Change in number of magnetic field
lines induces
A. current in coil
B. EMF in the coil
c. frequency in coil
D. both A and C


Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the
acceleration due to gravity on the surface of earth is \( g \) and that on the surface of the new planet is \( g^{\prime} \), then:
A \( \cdot g^{\prime}=3 g \)
B. \( g^{\prime}=\frac{g}{3} \)
c. \( g^{\prime}=9 g \)
D. \( g^{\prime}=27 g \)


The probable first prehistoric man was
A. Ramapithecus
B. Homo habilis
c. Australopithecus
D. zinjanthropus


How many permutations can be made with the letters of the word
'MEADOW \( S^{\prime} \) such that the vowels
occupy even places?
A. 720
в. 144
\( c \cdot 120 \)
D. 36


Cambium found in vascular bundles of
dicot stem is
A. Intercalary meristem
B. Fascicular cambium
c. secondary meristem
D. All of the above


Find the square root of 121 using repeated subtraction.


A wooden plank of length 1 m and
uniform cross section is hinged at one
end to the bottom of a tank as shown in
the figure. The tank is filled with water
up to a height of 0.5 m. The specific
gravity of the plank is \( 0.5 . \) If the angle \( \theta \) by the inclination of that the plank
makes with the vertical in the
equilibrium position (exclude the case
\( \theta=0 \) ). Find the value of \( \frac{1}{\cos ^{2} \theta} \)


If \( \frac{x^{2}+3}{x^{4}(x+3)}=\frac{A}{(x+3)}+\frac{B}{x}+\frac{C}{x^{2}}+\frac{D}{x^{3}}+\frac{E}{x^{4}} \)
then
Match the following with \( \mathrm{I}, \mathrm{II}, \mathrm{III}, \mathrm{IV}, \mathrm{V} \)
\( \begin{array}{ll}\text { I) } A & \text { a) } \frac{4}{9} \\ \text { (i) }\end{array} \) \begin{tabular}{ll|l}
II) \( C \) & b) \( \frac{4}{27} \) \\
(II) \( B \) & c) \( -\frac{1}{3} \) \\
IV) \( E \) & d) \( -\frac{4}{27} \) \\
V) \( D \) & e) 1
\end{tabular}
\( A \cdot b, a, d, e, c \)
B. \( b, a, e, d, c \)
\( \mathbf{c} \cdot \mathrm{d}, \mathrm{b}, \mathrm{e}, \mathrm{a}, \mathrm{c} \)
D. a,b,c,d,e


The following four wires of length \( L \) and radius \( r \) are made of the same material
Which of these will have the largest
extension, when the same tension is
applied?
A. \( L=100 \mathrm{cm}, r=0.2 \mathrm{mm} \)
В. \( L=200 c m, r=0.4 m m \)
c. \( L=300 c m, r=0.6 m m \)
D. \( L=400 \mathrm{cm}, r=0.8 \mathrm{mm} \)


Statement 1: An increase in entropy
leads to an increase of randomness.
Statement 2: The lower energy state of ordered crystals has a high entropy.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Which of the following are common to images formed by both Concave and Convex lens?
A. Real and Inverted
B. Real and Erectedd
c. virtual and Erected
D. Virtual and Real


A fly strikes the windshield of a moving
truck as shown. What can you say about
the forces: the force on the fly and the
force on the truck.
A. Force on the fly \( > \) Force on the truck
B. Force on the fly \( < \) Force on the truck
c. Force on the fly = Force on the truck
D. None of thes


Let \( \mathbf{A}(\mathbf{1}, \mathbf{2}) \) and \( \mathbf{B}(\mathbf{3}, \mathbf{4}) \) be two points.
Let
\( \mathbf{C}(x, y) \) be a point such that \( (x- \)
1) \( (x-3)+(y-2)(y-4)=0 . \) If area
of
\( (\Delta A B C)=1, \) then the maximum
number of positions of
\( \mathbf{C} \) in \( \boldsymbol{x} \boldsymbol{y} \) -plane is
A . 2
B. 4
c. 8
D. None of these


State True or False.
Except \( \boldsymbol{H}_{2} \) and \( \boldsymbol{H} \boldsymbol{e}, \) intermolecular attractions have longer range than repulsions.
A. True
B. False


5-litre vessel contains 2 moles of each
of gases \( A \) and \( B \) at equilibrium. If 1 mole each of \( A \) and \( B \) are removed.
Calculate \( K_{c} \) for the reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \) \( B(g) \)


In defining the specific heat,
temperature is represented in \( ^{o} \boldsymbol{F} \)
instead of \( ^{\circ} \mathrm{C} \). Then the value of specific
heat will:
A. decrease
B. increase
c. remain constant
D. be converted to heat capacity


Find the fourteenth term of \( (3-a)^{15} \)


An air conditioner is rated
\( 240 V, 1.5 k W . \) The air conditioner is
switched on 8 hrs each day. What is
electrical energy consumed in 30 days?
\( \mathbf{A} \cdot 2.88 k W h \)
в. \( 360 k W h \)
c. \( 120 k W h \)
D. \( 240 k W h \)


Give an example for each of the following energy conversion: (1) electrical energy to kinetic energy. chemical energy to electrical energy (3) sound energy to electrical energy


What is the sign of \( \triangle G \) for the process of ice melting at \( 283 \mathrm{K} ? \)
A. \( \triangle G>0 \)
в. \( \triangle G=0 \)
c. \( \Delta G<0 \)
D. None of these


The far point of a myopic person is 40 cm. To see the distant objects clearly, the focal length and the power of the
lens used should be:
A. \( -40 \mathrm{cm},-2.5 \mathrm{D} \)
B. \( -25 \mathrm{cm},-4.0 \mathrm{D} \)
\( c \cdot+40 \mathrm{cm},+2.5 \mathrm{D} \)
D. \( -40 \mathrm{cm},+2.5 \mathrm{D} \)


If \( A=\tan 6^{0} \tan 42^{0} \) and \( B= \)
\( \cot 66^{0} \cot 78^{0}, \) then
\( A \cdot A=2 B \)
B. A=1/3 B
\( c \cdot A=B \)
D. 3A=2B


Which of the following spectra was not explained by Bohr's Atomic model? This question has multiple correct options
A. Spectra of single electron system
B. Hydrogen spectra
c. spectra other than Hydrogen like atoms
D. spectra of helium atom


The transformation ratio in the step-up
transformer is
A .
B. Greater than one
c. Less than one
D. The ratio greater or less than one depends on the other factors


Iron rod is immersed in \( K C l K C l \)
solution such that half its length is exposed to air and the other half
immersed in \( K C l K C l \) solution. The
part corroded faster is


The movement of mineral ions into
plant root cells as a result of diffusion is called:
A. Osmosis
B. Passive absorption
c. Active absorption
D. Endocytosis


A cell of emf \( E \) is connected to a
resistance \( R_{1} \) for time \( t \) and the amount
of heat generated in it is \( H . \) If the
resistance \( R_{1} \) is replaced by another
resistance \( \boldsymbol{R}_{2} \) and is connected to the
cell for the same time \( t, \) the amount of
heat generated in \( \boldsymbol{R}_{2} \) is \( 4 \boldsymbol{H} \). Then
internal resistance of the cell is:
A. \( \frac{2 R_{1}+R_{2}}{2} \)
в. \( \sqrt{R_{1} R_{2}} \times \frac{2 \sqrt{R_{2}}-\sqrt{R_{1}}}{\sqrt{R_{2}}-2 \sqrt{R_{1}}} \)
c. \( \sqrt{R_{1} R_{2}} \times \frac{\sqrt{R_{2}}-2 \sqrt{R_{1}}}{2 \sqrt{R_{2}}-\sqrt{R_{1}}} \)
D. \( \sqrt{R_{1} R_{2}} \times \frac{\sqrt{R_{2}}-\sqrt{R_{1}}}{\sqrt{R_{2}}+\sqrt{R_{1}}} \)


\( \operatorname{Let} \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi \)
then prove that \( x^{2}+y^{2}+z^{2}+2 x y z= \)
1


A solution of compound \( Z \) gives a light blue precipitate with aqueous ammonia. The precipitate
dissolves in an excess of ammonia.
A flame test is done on compound \( Z \) What is the colour of the flame?
A. Blue-green
B. Lilac
c. Red
D. Yellow


The image of the point (1,6,3) in the \( \operatorname{line} \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is?
A. (1,0,7)
в. (7,0,1)
c. (2,7,0)
D. (-1,-6,-3)


Using long division method, divide the polynomial \( 4 p^{3}-4 p^{2}+6 p-\frac{5}{2} \) by \( 2 p-1 \)
A \( \cdot 2 p^{2}-p-\frac{5}{2} \)
В \( \cdot 2 p^{2}+p+\frac{5}{2} \)
c. \( _{2 p^{2}-p+\frac{5}{2}} \)
D. None of the above


A Simple harmonic oscillator has a period of \( 0.01 s \) and an amplitude of \( 0.2 m . \) The magnitude of the velocity in \( m \) \( \sec ^{-1} \) at the mean position will be
A \( .20 \pi \)
в. 100
c. \( 40 \pi \)
D. \( 100 \pi \)


Arun was going for a run in the morning. He travelled a distance of \( 4 k m \) in one
hour. What could be the speed of Arun in
\( \boldsymbol{k m} / \boldsymbol{h r} ? \)
A . 4
B. 8
c. 2
\( D \)


If the points \( (h, 3,-4),(0,-7,10) \) and \( (1, k, 3) \) are collinear, then \( h+k \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c. -4
D. 14


Give the function of HCl


One of the following is not the function
of bile.
A. Fat emulsification
B. Disinfection of food
c. Reduction of acidity
D. Reduction of lipase


Identify the decimal and whole number
from the following.
\( \mathbf{6 3 . 7 9 3} \)


A force acts on a \( 3 g \) particle in such a
way that position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in metre and \( t \) is in
sec. The work done during the first \( 4 s \) is
A. 570 mJ
B. 450 mJ
c. \( 490 \mathrm{mJ} \)
D. 528 mJ


N particles moving in a straight line have initial velocities of \( 1,2,3, \dots \dots \dots \dots \)
\( \mathrm{m} / \mathrm{s} \) and accelerations of \( 1,2,3, \ldots \ldots \)
\( \mathrm{m} / \mathrm{s}^{2} \) respectively. If the initial spacing
between any two consecutive particles is same then, select the correct
alternative(s).

This question has multiple correct options
A. The distance between any two particles remains constant throughout
B. The distance between any two consecutive particles is same for all particles and increases with time
C. The distance between any two consecutive particles is different and increases with time
D. The distance between any two consecutive particles increases parabolically with time


After \( 10 s \) of the start of motion of both
objects \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) find the value of
velocity of \( \boldsymbol{A} \) if \( \boldsymbol{u}_{\boldsymbol{A}}=\boldsymbol{6} \boldsymbol{m} \boldsymbol{s}^{-1}, \boldsymbol{u}_{\boldsymbol{B}}= \)
\( 12 m s^{-1} \) and at \( T \) velocity of \( A \) is
\( 8 m s^{-1} \) and \( T=4 s \)
\( \mathbf{A} \cdot 12 m s^{-1} \)
\( \mathbf{B} \cdot 10 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. None of these


What are isotopes and isobars?


Formula of ferrocene is:
\( A \)
\( \left[F e(C N)_{6}\right]^{4-} \)
в. \( \left[F e(C N)_{6}\right]^{3+} \)
\( \left.\mathrm{c} \cdot_{[\mathrm{Fe}}(\mathrm{CO})_{5}\right] \)
D. \( \left[\mathrm{Fe}\left(C_{5} \mathrm{H}_{5}\right)_{2}\right. \)


Find out the volume of gases evolved by
passing \( 0.965 A \) current for \( 1 h r \) through an aqueous solution of
\( C H_{3} C O O N a \) at \( 25^{\circ} C \) and 1 at \( m \)


A flux of \( 1 m W b \) passes through a strip
having an area \( A=0.02 m^{2} . \) The plane
of the strip is at an angle of \( 60^{\circ} \) to the
direction of a uniform field B. The value
of B is:
A . \( 0.1 T \)
B. \( 0.058 T \)
c. \( 4.0 m T \)
D. None of the above


Which of the following is true regarding
superconductivity?
A. The superconducting state cannot exist in the presence of a magnetic field lesser than a critical value, even at absolute zero
B. The superconducting state exists in the presence of a magnetic field greater than a critical value, even at absolute zero
C. The superconducting state exists in the presence of a magnetic field lesser than a critical value, even at absolute zero
D. The superconducting state cannot exist in the presence of a magnetic field greater than a critical value, even at absolute zero


In the adjoining figure, \( A B \) and \( C D \) are
parallel lines. The transversals \( P Q \) and
\( R S \) intersect at \( U \) on the line \( A B . \) Given
that \( \angle D W U=110^{\circ} \) and \( \angle C V P=70^{\circ} \)
find the measure of \( \angle Q U S \)


Which of the following are transition
elements?
\( \mathrm{K}, \mathrm{Mn}, \mathrm{Ca}, \mathrm{Cs}, \mathrm{Fe}, \mathrm{Cu}, \mathrm{Pb} \)


The atomic number of third alkali metal
is :
\( \mathbf{A} \cdot \mathbf{3} \)
B. 11
c. 19
D. 37


Evaluate \( \cos (A+B) \cdot \cos (A-B)= \)
\( A \cdot \sin ^{2} A-\cos ^{2} B \)
B. \( \cos ^{2} A+\sin ^{2} B \)
\( \mathbf{c} \cdot \cos ^{2} A-\sin ^{2} B \)
\( \mathbf{D} \cdot \cos ^{2} A+\cos ^{2} B \)


A wire \( 2 \mathrm{m} \) in length suspended vertically stretches by \( 10 \mathrm{mm} \) when the mass of \( 10 \mathrm{kg} \) is attached to the lower end. The elastic potential energy gain by the wire is? \( \left(\operatorname{take} g=10 m / s^{2}\right) \)
A . 0.5
B. 5 J
c. 50
D. 500 J


A solution of the differential equation \( \left(\frac{d y}{d x}\right)^{2}-x \frac{d y}{d x}+y=0 \)
\( \mathbf{A} \cdot y=2 \)
в. \( y=2 x \)
\( \mathbf{c} \cdot y=2 x-4 \)
D. \( y=2 x^{2}-4 \)


Why is it dangerous to jump out of a
moving bus?


The radius of a wire is decreased to one-
third and its volume remains the same.
The new length is how many times the original length?
A. 1 time
B. 3 times
\( c .6 \) times
D. 9 times


Identify a 'chemical twin' among the following.
A. Zr-Ta
B. Nb-Tc
c. Hf-Re
D. Nb-Ta


The coefficient of self induction of a coil
is given by
\( ^{\text {A }} \cdot L=\left(-\frac{d I}{d t}\right) \)
B. \( L=-\frac{e d I}{d t} \)
c. \( _{L}=\frac{d I}{e d t} \)
D. \( L=\frac{d I}{d t} e^{2} \)


A boat is traveling due east at \( 12 m s^{-1} \)
A flag on the boat flaps at \( 53 N \) of \( W \) Another flag on the shore flaps due
north.
This question has multiple correct options
A. speed of wind with respect to ground is \( 16 \mathrm{ms}^{-1} \)
B. Speed of wind with respect to ground is \( 20 \mathrm{ms}^{-1} \)
c. speed of wind with respect to boat is \( 20 \mathrm{ms}^{-1} \)
D. speed of wind with respect to boat is \( 16 \mathrm{ms}^{-1} \)


Consider the following cell:
\[
\begin{array}{c}
\boldsymbol{P t}, \boldsymbol{H}_{2}(\boldsymbol{g}) \mid \boldsymbol{2} \boldsymbol{M} \boldsymbol{C H}_{3} \boldsymbol{C O O N H}_{4}(\boldsymbol{a} \boldsymbol{q}) \| \mathbf{2} \boldsymbol{n} \\
20
\end{array}
\]
\( a+m \)
0.2 atm
Given, \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \boldsymbol{o} \boldsymbol{f} \boldsymbol{C H}_{3} \boldsymbol{C O O H}= \)
4.74 and \( p K_{b} \) of \( N H_{4} \) OHis4.74.
If \( E \) is e.m.f. of the cell in volt, then the value of \( 1000 \mathrm{E} \) is \( \left[\text { Take } \frac{2.303 R T}{F}=\right. \) 0.059]\( (\text { e.g. }, \text { if the value is } 56, \) then write
answer as \( 6) \)


Answer the following:
Define Hydrocarbons.


If \( \log _{10} a, \log _{10}, \log _{10} c \) are in A.P., then
\( a, b, c \) must be in
A. A.P.
в. G.P.
c. н.P.
D. None of these


A wire is bent in the form of a circular
arc with a straight portion \( \boldsymbol{A B} \)

Magnetic induction at \( O \) when current
is flowing in the wire, is
\( ^{\text {A } \cdot} \frac{\mu_{0}}{2^{r}}(\pi-\theta+\tan \theta) \)
в. \( \frac{\mu_{0} I}{2 \pi r}(\pi+\theta-\tan \theta) \)
c. \( \frac{\mu_{0} I}{2 \pi r}(\pi-\theta+\tan \theta) \)
D. \( \frac{\mu_{0} I}{2 \pi_{r}}(-\tan \theta+\pi-\theta) \)


Prove that:
\( 2 m+7=9 \)


Which one of the following is present as an active ingredient in bleaching powder for bleaching action?
\( \mathbf{A} \cdot C a(O C l)_{2} \)
в. \( C a O_{2} C l \)
c. \( C a C l_{2} \)
D. \( C a O C l_{2} \)


Find the squares of 510 using the identity
\( (a+b)^{2}=a^{2}+2 a b+b^{2} \)


For the reaction show:
\[
\mathbf{3} C_{2} H_{2} \leftrightharpoons C_{6} H_{6}
\]
This equilibrium is established when 0.5 mole of benzene is present at a certain temperature. If equilibrium
constant of the reaction is 4 litre \( ^{-2} \)
mole \( ^{2} \). The total number of moles of all
the substances present at equilibrium
is :
(Note : The reaction is performed in a \( 1- \) litre vessel.)
A. 0.5
B.
c. 1.5
D. 2


In a reversible process:
A. entropy of the system increases.
B. entropy of the system decreases.
C. entropy of the combined system and surroundings does not change
D. entropy of all systems in the universe is constant.


III effect of deforestation is that, it
A. Increases temperature of earth
B. Increases pollution level
C. Increases CO \( _{2} \) level of atmosphere
D. All of the above


Two equal charges \( A \) and \( B \) each of \( 1 / 3 \times 10^{-6} C \) are placed \( 200 \mathrm{cm} \) apart
in air. A particle carrying a charge of \( -1 / 3 \times 10^{-6} C \) is projected along the
perpendicular bisector from the point 0 midway between \( A \) and \( B \) with a kinetic
energy of \( 10^{-3} J . \) Before the particle
starts to return it will cover a distance
A. \( 1 m \)
B. \( \sqrt{2} \mathrm{m} \)
c. \( \sqrt{3} \mathrm{m} \)
D. \( 1 / \sqrt{3} \mathrm{m} \)


Keystone species deserve protection
because these
A. are capable of surviving in harsh environmental conditions
B. indicate presence of certain minerals in the soil
C. have become rare due to overexploitation
D. play an important role in supporting other species.


What is the physical state of water at
\( \mathbf{3 0}^{\circ} \mathbf{C} ? \)
A. Solid
B. Liquid
\( c . \) Gas
D. None of the above


What kind of compound is Magnesium
chloride or \( M g C l_{2} \)
This question has multiple correct options
A. lonic compound
B. Electrovalent compound
c. covalent compound
D. Co-ordinate covalent compound


Sand is pouring from a pipe at the rate of \( 12 \mathrm{cm}^{3} / \mathrm{s} \). The falling sand forms a cone on the ground in such a way that
the height of the cone is always onesixth of the radius of the base. How fast
is the height of the sand cone increasing when the height is \( 4 \mathrm{cm} \)


A body projected vertically up has a displacement of \( 20 \mathrm{m} \) in the first ' \( \mathrm{n}^{\prime} \) seconds while it was moving up. Find its magnitude of displacement in the last n' seconds while falling down.
A. \( 40 \mathrm{m} \)
B. 10 \( m \)
\( c \cdot 20 m \)
D. 30 m


The method preferred for determining the molecular weight of a polymer is
A. osmotic pressure
B. gas density
c. lowering of freezing point
D. direct weighing of a single molecule


Assertion
"Fungi imperfect does not show
alternation of generation.
Reason
The diploid phase is present in only
zygote.
A. If both the assertion and the reason are true and the
reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


The radius and acceleration due to
gravity of the moon are \( \frac{1}{4} \) and \( \frac{1}{5} \) that of
the earth, the ratio of the mass of the
earth to mass of the moon is :
\( \mathbf{A} \cdot 1: 80 \)
B. 80: 1
c. 1: 20
D. 20:1


If \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{1-\sin 2 \boldsymbol{x}}, \) then \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \) is
equal to:
This question has multiple correct options
A. \( -(\cos x+\sin x) \), for \( x \in(\pi / 4, \pi / 2) \)
B. \( (\cos x+\sin x) \), for \( x \in(0, \pi / 4) \)
c. \( -(\cos x+\sin x) \), for \( x \in(0, \pi / 4) \)
D. None of these


Lines \( l \) and \( m \) and two circles lie in a
plane. If \( l \) passes through the centers of the two circles and if \( m \) is parallel to \( l \)
which of the following could NOT be the number of points at which \( m \) intersects the circles?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 3 \)
D. 4
E . 5


If \( i_{1}=3 \sin \omega t \) and \( i_{2}=4 \cos \omega t, \) then \( i_{3} \)
is -
\( \mathbf{A} \cdot 5 \sin \left(\omega t+53^{\circ}\right) \)
B. \( 5 \sin \left(\omega t+37^{\circ}\right) \)
\( \mathbf{c} \cdot 5 \sin \left(\omega t+45^{\circ}\right) \)
\( \mathbf{D} \cdot 5 \cos \left(\omega t+53^{\circ}\right) \)


Describe the process of assimilation of
food.


In Hertz's experiment the
of the
electromagnetic waves is equal to the kinetic energy of the charges oscillating between two spheres.
A. Frequency
B. Energy
c. wavelength
D. Velocity


Who is known as the father of nuclear
physics?
A. Ernest Rutherford
B. Dalton
c. J.J. Thomson
D. E. Goldstein


State whether the following statements
are true or false

Taxonomic group belonging to any one
of the taxonomic categories is known
as a taxon.
A. True
B. False


\( n \) identical cells each of electromotive
force \( e \) and internal resistance \( r \) are
connected in series of this combination
The current through \( V \) is:
A \( \cdot \frac{2 e}{n} \)
в. \( \frac{n e}{n R+r} \)
c. \( \frac{e}{R+n r} \)
D. \( \frac{n e}{R+r} \)


"14
incline. A device on the cart launches a
ball, forcing the ball perpendicular to
the incline, as shown above. Air
resistance is negligible. Where will the
ball land relative to the cart, and why?
A. The ball will land in front of the cart, because the balls acceleration component parallel to the plane is greater than the carts acceleration component parallel to the plane
B. The ball will land in front of the cart, because the ball has a greater magnitude of acceleration than the cart
C. The ball will land in the cart, because both the ball and
the cart have the component of acceleration parallel to the plane
D. The ball will land in the cart, because both the ball and the cart have the same magnitude of acceleration


The angles of a pentagon in degrees are \( x, x+20, x+40, x+60 \) and \( x+80, \) then
the smallest angle of the pentagon is
\( \mathbf{A} \cdot 50^{\circ} \)
B. \( 68^{\circ} \)
\( c \cdot 78^{\circ} \)
D. \( 85^{\circ} \)


Subtract :
\( \frac{2}{7} \) from \( \frac{19}{21} \)


Equation(s) or the straight line(s),
inclined at \( 30^{\circ} \) to the \( x \) -axis such that
the length of its (each of their) line segment(s) between the coordinate axes is 10 units is/are
This question has multiple correct options
A. \( x+\sqrt{3} y+5 \sqrt{3}=0 \)
в. \( x-\sqrt{3} y+5 \sqrt{3}=0 \)
c. \( x+\sqrt{3} y-5 \sqrt{3}=0 \)
D. \( x-\sqrt{3} y-5 \sqrt{3}=0 \)


Assertion
Statement I : A physical quantity can be regarded as a vector, if magnitude as well as direction is associated with it.
Reason

Statement II : A physical quantity can be regarded as a scalar quantity, if it is associated with magnitude only.
A. Statement-I is false, Statement-II is true
B. Statement-I is true, Statement-II is false
c. statement-l is true, statement-ll is true ; statement-I is NOT a correct explanation for Statement-
D. Statement-l is true, Statement-II is true ; Statement-I is correct explanation for Statement-


A parallel plate capacitor of capacitance \( 5 \mu F \) and plate separation \( 6 \mathrm{cm} \) is connected to a \( 1 \mathrm{V} \) battery and charged. A dielectric of dielectric
constant 4 and thickness \( 4 \mathrm{cm} \) is
introduced between the plates of the
capacitor. The additional charge that flows into the capacitor from the battery is
A. \( 2 \mu C \)
в. \( 3 \mu C \)
\( c \cdot 5 \mu C \)
D. 10 \( \mu C \)


If the given figure, AB II CD. then
\( B P O+P O Q+D Q O \) is
4
3.90
\( c \cdot 180 \)
D. \( 360^{\circ} \)


Select the correct match of algal class and its characteristic flagellation.
A. Chlorophyceae - 2-8 equal, apical
B. Phaeophyceae - 2, unequal, latera
c. Rhodophyceae- Absent
D. All of these


The correct descending order of the priority of the following atoms or group is:
\( -\boldsymbol{C H O},-\boldsymbol{C H}_{2} \boldsymbol{O H},-\boldsymbol{C H}_{3},-\boldsymbol{O H} \)
A .2,4,1,3
B. 1,2,3,4
c. \( 4,3,2, \)
D. 1,4,2,3


Petiole part of the leaf is also known as
A. Epipodium
B. Mesopodium
c. Hypopodium
D. None of the above


At a school, \( 20 \% \) of the students are
seniors. If all of the seniors attended the
school play, and \( 60 \% \) of all the students
attended the play, then what percent of the non-seniors attended the play?
A . \( 20 \% \)
B. \( 40 \% \)
\( c .50 \% \)
D. \( 100 \% \)


Answer the following. What is meant by the power of accommodation of eye?


A wooden spoon is dipped in a cup of ice
cream. It's another end
A. Become cold by the process of conduction
B. Become cold by the process of convection
C. Become cold by the process of radiation
D. Does not become cold


If the intermolecular forces vanish
away, the volume occupied by the molecules of \( 4.5 k g \) water at \( S T P \) will
be:
\( \mathbf{A} \cdot 5.6 m^{3} \)
B. \( 5.6 L \)
c. \( 11.2 L \)
D. \( 11.2 m^{3} \)


An instrument commonly used for measurement of atmospheric pressure
is known as
A. Manometer
B. Barometer
c. Calorimeter
D. Potentiometer


The moment of inertia of a rod about its
perpendicular bisector is I. When the temperature of the rod is increased by \( \triangle T, \) the increase in the moment of
inertia of the rod about the same axis is
(Here, \( \alpha \) is the coefficient of linear
expansion of the rod)
\( \mathbf{A} \cdot \alpha I \Delta T \)
в. \( 2 \alpha I \Delta T \)
c. \( \frac{\alpha I \Delta T}{2} \)
D. \( \frac{2 I \triangle T}{\alpha} \)


Consider the following statements:
\( f(x)=\ln x \) is an increasing function
on \( (0, \infty) \)
2. \( f(x)=e^{x}-x(\ln x) \) is an increasing
function on \( (1, \infty) \) Which of the above statements is lare
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


A metal sphere of radius \( 1 m m \) and
mass \( 50 m g \) falls vertically in glycerine. Find the hydrostatic force exerted by the glycerine on the sphere.


For the cell (at \( 298 \mathrm{K} \) ), which of the
following is correct?
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s})| \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \mid \boldsymbol{A} \)
A. The cell emf will be zero when ( \( \left.\left[\mathrm{Ag}^{+}\right]\right) \) in anodic compartment \( =\left[\mathrm{Ag}^{+}\right] \) in cathodic compartment
B. The amount of AgCl(s) precipitate in anodic compartment will decrease will the working of the cell
C. The concentration of \( \left[\mathrm{Ag}^{+}\right]= \) constant, in anodic compartment during working of cell
D. \( E_{\text {cell}}=E_{A g^{+} \mid A g}^{0}-E_{C l^{-}|A g C l| A g}^{0}-\frac{0.059}{1} \log \frac{1}{\left[C l^{-}\right]_{a}} \)


Plastics are eco-friendly.
A. True
B. False


Telomeres with repetitive DNA
sequences
A. Act as replicons
B. Are transcription initiators
c. Help in chromosome pairing
D. Prevent chromosome loss


State whether the following statement
is True or False.

A convex lens is a convergent lens and is used as a magnifying glass
A. True
B. False


\( \ln \operatorname{an} A C \) generator, a coil with \( N \) turns, all of the same area \( A \) and total
resistance \( \boldsymbol{R} \), rotates with frequency \( \boldsymbol{\omega} \)
in a magnetic field \( B \). The
maximum value of e.m.f. generated in the coil is :
A. NABR \( \omega \)
B. NAB
c. NABR
D. NAB


If \( z(\neq-1) \) is a complex number such
that \( \frac{z-1}{z+1} \) is purely imaginary, then find
\( |z| \)


In the normal expiration, the diaphragm is
A. Arched
B. Flattened
c. Not involved
D. Perforated


A force \( F=(5 \hat{i}+3 \hat{j}) \) newtons is applied over a particle which displaces it from its origin to the point \( r=(2 \hat{i}- \)
1 \( \hat{\boldsymbol{j}} \) ) metres. The work done on the
particle is
A. -7 joules
B. +13 joules
c. +7 joules
D. +11 joules


The weight of 50 kg person at the surface of earth is
A . \( 50 N \)
B. \( 35 N \)
c. \( 380 N \)
D. \( 490 N \)


Find the maximum and minimum
values, if any of the following function given by:
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{\boldsymbol{3}}+\mathbf{1} \)


On adding \( A g N O_{3} \) solution into \( K I \)
solution, a negatively charged colloidal solution is obtained when they are in:
A \( \cdot 100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{AgNO}_{3}+100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{K} \)
B. 100 \( \mathrm{mL} \) of \( 0.1 \mathrm{M} \) AgNO \( _{3}+100 \mathrm{mL} \) of \( 0.2 \mathrm{M} \) KI
C. \( 100 \mathrm{mL} \) of \( 0.2 \mathrm{M} \) AgNO \( _{3}+100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) k
D. \( 100 \mathrm{mL} \) of \( 0.15 \mathrm{M} \mathrm{AgNO}_{3}+100 \mathrm{mL} \) of \( 0.15 \mathrm{M} \mathrm{K} \)


If \( \boldsymbol{x}, \mathbf{1}, \boldsymbol{z} \) are in \( \mathbf{A P} \) and \( \boldsymbol{x}, \boldsymbol{2}, \boldsymbol{z} \) are in \( \mathbf{G P} \)
then \( x, 4 ; z \) will be in
\( A \cdot A P \)
в. GP
c. нр
D. None of these


Systole brings about the
A. Entry of blood into lungs
B. Entry of blood into heart
C. Exit of blood from lungs
D. Exit of blood from ventricles


Write the products when \( P b_{3} O_{4} \) reacts
with \( \boldsymbol{H} \boldsymbol{C l} \)
This question has multiple correct options
\( \mathbf{A} \cdot P b O_{2} \)
в. \( P b C l_{2} \)
\( c \cdot C l_{2} \)
D. \( 2 H_{2} O \)


If \( X, Y \) are two matrices given by the equations \( \boldsymbol{X}+\boldsymbol{Y}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \boldsymbol{X}-\boldsymbol{Y}= \)
\( \left[\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \)
\( \operatorname{then} \boldsymbol{X} \boldsymbol{Y}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right], \) find \( \boldsymbol{a}-\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \)


Using ruler and compasses only, construct a triangle \( A B C \). having \( A B=47 \)
\( \mathrm{cm}, \mathrm{AC}=34 \mathrm{cm} \) and \( \angle B A C=75^{\circ} . \) Draw
the perpendicular bisector of BC and the bisector of angle BAC. If the perpendicular bisector and the angle bisector meet at a point \( \mathrm{M} \), measure
\( \angle B M C \)


A carbon resistance has a following
colour code. What is the value of the
resistance?
A \( .1 .64 M \Omega \pm 5 \% \)
B. \( 530 k \Omega \pm 5 \% \)
\( c \cdot 64 k \Omega \pm 10 \% \)
D. \( 5.3 M \Omega \pm 5 \% \)


Write the chemical reaction of the
photosynthesis and events occured during the process.


A computer producing factory has only two plants \( T_{1} \) and \( T_{2} \). Plant \( T_{1} \) produces
\( 20 \% \) and plant \( T_{2} \) produces \( 80 \% \) of total
computers produced. \( 7 \% \) of computers produced in the factory turn out to be defective. It is known that \( P \) (computer
turns out to be defective given that it is
produced in plant \( T_{1} \) ) \( =10 P \) (computer
turns out to be defective given that it is
produced in plant \( T_{2} \) ). where \( P(E) \) denotes the probability of
an event \( E . \) A computer produced in the factory is randomly selected and it does not turn out ot be defective. Then the
probability that it is produced in plant
\( T_{2} \) is
A \( \cdot \frac{36}{73} \)
в. \( \frac{47}{79} \)
c. \( \frac{78}{93} \)
D. \( \frac{75}{83} \)


As the air around the base of a candle
flame is heated, it rises and is replaced by cooler air due to which of following type of heat transfer?
A. Conduction
B. convection
c. Radiation
D. Diffraction
E. Latent heat


The random error in the arithmatic
mean of 10 observations is \( k . \) Then
random error in arithmatic mean of 25
observations would be
A. \( 0.1 k \)
\( k \)
в. \( 0.4 k \)
\( c .2 .5 k \)
D. \( 1.25 k \)


In the reaction, \( \boldsymbol{P}+\boldsymbol{Q} \longrightarrow \boldsymbol{R}+\boldsymbol{S} \). The
time taken for \( 75 \% \) reaction of \( P \) is
twice the time taken for \( 50 \% \) reaction of
P. The concentration of \( Q \) varies with
reaction time as shown in the figure.
The overall order of the reaction is:
A . 2
B. 3
c. 0
\( D \)


When the stems have dense soft
coatings all over their surface, such surfaces are called as
A. Ribbed
B. Pubescent
c. succulent
D. Hairy


Which of the following represents the
correct decreasing order of acidity of
the following compounds?
(i)
(ii)
(iii)
(iv)
\( A \cdot i i>i>i i i>i v \)
\( \mathbf{B} \). \( i \mathbf{v}> \) iii \( > \) ii \( >i \)
\( \mathbf{C} \cdot \) iii \( >i v>i>i \)
D. iv \( > \) iii \( >i> \) ii


A point within the lens, where a line drawn through the diameter of lens meets principal axis is known as
A. Focal length
B. Optic Center
c. Aperture
D. center of curvature


Which one of the following ions is the most stable in aqueous solution?
\( [A t . \text { no.; } T i=22, V-23, C r=24 ; M n=25] \)
A \( \cdot C r^{3} \)
в. \( V^{3} \)
\( \mathrm{c} \cdot T i^{3} \)
\( \mathbf{D} \cdot M n^{3} \)


Assertion
The law of conversation of mass apply to
the burning a candle.
Reason
During the burning of candle, the wax is converted into smoke, gas, soot and
melted wax.The mass of these products
is same as the melted wax.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For the matrix \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{4} & -\mathbf{4} & \mathbf{5} \\ -\mathbf{2} & \mathbf{3} & -\mathbf{3} \\ \mathbf{3} & -\mathbf{3} & \mathbf{4}\end{array}\right] \)


The distance covered by the second body when they meet is
\( A \cdot 8 m \)
B. 16 \( m \)
c. \( 24 \mathrm{m} \)
D. 32 m


What is the working principle of
generator?
A. Attractive property of magnets.
B. Conductors carrying current behave like magnets.
C. Electromagnetic induction.
D. none of the above


How does the height boys and girls change during puberty?


Find the components along the coordinate axes of the position vector of each of the following point:
\( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{2}) \)


Heavy rainfall during summer produces
A. Desert
B. Grassland
c. Forest
D. wetland


Solve \( \int \frac{\sin ^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\sin ^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}} d x \)


Find a vector in which two of the three
direction angles are \( \boldsymbol{\alpha}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \) and \( \boldsymbol{\beta}= \)
\( \mathbf{5 5}^{\circ} \)
\( \mathbf{A} \cdot v=\cos 55^{o} \hat{i}+\cos 75^{\circ} \hat{j}+\cos 39^{o} \hat{k} \)
B . \( v=\cos 75^{\circ} \hat{i}+\cos 55^{\circ} \hat{j}+\cos 39^{\circ} \hat{k} \)
c. \( v=\cos 55^{\circ} \hat{\imath}+\cos 39^{\circ} \hat{\jmath}+\cos 75^{\circ} \hat{k} \)
D . \( v=\cos 75^{\circ} \hat{i}+\cos 39^{\circ} \hat{j}+\cos 55^{\circ} \hat{k} \)


The electric field in the region with
radius \( r, \) where \( c>r>b, \) is


The moment of inertia of a uniform thin
sheet of mass \( M \) of the given shape
about the specified axis is (axis and
sheet both are in the same plane):
A \( \cdot \frac{7}{12} M a^{2} \)
B \( \cdot \frac{5}{12} M a^{2} \)
c. \( \frac{1}{3} M a^{2} \)
D. \( \frac{1}{12} M a^{2} \)


Sucrose on hydrolysis gives?
A . Glucose+Glucose
B. Glucose+Galactose
c. Glucose+Fructose
D. Glucose+Lactose


State the defect of vision Kavita is
suffering from.


The passage of electricity in the Daniell cell when \( Z n \) and \( C u \) electrodes are
connected is from:
A. \( C u \) to \( Z n \) in the cell
B. \( C u \) to \( Z n \) outside the cell
c. \( Z n \) to \( C u \) outside the cell
D. \( Z n \) to \( C u \) in the cell


A coil of area \( 500 \mathrm{cm}^{2} \) having 1000 turns
is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude \( 4 \times 10^{-5} \) weber \( / m^{2} \). If it is
rotated by 180 about an axis passing through one of its diameter in \( 0.1 \mathrm{sec} \), find the average induced emf
A. zero
B. 30 mv
c. \( 40 \mathrm{mv} \)
D. 50 mv


The most important mineral for blood coagulation is
A. Calcium
B. Magnesium
c. Sodium
D. Iron


The probability of a leap year having 53 Mondays is:
A \( \cdot \frac{2}{7} \)
B. \( \frac{1}{7} \)
\( c \cdot \frac{3}{7} \)
D.


Value of
\( \lim _{x \rightarrow 0} \frac{x+2 \sin x}{\sqrt{x^{2}+2 \sin x+1}-\sqrt{x-\sin ^{2} x}} \)
is
\( A \cdot 2 \)
B.
\( c \cdot 6 \)
D. - 2


How many atoms are present in the given reaction?
\( \boldsymbol{P b}\left(\boldsymbol{N O}_{3}\right)_{2}+2 \boldsymbol{K} \boldsymbol{I} \rightarrow \boldsymbol{P b I}_{2}+2 \boldsymbol{K} \boldsymbol{N O}_{3} \)
A . 5
B. 12
c. 13
D. 18
E . 26


The slope of the normal to the curve
\( y^{3}-x y-8=0 \) at the point (0,2) is
equal to:
A . -3
в. -6
\( c \cdot 3 \)
D. 6
E . 8


A thin wire is bent in the form of a ring
of diameter \( 3.0 \mathrm{cm} . \) The ring is placed
horizontally on the surface of soap solution and then raised up slowly. How much upward force is necessary to break the vertical film formed between
the ring and the solution?
A \( .5 .452 \times 10^{-3} \)
B. \( 4.452 \times 10^{-3} \)
c. \( 6.452 \times 10^{-3} \)
D. \( 9.452 \times 10^{-3} \)


The coefficient of middle term in the
expansion of \( (1+x)^{10} \) is
A . \( 10 ! / 5 ! 6 ! \)
B . \( 10 ! / 5 !^{2} \)
c. \( 10 ! \) 5! 7
D. None of these


The number of chromosomes in parents
and offsprings of a particular species remains constant due to
A. Doubling of chromosomes after zygote formation
B. Halving of chromosomes during gamete formation
c. Doubling of chromosomes after gamete formation
D. Halving of chromosomes after gamete formation


If \( y=\sqrt{\sin x+y} \) then \( \frac{d y}{d x} \) equals to
A \( \cdot \frac{\cos x}{2 y-1} \)
B. \( \frac{\cos }{1-2 y} \)
c. \( \frac{\sin x}{1-2 y} \)
D. \( \frac{\sin x}{2 y-1} \)


What is coal tar also known as when
used in shampoo, ointment etc?
A. Liquor carbonis detergens
B. Solidified carbonis detergents
c. soldified coke detergents
D. All of the above


How many kg (nearest integer value) of wet \( N a O H \) containing \( 12 \% \) water is
required to prepare 60 L of \( 0.50 M \)
Na \( O H \) solution? If the answer is \( x \) then
the nearest integral value of \( 1000 x \)


The magnetic force on a moving charge
in a magnetic field acts
A. Only at right angles to the direction of motion of the particle.
B. Only at right angles to magnetic field.
C. At right angles to the field and the direction of motion of the particle.
D. Parallel to the field as well as the direction of motion
of the particle.


Which of the following bond line
structural formulae is correct for the
four carbon branched primary alcohols?
\( A \)
B.
\( c \)
\( D \)


\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these


Greek word sexus means
A. Disjunction
B. Disintegration
C. Union
D. Both A and B


The following question relates to the partial energy level diagram for the hydrogen electron:
\( \mathbf{5 4 e V}_{-\text {一一一一一一一一一一一 }} \)
\( 85 e V_{4} \)
\( 1.51 e V_{3} \)
\( 3.4 e V_{2} \)
13.6 \( e V \) -
The question relates to a hydrogen
electron located at \( E_{3} \).What is the
emission energy when the electron falls
to \( E_{5} \) from \( E_{3} ? \)
A. \( \pm .66 e V \)
в. \( \pm .966 e V \)
c. \( \pm .1 .89 e V \)
D. \( \pm 10.2 e V \)
E . \( \pm 12.09 e V \)


The oxide of element \( X \) forms a solution
with \( p H 4 \)

The oxide of element \( Y \) forms a solution
that turns Universal Indicator blue.
Which row correctly classifies elements
\( X \) and \( Y ? \)
A. Element \( X \) - metal, Element \( Y \) - meta
B. Element \( X \) - metal, Element \( Y \) - non-metal
c. Element \( X \) - non-metal, Element \( Y \) - metal
D. Element \( X \) - non-metal, Element \( Y \) - non-metal


If \( \int_{0}^{\pi} \ln \sin x d x=k, \) then the value of
\( \int_{0}^{\pi / 4} \ln (1+\tan x) d x \) is:
A \( \cdot-\frac{k}{4} \)
в. \( \frac{k}{4} \)
\( c \cdot-\frac{k}{8} \)
D. None of these


A.P.
\( \mathbf{A} \cdot 2 a_{2}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{3}=0 \ldots(1) \)
B \( \cdot 2 a_{2}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{1}=0 \ldots(1) \)
C \( \cdot 2 a_{1}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{3}=0 \ldots(1) \)
D. \( 2 a_{1}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{1}=0 \ldots(1) \)


What is the missing number in the sequence \( 1,5,10,16,23,31,_{---} \)
A . 37
B. 38
c. 39
D. 40
E. 41


Which of the following halogen reacts with alkanes with explosive violence?
\( \mathbf{A} \cdot F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( l_{2} \)


A person was weighing \( 102.1 \mathrm{kg} \) last
week and gained \( 0.28 k g \) this week. His
weight as of now is correctly expressed
as:
A. \( 102.38 \mathrm{kg} \)
в. \( 102.3 \mathrm{kg} \)
c. \( 102.4 \mathrm{kg} \)
D. \( 102 \mathrm{kg} \)


In the figure shown, a force \( \boldsymbol{F} \) is applied
at the top of a disc of mass \( 4 k g \),and
radius \( 0.25 m . \) Find maximum value of
\( F(\text { in } N) \) for no slipping.


A vertical wire caries a current in
upward direction. An electron beam
sent horizontally towards the wire will
be deflected
A. towards right
B. towards left
c. upwards
D. downwards


What is the acceleration of free fall?


The work-energy theorem states that
the change in:
A. kinetic energy of a particle is equal to the work done on it by the net force
B. kinetic energy of a particle is equal to the work done by one of the forces acting on it
C. potential energy of a particle is equal to the work done on it by the net force
D. potential energy of a particle is equal to the work done by one of the forces acting on it
E. total energy if a particle is equal to the work done on it by the net force


The major contribution of Sir C.V.
Raman is:
A. principle of buoyancy
B. scattering of light by molecules of a medium
c. electromagnetic theory
D. explanation of photoelectric effect


A book seller has 28 Kannada and 72
English books. The books are of the
same size. These books are to be
packed in separate bundles and each bundle must contain the same number
of books. Find the least number of
bundles which can be made and also
the number of books in each bundle


The maximum power dissipated by external resistance \( \mathrm{R} \) by a cell of an external emf \( \mathrm{E} \) and internal resistance is \( \frac{E^{2}}{4 R} \) which is obtained for
\( A \cdot R<r \)
B. \( R>r \)
\( c \cdot R=r \)
D. any value of R.


Find the value of definite integrals as the limit of a sum (by first principle). \( \int_{a}^{b} e^{-x} d x \)


In TCA during the conversion of succinic acid to fumaric acid how many ATP are produced?
\( A \cdot 2 \)
B. 14
\( c \cdot 6 \)
D. 10


Why is the electrolytic dissociation represented by a reversible \( (\rightleftharpoons) \operatorname{sign} ? \)


Starch sheath is another name of
A. Hypodermis
B. Endodermis
c. Casparian strip
D. None of the above


The production of dihydrogen gas via water gas shift reaction
\( \boldsymbol{C O}_{(\boldsymbol{g})}+\boldsymbol{H}_{2} \boldsymbol{O}_{(\boldsymbol{g})} \stackrel{\Delta}{\longrightarrow} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2(\boldsymbol{g})} \)
The \( C O_{2} \) gas is removed by scrubbing with solution of?
A. sodium arsenite
B. Calcium oxide
c. Sodium phosphate
D. aluminium oxide


A work of \( 200 J \) is done in moving a charge of \( -5 C \) from infinity to a
particular point in an electrostatic field The potential of this point is...........
\( \mathbf{A} \cdot-20 V \)
в. \( -25 V \)
c. \( -30 V \)
D. \( -40 V \)


The circumference and area of a circle
of diameter \( 91 \mathrm{cm} \) are, respectively
A \( \cdot 367 \mathrm{cm}, 4986.5 \mathrm{cm}^{2} \)
B . \( 442 \mathrm{cm}, 6166.5 \mathrm{cm}^{2} \)
\( \mathbf{c} .286 \mathrm{cm}, 6506.5 \mathrm{cm}^{2} \)
D. \( 456 \mathrm{cm}, 5466.5 \mathrm{cm}^{2} \)


A disease can spread from one person
to population by
A. Improper sanitation in public places.
B. Improper sanitation in home
c. sharing of food.
D. Sharing of water bottle


In a parallelogram \( A B C D, \) if \( A B=2 x+5 \) \( \mathrm{CD}=\mathrm{y}+1, \mathrm{AD}=\mathrm{y}+5 \) and \( \mathrm{BC}=3 \mathrm{x}-4 \) then the
ratio of AB:BC is
A . 71:21
B. 12:11
\( c \cdot 31: 35 \)
D. 4: 7


Identify the property which does not reflect the periodicity of the elements.
A. Bonding behaviour
B. Electronegativity
c. lonization potential
D. Neutron-proton ratio


The lower limit of the modal class of the
following data is :
\( \begin{array}{lllll} & 0 & 10 & 20 & 30 \\ \text { c.l. } & - & - & - & - \\ & 10 & 20 & 30 & 40\end{array} \)
Frequency \( \quad 5 \quad 8 \quad \) 13 \( \quad \) 7
A . 10
B. 30
c. 20
D. 50


A wheel starts from the rest and attains
an angular velocity of 20 radian/s after being uniformly accelerated for 10 s.The
total angle in radian through which it has turned in 10 second is
A \( .20 \pi \)
в. \( 40 \pi \)
\( c .100 \)
D. \( 100 \pi \)


Unknown gas diffuses with \( \mathrm{CO}_{2} \). Rate of
diffusion of unknown gas is double than
that of \( \mathrm{CO}_{2} \). The molecular weight of the
unknown gas is:
A . 22
B . 30
c. 11
D. 44


toppr LOGIN JolN Now
Q Type your question_
changes that will take place as a result
of the increased plate separation?
\( \mathbf{A} \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor Property } & Effect of Increased Plate Separation \\
\hline Charge on Plates & increase \\
Voltage Across Plates & no effect \\
Capacitance & increase \\
\hline
\end{tabular}
B.
\begin{tabular}{|l|l|}
\hline Capacitor Property & Effect of Increased Plate Separation \\
\hline Charge on Plates & no effect \\
Voltage Across Plates & increase \\
Capacitance & decrease \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor Property } & Effect of Increased Plate Separation \\
\hline Charge on Plates & increase \\
Voltage Across Plates & decrease \\
Capacitance & no effect \\
\hline
\end{tabular}
D. \begin{tabular}{|l|l|}
\hline Capacitor Property & Effect of Increased Plate Separation \\
\hline Charge on Plates & decrease \\
Voltage Across Plates & increase \\
Capacitance & no effect \\
\hline
\end{tabular}
\( E \)
\begin{tabular}{|l|l|}
\hline Capacitor Property & Effect of Increased Plate Separation \\
\hline Charge on Plates & no effect \\
Voltage Across Plates & decrease \\
Capacitance & increase \\
\hline
\end{tabular}


f \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{4}, \boldsymbol{5}\}, \boldsymbol{B}=\{\boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}\} \) then
\( n(A \times B) \) is equal to-
\( A \cdot 6 \)
B. 9
\( c .3 \)
\( D \)


Show graphically that each one of the following systems of equations has infinitely many solutions:
\( \boldsymbol{x}-2 \boldsymbol{y}+11=\mathbf{0} \)
\( \mathbf{3} \boldsymbol{x}-\mathbf{6} \boldsymbol{y}+\mathbf{3 3}=\mathbf{0} \)


Find the geometric mean of the values
2,4,4,8
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
\( D \)


Part of active site of enzyme, where
substrate is supported is
A. Catalytic group
B. Buttressing group
c. Activation chamber
D. K constant


Name the method by which Hydra reproduces. Is this method sexual and asexual?


Harmful gases like \( S O_{2}, \) which harm the Taj Mahal, are present in:
A. industrial areas
B. forests
c. highly populated areas
D. hills


The area of a trapezium is \( 105 \mathrm{cm}^{2} . \) If
one of the parallel sides is \( 28 \mathrm{cm} \) and the distance the parallel sides is \( 5 \mathrm{cm} \) find the length of the other parallel side.


The radius of the blade of fan is \( 0.3 \mathrm{m} \). It
is making 1200 rev/min.The acceleration of a particle at the tip of the blade is:
A \( \cdot 3733 m / s^{2} \)
В. \( 2733 m / s^{2} \)
c. \( 4733 m / s^{2} \)
D. \( 5733 m / s^{2} \)


What is a bilateral symmetry?
A. Type of arrangement of the parts and organs of an animal in which the body can be divided into two halves.
B. Type of arrangement of the parts and organs of an animal in which the body can be divided into three halves.
C. Type of arrangement of the parts and organs of an animal in which the body can be divided into four equal halves.
D. None of these.


A work - force of 420 men with a
contractor can finish a certain piece of work in 9 months. How many extra men
must he employ to complete the job in 7 months?


Select the group which shares
maximum number of common
characters.
A. Two individuals of a species
B. Two species of a genus
c. Two genera of a family
D. Two genera of two families


The value of \( \frac{15 \times(-24) \times-18}{-(27) \times(20)} \) is
A . -16
B . -15
\( c \cdot-12 \)
D. 12


In the nuclear fusion reaction, \( _{1}^{2} \mathbf{H}+_{1}^{3} \) \( \mathbf{H} \rightarrow_{2}^{4} H e+n \) given that the repulsive potential energy between the two nuclei is \( 7.7 \times 10^{-14} J, \) the temperature at
which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant \( \mathbf{k}=\mathbf{1 . 3 8} \times \)
\( \left.\mathbf{1 0}^{-\mathbf{2 3} \mathbf{J}} / \mathbf{K}\right] \)
\( \mathbf{A} \cdot 10^{7} K \)
В. \( 10^{5} K \)
\( \mathbf{c} \cdot 10^{3} K \)
\( \mathbf{D} \cdot 10^{9} K \)


The ratio \( r \) of the rate of production of neutrons from uranium nucleus to the
rate of leakage of neutrons for
sustained chain reaction is
\( \mathbf{A} \cdot r>1 \)
В. \( 1>r \)
c. \( 1>r^{2} \)
D. \( r^{2}=1 \)


Identify which of the following list of numbers is an arithmetic progression?
A \( .1,1,2,3,5, \ldots \)
в. \( 2,3,5,7,11, \ldots \)
c. \( 10,100,1000, \ldots \)
D. \( 12,18,24,30, \ldots \)


Which of the following condition will occur, if the chromosomes of a
eukaryotic cell lack telomerase?
A. Have a greater potential to become cancerous than one with telomerase
B. Would be able to repair mismatched base pairs during replication
c. Not produce okazaki fragments
D. Become increasingly shorter with each cycle of replication
E. Be unable to take up extraneous DNA from the surrounding solution


Which of the following pteridophytes belong to class Pteropsida?
A. Equisetum and Psilotum
B. Lycopodium and Adiantummmmm
c. Selaginella and Pteris
E. Dryopteris and Psilotum


\( A, B, C \) and \( D \) are four coils of wires of 2,2
2 and 3 ohm resistances respectively and are arranged to form a Wheatstone bridge.The resistance which the coil 'D' must be shunted in order that the
bridge may be balanced is:
A . \( 4 \Omega \)
B. 6.
\( c .3 \Omega \)
D. \( 8 \Omega \)


Hydrogen is the most abundant element
on earth after oxygen
If this is true enter 1 , if false enter 0 .


Addition of \( \left(x^{2}+y^{2}\right) \) and \( \left(x^{2}-y^{2}\right) \)
is


A uniform rod of mass \( m \) and length \( l \) is resting on a smooth horizontal surface.
A particle of mass \( m / 2 \) travelling with a
speed \( v_{0} \) hits the rod normally and
elastically. Then,
This question has multiple correct options
A \( \cdot \) final velocity of the particle is \( -\frac{2}{15} v_{0} \)
B. final velocity of the particle is \( -\frac{1}{15} v_{0} \)
c. angular velocity of the rod \( \frac{8 v_{0}}{5 e} \)
D. angular velocity of the rod \( \frac{6 v_{0}}{5 \ell} \)


f \( n(A)=18, n(B)=12, \) and \( A \cap B= \)
\( \emptyset, \operatorname{then} n(A \cup B)= \)
\( A \cdot 6 \)
B. 12
\( c .30 \)
D. 20


The length of a rectangular verandah is
\( 3 m \) more than its breadth. The
numerical value of its area is equal to
the numerical value of its
perimeter. Taking \( x \) as the breadth of
the verandah, write an equation in \( x \)
that represents the above statement.
A \( \cdot x^{2}-x-6=0 \)
B. \( x^{2}-x+6=0 \)
c. \( x^{2}-x+5=0 \)
D. \( x^{2}-x-5=0 \)


Write the additive inverse of each of the
following rational numbers:
\( \frac{4}{9} ; \frac{-13}{7} ; \frac{5}{-11} ; \frac{-11}{-14} \)
A \( \cdot \frac{-4}{9} ; \frac{13}{7} ; \frac{5}{11} ; \frac{-13}{14} \)
В. \( \frac{-4}{9} ; \frac{1}{7} ; \frac{5}{11} ; \frac{-11}{14} \)
c. \( \frac{-4}{9} ; \frac{13}{7} ; \frac{5}{11} ; \frac{-11}{14} \)
D. \( \frac{-5}{9} ; \frac{13}{7} ; \frac{5}{11} ; \frac{-11}{14} \)


With the help of one example, explain how the neutron to proton ratio changes during alpha decay of a nucleus.


The equilibrium of formation of phosgene is represented as:
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O} \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The reaction is carried out in a \( 500 m L \)
flask. At equilibrium 0.3 mole of
phosgene, 0.1 mole of \( C O \) and 0.1 mole
of \( C l_{2} \) are present. The equilibrium
constant of the reaction
is
A . 30
B. 15
c. 5
D. 3


On which law does the study of calorimetry based?
A. Joule's law
B. Law of conservation of energy
c. Law of Kinetic energy
D. None


Assertion
If standard reduction potential for the
reaction \( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} \) is 0.80 volt,
then for the reaction \( 2 A g^{+}+2 e^{-} \rightarrow \)
2 Ag.lt will be 1.60 volt.
Reason
If concentration of \( A g^{+} \) ions is doubled
the standard electrode potential is also doubled.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What will happen if their is no tubular reabsorption in the nephrons of kidneys?


The reaction, \( _{92}^{235} U+_{0}^{1} n \longrightarrow_{56}^{140} B a+_{36}^{93} \)
\( K r+3 \) represents:
A. artificial radioactivity
B. nuclear fission
c. nuclear fusion
D. none of the above


Which of the following is/are NOT true?
A. Temperature also makes changes in air pressure
B. In cold air, the molecules are more closely packed together than in warm air, so cold air is more dense than warm air
C. Air pressure depends on the density of the air, or how close together its molecules are
D. None of the above


A tyre pumped to a pressure 3.375 atm
at \( 27^{\circ} C \) suddenly bursts. What is the
final temperature \( (\gamma=\mathbf{1 . 5}) ? \)
A \( \cdot 27^{\circ} \mathrm{C} \)
B . \( -27^{\circ} \mathrm{C} \)
\( c \cdot 0^{\circ} C \)
D. \( -73^{\circ} \mathrm{C} \)


A factory makes 1150 shirts on a day.
How many can be sent to shop if \( 6 \% \) of the shirt have defects in stitching?


A force \( F_{1} \) on a body of \( 2 \mathrm{kg} \) produces an
acceleration of \( 2.5 m / m^{2} \) and other
force \( F_{2} \) acting on another body of mass
5 kg produces an acceleration of \( 2 m / s^{2} \)
The ratio of \( \boldsymbol{F}_{2} / \boldsymbol{F}_{1} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


The angle between electric lines of force and equipotential surface is :
\( \mathbf{A} \cdot 0^{\circ} \)
B . \( 180^{\circ} \)
\( c \cdot 90^{\circ} \)
\( D \cdot 45^{\circ} \)


in
\( \theta=0 \)
\( \Delta-8 \)
\( \Delta \cdot \phi \)


A cubical region of side a has its centre
at the origin. It encloses three fixed point charges,- -q \( a t(0,-a / 4,0),+3 q \) at (0,0,0) and \( -q \) at \( (0,+a / 4,0) . \) Choose the correct
option(s):

This question has multiple correct options
A. The net electric flux crossing the plane \( x=+a / 2 \) is equal to the net electric flux crossing the plane \( x=-a / 2 \)
B. The net electric crossing the plane \( y=+a / 2 \) is more than the net electric flux crossing the plane \( y=-a / 2 \)
C. The net electric flux crossing the entire region is \( \frac{q}{\varepsilon_{0}} \)
D. The net electric flux crossing the piane \( z=+a / 2 \) is equal to the riet electric flux crossing the piane \( x= \) \( +a / 2 \)


Charging by friction is accompanied by loss or gain of electrons. State which
body loses electrons when an ebonite rod is rubbed with fur.
A . ebonite
B. fur
c. hand
D. Both fur and ebonite


In toroid magnetic field on axis will be
radius \( =0.5 \mathrm{cm}, \) current \( =1.5 \mathrm{A}, \) turns
\( =250, \) permeability \( =700 \)
\( \mathbf{A} \cdot 7.5 \) Tesla
B. 10.5 Tesla
c. 4.5 Tesla
D. 15.5 Tesla


Which of the following are the incorrect
orders of basic character?
\( A \)
B.
\( c \)
\( D \)


Sodium salt \( (A) \) of a dibasic acid \( \stackrel{H C l}{\longrightarrow} \)
gas \( (B) \)
Clear solution of \( \operatorname{gas}(B) \) turns
\( K_{2} C r_{2} O_{7} \) to green and also lime water
milky. Identify \( (\boldsymbol{A}) \) and \( (\boldsymbol{B}) \)
A \( \cdot(A)-N a_{2} S O_{4} \)
\( (B)-S O_{2} \)
в. \( (A)-N a_{2} S O_{3} \)
\( (B)-S O_{3} \)
c. \( (A)-N a_{2} S O_{4} \)
\( (B)-S O_{3} \)
D \( \cdot(A)-N a_{2} S O_{3} \)
\( (B)-S O_{2} \)


The frequencies of X-rays, \( \gamma \) -rays and ultraviolet rays are respectively a, b and
c. Then
\( \mathbf{A} \cdot a<b, b>c \)
В \( . a>b, b>c \)
c. \( a>b, b<c \)
D. \( a<b, b<c \)


The number of solutions of the equation \( x^{3}+2 x^{2}+5 x+2 \cos x=0 \) in \( [0,2 \pi] \) is:
A .
в.
\( c \cdot 2 \)
D. 3


The mid-point of the sides \( A B \) and \( A C \) of \( \triangle A B C \) are (3,5) and (-3,-3)
respectively. What is the length of the side BC?
A . 10
B . 20
c. 15
D. 30


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \stackrel{N i}{\rightarrow} \boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \) is
an addition reaction. \( \boldsymbol{C H} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \stackrel{N i}{\rightarrow} ? \)
Predict and write the products.


Boojhos uncle has set up an electroplating factory near his village. He should dispose off the waste of the factory
A. in the nearby river
B. in the nearby pond
c. in the nearby cornfield
D. according to the disposal guidelines of the local authority


For the reaction
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The forward reaction at constant
temperature is favoured by:
A. introducing inert gas at constant volume
B. introducing chlorine gas at constant volume
c. introducing inert gas at constant pressure
D. none of the above


For a particle in circular motion the centripetal acceleration should be
A. Equal to tangential acceleration
B. More than to is tangential acceleration
c. Less than to its tangential acceleration
D. May be more or less than its tangential acceleration


If the differential equation representing the family of all circles touching \( x- \) axis at the origin is \( \left(x^{2}-y^{2}\right) \frac{d y}{d x}= \)
\( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{y}, \) then \( \boldsymbol{g}(\boldsymbol{x}) \) equals:
A \( \cdot \frac{1}{2} x \)
в. \( 2 x^{2} \)
c. \( 2 x \)
D. \( \frac{1}{2} x^{2} \)


Work done during isothermal expansion depends on change in
A. volume
B. pressure
c. both (a) and (b)
D. none of these


Give reasons:
"The presence of nitro group \( \left(-N O_{2}\right) \) at ortho/para positions increase the reactivity of haloarenes towards nucleophilic substitution reaction".


For \( n=3 \) energy level, number of orbitals of all kind that are possible is:
A . 9
B. 7
\( c \cdot 8 \)
D. 10


\( A B C D \) is a square and \( \Delta P A D \) is
equilateral then \( \boldsymbol{P B}=\mathbf{2 P C} \)
A. True
B. False


Match the following
\( \begin{array}{ll}\text { Column-I } & \text { Column-II } \\ \text { A. Pressure } & \text { E. } M L^{-1} T^{-2} \\ \text {B. Stress } & \text { F. } N m^{-2} \\ \text {C. Energy per unit } & \text { G. } M^{0} L^{0} T^{0} \\ \text { volume } & \text { H. } J m^{-3} \\ \text {D. Strain } & \end{array} \)
\( \mathbf{A} \cdot A-E, F, H: B-E, F, H: C-E, F, H: D-G \)
\( B \cdot A-E, F: B-E, H: C-E, F, H: D-G \)
\( \mathbf{C} \cdot \mathbf{A}-\mathbf{E}, \mathbf{H}: \mathbf{B}-\mathbf{E}, \mathbf{F}: \mathbf{C}-\mathbf{E}, \mathbf{F}, \mathbf{H}: \mathbf{D}-\mathbf{G} \)
D. \( A-E, F, H: B-E, F: C-E, F, H: D-G \)


Discuss the applicability of Rolle's theorem for the following function on the indicated interval:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}-\mathbf{4} \boldsymbol{x}+\mathbf{5}, \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3}, \quad \mathbf{1}<\boldsymbol{x} \leq \mathbf{2}\end{array}\right. \)


A gas cylinder can hold 1 kg of hydrogen
at room temperature and pressure:
Find the number of moles of hydrogen
present.


When the temperature is increased, the
speed of a chemical reaction usually increases because the
(1) Pressure has decreased
(2) molecules collide less frequently
(3) fractional of the molecules
possessing the activation energy for the reaction increases
Which of the above option(s) is/ are
correct?
\( A \cdot \) If 1,2 and 3 are correct
B. If only 1 and 2 are correct
C. If only 2 and 3 are correct
D. If only 1 is correct
E. If only 3 is correct


The material that has largest specific
heat is :
A. mercury
B. water
c. iron
D. diamond


If \( p, q, r \) are simple proportions with
truth values \( T, F, T, \) then the truth
value of \( (\sim p \vee q) \wedge \sim r \Rightarrow p \) is
A. True
B. False
c. True, if \( r \) is false
D. True, if \( q \) is true


Find out the coefficient of range for the
following prices of shirts in a shop.
Rupees
150
250
100
500
175
450
300
280
A. 1.25
B. 0.666
c. 0.333
D. 0.30


Which of the following statment is
incorrect?
A. Greater the lowering of vapour pressure, greater is the boiling point of the solution
B. Greater the lowering of vapour pressure, greater is the freezing point of the solution
C. At the freezing point, the solute and the solvent have same vapour pressure
D. The units of molal depression constant are \( K m^{-1} \)


A body is projected vertically upwards
from the surface of the earth, then the
velocity time graph is :-
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.


Each of the resistors shown in Figure
has resistance \( R \). Find the equivalent
resistance between \( A \) and \( B \)
\( ^{A} \cdot \frac{7 R}{4} \)
в. \( \frac{5 R}{4} \)
c. \( \frac{9 R}{4} \)
D. \( \frac{11}{4} \)


Assertion
Hussain died turning blue in the body
colour.
Reason
This is due to deficiency of oxygen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( \frac{\bar{k}}{k} \)


Spindles are arrested by colchicine at
A. Anaphase
B. Metaphase
c. Telophase
D. Prophase


Solve by graphical method: \( y-2 x \leq \)
\( \mathbf{1}, \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{3}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


Evaluate \( \left(1-x^{2}\right) \frac{d y}{d x}-x y=1 \)


Why do we wear cotton clothes in
Summer?
A. Cotton is a bad conductor of heat and doesn't allow
passage of warmer air near body.
B. Cotton is a good conductor of heat and allows body heat to escape in the atmosphere.
C. Cotton absorbs sweat from the body, exposing it to atmosphere for easy evaporation
D. None of the above


Chlorine \( \left(C l^{17}\right) \) free radical contains how many electrons around the nucleus
\( ? \)
A . 16
B . 17
\( c \cdot 18 \)
D. 19


Find an anti derivative (or integral) of the given function by the method of inspection.
\( e^{2 x} \)


If latus rectum of ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \)
is double ordiante passing through
focus of parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a} \boldsymbol{x}, \) then find
the value of \( a \).


Which one of the following pairs is not correctly matched?
B. Capacitance - Coulomb/volt
c. Electric potential - - volt
D. Electric field - Volt/meter


When a man is standing, rain drops appear to him falling at \( 60^{\circ} \) from the
horizontal from his front side. When he
is travelling at \( 5 k m / h \) on a horizontal
road they appear to him falling at \( 30^{\circ} \) from the horizontal from his front side.
The actual speed of the rain is \( ( \) in
\( \boldsymbol{k m} / \boldsymbol{h}) \)
A . 3
B. 4
c. 5
D. 6


The angle of dip at a place where horizontal and vertical components of Earth's magnetic field are equal is
A \( .45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 0^{\circ} \)
D. \( 60^{\circ} \)
E \( .90^{\circ} \)


Which of the following have equal mass
of \( C l^{-} \) ions in \( 1.0 \mathrm{L} \) of each of the
following solutions? This question has multiple correct options
A. \( 5 \% \) NaCl (density \( =1.07 \) g/m \( L \) )
в. \( 5 \% \) KCl (density \( =1.06 \mathrm{g} / \mathrm{mL} \) )
c. 58.5 g of \( N a C l \)
D. \( 55.5 \mathrm{g} \) of \( \mathrm{BaCl}_{2} \)


Oxygen is insoluble in water.
A. True
B. False


A proton is moved \( 15 \mathrm{cm} \) on path parallel to the field lines of a uniform electric
field of \( 2.0 \times 10^{5} \mathrm{V} / \mathrm{m} \)
What are the possible change in potential ?consider both cases of a
moving the proton.


A heat engine is \( 20 \% \) efficient. If the engine does \( 500 J \) of work every second,
how much heat does the engine exhaust every second?
A . \( 2000 J \)
в. 2500 J
c. \( 400 J \)
D. \( 500 J \)


Streamline flow is more likely for liquids with
A. high density and high viscosity
B. low density and low viscosity
c. high density and low viscosity
D. low density and high viscosity


Give the correct IUPAC names of the
following:
Dimethyl ether


Ecosystem is defined as
A. Relation between plants and animals
B. Relation between biotic and physical components
C . Relation between producers and decomposers
D. None of the above


The saturation condition of transistor
implies that
A. Collector current has highest possible value
B. entire \( V_{c c} \) gets dropped across load resistor
C. it acts as a closed switch with negligible value of resistance
D. all of the above


Bleaching powder should not be used
for acidic water as it reacts with them
to :
A. liberate hydrogen gas
B. liberated free chlorine
c. form chlorine water
D. liberate carbon monoxide


For a coil having \( \boldsymbol{L}=2 \boldsymbol{m} \boldsymbol{H}, \) current
flow through it is \( I=t^{2} e^{-t} \) then the time
at which emf become zero: -
\( \mathbf{A} \cdot 2 s \)
B . \( 1 s \)
c. \( 4 s \)
D. \( 3 s \)


Sometimes, foaming is seen in river water near the place where sewage water is poured after treatment.
If true enter 1 else 0
\( A \)


In the first order reaction, \( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \)
\( B(g)+C(g), \) at constant volume and
temperature, the initial pressure of \( \boldsymbol{A} \) is
\( 11200 P a \) and the total pressure at the
end of 16 minutes is 14667 Pa.

Calculate the half life period of reaction.


Differentiate with respect to \( x \) :
\( e^{\sqrt{\cot x}} \)


The gravitational force between two bodies is decreased by \( 36 \% \) when the distance between them is increased by
\( 3 m . \) The initial distance between them
is:
A. \( 6 m \)
в. \( 9 m \)
\( c .12 m \)
D. \( 15 \mathrm{m} \)


A block of mass \( 3 k g \) which is on a
smooth inclined plane making an angle
of \( 30^{\circ} \) to the horizontal is connected by
second block of mass \( 2 k g \) hanging
vertically, What is the acceleration of each block and what is the tension of the
cord?
A \( \cdot 0.98 m / s^{2} ; 17.6 N \)
B . \( 1.98 m / s^{2} ; 19.6 N \)
c. \( 0.49 m / s^{2} ; 9.8 N \)
D. \( 1.47 m / s^{2} ; 4.9 N \)


Radius of the second Bohr orbit of a
singly ionised helium atom is
A \( .0 .53 A^{\circ} \)
B . \( 1.06 A^{\circ} \)
c. \( 0.265 A^{\circ} \)
D. \( 0.132 A^{\circ} \)


Form the differential equation of the family of curves represented by the equation(a being the parameter). \( (x-a)^{2}+2 y^{2}=a^{2} \)


(i) \( \ln \) a process 10 gm of ice at \( -5^{\circ} C \) is
converted into steam at \( 100^{\circ} \mathrm{C} \). If
specific heat of water 1 cal \( g^{-1 \circ} C^{-1}, \) the heat required to rise the temperature of water 10 g from \( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \)
A . \( 100 c a l \)
в. 1000call
\( \mathbf{c} \cdot 10^{4} \) cal
D. \( 10^{5} \) cal


Natural rubber or raw rubber consists of
basic material latex which is a
dispersion of isoprene. During the treatment, this isoprene forms a high molecular weight polymer of isoprene. Natural rubber can be obtained from
five hundred different species of plants. In the isoprene polymer all the isoprene have:
A. trans 1, 4 configuration
B. cis 1, 4 configuration
c. both cis and trans 1,4 configuration
D. none of these


A cow is tied to a pole, fixed to the
midpoint of a side of a square field of dimensions \( 40 m \times 40 m \), by means of
\( 14 m \) long rope. Find the area that the
cow can graze.
A \( .254 m^{2} \)
в. \( 308 m^{2} \)
c. \( 245 \mathrm{m}^{2} \)
D. \( 380 m^{2} \)


Write the names and structures of the
monomers of the following polymers:
(i) Buna-S
(ii) Buna-N
(iii) Dacron
(iv) Neoprene


Consider seperate solutions of
\( \mathbf{0 . 5 0 0} \boldsymbol{M} \boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{O H}(\boldsymbol{a q}), \mathbf{0 . 2 5 0} \boldsymbol{M} \boldsymbol{K} \boldsymbol{B r} \)
\( \mathbf{0 . 1 2 5} \boldsymbol{M} \boldsymbol{N a _ { 3 }} \boldsymbol{P O}_{4}(\boldsymbol{a q}) \) and
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{M} \boldsymbol{g}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) at \( \mathbf{2 5}^{\circ} \boldsymbol{C} \)
Which statement is true about these
solutions, assuming all salts to be strong electrolytes?
A \( \cdot 0.125 M N a_{3} P O_{4}(a q) \) has the highest osmotic
pressure
B. \( 0.500 M C_{2} H_{5} O H(a q) \) has the highest osmotic pressure.
C. They all have the same osmotic pressure.
D. \( 0.100 M M g_{3}\left(P O_{4}\right)_{2}(a q) \) has the highest osmotic pressure


\( \operatorname{Let} \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 \) for \( x>0, y>0, z>0 \)
Which of the following sets could be the possible values of \( (x-1)(y-1)(z-1) ? \) This question has multiple correct options
B. \( [11, \infty) \)
\( c \cdot[7, \infty) \)
D. \( [6, \infty) \)


Define magnetization. Write its Sl unit and dimensions.


Sphalerite is a mineral that is the chief
ore of zinc.
A . True
B. False


\begin{tabular}{|ccc}
If \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x}+ \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}+ \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \boldsymbol{x} \)
\end{tabular}
then \( f(100) \) is equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 100 \)
D \( .-100 \)


A light beam parallel to axis is incident
on the system of four convex lenses
\( A, B, C \) and \( D . \) Focal lengths of \( A, B, C \)
and \( D \) are \( 30 \mathrm{cm}, 10 \mathrm{cm}, 30 \mathrm{cm} \) and
\( 10 \mathrm{cm}, \) respectively as shown. Here, fixed distance \( B C=20 \mathrm{cm} . \) What
should be the distance between the lens
\( A \) and lens \( D \) so that after refractions,
rays will be parallel to axis in region I, III and V?
\( \mathbf{A} \cdot 40 \mathrm{cm} \)
B. \( 100 \mathrm{cm} \)
c. \( 80 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


During solidification, heat energy is


An orange solid \( (X) \) on heating, gives a colourless gas (Y) and a only green residue (Z). Gas (Y) on treatment with
Mg, produceds a white solid
substance
A. \( M g_{3} N_{2} \)
2
в. \( M g O \)
c. \( M g_{2} O_{3} \)
D. \( M g C l_{2} \)


The figure shows the cross-section of
two long coaxial tubes carrying equal
currents \( I \) in opposite directions. If \( B_{1} \)
and \( B_{2} \) are magnetic fields at point
and \( 2, \) as shown in figure then
\( \mathbf{A} \cdot B_{1} \neq 0 ; B_{2}=0 \)
B . \( B_{1}=0 ; B_{2}=0 \)
c. \( B_{1} \neq 0 ; B_{2} \neq 0 \)
D. \( B_{1}=0 ; B_{2} \neq 0 \)


A solid sphere of mass \( M \) and radius \( 2 R \) rolls down an inclined plane of
height \( h \) without slipping. The speed of its center of mass when it reaches the
bottom is
A \( \cdot \sqrt{\frac{6}{7} g h} \)
B. \( \sqrt{3 g h} \)
c. \( \sqrt{\frac{10}{7} g h} \)
D. \( \sqrt{\frac{4}{3} g h} \)


A sphere is inscribed in a cubical box
such that the sphere is tangent to all six faces of the box, What is the ratio of
the volume of the cubical box to the
volume of sphere?
A . \( 6 \pi \)
в. \( 36 \pi \)
c. \( \frac{4 \pi}{3} \)
D. \( \frac{6}{\pi} \)


Arrange the following alkyl chlorides in
order of decreasing reactivity in a \( \boldsymbol{S}_{N} \mathbf{1} \)
reaction.
(I) isopropyl bromide
(II) propyl bromide
(III) tert-butyl bromide
(IV) methyl bromide
\( A \cdot((11)>(1)>(11)>(1 v) \)
B. (I) > (III) > (IV) > (II)
\( c \cdot(\mid V)>(|| \mid)>(||)>(\mid) \)
\( D \cdot(1)>(\|)>(\| I)>(1 \vee) \)


A sphere and a disc of same radii and
mass are rolling on an inclined plane
without slipping. \( a_{s} \& a_{d} \) are
acceleration and \( g \) is acceleration due
to gravity. Then which statement is
correct?
\( \mathbf{A} \cdot a_{s}>a_{d}>g \)
В \( \cdot g>a_{s}>a_{d} \)
\( \mathbf{c} \cdot a_{s}>g>a_{d} \)
D \( \cdot a_{d}>a_{s}>g \)


Find the maxima of function \( 8-7 x^{2} \)


The linear density of a thin rod of length 1.0m varies as \( \boldsymbol{\lambda}=2 \mathrm{kg} / \mathrm{m}+\left(\frac{2 \mathrm{kg}}{\boldsymbol{m}^{2}}\right) \boldsymbol{x} \)
where \( x \) is the distance from its one end
The distance of its centre of mass from
its end is?
A \( \cdot \frac{2}{3} \mathrm{m} \)
в. \( \frac{5}{9} \mathrm{m} \)
c. \( \frac{4}{3} \mathrm{m} \)
D. \( \frac{1}{2} \) n


The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at \( 100 \mathrm{K} \). If \( 10^{-5} \) moles of \( \mathrm{A} \) and
100 moles of \( \mathrm{B} \) are present in a 10 litre vessel at equilibrium then rate constant for the backward reaction at
this temperature is:
A. \( 1.50 \times 10^{4} L \) mol \( ^{-1} s^{-1} \)
B . \( 1.5 \times 10^{11} L \) mol \( ^{-1} s^{-1} \)
c. \( 1.5 \times 10^{10} L m o l^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \) mol \( ^{-1} s^{-1} \)


Specify the co-ordination geometry
around and hybridization of \( N \) and \( B \)
atoms in a 1: 1 complex of \( B F_{3} \) and
\( \boldsymbol{N} \boldsymbol{H}_{3}: \)
\( \mathbf{A} \cdot N: \) tetrahedral, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)
B. \( N: \) pyramidal, \( s p^{3} ; B: \) pyramidal, \( s p^{3} \)
C. \( N: \) pyramidal, \( s p^{3} ; B: \) planar, \( s p^{2} \)
D. \( N: \) pyramidal, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)


The amount of thermal energy required to cause a liquid to freeze or a solid to melt is known as:
A. Latent heat of fusion
B. Latent heat of vaporization
c. Latent heat of condensation
D. Heat of fission


If there is a circular coil having n turns,
the field produced is
A. \( 1 / n \) times as that produced by single turn.
B. \( n \) times as large as that produced by a single turn.
C. \( 2 / n \) times as large as that produced by a single turn.
D. all


An unpolarised beam of intensity \( \boldsymbol{I}_{\mathbf{0}} \)
falls on a polaroid at an angle of \( 45^{0} . \) The intensity of the emergent light is
A \( \cdot \frac{I_{0}}{2} \)
в. \( I_{0} \)
c. \( \frac{I_{0}}{4} \)
D. zero


In which condition, adsorption will not
take place?
A. When \( \Delta H \) is negative
B. When \( \Delta H \) is positive \( \Delta S \) is positive
c. When \( \Delta H \) is positive and \( \Delta S \) is negative
D. When \( \Delta G \) is negative


Like poles of two magnets each
other.
A . attract
B. repel
c. exert no force on
D. neutralize


Convert the following ratio to
percentage
8: 4


Solid \( B e\left(N O_{3}\right)_{2} \) is gradually dissolved in a \( 1.0 \times 10^{-4} M N a_{2} C O_{3} \) solution. At
what concentration of \( B a^{2+} \) will a
percipitate begin to form?
\( \left(K_{S P} \text { for } B a C O_{3}=5 \times 10^{-9}\right) \)
A. \( 8.1 \times 10^{-8} M \)
в. \( 8.1 \times 10^{-7} M \)
c. \( 4.1 \times 10^{-5} M \)
D. \( 5.1 \times 10^{-5} M \)


Two wires of resistance \( R_{1} \) and \( R_{2} \) at 0
C have temperature coefficient of
resistance \( \alpha_{1} \) and \( \alpha_{2} \) respectively.These are joined in series.The effective temperature coefficient of resistance
is:-
A. \( \frac{\alpha_{1}+\alpha_{2}}{2} \)
B. \( \sqrt{\alpha_{1} \alpha_{2}} \)
c. \( \frac{\alpha_{1} R_{1}+\alpha_{2} R_{2}}{R_{1}+R_{2}} \)
D. \( \frac{\sqrt{R_{1} R_{2} \alpha_{1} \alpha_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}} \)


Which of the following statements is
not true?
A. The cartilage is not as hard as bones.
B. A snake moves by making loops.
C. All animals show exactly similar movements.
D. Snails move with the help of their muscular feet.


Acids are
A. sour
B. bitter
c. spicy
D. sweet


At equilibrium of the reaction
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \) the
concentrations of \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \) and \( \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
are 0.2 and 0.1 moles/lit.respectively \( \boldsymbol{K}_{c} \) is \( 0.05 . \) The equilibrium concentration
of \( C l_{2}\left(\text { moles.lit }^{-1}\right) \) is:
A. 0.5
B. 0.1
c. 1.5
D. 0.75


\( 37-(3 x+5) \geq 9 x-8(x-3) \)


Assertion
The "biological species" concept helps us to ask how species are formed.
Reason

The concept of biological species focusses our attention on the question
of how reproductive isolation comes about.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( f \) is a real-valued differentiable
function satisfying \( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})| \leq \)
\( (x-y)^{2}, \quad x, y \in R \) and \( f(0)=0, \) then
\( \boldsymbol{f}(\mathbf{1}) \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. 0
D. -


When a current is passed in a
conductor, \( 3^{\circ} C \) rise in temperature is
observed. If the strength of current is made thrice, then rise in temperature will approximately be:
A \( \cdot 36^{\circ} \mathrm{C} \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 18^{\circ} C \)
D. \( 9^{\circ} C \)


\( \frac{\sqrt{2}}{L} \)


What can you say about the prime factorisations of the denominators of
the following rationals:
(i) 43.123456789
(ii) \( 43 . \overline{123456789} \) (iii) \( \mathbf{2 7} \mathbf{.} \overline{\mathbf{1 4 2} \mathbf{8 5 7}} \) (iv) 0.120120012000120000


If the foot of the perpendicular from the origin to a plane is \( (1,2,3), \) then the equation of the plane is
A. \( 3 x+2 y+z=14 \)
B. \( x+2 y+3 z=14 \)
c. \( x+\frac{y}{2}+\frac{z}{3}=1 \)
D. \( x+2 y+3 z=6 \)


\( f(\alpha, \beta, \gamma \) are the zeros of the polynomial
\( \boldsymbol{x}^{3}+\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}+\boldsymbol{2} \) such that \( \boldsymbol{\alpha} \boldsymbol{\beta}+\mathbf{1}= \)
\( 0, \) find the value of \( 2 p+q+5 \)


Show that: \( \int_{0}^{\pi / 2} \frac{\sin ^{2} x}{\sin x+\cos x} d x= \)
\( \frac{1}{\sqrt{2}} \log (\sqrt{2}+1) \)


toppr
Q Type your question
4
\begin{tabular}{cc|c}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
B. \begin{tabular}{cc|c}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( c \)
\begin{tabular}{ll|l}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( D \)
\begin{tabular}{ll|l}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
& \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{-} \) & \( \mathbf{1} \) & \( \mathbf{0} \)
\end{tabular}


Give the decreasing order of reactivity of the following alkyl halides in the Williamson' s reaction.
i. \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C H}_{2} \boldsymbol{B r} \)
ii. \( \boldsymbol{C l C H}_{2} \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
iii. \( \boldsymbol{C l C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
¡v. \( B r C H_{2} C H_{2} C H_{3} \)
\( A \). ii \( > \) iv \( > \) iii \( >i \)
B. i>iii>iv>ii
c. ii > ii >iv > i
D. i > iv > iii > i


Which of the following order is correct?
A. Sound \( \rightarrow \) ear \( \rightarrow \) inner ear \( \rightarrow \) vibration of eardrum \( \rightarrow \)
brain \( \rightarrow \) hearing
B. Ear \( \rightarrow \) Vibration of eardrum \( \rightarrow \) Inner ear \( \rightarrow \) hearing \( \rightarrow \) brain \( \rightarrow \) vibration
C. Sound \( \rightarrow \) ear \( \rightarrow \) inner ear \( \rightarrow \) vibration of eardrum \( \rightarrow \) hearing \( \rightarrow \) brain
D. Sound \( \rightarrow \) ear \( \rightarrow \) vibration of eardrum \( \rightarrow \) inner ear \( \rightarrow \) brain \( \rightarrow \) hearing


A person bought a certain number of books for \( R s .80 . \) If he had bought 4
more books for the same sum, each
book would have cost \( R e .1 \) less. What is
the price of each book?
A . \( R s .10 \)
в. Rs.
c. \( R s . \)
D. Rs.


Assertion
Amperes circuital law holds for steady
currents which do not fluctuate with
time.
Reason
Amperes circuital law is similar to that
of Biot-savarts law.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A polynomial \( P \) is positive for \( x>0 \) and
the area of the region bounded by \( \boldsymbol{P}(\boldsymbol{x}) \)
the \( x- \) axis and the vertical lines \( x=0 \)
and \( x=\lambda \) is \( \frac{\lambda^{2}(\lambda+3)}{3} \) squnit. Then
polynomial \( \boldsymbol{P}(\boldsymbol{x}) \) is:
A \( \cdot x^{2}+2 x \)
B. \( x^{2}+2 x+1 \)
c. \( x^{2}+x+1 \)
D. \( x^{3}+2 x^{2}+2 \)


The vitamin which is neither soluble in
water nor in fat is:
A. Biotin
B. Phylloquinone
c. Thiamine
D. Pyridoxine


For a heater rated at \( 4.4 \mathrm{kW} ; 220 \mathrm{V} \) Calculate the current drawn by the heater.
A . 40 A
B. 20A
\( c \cdot 12.6 A \)
D. ô


The incorrect statement is
A. Calcium oxalate crystals in leaves are raphides.
B. Calcium carbonate crystals are cystoliths.
C . Hydrilla is an amphistomatic.
D. Gossypium has commercially important trichomes.


Find the product. \( (3+\sqrt{2})(2+\sqrt{3})(3-\sqrt{2})(2-\sqrt{3}) \)


Which letter represents the wavelength
of the light in the Young's double slit
experiment?
\( A \cdot A \)
B. B
\( c . c \)
D.
\( E \)


A \( 0.5 ~ M \) Na \( O H \) solution offers a
resistance of 31.6 ohm in a
conductivity cell at room temperature. What shall be the approximate molar conductance of this \( N a O H \) solution if
cell constant of the cell is \( 0.367 \mathrm{cm}^{-1} ? \)
A \( \cdot 234 S \mathrm{cm}^{2} \) mole \( ^{-1} \)
B. \( 23.2 \mathrm{S} \mathrm{cm}^{2} \) mole \( ^{-1} \)
c. \( 4645 S \mathrm{cm}^{2} \) mole \( ^{-1} \)
D. \( 5464 S \mathrm{cm}^{2} \) mole \( ^{-1} \)


Matching pairs in the two lists given below are
ListList-II
A) Gravitions
E) Hyperons
B) Baryons
F) Positrons
C) Pions
G) Particles with zero mass nd with a spin of unity
D) Leptons
H) Decay to -mesons
I) Massless
particles with a probable spin of two units
\( A \cdot A-E, B-H, C-G, D-1 \)
B. A-I,B-E,C-H,D-F
c. \( A-H, B-F, C-1, D-E \)
D. A-F,B-G,C-E,D-H


Which of the following reactions is not oxidation-reduction reaction?
\( \mathbf{A} \cdot H \oplus+O H^{\ominus} \rightarrow H_{2} O \)
B \( \cdot \frac{1}{2} H_{2}+\frac{1}{2} C l_{2} \rightarrow H C l \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \rightarrow \mathrm{CaO}+\mathrm{CO}_{2} \)
D. \( A \) and \( C \)


Discuss the various reactions that
occur in the Solvay process.


Explain the reactions involved in glycolysis. (flowchart or explanation)


Which among the following is not a true
tree?
A. coconut (cocus nucifera)
B. Peepal (Ficus religiosa)
c. Mango (Mangifera indica)
D. Banyan (Ficus benghalensis)


Which of the following pairs of physical quantities are not analogous to each other in case of translatory motion
and rotational motion,
A. force, torque
B. mass, moment of inertia
c. couple, torque
D. linear momentum, angular momentum


If the vertices of a triangle are
\( (1,-3),(4, p) \) and (-9,7) and its area is 15 sq. units, find the value(s) of \( p \)


Assertion
For small deformations, the stress and
strain are proportional to each other
Reason
A class of solids called elastomers does
not obey Hooke's law.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The chemical composition of slag formed during the smelting process in the extraction of copper is:
A \( \cdot C u_{2} O+F e S \)
в. Fesi Оз\( _{3} \)
\( \mathbf{c} \cdot \mathrm{CuFeS}_{2} \)
D. \( C u_{2} S+ \) Fe\( O \)


If \( \sin ^{4} \theta+\cos ^{4} \theta=1-\frac{1}{2} f(\theta) \) then
\( f\left(\frac{\pi}{4}\right)= \)
\( A \)
B.
\( c \cdot 1 / 2 \)
D. \( 1 / 4 \)


The atomic number of an element is
determined by:
A. the number of electrons in one atom
B. the number of neutrons in one atom
c. the valency of the element
D. the number of protons in one atom


Which one of the following molecules contains no \( \pi \) bonds?
A. \( C O_{2} \)
в. \( H_{2} \) о
\( c \cdot S O_{2} \)
D. \( N O_{2} \)


Coordination compounds
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}(\boldsymbol{N} \boldsymbol{C S})\right] \) and
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})\right] \) are examples of
which isomerism?
A. coordination
B. linkage
c. ionizaiton
D. optical


State the following statement is True or
False

If the chords of a circle intersect within
a circle, then the rectangle formed by the parts of the same chord have equal
area
A. True
B. False


In the Wheatstone's network given, \( \boldsymbol{P}= \)
\( \mathbf{1 0 \Omega}, \boldsymbol{Q}=\mathbf{2 0 \Omega}, \boldsymbol{R}=\mathbf{1 5 \Omega}, \boldsymbol{S}=\mathbf{3 0 \Omega}, \) the
current passing through the battery (of
negligible internal resistance) is
A \( .0 .36 A \)
B. Zero
\( c .0 .18 A \)
D. \( 0.72 A \)


Which one is a protozoan disease
A. AlDS
B. Taeniasis
c. Polio
D. Malaria


A vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of a vessel. The length of vessel is \( 90 \mathrm{cm} \) and the piston divides the cylinder in the ratio \( 2: 1 . \) Each
of the two parts contain 0.1 mole of
an ideal gas. The temperature of the gas
is \( 27^{\circ} \mathrm{C} \) in each part. The mass of the
piston is
A. \( 41.5 \mathrm{kg} \)
B. \( 8.97 \mathrm{kg} \)
c. \( 9.57 \mathrm{kg} \)
D. 11.57 kg


If molality of the dilute solution is doubled, the value of molal depression
constant \( \left(\boldsymbol{K}_{\boldsymbol{f}}\right) \) will be :
A. unchanged
B. doubled
c. halved
D. tripled


If a metallic cuboid weighs \( 16 \mathrm{kg} \), how much would a miniature cuboid of
metal weigh, if all dimensions are
reduced to one-fourth of the original?
A. \( 0.25 k g \)
B. \( 0.50 k g \)
c. \( 0.75 k g \)
D. \( 1 k g \)


The compound found in some stones deposited in kidneys is:
A. potassium oxalate
B. oxalic acid
c. potassium succinate
D. calcium oxalate


A sound wave travels at a speed of 339
\( \mathrm{m} / \mathrm{s} . \) If its wavelength is \( 1.5 \mathrm{cm}, \) what is
the frequency of the wave?
A \( .2600 H z \)
B . \( 2200 H z \)
c. \( 2260 H z \)
D. \( 22600 \mathrm{Hz} \)


When \( S O_{2} \) is passed in acidified potassium dichromate solution, the oxidation number of \( S \) is changed from:
\( A \cdot+4 \) to zero
B. +4 to +2
\( \mathbf{c} \cdot+4 \) to +6
D. +6 to +4


You have learnt that a travelling wave in one dimension is represented by a function \( y=f(x, t) \) where \( x \) and \( t \) must appear in the combination \( x-v t \) or \( x+v \)
t i.e. \( y=f(x \pm v t) . \) Is the converse true
? Examine if the following functions for y can possibly represent a travelling
wave:
(a) \( (x+v t)^{2} \)
(b) \( \log \left[(\boldsymbol{x}+\boldsymbol{v} \boldsymbol{t}) / \boldsymbol{x}_{\boldsymbol{o}}\right] \)
(c) \( 1 /(x+v t) \)


Heavy water is used in nuclear reactor
as
A. Coolant
B. Moderator
c. Both coolant and moderator
D. catalyst


Fill in the blanks by selecting the correct word from the brackets:
(i) If an element has a low ionization
energy then it is likely to be (metallic / non metallic).
(ii) If an element has seven electrons in
its outermost shell then it is likely to have the \( _{--}-_{--}- \) (largest / smallest) atomic size among all the elements in
the same period.


The modulus of elasticity is dimensionally equivalent to
A. Stress
B. Surface tension
c. Strain
D. coefficient of viscosity


Select incorrect statement.
A. Ionisation energies of 5d-elements are greater than those of \( 3 d \) and \( 4 d \) elements.
B. Cu(l) is diamagnetic while Cu(II) is paramagnetic.
\( \mathbf{c} \cdot\left[T i\left(H_{2} O\right)_{6}\right]^{3+} \) is coloured while \( \left[S c\left(H_{2} O\right)_{6}\right]^{3+} \)
colourless.
D. Transition elements cannot form complexes.


An ideal spring with spring constant \( k \) is hung from the ceiling and a block of mass \( M \) is attached to its lower end.
The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (Given acceleration due to gravity \( =g) \)
A \( \cdot \frac{4 M g}{k} \)
в. \( \frac{2 M g}{k} \)
c. \( \frac{M g}{k} \)
D. \( \frac{M g}{2 k} \)


Find the magnitude of the force on a charge of \( 12 \mu C \) placed at a point where the potential gradient has a magnitude of \( 6 \times 10^{5} V m^{-1} \)


For traffic moving at \( 60 k m / h r \) along a smooth circular track of radius \( 0.1 k m \)
the correct angle of banking should be:
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left[\frac{(100 \times 9.8)}{\left(\frac{50}{3}\right)^{2}}\right] \)
\( ^{\mathrm{B}} \tan ^{-1}\left[\frac{\left(\frac{50}{3}\right)^{2}}{(100 \times 9.8)}\right] \)
\( ^{\mathrm{c}} \tan ^{-1}\left(\frac{60^{2}}{0.1}\right) \)
D. \( \tan ^{-1} \sqrt{(60 \times 0.1 \times 9.8)} \)


Pigment free plastids are
A. Chloroplasts
B. Chromoplasts
c. Lysosomes
D. Leucoplasts


Which of the following species have undistorted octahedral structures?
1. \( \boldsymbol{S F}_{\mathbf{6}} \)
2. \( \boldsymbol{P F}_{\mathbf{6}}^{-} \)
3. \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{\boldsymbol{6}}^{2-} \)
4. \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \)
Select the correct answer using the codes given below.
\( \mathbf{A} \cdot 1,3 \) and 4
B. 1,2 and 3
C. 1,2 and 4
D. 2,3 and 4


Unpolarised light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be \( \frac{1}{2} . \) Now another identical polarizer \( \mathrm{C} \) is placed between \( \mathrm{A} \) and \( \mathrm{B} \). The intensity beyond B is now found to be \( \frac{1}{8} \) The angle between polarizer A and C is?
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 0^{\circ} \)
D. \( 30^{\circ} \)


The anode rays are also known as:
A . canal rays
B. positive rays
c. both A and B
D. electron rays


What is the percentage of oxygen in the atmosphere?
A . 78\%
B. 21\%
c. 12\%
D. 11\%


Calculate the difference between heat of
combustion of carbon monoxide gas at
constant pressure and at constant
volume at \( 27^{\circ} \mathrm{C} ?\left(\mathrm{R}=2 \text { cal. } K^{-1} \mathrm{mol}^{-1}\right. \)
\( \mathbf{A} \cdot 54 \mathrm{cal} \)
B. 600 call
c. -300 cal
D. 27 cal


A cylindrical tank of radius \( 10 m \) is being filled with wheat at the rate of 314
cubic metre per hour. then the depth of the wheat is increasing at the rate of
A \( \cdot 1 m^{3} / h \)
B. \( 0.1 m^{3} / h \)
\( \mathbf{c} \cdot 1.1 m^{3} / h \)
D. \( 0.5 m^{3} / h \)
E. None of these


Assertion
\( F r C l O_{4}, F r_{2} P t C l_{6} \) are low solubility
compounds of \( \boldsymbol{F r} \)
Reason
\( \boldsymbol{F r} \boldsymbol{C l O}_{4}, \boldsymbol{F r}_{2} \boldsymbol{P t C l}_{6} \) have larger alkali
metal ion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Mark the correct statement
A. Hard surfaces are good reflectors of sound.
B. Soft surfaces are poor reflector of sound.
C. Bad reflectors of sound are good absorbers of sound.
D. All


If \( \theta=\sin ^{-1} x+\cos ^{-1} x-\tan ^{-1} x, 1 \leq \)
\( x<\infty, \) the smallest interval in which \( \theta \)
lies is


The complex numbers \( \sin x+i \cos 2 x \)
and \( \cos x-i \sin 2 x \) are conjugate to
each other, for
A . \( x=n \pi \)
B. \( x=\left(n+\frac{1}{2}\right) \pi \)
c. \( x=0 \)
D. No value of \( x \)


Find whether 0 is a term of the A.P.
\( \mathbf{4 0}, \mathbf{3 7}, \mathbf{3 4}, \mathbf{3 1} \dots \)


The order of \( [\mathbf{x} \mathbf{y} \mathbf{z}]\left[\begin{array}{lll}\mathbf{a} & \mathbf{h} & \mathbf{g} \\ \mathbf{h} & \mathbf{b} & \mathbf{f} \\ \mathbf{g} & \mathbf{f} & \mathbf{c}\end{array}\right]\left[\begin{array}{l}\mathbf{x} \\ \mathbf{y} \\ \mathbf{z}\end{array}\right] \)
is
A . \( 3 \times 1 \)
B. 1x
\( c .1 \times 3 \)
D. 3x3


Which of the following is correct (where \( \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N}) \)


Assertion
Spongy bones are specialized to form
erythrocytes.
Reason
They contain osteocytes and
osteoblasts.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


Choose the correct statement:
A. A nucleus is relatively more stable for which total binding energy is more.
B. A nucleus is relatively more stable for which binding energy per nucleon is more.
C. A nucleus is relatively more stable for which total binding energy is low.
D. None of these


The monthly income (in rupees) of 7 households in village are
\( \mathbf{1 2 0 0}, \mathbf{1 5 0 0}, \mathbf{1 4 0 0}, \mathbf{1 0 0 0}, \mathbf{1 0 0 0}, \mathbf{1 6 0 0}, \mathbf{1 0 0} \)
(i) Find the median income of the house
holds.
(ii) If one more household with monthly
income of Rs. 1500 is added, what will
the median income be?
\( \begin{array}{ll} \text { A }. i) 1400 & \text { i) } 1450\end{array} \)
B. \( i \) ) 1450 ii) 1400
c. \( i) 1200 \) ii) 1450
D. \( i \) ) 1000 ii) 1250


Which of the following is pheromone?
A. Linalool
B. Disparlure
c. ВнА
D. Alitame


Suppose the resulting torque on a body is
(i) zero
(ii) not zero. What is the effect
of the acting torques on the body in the two cases?


Hertz stands for:
A. second
B. second \( ^{-1} \)
c. meter
D. meter


Obtain the differential equation whose solution is
\( \boldsymbol{y}=\boldsymbol{x} \sin (\boldsymbol{x}+\boldsymbol{A}), \mathbf{A} \) being constant
A \( \cdot\left(x y_{1}-y\right)^{2}+x^{2} y^{2}=x^{4} \)
B. \( \left(x y_{1}-y\right)^{2}-x^{2} y^{2}=x^{4} \)
c. \( \left(x y_{1}-y\right)^{2}+x^{2} y^{2}=x^{2} \)
D. \( \left(x y_{1}-y\right)^{2}-x^{2} y^{2}=x^{2} \)


\( X \) and \( Y \) are independent binomial \( \operatorname{variates} \boldsymbol{A}\left(\mathbf{5}, \frac{\mathbf{1}}{\mathbf{2}}\right) \) and \( \boldsymbol{B}\left(\mathbf{7}, \frac{\mathbf{1}}{\mathbf{2}}\right) \) then
\( \boldsymbol{P}(\boldsymbol{X}+\boldsymbol{Y}=\boldsymbol{3}) \)
A \( \cdot \frac{45}{1024} \)
в. \( \frac{55}{1024} \)
c. \( \frac{65}{1024} \)
D. \( \frac{60}{1024} \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} & -\mathbf{2} \\ \mathbf{2} & \mathbf{0} & \mathbf{3}\end{array}\right] \) then \( (\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \boldsymbol{A}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ccc}13 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 13\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{ccc}7 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{ccc}-7 & 0 & 0 \\ 0 & 0 & -7 \\ 0 & 0 & -7\end{array}\right] \)
D. \( \left[\begin{array}{ccc}11 & 0 & 0 \\ 0 & 11 & 0 \\ 0 & 0 & 11\end{array}\right] \)


Assertion
Iron is found in the free state in nature.
Reason
Iron is highly reactive element.
A. If both Assertion and Reason are correct and Reason is
the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.


Obturator foramen occurs in
A. Pelvic girdle
B. Pectoral girdle
c. Cranium
D. vertebrae


The value of \( \left|\begin{array}{llll}\boldsymbol{p} & \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{a} & \boldsymbol{q} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{r} & \boldsymbol{0} \\ \boldsymbol{d} & \boldsymbol{e} & \boldsymbol{f} & \boldsymbol{s}\end{array}\right| \) is
\( A \cdot p+q+r+s \)
B.
\( c \cdot a b+c d+e f \)
D. pqrs


The arrangement of megaspores tetrad in a gymnosperm is
A. Decussate
B. Tetrahedral
c. Linear
D. Isobilateral


Which of the following products obtained by destructive distillation of coal, is not properly matched?
A. Coal tar-dyes, explosives, paints
B. Coal gas - fuel
c. coke - drinking purposes
D. Ammoniacal liquor - fertilizers


A particle is executing simple harmonic motion between extreme positions
given by \( (-1 .-2 .-3) \mathrm{cm} \) and
\( (1,2,1) c m . \) Its amplitude of oscillation is :
\( A \cdot 6 c m \)
в. 4 ст
\( c .2 c m \)
D. \( 3 c m \)


The total probability of finding a particles in space under normalized condition according to quantum
mechanics is
A. zero
B. Infinity
c. one
D. Uncertain


Describe the bell jar experiment to
prove that sound requires a medium to
propagate.


Assertion
Detergents with a straight chain of hydrocarbons are preferred over a branched chain
Reason
Detergents with branched chain hydrocarbon part are expensive.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Represent the number on the number line: \( \frac{7}{4} \)


The method of zone refining of metals is
based on the principle of:
A. greater noble character of the solid metal than that of the impurity
B. greater solubility of the impurity in the molten state than in the solid
C . greater mobility of the pure metal than that of impurity
D. higher melting point of the impurity than that of the pure metal