For a common-emitter transistor, input
current is \( 5 \mu A, \beta=100 . \) Circuit is
operated at load resistance of \( 10 k \Omega \). The
voltage across collector emitter will be
A. \( 5 v \)
B. 10 \( v \)
c. \( 12.5 \mathrm{v} \)
D. 7.5 \( v \)


Scala Naturae was written by
A. Hippocrates
B. Thales
C. Aristotle
D. Theophrastus


Show that \( f(x)=|x-3| \) is continuous
but not differentiable at \( x=3 \)


A man is standing on a boat in still water. If he walks towards the shore the
boat will
A. move away from the shore
B. remain stationary
c. move towards the shore
D. sink


Say true or false.
f \( x(x-4)=0, \) then \( x=0 \) or \( x=4 \)
A. True
B. False


A prism has a refractive index \( \sqrt{\frac{3}{2}} \) and
refracting angle \( 90^{\circ} \). Find the minimum
deviation produced by prism.
\( A \cdot 40^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 49^{\circ} \)


\( \tan ^{2} \phi-\sin ^{2} \phi=\tan ^{2} \phi \cdot \sin ^{2} \phi \)


If \( S_{n}=n P+\frac{n(n-1) Q}{2}, \) where \( S n \)
denotes the sum of the first \( n \) terms of
an \( A P, \) then the common difference is
\( \mathbf{A} \cdot P+Q \)
в. \( 2 P+3 Q \)
c. \( 2 Q \)
D. \( Q \)


The mean of 10 observation is 20 . if
each observation is added by \( ^{\prime} 5^{\prime} \). Find the mean of new observation.


If the attacking species is an electrophile, the electrons are
transferred towards the positively charged atom. This is known as:
\( \mathbf{A} \cdot+R \) effect
B. \( -E \) effect
\( \mathbf{c} .+E \) effect
D. none of these


A coil has a self-inductance of 0.05
henry. Find magnitude of the emf induced in it when the current flowing through it is changing at the rate
\( 100 A s^{-1} \)


Ag can be obtained from purified Zn-Ag alloy by :
A. distillation
B. poling
c. liquation
D. reduction


What is a Tyndall effect? Write any two application of tyndal effect.


Determine the magnitude of frictional
force \( f \) in each of the following cases:
c)


Which of the following options are correct regarding the manufacture of
\( H_{2} S O_{4} \) by Contact process? The statements given below are
regarding the contact process for the
manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(a) Manufacture of \( S O_{2} \) from sulphur is a reversible process.
(b) High pressure, optimum temperature and specific catalyst is
required to obtain a better yield of \( S O_{3} \)
(c) \( S O_{3} \) is hydrolysed to get \( H_{2} S O_{4} \)
(d) Pyrosulphuric acid is hydrolysed to
\( \operatorname{get} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A \( . a \) and \( d \)
B. \( b \) and \( c \)
c. only \( d \)
D. \( b \) and \( d \)


In an octahedral complex, if ligands on one axis are displaced little away from their ideal positions, the crystal field splitting of d-orbitals for this complex is as given below
\( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \boldsymbol{d}_{z^{2}} \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}} \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)
The ligands are displaced on which axis/ axes:
A. x- and y
B. y-only
c. x-only
D. z-only


Let \( r \) be the range of \( n(\forall n \geq 1) \)
observations \( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \ldots, \boldsymbol{x}_{\boldsymbol{n}} \) if \( \boldsymbol{S}= \)
\( \sqrt{\frac{\sum_{t=1}^{n}\left(x_{i}-\bar{x}\right)^{2}}{n-1}}, \) then
\( ^{\mathbf{A}} \cdot_{S}<r \sqrt{\frac{n^{2}+1}{n-1}} \)
в. \( s \geq r \sqrt{\frac{n}{n-1}} \)
c. \( s=r \sqrt{\frac{n}{n-1}} \)
D. \( s<r \sqrt{\frac{n}{n-1}} \)


A successful study of morphology of viruses can be done by
A. Binocular microscope
B. Plane polarised microscope
c. Electron microscope
D. simple microscope


The force used by an archer to pull a bow is:
A. muscular force
B. friction force
c. gravitational force
D. elsatic spring force


The term ecosystem development to ecological succession was given by
A. Odum
B. Clements
c. Mishra
D. Blackman


What are intrinsic proteins?


A glass slab has a length of \( 6 \mathrm{cm} \) and
refractive index \( 1.5 . \) One of the outer
surfaces of the slab is silvered and
object is placed at a distance of \( 10 \mathrm{cm} \)
from the other end. The image formed in
the mirror will be at a distance of
from the object
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 32 \mathrm{cm} \)
\( \mathbf{c} \cdot 28 c m \)
D. \( 38 c m \)


Terylene is a condensation polymer of ethylene glycol and:
A. benzoic acid
B. phthalic acid
c. terephthalic acid
D. salicylic acid


A uniform rod of length \( L \) rests on a frictionless horizontal surface. The rod
is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed \( v \) strikes the rod at
its centre and becomes embedded in it.
The mass of the bullet is one-sixth the
mass of the rod. The ratio of the kinetic
energy of the system before the collision to the kinetic energy of the bullet after the collision is \( \frac{1}{x} . \) Find the value of \( x \)


What is wrong about kidney
A. Peripheral cortex and central medulla
B. Blood enters glomerulus through efferent arterioles
C. Malpighian capsules occur in cortex
D. Concave part of kidney is called hilus


An electric heater kept in vacuum is
heated continuously by passing electric
current. Its temperature:
A. will go on rising with time
B. will stop after sometime as it will loose heat to the surroundings by conduction
C. will rise for sometime and thereafter will starts falling
D. will become constant after sometime because of loss of heat due to radiation


The major product of the reaction
between m-dinitrobenzene and
\( N H_{4} H S \) is:
\( \mathbf{A} \)
B.
\( c \)
D.


Name the device which is used to
prevent electrical circuits.


For the reaction \( : 2 N O C l(g) \longrightarrow \)
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) The equilibrium
constant at \( 400 \mathrm{K}, \) if \( \Delta \boldsymbol{H}^{o}= \)
\( 77.18 k J m o l^{-1} \) and \( \Delta S^{o}= \)
\( \mathbf{0 . 1 2 2 k J K}^{-1} \mathbf{m o l}^{-\mathbf{1}} \mathbf{i s} \)
A \( \cdot 1.97 \times 10^{-3} \)
В. \( 1.97 \times 10^{-2} \)
c. \( 1.97 \times 10^{-4} \)
D. \( 1.97 \times 10^{-1} \)


In the circuit shown in figure cells of
emf 2,1,3 and \( 1 V \) respectively having
resistances \( 2 \Omega, 1 \Omega, 3 \Omega \) and \( 1 \Omega \) are
their internal resistances respectively.
The potential difference between D and B (in volts)
A \( \cdot \frac{5}{13} \)
в. \( \frac{2}{13} \)
c. \( \frac{10}{13} \)


It has \( d^{2} s p^{2} \) hybridisation. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) on heating gives a gas /vapour, which is also produced in significant quantity by:
(I) heating \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
(II) heating \( C u S O_{4} 5 H_{2} O \)
(III) heating \( B a\left(N_{3}\right)_{2} \)
(IV) treating \( N a N O_{3} \) with \( Z n \) in basic medium.
A. Only III
B. ।, IV
c. only IV
D. ॥, II


Find the sum of the perimeters of the
figures given below
A. \( 350 \mathrm{cm} \)
B. 360 cm
c. \( 370 \mathrm{cm} \)
D. \( 380 \mathrm{cm} \)


How will the following be affected on cutting the lens into two halves along the principle axis?
(a) focal length
(b) intensity of image formed by half lens


Two stationary particles of masses \( \mathbf{M}_{1} \)
and \( \mathrm{M}_{2} \) are at distance d apart. A third
particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from \( \mathbf{M}_{\mathbf{1}} \) is
\( ^{\mathrm{A}} \cdot \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{2}}}{\sqrt{\mathrm{M}_{1}}-\sqrt{\mathrm{M}_{2}}}\right) \)
В. \( \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{1}}}{\sqrt{\mathrm{M}_{1}}+\sqrt{\mathrm{M}_{2}}}\right) \)
\( ^{\mathrm{c}} \cdot \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{1}}}{\sqrt{\mathrm{M}_{1}}-\sqrt{\mathrm{M}_{2}}}\right) \)
D. \( \mathrm{d}\left(\frac{\mathrm{M}_{1}}{\mathrm{M}_{1}+\mathrm{M}_{2}}\right) \)


Solve
\( \cot ^{-1} \cot \left(\frac{5 \pi}{4}\right) \)


How far away should a deep sea diver be
from an under-sea rock so that he can
hear his own echo? (Speed of sound in water is \( 1500 \mathrm{m} / \mathrm{s} \) ).
A. \( 1500 \mathrm{m} \)
B. 750m
\( c \cdot 150 m \)
D. 75m


Nitrogen reaction with oxygen to form nitrous oxide.

What will be the volume ratio of the
reactants and products of the given reaction?
A \( \cdot 1: 1: 2 \)
B. 1: 2: 2
c. 3: 1: 2
D. 2:1:2


Sequences and Their limits. An
infinitely Decreasing Geometric Progression. limits of Functions. The sum of the terms of an infinitely decreasing geometric progression is equal to the greatest value of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{3} \boldsymbol{x}-\boldsymbol{9} \) on the
interval [-2,3]\( ; \) the difference between the first and the second terms of the
progression is \( \boldsymbol{f}^{\prime}(\mathbf{0}) . \) Find the common
ratio of the progression.


A current carrying wire produces a magnetic field in its surrounding space. The S.I. unit of magnetic flux density is
A . Henry
B. Tesla
c. \( A M^{2} \)
D. A-m


"Calcium and barium bicarbonates are
stable only in solution and decompose on removal of water to give carbonates." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


What is Ohm's law? Write any two
limitations of it.


Three similar spheres of mass \( \mathrm{m} \) and
radius r are moving down along three
inclined planes \( A, B \) and \( C \) of similar
dimensions. Sphere on inclined plane \( A \) rolls down in pure rolling, on B it partially
rolls and partially slides down the plane
whereas on plane \( \mathrm{C} \) it slides down
without rolling, then at the bottom of
planes
A. Velocities of all sphere are same.
B. Velocities on A and C are same whereas that on B is less
C. Velocities of sphere on \( A \) is least and that on \( C \) is maximum
D. Velocities of sphere A is maximum


A uniform cylinder of radius \( \boldsymbol{R} \)
is spinned about its axis to the angular
velocity \( \omega_{0} \) and then placed into a
corner. The coefficient of friction
between the corner walls and the
cylinder is \( \mu_{k} . \) How many turns will the
cylinder accomplish before it stops?


A piggy bank contains a hundred 50 paise coins, fifty Rs. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is
equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell
(i) will be a 50 paise win
(ii) will be of
value more than Rs. 1
(iiii) will be of
value less than Rs. 5 (iv) will be Rs. 1 or
Rs. 2 coin


Why does menstruation occur?


Iron carbonyl, \( \boldsymbol{F e C O}_{5} \) is:
A. Trinuclear
B. Mononuclear
c. Tetranuclear
D. Dinuclear


Not considering the electron spin, the degeneracy of second excited state is 9 while the generality of the first excited
state of \( \boldsymbol{H} \) atom is:
A.
B. 2
\( c \cdot 3 \)
\( D \)


A wheel with 4 spokes is placed with its
plane perpendicular to a uniform magnetic field B of magnitude 0.5 T. The field is directed into the plane of the paper and is present over the entire
region of the wheel as shown in fig. When the switch \( \mathrm{S} \) is closed, there is
initial current of 6 A between the axis
and the rim and the wheel begins to rotate. Resistances of the spokes are 1
2,4 and \( 8 \Omega, \) respectively. Resistance of rim is negligible
If current in \( 1 \Omega \) is \( 2 / X \) A. Find \( X ? \)


An organic compound on heating with
Cu O produces \( C O_{2} \) but no water it may
be
A \( \cdot C H_{4} \)
в. \( C_{2} H_{5} I \)
c. \( C H C l_{4} \)
D. \( C C l_{4} \)


Photons of energy 7 e \( V \) are incident on two metals \( A \) and \( B \) with work functions
\( 6 \mathrm{eV} \) and \( 3 \mathrm{eV} \) respectively. The minimum de Broglie wavelengths of the emitted photoelectrons with maximum
energies are \( \lambda_{A} \) and \( \lambda_{B}, \) respectively
where \( \boldsymbol{\lambda}_{\boldsymbol{A}} / \boldsymbol{\lambda}_{\boldsymbol{B}} \) is nearly:
A. 0.5
B. 1.4
\( c \cdot 4.0 \)
D. 2.0


A chemist prepares \( 1.00 g \) of pure \( _{6}^{11} C . \)
This isotope has half life of 21 minutes, decaying by the equation:
\[
_{6}^{11} C \rightarrow_{5}^{11} B+_{1}^{0} e
\]
(a) What is the rate of disintegration per second (dps) at start?
(b) What are the activity and specific activity of \( _{6}^{11} \mathrm{C} \) at start?
(c) How much of this isotope \( _{6}^{11} C \) is left
after 24 hours of its preparation?


Many lead salts are often used as pigments. If \( \boldsymbol{P b S O}_{4}\left(\boldsymbol{K}_{s p}=\mathbf{1 . 6} \times \mathbf{1 0}^{-8}\right) \)
were used in an unglazed ceramic bowl
how many milligrams of lead (II) could dissolve per liter of water?
\( A \cdot 43 \)
B. 35
\( c \cdot 11 \)
D. 38


Which of the following natural phenomenons releases chemicals which cause acid rains?
A. Volcanic eruptions
B. Lightning
c. Rotting vegetation
D. All


Find the differential equation of the family of all straight lines passing through the origin.


Which one of the following statements
about stable configuration is not correct?
A. They have their valence shell fully filled
B. They do not gain, lose or share electrons
C. They have 2 or 8 electrons in their outermost shell
D. Halogens belong to stable configuration


Leaching of \( A g_{2} S \) is carried out by heating it with a dilute solution of:
A. \( N a C N \) only
в. НС l
c. \( N a O H \)
D. \( N a C N \) in presence of \( O_{2} \)


A long solenoid of diameter 0.1 m has
\( 2 \times 10^{4} \) turns per metre.At the centre of
the solenoid, a coil of 100 turns and
radius \( 0.01 m \) is placed with its axis coinciding with the solenoid axis.The
current in the solenoid reduces at a
constant rate to \( 0 A \) from \( 4 A \) in 0.05 s.
If the resistance of the coil is \( 10 \pi^{2} \Omega \)
the total charge flowing through the coil during this time is.
\( \mathbf{A} \cdot 32 \pi \mu C \)
B. \( 16 \mu C \)
c. \( 32 \mu C \)
D. \( 16 \pi \mu C \)


The projections of a directed line segment on the coordinate axes 12,4,3 The direction cosines of the line are
A \( \cdot \frac{12}{13},-\frac{4}{13}, \frac{3}{13} \)
B. \( -\frac{12}{13},-\frac{4}{13}, \frac{3}{13} \)
c. \( \frac{12}{13}, \frac{4}{13}, \frac{3}{13} \)
D. none of these


How are non luminous objects visible to eye?
A. Non-luminous objects give away light
B. Non-luminous objects reflect the light falling on them
C. Non-luminous objects disperse the light falling on them
D. None of the above


If the area swept by the line joining the sun and the earth from Feb 1 to Feb 7 is
A, then the area swept by the radius vector from Feb 8 to Feb 28 is
\( A \cdot A \)
B. 2A
\( c \cdot 3 A \)
D. \( 4 A \)


Classify the following solids into different types Tetra phosphorous decoxide


A train moves northwards with speed
\( 80 k m h^{-1}, \) while a car moves towards
east with a speed of \( 60 k m h^{-1} . \) What is
the velocity of the train w.r.t the driver
of the car?


The science of diversity of organisms
is
A. Taxonomy
B. Systematics
c. Evolution
D. Paleontology


Two particles 1 and 2 are projected
simultaneously with velocities \( v_{1} \) and
\( v_{2}, \) respectively. Particle 1 is projected vertically up from the top of a cliff of height h and particle 2 is projected vertically up from the bottom of the cliff Find the time of meeting of particles, if the bodies meet (a) Above the top of the
cliff,
(b) Between the top and bottom of the cliff, and (c) below the bottom of the
cliff, find the time of the meeting of the particles.


Hydrogen differs from elements of \( \boldsymbol{I}- \)
\( A \) group as:
A. it can form ionic as well as covalent bond
B. all are metals
c. \( H^{+} \) is unstable in water
D. both \( A \) and \( B \)


Assertion
On plotting the length of the root against time, a linear curve is obtained.
Reason
An elongating root exemplifies arithmetic growth.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A point charge is moving in a circle with constant speed. Consider the magnetic field produced by the charge at a fixed
point \( \boldsymbol{P} \) (not at the center of circle) on
the axis of the circle.
A. it is constant in magnitude only
B. it is constant in direction only
c. it is constant both in direction and magnitude both
D. it is constant neither in magnitude nor in direction both


Approximate atomic weight is of an element is \( 26.89 g . \) If its equivalent weight is \( 8.9 g \), the exact atomic weight of element would be:
A . 29.8
B. 8.9
c. 17.8
D. 26.7


The factors, on which pressure depend
are surface area and
A. atmospheric pressure
B. force applied
c. shape of surface
D. mass of the body


The chief function of lymph nodes in mammalian body is to
A. Produce RBCs
B. Collect and destroy pathogens
c. Produce a hormone
D. Destroy the old and worn out red blood cells


In group I of alkali metals, the ionization potential decreases down the
group. Therefore lithium is a poor
reducing agent in gaseous state.
A. True
B. False


ff \( f(x)= \)
\( f(x-a)(x-b)(x-c)(x-d) \) then
prove that
\( \Delta=\left|\begin{array}{cccc}\boldsymbol{a} & \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{b} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{c} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{d}\end{array}\right|=\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{x} \boldsymbol{f}^{\prime}(\boldsymbol{x}) \)


A Point source generates 10 J of light energy in 2 s. The luminous flux of
source is:
A. 5 lumen
B. 10 lumen
c. 50 lumen
D. none of these


Solve the given pair of linear equations:
\( \frac{3}{\sqrt{x}}+\frac{4}{\sqrt{y}}=2, \frac{5}{\sqrt{x}}+\frac{7}{\sqrt{y}}= \)
\( \frac{41}{12}(x>0, y>0) \)


Largest ecosystem of the world are
A. Grasslands
B. Great lakes
c. oceans
D. Forests


In hydrogen evolution type of corrosion
with respect to hydrogen electrode which
of the following is correct?
A. the metal with more negative SRP value under the given conditions
B. the metal with more positive SRP value under the given conditions
C. the metal with both negative and positive SRP values
D. All the above


An airtight box, having a lid of area
\( 80 c m^{2}, \) is partially evacuated (i.e., has low pressure than outside atmosphere)
Atmosphere pressure is \( 1.01 \times 10^{5} P a \)
A force of \( 600 N \) is required to pull the
lid off the box. What was the pressure in
the box?


Represent set \( A, B, C \) such that \( A \subset \) \( \boldsymbol{B}, \boldsymbol{A} \cap \boldsymbol{C}=\boldsymbol{\phi} \) and \( \boldsymbol{B} \cap \boldsymbol{C} \neq \boldsymbol{\phi} \) by Venn
diagram. The number of separate
regions representing \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C}) \)
is/are:


Find the remainder obtained on dividing
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{1} \) by \( \boldsymbol{x}+\mathbf{1} \)


Curie is the unit of
A. decay constant
B. radio-activity
c. half-life
D. average life


Find the square of the distance between
the points whose cartesian coordinates
are:
(-1,1,3),(0,5,6)


What is meant by an equilibrium?


How many significant figures are present in the following?
(i) 0.0025
(ii) 208
(iii) 5005
(iv) 126,00
\( (v) 500.0 \)
(vi) 2.0034


The number of values \( k \) for which \( \left[x^{2}-\right. \)
\( \left.(k-2) x+k^{2}\right]\left[x^{2}+k x+(2 k-1)\right] \) is a
perfect square is
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. None of these


In Rutherford experiment, most of the alpha particles go straight through the foil because:
A. alpha particles are much heavier than electrons
B. alpha particles are positively charged
c. most part of the atom is empty space
D. alpha particles move with high velocity


In an LCR circuit, the capacitance is made one-fourth, when in resonance. Then what should be the change in inductance, so that the circuit remains
in resonance?
A. 4 times
B. (1/4) times
\( c .8 \) times
D. 2 times


Molar mass of carboxylic acid containing 2 carbon atoms, is:


In the adjoining figure \( \boldsymbol{A B}= \)
\( 12 c m, C D=8 c m, B D=20 \mathrm{cm} \)
\( \angle A B D=\angle A E C=\angle E D C=90^{\circ} . \) If
\( B E=x, \) then
A. \( x \) has two possible values whose difference is 4
B. \( x \) has two possible values whose sum is 28
c. \( x \) has only one value and \( x \geq 12 \)
D. \( x \) cannot be determined with the given information


Assertion If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{\pi} \\ \mathbf{0} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}^{100}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{1 0 0} \boldsymbol{\pi} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
Reason
If \( B \) is a \( 2 \times 2 \) matrix such that \( B^{2}=0 \)
then \( (I+B)^{n}=I+n B \) for each \( n \in \)
\( N \)
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 solenoid with a soft iron core is called
\( \mathbf{a} \)
A. Electromagnet
B. Magnettet
c. conducts
D. Insulator


What is not an essential condition for
an observable interference pattern to
occur between the waves two sources?
A. The frequencies of the two sources must be equal
B. The sources must be coherent
c. The sources must emit waves of equal amplitide
D. The waves from the two sources must overlap


What is meant by soil erosion?


For making cake, baking powder is taken. If you use baking soda instead of baking powder in cake. How will it effect
the taste of cake and why? How can
baking soda be converted into baking
powder?


Atomic number of calcium is ?
\( A \cdot 18 \)
B. 19
c. 20
D. 21


A tank is filled with water to a height of \( 12.5 \mathrm{cm} . \) The apparent depth of a needle lying at the bottom of the tank is
measured by a microscope to be \( 9.4 \mathrm{cm} \) What is the refractive index of water? If
water is replaced by a liquid of refractive index 1.63 up to the same
height, by what distance would the microscope have to be moved to focus on the needle again?


\( N H_{4} N O_{3} \) and \( N H_{4} N O_{2} \) on heating decomposes into:
A \( . N O_{2}, N_{2} \)
в. \( N O_{2}, N O_{3} \)
c. \( N_{2} O, N_{2} \)
D. \( N O_{3}, N O_{2} \)


If \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \) then
\( \frac{d y}{d x}=\frac{\log x}{(1-\log x)^{2}} \)
A . True
B. False


A plot of \( \boldsymbol{P} \boldsymbol{v} \boldsymbol{s} \boldsymbol{T} \) for a given mass of gas
of constant volume is a straight line.
P \( \boldsymbol{v} \boldsymbol{s} \boldsymbol{T} \) at constant volumes \( \boldsymbol{V}_{1} \) and \( \boldsymbol{V}_{2} \)
for an ideal gas are shown below:
Which of the following is correct?
\( A \cdot V_{1}>V_{2} \)
B. \( V_{1}<V_{2} \)
\( \mathbf{c} \cdot V_{1}=V_{2} \)
D. \( V_{1}=2 V_{2} \)


When the door of a refrigerator in a
room is kept open, the temperature of
the room
If Decreases - then write 0
if Increases then write 1


The solution set of \( x^{2}+2 \leq 3 x \leq \)
\( 2 x^{2}-5, \) is
\( A \cdot \phi \)
B. [1,2]
c. \( (\infty, 1) \cup[5 / 2, \infty) \)
D. None of these


During ecological succession
A. The changes lead to a community that is in near equilibrium with the environment and is called pioneer community.
B. The gradual and predictable change in species composition occurs in a given area.
C. The establishment of a new biotic community is very fast in its primary phase.
D. The numbers and types of animals remain constant.


Which of the following is not an acid anhydride?
A. \( C O_{2} \)
в. \( C O \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


The \( \alpha \) -hydroxy progesterone is a/an
A. Fatt
B. Acid
c. Dextran
D. steroid


When a compound X reacts with ozone in aqueous medium,a compound Y is produced.Ozone also reacts with Y and
produces compound \( z, z \) acts as an oxidising agent,then \( \mathrm{X}, \mathrm{Y} \) and \( \mathrm{Z} \) will be :
A \( \cdot X=H I, Y=I_{2} \) and \( Z=H I O_{3} \)
B. \( X=K I, Y=I_{2} \) and \( Z=H I O_{3} \)
C. \( X=K I, Y=I_{2} \) and \( Z=H I O_{4} \)
D. \( X=H I, Y=I_{2} \) and \( Z=H I O_{4} \)


Kirchoff's voltage law and current law are respectively in accordance with the conservation of
(a) charge and momentum
(b) charge and energy (c) energy and charge
(d) energy and
momentum


A resistor of \( 100 \Omega \), a pure inductance coil of \( L=0.5 \mathrm{H} \) and capacitor are in series in a circuit containing an a.c sources of \( 200 \mathrm{V}, 50 \mathrm{Hz} \). In the circuit, current is added is ahead of the voltage
by \( 30^{0} . \) Find the value of the capacitance
A . 1.46
B. 3
\( c \cdot 4 \)
D. 5


The lengths of two sides of a triangle are \( 7 \mathrm{cm} \) and \( 10 \mathrm{cm} . \) What is the possible
value range of the third side?
A. \( 3 \mathrm{cm}< \) third side \( <10 \mathrm{cm} \)
B. \( 7 \mathrm{cm}< \) third side \( <10 \mathrm{cm} \)
\( \mathrm{c} \cdot 3 \mathrm{cm}< \) third side \( <17 \mathrm{cm} \)
D. \( 7 \mathrm{cm}< \) third side


If \( \sin \alpha \sin \beta-\cos \alpha \cos \beta+1=0 \) then
show that \( 1+\cot \alpha \tan \beta=0 \)


A particle is moving in a plane with a velocity given by \( \vec{v}=\hat{i} u_{0}+\hat{j} a \omega \cos \omega t \) if
the particle is at origin at \( t=0 \) Distance of the particle from origin at
time \( 3 \pi / 2 \omega \) is
A \( \cdot \sqrt{a^{2}+\left(3 \pi u_{0} / 2 \omega\right)^{2}} \)
B . \( \sqrt{a^{2}+\left(2 \pi u_{0} / \omega\right)^{2}} \)
\( ^{\mathbf{c}} \cdot\left(\frac{\pi u_{0}}{\omega}\right)^{2}+a^{2} \)


A block of mass 2 kg collides with a horizontal massless spring of force constant \( 2 \mathrm{N} / \mathrm{m} \). The block compresses the spring \( 4 \mathrm{cm} \) from the rest position speed of the block at the instant of collision is in \( \mathrm{m} / \mathrm{s} \)


When a high energy (fast moving) electron approaches a heavy metal target, some of the electrons are significantly deflected by nuclei, and they lose much of their energy. This lost energy goes into the creation of high energy photons. What process is being described here?
A. compton scattering
B. The photoelectric effect
c. \( x \) -ray production
D. Pair production
E. Quantum tunneling


The impurity atoms with which pure silicon would be doped to make a p-type semiconductor are those of
This question has multiple correct options
A. Phosphorus
B. Boron
C. Antimony
D. Aluminium


Which of the following is true?
A. The continuous cycling of water among its three forms keeps the total amount of water on the earth constant even when the whole world is using it.
B. The continuous cycling of water among its three forms cannot keep the total amount of water on the earth constant even when the whole world is using it.
C. The continuous cycling of water among its three forms decreases the total amount of water on the earth when
the whole world is using it
D. The continuous cycling of water among its three forms keeps the total amount of water on the earth constant only if the whole world is not using it


A spontaneous reaction is impossible if
A. both \( \Delta H \) and \( \Delta S \) are negative
B. \( \Delta H \) and \( \Delta S \) are positive
c. \( \Delta H \) is negative and \( \Delta S \) is positive
D. \( \Delta H \) is positive and \( \Delta S \) is negative


Hormone which stimulate initiation of
flowering process is
A. Gibberllin
B. Ethylene
c. Both A and B
D. Florigen


According to the Kinetic-Molecular Theory, the kinetic energy of the
molecules increases when they are -
A. mixed with other molecules at lower temperature
B. frozen into a solid
C . condensed into a liquid
D. heated to a higher temperature
E. Collide with each other in a container at a lower temperature


The largest and the shortest distance of
the earth from the sun are \( r_{1} \) and \( r_{2} \). Its
distance from the sun when it is at
perpendicular to the major-axis of the orbit drawn from the sun is:
A \( \cdot \frac{r_{1}+r_{2}}{4} \)
в. \( \frac{r_{1}+r_{2}}{r_{1}-r_{2}} \)
c. \( \frac{2 r_{1} r_{2}}{r_{1}+r_{2}} \)
D. \( \frac{r_{1}+r_{2}}{3} \)


Assertion
\( \beta \) -particles are deflected more than \( \alpha \) particles in a given electric field.
Reason
Charge on \( \alpha \) -particles is larger than on
\( \beta \) -particles.
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 the Reason is correct


A copper slab of mass \( 2 g \) contains \( 2 x \)
\( 10^{22} \) atoms. The charge on the nucleus
of each atom is \( 29 e . \) What fraction of
the electrons must be removed from the
sphere to give it a charge of \( +2 \mu C ? \)
A \( .58 \times 10^{22} \)
B. \( 1.25 \times 10^{13} \)
c. \( 2.16 \times 10^{11} \)
D. \( 2.16 \times 10^{-11} \)


Prove that: \( \cot \left(\frac{\pi}{2}-2 \cot ^{-1} 3\right)=\frac{3}{4} \)


Identify the molecular formula of an alkane which has only three chain
isomer. Suggest a suitable method of separation of these isomers and draw a comparison of their dipole moments


Find the equation of the straight line which passes through the origin and
making angle \( 60^{\circ} \) with the line \( x+ \) \( \sqrt{3} y+3 \sqrt{3}=0 \)


The diameter of ball \( y \) is double that of
\( x \). The ratio of their terminal velocities
inside water will be:
A . 1: 4
B . 4: 1
c. 1: 2
D. 2: 1


The element with atomic number \( Z= \)
115 will be placed in :
A \( \cdot 7^{t h} \) period , 1 A group
B. \( 8^{t h} \) period , IV A group
C. \( 7^{t h} \) period \( , \) V A group
D. \( 6^{t h} \) period , \( \vee \) B group


Which of the following ores are concentrated by Froth Flotation.
A. Oxide ores
B. Chloride ores
c. sulphide ores
D. Nitride ores


Write the IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C}_{6} \boldsymbol{H}_{5} \)


Arrange the following alcohols in order of increasing reactivity towards sodium metal.
(i) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O H} \) (ii) \( \left(\boldsymbol{C H}_{3}\right) \mathbf{2 C H}- \)
\( O H \) (iii) \( C H_{3} C H_{2} O H \)
A. (iii) < (ii) < (i)
B. (ii) < (i) < (iii)
c. (i) < (ii) < (iii)
D. (iii) < (i) < (ii)


The p. \( m \). \( f \). \( X \) -number of major defects randomly selected appliance of a certain type is :
\[
x-x
\]
\( \begin{array}{lllll}\text { P(a) } & \text { 0.08 } & \text { 0.15 } & \text { 0.45 } & \text { 0.27 }\end{array} \)
Find the expected value and standard deviation of \( X \)


A magnetic needle suspended by a silk thread is vibrating in the earth's magnetic field if the temperature of the
needle is increased by \( 700^{\circ} \mathrm{C} \), then
A. time period decreases
B. time period increases
c. time period remains unchanged
D. the needle stops vibrating


The solubility of \( M g(O H)_{2} \) in pure
water is \( 9.57 \times 10^{-3} g L^{-1} . \) Calculate its
solubility in \( g L^{-1} \) in \( 0.02 M \)
\( M g\left(N O_{3}\right)_{2} \) solution.


What were the criteria used by Mendeleev in creating his period. Why do you think the noble gases are placed
in a separate group?


The toxic chemicals from industries
released in water lead to:
A. change in the color of water
B. eutrophication
c. change in the temperature of water
D. all of above


An automobile moves on a road with a
speed of \( 54 k m h^{-1} . \) The radius of its
wheel is \( 0.45 m \) and the moment of
inertia of the wheel about its axis of
rotation is \( 3 \mathrm{kgm}^{2} \). If the vehicle is
brought to rest in \( 15 s \), the magnitude of average torque transmitted by its brakes to the wheels is:
A . \( 2.86 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
B. \( 6.66 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
c. \( 8.58 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
D. \( 10.86 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)


The sum of absolute deviation is least
when taken from
A. Mean
B. Median
c. mode
D. None of the above


Arrange the following in the decreasing order of their boiling points.
I.
II.
III.
IV.
\( A \cdot(1)>(11)>(11)>(111) \)
B. (I) > (II) > (III) > (III)
\( c \cdot(\| I)>(1)>(\|)>(I V) \)
D. (IV) > (III) > (II) > (I)


Let \( A B C \), be a triangle such that the coordinates of the vertex \( \boldsymbol{A} \) are \( (-\mathbf{3}, \mathbf{1}) \) Equation of the median through \( B \) is
\( 2 x+y-3=0 \) and equation of the
angular bisector of \( \boldsymbol{C} \) is \( \mathbf{7} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}-\mathbf{1}= \)
0.Find the slope of line \( \boldsymbol{B C} \).


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C l} \stackrel{\boldsymbol{N a C N}}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{N i} / \boldsymbol{H}_{2}}{\longrightarrow} \)
\( \boldsymbol{Y} \stackrel{\text {aceticanhydride}}{\longrightarrow} \boldsymbol{Z} \)
In the above reaction sequence, \( Z \) is:
A. \( C H_{3} C H_{2} C H_{2} N H C O C H_{3} \)
B. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
c. \( C H_{3} C H_{2} C H_{2} C O N H C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C O N H C O C H_{3} \)


The gas used in the hydrogenation of
oils in presence of nickel as a catalyst to give vanaspathi is
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( C l_{2} \)


A tank is filled \( 10 \% \) in one hour and \( 8 \% \)
of the water is emptied in the next hour. If it is repeated again, find the percentage of tank filled with water?
A . 20\%
B . 4\%
c. \( 19.2 \% \)
D. 17.66\%


A uniform rod of mass \( m \) and length \( l \)
hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinged when the rod becomes vertical is
A \( \cdot \frac{m g}{4} \)
B. 5 \( \frac{-m g}{2} \)
c. \( \frac{m g}{6} \)
\( \stackrel{\mathrm{D}}{-}_{2}^{7} m g \)


The continuity of water column in xylem is maintained due to
A. Presence of air bubbles
B. Cohesive property of water
c. Evaporation power of water
D. None of the above


State True or False.
f \( x, y \) are positive real numbers such that \( x+y=1, \) then \( \left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right) \geqslant 9 \)
A. True
B. False


The minimum phase difference between two SHM's is:
\( \boldsymbol{y}_{1}=\sin \left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}\right) \sin (\boldsymbol{\omega} \boldsymbol{t})+\sin \left(\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \cos (\boldsymbol{\omega} \boldsymbol{t}) \)
\( \boldsymbol{y}_{2}=\cos \left(\frac{\pi}{6}\right) \sin (\omega t)+\sin \left(\frac{\pi}{3}\right) \cos (\omega t) \)
is:
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{6} \)
c. \( \frac{\pi}{12} \)
D.


Choose the correct statement(s) from
the following?
This question has multiple correct options
A. Mechanical waves need medium for their propagation.
B. Sound cannot travel through vacuum.
C. Mechanical waves transport energy from one place to another
D. Sound waves are non mechanical waves.


For the following grouped frequency distribution find the mode:
\( \begin{array}{llll}\text { Class: } & \begin{array}{l}3- \\ 6\end{array} & \begin{array}{l}\text { 6- } \\ \text { 9 }\end{array} & \begin{array}{l}\text { 9- } \\ 12\end{array}\end{array} \) 15
Frequency:
:
2 5
10
23


If the slopes of the lines given by the equation \( 24 x^{3}-a x^{2} y+26 x y^{2}- \)
\( 3 y^{3}=0 \) are in G.P., p is the greatest
perpendicular distance of the point (1,1) from these lines, then \( a^{2}+37 p^{2} \) is
equal to


The rational number lying exactly in between the numbers \( \frac{1}{5} \) and \( \frac{1}{3} \) is
A \( \cdot \frac{1}{2} \)
в.
c. \( \frac{2}{15} \)
D. \( \frac{4}{15} \)
E. \( \frac{8}{15} \)


The potential difference across the ends of a resistor is \( _{-}-_{-}-_{-}-_{-}- \) to the
current through it
A. directly proportional
B. inversely proportional
c. square proportional
D. none of these


\( \sinh ^{-1}\left(\frac{x}{4}\right) d x \) is equal to
A \( \cdot x \sinh ^{-1}\left(\frac{x}{4}\right)-\sqrt{x^{2}+16}+c \)
B. \( x \sinh ^{-1}\left(\frac{x}{4}\right)+\sqrt{x^{2}+16}+c \)
c. \( x \sinh ^{-1}\left(\frac{x}{4}\right)-\frac{1}{2} \sqrt{x^{2}+16}+c \)
D \( x \sinh ^{-1}\left(\frac{x}{2}\right)-x \sqrt{x^{2}+16}+c \)


A baker found that the cake prepared by
him is hard and small in size. Which
ingredient has he forgotten to add that would have made the cake fluffy?


The element which could be extracted by electrolytic reduction of its oxide dissolved in a high temperature
melt is:
A. Sodium
B. Potassium
c. Fluorine
D. Aluminium


Assertion
Vinylic halides are reactive towards nucleophilic substitution reaction.
Reason Reactivity is due to the polarity of carbon-halogen bond.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is incorrect


In the leaching of \( A g_{2} S \) with \( N a C N, \) a
stream of air is also passed. It is because of:

This question has multiple correct options
A . reversible namre of reaction between \( A g_{2} S \) and \( N a C N \)
B. oxidised \( N a_{2} S \) formed into \( N a_{2} S O_{4} \)
c. irreversible namre of reaction between \( A g_{2} S \) and \( ^{N a C N} \)
D. None of the above


The calculated spin-only magnetic moments (BM) of the anionic and
cationic species of \( \left[\boldsymbol{F} e\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]_{2} \) and
\( \left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right], \) respectively, are:
A .4 .9 and 0
B. 2.84 and 5.92
c. 0 and 4.9
D. 0 and 5.92


If \( A \) and \( B \) are independent events of \( a \) random experiment such that \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B)=\frac{1}{6} \) and \( P(\bar{A} \cap \bar{B})=\frac{1}{3}, \) then \( P(A) \)
is equal to
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{5}{7} \)
D. None of these


If the air density were uniform, then the height of the atmosphere above the sea level to produce a normal atmospheric
pressure of \( 1.0 \times 10^{5} \) Pa is (density of air is \( 1.3 \mathrm{kg} / \mathrm{m}^{3}, \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} \) ):
A. \( 0.77 \mathrm{km} \)
B. 7.7 km
c. \( 77 \mathrm{km} \)
D. 0.077 km


Identify the correct statement from the
following:
A. Wave nature of light was proposed by Huygens.
B. The direction of light ray and its wave front are opposite.
C. Huygen's wave theory could not explain phenomenon of reflection.
D. A monochromatic ray of light after passing through the prism should create a spectrum of seven colours.


In Young's double slit experiment, the slits are \( 2 \mathrm{mm} \) apart are illuminated by
photons of two wavelengths \( \boldsymbol{I}_{1}= \) \( 12000 A \) and \( I_{2}=10000 A \) at what
minimum distance from the common
central bright fringe on the screen \( 2 \mathrm{m} \) from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?
\( A \cdot 8 m m \)
B. 6 mm
\( c \cdot 4 m m \)
D. 3 mm


The symbiotic nitrogen fixing bacterium in root nodules of legumes is
A. Pseudomonas
B. Bacillus
c. Rhizobium
D. Nitrobacter


Which of the following is not correct statement for periodic classification of elements?
A. The properties of elements are the periodic functions of their atomic number
B. Non-metallic elements are less in number than metallic elements
c. For transition elements, the last electron enters into (n
- 2) d-subshell
D. None of these


What is the output of the combination?


State whether true or false.
The image formed by a plane mirror is of the same size as the object.
A. True
B. False


If \( \boldsymbol{A}=\left[\begin{array}{ccc}2 & 4 & -1 \\ -1 & 0 & 2\end{array}\right], B=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 2 & 1\end{array}\right] \)
find \( (A B)^{T} \)


The mass number of an atom is slightly less than the actual atomic mass. Give
reasons.


The truth tables of logic gates \( A, B, C, D \)
are given here. Identify them correctly.
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|} { Input } & \multicolumn{1}{c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1 \\
\hline
\end{tabular} \begin{tabular}{|l|c|c|}
\hline \multicolumn{2}{|c|} { Input } & Output \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 0 \\
1 & 1 & 1 \\
\hline
\end{tabular}
\begin{tabular}{|l|l|l|}
\hline \multicolumn{2}{|c|} { Input } & \multicolumn{1}{|c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0 \\
1 & 1 & 0 \\
\hline
\end{tabular} \begin{tabular}{|l|c|c|}
\hline \multicolumn{2}{|c|} { Input } & \multicolumn{1}{|c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\hline
\end{tabular}
A . A: OR
B: AND, C: NOR,
D: NAND
B. A: OR,
\( B: \) NOR, \( C: A N D \)
D: NAND
C. \( A: A N D \)
B: OR, C: NAND,
D: NOR
D. A: OR
B: NOR, C: NAND,
D: AND


Find the addition of \( -2 x+1 \) and
\( -2 x-2 \)


Biochemical Oxygen Demand(BOD)
value can be a measure of water
pollution caused by the organic matter.
Which of the following statements is
correct?
A. Polluted water has BOD value higher than 10 ppm
B. Aerobic bacteria decrease the BOD value
C. Anaerobic bacteria increase the BOD value
D. Clean water has BOD value higher than 10 ppm


Which of the following duct lead into the collecting tubules?
A. Tertiary duct
B. Duct of Bellini
c. Henle's loop
D. Bowman's capsule


For transmission of speeches, talks, music, dramas etc is used
A. radio broadcast transmittter
B. radio telegraph transmitter
c. navigation transmitter
D. None of these


Liver in our body stores
A. Vitamin A
B. Vitamin D
c. Vitamin \( B_{12} \)
D. All of the above


Two rods of the same length and
diameter having thermal
conductivities \( \boldsymbol{K}_{\mathbf{1}} \boldsymbol{K}_{\mathbf{2}} \) are joined in
parallel. The equivalent thermal conductivity of the combination is:
A. \( \frac{K_{1} K_{2}}{K_{1}+K_{2}} \)
в. \( K_{1}+K_{2} \)
c. \( \frac{K_{1}+K_{2}}{2} \)
D. \( \sqrt{K_{1} K_{2}} \)


The gravitational unit of force in the metric system is
A . gwt
B.
c. \( \mathrm{kg} \) wt
D. None of these


Plastochron is
A. Period between two successive leaf primordia
B. Distance between two successive leaf primordia
C. Region of origin of root branch
D. Region of origin of stem branch


The equation of parabola whose latus rectum is 2 units, axis is \( x+y-2=0 \)
and tangent at the vertex is \( x-y+ \)
\( 4=0 \) is given by
A \( \cdot(x+y-2)^{2}=4 \sqrt{2}(x-y+4)^{2} \)
B . \( (x-y-4)^{2}=4 \sqrt{2}(x+y-2) \)
C. \( (x+y-2)^{2}=2 \sqrt{2}(x-y+4) \)
D. \( (x-y-4)^{2}=2 \sqrt{2}(x-y+2)^{2} \)


Choose the most appropriate answer; Kidneys are excretory organs in
A. All chordates
B. Only mammals
C. Mammals, Reptiles and Amphibians
D. Mammals, Reptiles and Birds


In a complimentary gene interaction calculate the number of phenotype and genotype produced in a cross \( A a B b \times \)
\( a a B B \)
A. 1 phenotype, 2 genotypes
B. 2 phenotypes, 4 genotypes
c. 4 phenotypes, 4 genotypes
D. 2 phenotypes, 2 genotypes


The elements \( X \) and \( Y \) form two
compounds, \( \boldsymbol{X} \boldsymbol{Y}_{2} \) and \( \boldsymbol{X}_{3} \boldsymbol{Y}_{2} . \mathbf{0 . 1} \) mol of
former weighs 10 g while 0.05 mole of the latter weighs 9 g. Find the atomic
weight of \( \boldsymbol{X} \)


Convert part of the ratio to percentage:
\( \mathbf{1}: \mathbf{4} \)


The formula of meta phosphoric acid is :
A. \( \mathrm{H}_{2} \mathrm{PO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
\( \mathrm{c} \cdot \mathrm{HPO}_{3} \)
D. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)


The range of values of \( a \) such that the
angle \( \theta \) between the pair of tangents drawn from \( (a, 0) \) to the circle \( x^{2}+ \) \( y^{2}=1 \) satisfies \( \frac{\pi}{2}<\theta<\pi \), is
A \( .(1,2) \)
B. \( (1, \sqrt{2}) \)
c. \( (-\sqrt{2},-1) \)
(年) \( (-\sqrt{2},-1) \)
D. \( (-\sqrt{2},-1) \cup(1, \sqrt{2}) \)


\( \boldsymbol{x}+\boldsymbol{y}- \)
\( (z-x-[y+z-(x+y-\{z+x-(y \)
is equal to
A . \( x \)
B. \( 2 y \)
c.
D.


The momentum of a photon of energy 1MeV in kg.m/s will be:
A \( .0 .33 \times 10^{6} \)
B . \( 7 \times 10^{24} \)
\( c \cdot 10^{2} \)
D \( .5 \times 10^{-22} \)


Why starch turns blue black with iodine
\( ? \)


The energy released when a positron is
annihilated is
A. \( 0.51 \mathrm{MeV} \)
B. 0.58 MeV
c. \( 185 M e V \)
D. \( 200 \mathrm{MeV} \)


A line passes through the points whose position vectors are \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-2 \hat{\boldsymbol{k}} \) and \( \hat{\boldsymbol{i}}- \)
\( 3 \hat{j}+\hat{k} . \) The position vector of a point on it at unit distance from the first point
is


The direction angles of the line \( x= \)
\( \mathbf{4} z+\mathbf{3}, \boldsymbol{y}=\mathbf{2}-\mathbf{3} z \) are \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma, \) then
\( \cos \alpha+\cos \beta+\cos \gamma= \)
A \( \cdot \frac{2}{\sqrt{26}} \)
B. \( \frac{8}{\sqrt{26}} \)
c. 1
D. 2


Assertion: Hydrogen is a diatomic
molecule

Reason: Protium atom contains one
electron, one proton and one neutron
A. Both Assertion and Reson are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
c. The Assertion is true but Reason is false
D. The Assertion is false but Reason is true


Water entering root due to diffusion is a
part of
A. Endocytosis
B. Osmosis
c. Passive absorption
D. Active absorption


If \( f(x)=\frac{\sin 4 x}{5 x}+a, \quad \) for \( x>0 \)
\( =\boldsymbol{x}+\mathbf{4}-\boldsymbol{b} \quad \) for \( \boldsymbol{x}<\mathbf{0} \)
\( =1 \) for \( x=0 \) is continuous
\( a t x=0, \) find \( a \) and \( b \)


Complete the reaction
11


ntegrate the function \( \frac{\mathbf{5 x}}{(x+1)\left(x^{2}+9\right)} \)


What is water gas?


The frequency of \( B \) is \( 3 \% \) greater than \( A \)
The frequency of \( C \) is \( 2 \% \) less than that
of \( A, \) if \( B \) and \( C \) produce 8 beats \( / s, \) then the frequency of \( \boldsymbol{A} \) is


Diodes are used to
A. convert DC into AC
B. convert AC into DC
c. resistance control
D. current regulation


The magnetic force required to demagnetise the material is
A. retentivity
B. coercivity
c. energy loss
D. hysterisis


The armature of a dc motor has \( 15 \Omega \)
resistance. It draws a current of \( 1.6 \mathrm{A} \) when run by 220 V de supply. The value of back emf will be:
A. 24
B. \( 196 v \)
c. \( 220 v \)
D. 244 V


An electron that accelerates from a
point near a collection of positive source charges toward a point near a collection of negative source charges
experiences
A. A decrease in electrical potential energy as it moves toward a region at a lower electric potential
B. A decrease in electrical potential energy as it moves toward a region at a higher electric potential
C. An increase in electrical potential energy as it moves toward a region at a lower electric potential
D. An increase in electrical potential energy as it moves toward a region at a higher electric potential
E. No change in electrical potential energy


If the charge density at each small drop
be \( \sigma, \) then charge density in the larger drop is
A \( \cdot\left[4 n^{1 / 3} \sigma\right] \)
B . \( \left[n^{1 / 3} \sigma\right] \)
c. \( \left[3 n^{1 / 3} \sigma\right] \)
D. \( \left[2 n^{1 / 3} \sigma\right] \)


The IUPAC name of \( \left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{4}\right]\left[\mathrm{NiCl}_{4}\right] \) is :
A. tetrachloronickel (II)-tetraaminenickel (II)
B. tetramminenickel
(II)-tetrachloronickel (II)
c. tetraamminenickel (II)-tetrachloronickelate (II)
D. tetrachloronickel (II)-tetraaminenickelate (0)


Which of the following eukaryotes are devoid of histone proteins?
A. Golden algae
B. Euglenoids
c. Fire algae
D. Slime mould


Double helix model of DNA which was
proposed by Watson and Crick was of
A. C-DNA
B. B-DNA
c. D-DNA
D. z-DNA


\( \left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \dots\left(1-\frac{1}{n}\right) \)
equals
A.
B. \( \frac{2}{n} \)
c. \( \frac{3}{n} \)
D.


For a string clamped at both its ends, which of the following wave equation is/are valid for a stationary wave set up in it? (Origin is at one end of string) This question has multiple correct options
A. \( y=A \sin k x . \sin \omega t \)
B. \( y=A \cos k x \sin \omega t \)
c. \( y=A \sin k x . \cos \omega t \)
D. \( y=A \cos k x \cos \omega t \)


\( C_{P} 29 J m o l^{-1} K^{-1} \) in the process \( P T= \)
constant.


In one model of the electron, the electron
of mass \( m_{e} \) is thought to be a uniformly
charged shell of radius \( R \) and total charge \( e, \) whose electrostatic energy \( E \)
is equivalent to its mass \( m_{e} \) via
Einstein's mass energy relation \( \boldsymbol{E}= \) \( \boldsymbol{m}_{e} \boldsymbol{c}^{2} . \) In this model, \( \boldsymbol{R} \) is approximately
\( \left(\boldsymbol{m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, \boldsymbol{c}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \mathbf{m s}^{-\mathbf{1}}\right. \)
\( \mathbf{1} / \mathbf{4} \boldsymbol{\pi} \varepsilon_{\mathbf{0}}=\mathbf{9} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{F} \boldsymbol{a} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} \boldsymbol{s} \boldsymbol{n}^{-1} \)
magnitude of the electron charge \( = \) \( \left.\mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C}\right) \)
A. \( 1.4 \times 10^{-15} \mathrm{m} \)
B . \( 2 \times 10^{-13} m \)
c. \( 5.3 \times 10^{-11} m \)
D. 2.8 \( \times 10^{-35} \mathrm{m} \)


The contrapositive of "if in a triangle
\( A B C, A B>A C, \) then \( \angle C>\angle B^{\prime \prime}, \) is
\( \mathbf{A} \cdot \) If in a triangle \( A B C, \angle C>\angle B, \) then \( A B>A C \)
B. If in a triangle \( A B C, A B \not \) # A then \( \angle C \Varangle \angle B \).
C. If in a triangle \( A B C, \angle C \Varangle \angle B, \) then \( A B>A C \).
D. If in a triangle \( A B C, \angle C \Varangle \angle B, \) then \( A B \Varangle A C \).


Eight spherical rain drops of the same mass and radius are falling down with a
terminal speed of \( 6 \mathrm{cm} s^{-1} \). If they coalesce to form one big drop, what will be its terminal speed? Neglect the
buoyancy due to air:
A \( .1 .5 \mathrm{cm} \mathrm{s}^{-1} \)
B. \( 6 \mathrm{cms}^{-1} \)
c. \( 24 c m s^{-1} \)
D. \( 32 \mathrm{cms}^{-1} \)


Give examples of division pteridophyta
A. Adiantum and Lycopodiummm
B. Marsilea and Selaginella
c. Adiantum and Selaginella
D. All of above


An object of length \( 4 \mathrm{cm} \) is placed in front of a concave mirror at a distance
of \( 30 \mathrm{cm} . \) The focal length of mirror is
\( 15 \mathrm{cm} . \) What will be the length of image?
A. \( 1 ~ c m \)
в. 2 ст
\( c .4 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


The percentage of p-character in the orbitals forming P-PP-P is:
A . 25
B. 33
\( c .50 \)
D. 75


Which of the following statements is
incorrect?
A. No work is done if the displacement is perpendicular to the direction of the applied force
B. If the angle between the force and displacement vectors is obtuse, then the work done is negative
C. Frictional force is a non-conservative
D. All the central forces are non-conservative


A body of mass \( 5 k g \) is acted upon by
two perpendicular force \( 8 N \) and \( 6 N \) find the magnitude and direction the
acceleration:
A \( \cdot 3 m s^{-2}, \theta=\cos ^{-1}(0.8) \) from \( 8 N \)
B . \( 2 m s^{-2}, \theta=\cos ^{-1}(0.6) \) from \( 6 N \)
c. \( 3 m s^{-2}, \theta=\cos ^{-1}(0.9) \) from \( 6 N \)
D. \( 5 m s^{-2}, \theta=\cos ^{-1}(0.81) \) from \( 8 N \)


A proton with KE \( 6 M e V \) is travelling in a particle accelerator of circular orbit \( 0.75 m . \) What fraction of energy does it radiate per sec?


The current in an electrical circuit is
given by \( \boldsymbol{R} \boldsymbol{i}+\frac{\boldsymbol{q}}{\boldsymbol{c}}=\frac{\boldsymbol{E}}{\boldsymbol{R}} . \) The expression
for \( \boldsymbol{q} \) is?
A \( \cdot q=E C\left(1-e^{t / C R}\right) \)
в. \( q=E C\left(1+e^{-t / C R}\right) \)
c. \( q=E C\left(1-e^{-C R / t}\right) \)
D \( \cdot q=E C\left(1-e^{-t / C R}\right) \)


The lattice energy of NaCl is
\( 788 k J \) mol \( ^{-1} . \) This means that \( 788 k J \)
of energy is required:
A. to separate one mole of solid \( N a C l \) into one mole of \( N a(g) \) and one mole of \( C l(g) \) to infinite distance
B. to separate one mole of solid \( N a C l \) into one mole of \( N a^{+}(g) \) and one mole of \( C l^{-}(g) \) to infinite distance
C. to convert one mole of solid \( N a C l \) into one mole of
gaseous \( N a C l \)
D. to convert one mole of gaseous \( N a C l \) into one mole of solid \( N a C l \)
E. to separate one mole of gaseous \( N a C l \) into one mole of \( N a^{+}(g) \) and one mole of \( C l^{-}(g) \) to infinite distance


How many \( \sigma \) and \( \pi \) bonds are present in
\( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} ? \)
\( \mathbf{A} \cdot 9 \sigma, 4 \pi \)
в. \( 10 \sigma, 3 \pi \)
\( \mathbf{c} \cdot 6 \sigma, 6 \pi \)
D. \( 5 \sigma, 5 \pi \)


Two point charges \( +q \) and \( -2 q \) are kept \( d \) distance apart Find the location of the points on the line joining the two charges at which potential due to this system of charges is zero.


The liquefaction behaviour of temporary gases approaches that of permanent
gases as we go:
A. below critical temperature
B. above critical temperature
c. above absolute zero
D. below absolute zero


Ammonia is not a product in the :
A. hydrolysis of nitrolim
B. hydrolysis of aluminium nitride
c. decomposition of ammonium nitrite
D. hydrolysis of urea


In which phase of meiosis-I the two chromosome can align at the metaphase plate independently of each other
B. Metaphase- -
c. Anaphase-I
D. Telophase-


If the potential energy of two molecules is given by, \( U=\frac{A}{r^{12}}-\frac{B}{r^{6}} \) then at
equilibrium position, its potential energy is equal to:
A \( \cdot \frac{A^{2}}{4 B} \)
B. \( -\frac{B^{2}}{4 A} \)
c. \( \frac{2 B}{A} \)
D. 3A


Can a pendulum vibrate in an artificial
satellite?


A charge can exist without mass.
A. True
B. False


Consider the following species:
(i) \( \left[\boldsymbol{O}_{2}\right]^{2-} \)
(ii) \( [\boldsymbol{C O}]^{+} \)
(iii) \( \left[\boldsymbol{O}_{2}\right]^{+} \)
Among these sigma bond alone is
present in?
A. (i) alone
B. (ii) alone
c. (iii) alone
D. (i) and (ii)
E. (i), (ii) and (iii)


Let \( \boldsymbol{a}=\boldsymbol{m} \boldsymbol{i n}\left\{\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}, \boldsymbol{x} \epsilon \boldsymbol{R}\right\} \) and
\( \boldsymbol{b}=\lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\mathbf{1}-\cos \boldsymbol{\theta}}{\boldsymbol{\theta}^{2}} \)
The value of \( \sum_{r=0}^{n} a^{r} . b^{n-r} \) is?
\( ^{\text {A } \cdot \frac{2^{n+1}-1}{3.2^{n}}} \)
B. \( \frac{2^{n+1}+1}{3.2^{n}} \)
c. \( \frac{4^{n+1}-1}{3.2^{n}} \)
D. none of these


If the temperature of a conductor is increased, its resistance will
A. not increase
B. increase.
c. decrease.
D. change according to the whether


If at a given temperature pKa of buffer
is constant, then
A. pkb is constant
B. pH is constant
c. both pKb and pH are constants
D. \( \mathrm{pH}=7 \)


A object of mass \( 40 k g \) having velocity
\( 4 m / s \) collides with another object \( m= \)
\( 60 k g \) having velocity \( 2 m / s . \) The
collision is perfectly inelastic. The loss in energy is
A . \( 110 J \)
в. \( 48 J \)
\( \mathrm{c} .3925 \)
D. \( 440 J \)


Find the square root of the following numbers using division method:
0.431649


Green chemistry is:
A. way of thinking and utilising the existing knowledge and principles of chemistry and other sciences
B. study of plants for making the environment clean
C. both \( A \) and \( B \)
D. None of the above


Draw the structure of the molecule
\( C l F_{3} \) and state its geometry.


If \( \mu_{0} \) is absolute permeability of
vacuum and \( \mu_{r} \) is relative magnetic permeability of another medium, then permeability \( \mu \) of the medium is
A . \( \mu_{0} \mu_{r} \)
B. \( \mu_{0} / \mu_{r} \)
\( \mathbf{c} \cdot \mu_{r} / \mu_{0} \)
D. \( I / \mu_{0} \mu_{r} \)


What happens when two inflated
balloons are rubbed with a silk cloth
and brought close to each other?
A. Balloons repel each other
B. Balloons attract each other
C. Balloons neither attract nor repel.
D. Baloons either attract or repel


A man in a minivan rounds a circular
turn at a constant speed. Which of the
following would cause the minivan to
experience less acceleration?
A. traveling faster
B. traveling around a turn with a smaller circular radius
C. traveling with more weight in the van
D. traveling around a turn with a greater circular radius
E. traveling the opposite direction around the same turn


Air baldder or swim bladder functions
as a lung in
A. Scoliodon
B. Rhinobatos
c. Protopterus
D. Betta


Why is there a need for harnessing nonconventional sources of energy? How
can energy be harnessed from the sea
indifferent ways?


Bamboo, grass and mint stem elongate by the activity of
A. Primary meristem
B. Secondary meristem
c. Intercalary meristem
D. Apical meristem


If the difference between the mean and
variance of a binomial distribution for 5 trials is \( \frac{5}{9}, \) then the distribution is
\( ^{A} \cdot\left(\frac{1}{9}+\frac{2}{9}\right)^{5} \)
\( ^{\mathrm{B}}\left(\frac{1}{4}+\frac{3}{4}\right)^{5} \)
\( ^{c}\left(\frac{2}{3}+\frac{1}{3}\right)^{5} \)
\( ^{\mathrm{D}}\left(\frac{3}{4}+\frac{1}{4}\right)^{5} \)


Represent graphically a displacement
of
\( 50 k m, 30^{\circ} \) east of north


Two particles \( A \) and \( B \) are in motion. If the wavelength associated with particle \( A \) is \( 5 \times 10^{-8} \) m. Calculate the
wavelength associated with particle B if its momentum is half of \( A \)
A. \( 5 \times 10^{-8} \mathrm{m} \)
B. \( 10^{-5} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-6} \mathrm{cm} \)
D. \( 5 \times 10^{-8} \mathrm{cm} \)


The functional group contained in the
compound \( \boldsymbol{C H} \equiv \boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \)
\( \boldsymbol{C H} \) is:
A. alkene
B. alkyne
c. diene
D. none of these


\( f x, Y, z \) are the three sums of money such that \( Y \) is a simple interest on \( x \) and \( z \) is a simple interest on \( Y \) for same time and rate, then
\( \mathbf{A} \cdot X^{2}=Y Z \)
B . \( Y^{2}=Z X \)
\( \mathbf{c} \cdot Z^{2}=X Y \)
D. \( X Y Z=1 \)


In a dicotyledonous stem, the sequence of tissues from the outside to the inside
is
A. Phellem-pericycle-endodermis-phloem
B. Phellem-phloem-endodermis-pericycle
c. Phellem-endodermis-pericycle-phloem
D. Pericycle-phellem-endodermis-phloem


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O N H}_{2} \frac{\boldsymbol{B r}_{2}}{N a O \boldsymbol{H}} \boldsymbol{A} \)
Aqueous solution of \( \boldsymbol{A} \)
A. Turns blue litmus to red
B. Turns red litmus to blue
c. Does not affect the litmus
D. Decolourise the litmus


Let \( A \) be a square matrix of order \( 3 \times 3 \) then \( |\mathbf{5} \boldsymbol{A}|=? \)
A. \( 5|A| \)
в. \( 125|A| \)
c. \( 25|A| \)
D . \( 15|A| \)


A vehicle is running with a velocity of \( 5 m / s . \) If the momentum of the vehicle
is \( 5000 \mathrm{kg} \mathrm{m} / \mathrm{s}, \) What is its mass?
A. \( 1 \mathrm{kg} \)
в. \( 100 \mathrm{kg} \)
c. \( 1000 k g \)
D. \( 1.1 \mathrm{kg} \)


Write the logic symbols and prepare the truth tables of the following gates.
(i) AND
(ii) NOR.


The angle between the lines \( k x+y+ \)
\( 9=0, y-3 x=4 \) is \( 45^{\circ}, \) then the value
of \( k \) is :
A. 2 only
B. 2 or \( -\frac{1}{2} \)
c. -2 only
D. -2 or \( -\frac{1}{2} \)


Given \( : \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 6 9} \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{E}^{\ominus}=\mathbf{1 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{I}^{\ominus} \rightarrow+\mathbf{2} e^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 5 3 5} \boldsymbol{V} \)
Which of the following statements is / (are) correct?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} O_{2} \) behaves as an oxidant for \( I_{2} / I^{\ominus} \)
B. \( H_{2} O_{2} \) behaves as an reductant for \( I_{2} / I^{\ominus} \)
C \( \cdot I^{\ominus} / I_{2} \) behaves as an reductant for \( H_{2} O_{2} \)
D. None of these is correct.


What is (a) mass defect, and (b)
binding energy in Oxygen \( _{8}^{16} O, \) whose nuclear mass is 15.995 amu. \( \left(m_{p}=\right. \) \( \mathbf{1 . 0 0 7 8 a m u} ; \boldsymbol{m}_{n}=\mathbf{1 . 0 0 8 7 a m u} \)


The enolic for of acetone contains:
A. 9 -sigma, 1 pi-bond and 2 lone pairs
B. 8 -sigma, 2 pi-bond and 2 lone pairs
C. 10 -sigma, 1 pi-bond and 1 lone pair
D. 9 -sigma, 2 pi-bond and 1 lone pair


Infrared lamps are used in restaurants to keep the food warm. The infrared
radiation is strongly absorbed by water, raising its temperature and that of the food. If the wavelength of infrared
radiation is assumed to be \( 1500 n m \)
then the number of photons per second of infrared radiation produced by an infrared lamp, that consumes energy at
the rate of \( 100 W \) and is \( 12 \% \) efficient
only, is \( \left(x \times 10^{19}\right) . \) The value of \( x \) is:
\( \left[\text { Given: } \boldsymbol{h}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right] \)


Assertion
Acetic acid is a colourless liquid that when undiluted is called glacial acetic
acid.
Reason
Acetic acid has a distinctive sour taste
and pungent smell
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


Assertion
Sound waves cannot be polarised.
Reason
Sound waves are longitudinal in nature.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not
the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.


The function of enzyme trypsin is to
A. Breakdown fats
B. Breakdown proteins
C . Synthesise proteins
D. Breakdonwn carbohydrates


Through two parallel wires \( A \) and \( B, 10 A \)
and \( 2 A \) of currents are passed
respectively in opposite directions. If the wire \( A \) is infinitely long and the length of the wire \( \mathrm{B} \) is \( 2 \mathrm{m} \), then force on the conductor \( \mathrm{B} \), which is situated at 10
\( \mathrm{cm} \) distance from \( \mathrm{A}, \) will be
\( \mathbf{A} \cdot 8 \times 10^{-7} N \)
B \( .8 \times 10^{-5} N \)
c. \( 4 \times 10^{-7} N \)
D. \( 4 \times 10^{-5} N \)


If \( \sum_{k=0}^{100} i^{k}=x+i y, \) then the values of \( x \) and y are
A. \( x=-1, y=0 \)
B. \( x=1, y=1 \)
c. \( x=1, y=0 \)
D. \( x=0, y=1 \)


f \( A=\{a, b\} \) and \( B=\{1,2,3\} \) find
\( A \times A \) and \( B \times B \)


Here, A in the above sequence is :
A. ethanol
B. ethyl chloride
c. ethane
D. acetic acid


Which of the following number has same unit digit as its cube?
\( \begin{array}{l}\text { A } \cdot 122^{3} \\ ^{3}\end{array}^{1}^{32} \)
B. \( 168^{3} \)
\( \mathbf{c} \cdot 137^{3} \)
D. \( 184^{3} \)


Which of the following statements is
correct (for zero order reaction)?
A. The rate of a reaction decreases with passage of time as the concentration of reactants decreases.
B. The rate of a reaction is same at any time during the reaction.
C. The rate of a reaction is independent of temperature change.
D. The rate of a reaction decreases with increase in concentration of reactant(s).


What happens on connecting too many appliances at a time to a single socket?


Prove that a median divides a \( \triangle \) into
two \( \triangle^{\prime} s \) of equal area.


Most insecticides attack upon insects
on their
A. Digestive system
B. Reproductive system
c. Nervous system
D. Respiratory system


Q Type your question-
each of different cross-sections and
each part having a piston which can move smoothly in respective tubes. The
two pistons are joined together by an in extensible wire. The combined mass of
the two pistons is 5 kg and area of the cross-section of the upper piston is 10
\( c m^{2} \) greater than that of the lower
piston. Amount of gas enclosed by the pistons is one mole. When the gas is heated slowly, pistons move by \( 50 \mathrm{cm} \). Find rise in temperature of the gas, in the form
\( \frac{15 x}{R} K, \) where \( R \) is universal gas
constant. Use \( g=10 m / s^{2} \) and outside
pressure \( \left.=10^{5} N / m^{2}\right) . \) Fill value of \( ^{\prime} x^{\prime} \)


\( \boldsymbol{A} \stackrel{P h-S O_{2} C l}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{K O H}}{\longrightarrow} \boldsymbol{C} \stackrel{C_{2} \boldsymbol{H}_{5} \boldsymbol{I}}{\longrightarrow} \boldsymbol{D} \)
'C' is water soluble.
Correct structure of \( A \) and \( D \) are?
A \( . R-N H_{2}, P h-S O_{2}-N(R)-\left(C_{2} H_{5}\right)_{2}+I^{-} \)
B. \( R-N H-R, P h-S O_{2}-N R_{2}-C_{2} H_{5} \)
c. \( R-N H_{2}, P h-S O_{2}-N R-I \)
D. \( R_{2} N H, P h-S O_{2}-N R_{2}-\left(C_{2} H_{5}\right)^{+} I^{-} \)


How will you distinguish between fire
extinguishing action of water and \( C O_{2} \)
\( ? \)
A. Water helps to extinguish a fire in two ways: (1) It brings the temperature of the combustible material below its ignition temperature.
(2) The water vapour formed due to the heat of fire cuts the supply of oxygen.
B. Carbon dioxide is highly volatile. So, it immediately vaporises to cut off the supply of air. In the absence of supporter of combustion, fire is extinguished.
\( c . \) Both \( A \) and \( B \)
D. None of the above


Find the mean, variance and standard
deviation for the following frequency distribution.
Classes \( \begin{array}{lll}0- & 10- & 2 \\ 10 & 20 & 3\end{array} \) 30 40
Frequency
१५ 16


Porphyra and Dictyota contain the following pigments respectively
A. Phycoerythrin and fucoxanthin
B. Xanthophyll and \( \gamma \) -phycoerythrin
c. chlorophyll d and chlorophyll b
D. Fucoxanthin and phycoerythrin


Find the value of the polynomial \( 5 x- \)
\( 4 x^{4}+3 \) at
\( \boldsymbol{x}=\mathbf{2} \)


Identify the incorrect order in terms of
atomic radii.
\( \mathbf{A} \cdot N^{3-}>P^{3} \)
B. \( O^{2-}>F^{-} \)
\( \mathrm{c} \cdot \mathrm{Ca}^{2+}>\mathrm{Sr}^{2} \)
D \( \cdot S^{-}>S^{2-} \)
E \( . S^{2-}>O^{-} \)


Filling the blanks. Both elements and compounds are substances.


What happens to the centripetal acceleration of a revolving body if you
double the orbital speed \( v \) and half
angular velocity \( \omega \)
A. It remains unchanged
B. It is halvedd
c. It is doubleo
D. It is quadrupled


Gold is a shining metal which is highly malleable.
A . True
B. False


Assertion
A reflecting type telescope is preferred in astronomy
Reason
Weight of the mirrors are less as
compare the lenses.
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


fthe area of the region bounded by point \( (x, y) \) satisfying the condition
\( \left\{(x, y) ; 0 \leq y \leq x^{2}+1,0 \leq y \leq x+1\right. \)


fixed plane inclined at angle \( \boldsymbol{\theta} \) with
horizontal. A light string is tied to the cylinder at the right most point, and a
mass \( m \) hangs from the string, as
shown in. Assume that the coefficient of
friction between the cylinder and the
inclined plane is sufficiently large to
prevent slipping. For the cylinder to
remain static, the value of m is
\( A \cdot \frac{M \sin \theta}{1-\sin \theta} \)
B. \( \frac{M \cos \theta}{1+\sin \theta} \)
\( c \cdot \frac{M \sin \theta}{1+\sin \theta} \)
D. \( \frac{M \cos \theta}{1-\sin \theta} \)


Figure shown a DC voltage regulator
circuit, with a Zener diode of breakdown
voltage \( =6 V . \) If the unregulated input
voltage varies between \( 10 V \) to \( 16 V \)
then what is the maximum Zener
current?
A. \( 2.5 \mathrm{mA} \)
B. \( 3.5 \mathrm{mA} \)
c. \( 7.5 m A \)
D. \( 1.5 \mathrm{mA} \)


Find \( \frac{d y}{d x} \) for \( y=\log _{e}(x+\sqrt{x^{2}-a^{2}}) \)


A railway wagon of mass \( 10^{5} k g \) is
moving with a velocity of \( 0.5 m s^{-} 1 \) beneath a stationary coal dumper.
When \( 2 \times 10^{5} k g \) of coal is dropped into
it, the velocity of the wagon would be
A \( \cdot 0.333 m s^{-1} \)
В. \( 0.167 m s^{-1} \)
c. \( 0.233 m s^{-1} \)
D. \( 0.133 m s^{-1} \)


How many neutrons are present in tritium nucleus?
A. 0
B.
\( c \cdot 2 \)
\( D \)


Find the A.P whose \( 7^{t h} \) and \( 13^{t h} \) terms
are respectively 34 and 64


A small current element of length \( d l \) and carrying current is placed at (1,1,0) and is carrying current in ' \( +z^{\prime} \) direction. If magnetic field at origin be \( \vec{B}_{1} \) and at point (2,2,0) be \( \vec{B}_{2} \) then
A \( \cdot \vec{B}=\vec{B} \)
B . \( \left|\vec{B}_{1}\right|=\left|2 \vec{B}_{2}\right| \)
c. \( \vec{B}_{1}=-\vec{B}_{2} \)
D . \( \vec{B}_{1}=-2 \vec{B}_{2} \)


Boiling of liquid can take place at any temperature.
A . True
B. False


Six grams of hydrogen gas at a temperature of \( 273 K \) was isothermally expanded to five times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. Find the total amount of heat
absorbed by the gas during the entire process (in joules).
A . 78919.4
в. 78990.2
c. 80281.6
D. 80110.8


In a company the average salary of male employees is Rs 9200 and that of female employees is Rs 8200 If the average salary per employees is Rs 8900 the percentage of female
employees of the total employees is
A . 30
B. 40
\( c .50 \)
D. 25


Give a few applications of Faradays law of induction in daily life.


How much work does a person do in
pushing a box with a force of 20 N over a distance of \( 8.0 \mathrm{m} \) in the direction of the
force?
A . 1.6
B . 16 J
c. 160
D. 1600
E. 16000


The Venn diagram shows sets \( \boldsymbol{\xi}, \mathrm{P} \) and
\( Q \)
The shaded region in the Venn diagram
represents set:
\( A \cdot P \cap Q \)
в. \( P^{\prime} \cap Q \)
c. \( P \cap Q^{\prime} \)
D. \( P^{\prime} \cap Q^{\prime} \)


If \( p, q, r \) have truth values \( T, F, T \) respectively, then which of the following
is True?
A \( \cdot(p \rightarrow q) \wedge r \)
в. \( (p \rightarrow q) \wedge \sim r \)
c. \( (p \wedge q) \wedge(p \vee r) \)
D. \( q \rightarrow(p \wedge r) \)


Consider the following transformations:
(I) \( \quad X e F_{6}+N a F \rightarrow N a^{+}\left[X e F_{7}\right]^{-} \)
(II) \( 2 P C l_{5}(s) \rightarrow\left[P C l_{4}\right]^{+}\left[P C l_{6}\right]^{-} \)
(III) \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+}+H_{2} O \rightarrow \)
\( \left[A l\left(H_{2} O\right)_{5} O H\right]^{2+}+H_{3} O^{+} \)
Correct transformations are :
A . ।,
в. ।,॥
\( c \cdot \) ।,
D. ॥,॥


Bond dissociation enthalpies of \( \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \) and \( N_{2(g)} \) are \( 436.0 K J \) mol \( ^{-1} \) and 941.8
\( K J \) mol \( ^{-1}, \) respectively and enthalpy of
formation of \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}(\boldsymbol{g})} \) is \( -\mathbf{4 6} \boldsymbol{K} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
What is the enthalpy of atomization of
\( N H_{3}_{(g)} \) and the average bond enthalpy
of \( N-H \) bond respectively \( (\text { in } K J \)
\( \left.m o l^{-1}\right) ? \)
A. 1170.9,390.3
B. 117,300
c. 300,200
D. 2000, 1975


Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to
Bohr's atomic model?
A . 0.65 ev
B. 1.9 eV
c. \( 11.1 \mathrm{ev} \)
D. 13.6 ev


Explain the hydrogen bonding in
molecules of \( \boldsymbol{H} \boldsymbol{F}, \boldsymbol{H}_{2} \boldsymbol{O} \) and \( \boldsymbol{N} \boldsymbol{H}_{3} \)


A manufactacturer buys raw material
for Rs. 60,000 and pays \( 4 \% \) tax. He sells the ready stocks for Rs. 92,000 and charges \( 12.5 \% \) tax. Find the VAT paid by the manufacturer.
A . \( R s .13,870 \)
B. \( R s .12,160 \)
c. \( R s .10,370 \)
D. \( R s .9,100 \)


Calculate the total pressure of a mixture of 8 g of oxygen and 4 g of hydrogen confined in vessel of \( 1 d m^{3} \) at
\( 27^{0} C \)
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 3} \quad \text { bar } \quad \boldsymbol{d m}^{3} \boldsymbol{k}^{-1} \boldsymbol{m o l}^{-1}\right) \)


Match list I with list II and select the
correct answer using the codes given
below the lists.
List I List II
I. Cyanide e Ge and e process
A. Ultrapure
\( \| \)
Floatation process Pine oil
B.
III. Electrolytic reduction
C. Extraction of \( A l \)
Iv. Zone refining
D. Extraction of f \( A u \)
\( \mathbf{A} \cdot I-C, I I-A, I I I-D, I V-B \)
B . \( I-D, I I-B, I I I-C, I V-A \)
\( \mathbf{c} \cdot I-C, I I-B, I I I-D, I V-A \)
D . \( I-D, I I-A, I I I-C, I V-B \)


we have taken a saturated solution of
AgBr. Ksp of AgBr is \( 12 \times 10^{-4} \) if \( 10^{-7} \)
mole of \( A g N O_{3} \) are added to 1 litre of
this solution then the conductivity of solution in terms of \( 10^{-7} S m^{-1} \) units
will be \( ? \mathrm{GIVEN} \boldsymbol{\lambda} \boldsymbol{A} \boldsymbol{g}+=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{3}} ; \boldsymbol{\lambda} \)
\( \mathrm{Br}_{-}=6 \times 10^{-3} \mathrm{Sm}^{2} \boldsymbol{m} \)


Form the differential equation
representing the family of curves \( \boldsymbol{y}= \) \( a \sin (x+b), \) where \( a, b \) are arbitrary
constants.


Find the number of electrons
transferred between two points kept at a potential difference of \( 20 \mathrm{V}, \) if 401 of
work is done

Name the colorless transporting fluid found in humans


Among '3d' series of elements, the one
that cannot liberate hydrogen with dil
acids is:
A. cu
B. Sç
\( c \cdot z n \)
D. Mn


Short / Long Answer Types:
What is fermentation and how does it
differ from glycolysis? Mention the benefit of pyruvate reduction during fermentation. What types of organisms carry out lactate fermentation, and
what types carry out alcoholic fermentation?


Sex of a human child is determined by
A. Size of the egg at the time of fertilization
B. Size of the sperm at the time of fertilization
c. Sex chromosome of father
D. Sex chromosome of mother


A ray of light \( O P \) passes through a right
angled prism as shown in the diagram.
Name the phenomenon which the ray
suffers at the face \( \boldsymbol{A C} \)
A. Total Internal Reflection
B. Minimum Deviation
c. Refraction
D. Dispersion


A body falls from a height of 200 m. If gravitational attraction ceases after 2
s, further time taken by it to reach the ground is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A . \( 5 s \)
B. \( 9 s \)
c. \( 13 s \)
D. 17 s


State difference between the blood
vessels-artery,vein and capillary?


Find the \( 12^{t h} \) term of G.P \( 3,6,12,24, \dots . . . \)


Choose the correct answers from the
alternatives given Which one of the following is homologous to the wing of a bat?
A. Tail of a kangaroo
B. Wing of a butterfly
c. Tail fin of a fish
D. Arm of a human


Which is the strongest base?
A. Pyrole
B. Aniline
c. Pyridine
D.


\( \mathrm{XeF}_{2} \) has \( _{-}-\ldots_{-} \) geometry
A. linear
B. tetrahedral
c. coplanar
D. octahedral


Given chemical reaction.
\( \boldsymbol{x} \boldsymbol{S} \boldsymbol{O}_{3}^{2-}+\boldsymbol{y} \boldsymbol{N} \boldsymbol{O}_{2}^{-}+\boldsymbol{2} \boldsymbol{H}^{+} \longrightarrow \boldsymbol{S} \boldsymbol{O}_{4}^{2}+ \)
\( \boldsymbol{z} \boldsymbol{N} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Then \( x+y+z \) is


Which of the following has electrons in
\( \boldsymbol{f} \) orbitals?
A \( \cdot F e^{2} \)
в. \( C l \)
\( c \cdot K^{+} \)
D. \( C s \)
E . \( A u \)


Are breathing \& heartbeat visible
movement??


\( A \triangle A B C \) is right angled at \( A . L \) is a
point on \( B C \) such that \( A L \perp B C \) that
\( \angle B A L=\angle A C B \)


Read the bar graph shown in fig.23.8
and answer the following questions:
How many tickets of Assam State
Lottery were sold by the agent?
graph lotteries sold by an agent on a day


A particle moves along positive X-axis
from \( x=0 \) to \( x=5 \) under influence of force
is given by \( F=x^{2}-2 x-8 . \) The work
done by the force is
A . - 69 units
B. -23.33 units
c. - - - units
D. zero


Which from the following works on the principle of electromagnetism?
A. Bar megnet
B. Electric bell
c. Fuse
D. Earthing


Find how the total acceleration \( \omega \) of the
balloon depends on the height of ascent.
A. \( \omega=2 a v_{0} \)
B. \( \omega=-2 a v_{0} \)
c. \( \omega=a v_{0} \)
D. \( \omega=-a v_{0} \)


A straight line \( r=a+\lambda b \) meets the
plane \( r . n=0 \) in \( P . \) The position vector
of \( \boldsymbol{P} \) is
A \( \cdot a+\frac{a \cdot n}{b \cdot n} b \)
B. \( a+\frac{b . n}{a . n} b \)
c. \( _{a-} \frac{a . n}{b . n} b \)
D. None of these


The phenomenon of electromagnetic
induction is :
A. the process of charging a body
B. the process of generating magnetic field due to a current passing through a coil
C. producing induced current in a coil due to relative motion between a magnet and the coil
D. the process of rotating a coil of an electric motor


The mean and variance of Binomial
Distribution are 4 and 2 respectively, then the probability of success is
A \( \cdot \frac{128}{256} \)
в. \( \frac{219}{256} \)
c. \( \frac{37}{256} \)
D. \( \frac{28}{256} \)


Match list I and list II.
List I

List II
\( \mathbf{A} \cdot_{\mathbf{1}}^{2} \boldsymbol{H}+_{\mathbf{1}}^{\mathbf{3}} \boldsymbol{H} \rightarrow_{\mathbf{2}}^{\mathbf{4}} \boldsymbol{H} \boldsymbol{e}+_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n}+\mathbf{1 7} \mathbf{. 6} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} \)
1. Artificial radioactivity
B. \( _{92}^{235} U+_{0}^{1} n \rightarrow_{56}^{143} B a+_{36}^{90} K r+3_{0}^{1} n+ \)
\( 200 M e v \quad \) 2. Isodiaphers
\( \mathrm{C} \cdot_{13}^{23} A l+_{2}^{4} H e \rightarrow_{14}^{30} S i+_{1}^{1} H \)
3. Atom Bomb
\( \mathrm{D} \cdot_{Z}^{m} \boldsymbol{A} \stackrel{-\alpha^{m-4}}{\rightarrow}_{Z-2} \boldsymbol{B} \)
4. Nuclear Fissio
5. Nuclear Fusion
\( A \cdot A-5 ; B-3,4 ; C-1 ; D-2 \)
B. A - 2; B - 3,4; C - 1; D - 5
c. \( A-1,5 ; B-3 ; C-4 ; D-2 \)
D. A - 3,4; B - 1; C - 5; D - 4,2


Write the monomers used for getting
the following polymers.
(i) Polyvinyl chloride
(ii) Teflon
Bakelite


Evaluate :
\( \frac{6 x^{2}-x-2}{3 x-2} \)


An object starting from rest travels 20 \( \mathrm{m} \) in first \( 2 \mathrm{s} \) and \( 160 \mathrm{m} \) in next \( 4 \mathrm{s} \)
What will be the velocity \( (\text { in } \boldsymbol{m} / \boldsymbol{s}) \) after 7 s from the start.
A. 0
B. 10
\( c \cdot 65 \)
D. 70


Solubility product of \( B a(O H)_{2} \) and
\( A l(O H)_{3} \) are \( 1.8 \times 10^{-10} \) and \( 2.4 \times \)
\( 10^{-20} \) respectively. If both \( A l^{+3} \) and
\( B a^{+2} \) ions are present is a solution,
which one will be ppt on addition of ammonium hydroxide solution
A \( \cdot \operatorname{Ba}(O H)_{2} \)
в. \( _{A l}(O H)_{3} \)
c. Both are precipitated at same time
D. Both are not precipitated


Solution of \( (x+y)^{2} \frac{d y}{d x}=a^{2}\left(^{\prime} a^{\prime} \) being a \right.
constant) is:
A \( \cdot \frac{(x+y)}{a}=\tan \frac{y+c}{a}, c \) is an arbitrary constant
B. \( x y=a \tan c x, c \) is an arbitrary constant
c. \( \frac{x}{a}=\tan \frac{y}{c}, c \) is an arbitrary constant
D. \( x y=\tan (x+c), c \) is an arbitrary constant


If \( \vec{P}(1,5,4) \) and \( \vec{Q}(4,-1,-2), \) find the direction ratio of \( \overrightarrow{P Q} \)


An uncharged insulator can be charged by with another suitable body
A. diverging
B. induction
c. rubbing
D. excess


EEG can help in diagnosing certain conditions like
A. Epilepsy
B. Encephalitis
c. Dementia
D. All of the above


Which of the following is true about the reaction \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{S} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} ? \)
This question has multiple correct options
A \( \cdot F e+2 e^{-} \rightarrow F e^{2+} \)
B. \( F e \rightarrow F e^{2+}+2 e^{-} \)
C \( \cdot F e^{2+} \rightarrow F e+2 e^{-} \)
D. \( S \rightarrow S^{2-}+2 e^{-} \)
E \( . S+2 e^{-} \rightarrow S \)


(a) NAND gates are also called universal gate. Why?
(b) Draw a logic symbol of OR gate.
(c) Write the value of output \( y \) in the
given circuit:
(d) Write the name of the diode used in
voltage regulation.
Input \( a=1-\square \) output \( y \)


Which of the following represents
petiole?
\( A \)
\( B \)
\( c \)
\( D \)


A cradle is \( h \) meters above the ground
at the lowest position and \( H \) meters
when it is at the highest point. If \( v \) is the maximum speed of the swing having
total mass \( m \), then the relation between
\( \boldsymbol{h} \) and \( \boldsymbol{H} \) is:
A \( \cdot m v^{2}+h=H \)
в. \( \frac{v^{2}}{2 g}+h=H \)
c. \( \frac{v^{2}}{2 g}+2 h=H \)
D. \( \frac{v^{2}}{2 g}+H=h \)


Example of proper fraction from the given options is
A \( \cdot \frac{5}{7} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{16}{15} \)
D. \( \frac{22}{21} \)


Differentiate \( 5^{\log \sin x} \) w.r.t. \( x \)


A slit of width a is illuminated by the
red light of wavelength \( 6500 A^{0} . \) If the
first minimum falls at \( \theta=30^{\circ}, \) the value
of a is
A \( \cdot 6.5 \times 10^{-4} m m \)
B. 1.3 micron
c. \( 3250 A^{\circ} \)
D. \( 2.6 \times 10^{-4} \mathrm{cm} \)


The term photorespiration was coined by
A. Decker and Tio.
B. Julius von Sachs
c. Rouhani.
D. O-leri


If \( \boldsymbol{x}=(-\mathbf{3}), \) then find the value of
\( \left(x^{2}\right)^{3} \times\left(\frac{1}{x}\right)^{4} \times x \)
A \( \cdot(-25) \)
B . (-27)
c. (-15)
D. None of these


If the body covers a circular path with
constant angular speed \( 4 \pi \) rad/sec. Then frequency of the body is
\( A \cdot 1 H z \)
B. 0.5 Hz
c. 2 н \( z \)
D. 1.5 Нz


The slope of the line joining the point (-8,-3) and (8,3) is
A \( \cdot \frac{8}{3} \)
в. \( \frac{3}{8} \)
\( c \cdot 0 \)
D. -


In the equation \( y=k x+3, k \) is a
constant. If \( \boldsymbol{y}=\mathbf{1 7} \) when \( \boldsymbol{x}=\mathbf{2}, \) what is
the value of \( \boldsymbol{y} \) when \( \boldsymbol{x}=\mathbf{4} ? \)
A . 34
B. 31
c. 14
D. 11
\( E .7 \)


What forms the backbone of a
polynucleotide strand of a nucleic acid?


Compound (A) is:
\( \mathbf{A} \)
\[
C H_{3}-\underset{_{C H_{3}}^{\mid}}{C}^{\text {сснз }}-C H_{2} C H_{2} B r
\]
В. \( C H_{3}-\begin{array}{c}C H-C H-C H_{2} B r \\ _{I H_{3}}^{\mid}\end{array} \)
D.
\[
C H_{3}-\underbrace{C}_{C H_{3}}^{\text {СС }}-C_{\text {। }} H-C H_{3}
\]


Among the following, the surfactant that will form micelles in aqueous
solution at the lowest molar
concentration at ambient conditions is :
A \( \cdot \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{15} \mathrm{N}^{+}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Br} \)
B. \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{OSO}_{3}^{-} \mathrm{Na}^{+} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{COO}^{-} \mathrm{Na}^{+} \)
D. \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{N}^{+}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Br} \)


Select incorrect statements.
A. \( N H_{3} \) is soluble in water due to hydrogen bonding as well as due to formation of ions.
B. Gases which can be liquefied easily are more soluble in water then the gases which cannot be liquefied.
C. The solute follows Henry law at all pressure of gas.
D. The solute follows Henry law at low pressure of gas.


The de-Broglie wavelength of a proton accelerated by \( 400 \mathrm{V} \) is
A \( .0 .005 \AA \)
B . 1.0528 ,
c. \( 0.0568 \dot{A} \)
D. \( 0.0143 \dot{A} \)


What bring the rolling ball to rest?
A. Force of friction
B. Gravitational force
c. Air drag
D. Buoyant force


Which one of the following pair is
mismatched?
A. Nuclear power-radioactive wastes
B. Solar energy-greehouse effect
C. Fossil fuel burning- release of \( \mathrm{CO}_{2} \)
D. Biomass burning- release of \( \mathrm{CO}_{2} \)


Read the given statements and select
the correct option
Statement 1: Ethylene is a gaseous hormone.
Statement 2 : Ethylene causes climacteric ripening of fruits.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect


The function \( \boldsymbol{f}:[\mathbf{0}, \infty) \rightarrow \boldsymbol{R} \) given by
\( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\boldsymbol{x}+\mathbf{1}} \) is
A. one-one and onto
B. one-one but not onto
c. onto but not one-one
D. neither one-one nor onto


Identify the correct statement from
below:
\( \mathbf{A} \cdot \) A will be at higher potential
B. B will be at higher potential
C. Both will be at same potential
D. Can't be said


Column Column II (Compouds) \( \quad \) (Characteristic property)


The area of the figure bounded by two branches of the curve \( (\boldsymbol{y}-\boldsymbol{x})^{2}=\boldsymbol{x}^{3} \)
and the straight line \( x=1 \) is:
A \( \cdot \frac{1}{3} \) sq.unit
B \( \cdot \frac{4}{5} \) sq.unit
c. \( \frac{5}{4} \) sq.unit
D. 3 sq.unit


Find sides a cube is \( 17.5 \mathrm{cm} \) find volum
of cube


If the centroid of tetrahedron \( O A B C \)
where \( A, B, C \) are given by \( (a, 2,3),(1, b, 2) \) and \( (2,1, c) \)
respectively is \( (1,2,-2), \) then distance of \( \boldsymbol{P}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) from origin is
\( \mathbf{A} \cdot \sqrt{195} \)
в. \( \sqrt{14} \)
c. \( \sqrt{\frac{107}{14}} \)
D. \( \sqrt{13} \)


If \( N a C l O \) is added to water, then the
ion that undergoes hydrolysis is:
A . \( N a^{\text {t }} \)
B. \( C l O^{-} \)
c. both \( N a^{+} \) and \( C l O^{-} \)
D. \( C l \)


The work done in turning a magnet of magnetic moment \( M \) by an angle of \( 90^{\circ} \)
from the meridian is \( n \) times the
corresponding work done to turn it through an angle of \( 60^{\circ} \) from the
meridian, where \( n \) is given by :
A \( \cdot \frac{1}{2} \)
B. 2
\( c \cdot \frac{1}{4} \)
D.


If \( m \) is the mass of drop of a liquid of radius \( r, \) then \( \frac{m g}{\pi r} \) has the same dimensions of :
A. Surface tension
B. Tension
c. Young's Modulus
D. coefficient of viscosity


A boat at anchor is rocked by waves
whose crests are \( 100 m \) apart and
velocity is \( 25 m / s \). The boat bounces up once in every:
\( \mathbf{A} \cdot 2500 s \)
в. \( 75 s \)
c. \( 4 s \)
D. \( 0.25 s \)


Evaluate the following limits. \( \lim _{x \rightarrow 2} \frac{x^{3}-8}{x^{2}-4} \)


Obtain a differential equation by
eliminating \( c \) when it is given
\( \tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} c \)


Acetamide on treatment with \( L i A l H_{4} \)
forms:
A. ethyl amine
B. ethanoic acid
c. ethanimine
D. none of these


A closed curve has no
This question has multiple correct options
A. joints
B. starting points
C . end points
D. All of the above


In which of the following species maxium atom lie in same plane?
A. \( X e F_{2} O_{2} \)
в. \( P C l_{5} \)
c. \( A s H_{4}^{\text {t }} \)
D. \( X e F_{4} \)


The smallest integer n such that \( \left(\frac{1+i}{1-i}\right)^{n}=1 \) is
A . 16
B. 12
\( c \cdot 8 \)
D.


Statement-1: If the Earth suddenly contracts to \( \frac{1}{n} \) th of its present size without any change in its mass.

Statement-2:The duration of the new
day will be \( \frac{24}{n} \) hrs.
A. Statement-1 is True, Statement-2 is True; Statement-2
is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Write any two arithmetic progressions
with common difference 3


In the given Figure, \( A B C \) is a straight
line what is the value of \( z ? \)
\( \mathbf{A} \cdot 112^{\circ} \)
B. \( 92^{\circ} \)
c. \( 132^{\circ} \)
D. \( 106^{\circ} \)


Nitrogen reacts with a metal \( M \) to produce a compound \( X . \) This compound \( X \) when dissolved in water forms
pungent gas \( Y \) which can be identified
easily by the formation of white fumes
in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify \( Y: \)
A. Nitrogen dioxide
B. Ammonia
c. Nitrous oxide
D. Nitric oxide


Which has the highest \( p H ? \)
A. \( C H_{3} C O O N H_{4} \)
в. \( N a_{2} C O_{3} \)
c. \( N H_{4} C l \)
D. \( N a N O_{3} \)


Find the value of the multiplication \( 3.124 \times 4.576 \) correct to three
significant figures.


A weightless string passes through a slit over a pulley. The slit offers
frictional force \( \boldsymbol{f} \) to the string. The
string carries two weights having
masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) where \( \boldsymbol{m}_{2}>\boldsymbol{m}_{1} \)
then acceleration of the weights is:
A \( \cdot \frac{\left(m_{2}-m_{1}\right) g-f}{m_{1}+m_{2}} \)
B. \( \frac{f-\left(\left(m_{2}-m_{1}\right) g\right.}{\left(m_{1}+m_{2}\right)} \)
C \( \cdot \frac{\left(m_{1}+m_{2}\right) g-f}{m_{1}-m_{2}} \)
D. \( \frac{m_{2} g-f}{\left(m_{1}+m_{2}\right)} \)


Match the column with types of polymer
in list I with their examples in list II.
List -
List - II
A) Natural Polymer
1) PVC
B) Ehene Polymer
2) Nylon - 6,6
C) Polyamide polymer
3) Silk
D) Vinylchloride polymer
4) Polyethylene
A. \( A-2, B-3, C-4, D-1 \)
в. \( A-3, B-2, C-1, D-4 \)
c. \( A-3, B-4, C-2, D-1 \)
D. \( A-3, B-2, C-4, D-1 \)


Position vectors of mid point of the
vector joining the points \( \boldsymbol{P}(\mathbf{2}, \mathbf{3}, \mathbf{4}) \) and \( Q(4,1,-2) \) is
\( \mathbf{A} \cdot 2 \hat{i}+\widehat{j}+\widehat{k} \)
B. \( 3 \hat{i}+2 \hat{j}+\widehat{k} \)
c. \( -3 \hat{i}-\hat{j}+\widehat{k} \)
D. None


A charged particle 'q' lies at 'P' and the line \( \mathrm{PC} \) is perpendicular to the surface of \( A B C \) (part of disc). Find the flux passing through the surface ABC.
A \( \cdot \frac{q}{4 \varepsilon_{0}} \)
в. \( \frac{q}{16 \varepsilon_{0}} \)
c. \( \frac{q}{32 \varepsilon_{0}} \)
D. \( \frac{q}{48 \varepsilon_{0}} \)


For what value of \( k \) the function \( f(x)= \) \( \left\{\begin{array}{l}\frac{\sin 5 x}{3 x}, i f, x \neq 0 \\ k, \text { if } x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)


Integrate:
\( \int \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}} d x \)


A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact
lasts for time \( \Delta t \), Then :
This question has multiple correct options
A. the average elastic force acting on the ball is \( [m(u+ \)
\( v)] / \Delta t \)
B. the average elastic force acting on the ball is \( [2 m(u+ \)
\( v)] / \Delta t \)
c. the kinetic energy of the ball increases by 2 mu \( (u+v) \)
D. the kinetic energy of the ball remains the same after the collision


The correct order of lattice energy is:
\( \mathbf{A} \cdot L i F>C a F_{2}>M g O \)
B. \( M g O>C a F_{2}> \) LiF
\( \mathbf{c} \cdot C a F_{2}>M g O>L i F \)
D. \( C a F_{2}>L i F>M g O \)


Ethylene is used for
A. Decrease the senescence
B. Increase the height of stem
C. Ripening of fruits
D. Prevention of leaf fall


Let \( x=\log _{4} 9+\log _{9} 28 \)
show that \( [x]=3, \) where \( [x] \) denotes the
greatest integer less than or equal to \( x \)


Evaluate the following integration w.r.t.
\( \boldsymbol{x} \)
\( \int \frac{1}{(4 x+5)^{2}+1} d x \)


Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The
area around the magnets is divided into
four zones. Given that there is a neutral
point it is located in.
A. Zone I
B. Zone II
C. Zone III
D. Zone IV


The harmonic mean and geometric mean of two positive numbers are in the
ratio \( 4: 5, \) then two numbers are in the
ratio
A . 4: 1
B. 3: 1
\( c \cdot 2: 1 \)
\( D .5: \)


In which of the following algae like characters are presents?
A . Riccia
B. Marchantia
c. Ricciocerpus
D. Anthoceros


Calculate the inductance of a unit
length of a double tape line as shown in
figure. The tapes are separated by a
distance \( h \) which is considerably less
than their width \( b \)
A \( \cdot \frac{\mu_{0}}{b} \)
B. \( \frac{\mu_{0} h}{\text { sh } h} \)
c. \( \frac{2 \mu_{0} h}{b} \)
D. \( \frac{\sqrt{2} \mu_{0} h}{b} \)


The radius of the stationary state which is also called Bohr radius is given by the
expression \( r_{n}=n^{2} a_{0} \) where the value
of \( a_{0} \) is:
A. 52.9 pm
B. 5.29 pm
c. \( 529 \mathrm{pm} \)
D. 0.529 pm


Assertion
An emf \( \vec{E} \) is induced in a closed loop
where magnetic flux is varied. The induced \( \vec{E} \) is not a conservative field.
Reason The line integral \( \overrightarrow{\boldsymbol{E}} \cdot \boldsymbol{d l} \) around
the closed loop is nonzero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A body of weight \( w \) is lying at rest on a rough horizontal surface. If the angle of friction is \( \theta \), then the minimum force
required to move the body along the surface will be:
A . \( w \cos \theta \)
B. \( w \tan \theta \)
c. \( w \sin \theta \)
D. \( w \cot \theta \)


Permanent hardness is due to the
presence of soluble salts of Mg and Ca in the form of chlorides and sulphates
in \( H_{2} O . \) It can be removed by:
A. boiling
B. the Clark's method
c. treatment with \( N a_{2} C O_{3} \)
D. all of these


Let \( a, b, c \epsilon R \) such that \( a+b+c=0 \) and
\( a+b-c=0, \) then the polynomial function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} ;(\boldsymbol{a}>\boldsymbol{0}) \)
attains its least value at 'x' equal to
\( A \cdot O \)
в.
\( c \cdot \frac{1}{2} \)
D. not possible


If \( \angle B A D \) and \( \angle D A C \) form a linear pair
and \( a^{\circ}-b^{\circ}=60^{\circ} \) then find the values
of \( a \) and \( b \)


Given the polymers
\( A= \) Nylon 6,\( 6 ; B= \) Buna-S; \( C= \) Polythene.
Arrange these in decreasing order of their intermolecular forces.
\( A \cdot A>B>C \)
в. \( B>C>A \)
c. \( B<C<A \)
D. \( C<A<B \)


In figure. the galvanometer shows no deflection. What is the resistance \( X ? \)
\( A \cdot 7 \Omega \)
в. \( 14 \Omega \)
\( c .21 \Omega \)
D. \( 28 \Omega \)


If \( A \) and \( B \) are two sets containing four and two elements, respectively. Then the
number of subsets of the set \( \boldsymbol{A} \times \boldsymbol{B} \)
each having at least three elements is
A .219
в. 256
c. 275
D. 510


Two sides of a rhombus are along the
lines, \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{7} \boldsymbol{x}-\boldsymbol{y}-\mathbf{5}= \)
0. If its diagonals intersect at (-1,-2)
then which one of the following is a
vertex of this rhombus??
\( ^{\mathrm{A}} \cdot\left(-\frac{10}{3},-\frac{7}{3}\right) \)
в. (-3,-9)
c. (-3,-8)
D. \( \left(\frac{1}{3},-\frac{8}{3}\right) \)


If Rolle's theorem is applicable to the function \( f(x)=\frac{\ln x}{x},(x>0) \) over the interval \( [a, b] \) where \( a \epsilon I, b \epsilon I, \) then the value of \( a^{2}+b^{2} \) can be
A . 20
B . 25
c. 45
D. 10


Which selection applies to the process shown below?
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(l) \rightarrow \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) \)
A. \( \Delta H_{f u s} \)
в. \( \Delta H_{c} \)
c. \( \Delta H_{s o l n} \)
D. \( \Delta H_{v a p} \)


State Gauss' law. Using this find an expression for electric field due to an infinitely long straight charged wire uniform charge density


For an ideal binary liquid solution with
\( P_{A}^{\circ}>P_{B}^{\circ}, \) which relation between \( X_{A} \)
(mole fraction of \( A \) in liquid phase) and
\( Y_{A}(\text { mole fraction of } A \text { in vapour phase }) \)
is correct?
\( \mathbf{A} \cdot Y_{A}<Y_{B} \)
В . \( X_{A}>X_{B} \)
c. \( \frac{Y_{A}}{Y_{B}}>\frac{X_{A}}{X_{B}} \)
D. \( \frac{T_{A}}{Y_{B}}<\frac{X_{A}}{X_{B}} \)


'Abirin' and 'ricin' are toxic plant
proteins which inhibit the protein synthesis in eukaryotic ribosomes by inactivating the
A. 40 s subunit
B. 60S subunit
\( c \cdot 60 s \) and \( 40 S \)
D. Genetic code


Element showing the phenomenon of allotropy is:
A . \( A l \)
в. \( P b \)
\( c \cdot s n \)
D. \( C u \)


Two conducting spheres of radii \( r_{1} \) and
\( r_{2} \) are charged to the same surface
charge density. The ratio of electric
fields near their surface is :
A \( \cdot r_{1}^{2} / r_{2}^{2} \)
B . \( r_{2}^{2} / r_{1}^{2} \)
\( \mathbf{c} \cdot r_{1} / r_{2} \)
D. 1: 1


The specific conductance of a saturated
solution of silver bromide is \( \kappa \mathbf{S} \mathrm{cm}^{-1} \)
The limiting ionic conductivity of
\( A g^{+} \) and \( B r^{-} \) ions are \( x \) and \( y \)
respectively. The solubility of silver bromide in \( \mathrm{gL}^{-1} \) is:
[molar mass of \( \mathrm{AgBr}=188 \)
A. \( \frac{\kappa \times 100}{x-y} \)
B. \( \frac{\kappa}{x+y} \times 188 \)
c. \( \frac{\kappa \times 1000 \times 188}{x+y} \)
D. \( \frac{x \times y}{\kappa} \times \frac{1000}{188} \)


Find \( \frac{d y}{d x}, \) if \( y=\sin ^{3} x \cos ^{5} x \)


At what depth in an ocean will a bubble
of air have one fourth the volume it will
have on reaching the surface?
(Atmospheric pressure \( =\mathbf{7 6} \) cm of \( \boldsymbol{H} \boldsymbol{g} \)
and density of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} \boldsymbol{c m}^{-3} \mathbf{)} \)


The rate of photosynthesis does not depends upon
A. Light duration
B. Light intensity
c. Light quality (colour)
D. Temperature


Saliva has the enzyme
A. Pepsin
B. Ptyalin
c. Trypsin
D. Rennin