Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2 . 0 cm $^{2}$ .
The area of cross section at the outlet is 10 mm $^{2}$ . If the piston is pushed at a speed of 4 cm s $^{-1}$ , the speed
of outgoing fluid is _____ cm s $^{-1}$
✓ Accepted Answer:80
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Q2mcq
A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the
magnet will
a.
Move down with an acceleration equal to g
b.
Oscillate inside the tube
c.
Move down with almost constant speed
Correct Answer
d.
Move down with an acceleration greater than g
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Q3nat
A force of -ππ $^{^}$ acts on the origin of the coordinate system. The torque about the point ( 2, - 3 ) is π(π $^{^}$ π+ π $^{^}$ π)
, The ratio of $\frac{π}{π}$ is $\frac{π₯}{2}$ . The value of π₯is
✓ Accepted Answer:3
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Q4mcq
Given below are two statements:
Statement I: For diamagnetic substance -1 $\leq$x < 0, where xis the magnetic susceptibility.
Statement II: Diamagnetic substance when placed in an external magnetic field, tend to move from stronger
to weaker part of the field. In the light of the above statements, choose the correct answer from the options
give below.
a.
Both Statement Iand Statement IIare False
b.
Statement Iis correct but Statement IIis false
c.
Statement Iis incorrect but Statement IIis true
d.
Both Statement Iand Statement IIare true
Correct Answer
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Q5nat
A rectangular parallelopiped is measured as 1 cm $\times$ 1 cm $\times$ 100 cm. If its specific resistance is
3 $\times$ 10 $^{-7}$ $\Omega$ m, then the resistance between its two opposite rectangular faces will be _____$\times$ 10 $^{-7}$ $\Omega$.
✓ Accepted Answer:3
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Q6mcq
Given below are two statements:
Statement I: Rotation of the earth shows effect on the value of acceleration due to gravity ( π).
Statement II: The effect of rotation of the earth on the value of πat the equator is minimum and that at the
pole is maximum.
In the light of the above statements, choose the correct answer from the options given below
a.
Statement I is false but statement II is true
b.
Both Statement I and Statement II are true
c.
Both Statement I and Statement II are false
d.
Statement I is true but statement II is false
Correct Answer
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Q7mcq
Given below are two statements: one is labelled as Assertion Aand the other is labelled as Reason R
Assertion A: An electric fan continues to rotate for some time after the current is switched off.
Reason R: Fan continues to rotate due to inertia of motion.
In the light of above statements, choose the most appropriate answer from the options given below.
a.
Ais correct but Ris not correct
b.
Ais not correct but Ris correct
c.
Both Aand Rare correct and Ris the correct
explanation of A
Correct Answer
d.
Both Aand R are correct but Ris NOTthe
correct explanation of A
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Q8nat
A rectangular block of mass 5 kgattached to a horizontal spiral spring executes simple harmonic motion of
amplitude 1 mand time period 3 . 14 s. The maximum force exerted by spring on block is ___ N.
✓ Accepted Answer:20
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Q9mcq
In an experiment with vernier callipers of least count 0 . 1 mm, when two jaws are joined together the zero of
vernier scale lies right to the zero of the main scale and 6 $^{th}$ division of vernier scale coincides with the main
scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between
3 . 2 cmand 3 . 3 cmmarks and 4 $^{th}$ division of vernier scale coincides with the main scale division. The
diameter of bob is measured as
a.
3 . 22 cm
b.
3 . 18 cm
Correct Answer
c.
3 . 26 cm
d.
3 . 25 cm
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Q10nat
A straight wire carrying a current of 14 Ais bent into a semicircular arc of radius 2 . 2 cmas shown in the
figure. The magnetic field produced by the current at the centre πof the arc is ____ $\times$ 10 $^{- 4}$ T
✓ Accepted Answer:2
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A gas mixture consists of 2moles of oxygen and 4moles of neon at temperature π. Neglecting all vibrational
modes, the total internal energy of the system will be:
a.
11π π
b.
8π π
c.
4π π
d.
16π π
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A point object πis placed in front of two thin symmetrical coaxial convex lenses πΏ $_{1}$ and πΏ $_{2}$ with focal length
24 cmand 9 cmrespectively. The distance between two lenses is 10 cmand the object is placed 6 cm
away from lens πΏ $_{1}$ as shown in the figure. The distance between the object and the image formed by the system
of two lenses is _____________ cm
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The variation of stopping potential V $_{0}$ as a function of the frequency ( π)of the incident light for a metal is
shown in figure. The work function of the surface is
a.
2 . 98 eV
b.
2 . 07 eV
c.
1 . 36 eV
d.
18 . 6 eV
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A square loop of side 2 . 0 cmis placed inside a long solenoid that has 50turns per centimetre and carries a
sinusoidally varying current of amplitude 2 . 5 Aand angular frequency 700 rad s $^{-1}$ . The central axes of
the loop and solenoid coincide. The amplitude of the emf induced in the loop is π₯$\times$ 10 $^{-4}$ V. The value of π₯is
___________
( Take, π= $\frac{22}{7}$
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Youngβs moduli of the material of wires Aand Bare in the ratio of 1 : 4, while its area of cross sections are
in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation
produced in the wires A and B will be in the ratio of [Assume length of wires Aand Bare same]
a.
12 : 1
b.
1 : 36
c.
36 : 1
d.
1 : 12
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The distance between two plates of a capacitor is πand its capacitance is πΆ $_{1}$ , when air is the medium between
the plates. If a metal sheet of thickness $\frac{2π}{3}$ and of the same area as plate is introduced between the plates, the
capacitance of the capacitor becomes πΆ $_{2}$ . The ratio $\frac{πΆ2}{πΆ1}$ is
a.
3 : 1
b.
2 : 1
c.
4 : 1
d.
1 : 1
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The time period of a satellite, revolving above earth's surface at a height equal to Rwill be (Given
π= π $^{2}$ m s $^{-2}$ , π = radius of earth)
a.
$\sqrt$2R
b.
$\sqrt$8R
c.
$\sqrt$32R
d.
$\sqrt$4R
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A person travels π₯distance with velocity π£ $_{1}$ and then π₯distance with velocity π£ $_{2}$ in the same direction. The
average velocity of the person is π£, then the relation between π£, π£ $_{1}$ and π£ $_{2}$ will be
Two projectiles are projected at 30$^{\circ}$and 60$^{\circ}$with the horizontal with the same speed. The ratio of the maximum
height attained by the two projectiles respectively is:
a.
$\sqrt$3 : 1
b.
1 : $\sqrt$3
c.
2 : $\sqrt$3
d.
1 : 3
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The ratio of intensities at two points Pand Qon the screen in a Young's double slit experiment where phase
difference between two waves of same amplitude are $\frac{$\pi$}{3}$ and $\frac{$\pi$}{2}$ , respectively are
a.
2 : 3
b.
1 : 3
c.
3 : 1
d.
3 : 2
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If the maximum load carried by an elevator is 1400 kg ( 600 kg-Passengers + 800 kg-elevator ) ,
which is moving up with a uniform speed of 3 m s $^{-1}$ and the frictional force acting on it is 2000 N, then
the maximum power used by the motor is _____________kW . π= 10 m s $^{-2}$
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An electron revolves around an infinite cylindrical wire having uniform linear charge density 2 $\times$ 10 $^{-8}$ C m $^{-1}$
in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of
electron with which it is revolving is ______________ $\times$ 10 $^{6}$ m s $^{-1}$ . Given mass of electron
= 9 $\times$ 10 $^{-31}$ kg
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The amplitude of magnetic field in an electromagnetic wave propagating along π¦-axis is 6 . 0 $\times$ 10 $^{- 7}$ T.
The maximum value of electric field in the electromagnetic wave is
a.
2 $\times$ 10 $^{15}$ V m $^{- 1}$
b.
180 V m $^{- 1}$
c.
6 . 0 $\times$ 10 $^{- 7}$ V m $^{- 1}$
d.
5 $\times$ 10 $^{14}$ V m $^{- 1}$
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The correct relationships between unit cell edge length βaβ and radius of sphere βrβ for face-centred and body-
centred cubic structures respectively are:
a.
2$\sqrt$2r = aand $\sqrt$3r = 4a
b.
r = 2$\sqrt$2aand 4r = $\sqrt$3a
c.
r = 2$\sqrt$2aand $\sqrt$3r = 4a
d.
2$\sqrt$2r = aand 4r = $\sqrt$3a
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The number of molecules from the following which contain only two lone pair of electrons is _____________
H $_{2}$ O, N $_{2}$ , CO, XeF $_{4}$ , NH $_{3}$ , NO, CO $_{2}$ , F $_{2}$
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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 energy required to form Mg $^{2 +}$ from Mgis much higher than that required to produce Mg $^{+}$
Reason R:Mg $^{2 +}$ is small ion and carry more charge than Mg $^{+}$
In the light of the above statements, choose the correct answer from the options given below.
a.
Both Aand Rare true but Ris NOTthe correct
explanation of A
b.
Ais true but Ris false
c.
Ais false but Ris true
d.
Both Aand Rare true and Ris the correct
explanation of A
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The correct order for acidity of the following hydroxyl compound is
(A) CH $_{3}$ OH
(B) CH $_{33}$ COH
(C)
(D)
(E)
Choose the correct answer from the options given below:
a.
C > E > D > B > A
b.
E > D > C > B > A
c.
D > E > C > A > B
d.
E > C > D > A > B
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The number of incorrect statement/s from the following is ______________
A. The successive half lives of zero order reactions decreases with time.
B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction
C. Order and molecularity of a chemical reaction can be a fractional number
D. The rate constant units of zero and second order reaction are molL $^{-1}$ s $^{-1}$ and mol $^{-1}$ L s $^{-1}$ respectively
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An aqueous solution of volume 300 cm $^{3}$ contains 0 . 63 gof protein. The osmotic pressure of the solution at
300 Kis 1 . 29 mbar. The molar mass of the protein is gmol $^{-1}$ .
Given : R = 0 . 083 L $_{bar}$ K $^{-1}$ mol $^{-1}$
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The electron in the n $^{th}$ orbit of Li $^{2 +}$ is excited to ( n + 1 ) orbit using the radiation of energy
1 . 47 $\times$ 10 $^{-17}$ J(as shown in the diagram). The value of nis ___________
Given : R $_{H}$ = 2 . 18 $\times$ 10 $^{-18}$ J
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Match List-I with List-II
List-I List-II
A 16 gof CH $_{4}$ ( g ) I Weighs 28g
B 1 gof H $_{2}$ ( g ) II 60 . 2 $\times$ 10 $^{23}$ electrons
C 1 moleof N $_{2}$ ( g ) III Weighs 32g
D 0 . 5 mol of SO $_{2}$ ( g ) IV Occupies11 . 4 Lvolume at STP
Choose the correct answer from the options given below:
a.
A-II, B-III, C-IV, D-I
b.
A-II, B-IV, C-I, D-III
c.
A-I, B-III, C-II, D-IV
d.
A-II, B-IV, C-III, D-I
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In Carius tube, an organic compound ' X' is treated with sodium peroxide to form a mineral acid ' Y'. The
solution of BaCl $_{2}$ is added to ' Y' to form a precipitate ' Z'. ' Z' is used for the quantitative estimation of an
extra element. ' X' could be
a.
Cytosine
b.
A nucleotide
c.
Methionine
d.
Chloroxylenol
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The number of endothermic process/es from the following is _______.
A. I $_{2}$ ( g ) $\rightarrow$2I ( g )
B. HCl ( g ) $\rightarrow$H ( g ) + Cl ( g )
C. H $_{2}$ O ( l ) $\rightarrow$H $_{2}$ O ( g )
D. C ( s ) + O $_{2}$ ( g ) $\rightarrow$CO $_{2}$ ( g )
E. Dissolution of ammonium chloride in water
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Given below are two statements: one is labelled as Assertion Aand the other is labelled as Reason R.
Assertion A: Physical properties of isotopes of hydrogen are different.
Reason R: Mass difference between isotopes of hydrogen is very large.
In the light of the above statements, choose the correct answer from the options given below:
a.
Both A and Rare true and Ris the correct
explanation of A
b.
Ais false but Ris true
c.
Ais true but Ris false
d.
Both Aand Rare true but Ris NOTthe correct
explanation of A
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A ( g ) $\rightleftharpoons$2 B ( g ) + C ( g )
For the given reaction, if the initial pressure is 450 mmHgand the pressure at time tis720 mmHgat a
constant temperatureTand constant volume V. The fraction of A ( g ) decomposed under these conditions is
x $\times$ 10 $^{-1}$ . The value of xis (nearest integer)
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The correct order of the number of unpaired electrons in the given complexes is
(A) [Fe ( CN ) $_{6}$ ] $^{3 -}$
(B) FeF $_{6}^{3 -}$
(C) CoF $_{6}^{3 -}$
(D) Cr ( oxalate $^{3 -}$
) $_{3}$
(E) Ni ( CO ) $_{4}$
Choose the correct answer from the options given below:
a.
E < A < D < C < B
b.
E < A < B < D < C
c.
A < E, C < B < D
d.
A < E < D < C < B
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The specific conductance of 0 . 0025Macetic acid is 5 $\times$ 10 $^{-5}$ S cm $^{-1}$ at a certain temperature. The
dissociation constant of acetic acid is ___________ $\times$ 10 $^{-7}$ .(Nearest integer)
Consider limiting molar conductivity of CH $_{3}$ COOHas 400 S cm $^{2}$ mol $^{-1}$
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Given below are two statements: one is labelled as Assertion Aand the other is labelled as Reason R.
Assertion A: 3 . 1500 π of hydrated oxalic acid dissolved in water to make 250 . 0 ππΏsolution will result
in 0 . 1 πoxalic acid solution.
Reason R: Molar mass of hydrated oxalic acid is 126 π πππ $^{- 1}$ .
In the light of the above statements, choose the correct answer from the options given below:
a.
Both Aand Rare true but Ris NOTthe correct
explanation of A
b.
Ais true but Ris false
c.
Both Aand Rare true and Ris the correct
explanation of A
d.
Ais false but Ris true
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Let πbe the mean and πbe the standard deviation of the distribution
π $_{π}$ 0 1 2 3 4 5
π $_{π}$ π+ 2 2π π $^{2}$ - 1 π $^{2}$ - 1 π $^{2}$ + 1 π- 3
where π΄π $_{π}$ = 62. If π₯denotes the greatest integer $\leq$π₯, thenπ $^{2}$ + π $^{2}$ is equal to
a.
9
b.
8
c.
7
d.
6
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2
Let f be a continuous function satisfying $\int$ $^{t}_{0}$ f ( x ) + x $^{2}$ dx = $\frac{4}{3}$ t $^{3}$ , $\forall$t > 0. Then f $\frac{$\pi$2}{4}$ is equal to
a.
$\pi$ $^{2}$ 1 - $\frac{$\pi$2}{16}$
b.
-$\pi$1 + $\frac{$\pi$3}{16}$
c.
$\pi$1 - $\frac{$\pi$3}{16}$
d.
-$\pi$ $^{2}$ 1 + $\frac{$\pi$2}{16}$
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Let π΄be the point 1, 2and π΅be any point on the curve π₯ $^{2}$ + π¦ $^{2}$ = 16. If the centre of the locus of the point π,
which divides the line segment π΄ π΅in the ratio 3: 2is the point πΆπΌ, π½, then the length of the line segment π΄πΆ
is
a.
$\frac{3$\sqrt{\,}$5}{5}$
b.
$\frac{4$\sqrt{\,}$5}{5}$
c.
$\frac{2$\sqrt{\,}$5}{5}$
d.
$\frac{6$\sqrt{\,}$5}{5}$
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Let ππ₯= ππ₯+ π1 - π₯and π $^{"}$ π₯> 0, π₯$\in$0, 1. If πis decreasing in the interval 0, πΌand increasing in the interval
πΌ, 1, then tan $^{-1}$ 2πΌ+ tan $^{-1 1}_{πΌ}$ + tan $\frac{-1πΌ+ 1}{πΌ}$ is equal to
a.
$\pi$
b.
$\frac{5$\pi$}{4}$
c.
$\frac{3$\pi$}{4}$
d.
$\frac{3$\pi$}{2}$
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Let the quadratic curve passing through the point -1, 0and touching the line π¦= π₯at 1, 1be π¦= ππ₯. Then the
π₯-intercept of the normal to the curve at the point πΌ, πΌ+ 1in the first quadrant is
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If the points πand πare respectively the circumcenter and the orthocentre of a βπ΄π΅πΆ, then $^{$\rightarrow$}$ ππ΄+ $^{$\rightarrow$}$ ππ΅+ $^{$\rightarrow$}$ ππΆis
equal to _______
$\rightarrow$ $\rightarrow$
a.
2ππ
b.
2ππ
c.
$^{$\rightarrow$}$ ππ
d.
$^{$\rightarrow$}$ ππ
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Let the tangent at any point Pon a curve passing through the points 1, 1and $\frac{1}{10}$ , 100, intersect positive x-axis
and y-axis at the points Aand Brespectively. If π π΄: π π΅= 1: πand y = yxis the solution of the
differential equation π $\frac{ππ¦}{ππ₯}$ = ππ₯+ $\frac{π}{2}$ , π¦0 = π, then 4y1 - 5log $_{e}$ 3is equal to _______________
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Let πbe the set of values of $\lambda$, for which the system of equations
6ππ₯- 3π¦+ 3π§= 4π $^{2}$ , 2π₯+ 6ππ¦+ 4π§= 1and 3π₯+ 2π¦+ 3ππ§= πhas no solution. Then,12 $\sum$ $_{π$\in$π}$ πis equal to
_______.
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Let the equations of two adjacent sides of a parallelogram π΄π΅πΆπ·be 2π₯- 3π¦= - 23and 5π₯+ 4π¦= 23. If the
equation of its one diagonal π΄πΆis 3π₯+ 7π¦= 23and the distance of π΄from the other diagonal is π, then 50π $^{2}$
is equal to ______________
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Let a die be rolled ntimes. Let the probability of getting odd numbers seven times be equal to the probability
of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{π}{215}$ , then πis equal to
a.
60
b.
15
c.
90
d.
30
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In the figure, $\theta$ $_{1}$ + $\theta$ $_{2}$ = $\frac{$\pi$}{2}$ and $\sqrt$3BE = 4AB. If the area of βCABis 2$\sqrt$3 - 3 unit $^{2}$ , when $\frac{$\theta$2}{$\theta$1}$ is the largest,
then the perimeter (in unit) of βCEDis equal to
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Let the image of the point P ( 1, 2, 6 ) in the plane passing through the points A ( 1, 2, 0 ) and
B ( 1, 4, 1 ) C ( 0, 5, 1 ) be Q ( $\alpha$, $\beta$, $\gamma$ ). Then $\alpha$ $^{2}$ + $\beta$ $^{2}$ + $\gamma$ $^{2}$ equal to
a.
65
b.
62
c.
76
d.
70
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Let the foot of perpendicular from the point π΄4, 3, 1on the plane π: π₯- π¦+ 2π§+ 3 = 0be π. If
π΅( 5, πΌ, π½) , πΌ, π½$\in$β€is a point on plane πsuch that the area of the triangle π΄π΅πis 3$\sqrt$2, then πΌ $^{2}$ + π½ $^{2}$ + πΌπ½is
equal to _____________
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Let the number ( 22 ) $^{2022}$ + ( 2022 ) $^{22}$ leave the remainder $\alpha$when divided by 3and $\beta$when divided by 7
. Then ($\alpha$ $^{2}$ + $\beta$ $^{2}$ )is equal to
a.
20
b.
13
c.
5
d.
10
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Eight persons are to be transported from city Ato city Bin three cars of different makes. If each car can
accommodate at most three persons, then the number of ways, in which they can be transported, is
a.
1120
b.
3360
c.
1680
d.
560
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Let a circle of radius 4be concentric to the ellipse 15π₯ $^{2}$ + 19π¦ $^{2}$ = 285. Then the common tangents are
inclined to the minor axis of the ellipse at the angle
a.
$\frac{$\pi$}{3}$
b.
$\frac{$\pi$}{4}$
c.
$\frac{$\pi$}{6}$
d.
$\frac{$\pi$}{12}$
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Suppose π $_{1}$ , π $_{2}$ , 2, π $_{3}$ , π $_{4}$ be in an arithmetico-geometric progression. If the common ratio of the corresponding
geometric progression is 2and the sum of all 5terms of the arithmetico-geometric progression is $\frac{49}{2}$ , then π $_{4}$ is
equal to ______________
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Let the line $\frac{π₯}{1}$ = $\frac{6 - π¦}{2}$ = $\frac{π§+ 8}{5}$ intersect the lines $\frac{π₯- 5}{4}$ = $\frac{π¦- 7}{3}$ = $\frac{π§+ 2}{1}$ and $\frac{π₯+ 3}{6}$ = $\frac{3 - π¦}{3}$ = $\frac{π§- 6}{1}$ at the points Aand B
respectively. Then the distance of the mid-point of the line segment π΄π΅from the plane 2π₯- 2π¦+ π§= 14is
a.
3
b.
$\frac{11}{3}$
c.
4
d.
$\frac{10}{3}$
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Let π΄= 2, 3, 4and π΅= 8, 9, 12. Then the number of elements in the relation
π = π $_{1}$ , π $_{1}$ , π $_{2}$ , π $_{2}$ $\in$π΄$\times$ π΅, π΄$\times$ π΅: π $_{1}$ divides π $_{2}$ and π $_{2}$ divides π $_{1}$ is
a.
36
b.
24
c.
18
d.
12
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If the domain of the function ππ₯= sec $^{-1}\frac{2π₯}{5π₯+ 3}$ is [πΌ, π½) $\cup$( πΎ, πΏ], then 3πΌ+ 10π½+ πΎ+ 21πΏis equal to
__________
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