Ramu and Somu are running towards north with \( 3 \mathrm{m} / \mathrm{s} \) and \( 4 \mathrm{m} / \mathrm{s} \). Their friend
Srinu is running towards south with 2 \( \mathrm{m} / \mathrm{s} . \) Then the magnitude of relative velocity of Somu w.r.t Ramu
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 m/s
\( c \cdot 3 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)


If \( x \sin y=3 \sin y+4 \cos y, \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot \frac{-\sin ^{2} y}{4} \)
B. \( \frac{\sin ^{2} y}{4} \)
\( \mathbf{c} \cdot \frac{-\cos ^{2} y}{4} \)
D. \( \frac{\cos ^{2} y}{4} \)


Q Type your question
4
\( B \)
\( c \)
ne of thes


If you were looking at the 3 D shape from the left side what would you see?
\( A \)
в.
\( c \)
D.


Evaluate the following integrals.
\( \int \frac{d x}{\sqrt{2 x-3 x^{2}+1}} \)


1 fermi is equal to
\( \mathbf{A} \cdot 10^{-15} \mathrm{m} \)
B. \( 10^{15} \mathrm{m} \)
\( \mathbf{C} \cdot 10^{-12} \mathrm{m} \)
\( D \cdot 10^{12} m \)


Total number of isomers for \( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{6}} \boldsymbol{B} \boldsymbol{r}_{2} \)
containing cyclobutane ring are (including stereoisomers) are:
\( A \cdot 6 \)
B. 7
\( c \cdot 4 \)
D. 5


The heat of sun focussed by a convex lens on a piece of paper is capable of
A. Cooling the paper
B. Just heating the paper
c. Burning the paper
D. Folding the paper


Which molecule is relatively more stable?
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( L i_{2} \)
D. \( N_{2} \)


Two gases \( A \) and \( B \) are taken in same volume containers under similar
conditions of temperature and
pressure. In container A, there are '2N' molecules of gas A. How many number molecules does container B have?
A . 2N
B. 4N
\( c \cdot N \)
D. 8N


The correct sequence of stages in the
evolution of the modern man (Homo
sapiens) is
A. Neanderthal man, Australopithecus, Cro-magnon man, Homoerectus, Modern man
B. Australopithecus, Homo sapiens, Neanderthal man, Cro-magnon man, Modern man
C. Homo erectus, Australopithecus, Neanderthal man, Cro-magnon man, Modern man
D. Australopithecus, Homo erectus, Neanderthal man, Cro-magnon man, Modern man


Largest blood vessel in body is
A. carotid artery
B. Dorsal aorta
c. Phrenic artery
D. Coronary artery


If \( A, B, C, D \) be any four points and \( E \) and \( F \) be the mid-points of \( A C \) and \( B D \) respectively, then \( \overrightarrow{\boldsymbol{A B}}+\overrightarrow{\boldsymbol{C B}}+\overrightarrow{\boldsymbol{C D}}+ \)
\( \overrightarrow{A D} \) is equal to
A \( .3 \overrightarrow{E F} \)
B. \( 4 \overrightarrow{E F} \)
c. \( 4 \overrightarrow{F E} \)
D. \( 3 \overrightarrow{F E} \)


A person travels along a straight road \( \boldsymbol{t} \)
for the first \( \frac{v}{3} \) time with a speed \( v_{1} \) and for the next \( \frac{2 t}{3} \) time with a speed \( v_{2} \) Then the mean speed \( v \) is given by :


What is abbreviated as 'H'?
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate


A horizontal overhead power line carries a current of \( 90 \mathrm{A} \) in east to west
direction. Magnitude of magnetic field due to the current \( 1.5 \mathrm{m} \) below the line is
A . 1.27
в. \( 1.2 \times 10^{-10} T \)
c. \( 0 T \)
D. \( 1.2 \times 10^{-5} T \)


Baking soda is a compound.
A. True
B. False
c. Either
D. Neither


What is the principle of cyclotron?


Find the probability that one will get 75 marks in the question paper of 100 marks.
A \( \cdot \frac{1}{101} \)
в. \( \frac{75}{100} \)
c. \( \frac{1}{100} \)
D. \( \frac{75}{101} \)


Most organelles show duplication in cell cycle during
A \( \cdot G_{1} \) - phase
B. \( G_{0} \) - phase
c. \( S \) -phase
D. \( G_{2} \) - phase


In an organic compound with molar mass \( 108 \mathrm{g}, \mathrm{C}, \mathrm{H}, \) and \( \mathrm{N} \) are present in the ratio 9: 1: 3.5 by mass. Molecular formula of the compound is:
A \( \cdot C_{6} H_{8} N_{2} \)
В. \( C_{7} H_{10} N \)
\( \mathbf{c} \cdot C_{5} H_{6} N_{3} \)
D. \( C_{4} H_{5} N_{3} \)


Alternation of generations is not found in bacterium E. coli due to the lack of
A. Syngamy
B. Reduction division
c. Nucleus
D. Chromosomes


Linnaeus proposed an outline of plant classification in
A. Genera Plantarum
B. Species Plantarurn
c. systema Naturae
D. Philosophia Botanica


An insoluble substance or mixture that
collects at the anode in an electrolytic \( r \) efining or plating process is known as
anode mud.
State True or False.
A . True
B. False
c. Cannot be determined
D. None of the above


How many molecules of ATP and NADPH
are require in formation of two molecules of glucose? How many Calvin cycles are required?
A. 36 ATP, 24 NADPH, 12 Calvin cycles
B. 18 ATP, 12 NADPH, 6 Calvin cycles
c. 36 ATP, 24 NADPH, 6 Calvin cycles
D. 24 ATP, 36 NADPH, 12 Calvin cycles


Monomer used to prepare orlon
is
\( \mathbf{A} \cdot H_{2} C=C H-C l \)
B \( \cdot F_{2} C=C F_{2} \)
\( \mathbf{c} \cdot H_{2} C=C H C N \)
D. \( H_{2} C=C(C l)-C H=C H_{2} \)


Principle behind the working of electric
generator?
A. When a conductor is moved in a magnetic field then voltage is induced in the conductor
B. When a conductor is moved in a magnetic field then current is induced in the conductor
\( c \cdot \) both
D. none


The magnetic field at the center of the
coil of radius \( r \) and carrying a current \( I \)
as shown in the figure is : (the wires crossing at \( P \) are insulated from each
other)
A \( \cdot \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(1+\pi) \)
в. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(\pi-1) \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}\left(\pi^{2}+1\right) \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{2 \pi I}{r} \)


A charge \( q \) is placed at the centre of the line joining two equal charges \( Q \). The system of three charges will be in equilibrium if \( q \) is equal to:
A \( \cdot-\frac{Q}{2} \)
в. \( -\frac{Q}{4} \)
\( c \cdot+\frac{Q}{4} \)
D. \( +\frac{Q}{2} \)


Why is that in certain plants deficiency
symptoms appear first in younger parts
of the plants while in others they do so in mature organ?


ldentify the unlabelled part of the
diagram.
A. Reflex arc
B. Impulse
C. Motor neuron
D. None of the above


Which ecological pyramid can never
occur in an inverted form?
A. Pyramid of number
B. Pyramid of biomass
c. Pyramid of energy
D. Pyramid of species richess


Match the following
List I
a. Static \( \quad \) e. constant for a given pair of friction \( \quad \) surfaces
b. Limiting \( \quad \) f. independent of area of contact friction
c. Kinetic \( \quad \) g. self adjusting friction
d. Rolling \( \quad \) h. has the least magnitude for a friction \( \quad \) given normal reaction
\( \mathbf{A} \cdot a \rightarrow e ; b \rightarrow f ; c \rightarrow g ; d \rightarrow h \)
B \( \cdot a \rightarrow h ; b \rightarrow f ; c \rightarrow e ; d \rightarrow g \)
\( \mathbf{c} \cdot a \rightarrow g ; b \rightarrow e ; c \rightarrow f ; d \rightarrow h \)
\( \mathbf{D} \cdot a \rightarrow g ; b \rightarrow h ; c \rightarrow f ; d \rightarrow e \)


Conjugate acid-base pair differ by:
A. electron
B. proton
c. neutron
D. hydroxyl group


Correct statement(s) in case of n-
butanol and t-butanol is (are):
This question has multiple correct options
A. both are having equal solubility in water
B. t-butanol is more soluble in water than n-butanol.
C. boiling point of t-butanol is lower than n-butanol.
D. boiling point of n-butanol is lower than t-butanol.


During the working of a galvanic cell and with the passage of time:
This question has multiple correct options
A. spontaneity of the cell reaction decreases, \( E_{c c l} \) decreases
B. reaction quotient Q decreases, E \( _{\text {cell } \text {increases }} \)
C . reaction quotient \( Q \) increases, \( E_{c e l l} \) decreases
D. at equilibrium, \( Q=K_{e q}, E_{c e l l}=0 \)


Which of the compounds is least soluble in water?
\( A \cdot A g F F \)
в. AgCI
c. AgBr
D. Agl


For real numbers \( x \) and \( y \) we write \( _{x} R_{y} \) iff \( \boldsymbol{x}-\boldsymbol{y}+\sqrt{\mathbf{2}} \) is an irrational numbers.
Then relation \( R \) is reflexive.


Find the square of the following
number.
68


\( A B C \) and \( B D E \) are two equilateral
triangles such that \( D \) is the midpoint of
\( B C . \) Ratio of the areas of triangles \( A B C \)
and \( B D E \) is
A .2: 1
B. 1: 2
\( c \cdot 4: 1 \)
D. 1: 4


Describe the functions of the heart.


According to JJ Thomson
model,Electrons in atom are
A. revolving around nucleus
B. embeded in nucleus
c. static around the nucleus
D. none of these


The law of triads was given by :
A. Dobereiner
B. Lewis
c. Mendeleev
D. Dalton


The number of metals from the
following:
\( \boldsymbol{A} \boldsymbol{s}, \boldsymbol{F} \boldsymbol{e}, \boldsymbol{X} \boldsymbol{e}, \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B}, \boldsymbol{C l}, \boldsymbol{B} \boldsymbol{a}, \boldsymbol{P}, \boldsymbol{I}, \boldsymbol{S} \boldsymbol{i} \)


Solve \( \int \frac{x^{3}+4 x^{2}-7 x+5}{x+2} d x \)


In the diagram the area of cross section
of the pistons \( A \) and \( B \) are \( 8 c m^{2} \) and
\( 320 c m^{2} \) respectively then the thrust on
the piston at \( B \) is
A . \( 160 k g f \)
в. \( 320 k g f \)
c. \( 420 k g f \)
D. \( 80 k g f \)


Brown mottling of teeth occurs when
\( F^{-} \) ion concentration in drinking
water becomes:
A. less than 1 ppm
B. greater than 1 ppm
c. greater than 5 ppm
D. it does not depend on \( F^{-} \) ion concentration


The disease diabetes mellitus is
caused by the deficiency of:
A . lodine.
B. Insulin
c. Phenyl alanine hydroxylase.
D. Lysine


\( f\left|\begin{array}{ccc}6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i\end{array}\right|=x+i y \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)


Number of integral solutions satisfy
inequality \( |\boldsymbol{x}-\mathbf{3}|-|\mathbf{2 x}+\mathbf{5}| \geq|\boldsymbol{x}+\mathbf{8}| \)
is
A . 5
B. 6
\( c \cdot 7 \)
D.


Which of the following can travel through vacuum?

This question has multiple correct options
A . Light waves
B. Heat waves
c. \( x \) -rays
D. sound waves


Which term describes the tendency of elements to participate in a chemical change process?
A. Ionic radius
B. Reactivity
c. lonization enthalpy
D. Atomic radius


Choose the correct answer from the
alternatives given
Plant hormones
A. interact with one another
B. are influenced by environmental cues
c. are active in plant embryos within seeds
D. all of the above


Which of the following statements is true regarding the typical element belonging to \( 1^{s t} \) group of \( p \) - block elements?

This question has multiple correct options
A. The element forms amphoteric oxide
B. The element forms a sulphate of formula \( M_{2}\left(S O_{4}\right)_{3} \)
c. The element shows variable valency
D. The element is a metalloid


Plant tissue responsible for stiffness in husk of coconut is
A. Sclerids
B. Phloem cells
c. xylem fibres
D. Sclerenchyma fibres


A total of 28 handshakes was
exchanged at the conclusion of a party. Assuming that each participant was equally polite towards all the others, the number of people present was:
A . 14
B . 28
c. 56
D. 8
\( E .7 \)


Which one of the following is correctly matched?
A. Emulsion-Smoke
B. Gel-Butter
c. Sol-Whipped Cream
D. Aerosol-Hair cream
E. Foam-Mist


Assertion
A laser beam of \( 0.3 W \) can drill a hole
through metal sheet, whereas light of \( 1000 W \) can not do so
Reason
Laser beam has very high frequency
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


Given that she does not achieve
success, the chance she studied for 4
hour, is
A \( \cdot \frac{18}{26} \)
в. \( \frac{19}{26} \)
c. \( \frac{20}{26} \)
D. \( \frac{21}{26} \)


Which of the following is correct about
\( (A),(B) \) and \( (C) ? \)
A. \( A, B \) and \( C \) are anomers
B. A and C are anomers
\( \mathrm{c} \cdot \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are metamers
D. None of the above


During complete combustion of one
mole of butane, \( 2658 k J \) of heat is
released. The thermochemical reaction
for above change is:
\( \mathbf{A} \cdot 2 C_{4} H_{10}(g)+13 O_{2}(g) \rightarrow 8 C O_{2}(g)+10 H_{2} O(l) \Delta_{c} H= \)
\( -2658.0 k J \mathrm{mol}^{-1} \)
B.
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(g) \Delta_{c} H=
\]
\( -1329.0 k J \mathrm{mol}^{-1} \)
\( c \)
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(l) \Delta_{c} H=
\]
\( -2658.0 k J m o l^{-1} \)
D.
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(l) \Delta_{c} H=
\]
\( +2658.0 k J \mathrm{mol}^{-1} \)


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


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |\vec{c}|=\sqrt{3} \) then
A. \( \alpha=1, \beta=-1 \)
В. \( \alpha=1, \beta=\pm 1 \)
c. \( \alpha=-1, \beta=\pm 1 \)
D. \( \alpha=\pm 1, \beta=1 \)


The area of three adjacent faces of a
cuboid are \( x, y \) abd \( z . \) If the volume is \( V \)
prove that \( V^{2}=x y z \)


A block of mass \( m \) is projected with velocity \( u \) forwards another identical
block with has a massless spring attached to its face. The spring constant of the spring is \( k \) and blocks are on smooth horizontal surface.

Maximum compression in the spring is:
A \( \cdot u \sqrt{\frac{2 m}{k}} \)
в. \( u \sqrt{\frac{m}{k}} \)
c. \( u \sqrt{\frac{m}{2 k}} \)
D. \( u \sqrt{\frac{m}{4 k}} \)


The electric field intensity at point 0 is
A. zero
В \( \cdot \frac{q}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{1}{R_{1}^{2}}+\frac{1}{R_{2}^{2}}\right] \)
c. \( \frac{q}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{1}{R_{1}^{2}}\right] \)
D. None of these


A parallel beam of light \( \lambda=5000 A^{\circ} \)
falls normally on a single narrow slit of
width \( 0.001 m m . \) The light is focused by a convex lens on a screen placed in the focal plane. The first minimum will be
formed for the angle of diffraction are equal to:
A . \( 0^{\circ} \)
В. \( 15^{\circ} \)
\( c \cdot 30^{0} \)
D. \( 50^{\circ} \)


Assertion
The mass of a substance is constant
whereas its weight may vary from one place to another.
Reason
Mass of a substance is the amount of
matter present in it while weight is the force exerted by gravity on an object.
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 battery and a variable resistor are in
series with a small fan. A switch is
closed, and the fan runs. When the variable resistor is moved slightly to the left, the fan slows down a little. When
the variable resistor is moved slightly to the right, the fan speeds up a little. If the variable resistor in the circuit is set
all the way to the right, what happens in the circuit?
I. The fan runs faster
II. The voltage decreases.
III. The current increases.
A . I only
B. Il only
c. I and III only
D. I I and III only
E . I, II, and III


A \( 100 m H \) inductor, a \( 25 \mu F \) capacitor
and a \( 15 \Omega \) resistor are connected in
series to a \( 120 V, 50 H z \) ac source.
Calculate
(a) impedance of the circuit at
resonance
(b) current at resonance
(c) resonant frequency
A \( . \) (a) \( 16 \Omega \) (b) \( 9 A \) (c) \( 100 H z \) \( z \)
B. (a) \( 15 \Omega \) (b) \( 8 A \) (с) \( 100 H z \)
c. \( (\text { a) } 15 \Omega \)
(b) \( 8 A \) (с) \( 120 H z \)
D. (a) \( 15 \Omega \) (b) \( 7 A \) (с) \( 100 H z \)


It is given that event \( A \& B \) are such \( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{B}}\right)= \)
\( \frac{1}{2}, P\left(\frac{B}{A}\right)=\frac{2}{3}, \) then \( P(B)= \)
\( A \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D.


A charge q is situated at the centre of a square of side d. The electric field
intensity at the midpoint of a side is \( \mathrm{E}_{1} \)
and at one corner of the square is \( \mathrm{E}_{2} \)
Then, the ratio of \( E_{1} / E_{2} \) is :
A . 0.5
в. 0.7
c. 1
D.


A spherically symmetric charge distribution is characterised by a
charge density having the following variation:
\( \boldsymbol{p}(\boldsymbol{r})=\boldsymbol{p}_{o}\left(\mathbf{1}-\frac{r}{R}\right) \) for \( \boldsymbol{r}<\boldsymbol{R} \)
\( \boldsymbol{p}(\boldsymbol{r})=\mathbf{0} \) for \( \boldsymbol{r} \geqslant \boldsymbol{R} \)
Where \( r \) is the distance from the centre
of the charge distribution and \( p_{o} \) is a
constant. The electric field at an
internal point
\( ^{\text {A }} \cdot \frac{p_{o}}{4 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
в. \( \frac{p_{o}}{\epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
c. \( \frac{p_{o}}{3 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
D. \( \frac{p_{o}}{12 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)


The order of boiling point of primary (1) secondary (2) and tertiary (3) alcohols is:
A \( \cdot 1>2>3 \)
B. 3 > 2 >1
\( c \cdot 2>1>3 \)
D. 2 >3>1


Relative permittivity of water is \( 81 . \) If \( \epsilon_{w} \)
and \( \epsilon_{0} \) are permittivities of water and
vacuum respectively, then :
A \( \cdot \epsilon_{0}=9 \epsilon_{w} \)
В . \( \epsilon_{0}=81 \epsilon_{w} \)
\( \mathbf{c} \cdot \epsilon_{w}=9 \epsilon_{0} \)
D. \( \epsilon_{w}=81 \epsilon_{0} \)


Three numbers \( x, y \) and \( z \) are in
arithmetic progressions. If \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}= \)
-3 and \( x y z=8, \) then \( x^{2}+y^{2}+z^{2} \) is
equal to
\( A \cdot 0 \)
B. 10
\( c \cdot 21 \)
D. 20


Two billiard balls each of mass \( 0.05 k g \)
moving in opposite directios with speed
\( 6 m s^{-1} \) collide and rebound with the
same speed. What is the impulse imparted to each ball due to the other.


Given, \( C_{\text {graphite }}+O_{2}(g) \rightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}= \)
\( -285.8 k J m o l^{-1} \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+ \)
\( \mathbf{2} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) ; \boldsymbol{\Delta}^{r} \boldsymbol{H} \mathbf{6} \boldsymbol{o}=+\mathbf{8} \mathbf{9 0 . 3} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
Based on the above thermochemical
wquations, the value of Delt\( a_{r} H^{o} \) at
\( 298 K \) for the reaction,
\( \boldsymbol{C}_{(g r a p h i t e)}+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \) will be:
A. \( -78.8 k J \) mol \( ^{-1} \)
B. \( +144.0 k J \) mol \( ^{-1} \)
c. \( +74.8 k J \) mol \( ^{-1} \)
D. - 144.0kJ mol \( ^{-1} \)


Chiral carbon is:
A. carbon in which all four valencies are satisfied with four different atoms or group of atoms
B. carbon in which at least two of their valency are satisfied with four different atoms or group of atoms
C. carbon in which all four valences satisfied with same
atoms
D. none of these


Match the following:


Three containers of the same volume
contain three gases. The masses of their
molecules being \( \mathrm{m}_{1}, \mathrm{m}_{2} \) and \( \mathrm{m}_{3} \) and
number of molecules in these containers
is \( \mathrm{N}_{1}, \mathrm{N}_{2} \) and \( \mathrm{N}_{3} \). The pressure in
the containers are \( \mathrm{P}_{1}, \mathrm{P}_{2} \) and \( \mathrm{P}_{3} \)
respectively. All the gases are now mixed up and put in these containers. The
pressure \( \mathrm{P} \) of the mixture is
\( \mathbf{A} \cdot P<\left(P_{1}+P_{2}+P_{3}\right) \)
B. \( P=\frac{P_{1}+P_{2}+P_{3}}{3} \)
\( \mathbf{c} \cdot P=P_{1}+P_{2}+P_{3} \)
D \( \cdot P>\left(P_{1}+P_{2}+P_{3}\right) \)


On which factors from below does
Coulomb's law(i.e. law of electrostatic
attraction and repulsion) depends?
A. Magnitude of charges
B. Distance between charges
c. Both magnitude and distance between charges
D. None of the above


Number of double bond in \( H_{2} N O H \) is:


A steel scale is correct at \( 0^{\circ} \mathrm{C} \), the
length of a brass tube measured by it at
\( 40^{\circ} \mathrm{C} \) is \( 5 \mathrm{m} . \) The correct length of the
tube at \( 0^{\circ} \mathrm{C} \) is (Coefficients of linear
expansion of steel and brass are \( 11 \times \) \( \mathbf{1 0}^{-\mathbf{6} /^{\circ} C} \) and \( \mathbf{1 9} \times \mathbf{1 0}^{-\mathbf{6} /^{\circ} \mathbf{C}} \) respectively
A. \( 4.001 \mathrm{m} \)
в. \( 5.001 m \)
\( c .4 .999 m \)
D. \( 4.501 m \)


Calculate maximum number of
electrons in \( _{25} M n \) which have \( n=3, m=0 \)
and \( s==1 / 2 \)


The sodium compound which is used for softening hard water:
A. washing soda.
B. bleaching powder.
c. caustic soda
D. lime soda.


Why is the ratio of the velocities of light
of wavelengths \( 4000 A \) and \( 8000 A \) in
vacuum \( 1: 1 ? \)


A cylinder of height \( 90 \mathrm{cm} \) and base
diameter \( 8 c m \) is melted and recast into
spheres of diameter \( 12 \mathrm{cm} \). Find the number of spheres.


A uniform metre rule \( A B \) is supported
at its centre of gravity by a knife-edge. A force of \( 4 N \) is applied at a point which
is \( 20 \mathrm{cm} \) from end \( \mathrm{A} \) of the rule.
Calculate the force which must be
applied to end B to restore the
equilibrium of the rod
\( A \cdot 4 N \)
B. 2.4
c. \( 1.2 \mathrm{N} \)
D. 4.8 N


Which of the following is not a Lewis acid?
A. Aluminum chloride
B. Ammonia
c. sulphur trioxide
D. cupric ion


Which of the following has the shortest
wavelength?
A. Red light
B. Blue light
c. Gamma rays
D. x rays
E. Radio waves


If \( \theta \) is the angle between the pair of
straight lines \( x^{2}-5 x y+4 y^{2}+3 x- \)
\( 4=0, \) then \( \tan ^{2} \theta \) is equal to
\( A \cdot \frac{9}{16} \)
в. \( \frac{16}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{21}{25} \)
E \( \cdot \frac{25}{9} \)


Which of the following property is generally not shown by metal?
A . Electrical conduction
B. Sonorous in nature
c. Dullness
D. Ductility


Determine the value of \( k \) so that the
following linear equations has no
solution:
\( (3 k+1) x+3 y-2=0 \) and \( \left(k^{2}+\right. \)
1) \( \boldsymbol{x}+(\boldsymbol{k}-\mathbf{2}) \boldsymbol{y}-\mathbf{5}=\mathbf{0} \)
A. \( k=-1 \)
B. \( k=3 \)
c. \( k=-7 \)
D. \( k=8 \)


State whether true or false.
An increase in the base area leads to
the decrease in stability of the object.
A. True
B. False


The solution set of \( f^{\prime}(x)>g^{\prime}(x) \) where
\( f(x)=\left(\frac{1}{2}\right) 5^{2 x+1} \) and \( g(x)=5^{x}+ \)
\( 4 x \log 5 \) is
\( A \cdot(1, \infty) \)
B \( \cdot(0,1) \)
\( c \cdot[2, \infty) \)
D. \( (0, \infty) \)


A wire has a resistance of \( 10 \Omega \). It is
stretched by \( 1 / 10 \) of its original length. Then its resistance will be
A. \( 9 \Omega \)
B. \( 10 \Omega \)
c. \( 11 \Omega \)
D. \( 12.1 \Omega \)


The role of gibberellin is
A. Inhibits lateral buds
B. Stimulates fruit ripening
C. Maintains seed dormancy
D. Stimualtes rapid stem elongation
E. All of the above


Which heat depends on the direction of
current?
A. Joule heat
B. Peltier heat
c. Thompson effect
D. None of these


Which of the following is not a measure of central location?
A. Mean
B. Median
c. mode
D. Variance


Two isosceles triangles have equal vertical angles and their areas are in the ratio \( 9: 16 . \) What is the ratio of their
corresponding altitudes?
A .2: 3
B. 3: 2
c. 3: 4
D. 4: 3


If the line joining the points (-1,2,3),(2,-1,4) is perpendicular to the line joining the points \( (x,-2,4),(1,2,3) \) then \( x= \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 10
\( c \cdot \frac{-3}{10} \)
D. \( \frac{-10}{3} \)


Antichlor is a compound that converts
\( C I_{2} \) into \( _{-}-_{-} ? \)
A. hydrochloride acid
B. kcl
C. nitric acid
D. Nacl


How is 1-propoxypropane synthesised from propan-1-ol? Write mechanism of
this reaction.


The relation \( R \) define on the set of
natural numbers as \( \{(a, b): a \) differs
from b by \( 3\} \) is given.
A \( \cdot\{(1,4),(2,5),(3,6), \ldots \ldots . .\} \)
в. \( \{(4,1),(5,2),(6,3), \ldots \ldots .\} \)
c. \( \{(1,3),(2,6),(3,9), \ldots \ldots .\} \)
D. None of above


What are the main function of
connective tissue?


A rod of length \( l \) is translating at
velocity \( v \) making an angle \( \theta \) with the
length as shown. If its resistance is \( \boldsymbol{R} \)
then find emf and current in the rod?


The motion described by the string of violin is -
A. oscillatory motion
B. vibratory motion
c. non-periodic motion
D. rectilinear motion


A lake near village suffered heavy mortality of fishes within a few days. Consider the following reasons for this.
(i) Lots of urea and phosphate fertiliser were used in the crops in the vicinity.
(ii) The area was sprayed with DDT by an aircraft.
(iii) The lake turned green and stinky.
(iv) Phytoplankton population in the lake declined initially thereby greatly reducing photosynthesis. Which two of the above were the main
causes of fish mortality in the lake?
A . (i), (ii)
B. (ii), (iii)
\( c . \) (iii), (iv)
D. (i), (iii)


In several fungi and plants the bisexual condition is denoted by
A. Homothallic and monoecious
B. Heterothallic and Monoecious
c. Homothallic and dioecious
D. Heterothallic and dioecious


Which of the following statements are
correct about dissociation?
A. Dissociation generally refers to breaking a compound into smaller pieces, usually reversibly.
B. Dissociation can happen without the formation of charged species
\( c . \) Both \( A \) and \( B \)
D. None of these


If the standard deviation of a set of
scores is 1.2 and their mean is \( 10, \) then the coefficient of variation of the scores
is
A . 12
B. 0.12
c. 20
D. 120


Nitrogen oxides released in the
stratosphere cause ozone depletion due
to
A. catalysing conversion of ozone to oxygen
B. Binding ozone
c. Reacting with ozone
D. All of the above


A body is projected up such that its
position vector with time as \( \vec{r}= \)
\( \left\{3 t \hat{i}+\left(4 t-5 t^{2}\right) \hat{j}\right\} m . \) Here, tis in
seconds.
Find the time and \( x- \) coordinate of
particle when its \( y- \) coordinate is zero.


If \( a, b, c \) are in \( A . P ., \alpha, \beta, \gamma \) in H.P., \( \boldsymbol{a} \boldsymbol{\alpha}, \boldsymbol{b} \boldsymbol{\beta}, \boldsymbol{c} \gamma \) in G.P. (with common ratio
not equal to \( 1 . \) ), then prov that \( a: b: c= \) \( \frac{1}{\gamma}: \frac{1}{\beta}: \frac{1}{\alpha} \)


\( \lim _{n \rightarrow \infty} \frac{n(2 n+1)^{2}}{(n+2)\left(n^{2}+3 n-1\right)} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot 4 \)
\( D \)


If \( h(x)>[2 x-f n(f(x))] f(x) \) and
\( f(x)>0 \) satisfy for \( \forall x>0, \) if \( h(x)= \) \( \int_{0}^{x}(f(t)-t) d t, \) then
A. \( h(x) \) is increasing function
B. \( h(x) \) is decreasing function
\( c \cdot h(1)>1 \)
D. \( h(1)>e-1 \)


In the following redox reaction:
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \)
\( Z n^{2+}(a q)+N H_{4}^{+}(a q) \)
\( Z n(s) \) and \( N O_{3}^{-}(a q) \) respectively are
respectively:
A. oxidant and reductant
B. reductant and oxidant
c. both oxidant
D. both reductant


The pH of rain water is \( 7 . \) Is it true or
false?


Classify the following polynomial based on their degrees:
\( \boldsymbol{y}^{2}-\boldsymbol{4} \)


Which of the following is NOT a Absolute Temperature Scale?
A. Celsius Scale
B. Rankine Scale
c. Kelvin Scale
D. None of these


Which is the largest open university in India?
A. Indira Gandhi National Open University
B. Dr. B.R. Ambedkar Open University
c. Nalanda Open University
D. Yashwantrao Chavan Maharashtra open University


Let \( \boldsymbol{f}: \boldsymbol{I} \boldsymbol{R} \rightarrow \boldsymbol{I} \boldsymbol{R} \quad \) be defined as
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+\left|\boldsymbol{x}^{2}-1\right| . \) The total number
of points at which \( f \) attains either a
local maximum or local minimum is


An airplane with wingspan \( 50 m \) is flying horizontally with a speed of
\( 360 k m h r^{-1} \) over a place where the
vertical component of the earth's magnetic field is \( 2 \times 10^{-2} \). The
potential difference between the tips of the wings would be
A. \( 100 V \)
в. \( 1.0 V \)
\( c .0 .2 V \)
D. \( 0.01 V \)


Two positive charges \( \boldsymbol{q}_{1}=\boldsymbol{4} \times \mathbf{1 0}^{-\mathbf{6}} \boldsymbol{C} \)
and \( q_{2}=9 \times 10^{-6} C \) are placed \( 10 \mathrm{cm} \)
a part in air. The position of a third charge to be placed between them, such that there will be no resultant force on it
is:
A \( .6 \mathrm{cm} \) from \( q_{1} \)
B. \( 3 \mathrm{cm} \) from \( q_{1} \)
c. \( 4 \mathrm{cm} \) from \( q_{1} \)
D. \( 7 \mathrm{cm} \) from \( q_{1} \)


Velocity of sound in air is about :
A. \( 330 \mathrm{m} / \mathrm{s} \)
B. \( 460 \mathrm{m} / \mathrm{s} \)
c. \( 380 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)


The \( (x, y, z) \) coordinates of two points \( A \) and \( \mathrm{B} \) are given respectively as (0,4,-2) and \( (-2,8,-4) . \) The displacement vector
from \( A \) to \( B \) is:
A \( \cdot-2 \hat{i}+4 \hat{j}-2 \hat{k} \)
B. \( 2 \hat{i}-4 \hat{j}+2 \hat{k} \)
c. \( 2 \hat{i}+4 \hat{j}-2 \hat{k} \)
D. \( -2 \hat{i}-4 \hat{j}-2 \hat{k} \)


The eccentricity of the conic is \( \frac{l}{r}= \) \( 2+3 \cos \theta+4 \sin \theta \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
\( c .5 \)
D.


Conifer gymnosperm, amongst the following is
A. Gnetum
B. Sequoia
c. cycas
D. Ginko


Conduct an experiment to prepare
nitrogen gas objective :
1.5 :Formation of nitrogen (N \( _{2} \) )


in the given figure sides of the angles
are parallel. Find \( \boldsymbol{x} \) and \( \boldsymbol{y} \) if \( \angle \boldsymbol{A}=\mathbf{5 5}^{\circ} \)


Which of the two components of starch
is water soluble?


Which one of the following oxy acid of fluorine exists?
\( \mathbf{A} \cdot H O F \)
в. \( H F O_{3} \)
c. \( H F O_{4} \)
D. \( H F O_{2} \)


A long elastic spring is stretched by \( 2 \mathrm{cm} \) and its potential energy is \( U \). If the
spring is stretched by \( 10 \mathrm{cm} \), the P.E., will be
A . \( 5 U \)
в. \( 25 U \)
c. \( U / 5 \)
D. \( U / 20 \)


If \( A \) and \( B \) are acute positive angles satisfying the equations \( 3 \sin ^{2} A+ \) \( 2 \sin ^{2} B=1 \) and \( 3 \sin 2 A-2 \sin 2 B= \)
\( 0, \) then \( A+2 B \) is equal to
A \( \cdot \frac{\pi}{4} \)
в.
\( \mathrm{c} \cdot_{3} \frac{\pi}{4} \)
D. \( \frac{2 \pi}{3} \)


Consider a parallel plate capacitor with plates \( 20 \mathrm{cm} \) by \( 20 \mathrm{cm} \) and separated by \( 2 \mathrm{mm} . \) The dielectric constant of the material between the plates is 5.The plates are connected to a voltage source
of \( 500 \mathrm{V} \). The energy density of the field
between the plates will be close to
A \( \cdot 2.65 \mathrm{J} / \mathrm{m}^{3} \)
B . \( 1.95 \mathrm{J} / \mathrm{m}^{3} \)
C. 1.38 J \( / m^{3} \)
D. 0.69 J \( / m^{3} \)


\( Z n \mid Z n^{2+}(a=0.1 M) \| F e^{2+}(a= \)
\( \mathbf{0 . 0 1} \boldsymbol{M}) \mid \boldsymbol{F} e \)
The EMF of the above cell is \( 0.2905 . \) The
equilibrium constant for the cell reaction is:
B . \( 10^{0.32 / 0.0295} \)
D. \( e^{0.32 / 0.0295} \)


Explain 'Electric generator' with the help of the following points :
i. Principle of an electric generator.
ii. Function of slip rings.
iii. Any two uses of a generator.


Power of lens is:
A. \( \frac{1}{\text { focal length in centimetre }} \)
B. \( \frac{1}{\text { focal length in metre }} \)
C \( \frac{100}{\text { focal length in kilometre }} \)
D. None


Biological Oxygen Demand (BOD) is a
measure of
A. Industrial wastes poured into water bodies
B. Extent to which water is polluted with organic compounds.
c. Amount of carbon monoxide inseparably combined with haemoglobin
D. Amount of oxygen needed by green plants during night


Evaluate \( \int \frac{\sin \theta}{\sin 3 \theta} d \theta \)


If \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / \mathbf{4}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \)
\( B)=1 / 2 \) show that \( A \) and \( B \) are
independence events.


If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0 \) then find the roots of the equation
\( a x^{2}-b x(x-1)+c(x-1)^{2}=0 \)


The ratio of hydraulic stress to the
corresponding strain is known as
A. Compressibility
B. Bulk modulus
c. Young's modulus
D. Rigidity modulus
E. Expansion coefficient


Cr atom is ........... hybridized.
\( \mathbf{A} \cdot s p^{3} d^{2} \) in both complexes
B. \( d^{2} s p^{3} \) in both complexes
\( \mathbf{C} \cdot s p^{3} d^{2} \) in \( A \) and \( d^{2} s p^{3} \) in \( B \)
D. \( d^{2} s p^{3} \) in \( A \) and \( s p^{3} d^{2} \) in \( B \)


Which of the following practices adversely effect the environment?
A. Aeration
B. Ploughing
c. weeding
D. None of the above


Find the differential equation of \( y=A \) \( \operatorname{cox}+B \sin x \)


Find the angle between the following pairs of lines:
\( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{-3} \) and \( \frac{x+3}{-1}= \)
\( \frac{\boldsymbol{y}-\mathbf{5}}{\mathbf{8}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{4}} \)


The coordinate of the point dividing internally the line joining the points (4,-2) and (8,6) in the ratio 7: 5 is
A \( .(16,18) \)
в. (18,16)
\( ^{C} \cdot\left(\frac{19}{3}, \frac{8}{3}\right) \)
D. \( \left(\frac{8}{3}, \frac{19}{3}\right) \)
E . (7,3)


Consider the following statements A and B identify the correct statement from the following.
A) The width of the depletion layer in a
p-njjunction diode increases in forward bias.
B) In an intrinsic semiconductor, the
Fermi energy level is exactly in the middle of the forbidden gap.
A. A is true and B is false.
B. Both A and B are false
c. A is false and B is true
D. Both A and B are true


The oxidation state of bismuth in
lithium bismuthate is:
\( A \cdot+5 \)
\( B \cdot+3 \)
\( c \cdot+2 \)
\( D \cdot+4 \)


\( \lim _{\mathbf{x} \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(\mathbf{x}-\mathbf{2})\}}}{\mathbf{x}-\mathbf{2}}\right) \)
A. does not exist
B. equals \( \sqrt{2} \)
c. equals \( -\sqrt{2} \)
D. equals \( \frac{1}{\sqrt{2}} \)


Events \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are such that \( \boldsymbol{P}(\boldsymbol{A})= \) \( \frac{1}{2}, P(B)=\frac{7}{12} \) and
\( P(\text { not } A \text { or } \operatorname{not} B)=\frac{1}{4} . \) State whether
\( A \) and \( B \) are independent?
A. True
B. False


For any two complex numbers \( z_{1}, z_{2} \) we
have \( \left|z_{1}+z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}, \) then
A \( \cdot \operatorname{Re}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
в. \( \operatorname{Im}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
c. \( \operatorname{Re}\left(z_{1} z_{2}\right)=0 \)
D・Im \( \left(z_{1} z_{2}\right)=0 \)


Statement : Baking soda or baking powder is different.
Answer whether the above statement is
true or false.
A. True
B. False


\( " P O C l_{3}, \) like \( P_{2} O_{5} \) is also used as
dehydrating agent." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Which of the following molecule having resonating electronic configuration?
\( A \cdot S O_{2} \)
в. \( C_{2} H_{6} \)
\( c \cdot C l_{2} \)
D. \( H B r \)
E . \( N a C l \)


Evaluate, without using trigonometric
tables:
\( \frac{\sin ^{2} \theta+\sin ^{2}\left(90^{\circ}-\theta\right)}{3\left(\sec ^{2} 61^{\circ}-\cot ^{2} 29^{\circ}\right)} \)
\( \frac{3 \cot ^{2} 30^{\circ} \cdot \sin ^{2} 54^{\circ} \cdot \sec ^{2} 36^{\circ}}{2\left(\csc ^{2} 65^{\circ}-\tan ^{2} 25 o\right)} \)


\( \operatorname{Let} A=\{x, y, z\} \) and \( B=\{1,2\} . \) Find
the number of relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)


During photosynthesis
A. Water is reduced and \( C O_{2} \) is oxidized.
B. \( C O_{2} \) is reduced and water is oxidized.
C \( . \) Both \( C O_{2} \) and water get reduced.
D. Both \( C O_{2} \) and water get oxidized.


The source frequency for which a \( 5 \mu \mathrm{F} \)
capacitor has a reactance of \( 1000 \Omega \) is
A \( \cdot \frac{100}{\pi} \) Hz
в. \( \frac{1000}{\pi} \) Н \( z \)
\( c .200 H z \)
D. \( 5000 \mathrm{Hz} \)


Which does not contain cytoplasm?
A. Liver cell
B. Palisade tissue
c. Red blood cell
D. xylem vessel


Three tubes \( A, B \) and \( C \) are connected to a horizontal pipe in which liquid is flowing. The radii of pipe at the joints of \( A, B \) and \( C \) are \( 2 c m, 1 c m \) and \( 2 c m \) respectively. The height of liquid:
\( A \). in A and B is equal
B. in A is maximum
\( c . \) in \( A \) and \( C \) is same
D. is same in all three


What is the mass of one atom of \( C-12 \)
in grams?
\( \mathbf{A} \cdot 1.992 \times 10^{-23} \mathrm{gm} \)
B . \( 1.989 \times 10^{-23} \mathrm{gm} \)
C \( \cdot 1.892 \times 10^{-23} \mathrm{gm} \)
D. \( 1.965 \times 10^{-23} \mathrm{gm} \)


Which of the following is the graph showing stress-strain variation for
elastomers?
(1)
(2)
(3)
(4)


The number of permutations or the letters of the word EXAMINATION taken
4 at a time is
A . 136
в. 2454
\( c .2266 \)
D. None of these


Assertion
Tapeworm, roundworm and pinworm are
endoparasites of human intestine.
Reason
Improperly cooked food is the source of
all intestinal infections.
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 radioactive sample \( A \) and \( B \) have
half \( T_{1} \) and \( T_{2}\left(T_{1}>T_{2}\right) \) respectively. At
\( T=0, \) the activity of a \( B \) was twice the activity of A. Their activity will become equal after a time:
A. \( \frac{T_{1} T_{2}}{T_{1}-T_{2}} \)
в. \( \frac{T_{1}-T_{2}}{2} \)
c. \( \frac{T_{1}+T_{2}}{2} \)
D. \( \frac{T_{1} T_{2}}{12} \)


Now, we construct rectangles with class-limits as bases and respective adjusted frequencies as heights. Draw a histogram for the marks of students given below:
\begin{tabular}{|l|c|c|c|c|c|}
\hline Marks: & \( 0-10 \) & \( 10-30 \) & \( 30-45 \) & \( 45-50 \) & \( 50-60 \) \\
\hline No. of students: & 8 & 32 & 18 & 10 & 6 \\
\hline
\end{tabular}


Reproductive health is related to
A. Physical fitness
B. Emotional compatibility
c. Behavioural inter relationships
D. All of the above


Regular reflection takes place when light is incident on:
A. a rough curved surface
B. a highly polished plane surface
c. either of A and B
D. neither of A and B


The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the \( y \) -axis is:
A \( \cdot y y^{\prime}+2 x y+1=0 \)
В . \( x y^{\prime}+y+1=0 \)
c. \( x y^{\prime}+2 y+2=0 \)
D. \( x y^{\prime}-y-1=0 \)


Radiation coming from transitions \( n= \)
2 to \( n=1 \) of hydrogen atoms falls on
helium ions in \( n=1 \) and \( n=2 \) states.
What are the possible transition of helium ions as they absorb energy from the radiation?


Which of the following changes increases the overall density of the object?
A. A block of iron is formed into a hollow shape
B. A submarine fills its ballast tanks with water
c. A submarine fills its ballast tanks with air
D. A fish increases the amount of gas in its swim bladder


Which of the following is not a
monovalent group?
A. Aldehydic
B. Ketonic
c. carboxylic
D. Hydroxy


Choose the correct answers from the
alternatives given:
Vascular bundles are scattered in
A. Monocot root
B. Dicot root
c. Monocot stem
D. Dicot stem


While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because:
A. the resources are limited in supply
B. the objective function as a linear function
c. the constraints are linear equations or inequalities
D. all of the above


Identify the wrong pair of statements
I.During plant succession some species colonise an area and populations becomes more numerous whereas
populations of other species decline and even disappear II.Both hydrarch and xerarch successions lead to mesic conditions
III. Secondary succession is a slow process as compared to primary succession
IV.In successive seral stages there is no change in the diversity of species of organisms
A . ॥ , ॥ ॥
в. ।, ॥
c. ॥॥ , । v
D. 1, Il


Which layer protects us from harmful ultraviolet rays of the sun?
A. First layer
B. Second layer
c. Ozone layer
D. Exosphere


The moment of inertia of a solid cylinder
about its own axis is the same at its
moment of inertia about an axis
passing through its cenre of gravity and perpendicular to its length. The relation between its length \( L \) and radius \( R \) is
В. \( L=\sqrt{3} R \)
c. \( L=3 R \)
D. \( L=R \)


Give the products formed on reductive ozonolysis with LAH and oxidative
ozonolysis with \( H_{2} O_{2} \), from the compound 2mol butan - 2 - one.


In an experimental set-up for the measurement of emf of a half-cell using a reference electrode and a salt bridge, when the salt bridge is removed, the voltage:
A. does not change
B. increases to maximum
c. decreases half the value
D. drops to zero


For a CB amplifier current gain is \( 0.54 . \) I the emitter current is \( 6.8 m A \), the
collector current will be
A . \( 1.7 \mathrm{mA} \)
в. \( 2.7 \mathrm{mA} \)
\( c .3 .7 m A \)
D. \( 4.7 \mathrm{mA} \)


Mention important characteristics and applications of a diode.


Oxidation state of phosphorous in
\( \boldsymbol{P O}_{4}^{3-} \) is:
\( A \cdot+2 \)
B. +5
\( c \cdot+4 \)
\( D \cdot+1 \)
E. none of the above


In the figure shown below the
conducting shell \( A \) having radius \( R \) is
given charge \( Q \) initially. The shell \( A \) is connected to shell \( B \) of radius \( 2 R \) via
switch \( S \) and a conducting wire. The
switch \( S \) is closed at \( t=0, \) then charge density on the shell \( B \) is (Assuming separation between \( \boldsymbol{A} \) and
\( B \) is very very large)
\( A \)
в. \( \frac{Q}{24 \pi R^{2}} \)
c. \( \frac{Q}{12 \pi R^{2}} \)
D. \( \frac{Q}{6 \pi R^{2}} \)


How many different numbers, greater
than 50000 can be formed with the
\( \operatorname{digits} \mathbf{0}, \mathbf{1}, \mathbf{1}, \mathbf{5}, \mathbf{9} \)


The applied potential difference in the
circuit shown is \( V=10 \sin 100 t \) where
\( V \) is in volt and \( t \) is in second. If the
power factor of the circuit is \( \frac{1}{\sqrt{2}}, \) then
the value of capacitance \( C \) of the
circuit, nearly is:
A. \( 111 \mu F \)
в. \( 333 \mu F \)
c. \( 222 \mu F \)
D. \( 444 \mu F \)


A swimmer swims in still water at a
speed \( =5 k m / h r . \) He enters a \( 200 m \) wide
river, having river flow speed \( =4 k m / h r \) at a point \( A \) and proceeds to swim at an
angle of \( 127^{0}\left(\sin 37^{*}-0.6\right) \) with the
river flow direction. Another point B is located directly across \( A \) on the other side. The swimmer lands on the river
bank at a point C. from which he walks the distance \( \mathrm{CB} \) with a speed \( =3 k m / h r \) The total time in which he reach from \( \mathbf{A} \)
to B is
\( \mathbf{A} \cdot 5 \min \)
B. 4 min
c. 3 min
D. None


Hydraulic lifts are used to lift the heavy loads primarily because:
A. they look good
B. they amplify the force applied by a large extent
c. they are sturdy
D. they have better tensile strength


Jelly fish is placed in which class of coelenterate?
A. Anthozoa
B. Scyphozoa
c. Hydrozoa
D. None of the above


How many significant digits does the measurement \( 0.0384 g \) possess?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
E . 5


While opening a tap with two fingers, the forces applied are
A . equal in magnitude
B. parallel to each other
c. opposite in direction
D. All of the above


\( 4 s^{2} \) is the configuration of the outermost orbit of an element. Its
atomic number would be:
A . 29
B. 24
\( c . \) 30
D. 19


Gas B is paramagnetic and support the combustion compound B is :
A. \( N_{2} \)
в. \( N_{2} \),
\( c \cdot O_{2} \)
D. \( N a_{2} O \)


What is the vertical cross-section of a
solid cylindrical pipe shown in the
figure?
A. An ellipse
B. A circle
C. A cylinder
D. A rectangle


A carbon resistor of \( (47 \pm 4.7) k \Omega \) is to
be marked with rings of different
colours for its identification. The colour
code sequence will be:
A. Yellow-Green-Violet-Gold
B. Violet-Yellow-Orange-Silver
c. Green-orange-violet-Gold
D. Yellow-violet-orange-silver


The earliest site where human
civilization and crop cultivation started
was presumably
A. Around Caspian and Mediterranean seas
B. Around river Nile
c. chinese river valley
D. All of the above


What is the number of aromatic
isomers for \( C_{7} H_{8} O ? \)


Mention any two differences between
ideal and non ideal solution.


A rain drop of radius \( 1.5 \mathrm{mm} \)
experience a drag force \( \boldsymbol{F}=(12 \times \)
\( \left.\mathbf{1 0}^{-5} \boldsymbol{v}\right) N, \) while falling through air from
a height \( 2 \mathrm{km}, \) with a velocity v. The terminal velocity of the rain drop will be nearly \( \left(u s e g=10 m / s^{2}\right) \)
A. \( 200 \mathrm{m} / \mathrm{s} \)
B. \( 80 \mathrm{m} / \mathrm{s} \)
\( c \cdot 7 m / s \)
D. \( 3 \mathrm{m} / \mathrm{s} \)


Simplify:\( 2 \times(9)^{\frac{3}{2}} \times(9)^{\frac{-1}{2}} \)


Corrosion can not be prevented by which of the following method?
A. Use of an anode connected to a direct current power
B. Create a barrier between the object being corroded and oxygen
c. Painting
D. Exposing it to sunlight


During the preparation of ethane by Kolbe's electrolytic method using inert electrodes the pH of the electrolyte:
A. increases progressively as the reaction proceeds
B. decreases progressively as the reaction proceeds
c. remains constant throughout the reaction
not very high


For a positively charged particle moving
in a \( x \) -y plane initially along the \( x \) -axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond P. The curved path is shown in the \( x \) -y plane and is found to be non-circular.Which one of
the following combinations is possible?
A \( \cdot \vec{E}=0, \vec{B}=b \hat{i}+c \hat{k} \)
в. \( \vec{E}=a \hat{i}, \vec{B}=c \hat{k}+a \hat{i} \)
c. \( \vec{E}=0, \vec{B}=c \hat{j}+b \hat{k} \)
D. \( \vec{E}=a \hat{i}, \vec{B}=c \hat{k}+b \hat{j} \)


\( \boldsymbol{8} \boldsymbol{p}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)


Pankaj is planning lunch for his wedding anniversary. At one restaurant, the cost per person for lunch is \( \$ 15 \) with an additional one-time set-up
charge of \( \$ 35 . \) Pankaj has a maximum
budget of \( \$ 150 . \) If \( p \) represents the
number of people (including Pankaj) who will attend the lunch, which of the
following inequalities represents the number of people who can attend within
budget?
A. \( 15 p \leq 150+35 \)
B. \( 35 \leq 150-15 p \)
c. \( 15 p \geq 150-35 \)
D. \( 35 \geq 150-15 p \)


A capacitor is connected to an A.C. circuit, then the phase difference between current and the voltage is :
A . \( \pi \)
в.
c. \( \frac{-\pi}{2} \)
D. zero


\( A B C \) is a right angled triangle. Calculate
the magnitude of force on charge - \( Q \)


Most common oxidation states shown
by cerium are:
\( \mathbf{A} \cdot+2,+4 \)
B. +3,+4
\( \mathrm{c} \cdot+3,+5 \)
D. +2,+3


If instead of \( M g F_{2}, \) the coating of the substance whose refractive indices is
larger than the refractive index of glass
was made then interference
A. would not have occurred
B. would have occurred due to total internal reflection of light
c. would have occurred due to refraction of light
D. would have occurred due to strong reflection


Consider the points \( \boldsymbol{P}=(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}=(\cos (\beta-\boldsymbol{\alpha}), \sin \beta) \)
and \( \boldsymbol{R}=(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})) \)
where \( 0<\alpha, \beta<\frac{\pi}{4} \) then
A. \( P \) lies on the line segment \( R Q \)
B. \( Q \) lies on the line segment \( P R \)
c. \( R \) lies on the line segment \( Q P \)
D. \( P, Q, R \) are non-collinear


Differentiate between oxygenic and anoxygenic photosynthesis?


Which of the following is not correct for
enzyme catalysis?
A. The enzyme activity is maximum at optimum pH which is between \( 5-7 \).
B. Each enzyme is specific for a given reaction.
C. The favourable temperature range of enzyme activity is between \( 50-60^{\circ} \mathrm{C} \)
D. The enzymatic activity is increased in presence of certain substances called co-enzymes.


State whether the given statement is True or False :

The earth moves around the sun with a
uniform velocity.
A. True
B. False


During an adiabatic change the density
becomes \( \frac{1}{16} t h \) of the initial value, then \( \frac{\boldsymbol{P}_{1}}{\boldsymbol{P}_{2}} \) is \( :(\gamma=\mathbf{1 . 5}) \)
A . 16
B. 4
c. 32
D. 64


Carboxylic acids dimerise due to:
A. high molecular weight
B. coordinate bonding
C. intermolecular hydrogen bonding
D. covalent bonding.


Electroplating does not help
A. fine finish to the surface
B. shining appearance
C. metals to become hard
D. protect metals against corrosion


Find the modulus, argument and the principal argument of the complex numbers.
\( z=1+\cos \frac{10 \pi}{9}+i \sin \left(\frac{10 \pi}{9}\right) \)
A . Principal Arg \( z=-\frac{4 \pi}{9} ;|z|=2 \cos \frac{4 \pi}{9} ; \operatorname{Arg} z=2 k \pi- \)
\( \frac{4 \pi}{9} k \epsilon l \)
B. Principal Arg \( z=-\frac{10 \pi}{9} ;|z|=2 \cos \frac{10 \pi}{9} ; \) Argz\( =2 k \pi- \)
\( \frac{10 \pi}{9} k \epsilon l \)
C . Principal Arg \( z=-\frac{-10 \pi}{9} ;|z|=2 \cos \frac{-10 \pi}{9} ; \) Argz\( = \)
\( 2 k \pi-\frac{4 \pi}{9} k \epsilon l \)
D. Principal Arg \( z=-\frac{-4 \pi}{9} ;|z|=2 \cos \frac{-4 \pi}{9} ; \) Argz\( =2 k \pi- \)
\( \frac{4 \pi}{9} k \epsilon l \)


A composite wire consits of a steel wire of length \( 1.5 ~ m \) and a copper wire of
length \( 2.0 m, \) with a uniform cross-
sectional area of \( 2.5 \times 10^{-5} m^{2} . \) It is
loaded with a mass of 200 kg. Find the
extension produced. Young's modulus of copper is \( 1.0 \times 10^{11} N m^{-2} \) and that of
steel is \( 2.0 \times 10^{11} N m^{-2} \)
Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} \boldsymbol{s}^{-2} \)


f \( \left|x^{2}-7\right| \leq 9 \) then find the values of \( x \)


Find the potential difference (in \( V \) ) between points \( A \) and \( B \) shown in the
circuit.


A rod of mass \( m \) and length \( L \), lying
horizontally, is free to rotate about a vertical axis through its centre. \( \mathbf{A} \) 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.
A \( \cdot \frac{3 F t^{2}}{5 m L} \)
B. \( \frac{5 F t^{2}}{2 m L} \)
c. \( \frac{3 F t^{2}}{2 m L} \)
D. \( \frac{2 F t^{2}}{3 m L} \)


Dissolving \( 120 g \) of urea in \( 1000 g \) of water gave a solution of density \( \mathbf{1 . 1 5} g / \boldsymbol{m} \boldsymbol{L} . \) The molarity of the solution is:
A \( .1 .79 M \)
в. \( 2 M \)
\( c .2 .05 M \)
D. 2.22 \( M \)


\( \lim _{x \rightarrow \frac{n}{2}} \frac{1-(\sin x)^{\frac{-1}{3}}}{1-(\sin x)^{\frac{-2}{3}}} \) is?
\( A \)
B. \( \frac{3}{2} \)
\( c \cdot 1 \)
2
\( D \)


Which of the following group is diamagnetic?
A. Copper, hydrogen, silver
B. Copper, hydrogen, argon
c. Hydrogen, oxygen, argon
D. Copper, silver, oxygen


Assertion
\( Z r \) and \( H f \) occur together in nature and are difficult to separate.
Reason
\( Z r \) and \( H f \) have identical radii due to lanthanide contraction.
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 addition of pentavalent impurities
of the semiconductor.
A. brings no change to the conductivity
B. decreases the conductivity
c. increases the conductivity
D. reduces the formation of free electrons


Find the increment in the length of a
steel wire of length \( 5 m \) and radius
6 mm under its own weight.Density of steel \( =8000 k g / m^{3} \) and Young's
modulus of steel \( =2 \times 10^{11} N / m^{2} \)
What is the energy stored in the wire? \( \left(\text { Take } g=9.8 m / s^{2}\right) \)


Find radian measure corresponding to
the degree measure \( -37^{\circ} 30^{\prime} \)


In classical physics the force \( F \) acting on a body is assumed to be the product of mass \( \mathrm{m} \) and acceleration a.lf \( \mathrm{m}=2.31 \)
\( \mathrm{kg} \) and acceleration is \( 3.123 \mathrm{m} / \mathrm{s}^{2} \), then taking into account significant figures the force \( F \) should be reported as
A. \( 7.21413 \mathrm{N} \)
B. 7.2141
c. 7.214 N
D. 7.21 N


A charge q is enclosed as shown in all
figure, the electric flux is
(i)
(iii)
A. maximum in (i)
B. maximum in (ii)
c. maximum in (iii)
D. equal in all


Evaluate: \( \int_{0}^{\pi / 2} \frac{8 \sin \theta+4 \cos \theta}{\sin \theta+\cos \theta} \)


Identify the graph of the exponential
function \( \boldsymbol{f} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{(\boldsymbol{x}+\mathbf{2})} \)


The time from sunrise to sunset is
lengthened by about 4 minutes on the earth because
A. the earth revolves slowly around the sun
B. the earth rotates slowly on its axis
c. the earth is losing its round shape
D. the earth has atmosphere


A man gets \( R s .7920 \) for working 48
hours a week. How much does he get
when he works 36 hours a week?
A. \( R s .7150 \)
в. \( R s .5940 \)
c. \( R s .6660 \)
D. Rs. 4000


Which of the following shows allotropy?
A. Silver
B. Sulphur
c. Hydrogen
D. Nitrogen


Molar heat capacity of a gas does not depend on
A. Its temperature
B. Its molecular weight
c. Its atomicity
D. The conditions under which heat is supplied


Find whether the following statement is true or false:
Equivalent rational numbers of a positive rational numbers are all positive.
A. True
B. False


The magnetic flux in a coil of 100 turns increases by \( 12 \times 10^{3} \) Maxwell in 0.2
second due to the motion of a magnet. The emf induced in the coil will be
\( A \cdot 6 v \)
B. \( 0.6 v \)
c. \( 0.06 v \)
D. 60 V


A A ratery is cumectuatuss AD as
shown in the figure. The value of the current supplied by the battery when in one case, battery's positive terminal is connected to A and in other case when
positive terminal of battery is connected to B will respectively be
в. \( 0.1 A \) and \( 0.2 A \)
c. 0.2 A and 0.4 A
D. \( 0.4 \mathrm{A} \) and \( 0.2 \mathrm{A} \)


A cyclotron is used to accelerate
protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the
cyclotron is \( 2 T, \) find the radius and the frequency needed for the applied alternating voltage of the cyclotron.
(Given: Velocity of proton \( =3 x \)
\( \left.10^{7} m / s\right) \)


Let \( x . y . z=105 \) where \( x, y, z \in N . \) Then
number of ordered triplets \( (x, y, z) \) satisfying the given equation is
A . 15
B. 27
\( c \cdot 6 \)
D. 33


The distance between any two crests or troughs is \( 0.5 \mathrm{m} \) in a travelling wave. Find the wavelength of the wave
A . \( 0.5 \mathrm{m} \)
B. \( 1 \mathrm{m} \)
c. \( 0.25 \mathrm{m} \)
D. 1.5 \( m \)


A tall man of height 6 feet wants to see his full image. Then the minimum required length of the mirror will be
A . 12 feet
B. 3 feet
c. 6 feet
D. Any length


\( \int_{-1}^{1} \sqrt{\left(\frac{x+2}{x-2}\right)^{2}}+\left(\frac{x-2}{x+2}\right)^{2}-2 d x \)
A \( \cdot \sin \frac{4}{3} \)
B. \( \operatorname{sln} \frac{3}{4} \)
c. \( 4 \ln \frac{4}{3} \)
\( D \)


Activity of succinic dehydrogenase involves which of the following in TCA cycle?
A. NAD
B. FAD
c. GDP
D. ATP


Assertion
When a ball of mass \( \mathrm{m} \) hits normally a
wall with a velocity \( v \) and rebounds with
same velocity \( v, \) impulse imparted to
the wall is \( 2 m v \)
Reason
Impulse = change in linear momentum
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


Water from a tap emerges vertically downwards with an initial speed of
\( 1.0 m s^{-1} . \) The cross-sectional area of
the tap is \( 10^{-4} m^{2} \). Assume that the
pressure is constant throughout the stream of water and that the flow is
steady. The cross-sectional area of the
stream \( 0.15 m \) below the tap is \( (g= \)
\( 10 m s^{-2} \)
В. \( 1.0 \times 10^{-5} \mathrm{m}^{2} \)
D. \( 2.0 \times 10^{-5} \mathrm{m}^{2} \)


If \( \vec{A} \times \vec{B}=\vec{B} \times \vec{C}=\vec{C} \times \vec{A} \) then \( \vec{A}+ \)
\( \vec{B}+\vec{C} \) is equal to:
A. zero
B. sum of magnitudes
c. twice of the sum of magnitudes.
D. unity.


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & 3 \\ 1 & 1 & 1\end{array}\right], \) Find \( A^{-1} . \) Using
\( A^{-1} \), solve the following system or liner
equation.
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{4} ;-\boldsymbol{z}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0} ; \boldsymbol{x}- \)
\( \mathbf{3} \boldsymbol{y}+\boldsymbol{z}=\mathbf{2} \)


Burning of wood is a \( _{-}-_{-}-_{-} \) change.
A . reversible
B. physical
c. irreversible
D. all of these


In the aqueous solution of sodium acetate the ion that undergoes hydrolysis is :
A. \( C H_{3} C O O^{-} \)
В. \( N a^{+} \)
c. \( N a^{+} \) and \( C H_{3} C O O \)
D. \( N a^{-} \)


Read the bar graph shown in Fig. 23.8 and answer the following questions
What is the information given by the bar
graph?

Bar graph of the tickets of different state lotteries sold by an agent on a day.


If an equiconvex lens is cut into two
halves along (i) \( X O X^{\prime} \) and (ii) \( Y O Y^{\prime} \)
as shown in the figure. Let \( f, f^{\prime}, f^{\prime \prime} \) be the focal lengths of complete lens of each, in case (i) and of each half in case
(ii) respectively.
Choose the correct statement from the
following?
\( \mathbf{A} \cdot f^{\prime}=f, f^{\prime \prime}=f \)
B . \( f^{\prime}=2 f, f^{\prime \prime}=2 f \)
C. \( f^{\prime}=f, f^{\prime \prime}=2 f \)
D. \( f^{\prime}=2 f, f^{\prime \prime}=f \)


Determine the standard reduction
potential for the half reaction.
\[
\boldsymbol{C l}_{2}+\mathbf{2} e^{-} \rightarrow \mathbf{2} \boldsymbol{C l}^{-}
\]
Given: \( \boldsymbol{P t}^{2+}+\mathbf{2} \boldsymbol{C l}^{-} \rightarrow \boldsymbol{P t}+ \)
\[
\begin{array}{l}
\boldsymbol{C l}_{2}, \boldsymbol{E}_{c e l l}=-\mathbf{0 . 1 5} \boldsymbol{V} \\
\boldsymbol{P t}^{2+}+\boldsymbol{2} e^{-} \rightarrow \boldsymbol{P t}, \boldsymbol{E}=1.20 \boldsymbol{V}
\end{array}
\]


Which will have least inertia?
\( A \). A football
B. A needle
C. A thread
D. A refrigerator


Two waves are said to have destructive
interference if
A. their frequencies are same
B. their frequencies are doubled
c. the phase difference is same
D. the phase difference is \( 180^{\circ} \)


The bond order of \( C O \) molecule on the
basis of molecular orbital theory is:
A. zero
B . 2
\( c .3 \)
D.


The diagram represents an atom 'X'. Answer the following.
f atom 'X' has 1 electron in its outer
shell, is it a non-metal.
A. True
B. False


Einstein's equation is given as-


A particle covers \( 150 \mathrm{m} \) in 8 thsecond
starting from rest, its acceleration is:
A \( \cdot 15 m / s^{2} \)
B. \( 20 m s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 8 m / s^{2} \)


Biodegradable pollutant is
A. Plastic
B. Asbestors
c. sewage
D. Mercury


Two vibrating strings of the same material but lengths \( L \) and \( 2 L \) have
radii \( 2 r \) and \( r \) respectively. They are
stretched under the same tension.
Both the strings vibrate in their fundamental modes, the one of length \( L \)
with frequency \( v_{1} \) and the other with frequency \( v_{2} . \) The ratio \( \frac{v_{1}}{v_{2}} \) is given by
\( A \cdot 2 \)
B. 4
\( c .8 \)
D.


\( \angle 1 \) and \( \angle 2 \) are adjacent angles.
It is given that \( \angle A O B=140^{\circ} . \) What is
value of \( \angle \mathbf{1}+\angle \mathbf{2} \)
A \( \cdot 210^{\circ} \)
B \( .220^{\circ} \)
\( c \cdot 230^{\circ} \)
D. \( 240^{\circ} \)


Is there any change in the hybridisation
of \( B \) and \( N \) atoms as a result of the
following reaction?
\( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow\left[\boldsymbol{F}_{3} \boldsymbol{B} \cdot \boldsymbol{N} \boldsymbol{H}_{3}\right] \)


\( 9^{t h} \) term in the expansion of
\( \left(\frac{x}{a}-\frac{3 a}{x^{2}}\right)^{12} \)
A \( \cdot^{12} C_{9} \cdot 3^{9} x^{-12} a^{6} \)
В. \( ^{12} C_{6} \cdot 3^{8} x^{-16} a^{6} \)
C \( .^{12} C_{4} \cdot 3^{8} x^{-12} a^{4} \)
D. none of the above


Draw a ray diagram for concave mirror when the object is between center of
curvature and focus


Metals extracted by electrolysis of their fused salts are :
A. highly electropositive
B. highly electronegative
c. Both A and B
D. None of the above


Molecular formula of pyrophosphoric acid is :
A. \( H_{4} P_{2} O_{7} \)
в. \( H_{4} P_{2} O_{6} .2 H_{2} O \)
c. \( H_{4} P_{2} O_{8} \)
D. \( H P O_{3} \)


A motor rated \( 500 \mathrm{W}, 230 \mathrm{V} \) utilizes 3
units of electrical energy. Calculate the time for which the motor works.


A stationary object at \( 4^{\circ} \mathrm{C} \) weighing 3.5 kg falls from a height \( 2000 \mathrm{m} \) on a snow
mountain at \( 0^{\circ} \mathrm{C} \). If the temperature of the object before comes to rest
immediately \( \left(g=10 m / s^{2}\right) \) and latent
heat of ice \( =3.5 \times 10^{6} J / s \) ), then the
object :
A. 2 gm of ice
B. 200 gm of ice
c. 20 gm of ice
D. 2 kg of ice


Which of the following is used as freezing mixture?
A. Mixture of ether and liquid \( C O_{2} \)
B. Mixture of ether and ethyl alcohol
C. Mixture of ether and dry ice
D. Mixture of ethyl alcohol and dry ice


Solve the following equation:
\( 2^{\sin ^{2} x}+2^{\cos ^{2} x}=2 \sqrt{2} \)


\( A B \) is a chord of a circle with center 0
The tangent at B cuts AO produced at T
if \( \angle B A T=25^{\circ} \) Then the value of
\( \angle B T A \) is
A . \( 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 25 \)
D. \( 40^{\circ} \)


By which of the following relations, the equilibrium constant varies with
temperature?
\( ^{\mathrm{A}} \cdot \ln K_{2}-\ln K_{1}=\frac{\Delta H^{\circ}}{R} \int_{T_{1}}^{T_{2}} d\left(\frac{1}{T}\right) \)
в. \( \ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{1 T_{1}^{1} T_{1}}^{1 / T_{2}} d\left(\frac{1}{T^{2}}\right) \)
\( ^{\mathrm{c}} \cdot \ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{T_{1}^{T_{1}}}^{T_{2}}\left(\frac{1}{T}\right) \)
D. \( _{\ln K_{2}-\ln K_{1}=-\frac{\Delta H^{o}}{R} \int_{1 / T_{2}}^{1 / T_{1}} d}\left(\frac{1}{T}\right) \)


As many as different
combination of water are possible from
\( 1 H^{1}, 1 H^{2}, 1 H^{3} \) and \( _{8} O^{16},_{8} O^{17} \) and \( _{8} O_{18} \)


What is the mode of nutrition in fungi?
A. Saprophytic
B. Holozoic
c. Parasitic
D. All of the above


A uniform magnetic field \( \vec{B}=B_{0} \hat{j} \)
exists in a space. A particle of mass \( m \)
and charge q is projected towards
negative \( x \) -axis with speed \( v \) from the a
point \( (d, 0,0) . \) The maximum value v for
which the particle does not hit \( y \) -z plane is?
\( \mathbf{A} \cdot \frac{2 B q}{d m} \)
B. \( \frac{B q d}{m} \)
\( \mathbf{c} \cdot \frac{B q}{2 d m} \)
D. \( \frac{B q d}{2 m} \)


Plane \( a x+b y+c z=1 \) intersect axes \( \operatorname{in} A, B, C \) respectively. If \( G\left(\frac{1}{6},-\frac{1}{3}, 1\right) \)
is a centroid of \( \triangle A B C \) then \( a+b+ \)
\( 3 c=-1 \)
A \( \cdot \frac{4}{3} \)
B. 4
\( c \cdot 2 \)
D.


For the cell :
\[
\begin{array}{l}
\boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z} \boldsymbol{n}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+}\right| \boldsymbol{C} \boldsymbol{u} \\
\boldsymbol{E}_{\boldsymbol{z n}}^{\ominus}=\boldsymbol{0 . 7 3 6} \boldsymbol{V} ; \boldsymbol{E}_{(c u)}^{\ominus}=-\boldsymbol{0 . 3 5} \boldsymbol{V}
\end{array}
\]
Calculate the cell EMF.


Lead nitrate of heating decomposes to give
\( 2 P b\left(N O_{3}\right)_{2} \rightarrow 2 P b O+4 N O_{2}+O_{2} \)
What is the total volume of gases
produced when 13.24 g of lead nitrate is heated? All gases are measured at STP. \( (P b=207 ; N=14 ; O=16) \)
A. 4.24 litres
B. 1.24 litres
c. 3.24 litres
D. 2.24 litres


An open box is made of 3cm thick. Its
external length, breadth, and hights are \( 1.48 \mathrm{m}, 1.16 \mathrm{m}, 8.3 \mathrm{dm} . \) Find the cost of
painting the inner surface at 50 p per \( 100 \mathrm{cm}^{2} \)


Electrical power \( P \) is given by expression : \( \boldsymbol{V} \times \boldsymbol{x} . \) What is \( \boldsymbol{x} \) ?
A. Charge
B. current
c. Resistance
D. None of these


A tap supplies water at \( 22^{0} \) C.A man
takes 1 litre per minute at \( 37^{0} \) from the
geyser. If the mains supply is \( 210 \mathrm{V} \), then the current flowing in the geyser is :
A. 7.5A
B. 2.5A
c. \( 5.0 A \)
D. 10A


Which of the following statement is true about the complex \( \left[\boldsymbol{C r} \boldsymbol{C l}_{3}(\boldsymbol{O H})_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\right]^{2-} \) ion?
This question has multiple correct options
A. It has three geometrical isomers.
B. Only one space isomers is optically active and remaining are inactive
c. There are total four space isomers.
D. The magnetic moment of complex ion is 3.89 BM.


Give two examples of root parasites of plants. Mention the special structures present in them to draw the nutrients
from the host plant.


Solve the following question:
Find the slope of the line passing through the points \( A(2,3) \) and \( B(4,7) \)


In fire extinguishers, which of the following is used?
A. \( C H C l_{3} \)
в. \( C S_{2} \)
c. \( C C l_{4} \)
D. \( C H_{2} C l_{2} \)


Two nitrogen atom form a nitrogen molecule by sharing
A. 2 pairs of electrons.
B. 3 pairs of electrons.
c. 4 pairs of electrons
D. 1 pairs of electrons


In a metre bridge experiment, null point
is obtained at \( 20 \mathrm{cm} \) from one end of the
wire when resistance \( X \) is balanced
against another resistance \( \boldsymbol{Y} \). If \( \boldsymbol{X}<\boldsymbol{Y} \)
then the new position of the null point from the same end, if one decides to
balance a resistance of \( 4 X \) against \( Y \)
will be at:
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
в. \( 80 \mathrm{cm} \)
\( \mathbf{c} .40 \mathrm{cm} \)
D. \( 70 \mathrm{cm} \)


Who proposed Lock and key hypothesis to explain the mechanism of enzymatic action?
A. Fischer
B. Jacob
c. Koshland
D. Sumner


Which of the following objects are soluble in water?
A. Fodder
B. Table salt
c. chalk powder
D. clay


When is \( P_{\text {inst}} \) negative?
A. From base to highest point.
B. From highest point to base.
c. At the base
D. At the highest point.


When conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) comes in contact with sugar, it becomes black due to
A. hydrolysis
B. hydration
c. decolourisation
D. dehydration


Munch hypothesis is based on
A. Translocation of food due to turgor pressure (TP) gradient and imbibition force
B. Translocation of food due to turgor pressure (TP) gradient
C. Translocation of food due to imbibition force
D. None of the above


Which one is required for muscle contraction and nerve impulse transmission?
A \( \cdot C a^{2} \)
в. \( M g^{2+} \)
\( \mathrm{c} \cdot F e^{2} \)
D. Both A and B


The correct sequence of plants in a hydrosere is
\( \mathbf{A} \cdot O a k \rightarrow \)Lantana\( \rightarrow V o l v o x \rightarrow H y d r i l l a \rightarrow P i s t i a \rightarrow \)
Scirpus
B. \( O a k \rightarrow \)Lantana\( \rightarrow \)Scirpus\( \rightarrow \)Pistia\( \rightarrow \)Hydrilla\( \rightarrow \)
Volvox
C . \( V \) olvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus \( \rightarrow \)
Lantana\( \rightarrow \)Oak
D. Pistia \( \rightarrow \) Volva \( \rightarrow \) Scirpus \( \rightarrow \) Hydrilla\( \rightarrow \) Oak \( \rightarrow \)
Lantana


The sound heard after reflection from a
rigid surface is
called


In adolescents, acne develops into
A. Males in response to androgen
B. Females in response to oestrogen
C. Both males and females in response to androgen
D. Both males and females in response to oestrogen


Photochemical smog brings about.
A. Defoliation
B. Bleaching and blazing of foliage
c. Floral bud shedding
D. Discolouration and curling of petals


n the adjoining figure ABC is a triangle
in which \( \mathrm{D} \) and \( \mathrm{E} \) are the mid points \( \mathrm{AB} \)
and \( A C \) respectively if \( B C=4.6 \mathrm{cm} \) then
\( D E= \)
A. \( 9.2 \mathrm{cm} \)
B. 2.3 \( \mathrm{cm} \)
\( c .5 .0 \mathrm{cm} \)
D. \( 6.4 \mathrm{cm} \)


Consider the following statements with respect to lanthanides:
1. The basic strength of hydroxides of
lanthanides increases from \( \boldsymbol{L} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{3} \)
to \( \boldsymbol{L} \boldsymbol{u}(\boldsymbol{O} \boldsymbol{H})_{3} \)
2. The lanthanide ions
\( L u^{3+}, Y b^{2+} \) and \( C e^{4+} \) are diamagnetic.
Which of the statement(s) given above is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


If \( \boldsymbol{u}=\mathbf{3}-\mathbf{5} \boldsymbol{i} \) and \( \boldsymbol{v}=-\boldsymbol{6}+\boldsymbol{i}, \) then the
value of \( (u+v)^{2} \) is
A. \( -7+24 i \)
B. \( 9+8 i \)
\( \mathrm{c} \cdot 9+16 i \)
D. \( 25-24 i \)


An uncharged metal object \( M \) is
insultated from its surroundings.A
positively charges metal sphere \( \boldsymbol{S} \) is
then brought near to \( M . \) Which diagram
illustrate the resultant distribution of
charge on \( S \) and \( M \)
\( A \)
в.
\( c \)
D.


A plano convex lens of focal length 30 \( \mathrm{cm} \) has its plane surface silvered. An object is placed \( 40 \mathrm{cm} \) from the lens on
the convex side. The distance of the
image from the lens is:
\( A \cdot 18 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


If \( f(x) \) is a polynomial in \( x, \) then
the second derivative of \( f\left(e^{x}\right) \) at \( x=1 \)
is
A \( \cdot e f^{\prime \prime}(e)+f^{\prime}(e) \)
B . \( \left(f^{\prime \prime}(e)+f^{\prime}(e)\right) e^{2} \)
c. \( e^{2} f^{\prime \prime}(e) \)
D. \( \left(f^{\prime \prime}(e) e+f^{\prime}(e)\right) e \)


Who is know as father of Genetics?


\( H C l \) can be used to remove rust from
iron.
A. True
B. False


The degree of unsaturation in the
structure of the product is:


For the change, \( C_{\text {diamond}} \longrightarrow \)
\( C_{g r a p h i t e} ; \Delta H=-1.89 k J, \) if \( 6 g \) of
diamond
and \( 6 g \) of graphite are separately burnt
to yield \( C O_{2} \) the heat liberated in first
case is:
A. Less than in the second case by \( 1.89 k J \)
B. Less than in the second case by \( 11.34 k J \)
c. Less than in the second case by \( 14.34 k J \)
D. More than in the second case by \( 0.945 k J \)


A plano-convex lens fits exactly into a plano-concave lens. Their plane surface are parallel to each other. If lenses are
made of different materials of refractive
indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is the radius
of curvature of the curved surface of the
lenses, then the focal length of the combination is
A.
\[
\frac{R}{2\left(\mu_{1}+\mu_{2}\right)}
\]
B.
\[
\frac{R}{2\left(\mu_{1}-\mu_{2}\right)}
\]
c. \( \frac{R}{\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{\left(\mu_{2}-\mu_{1}\right)} \)


A square and a regular hexagon have equal perimeters. Their areas are in the
ratio:
A .2: 1
B. \( 2 \sqrt{3}: 1 \)
c. \( \sqrt{3}: 2 \)
D. 3: 2


Two unbiased dice are rolled once. Find
the probability of getting a doublet.
A \( \cdot \frac{1}{6} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{2}{3} \)
D.


\( P \) makes a bet with \( Q \) of 8 pounds to
120 pounds that three races will be won by the three horses \( A, B, C, \) against which the betting is 3 to 2,4 to \( 1, \) and 2 to 1 respectively. The first race having been a on by \( A \), and it being known that
the second race was won either by \( B \), or
by a horse \( D \) against which the betting
was 2 to 1 , find the value of \( P^{\prime} s \)
expectation.


Chemical equilibrium for a reversible
change means for:
This question has multiple correct options
A. the forward reaction proceeds as fast as the backward reaction, i.e., velocity of opposing reaction is equal
B. no change in concentration of reaction species with time
C . dynamic equilibrium
D. none of the above


List I contains either an action or an
observation. Match each of these,
respectively to the correct effect, or a reason from list II.
List 1 List II
\( a \)
. Two rotating discs
e. Generated force of in contact- friction is equal to are brought in contact-
coaxially
b. A contact force
exists between exists between
a rough surface and
body placed on it y placed on it d a partially into heat
Attributed to g. resultant of "
" I reaction and c. For a body on a rough
surface, maintaining
motion is easier
as compared to
initiating it normal coefficient of
friction between t the surfaces

Is \( \quad \) h. As kinetic friction \( \begin{array}{l}\text { d. Static friction is } \\ \begin{array}{l}\text { less than limiting } \\ \text { friction }\end{array} & \begin{array}{l}\text { h. AS } \\ \text { is less than static } \\ \text { friction }\end{array}\end{array} \)
\( A \cdot a-f, b-g, c-h, d-e \)
B. a-g, b-f, c-e, d-h
c. a-h, b-e, c-f, d-g
D. a-e


A card is drawn from the pack of 25
cards labelled with numbers 1 to 25
Write the sample space for this random experiment.


The distance of the point (1,-2,3)
from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
measured parallel to the line whose direction cosines are proportional to
2,3,-5 is
A \( \cdot \frac{9}{7} \)
B. \( \frac{11}{7} \)
c. \( \frac{15}{7} \)
D. None of these


If \( |\vec{a}|=3,|\vec{b}|=4, \) then a value of \( \lambda \) for which \( \vec{a}+\lambda \vec{b} \) is perpendicular to \( \vec{a}- \) \( \lambda \vec{b} \) is
A \( \cdot \frac{9}{16} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{4}{3} \)


The correct order of decreasing polarity
¡s:
\( \mathbf{A} \cdot H F>S O_{2}>H_{2} O>N H_{3} \)
B \( \cdot H F>H_{2} O>S O_{2}>N H_{3} \)
\( \mathbf{C} \cdot H F>N H_{3}>S O_{2}>H_{2} O>H F \)
D. none of the above


The solution of the differential equation
\( \boldsymbol{x} \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{y}-\left(\boldsymbol{x}^{3}+\boldsymbol{y}^{3}\right) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \) is
A \( \cdot y^{3}=3 x^{3}+c \)
B . \( y^{3}=3 x^{3} \log (c x) \)
c. \( y^{3}=3 x^{3}+\log (c x) \)
D. \( y^{3}+3 x^{3}+\log (c x) \)


Prove that if the lengths of two altitudes of a triangle are equal, then the triangle is isosceles.


The numbers of lone pair(s) on Xe in
\( X e F_{2} \) and \( X e F_{4} \) are, respectively:
A. 2 and 3
B. 4 and 1
c. 3 and 2
D. 4 and 2


Let \( \boldsymbol{A}=\{1,2,3, \dots, 10\} \) and \( B= \)
\( \{101,102,103, \dots, 1000\} . \) Then set \( A \)
and \( B \) are
A. Both finite sets
B. Infinite and finite set respectively
c. Both Infinite sets
D. Finite and infinite set respectively


The operating temperature of the filament of lamp is \( 2000^{\circ} \mathrm{C} \). The temperature coefficient of the material
of filament is \( 0.005 /^{\circ} \mathrm{C} \). If the
atmospheric temperature be \( 0^{\circ} C, \) the current in the \( 100 \mathrm{W} \) and \( 2000 \mathrm{V} \) lamp when it is switched on its nearest to:
A. 2.5
B. 0.05 A
c. 4.5 A
D. \( 5.5 \mathrm{A} \)


What is hybridization?
A. The mixing of two or more atomic orbitals to form new orbitals that describe the covalent bonding in molecules.
B. The mixing of electrons in the electron sea model to account for the number of bonds in a molecule.
C. The mixing of two or more atomic orbitals to form new orbitals that describe the location of electrons in
atoms.
D. The mixing of two or more molecules
E. The mixing of two or more atoms to make a new compound or molecule.


Draw. Wheatstone's bridge circuit and write the condition for its balance.


Albert Einstein used corpuscular theory to explain:
A \( . E=m c^{2} \)
B. The photoelectric effect
c. Quantisation of charge
D. magic of light


The resistivity of a wire varies with its
A . length
B. cross-section
c. mass
D. material


The Big Bang Theory explains:
A. the beginning of life
B. origin of the universe
c. law of Gravity
D. why the universe was created


Difference between oxidation and
reduction


Discuss the continuity of the following function \( : f(x)=\sin x . \cos x \)


\( f ; A \rightarrow B \) defined by \( f(x)=2 x+3 \)
and if \( \boldsymbol{A}=\{-\mathbf{2},-\mathbf{1}, \mathbf{0}, \mathbf{1}, \mathbf{2}\}, \boldsymbol{B}= \)
\( \{-1,1,3,5,7\}, \) then which of function
is f?
A. One-one
B. onto
c. Bijection
D. constant


Assertion
Agriculture output increased several
times after introduction of DDT.
Reason
DDT was the first insecticide used on a
wide scale.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If \( \vec{A}+\vec{B} \) is a unit vector along \( x \) -axis and \( \vec{A}=\hat{i}-\hat{j}+\hat{k} \) then what is \( \vec{B} ? \)
\( \mathbf{A} \cdot \hat{j}+\hat{k} \)
B. \( \hat{j}-\hat{k} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( \hat{i}+\hat{j}-\hat{k} \)


During the formation of \( N a C l \), transfer
of electron is from \( X \) orbital of \( N a \) to
the \( Y \) orbital of \( C l . \) Then \( X \) and \( Y \) are
respectively:
A. \( 3 s \) and \( 3 s \)
B. \( 3 s \) and \( 3 p \)
c. \( 3 p \) and \( 3 s \)
D. \( 3 p \) and \( 3 p \)


Give the characteristics of free energy.


What is the number of outcomes when
a coin is tossed and then a die is rolled
only in case a head is shown on the
coin?
A . 6
B. 7
c. 8
D. None of the above


The diagram in Fig. shows the displacement- time graph of a vibrating
body. Why is the amplitude of vibrations
gradually decreasing?


f \( \boldsymbol{P Q \perp P S}, \boldsymbol{P Q} \| \boldsymbol{S R}, \angle \boldsymbol{S O R}=\mathbf{2 8}^{\boldsymbol{o}} \)
and \( \angle Q R T=65^{\circ}, \) then find \( x \& y \)


Give reasons for the following observations:
(i) Leather gets hardened after tanning.
(ii) Lyophilic sol is more stable than Iyophobic sol.
(iii) It is necessary to remove \( \mathrm{CO} \) when ammonia is prepared by Haber's
process.


The atomic number of an element
having 12 neutrons and a mass number of 23 is equal to:
A. \( z=1 \)
B. \( z=12 \)
\( c \cdot z=10 \)
D. \( z=13 \)


Charge density is a measure of electric charge per unit volume of
space,
A. in one dimension
B. in two dimensions
c. in three dimensions
D. All of the above


One of the following represents feed
back inhibition
A. Reaction of snake venom with neuro - transmitter
B. Malate inhibiting succinic dehydrogenase
C . Cyanides inhibiting cytochrome a
D. Allosteric compound ATP inhibiting hexokinase enzyme


Simultaneous solubility of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N} \boldsymbol{S}(\boldsymbol{a}) \)
and \( A g B r(b) \) in a solution of water will
be
\( \boldsymbol{K}_{s p_{(A g B r)}}=\mathbf{5} \times \mathbf{1 0}^{-13} \) and \( \boldsymbol{K}_{s p_{(A g C N S)}}= \)
\( 10^{-12} \)
A \( \cdot a=4.08 \times 10^{-7} \) mol litre \( ^{-1} ; b=8.16 \times 10^{-7} \) mollitre \( ^{-1} \)
В . \( a=4.08 \times 10^{-7} \) mol litre \( ^{-1} ; b=4.08 \times 10^{-7} \) mollitre \( ^{-1} \)
\( \mathbf{c} \cdot a=8.16 \times 10^{-7} \)mollitre\( ^{-1} ; b=4.08 \times 10^{-7} \)mollitre\( ^{-1} \)
D. None of these


Which of the following is the inverse of the proposition : 'If a number is a prime then it is odd"?
A. If a number is not a prime then it is odd
B. If a number is not a prime then it is not odd
c. If a number is not odd then it is not prime
D. If a number is odd then it is a prime


A force of \( 10 N \) is applied along \( x- \) axis calculate amount of work done to
displace body from (2,3) to (-1,4)


What is the activation energy for the reverse of this reaction?
\( N_{2} O_{4}(g) \longrightarrow 2 N O_{2}(g) \)
Data for the given reaction is: \( \Delta \boldsymbol{H}= \)
\( +54 k J \) and \( E_{f}=+57.2 k J \)
A \( .-54 k J \)
в. \( +3.2 k J \)
\( \mathbf{c} .+60.2 k J \)
D. \( +111.2 k J \)


An increase in pressure will change the equilibrium by:
A. shifting to the side where a smaller volume results
B. shifting to the side where a larger volume results
C. favoring the endothermic reaction
D. favoring the exothermic reaction
E. none of the above


\( \underset{92}{238} U(I I I B) \) changes to \( 284 T h \) by emission of \( \alpha \) -particle. Daughter element will be in:
A . IIIB
в. \( I B \)
c. \( V B \)
D. IIA


Ratio of \( S I \) unit of torque to its CGS unit is
\( \mathbf{A} \cdot 10^{5}: 1 \)
B . \( 10^{7}: 1 \)
\( \mathbf{c} \cdot 10^{6}: 1 \)
D. \( 10^{17}: 1 \)


Arrange the elements in increasing order of atomic radius \( \mathrm{Na}, \mathrm{Rb}, \mathrm{K}, \mathrm{Mg} \)
A. \( \mathrm{Na}<\mathrm{K}<\mathrm{Mg}<\mathrm{Rb} \)
B. \( K<N a<M g<R b \)
\( \mathrm{c} \cdot \mathrm{Mg}<\mathrm{Na}<\mathrm{K}<\mathrm{Rb} \)
D. \( R b<K<M g<N a \)


Explain why apparatus for laboratory preparation of hydrogen should be air tight and away from a naked flame?


Subtract the sum of \( 36-4 m-7 x^{2} \)
and \( 2 t-3 m-4 x^{2} \) from the sum of
\( 96+2 m-3 x^{2} \) and \( -36+m+4 x^{2} \)


SONAR can be used
A. for determination of a depth of a sea
B. in the ships to locate underwater rocks, icebergs
C. to measure distance, direction and speed of underwater objects, such as hills,valleys etc
D. for all the above


Observe the following reaction \( : 2 A+ \)
\( B \rightarrow C . \) The rate of formation of \( C \) is
\( 2.2 \times 10^{-3} \) mol \( l^{-1} \) min \( ^{-1} . \) The is the
value of \( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}\left(\text { in } \boldsymbol{m o l} \boldsymbol{l}^{-1} \boldsymbol{m} \boldsymbol{i} \boldsymbol{n}^{-1}\right) \)
A \( .2 .2 \times 10^{-3} \)
В. \( 1.1 \times 10^{-3} \)
c. \( 4.4 \times 10^{-3} \)
D. \( 5.5 \times 10^{-3} \)


A string of length \( 0.5 m \) carries a bob
with a period \( 2 \pi s . \) Calculate the angle of
inclination of string with vertical and
tension in the string.


Exactly 6 on each of 3 successive throws
A \( \cdot \frac{5^{3}}{16^{3}} \)
в. \( \frac{5}{16^{3}} \)
c. \( \frac{5^{2}}{16^{3}} \)
D. \( \frac{1}{16^{3}} \)


Q Type your questior
perpendicular to a constantmagnetic
field of magnitude \( 1 \mathrm{T} \) as shown in figure. One end of a resistanceless rod is
hinged at thecentre of ring 0 and other
end is placed on the ring. Now rod is rotated with constant angular velocity \( 4 \mathrm{rad} / \mathrm{s} \) by some external agent and circuit is connected as shown in the
figure, initially switch is open andcapacitor is uncharged. If switch S
is closed at \( t=0, \) then calculate heat
\( \operatorname{loss}(\operatorname{in} \mu \mathrm{J}) \) from the resistor \( \boldsymbol{R}_{1} \) from \( \mathrm{t} \)
\( =0 \) to the instant when voltage across the capacitor becomes half of steady state voltage. (Assume plane of ring to be horizontal and friction to be absent
at all the contacts)


The construction of \( \triangle A B C \) in which
\( A B=6 \mathrm{cm}, \angle A=30^{\circ}, \) is not possible
when \( \boldsymbol{A C}+\boldsymbol{B C}= \)
\( \mathbf{A} \cdot 6.3 \mathrm{cm} \)
B. \( 7.2 \mathrm{cm} \)
\( c .5 .6 \mathrm{cm} \)
D. \( 6.9 \mathrm{cm} \)


Represent the following data using a suitable graphical representation.
\( \begin{array}{lllll}\text { class- } & 0- & 5- & 10- & 1 \\ \text { intervals } & 5 & 10 & 15 & 2\end{array} \)
Frequency \( \begin{array}{ll}\text { 1. } & 5\end{array} \) 6


Consider the following pairs of quantities:
1. Young's modulus; pressure
2. Torque; energy
3. Linear momentum; work
4. Solar day; light year In which cases are the dimensions,
within a pair, same?
A . 1 and 3
B. 1 and 4
\( c \cdot 1 \) and 2
D. 2 and 4


Select the correct answer from the
choices given below. The three states of
matter are classified on the basis of
differences of certain
A. chemical properties
B. physical properties
c. physical and chemical properties
D. none of the above


\( \boldsymbol{T} \boldsymbol{i}^{3+}(\boldsymbol{a} \boldsymbol{q}) \) is purple while \( \boldsymbol{T} \boldsymbol{i}^{4+}(\boldsymbol{a} \boldsymbol{q}) \) is
colourless because:
Tetrahedral field
A. there is no crystal field effect in \( T i^{4-} \)
B. there energy difference between \( t_{2 g} \) and \( e_{g} \) of Tir\{ \( 4-3 \$ \$ \) is quite high and does not fall in the visible region
\( \mathrm{C} \cdot T i^{4-} \) has \( d^{0} \) configuration.
D. \( T i^{4-} \) is very stabilization energy for \( \left[C o F_{6}\right]^{3-} \) in terms of parameter Dq is - \( (\Delta=100 D q) \)


A perpendicular force is applied to a
certain area and produces a pressure \( \boldsymbol{P} \) If the same force is applied to a twice bigger area, the new pressure on the surface is:
A \( \cdot \frac{P}{2} \)
в. \( \frac{P}{3} \)
c. \( \frac{P}{4} \)
D. none


Observe the following patterns \( \mathbf{1}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{1} \times(\mathbf{1}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{2} \times(\mathbf{2}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}+\mathbf{3}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{3} \times(\mathbf{3}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{4} \times(\mathbf{4}+\mathbf{1})) \)
and find the value of each of the
following
\[
\mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\ldots+\mathbf{5 0}
\]


Write an essay on growth regulation in plants.


If \( \mathbf{3} \boldsymbol{A}-\mathbf{2 B}=\left(\begin{array}{cc}\mathbf{1} & \mathbf{- 2} \\ \mathbf{3} & \mathbf{0}\end{array}\right) \) and \( \mathbf{2} \boldsymbol{A}- \)
\( \mathbf{3} \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{- 3} & \mathbf{3} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right) \) then find \( \boldsymbol{B} \)


The transfer of energy in mechanical waves happens through molecules
A. through collisions
B. through interactions
c. through cohesive forces
D. through electrical forces


How many meiotic divisions are required for the formation of 50
zygotes?
A. 62
B. 63
\( c \cdot 61 \)
D. 50


Which among the given haloalkanes develop colour when exposed to light?
A. \( R-B r \) and \( R-C l \)
B. \( R-I \) and \( R-F \)
c. \( R-C l \) and \( R-B r \)
D. \( R-B r \) and \( R-I \)


The density of a \( 3 \mathrm{M} \) solution of NaCl is 1.25g/ml. Calculate the molality of the solution.


The total number of electrons that take
part in forming the bond in \( N_{2} \) is :
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 10


The following reactions take place in the blast furnace in the preparation of impure iron.Identify the reaction pertaining to the formation of the slag.
A \( \cdot 2 C(s)+O_{2}(g) \rightarrow 2 C O(g) \)
B. \( F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(\ell)+3 C O_{2}(g) \)
c. \( C a C O_{3}(s) \rightarrow C a O(s)+C O_{2}(g) \)
D. \( \operatorname{CaO}(s)+\operatorname{Si} O_{2}(s) \rightarrow \operatorname{CaSiO}_{3}(s) \)


Phosphate pollution is caused by:
A. weathering of phosphate rocks only
B. agriculatural fertilizers only
C . phosphate rocks and sewage
D. sewage and agricultural fertilizers


A 0.1 molal solution of a monobasic
acid is \( 45 \% \) ionized. Calculate the
depression in freezing point:
(Molecular weight of the acid \( =300 \)
\( \left.\mathrm{g} / \mathrm{mol}, \boldsymbol{K}_{f}=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g}\right) \)
A \( .--0.199^{\circ} \mathrm{C} \)
B . \( 2.00^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 0^{\circ} \mathrm{C} \)
D. \( 0.269^{\circ} \mathrm{C} \)


An object is thrown from the height of \( 125 \mathrm{cm} \) take \( \mathrm{g}=10 \mathrm{m} / \mathrm{s} \). Find the ratio of distance covered by object in the 1 st and last 1 sec
A . 1: 9
B. 4:
\( c \cdot 4: 4 \)
D. 2:


Which meristem does produce growth in length?


What mass of solid ammonium
carbonate \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C O O N} \boldsymbol{H}_{4}, \) when
vaporized at \( 273^{\circ} C, \) will have a volume
of 8.961 at \( 760 m m \) of pressure.
Assume that the solid completely
decomposes as
\( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C O O N} \boldsymbol{H}_{4}(\boldsymbol{s}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
A . \( 15.6 g \)
в. \( 5.2 g \)
c. \( 46.8 g \)
D. \( 7.8 g \)


A person cannot clearly see objects farther than \( 12 \mathrm{m} \) from the eye. Name the defect in vision he is suffering from
and the lens that should be used to
correct this defect.


Major product of this reaction:
(A)
\( A \)
B.
\( c \)
D.


The measured mass and volume of a
body are \( 53.63 g \) and \( 5.8 \mathrm{cm}^{3} \) respectively, with possible errors of \( 0.01 g \) and \( 0.1 \mathrm{cm}^{3} . \) The
maximum percentage error in density is about:
A . \( 0.2 \% \)
в. \( 1.74 \% \)
c. \( 5 \% \)
D. \( 10 \% \)


If the ratio of lengths, radii and Young's modulus of steel and brass wires shown
in the figure are \( a, b \) and \( c \) respectively, the ratio between the increase in
lengths of brass and steel wires would
be :
A \( \cdot \frac{b^{2}}{2 c} \)
в. \( \frac{b c}{2 a^{2}} \)
\( c \cdot \frac{b a^{2}}{2 c} \)
D. \( \frac{2 b^{2} c}{a} \)


Find the acceleration of a particle placed on the surface of the earth at the equator due to the earth's rotation. The
diameter of the earth is \( 12800 \mathrm{km} \) and
it takes 24 hours for the earth to
complete one revolution about its axis.


The particle of mass \( m \) and charge \( q \) will touch the infinitely large plate of uniform charge density \( \sigma \) if its velocity \( v \) is more than:(Given that \( \sigma q>0 \) )
A . 0
в. \( \sqrt{\frac{4 \sigma q d}{m \varepsilon_{0}}} \)
c. \( \sqrt{\frac{\sigma q d}{m \varepsilon_{o}}} \)
D. none of these


The intensity of an electric field at some point distant \( r \) from the axis of infinity long pipe having charged per unit length as q will be:
A. Proportional to \( r^{2} \)
B. Proportional to \( r^{3} \)
c. inversely proportional to \( r \)
D. inversely Proportional to \( r^{2} \)


Complete the following equations:
(i) \( P_{4}+H_{2} O \rightarrow \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{O}_{2} \boldsymbol{F}_{2} \rightarrow \)


In the given figure, find the area of the shade region. [use \( \pi=22 / 7 \text { ] [use } \pi=227] \)


In III group precipitation, \( N H_{4} C l \) is
added before adding \( N H_{4} O H \) to
A . Decrease conc. of \( O H^{-} \)
B. Prevent interference of \( P O_{4}^{3-} \)
c. Increase conc. of \( C l^{-} \)
D. Increase conc. of \( O H^{-} \) ion


PQRS is a parallelogram and PA, SB, RC,
QD are angle bisectors. If \( P Q=Q D=6 \)
units, find \( \boldsymbol{m} \angle \boldsymbol{P Q R} \)
\( A \cdot 30^{\circ} \)
B. 60
\( c \cdot 120 \)
D. Indeterminate


Which one of the following sets of quantum numbers represents the highest energy level in an atom?
B. \( n=3, l=1, m=1, s=+1 / 2 \)
c. \( n=3, l=2, m=-2, s=+1 / 2 \)
D. \( n=3, l=0, m=0, s=+1 / 2 \)


The efficiency of the heat engine is
A . 75\%
B. 33\%
c. 50\%
D. 25\%
E . \( 100 \% \)


Assertion
The electrical resistance of any object decreases with increase in its length.
Reason
Electrical resistance of any object
increases with increase in its area of
cross-section.
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


\( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}-\{1,2,3\} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{3} \) is
A. one-one only
B. onto only
c. bijective
D. neither one-one nor onto


Assertion
\( \boldsymbol{H}_{2}+\boldsymbol{O}_{2} \) fuel cell gives a constant
voltage throughout its life.
Reason
In this fuel cell, \( H_{2} \) reacts with \( O H^{-} \) ions, yet the overall concentration of
\( O H^{-} \) ions does not change.
A. assertion is true, reason is true; reason is correct explanation for assertion.
B. assertion is true, reason is true; reason is NOT a correct explanation for assertion
c. assertion is true, reason is false
D. assertion is false, reason is true


The alkali metal which acts as a
nutrient for plants is:
A. \( N a \)
в. \( K \)
\( c \cdot L i \)
D. \( R b \)


Choose the correct answer from the
alternatives given Hypothyroidism in children results in:
A. dwarfism
B. acromegaly
c. high blood pressure
D. high body temperature


Why do we apply paint on iron articles?


A chemical process in which a
substance reacts with oxygen to give off heat is called?
A . lgnition
B. Combustion
c. conduction
D. None of the above


According to the formula, what will be t
he number of plants two years from now if \( K=4000 \) (Round your answer to the
nearest whole number.)


Isotope of which metal is used in cancer therapy?
A . \( R a \)
в. \( N i \)
c. \( P_{o} \)
D. \( C o \)


The angle between magnetic meridian
and geographical meridian is known as:
A. magnetic dip
B. magnetic latitude
C. magnetic declination
D. magnetic longitude


How many moles of sodium chloride are
present in a sample that has a mass of \( 1.17 g ? \)
A. 0.005 mol
B. \( 0.01 \mathrm{mol} \)
c. 0.02 mol
D. 0.03 mol


The metallic cuboid \( 100 \mathrm{cm} \times 80 \mathrm{cm} \times \)
\( 64 \mathrm{cm} \) is recast into a cube. The surface
area of the cube is
A \( \cdot 19200 \mathrm{cm}^{2} \)
B. \( 31600 \mathrm{cm}^{2} \)
c. \( 38400 \mathrm{cm}^{2} \)
D. \( 25600 \mathrm{cm}^{2} \)


Prove that \( : \sin ^{-1}\left(\frac{5}{13}\right)+ \)
\( \cos ^{-1}\left(\frac{4}{5}\right)=\frac{1}{2} \sin ^{-1}\left(\frac{3696}{4225}\right) \)


If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) are in A.P. show that \( \cot \boldsymbol{\beta}= \)
\( \frac{\sin \alpha-\sin \gamma}{\cos \gamma-\cos \alpha} \)


Find the square root of the following number by factorisation.
\( \mathbf{1 1 5 6} \)


2.5 litre of \( 1 \mathrm{M} \) NaOH solution mixed
with another 3 litre of \( 0.5 ~ M \) NaOH
solution. Then find out molarity of resultant solution.
в. \( 1.0 \mathrm{M} \)
c. 0.73 М
D. \( 0.50 M \)


Zeroth law of thermodynamic signifies:
A . Mass
B. Heat
c. Temperature
D. Inertia


Find :
\( \int \frac{2}{(1-x)\left(1+x^{2}\right)} d x \)


A compound of platinum, ammonia and chlorine produces which complex
compound?


Prokaryotic cells are characterised by
A. Absence of nuclear envelope
B. Presence of nuclear envelope
C. Presence of distinct chromosome
D. Absence of chromatin material


Find the frequency of 1 MeV photon. Given wavelength of a \( 1 \mathrm{keV} \) photon is \( 1.24 \times 10^{-9} m \)
Hint: \( \boldsymbol{E}=\boldsymbol{h} \boldsymbol{\nu} \)


Assertion
It is hotter over the top of a fire than at the same distance of the sides.
Reason
Air surrounding the fire conducts more heat upwards.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the following sequence of reactions, identify the end product (D). \( N a_{2} C O_{3} \stackrel{S O_{2}}{\rightarrow}(A) \stackrel{N a_{2} C O_{3}}{\longrightarrow}(B) \)
Elemental \( S, \Delta \)
\( (\boldsymbol{C}) \stackrel{\boldsymbol{I}_{2}}{\rightarrow}(\boldsymbol{D}) \)
A \( \cdot N a_{2} S O_{4} \)
в. \( N a_{2} S_{4} O_{6} \)
c. \( N a_{2} S \)
D. \( N a_{2} S_{2} O_{3} \)


In the following triplet pythagorean? show working (18,79,82)


A \( 10 \% \) solution of \( N a C l \) means that in
\( 100 g \) of solution there is:
A. \( 5.85 g \) NaCl
в. \( 58.5 g \) NaCl
c. \( 10 g \) NaCl
D. \( 94 g \) NaCl


For a solution of density, \( d \) in \( g / m \) containing solute of molecular weight \( W, \) the molarity \( M \) and molality \( m \) are
related by:
A \( \cdot \frac{d}{M}=\frac{1}{m}+\frac{W}{1000} \)
в. \( \frac{d}{m}=\frac{1}{M}+\frac{W}{1000} \)
c. \( \frac{W}{M}=\frac{1}{m}+\frac{d}{1000} \)
D. \( \frac{d}{m}=\frac{W}{M}+\frac{1}{1000} \)


An ellipse with centre (0,0) cuts y axis \( \operatorname{at}(0,6) \) and \( (0,-6) . \) If its \( e=\frac{\sqrt{3}}{2} \) then the length of major axis is:
A . 18
B. 36
c. 20
D. 24


Let \( R \) be a reflexive on a finite \( \operatorname{set} A \)
having \( n \) elements, and let there be \( m \)
ordered pairs in \( R \) Then
A \( . m \geq n \)
в. \( m \leq n \)
c. \( m=n \)
D. None of these


What are inter halogen compounds? Give one preparation.


The hormone that promotes rapid elongation of intermodes or leaf base in deep water rice plant is
A. Abscisic acid
B. Ethylene
c. cytokinin
D. Gibberellin


Assume that the potential energy of a hydrogen atom in its ground state is
zero. Then its total energy in the first
excited state will be:
A . \( 13.6 e V \)
в. 27.2eV
c. \( 23.8 e V \)
D. \( 10.2 e V \)


State whether the following statements
are true or false.
Climax indicates a final and stable community in a successional series
A. True
B. False


Number of elements in Lanthanide
family is:


In the figure \( Q-26 \) the potential at \( A \) is
when the potential at B is zero.