At Curie temperature, in ferromagnetic
materials
A. the atomic dipoles get aligned
B. the atomic dipoles remains stationary
C. the atomic dipoles lose alignment
D. magnetism is zero


In elastic collision, \( A \) is conserved while
in inelastic collision \( B \) is conserved.
I.Momentum
II.Kinetic Energy
III.Potential Energy
A. \( A= \) ।, ॥ \( B=1, \) II
в. \( A= \) ।, ॥ \( B=1 \)
c. \( A=\| \) \( B= \) ॥, ॥ ॥
D. \( A=\| \) \( B=1, \) II


The atom is made of 3 subatomic
particles. The subatomic particle found in the nucleus with a positive charge is


If \( \boldsymbol{x}=\boldsymbol{a}\left(\boldsymbol{1}-\cos ^{3} \boldsymbol{\theta}\right), \boldsymbol{y}=\boldsymbol{a} \sin ^{3} \boldsymbol{\theta}, \) prove
that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\frac{\boldsymbol{3} \mathbf{2}}{\mathbf{2 7} \boldsymbol{a}} \) at \( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{6}} \)


A conic passes through the point (2,4) and is such that the segment of any of its tangents at any point contained between the coordinate axes is bisected
at the point of tangency. Then equation of auxiliary circle of the conic is
A \( \cdot x^{2}+y^{2}=16 \)
B . \( x^{2}+y^{2}=25 \)
c. \( x^{2}+y^{2}=4 \sqrt{2} \)
D. none of these


What do you mean by a solenoid?


Isotopes are atoms with the same number of protons, but differing numbers of neutrons. Isotopes are different forms of a single element.
A. True
B. False


In YDSE of equal width slits, if intensity
at the centre of screen is \( I_{0}, \) then
intensity at a distance of \( \beta / 4 \) from the
central maxima is \( (\beta \) is the fringe
width) :
A \( \cdot I_{0} \)
в. \( \frac{I_{0}}{2} \)
c. \( \frac{I_{0}}{4} \)
D. \( \frac{I_{0}}{3} \)


In how many years will a sum of Rs. 800 at \( 10 \% \) per annum compounded, semiannually become Rs. 926.10 ?
A \( \cdot 1 \frac{1}{3} \)
в. \( 1 \frac{1}{2} \)
c. \( _{2} \frac{1}{3} \)
D. \( _{2} \frac{1}{2} \)


The plates of a parallel plate capacitor are charged upto \( 100 V . \) now, after removing the battery, a \( 2 m m \) thick plate is inserted between the plates. Then, to maintain the same potential difference, the distance between the
capacitor plates is increased by \( 1.6 m m \) The dielectric constant of the plate is :
A . 5
B. 1.25
\( c \cdot 4 \)
D. 2.5


The value of \( \sin ^{-1}(\sin 12)- \)
\( \cos ^{-1}(\cos 12)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в.
\( c \cdot 8 \pi+24 \)
D. \( 8 \pi-24 \)


If a current increases from zero to one
ampere in 0.1 second in a coil of \( 5 \mathrm{mH} \)
then the magnitude of the induced e.m.f. will be
A . 0.005 volt
B. 0.5 volt
c. 0.05 volt
D. 5 volt


Arrange according boiling point:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{C H}_{3} \boldsymbol{C H O}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C} \)


\( n \) charged drops, each of radius \( r \) and
charge \( q, \) coalesce to form a big drop of
radius \( R \) and charge \( Q . \) If \( V \) is
the electric potential and \( \boldsymbol{E} \) is the electric field at the surface of a drop,
then :
A \( \cdot E_{\text {big}}=n^{2 / 3} E_{\text {small}} \)
B. \( V_{\text {big}}=n^{1 / 3} V_{\text {small}} \)
C. \( E_{\text {small}}=n^{2 / 3} E_{\text {big}} \)
D. \( V_{\text {big}}=n^{2 / 3} V_{\text {small}} \)


In the series \( 20,18,16, \ldots \ldots \ldots,-2 \) is the
term
\( \mathbf{A} \cdot 10^{t h} \)
B. \( 11^{\text {th }} \)
\( \mathbf{c} \cdot 12^{t h} \)
D. \( 13^{\text {th }} \)


Define roasting.
A. Heating of sulphide ores in the presence of excess air to convert them into oxides
B. Heating of carbonate ores in the limited supply of air to convert them into oxides
C. Heating of oxides of metals to turn them into metal
D. Heating of carbonate ores in the limited supply of air to convert them into sulphide


When calyx and corolla are not
distinguishable, then member of their collective whorl termed as
A. Perianth
B. Sepal
c. Petal
D. Tepal


The fluid mosaic model of plasma
membrane was given by
A. Robertson
B. Robert Hooke
c. singer and Nicholson
D. Gorter and Grende


Liquid is used in rocket
fuels.
A. nitrogen.
B. oxygen
c. hydrogen
D. both B and C


Which term of the sequence 3,6,12 is \( 1536 ? \)


Trans \( -1,2- \) dibromo \( -1- \)
methylcyclohexane.
\( A \)


Give the differences between right and left lungs of humans.


If an earthworm is left in \( 40 \% \) KOH
solution for a long time, which part would be left undissolved?
A . Setae
B. Spermatheca
c. sand particles
D. circular muscles


The function of zymase is to:
A. change starch into sugar
B. ferment glucose to alcohol and carbon dioxide
c. change malt sugar into glucose
D. change starch into malt sugar and dextrin


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}2 a-x, & \text { if }-a<x<a \\ 3 x-2 a, & \text { if } a \leq x\end{array} . \) Then \right.
which of the following is true?
A. \( f(x) \) is discontinuous at \( x=a \)
B. \( f(x) \) is not differentiable at \( x=a \)
c. \( f(x) \) is differentiable at \( x \geq a \)
D. \( f(x) \) is continuous at all \( x<a \)


In the mechanism of action of a protein hormone, one of the second messengers is?
A. Cyclic AMP
B. Insulin
\( c \cdot T_{3} \)
D. Gastrin


\( y=(x-8)^{4}(x-9)^{5}, 0 \leq x \leq 10, \) In
this interval \( y \) will attain max. and min.
value at \( \boldsymbol{x}= \)
\( A \cdot 8,9 \)
в. \( _{8, \frac{76}{9}} \)
\( \mathrm{c} .9,10 \)
D. \( _{9, \frac{76}{9}} \)


When the distance covered by an object is directly proportional to the time interval, it is said to travel with:
A. Constant speed
B. Zero velocity
c. Constant acceleration
D. Uniform velocity


When zinc reacts with very dilute
\( H N O_{3}, \) the oxidation state of nitrogen
changes from:
A. +5 to +1
B. +5 to -3
\( c \cdot+5 t o+4 \)
D. +5 to +3


Solve the inequality and show the graph
of the solution on number line:
\( 3 x-2<2 x+1 \)


\( \sigma_{i}^{i} \)
\( \Phi_{i}^{i} \)
\( \Phi_{i-i}^{i-1} \)
\( \sigma_{i}^{i} \)


Which one of the following species does not represent cationic species of vanadium formed in aqueous solution?
A \( \cdot V O_{2}^{+} \)
B. \( V O^{2+} \)
c. \( \left[V\left(H_{2} O\right)_{6}\right]^{3+} \)
D. \( V O_{2}^{2+} \)


A pure capacitor is connected in an \( A C \) circuit.The power factor of the circuit will be
\( A \)
B. infinity
c. zero
D. 0.5


The amount of oil available for use are
from oil
A . reserve
B. reservoir
c. resources
D. barrelss


A \( 1000 \Omega \) resistance and a capacitor of
100 \( \Omega \) resistance are connected in
series a \( 220 V \) source. when the
capacitor is \( 50 \% \) charged, the value of the displacement current is.
A \( .11 . \sqrt{2} A \)
в. \( 2.2 A \)
\( c .11 A \)
D. \( 4.4 A \)


If \( P(1,4), Q(9,-2), \) and \( R(5,1) \) are collinear
then
A. P lies between \( Q \) and \( R \)
B. Q lies between P and R
c. R lies between P and Q
D. none of these


A rock is \( 12.5 \times 10^{9} \) years old. The rock
contains \( ^{238} U \) which disintegrates to
form \( ^{206} U . \) Assume that there was no
\( ^{206} P b \) in the rock initially and it is the only stable product formed by the decay
The ratio of number of nuclei of \( ^{238} U \) to that of \( ^{206} P b \) in the rock is \( \frac{1}{2^{1 / x}-1} \)
Find \( x \) (Approximately). Half-life of \( ^{238} \boldsymbol{U} \) is \( 4.5 \times 10^{9} \) years.\( \left(2^{1 / 3}=1.259\right) \)


Which of the following are paramagnetic? This question has multiple correct options
\( A \cdot B_{2} \)
в. \( O_{2} \)
\( c \cdot N_{2} \)
D. \( H e_{2} \)


If you dilute \( 25.0 \mathrm{mL} \) of \( 1.5 \mathrm{M} H C l \) to \( 500 \mathrm{mL}, \) then the molar concentration of
each ions becomes \( \boldsymbol{Y} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} . \) Here \( \boldsymbol{Y} \)
is:


What is the shape of f-orbital?
A. spherical
B. dumb bell
c. double dumb bell
D. no definite shape


If \( i z^{3}+z^{2}-z+i=0, \) then \( |z|=? \)
B . |z| = 2
c. \( |z|=3 \)
D. \( |z|=4 \)


Which among the following is/are
correct?
This question has multiple correct options
A. If an operations can be performed in 'm' different ways and a second operation can be performed in 'n different ways, then both of these operations can be performed in \( ^{\prime} m \times n^{\prime} \) ways together
B. The number of arrangements of n different objects taken all at a times is n!
C. The number of permutations of n different things taken \( r \) at a time, when each thing may be repeated any number of times is \( n \)
D. The number of circular permutations of 'n' different things taken all at a time is \( \frac{1}{2}(n-1) ! \). if clockwise and anticlockwise orders are taken as different.


Freons are:
A. chlorofluorocarbons of methane
B. chlorofluorocarbons of ethane
C. both chlorofluorocarbons of methane and
chlorofluorocarbons of ethane
D. chlorofluorocarbons of butane


If \( A \) is any event in a sample space then \( P\left(A^{\prime}\right) \) is
\( A \cdot P(A) \)
B. \( 1+P(A) \)
c. \( 1-P(A) \)
D. 1-2P(A)


State True or False.
\( 1+\frac{1}{5}+\frac{3}{5^{2}}+\frac{5}{5^{3}}+\ldots . . \infty=\frac{13}{8} \)
A . True
B. False


From a survey of 100 college students, a marketing research company found
that 75 students owned stereos, 45
owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo?
A . 85
B. 47
\( c .68 \)
D. None of these


The equi-potential surface for an
electric dipole is:
A. the dipole axis
B. the perpendicular bisector of the dipole axis
C. a line parallel to the dipole axis
D. a line passing through one of the charges


Describe the following:
Carius method for the estimation of
halogens in an organic compound.


Maximum value of \( r \) where \( \frac{c^{2}}{r^{2}}= \) \( \frac{\mathbf{a}^{2}}{\sin ^{2} \theta}+\frac{b^{2}}{\cos ^{2} \theta} \) where \( c, a, b \)
are constants is
A. \( \frac{c}{a+b} \)
B. \( \frac{c}{a-b} \)
c. \( \frac{a^{2}+b^{2}}{c^{2}} \)
D. \( \frac{c^{2}}{a^{2}+b^{2}} \)


What is intensive property? Give one example.


If ovaries from a pregnant woman are removed in \( 4^{t h} \) month of pregnency,
then
A. Development of embryo becomes abnormal
B. Abortion occurs after some time
C. Embryo develops normally till birth
D. None of the above


Two circular loops \( P \) and \( Q \) are
concentric and coplanar as shown in
figure. The loop \( Q \) is smaller than \( P . \) If
the current \( I_{1} \) flowing in loop is decreasing with time, then the current
\( I_{2} \) in the \( \operatorname{loop} Q \)
A. flows in the same direction as that of \( P \)
B. flows in the opposite direction as that of \( Q \)
c. is zero
D. None of these


In the following figure, \( \Delta A B C \) is an isosceles triangles with perimeter
\( 40 \mathrm{cm} . \) The base \( A C \) is of length \( 10 \mathrm{cm} \)
Side \( A B \) and side \( B C \) are congruent. \( A \)
circle touches the three sides as shown
in the figure below. Find the length of
the tangent segment from point \( B \) to
the circle.


Which of the following hypotheses was made by Newton?
A. Heavier body in the universe exerts a gravitational force on the lighter bodies.
B. Every body in the universe exerts a gravitational force on every other body.
c. Only the sun gravitational force is responsible for all the motion in this universe
D. None of the above


Assertion
Collision between two billiard's ball are
inelastic.
Reason
Momentum remains conserve during
the collision.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If coulomb's law involved \( 1 / r^{3} \) instead
of \( \left(1 / r^{2}\right), \) would Gauss's law still be
true?


Find common difference of the following \( 8,15,22,29, \dots \)
A. 5
B. 6
c. 7
\( D \)


Which \( \beta-k e t o \) acid shown will not
undergo decarboxylation?
\( A \)
B.
\( c \)
D.


State one way to obtain a greater
moment of a force about a given axis of
rotation.


The hybridization and shape of \( X e F_{2} \) is
\( \mathbf{A} \cdot s p^{3}, \) bent
B. \( d s p^{2}, \) linear
c. \( s p^{3} d^{2}, \) linear
D. \( s p^{3} d, \) linear


Which of the following statements
is/are correct regarding inter-halogen
compounds of ABX types?
This question has multiple correct options
\( A \cdot X \) may be 1,3,5 and 7
B. A is a more-electronegative halogen than B
\( \mathrm{C} \cdot F B r_{3} \) is a stable inter-halogen compound
D. the structures of \( C I F_{3} \) and \( I F_{2} \) show deviation from
normal structures and could be explained on the basis of VSEPR theory


Assertion
Air bladder is absent in fishes.
Reason
Fishes generally respire through gills.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect Reason is correct.


On reduction of glycolic acid with \( \boldsymbol{H} \boldsymbol{I} \) the product formed is:
A . acetic acid
B. iodo aectic acid
c. formic acid
D. none of these


The mixture of \( X \) and \( Y \) were taken in a
condenser flask and were then heated.
After keepint it for cooling, crystals of \( Y \) were found on the walls of the flask and
X was present as such at the bottom of
flask. Identify \( X \) and \( Y: \)
A. \( X=N a C l, Y=K C l \)
B. \( X= \) Anthracene, \( Y= \) Naphthalene
c. \( X=N a C l, Y= \) Naphthalene
D. \( X= \)Anthracene, \( Y=N a C l \)


Two soap bubbles of radii \( a \) and \( b \)
combine under isothermal conditions to
form a single bubble of radius \( c \) without
any leakage of air. If \( \boldsymbol{P}_{\mathbf{0}}= \)
atmospheric pressure and \( \boldsymbol{T}= \) surface
tension of soap solution, show that \( \boldsymbol{P}_{0}=\frac{\boldsymbol{4} \boldsymbol{T}\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}-\boldsymbol{c}^{2}\right)}{\boldsymbol{c}^{3}-\boldsymbol{a}^{3}-\boldsymbol{b}^{3}} \)


If impulse \( I \) varies with time \( t \) as
\( f\left(k g m s^{-1}\right)=20 t^{2}-40 t . \) The change in
momentum is minimum at
\( \mathbf{A} \cdot t=1 s \)
B . \( t=2 s \)
c. \( _{t=\frac{1}{2} s} \)
D. \( t=\frac{3}{2} s \)


If the \( 10^{t h} \) term of a G.P. is 9 and \( 4^{t h} \)
term is \( 4, \) then its \( 7^{t h} \) term is
A. 6
B. 14
c. \( \frac{27}{14} \)
D. \( \frac{56}{15} \)


Chemical hypothesis first emerged in Classical Greece by:
A. Einstein
B. Louis Pasteur
C. Aristotle
D. Leuweenhock


State whether true or false.
Ebonite is a good conductor of electricity.
A. True
B. False


When two charged objects attract each other, the objects carry:
A. same charges
B. opposite charges
c. no charges
D. none of the above


Find the temperature of Hydrogen gas which has the same velocity as that of
oxygen at a temperature of \( 0^{0} C \)
A. \( 273 \div 16 K \)
В . \( 273 \times 8 K \)
c. \( 273 \times 32 K \)
D. \( 273 \times 4 K \)


In a first order reaction, the concentration of product 'x' at time 't' is given by the expression:
(where,a = initial concentration, \( \mathbf{k}= \)
rate constant, \( n=\text { order }) \)
A \( \cdot x=a\left(1-e^{-k t}\right) \)
в. \( x=\frac{1}{(a-x)} \)
c. \( _{x}=\frac{1}{2^{n-1}} \)
D. \( x=\frac{a}{(a-x)} \)


When a mixture to \( t- \)butyl alcohol and
ethyl alcohol is heated with conc.
\( H_{2} S O_{4} \) a single ether product is obtained. Identify the product giving
proper reasons.


STATEMENT - 1: If tangents OR, PR, PQ and drawn respectively at \( A, B, C \) to the circle circumscribing an acute-angled
\( \Delta A B C \) so as the form another \( \Delta P Q R \) then the \( \angle R P Q=\angle B A C \)
STATEMENT - 2: \( \Delta A B C \) is similar to \( \Delta \)
CPB.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement-1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. Statement - 1 is True, Statement- - 2 is False
D. Statement-1 is False, Statement - 2 is True


If tangents \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) from a point \( \boldsymbol{P} \)
to a circle with centre \( O \) are inclined to
each other at angle of \( 80^{\circ}, \) then \( \angle P O A \) is equal to.
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 80^{\circ} \)


Examine the table. (Each figure is
divided into triangles and the sum of the angles deduced from that)

What can you say about the angle sum
of a convex polygon with number of \( \operatorname{sides}(n)=10 ? \)
\begin{tabular}{|l|c|c|c|c|}
\hline Figure & & & & & \\
\hline side & 3 & & & & \\
\hline Ange sum & \( 180^{\circ} \) & \( 2 \times 180^{\circ} \) & 5 & 6 \\
\hline
\end{tabular}
A \( .720^{\circ} \)
B. \( 960^{\circ} \)
\( c \cdot 1080^{\circ} \)
D. \( 1440^{\circ} \)


\( p H \) of a dilute solution of \( H C l \) is 6.95
Calculate molarity of \( H C l \) solution. \( \left[\begin{array}{c}10^{-6.95}=11.22 \times 10^{-8} \\ 10^{-7.05}=8.90 \times 10^{-8}\end{array}\right] \)


Number of chiral centre present in cyclic structure of glucose:


Small chromosomes which do not
produce any detectable phenotypic expression are termed as
A. Heterochromatic chromosomes
B. Supernumerary chromosomes
c. Nonsense chromosomes
D. Nucleoids


Two thin, long, parallel wires, separated by a distance 'd' carry a current of 'i' A in
the same direction. They will
A \( . \) repel each other with a force of \( \mu_{0} i^{2} /(2 \pi d) \)
B. attract each other with a force of \( \mu_{0} i^{2} /(2 \pi d) \)
C . repel each other with a force of \( \mu_{0} i^{2} /\left(2 \pi r d^{2}\right) \)
D. attract each other with a force of \( \mu_{0} i^{2} /\left(2 \pi d^{2}\right) \)


Masses of neutron, proton and electron are \( 1.0087 \cup, 1.0073 \mathrm{u} \) and \( 0.0005 \mathrm{u} \)
respectively. If a neutron decays into a proton and an electron, the energy released would be about.
A. \( 0.68 \mathrm{MeV} \)
B. 0.84 Mev
c. \( 0.75 \mathrm{MeV} \)
D. \( 1.22 \mathrm{MeV} \)


Assertion:PV/T=constant for 1 mole of gas.
This constant is same for all gases.
Reason: 1 mole of different gases at \( \mathrm{NTP} \)
Occupy same volume of 22.4 litres.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true


Which term of the following sequences:
\( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots \) is \( \frac{1}{19683} ? \)


If \( Q_{1} \) and \( Q_{2} \) are the energies released in the fusion of hydrogen in Carbon nitrogen cycle and proton - proton cycle respectively, then
A \( \cdot Q_{1}>Q_{2} \)
в. \( Q_{1}=Q_{2} \)
c. \( Q_{1}<Q_{2} \)
D. \( Q_{1}=2 Q_{2} \)


During the discharge of a lead storage battery, the density of sulphuric acid
fell from 1.294 to \( 1.139 g m L^{-1} . H_{2} S O_{4} \) of
density \( 1.294 g m L^{-1} \) is \( 39 \% \) and that of
density \( 1.139 g m L^{-1} \) is \( 20 \% \)
by weight.The battery holds 3.5 L of acid and the volume practically remains constant during discharge. The number of ampere hours for which the battery must have been used are..

The discharging and charging reactions
are:
\( \boldsymbol{P b}+\boldsymbol{S O}_{4}^{2-} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2} \boldsymbol{e}^{-} \)
(charging) \( \boldsymbol{P b O}_{2}+\mathbf{4 H}^{+}+\boldsymbol{S O}_{4}^{2-}+\boldsymbol{2 e}^{-} \rightarrow \)
\( P b S O_{4}+2 H_{2} O \) (discharging)


The number of steps in which orthophosphoric acid is ionized is :
A.
B. 2
\( c \cdot 3 \)
\( D \)


a speparanationa
varies as follows.
\( 1 / 1 \)
What
1
\( M \)


Write one merit and one de-merit of
alternating current in comparison of direct current. Obtain expression for
following in a pure inductive alternating current circuit
i) Instantaneous value of current
ii) Reactance of circuit
iii) Peak value of current Draw curve for
power in pure inductive circuit.


The value of \( k \) for which the system of equations \( 3 x+5 y=0 \) and \( k x+ \)
\( 10 y=0 \) has a non-zero solution, is
\( A \cdot 0 \)
B . 2
\( c \cdot 6 \)
D. 8


Chloral is :
A \( \cdot C C l_{3} C O C H_{3} \)
в. \( C C l_{3} \) СН \( _{2} \) ОН
c. \( C C l_{3} C H O \)
D. \( C C l_{3} \) СОСС\( l \)


A light year is unit of
A. acceleration
B. distance
\( \mathbf{C} \cdot \) speed
D. velocity
E . time


The diagonals of a rectangle \( A B C D \)
intersect each other in \( O . \) If angle \( A O D \)
is \( 30^{0}, \) then find angle \( O C D \)


A spherical capacitor has an inner sphere of radius \( 12 \mathrm{cm} \) and an outer
sphere of radius \( 13 \mathrm{cm} . \) The outer sphere is earthed and the inner sphere is given
a charge of \( 2.5 \mu C . \) The space between
the concentric spheres is filled with a liquid of dielectric constant 32
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated
sphere of radius 12 cm. Explain why the latter is much smaller.


Assertion
Stress is the internal force per unit area
of a body.
Reason
Rubber is more elastic than steel.
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


What will happen to the volume of the cube, if its edge is
(a) tripled (b) reduced to one-fourth?


The resistance of \( n \) wires each of
resistance \( r \) ohms is \( R \), when they are connected in parallel. When these resistance are connected in series the
resultant resistance will be :-
A \( \cdot \frac{R}{n} \)
в. \( \frac{R}{n^{2}} \)
\( c \cdot n R \)
D. \( n^{2} R \)


(a) Two identical vessels \( A \) and \( B \)
containing equal volume of water are placed in sun. The outer surface of one vessel A is blackened, while of other
vessel B is polished. Thermometer \( \boldsymbol{T}_{1} \)
and \( T_{2} \) are used to measure the
temperature of vessel \( A \) and \( B \) respectively. Which thermometer will
record a higher temperature? Give a reason for your answer
(b) If the two vessels \( A \) and \( B \) as
described in part (a) are filled with
boiling water and placed inside the room, which thermometer will show a
higher temperature after 15 minutes? Give a reason for your answer


Find the slope of a line. Which bisects the first quadrant angle.


Hormone involved in discharge of pancreatic secretions is
A. Gastrin
B. cholecystokinin
c. secretin
D. Both B and C


find the value
\( \tan 11 \frac{\pi}{3} \)


A student prepared methanol in the laboratory by the addition of \( 266 g \) of \( C O \) and \( 60 g \) of \( H_{2}, \) as shown below. \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l}) \)
(a) Find out the limiting reagent
(b) Calculate the amount of methanol produced and the amount of excess reactant remaining after the completion of the reaction.


\( A, B, \) and \( C \) are three points on a circle
with centre \( \boldsymbol{O} \) such that \( \boldsymbol{B O C}=\mathbf{3 0}^{\mathbf{o}} \)
and \( \angle A O B=60^{\circ} . \) If \( D \) is a point on the
circle other than the arc \( A B C \), find
\( \angle A D C \)
\( A \cdot 45 \)
В. 60
\( c \cdot 22.5^{\circ} \)
0.30


Which of the following statements is
false?
A. The main reason for river water pollution is industrial and domestic sewage discahrge
B. Surface water contains a lot of organic matter mineral nutrients and radioactive materials
c. oil spills in sea water causes heavy damage to fishery
D. oil slick in a sea water increases DO value


Which gas is more soluble in water, \( \boldsymbol{O}_{2} \)
or \( N_{2} ? \)


Calculate the scalar product of the following vectors. Find the vector c being given that it is perpendicular to the vectors \( \boldsymbol{a}= \)
\( \{2,3,-1\}, b=\{1,-2,3\} \) and
satisfies the condition
\( \boldsymbol{c} \cdot\{\boldsymbol{2} \boldsymbol{i}-\boldsymbol{j}+\boldsymbol{k}\}=-\boldsymbol{6} \)


If a mole of hydrogen molecule is heated to a high temoerature then which of the following reactions take place?
A \( \cdot H_{2}(g)+436 k J m o l^{-1} \rightarrow H(g)+H(g) \)
B . \( 2 H 2(g)+820 k J m o l^{-1} \rightarrow 2 H_{2}(g) \)
C \( \cdot H_{2}(g)+H_{2}(g)+436 k J m o l^{-1} \rightarrow H_{(a q)}^{+}+H_{(a q)}^{-} \)
D. \( H_{2}(g)+200 k J m o l^{-1} \rightarrow H_{(g)}+H_{(g)} \)


If \( A B C D \) is a parallelogram with two adjacent angles \( A \) and \( B \) equal to each other, then the parallelogram is?
A. Rhombus
B. Trapezium
c. Rectangle
D. None of These


Which of the following are examples of celestial objects?
A. Asteroids
B. Moons
c. Planets
D. All of above


Which of the following species are having peroxy linkages? This question has multiple correct options
\( \mathbf{A} \cdot B r O_{4}^{-} \)
в. \( S_{2} O_{8}^{2} \)
\( \mathrm{c} \cdot P_{2} \mathrm{O}_{8}^{4} \)
D. \( P O_{5}^{3} \)


Five resistance are connected as shown
in figure. If total current flowing is \( 0.5 A \)
then the potential difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{A}_{\boldsymbol{B}} \)
is:
\( A \cdot 8 V \)
в. \( 6 V \)
\( c \cdot 2 V \)
D. \( 4 V \)


The statements regarding ozone
i) It oxidises \( C l_{2} \) to \( H C l \)
ii) It oxidises \( P b S \) to \( P b S O_{4} \)
iii) It oxidises \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) to
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
The correct combination is:
A. All are correct
B. (ii) and (iii) are correct
c. only (ii) is correct
D. Only (iii) is correct


Ileum is
A. First part of the small intestine
B. Middle part of the small intestine
C. Last part of the small intestine
D. Not a part of the small intestine


Which carbon is the most
electronegative?
A \( \cdot s p^{3}- \) hybridized carbon
B. \( s p \) - hybridized carbon
c. \( s p^{2}- \) hybridized carbon
D. Always same irrespective of its hybrid state


A prism of \( \boldsymbol{R} . \boldsymbol{I} .=1.5 \) is immersed in
water of \( \boldsymbol{R} . \boldsymbol{I} .=\mathbf{4} / \mathbf{3} \) as shown in the
figure. For the total internal reflection
the correct choice is:
A \( \cdot \sin \theta<\frac{8}{9} \)
B. \( \sin \theta>\frac{8}{9} \)
\( \mathrm{c} \cdot \sin \theta=\frac{8}{9} \)
D. \( \sin \theta \leq \frac{8}{9} \)


In Young's double-slit experiment, the angular width of a fringe formed on
a distant screen is \( 1^{\circ} . \) The slit
separation is \( 0.01 \mathrm{mm} . \) The wavelength of the light is
A. \( 0.174 \mathrm{nm} \)
в. 0.174 А
c. \( 0.174 \mu m \)
D. \( 0.174 \times 10^{-4} \mathrm{m} \)


\( \int_{0}^{1} x e^{x} d x= \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
D.


Which fat soluble vitamin in necessary for blood clotting?
\( A \cdot A \)
B.
\( c \cdot E \)
D.


State and prove Addition theorem on
probability.


A solution has a \( p H \) of \( 7 . \) Explain how
would you:
Increase its \( p H \)
Decrease its \( p H \)


The radii of curvature of the surfaces of
a double convex lens are \( 20 \mathrm{cm} \) and 40
\( \mathrm{cm} \) respectively, and its focal length is \( 20 \mathrm{cm} . \) What is the refractive index of
the material of the lens.?
A \( \cdot \frac{5}{2} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{4}{5} \)


Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.


There are \( n \) persons sitting in a row. Two of them are selected at random. The
probability that the two selected
persons are not together, is
A \( \cdot \frac{2}{n} \)
в. \( _{1-} \frac{2}{n} \)
c. \( \frac{n(n-1)}{(n+1)(n+2)} \)
D. None of these


Veena and Rani are on the moon, Veena
calls out her friend, but Rani does not hear Veena's call even though she is near. Discuss.


The interior angles of a polygon are in arithmetic progression. The smallest angle is \( 120^{\circ} \) and the common
difference is \( 5 . \) Find the number of sides
of the polygon.


Simplify:
\( \left(\frac{2 i}{1+i}\right)^{2} \)


The hybridisation involved in
\( \left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \) is \( ? \)
A \( \cdot s p^{3} d^{2} \)
B. \( s p^{3} d^{3} \)
c. \( d s p^{3} \)
D. \( d^{2} s p^{3} \)


Concept of stationary orbit was introduced by :
A. Bohr
B. Rutherford
c. Sommerfeld
D. Thomson


Which of the following is not correctly
matched?
\( \begin{array}{clc}\text { Complex ion } & \text { CFSE } \\ \text { a } & {\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+}} & 24 D q \\ \text { b } & {\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+}} & 12 D q \\ \text { c } & {\left[F e F_{6}\right]^{3-}} & 4 D q \\ \text { d } & {\left[F e(C N)_{6}\right]^{3-}} & 20 D q\end{array} \)


The equilibrium constant \( K \) for the
reaction \( : 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \) at
room temperature is 2.85 and that at \( 698 K \) is \( 1.4 \times ! 0^{-2} . \) This implies that
the forward reaction is:
A. exothermic
B. endothermic
c. slow
D. unpredictable


A fungal spore
A. Contains an embryonic organism
B. Germinates directly into an organism
C. Is always windblown
D. Both
(b) and (c)


Zinc can be coated on iron to produce galvanized iron but the reverse is not possible. It is because:
A. zinc has lower negative electrode potential than iron
B. zinc has higher negative electrode potential than iron
c. zinc is lighter than iron
D. zinc has lower melting point than iron


Assertion(A): The minimum value
of \( 16 \cot x+9 \tan x \) is 3
Reason (R): For two positve real
numbers a and b, \( \boldsymbol{A} . \boldsymbol{M} \geq \boldsymbol{G} . \boldsymbol{M} \)
This question has multiple correct options
A. Both A and R are true and \( R \) is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
\( \mathrm{c} . \) A is true and \( \mathrm{R} \) is false
D. A is false and R is true


A long straight cable of lenght \( l \) is
placed symmetrically along z - axis has radius \( a(<<l) \). The cable consists of a
thin wire and a coaxial conducting tube
An alternating current \( \boldsymbol{I}(\boldsymbol{t})= \)
\( I_{0} \sin (2 \pi v t) \) flows down the central thin
wire and return along the coaxial conducting tube. The induced electric field at a distance s from the wire inside
the cable is \( \boldsymbol{E}(\boldsymbol{s}, \boldsymbol{t})= \)
\( \mu_{o} I_{o} v \cos (2 \pi v t) \ln \left(\frac{s}{a}\right) \hat{k} . \) The
displacement current density inside the cable is
A \( \cdot \frac{2 \pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
в. \( \frac{I}{\lambda^{2}} I_{0} \) ln \( \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
c. \( \frac{\pi}{\lambda^{2}} I_{0} \ln \left(\frac{a}{s}\right) \sin (2 \pi v t) \hat{k} \)
D. Zero


If the perimeter is half of the area of the
circle numerically then find the radius of the circle.


A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs \( 40 . \) If he sells the cooler for Rs 1550 , determine
his profit (in percent).


Silkworm larva spins silk from
A. Inside to outside
B. Outside to inside
c. Random fashion
D. Anterior to posterior side


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\cos ^{2}\left(\tan ^{-1}\left(\sin \left(\cot ^{-1} x\right)\right)\right)\right]= \)
A. \( \frac{2}{\left(x^{2}+2\right)^{2}} \)
B. \( \frac{2 x}{\left(x^{2}+2\right)^{2}} \)
c. \( \frac{\left(x^{2}+1\right)}{\left(x^{2}+2\right)} \)
D. \( \frac{-2 x}{\left(x^{2}-1\right)^{2}} \)


f the following function is continuous at \( x=\frac{\pi}{2}, \) then find \( a \) and \( b \) \( f(x)=\left\{\begin{array}{l}\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, \text { if } x<\frac{\pi}{2} \\ a, \text { if } x=\frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, \text { if } x>\frac{\pi}{2}\end{array}\right. \)


When the temperature of an iron sphere
of mass \( 1 k g \) falls from \( 30^{\circ} C \) to \( 25^{\circ} C \)
then 550 cal of heat is released. The
heat capacity of the iron sphere will be
in \( \left.\operatorname{cal}^{\circ} C^{-1}\right) \)
A . 440
в. 330
\( c \cdot 220 \)
D. 110


Choose the correct statements -
This question has multiple correct options
\( \mathbf{A} \cdot C_{2} H_{6}+O_{2} \rightarrow C O_{2}+H_{2} O \) is an unbalanced
combustion reaction.
B. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \) is a balanced combustion
reaction.
C \( . A+B C \rightarrow A C+B \) represents a single replacement
reactions.
D. \( H N O_{3}+C a(O H)_{2} \rightarrow C a\left(N O_{3}\right)_{2}+2 H_{2} O \) is an
unbalanced neutralization reaction.


One mole of a monoatomic gas is mixed with 3 mole of a diatomic gas. The
molar heat capacity at constant volume of mixture (in cal) is :
A . 4.5
B. 2
\( c \cdot 4 \)
D.


The solution of the differential equation,
\( \boldsymbol{e}^{\boldsymbol{x}}(\boldsymbol{x}+\mathbf{1}) \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{y} \boldsymbol{e}^{\boldsymbol{y}}+\boldsymbol{x} \boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
with initial condition \( f(0)=0, \) is-
A \( \cdot x e^{x}+2 y^{2} e^{y}=0 \)
В \( \cdot 2 x e^{x}+y^{2} e^{y}=0 \)
C. \( x e^{x}-2 y^{2} e^{y}=0 \)
D. \( 2 x e^{x}-y^{2} e^{y}=0 \)


Three cations \( A, B, C \) are allowed to
react with ammonium hydroxide solution. \( A \) and \( B \) produce a dirty green
precipitate and a reddish brown precipitate respectively, both of which do not dissolve on further addition of
\( N H_{4} O H . C \) gives pale blue colour precipitate with less amount of ammonium hydroxide and on further
addition of \( N H_{4} O H, \) precipitate becomes soluble and deep blue colour
solution is formed:
A \( \cdot F e^{+2}, F e^{+3}, C u^{+2} \)
B. \( F e^{+3}, F e^{+2}, C u^{+2} \)
c. \( C u^{+2}, F e^{+2}, F e^{+3} \)
D. \( C u^{+2}, F e^{+3}, F e^{+2} \)


What is the volume of water consumed
during acid hydrolysis of \( 1.368 K g \) of
sucrose?
(Given - molar masses of sucrose \( =\mathbf{3 4 2} \)
water \( =18, \) density of water \( =1 g / c m^{3} \)
В. \( 0.720 d m^{3} \)
c. \( 0.18 d m^{3} \)
D. \( 0.018 d m^{3} \)


When a substance is dissolved in a
solvent, the vapour pressure of solvent decrease. It brings This question has multiple correct options
A. a decrcase in boilings point of solution
B. an increase in boiling point of the solution
c. a decrease in freezing point of the solution
D. an increase in freezeing point of the solution


A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12
\( \mathrm{cm} . \) The coil is in a vertical plane
making an angle of \( 45^{\circ} \) with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west
to east.
(a) Determine the horizontal component of the earth's magnetic field at the location.
(b) The current in the coil is reversed, and the coil is rotated about its vertical
axis by an angle of \( 90^{\circ} \) in the anticlockwise sense looking from above. Predict the direction of the
needle. Take the magnetic declination at the places to be zero.


Which is the correct sequence of cranial
capacities according to increasing
manner?
A. Australopithecus - Homo erectus - Cro magnon man Neanderthal man
B. Homo erectus Ramapithecus Homo habilis Neanderthal man
C. Australopithecus - Homo habilis - Homo erectus Neanderthal man
D. Cro-Magnon man- Dryopithecus - Heidelberg man Neanderthal man


The equation of the hyperbola whose foci are \( (\mathbf{6}, \mathbf{5}),(-\mathbf{4}, \mathbf{5}) \) and eccentricity \( \mathbf{5} / \mathbf{4} \) is?
A \( \cdot \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=1 \)
В. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \)
c. \( \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=-1 \)
D. \( \frac{(x-1)^{2}}{4}-\frac{(y-5)^{2}}{9}=1 \)


For a solution of an electrolyte at a
particular concentration and temperature, which of the following is not the function of cell constant?
1) specific conductance
2) molar conductance
3) equivalent conductance
4) conductance
A \( \cdot 1,2 \)
B. 1,2,3
c. 2,3,4
D. 1,4


Which if the following is used in making smoke bombs?
A. Sulphur
B. Phosphorus
c. Hydrogen
D. carbon


\( \lim _{x \rightarrow 1} \frac{\sqrt{3+x}-\sqrt{5-x}}{x^{2}-1} \)


Define following:
Position vector


When a bar of iron \( 50.0 \mathrm{cm} \) long at \( 15^{\circ} \mathrm{C} \) is heated in a furnace, it becomes
\( 50.4 \mathrm{cm} . \) If the coefficient of linear
expansion of iron is \( 1.1 \times 10^{-5} C^{o-1} \)
find the temperature of furnace.


A liquid takes 5 minutes to cool from 80
\( ^{o} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \). How much time will it take
to cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} ? \)
(Temperature of the surrounding \( \left.=20^{\circ} \mathrm{C}\right) \)
A. 10 minutes
B. 15 minutes
c. 5 minutes
D. 7.5 minutes


The area of the smaller part of the circle \( x^{2}+y^{2}=a^{2}, \) cut off by the line \( x=\frac{a}{\sqrt{2}} \)
is given by:
\( ^{\text {A }} \cdot \frac{a^{2}}{2}\left(\frac{\pi}{2}+1\right) \)
в. \( \frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right) \)
c. \( a^{2}\left(\frac{\pi}{2}-1\right) \)
D. None of these


An object falls from rest with an
acceleration \( g \). The uncertainty in the value of the time is \( \pm 6 \% \) and the
uncertainty in the value of \( g \) is \( \pm 4 \% \). The
best estimate for the uncertainty of the position of the of the object is:-
\( \mathbf{A} \cdot \pm 16 \% \)
B . \( \pm 10 \% \)
\( c . \pm 5 \% \)
D. \( \pm 8 \% \)


The time required to produce \( 2 \mathrm{F} \) of electricity with a current of 2.5 amperes is:
A. 21.44
B. 1200 min
c. 50000 s
D. 1.5 \( h \)


Evaluate :
\( \int \frac{x+1}{x^{2}+3 x+12} d x \)


Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen. sulphur, and halogens.


When two nonmetals react, what do
they form?
A. A covalent bond
B. An ionic bond
c. A synthesis reaction
D. A decomposition reaction
E. A hybrid bond


If \( a^{2}+10 b^{2}+5 c^{2}+6 a b+2 b c-16 c+ \)
\( \mathbf{1 6}=\mathbf{0} \) then the possible value of \( \boldsymbol{a}- \)
\( b+c= \)
A . 5
B. -3
\( c \cdot-2 \)
D. 10


The diagram in Fig. shows a three-pin
socket marked as 1,2 and \( 3 . \) To which wire is the fuse connected?
4
\( c \)
D. 1 and 3


Base surface area of a cylinder is 20
\( c m^{2} \) and its height is \( 10 \mathrm{cm} . \) Find the
volume of the cylinder.


In eukaryotic cell cycle, cell fusion
experiments show that
A. When an S phase cell is fused with a G_phase cell, \( G_{1} \)
phase cell is stimulated to synthesize DNA
B. When an S phase cell is fused with a Ga phase cell, DNA
synthesis is induced in \( \mathrm{G}_{2} \) phase cell
C. When a Gi phase cell is fused with a Ga phase cell, DNA
synthesis is induced in both \( \mathrm{G}_{1} \) and \( \mathrm{G}_{2} \) phase cells
D. When a Gi phase cell is fused with an M phase
cell both \( \mathrm{G}_{1} \) and \( \mathrm{M} \) phase cells are stimulated to synthesise DNA


Study of effect of potassium bisulphate as food preservative under various conditions (temperature, concentration,
time etc.)


Which of the following was not proposed by Thomson?
A. The negative and positive charges are equal in magnitude
B. The electrons revolve around the nucleus in circular paths
C. The electrons are embedded in a positive sphere
D. Atoms are electrically neutral


A rectangular tank is \( 80 m \) long and \( 25 m \) broad. Water flows into it through
a pipe whose cross-section is \( 25 \mathrm{cm}^{2}, \) at
the rate of \( 16 k m \) per hour. How much
the level of the water rises in the tank in
45 minutes?


During extraction of \( N a C l \), sodium is deposited at :
A. anode
B. cathode
c. Depends on \( N a C l \)
D. No deposition takes place


Integrate w.r.t \( \times \frac{3 x}{1+2 x^{4}} \)
A \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
B. \( \frac{3}{2 \sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
\( \frac{3}{2 \sqrt{2}} \tan ^{-1} 2 x^{2}+c \)
D \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} x^{2}+c \)


The process of separation of cream from milk is called:
A. emilsification
B. demulsification
c. electro-osmosis
D. peptization


The measure of an angle in degrees,
grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2 C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following
questions :The angles between the hour hand and minute hand of a clock at half
past three is -
\( A \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{5 \pi}{12} \)
D. \( \frac{7 \pi}{12} \)


Which of the following does not react
with cold water?
A . \( S i C \)
в. АIN
c. \( C a C_{2} \)
D. \( A l_{4} C_{3} \)


A magnified, inverted image is located
a distance of \( 32.0 \mathrm{cm} \) from a concave
mirror with a focal length of \( 12.0 \mathrm{cm} \) Determine the object distance and tell whether the image is real or virtual.


If \( A \) is a singular matrix, then \( A(\operatorname{adj} A) \)
is a
A. scalar matrix
B. zero matrix
c. identity matrix
D. orthogonal matrix


The most abundant metal in the earth's
crust is :
A . Silver
B. Aluminium
c. Calcium
D. Gold


Define peptide linkage.


A cricket ball of mass \( 500 \mathrm{g} \) is moving with speed of \( 36 k m h^{-1} . \) It is reflected
back with the same speed. What is the
impulse applied on it?
A. \( 20 \mathrm{Kg} \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. none of the above


If \( f(x)=(x-[x]) \sin \frac{1}{x}, \) then at \( x=0 \)


In the equation of \( \boldsymbol{A C}, \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
the current amplitude and frequency will respectively be
A \( \cdot I_{0}, \frac{\omega}{2 \pi} \)
В. \( \frac{I_{0}}{2}, \frac{\omega}{2 \pi} \)
\( c \cdot I_{r m s}, \frac{\omega}{2 \pi} \)
D. \( I_{0}, \omega \)


Chromatography is used to separate:
A . molecules
B. atoms
C. solution
D. mixtures


Which one of the following is the unit vector perpendicular to both \( \overrightarrow{\boldsymbol{a}}=-\hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ? \)
A \( \cdot \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
в. \( \hat{k} \)
\( c \cdot \frac{\hat{j}+\hat{k}}{\sqrt{2}} \)
D. \( \frac{\hat{i}-\hat{\jmath}}{\sqrt{2}} \)


A body of mass 2 kg moving with velocity of \( 6 \mathrm{m} / \mathrm{s} \) strike another body of same mass at rest and sticks to it. The
amount of heat evolved during collision is:
A . 18 J
B. 36 J
c. 9 J
D. 3


Write the structure of 2-hydroxybenzoic acid.


Fibres with tapering ends and spindle shape are seen in case of
A . Striated muscle
B. Cardiac muscle
c. skeletal muscle
D. Smooth muscle


If \( \lambda \) is the wavelength of hydrogen atom
from the transition \( n=3 \) to \( n=1 \), then
what is the wavelength for doubly ionised lithium ion for same transition?
\( A \cdot \frac{\lambda}{3} \)
B. \( 3 \lambda \)
\( c \cdot \frac{\lambda}{9} \)
D. \( 9 \lambda \)


In parallelogram \( A B C D, A B=10 \mathrm{cm}, A D= \)
\( 24 \mathrm{cm} \) and \( \mathrm{BD}=26 \mathrm{cm}, \) find the area
of parallelogram(in \( \mathrm{cm}^{2} \) )


The nuclear material without nuclear
membrane is observed in
A. Bacteria and green algae
B. Cyanobacteria and red algae
c. Bacteria and cyanobacteria
D. Mycoplasma and green algae


Silicon has 4 electrons in its outer most
orbit. In forming the bond:
A. it gains electrons
B. it loses electrons
c. it shares electrons
D. none of the above


A charged body is brought near an uncharged gold leaf electroscope. What will be your observation if the body is charged?
A. leaves will diverge
B. leaves will converge
c. leaves will remain unaffected
D. none


If \( S_{n}=2+0.4 n, \) find initial velocity
and acceleration
A . 2.2 units, 0.4 units
B. 2.1 units, 0.3 units
c. 1.2 units, 0.4 units
D. 2.2 units, 0.3 units


(a) State Joule's law of heating. Name two gases which are filled in electric bulbs and explain why these gases are filled in electric bulbs.
(b) An electric iron consumes energy at
a rate of \( 840 \mathrm{W} \), when heating is at the maximum rate. The voltage of electric
source is \( 220 \mathrm{V} \). Calculate the value of
current and the resistance


The solution of the D.E \( y y_{1}= \)
\( \left[\frac{\boldsymbol{y}^{2}}{\boldsymbol{x}^{2}}+\frac{\boldsymbol{f}\left(\boldsymbol{y}^{2} / \boldsymbol{x}^{2}\right)}{\boldsymbol{f}^{\prime}\left(\boldsymbol{y}^{2} / \boldsymbol{x}^{2}\right)}\right] \) is:
\( ^{A} \cdot f\left(\frac{y^{2}}{x^{2}}\right)=c x^{2} \)
B. \( x^{2} f\left(\frac{y^{2}}{x^{2}}\right)=c^{2} y^{2} \)
C \( \cdot x^{2} f\left(y^{2} / x^{2}\right)=c \)
D. \( f\left(\frac{y^{2}}{x^{2}}\right)=c y / x \)


Which statements is/ are correct?
This question has multiple correct options
A. When \( F e C l_{3} \) is added to excess of hot water, a
positively charged colloidal solution form
B. Amount of electrolyte required to cause coagulation is higher for lyophobic than Iyophillic colloids
C. High pressure is favaourable for physical as well as chemical adsorption
D. Physical and chemical adsorption both decrease entropy of universe


If the vertices of a \( \Delta A B C \) are \( A= \)
\( (1,-1,-3), B=(2,1,-2) \) and \( C= \)
(-5,2,-6) then the length of the
internal bisector of angle \( \boldsymbol{A} \) is
A \( \cdot \frac{3 \sqrt{10}}{2} \)
в. \( \frac{3 \sqrt{10}}{5} \)
c. \( \frac{3 \sqrt{10}}{7} \)
D. \( \frac{3 \sqrt{10}}{4} \)


When 1 coulomb of charge flows through a conductor in 1 sec, then the current passing through the conductor is?
A. \( 1 \mathrm{Hp} \)
B. 1A
c. \( 1 \mathrm{C} \)
\( D \cdot 1 P \)


Sum the series to \( n \) terms
\( \frac{1}{2.4 .6}+\frac{1}{4.6 .8}+\frac{1}{6.8 .10}+\dots \)


\( 2 g \) of \( N a O H \) are dissolved in water to
make 1 litre solution. What is pH of
solution?


Find the real values of \( x \) and \( y, \) if
\( (x+i y)(2-3 i)=4+i \)


In above shown figure, fringe pattern is produced by a monochromatic light passing through two narrow slit. If the fringe width is \( 2 \mathrm{cm} \) then, which of the following changes would increase the distance between the bands?
A. Moving the slits closer together
B. Making the light source brighter
c. Moving the slits closer to the screen
D. Increasing the frequency of the light
E. shortening the wavelength of the light


Draw the graph of the following linear
equation
\( -\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6} \)


A point charge \( +\boldsymbol{q} \& \) mass \( 100 g \boldsymbol{m} \)
experiences a force of \( 100 N \) at a point
at a distance \( 20 \mathrm{cm} \) from a long infinite uniformly charged wire. If it is released its speed is \( 20 \sqrt{\ln x} \) m/ \( s \) when
it is at a distance \( 40 \mathrm{cm} \) from wire. Find
\( \boldsymbol{x} \)


A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius 'R'. The magnetic field 'B' produced at a perpendicular distance 'd' from the axis
of the cylinder is plotted in a graph Which of the following figures looks like the plot?
\( A \)
в.
\( c \)
D.


Aquatic ancestry of bryophytes is evidenced by
A. Theirgreen colour
B. Algae like protonema
C. Many aquatic bryophytes
D. Flagellated male gametes


A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.


At \( 25^{\circ} \mathrm{C} \) the saturated vapour pressure
of water is 3.165 kPa \( (23.75 \mathrm{mm} \mathrm{Hg}) \) Find the saturated vapour pressure of a \( 5 \% \) aqueous solution of urea (carbamide) at the same temperature.
(Molar mass of urea \( =\mathbf{6 0 . 0 5} \) g \( \boldsymbol{m o l}^{-1} \) )


Arrange the following as per the
instructions given in the brackets:
\( N a, K, C l, S, S i \) (increasing order of ionization energy)


An AP consists of 23 terms. If the sum of the 3 terms in the middle is 141 and the
sum of the last 3 terms is 261 , then the
first term is
A . 6
B. 5
\( c \cdot 4 \)
D. 3
E . 2


Which of the reactant act as oxidant?
\( \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{P C l}_{5} \)
A \( \cdot C l_{2} \)
в. \( P C l_{3} \)
c. Both of these
D. None of these


Prove that the area enclosed between
two parabolas \( y^{2}=4 a x \) and \( x^{2}=4 a y \)
is \( \frac{16 a^{2}}{3} \)


A cross between two tall garden pea plants produced all tall plants. The possible genotypes of the parents are
I) \( \pi, \) T
II) TT, Tt
III) \( T t, t \)
IV) \( \mathrm{Tt}, \mathrm{Tt} \)
A . ॥I, IV
B. I, IV
\( c \cdot 1,1 \)
D. II, III


The isotope of hydrogen, \( D_{2} \) forms heavy
water, \( D_{2} O . \) It is qualified as \( D_{2} O \) because it is:
A. a heavy liquid
B. an oxide of heavier isotope of oxygen
c. an oxide of deuterium
D. denser than water


Three sides \( A, B \) and \( C \) are moving in a straight line in same direction such that relative velocity of \( A \) wrt \( B \) is \( 2 m / s \) relative velocity of B wrt C is -5m/s. Find relative velocity of \( C \) wrt A. Also write which body is moving in b/w of remaining two bodies.


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \frac{A l \operatorname{co.KOH}}{\Delta} \boldsymbol{B} \stackrel{\boldsymbol{H B r}}{\longrightarrow} \)
\( C \stackrel{N a / \text {ether}}{ } D \) the compound D is
A. ethane
B. propane
c. n-butane
D. n-pentane


The excess pressure across a soap bubble of radius \( r \) is \( p=\frac{4 \sigma}{r}, \) where \( \sigma \)
is the surface tension of soap solution.
What is the excess pressure across an
air bubble of the same radius \( r \) formed
inside a container of soap solution?
A \( \cdot \frac{\sigma}{r} \)
в. \( \frac{2 \sigma}{r} \)
c. \( \frac{4 \sigma}{r} \)
D. none of these


Number of revolution per second made by electron in Bohr orbit is called orbital
frequency. If \( \boldsymbol{u}_{n}, \boldsymbol{r}_{n}, \boldsymbol{E}_{n} \) are velocity,
radius and energy level of \( n \) th orbit respectively?
A \( \cdot \frac{u_{n}}{2 \pi r_{n}} \)
B. \( -\frac{2 E_{n}}{n h} \)
c. \( -\frac{2 E_{1}}{n^{3} h} \)
D. either of these


An angle is \( 45^{\circ} \) less than two times of
its supplement, then the greater angle is
A \( .75^{\circ} \)
B . \( 100^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 105^{\circ} \)


Write the number of significant digits in \( 6.032 ? \)
A . 4
B. 3
\( c \cdot 2 \)
D. none of the above


The duration of the day form the moment the sun is overhead today to the moment the sun will be overhead
tomorrow is determined by
A. the rotation of the earth's on its axis only
B. the revolution of the earth round the sun only.
c. the rotation of the earth on its axis as well the revolution of the earth around the sun
D. the inclination of the axis of rotation of the earth to its plane of revolution.


Pure \( S e \) at \( 300 K \) has equal electron \( \left(n_{e}\right) \)
and hole \( \left(n_{h}\right) \) concentration of \( 1.5 \times \)
\( 10^{6} m^{-3} . \) Doping by indium increases
\( \boldsymbol{n}_{\boldsymbol{h}}=\mathbf{4 . 5} \times \mathbf{1 0}^{\mathbf{2 2}} \boldsymbol{m}^{-\mathbf{3}} . \) Calculate the
doped silicon.


Which equation has the solution shown
on the number line?
\( \mathbf{A} \cdot x \geq 1 \)
в. \( x \geq-6 \)
c. \( x \neq 1 \)
D. \( x<0 \)


Name the source from which litmus
solution is obtained. What is the use of
this solution?


What is the degree of the given monomial \( 7 y ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D.


Colloidal solutions are classified on the
basis of :
A. molecular size
B. orgainc or inorganio
c. surface tension value
D. pH value


\( (A g+P b) \) alloy \( \frac{M e l t a n d}{Z i n c i s a d d e d}(A g+P b+ \)
\( Z n) m e l t \stackrel{C o o l}{\longrightarrow} \frac{\text {Layer} X}{\text {Layer} Y} \)
Select the correct statement based on
the above scheme:
A. Layer X contains Zn and Ag
B. Layer Y contains Pb and Ag but amount of silver in this layer is smaller than in layer \( x \)
c. \( x \) and \( Y \) are immiscilbe layer
D. All the correct statements


\( \lim _{x \rightarrow 1} 2 x+1 \)


If \( f(x)=x^{2 / 3}, x \geq 0 . \) Then,the area of
the region enclosed by the curve \( y= \) \( f(x) \) and the three lines \( y=x, x=1 \)
and \( x=8 \) is
\( ^{\mathrm{A}} \cdot \frac{63}{2} \)
в. \( \frac{93}{5} \)
\( ^{c} \cdot \frac{105}{7} \)
D. \( \frac{129}{10} \)


What do you observe when water droplets fall on blue cobalt chloride?


For the redox reaction \( Z n(S)+C u^{2+}(0.1 M) \rightarrow \)
\( Z n^{2+}(1 M)+C u(s) \) taking place in a cell, \( E_{c e l l}^{0} \) is
1.10 volt. \( E_{\text {cell}} \) for the cell will be:
\( \left(2.303 \frac{R T}{F}=0.0591\right) \)
\( \mathbf{A} \cdot 2 \cdot 14 V \)
B. \( 1.80 V \)
c. \( 1.07 V \)
D. \( 0.82 V \)


What is meant by peptide linkage and biocatalysts?


The elements of \( (\boldsymbol{A}-\boldsymbol{B}) \) are:


Find differentiation of \( \sec ^{-1} \tan x \)


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( \mathbf{0 . 4 2 5} \)
A \( \cdot \frac{12}{40} \)
в. \( \frac{19}{40} \)
c. \( \frac{41}{40} \)
D. \( \frac{17}{40} \)


If \( a^{2}, b^{2}, c^{2} \) are in A.P., then the following
are also in A.P.
\( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \)


If the chromosome number in the
somatic cell of gymnosperm is 8. Then the number of chromosomes in the
nucellus of \( C y c a s \) is
A. 08
B. 04
\( c \cdot 16 \)
D. 32


Find the exact position solution of the
equation \( x^{2}+x=30 \)


When a glass rod is rubbed with silk
A. Negative charge is produced on silk but not charge on the glass rod
B. Equal but opposite charge are produced on the both
C. Equal and similar charges are produced on the both
D. Positive charge is produced on the glass rod but no charge on the silk


f \( \sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} \) then
\( a \) value of \( x \) is:
\( A \)
B. 3
\( c \cdot 4 \)
D. 5


Show that:
\( \int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x, \) if \( f(x) \) is an
even function. \( \boldsymbol{I}=\mathbf{0}, \) if \( \boldsymbol{f}(\boldsymbol{x}) \) is an odd
function.


There are 40 students in a chemistry class and 60 students in a physics class. Find the number of students
which are either in physics class or
chemistry class in the following case:
The two classes meet at different hours
and 20 students are enrolled in both the
subjects


An alloy consists of \( 3 \frac{1}{2} g m \) of copper and \( 2 \frac{3}{4} g m \) of tim. Find the ratio of copper so that of tim in the alloy in the simplest form.


Why is \( N_{2} \) less reactive at room
temperature?


How many electrons does oxygen have in its outermost shell?


The focal length of a convex mirror is 10cm. Its radius of curvature will be:
A . \( 5 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 20 \mathrm{cm} \)
D. \( 30 c m \)


The term ecosystem was coined by
A. E.P. Odum
B. A.G. Tansley
c. E. Haeckel
D. E. Warming


Prove that \( 2 \sec ^{2} \theta-\sec ^{4} \theta- \)
\( 2 \cos e c^{2} \theta+\cos e c^{4} \theta=\cot ^{4} \theta-\tan ^{4} \theta \)


An outstanding book on the wave nature of light titled "An Introduction to the
Study of Wave Mechanics" was
published in \( 1930 . \) Who was its author?
A. E. Shroedinger
B. A. Sommerfield
c. P.A.M. Dirac
D. Louis de Broglie


The rate law of gaseous reaction:
\( \boldsymbol{A}_{(g)}+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \) product is given by
\( \boldsymbol{K}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) If the \( ^{\prime} \mathbf{V}^{\prime} \) of one reaction
vessel is suddenly doubled, which of the following will happen?
A. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Two times.
B. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Four times.
c. The rate \( w . r . t^{\prime} B^{\prime} \) will decrease Two times
D. The overall rate will decrease Eight Times of the original Value.


The input signal given to a a CE
amplifier having a voltage gain of 150 is \( V_{i}=2 \cos \left(15 t+\frac{\pi}{3}\right) . \) The
corresponding output signal will be
A \( \cdot 300 \cos \left(15 t+\frac{4 \pi}{3}\right) \)
B. \( 300 \cos \left(15 t+\frac{\pi}{3}\right) \)
c.
\( 75 \cos \left(15 t+\frac{2 \pi}{3}\right) \)
D. \( 2 \cos \left(15 t+\frac{5 \pi}{6}\right) \)


The electronic configuration of an atom/ion can be defined by which of the following?
A. Aufbau principle
B. Pauli's exclusion principle
c. Hund's rule of maximum multiplicity
D. All of the above


A tube of light emits light of wavelength \( \mathbf{5 2 9 6} \) A. The bulb is rated as 200watt
and \( 20 \% \) of the energy is converted into light. If the whole light emitted is allowed to fall on a metal surface
having work function \( 3.00 \times 10^{-19} J \)
calculate the no. of electrons ejected in
\( \mathbf{1 0} \boldsymbol{s} \)


From a point \( Q, \) the length of the
tangent to a circle is \( 24 \mathrm{cm} \) and the
distance of \( Q \) from the centre is \( 25 \mathrm{cm} \) The radius of the circle is


Production of electricity from magnetism is called
A . electric field
B. magnetic field lines
c. electromagnetic induction
D. magnetic induction


The lower edge of a square slab of side \( 50 \mathrm{cm} \) and thickness \( 20 \mathrm{cm} \) is rigidly
fixed to the base of a table. A tangential force of \( 30 \mathrm{N} \) is applied to the slab. If the shear moduli of the material is \( 4 \times \)
\( 10^{10} N / m^{2}, \) then displacement of the
upper edge, in maters is?
A \( .4 \times 10^{-12} \)
В. \( 4 \times 10^{-10} \)
c. \( 6 \times 10^{-10} \)
D. \( 6 \times 10^{-12} \)
E . \( 8 \times 10^{-10} \)


Momentum is a measure of
A. Weight
B. Mass
C . Quantity of motion
D. Velocity


Factorize:
\( (x-y)^{3}-8 x^{3} \)
\( \mathbf{A} \cdot-2(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)
B . \( -(x-y)\left(x^{2}-4 x y+6 y^{2}\right) \)
\( \mathbf{c} \cdot-(x+2 y)\left(x^{2}-4 x y+y^{2}\right) \)
\( \mathbf{D} \cdot-(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)


If heads means one and tail means two,
then coefficients of quadratic equation
\( a x^{2}+b x+c=0 \) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A \( \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{7}{8} \)
D.


What is the probability of getting a king if a card is drawn from a pack of 52
cards?
A \( \cdot \frac{1}{52} \)
в. \( \frac{2}{52} \)
c. \( \frac{3}{52} \)
D. \( \frac{4}{52} \)


The rate of a certain reaction increases
by 2.3 times when the temperature is raised from \( 300 \mathrm{K} \) to \( 310 \mathrm{K} \). If \( \mathrm{k} \) is the
rate constant at \( 300 \mathrm{K} \), then the rate
constant at \( 310 \mathrm{K} \) will be equal to:
\( A \cdot 2 k \)
B.
\( c \cdot 2.3 k \)
\( D \cdot 3 k^{2} \)


Order and degree of \( \left(\frac{d y}{d x}\right)^{2}-5 y=3 \cos x \)
are:
A . 2,3
B. 1,2
\( c \cdot 2,2 \)
D. 1,1


Let \( A \) and \( B \) be two symmetric matrices
of order 3
Statement-1:
\( \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}) \) and \( (\boldsymbol{A B}) \boldsymbol{A} \) are symmetric
matrices.
Statement-2:
\( A B \) is symmetric matrix if matrix
multiplication of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
commutative.
A. Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- 1 .
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true.


A spark is produced between two insulated surfaces maintained at a
potential difference of \( 5 \times 10^{6} V . \) If the
energy output is \( 10^{-5} J \), the charge
transferred during the spark is :
A \( \cdot 5 \times 10^{11} C \)
В. \( 5 \times 10^{-11} C \)
C \( \cdot 2 \times 10^{12} C \)
D. \( 2 \times 10^{-12} C \)


The given plane figure is to be coloured.
What will be the expenditure at the rate
of \( \boldsymbol{R} \boldsymbol{s} 15 \) per \( \boldsymbol{m}^{2} ? \)
A . \( R s 450 \)
B. \( R s 480 \)
c. \( R s 570 \)
D. Rs780


Carius method is used for the
quantitative
estimation of
A. \( c \) and
B. Halogens, S, and P
\( c \cdot N \)
D. All


Let \( P(n)=n(n+1) \) is an even
number, then which of the following
satisfy \( \boldsymbol{P}(\boldsymbol{n}) \)
A \( . P(3) \)
B. \( P(100) \)
c. \( P(50) \)
D. All of these


Define the following terms:
(i) Glycosidic linkage
(ii) Invert sugar
(iii) Oligo saccharides


A bar magnet is dropped along the axis of copper ring held horizontally. The acceleration of fall is
A. equal to g at the place.
B. less than \( g \)
c. more than \( g \)
D. depends upon diameter of the ring and length of the magnet


The pressure \( v / s \) volume graph of an
ideal gas is given in different thermodynamics process which of the
following option in relevant order:
(Isochoric, isobaric, isothermal, adiabatic)
A \( \cdot d, \) a, b,
B. a, d, c,
\( c \cdot a, c, d, b \)
D. a, b, c,


If \( \boldsymbol{R} \) is the largest equivalence relation
on a set \( A \) and \( S \) is any relation on \( A \)
then
A \( . R \subset S \)
в. \( S \subset R \)
c. \( R=S \)
D. none of these


What should retarding potential difference be applied between
electrodes of the photocell for the photocurrent to drop to zero?
A. \( 1.5 V \)
в. \( 2.0 V \)
c. \( 1.8 V \)
D. 2.3V


Define standard enthalpy of reaction.


The molecular formula of diphenyl
methane is \( C_{13} H_{12} . \) How many structural isomers are possible when one of the hydrogen is replaced by a chlorine atom?
\( A .8 \)
B. 7
\( c .6 \)
\( D \)


Consider the following statements regarding gymnosperms and choose the
correct option.
(A) In gymnosperms, the male and female gametophytes have an independent existence.
(B) The multicellular female
gametophyte is retained within the
megasporangium.
(C) The gymnosperms are heterosporous.
\( A \cdot(A) \) and
(B) are true but (C) is false.
B. (A) and
(C) are true but (B) is false.
c. (B) and
(C) are false but (A) is true
D. (A) and
(C) are false but (B) is true.
E. (B) and
(C) are true but (A) is false.


figure bounded by non coplanar triangular planes. So, a tetrahedron has four non-coplanar points as its vertices. Suppose a tetrehedron has points
A,B,C,D as its vertices which have
coordinates \( \left(\boldsymbol{x} \mathbf{1}, \boldsymbol{y} \mathbf{1}, \boldsymbol{z}_{1}\right)\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}, \boldsymbol{z}_{2}\right) \)
\( \left(x_{3}, y_{3}, z_{3}\right) \) and \( \left(x_{4}, y_{4}, z_{4}\right), \) respectively
in a rectangular three dimensional
space. Then, the coordinates of
its centroid are \( \left[\frac{\boldsymbol{x}_{1}+\boldsymbol{x}_{2}+\boldsymbol{x}_{3}+\boldsymbol{x}_{4}}{\boldsymbol{4}}, \frac{\boldsymbol{y}_{1}+\boldsymbol{y}_{2}+\boldsymbol{y}_{3}+\boldsymbol{y}_{4}}{\boldsymbol{4}}\right. \)
Let a tetrahedron have three of its
vertices represented by the points (0,0,0),(6,5,1) and (4,1,3) and
its centroid lies at the point (1,2,5) Now, answer the following question. The coordinate of the fourth vertex of the
tetrahedron is:
A \( \cdot(-6,2,16) \)
B. (1,-2,13)
c. (-2,4,-2)
D. (1,-1,1)


A ware house worker exerts a constant
horizontal force of magnitude \( 85 N \) on a
\( 40 k g \) box that is initally at rest on the floor of the ware house. After moving a
distance of \( 2 m \) the speed of the box is
\( 1 m s^{-1} . \) The coefficent of friction
between the box and the ware house
floor is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A \( .5 / 16 \)
в. \( 3 / 16 \)
c. \( 19 / 80 \)
D. \( 0.25 / 16 \)


A particle vibrates 10 times in 1 sec. What is the time period of vibration of
the particle
A . \( 10 \mathrm{Sec} \)
B. 1 Sec
c. \( 0.1 \mathrm{sec} \)
D. 0.01 sec


A block of mass \( M \) is hanging over a
smooth and light pulley through a light string. The other end of the string is
pulled by a constant force \( F \). If kinetic energy of the block increases by \( 20 J \) in
1 s. Then:
A. Tension in the string is \( M g \)
B. Tension in the string is \( F \)
c. work done by the tension on the block is \( 20 \mathrm{J} \) in 1 sec
D. Work done by the force of gravity is \( -20 \mathrm{J} \) in 1 sec.


In how many acids among following, the basicity is greater than \( 1 ? \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \)


Water is poured into a pan and heated over a flame. After some time, the hot water begins rising to the top. Which type of heat transfer is involved in this?
A. conduction
B. convection
c. radiation
D. thermal expansion
E. specific heat


In which of the following animals are bones not present?
A. Earthworm
B. Snail
c. cockroach
D. All of the above


Match the appropriate pairs from Lists
and \( \|: \)
ListList - II
e) Continuous
a) Nitrogen molecule \( \quad \) spectrum
f) Absorption
b) Incandescent solids \( \quad \) spectrum
c) Fraunhofer lines
g) Band spectrum
d) Electric arc between iron
h) Emission rods \( \quad \) spectrum
\( A \cdot a-g, b-e, c-f, d-h \)
B. \( a-f, b-e, c-h, d-g \)
\( \mathbf{C} \cdot a-h, b-e, c-f, d-g \)
D. a-e, b-g, c-h, d-f


Which of the following gives nitrogen on thermal decomposition?
This question has multiple correct options
A. Ammonium nitrite
B. Ammonia
c. Ammonium dichromate
D. Air


\( \boldsymbol{x}_{1}=\boldsymbol{A} \sin (\omega \boldsymbol{t}-\mathbf{0 . 1} \boldsymbol{x}) \) and \( \boldsymbol{x}_{2}= \)
\( A \sin \left(\omega t-0.1 x-\frac{\phi}{2}\right) . \) The resultant
amplitude of combined wave is:-
A \( \cdot 2 A \cos \frac{\phi}{4} \)
B. \( A \sqrt{2 \cos \frac{\phi}{2}} \)
\( \mathrm{c} \cdot_{2 A \cos \frac{\phi}{2}} \)
D. \( A \sqrt{2\left(1+\cos \frac{\phi}{4}\right)} \)


An electric dipole is placed near a positive charge. It will experience:
A. a torque only
B. a force only
c. both torque and force
D. it will depend on the orientation of the dipole with respect to the charge


A "moving sidewalk" in a busy airport terminal moves \( 1 m / s \) and is \( 200 m \)
long. A passenger steps onto one end and walks, in the same direction as the
sidewalk is moving, at a rate of \( 2.0 \mathrm{m} / \mathrm{s} \) relative to the moving sidewalk. How much time does it take the passenger
to reach the opposite end of the walkway? (in seconds)
A . 66.7
B. 67.3
c. 63
D. 66


There are 8 types of pant pieces and 9 types of shirt pieces with a man. The number of ways in which a pair (1 pant,
1 shirt) can be stitched by the tailor is
A . 17
B. 56
c. 64
D. 72


If \( \boldsymbol{x}=\frac{\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}}}{\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}}} \) find \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \)


A covalent bond is formed when:
A. transfer of electrons take place
B. sharing of electrons take place
C. both sharing and transfer of electrons takes place
D. neither sharing nor transfer of electrons takes place


A and \( \mathrm{B} \) are facing the mirror and
standing in such a way that \( A \) can see \( B \)
and \( B \) can see A. Explain this
phenomenon.


Which one of the following statement is false with respect to deep red
colouration produced with \( N H_{4} S C N ? \)
A. The deep red colour is bleached by \( H g(I I) \) jon
B. The deep red colouration is due to the formation of a non-dissociated iron \( (I I I) \) thiocyanate complex.
c. The deep red coloured compound can be extracted by ether or amyl alcoho
D. None of the above


Assertion
\( \gamma \) -radiation emission occurs after \( \boldsymbol{\alpha} \) and
\( \beta \) decay.
Reason
Energy levels occur in nucleus.
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.


Sulphur dioxide is a strong reducing agent. However, it can also act as an
oxidizing agent. Which of the following reactions shows its oxidizing nature?
A. Bleaching flower petalss
B. Decolourising of acidfied KMnO \( _{4} \) solution
c. Reaction with \( H_{2} S \) to give sulphur
D. Turning acidified dichromate paper green


The surface of the head of a match stick
and sides of a match box are
deliberately made rough to:
A. increase friction
B. decrease friction
c. increase amount of heat
D. decrease amount of heat


The electric potential at a point in free
space due to a charge \( Q \) coulomb is \( Q \times 10^{11} V . \) The electric field at that
point is
A \( \cdot 12 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
B . \( 4 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
C \( .12 \pi \varepsilon_{0} Q \times 10^{20} \mathrm{Vm}^{-1} \)
D. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V m^{-1} \)


Solve:
(i) \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}}+\boldsymbol{x}^{2} \boldsymbol{e}^{-\boldsymbol{2} \boldsymbol{y}} \)


What is potentimeter? Write its
principle.


The twisting couple per unit twist for a
solid cylinder of radius \( 4.9 \mathrm{cm} \) is \( 0.1 N / m . \) The twisting couple per unit twist for a hollow cylinder of same material with outer and inner radii of
\( 5 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively, will be
A. \( 0.64 N / m \)
В. \( 0.64 \times 10^{-1} N / m \)
c. \( 0.64 \times 10^{-2} N / m \)
D. \( 0.64 \times 10^{-3} N / m \)


If \( D E \| B C \) in \( \triangle A B C, A D= \)
\( 1.5 \mathrm{cm}, B D=3 \mathrm{cm} \) and \( A E=1 \mathrm{cm}, \)
then find \( E C(\text { in } \mathrm{cm}) . \)


\( X \) -rays are produced when a stream of
electrons in an \( X \) -ray tube:
A. hits the glass wall of the tube
B. strikes the metal target
c. passes through a strong magnetic field
D. none of the above


toppr
Q Type your question
secondary coil, current through the primary coil and input power are given.
(a) Let the given data be taken as \( \frac{N_{1}}{N_{2}} \)
(turn-ratio), \( i_{1}, \) (input current) and \( P \)
(input power).
(b) Substitute the given values of \( \frac{N_{1}}{N_{2}} \)
and \( i_{1}, \) in the above formula and get the
value of \( i_{2} \)
(c) Write the relation between turn-ratio
and the currents as \( \frac{N_{1}}{N_{2}}=\frac{i_{2}}{i_{1}}, \) where \( i_{2} \) is the current in the secondary coil.
(d) Write the relation between input
power and output power in terms of
\( V_{1}, i_{1}, V_{2}, i_{2} \) i.e. \( V_{1} i_{1}=V_{2} i_{2}=P, \) where
\( V_{1} \) and \( V_{2} \) are the voltage in the primary and secondary coils respectively.
(e) Substitute the values of \( i_{2} \) and \( P \) in
the above relation to get the value of \( V_{2} \)
A \( . \) abdce
B. bcade
c. acbde
D. \( d b c a e \)


A uniform aluminium wire of length \( 3 \mathrm{m} \)
and area of cross-section \( 2 m m^{2} \) is
extended through 12 mm. The energy stored in the wire is
\( \boldsymbol{Y}_{\boldsymbol{A l}}=\boldsymbol{7} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2} \mathbf{)} \)
A . \( 336 J \)
B. 33.6 \( J \)
c. \( 3.36 J \)
D. 0.336 J


Starting with an expression for
refraction at a single spherical surface,
obtain an expression for lens maker's formula.


The graph shows position as a function
of time for two trains \( A \) and \( B \) running
on parallel tracks. For time greater than
\( t=0, \) which of the following statement is
true ?
A. Both trains have the same velocity at timet \( _{B} \)
B. Both trains speed up all the time.
c. Both trains may have the same velocity at some time earlier than \( t_{E} \)
D. Graph indicates that both trains have the same acceleration at a given time


Consider the following relations
\( (1) \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{A}-(\boldsymbol{A} \cap \boldsymbol{B}) \)
(2) \( \boldsymbol{A}=\boldsymbol{A}-(\boldsymbol{A} \cap \boldsymbol{B}) \cup(\boldsymbol{A}-\boldsymbol{B}) \)
(3) \( \boldsymbol{A}-(\boldsymbol{A} \cup \boldsymbol{C})=(\boldsymbol{A}-\boldsymbol{B}) \cup(\boldsymbol{A}-\boldsymbol{C}) \)
Which of these is correct
A . 1 and 3
B. 2 only
\( c \cdot 2 \) and 3
D. 1 and 2


In qualitative analysis, the metals of Group I can be separated from other ions by precipitating them as chloride
salts. A solution initially contains \( A g^{+} \)
and \( P b^{2+} \) at a concentration of 0.10 M.
Aqueous HCl is added to this solution
until the \( C l^{-} \) concentration is 0.10 M.
What will the concentration of \( A g^{+} \) and
\( P b^{2+} \) be at equilibrium? \( \left(K_{s p} \text { for } A g C l=1.8 \times 10^{-10}, K_{s p} \) for \right.
\[
\left.P b C l_{2}=1.7 \times 10^{-5}\right)
\]
\( \mathbf{A} \cdot\left[A g^{+}\right]=1.8 \times 10^{-11} M \)
\[
\left[P b^{2+}\right]=1.7 \times 10^{-4} M
\]
B . \( \left[A g^{+}\right]=1.8 \times 10^{-7} M \)
\[
\left[P b^{2+}\right]=1.7 \times 10^{-6} M
\]
c. \( \left[A g^{+}\right]=1.8 \times 10^{-11} M \)
\[
\left[P b^{2+}\right]=8.5 \times 10^{-5} M
\]
D \( \cdot\left[A g^{+}\right]=1.8 \times 10^{-9} M \)
\[
\left[P b^{2+}\right]=1.7 \times 10^{-3} M
\]


Reduce the equation \( x+2 y-3=0 \) to
slope-intercept form and find its slope
and \( \boldsymbol{y}- \) intercept.


If \( \frac{a^{3}+3 a b^{2}}{3 a^{2} b+b^{3}}=\frac{x^{3}+3 x y^{2}}{3 x^{2} y+y^{3}}, \) then
A \( \cdot b x=a y \)
в. \( b y=a x \)
\( \mathbf{c} \cdot b^{2} y=a^{2} x \)
D. \( b^{2} x=a^{2} y \)


Two particles having the same phase
must be at
A. a crest and a trough respectively at the same time
B. a crest and at the mean position respectively at the same time
C. a trough and at the mean position respectively at the same time
D. Two consecutive crests respectively at the same time


Give reasons why Distance and
displacement are different concepts.


How many ATPs are required by \( \boldsymbol{C}_{4} \) plants in synthesis of one molecule of glucose
A . 18 ATP
в. 30 АтР
c. 12 Атр
D. None of the above


In the following circuit diagram,
A. the diode is forward biased
B. the diode is reverse biased
C. current due to majority charge carriers flow from \( A \) to \( B \)
D. current due to majority charge carriers flows from \( B \) to \( A \)


Which of the following is the only coaltar derived analgesic, still in use today?
A. Acetaldehyde
B. Paracetamol
c. Penicillin
D. Formaldehyde


\( \frac{-}{0} \)
0
0
0


The force of repulsion between two
parallel wires is \( \boldsymbol{F} \) when each one of
them carries a certain current I. If the
current in each is doubled, the force
between them would be
\( A \cdot 8 F \)
в. \( 4 F \)
\( c \cdot 2 F \)
D. \( F \)


An acid with molecular formula
\( C_{7} H_{6} O_{3} \) forms three types sodium salts, i.e., \( C_{7} H_{5} O_{3} N a, C_{7} H_{4} O_{3} N a_{2} \)
and \( C_{7} H_{3} O_{3} N a_{3} . \) The basicity of the
acid is:
A. one
B. Two
c. Three
D. Four


A plane mirror is inclined at \( 40^{\circ} \) to the
floor. An incident ray parallel to the floor
strikes the mirror and a reflected ray is
formed. What is the angle of reflection?
A \( \cdot 40^{\circ} \)
B. \( 50^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 70^{\circ} \)


The pH of a solution of hydrochloric acid is \( 4 . \) The molar concentration of this solution is:
A . 4.0
B. 0.4
c. 0.000
D. 0.04


If \( a^{2}+b^{2}=1, \) then \( \frac{1+b+i a}{1+b-i a}=? \)
\( A \)
B. 2
c. \( b+i a \)
\( \mathbf{D} \cdot a+i b \)


Intensity of an electric field (E) depends on distance \( r . \) In case of dipole, it is
related as:
\( ^{\mathrm{A}}=_{E} \propto \frac{1}{r} \)
в. \( \quad E \propto \frac{1}{r^{2}} \)
c. \( \quad E \propto \frac{1}{r^{3}} \)
D. \( \quad E \propto \frac{1}{r^{4}} \)


If the area enclosed by the parabolas \( y=a-x^{2} \) and \( y=x^{2} \) is \( 18 \sqrt{2} \) sq.
units Find the value of 'a'
A \( . a=-9 \)
B. \( a=6 \)
\( \mathbf{c} \cdot a=9 \)
D. \( a=-6 \)


If the kinetic energy of the molecules in 5 litres of helium at 2 at \( m \) is \( E \). What is
the kinetic energy of molecules in 15
litres of oxygen at 3 at \( m \) in terms of \( E ? \)
A . \( 7.5 E \)
в. \( 7 E \)
\( c .8 .5 E \)
D. \( 8 E \)


The solubility product of an electrolyte is \( 6912 \times s^{n} \) ? How many ions \( (n) \) will be
obtained by the ionization of one molecule of electrolyte?


In a DNA molecule distance between
two bases is
\( \mathbf{A} \cdot 2 n m / 20 \stackrel{\circ}{A} \)
B \( \cdot 0.2 n m / 2 \stackrel{\circ}{A} \)
c. \( 3.4 n m / 34^{\circ} \)
D. \( 0.34 n m / 3.4^{\circ} \)


The binding energy of \( e^{-} \) in the ground
state of the hydrogen atom is \( 13.6 e V \) The energies required to eject out an
electron from three lowest states of \( \mathrm{He}^{+} \)
atom will be (in eV):
A . 13.6,10.2,3.4
в. 13.6,3.4,1.5
c. 13.6,27.2,40.8
D. 54.4,13.6,6


The nth term of the geometric
progression \( -3,6,-12,24 \dots \) is
A. \( -3(-2)^{n+1} \)
B. \( 3(-2)^{n-1} \)
c. \( -3(2)^{n-1} \)
D. \( -3(-2)^{n-1} \)


Among the following has the
highest retentivity.
A. aluminium
B. steel
c. nickel
D. soft iron


Assertion
O \( _{2} \) is paramagenetic in nature.
Reason
Bond-order of oxygen is two.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Prove that, \( (\cos \alpha+\cos \beta)^{2}+ \)
\( (\sin \alpha+\sin \beta)^{2}=4 \cos ^{2}\left(\frac{\alpha-\beta}{2}\right) \)


Statement
As ice absorbs heat and begins to melt,
its temperature remains constant Because
Statement II
Changes of state bring about changes in a substances potential energy, not in its kinetic energy
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct


The reagent used to detect phosphorous in an organic compound is :
A. \( F e S O_{4} \)
в. \( A g N O_{3} \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{2} M o O_{4} \)
D. \( B a C l_{2} \)


Histone occupies the major grooves of DNA at an angle of
\( A \cdot 15^{\circ} \)
B. \( 90^{\circ} \)
\( \mathrm{c} \cdot 45^{\circ} \) to the helix axis
D. 30 to the helix axis


If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are the position vectors of the points \( A, B, C, D \) respectively such that \( 3 \vec{a}+5 \vec{b}-3 \vec{c}-5 \vec{d}=0 \) then \( A B \)
intersects \( C D \) in the ratio
A .2: 3
B. 3: 2
c. 3: 5
D. 5: 3


In the xy-plane, the point of intersection of the lines \( x-7 y=25 \) and \( 7 x+ \)
\( 49 y=31 \) is given by
A \( \cdot(0,-3) \)
в. (4,3)
c. (-3,4)
D. \( \left(\frac{103}{7}, \frac{-72}{49}\right) \)


The ratio of the values in SI units to
values in CGS units of density is
\( \mathbf{A} \cdot 10^{3}: 1 \)
B \( \cdot 10^{2}: 1 \)
\( \mathbf{c} \cdot 10^{-2}: 1 \)
D. \( 10^{-3}: 1 \)


aqueous \( N a O H+P_{4}(w h i t e) \longrightarrow \)
\( \boldsymbol{P H}_{3}+\boldsymbol{X} . \) Compound \( \mathbf{X} \) is:
A. \( N a H_{2} P O_{2} \)
в. \( N a_{2} H P O_{4} \)
c. \( N a_{2} C O_{3} \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


Which substance is in higher concentration in blood than in glomerular filtrate?
A. Urea
B. Plasma proteins
c. water
D. Glucose


If \( P(2,-1), Q(3,4), R(-2,3) \) and
\( S(-3,-2) \) be four points in a plane,
show that PQRS is a rhombus but not a square. Find the area of the rhombus.


Find the matrix \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right], \) which
of the following is correct
A. \( A^{3}+3 A^{2}-I=0 \)
B. \( A^{3}-3 A^{2}-I=0 \)
c. \( A^{3}+2 A^{2}-I=0 \)
D. \( A^{3}-A^{2}+I=0 \)


Binomial system of nomenclature for plants is effective from
A. 5.8.1771
в. 1.5.1753
c. 1.8 .1758
D. 6.7.1736


\( 100 \mathrm{ml} \) of tap water containing
\( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2} \) was titrated with \( \mathrm{N} / 50 \)
\( \boldsymbol{H} \boldsymbol{C l} \) with methyl orange as indicator. If
\( 30 \mathrm{ml} \) of \( H C l \) were required, calculate
the temporary hardness as part of \( \mathrm{CaCO}_{3} \) per \( 10^{6} \) parts of water.
A. 150 ppm
B. 300 ppm
c. 450 ppm
D. 600 ppm


The volume of \( 1.0 g \) of hydrogen at NTP
is:
A \( .2 .24 L \)
B. 22.4 L
c. \( 1.12 L \)
D. \( 11.2 L \)


The equivalent circuit is :
A. NAND gates
B. OR gates
c. AND gates
D. NOR gates


Write the complete symbol for the atom with the given atomic number (Z) and atomic mass \( (A) \)
(i) \( z=17, A=35 \)
(ii) \( z=92, A=233 \)
(iii) \( Z=4, A=9 \)


An Incomplete rrequency alstrıbution IS
given below Median value is \( 46, \) the
missing frequency is
\( \begin{array}{lll}\text { Variate } & \text { Frequency } \\ 10-20 & 12 \\ 20-30 & 30 \\ 30-40 & ? \\ 40-50 & 65 \\ 50-60 & 45 \\ 60-70 & 25 \\ 70-80 & 18 \\ \text { Total } & 229\end{array} \)
A . 33
B. 35
\( c \cdot 34 \)
D. 2


Assertion
STATEMENT 1: Domain of \( \tan ^{-1} x \) and
\( \cot ^{-1} x \) is \( R \)
Reason
STATEMENT 2: \( \boldsymbol{f}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \cot x \) are unbounded function
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT1
C. STATEMENT1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE


Methylethylpropyl amine is optically inactive because
(i) It is not tetrahedral
(ii) Its molecule is superimposable on its mirror image
(iii) The enantiomers are rapidly interconverted
(iv) The nitrogen is \( s p^{2} \) hybridized Which of the above statement(s) is(are)
true?
A. only (i)
B. only (iii)
c. (i) and (iii)
D. All the four


Some hydrogen like atoms in ground state absorb n photons having same energy \( \& \) on de-excitation they emit exactly n photons. Then the energy of absorbed photon may be:
A . 91.8 ev
B. 40.8 ev
\( c .48 .4 \mathrm{ev} \)
D. 54.4 ev


Which of following molecules is not linear?
\( \mathbf{A} \cdot \mathbf{O}=\mathbf{C}=\mathbf{C}=\mathbf{C}=\mathbf{0} \)
B. \( \mathrm{H}_{2} \mathrm{C}=\mathrm{C}=\mathrm{O} \)
c. \( \mathrm{HC} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{CH} \)
D. \( \mathrm{HC} \equiv \mathrm{CH} \)


Distinguish between the following pairs of compounds using the test given within brackets:

Sodium nitrate and sodium sulphite (using dilute sulphuric acid)


State whether true or false.
Gravitational forces can also be
repulsive like that of electrostatic forces.
A. True
B. False


Assertion
According to Lenz Law, since the same
magnetic flux passes through both the primary and secondary windings in an ideal transformer,a voltage is induced
in each winding.
Reason
Voltage induced is same in both the
windings, ideally.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Equation of gas in terms of pressure \( p \)
absolute temperature \( T \) and density \( d \) is :
\( \mathbf{A} \cdot \frac{p_{1}}{d_{1} T_{1}}=\frac{p_{2}}{d_{2} T_{2}} \)
В \( \cdot \frac{p_{1} T_{1}}{d_{1}}=\frac{p_{2} T_{2}}{d_{2}} \)
\( \mathbf{c} \cdot \frac{p_{1} d_{2}}{T_{2}}=\frac{p_{2} d_{1}}{T_{1}} \)
D. \( \frac{p_{1} d_{1}}{T_{1}}=\frac{p_{2} d_{2}}{T_{2}} \)


Construct a triangle \( A B C \) in which
\( A B=5.6 c m, B C=5.4 c m \) and \( \angle B= \)
\( 40^{\circ} \)


Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\cos ^{-1}\left(\frac{\boldsymbol{4} \boldsymbol{x}^{\boldsymbol{3}}}{\mathbf{2 7}}-\boldsymbol{x}\right)\right\} \)
\( ^{A} \cdot \frac{4}{\sqrt{9-x^{2}}} \)
В. \( \frac{1}{\sqrt{9-x^{2}}} \)
c. \( \frac{-3}{\sqrt{9-x^{2}}} \)
D. \( \frac{-1}{\sqrt{9-x^{2}}} \)


Show for positive number \( a, b, c \frac{b c}{a}+ \) \( \frac{a c}{b}+\frac{a b}{c} \leq a+b+c \)


Three identical point charges, each of mass \( \mathrm{m} \) and charge \( \mathrm{q}, \) hang from three strings as shown in figure and assume
the system is in equilibrium. The value of \( q \) in terms of \( m, L, \) and is:
A \( \cdot q=\sqrt{(16 / 5) \pi \varepsilon_{0} m g L^{2} \sin ^{2} \theta \tan \theta} \)
в. \( q=\sqrt{(16 / 25) \pi \varepsilon_{0} m g L^{2} s i n^{2} \theta \tan \theta} \)
c. \( q=\sqrt{(15 / 16) \pi \varepsilon_{0} m g L^{2} s i n^{2} \theta \tan \theta} \)
D. none of these


n \( \Delta A B C, \angle A B C=90^{\circ} \) and \( P \) is a
point on \( A C \) such that \( \angle P B C= \)
\( \angle P C B . \) Show that \( : P A=P B . \) Enter 1 if
true else 0


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \)
then what is determinant of AB?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 10
D. 20


Thermoplastics are
A. linear polymers
B. soften or melt on heating
C. molten polymer can be moulded in desired shape
D. all of the above


One \( k g \) of diatomic gas is at a pressure
of \( 8 \times 10^{4} N / m^{2} . \) The density of the gas
is \( 4 k g / m^{3} . \) What is the energy of the gas due to its thermal motion?
A \( .5 \times 10^{4} J \)
B . \( 6 \times 10^{4} J \)
c. \( 7 \times 10^{4} J \)
D. \( 3 \times 10^{4} J \)


Find the point on the parabola \( y^{2}=18 x \)
at which the ordinate increases at twice
the rate of the abscissa.


In an ellipse the distance between the foci is one third of the distance between
the directrices, then its \( e \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \frac{2 \sqrt{2}}{3} \)
D. \( \frac{1}{3} \)


In a vessel containing \( S O_{3}, S O_{2} \) and \( O_{2} \)
at equilibrium, some helium gas is introduced so that total pressure
increases while temperature and volume remain the same. According to Le Chatelier's principle the dissociation
of \( \boldsymbol{S O}_{3} \)
A. increases
B. decreases
c. remains unaltered
D. changes unpredictably


Explain the different zones of a candle flame.


The centre of the hyperbola \( 9 x^{2}-36 x- \)
\( 16 y^{2}+96 y-252=0 \) is
A \( .(2,3) \)
в. (-2,-3)
c. (-2,3)
D. none of these


The value of \( \int_{0}^{\pi} \sin ^{50} x \cos ^{49} x d x \) is
A .
в.
c. \( \frac{\pi}{2} \)
D.


Define electric potential.


Which of the following is true?
A. Rusting will take place in absence of water.
B. Rusting will take place in absence of air.
C. Rusting will not take place in presence of water and air
D. None of the above


If \( 27 a+9 b+3 c+d=0, \) then the
equation \( 4 a x^{3}+3 b x^{2}+2 c x+d=0 \)
has atleast one real root lying between
A. 0 and 1
B. 1 and 3
c. 0 and 3
D. None


Name and state the law which is used
to determine the direction of force on
a current carrying conductor placed in a magnetic field.


Assertion
Most polycyclic aromatic hydrocarbon
do not dissolve easily in water.
Reason
They stick to solid particles and settle to the bottoms of lakes or rivers.
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


Calculate the value of \( \frac{\left(290 K \times 300^{\circ} C\right)}{0^{o} C} \) in Kelvin scale.
A. 708.6
в. \( 608.6 \mathrm{k} \)
c. \( 508.6 \mathrm{k} \)
D. 408.6


What are resonating frequency for two circuits.


Which of the following is tetrabasic acid?
A. orthophosphoric acid
B. Hypophosphorus acid
c. Metaphosphoric acid
D. Pyrophosphoric acid


toppr \( E \)
Q Type your question-
product?
\( A \)
\( (\mathrm{A}) \)
\( B \)
\( (\mathrm{B}) \)
\( c \)
\( (\mathrm{C}) \)
\( D \)
\( (\mathrm{D}) \)


Which of the following is incorrect statement about Mendeleev's
classification of elements?
A. He could classify all the elements including noble gases
B. He left gaps for some yet to be discovered elements
c. He predicted the properties of some undiscovered elements
D. There was no place for isotopes in his table


\( \frac{\sin (\alpha+\beta)}{\sin (\alpha-\beta)}=\frac{a+b}{a-b} \) then prove that
\( \boldsymbol{a} \tan \boldsymbol{\beta}=\boldsymbol{b} \tan \boldsymbol{\alpha} \)


Two sound waves having a phase
difference of \( 60^{\circ}, \) have a path difference
of :
\( A \cdot \frac{\lambda}{3} \)
B. \( \frac{\lambda}{6} \)
\( c \cdot \frac{\lambda}{9} \)
D. \( \lambda \)


The monomeric actin is called as
A. F- actin
B. M- actin
c. G- actin
D. N- actin


Sound waves cannot travel through
A. Solids
B. Liquids
c. Gases
D. vacuum


The gas mixture constists of 3 moles of oxygen and 5 moles of argon at temperature \( T . \) Considering only
translational and rotational modes, the
total internal energy of the system is:
A . \( 12 R T \)
в. \( 20 R T \)
c. \( 15 R T \)
D. \( 4 R T \)


A good fuel has high calorific values.
A. True
B. False


The plane face of a plano convex lens is
silvered. If \( \mu \) be the refractive index and
R, the radius of curvature of curved
surface, then system will behave like a concave mirror of curvature.
A \( . \mu R \)
в. \( R^{2} / \mu \)
\( \mathbf{c} \cdot R /(\mu-1) \)
D. \( [(\mu+1) /(\mu-1)] R \)


Name and state the law which is kept in
mind while balancing equations.


Oxidation state of \( \boldsymbol{C r} \) in \( \boldsymbol{K}_{3}\left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \)
is :


Select the correct I.U.P.A.C. name for
\( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right] \mathrm{SO}_{4} \)
A. Pentaaqua nitrosonium iron
(I) sulphate
B. Pentaaqua nitrosylium iron (I) sulphate
c. Pentaaqua nitrosylium iron
(II) sulphate
D. Pentaaqua nitrosonium ferrate
(II) sulphate


Two wires of resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) at
\( 0^{\circ} C \) have temperature coefficient of
resistance \( \alpha_{1} \) and \( \alpha_{2}, \) respectively. These are joined in series. The effective temperature coefficient of resistance is
:-
A \( \cdot \frac{\alpha_{1}+\alpha_{2}}{2} \)
в. \( \sqrt{\alpha_{1} \alpha_{2}} \)
c. \( \frac{\alpha_{1} R_{1}+\alpha_{2} R_{2}}{R_{1}+R_{2}} \)
D. \( \frac{\sqrt{R_{2} R_{1} \alpha_{1} \alpha_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}} \)


If the relation is defined on \( \boldsymbol{R}-\{\mathbf{0}\} \) by
\( (x, y) \in S \Leftrightarrow x y>0, \) then \( S \) is
A. an equivalence relation
B. symmetric only
c. reflexive only
D. transitive only


Define principal focus of a convex lens. Draw light ray diagram of an image formed, when the object is placed in
between principal focus \( \boldsymbol{F} \) and \( 2 \boldsymbol{F} \) Write lens formula.

Calculate power of a lens if its focal
length is \( 0.5 m \)


Mono atomic element among the following is:
A. phosphorus
B. oxygen
c. krypton
D. sulphur


Draw a circuit diagram of an \( n-p-n \)
transistor with its emitter-base
junction foward biased and base-
collector junction reverse biased. Briefly describe its working Explain how a transistor in active
states exhibits a low resistance at its
emitter-base junction and high resistance at its base-collector
junction.


Calculate the energy required to excite
1 L of hydrogen gas at 1 atm and 298K to the first excited state of atomic
hydrogen. The energy for the dissociation of \( \boldsymbol{H}-\boldsymbol{H} \) bond is
\( 436 k J m o l^{-1} \)


The insecticide chlordane is warmed
with dilute NaOH solution for some
time. The no. of NaOH consumed:


Evaluate: \( \int_{3}^{9} \frac{\sqrt[3]{12-x}}{\sqrt[3]{x}+\sqrt[3]{12-x}} d x \)


Convert the complex number \( \frac{-16}{1+i \sqrt{3}} \) into polar form.


One mega joule approximately equals
\( A \cdot 240 \mathrm{kcal} \)
B. 2400 kcal
c. 24 kcasl
D. 2.4 kcal


The sky appears dark instead of blue to
an astronaut.Why?


The number of spectral lines that are
possible when electrons in fourth energy level in different hydrogen atoms return to ground state.
A .4
B. 8
\( c \cdot 6 \)
\( D \)


Match the columns I, II and III and mark
the appropriate choice.
\begin{tabular}{lll}
Column I & Column II & Column III \\
(A) Bromine & (i) Noble metal & (p) Amalgam \\
(B) Gold & (ii) Crystalline non-metal & (q) \( 4 s^{2} 4 p^{5} \) \\
(C) Mercury & (iii) Liquid non-metal & (r) Transition metal \\
(D) lodine & (iv) Liquid metal & (s) Violet \\
\hline
\end{tabular}
\( A \)
(A) \( \rightarrow(\text { iii }, q) ;(B) \rightarrow(i, r) ;(C) \rightarrow(i v, p) ;(D) \rightarrow(\text { ii, s }) \)
в. \( (A) \rightarrow(i i, p) ;(B) \rightarrow(i, s) ;(C) \rightarrow(i i i, q) ;(D) \rightarrow(i v, r) \)
\( c \)
(A) \( \rightarrow(\mathrm{i}, \mathrm{s}) ;(\mathrm{B}) \rightarrow(\mathrm{ii}, \mathrm{p}) ;(\mathrm{C}) \rightarrow(\mathrm{i} \vee, \mathrm{r}) ;(\mathrm{D}) \rightarrow(\text { iii }, \mathrm{q}) \)
\( D \cdot(A) \)
\( \rightarrow \) ii व)
\( (c) \)
\( \rightarrow \)
D) \( \rightarrow(i \) \( p \)


Members of which of the following have similar chemical properties?
A. Isotope
B. Isobars
c. Allotropes
D. Both isotopes and allotropes


Where is the tricuspid valve found?


If \( f(x)=\left\{\begin{array}{ll}\frac{x}{1+e^{1 / x}} & x \neq 0 \\ 0 & x=0\end{array} \), then the \right.
function \( f(x) \) is differentiable for:
\( \mathbf{A} \cdot x \in R^{+} \)
B. \( x \in R \)
c. \( x \in R-\{0\} \)
D. \( x \in R-\{0,1\} \)


The elements that reacts with cold
water:
A . Mg
B. Са
\( c . \) Ве
D. Mg \& Ca


The density of a cuboid of mass \( 200 g \)
with dimensions \( 2 \mathrm{cm} \times 4 \mathrm{cm} \times 5 \mathrm{cm} \) is
A \( \cdot 1000 \mathrm{kg} \mathrm{m}^{-3} \)
в. 3000 kg \( m^{-3} \)
c. \( 5000 \mathrm{kg} \mathrm{m}^{-3} \)
D. 2000 kg m \( ^{-3} \)


The number of significant figures in
3400 is :
A . 4
B.
\( c \cdot 3 \)
\( D \)


Soid PCI \( _{5} \) exists as ?


\( \frac{1}{(216)^{\frac{-2}{3}}}+\frac{1}{(256)^{\frac{-3}{4}}}+\frac{1}{(243)^{\frac{-1}{5}}} \) is equal
to:
A. 103
в. 105
\( c .107 \)
D. 101


Solve for \( a, b \)
\( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}-\mathbf{4} \boldsymbol{a}+\mathbf{1 6} \boldsymbol{b}+\mathbf{6 8}=\mathbf{0} \)


At a place, the horizontal and vertical components of earth's magnetic field are equal. What is the angle of dip at that place?
A . 45
B. 55
\( c \cdot 65 \)
D. 76


A thin prism of glass is placed in air and water successively. If \( \mu=\frac{3}{2} \) and \( \mu=\frac{4}{3} \)
then the ratio of deviations produced by the prism for a small angle of incidence when placed in air and water is
\( A \cdot 4: 1 \)
B. 3:4
\( c \cdot 1: \)
D. 9: 16


The image of a candle flame formed by a lens is obtained on a screen placed on
the other side of the lens. If the image is
three times the size of the flame and
the distance between lens and image is \( 80 \mathrm{cm}, \) at what distance should the candle be placed from the lens?
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( -36.67 \mathrm{cm} \)
\( \mathbf{c} .-26.67 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)


The exact location of an electron can not
be determined in space.
A. Heisenberg Uncertainty principle
B. Pauli Exclusion Principle
c. schrodinger Wave Equation
D. Hunds Rule
E. Bohr model of the hydrogen atom


Given the first two terms of an infinitely decreasing geometric progression \( \sqrt{\mathbf{3}}, \frac{\mathbf{2}}{\sqrt{\mathbf{3}}+\mathbf{1}} \)
Find the common ratio and the sum of
the progression.


The bulk modulus of elasticity with increase in pressure
A. increases
B. decreases
c. remains constant
D. increases first up to certain limit and then decreases


How much \( C O_{2} \) can be carried by 100
\( \mathrm{ml} \) of blood?
A . 20 \( \mathrm{m} \)
B. 0.3 \( m \)
c. 3.7 \( m \)
D. \( 6.3 \mathrm{m} \)


Find the sum of the series.
\( \mathbf{1 1}^{\mathbf{3}}+\mathbf{1 2}^{\mathbf{3}}+\mathbf{1 3}^{\mathbf{3}}+\ldots+\mathbf{2 8}^{\mathbf{3}} \)


The vector \( \frac{1}{3}(2 \hat{i}-2 \hat{j}+\hat{k}) \) is
This question has multiple correct options
A. unit vector
B. Makes an angle \( \pi / 3 \) with vector \( 2 \hat{i}-4 \hat{j}+3 \hat{k} \)
C. parallel to the vector \( -\hat{i}+\hat{j}-(1 / 2) \hat{k} \)
D. perpendicular to the vector \( 3 \hat{i}+2 \hat{j}-2 \hat{k} \)


A geostationary satellite is at a height
above the surface of earth. If earth
radius is \( \mathrm{R} \)
A. The minimum colatitude on earth upto which the satellite can be used for communication is \( \sin ^{-1}(\mathrm{R} / \mathrm{R} \)
\( +h) \)
B. The maximum colatitudes on earth upon which the satellite can be used for communication is \( \sin ^{-1}(R / R+h) \)
c. The area on earth escaped from this satellite is given as \( 2 \pi R^{2}(1+\sin \theta) \)
D. The area on earth escaped from this satellite is given as \( 2 \pi R^{2}(1+\cos \theta) \)


You place \( 2.56 \mathrm{g} \) CaCO\( _{3} \) (calcium carbonate) in a beaker containing 250
\( \mathrm{mL} \) of \( 0.125 \mathrm{M} \) HCl. What mass of
\( \mathrm{CaCl}_{2} \) can be produced? (Answer in nearest integer)
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q}) \rightarrow \)
\( \boldsymbol{C a C l}_{2}(\boldsymbol{a q})+\boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)


If the vectors \( \vec{A}=2 \hat{i}+4 \hat{j} \) and \( \vec{B}= \) \( \mathbf{5} \hat{\mathbf{i}}-\boldsymbol{P} \hat{\boldsymbol{j}} \) are parallel to each other, the
magnitude of \( \vec{B} \) is:
A \( 5 \sqrt{5} \)
5
B. 10
c. 15
D. \( 2 \sqrt{5} \)


The molar mass of \( C a C O_{3} \) is :
\( \mathbf{A} \cdot 68 \mathrm{g} / \mathrm{mol} \)
B. \( 75 \mathrm{g} / \mathrm{mol} \)
c. 82 g/mol
D. \( 100 \mathrm{g} / \mathrm{mol} \)
E . \( 116 \mathrm{g} / \mathrm{mol} \)