A freshly prepared radioactive source of half life 2hours 30minutes emits radiation which is 64times the
permissible safe level. The minimum time, after which it would be possible to work safely with source, will be
_____ hours.
✓ Accepted Answer:15
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Q2mcq
Two capacitors, each having capacitance 40πFare connected in series. The space between one of the
capacitors is filled with dielectric material of dielectric constant πΎsuch that the equivalence capacitance of the
system became 24πF. The value of πΎwill be :
a.
1 . 5
Correct Answer
b.
2 . 5
c.
1 . 2
d.
3
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Q3mcq
As shown in the figure, a metallic rod of linear density 0 . 45 kg m $^{-1}$ is lying horizontally on a smooth
incline plane which makes an angle of 45$^{\circ}$with the horizontal. The minimum current flowing in the rod
required to keep it stationary, when 0 . 15 Tmagnetic field is acting on it in the vertical upward direction, will
be
(Use π= 10 m s $^{-2}$ )
a.
30 A
Correct Answer
b.
15 A
c.
10 A
d.
3 A
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Q4nat
Two electric dipoles of dipole moments 1 . 2 $\times$ 10 $^{-30}$ cmand 2 . 4 $\times$ 10 $^{-30}$ cmare placed in two difference
uniform electric fields of strengths 5 $\times$ 10 $^{4}$ N C $^{-1}$ and 15 $\times$ 10 $^{4}$ N C $^{-1}$ respectively. The ratio of maximum
torque experienced by the electric dipoles will be $\frac{1}{π₯}$ . The value of π₯is _____ .
✓ Accepted Answer:6
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Q5nat
The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{$\sqrt{\,}$2}$ times its maximum value,
are 212 rad s $^{-1}$ and 232 rad s $^{-1}$ . The value of resistance in the circuit is π = 5 $\Omega$. The self inductance in
the circuit is _____ mH.
✓ Accepted Answer:250
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Q6mcq
The equation π= $\frac{1 . 227}{x}$ nmcan be used to find the de-Broglie wavelength of an electron. In this equation π₯
stands for :
Where,
π= mass of electron
π=momentum of electron
πΎ= Kinetic energy of electron
π= Accelerating potential in volts for electron
a.
$\sqrt$ππΎ
b.
$\sqrt$π
c.
$\sqrt$πΎ
d.
$\sqrt$π
Correct Answer
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Q7nat
In a Young's double slit experiment, a laser light of 560 nmproduces an interference pattern with consecutive
bright fringes' separation of 7 . 2 mm. Now another light is used to produce an interference pattern with
consecutive bright fringes' separation of 8 . 1 mm. The wavelength of second light is _____ nm .
✓ Accepted Answer:630
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Q8nat
The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density $1750
\mathrm{~kg} / \mathrm{m}^3$ at the rate of $0.35 \mathrm{~cm} / \mathrm{s}$. Coefficient of viscosity of
the solution is ______ (Assume mass of the bubble to be negligible) (Answer in Poise to the nearest integer)
✓ Accepted Answer:11
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Q9nat
A block of mass 'π' (as shown in figure) moving with kinetic energy πΈcompresses a spring through a distance
25 cmwhen, its speed is halved. The value of spring constant of used spring will be ππΈ N m $^{-1}$ for π=
_____.
✓ Accepted Answer:24
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Q10mcq
A balloon has mass of 10 gin air. The air escapes from the balloon at a uniform rate with velocity
4 . 5 cm s $^{-1}$ . If the balloon shrinks in 5 scompletely. Then, the average force acting on that balloon will be
(in dyne).
a.
3
b.
9
Correct Answer
c.
12
d.
18
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A NCC parade is going at a uniform speed of 9 km h $^{-1}$ under a mango tree on which a monkey is sitting at a
height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose
distance from the tree at time of drop is :
(Given π= 9 . 8 m s $^{-2}$ )
a.
5 m
b.
10 m
c.
19 . 8 m
d.
24 . 5 m
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As shown in the figure, a potentiometer wire of resistance 20 $\Omega$and length 300 cmis connected with
resistance box (R.B.) and a standard cell of emf 4 V. For a resistance 'π ' of resistance box introduced into the
circuit, the null point for a cell of 20 mVis found to be 60 cm. The value of 'π ' is _____ $\Omega$.
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A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40$^{\circ}$C, its efficiency increases
by 30%. The temperature of the source will be :
a.
166 . 7 K
b.
255 . 1 K
c.
266 . 7 K
d.
367 . 7 K
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The force required to stretch a wire of cross-section 1 cm $^{2}$ to double its length will be :
(Given Yong's modulus of the wire = 2 $\times$ 10 $^{11}$ N m $^{-2}$ )
a.
1 $\times$ 10 $^{7}$ N
b.
1 . 5 $\times$ 10 $^{7}$ N
c.
2 $\times$ 10 $^{7}$ N
d.
2 . 5 $\times$ 10 $^{7}$ N
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As shown in the figure, after passing through the medium 1. The speed of light π£ $_{2}$ in medium 2will be :
(Given π= 3 $\times$ 10 $^{8}$ m s $^{-1}$ )
a.
1 . 0 $\times$ 10 $^{8}$ m s $^{-1}$
b.
0 . 5 $\times$ 10 $^{8}$ m s $^{-1}$
c.
1 . 5 $\times$ 10 $^{8}$ m s $^{-1}$
d.
3 . 0 $\times$ 10 $^{8}$ m s $^{-1}$
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In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm. The
focal length of the objective, when the angular magnification of the telescope is 2, will be:
a.
20 cm 30 cm
c.
10 cm
d.
15 cm
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The frequency of echo will be _____ Hzif the train blowing a whistle of frequency 320 Hzis moving with a
velocity of 36 km h $^{-1}$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air
is 330 m s $^{-1}$ .
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In two different experiments, an object of mass 5 kgmoving with a speed of 25 ms $^{-1}$ hits two different walls
and comes to rest within
(i) 3second, (ii) 5seconds, respectively.
Choose the correct option out of the following :
a.
Impulse and average force acting on the object
will be same for both the cases.
b.
Impulse will be same for both the cases but the
average force will be different.
c.
Average force will be same for both the cases but
the impulse will be different.
d.
Average force and impulse will be different for
both the cases.
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Four identical discs each of mass 'π' and diameter 'π' are arranged in a small plane as shown in figure. If the
moment of inertia of the system about ππ $'$ is $\frac{π₯}{4}$ ππ $^{2}$ . Then, the value of π₯will be _____ .
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Given below are two statements:
Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II :The rms speed of oxygen molecules in a gas is π£. If the temperature is doubled and the oxygen
molecules dissociate into oxygen atoms, the rms speed will become 2π£.
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.
Both Statement I and Statement II are false
c.
Statement I is true but Statement II is false
d.
Statement I is false but Statement II is true
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The current sensitivity of a galvanometer can be increased by :
(A) decreasing the number of turns
(B) increasing the magnetic field
(C) decreasing the area of the coil
(D) decreasing the torsional constant of the spring
Choose the most appropriate answer from the options given below :
a.
(B) and (C) only
b.
(C) and (D) only
c.
(A) and (C) only
d.
(B) and (D) only
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The equation of current in a purely inductive circuit is 5sin49ππ‘- 30$^{\circ}$. If the inductance is 30mHthen the
equation for the voltage across the inductor, will be
a.
1 . 47sin49ππ‘- 30$^{\circ}$
b.
1 . 47sin49ππ‘+ 60$^{\circ}$
c.
23 . 1sin49ππ‘- 30$^{\circ}$
d.
23 . 1sin49ππ‘+ 60$^{\circ}$
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A wire of resistance π $_{1}$ $R_{1}$ is drawn out so that its length is increased by twice of its original length. The
ratio of new resistance to original resistance is:
a.
9: 1
b.
1: 9
c.
4: 1
d.
3: 1
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In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or
identical?
(A) Rband Cs
(B) Na and K
(C) Arand Kr
(D) Iand At
Choose the correct answer from the options given below
a.
A & Bonly
b.
B & Conly
c.
A & Conly
d.
C & Donly
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Statements about Enzyme Inhibitor Drugs are given below :
(A) There are Competitive and Non-competitive inhibitor drugs.
(B) These can bind at the active sites and allosteric sites.
(C) Competitive Drugs are allosteric site blocking drugs.
(D) Non-competitive Drugs are active site blocking drugs.
Choose the correct answer from the options given below
a.
A, Donly
b.
A, Conly
c.
A, Bonly
d.
A, B, Conly
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Match List-I with List-II.
List-I List-II
A Cds + 2NiOH $_{3}$ s $\rightarrow$CdOs + 2NiOH $_{2}$ s + H $_{2}$ Ol I Primary battery
Discharging of secondary
BZnHg + HgOs $\rightarrow$ZnOs + Hgl II
battery
C2PbSO $_{4}$ s + 2H $_{2}$ OI $\rightarrow$Pbs + PbO $_{2}$ s + 2H $_{2}$ SO $_{4}$ aq III Fuel cell
Charging of secondary
D 2H $_{2}$ g + O $_{2}$ g $\rightarrow$2H $_{2}$ Ol IV
battery
Choose the correct answer from the options given below
a.
A - I, B - II, C - III, C - IV
b.
A - IV, B - I, C - IV, C - III
c.
A - II, B - I, C - IV, C - III
d.
A - II, B - I, C - III, C - IV
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In the given reaction,
X + Y + 3Z βXYZ $_{3}$
if one mole of each of Xand Ywith 0 . 05 molof Zgives compound XYZ $_{3}$ . (Given : Atomic masses of X, Y
and Zare 10,20 and 30amu, respectively). The yield of XYZ $_{3}$ is____g.
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Match List-I with List-II, match the gas evolved during each reaction.
List-I List-II
π₯
A I H
NH $_{42}$ Cr $_{2}$ O $_{7}$ $\longrightarrow$ $^{2}$
B KMnO $_{4}$ + HCl $\rightarrow$ II N $_{2}$
C Al + NaOH + H $_{2}$ O $\rightarrow$ III O $_{2}$
$\Delta$
D IV Cl
NaNO $_{3}$ $\longrightarrow$ 2
Choose the correct answer from the options given below
a.
A - II, B - III, C - I, D - IV
b.
A - III, B - I, C - IV, D - II
c.
A - II, B - IV, C - I, D - III
d.
A - III, B - IV, C - I, D - II
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Match List-I with List-II.
List-I List-II
A4NH $_{3}$ g + 5O $_{2}$ g $\rightarrow$4NOg + 6H $_{2}$ Og I NOg
BN $_{2}$ g + 3H $_{2}$ g $\rightarrow$2NH $_{3}$ g II H $_{2}$ SO $_{4}$ l
CC $_{12}$ H $_{22}$ O $_{11}$ aq + H $_{2}$ Ol $\rightarrow$C $_{6}$ H $_{12}$ O $_{6}$ Glucose + C $_{6}$ H $_{12}$ O $_{6}$ Fructose III Pts
D2SO $_{2}$ g + O $_{2}$ g $\rightarrow$2SO $_{3}$ g IVFes
Choose the correct answer from the options given below
a.
A - II, B - III, C - I, D - IV
b.
A - III, B - II, C - I, D - IV
c.
A - III, B - IV, C - II, D - I A - III, B - II, C - IV, D - I
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Match List-I with List-II.
List-I List-II
A I Spiro compound
B II Aromatic compound
C III Non-planar Heterocyclic compound
D IV Bicyclo compound
Choose the correct answer from the options given below
a.
A - II, B - I, C - IV, D - III
b.
A - IV, B - III, C - I, D - II
c.
A - III, B - IV, C - I, D - II
d.
A - IV, B - III, C - II, D - I
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The number of inter halogens from the following having square pyramidal structure is
ClF $_{3}$ , IF $_{7}$ , BrF $_{5}$ , BrF $_{3}$ , I $_{2}$ Cl $_{6}$ , IF $_{5}$ , ClF, ClF $_{5}$
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An element Mcrystallises in a body centred cubic unit cell with a cell edge of 300pm. The density of the
element is 6 . 0 g cm $^{-3}$ . The number of atoms present in 180 gof the element is____$\times$ 10 $^{23}$ . (Nearest
integer)
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Given below are two statements :
Statement I : In polluted water values of both dissolved oxygen and BODare very low.
Statement II : Eutrophication results in decrease in the amount of dissolved oxygen.
In the light of the above statements, choose the most appropriate answer from the options given below
a.
Both Statement I and Statement II are true
b.
Both Statement I and Statement II are false
c.
Statement I is true but Statement II is false
d.
Statement I is false but Statement II is true
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On complete combustion of 0 . 492 gof an organic compound containing C, Hand O, 0 . 7938 gof CO $_{2}$ and
0 . 4428 gof H $_{2}$ Owas produced. The %composition of oxygen in the compound is____. (Nearest Integer)
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For kinetic study of the reaction of iodide ion with H $_{2}$ O $_{2}$ at room temperature :
(A) Always use freshly prepared starch solution.
(B) Always keep the concentration of sodium thiosulphate solution less than that of KIsolution.
(C) Record the time immediately after the appearance of blue colour.
(D) Record the time immediately before the appearance of blue colour.
(E) Always keep the concentration of sodium thiosulphate solution more than that of KIsolution.
Choose the correct answer from the options given below
a.
A, B, Conly
b.
A, D, Eonly
c.
D, Eobly
d.
A, B, Eonly
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150 gof acetic acid was contaminated with 10 . 2 gascorbic acid C $_{6}$ H $_{8}$ O $_{6}$ to lower down its freezing point
by x $\times$ 10 $^{-1}$ $^{\circ}$C. The value of xis____ (Nearest integer). [Given K $_{f}$ = 3 . 9 K kg mol $^{-1}$ ; Molar mass of
ascorbic acid = 176 g mol $^{-1}$ ]
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For the given first order reaction A $\rightarrow$Bthe half life of the reaction is 0 . 3010 min. The ratio of the initial
concentration of reactant to the concentration of reactant at time 2 . 0 minwill be equal to _____. (Nearest
integer)
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The number of paramagnetic species among the following is B $_{2}$ , Li $_{2}$ , C $_{2}$ , C $^{-}_{2}$ , O $^{2 -}_{2}$ , O $^{+}_{2}$ and He $^{+}_{2}$
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The disproportionation of MnO $^{2 -}_{4}$ in acidic medium resulted in the formation of two manganese compounds A
and B. If the oxidation state of Mnin Bis smaller than that of A, then the spin-only magnetic moment $\mu$value
of Bin BMis____ . (Nearest integer)
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Let πΆbe the centre of the circle π₯ $^{2}$ + π¦ $^{2}$ - π₯+ 2π¦= $\frac{11}{4}$ and πbe a point on the circle. A line passes through the
point πΆ, makes an angle of $\frac{π}{4}$ with the line πΆπand intersects the circle at the points πand π . Then the area of
the triangle πππ (in unit $^{2}$ ) is
a.
2
b.
2$\sqrt$2
c.
8sin $\frac{π}{8}$
d.
8cos $\frac{π}{8}$
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Let the solution curve of the differential equation π₯ππ¦= $\sqrt$π₯ $^{2}$ + π¦ $^{2}$ + π¦ππ₯, π₯> 0, intersect the line x = 1at
π¦= 0and the line π₯= 2at π¦= πΌ. Then the value of πΌis
a.
$\frac{1}{2}$
b.
$\frac{3}{2}$
c.
- $\frac{3}{2}$
d.
$\frac{5}{2}$
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Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the
equation cos $^{-1}$ π₯- 2sin $^{-1}$ π₯= cos $^{-1}$ 2π₯is equal to
a.
0
b.
1
c.
$\frac{1}{2}$
d.
- $\frac{1}{2}$
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Out of 60%female and 40%male candidates appearing in an exam, 60%candidates qualify it. The number of
females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from
the qualified candidates. The probability, that the chosen candidate is a female, is
a.
$\frac{2}{3} \frac{11}{16}$
c.
$\frac{23}{32}$
d.
$\frac{13}{16}$
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For π, π$\in$π , consider the real valued function ππ₯= π₯- π $^{2}$ - π, π₯$\in$π and π> 0. Let π $_{1}$ , π $_{2}$ , π $_{3}$ and π $_{4}$ be in an
arithmetic progression with mean πand positive common difference. If ππ $_{π}$ = 500for all π= 1, 2, 3, 4, then
the absolute difference between the roots of ππ₯= 0is
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Considering only the principal values of the inverse trigonometric functions, the domain of the function
ππ₯= cos $\frac{-1 π₯2- 4π₯+ 2}{π₯2+ 3}$ is
a.
- $\infty$, $\frac{1}{4}$
b.
- $\frac{1}{4}$ , $\infty$
c.
- $\frac{1}{3}$ , $\infty$
d.
- $\infty$, $\frac{1}{3}$
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If π¦= π¦π₯, π₯$\in$0, $\frac{π}{2}$ be the solution curve of the differential equation
sin $^{2}$ 2π₯ $\frac{ππ¦}{ππ₯}$ + 8sin $^{2}$ 2π₯+ 2sin4π₯π¦=
2π $^{-4π₯}$ 2sin2π₯+ cos2π₯,with π¦ $\frac{π}{4}$ = π $^{-π}$ , then π¦ $\frac{π}{6}$ is equal to
The foot of the perpendicular from a point on the circle π₯ $^{2}$ + π¦ $^{2}$ = 1, π§= 0to the plane 2π₯+ 3π¦+ π§= 6lies
on which one of the following curves?
Let πbe the set of all passwords which are six to eight characters long, where each character is either an
alphabet from π΄, π΅, πΆ, π·, πΈor a number from 1, 2, 3, 4, 5with the repetition of characters allowed. If the number
of passwords in πwhose at least one character is a number from 1, 2, 3, 4, 5is πΌ$\times$ 5 $^{6}$ , then πΌis equal to
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Let π-2, - 1, 1and π $\frac{56}{17}$ , $\frac{43}{17}$ , $\frac{111}{17}$ be the vertices of the rhombus ππ ππ. If the direction ratios of the diagonal π π
are πΌ, - 1, π½, where both πΌand $\beta$ are integers of minimum absolute values, then πΌ $^{2}$ + π½ $^{2}$ is equal to
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The minimum value of the twice differentiable function ππ₯= $\int$ $^{π₯}_{0}$ π $^{π₯- π‘}$ π $'$ π‘ππ‘- π₯ $^{2}$ - π₯+ 1π $^{π₯}$ , π₯$\in$π , is
a.
- $\frac{2}{$\sqrt{\,}$π}$
b.
-2$\sqrt$π
c.
-$\sqrt$π
d.
$\frac{2}{π}$
$\sqrt$
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For the hyperbola π»: π₯ $^{2}$ - π¦ $^{2}$ = 1and the ellipse πΈ: $\frac{π₯2}{π2}$ + $\frac{π¦2}{π2}$ = 1, π> π> 0, let the
(1) eccentricity of $\frac{πΈ}{5}$ be reciprocal of the eccentricity of π», and
(2) the line π¦= $\sqrt$ $_{2}$ π₯+ πΎbe a common tangent of πΈand π».
Then 4π $^{2}$ + π $^{2}$ is equal to
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For π‘$\in$0, 2π, if π΄π΅πΆis an equilateral triangle with vertices π΄sinπ‘, - cosπ‘, π΅cosπ‘, sinπ‘and πΆπ, πsuch that its
orthocentre lies on a circle with centre 1, $\frac{1}{3}$ , then π $^{2}$ - π $^{2}$ is equal to
a.
$\frac{8}{3}$
b.
8
c.
$\frac{77}{9}$
d.
$\frac{80}{9}$
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0 1 0
Let the matrix π΄= 1 0 0 and the matrix π΅ $_{0}$ = π΄ $^{49}$ + 2π΄ $^{98}$ . If π΅ $_{π}$ = Adjπ΅ $_{π- 1}$ for all π$\geq$1, then det π΅ $_{4}$ is
0 0 1
equal to
a.
3 $^{28}$
b.
3 $^{30}$
c.
3 $^{32}$
d.
3 $^{36}$
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For πΌ$\in$π, consider a relation π on πgiven by π ={π₯, π¦: 3π₯+ πΌπ¦is a multiple of 7}. The relation π is an
equivalence relation if and only if
a.
πΌ= 14
b.
πΌis a multiple of 4
c.
4is the remainder when πΌis divided by 10
d.
4is the remainder when πΌis divided by 7
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If the tangents drawn at the points πand πon the parabola π¦ $^{2}$ = 2π₯- 3intersect at the point π 0, 1, then the
orthocentre of the triangle πππ is
a.
0, 1
b.
2, - 1
c.
6, 3
d.
2, 1
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Let π₯ $_{1}$ , π₯ $_{2}$ , π₯ $_{3}$ , β¦ . . , π₯ $_{20}$ be in geometric progression with π₯ $_{1}$ = 3and the common ration $\frac{1}{2}$ . A new data is
constructed replacing each π₯ $_{π}$ by π₯ $_{π}$ - π $^{2}$ . If π₯is the mean of new data, then the greatest integer less than or equal
to π₯is
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Let a vector $^{$\rightarrow$}$ πhas a magnitude 9. Let a vector $^{$\rightarrow$}$ πbe such that for every π₯, π¦π $\times$ π - 0, 0, the vector π₯ $^{$\rightarrow$}$ π+ π¦ $^{$\rightarrow$}$ πis
perpendicular to the vector 6π¦ $^{$\rightarrow$}$ π- 18π₯ $^{$\rightarrow$}$ π. Then the value of $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ πis equal to
a.
9$\sqrt$3
b.
27$\sqrt$3
c.
9
d.
81
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Let π: 0, 1 $\rightarrow$π be a twice differentiable function in 0, 1such that π0 = 3and π1 = 5. If the line π¦= 2π₯+ 3
intersects the graph of πat only two distinct points in 0, 1, then the least number of points π₯$\in$0, 1, at which
π $''$ π₯= 0, is
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1 -1 π½1 $_{2}_{2}$ 2 2
Let π΄= and π΅= , πΌ, π½$\in$π . Let πΌ $_{1}$ be the value of πΌwhich satisfies π΄+ π΅ = π΄ + and
2 πΌ 1 0 2 2
πΌ $_{2}$ be the value of πΌwhich satisfies π΄+ π΅ $^{2}$ = π΅ $^{2}$ . Then πΌ $_{1}$ - πΌ $_{2}$ is equal to
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Let πΌ, π½and πΎbe three positive real numbers. Let ππ₯= πΌx $^{5}$ + π½x $^{3}$ + πΎx, x $\in$Rand π: π $\rightarrow$π be such that
πππ₯= π₯for all π₯$\in$π . If π $_{1}$ , π $_{2}$ , π $_{3}$ , β¦ , π $_{π}$ be in arithmetic progression with mean zero, then the value of
ππ $\frac{1}{π}$ $\sum$ $^{π}_{π= 1}$ ππ $_{π}$ is equal to
a.
0
b.
3
c.
9
d.
27
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