A bag contains 15 red, 8 blue and
several green marbles. A marble is selected at random. The probability of drawing a blue marble is \( \frac{1}{5} \)
5 green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing
a green marble
A \( \cdot \frac{3}{10} \)
В. \( \frac{12}{35} \)
c. \( \frac{23}{40} \)
D. \( \frac{17}{35} \)


Calculate standard deviation of the
following data.
\[
\begin{array}{lllll}
x & 0- & 10- & 20- & 30- \\
& 10 & 20 & 30 & 40
\end{array}
\]
10
A . -12
B. 12
c. 12.36
D. 152.77


If \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}-\sqrt{\mathbf{9} \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{6}}} \) to
evaluate \( I \), one of the most proper
substitution could be
A. \( \sqrt{9 x^{2}+4 x+6}=u \pm 3 x \)
B. \( \sqrt{9 x^{2}+4 x+6}=3 u \pm x \)
c. \( _{x}=\frac{1}{t} \)
D. \( 9 x^{2}+4 x+6=\frac{1}{t} \)


The time interval between a lightning
flash and the first sound of thunder
was found to be 5 s. If the speed of sound in air is \( 330 m s^{-1}, \) find the
distance of the flash from the observer.


Which of the following is not a target molecule for drug function in body?
A. Vitamins
B. Proteins
c. Lipids
D. Carbohydrates


toppr
Q Type your question
to the other end of the piston, it moves down. If air in the enclosure is cooled
from temperature \( \boldsymbol{T} \) to \( \boldsymbol{T}-\triangle \boldsymbol{T}, \) the
piston moves back to its original
position. Then \( \triangle \boldsymbol{T} / \boldsymbol{T} \) is close to
(Assuming air to be an ideal gas, \( \boldsymbol{g}= \)
\( 10 m / s^{2}, \) atmospheric pressure is \( 10^{5} \)
Pascal)
\( \mathbf{A} \cdot 0.01 \)
B. 0.02
c. 0.04
D. 0.09


The oxidation states exhibited by Tin
are:
\( \mathbf{A} \cdot+2 \) and +4
B. +1 and +2
c. +3 and +4
D. +4 only


The formula of prussian blue is:
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{6}\right] \)
В. \( \operatorname{Fe}(C N)_{2} \)
c. \( \operatorname{Fe}(C N S)_{3} \)
D. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)


A river is flowing from west to east at a speed of \( 5 \mathrm{m} / \mathrm{min}^{-1} \). A man on the south
bank of the river, capable of swimming at \( 10 m / m i n^{-1} \) in still waters wants to swim
the river in the shortest time. In which
direction should swim in a direction
A \( .30^{\circ} \) west of north
B. \( 60^{\circ} \) east of north
\( \mathbf{c} \cdot 30^{\circ} \) east of north
D. due north


The co-ordinates of a moving particle at a time \( t, \) are given by \( \boldsymbol{x}= \)
\( 5 \sin 10 t, y=5 \cos 10 t . \) The speed of
the particle is
\( \mathbf{A} \cdot 25 \)
B. 50
c. 10
D. \( 50 \sqrt{2} \)


If \( y \) represents pressure and \( x \) represents velocity gradient, then the dimensions of \( \frac{d^{2} y}{d x^{2}} \) are
\( \mathbf{A} \cdot\left[M L^{-1} T^{-2}\right] \)
B. \( \left[M^{2} L^{-2} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{0}\right] \)
D \cdot \( \left[M^{2} L^{-2} T^{-4}\right] \)


Graph between log k and 1/T [k is rate
constant \( \left(s^{-1}\right) \) and \( T \) the temperature
(K) \( ] \) is a straight line with \( 0 X=5, \theta= \)
\( \tan ^{-1}(1 / 2.303) . \) Hence \( -E_{a} \) will be :
A . 2.303 2 cal
B. 2/2.303 cal
c. 2 cal
D. None


Steel wire of length ' \( L \) ' at \( 40^{\circ} \mathrm{C} \) is suspended from the ceiling and then a mass ' \( m^{\prime} \) is hung from its free end. The
wire is cooled down from \( 40^{\circ} C \) to \( 30^{\circ} C \)
to regain its original length \( ^{\prime} L^{\prime} . \) The coefficient of linear thermal expansion
of the steel is \( 10^{-5} /^{\circ} C, \) Young's modulus of steel is \( 10^{11} N / m^{2} \) and radius of the wire is \( 1 \mathrm{mm} \). Assume that
\( L>> \) diameter of the wire. Then the
value of ' \( m \) ' in kg is nearly
A . 3
B. 2
\( c .9 \)
D. 5


\( \mathbf{A} \)
G.P. consists of an even number of
terms. If the sum of all the terms is 5
times the sum of the terms occupying the odd places. Find the common ration of the G.P.


If \( \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{2} \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{o})=-\mathbf{1}, \boldsymbol{f}(\boldsymbol{o})=\mathbf{1} \)
then \( \boldsymbol{f}(2)= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-1 \)
D. \( \frac{-1}{2} \)


The freezer in a refrigerator is located at
the top section so that;
A. The entire chamber of the refrigerator is cooled quickly due to convection
B. The motor is not heated
C. The heat gained from the environment is high
D. The heat gained from the environment is low


\( y=5 x \) then \( \frac{d y}{d x} \)


The armature of a demonstrator
generator consists of a flat square coil
of side \( 4 c m \) and 200 turns. The coil
rotates in a magnetic field of 0.75 T. The
angular speed so that a maximum emf of \( 1.6 V \) is generated is:
A \( \cdot \frac{20}{3} \) rad/s
B. \( \frac{10}{3} \) rotations/s
c. \( \frac{40}{3} \) rpm
D. None of these


Trochlea of which bone fits in the
trochlear notch of ulna?
A. Humerus
B. Radius
c. Femur
D. Scaphoid


Which of the following is true about
Bryophytes?
A. They possess archegonia
B. They contain chloroplast
c. They are thalloid
D. All of the above


A particle moves along a circle of radius \( 2 m \) with a constant speed of \( 8 m / s . \) It
covers the quarter of circle in sec?
A \( \cdot \frac{\pi}{16} \)
в.
\( c \cdot \frac{\pi}{4} \)
D.


Which of the following elements is oxidised by fluorine and not by
chlorine?
A. Sodium
B. Aluminum
c. sulphur
D. oxygen


\( 2 N O_{2} \rightleftharpoons N_{2} O_{4} \) The dimerisation of
\( N O_{2} \) is accompainied with :
This question has multiple correct options
A. decrease in paramagnetism
B. change in color
C. increase in temperature
D. increase in paramagnetism


In the complex \( F e(C O)_{x}, \) the value of \( x \)
is:
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Scavenger cells of alveoli is called as
A. Melanophage
B. Monocytes / macrophage
c. Dust cell
D. Microglial cell


Which property of water make it easy to
contaminate and difficult to purify?
A. Water is a universal solvent
B. Tendency to dissolve a large number of substances
C. Both A and B
D. None of the above


If
\( a, b, c \) are real numbers such that ac
\( \neq 0, \) then show that at least one of the
equations \( a x^{2}+b x+c=0 \) and \( -a x^{2}+b x \)
\( +c=0 \) has real roots.


Bleaching action of \( S O_{2} \) is due to:
A. reduction
B. Oxidation
c. hydrolysis
D. None of the above


The value of ionisation potential for inert gases is :
A . zero
B. low
c. high
D. negative


An object is lying at a distance of \( 90 \mathrm{cm} \) from a concave mirror of focal length
\( 30 \mathrm{cm} . \) The position and nature of image formed by it will be:
A. \( 45 \mathrm{cm} \), of the size to object
B. \( 95 \mathrm{cm} \), smaller than object
c. \( 35 \mathrm{cm} \), bigger than object
D. \( -45 \mathrm{cm}, \) smaller than object


Why does the flow of acid rain water
into a river make the survival of aquatic life in the river difficult??


fthe matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{I}+\boldsymbol{A}+ \)
\( A^{2}+\ldots \ldots \ldots . \) upto \( A^{\infty}=\ldots \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}\frac{1}{2} & \frac{1}{3} \\ \frac{1}{-2} & 0\end{array}\right] \)
C. \( \left[\begin{array}{ll}\frac{-1}{2} & \frac{1}{-3} \\ \frac{1}{-2} & 0\end{array}\right] \)
D. \( \left[\begin{array}{cc}\frac{1}{2} & \frac{1}{-3} \\ \frac{1}{-2} & 0\end{array}\right] \)


The Sl unit of inductance is


Which of the following is an example of oscillatory motion?
A. Heart beat of a persion
B. Motion of earth around the sun
c. Motion of Hally's comet around the sun
D. oscillations of a simple pendulam


Fill in the blanks with \( >,< \) or \( =\operatorname{sign} \) \( \$ \$-45-(-11) \)
\( -57+(-4) \$ \$ ? \)


In dihybrid cross, out of 16 plants obtained, the maximum number of
different genotypes possible are
\( A \cdot 4 \)
B. 9
\( c \cdot 16 \)
\( D \cdot 12 \)


In North west corner rule the allocation
is done in
A. upper left corner
B. upper right corner
c. middle cell in the transportation table
D. cell with the lowest cost


A particle would take time \( t_{1} \) to move
down a straight tube from the surface of earth (supposed to be homogeneous sphere) to its centre. If gravitational acceleration were to remain constant
time would be \( t_{2} \). The ratio \( t / t^{\prime} \) will be
A \( \cdot \frac{\pi}{2 \sqrt{2}} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{\pi}{\sqrt{3}} \)


In alveolar air, the partial pressure of
\( C O_{2} \) is
A. \( 40 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 42 \mathrm{mm} \) of \( \mathrm{Hg} \)
c. \( 44 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 46 \mathrm{mm} \) of \( \mathrm{Hg} \)


\( \int \frac{(x-1) e^{x}}{(x+1)^{3}} d x \) is
A \( \cdot \frac{e^{x}}{x+1} \)
В. \( e^{x}\left(\frac{x}{x+1}\right) \)
c. \( \frac{e^{x}(x-1)}{(x+1)^{2}} \)
D. \( \frac{e^{x}}{(x+1)^{2}} \)


\( 25 \mathrm{ml} \) of \( H_{2} O_{2} \) solution were added to
excess of acidified \( K I \) solution. The
iodine so liberated required \( 20 \mathrm{ml} \) of
\( 0.1 \mathrm{N} N a_{2} S_{2} O_{3} \) for titration
Calculate strength of \( H_{2} O_{2} \) in terms of
normality and percentage?
A. \( 0.04 \mathrm{N}, 0.136 \% \)
В. \( 0.08 \mathrm{N}, 0.136 \% \)
c. \( 0.04 \mathrm{N}, 0.163 \% \)
D. \( 0.02 \mathrm{N}, 0.163 \% \)


The heat of combustion of acetylene is
312 kcal. If heat of formation of \( C O_{2} \) and
\( H_{2} O \) are 94.38 and 68.38 kcal
respectively, \( C \equiv C \) bond energy is
\( x k c a l . \) Given that heat of atomisation of
C and H are 150.0 and 51.5 kcal
respectively and \( C-H \) bond energy is
\( 93.64 \mathrm{kcal} \)
Value of \( x \) (nearest integer value) is


The signs of \( \Delta \mathrm{H}, \Delta \mathrm{S} \) and \( \Delta \mathrm{G} \) for a non
spontaneous reaction at all temperatures would be:
\( A \cdot+,+, \)
\( B .+. .,+ \)
\( c \ldots- \)
D. \( +,+,+ \)


In the figure given below, there are two
convex lens \( L_{1} \) and \( L_{2} \) having focal
length of \( f_{1} \) and \( f_{2} \) respectively. The
distance between \( L_{1} \) and \( L_{2} \) will be
\( A \cdot f_{1} \)
B \( \cdot f_{2} \)
\( c \cdot f_{1}+f_{2} \)
D. \( f_{1}-f_{2} \)


State the following statement as True or False.
Multiplication and Division of two negative numbers is always a negative
number.
A. True
B. False


The plate separation in a parallel plate capacitor is \( d \) and plate area is \( A \). If it is charged to \( V \) volts then calculate the work done in increasing the plate separation to \( 2 d \) then


Acetic acid is a more volatile than
\( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
A. True
B. False


What will Rs. 500 amounts to in 10
years after its deposit in a bank which pays annual interest rate of \( 10 \% \)
compounded annually.


The density of a gas is 10 times more than that of hydrogen. The molecular weight of gas \( \boldsymbol{X} \) is


Three equal resistors connected in series across a source of e.m.f together dissipate 10W power. The power dissipated if the same resistors are connected in parallel across the same source of emf is
A \( . \) 1) \( 10 w \)
B. 2) 30w
\( c \cdot 3) \) 90w
D. 4 cow


Match List-I (Atomic masses M) with
List-II (\% composition of heavier isotope).


Find the ratio of the power developed in
segment AE to that in segment HM.
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


\( \underbrace{\frac{i}{i}}{k} \)


The coil in a MCG has an area of \( 4 \mathrm{cm}^{2} \)
and 500 turns. The intensity of magnetic induction is 2T. When a
current of \( 10^{-4} \) A is passed through it,
the deflection is \( 20^{0} \). The couple per
unit twist is (N-m)
A. \( 3 \times 10^{-6} \)
B. \( 2 \times 10^{-6} \)
\( \mathbf{c} \cdot 4 \times 10^{-6} \)
D. \( 5 \times 10^{-6} \)


Factorise: \( \boldsymbol{x}^{2}-\mathbf{3 6} \)


Which of the following in the blood stream is reduced most by excessive vomiting and diarrhoea?
A. Calcium
B. Sodium
c. Potassium
D. Iron


Progesterone is secreted by
A. Corpus luteum
B. Thyroid
c. Thymus
D. Testis


With rise in temperature the resistance of germanium,
A. increases
B. decreases
c. remains the same
D. first increases then decreases


The projections of a directed line segment on the coordinate axes are
12,4,3 respectively.

What are the direction cosines of the
line segment?
A \( \cdot(12 / 13,4 / 13,3 / 13) \)
B . \( (12 / 13,-4 / 13,3 / 13) \)
c. \( (12 / 13,-4 / 13,-3 / 13) \)
D. \( (-12 / 13,-4 / 13,3 / 13) \)


For the reaction, \( \left[A g\left(C N_{2}\right)\right]^{-} \rightleftharpoons \)
\( A g^{+}+2 C N^{-} \) the equilibrium constant
at \( 298 \mathrm{K} \) is \( 4.0 \times 10^{-10} . \) The silver ion
concentration in a solution which was
originally 0.12 molar \( n K C N \) and 0.04
molar in \( A g N O_{3}, \) is:
A \( \cdot 1 \times 10^{-10} \mathrm{M} \)
В. \( 1 \times 10^{-8} M \)
c. \( 1 \times 10^{-12} M \)
D. \( 1 \times 10^{-4} M \)


Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of \( 30^{0} \) with each other. When suspended in a liquid
of density \( 0.8 \mathrm{gcm}^{-3}, \) the angle remains
the same. If density of the material of
the sphere is \( 1.6 \mathrm{gcm}^{-3} \), the dielectric
constant of the liquid is :
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Which of the follwing is the correct electronic configuration of
\( \boldsymbol{F} \boldsymbol{e}^{+3} \boldsymbol{i o n}\left(\boldsymbol{Z}_{\boldsymbol{F} e}=\boldsymbol{2} \boldsymbol{6}\right) ? \)
\( \mathbf{A} \cdot[A r] 3 d^{6} \)
B . \( [A r] 3 d^{5} \)
\( \mathbf{c} \cdot[A r] 3 d^{6} 4 s^{2} \)
D \cdot \( [A r] 3 d^{6} 4 s^{1} \)


Explain the significance of quantum
number?


Meitnerium is IUPAC official name of an
element with atomic number?
\( A \cdot 113 \)
B. 118
\( c \cdot 104 \)
D. 109


The total number of structural isomers
possible for a compound with the formula \( C_{6} H_{12}, \) having only one cyclopropane ring, is :


Give one equation each to show the following properties of sulphuric acid:
Acidic nature.


Which of the following shows the sex chromosomes in the body cells and in the sex cells in a female?
A. Body cells- \( x x \), sex cells-all \( x \)
B. Body cells- XX, Sex cells- all XX
c. Body cells- XY, Sex cells- x or Y
D. Body cells- XY, Sex cells- all XY


If \( 4 A M^{\prime} s \) are inserted between \( \frac{1}{2} \) and 3
then third \( A M \) is
A . -2
B. 2
\( c \cdot-1 \)
D.


Particles of a colloidal solution can be
filtered through a filter paper
If true enter 1 , else enter 0 .


The D.E whose solution is \( y=C^{2}+\frac{C}{x} \)
is:
A \( \cdot y=x^{4} y_{1}-x y_{1}^{2} \)
B . \( y=x^{4} y_{1}^{2}-x^{2} y_{1} \)
C \( \cdot y=x^{4} y_{1}^{2}-x y_{1} \)
D. \( y=x^{4} y_{1}^{2}+x y_{1} \)


Which of the following are responsible for a beam of light being separated into its seven components when it is passed through a prism?
1. Total internal reflection
2. The index of refraction of prism medium with respect to air varies with wavelength
3. The index of refraction of prism
medium with respect to air is independent of wavelength
4. Velocity of light in prism depends on wavelength.
A. 1 and 4 only
B. 2 and 4 only
c. 1 and 2 only
D. 2 and 3 only


Which one of the following measures is determined only after the construction of cumulative frequency distribution?
A. Arithmetic mean
B. Mode
c. Median
D. Geometric mean


soils tend to be light, well aerated and rather dry.
A. Red soil
B. Black soil
c. sandy soil
D. Clayey soil


The velocity of a particle is \( \boldsymbol{v}=\boldsymbol{v}_{0}+ \)
\( g t+f t^{2} . \) If its position is \( x=0 \) at \( t=0 \)
then its displacement after unit time \( (\mathrm{t} \)
\( =1) \) is:
A \( \cdot v_{0}+2 g+3 f \)
В. \( v_{0}+\frac{g}{2}+\frac{f}{3} \)
\( \mathbf{c} \cdot v_{0}+g+f \)
D. \( v_{0}+\frac{g}{2}+f \)


\( \boldsymbol{p}=\mathbf{3 . 8 2}, \boldsymbol{q}=-\mathbf{4 . 3 9} \)
\( [p+q] \) is equal to
A . -2
B . 2
\( c \cdot 0 \)
D. -1


A circular current loop of radius a is
placed in a radial field B as shown. The
net force acting on the loop is:
A. zero
B. \( 2 \pi B a l \cos \theta \)
c. \( 2 \pi B a l \sin \theta \)
D. None


From a uniform disk of radius \( \boldsymbol{R} \), a
circular hole of radius \( \boldsymbol{R} / 2 \) is cut out.
The centre of the hole is at \( R / 2 \) from the centre of the original disc.Locate the
centre of gravity of the resulting flat body.


The time required for the completion of first order reaction is:
A . Infinity
B. Thrice that of time required for 90\% completion
c. \( 3 / 2 \) that of time required for \( 90 \% \) completion
D. ten times that of time required for \( 90 \% \) completion


8
8
8
8


What is not true about polymers?
A. Polymers do not carry any change.
B. Polymers have high viscosity.
C. Polymers scatter light.
D. Polymers have low molecular weight.


Calculate the weight of lime \( (C a O) \) that
can be obtained by heating 200 kg of limestone which is \( 93 \% \) pure. How many moles of impure potassium chlorate of \( 75 \% \) purity is required to produce 48 g of oxygen?


A body is weighed at the poles and at the equator. The weight:
A. at the equator it will be more than at the poles
B. at the poles it will be greater than at the equator
C. at the poles it will be equal to the weight at the equator
D. depends upon the object


The resistance of a conductor is:
A. Inversely proportional to the length
B. Directly proportional to the square of the radius
C. Inversely proportional to the square of the radius
D. Directly proportional to the square root of the length


The cycle on a \( P V \) diagram is
represented as
\( A \)
B.
\( c \)
D. none of these


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & -\mathbf{1} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \) then
what is \( B^{-1} A^{-1} \) equal to?
\begin{tabular}{ll}
A. \( \left[\begin{array}{cc}1 & -3 \\
-3 & 2\end{array}\right] \) \\
\hline
\end{tabular}
B. \( \left[\begin{array}{cc}-1 & 3 \\ 1 & -2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 3 \\ -1 & -2\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & 1 \\ -3 & -2\end{array}\right] \)


Angular diameter of the Jupiter is \( 36 " . \)
the distance of the Jupiter form the
Earth is 825 million kilometer, find the diameter of Jupiter.


Which of the following complex will show geometrical as well as optical isomerism?
\( A \)
\( \left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
в. \( \left[P t\left(N H_{3}\right)_{2} C l_{4}\right] \)
c. \( \left[P t(e n)_{3}\right]^{4} \)
D \( \cdot\left[P t(e n)_{2} C l_{2}\right] \)


The depth at which the value of acceleration due to gravity becomes \( \frac{1}{n} \) times the value at the surface is (R be
the radius of the earth):
A \( \cdot \frac{R}{n} \)
в. \( \frac{R}{n^{2}} \)
c. \( \frac{R(n-1)}{n} \)
D. \( \frac{R n}{(n-1)} \)


\( 1.5 g \) of \( C d C l_{2} \) was found to contain \( 0.9 g \) of \( C d . \) Calculate, the atomic weight of \( \boldsymbol{C} \boldsymbol{d} \)
A . 118
в. 112
c. 106.5
D. 53.25


A \( 0.098-k g \) block slides down a
frictionless track as shown in Fig. The time taken by the block to move
from \( A \) to \( B \) is:
\( ^{A} \cdot \frac{1}{\sqrt{g}} \)
в. \( \frac{2}{\sqrt{g}} \)
c. \( \frac{3}{\sqrt{g}} \)
D. \( \frac{4}{\sqrt{g}} \)


The mean and standard deviation of a
set of values are 5 and 2 respectively. If
5 is added to each value, then what is
the coefficient of variation for the new
set of values?
A . 10
B . 20
c. 40
D. 70


Equation of tangent at that point of the curve \( \boldsymbol{y}=\mathbf{1}-\boldsymbol{e}^{\frac{x}{2}}, \) where it meets \( \mathbf{y} \) -axis
\( \mathbf{A} \cdot x+2 y=0 \)
в. \( 2 x+y=0 \)
c. \( x-y=2 \)
D. None of these


Area under force-time graph gives:
A. Velocity
B. Impulse
c. Displacement
D. Kinetic energy


The balanced equation in acidic
medium is :
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}+\boldsymbol{S} \boldsymbol{b}_{2} \boldsymbol{O}_{5} \stackrel{\boldsymbol{H}^{+}}{\rightarrow} \boldsymbol{S b} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)
A \( \cdot 3 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+6 H^{+} 3 H_{2} O \rightarrow 4 S b O+6 H_{2} S O_{3} \)
B . \( 2 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+6 H^{+} 3 H_{2} O \rightarrow 4 S b O+4 H_{2} S O_{3} \)
\( \mathrm{c} \cdot 3 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+4 H^{+} 2 H_{2} O \rightarrow 4 S b O+2 H_{2} S O_{3} \)
D. none of these


In which of the following cases is the
displacement zero?
A. When displacement and distance traveled are equal
B. When the object is travelling in a straight line
c. If there is a unique path between two points
D. If an object starts mowing from point \( A \) and comes back to \( A \) an a circular path


Let there be a spherically symmetric
charge distribution with charge density \( \operatorname{varying} \operatorname{as} \rho(r)=\rho_{0}\left(\frac{5}{4}-\frac{r}{R}\right) \) upto \( r= \)
\( R, \) and \( \rho(r)=0 \) for \( r>R, \) where \( r \) is
the distance from the origin. Find the
electric field at a distance \( r(r<R) \)
from the origin.
A \( \cdot \frac{3 \rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
В \( \cdot \frac{4 \rho_{0} r}{3 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
C \( \cdot \frac{\rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
D. \( \frac{3 \rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{4}-\frac{r}{R}\right) \)


A reaction mixture containing \( \boldsymbol{H}_{2}, \boldsymbol{N}_{2} \)
and \( N H_{3} \) has partial pressure
2 atm, 1 atm and 3 atm respectively at
\( 725 K . \) If the value of \( K_{P} \) for reaction
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \) is \( 4.28 \times \)
\( 10^{-5} a t m^{-2} \) at \( 725 K \), in which direction
the net reaction will go :
A. Forward
B. Backward
c. No net reaction
D. Direction of reaction cannot be predicted


Acid rain:
A. reduces fertility of soil
B. damage vegetation
C. affects marble monuments
D. all of these


Select the correct IUPAC name from
following.
A. Diamminesilver (I) chloride: \( \left[\operatorname{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl} \)
B. Potassium cyanidoferrate (III) : K \( _{3} \) [Fe(CN) \( _{6} \) ]
C. Tetraamminecopper sulphate : [Cu(NHz),]SO
D. Hexamminecobalto
(III) chloride : [Co(NH_) \( \left._{6}\right] \) Сз \( _{3} \)


During the course of evolution, which part of the brain has shown maximum increase in size.
A. Midbrain
B. Forebrain
c. Hindbrain
D. All of the above


The probability of sample space is
A .
B.
\( c \cdot 1 \)
D. None of these


A cylinderical vessel is filled with equal
amount of weight of mercury and water.The overall height of the two layer is \( 29.2 \mathrm{cm}, \) specific gravity of mercury is 13.6.Then the pressure of the liquid at the bottom of the vessel is:
\( \mathbf{A} \cdot 29.2 \mathrm{cm} \) of water
в. \( \frac{29.2}{13.6} \mathrm{cm} \) of mercury
c. \( 4 c m \) of mercury
D. \( 15.6 \mathrm{cm} \) of mercury


Correct statement regarding this
reaction
\( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow\left[\boldsymbol{F}_{3} \boldsymbol{B} \leftarrow \boldsymbol{N} \boldsymbol{H}_{3}\right] \)
A. Hybridiration of \( N \) is changed
B. Hybridiration of \( B \) is changed
\( \mathrm{c} . N H_{3} \) act as a Lewis Base
D. (2)\( \&(3) \) both


The single-bonded metallic radius of Na is 157 pm. What is the reasonable estimate of the radius of Na assuming that the increment between radii of
different magnitudes is 60 pm?
\( A \cdot 97 \mathrm{pm} \)
B. 95 pm
\( c \cdot 93 p m \)
D. 99 pm


Consider the given reaction, the product
\( A^{\prime} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} O H \)
в. \( C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C l \)
D. \( C_{6} H_{5} C H O \)


If a star can convert all the \( H e \) nuclei
completely into oxygen nuclei, the energy released per oxygen nuclei is [Mass of \( H e \) nucleus is \( 4.0026 a m u \) and
mass of oxygen nucleus is \( 15.9994 a m u \)
A. \( 7.6 \mathrm{MeV} \)
B. 56.12 MeV
c. \( 10.24 \mathrm{MeV} \)
D. \( 23.9 \mathrm{MeV} \)


Which of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?
\( A \cdot S r S O_{4} \)
в. \( \mathrm{CaSO}_{4} \)
c. \( B e S O_{4} \)
D. \( B a S O_{4} \)


Which of the following statements
is/are true?
This question has multiple correct options
A. Work done by kinetic friction on an object may be positive
B. A rigid body rolls up an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
C. A rigid body rolls down an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
D. A rigid body is left from rest and having no angular velocity from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be up the incline.


A liquid with coefficient of volume
expansion \( \gamma \) is filled in a container of a
material having coefficient of linear
expansion \( \alpha \). If the liquid overflows on
heating, then:
A \( \cdot \gamma=3 \alpha \)
в. \( \gamma>3 \alpha \)
c. \( \gamma<3 \alpha \)
D . \( \gamma=a^{3} \)


Baking powder is more commonly used to make cakes or bread "rise". Filler in
baking powder is:
A. \( \operatorname{NaH} \mathrm{CO}_{3} \)
в. \( \operatorname{Ca}\left(\text { На }_{2} \text { РО }_{4} \) ) \right.
c. starch
D. \( \operatorname{NaAl}\left(S O_{4}\right)_{2} \)


Hydrogen differs from elements of \( 1-A \)
group as:
This question has multiple correct options
A. hydrogen is gas but others are solid at room temperature
B. all are metals
C. hydrogen is a non-metal but others are metal
D. they donate one electron to become cation


Given appropriate biological/ technical terms for the following:
The antiseptic substance in tears.


If \( x \) is \( 90 \% \) of \( y, \) then what percent of \( x \) is
\( \boldsymbol{y} ? \)
A \( .90 \% \)
B. \( 190 \% \)
c. \( _{101} \frac{1}{9} \% \)
D. \( 111 \frac{1}{9} \% \)


Carbon monoxide is a poisonous gas.
A. True
B. False


Ferromagnetism is not found in
A. conductors
B. semiconductors
c. cobalt
D. gases


The values of \( \lambda \) such than \( (x, y, z) \neq \) (0,0,0)
and \( (i \hat{+} \hat{j}+3 \hat{k}) x+(3 \hat{i}-3 \hat{j}+\hat{k}) y+ \)
\( (-4 \hat{i}+5 \hat{j}) z=\lambda(x \hat{i}+y \hat{j}+z \hat{k}) \) are


Which of the following characteristic property of clay soil make it useful to
grow plants?
A. Retain water and moisture
B. Do not retain water and moisture
c. Holds lot of sand
D. None of the above


\( 150 \mathrm{J} \) of heat has been added to the gas
When 1 kg of ice at \( 0^{\circ} \mathrm{C} \) melts to water
at \( 0^{\circ} \mathrm{C} \) the resulting change in its
entropy latent heat of ice to be \( 80 \mathrm{cal} /^{\circ} \mathrm{C} \)
is
A. \( 273 \mathrm{cal} / \mathrm{K} \)
B. \( 8 \times 104 \mathrm{cal} / \mathrm{K} \)
c. 80 салК
D. \( 293 \mathrm{cal} / \mathrm{K} \)


Rancidity of fats can be prevented by antioxidants.
A . True
B. False


The compound with negative value of heat of formation is called:
A. endothermic compound
B. exothermic compound
c. heat of formation compound
D. none of the above


From what minimum height, a block of ice has to be dropped in order that it may melt completely on hitting the
ground:
\( A \cdot m g h \)
в. \( \frac{m g h}{l} \)
c. \( \frac{l}{g} \)
D. \( \frac{h}{l g} \)


Which of the following can exhibit ring chain isomerism?
A. \( C_{6} H_{14} \)
B. \( C_{4} H_{10} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{10} H_{2} \)


The current voltage relationship of a
diode is \( I=I_{x}\left[\exp \left(\frac{e V}{k T}\right)-1\right] \) where e is
charge on an electron, \( V \) is voltage applied, k is Boltzmann's constant, T is
temperature in Kelvin. Find the
resistance of the diode if \( \mathrm{I},=1.5 \mathrm{m} A \)
and \( \boldsymbol{T}=\mathbf{3 9 8 K} \)
A \( \cdot \frac{100}{3} \Omega \)
B. \( \frac{50}{3} \Omega \)
\( c \cdot \frac{500}{3} \Omega \)
D. \( \frac{200}{3} \Omega \)


Select the incorrect statement(s):
This question has multiple correct options
\( \mathbf{A} \cdot N F_{3} \) has a highest dipole moment among \( C O, N H_{3} \) and \( N F_{3} \)
B. \( H F \) has a highest boiling point among \( C H_{4}, N H_{3} \) and
\( H F \)
\( \mathrm{C} \cdot \mathrm{Cl}_{2} \) has a lowest boiling point among \( \mathrm{Cl}_{2}, \mathrm{Br}_{2} \) and \( I_{2} \)
D. \( H C l O_{3} \) is weakest acid among \( H I O_{3}, H B r O_{3} \) and
\( H C l O_{3} \)


Two arithmetic progressions have the
same common difference. The
difference between their 100 th terms is
100, what is the difference between
their 1000 th terms?


In the given circuit the potential at
point \( \boldsymbol{E} \) is:
A. Zero
B. \( -8 V \)
\( c \cdot-\frac{4}{3} V \)
\( D \cdot \underline{4}-v \)


A carbon resistance with color band is
\( 200 \Omega . \) If red band is replaced by green band then the new resistance is:
\( \mathbf{A} \cdot 500 \Omega \)
в. 300\Omega
c. \( 400 \Omega \)
D. \( 100 \Omega \)


In a circle with centre \( \boldsymbol{O}, \boldsymbol{O} \boldsymbol{D} \perp \) chord
\( A B . \) If \( B C \) is the diameter, then which
of the following option is correct:
\( \mathbf{A} \cdot A C=B C \)
В \( . O D=B D \)
c. \( A C=2 \times O D \)
D. None of these


Describe the post-fertilization changes
in a flower.


The circular motion of a particle with
constant speed is
A. Periodic but not SHM
c. Periodic and also SHM
D. Neither periodic nor SHM


\( \mathrm{IF}^{n} \boldsymbol{C}_{r}=^{n} \boldsymbol{P}_{r} \) then \( r \) can be
A .
B. 1
\( c \cdot 3 \)
D. Either(1) or (2)


Write the IUPAC names of the given
compounds:


Vitamin K is required for
A. Formation of thromboplastin
B. Conversion of fibrinogen to fibrin
C. Conversion of protrombin to thrombin
D. Synthesis of prothrombin


Value of \( \left|\begin{array}{lll}\sin \alpha & \cos \alpha & \sin \alpha+\cos \beta \\ \sin \beta & \cos \alpha & \sin \beta+\cos \beta \\ \sin \gamma & \cos \alpha & \sin \gamma+\cos \beta\end{array}\right| \) is
\( A \cdot \sin \alpha+\sin \beta+\sin \gamma \)
B. \( \cos \alpha+\cos \beta+\cos \gamma \)
\( \mathbf{c} \cdot \sin \alpha-\sin (\alpha+\beta)-\cos \alpha+\cos (\gamma+\beta) \)
\( D \)


Blind spot in the eye is located
A. In the centre of pupil
B. In the centre of lens
c. In fovea centralis
D. Where optic nerves leaves retina


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x^{\alpha} \cos \left(\frac{1}{x}\right), & \text { if } & x \neq 0 \\ 0 & , \text { if } & x=0\end{array}\right. \)
continuous at \( x=0 \) then
\( \mathbf{A} \cdot \alpha<0 \)
В . \( \alpha>0 \)
c. \( \alpha=0 \)
D. \( \alpha \geq 0 \)


Roots developing from plant parts other than radicle are
A. Epiphyllous
B. Epicaulose
c. Adventitious
D. Fibrous


f a body be projected vertically upward from the surface of the earth so as to
reach a height \( n R \) above the surface;
the increase in its potential energy is \( \left(\frac{n}{n+a}\right) m g R, \) where \( a=? \)


If a body is charged by rubbing it, its weight
A. Remains precisely constant
B. Increases slightly
c. Decreases slightly
D. May increase or decrease slightly


If one side of rhombus has end points (4,5) and (1,1) then the maximum area of the rhombus is:
A. 50 sq. units
B. 25 sq. units
c. 30 sq. units
D. 20 sq. units


\( \left(49 x^{2} y z+35 p\right) \div 7 \) is equal to
A \( \cdot 7 x^{2} y z-35 p \)
B. \( 7 x^{2} y z+35 p \)
c. \( 7 x^{2} y z-5 p \)
D. \( 7 x^{2} y z+5 p \)


Consider the following two compounds:
Identify which of these two compounds
has greater resonance stabilization
Compound \( \mathbf{A} \)

Compound


A current I is passing through a wire having two sections \( \mathrm{P} \) and \( \mathrm{Q} \) of uniform diameters d and \( d / 2 \) respectively if the mean drift velocity of electrons in section \( \mathrm{P} \) and \( \mathrm{Q} \) is denoted by and
respectively then.


If \( p H \) of solution is 13 , it means that it
is:
A. weakly acidic
B. weakly basicç
c. strongly acidic
D. strongly basic


Calculate the electron gain enthalpy of fluorine atom using the following data.
All the values are in \( k J \) mol \( ^{-1} \) at \( 25^{\circ} C \)
\( \Delta \boldsymbol{H}_{d i s s}\left(\boldsymbol{F}_{2}\right)=\mathbf{1 6 0}, \boldsymbol{\Delta}_{f} \boldsymbol{H}(\boldsymbol{N a F}(s))= \)
\( -\mathbf{5 7 1}, \) ।.E. \( [\boldsymbol{N a}(\boldsymbol{g})]= \)
\( \mathbf{4 9 4}, \mathbf{\Delta H}_{\mathbf{v a p}}[\mathbf{N a}(s)]=\mathbf{1 0 1 .} \) Lattice
enthalpy of \( N a F(s)=894 \) Also, make Born - Haber's cycle.


\( P \) represents the variable complex
number \( z . \) Find the locus of \( \boldsymbol{P}, \) if \( \mid \boldsymbol{z}- \)
\( \mathbf{5 i}|=| \boldsymbol{z}+\mathbf{5 i} \mid \)


On the basis of following features, identify the correct tissue.
It is the covering or protective tissues in the animal body.

It forms a barrier to keep different body
systems separate.
The skin, the lining of the mouth, the
lining of blood vessels, lung alveoli and
kidney tubules are made up of this type
of tissue.
A. Epithelial tissue
B. Connective tissue
c. Muscular tissue
D. Nervous tissue


Differentiate between roasting and
calcination.


Modern vacuum pumps can evacuate a
vessel down to a pressure of \( 4.0 \times \) \( 10^{-15} \) atm. At room temperature
\( (300 K), \) taking \( R= \)
\( \mathbf{8 . 3 J K}^{-1} \quad \boldsymbol{m o l e}^{-1}, \mathbf{1} \quad \boldsymbol{a t m}= \)
\( \mathbf{1 0}^{5} \boldsymbol{P a} \quad \) and \( \boldsymbol{N}_{\text {Avagadro }}=\mathbf{6} \times \)
\( 10^{23} \) mole \( ^{-1} \), the mean distance
between the molecules of gas in an evacuated vessel will be of the order of :
\( \mathbf{A} \cdot 0.2 \mu m \)
B. \( 0.3 \mu \) m
\( c .0 .2 \mathrm{mm} \)
D. \( 0.2 n m \)


Among the following, the extensive variables are
This question has multiple correct options
A. H (Enthalpy)
B. P (Pressure)
c. E (Internal energy)
D. v (Volume)


If a spark is produced on removing the load from an AC circuit then the
element connected in the circuit is
A. high resistance
B. high capacitance
c. high inductance
D. high impedance


Which base is used in manufacture of
soap?
\( \mathbf{A} \cdot C a(O H)_{2} \)
в. маОН
c. \( N H_{3} \)
D. \( N H_{4} O H \)


Evaluate: \( \sqrt{\mathbf{1 0 0}}+\sqrt{\mathbf{4 9}} \)
A. \( \sqrt{149} \)
B. \( \sqrt{490} \)
c. \( \sqrt{10}+\sqrt{14} \)
D. 17


Find the work done by a gas when it
expands isothermally at \( 37^{\circ} \mathrm{C} \) to four times its initial volume.
A . 3753J
B . 3573J
c. 7533J
D. 5375J


Which one of the amino acids can be
synthesised in the body?
A. Alanine
B. Lysine
c. valine
D. Histidine


Convert t-Butanol to the given
compound.


Q Type your question
B.
\( c \)
\( D \)


How much intense is \( 80 d B \) sound in
comparison to \( 40 d B ? \)
A \( \cdot 10^{4} \)
B . \( 10^{2} \)
\( c \cdot 2 \)
D.


Find the angle subtended at the origin
by the line segment whose end points \( \operatorname{are}(0,100) \) and (10,0)


Assertion
If light enters from medium- 1 into
medium-2 and bends towards the
normal, its wavelength in medium-2 is smaller than its wavelength in medium-
1
Reason
According to Cauchy's relation, \( \mu= \) \( A+\frac{B}{\lambda^{2}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is the force in \( y \) direction if the
plate is given a constant velocity ' \( u \) ' in
the direction of \( v ? \)
A \( \cdot \rho A(v-u)^{2} \sin 2 \theta \)
В \( \cdot_{\rho A}(v-u)^{2} \sin \theta \)
c. \( \rho A\left(v^{2}-u^{2}\right) \sin \theta \)
D. None of these


A stretched string is vibrating in the second overtone, then the number of
nodes and antinodes between the ends
of the string are respectively:
A. 4 and 3
B. 3 and 2
\( c .3 \) and 4
D. 2 and 3


A solid in hemisphere at the bottom and conical above. If the surface are of the
part our equal, find the ratio of radius and height of conical part.


Which of the following reactions is known as slaking of lime?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( C a C O_{3}+H_{2} O \rightarrow C a(O H)_{2}+C O_{2} \)
D. \( C a O+H_{2} O \rightarrow C a(O H)_{2} \)


Equilibrium, \( \boldsymbol{X} \rightleftharpoons \mathbf{2} \boldsymbol{Y} \) and \( \boldsymbol{Z} \rightleftharpoons \boldsymbol{P}+\boldsymbol{Q} \)
are established with 1 mole of \( z \) and \( z \)
taken initially in separate vessels with
equilibrium pressures of 1 atm and 36 atm respectively. If the degree of
dissociations are same. Then \( \boldsymbol{K}_{\boldsymbol{P} \mathbf{2}}= \)
\( \boldsymbol{n} \boldsymbol{K}_{\boldsymbol{P} 1} . \) What is the value of \( n ? \)


Distinguish between simple gland and compound gland.


Which laboratory technique would allow students to determine the energy content of a food sample?
A. conductivity
B. Calorimetry
c. Precipitation
D. spectophotometry


A wave is represented by an equation; \( Y=A \cos k x \sin \omega t, \) then
A. It is a progressive wave with amplitude \( A \)
B. It is a progressive wave with amplitude \( A \) cos \( k x \)
c. It is a stationary wave with amplitude \( A \)
D. It is a stationary wave with amplitude \( A \cos k x \)


How does deforestation reduce rainfall
on the one hand and lead to floods on
the other?


How long will it be moving until it stops for the first time?
A \( \cdot t=2 \frac{\pi}{\omega} \)
В \( \cdot t=3 \frac{\pi}{\omega} \)
c. \( t=4 \frac{\pi}{\omega} \)
D・ \( t=\frac{\pi}{\omega} \)


What is the action of hot concentrated
nitric acid on carbon?


I. \( P b O_{2} \rightarrow P b O \Delta G_{298}<0 \)
\( \| S n O_{2} \rightarrow S n O \Delta G_{298}>0 \)
Which of the above is/are true?
\( A \)
B. I
\( c . \) both (a) \& (b)
D. none of these


Action potential is generated by
A . \( N a^{+} \)
в. \( K^{+} \)
c. \( C a^{+} \)
D. \( C l^{-} \)


Use graph paper for this question. Take
\( 2 c m=2 \) units on \( x \) -axis and \( 1 c m=1 \)
unit on \( y \) -axis. Solve graphically the following
equations:
\( 3 x+5 y=12 ; 3 x-5 y+18=0 \)
(Plot only three points per line)
A. \( x=-1 ; y=3 \)
в. \( x=-1 ; y=7 \)
c. \( x=-1 ; y=5 \)
D. \( x=-1 ; y=2 \)


What is electrolysis? A solution of
\( C u S O_{4} \) is electrolysed for 10 minutes
with a current of 1.5 amperes. What is
the mass of copper deposited at the cathode?


Prove that the angle in a semicircle is a
right angle.


Assertion
(A): Thermal radiations are
electromagnetic radiation with wave lengths greater than visible light.
Reason
(R): Thermal radiations can
propagate through vacuum.
A. both A and R are true and the R is correct explanation of the A
B. both A and R are true, but R is not correct explanation of the A
c. A is true, but the R is false.
D. A is false, but the R is true.


Sonar is a device for
A. Location and ranging of aircrafts
B. Location and ranging of submarines
C. Producing a musical note of high quality
D. Measuring frequency of musical notes


In the destructive distillation of coal, at
\( 443-503 \mathrm{K} \) temperature, a middle oil or carbolic oil fraction is obtained. This
fraction contains:
This question has multiple correct options
A. Phenol
B. xylenes
c. Naphthalene
D. Benzene


ff \( \boldsymbol{P}=\left[\begin{array}{ccc}2 & 3 & 1 \\ 0 & -1 & 5\end{array}\right] \) and \( Q= \)
\( \left[\begin{array}{ccc}1 & 2 & -6 \\ 0 & -1 & 3\end{array}\right], \) Evaluate \( 3 P-4 Q \)
\( \mathbf{3} P-4 Q=\left[\begin{array}{lll}a & b & c \\ d & e & f\end{array}\right], \) find sum of
\( a, b, c, d, e, f \)


Eutrophication is caused by
A. Sewage and detergents
B. Petrochemical and fertilizer plant effluents
C. \( \mathrm{NO}-13 \) and \( \mathrm{SO}-24 \) present in acid rains
D. Mine effluents


Find the volume of the cuboid with
dimensions \( (x-1),(x-2) \) and \( (x- \)
\( \mathbf{3}) \)


Fill in the blanks with suitable words
Electrica is a Latin word which means


Which of the following statements is
(are) correct?
This question has multiple correct options
A. graphite is much less dense than diamond
B. graphite is black and soft
C . graphite has low melting point
D. graphite feels smooth and slippery


toppr
Q Type your question
finches with large, thick beaks survived
the drought as they subsisted on cactus, which are drought tolerant
plants.

In the early 1980 's, the Galapagos
Islands underwent an El Nino event that
led to higher annual levels of
precipitation than normal. This climate
event occurred just a few years after the
drought. The increase in rainfall led to a
dramatic increase in growth of seed-
producing plants, which led to an abundance of foods for seed-eating
finches, which have small, short beaks.
The increase in rainfall also decreased
the availability of cactuses on the islands. Which of the following would
you predict occurred in the finch population as a result of the second
change in climate?
A. The variety present in the finch population did not change due to changes in climate
B. The population of short-beaked finches increased while the population of large beaked birds decreased.
C. The large-beaked finches increased in number while the short-beaked finches decreased in number
D. The number of finches of each type both decreased due to the change in climate
E. The large-beaked finches hybridized with the shortbeaked finches.


In the meter bridge shown, the
resistance \( X \) has a negative
temperature coefficient of resistance.
Neglecting the variation in other
resistors, when current is passed for
some time, in the circuit balance point
should shift towards:
\( A \cdot A \)
в. \( B \)
\( c . \) First \( A \) then \( B \)
D. It will remain at


Areolar connective tissue joins
A. Fat body with muscles
B. Integument with muscles
c. Bones with muscles
D. Bones with bones


The liquid meniscus in a capillary tube will be convex, if the angle of contact is :
A . greater than \( 90^{\circ} \)
B. less than \( 90^{\circ} \)
C . equal to \( 90^{\circ} \)
D. equal to zero


If \( f(x)=\frac{1}{x^{2}-17 x+66} \) then \( f\left(\frac{2}{x-2}\right) \)
is discontinuous at \( x \) is equal to
A \( \cdot \quad, \frac{7}{3}, \frac{25}{11} \)
в. \( 2, \frac{8}{3}, \frac{24}{11} \)
c. \( \quad_{2}, \frac{7}{3}, \frac{24}{11} \)
D. 2,6,11


If \( a, b \) and \( c \) are positive real numbers then \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \) is greater than or
equal to.
\( A \cdot 3 \)
B. 6
\( c \cdot 27 \)
D. 5


Find IUPAC name of the hydrate isomer
of \( C r C l_{3} .6 H_{2} O, \) which is having lowest
electrical conductivity
A. Hexaaquachromium(III)chloride
B. Tetraaquadichloridochromium(III)chloridedihydrate
c. Pentaaquachloridochromium(III)chloridemonohydrat
D. Triaquatrichloridochrominum(III)trihydrate


Find all zeroes of \( 2 x^{4}-3 x^{3}-3 x^{2}+ \)
\( 6 x-2 \) if 2 zeroes \( \sqrt{2} \) and \( -\sqrt{2} \)


Find the value of \( 5 \sin 30^{0}+3 \tan 45^{0} \)


If \( y=\frac{x^{4}-x^{2}+1}{x^{2}+\sqrt{3} x+1} \) and \( \frac{d y}{d x}=a x+b \)
then the value of \( a+b \) is equal to
A \( \cdot \cot \frac{5 \pi}{8} \)
B. \( \cot \frac{5 \pi}{12} \)
c. \( \tan \frac{5 \pi}{12} \)
D. \( \tan \frac{5 \pi}{8} \)


The Hertzsprung-Russell Diagram
A. is based on the principle that the intrinsic brightnesses of most stars are related to their temperatures.
B. most stars have the same temperature.
C. was developed in the 1950 s by two American astronomers working for NASA.
D. while of great utility for most large stars, has proven of little value in classifying small stars like our sun.


The compound having the molecular
formla \( C_{4} H_{10} \) does not show isomerism.
A. True
B. False


At what \( \left[O H^{-}\right] \) does the following half-
reaction have a potential of \( 0 V \) when other species are at 1 M?
\( N O_{3}^{-}+H_{2} O+2 e^{-} \rightarrow N O_{2}^{-}+ \)
\( \mathbf{2 O H}^{-}, \boldsymbol{E}_{c e l l}^{\circ}=\mathbf{0 . 0 1} \boldsymbol{V} \)


\( \operatorname{Let} f(x)=3 x^{2} \cdot \sin \frac{1}{x}- \)
\( \boldsymbol{x} \cos \frac{1}{\boldsymbol{x}}, \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{f}(\mathbf{0})=\mathbf{0} \boldsymbol{f}\left(\frac{\mathbf{1}}{\boldsymbol{\pi}}\right)=\mathbf{0} \)
then which of the following is/are not
correct.
This question has multiple correct options
A. \( f(x) \) is continuous at \( x=0 \)
B. \( f(x) \) is non-differentiable at \( x=0 \)
c. \( f(x) \) is discontinuous at \( x=0 \)
D. \( f(x) \) is differentiable at \( x=0 \)


Which of the following categories possesses the maximum number of related characters?
A. Order
B. Phylum
c. class
D. species


A tennis ball and a cricket ball, both are
stationary. To start motion in them
A. a less force is required for the cricket ball than for the tennis bal
B. a less force is required for the tennis ball than for the cricket ball
c. same force is required for both the balls
D. nothing can be said


A solid uniform disk of mass \( m \) and
radius \( R \) is pivoted about a horizontal
axis through its centre and a small body of mass \( m \) is attached to the rim of the
disk. If the disk is released from rest
with the small body, initially at the
same level as the centre, find the
angular velocity when the small body reaches the lowest point of the disk.


Evaluate
\( \left[\begin{array}{l}3 \\ 4 \\ 1\end{array}\right]\left[\begin{array}{lll}2 & -1 & 3\end{array}\right] \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}-\mathbf{3}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{3}, \) then
\( \left(g o f^{-1}\right)(3)= \)
A \( \cdot \frac{25}{3} \)
в. \( \frac{111}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{25}{111} \)


The azeotropic mixture of water and
\( H C l \) boils at \( 108.5^{0} C . \) This solution is:
A . ideal
B. non-ideal with positive deviation
c. non-ideal with negative deviation
D. cannot be predicated


In electromagnetic wave, according to Maxwell, changing electric field gives
A. stationary magnetic field
B. conduction current
c. eddy current
D. displacement current


At the starts of a motion along a line the initial velocity is \( u \) and acceleration is
at. The final velocity v is
A . v=u+at
B. v=u+at \( ^{2} \)
C \( \cdot v=u+\frac{1}{2} a t^{2} \)
D. \( v=a t^{2} \)


Let \( p \in I R \) then the differential
equation of the family of curves \( y= \)
\( (\alpha+\beta x) e^{p x}, \) where \( \alpha, \beta \) are arbitrary
constants, is:
A \( \cdot y^{\prime \prime}+4 p y^{\prime}+p^{2} y=0 \)
в. \( y^{\prime \prime}-2 p y^{\prime}+p^{2} y=0 \)
c. \( y^{\prime \prime}+2 p y^{\prime}-p^{2} y=0 \)
D. \( y^{\prime \prime}+2 p y^{\prime}+p^{2} y=0 \)


Derive the coordinates of the points \( R(x, y, z) \) dividing the line joining the
points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1}\right) \) and \( \boldsymbol{Q}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}, \boldsymbol{z}_{2}\right) \)
internally in the ratio \( m: n \)


In Opuntia, the function of photosynthesis is carried out by
A. cladode
B. phyllode
c. phyllociade
D. stipules


When two molecules of hydrogen react
with a molecule of oxygen, the mass of
reactants is \( 36, \) what is the mass of
products?
A . 40
B. 36
\( c \cdot 38 \)
D. 33


A parallel plate capacitor having plates
of area \( S \) and plate separation \( d, \) has
capacitance \( C_{1} \) in air. When two
dielectrics of different relative
permittivities \( \left(\epsilon_{1}=1 \text { and } \epsilon_{2}=4\right) \) are
introduced between the two plates as
shown in the figure, the capacitance
become \( C_{2} . \) The ratio \( \frac{C_{2}}{C_{1}} \) is
\( A \cdot 6 / 5 \)
В. \( 5 / 3 \)
\( c .7 / 5 \)
\( D \)


What will be the major product formed?


A solar energy system uses a photovoltaic panel to convert solar energy into electricity, to charge a battery, and provide electricity as needed by the consumer. The photovoltaic pannel intercepts 1000 units of solar energy and convert \( 20 \% \) of that into electricity. There is a loss of 10 \( \% \) energy while charging the battery. The battery can be used to supply only half of the stored energy to the consumer. Assuming \( 40 \% \) energy loss in the distribution, the number of units of
energy received by the customers is
\( A \cdot 6 \)
в. 36
\( c \cdot 54 \)
D. 80


Assertion
limiting line in the Balmer series has a wavelength of \( 364.4 \mathrm{nm} \)
Reason
limiting line is obtained for a jump of electron from \( n= \) infinity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{x}=\mathbf{7}+\mathbf{4} \sqrt{\mathbf{3}}, \boldsymbol{y}=\mathbf{7}-\mathbf{4} \sqrt{\mathbf{3}}, \) then \( \frac{\mathbf{1}}{\boldsymbol{x}}+ \)
\( \frac{1}{y}= \)
A . 11
B. 14
c. 8
D. 6


O' is the centre of the circle \( \angle Q P S= \)
\( \mathbf{6 5}^{\circ} ; \angle \boldsymbol{P} \boldsymbol{R} \boldsymbol{S}=\mathbf{3 3}^{\circ}, \)then \( \angle \boldsymbol{P S Q}= \)
A .90
B. \( 82^{\circ} \)
\( c \cdot 102 \)
\( D \cdot 42 \)


lonic product of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is \( \mathbf{1 0}^{-14} \). The \( \boldsymbol{H}^{+} \)
ion concentration in \( 0.1 M \) NaOH
solution is:
A \( \cdot 10^{-11} M \)
В . \( 10^{-13} M \)
\( \mathbf{c} \cdot 10^{-1} M \)
D. \( 10^{-4} M \)


Pubertal changes in boys include
A. Development of gonads
B. Voice change
C. Facial hair
D. All of the above


An object has an initial velocity \( u \) and an acceleration \( a \). The object moves in a straight line through a displacement s and has final velocity \( v \) The above quantities are related by the equation shown \( \boldsymbol{v}^{2}=\boldsymbol{u}^{2}+\mathbf{2} \boldsymbol{a} \boldsymbol{s} \)
Which condition must be satisfied in
order for this equation to apply to the motion of the object?
A. The direction of \( a \) is constant and the direction of \( a \) is the same as the direction of \( s \)
B. The direction of \( a \) is constant and the direction of \( a \) is the same as the direction of \( u \)
c. The magnitude of \( a \) is constant and the direction of \( a \) i constant
D. The magnitude of \( a \) is constant and the direction of \( a \) is the same as the direction of \( v \)


In the set of all \( 3 \times 3 \) real matrices a
relation is defined as follows. A matrix
\( A \) is related to a matrix \( B \), if and only
there is a non-singular \( 3 \times 3 \) matrix \( P \)
such that \( B=P^{-1} A P . \) This relation is
A. reflexive,symmetric but not transitive
B. reflexive, transitive but not symmetric
c. symmetric, transitive but not reflexive
D. an equivalence relation


Which of the following statement is
wrong?
A. Ozone is not responsible for greenhouse effect.
B. Ozone can oxidise sulphur dioxide present in the atmosphere to sulphur trioxide.
C. Ozone hole is thinning of ozone layer present in the stratosphere.
D. Ozone is produced in upper stratosphere by the action of UV rays on oxygen.


The climate of North-Eastern part of our
country is?
A. Dry
B. Hot
c. wet
D. cold


A yellow crystalline allotropic form of sulphur \( (A) \) on heating at \( X^{o} C \) converts
to another allotropic sulphur \( (B) \) that
has needle shape. Identify \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{X} \)


A ray of light strikes a transparent rectangular slab of refractive index \( \sqrt{2} \) at an angle of incidence of \( 45^{\circ} . \) The angle between the reflected and refracted rays is :
A \( .75^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 105 \)
D. \( 120^{\circ} \)


Which of the following statements
is/are false?
A. Mass, speed and energy are scalar quantities
B. Momentum, force and torque are vector quantities
C. Distance is a scalar quantity but displacement is a vector quantity
D. A vector has only magnitude, whereas a scalar has both magnitude and direction


Given is a diagrammatic cross section
of a single loop of human cochlea.
Which one of the following options correctly represents the names of three
different parts?
A. D- Sensory A- Endolymph, BTectorial
B. A- Perilymph, B- Tectorial membrane, C- Endolymph
c. B- Tectorial membrane, C- Perilymph, D Secretory cells
D. C- Endolymph, D- Sensory hair cells, A- Serum


horizontal force,


The decreasing order of the rate of nitration of the following compounds is:
I. Benzene \( I I . C_{6} D_{6} \)
III. Nitrobenzene \( I V . \) Chlorobenzene
A \( \cdot(I)>(I I)>(I I I)>(I V) \)
в. \( (I)>(I I)>(I V)>(I I I) \)
c. \( (I)=(I I)>(I V)>(I I I) \)
D. \( (I)=(I I)>(I I I)>(I V) \)


What is the phenomenon shown by ferromagnetic substances whereby the magnetic flux through the medium on magnetising field as well as previous
state of the substance?
A. Irradiation
B. Hysteresis
c. Inversion
D. Magnetostriction


Which of the following family form negative ions in an ionic bond?
A. Alkali metalss
B. Alkaline earth metals
c. Noble gases
D. Halogens
E. Transition metals


State whether the given statement is True or False:
Six negative point charges are arranged symmetrically around a circle centered at point \( P \) as shown in the diagram below. All points charges are of the same magnitude Electric Field at \( \mathrm{P} \) will be zero while
electric potential at point \( P \) will be non
zero.
A. True
B. False


For a radioactive substance, show the
variation of the total mass
disintegrated as a function of time \( t \)
graphically.


Arrange the following in increasing order of their atomic radii.
\( \mathrm{Li}, \mathrm{Be}, \mathrm{Ne}, \mathrm{C}, \mathrm{B} \)
A. \( N e<C<B<B e<L i \)
в. \( L i>N e>C>B>B e \)
c. \( N e>C>B>B e>L i \)
D. \( L i>N e>B>C>B e \)


A ferris wheel with a radius of \( 8.0 m \)
makes 1 revolution every 10 s.When a
passenger is at the top essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 1.0 \mathrm{m} \)
\( c .8 .0 m \)
D. \( 9.1 \mathrm{m} \)


Factorise: \( \boldsymbol{x}^{4}-\mathbf{2} \boldsymbol{x}^{2} \boldsymbol{y}^{2}+\boldsymbol{y}^{4} \)


For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?
A. \( A l C l_{3} \)
в. \( N a C l \)
c. \( B a C l_{2} \)
D. \( N a_{3} P O_{4} \)


\( \boldsymbol{E}^{\circ} \) for \( \boldsymbol{M}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{M}(\boldsymbol{s}) \)
(where \( M=C a, S r \text { or } B a) \) is nearly
constant.


How many types of substituted alcohols (stereoisomers not considered) are
possible in the given reaction?
A. One
B. Two
c. Three
D. Four


Convert \( 3 \frac{920}{1331} \) into improper fraction


Consider a Wheatstone bridge with
resistance and capacitance connected as shown.

Find the condition on the resistance and
the capacitance such that the bridge remains balanced at all times.


The vertical height of the mercury column in a barometer remains
unaffected even if the tube is tilted.
A. True
B. False


Bulk modulus of water is \( 2 \times 10^{9} N / m^{2} \)
The change in pressure required to increase the density of water by \( 0.1 \% \) is.
A \( \cdot 2 \times 10^{9} N / m^{2} \)
B . \( 2 \times 10^{8} N / m^{2} \)
c. \( 2 \times 10^{6} N / m^{2} \)
D. \( 2 \times 10^{4} N / m^{2} \)


Out of the two concentric circles, the
radius of the outer circle is \( 5 \mathrm{cm} \) and
the chord \( A C \) of length \( 8 \mathrm{cm} \) is a tangent to the inner circle. Find the radius of
the inner circle.
\( A .3 c m \)
B. \( 6 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. 7 cm


The basic character of the transition
metal monoxides follows the
(At. no. of \( \boldsymbol{T} \boldsymbol{i}=\mathbf{2} 2, \boldsymbol{V}=\mathbf{2 3}, \boldsymbol{C r}= \)
\( 24, F e=26) \)
A \( . T i O>V O>C r O>F e O \)
в. \( V O>C r O>T i O>F e O \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}>\mathrm{VO}>\mathrm{FeO}>\mathrm{TiO} \)
D. \( T i O>F e O>V O>C r O \)


Orbits or shells are represented by:
A. The letters \( K . L, M, N, \ldots \) or the numbers, \( n=1,2,3,4, \ldots \)
B. Only by the numbers \( n=1,2,3,4 \)
C. Only by the letter \( \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N} \)
D. None of the above


Definition of chemistry is:
A. physical science that studies the composition, structure, properties and change of matter
B. biological science that helps to study the basic functioning of nervous system
C. science that helps in studying the galaxy
D. physical science that studies the biotic and abiotic aspects of environment


Hydrolysis of \( X e F_{4} \) with excess water
gives:
A \( . \quad \) Xe OF\( _{4} \)
в. \( X e O_{2} F_{2} \)
\( c \cdot X e \)
D. \( X e O_{4} \)


Which of the following is NOT a protein?
\( A \). Wool
B. Cellulose
c. Hair
D. Nail


A constant valume gas thermometer shows pressure reading of \( 50 \mathrm{cm} \) and
\( 90 \mathrm{cm} \) of mercury at \( 0^{0} \mathrm{C} \) and \( 100^{0} \mathrm{C} \)
respectively. When the pressure reading
is \( 60 \mathrm{cm} \) of mercury, the temperature is:-
\( \mathbf{A} \cdot 25^{0} C \)
в. \( 40^{\circ} \mathrm{C} \)
c. \( ^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)


What is the path difference for the first, second and third order maxima of
wavelengths \( 4000 A \) and \( 7000 A \)


Chlorine gas removes hydrogen from
water \( \boldsymbol{H}_{2} \boldsymbol{O} \) giving out oxygen gas.
A. True
B. False


Check the commutativity and associativity of the following binary operation:
\( ^{\prime} *^{\prime} \) on \( Q \) defined by \( a * b=\frac{a b}{4} \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Q} \)


Derive lens maker's formula for a
biconvex lens.


The outermost electronic configuration of the most electronegative element is:
\( \mathbf{A} \cdot n s^{2} n p^{3} \)
В. \( n s^{2} n p^{6} \)
\( c \cdot n s^{2} \)
D. \( n s^{2} n p^{5} \)


An increase in pressure in this reaction
would:
A . produce more \( I^{-}(a q) \)
B. produce more \( H_{2} \)
c. not affect the system
D. drive it to the right


If the radius of curvature of the curved
surface of a planoconvex lens is \( 50 \mathrm{cm} \)
its focal length is \( (\mu=1.5) \)
A . \( -0.5 m \)
в. \( -0.75 m \)
c. \( -1.25 m \)
D. \( -0.25 m \)
E. \( 1 m \)


A. liquid drop of radius 'R' breaks into
64 tiny droplets each of radius 'r'. If the surface tension of the liquid is 'T' then
gain in energy is:
\( \mathbf{A} \cdot 48 \pi R^{2} T \)
В. \( 12 \pi r^{2} T \)
\( \mathbf{c} \cdot 96 \pi r^{2} T \)
D. \( 192 \pi r^{2} T \)


The heat of combustion of \( C_{(g\text { raphite) } } \) is \( -393.5 k J \) mol \( ^{-1} . \) The heat of formation
of \( C O_{2} \) from graphite is \( k J m o l^{-1} \)
A. 393.5
B. -393.5
c. -787.0
D. 787.0


Benzyl chloride \( C_{6} H_{5} C H_{2} C l \) can be
prepared from toluene by chlorination
with:
A \( \cdot C l \)
в. \( S O_{2} C l_{2} \)
c. \( \operatorname{socl}_{2} \)
D. \( N a O C l \)


Balance the following equation by
oxidation number method.
\( A l+K M n O_{4}+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{A l}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Find the value of \( \sin ^{-1}\left(2 \cos ^{2} x-1\right)+ \)
\( \cos ^{-1}\left(1-2 \sin ^{2} x\right) \)
A \( \cdot \frac{\pi}{2} \)
в.
c.
D.


Which condition of zygote cell will lead to birth of a normal human female child
A. one X-chromosome
B. one \( x \) and one \( Y \) chromosome
c. two X-chromosomes
D. one Y-chromosome


Given is a diagram of a human blood smear. Study the diagram and answer the question that follows. Component numbered 1 do not have
certain organelles but are very efficient in their function. Explain.


Which of the following types of reproduction leads to the variation in
the population?
A. Sexual reproduction
B. Asexual reproduction
c. Both of these
D. None of these


Find the nature and order of the
interference at 0
\( A \cdot 20^{t h} \operatorname{minimal} \)
B. \( 20^{\text {th }} \) maxima
\( \mathrm{c} \cdot 10^{t h} \) maxima
\( D \cdot 10^{t h} \operatorname{minimaa} \)


Let \( f(x)=(x-2)^{33}(x-3)^{44} \) then
which of the following is true
A. \( x=2 \) is point of inflexion
B. \( x=3 \) is point of minima
c. \( _{x}=\frac{17}{7} \) is point of maxima
D. All of these


Evaluate \( \int_{0}^{1} \cot ^{-1}\left(1-x+x^{2}\right) d x \)


The gas responsible for causing Bhopal
tragedy was:
A. methyl isocyanate
B. potassium isothiocyanate
c. sodium isothiocyante
D. ethyl isothiocyante


Find the VAT paid by the shopkeeper to
the government


Which of the following is the radio isotope in this pair? \( \mathbf{1 2} \mathbf{C}, \mathbf{1 4} \mathbf{C} \)
\( \mathbf{6} \)
A \( \cdot \frac{12 C}{6} \)
B. \( 14 C \)
c. Both of them
D. None of them


Valence electron of zinc atom possesses
the quantum numbers
A \( \cdot n=4,1=0, m=0 \)
B. \( n=4,1=1, m=0 \)
\( c \cdot n=4,1=2, m=3 \)
D. \( n=4,1=3, m=5 \)


The cartesian from of equation a line passing through the point position vector \( 2 \hat{i}-\hat{j}+2 \hat{k} \) and is in the direction of \( -2 \hat{i}+\hat{j}+\hat{k}, \) is
A \( \frac{x-2}{-2}=\frac{y+1}{1}=\frac{z-2}{1} \)
B. \( \frac{x+4}{-2}=\frac{y-1}{1}=\frac{z+2}{1} \)
c. \( \frac{x+2}{4}=\frac{y-1}{-1}=\frac{z-1}{2} \)
D. None of these


The volume of an air bubble increases by
\( x \% \) as it rises from the bottom of a lake to
its surface. If the height of the water barometer is \( \mathrm{H} \), the depth of the lake is
\( A \)
в. \( \frac{H x}{(100+x)} \)
\( c \cdot \frac{H x}{100} \)
D. 100 \( H / x \)


\( (-144) \div(+16) \)
\( A \cdot+9 \)
B. +11
\( c .-9 \)
D. -11


During one cycle of a heat engine 2000 calories of heat is supplied and 1500 calories rejected. The amount of work
done equals:
A .2093 J
B. \( 4186 J \)
c. \( 1042 J \)
D. 0


Which of the following group 14 elements shows maximum tendency
towards catenation?
A. Iead
B. germanium
c. silicon
D. carbon


Maximum bond angle is in:
A. \( A l C l_{3} \)
в. \( C C l_{4} \)
\( c \cdot C O_{2} \)
D. \( P C l_{5} \)


A highly conducting sheet of aluminium foil of negligible thickness is placed between the plates of a parallel plate capacitor. The foil is parallel to the plates at distance \( \frac{d}{2} \) from positive plate where \( d \) is distance between plates. If the capacitance before the insertion of
foil was \( 10 \mu F \), its value after the insertion of foil will be:
\( \mathbf{A} \cdot 20 \mu F \)
в. \( 10 \mu F \)
\( \mathrm{c} .5 \mu F \)
D. zero


\( \int \frac{d x}{x^{2}+2 x+2} \) is equal to:
\( \mathbf{A} \cdot \sin ^{-1}(x+1)+c \)
B. \( \sinh ^{-1}(x+1)+c \)
c. \( \tanh ^{-1}(x+1)+c \)
D. \( \tan ^{-1}(x+1)+c \)


The productive area required to produce all the resources for humanity to consume and to absorb all its waste is
known as
A. A habitat
B. An ecosystem
c. An ecological footprint
D. The biosphere
E. The carrying capacity


Which of the following substances, if introduced into the blood stream,
would cause coagulation of blood at the site of its introduction
A. Thromboplastin
B. Fibrinogen
c. Heparin
D. Prothrombin


Let \( V \) and \( E \) denote the gravitational
potential and gravitational field at a point. It is possible to have
A \( . V=0 \) and \( E=0 \)
B. \( V=0 \) and \( E \neq 0 \)
c. \( V \neq 0 \) and \( E=0 \)
D. All of the above


How many number of enolic form are
possible for the compound
\( A \)
B.
\( c \cdot 3 \)
\( D \)


\( X \) is a set of factors of 24 and \( Y \) is a set
of factors of \( 36, \) then find the sets \( X \cup \)
\( \boldsymbol{Y} \) and \( \boldsymbol{X} \cap \boldsymbol{Y} \)


Heat of reaction for; \( \boldsymbol{C O}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) \) at constant \( V \) is
-67.71 cal \( 17^{\circ} C . \) The heat of reaction at
constant \( P \) at \( 17^{\circ} C \)
A. \( -68.0 K \) cal
в. +68.0 Кса
c. -67.42 К \( c a l \)
D. None of these


The basic character of the transition
metal monoxides follows the order:
(Atomic number \( \mathrm{Ti}=22, \mathrm{V}=23, \mathrm{Cr}=24 \)
\( F e=26) \)
A. TiO > Fe0 > VO > cro
в. тio > vo > cro > Feo
c. тio \( > \) Cro \( > \) vo \( > \) Feo
D. crosvo \( > \) Fe0 > Tio


is the change of gaseous state directly to solid state without going through liquid the state.
A. sublimation
B. Precipitation
c. Evaporation
D. freezing


A solid copper sphere of radius \( R \) and \( a \)
hollow copper sphere of outer radius \( \boldsymbol{R} \)
are heated to the same temperature
and allowed to cool in the same
surroundings. Then
A. Solid sphere cools faster
B. Hollow sphere cools faster
c. Both cool equally
D. cannot be decided


Which one of the given elements shows
maximum number of different
oxidation states in its compounds?
\( A \cdot A m \)
в. \( F m \)
\( c . L a \)
D. \( G d \)


Which one of the following is an inner orbital complex as well as diamagnetic in behaviour?
A \( \cdot\left[\operatorname{Zn}\left(N H_{3}\right)_{6}\right]^{2} \)
в. \( \left[Z i\left(N H_{3}\right)_{6}\right]^{2+} \)
\( \mathbf{c} \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{3} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)


A tuning fork vibrating with a sonometer having \( 20 \mathrm{cm} \) wire produces 5 beats/s. The beat frequency does not
change, if the length of the wire is changed to \( 22 \mathrm{cm} . \) The frequency of the tuning fork (in Hz) must be
A . 200
B. 210
\( c \cdot 105 \)
D. 125


A mixture of chlorobenzene and wate
(immiscible) boils at \( 90.3^{\circ} \mathrm{C} \) at an
external pressure of \( 740.2 \mathrm{mm} . \) The vapour pressure of pure water at
\( 90.3^{\circ} \mathrm{C} \) is \( 530.1 \mathrm{mm} \). Calculate the \( \% \)
composition of distillate:
A. \( H_{2} O=35 \% \)
в. \( H_{2} O= \) 22\%
c. \( H_{2} O= \) २९\% \( \%= \)
D. \( H_{2} O=71 \% \)


An example of irreversible inhibition is
the action of nerve gas poisons on
A. Lipase
B. Acetylcholinesterase
c. Urease
D. Amylase


Simplify:
\( \frac{3}{17} \div \frac{8}{17} \times \frac{2}{3}+\left(-\frac{2}{7}\right) \times \frac{35}{33} \div \)
\( \left(-\frac{7}{11}\right) \)


The number of mole of \( A g I \) which may
be dissolved in 1.0 litre of \( 1.0 M C N^{-} \)
solution whose
\( \boldsymbol{K}_{s p} \) for \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \) and \( \boldsymbol{K}_{c} \) for \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}^{-} \) are
\( 1.2 \times 10^{-17} \) and \( 7.1 \times 10^{19} M^{-2} \)
respectively.
A. \( 0.40 \mathrm{mol} \)
B. \( 0.45 \mathrm{mol} \)
c. 0.50 mol
D. None of these


Which artificial sweetener contains
chlorine?
A. Sucralose
B. Alitame
c. saccharin
D. Aspartame


If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y}) \cdot \boldsymbol{f}(\boldsymbol{z}) \) for all
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) and \( \boldsymbol{f}(\boldsymbol{2})=\boldsymbol{4}, \boldsymbol{f}^{\prime}(\boldsymbol{0})=\boldsymbol{3}, \) then
\( f^{\prime}(2) \) equals
A . 12
B. 9
c. 16
D. 6


If \( A \) is a \( 3- \) rowed square matrix and
\( |\boldsymbol{A}|=\mathbf{4} \) then \( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=? \)
A \( .4 A \)
в. \( 16 A \)
\( c \cdot 64 A \)
D. None of these


A die is thrown 100 times with the
frequencies for the outcomes 1,2,3,4,5
and 6 as given in following table:
Outcome 1 2 3. 3
Frequency 13 18 २६
If a die is thrown at random, find the
probability of getting (i) 1 (ii) 2 (iii) 3
(iv) \( 4(v) 5(v i) 6 \)


Element with similar chemical
properties:
A. occur only within the same period
B. have identical atomic mass(weight)
C. have identical number of neutrons
D. have the same number of electrons in the outer shell


The inequality \( |z-4|<|z-2| \)
represents the region given by:
A. \( \operatorname{Re}(z) \geq 0 \)
в. \( \operatorname{Re}(z)<0 \)
c. \( \operatorname{Re}(z)>0 \)
D. None of these


In earthworms setae are present in all
segments except
A. First and the last segment
B. First and the clitellum
c. First segment
D. Clitellum and last segment
E. First, clitellum and last segment


Electromotive force of a battery
represents
\( A \cdot \) force
B. energy
C. electric potential energy per unit charge
D. current


Match the statements in Column \( A \)


The breaking stress of aluminium is \( \mathbf{7 . 5} \times \mathbf{1 0}^{7} \mathbf{N m}^{-\mathbf{2}} . \) Find the greatest
length of aluminium wire that can hang vertically without breaking. Density of aluminium is \( 2.7 \times 10^{3} \mathrm{Kgm}^{-3} \)


If a line makes \( \theta_{1}, \theta_{2}, \theta_{3} \) angles with the
co-ordinates axes, then prove that
\( \cos 2 \theta_{1}+\cos 2 \theta_{2}+\cos 2 \theta_{3}+1=0 \)


A metal block is exposed to beams of \( X \) ray of different wavelength. X-rays of which wavelength penetrate most?
\( A \cdot 2 A \)
в. 4 А
\( c \cdot 6 \hat{A} \)
\( D \cdot 8 A^{\circ} \)


Assertion
Following reaction fail to produce benzoic acid
Reason
Aryl halides do not usually undergo \( S_{N} 2 \)
reaction
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In a circle of radius \( 6 \mathrm{cm}, \) a chord of
length \( 10 \mathrm{cm} \) makes an angle of \( 110^{\circ} \mathrm{at} \)
the centre of the circle. Find the
circumference of the circle.


Assertion
Fat is digested in the intestine by
emulsification.
Reason
Bile salts stabilize the emulsion so
formed.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A black body is at a temperature of \( 2880 K . \) The radiation energy emitted by this object with wavelength in between
\( 499 n m \) and \( 500 n m \) is \( U_{1}, \) between 999
nm and 1000 nm is \( U_{2} \) and between
\( 1499 \mathrm{nm} \) and \( 1500 \mathrm{nm} \) is \( U_{3} . \) If Wein
constant is \( 2.8 \times 10^{6} \mathrm{nmK} \), then
A \( \cdot U_{1}=0 \)
в. \( U_{3}=0 \)
\( \mathbf{c} \cdot U_{1}>U_{2} \)
D. \( U_{2}>U_{1} \)


\( 0.5264 \mathrm{gm} \) silver bromide is obtained from 0.5124 gm of an organic compound. Calculate the percentage of bromine in the compound rounded to the nearest integer.


The line \( 3 x-4 y+8=0 \) is rotated
through an angle \( \frac{\pi}{4} \) in the clockwise direction about the point \( (0,2) . \) The equation of the line in its new position
is
A. \( 7 y+x-14=0 \)
в. \( 7 y-x-14=0 \)
c. \( 7 y+x-2=0 \)
D. \( 7 y-x=0 \)


Heating pyrites to remove sulphur is called:
A. smelting
B. calcination
c. liquation
D. roasting


When electric current passes through
the filaments of a bulb, it starts
emitting light due to :
A. heating effect of electric current.
B. magnetic effect of electric current.
c. chemical effect of electric current
D. lighting effect of electric current.


The author of Species Plantarum is


The instrument that can be used to see
things from a concealed position
A. Periscope
B. Kaleidoscope
c. Telescope
D. Microscope


Human baby will be a female, if its \( 23^{r d} \)
chromosome pair is
A. \( x x \)
B. XY
c. \( \gamma \) r
D. xyr


Represent the following families of curves by forming the corresponding differential equation.(a, b being parameters). \( x^{2}-y^{2}=a^{2} \)


Using Molecular Orbital theory complete the relative of the fall species and indicate their magnetic behaviour. \( \rightarrow \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{+}, \boldsymbol{O}_{2}^{-}, \boldsymbol{O}_{2}^{2-} \)


n the above figure find the ratio
between the \( \triangle A O B \) and \( \triangle C O D, \) if \( A B= \)
\( \mathbf{3} C D \)


How is the sex of an offspring determined in humans?
A. Sex chromosome of mother
B. Size of ovum
c. Size of sperm
D. Sex chromosome of father


Nitrogen dioxide gas turns moist blue litmus
A. white
B. red
c. yellow
D. black


Which amongst the following is also called as a sesqui oxide?
A. \( B_{2} O_{3} \)
a
в. \( A l_{2} O_{3} \)
\( \mathrm{c} \cdot \operatorname{Ti}_{2} \mathrm{O}_{3} \)
D. All of the above


Use Euclid's division algorithm to find
the HCF of the following number: 55 and
210


What are representative elements?


Convert 0.55 in to a fraction.
A \( \cdot \frac{11}{20} \)
в. \( \frac{2}{9} \)
\( c \cdot \frac{3}{9} \)
D. \( \frac{4}{9} \)


True or False.
Coins can be made up of pure metals.


The ratio of slit widths in Young's double
slit experiment is \( 4: 9 . \) The ratio of
maximum and minimum intensities
will be
A. 169: 25
B. 81: 16
c. 13: 5
D. 25: 1


In the case of a fluid, Bernoulli's theorem expresses the application of the principle of conservation of:
A. linear momentum
B. energy
c. mass
D. angular momentum


In a torch there are two cells each of
1.45 volt and \( 0.15 \Omega . \) Each cell gives a
current to filament of a lamp of \( 1.5 \Omega \) then the value of current in ampere is :-
A. 16.11
B. 1.611
c. 0.1611
D. 2.6


Six particles each of mass \( m \) are placed
at the corners of a regular hexagon of
edge length \( a \). If a point mass \( m_{0} \) is
placed at the centre of the hexagon, then the net gravitational force on the
point mass \( \boldsymbol{m}_{0} \) is :
A \( \cdot \frac{6 G m^{2}}{a^{2}} \)
в. \( \frac{6 G m m_{0}}{a^{2}} \)
c. zero
D. none of these


Which of the following affects the elasticity of a substance?
A. Hammering and annealing
B. Change in temperature
c. Impurity in substance
D. All of the above


Centigrade (Celsius) scale can be
converted into Kelvin scale by formula
\( \mathbf{A} \cdot \Omega^{0} C= \) Temperature in \( \mathrm{Kelvin}+273.15 \)
B \( \cdot \Omega^{0} C= \) Temperature in Kelvin -273.15
\( \mathbf{C} \cdot \Omega^{0} C= \) Temperature in Fahrenheit +273.15
D. \( \Omega^{0} C= \) Temperature in Fahrenheit -273.15


A nail of mass \( ^{\prime} m_{1}^{\prime} \) kg is being hammered by a hammer of mass \( ^{\prime} \boldsymbol{m}_{2}^{\prime} \)
kg with a velocity of 'v' \( \mathrm{m} \mathrm{s}^{-1} \) such that the nail drives by 's' m into a wall. Find
the average resistance offered by the wall to the penetration of nail.
A. \( \left[\frac{m_{2} v}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
В \( \cdot\left[\frac{m_{2} v^{2}}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
\( ^{\mathbf{c}} \cdot\left[\frac{m_{2}^{2} v}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
D. \( \left[\frac{m_{2}^{2} v^{2}}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)


Quantity \( X \) has a fractional uncertainty
of \( x . \) Quantity \( Y \) has a fractional uncertainty of \( y \) What is the fractional uncertainty in \( \frac{\boldsymbol{X}}{\boldsymbol{Y}^{2}} \)
\( \mathbf{A} \cdot x+y \)
в. \( x-y \)
c. \( x+2 y \)
D. \( x-2 y \)


Distinction of prokaryota and eukaryota is mainly based on
A. Nucleus
B. Cell organelles
c. chromosomes
D. All of the above


Which one given below is a nonreducing sugar?
A. Maltose
B. Lactose
c. Glucose
D. sucrose


The hydrolysis constant is \( \boldsymbol{K}_{\boldsymbol{H}}=\boldsymbol{X} \times \)
\( 10^{-2} . \) The value of \( X \) is:


If the bisector of the exterior vertical
angle of a triangle is parallel to the base, show that the triangle is isosceles.


\( \ln \) YDSE, \( d=2 m m, D=2 m \) and \( \lambda= \)
\( 500 n m . \) If intensities of two slits are \( I_{0} \)
and \( 9 I_{0}, \) then find intensity at \( y= \)
\( \frac{1}{6} m m \)
A \( \cdot 7 I_{0} \)
в. \( 10 I_{0} \)
\( c \cdot 16 I_{0} \)
D. \( 4 I_{0} \)


Short / Long answer type questions.
(a) Explain the phenomena of multiple allelism and co-dominance taking ABO blood group as an example.
(b) What is
the phenotype of the following: (i) \( A \) i,
(ii) ii


Assertion: In prokaryotes, there are three initiation factors used for protein synthesis.

Reason: All the initiation factors have
their own functions.
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


What is meant by positive and negative
deviations from Raoult's law and how is
the sign of \( \Delta_{m i x} H \) related to positive
and negative deviations from Raoult's law?


Which of the following aqueous solutions will have maximum freezing point. [Assume dilute solutions]
A. \( C_{6} H_{5} N H_{3} C I \) solution having \( 0.01 m \)
B. \( C a\left(N O_{3}\right)_{2} \) solution having \( 0.005 m \)
C. \( A I\left(N O_{3}\right)_{3} \) solution having \( 0.004 m \)
D. Glucose solution having \( 0.04 \mathrm{m} \)


A monomeric anhydrous complex of Co gives the following results:
\( C o: 21.24 \% \)
\( N H_{3}: 24.77 \% \)
\( C l^{-}: 12.81 \% \)
\( S O_{4}^{2-}: 34.65 \% \)
\( H_{2} O: 6.53 \% \)
\( (c o: 58, C l=35.5, s=32, N=14) ; Z(C 0= \)
27)
The compound is diamagnetic and
gives white ppt with \( B a C l_{2} . \) What is its empirical formula?
A \( \cdot \operatorname{Co}\left(N H_{3}\right)_{4} S O_{4} \cdot H_{2} O C l_{2} \)
в. \( \operatorname{Co}\left(N H_{3}\right)_{2} S O_{2} \cdot H_{2} O C l \)
c. \( \operatorname{Co}\left(N H_{3}\right)_{4} \operatorname{SO}_{4} \cdot H_{2} \) OCl
D. None of the above


Given: \( \left(\frac{1}{2^{3}}\right)^{2}=\frac{1}{2^{m}} . \) The value of \( m \) is


A wave is travelling in a medium with frequency \( \boldsymbol{f}=\mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{H} \boldsymbol{z} \) and speed \( \boldsymbol{v}= \)
\( 100 m / s, \) Find out its wavelength?
B. \( 10^{-12} m \)
c. \( 10^{10} m \)
\( \mathbf{D} \cdot 10^{12} m \)
E \( .10^{16} m \)


The ozone layer absorbs and protects the living beings of the earth.
A. water vapour
B . light
c. infrared rays
D. ultraviolet rays


Assertion
Statement -1: Coordination isomerism
occurs when both cation and anion are
complex.
Reason
Statement -2: The complexes with coordination number 6 form octahedral
complexes involving either \( s p^{3} d^{2} \) or
\( d^{2} s p^{3} \) hybridization.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1.
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. Statement -1 is true, Statement -2 is false
D. Statement - 1 is false, Statement - 2 is true


A particle is moving in a potential region given by \( U=K\left(x^{2}+y^{2}+z^{2}\right) \)
The force acting on the particle is given by:
A . \( -2 K(x \hat{i}+y \hat{j}+z \hat{k}) \)
B . \( K(x \hat{i}+y \hat{j}+z \hat{k}) \)
c. \( \frac{K}{2}(x \hat{i}+y \hat{j}+z \hat{k}) \)
D. \( K\left(x^{2} \hat{\imath}+y^{2} \hat{\jmath}+z^{2} \hat{k}\right) \)


Draw labelled diagram of Hall-Heroult Electrolytic cell for the extraction of aluminium. Write anode and cathode
reactions.


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


In series combination of \( \boldsymbol{R}, \boldsymbol{L}, \boldsymbol{C} \) with an
A.C source at resonanace, if \( \boldsymbol{R}=\mathbf{2 0} \)
ohm, then impedence \( Z \) of the combination is
A. 20 ohm
B. zero
c. 10 ohm
D. 400 ohm


Which of the following reacts with phenol to give salicylaldehyde after hydrolysis?
A. Dichloro methane
B. Trichloro methane
c. Methyl chloride
D. None of the above


Find the 12 th term from the end of the
following arithmetic progressions. \( \mathbf{1}, \mathbf{4}, \mathbf{7}, \mathbf{1 0}, \dots \dots \dots, \mathbf{8 8} \)


A mirage occurs because
A. The refractive index of atmosphere increases with height
B. The refractive index of atmosphere decreases with height
C. The hot ground acts like a mirror
D. Refractive index remains constant with height


Carbon dioxide is neither combustible
nor a supporter of combustion.
A. True
B. False


For a zero order reaction at \( 200 K \)
reaction complete in 5 minutes while at
\( 300 K, \) same reaction, completes in 2.5
minutes. What will be the activation
energy in calorie? \( (\boldsymbol{R}= \)
\( \mathbf{2} \text { Cal } /(\text { mol. } \boldsymbol{K}) ; \boldsymbol{l n} \mathbf{2}=\mathbf{0 . 7}) \)


The power of a lens is negative. State
whether it is convex or concave?
A. Concave
B. Convex
c. Both \( A \& B \)
D. can't say


Say true or false.
The total savings (in \( R s . \) ) after every
month for 10 months when \( R s .50 \) are
saved each month are
\( \mathbf{5 0 , 1 5 0}, 200,250,300,350,400,450,500 \)
represent G.P.
A . True
B. False


\( \sqrt{9} \) is a rational number. It is equal to
A . 4.5
B. 3
\( c \cdot 27 \)
D. 18


Use the following figure to find \( A E \), if
\( B D=4.1 \mathrm{cm} \)
A . \( 4.1 \mathrm{cm} \)
B. \( 8.2 \mathrm{cm} \)
c. \( 16.4 \mathrm{cm} \)
D. Data insufficient


On a two-lane road, car \( A \) is travelling
with a speed of \( 36 k m h^{-1} . \) Two cars \( B \)
and \( C \) approach car \( A \) in opposite
directions with a speed of \( 54 k m h^{-1} \) each. At a certain instant, when the
distance \( A B \) is equal to \( A C, \) both being
\( 1 k m, B \) decides to overtake \( A \) before \( C \)
does. What minimum acceleration of
\( \operatorname{car} B \) is required to avoid an accident?


\( \operatorname{Let} \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3}, \dots, \boldsymbol{H}_{n} \) be mutually
exclusive and exhaustive events with
\( \boldsymbol{P}\left(\boldsymbol{H}_{i}\right)>0 ; \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \ldots, \boldsymbol{n} . \) Let \( \mathrm{E} \) be any
other event with \( 0<P(E)<1 \)
STATEMENT-1: \( \boldsymbol{P}\left(\boldsymbol{H}_{\boldsymbol{i}} \mid \boldsymbol{E}\right)> \)
\( \boldsymbol{P}\left(\boldsymbol{E} \mid \boldsymbol{H}_{i}\right) \cdot \boldsymbol{P}\left(\boldsymbol{H}_{i}\right) \) for \( \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \dots, \boldsymbol{n} \)
STATEMENT-2 \( \sum_{i=1}^{n} P\left(H_{i}\right)=1 \)
A. Statement-1 is True, Statement-2 is True; Statement - is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True; Statement - is Not a correct explanation for Statement- 1
c. Statement- - - is True, Statement - 2 is False
D. Statement-1 is False, Statement-2 is True


If an element X has mass number and
number of proton 8 then identify element \( X \)
A .
B.
\( c \cdot 0 \)
D. Ar


Assertion
Benzene \( \left(C_{6} H_{6}\right) \) can be drawn as a
series of resonance structures.
Reason
Its bonds are a hybrids of single and double bond character.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The magnetic field at \( O \) due to current
in the wire segment BC of the infinite wire forming a loop as shown in figure
is
\( ^{A} \cdot \frac{\mu_{0} I}{4 \pi d}\left(\cos \phi_{1}+\cos \phi_{2}\right) \)
в. \( \frac{\mu_{0}}{4 \pi} \)
c. \( \frac{\mu_{0} I}{4 \pi d}\left(\sin \phi_{1}+\sin \phi_{2}\right) \)
D. \( \frac{\mu_{0}}{4 \pi} \)


The amine 'A' when treated with nitrous
acid gives yellow oily substance. The amine A is :
A. triethylamine
B. trimethylamine
c. aniline
D. methylphenylamine


A river \( 10 m \) deep is flowing at \( 5 m / s \)
The shearing stress between horizontal layers of the river is \( (\boldsymbol{\eta}= \)
\( 10^{-3} \) SI units
\( \mathbf{A} \cdot 10^{-3} N / m^{2} \)
B. \( 0.8 \times 10^{-3} N / m^{2} \)
C. \( 0.5 \times 10^{-3} N / m^{2} \)
D. \( 1 \mathrm{N} / \mathrm{m}^{2} \)


There are 720 permutations of the digits \( 1,2,3,4,5,6 . \) suppose these permutations are arranged from smallest to largest numerical of values, beginning from 123456 and ending with \( 654321 . \) (a)what number falls on
\( 124^{t h} \) position?
(b) what is the position
of 321546?


Density is least in
A. Sold
B. Liquid
c. Both A and B
D. Gas


\( \boldsymbol{H}_{2} \stackrel{14}{C}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \frac{\operatorname{low} \operatorname{conc.of} B r_{2}}{\operatorname{orhightemp}}(?) \)
Product of the above reaction is :
A \( \cdot H_{2}^{14}=C H-C H_{2}-B r \)
в. \( _{H_{2}} C=C H-_{C H_{2}}^{14}-B r \)
D. both (a) and (b)


More number of oxidation states are
exhibited by the actinoids than by lanthanoids. The main reason for this is:
A. greater metallic character of the lanthanoids than that of the corresponding actinoids.
B. more active nature of the actinoids
c. more energy difference \( 5 f \) and \( 6 d \) -orbitals than that between \( 4 f \) and \( 5 d \) -orbitals
D. lesser energy difference between \( 5 f \) and \( 6 d \) -orbitals than that between \( 4 f \) and \( 5 d \) -orbitals


What are the limitations of
J.J.Thomson's model of the atom?


How do chlorofluorocarbons (CFSs)
enter the atmosphere and how do they affect humans? Explain.


Two masses \( M_{1} \) and \( M_{2} \) are attached
to the ends of a string which passes
over a attached to the of a double
inclined plane of angles of inclination \( \alpha \)
and \( \beta . \) If \( \mathrm{M}_{2}>\mathrm{M}_{1} \) the acceleration a of
the system can be given by (neglect friction)
A \( \frac{M_{2} g(\sin \beta)}{M_{1}+M_{2}} \)
B. \( \frac{M_{1} \sin \alpha}{M_{q}+M_{2}} \)
\( c \)
D. zero


A fighter plane is flying horizontally at an altitude of \( 1.5 \mathrm{km} \) with speed 720
\( \mathrm{km} / \mathrm{h} . \) At what angle of sight (w.r.t. horizontal) when the target is seen should the pilot drop the bomb in order
to attack the target than?
A \( \cdot 23^{\circ} 4^{\prime} \)
B . \( 43^{\circ} 4^{\prime} \)
c. \( 33^{\circ} 4^{\prime} \)
D. \( 53^{\circ} 4^{\prime} \)


Select the correct I.U.P.A.C. name for
\( \left[\left(\mathrm{NH}_{3}\right)_{4} \mathrm{CoNH}_{2} \mathrm{NO}_{2} \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]\left(\mathrm{NO}_{3}\right)_{4} \)
This question has multiple correct options
A. Tetraamminecobalt (III)- \( \mu \) -amido- \( \mu \) -nitrito-n
tetraamminecoball (III) nitrate
B. \( \mu \) -Amido- \( \mu \) -nitrito- N-octaamminedicobalt (III)
nitrate
C \( . \mu \) - Amido- \( \mu \) -nitrito - N-bis(tetraammine)dicobalt
(III) nitrate
D. \( \mu \) -Amido- \( \mu \) -nitrito-O-octaamminedicobaltate (III)
nitrate


\( \ln \Delta A B C, 2 \angle A=3 \angle B=6 \angle C . \) Find
\( \frac{\angle A+\angle B}{\angle C} \times \angle B \)


Calculate the \( 7^{t h} \) term in the G.P.
\( 1,-3,9,-27 \dots \)
A . 429
B. 529
\( c \cdot 629 \)
D. 729


Ine velocıty or poınt \( \mathrm{K} \) or tne roa just
after impact with the bumper is (in
\( m / s) \)
A \( .1 .2 \sqrt{5} \)
B . 1.2
c. \( 1.2 \sqrt{5(2-\sqrt{3})} \)
D. \( 1.2 \sqrt{5(2+\sqrt{3})} \)


Which one of the following
arrangements does not give the correct
picture of the trends indicated against
it?
This question has multiple correct options
\( \mathbf{A} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}: \) Bond dissociation energy
\( \mathbf{B} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}: \) Electronegativity
\( \mathbf{C} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}: \) Oxidizing nature
D. \( F_{2}>C l_{2}>B r_{2}>I_{2}: \) Electron gain enthalpy


Short / Long answer type questions.
What is a nerve fibre? Describe the
structure of a myelinated fibre.


The number of electrons for one
coulomb of charge are:
A \( \cdot 6.25 \times 10^{23} \)
B. \( 6.25 \times 10^{21} \)
c. \( 6.25 \times 10^{18} \)
D. \( 6.25 \times 10^{19} \)


Statement 1: The temperature of a substance always increases as heat energy is added to the system.
Statement 2: The average kinetic energy of the particles in the system
increases with an increase in
temperature.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


The gases produced by thermal decomposition of nitric acid are :
A. nitric oxide and oxygen
B. nitrous oxide and nitrogen
c. nitrogen dioxide and oxygen
D. nitrogen and oxygen


Match items of Column I with the items
of Column II and assign the correct code
with respect to Column I:
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \begin{array}{l}\text { Cyanide } \\ \text { process }\end{array} & \text { (i) } & \begin{array}{l}\text { Ultrapure } \\ \text { Ge }\end{array} \\ \text { (b) } & \begin{array}{l}\text { Froth } \\ \text { floatation } \\ \text { process }\end{array} & \text { (ii) } & \begin{array}{l}\text { Dressing of } \\ Z n S\end{array} \\ \text { (c) } & \begin{array}{l}\text { Electrolytic } \\ \text { reduction }\end{array} & \text { (iii) } & \begin{array}{l}\text { Extraction } \\ \text { of } A l\end{array} \\ \text { (d) } & \text { Zone refining } & \text { (iv) } & \begin{array}{l}\text { Extraction } \\ \text { of } A u\end{array} \\ & \text { (v) } & \begin{array}{l}\text { Purification } \\ \text { of } N i\end{array}\end{array} \)
\( \mathbf{A} \cdot(i v),(i i),(i i i),(i) \)
B. (ii), (iii), (i), (v)
\( \mathbf{C} \cdot(\mathrm{i}),(\mathrm{ii}),(\mathrm{iii}),(\mathrm{iv}) \)
D. (iii),(iv),(v), (i)


The altitude of a cone is \( 20 \mathrm{cm} \) and its
semi-vertical angle is \( 30^{0} . \) If the semivertical angle is increasing at the rate
of \( 2^{0} \) per second, then the radius of the base is increasing at the rate of
A. \( 30 \mathrm{cm} / \mathrm{sec} \)
в. \( \frac{160}{3} \mathrm{cm} / \mathrm{sec} \)
c. \( 10 \mathrm{cm} / \mathrm{sec} \)
D. \( 160 \mathrm{cm} / \mathrm{sec} \)


Nylon-6 is formed from caprolactam
which is formed
from
A. cyclohexanone and hydroxyl amino
B. cyclohexanone and hydrazine
c. benzophenone and hydrazine
D. benzophenone and hydroxylamine


Strongest hydrogen bond is present in
A. \( H C l \)
в. \( H B r \)
c. \( H F \)
D. \( H I \)


Give the IUPAC name for the following alcohols. Classify as primary or secondary or teritiary alcohol \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)


The PDI (polydisersity index) is the ratio of weight to number-average molecular masses, \( M \bar{w} / M \bar{n} . \) In natural polymers, which are generally monodispersed, PDI is ............... and in synthetic polymers which are always polydispersed, PDI is
because \( M \bar{w} \) is always than \( M \bar{n} \)
Fill in the blanks.
A. greater than 1,1 , higher
B. 1, greater than 1, higher
c. less than 1,1 , lower
D. 1, less than 1, lower


Find the value of the constant \( k \) so that
the given function is continuous at the
indicated point:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{k} \boldsymbol{x}+\mathbf{1}, \text { if } \boldsymbol{x} \leq \mathbf{5} \\ \boldsymbol{3} \boldsymbol{x}-\mathbf{5}, \text { if } \boldsymbol{x}>\mathbf{5}\end{array} \text { at } \boldsymbol{x}=\mathbf{5}\right. \)


An electric dipole with dipole moment \( \overrightarrow{\boldsymbol{p}}=(3 i+4 j) \times 10^{-30} C-m \) is placed
in an electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{4 0 0 0 \hat { \boldsymbol { i } }}(\boldsymbol{N} / \boldsymbol{C}) \)
An external agent turns the dipole and its dipole moment becomes \( (-4 \hat{\mathbf{i}}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}) \times \mathbf{1 0}^{-\mathbf{3 0}} \boldsymbol{C}-\boldsymbol{m} . \) The work done by
the external agent is equal to:
A \( \cdot 4 \times 10^{-27} J \)
в. \( -4 \times 10^{-27} \mathrm{J} \)
c. \( 2.8 \times 10^{-26} J \)
D. \( -2.8 \times 10^{-26} J \)


At a certain place, the angle of dip is
\( 60^{\circ} \) and the horizontal component of
earth's magnetic field \( \left(B_{H}\right) \) is \( 0.8 \times \)
\( \mathbf{1 0}^{-4} \boldsymbol{T} . \) The earth's overall magnetic
field is:
A \( .1 .5 \times 10^{-4} T \)
в. \( 1.6 \times 10^{-3} T \)
c. \( 1.5 \times 10^{-3} T \)
D. \( 1.6 \times 10^{-4} T \)


A body is revolving with a constant
speed along a circular path. If the
direction of its velocity is reserved,
keeping speed unchanged, then at that
instant.
A. centripetal force disappears
B. centripetal force will be doubled
C. the centripetal force does not suffer any change in magnitude and direction both
D. the centripetal force does not suffer any change in magnitude but its direction is reserved.


The activation energy for a chemical reaction depends upon:
A. reaction
B. nature of reacting species
c. frequency factor
D. concentration of reacting species


The value of \( \frac{1}{97}+\frac{2}{97}+\ldots . .+\frac{96}{97} \) is
A . 48
в. -48
\( c \cdot 1 \)
D. None of the above


A hosewife saved rs. 2.50 in buying an item on sale. If she spent rs. 25 for thye item, approximately how much percent did she save in the translation?
A. 8\%
B. 9\%
c. \( 10 \% \)
D. 11\%


A pulse waveform has a high time of 8 ms and a pulse width of 32 ms. The duty cycle is
A . 25\%
B. 50\%
c. 1\%
D. 100\%


With a monochromatic light, the fringe-
width obtained in a Young's double slit
experiment is \( 0.133 \mathrm{cm} . \) The whole setup is immersed in water of refractive index 1.33 , then the new fringe-width is
A. \( 0.133 \mathrm{cm} \)
B. 0.1 \( \mathrm{cm} \)
c. \( 1.33 \times 1.33 \mathrm{cm} \)
D. \( \frac{1.33}{2} \mathrm{cm} \)


What is the process of leaching in case of low grade copper ores?
A . Leaching is carried out with \( N a O H \) and \( O_{2} \)
B. Leaching is carried out with \( N a C N \)
C. Leaching is carried out with acids in presence of \( O_{2} \)
D. Leaching is carried out by boiling the ore with water


In order to prepare a buffer of \( P^{H} 8.26 \)
the amount of \( \left(N H_{4}\right)_{2} S O_{4} \) required to
be mixed with 1L of 0.1 M \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}\left(\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}}=\right. \)
4.74) is:
A . 5 mol
B. 0.5 mol
c. 10 mol
D. 1 mol


Which metal is refined by Mond Process?
A. Titanium
B. Copper
c. Nickel
D. zinç


The pathway which water moves through cell wall without crossing any membrane
A. apoplast pathway
B. symplast pathway
c. vacuolar pathway
D. transmembrane pathway


Which of the following figures
represents the magnetic lines of force
due to an isolated north pole?
\( A \)
B.
\( c . \) Both
D. None


If a \( \$ 12,000 \) car loses \( 10 \% \) of its value
every year, what is the worth after 3
years?
\( A \cdot 8748 \)
B. 8750
c. 8752
D. 8744


\( \frac{-7}{5}+\left(\frac{2}{-11}+\frac{-13}{25}\right)= \)
\( \left(\frac{-7}{5}+\frac{2}{-11}\right)+\frac{-13}{25} \)
This property is
A . closure
B. commutative
c. associative
D. identity


Mrs. Mehra, who is 32 years old
underwent a surgery to get her oviducts removed after having a girl. Now, she wants to another baby. Do you think she can have another baby?
A. Yes, she can have another baby as her ovaries are still functional to produce an egg
B. No, she cannot have another baby because of fertilization of egg place in the oviducts
c. Yes, she can have another baby
D. No, she cannot have another baby as the hormones associated with the oviduct will not be present


The structure of Adenosine
triphosphate (ATP) molecule is given
above. The value of \( n_{1}+n_{2} \) is (where \( n_{1} \)
is the net negative charge in neutral
medium and \( n_{2} \) is number of chiral
carbon atoms)


If \( ^{6} C_{n}+2^{6} C_{n+1}+^{6} C_{n+2}>^{8} C_{3} \),then
the quadratic equations whose roots \( \operatorname{are} \alpha, \beta \) and \( \alpha^{n-1}, \beta^{n-1} \) have
A. 2 common root
B. 1 common root
c. no common roots
D. imaginary roots


The diameter of the base of the cylinder
is \( 12 \mathrm{cm} \) and the height is \( 8 \mathrm{cm} . \) Find the surface area of the solid cylinder.
A \( \cdot 520 \mathrm{cm}^{2} \)
B. \( 524 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 528 \mathrm{cm}^{2} \)
D. \( 532 \mathrm{cm}^{2} \)


When phenol is treated with \( C H C l_{3} \)
and \( N a O H, \) the product formed is :
A. Benzaldehyde
B. Salicylaldehyde
c. Salicyclic acid
D. Benzoic acid


The limits for the value of c for which
such collision is possible.


How is boron absorbed by plants?


Rahul is standing on the street and wants to throw an \( 8 k g \) book up to his
friend who is leaning out of a window
\( 5 m \) above street level. With what
velocity Rahul must throw the book so
that it reaches his friend in the window?
A. \( 5 m / s \)
в. \( 8 m / s \)
c. \( 10 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)
E \( .50 \mathrm{m} / \mathrm{s} \)


Haber's process is a/an:
A. endothermic process
B. exothermic process
c. spontaneous with no heat liberation
D. None


In the given figure, \( O \) is the centre of the
circle and \( \angle Q P R=x^{\circ} ; \angle O R Q=y^{\circ} \)
Which statement is true about \( x^{\circ} \) and
\( \boldsymbol{y}^{\circ} ? \)
A \( \cdot x^{\circ}+y^{\circ}=120^{\circ} \)
В . \( x^{\circ}+y^{\circ}=180^{\circ} \)
c. \( x^{\circ}+y^{\circ}=90^{\circ} \)
D. \( x^{\circ}+y^{\circ}=150^{\circ} \)


The solution set of the equation
\( \sin ^{-1} x=2 \tan ^{-1} x \)
\( \mathbf{A} \cdot\{1,2\} \)
B \( \cdot\{-1,2\} \)
\( \mathbf{c} \cdot\{-1,1,0\} \)
D. \( \left\{1, \frac{1}{2}, 0\right\} \)


Match the columns
(Gases)
(Behaviour)


Discuss the relation between \( \boldsymbol{K}_{\boldsymbol{p}} \) and
\( K_{c} \) for this equilibrium:
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\mathbf{2} \boldsymbol{C} \boldsymbol{l}_{2(\boldsymbol{g})} \rightleftharpoons \boldsymbol{4} \boldsymbol{H} \boldsymbol{C l}_{(\boldsymbol{g})}+ \)
\( \boldsymbol{O}_{2(\boldsymbol{g})} \)
A. \( K_{p}=K_{c} \)
\( \mathbf{B} \cdot K_{p}>K_{c} \)
c. \( K_{p}<K_{c} \)
\( ^{\mathrm{D}} K_{p}=\frac{1}{K_{c}} \)


The sum of place value of digit 2 in the
number 21.236 is
A . 20
B. 20.2
c. 22
D. 2.2


Very large particles may scatter light of which color?
A. Blue
B. Violet
c. Indigo
D. white