The interference pattern is obtained with two coherent light sources of intensity ratio 4: 1. And the ratio
$\frac{πΌmax+ πΌmin}{πΌmax- πΌmin}$ is $\frac{5}{π₯}$ . Then, the value of π₯will be equal to :
a.
3
b.
4
Correct Answer
c.
2
d.
1
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Q2mcq
The ratio of specific heats $\frac{πΆπ}{πΆπ}$ in terms of degree of freedom πis given by :
a.
1 + $\frac{π}{3}$
b.
1 + $\frac{2}{π}$
Correct Answer
c.
1 + $\frac{π}{2}$
d.
1 + $\frac{1}{π}$
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Q3mcq
$\rightarrow$
For a particle in uniform circular motion, the acceleration π at any point ππ , πon the circular path of radius π
is (when πis measured from the positive π₯-axis and π£is uniform speed):
- $\frac{π£2}{π }^{^}$ i + $\frac{π£2}{π }^{^}$ j
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Q4mcq
A proton, a neutron, an electron and an πΌ-particle have same energy. If π $_{π}$ , π $_{π}$ , π $_{π}$ and π $_{πΌ}$ are the de Broglie's
wavelengths of proton, neutron, electron and πΌparticle respectively, then choose the correct relation from the
following
27identical drops are charged at 22 Veach. They combine to form a bigger drop. The potential of the bigger
drop will be _____ V.
✓ Accepted Answer:198
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Q6nat
The length of a given cylindrical wire is increased to double of its original length. The percentage increase in
the resistance of the wire will be _____ %
✓ Accepted Answer:300
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Q7mcq
If πrepresents the actual number of deflections in a converted galvanometer of resistance πΊand shunt
resistance π. Then the total current πΌwhen its figure of merit is πΎwill be
a.
$\frac{πΎπ}{π+ πΊ}$
b.
$\frac{πΊ+ π}{ππΎπ}$
c.
$\frac{ππΎπ}{πΊ+ π}$
d.
$\frac{ππΎπΊ+ π}{π}$
Correct Answer
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Q8mcq
Which of the following figure represents the variation of ln $\frac{π }{π 0}$ with lnπ΄(if π =radius of a nucleus and π΄=
its mass number)
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Q9mcq
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A:Two identical balls π΄and π΅thrown with same velocity 'π’' at two different angles with horizontal
attained the same range π . If A and π΅reached the maximum height β $_{1}$ and β $_{2}$ respectively, then π = 4$\sqrt$β $_{1}$ β $_{2}$
Reason R:Product of said heights. β $_{1}$ β $_{2}$ = $\frac{π’2sin2π}{2π}$ Β· $\frac{π’2cos2π}{2π}$
a.
Both A and R are true and R is the correct
explanation of A.
Correct Answer
b.
Both A and R are true but R is NOT the correct
explanation of A.
c.
A is true but R is false.
d.
A is false but R is true.
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Q10nat
Two satellites π $_{1}$ and π $_{2}$ are revolving in circular orbits around a planet with radius π $_{πΌ}$ = 3200 kmand
π $_{2}$ = 800 kmrespectively. The ratio of speed of satellite π $_{1}$ to the speed of satellite π $_{2}$ in their respective
orbits would be $\frac{1}{π₯}$ where π₯=
✓ Accepted Answer:2
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Given below are two statements :
Statement - I :Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in
temperature.
Statement - II :Diamagnetism is a result of orbital motions of electrons developing magnetic moments
opposite to the applied magnetic field.
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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A block of mass 200 gis kept stationary on a smooth inclined plane by applying a minimum horizontal force
πΉ= $\sqrt$π₯ Nas shown in figure.
The value of π₯= _____.
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Two metallic plates form a parallel plate capacitor. The distance between the plate is 'π'. A metal sheet of
thickness $\frac{π}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the
new capacitance to the original capacitance of the capacitor?
a.
1: 2
b.
2: 1
c.
1: 4
d.
4: 1
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A disc with a flat small bottom beaker placed on it at a distance π from its center is revolving about an axis
passing through the center and perpendicular to its plane with an angular velocity π. The coefficient of static
friction between the bottom of the beaker and the surface of the disc is π. The beaker will revolve with the disc
if :
Moment of Inertia (M.I.) of four bodies having same mass πand radius 2π are as follows
πΌ $_{1}$ = M.I. of solid sphere about its diameter
πΌ $_{2}$ = M.I. of solid cylinder about its axis
πΌ $_{3}$ =M.I. of solid circular disc about its diameter
πΌ $_{4}$ = M.I. of thin circular ring about its diameter
If 2πΌ $_{2}$ + πΌ $_{3}$ + πΌ $_{4}$ = π₯πΌ $_{1}$ then the value of π₯will be _____ .
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A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be
30 m s $^{-1}$ without skidding. If radius of curved road is changed to 48 mand the coefficient of friction
between the tyres and the road remains same, then maximum allowed speed would be _____ m s $^{-1}$ .
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Match List I with List II
List I List II
(A) Facsimile (I) Static Document Image
(B) Guided media Channel (II) Local Broadcast Radio
(C) Frequency Modulation (III) Rectangular wave
(D) Digital Signal (IV) Optical Fiber
Choose the correct answer from the following options
a.
A - IV, B - III, C - II, D - I
b.
A - I, B - IV, C - II, D - III
c.
A - IV, B - II, C - III, D - I
d.
A - I, B - II, C - III, D - IV
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Two cells of the same EMF πΈbut different internal resistances π $_{1}$ and π $_{2}$ are connected in series with an external
resistance π as shown in the figure. The terminal potential difference across, the second cell is found to be zero.
The external resistance π must then be:
a.
π $_{1}$ π $_{2}$
b.
π $_{1}$ - π $_{2}$
c.
π $_{2}$ - π $_{1}$
d.
π $_{1}$ + π $_{2}$
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When a gas filled in a closed vessel is heated by raising the temperature by 1$^{\circ}$C, its pressure increases by
0 . 4%The initial temperature of the gas is _____ πΎ.
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For π§= π $^{2}$ π₯ $^{3}$ π¦ $\frac{1}{2}$ , where 'π' is a constant. If percentage error in measurement of 'π₯' and 'π¦' are 4%and 12%,
respectively, then the percentage error for 'π§' will be _____%.
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A solid metallic cube having total surface area 24 m $^{2}$ is uniformly heated. If its temperature is increased by
10$^{\circ}$C, calculate the increase in volume of the cube. (Given πΌ= 5 . 0 $\times$ 10 $^{-4$\circ$}$ C $^{-1}$ ).
a.
2 . 4 $\times$ 10 $^{6}$ cm $^{3}$
b.
1 . 2 $\times$ 10 $^{5}$ cm $^{3}$
c.
6 $\times$ 10 $^{4}$ cm $^{3}$
d.
4 . 8 $\times$ 10 $^{5}$ cm $^{3}$
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In an experiment of πΆπΈconfiguration of π- π- πtransistor, the transfer characteristics are observed as given in
figure.
If the input resistance is 200$\Omega$and output resistance is 60$\Omega$, the voltage gain in this experiment will be _____ .
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Two buses πand πstart from a point at the same time and move in a straight line and their positions are
represented by π₯ $_{π}$ π‘= πΌπ‘+ π½π‘ $^{2}$ and π₯ $_{π}$ π‘= ππ‘- π‘ $^{2}$ . At what time, both the buses have same velocity ?
a.
$\frac{πΌ- π}{1 + π½}$
b.
$\frac{πΌ+ π}{2π½- 1}$
c.
$\frac{πΌ+ π}{21 + π½}$
d.
$\frac{π- πΌ}{21 + π½}$
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A long solenoid carrying a current produces a magnetic field π΅along its axis. If the current is doubled and the
number of turns per cmis halved, the new value of magnetic field will be equal to
a.
2π΅
b.
4π΅
c.
$\frac{π΅}{2}$
d.
π΅
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The electromagnetic waves travel in a medium at a speed of 2 . 0 $\times$ 10 $^{8}$ m s $^{-1}$ . The relative permeability of
the medium is 1 . 0. The relative permittivity of the medium will be
a.
2 . 25
b.
4 . 25
c.
6 . 25
d.
8 . 25
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In a series LCR circuit, the inductance, capacitance and resistance are πΏ= 100 mH, C = 100 πFand
π = 10 $\Omega$respectively. They are connected to an ACsource of voltage 220 Vand frequency of 50 Hz. The
approximate value of current in the circuit will be _____ π΄.
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A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on
the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the
prism.
a.
Reflected and refracted rays will be
perpendicular to each other.
b.
Wave will propagate along the surface of prism.
c.
No refraction, and there will be total reflection of
light.
d.
No reflection. and there will be total transmission
of light.
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A copper block of mass 5 . 0 kgis heated to a temperature of 500$^{\circ}$Cand is placed on a large ice block. What is
the maximum amount of ice that can melt?
[Specific heat of copper : 0 . 39Jg $^{-1$\circ$}$ C $^{-1}$ and latent heat of fusion of water : 335 Jg $^{-1}$ ]
a.
1 . 5 kg
b.
5 . 8 kg
c.
2 . 9 kg
d.
3 . 8 kg
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A sinusoidal voltage ππ‘= 210sin3000π‘volt is applied to a series LCR circuit in which
πΏ= 10 mH, πΆ= 25 $\mu$Fand π = 100$\Omega$. The phase difference π·between the applied voltage and resultant
current will be
a.
tan $^{-1}$ 0 . 17
b.
tan $^{-1}$ 9 . 46
c.
tan $^{-1}$ 0 . 30
d.
tan $^{-1}$ 13 . 33
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A solution of Fe $_{2}$ SO $_{43}$ is electrolyzed for 'x' min with a current of 1 . 5 Ato deposit 0 . 3482 gof Fe. The
value of xis - [nearest integer]
Given : 1 F = 96500 Cmol $^{-1}$ . Atomic mass of Fe = 56 gmol $^{-1}$
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Solute A associates in water. When 0 . 7 gof solute Ais dissolved in 42 . 0 gof water, it depresses the
freezing point by 0 . 2 $^{\circ}$C. The percentage association of solute Ain water, is
[Given: Molar mass of A = 93 g mol $^{-1}$ . Molal depression constant of water is 1 . 86 K kg mol $^{-1}$ ]
a.
50%
b.
60%
c.
70%
d.
80%
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The neutralization occurs when 10 mLof 0 . 1 Macid 'A' is allowed to react with 30 mLof 0 . 05 Mbase
MOH $_{2}$ . The basicity of the acid 'A' is
[Mis a metal]
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Given below are two statements.
Statement I: During electrolytic refining. blister copper deposits precious metals.
Statement II: In the process of obtaining pure copper by electrolysis method, copper blister is used to make the
anode.
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 correct order of reduction potentials of the following pairs is
A. Cl $_{2}$ / Cl $^{-}$
B. I $_{2}$ / I $^{-}$
C. Ag $^{+}$ / Ag
D. Na $^{+}$ / Na
E. Li $^{+}$ / Li
Choose the correct answer from the options given below.
a.
A > B > C > E > D
b.
A > C > B > E > D
c.
A > B > C > D > E
d.
A > C > B > D > E
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Given below are two statements: one is labelled as Assertion and the other is labelled as Reason.
Assertion: A mixture contains benzoic acid and napthalene. The pure benzoic acid can be separated out by the
use of benzene.
Reason: Benzoic acid is soluble in hot water.
In the light of the above statements, choose the most appropriate answer from the options given below.
a.
Both Assertion and Reason are true and Reason is
the correct explanation of Assertion.
b.
Both Assertion and Reason are true but Reason is
not the correct explanation of Assertion.
c.
Assertion is true but Reason is false.
d.
Assertion is false but Reason is true.
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A rigid nitrogen tank stored inside a laboratory has a pressure of 30atm at 06: 00am when the temperature is
27 $^{\circ}$C. At 03: 00pm, when the temperature is 45 $^{\circ}$C, the pressure in the tank will be _____ atm. [nearest
integer]
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The number of bridged oxygen atoms present in compound Bformed from the following reactions is
673 K
PbNO $_{32}$ $\longrightarrow$ A + PbO + O $_{2}$
Dimerise
A $\longrightarrow$ B
a.
0
b.
1
c.
2
d.
3
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Amongst FeCl $_{3}$ . 3H $_{2}$ O, K $_{3}$ FeCN $_{6}$ and CoNH $_{36}$ Cl $_{3}$ , the spin-only magnetic moment value of the inner-orbital
complex that absorbs light at shortest wavelength is B.M. [nearest integer]
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The minimum energy that must be possessed by photons in order to produce the photoelectric effect with
platinum metal is:
[Given: The threshold frequency of platinum is 1 . 3 $\times$ 10 $^{15}$ s $^{-1}$ and h = 6 . 6 $\times$ 10 $^{-34}$ Js]
a.
8 . 58 $\times$ 10 $^{-19}$ J
b.
9 . 76 $\times$ 10 $^{-20}$ J
c.
3 . 21 $\times$ 10 $^{-14}$ J
d.
6 . 24 $\times$ 10 $^{-16}$ J
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A protein 'A' contains 0 . 30%of glycine (molecular weight 75). The minimum molar mass of the protein 'A'
is____$\times$ 10 $^{3}$ g mol $^{-1}$ [nearest integer]
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At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55 . 5 kPawas
340 s. When the pressure was 27 . 8 kPa, the half life was found to be 170 s. The order of the reaction is -
[integer answer]
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At 25 $^{\circ}$Cand 1 atmpressure, the enthalpy of combustion of benzene 1and acetylene gare
-3268 kJ mol $^{-1}$ and -1300 kJ mol $^{-1}$ , respectively. The change in enthalpy for the reaction
3C $_{2}$ H $_{2}$ g $\rightarrow$C $_{6}$ H $_{6}$ l, is
a.
+324 kJ mol $^{-1}$
b.
+632 kJ mol $^{-1}$
c.
-632 kJ mol $^{-1}$
d.
-732 kJ mol $^{-1}$
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Given below are two statements: one is labelled as Assertion and the other is labelled as Reason.
Assertion:Polluted water may have a value of BODof the order of 17ppm.
Reason: BODis a measure of oxygen required to oxidise both the biodegradable and non-biodegradable
organic material in water.
In the light of the above statements, choose the most appropriateanswer from the options given below.
a.
Both Assertion and Reason are true and Reason is
the correct explanation of Assertion.
b.
Both Assertion and Reason are true but Reason is
NOT the correct explanation of Assertion.
c.
Assertion is true but Reason is false.
d.
Assertion is false but Reason is true.
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Let π $_{1}$ be the line in π₯π¦-plane with π₯and π¦intercepts $\frac{1}{8}$ and $\frac{1}{4$\sqrt{\,}$2}$ respectively, and π $_{2}$ be the line in π§π₯-plane
with π₯and π§intercepts - $\frac{1}{8}$ and - $\frac{1}{6$\sqrt{\,}$3}$ respectively. If πis the shortest distance between the line π $_{1}$ and π $_{2}$ , then π $^{-2}$
is equal to _____.
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Let π, π$\in$π be such that the equation ππ₯ $^{2}$ - 2ππ₯+ 15 = 0has repeated root πΌand if πΌand π½are the roots of
the equation π₯ $^{2}$ - 2ππ₯+ 21 = 0, then πΌ $^{2}$ + π½ $^{2}$ is equal to:
a.
37
b.
58
c.
68
d.
92
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If the angle made by the tangent at the point π₯ $_{0}$ , π¦ $_{0}$ on the curve π₯= 12π‘+ sinπ‘cosπ‘,
π¦= 121 + sinπ‘ $^{2}$ , 0 < π‘< $\frac{π}{2}$ , with the positive π₯-axis is $\frac{π}{3}$ , then π¦ $_{0}$ is equal to
a.
63 + 2$\sqrt$2
b.
37 + 4$\sqrt$3
c.
27
d.
48
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If the line π¦= 4 + ππ₯, π> 0, is the tangent to the parabola π¦= π₯- π₯ $^{2}$ at the point πand πis the vertex of
the parabola, then the slope of the line through πand πis
a.
$\frac{3}{2}$
b.
$\frac{26}{9}$
c.
$\frac{5}{2}$
d.
$\frac{23}{6}$
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If the mean deviation about the mean of the numbers 1, 2, 3, β¦ β¦ , π, where πis odd, is $\frac{5π+ 1}{π}$ , then πis equal
to ______.
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Let ππ₯= π₯- 1π₯ $^{2}$ - 2π₯- 3 + π₯- 3, π₯$\in$β. If πand πare respectively the number of points of local minimum
and local maximum of πin the interval 0, 4, then π+ πis equal to _____.
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If the sum of the co-efficients of all the positive even powers of π₯in the binomial expansion of 2π₯ $^{3}$ + $\frac{3}{π₯}^{10}$ is
5 $^{10}$ - π½Β· 3 $^{9}$ , then π½is equal to _____.
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Water is being filled at the rate of 1cm $^{3}$ sec $^{-1}$ in a right circular conical vessel (vertex downwards) of height
35cmand diameter 14cm. When the height of the water level is 10cm, the rate (in cm $^{2}$ sec $^{-1}$ ) at which the
wet conical surface area of the vessel increases is
a.
5
b.
$\frac{$\sqrt{\,}$21}{5}$
c.
$\frac{$\sqrt{\,}$26}{5}$
d.
$\frac{$\sqrt{\,}$26}{10}$
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Let the eccentricity of the hyperbola $\frac{π₯2}{π2}$ - $\frac{π¦2}{π2}$ = 1be $\frac{5}{4}$ . If the equation of the normal at the point $\frac{8}{$\sqrt{\,}$5}$ , $\frac{12}{5}$ on the
hyperbola is 8$\sqrt$5π₯+ π½π¦= π, then π- π½is equal to _____.
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The line π¦= π₯+ 1meets the ellipse $\frac{π₯2}{4}$ + $\frac{π¦2}{2}$ = 1at two points πand π. If πis the radius of the circle with ππ
as diameter then 3π $^{2}$ is equal to
a.
20
b.
12
c.
11
d.
8
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Let π§ $_{1}$ and π§ $_{2}$ be two complex numbers such that π§ $^{-}_{1}$ = ππ§ $^{-}_{2}$ and arg $\frac{π§1}{π§-2}$ = π, then the argument of π§ $_{1}$ is
a.
arg π§ $_{2}$ = $\frac{$\pi$}{4}$
b.
arg π§ $_{2}$ = - $\frac{3$\pi$}{4}$
c.
arg π§ $_{1}$ = $\frac{$\pi$}{4}$
d.
arg π§ $_{1}$ = - $\frac{3$\pi$}{4}$
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If π¦= π¦π₯is the solution of the differential equation 2π₯ $\frac{2ππ¦}{ππ₯}$ - 2π₯π¦+ 3π¦ $^{2}$ = 0such that π¦π= $\frac{π}{3}$ , then π¦1is equal
to
a.
$\frac{1}{3}$
b.
$\frac{2}{3}$
c.
$\frac{3}{2}$
d.
3
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$\rightarrow$ $^{^}^{^}^{^}$ $\rightarrow$πΒ· 2 $^{^}^{^}^{^}$
Let πbe the plane passing through the intersection of the planes πΒ· π+ 3π- π= 5and π- π+ π= 3, and
the point 2, 1, - 2. Let the position vectors of the points πand πbe $^{^}$ π- 2 $^{^}$ π+ 4π $^{^}$ and 5 $^{^}$ π- $^{^}$ π+ 2π $^{^}$ respectively.
Then the points
a.
πand π+ πare on the same side of π
b.
πand π- πare on the opposite sides of π
c.
πand πare on the opposite sides of π
d.
π+ πand π- πare on the same side of π
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2 -2 -1 2
Let π΄= andπ΅= . Then the number of elements in the set {π, π: π, π$\in$1, 2, β¦ β¦ . 10and
1 -1 -1 2
ππ΄ $^{π}$ + ππ΅ $^{π}$ = πΌ} is _____.
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2π₯- 3, π₯< 0
Let ππ₯= 2π₯ $^{2}$ + 1and ππ₯= , where π‘is the greatest integer $\leq$π‘. Then, in the open interval
2π₯+ 3, π₯$\geq$0
-1, 1, the number of points where fog is discontinuous is equal to ______.
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If π $_{π}$ = $\int$ $_{0}\frac{π}{2} \frac{cos2ππ₯}{sinπ₯}$ ππ₯, π$\in$β, then
a.
π $_{3}$ - π $_{2}$ , π $_{4}$ - π $_{3}$ , π $_{5}$ - π $_{4}$ are in an A.P. with $\frac{1}{π3- π2}$ , $\frac{1}{π4- π3}$ , $\frac{1}{π5- π4}$ are in an A.P. with common
common difference-2 difference
2
c.
π $_{3}$ - π $_{2}$ , π $_{4}$ - π $_{3}$ , π $_{5}$ - π $_{4}$ are in a G.P.
d.
$\frac{1}{π3- π2}$ , $\frac{1}{π4- π3}$ , $\frac{1}{π5- π4}$ are in an A.P. with common
difference -2
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A biased die is marked with numbers 2, 4, 8, 16, 32, 32on its faces and the probability of getting a face with
mark πis $\frac{1}{π}$ . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is
a.
$\frac{7}{211}$
b.
$\frac{7}{212}$
c.
$\frac{3}{210}$
d.
$\frac{13}{212}$
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