Two identical thin metal plates has charge π $_{1}$ and π $_{2}$ respectively such that π $_{1}$ > π $_{2}$ . The plates were brought
close to each other to form a parallel plate capacitor of capacitance πΆ. The potential difference between them is
:
a.
$\frac{π1+ π2}{πΆ}$
b.
$\frac{π1- π2}{πΆ}$
c.
$\frac{π1- π2}{2πΆ}$
Correct Answer
d.
$\frac{2π1- π2}{πΆ}$
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Q2mcq
Two identical metallic spheres π΄and π΅when placed at certain distance in air repel each other with a force of πΉ
. Another identical uncharged sphere πΆis first placed in contact with π΄and then in contact with π΅and finally
placed at midpoint between spheres π΄and π΅. The force experienced by sphere πΆwill be :
a.
$\frac{3πΉ}{2}$
b.
$\frac{3πΉ}{4}$
Correct Answer
c.
πΉ
d.
2πΉ
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Q3mcq
Light enters from air into a given medium at an angle of 45$^{\circ}$with interface of the air-medium surface. After
refraction, the light ray is deviated through an angle of 15$^{\circ}$from its original direction. The refractive index of
the medium is :
a.
1 . 732
b.
1 . 333
c.
1 . 414
Correct Answer
d.
2 . 732
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Q4mcq
An πΌparticle and a proton are accelerated from rest through the same potential difference. The ratio of linear
momenta acquired by above two particals will be :
a.
$\sqrt$2: 1
b.
2$\sqrt$2: 1
Correct Answer
c.
4$\sqrt$2: 1
d.
8: 1
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Q5mcq
Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.
a.
(A) and (D) only.
b.
(A) and (E) only.
Correct Answer
c.
(B) and (E) only.
d.
(A) and (C) only
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Q6nat
A metal wire of length 0 . 5 mand cross-sectional area 10 $^{-4}$ m $^{2}$ has breaking stress 5 $\times$ 10 $^{8}$ N m $^{-2}$ . A
block of 10 kgis attached at one end of the string and is rotating in a horizontal circle. The maximum linear
velocity of block will be _____ m s $^{-1}$ .
✓ Accepted Answer:50
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Q7nat
The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If
the metallic bob is immersed in water, then the new time period becomes 5$\sqrt$π₯ s. The value of π₯will be
_____ .
✓ Accepted Answer:5
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Q8nat
A tube of length 50 cmis filled completely with an incompressible liquid of mass 250 gand closed at both
ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity
π₯$\sqrt$πΉ rad s $^{-1}$ . If πΉbe the force exerted by the liquid at the other end then the value of π₯will be _____ .
✓ Accepted Answer:4
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Q9mcq
A 1 mlong wire is broken into two unequal parts πand π. The πpart of the wire is stretched into another
wire π. Length of πis twice the length of πand the resistance of πis twice that of π. Find the ratio of length
of πandπ.
a.
1: 4
b.
1: 2
Correct Answer
c.
4: 1
d.
2: 1
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Q10mcq
The vertical component of the earth's magnetic field is 6 $\times$ 10 $^{-5}$ Tat any place where the angle of dip is 37$^{\circ}$.
The earth's resultant magnetic field at that place will be (Given tan37$^{\circ}$ = $\frac{3}{4}$ )
a.
8 $\times$ 10 $^{-5}$ T
b.
6 $\times$ 10 $^{-5}$ T
c.
5 $\times$ 10 $^{-4}$ T
d.
1 $\times$ 10 $^{-4}$ T
Correct Answer
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A capacitor of capacitance 500 πFis charged completely using a de supply of 100 V. It is now connected to
an inductor of inductance 50 mHto form an LC circuit. The maximum current in LC circuit will be _____ A.
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A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest
position, he throws the next ball. Assuming the juggler throws πballs per second, the maximum height the balls
can reach is
a.
$\frac{π}{2π}$
b.
$\frac{π}{π}$
c.
2ππ
d.
$\frac{π}{2π2}$
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A thermodynamic system is taken from an original state π·to an intermediate state πΈby the linear process
shown in the figure. Its volume is then reduced to the original volume from πΈto πΉby an isobaric process. The
total work done by the gas from π·to πΈto πΉwill be
a.
-450 J
b.
450 J
c.
900 J
d.
1350 J
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The torque of a force 5 $^{^}$ π+ 3 $^{^}$ π- 7π $^{^}$ about the origin is π. If the force acts on a particle whose position vector is
2 $^{^}$ π+ 2 $^{^}$ π+ π $^{^}$ , then the value of πwill be
a.
11 $^{^}$ π+ 19 $^{^}$ π- 4π $^{^}$
b.
-11 $^{^}$ π+ 9 $^{^}$ π- 16π $^{^}$
c.
-17 $^{^}$ π+ 19 $^{^}$ π- 4π $^{^}$
d.
17 $^{^}$ π+ 9 $^{^}$ π+ 16π $^{^}$
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A modulating signal 2sin6 . 28 $\times$ 10 $^{6}$ π‘is added to the carrier signal 4sin12 . 56 $\times$ 10 $^{9}$ π‘for amplitude
modulation. The combined signal is passed through a non-linear square law device. The output is then passed
through a band pass filter. The bandwidth of the output signal of band pass filter will be _____ MHz.
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An unpolarised light beam of intensity 2πΌ $_{0}$ is passed through a polaroid πand then through another polaroid π
which is oriented in such a way that its passing axis makes an angle of 30$^{\circ}$relative to that of π. The intensity
of the emergent light is
a.
$\frac{πΌ0}{4}$
b.
$\frac{πΌ0}{2}$
c.
$\frac{3πΌ0}{4}$
d.
$\frac{3πΌ0}{2}$
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The root mean square speed of smoke particles of mass 5 $\times$ 10 $^{-17}$ kgin their Brownian motion in air at NTP is
approximately.
[Given π= 1 . 38 $\times$ 10 $^{-23}$ J K $^{-1}$ ]
a.
60 mm s $^{-1}$
b.
12 mm s $^{-1}$
c.
15 mm s $^{-1}$
d.
36 mm s $^{-1}$
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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: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R:Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.
a.
Both A and R are true and R is the correct
explanation of A
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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A circuit element πwhen connected to an AC supply of peak voltage 100 Vgives a peak current of 5 A
which is in phase with the voltage. A second element πwhen connected to the same AC supply also gives the
same value of peak current which lags behind the voltage by $\frac{π}{2}$ . If πand πare connected in series to the same
supply, what will be the rms value of the current in ampere?
a.
$\frac{10}{$\sqrt{\,}$2}$
b.
$\frac{5}{$\sqrt{\,}$2}$
c.
5$\sqrt$2
d.
$\frac{5}{2}$
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Match List I with List II.
List I List II
(A) Torque (I) Nms $^{-1}$
(B) Stress (II) Jkg $^{-1}$
(C) Latent Heat (III) Nm
(D) Power (IV) Nm $^{-2}$
Choose the correct answer from the options given below:
a.
A - III, B - II, C - I, D - IV
b.
A - III, B - IV, C - II, D - I
c.
A - IV, B - I, C - III, D - II
d.
A - II, B - III, C - I, D - IV
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Nearly 10%of the power of a 110 Wlight bulb is converted to visible radiation. The change in average
intensities of visible radiation, at a distance of 1 mfrom the bulb to a distance of 5 mis π$\times$ 10 $^{-2}$ W m $^{-2}$ .
The value of 'π' will be
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The velocity of a small ball of mass 0 . 3 gand density 8 g cc $^{-1}$ when dropped in a container filled with
glycerine becomes constant after some time. If the density of glycerine is 1 . 3 g cc $^{-1}$ , then the value of
viscous force acting on the ball will be π₯$\times$ 10 $^{-4}$ N, the value of π₯is _____ .
[use π= 10 m s $^{-2}$ ]
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Two bodies of masses π $_{1}$ = 5 kgand π $_{2}$ = 3 kgare connected by a light string going over a smooth light
pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined
plane on the body of mass π $_{1}$ will be : [Take π= 10 m s $^{-2}$ ]
β
a.
30 N
b.
40 N
c.
50 N
d.
60 N
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The speed of a transverse wave passing through a string of length 50 cmand mass 10 gis 60 m s $^{-1}$ . The
area of cross-section of the wire is 2 . 0 mm $^{2}$ and its Young's modulus is 1 . 2 $\times$ 10 $^{11}$ N m $^{-2}$ . The extension
of the wire over its natural length due to its tension will be x $\times$ 10 $^{-5}$ m. The value of π₯is _____ .
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An object of mass 1 kgis taken to a height from the surface of earth which is equal to three times the radius of
earth. The gain in potential energy of the object will be
[If, π= 10 m s $^{-2}$ and radius of earth = 6400 km]
a.
48MJ
b.
24MJ
c.
36MJ
d.
12MJ
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A ball is released from a height β. If π‘ $_{1}$ and π‘ $_{2}$ be the time required to complete first half and second half of the
distance respectively. Then, choose the correct relation between π‘ $_{1}$ and π‘ $_{2}$ .
Two radioactive materials π΄and π΅have decay constants 25πand 16πrespectively. If initially they have the
same number of nuclei, then the ratio of the number of nuclei of π΅to that of A will be "π" after a time $\frac{1}{ππ}$ . The
value of πis _____ .
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A 8VZener diode along with a series resistance π is connected across a 20 Vsupply (as shown in the figure).
If the maximum Zener current is 25 mA, then the minimum value of π will be _____ $\Omega$.
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A wire πof length 50 cmcarrying a current of 2 Ais placed parallel to a long wire πof length 5 m. The
wire πcarries a current of 3 A. The distance between two wires is 5 cmand currents flow in the same
direction. The force acting on the wire πis :
β
a.
1 . 2 $\times$ 10 $^{-5}$ Ndirected towards wire π.
Consider, PF $_{5}$ , BrF $_{5}$ , PCl $_{3}$ , SF $_{6}$ , ICl $_{4}^{-}$ , ClF $_{3}$ and IF $_{5}$
Amongst the above molecule(s) ion(s), the number of molecule(s)/ion(s) having sp $^{3}$ d $^{2}$ hybridisation is
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A 1 . 84mgsample of polyhydric alcoholic compound 'X' of molar mass 92 . 0 g / molgave 1 . 344 mLof H $_{2}$
gas at STP. The number of alcoholic hydrogen present in compound 'X' is
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A compound 'X' is a weak acid and it exhibits colour change at pHclose to the equivalence point during
neutralization of NaOHwith CH $_{3}$ COOH. Compound 'X' exists in ionized form in basic medium. The compound
'X' is
a.
methyl orange
b.
methyl red
c.
phenolphthalein
d.
erichrome Black T
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Compound 'A' undergoes following sequence of reactions to give compound 'B'. The correct structure and
chirality of compound 'B' is [where Etis -C $_{2}$ H $_{5}$ ]
β
Compound 'A'
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'x' gof molecular oxygen O $_{2}$ is mixed with 200 gof neon Ne. The total pressure of the nonreactive mixture of
O $_{2}$ and Nein the cylinder is 25bar. The partial pressure of Neis 20bar at the same temperature and volume.
The value of 'x' is
[Given: Molar mass of O $_{2}$ = 32 g mol $^{-1}$ . Molar mass of Ne = 20 g mol $^{-1}$ ]
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1 . 80 gof solute A was dissolved in 62 . 5 cm $^{3}$ of ethanol and freezing point of the solution was found to be
155 . 1 K. The molar mass of solute Ais gmol $^{-1}$ . [Given: Freezing point of ethanol is 156 . 0 K. Density of
ethanol is 0 . 80 g cm $^{-3}$ . Freezing point depression constant of ethanol is 2 . 00 K kg mol $^{-1}$ ]
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Assuming 1$\mu$gof trace radioactive element Xwith a half life of 30years is absorbed by a growing tree. The
amount of Xremaining in the tree after 100years is_____$\times$ 10 $^{-1}$ $\mu$g. [Given : ln10 = 2 . 303; log2 = 0 . 30]
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Given below are two statements. One is labelled as Assertion Aand the other is labelled as Reason R.
Assertion A: Amylose is insoluble in water.
Reason R: Amylose is a long linear molecule with more than 200glucose units.
In the light of the above statements, choose the correct answer from the options given below.
a.
Both Aand Rare correct and Ris the correct
explanation of A.
b.
Both Aand Rare correct and Ris NOT the
correct explanation of A.
c.
Ais correct but Ris not correct.
d.
Ais not correct but Ris correct.
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Consider the following sulphure based oxoacids. H $_{2}$ SO $_{3}$ , H $_{2}$ SO $_{4}$ , H $_{2}$ S $_{2}$ O $_{8}$ and H $_{2}$ S $_{2}$ O $_{7}$ . Amongst these
oxoacids, the number of those with peroxo O - Obond is
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Dinitrogen is a robust compound, but reacts at hig altitude to form oxides. The oxide of nitrogen the can
damage plant leaves and retard photosynthes is
a.
NO
b.
NO $^{-}_{3}$
c.
NO $_{2}$
d.
NO $^{-}_{2}$
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Given below are two statements.
Statement I : Stannane is an example of a molecular hydride.
Statement II : Stannane is a planar molecule. In the light of the above statement, 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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Cs + O $_{2}$ g $\rightarrow$CO $_{2}$ g + 400 kJ
Cs + $\frac{1}{2}$ O $_{2}$ g $\rightarrow$COg + 100 kJ
When coal of purity 60%is allowed to burn in presence of insufficient oxygen, 60%of carbon is converted
into ' CO' and the remaining is converted into 'CO $_{2}$ '.
The heat generated when 0 . 6 kgof coal is burnt is
a.
1600 kJ
b.
3200 kJ
c.
4400 kJ
d.
6600 kJ
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Octahedral complexes of copper IIundergo structural distortion (Jahn-Teller). Which one of the given copper
IIcomplexes will show the maximum structural distortion?
(en-ethylenediamine; H $_{2}$ N - CH $_{2}$ - CH $_{2}$ - NH $_{2}$ )
a.
CuH $_{2}$ O $_{6}$ SO $_{4}$
b.
CuenH $_{2}$ O $_{4}$ SO $_{4}$
c.
cis-Cuen $_{2}$ Cl $_{2}$
d.
trans-Cuen $_{2}$ Cl $_{2}$
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Given below are the quantum numbers for 4electrons.
A. n = 3, l = 2, m $_{1}$ = 1, m $_{s}$ = + $\frac{1}{2}$
B. n = 4, l = 1, m $_{1}$ = 0, m $_{s}$ = + $\frac{1}{2}$
C. n = 4, l = 2, m $_{1}$ = - 2, m $_{s}$ = - $\frac{1}{2}$
D. n = 3, l = 1, m $_{1}$ = - 1, m $_{s}$ = + $\frac{1}{2}$
The correct order of increasing energy is
a.
D < B < A < C
b.
D < A < B < C
c.
B < D < A < C
d.
B < D < C < A
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Given below are the critical temperatures of some of the gases:
Gas Critical temperature K
He 5 . 2
CH $_{4}$ 190
CO $_{2}$ 304 . 2
NH $_{3}$ 405 . 5
The gas showing least adsorption on a definite amount of charcoal is
a.
He
b.
CH $_{4}$
c.
CO $_{2}$
d.
NH $_{3}$
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When enthanol is heated with conc. H $_{2}$ SO $_{4}$ , a gas is produced. The compound formed, when this gas is treated
with cold dilute aqueous solution of Baeyer's reagent, is
a.
Formaldehyde
b.
Formic acid
c.
Glycol
d.
Ethanoic acid
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Consider the reaction
4HNO $_{3}$ l + 3KCls $\rightarrow$Cl $_{2}$ g + NOClg + 2H $_{2}$ Og + 3KNO $_{3}$ s
The amount of HNO $_{3}$ required to produce110 . 0 gof KNO $_{3}$ is
(Given : Atomic masses of H, O, Nand Kare 1, 16, 14and 39, respectively.)
a.
32 . 2 g 69 . 4 g
c.
91 . 5 g
d.
162 . 5 g
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Given below are two statements.
Statement I : The compound is optically active.
Statement II : β is mirror image of above compound A.
In the light of the above statement, choose the most appropriate answer from the options given below.
a.
Both Statement I and Statement II are correct
b.
Both Statement I and Statement II are incorrect.
c.
Statement I is correct but Statement II is
incorrect.
d.
Statement I is incorrect but Statement II is
correct.
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$\frac{logπ1 + 5π₯- logπ1 + πΌπ₯}{π₯}$ if π₯$\neq$0
Let the function ππ₯= be continuous at π₯= 0. Then πΌis equal to
10 if π₯= 0
a.
10
b.
-10
c.
5
d.
-5
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The sum and product of the mean and variance of a binomial distribution are 82 . 5and 1350respectively.
They the number of trials in the binomial distribution is
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Let πΌ, π½πΌ> π½be the roots of the quadratic equation π₯ $^{2}$ - π₯- 4 = 0. If π $_{π}$ = πΌ $^{π}$ - π½ $^{π}$ , π$\in$β, then
$\frac{π15π16- π14π16- π215+ π14π15}{π13π14}$ is equal to _____.
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Let πbe the foot of perpendicular drawn from the point π1, 2, 3to the plane π₯+ 2π¦+ π§= 14. If π is a point
on the plane such that $\angle$ππ π= 60$^{\circ}$, then the area of βπππ is equal to
a.
$\frac{$\sqrt{\,}$3}{2}$
b.
$\sqrt$3
c.
2$\sqrt$3
d.
3
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Bag Icontains 3red, 4black and 3white balls and Bag IIcontains 2red, 5black and 2white balls. One ball is
transferred from Bag Ito Bag IIand then a ball is draw from Bag II. The ball so drawn is found to be black in
colour. Then the probability, that the transferred ball is red, is
a.
$\frac{4}{9}$
b.
$\frac{5}{18}$
c.
$\frac{1}{6}$
d.
$\frac{3}{10}$
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If the tangent to the curve π¦= π₯ $^{3}$ - π₯ $^{2}$ + π₯at the point π, πis also tangent to the curve π¦= 5π₯ $^{2}$ + 2x - 25at
the point 2, - 1, then 2π+ 9πis equal to ______.
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If the solution curve of the differential equation $\frac{ππ¦}{ππ₯}$ = $\frac{π₯+ π¦- 2}{π₯- π¦}$ passes through the point 2, 1and π+ 1, 2, k > 0,
then
+ 1 + 1
Let $^{$\rightarrow$}$ π, $^{$\rightarrow$}$ π, $^{$\rightarrow$}$ πbe three coplanar concurrent vectors such that angles between any two of them is same. If the
product of their magnitudes is 14and $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ πΒ· $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π+ $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ πΒ· $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π+ $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ πΒ· $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π= 168then $^{$\rightarrow$}$ π+ $^{$\rightarrow$}$ π+ $^{$\rightarrow$}$ πis
equal to
a.
10
b.
14
c.
16
d.
18
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Let π΄πΌ, - 2, π΅πΌ, 6and πΆ $\frac{πΌ}{4}$ , - 2be vertices of a βπ΄π΅πΆ. If 5, $\frac{πΌ}{4}$ is the circumcentre of βπ΄π΅πΆ, then which of the
following is NOT correct about βπ΄π΅πΆ
a.
ares is 24
b.
perimeter is 25
c.
circumradius is 5
d.
inradius is 2
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Let π¦= π¦π₯be the solution curve of the differential equation $\frac{ππ¦}{ππ₯}$ + $\frac{2π₯2+ 11π₯+ 13}{π₯3+ 6π₯2+ 11π₯+ 6}$ π¦= $\frac{π₯+ 3}{π₯+ 1}$ , π₯> - 1, which
passes through the point 0, 1. Then π¦1is equal to
a.
$\frac{1}{2}$
b.
$\frac{3}{2}$
c.
$\frac{5}{2}$
d.
$\frac{7}{2}$
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The number of natural numbers lying between 1012and 23421that can be formed using the digits 2, 3, 4, 5, 6
(repetition of digits is not allowed) and divisible by 55is _____.
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Let π= π§= π₯+ ππ¦: π§- 1 + π$\geq$π§, π§< 2, π§+ π= π§- 1. Then the set of all values of π₯, for which
π€= 2π₯+ ππ¦$\in$πfor some π¦$\in$β, is
If the system of equations
π₯+ π¦+ π§= 6
2π₯+ 5π¦+ πΌπ§= π½
π₯+ 2π¦+ 3π§= 14
has infinitely many solutions, then πΌ+ π½is equal to
a.
8
b.
36
c.
44
d.
48
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Let π $_{1}$ , π $_{2}$ be the slopes of two adjacent sides of a square of side πsuch that π $^{2}$ + 11π+ 3 π $^{2}_{1}$ + π $^{2}_{2}$ = 220.
If one vertex of the square is 10cosπΌ- sinπΌ, 10sinπΌ+ cosπΌ, where πΌ$\in$0, $\frac{π}{2}$ and the equation of one diagonal is
cos$\alpha$ - sin$\alpha$π₯+ sinπΌ+ cosπΌπ¦= 10, then 72sin $^{4}$ πΌ+ cos $^{4}$ πΌ+ π $^{2}$ - 3π+ 13is equal to
a.
119
b.
128
c.
145
d.
155
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If π‘denotes the greatest integer $\leq$π‘, then number of points, at which the function ππ₯= 42π₯+ 3 +
9π₯+ $\frac{1}{2}$ - 12π₯+ 20is not differentiable in the open interval -20, 20, is ______.
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Let π΄π΅be a chord of length 12of the circle
π₯- 2 $^{2}$ + π¦+ 1 $^{2}$ = $\frac{169}{4}$
If tangents drawn to the circle at points π΄and π΅intersect at the point π, then five times the distance of point π
from chord π΄π΅is equal to _____.
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