If the potential energy of the electron in
the first allowed orbit in hydrogen atom is \( E ; \) its
This question has multiple correct options
A. lonization potential is \( -E / 2 \)
B. Kinetic energy is \( -E / 2 \)
c. Total energy is \( E / 2 \)
D. None of these


A simple pendulum, made of a string of
length \( l \) and a bob of mass \( m \), is
released from a small angle \( \theta_{0} . \) It
strikes a block of mass \( M, \) kept on a
horizontal surface at its lowest point of oscillations, elastically. It bounces back
and goes up to an angle \( \theta_{1} . \) Then \( M \) is given by :
A \( \cdot m\left(\frac{\theta_{o}+\theta_{1}}{\theta_{o}-\theta_{1}}\right) \)
B. \( \frac{m}{2} \frac{\theta_{o}-\theta_{1}}{\theta_{o}+\theta_{1}} \)
c. \( \frac{m_{o}+\theta_{1}}{2}\left(\frac{\frac{\theta_{o}}{\theta_{o}-\theta_{1}}}{)}\right. \)
D. \( \quad m\left(\frac{\theta_{o}-\theta_{1}}{\theta_{o}+\theta_{1}}\right) \)


The radius of base of a right circular cylinder is halved and its height is increased by \( 50 \% \). The ratio of volume of the new cylinder to that of the original cylinder will be
A . 3: 8
B. 2:
\( c \cdot 3: 1 \)
\( D \cdot 4: \)


Prove that:
\( \frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}=1 \)


Vessels and companian cells are found
in
A. Pteridophyte
B. Gnetum
c. Ephedra
D. Angiosperm


\( A_{n \times n} \) and \( B_{n \times n} \) are diagonal matrices
then \( A B=_{-\dots} \dots \dots \dots . . . \) matrix
This question has multiple correct options
A. square
B. diagonal
c. scalar
D. rectangular


Numbers of real roots of \( \boldsymbol{P}(\boldsymbol{x})=\mathbf{0}, \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
c. 5
D. 2


Prove the following identities
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \boldsymbol{a}^{2} & \mathbf{1} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}\end{array}\right|=\left(\boldsymbol{a}^{3}-\mathbf{1}\right)^{2} \)


\( \int \frac{2 x+5}{x^{2}+5 x-3} d x \)


What are food preservatives?


\( \boldsymbol{I}=\int \sqrt{\frac{a+x}{a-x}} d x \)


Define mixtures.
(a) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
\[
\boldsymbol{\Delta} \boldsymbol{H}_{298 K}^{o}=-285.9 \boldsymbol{k J m o l}^{-1}
\]
(b) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\[
\boldsymbol{\Delta} \boldsymbol{H}_{298 K}^{o}=-241.8 \boldsymbol{k J m o l}^{-1}
\]
The molar enthalpy of vapourisation of water will be:
B. 22.0 kJ mol-
c. \( 44.1 \mathrm{kJ} \mathrm{mol}^{-} \)
D. \( 527.7 k J \) mol\( ^{-} \)


If \( f \) and \( g \) are functions such that fog is onto then
A. \( f \) is onto
B. \( g \) is onto
c. \( g o f \) is onto
D. Neither \( f \) nor \( g \) is onto


The rate of recombination or generation
are governed by the law(s) of
A. Mass conservation
B. Electrical neutrality
c. Thermodynamics
D. chromodynamics


A conducting loop (as shown) has total
resistance \( R \). A uniform magnetic field
\( B=\gamma t \) is applied perpendicular to
plane of the loop where \( \gamma \) is a constant
and \( t \) is time. The induced current
flowing through loop is:
\( A \)
B. \( \frac{\left(b^{2}-a^{2}\right) \gamma}{R} \)
c. \( \frac{\left(b^{2}-a^{2}\right) \gamma t}{R} \)
D. \( \frac{\left(b^{2}+a^{2}\right) \gamma}{R} \)


The colour of methyl orange indicator in a solution is yellow. The pH of this solution is likely to be:
A. 7
B. less than 7
\( c \cdot 0 \)
D. more than 7


The coefficient of friction between the
block A of mass \( \mathrm{m} \) and the triangular
wedge B of mass M is \( \mu \). There is no friction between the wedge and the
plane. If the system (block \( A+\text { wedge B }) \) is released so that there is no sliding
between \( A \) and \( B \). Find the inclination \( \theta \)


Differentiate \( e^{\sin x} \)
\( \mathbf{A} \cdot e^{\sin x} \cos x \)
B. \( -e^{\sin x} \cos x \)
\( \mathbf{c} \cdot e^{-\sin x} \cos x \)
\( \mathbf{D} \cdot e^{\cos x} \sin x \)


Calculate the area bounded by the line
\( x+y=10 \) and both the coordinates
axes.


Which of the following is used for the formation of thermistor?
A. copper oxide
B. Nickel oxide
c. Iron oxide
D. All of the above


MTP is considered safe upto how many weeks of pregnancy?
A. six
B. Eight
c. Twelve
D. Eighteen


Which of the following is required in lowest concentration for coagulating a sol having positively charged colloidal particle?
A. \( K C l \)
в. \( K_{2} S O_{4} \)
c. \( Z n C l_{2} \)
D. \( K_{4}\left[F e(C N)_{6}\right. \)


The condition for constructive
interference is path difference should
be equal to :
A. odd integral multiple of wavelength
B. Integral multiple of wavelength
c. odd integral multiple of half wavelength
D. Integral multiple of half wavelength


conversion of glucose into ethanol, a
key process of anaerobic energy
transformation in some organisms.
The best explanation for this is that
A. Step 1 illustrates that ATP hydrolysis is an energetically favorable exergonic reaction that couples the free energy released when ATP forms ADP and Pi (inorganic phosphate) with the endergonic conversion of glucose into pyruvate.
B. NADH is oxidized during step 1 and reduced during step
3
c. Step 1 illustrates the phosphorylation of ADP into ATP, which is coupled to the energetically favorable conversion of glucose into pyruvate
D. In step 1 ATP is oxidized and glucose is reduced, and it is this coupling that provides the energy to drive ethanol production


The \( 6 V \) Zener diode is shown in figure
has negligible resistance and a knee
current of \( 5 m A \). The minimum value of
\( R(i n \Omega) \) so that the voltage across it
does not fall below \( 6 V \) is
A. 40
в. 60
\( c \cdot 72 \)
D. 80
\( E .120 \)


What is the angle between electric field and equipotential surfaces?
A. 90 always
B. O always
\( c \cdot 0 \) to 90
D. 0 to 180


A block is attached to the end of an
ideal spring and moved from coordinate
\( x_{i} \) to coordinate \( x_{f} . \) The relaxed position
is at \( x=0 . \) The work done by spring is
positive if.
A \( \cdot x_{i}=2 c m \) and \( x_{f}=4 \mathrm{cm} \)
B . \( x_{i}=-2 \mathrm{cm} \) and \( x_{f}=4 \mathrm{cm} \)
C \( \cdot x_{i}=-4 \mathrm{cm} \) and \( x_{f}=4 \mathrm{cm} \)
D. \( x_{i}=4 \mathrm{cm} \) and \( x_{f}=-2 \mathrm{cm} \)


In an experiment, addition of \( 4.0 \mathrm{mL} \) of
\( 0.005 M B a C l_{2} \) to \( 16.0 \mathrm{mL} \) of arsenious
sulphide sol just causes the complete coagulation in 2 h. The flocculating value of the effective ion is:
A . 3.0
B . 2.
c. 1.0
D. 0.5


What are monosaccharides?


\( 4.9 g \) of \( H_{2} S O_{4} \) is present in \( 100 m L \) of the solution. What is the molarity of the
solution? Calculate its normality also.


When some liquid evaporates, the average speed of the molecules
remaining will
A. Increase because the more energetic molecules have left
B. Decrease because the more energetic molecules have left
c. Remain unchanged because all molecules have about the same speed
D. Increase because there are fewer molecules


Fill in the blank space shown in the
image of groundwater process.
A. Infiltration
B. Absorption
C. Diffusion
D. Sedimentation


In a \( D C \) generator, the induced e.m.f, in
the armature is
A \( . D C \)
в. \( A C \)
c. Fluctuating \( D C \)
D. Both \( A C \) and \( D C \)


Choose the correct statement:
A. Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.
B. The difference of two sides of a triangle is equal to the third side.
C. The sum of the three sides of a triangle is less than the sum of its three medians.
D. If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.


If the equation \( (10 x-5)^{2}+(10 y- \)
4)\( ^{2}=\lambda^{2}(3 x+4 y-1)^{2} \) represents a
hyperbola, then :
A \( .-2<\lambda<2 \)
B \( . \lambda>2 \)
c. \( \lambda<-2 \) or \( \lambda>2 \)


1200 men can finish a stock of food in
35 days. How many more men should
join them so that the same stock may
last for 25 days?


At which stage of mitosis, the two daughter chromatids separate from each other, migrate towards the opposite poles and are now referred to as chromosomes of the future daughter nuclei?
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


If the amplitude of two light waves is 1
and 2 units respectively then the average intensity will be
A. 3 units
B. 1 units
c. 5 units
D. \( \sqrt{3} \) units


The bond energies of \( F_{2}, C l_{2}, B r_{2}, \) and
\( I_{2} \) are \( 155 \mathrm{kJ} \) mol \( ^{-1}, 244 \mathrm{kJ} \mathrm{mol}^{-1}, 193 \)
kJ \( m o l^{-1} \) and 151 kJ \( m o l^{-1} \) respectively. The weakest bond will be in:
A. \( B r_{2} \)
в. \( C l_{2} \)
\( c \cdot F_{2} \)
D. \( I_{2} \)


\( O_{2} \) is paramagnetic in nature because it has two unpaired electrons. if true enter 1 , else enter 0
\( A \)


Brownian movement explains the property of colloidal solutions


Consider the following events for a family with children
\[
A=\{o f \text { both sexes }\} ; B=
\]
\( \{a t \text { most one boy }\} \)
In which of the following (are/is) the events \( A \) and \( B \) are independent
(a)If a family has 3 children
(b) If a
family has 2 children Assume that the birth of a boy or a girl is equally likely mutually exclusive and exhaustive


If \( i \) is the angle of incidence, the angle
between the incident wave front and the
normal to the reflecting surface is
\( \mathbf{A} \cdot i \)
B. \( 90^{\circ}-i \)
\( \mathbf{c} \cdot 90^{\circ}+i \)
D . \( i-90^{\circ} \)


The force \( F \) is exerted on a particle of mass 5 kg. If the particle starts from rest from origin and its position after 3
s is \( (4.5 \hat{i}+13.5 \hat{j}) m, \) then find \( \vec{F} \).
A \( \cdot(5 \hat{i}+13.5 \hat{j}) N \)
B . \( (5 \hat{i}+15 \hat{j}) N \)
c. \( (5 \hat{i}+13 \hat{j}) N \)
D. \( (15 \hat{i}+5 \hat{j}) N \)


Fatty acid and glycerol are first taken up from alimentary canal by
A. villi
B. Blood capillaries
c. Hepatic portal vein
D. Lymph vessels


a. Write additive inverse of \( \frac{2}{8} \) and \( \frac{-6}{-5} \)
b. Write multiplicative inverse of
\( -13 a n d \frac{-13}{19} \)


Which of the following hormones
contains iodine?
A. Insulin
B. Thyroxine
c. Adrenaline
D. Testosterone


Construct a cyclic quadrilateral PQRS
\( \operatorname{given} P Q=5 \mathrm{cm}, Q R=4 \mathrm{cm} \)
\( \angle Q P R=35^{\circ} \) and \( \angle P R S=70^{\circ} \)


When sound wave is refracted from air
to water, which of the following will remain unchanged?
A. wave number
B. wavelength
c. wave velocity
D. frequency


Define capacitor reactance. Write its S.I.
units


The correctly reported answer of the addition of 154.21,6.142 and 23 will be:
A. 183.352
B. 183.35
\( c \cdot 183.4 \)
D. 183


Write the inclination of a line which is
perpendicular to x-axis.


Which among these is required in the experiment to measure Gravitational Constant?
This question has multiple correct options
A. 2 big spheres
B. 2 small spheres
c. a rod
D. physical balance


Consider the ester benorylate (an
analgesic) shown below.
The correct statement regarding the
rate of base-catalyzed hydrolysis of
benorylate is:
This question has multiple correct options
A . a nitro group substitution at \( C 4 \$ \) will increase the rate
B. a methoxy group substitution at \( C 4 \) will decrease the rate
c. a nitro group substitution at \( C 4 \) will decrease the rate
D. a methoxy group substitution at \( C 4 \) will increase the rate


Identify the decimal and whole number
from the following.
\( \mathbf{1 . 2 1} \)


The terms \( \frac{1}{\sqrt{5}+\sqrt{6}}, \frac{1}{\sqrt{6}+\sqrt{4}}, \frac{1}{\sqrt{4}+\sqrt{5}} \) are in
\( A \cdot A \cdot P \)
B. G.P.
c. н.P
D. A.G.P.


The number of structural and
configurational isomers of a bromo
compound \( C_{5} H_{9} B r, \) formed by the addition of HBr to 2-pentyne respectively are :
A. 1 and 2
B. 2 and 4
c. 4 and 2
D. 2 and 1


\( 4 \frac{1}{3}+5 \frac{2}{3}= \)
A \( \cdot \frac{13}{3} \)
B. 30
c. \( \frac{14}{3} \)
D. 10


Assertion
The mass number of an atom is the
sum of number of protons and neutrons it contains.
Reason
The mass number of an atom can never
be smaller than the atomic number.
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 condition that the chord \( x \cos \alpha+ \)
\( \boldsymbol{y} \sin \boldsymbol{\alpha}-\boldsymbol{p}=\mathbf{0} \) of \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{a}^{2}=\mathbf{0} \) may
subtend a right angle at the centre of the circle is
A \( \cdot a^{2}=2 p^{2} \)
B \( \cdot p^{2}=2 a^{2} \)
c. \( a=2 p \)
D. \( p=2 a \)


Give a brief account on absorption of
food in small intestine.


A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 \( \mathrm{mm} \) at \( 300 \mathrm{K} . \) The vapour pressure of propyl alcohol is \( 200 \mathrm{mm} \). If the mole
fraction of ethyl alcohol is \( 0.6, \) its vapour pressure(in \( \mathrm{mm} \) ) at the same temperature will be:
A . 350
в. 300
c. 700
D. 360


Using dimensional anaysis,shown that the kinetic energy of a body of mass \( \mathrm{m} \)
moving with a velocity v varies as \( m v^{2} \)


The change in volume \( V \) with respect to
an increase in pressure P has been
shown in the adjoining figure for a non-
ideal gas at four different temperatures
\( T_{1}, T_{2}, T_{3} \) and \( T_{4} . \) The critical
temperature of the gas is:
A \( \cdot T_{1} \)
\( \mathbf{B} \cdot T_{2} \)
\( c \cdot T_{3} \)
\( \mathbf{D} \cdot T_{4} \)


A chord attached to a vibrating form divides it into 6 loops, when its tension
is \( 36 N . \) The tension at which it will
vibrate in 4 loops is
A \( .24 N \)
в. \( 36 N \)
\( c \cdot 64 N \)
D. \( 81 N \)


The planets revolve round the sun in orbits.
A. circular
B. spiral
c. elliptical
D. helical


Four particles having masses \( \mathrm{m}, 2 \mathrm{m}, 3 \mathrm{m} \) and \( 4 \mathrm{m} \) are placed at the four corners
of a square of edge a. Find gravitational force acting on a
particle of mass \( \mathrm{m} \) place at the center.


A stone us dropped into a well of \( 20 m \)
deep. Another stone is thrown downward
with velocity \( v \) one second later. If both
stones reach the water surface in the
well simultaneously \( v \) is equal to \( (g= \) \( \left.10 m s^{-2}\right) \)
A \( \cdot 30 m s^{-1} \)
B. \( 15 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


What is the value (including the sign) of the electron gain enthalpy or electron
affinity of \( N a^{+} \) ion in electron -volts?
The first ionization potential for Na is \( 118 \mathrm{k} \) cal/mole.


The lines \( p\left(p^{2}+1\right) x-y+q=0 \) and
\( \left(p^{2}+1\right)^{2} x+\left(p^{2}+1\right) y+2 q=0 \) are
perpendicular to a common line for:
A. exactly one value of
B. exactly two values of \( \mathrm{p} \)
C. more than two values of \( \mathrm{p} \)
D. no value of


The degree of ionisation does not
depend upon:
A. its nature
B. its volume
c. its dilution
D. its temperature


The characteristics of hydrogen resemble the elements of \( _{-1-} \) as well
A. IIA and VA
B. IIIA and VIA
c. IIA and VIA
D. IA and VIIA


Find the conjugate of \( \frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)} \)


The distance of point (-1,-5,-10) from the point of intersection of \( \frac{x-2}{3}=\frac{y+1}{4}=\frac{-2}{12} \) and plane \( x \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) is :
A . 10
B. 8
\( c \cdot 2 \)
D. 13


There are four complexes of Ni. Select the complex(es) which will be attracted by a magnetic field.
(1)\( \left[N i(C N)_{4}\right]^{2-} \)
(II) \( \left[N i C l_{4}\right]^{2-} \)
\( \left[N i(C O)_{4}\right] \quad(I V)\left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)
A. I only
B. IV only
c. ॥, Ill and IV
D. II and IV


Find the coordinates of the points of trisection of the line segment joining (1,-2) and (-3,4)


On what factor does the resistance of a
material depend? Define resistivity.


Arrange the following monomers in order of decreasing ability to undergo cationic polymerisation.
\( \mathbf{I} . \boldsymbol{C} \boldsymbol{H}_{\mathbf{2}}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{4}}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right) \)
\( \| . C H_{2}=C H-C_{6} H_{4}\left(C H_{3}\right) \)
\( \| I \cdot C H_{2}=C H-C_{6} H_{4}\left(O C H_{3}\right) \)
A. \( I>I I>I I I \)
В. \( I I>I>I I \)
c. \( I I I>I I>I \)
D. \( I>I I I>I I \)


For \( x \in R, \) the range of the given expression \( \frac{x^{2}+34 x-71}{x^{2}+2 x-7} \) is


Standard deviation of four observations
-1,0,1 and \( k \) is \( \sqrt{5} \) then \( k \) will be?
A \( \cdot 2 \sqrt{6} \)
B.
\( c \cdot 2 \)
D. \( \sqrt{6} \)


Two charges \( +5 \mu C \) and \( -5 \mu C \)
separated by \( 4 m m \) form an electric dipole. The dipole is placed in a uniform
electric field of \( 4 \times 10^{5} N / C . \) The work
done in rotating the electric dipole
through \( 180^{\circ}, \) if it starts from the
positions of \( \boldsymbol{\theta}=\mathbf{0} \) is
A. \( 4 m J \)
в. \( 8 m J \)
c. \( 12 m J \)
D. \( 16 m J \)


The resistivity of a conductor with a
current density of \( 2.5 A m^{-2} \) when an
electric field \( 5 \times 10^{-8} V m^{-1} \) is applied
to it, is
A \( \cdot 1.0 \times 10^{-8} \Omega m \)
в. \( 2.0 \times 10^{-8} \Omega \) т
\( \mathbf{c} \cdot 0.5 \times 10^{-8} \Omega m \)
D. \( 12.5 \times 10^{-8} \Omega m \)


Which part of eye is transplanted?
A. cornea
B. Pupil
c. Retina
D. All


Define Raoult's law for the elevation of
boiling point of a solution.


can be one of the term in
Arithmetic progression 4,7,10
A. 103
B. 123
c. 17
D. 99


mounted on one end of a balance beam
and introduced between the poles of an
electromagnet as shown in fig. The area
of the coil is \( S=1 c m^{2}, \) the length of the
right arm of the balance beam is \( l= \)
\( 30 \mathrm{cm} . \) When there is no current in the
coil the balance is in equilibrium. On
passing a current \( I=22 m A \) through
the coil, equilibrium is restored by
putting an additional weight of mass
\( \boldsymbol{m}=\mathbf{6 0} \mathrm{mg} \) on the balance pan. Find the
magnetic induction field (in terms of
\( \left.\times 10^{-1} T\right) \) between the poles of the electromagnet, assuming it to be uniform:


Which of the following are done to
increase friction?
A. Greasing the machines
B. Treanding the tyres
c. sprinkling powder on the carom board
D. All of the above


A cord is used to lower vertically a block
of mass \( M \) by a distance \( d \) with
constant downward acceleration \( \boldsymbol{g} / \mathbf{4} \) Work done by the cord on the block is:
A \( \cdot_{M g} \frac{d}{4} \)
в. \( 3 M g \frac{d}{4} \)
c. \( _{-3 M g_{\overline{4}}^{d}} \)
D. \( M g d \)


The commonly used barometric liquid
in a barometer is


Electrons traveling at a velocity of
\( 2.4 \times 10^{6} m s^{-1} \) enter a region of cross
electric and magnetic fields as shown in fig. If the electric field is \( 3.0 x \)
\( 10^{6} V m \) and the flux density of the
magnetic field is \( 1.5 \mathrm{T} \), the electron upon
entering the region of the crossed fields
will
A. continue to travel undeflected in their original direction
c. be deflected downward on the plane of the diagram
D. none of the above


The correct match forcolumn A given in
column B is
\begin{tabular}{llll}
Sr.No & Column I & Sr.No & Column \\
1. & Nylon-6 & a. & Zeigler N catalyst \\
2. & Novolac & b. & Peroxide catalyst \\
3. & High-density polythene & c. & Condens. athighT P \\
4. & Polyacrylonitrile & d. & catalyzec an acid-ter \\
\hline
\end{tabular}
A. \( 1-d, 2-a, 3-c, 4-b \)
B. \( 1-a, 2-c, 3-b, 4-d \)
c. \( 1-c, 2-d, 3-a, 4-b \)
D. \( 1-b, 2-c, 3-a, 4-d \)


The decomposition of certain mass of
\( \mathrm{CaCO}_{3} \) gave \( 11.2 \mathrm{dm}^{3} \) of \( \mathrm{CO}_{2} \) gas at
STP. The mass of KOH required to completely neutralise the gas is :
A. \( 56 g \)
в. 28 \( g \)
c. 42 g
D. 20


The concentration of \( Z n^{2+} \) in first
compartment after passage of \( 0.1 F \)
charge will be:
A \( .1 ~ M \)
В. 1.05 М
c. 1.025 М
D. \( 0.5 ~ M \)


A radar sends a signal to an aircraft at a distance of \( 30 k m \) away and receives it
back after \( 2 \times 10^{-4} \) second. What is the
speed of the signal?


What is the order of increasing heat of hydrogenation for the following
compounds (lowest first)?
\( \mathbf{A} \cdot|,| 1,|1|, 1 V \)
B. II, IV, I, III
c. ।, ॥ा, IV, ॥
D. IV, II, III, ,


The jawless vertebrate is
A. Crocodile
B. Loris
c. Hyla
D. Fox
E. Petromyzon


Sea weeds are an important source of :
A. Iron
B. Chlorine
c. lodine
D. Bromine


The number of arbitarary constants in the solution of a differential equation of
degree 2 and order 3 is:
\( A \cdot 2 \)
B. 3
\( c \cdot 5 \)
D.


Find the equation of tangents to the hyperbola \( 3 x^{2}-4 y^{2}=12, \) which make
equal intercepts on the axes.


Classify the following salts as acid
salt or normal salt:
(a) \( N a H_{2} P O_{3} \)


The radii of the press plunger and the pump plunger are in the ratio \( 30: 4 . \) If
an effort of \( 32 k g f \) acts on the pump
plunger. Find the maximum effort the press plunger can overcome. ( in kgf)


The unit of rate constant for a second
order reaction is:
A . lit.sec
B. lit.mole.sec
c. moles \( ^{-1} . \) lit.sec \( ^{-1} \)
D. moles.sec


Polymerisation may occur through
intermediate formation
of
This question has multiple correct options
A. carbocations
B. carbanions
c. free radicals
D. carbenes


If \( A \) and \( B \) are two objects with masses
100 kg and 200kg respectively, then which object will have less inertia?
A . \( 200 k g \)
в. \( 100 k g \)
c. Both
D. None


Electrolysis of water is carried out in hoffman voltameter. Litmus is added to
both cathodic and anodic
compartments.What changes do you observe in the above process at the end of electrolysis? Justify.


How is the velocity of thermal radiations ( \( v \) ) related to the velocity of
light \( (c) ? \)
\( \mathbf{A} \cdot v<c \)
В \( . v>c \)
\( \mathbf{c} \cdot v=c \)
D. the relation depends upon the wavelength of the radiations


The mass of earth is 80 times that of
moon and its diameter is double that of
moon. If the value of acceleration due to
gravity on earth is \( 9.8 m s^{-2} \) then the
value of acceleration due to gravity on
moon will be?
A \( \cdot 0.98 \mathrm{ms}^{-2} \)
В. \( 0.49 \mathrm{ms}^{-2} \)
c. \( 9.8 \mathrm{ms}^{-2} \)
D. \( 4.9 \mathrm{ms}^{-2} \)


Energy enters a food chain through
A. Producers
B. Decomposers
c. Herbivores
D. Carnivores


A student has performed an experiment in the laboratory. He mixed water with hexane and found two layers separated. A second time he mixed chloroform with
water and he again found two layers in the test tube. Explain which will be an
upper layer and which one will be a lower layer in both the experiments.


State whether the statement is
true/false.
The lines \( 2 x+3 y=19 \) and \( 2 x+3 y+ \)
\( \mathbf{7}=\mathbf{0} \) are not equidistant from the line
\( 2 x+3 y=6 \)
A. True
B. False


The hybridizations of \( N i(C O)_{4} \) and
\( \boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}^{2+}, \) respectively, are:
A \( \cdot s p^{3} \) and \( d^{3} s p^{2} \)
B. \( d s p^{2} \) and \( d^{2} s p^{3} \)
c. \( s p^{3} \) and \( d^{2} s p^{3} \)
D. \( d s p^{2} \) and \( s p^{3} d^{2} \)


Study the given statements about gymnosperms and select the correct
option.
(i) Mode of fertilisation is siphonogamy.
(ii) Male and female cones are borne on same tree in Pinus
(iii) Endosperm represents female gametophyte.
A. Statements (i) and (ii) are correct
B. Statements (ii) and (iii) are correct
c. Statements (i) and (iii) are correct.
D. Statements (i), (ii) and (iii) are correct.


A beam of light striking the surface of a
glass plate from the air as shown in
above figure.
If the angle between reflected beam and
refracted beam is 90 degree, Find out
the index of refraction of the glass?
\( A \cdot \sin 55^{\circ} \)
B. \( \frac{1}{\sin 55^{\circ}} \)
c. \( \frac{1}{\sin 35^{\circ}} \)
D. \( \frac{\sin 55^{\circ}}{\sin 35^{\circ}} \)
E \( \cdot \frac{\sin 35^{\circ}}{\sin 55^{\circ}} \)


The vapour pressure of pure water is
\( 23.8 \mathrm{mm} \mathrm{Hg} \) at \( 25^{0} \mathrm{C} \) What is the vapour
pressure of 2.50 molal \( C_{6} H_{12} O_{6} \)


The intensity falls as we move to
successive maxima away from the centre on either side.


If a large number of people are enclosed
in a room, then
A. Oxygen decreases and carbon dioxide increases
B. Oxygen increases and carbon dioxide decreases
C. Both oxygen and carbon dioxide decrease
D. Both oxygen and carbon dioxide increase


N-methyl aniline is a stronger base
than aniline
Write True or False.


and we (i) (i)


Alisha has Rs 4900 with her and spends
\( 36 \% \) of it on groceries. How much money is left with her
A . Rs 1764
B. Rs 3136
c. Rs 3276
D. Rs 3336


A body of \( 6 k g \) rests in limiting equilibrium on an inclined plane whose
slope is \( 30^{\circ} . \) If the plane is raised to
slope of \( 60^{\circ}, \) then force \( (\operatorname{in} k g-w t) \)
along the plane required to support it is
A . 3
B. \( 2 \sqrt{3} \)
\( c \cdot \sqrt{3} \)
D. \( 3 \sqrt{3} \)


Evaluate:
\( \int_{-1}^{1} \sin ^{5} x \cos ^{4} x d x \)


State whether true or false.
One mega watt is 10 times that of one kilowatt.
A. True
B. False


Explain saponification of oils/fats with
equation.


Find the adjoint of \( \left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right] \)


Acid rain pollutes:
This question has multiple correct options
\( A \). air
B. water
c. soil
D. all of these


A magnetic field of flux density 10 T acts normal to a coil of 50 turns having 100 em-area. The e.m.f. induced if the coil is
removed from magnetic field in \( 0 . \) second is:
A. \( 50 v \)
B. 60V
\( c \cdot 80 v \)
D. 40v


Match molecules/ions (in List \( \boldsymbol{I} \) ) with
their shapes \( (\text {in } \boldsymbol{L i s t} \boldsymbol{I} \boldsymbol{I}) \)


In a certain region of space, there exists
a uniform electric field of \( 2 \times \) \( 10^{2} \hat{k} V m^{-1} . \) A rectangular coil of
dimension \( 10 \mathrm{cm} \times 20 \mathrm{cm} \) is placed in
\( \boldsymbol{x}-\boldsymbol{y} \) plane. The electric flux through
the coil is
A. zero
в. \( 30 \mathrm{Vm} \)
c. \( 40 \mathrm{Vm} \)
D. \( 50 \mathrm{Vm} \)


In a triangle \( A B C, \) with usual notations, if \( \left|\begin{array}{ccc}1 & a & b \\ 1 & c & a \\ 1 & b & c\end{array}\right|=0, \) then \( 4 \sin ^{2} A+ \)
\( 24 \sin ^{2} B+36 \sin ^{2} C \) is equal to
A . 48
B. 50
c. 44
D. 34


Assertion
\( \boldsymbol{T} e \boldsymbol{B} \boldsymbol{r}_{4} \) and \( \boldsymbol{P o} \boldsymbol{B r}_{4} \) are quite stable
while \( S B r_{4} \) and \( S e B r_{4} \) are unstable
Reason
Inert pair effect is greater in tetra bromides of \( S \) and \( S e \) than in \( T e \) and
Po.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which term of the A.P. \( 3,15,27,39, \dots \)
will be 132 more than its \( 54^{t h} \) term?


In which organ the digestion of protein starts in the human digestive tract?
A. Mouth
B. Oesophagus
c. Stomach
D. Small intestine


Jaundice is a disease of
A. Kidney
B. Liver
c. Pancreas
D. Duodenum


\( \boldsymbol{P t}\left|\boldsymbol{O}_{2}(\boldsymbol{g}, \boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{C l}^{-}(\boldsymbol{1} \boldsymbol{M}) \mid \)
For the given cell, the cell reaction is:


A body of mass \( 3 \mathrm{kg} \) is under a force, which causes a displacement in it given by \( S=\frac{t^{3}}{3}\left(\text { in }^{\prime} m^{\prime}\right) . \) Find the work
done by the force in first 2 seconds.


Show that each of the relation \( R \) in the
\( \operatorname{set} A=\{x \in Z: 0 \leq x \leq 12\}, \) given by
is an equivalence relation. Find the set of all elements related to 1 in each case
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}=\boldsymbol{b}\} \)


If charge density of an infinite charged plate is doubled and the distance of
point charge is tripled from the infinite charged plate, then electric field is increased \( _{\text {thes }} \)


If \( \mathbf{A} \) is an unitary matrix then \( |\boldsymbol{A}| \) is
equal to:
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c .\pm 1 \)
D. 2


Which of the following were released during accidental leakage in Chernobyl, the three-mile island?
A . Low-level radiations
B. Intermediate level radiation
c. High level radiation
D. No radiations were released


Myelin sheath is a layer covering
A. A nerve fibre in a vertebrate
B. A chick embryo
c. A muscle fibre in a vertebrate
D. None of the above


Which of the following does not depict
the correct link between technology and physics.?
A. Photocell - Photoelectric effect
B. Rocket propulsion - Laws of thermodynamics
c. optical fibres - Total internal reflection of light
D. Fusion test reactor - Magnetic confinement of plasma


The angle between the internal bisector and the external bisector of an angle is:
\( \mathbf{A} \cdot 60 \)
B. 90
\( c \cdot 120 \)
D. 135


Cretinism in young children is due to hyposecretion of
\( A \). Vitamin D
B. Growth hormone
c. calcitonin
D. Thyroxine


If a proton is completely converted into the energy, then the energy produced will be:
A. \( 0.51 \mathrm{MeV} \)
B. 1.02 MeV
c. \( 185 \mathrm{MeV} \)
D. 932 MeV


A ship \( A \) is moving westward with a speed of \( 10 k m h^{-1} \) and a ship \( B 100 k m \) south of \( A \) is moving northwards with a speed of \( 10 \mathrm{km} \mathrm{h}^{-1} \) The time after which the distance
between them becomes shortest is:
A. \( 5 \sqrt{2} h \)
hon
В. \( 10 \sqrt{2} h \)
\( c \cdot 1 h \)
D. \( 5 h \)


\( \boldsymbol{O H} \)
\( \boldsymbol{C H}_{3}-\dot{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\stackrel{\boldsymbol{O}}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{H} \)
The IUPAC name of the compound is
A. 2 - Hydroxypentan - 4 - one
B. 4 - Hydroxypentan - 2 - one
c. 4 - oxopentan -2 - ol
D. 2 - oxopentan \( -4- \) o


The product of two numbers is 120 and the sum of their squares is \( 289 . \) The sum of the numbers is :
A . 20
B. 23
\( c \cdot 16 \)
D. None of these


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


Tin cans, used for storing food are made by electroplating:
A. chrome onto tin
B. iron onto tin
c. tin onto iron
D. chrome onto iron


Which compound is used in photography?
A \( . A g N O_{3} \)
в. \( A g O \)
c. \( A g B r \)
D. \( A g C l \)


Find the lateral or curved surface area
of a closed cylindrical petrol storage tank that is \( 4.2 m \) in diameter and
\( 4.5 m \) high.


Find which of the number of the form
\( \left(n \pi-t a n^{-1} 3\right), \) where \( n \epsilon l, \) are
solution for \( 12 \tan 2 x+\frac{\sqrt{10}}{\cos x}+1=0 \)
\( \mathbf{A} \cdot n=k, k \epsilon z \)
B. \( n=(3 k+1), k \epsilon z \)
c. \( n=(2 k+1), k \epsilon z \)
D. \( n=(4 k+1), k \epsilon z \)


A sheet of \( 15.0 g \) of gold at \( 25.0 C \) is
placed on a \( 30.0 g \) sheet of copper at \( 45.0 C . \) What is the final temperature of
the two metals assuming that no heat is lost to the surroundings. The specific heats of gold and copper are
\( 0.129 J / g C \) and \( 0.385 J / g C \)
respectively.


What is the average sales of laptop of all the states (in hundred numbers) for
the year \( 2005 ? \)
laptop
A .12 .24
В. 13.14
\( c .14 .45 \)
D. 15.23


\( \cos ^{-1}\left(\cos \left(\frac{5 \pi}{4}\right)\right) \) is given by
\( \mathbf{A} \cdot 5 \pi / 4 \)
B . \( 3 \pi / 4 \)
\( \mathbf{c} .-\pi / 4 \)
D. None of these


The sum of three expressions is \( x^{2}+ \) \( y^{2}+z^{2} . \) If two of them are \( 4 x^{2}-5 y^{2}+ \)
\( 3 z^{2} \) and \( -3 x^{2}+4 y^{2}+2 z^{2}, \) the third
expression is
A \( \cdot 2 x^{2}+2 z^{2} \)
в. \( 2 y^{2} \)
c. \( 2 x^{2}+2 y^{2}-z^{2} \)
D. \( 2 y^{2}-4 z^{2} \)


In which of the following pairs of solutions will the values of the Van't
Hoff factor be the same?
A \( \cdot_{0.05} \) M \( K_{4}\left[\text { Fe }(C N)_{6}\right] \) and 0.10 M FeSO\( _{4} \)
B. 0.20 М NaCl and 0.10 М Ва С\( l_{2} \),
c. \( _{0.05} \) M FeSO\( _{4}\left(N H_{4}\right)_{2} \) SO\( _{4} \). \( 6 H_{2} \) O and 0.02 M
КСl.М \( g C l_{2} .6 H_{2} O \)
D. All have same value


Prove that:
\( 2 \tan ^{-1}\left(\frac{1}{5}\right)+\sec ^{-1}\left(\frac{5 \sqrt{2}}{7}\right)+ \)
\( 2 \tan ^{-1}\left(\frac{1}{8}\right)=\frac{\pi}{4} \)


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\left(\frac{3}{\sqrt{1-a^{2}}}+1\right) \)


Find the value of \( k \) is continuous at \( x= \)
where
2
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{\boldsymbol{k} \cos \boldsymbol{x}}{\boldsymbol{\pi}-\mathbf{2} \boldsymbol{x}}, \text { if } \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\mathbf{2}} \\ \boldsymbol{3}, \quad \text { if } \boldsymbol{x}=\frac{\boldsymbol{\pi}}{2}\end{array}\right. \)


If \( A=\{a, b, c, d, e\}, B=\{a, c, e, g\} \) and \( C= \)
\( \{b, d, e, g\} \) then which of the following is
true?
A \( \cdot C \subset(A \cup B) \)
B . \( C \subset(A \cap B) \)
c. \( A \cup B=A \cup C \)
D. Both(1) and (3)


Vulture, hyena and eagle are examples
of
A. Producers
B. Herbivores
c. Decomposers
D. Scavengers


Write the structures of the following:
(i) \( \boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{3} \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)


Square of any -ve integer is
A. Negative
B. Positive
\( c \cdot 0 \)
D. none of these


Vivekbhai bought a TV for Rs \( 16,000 . \) Rs 200 was spent on transportation and labour. For earning 12 \% profit, what price should it be sold?
A. \( R s 30,144 \)
B. \( R s 18,144 \)
c. \( R s 20,144 \)
D. None of these


Yellow precipitate in the detection of phosphorous when an organic
compound is heated with \( N a_{2} O_{2} \) and
then boiled with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) followed
by the addition of ammonium molybdate is due to the formation
of
A \( \cdot\left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 12 M o O_{3} \)
B . \( \left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 6 M o O_{3} \)
c. \( \left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 12 M o O_{2} \)
D. \( \left(N H_{4}\right)_{3} P O_{4} \cdot 6 M o O_{2} \)


What is WBC, RBC and platelet?


\( 3.2 \mathrm{g} \) sulphur combines with \( 3.2 \mathrm{g} \) of oxygen to form a compound in one set of conditions. In another set of conditions,
\( 0.8 \mathrm{g} \) of sulphur combines with \( 1.2 \mathrm{g} \) of oxygen to form another compound. State the law illustrated by these
chemical combinations.
A. Law of constant composition
B. Law of reciprocal proportion
c. Law of multiple proportion
D. None of the above


The false foot in amoeba is known as
A. Pseudopodia
B. Food vacuole
c. water vacuole
D. None of the above


A liquid disturbed by stirring comes to rest after sometime due to its property
of
A. compressibility
B. diffusion
c. viscosity
D. all of these


The total vapour pressure of a mixture of 1 mol \( A\left(P_{A}^{O}=150 \text { tor } r\right) \) and 2 mol \( B \)
\( \left(P_{B}^{o}=240 \text { tor } r\right) \) is \( 200 \mathrm{mm} . \) In this
case:
A. there is positive deviation from Raoult's law
B. there is negative deviation from Raoult's law.
c. there is no deviation from Raoult's law
D. molecular masses of A and B are also required.


Find the equation of the hyperbola satisfying the give conditions: Foci
(0,±13) the conjugate axis is of length
\( \mathbf{2 4} \)


A particle executes SHM whose instantaneous displacement is given by \( \boldsymbol{x}=\boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\pi} / 2) . \) What will be its
acceleration at \( t=T / 4 \)
\( \mathbf{A} \cdot a=0 \)
B . \( a=2 \omega^{2} A \)
\( \mathbf{c} \cdot a=\omega^{2} A \)
D. \( a=\omega^{2} A / 2 \)


The word cytokinin which induces cell
division was given by
A. Yabuta
B. Brown
c. Letham
D. Fitting


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \) is a
A. monomer
B. polymer
c. isomer
D. equimer


A body of mass \( 3 \mathrm{kg} \) collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body?
\( A \cdot 1 \mathrm{kg} \)
B. 2.5 \( \mathrm{kg} \)
\( c \cdot 2 k g \)
\( D .5 \mathrm{kg} \)


Which of the following are correct
statements?

This question has multiple correct options
A. In less acidic solution \( K_{2} C r_{2} O_{7} \) and \( H_{2} O_{2} \) gives violet
coloured diamagnetic \( \left[\mathrm{CrO}\left(\mathrm{O}_{2}\right)(\mathrm{OH})\right]^{-} \) ion
B. In alkaline \( H_{2} O_{2}, K_{2} C r O_{8} \) (with tetraperoxo species \( \left.\left[C r O\left(O_{2}\right)(O H)\right]^{3-}\right) \) is formed
C. In Ammoniacal solution, \( \left(N H_{3}\right) C r O_{4} \) is formed
D. \( C r O_{4}^{2-} \) changes to \( C r_{2} O_{7}^{2-} \) by oxidation


Consider air to be a diatomic gas with
average mole moasses \( 29 \mathrm{g} / \mathrm{mole} . \) A mass \( 1.45 \mathrm{kg} \) of air is contained in a
cylinder with a piston at \( 27^{0} C \) and
pressure \( 1.5 \times 10^{5} N / m^{2} . \) Energy is
given to the system as heat and the system is allowed to expand till the fina
pressure \( 3.5 \times 10^{5} N / m^{2} . \) As the gas
expands, pressure and volume follow
the relation
\( \boldsymbol{V}=\boldsymbol{K} \boldsymbol{P}^{2} \) where \( \mathrm{K} \) is constant \( (\mathrm{R} \)
\( =8.3 \mathrm{J} /(\mathrm{mole}-\mathrm{K}) \)
Which solutionn.will give a white ppt.
when either dil. \( H C l \) or dil. \( H_{2} S O_{4} \) is
added to it?


A hemisphere and a solid cone have a
common base. The center of mass of the
common structure coincides with the
centre of the common base. If \( \boldsymbol{R} \) is the
radius of hemisphere and \( h \) is height of
the cone then:
A \( \cdot \frac{h}{R}=\sqrt{3} \)
в. \( \frac{h}{R}=\frac{1}{\sqrt{3}} \)
c. \( \frac{h}{R}=3 \)
D. \( \frac{h}{R}=\frac{2}{\sqrt{3}} \)


Bat is a mammal because
A. Bats have wings like birds
B. Bats have tail like other mammals
C. Bats have milk-secreting gland
D. Bat is a cold blooded animal


A uniform disc of mass \( M \) and radius \( R \)
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and
a steady downward pull \( T \) is exerted on
the cord. If we hang a body of mass \( m \) with the cord, the tangential acceleration of the disc will be
A. \( \frac{m g}{M+m} \)
в. \( \frac{m g}{M+2 m} \)
c. \( \frac{2 m g}{M+2 m} \)
D. \( \frac{M+2 m}{2 m g} \)


A rubbed comb can lift paper pieces.
why?


Available chlorine in a good sample of bleaching powder is:
A . 75\%
B. 20-25\%
c. 50-75\%
D. 35-38\%


Which solid dissolve exothermically in
water?
A. \( N a C l \)
в. \( C a O \)
\( \mathbf{c} \cdot N H_{4} N O_{3} \)
D. \( C u S O_{4} \)


\( \frac{\sqrt{1}}{\frac{1}{x}} \)


Bohr modified the adding that the electrons move in orbits
of fixed size and energy.
A. Rutherford's model
B. Dalton's model
c. chadwick's model
D. Goldstein's model


Two south poles each of pole strength 16 A m are placed at corners \( P, R \) of a square PQRS. The pole that should
placed at 'Q' to make S as null point is :
A. South pole of pole strength 32 A m
B. South pole of pole strength \( 32 \sqrt{2} \) A \( m \)
c. North pole of pole strength 32 A m
D. North pole of pole strength \( 32 \sqrt{2} \) A \( m \)


Heating of sugar solution is a chemical
change. State whether the statement is true or false
A. True
B. False
c. Either
D. Neither


The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure
difference across the ends) \( ^{n} \) and
(average velocity of the liquid ) \( ^{m} \). Which
of the following relations between \( \boldsymbol{m} \)
and \( n \) is correct?
A \( . m=n \)
B. \( m=-n \)
c. \( m^{2}=n \)
D. \( m=-n^{2} \)


The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
\( A \cdot 1: 2 \)
B. 1:3
\( c .3: 2 \)
D. None of these


In Young's double slit experiment, when
wavelength used is \( 6000 A \) and the
screen is \( 40 \mathrm{cm} \) from the slits, the
fringes \( 0.012 \mathrm{cm} \) wide. What is the distance between the slits?
A \( .0 .24 \mathrm{cm} \)
B. \( 0.2 \mathrm{cm} \)
\( \mathrm{c} \cdot 2.4 \mathrm{cm} \)
D. \( 0.024 \mathrm{cm} \)


Alkyl halides are immiscible in water
though they are polar because?
A. they react with water to give alcohols
B. they cannot form hydrogen bonds with water
C. \( C-X \) bond cannot be broken easily
D. they are stable compounds and are not reactive.


Consider the differential equation:
\( \frac{\left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}}{\frac{d^{2} y}{d x^{2}}}=c \)
Find order and degree.


An ecosystem is a
A. group of components that interact with one another
B. group of interacting chemicals and their cycles
C . group of interacting species in one place at one time
D. biologic community and components of the physical environment with which the community interacts


Which of the following are examples of
pseudo-unimolecular reactions?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O_{2} C_{2} H_{5}+H_{2} O \stackrel{H^{+}}{\longrightarrow} C H_{3} C O_{2} H+C_{2} H_{5} O H \)
\( \mathbf{B} \cdot C_{12} H_{22} O_{11}+H_{2} O \stackrel{H^{+}}{\rightarrow} C_{6} H_{12} O_{6}(g l u c o s e)+C_{6} H_{12} O_{6} \)
(fructose)
\( \mathbf{c} \cdot C H_{3} C O C l+H_{2} O \rightarrow C H_{3} C O_{2} H+H C l \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{OH}^{-}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)


Show the product of these elimination
reactions:


What are the two most common defects
of vision (or defect of eye)? How are they
corrected?


If \( \mathrm{CO}_{2} \) is absent in atmosphere of earth
then
A. Temperature will decrease
B. Temperature will increase
C. Plants will flourish well
D. No effect


\( f(\operatorname{mis} 100 g) R \) is \( 4 \mathrm{cm}, h \) is \( 10 \mathrm{cm} \) and \( \omega \)
is 10 rad/s then find the value of \( \omega \)
\( A \cdot 10 \operatorname{rad} / \)
B. 62,5 rad/s
\( c \cdot 31,25 \mathrm{rad} / \mathrm{s} \)
D. None


If \( \theta \) be the angle between the vectors \( i+ \) \( j \) and \( j+k, \) then \( \theta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D . \( \pi / 3 \)


Diploid cells have
A. Two chromosomes
B. One set of chromosomes
C. Two pairs of chromosomes
D. Two sets of chromosomes


Nitrogen dioxide is not produced on
heating:
A. \( K N O_{3} \)
B. \( P b\left(N O_{3}\right)_{2} \)
c. \( C u\left(N O_{3}\right)_{2} \)
D. \( A g N O_{3} \)


Assertion: Artificial sweeteners are
added to the food to control the intake of
calories.
Reason: Most of the artificial
sweeteners are inert and do not
metabolise in the body.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct.


Look at the given picture. Describe the
changes in the nuclear material from
stage \( A \) to stage \( B \)


The cost of a chair at a shop was Rs.220. The sales tax charged was \( 5 \% \). Calculate
the bill amount.


With regard to the exhibiting oxidation states the correct statement would be:
A. Lanthanides form largest number of oxidation states
B. Actinides form largest number of oxidation states
c. Lanthanides and actinides have almost same tendency to exhibit various oxidation states
D. Actinides exhibit least number of oxidation states


Two bodies of masres \( 1 k g \) and \( 3 k g \) have position vectors \( \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( -\boldsymbol{3} \boldsymbol{i}- \)
\( 2 \hat{j}+\hat{k} \) respectively. The centre of mass
of this system has a position vector
B . \( -2 \hat{i}-1 \hat{j}+\hat{k} \)
c. \( 2 \hat{i}-\hat{j}-2 \hat{k} \)
D. \( -\hat{i}+\hat{j}+\hat{k} \)


Maximum fats is present in seeds of
A. Arachis hypogea
B. Oryza sativa
c. Cicer arietinum
D. Hibiscus esculentus


Solve the equation obtained \( x^{2}-x- \)
\( 6=0 \) and hence find the dimensions of
the verandah. Verandah is in
rectangular shape having area and perimeter equal.
A. \( x=3 ; \) length \( =6 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)
B. \( x=3 ; \) length \( =6 \mathrm{m} \) and breadth \( =4 \mathrm{m} \)
c. \( x=3 ; \) length \( =4 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)
D. \( x=4 ; \) length \( =6 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)


Equivalent weight of \( B r_{2} \) is 96 in the following disproportionation reaction:
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{B} \boldsymbol{r}^{-}+\boldsymbol{H}_{2} \boldsymbol{O}+? \)
(oxidized product) The oxidation state of Br in the oxidized product is \( (\mathrm{Br}=80) \)


Which of the following is absent in the segment of cockroach's leg
A . Fibula
B. Coxa
c. Tibia
D. Femur


The sum of Rs. 1000 is compounded continuously, the nominal rate of interest being four percent per annum. In how many years will the amount be
twice the original principal? \( \left(\log _{e} 2=\right. \)
\( \mathbf{0 . 6 9 3 1}) \)


The perimeters of an equilateral
triangle and a square are same The area of triangle : area of square is
A . 1: 1
в. \( 4: 3 \sqrt{3} \)
c. 4: 3
D. 3: 2


Choose the correct answer from the
alternatives given
Aldosterone causes the:
A. kidneys to release renin
B. kidneys to reabsorb sodium
c. blood volume to increase
D. all of the above


\( 4^{t h} \) period ends with :
A . argon
B. neon
c. krypton
D. radon


In budding
A. Outgrowth develops earlier than nuclear division
B. Nucleus divides earlier than development of outgrowth
C. Both occur simultaneously
D. There is no fixed sequence


Which of the following activity would not be possible in the absence of
friciton?
A. holding a glass
B. writing on a paper
c. sitting on a chair
D. all of the above


Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) in each of
the reaction will be respectively:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{H}_{3} \boldsymbol{P O}_{4}+\boldsymbol{3} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{P} \boldsymbol{O}_{4}^{3-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . 98,49,32.67
B. 49, 98, 32.67
c. 98,32.67,49
D. 32.67, 49, 98


A plane electromagnetic wave in a non magnetic dielectric medium is given by \( \overline{\boldsymbol{E}}=\overline{\boldsymbol{E}}_{0}\left(\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{x}-\mathbf{5 0} \boldsymbol{t}\right) \) with
distance being in meter and time in seconds. The dielectric constant of the
medium is:
A . 5.8
B. 2.4
c. 1.6
D. 3.5


n figure, find the values of \( x, y \) and \( z \)
\( \mathbf{A} \cdot x=155^{\circ} \)
B . \( y=25^{\circ} \)
\( \mathbf{c} \cdot z=155^{\circ} \)
D. All of these


Mode of the following data.
\begin{tabular}{lllll}
Interval & \( 0- \) 20 & \( 20- \) 40 & 40-60 & 60-80 \\
Frequency & 6 & 8 & 12 & 10 \\
\hline
\end{tabular}


When hydrogen reacts with oxygen, oxygen is reduced and water is formed
A. True
B. False


A particle of mass \( m \) is moving in a circular path of constant radius r such
that its centripetal acceleration \( a_{c} \) is
varying with time \( t \) as \( a_{c}=k^{2} r t^{2}, \) where
k is a constant. The power delivered to the particle by the forces acting on it is:
A. zero
B. \( m k^{2} r^{2} t^{2} \)
\( \mathrm{c} \cdot m k^{2} r^{2} t \)
\( \mathbf{D} \cdot m k^{2} r t \)


If the two members of a Dobereiner triad
are phosphorus and antimony, the third member of this triad is :
A. arsenic
B. sulphur
c. iodine
D. calcium


What is the shape of arsenic
pentachloride?
A. Trigonal planar
B. Octahedral
c. Trigonal bipyrimidal
D. Tetrahedral


The conjugate acid of \( N H_{2}^{-} \) is:
A. \( N H_{4}^{-} \)
в. \( N H_{3} \)
c. \( N H_{2} O H \)
D. \( N_{2} H_{4} \)


Formation of phosphoenol pyruvate from 2-pliosphoglycerate is
A. Dehydration
B. Dehydrogenation
c. oxidation
D. Hydration


Body requires calcium phosphate for the formation of:
A. bones
B. tooth enamel
c. both a and \( b \)
D. none of the above


Which of the following aqueous solutions will conduct an electric
current quite well?
A . Sugar
в. нс
c. Pure water
D. Alcohol


Aluminium is obtained from \( A l_{2} O_{3} \) by
A. Thermal reduction
B. Hydro metallurgical method
c. Electrolytic reduction
D. Reduction by iron


The noble gas which has abnormal
behaviour in its liquid state
is
A . He
B. Ar
\( c \cdot x e \)
D. Ne


For the precipitation of \( A g C l \) by \( A g^{+} \)
ions and \( \boldsymbol{H} \boldsymbol{C l} \) :
A. \( \Delta H=0 \)
в. \( \Delta G=0 \)
c. \( \Delta G=-v e \)
D. \( \Delta H=\Delta G \)


Which are correct statements?
This question has multiple correct options
\( \mathbf{A} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is linear with sp hybridised \( A g^{+} \) ion.
B. \( N i C l_{4}^{2-}, V O_{4}^{3-} \) have tetrahedral geometry.
\( \mathbf{C} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+},\left[P t\left(N H_{3}\right)_{4}\right]^{2+} \) and \( \left[N i(C N)_{4}\right]^{2-} \) have
\( d s p^{2} \) hybridisation of the metal ion.
D. \( F e(C O)_{5} \) have bipyramidal structure with \( d s p^{3} \) hybridised iron.


Plant group with largest ovule, largest
tree and largest gametes is
A. Gymnosperm
B. Angiosperm
c. Bryophyta
D. Pteridophyta


\( f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1\end{array}\right| \) then
\( \lim _{x \rightarrow 0} f(x)= \)
\( A \cdot O \)
B.
\( c \cdot-2 \)
\( D \)


Consider two curves \( C_{1}: y=\frac{1}{x} \) and \( C_{2} \)
\( \boldsymbol{y}=\ln x \) on the xy plane Let \( \boldsymbol{D}_{1} \) denotes
the region surrounded by \( C_{1}, C_{2} \) and the
line \( x=1 \) and \( D_{2} \) denotes the region
surrounded by \( C_{1}, C_{2} \) and the line \( x=a \)
If \( D_{1}=D_{2} \) then the value of 'a':
A \( \cdot \frac{e}{2} \)
в.
\( \mathbf{c} \cdot e-1 \)
D. \( 2(e-1) \)


Give reasons:
p-nitro phenol is more acidic than \( p \) methyl phenol.


When hydrochloric acid is added to
cobalt nitrate solution at room
temperature, the following reaction takes place and the reaction mixture
becomes blue. On cooling the mixture, it
becomes pink. On the basis of this information mark the correct answer.
\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]_{(a q)}^{3+}+\boldsymbol{4} \boldsymbol{C l}_{(a q)}^{-} \rightleftharpoons \)
\( \left[\boldsymbol{C o C l}_{4}\right]_{(a q)}^{2-}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
A. \( \triangle H>0 \) for the reaction
B. \( \triangle H<0 \) for the reaction
c. \( \triangle H=0 \) for the reaction
D. The sign of \( \triangle H \) cannot be predicted on the basis of this information


The Sl unit of inductance, the henry, can
be written as:
A. Weber ampere \( ^{-1} \)
B. Volt-s ampere-
c. Joule ampere-
D. ohm \( s^{-1} \)


Four thin metal rods, each of mass \( M \)
and length \( L, \) are welded to form a
square. The moment of inertia of the
composite structure about a line which bisects any two opposite rods is:
\( ^{\mathrm{A}} \cdot \frac{M L^{2}}{6} \)
B. \( \frac{M L^{2}}{3} \)
c. \( \frac{M L^{2}}{2} \)
D. \( \frac{2 M L^{2}}{3} \)


OA and OB are opposite rays.
f \( x=75^{\circ}, \) what is the value of \( y ? \)
\( A \cdot 105^{\circ} \)
B \( .75^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D \( .15^{\circ} \)


Sex organ in bryophytes are
A. Unicellular and jacketedd
B. Unicellular and non-jacketed
c. Multicellular and jacketed
D. Multicellular and non jacketed


A binomial nomenclature has how
many words/parts?
A . Five
B. Three
c. Two
D. one


A scooty is sold for 13,600 and fetches
a loss of \( 15 \% \). Find the cost price of the
scooty.


Give reasons: Silver articles becomes
black after exposure to air.


PQRS is a parallelogram and diagonals PR and \( \$ Q \) bisect at \( 0 . \) If \( P O=3.5 \mathrm{cm} \) and
\( 0 Q=4.1 \mathrm{cm} . \) What is the length of the
diagonals?


The velocity acquired by a body moving with uniform acceleration is \( 30 m / s \) in
2 seconds and \( 60 m / s \) in 4 seconds. The initial velocity is:
A. Zero
B. \( 2 m / s \)
c. \( 4 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


The wires which connect the battery of
an automobile to its starting motor
carry a current of 300 A (for a short
time). What is the force per unit length
between the wires if they are \( 70 \mathrm{cm} \) long
and \( 1.5 \mathrm{cm} \) apart? Is the force attractive or repulsive?


A number of capacitors, each of equal
capacitance \( C, \) are arranged as shown
in the figure. The equivalent
capacitance between \( A \) and \( B \) is :
A \( \cdot n^{2} C \)
B. \( (2 n+1) C \)
c. \( \frac{(n-1) n}{2} C \)
D. \( \frac{(n+1) n}{2} C \)


Three point masses \( m_{1}, m_{2} \) and \( m_{3} \) are
located at the vertices of an equilateral
triangle of length \( a \). Determine the
moment of inertia of the system anout
an axis along the altitude of the triangle
passing through \( \boldsymbol{m}_{1} \)


The largest bond angle is in :
A. \( A s H_{3} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( P H_{3} \)


A cube of side 5 has one vertex at the
point \( (1,0,-1), \) and the three edges from this vertex are, respectively, parallel to the negative \( x \) and \( y \) axes and positive z-axis. Find the coordinates of the other
vertices of the cube.
A. (1,0,1)
B. (0,-1,0)
c. (0,0,-1)
D. (1,0,0)


The basic oxides react with acids to
form:
This question has multiple correct options
A . salt
B. water
c. metalloid
D. hydrogen


Two dice are thrown:
\( P \) is the event that the sum of the
scores on the uppermost faces is a
multiple of 6
\( Q \) is the event that the sum of the
scores on the uppermost faces is at
least 10
\( R \) is the event that same scores on both
dice.

Which of the following pairs is mutually exclusive?
A. \( P, Q \)
в. \( P, R \)
\( \mathbf{c} \cdot Q, R \)
D. None of these


In the law of mean, the value of \( \theta \)
satisfies the condition
\( \mathbf{A} \cdot \theta>0 \)
B . \( \theta<0 \)
\( \mathbf{c} \cdot \theta>1 \)
\( 0.0<\theta<1 \)


A ball with charge -50e is placed at the
centre of a hollow spherical shell has a
net charge of -50e. What is the charge on the shell's outer surface?
A . - -50e
B. zero
\( c \cdot-100 e \)
D. \( +100 e \)


\( \ln a \Delta A B C, \) if \( \cos A \cos B \cos C= \)
\( \frac{\sqrt{3}-1}{8} \) and \( \sin A . \sin B . \sin C= \)
\( \frac{\mathbf{3}+\sqrt{\mathbf{3}}}{\mathbf{8}} \)
then- \( 0 n \) the basis of above information, answer the following questions:The
value of \( \tan A+\tan B+\tan C \) is:
A \( \frac{3+\sqrt{3}}{\sqrt{3}-1} \)
B. \( \frac{\sqrt{3}+4}{\sqrt{3}-1} \)
c. \( \frac{6-\sqrt{3}}{\sqrt{3}-1} \)
D. \( \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-1} \)


Write each of the following polynomials in the standard form. Also, write their
degree:
\( \left(x^{3}-1\right)\left(x^{3}-4\right) \)


Why is a solution of potassium hydroxide used to absorb carbon dioxide evolved during the estimation of carbon present in an organic compound?


Normal force can occur
A. only on rough surfaces
B. only on smooth surfaces
C. on all surfaces
D. None


Rotational Analogue of force in linear motion is
A. weight
B. Angular Momentum
c. Moment of Inertia
D. Torque


The transition series that possess
elements with maximum oxidation state
of +8:
A. 1 and 2 series
B. 1 and 3 series
c. 1,2 and 3 series
D. 2 and 3 series


Balance the following equation.
\( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}_{2} \boldsymbol{O}_{3}+ \)
\( \boldsymbol{S}_{8}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( \mathbf{A} \cdot 24 H_{2} S+8 C r_{2} O_{7}^{2-}+16 H^{+} \rightarrow 8 C r_{2} O_{3}+3 S_{8}+32 H_{2} O \)
B \( \cdot 24 H_{2} S+3 C r_{2} O_{7}^{2-}+6 H^{+} \rightarrow 7 C r_{2} O_{3}+3 S_{8}+32 H_{2} O \)
\( \mathbf{c} \cdot 24 H_{2} S+8 C r_{2} O_{7}^{2-}+5 H^{+} \rightarrow 6 C r_{2} O_{3}+4 S_{8}+32 H_{2} O \)
D. None of these


A smooth horizontal disc rotates with a
constant angular velocity \( \omega \) about a stationary vertical axis passing through
its centre, the point \( O . A t \) a moment \( t= \)
0 a disc is set in motion from that point
with velocity \( v_{0} . \) Find the angular
momentum \( \boldsymbol{M} \)
\( (t) \) of the disc relative to the point \( O \) in the reference frame fixed
to the disc. Make sure that this angular momentum is caused by the Coriolis force.


Arrange the following in the increasing order of basicity:
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \)


Lassaigne's test is not shown by diazonium salts because they:
\( \mathbf{A} \cdot \) form \( N H_{3} \) gas on heating much before the reaction with sodium.
B. form \( N_{2} \) gas on heating much before the reaction with sodium
C . are highly volatile and evaporate before the reaction with sodium
D. all of the above


Parallax method is based on which of
the following principle?
A. Disparity
B. Lutz Kelker bias
c. Trilateration
D. Triangulation


On oxidation with acidified \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}}, \) an
compound gives a ketone which contains same number of carbon atoms
as in initial compound. The compound
is:
A. aldehyde
B . \( 1^{0} \) alcohol
C \( \cdot 2^{0} \) alcohol
D. both \( 1^{0} \) and \( 2^{0} \) alcohols


Endosperm of gymnosperms is
A. Haploid
B. Tetraploid
c. Diploid
D. None of these


A flag is mounted on a car moving due North with a velocity of \( 20 k m / h \). Strong winds are blowing due East with the
velocity of \( 20 k m / h \). The flag will point in direction:
A. East
B. North-East
c. south-East
D. south-west


In what ratio are the mixture of cement,
gravel and sand mixed to form concrete?
A .1: 2: 4
B. 1: 3: 6
c. Both \( A \) and \( B \)
D. 1: 1: 1


A man throws the brick to the height of 12 \( \mathrm{m} \) where they reach with a speed of 12 \( \mathrm{m} / \mathrm{s} . \) If he throws the bricks such that
theyjust reach this height, then what percentage of energy will be save?
A . 19\%
в. 38\%
c. 57\%
D. 76\%


An ideal gas is compressed in a closed container its U?
A. Increases
B. Decreases
c. Remains same
D. Both (1) \& (2)


A non-conducting hollow sphere of
mass \( m \) and radius \( R \) having total charge 'q' is rotating with constant
angular velocity ' \( \omega^{\prime} \) about a vertical
axis as shown in the figure. The sphere is then gently placed on the horizontal
surface having a magnetic field applied in the horizontal direction as shown. If
there is sufficient friction to prevent
any slipping, then the friction force acting on the sphere at \( t=0 \) is \( \frac{q \omega R B}{n} \)
Find the value of \( n \)


\( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], B=\left[\begin{array}{ll}-1 & -1 \\ -1 & -1\end{array}\right], C=\left[\begin{array}{ll}x & y \\ z & r\end{array}\right] \)
If \( \boldsymbol{A}+\mathbf{3} \boldsymbol{B}=\boldsymbol{C}, \) then \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}+\boldsymbol{r} \) is
\( A \)
B. - 2
\( c .-1 \)
\( D \)


If \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}), \mathbf{P}=(\mathbf{4}, \mathbf{3},-\mathbf{5}), \mathbf{Q}= \)
\( (-2,1,-8), \cos \angle P O Q=\frac{a}{\sqrt{b} \sqrt{c}} \) and
\( \mathbf{b}>\mathbf{c}, \) then \( \sqrt{\boldsymbol{b}}-\sqrt{\boldsymbol{c}} \) is
A . 19
B . \( \sqrt{69}-\sqrt{50} \)
c. -19
D. 17


A glass rod when rubbed with silk cloth, acquires a charge of \( 1.6 \times 10^{-11} C \), then
the charge on silk cloth will be:
A. \( -3.2 \times 10^{-11} C \)
B . \( -2.4 \times 10^{-13} C \)
c. \( -1.6 \times 10^{-13} C \)
D. \( -1.6 \times 10^{-11} C \)


Find the expected value, variance and standard deviation of a random variable
whose \( p . m . f \) is.
\[
\begin{array}{lllll}
\boldsymbol{X}=\boldsymbol{x} & & 1 & 2 & 3 \\
p(X=x) & \frac{1}{5} & \frac{2}{5} & \frac{2}{5} & \frac{2}{5}
\end{array}
\]


Valency of carbon is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 3 \)
D. 2


\( \frac{\boldsymbol{d}(\sin \boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}} \)
\( A \cdot \cos x \)
B. \( \sec x \)
\( c .-\cos x \)
D. - \( \tan x \)


The angle between two vectors given by \( (6 \hat{i}+6 \hat{j}+3 \hat{k}) \) and \( (7 \hat{i}+4 \hat{j}+4 \hat{k}) \) is
A \( \cdot \cos ^{-1}\left(\frac{26}{27}\right) \)
B. \( \cos ^{-1}\left(\frac{5}{3 \sqrt{3}}\right) \)
c. \( \sin ^{-1}\left(\frac{2}{3 \sqrt{3}}\right) \)
D. \( \sin ^{-1}\left(\frac{-2}{27}\right) \)


At \( 700 K \), equilibrium constant for the reaction: \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is
64. If 0.5 mol \( L^{-1} \) of \( H I(g) \) is present at
equilibrium at \( 700 K \), what are the
concentration of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{I}_{2}(\boldsymbol{g}) \)
assuming that we initially started with \( H I(g) \) and allowed it to reach equilibrium at \( 700 K ? \)
A. \( 0.0625 M \)
в. 0.034 М
\( c .0 .136 M \)
D. \( 0.68 M \)


NaCl molecule is bound due to the
electric force between the sodium and
the chlorine ions when one electron of
sodium is transferred to chlorine.

Taking the separation between the ions to be \( 2.75 \times 10^{-8} \mathrm{cm}, \) find the force of
attraction between them. State the
assumptions (if any) that you have made.


Assume that if the shear stress in stee
exceeds about \( 4.00 \times 10^{8} N / m^{2}, \) the steel reptures. Determine. the shearing force necessary to (a) shear a steel bolt \( 1.00 \mathrm{cm} \) in diameter and
(b) punch a
1.00-cm-diameter hole in a steel plate \( 0.500 \mathrm{cm} \) thick.


Which of the following situation refers to lactational amenorrhea?
A. It is the absence of menstruation
B. It is the absence of menstruation during the period of intense lactation following parturition
C. A method in which couples avoid from coitus from day 10 to 17 of the menstrual cycle when ovulation could be expected
D. None of the above


Valency of an element is the number of
electrons \( _{--}--- \) by an atom
A . lost
B. gained
c. shared
D. any of these


The ratio of contributions made by the electric field and magnetic field
components to the intensity of an electromagnetic wave is:
A \( . c: 1 \)
B . \( c^{2}: 1 \)
\( c \cdot 1: 1 \)
D. \( \sqrt{c}: 1 \)


4
The IUPAC name of \( C H_{3}-C H- \)
\( \boldsymbol{C H}_{3} \)
\( C H_{2}-C H-C H O: \)
A. 4 -hydroxy - 2 - methyl pentanal
B. 2-hydroxy -4- methyl pentanal
C. 4 -hydroxy-2-methyl pentanol
D. 2-hydroxy-4- methyl pentanol


In the circuit shown, a \( 30 \mathrm{V} \) d.c source
gives a current \( 2.0 \mathrm{A} \) as recorded in the
ammeter \( A \) and \( 30 V \) a.c. source of
frequency \( 100 \mathrm{Hz} \) gives a current \( 1.2 \mathrm{A} \)
The inductive reactance is
\( A \cdot \) 10ohm
B. 20 ohm
\( \mathbf{c} \cdot 5 \sqrt{34} \) ohm
D. 40 ohm


The following data give the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year 1992 \( \quad 1993 \quad 1994 \quad 1995 \)
Loan
(in
crores \( 28 \quad 33 \quad 55 \) of
upee
Represent the above data with the help of a bar graph.


When tree grows older, which of the following increase rapidly in thickness?
A. Heart wood
B. Sap wood
c. cortex
D. Phloem


State whether given statement is True or False

The dielectric constant is the ability of a material to establish an electric field.
A. True
B. False


Go through the following flow chart for
division of subphylum vertebrata. Fill
the gaps \( A, B, C \) and \( D \) and select the
correct option.
A. A-Ostracodermi, B-Cyclostomata, C-Pisces, DTetrapoda
B. A-Cyclostomata, B-Ostracodermi, C-Pisces, DTetrapoda
C. A-Ostracodermi, B-Tetrapoda, C-Cyclostomata, DPisces
D. A-Pisces, B-Ostracodermi, C-Tetrapoda, DCyclostomata


Fuel cell involves which of the following
reaction(s)?
This question has multiple correct options
\( \mathbf{A} \cdot O_{2}(g)+2 H_{2} O(l)+4 e^{-} \rightarrow 4 O H^{-}(a q .)(\text { at cathode }) \)
B. \( O_{2}(g)+2 H_{2} O(l)+4 e^{-} \rightarrow 4 O H^{-}(a q .) \) (at anode)
\( \mathbf{c} \cdot 2 H_{2}(g)+4 O H^{-}(a q) \rightarrow 4 H_{2} O(l)+4 e^{-}(a t \text { anode }) \)
D. \( 2 H_{2}(g)+4 O H^{-}(a q .) \rightarrow 4 H_{2} O(l)+4 e^{-} \) (at cathode)


In comparing e.m.f. of two cells with the help of a potentiometer, at the balance
point, the current flowing through the wire is taken from
A. one of these cells
B. both of these cells
c. the battery in the main circuit
D. none of these


The concentrated acid present in three parts in aqua regia
\( A \). nitric acid
B. sulphuric acid
c. hydrochloric acid
D. nitrosyl chloride


Which colour of light deviates the maximum in the dispersion of white light by the prism?
A . Violet
B. Blue
c. Green
D. Red


Reaction; \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D}, \) follows
rate law; \( r a t e=k[A]^{2}[B]^{2} . \) Starting
with initial concentration of \( 1 M \) of \( A \)
and \( B \) each, what is the time taken for
concentration of \( A \) to become \( 0.25 M ? \)
Given: \( k=2.303 \times 10^{-2} s e c^{-1} \)
A . 300 sec
B. 600 sec
c. 900 sec
D. 1200sec


The induction coil works on the
principle of
A. self induction
B. mutual induction
c. amperes rule
D. fleming's right hand rule


The primary and secondary coils of a transformer have 50 and 1500 turns
respectively. If the magnetic flux \( \phi \) linked with the primary coil is given by \( \phi=\phi_{0}+4 t, \) where \( \phi \) is in weber, t is
time in seconds and \( \phi_{0} \) is a constant.
The output voltage across the secondary coil is
A \( .90 V \)
\( V \)
в. \( 6000 V \)
c. \( 220 V \)
D. 30 \( V \)


Gravity is what makes objects orbit around other objects, and gravity is a reflection of an object's mass. So why
doesn' the mass of the objects appear in Kepler's third law??


Define osmosis.


The periodic time of a linear harmonic
oscillator is \( 2 \pi \) seconds, with
maximum displacement of \( 1 c m \), if the
particle starts from extreme position, find displacement of the particle after \( \frac{\pi}{3} \) seconds


A number was divided successively in order by 4,5 and 6 The remainders were respectively 2,3 and 4 Then find out the number


Which period is incomplete in the modern periodic table?
A . \( 1 s \)
B. 2nd
\( c \cdot \) 6th
D. 7th


Assertion
Mutual inductance of a pair of coils depend on their separation as well as their relative orientation.
Reason
Mutual inductance depend upon the
length of the coil only.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Balance the following equation:
\( \boldsymbol{C u O}+\boldsymbol{N H}_{3} \rightarrow \boldsymbol{N}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C u} \)


Imagine a light planet revolving around a very massive star in a circular orbit of
radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is
proportional to \( r^{5 / 2}, \) then the square of the time period will be proportional to.
A \( \cdot r^{3} \)
в. \( r^{2} \)
\( c \cdot r^{2.5} \)
D. \( r^{3.5} \)


The curve \( y=a x^{3}+b x^{2}+c x+d \) has a
point on inflexion at \( x=1 \) then
\( \mathbf{A} \cdot a+b=0 \)
B . \( a+3 b=0 \)
c. \( 3 a+b=0 \)
D. \( 3 a+b=1 \)


Four fifth of a number is more than
three-fourth of the same number by 40
Find the number.


Loop of Henle is concerned with
A. Excretory system
B. Reproductive system
C. Nervous system
D. Muscular system


Iron and rust are the same things.
A. True
B. False


Aldol condensation reaction is not given
by:
A. \( C_{6} H_{5} C H_{2} C H O \)
в. \( C_{6} H_{5} C H O \)
c. \( C H_{3} C H O \)
D. \( C H_{3} C O C H_{3} \)


If the kinetic energy of a particles is reduced to half, de broglie wave length becomes:
A. 2 times
B. \( \frac{1}{\sqrt{2}} \) times
c. 4 times
D. \( \sqrt{2} \) times


Among the following which is used in the nuclear reactor as a moderator?
A. copper
B. boron
c. graphite
D. None of these


Ficus benghalensis is the common name
of
A. Orchid
B. 4 o'clock plant
c. Banyan tree
D. Mango tree


Human ancestors, who left cave
paintings were
A. Neanderthal man
B. Cro-magnon mann
c. Java ape man
D. Peking man


Find \( \int\left(\sqrt{\boldsymbol{x}}+\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}}}\right) \boldsymbol{d} \boldsymbol{x} \)


Lanthanoid contraction is caused due
to:
A. the same effective nuclear charge from \( C e \) to \( L u \)
B. the imperfect shielding on outer electrons by \( 4 f \) electrons from the nuclear charge
C. the appreciable shielding on outer electrons by \( 4 f \) electrons from the nuclear charge
D. the appreciable shielding on outer electrons by \( 5 d \) electrons from the nuclear charge


The value of \( g \) near the earth's surface is
A \( \cdot 8.9 m / s^{2} \)
в. \( 8.9 m / s \)
\( \mathrm{c} \cdot 9.8 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 9.8 m / s \)


Parathyroid hormone
A. Is produced by the thyroid gland
B. Is released when blood calcium levels fall
C. Stimulates osteoblasts to lay down new bone
D. Stimulates calcitonin release


In a reaction; \( 2 A \rightarrow \) Products, the
concentration of \( \boldsymbol{A} \) decreases from
0.5 mol litre \( ^{-1} \) to 0.4 mol litre\( ^{-1} \) in 10
minutes. Calculate rate during this interval.


What are emulsions? What are their
different types? Give one example of
each type.


Expressing \( \vec{a} \) and \( \vec{b} \) as linear combinations of \( \vec{c} \) and \( \vec{d} \) we \( \operatorname{get} \vec{a}= \) \( \boldsymbol{k} \overrightarrow{\boldsymbol{c}}+\boldsymbol{m} \overrightarrow{\boldsymbol{d}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{h} \overrightarrow{\boldsymbol{c}}+\boldsymbol{r} \overrightarrow{\boldsymbol{d}} \)
Find integer part of \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{h}+\boldsymbol{r} ? \)
\( -\boldsymbol{a}+\boldsymbol{b}=-\boldsymbol{c} ; \mathbf{2} \boldsymbol{a}-\boldsymbol{b}=\boldsymbol{c}+\boldsymbol{d} \)


The equilibrium constant of the reaction
\( \boldsymbol{C}_{\boldsymbol{u}}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) ; \boldsymbol{E}^{0}=\mathbf{0 . 4 6} \boldsymbol{V} \boldsymbol{a} \boldsymbol{t} \mathbf{2} \boldsymbol{9} \boldsymbol{8} \boldsymbol{K} \) is:
\( \mathbf{A} \cdot 4.0 \times 10^{15} \)
B . \( 2.4 \times 10^{10} \)
c. \( 2.0 \times 10^{10} \)
D. \( 4.0 \times 10^{10} \)


If the \( 5 t h \) and \( 8 t h \) term of an \( A P \) are 6
and 15 respectively, find the 19 th term
A . 48
B . 54
c. 19
D. 57


A mass \( \boldsymbol{m}=\mathbf{1 4 k g} \) performing \( \boldsymbol{S H} \boldsymbol{M} \) as
displacement, \( \boldsymbol{x}=(\mathbf{0 . 5 m}) \sin (\boldsymbol{6} \boldsymbol{t}+\boldsymbol{\pi}) \)
Determine maximum K.E. of the mass
during its motion \( (\text { in } \boldsymbol{J}) \)
A. \( \frac{7 \pi^{2}}{4} \)
B . 49
c. 63
D. Data insufficient


Assertion
lodine shows oxidation state of +1 and
+3 in the compounds ICl and \( I C l_{3} \)
respectively.
Reason
lodine coming below the halogens \( \mathrm{F} \), \( \mathrm{Cl} \) and Br in the halogen group of elements in the periodic table shows a higher degree of electropositive nature.
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


Write formulae for the first five
members of each homologous series beginning with the following compound,
\( \boldsymbol{H}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)


The energy required to break one mole
\( C l-C l \) bonds in \( C l_{2} \) is \( 242 K J m o l^{-1} \)
The longest wavelength of light capable of breaking a single \( C l-C l \) bond is:
\( A .594 n m \)
B. 640 nm
\( c .700 n m \)
D. 494 ит


What is a solenoid? Draw a sketch to
show the magnetic field pattern produced by a current carrying solenoid


When two unknown resistances are
placed in the gaps of meterbridge, the null point is found to be \( 40 \mathrm{cm} \) from one
end of the bridge wire. When one of the
resistances is shunted with a 10
ohm coil, the null point is \( 25 \mathrm{cm} \) from the same end. The value of each of the
unknown resistances is
\( \mathbf{A} \cdot 15 \Omega, 10 \Omega \)
в. \( 10 \Omega, 15 \Omega \)
\( \mathbf{c} \cdot 20 \Omega, 30 \Omega \)
D. \( 30 \Omega, 20 \Omega \)


The value of \( K_{c}=4.24 \) at \( 800 K \) for the
reaction
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Calculate equilibrium concentrations of
\( C O_{2}, H_{2}, C O \) and \( H_{2} O \) at \( 800 K, \) if only
\( C O \) and \( H_{2} O \) are present initially at concentration of \( 0.10 M \) each?


For biogas production besides dung, which one of the following weed is recommended in our country?
A. Eichhornia crassipes
B. Coffea arabica
c. Mangifera indica
D. Solanum nigrum


Organs responsible for breathing in humans and fishes respectively are
A. Lungs in both
B. Gills and lungs
c. Gills in both
D. Lungs and gills


Write the formula to calculate the mole
fraction?


\( S_{N} 1 \& S_{N} 2 \) is not favourable in:
This question has multiple correct options
A \( \cdot H_{2} C=C H-C l \)
в. \( P h-C h_{2}-C l \)
c. \( P h-C l \)
D. \( H_{2} C=C H-C H_{2}-C l \)


Identify the correct statement(s):
This question has multiple correct options
A. The oxidation number of \( C r \) in \( C r O_{5} \) is +6
B. \( \Delta H>\Delta U \) for the reaction \( N_{2} O_{4}(g) \rightarrow 2 N O_{2}(g) \)
provided both gases behave ideally.
C \( . \) pH of \( 0.1 N H_{2} S O_{4} \) is less than that of \( 0.1 \mathrm{N} \mathrm{HCl} \) at
\( 25^{\circ} C \)
D \( \cdot\left(\frac{R T}{F}\right)=0.0591 \) volt at \( 25^{\circ} \mathrm{C} \)


Containers \( X, Y \) and \( Z \) of the equal
volume contain oxygen, neon and methane respectively at the same temperature and pressure. The correct increasing order of their masses is:
A. \( X<Y<Z \)
в. \( Y<Z<X \)
c. \( Z<X<Y \)
D. \( Z<Y<X \)


The rate of cooling of a body is :
A. independent of the nature of the surface of the body
B. independent of the area of the body
C. dependent on the excess of temperature of the body above that of the surroundings
D. independent of the temperature of the surroundings


Using vectors, prove that angle in a semicircle is a right angle.


Three charges \( -\mathbf{q}_{1},+\mathbf{q}_{2} \) and \( -\mathbf{q}_{3} \) are
placed as shown in the figure. The \( x \)
component of the force on \( -q_{1} \) is proportional to:
A \( \cdot \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}-\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \cos \theta \)
B. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}+\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \sin \theta \)
c. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}+\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \cos \theta \)
D. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}-\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \sin \theta \)


Assertion
Ammonia acts as a ligand.
Reason
A lone pair of electrons on nitrogen can
be donated to acceptor.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Temperature and soil moisture are the important climatic factors that
regulate the process of decomposition.
Reason

Warm and moist environment favours
decomposition whereas low temperature and anaerobiosis inhibit decomposition.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Algae show only anisogamous type of
reproduction.
Reason
In algae, gametes can never be non
flagellated.
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


Why \( ^{12} \mathrm{C} \) is the basis of the modern
atomic mass unit??


The minimum distance between two
particles in same phase is \( 18 \mathrm{cm} \). If the
velocity of the wave is \( 36 m s^{-1}, \) then find the time interval after which the
given particle undergoes a phase change of \( \pi \)


\( \boldsymbol{n} \) identical cells, each of emf \( \boldsymbol{E} \) and
internal resistance \( r, \) are joined in series to form a closed circuit. One of
the cell \( A \) is joined with reversed polarity. The potential difference across each cell except \( A \), is
A \( \cdot \frac{2 \varepsilon}{n} \)
в. \( \frac{n-1}{n} \)
c. \( \frac{n-2}{n} \)
D. \( \frac{2 n}{n-2} \)


Using Mean-Value Theorem, the best upper bound of \( \int_{0}^{1} \frac{\sin x}{1+x^{2}} d x \) is
A \( \cdot \frac{\pi}{4} \sin 1 \)
B. \( \pi \sin 1 \)
c. \( \frac{\pi}{2} \sin 1 \)
D. \( \frac{\pi}{4} \sin \left(\frac{1}{2}\right) \)


There is life on Earth because of:
A. optimum sunlight
B. presence of water and atmosphere
c. presence of ozone layer
D. all of the above


Pteridophytes are advanced than bryophytes in having
A. Swimming antherozoids
B. Sporophyte as dominant phase
c. Archegonia
D. Gametophyte as dominant phase


An object is placed in front of a spherical mirror whose 2 times magnified images is formed on the screen. Then choose the
CORRECT option:
A. Mirror is concave \( \mathrm{m}=+2 \)
B. Mirror is concave \( m=-2 \)
c. Mirror is convex \( \mathrm{m}=+2 \)
D. Mirror is convex \( \mathrm{m}=-2 \)


Which of the following statements is
false?
A. Photon has momentum as well as wavelength
B. Frequency of emitted radiation from a lower wavelength to higher wavelength as the temperature increases
C. Rydberg constant has unit of energy
D. Splitting of spectral lines an electrical field is called Stark effect


ntegrate the function \( \frac{x^{2}+x+1}{(x+1)^{2}(x+2)} \)


If they start together at \( t=0 \) at what
time does each reach the bottom?


The car \( A \) of mass \( 1500 k g \) travelling at
\( 40 m / s \) collides with another car \( ^{\prime} B^{\prime} \) of
mass \( 1250 k g \) travelling at \( 25 m / s \) in the same direction. After collision the
velocity of car ' \( A^{\prime} \) becomes \( 30 m / s \)
calculate the velocity of car \( ^{\prime} B^{\prime} \) after the
collision.


Common examples of family Liliaceae
are
A. Allium cepa, Aloe vera and Tamarindus indica
B. Saraca indica, Allium cepa and Aloe vera
C. Allium sativum, Allium cepa and Aloe vera


A particle of mass \( 10 g \) is undergoing SHM of amplitude \( 10 \mathrm{cm} \) and period
\( 0.1 s . \) The maximum value of force on
particle is about
A \( .5 .6 N \)
B. 2.75 N
c. \( 3.5 N \)
D. \( 4 N \)


The concept of 'Reduce, Reuse and
Recycle' helps us to:
A. minimize the dependence on producing new things.
B. minimize the dependence on producing old things.
C. maximize the dependence on producing new things.
D. All of the above.


In the following diagram, the value of
emf of A.C. source will be :
A . \( 40 V \)
B . \( 40 \sqrt{2} V \)
c. \( \frac{40}{\sqrt{2}} V \)
D. \( 160 V \)


Make a list of the uses of artificial
satellites.


The production of sulphuric acid by the assistance of the oxides of the nitrogen is carried out in the
A. furnace
B. vitrol chambers
c. heating pans
D. none of the above


Low \( C a^{++} \) in the body fluid may be the
cause of
A. Gout
B. Tetany
c. Anaemia
D. Angina pectoris


The coxal bone of the-pelvic girdle Is formed by the fusion of
A. llium, ischium, and pubis
B. scapula and clavicle
c. ilium and scapula
D. ilium, scapula and ischium


A system is shown in the figure. Block \( \boldsymbol{A} \)
moves with velocity \( 10 m / s . \) The speed
of the mass \( B \) will be: \( \left(\sin 15^{\circ}=\right. \)
\( \left.\frac{\sqrt{3}-1}{2 \sqrt{2}}\right) \)
A. \( 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)
в. \( 5 \sqrt{3} \) m/
c. \( \frac{20}{\sqrt{3}} m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Find the areas of rectangles with the following pairs of monomials as their
lengths and breadths respectively \( (p, q) ;(10 m, 5 n) ;\left(20 x^{2}, 5 y^{2}\right) ;\left(4 x, 3 x^{2}\right) \)
A \( \cdot 100 x^{2} y^{2} ; 12 x^{3} ; 12 m n^{2} p \)
B . \( 100 x^{2} y^{2} ; 12 x^{2} ; 12 m n^{2} p \)
C \( \cdot 100 x^{2} y ; 12 x^{3} ; 12 m n^{2} p \)
D. \( 100 x^{2} y^{2} ; 12 x^{3} ; 12 m n p \)


In figure, write down each pair of
vertically opposite angles


Describe in details the industrial
electrolysis of sodium chloride. Comment on the purity of the products.


Vertebrates are mainly divided into
groups
A. Four
B. Three
c. Five
D. Two


Why we should try to preserve the biodiversity we have inherited?


Find the value of following \( (625)^{\frac{-3}{4}} \)


Aspirin is pain relieving antiinflamatory drug but can be used to prevent heart attack.
A. True
B. False


If the speed of electrons in Bohr's first
obtain of hydrogen is \( ^{\prime} X^{\prime} \) the speed of
electrons in third orbit is:
\( A \cdot \frac{X}{9} \)
в. \( \frac{x}{3} \)
\( c .3 x \)
D. 9.8


A rod \( 70 \mathrm{cm} \) long is clamped from middle. The velocity of sound in the
material of the rod is 3500 ms\( ^{-1} \). The
frequency of fundamental note
produced by it is :
A. \( 3500 \mathrm{Hz} \)
B . \( 2500 H z \)
c. \( 1250 H z \)
D. \( 700 \mathrm{Hz} \)


\( f(x)=\left\{\begin{array}{lc}\frac{x^{2}}{a} \quad ; & 0 \leq x<1 \\ -1 & 1 \leq x<\sqrt{2} \\ \frac{2 b^{2}-4 b}{x^{2}} & ; \sqrt{2} \leq x<\infty\end{array}\right. \)
then find the value of \( a \) and \( b \) if \( f(x) \) is
continuous in \( [\mathbf{0}, \infty) . \) Find \( \boldsymbol{a}+\boldsymbol{b} \)


Which of the following rational numbers is in the standard form?
A \( -\frac{8}{-36} \)
в. \( \frac{-7}{56} \)
c. \( \frac{3}{-4} \)
D. None


If \( \sin \alpha+\operatorname{cosec} \alpha=2, \) find the value of
\( \sin ^{n} \alpha+\operatorname{cosec}^{n} \alpha, n \epsilon Z \)


State the physical and chemical properties of nitrogen is....


Arteries are the
A. Blood vessels which carry only oxygenated blood
B. Blood vessels which carry only deoxygenated blood
C. Blood vessels which carry blood from the heart to different organs of the body
D. Blood vessels which carry blood from different organs of the body to the heart


A collimated beam of light of flux
density \( 3 k W m^{-2} \) is incident normally
on a \( 100 m m^{2} \) completely absorbing screen. If \( P \) is the pressure exerted on the screen and \( \Delta p \) is the momentum transferred to the screen during a 1000 s interval, then
This question has multiple correct options
A. \( P=10^{-3} N m^{-2} \)
В. \( P=10^{-4} N m^{-2} \)
c. \( \Delta p=10^{-4} \)Kgms\( ^{-} \)
D. \( \Delta p=10^{-5} \mathrm{Kgms}^{-1} \)


1.375 g of cupric oxide was reduced by heating in a current of hydrogen and the weight of copper obtained was 1.098 g. In another experiment, 1.179 g of copper was dissolved in nitric acid and the
resulting solution was evaporated to dryness. The residue of copper nitrate when strongly heated was converted into 1.4476 g of cupric oxide. The result of this process show:
A. law of reciprocal proportion
B. law of multiple proportion
c. law of constant proportion
D. none of these


Which one is solid at room
temperature?
A. Nitrogen
B. Potassium permanganate
c. Bromine
D. Helium


The change in output voltage is approximately:
\( \mathbf{A} \cdot 0.8 \mu V \)
в. \( 2 m V \)
\( \mathrm{c} .3 .2 \mathrm{V} \)
\( \mathbf{D} \cdot 80 \mu V \)


What is the optimum band gap energy
for a material to be considered as a
semiconductor?
A. greater than \( 6 e V \)
B. less than \( 6 e V \)
c. \( 0 e V \)
D. \( 0.5-3 e V \)


In the following circuit diagram, what is
the value recorded by the voltmeter if
the potential across the diode is \( 1 V \) and
both ammeter and voltmeter are ideal?
A \( .4 .5 \mathrm{v} \)
B. 5.5 v
c. 3.2
D. \( 8.4 \mathrm{V} \)


Which one of the following is a bioindicator of air pollution?
A. Fern
B. Lichen
c. Money Plant
D. Dodder


A parallel-plate air capacitor of
capacitance \( C_{0} \) is connected to a cell of emf \( V \) and then disconnected from it. \( A \)
dielectric constant \( K, \) which canjust fill the air gap of capacitor, is now inserted in it. Which of the following is incorrect?
A. The potential difference between the plates decreases \( K \) times
B. The energy stored in the capacitor decreases \( K \) times.
C ' the change in energy is \( \frac{1}{2} C_{0} \varepsilon^{2}(K-1) \)
D. The change in energy is \( \frac{1}{2} C_{0} \varepsilon^{2}\left(1-\frac{1}{k}\right) \)


From a pack of 52 playing cards, face
cards and tens are removed and kept aside then a card is drawn at random
from the remaining cards. If
A : The event that the card drawn is an
ace
\( \mathrm{H}: \) The event that the card drawn is a
heart
S : The event that the card drawn is a
spade then which of the following holds?
This question has multiple correct options
\( \mathbf{A} \cdot 9 P(A)=4 P(H) \)
B . \( P(S)=4 P(A \cap H) \)
c. \( 3 P(H)=3 P(A \cup S) \)
D. None of these


The given diagram represents


What should be the parents task?


State True or False.
The following reaction is a
disproportionation reaction. \( N H_{4} N O_{3} \stackrel{\Delta}{\longrightarrow} N_{2} O+2 H_{2} O \)


Given right triangle \( \boldsymbol{R} \boldsymbol{S} \boldsymbol{T} \) in figure
calculate the length of \( \overline{S T} \), to the
nearest hundredth. (Use \( \cos 42^{0}= \)
\( \mathbf{0 . 7 4 3 2}) \)
\( \mathbf{A} \cdot 12.04 m m \)
B. \( 13.38 \mathrm{mm} \)
c. \( 16.21 \mathrm{mm} \)
D. 24.22 \( m m \)
E \( .26 .90 m m \)


Construct a AND gate using only NOR gates only


Fleming's right hand is also called as
A. generator rule
B. dynamo rule
c. system rule
D. none


Degree of ionization refers to the ratio of
concentration of ionized compound to neutral particles.
A. True
B. False


Differentiate between antiseptics and
antibiotics.


In hydraulic machine, the two pistons
are of area of cross section in the ratio
1: 10. What force is needed on the
narrow piston to overcome a force of \( 100 N \) on the wider piston?


f the percentage production of \( P \) type cars in 2001 was the same as that in
\( 2000, \) then the number of \( P \) type cars
produced in 2001 would have been?
A \( \cdot 1,40,000 \)
В. 1,32,000
\( c \cdot 1,17,000 \)
D . 1,05,000


in the horizontal plane of the circle as shown in the figure. The path
consists of eight arcs with alternating
radii \( r \) and \( 2 r . \) Each segment of arc
subtends equal angle at the common
centre \( P . \) The magnetic field produced
by current path at point \( \boldsymbol{P} \) is
A \( \cdot \frac{3}{8} \frac{\mu_{0} I}{r} ; \) perpendicular to the plane of the paper and directed inward.
B. \( \frac{3}{8} \frac{\mu_{0} \mathrm{I}}{\mathrm{r}} ; \) perpendicular to the plane of the paper and directed outward.
C \( \cdot \frac{1}{8} \frac{\mu_{0} I}{r} ; \) perpendicular to the plane of the paper and directed inward.
D. \( \frac{1}{8} \frac{\mu_{0} \mathrm{I}}{\mathrm{r}} ; \) perpendicular to the plane of the paper and directed outward


The expression \( (\tan \Theta+\sec \theta)^{2} \) is
equal to
A \( \cdot \frac{1+\cos \Theta}{1-\cos 0} \)
B. \( \frac{1+\sin \Theta}{1-\sin 0} \)
c. \( \frac{1-\cos \Theta}{1+\cos 0} \)
D. \( \frac{1-\sin \Theta}{1+\sin \Theta} \)


Explain the synthesis of ammonia occurs by Haber's process.


A solenoid has 2000 turns wound over a
length of \( 0.3 m . \) The area of its cross section is \( 1.2 \times 10^{-3} m^{2} . \) Around its
cross section a coil of 300 turns is
wound. If an initial current of \( 2 A \) is
reversed in \( 0.25 s, \) the emf induced in
the coil is equal to
A \( \cdot 6 \times 10^{-4} V \)
В. \( 4.8 \times 10^{-2} V \)
c. \( 2.4 \times 10^{-2} V \)
D. \( 48 k V \)


Differentiate between inherited and
acquired traits.


Well known formula one racing car has
a body with
A. laminated design
B. turbulent design
c. flat design
D. streamlined design


The length of a rectangle with area
\( 35 c m^{2} \) is \( 7 c m \) What is its breadth.


An airplane pilot sets a compass course due west and maintains an air speed of \( 240 \mathrm{km} / \mathrm{h} . \) After flying for \( \frac{1}{2} h, \) he finds himself over a town that is \( 150 \mathrm{km} \) west
and \( 40 \mathrm{km} \) south of his starting point. The wind velocity (with respect to ground).
A \( \cdot 100 k m / h, 37^{\circ} \) Wof \( S \)
в. \( 100 k m / h, 37^{\circ} \) Sof \( W \)
c. \( 120 k m / h, 37^{\circ} \) Wof \( S \)
D. \( 120 k m / h, 37^{\circ} \) Sof \( W \)


The function \( f \) is defined as \( f(x)= \) \( \left\{\begin{array}{ll}x^{2}+a x+b, & \text { if } 0 \leq x<2 \\ 3 x+2, & \text { if } 2 \leq x \leq 4, \text { If } f \text { is } \\ 2 a x+5 b, & \text { if } 4<x \leq 8\end{array}\right. \)
continuous in [0,8] find the values of \( a \)
and \( b \)


The photovoltaic effect is the creation of
a material upon exposure to light and is a physical and chemical phenomenon.
A. voltage or electric current
B. voltage
c. current
D. none of the above


Solve the following inequation:
\( (x-5)(x+9)(x-8)<0 \)


(ii) while climbing up a slope of height
\( 10 \mathrm{m}\left(g=10 m s^{-2}\right) ? \)
A \( .5 k J^{2} \)
\( \begin{array}{ll}2 & \text { 2 } \\ \text { 2 } & \text { 2 }\end{array} \)
в. \( 50 k J \)
c. \( 100 k J^{2} \)
D. \( 5 k J \)


Three school \( A, B \) and \( C \) organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold
hand made fans, mats and plates from
recycled material at a cost of Rs \( 25, \) Rs
100 and \( R s 50 \) each. The number of
articles sold are given below:
school \( \begin{array}{lll}\text { School } & \text { School } & \text { Sc } \\ \text { A } & \text { B } & \text { c }\end{array} \) Articles
Hand40 25 fans
Mats 50 40
Plates 20 30 40
Find the fund collected by each school
separately by selling the above articles. Also, find the total funds collected for
the purpose.


The angles of an isosceles triangle are
in the ratio \( 1: 4: 4 . \) Find the measure of
the base angle of the triangle.


Ratio of frequency of revolution of
electron in second excited state of \( \boldsymbol{H} \boldsymbol{e}^{+} \)
and first excited state of \( \boldsymbol{H} \) is \( \frac{\boldsymbol{2}^{x}}{\mathbf{3}^{y}} . \) Then
the value of \( x+y \) is:


The greatest and least value of
\( \left(\sin ^{-1} x\right)^{2}+\left(\cos ^{-1} x\right)^{2} \) are respectively
A \( \cdot \frac{\pi^{2}}{4} a n d 0 \)
B . \( \frac{\pi}{2} a n d-\frac{\pi}{2} \)
C. \( \frac{5 \pi^{2}}{4} \) and \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{4} \) and \( \frac{-\pi}{4} \)


The work function for the surface of
aluminium is \( 4.2 \mathrm{eV} \). How much
potential difference will be required to stop the emission of maximum energy electrons emitted by light of \( 2000 \dot{A} \) wavelength? What will be the wavelength of that incident light for
which stopping potential will be \( 0 ? \)


Which substances are needed for iron
to rust?
A. Carbon dioxide and oxygen
B. Oxygen only
c. water and carbon dioxide
D. water and oxygen


Write one structural difference between
the composition of artery and veins.


A silver electrode is immersed in
saturated \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S} \boldsymbol{O}_{4(a q)} . \) The potential
difference between silver and the
standard hydrogen electrode is found to be \( 0.711 V . \) Determine \( K s p\left(A g_{2} S O_{4}\right) \)
\( \left[\operatorname{Given} \boldsymbol{E}_{A \boldsymbol{g}^{+} / A \boldsymbol{g}}^{\circ}=\mathbf{0 . 7 9 9} \boldsymbol{V}\right] \)


If the width of slit is gradually increased, it will be observed experimentally that :
A. bright fringes become reduced in intensity
B. bright fringes become increased in intensity
c. the intensity of minima is strictly zero
D. the fringes become more distinct


Which of the following compound removes both oxygen and nitrogen from the air when it is passed over it at
\( 1000^{\circ} \mathrm{C} ? \)
A. \( C a C_{2} \)
в. \( C a C l_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCN}_{2} \)
D. \( \operatorname{CaSO}_{4} \)


Read the following statements carefully
1. Photochemical smog always contains
ozone
2. The toxic effect of carbon monoxide is
due to its greater affinity for haemoglobin as compared to oxygen.
3. Lead is the most hazardous metal
pollutant of automobile exhaust. Which of the above statements is not
true?
A.
B. 2
\( c .3 \)
D. None of these


Evaluate the given integral. \( \int \frac{\sqrt{1-\cos 2 x}}{2} d x \)


Two vectors are necessarily mutually perpendicular when
\( \mathbf{A} \cdot \vec{A}+\vec{B}=\overrightarrow{0} \)
\( \mathbf{B} \cdot \vec{A}-\vec{B}=\overrightarrow{0} \)
\( \mathbf{c} \cdot \vec{A} \times \vec{B}=\overrightarrow{0} \)
D . \( \vec{A} . \vec{B}=0 \)


Ashwin distributes 30 sweets between
Shweta and pallavi in the ratio 2:3. How many and what percentage of sweets do Shweta and Pallavi get?


Law of multiple proportions is illustrated by which one of the following pairs?
A \( . H_{2} S \) and \( S O_{2} \)
B. \( N H_{3} \) and \( N O_{2} \)
c. \( N_{2} O \) and \( N O \)
D. \( N_{2} S \) and \( N a_{2} O \)


A famous relation in physics relates
'moving mass' \( \mathrm{m} \) to the 'rest mass' \( \boldsymbol{m}_{\mathbf{0}} \) of a particle in terms of its speed v and the speed of light, c. (This relation first arose asa consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He
writes:
\( \boldsymbol{m}=\frac{\boldsymbol{m}_{o}}{\left(\mathbf{1}-\boldsymbol{v}^{2}\right)^{1 / 2}} \)
Guess where to put the missing c.


Given two functions
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\mathbf{1 0 0} \)
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{3}^{\boldsymbol{x}} \)
Calculate at what minimum integral value of \( \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})>\boldsymbol{f}(\boldsymbol{x}) \)
A . 5
B. 3
\( c \cdot 4 \)
D. 6


The position vectors of \( \mathbf{A}, \mathbf{B} \) are \( \mathbf{a}, \mathbf{6} \) respectively. The position vector of \( \mathbf{C} \) is \( \frac{5 \bar{a}}{3}-\bar{b} . \) Then 3
\( \mathbf{A} \cdot \mathrm{C} \) is inside the \( \Delta O A B \)
B. \( C \) is outside the \( \Delta O A B \) but inside the angle OAB
C. \( \mathrm{C} \) is outside the \( \Delta O A B \) but inside the angle \( \mathrm{OBA} \)
D. None of these


The chord of contact of tangents from a
point \( \boldsymbol{P} \) to a circle passes through \( \boldsymbol{q} \). If
\( l_{1} \) and \( l_{2} \) are the lengths of the tangents
from \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) to the circle, then \( \boldsymbol{P} \boldsymbol{Q} \) is
equal to
A. \( \frac{l_{1}+l_{2}}{2} \)
в. \( \frac{l_{1}-l_{2}}{2} \)
C \( . \sqrt{\left|l_{1}^{2}-l_{2}^{2}\right|} \)
D. \( \sqrt[2]{l_{1}^{2}+l_{2}^{2}} \)


What is the S.I. unit of charge?
A. Ampere
B. Charge
c. coulomb
D. volt


The cross between recessive to it's
hybrid or it's \( F_{1} \) plant is called as
A. Back cross
B. Test cross
c. Monohybrid cross
D. Dihybrid cross


The moon is a natural source of light. State whether true or false.
A. True
B. False


Tendons or ligaments are
A. Connective tissue
B. Vascular tissue
C . Epithelial tissue
D. Skeletal tissue


If \( \boldsymbol{A}=(\mathbf{3}-\mathbf{4} \boldsymbol{i}) \) and \( \boldsymbol{B}=(\mathbf{9}+\boldsymbol{k} \boldsymbol{i}), \) where
\( k \) is a constant.
If \( A B-15=60, \) then the value of \( k \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B . 24
c. 12
D. 3


Write about Female Reproductive
System.


On a displacement/time graph, two
straight lines make angles at \( 30^{\circ} \) and
\( 60^{\circ} \) with the time axis. The ratio of the
velocities represented by them is:
A .1: 2
B. 1: 3
c. 2: 1
D. 3: 1


What is the value of \( x, \) when \( f(x)= \)
\( 6+(x-2)^{2} \) is at its minimum?
A . -6
B. -
c. 0
D. 2
E . 5


Show that the relation \( R \) in the set \( \mathbb{Z} \) of
integers given by \( \boldsymbol{R}= \)
\( \{(a, b): 2 \text { divides }(a-b)\} \) is
equivalence relation.


If the equilibrium constants of the
following reactions \( 2 A \rightleftharpoons B \) is \( K_{1} \) and
\( B \rightleftharpoons 2 A \) is \( K_{2} \) then:
A \( . K_{1}=2 K_{2} \)
B. \( K_{1}=\frac{1}{K_{2}} \)
c. \( K_{2}=\left(K_{1}\right)^{2} \)
D. \( _{K_{1}=} \frac{1}{K_{2}^{2}} \)


Two identical spheres are placed in contact with each other. The force of
gravitation between the spheres will be proportional to (R = radius of each sphere \( ) \)
\( A \cdot R \)
B . \( R^{3} \)
\( c \cdot R^{4} \)
D. None of these


A current \( I \) ampere flows along an infinitely long straight thin walked tube, then the magnetic induction at any point inside the tube is
A . infinite
B. zero
c. \( \frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \) tesla
D \( \frac{2 i}{r} \) tesla