\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{5} & \mathbf{5} \boldsymbol{\alpha} & \boldsymbol{\alpha} \\ \mathbf{0} & \boldsymbol{\alpha} & \mathbf{5} \boldsymbol{\alpha} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] ; \) If \( \left|\boldsymbol{A}^{2}\right|=\mathbf{2 5}, \) then
\( |\boldsymbol{\alpha}|= \)
A . 5
B \( .5^{2} \)
\( c \cdot 1 \)
\( D \)
\( \therefore \)


When galena is treated with ozone,the
colour change occur from
A. black to red
B. red to white
c. black to white
D. white to black


The work done when 2 moles of an ideal
gas is compressed from a volume of
\( 5 m^{3} \) to \( 1 d m^{3} \) at an initial temperature
of \( 300 K, \) under a pressure of \( 100 k P a \)
is:
A. \( 499.9 k J \)
в. \( -499.9 k J \)
\( \mathbf{c} .-99.5 k J \)
D. \( 42495 k J \)


In Haber process 30 litres of dihydrogen and 30 litres of dinitrogen were taken for reaction which yielded only \( 50 \% \) of the expected product. What will be the composition of gaseous mixture under these condition in the end.


Cassiterite is an ore of:
A. Mn
B. Ni
\( c \cdot s b \)
D. sn


Brown ring is made form
1. \( \boldsymbol{N} \boldsymbol{O}_{\mathbf{3}}^{-} \)
2. \( C l^{-} \)


Which of the following substances yield less than 4 Kcal/mol when its
phosphate bond is hydrolysed?
A. Creatine phosphate
B. ADP
c. Glucose-6-phosphate
D. ATP


A ball of superconducting material is dipped in liquid nitrogen and placed near a bar magnet. In which direction will it move then?
A. Away from bar magnet
c. Around the bar magnet
D. Remains constant


If \( y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right), \) then
\( \frac{d y}{\operatorname{isequal}} \) to
\( d x \)
\( A \cdot 2 \)
B. -
\( c \cdot a \)
\( D \)


Find the amount and the compound
interest on 50000 for \( 1 \frac{1}{2} \) years at \( 8 \% \)
per annum, the interest is compounded
semi-annually.


For one mole of a pure substance free energy is identical with:


Inner lining of gut, stomach and liver is composed of
A. Simple squamous epithelium
B. Simple columnar epithelium
c. simple cuboidal epithelium
D. compound epithelium


Find general solution of the following equations:
\( \sin \theta=\frac{1}{2} ? \)


The interior region of earth between the crust and the central core is called
A. Mantle
B. lava
c. мagma
D. none of these


The coefficient of \( x^{5} \) in the expansion of
\( \left(1+x^{2}\right)^{5}(1+x)^{4} \) is \( ? \)
\( \mathbf{A} \cdot 61 \)
B. 59
c. zero
D. 60


This section contains questions each
with two columns-I and II. Match the
column I with column II.


Which plastid does not contain stored food material?
A. Elaioplasts
B. Aleuroplasts
c. Amyloplasts
D. chromoplasts


Assertion
The force exerted by the fluid is due to
the collisions of molecules with their
surroundings.
Reason
The normal force exerted by the fluid
particles on the walls of the container
results pressure.
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


Two liquids \( A \) and \( B \) of equal volumes have their specific heats in the ratio 2 :
3. If they have same thermal capacity, then the ratio of their densities is
A . 1:
B. 2:3
\( c \cdot 3: 2 \)
D. 5: 6


When without change in temperature, a gas is forced in a smaller volume, its
pressure increases because its
molecule :
A. strike the unit area of the container, wall more often
B. strike the unit area of the container, wall more at higher speed
c. strike the unit area of the container, wall with greater force
D. have more energy


A pair of dice is thrown 6 times. If
getting a total of 9 is considered as a success, what is the probability of getting at least 5 successes?


Assertion
If \( A \) is a non-singular symmetric matrix, then its inverse is also symmetric. Because
Reason
\( \left(A^{-1}\right)^{T}=\left(A^{T}\right)^{-1}, \) where \( A \) is a non-
singular symmetric matrix.
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 arithmetic mean of the nine
numbers in the given set
\{9,99,999,999999999\} is a 9 digit
numbers \( N, \) all whose digits are
distinct. The number \( N \) does not
contain the digit


Solve \( \int \frac{d x}{2 x^{2}-5 x+6} \)


Aluminium containers can be used for
storing conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} . \) Why?


Find inclination (in degrees) of a line
parallel to \( y \) -axis.


Magnetic moment \( \sqrt{35} \) is true for which
of the following pair:
A. \( C o^{+2}, F e^{+2} \)
B . \( F e^{+3}, M n^{+2} \)
c. \( C o^{+3}, C r^{+2} \)
D. \( F e^{+2}, M n^{+2} \)


A population grows at the rate of \( 8 \% \) per year. How long does it take for the
population to double ? Use differential equation for it.


An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top card is a red card.


\( a^{x} \)
\( a^{x} \)
\( a^{x} \)
\( a^{x} \)


n-butyl benzene on oxidation will give:
A. benzoic acid
B. butanoic acid
c. benzyl alcohol
D. benzaldehyde


An object of mass 500 g falls from height of \( 2 \mathrm{m} . \) If \( g=9.8 m / s^{2}, \) what is its kinetic energy when it just touches the ground?
A. zero
B. 19.6
c. \( 9.8 \mathrm{J} \)
D. 9800 J


Using the properties of determinant and without expanding, prove that:
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{y} & \boldsymbol{b} & \boldsymbol{y}+\boldsymbol{b} \\ \boldsymbol{z} & \boldsymbol{c} & \boldsymbol{z}+\boldsymbol{c}\end{array}\right|=\mathbf{0} \)


Two fixed charges separated by a distance \( \boldsymbol{d} \) experience a force \( \boldsymbol{F} \). \( \boldsymbol{A} \) dielectric medium of thickness \( \frac{d}{4} \) and dielectric constant 4 is introduced in
the space between them. Find the new
force between the charges.
A \( \cdot \frac{F}{4} \)
в. \( \frac{F}{3} \)
\( c . F \)
D. \( \frac{16 F}{25} \)


Write the name of adsorbent used in
following:
(i) To remove colouring matter from solution.
(ii) In gas mask.


Which of the following statements given below is incorrect?
A. \( O N F \) is isoelectronic with \( O_{2} N^{-} \)
B. \( O F_{2} \) is an oxide of fluorine
c. \( C l_{2} O_{7} \) is an anhhydride of perchloric acid
D. \( O_{3} \) molecule is bent.


A rod of mass \( m \) and length \( L \), lying horizontally, is free to rotate about a vertical axis through its centre. \( A \) horizontal force of constant magnitude \( F \) acts on the rod at a distance of \( L / 4 \) from the centre. The force is always perpendicular to the rod. Find the angle rotated by the rod during the time \( t \) after the motion starts.


Which of the following statement is not
correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series ionic radius of \( L n^{3+} \) ion
decreases.
C. La is actually an element of transition series rather lanthanide.
D. Atomic radius of Zr and Hf are same because of lanthanide contraction.


f we write equation as \( a x+b y+c=0 \)
then \( a=? \)
4
B.
\( c \)
\( D \)


The expression for equilibrium
constant, \( K_{c} \) for the following reaction
is :
\( \left.\boldsymbol{F} \boldsymbol{e}_{(}^{\boldsymbol{3}+} \boldsymbol{a} \boldsymbol{q}\right)+\boldsymbol{3} \boldsymbol{O} \boldsymbol{H}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{\boldsymbol{3}(\boldsymbol{s})} \)
A \( \cdot K_{c}=\frac{\left[F e\left(O H_{3}\right)\right]}{\left[F e^{3+} \mid D P H\right]^{5}} \)
C . \( K_{c}=\frac{1}{\left[F e^{s+1}\right]\left(0 H^{-}\right]^{s}} \)
D. \( K_{c}=\left[\mathrm{Fe}\left(\mathrm{OH}_{3}\right)\right] \)


Equation of a straight line passing through the point (2,3) and inclined at an angle of \( \tan ^{-1} \frac{1}{2} \) with the line \( y+ \) \( 2 x=5, \) is:
\( \mathbf{A} \cdot y=3 \)
B. \( x=2 \)
c. \( 3 x+4 y-18=0 \)
D. \( 4 x+3 y-17=0 \)


Under what condition real gases obey ideal gas behaviour?


Explain the underlying principle and working of electric generator by drawing
a labelled diagram. What is the function of brushes?


Acidified \( K_{2} C r_{2} O_{7} \) solution turns
green when \( N a_{2} S O_{3} \) is added to it. This is due to the formation of:
A \( \cdot C r O_{4}^{2-} \)
В \( \cdot C r_{2}\left(S O_{3}\right)_{3} \)
\( \mathrm{c} \cdot \mathrm{CrSO}_{4} \)
D \( \cdot C r_{2}\left(S O_{4}\right)_{3} \)


If \( y=e^{\sqrt{x}}+e^{-\sqrt{x}} \) then \( \frac{d y}{d x} \) equals
This question has multiple correct options
A \( \cdot \frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 \sqrt{x}} \)
\( \frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 x} \)
c. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}-4} \)
D. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}+4} \)


Input credit is payable on account of paid on capital goods.
A. profit
B. vat
c. sales tax
D. discount


In the thunderstorm, the charges accumulate near the upper edges of
clouds are
A . negatively charged
B. positively chargedd
c. neutral
D. none of these


The internal energy of a monoatomic ideal gas is :
A. only kinetic
B. only potential
c. partly kinetic and partly potential
D. none


Our universe is very big, with millions of bright galaxies and stars that are much bigger than the sun and the earth. The universe is made up of:
A. burning coal
B. hydrogen
c. oxygen
D. iron burning in a hot flame of oxygen


Find the square of 83 without actual multiplication
A . 6880
B. 3881
\( c .3889 \)
D. 6889


Kate and Nora each have a sum of
money. The ratio of the amount of
money Kate has to that of Nora is 3: 5
After Nora gives Rs. 150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes \( 7: 9 . \) Find the
sum of money Kate had initially.


If the energy density and velocity of a wave are \( u \) and \( c \) respectively then the
energy propagating per second per unit area will be
\( \mathbf{A} \cdot u / c \)
B . \( c^{2} u \)
c. \( u \)
D. \( c / u \)


The change in free energy accompanied by the isothermal reversible expansion of 1 mole of an ideal gas when it doubles
its volume is \( \Delta G_{1} \). The change in free energy accompanied by sudden isothermal irreversible doubling volume
of 1 mole of the same gas is \( \Delta G_{2} \). Ratio
of \( \Delta G_{1} \) and \( \Delta G_{2} \) is:
\( A \)
B.
\( c \cdot-1 \)
D. \( \frac{-1}{2} \)


Explain the principle of a device that can build up high voltage of the order of few million volts

Draw a schematic diagram and explain the working of this device Is there any restriction on the upper
limit of high voltage set up in this machine? Explain.
OR
(a) Define electric flux. Write its S.
units
(b) Using Gauss's law, prove that the electric field at a point due to a uniformly charge infinite plane sheet is independent of the distance from it
(c) How is the field directed if (i) the
sheet is positively charged,(ii) negatively charged?


A machine gun fires a bullet of mass
\( 40 g \) with a velocity \( 1200 m / s . \) The man holding it can exert a maximum force of
\( 144 N \) on the gun. How many bullets can be fired per second at the most?
A. Only one
B. Three
c. can fire any number of bullets
D. \( 144 \times 48 \)


Why is denatured alcohol not used for
drinking?


Which of the following equations shows
the shaded region in the above figure?
A \( \cdot x\left(y-\frac{2}{3} x\right) \geq 0 \)
B. \( x\left(y-\frac{3}{2} x\right) \geq 0 \)
c. \( x\left(y+\frac{3}{2} x\right) \geq 0 \)
D \( \cdot x\left(y+\frac{2}{3} x\right) \geq 0 \)
E \( \cdot x\left(y+\frac{3}{2} x\right) \leq 0 \)


A particle executing S.H.M. completes a distance (taking friction as negligible) in one complete one time period.
A. Four times the amplitude
B. Two times the amplitude
c. one times the amplitude
D. Eight times the amplitude


The marine plants living at different depths of ocean are adapted to survive
A. In UV component of solar radiation
B. Without any component of solar spectrumm
C. In only some components of solar radiation
D. By using chemical source of energy for photosynthesis


Prove that \( \int_{0}^{\frac{32 \pi}{3}} \sqrt{1+\cos 2 x} d x= \)
\( 22 \sqrt{2}-\sqrt{\frac{3}{2}} \)


A cylindrical rod of iron whose height is four times its radius is melted and cast
into the spherical balls of the same
radius then the number of balls is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Which of the following statements
about anhydrous aluminium chloride is
correct?
A. It fumes in moist air.
B. It exists as dimer both in the vapour state below \( 350^{\circ} \mathrm{C} \)
and in non-polar solvents.
C. It is prepared by heating \( A l_{2} O_{3} \) in a stream of sulphur
chloride \( \left(S_{2} C l_{2}\right) \) vapour and chlorine.
D. All of these.


In the following, equilibrium partial
pressure of \( N H_{3}, N_{2} \) and \( H_{2} \) gasses are 4,1 and 2 atm respetively at \( 300 \mathrm{K} \)
what is value of \( \boldsymbol{K}_{\boldsymbol{p}} \) ?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)


\( B r^{-} \) and \( B r O_{x}^{-} \) in acidic medium
forms \( B r_{2}, \) where \( x= \)


A rocket has been fired upwards to launch a satellite in its orbit. Name the
two forces acting on the rocket immediately after leaving the launching pad.


Silk worm is a
A. Fly
B. worm
c. Moth
D. Beetle


Assertion
At the college entrance examination
each candidate is admitted or rejected
according to whether he has passed or failed the tests. Of the candidates who
are really capable, \( 80 \% \) pass the test
and of the incapable, \( 25 \% \) pass the test.
Given that \( 40 \% \) of the candidates are
really capable, then the proportion of
capable college students is about \( 68 \% \)
Reason
\( P\left(\frac{A}{B}\right)=\frac{P(A) P\left(\frac{B}{A}\right)}{P(A) P\left(\frac{B}{A}\right)+P\left(A^{\prime}\right) P\left(\frac{B}{A^{\prime}}\right)} \)
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


Which one of the following is the white silk cotton plant?
A. sida
B. Ceiba
c. Malvaviscus
D. Kydia


Solve the following differential equation \( \cos x \frac{d y}{d x}-\cos 2 x=\cos 3 x \)


Metals react with oxygen to form:
A. Basic oxides
B. Acidic oxides
C. Both A and B
D. None of the above


Full name of the unit named in the
honour of a scientist is written with
A. Lower initial letter
B. Initial capital letter
c. Lower letter
D. All


In mammals, veins differ from arteries
in having
A. Thicker walls
B. Deeply present
D. Internal valves


The reaction \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}_{2}+ \)
\( \boldsymbol{H}_{2} \underbrace{\frac{N i}{250-300^{\circ}}} \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C H}_{3} \) is called
A. Wurtz reaction
B. Kolbe's reaction
c. Sabatier - Sendern's reaction
D. Cabylamine reaction


State Gauss's law in electrostatics.


If \( \bar{a}, \bar{b}, \bar{c} \) are three non-coplanar, non-
zero vectors and \( \bar{r} \) is any vector then \( \bar{r} \) can be represented as \( \boldsymbol{x} \overline{\boldsymbol{a}}+\boldsymbol{y} \overline{\boldsymbol{b}}+\boldsymbol{z} \overline{\boldsymbol{c}} \)
A. always
B. never
c. is one and only one way
D. None of these


A reference frame attached to the earth
This question has multiple correct options
A. is an inertial frame by definition.
B. cannot be an inertial frame because the earth is
revolving around the sun.
C. is an inertial frame because Newtons laws are applicable in this frame.
D. cannot be an inertial frame because the earth is rotating about its own axis.


"If Tom buys a red skateboard then
Amanda buys green in-line skates".
Which statement below is logically equivalent?
A. If Amanda does not buy green in-line skates then Tom does not buy a red skateboard
B. If Tom does not buy a red skateboard then Amanda does not buy green in-line skates
C. If Amanda buys green in-line skates then Tom buys a red skateboard
D. If Tom buys a red skateboard then Amanda does not buy green in-line skates


Which of the following is an energy dependent process?
A. Facilitated diffusion
B. Active transportt
c. Endosmosis
D. Exosmosis


Book of mass \( 2 \mathrm{kg} \) is lifted from floor to the table. The height between floor and the table is \( 1.5 \mathrm{m} \). Calculate the work
done by gravitational force.
A . -30
B . -15 J
c. о
D. 15 J
E. 30


Use Lenz's law to determine the
direction of induced current in
the situations described by Fig.(a) \( A \) wire of irregular shape turning into a circular shape;(b) A circular loop being
deformed into a narrow straight wire.


If \( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{5} \\ \mathbf{5} & \mathbf{0} \\ -\mathbf{7} & \mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{- 5} & \mathbf{7} \\ \mathbf{- 5} & \mathbf{0} & \mathbf{- 4}\end{array}\right], \) then find \( \boldsymbol{A}+\boldsymbol{B}^{\boldsymbol{T}} \)
A . 0
в. \( 2 B \)
c. \( 2 A^{\text {न }} \)
D. \( 2 B^{\text {T }} \)


Identify the incorrect statement from the following
A. Oxides of nitrogen in the atmosphere can cause the depletion of ozone layer
B. Ozone absorbs the intense ultraviolet radiations of the
sun
c. Depletion of ozone layer is because of its chemical reactions with CFC
D. Ozone absorbs infrared radiations


Power consumed in an AC circuit
becomes zero if
A. inductance and resistance are both high.
B. inductance and resistance are both low.
C. inductance is very high and resistance is negligible.
D. inductance is low and resistance is high.


Which is the amorphous form of silica?
A. Quartz
B. Tridymite
c. onyx
D. crystobalite


Which compound did Wohler make in
the laboratory first?


Which one of the following is true with
respect to \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} ? \)
A. Linear, acidic
B. Linear, basic
c. Tetrahedral, acidic
D. Angular, basic


In p-njunction, avalanche current flows in circuit when biasing is
A. forward
B. reverse
c. zero
D. excess


What is the distance travelled by a point during the time t. if it moves in \( x \) Y plane according to relation.
\[
\begin{array}{l}
\boldsymbol{X}=\boldsymbol{a} \boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{\omega} \boldsymbol{t} \\
\boldsymbol{Y}=\boldsymbol{a}(1-\boldsymbol{c o s} \boldsymbol{\omega} \boldsymbol{t})
\end{array}
\]


Phosgene is formed by aerial oxidation
of \( \boldsymbol{C H} \boldsymbol{C l}_{3} \)
\( \boldsymbol{C H} \boldsymbol{C l}_{3}+\frac{1}{2} \boldsymbol{O}_{2} \longrightarrow \boldsymbol{C O C l}_{2}+\boldsymbol{H C l} \)
If true enter 1 , else enter 0 .


The given diagram shows a series of images of moving ball captured by a
camera.
The ball was moving at a constant speed and the image were taken
constant rate of 10 per second.What is
the speed of ball?
A. \( 30 m s^{-1} \)
B. \( 20 m s^{-1} \)
c. \( 45 m s^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \)


An atom of neon has a mass of \( 3.35 \times \)
\( 10^{-23} g . \) How many atoms of neon are
there in \( 20 g \) of the gas?


State whether the following sentences
are always true, always false or
ambiguous.Justify your answer. There are 27 days in a month.


Differentiate between NPN \& PNP
transistors.?


If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
A. 48 paise
B. 54 paise
c. 56 paise
D. 72 paise


Which units of pressure are needed if you are going to use 0.0821 as your ideal gas constant?
A. Atmospheric
B. Torr
\( c . \) Psi
D. mmHg
E. Pascals


A bomb explodes on the moon. How long will it take for the sound to reach the
earth?
A . 10 seconds
B. 1000 seconds
c. 1 day
D. It does not reach the earth


Analyse the given circuit diagram of a half wave rectifier and answer the
following questions.
a.Identify the components labelled as
\( M \) and \( N \)
What are the changes to be made in
the following components for the
converting this to a full wave rectifier
I. Transformer
ii. No.of Dioder
iii. Draw the output form of a fill
rectifier.


The amino acid which is not optically active is:
A . lactic acid
B. serine
c. alanine
D. glycine


A mixture of \( S O, \) and \( O_{2} \) under
atmospheric pressure in the ratio of 2:
1 is passed over a catalyst at \( 1170^{\circ} \mathrm{C} \) After equilibrium has reached, the gas coming out has been found to contain
\( 87 \% S O_{3} \) by volume. Calculate \( K_{p} \) for \( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3} \)


The speed of the disc \( M \) is
\( A \cdot 0 \)
B. \( \frac{v_{0}}{2} \)
\( c \cdot \frac{200}{\sqrt{5}} \)
\( D \cdot v_{0} \)


A current is flowing in a circuit consisting of a resistor and a battery. What happens to the power dissipated in the resistor when the resistance is
quadrupled and the voltage remains
constant?
A. It is doubleo
B. It is quadrupled
c. It is halvedd
D. It is quartered
E. It remains the same


The elastic limit of steel is \( 8 x \)
\( 10^{8} N m^{-2} \) and its Young modulus \( 2 \times \)
\( 10^{11} N m^{-2} . \) Find the maximum
elongation of a half-metre steel wire that can be given without exceeding the elastic limit.


\( A \cdot A-1, B-2, C-4, D-3 \)
B. \( A-2, B-1, C-4, D-3 \)
\( C \cdot A-1, B-4, C-2, D-3 \)
D. \( A-1, B-2, C-3, D-4 \)


Why does toroid have a higher magnetic field than a solenoid?
A. It is magnetically efficient.
B. It is a straight core
c. It has an open loop core.
D. It has a closed loop core


If the ratio of the areas of the two circles
is \( 25: 16, \) then the ratio of their
circumferences is

This question has multiple correct options
A \( \cdot \frac{625}{500} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{500}{625} \)


\( N a, M g \) and \( A l \) are the elements of the
\( 3^{r d} \) period of the Modern Periodic Table having group number 1,2 and 13 respectively. Which one of these elements has the
(a) highest valency,
(b) largest atomic radius, and (c)
maximum chemical reactivity? Justify
your answer starting the reason for each.


Sometimes moulds (fungus) grow on bread or grains,like rice, corn and beans. These moulds (fungus) produce a carcinogenic (cancer-causing) poison,namely:
A. aflatoxin
B. cyanide
c. sodium phosphate
D. alfalfa


How many of the following compounds has \( X X \) bonds i.e. single covalent bond between two same elements in their
molecules:
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}, \boldsymbol{N}_{2} \boldsymbol{O}, \boldsymbol{N}_{2} \boldsymbol{O}_{3} \)
\( A \cdot 3 \)
B. 8
\( c \cdot 4 \)
D. 6


The H.C.F. of two expressions is \( x \) and their L.C.M is \( x^{3}-9 x \) IF one of the
expression is \( x^{2}+3 x \) then,the other
expression is
A \( \cdot x^{2}-3 x \)
B. \( x^{3}-3 x \)
c. \( x^{2}+9 x \)
D. \( x^{2}-9 x \)


If \( \lim _{x \rightarrow 2^{-}} \frac{x-3}{x^{2}-4}=a \) then \( \frac{1}{a} \) is equal
to


For instantaneous speed, the distance
traveled by the object and the time taken are both equal to zero.
A. True
B. False


The diameter of a sphere is decreased by \( 25 \% \). By what percent its curved
surface area decrease?


Identify the following force:
1)Force between the charged particles.
2)Attractive for unlike charges and
repulsive for like charges.
3) It does not need any intervening medium.
4) It is not the strongest force.
A. Gravitational Force
B. Electromagnetic force
c. strong nuclear force
D. Weak nuclear force


Acrylonitrile, butadiene and styrene are a kind of:
A. addition polymer
B. co-polymer
c. homopolymer
D. thermosetting polymer


Solve
\( \lim _{x \rightarrow 0} \frac{\tan 8 x}{\sin 2 x} \)


Define the following with a suitable example, of each:
(a) Cogulation
(b) Multimolecular colloid
(c) Gel


The element which has not yet been
reacted with \( \boldsymbol{F}_{2} \) is:
\( A \cdot A r \)
в. \( x_{e} \)
\( c \cdot k r \)
D. Rn


The conduction current in ideal case
through a circuit is zero when charge on capacitor is


If \( \omega \) is a complex cube root of unity, the \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \boldsymbol{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{\omega}\end{array}\right| \) is equal to
A . -1
B.
\( c \cdot 0 \)
D.


Newton postulated his corpuscular theory of light on the basis of:
A. Newton's rings.
B. rectilinear propagation of light
c. colour through thin films.
D. Dispersion of white light into colours.


If \( \sin ^{-1} x-\sin ^{-1} y=\frac{\pi}{2}, \) then
A \( \cdot x^{2}+y^{2}=1 \)
в. \( y=-\sqrt{1-x^{2}}, 0 \leq x \leq 1,-1 \leq y \leq 0 \)
C \( \cdot y=\sqrt{1-x^{2}},|x|<1 \)
D. None of these


When two dice are thrown
simultaneously the probability that the
sum of the two numbers that turn up is
more than 11 is:
A \( \cdot \frac{11}{12} \)
в. \( \frac{1}{36} \)
\( c \cdot \frac{2}{12} \)
D. \( \frac{1}{8} \)


Two radioactive sources \( X \) and \( Y \) of
half lives \( 1 h \) and \( 2 h \) respectively
initially contain the same number of
radioactive atoms. At the end of \( 2 h \)
their rates of disintegration are in the ratio of :
A .4: 3
B. 3: 4
\( c \cdot 1: 2 \)
D. 2: 1


A copper wire of negligible mass, \( 1 \mathrm{m} \)
length and cross-sectional area
\( 10^{-6} m^{2} \) is kept on a smooth horizontal
table with one end fixed. A ball of mass
\( 1 \mathrm{kg} \) is attached to the other end. The
wire and the ball are rotating with an angular velocity of 20 rad/s. If the
elongation in the wire is \( 10^{-3} \mathrm{m} \)
b. If for the same wire as stated above, the angular velocity is increased to 100 rad/s and the wire breaks down, find the
breaking stress (in terms of \( \left.\times 10^{10} N / m^{2}\right) \)


Find the average acceleration in first 20
s.


In the reaction between \( N O \) and \( H_{2} \) the
following data are obtained
Experiment \( 1: P_{H_{2}}= \) constant
\[
(\mathrm{mm} \text { of } \mathrm{Hg}) \quad \text { 359 } \quad \text { 300 }
\]
\( -\frac{P_{H_{2}}}{d t} \) 1.50 \( \quad 1.03 \quad \) 0.25
Experiment \( 2: P_{N O}= \) constant
\[
\boldsymbol{P}_{H_{2}}(\mathrm{mm} \text { of } \mathrm{Hg}) \quad 289 \quad 205
\]
\( -\frac{P_{H_{2}}}{d t} \) \( 1.60 \quad 1.10 \)
The orders with respect of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{N} \boldsymbol{O} \)
are:
A \( \cdot 1 \) with respect to \( N O \) and 2 with respect to \( H_{2} \)
B. 2 with respect to \( N O \) and 1 with respect to \( H_{2} \)
c. 1 with respect to \( N O \) and 3 with respect to \( H_{2} \)
D. 2 with respect to \( N O \) and 2 with respect to \( H_{2} \)


Sodium forms \( N a^{+} \) ion but it does not
form \( N a^{2+} \) because of the:
A. very low value of (IE) and (IE) 2
B. very high value of (IE) and (IE)
c. low value of (IE) and low value of (IE) 2
D. low value of (IE) and high value of (IE) 2


The number of protons in an ion from which \( (Z-1) \) electrons are removed
having its ionization energy \( 11800 k J \)
\( m o l^{-1} \) is :
A. three
B. five
c. four
D. insufficient information


Argon has three isotopes with relative atomic masses of 36,38 and \( 40 . \) Given that the average relative atomic mass of naturally occurring argon is 39.95 Which of the following statements must
be correct?
A. 40 Ar is less abundant than \( ^{38} \) Ar
B. \( 40 \mathrm{Ar} \) is more abundant than either \( ^{36} \mathrm{Ar} \) or \( ^{38} \mathrm{Ar} \)
C. \( 40 \mathrm{Ar},^{38} \mathrm{Ar} \) and \( ^{36} \mathrm{Ar} \) are equally abundant
D. \( 36 A r \) is more abundant than \( ^{40} A r \)


Which of the following statements are
correct about \( \boldsymbol{S} \boldsymbol{F}_{4} ? \)
A. It is prepared by reacting sulphur directly with fluorine
B. Sulphur tetrafluoride hydrolyzed by water to give \( S O_{2} \) and нF
\( \mathrm{c} . S F_{4} \) has a square planar shape with \( \mathrm{S} \) having two lone pair of electrons
D. S-atom has a expanded octet.


There are 5 letters and 5 addressed
envelopes.The number of ways in which the letters can be placed in the envelopes so that none of them goes
into the right envelope is
A . 22
B. 44
\( c \cdot 120 \)
D. 119


Haversian canal is situated in
A. Glandular connective tissue
B. Skeletal connective tissue
c. Fibrous connective tissue
D. Nervous tissue


In heart cells, which one serves as a second messenger, speeding up muscle cell contraction in response to
adrenaline?
A . cAMP
B. сGMP
c. Gтр
D. ATP


The oil used as frothing agent in froth floatation process is:
A. coconut oil
B. castor oil
c. palmitic oil
D. pine oil


The parallel sides of a trapezium are \( x \)
and \( y \) in length. The length of the line segment joining the mid points of the non parallel sides is:
A. \( \frac{x+y}{2} \)
B. \( x+y \)
c. \( \frac{2 x+3 y}{2} \)
D. \( \frac{x y}{2} \)


Four forces of magnitude \( P, 2 P, 3 P \) and \( 4 P \) act along the four sides of a square ABCD in cyclic order. Use the vector method to find the resultant force.
A \( \cdot 2 \sqrt{2} P \)
В. \( 3 \sqrt{2} P \)
c. \( \sqrt{2} P \)
D. \( -2 \sqrt{2} P \)


Assertion: \( P H_{3} \) is more basic than
\( N H_{3} \)
Reason: EN of N is more than that of P
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. The Assertion is true and Reason is false
D. Assertion is false but Reason is true


Standard form of \( 900000000+3000+ \)
7 is equal to
A .90,00,03,007
7
B. 9,00,03,007
\( \mathrm{c} .90,00,03,000 \)
D. none of these


A steam of water flowing horizontally
with a speed of \( 25 m s^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-3} m^{2} \)
and hits at a vertical wall nearby. What is the force exerted on the wall by the impact of water?
A . \( 125 N \)
в. 625 N
c. \( -650 N \)
D. \( -1125 N \)


Our body can conduct electric current.
A. True
B. False


Sols are colloidal systems in which the dispersion medium is liquid (such as water) and the dispersed phase is solid
State whether True or False.


The V-I graph for conductor at
temperatures \( T_{1} \) and \( T_{2} \) are shown in
the figure. \( \left(T_{2}-T_{1}\right) \) is proportional to
A \( . \cos 2 \theta \)
B. \( \sin 2 \theta \)
\( c \cdot \cot 2 \theta \)
D. \( \tan 2 \theta \)


Two identical capacitors having plate
separation \( d_{0} \) are connected parallel to
each other across the points \( A \) and \( B \)
as shown in figure. A charge \( Q \) is imparted to the system by connecting
battery across \( A \) and \( B \) and the battery is removed. Now the first plate of the
first capacitor and the second plate of the second capacitor start moving with
constant velocity \( u_{o} \) toward left. The magnitude of the current flowing in the loop during this process is given as
\( \frac{Q u_{0}}{x d_{0}} . \) Find \( x \)


How can a scuba diver keep from
floating back to the surface of the
water?


A species lacking sexual reproduction and delimited by asexual traits is called
A. Sibling species
B. Agamospecies
c. Biospecies
D. Allochronic species


Find the vector equation of the plane
passing through points \( 4 i-3 j- \)
\( k, 3 i+7 j-10 k \) and \( 2 i+5 j-7 k \) and
show that the point \( i+2 j-3 k \) lies in
the plane.


A transformer having the efficiency of \( 90 \% \) is working on \( 200 V \) and \( 3 k W \) power supply. If the current in the secondary coil is \( 6 A \), the voltage across the secondary coil and the
current in the primary coil respectively are:
A. \( 300 V, 15 A \)
в. \( 450 V, 15 A \)
c. \( 450 V, 13.5 A \)
D. \( 600 V, 15 A \)


The terminal and bridged \( C O \) ligands in
the compound \( \left[\boldsymbol{C o}_{2}(\boldsymbol{C O})_{8}\right] \) are respectively:
\( A \cdot 0,2 \)
в. 6,1
\( c \cdot 5,2 \)
D. 6,2


Choose the correct statements about
phase changes.
A. When a liquid freezes, it releases thermal energy into its immediate environment
B. When a solid melts, it releases thermal energy into its immediate environment
C. For most substances, the latent heat of fusion is
greater than the latent heat of vaporization
D. As a solid melts, its temperature increases
E. As a liquid freezes, its temperature decreases


Increase in concentration of a toxicant
at successive trophic levels is called
A. Algal bloom
B. Biomagnification
c. Eutrophication
D. Accelerated eutrophication
E. Decelerated eutrophication


The diagram given below represents those students who play Cricket, Football and Kabaddi. Study the
diagram and identify the students who play all the three games.
\( \mathbf{A} \cdot P+Q+R \)
в. \( S \)
\( \mathbf{c} \cdot S+T+V \)
D. \( V+T \)


Two horizontal metal plates having a
potential difference of \( 800 \mathrm{V} \) are \( 0.02 \mathrm{m} \) apart. A particle of mass \( 1.92 \times \) \( 10^{-15} \mathrm{kg} \) is suspended in equilibrium
between the plates. Ife is the elementry charge, then charge on the particle is:
\( A \)
B . 3 e
c. \( 6 \mathrm{e} \)
D. \( 8 \mathrm{e} \)


Find the smallest number which when
multiplied with 53240 will make the product a perfect cube.


All viruses contain
A. Protein coat
B. Cell membrane
C. Membrane-bound organelles
D. Endoplasmic Reticulum
E. Mitochondrial DNA


Evaluate the integral \( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


Concentrate nitric acid oxidises
phosphorus to phosphoric acid according to the following equation:
\( \boldsymbol{P}+\mathbf{5} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{c} \boldsymbol{o} \boldsymbol{n} \boldsymbol{c} .) \rightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}+\mathbf{5} \boldsymbol{N} \boldsymbol{O}_{2} \)
What mass of phosphoric acid can be
prepared from \( 6.2 g \) of phosphorous?


What is the SI unit of mass? How is it
defined?


The temperature of a metal coin is
increased by \( 100^{\circ} \mathrm{C} \) and its diameter increases by \( 0.15 \% \). Its area increases by nearly:
A . 0.15\%
B. 0.60\%
c. 0.30\%
D. 0.0225\%


Flux \( \Phi \) (in weber) in a closed circuit of
resistance 10 ohm varies with time \( t \) (in
sec) according to the equation \( \Phi=6 t^{2}- \)
\( 5 t+1 . \) What is the magnitude of the
induced current at \( t=1 \) sec?
A . \( 0.5 A \)
в. \( 0.6 A \)
\( c .0 .7 A \)
D. \( 0.8 A \)


Interfascicular cambium develops from the cell of
A. Medullary rays.
B. Xylem parenchyma.
c. Endodermis.
D. Pericycle.


When two deuterium nuclei fuse
together to form a tritium nucleus, we
\( \operatorname{get} a \)
A. neutron
B. deuteron
c. alpha particle
D. proton


Magnetic moment of \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) ion
is?
A \( \cdot 1.414 \)
B. 1.73
c. 2.23
D. 2.38


If \( P(x, y, z) \) is point in the space at a
distance \( r \) from the origin \( O \), then
direction cosines of the line \( O P \) are


A gas has an average speed of \( 10 \mathrm{m} / \mathrm{s} \)
and a collision frequency of \( 10 s^{-1} . \) What
is its mean free path?
A. \( 1 m \)
в. \( 2 m \)
c. \( 3 m^{\text {- }} \)
D. \( 4 m \)


The value of \( ^{n} C_{n} \) is
\( A \cdot n \)
B.
c. 1
D. \( n ! \)


A circular loop of radius R carries
current \( I_{2} \) in a clockwise direction as
shown in figure. The centre of the loop is a distance D above a long,straight wire.What are the magnitude and
direction of the current \( I_{1} \) in the wire if
the magnetic field at the centre of loop
is zero?


Solution of sodium metal in liquid ammonia is strongly reducing due to the presence of
A. sodium hydride
B. sodium amide
c. sodium atoms
D. solvated electrons


Dispersion forces:
A. Water
B. Hydrogen bromide
C. Iron
D. Argon
E . Sodium chloride


If first ionization potential of an atom is \( 16 \mathrm{V} \) then determine the first excitation
potential value for it.
A . 12 \( v \)
B. 14
\( c \cdot 19 v \)
D. 20


The most commonly used food preservative is:
A. Sodium cyclamate
B. Sodium benzoate
c. sodium acetate
D. vanillin


Boiling hard water with washing soda removes permanent hardness.
A. True
B. False


i) Space Stations are used to study the effects of long-space flight on the human body. Justify.
ii) \( \boldsymbol{F}=\boldsymbol{G} \boldsymbol{m}_{1} \boldsymbol{m}_{2} / \boldsymbol{d}^{2} \) is the
mathematical form of Newton's law of
gravitation, \( G- \) gravitational constant
\( m_{1} m_{2}, \) are the masses of two bodies
separated by a distance \( d \), then given
the statement of Newton's law of
gravitation.


The combustion of candles, containing
paraffin wax, to carbon dioxide and water vapour is sublimation.
A. True
B. False


A bomb explodes on the moon. How long will it take for the sound to reach the
earth?
\( \mathbf{A} \cdot 10 \sec \)
B. 1000sec
c. \( 1 d a y \)
D. None of these


From the following data, state if \( \triangle A B C \sim \triangle D E F \) or not
\( \angle B=65^{\circ}, \angle C=82^{\circ}, \angle D=33^{\circ}, \angle F= \)
\( \mathbf{6 5}^{\circ} \)


Chlorine acts as a bleaching agent only
in the presence of :
A. dry air
B. moisture
c. sunlight
D. pure oxygen


The soft-iron core of an electromagnet loses its magnetism once the current passing through the electromagnetic coil stops because.
A. Domains lose their alignment when the current is stopped
B. Iron cannot hold alignment for longer time even when the current is passing through the coil
c. Magnetic properties of iron are weak
D. Domains inside the iron get aligned in north to south direction


Let us list some of the factors, which could possibly influence the speed of wave propagation:
(i) nature of the source.
(ii) direction of propagation.
(iii) motion of the source and/or
observer.
(iv) wavelength.
(v) intensity of the wave. On which of these factors, if any, does
(a) The speed of light in vacuum
(b) The speed of light in a medium (say, glass or water), depend?


Find which of the function are one-one
,onto, many-one,one-many. Justify your
answer
\( \boldsymbol{f}=\{(1, \mathbf{3}),(\mathbf{2}, \mathbf{6}),(\mathbf{3}, \mathbf{9}),(\mathbf{4}, \mathbf{1 2})\} \) define
from \( A \) and \( B \) where
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \boldsymbol{B}=\{\mathbf{3}, \mathbf{6}, \mathbf{9}, \mathbf{1 2}, \mathbf{1 5}\} \)


Find the maximum value of \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\sin \boldsymbol{\theta} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\cos \boldsymbol{\pi}\end{array}\right| \)


Find the remainder when \( 4 x^{3}-3 x^{2}+ \)
\( 4 x-2 \) divided by \( (\text { i) } x-1 \)
(ii) \( x-2 \)


A silicon diode has a "knee voltage of
threshold voltage" value of \( 0.7 \mathrm{V} \). This \( \mathrm{Si} \)
diode is connected in a circuit as shown
in the figure

Potential \( V_{0} \) of point \( p \) in the circuit will
be:
A . \( -0.44 v \)
B. 0.44V
c. \( 4.4 v \)
\( D,-4,4\rangle \)


Which one of the following compounds do not give a primary alcohol on reduction?
A. Propanal
B. Propanoic acid
c. Methyl propanoate
D. Propan-2-one


Two blocks of masses \( m_{1} \) and \( m_{2} \) are
connected by spring constant \( \boldsymbol{K} \) Initially the spring is at its natural length. The coefficient of friction between the bars and the surface is \( \mu \)
What minimum constant force has to
be applied in the horizontal direction on
the block of mass \( m_{1}, \) in order to shift
the other block?
\( A \)
\[
F=\mu\left(2 m_{1}+\frac{m_{2}}{2}\right) g
\]
В \( \cdot F=\mu\left(2 m_{1}+m_{2}\right) g \)
\( ^{\mathbf{c}} \cdot_{F}=\mu\left(m_{2}+\frac{m_{1}}{2}\right) g \)
\( ^{\mathrm{D}} F=\mu\left(m_{1}+\frac{m_{2}}{2}\right) g \)


Which of the following is a correct sequence of layers in typical monocot root (from outer surface to inside)?
A. Pericycle, cortex, endodermis, epiblema
B. Epiblema, endodermis, cortex, pericycle
c. Epiblema, cortex, endodermis, pericycle
D. Epiblema, pericycle, cortex, endodermis


A circuit consists of a coil with
inductance \( L \) and an uncharged capacitor of capacitance C.The coil is in a constant uniform magnetic field such
that the flux through the coil is \( \mathbf{\Phi} . \mathbf{A t} \)
time \( t=0, \) the magnetic field is
abruptly switched off. Let \( \omega_{0}=1 / \sqrt{L C} \)
and ignore the resistance of the circuit.
Then:
A . current in the circuit is \( I(t)=(\Phi / L) \cos \omega_{0} t \)
B. Magnitude of the charge on the capacitor is \( |Q(t)|= \) \( 2 C \omega_{0} \mid \sin \omega_{0} t \)
C. initial current in the circuit is infinite
D. initial charge on the capacitor is \( C \omega_{0} \Phi \)


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


When excess of ammonia is used:
\( \mathbf{3} C l_{2}+\mathbf{8} N H_{3} \longrightarrow A+B \)
When excess of chlorine is used:
\( \mathbf{3} C l_{2}+\mathbf{4} N H_{3} \longrightarrow C+D \)
The oxidation state of nitrogen in
compound \( \boldsymbol{A} \) is:
A. -3
B. +3
\( c .+5 \)
D.


For an ideal toroid, in which turns are closely spaced, the external magnetic field is
A. Very high
B. Infinity
c. zero
D. one


The IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{O H}) \boldsymbol{C H}_{2}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \) is:
A. 2,4-Dimethylpentan-2-ol
B. 2,4-dimethylpentan-4-ol
c. 2, 2-dimethylbutane
D. 2,4,4-trimethylbutan-2-ol


What is the name of the alkane shown
in the image?
A. 2 -dimethylhexane
B. 3-dimethylhexane
C. 2,2 -dimethylhexane
D. 3,3-dimethylhexane


The vital capacity of the lung signifies
the volume of air
A. Breathe in during normal inspiration
B. Breathe out with forcible expiration
c. Breathe in with forcible inspiration
D. Volume of air expelled with forcible expiration after deep inspiration


Active transport across cell membrane
requires
A. Glucose
B. Steroids
c. Energy in the form ATP
D. Proteins and glucose


Explain reflex arc with diagram.


Blister copper is:
A. impure copper
B. obtained in self-reduction process during bessemerisation
c. both are correct
D. none is correct


Let \( \boldsymbol{A}=\{\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}, \boldsymbol{z}\} ; \boldsymbol{B}=\{\mathbf{3}, \mathbf{5}\}, \) then
the number of relations from \( A \) to \( B \) is
A . 256
B. 1024
c. 512
D. 64


The mass of photon having wavelength
1n \( m \) is:
\( \mathbf{A} \cdot 2.21 \times 10^{-35} k g \)
B . 2.21 \( \times 10^{-33} g \)
C \( .2 .21 \times 10^{-33} k g \)
D . \( 2.21 \times 10^{-26} \mathrm{kg} \)


The positive integer whose product with
-1 is
A. positive
B. negative
c. 0
\( D \cdot \) none


Which heat is produced throughout the conducting wire?
A. Petlier heat
B. Thomson effect heat
c. Joule heat
D. none of these


The ratio of the size of the image to the size of the object is known as
A. focal plane
B. transformation ratio
c. efficiency
D. magnification


Which of the following method of preparation of chloroform is not preferable?
A. Distillation of ethyl alcohol with bleaching powder
B. Chlorination of methane
c. Reduction of carbon tetrachloride with iron and water
D. Distillation of chloral hydrate with \( N a O H \)


Evaluate the definite integral \( \int_{0}^{\frac{\pi}{2}} \cos ^{2} x d x \)


RQ (Respiratory Quotient) is defined as
A. Volume of \( \mathrm{CO}_{2} \) evolved \( = \)
volume of \( \mathrm{O}_{2} \) consumed
\begin{tabular}{llll}
B. Volume of & O \( _{2} \) consumed \\
\cline { 2 - 3 } Volume of & \( \mathrm{CO}_{2} \) & evolved
\end{tabular}
\begin{tabular}{llll}
C. Volume & of & C O \( _{2} \) evolved \\
\cline { 2 - 3 } Volume & of & \( \mathrm{O}_{2} \) & consumed
\end{tabular}
D. \( \frac{\text { Volume of } O_{2}}{\text { Volume of } C O_{2}} \) consumed


A sound wave has a frequency of \( 192 \mathrm{Hz} \) and travels the length of a football field, \( 91.4 \mathrm{m}, \) in \( 0.27 \mathrm{s} . \) What is the speed of the wave?
A. \( 338.5 \mathrm{m} / \mathrm{s} \)
В. \( 348.5 \mathrm{m} / \mathrm{s} \)
c. \( 358.5 \mathrm{m} / \mathrm{s} \)
D. \( 368.5 \mathrm{m} / \mathrm{s} \)


A turn of radius \( 20 \mathrm{m} \) is banked for the
vehicles going at a speed of \( 36 k m / h \). If
the coefficient of static friction between
the road and the tyre is \( 0.4 . \) What are the possible speeds of a vehicle so that it neither slips down nor skids up?
\( \left(g=9.8 m / s^{2}\right) \)
A \( \cdot 2.2 m s^{-1} \leq v \leq 4.2 m s^{-1} \)
B. \( 4.2 m s^{-1} \leq v \leq 15 m s^{-1} \)
c. \( 15 m s^{-1} \leq v \leq 18.5 m s^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \leq v \leq 22.5 \mathrm{ms}^{-1} \)


Write the relation for binding energy
(B.E) (in MeV) of a nucleus of mass \( _{Z}^{A} M \) atomic number \( (z) \) and mass number
(A) in terms of the masses of its
constituents - neutrons and protons.


Which of the following is pyrogallol?
A.
в.
\( c \)
D.


Add the given expression: \( 5 \sqrt{x}- \) \( 4 \sqrt{y}+2 ; 2 \sqrt{x}+7 \sqrt{y}-5 \)
A. \( 7 \sqrt{x}+3 \sqrt{y}-3 \)
В. \( 7 \sqrt{x}+3 \sqrt{y}-5 \)
c. \( 7 \sqrt{x}+3 \sqrt{y}-8 \)
D. \( 7 \sqrt{x}+2 \sqrt{y}-3 \)


Find the difference of the areas of two
segments of a circle formed by a chord of length \( 5 \mathrm{cm} . \) Subtending an angle of
\( 90^{\circ} \) till the centre.
A. 32.14 sq. \( \mathrm{cm} \)
в. 35.42 sq. \( \mathrm{cm} \)
c. 38.96 sq. \( \mathrm{cm} \)
D. 42.43 sq. \( \mathrm{cm} \)


At \( 300 K \), two pure liquids \( A \) and \( B \)
have vapour pressures \( 150 \mathrm{mm} \mathrm{Hg} \)
and 100 mm \( H g \) respectively. In an equimolar liquid mixture of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) the mole fraction of \( B \) in the vapour
mixture at this temperature is:
A . 0.6
B. 0.5
c. 0.8
D. 0.4


In Krebs cycle, the Hydrogen atoms removed at succinate level are
accepted by
A. FAD
B. ADP
c. Атр
D. NAD


Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \dots \dots(1+ \)
\( (n+1)^{2} \)


Study the following statements and select the incorrect ones.
(i) Physical removal of large and small particles through filtration and sedimentation is called primary sewage
treatment.
(ii) Secondary sewage treatment is mainly a mechanical process.
(iii) Activated sludge sediment in a sewage treatment plant is a rich source of aerobic bacteria.
(iv) Biogas, commonly called as gobar
gas, is pure methane.
A . A-(iii), B-(i), C-(iv), D-(ii)
B. A-(i), B-(iii), C-(iv), D-(ii)
c. A-(iii), B-(ii), C-(iv), D-(i)
D. A-(iii), B-(i), C-(ii), D-(iv)


If \( f(x)=\frac{\sin ([x] \pi)}{x^{2}+x+1}, \) where \( [x] \) denotes
the integral part of \( x . \) Show that \( f(x) \) is
a constant function.


In Haber's process \( 50.0 g \) of \( N_{2}(g) \) and
\( 10.0 g \) of \( H_{2}(g) \) are mixed to produced \( N H_{3}(g) . \) What are the number of moles
of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) formed?
A . 3.33
в. 2.36
c. 2.01
D. 5.36


Bunty mixed 440 gm of ice at \( 0^{\circ} \mathrm{C} \) with
\( 540 \mathrm{gm} \) of water at \( 80^{\circ} \mathrm{C} \) in a bowl. Then what would remain after sometime in
the bowl?
A . only ice
B. only water
c. ice and water in same amount
D. ice and water will vapourise


The waves that are propagated by simultaneous periodic variations of electric and magnetic field intensity known as:
A. Transverse wave
B. Longitudinal wave
c. Electromagnetic wave
D. None of the above


Which is correct for secondary
succession?
A. It follows primary succession
B. It is similar but faster than primary succession
C. It begins on bare rock
D. It occurs on deforested site


Solve:
\( \left(\frac{2 i}{1+i}\right)^{2} \)
\( \mathbf{A} \cdot-i \)
B. \( i \)
\( \mathbf{c} \cdot 2 i \)
D. \( 1-i \)


Calculate focal length of a spherical mirror from the following observations.
Object distance, \( \boldsymbol{u}=(\mathbf{5 0 . 1} \pm \mathbf{0 . 5}) \mathrm{cm} \)
and image distance, \( \boldsymbol{v}=(\mathbf{2 0 . 1} \pm \mathbf{0 . 2}) \)
\( \mathrm{cm} \)
\( \mathbf{A} \cdot f=(14.3 \pm 0.2) \mathrm{mm} \)
B . \( f=(14.3 \pm 0.2) \mathrm{cm} \)
C \( \cdot f=(14.3 \pm 0.4) \mathrm{cm} \)
D. None of these


The function \( f(x) \) whose graph passes
through the point \( \left(0, \frac{7}{3}\right) \) and whose derivatives is \( x \sqrt{1-x^{2}} \) is given by


In the figure, the cross-sectional area of
the smaller tube is \( a \) and that of the
larger tube is \( 2 a . \) A block of mass \( m \) is
kept in the smaller tube having the
same base area \( a \), as that of the tube
The difference between water levels of
the two tubes is
A \( \cdot \frac{P_{0}}{\rho g}+\frac{m}{a \rho} \)
в. \( \frac{P_{0}}{\rho g}+\frac{m}{2 a \rho} \)
c. \( \frac{m}{a \rho} \)
D. \( \frac{m}{20} \)


Calculate \( \boldsymbol{E}^{\circ} \) values of the following
reactions.
\[
\mathbf{2} \boldsymbol{A} \boldsymbol{g}+\boldsymbol{Z} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{Z} \boldsymbol{n}
\]
Given that: \( \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+} / A \boldsymbol{g}}^{\circ}= \)
\[
\mathbf{0 . 8 0 V}, \boldsymbol{E}_{\mathbf{Z n}^{2+} / \mathbf{Z n}}^{\circ}=\mathbf{- 0 . 7 6 V}
\]
A. \( -1.10 V \)
B. \( 1.10 V \)
c. \( -1.56 V \)
D. \( 1.56 V \)


\( 0.28 \mathrm{g} \) of a nitrogenous compound was Kjeldahlised to produce 0.17 g of \( \mathrm{NH}_{3} \). The percentage of nitrogen in the organic compound is:
A. 5
B. 30
\( c .50 \)
\( D \cdot 80 \)


For the circuit shown in the figure. The
equivalent resistance between point \( \mathbf{A} \)
and \( \mathrm{B} \) for the two cases \( (\mathrm{i}) \boldsymbol{V}_{\boldsymbol{A}}>\boldsymbol{V}_{\boldsymbol{B}} \)
(ii) \( V_{B}>V_{A} \quad \) respectively is
\( \mathbf{\Omega} \) and
respectively \( \left(D_{1} \text { and } D_{2} \) are ideal \right.
diodes)
\( A \cdot 25, \infty \)
B. \( 50, \infty \)
\( \mathrm{c} \cdot \infty, 25 \)
D. 50.5


A raw material feedstock should be
renewable rather than depleting, whenever technically and ecomonically practical, is an objective of:
A. Green revolution
B. Green chemistry
c. waste management
D. revolution resource recovery


A particle is moving with uniform acceleration.Its displacement at any instant \( t \) is given as \( s=10 t+49 t^{2} \)
What is the initial velocity,velocity at t= 3sec and uniform acceleration.


\( P(1,1,1) \) and \( Q(\lambda, \lambda, \lambda) \) are two points in the space such that \( P Q=\sqrt{27} \), then the value(s) of \( \lambda \) can be
A . -4
в. -2,4
\( c \cdot 2 \)
D. 4,3


The focal length of a convex mirror is
given as \( 2 \mathrm{cm} . \) Find the radius of
curvature, \( \boldsymbol{R} \), of the mirror?
A . \( 1.0 \mathrm{cm} \)
B. \( 2.0 \mathrm{cm} \)
c. \( 4.0 \mathrm{cm} \)
D. \( 8.0 \mathrm{cm} \)


Calculate the mole fraction of Benzene
\( \left(C_{6} H_{6}\right) \) in a solution containing \( 30 \% \) by \( \operatorname{mass} \operatorname{in} H C l .(C l=35.5) \)


Which of the following microbes produces nitrogen fixing nodules in non leguminous plants?
A. Rhizobium
B. Frankia
c. Azotobacter
D. Pseudomonas


Which one of the following is a metalloid?
\( A \cdot B i \)
B.
\( c \cdot \) Ge
D. Pb


How do you appreciate the role of electronic configuration of the atoms of elements in periodic classification?


In a potention meter of one metre length an unknown emf voltage source is balanced at \( 60 \mathrm{cm} \) length of potention meter wire, while a \( 3 v \) battery is balanced at \( 45 \mathrm{cm} \) length. Then, the emf of the unknown voltage source is :
\( A \cdot 3 v \)
B. 2.25
\( c \cdot 4 v \)
D. \( 4.5 \mathrm{v} \)


Two particles each of mass m move in opposite direction along Y-axis. One particle moves in positive direction
with velocity v while the other particle moves in negative direction with speed
2v. The total angular momentum of the system with respect to origin is:
A. Is zero
B. Goes on increasing
c. Goes on decreasing
D. None of these


The potential of hydrogen electrode having a solution of \( \mathrm{pH}=4 \) at \( 298 \mathrm{K} \) is:
A. \( -0.177 V \)
B. \( -0.236 V \)
c. \( 0.177 V \)
D. \( 0.236 V \)


Addition of water to \( \boldsymbol{X} \) solution will not
change concentration of \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} . \boldsymbol{X} \) is:
A. chemical pH indicator
B. acid/base buffer
c. anhydrous solution
D. hypotonic solution
E. supersaturated solution


A galvanic cell consists of a metallic.
zinc plate immersed in \( 0.1 \mathrm{M} \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} \)
solution and metallic plate of lead in
\( 0.02 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) solution. Calculate
the emf of the cell write the chemical
equation for the electrode reactions and
represent the cell. (Given \( \mathbf{E}_{Z n^{2+}, Z n}^{\circ}= \)
\( \left.-\mathbf{0 . 7 6} V, E_{P b^{2+}, P b}^{\circ}=\mathbf{0 . 1 3} V\right) \)


By using \( L M V T \), prove that \( \frac{\beta-\alpha}{1+\beta^{2}}<\tan ^{-1} \beta-\tan ^{-1} \alpha< \)
\( \frac{\beta-\alpha}{1+\alpha^{2}}, \beta-\alpha<0 \)


Oleum is:
A. castor oil
B. oil of vitriol
C. fuming sulphuric acid
D. none of these


Due to the nature of catenation, carbon
can form:
A. Open chain compounds as well as branched chain compounds.
B. Open chain compounds as well as closed chain compounds.
C. Both \( A \) and \( B \) are correct
D. None of these.


Find minimum normal force to be
applied by each hand to hold three identical books in a vertical position. Each book in a vertical position. Each
book has mass \( \mathrm{m} \) and the value of the
coefficient of friction between the books
as well as between hand the book is \( \mu \)


\( \lim _{x \rightarrow 5} \frac{2 x^{2}+9 x-5}{x+5} \)


Which figure shows the rotation image
of pentagon \( A \) after a \( 216^{\circ} \) clockwise
rotation about its centre?
A. Figure iii
B. Figure
c. Figure iv
D. Figure i


Solve it
\( \mathbf{2} \boldsymbol{I}=\int_{\boldsymbol{O}}^{\boldsymbol{Q}} \boldsymbol{d} \boldsymbol{x} \)


What is the valency of potassium with atomic number \( 19 ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


Find the principal value of:
\( \sec ^{-1}(\sqrt{2})+2 \operatorname{cosec}^{-1}(-\sqrt{2}) \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 2} \\ \mathbf{5} & \mathbf{4}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{4} \\ \mathbf{6} & -\mathbf{7}\end{array}\right], \) then
find the matrix \( A-4 B+7 I \), where lis
the unit matrix of order 2
\( =\left(\begin{array}{rr}3 & -2 \\ 5 & 4\end{array}\right], \mathbf{B}=\left[\begin{array}{rr}1 & 4 \\ 6 & -7\end{array}\right] \)


In bringing an electron towards another electron, the electrostatic potential
energy of the system:
A . decreases
B. increases
c. remains same
D. becomes zero


What will not be obtained in the
sublimate when a mixture of sand,
sulphur, common salt and iodine is
sublimed?
A. sand
B. lodine
c. sulphur
D. common salt


The standard electrode potentials of \( Z n \)
and \( N i \) respectively are \( -0.76 \mathrm{V} \) and
\( -0.25 \mathrm{V} . \) Then the standard emf of the
spontaneous cell by coupling these under standard conditions is:
\( A \cdot+1.01 v \)
B. - 0.51 V
\( c \cdot+0.82 v \)
\( D \cdot+0.25 v \)
\( \mathrm{E} \cdot+0.51 \mathrm{v} \)


Which type of polynomial is \( 5 t-\sqrt{7} ? \)
A. Linear Polynomial
B. Quadratic polynomial
c. cubic Polynomial
D. None of above


Three vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are as shown in figure. If magnitude of \( \vec{A} \) is \( 4 \mathrm{m} \) and \( \vec{A}+\vec{B}+\vec{C}=0, \) then the magnitude of \( \vec{B} \) and \( \vec{C} \) are respectively
A. \( 4 m, 4 m \)
в. \( 4 \sqrt{3} m, 4 \sqrt{3} m \)
c. \( 4 m, 4 \sqrt{3} m \)
D. \( 4 \sqrt{3} m, 4 m \)


Which of the following hydride is thermally stable?
A \( . P H_{3} \)
B. \( A s H_{3} \)
c. \( N H_{3} \)
D. \( B i H_{3} \)


Flux in the smelting process is added to
A. decrease the solubility of impurities
B. increase the fusion temperature of roasted ore
c. convert impurities into slag
D. all of the above


The Venn diagram shows the sets
\( \xi, P, Q \) and \( R . \) Which of the following is
not true?
\( \mathbf{A} \cdot P \cap Q \neq \emptyset \)
в. \( R \subset Q \)
\( \mathbf{c} \cdot(P \cap R) \subset Q \)
D. \( (P \cap Q)=R \)


Considering only lattice enthalpy, arrange them in the increasing order of their stability:
Na \( C l, M g C l_{2}, M g O \)
A. \( N a C l, M g O, M g C l_{2} \)
в. маСl, М \( g \) Са\( _{2}, \) М \( g \) О
c. \( M g C l, M g O, M g C l_{2} \)
D. none of these


Assertion
\( C_{P}-C_{V}=R \) for ideal gas.
Reason
\( R \) is the work done when temperature of
one mole of an ideal gas is increased by
\( \mathbf{1}^{o} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( A s p^{3} \) hybrid orbital contains:
A. \( 1 / 4 \) th \( s \) -character
B. 1/2 ths - character
c. \( 2 / 3 \) th \( s \) -character
D. \( 3 / 4 \) th s-character


What is an optical fiber? Write its advantages.


A body of mass 400 g slides on a rough horizontal surface. If the frictional force
is \( 3.0 \mathrm{N} \). Find the angle made by the contact force on the body with the vertical.
A \( .37^{\circ} \)
В. \( 53^{\circ} \)
\( c \cdot 63^{0} \)
D. \( 27^{\circ} \)


List I contains the type of colloid while
List II contains the examples.
\( \begin{array}{ll}\text { List } 1 & \text { List II } \\ \text { A. Sol } & \text { p. Dust } \\ \text { B. Aerosol } & \text { q. Cheese } \\ \text { C. Gel } & \text { r. Soap lather } \\ \text { D. Foam } & \text { s.Plant cell fluid }\end{array} \)
A. A-s B-r C-p D-q
B. A-s B-p C-q D-r
c. A-r B-s C-q D-p
D. \( A-r B-p C-s D-q \)
E. A-p B-r C-s D-q


A thin uniform square lamina of side \( a \)
is placed in the \( X Y \) plane with its sides
parallel to \( X \) and \( Y \) axes and with its
centre coinciding with the origin. Its moment of inertia about an axis
passing through a point on the \( Y \) axis at
a distance \( y=2 a \) and parallel to \( X \)
axis is equal to its moment of inertia
about an axis passing through a point on the \( X \) axis at a distance \( x=d \) and
perpendicular to \( X Y \) plane. The value of
\( \boldsymbol{d} \) is:
A \( \cdot \frac{7}{3} a \)
B. \( \sqrt{\frac{47}{12}} a \)
c. \( \frac{9}{5} a \)
D. \( \sqrt{\frac{51}{12}} a \)


From the symbol \( _{2} H e^{4} \) for the element helium, write down the mass number
and the atomic number of the element.


Name the four types of elements of the periodic table based on the electronic configuration. Write one characteristic of each type.


NADPH is produced in
photosynthesis during
A. Dark reaction
B. Non-cyclic photophosphorylation
C. Pseudocyclic photophosphorylation
D. Cyclic photophosphorylation


If \( \boldsymbol{x}=\cos ^{n} \boldsymbol{\theta}, \boldsymbol{y}=\sin ^{n} \boldsymbol{\theta} \operatorname{then} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}= \)
A \( \cdot \frac{n}{n-1} \cdot \frac{\cos ^{2 n-1} \theta}{\sin ^{n-3} \theta} \)
B. \( \frac{n-2}{n} \cdot \frac{\tan ^{n-3} \theta}{\cos ^{n+1} \theta \sin \theta} \)
c. \( n-1 . \tan ^{n-2} \theta \cdot \sec ^{2} \theta \)
D. \( \quad n \frac{\sin ^{n-1} \theta}{\cos ^{n-2} \theta} \)


A ball is dropped from rest at a height of \( 60 \mathrm{m} . \) On striking the ground, it loses \( 25 \% \) of its of its energy. To what height
does it rebound?


Differentiate between Rectilinear
motion and Curvilinear motion.


The value of \( \lim _{x \rightarrow-\infty}\left[\frac{x^{4} \sin \left(\frac{1}{x}\right)+x^{2}}{1+|x|^{3}}\right] \) is
equal to
\( A \cdot 1 \)
B. -
c. 0
\( D \cdot \alpha \)


In a stationary wave along a string the strain is
A. Zero at the antinodes
B. Maximum at the antinodes
c. zero at the nodes
D. Maximum at the nodes


Draw venn diagram \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C}) \)


I. Oxidizing agents must include
oxygen.
II. Oxygen is a good electron acceptor.
A. Statement \( I \) is true, statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
B. Statement I is true, statement II is false
c. statement I is false, statement \( I I \) is true
D. Statement I is false, Statement \( I I \) is false


A toy is in the form of a cone of radius
\( 3.5 \mathrm{cm} \) mounted on a hemisphere of
same radius. The total height of the toy is \( 15.5 \mathrm{cm} . \) Find the total surface area of
the toy.


What is \( (\sin x \cos y+ \)
\( \cos x \sin y)(\sin x \cos y-\cos x \sin y) \)
equal to?
A \( \cdot \cos ^{2} x-\cos ^{2} y \)
B. \( \cos ^{2} x-\sin ^{2} y \)
\( c \cdot \sin ^{2} x-\cos ^{2} y \)
D. \( \sin ^{2} x-\sin ^{2} y \)


Calculate the area of the rectangle whose length \( 20 m \) and breadth \( 11 m \)


One hundred identical coins, each with
probability, \( p, \) of showing up heads are
tossed once. If \( 0<p<1 \) and the
probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of \( p \) is :
A . \( 1 / 2 \)
B . \( 49 / 101 \)
c. \( 50 / 101 \)
D. \( 51 / 101 \)


Assertion
In rolling a dice, the probability of getting number 8 is zero.
Reason

Its an impossible event.
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 one ampere is passed
through a straight wire of length 2 metre. The magnetic field at a point in
air at a distance of \( 3 \mathrm{m} \) from one end of
the wire but lying on the axis of the wire will be:
A \( \cdot \mu_{0} / 2 \pi \)
B . \( \mu_{0} / 4 \pi \)
c. \( \mu_{0} / 8 \pi \)
D. zero


From any point on the hyperbola \( \frac{x^{2}}{a^{2}}- \) \( \frac{y^{2}}{b^{2}}=1 \) tangents are drawn to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=2 . \) The area cut-off
by the chord of contact on the
asymptotes is equal to
A \( \cdot \frac{a b}{2} \)
B. ab
\( c \cdot 2 a b \)
\( D \cdot 4 a b \)


A coin is tossed 100 times with
following frequency. Head : 25, Tail : 75
How many outcomes are possible here?
A. one
B. Two
c. three
D. Four


If \( z=\frac{1+i \sqrt{3}}{\sqrt{3}+i}, \) then \( (\bar{z})^{100} \) lies in
A. \( I \) quadrant
B. II quadrant
c. \( I I I \) quadrant
D. \( I V \) quadrant


What are termination codons?


Which of the following are isomers?
A. Ethane and propane
B. Ethane and ethene
C. Ethane and ethyne
D. \( n \) -Butane and isobutane


The substance used as a moderator in
atomic reactors is:
A. boron
B. cadmium
c. uranium -235
D. heavy water


Sodium bicarbonate is also known as:
A. washing soda
B. baking soda
c. glauber's salt
D. lime soda


\( A \) point \( C \) with position vector \( \frac{3 a+4 b-5 c}{3} \)
(where \( a, b \) and \( c \) are non co-planar
vectors) divides the line joining \( A \) and \( B \) in the ratio \( 2: 1 . \) If the position vector
of \( A \) is \( a-2 b+3 c, \) then the position
vector of \( \boldsymbol{B} \) is
A \( .2 a+3 b-4 c \)
B . \( 2 a-3 b+4 c \)
c. \( 2 a+3 b+4 c \)
D. \( a+3 b-4 c \)


List out the major air pollutants.


Explanation of the presence of three unpaired electrons in nitrogen atom is given by:
A. Pauli's principle
B. Hund's rule
c. Aufbau principle
D. Uncertainty principle


The closest relative of modern day man
is considered to be
A. Chimpanzee
B. Orangutan
c. Apes
D. Gibbon


n the transformer shown in figure, the
load resistor is \( 50 \Omega \). The turns ratio
\( N_{1}: N_{2} \) is 10: 2 and the source voltage
is \( 200 \mathrm{V}(\mathrm{r} . \mathrm{m} . \mathrm{s}) . \) If a voltmeter across the
load measures \( 25 \mathrm{V} \) (r.m.s.), then the
source resistance \( R_{S} \) is (power loss is
negligible)
\( A \cdot 450 \Omega \)
в. \( 750 \Omega \)
c. \( 2000 \Omega \)
D. 100\Omega


Which of the following is not an advantage of Integrated Circuits (ICs).
A. Extremely small in size
B. High power consumption
c. Low cost
D. Less weight


If the mean and S.D. of n observation
\( x_{1}, x_{2}, \dots \dots x_{n} \) are \( \bar{x} \) and \( \sigma \) resp, then the sum of squares of observations is
A \( \cdot n\left(\sigma^{2}+\bar{x}^{2}\right) \)
В \( \cdot n\left(\sigma^{2}-\bar{x}^{2}\right) \)
c. \( n\left(\overline{x^{2}}-\sigma^{2}\right) \)
D. none of these


Match the species in Column I with the corresponding properties in Column II.


A solid sphere and a solid cylinder having the same mass and radius, rol
down the same incline. What will the
ratio of their acceleration be?


Which of the following halide of nitrogen is stable in nature?
A. \( N F_{3} \)
в. \( N C l_{3} \)
c. \( N B r_{3} \)
D. \( N I_{3} \)


In an entrance test is graded on the basis of two examinations, the
probability of a randomly chosen
student passing the first examination
is 0.8 and the probability of passing the second examination is 0.7 . The
probability of passing at least of them is \( 0.95 . \) What is the probability of passing both?


The angle between the lines whose
direction cosines satisfy the equations \( l+m+n=0 \) and \( l^{2}+m^{2}+n^{2} \) is
A \( \cdot \frac{\pi}{2} \)
в.
c.
D. \( \frac{\pi}{6} \)


The complex number \( z \) is such that \( |z|=1, z \neq-1 \) and \( \omega=\left(\frac{z-1}{z+1}\right) . \) Then
the real part of \( \omega \) is


The relation between \( \left[\in_{0}\right] \) and \( \left[\mu_{0}\right] \) is
A \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right][L]^{2}[T]^{-2} \)
B . \( \left[\mu_{0}\right]=\left[\epsilon_{0}\right][L]^{-2}[T]^{2} \)
C \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right]^{-1}[L]^{2}[T]^{-2} \)
D \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right]^{-1}[L]^{-2}[T]^{2} \)


Represent the complex number \( -1-i \)
in the polar form


Which of the following has an equal
number of neutrons and protons?
A. Hydrogen
B. Deuterium
c. Fluorine
D. Chlorine


Solve \( : \cos ^{-1} \sqrt{\frac{1+\cos x}{2}} \)


Which of the following compounds is known as baking soda?
A. Sodium carbonate
B. Calcium carbonate
c. Sodium bicarbonate
D. Calcium bicarbonate


The loop of Henle is most highly developed in
A. Freshwater fishes
B. Salamanders
c. Desert lizards
D. Mammals


Calculate the number of neutrons in the
remaining atom after emission of an alpha particle from \( _{92}^{238} U \) atom.


The ground glass stopper is often seen
to get stuck in the neck of glass bottles
containing aq NaOH solution This is
due to:
A. formation of solid \( N a_{2} C O_{3} \) around the neck of the
bottle due to NaoH reacting with atmospheric \( C O_{2} \)
B. formation of solid \( N a_{2} S i O_{3} \) around the neck of the
bottle
C. creation of partial vacuum due to highly hygroscopic nature of \( N a O H \)
D. high coefficient of thermal expansion of glass


The maximum velocity reached.


Draw the graph of i) \( y=2 x+5, \) ii)
\( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{5}, \) iii) \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x} \) and find the
point of intersection on \( x \) -axis. Is the \( x \)
coordinates of these points also the zero of the polynomial?


Identify the correct statement regarding
enzyme inhibition.
A. Non-competitive inhibition of an enzyme can be overcomed by adding large amount of substrate.
B. Competitive inhibition is seen when a substrate competes with an enzyme for binding to an inhibitor protein.
C. Competitive inhibition is seen when the substrate and the inhibitor compete for the active site on the
enzyme.
D. Non-competitive inhibitors often bind to the enzyme irreversibly.


OABC is a tetrahedron express the vectors \( \overrightarrow{B C}, \overrightarrow{C A}, \) and \( \overrightarrow{A B} \) in terms of the vectors \( \overrightarrow{\boldsymbol{O A}}, \overrightarrow{\boldsymbol{O B}} \) and \( \overrightarrow{\boldsymbol{O C}} \)
A \( \cdot \overrightarrow{B C}=\overrightarrow{O C}+\overrightarrow{O B} \quad ; \overrightarrow{C A}=\overrightarrow{O A}+\overrightarrow{O C} \quad ; \overrightarrow{A B}=\overrightarrow{O B}+ \)
\( \overrightarrow{O A} \)
в . \( \overrightarrow{B C}=\overrightarrow{O C}-\overrightarrow{O B} \quad ; \overrightarrow{C A}=\overrightarrow{O A}-\overrightarrow{O C} \quad ; \overrightarrow{A B}=\overrightarrow{O B} \)
\( \overrightarrow{O A} \)
c. \( \overrightarrow{B C}=\overrightarrow{O C}-\overrightarrow{B O} \quad ; \overrightarrow{C A}=\overrightarrow{O A}-\overrightarrow{C O} \quad ; \overrightarrow{A B}=\overrightarrow{O B} \)
\( \overrightarrow{A O} \)
D. none of these


Write the range of frequencies of electromagnetic waves which propagate through sky wave mode.


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{x} \)
satisfying \( \mathbf{0}<\boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}} \) when \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}}=\boldsymbol{I} \)


Draw a triangle of 3,4 and \( 6 \mathrm{cm} \)


The atmospheric pressure at sea level is \( _{-}-_{-}- \) of \( \boldsymbol{H} \boldsymbol{g} \)
\( \mathbf{A} \cdot 76 k m \)
B. \( 76 \mathrm{cm} \)
\( \mathrm{c} .76 \mathrm{mm} \)
D. \( 76 m \)


Human cells in culture show a cell cycle
to be completed in approximately
A. 42 hours
B. 24 hours
c. 24 minutes
D. 24 seconds


Write the formula of Biot-Sevart law in
vector form. Obtain an expression of magnetic field on the axis of a current
carrying circular loop. Draw necessary diagram.


The other name of glycolysis is
A. EMP-pathway
B. TCA-pathway
c. HMS-pathway
D. Carbon-pathway


The weight in grams of a non-volatile
solute \( (M . w t: 60) \) to be dissolved in
\( 90 g \) of water to produce a relative
lowering of the vapour pressure of 0.02 is:
A . 4
B. 8
\( c .6 \)
D. 10


Use suitable identities to find the
product of
\( (x+5)(x+2) \)


The angle between the two vectors \( -2 \hat{i}+3 \hat{j}+\hat{k} \) and \( \hat{i}+2 \hat{j}-4 \hat{k} \) is:
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
\( D \cdot 45^{\circ} \)


A flat car is pulled with a constant
acceleration \( 2 m / s^{2} . \) The mass of the
block is \( 50 \mathrm{kg} \). There is friction between
the flat car surface and the block. The
wheels of the car are rolling without slipping. Then
This question has multiple correct options
A. tension in the string is \( 350 \mathrm{N} \)
B. frictional force is 150 N
C. acceleration of the block is \( 4 m / s^{2} \)
D. acceleration of center of the weel is \( 1 \mathrm{m} / \mathrm{s}^{2} \)


The approximate radius of a \( \boldsymbol{H}- \) atom
is \( 0.05 n m, \) and that of proton is \( 1.5 \times \) \( 10^{-15} . \) Assuming both the hydrogen and
the proton to be spherical, calculate
fraction of the space in an atom of hydrogen that is occupied by the nucleus.


The values of constants a and b so that \( \lim _{x \rightarrow \infty}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=\frac{1}{2}, \) are
A \( a=1, b=-\frac{3}{2} \)
в. \( a=-1, b=\frac{3}{2} \)
c. \( a=0, b=0 \)


\( \operatorname{Let} \mathbf{f}(\mathbf{x})=\mathbf{x}+\tan ^{-1} \mathbf{x}, \mathbf{g}(\mathbf{x})= \)
\( \frac{x}{1+x^{2}}(x>0) \) Then
A \( \cdot \mathrm{f}(\mathrm{x})<\mathrm{g}(\mathrm{x}), \mathrm{x}>0 \)
B. \( f(x)>g(x), x>0 \)
c. \( f(x)<g(x) \) in \( [1, \infty) \)
D. None of these


A person is throwing two balls in the air one after the other. He throws the
second ball when the first ball is at the
highest point. If he is throwing the balls every second, how high do they rise?
A. \( 5 m \)
B. \( 3.75 \mathrm{m} \)
c. \( 2.50 m \)
D. \( 1.25 \mathrm{m} \)


Select the correct answer from \( A, B, C, D \)
and E for each of the metals given below
A metal which is highly malleable and used in flexible pipes.
A. Aluminium
в. copper
c. Lead
D. Potassium
E. Iron
F. Sodium


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


Which among the following is/are the correct statement(s)?
A. Antibiotics kill bacteria
B. Analgesics relieve pain
c. Antipyretics reduce body temperature.
D. All of the above


Formula of the bleaching powder is:
\( \mathbf{A} \cdot C a(O H)_{2} \)
в. \( C H C l_{3} \)
c. \( C C l_{3} C H O \)
D. \( C a O C l_{2} \)


(a) \( A \) ball of mass \( m \) is thrown vertically upward from the ground with an initial speed \( v, \) its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall
downward and attains the speed again before striking the ground. It implies that the magnitude of initial and final momentum of the ball are same. Yet, it
is not an example of conservation of momentum. Explain why?
(b) A bullet of mass 20 g is horizontally
fired with a velocity \( 150 m s^{1} \) from a pistol of mass 2 kg. What is the recoil velocity of the pistol?


The equation of the ellipse whose foci \( \operatorname{are}(\pm 5,0) \) and of the directrix is \( 5 x= \)
\( 36, \) is
A \( \frac{x^{2}}{36}+\frac{y^{2}}{11}=1 \)
B. \( \frac{x^{2}}{6}+\frac{y^{2}}{\sqrt{11}}=1 \)
c. \( \frac{x^{2}}{6}+\frac{y^{2}}{11}=1 \)
D. None of these


For an A.P.. \( \mathrm{S}_{2 n}=3 S_{n} . \) The value of \( \frac{S_{3 n}}{S_{n}} \)
is equal to
A . 4
B. 6
c. 8
D. 10


Statoreceptors are located in
A. Cristae
B. Maculae
c. Both A and B
D. cochlea


Which of the following is true about ethylene?
A. Removal of ethylene prevents fruit ripening
B. Ethylene inhibits the stem elongation.
c. It abolishes positive geotropism
D. All of the above


Which of the following is most stable
\( \operatorname{among} \boldsymbol{C u}^{+}, \boldsymbol{F e}^{+}, \boldsymbol{F e}^{2+}, \boldsymbol{a n d} \boldsymbol{F e}^{3+} \)
A \( \cdot C u^{+} \)
B. \( F e^{+} \)
\( \mathrm{c} \cdot F e^{2} \)
D. \( F e^{3} \)


You are provided with one low
resistance \( R_{L} \) and one high resistance
\( R_{H} \) and two galvanometers. One
galvanometer is to be converted to an ammeter and the other to a voltmeter.
Show how you will do this with the help of simple, labelled diagrams


\( C u^{2+} \) is stable in aqueous medium due
to
A . \( d^{10} \) configuration
B. \( d^{9} \) configuration
c. \( I P_{2}>I P_{1} \)
D. Hydtation energy overcomes the other endothermic processes


f \( \boldsymbol{A}=\operatorname{diag}(\mathbf{2}-\mathbf{5} \mathbf{9}), \boldsymbol{B}=\operatorname{diag}(\mathbf{1} \mathbf{1}- \)
4) and \( C=\operatorname{diag}(-634), \) then find \( B+ \)
\( C-2 A \)


\( \mathrm{Cl}_{2} \) cannot replace:
A. F from NaF
B. Br from NaBr
c. I from Nal
D. Br from KBr


The correct statement(s) about the
following reaction sequence is(are):
Cumene \( \left(C_{9} H_{12}\right) \frac{i) O_{2}}{i i) H_{3} O^{+}} \)
\( P \frac{C H C l_{3} / N a O H}{ } Q(\text { major })+ \)
\( \boldsymbol{R}(\boldsymbol{m} \boldsymbol{i n} \boldsymbol{o r}) \boldsymbol{Q} \frac{\boldsymbol{N a O H}}{\boldsymbol{P h C H}_{2} \boldsymbol{B r}} \boldsymbol{S} \)
This question has multiple correct options
A. \( R \) is steam volatile
B. Q gives dark violet coloration with \( 1 \% \) aqueous \( F e C l_{3} \) solution
c. \( \operatorname{sgives} \) yellow precipitate with \( 2,4- \) dinitrophenylhydrazine
D. s gives dark violet coloration with \( 1 \% \) aqueous \( F e C l_{3} \) solution.


Find the volume of a sphere \( \left(\operatorname{in} m^{3}\right) \)
whose diameter is : 2.1 \( \mathrm{m} \)


High BOD indicates
A . Highly polluted \( H_{2} O \)
B. Less pollution in \( H_{2} O \)
c. Less sewage
D. Less microorganism


Which vessels of the cardiovascular
system (arteries, veins, or capillaries) produce lymph?


What do oxygen atom and oxide ion have in common?
A. Same size
B. Same number of electrons
c. Same electronic configuration
D. Same number of protons


\( \mathbf{F e S O}_{4} \) forms brown ring with:
\( A \cdot N O_{3} \)
в. NO
\( c \cdot \mathrm{NO}_{2} \)
D. \( \mathrm{N}_{2} \mathrm{O}_{3} \)


For the growth of plants which of the following top soil is suitable the most:
A. Clay soil
B. Black soil
c. Loam soil
D. Sandy soil


Lightning is formed in unstable atmospheric zones where there is
typically a lot of and
\( \mathbf{A} \). Heat, moisture
B. Heat, vapour
c. Heat, gas
D. Heat, lava


A resistance of \( 100 \Omega \) and inductance \( L \)
henry are connected in series with a
battery of 20 volts.The current at any instant, if the relation between is \( \boldsymbol{L}, \boldsymbol{R}, \boldsymbol{E} \) is \( \boldsymbol{L} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\boldsymbol{R} \boldsymbol{i}=\boldsymbol{E} \) is given by?
A \( . i=0.6\left(-e^{-200 t}\right) \)
В \( \cdot i=0.4\left(-e^{-200 t}\right) \)
c. \( \quad i=0.2\left(1-e^{\frac{-100}{L} t}\right) \)
D . \( i=0.8\left(-e^{-200 t}\right) \)


If \( x \) denotes displacement in time \( t \) and
\( \boldsymbol{x}=\boldsymbol{a} \cos \omega \boldsymbol{t}, \) then for \( \boldsymbol{\omega}=\mathbf{1}, \) the
acceleration will be
\( \mathbf{A} \cdot a \cos t \)
B. - a cost
\( \mathbf{c} \cdot a \sin t \)
D. - \( a \sin t \)


The commonly used name of the
insecticide DDT is:
A. dichlorodiphenyl toluene
B. dichlorodiphenyltrichloroethane
C . dibromodiphenyltrichloroethane
D. dichlorodiphenylthiosemicarbazide


The HCF of 135 and 225 using Euclid algorithm is
\( \mathbf{A} \cdot 41 \)
B. 42
c. 43
D. 45


A convex lens of focal length \( 10 \mathrm{cm} \) is
painted black at the middle portion as
shown in Fig. An object is placed at a
distance of \( 20 \mathrm{cm} \) from the lens. Then
A. only one image will be formed by the lens
B. The distance between the two images formed by such a lens is \( 6 \mathrm{mm} \)
c. The distance between the images is \( 4 \mathrm{mm} \)
D. The distance between the images is 2 mm


Construct a right angled triangle whose
hypotenuse measure \( 6.5 \mathrm{cm} \) and one of
its acute angle measure \( 60^{\circ} \)


Choose the best possible option. \( x^{3}-5 x+2 x^{2}+1=0 \) is
quadratic equation.
A. Yes
B. No
c. can't predict
D. None


A function \( f \) such that \( f^{\prime}(2)=f^{\prime \prime}(2)= \)
0 and \( f \) has a local maximum of -17 at \( x \)
\( =2 \) is :
A \( \cdot(x-2)^{4} \)
B . \( 3-(x-2)^{4} \)
c. \( -17-(x-2)^{4} \)
D. None of these


Surface charge density of the plate is
equal to
\( \mathbf{A} \cdot 8.85 \times 10^{-10} \mathrm{C} / \mathrm{m}^{2} \)
B . \( -8.85 \times 10^{-10} C / m^{2} \)
C \( \cdot 17.7 \times 10^{-10} \mathrm{C} / \mathrm{m}^{2} \)
D. \( -17.7 \times 10^{-10} C / m^{2} \)


Find the \( A M, G M \) and HM between 9 and
18


If a disc slides from top to bottom of an
inclined plane, it takes time \( t_{1} . \) If it rolls, it takes time \( t_{2} . \) Now \( \frac{t_{2}^{2}}{t_{1}^{2}} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{5} \)


If Pt is used as catalyst in the
decomposition of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) then it is an example of:
A. homogeneous catalysis
B. heterogenous Catalysis
c. negative Catalysis
D. auto Catalysis


Partial roasting of galena gives:
A. Only PbS
B. Only Pbo
c. \( P b S+P b O \)
\( \mathbf{D} \cdot P b O+P b \)


The atomic weight of noble gases is obtained by using the relationship:
A. Atomic weight = equivalent weight \( x \) valency
B. Atomic weight = equivalent weight/valency
C. At. weight = valency/equivalent weight
D. 2 x V.D. = molecular weight = atomic weight


Calculating the principal value, find the value of \( \sin \left[2 \sin ^{-1}\left(\frac{4}{5}\right)\right] \)


Calculate hydrolysis constant for 0.01
(N) solution of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{O}_{2} \boldsymbol{N} \boldsymbol{a}\left(\boldsymbol{K}_{\boldsymbol{a}} \) for \right.
\( \boldsymbol{C H}_{3} \boldsymbol{C O}_{2} \boldsymbol{H}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{)} \)


\( a \)
\( b \)
\( c \)


Hydrogen has the tendency to lose one electron and form \( \boldsymbol{H}^{+} . \) In this respect, it
resembles:
A. alkali metals
B. carbon
c. alkaline earth metals
D. halogens


A copper wire is in the form of a circle
with radius \( 35 \mathrm{cm} \). It is bent into a
square. Determine the side of the
square.


On analysis, a certain compound was
found to contain 254 g of iodine and 80
g of oxygen. The formula of the compound is:
A . \( I O \)
B. \( I_{2} O \)
\( \mathrm{c} \cdot I_{5} \mathrm{O}_{3} \)
D. \( I_{2} O_{5} \)


\( \ln \operatorname{eq} x^{2}+y=6 x-14 \)
f \( x=0,1,2 \)
then the values of \( y \) are


Which one of the following classes are included under gymnosperms?
A. Lycopsida
B. Bryopsida
c. cycadopsida
D. Pteropsida
E. sphenopsida


Statement - I: \( 1 \mathrm{M} \) solution of NaCl has a
higher osmotic pressure than 1 M solution of glucose at the same temperature. Statement - II: The number of particles present in 1 M NaCl solution are more
than those present in 1 M glucose solution and osmotic pressure depends upon number of particles present in the
solution.
A. Statement-lis True, Statement - II is True; Statement I is a correct explanation for Statement -
B. Statement-lis True, Statement - /I is True; Statement I is NOT a correct explanation for Statement- -
c. Statement - - is True, Statement - II is False
D. Statement-lis False, Statement - II is True


Name the term used to describe a
single dominant species that dictates
community structure
A. Pioneer species
B. Transitional species
C. Key stone species
D. Indigenous species
E. Exogenous species


Which of the following relations for the displacement of a partide undergoing simple harmonic motion is not correct
dimensionally?
A \( \cdot Y=a \sin \frac{2 \pi t}{T} \)
B. \( Y=a \cos \omega t \)
c. \( Y=\frac{a}{T} \sin \left(\frac{t}{a}\right. \)
\( V=a \sqrt{2}\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right) \)


Dampers are found on bridges
A. to allow natural oscillations to occur
B. to prevent them from swaying due to wind
c. to prevent resonance of frequencies.
D. None of these.


The release of chlorofluorocarbons by
the use of refrigerators, air conditioners, deodorants, etc., are
destroying the \( _{\text {一一一一一一一一 }} \) layer of the atmosphere.
A. Mesosphere
B. Ionosphere
c. Humidity
D. Ozone


In taxonomic hierarchy, various
categories are arranged in series.


Complete the following reactions:
(i) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{M}_{m} \boldsymbol{O}_{o}(\boldsymbol{s}) \stackrel{\boldsymbol{\Delta}}{\rightarrow} \)
(ii) \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \frac{\boldsymbol{\Delta}}{\text {catalyst}} \)
(iii) \( C_{3} H_{8}(g)+3 H_{2} O(g) \frac{\Delta}{\text { catalyst }} \)
\( (\mathrm{iv}) C_{3} H_{8}(g)+3 H_{2} O(g) \frac{\Delta}{\text {catalyst}} \)


Which one of the following is heterosporous?
A. Adiantum
B. Equisetum
c. Dryopteris
D. Salvinia


In Bredig's arc method, an electric arc is
struck between the metal electrodes
under the surface of water containing
some stabilizing agent. The process involves:
A. mechanical dispersion
B. condensation
c. both dispersion and condensation
D. ultrasonic dispersion


A first order reaction is found to have a
rate constant, \( k=5.5 ; \) find the half life of
the reaction.


A \( 3 m \) wide path runs outside and
around a rectangular park of length \( 125 m \) and breadth 65 m. Find the area
of the path.


In which bias can a zener diode be used
as voltage regulator?


Permutit is the trade name of a mixture
of?
A. Hydrated silicates of Ca and Mg
B. Hydrated silicates of Al and Na
c. Hydrated aluminates of Ca and No
D. None of these


Give two different examples of pair of
(ii) non-similar figures.


More is the coagulation value of electrolyte, its coagulation power is
1. more
2. less
3. unchanged
4. none of the above
Choose the correct answer.


Three reactions involving \( \mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-} \) are given below:
(i) \( \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}+\mathbf{H}_{2} \mathbf{O} \rightarrow \mathbf{H}_{3} \mathbf{O}^{+}+\mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-} \)
(ii) \( \mathbf{H}_{2} \mathbf{P} \mathbf{O}_{4}^{-}+\mathbf{H}_{2} \mathbf{O} \rightarrow \mathbf{H} \mathbf{P} \mathbf{O}_{4}^{2-}+\mathbf{H}_{3} \mathbf{O}^{+} \)
(iii) \( \mathbf{H}_{2} \mathbf{P O}_{4}^{-}+\mathbf{O H}^{-} \rightarrow \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}+\mathbf{O}^{2-} \)
In which of the above reactions, does
\( H_{2} P O_{4}^{-} \) act as an acid?
A . (ii) only
B. (i) and (ii)
\( c . \) (iii) only
D. (i) and (iii)


If the skeletal muscle fibres are soaked
and treated with high concentration of salts, large quantities of proteins are removed. The fibres can no longer contract and the A-bands disappear This shows that
A. Myosin is essential for contraction of the fibres
B. Actin is essential for contraction
c. Both myosin and actin are essential for contraction
D. Proteins do not play any role in the contraction of fibres


Identify the incorrect statement.
A. Forest prevents soil erosion.
B. Forest influences climate and water cycle.
C. Soil helps forest to regenerate.
D. Plants and animals in the forest are not dependent on one another.


Determine \( n \) if \( ^{2 n} C_{2}:^{n} C_{2}=12: 1 \)


During an experiment an ideal gas is found to obey an additional law \( \mathrm{V}^{2} \mathrm{P}= \)
constant. The gas is initially at a temperature \( T \) and volume \( V \). When it expands to a volume 2 V, the temperature becomes
A. \( T \)
в. 2T
c. \( T \sqrt{2} \)
D. \( T / 2 \)


The number of p-electrons in bromine
atom is:
A . 17
B. 7
c. 15
\( D \cdot 13 \)


Show that the elements on the main
diagonal of a skew-symmetric matrix are all zero.


Total sales of branch \( B_{6} \) for both the
years is what percent of the total
sales of branch \( B_{3} \) for both the years?
A. \( 68.54 \% \)
в. \( 71.11 \% \)
\( c .73 .17 \% \)
D. \( 75.55 \% \)


An electric dipole is placed at the centre
of a sphere. Mark the correct option:
This question has multiple correct options
A. the flux of the electric field through the sphere is zero
B. the electric field is zero at every point of the sphere
C. the electric field is not zero anywhere on the sphere
D. the electric field is zero on a circle on the sphere


Match the following.


If a soft iron is placed inside the current carrying coil, what is the name given to the device?


Three charges \( -q, Q,-q \) are placed at equal distance on a straight line. If the total potential energy of the system is zero, then \( Q: q \) is:
A .1: 4
B. -1: 4
c. 1: 2
D. 2: 1


Express each of the complex number given in the Exercises 1 to 10 in the form \( a+i b \)
\( (\mathbf{5} i)\left(-\frac{\mathbf{3}}{\mathbf{5}} \boldsymbol{i}\right) \)


The radius of a circle is given as \( 15 \mathrm{cm} \)
and chord AB subtends an angle of \( 131^{\circ} \)
at the centre \( C \) of the circle.Using trigonometry ,calculate:
(i) the length of \( A B \)
(ii) the distance of \( A B \) from the centre \( C \)


If \( I=\int_{1}^{\infty} \frac{x^{2}-2}{x^{3} \sqrt{x^{2}-1}} d x, \) then \( I \) equals
A . -1
B.
c. \( \pi / 2 \)
D. \( \pi-\sqrt{3} \)


Choose the correct statement. The use
\( ^{12} C \) scale has superseded the older scale of atomic mass based on
\( ^{16} \boldsymbol{O} \) isotope, one important advantage of the former being:
A. The atomic masses on \( ^{12} C \) scale became whole
numbers
B. 12 C is more abundant in the earths crust than \( ^{16} \) O
c. The difference between the physical and chemical atomic masses got narrowed down significantly
D. \( 12 \mathrm{C} \) is situated midway between metals and nonmetals in the periodic table


Simplify: \( (\boldsymbol{a}+\boldsymbol{b})^{\boldsymbol{3}} \)


In the electrolytic refining for aluminium extraction the electrolyte
used is:
A. fluorides of \( A l, N a \) and \( C a \)
в. \( A l(O H)_{3} \) in \( N a O H \) solution
c. an aqueous solution of \( A l_{2}\left(S O_{4}\right)_{3} \)
D. molten \( A l_{2} O_{3} \)


The length of vector AG is?
A \( . \sqrt{17} \)
в. \( \frac{\sqrt{51}}{3} \)
c. \( \frac{\sqrt{51}}{9} \)
D. \( \frac{\sqrt{59}}{4} \)


Write the difference between order and
molecularity of a reaction.


Use the given standard enthalpies of formation to determine the heat of
reaction of the following reaction:
\[
\begin{array}{c}
2 L i O H+C O_{2}(g) \longrightarrow \\
L i_{2} C O_{3}(s)+H_{2} O(l) \\
\Delta H_{f} L i O H(s)=-487.23 k J / \text {mole} \\
\Delta H_{f} L i_{2} C O_{3}(s)=-1215.6 k J / \text {mole} \\
\Delta H_{f} H_{2} O(l)=-285.85 k J / \text {mole} \\
\Delta H_{f} C O_{2}(g)=-393.5 k J / \text {mole}
\end{array}
\]
A . \( +303 . \)
в. -133.5
c. -198.6
D. +198.6


\( E^{o} \) of an electrode half reaction is
related to \( \Delta G^{o} \) by the equation, \( E^{o}= \)
\( -\Delta G^{o} / n F . \) If the amount of \( A g^{+} \) in the
half reaction \( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} \) is tripled
then:
A . n is tripled
B. \( \Delta G^{o} \) increases to three times
c. \( E^{o} \) reduces to one third
D. All the above


A colourless gas ' \( x \) ' forms a brown
coloured gas ' \( y^{\prime} \) when mixed with air. \( x \)
and \( y \) could be :
A. \( N O, N O_{2} \)
в. \( N O, O_{2} \)
c. \( N O_{2}, N_{2} O_{4} \)
D. \( N O, N_{2} O_{4} \)


Find the area of the smaller region bounded by the ellipse \( \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 \) and the line \( \frac{x}{3}+\frac{y}{2}=1 \)


Find the value of the limit:
\( \lim _{x \rightarrow 1} \frac{x^{2}-6 x+5}{x^{2}+3 x-4} \)
A . -1.25
в. -0.80
c. 0.80
D. 1.25
E. The limit does not exists


If \( n(A)=5 \) and \( n(B)=7, \) then the
number of relations on \( \boldsymbol{A} \times \boldsymbol{B} \) is :
\( \mathbf{A} \cdot 2^{3} \)
B. \( 2^{4} \)
\( c \cdot 2^{25} \)
D. \( 2^{70} \)
E \( .2^{35 \times 35} \)


Q Type your question-
uniform transverse magnetic field B.
The field occupies a region of space by width 'd'. If ' \( \alpha \) ' be the angle of deviation
of proton from initial direction of motion (see figure), the value of \( \sin \alpha \) will be:
\( ^{\text {A }} \cdot B d \sqrt{\frac{q}{2 m V}} \)
B. \( \frac{B}{d} \sqrt{\frac{q d}{m V}} \)
\( ^{\mathbf{C}} \cdot q V \sqrt{\frac{B d}{2 m}} \)
D. \( \frac{B}{d} \sqrt{\frac{q}{2 m V}} \)


Formulate a call for each of the
following reactions; \( S n^{2+}(a q)+2 A g C l(s) \longrightarrow S n^{4+}(a q)+ \)
\( 2 A g(s)+2 C l^{-}(a q) \)
\( M g(s)+B r_{2}(l) \longrightarrow M g^{2+}(a q)+ \)
\( 2 B r^{-}(a q) \)


Find the area of the triangle formed by the line \( 3 x+4 y=12 \) and the \( c o \)
ordinate axes.


Assertion
Meniscus is formed in case of confined
liquids.
Reason
It is not due to the force of surface
tension
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 absolute configuration of a molecule changes during:
\( A \cdot S_{N} \)
в. \( S_{N} 2 \)
c. free radical substitution
D. \( S_{E} \) ?


\( \operatorname{Let} \boldsymbol{E}=\left[\frac{\mathbf{1}}{\mathbf{3}}+\frac{\mathbf{1}}{\mathbf{5 0}}\right]+\left[\frac{\mathbf{1}}{\mathbf{3}}+\frac{\mathbf{2}}{\mathbf{5 0}}\right]+\ldots+ \)
up to 50 terms, then which of the
following is true? Here \( \square \) denotes the greatest integer function.
This question has multiple correct options
A. \( E \) is divisible by exactly 2 primes
B. \( E \) is prime
c. \( E \leq 30 \)
D. \( E \geq 35 \)


The accuracy in the measurement of the diameter of hydrogen atom measured as \( 1.06 \times 10^{-10} \mathrm{m} \) is :
A .0 .01
В. \( 106 \times 10^{-10} \)
c. \( \frac{1}{106} \)
D. \( 0.01 \times 10^{-10} \)


Solve the following systems of equations by the method of crossmultiplication:
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
\( 2 x-3 y-12=0 \)


Which element with lowest atomic
number follows rule (b)?
\( A \cdot 19^{k} \)
B. 24 \( ^{c} \)
\( c \cdot 11^{N a} \)
D. \( 29^{c} \)


Molar conductivity of 0.15 M solution of KCl at \( 298 \mathrm{K} \), if its conductivity is \( 0.0152 \mathrm{S} \mathrm{cm}^{-1} \) will be:
A \( \cdot 124 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-} \)
B. \( 204 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-} \)
c. \( 101 \Omega^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
D. \( 300 \Omega^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)


These are generally the bad conductors of heat :
A. Graphite
B. Copper
c. Iron
D. Plastics


Along the \( X \) -axis, three charges \( \frac{q}{2},-q \) and \( \frac{q}{2} \) are placed at \( x=0, x=a \) and \( x=2 a \) respectively. The resultant electric potential at \( x=a+r(\text { if }, a<r) \) is :
\( \left(\epsilon_{0} \) is the permittivity of free space) \right.
A \( \cdot \frac{q a}{4 \pi \epsilon_{0} r^{2}} \)
в. \( \frac{q a^{2}}{4 \pi \epsilon_{0} r^{3}} \)
\( ^{\mathbf{C}} \cdot \frac{q\left(a^{2} / 4\right)}{4 \pi \epsilon_{0} r^{3}} \)
D. \( \frac{q}{4 \pi \epsilon_{0} r} \)


Which type of isomerism can not be shown by benzaldoxime?
A. Optical isomerism
B. Functional group isomerism
c. Geometrical isomerism
D. configuration isomerism


If length of the largest side of a triangle is \( 12 \mathrm{cm} \) then other two sides of triangle
can be :
\( A \cdot 4.8 \mathrm{cm}, 8.2 \mathrm{cm} \)
B. 3.2 \( \mathrm{cm}, 7.8 \mathrm{cm} \)
c. \( 6.4 \mathrm{cm}, 2.8 \mathrm{cm} \)
D. \( 7.6 \mathrm{cm}, 3.4 \mathrm{cm} \)


In a reaction, 5 g ethyl acetate is hydrolyzed per litre in the presence of
dil. HCl in 300 min.lf the reaction is of
the first order and the initial
concentration of ethyl acetate is 22 g
\( L^{-1}, \) the rate constant of the reaction is:
A. \( k=8.6 \times 10^{-4} \min ^{-1} \)
В. \( k=1.4 \times 10^{-4} \min ^{-1} \)
c. \( k=6.9 \times 10^{-4} \min ^{-1} \)
D. None of these


The equilibrium of which of the following reactions will not be disturbed by the addition of an inert gas at
constant volume?

This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) \)
D. \( C(s)+H_{2} O(g) \rightleftharpoons C O(g)+H_{2}(g) \)


Formic acid is considered as a
resonance hybrid of the four structures
Which of the above order is correct for
the stability of the four contributing
structures:
\( \boldsymbol{O} \)
\( \boldsymbol{H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O} \boldsymbol{H} \leftrightarrow \boldsymbol{H}-\dot{\boldsymbol{C}}=\boldsymbol{O} \boldsymbol{H} \leftrightarrow \boldsymbol{H} \)
\( o \)
\( \stackrel{1+}{C}-O-H \leftrightarrow H-C-O-H \)
\( \boldsymbol{I} \quad \boldsymbol{I I} \)
\( \boldsymbol{I} \boldsymbol{V} \)
A \( . I>I I>I I I>I V \)
В . \( I>I I>I V>I I I \)
c. \( I>I I I>I I>I V \)
D. \( I>I V>I I I>I I \)
1


Consider a plane flying due West at 200 MPH. The co-pilot is firing a gun in the opposite direction the plane is flying due East. If the co-pilot clocks the bullets at \( 500 \mathrm{MPH} \), how fast would the
bullets be clocked from the ground?
A. 300 MPH East
в. 700 МРн Еазн
c. 500 MPH West
D. 200 MPH West
E. cannot determine with information provided


Which of the following compounds is found in abundance in nature?
A. Fructose
B. Glucose
c. starch
D. Cellulose


In Boolean algebra, \( \boldsymbol{A}+\boldsymbol{B}=\boldsymbol{Y} \) implies
that
A. sum of \( A \) and \( B \) is \( Y \).
B. \( Y \) exists when \( A \) exists or \( B \) exists or both \( A \) and \( B \) exist
c. \( Y \) exists only when \( A \) and \( B \) both exist
D. \( Y \) exists when \( A \) or \( B \) exist but not when both \( A \) and \( B \) exist


\( \boldsymbol{P h}-\boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \stackrel{\boldsymbol{S O C l}_{2}}{\longrightarrow} \boldsymbol{P h C l}- \)
\( \quad \) Specific Rotaion \( =+\boldsymbol{5 0}^{o} \)
\( \boldsymbol{C H}_{3} \)
What is the specific rotation of the product?
A. \( +50^{\circ} \)
B. \( +60^{\circ} \)
\( c .-60^{\circ} \)
D. zero


What is a generator state the principle
on which generators work


Fill in the blanks:
In Ursa Major, stars form the
shape of the handle and stars
form the shape of the bowl of the ladle
respectively.
A . 4,3
в. 5,6
\( c .3,4 \)
D. 2,


Force for passive water absorption develops in
A. Xylem
B. Aerial parts
c. Root
D. Root hairs


Give any two reasons for land
degradation.


Assertion
The plot of volume \( (V) \$ \) versus
pressure \( (P) \) at constant temperature
is a hyperbola in the first quadrant.
Reason
\( \boldsymbol{V} \propto \mathbf{1} / \boldsymbol{P} \) at constant temperature
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


Hydrolysis of \( \mathrm{Mg}_{3} \mathrm{N}_{2} \) gives:
A . \( \mathrm{NH}_{3} \)
в. NO
c. \( \mathrm{H}_{2} \)
D. \( \mathrm{cO}_{2} \)


The score of the player placing II was
A \( \cdot 5 \frac{1}{2} \)
в. \( 6 \frac{1}{2} \)
\( c \cdot 6 \)
D. \( \operatorname{can}^{\prime} t \) say


White light is passed through sodium vapours contained in a thin walled
glass flask and the transmitted light is examined with the help of a spectrometer. The spectrum so obtained is.
A. Absorption spectrum
B. Solar spectrum
c. Band spectrum
D. Continuous spectrum


A particle is executing SHM with time
period T. Starting from mean position, time taken by it to complete \( 5 / 8 \) oscillations, is


Red lead is:
\( \mathbf{A} \cdot P b O \)
\( \mathbf{B} \cdot P b O_{2} \)
\( \mathbf{C} \cdot P b_{3} O_{4} \)
\( \mathbf{D} \cdot P b_{2} O_{4} \)


The numbers of \( 3 \times 3 \) matrices A whose
entries are either 0 or 1 and for which the system \( \boldsymbol{A}\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right]=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \) has exactly
two distinct solutions is?
A .
B . \( 2^{9}-1 \)
\( c .168 \)
D.


\( \mathbf{A}=\left|\begin{array}{lll}\mathbf{5} & \mathbf{3} & \mathbf{8} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right|, \) write the cofactor of
the element \( a_{32} \)