Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side $10\, cm, 50$ turns and
carrying current $I$ (Ampere) in units of $\frac{\mu _{0}I}{\pi}$ is :
a.
$250\sqrt{3}$
b.
$50\sqrt{3}$
c.
$500\sqrt{3}$
Correct Answer
d.
$5\sqrt{3}$
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Q2mcq
The magnetic field of a plane electromagnetic wave is $\vec{B}=3 \times 10^{-8} sin[200\pi (y+ct)]ˆi\,T$ . Where,
$c=3 \times 10^{8\,}m\,s^{-1}$ is the speed of light the corresponding electric filed is :
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the
earth's radius $R_{e}.$ By firing rockets attached to it, its speed is instantaneously increased in the direction of its
motion so that it become $\sqrt{\frac{3}{2}}$ times larger. Due to this the farthest distance from the centre of the earth that the
satellite reaches is $R$ . Value of $R$ is :
a.
$4R_{e}$
b.
$2. 5R_{e}$
c.
$3R_{e}$
Correct Answer
d.
$2R_{e}$
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Q4mcq
When a diode is forward biased, it has a voltage drop of $0. 5\,V$ . the safe limit of current through the diode is
$10\, mA$ . If a battery of emf $1. 5\,V$ is used in the circuit, the value of minimum resistance to be connected in
series with the diode so that the current does not exceed the safe limit is :
a.
$300\,\Omega$
b.
$50\,\Omega$
c.
$100\,\Omega$
Correct Answer
d.
$200\,\Omega$
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Q5mcq
A charged particle carrying charge $1\,\mu C$ is moving with velocity $(2ˆi+ 3ˆj+ 4ˆk)\,m\,s^{-1}$ . If an external
magnetic field of $(5ˆi+ 3ˆj-6ˆk)\times 10^{-3}T$ exists in the region where the particle is moving then the force on
the particle is $\vec{F}\times 10^{-9}\,N$ . the vector $\vec{F}$ is :
a.
$-0. 30ˆi + 0. 32ˆj -0. 09ˆk$
b.
$-30ˆi + 32ˆj -9ˆk$
Correct Answer
c.
$-300ˆi+ 320ˆj-90ˆk$
d.
$-3. 0ˆi+ 32ˆj-0. 9ˆk$
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Q6mcq
When the wavelength of radiation falling on a metal is changed from $500 nm \, to \,200 nm$ , the maximum
kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:
a.
$0. 81 eV$
b.
$1. 02 eV$
c.
$0. 52 eV$
d.
$0. 61 eV$
Correct Answer
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Q7nat
An observer can see through a small hole on the side of a jar (radius $15\, cm$ ) at a point at height of $15\, cm$
from the bottom (see figure). The hole is at a height of $45\, cm$ . When the jar is filled with a liquid up to a
height of $30\, cm$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid
is $\frac{N}{100},$ where $N$ is an integer, the value of $N$ is
✓ Accepted Answer:158
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Q8mcq
In the circuit shown in the figure, the total charge is $750\,\mu C$ and the voltage across capacitor $C_{2}$ is $20\,V$ . Then
the charge on capacitor $C_{2}$ is :
a.
$450\,\mu C$
b.
$590\,\mu C$
Correct Answer
c.
$160\,\mu C$
d.
$650\,\mu C$
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Q9mcq
An elliptical loop having resistance $R$ , of semi major axis $a$ , and semi minor axis $b$ is placed in a magnetic
field as shown in the figure. If the loop is rotated about the $x$ -axis with angular frequency $\omega$ , the average power
loss in the loop due to Joule heating is :
In a radioactive material, a fraction of active material remaining after the time $t is \frac{9}{16}$ . The fraction that
was remaining after the time $\frac{t}{2}$ is :
a.
$\frac{4}{5}$
b.
$\frac{3}{5}$
c.
$\frac{3}{4}$
Correct Answer
d.
$\frac{7}{8}$
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Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid
rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:
a.
$\frac{5}{2}RT$
b.
$\frac{3}{2}RT$
c.
$\frac{9}{2}RT$
d.
$3RT$
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In a Young's double slit experiment, light of $500 nm$ is used to produce and interference pattern. When the
distance between the slits is $0. 05 mm,$ the angular width (in degree) of the fringes formed on the distance
screen is close to :
a.
$0. 17^{\circ}$
b.
$0. 57^{\circ}$
c.
$1. 7^{\circ}$
d.
$0. 07^{\circ}$
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A cricket ball of mass $0. 15\, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum
height of $20\,m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball
applies a constant force $F$ on the ball and moves horizontally a distance of $0. 2\,m$ while launching the ball, the
value of $F(in \,N)$ is $(g= 10\,m\,s^{-2})$
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A uniform thin rope of length $12\,m$ and mass $6\, kg$ hangs vertically from a rigid support and a block of mass
$2\, kg$ is attached to its free end. A transverse short wave train of wavelength $6\, cm$ is produced at the lower and
the rope. What is the wavelength of the wave train (in $cm$ ) when it reaches the top of the rope?
a.
$3$
b.
$6$
c.
$12$
d.
$9$
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A block of mass $m = 1\, kg$ slides with velocity $v = 6\,m\,s^{-1}$ on a frictionless horizontal surface and collides
with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $O$ and swings as a result of the
collision making angle $\theta$ before momentarily coming to rest. if the rod has mass $M = 2\, kg,$ and length
$\ell = 1\,m,$ the value of $\theta$ is approximately $(take \,g = 10\,m\,s^{-2})$
a.
$63^{\circ}$
b.
$55^{\circ}$
c.
$69^{\circ}$
d.
$49^{\circ}$
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Using screw gauge of pitch $0. 1 cm$ and $50$ divisions on its circular scale, the thickness of an object is
measured. It should correctly be recorded as,
a.
$2. 121 cm$
b.
$2. 124 cm$
c.
$2. 125 cm$
d.
$2. 123 cm$
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A $750\, Hz, \,20\,V(rms)$ source is connected to a resistance of $100\,\Omega ,$ an inductance of $0. 1803\,H$ and a
capacitance of $10\,\mu F$ all in series. The time in which the resistance (heat capacity $2\,J/^{\circ}C$ ) will get heated by
$10^{\circ}C.$ (assume no loss of heat to the surroundings) is close to :
a.
$418\,s$
b.
$245\,s$
c.
$365\,s$
d.
$348\,s$
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A person of $80\, kg$ mass is standing on the rim of a circular platform of mass $200\, kg$ rotating about its axis at $5$
revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be
the rotational speed (in $rpm$ ) of the platform when the person reaches its centre....
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Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3}R$ and $\frac{1}{3} R$ have $12\,\mu C$ and $-3\,\mu C$ charges,
respectively, and are at a large distance from each other, They are now connected by a conducting wire. A long
time after this is done the charges on $S_{1}$ and $S_{2}$ are respectively:
a.
$4. 5\,\mu C\, of \, both$
b.
$+4. 5\,\mu C\, and \, -4. 5\,\mu C$
c.
$3\,\mu C\, and \,6\,\mu C$
d.
$6\,\mu C\, and \,3\,\mu C$
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A bakelite beaker has volume capacity of $500\, cc$ at $30^{\circ}C$ . When it is partially filled with $V_{m}$ volume (at $30^{\circ}C$
) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If
$\gamma _{bester\,} = 6 \times 10^{-6}0^{\circ}C^{-1},$ where $\gamma$ is the coefficient of volume expansion, then $V_{m}$ (in $cc$ ) is close to $…$
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When a long glass capillary tube of radius $0. 015 cm$ is dipped in a liquid, the liquid rises to a height of $15\, cm$
within it. If the contact angle between the liquid and glass to close to $0^{\circ}$ , the surface tension of the liquid, in
milliNewton $m^{-1},$ is $[\rho _{(liqued)\,} = 900\, kg \,m^{-3}, g = 10\,m\,s^{-2}]$ (Given answer in closed integer)
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Moment of inertia of a cylinder of mass $m,$ length $L$ and radius $R$ about an axis passing through its centre and
perpendicular to the axis of the cylinder is $I =M(\frac{R^{2}}{4} + \frac{L^{2}}{12}).$ If such a cylinder is to be made for a given mass
of a material, the ratio $\frac{L}{R}$ for it to have minimum possible $I$ is:
a.
$\frac{2}{3}$
b.
$\frac{3}{2}$
c.
$\sqrt{\frac{3}{2}}$
d.
$\sqrt{\frac{2}{3}}$
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Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $a$ and a concentric thin
cylindrical shell of radius $b$ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is
connected to a resistance of value $R$ , the maximum Joule heating in $R$ will take place for :
a.
$R= \frac{\rho}{2\pi \ell}(\frac{b}{a})$
b.
$R = \frac{\rho}{2\pi \ell} ln(\frac{b}{a})$
c.
$R= \frac{\rho}{\pi \ell} In(\frac{b}{a})$
d.
$R = \frac{2\rho}{\pi \ell} ln(\frac{b}{a})$
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Let $C_{NaCl}$ and $C_{BaSO4}$ , be the conductances (in S) measured for saturated aqueous solutions of $NaCl$ and
$BaSO_{4}$ respectively, at a temperature T. Which of the following is false?
a.
lonic mobilities of ions from both salts increase with T.
b.
$C_{BaSO_{4}}(T_{2}) > C_{BaSO_{4}}(T_{1}) for T_{2} > T_{1}$
c.
$C_{NaCl}(T_{2}) > C_{NaCl}(T_{1}) for T_{2} > T_{1}$
d.
$C_{NaCl} \gg C_{BaSO_{4}}$ at given $T$
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The mechanism of Sn1 reaction is given as:
$R -X\longrightarrow R^{\oplus }X^{\ominus } \longrightarrow R^{\oplus } \,X^{\ominus } \rightarrow R -Y + X\rightarrow^{Y^{\ominus }}^{\ominus }$
$\,\,\,\,\,\,\,\,\,\,\,\,\,\, lon \, pair \,\,\,\,\,\, Solvent$
$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, Speparated \, ion$
$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, pair$
A student writes general characteristics based on the given mechanism as :
(a) The reaction is favoured by weak nucleophiles.
(b) $R^{\oplus }$ would be easily formed if the substituents are bulky $y$
(c) The reaction is accompanied by recemization
(d) The reaction is favoured by non-polar solvents.
Which observations are correct?
a.
(a) and (b)
b.
(a) and (c)
c.
(a), (b) and (c)
d.
(b) and (d)
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The electronic spectrum of $[Ti (H_{2}O)_{6}]^{3+}$ shows a single broad peak with a maximum at $20, 300 cm^{-1}.$
The crystal field stabilization energy (CFSE) of the complex ion, in $kJmol^{-1},$ is : $(1 kJmol^{-1} = 83. 7 cm^{-1})$
a.
145.5
b.
242.5
c.
83.7
d.
97
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An organic compound [A], molecular formula $C_{10}H_{20}O_{2}$ was hydrolyzed with dilute sulphuric acid to given a
carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with $CrO_{3}-H_{2}SO_{4}$ produced [B]. Which of the
following structures are not possible for $[A]$
c.
$CH_{3}CH_{2}CH_{2}COOCH_{2}CH_{2}CH_{2}CH_{3}$
d.
$(CH_{3})_{3}-C -COOCH_{2}C(CH_{3})_{3}$
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An element with molar mass $2 .7 \times 10^{-2}\, kg \, mol^{-1}$ forms a cubic unit cell with edge length $405\, pm.$ If its
density is $2. 7 \times 10^{3}\, kg \,m^{-3}$ , the radius of the element is approximately $… … … . \times 10^{-12}m$ (to the nearest
integer)
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Henry's constant (in kbar) for four gases $\alpha$ $,$ $\beta$ $,$ $\gamma$and $\delta$ in water at $298\,K$ is given below :
$\alpha$ $\beta$ $\frac{$\gamma$}{-5}$ $\delta$
$K_{H} 50 2 2 \times 10 0. 5$
(density of water $= 10^{3}\,k\, gm^{-3}$ at $298\,K$ ) This table implies that :
a.
$\alpha$ has the highest solubility in water at a given pressure
b.
solubility of $\gamma$ at $308K$ is lower than at $298K$
c.
The pressure of a $55. 5$ molal solution of is $\delta$ $250$ bar
d.
The pressure of $55. 5$ molal solution of $\gamma$is $1\, bar$ .
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$\parallel$
The mole fraction of glucose $(C_{6}H_{12}O_{6})$ in an aqueous binary solution is $0. 1.$ The mass percentage of water
in it, to the nearest integer, is $… … …$
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The volume strength of $8. 9\, MH_{2}O_{2}$ solution calculated at $273\,K$ and 1 atm is
$........(R = 0 .0821 L\, atm \,K^{-1}\, mol^{-1})$ (rounded off to the nearest integer)
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The total number of monohalogenated organic products in the following (including stereoisomers) reaction is
$-_{(Simplest \, optically active \, alkene)}A^{(i)\,H}_{(ii)\,X}^{_{2}/ Ni /\Delta }_{_{2}/\Delta }\rightarrow \rightarrow$
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The photoelectric current from Na (work function, $w_{0} = 2. 3 eV$ ) is stopped by the output voltage of the cell
$Pt(s)\parallel H_{2}(g, 1 bar)| HCl(aq\cdot , pH = 1)| AgCl(s) |Ag(s)$
the $pH$ of aq. $HCl$ required to stop the photoelectric current from $K(w_{0} = 2. 25 eV)$ , all other conditions
remaining the same, is $… … … . \times 10^{-2}$ (to the nearest integer).
Given $2. 303\frac{RT}{F} = 0. 06V; E^{0}_{AgCl / Ag /Cl} = 0. 22V$
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If $_{x}lim_{\rightarrow 0\rightarrow } {\frac{1}{x^{8}}(1 -cos \frac{x^{2}}{2} -cos \frac{x^{2}}{4} + cos \frac{x^{2}}{2}cos \frac{x^{2}}{4} )}= 2^{-k}$ then the value of k is
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For the frequency distribution: Variate $(x) :x_{1}, \,x_{2}, \,x_{3}, … ,x_{15}$
Frequency $(f) :f_{1}, \,f_{2}, \,f_{3}, … ,f_{15}$
where $0 <x_{1} <x_{2} <x_{3} < … <x_{15} = 10$ and $\sum ^{15}_{i=1} f_{i} > 0,$ the standard deviation cannot be
a.
$4$
b.
$1$
c.
$6$
d.
$2$
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The value of ( $2 \cdot ^{1} P_{0}-3 \cdot ^{2} P_{1}+ 4 \cdot ^{3} P_{2}-. . . . . . . .$ up to $51^{th}$ term) $+$ ( $1! -2! + 3!-. . . . . . .$ up to $51^{th}$ term) is
equal to
a.
$1 -51(51)!$
b.
$1 + (51)!$
c.
$1 + (52)!$
d.
$1$
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The foot of the perpendicular drawn from the point $(4, \,2, \,3)$ to the line joining the points $(1, \, -2, \,3)$ and
$(1, \,1, \,0)$ lies on the plane
a.
$2\,x+y- z= 1$
b.
$x- y-2\,z= 1$
c.
$x-2\,y+z= 1$
d.
$x+ 2\,y- z= 1$
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Let $P$ be a point on the parabola, $y^{2} = 12x$ and $N$ be the foot of the perpendicular drawn from $P$ , on the axis
of the parabola. A line is now drawn through the mid-point $M$ of $PN$ , parallel to its axis which meets the
parabola at $Q$ . If the $y-$ intercept of the line $NQ$ is $\frac{4}{3},$ then :
a.
$PN = 4$
b.
$MQ= \frac{1}{3}$
c.
$MQ= \frac{1}{4}$
d.
$PN = 3$
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If $\alpha$ and $\beta$ are the roots of the equation $x^{2} +px+ 2 = 0$ and $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ are the roots of the equation
$2x^{2} + 2qx+ 1 = 0,$ then $(\alpha - \frac{1}{\alpha})(\beta - \frac{1}{\beta})(\alpha + \frac{1}{\beta} )(\beta + \frac{1}{\alpha})$ is equal to :
a.
$\frac{9}{4}(9 +q^{2})$
b.
$\frac{9}{4}(9 - q^{2})$
c.
$\frac{9}{4}(9 +p^{2})$
d.
$\frac{9}{4}(9 - p^{2})$
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If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then
the common difference of this $A.P.$ is
a.
$\frac{1}{6}$
b.
$\frac{1}{5}$
c.
$\frac{1}{4}$
d.
$\frac{1}{7}$
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A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$ .
Then the conditional probability that the score $4$ has appeared at least once is
a.
$\frac{1}{4}$
b.
$\frac{1}{3}$
c.
$\frac{1}{8}$
d.
$\frac{1}{9}$
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A hyperbola having the transverse axis of length, $\sqrt{2}$ has the same foci as that of the ellipse, $3x^{2} + 4y^{2} = 12$
then this hyperbola does not pass through which of the following points?
a.
$( \frac{1}{\sqrt{2}}, 0)$
b.
$(-\sqrt{\frac{3}{2}} , 1)$
c.
$(1, -\frac{1}{\sqrt{2}} )$
d.
$(\sqrt{\frac{3}{2}}, \frac{1}{\sqrt{2}})$
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Let $[t]$ denote the greatest integer $\leq t$ . If $\lambda \epsilon R-{0, \,1}, \,\, lim_{x\rightarrow 0\rightarrow } \frac{1-x+|x|}{\lambda -x+[x]} =L$ , then $L$ is equal to
a.
$1$
b.
$2$
c.
$\frac{1}{2}$
d.
$0$
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If $(\frac{1+i}{1-i})\frac{m}{2} =(\frac{1+i}{i-1})\frac{n}{3} = 1, \,\,(m, \,n\in N)$ then the greatest common divisor of the least values of $m$ and $n$ is
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