The pressure of a gas changes linearly with volume from π΄to π΅as shown in figure. If no heat is supplied to or
extracted from the gas then change in the internal energy of the gas will be
a.
6 J
b.
Zero
c.
-4 . 5 J
d.
4 . 5 J
Correct Answer
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Q2mcq
Two polaroids π΄ and π΅are placed in such a way that the pass-axis of polaroids are perpendicular to each
other. Now, another polaroid πΆis placed between π΄ and π΅bisecting angle between them. If intensity of
unpolarised light is πΌ $_{0}$ then intensity of transmitted light after passing through polaroid π΅will be :
a.
$\frac{πΌ0}{4}$
b.
$\frac{πΌ0}{2}$
c.
$\frac{πΌ0}{8}$
Correct Answer
d.
Zero
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Q3nat
The speed of a swimmer is 4 km h $^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of
river of width 1 km, he reaches a point 750 mdown the stream on the opposite bank. The speed of the river
water is ______ km h $^{-1}$ .
✓ Accepted Answer:3
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Q4nat
An inductor of 0 . 5 mH, a capacitor of 20 $\mu$Fand resistance of 20 $\Omega$are connected in series with a 220 V
ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt$π₯ A. The value of
π₯is-
✓ Accepted Answer:242
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Q5mcq
If 1000droplets of water of surface tension 0 . 07 N m $^{-1}$ . having same radius 1 mmeach, combine to from a
single drop. In the process the released surface energy is-
Take $\pi$ = $\frac{22}{7}$
a.
7 . 92 $\times$ 10 $^{-6}$ J
b.
7 . 92 $\times$ 10 $^{-4}$ J
Correct Answer
c.
9 . 68 $\times$ 10 $^{-4}$ J
d.
8 . 8 $\times$ 10 $^{-5}$ J
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Q6mcq
A bar magnet with a magnetic moment 5 . 0 A m $^{2}$ is placed in parallel position relative to a magnetic field of
0 . 4 T. The amount of required work done in turning the magnet form parallel to antiparallel position relative
to the field direction is ________.
a.
4 J
Correct Answer
b.
1 J
c.
2 J
d.
Zero
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Q7mcq
The amplitude of 15sin ( 1000$\pi$π‘)is modulated by 10sin ( 4$\pi$π‘) signal. The amplitude modulated signal
contains frequency (ies) of
( π΄) 500 Hz
( π΅) 2 Hz
( πΆ) 250 Hz
( π·) 498 Hz
( πΈ) 502 Hz
Choose the correct answer from the options given below:
a.
A only
b.
A, D and E only
Correct Answer
c.
B only
d.
A and B only
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Q8nat
In a medium the speed of light wave decreases to 0 . 2times to its speed in free space. The ratio of relative
permittivity to the refractive index of the medium is π₯: 1. The value of π₯is ______.
(Given speed of light in free space = 3 $\times$ 10 $^{8}$ m s $^{-1}$ and for the given medium π $_{π}$ = 1)
✓ Accepted Answer:5
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Q9mcq
At a certain depth πbelow surface of earth, value of acceleration due to gravity becomes four times that of its
value at a height 3π above earth surface. Where π is Radius of earth (Take π = 6400 km). The depth πis
equal to
a.
5260 km
b.
640 km
c.
2560 km
d.
4800 km
Correct Answer
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Q10nat
In the figure given below. a block of mass π= 490 gplaced on a frictionless table is connected with two
springs having same spring constant (πΎ= 2 N m $^{-1}$ ). If the block is horizontally displaced through π mthen
the number of complete oscillations it will make in 14πseconds will be ______.
✓ Accepted Answer:20
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A thin rod having a length of 1 mand area of cross-section 3 $\times$ 10 $^{-6}$ m $^{2}$ is suspended vertically from one
end. The rod is cooled from 210$^{\circ}$Cto 160$^{\circ}$C. After cooling, a mass πis attached at the lower end of the rod
such that the length of rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the
rod are 2 $\times$ 10 $^{11}$ N m $^{-2}$ and 2 $\times$ 10 $^{-5}$ K $^{-1}$ , respectively. The value of πis ______ kg. (Take π= 10 m s $^{-2}$
)
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Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height.
Choose the correct statement out of the following {Assume negligible air friction}
(1) Time taken by them to reach the earth's surface (2) Insulating ball will reach the earth's surface
will be independent of the properties of their earlier than the metal ball
materials
(3) Both will reach the earth's surface simultaneously (4) Metal ball will reach the earth's surface earlier
than the insulating ball
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For hydrogen atom, π $_{1}$ and π $_{2}$ are the wavelengths corresponding to the transitions 1and 2respectively as
shown in figure. The ratio of π $_{1}$ and π $_{2}$ is $\frac{π₯}{32}$ . The value of π₯is ______.
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Which of the following correctly represents the variation of electric potential ( π) of a charged spherical
conductor of radius ( π ) with radial distance ( π) from the centre?
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If a source of electromagnetic radiation having power 15 kWproduces 10 $^{16}$ photons per second, the
radiation belongs to a part of spectrum is :
(Take Planck constant β = 6 $\times$ 10 $^{-34}$ J s)
a.
Micro waves
b.
Ultraviolet rays
c.
Gamma rays
d.
Radio waves
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The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of
oscillation. At $\frac{π΄}{2}$ , the kinetic energy of the block is
a.
37 . 5 J
b.
9 . 75 J
c.
18 . 75 J
d.
12 . 5 J
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A solid sphere of mass 1 kgrolls without slipping on a plane surface. Its kinetic energy is 7 $\times$ 10 $^{-3}$ J. The
speed of the centre of mass of the sphere is ______ cm s $^{-1}$ .
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As shown in figure, a 70 kggarden roller is pushed with a force of πΉ= 200 N $^{$\rightarrow$}$ at an angle of 30$^{\circ}$with
horizontal. The normal reaction on the roller is (Given π= 10 m s $^{-2}$ )
a.
800$\sqrt$2 N
b.
600 N
c.
800 N
d.
200$\sqrt$3 N
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The drift velocity of electrons for a conductor connected in an electrical circuit is π $_{π}$ . The conductor is now
replaced by another conductor with same material and same length but double the area of cross-section. The
applied voltage remains same. The new drift velocity of electrons will be
a.
π $_{π}$
b.
$\frac{ππ}{2}$
c.
$\frac{ππ}{4}$
d.
2π $_{π}$
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A rod with circular cross-section area 2 cm $^{2}$ and length 40 cmis wound uniformly with 400turns of an
insulated wire. If a current of 0 . 4 Aflows in the wire windings, the total magnetic flux produced inside
windings is 4$\pi$ $\times$ 10 $^{-6}$ Wb. The relative permeability of the rod is
(Given : Permeability of vacuum $\mu$ $_{0}$ = 4$\pi$ $\times$ 10 $^{-7}$ N A $^{-2}$ )
a.
12 . 5
b.
$\frac{32}{5}$
c.
125
d.
$\frac{5}{16}$
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Expression for an electric field is given by $^{$\rightarrow$}$ πΈ= 4000 π₯ $^{2}^{^}$ i V m $^{-1}$ . The electric flux through the cube of
side 20 cmwhen placed in electric field (as shown in the figure) is ______ V cm.
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Two identical cells, when connected either in parallel or in series gives same current in an external resistance
5 $\Omega$. The internal resistance of each cell will be ______ $\Omega$.
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If π , π $_{πΏ}$ and π $_{πΆ}$ represent resistance, inductive reactance and capacitive reactance. Then which of the
following is dimensionless:
a.
π π $_{πΏ}$ π $_{πΆ}$
b.
$\frac{π }{$\sqrt{\,}$ππΏππ}$
c.
$\frac{π }{ππΏππ}$
d.
π $\frac{ππΏ}{ππ}$
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion A :The beam of electrons shows wave nature and exhibit interference and diffraction.
Reason R :Davisson Germer Experimentally verified the wave nature of electrons.
In the light of the above statements. Choose the most appropriate answer from the options given below :
a.
A is correct but R is not correct
b.
A is not correct but R is correct
c.
Both A and R are correct but R is Not the correct
explanation of A
d.
Both A and R are correct and R is the correct
explanation of A
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100balls each of mass πmoving with speed π£simultaneously strike a wall normally and reflected back with
same speed, in time π‘ s. The total force exerted by the balls on the wall is
a.
$\frac{100ππ£}{π‘}$
b.
$\frac{200ππ£}{π‘}$
c.
200 ππ£π‘
d.
$\frac{ππ£}{100π‘}$
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The initial speed of a projectile fired from ground is π’. At the highest point during its motion, the speed of
projectile is $\frac{$\sqrt{\,}$3}{2}$ π’. The time of flight of the projectile is:
a.
$\frac{π’}{2π}$
b.
$\frac{π’}{π}$
c.
$\frac{2π’}{π}$
d.
$\frac{$\sqrt{\,}$3π’}{π}$
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A lift of mass π= 500 kgis descending with speed of 2 m s $^{-1}$ . Its supporting cable begins to slip thus
allowing it to fall with a constant acceleration of 2 m s $^{-2}$ . The kinetic energy of the lift at the end of fall
through to a distance of 6 mwill be ______ kJ.
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The total pressure of a mixture of non-reacting gases X ( 0 . 6 g ) and Y ( 0 . 45 g ) in a vessel is 740 mmof
Hg. The partial pressure of the gas Xis mmof Hg . (Nearest Integer)
(Given : molar mass X = 20and Y = 45 g mol $^{-1}$ )
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For reaction: SO $_{2}$ ( g) + $\frac{1}{2}$ O $_{2}$ ( g) $\rightleftharpoons$SO $_{3}$ ( g) K $_{P}$ = 2 $\times$ 10 $^{12}$ at 27$^{\circ}$Cand 1 atmpressure. The K $_{c}$ for
the same reaction is $\times$ 10 $^{13}$ . (Nearest integer)
(Given R = 0 . 082 L atm K $^{-1}$ mol $^{-1}$ )
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A $\rightarrow$B
The rate constants of the above reaction at 200 Kand 300 Kare 0 . 03 min $^{-1}$ and 0 . 05 min $^{-1}$
respectively. The activation energy for the reaction is J(Nearest integer)
(Given : In 10 = 2 . 3
R = 8 . 3 J K $^{-1}$ mol $^{-1}$
log 5 = 0 . 70
log 3 = 0 . 48
log2 = 0 . 30
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Consider the following reaction
( i ) dil . NaOH
Propanal + Methanal = $\rightarrow$ $_{+}$ Product B
(ii) $\Delta$(iii) NaCN(iv) H3O ( C5H8O3)
The correct statement for product π΅is. It is
a.
optically active and adds one mole of bromine
b.
racemic mixture and is neutral
c.
racemic mixture and gives a gas with saturated
NaHCO $_{3}$ solution
d.
optically active alcohol and is neutrall
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Match List I with List II
List I List II
A. XeF $_{4}$ I.See-saw
B. SF $_{4}$ II. Square planar
C. NH $^{+}_{4}$ III. Bent T - shaped
D.BrF $_{3}$ IV. Tetrahedral
Choose the correct answer from the options given below :
a.
A - IV, B - III, C - II, D - I
b.
A - II, B - I, C - III, D - IV
c.
A - IV, B - I, C - II, D - III
d.
A - II, B - I, C - IV, D - III
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The enthalpy change for the conversion of $\frac{1}{2}$ Cl $_{2}$ (g) to Cl $^{-}$ ( aq ) is ( - )
kJmol $^{-1}$ (Nearest integer)
Given : π₯ $_{dis}$ H $_{Cl}^{0}_{2 (}_{g )}$ = 240kJmol $^{-1}$ .
π₯ $_{eg}$ H $_{Cl ( g )}^{o}$ = - 350kJmol $^{-1}$ ,
π₯ $_{hyd}$ H $^{o}_{Cl( g )}$ - = - 380kJmol $^{-1}$
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The methods NOT involved in concentration of ore are
(A) Liquation
(B) Leaching
(C) Electrolysis
(D) Hydraulic washing
(E) Froth floatation
Choose the correct answer from the options given below:
a.
B, D and C only
b.
C, D and E only
c.
A and C only
d.
B, D and E only
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The logarithm of equilibrium constant for the reaction Pd $^{2 +}$ + 4Cl $^{-}$ $\rightleftharpoons$PdCl $^{2 -}_{4}$ is
(Nearest integer)
Given: $\frac{2 . 303RT}{F}$ = 0 . 06 V
Pd $^{2 +}_{( aq )}$ + 2e $^{-}$ $\rightleftharpoons$Pd(s) E $^{π}$ = 0 . 83 V
PdCl $^{2 -}_{4}$ (aq) + 2e $^{-}$ $\rightleftharpoons$Pd(s) + 4Cl $^{-}$ (aq)
E $^{o}$ = 0 . 65 V
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An organic compound ' π΄' with empirical formula C $_{6}$ H $_{6}$ Ogives sooty flame on burning. Its reaction with
bromine solution in low polarity solvent results in high yield of π΅ . π΅is
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When Cu $^{2 +}$ ion is treated with KI, a white precipitate, Xappears in solution. The solution is titrated with
sodium thiosulphate, the compound Yis formed. Xand Yrespectively are
a.
X = Cu $_{2}$ I $_{2}$ , Y = Na $_{2}$ S $_{4}$ O $_{5}$
b.
X = Cu $_{2}$ I $_{2}$ , Y = Na $_{2}$ S $_{4}$ O $_{6}$
c.
X = CuI $_{2}$ , Y = Na $_{2}$ S $_{4}$ O $_{3}$
d.
X = CuI $_{2}$ , Y = Na $_{2}$ S $_{4}$ O $_{6}$
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Cobalt chloride when dissolved in water forms pink colored complex Xwhich has octahedral geometry. This
solution on treating with cone HClforms deep blue complex, Ywhich has a Zgeometry. X, Yand Z,
respectively, are
, , , ,
a.
X = CoH $_{2}$ O $_{6}^{2 +}$ Y = CoCl $_{4}^{2 -}$ Z = Tetrahedral
, ,
b.
X = CoH $_{2}$ O $_{6}^{2 +}$ Y = CoCl $_{6}^{3 -}$ Z = Octahedral
,
c.
X = CoH $_{2}$ O $_{6}^{3 +}$ Y = CoCl $_{6}^{3 -}$ Z = Octahedral
d.
X = CoH $_{2}$ O $_{4}$ Cl $_{2}^{+}$ , Y = CoCl $_{4}^{2 -}$ Z = Tetrahedral
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Match items of column I and II
Column I (Mixture of compounds) Column II (Separation Technique)
A. H $_{2}$ O / CH $_{2}$ Cl $_{2}$ i. Crystallization
ii. Differential solvent extraction
B.
C. Kerosene/Naphthalene iii. Column chromatography
D. C $_{6}$ H $_{12}$ O $_{6}$ / NaCl iv. Fractional Distillation
a.
A - ( iii ) , B - ( iv ) , C - ( ii ) , D - ( i )
b.
A - ( ii ) , B - ( iii ) , C - ( iv ) , D - ( i )
c.
A - ( i ) , B - ( iii ) , C - ( ii ) , D - ( iv )
d.
A - ( ii ) , B - ( iv ) , C - ( i ) , D - ( iii )
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Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced
at STP from the reaction of 11 . 5 gof zinc with excess HClis L(Nearest integer)
(Given : Molar mass of Znis 65 . 4 g mol $^{-1}$ and Molar volume of H $_{2}$ at STP = 22 . 7 L)
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At 27$^{\circ}$C, a solution containing 2 . 5 gof solute in 250 . 0 mLof solution exerts an osmotic pressure of
400 Pa. The molar mass of the solute is g mol $^{-1}$ (Nearest integer)
(Given : R = 0 . 083 Lbar $^{-1}$ mol $^{-1}$ )
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2
Let $^{$\rightarrow$}$ πand $^{$\rightarrow$}$ πbe two vector such that $^{$\rightarrow$}$ π= $\sqrt$14, $^{$\rightarrow$}$ π= $\sqrt$6and $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π= $\sqrt$48. Then $^{$\rightarrow$}$ πΒ· $^{$\rightarrow$}$ π is equal to _____ .
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A bag contains 6balls. Two balls are drawn from it at random and both are found to be black. The probability
that the bag contains at least 5black balls is
a.
$\frac{5}{7}$
b.
$\frac{2}{7}$
c.
$\frac{3}{7}$
d.
$\frac{5}{6}$
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30
Let πΌ> 0, be the smallest number such that the expansion of π₯ $\frac{2}{3}$ + $\frac{2}{π₯3}$ has a term π½π₯ $^{-πΌ}$ , π½$\in$π. Then πΌis
equal to _____ .
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π₯, π₯< 0
Let for π₯$\in$π , ππ₯= $\frac{π₯+ π₯}{2}$ and ππ₯= . Then area bounded by the curve π¦= ππππ₯and the lines
π₯ $^{2}$ , π₯$\geq$0
π¦= 0, 2π¦- π₯= 15is equal to _____ .
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Let the shortest distance between the lines L: $\frac{π₯- 5}{-2}$ = $\frac{π¦- π}{0}$ = $\frac{π§+ π}{1}$ , π$\geq$0and L $_{1}$ : π₯+ 1 = π¦- 1 = 4 - π§be 2$\sqrt$6.
If ( πΌ, π½, πΎ) lies on L, then which of the following is NOT possible?
a.
πΌ+ 2πΎ= 24
b.
2πΌ+ πΎ= 7
c.
2πΌ- πΎ= 9
d.
πΌ- 2πΎ= 19
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Let the line πΏ: $\frac{π₯- 1}{2}$ = $\frac{π¦+ 1}{-1}$ = $\frac{π§- 3}{1}$ intersect the plane 2π₯+ π¦+ 3π§= 16at the point π. Let the point πbe the
foot of perpendicular from the point π 1, - 1, - 3on the line πΏ. If πΌis the area of triangle πππ . then πΌ $^{2}$ is equal
to _____ .
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Let πbe the angle between the planes π $_{1}$ = $^{$\rightarrow$}$ πΒ· $^{^}$ π+ $^{^}$ π+ 2π= 9 $^{^}$ and π $_{2}$ = $^{$\rightarrow$}$ πΒ· 2 $^{^}$ π- $^{^}$ π+ π= 15 $^{^}$ . Let Lbe the line
that meets π $_{2}$ at the point 4, - 2, 5and makes an angle πwith the normal of π $_{2}$ . If πΌis the angle between πΏand
π $_{2}$ then tan $^{2}$ πcot $^{2}$ πΌis equal to _____ .
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If the maximum distance of normal to the ellipse $\frac{π₯2}{4}$ + $\frac{π¦2}{π2}$ = 1, π< 2, from the origin is 1, then the eccentricity
of the ellipse is:
a.
$\frac{1}{$\sqrt{\,}$2}$
b.
$\frac{$\sqrt{\,}$3}{2}$
c.
$\frac{1}{2}$
d.
$\frac{$\sqrt{\,}$3}{4}$
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Let a circle πΆ $_{1}$ be obtained on rolling the circle π₯ $^{2}$ + π¦ $^{2}$ - 4π₯- 6π¦+ 11 = 0upwards 4units on the tangent Tto
it at the point 3, 2. Let πΆ $_{2}$ be the image of πΆ $_{1}$ in π. Let π΄and π΅be the centers of circles πΆ $_{1}$ and πΆ $_{2}$ respectively,
and πand πbe respectively the feet of perpendiculars drawn from π΄and π΅on the π₯-axis. Then the area of the
trapezium AMNB is:
a.
22 + $\sqrt$2
b.
41 + $\sqrt$2
c.
3 + 2$\sqrt$2
d.
21 + $\sqrt$2
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A wire of length 20 mis to be cut into two pieces. A piece of length $\ell$ $_{1}$ is bent to make a square of area π΄ $_{1}$
and the other piece of length $\ell$ $_{2}$ is made into a circle of area π΄ $_{2}$ . If 2 π΄ $_{1}$ + 3 π΄ $_{2}$ is minimum then π$\ell$ $_{1}$ : $\ell$ $_{2}$ is
equal to:
a.
6: 1
b.
3: 1
c.
1: 6
d.
4: 1
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Let π¦= ππ₯represent a parabola with focus - $\frac{1}{2}$ , 0and directrix π¦= - $\frac{1}{2}$ . Then
π= π₯$\in$β: tan $^{-1}$ $\sqrt$ππ₯+ sin $^{-1}$ $\sqrt$ππ₯+ 1 = $\frac{π}{2}$ :
a.
contains exactly two elements
b.
contains exactly one element
c.
is an infinite set
d.
is an empty set
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Let a differentiable function πsatisfy ππ₯+ $\int$ $_{3} \frac{π₯ππ‘}{π‘}$ ππ‘= $\sqrt$π₯+ 1, π₯$\geq$3. Then 12π8is equal to:
a.
34
b.
19
c.
17
d.
1
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Let 5digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9with repetition allowed, and are arranged in
ascending order with serial numbers. Then the serial number of the number 42923is _____ .
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