The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest
wavelength is
a.
π·
Correct Answer
b.
π΄
c.
π΅
d.
πΆ
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Q2mcq
The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the uniform magnetic field
Choose the correct answer from the options given below:
a.
π΅and πΆonly
b.
π΄and πΆonly
c.
πΆand π·only
Correct Answer
d.
π΅and π·only
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Q3mcq
Given below are two statements: one is labelled as Assertion π΄and the other is labelled as Reason π .
Assertion A: When a body is projected at an angle 45$^{\circ}$,its range is maximum.
Reason R: For maximum range, the value of sin 2πshould be equal to one.
In the light of the above statements, choose the correct answer from the options given below:
a.
π΄is false but π is true
b.
π΄is true but π is false
c.
Both π΄and π are correct and π is the correct Both π΄and π are correct but π is NOT the correct
explanation of π΄ explanation of π΄
Correct Answer
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Q4mcq
Two resistance are given as π $_{1}$ = ( 10 $\pm$ 0 . 5 ) $\Omega$and π $_{2}$ = ( 15 $\pm$ 0 . 5 ) $\Omega$ . The percentage error in the
measurement of equivalent resistance when they are connected in parallel is
a.
6 . 33
b.
2 . 33
c.
5 . 33
d.
4 . 33
Correct Answer
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Q5nat
An ideal transformer with purely resistive load operates at 12 kVon the primary side. It supplies electrical
energy to a number of nearby houses at 120 V . The average rate of energy consumption in the houses served
by the transformer is 60 kW . The value of resistive load ( π $_{π }$ ) required in the secondary circuit will be
_________m$\Omega$ .
✓ Accepted Answer:240
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Q6mcq
A monochromatic light wave with wavelength π $_{1}$ and frequency π $_{1}$ in air enters another medium. If the angle
of incidence and angle of refraction at the interface are 45$^{\circ}$and 30$^{\circ}$respectively, then the wavelength π $_{2}$ and
frequency π $_{2}$ of the refracted wave are:
A small block of mass 100 gis tied to a spring of spring constant 7 . 5 N m $^{-1}$ and length 20 cm . The other
end of spring is fixed at a particular point π΄. If the block moves in a circular path on a smooth horizontal
surface with constant angular velocity 5 rad s $^{-1}$ about point π΄, then tension in the spring is
a.
0 . 75 N
Correct Answer
b.
0 . 25 N
c.
0 . 50 N
d.
1 . 5 N
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Q8nat
A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2 . 15 mwithin water
when sunlight is incident at an angle of 30$^{\circ}$with the surface of water. If swimming pool is filled to a height of
1 . 5 m, then the height of the pole above the water surface in centimeters is (π $_{π€}$ = $\frac{4}{3}$ ) ________ .
✓ Accepted Answer:50
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Q9nat
A particle of mass 10 g moves in a straight line with retardation 2π₯,where π₯is the displacement in SIunits.
Its loss of kinetic energy for above displacement is $\frac{10}{π₯}^{-π}$ J .The value of πwill be ________ .
✓ Accepted Answer:2
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Q10nat
A person driving car at a constant speed of 15 m s $^{-1}$ is approaching a vertical wall. The person notices a
change of 40 Hzin the frequency of his carβs horn upon reflection from the wall. The frequency of horn is
_______Hz .
(Given: Speed of sound: 30 m s $^{-1}$ )
✓ Accepted Answer:420
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A source supplies heat to a system at the rate of 1000 W . If the system performs work at a rate of 200 W .
The rate at which internal energy of the system increases is
a.
600 W
b.
800 W
c.
500 W
d.
1200 W
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A mass πis attached to two springs as shown in figure. The spring constants of two springs are πΎ $_{1}$ and πΎ $_{2}$ .For
the frictionless surface, the time period of oscillation of mass πis
a.
2π$\sqrt$ $\frac{π}{K1+ K2}$
b.
$\frac{1}{2π}$ $\sqrt$ $\frac{K1- K2}{π}$
c.
2π$\sqrt$ $\frac{π}{K1- K2}$
d.
$\frac{1}{2π}$ $\sqrt$ $\frac{K1+ K2}{π}$
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Two identical solid spheres each of mass 2 kgand radii 10 cm are fixed at the ends of a light rod. The
separation between the centres of the spheres is 40 cm . The moment of inertia of the system about an axis
perpendicular to the rod passing through its middle point is______ $\times$ 10 $^{- 3}$ kg m $^{2}$ .
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The number of air molecules per cm $^{3}$ is increased from 3 $\times$ 10 $^{19}$ to 12 $\times$ 10 $^{19}$ . The ratio of collision
frequency of air molecules before and after the increase in number respectively is :
a.
0 . 75
b.
1 . 25
c.
0 . 50
d.
0 . 25
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A particle is moving with constant speed in a circular path. When the particle turns by an angle 90$^{\circ}$, the ratio of
instantaneous velocity to its average velocity is π: π₯$\sqrt$2 .The value of π₯will be
a.
2
b.
5
c.
1
d.
7
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A small ball of mass πand density πis dropped in a viscous liquid of density π $_{0}$ . After some time, the ball falls
with a constant velocity. What is the viscous force on the ball?
a.
πΉ= ππ1 + $\frac{π0}{π}$
b.
πΉ= ππ1 + $\frac{π}{π0}$
c.
πΉ= ππ1 - $\frac{π0}{π}$
d.
πΉ= ππ1 $\pm$ ππ $_{0}$
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A long straight wire of circular cross-section (radius π) is carrying steady current I . The current Iis uniformly
distributed across this cross-section. The magnetic field is
a.
inversely proportional to πin the region π< π
and uniform throughout in the region π> π
b.
directly proportional to πin the region π< πand
inversely proportional to πin the region π> π
c.
Zero in the region π< πand inversely
proportional to πin the region π> π
d.
uniform in the region π< πand inversely
proportional to distance πfrom the axis, in the
region π> π
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The kinetic energy of an electron, πΌ-particle and a proton are given as 4πΎ, 2πΎand πΎrespectively. The de-
Broglie wavelength associated with electron ( π $_{π}$ ) , πΌ-particle ( π $_{πΌ}$ )and the proton (π $_{π}$ )are as follows:
a.
π $_{πΌ}$ = π $_{π}$ > π $_{π}$
b.
π $_{πΌ}$ < π $_{π}$ < π $_{π}$
c.
π $_{πΌ}$ = π $_{π}$ < π $_{π}$
d.
π $_{πΌ}$ > π $_{π}$ > π $_{π}$
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A steel rod has a radius of 20 mmand a length of 2 . 0 m . A force of 62 . 8 kNstretches it along its length.
Young's modulus of steel is 2 . 0 $\times$ 10 $^{11}$ N m $^{-2}$ . The longitudinal strain produced in the wire is _________ $\times$ 10 $^{-5}$ .
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The length of a metallic wire is increased by 20%and its area of cross-section is reduced by 4 % . The
percentage change in resistance of the metallic wire is ________ .
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A parallel plate capacitor with plate area π΄and plate separation πis filled with a dielectric material of
dielectric constant πΎ= 4 . The thickness of the dielectric material is π₯, where π₯< π.
Let πΆ $_{1}$ and πΆ $_{2}$ be the capacitance of the system for π₯= $\frac{1}{3}$ πand π₯= $\frac{2π}{3}$ ,respectively. If πΆ $_{1}$ = 2 $\mu$F, the value
of πΆ $_{2}$ is _____ $\mu$F .
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Two identical circular wires of radius 20 cmand carrying current $\sqrt$2Aare placed in perpendicular planes as
shown in figure. The net magnetic field at the centre of the circular wires is________ $\times$ 10 $^{-8}$ T .
(Take π= 3 . 14)
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Given below are two statements: one is labelled as Assertion Aand the other is labelled as Reason R.
Assertion A:Earth has atmosphere whereas moon doesnβt have any atmosphere.
Reason R:The escape velocity on moon is very small as compared to that on earth.
In the light of the above statements, choose the correct answer from the options given below:
a.
Both π΄and π are correct but π is NOTthe correct
explanation of π΄
b.
π΄is false but π is true
c.
Both π΄and π are correct and π is the correct
explanation of π΄
d.
π΄is true but π is false
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A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing π
on earth will weigh on that planet:
a.
2 $\frac{1}{4}$ W
b.
2 $\frac{1}{3}$ W
c.
2W
d.
2 $\frac{2}{3}$ W
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For the plane electromagnetic wave given by πΈ= πΈ $_{0}$ sin ( ππ‘- ππ₯)and π΅= π΅ $_{0}$ sin ( ππ‘- ππ₯) ,the ratio of
average electric energy density to average magnetic energy density is
a.
$\frac{1}{2}$
b.
2
c.
4
d.
1
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For a concentrated solution of a weak electrolyte (K $_{eq}$ =equilibrium constant) A $_{2}$ B $_{3}$ of concentration βCβ, the
degree of dissociation β$\alpha$βis
a.
$\frac{Keq}{5c4} \frac{1}{5}$
b.
$\frac{Keq}{108c4} \frac{1}{5}$
c.
$\frac{Keq}{25c2} \frac{1}{5}$
d.
$\frac{Keq}{6c5} \frac{1}{5}$
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Mass of Urea NH $_{2}$ CONH $_{2}$ required to be dissolved in 1000 gof water in order to reduce the vapour pressure
of water by 25%is _______ g . (Nearest integer)
Given : Molar mass of N, C, Oand Hare 14, 12, 16and 1 g mol $^{-1}$ respectively.
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Given below are two statements, one is labelled as Assertion Aand the other is labelled as Reason R .
Assertion A: The spin only magnetic moment value for $^{3 -}$ is whereas for [Fe(H2O)6]
Fe ( CN ) $_{6}$ 1 . 74 BM,
FeH $_{2}$ O $_{6}^{3 +}$ is 5 . 92 BM .
Reason B: In both complexes, Feis present in +3oxidation state.
In the light of the above statements, choose the correct answer from the options given below:
a.
Ais false but Ris true
b.
Ais true but Ris false
c.
Both Aand Rare true but Ris NOTthe correct
explanation of A
d.
Both Aand Rare true andRis the correct
explanation of A
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For the adsorption of hydrogen on platinum, the activation energy is 30 kJ mol $^{- 1}$ and for the adsorption of
hydrogen on nickel, the activation energy is 41 . 4 kJ mol $^{- 1}$ . The logarithm of the ratio of the rates of
chemisorption on equal areas of the metals at 300 Kis _______(Nearest integer)
Given: In10 = 2 . 3
R = 8 . 3 J K $^{-1}$ mol $^{-1}$
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Match List I and List II
List I List II
Vitamin Deficiency disease
A Vitamin A I Beri-Beri
B Thiamine II Cheilosis
C Ascorbic acid III Xerophthalmia
D Riboflavin IV Scurvy
Choose the correct answer from the options given below
a.
A - III, B - I, C - IV, D - II
b.
A - IV, B - I, C - III, D - II
c.
A - IV, B - II, C - III, D - I
d.
A - III, B - II, C - IV, D - I
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If 5moles of BaCl $_{2}$ is mixed with 2moles of Na $_{3}$ PO $_{4}$ , the maximum number of moles of Ba $_{3}$ PO $_{42}$ formed is
_________(Nearest integer)
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Which of the following options are correct for the reaction?
$^{-}$ (aq) + Zn(s) $\rightarrow$2Au(s) $^{2 -}$ (aq)
2Au ( CN ) $_{2}$ + Zn ( CN ) $_{4}$
A. Redox reaction
B. Displacement reaction
C. Decomposition reaction
D. Combination reaction
Choose the correct answer from the options given below:
a.
A only
b.
A and D only
c.
A and B only
d.
C and D only
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The wavelength of an electron of kinetic energy 4 . 50 $\times$ 10 $^{-29}$ Jis ________ $\times$ 10 - 5 m . (Nearest integer)
Given: mass of electron is9 $\times$ 10 - 31 kg, h = 6 . 6 $\times$ 10 - 34 Js
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A compound is formed by two elements Xand Y . The element Yforms cubic close packed arrangement and
those of element Xoccupy one third of the tetrahedral voids. What is the formula of the compound?
a.
X $_{2}$ Y $_{3}$
b.
X $_{3}$ Y $_{2}$
c.
X $_{3}$ Y
d.
XY $_{3}$
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The number of species from the following which have square pyramidal structure is _______
PF $_{5}$ , BrF $^{-}_{4}$ , IF $_{5}$ , BrF $_{5}$ , XeOF $_{4}$ , ICl $^{-}_{4}$
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Match List I with List II
LIST I - Enzymatic reaction LIST II - Enzyme
A Sucrose$\rightarrow$ Glucose and Fructose I Zymase
B Glucose $\rightarrow$ ethyl alcohol and CO $_{2}$ II Pepsin
C Starch $\rightarrow$ Maltose III Invertase
D Proteins $\rightarrow$ Amino acids IV Diastase
Choose the correct answer from the options given below.
a.
A - I, B - II, C - IV, D - III
b.
A - III, B - I, C - IV, D - II
c.
A - III, B - I, C - II, D - IV
d.
A - I, B - IV, C - III, D - II
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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: Loss of electron from hydrogen atom results in nucleus of ~1 . 5 $\times$ 10 $^{- 3}$ pmsize.
Reason R: Proton H $^{+}$ always exists in combined form.
In the light of the above statements, choose the most appropriate answer from the options given below:
a.
Both Aand Rare correct and Ris the correct
explanation of A
b.
A is correct but R is not correct
c.
A is not correct but R is correct
d.
Both Aand Rare correct but Ris NOTthe correct
explanation of A
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Match List I with List II
List I List II
Oxide Type of bond
A N $_{2}$ O $_{4}$ I 1 N = O bond
B NO $_{2}$ II 1 N - O - N bond
C N $_{2}$ O $_{5}$ III 1 N - N bond
D N $_{2}$ O IV 1 N = N / N $\equiv$ N bond
Choose the correct answer from the options given below :
a.
A - III, B - I, C - II, D - IV
b.
A - II, B - IV, C - III, D - I
c.
A - III, B - I, C - IV, D - II
d.
A - II, B - I, C - III, D - IV
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Consider the graph of Gibbs free energy G vs extent of reaction. The number of statement/s from the following
which are true with respect to points (a), (b) and (c) is ______
A. Reaction is spontaneous at (a) and (b)
B. Reaction is at equilibrium at point (b) and non-spontaneous at point (c)
C. Reaction is spontaneous at (a) and non-spontaneous at (c)
D. Reaction is non-spontaneous at (a) and (b)
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Match List-I with .
List-I List-II
Name of reaction Reagent used
AHell-Volhard Zelinsky reaction I NaOH + I $_{2}$
BIodoform reaction II ( i ) CrO $_{2}$ Cl $_{2}$ , CS $_{2}$ ( ii ) H $_{2}$ O
CEtard reaction III ( i ) Br $_{2}$ / red phosphorus ( ii ) H $_{2}$ O
DGatterman-Koch reaction IV CO, HCl, anhyd . AlCl $_{3}$
Choose the correct answer from the options given below:
a.
A $\rightarrow$III; B $\rightarrow$I; C $\rightarrow$II; D $\rightarrow$IV
b.
A $\rightarrow$I; B $\rightarrow$II; C $\rightarrow$III; D $\rightarrow$IV
c.
A $\rightarrow$III; B $\rightarrow$II; C $\rightarrow$I; D $\rightarrow$IV
d.
A $\rightarrow$III; B $\rightarrow$I; C $\rightarrow$IV; D $\rightarrow$II
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Match List-I with List-II.
List-I List-II
Element detected Reagent used/Product formed
A Nitrogen I Na $_{2}$ FeCN $_{5}$ NO
B Sulphur II AgNO $_{3}$
C Phosphorus III Fe $_{4}$ FeCN $_{63}$
D Halogen IV NH $_{42}$ MoO $_{4}$
Choose the correct answer from the options given below:
a.
A $\rightarrow$III; B $\rightarrow$I; C $\rightarrow$IV; D $\rightarrow$II
b.
A $\rightarrow$II; B $\rightarrow$IV; C $\rightarrow$I; D $\rightarrow$ III
c.
A $\rightarrow$IV; B $\rightarrow$II; C $\rightarrow$I; D $\rightarrow$III
d.
A $\rightarrow$II; B $\rightarrow$I; C $\rightarrow$IV; D $\rightarrow$III
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Let the point π, π+ 1lie inside the region πΈ= π₯, π¦: 3 - π₯$\leq$π¦$\leq$$\sqrt$9 - π₯ $^{2}$ , 0 $\leq$π₯$\leq$3 .If the set of all values of
πis the interval π, π,then π $^{2}$ + π- π $^{2}$ is equal to ________ .
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Let the image of the point π( 1, 2, 3 ) in the plane 2π₯- π¦+ π§= 9be π.If the coordinates of the point π
are ( 6, 10, 7 ) , then the square of the area of the triangle πππ is _______ .
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If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $^{4}$ $\sqrt$2 + $\frac{1}{^{4}$\sqrt{\,}$3}^{π}$ is
$\sqrt$6: 1, then the third term from the beginning is:
a.
30$\sqrt$2
b.
30$\sqrt$3
c.
60$\sqrt$2
d.
60$\sqrt$3
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If the area of the region π= ( π₯, π¦) : 2π¦- π¦ $^{2}$ $\leq$π₯ $^{2}$ $\leq$2π¦, π₯$\geq$π¦is equal to $\frac{π+ 2}{π+ 1}$ - $\frac{π}{π- 1}$ ,then the natural number
πis equal to _______
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One vertex of a rectangular parallelopiped is at the origin πand the lengths of its edges along π₯, π¦and π§axes
are 3, 4and 5units respectively. Let πbe the vertex ( 3, 4, 5 ) . Then the shortest distance between the
diagonal ππand an edge parallel to π§axis, not passing through πor πis
a.
$\frac{12}{$\sqrt{\,}$5}$
b.
12$\sqrt$5
c.
$\frac{12}{5$\sqrt{\,}$5}$
d.
$\frac{12}{5}$
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A pair of dice is thrown 5times. For each throw, a total of 5is considered a success. If the probability of at
least 4successes is $\frac{π}{311}$ , then πis equal to
a.
82
b.
75
c.
164
d.
123
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A circle passing through the point ππΌ, π½in the first quadrant touches the two coordinate axes at the points π΄
and π΅. The point πis above the line π΄π΅. The point πon the line segment π΄π΅is the foot of perpendicular
from πon π΄π΅.If ππis equal to 11units, then the value of πΌπ½is _______
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Let the position vectors of the points π΄, π΅, πΆand π·be 5 $^{^}$ i + 5 $^{^}$ j + 2$\lambda$k, $^{^}^{^}$ i + 2 $^{^}$ j + 3k, $^{^}$ - 2 $^{^}$ i + $\lambda$ $^{^}$ j + 4k $^{^}$ and
- $^{^}$ i + 5 $^{^}$ j + 6k . $^{^}$ Let the set π= {π$\in$β: the points π΄, π΅, πΆand π·are coplanar} . The $\sum$ $_{π$\in$π}$ (π+ 2 ) $^{2}$ is equal
to
a.
25
b.
$\frac{37}{2}$
c.
14
d.
41
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Let π$\in$β€and π‘be the greatest integer $\leq$π‘, then the number of points, where the function
ππ₯= π+ 13 sinπ₯, π₯$\in$0, πis not differentiable, is ____________
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If the system of equations
π₯+ π¦+ ππ§= π
2π₯+ 5π¦+ 2π§= 6
π₯+ 2π¦+ 3π§= 3
has infinitely many solutions, then 2π+ 3πis equal to
a.
25
b.
20
c.
23
d.
28
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Let π΄= π $_{ππ2 $\times$ 2}$ ,where π $_{ππ}$ $\neq$0for all π, πand π΄ $^{2}$ = πΌ, Let abe the sum of all diagonal elements of π΄and π= π΄
Then 3π $^{2}$ + 4π $^{2}$ is equal to
a.
4
b.
14
c.
7
d.
3
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If the equation of the plane passing through the line of intersection of the planes
2π₯- π¦+ π§= 3, 4π₯- 3π¦+ 5π§+ 9 = 0and parallel to the line $\frac{π₯+ 1}{-2}$ = $\frac{π¦+ 3}{4}$ = $\frac{π§- 2}{5}$ is ππ₯+ ππ¦+ ππ§+ 6 = 0,
then π+ π+ πis equal to
a.
12
b.
14
c.
16
d.
13
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The straight lines π $_{1}$ and π $_{2}$ pass through the origin and trisect the line segment of the line πΏ: 9π₯+ 5π¦= 45
between the axes. If π $_{1}$ and π $_{2}$ are the slopes of the lines π $_{1}$ and π $_{2}$ , then the point of intersection of the line
π¦= ( π $_{1}$ + π $_{2}$ ) π₯with πΏlies on
a.
π¦- 2π₯= 5
b.
6π₯+ π¦= 10
c.
π¦- π₯= 5
d.
6π₯- π¦= 15
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From the top π΄of a vertical wall π΄π΅of height 30 m, the angles of depression of the top πand bottom πof a
vertical tower ππare 15 $^{$\circ$}$ and 60 $^{$\circ$}$ respectively, π΅and πare on the same horizontal level. If πΆis a point on π΄π΅
such that πΆπ΅= ππ, then the area (in m $^{2}$ ) of the quadrilateral π΅πΆππis equal to
a.
300 ( $\sqrt$3 - 1 )
b.
300 ( $\sqrt$3 + 1 )
c.
600 ( $\sqrt$3 - 1 )
d.
200 ( $\sqrt$3 - 1 )
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The mean and variance of a set of 15numbers are 12and 14respectively. The mean and variance of another
set of 15numbers are 14and π $^{2}$ respectively. If the variance of all the 30numbers in the two sets is 13, then
π $^{2}$ is equal to
a.
10
b.
11
c.
9
d.
12
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Let π $_{1}$ , π $_{2}$ , π $_{3}$ , . . . . , π $_{π}$ be npositive consecutive terms of an arithmetic progression. If π> 0is its common
difference, then $_{π$\rightarrow$$\infty$}$ lim $\sqrt$ $\frac{π}{π} \frac{1}{$\sqrt{\,}$π1+$\sqrt{\,}$π2}$ + $\frac{1}{$\sqrt{\,}$π2+$\sqrt{\,}$π3}$ + β¦ + $\frac{1}{$\sqrt{\,}$ππ- 1+$\sqrt{\,}$ππ}$ is
a.
$\frac{1}{$\sqrt{\,}$π}$
b.
$\sqrt$π
c.
1
d.
2
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Let the tangent to the curve π₯ $^{2}$ + 2π₯- 4π¦+ 9 = 0at the point π1, 3on it meet the π¦-axis at π΄.Let the line
passing through πand parallel to the line π₯- 3π¦= 6meet the parabola π¦ $^{2}$ = 4π₯at π΅.If π΅lies on the line
2π₯- 3π¦= 8,then π΄π΅ $^{2}$ is equal to _______ .
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