Point charge \( +4 q,-q \) and \( +4 q \) are kept
on the \( x \) -axis at points \( x=0, x=a \) and
\( x=4 a \) respectively. Then:
A. Only-q is in stable equilibriummmmmm
B. None of the charges are in equilibrium.
c. All the charges are in unstable equilibrium.
D. All the charges are in stable equilibrium.


Calculate the quantity of electricity that would be required to reduce 12.3 g of nitrobenzene to aniline, if the current efficiency for the process is 50 percent. If the potential drop across the cell is 3.0 volts, how much energy will be
consumed?


In which form does the food get
transported in plants?
A. sucrose
B. Fructose
c. Glucose
D. Lactose


The length of an elastic string is \( 5 m \)
when the longitudinal tension is \( 4 N \)
and \( 6 m \) when the tension is \( 5 N . \) If the
length of the string (in meter) is "2 \( X^{\prime \prime} \)
when the longitudinal tension is \( 9 N \) (assume Hooke's law is valid) then the value of \( \boldsymbol{X} \) will be :


Sl unit of moment of couple is
A \( \cdot N^{2} m \)
в. \( N m \)
\( \mathrm{c} \cdot \mathrm{Nm}^{2} \)
D. \( N / m^{2} \)


How many ponds had \( 20-39 \) ducks?
Ducks per pond
A .25
B. 30
\( c \cdot 20 \)
D. 15


What is the type of the semiconductor,
for the energy band diagram shown in
the figure?
A. N-type semiconductor
B. P-type semiconductor
c. Intrinsic semiconductor
D. Both \( N \) and \( P \) type semiconductors


Who proposed wave nature of light?
A. Huygen
B. Youngg
c. Fresnel
D. Maxwell


The second division of meiosis is
A. Equational division
B. Reductional division
c. Multiplied division
D. None of the above


The following some statements about
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) are :
i)It acts as both oxidising and reducing
agent.
ii) It is a strong acid.
iii) Its anhydride in pure state exists as pale blue liquid The correct combination is :
A. All are correct
B. i, iii are correct
c. ii, iii are correct
D. i, ii are correct


In the following first-order competing reactions:
\( A+ \) Reagent \( \longrightarrow \)
Product; \( \quad B+ \) Reagent \( \longrightarrow \)
Product
The ratio of \( \frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}} \) if only \( 50 \% \) of \( \mathrm{B} \) will have been reacted when \( 94 \% \) of \( A \) has been
reacted is: (as nearest integer)


lonic species are stabilised by the dispersal of charge Which of the following carboxylate ion is the most stable :
\( \mathbf{A} . \)
\( C H_{3}-C-O^{\circ} \)
в.
\[
C l-C H_{2}-C-O
\]
\( c \)
\( F-C H_{2}-C-O^{\circ} \)
D. \( F>C H-C-O^{6} \)
\( F> \)


Select the correct statements:
This question has multiple correct options
A. s-block metal oxides are basic in nature, except \( B e O \) which is amphoteric
B. p-block metal oxides are acidic in nature, except \( N O \) \( N_{2} O, C O \)
C. d-block metal oxides are basic, acidic, and amphoteric in nature.
D. d-block metal oxides are only basic in nature.


A bomb at rest at the summit of a cliff
breaks into two equal fragments. One of
the fragments attains a horizontal velocity of \( 20 \sqrt{3} m / s . \) The horizontal
distance between the two fragments, when their displacement vectors is inclined at \( 60^{0} \) relative to each other is
\( (g=10), m / s^{\wedge} 2 \$ \$ \)
A \( \cdot 40 \sqrt{3} m \)
B. \( 80 \sqrt{3} m \)
c. \( 120 \sqrt{3} \mathrm{m} \)
.
D. \( 480 \sqrt{3} \mathrm{m} \)


The most non-metallic element among the following is:
A.
B.
\( c \cdot 0 \)
D. c


Consider the following statements.
A. The coefficient of linear expansion has dimension \( K^{-1} \)
B. The coefficient of volume expansion has dimension \( K^{1} \)
C. \( A \) and \( B \) are both correct.
D. A is correct but B is wrong.


\( f\left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \mathbf{1} & \boldsymbol{6}\end{array}\right|=\left|\begin{array}{ll}\mathbf{1} & \mathbf{8} \\ \mathbf{1} & \mathbf{6}\end{array}\right| \) then \( \mathbf{x}+2 \mathbf{y}= \)
\( A \cdot 9 \)
B. 17
c. 10
\( D \)


Describe briefly: Arithmetic growth
\( (b) \)
Geometric growth
(c) Sigmoid growth
curve
(d) Absolute and relative growth
rates


Which statement about cathode rays is
correct?
This question has multiple correct options
A. They travel in straight lines towards cathode
B. They produce fluorescent discharge through the walls of the tube
C. They produce heating effect
D. They can affect photographic plate


The projections of a line segment on \( x, y \) and \( z \) axes are respectively \( \sqrt{2}, 3,5 \) The length of the line segment is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 11
c. 8
D. 5


Very short answer type. Name the source gland and give one
main action of the following hormones:
aldosterone


When a \( 4 k g \) mass is hung vertically on a light spring that obeys Hooke's law,
the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by \( 5 c m s \) will
be \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s e c}^{2}\right) \)
A. 4.900 joule
B . 2.450 joule
c. 0.495 joule
D. 0.245 joule


Small intestine receives secretions
from the
A. Only liver
B. Only pancreas
c. Both A and B
D. None of the above


According to Munch hypothesis osmotic pressure remains high in the mesophyll cells due to
A. Accumulation of food brought by phloem
B. Accumulation of salts brought by xylem
c. conversion of starch into sugar
D. synthesis of soluble carbohydrates due to photosynthesis


\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{x} \\ \boldsymbol{x}^{2} & \boldsymbol{x} & \boldsymbol{6} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{6}\end{array}\right|=\boldsymbol{a} \boldsymbol{x}^{4}+\boldsymbol{b} \boldsymbol{x}^{3}+\boldsymbol{c} \boldsymbol{x}^{2}+ \)
\( \boldsymbol{d} \boldsymbol{x}+\boldsymbol{e}, \) then \( \boldsymbol{5} \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b}+\boldsymbol{3} \boldsymbol{c}+\boldsymbol{2} \boldsymbol{d}+\boldsymbol{e} \) is
equal to
A. 11
B. -11
c. 12
D. -12
E . 13


Two pieces, one of mass \( \mathrm{M} \) and the other of mass \( 4 \mathrm{M} \). After the explosion, the mass \( \mathrm{M} \) ends up traveling in the same circular orbit, but in opposite direction.
After the explosion the mass \( 4 \mathrm{M} \) is :
\( A \). In a circle orbit
B. unbound
c. elliptical orbit
D. data is insufficient to determent the nature of the orbit


The instantaneous angular position of a point on a rotating wheel is given by the equation \( \boldsymbol{\theta}(\boldsymbol{t})=2 \boldsymbol{t}^{3}-\boldsymbol{6} \boldsymbol{t}^{2} . \) The torque on
the wheel becomes zero at :
\( \mathbf{A} \cdot t=1 s \)
B. \( t=0.5 s \)
c. \( t=0.25 s \)
\( \mathbf{D} \cdot t=2 s \)


Two spheres of masses \( m \) and \( M \) are situated in air and the gravitational force between them is F. The space around the masses is now filled with a
liquid of specific gravity \( 3 . \) The new gravitational force will be :
\( A \cdot F \)
в. \( \frac{F}{3} \)
\( c .3 F \)
D. \( \frac{F}{9} \)


What will happen if one kidney is removed from the body of a human
being?
A. Death due to poisoning
B. Ureamia and death
c. Stoppage of urination
D. The person will survive and remain normal. The other kidney will become hypertrophied.


Evaluate the given integral: \( \int_{0}^{1}(1+ \)
\( x)^{5} d x \)


Braille is a
based on \( _{-}-_{-}-_{-}- \) system.
A. binary, binary
B. coded, logical
c. binary, coded
D. logical, binary


Hybridisation of each carbon in benzene is:
\( A \cdot s p^{3} \)
B. \( s p \)
\( c \cdot s p^{2} \)
D. \( s p \) and \( s p^{2} \)


A uniform bar of mass \( M \) and length \( L \)
is horizontally suspended from the ceiling by two vertical cables as shown
in the above figure. Cable \( A \) is
connected \( 1 / 4 t h \) distance from the left
end of the bar. Cable \( B \) is attached at
the far right end of the bar. What is the
tension in cable \( A \) ?
A. \( 1 / 4 M g \)
B. \( 1 / 3 v M g \)
\( \mathbf{c} \cdot 2 / 3 M g \)
D. \( 3 / 4 M g \)


Let \( f, g \) and \( h \) are differentiable functions. If \( \boldsymbol{f}(\mathbf{0})=\mathbf{1} ; \boldsymbol{g}(\mathbf{0})=\mathbf{2} ; \boldsymbol{h}(\mathbf{0})= \)
3 and the derivative of their pair wise
products at \( x=0 \) are \( (f g)^{\prime}(0)= \)
\( \mathbf{6} ;(\boldsymbol{g} \boldsymbol{h})^{\prime}(\mathbf{0})=\mathbf{4} \) and \( (\boldsymbol{h} \boldsymbol{f})^{\prime}(\mathbf{0})=\mathbf{5} \) then
compute the value of \( (f g h)^{\prime}(0) \)
A . 12
B . 15
c. 16
D. None of these


What is the nature of Gaussian surface
involved in Gauss law of electrostatic?
A. Scalar
B. Electrical
c. Magnetic
D. vector


To find out the concentration of \( S O_{2} \) in
the air(in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
concentration \( \begin{array}{llll}0.00 & 0.04 & 0.08\end{array} \)
of \( s o_{2} \) in 0.08 ppm \( 2^{11} \) 0.04 0.12
Frequency
The mean concentration of \( S O_{2} \) in the
\[
\operatorname{air} \mathbf{0 . 0 9 8 6 6 7}
\]
A. True
B. False


Which of the following phosphorus is the most reactive?
A. Red phosphorus
B. White phosphorus
c. Scarlet phosphorus
D. Violet phosphorus


The Langmuir adsorption isotherm is
deduced by assuming that:
A. the heat of adsorption varies with coverage
B. the adsorbed molecules interact with each other
C. the adsorption takes place in multi-layers
D. the adsorption sites are equivalent in their ability to adsorb the particles


Growth of plants is a:
A. physical change
B. chemical change
\( c . \) both \( A \) and \( B \)
D. none of the above


If a ray of light goes from a rarer medium to a denser medium, will it bend towards the normal or away from it ?
A. bends away from the normal
B. bends towards the normal
c. goes undeviated
D. is reflected back


Suppose you are in a car and it is raining heavily with thunderstorms. Then what is the best way to protect yourself from a possible thunder-strike?
A. To remain in the car
B. To get out of the car and take cover under the car
c. To run to a nearby tree
D. To get out and stand under an electric pole


Small fishes are called as
A. Hatchling
B. Fry
c. Both A and B
D. None of the above


Find a value of \( \boldsymbol{x} \) if \( \left|\begin{array}{cc}\boldsymbol{x} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{6}\end{array}\right| \)


Which of the following statements is
incorrect?
A. Calamine and Siderite are carbonates.
B. Argentite and Cuprite are oxides.
C. Zinc blende and Pyrites are sulphides.
D. Malachite and Azurite are ores of copper.


Three resistance \( P, Q, R \) each of \( 2 \Omega \) and
an unknown resistance S form the four
arms of a Wheatstone's bridge circuit. When a resistance of \( 6 \Omega \) is connected
in parallel to \( \mathrm{S} \) the bridge gets balanced What is the value of S?
A . \( 2 \Omega \)
B. 3\Omega
\( c \cdot 6 \Omega \)
D. 1\Omega


A man crosses a \( 320 \mathrm{m} \) wide river
perpendicular to the current in 4 min. If in still water he can swim with a speed
\( 5 / 3 \) times that of the current, then the
speed of the current, in \( m \) min\( ^{-1} \) is?
A . 30
B . 40
c. 50
D. 60


Strength of earth's magnetic field is of
the order of :
\( \mathbf{A} \cdot 10^{-4} T \)
B. \( 10^{-3} T \)
c. \( 10^{-5} T \)
D. \( 10^{-6} T \)


Which of the following is not formed by Sandmeyer reaction?
A. \( C_{6} H_{5} I \)
B . \( C_{6} H_{5} C l \)
\( \mathbf{c} \cdot C_{6} H_{5} B r \)
D. \( C_{6} H_{5} C N \)


A ball of mass 'm' moves normal to a
wall with a velocity 'u' and rebounds
with a velocity 'v'. The change in momentum of the ball is (surface of the
wall is smooth):
A. \( m(u+v) \) towards the wall
B. \( m(u-v) \) towards the wall
c. \( m(u+v) \) away from the wall
D. \( m(u-v) \) away from the wall


If \( 2^{x}+2^{y}=2^{x+y}, \) then the value of \( \frac{d y}{d x} \)
at (1,1) is equal to
A . -2
B. -
\( c \cdot 0 \)
D. 1
\( E \)


The reaction between carbon and
oxygen can be represented as
\( C_{(s)}+O_{2(x)} \rightarrow C O_{2(g)}+ \)heat
In which of the following type(s), the above reaction can be classified?
I. Combustion reaction
Il. Displacement reaction
III. Endothermic reaction
IV. Combination reaction
\( A \). (I) and (III)
B. (I), (II) and (IV)
c. (I) and (IV)
D. (I) only


Eustachian tube connects
A. Pharynx with middle ear
B. Middle ear with internal ear
C. Middle ear with external ear
D. External ear with internal ear


The field of organic chemistry focuses mainly on:
A. oxygen-containing compounds
B. carbon-containing compounds
c. proteins and enzymes
D. halogens
E. nitrogen-containing compounds


One atomic mass unit (a.m.u) is equal
to:
A \( .2 .67377 \times 10^{-27} \)
В. \( 1.67377 \times 10^{-22} \)
c. \( 0.67377 \times 10^{-27} \)
D. \( 1.67377 \times 10^{-27} \)


The passage of electricity in the Daniell cell when \( \mathrm{Zn} \) and \( \mathrm{Cu} \) electrodes are
connected:
A. from Cu to Zn inside the cell
B. from Cu to Zn outiside the cell
c. from zn to Cu outside the cell
D. none of the above


Plastic sulfur has an octahedral shape.
A. True
B. False


Assertion
n a reaction
\( Z n(s)+C u S O_{4}(a q) \rightarrow Z n S O_{4}(a q)+ \)
\( \boldsymbol{C u}(\boldsymbol{s}) \)
Zn is a reductant but itself get oxidized.
Reason

In a redox reaction, oxidant is reduced
by accepting electrons and reductant is oxidized by losing electrons.
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


Two resistances are connected in two
configurations- series or parallel. Which represents the parallel combination?
\( A, A \)
B. A and B both
\( c . \)
D. none of these


is the contamination of water
by substances harmful to life.
A. Water pollution
B. Air pollution
c. Noise pollution
D. None of the above


single heart circuit occurs in
A. Fishes
B. Frog
c. Reptiles
D. Man


For the following reaction, which of the
following statements is correct?
A. Ring (A) is oxidised
B. Ring
(B) is oxidised
C. Both are oxidised
D. None is oxidised


The compound formed as a result of
oxidation of ethyl benzene by \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
is:
A. acetophenone
B. benzophenone
c. benzoic acid
D. benzaldehyde


The number of moles of carbon
present in three moles of ethane gas
\( \left(C_{2} H_{6}\right) \) is :


The colour of bleaching powder is :
A. green
B. pale yellow
c. blue
D. white


How many minimum squares must be
shaded to make the given figure
symmetric ?
\( A \)
B.
\( c \)
\( D \)


Two blocks of masses \( 2 \mathrm{kg} \) and \( 1 \mathrm{kg} \) are
placed on a smooth horizontal table i contact with each other.A horizontal
force of 3 newton is applied on the first
so that the block moves with a constant
acceleration. The force between the
blocks would be:-
\( A \cdot 3 N \)
B. 2 N
c. \( 1 \mathrm{N} \)
D. ZERO


\( (x+y-z)^{2}= \)
A \( \cdot x^{2}+y^{2}-z^{2}+2 x y+2 x z-2 y z \)
B \( \cdot x^{2}+y^{2}+z^{2}+2 x y-2 x z-2 y z \)
C \( \cdot x^{2}+y^{2}-z^{2}-2 x y+2 x z+2 y z \)
D. None of the above


In the figure shown, a block A moving with velocity \( 10 ~ m / s \) on a horizontal surface collides with another block B at
rest initially. The coefficient of restitution is \( \frac{1}{2} . \) Neglect friction everywhere. The distance between the blocks at \( 5 s \) after the collision takes
place is \( 5 x(\text { in } m) . \) Then \( x \) is


Consider the following statements:
1. Determinant is a square matrix.
2. Determinant is a number associated
with a square matrix. Which of the above statements is/are
correct?
A . 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


A thin ring has mass \( 0.25 \mathrm{kg} \) and radius
\( 0.5 m . \) Its moment of inertia about an
axis passing through its centre and perpendicular to its plane is
A \( \cdot 0.0625 \mathrm{kgm}^{2} \)
B. \( 0.625 \mathrm{kgm}^{2} \)
c. \( 6.25 \mathrm{kgm}^{2} \)
D. \( 62.5 \mathrm{kgm}^{2} \)


Only the current inside the Amperian loop contributes in
A. finding magnetic field at any point on the Ampere's loop
B. line integral of magnetic field
\( c . \) in both of the above
D. in neither of them


Which of the following is a mixed oxide?
A. \( F e_{2} O_{3} \)
в. \( P b O_{2} \)
\( \mathbf{c} \cdot B a O_{2} \)
\( \mathbf{D} \cdot P b_{3} O_{4} \)


Root mean square speed of the molecules of ideal gas is \( v \). If pressure
is increased two times at constant
temperature, the \( r m s \) speed will
become:
A \( .2 v \)
в. \( \frac{v}{2} \)
c. \( 4 v \)
D.


The point on the \( x \) -axis which is equidistant from the points (5,4) and (-2,3) is
A. (-2,0)
в. (2,0)
D. (2,2)


Which particle is used to bombard \( 13 A I^{28} \) togive \( _{15} P^{31} \) and a neutron?
A. \( \alpha \) -particle
B. Deuteron
c. Proton
D. Neutron


RNA contains which of the following base, in place of thymine of DNA.
A. Cytosine
B. Uracil
c. Adenine
D. None of the above


Name the four classes of pteridophyta with one example?


A wire of radius \( 1 \mathrm{mm} \) is bent in the
form of a circle of radius \( 10 \mathrm{cm} . \) The
bending moment will be \( (Y=2 \times \) \( \left.\mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}}\right) \)
\( A \cdot 3.14 \mathrm{N} / \mathrm{m} \)
B. \( 6.28 \mathrm{N} / \mathrm{m} \)
c. \( 1.57 \mathrm{N} / \mathrm{m} \)
D. 15.7 N/m


If three angles of a triangle are in the ratio \( 2: 3: 5, \) determine three angles.


Consider the following statements:
i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle
respectively, then the two triangles are
congruent.
A . (i) is correct and (ii) is false
B. Both (i) and (ii) are false
c. Both (i) and (ii) are correct
D. (i) is false and (ii) is correct


A white solid imparts a violet colour to a Bunsen flame. On being heated with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) the solid gives
violet vapours that turns starch paper blue. The salt may be :
A. Nal
B. KI
c. \( C a B r_{2} \)
D. \( M g I_{2} \)


Identify the correct order of boiling
point:
This question has multiple correct options
\( \mathbf{A} \cdot H F<H C l<H B r<H I \)
B. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \)
\( \mathbf{c} \cdot C H_{4}<S i H_{4}<G e H_{4}<S n H_{4} \)
D. \( H_{2} S<H_{2} S e<H_{2} T e<H_{2} O \)


If a satellite is moving around a planet of mas \( \mathrm{M} \) in a elliptical orbit of semi major axis a.The orbital speed (V) of the satellite when it is at a distance r from
the focus will be given by


Select the correct statement regarding the specific disorder of muscular or
skeletal system.
A. Myastenia gravis - Auto immune disorder, which inhibits sliding of myosin filments
B. Osteoporosis - Decrease in bone mass and higher chances of fractures with advancing age
c. Gout- Inflammation of joints due to extra deposition of calcium
D. Muscular dystrophy - Age related shortening of muscles


Which are the areas influenced by
electronics?


ATP-ADP system was discovered in
A . 1940
B. 1944
\( c \cdot 1943 \)
D. 1840


An electrolytic cell contains a solution
of \( A g_{2} S O_{4} \) and has platinum
electrodes. A current is passed until
\( 1.6 g \) of \( O_{2} \) has been liberated at anode. The amount of silver deposited at cathode will be
A. \( 108 g \)
B. \( 1.6 g \)
\( \mathrm{c} .0 .8 \mathrm{g} \)
D. 21.60 \( g \)


By using elementary transformation
find the inverse of the matrix \( \boldsymbol{A}= \) \( \left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right] \)


Two point charges \( 2 q \) and \( 8 q \) are placed at a distance r apart. Where should a third charge -q be placed between them so that the electrical potential energy of the system is a minimum.
A. At a distance of r/3 from 2 q.
B. At a distance of 2 r/3 from 2 2
c. At a distance of r/16 from 2q.
D. There is no such position


Among the hydrides of Group - 15 elements, which have the:-
A. Lowest boiling point - phosphine.
B. Maximum basic character - ammonia.
c. Highest bond angle - ammonia.
D. All are correct.


Abscission layer is made up of
A. Cork cells
B. Sclerenchymatous cells
c. collenchymatous cells
D. Parenchymatous cells


\( A B C D \) is a trapezium in which \( A B \| \)
\( D C, B D \) is a diagonal and \( E \) is the
mid-point of \( A D . A \) line is drawn
through \( E \) parallel to \( A B \) intersecting \( B C \) at \( F \) (see Fig). Show that \( F \) is the
mid-point of \( \boldsymbol{B C} \)


\( \boldsymbol{z}=\mathbf{3 0} \boldsymbol{x}+\mathbf{2 0} \boldsymbol{y}, \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{8}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \geq \)
\( 4,6 x+4 y \geq 12, x \geq 0, y \geq 0 \) has
A. Unique solution
B. Infinitely many solution
C . Minimum at (4,0)
D. Minimum 60 at point (0,3)


\( \cos \frac{\pi}{5} \cos \frac{2 \pi}{5}=\frac{1}{4} \) and \( \cos \frac{\pi}{5}+ \)
\( \cos \frac{3 \pi}{5}=\frac{1}{2} \) without using standard
value


In the following four elements, the
ionisation potential of which one is the highest?
A. Oxygen
B. Argon
c. Barium
D. cesium


A Volume \( V \) absolute temperature \( T \)
diagram was obtained when a given
mass of gas was heated. During the heating process fro nm state 1 to 2 , the
pressure
A. remains constant
B. Decreased
c. changed eratically
D. Increased


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{c}x \\ \frac{a e^{|x|}+3 . e^{\frac{-1}{x}}}{1} \\ (a+2) e^{\frac{1}{|x|}-e^{\frac{-1}{x}}}\end{array}\right) \begin{array}{l}x \neq 0 \\ 0\end{array} \)
differentiable at \( \boldsymbol{x}=\mathbf{0} \) then \( [\boldsymbol{a}]=_{--}(\mathbb{D} \)
denotes greatest integers function
4
B. -1
\( c \cdot 2 \)
\( 0 .-3 \)


\( H_{2} O \) molecule is linear.
If the statement is true enter 1 , else
enter 0


Which of the following is a reducing agent and undergoes hydrolysis?
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( S i H_{4} \)


form oxocations.
A. Lanthanides
B. Actinides
c. Nobel gases
D. Alkali metalss


If \( a \neq 0 \) and \( a-\frac{1}{a}=4, \) find:
\( a^{4}+\frac{1}{a^{4}} \)
A .92
в. 112
\( c .322 \)
D. 122


What is the physical state of \( \boldsymbol{P} \boldsymbol{C l} \) late under normal condition?
A. Solid
B. Liquid
c. Gaseous
D. None of these


If the equation \( \frac{\lambda(x+1)^{2}}{3}+ \) \( \frac{(y+2)^{2}}{4}=1 \) represents a circle then
\( \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{3}{4} \)
c. 0
D. \( -\frac{3}{4} \)


Potential (in V) at \( r=1.25 \mathrm{cm} \)


t is given that \( A B=B C \) and \( A D= \)
EC. The \( \triangle A B E \cong \triangle C B D \) by
congruency
A. \( S S S \)
B. \( A S A \)
\( c . S A S \)
D. \( A A S \)


If \( a, b \in Z^{+} \) then maximum value of
\( \log \left[(x-a)^{a}(x-b)^{b}\right] \) occurs at \( x= \)
\( A \cdot \frac{a+b}{2} \)
B. \( \sqrt{a b} \)
c. \( \frac{2 a b}{a+b} \)
\( D \cdot a+b \)


Fill in the blank with appropriate word to complete the sentence.

The planets do not possess their own and


The ratio of time periods of oscillations of situations shown in figures (i) and
(ii) is:
A .2: 3
B. \( 3: \sqrt{2} \)
\( c \cdot 4: 3 \)
D. 1: 1


The tricuspid valve is present at the origin of
A. Carotid arch
B. Pulmonary arch
c. Truncus arteriosus
D. systemic arch


Find the value of 'a' \( \operatorname{in} 4 x^{2}+a x+ \)
\( \mathbf{9}=(\mathbf{2} \boldsymbol{x}+\mathbf{3})^{2} \)
A \( . a=34 \)
B. \( a=11 \)
c. \( a=12 \)
D. \( a=33 \)


An equiconvex lens is cut into two halves along (i) \( \mathrm{XOX}^{\prime} \) and (ii) YOY" as shown in fig. Let \( f, f^{\prime}, f^{\prime} \) be the focal
length of the lens, of each half in case
(i), and of each half in case (ii),
respectively, choose the correct
statement from the following
A \( \cdot f^{\prime}=f, f^{\prime \prime}=2 f \)
B . \( f^{\prime}=2 f, f^{\prime \prime}=f \)
\( \mathbf{C} \cdot f^{\prime}=f, f^{\prime \prime}=f \)
D. \( f^{\prime}=2 f^{\prime}, f^{\prime \prime}=2 f \)


Consider the following statements;
(I) Rutherford name was associated
with the development of periodic table.
(II) A metal M having electronic configuration \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 2 p^{6}, 3 d^{10}, 4 s^{1} \) is d-
block element.
(III) Diamond is not an element.
(IV) The electronic configuration of the
most electronegative element is \( 1 s^{2}, 2 s^{2}, 2 p^{5}, \) Select the correct option
from the given codes.
A . ।, ॥।, IV
B. I, II, III, IV
c. ॥, IV
D. I, III, IV


An element, which never as a positive oxidation state in any of its compounds is:
A. boron
B. oxygen
c. chlorine
D. fluorine


If the cost price of 21 cell phones is
equal to selling price of 18 cell phones, find the profit percent


In the given figure, \( A C \) is diameter of \( a \)
circle with radius \( 5 \mathrm{cm} \). if \( \mathrm{AB}=\mathrm{BC} \) and
\( \mathrm{CD}=8 \mathrm{cm}, \) the area of the shaded region
to the nearest whole number is-
\( A \cdot 28 c m^{2} \)
B \( \cdot 29 c m^{2} \)
\( c \cdot 30 c m^{2} \)
\( \mathbf{D} \cdot 45 \mathrm{cm}^{2} \)


Let \( \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{G} \) be pairwise independent events with \( P(G)>0 \) and \( P(E \cap F \cap \)
\( G)=0 . \) Then \( P\left(E^{\prime} \cap F^{\prime} \mid G\right) \) equals
\( \mathbf{A} \cdot P\left(E^{\prime}\right)+P\left(F^{\prime}\right) \)
B . \( P\left(E^{\prime}\right)-P\left(F^{\prime}\right) \)
c. \( P\left(E^{\prime}\right)-P(F) \)
D. \( P(E)-P\left(F^{\prime}\right) \)


Solve:
\( \frac{3(y-5)}{4}-4 y=3-\frac{(y-3)}{2} \)


\( \boldsymbol{I}_{2}+\boldsymbol{I}^{-} \rightleftharpoons \boldsymbol{I}_{3}^{-} \) This reaction is set-up in
aqueous medium. We start with one
mole of \( I_{2} \) and 0.5 mol of \( I^{-} \) in \( 1 L \) flask.
After equilibrium is reached, excess of
\( A g N O_{3} \) gave 0.25 mol of yellow
precipitate. Equilibrium constant is
A . 1.33
B . 2.66
\( c .2 .00 \)
D. 3.00


Ratio of kinetic energy at mean position to potential energy at \( A / 2 \) of a particle performing SHM.
A . 2: 1
B . 4: 1
c. 8: 1
D. 1: 1


Define cell cycle?


Fill in the blank with appropriate
answer:

A compound microscope is used because a realistic simple microscope
does not have
magnification.


Which of the following act as a substrate for an enzyme that charges
tRNA molecules?
I. Amino acid
I. ATP
III. tRNA
IV. snRNA
A. I only
B. II only
c. ॥ा only
D. I, II, and III
E . ।, ॥, ॥ा, and IV


The volume of a cube is numerically equal to the sum of its edges. What is the total surface area in square units?
\( \mathbf{A} \cdot 66 \)
в. 183
\( c .36 \)
D. 72


The order of boiling point of the following substances is :
\[
\begin{array}{c}
\boldsymbol{N H}_{3}>\boldsymbol{P H}_{3}>\boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3}>\boldsymbol{S b} \boldsymbol{H}_{3}> \\
\boldsymbol{B i H}_{3}
\end{array}
\]
If the given order is true enter 1 else 0


What is the percentage of ab gametes
produced by parents of genotype \( \boldsymbol{A} \boldsymbol{a} \boldsymbol{B} \boldsymbol{b} \)
\( ? \)
A . 20
B. 25
\( c .50 \)
D. 75


State whether true or false.
Light is a form of energy that causes a sensation of smell.
A. True
B. False


Nitrogen (I) oxide is produced by:
This question has multiple correct options
A. thermal decomposition of ammonium nitrate
B. disproportionation of \( N_{2} O_{4} \)
C. thermal decomposition of ammonium nitrite
D. interaction of hydroxylamine and nitrous acid


Find the inverse of \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{1} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{A}^{-1}=\left[\begin{array}{ccc}1 / 2 & -1 / 2 & 1 / 2 \\ a & 3 & b \\ c & -3 / 2 & 1 / 2\end{array}\right] \)
Find \( |\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}| ? \)


State True or False
Let \( \boldsymbol{A}=\{1,2\} \) and \( \boldsymbol{B}=\{2,3,4\}, \) then \( \boldsymbol{A} \)
\( \times \mathrm{B}=\mathrm{B} \times \mathrm{A} ? \)
A. True
B. False


The pressure of a gas in a container is
\( 10^{-11} \) pascal at \( 27^{\circ} \mathrm{C} . \) The number of molecules per unit volume of vessel will
be
A \( \cdot 6 \times 10^{23} \mathrm{cm}^{-3} \)
В. \( 2.68 \times 10^{19} \mathrm{cm}^{-3} \)
c. \( 2.5 \times 10^{6} \mathrm{cm}^{-3} \)
D. \( 2400 \mathrm{cm}^{-3} \)


What structural feature distinguishes
glycine from other natural \( \alpha \)
aminoacids?
A. It is optically inactive.
B. It contains aromatic group.
c. It is a dicarboxylic acid.
D. It has a secondary amine.


Find the derivative of \( \sqrt{\tan x} \) with respect to \( x \) using the first principle.
A \( \cdot \frac{\sec ^{2} x}{2 \sqrt{\tan x}} \)
в. \( \frac{s e c x}{2 \sqrt{\tan x}} \)
\( ^{\mathrm{c}} \cdot \frac{\sec ^{2} x}{\sqrt{\tan x}} \)
D. \( \frac{\sec ^{2} x}{2 \sqrt{\tan } x} \)


If \( f(x)=\frac{2 x-4}{x^{2}-1} \) and \( f^{\prime}(x)=\frac{p}{\left(x^{2}-1\right)^{2}} \)
then p equals-
A \( \cdot x^{2}-8 x-2 \)
B. \( -2 x^{2}+8 x+2 \)
c. \( 4 x+2 \)
D. \( -2 x^{2}+8 x-2 \)


Find the coordinates of the foci, the
vertices the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{25}=1 \)


The range of clinical thermometer is \( 35^{0} \) to \( 43^{0} \)
A. True
B. False


Phosphor-Bronze wire is used for suspension in a moving coil galvanometer because it has.
A. High conductivity
B. High resistivity
c. Large couple per unit twist
D. Small couple per unit twise


Green chemistry involves?
A. production of chemicals of our daily use from green house gases
B. such chemical processes in which green plants are used
C. those reaction which are of biological origin
D. use of non-toxic reagents and solvents to produce environment friendly products.


Electronic configuration of element T is 2,8,7
What is the group number of T?
A . 15
B. 16
\( c \cdot 17 \)
D. 18


Show that: \( \int_{0}^{\frac{\pi}{4}} \log (1+\tan x) d x= \)
\( \frac{\pi}{8} \log 2 \)


Match the excretory functions with the
parts of the excretory system.choose the correct combination from among the
answers given.
List 1
1. Ultra filtration
a. Henle's loop
2. Concentration of
b. Ureter าe
3. Transport of urine
c. Urinary bladder
d. Malpighian
4. Storage of urine \( \quad \) corpuscle
A. \( 1-d, 2-a, 3-b, 4-c \)
B. \( 1-\mathrm{d}, 2-\mathrm{c}, 3-\mathrm{b}, 4-\mathrm{a} \)
c. \( 1-\mathrm{e}, 2-\mathrm{d}, 3-\mathrm{a}, 4-\mathrm{b} \)
D. \( 1-d, 2-a, 3-c, 4-b \)


Ozone hole over Antarctica was first
detected by
A. Molina and Rowland
B. Farman et al
c. Augus
D. Molina and Molina


2 moles of \( P C l_{5} \) were heated in a closed
vessel of 2 litre capacity. At
equilibrium, \( 40 \% \) of \( P C l_{5} \) is
dissociated into \( P C l_{3} \) and \( C l_{2} . \) The
value of equilibrium constant is:
\( \mathbf{A} \cdot 0.266 \)
B. 0.53
\( c .2 .66 \)
D. 5.3


\( 45 g \) of water at \( 50^{\circ} \mathrm{C} \) in a beaker is
cooled when \( 50 g \) of copper at \( 18^{\circ} \mathrm{C} \) is added to it. The contents are stirred till
a final constant temperature is reached Calculate this final temperature. The specific heat capacity of copper is
\( 40.39 J g^{-1} K^{-1} \) and that of water is \( 4.2 J g^{-1} K^{-1} \)
A \( \cdot 17^{\circ} \mathrm{C} \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 47^{\circ} \mathrm{C} \)
D. none of the above


The maximum charge on the capacitor is given as \( (\text { in } n C) \)


Which of the following is independent of the remaining three for a sound wave?
A. Frequency
B. wavelength
c. velocity
D. Amplitude


Which of the following represents the
correct order of the acidity in the given
compound?
\( \mathbf{A} \cdot C l C H_{2} C O O H<B r C H_{2} C O O H<C H_{3} C O O H< \)
\( F C H_{2} C O O H \)
B. \( C H_{3} C O O H<B r C H_{2} C O O H<C l C H_{2} C O O H< \)
\( F C H 2 C O O H \)
\( \mathrm{c} \cdot F C H_{2} C O O H<C l C H_{2} C O O H<B r C H_{2} C O O H< \)
\( C H_{3} C O O H \)
D. \( C H_{3} C O O H<F C H_{2} C O O H<C l C H_{2} C O O H< \)
\( B r C H_{2} C O O H \)


The process by which synthesis of protein takes place based on the genetic information present in \( \mathrm{m} \) -RNA
is called :
A. translation
B. transcription
c. replication
D. messenger hypothesis


Which among the following are the examples of Reptilia?
A. Snakes
B. Turtles
c. Lizards
D. All of the above


What is the relation between distance
and displacement.
A. Distance is always less than displacement
B. Distance is always greater than displacement
C. Distance is always equal to displacement
D. None of the above


Hydroponics is the
A. Growing of aquatic plants.
B. Growing of floating aquatic plants.
C. Growing of plants in sand.
D. Growing of plants in nutrient balanced aqueous medium.


A cylinder containing \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) and
\( N_{2}(g) \) at \( 25^{\circ} C \) recorded a pressure of 500 mbar. The volume of cylinder is reduced to half by forcing the piston downward at the same temperature, the
new pressure reading would be (aqueous tension \( =23 \) mbar):
A. 977 mbar
B. 1000 mbar
c. 1100 mbar
D. 1023 mbar


If \( \mathrm{E} \& \mathrm{F} \) are events with \( \boldsymbol{P}(\boldsymbol{E}) \leq \boldsymbol{P}(\boldsymbol{F}) \& \)
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})>0, \) then
A. occurrence of \( E \Rightarrow \) occurrence of \( F \)
B. occurrence of F\Rightarrow occurrence of E
c. non occurrence of \( E \Rightarrow \) non occurrence of \( F \)
D. none of the above implications holds


Sulphur dioxide bleaches colouring matter by
A. dehydration
B. oxidation
c. decomposition
D. reduction


A kangaroo moves around by leaping with its strong hind legs. When moving its thick strong tail helps it to
A. Defend against enemies
B. Maintain balance
c. Have a firm grip on branches
D. catch food on its way


A particle of mass \( m \) is moving with
constant velocity \( v \) parallel to the \( x- \)
axis as shown in the figure. Its angular
momentum about origin \( O \) is
A . \( m v b \)
B. mva
c. \( m v \sqrt{a^{2}+b^{2}} \)
D. \( m v(a+b) \)


Chlorobenzene can be prepared by
reacting aniline with:
A \( . \) Hydrochloric acid \( (H C l) \)
B. Cuprous chloride \( \left(C u_{2} C l_{2}\right) \)
C. Chlorine in the presence of anhydrous aluminium chloric
D. Nitrous acid followed by heating with cuprous chloride(c


Living organisms has not effect on the abiotic factor around them in an
ecosystem
A. True
B. False
c. Ambiguous
D. Data insufficient


\( \ln \) a \( \triangle A B C, A(-2,3), B(2,1) \) and
\( C(1,2) . \) What is the foot of the altitude
from the vertex \( A \) of the triangle \( A B C ? \)
A \( .(1,4) \)
в. (-1,3)
c. (-2,4)
D. (-1,4)


Permanent hardness of water cannot be
removed by:
A. washing soda method.
B. permutit method
c. ion exchange method.
D. boiling


When conc. \( H_{2} S O_{4} \) is added to hydrated copper [ll] sulphate:
A. white crystals is changed to black powder as water is removed.
B. brown crystals is changed to black powder as water is removed.
c. black crystals is changed to white powder as water is removed.
D. blue crystals is changed to white powder as water is removed


Express \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{N}, \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x} \) where
\( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N}, \boldsymbol{x} \leq 10\} . \) Determine
range of the function.


Which is present in the kidney?
A . Glomerulus
B. Neurons
c. Middle kidney duct
D. Nephridia


The IUPAC name of the following compound is ethyl 4 - acetylbenzoate.
A. True
B. False


The two ions which are formed when
ammonia dissolves in water are
ammonium ion and
A \( . O H^{-} \)
B. \( H_{3} O^{+} \)
\( \mathrm{c} \cdot H^{+} \)
D. \( O^{-2} \)


Select incorrect statement:
A \( \cdot C l O_{2} \) and \( C l_{2} O \) are used as bleaching agents for paper pulp and textiles.
B. \( O C l^{-} \) (hypohalites) salts are used as detergent.
C . \( O C l^{-} \) disproportionates in alkaline medium.
D. \( B r O_{3}^{-} \) is oxidised to \( B r_{2} \) by \( B r^{-} \) in acidic medium.


A solid cylinder of glass whose diameter
is \( 1.5 \mathrm{m} \) and height \( 1 \mathrm{m} \) is melted and recasted into a sphere, then the radius of the sphere is
\( A \cdot 1 m \)
B. \( 0.75 \mathrm{m} \)
c. \( 1.25 \mathrm{m} \)
D. \( 1.5 \mathrm{m} \)


The current \( I \) through a rod of a certain metallic oxide is given by \( \boldsymbol{I}=\mathbf{0 . 2} \boldsymbol{V}^{\mathbf{5} / \mathbf{2}} \)
where \( V \) is the potential difference across it. The rod is connected in series
with a resistance to a \( 6 V \) battery of negligible internal resistance. What value should the series resistance have
so that the power dissipated in the rod is twice that dissipated in the resistance?


The reduction of an oxide by aluminium is called
A. Ellingham process
B. Goldschmidts aluminothermite process
c. Krolls process
D. Van Arkel process


8
\( b \)
8
8


\( M e-\stackrel{\|}{C}-O-C H_{2}-C H_{2}- \)
\( \stackrel{\ominus}{\boldsymbol{N}} \boldsymbol{H}_{3} \stackrel{N a O \boldsymbol{H}}{\longrightarrow} \boldsymbol{Q} \) is
A \( \ldots_{M e-C-O-C H_{2}-C H_{2}-N H_{2}} \)
в. \( \quad_{M e-C-N H-C H_{2}-C H_{2}-O H}^{\circ} \)
\( c \)
D. \( M e C O O N a+H O C H_{2} C H_{2} N H_{2} \)


The value of \( n \) in the following reaction
is :
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{n} e^{-}+\mathbf{1 4 H}^{+} \rightarrow \boldsymbol{2 C r}^{3+}+ \)
\( \mathbf{7} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \)


(a) Taking an example of a small pond,
explain how the four components of an
ecosystem function as a unit.
(b) Name the type of food chain that exists in a pond.


A beam of protons enters a uniform magnetic field of \( 0.3 T \) with a velocity of \( 4 \times 10^{5} m / s \) in a direction making an
angle of \( 60^{\circ} \) with the direction of magnetic field. What will be the pitch of the helix formed by moving particles? (Given charge of proton \( e=1.6 \times \)
\( 10^{-19} C, \) mass of proton \( m=1.67 \times \)
\( \left.10^{-27} k g\right) \)
A \( .4 .37 m \)
В. 0.437 т
\( c .0 .0437 m \)
D. \( 0.00437 m \)


If the area above \( x \) -axis bounded by the curves \( \boldsymbol{y}=\mathbf{2}^{k x}, \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\mathbf{2} \) is
\( \frac{3}{\log 2}, \) then the value of \( k \) is
A \( \cdot \frac{1}{2} \)
B.
c. -1
D.


In Rabbit and Hare, the incisors of upper and lower jaw halves are
\( A \cdot 1 / 1 \)
B. 2 / 1
\( c \cdot 2 / 2 \)
D. 2 /


Assertion:With increase in temperature
the pressure of given gas increases
Reason:Increase in temperature causes
decrease in no. of collision of molecules
with walls of container.
A. Both assertion (A) and reason
(R) are correct and gives the correct explanation
B. Both assertion (A) and reason
(R) are correct but \( R \) doesnt give the correct explanation
c. \( A \) is true but \( R \) is false
D. A is false but R is true


A convenient reagent for the conversion of bromobenzene into benzonitrile is:
A . alc. \( K C N \) alone
B. \( K C N \) and pyridine
c. silver cyanide
D. \( C u C N \) and pyridine


Compute Mean deviation about median for the following Frequency distribution.
Variable(
\( x \)
\( \mathbf{1 0} \)
\( \mathbf{1 5} \quad \mathbf{2 0} \quad \mathbf{2 5} \)
Frequency
\[
f)
\]
A . 10.5
в. 10.1
c. 13.2
D. 12.1


The Van der Wall equation for 1 mole of a real gas is \( \left(\boldsymbol{P}+\frac{\boldsymbol{a}}{\boldsymbol{V}^{2}}\right)(\boldsymbol{V}-\boldsymbol{b})=\boldsymbol{R} \boldsymbol{T} \)
where \( P \) is the pressure, \( V \) is the
volume, \( \boldsymbol{T} \) is the absolute temperature \( R \) is the molar gas constant and \( a, b \) are Van der Wall constants. The dimensions
of \( a \) are the same as those of :
A . \( P V \)
в. \( P V^{2} \)
c. \( P^{2} V \)
D. \( P / V \)


Statement: Cyclopentadecene reacts
with \( B r_{2} / C C l_{4} \) and \( N a N H_{2} \) to give
cyclopentadecyne If the statement is true enter 1 , else
enter 0


For 3 events \( A, B \) and \( C, P( \) exactly one of the events \( A \text { or } B \text { occurs })=P( \) exactly one of the events \( \mathrm{B} \text { or } \mathrm{C} \text { occurs })=\mathrm{P}( \) exactly one of the events \( C \text { or } A \text { occurs })=p \& P \) (all the three events occurs
simultaneously) \( =p^{2} . \) Where \( o<p<\frac{1}{2} \)
then the probability of at lest one of
three events, \( A, B \& C \) occurring is
A \( \cdot \frac{3 p+2 p^{2}}{2} \)
B. \( \frac{p+2 p^{2}}{2} \)
c. \( \frac{3 p+p^{2}}{2} \)
D. \( \frac{3 p+2 p^{2}}{4} \)


Find whether the following statements
are true or false.
\( \pi \) is an irrational number.
A. True
B. False


Which of the following statement is correct regarding hydrogen?
A. Hydrogen shows +1 and - - - oxidation states
B. Hydrogen is never liberated at anode
c. Hydrogen has same ionisation enthalpy as that of alkali metals
D. Hydrogen has same electronegativity as of halogens


The total revenue received from the sale
of \( x \) units is given by \( R(x)=10 x^{2}+ \)
\( 20 x+1500 . \) The marginal revenue
when \( x=2015, \) is
A. 4032
B. 40320
\( c .403 \)
D. 40300


The number of arrangements of the letters of the word BANANA in which two
N's do not appear adjacently is
A . 40
B. 60
c. 80
D. 100


In a silicon diode, the reverse current increases from \( 10 \mu A \) to \( 20 \mu A \). when the
reverse voltage change from \( 2 V \) to \( 4 V \)
The reverse ac resistance of the diode is
A \( \cdot 1 \times 10^{5} \Omega \)
В. \( 3 \times 10^{5} \Omega \)
c. \( 2 \times 10^{5} \Omega \)
D. \( 4 \times 10^{5} \Omega \)


Peptization is:
A. Formation of colloid from precipitate
B. Formation of precipitate from colloid
C. Formation of colloid from solution
D. Addition of colloid is solvent.


Green carbonate which turns black on
heating is:
A. copper carbonate
B. sodium carbonate
c. potassium carbonate
D. none of these


Glucose or fructose is converted into
\( C_{2} H_{5} O H \) in the presence of:
A . invertase
B. diastase
c. maltase
D. zymase


Ernest Rutherford carried out his work
on discovery of nucleus of an atom with:
A. silver foil experiment
B. gold foil experiment
c. \( \alpha \) - particle experiment
D. none of the above


Find the distance of centre of mass of
\( H_{2} O \) molecule


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}-\boldsymbol{x}^{3}+\log _{2} \boldsymbol{b}, & \mathbf{0} \leq \boldsymbol{x}<\mathbf{1} \\ \mathbf{3} \boldsymbol{x}, & \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3}\end{array}\right. \)
The set of real values of b for which \( f(x) \)
has smallest value at \( x=1 \), is?
A . (0,8]
B. \( [8, \infty) \)
c. \( [16, \infty] \)
\( D . \quad(0,16 \)


In what pressure range will the naphthalene compound sublime faster?
A. Less than 0.5 atm
B. Between 0.5 and 1.0
c. Between 1.0 and 2.0
D. This compound won't sublime
E. None of these


A black compound of manganese reacts with a halogen acid to give greenishyellow gas. When an excess of this gas
reacts with \( N H_{3} \) an unstable trihalide
is formed. In this process the oxidation state of nitrogen changes from :
\( A \cdot-3 \) to +3
B. - - - to O
\( c .-3 \) to +5
\( D \cdot O \) to -3


In a simultaneous throw of a pair of dice, if the probability of getting neither 9 nor 11 as the sum of the numbers on the faces is \( \frac{5}{a} . \) Find \( a \)


Rate of formation of \( S O_{3} \) in the
following reaction \( 2 S O_{2}+O_{2} \longrightarrow \)
\( 2 S O_{3} \) is \( 100 g \quad \) min \( ^{-1} . \) Hence
disappearance of \( \boldsymbol{O}_{2} \) is:
\( \begin{array}{ll}\text { A. } 50 g & \min ^{-1}\end{array} \)
B. \( 40 g \) min\( ^{-1} \)
c. \( 200 g \) min\( ^{-1} \)
D. \( 20 g \) min\( ^{-1} \)


A grind-stone starts revoiving from rest,
it its angular acceleration is 4.0 rad / sec \( ^{2} \) (uniform) then after 4 sec.
What is its angular displacement \& angular velocity respectively -
A. 32 rad, 16 rad/sec
B. 16 rad, 32 rad/sec
c. 64 rad, 32 rad/sec
D. 32 rad, 64 rad/sec


Naphthalene is a volatile solid. It is best purified by:
A. Crystallisation
B. Distillation
c. Steam distillation
D. Sublimation


When baking soda reacts with vinegar, is formed.
A. sodium carbonate
B. sodium hydrogen carbonate
c. sodium acetate
D. none of above


When France Sneezes, the rest of Europe catches cold? This was the remark of ?
\( A \). Bismarck
B. Metternich
C. Mazzini
D. Napoleon


A force of \( 15 N \) acts on an area of \( 50 c m^{2} \)
What is the pressure in pascal.


Make a proper pair:
a) Fullerene
b) SWNT
c) MWNT
d) Carbon nano buds
A. \( a-2, b-4, c-1, d-3 \)
B . \( a-3, b-1, c-2, d-4 \)
c. \( a-4, b-2, c-1, d-3 \)
D . \( a-1, b-3, c-4, d-2 \)


A glass prism of refractive index 1.5 is
immersed in water (refractive index
4/3). A light beam normally on the face
\( A B \) is totally reflected to reach on the
face \( B C \) if
A \( \cdot \sin \theta \geq \frac{8}{9} \)
В \( \cdot \frac{2}{3}<\sin \theta \geq \frac{8}{9} \)
\( ^{\mathbf{C}} \cdot \sin \theta \leq \frac{2}{3} \)
\( \mathrm{D} \cdot \sin \theta \leq \frac{8}{9} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}-\boldsymbol{b}|\boldsymbol{x}|, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants. Then at \( x=0, f(x) \) has
This question has multiple correct options
A. A maxima whenever \( a>0, b>0 \)
B. A maxima whenever \( a>0, b<0 \)
c. A minima whenever \( a>0, b<0 \)
D. Neither minima nor a maxima whenever \( a>0, b<0 \)


toppr
R type your question.
Q Type you
on
B.
\( c \)
\( D \)
\( \because \)


The point (3,4) is the focus and \( 2 x- \)
\( 3 y+5=0 \) is the directrix of a parabola
Its latus rectum is
A \( \cdot \frac{2}{\sqrt{13}} \)
в. \( \frac{4}{\sqrt{13}} \)
c. \( \frac{1}{\sqrt{13}} \)
D. \( \frac{3}{\sqrt{13}} \)


toppr
Q Type your question-
corresponding \( \boldsymbol{P}-\boldsymbol{V} \) diagram for the
process is (all figures are schematic
and not drawn to scale)
\( A \)
B.
\( c \)
\( D \)


The water table of a place:
A. changes from time to time
B. changes from palce to place
C . goes down when rains are less
D. all of these


Describe the laboratory method for preparation of diethyl ether and write
the reaction with \( H_{2} O \) and cold \( H I \)


Phyllosphere bacteria are present around the
A. Leaf surface of desert plants
B. Leaf surface of tropical rain forest plants
c. shoot surface
D. Root of higher plants


Use Euclid's division algorithm to find
the \( H C F \) of 4052 and 12576


Find the intersection of \( A \) and \( B, \) by
representing using Venn diagram:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{5}, \mathbf{7}, \mathbf{1 0}, \mathbf{1 2}\} \)
\( \mathbf{A} \cdot\{1,3,5,7\} \)
B \( \cdot\{5,7\} \)
\( \mathbf{c} \cdot\{1,2,3,5,7,10\} \)
D. None of these


Fill in the blanks.
In solid state, nitrogen occurs as


Q Type your question
steel, a student can record the
following values:
length of wire \( \mathrm{I}=\left(\ell_{0} \pm \Delta \mathrm{I}\right) \boldsymbol{m} \)
diameter of wire \( \boldsymbol{d}=\left(\boldsymbol{d}_{0} \pm \boldsymbol{\Delta} \boldsymbol{d}\right) \mathrm{mm} \)
force applied to wire \( \boldsymbol{F}=\left(\boldsymbol{F}_{0} \pm \boldsymbol{\Delta} \boldsymbol{F}\right) \boldsymbol{N} \)
extension of wire \( e=\left(e_{0} \neq \Delta e\right) \mathrm{mm} \)
In order to obtain more reliable value for
\( Y, \) the following three techniques are
suggested

Technique (i) A shorter wire Is to be used.
Technique
(ii) The diameter shall be
measured at several places with a
micrometer screw gauge. Technique (iii) Two wires are made irom the same ntaterial and of same length. One is loaded at a fixed weight and acts as a reference for the extension of the
other which is load- tested Which of the above techniques is/are useful?
A. i and ii only
B. ii and iii only
c. i only
D. iii only


Why is it difficult to read the image of the text of a page formed due to reflection by plane mirror?
A. Due to lateral inversion
B. It is virtual
c. Due to reflection
D. No difficulty


The increase in pressure required in \( k P a, \) to decrease the 200 litres volume
of a liquid by \( 0.004 \% \) is (bulk modulus of the liquid \( =2100 M P a) \)
A . 8.4
B. 84
c. 92.4
D. 16


A 0.004 M solution of \( N a_{2} S O_{4} \) is
isotonic with a \( 0.010 \mathrm{M} \) solution of
glucose at same temperature. The apparent degree of dissociation of
\( N a_{2} S O_{4} \) is:
A . \( 25 \% \)
B . 50\%
c. \( 75 \% \)
D. 85\%


If \( P(x, y, z) \) is a point on the line segment joining \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}, \mathbf{4}) \) and
\( B(3,5,6) \) such that projection of \( \overrightarrow{O P} \) on axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \) respectively, then \( P \) divide AB in the ratio
A .3: 2
B. 2: 3
c. 1: 2
D. 1: 3


The number of terms is given by
in the expression \( t_{n}=a+ \)
\( (n-1) d \)
A \( \cdot t_{n} \)
B. \( n \)
\( c \cdot a \)
D. \( d \)


\( \ln \) a \( \Delta A B C, i f \angle A=\angle B+ \)
\( \angle C \) then \( \angle A=\dots \dots \dots \)
A . \( 60^{\circ} \)
B . \( 45^{\circ} \)
\( c .90^{\circ} \)
D. none


Bohrs model can not explain the emission spectrum of :
A. \( B \)
B. \( L i^{2} \)
\( c . H \)
D. \( H e^{+} \)


An amorphous solid (X) burns in air to form a gas (Y) which turns lime water milky. This gas decolourises aqueous solution of acidified \( K M n O_{4} . \) Gas \( (Y) \)
reacts with oxygen to give another gas
(z) which is responsible for acid rain. \( \mathbf{X} \)
\( Y, \) and \( z \) are:
A \( \cdot C(X), C O(Y), C O_{2}(Z) \)
B. \( S(X), S O_{2}(Y), S O_{3}(Z) \)
c. \( P(X), P_{2} O_{3}(Y), P_{2} O_{5}(Z) \)
D. \( S(X), S O_{3}(Y), C O_{2}(Z) \)


When cell division fails after \( S \) - phase
(DNA replication) in a diploid cell, the
ploidy is
A. Haploid
B. Diploid
c. Tetraploid
D. Triploid


The momentum P and kinetic energy E of a body of mass \( \mathrm{m} \) are related as :
A \( . P=\sqrt{2 m E} \)
B. \( P=\frac{1}{2} m E \)
\( ^{\mathrm{c}} \cdot_{P}=\frac{2 m}{E} \)
D. \( P=2 m E \)


A die is thrown 100 times and outcomes
are noted as given below:
Outcome: 1 3 4
Frequency:
\( \begin{array}{llll}21 & 9 & 14 & 23\end{array} \)
If a die is thrown at random, find the probability of getting a/an. 5


Assertion
Fermentation is the incomplete oxidation of glucose into lactic acid or ethanol
Reason
It takes place under anaerobic condition in prokaryotes only.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A parachute after bailing out falls \( 50 \mathrm{m} \) without friction. When a parachute opens it decelerates at \( 2 m s^{-2} . \) He
reaches the ground with a speed of 3
\( m s^{-1} . \) At what height did he bail out?


In figure the upper wire is made of steel
and the lower of copper. The wires have equal cross section. Find the ratio of the
ongitudinal strains developed in the
two wires.


In physical equilibrium, forces responsible for equilibrium are in nature
A. physical
B. chemical
c. strong
D. weak


Which of the given pair of \( S N_{1} \) reaction
would you expect to proceed faster? Explain your answer.


Factorize: \( 3 a^{2} b-12 a^{2}-9 b+36 \)


Describe kepler's law of planetrary
motion?


\( K \) is the force constant of a spring. The
work done in increasing its extension
from \( l_{1} \) to \( l_{2} \) will be:
\( \mathbf{A} \cdot K\left(l_{2}-l_{1}\right) \)
в. \( \frac{K}{2}\left(l_{2}+l_{1}\right) \)
\( \mathbf{c} \cdot K\left(l_{2}^{2}-l_{1}^{2}\right) \)
D. \( \frac{K}{2}\left(l_{2}^{2}-l_{1}^{2}\right) \)


Why does bread mould grow profusely on a moist slice of bread rather than on
a dry slice of bread?
A. Moisture is an important factor for growth of mould
B. Moisture is not an important factor for growth of mould
c. softness of bread is an important factor for growth of mould as mould can not tolerate tough surface
D. All of the above


Explain why the given names in the following are wrong. Give the correct name in each case:
1-chloro-1-methylpropan-2-ol


The moment of inertia and rotational
kinetic energy of a fly wheel are \( 20 k g-m^{2} \) and 1000 joule
respectively. Its angular frequency per minute would be
A. \( \frac{600}{\pi} \)
B. \( \frac{25}{\pi^{2}} \)
c. \( \frac{5}{\pi} \)
D. \( \frac{300}{\pi} \)


If the solubility of lithium sodium
hexafluoridoaluminate, \( \boldsymbol{L} \boldsymbol{i}_{3} \boldsymbol{N} \boldsymbol{a}_{3}\left[\boldsymbol{A l} \boldsymbol{F}_{6}\right]_{2} \)
is 's' \( m o l L^{-1}, \) its solubility product is:
(Assume no ionisation of \( \left.\left[A i F_{6}\right]^{3-}\right) \)
A . \( 18 s^{3} \)
B. \( 186624 s^{8} \)
\( \mathbf{c} \cdot 1458 s^{8} \)
D. \( 2916 s^{8} \)


The converse of \( \boldsymbol{p} \Rightarrow \boldsymbol{q} \) is
\( \mathbf{A} \cdot p \Rightarrow q \)
в. \( q \Rightarrow p \)
c. \( -p \Rightarrow-q \)
\( \mathbf{D} \cdot-q \Rightarrow-p \)


The no. of ways can a group of 5 letters
be formed out of \( 5 a^{\prime} s, 4 b^{\prime} s, 3 c^{\prime} s .2 d^{\prime} s \)
and \( 1 e^{\prime} s \) is
A \( \cdot^{5} C_{4} \times 5 \)
B . \( ^{5} C_{4} \times 4 \)
c. 71
D. 75


In a single throw of a die, the events \{1,2\},\{2,3\} are mutually exclusive. Write 1 if true and 0 if false.


Which of the following statement is/ are
correct.?
A. A gas has two specific heats only
B. A material will have only one specific heat, if and only if its coefficient of thermal expansion is equal to zero.
C. A gas has infinite number of specific heat
D. None of these


For the system \( \boldsymbol{A}_{(g)}+\mathbf{2} \boldsymbol{B}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C}_{(g)}, \) the
equilibrium concentrations are \( \boldsymbol{A}=\mathbf{0 . 0 6} \boldsymbol{m o l} \boldsymbol{L}^{-1} \)
\( \boldsymbol{B}=\mathbf{0 . 1 2} \boldsymbol{m o l} \boldsymbol{L}^{-1} \)
\( \boldsymbol{C}=\mathbf{0 . 2 1 6} \boldsymbol{m o l} \boldsymbol{L}^{-1} \)
Then \( K_{c} \) for the reaction is
A . 250
в. 416
\( c .450 \)
D. 525


The speci/species which do not support octet rule are:
\( (a) H_{2} O(b) C l_{2} O(c) N O \)
\( (d) P C l_{5} \)
\( A \cdot a, b \) and \( c \)
B. c and d
\( c . b, c \) and \( d \)
\( D . \quad b, d \) and \( a \)


Choose the correct answers from the
alternatives given

External ears are characteristics of
A. cartilaginous fishes
B. sea horse
c. mammals
D. newts


What is the biggest advantage of
nuclear energy?
A. It is clean.
B. Huge amount of energy is produced.
C. The radioactive emissions from a nuclear power plant are healthy.
D. Nuclear power plant can be easily set up in urban areas.


In Euclid's Division Lemma, when
\( a=b q+r \) where \( a, b \) are positive integers then what values r can take?


If \( \sin 25^{\circ} \cdot \sin 35^{\circ} \cdot \sin 85^{\circ}=\frac{\cos x^{\circ}}{a} \) wher
argument of \( \cos \) is acute and positive then find the value of \( (x+a) \)


Disjunction is
A. Chromosome separition during interphase
B. Chromosome separation during prophas I
C. Chromosome separation in anaphase I
D. Chromosome separation duri metaphase


What happens when acetic acid is
treated with carbonate salt? Name the
gas produced. What happens when this gas is treated with lime water? Support
your answer with equations


toppr
Q Type your question
membrane. It allows small molecules,
such as water, to pass through easily, while larger molecules, such as sucrose, are restricted. Movement of
molecules across the tubing is due to concentration gradients. In an experiment designed to study osmosis, several pieces of dialysis tubing were filled with sucrose solutions of varying concentration and placed in beakers containing distilled water. The rate and direction of water movement was
determined by weighing the bags before and after placing them in the distilled water. The data are recorded below.Table
\( \begin{array}{llll}\text { Tube } & \begin{array}{c}\text { Tube } \\ \text { contents }\end{array} & \begin{array}{c}\text { Mass }(\mathrm{g}) \\ 0\end{array} & \begin{array}{c}\text { Mas } \\ (\mathrm{g})\end{array} \\ \text { number } & \begin{array}{l}\text { (beaker } \\ \text { contents) }\end{array} & \text { minutes } & \begin{array}{l}15 \\ \text { minn }\end{array}\end{array} \)
Distilled water
(distilled
water)
10\% sucrose the and suistilled water)
\( 40 \% \)
sucrose 'distilled
a water
Distilledd water
(40\%)
sucrose)
Cell membranes are also
semipermeable, allowing water but not other substances to cross easily. A red blood cell placed in a \( 0.9 \% \) NaCl solution will neither swell nor shrivel. Based on
this knowledge, and the information presented in Table 1 , what would happen to a red blood cell placed in a \( 20 \% \) NaCl solution?
A. Water would be drawn out of the cell and the cell would swell
B. Water would be drawn into the cell and the cell would swell
c. water would be drawn out of the cell and the cell would shrivel
D. water would be drawn into the cell and the cell would shrive
E. NC


Calculate the enthalpy change on freezing of 1.0 mol of water at \( 10.0^{\circ} \mathrm{C} \) to
ice at \( -10.0^{\circ} \mathrm{C} \)
\( \triangle_{f u s} H=6.03 K J m o l^{-1} \) at \( 0^{\circ} C \)
\( \boldsymbol{C}_{\boldsymbol{p}}\left[\boldsymbol{H}_{2} \boldsymbol{O}(1)\right]=\mathbf{7 5 . 3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \)
\( \boldsymbol{C}_{\boldsymbol{p}}\left[\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})\right]=\boldsymbol{3} \boldsymbol{6} \cdot \boldsymbol{8} \boldsymbol{J} \boldsymbol{m} \boldsymbol{o l}^{-1} \boldsymbol{K}^{-1} \)


In a series LCR circuit connected to an
ac source of variable frequency and voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t}, \) draw a plot
showing the variation of current (I) with angular frequency ( \( \omega \) ) for two different values of resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{1}>\right. \)
\( \left.R_{2}\right), \) Write the condition under which
the phenomenon of resonance occurs. For which value of the resistance out of
the two curves a sharper resonance is produced? Define \( Q \) -factor of the circuit and give its significance


The surface area of the reacting particle can be increased by:
A. Mixing
B. Powdering
c. cooling
D. Both a and


Pluto is termed as the
planet.
A. inner
B. outer
c. dwarf
D. giant


Assertion
Histamine is related with allergic and
inflammatory reactions
Reason
Histamine is a vasodilator
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the
reason
is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


What are Eddy currents? Describe the ways in which they are used to
advantage.


The total number of electrons in the
oxide of Nitrogen with molecular weight
30 is :
A . 22
B. 23
c. 15
D. 26


If \( z \) is purely real and \( R e(z)<0, \) then
\( \arg (x) \) is
A . 0
в. \( \pi \)
c. \( -\pi \)
D.


The area bounded by the region by the curves \( |x|=1-y^{2} \) and \( |x|+|y|=1 \) is
A \( \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{1}{2} \)
\( D \cdot \frac{2}{3} \)


In the circuit shown in the figure, the
heat produced in the \( 5 \Omega \) resistor due to
the current flowing through it is
\( \mathbf{1 0} \) cal \( s^{-1} \)
The heat generated in the \( 4 \Omega \) resistor is
A \( \cdot 1 \) cal \( s^{-1} \)
B. 2 cal \( s^{-1} \)
c. 3 cal \( s^{-1} \)
D. 4 cal \( s^{-} \)


A charge \( Q \) is placed at a distance \( a / 2 \)
above the centre of the square surface
of edge a as shown in the figure. The
electric flux through the square surface
is :
A \( \cdot \frac{Q}{3 \epsilon_{0}} \)
в. \( \frac{Q}{6 \epsilon_{0}} \)
c. \( \frac{Q}{2 \epsilon_{0}} \)
D. \( \frac{Q}{\epsilon_{0}} \)


When crystals of lead nitrate heated
strongly, it produces \( _{-}---- \) gas
A \( \cdot N O_{2} \)
B. \( N O \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O} \)
D. \( N_{2} O_{4} \)


Fill in the blanks.
At any point in a circular motion the
direction of linear velocity of the
particle is


Using a heating blanket to get warm is an example of-
A. Conduction
B. Convection
c. Radiation
D. none of these


The formula of the most abundant salt
of sodium in nature is:
A. \( N a N O_{3} \)
B. \( N a C l \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( N a_{2} S O_{4} \)


For the given circuit shown in fig to act as full wave rectifier - ac input should
be connected across and \( \ldots \ldots . \) the d.c.
output would appear across ......... and
\( A \cdot A, C, B, D \)
\( B . B, D, A, C \)
\( \mathbf{c} \cdot A, B, C, D \)
\( D \cdot C, A, D, B \)


Equipotential surface due to an electric
dipole
A. Does not exist
B. Bisects the line joining two charge of the diople
c. contains the two charge of the dipole
D. Exists in an axial plane


Find the area of the following
parallelogram


Write a balanced equation for each of the following observations:
\( H N O_{3} \) turns brown when exposed to
air.
A \( \cdot 2 H N O_{3} \longrightarrow H_{2} O+2 N O+3(O), 2 N O+O_{2} \rightarrow \)
\( 2 N O_{2} \)
в. \( 2 H N O_{3} \rightarrow H_{2} O+2 N O+2(O), 2 N O+O_{2} \rightarrow \)
\( 2 N O_{2} \)
c. \( 2 H N O_{3} \longrightarrow H_{2} O+N O+3(O), N O+O_{2} \longrightarrow 2 N O_{2} \)
D. \( 2 H N O_{3} \rightarrow H O+2 N O_{2}+3(O), 2 N O_{2}+O_{2} \longrightarrow \)
\( 2 N O_{2} \)


In the different experiments, \( \alpha- \) particles, proton, deuteron and neutron are projected towards gold nucleus with
the same kinetic energy. The distance of closest approach will be minimum for
A. \( \alpha \) - particle
B. proton
c. deuteron
D. neutron


Deformation of surfaces occurs due to
which type of friction among the following?
A. Static friction
B. Rolling friction
C. Fluid friction
D. None of these


The rational numbers whose absolute value is \( \frac{4}{3}, \) is
\( A \cdot \frac{8}{6} \)
в. \( \frac{16}{9} \)
\( c .1 \)
D. -


Ozone layer of upper atmosphere is being destroyed by
A. Sulphurdioxide
B. Carbondioxide
c. chlorofluorocarbon
D. Smogg


Given lines \( : 4 x+3 y=3 \) and \( 4 x+ \)
\( 3 y=12 . \) One of the possible equations
of straight line passing through (-2,-7) and making an intercept of length 3 between the given lines is
A . \( y=-7 \)
В. \( 4 x+3 y=-29 \)
c. \( 3 x-4 y=22 \)
D. \( 7 x+24 y+182=0 \)


The pair of boiling point and compound
are given as,
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}, \quad \boldsymbol{C H}_{3} \boldsymbol{O H} \quad \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N O}_{2} \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
\( \mathbf{8 0}^{\circ} \boldsymbol{C} \quad \mathbf{6 5}^{\circ} \boldsymbol{C} \quad \mathbf{2 1 2}^{\boldsymbol{o}} \boldsymbol{C} \)
\( 184^{\circ} \mathrm{C} \)
(1)
\( (\|) \)
(III)
Which will show lowest vapour pressure
at room temperature?
A. \( C_{6} H_{6} \)
в. \( C H_{3} \) ОН
\( \mathbf{c} \cdot C_{6} H_{5} N O_{2} \)
D. \( C_{6} H_{5} N H_{2} \)


The number of significant figures in
0.010200 is :
A. 6
B. 5
\( c \cdot 4 \)
\( D \)


Matrix is defined as:
A. the unwanted foreign material present in the ore
B. the flux added to remove the unwanted impurities from ore
C. the slag formed as a result of the reaction of flux with
gongue
D. the material used in the reduction of metal oxide to
metal


\( X \) is an optically active alkane having lowest molecular mass. Predict the
structure of the major product obtained
on monochlorination of \( \boldsymbol{X} \)
A \( \cdot C H_{3}-C H_{2}-C H_{2}-C(C l)\left(C H_{3}\right)-C H_{2}-C H_{3} \)
B. \( C H_{3}-C H_{2}-C H_{2}-C H\left(C H_{3}\right)-C H(C l)-C H_{3} \)
c. \( C H_{3}-C H_{2}-C H_{2}-C H\left(C H_{3}\right)-C H_{2}-C H_{2}-C l \)
D. \( C l-C H_{2}-C H_{2}-C H_{2}-C H\left(C H_{3}\right)-C H_{2}-C H_{3} \)


Proteins are made up of organic
molecules with a divalent functional
group.
A. True
B. False


Q Type your question
Why
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


A slide with an image \( 4 \mathrm{cm} \times 2 \mathrm{cm} \) is
placed at a distance of \( 10 \mathrm{cm} \) behind a converging lens and a clear image is formed on a screen \( 1.1 \mathrm{m} \) from the slide.
What is the size of the image on the
screen?


An epithelial tissue which has thin and flat cells arranged edge to edge so as to appear like closely packed tiles, is found at the
A. Inner lining of stomach
B. Inner lining of cheeks
c. outer surface of ovary
D. Inner lining of fallopian tube


One of the common fungal diseases of
human is
A. cholera
B. Plague
c. Typhoid
D. Ring worm


The value of Henry's law constant for
some gases at \( 293 K \) is given below. Arrange the gases in the increasing order of their solubility. \( \boldsymbol{H} \boldsymbol{e}= \)
\( \mathbf{1 4 4 . 9 7 k b a r} ; \mathbf{H}_{\mathbf{2}}=\mathbf{6 9 . 1 6 k b a} \)
\( N_{2}=76.48 k b a r ; O_{2}=34.86 k b a r \)
A. \( H e<N_{2}<H_{2}<O_{2} \)
B. \( O_{2}<H_{2}<N_{2}<H e \)
c. \( H_{2}<N_{2}<O_{2}<H e \)
D. \( H e<O_{2}<N_{2}<H_{2} \)


For the process \( \frac{3}{2} A \rightarrow B, \) at
\( \mathbf{2 9 8 K}, \mathbf{\Delta G ^ { \circ }} \) is \( \mathbf{1 6 3} \mathbf{k J} \mathbf{m o l}^{-1} . \) The
composition of the reaction mixture is \( [\boldsymbol{B}]=\mathbf{1} \) and \( [\boldsymbol{A}]=\mathbf{1 0 0 0 0} . \) Predict the
direction of the reaction and the
relation between reaction quotient (Q) and the equilibrium constant (K)
A. Forwards direction because \( Q>K \)
B. Reverse direction because \( Q>K \)
c. Forwards direction because \( Q<K \)
D. Reverse direction because \( Q<K \)
E. It is at equilibrium as \( Q=K \)


Which of the following has no muscular walls?
A. Artery
B. Arteriole
c. capillary
D. vein


The value of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x^{2}-3 x+2}{x^{2}+x-6} \) lies in the interval
\( ^{\mathbf{A}} \cdot(-\infty, \infty) /\left\{\frac{1}{5}, 1\right\} \)
B \( \cdot(-\infty, \infty) \)
\( \mathrm{c} \cdot(-\infty, \infty) / 1 \)
D. None of these


Two moles of an ideal monoatomic gas
at \( 27^{\circ} \mathrm{C} \) occupies a volume of \( V \). If the
gas is expanded adiabatically to the
volume \( 2 V \), then the work?


A solenoid has a core of a material with
relative permeability of 500. The windings of the solenoid are insulated
from the core and carry a current of \( 2 \mathrm{A} \) If the number of turns is 1000 per
meter, then magnetisation will be then
A . \( 7.78 \times 10^{5} \mathrm{Am}^{-1} \)
В. \( 8.88 \times 10^{5} \mathrm{Am}^{-1} \)
c. \( 9.98 \times 10^{5} \mathrm{Am}^{-} \)
D. \( 10.2 \times 10^{5} \mathrm{Am}^{-1} \)


For an irregularly shaped charged
conductor the potential is :
A. more at the flat parts
B. more at the spherical parts
C. more at the sharp edges
D. same everywhere


What is the most common type of electrometallurgical processes to obtain pure metal?
A. Electro-refining
B. Electrowinning
c. Both a and
D. Oxidation


If for the complex numbers \( z_{1}, z_{2}, \dots ., z_{n} \)
\( \left|z_{1}\right|=\left|z_{2}\right|=\ldots . .=\left|z_{n}\right|=1 . \) Then prove
that \( |\overline{z_{1}+z_{2}+\ldots . .+z_{n}}|= \)
\( \left|\frac{\mathbf{1}}{z_{1}}+\frac{1}{z_{2}}+\ldots \ldots+\frac{1}{z_{n}}\right| \)


The decreasing order of the second
ionization potential of \( M g, C a \) and \( B a \)
is:
A. \( M g>C a>B a \)
в. \( C a>B a>M g \)
с. \( B a>M g>C a \)
D. \( M g>B a>C a \)


Calculate the wavelength, frequency and wavelength of a light wave whose time period is \( 2.0 \times 10^{-10} \)sec


When the temperature of a copper coin
is raised by \( 80^{0} \mathrm{C}, \) its diameter
increases by \( 0.2 \% \) This question has multiple correct options
A. percentage rise in the area of a face is \( 0.4 \% \)
B. percentage rise in the thickness is \( 0.4 \% \)
c. percentage rise in the volume is \( 0.6 \% \)
D. coefficient of linear expansion of copper is 0.25 x \( 10^{-4} /^{0} C \)


A condenser of capacity \( 20 \mu F \) is first charged and then discharged through a
10 \( m H \) inductance. Neglecting the
resistance of the coil, the frequency of the resulting vibrations will be
A. 356 cycle/s
B. 35.6 cycle/s
\( \mathbf{c} \cdot 356 \times 10^{3} \) cycle \( / \mathrm{s} \)
D. 3.56 cycle/s


The \( M n^{3+} \) ion is unstable in solution
and undergoes disproportionation to \( \operatorname{give} M n^{2+}, M n O_{2} \) and \( H^{+} \) ion. Write a
balanced ionic equation for the reaction.


A bullet emerge from a barrel of length \( 1.2 \mathrm{m} \) with a speed of \( 640 \mathrm{ms}^{-1} \)
Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is
A. \( 4 \mathrm{ms} \)
B. 40 ms
c. \( 400 \mu s \)
D. 1 s


\( \int_{-}\left(3 \sin x-4 \cos x+5 \sec ^{2} x-2 \cos e c^{2}\right. \)


Determine an \( A . P \) whose third term is 9
and when fifth term is subtracted from
\( 8 t h \) term we get 6


Chernobyl tragedy occurred in
A. 26th May, 1966
B. 26th April, 1986
c. 6th August, 1947
D. 9th May, 1945


Polarisation of light establishes
A. corpuscular theory of light
B. quantum nature of light
c. transverse nature of light
D. all of the above


A buffer is a solution of weak acid and
its conjugate base or a weak base and
its conjugate acid. It resists the change in \( p H, \) when small amount of strong acid or base is added to it. Buffer
solutions have wide applications. \( H C l \) gas is passed through an aqueous solution of \( 0.1 \mathrm{M} \) 1-aminopropane
\( \left(P r N H_{2}\right) \) till the \( p H \) reaches 9.71 Calculate the ratio of
\( \left[\boldsymbol{P r} \boldsymbol{N} \boldsymbol{H}_{2}\right] /\left[\boldsymbol{P r} \boldsymbol{N} \boldsymbol{H}_{3}^{+}\right] \) in this solution
\( \left[\boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{P r} \boldsymbol{N} \boldsymbol{H}_{3}^{+}\right)=\mathbf{1 . 9 6} \times \mathbf{1 0}^{-11}\right. \)
A. \( 0 . \)
B. 0.2
\( c \cdot 0.3 \)
D. 0.15


Find the derivative of the following functions(it is to be understood that
\( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero
constants and \( m \text { and } n \text { are integers }) \) \( \frac{1}{a x^{2}+b x+c} \)


The volume \( V \) of a liquid crossing through a tube is related to the area of cross-section \( A \), velocity \( v \) and time \( t \) as
\( \boldsymbol{V} \propto \boldsymbol{A}^{\boldsymbol{a}} \boldsymbol{v}^{b} \boldsymbol{t}^{c} . \) Which of the following is
correct given that \( a \neq 1 ? \)
A. \( a \neq b \) and \( b \neq c \)
B. \( a=b \) and \( b=c \)
c. \( a \neq b \) and \( b=c \)
D. \( a=b \) and \( b \neq c \)


A girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position.
Her displacement-time graph is shown in the figure. Find the average velocity
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot-2 m / s \)
D. \( 0 \mathrm{m} / \mathrm{s} \)


A single electron ion has nuclear charge
\( +Z e \) where \( Z \) is atomic number and \( e \)
is electronic charge. It requires \( 16.52 e V \) to excite the electron from the
second Bohr orbit. Find
(a) The atomic number of element?
(b) The energy required for transition of electron from first to third orbit??
(c) Wavelength of photon required to remove electron from first Bohr orbit to
infinity?
(d) The kinetic energy of electron in first
Bohr orbit?


The rate of transfer of energy in a wave
depends
A. directly on the square of the wave amplitude and square of the wave frequency
B. directly on the square of the wave amplitude and square root of the wave frequency
C. directly on the wave frequency and square of the wave amplitude
D. directly on the wave amplitude and square of the wave frequency


Gymnosperms differ from pteridophytes in having
A. Presence of tracheids
B. Presence of embry
c. Presence of ovule
D. Companian cell


Calculate the amount to heat produced per second when a bulb of \( 50 \mathrm{W}, 200 \mathrm{V} \) glows assuming that only \( 20 \% \) of the electric energy is converted into light.
A. 20
B. 400
\( c . \) 50
D. 200


Show that the relation \( \geq \) on the set \( \mathbb{R} \) of
all real numbers is reflexive and
transitive but not symmetric.


paragraph, find the resultant vectors \( \boldsymbol{A} \)
and \( B \) in figure.
\( |\vec{R}|=13.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 8 m s^{-1} \)
vector
3 \( |\vec{R}|=15.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 8 m s^{-1} \)
vector
\( ^{\mathrm{C}}|\vec{R}|=15.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 9 m s^{-1} \)
vector
\( |\vec{R}|=13.54 m s^{-1}, \tan \beta=\frac{3}{13.196} \) with respect to \( 9 m s^{-} \)
vector


The S.I. unit of pressure is pascal
A. True
B. False


If \( \theta \) is the angle between two lines
whose d.cs are \( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \)
then
\( \frac{\Sigma\left(l_{1}+l_{2}\right)^{2}}{4 \cos ^{2}\left(\frac{\theta}{2}\right)}+\frac{\Sigma\left(l_{\mathrm{I}}-l_{2}\right)^{2}}{4 \sin ^{2}\left(\frac{\theta}{2}\right)}= \)
\( A \)
B.
c. -1
\( D \)


Pollution can bring about change in
A. Biogeochemical cycling
B. Abiotic environment
c. Biotic environment
D. None of the above


The diagram shows the outline of a 50
cent coin from Fiji

How many lines of symmetry does it
have?
A \( \cdot 12 \)
B.
\( c \)
\( D \)


Calculate the number of roots of \( \boldsymbol{f}(|\boldsymbol{x}|) \) if \( f(x)=(x-2)(x+3)(x-4) \)
\( A \cdot 3 \)
B. 6
\( c \cdot 0 \)
D. 4


Find a vector in the direction of vector \( \vec{a}=\hat{i}-2 \hat{j} \) that has magnitude 7 units.
A \( \cdot \frac{7}{\sqrt{5}}(\hat{i}-2 \hat{j}) \)
B. \( \frac{7}{\sqrt{5}}(\hat{i}+2 \hat{j}) \)
c. \( \frac{7}{\sqrt{5}}(-\hat{i}-2 \hat{j}) \)
D. None of these


Assertion
Adrenal medullary hormones help in combating the stress condition.
Reason
Both adrenaline and noradrenaline act
on same organs and produce similar effects.
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


Let \( \vec{a} \) and \( \vec{b} \) be unit vectors inclined at
an variable angle \( \boldsymbol{\theta}\left(\boldsymbol{\theta \epsilon}\left(\mathbf{0}, \frac{\pi}{2}\right)\left(\frac{\pi}{2}, \boldsymbol{\pi}\right)\right) \)
\( \operatorname{Let} g(\theta)=\int_{-(\vec{\alpha} . \vec{b})^{2}}^{-\lambda} f^{2}(x) d x+ \)
\( \int_{\lambda}^{|\vec{a} \times \vec{b}|^{2}} f^{2}(x) d x-\frac{2}{\lambda}, w h e r e \lambda>0, \) is
function satisfying \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})= \)
\( \frac{\boldsymbol{x}+\boldsymbol{y}}{\boldsymbol{x} \boldsymbol{y}}, \boldsymbol{x}, \boldsymbol{y} \epsilon \boldsymbol{R}-[\mathbf{0}] \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{h}(\boldsymbol{\theta})= \)
\( -g(\theta)+|\vec{a} \times \vec{b}|^{2} \cdot\left(\vec{a} \cdot \vec{b}_{1}\right)^{2}, \vec{b}_{1}=2 \vec{b} \)
\( \mathbf{f}|\boldsymbol{g}(\boldsymbol{\theta})| \) is attaining its minimum value, then minimum distance between origin and the point of intersection of lines \( \vec{r} \times \vec{a}=\vec{a} \times \vec{b} \) and \( \vec{r} \times \vec{b}=\vec{b} \times \vec{a} \)
is
A. \( \sqrt{2-\sqrt{2}} \)
в. \( \sqrt{2+\sqrt{2}} \)
c. \( \sqrt{\sqrt{2}+1} \)
D. \( \sqrt{\sqrt{2}-1} \)


Polygons that have no portions of their diagonals in the exterior are called
A. squares
B. triangles
c. convex
D. concave


The equations of two planes are \( P_{1} \)
\( 2 x-y+z=2, \) and \( P_{2}: x+2 y-z= \)
3. The equation of the plane which
passes through the point (-1,3,2) and is perpendicular to each of the planes
\( P_{1} \) and \( P_{2} \) is
A \( \cdot x+3 y-5 z+2=0 \)
B. \( x+3 y+5 z-18=0 \)
c. \( x-3 y-5 z+20=0 \)
D. \( x-3 y+5 z=0 \)


Which of the statements given below are applicable for an object to move in a
circle?
A. The object must continuously slow down.
B. The object must accelerate
c. The object must be acted on by external balanced forces
D. The object must move with uniform velocity.


Magnification of a concave lens is
\( A .>0 \) and \( <1 \)
B. >1 or \( <-1 \)
\( c \cdot>-1 \) and \( <1 \)
D. Insufficient information


If \( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the A.M. between \( a \) and
\( b, \) then find the value of \( n \)


An object (O) is placed in a medium M
of refractive index \( 5 / 3 \). A convex lens of
focal length \( 15 \mathrm{cm} \) is placed in front of the object as shown in the figure. Determine the position of the image
formed by the lens.
\( A \cdot 15 \mathrm{cm} \)
B. 20 cm
c. 30 \( \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


Construct a quadrilateral \( A B C D \) such
that \( A B=3 c m, B C=4 c m, \angle A= \)
\( 90^{O}, \angle B=65^{\circ} \) and \( \angle C=110^{\circ} \)


Each face of a cube has perimeter equal
to \( 32 \mathrm{cm} \). Find its surface area


The position of \( -B r \) in the compound in
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C}(\boldsymbol{B r})\left(\boldsymbol{C H}_{3}\right)_{2} \) can be
classified as
A. viny!
B. Secondary
c. Ally
D. Ary


The equation of the plane which is parallel to \( x y \) plane and cuts intercept of length 3 from the z-axis
\( \mathbf{A} \cdot x=3 \)
B. \( y=3 \)
\( \mathbf{c} \cdot z=3 \)
D. \( x+y+z=3 \)


In the alkane
\( \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
identify \( 1^{\circ}, 2^{\circ}, 3^{\circ} \) carbonatoms and give the number of H atoms bonded to
each one of these.


What is dead space air?
A. Air in the alveoli
B. Air in the lungs
C. Air in the pharynx
D. Air in the trachea and bronchi


Two identical charges, \( 5 \mu C \), each are
fixed at a distance \( 8 \mathrm{cm} \) and a charged particle of mass \( 9 \times 10^{-6} k g \) and charge
\( -10 \mu C \) is placed at a distance \( 5 \mathrm{cm} \)
from each of them and is released. Find
the speed of the particle when it is
nearest to the two charges.


If \( (a+i b)(c+i d)(e+i f)(g+i h)= \)
\( A+i B, \) then show that
\( \left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)\left(e^{2}+f^{2}\right)\left(g^{2}+h^{2}\right)= \)
\( A^{2}+B^{2} \)


Which of the tissue is more important for translocation of sucrose?
A. Xylem
B. Phloem
c. Both of the above
D. None of the above


Determine the values of \( a, b, c \) for which
\[
\left\{\begin{array}{ll}
f(x)=\frac{\sin (a+1) x+\sin x}{x} & \text { for } x< \\
=c & \text { for } x= \\
\frac{\left(x+b x^{2}\right)^{\frac{1}{2}}-x^{\frac{1}{2}}}{1} & \text { for } x>
\end{array}\right.
\]
is continuous at \( \boldsymbol{x}=\mathbf{0} \)


Explain briefly the reason for the blue
colour of the sky.


Hydrogen is not a metal but it has been
assigned aplace in the reactivity series of metals.Explain.


The sides of rectangle block are 23 and
\( 4 \mathrm{cm} \) The ratio of the maximum to
minimum resistance between its
parallel force is.


The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994 \\ 4\end{array} \)
Loanfin crores 28 33 of rupees
Represent the above data with the help of a bar graph.


A stone \( A \) is dropped from a height \( h \) above the ground. A second stone B is simultaneously thrown vertically up from a point on the ground with velocity
v. The line of motion of both the stones
is same. The value of v which would
enable the stone \( B \) to meet the stone \( A \)
midway ( at midpoint) between their initial position is:
\( A \cdot 2 g h \)
в. \( 2 \sqrt{g h} \)
\( c \cdot \sqrt{g h} \)
D. \( \sqrt{2 g h} \)


Find the average of 2,3,4,5,10,13


When can the instantaneous velocity of
an object be equal to the average velocity of an object?
A. It can never equal the average velocity
B. It can only equal the average velocity during acceleration
C. It can only equal the average velocity when the velocity is constant
D. It is always equal at the end of a displacement
E. They are equal at the end of a displacement


The half life of a radioactive nucleus is
50 days.The time interval \( \left(t_{2}-t_{1}\right) \)
between the time \( t_{2} \) when \( \frac{2}{3} \) of it has
decayed and the time \( t_{1} \) when \( \frac{1}{3} \) of it
had delayed is-
A. 50 days
B. 60 days
c. 15 days
D. 30 days


Oxidation number of \( N a \) in \( N a-H g \)
amalgam is zero.
If true enter 1 , else enter 0 .
\( A \cdot 1 \)


A substance A decomposes in solution following the first order kinetics. Flask contains 1 L of 1 M solution of \( A \) and flask
II contains \( 100 \mathrm{mL} \) of \( 0.6 \mathrm{M} \) solution
After \( 8 \mathrm{hr} \), the concentration, of \( \mathrm{A} \) in the flask I becomes 0.25 M. What will be the
time for the concentration of \( A \) in flask
to become 0.3 M?
A . \( 0.4 \mathrm{hr} \)
B. 2.4 hr
c. \( 4.0 \mathrm{hr} \)
D. Unpredictable as rate constant is not given


A particle of rest mass \( m_{0} \) moves with a
speed \( \frac{C}{2} \) its total energy and kinetic
energy are:
\( ^{\mathrm{A}} \cdot \frac{\sqrt{3}}{2} m_{0} C^{2} ; \frac{\sqrt{3}}{2} m_{0} C \)
в. \( \frac{2}{\sqrt{3}} m_{0} C^{2} ; \frac{0.25}{\sqrt{3}} m_{0} C^{2} \)
c. \( \frac{2}{\sqrt{3}} m_{0} C^{2} ; \frac{0.27}{\sqrt{3}} m_{0} C^{2} \)
D. None of these


Given, \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}-|\boldsymbol{x}-\mathbf{2}| \) for \( \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3} \)
and \( f(3 x)=a f(x) \) for all other values
of \( x . \) If \( a=3 \), then \( \lim _{x \rightarrow 10^{+}} f(x)=? \) and \( \lim _{x \rightarrow 10^{-}} f(x)=? \)


Which subshell is filled up
progressively in actinides?
A . \( 4 f \)
B. \( 5 f \)
c. \( 6 d \)
D. \( 7 s \)


Nucleic acids/nuclein were first
discovered by
A. Altmann
B. Fleming
c. Miescher
D. Koch


Which of the followings are dissociation?
1. \( M g C l_{2} \rightarrow M g^{2+}+2 C l^{-} \)
2. \( P b B r_{2} \rightarrow P b^{2+}+2 B r^{-} \)
3. \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \rightarrow \boldsymbol{N} \boldsymbol{a}^{+}+\boldsymbol{C l}^{-} \)
A. Only 1 and 2
B. Only 1 and 3
c. only 2 and 3
D. All 1,2 and 3


What is the value of \( \Delta H_{m i x} \) for an ideal
solution?


The artificial sweetener containing chlorine that has the appearance and taste as that of sugar and is stable at cooking temperature is:
A. Aspartame
B. Saccharin
c. sucralose
D. Alitame


Fill in the blanks with approprite words.
...involves the fusion of two naked
gametes, one of both of which are
motile


The hydro static pressure P of a liquid column depends on density d of the liquid column h and acceleration due to gravity g. Using dimensional analysis suggest a formula for hydrodynamic
pressure.


Evaluate: \( \int_{0}^{\frac{\pi}{2}} \sqrt{1+\sin x} d x \)


If a wire having initial diameter of \( 2 m m \)
produced the longitudinal strain of 0.1
\( \%, \) then the final diameter of wire is
\( (\sigma=\mathbf{0 . 5}) \)
A \( .2 .002 m m \)
B. \( 1.999 \mathrm{mm} \)
c. \( 1.998 \mathrm{mm} \)
D. \( 2.001 m m \)


The main reason for deviation of gases
from ideal behaviour is few
assumptions of kinetic theory. These
are
(i) there is no force of attraction
between the molecules of a gas
(ii) volume of the molecules of a gas is negligibly small in comparison to the volume of the gas
(iii) Particles of a gas are always in constant random motion.
A. (i) and (ii)
B. (ii) and (iii)
C . (i), (ii) and (iii)
D. (iii) only


Name the physical quantity which causes motion in a body.
A. Force
B. Work
c. Energy
D. Power


Sam scored 36 marks out of \( 60 . \) Express
the marks in percentage.
A . \( 50 \% \)
B. \( 56 \% \)
\( c \cdot 60 \% \)
D. \( 65 \% \)


Two spheres each of mass \( 10^{5} k g \) and
radius \( 10 m \) are kept in constant. Find the force of gravitational acting between them.
\( \mathbf{A} \cdot 10^{-3} N \)
В \( \cdot 6.67 \times 10^{-3} N \)
c. \( 6.67 \times 10^{-11} N \)
D. \( 10^{-11} N \)


To produce an \( 800 H z \) sine wave, a four
pole generator must be operated at
A. 200 rps
в. 400 rps
c. 800 rps
D. 1,600 rps


Sugars are seperated by using the
solvent BAW (n-butanol acetic acid
\( \left.-H_{2} O\right) \) and detected by spraying the
plate with:
A. Aniline hydrogen phthalate solution
B. Hydrogen peroxide solution
C. crystals of \( I_{2} \)
D. cupric oxide


The figure shows four animals (a), (b),
(c) and (d). Select the correct answer
with respect to a common characteristics of two of these animals.
(a)
(b)
(d)
A . (a) and
(d) respire mainly through body wall.
B. (b) and
(c) show radial symmetry.
\( c \cdot(a) \) and
(b) have cnidoblasts for self-defense.
D. (c) and
(d) have a true coelom.


Prove that if chords of congruent circles subtend equal angle at their centres, then the chords are equal.


The part of the neuron through which information travels as an impulse is
A. Dendrite
B. Axon
c. Cell body
D. Nerve ending


Evaluate \( \frac{d}{d x} 3^{\log _{3} \sqrt{x}}=\dots \dots \dots \)
\( A \cdot \frac{1}{\sqrt{x}} \)
B. \( \sqrt{x} \)
c. \( \frac{1}{2 \sqrt{x}} \)
D. \( -\frac{1}{\sqrt{x}} \)


Equivalent conductivity of acetic acid at infinite dilution is \( 390.7 \mathrm{mho} \mathrm{cm}^{2} \mathrm{gm} \)
equiv and for \( 0.1 \mathrm{M} \) acetic acid is 5.2
mho \( c m^{2} \) gm.equiv \( ^{2} \). Calculate degree
of dissociation, \( \boldsymbol{H}^{+} \) ion concentration
and dissociation constant of the acid.


Measure of angle \( \angle A C D \) in the given
figure is:
A \( .130^{\circ} \)
B. 120
\( c \cdot 150 \)
D. \( 115^{\circ} \)


Phyllotaxy is the arrangement of leaves on the stem. Identify the three types of phyllotaxy shown in the given figures, \( x \) Y and Z.
When
A. X-Alternate, Y-Opposite, Z-Whorled
B. X-opposite, Y-Whorled, Z-Alternate
c. x-whorled, Y-Alternate, Z-Opposite
D. x-opposite, Y-Alternate, Z-Whorled


Which of the following distinguishes bleaching powder from carbonyl chloride?
A. Number of chlorine atoms
B. Number of oxygen atoms
c. Calcium atom.
D. Hydrogen atom.


The coefficients of variation of two
series are \( 58 \% \) and \( 69 \% \). If their
standard deviations are 21.2 and 15.6
then their A.M's are
A \( .36 .6,22.6 \)
в. 34.8,22.6
c. 36.6,24.4
D. None of these


What coefficients are required to balance the following equation? \( \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{H C l} \rightarrow \boldsymbol{C a C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A .2,4,2,4
в. 1,2,2,2
\( \mathrm{c} .1,2,1,1 \)
D. 1,2,1,2


A boat whose speed in \( 15 k m / h r \) in still
water goes \( 30 \mathrm{km} \) downstream and
comes back in a total of 4 hours 30
minutes. the speed of the stream (in \( \mathrm{km} / \mathrm{hr}) \) is :


How many numbers greater than a
million can be formed with the digits
\( \mathbf{2}, \mathbf{3}, \mathbf{0}, \mathbf{3}, \mathbf{4}, \mathbf{2}, \mathbf{3} ? \)


A vessel of \( 5.0 l \) capacity contains \( 1.4 g \)
nitrogen at \( 1800 \mathrm{K} \). Assuming that at this temperature, \( 40 \% \) of molecules are
dissociated into atoms and the gas is ideal, what is the gas pressure?
A .2 .07 atm
B. 1.476 atm
c. 1.05 atm
D. 2.67 atm


Choose the correct statement.
A. Polar molecules have permanent electric dipole moment.
B. \( C O_{2} \) molecule is a polar molecule.
C \( . H_{2} O \) is a non-polar molecule.
The dipole field at large distances falls of as \( \frac{1}{r^{2}} \)


Ram was riding in a car travelling at
a speed of \( 20 m s^{-1} \) toward east. Shyam
was standing on the sideway when the car passed him. Just before the car passed close to Shyam (when it was north-west of him); Ram had thrown a
banana peel with velocity \( 10 m s^{-1} \)
relative to him as \( \boldsymbol{v}_{\text {Banana}, \text {Ram}}= \)
\( (-10) \hat{i}+(-10) \hat{j} . \) The banana peel had
velocity components \( 10 m s^{-1} \) toward
south and \( 10 m s^{-1} \) towards west in
Ram's reference frame. When Ram met
Shyam later, Shyam accused that Ram had thrown the banana peel at him.
Explain this with the help of a velocity diagram.


The compound(B) in the below reaction
is :
\( C_{2} H_{5} C l \stackrel{K C N}{\rightarrow} A^{H_{3}} Q^{+} B \)
A. ethylene chloride
B. acetic acid
c. propionic acid
D. ethyl cyanide


The chambers in heart of fish are
A. 1 ventricle and 1 auricle
B. 1 ventricle and 2 auricles
c. 2 ventricles and 2 auricles
D. 2 ventricles and 1 auricle


A goldfish swims through an aquarium by moving its fins and tail. What causes the fish to move forward?
I. The force exerted by the water on the goldfish
II. The force exerted by the tail of the goldfish on the water
III. The force exerted by the fins of the goldfish on the water
A . Ionly
B. II only
c. I and III only
D. II and III only
E. I, II, and III


If equation of sound wave is \( \boldsymbol{y}= \)
\( 0.0015 \sin (62.8 x+314 t) \) then its
wavelength will be:
A. 0.1 unit
B. 0.2 unit
c. 0.3 unit
D. 2 unit


Write an example of food preservative.


What is the correct formula for lithium
fluoride?
A . \( L i F \)
в. \( L i_{2} F_{2} \)
\( \mathbf{c} \cdot L i_{3} F_{9} \)
D. \( L i F_{7} \)
E \( . L i_{7} F_{19} \)


Select correct IUPAC naming of given
compound:
A. but-3-ene
B. but-3-yne
c. butene
D. butane


Solve:
\( \int_{0}^{\frac{\pi}{2}}(\sin 2 x) \sin x d x \)


The Sl unit of displacement is


Find the \( T . S . D \) of a cube, whose volume
is \( 3 \sqrt{3} a^{3} \) cubic units.


Two forces of \( 1 N \) and \( P N \) act at a point so that the magnitude of resultant is \( \mathbf{1} N \) and it is perpendicular to \( 1 N . \) The
value of \( \boldsymbol{P} \) in newtons and the angle
between the \( 1 N \) and \( P N \) are:
A \( \cdot \sqrt{2}, 135^{\circ} \)
B . \( \sqrt{2}, 120^{0} \)
c. \( 1,45^{\circ} \)
D. \( 2,150^{\circ} \)


At absolute zero, the entropy of a pure
crystal is zero. This statement is:
A. first law of thermodynamics
B. second law of thermodynamics
C. third law of thermodynamics
D. zeroth law of thermodynamics.


Which of the following is not correct regarding terylene?
A. Step-growth polymer
B. Synthetic fibre
c. condensation polymer
D. Thermosetting plastic


What are the different shapes found in
bacteria? Give examples.


The points \( A(2 a, 4 a), B(2 a, 6 a) \) and
\( C(2 a+\sqrt{3} a, 5 a)(\text { when } a>0) \) are
vertices of
A. an obtuse angled triangle
B. an equilateral triangle
c. an isosceles obtuse angled triangle
D. a right angled triangle


Evaluate \( \int e^{x}\left(\log x+\frac{1}{x^{2}}\right) d x \)
A \( \cdot e^{x} \log x+c \)
B. \( e^{x}\left(\log x-\frac{1}{x}\right)+c \)
c. \( e^{x}\left(\log x+\frac{1}{x}\right)+c \)
D. \( \frac{e^{x}}{x^{2}}+c \)


Divide 1000 into 2 parts such that 10
\( \% \) of one part equals \( 20 \% \) of the other Find the bigger part.
A \( \cdot \frac{2000}{3} \)
в. \( \frac{1000}{3} \)
c. \( \frac{150}{3} \)
D. None of the above


The general solution of the differential
equation \( (x+y) d x+x d y=0 \) is
A \( \cdot x^{2}+y^{2}=C \)
B . \( 2 x^{2}-y^{2}=C \)
c. \( x^{2}+2 x y=C \)
D. \( y^{2}+2 x y=C \)


Find the position vector of the midpoint of the vector joining the points \( P(2,3,4) \) and \( Q(4,1,-2) \)


55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?


\( A B C D \) is a quadrilateral, \( E \) is the point of intersection of the line joining the
middle points of the opposite sides. If \( \boldsymbol{O} \) is any point, then \( \hat{O} A+\hat{O} B+\hat{O C}+ \) \( \hat{O} D= \)
A \( \cdot 4 O E \)
в. 3 О
\( \mathrm{c} \cdot 2 O \hat{E} \)
D. \( O E \)


State whether given statement is True or False.

Aryabhata is the first Indian satellite.
A. True
B. False


The domain of \( \frac{1}{\sqrt{x-x^{2}}}+\sqrt{3 x-1-2 x^{2}} \)
is:


Balance the following equation:
\( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H} \boldsymbol{C l O}_{4}+\boldsymbol{C l O}_{2} \)
A \( \cdot 3 K C l O_{3}+3 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+H C l O_{4}+2 C l O_{2}+ \)
\( H_{2} O \)
в. \( K C l O_{3}+5 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+3 H C l O_{4}+2 C l O_{2}+ \)
\( 3 H_{2} O \)
c. \( 3 K C l O_{3}+4 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+2 H C l O_{4}+ \)
\( 2 C l O_{2}+H_{2} O \)
D. None of these


A body acted upon by three forces \( \vec{F}_{1}, \vec{F}_{2} \) and \( \vec{F}_{3} \) is under equilibrium. Given \( \left|\vec{F}_{1}\right|=10 N,\left|\vec{F}_{2}\right|=6 N \)
This question has multiple correct options
\( A \cdot F_{3}=8 N \)
В \( \cdot F_{3}=6 N \)
\( \mathbf{c} \cdot \theta=53 \)


When in going east at \( 10 \mathrm{km} / \mathrm{h} \) a train moving with constant velocity appears to be moving exactly north - east. when my velocity is increased to \( 30 \mathrm{km} / \mathrm{h} \) east it appears to be moving north What is the velocity of train along north (in \( \mathrm{Kmph}) \) ?
\( A \cdot 30 \mathrm{km} / \mathrm{h} \)
B. 20 km/h
\( c \cdot 50 \mathrm{km} / \mathrm{h} \)
D. \( 10 \mathrm{km} / \mathrm{h} \)


What is electrostatic shielding? Mention one application of it.


Two sources of sound \( S_{1} \) and \( S_{2} \)
produce sound waves of same frequency \( 660 H z . \) A listener is moving
from source \( S_{1} \) towards \( S_{2} \) with a
constant speed \( u \) m/ \( s \) and he hears
10 beats/s. The velocity of sound is
\( 330 m / s . \) Then, \( u \) equals:
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
в. \( 15.0 \mathrm{m} / \mathrm{s} \)
\( c .5 .5 m / s \)
D. \( 10.0 \mathrm{m} / \mathrm{s} \)


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


Why we are hurt less when we jump on a muddy floor in comparison to a hard
floor?


Three charges \( +4 q, Q \) and \( +q \) are
placed in a straight line with \( Q \) midway
in between the other two charges. If net
force on \( +\boldsymbol{q} \) is zero, the charge \( \boldsymbol{Q} \) must
be:
A. \( -q \)
в. \( -2 q \)
c. \( \frac{-q}{2} \)
D.


\( \cos ^{-1}\left(\frac{3+5 \cos x}{5+3 \cos x}\right)= \)
A \( \cdot \tan ^{-1}\left(\frac{1}{2} \tan \frac{x}{2}\right) \)
B \( \cdot 2 \tan ^{-1}\left(-\frac{1}{2} \tan \frac{x}{2}\right) \)
c. \( \frac{1}{2} \tan ^{-1}\left(2 \tan \frac{x}{2}\right) \)
D. \( 2 \tan ^{-1}\left(\frac{1}{2} \tan \frac{x}{2}\right) \)


Alanine forms Zwitter ion which exists
as
A. \( C H_{3}-\quad C \quad H C O O^{-} \) in a medium of \( p H=12 \)
\( C H_{3}-C_{\uparrow} H C O O \)
\( +N H_{3} \)
B. \( C H_{3}-\underset{t_{1}}{C} H C O O H \) in a medium of \( p H=4 \)
c. \( C H_{3}-C H-C O O^{-} \) in a medium of \( p H=7 \) \( C H_{3}-C H-C O O \)
\( _{N H_{2}} \)
D. None of these


The density of air at NTP is
\( 1.293 k g m^{-3} \) and density of mercury at
\( \mathbf{0}^{\circ} \boldsymbol{C} \) is \( \mathbf{1 3 . 6} \times \mathbf{1 0}^{\mathbf{3}} \mathbf{k g m}^{-\mathbf{3}} . \) If \( \boldsymbol{C}_{\boldsymbol{p}}= \)
\( 0.2417 \mathrm{calkg}^{-10} \mathrm{C}^{-1} \) and \( C_{v}=0.1715 \)
the speed of sound in air at \( 100^{\circ} \mathrm{C} \) will
be \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{N} \boldsymbol{k} \boldsymbol{g}^{-1}\right) \)
A \( .260 m s^{-1} \)
B . \( 332 \mathrm{ms}^{-1} \)
c. \( 350.2 \mathrm{ms}^{-1} \)
D. \( 369.4 \mathrm{ms}^{-1} \)


Define density. What is the Sl units of density?


A balloon is rising with constant acceleration \( 2 m / s e c^{2} . \) Two stones are
released from the balloon at the interval
of 2 sec. Find out the distance between
the two stones 1 se \( c \). after the release of
second stone.
\( \mathbf{A} \cdot 48 m \)
в. \( 84 m \)
\( c .40 m \)
D. \( 60 m \)


Stomata can open at night in
A. Xerophyte
B. Gametophyte
c. Hydrophyte
D. None of the above


\( \sin ^{-1} \sin 15+\cos ^{-1} \cos 20+ \)
\( \tan ^{-1} \tan 25=? \)
A . 1.04719754
в. 11.04719754
c. 111.04719754
D. 1111.04719754


Binary operation \( ^{*} \) on \( \mathrm{R}-\{-1\} \) defined by \( \boldsymbol{a} * \boldsymbol{b}=\frac{\boldsymbol{a}}{\boldsymbol{b}+\mathbf{1}} \) is
\( A .^{*} \) is associative and cummutative
B. \( ^{*} \) is neither associative nor commutative
c. \( ^{*} \) is commutative but not associative
D. \( ^{*} \) is associative but not commutative


A circular coil of mean radius of \( 7 \mathrm{cm} \)
and having 4000 tums is rotated at the rate of 1800 revolutions per minute in the earth's magnetic field \( (\mathrm{B}=0.5 \) Gauss ), The peak value of emf induced is
A . \( 1.158 \mathrm{v} \)
B. 0. 58 v
c. \( 0.29 v \)
D. 5.8


What are the differences between a
thorn and prickle? Describe with
examples.


The equation of the plane passing through the point (1,1,1) and perpendicular to the planes \( 2 x+y- \)
\( 2 z=5 \) and \( 3 x-6 y-2 z=7 \) is?
A. \( 14 x+2 y-15 z=1 \)
B. \( -14 x+2 y+15 z=3 \)
c. \( 14 x-2 y+15 z=27 \)
D. \( 14 x+2 y+15 z=31 \)


The direction cosines to two lines at
right angles are (1,2,3) and \( \left(-2, \frac{1}{2}, \frac{1}{3}\right), \) then
the direction cosine perpendicular to both given lines are:
A \( \cdot \sqrt{\frac{25}{219}} \cdot \sqrt{\frac{19}{2198}} \cdot \sqrt{\frac{729}{21988}} \)
B. \( \sqrt{\frac{24}{2198} \cdot \sqrt{\frac{38}{2198}}} \sqrt{\frac{730}{21988}} \)
c. \( \frac{1}{3},-2, \frac{-7}{2} \)
D. None of the above


Match the compounds and their
chemical units.
Compound Units
A. \( \quad \) p. Unbranched polymer of glucose Amylopectin
B. Lignin \( \quad \) q. Branched polymer of glucose
Complex polymer of aromatic
C. Chitin \( \quad \) alcohols
D. Proteins \( \quad \) s. Polymer of acetyl glucosamine
t. Polymer of amino acids
\( A \cdot A-p, B-r, C-s, D-t \)
B. \( A-q, B-r, C-s, D-t \)
c. \( A-q, B-p, C-s, D-t \)
\( D \cdot A-p, B-r, C-p, D-t \)


What is the amount of Al deposited on
the electrolysis of molten \( A l_{2} O_{3} \) when a current of \( 9.65 \mathrm{A} \) is passed for \( 10.0 \mathrm{s} \)


The sequence of communities of
primary succession in water is?
A. Phytoplankton, sedges, free-floating hydrophytes, rooted hydrophytes, grasses and trees
B. Phytoplankton, free-floating hydrophytes, rooted hydrophytes, sedges, grasses and trees
C. Free-floating hydrophytes, sedges, phytoplankton, rooted hydrophytes, grasses and trees
D. Phytoplankton, rooted submerged hydrophytes, floating hydrophytes, reed swamp, sedges, meadow and trees


Examples of Iyophilic colloids are:
This question has multiple correct options
A. albumin
в. RВС
c. smoke
D. metalsulphide


\( f\left(m_{1}, m_{2} \) are masses of an ideal gas, \right.
then which of the graph represents
\( \boldsymbol{m}_{2}>\boldsymbol{m}_{1} ? \)
İ
\( (1 v) \)
A . I, Il only
в. ।, III only
c. ।, Iv only
D . ।, и, II, Iv