Find derivative of \( \tan ^{-1} \frac{\cos x-\sin x}{\cos x+\sin x} \)
w.r.t. \( \boldsymbol{x} \)
A . -1
B.
c. 1
D.


If \( A \) be a \( 3 \times 3 \) matrix and \( I \) be the unit
matrix of that order such that \( \boldsymbol{A}= \)
\( A^{2}+I \) then \( A^{-1} \) is equal to
A . \( A \)
в. \( A+I \)
c. \( I-A \)
D. \( A-I \)


Choose the correct answer from the
alternatives given Water enters capillaries on the venule side as a result of:
A. higher red blood cell concentration on this side
B. increased blood pressure on this side
c. an osmotic pressure gradient
D. active transport from tissue fluid


Which of the following compound has
three \( 1^{\circ} \), one \( 2^{\circ} \) and one \( 3^{\circ} \) carbon?
A \( \cdot C H_{3}\left(C H_{2}\right)_{4} C H_{3} \)
в. \( C H_{3} C H\left(C H_{3}\right) C H_{3} \)
c. \( C H_{3}\left(C H_{2}\right)_{3} C H_{3} \)
D. \( C H_{3} C H\left(C H_{3}\right) C H_{2} C H_{3} \)


If
A.C. voltage is applied to a pure capacitor, then voltage across the
capacitor
A \( \cdot \) Leads the current by phase angle \( \left(\frac{\pi}{2}\right) \) rad.
B. Leads the current by phase angle \( (\pi) \) rad.
C - Lags behind the current by phase angle \( \left(\frac{\pi}{2}\right) \) rad.
D. Lags behind the current by phase angle \( (\pi) \) rad.


Assertion
A substance that can either act as an
acid or a base is called ampholyte.
Reason
Bisulphide ion \( \left(\boldsymbol{H} \boldsymbol{S}^{-}\right) \) and bicarbonate
ion \( \left(H C O_{3}^{-}\right) \) are ampholytes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A current of \( 5 A \) is passing through a metallic wire of cross-sectional area
\( 4 \times 10^{-6} m^{2} . \) If the density of charge
carriers of the wire is \( 5 \times 10^{26} m^{-3}, \) the
drift velocity of the electrons will be :
A. \( 1 \times 10^{2} \mathrm{ms}^{-1} \)
В. \( 1.56 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 1.56 \times 10^{-3} m s^{-1} \)
D. \( 1 \times 10^{-2} \mathrm{ms}^{-1} \)


Which of the following reactions involves the combination of two
elements?
A \( \cdot C a O+C O_{2} \rightarrow C a C O_{3} \)
в. \( 4 N a+O_{2} \rightarrow 2 N a_{2} O \)
c. \( s o_{2}+\frac{1}{2} o_{2} \rightarrow S O_{3} \)
D. \( N H_{3}+H C l \rightarrow N H_{4} C l \)


A large quantity of urban sewage is drained into nearby village river. Which among the given conditions would happen after mixing of sewage into the river?
(i) Biochemical oxygen demand (BOD) of receiving water body increases.
(ii) Dissolved oxygen of receiving water body decreases.
(iii) It will not cause mortality among fishes and other aquatic creatures.
(iv) It will lead to the nutrient
enrichment of receiving water body.
A \( \cdot \) (i), (ii) and (iii)
B. (i), (ii) and (iv)
C. (ii) and (iii) only
D. (iii) and (iv) only


The potential in certain region is given
as \( V=2 x^{2}, \) then the charge density of
that region is
A \( \cdot-\frac{4 x}{\varepsilon_{0}} \)
в. \( -\frac{4}{\varepsilon_{0}} \)
\( \mathbf{c} .-4 \varepsilon_{0} \)
D. \( -2 \varepsilon_{0} \)


The first ionization energy for \( N a \) is \( 495 k J / m o l \)
The BEST estimate for sodium's second
ionization energy would be
A. \( 367 k J / \) mol
в. \( 584 k J / m o l \)
c. \( 690 k J / \) mol
D. \( 4560 k J / \) mol


A person goes to work by car, train or bus. The probabilities of person travelling by there modes are \( 3 / 10,1 / 2 \) and \( 1 / 5 \) respectively. It is found that chance of person being late for work are \( \mathbf{3} / \mathbf{7}, \mathbf{1} / \mathbf{7} \) and \( \mathbf{5} / \mathbf{7} \) by respective modes
Given that on particular day person reaches late, find the probability that on that day he had travelled by train


If the unit of length is doubled the
numerical value of Area will become
times its original value.
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot 2 \)
D. 4


Correct order of boiling point is:
A. Methanol < ethylene glycol < ethanol
B. Methanol < ethanol < ethylene glycol
C. Ethanol < ethylene glycol < methanol
D. Ethylene glycol < methanol < ethanol


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{1+3 x}-\sqrt{1-3 x}}{x} \)


Assertion
In a Daniell cell, if the concentration of
\( C u^{2+} \) and \( Z n^{2+} \) ions are doubled, the
EMF of the cell will be doubled.
Reason
f the concentration of ions in contact
with metals is doubled, the electrode
potential is doubled.
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


In the following sequence of reaction all stereoisomers of (X) have been taken.
Find \( Q \) and \( R \)

Here \( Q= \) Total number of stereoisomers
of \( Y \)
\( \mathrm{R}= \) Total number of stereoisomers of \( \mathrm{Z} \)
What is the sum of \( Q \) and \( R ? \)


When the input of a two input logic gate are 0 and \( 0, \) the output is \( 1 . \) When the inputs are 1 and 0 , the output is zero. The type of logic gate is
A. xor
B. NAND
c. NOR
D. or


A particle moves along +x-axis with initial velocity \( 5 \mathrm{m} / \mathrm{s} \). If acceleration (a)
varies with time (t) as shown in a-tt
graph, then the velocity of the particle
just after 4 second is
A \( .2 .5 m / s \)
B. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( -1.25 m / s \)
D. \( -5 m / s \)


Construct a \( \triangle A B C \) in which \( A B= \) \( 4 \mathrm{cm}, B C=5 \mathrm{cm} \) and \( A C=6 \mathrm{cm} \)
Now, construct a triangle similar to
\( \triangle A B C \) such that each of its sides is
two-third of the corresponding sides of \( \triangle A B C . \) Also, prove your assertion.


Starch is made by photosynthesis in the leaves of plants. It is found in rice, potatoes, and many vegetables sources.
It can be detected with a drop of iodine.
In the presence of starch, iodine:
A. vapourises
B. turns blue
c. decolourises
D. turns into a black solid


As per given sequence of reaction, His:
\[
\begin{aligned}
\mathrm{Ca}+\mathrm{H}_{2} & \frac{\Delta}{\Delta} \rightarrow \mathrm{F} \text { (Solid) } \\
(\mathrm{F})+\mathrm{CaCl}_{2} & \longrightarrow(\mathrm{G}) \text { Solid } \\
(\mathrm{G})+\mathrm{H}_{2} \mathrm{O} & \longrightarrow(\mathrm{H}) \text { gas }
\end{aligned}
\]
\( \mathbf{A} \cdot H C l \)
в. \( C a H C l \)
\( c \cdot C l_{2} \)
D. \( H_{2} \)


Energy band gap between valence band and conduction band for semiconductor
is:
A. approximately 1 ev
B. less than conductors
c. equal to conductors
D. more than insulator


There are three Newton's laws of motion
namely first,second and third laws.We
can derive
A. Second and third laws from the first law
B. First and second laws from the third law
c. Third and first laws from the second law
D. All the three laws are independent of each other


The structure of bicyclo [1.1.0] butane is:
\( \mathbf{A} \)
B.
\( c \)
D.


A stone is released from the top of a
tower of height \( 19.6 \mathrm{m} \). Calculate its
final velocityjust before touching the ground.


Which enzyme converts glucose to ethanol?
A . Diesterase
B. Invertase
c. zymase
D. Both (2) and (3)


State whether true or false.
The other name for the voice box in
humans is Larynx.
A. True
B. False


A small ball of mass \( m \) collides with a
rough wall having coefficient of friction
\( \mu \) at an angle \( \theta \) with the normal to the
wall. If after collision the ball moves
angle \( \alpha \) with the normal to the wall and
the coefficient of restitution is \( e \), then
find the reflected velocity \( \nu \) of the ball
just after collision.


An artery can be distinguished from a vein in having
A. Thicker wall
B. Oxygenated blood
c. More haemoglobin
D. Both A and B


For measuring time in sports events
like sprinting, milisecond\( (\boldsymbol{m s}) \) is a commonly used unit of time. 1 ms \( =? \)
\( \mathbf{A} \cdot 10^{-12} s \)
B. \( 10^{-9} s \)
\( \mathbf{c} \cdot 10^{-3} s \)
D. None of these


The angular momentum of a flywheel having a moment of inertia of \( 0.4 k g m^{2} \)
decreases from 30 to \( 20 \mathrm{kg} m^{2} / s \) in a period of 2 second. Find the average torque in \( \mathrm{Nm} \) acting on the flywhee during this period.


f \( x \) is the \( n^{t h} \) term of the \( A P \)
\( 5 \frac{1}{2}, 11,16 \frac{1}{2}, 22 \ldots \ldots \) with \( x=550 \)
find \( ^{\prime} \boldsymbol{n}^{\prime} \)


In the process of respiration, the largest amount of energy is produced during
A. Anaerobic respiration.
B. Krebs cycle and oxidative phosphorylation
c. Glycolysis.
D. None of the above


What is the order of magnitude of the resistance of a dry human body?
A . \( 10 \Omega \)
B . \( 10^{4} \Omega \)
c. 10 М\Omega
D. \( 10 \mu \Omega \)


All samples of carbon dioxide contain carbon and oxygen in the mass ratio of
\( \mathbf{3}: 8 . \) This is in agreement with the law
of :
A. conservation of mass
B. constant proportion
c. multiple proportions
D. gaseous volumes


Consider a ball at rest in the middle of a
toy wagon. When the wagon is pulled forward, the ball:
A. Rolls forward
B. Stays stationary
c. Rolls sidewards
D. Rolls backwards


The atoms of different elements which
have the same mass number but different atomic number are
called
A. Isotopes
B. Isobars
c. Isotones
D. None of the above


If \( y=\sin \left(\log _{e} x\right) \) prove that \( \frac{d y}{d x}= \)
\( \frac{\sqrt{1-y^{2}}}{x} \)


Write equations of the following
reactions:
(i) Friedel-Crafts reaction alkylation of
anisole.
(ii) Nitration of anisole.
(iii) Bromination of anisole in ethanoic
acid medium.
(iv) Friedel-Crafts acetylation of anisole.


Which of the following is not correctly matched?
A . Acidic oxides \( -P_{2} O_{5}, N O_{2}, C l_{2} O_{7} \)
B. Basic oxides - \( N a_{2} O, C a O, M g O \)
c. Neutral oxides \( -C O_{2}, C O, B e O \)
D. Amphoteric oxides - \( Z n O, S n O, A l_{2} O_{3} \)


Assertion
The heat absorbed during the isothermal expansion of an ideal gas against vacuum is zero.
Reason
The volume occupied by the molecules of an ideal gas is zero.
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


The osmotic pressure at \( 293 \mathrm{K} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 4.805


Define molar conductivity. How it is
related with conductivity.


0.6 mole of \( N H_{3} \) in a reaction vessel of
\( 2 d m^{3} \) capacity was brought to
equilibrium. The vessel was then found
to contain 0.15 mole of \( H_{2} \) formed by
the reaction
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
Which of the following statements is
true?
A. 0.15 mole of the original \( N H_{3} \) had dissociated at equilibrium
B. 0.55 mole of ammonia is left in the vessel
C . At equilibrium the vessel contained 0.45 mole of \( N_{2} \)
D. The concentration of \( N H_{3} \) at equilibrium is 0.25 mole per \( d m^{3} \)


\( \mathbf{A} \) time \( \boldsymbol{t}=\mathbf{0} \) a particle starts moving
along the \( x \) axis. If its kinetic energy
increases uniformly with \( t, \) the net force acting on it must be
A. Constant
B. Proportional to \( t \)
C . Inversely proportional to \( t^{2} \)
D. Proportional to \( 1 / \sqrt{t} \)


Three persons \( A, B \) and \( C \) apply for a job of Manager in a Private company. Chance of their selection \( (A, B \text { and } C) \)
are in the ratio \( 1: 2: 4 . \) The probability
that \( A, B \) and \( C \) can introduce changes to improve profits of company are 0.8,0.5 and 0.3 respectively, if the changes does not take place, find the probability that it is due to the
appointment of \( \boldsymbol{C} \)


Find mole fraction of \( N a O H \) in its \( 10 \% \)
aqueous solution.


571787 is a perfect cube
Find the cube root of the following number:


If \( A, B \) and \( C \) are mutually exclusive and exclusive events of a random
experiment such that \( \boldsymbol{P}(\boldsymbol{B})=\frac{\boldsymbol{3}}{2} \boldsymbol{P}(\boldsymbol{A}) \)
and \( P(C)=\frac{1}{2} P(B), \) then \( P(A \cup C)= \)
A \( \cdot \frac{10}{13} \)
в. \( \frac{3}{13} \)
c. \( \frac{6}{13} \)
D. \( \frac{7}{13} \)


The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.
A . 2.00
B . 2.25
c. 2.50
D. 2.75


Find the vector equation of the plane passing through (1,2,3) and perpendicular to the plane
\( \vec{r} \cdot(\hat{i}+2 \hat{j}-5 \hat{k})+9=0 \)


A car was travelling at a speed of 10 \( \mathrm{m} / \mathrm{s} . \) After the brakes were applied, it start to decelerate at a rate of \( 2 m / s^{2} \) and finally came to rest. Find the distance traveled by the car before coming to rest.
A. \( 10 \mathrm{m} \)
B. 15 \( m \)
c. \( 25 \mathrm{m} \)
\( D \cdot 35 \mathrm{m} \)


Ethanol is denatured (made unfit for
human consumption) by adding a poisonous substance. Identify it
A. Tartaric acid
B. Methyl alcohol
c. Acetic acid
D. Stearic acid


A body of mass \( 3 \mathrm{kg} \) is under a force which causes a displacement in it, given by \( s=t^{2} / 3(\text { in } \mathrm{m}) . \) Find the work
done by the force in 2 second.
A . 2
B . 3.8
c. 5.2 J
D . 2.6


The impression of an image does not vanish immediately from the retina. It persists there for about \( 1 / 6^{t h} \) of \( a \) second
A. True
B. False


A man stands on the surface of the
earth. The number of action reaction
pairs that can be seen here is/are
\( A \)
B. 2
\( c \cdot 4 \)
D. 5


Define mobility of a charge carrier
What is its relation with relaxation
time?


Masses of two isobars \( _{29}^{64} \mathrm{Cu} \) and \( _{30}^{64} \mathrm{Zn} \) are \( 63.9298 a m u \) and \( 63.9292 a m u \)
respectively. It can be concluded from these data that
A. Both the isobars are stable
B. \( 64 Z n \) is radioactive, decaying to \( ^{64} C u \) through \( \beta- \) decay
c. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \lambda \) \( \operatorname{decay} \)
D. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \beta- \) decay


Find the total force exerted by liquid \( \boldsymbol{A} \)
on the cylinder


\( \sim(p \leftrightarrow q) \) is equivalent to
\( \mathbf{A} \cdot \sim p \wedge \sim q \)
\( \mathbf{B} \cdot \sim p \vee \sim q \)
\( \mathbf{c} \cdot(p \wedge \sim q) \vee(\sim p \wedge q) \)
D. none of these


If \( f(x)=\ln \frac{1+x}{1-x} \) and \( g(x)=\frac{3 x+x^{3}}{1+3 x^{2}} \)
then \( \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})] \) equals.
A. \( f(x) \)
B . \( [f(x)]^{3} \)
\( \mathbf{c} \cdot 3 f(x) \)
D. \( f(x)^{2} \)


A mixture of \( \alpha \) -amino acids is obtained
when proteins are hydrolysed by:
A. acids
B. bases
c. enzymes
D. all of the above


Find the \( x \) and \( y \) in the following figure:


If \( \cos A=\frac{12}{13}, \) then calculate cot \( A \)


The force responsible for raising water
in \( 100 \mathrm{ft} \) tall plant is
A. Transpiration pull
B. Root pressure
c. Air pressure
D. Capillary action


ff \( y=\operatorname{en}\left\{\frac{x+\sqrt{\left(a^{2}+x^{2}\right)}}{a}\right\}, \) then the
value of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is
A \( \cdot \sqrt{a^{2}-x^{2}} \)
B. \( a \sqrt{a^{2}+x^{2}} \)
c. \( \frac{1}{\sqrt{a^{2}+x^{2}}} \)
D. \( x \sqrt{a^{2}+x^{2}} \)


The ore that is concentrated by froth floatation process is
A. cinnabar
B. bauxite
c. malachite
D. zineite


To construct a triangle similar to a
\( \operatorname{given} A B C \) with its sides \( \frac{7}{3} \) of the corresponding sides of \( \Delta A B C, \) draw a
ray \( B X \) making acute angle with \( B C \)
and \( X \) lies on the opposite side of \( A \)
with respect to \( B C . \) The points
\( B_{1}, B_{2}, \dots, B_{7} \) are located at equal
distances on \( B X, B_{3} \) is joined to \( C \)
A. True
B. False


A particle of mass \( \mathrm{M} \) is situated at the
centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be
A. \( -\frac{3 G M}{a} \)
В. \( -\frac{2 G M}{a} \)
c. \( -\frac{G M}{a} \)
D. \( -\frac{4 G M}{a} \)


A particle moves in a circle of radius
1.0 \( c m \) with a speed given by \( v=2 t \)
where \( v \) is in \( c m / s \) and \( t \) in
seconds. Find the radial acceleration of
the particle at \( t=1 s: \)
\( \mathbf{A} \cdot 2.0 \mathrm{cms}^{-2} \)
B. \( 3.0 \mathrm{cms}^{-2} \)
c. \( 4.0 \mathrm{cms}^{-2} \)
D. \( 5.0 \mathrm{cms}^{-2} \)


\( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A}) \neq 0 . \) Find \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A}), \) if
(i) \( A \) is a subset of \( B \)
(ii) \( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{\phi} \)


Calculate the following limits. \( \lim _{x \rightarrow-3} \frac{x+3}{\sqrt{x+4}-1} \)


Explain how does nitrogen exhibit anomalous behaviour amongst group
15 elements.


A certain region of a soap bubble reflects red light of vacuum wavelength \( \lambda=650 n m . \) What is the minimum
thickness that this region of the soap bubble could have? Take the index of
reflection of the soap film to be 1.41
A. \( 1.2 \times 10^{-7} \mathrm{m} \)
B. \( 650 \times 10^{-9} \mathrm{m} \)
c. \( 120 \times 10^{7} m \)
D. \( 650 \times 10^{5} \mathrm{m} \)


\( \boldsymbol{D}=\left|\begin{array}{ccc}\mathbf{1 8} & \mathbf{4 0} & \mathbf{8 9} \\ \mathbf{4 0} & \mathbf{8 9} & \mathbf{1 9 8} \\ \mathbf{8 9} & \mathbf{1 9 8} & \mathbf{4 4 0}\end{array}\right|= \)
\( A \)
B. -
c. zero
\( D \)


Identify all the possible monochloro structural isomers expected to be
formed on free radical
monochlorination of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}_{2} \boldsymbol{C H}_{3} \)
In the given molecule, there are four
different types of hydrogen atoms. Replacement of these hydrogen atoms will give the following?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H C H_{2} C H_{2} C l \)
B \( \cdot\left(C H_{3}\right)_{2} C H C H(C l) C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C(C l) C H_{2} C H_{3} \)
D. \( C H_{3} C H\left(C H_{2} C l\right) C H_{2} C H_{3} \)


Divide:
459.5 by 100


Select the correct options.
This question has multiple correct options
A. Isoelectric point is the \( \mathrm{pH} \) at which an amino acid exists primarily in its neutral from
B. Isoelectric point is the average of \( p K_{a} \) value of \( \alpha \) \( C O O H \) amino \( \alpha-N H_{3}^{+} \) groups[valid only for neutral amino acid]
C . Glycine is characterised by two \( p K_{a} \) values
D. For neutral amino acid, the concentration of zwitter ion is maximum at its isoelectric point


Calculate the work required to be done to stop a car of \( 1500 \mathrm{kg} \) moving at a velocity of \( 60 \mathrm{km} / \mathrm{h} ? \)


Solve:
\( x \sin 45^{\circ} \cdot \cos 45^{\circ} \cdot \tan 60^{\circ}=\tan 45^{\circ} \)
\( \cos 60^{\circ} \)


Between \( t=10 \) s and \( t=20 s, \) the
merry-go-round.
A. rotates clockwise, at a constant rate
B. rotates clockwise, and slows down
C. rotates counterwise, at a constant rate
D. rotates counterclockwise, and slows, down


The probability of event is 0
A. Sure
B. Impossible
c. Exclusive
D. None of these


Give reason for these type of disorder.
What dife beara degensiation of What and ovaries etcrint their growing period


The value of \( \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right) \) is equal to
A \( \cdot \frac{7 \pi}{6} \)
в. \( \frac{5 \pi}{6} \)
\( c \cdot \frac{\pi}{3} \)
D.


The correct order of the calculated spinonly magnetic moments of complexes
(A) to (D) is:
\( (A) N i(C O)_{4} \)
(B) \( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{2} \)
\( (\mathrm{C}) N a_{2}\left[N i(C N)_{4}\right] \)
(D) \( P d C l_{2}\left(P P h_{3}\right)_{2} \)
A \( \cdot(C)<(D)<(B)<(A) \)
B. \( (C) \approx(D)<(B)<(A) \)
c. \( (A) \approx(C)<(B) \approx(D) \)
D. \( (A) \approx(C) \approx(D)<(B) \)


Containers which are light weight, lower price, good strength and easy to handle is made up of :
A. Plastic
B. Metal
c. wood
D. Brick


The horizontal flow of fluid depends
upon
A. Pressure difference
B. Amount of fluid
c. Density of fluid
D. All the above


Which of the following is not a method of extraction of metals?
A. Enrichment of ore
B. Refining
c. Magnetic separation
D. None of the above


If in a triangle \( A B C, 2 \cos A= \)
\( \sin B \operatorname{cosec} C, \) then
\( \mathbf{A} \cdot a=h \)
в. \( b=c \)
\( \mathbf{c} \cdot c=a \)
D. \( 2 a=b c \)


In the detection test of halogen, the
sodium fusion extract is acidified with
and then treated with
A. nitric acid, silver chloride
B. sulphuric acid, silver nitrate
C. nitric acid, silver nitrate
D. sulphuric acid, silver chloride


What are alkyl halides? How is n-propyl bromide prepared from propylene?


\( \boldsymbol{\alpha}-\boldsymbol{D}-\boldsymbol{G} \boldsymbol{l} \boldsymbol{u} \operatorname{cose} \) and \( \boldsymbol{\beta}-\boldsymbol{D}- \)
Glucose are not:
A. Epimers
B. Anomers
c. Enationers
D. Diastereomers


If
\( \int \frac{2 d x}{[(x-5)+(x-7)] \sqrt{(x-5)(x-7)}} \)
\( \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})]+\boldsymbol{c}, \) then
A \( \cdot f(x)=\sin ^{-1} x, g(x)=\sqrt{(x-5)(x-7)} \)
B . \( f(x)=\sin ^{-1} x, g(x)=(x-5)(x-7) \)
C \( \cdot f(x)=\tan ^{-1} x, g(x)=\sqrt{(x-5)(x-7)} \)
D. \( f(x)=\tan ^{-1} x, g(x)=(x-5)(x-7) \)


A reaction time for an automobile driver
is 0.7 sec. If the automobile can be
declared at \( 5 ~ m / s^{2} \) calculate the total distance travelled in coming to stop from an initial velocity of \( 8.33 m / s \) after a signal is observed.
A . \( 12.77 m \)
в. \( 14.82 m \)
\( c .16 .83 m \)
D. \( 19.65 m \)


When potential difference is applied across an electrolyte, then Ohm's law is obeyed at
A. zero potential
B. very low potential
c. negative potential
D. high potential


Without actually calculating the cubes, find the value of each of the following:
\( (28)^{3}+(-15)^{3}+(-13)^{3} \)
This question has multiple correct options
A . 17530
B. 14850
c. 12022
D. 16380


With the increasing altitude, gauge
pressure:
A. increases
B. decreases
c. remains same
D. becomes zero


Find the value of \( \lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a} \)
A \( \cdot n a^{n} \)
В \( \cdot n a^{n-1} \)
\( c \cdot n a \)
D.


if \( \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{2} \boldsymbol{\pi}] \) and \( \sin \boldsymbol{x}+\sin \boldsymbol{y}=\boldsymbol{2} \) then
the value of \( x+y \) is
A . \( \pi \)
в.
\( c .3 \pi \)
D. None of these


What are emulsions? Give examples


In a p-n-p transistor, working as a common base amplifier, current gain is 0.96 and emitter current is \( 7.2 \mathrm{mA} \). The
base current is
\( A \cdot 0.20 \mathrm{mA} \)
B. 0.36 mA
c. \( 0.29 \mathrm{mA} \)
D. \( 0.45 \mathrm{mA} \)


What will happen if the strip in a doorbell loses its flexibility?
A. Striker may break if current is large.
B. After hitting the metal gong, it never returns to original position and only a single sound is produced
c. system of doorbell breaks
D. Both A and B


What is the minimum number of rays
required for locating the image formed by a concave mirror for an object. Draw a ray diagram to show the formation of a virtual image by a concave mirror


A parallel plate capacitor is charged by a battery. The battery is disconnected and a
dielectric slab is inserted to completely fill the space between the plates. How will
(i) its capacitance,
(ii) electric
field between the plates and (iii) energy stored in the capacitor be affected? Justify your answer giving necessary mathematical expressions for each
case.


Which of the statement is wrong:-
A. when all resistance are equal, then the sensitivity of wheatstone bridge is maximum.
B. when the galvanometer and the cell are interchanged, then the balancing of wheat stone bridge will be effected.
C. Kirchoff's first law for the currents meeting at the Junctions in an electric circuit shows the conservation of charge.
D. Rheostat can be used as potential divider.


The tympanum is absent is
A. Dog fish
B. Cat fish
c. Bony fishes
D. All the fishes


What change, if any, is observed in
frequency and wavelength when light travels fro air to glass?


Name the purine bases and pyrimidine
bases present in RNA and DNA.


A small sphere of mass \( m=2 k g \) moving with a velocity \( \bar{u}=\hat{4} i-7 \hat{j} m / s \) collides
with a smooth wall and returns with a velocity \( \bar{v}=\hat{i}-3 \hat{j} m / s . \) The magnitude
of the impulse received by the ball is
\( \mathbf{A} \cdot 5 k g m s^{-1} \)
В. \( 10 k g m s^{-1} \)
c. \( 20 \mathrm{kgms}^{-1} \)
D. \( 15 k g m s^{-1} \)


To determine the solubility of a solute in water, a solution must be prepared that is
A. saturated
B. unsaturated
c. concentrated
D. supersaturated


How many numbers between 5000 and
10,000 can be formed using the digits \( \mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9} \) each digit
appearing not more than once in each number
\( A \cdot 5 \times^{8} P_{3} \)
В. \( 5 \times^{8} C_{3} \)
c. \( 5 ! \times^{8} P_{3} \)
D. \( 5 ! \times^{8} C_{3} \)


The most abundant isotope of hydrogen is:
A. tritium
B. deuterium
c. protium
D. para hydrogen


The by-product formed in most of the
cases with the use of hydrogen is:
A. water
B. oxygen
c. carbon-dioxide
D. none of above


Which of the following cyclopentane
derivative is optically inactive?
\( A \)
B.
\( c \)
\( D \)


A uniform rod \( A B \) of length \( l \) and mass
\( m \) hangs from point \( A \) in a car moving
with velocity \( v_{0} \) on an inclined plane as
shown in the figure. The rod can rotate
in vertical plane about the axis at point
A. If the car suddenly stops, the angular
speed with which the rod starts rotating
is :
A \( \cdot \frac{3}{2} \frac{v_{0}}{l} \cos \theta \)
B. \( \frac{v_{0}}{2} \frac{\cos \theta}{l} \)
c. \( \frac{3}{2} \frac{v_{0}}{l} \sin \theta \)
\( D \)


The excess temperature of a body falls
from \( 12^{\circ} \mathrm{C} \) to \( 6^{\circ} \mathrm{C} \) in 5 minutes, then the
time to fall the excess temperature
from \( 6^{\circ} \mathrm{C} \) to \( 3^{\circ} \mathrm{C} \) is (assume the
Newton's cooling is valid)
A . 10 minutes
B. 7.5 minutes
c. 5 minutes
D. 2.5 minutes


The block shown moves with constant
velocity on a horizontal surface. Two of
the forces on it are shown. A frictiona
force exerted by the surface is the only other horizontal force on the block. The
frictional force is
\( A \)
c. \( 2 \mathrm{N} \), rightward
D. slightly more than 2 N, leftward


For given reaction:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \stackrel{\boldsymbol{H}^{+}}{\longrightarrow} \boldsymbol{C r}^{3} \)
Eq.wt of \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \) is:
A. mol. wt. \( / 6 \)
B. mol. wt./3
c. mol. wt. \( / 4 \)
D. mol. wt./1


The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and \( 2.626 \mathrm{cm} \)
Calculate absolute error in each
measurement.
A \( . \Delta a_{5}=2.626-2.626=+0.000 \mathrm{cm} \)
в. \( \Delta a_{4}=2.626-2.626=0.000 \mathrm{cm} \)
C. \( \Delta a_{3}=2.626-2.630=-0.004 \mathrm{cm} \)
D. All of these


Loss of an electron is called :
A. reduction
B. oxidation
c. \( A \) or \( B \)
D. none of the above


Write any 2 properties of thermal
radiations?


In a mixture of kerosene and water,
kerosene forms the:
A. Lower layer
B. Upper layer
c. It mixes with water and forms no layer
D. Data insufficient


Very short answer type. How much blood is in each ventricle at
the end of ventricular diastole and what
is this volume called?


Astronauts on the orbiting space
station are weightless because...
A. there is no gravity in space and they do not weigh anything.
B. space is a vacuum and there is no gravity in a vacuum.
C. space is a vacuum and there is no air resistance in a
vacuum
D. None of the reasons given above are correct


Six particles situated at the corners of a regular hexagon of side a move at a constant speed \( v . \) Each particle maintains a direction towards the
particle at the next corner. Calculate the time particles will take to meet each other.


Choose correct statement.
A. Nitrogen is transported in plant xylem mainly in organic form
B. \( P \) and \( S \) are carried mainly in organic compounds in plants
C. There is no exchange of material between xylem and phloem
D. Xylem transport only inorganic nutrients


The IUPAC name of the following compound is \( 1,2,5- \) tribromo \( -3,4,6- \)
trichlorobenzene
A. True
B. False


When chlorine reacts with cold and
dilute solution of sodium hydroxide, the products obtained are:
A \( \cdot C l^{-}+C l O^{-} \)
в. \( C l^{-}+C l O_{2} \)
c. \( C l^{-}+C l O_{3} \)
D. \( C l^{-}+C l O_{4} \)


Assertion
Helium will have fewer dispersion forces between its atoms than the other
noble gases
Reason
As the mass of nonpolar atoms and molecules increases, dispersion forces increase
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 \( x \% \) of \( 250+25 \% \) of \( 68=67, \) then the
value of \( x \) is
A . 10
B . 15
c. 20
D. 25


\( \ln \) an \( A . P ., \) sum of \( p \) terms \( = \)
sum of q terms, then sum of \( (\boldsymbol{p}+\boldsymbol{q}) \)
terms equal to?
A . 0
B. 2
c. \( -p q \)
\( \mathbf{D} \cdot-(p+q) \)


The mobility of free electrons (charge =e, mass = m and-relaxation
time \( \tau \) ) in a metal is proportional to:
A \( \cdot \frac{e}{m} \tau \)
в. \( \frac{m}{e} \tau \)
\( c \cdot \frac{e}{m \tau} \)
D. \( \frac{m}{e \tau} \)


The formula \( Y=3 B(1-2 \sigma) \) relates
young's modulus and bulk's modulus with poisson's ratio. A theoretical physicist derives this formula incorrectly as \( Y=3 B(1-4 \sigma) \)
According to this formula, what would be the theoretical limits of poisson's
ratio:
A. Poisson's ratio should be less than 1
B. Poisson's ratio should be less than 0.5
c. Poisson's ratio should be less than 0.25
D. Poisson's ratio should be less than 0


An area of soil is thoroughly wetted and allowed to drain until capillary movement of water stopped. The water contents of the soil will give an
estimate of its
A. Capillary water
B. Storage water
c. Field capacity
D. Gravitational water


For the cell reaction \( : C u^{2+}(a q)\left(C_{1}\right)+ \)
\( Z n(s) \rightarrow Z n^{2+}(a q)\left(C_{2}\right)+C u(s) \) the
change in free energy \( \Delta G \) at a given temperature is a function of
\( A \cdot \ln C_{1} \)
в. \( \ln \left(\frac{C_{2}}{C_{1}}\right) \)
\( \mathrm{c} \cdot \ln \left(C_{2}+C_{2}\right) \)
D. \( \ln \left(C_{2}\right) \)


In \( 1902, \) periscope was used in submarine by:
A. Jefferson Simon
B. Charles Simon
c. simon Lake
D. George Lake


n the given figure, the measure of
\( \angle B A C \) is
A \( \cdot 65^{\circ} \)
\( 3 \cdot 50^{\circ} \)
\( c \cdot 55^{\circ} \)
0.60


What is the total number of candidates
at an examination, if \( 31 \% \) fail and the
number of failing students is 248
A. 800
B. 900
c. 1,000
D. 1,100


Occupational lung diseases that occurs in humans, among those given below is
A. Dyspnea
B. Anthracosis
c. Atelectasis
D. Cyanosis


Java man was discovered by
A . Leakey
B. Levis
c. Dubois
D. Oparine


Calculate the useful work of the
reaction \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\mathbf{1} / \mathbf{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \)
\( A g C l(s) \)
\( \operatorname{Given} \boldsymbol{E}_{c_{2} / C l^{-}}^{0}=+\mathbf{1 . 3 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{A \boldsymbol{g}|A \boldsymbol{g} C l| C l^{-}}^{0}=\mathbf{0 . 2 2} \boldsymbol{V} \) if \( \boldsymbol{P}_{C l_{2}}=\mathbf{1} \boldsymbol{a} \boldsymbol{t m} \)
and \( \boldsymbol{T}=\mathbf{2} \mathbf{9} \mathbf{8} \boldsymbol{K} \)
A. 110 kJ/mol
B. 220 kJ/mol
c. 55 kJ/mol
D. 1000 kJ/mol


Q Type your question-
nuticy. uuuy ur uiagial carefully and answer the questions that
follow:
(i) Label the parts numbered 1 to 4
(iii) Why does part' '2' have striped
appearance?
(iiii) What is the fluid that passes down
part ' 4 '? Name the main nitrogenous
waste present in it.
(iv) Mention the structural and
functional units of kidneys.
\( (v) \) Name the two major steps in the formation of the fluid mentioned in \( (\boldsymbol{i} \boldsymbol{i} \boldsymbol{i}) \)


Explain how hypothyroidism and hyperthyroidism can effect the body?


"The final Agent Orange raid in Vietnam took place in 1970 areas
have begun to bloom in 1970. But 19
years after the war's end, it seem plain that Agent Orange is killing and maiming human beings, something it never intended to do. The apparent toxic fallout from those clouds \( _{---} \) is a crop
of human miseries including cancers, miscarriages and birth defects - that
may persist for decades." The offensive substance referred to in
this quotation is
A. A complex minute of DDT and other insecticides used as aerial sprays for protection against malaria and other tropical diseases
B. A complex mixture of herbicides and weedicides used to increase agricultural output in the South Vietnam under the U.S. aid programme
c. Dot used as an insecticide
D. Dioxin used as defoliants


Marshalls acid is prepared by the
electrolytic oxidation of \( H_{2} S O_{4} \) as
\( 2 H_{2} S O_{4} \rightarrow H_{2} S_{2} O_{8}+2 H^{\oplus}+2 e^{-} \)
Oxygen and hydrogen are byproducts. In
such Electrolysis 2.24 L of \( H_{2} \) amd \( 0.56 \mathrm{L} \)
\( O_{2} \) were produced at STP. The weight of
\( H_{2} S_{2} O_{8} \) formed is:
A \( .9 .7 g \)
в. \( 19.4 g \)
c. \( 14.55 g \)
D. \( 29.1 g \)


The centripetal force acting on a
satellite revolving round the earth is \( \boldsymbol{F} \) The gravitational force on that planet is also \( F . \) The resultant force on the
satellite is
A . zero
в. \( F \)
c. \( 2 F \)
D. \( \frac{F}{2} \)


If wavelength of a wave is \( 100 \mathrm{m} \), then
100 waves will cover distance.
\( A \cdot 10 \mathrm{km} \)
B. \( 1 \mathrm{km} \)
\( c .100 \mathrm{km} \)
D. \( 100 \mathrm{m} \)


Ammonia, \( N H_{3} \) and hydrazine \( N_{2} H_{4} \)
are both binary compounds of nitrogen and hydrogen. Based on the law of
multiple proportions, how many milligrams of hydrogen would you expect \( 2.34 g \) of nitrogen to combine with to yield ammonia?


Factories \( : \boldsymbol{p}^{2}+\mathbf{6} \boldsymbol{p}+\mathbf{8} \)


Find the energy needed to remove a
proton from nucleus.


Assertion
\( X e F_{4} \) may be estimated by titrating the
\( I_{2} \) by reaction with \( K I \)
Reason
Equivalent weight of \( N a_{2} S_{2} O_{3} \) can be determined by iodimetric titration.
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 true but Reason is false
D. Assertion is false but Reason is true


Write the IUPAC name of the given compound and classify it into primary, secondary and teritiary amine
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)\left(\boldsymbol{C} \boldsymbol{H}_{2}\right)_{2} \boldsymbol{N} \boldsymbol{H}_{2} \)


One volume of nitrogen combines with one volume of oxygen to form two
volumes of nitric oxide. Calculate the
amount of each reactant required to produce \( 250 \mathrm{ml} \) of nitric oxide.
A \( \cdot N_{2}=100 \mathrm{ml}, \mathrm{O}_{2}=100 \mathrm{ml} \)
в. \( N_{2}=120 \mathrm{ml}, \mathrm{O}_{2}=120 \mathrm{ml} \)
c. \( N_{2}=125 \mathrm{ml}, \mathrm{O}_{2}=125 \mathrm{ml} \)
D. \( N_{2}=100 \mathrm{ml}, \mathrm{O}_{2}=125 \mathrm{ml} \)


Assertion
The diamond shines due to multiple
total internal reflections
Reason
The critical angle for diamond is \( 24.4^{\circ} \)
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


Para hydrogen is:
A. less stable than ortho hydrogen
B. more stable than ortho hydrogen
C . as stable as ortho hydrogen
D. None of these


In the given figure \( A B \) is the diameter where \( \boldsymbol{A P}=\mathbf{1 2} \mathrm{cm} \boldsymbol{P B}=\mathbf{1 6 c m} \) taking
the value of \( \pi=3 \) find the perimeter of
the shaded region


The diagram below shows a part of the
skelecton of the periodic table in which
elements are indicated by letters which
are not their usual symbols.

Which one of the following statement is
correct?
A. The greatest ionic character of compounds formed by reaction of pairs of the listed elements would be
exhibited by the compounds with the formula \( M_{2} \)
B. The \( J^{2+} \) ion is colored and has an electronic
configuration of \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{7} \)
C. Element \( R \) is a gas at room temperature
D. Element T is an inert gas with an electronic configuration \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{10}, 4 s^{2}, 4 p^{6} \)


In figure a wire perpendicular to a long straight wire is moving parallel to the later with speed \( \boldsymbol{v}=\mathbf{1 0 m} / \boldsymbol{s} \) in the
direction of the current flowing in the
later. The current is \( 10 A \). What is the
magnitude of the potential difference between the ends of the moving wire?
A \( \cdot\left(5 \times 10^{-4}\right) \ln (10) V \)
B \( \cdot\left(7 \times 10^{-4}\right) \ln (10) V \)
\( \mathbf{c} \cdot\left(2 \times 10^{-4}\right) \ln (2) V \)
D. \( \left(2 \times 10^{-5}\right) \ln (10) V \)


A hydraulic lift at a service station can
lift cars with a mass of 3500 kg. The
area of cross section of the piston
carrying the load is \( 500 \mathrm{cm}^{2} \). What
pressure does the smaller piston
experience? \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)


Sublimation is a process in which a
solid.
A. Changes into another allotropic form
B. Changes into liquid form
c. changes into vapour form
D. None of the above


The density of ammonia at \( 30^{\circ} \mathrm{C} \) and 5
atm pressure is:
A .3 .42 g/
B. 2.42 g/L
c. \( 1.171 g / L \)
D. \( 3.84 \mathrm{g} / \mathrm{L} \)


Which of the following represents a conjugate acid/base pair?
A. \( N a^{+} / C l^{-} \)
в. \( H C l / H^{+} \)
c. \( H_{2} C O_{3} / C O_{3}^{2} \)
D. \( N H_{3} / N H_{4}^{+} \)
E . \( K^{+} / O H^{-} \)


A card is thrown from a pack of 52 cards
so that each cards equally likely to be
selected. Determine whether in the
following case are the events \( A \) and \( B \) independent. \( A= \) the card is drawn is a spade, \( B= \) the card is drawn in an ace.


A particle moving rectilinearly with constant acceleration is having initia velocity of \( 10 \mathrm{m} / \mathrm{s} \). After some time, its velocity becomes \( 30 \mathrm{m} / \mathrm{s} \). Find out velocity of the particle at the mid point of its path?
A \( \cdot 10 \sqrt{5} \mathrm{m} / \mathrm{s} \)
B. \( 50 \sqrt{5} \mathrm{m} / \mathrm{s} \)
c. \( 60 \sqrt{5} \mathrm{m} / \mathrm{s} \)
D. \( 5 \sqrt{5} \mathrm{m} / \mathrm{s} \)


Which of the following base is used in the manufacturing of bleaching powder?
A. Sodium hydroxide
B. Calcium hydroxide
c. Magnesium oxide
D. Ammonium hydroxide


Solve: \( 3 n+7=1 \)


A box contains 10 white, 6 red and 10
black balls. A ball is drawn at random
from the box. What is the probability
that the ball drawn is either white or
red?
A \( \cdot \frac{7}{13} \)
в. \( \frac{7}{12} \)
c. \( \frac{8}{13} \)
D. \( \frac{9}{15} \)


A gas is taken through the cycle \( A B C A \)
as shown. What is the net work done by
the gas?
\( A \cdot 3000 J \)
в. \( 1000 J \)
c. zer
D. 2000J


contains how many \( 2^{\circ} \) carbons?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Water of crystallization is the fixed number of water molecules chemically attached to a unit of a salt in its
crystalline form.
A. True
B. False


Which of the following sets of quantum numbers represents the 19th electron of \( \boldsymbol{C r}(\boldsymbol{Z}=\mathbf{2 4}) ? \)
\( ^{\mathbf{A}} \cdot\left(4,1,-1,+\frac{1}{2}\right) \)
в. \( \left(4,0,0,+\frac{1}{2}\right) \)
c. \( \left(3,2,0,-\frac{1}{2}\right) \)
D. \( \left(3,2,-2,+\frac{1}{2}\right) \)


Find the sum of \( n \) terms of the A.P.
whose kth terms is \( 5 k+1 \)


The laws of forces that govern the force between two electric charges were discovered by :
A. Faraday
B. Ampere
\( c . \) onm
D. Coulumb


What is the most important change marked by puberty?


Which gas emits on burning of rice
straw?
\( A \cdot S O_{2} \)
в. \( N H_{3} \)
\( c \cdot O_{3} \)
D. \( H_{2} \).


Which of the following has more acidic
in nature?
A. HCIO
в. нсЮо
c. нс \( \operatorname{lo}_{3} \)
D. \( \mathrm{HClO}_{4} \)


In a SHM, when the displacement is one half the amplitude, what fraction of the total energy is kinetic?
A. zero
B. \( 1 / 4 \)
\( c \cdot 1 / 2 \)
D. 3/4


Based on development stage, tissues can be
A. Apical and intercalary meristems
B. Meristematic and permanent
c. Primary and secondary meristem
D. Promeristem and primordial meristems


A metallic rod of \( ^{\prime} \boldsymbol{L}^{\prime} \) length is rotated
with angular frequency of \( ^{\prime} \omega^{\prime} \) with one
end hinged at the centre and the other
end at the circumference of a circular
metallic ring of radius \( L \) about an axis
passing through the centre and perpendicular to the plane of the ring. \( \mathbf{A} \)
constant and uniform magnetic field \( \boldsymbol{B} \) parallel to the axis is present
everywhere. Deduce the expression for
the emf between the centre and the
metallic ring.
(a)
\( (b) \)


Two rings of radius \( R \) and \( n R \) made up of same material have the ratio of
moment of inertia about an axis
passing through centre \( 1: 8 . \) The value
of \( n \) is
A .2
B. \( 2 \sqrt{2} \)
\( c \cdot 4 \)
D. \( \frac{1}{2} \)


Divide \( \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}+\boldsymbol{3}) \) by
\( (x+3)(x+2) \)
A. \( x(x+3) \)
в. \( x(x+2) \)
c. \( (x+1) \)
D. \( x(x+1) \)


An electric circuit is composed of three
conducting rods \( M O, O N \) and \( P Q \) as
shown in figure. The resistance of the
rods per unit length is \( \lambda \). The rod \( P Q \)
slides, as shown in the figure, at a constant velocity \( v, \) keeping its tilt
angle relative to \( O N \) and \( N=M O \)
fixed \( 45^{\circ} . \) At each instance, the circuit
is closed. The whole system is embedded in a uniform magnetic field
\( B, \) which is directed perpendicularly into the page. Compute the timedependent induced electric current induced in the rods?


In a reaction involving one single reactant, the fraction of the reactant
consumed may be defined as \( \boldsymbol{f}= \) \( \left(1-\frac{C}{C_{0}}\right) \) where \( C_{0} \) and \( C \) are the concentrations of the reactant at the
after time, t. For a first order reaction:
A \( \cdot \frac{d f}{d t}=k(1-f) \)
B. \( -\frac{d f}{d t}=k f \)
c. \( -\frac{d f}{d t}=k(1-f) \)
D. \( \frac{d f}{d t}=k f \)


In fungi, sporangiospores and ascospores are found in bag-like
structures but are always present in
even numbers. These spore types are not same because
A. They are basically the same, but the sporangiospores are always larger.
B. Ascospores are formed as a result of meiosis, while sporangiospores are a result of mitosis
c. Sporangiospores are produced by sexual recombination, while ascospores are produced asexually.
D. They are basically the same, but ascospores are always larger.
E. The structure are the same, but they were named differently before they were determined to have the same function


Rutherford experiment of scattering of \( \alpha \) particles showed for the first time
that the atom has:
A . electron
B. protons
c. nucleus
D. all of these


The direction ratios of the line joining the points (4,3,-5) and (-2,1,-8) are
A \( \cdot \frac{6}{7}, \frac{2}{7}, \frac{3}{7} \)
в. 6,2,3
c. 5,8,0
D. 3,7,9


The final step for the extraction of
copper pyrites in Bessemer converter involves the reaction
A \( \cdot C u_{2} S+2 F e O \rightarrow 2 C u+2 F e+S O_{2} \)
в. \( C u_{2} S+2 C u_{2} O \rightarrow 6 C u+S O_{2} \)
c. \( 4 C u_{2} O+F e S \rightarrow 8 C u+2 F e S O_{4} \)
D. \( 2 C u_{2} O+F e S \rightarrow 4 C u+F e+S O_{2} \)


Which among the following is a paramagnetic compound?
A \( \cdot N_{2} O \)
B. \( N O \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( N_{2} O_{4} \)


Assertion
Neural signals through sympathetic nerves can increases the strength of ventricular contraction
Reason
Parasympathetic neural signals synergistically act with sympathetic
neural signal to increase the cardiac
output.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The nature of the magnetic field in a moving coil galvanometer is Radial magnetic field. State True or False.


The real and imaginary parts of \( \log (1+i)= \)
\( ^{A} \cdot\left(\frac{1}{2}, \frac{\pi}{4}\right) \)
B \( \cdot\left(\log 2, \frac{\pi}{4}\right) \)
\( ^{\mathbf{c}} \cdot\left(\log \sqrt{2}, \frac{\pi}{4}\right) \)
\( ^{\mathrm{D}} \cdot\left(\log \frac{1}{2}, \frac{\pi}{4}\right) \)


A metallic wire is subjected to stress and compression periodically with very high stresses. How will the plot of the
stress-strain relationship be indicated
A. Straight line
B. Circle
c. Hysteresis curve
D. Elliptical


Gastric acid mainly consists of:
A. \( H_{2} S O_{4} \)
в. \( H_{2} \).
c. \( H C l \)
D. all of the above


Maximum safe speed does not depend
upon
A. radius of curvature
B. angle of inclination with the horizontal
c. mass of the vehicle
D. acceleration due to gravity


In a volume of \( 5 d m^{3}, 26 \) moles of pure \( A \)
and 4 moles of pure \( B \) were placed. At
equilibrium 1 mol of \( C \) was present.
Calculate \( K_{c} \) for the reaction, \( \boldsymbol{A}+\boldsymbol{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{C} \)


The distance PQ is?
\( \mathbf{A} \cdot 20 \mathrm{m} \)
\( \mathbf{B} \cdot 10 \sqrt{3} \mathrm{m} \)
\( c \cdot 10 m \)
D. 5 m


A small metal sphere carrying charge
\( +Q \) is located at the centre of a spherical cavity in a large uncharged metallic
spherical shell. Write the charges on the
inner and outer surfaces of the shell.
Write the expression for the electric
field at the point \( P_{1} \) is \( E=\frac{x Q}{4 \pi \epsilon_{0} r_{1}^{2}} . \) Then
the value of \( x \) is :


Two masses as shown are suspended
from a massless pulley. Calculate the
acceleration of the 10 kg mass when
masses are left free
\( \mathbf{A} \cdot \frac{2 g}{3} \)
B. \( \frac{g}{3} \)
c. \( \frac{g}{9} \)
\( D \cdot \underline{g} \)


The figure shows a mechanical set-up.
The mechanism can be suitably
described as :
A. conversion of the rotational motion of crank into
linear motion of slider
B. conversion of linear motion of slider into the
rotational motion of crank
c. conversion of the rotational motion of slider into
linear motion of crank.
D. conversion of linear motion of crank into the rotational motion of slider


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{2 \times 2} \) and \( \boldsymbol{a}_{i j}=\boldsymbol{i}+\boldsymbol{j}, \) then \( \boldsymbol{A}= \)
\( A \cdot\left(\begin{array}{l}12 \\ 3\end{array}\right) \)
в. \( \left(\begin{array}{c}23 \\ 3\end{array}\right) \)
\( c \cdot\left(\begin{array}{cc}2 & 3 \\ 4 & 5\end{array}\right) \)
D. \( \left(_{6}^{4} \begin{array}{r}5 \\ \end{array}\right) \)


Particles in water at \( 273 \mathrm{K} \) have
energy as compared to particles in ice at the same temperature.
A . less
B. more
c. same
D. Can't say


Find the values of other trigonometric
function \( (\sin , \cos , \tan ) \) in each of the
following problems
i) \( \sin \theta=3 / 5: \theta \) in \( I^{s t} \) quadrant
ii) \( \cos \theta=-1 / 2: \theta \) in \( I I^{s t} \) quadrant
iii) \( \sin \theta=3 / 4: \theta \) in \( I I I^{s t} \) quadrant \( \$ \$ \)


The wavelength of light is 8000 A. The no. of photon required to provide 20 J of energy is approximately:
A \( \cdot 4.56 \times 10^{18} \)
B . \( 8 \times 10^{19} \)
c. \( 7 \times 10^{19} \)
D. \( 4 \times 10^{7} \)


When viewing through a compound microscope, our eye should be
positioned not on the eye-piece but a short distance away from it for best viewing why? How much should be that short distance between the eye and eyepiece?


Which of the following has \( \boldsymbol{p} \boldsymbol{\pi}-\boldsymbol{d} \boldsymbol{\pi} \)
bonding?
A \( . N O_{3}^{-} \)
в. \( S O_{3}^{2} \)
\( \mathrm{c} \cdot B O_{3}^{3-} \)
D. \( C O_{3}^{2-} \)


\( \vec{y} \)
類 4


Show that the function \( f \) fiven below by:
\( \left\{\begin{array}{ll}\frac{e^{1 / x}-1}{e^{1 / x}+1} & , \text { if } x \neq 0 \\ -1 & , \text { if } x=0\end{array} \) is discontinuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\frac{x^{2}-2 x-3}{x+1^{2}}, & \text { when } x \neq-1 \\ k, & \text { when } x=-1\end{array}\right. \)
If \( f(x) \) is continuous at \( x=-1 \) then
\( \boldsymbol{k}=? \)
A . 4
B. -4
c. -3
D.


The most important muscular structure in respiratory system of rabbit is
A. External intercostal muscles
B. Internal intercostal muscles
c. Diaphgram
D. Vertebral column


Three unbiased coins are tossed. What
is the probability of getting at most two tails or two heads?
\( A \cdot \frac{3}{2} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{7}{2} \)


f \( \boldsymbol{A}=[\mathbf{2}, \mathbf{4}, \mathbf{5}], \boldsymbol{B}=[\mathbf{7}, \mathbf{8}, \mathbf{9}] \) then \( \boldsymbol{n}(\boldsymbol{A} \times \)
\( B \) ) is equal to?


If the line \( (2 x+y+1)+\lambda(x-y+ \)
1) \( =0 \) is parallel to \( y-a x i s \) then value
of \( \lambda \) is \( ? \)
A .
B. -
\( c \cdot \frac{1}{2} \)
\( D \)


Calculate the solid angle subtended by an octant of a sphere at the centre of the
sphere
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{3} \)
\( c \cdot \frac{\pi}{2} \)
\( D \)


Which of the following is a source of income of the Gram Panchayats?
A. Income Tax
B. Sales Tax
c. Professional Tax
D. Levy duties


\( \text { If }\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \sec \boldsymbol{x}-\boldsymbol{b} \tan \boldsymbol{x}, \boldsymbol{a}\rangle \boldsymbol{b}\rangle \boldsymbol{0}, \) then
the minimum value of \( f(x) \) is
A \( \cdot \sqrt{a^{2}+b^{2}} \)
B. \( 2 \sqrt{a^{2}-b^{2}} \)
c. \( \sqrt{a^{2}-b^{2}} \)
D. \( a-b \)


An object is resting upon a table, the normal force on the object is
and in direction to the
gravitational force applied on the object. Fill in the blank.
A. equal,opposite
B. unequal,opposite
c. equal,in the same
D. unequal,in the same


Find \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \) when \( \boldsymbol{P}(\boldsymbol{A})= \)
\( \frac{\mathbf{5}}{\mathbf{1 1}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{6}}{\mathbf{1 1}} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\mathbf{7}}{\mathbf{1 1}} \)


A shopkeeper sells 6 more products in February compared to January. If the shopkeeper sells \( 15 \% \) more products in February than in January, what is the total amount of products he sold in February?
A . 25
B . 29
c. 16
D. 46


Find the value of \( a \) if \( f(x)=2 e^{x}- \)
\( a e^{-x}+(2 a+1) x-3 \) is increasing for
all values of \( x \)


The coefficient of \( x \) in the expansion of
\( \left(1-x-x^{2}+x^{3}\right)^{6} \) is ?
\( A \cdot 6 \)
B. -6
c. -12
D. 12


How many positional isomers would result on dichlorination of \( 2,4- \)
dimethylpentane?


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


87,78,69
Write the next
number of the series.
A . 26
B. 60
c. 12
D. zero


Which can reduce \( R C O O H \longrightarrow \)
\( R C H_{2} O H ? \)
A \( . \) NaBH \( _{4} \)
в. \( N a / C_{2} H_{5} O H \)
c. \( B H_{3} / T H F / H_{3} O^{+} \)
D. \( H_{2} / \) catalyst


The wavelength of monochromatic light is \( 6000 A^{0} . \) Write this value in \( n m \)


The area of a man's foot is \( 80 \mathrm{cm}^{2} . \) How
much pressure will the man exert on
the ground, while standing, if weight is
80kgf?


A woman buys toffees at Rs 2.50 a
dozen and an equal number at Rs. 3 a score. She sells them at Rs. 3.60 a score
and thus makes a profit of Rs. 10. How many toffees did she buy?
A . 10000
B. 12000
c. 5000
D. 6000


Which of the following hydrogen like species will have same radius as that of
a Bohr orbit of hydrogen atom?
A \( \cdot n=2, L i^{2+} \)
B . \( n=2, B e^{3+} \)
C \( \cdot \mathrm{n}=2, \mathrm{He}^{+} \)
D. \( n=3, L i^{2+} \)


The parallel plate capacitors with different distance between the plates
are connected in parallel to voltage
source as shown in the figure. A point
positive charge is moved from a point
that is exactly in the middle between
the plates of the capacitor \( c_{1} \) to a point
2 in capacitor \( c_{2} \) that lies at the plates
of \( c_{1} \). Then the work done by the electric
force is.
A. positive
B. negative
c. zero
D. data insufficient.


When a real gas show behaviour same as ideal gas:
A. At low temperature and low pressure
B. At high temperature and high pressure
C. At low temperature and high pressure
D. At high temperature and low pressure


The orbital angular momentum of an
electron in 2 s orbitals is:
A \( \cdot+\frac{1}{2} \frac{h}{2 \pi} \)
B. zero
\( c \cdot \frac{h}{2 \pi} \)
D. \( \sqrt{2} \frac{h}{2 \pi} \)


Iron
(III) oxide on heating with carbon
monoxide gas form solid iron and liberates carbon dioxide gas. This is a:
A. precipitation reaction
B. double decomposition reaction
c. synthesis reaction
D. redox reaction


Sodium hexametaphosphate is known
as:
A. Calgon
B. Permutit
c. Natalite
D. Nitrolim


A fair price shopkeeper takes \( 10 \% \) profit on his goods. He lost \( 20 \% \) goods during theft. His loss percent is
A . 12
B. 15
c. 20
D. 25


Define curie.


Match the compounds in column-I with
their structure given in column-
II. Matching can be one or more than
one.


Which system transmits impulses between different parts of the body?
A. Musculoskeletal system
B. Endocrine system
D. Nervous system
E. Reproductive system


\( \bar{a}, \bar{b}, \bar{c} \) are three non-zero vectors such that any two of them are non-collinear. If \( \bar{a}+\bar{b} \) is collinear with \( \bar{c} \) and \( \bar{b}+\bar{c} \) is
collinear with \( \bar{a} \), then what is their sum?
A . -1
B. 0
c. 1
D. 2


Bicuspid and tricuspid valves are open during
A. Ventricular systole
B. Ventricular diastole
c. Atrial systole
D. Late joint diastole


The ratio of the isothermal elasticity of gas to its adiabatic elasticity is :
\( A \cdot \gamma \)
B. \( \frac{1}{\gamma} \)
c. \( 1-\gamma \)
D. \( \frac{1}{1-\gamma} \)


A circular loop of radius \( 2 \mathrm{cm}, \) is placed in a time varing magnetic field with rate of \( 2 \mathrm{T} / \mathrm{sec} . \) Then induced electric
field in this loop will be
A. 0
B. 0. \( 02 \mathrm{V} / \mathrm{m} \)
\( c \cdot 0.01 v / m \)
D. \( 2 v / m \)


Two identical cycle wheels (geometrically) have different number of spokes connected from center to rim.
One is having 20 spokes and the other
having only 10 (the rim and the spokes are resistanceless). One resistance of
value \( R \) is connected between center
and rim. The current in \( \boldsymbol{R} \) will be
A. double in the first wheel than in the second wheel
B. four times in the first wheel than in the second wheel
c. will be double in the second wheel than that of the first whee
D. will be equal in both these wheels
E . answer required


A man has 7 trousers and 10 shirts How
many different outfits can he wear?


If the percentage of nitrogen in an organic compound is \( 12.5 \% \), then how much of the organic compound should
be taken? so as to produce \( 50 m l \) of \( N_{2} \)
at \( 300 K \) and 715 mm pressure. [Aq. tension \( =15 \) mm]
A. \( 0.419 g \)
\( g \)
в. \( 0.0149 g \)
c. \( 0.914 g \)
D. \( 0.941 g \)


Why it is more hotter for same distance
over the top of a candle than it in the
side of its flame?
A. Conduction of heat in air is upward
B. Heat is maximum radiated in upward direction
c. Radiation and conduction both contribute in transferring heat upwards
D. convection takes more heat in upward direction


What is the position of centre of gravity
of a cylinder?
A. At the center of base circle
B. At the center of top circle
c. cannot be determined
D. At the mid point on the axis of cylinder


An ecosystem contains
A. only the biotic components of the environment
B. only the energy flow components of an environment
C. both the living organisms and the abiotic components of the environment
D. only the food relationships found m an environment


In case of a virtual and erect image, the magnification of a mirror is :
A. Positive
B. Negative
c. Unity
D. Infinity


If the kinetic energy of a body increases
b \( 4 \% \) the momentum:
A. increases by 2\%
B. increases by 4\%
c. increases by \( 8 \% \)
D. increases by 16\%


Chloroform reacts with oxygen in the presence of light to give:
A. carbon tetrachloride
B. carbonyl chloride
c. methyl chloride
D. methylene dichloride
E . acetaldehyde


White phosphorus reacts with \( N a O H \)
forming \( P H_{3} \) and \( H_{2} P O_{2}^{-} . \) This is an example of :
A. neutealisation
B. thermal decomposition
c. redox reaction
D. disproportionation


Find the range of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\sin \left(\pi\left[x^{2}+1\right]\right)}{x^{4}+1} \) where [.] is greatest
integer function
A . [0,1]
в. [-1,1]
c. 0
D. None of these


Maximum silk production is in which of the following state?
A. Assam
B. Karnataka
c. Gujarat
D. Kerala


A ray of light is incident from one medium \( (\mu=1.5) \) into another medium. If the angle of incidence and
refraction are, respectively, 60 and 45 then what will be the refractive index of the denser medium?
A . 1.63
в. 1.43
c. 1.83
D. Data insufficient


Carbon dioxide is used in fire
extinguisher.
A. True
B. False


Two copper rods \( P, Q \) of thickness in the ratio 2: 5 taken. If both the rods \( P, Q \) of
lengths \( 10 \mathrm{cm} \) are heated to same temperature rise, then the ratio of the linear expansions of \( P \) to that of rod \( Q \) is:
A .2: 5
B. 5: 2
\( c \cdot 1: 1 \)
\( D \cdot 4: \)


In the circuit shown, the ammeter
reading is zero. Then, the value of the
resistance R is:
\( A \cdot 50 \Omega \)
B. \( 100 \Omega \)
c. \( 200 \Omega \)
0.4005


The increasing dipole moments of the
given compounds is:
B. II = IV < III <
c. \( \|=1<1 V<\| \)
D. III <I<II IV


Shell fish taken from water during a red tide would be
A. Rich in proteins
B. Poisoned with neurotoxin
c. Dead
D. Rich in fats


The anaerobic respiration is also called
as.
A. Fermentation
B. Fragmentation
c. oxidation
D. Reduction


Exercise:
[ A transverse harmonic wave on a
string is described by \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{3} . \mathbf{0} \sin (\mathbf{3 6} \boldsymbol{t}+\mathbf{0 . 0 1 8} \boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) \)
where \( x \) and \( y \) are in \( c m \) and \( t \) in s. The
positive direction of \( x \) is from left to right. For the wave described in the above
Exercise, plot the displacement \( (y) \)
versus
(t) graphs for \( x=0,2 \) and \( 4 \mathrm{cm} \) What are the shapes of these of these
graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another:
amplitude, frequency or phase?


The acceleration of a particle is given by \( \vec{a}=\left\lfloor 2 \hat{i}+6 t \hat{j}+\frac{2 \pi^{2}}{9} \cos \frac{\pi t}{3} \hat{k}\right\rfloor m / s^{2} \)
\( \mathbf{A t} t=\mathbf{0}, \overrightarrow{\boldsymbol{r}}=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{v}}=(\mathbf{2} \overrightarrow{\mathbf{i}}+\hat{\boldsymbol{j}}) \boldsymbol{m} \boldsymbol{s}^{1} \)
The position vector at \( t=2 s \) is
\( \mathbf{A} \cdot(8 \hat{i}+10 \hat{j}+\hat{k}) m \)
B . \( (8 \hat{i}+10 \hat{j}+3 \hat{k}) m \)
c. \( (3 \hat{i}+8 \hat{j}+10 \hat{k}) m \)
D. \( (10 \hat{i}+3 \hat{j}+8 \hat{k}) m \)


Yeast and mushroom are different from
spirogyra because they
A. Cannot carry out photosynthesis
B. Lack cellulosic cell wall
c. Reproduce by sexual methods
D. Are terrestrial as well as aquatic


A transformer connected to 220 volt line
shows an output of \( 2 A \) at \( 11000 V . \) The
efficiency is \( 100 \% \). The current drawn from the line is:
\( \mathbf{A} \cdot 100 A \)
в. \( 200 A \)
\( c .22 A \)
D. \( 11 A \)


Assertion
2,2-Dimethylbutane does not have any
tertiary carbon atom.
Reason Tertiary carbon atom is attached to
three carbon atoms.
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 are the properties of \( R \) used in the
following? \( \boldsymbol{\pi} \times \mathbf{1}=\boldsymbol{\pi} \)


\( \boldsymbol{L} \) and \( \boldsymbol{M} \) are two points with position vectors \( 2 \bar{a}-\bar{b} \) and \( a+2 \bar{b} \) respectively.
The position vector of the point \( N \) which
divides the line segment \( L M \) in the ratio 2: 1 externally is
\( \mathbf{A} \cdot 3 \bar{b} \)
в. \( 4 \bar{b} \)
\( c .5 \bar{b} \)
D. \( 3 \bar{a}+4 \bar{b} \bar{\hline} \bar{b}+4+4 \bar{a} \bar{a} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \bar{b} \)


A convex lens forms a real image of a
point object at a distance of \( 50 \mathrm{cm} \) from the convex lens. A concave lens is
placed. \( 10 \mathrm{cm} \) behind the convex lens on the image side. On placed a plane mirror an the image side and facing the concave lens. It is observed that the
final image now coincides with the
object itself. The focal length of the concave lens is:
A. \( 50 \mathrm{cm} \)
B. 20 cm
\( c .40 \mathrm{cm} \)
D. 25 cm


The investment (in ten crores of rupees)
of Life Insurance Corporation of India in different sectors are given below:
Investment sectors rupees
Central Government Securities
State Government Securities
Securities guaranteed by the Government
Private Sectors
Socially oriented sectors (Plan)
Socially orient (Non-Plan)
Represent the above data with the help
of a bar graph.


\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{A} \boldsymbol{X}+\boldsymbol{B} \boldsymbol{Y} \longrightarrow \boldsymbol{H} \boldsymbol{A}+\boldsymbol{O} \boldsymbol{Y}+ \)
\( \boldsymbol{X}_{2} \boldsymbol{B} \)
In the above-unbalanced redox
reaction, the oxidation number of \( \boldsymbol{X} \) is
-2 and neither \( X \) nor water is involved
in the redox process. If the above reaction is balanced with
the smallest whole-number
coefficients, the sum of the
stoichiometric coefficients of all the
compounds is :
\( A \cdot 9 \)
B. 8
\( c .7 \)
D. 6


An electrolysis of a oxytungsten complex ion using \( 1.10 A \) for 40 min produces \( 0.838 g \) of tungsten. What is the charge of tungsten in the material? (Atomic weight: \( \boldsymbol{W}=\mathbf{1 8 4} \) )
A . 6
B. 3
\( c .5 \)
D.


The distances of Neptune and Saturn
from the Sun are respectively \( 10^{13} \) and
\( 10^{12} \) meters and their periodic times
are respectively \( T_{n} \) and \( T_{S} \). If their orbits are assumed to be circular, the value of \( \frac{T_{n}}{T_{S}} \) is :
A. 100
в. \( 10 \sqrt{10} \)
c. \( \frac{1}{10 \sqrt{10}} \)
D. 10


If \( D_{1} \) and \( D_{2} \) are two \( 3 \times 3 \) diagonal
matrices, then
A. \( D_{1} D_{2} \) is a diagonal matrix
B. \( D_{1}+D_{2} \) is a diagonal matrix
c. \( D_{1}^{2}+D_{2}^{2} \) is a diagonal matrix
D. 1,2,3 are correct


A rope ladder with a length 1 m carrying
a man with a mass \( m \) at its end is
attached to the basket of a balloon with
a mass M. The entire system is in
equilibrium in the air. As the man climbs up the ladder into the balloon,
the balloon descends by a height \( h \). Then the potential energy of the man (in \( J \) ):
A. increases by \( m g(1-h) \)
B. increases by \( m g l \)
c. increases by \( m g h \)
D. increases by \( m g(21-h) \)


A body moving uniformly along a circular path has:
A. a constant speed
B. a constant velocity
c. zero tangential velocity
D. zero radial acceleration


The circuit below shows a 6.0 V battery
In a circuit with three resistors, labeled
1,2 and \( 3 . \) If each resistor has a
resistance of 6.0 ohms, what is the rate
at which energy is used by resistor \( 2 ? \)
\( A \cdot 10 W \)
B. 36.0 W
c. \( 6.0 \mathrm{w} \)
D. \( 24.0 \mathrm{W} \)
E. \( 18.0 \mathrm{w} \)


The molar heat capacity \( \left(C_{p}\right) \) of \( C D_{2} O \)
is 10 cals at \( 1000 K . \) The change in entropy associated with cooling of \( 32 g \)
of \( C D_{2} O \) vapour from \( 1000 K \) to \( 100 K \)
at constant pressure will be:
\( (D=\text { deutrium, at. mass }=2 u) \)
A. -23.03 cal deg \( ^{-1} \)
в. 2.303 саг de \( g^{-1} \)
c. 23.03 cal deg \( ^{-1} \)
D. -2.303 cal de \( g^{-1} \)


The number of partial fraction of \( \frac{3 x^{2}+70 x+93}{(x-1)^{4}} \) is
A . 3
B. 4
\( c .5 \)
D. 2


The equivalent capacitance between \( x \)
and \( y \) is :
\( A \cdot 5 / 6 \mu F \)
B. \( 7 / 6 \mu F \)
\( c \cdot 8 / 3 \mu F \)
D. \( 1 \mu F \)


Moon does not emit light yet it is visible Choose the most appropriate reason behind it :
A. At night the moon starts emitting light because the moon is covered by sun at night
c. Both are true
D. None is true


Arrange the following physical quantities in the decreasing order of dimension of length.
I. Density
II. Pressure
III. Power
IV. Impulse
\( \mathbf{A} \cdot \) ।, ॥, ॥ा, ।V
B. ॥II, II, I, IV
c. \( 1 \mathrm{V}, \) । ॥ \( , \) ॥)
D. III, IV, II, I


Q Type your question-
(a) Colour the map as follows: BlueWater, Red-Fire station, Orange-Library,
Yellow-Schools, Green-park, PinkCollege, Purple-Hospital, BrownCemetery.
(b) Mark a green \( ^{\prime} X^{\prime} \) at the intersection
of Road \( ^{\prime} C^{\prime} \) and Nehru Road, Green \( ^{\prime} Y^{\prime} \)
at the intersection of Gandhi Road and
Road \( \boldsymbol{A} \)
(c) In red, draw a short street route from
Library to the bus depot.
(d) Which is further east, the city park
or the market?
(e) Which is further south, the primary
school or the Sr. Secondary School?


Three right angled prisms of refractive
indices \( \mu_{1}, \mu_{2} \) and \( \mu_{3} \) are joined
together ao that the faces of the middle
prism are each in contact with one of
the outside prisms. If the ray passes through the composite block undeviated, then
A \( \cdot 1+\mu_{2}^{2}=\mu_{1}^{2}+\mu_{3}^{2} \)
B \( \cdot \mu_{1}^{2}-\mu_{3}^{2}+\mu_{2}^{3}=1 \)
C. \( \mu_{1}^{2}-\mu_{3}^{2}-\mu_{2}^{3}=1 \)
D \( \cdot \mu_{2}^{2}+\mu_{3}^{3}-\mu_{2}^{1}=1 \)


The photo electric work function for a metal surface is 4.125 eV. The cut-off
wavelength for this surface
A \( \cdot 4125 ~ A^{\circ} \)
B. 2062.5 \( A^{\circ} \)
c. \( 3000 A^{\circ} \)
D. 6000A \( ^{\text {о }} \)


A surface \( d s=10 \hat{j} \) is kept in an electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}+7 \hat{\boldsymbol{k}} . \) How much
electric flux will come out through the surface?
A . 40 unit
B. 50 unit
c. 30unit
D. 20 unit


Find the average speed of the train.
A. \( 20 k m p h \)
B. \( 40 k m p h \)
\( c .60 k m p h \)
D. \( 80 k m p h \)


The critical temperature of water is
higher than that of \( O_{2} \) because the
\( H_{2} O \) molecule has:
A. a fewer electrons than \( O_{2} \)
B. a dipole moment
c. a v shape structure
D. two covalent bonds


In which of the following pairs of compounds xenon is involved in \( s p^{3} \) hybridisation:
A. \( X e F_{2}, X e F_{4} \)
в. \( X e F_{2}, X e F_{6} \)
c. \( X e F_{4}, X e F_{6} \)
D. \( X e O_{3}, X e O_{4} \)


The gases chlorine, nitrogen, ammonia
and sulphur dioxide are collected under the same conditions of temperature
and pressure. If 20 litres of nitrogen contains 'x' no. of molecules, state the no. of molecules in 20 litres of
ammonia.
A. \( x \)
в. x/2
\( c \cdot x / 4 \)
D. 2x


In figure, \( D E F \) is an isosceles triangle
and \( D G \) is the altitude on \( F E \) is \( D G \)
also a median.


Three lenses of power \( +1.5 D \) and
\( -0.5 D \) are kept in contact on their
principal axis. What is the effective power of the combination?


If \( \boldsymbol{u}_{n}= \)
then \( \boldsymbol{u}_{n}=\boldsymbol{a}_{n} \boldsymbol{u}_{n-1}+\boldsymbol{u}_{n-2} \)
f true enter 1 else enter


Number of unpaired electron(s) in \( \boldsymbol{O}_{2} \) is/are:


In a reversible process, system goes from an initial state \( A \) to a final state \( B \)
Which of the following is true?
A. The heat required from state A to state B is zero.
B. The work done from state A to state B is zero
c. The heat required from state A to state B and back to state A is zero
D. The heat required from state A to state B and back to state A is non-zero


If an air bubble rises from the bottom of
the lake to its surface at constant
temparature, its volume
A . decreases
B. increases
c. remain same
D. can't say


Active transport?


Two point charges \( q_{1} \) and \( q_{2} \) are placed as shown. Resultant electric field origin is along -y-axis, \( \left(\frac{\boldsymbol{q}_{1}}{\boldsymbol{q}_{2}}\right) \) equals to:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2 \sqrt{2}} \)
\( c \cdot \sqrt{2} \)
\( D \)


\( P \) and \( Q \) are two elements which form
\( P_{2} Q_{3} \) and \( P Q_{2} . \) If 0.15 mole of \( P_{2} Q_{3} \)
weight \( 15.9 \mathrm{g} \) and 0.15 mole of \( P Q_{2} \) weight 9.3 g. what are atomic weights of
\( P \) and \( Q ? \)
\( A \cdot 18 \) and 26
B. 26 and 26
c. 26 and 18
D. 18 and 18


Find the equation of the plane bisecting the line segment joining the points
(-3,-2,1) and (1,6,-5)
perpendicularly.


The force exerted on a current-carrying wire placed in a magnetic field is zero when the angle between the wire and the direction of magnetic field is.
A \( .180^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)


Which of the following is neutral?
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
c. \( N_{2} O_{4} \)
D. \( N_{2} \),


In the figure, ABCDEF is a regular hexagon, and its centre is point 0. What
is the value of \( x ? \)
A \( \cdot 80^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 40^{\circ} \)
\( D .30 \)


Two moles of an ideal monoatomic gas,
initially at pressure \( P_{1} \) and volume \( V_{1} \) undergo an adiabatic compression
until its volume is \( V_{2} . \) Then the gas is
given heat \( Q \) at constant volume \( V_{2} \) Find the total work done by the gas, the total change in its internal energy and the final temperature of the gas.[Give
your answers in terms of \( \boldsymbol{P}_{1}, \boldsymbol{V}_{1}, \boldsymbol{V}_{2} \mathrm{Q} \)
and \( \mathrm{R}] \)
A. \( \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{3 R} \)
в.
(ii) \( \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{4 R} \)
\( ^{\mathrm{C}} \cdot \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{5 R} \)
D. \( \frac{P_{1} V_{1}^{5 / 3} v_{2}^{-2 / 3}}{5 R}+\frac{Q}{3 R} \)


Wavelength of the de-Broglie wave of an electron revolving in the sixth orbit of
the hydrogen atom is: \( \left(r_{0} \) is the Bohr's \right. radius \( =0.529 A \)
A \( \cdot \pi r_{0} \)
В. \( 12 \pi r_{0} \)
\( c \cdot 6 \pi r_{0} \)
D. \( 4 \pi r_{0} \)


The ray of light which falls on a mirror is called-
A. Reflected ray
B. Emergent ray
c. Incident ray
D. Transmitted ray


Lymph is colourless because
A. WBC are absent
B. WBC are present
C. Platelet is absent
D. \( R B C \) are absent


A coil carrying current behaves as a/an
A. magnet
B. motor
c. dynamo
D. electric dipole


Which one of the following is an example of homogeneous catalysis?
A. Haber's process of synthesis of ammonia
B. catalytic conversion of \( S O_{2} \) to \( S O_{2} \) in contact process
c. catalytic hydrogenation of oils
D. Acid hydrolysis of methyl acetate


Find the area of the figure contained
between the parabola \( x^{2}=4 y \) and the
curve \( \boldsymbol{y}=\frac{\boldsymbol{8}}{\boldsymbol{x}^{2}+\boldsymbol{4}} \)


Two intersecting straight lines move
with speeds \( 3 m / s \) and \( 4 m / s \) parallel to themself. If angle between the lines is
\( 90^{\circ} \) then speed of intersection point is
A. \( 5 m / s \)
B. \( 3 m / s \)
c. \( 4 m / s \)
D. None


Covalent compounds are.........conductors of electricity
A. heavy
B. poor
c. can't be said
D. partial


If a diamagnetic substance is brought near north and south pole of a bar
magnet, it is
A. attracted by poles
B. repelled by poles
c. replaced by north pole and attracted by south pole
D. attracted by north pole and repelled by south pole


Set up an equation of a tangent to the graph of the following function. \( y=4 x-x^{2} \) at the points of its
intersections with the \( 0 x \) axis.


A spring balance is calibrated at sea
level. If this balance is used to measure
the weight of a body at successive increasing heights from the surface of the earth, then the weight indicated by spring balance will
A. decrease continuously
B. increase continuously
c. first decrease, then increase
D. remains constant


Match the following:
Quantity Formula
x linked a coil
1) Magnetic c flux with
a) \( -N \frac{d \phi}{d t} \)
2)
Induced emf
b) \( \mu_{r} \mu_{0} n_{1} n_{2} \pi r_{1}^{2} l \)
3) Force on a charged particle
\( \cdots \) moving in a electric and
c) \( B A \cos \theta \)
magnetic field
\( f a \) 4) Mutual inductance of
solenoid d)
\[
q(\bar{E}+\bar{v} \times \bar{B})
\]
\( A \cdot 1-c, 2-d, 3-b, 4-a \)
B. \( 1-c, 2-a, 3-d, 4-b \)
\( \mathbf{C} \cdot 1-\mathbf{b}, 2-\mathbf{a}, \mathbf{3}-\mathbf{c}, \mathbf{4}-\mathbf{d} \)
D. \( 1-a, 2-b, 3-d, 4-c \)


Rain is falling vertically with \( 3 m s^{-1} \) and a man is moving due North with \( 4 m s^{-1} . \) In which direction he should
hold the umbrella to protect himself from rains?
A \( \cdot 37^{\circ} \) North of vertical
B. \( 37^{\circ} \) South of vertical
C. \( 53^{\circ} \) North of vertical
D. \( 53^{\circ} \) South of vertical


Two electric charges of \( 9 \mu C \) and \( -3 \mu C \) are placed \( 0.16 \mathrm{m} \) apart in air. There are two points \( A \) and \( B \) on the line joining the two charges at distances of (i) \( 0.04 m \) from \( -3 \mu C \) and in between the charges
and
(ii) \( 0.08 m \) from \( -3 \mu C \) and out side
the two charges. The potentials at \( A \) and
B are :
A. \( 0 V, 5 V \)
в. \( 0 V, 0 V \)
c. \( 5 V, 0 V \)
D. \( 5 V, 10 V \)


Using equipartition of energy, the specific heat \( \left(\operatorname{in} J k g^{-1} K^{-1}\right) \) of aluminium at high temperature can be estimated to be (atomic weight of aluminium \( =27) \)
A . 25
B. 1850
\( c \cdot 410 \)
D. 923


Three numbers are chosen at random
withoutreplacement from the set of integers \( 1,2,3, \ldots .10 . \) The probability that the minimum of thechosen
numbers is 3 or the maximum of
thechosen numbers is \( 7, \) is equal to
A . \( 23 / 120 \)
B. \( 13 / 120 \)
c. \( 13 / 60 \)
D. \( 11 / 40 \)


1 parsec equals to:
\( \mathbf{A} \cdot 3.26 \) light years
B . \( 3.1 \times 10^{13} \mathrm{km} \)
C \( .1 .92 \times 10^{13} \) miles
D. all of the above


Assertion(A): The possibility of an electric bulb fusing is higher at the time of switching on and off
Reason(R): Inductive effects produce a large current at the time of switch-on
and switch-off.
A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of \( A \)
c. A is true but R is false
D. Both A and R are false


If in triangle \( \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z}, \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{X} \boldsymbol{Z} \) and
\( M, N \) are the mid points of \( X Y, Y Z \) then which one of the following is correct?
\( \mathbf{A} \cdot M N=Y Z \)
в. \( N Y=N Z=M N \)
c. \( M X=M Y=N Y \)
D. \( M N=M X=M Y \)


An urn contains five balls alike in every respect save colour. If three of these
balls are white and two are black and
we draw two balls at random from this
urn without replacing them. If A is the event that the first ball drawn is white and \( \mathrm{B} \) the event that the second ball
drawn is black, are \( A \) and \( B \)
independent? If \( A \) and \( B \) are independent then enter 1 , else enter 0 .


The difference between an exterior
angle of \( (n-1) \) sided regular polygon and an exterior angle of \( (n+2) \) sided regular
polygon is \( 6^{\circ} . \) Find the value of \( n \)
\( A \cdot 13 \)
B. 12
\( c \cdot 16 \)
D. 18


Which of the following has only one subset?
A \( \cdot\{0,1\} \)
B . \{1\}
\( c \cdot\{0\} \)
\( D \cdot\{\} \)


Show that the minimum size of a plane
mirror required to see the full image of
an observer is half the size of that
observer.


Bacterium, Escherichia coli have flagella around the periphery of the cell. This condition is known as
A. Peritrichate
B. Monotrichat
c. Lophotrichate
D. Amphitrichate


In an eleventh storey building 9 people enter a lift cabin. It is known that they will leave the lift in group of 2,3 and 4 at different residential storey. Find the number of ways in which they can get down


The median of 21 observations is \( 18 . \) If
two observations 15 and 24 are
included to the observations, then the median of new series is
A . 15
B . 18
\( c \cdot 24 \)
D. 16


For most of the cities water is drawn
from
A. Rivers
B. Lakes
c. Ponds or wells
D. All of the above.


An Earth's satellite is moving in a circular orbit with a uniform speed \( \boldsymbol{v} \). If
the gravitational force of the Earth suddenly disappears, the satellite will
A. vanish into outer space
B. continue to move with velocity \( v \) in original orbit
c. fall down with increasing velocity.
D. fly off tangentially from the orbit with velocity \( v \)


State whether true or false:
Cutting a log of wood into pieces is a chemical change.
A. True
B. False


Solve :
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\left(\boldsymbol{1}+\boldsymbol{x}^{2}\right)\left(\boldsymbol{1}+\boldsymbol{y}^{2}\right) \)


Expand each of the following, using suitable identities:
\( (3 a-7 b-c)^{2} \)


At certain temperature, \( 1.6 \% \) solution of an unknown substance is isotonic with
\( 2.4 \% \) solution of urea. If both the
solutions have the same solvent and
both the solution have same density \( 1 g m / c m^{3}, \) what will be the molecular mass of unknown substance in
\( \boldsymbol{g} \boldsymbol{m} / \boldsymbol{m} \boldsymbol{o l} \)
(Molecular mass of urea 60 gm / mol)
A. 30
B. 40
c. 80
D. 90


The S.I unit of mass is
A. kilogram
B. gram
c. decigram
D. milligram


The masses of the three wires of copper
are in the ratio \( 1: 3: 5 . \) And their
lengths are in the ratio \( 5: 3: 1 . \) The
ratio of their electrical resistance is
A. 1: 3: 5
B. 5: 3: 1
c. 1: 15: 125
D. 125: 15: 1


\( A D, B E \) and \( C F \) are the altitudes of a
triangle \( A B C \) whose vertex \( A \) is the
point \( (-4,5) . \) The coordinates of the points \( D, E, F \) are respectively \( \left(\frac{16}{5},-\frac{23}{5}\right),(4,1) \) and \( (-1,-4) . \) Find
the equation of the sides of the triangle and the coorindates of the other two
vertices of the triangle.


Assertion
\( \beta \) -particles are deflected less than \( \alpha \) particles in electrical field.
Reason
\( \beta \) -particles have very low mass.
A. \( A \) is correct but \( R \) is wrong
B. \( A \) is wrong but \( R \) is correct
c. Both \( A \) and \( R \) are correct and \( R \) is correct explanation of \( A \)
D. Both \( A \) and \( R \) are correct but \( R \) is not correct explanation of \( A \)


A person wearing a wrist watch that
keeps correct time at the equator goes to N-pole. His watch will
A. Keep correct time
B. gain time
c. loose time
D. cannot say


If a \( 0.1 \mathrm{M} \) solution of \( \mathrm{HCN} \) is \( 0.01 \% \)
ionised, the ionisation constant for
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) is:
A \( \cdot 10^{-9} \)
B. \( 10^{-7} \)
\( c \cdot 10^{-5} \)
D. \( 10^{-3} \)


Write down all possible factors of \( 3 x^{2} y \)


Find a particular solution of the differential equation \( \frac{d y}{d x}+y \cot x= \) \( 4 x \operatorname{cosec} x(x \neq 0), \) given that \( y=0 \)
when \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)


The factor which is not affecting the
conductivity of any solution is
A. temperature
B. dilution
c. nature of electrolyte
D. none of the above


A vertical circular coil of radius \( 0.1 m \)
and having 10 turns carries a steady current. When the plane of the coil is normal to the magnetic meridian, a neutral point is observed at the centre
of the coil. If \( \boldsymbol{B}_{\boldsymbol{H}}=\mathbf{0 . 3 1 4} \times \mathbf{1 0}^{-\mathbf{4}} \boldsymbol{T} \)
the current in the coil is :
\( \mathbf{A} \cdot 0.5 A \)
B. 0.25 A
\( c \cdot 2 A \)
D. \( 1 A \)


The main cause of Zener breakdown is
A. the base semiconductor being germanium.
B. production of electron-hole pairs due to thermal excitation.
C . low doping.
D. high doping.


Find the equation of the ellipse whose
foci are \( (\mathbf{0}, \pm \mathbf{6}) \) and length of the minor
axis is 22


State some characteristics of magnetic
field due to a Current through a Straight Conductor.


Lead obtained from galena ore (PbS) by
air reduction or carbon reduction
process contains base metal (Cu, Bi, As, Sn, \( Z n \) ) as impurities. Gelatin acts as an addition agent in the electrolysis of
Pb. In the presence of gelatin, Pb becomes:
A. hard and brittle
B. soft and rubbery
c. smooth and uniform
D. only brittle


The path of a ray of light passing
through a glass prism is shown below:
In this diagram the angle of prism, angle of incidence, angle of emergence and angle of deviation respectively have
been represented by:
A. \( 0, Y, Z \) and \( N \)
B. P, Y, M and Z,
c. \( 0, x, M \) and \( z \)
D. \( P, X, Z \) and \( N \)


Find the value of \( p: \)
\( (p-3)(p+3)-p(p+8)=15 \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. -3
c. \( \frac{-1}{3} \)
D.


Explain the function of the coronary
artery


Bullets of mass \( 10 g \) each are fired from
a machine gun at a rate of 6 bullets/minute. The muzzle velocity of
bullets is \( 100 \mathrm{m} / \mathrm{s} \). The thrust force (in
N) due to firing bullets experienced by the person holding the gun stationary is
\( 10^{-x} . \) Find \( x \)


The value of \( \sin ^{-1}(\sin 2) \) is?
A \( .2+n \pi \)
B. \( 2-\pi \)
\( c \cdot-2+\pi \)
D. \( 2-2 n \pi \)


Write the name of the following cations. \( N O_{2}^{+}, N O^{+}, H_{3} O^{+}, N H_{4}^{+}, N_{2} H_{5}^{+}, C_{6} H \)


Write structure of Butane \( 1,4- \) dial.


The \( p H \) of three solutions \( A, B, C \) is 6 4, 8 receptivity which of the following is the correct option?
A. \( A>B>C \) decreasing acidic strength
B. \( C>B>A \) increasing acidic strength
c. \( B>A>C \) is decreasing acidic strength
D. \( C>B>A \) decreasing acidic strength


A coil is used in a circuit in which an
A.C. of frequency \( 50 \mathrm{Hz} \) is flowing. The self-inductance of the coil, in order to
produce an impedance of \( 100 \Omega, \) will be
\( H \)
A . \( \pi \)
B.
c. \( \pi^{2} \)
D. \( \frac{1}{\pi^{2}} \)


Fig. shows a brick of weight 2 kgf and
dimensions \( 20 \mathrm{cm} \times 10 \times \mathrm{cm} \times 5 \mathrm{cm} \)
placed in three different positions on
the ground. Find the pressure exerted by the brick in each case.


A fruit (mass \( =50 g \) ) falls from a tree
because of gravitational attraction between the earth and the fruit. Which
of the following statements is true if \( x \) is the force exerted by the earth on the fruit and \( y \) is the force exerted by the fruit on the earth?
A. x is much greater than y
B. \( x \) and y are equal
c. y is greater than \( x \)
D. y is equal to zero


The tension, length, diameter and density of a string \( \mathrm{B} \) are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?
A . \( 1 s \)
B. 2nd
\( c .3 r d \)
D. 4 th


What are sex hormones? Why are they
named so? State their function


For a non-ideal solution exhibiting positive deviation from Raoult's law,
\( \Delta_{m i x} H \) has a
(nonzero)
A. positive
B. negative
c. zero
D. none


If a body is executing simple harmonic motion and its current displacement is \( \frac{\sqrt{3}}{2} \) times the amplitude from its mean position, then the ratio between potential energy and kinetic energy is:
A . 3: 2
B. 2: 3
c. \( \sqrt{3}: 2 \)
D. 3: 1


The volume of a cylindrical toy is 628
\( c m^{3} . \) The radius of its base is \( 10 \mathrm{cm} \)
Find the height of the toy. \( (\pi=3.14) \)


The diamagnetic species is:
A . \( N O \)
в. \( N O_{2} \)
\( c \cdot O_{2} \)
\( D \cdot C O_{2} \)


Assertion
An emulsion becomes stable if soap is
added to it.
Reason
Soap contains hydrophobic and hydrophilic parts.
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


Write three conclusion made by
Rutherford on the basis of alpha
particle scattering experiment.


Sudhir brought an almirah for
Rs. 13600 and spent \( R s .400 \) on its
transportation. He sold it for \( \boldsymbol{R} \boldsymbol{s} \). \( \mathbf{1 6} \boldsymbol{8} \mathbf{0 0} \)
Find his gain percent.


Find the area of the following
parallelogram


Dipole moment is shown by:
This question has multiple correct options
A. 1,4 -dichloro benzene
B. cis-1, 2-dichloro ethene
C. trans-1, 2-dichloro ethene
D. trans-1, 2-dichloro-2-pentene


How much will a bar of aluminium
\( 100 \mathrm{cm} \) long, expand when heated from
\( 20^{\circ} C \) to \( 100^{\circ} C ? \) Coefficient of linear
expansion of aluminium is \( 2.5 \times \) \( 10^{-5} C^{-1} \)


is used for making
parachutes and stockings.
A. cotton
B. Nylon
c. wool
D. Bakelite


Rate limiting step in glycolysis is
A. Glucose to glucose 6 -phosphate
B. Fructose 6- phosphate to fructose 1,6-diphosphate
C. Glyceraldehydde -3 phosphate to 3-phosphoglyceric acid
D. Both A and B


A wire is wound on a long rod of
material of relative permeability \( \mu_{r}= \)
4000 to make a solenoid. If the current
through the wire is \( 5 A \) and number of
turns per length is 1000 per meter, then the magnetic field inside the solenoid is:
A. \( 25.12 \mathrm{mT} \)
B. \( 12.56 \mathrm{mT} \)
c. \( 12.56 T \)
D. 25.12 T


The second stage of hydrosere is occupied by plants like
A. Typha
B. Salix
c. vallisneria
D. Azolla


Consider two nuclei of the same
radioactive nuclide. One of the nuclei
was created in a supernova explosion 5 billion years ago. The probability of decay during the next time is.
A. Different for each nuclei
B. Nuclei created in explosion decays first
c. Nuclei created in the reactor decays first
D. Independent of the time of creation


The ratio of the difference in energy of
electron between the first and second
Bohr's orbits to that between second
and third Bohr's orbits is :
A. \( 1 / 3 \)
в. 27/5
\( c \cdot 9 / 4 \)
D. \( 4 / 9 \)


The longest side of a triangle is 3 times the shortest side and the third side is 2
\( \mathrm{cm} \) shorter than the longest side. If the
perimeter of the triangle is at least 61 \( \mathrm{cm}, \) find the minimum length in cm. of
the shortest side.


The reaction of \( \boldsymbol{C H}_{3} \boldsymbol{O C}_{2} \boldsymbol{H}_{5} \) with \( \boldsymbol{H} \boldsymbol{I} \)
gives:
\( \mathbf{A} \cdot C H_{3} I \)
в. \( C_{2} H_{5} O H \)
c. \( C H_{3} I+C_{2} H_{5} O H \)
D. \( C_{2} H_{5} I+C H_{3} O H \)


The number of particles crossing unit area perpendicular to X-axis in unit time is given by \( \frac{D\left(n_{2}-n_{1}\right)}{\left(x_{2}-x_{1}\right)} \) where
\( n_{1} \) and \( n_{2} \) are number of particle per
unit volume respectively at and \( x_{2} \) The dimension of the diffusion constant \( D \)
are
\( \mathbf{A} \cdot\left[L T^{-1}\right] \)
в. \( \left[L^{2} T^{-1}\right] \)
c. [LT]
D. \( \left[L^{-1} T\right] \)


Centre of gravity of a rectangle will be at its:
A. Centre
B. At its periphery
c. Intersection of its diagonal
D. None


STATEMENT-1: At two different points on
the same stream line in streamline flow
velocity of a particle may be different. STATEMENT-2: Pressure and height may be different at two different points on a
streamline.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True


Let \( f(x)=x^{3} e^{-3 x}, x>0 . \) Then the
maximum value of \( f(x) \) is
A \( \cdot e^{-3} \)
B. \( 3 e^{-3} \)
\( \mathbf{c} \cdot 27 e^{-9} \)
D. \( \infty \)


State the function of bile.


The energy of the second Bohr orbit of hydrogen atom is - 3.41 eV. The energy of
the second orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) would be:
A . - \( 0.85 \mathrm{ev} \)
B . -13.6ev
c. -1.70ev
D. - \( 6.82 \mathrm{eV} \)


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


A compound with molecular weight
equal to 72 g/mol gives a single monochloride and two dichloride on
photochlorination. The hydrocarbon which is consistent with the given
information is \( 2,2- \) dimethylpropane.
State whether the given statement is correct or not.


The order and degree of the differentia
equation \( \left[1+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)\right]^{3 / 4}=\frac{d^{2} y}{d x^{2}} \)
are:
A. order \( =2 ; \) degree \( =3 \)
B. order= \( 2 ; \) degree \( =4 \)
\( ^{\mathrm{c}} \cdot_{\mathrm{order}=} 2 ; \) degree \( =\frac{3}{4} \)
D. order= \( 2 ; \) degree \( = \) not defined


Compound \( \quad \Delta \boldsymbol{H}_{t}(\boldsymbol{k} c a l / \boldsymbol{m o l}) \) \( H_{2} O(g) \) \( C_{2} H_{4}(g) \) 5
\( C O_{2}(g) \) -94.1
What is the heat of combustion of
one mole of \( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \) ?
A . \( +316.3 \mathrm{kcal} \)
B . -12.5 kcall
c. -291.3 kcal
D. - 374.1 kcal
E . \( -57.8 \mathrm{kcal} \)


Sound of frequency 1000 Hz from a stationary source is reflected from an object approaching the source at 30 \( \mathrm{m} / \mathrm{s}, \) back to a stationary observer located at the source. The speed of sound in air is \( 330 \mathrm{m} / \mathrm{s} \). The frequency
of the sound heard by the observer is
A . \( 1200 \mathrm{Hz} \)
в. 1000нz
c. 1090 н \( z \)
D. 1100нz


Which of the following Newton's law(s) is/are not applicable in non-inertial reference frame.
A. Newton's first law
B. Newton's second law
c. Newton's third law
D. All of these


Phosphide and phosphate ions are:
\( \mathbf{A} \cdot P O_{4}^{3-} \) and \( P^{3-} \)
B. \( P^{3-} \) and \( P O_{4}^{3-} \)
\( \mathrm{C} \cdot P O_{3}^{4-} \) and \( P^{4-} \)
D. \( P^{4-} \) and \( P O_{3}^{4-} \)


Indicate the correct statements.
This question has multiple correct options
A. Conductivity cells have cell constant values independent of the solution filled into the cell
B. DC (direct current) is not used for measuring the resistance of a solution
C. Kohlrausch law is valid both for strong and weak electrolytes
D. The k decreases but \( \lambda_{M} \) and \( \lambda_{E} \) increase on dilution


A moving coil galvanometer has 48 turns and area of coil is \( 4 \times 10^{-2} m^{2} . \) If
the magnetic field is \( 0.2 T, \) then to increase the current sensitivity by \( 25 \% \) without changing area (A) and field (B) the number of turns should become:
A . 24
B. 36
\( c \cdot 60 \)
\( D \cdot 54 \)


If in Young's double slit experiment, the
distance between the two slits is halved
and the distance between the slit and
screen id doubled, then the fringe width will become
A . half
B. double
c. four times
D. unchanged


Is the following reaction is a redox
reaction?
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \)


Find the coordinates of the foot of the
perpendicular drawn from the origin to the plane \( 5 y+8=0 \)


An extremely small and dense neutron star of mass \( M \) and radius \( R \) is
rotating at an angular frequency \( \omega . \) If an object is placed at its equator, it will remain stuck to it due to gravity if
A \( \cdot M>\frac{R \omega}{G} \)
в. \( _{M}>\frac{R^{2} \omega^{2}}{G} \)
\( ^{\mathbf{C}} \cdot M>\frac{R^{3} \omega^{2}}{G} \)
D. \( M>\frac{R^{2} \omega^{3}}{G} \)


Two tuning forks of frequency 256 and 258 vibrating per second are sounded together, then time interval between
consecutive maxima heard by the observer is.
A . 2 sec
B. 1 sec
c. \( 0.5 \mathrm{sec} \)
D. 1/4 sec


Which of the following are features of Rutherford nuclear model of an atom?
A. There is a positively charged centre in an atom called the nucleus
B. The electrons revolve around the nucleus in circular paths
C. The size of the nucleus is very small as compared to the size of the atom
D. All of the above


For constructive interference, the path difference between two waves must be
A \( \cdot(2 n+1) \lambda / 2 \)
B. \( (2 n+1) \lambda \)
c. \( _{n \frac{\lambda}{2}} \)
D. \( n \lambda \)


Each of the 11 letters \( A, H, I, M, O, T, U, V, W, X \)
and \( Z \) appears same when looked at in a mirror. they are called symmetric letters. other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?