Water jet is coming out of a hose pipe of diameter \( 20 \mathrm{cm} \) with speed \( 20 \mathrm{cm} / \mathrm{sec} \)
It strike a man inelastically. Find the force exerted by water jet on the person.
A . \( 5.04 N \)
B. \( 1.26 N \)
c. \( 2.52 N \)
D. \( 9.4 N \)


Read the assertion and reason carefully to mark the correct option out of the
options given below:

Assertion: An astronaut in a satellite
feels weightlessness.
Reason: As observed by another
astronauts in the same satellite, force
of gravity and centrifugal force balance
each other.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
C. If assertion is true but reason is false
D. If assertion is false but reason is true


AC generator means
A. Acquired continuity generator
B. Assistant current generator
C . Alternating current generator
D. none


In some places a hard, cement concrete structure with pores is desired. The concrete pores can be made by the release of oxygen gas from inside the concrete by:
A. steam
B. hydrogen peroxide
c. sodium peroxide
D. ozone


A volume of \( 2.5 ~ L \) of a sample of a gas
at \( 27^{\circ} \mathrm{C} \) and 1 bar pressure is
compressed to a volume of 500 ml keeping the temperature constant, the percentage increase in pressure is?
\( \mathbf{A} \cdot 100 \% \)
B. \( 400 \% \)
c. \( 500 \% \)
D. \( 80 \% \)


Find the number of an element(s) which
is/are present in group-II. \( \boldsymbol{B} \boldsymbol{a}, \boldsymbol{K}, \boldsymbol{C} \boldsymbol{a}, \boldsymbol{C} \boldsymbol{s}, \boldsymbol{R} \boldsymbol{b}, \boldsymbol{n} \)


Which of the following diagrams shows a non-luminous flame?
A. I only
B. II only
c. I and II
D. II and IV


Which of the following is the most effective in causing coagulation of ferric hydroxide solution?
A. \( K C l \)
в. \( K N O_{3} \)
\( \mathrm{c} \cdot K_{2} \mathrm{SO}_{4} \)
D \( \cdot_{K_{3}}\left[F e(C N)_{6}\right] \)


Express 0.000840 in scientific notation.
A. \( 8.4 \times 10^{-3} \)
B. \( 8.40 \times 10^{4} \)
c. \( 8.40 \times 10^{-4} \)
D. \( 8.4 \times 10^{4} \)


Four curves \( A, B, C \) and \( D \) are drawn in
figure for a given amount of gas. The curves which represent adiabatic and
isothermal changes are.
A. \( C \) and \( D \), respectively
B. \( D \) and \( C \), respectively
c. \( A \) and \( B \), respectively
D. \( B \) and \( A \), respectively


The algebraic sum of the deviations of a
set of \( n \) values from their mean is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( n-1 \)
\( c \cdot 1 \)
D.


Mitochondria is the site for
A. Krebs cycle
B. Calvin cycle
C. Anaerobic respiration
D. Trapping of sun light


Physical adsorption is appreciable at temperature
A. low
B. highh
C. very high
D. moderate


Ethane, with the molecular formula
\( C_{2} H_{6} \) has:
A. 6 covalent bonds
B. 7 covalent bonds
c. 8 covalent bonds
D. 9 covalent bonds


Which polynomial represents this plot?
A. cubic
B. biquadratic
c. quadratic
D. linear


The length of side \( \boldsymbol{P S}= \)
A. \( 4.2 \mathrm{cm} \)
в. \( 6.7 \mathrm{cm} \)
c. \( 5.1 \mathrm{cm} \)
D. \( 3.5 \mathrm{cm} \)


n figure, \( \boldsymbol{k}=\mathbf{1 0 0} \boldsymbol{N} / \boldsymbol{m}, \boldsymbol{M}= \)
1 kgand \( F=10 N . \) A sharp blow by
some external agent imparts a speed of \( 2 m / s \) to the block towards left. Find the
sum of the potential energy of the spring and the kinetic energy of the block at this instant.
A . \( 0.25 J \)
в. 1.5
\( c \cdot 2 J \)
D. 2.5 5


An ideal heat engine working between
temperatures \( T_{1} \) and \( T_{2} \) has an
efficiency \( \eta \). The new efficiency if the temperatures of both the source and sink are doubled, will be
\( A \cdot \frac{\eta}{2} \)
B. \( \eta \)
c. \( 2 \eta \)
D. \( 3 \eta \)


Solve:
\( \mid \begin{array}{ccc}x^{2}-1 & x^{2}+2 x+1 & 2 x^{2}+3 x \\ 2 x^{2}+x-1 & 2 x^{2}+5 x-3 & 4 x^{2}+4 x \\ 6 x^{2}-x-2 & 6 x^{2}-7 x+2 & 12 x^{2}-5\end{array} \)
0. Let sum of all values of \( x \) be \( k \). Find
\( -2 k \)


Consider the double helix structure of
DNA. In this base pairs are present
A. part of the back bone structure
B. inside the helix
c. outside the helix
D. none of these


The correct order of basicity of the following amines is:
A \( . I>I I>I I I>I V \)
В. \( I>I I I>I I>I V \)
c. \( I I I>I I>I>I V \)
D. \( I V>I I I>I I>I \)


Fill in the blank:
The member of our solar system, with highly tilted orbit, is
A. Earth
B. Pluto
c. Mars
D. Saturn


The soultion of \( 3 e^{x} \cos ^{2} y d x+(1- \)
\( \left.e^{x}\right) \cot y d y=0 \) is


The adjoining figure shows a negatively charged electroscope. If a positively
charged rod touches the knob, the two
leaves will
A. move closer together
B. move farther apart
c. not move at all
D. become positively chargedd


Factorize:
\( 169 p^{2}-625 q^{2} \)


A solid sphere of diameter \( 12 \mathrm{cm} \) is melted and draw into a wire of radius \( \mathbf{1} \)
\( \frac{1}{5} c m \) then the length of the wire is
A . \( 108 \mathrm{m} \)
в. 72 \( \mathrm{m} \)
\( c \cdot 84 m \)
D. None


An astronaut accidentally gets separated out of his small spaceship accelerating in inter steller space at a
constant rate of \( 100 m s^{-2} \). What is the
acceleration of the astronaut the
instant after he is outside the
spaceship? (Assume that there are no
nearby stars to exert gravitational force on him.)


State the following statement is True or
False
The truth value of "4 is even and 8 is
odd" is True
A. True
B. False


The presence of electrolytes the
rate of corrosion.
A. increases
B. decreases
c. sharply decreases
D. does not effect


Parallax method is suitable for the
measurement of:
A . ball
B. planet
c. vehicle
D. distance between cities


For a given reaction of first order, it takes 20 minutes for the concentration
to drop from \( 1.0 \mathrm{M} \) to \( 0.6 \mathrm{M} \). The time
required for the concentration to drop from \( 0.6 ~ M \) to \( 0.36 M \) will be:
A. more than 20 minutes
B. less than 20 minutes
c. equal to 20 minutes
D. infinite time


I. The ideal gas law can be applied to a
sample of xenon at a temperature of
\( -273^{\circ} C \)
II. Xenon is a noble gas.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement \( I I \) is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)


Which of the following is correct about
the adsorption of \( N_{2} \) over iron?
A. It is always physically adsorbed
B. Extent of adsorption over iron decreases with the increase in temperature first and then increases
c. It is always chemically adsorbed
D. \( N_{2} \) is never adsorbed over iron


At what temperature the linear kinetic energy of a gas molecule will be equal to that of an electron accelerated through a potential difference of 10 volt?
A . \( 77.3 \times 10^{3} \mathrm{K} \)
B. 38.65 x 10 \( ^{3} \) к
c. \( 19 . \times 10^{3} \mathrm{K} \)
D. 273 K


Express \( q \) as a function of time.
A \( \cdot 10^{4} \cos \left(6.28 \times 10^{3} t\right) \)
B \( \cdot 10^{-4} \cos \left(9.28 \times 10^{3} t\right) \)
\( \mathbf{c} \cdot 10^{-4} \cos \left(6.28 \times 10^{3} t\right) \)
D \( \cdot 10^{-4} \cos \left(6.28 \times 10^{-3} t\right) \)


Draw a circle with centre 0 and radius 3.5
\( \mathrm{cm} . \) Take point \( \mathrm{P} \) at a distance \( 5.7 \mathrm{cm} \) from
the centre. Draw tangents to the circle from point \( P \)


\( 90 \% \) of a first order reaction was
completed in 100 min. What is the half
life of the reaction?
\( A \cdot 63.3 \min \)
B. 53.3 min
c. 43.3 min
D. 30 min


The magnetic flux linked with a coil is
\( \phi \leq 8 t^{2}+3 t+5 \) Weber. The induced
emf in fourth second will be
\( \mathbf{A} \cdot 16 V \)
B. \( 139 V \)
\( c .67 V \)
D. \( 145 V \)


A ray of light travelling in air falls on the surface of a rectangular slab of a plastic material whose refractive index is \( 1.6 . \) If the incident ray makes an angle of \( 53^{\circ} \) with the normal \( \left(\sin 53^{\circ}=4 / 5\right) \)
find the angle made by the refracted ray with the normal.


The coefficient of mutual induction
between two coils is \( 4 \mathrm{H} \). If the current in
the primary reduces from 5 A to zero in \( 10^{-3} \) second then the induced emf in the
secondary coil will be
A \( \cdot 10^{4} v \)
B . \( 25 \times 10^{3} \mathrm{V} \)
C \( \cdot 2 \times 10^{4} \mathrm{V} \)
\( \mathbf{D} \cdot 15 \times 10^{3} \mathbf{v} \)


represent the motion of a raindrop?
\( A \)
B.
\( c \)
\( D \)


(a) Three resistors \( 2 \Omega, 4 \Omega \) and \( 5 \Omega \) are
combined in parallel. What is the total resistance of the combination?
(b) If the combination is connected to a
battery of emf \( 20 \mathrm{V} \) and negligible internal resistance, determine the
current through each resistor, and the total current drawn from the battery.


\( A \equiv(1,2) \) and \( B \equiv(7,10) \) are two points. If \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is a point such that
\( \angle A P B=60^{\circ} \) and area of \( \Delta A P B \) is
maximum, then which of the following is (are) TRUE?
This question has multiple correct options
A. \( P \) lies on any line perpendicular to \( A B \)
B. \( P \) lies on the perpendicular bisector of \( A B \)
c. \( P \) lies on the line \( 3 x+4 y=36 \)
D. Radius of circumcircle of \( \Delta P A B \) is 10 units


An under-water swimmer cannot see
very clearly even in absolutely clear water because of:
A. Absorption of light in water
B. Scattering of light in water
c. Reduction of speed of light in water
D. Change in the focal length of eye lens.


A conducting circular loop of radius carries a constant current I. It is placed in a uniform magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force acting on the loop is
\( \mathbf{A} \cdot \) Вᅵ
В. 2 \( \pi \) (ВЮА)
c. zero
D. \( \pi \) (ВIR)


Ozone turns trimethyl paper:
A. green
B. violet
\( c \cdot \) red
D. black


Which of the following is an isotope of hydrogen?
A. Deuterium
B. Trinium
c. Promium
D. All of the above


How many periods are there in the long form of the periodic table?
A. 6
B. 7
\( c \cdot 8 \)
\( D \)


Balance the following equation by
oxidation number method.
\( \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


A person skilled in taxidermy is called
as
A. Taxonomist
B. Taxidermist
c. Archeologist
D. Scientist


Explain why \( O_{2} \) molecule is paramagnetic in nature? Write
Molecular Orbital configuration of \( \boldsymbol{O}_{2} \)


A stone is thrown vertically up from the top of a tower with some initial velocity
and it arrives on the ground after \( t_{1} \) seconds. Now if the same stone is
thrown vertically down from the top of the same tower with the same initial
velocity, it arrives on ground after \( t_{2} \) seconds. How much time will the stone
take to reach the ground if it is dropped
from the same tower?
\( \mathbf{A} \cdot \sqrt{t_{1} t_{2}} \)
B . \( t_{1}+t_{2} \)
\( \mathbf{c} \cdot\left(t_{1}+t_{2}\right) / 2 \)
D. None of these


The relation P defined from R to R as a P
\( \mathbf{b} \Leftrightarrow 1+\mathbf{a b}>\mathbf{0}, \) for all \( \mathbf{a}, \mathbf{b} \boldsymbol{\epsilon} \mathbf{R} \) is
A . reflexive only
B. reflexive and symmetric only
c. transitive only
D. equivalence


Given the standard half-cell potentials
\( \left(E^{o}\right) \) of the following as
\( Z n=Z n^{2+}+2 e^{-} ; \quad E^{o}=+0.76 \mathrm{V} \)
\( \boldsymbol{F e}=\boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \quad \boldsymbol{E}^{o}=+\mathbf{0 . 4 1} \mathbf{V} \)
Then the standard e.m.f. of the cell with
the reaction \( \boldsymbol{F e}^{2+}+\boldsymbol{Z n} \rightarrow \boldsymbol{Z n}^{2+}+\boldsymbol{F e} \)
is?
A . \( -0.35 v \)
B. \( +0.35 v \)
c. \( +1.17 v \)
D. \( -1.17 v \)


Given reasons for the following:
Dioxygen is a gas but sulphur a solid.


A myopia person cannot see distinctly objects that are :
A. near
B. far
c. Neither
D. horizontal and vertical signs


Write the degree of the following polynomial :
\( 5 x^{2} y z^{3}+x y^{4} z^{2} \)
\( A \cdot 3 \)
B. 2
\( c \cdot 7 \)
D.


Find out the velocity of the centre of mass of two \( 1 k g \) masses moving toward
each other, one mass with velocity \( \boldsymbol{v}_{1}= \)
\( \mathbf{1 0 m} / \boldsymbol{s}, \) the other with velocity \( \boldsymbol{v}_{\mathbf{2}}= \)
\( 20 m / s \)
A. \( 0 m / s \)
B. \( 5 m / s \) to the left
c. \( 10 m / s \) to the left
D. \( 15 \mathrm{m} / \mathrm{s} \) to the left
E . \( 20 \mathrm{m} / \mathrm{s} \) to the left


In Young's double-slit experiment, the \( y- \) coordinates of central maxima and 10 th
maxima are \( 2 c m \) and \( 5 c m \), respectively
When the YDSE apparatus is immersed
in a liquid of refractive index \( 1.5, \) the corresponding y-coordinates will be
\( \mathbf{A} \cdot 2 c m, 7.5 c m \)
B. \( 3 \mathrm{cm}, 6 \mathrm{cm} \)
\( \mathbf{c} .2 \mathrm{cm}, 4 \mathrm{cm} \)
D. \( 4 / 3 c m, 10 / 3 c m \)


\( \int\left(\frac{\cos ^{3} x+\cos ^{5} x}{\sin ^{2} x+\sin ^{4} x}\right) d x= \)
A \( \cdot \sin x-\frac{2}{\sin x}-6 \tan ^{-1}(\sin x)+c \)
в.
c. \( \sin x+\frac{2}{\sin x}-6 \tan ^{-1}(\sin x)+c \)
D. \( \sin x+\frac{2}{\sin x}+6 \tan ^{-1}(\sin x)+c \)
sin \( x+6 \tan ^{-1}(\sin x)+c \)


The minimum and maximum speeds
are
\( ^{\mathbf{A}} \cdot \sqrt{\frac{G M}{9 R}}, \sqrt{\frac{2 G M}{R}} \)
в. \( \sqrt{\frac{G M}{5 R}}, \sqrt{\frac{3 G M}{2 R}} \)
c. \( \sqrt{\frac{G M}{6 R}}, \sqrt{\frac{2 G M}{3 R}} \)
D. \( \sqrt{\frac{G M}{3 R}}, \sqrt{\frac{5 G M}{2 R}} \)


Graphite is a conductor of
electricity whereas diamond is a
conductor of electricity.
A. bad, bad
B. good, bad
c. bad, good
D. good, goodd


Which on adding to freshly precipitated aluminium hydroxide and shaking produces sol of aluminium hydroxide?
A . insufficient quantity of conc \( H C l \)
B. sufficient quantity of conc \( H C l \)
c. insufficient quantity of very dil \( H C l \)
D. sufficient quantity of very dil \( H C l \)


Find the formal charge of each \( ^{\prime} O^{\prime} \) in
ozone.


Which of the following reducing agent is used in chemical reduction?
A. \( C \)
в. \( C O \)
c. \( A l \)
D. all of these


\( \int \frac{\boldsymbol{x}^{3 / 2}+\boldsymbol{x}^{5 / 2}+\boldsymbol{x}}{\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}^{1 / 2}+\boldsymbol{x}+1} \boldsymbol{d} \boldsymbol{x} \) equals
A. \( \frac{2}{3} x^{3 / 2}+x-\tan ^{-1} x^{1 / 4}+C \)
B. \( \frac{2}{3} x^{5 / 2}-x+\tan ^{-1} x^{1 / 2}+C \)
C. \( \frac{2}{3} x^{1 / 2}-x-\tan ^{-1} x^{1 / 4}+C \)
D. \( \frac{2}{3} x^{3 / 2}-x+\tan ^{-1} x^{1 / 4}+C \)


A solid iron pole consists of a cylinder of height \( 220 \mathrm{cm} \) and base diameter 24 \( \mathrm{cm}, \) which is surmounted by another
cylinder of height \( 60 \mathrm{cm} \) and radius 8
cm. Find the mass of the pole, given that \( 1 \mathrm{cm}^{3} \) of iron has approximately \( 8 \mathrm{g} \) mass. (Use \( \pi=3.14) \)


The list gives four experiments done with calcium carbonate.
acid added
2 alkali added
3 heated strongly
4 water added
Which experiments produced carbon dioxide?
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 2 and 4


In humans, the composition of a zygote that will develop into a female is
\( \mathbf{A} \cdot 44 A+X X \)
B. \( 44 A+X Y \)
\( c \cdot 22+X \)
D. \( 23 A \)


In an electron gun, the control grid is given negative potential, relative to cathode in order to
A. accelerate the electrons
B. decrease KE of electrons
C. repel the electrons
D. decelerate the electrons


Match column A with column B and
select the correct option-


Jayanti purchase a commodity for
Rs. 2500 and paid an amount of
Rs. 2700 including the sales tax. Find
the rate of sales tax
A . \( 5 \% \)
B. \( 8 \% \)
\( c \cdot 10 \% \)
D. \( 12 \% \)


A ray of light falls on the surface of a spherical glass paperweight making an angle \( a \) with the normal and is refracted
in the medium at angle \( b \). The angle of deviation of the emergent ray from the
direction of incident ray is :
A \( . a-b \)
в. \( 2(a-b) \)
c. \( \frac{(a-b)}{2} \)
D. \( b-a \)


If 0.765 gm of an acid gives 0.535 gm of \( C O_{2} \) and \( 0.138 \mathrm{gm} \) of \( H_{2} O . \) Then, the ratio of the percentage of carbon and hydrogen is :
\( \mathbf{A} \cdot 19: 2 \)
B. 18: 12
c. 20: 17
D. 1: 7


Form the differential equation
corresponding to \( y=\left(\sin ^{-1} x\right)^{2}+ \)
\( A \cos ^{-1} x+B \) where \( A, B \) are arbitrary
constants.


The power loss in an \( A C \) circuit is \( E_{r m s} \)
\( I_{r m s}, \) when in the circuit there is only
A. \( C \)
в. \( L \)
\( c . R \)
D. \( L, C \) and \( R \)


Which of the following statements is
correct about the water-gas shift
reaction used for the commercial
preparation of hydrogen gas?
A. It involves the selective oxidation of \( \mathrm{CO} \) of water gas to
\( C O_{2} \) with the help of steam in the presence of iron chromate as catalyst
B. It involves the separation of \( \mathrm{CO} \) and \( \mathrm{H}_{2} \) by solvent extraction method
C. It involves the absorption of \( \mathrm{CO} \) in aqueous copper (I) chloride solution
D. It involves the removal of \( H_{2} \) through occlusion with
\( P d \)


Balance the following equation by ion electron method.
\( \boldsymbol{C o}^{2+}+\boldsymbol{N} \boldsymbol{O}_{2}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C} \boldsymbol{o}^{3+}+ \)
\( N O+H_{2} O \)


Obtains all other zeroes of \( x^{4}-3 x^{3}- \)
\( x^{2}+9 x-6, \) if two of its zeroes are \( \sqrt{3} \)
and \( -\sqrt{3} \)


Hydrogen bonding originates from the dipole-interaction between H-atom and any of the other atom like \( F, O, N \) and in
some cases with Cl atom. There are two
types of H-bonding namely, intermolecular and intra-molecular H-
bonding. Which of the following molecule does not consist of intramolecular H-
bonding?
A. chloral
B. chloral hydrate
c. ortho-hydroxybenzaldehyde
D. ortho-chloropheno


Reactions s with dil \( \boldsymbol{H C l} \) Appearance
Unknown
metal #1 bubbl \( \begin{array}{ll}\text { Dull gray } & \text { Dissolved with } 6 \\ \text { solid } & \text { of clear gas } \\ \text { with white } & \\ \text { oxide coating } & \end{array} \)
Unknown metal #2 Solid;
lustrous,
smooth
silver-gray
surface
Unknown metal #1 could be:
A. mercury
B. copper
\( c \cdot \) zinc
D. iron


Name the following compound. An acid which dissociates in aqueous
solution giving low concentration of \( \boldsymbol{H}^{+} \)
ion.


In a circle with centre \( 0, O D \perp \) chord \( A B \). If \( B C \) is the diameter, then
\( \mathbf{A} \cdot A C=B C \)
В. \( O D=B D \)
c. \( A C=2 O D \)
D. none of these


Which of the following contains acidic hydrogen?
A. Ethene
B. Ethane
c. Ethyne
D. \( B u t-1-y n e \)


Identify the incorrect statement among
the following.
A. Lanthanide contraction is the accumulation of
successive shrinkages.
B. As a result of lanthanoid contraction, the properties of 4d series of the transition elements have no
similarities with the \( 5 \mathrm{d} \) series of elements.
C. Sheilding power of 4f electrons is quite weak.
D. There is a decrease in the radii of the atoms or ions as one proceeds from La to Lu.


An electron passes undeflected
through perpendicular electric and magnetic fields of intensity \( 3.4 \times \)
\( \mathbf{1 0}^{\mathbf{3}} \boldsymbol{V} / \boldsymbol{m} \) and \( \mathbf{2} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{W} \boldsymbol{b} / \boldsymbol{m}^{\mathbf{2}} \)
respectively. Then its velocity is:
A \( .1 .7 \times 10^{6} \mathrm{m} / \mathrm{s} \)
B . \( 6.8 \times 10^{6} \mathrm{m} / \mathrm{s} \)
\( c \cdot 6.8 m / s \)
D. \( 1.7 \times 10^{8} \mathrm{m} / \mathrm{s} \)


Construct a triangle, \( \triangle A B C \) with \( A B=5, B C=12 \) and \( A C=13 . \) What
is the measure of \( \angle A B C \)
A \( .90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 40^{\circ} \)
D. \( 75^{\circ} \)


Choose incorrect statement.
A. Particle \( A, B \) and \( C \) changes their direction during motion one time
B. Acceleration of particle \( A, B \) and \( D \) are constant
C. Particle A and B retarded initially then speed up
D. Direction of motion of particle D remain unchanged


The number of ionization energies
carbon can have are:
A . 1
B. 2
\( c \cdot 4 \)
\( D \)


Which of the following characteristics is not correct for physical adsorption?
A. Adsorption is spontaneous.
B. \( \Delta H \) and \( \Delta S \) are negative
c. It is reversible in nature
D. Degree of adsorption increa ture


Parasexual cycle first discovered by
A. Lederberg and Tatum
B. Pontecorvo and Roper
c. Blaksle
D. Wollman


A metal ring kept (supported by a card
board) on the top of a fixed solenoid
carry a current I as shown in figure. The centre of the ring coincides with the axis of the solenoid. If the current in the
solenoid is switched off, then
A. magnetic flux linked with the metal ring increases.
B. current induced in the metal ring in clockwise direction
c. metal ring will not remain on the cardboard
D. both
(a) and
(b) are correct


If direction ratios of the normal of the
plane which contains the lines \( \frac{x-2}{3}= \) \( \frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{1}}{\boldsymbol{1}} \& \frac{\boldsymbol{x}-\boldsymbol{6}}{\boldsymbol{3}}=\frac{\boldsymbol{y}+\boldsymbol{2}}{\boldsymbol{2}}= \)
\( \frac{z-2}{1} \) are \( (a, 1,-26), \) then \( a \) is equal
to
A . 5
B. 6
\( c \cdot 7 \)
D.


Citric acid \( \left(\boldsymbol{H}_{3} \boldsymbol{A}\right) \) is a polyprotic acid
with \( K_{1}, K_{2}, \) and \( K_{3} \) equals to \( 7.4 \times \)
\( 10^{-4}, 1.7 \times 10^{-5}, \) and \( 4.0 \times 10^{-7} \)
respectively. Calculate the
\( \left[\boldsymbol{H}^{\oplus}\right],\left[\boldsymbol{H}_{2} \boldsymbol{A}^{\ominus}\right],\left[\boldsymbol{H} \boldsymbol{A}^{2-}\right], \) and \( \left[\boldsymbol{A}^{3-}\right] \) in
\( 0.01 M \) citric acid.
\( \mathbf{A} \cdot\left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-3} M,\left[H A^{2-}\right]=1.7 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-9}
\]
B . \( \left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-6} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-6}
\]
C \( \cdot\left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-5} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-8}
\]
D. \( \left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-7} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-6}
\]


Sound travels faster in gases as compared to solids and liquids.
A. True
B. False


Which is more stable in the below
given pair?
\( M n_{2} O_{7}_{-}-_{-}--R e_{2} O_{7} \)
A \( \cdot M n_{2} O_{7}=R e_{2} O_{7} \)
в. \( M n_{2} O_{7}<R e_{2} O_{7} \)
c. \( M n_{2} O_{7}>R e_{2} O_{7} \)
D. None of these


The part of a transistor which is heavily dopped to produce a large number of majority carriers is:
A. Base
B. Emitter
c. collector
D. None of these


An object placed \( 10 \mathrm{cm} \) in front of a lens has an image \( 20 \mathrm{cm} \) behind the lens. What is the power of the lens (In dioptre)?
A . 0.15
B. 3.0
\( c \cdot-5.0 \)
D. +15.0


For the situation described in figure
the magnetic field changes with time
\( \operatorname{according} \) to \( \boldsymbol{B}=\left(\mathbf{2} . \mathbf{0 0} \boldsymbol{t}^{3}-\mathbf{4 . 0 0} \boldsymbol{t}^{2}+\right. \)
0.8)\( T \) and \( r_{2}=2 R=5.0 \mathrm{cm} \)
a) Calculate the force on an electron
located \( a t P_{2} \) at \( t=2.00 s \)
b) What are the magnitude and
direction of the electric field at \( P_{1} \) when
\( t=3.00 \mathrm{s} \) and \( r_{1}=0.02 m \)


Given two vectors \( a=2 i-3 j+6 k \) on
\( b=2 i+3 j-k \) and \( \lambda= \)
\( \frac{\text {the projection of } a \text { on } b}{\text {the projection of bon } a}, \) then the
value of \( \lambda \) is
A. 3/
в. \( 7 / 3 \)
\( c \cdot 3 \)
D. 7


How many P-O-P bonds in cyclic meta phosphoric acid also give its structure?


Given two independence events \( A \) and
\( B, \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


If \( \left|\begin{array}{ccc}2 a & x_{1} & y_{1} \\ 2 b & x_{2} & y_{2} \\ 2 c & x_{3} & y_{3}\end{array}\right|=\frac{a b c}{2} \neq 0, \) then the
area of the triangle whose vertices are \( \left(\frac{x_{1}}{a}, \frac{y_{1}}{a}\right),\left(\frac{x_{2}}{b}, \frac{y_{2}}{b}\right) \) and \( \left(\frac{x_{3}}{c}, \frac{y_{3}}{c}\right) \) is
A \( \cdot \frac{1}{4} a b c \)
B. \( \frac{1}{8} a b c \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{8} \)
E \( \cdot \frac{1}{12} \)


If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{1-\cos 4 x}{8 x^{2}}, x \neq 0 \\ k, x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{k}=? \)
A . 1
B . 2
\( c \cdot \frac{1}{2} \)
D. \( \frac{-1}{2} \)


Which of the following form an alloy?
A. \( Z n+P b \)
в. \( F e+H g \)
c. \( P t+H g \)
D. \( F e+C \)


Which group is meta directing?
A \( .-C C l_{3} \)
B. \( -O H \)
\( \mathrm{c} \cdot-N H_{2} \)
D. \( -C H_{3} \)


Which fin are paired in fishes?
A. Dorsal fin
B. Anal fin
c. Pelvic fin
D. None of the above


Imparipinnate leaf is the one where
A. Leaflets are borne in pairs
B. Leaflets are small
c. Leaflets are large
D. Rachis is terminated by an odd leaflet


Area of a rhombus if its vertices are \( (3, \)
0), (4,5),(-1,4) and (-2,-1) taken in order
is
A . 24. sq. units
B. 36 sq. units
c. 48 sq. units
D. \( 48 \sqrt{2} \) sq. units


Malpighian tubules are the excretory
organs in
A. Cockroach
B. Platyhelminthes
c. Ascaris
D. Pila


One day Chetan's mother developed a severe stomach ache all of a sudden.
She was rushed to the doctor who
suggested for an immediate endoscopy test and gave an estimate of
expenditure for the same. Chetan immediately asked her class teacher and arranged the money and rushed to the hospital. On realizing that Chetan belonged to a below average income group family even the doctor offered concession for the test fee. The test was
conducted successfully. Answer the following questions based on the above information;
(a) Which principle in optics is made use of in endoscopy.?
(b) Briefly explain the values reflected in the action taken by the teacher
(c) In what way do you appreciate the response of the doctor on the given situation?


The mass and energy equivalent to
1 amu are respectively
A \( \cdot 1.67 \times 10^{-27} g m, 9.30 \mathrm{MeV} \)
В. \( 1.67 \times 10^{-27} \) к \( g \), 930 Ме \( V \)
C . \( 1.67 \times 10^{-27} \mathrm{kg}, 1 \mathrm{MeV} \)
D. \( 1.67 \times 10^{-34} k g, 1 M e V \)


EMF of the cell
\( Z n\left|Z n S O_{4}(a=0.2)\right|\left|Z n S O_{4}\left(a_{2}\right)\right| Z n \)
is \( -0.0088 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). Calculate the
value of \( a_{2} \)
A \( \cdot a_{2}=0.1006 \mathrm{M} \)
В . \( a_{2}=0.2012 M \)
\( \mathbf{c} \cdot a_{2}=0.3018 M \)
D. None of these


Construction of dams
A. Is always an advantageous process
B. Has only disadvantages
c. Both
D. None


\( \frac{1}{3} x-\frac{1}{6} y=4 \)
\( 6 x-a y=8 \)
In the system of equations above, \( a \) is a
constant. If the system has no solution,
what is the value of \( \boldsymbol{a} \)
A \( \cdot \frac{1}{3} \)
B.
\( c .3 \)
D.


Let \( z \) be a complex number such that the principal value of argument, arg \( z<0 . \) Then \( \arg (-z)-\arg (z) \) is
A \( \cdot \frac{\pi}{2} \)
B. \( \pm \pi \)
\( c . \pi \)
D. -


A lift starts from the top of a mine shaft and descends with a constant speed of \( 10 m / s .4 s \) later a boy throws a stone vertically upwards from the top of the shaft with a speed of \( 30 m / s . \) If stone
hits the lift at a distance \( x \) below the
shaft write the value of \( \frac{x}{3}(\text { in } \mathrm{m} \) ). (Take:
\( \left.\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right](\text { Give value of } \mathbf{2 0} \sqrt{\mathbf{6}}=\mathbf{4 9}) \)


Write the polynomial in standard form
and also write down their degree. \( 4 p+15 p^{6}-p^{5}+4 p^{2}+3 \)


Select the correct order of ionic
conductance of the following cations in
an aqueous solution.
A \( . L i^{+}<N a^{+}<K^{+}<R b^{+} \)
B . \( L i^{+}>N a^{+}>K^{+}>R b^{+} \)
c. \( L i^{+}<N a^{+}>K^{+}>R b^{+} \)
D. \( L i^{+}=N a^{+}<K^{+}<R b^{+} \)


Assertion
Systematics is the branch of biology
that deals with classification of living organisms.
Reason
The aim of classification is to group the
organisms.
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


Complete the following equations:
\( \begin{array}{l}\text { i) } 2 N a O H_{2} \rightarrow \\ \text { cold and dilute }\end{array}+C l_{2} \rightarrow \)
ii) \( 2 F e S O_{4}+H_{2} S O_{4}+C l_{2} \rightarrow \)
iii) \( C l_{2}+3 F_{2} \stackrel{573 K}{\text { excess }} \)


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}, \) then find a
vector \( \vec{c} \) such that \( \vec{a} \times \vec{c}= \)
\( \overrightarrow{\boldsymbol{b}} \quad \) and \( \quad \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{c}}=\mathbf{3} \)


Assertion
The smaller the orbit of a planet around
the Sun, the shorter is the time it takes
to complete.
Reason
According to Kepler's third law of planetary motion, square of time period is proportional to cube of mean distance from Sun.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the figure shown
\( \mathbf{A} \cdot \) impulse in the two cases will be same if \( A_{1}=A_{2} \)
B. maximum force is greater in case I
C. impulse in two cases may or may not be equal and it does not depend on area under the curve
D. none of these


The potential energy of a particle of
mass \( 1 k g \) in motion along the \( x \) -axis is given by \( U=4(1-\cos 2 x) J . \) Here \( x \) is
in meter. The period of small oscillations (in sec) is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
D. \( \sqrt{2 \pi} \)


Data force \( , f=2 \hat{i}+3 \hat{j}-4 \hat{k} \)
displacement \( s=2 \hat{i}+3 \hat{j}-4 \hat{k} \) find
work?


A particle has initial velocity \( 4 i+ \) \( 4 j m s^{-1} \) and an acceleration
\( -0.4 i m s^{-2}, \) at what time will its speed
be \( 5 m s^{-1} ? \)
A . \( 2.5 s \)
B. \( 17.5 s \)
\( c \)
D. \( 8.5 s \)


The heat of combustion of carbon to
\( C O_{2} \) is \( -393.5 \mathrm{kJ} / \mathrm{mol} \). The heat released
upon formation of \( 35.2 \mathrm{g} \) of \( C O_{2} \) from
carbon and oxygen gas is:
A . - 315kJ
B. +315kJ
c. -630Kj
D. +3.15kJ


\( \begin{array}{|ccc|}\text { If } \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}= & \mathbf{0} \text { ,find } \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{x}^{\mathbf{2}} & \boldsymbol{y}^{\mathbf{2}} & \boldsymbol{z}^{\mathbf{2}} \\ \boldsymbol{y}+\boldsymbol{z} & \boldsymbol{z}+\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y}\end{array} \)


Compounds that have the same composition but differ in structural formulas:
A. are used for substitution products
B. are called polymers
c. are usually alkanes
D. have the same properties
E. are called isomers


Give the equation for the discharge of ion at the cathode during the electrolysis of acidified water?


The pair in which both species have same magnetic moment (spin only value) is :
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right]^{2+},\left[\operatorname{CoCl}_{4}\right]^{2-} \)
B . \( \left[C r\left(H_{2} O\right)_{6}\right]^{2+},\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
C. \( \left[M n\left(H_{2} O\right)_{6}\right]^{2+},\left[C r\left(H_{2} O\right)_{6}\right]^{2} \)
D. \( \left[C o C l_{4}\right]^{2-},\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)


consist of atoms that have valence electrons in a \( \boldsymbol{d}- \)
subshell.
A. Alkali metals
B. Alkaline earth metals
c. Transition metals
D. Halogens


Let \( z \) be a complex number of constant modulus such that \( z^{2} \) is purely
imaginary then the number of possible values of z is
A . 2
в. 1
\( c . \)
D. infinite


Mass defect of 1 g gives energy equal to
This question has multiple correct options
\( \mathbf{A} \cdot 9 \times 10^{13} J \)
B \( .5 .625 \times 10^{32} e V \)
C \( .2 .15 \times 10^{10} \) kcal
D. \( 9 \times 10^{6} \) ergs


Which compound is four
carbon compound in the \( C_{3} \) cycle?
A. Erythrose - 4 - phosphate
B. Dihydroxy acetone phosphate
C. 3- Phosphoglyceraldehyde
D. Oxalo acetic acid


Indusium is found in
A . Algaa
B. Ferns
c. Moss
D. cycas


Most of the unicellular organisms show
A. Sexual reproduction
B. Asexual reproduction
c. Vegetative reproduction
D. None of the above


Energy released in nuclear reaction is related to mass by
A \( . E=1 / 2 m v^{2} \)
B . \( E=m v^{2} \)
\( \mathbf{c} \cdot E=m c^{2} \)
D. \( E=1 / 2 m c^{2} \)


There are 14 elements in actinoid series.
Which of the following elements does not belong to this series?
A. \( U \)
в. \( N p \)
\( c . T m \)
D. \( P m \)


At present about animal
phyla have been recognized.
A . 10
B. 20
c. 30
D. 40


The coefficient of variation of two
distributions are 60 and \( 70 . \) The
standard deviation are 21 and 16
respectively, then their mean is This question has multiple correct options
A . 35
B . 23
c. 28.25
D. 22.85


The number of integral solutions \( (x, y) \) of the equations \( \boldsymbol{x} \sqrt{\boldsymbol{y}}+\boldsymbol{y} \sqrt{\boldsymbol{x}}=\mathbf{2 0} \)
and \( \boldsymbol{x} \sqrt{\boldsymbol{x}}+\boldsymbol{y} \sqrt{\boldsymbol{y}}=\boldsymbol{6 5} \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these


A maximum number of electrons in a
subshell of an atom determined by the
formula:
\( \mathbf{A} \cdot 4 l+2 \)
B \( \cdot 2 n^{2} \)
c. \( 4 l-2 \)
D. \( 2 l+1 \)


Choose the correct option from the options given below.We can derive
Newton's:
A. second and third laws from the first law
B. first and second laws from the third law
c. third and first laws from the second law
D. all the three laws are independent of each others


The series combination of two batteries,
both of the same emf \( 10 V \), but different
internal resistance of \( 20 \Omega \) and \( 5 \Omega \), is
connected to the parallel combination of two resistors \( 30 \Omega \) and \( R \Omega \). The
voltage difference across the battery of internal resistance \( 20 \Omega \) is zero, the
value of \( R\left(\text { in } \Omega \text { is }_{-}-\dots\right. \)


During extraction of Fe:
A . carbon is ultimately converted to \( C O_{2} \) in the combustion zone in the blast furnace
B. \( C O_{2} \) is one of the by-products of reduction zone of blast furnace
C. cast iron is obtained from blast furnace
D. uppermost zone of blast furnace is slag formation zone


Deformation of sensory dendrites is required to establish a nerve impulse in
all of the following except
A . gustatory hair cells
B. organ of Corn
c. Pacinian corpuscles
D. lateral line organs


\( 500 m L \) of a hydrocarbon gas, burnt in
excess og oxygen, yields \( 2500 m L C O_{2} \)
and 3 liters of water vapour, all volumes
being mesured at the same temperature and pressure, what is the formula of the hydrocarbon?
A \( \cdot C_{4} H_{8} \)
B. \( C_{5} H_{12} \)
c. \( C_{5} H_{1} \)
D. \( C_{2} H_{6} \)


The main waste products of plants are
\( A \cdot C O_{2} \) and \( N O_{2} \)
B. \( \mathrm{cO}_{2} \) and water vapour.
\( \mathrm{c} \cdot \mathrm{co}_{2}, \mathrm{O}_{2} \) and water vapour
D. None of the above


Enzymes are known to increase the rate of reaction by :
A \( \cdot 10^{2} \) times
B. \( 10^{-2} \) times
c. \( 10^{5} \) times
D. \( 10^{12} \) times


Green potatoes are toxic due to
A. Phytoalexins
B. Solanine
c. Triazine
D. Hormones


Write five rational numbers which are
smaller than 2
A \( \cdot_{1, \frac{1}{2}, 0,-1,-\frac{1}{2}} \)
в. \( 0,1,1.414, \sqrt{3},-1 \)
D. \( 0,1,1.732, \sqrt{2},-1 \)


An electric dipole (dipole moment \( =p \) )
is placed in a uniform electric field in
stable equilibrium position at rest. Now it is rotated by a small angle and released. The time after which it comes
to the equilibrium position again (for first time) is \( t . \) Then the moment of
inertia of the dipole about the axis of
rotation is :
A \( \cdot \frac{4 t^{2} p E}{3 \pi^{2}} \)
в. \( \frac{1 t^{2} p E}{4 \pi^{2}} \)
c. \( \frac{2 t^{2} p E}{3 \pi^{2}} \)
D. \( _{4} \frac{t^{2} p E}{\pi^{2}} \)


The decay constant of a radioactive
sample is \( \gamma \). Its half-life is \( T_{1 / 2} \) and mean life is \( \boldsymbol{T} \).
\( A \cdot T_{1 / 2}=\frac{1}{\lambda}, T=\frac{I n 2}{\lambda} \)
B・ \( T_{1 / 2}=\frac{I n 2}{\lambda}, T=\frac{1}{\lambda} \)
\( \mathbf{c} \cdot_{T_{1 / 2}=\lambda \operatorname{In} 2, T}=\frac{1}{\lambda} \)
D. \( T_{1 / 2}=\frac{\lambda}{I n 2}, T=\frac{I n 2}{\lambda} \)


\( \int_{0}^{1} \tan ^{-1}\left[\frac{2 x-1}{1+x-x^{2}}\right] d x= \)
A .
B. \( 1 / 2 \)
\( c \)
D . \( \pi / 6 \)


In roots, lateral branches grow from
A. Epiblema
B. Pericycle
c. cortex
D. Endodermis


Write down the truth table for the given
logic circuit with Boolean expression


The circuit shown given contains two
ideal diodes, each with a forward
resistance of \( 50 \Omega \). If the battery voltage
is \( 6 \mathrm{V} \), the current through the \( 100 \Omega \) resistance (in Amperes) is?
A .0 .027
В. 0.020
\( c .0 .030 \)
D. 0.036


Which one among the following has a
filled \( 4 p \) orbital?
A . Na
B. Fe
\( c \cdot c l \)
D. \( R b \)
E \( . C a^{+} \)


State True or False
Cube of any odd number is even
A. True
B. False
c. Ambiguous
D. Data insufficient


If the absolute refractive indices of glass and water are \( \frac{3}{2} \) and \( \frac{4}{3} \) respectively, what will be the velocity of light in water?
(If velocity of light in glass \( \left.=2 \times 10^{8}\right) \)
\( \mathbf{A} \cdot 2.25 \times 10^{8} m / s \)
B . \( 3.25 \times 10^{8} m / s \)
C \( .2 .25 \times 10^{7} \mathrm{m} / \mathrm{s} \)
D. \( 2.15 \times 10^{8} \mathrm{m} / \mathrm{s} \)


From \( 2012-2016, \) the amount (in crores)
spent on natural gas \( \mathrm{N} \) and electricity \( \mathrm{E} \) by Indian residents can be described by the following expressions, where t is the number of years since 2012 Gas spending model, \( \mathrm{N}=2.13 t^{2}-4.21 t+37.40 \)
Electricity spending model, \( \mathrm{E}=-0.209 t^{2}+5.393 t+307.735 \)
What is the total amount A spent on
natural gas and electricity by Indian residents from 2012 to 2016?
A. \( 1.467 t^{2}+7.423+121.721 \)
1
B. \( 1.339 t^{2}-8.729 t+76.245 \)
c. \( 1.01 t^{2}+7.083+97.83 \)
D. \( 1.921 t^{2}+1.183 t+345.135 \)


0.5 Faraday of electricity was passed to deposit all the copper present in \( 500 \mathrm{m} \) of \( C u S O_{4} \) solution. What was the
molarity of this solution?
A. 1 м
B. 0.5 M
c. \( 0.25 \mathrm{M} \)
D. 2.5м


Assertion
Oceans and lakes tend to maintain a
relatively constant temperature.
Reason
Water has high heat capacity and it can withhold large amounts of heat.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \operatorname{Matrix} \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{3} & \boldsymbol{2} \\ \boldsymbol{1} & \boldsymbol{y} & \boldsymbol{4} \\ \boldsymbol{2} & \boldsymbol{2} & \boldsymbol{z}\end{array}\right], \) if \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\boldsymbol{6} \mathbf{0} \)
and \( 8 x+4 y+3 z=20, \) then \( A(a d j A) \)
is equal to
A. \( \left|\begin{array}{lll}64 & 0 & 0 \\ 0 & 64 & 0 \\ 0 & 0 & 64\end{array}\right| \)
B. \( \mid \begin{array}{ccc}68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68\end{array} \)
\begin{tabular}{l|lll}
38 & 0 & 0 \\
0 & 38 & 0 \\
0 & 0 & 38
\end{tabular}
D. \( \mid \begin{array}{ccc}32 & 0 & 0 \\ 0 & 32 & 0 \\ 0 & 0 & 32\end{array} \)


Male child will be born if
A. Father is sexually more excited
B. Sperm of male with Y chromosome fertilizes the egg
C. Sperm of male with \( X \) chromosome fertilizes the egg
D. None of the above


Covalent bond between atoms is formed
by :
A. loss of electrons
B. gain of electrons
c. sharing of electrons
D. loss and gain of electrons boh


Which of the following occurs, when two hydrogen atoms bond with each other?
A. Potential energy is lowered
B. Kinetic energy is lowered
c. Electronic motion creases
D. Energy is absorbed


If the eccentricity of an ellipse is \( \frac{5}{8} \) and
the distance between its foci is \( 10, \) then
find the latusrectum of the ellipse.


Area bounded by \( x^{2}=4 a y \) and \( y= \)
\( \frac{8 a^{3}}{x^{2}+4 a^{2}} \) is :


Water found in wells:
A. contain sodium carbonate
B. is underground water
C. contain distilled water
D. contain ice


A ball of mass \( m \) moving with velocity \( v \) collides elastically with wall and rebounds. The change in momentum of
the ball will be :
A. \( 4 m v \)
B. \( 2 m v \)
\( c . m v \)
D. zero


Evaluate the following integral:
\( \int_{0}^{3} x^{2} d x \)


An electric charge \( q \) is placed at the centre of a cube of side \( a \) The electric
flux through one of its faces is
A \( \cdot \frac{q}{6 \epsilon_{0}} \)
B. \( \frac{q}{6 \epsilon_{0} a^{2}} \)
c. \( \frac{q}{6 \pi \epsilon_{0} a^{2}} \)
D. \( \frac{q}{\epsilon_{0}} \)


The water table is:
A. the upper level of an underground surface in which the soil or rocks are permanently saturated with water.
B. the upper level of an underground surface in which the soil or rocks are unsaturated with water.
C. the lower level of an underground surface in which the soil or rocks are permanently saturated with water.
D. the lower level of an underground surface in which the soil or rocks are unsaturated with water.


Which of the following compounds has
maximum volatility?
\( A \)
в.
\( c \)
D.


Percentage of fresh water in
hydrosphere is
A. Less than 10\%
B. Less than 25\%
c. Less than \( 3 \% \)
D. Less than 17\%


\( \int \frac{x}{1+\cos x} d x= \)
\( \mathbf{A} \cdot x \tan \frac{x}{2}-2 \log |\sec x / 2|+c \)
B. \( -x \tan x / 2-\frac{1}{2} \log |\sec x / 2|+c \)
c. \( _{x \tan x / 2+\frac{1}{2} \log |\sec x / 2|+c} \)
D. \( x \cot x / 2-\frac{1}{2} \log |\csc x / 2|+c \)


80 g of water at \( 30^{\circ} \mathrm{C} \) are poured on a
large block of ice at \( 0^{\circ} \mathrm{C} \) The mass of ice that melts is
A. \( 30 g \)
в. 80 \( g \)
\( c \cdot 1600 g \)
D. \( 150 \mathrm{g} \)


Which of the following is major sink for carbon monoxide?
A. water
B. Soil
c. Animal respiration
D. Salts dissolved in ocean water


Blood platelets
A. Help in the production of red blood cells in the bone
marrow.
B. Clot the blood.
C . Are produced in liver.
D. Fight disease-causing germs.


Catalyst used in contact process is:
A . platinum
B. ferric oxide + copper oxide
c. vanadium pentoxide
D. All of the above


The direction of \( \boldsymbol{\tau} \) is :
\( \mathbf{A} \cdot \) parallel to the plane of \( \bar{r} \) and \( \bar{F} \)
B. perpendicular to the plane of \( \bar{r} \) and \( \bar{F} \).
C. parallel to the plane of \( \bar{r} \) and \( \bar{P} \).
D. perpendicular to the plane of \( \bar{r} \) and \( \bar{P} \).


\( H_{2} S \) is not :
A. reducing agent
B. oxidising agent
c. acidic
D. None of the above


In a first order reaction the
concentration of reactant decreases
from \( 800 \mathrm{mol} / \mathrm{dm}^{3} \) to \( 50 \mathrm{mol} / \mathrm{dm}^{3} \) is
\( 2 \times 10^{4} \) sec. The rate constant of
reaction in \( \sec ^{-1} \) is:
A \( \cdot 2 \times 10^{4} \)
В. \( 3.45 \times 10^{-5} \)
\( \mathbf{c} \cdot 1.386 \times 10^{-4} \)
D. \( 2 \times 10^{-4} \)


\( \int \sqrt{\left(\frac{x-1}{x+1}\right)} d x \)


A line \( P Q \) makes intercepts of length 2
units between the lines \( y+2 x=3 \) and
\( \boldsymbol{y}+\mathbf{2} \boldsymbol{x}=\mathbf{5} . \) If the coordinates of \( \boldsymbol{P} \) are
\( (2,3), \) coordinates of \( Q \) can be
This question has multiple correct options
в. (2,3)
c. \( \left(0, \frac{9}{2}\right) \)
D. (3,2)


Which of the following maintains the volume of air in the chest cavity during breathing?
A. Diaphragm
B. Lungs
c. Breastbone
D. None of the above


Show that \( f(x)=\tan ^{-1}(\sin x+\cos x) \)
is a decreasing function on the interval \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)


Which of the following compounds is isomeric with trimethyl amine?
A. 1-Propanamine
B. 2-Propanamine
c. Both 1 and 2
D. 2-Butanamine


When \( P b O_{2} \) reacts with concentrated
\( H N O_{3}, \) the gas evolved is
A \( . N O_{2} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( N_{2} \) O


Mass flow hypothesis was first described by
A. Swanson
B. Buchman
c. Kursanov
D. Munch


Kinetic energy is proportional to
This question has multiple correct options
A. velocity
B. mass
C . square of velocity
D. acceleration


Does \( C u^{+} \) ion show colour?


Natural sink of stratospheric ozone is?
A. Sulphuric dioxide
B. Sulphur fluxes of oceans
c. Freons
D. нсFсs


wavelength and are initially in phase.
They then travel through plastic layer
with thicknesses of \( L_{1}=3.5 m m \) and
\( \boldsymbol{L}_{2}=\mathbf{5 . 0 m m} \) and indices of refraction
\( \boldsymbol{n}_{1}=\mathbf{1 . 7} \) and \( \boldsymbol{n}_{2}=1.25 \) as shown in
figure. The rays later arrive at a
common point. The longest wavelength of light for which constructive
interference occurs at the point is
\( \mathbf{A} \cdot 0.8 m m \)
\( \mathbf{B} \cdot 1.2 m m \)
c. \( 1.7 m m \)
\( \mathbf{D} \cdot 2.9 m m \)


Four charges \( 10^{-8},-2 \times 10^{-8},+3 x \)
\( 10^{-8} \) and \( 2 \times 10^{-8} \mathrm{C} \) are placed at the
four corners of a square of 1 meter
\( \mathbf{1} / \mathbf{4} \boldsymbol{\pi} \varepsilon_{\mathbf{0}}=\mathbf{9} \times \mathbf{1 0}^{\mathbf{9}} \mathbf{N}-\boldsymbol{m}^{2} / \boldsymbol{C}^{\mathbf{2}} \) its
potential at the centre Of the square is
A . 206
B. 308
c. \( 360 \sqrt{2} \mathrm{V} \)
D. 90


The wavelength \( \lambda_{e} \) of an electron and \( \lambda_{p} \)
of a photon of same energy \( \boldsymbol{E} \) are
related by:
\( A \cdot \lambda_{p} \propto \lambda_{e} \)
B. \( \lambda_{p} \propto \sqrt{\lambda_{e}} \)
c. \( \lambda_{p} \propto \frac{1}{\sqrt{\lambda_{e}}} \)
D. \( \lambda_{p} \propto \lambda_{e}^{2} \)


A potential barrier of \( 0.5 \mathrm{V} \) exists
across a p-njjunction. If the width of depletion layer is \( 10^{-6} m \), then intensity
of electric field in this region will be
A \( .1 \times 10^{6} V / m \)
в. \( 5 \times 10^{5} \mathrm{V} / \mathrm{m} \)
c. \( 4 \times 10^{4} V / m \)
D. \( 2 \times 10^{6} \mathrm{V} / \mathrm{m} \)


A body is acted upon by a force which is proportional to the distance covered. If distance covered is represented by \( s \)
then work done by the force will be
proportional to.
\( A \)
B \( \cdot s^{2} \)
c. \( \sqrt{s} \)
D. None of the above


The heart is covered by a membrane called
A. Epidermis
B. Dermis
c. Epicardium
D. Pericardium


The product as a result of reaction of
\( \boldsymbol{C H}_{3} \boldsymbol{M g I} \) with \( \boldsymbol{C O}_{2} \) on further
hydrolysis gives:
A \( \cdot C H_{3} C O O H \)
в. \( H C O O H \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C O O H-C O O H \)


A person sitting in a satellite orbiting earth feels weighlessness due to
A. Centripetal acceleration
B. Tangential velocity
c. Large distance from earth
D. zero gravity


Why are part of the space shuttles
covered with black tiles?
A. To allow more loss of heat through the surface.
B. To allow less loss of heat through the surface.
C. To allow more gain of heat through the surface.
D. To allow less gain of heat through the surface.


A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 m s^{-1} \) at an angle of \( 24^{\circ} \) to the
horizontal. The path of the man is shown
n Fig
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)
The pressure of the still air at \( A \) is
\( 63 k P a \) and at \( B \) is \( 92 k P a . \) Assume the
density of the air in constant between \( \boldsymbol{A} \)
and \( B \)
Determine the density of the air between \( A \) and \( B \)
density \( = \)


In the pentagon \( A B C D E \) shown above,
the measures of angles \( A, E \) and \( C \) are
given. It is known that the measures of
angles \( B \) and \( D \) are equal.Then which of
the following is true?
\( \mathbf{A} \cdot \overline{A B} \| \overline{C D} \)
\( \mathbf{B} \cdot \overline{B C} \| \overline{A E} \)
\( \mathbf{c} \cdot \overline{A B} \| \overline{D E} \)
D. \( \overline{C D} \| \overline{A E} \)


At what temperature in \( ^{\circ} \boldsymbol{C}, \) the \( \boldsymbol{U}_{r m s} \) of
\( \boldsymbol{S} \boldsymbol{O}_{2} \) is equal to the average velocity of
\( O_{2} \) at \( 27^{\circ} C ? \)
A \( \cdot 118.1^{\circ} \mathrm{C} \)
B . \( 236.3^{\circ} \mathrm{C} \)
C \( .472 .6^{\circ} \mathrm{C} \)
D. None of these


If \( A \) got \( 40 \% \) marks more than \( B \) in exam, by what \( \% \) is \( B s \) marks less than
\( A s ? \)
A . \( 28.57 \% \)
B. \( 7.14 \% \)
\( \mathrm{c} .9 .09 \% \)
D. \( 40 \% \)


What is meant by transposing of a
matrix? Give an example.


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{3 \times 3} \) is a square matrix so
that \( a_{i j}=i^{2}-j^{2}, \) then \( A \) is a
A. unit matrix
B. symmetric marix
c. skew symmetric matrix
D. orthogonal matrix


Explain the reasons for the following in
a power generator.
a.armature is used as stator.
b. Strong electromagnets are used as field magnet.
c. Three armature coil are arranged at
\( 120^{\circ} \) angular separation


Give the decreasing order of reactivity
of the following compounds with HBr.
\( (I) \)
\( (\mathrm{II}) \)
\( (\mathrm{III}) \)
\( (\mathrm{IV}) \)
\( \mathbf{A} \cdot I I I>I V>I I>I \)
В. \( I I I>I I>I V>I \)
c. \( I I I>I I>I>I V \)
D. \( I I>I I I>I V>I \)


Match the following.
SET-A SET-B
Type of hormone

Name of
hormone
1) Steroid hormone
a) Cytokinins
2) Non Steroid
b) Estrogens
3) Plant hormone
c) Auxins
4) Peptide hormone
d) Insulin
A. \( 1-b, 2-b, 3-c, 4-d \)
B. 1-b, 2-a, 3-d, 4-c
c. 1-b, 2-a,d 3-a,c, 4-d
D. 1-c, 2-a, 3-d, 4-b


Protons and neutrons are also called
A . nucleons
B. isotope
c. isobars
D. elements


Assertion: In series LCR circuit
resonance can take place.
Reason: Resonance takes place if inductance and capacitive reactances are equal and opposite.
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


A metallic wire bent into a right \( \Delta \) abc
moves with a uniform velocity \( \boldsymbol{v} \) as
shown in figure. B is the strength of
uniform magnetic field perpendicular
outwards the plane of triangle. The net
emf is ................. and emf along ab is
A. zero, zero
B. zero, \( B v(b c) \) with \( b \) positive
C. zero, \( B v(b c) \) with \( a \) positive
D. \( B v(b c) \) with \( c \) positive, zero
E. \( B v(b c) \) with \( b \) positive, zero


Assertion
Statement-1: Echo is produced when
sound is incident on hard and polished
surface.
Reason
Statement-2: Sound energy can be totally reflected by objects with soft and loose texture.
A. Both Statements-1 and 2 are true and Statement-2 is the correct explanation of Statement- 1
B. Both Statements-1 and 2 are true but Statement-2 is not the correct explanation of Statement- 1
c. Statement-1 is true and Statement-2 is false
D. Both Statements-1 and 2 are false


ff \( a+b-12=0 \) and \( a b=27 \), then find
\( \boldsymbol{a}^{\boldsymbol{3}}+\boldsymbol{b}^{\boldsymbol{3}} \)


Consider following equilibrium \( 3 F e(s)+C(s) \rightleftharpoons F e_{3} C(s), \quad \Delta H^{\circ}>0 \)
What is the effect of increasing temperature on this equilibrium?
A. reaction proceeds in forward
c. no effects
D. none of these


The following relations are defined on the set of real numbers check them for
\( \mathrm{R}, \mathrm{S}, \mathrm{T} \)
\( \operatorname{arbiff}|a-b|>0 \)


A plane electromagnetic wave propagating along \( x \) direction can have the following pairs of \( \vec{E} \) and \( \vec{B} \).
A. \( E_{y}, B_{z} \)
в. \( E_{z}, B_{y} \)
c. \( E_{x}, B_{y} \)
D. both (a) and (b)


A solid sphere is rolling down on
inclined plane from rest and rectangular block of same mass is also slipping down simultaneously from rest on a similar smooth inclined plane.
A. Both of them will reach the bottom simultaneously.
B. The sphere will reach the bottom first
c. The rectangular block will reach the bottom first
D. Depends on density of materia


If \( n \) is a positive integer, which of the following CANNOT be the units digit of
\( \mathbf{3}^{n} ? \)
A .
B. 3
\( c .5 \)
D.


Under high pressure and in presence of nickel cyanide catalyst, acetylene on polymerisation gives:
A. Benzene
B. Mesitylene
c. cyclo-octatetraene
D. vinyl acetylene


An electric dipole of dipole moment \( 20 \times 10^{-6} C \) is enclosed by closed
surface. What is the net electric flux
coming out of this surface?


The hormone which controls
the processes of burning of fats, proteins and carbohydrates and liberates energy in the body is:
A. Thyroxine
B. Adrenaline
c. Insulin
D. cortisone


Pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature. This law is popularly known as:
A. Boyle's law
B. Charles'law
c. Gay Lusac's law
D. Avogadro law


Sulphanilamide is a/an:
This question has multiple correct options
A. sulpha drugg
B. antibiotic drug
c. disinfectant
D. antacid


If \( U=\cot ^{-1} \sqrt{\cos 2 \theta}-\tan ^{-1} \sqrt{\cos 2 \theta} \)
then \( \sin U \) is equal to
\( A \cdot \sin ^{2} \theta \)
B. \( \cos ^{2} \theta \)
\( \mathbf{c} \cdot \tan ^{2} \theta \)
\( \mathbf{D} \cdot \tan ^{2} 2 \theta \)


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{\sqrt{x+8}}{\sqrt{x}} \)


Fill in the blanks in the following
statements:
(a) To draw water from a well we have to
at the rope
(b) A charged body an
uncharged body towards it.
(c) To move a loaded trolley we have to
¡t.
(d) The north pole of a magnet
the north pole of
another magnet.


Find the area of the region enclosed by
parabola \( \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{2} \) and lines \( \boldsymbol{y}= \)
\( \boldsymbol{x}, \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{x}=\mathbf{0} \)


The oxidation states exhibited by
hydrogen in its various molecular forms/compounds are :
A . - - ' only
B. zero only
\( c \cdot+1,-1 \) and 0
D. +1 only


litre mixture of \( C O \) and \( C O_{2} \) is taken
This is passed through a tube containing red-hot charcoal. The volume now becomes 1.6 liters. The volumes. are
measured under the same conditions.
Find the composition of the mixture by volume


The film of camera is compared to which part of human eye?
A. Lens
B. Retina
c. Iriss
D. choroid


The distance between an electric lamp
and a screen is \( d=1 \) m. A convergent
lens of focal length \( \boldsymbol{f}=21 \mathrm{cm} \) is placed
between the lamp and the lens such
that a sharp image of the lamp
filaments is formed on the screen.
This question has multiple correct options
A. The positions of the lens from the lamp for which sharp images are formed on the screen are \( 35 \mathrm{cm} \) and \( 65 \mathrm{cm} \)
B. The position of the lens from the lamp for which sharp images are formed on the screen are \( 30 \mathrm{cm} \) and \( 70 \mathrm{cm} \)
c. Magnitude of the difference in magnification is \( 40 / 21 \)
D. The size of the lamp filament for which there are two sharp images of \( 4.5 \mathrm{cm} \) and \( 2 \mathrm{cm} \), is \( 3 \mathrm{cm} \)


Match List-1 with List-2.
List -1
List-2
A) \( C H_{3} C O O N a+C H_{3} C O O H \)
1)Acidic due to cationic hydrolysis
B) \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \)
2) Basic due to anionic hydrolysis
C) aqueous \( A l C l_{3} \)
Basic buffer solution
D) aqueous \( N a_{2} C O_{3} \)
4)Acidic buffer solution
\( A \cdot A-1 ; B-2 ; C-3 ; D-4 \)
B. \( A-4 ; B-3 ; C-1 ; D-2 \)
c. \( A-2 ; B-3 ; C-1 ; D-4 \)
D. \( A-4 ; B-3 ; C-2 ; D-1 \)


Let \( R \) be relation on I defined as mRn iff
\( \boldsymbol{m} \leq \boldsymbol{n} . \) Check if \( \boldsymbol{R} \) is an equivalence
relation.


Wave number is given by:
A. \( \frac{2 \pi}{\text { wavelength }} \)
в. \( \frac{2 \pi}{\text { frequency }} \)
c. \( \frac{2 \pi}{\text { time period }} \)
D. none of these


Which one of the following is the first group of vascular plants?
A. Thallophyta
B. Bryophyta
c. Pteridophyta
D. Spermatophyta


Which of the following is the best thing to do during heavy lightning?
A. Lying on the ground in an open place
B. Going into the nearest water body
c. staying indoors, away from metallic doors or windows
D. standing under a tall tree


In which phase proteins for spindle fibre formation are synthesized?
\( A \cdot G_{1}- \) phase
B. G_-phase
c. s-phase
D. Anaphase


The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.


A lake with an inflow of domestic
sewage, rich in organic waste, may result in
A. Drying of the lake very soon due to algal bloom
B. An increased production of fish due to lot of nutrients
c. Death of fish due to lack of oxygen
D. Increased population of aquatic web organisms


f \( r_{2}=3 r_{1} \) and time period of revolution
for \( B \) be \( T \) than time taken by \( A \) in
moving from position 1 to position 2 is :
\( ^{A} \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
3. \( T \frac{\sqrt{3}}{2} \)
c. \( \frac{T \sqrt{2}}{3 \sqrt{3}} \)
D. \( \frac{T \sqrt{2}}{3} \)


Hydrogen atom in ground state takes
up a photon of \( \lambda=50 \) nm (uv light)
Find the \( K E \) with which it is emitted.
A . \( 14.4 e V \)
B. \( 12.2 e V \)
c. \( 13.6 e V \)
D. \( 11.2 e V \)


Two symmetrical dice are thrown. The probability of getting a sum of 6 points
is
A \( \cdot \frac{4}{36} \)
в. \( \frac{5}{36} \)
c. \( \frac{6}{36} \)
D. \( \frac{1}{36} \)


A smooth block is released at rest on a
\( 45^{\circ} \) incline and then slides a distance \( d \)
The time taken to slide is \( n \) times as
much to slide on rough incline than on a
smooth incline. The coefficient of
friction is:
A
в. \( _{\mu_{k}}=\sqrt{1-\frac{1}{n^{2}}} \)
c. \( _{\mu_{s}=1-\frac{1}{n^{2}}} \)
D. \( _{\mu_{s}}=\sqrt{1-\frac{1}{n^{2}}} \)


If \( A \) and \( B \) be two sets containing 4 and
8 elements respectively, what can be
the maximum number of elements in
\( A \cup B ? \) Find also, the minimum number
of elements in \( (\boldsymbol{A} \cup \boldsymbol{B}) \) ?
A. Maximum number of elements \( =12 \)
Minimum number of elements = 8
B. Maximum number of elements \( =14 \) Minimum number of elements \( =8 \)
c. Maximum number of elements \( =12 \)
Minimum number of elements = 9
D. Maximum number of elements \( =14 \)
Minimum number of elements \( =7 \)


In an equilateral triangal \( A B C, D \) is a point on side \( \mathrm{BC} \) such that \( B D=\frac{1}{3} B C \)
Prove that \( 9 A D^{2}=7 A B^{2} \)


The thyroid hormones are strored as
A. Glycoproteins
B. Thyroglobulin
\( c . \) T3 and T4
D. Polycyclic hydrocarbons


Find the principal value of \( \tan \left(\cos ^{-1} \frac{1}{2}\right) \)


Pick out the isoelectronic species from the following:
\( (\boldsymbol{I}) \boldsymbol{C} \boldsymbol{H}_{3}^{+} \)
\( (\boldsymbol{I I}) \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( (I I I) N H_{3} \)
A. I and II
B. III and IV only
c. I and III
D. II, III, IV


Which of the following solution in water will have the lowest vapour pressure?
A. \( 0.1 M, \) NaCI
B. \( 0.1 M, \) Sucrose
с. \( 0.1 M, \)ВаС\( I_{2} \)
D. \( 0.1 M N a_{3} P O_{4} \)


For an \( A . P, \) if \( T_{1}=22, T_{n}=-11 \) and
\( \boldsymbol{S}_{\boldsymbol{n}}=\boldsymbol{6 6}, \) then find \( \boldsymbol{n} \)


Hydrogen bond is strongest in:
A . \( H F \)
в. НС l
c. \( H B r \)
D. \( H l \)
E. \( H A l \)


Which of the following pollutants is main product of automobiles exhaust?
A. \( C O \)
в. \( C O_{2} \)
c. No
D. Hydrocarbons


\( \lim _{n \rightarrow \infty} \frac{\sqrt{\mathbf{1}}+\sqrt{\mathbf{2}}+\ldots \ldots+\sqrt{n-1}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}=\mathbf{0} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D. 0 (zero)


If \( a, b, c \) are positive and are the \( p \) th \( , q t h \)
and \( r t h \) terms, respectively, of a G.P. \( \operatorname{then} \Delta=\left|\begin{array}{lll}\log a & p & 1 \\ \log b & q & 1 \\ \log c & r & 1\end{array}\right| \) is
\( A \)
B. \( \log (a b c) \)
c. \( -(p+q+r) \)
D. none of these


Three forces
\( (\hat{i}+3 \hat{j}+\hat{k}), \frac{5}{7}(-2 \hat{i}+9 \hat{k}) \) and
\( 11(2 \hat{i}+\hat{j}+6 \hat{k}) \) are acting on a
particle. Calculate the work done in displacing the particle from point (4,-1,1) to point (11,6,8)


The contraction of the rubber-band is a
spontaneous, natural process because it is accompanied by:
A. an increase in the kinetic energy
B. a decrease in the free-energy in the rubber-band
c. an increase in heat in the rubber-band
D. an elastic force


The middle term in the expansion of \( \left(1-\frac{1}{x}\right)^{n}(1-x)^{n}, \) is
A \( \cdot^{2 n} C_{n} \)
в. \( ^{-2 n} C_{n} \)
\( \mathrm{c} .^{-2 n} C_{n-1} \)
D. none of these


The primary threshold substance
are
A. Urea and uric acid
B. Potassium and calcium
c. Glucose and amino acids
D. Plasma proteins


\( \frac{d^{2} y}{d x^{2}}+\sin \left(\frac{d y}{d x}\right)+y 0 \) Find order and
degree of this \( D E \)


What is the difference between direct
and indirect development?


The valency of elements in group I A is:
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


The symbol for a unit which is not named in the honour of some scientist
is written in
A. Lower initial letter
B. Initial capital letter
c. Lower letter
D. All


The best method to purify impure
acetone is:
A. \( \quad C H_{3} C O C H_{3}+H C l \rightarrow C H_{3}-C_{I l}^{D H}-C H_{3} \stackrel{h e a t}{\longrightarrow} \)
\( C H_{3} C O C H_{3} \)
B. \( \quad C H_{3} C O C H_{3}+N a H S O_{3} \rightarrow C H_{3}-C_{I}^{D H}- \)
\( S O_{3} N a \stackrel{N a_{2} C O_{3}}{\longrightarrow} C H_{3} C O C H_{3} \)
\( \mathrm{c} \)
\( C H_{3} C O C H_{3} \)
D.
\[
C H_{3} C O C H_{3}+H_{2} S O_{4} \rightarrow C H_{3}-\quad C_{1}^{\prime} C_{3}-C H_{3} \stackrel{\text { Heat}}{\longrightarrow}
\]
\( C H_{3} C O C H_{3} \)


Divide \( :\left(51 m^{3} p^{2}-34 m^{2} p^{3}\right) \) by \( 17 m p \)
\( \mathbf{A} \cdot m^{2} p \)
В \( \cdot m p^{2} \)
c. \( 3 m^{2} p-2 m p^{2} \)
D. \( m \)


In tetrad, the number of non-cross over
chromatids is normally
A. Four
B. Two
c. one
D. None of the above


A candle is placed in front of an optical instrument, and an image is obtained as erect, virtual, and reversed from left
to right. Identify the device that would produce the types of images described
above.
A. Concave mirror
B. Convex mirror
c. concave lens
D. Convex lens
E. Flat mirror


A battery of e.m.f. \( 3.0 \mathrm{V} \) supplies current through a circuit in which the
resistance can be changed. A high resistance voltmeter is connected
across the battery. When the current is
\( 1.5 \mathrm{A}, \) the voltmeter reads \( 2.7 \mathrm{V} \). The
internal resistance of the battery is
A . \( 4 \Omega \)
в. \( 1.2 \Omega \)
c. \( 0.2 \Omega \)
D. 2\Omega


\( 1 m A= \)
\( \mathbf{A} \cdot 1000 A \)
B. \( 10^{-3} A \)
\( \mathbf{c} \cdot 1 C s^{-1} \)
D. None


Assertion (A): The enthalpy of formation of \( H_{2} O_{(l)} \) is greater than that of \( H_{2} O(g) \) Reason (R): Enthalpy change is negative for the condensation reaction \( H_{2} O(g) \rightarrow \)
\( H_{2} O(l) \)
A. Both assertion and reason are correct, reason is the correct explanation of the assertion
B. Both assertion and reason are correct reason is the not correct explanation of the assertion
c. Assertion is correct, reason is incorrect
D. Assertion is incorrect, reason is correct


An electric dipole has the magnitude of its charge as \( q \) and its dipole moment is
\( \boldsymbol{p} . \) It is placed in uniform electric field \( \boldsymbol{E} \) If its dipole moment is along the direction of the field, the force on it and
its potential energy are respectively
A. \( q . E \) and max
в. 2q.E and min
c. \( q . E \) and min
D. zero and min


A radiation is incident on a metal of
work function \( 2.3 e V . \) The incident
radiation is \( 600 n \) m.lf the total energy of
incident radiation is \( 23 J \), then the
number of photoelectrons is
A. zero
B \( .<10^{4} \)
\( \mathbf{c} .=10^{4} \)
D. \( \infty \)


Select the characters which are not
applicable to the anatomy of dicot roots:
(a) Conjunctive tissue present (b) Presence of protein compound in casparian strips
(c) Polyarch xylem bundles (d) Presence of pericycle
\( A \cdot(a) \) and \( (b) \)
B. (b) and (d)
\( c \cdot(c) \) and \( (d) \)
\( D \cdot(a) \) and \( (d) \)
E. (b) and (c)


The process of changing water vapour into water is called


How are convection currents formed
when a liquid is heated?


A drop of liquid is broken down into 27 identical liquid drops. If the terminal
velocity of original liquid drop is \( V_{T} \) then find the terminal velocity of the new liquid drop thus formed.
A \( \cdot \frac{V_{T}}{3} \)
в. \( \frac{V_{T}}{9} \)
c. \( \frac{V_{T}}{27} \)
D. \( \frac{9 V_{T}}{9} \)


Which term of the sequence
\( \mathbf{3}, \mathbf{8}, \mathbf{1 3}, \mathbf{1 8}, \dots \dots . . \) is \( \mathbf{4 9 8} \)
A. 95 th
B. 100 th
c. \( 102 t h \)
D. \( 101 t h \)


Incomes of the families in a locality are given. Find the mode of the data.
\( \begin{array}{lllll}\text { Income } & 1- & 201 & 401 & 600 \\ \text { (in Rs.) } & 200 & 400 & 600 & 800\end{array} \)
10 16 Number
of
families


The interior of the urinary bladder is
lined by
A. Columnar epithelium
B. Squamous epithelium
c. Transitional epithelium
D. Goblet cells


The sum of three terms of a geometric sequence is \( \frac{39}{10} \) and their product is 1 Find the common ratio and the terms


A vertical off-shore structure is built to
withstand a maximum stress of \( 10^{9} \) Pa.
Is the structure suitable for putting up
on top of an oil well in the ocean ? Take
the depth of the ocean to be roughly 3 \( \mathrm{km}, \) and ignore ocean currents.


The most electronegative element is:
A. nitrogen
B. fluorine
c. oxygen
D. chlorine


State whether the following statement is true or false. Give reason to support
your answer.

A set can have infinitely many subsets.
A. True
B. False


A stone is dropped into a pond from the top of the tower of height, \( h \). If \( \nu \) is the speed of sound in air, then the sound of splash will be heard at the top of the tower after a time
A \( \cdot \sqrt{\frac{2 h}{g}}+\frac{h}{\nu} \)
B. \( \sqrt{\frac{2 h}{g}}-\frac{h}{\nu} \)
c. \( \sqrt{\frac{2 h}{q}} \)
D. \( \sqrt{\frac{2 h}{g}}+\frac{2 h}{\nu} \)


Excretion means
A. Removal of useless substances and substances
present in excess.
B. Formation of those substances which have some role
in the body.
c. Removal of such substances which have never been
part of the body.
D. All of the above.


Assertion
Electromagnetic waves carry energy
and momentum.
Reason
Electromagnetic waves can be
polarised.
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


When electricity is passed through a solution of \( A l C l_{3}, 13.5 \) g of Al are deposited. The number of Faradays of electricity passed is: ( write your answer to nearest integer)


The earthy impurities present in the mineral are called:
A . flux
B. slag
c. gangue
D. refractory material


A proton, deutron and an \( \alpha \) -particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths?
A .1: 2: 2
B. 2:1:1
c. 1: 1: 2
D. 1: 2: 1


A planar coil of area \( 7 \mathrm{m}^{2} \) carrying an anti-clockwise current 2 A is placed in an extemal magnetic field \( \vec{B}=(0.2 \hat{i}+ \) \( 0.2 \hat{j}-0.3 \hat{k}), \) such that the normal to the plane is along the \( \operatorname{line}(3 \hat{i}-5 \hat{j}+ \)
4 \( \hat{k} \) ). Select correct statements from the
following. ( Consider Normal of the coil and Magnetic moment vectors to be in the same direction
This question has multiple correct options
A. The potential energy of the coil in the given orientation is 6.4
B. The angle between the normal (positive) to the coil and the external magnetic field is \( \cos ^{-1}(0.57) \)
c. The potential energy of the coil in the given orientation is 3.2
D. The magnitude of magnetic moment of the coil is about \( 14 A m^{2} \)


The mass of block is \( m_{1} \) and that of
liquid with the vessel is \( m_{2} . \) The block is
suspended by a string(tension \( \boldsymbol{T} \) )
partially in the liquid. The reading of the weighing machine placed below the
vessel:
A \( \cdot \) can be \( \left(m_{1}+m_{3}\right) g \)
B. can be greater than \( \left(m_{1}+m_{2}\right) g \)
C . is equal to \( \left(m_{1} g+m_{5} g-T\right) \)
D. can be less than \( \left(m_{1}+m_{2}\right) g \)


A siren of frequency n approaches a stationary observer and then recedes from the observer. If the velocity of
source (V) < the velocity of sound(C), the apparent change in frequency is :
A. 2nv/C
B. 2nC/V
\( c \cdot n / V \)
D. 2VC/n


The order of magnitude of 379 is
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


Three resistors are connected to a \( 6 \mathrm{V} \)
battery as shown in the figure given
Calculate the potential difference
across the \( 7.2 \Omega \) resistor


State Newton's third law of motion.


Paraffin dissolve in:
A. salt water
B. distilled \( H_{2} \) O
\( \mathbf{c} \cdot C H_{3} O H \)
D. benzene


A thin film with index of refraction 1.33
coats a glass lens with index of
refraction \( 1.50 . \) Which of the following
choices is the smallest film thickness
that will not reflect light with
wavelength \( 640 n m ? \)
A . \( 160 n m \)
B. \( 240 n m \)
\( c .360 n m \)
D. \( 480 n m \)


Find the following limit:
\( \lim _{x \rightarrow 0} x \cot 3 x \)


If \( \int \frac{x^{2}-x+1}{\left(x^{2}+1\right)^{\frac{3}{2}}} e^{x} d x=e^{x} f(x)+c, \) then
This question has multiple correct options
\( A . f(x) \) is an even function
B. \( f(x) \) is a bounded function
c. the range of \( f(x) \) is (0,1]
D. f(x) has two points of extrema


The de Broglie wavelength of 1 mg grain
of sand blown by a \( 20 m s^{-1} \) wind is:
A \( \cdot 3.3 \times 10^{-29} \mathrm{m} \)
В. \( 3.3 \times 10^{-21} \mathrm{m} \)
c. \( 3.3 \times 10^{-49} \mathrm{m} \)
D. \( 3.3 \times 10^{-42} \mathrm{m} \)


Gluconeogenesis is controlled by
A. Cortisol
B. Corticosterone
c. Thyroxine
D. All of the above


Explain the following:
(a) Disinfectants
(b) Food preservatives
(c) Tranquilizers


Which is the incorrect order for
compounds?
Compound \( : N H_{3}, P H_{3}, A s H_{3}, S b H_{3} \)
A \( \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3}(\text { Bond angle }) \)
B . \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \) (Bond energy)
C. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \) (Boiling point)
D. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \) (Reducing power)


A shoe shop in Chennai sold hundred
pairs of shoes of a particular brand in a certain day with the following
distribution.
\[
\begin{array}{lcccc}
\text { size } & & & & \\
\text { of } & 4 & 5 & 6 & 7 \\
\text { shoe } & & & &
\end{array}
\]
No
\[
\begin{array}{l}
\text { of } \\
\text { pairs } \\
\text { sold }
\end{array}
\]
23
Find the mode of the following distribution.


Find the general solution of the differential equation:
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}-\boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\sqrt{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}} \boldsymbol{d} \boldsymbol{x} \)


For soft iron, in comparison with steel:
A. hysteresis loss is more
B. hysteresis loss is same
C. hysteresis loss is less
D. hysteresis loss is negligible


\( A 1^{\circ} C \) rise in temperature is observed in a conductor by passing a certain current. If the current is doubled, then
the rise in temperature is approximately
\( \mathbf{A} \cdot 2.5^{\circ} \mathrm{C} \)
B . \( 4^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 2^{\circ} \mathrm{C} \)
D. \( 1^{\circ} \mathrm{C} \)


An organism was found to be multinucleated and possessed a naked cytoplasm. It exhibited saprophytic
mode of nutrition. To which of the
following kingdom would you classify this organism?
A. Monera
B. Protista
c. Mycota
D. Plantae


Assertion
The metals of group 2 (except Be) form
ionic compounds.
Reason
Electropositive character and the
reducing property increase on moving
down the group.

Read the above assertion and reason and
choose the correct statement regarding
it.
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


\( \underbrace{x}_{L} \)


The oxidation of iodide ion by
perdisulphate ion is described as follows :
\( \boldsymbol{I}^{\Theta}+\boldsymbol{S}_{2} \boldsymbol{O}_{8}^{2-} \rightarrow \boldsymbol{I}_{3}^{\Theta}+\boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
If the rate disappearance of \( S_{2} O_{8}^{2-} \) ions is \( 1.5 \times 10^{-3} M s^{-1}, \) the rate of
formation of \( \boldsymbol{S O}_{4}^{2-} \) ions is:
\( \mathbf{A} \cdot 3.0 \times 10^{-3} M s^{-1} \)
B . \( 2.5 \times 10^{-3} M s^{-1} \)
C \( .2 .75 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1} \)
D. None of these


The filtrate from the glomerulus contains
A. Urea and uric acid
B. Urea, uric acid and ammonia
c. Urea, uric acid, ammonia and water
D. Urea, uric acid, glucose and water


\( \boldsymbol{B r} \boldsymbol{O}_{3}^{-}(\boldsymbol{a q})+\mathbf{5 B r}_{(a q)}^{-}+\boldsymbol{6 H}^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B r}_{2}(\mathbf{1})+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(1)} \).The rate of
apprearance of bromine \( \left(B r_{2}\right) \) is related
to rate of disappearance of bromide ions as following:
A \( \cdot \frac{d\left(B r_{2}\right)}{d t}=-\frac{5}{3} \frac{d\left(B r^{-}\right)}{d t} \)
B. \( \frac{d\left(B r_{2}\right)}{d t}=\frac{5}{3} \frac{d\left(B r^{-}\right)}{d t} \)
C \( \cdot \frac{d\left(B r_{2}\right)}{d t}=\frac{3}{5} \frac{d(B r)}{d t} \)
D. \( \frac{d\left(B r_{2}\right)}{d t}=-\frac{3}{5} \frac{d\left(B r^{-}\right)}{d t} \)


Which of the following does not give white precipitate when boiled with alcoholic silver nitrate:
A. allyl chloride
B. t-butyl chloride
c. chlorobenzene
D. benzyl chloride


Water turns blue cobalt chloride paper:
A. no change
B. red
\( c \cdot \operatorname{pink} \)
D. orange


Wo are
kept in two identical vessels, which are
placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure shows the temperature T vs time \( t \) plot for the two
material. We denote the specific heat of materials in the liquid(solid) states to
be \( C_{L 1}\left(C_{S 1}\right) \) and \( C_{L 2}\left(C_{S 2}\right) \) respectively. Choose the correct option.
A \( \cdot C_{L 1}<C_{L 2} \) and \( C_{S 1}<C_{S 2} \)
B . \( C_{L 1}>C_{L 2} \) and \( C_{S 1}<C_{S 2} \)
C. \( C_{L 1}>C_{L 2} \) and \( C_{S 1}>C_{S 2} \)
D. \( C_{L 1}<C_{L 2} \) and \( C_{S 1}>C_{S 2} \)


If radii of two concentric circles are 4
\( \mathrm{cm} \) and \( 5 \mathrm{cm}, \) then the length of each chord of one circle which is tangent to the circle is
A. \( 3 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .9 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)


The Sales Tax amount a customer has
to pay.
A. Rs. 1,530
B. Rs. 1,260
c. Rs. 1,950
D. Rs. 1,420


Simplify: \( \left(\boldsymbol{m}^{2}+\boldsymbol{2} \boldsymbol{n}^{2}\right)^{2}-\boldsymbol{4} \boldsymbol{m}^{2} \boldsymbol{n}^{2} \)


Which of the following is not true about high density polythene?
A. Tough
c. Inert
D. Highly branched


The elements which have taken the
place of Eka aluminium is :
A. Germanium
B. Gallium
c. silicon
D. Aluminium


What are monosaccharides? Explain denaturation of proteins.


Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}= \)
\( \mathbf{1 4} \)
Hence, find 'a' if \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \)
A \( \cdot x=1, y=6 \) and \( a=3 \frac{2}{5} \)
B. \( x=3, y=12 \) and \( a=7 \frac{6}{5} \)
c. \( _{x}=3, y=2 \) and \( a=1 \frac{1}{3} \)
D. \( x=12, y=16 \) and \( a=4 \frac{31}{3} \)


A count rate meter shows a count of 240
per minute from a given radioactive source. One hour later the meter shows
a count rate of 30 per minute. The halflife of the source is?
A. 80 min
B. 120 min
c. 20 min
D. 30min


A mineral is rich in \( \mathrm{ZnS} \) and Pbs. If it
can be concentrate by froth flotation process enter 1 else 0.


Acid hydrolysis of sucrose is accompanied by a change in optical rotation.
A. True
B. False


The ratio of magnetic field at centre of circular loop to the magnetic field at the centre of square loop, which are made by a constant length current carrying wire :
A \( \cdot \frac{\pi^{2}}{16} \)
в. \( \frac{\pi^{2}}{8 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{4 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{2 \sqrt{2}} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}, \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \)
are rational, and \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z}, \) where \( \boldsymbol{Z} \) is
the set of integers. Then \( a+b \) is
A. a negative integer
B. an integer
c. nonintegral rational number
D. none of these


Conductors are materials having an
electrical conductivity :
A . greater than \( 10^{3} \) s/cm
B. between \( 10^{-8} \) to \( 10^{3} \) s/cm
C . equal to \( 10^{-8} \mathrm{S} / \mathrm{cm} \)
D. zero


The \( E_{c e l l}^{o} \) for \( C u\left|C u^{2+}\right|\left|A g^{+}\right| A g \) in volt is
A. +0.449
B. +0.474
c. -0.449
D. -0.474


\( v-t \) graph for rectilinear motion is
given as shown in the figure. Matched
the column on the basic of the \( v-t \)
graph.


The planet also known as morning star
is:
A. Mars
B. Mercury
c. Earth
D. Venus


n fig, \( A B C D \) is a parallelogram and
\( B C \) is produced to a point \( Q \) such that
\( \boldsymbol{A D}=\boldsymbol{C Q} . \) If \( \boldsymbol{A Q} \) intersect \( \boldsymbol{D} \boldsymbol{C} \) at \( \boldsymbol{P} \)
show that \( a r(B P C)=a r(D P Q) \)


A \( 600 n m \) light is perpendicularly
incident on a soap film suspended in
air. The film is \( 1.00 \mu m \) thick with \( n= \)
1.35. Which statement most accurately
describes the interference of light reflected by the two surfaces of the film?
A. The waves are close to destructive interference
B. The waves are close to constructive interference
c. The waves show complete destructive interference
D. The waves show complete constructive interference


is formed by the transformation of trees buried inside the earth millions of
years ago.
A. Biogas
B. coal
c. Diesel
D. Iron


Heat energy required of melt \( 1 g \) of ice to
\( 1 g \) of water at \( 0^{0} C \) is :


What could be the reason for maida
flour to increase in size?
A. Fermentation
B. Preservation
c. Fumigation
D. Both A and B


Foramen ovale/fossa ovalis is present in
A. Partition between inner and middle ear
B. Inter-auricular septum
C. Inter-ventricular septum
D. Aortic and pulmonary arches


If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be This question has multiple correct options
A. Going up with increasing speed
B. Going down with increasing speed
c. Going up with uniform speed
D. Going down with uniform speed


Assertion
Neurons are said to possess the
property of excitability.
Reason
Neurons can get excited by a given
stimulus.
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


Minamata disease is because of
pollution of:
A. organic waste going into drinking water
B. oil spill in water
c. industrial waste containing mercury into fishing water
D. arsenic going into the atmosphere


What amount of heat (in \( \mathrm{kJ} \) ) is released
in forming \( 31.2 g \) of \( A s H_{3} \) by the
following reaction? (Given : At. wt. As = 75, H = 1) Given \( : 2 A s(s)+3 H 2(g) \rightarrow 2 A s H 3(g) \)
\( \Delta H=-780 k J \)
A. 312
B. 390
\( c \cdot \) १५
D. 780


Three particles, each of mass m are
placed at the vertices of a right angled triangle as shown in figure. The position
vector of the center of mass of the
system is:
(O is the origin and \( \hat{i}, \hat{j}, \hat{k} \) are unit vectors)
A \( \cdot \frac{2}{3}(a \hat{i}+b \hat{j}) \)
B \( \cdot \frac{2}{3}(a \hat{i}-b \hat{j}) \)
c. \( \frac{1}{3}(a \hat{i}+b \hat{j}) \)
D \( \cdot \frac{1}{3}(a \hat{i}-b \hat{j}) \)


The range of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}} \)
is


Water containing impurities doesn't freeze at \( 0 . \) Explain?


formula \( \left(C_{8} H_{10}\right) .(A) \) is oxidized by a strong oxidizing agent to (B). (B) on dehydration and subsequent reaction with ammonia forms an imide, (C). (C) is then reacted with a strong inorganic
base to form a compound that undergoes Hoffman bromamide reaction to give (D). (D) is treated with sodium nitrite in an ice cold acidic
solution to form the product (E). (E) is a
steam volatile compound and on nitration gives two mononitro derivatives. (E) is treated with sodium
hydroxide to form the salt (F). On heating a solution of (F), bubble are
formed due to release of gas. This gas does not burn. On analysis it was found
that the gas has two components, one
lighter than air and one heavier than air.
Compound \( (B) \) is :
A. Phthalic acid
B. Isophthalic acid
c. Terephthalic acid
D. Benzoic acid


\( \cos ^{-1}\left(\cos \left(2 \cot ^{-1}(\sqrt{2}-1)\right)\right) \) is equal to
A \( \cdot \sqrt{2}-1 \)
в.
\( c \cdot \frac{3 \pi}{4} \)
D. none of these


Constellation Orion can be seen only with a telescope.
A . True
B. False


Name the parts of human forebrain
indicating their respective function


Three different vibrating bodies produce three types of sounds \( X, Y \) and \( Z \) Sounds \( X \) and \( Y \) cannot be heard by a
man having normal range of hearing but sound \( Z \) can be heard easily. The sound \( X \) is used to find faults and
cracks in metals.The sound similar to
that which is produced during an earthquake before the main shock wave is generated.
Name one device which can produce
sound like \( X \)
A. Megaphone
B. SONAR
c. Bulb horn
D. Ear mufflers


Nucleolemma is a part of
A. Nuclear membrane
B. Nuclear reticulum
C. Nucleolus
D. Nucleoplasm


The pattern of the magnetic field around a conductor due to an electric
current flowing through it depends on
A. amount of current flowing through the conductor
B. amount of voltage supplied to the conductor
c. size of conductor
D. shape of the conductor


\( \int \frac{1}{\sqrt{4+x^{2}}} d x \)


A car travels \( 6.0 \mathrm{km} \) along a main road
in 6.0 minutes. It then travels \( 2.0 \mathrm{km} \)
along a minor road in 6.0 minutes. Which calculation of average speed for
the whole journey is correct?
A. \( 8.0 \div 12.0=0.67 \mathrm{km} / \mathrm{minute} \)
в. \( 12.0 \div 8.0=1.57 \mathrm{km} / \mathrm{minute} \)
c. \( 8.0+12.0=20 \mathrm{km} / \mathrm{minute} \)
D. \( 8.0 \times 12.0=96 \mathrm{km} / \mathrm{minute} \)


You are provided with a narrow and parallel beam of light. State how you will determine experimentally, whether it is a beam of ordinary(unpolarised) light, partially polarised light or completely polarised light.


If it is known that the third term of the
binomial expansion \( \left(x+x^{\log _{10} x}\right)^{3} \) is \( 10^{6} \)
then \( x \) is equal to
A . 10
B. \( 10^{\frac{5}{2}} \)
c. 100
D. 5


Meteors are commonly known as:
A. comets
B. Stars
c. Asteroids
D. shooting stars


Which of the following represents sublimation?
A. Solid \( \Leftrightarrow \) Gas
B. Solid \( \Leftrightarrow \) liquid
c. Liquid\( \Leftrightarrow g a s \)
D. Solid \( \Leftrightarrow \) liquid \( \Leftrightarrow g a s \)


A rectangle has
A. one line of symmetry
B. two lines of symmetry
C. three lines of symmetry
D. None of these


The conductance of an emulsion
increases on adding common salt. What type of emulsion is this?


Chlorine on compression to the same pressure will conduct electricity.
A. True
B. False


Marchantia is Bryophyte because it lacks
A . Roots
B. Independent sporophyte
c. seeds
D. Vascular tissue


\( 0.40 g \) of an organic compound \( (A) \)
(Molecular formula \( C_{5} H_{8} O \) ) reacts
with \( x \) mole of \( C H_{3} M g B r \) to liberate
\( 224 m L \) of a gas at STP.With excess of
\( \boldsymbol{H}_{2},(\boldsymbol{A}) \) gives pentan-1-ol. The correct structure of \( (A) \) is:
A \( \cdot C H_{3}-C \equiv C-C H_{2}-C H_{2}-O H \)
в. \( C H_{3}-C H_{2}-C \equiv C-C H_{2}-O H \)
c. \( H-C \equiv C-C H_{2}-C H_{2}-C H_{2}-O H \)
D. \( H-C \equiv C-C H_{2}-C H-C H_{3} \)
扎


Which of the following quantity decrease as sound wave travels through
a medium:
A. Amplitude
B. Frequency
c. velocity
D. wavelength


State whether the statement is True or
False. The cube of \( \left(2 x+\frac{1}{x}\right) \) is equal to \( 8 x^{3}+ \) \( 12 x+\frac{6}{x}+\frac{1}{x^{3}} \)
A. True
B. False


Curved surface area of a hollow cylinder
is \( 4224 \mathrm{cm}^{2} . \) A rectangular sheet having
width \( 33 \mathrm{cm} \) is formed cutting it along
its height. Find perimeter of sheet.


The total number of elements present in 6th period are:
\( A \cdot 18 \)
B. 31
c. 32
D. 17


Water used as moderator in nuclear
reactor is called:
A. heavy water
B. hard water
c. nuclear water
D. critical water


The sparks produced during sharpening of a knife against a grinding whee leaves the rim of the wheel tangentially. This is due to which of the following?
A. Inertia of rest
B. Inertia of motion
c. Inertia of direction
D. Force applied


An element with atomic number '32'
belongs to
A. 4th period, VIA group
B. 3rd period, IV A group
c. 4 th period, IV A group
D. 5th period, va group


Find the lateral surface area and total
surface area of the following right
prisms.


Which is not true for Second Law of
Thermodynamics?
A. The second law of thermodynamics states that the total entropy of an isolated system always increases over time, or remains constant in ideal cases where the system is in a steady state or undergoing a reversible process.
B. It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects
C. It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.
D. The second law of thermodynamics states that the total energy of an isolated system is constant.


An example for Pasteur effect can be
found in
A. Nostoç
B. Saccharomyces
c. Pinnularia
D. Penicillium


An uncharged metal object \( M \) is
insulated from its surroundings. A
positively charged metal sphere \( \boldsymbol{S} \) is
then brought near to \( M . \) Which diagram
best illustrated the resultant
distributions of charge on \( S \) and \( M ? \)
\( A \)
в.
\( c \)
D.


The basicity is high for :
A. Phosphorus acid
B. Metaphosphoric acid
c. ortho phosphoric acid
D. Hypo phosphorus acid


The value of G does not depend upon:
A. nature of the interacting bodies
B. size of the interacting bodies
c. mass of the interacting bodies
D. all of these


Differentiate the given function w.r.t. \( x \)
\( \boldsymbol{y}=\log \left(\cos e^{x}\right) \)


(I) Ref. images
(II) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{N} \boldsymbol{H}_{2} \)
(III) \( \left(\boldsymbol{C H}_{3}\right)_{2} \)
\( o \)
\( (\mathrm{IV}) C H_{3}-\stackrel{\|}{C}-N H_{2} \)
What is the correct order of basicity among the following compounds?
A. \( I I>I>I I I>I V \)
В. \( I>I I>I I I>I V \)
c. \( I I I>I>I I>I V \)
\( . I>I I I>I I>I V \)
\( V \)


Which two of these vegetables correctly represent the homologous structures? Potato, Tomato, Radish, Brinjal, Carrot,
Bottle-ground
A. Carrot and Tomato
B. Potato and Brinjal
c. Radish and Carrot
D. Radish and Bottle-ground


Write the balanced chemical equation for the last step of oxidation test of
sulphur.
A \( . B a C l_{2}+N a_{2} S O_{4} \rightarrow B a S O_{4}+2 N a C l \)
в. \( H C l+N a_{2} S O_{4} \rightarrow N a H S O_{4}+N a C l \)
c. \( B a C l_{2}+2 H C l \rightarrow 2 C l_{2}+B a+H_{2} \)
D. None of the above


After terminal velocity is reached the acceleration of a body falling through a viscous fluid is:
A. zero
B. \( g \)
c. less thang
D. greater than g


what is the net charge on a conducting sphere of radius \( 19 \mathrm{cm} \) ? given that the
electric field \( 15 \mathrm{cm} \) from the centre of
the sphere is equal to \( 3 \times 10^{3} \mathrm{N} / \mathrm{C} \) and
is directed inward
A. \( -7.5 \times 10^{-5} \mathrm{C} \)
в. \( -7.5 \times 10^{-9} \mathrm{C} \)
c. \( 7.5 \times 10^{-5} C \)
D. \( 7.5 \times 10^{-9} C \)


If more than one code designates the single amino acid it is
A. Degenaracy of codon
B. Overlapping of codon
c. Nonsense codons
D. None of the above


Which one is not correctly matched?
A. Streptomyces - Antibiotic
B. Serratia - Drug addiction
C. Rhizobium - Biofertilizer
D. spirulina - single cell protein


Match the excretory organs listed under
column I with the animals given under
column II and select the correct option.
Column I (Excretory organs)
A. Nephridia \( \quad \) (i) \( \quad \) Hydra
Malpighian \( \quad \) (ii) \( \quad \) Leech
B. tubules
C. Protonephridia
(iii) Shark
D. Kidneys
(iv) \( \quad \) Roundworms
(v) Cockroach
A. A-(ii), B-(v), C-(iv), D-(iii)
B. A-(iv), B-(ii), C-(i), D-(v)
c. \( A-(v), B-(\text { ii) }, C-(i v), D-( \text { iii) } \)
D. A-(ii), B-(iv), C-(v), D-(i)


White phosphorous catches fire in air to produce dense white fumes. This is due to the formation of
\( \mathbf{A} \cdot P_{4} O_{10} \)
в. \( P H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{3} \)
D. \( H_{3} P O_{2} \)


Copper wire of length \( 3 m \) and the area
of cross section \( 1.7 \times 10^{-6} m^{2} \) has a
resistance of \( 3 \times 10^{-2} m^{2} \) ohms.
Calculate the resistivity of copper?


Which of the following is a good conductor of heat?
A. steel
B. Glass
c. wood
D. Rubber


The pendulum of a bob undergoes SHM with an amplitude A is given by the equation \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{s} \boldsymbol{i n} \boldsymbol{\omega} \boldsymbol{t} . \) The
corresponding angular SHM equation can be written as
A \( \cdot \theta=\phi \cos (\omega t) \)
в. \( \theta=\phi \sin (\omega t) \)
c. \( \theta=\phi \tan (\omega t) \)
D. \( \theta=\phi(\omega t) \)


When a glass filled with water is struck with a stick, ripples are produced in the water. This indicates that
A. the glass is not vibrating
B. the glass may or may not be vibrating.
c. the glass is vibrating.
D. none of the above is true


Draw the graph of the above linear
equation having Celsius on X-axis and Fahrenheit on Y-axis.


\( \Omega \)
2
2
2


What is the average sales of all the
branches (in thousand numbers) for the
year \( 2000 ? \)
A . 73
B. 80
\( c \cdot 83 \)
D. 88


At what temperature is the Fahrenheit scale reading equal to twice of Celsius?
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 160^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 80^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)


Which of the following pairs belong to the category of cold blooded animals?
A. Snakes and birds
B. Bat and rats
c. Frog and snakes
D. Birds and monkey


In the given diagram of a leg of
cockroach, parts have been indicated by
alphabets. Select the answer in which
these alphabets have been
correctly matched with the parts which
they indicate.
A. A- Coxa; B- Tibia; C- Tarsus; D- Femur; E- Trochanter
B. A- Coxa; B- Femur; C- - Trochanter
D- Tarsus; E- Tibia
C. A- Coxa; B- Tarsus; C- Femur; D- Tibia; E- Trochanter
D. A- Coxa; B- Trochanter; C- Femur; D- Tibia; E- Tarsus


The distance between the parallel lines
\( 9 x^{2}-6 x y+y^{2}+18 x-6 y+8=0 \) is?
A \( \cdot \frac{1}{\sqrt{10}} \)
B. \( \frac{2}{\sqrt{10}} \)
c. \( \frac{4}{\sqrt{10}} \)
D. \( \sqrt{10} \)


Which one of the following statements
İs incorrect?
A. The residual air in lungs slightly decreases the efficiency of respiration in mammals
B. The presence of non-respiratory air sacs, increases the efficiency of respiration in birds
C. In insects, circulating body fluids serve to distribute oxygen to tissues
D. The principle of counter current flow facilitates efficient respiration in gills of fishes


Fill the vacant space with the suitable
option. A wave transfers from
one location to another.
A. energy, but not matter
B. matter, but not energy
c. both energy and matter
D. neither energy nor matter
E. Waves do not transfer anything across locations


Argon is a greenhouse gas.
A. True
B. False


Which of the following is called the artificial kidney?
A. Dializer
B. Haemocytometer
c. Auto analyser
D. Artificial Pacemaker


The rate constant for a first order
reaction is \( 7.0 \times 10^{-4} s^{-1} . \) If initial
concentration of reactant is \( 0.080 M \)
what is the half life of reaction?
\( \mathbf{A} \cdot 990 s \)
B . \( 79.2 s \)
c. 12375 s
D. \( 10.10 \times 10^{-4} \mathrm{s} \)


State True or False.
Use of herbicides and pesticides should be reduced to prevent soil pollution.
A. True
B. False


Role of chromosomes in sex
determination was proposed by
A. Sutton and Boveri
B. Henking
c. Mc clung
D. Morgan


A body of mass M was slowly hauled up a rough hill by a force \( F \) which at each point was directed along a tangent to the hill. Work done by the force.
This question has multiple correct options
A. Is independent of the shape of trajectory
B. Depends upon the vertical component of displacemen but is independent of horizontal component
c. Depends upon both the component
D. Does not depend upon the coefficient of friction


Explain the geometry of \( \left[\boldsymbol{C o}\left(\boldsymbol{M} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)
on the basis of hybridization. \( (\mathrm{Z} \text { of } \mathrm{Co}= \)
27)


If \( a x^{2}+2 x y+b y^{2}=0 \) then find \( \frac{d y}{d x} \)


Gravity separation process is used for the concentration of
Haematite
2. Chalcopyrite
3. Bauxite
Choose the correct one from the given options.


A distribution has mean=8.7, median
\( =8.5 \) and mode \( =7.3 . \) The distribution is
A. Positively skewed
B. negatively skewed
c. symmetrical
D. none of these


\( f\left\{f_{i} x_{i}=75 \text { and } \sum f_{i}=15, \) then find \right.
the mean \( \bar{x} \)


Let \( A \) and \( B \) be two sets such that
\( \boldsymbol{A}= \)
\( \boldsymbol{x}: \boldsymbol{f}(\boldsymbol{x})=\left[\boldsymbol{x}^{2}\right], \) is discontinuous in \( [\mathbf{0}, \mathbf{2}] \)
\( \boldsymbol{B}= \)
\( \boldsymbol{x}: \boldsymbol{f}(\boldsymbol{x})=\left[\tan ^{2} \boldsymbol{x}\right]\left[\cot ^{2} \boldsymbol{x}\right], \) is non \( - \) diff
If \( m \) is the total number of onto
functions from \( A \) to \( B \) then find the
total number of divisors of \( \boldsymbol{m} .[\mathrm{Note}:[\boldsymbol{k} \)
denotes the greatest integer less than or equal to \( k .] \)


The deviation of gases from the behaviour of ideal gas is due to
A. colourless molecules
B. covalent bonding of molecules
c. attraction of molecules
D. absolute scale of temperature


A plane \( \pi \) makes intercepts 3 and 4
respectively on \( z- \) axis. If \( \pi \) is parallel to \( \boldsymbol{y}- \) axis, then its equation is ?
A. \( 3 x+4 z=12 \)
B. \( 3 z+4 x=12 \)
c. \( 3 y+4 z=12 \)
D. \( 3 z+4 y=12 \)


Which of the following solids are known to undergo sublimation?
¡. \( C O_{2} \)
ii. \( \boldsymbol{I}_{2} \)
iii. Naphthalene
A. i only
B. ii only
c. i and ii only
D. ii and iii only
E. i, ii and iii


A parallel-plate capacitor with plate
area \( A \) and separation between the
plates \( d, \) is charged by a constant
current \( i . \) Consider a plane surface of area \( A / 2 \) parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.


Find the direction cosines of a line
which makes equal angles with the coordinate axes.


For the reaction, \( \boldsymbol{C O}_{(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})} \rightleftharpoons \)
\( C O C l_{2(g)}, \) the value of \( K_{p} / K_{c} \) is equal
to?
A . 1.0
в. RT
c. \( \sqrt{R T} \)
D. \( \frac{1}{R T} \)


What is the inheritance of colour
blindness of both parents having a normal vision but mother having a recessive gene for colour blindness?
A. Son - 50\%; Daughter - nil
B. Son-100\%; Daughter-nil
c. son - nil ; Daughter - 100\%
D. son-nil; Daughter-nil


If \( 3 p+2 q=i+j+k \) and \( 3 p-2 q= \)
\( i-j-k, \) then the angle between \( p \) and
\( q \) is
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)
\( E \)


Migration of colloidal particles under
the effect of
called electrophoresis.
A . electric
B. magnetic
c. both
D. none


A current source sends a current i \( = \)
\( i_{0} \cos (\omega t) . \) When connected across an
unknown load gives a voltage output of,
\( \boldsymbol{v}=\boldsymbol{v}_{0} \sin (\omega t+\boldsymbol{\pi} / 4) \) across that load
Then voltage across the current source
may be brought in phase with the
current through it by
A. connecting an inductor in series with the load
B. connecting a capacitor in series with the load
C. connecting an inductor in parallel with the load
D. connecting a capacitor in parallel with the load.