If one were to apply the Bohr model to a particle of mass $'m'$ and charge $'q'$ moving in a plane under the
influence of a magnetic field 'B', the energy of the charged particle in the $n^{th}$ level will be:
a.
$n(\frac{hqB}{\pi m})$
b.
$n(\frac{hqB}{4\pi m})$
Correct Answer
c.
$n(\frac{hqB}{2\pi m})$
d.
$n(\frac{hqB}{8\pi m})$
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Q2mcq
In an unbiased p - n junction electrons diffuse from n-region to p-region because:
a.
electrons travel across the junction due to
potential difference
b.
only electrons move from n to p region and not
the vice - versa
c.
electron concentration in n - region is more as
compared to that in p - region
Correct Answer
d.
holes in p - region attract them
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Q3mcq
A uniform solid cylindrical roller of mass $m$ is being pulled on a horizontal surface with force $F$ parallel to the
surface and applied at its centre. If the acceleration of the cylinder is $a$ and it is rolling without slipping then the
value of $F$ is:
a.
$\frac{3}{2} ma$
Correct Answer
b.
$2\,ma$
c.
$\frac{5}{3} ma$
d.
$ma$
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Q4mcq
A bat moving at $10\,m\,s^{-1}$ towards a wall sends a sound signal of $8000\,Hz$ towards it. On reflection, it hears a
sound of frequency $f$ . The value of $f$ in $Hz$ is close to
$(speed\,of\,sound = 320 m\,s^{-1})$
a.
$8258$
b.
$8424$
c.
$8000$
d.
$8516$
Correct Answer
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Q5mcq
De-Broglie wavelength of an electron accelerated by a voltage of $50 V$ is close to
$(|e| = 1.6 \times 10^{-19}\,C, \,m_{e} = 9.1 \times 10^{-31}\,kg, \,\,h= 6.6 \times 10^{-34}\,J\,s)$
a.
$0.5\,$ Å
b.
$1.2\,$ Å
c.
$1.7\,$ Å
Correct Answer
d.
$2.4\,$ Å
No explanation saved for this question yet.
Q6mcq
You are asked to design a shaving mirror assuming that a person keeps it at $10\, cm$ from his face and views the
magnified image of the face at the closest comfortable distance of $25\, cm$ . The radius of curvature of the mirror
would then be:
a.
$24\, cm$
b.
$30\, cm$
c.
$60\, cm$
Correct Answer
d.
$-24\, cm$
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Q7mcq
If a body moving in a circular path maintains constant speed of $10\,m\,s^{-1}$ , then which of the following correctly
describes the relation between acceleration and radius?
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Q8mcq
An electromagnetic wave travelling in the $x-$ direction has frequency of $2 \times 10^{14}\,H\,z$ and electric field
amplitude of $27\,V\,m^{-1}$ oscillates in $Y-$ direction. From the options given below, which one describes the
magnetic field for this wave?
An ideal gas goes through a reversible cycle $a\rightarrow \rightarrow b\rightarrow \rightarrow c\rightarrow \rightarrow d$ has the V - T diagram shown below. Process
$d\rightarrow \rightarrow a and b\rightarrow \rightarrow c$ are adiabatic.
The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
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Q10mcq
Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale
(MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements
for a ball are given as:
S.No. MS (cm) VS divisions
1. 0.5 8
2. 0.5 4
3. 0.5 6
If the zero error is - 0.03 cm, then mean corrected diameter is:
a.
$0. 53\, cm$
b.
$0. 56\, cm$
c.
$0. 59\, cm$
Correct Answer
d.
$0. 52\, cm$
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In the given circuits $(a)$ and $(b)$ , switches $S_{1}$ and $S_{2}$ are closed at $t= 0$ and kept close for a long time. The
variation of currents in the two circuits for $t\geq 0$ are shown in the options. (Figures are schematic and not
drawn to scale.)
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A $10 V$ battery with internal resistance $1 \Omega$ and a $15 V$ battery with internal resistance $0.6\,\Omega$ are connected in
parallel to a voltmeter (see figure). The reading in the voltmeter will be close to:
a.
$11.9\,V$
b.
$13.1\,V$
c.
$12.5\,V$
d.
$24.5\,V$
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A proton (mass $m$ ) accelerated by a potential difference $V$ flies through a uniform transverse magnetic field $B$ .
The field occupies a region of space by width $d$ . If $\alpha$ be the angle of deviation of proton from the initial
direction of motion (see figure), the value of $sin\alpha$ will be:
a.
$\frac{B}{2}\sqrt{\frac{qd}{mV}}$
b.
$Bd\sqrt{\frac{q}{2mV}}$
c.
$\frac{B}{d}\sqrt{\frac{q}{2mV}}$
d.
$qV \sqrt{\frac{Bd}{2m}}$
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In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container
depends on $T as T^{q}$ . A good estimate for q is:
a.
$2$
b.
$\frac{1}{2}$
c.
$1$
d.
$\frac{1}{4}$
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A telescope has an objective lens of focal length $150\, cm$ and an eyepiece of focal length $5\, cm$ . If a $50\,m$ tall
tower at a distance of $1\, km$ is observed through this telescope in a normal setting, the angle formed by the
image of the tower is , then is close to$\theta$ $\theta$
a.
$30^{\circ}$
b.
$15^{\circ}$
c.
$1^{\circ}$
d.
$86^{\circ}$
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A parallel beam of electrons travelling in x - direction falls on a slit of width d (see figure). If after passing the
slit, an electron acquires momentum $p_{y}$ in the y - direction then for a majority of electrons passing through the
slit (h is Planck's constant):
a.
$|p_{y}|d<h$
b.
$|p_{y}|d>h$
c.
$|p_{y}|d\simeq h$
d.
$|p_{y}|d>>h$
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If the capacitance of a nanocapacitor is measured in terms of a unit $u$ , made by combining the electronic
charge $e$ , Bohr radius $a_{0},$ Planck's constant $h$ and speed of light $c$ then
a.
$u= \frac{e^{2}a_{0}}{hc}$
b.
$u= \frac{hc}{e^{2}a_{0}}$
c.
$u= \frac{e^{2}c}{ha_{0}}$
d.
$u= \frac{e^{2}h}{ca_{0}}$
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If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}} cm$ then the Reynolds number for
the flow is (density of water = $10^{3\,\,}kg/m^{3} and viscosity of water= 10^{-3} Pa.s$ ) close to:
a.
$5500$
b.
$550$
c.
$1100$
d.
$11,000$
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A very long (length $L$ ) cylindrical galaxy is made of uniformly distributed mass and has radius $R\,(R<<L)$ . A
star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its
centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$ , then
a.
$T\, \propto \,\sqrt{r}$
b.
$T\, \propto r$
c.
$T\, \propto r^{2}$
d.
$T^{2} \propto r^{3}$
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$| |$
A $25\, cm$ long solenoid has the radius $2\, cm$ and $500$ turns. It carries a current of $15\,A$ . If it is equivalent to a
$--$
magnet of the same size and magnetization $\vec{M} ( \frac{Magneticmoment}{volume}),$ then $\vec{M}$ is:
a.
$3$ $\pi$ $\,A\,m^{-1}$
b.
$30000\,A\,m^{-1}$
c.
$30000$ $\pi$ $\,A\,m^{-1}$
d.
$300\,A\,m^{-1}$
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A thin disc of radius $b= 2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface
charge $\sigma$ on it. If the electric field on its axis at a height $h(h << a)$ from its centre is given as $Ch$ then the
value of $C$ is
a.
$\frac{\sigma}{4\,a\epsilon _{0}}$
b.
$\frac{\sigma}{a\epsilon _{0}}$
c.
$\frac{\sigma}{5a\epsilon _{0}}$
d.
$\frac{\sigma}{2a\epsilon _{0}}$
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Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are
kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma _{1}$ is the surface charge on the
inner surface and $Q_{1}$ net charge on it and $\sigma _{2}$ the surface charge on the outer surface and $Q_{2}$ net charge on it
then:
A block of mass $m= 10\, kg$ rests on a horizontal table. The coefficient of friction between the block and the
table is $0. 05$ . When hit by a bullet of mass $50\,g$ moving with speed $v$ , that gets embedded in it, the block moves
and comes to stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$
after being dropped from height $H$ , then neglecting energy losses and taking $g= 10\,m\,s^{-2}$ , the value of $H$ is
close to
a.
$0. 2\, km$ .
b.
$0. 5\, km$ .
c.
$0. 4\, km$ .
d.
None of these.
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A simple harmonic oscillator of angular frequency $2\, rad \,s^{-1}$ is acted upon by an external force $F = sint N .\,$
If the oscillator is at rest in its equilibrium position at $t= 0,$ its position at later times is proportional to:
a.
$sint+ \frac{1}{2}cos 2t$
b.
$cost- \frac{1}{2}sin 2t$
c.
$sint- \frac{1}{2}sin 2t$
d.
$sint+ \frac{1}{2} sin 2t$
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A block of mass $m= 0.1\, kg$ is connected to a spring of unknown spring constant k. It is compressed to a
distance $x$ from its equilibrium position and released from rest. After approaching half the distance $(\frac{x}{2})$ from
the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with
velocity $\,3\,m\,s^{-1}$ . The total initial energy of the spring is:
a.
$0 .6 \,J$
b.
$0 .8 \,J$
c.
$1 .5 \,J$
d.
$0 .3 \,J$
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If two glass plates have water between them and are separated by very small distance (see figure), it is very
difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives
rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and
surface tension of water is T then the pressure in water between the plates is lower by:
a.
$\frac{T}{R}$
b.
$\frac{T}{4R}$
c.
$\frac{4T}{R}$
d.
$\frac{2T}{R}$
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Suppose the drift velocity $v_{d}$ in a material varied with the applied electric field E as $v_{d} \propto \sqrt{E}$ . Then $V - I$
graph for a wire made of such a material is best given by:
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The heat of atomization of methane and ethane are $360\, kJ \, mol^{-1}$ and $620\, kJ \, mol^{-1}$ , respectively. The
longest wavelength of light capable of breaking the $C -C$ bond is (Avogadro's number
$= 6.023 \times 10^{23}, \,h = 6.62 \times 10^{-34}\,J\,s$ )
a.
$2.48 \times 10^{4}\,\,nm$
b.
$1.49 \times 10^{4}\,\,nm$
c.
$2.48 \times 10^{3}\,\,nm$
d.
$1.49 \times 10^{3}\,\,nm$
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A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed.
The dried sample weighed 52 g. The formula of the hydrated salt is: (atomic mass, Ba = 137 amu, Cl = 35.5
amu)
a.
$BaCl_{2}\cdot H_{2}O$
b.
$BaCl_{2}\cdot 3H_{2}O$
c.
$BaCl_{2}\cdot 4H_{2}O$
d.
$BaCl_{2}\cdot 2H_{2}O$
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After understanding the assertion and reason, choose the correct option.
Assertion: In the bonding molecular orbital (MO) of $H_{2},$ electron density is increased between the nuclei.
Reason:The bonding MO is ψ $_{A}+$ ψ $_{B}$ , which shows destructive interference of the combining electron
waves.
a.
Assertion and Reason are correct, but Reason is
not the correct explanation for the Assertion.
b.
Assertion and Reason are correct and Reason is
the correct explanation for the Assertion.
c.
Assertion is incorrect, Reason is correct.
d.
Assertion is correct, Reason is incorrect.
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The correct statement on the isomerism associated with the following complex ions.
(a) $[Ni(H_{2}O)_{5}NH_{3}]^{2+}$
(b) $[Ni(H_{2}O)_{4}(NH_{3})_{2}]^{2+}$ and
(c) $[Ni(H_{2}O)_{3}(NH_{3})_{3}]^{2+}$ is:
a.
(a) and (b) show only geometrical isomerism
b.
(a) and (b) show geometrical and optical
isomerism
c.
(b) and (c) show geometrical and optical
isomerism
d.
(b) and (c) show only geometrical isomerism
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A variable, the opposite external potential $(E_{ext})$ is applied to the cell $Zn\, \,Zn^{2+}\,(1M) \parallel Cu^{2+}\,(1\,M) Cu$ , of
potential $1. 1\,V$ . When $E_{ext} < 1.1\,V$ and $E_{ext} > 1.1\,V$ , respectively electrons flow from
a.
anode to cathode in both the cases.
b.
anode to cathode and cathode to anode.
c.
cathode to anode and anode to cathode.
d.
cathode to anode in both cases.
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An aqueous solution of a salt X turns blood red on treatment with $SCN^{-}$ and blue on treatment with
$K_{4}[Fe(CN)_{6}]$ , X also gives a positive chromyl chloride test. The salt X is:
a.
$FeCl_{3}$
b.
$Fe(NO_{3})_{3}$
c.
$CuCl_{2}$
d.
$Cu(NO_{3})_{2}$
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Gaseous $N_{2}O_{4}$ dissociates into gaseous $NO_{2}$ according to the reaction $N_{2}O_{4}(g) \rightleftharpoons 2NO_{2}(g)$
At $300\,K$ and $1\, atm$ pressure, the degree of dissociation of $N_{2}O_{4}$ is $0. 2$ . If one mole of $N_{2}O_{4}$ gas is contained
in a vessel, then the density of the equilibrium mixture is $:$
a.
$3. 11\,g/L$
b.
$1. 56\,g/L$
c.
$4. 56\,g/L$
d.
$6. 22\,g/L$
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In the presence of a small amount of phosphorous, aliphatic carboxylic acid reacts with chlorine or bromine to
yield a reaction in which, $\alpha$ $-$ hydrogen is been replaced by halogen. This reaction is known as
a.
Etard reaction
b.
Wolff-Kischner reaction
c.
Rosenmund reaction
d.
Hell-volhard-zelinsky reaction
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A solution at $20^{o}C$ is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure
benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr respectively, then the total vapour
pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively:
a.
30.5 torr and 0.389
b.
35.0 torr and 0.480
c.
38.0 torr and 0.589
d.
35.8 torr and 0.280
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The reaction $2N_{2}O_{5}(g) \rightarrow 4NO\rightarrow_{2}(g) + O_{2}(g)$ follows first order kinetics. The pressure of a vessel containing
only $N_{2}O_{5}$ was found to increase from 50 mm Hg to 87.5 mm Hg in 30 min. The pressure exerted by the gases
after 60 min. Will be (Assume temperature remains constant) :
a.
106.25 mm Hg
b.
125 mm Hg
c.
116.25 mm Hg
d.
150 mm Hg
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Match the polymers in column-Awith their main uses in column-Band choose the correct answer:
Column - A Column - B
A. Polystyrene i. Paints and lacquers
B. Glyptal ii. Rain coats
C. Polyvinyl chloride iii. Manufacture of toys
D. Bakelite iv. Computer discs
a.
A - iii , B - i , C - ii , D - iv
b.
A - ii , B - i , C - iii , D - iv
c.
A - ii , B - iv , C - iii , D - i
d.
A - iii , B - iv , C - ii , D - i
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1.4 g of an organic compound was digested according to Kjeldahl's method and the ammonia evolved was
absorbed in 60 mL of M/10 $H_{2}SO_{4}$ solution. The excess sulphuric acid required 20 mL of M/10 NaOH
solution for neutralization. The percentage of nitrogen in the compound is:
a.
24
b.
3
c.
5
d.
10
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A compound $A$ with molecular formula $C_{10}H_{13}Cl$ , gives a white precipitate on adding silver nitrate solution.
$A$ on reacting with alcoholic $KOH$ gives compound $B$ as the main product. $B$ on ozonolysis, gives $C$ and $D$ . $C$
gives Cannizaro reaction, but not aldol condensation. $D$ gives aldol condensation, but not Cannizaro reaction.
$A$ is
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Let the sum of the first three terms of an A.P. be $39$ and the sum of its last four terms be $178$ . If the first term of
this A.P. is $10,$ then the median of the A.P. is :
a.
$26. 5$
b.
$29. 5$
c.
$28$
d.
$31$
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Let the tangents drawn to the circle, $x^{2} +y^{2} = 16$ from the point $P(0,h)$ meet the $x$ -axis at points $A$ and $B$ . If
the area of $\Delta APB$ is minimum, then positive value of $h$ is:
a.
$4\sqrt{2}$
b.
$3\sqrt{2}$
c.
$4\sqrt{3}$
d.
$3\sqrt{3}$
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If the shortest distance between the line $\frac{x-1}{\alpha} = \frac{y+1}{-1} = \frac{z}{1}, (\alpha \neq -1)\,$ , and
$x+y+z+ 1 = 0 = 2x- y+z+ 3\,$ is $\frac{1}{\sqrt{3}}$ ,then value of $\alpha$ is :
a.
$-\frac{19}{16}$
b.
$\frac{32}{19}$
c.
$-\frac{16}{19}$
d.
$\frac{19}{32}$
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If the tangent to the conic, $y-6 =x^{2}$ at $(2, 10)$ touches the circle, $x^{2} +y^{2} + 8x-2y=k$ (for some fixed $k$ )
at a point $(\alpha , \,\beta );$ then $(\alpha , \,\beta )$ is
a.
$(-\frac{7}{17}, \,\frac{6}{17})$
b.
$(-\frac{8}{17}, \,\frac{2}{17})$
c.
$(-\frac{6}{17}, \,\frac{10}{17})$
d.
$(-\frac{4}{17}, \frac{1}{17} )$
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If the coefficient of the three successive terms in the binomial expansion of $(1 +x)^{n}$ are in the ratio $1 : 7 : 42$ ,
then the first of these terms in the expansion is
a.
$9^{th}$
b.
$6^{th}$
c.
$8^{th}$
d.
$7^{th}$
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Let $L$ be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate
axes is bisected at $P$ . If $L_{1}$ is the line perpendicular to $L$ and passing through the point $(-2, \,1)$ , then the point
of intersection of $L$ and $L_{1}$ is
a.
$(\frac{3}{5} , \frac{23}{10})$
b.
$(\frac{4}{5}, \frac{12}{5})$
c.
$(\frac{11}{20}, \frac{29}{10})$
d.
$(\frac{3}{10}, \frac{17}{5})$
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In a certain town, $25%$ of the families own a phone and $15%$ own a car; $65%$ families own neither a phone nor
a car and $2000$ families own both a car and a phone. Consider the following three statements:
$(i) 5%$ families own both a car and a phone.
$(ii) 35%$ families own either a car or a phone.
$(iii) 40000$ families live in the town.
Then,
a.
Only $(ii)$ and $(iii)$ are correct
b.
Only $(i)$ and $(ii)$ are correct
c.
All $(i), \,(ii)$ and $(iii)$ are correct
d.
Only $(i)$ and $(iii)$ are correct
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The largest value of $r$ , for which the region represented by the set ${\omega \in C||\omega -4 - i| \leq r}$ is contained in the
region represented by the set ${z\in C||z-1| \leq |z+i|}$ , is equal to :
a.
$2\sqrt{2}$
b.
$\frac{3}{2}\sqrt{2}$
c.
$\sqrt{17}$
d.
$\frac{5}{2}\sqrt{2}$
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Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a}+ \vec{b} = \sqrt{3}$ . If $\vec{c}= \vec{a}+ 2\vec{b}+(\vec{a}\times \vec{b})$ , then $2 \vec{c}$ is equal to:
a.
$\sqrt{51}$
b.
$\sqrt{37}$
c.
$\sqrt{43}$
d.
$\sqrt{55}$
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A factory is operating in two shifts, day and night, with $70$ and $30$ workers, respectively.If per day mean wage
of the day shift workers is, ₹ $54$ and per day mean wage of all the workers is ₹ $60$ , then per day mean wage of
the night shift workers (in ) is :₹
a.
$75$
b.
$74$
c.
$69$
d.
$66$
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If $y\,(x)$ is the solution of the differential equation $(x+ 2) \frac{dy}{dx} =x^{2}+ 4x-9, \,\,x\, \neq \, -2\,$ and $y(0) = 0,$ then
$y(-4)$ is equal to
a.
$-1$
b.
$1$
c.
$0$
d.
$2$
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Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from
$P(X)$ , with replacement, then the probability that $A$ and $B$ have equal number of elements is:
a.
$\frac{(2^{10}-1)}{2^{20}}$
b.
$\frac{^{20}C_{10}}{2^{20}}$
c.
$\frac{^{20}C_{10}}{2^{10}}$
d.
$\frac{(2^{10}-1)}{2^{10}}$
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An ellipse passes through the foci of the hyperbola, $9x^{2} -4y^{2} = 36$ and its major and minor axes lie along the
transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is
$\frac{1}{2},$ then which of the following points does not lie on the ellipse?
a.
$(\frac{\sqrt{39}}{2}, \,\sqrt{3})$
b.
$(\frac{\sqrt{13}}{2}, \,\frac{\sqrt{3}}{2})$
c.
$(\sqrt{\frac{13}{2}}, \,\sqrt{6})$
d.
$(\sqrt{13}, \,0)$
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If the points $(1, \,1, \,\lambda )\,&\,(-3, \,0, \,1)$ , are equidistant from the plane, $3x+ 4y-12z+ 13 = 0,$ then $\lambda$ satisfies
the equation:
a.
$3x^{2} + 10x+ 7 = 0$
b.
$3x^{2} + 10x-13 = 0$
c.
$3x^{2} -10x+ 7 = 0$
d.
$3x^{2} -10x+ 21 = 0$
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The least value of the product $xyz$ (such that $x,y\,and\,z$ are positive real numbers) for which the determinant
$x 1 1$
$1 y 1$ is non-negative is
$1 1 z$
a.
$-1$
b.
$-16\sqrt{2}$
c.
$-8$
d.
$-2\sqrt{2}$
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