ .
a.
Statement I is incorrect but Statement II is
correct.
b.
Both Statement I and Statement II are correct.
c.
Statement I is correct but Statement II is
incorrect.
d.
Both Statement I and Statement II are incorrect.
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Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E : \frac{(x-1)^{2}}{100} + \frac{(y-1)^{2}}{75} = 1$ and the eccentricity
of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$ . If the length of the transverse axis of
$H$ is $\alpha$ and the length of its conjugate axis is $\beta$ , then $3\alpha ^{2} + 2\beta ^{2}$ is equal to
a.
237
b.
242
c.
205
d.
225
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Let $\alpha ,\beta ;\alpha >\beta$ , be the roots of the equation $x^{2} - \sqrt{2}x- = 0\sqrt{3}$ . Let $P_{n} =\alpha ^{\vec{n}} - \beta ^{n},n\in N$ . Then
$(11 -10)P\sqrt{3} \sqrt{2}_{10}+ (11 + 10)P\sqrt{2}_{11}-11P_{12}$ is equal to
a.
$10P\sqrt{3}_{9}$
b.
$11\sqrt{3}P_{9}$
c.
$10P\sqrt{2}_{9}$
d.
$11P\sqrt{2}_{9}$
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Let $a,ar,ar^{2}$ , be an infinite G.P. If $\sum ^{\infty }_{n=0} ar^{n} = 57$ and $\sum ^{\infty }_{n=0} a^{3}r^{3n} = 9747$ , then $a+ 18r$ is equal to
a.
46
b.
38
c.
31
d.
27
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Let $A,B$ and $C$ be three points on the parabola $y^{2} = 6x$ and let the line segment $AB$ meet the line $L$ through
$C$ parallel to the $x$ -axis at the point $D$ . Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and
$B$ on $L$ . Then $( \frac{AM\cdot BN}{CD})^{2}$ is equal to _________
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If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{th\,}$ roll than the
number obtained in the $(i-1)^{th\,}$ roll, $i= 2, 3$ , is equal to
a.
$3/54$
b.
$2/54$
c.
$1/54$
d.
$5/54$
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Let the range of the function $f(x) = \frac{1}{2+sin 3x+cos 3x},x\in R$ be $[a,b]$ . If $\alpha$ and $\beta$ are respectively the A.M. and
the G.M. of $a$ and $b$ , then $\frac{\alpha}{\beta}$ is equal to
a.
$\pi$
b.
$\sqrt{\pi}$
c.
2
d.
$\sqrt{2}$
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$2 -5 20 x$
Consider the matrices : $A=[ ],B=[ ]$ and $X =[ ]$ . Let the set of all $m$ , for which the system of
$3 m m y$
equations $AX =B$ has a negative solution (i.e., $x< 0$ and $y< 0$ ), be the interval $(a,b)$ . Then $8\int _{a}^{b} |A|dm$ is
equal to_________
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If the variance of the frequency distribution $\frac{x}{f}\frac{c}{2}\frac{2c}{1}\frac{3c}{1}\frac{4c}{1}\frac{5c}{1}\frac{6c}{1}$ is 160, then the value of $c\in N$ is
a.
7
b.
8
c.
5
d.
6
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$1 3$
Let $B=[ ]$ and $A$ be a $2 \times 2$ matrix such that $AB^{-1} =A^{-1}$ . If $BCB^{-1} =A$ and $C^{4} +\alpha C^{2} +\beta I =O$ ,
$1 5$
then $2\beta - \alpha$ is equal to
a.
16
b.
2
c.
8
d.
10
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The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x-1}{3} = \frac{y}{2} = \frac{z-2}{4}$ , from the origin is
_________
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Let the set of all values of $p$ , for which $f(x) =(p^{2} -6p+ 8) (sin^{2} 2x-cos^{2} 2x)+ 2(2 - p)x+ 7$ does not
have any critical point, be the interval $(a,b)$ . Then $16ab$ is equal to _______
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Two vertices of a triangle $ABC$ are $A(3, -1)$ and $B(-2, 3)$ , and its orthocentre is $P(1, 1)$ . If the coordinates of
the point $C$ are $(\alpha ,\beta )$ and the centre of the of the circle circumscribing the triangle $PAB$ is $(h, k)$ , then the
value of $(\alpha +\beta ) + 2(\,h + k)$ equals
a.
5
b.
81
c.
15
d.
51
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