ABCD is a square of length a, \( a \epsilon N, a>1 \)
Let \( L_{1}, L_{2}, L_{3}, \dots \) be points on BC such
that \( B L_{1}=L_{1} L_{2}=L_{2} L_{3}=\ldots=1 \) and
\( M_{1}, M_{2}, M_{3}, \ldots \) be points on CD such
that \( \boldsymbol{C M}_{\mathbf{1}}=\boldsymbol{M}_{\mathbf{1}} \boldsymbol{M}_{\mathbf{2}}=\boldsymbol{M}_{\mathbf{2}} \boldsymbol{M}_{\mathbf{3}}=\ldots=\mathbf{1} \)
Then \( \sum_{n=1}^{a-1}\left(A L_{n}^{2}+L_{n} M_{n}^{2}\right) \) is equal to
A \( \cdot \frac{1}{2} a(a-1)^{2} \)
в. \( \frac{1}{2} a(a-1)(4 a-1) \)
c. \( \frac{1}{2} a(a-1)(2 a-1)(4 a-1) \)
D. none of these


A question paper consists of 11 question divided into two section 1 and
2. section 1 consits of 5 questions and
section 2 consists of 6 questions. In how
many ways can a student select 6 questions, taking at least 2 questions from each section?


Assertion
In SHM let \( x \) be the maximum speed, \( y \)
the frequency of oscillation and \( z \) the maximum acceleration then \( \frac{x y}{z} \) is a
constant quantity.
Reason
This is because \( \frac{x y}{z} \) becomes a
dimensionless quantity
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


A planet has twice the mass of earth
and of identical size. What will be the
height above the surface of the planet where its acceleration due to gravity
reduces by \( 36 \% \) of its value on its surface?


What is the shape of equipotential
surface for a given point charge \( \boldsymbol{q} \)


The rate constant of the reaction \( \boldsymbol{A} \rightarrow \)
\( 2 B \) is \( 1.0 \times ! 0^{-3} \) mol \( l i t^{-1} \) min \( ^{-1}, \) if the
initial concentration of \( \boldsymbol{A} \) is 1.0 mole
\( l i t^{-1}, \) what would be the concentration
of \( B \) after 100 minutes?
A. \( 0.1 \mathrm{mol} \) lit\( ^{-1} \)
B. 0.2 mol lit \( ^{-1} \)
c. 0.9 mol lit \( ^{-1} \)
D. 1.8 mollit\( ^{-1} \)


Which of the following statement about
condensation is not true?
A. Protein synthesis result from them.
B. Polysaccharide synthesis result from them.
C. Nucleic acid synthesis result from them.
D. They consume water as a reactant.
E. Different condensation reactions produce different kinds of macromolecules.


Water gas is a mixture of -
A \( \cdot C O_{2} \) and \( O_{2} \)
в. \( O_{2} \) and \( H_{2} \)
c. \( H_{2}, N_{2} \) and \( O_{2} \)
D. \( C O, N_{2} \) and \( H_{2} \)


When a bomb explodes into two pieces, they move in opposite directions. This motion in opposite direction can be explained by
A. Law of conservation of energy
B. Law of conservation of momentum
c. Law of conservation of mass
D. Law of conservation of charge


The magnification of plane mirror is always -
\( \mathbf{A} \cdot<1 \)
B \( .>1 \)
\( c .=1 \)
D. zero


The near point of a normal human eye is
A \( .25 m \)
в. \( 17 m \)
\( c .1 m \)
D. \( 25 \mathrm{cm} \)


Which of the bryophyte has hyalline and chlorophyllose cells in its thallus (lacking rhizoids)?
A. Funaria
B. Sphagnum
c. Marchantia
D. Riccia


The scientific naming of plants begin with publication of Linnaeus book,
named
A. Charaka Samhita
B. Systema Naturae
c. species Plantarum
D. None of the above


1 kg of water is converted into steam at
the same temperature and at 1 atm (100
kPa). The density of water and steam
are \( 1000 \mathrm{kgm}^{-3} \) and \( 0.6 \mathrm{kgm}^{-3} \)
respectively. The latent heat of
vaporisation of water is \( 2.25 \times \) \( 10^{6} J k g^{-1} . \) What will be increase in
energy?
A \( .3 \times 10^{5} J \)
В . \( 4 \times 10^{6} J \)
c. \( 2.08 \times 10^{6} J \)
D. None of these


Find the approximate value of \( \angle A \) in
\( \Delta A B C \) if \( 8 \angle A=9 \angle B=4 \angle C \)
A \( .40^{\circ} \)
B. \( 74^{\circ} \)
\( c \cdot 86^{\circ} \)
D. \( 46.3^{\circ} \)


A zygote which has an \( X \) chromosome inherited from the father will become
A. Boy
B. Girl
C. Either girl or boy
D. cannot be predicted


The stable oxidation state of \( \boldsymbol{C} \boldsymbol{e}(\boldsymbol{Z}= \)
\( \mathbf{5 8} \) ) is:
\( A \cdot+4 \)
\( B \cdot+3 \)
\( c \cdot+2 \)
\( D \cdot+5 \)


Negative electric flux indicates that electric lines of force are directed
A. outwards
B. inwards
c. either (a) or (b)
D. none of these


A steady current I flows along an infinitely long hollow cylindrical
conductor of radius R. This cylinder is placed coaxially inside an infinite
solenoid of radius \( 2 R \). The solenoid has
n turns per unit length and carries a
steady current I. Consider a point \( P \) at a distance r from the common axis. The
correct statement(s) is(are)?
A. In the region \( 0<r<R \), the magnetic field is non-zero
B. In the region \( R<r<2 R \), the magnetic field is along
the common axis
C. In the region \( R<r<2 R \), the magnetic field is tangential to the circle of radius \( r, \) centered on the axis
D. In the region \( r>2 R \), the magnetic field is non-zero


(A) Write with the help of a diagram the principle of a potentionmeter.
(B) Using a potentionmeter how do you determine the internal resistance of a
cell?


State whether the given statement is True or False:

Acceleration due to gravity, \( \boldsymbol{g}=\frac{G M}{R^{2}} \)
where symbols have their usual meanings.
A. True
B. False


Which of the following is a soft material
in the tooth?
A. Dentine
B. Pulp
c. Enamel
D. Root


Which one of the following is correct
with respect to molar ionic
conductance of ions in aqueous
solution?
\( \mathbf{A} \cdot L i^{+}<N a^{+}<K^{+}<R b^{+} \)
B \( \cdot R b^{+}<K^{+}<N a^{+}<L i^{+} \)
\( \mathbf{c} \cdot S r^{2+}<C a^{2+}<M g^{2+}<B e^{2+} \)
D. \( N a^{+}<K^{+}<L i^{+}<R b^{+} \)


Arrange the direction of nerve
transmission in sequential order.
a) Cyton
b) Axon
c) Dendron
d) Nerve terminal
\( A \cdot c, a, b, d \)
в. \( a, c, b, d \)
\( c \cdot c, a, d, b \)
D. \( \mathrm{c}, \mathrm{b}, \mathrm{a}, \mathrm{d} \)


Is the Galileo principle adopted by Newton is known as law of inertia?


Describe the change in hybridisation of the \( A l \) atom in the following reaction:
\( \boldsymbol{A l C l}_{3}+\boldsymbol{C l}^{-} \rightarrow \boldsymbol{A l} \boldsymbol{C l}_{4}^{-} \)


Write the formulas for the following coordination compounds:
Amminebromidochloridonitrito-N-
platinate(II)


Calcium hydroxide is used for making
soap.
A . True
B. False


\( \lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin 2 x}= \)
\( A \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{3}{4} \)
D.


Bond angle is minimum for:
A \( . H_{2} O \)
в. \( H_{2} S_{2} \)
\( \mathbf{c} \cdot H_{2} S e \)
D. \( H_{2} T e \)


The power of a lens having a focal length of \( 1 \mathrm{cm} \) is :
\( A \cdot 1 D \)
в. \( 10 D \)
c. \( \frac{1}{10} D \)
D. \( 100 D \)


\( ^{210} 84^{\circ} \mathrm{o} \longrightarrow_{82}^{206} \mathrm{Pb}+_{2}^{4} \mathrm{He} \)
In this reaction, predict the position of group of \( P o \) in periodic table when lead
is in the \( I V A \) group:
A . IIA
в. \( I V B \)
c. \( V I A \)
D. \( V I B \)


The angle of inclination of the axis of
the magnetic needle to the horizontal plane when suspended freely and is at rest is known as
A. Angle of inclination
B. Angle of variation
c. Angle of declination
D. None of the above


Substances necessary for autotrophic nutrition are
\( A \cdot C O_{2} \) and \( H_{2} O \)
B. Chlorophyll
c. sun light
D. All of the above


The term used to indicate the
development of unpleasant smell and taste in fat and oil-containing foods due to aerial oxidation is:
A . acidity
B. radioactivity
c. rabidity
D. rancidity


(R)-2 -lodobutane is treated with Nal in
acetone and allowed to stand for a long
time.The product eventually formed is:
A \( \cdot(R)-2- \) iodobutane
B . \( (S)-2- \) iodobutane
C. \( (\pm)-2- \) iodobutane
D. (土) - 1,2 - diiodobutane


Name a material which exhibits
fluorescence when cathode rays fall on ¡t.


f \( f: R \rightarrow R \) be defined by \( f(x)=3 x+ \)
\( 2, \) find \( f(f(x)) \)


Willemite is
\( \mathbf{A} \cdot Z n_{2} S i O_{4} \)
\( \mathbf{B} \cdot H_{2} P t C l_{6} \)
\( c \cdot Z n O \)
D. \( Z n O F e_{2} O_{3} \)


In ethyne, the two carbon atoms
contain:
A. one sigma bond and two pi bonds
B. one sigma bond and one pi bond
C. two sigma bonds and one pi bond
D. two sigma bonds and no pi bond


Show that for reaction \( A B(g) \rightleftharpoons A(g)+ \) \( \mathrm{B}(\mathrm{g}), \) the total pressure at which \( \mathrm{AB} \) is \( 50 \% \) dissociated is numerically equal to
three times of \( \boldsymbol{K}_{\boldsymbol{p}} \)


If the volume of \( C O_{2} \) liberated during
respiration is more than the volume of
\( O_{2} \) used the respiratory substances will
be
A. Fats
B. organic acid
c. Proteins
D. Carbohydrate


Which oxides will not give metal on heating?
A. \( H g O \)
в. \( Z n O \)
c. \( A g_{2} O \)
D. All of these


At puberty,
A. Thigh bones elongate
B. Skull bones expand
C. Increase in number of bones of rib cage
D. Hip joint grows bigger


An electric cell does 5 joules of work in carrying 10 -coulomb charge around the closed circuit. The electromotive force
of the cell is :
A . 2 volt
B. 0.5 volt
c. 4 volt
D. 1 volt


The coefficient of \( t^{24} \) in the expansion of
\( \left(1+t^{2}\right)^{12}\left(1+t^{12}\right)\left(1+t^{24}\right) \) is
A. \( ^{12} C_{6}+2 \)
B. \( ^{12} C_{5} \)
\( \mathbf{c} \cdot^{12} C_{6} \)
D. \( ^{12} C_{7} \)


Average Kinetic energy in one time
period in an SHM is (Where \( m, \omega \) and \( y_{0} \)
are mass of particle, angular velocity and maximum displacement respectively)
\( ^{A} \cdot \frac{m \omega^{2} y_{0}^{2}}{2} \)
B . \( m \omega^{2} y_{0}^{2} \)
c. \( \frac{m \omega^{2} y_{0}^{2}}{3} \)
D. \( \frac{m \omega^{2} y_{0}^{2}}{4} \)


What is meant by magnification? obtain the formula for finding
magnification image formed by a
mirror.


A sphere, a cube and a thin circular disc all made of the same material, have
same mass. Their initial temperature is
\( 3 \times 10^{3}^{\circ} \mathrm{C} . \) The body which cools
rapidly is :
A. sphere
B. cube
c. both sphere and cube
D. circular plate


A salt which in solution gives a bluish
white precipitate with \( N a O H \) solution
and a white precipitate with \( B a C l_{2} \) solution is:
A \( . C u S O_{4} \)
в. \( F e S O_{4} \)
c. \( F e_{2}\left(S O_{4}\right)_{3} \)
D. \( C u C l_{2} \)


Fill in the blanks.
\( \ln 1609 \)
designed a telescope.
A. Newton
B. Galileo
c. Einstein
D. Archimedes


A ball weighing \( 10 g \) hits a hard surface
vertically with a speed of \( 5 m / \)sec and rebounds with the same speed. The ball remains in contact with the surface for
\( 1 / 100 s e c . \) The average force exerted by the surface on the ball is
\( \mathbf{A} \cdot 100 N \)
в. \( 10 N \)
\( c \cdot 1 N \)
D. \( 0.1 N \)


Three arrangements are shown for the
\( \operatorname{complex}\left[\operatorname{CoBr}_{2}\left(N H_{3}\right)_{2}(e n)\right]^{\oplus} . \) Which
one is wrong statement?
A. I and II are geometrical isomers
B. Il and III are optically active isomers
c. I and III are optically active isomers
D. II and III are geometrical isomers


Long-sightedness is caused by the eyeball being too short. It can be
corrected by the use of a:
A. convergent lens
B. plane mirror
c. divergent lens
D. None of these


Write a value of \( \int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x \)


\( \left.\begin{array}{l}\text { Find } \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d} \text { if }\left[\begin{array}{cc}\boldsymbol{d}+\mathbf{1} & \mathbf{1 0}+\boldsymbol{a} \\ \mathbf{3} \boldsymbol{b}-\mathbf{2} & \boldsymbol{a}-\mathbf{4}\end{array}\right]= \\ \mathbf{2} \quad \mathbf{2} \boldsymbol{a}+\mathbf{1} \\ \boldsymbol{b}-\mathbf{5} \quad \boldsymbol{4} \boldsymbol{c}\end{array}\right] \)


Find the angle between the vectors \( 3 i+ \)
\( 2 j-6 k \) and \( 4 i-3 j+k \)


If \( \sin \theta+\cos \theta=\sqrt{2} \cos \theta, \) then the
general value of \( \boldsymbol{\theta} \) is


I.F. of \( \frac{d y}{d x}=y \tan x+2 \sin x \) is:
A . sec \( x \)
B. \( \sin x \)
\( c \cdot \csc x \)
D. \( \cos x \)


A nectar-secreting gland cell
characteristically contains
A. Granular cytoplasm filling the cell and a small nucleus.
B. Granular cytoplasm living a central vacuole and a small nucleus.
C. Granular cytoplasm filling the cell and a large conspicuous nucleus.
D. Vacuolated cytoplasm but with a large nucleus.


In the given figure, if area of parallelogram \( A B E F \) is \( 96 \mathrm{cm}^{2} ; \) state
giving reason, the area of parallelogram
\( A B C D \)
\( \mathbf{A} \cdot 96 \mathrm{cm}^{2} \)
B. \( 86 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 76 \mathrm{cm}^{2} \)
\( \mathrm{D} \cdot 36 \mathrm{cm}^{2} \)


Assertion
Across the period effective nuclear charge decreases.
Reason
The third period contains only 8
elements and not 18 like 4 th period.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Three concentric spherical shells have radii \( a, b \) and \( c(a<b<c) \) and have
surface charge densities \( +\boldsymbol{\sigma},-\boldsymbol{\sigma},+\boldsymbol{\sigma} \)
respectively. If \( V_{A}, V_{B} \) and \( V_{C} \) denote the potentials of three shells, then for \( c=a+b, \) we have
A. \( V_{C}=V_{B}=V_{A} \)
B. \( V_{C}=V_{B} \neq V_{A} \)
c. \( V_{C} \neq V_{B}=V_{A} \)
D. \( V_{C} \neq V_{B} \neq V_{A} \)


Which of the given labeled parts is
responsible for the decrease in the
amount of stored glycogen in the liver?
\( A \cdot D \)
B.
\( c . \) в
\( D \)


Find the degree of the given algebraic
expression
\( 3 x-15 \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 2 \)
D. -15


The fine structure of hydrogen spectrum can be explained by
A. the presence of neutrons in the nucleus
B. the finite size of nucleus
c. the orbital angular momentum of electrons
D. the spin angular momentum of electrons


The solubility of \( B a_{3}\left(A s O_{4}\right)_{2} \) (formula
mass \( =\mathbf{6 9 0} \) ) is \( \mathbf{6 . 9} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{g} / \mathbf{L} . \) What is
the \( \boldsymbol{K}_{s p} ? \)
A \( .1 .08 \times 10^{-11} \)
B . \( 1.08 \times 10^{-13} \)
c. \( 1.0 \times 10^{-15} \)
D. \( 6.0 \times 10^{-13} \)


When a solid ball of volume \( V \) is falling through a viscous liquid, a viscous force \( F \) acts on it. If another ball of
volume 2 V of the same material
is falling through the same liquid then the viscous force experienced by it will be (when both fall with terminal
velocities).
\( A \cdot 4 F \)
в. \( \frac{F}{2} \)
\( c \cdot 2 F \)
D. \( \frac{F}{4} \)


A concave lens of focal length \( 15 \mathrm{cm} \) form an image \( 10 \mathrm{cm} \) from the lens. How far is the object placed from the lens? Draw the ray diagram also.


A moving charge produces
A. Neither electric field nor magnetic field
B. Electro-static field only
C. Magnetic field only
D. Both magnetic and electro-static field


Find the inverse of the following matrix
using transformation method. \( \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right] \)


The value of equilibrium constant for a
feasible cell reaction is:
\( \mathbf{A} \cdot<1 \)
в. \( =1 \)
\( c \cdot>1 \)
D. zero


The motion of copper plate is damped
when it is allowed to oscillate between
the two poles of a magnet. What is the cause of this damping?


When benzene diazonium chloride is
treated with cuprous chloride in \( \boldsymbol{H} \boldsymbol{C l} \) chlorobenzene is formed. This reaction
is called:
A. Perkin reaction
B. Hinsberg reaction
c. Gattermann reaction
D. Sandmeyer reaction


\( A \) and \( B \) are two different chemical
species undergoing 1st order decomposition with half lives equal to 5 \( \sec \) and 7.5 sec respectively. If the initial concentration of \( A \) and \( B \) are in
the ratio \( 3: 2 . \) Calculate \( \frac{C_{A_{1}}}{C_{B_{1}}} \) after three
half lives of \( A \). Report your answer after
multiplying it with 100


Find out the frequency of orange light
whose wavelength is \( 6 \times 10^{-7} \) m. The
speed of light is \( 3 \times 10^{8} m / s \)
A \( \cdot 2 \times 10^{15} \mathrm{Hz} \)
B . \( 2 \times 10^{-15} \mathrm{Hz} \)
c. \( 5 \times 10^{14} H z \)
D. \( 5 \times 10^{-14} \mathrm{Hz} \)
E . \( 2 \times 10^{14} H z \)


A man wants to measure current \( \sim \boldsymbol{m} \boldsymbol{A} \)
He should use
A. photo multiplier tube
B. photo cell and amplifier
c. photo multiplier tube and amplifier
D. photo cell and two stage amplifier


The magnitude of acceleration due to
gravity decreases
A. as the height from the surface of the earth increases
B. as the depth from the surface of the earth increases
C. as one moves from the pole of the earth to its equator
D. All the above


A unit vector is represented as \( 0.8 \hat{i}+ \) \( b \hat{j}+0.4 \hat{k} . \) Hence the value of \( b \) must be
A . 0.4
B. \( \sqrt{0.6} \)
\( c .0 .2 \)
D. \( \sqrt{0.2} \)


IUPAC name of given compound is:
A. 4 -methylpentanal
B. 4 -methylpentanol
C. 4 -methylpentenal
D. 4 -methylpentanone


Consider two points 1 and 2 in a region outside a charged sphere. Two points are not vary far away from the sphere. If \( \boldsymbol{E} \) and \( \boldsymbol{V} \) represent the electric field vector and the electric potential, which of the following is not possible?
A \( \cdot\left|\vec{E}_{1}\right|=\left|\vec{E}_{2}\right|, V_{1}=V_{2} \)
в. \( \left|\vec{E}_{1}\right| \neq\left|\vec{E}_{2}\right|, V_{1} \neq V_{2} \)
c \( \cdot\left|\vec{E}_{1}\right| \neq\left|\vec{E}_{2}\right|, V_{1}=V_{2} \)
D . \( \left|\vec{E}_{1}\right|=\left|\vec{E}_{2}\right|, V_{1} \neq V_{2} \)


In a game of tug of wars, a condition of equilibrium exists. Both the teams pull
the rope with a force of \( 10^{4} \) N. The
tension in the rope is :
\( A \cdot 10^{4} N \)
B . \( 10^{5} \mathrm{N} \)
\( c \cdot 0 \)
D. \( 2 \times 10^{4} \mathrm{N} \)


Which of the following is the smallest temperature?
A \( \cdot 1^{\circ} R \)
B. \( 1^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 1^{o} F \)
D. \( 1 K \)


If the change in internal energy of an ideal gas is equal to negative of the work done by the system, then
A. the process may be adiabatic
B. the process may be isothermal
c. the process must be isobaric
D. the temperature must decrease


The vectors \( \overrightarrow{A B}=3 \hat{i}+5 \widehat{j}+4 \widehat{k} \) and
\( A C=5 \hat{i}-5 \hat{j}+2 \widehat{k} \) are the sides of \( a \)
triangle ABC. The length of the median through \( A \) is


Which force is weakest of
all fundamental forces?
A. Gravitational force
B. Electromagnetic force
c. Weak nuclear force
D. Strong nuclear force


The angle of elevation of the top of a vertical tower from a point \( A, \) due east
of it is \( 45^{\circ} . \) The angle of elevation of the
top of the same tower from a point \( \boldsymbol{B} \)
due south of \( A \) is \( 30^{\circ} . \) If the distance
between \( A \) and \( B \) is \( 54 \sqrt{2} m, \) then
the height of the tower (in metres), is :
A. \( 36 \sqrt{3} \)
в. 108
\( c .54 \)
D. \( 54 \sqrt{3} \)


The surface area of a sphere when its volume is increasing at the same rate as its radius is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{1}{2 \sqrt{\pi}} \)
c. \( 4 \pi \)
D. \( \frac{4 \pi}{3} \)


The kinetic energy of \( 1 g \) molecule of a
gas at normal temperature and
pressure is :
\( \mathbf{A} \cdot 1.3 \times 10^{2} J \)
B . \( 2.7 \times 10^{2} J \)
c. \( 0.56 \times 10^{4} J \)
D. \( 3.4 \times 10^{3} J \)


Find the mode of the following frequency distribution of marks
obtained by 50 students.
\( \begin{array}{llll}\text { Marks } & 0- & 10- & 20- \\ \text { obtained } & 10 & 20 & 30\end{array} \)
No. of
students 12 20


Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel
A. Increases continuously
B. Decreases continuously
c. First increases and then decreases
D. First increases and then becomes cosntant


The frequency of A.C mains in India is
\( \mathbf{A} \cdot 30 H z \)
B. \( 50 H z \)
\( \mathbf{c} \cdot 60 H z \)
D. \( 120 H z \)


Minimum number of carbon atoms
required for an alkane to show any kind of isomerism.


Thermal radiation is also called
A . infrared radiation
B. EM radiation
c. nuclear radiation
D. None


Phenylalanine is a:
A. aromatic amino acid
B. aliphatic amino acid
c. dipeptide
D. glycoprotein


Evaluate the following integral as limit
of sum:
\( \int_{1}^{4}\left(x^{2}-x\right) d x \)


Compare the acceleration due to gravity on the surface of a planet, whose mass
and diameter are double that of the
earth, with the acceleration due to
gravity on the surface of the earth.
A . 1: 2
B . 2: 1
c. 3: 4
D. 4: 1


Two particles are in SHM in parallel straight lines close to each other. Amplitude \( A \) and time period \( T \) of both
the particles are equal. At \( t=0, \) one
particle is at displacement \( \boldsymbol{x}_{\mathbf{1}}=+\boldsymbol{A} \) and other at \( x_{2}=-\frac{A}{2} \) an they are
approaching towards each other, after what time they will cross each other?
A. \( T / 3 \)
в. \( T / 4 \)
\( \mathrm{c} \cdot 5 T / 6 \)
D. \( T / 6 \)


A body projected vertically upwards with a velocity of \( 19.6 \mathrm{ms}^{-1} \) reaches a
height of \( 19.6 ~ m \) on earth. If it is
projected vertically up with the same velocity on moon, then the maximum
height reached by it is \( \left(g_{\text {earth}}=g m s^{-2}\right. \) \( \left.\boldsymbol{g}_{m o o n}=\frac{\boldsymbol{g}}{\boldsymbol{6}} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . \( 19.18 \mathrm{m} \)
B. 3.3 \( m \)
c. \( 9.9 \mathrm{m} \)
D. 117.6 \( m \)


Find out the value of \( \mathrm{E} \) in the circuit
shown in figure.
A \( .+14 V \)
B . \( -14 V \)
\( c .-7 V \)
\( D \cdot+7 V \)


Factorise the following: \( a^{6}-b^{6} \)
\( \mathbf{A} \cdot(a+b)(a-b)\left(a^{2}+b^{2}+a b\right)\left(a^{2}-b^{2}+a b\right) \)
B \( \cdot(a+b)(a-b)\left(a^{2}+b^{2}+a b\right)\left(a^{2}+b^{2}-a b\right) \)
\( \mathbf{c} \cdot(a+b)(a-b)\left(a^{2}-b^{2}-a b\right)\left(a^{2}+b^{2}-a b\right) \)
D. None of these


The function \( f(x)=x^{2}+\frac{\lambda}{x} \) then:
A. minimum at \( x=2 \) if \( \lambda=16 \)
B. maximum at \( x=2 \) if \( \lambda=16 \)
c. maximum for no real value of \( \lambda \)
D. point of inflection at \( x=1 \) if \( \lambda=-1 \)


Which one of the following is least volatile?
\( \mathbf{A} \cdot H C N \)
в. \( H F \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C S_{2} \)


Which of the following is stress
hormone?
\( \mathbf{A} \cdot A B A \)
в. \( C_{2} H_{4} \)
\( \mathrm{c} \cdot G A_{7} \)
D. IAA


In triangle \( A B C, \) right-angled at \( B \), if \( \tan A=\frac{1}{\sqrt{3}} \) find the value of:
(i) \( \sin A \cos C+\cos A \sin C \)


\( \operatorname{Let}\left(1+x^{2}\right)^{2}(1+x)^{n}=A_{0}+A_{1} x+ \)
\( A_{2} x^{2}+\ldots . \) If \( A_{0}, A_{1}, A_{2} \) are in A.P, then
the value of \( n \)
\( A \cdot 2 \)
B. 3
\( c \cdot 5 \)
D. 7


Assertion
He and Ne do not form clatharates.
Reason

They are difficult to polarise due to
smaller size.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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 true but Reason is false
D. Assertion is false but Reason is true


The dimensions of cuboid are in the
ratio \( 3: 2: 1 . \) Its volume is \( 1296 m^{3} \)
Find its height.
\( \mathbf{A} \cdot 6 m \)
B. \( 0.8 m \)
\( c .6 \mathrm{cm} \)
D. None of these


Six point charges are kept at the
vertices of a regular hexagon of side \( \boldsymbol{L} \)
and centre \( O \), as shown in the figure. Given that \( K=\frac{1}{4 \pi \epsilon_{0}} \frac{q}{L^{2}}, \) which of the following statement(s) is(are) correct?
This question has multiple correct options
A. The electric field at \( O \) is \( 6 K \) along \( O D \)
B. The potential at \( O \) is zero
c. The potential at all points on the line \( P R \) is same
D. The potential at all points on the line \( S T \) is same


A transverse wave of amplitude \( 0.01 m \)
and frequency \( 500 H z \) is travelling
along a stretched string with a speed of \( 200 m / s . \) Find the displacement of a particle at a distance of \( 0.7 \mathrm{m} \) from the
origin after \( 0.01 s . \) Also find the phase difference between the point where
wave reaches from the origin


\( ^64 C u \) (half-life-12.8 hr) decays by \( \beta^{-} \)
emission \( (38 \%), \beta^{+} \) -emission \( (19 \%) \) and
electron capture \( (43 \%) . \) Calculate partial half lives for electron capture?
\( \mathbf{A} \cdot 29.78 h r \)
B. \( 28.78 h r \)
\( \mathrm{c} .59 .56 \mathrm{hr} \)
D. \( 57.56 h r \)


A current of \( 3.7 \mathrm{A} \) is passed for six hours between \( N i \) electrode in 0.5 litre of \( 2 M \)
solution of \( N i\left(N O_{3}\right)_{2} . \) The molarity of
solution at the end of electrolysis is:


By many evidences, it can be known
that the downward movement of food
takes place through
A. Phloem
B. Xylem
c. collenchyma
D. Sclerenchyma


Which of the following statement is not
true?
A. The resistance of an intrinsic semiconductor
decreases with increase in temperature
B. Doping pure \( S i \) with trivalent impurities gives \( p \) -type semiconductor
C. The majority carriers in n-type semiconductor are holes
D. a p-njunction can act as a semiconductor diode


If the distance traveled by a body in the nth second is given by \( (4+6 n) m \) then find the initial velocity and acceleration
of the body.
A \( \cdot 6 \mathrm{m} \mathrm{s}^{-2}, 7 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 6 \mathrm{m} \) s \( ^{-2} \), 3 \( \mathrm{m} \) s \( ^{-1} \)
C \( \cdot 16 \mathrm{m} \mathrm{s}^{-2}, 17 \mathrm{m} \mathrm{s}^{-1} \)
D. 26 m \( s^{-2} \), 7 \( \mathrm{m} s^{-1} \)


Choose the correct answer from the
alternatives given

Whether a molecule can cross the
plasma membrane depends upon the
A. Size of the molecule
B. Shape of the molecule
c. charge of the molecule
D. All of these


Match the following lists and choose the correct combination.
List-I List-II
(A)Trichomes \( \quad \) (i)Gaseous exchnage
(B)Tracheid \( \quad \) (ii)Mechanical strength
(C)Bast fiber
(iii)Prevent water loss
(iv)Water conduction (D)Guard cells food pf (v)Synthesis
\( A \)
A- (iii), B- (v), C- (iv), D- (ii)
B. A- (iii), B- (iv), C- (ii), D- (i)
\( c \)
A- (i), B- (iv), C- (ii), D- (iii)
\( A-(v) \) C- (iv), D- (ii)
D. B- (iii)


Out of \( 1 \mathrm{M} \) glucose and \( 2 \mathrm{M} \) glucose. \( 2 \mathrm{M} \) glucose has a higher boiling point.
A. True
B. False


Which one of the following statements
is not true regarding diborane?
A. It has two bridging hydrogens and four perpendicular to the rest.
B. When methylated, the product is \( M e_{4} B_{2} H_{2} \)
C. The bridging hydrogens are in a plane perpendicular to the rest.
D. All the B - H bond distances are equal


The following is the bond of maximum bond energy:
A. s-s
B. 0-0
c. se-se
D. Te-Te


In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in Hindi and Mathematics but not in
English?
A . 18
в. 12
\( c \cdot 10 \)
\( D \)


Arrange the following compounds in
increasing order of their boiling points:
\( \mathbf{C H}_{3} \mathbf{C H}_{2} \mathbf{C H}_{2} \mathbf{C H O}, \mathbf{C H}_{3} \mathbf{C H}_{2} \mathbf{C H}_{2} \mathbf{C H}_{2} \)


Carbohydrates contain hydrogen and oxygen atoms in the ratio of
A . 1:
B. 2:
\( c \cdot 2: 3 \)
D. 1:


The ratio of work done by an ideal diatomic gas to the heat supplied by the gas in an isobaric process is
A \( \cdot \frac{5}{7} \)
в. \( \frac{3}{5} \)
\( c \cdot \frac{2}{7} \)
D. \( \frac{5}{3} \)


Write the abscissa of the following
point
(0,5)


The angle between force of friction and instantaneous velocity of the body moving over a rough surface is
A. zero
в. \( \pi / 2 \)
\( c . \pi \)
D. Insufficient data


Three wires \( A, B, C \) made of different
materials elongated by \( 1.5,2.5,3.5 \mathrm{mm} \) under a load of 5kg. If the diameters of the wires are the same,the most elastic material is that of
\( A \cdot A \)
B. B
\( c \cdot c \)
D. All


The volume of metal in a hollow sphere
is constant.If the inner radius is
increasing at the rate of \( 1 \mathrm{cm} / \mathrm{sec} \), then the rate of increase of the outer radius
when the radii are \( 4 c m \) and \( 8 c m \)
respectively is.
A. \( 0.75 \mathrm{cm} / \mathrm{sec} \)
B. \( 0.25 \mathrm{cm} / \mathrm{sec} \)
\( \mathrm{c} \cdot 1 \mathrm{cm} / \mathrm{sec} \)
D. \( 0.50 \mathrm{cm} / \mathrm{sec} \)


\( (1+i)^{8}+(1-i)^{8}= \)
A . 16
B. -16
\( c .32 \)
D. -32


What happens when the lower end of the lightning conductor is not properly buried in the ground?
A. No earthing
B. Building are protected
c. Damage building and even life
D. Both a \&


Which group of plant are not benefited
by \( C O_{2} \) fertilisation effect?
A. Plant requiring 3 ATP per \( C O_{2} \) fixation
B. Plant with kranz anatomy
c. Plant having high rate of photorespiration
D. Plant having single carboxylation


Which one of the following metal oxides shows both acidic and basic
characters?
A. \( N a_{2} O \)
в. \( K_{2} \) о
c. \( C u O \)
D. \( A l_{2} O_{3} \)


Find the square of the following
numbers using the identity \( (a+b)^{2}= \)
\( a^{2}+2 a b+b^{2}: \)
510


The velocity of an earth satellite is
A. constant
B. maximum at perigee.
c. maximum at apogee.
D. None of the above


The rate at which energy is radiated
from a hot body depends upon:
This question has multiple correct options
A. the nature of its surface
B. the area of its surface
C. the temperature of its surface
D. the temperature of the surroundings


\( f F \) is 200 N then find acceleration of \( B \)
A \( \cdot 5 m / s^{2} \)
\( 3 \cdot 10 m / s^{2} \)
c. \( 4 m / s^{2} \)
D. zer


Subtract \( 3.2 \times 10^{-6} \) from \( 4.7 \times 10^{-4} \)
with due regard to significant figures.
В. \( 7 \times 10^{-4} \)
c. \( 5.7 \times 10^{-4} \)
D. \( 4.7 \times 10^{-5} \)


\( N H_{3}+I^{-} \longrightarrow(E)(\text { violet vapours }) \)
What is (E) ?
\( \mathbf{A} \cdot I_{2} \)
в. \( I_{2} \)
c. \( I \)
D. \( I_{3}^{-} \)


Electric field at point \( \boldsymbol{A} \) depends on
\( A \)
в. \( q_{2} \)
\( c \cdot \) both \( q_{1} \) and \( q_{2} \)
D. None of these


A regular hexagon is inscribed in a
circle. If the area of hexagon is
\( 24 \sqrt{3} \mathrm{cm}^{2}, \) find the area of the circle.
(Use \( \boldsymbol{\pi}=\mathbf{3 . 1 4} \) ).


Bonding in ferric chloride is
A. Covalent
B. Ionic
c. co-ordinate
D. None of the above


\( A \) and \( B \) each have a certain number of
mangoes. A says to B "If you give me 30 of your mangoes, I will have twice as many as left with you." B replies, "If you give me \( 10, \) I will have thrice as many as left with you." How many mangoes does each have?


Solve the given quadratic equation by factorization
\( 8 x^{2}-22 x-21=0 \)


The reactant which is not used in
preparation of benzaldehyde in Etard method is:
This question has multiple correct options
A. toluene
B. ethylbenzene
c. benzoyl chloride
D. sodium benzoate


What is use of standard molar entropy?


If the activity of 108 Ag is 3 micro curie, the number of atoms present in it are \( \lambda=0.005 \mathrm{sec}^{-1} \)
A. \( 2.2 \times 10^{7} \)
B. 2.2 \( \times 10^{6} \)
c. \( 2.2 \times 10^{5} \)
D. 2.2 \times 10 \( ^{4} \)


Prove that \( : \frac{1+\cos A+\sin A}{1+\cos A-\sin A}= \)
\( \frac{1+\sin A}{\cos A} \)


An accurate celsius scale and faulty
Fahrenheit thermometer read \( 65^{\circ} \mathrm{C} \) and
\( 154^{\circ} F \) respectively when placed in a hot
liquid. Find the error in the latter.


Let \( ^{\prime} \boldsymbol{A}^{\prime} \) be the area swept by the radial vector connecting the earth and the sun in April and May months. Then, find the area swept by the same radial vector connecting the earth and the sun in
November and December months
interms of \( \boldsymbol{A} \)
A. \( A \)
в. \( 2 A \)
c. \( \frac{30 A}{31} \)
D. \( \frac{31 A}{30} \)


Choose the correct statement from the
following?
This question has multiple correct options
A. Pressure is same at all points in the horizontal plane
B. A liquid seeks its own level
C. The lateral pressure exerted by a liquid decreases with the increase in depth of the liquid
D. The upper surface of a stationary liquid is always horizontal


Which one of the following components has largest dipole moment?
A. chlorobenzene
B. \( 1,4- \)-dichlorobenzene
c. \( 1,2,3- \) trichlorobenzene
D. \( 1,2,4,5- \) tetrachlorobenzene


Name of metals and non-metals which
obtained by electrolysis is/are respectively? This question has multiple correct options
A. Sodium, Chlorine
B. Magnesium, lodine
c. Aluminium, Fluorine
D. Iron, Cobalt


Which of the following equipment does not work on principle of Joule's law?
A . Electric Heater
B. Electric Iron
c. Electric Bulb
D. Electric Fan


Choose the correct answer from the
alternatives given :
Amino acids which are specified by single codons are
A. Phenylalanine and arginine
B. Tryptophan and methionine
c. Valine and proline
D. Methionine and arginine


Given: \( C a O+C O_{2} \rightarrow C a C O_{3}+ \)
\( 40 \mathrm{kcal} / \mathrm{mole.} \) If \( 176 \mathrm{g} \) of \( \mathrm{CO}_{2} \) are
consumed, then how many \( k c a l \) of heat
are released?
A. \( 80 \mathrm{kcal} \)
в. 100 kcal
c. 120 kcal
D. 160 kcal


What is the molecular formula of silver
glance?
A. \( A g_{2} S \)
B. AgCl
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( A l_{2} O_{3} \)


Hydrogen burns in air with a:
A. light bluish flame
B. yellow flame
c. crimson red flame
D. green flame


Concentration of pure solid and liquid is not included in the expression of equilibrium constant because:
A. solid and pure liquid concentrations are independent of their quantities
B. solid and liquids react slowly
c. solid and liquids at equilibrium do not interact with gaseous phase
D. the molecules of solids and liquids cannot migrate to the gaseous phase


In bases, methyl orange turns:
A . red
B. green
c. yellow
D. blue


Light with an energy flux of \( 18 W / c m^{2} \) falls on a non-reflecting surface at normal incidence. The pressure exerted on the surface is:
A. \( 2 N / m^{2} \)
B . \( 2 \times 10^{-4} N / m^{2} \)
c. \( 6 N / m^{2} \)
D. \( 6 \times 10^{-4} N / m^{2} \)


20 card are numbered from 1 to \( 20 . \) One
card is drawn at random. What is the
probability that the number on the card is greater than \( 12 ? \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{5} \)
D. None of these


What is the reason to operate the
photodiodes in reverse bias?
A. fractional change due to the photo-effects on the majority carrier dominated forward bias current is more easily measurable than the fractional change in the reverse bias current.
B. reverse bias is more efficient than forward bias.
C. fractional change due to the photo-effects on the minority carrier dominated reverse bias current is more easily measurable than the fractional change in the forward bias current.
D. reverse bias configuration result in larger amount of current \( (\operatorname{in} \mu A) \)


Assertion: There is a scientific
explanation for the feeling of
depression.
Reason: In people who are depressed, the mood-regulating neurotransmitters fail to function normally, so that the signal is either depleted or disrupted before passing to the next nerve cell. In all depressions, it is likely that the transmission of serotonin is reduced or
disrupted.
Choose the correct options.
A. Both Assertion and Reason are correct
B. Assertion is correct but Reason is incorrect
c. Both Assertion and Reason are incorrect
D. Assertion is incorrect but reason is correct


Autoradiography technique was used
to
A. trace the path of carbon in photosynthesis
B. establish that the oxygen evolved during phtosynthesis is by photolysis of water molecule.
C. study photorespiration in certain plants.
D. find out the absorption maximum of chlorophyll pigments.


Which of the following processes cannot take place in the absence of oxygen?
A. Combustion
B. Respiration
c. oxidation
D. All of these


When a sperm containing Y chromosome fertilises an egg with \( x \) chromosome, the zygote develops into a
child.
A. Female
B. Either male or a female
c. Male
D. No child


\( C r_{2} O_{7}^{2-p H>a} C r O_{4}^{2-p H \leqslant b} C r_{2} O_{7}^{2-} \)
Find the value of \( \frac{\boldsymbol{a}}{\boldsymbol{b}}: \)


The allotrope of carbon which is a good conductor of heat and electricity is:
A. diamond
B. sugar charcoal
c. graphite
D. wood charcoal


Why does light from a clear blue portion of the sky show a rise and fall of intensity when viewed through a polaroid which is rotated? Explain by drawing the necessary diagram.


A metal ion required for normal functioning of an enzyme is
A. Holoenzyme
B. Coenzyme
c. cofactor
D. Prosthetic group


There are two solar energy collectors made up of thin aluminium sheet. They
are flat and uncoated. Collector ' \( \boldsymbol{A}^{\prime} \) is
rectangular measuring \( 20 \mathrm{cm} \) long and \( \mathbf{1 5} \mathrm{cm} \) wide while collector' \( \boldsymbol{B}^{\prime} \) is
circular having \( 20 \mathrm{cm} \) diameter. If
they are kept under mid-day sun for long time then,
A. both the collectors \( A \) and \( B \) will show nearly the same temperature
B. collector \( A \) will show higher temperature than \( B \)
c. collector \( B \) will show higher temperature than \( A \)
D. there will be no rise in the temperature of the two collectors, as they are uncoated


The value of \( K_{f} \) for water is \( 1.86^{\circ} \) calculated from glucose solution.The
value of \( \boldsymbol{K}_{f} \) for water calculated for
Na Cl solution will be :
\( \mathbf{A} .=1.86 \)
B. \( <1.86 \)
\( c \cdot>1.86 \)
D. zero


Which of the following compounds
would exhibit co-ordination isomerism?
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{5}\right] C l_{2} \)
B . \( \left[C r\left(N H_{3}\right)_{5}\right]\left[C o(C N)_{5}\right] \)
\( \mathrm{c} \cdot\left[\mathrm{Cr}(\mathrm{en})_{2}\right] \mathrm{NO}_{2} \)
D. \( \left[N i\left(N H_{3}\right)_{5}\right]\left[B F_{4}\right]_{3} \)


Choose the odd one out from the
following and give reason for your choice.
A. Natural Gas
B. Sun
c. Biomass
D. wind


Reindeer moss is common name of
A. Usnea comosa
B. cladonia rangiferina
c. Funaria hygrometrica
D. sphagnum angustifolium


Use Euclid's division lemma to find the
HCF of the following
27727 and 53124
A .233
B . 200
c. 154
D. 212


The focal length of a spherical mirror is half of the radius of curvature
A. For all rays
B. Only for paraxial rays near the principal axis
C. For those rays which are far from the principal axis
D. For those rays which subtend extremely large angles with the axis


The value of \( \lim _{n \rightarrow \infty} \frac{\sqrt[4]{n^{5}+2}-\sqrt[3]{n^{2}+1}}{\sqrt[5]{n^{4}+2}-\sqrt[2]{n^{3}+1}} \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. -1
D. \( \infty \)


Bond order of \( \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{+}, \boldsymbol{O}_{2}^{-} \) and \( \boldsymbol{O}_{2}^{2-} \) is in
order
A \( \cdot O_{2}^{-}<O_{2}^{2-}<O_{2}<O_{2}^{+} \)
B. \( O_{2}^{2-}<O_{2}^{-}<O_{2}<O_{2}^{-} \)
c. \( O_{2}^{+}<O_{2}<O_{2}^{-}<O_{2}^{2} \)
D. \( O_{2}<O_{2}^{+}<O_{2}^{-}<O_{2}^{2} \)


Which of the following sets of ions represents a collection of isoelectronic
species?
A \( \cdot N^{3}, O^{3}, F^{-}, S^{2-} \)
B . \( L i^{+}, N a^{+}, M g^{2+}, C a^{2+} \)
C \( \cdot K^{+}, C l^{-}, C a^{2+}, S c^{3+} \)
D. \( B a^{2+}, S r^{2+}, K^{+}, C a^{2+} \)


Magnitude of \( e / m \) for \( O^{-} \)
\( \mathbf{A} \cdot 10^{-12} \)
B. \( 10^{-20} \)
c. \( 10^{-22} \)
a
D . \( 10^{-18} \)


Which atoms should have smaller value
of \( (\boldsymbol{I} \boldsymbol{E})_{1} ? \)
(a) Oxygen or sulphur
(b) Nitrogen or phosphorus
\( \begin{array}{ll}\text { A } \cdot \text { (a) } S(b) & P\end{array} \)
B. (a) \( O \) (b) \( P \)
c. (a) \( S \) (b) \( N \)
D. Noneofthese


A bacterium divides every 35 minutes. If
a culture containing \( 10^{5} \) cells/ml is
grown in 175 minutes, what will be cell
concentration after that period
A \( \cdot 175 \times 10^{5} \)
В. \( 35 \times 10^{5} \)
c. \( 5 \times 10^{5} \)
D. \( 32 \times 10^{5} \)


Two cylindrical vessels fitted with pistons \( A \) and \( B \) of area of cross section
\( 8 \mathrm{cm}^{2} \) and \( 320 \mathrm{cm}^{2} \) respectively are
joined at their bottom by a tube and they are completely filled with water. When a mass of \( 4 \mathrm{kg} \) is placed on piston
A, find:
(i) the pressure on piston \( A,( \) ii) the pressure on piston \( \mathrm{B} \), and (iii) the thrust on piston B.


How many different signals can be made by hoisting 6 differently coloured flags one above the other, when any number of them may be hoisted at
once?
A . 1956
B . 1955
\( c \cdot 1900 \)
D. 1901


The current gain \( (\beta) \) of a transistor in
common base mode is \( 40 . \) To change
the collector current by \( 160 \mathrm{mA} \), the necessary change in the base current is
(at constant \( \mathbf{V}_{C E} \) )
A. \( 0.25 \mu \)
B. \( 4 \mu \) A
\( c \cdot 4 m A \)
D. \( 40 \mathrm{mA} \)


List three differences between arteries
and veins


A prism having an apex angle 40 and
refractive index 1.5 is located in front of
a vertical plane mirror as shown in
figure. Through what total angle is the ray deviated after reflection from the
A \( \cdot 176^{\circ} \)
\( \mathbf{B} \cdot 4^{0} \)
\( c \cdot 178 \)
\( D \cdot 2 \)


Blood vessels which carry blood from different organs of the body to the heart
A. Veins
B. Arteries
c. capillaries
D. None of the above


The diagram given shows a special method of reproduction in an organism. Which of the following organisms also reproduces in a similar way?
A. Amoeba
B. Hydra
c. Paramecium
D. Euglena


In cockroach, the ootheca is formed by the secretion of
A. phallic gland
B. collaterial gland
c. mushroom gland
D. conglobate gland


Match the following
Set-I (Cl-O bond length) \( \quad \operatorname{Set}-\|\left(\mathbf{A}^{0}\right) \)
A) \( \boldsymbol{H} \mathbf{C l O} \)
1)1.64
\( \mathbf{B}) \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{2} \)
2)1.70
\( \mathbf{C}) \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{3} \)
3) 1.45
D) \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{\boldsymbol{4}} \)
4) 1.57
The correct matching is:
B. A-2, B-3, C-4, D-1
c. A-2, B-1, C-4, D-3
D. A-2, B-1, C-3, D-4


The area of the region between the curve
\( \boldsymbol{y}=\mathbf{4} \boldsymbol{x}^{2} \) and the line \( \boldsymbol{y}=\mathbf{6} \boldsymbol{x}-\mathbf{2} \) is:
A \( \cdot \frac{1}{9} \) sq. units
B. \( \frac{1}{12} \) sq. units
c. \( \frac{3}{2} \) sq. units
D. \( \frac{1}{5} \) sq. units


Identify the substance oxidised, reduced, oxidising agent and reducing agent for the following reaction.
\( \boldsymbol{H} \boldsymbol{C H O}_{(l)}+\mathbf{2}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]_{(a q)}^{+}+ \)
\( \mathbf{3} \boldsymbol{O} \boldsymbol{H}_{(\boldsymbol{a q})}^{-} \rightarrow \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(s)}+\boldsymbol{H} \boldsymbol{C O O}_{(\boldsymbol{a q})}^{-}+ \)
\( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3(a q)}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)


Which of the following pairs represents isobars?
A \( \cdot 2^{3} \mathrm{He} \) and \( _{2}^{4} \mathrm{He} \)
B \( \cdot \frac{24}{12} \mathrm{Mg} \) and \( _{12}^{25} \mathrm{Mg} \)
\( \mathbf{c} \cdot_{19}^{40} K \operatorname{and}_{20}^{40} C a \)


Normal of the parabola \( x^{2}=8 y \) at (2,1)
is
A. \( 2 x+y+5=0 \)
в. \( 2 x+y=5 \)
\( \mathbf{c} \cdot 2 x-y+5=0 \)
D. \( 2 x-y-5=0 \)


A soap bubble of radius \( 3 \mathrm{cm} \) is charged with surface charge density \( \sigma \) such that \( \frac{\sigma^{2}}{\epsilon_{0}}=0.4 S I \) units. The excess
pressure inside the bubble in SI unit
(surface tension of soap solution \( =3 \times \)
\( 10^{-3} \mathrm{N} / \mathrm{m} \) ) is:
A . \( 0 . \)
B. 0.2
c. 0.5
D. 0.25


Energy of an electron in an orbit of \( \boldsymbol{H}- \) atom is \( -\frac{\boldsymbol{R}_{\boldsymbol{H}}}{\boldsymbol{4}} . \) The no. of degenerate orbitals in this orbit are :
A .4
B. 3
\( c .5 \)
D.


Polluted water can be purified by using
A. Microorganisms
B. Algae
c. Pesticides
D. Fishes


Thermal conduction takes place in
A. solid, liquid
B. liquid, gas
c. gas, solid
D. solid, liquid, gas


Mercury, Venus, Earth and Mars are not
among the planets.
A. outer
B. inner
c. warmer
D. lighter


A body takes 10 minutes to cool from
\( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} . \) The temperature of
surroundings is constant at \( 25^{\circ} \mathrm{C} \). Then, the temperature of the body after next
10 minutes will be approximately
A \( \cdot 43^{\circ} \mathrm{C} \)
В . \( 47^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 41^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \)


A particle suspended from a fixed point, by a light inextensible thread of length is projected horizontally from its lowest position with velocity \( \sqrt{\frac{\mathbf{7 g L}}{\mathbf{2}}} . \) The thread will slack after swinging through
an angle \( \theta, \) such that \( \theta \) equal
A \( .30^{\circ} \)
B. \( 135^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 150^{\circ} \)


in the given figure if DEllAC and DCIIAP
then which of the
following is ture
A \( \cdot \operatorname{BE}(\mathrm{AD}+\mathrm{CP})=\mathrm{BE}^{2} \)
B. \( \mathrm{BE} \times \mathrm{CP}=\mathrm{EC} \times \mathrm{BC} \)
c. \( \mathrm{BC} \times \mathrm{CP}=\mathrm{EC} \times \mathrm{BC} \)
D. \( B D \times D E \times=B E^{2} \)


Two thin blankets are warmer than one
blanket of their combined thickness,
this happens, because
A. one blanket is heavier
B. Double layer prevent transmission of heat
c. Two blankets have large mass
D. None of the above


Verify whether the following are zeroes of the polynomial, indicated against them. \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{l} \boldsymbol{x}+\boldsymbol{m}, \boldsymbol{x}=-\frac{\boldsymbol{m}}{\boldsymbol{l}} \)


Write the negations of the following
statements:
(a) All students of this college live in the
hostel.
(b) 6 is an even number or 36 is a
perfect square


A gaseous hydrocarbon upon
combustion gives 0.72 g of \( H_{2} O \) and \( 3.08 \mathrm{g} \) of \( C O_{2} . \) The empirical formula of the hydrocarbon is :
A. \( C_{6} H_{5} \)
в. \( C_{7} H_{8} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{3} H_{4} \)


Explain only reaction mechanism for alkaline hydrolysis of tert-butylbromide.


The graph given represents the I-V
characteristics of a Zener diode. Which
part of the characteristic curve is most
relevant for its operation as a voltage
regulator?
\( A \cdot a \)
3. \( b c \)
\( c \cdot c d \)
\( 0 . d \)


Find the derivative of the following functions (it is to be understood that \( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero
constants and \( m \) and \( n \) are integers) \( \sec x-1 \)
\( \sec x+1 \)


When a plastic comb rubbed on hair is brought near bits of paper, it attracts them because:
A. The comb and the paper get similarly charged.
B. They get oppositely charged.
c. The paper bits are very light.
D. None of these


Give reasons for the following
statements
Why covalent compounds
(i) are bad conductors of electricity.
(ii) have low melting and boiling points.


Show that the Signum Function \( \boldsymbol{f} \)
\( R \rightarrow R, \) is neither one one nor onto?
\[
f(x)=\left\{\begin{array}{l}
1, \text { if } x>0 \\
0, \text { if } x=0 \\
-1, \text { if } x<0
\end{array}\right.
\]


What is the half - life of a radioactive
substance if \( 75 \% \) of any given amount of the substance disintegrates in 60
minutes?
A. 2 Hours
B. 30 Minutes
c. 45 Minutes
D. 20 Minutes


Identify the pair of metals present in the gun powder:
A. iron, tin
B. copper, tin
c. iron, brass, tin
D. iron, zinc, titanium


If \( \boldsymbol{4} \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{6} \boldsymbol{P}(\boldsymbol{B})=\mathbf{1 0 P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{1} \)
\( \operatorname{then} P\left(\frac{B}{A}\right)= \)
\( A \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{7}{10} \)
D. \( \frac{19}{60} \)


Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( x y<1 \)
\[
\pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\]
Prove
(a) \( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}=\frac{\pi}{2} \)
(b) \( \sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{8}{17}=\cos ^{-1} \frac{36}{85} \)
\( (c) \sin ^{-1} \frac{3}{5}+\cos ^{-1} \frac{12}{13}=\cos ^{-1} \frac{33}{65} \)


If the Mass of gun \( =2 k g \)
Mass of bullet \( =20 g m \)
Velocity of bullet after firing \( =200 m / s \)
Then the Velocity of gun after firing will be


Yeast produces its clone naturally. This process is called as
A. Budding
B. Cloning
c. Growth
D. None of the above


The area bounded by the curve \( |x|= \)
\( \cos ^{-1} y \) and the line \( |x|=1 \) and the \( x \)
axis is
A . \( \cos 1 \)
B. \( \sin 1 \)
c. \( 2 \cos 1 \)
D. \( 2 \sin 1 \)


The vibration in the stem of tuning fork
are
A. transverse
B. longitudinal
c. both
D. none of these


Covalent bonds are non-directional
bonds.
A. True
B. False


What is labelled as A and what is the pH
of media A?
A . Nutrient solutions with essential minerals with pH
B. Nutrient solutions with essential minerals with pH
c. Water with essential minerals with \( \mathrm{pH} \) 7
D. water with pH7


Which of the following contains Actinomycetes?
A. Kingdom Fungi
B. Kingdom Moneraara
c. Kingdom Plantae
D. Kingdom Protoctista


The diameter of a solid disc is \( 0.5 m \) and
its mass is \( 16 k g \)
At what rate is the work done by the torque at the end of eighth second?
\( \mathbf{A} \cdot \pi W \)
в. \( \pi^{2} W \)
\( \mathbf{c} \cdot \pi^{3} W \)
D. \( \pi^{4} W \)


A body of mass \( m \) starts moving with
velocity \( V_{0} \) at point \( A \) on a frictionless
path as shown in the figure.

The speed of the body at point \( B \) will be:
A \( . \) zero
B. \( V_{0} \)
c. \( \frac{v_{0}}{2} \)
D. \( 2 V_{0} \)


Select the correct answer from \( A, B, C, D \)
and E for each of the metals given below
A metal present in duralumin but not in magnalium.
A. A: Aluminium
B. B :Copper
c. \( c: \) Lead
D. D: Potassium
E. E : Iron
F. F: manganese


Find the value of an inductance which
should be connected in series with a
capacitor of \( 5 \mu F, \) a resistance of \( 10 \Omega \)
and an ac source of \( 50 H z \) so that the
power factor of the circuit is unity.
A \( \cdot \frac{20}{\pi^{4}} \)
в. \( \frac{20}{\pi^{2}} \)
c. \( \frac{20}{\pi^{3}} \)
D. \( \frac{20}{\pi^{5}} \)


What current density is required to
provide a pressure difference of 1 atm
between any two points if \( B=2.2 T \) and
\( l=35 m m \)
A \( .1 .4 \times 10^{3} \mathrm{Am}^{-2} \)
в. \( 7.2 \times 10^{6} \) Ат \( ^{-} \)
c. \( 1.3 \times 10^{5} \mathrm{Am}^{-2} \)
D. \( 1.3 \times 10^{6} \mathrm{Am}^{-2} \)


enzymes have heme as a
prosthetic group.
(i) Catalase
(ii) Carboxypeptidase
(iii) Succinic dehydrogenase
(iv) Peroxidase
\( A \). (i) only
B. (i) and (ii) only
c. (ii) and (iii) only
D. (iii) and (iv) only
E. (i) and (iv) only


If mean and variance of 7 variates are 8
and 16 respectively and five of them are 2,4,10,12,14 then find the product of remaining two variates
\( \mathbf{A} \cdot 49 \)
B. 48
c. 45
D. 40


A student has to secure \( 40 \% \) marks to
pass. He gets 40 marks and fails by 40 marks. The maximum number of marks
is
A . 200
B. 160
\( c \cdot 180 \)
D. 320


In Young's interference experiment, if
the slits are of unequal width, then
A. no fringes will be formed
B. the positions of minimum intensity will not be completely dark
C. bright fringe as displaced from the original central position
D. distance between two consecutive dark fringes will not be equal to the distance between two consecutive right fringes.


Let \( R \) be arelation on the set \( A \), then \( R \)
is symmetric. Prove that \( \boldsymbol{R}^{-1} \) is symmetric.


The value of atomic number(z) is:


Find the total surface area of a cuboid
whose length, breadth and height are 20 \( \mathrm{cm}, 12 \mathrm{cm} \) and \( 9 \mathrm{cm} \) respectively


During an explosion, a large amount of is given out


In a meter bridge experiment, we try to
obtain the null point at the middle. This
reduces:
A. systematic error as well as random errors
B. systematic error but not the random error
c. random error but not the systematic error
D. neither systematic error nor the random error


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \max \{1+\sin x, 1,1-\cos x\}, x \in \)
\( [0,2 \pi] \) and \( g(x)= \)
\( \max \{1,|x-1|\}, x \in R, \) then
This question has multiple correct options
A. \( g(f(0))=1 \)
B. \( g(f(1))=1 \)
c. \( f(g(1))=1 \)
D. \( f(g(0))=\sin 1 \)


A metal sheet \( 27 \mathrm{cm} \) long, \( 8 \mathrm{cm} \) broad
and \( 1 \mathrm{cm} \) thick is melted to form a cube
The difference between the surface
areas of the two solids is
A \( \cdot 284 \mathrm{cm}^{2} \)
B . \( 286 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 296 \mathrm{cm}^{2} \)
D. \( 280 \mathrm{cm}^{2} \)


A closed water tank has internal size of
\( 10 m \times 15 m \times 20 m . \) It needs to be lined
with waterproofing cement on all its internal side. At the rate of Rs.
250 per \( m^{2}, \) the total cost of lining will
be Rs.
A. 237,500
0
в. 325,000
c. 400,000
D. 475,000


Which one of the following is a sign of water scarcity?
A. Dried fields having cracks on them
B. Nutrient deficient plants
C. Struggle to obtain water from bore wells
D. All of the above


If \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) are the arguments of \( z_{1} \) and
\( \bar{z}_{2}, \) then the value of \( \arg \left(z_{1} z_{2}\right) \) is
A \( \cdot \frac{5 \pi}{12} \)
в. \( \frac{\pi}{12} \)
c. \( \frac{7 \pi}{12} \)
D. None of these


Find the common difference of an AP.
whose first term is 100 and the sum of
whose first six terms is five times the
sum of the next six terms.
A . 10
B. -10
\( c .5 \)
D. - 5


Simplify \( \frac{2 x+7}{5}-\frac{3 x-11}{2}=\frac{2 x+8}{3}-5 \)


The figure shown speed-time graph of a
car
Calculate displacement from the
graph?


If the cell of an organism heterozygous for two pairs of genes represented by \( x x, z z \) undergoes meiosis, then the
possible genotypic combination of
gametes will be
A. \( x z ; x z ; x z ; x z \)
B. \( x z ; x z ; x z \)
c. \( x x ; Z z ; x z \)
D. Data incomplete


Chipko movement originated in
A. Silent Valley of Kerala
B. Kangra Valley of Himachal Pradesh
C. Tehri Garwal of U.P
D. Pachmari of M.P


Let \( [x] \) denote the integral part of \( x \in \) \( \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] . \) Let \( \boldsymbol{f}(\boldsymbol{x}) \) be any
continuous function with \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}(\mathbf{1}) \)
then the function \( h(x)=f(g(x)) \)
A. has finitely many discontinuities
B. is discontinuous at some \( x=c, c \in I \)
c. is continuous on \( R \)
D. is a constant function


Find the direction cosines of the vector
joining the point \( A(1,2,-3) \) and \( B(-1,-2,1), \) directed from \( A \) and \( B \)


\( \mathbf{f}\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\mathbf{0} . \) Prove
that \( a, b, c \) are in G.P. or \( \alpha \) is a root of
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)


The distance of two planets (Neptune and Saturn) from the sun are \( 10^{13} m \)
and \( 10^{12} m \) respectively. Find the ratio of
the time periods of the planets.
A . 100: 1
B. \( 1: \sqrt{10} \)
\( c \cdot \sqrt{10}: 1 \)
D. \( 10 \sqrt{10}: 1 \)


If \( n \) equal resistors are first connected
in series and then parallel, what will be the ratio of the maximum to minimum
resistance?
A \( . n \)
B . \( 1 / n^{2} \)
\( c \cdot n^{2} \)
D. \( 1 / n \)


The element having greatest difference between its first and second ionization
energies is:
A. \( C a \)
в. \( K \)
\( c . B a \)
D. \( S e \)


Assertion
The only element that dissipates energy in an ac circuit is the resistive element
Reason

There are no power losses associated
with pure capacitances and pure inductances in an ac circuit
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 \( \tan \theta=\frac{x \sin \phi}{1-x \cos \phi}, \tan \phi= \)
\( \frac{y \sin \theta}{1-y \cos \theta}, \) then \( \frac{x}{y}= \)
A. \( \frac{\sin \phi}{\sin \theta} \)
B. \( \sin \theta \)
sin \( \phi \)
c. \( \frac{1-\cos \phi}{1-\cos \theta} \)
D. \( \frac{1-\cos \theta}{1-\cos \phi} \)


In mitochondrion, the proton gradient required for ATP synthesis develops
across
A. Inner membrane
B. Inter membrane space
c. Outer membrane
D. \( F_{0}-F_{1} \) particles


Which of the following compounds has zero dipole moment?
A. 1,4 - dichlorobenzene
B. 1, 2 - dichlorobenzene
c. 1,3 - dichlorobenzene
D. 1 - chloro - 2 - methyl benzene


Let \( f(x)=\sqrt{3 x-3} \) and \( c \) be the
number that satisfies the Mean value
theorem for \( f \) on the interval [4,13] What is the value of \( c \) ?
A . 11.5
в. 7.75
c. 7.5
D. 5.5


The species having bond order different
from that in CO is:
A . \( N O \)
B. \( N O^{+} \)
c. \( C N^{-} \)
D. \( N_{2} \)


The difference between the mass
number and the atomic number gives
the
A. number of neutrons
B. number of electrons
c. charge of an element
D. number of protons


The truth table for NOT gate is
\( A \)
\[
\left[\begin{array}{ll}
1 & 1 \\
0 & 0
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ll}
1 & 0 \\
0 & 0
\end{array}\right]
\]
c.
\[
\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ll}
0 & 1 \\
1 & 1
\end{array}\right]
\]


Express the sexagesimal measure \( 15^{\circ} \)
as radian measure


11. If
with different initial concentrations of \( \mathbf{A} \)
and \( \mathrm{B} \), the initial rate of reaction were
determined graphically in four
experiments. Find the rate of reaction \( (r \)
)
\( A \)
\( r=k[A]^{2}[B]^{2} \)
\( \mathbf{B} \cdot r=k[A]^{2}[B] \)
\( \mathbf{c} \cdot r=k[A][B]^{2} \)
D. \( r=k[A][B \)


If we suspend lamina at different positions, its center of gravity will still lie along the :
A. plumb line
B. line of force
c. line of weight
D. gravity line


The present population of a town is \( 35,000 . \) If the population becomes
35,700 next year, the rate of growth is
A . \( 2 \% \)
B. 20\%
c. \( 70 \% \)
D. \( 7 \% \)


The equivalent conductances of two strong electrolytes at infinite dilution in
\( H_{2} O \) (where ions move freely through a
solution) at \( 25^{\circ} \mathrm{C} \) are given below
\[
\boldsymbol{C H}_{3} \boldsymbol{C O O N a}=91.0 \boldsymbol{S c m}^{2} / \boldsymbol{e q u i v}
\]
\( H C l=426.2 \mathrm{Scm}^{2} / \)equiv
What additional information/quantity one needs to calculate the equivalent conductances an aqueous solution of acetic acid?
A. The limiting equivalent conductance of Naç
B. The limiting equivalent conductance of \( \mathrm{CH}_{3} \mathrm{COOH} \)
C. The limiting equivalent conductance of \( \mathrm{H}^{+} \)
D. The limiting equivalent conductance of chloroacetic \( \operatorname{acid}\left(\mathrm{ClCH}_{2} \mathrm{COOH}\right) \)


State whether the given statement is
True or False :

The energy of an object that is due to the object's motion is called kinetic
energy.
A. True
B. False


In which of the following animal dimorphic nucleus is found
A. Amoeba proteus
B. Plasmodium vivax
c. Paramecium coudatum
D. Trypanosoma gambiense


If \( f(x)=x+2, g(x)=x^{2}-x-2 \)
then find \( \frac{g(1)+g(2)+g(3)}{f(-4)+f(-2)+f(2)} \)


The system of classification based on evolutionary and genetic relationships among organisms, ignoring the morphological similarities or differences, is called as
A. Cladistics
B. Phenetics
c. classical systematics
D. New systematics


Metal which give out a musical note when struck are called
A. ductile
B. sonorous
c. malliable
D. all of these


Q Type your question
Why
given under Column-II. Select the
correct choice from those given below:
Column Column - I (Contraceptive Method)
Tubectomy
\( A \)
Chemical \( \quad \) p. \( \quad \) and Vasectomy
B. IUDS Copper T and
q. \( \quad \) Loop
\( \mathrm{C} \)
Barriers Condom and
Cervical cap
Spermicidal
D. Sterilization
s. \( \quad \) Jelly and foam
Coitus
\( \mathrm{t} \)
interruptus
and calendar and calendar and calen
method
\( A \cdot A=s, B=q, C=r, D=p \)
B. \( A=s, B=t, C=q, D=r \)
\( C \cdot A=p, B=r, C=q, D=t \)
D. \( A=s, B=q, C=t, D=p \)


The price of a garment has been reduced by \( 15 \% \) in a sale to Rs. 306 Find its original price.


\( \boldsymbol{p}(\boldsymbol{x})=\left(\boldsymbol{x}^{2}-\mathbf{1 0} \boldsymbol{x}-\mathbf{2 4}\right), \) when divided
by \( x+2 \) and \( x \neq-2 \) gives the quotient
Q. Find \( Q \)
A . \( x-22 \)
B. \( x-12 \)
c. \( x+12 \)
D. \( x+22 \)


\( \int \frac{(\sin x)^{99}}{(\cos x)^{101}} d x=-\ldots-\ldots+c \)
A \( \cdot \frac{(\tan x)^{97}}{97} \)
в. \( \frac{\tan x}{2} \)
C \( \cdot \frac{(\tan x)^{100}}{100} \)
D. \( \frac{(\tan x)^{98}}{98} \)


Solve :
\( 3 x-2 y=1 \)
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{y}=\mathbf{3} \)


Assertion
\( N_{2} \) is adsorbed on iron surface at \( 83 \mathrm{K} \)
which decreases rapidly with increase
in temperature and at room temperature, practically no adsorption
of \( N_{2} \) occurs. The adsorption, however,
becomes significant at \( 773 \mathrm{K} \)
Reason
At lower temperature, adsorption of \( N_{2} \)
molecules on iron surface is
physisorption and at high
temperatures, \( N_{2} \) shows chemisorption
of \( N \) atoms on iron surface.
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


In basic medium, which of the following
colour is obtained when
phenolphthalein is added?
A. Pink
B. Colourless
c. Yellow
D. Green


A student noted that the number of cars
passing through the spot on the road for 200 periods each of 10 minutes and
summarized in a table given below. Find
the mode of the data.
Number \( \begin{array}{ll}5- & 1 \\ 10 & 1\end{array} \)
\( \mathbf{n} \)
5
\( 20- \)
of cars 15 20 25
frequency 12 1. If 24 \( 15 \quad 10 \)
A . 15.5
B. 20.50
c. 25.45
D. 19.4


Find the period of \( f(x)=[\sin 3 x]+ \)
\( |\cos 6 x| \) where \( [.] \) is a greatest integer
function and / is a modulus function.


Evaluate : \( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\boldsymbol{d x}}{1+\sqrt{\tan x}} \)
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{\pi}{12} \)
D.


An arc of radius r carries change. The linear density of charge is \( \lambda \) and the arc
subtends a angle \( \frac{\pi}{3} \) at the center. What
is electric potential at the center
\( ^{A} \cdot \frac{\lambda}{4 \varepsilon_{0}} \)
в. \( \frac{\lambda}{8 \varepsilon_{0}} \)
\( c \cdot \frac{\lambda}{12 \varepsilon_{0}} \)
D. \( \frac{\lambda}{16 \varepsilon_{0}} \)


In a nuclear reactor, nuclear energy is
converted into


Arrange the following alkanes in the increasing order of their boiling point:
pentane, hexane, \( 2-3- \) dimethyl \( - \)
butane
A. pentane \( <2,3 \) - dimethylbutane \( < \) hexane
B. hexane \( <2,3 \) - dimethylbutane \( < \) pentane
c. pentane \( < \)hexane\( <2,3 \) - dimethylbutane
D. none of the above


Which one is partially submerged and fixed in mud
A. Marsilea
B. Cyperus
c. Eichhornia
D. Typha


Column I gives some devices and Column II gives some process on which the functioning of these devices depend Match the devices in Column I with the
processes in Column II and indicate
your answer by darkening appropriate bubbles in the 44 matrix given in the
ORS.


Two loudspeakers \( L_{1} \) and \( L_{2} \) driven by a
common oscillator and amplifier, are
arranged as shown. The frequency of the oscillator is gradually increased from
zero and the detector at \( D \) records a
series of maxima and minima. If the
speed of sound is 330 ms \( ^{-1} \) then the frequency at which the first maximum
is observed is:
A. \( 165 \mathrm{Hz} \)
В. \( 330 H z \)
\( \mathbf{c} \cdot 495 H z \)
D. \( 660 H z \)


At the same conditions of pressure,
volume and temperature, work done is maximum for which gas if all gases
have equal masses?
A \( . N H_{3} \)
в. \( N_{2} \)
\( c \cdot C l_{2} \)
D. \( H_{2} S_{S} \)


The area(in sq. units) of the smaller portion enclosed between the curves, \( x^{2}+y^{2}=4 \) and \( y^{2}=3 x, \) is
A \( \cdot \frac{1}{\sqrt{3}}+\frac{4 \pi}{3} \)
в. \( \frac{1}{2 \sqrt{3}}+\frac{\pi}{3} \)
c. \( \frac{1}{2 \sqrt{3}}+\frac{2 \pi}{3} \)
D. \( \frac{1}{\sqrt{3}}+\frac{2 \pi}{3} \)


What is the scientific name of human
being?
A. Homo sapiens
B. Rana tigrina
c. Pavo cristatus
D. Brassica rapa


The numbers 2.745 and 2.735 on
rounding off to 3 significant figures will give:
A. 2.75 and 2.74
B. 2.74 and 2.73
c. 2.75 and 2.73
D. 2.74 and 2.74


The lines of symmetry in the double-
headed arrow AB are
\( A \)
B. 1
\( c \)
\( D \)


\( \vec{B}=-(0.31 T) \hat{i} \) what will be the angle between \( \hat{\text { iand }} \) B. (length of wire is 0.01m)
A .
в. \( (0.01085 N) \hat{k} \)
c. \( (-0.01085 N) \hat{k} \)
D. \( (0.01085 N) \hat{i} \)


\( Q \) amount of electric charge is present
on the surface of a sphere having radius
\( \boldsymbol{R} \). Then electrical potential energy of this system is
\( \mathbf{A} \cdot \frac{K Q^{2}}{R^{2}} \)
в. \( \frac{K Q^{2}}{R} \)
c. \( \frac{1}{2} \frac{K Q^{2}}{R} \)
D. \( \frac{1}{2} \frac{K Q^{2}}{R^{2}} \)


The substance used for preparing electro
magnets is :
A. soft iron
B. steel
c. nickel
D. copper


The solubility of II group hydroxides
increases with molecular weight. This is
because:
A. lattice energy is same but hydration energy decreases down the group.
B. hydration energy is same but lattice energy decreases down the group
C. both lattice and hydration energy increase down the group
D. decrease in lattice energy down the group is faster than decrease in hydration energy.


A jeep carries trailor on a level road at constant speed of \( 10 \mathrm{m} / \mathrm{sec} \) calculate
the power excerted on the trailer if the
tension in the coupling is 2000 Newton?


\( A t 46^{\circ} C, K_{p} \) for the reaction
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) is 0.667 atm.
Compute the percent dissociation of
\( N_{2} O_{4} \) at \( 46^{\circ} C \) at a total pressure fo 380
Torr.
A . 50\%
B. 70\%
c. \( 40 \% \)
D. 20\%


Water is a mixture.
A. True
B. False


If the length of the filament of a heater
is reduced by \( 10 \% \), the power of the heater will
A. increase by about 9\%
B. increase by about 11\%
c. increase by about \( 19 \% \)
D. decrease by about \( 10 \% \)


\( \boldsymbol{C d}(s)\left|\boldsymbol{C d C l}_{2}(\mathbf{0 . 1 0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g}(s \)
The EMF of the above cell is 0.6315 V at
\( 0^{\circ} \mathrm{C} \) and \( 0.6753 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). The \( \Delta H \) of
reaction in \( \mathrm{kJ} \) at \( 25^{\circ} \mathrm{C} \) is:
A . - 176
B. - 234.7
c. 123.5
D . - 167.6


When light propagates in vaccum there is an electric field and a magnetic field.
Which of the following is not true about these field?
A. They are constant in time
B. They have zero average value
C. They are perpendicular to the direction of propagation of light
D. They are mutually perpendicular


How many lone pairs are present in the
\( N_{2} O_{4} ? \)


A current of 30 amp is flowing in a
conductor as shown in the figure. The
magnetic induction at point 0 will be :
A . 1.5 Tesla
B . \( 4.71 \times 10^{-4} \) Tesla
c. zero
D. 0.15 Tesla


What happens if forest disappears?
A. Climate change
B. Flood
c. Soil erosion
D. All of the above


Assertion: Preservatives are added to
food items
Reason : Preservatives inhibit the
growth of microorganisms
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct


groups, e.g.
\( O \)
\( -\boldsymbol{C H O} \)
\[
\begin{array}{ccc}
& \| & , & \| \\
- & \boldsymbol{C} & -\boldsymbol{R}- & \boldsymbol{C} & -\boldsymbol{O} \boldsymbol{R}
\end{array}
\]
\( N,-N O_{2} \) activates nucleophilic attack
in halobenzene. The order of reactivity of
these groups is:
A.
\[
\begin{array}{c}
0 \\
-N O_{2}>-C \equiv N>\quad\|\quad \quad>\quad\| \\
0 \\
-\quad C \quad-H \quad-\quad C \quad-R \\
-\quad C \quad-O R
\end{array}
\]
B.
\[
\begin{array}{l}
\|\quad>\quad\| \\
C \quad-H \quad-\quad C
\end{array}
\]
11
\[
>-C \equiv
\]
\[
\begin{array}{c}
-C-H \\
N>-N O_{2}
\end{array}
\]
\( -C-R-C-O R \)
\( c \)
\[
\begin{aligned}
-C \equiv N>-N O_{2}>& 0 \\
-& C-H-C-R
\end{aligned}
\]
\( O \)
11
\[
-C \quad O R
\]
D.
\[
\begin{array}{rl}
0 & 0 \\
\| & >-N O_{2}>-C \equiv N> \\
- & C \\
0 & -H & \| \\
& \| \\
- & C
\end{array}
\]


Consider a thin target \( \left(10^{-2} \mathrm{m} \) square \right.
\( \left.10^{-3} m \text { thickness }\right) \) of sodium, which
produces a photo-current of \( 100 \mu A \) when a light of intensity \( 100 W / m^{2}(\lambda=660 n m) \) falls on it.
Find the probability that a photoelectron is produced when a photon strikes a sodium atom.
[ Take density of \( \left.\boldsymbol{N} \boldsymbol{a}=\mathbf{0 . 9 7} \boldsymbol{k} \boldsymbol{g} / \boldsymbol{m}^{3}\right] \)


Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
Which factor was varied in all these
experiments?
A. Light intensity
B. Rate of photosynthesis
c. Both A and B
D. None of the above


f \( A \) and \( B \) are two matrices such that
\( A B=B \) and \( B A=A \) and
\( \left(A^{2}+B^{2}\right)=\lambda(A+B) . \) Considering
\( \boldsymbol{f}(\boldsymbol{x})=|[\sin \boldsymbol{x}]+[\cos \boldsymbol{x}]| ; \) where [] is
greatest integer function find \( \boldsymbol{f}(\mathbf{4} \boldsymbol{\lambda}) \)


For which of the following reaction
\( \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{K}_{c} ? \)
\( \mathbf{A} \cdot N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \)
B. \( 2 \mathrm{NOCl}_{(g)} \rightleftharpoons 2 \mathrm{NO}_{(g)}+\mathrm{Cl}_{2(g)} \)
C. \( H_{2(g)}+I_{2(g)} \rightleftharpoons 2 H I_{(g)} \)
D. \( C O_{2(g)}+C_{(s)} \rightleftharpoons 2 C O_{(g)} \)


Na \( 0 . H \) can also be prepared by electrolysis of aqueous \( N a C l . \) Amount of \( N a O H \) formed when \( 0.445 L \) of
\( N a C l(a q) \) is electrolysed for 137 s with a current of \( 1.08 A \) is \( 0.06 g . \) The pH of this solution is :
A . 11.70
B. 11.53
c. 11.83
D. data is incomplete


There is \( _{--} \) - tangent to a circle passing through a point lying inside the circle.
\( A \cdot \) no
B. one
c. two
D. three


Three capacitors \( \boldsymbol{C}_{\mathbf{1}}=\boldsymbol{6} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{C}_{2}= \)
\( 12 \mu F \) and \( C_{3}=20 \mu F \) are connected to
a \( 100 V \) battery, as shown following
figure below:
Calculate:
Charge on each plate of capacitor \( C_{1} \)


A group of students took an old shoe
box and covered it with a black paper
from all sides. They fixed a source of light (a torch) at one end of the box by making a hole in it and made another
hole on the other side to view the light They placed a milk sample contained in a beaker/tumbler in the box as shown
in the Fig.2.4. They were amazed to see that milk taken in the tumbler was
illuminated. They tried the same activity by taking a salt solution but found that light simply passed through it?

Same results were not observed with a
salt solution. Explain.


Prove \( \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots+\frac{1}{2^{n}}=1-\frac{1}{2^{n}} \)


Calculate the dissociation constant of
\( N H_{4} O H \) at \( 298 \mathrm{K}, \) if \( \triangle H^{\ominus} \) and \( \Delta S^{\ominus} \) for
the given changes are as follows:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}^{\oplus} \rightleftharpoons \stackrel{\oplus}{\boldsymbol{N}} \boldsymbol{H}_{4} \)
\( \Delta H^{\ominus}=-52.2 k J m o l^{-1}, \Delta S^{\ominus}= \)
\( \mathbf{1 . 6 7} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}^{\oplus}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} ; \boldsymbol{\Delta} \boldsymbol{H}^{\ominus}= \)
\( \mathbf{5 6 . 6} k J \mathbf{m o l}^{-1} \)
\( \Delta S^{\ominus}=-76.53 J K^{-1} m o l^{-1} \)
\begin{tabular}{l}
A. \( K_{b}=1.7 \times 10^{-5} \) \\
\hline
\end{tabular}
в. \( K_{b}=1.7 \times 10^{-3} \)
c. \( K_{b}=1.7 \times 10^{-1} \)
D. \( K_{b}=3.4 \times 10^{-5} \)


Action of concentrated nitric acid on
metallic tin produces:
This question has multiple correct options
A. stannous nitrite
B. stannous nitrate
c. stannic nitrate
D. stannic oxide


The median of 21 observations is 18 If
two observations 15 and 24 are included
to the observation then the median of
new series is
A . 15
B . 18
\( c \cdot 24 \)
D. 16


Solve \( :-\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}} \)


A long solenoid has magnetic field strength of \( 3.14 \times 10^{-2} \mathrm{T} \) inside it
when a current of \( 5 A \) passes through
¡t. The number of turns in 1 m length of the solenoid is
A. 1000
в. 3000
\( c .5000 \)
D. 10000


Derive the equation of the locus of a point equivalent from the points (1,-2,3) and (-3,4,2)


Percentage of precipitation that can be stored in dams of India is
A . 10
B. 18
\( c \cdot 43 \)
D. 55


According to Bohr's theory of hydrogen atom, which of the following is quantized for an electron?
A. Acceleration
B. Velocity
c. Angular momentum
D. Angular acceleration


If \( M N \) is a straight line on a cartesian
plane. The co-ordinates of \( \mathrm{N} \) are (12,13)
and \( M N=9 \) units. Find the co-
ordinates of \( \mathrm{M} \)
A \( .(21,13) \)
B. (12,22)
c. (12,4)
D. (3,13)


The heat of hydrogenation of one double bond in cyclohexene is \( 28.6 \mathrm{kcal} \) mol \( ^{-1} \) and the heat of hydrogenation of benzene to cyclohexane is \( 50 \mathrm{kcal} \) mol \( ^{-1} \). What will be the resonance
stabilization energy of benzene?
A . 28.6 kcal mol-1
B. 55.0 kcal mol-1
c. 85.8 kcal \( m o l^{-1} \)
D. 35.8 kcal mol-1


A dye absorbs a photon of wavelength lambda and re-emits the same energy
into two photons of wavelengths of \( \lambda_{1} \)
and \( \lambda_{2} \) respectively. The wavelength
lambda is related with \( \lambda_{1} \) and \( \lambda_{2} \) as:
\( A \cdot \lambda=\frac{\lambda_{1}+\lambda_{2}}{\lambda_{1} \lambda_{2}} \)
B. \( \lambda=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
\( c \cdot \lambda=\frac{\lambda_{1}^{2} \lambda_{2}^{2}}{\lambda_{1}+\lambda_{2}} \)
D. \( \lambda=\frac{\lambda_{1} \lambda_{2}}{\left(\lambda_{1}+\lambda_{2}\right)^{2}} \)


The value of \( [\sin x]+[1+\sin x]+2+ \)
\( [\sin x]+3+[\sin x] \) in \( \left(\pi, \frac{3 \pi}{2}\right] \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 2 \)
D. 3


A straight wire of 0.3 m carrying a current of \( 2 \mathrm{A} \) in the downward direction
is placed in a magnetic field of \( 0.1 \mathrm{T} \) as shown in the figure. Find out the magnitude of the force on the wire?
A . \( 0.06 N \)
B. 2.0 N
c. \( 6.7 \mathrm{N} \)
D. 0.15N
E. 0.015N


Figure here shows the vertical cross-
section of a vessel filled with a liquid of
density \( \rho \)

The normal thrust per unit area on the
walls of the vessel at point \( P \) as shown
will be :
A \( . \) hog
в. Нр р
\( \mathbf{c} \cdot(H-h) \rho g \)
D \( \cdot(H-h) \) pgcos


If \( b>a, \) and \( I=\int_{a}^{b} \sqrt{\frac{x-a}{b-x}} d x, \) then \( I \)
equals
A \( \cdot \frac{\pi}{2}(b-a) \)
в. \( \pi(b-a) \)
c. \( \pi / 2 \)
D. \( 2 \pi(b-a) \)


A dinoflagellate with nematocysts is
A. Nematodinium
B. Ceratium
c. Gonyaulax
D. symbodinium


A gas undergoes expansion in such a
manner that its p-V diagram plot is a
downward sloping straight line as shown in he figure below. What happens to the temperature during the process?
A. It increases first then decreases
B. It decreases first then increases
c. It continuously decreases
D. Data insufficient


The value of \( \left(8^{-25}-8^{-26}\right) \) is
A \( \cdot 7 \times 8^{-25} \)
В. \( 7 \times 8^{-26} \)
c. \( 8 \times 8^{-26} \)
D. None of these


Calculate the electric potential at the
center of the square in figure.


Find the difference between \( \boldsymbol{P}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{4}-\boldsymbol{3} \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{5}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{1}-\boldsymbol{x} \)


Diamond is the hardest allotrope of
carbon. Give reason for its hardness??


If the sum of two numbers is 11 and
sum of their cubes is \( 737, \) find the sum
of their squares.


A pulse is a wave:
A. Of high duration
B. Of short duration
C. Which travels in vacuum only
D. Which travels in solids only


A swimmer swims in still water at a
speed \( =5 k m / h . \) He enters a \( 200 m \)
wide river, having river flow speed \( = \)
\( 4 k m / h r \) at point \( A \) and proceeds to
swim at an angle of \( 127^{\circ} \) with the river flow direction. Another point B is located
directly across \( A \) on the other side. The
swimmer lands on the other bank at a
point \( C, \) from which he walks the
distance \( \mathrm{CB} \) with a speed \( =3 k m / h r \)
The total time in which he reaches from
\( A \) to \( B \) is
A . 5 minutes
B. 4 minutes
c. 3 minutes
D. none


The \( p H \) at which \( M g(O H)_{2} \) begins to precipitate from a solution containing \( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{M} \boldsymbol{g}^{\mathbf{2 +}} \) ions. \( \boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}_{M g(O H)_{2}}}=\mathbf{1 0}^{-\mathbf{1 1}} \) is


The foot of an elephant has an area of \( 275 c m^{2} . \) If the mass of elephant is
\( 2200 k g, \) find the pressure exerted by the elephant on the ground, \( (g=10 m \)
\( s^{-2} \) ).


Assertion
The total momentum of an isolated
system of particles is conserved.
Reason
The law of conservation of momentum
follows from the second and third law of
motion.
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 \( \boldsymbol{x}=\boldsymbol{y} \cos \frac{\boldsymbol{2} \boldsymbol{\pi}}{\mathbf{3}}=\boldsymbol{z} \cos \frac{\boldsymbol{4} \boldsymbol{\pi}}{\boldsymbol{3}}, \) then \( \boldsymbol{x} \boldsymbol{y}+ \)
\( y z+z x \) is equal to
\( \mathbf{A} \cdot-4 x^{2} \)
B.
\( c \cdot 1 \)
D.


A copper ring is suspended by a thread
in a vertical plane. If one end of a magnet is brought horizontally towards the ring in plane of ring as shown, the
ring will
B. not change its position
c. move away from the magnet.
D. first move towards and then move away from the magnet


Q Type your question
The and
of incidence and reflection in
accordance with the laws of reflection?
\( A \)
B.
\( c \)
\( D \)


A compound (A) when reacted with ammonia gave (B),(B) when treated with bromine and caustic powder produced (C), (C) on treatment with
\( N a N O_{2} \) and \( H C l \) at \( 0^{\circ} \mathrm{C} \) and then
produce ortho-cresol. Compound (A) is:
A. o-chlorotoluene
B. o-toluic acid
c. m-toluic acid
D. n-bromotoluene


When a force is applied on a wire of uniform cross-sectional area \( 3 \times \)
\( 10^{-6} m^{2} \) and length \( 4 m, \) the increase in
length is 1 \( m m . \) Energy stored in it will
be \( \left(Y=2 \times 10^{11} N / m^{2}\right) \)
A . \( 6250 J \)
в. 0.177 Л
c. \( 0.075 J \)
D. \( 0.150 J \)


\( O_{2}^{+} P t F_{6}^{-} \) (an orange coloured compound) was prepared and thus,
formation of compound \( \boldsymbol{X} \boldsymbol{e}^{+} \boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{\boldsymbol{6}}^{-} \)
was feasible based on ionisation energy of Xe (which is very similar to that of \( \boldsymbol{O}_{2} \)
)
If true enter 1 , else enter 0


Assertion
Ionic compounds are bad conductors of
electricity.
Reason
In ionic compounds mobile ions exists.
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 a gaseous reaction the rate equation is \( \boldsymbol{v}=\boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] . \) If the volume of
the gaseous system is suddenly reduced to \( 1 / 3 \) of initial volume. The rate would become:
A. \( 1 / 9 \) times
B. 9 times
c. \( 1 / 6 \) times
D. 6 times


Three charges are placed at the vertices
of an equilateral triangle of side 'a' as shown in the following figure. The force experienced by the charge placed at the
vertex \( A \) in a direction normal to \( B C \) is
A \( \cdot Q^{2} /\left(4 \pi \epsilon_{0} a^{2}\right) \)
B \( \cdot-Q^{2} /\left(4 \pi \epsilon_{0} a^{2}\right) \)
\( c . \) Zero
D. \( Q^{2} /\left(2 \pi \epsilon_{0} a^{2}\right) \)


The function(s) of oxytocin is/are to :
A. stimulate the release of milk from the mother's mammary glands when her baby is nursing.
B. cause the uterus to contract
c. induce labor
D. all of the above


Express the following percentages as
ratios in the reduced form.
\( 0.64 \% \)


Teeth are the only part of the digestive
system that physically breaks down food.
A. True
B. False


A Ge specimen is doped with Al. The
concentration of acceptor atoms is \( \sim \) \( 10^{21} \) atoms \( / m^{3} . \) Given that the intrinsic
concentration of electron-hole pairs is
\( 10^{19} / m^{3} . \) The concentration of electrons in the specimen is:
\( \mathbf{A} \cdot 10^{17} / m^{3} \)
B . \( 10^{15} / m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{2} / m^{3} \)


Which of the following ions has the maximum magnetic moment?
\( \mathbf{A} \cdot M n^{+2} \)
B. \( F e^{+2} \)
\( c \cdot T i^{+2} \)
D. \( C r^{+2} \)


Ideal solutions doesn't obey Roult's law.
A. True
B. False


The chief ore of aluminium is :
A. bauxite
B. cryolite
c. alunite
D. feldspar


Which of the following is not true about
transition metals?
A. They are diamagnetic substances
B. They are paramagnetic substances
C. They can form complexes
D. They can show variable oxidation states


Ordered pairs \( (a, 3) \) and \( (5, x) \) are equal the values of \( a \) and \( x \) are
A .2 and 4
B. 3 and 6
c. 5 and 3
D. 1 and -1


There is a regular bus service between towns \( A \) and \( B \), with a bus leaving towns A and B every \( T \) minutes. A cyclist
moving with a speed of \( 20 \mathrm{kmh}^{-1} \) in the direction \( A \) to \( B \) notices that a bus goes
past him every 18 mins in his direction
and every 6 mins in the opposite direction. What is the period \( \boldsymbol{T} \)
of bus service?
A. 9 minutes
B. 12 minutes
c. 15 minutes
D. 18 minutes


Oxygen in expired air
A . \( 10 \% \)
B . 16\%
c. \( 19 \% \)
D. 4\%


Identify the product obtained when
following acid prolonged heating


Find the slope of line which passes through the point (7,11) and (9,15)


Water flows at the rate of \( 10 \mathrm{m} \) per min from cylindrical pipe \( 5 \mathrm{mm} \) in diameter How long will it take to fill up a conical vessel whose diameter at the base is 40
\( \mathrm{cm} \) and depth \( 24 \mathrm{cm} ? \)
A. 48 min 15 sec
B. 51 min 12 sec
c. 52 min 1 sec
D. 55 min


Assertion
If \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2})(\boldsymbol{x}-\mathbf{3}), \) then
area enclosed by \( |\boldsymbol{f}(\boldsymbol{x})| \) between the
lines \( x=2.2, x=2.8 \) and \( x- \) axis is equal to \( \int_{2.2}^{2.8}(x-1)(x-2)(x-3) d x \)
Reason
\( (x-1)(x-2)(x-3) \leq 0 \) for all \( x \in \)
[2.2,2.8]
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


Which of the following does not come under antimicrobial?
A. Antibiotic
B. Tranquilizer
c. Disinfectant
D. Antiseptic


The type of resource obtained from Biosphere that contains life is.
A . Abiotic resource
B. Human made resource
c. Nonrenewable resource
D. Biotic resource


Fill in the blanks with suitable words:
Light waves travel in the form of
waves


Electrons are particles of negligible mass carrying unit negative charge.
A. True
B. False


Write the equation of tangent at (1,1) on the curve \( 2 x^{2}+3 y^{2}=5 \)


Which of the following points are the vertices of an equilateral triangle?
A \( \cdot(a, a),(-a,-a),(2 a, a) \)
В \( \cdot(a, a),(-a,-a),(-a \sqrt{3}, a \sqrt{3}) \)
c. \( (\sqrt{2} a,-a),(a, \sqrt{2} a),(a,-a) \)
D. \( (0,0),(a,-a),(a, \sqrt{2} a) \)


What is meant by heredity?


Blood clotting requires
\( A \cdot N a^{+} \) and \( K^{+} \)
B. \( \mathrm{Na}^{+} \) and prothrombin
C \( \cdot \mathrm{Na}^{+} \) and thromboplastin
D. \( \mathrm{Ca}^{++} \) and thromboplastin


Which plays a major role in the formation of complex compound?
A. Transition metal
B. Lanthanides \& Actinoides
c. Representative elements
D. p-Block elements


Form the differential equation of the family of circles having centre on y-axis and radius 3 units.


Show that \( 1.272727 \ldots=1 . \overline{27} \) can be
expressed in the form \( \underline{\boldsymbol{p}} \) \( \overline{\boldsymbol{q}} \)


If \( \boldsymbol{A} * \boldsymbol{B}=\boldsymbol{A} \cap \boldsymbol{B} \) on \( \boldsymbol{P}(\boldsymbol{X}), \) then identify
for \( * \) is \( _{-}--_{-}---(X \neq \phi) \)
\( A \cdot \phi \)
B. \( X \)
\( c \cdot U \)
D.


The equations representing the given
graph is
A. \( 7 x+2 y=11 ; y-2 x=3 \)
B. \( 2 x+7 y=11 ; 5 x+(35 y / 2)=25 \)
c. \( 3 x-7 y=10 ; 8 y-6 x=4 \)
D. \( 3 x-4 y=1 ; 3 x-4 y x+2=0 \)


Divide \( 2 x^{3}-9 x^{2}+10 x \) by \( (2 x+5) \) and
also verify the result.


The equilibrium constant for the given
reaction: \( \boldsymbol{S O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) ; K_{c}=4.9 \times \)
\( 10^{-2} m o l^{1 / 2} l i t r e^{-1 / 2} \)
What is the value of \( K_{c} \) for the reaction:
\( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) ? \)
A. 416 litre \( m o l^{-1} \)
B . \( 2.40 \times 10^{-3} \) litre \( \mathrm{mol}^{-1} \)
c. \( 9.8 \times 10^{-2} \) litre mole\( ^{-1} \)
D. \( 4.9 \times 10^{-2} \) litre \( m o l^{-1} \)


The given figure shows a parallelogram
\( A B C D \) with area \( 324 \mathrm{cm}^{2} . P \) is a point
in \( A B \) such that \( A P: P B=1: 2 \)
Find the area of \( \triangle \boldsymbol{A} \boldsymbol{P} \boldsymbol{D} \)
\( \mathbf{A} \cdot 34 \mathrm{cm}^{2} \)
B. \( 44 \mathrm{cm}^{2} \)
c. \( 24 \mathrm{cm}^{2} \)
D. \( 54 \mathrm{cm}^{2} \)


In which of the following reactions, does a non-metal act as a reducing agent?
A. \( \operatorname{SiO}_{2}+2 C \rightarrow S i+2 C O \)
в. \( A l N+3 H_{2} O \rightarrow A l(O H)_{3}+N H_{3} \)
\( \mathbf{c} \cdot 2 M g+N_{2} \rightarrow M g_{3} N_{2} \)
D. \( H g C l_{2}+2 K I \rightarrow H g I_{2}+2 K C l \)


If four resistances are connected as
shown in the fig. between \( A \) and \( B \), the
effective resistance is:
A . \( 3 \Omega \)
B. \( 1 \Omega \)
c. \( 2.4 \Omega \)
D. 25


Difluorodiphenyl trichloroethane (DDFT) is a/an:
A. refrigerant
B. fungicide
c. plastic
D. antiseptic


The de-Broglie wavelength associated with the motion of earth orbiting around the sun at a speed of \( 3 \times 10^{6} \mathrm{m} / \mathrm{s} \) is:
[mass of earth \( \left.6 \times 10^{24} K g\right] \)
A . \( 3.68 \times 10^{-65} \mathrm{m} \)
В . \( 3.68 \times 10^{-56} \mathrm{m} \)
c. \( 4.76 \times 10^{-65} \mathrm{m} \)
D. \( 4.76 \times 10^{-56} m \)


A semiconductor at \( 0 K \) behaves as :
A. conductor
B. insulator
c. super conductor
D. extensive semiconductor


Assuming the complete dissociation of HCl and lead salt, calculate how much
\( \mathrm{HCl} \) is added to \( 0.001 \mathrm{m} \) lead salt
solution to just precipitate when
saturated with \( H_{2} S . \) The concentration
of \( \boldsymbol{H}_{2} \boldsymbol{S} \). The concentration of \( \boldsymbol{H}_{2} \boldsymbol{S} \) is \( \boldsymbol{0 . 1} \)
\( \mathbf{M} \)


Which of the following alkenes is the most stable on account of maximum
hyperconjugation?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C C H=C H_{2} \)
в. \( C H_{3} C H=C H_{2} \)
c. \( \left(C H_{3}\right)_{2} C H C H=C H_{2} \)
D. \( C H_{4} C H_{2} C H=C H_{2} \)


A satellite is revolving around earth in a
circular orbit. The radius of orbit is half
of the radius of theorbit of moon.

Satellite will complete one revolution in.
A \( \cdot 1 / 2^{3 / 2} \) lunar month
B . \( 1 / 2^{2 / 3} \) |unar month
C. \( 2^{3 / 2} \) lunar month
D. \( 2^{2 / 3} \) lunar month


Which of the following compounds would be predicted to have the highest melting point?
A \( \cdot C S_{2} \)
в. \( H I \)
c. \( H_{2} \)
D. \( H_{2} O \)
E . \( M g O \)


The distance between the lines \( y= \)
\( 2 x+4 \) and \( 3 y=6 x-5 \) is equal to
A .
B. \( 3 / \sqrt{5} \)
c. \( \frac{17 \sqrt{5}}{15} \)
D. \( \frac{17}{\sqrt{3}} \)


A sum of Rs. 24000 is borrowed for \( 1 \frac{1}{2} \) years at the rate of interest \( 10 \% \) per
annum compounded semiannually. What is the compound interest \( (x) ? \)
A \( . x> \) Rs. 3000
B. Rs. 3000 < \( x< \) Rs. 4000
c. Rs. \( 4000<x<5000 \)
D. \( x> \) Rs. 5000


f \( n(A)=1 \) and \( n(S)=13, \) then find \( \boldsymbol{P}(\boldsymbol{A}) \)


Given \( A \leftrightharpoons B . K_{f} \) is the equilibrium
constant and \( K_{b} \) is the equilibrium constant for backward reaction. Find
the equilibrium constant \( \boldsymbol{K} \)
A. \( K_{f} / K_{b} \)
в. \( K_{b} / K_{f} \)
\( \mathbf{c} \cdot K_{b} \times K_{f} \)
D. \( K_{b}+K_{f} \)


If the height of cylinder increases from 8 inches to 12 inches, then its volume
increases from \( 72 \pi \) to \( V \). Find the value
of \( \boldsymbol{V} \)
\( \mathbf{A} \cdot 76 \pi \)
в. \( 108 \pi \)
\( c .328 \pi \)
D. \( 576 \pi \)


Which of the following option best describe the hydrogen economy?
A. Using dihydrogen in an efficient manner
B. Dihydrogen is carried and stored in the form of liquid or gas
c. Addition of dihydrogen to the reactant
D. Both (a) and (b)


Which one of the following is not the
correct statement?
A. Chemisorption is reversible in nature.
B. Chemisorption takes place at high temperature
c. Chemisorption depends on the nature of gas.
D. chemisorption requires activation energy


If the \( z x \) -plane divides the line segment joining (1,-1,5) and (2,3,4) in the ratio \( p: 1, \) then \( p+1= \)
A \( \cdot \frac{1}{3} \)
B. 1: 3
\( c \cdot \frac{3}{4} \)
D. \( \frac{4}{3} \)


Gold is chosen by Rutherford for his \( \alpha \)
ray scattering experiment because:
A. gold has high malleability
B. gold has high ductility
c. gold has high density
D. gold is the least reactive element


Assertion
Snow is better insulator than ice.
Reason
Snow contain air packet and air is good insulator of heat.
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


Which of the following is organometalic compound
A. Methyl lithium
B. Lithium methoxide
c. Lithium dimethyl amide
D. Lithium acetate


Among the following, the species with the highest bond order is:
\( A \cdot O_{2} \)
B . \( F_{2} \)
\( c \cdot O_{2}^{+} \)
D. \( F_{2}^{-} \)


What are semiconductors? Give
examples.


A die is throw once. Find the probability
of getting
(1)an even number
(2)a number less than 5
(3)a number greater than 2
(4)a number between 3 and 6
(5)a number other than 3
(6)the number 5


Draw a plot showing the variation of (i) electric field (E) and
(ii) electric
potential (V) with the distance r due to a point charge \( Q \)


If \( \sin y=x \sin (a+y), \) then show that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\sin ^{2}(\boldsymbol{a}+\boldsymbol{y})}{\sin \boldsymbol{a}} \)


If \( z \) be a complex number satisfying
\( z^{4}+z^{3}+2 z^{2}+z+1=0, \) then find the
value of \( |\vec{z}| \)


\( \int_{0}^{\pi / 2} f(\sin 2 x) \sin x d x= \)
\( K \int_{0}^{\pi / 2} f(\cos 2 x) \cos x d x \) where \( k \)
equals to
A . 2
B. 4
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)


\( \delta_{j} \)


A coin is tossed twice, the probability of getting head both times is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{4} \)
D.


An enzyme absent in mitochondrial ETS
is
A. FeS protease
B. Glucose 6-phosphate dehydrogenase
c. NADH dehydrogenase
D. cytochrome c-oxidase


Write balanced chemical equations involved in the following reactions:
(a) Fluorine gas reacts with water
(b) Phosphine gas is absorbed in copper sulphate solution.


Differentiate between Uniform and non-
Uniform motion


Soaps are sodium salts of :
A. mineral acids
B. fatty acids
\( \mathbf{C} \). bases
D. carbonic acid


Express as centimeter (cm) using
decimals:
175 mm


The figure shows velocity-time graph of
a stone thrown vertically upwards till it
comes back to the ground. Find the net
displacement of the stone.
\( A \cdot 0 m \)
B. \( 160 m \)
\( c .80 m \)
D. \( 100 m \)


Two particle of equal mass \( m \) and
charge \( q \) are placed at a distance of
16cm. They do not experience any force.
The value of \( \frac{\boldsymbol{q}}{\boldsymbol{m}} \) is :
A. \( \sqrt{\frac{\pi \varepsilon_{0}}{G}} \)
в. \( L \)
c. \( \sqrt{\frac{G}{\pi \varepsilon_{0}}} \)
D. \( \sqrt{4 \pi \varepsilon_{0} G} \)


Hardening of oil is done by:
A. dehydrogenation
B. hydrogenation
c. dehydrohalogenation
D. dehydration


If \( 6 \operatorname{Sin}^{-1}\left(x^{2}-6 x+12\right)=2 \pi, \) then the
value of \( x, \) is


(a) Write down the general form of the Schrodinger equation and define each of the terms in it.
(b) Solutions to the wave equation that is physically possible must have four special properties.What are they?


A man standing on a high bridge over a creek throws a rock straight down. Just as he throws the rock he accidentally drops another rock. Neglecting air resistance, which statement best describes the situation just after the
rocks reach the water?
A. The acceleration of the thrown rock is greater
B. The acceleration of the dropped rock is greater
c. The acceleration of both rocks is same
D. The average velocity of both rocks is the same
E. The final velocity of both rocks is the same


The complete balanced equation is:
\( \boldsymbol{C l}_{2}+\boldsymbol{I O}_{3}^{-}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot C l_{2}+I O_{3}^{-}+2 O H^{-} \rightarrow I O_{4}^{-}+2 C l^{-}+H_{2} O \)
в. \( 4 C l_{2}+I O_{3}^{-}+4 O H^{-} \rightarrow I O_{4}^{-}+C l^{-}+H_{2} O \)
c. \( C l_{2}+I O_{3}^{-}+3 O H^{-} \rightarrow I O_{4}^{-}+2 C l^{-}+H_{2} O \)
D. none of these


In India, per capita forest cover is
A . 1.06 ha
B. 0.06 ha
c. 0.6 ha
D. 1.6 ha


\( \beta \) -Elimination or anti-elimination
reaction is carried out with base \( \left(B^{\ominus}\right) \)
as shown.
The following bases are used. \( (I) \stackrel{\ominus}{O} H(I I) R O^{\ominus}(I I I) R C O O^{\ominus} \)
\( (I V) \stackrel{\ominus}{C} N(V) N O_{3}^{\ominus} \)
The decreasing order of reactivity for the above elimination is :
A. \( (I I)>(I)>(I V)>(I I I)>(V) \)
в. \( (V)>(I I I)>(I V)>(I)>(I I) \)
c. \( (I I)>(I)>(I I I)>(I V)>(V) \)
D. \( (I)>(I I)>(I I I)>(I V)>(V) \)


If \( A \) be the \( A . M . \) and \( H \) the H.M. between
two numbers \( a \) and \( b \), then show
\( \frac{\boldsymbol{a}-\boldsymbol{A}}{\boldsymbol{a}-\boldsymbol{H}} \times \frac{\boldsymbol{b}-\boldsymbol{A}}{\boldsymbol{b}-\boldsymbol{H}}=\frac{\boldsymbol{A}}{\boldsymbol{H}} \)


The structure of white phosphorus is:
A. square planar
B. pyramidal
c. tetrahedral
D. trigonal planar


The unit of molar susceptibility is
A \( \cdot k g^{-1} m^{3} \)
в. \( k g m^{3} \)
\( c \cdot m^{3} \)
D. Unit less


If \( \boldsymbol{A}=\left\{\boldsymbol{x}: \boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}=\boldsymbol{0}\right\} \) and \( \boldsymbol{B}= \)
\( \left\{x: x^{2}+4 x-5=0\right\} \) then the value of
\( A-B \) is
\( \mathbf{A} \cdot\{1,2\} \)
B . \{2\}
\( c \cdot\{1\} \)
D \( \cdot\{5,2\} \)


A train of \( 150 \mathrm{m} \) length is going towards
north direction at a speed of \( 10 \mathrm{ms}^{-1} . \mathrm{A} \)
parrot flies at a speed of \( 5 m s^{-1} \) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:
A . 12
B. 8 s
\( c \cdot 15 s \)
D. 10 s


Write the properties of hormone.


In Fig. voltmeter is not ideal. If the
voltmeter is removed from \( \boldsymbol{R}_{1} \) and then
put across \( R_{2}, \) what will be the effect on
current I? Given \( \boldsymbol{R}_{1}>\boldsymbol{R}_{2} \)
This question has multiple correct options
A . decreases
B. remains same
\( c \). increases
D. it would have been same if voltmeters were idea


If the area of circle increases at a
uniform rate, then prove that the perimeter varies inversely as the radius.


Which of the following carbohydrates is an essential constituent of all cell
walls?
A. Starch
B. Maltose
c. cellulose
D. sucrose


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( \boldsymbol{a}_{\boldsymbol{i} j} \) is \( \boldsymbol{a}_{\boldsymbol{i} j}=\frac{|\mathbf{2} \boldsymbol{i}-\boldsymbol{3} \boldsymbol{j}|}{\boldsymbol{2}} \)


Which of the following groups of organic compounds represent the proteins present in human blood?
A. Pepsin, trypsin and chymotrypsin
B. Albumins, globulins and prothrombin
c. valine, glycine and alanine
D. Glucose, fructose and galactose