Consider the cell:
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}), \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s})|\boldsymbol{K} \boldsymbol{C l}(\boldsymbol{0} \cdot \mathbf{1} \boldsymbol{M})| \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2}(\boldsymbol{s}) \)
The cell potential
This question has multiple correct options
A . increases on increasing concentration of \( C l^{-} \) ions
B. decreases on decreasing concentration of \( C l^{-} \) ions
c. is independent of concentration of \( C l^{-} \) ions.
D. is independent of amounts of \( A g C l \) and \( H g_{2} C l \)


Which of the following sugar is found in
ATP?
A. Deoxyribose
B. Ribose
c. Trehalose
D. Glucose


Find the product of:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}}+\underset{(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s})} \rightarrow ? \)
\( \mathbf{A} \cdot O H-C H_{2} C H_{2} O H, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}-I \)
B \( \cdot C_{6} H_{5} C H_{2}-O H, C H_{3} C H_{2}-I, I-C H_{2} C H_{2}-O H \)
\( \mathbf{c} \cdot I-C H_{2} C H_{2}-I, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}-O H \)
D. \( H O-C H_{2} C H_{2}-O H, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}- \)
\( O H \)


Kepler's third law of planetary motion states that : (Symbols have their usual
meaning)
A. \( V_{0}=\sqrt{R g} \)
B . \( \overrightarrow{F_{12}}=-\overrightarrow{F_{21}} \)
\( \mathbf{c} \cdot r^{2} \propto T^{3} \)
\( \mathbf{D} \cdot r^{3} \propto T^{2} \)


Always in a physical quantity, the numerical value is inversely proportional to its units. \( N \propto \frac{1}{U} \)


Choose the correct answer from the
alternatives given. An electromagnetic wave of frequency \( \nu=3 M H z \) passes from vacuum into
a dielectric medium with permittivity
\( \varepsilon=4 . \) Then
A. wavelength and frequency both become half.
B. wavelength is doubled and frequency remains unchanged
c. wavelength and frequency both remain unchanged.
D. wavelength is halved and frequency remains unchanged


Describes a solution containing solute particles of intermediate size that do
not settle but do scatter light
A. Miscible
B. Suspension
c. colloid
D. Saturated
E. Supersaturated


An artificial satellite moves in a
circular orbit around the earth. Total
energy of the satellite is given by \( \boldsymbol{E} \). The
potential energy of the satellite is:
A . \( -2 E \)
в. \( 2 E \)
c. \( \frac{2 E}{3} \)
D. \( -\frac{2 E}{3} \)


Kieselguhr contains:
A. carbon
B. silicon
c. boron
D. iodine


The colour of ammonium
phosphomolybdate is:
A. green
B. yellow
\( c . \) bhue
D. colourless


\( \boldsymbol{A}(\mathbf{5}, \mathbf{7}), \boldsymbol{B}(\mathbf{4}, \mathbf{1 2}), \boldsymbol{C}(\mathbf{9}, \mathbf{1 1}) \) and \( \boldsymbol{D}(\mathbf{1 0}, \mathbf{6} \)
are four points. Show that \( A B C D \) is a
rhombus


Construct the logic symbol, Boolean expression, circuit diagram and truth
table for an OR gate.


A copper wire of \( 3 m m^{2} \) cross sectional
area carries a current of 5 ampere. The magnitude of the drifty velocity for the electrons in the wire, (Assume copper to
be monovalent, \( M_{C u}=63.5 k g / k \) mol
and density of copper \( =\mathbf{8 9 2 0} \mathbf{k g} / \mathbf{m}^{\mathbf{3}} \) ).
A. \( 0.24 \mathrm{m} / \mathrm{s} \)
В. \( 0.12 \mathrm{m} / \mathrm{s} \)
c. \( 2.4 \mathrm{m} / \mathrm{s} \)
D. \( 0.06 \mathrm{m} / \mathrm{s} \)


What do you understand by the term
latent heat?


A stick is thrown in the air and lands on
the ground at some distance from the
thrower. The centre of mass of the stick
will move along a parabolic path
A. in all cases
B. only if the stick is uniform
c. only if the stick has linear motion but no rotational motion
D. only if the stick has a shape such that its centre of


Rutherford in his atomic model could
not explain behaviour of :
A. electrons
B. protons
c. neutrons
D. neutrino


The areas of two similar triangles are \( 81 \mathrm{cm}^{2} \) and \( 49 \mathrm{cm}^{2} \) respectively. Find
the ratio of their corresponding heights. What is the ratio of their corresponding medians?


Two coherent sources separated by
distance d are radiating in phase having wavelength \( \lambda \). A detector moves
in a big circle around the two sources in
the plane of the two sources. The angular position of \( n=4 \) interference maxima is given as
A \( \cdot \sin ^{-1} \frac{n \lambda}{d} \)
B. \( \cos ^{-1} \frac{4 \lambda}{d} \)
c. \( \tan ^{-1} \frac{d}{4 \lambda} \)
D. \( \cos ^{-1} \frac{\lambda}{4 d} \)


Given \( \sin \phi=\frac{15}{17}, \) find the value of \( \frac{3-4 \sin ^{2} \phi}{4 \cos ^{2} \phi-3} \)


On basis of which theory Langmuir
derived isotherm equation?
A. Collosion theory
B. Kinetic theory of gases
c. Thermodynamics
D. wave mechanic theory


Fruit in members of Solanaceae is
A . Drupe
B. Capsule or berry
c. siliqua
D. Pod or achene


An induced emf has
A. A direction same as field direction
B. A direction opposite to the field direction
C. No direction of its own
D. Non of these


An isosceles right-angled prism and a
convex lens (focal length \( =40 \mathrm{cm} \) ) are
placed as shown in the above figure,
and a \( 5 \mathrm{cm} \) wide strip with the letter
LIGHT' written on it placed as indicated.
What is the nature and position of the
image formed after refraction through the prism and the lens?
[Given the critical angle of the glass
used for the prism and the lens is \( 42^{\circ} . \)


Assertion
The solutions which show large positive
deviations from Raoult's law form
maximum boiling azeotropes.
Reason
\( 95 \% \) aqueous solution of ethanol is maximum boiling azeotrope
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


Two protons and two neutrons combine to form a nucleus of \( _{2} H e^{4} . \) Find the energy released during the process. Take masses of proton, neutron and helium nuclues as
\( \mathbf{1 . 0 0 7 u}, \mathbf{1 . 0 0 9 u}, \mathbf{4 . 0 0 2 u} \) respectively
B. 84.67 MeV
c. 94.82 Mev
D. 24.12 Mev


A catalyst :
A. Changes \( \Delta G \) for an equation
B. Acts by increasing the rate of the forward reaction more than the reverse reaction
C. Raises the equilibrium constant of a system
D. May have molecular weight as low as 1 or higher than 200,000
E. Does not react chemically during the course of a reaction


A square and an equilateral triangle have the same perimeter. If the diagonal of the square is \( 12 \sqrt{2} \mathrm{cm} \), then the area
of the triangle is:
A \( \cdot 24 \sqrt{3} \mathrm{cm}^{2} \)
B \( \cdot 24 \sqrt{2} \mathrm{cm}^{2} \)
c. \( 64 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 32 \sqrt{3} \mathrm{cm}^{2} \)


The same kinds of plants growth and
cultivated on a large scale at place is called


If a man is walking, then the direction of
friction is:
A. opposite to direction of motion
B. same as that of direction of motion.
c. perpendicular to direction of motion.
D. \( 45^{\circ} \) to the direction of motion


Solve \( \frac{1}{1.3}+\frac{2}{1.3 .5}+\frac{3}{1.3 .5 .7}+ \)
\( \frac{4}{1.3 .5 .7 .9}+\dots \)


How many significant characteristics are defined for the pressure exerted on fluids by container?
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
D.


Early blight of potato is caused by
A. Fusarium
B. Alternaria
c. Pythium
D. Cercospora


Find out the number of dimerize
products obtained by following reaction \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C l}+\boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2}-\boldsymbol{C l}+ \)
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \frac{N \boldsymbol{a}}{\text {Dryether}} \)


A ring of smooth muscles present
between the stomach and the
duodenum is
A. Cardiac Sphincter
B. Pyloric Sphincter
c. Ileocaecal valve
D. Anal Sphincter


What is the amount of heat required to
heat \( 1 \mathrm{kg} \) of ice from \( -10^{\circ} \mathrm{C} \) to \( 0^{\circ} \mathrm{C} ? \)


Draw the geometry of \( O S F_{4} \) using
VSEPR theory.


A reversible engine operates between
temperatures \( 900 \mathrm{K} \& T_{2}\left(T_{2}<900 \mathrm{K}\right) \)
\( \& \) another reversible engine between \( T_{2} \)
\( \& 400 \mathrm{K}\left(\mathrm{T}_{2}>400 \mathrm{K}\right) \) in series. What is
the value of \( T_{2} \) if work outputs of both
the engines are equal?
\( A \cdot 600 K \)
B. 625K
\( c .650 k \)
D. 675K


The relation between the magnitudes of
lattice energy of crystal and its formation energy is:
A. lattice energy > formation energy
B. lattice energy = formation energy
c. lattice energy \( < \) formation energy
D. none of the above


Crystalisation takes place by the
process of :
A. evaporation
B. condensation
c. sublimation
D. liquefication


The IUPAC name of
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N O})\right] \boldsymbol{S} \boldsymbol{O}_{4} \) is penta
aquanitrosylium iron ( I) sulphate.
A. True
B. False


A coil has 200 turns and area of \( 70 \mathrm{cm}^{2} \)
The magnetic field perpendicular to the plane of the coil is \( 0.3 W b / m^{2} \) and take
\( 0.1 \sec \) to rotate through \( 180^{\circ} . \) The value of the induced e.m.f. will be
A. \( 8.4 \mathrm{v} \)
B. 84
c. 42 v
D. 4.2 v


Convert benzene to \( 1- \)bromo -3
ethylbenzene


\( \square_{0} \)
0
\( \Delta \)


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a polynomial function of degree 2 and \( f(x)>0 \) for all \( x \in R \) If \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}^{\prime}(\boldsymbol{x})+\boldsymbol{f}^{\prime \prime}(\boldsymbol{x}), \) then for
any \( \boldsymbol{x} \)
A \( . g(x)<0 \)
В \( . g(x)>0 \)
\( \mathbf{c} \cdot g(x)=0 \)
D. \( g(x) \geq 0 \)


A gas is expanded from volume \( V_{1} \) to
volume \( V_{2} \) in three processes, shown in
the figure. If \( U_{A}, U_{B} \) and \( U_{C} \) and \( U_{D} \)
represent the internal energies of the
gas in state \( A, B, C \) and \( D \) respectively,
the which of the following is not correct.
A. \( U_{B}-U_{A}>0 \)
B. \( U_{C}-U_{A}=0 \)
c. \( U_{D}-U_{A}<0 \)
D. \( U_{B}=U_{C}=U_{D} \)


Tuft of capillary vessels which is surrounded by Bowman's capsule is
A. Malpighian corpuscle
B. Juxtaglomerular apparatus
c. Glomerulus
D. Loop of Henle


if \( \overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}=|\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}| \cdot \) then the resultant \( \overrightarrow{\boldsymbol{A}} \)
and \( \vec{B} \) is
\( A \cdot \vec{A}+\vec{B} \)
B . \( \vec{A}-\vec{B} \)
c. \( \sqrt{A^{2}+B^{2}} \)
D. \( \sqrt{A^{2}+B} \)


The metal not present in hard water is:
A. \( C a \)
в. \( N a \)
c. \( M g \)
D. \( F e \)


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


\( 10 g \) fairly concentrated solution of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is electrolysed using \( \mathbf{0 . 0 1} \)
faraday of electricity. Calculate the mass of the resulting solution.
A. \( 7.6025 g \)
в. \( 9.6025 g \)
c. \( 6.6025 g \)
D. \( 77.6025 g \)


The ratio of intensities of magnetic fields due to a short magnet in tan \( A \)
and tan B position is
A .2:
B. 1: 2
\( c \cdot 3: \)
\( D \cdot 1: 3 \)


The graph shows the number of
basketball titles won by the boys team
and the girls team for three different
school teams.
Based on the data in the graph, which of the following statements is true?
A. The \( F . P . S \) teams together have won the greatest total number of basketball titles
B. The girls L.P.S team has won exactly twice as many titles as the \( G . P . S \) boys and girls teamsm together
C. The girls \( F . P . S \) team has won more titles than the girls \( L . P . S \) team
D. The \( L . P . S \) teams together have won the greatest total number of basketball titles


What hybrid orbitals are employed by carbon atoms 1,2 nad \( 3, \) respectively, as labeled in the compound shown? 0
\( \boldsymbol{H}_{3} \boldsymbol{C}-\underset{2}{\boldsymbol{C}}-\underset{3}{\boldsymbol{1}} \equiv \boldsymbol{N} \)
\( \mathbf{A} \cdot s p^{3}, \mathbf{s p}, \mathbf{s p} \)
B \( \cdot s p^{2}, s p^{2}, \) sp
\( \mathbf{c} \cdot s p^{3}, s p^{2}, \mathbf{s p} \)
D. \( s p^{3}, s p^{2}, s p^{2} \)


If \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)-\cos ^{1}\left(\frac{1-b^{2}}{1+b^{2}}\right)= \)
\( \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right), \) then what is the value
of \( x ? \)
\( A \cdot \frac{a}{b} \)
B. \( a b \)
\( c \cdot \frac{b}{a} \)
D. \( \frac{a-b}{1+a b} \)


Probability of an impossible event is
\( A \)
B. -
\( c \cdot 0 \)
D.


The average lifespan of an earthworm is
A. 13-15 years
B. 28-30 years
c. \( 6-9 \) years
D. 24-28 years


If \( \boldsymbol{P}=\left[\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{b} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{c}\end{array}\right] \) then, \( \operatorname{det}\left(\boldsymbol{P}^{-1}\right) \)
A \( . a b c \)
B. \( a^{2} b^{2} c^{2} \)
c. \( \frac{1}{a b} \)
D. \( \frac{1}{a^{2} b^{2} c^{2}} \)


Which of the following pairs of carbonyl compounds and Grignard reagent should be chosen as reactants to
prepare 2,4 -dimethyl-3-pentanol?
A. \( C H_{3} C H_{2} C H_{2} C H O \) and \( C H_{3} C H_{2} C H_{2} M g B r \)
в. \( \left(C H_{3}\right)_{2} C H C H O \) and \( \left(C H_{3}\right)_{2} C H M g B r \)
c. \( C H_{3} C H_{2} C O C H_{3} \) and \( \left(C H_{3}\right)_{2} C H M g B r \)
D. \( \left(C H_{3}\right)_{2} C H C H O \) and \( C H_{3} C H_{2} C H_{2} M g B r \)


Wilting of plant is present in
A. Moss
B. Fern
c. Algae
D. Gymnosperm


Which of the following represents
correct statement(s)?
A. Two sets of yarn are woven to make a fabric.
B. The weaving of fabric is done in looms.
C. The looms are either hand operated or power operated.
D. All of the above


The mass ' \( M^{\prime} \) of a stone that can be
moved by water current depends upon velocity ' \( V^{\prime} \) of the stream, density of
water ' \( d \) and acceleration due to gravity
'g'. The relation between the mass and velocity is:
\( \mathbf{A} \cdot M \propto V^{6} \)
B. \( M \propto V^{2} \)
c. \( M \propto d^{2} \)
D. \( M \propto V \)


Find the area of the parallelogram whose two sides are \( 2 \bar{i}-3 \bar{j} \) and \( 3 \bar{i}-\bar{j} \)


A car, starting from rest, accelerate at
the rate \( f \) through a distance \( s, \) then continuous at constant speed for the
some time \( t \) and the decelerates at the
rate \( \boldsymbol{f} / 2 \) to come to rest. If the total
distance is \( 5 s, \) then prove that \( s=\frac{1}{2} f t^{2} \)
A . 24
B . 25
c. 30
D. 20


Name a metal among the following having highest heat conductivity.
A . Silver
B. Copper
c. Aluminium
D. Brass


Covalent compounds dissolve in
organic solvents. Explain.


Find two consecutive natural numbers
whose sum is 63
A. 31 and 36
B. 30 and 32
c. 31 and 32
D. 54 and 32


The \( B C l_{3} \) is a planar molecule whereas
\( N C l_{3} \) is pyramidal, because:
A. \( B-C l \) bond is more polar than \( N-C l \) bond
B. \( N-C l \) bond is more covalent than \( B-C l \) bond
c. nitrogen atom is smaller than boron atoms
D. \( B C l_{3} \) has no lone pair but \( N C l_{3} \) has a lone pair of electrons


Match the Column-I with Column-II.
Choose the correct' one from the
alternatives \( (a),(b),(c) \) and \( (d) \)
Column Column-II
trans P. Wilkinson catalyst I. \( \operatorname{Ir} C l(C O)\left(P P h_{3}\right)_{2} \)
Q. Speier catalyst
Il. Hydrosilylation
gas shift
R. Water
III. \( R h C l\left(P P h_{3}\right)_{3} \) catalyst
ZSM-5
S. Zeolite
IV. Synthetic gasoline catalyst
V. Hydroformylation
VI. Zinc-copper oxide
P- III (b) P-I (c) P- -IV (d) P-III
\( A \cdot(a) \)
B. (a) Q-II (b) Q-V (c) Q-II (d) Q-IV
C. (a) R-VII (b) R-III (c) R-VI (d) R-IV
D. (a) S-IV (b) S-IV (c)
S-IV (d) S-II


Sodium salts of some acids are very
useful as food preservatives.
If true enter 1 else 0
\( A \)


A washing machine was purchased 3 years ago for Rs 19,440 . Its value
depreciates at \( 16 \frac{2}{3} \% \) per annum. Calculate its value after 1 year
A . Rs. 11,\( 250 ; \) Rs. 9,375
B. Rs. 9,375; Rs. 11,250
c. Rs. 13,\( 500 ; \) Rs. 7,812
D. Rs. 7812; Rs. 13,500


Which of the following can absorb over
\( 90 \% \) of its own mass of water and also
does not stick to wounds?
A. Saran
B. Thiokol
c. Rayon
D. Gun cotton


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal.
1
\( (255)^{\overline{4}} \)


A point object is placed on the principle axis of a convex lens of focal length f at
a distance of \( 2 f \) to the left of it. The
diameter of the lens is d. An eye is placed at a distance of \( 3 f \) to the right of the lens and a distance h below the
optic axis. The maximum value of \( h \) to see the image is?
A. \( d \)
в. \( d / 2 \)
c. \( d / 3 \)
D. \( d / 4 \)


Choose the correct answer from the
alternatives given
If the expression \( 2 x^{2}+14 x-15 \) is divided
by \( (x-4) \). then the remainder is
A . 65
B. 0
\( c \cdot 73 \)
D. 45


The numbers \( 7.478478 \ldots . . \) and
\( 1.101001000100001 \ldots \) are
A. Rational and irrational respectively
B. Both rationals
c. Both irrationals
D. None of these


The co-ordinates of the focus of
parabola \( \boldsymbol{y}^{2}=\mathbf{2 0} \boldsymbol{x} \) are
A. (5,5)
(年) 5,5,5
B. (3,5)
c. (0,5)
(年. (0,5)
D. (5,0)


The geometry of the compound is :
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
A. tetrahedral
B. linear
c. planar
D. pyramidal


With \( C r_{2} O_{3}, \) colour of the bead in
sodium carbonate bead test is:
A . red
B. blue
c. yellow
D. green


In section \( A, \) there are some organic
compounds and in section \( \mathrm{B} \), their uses are mentioned. Match the correct
options.
Section A Section B
1. Ethanol
(a) Nail polish remover
2. Formalin
(b) To have sour taste in food
3. Acetone
(c) In fragrant materials like perfumes
4. Ethanoic
(d) To preserve dead bodies Acid
\( A \cdot(1-c),(2-d),(3-a),(4-b) \)
B. (1-a), (2-d), (3-c), (4-b)
C. \( (1-b),(2-a),(3-d),(4-c) \)
D. (1-d), (2-c), (3-b), (4-a)


Given \( : \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{e}^{\oplus}=-\mathbf{0 . 6 9} \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{E}^{\oplus}=\mathbf{1} . \mathbf{7 7} \boldsymbol{V} \)
\( \mathbf{2} \boldsymbol{I}^{\ominus} \rightarrow \boldsymbol{I}_{\mathbf{2}}+\mathbf{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 5 3 5} \boldsymbol{V} \)
Assertion: \( H_{2} O_{2} \) acts as an oxidizing
agent for \( \boldsymbol{I}^{\ominus} \)
Reason: \( \boldsymbol{E}^{\ominus} \) is positive.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Assertion is false but Reason is true Both Assertion and Reason are false


Biomolecules are formed by certain
specific linkages between simple
monomeric units. Write the names of
linkages and monomeric units in the following class of biomolecules.
(i) Starch
(ii) Protein
(iii) Nucleic acid.


\( 50 \% \) of a first order reaction is
completed in 30 min. The velocity constant of the reaction is:
A .0 .23
B. 2.31
\( c \cdot 0.0023 \)
D. 0.0231


The figure shows the position time \( (x- \)
t) graph of one-dimensional motion of a
body of mass 0.4 kg. The magnitude of each impulse is
A. \( 0.4 \mathrm{Ns} \)
B. 0.8 Ns
c. \( 1.6 \mathrm{Ns} \)
D. \( 0.2 \mathrm{Ns} \)


The horizontal range of a projectile fired at an angle of \( 15^{\circ} \) is \( 50 \mathrm{m} \). If it is fired with the same speed at an angle of \( 45^{\circ} \) its range will be:
A. \( 60 \mathrm{m} \)
B. 71
c. \( 100 \mathrm{m} \)
D. \( 141 \mathrm{m} \)


A fusion reaction consists of combining
four protons into an \( \alpha \) - particle. The
mass of \( \boldsymbol{\alpha} \) - particle is 4.002603 amu
and that of proton is 1.007825 amu
This question has multiple correct options
\( \mathbf{A} \cdot \) the equation \( 4 p_{1}^{1} \rightarrow H e_{2}^{4} \) does not satisfy
conservation of charge
B. the correct reaction equation may be \( 4 p_{1}^{1} \rightarrow H e_{2}^{4}+ \)
\( 2 \beta^{+}+2 v \) where \( \beta^{+} \) is positron and \( v \) is the neutrino
(zero rest mass and uncharged)
c. loss of mass in the reaction is \( 0.028697 a m u \)
D. the energy equivalent of the mass defect is \( 26.7 \mathrm{MeV} \)


On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the
rates of the tickets were Rs. 20 and Rs.
40 per ticket and the total collection
was Rs. \( 900, \) find the number of tickets
sold of each rate.


A gas has a molecular diameter of \( 0.1 \mathrm{m} \) It also has a mean free path of \( 2.25 \mathrm{m} \) What is its density?
A \( \cdot 10^{-3} \)
B . \( 10^{-2} \)
\( \mathbf{c} \cdot 10^{-4} \)
D. \( 10^{-5} \)


The species among the following, which can act as acid as well as base is?
A \( . H S O_{4}^{-} \)
B. \( S O_{4}^{2} \)
c. \( H_{3} O^{+} \)
D. \( C l \)


At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along
A. north
B. south
c. north-south
D. east-west


An astronaut whose mass is \( 84 \mathrm{kg} \) on earth will have a mass of approximately
\( 14 \mathrm{kg} \) on the moon.
A. True
B. False


If \( \overrightarrow{\boldsymbol{a}} \cdot \hat{\boldsymbol{i}}=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}})=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
then find the unit vector \( \vec{a} \).


Arithmetic mean of marks (out of 25 )
scored by 10 students was \( 15 . \) One of the student, named Karishma enquired
the other 9 students and find the
deviations from her marks are noted as
\( -8,-6,-3,-1,0,2,3,4,6 . \) Find
Karishmas marks


Match the correct pair.


Assertion
When 1 mole of hypophosphorous acid is treated with excess of iodine in acidic
solution, 1 mole of iodine is reduced; on making the solution alkaline, another mole of iodine is consumed.
Reason
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}+\boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+ \)
\( 2 I^{-}+2 H^{+} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+\boldsymbol{I}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+ \)
\( 2 I^{-}+H_{2} O \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A spring of force constant \( \mathrm{k}=300 \mathrm{N} / \mathrm{m} \) connects two blocks having masses 2 kg and 3 kg, lying on a smooth horizontal plane. If the spring block system is released from a stretched position, find the number of complete oscillations in 1 minute. Take \( \pi=\sqrt{10} \)
A .44
B. 150
\( c \cdot 34 \)
D. 55


Determine the volume contraction of a
solid copper cube, \( 10 \mathrm{cm} \) on an edge, when subjected to a hydraulic pressure of \( 7.0 \times 10^{6} \) Pa. (Bulk modulus of
copper, \( \left.\boldsymbol{B}=\mathbf{1 4 0} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{P a}\right) \)


Name some modern fabrics formed by
unstitched piece of fabric.


An electric dipole is placed in an electric field generated by a point charge. Then
A. net electric force on the diploe must be zero
B. net electric force on the diploe may be zero
c. torque on the dipole due to the field must be zero
D. torque on the dipole due to the field may be zero


How many 4 -digit numbers can be
formed from digit 1,1,2,2,3,3,4,4,5,5
\( ? \)


The magnetic induction due to circular current-carrying conductor of radius \( a \)
at its centre is \( B_{c} \). The magnetic
induction on its axis at a distance \( a \)
from its centre is \( B_{a} . \) The value of \( B_{c}: \)
\( \boldsymbol{B}_{\boldsymbol{a}} \) will be :
A \( \cdot \sqrt{2}: 2 \)
B. \( 1: 2 \sqrt{2} \)
c. \( 2 \sqrt{2}: 1 \)
D. \( 2: \sqrt{2} \)


\( \operatorname{Let} f(x)=\frac{x^{2}-4}{x^{2}+4} \) for \( |x|>2, \) then the
function \( \boldsymbol{f}:(-\infty,-2) \cup[\mathbf{2}, \infty) \rightarrow \)
(-1,1) is
A. One-one into
B. One-one onto
c. Many one into
D. Many one onto


If \( a>0, \) then the expression \( a x^{2}+ \)
\( b x+c \) is positive for all values of \( x \)
provided
A \( . b^{2}-4 a c>0 \)
В. \( b^{2}-4 a c<0 \)
\( \mathbf{c} \cdot b^{2}-4 a c=0 \)
D. \( b^{2}-a c<0 \)


Find out the correct option from the
following.
(a) The magnification is positive for all virtual images and is negative for all
real images.
(b) The magnification of concave lens and convex mirror is always positive where as the magnification of convex lens and concave mirror can be positive
or negative depending on the position of the object before the lens.
A. Only A is true
B. Only B is true.
c. Both \( A \) and \( B \) are true
D. Both A and B are false


Bakane disease of Rice is due to
A. Erysiphe
B. Gibberella
c. Phytophthora
D. Albugo


A hollow spherical conducting shell of
inner radius \( r_{1} \) and other radius \( r_{2} \) has
a charge \( Q . A \) charge \( -q \) is placed at the centre of the sphere. The surface charge densities on the inner and outer
surfaces of the sphere will be
respectively:-
\( ^{\mathbf{A}} \cdot \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{q}{4 \pi r_{2}^{2}} \)
В \( \cdot \frac{-q}{4 \pi r_{1}^{2}} \) and \( \frac{Q+q}{4 \pi r_{2}^{2}} \)
c. \( \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q-q}{4 \pi r_{2}^{2}} \)
D. \( _{\text {O and }} \frac{Q-q}{4 \pi r_{2}^{2}} \)


For a reaction, the rate constant is
expressed as, \( k=A . e^{-40000 / T} \)
The energy of the activation is:
A. 40000 cal
в. 88000 са\( l \)
c. \( \quad 80000 \) cal
D. 8000 cal


Which of the following is/are example(s) of isotones?
\( A \cdot_{6} C^{12} \) and \( _{6} C^{13} \)
B . \( _{11} N a^{23} \) and \( _{12} M g^{23} \)
\( \mathbf{c} \cdot_{14} S i^{30} \) and \( _{16} S^{32} \)
D・ \( _{83} B i^{210} \) and \( _{84} P o^{21} \)


For the circuit shown, with \( \boldsymbol{R}_{1}= \)
\( \mathbf{1 . 0 \Omega}, \boldsymbol{R}_{\mathbf{2}}=\mathbf{2 . 0 \Omega}, \boldsymbol{E}_{\mathbf{1}}=\mathbf{2} \boldsymbol{V} \) and \( \boldsymbol{E}_{\mathbf{2}}= \)
\( E_{3}=4 V, \) the potential difference
between the points \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \) is
approximately (in \( V \) )
\( A \cdot 2.7 \)
в. 3.3
\( c .2 . \)
3.3 .3


Match the following:
\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { a) Angular velocity } & \text { e) null vector } \\ \text { b) Power } & \text { f) Scalar } \\ \text { c) If } \overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}} \text { then } \overrightarrow{\mathrm{B}} \text { is } & \text { g) unit vector } \\ \mathrm{d}) \frac{\vec{A}}{|\vec{A}|} & \text { h) axial vector }\end{array} \)
\( \mathbf{A} \cdot \mathbf{a} \rightarrow \mathbf{f} ; \mathbf{b} \rightarrow \mathbf{h} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathrm{d} \rightarrow \mathbf{f} \)
B \( \cdot a \rightarrow h ; b \rightarrow f ; c \rightarrow g ; d \rightarrow e \)
\( \mathbf{C} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{e} ; \mathbf{c} \rightarrow \mathbf{h} ; \mathbf{d} \rightarrow \mathbf{f} \)
\( \mathbf{D} \cdot \mathbf{a} \rightarrow \mathbf{h} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathbf{d} \rightarrow \mathbf{g} \)


Which compound processes the greatest lattice energy?
\( \mathbf{A} \cdot L i B r \)
в. LiCl
c. \( L i I \)
D. \( L i F \)


Allene,CH2=C=CH2CH2=C=CH2 groups at
its ends to be at right to each other
allene


The correct order of reducing abilities of
hydrides of \( V \) group elements is:
A. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3}<B i H_{3} \)
В. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3}>B i H_{3} \)
c. \( N H_{3}<P H_{3}>A s H_{3}>S b H_{3}>B i H_{3} \)
D. \( S b H_{3}>B i H_{3}>A s H_{3}>N H_{3}>P H_{3} \)


A stationary man observes that the rain
strikes him at an angle of \( 60^{\circ} \) to the horizontal. When he begins to move with
the velocity of \( 25 m / s \) then the drops
appear to strike him at an angle \( 30^{\circ} \)
from horizontal. The velocity of the rain drops is :
\( \mathbf{A} \cdot 25 m / s \)
B. \( 50 \mathrm{m} / \mathrm{s} \)
c. \( 12.5 m / s \)
D. \( 25 \sqrt{2} \)


The specific gravity of the stainless steel spherical balls used in ball-
bearings are \( 10.2 . \) How many iron atoms are present in each ball of diameter 1
\( \mathrm{cm} \) if the balls contain 84 per iron by mass? The atomic mass of iron is 56
A \( \cdot 4.12 \times 10^{21} \)
B. \( 4.82 \times 10^{22} \)
D. None of these


Which of the following numbers have different significant figures?
A. 0.060
B. 0.60
\( c .6 . \)
D. 60


In Cycas, fertilization is
A. Zooidogamy
B. Siphonogamy
C. Both A and B
D. Chalazogamy


The points \( (-a,-b),(0,0),(a, b) \) and \( \left(a^{2},\right. \)
ab) are
A. collinear
B. vertices of a rectangle
c. vertices of a parallelogram
D. None of these


The following results have been obtained during the kinetic studies of
the reaction:
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
Experiment \( \quad[A] / m o l L^{-1} \quad[B] / m o l L^{-1} \) \begin{tabular}{lll}
1 & 0.1 & 0.1 \\
\hline 11 & 0.3 & 0.2 \\
\hline \( \mathrm{III} \) & 0.3 & 0.4 \\
& & \\
& & \\
& & \\
\( \mathrm{V} \) & 0.4 & 0.1 \\
& &
\end{tabular}
Determine the rate law and the rate
constant for the reaction.


A solenoid of \( 1.5 \mathrm{m} \) length and \( 4.0 \mathrm{cm} \) diameter possesses 100 turns per meter. A current of 5 amperes is flowing through it. The magnetic induction at axis inside the solenoid is:
A \( \cdot 2 \pi \times 10^{-4} \mathrm{T} \)
В . \( 2 \pi \times 10^{-5} \) Т
c. \( 2 \pi \times 10^{-2} \) gauss
D. \( 2 \pi \times 10^{-5} \) gauss


If a musical instrument is played on very high pitch then its frequency is:
A. same
B. highh
c. low
D. zero


Describe the preparation of potassium dichromate from iron chromite ore.
What is the effect of increasing pH on a solution of potassium dichromate?


Find the ratio of the given statement in the simplest form.
75 paise to Rs. 3


The equation of tangent to \( x^{2}=y^{3} \) at
(1,1) is


Which of the following carries anomalous expansion?
A. Mercury
B. water
c. copper
D. sodium


Find and write down structures of 10
interesting small molecular weight biomolecules. Find if there is any
industry which manufactures the compounds by isolation. Find out who are the buyers?


Use of the Data Booklet is relevant to
this question. The gas laws can be summarised in the ideal gas equation below. \( \boldsymbol{p} \boldsymbol{V}=\boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
The volume of a sample of methane is
measured at a temperature of \( 60^{\circ} \mathrm{C} \) and a pressure of \( 103 k \) Pa. The volume
measured is \( 5.37 \times 10^{-3} m^{3} \)
Assume the gas behaves as an ideal
gas. What is the mass of the sample of methane, given to two significant figures?
A. \( 0.00018 g \)
в. \( 0.0032 g \)
\( c \cdot 0.18 g \)
D. 3.29


Find the sum of 90 terms of A.P
\( 4,8,12, \dots \)


Antibiotic inhibiting interaction between tRNA and mRNA during protein synthesis in bacteria is
A. Tetracycline
B. Neomycin
c. Erythromycin
D. Streptomycin


If \( \boldsymbol{y}=\frac{\mathbf{1}}{\mathbf{1}+\boldsymbol{x}^{\boldsymbol{\beta}-\boldsymbol{\alpha}}+\boldsymbol{x}^{\boldsymbol{\gamma}-\boldsymbol{\alpha}}}+ \)
\( \frac{1}{1+x^{\alpha-\beta}+x^{\gamma-\beta}}+\frac{1}{1+x^{\alpha-\gamma}+x^{\beta-\gamma}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{r}} \) is equal to
A . 0
B. 1
C \( \cdot(a+\beta+\gamma) X^{\alpha+\beta+\gamma-1} \)
D. None of these


If \( A \) and \( B \) are any two events such that
\( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(\text {Aand} B)=\boldsymbol{P}(\boldsymbol{A}) \)
then
\( \mathbf{A} \cdot P(B \mid A)=1 \)
B . \( P(A \mid B)=1 \)
c. \( P(B \mid A)=0 \)
D \cdot \( P(A \mid B)=0 \)


In which of the following molecule, all the atoms lie in same plane? This question has multiple correct options
A. \( X e F_{4} \)
в. \( B F_{3} \)
c. \( P F_{5} \)
D. \( N H_{3} \)


Subtract \( 3 x y+2 z^{2} \) from \( 5 x y+3 z^{2}- \)
\( x z \)


Which is the site of cellular respiration in prokaryotes?
A. Mitochondrion
B. Plasmids
c. Plasma membrane
D. cytosol


Soft drinks and baby-feeding bottles are generally made of:
A. Polyurea
B. polyurethane
c. Polyester
D. Polyamide
E . polystyrene


The number of distinct real values of \( \alpha \)
for which the vectors \( \boldsymbol{\alpha}^{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}},-\hat{\boldsymbol{i}}- \)
\( \boldsymbol{\alpha}^{2} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}},-\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\boldsymbol{\alpha}^{2} \hat{\boldsymbol{k}} \) will lie in the
same place is
\( A \cdot 1 \)
B . 2
\( c .3 \)
D.


The IUPAC name of the compound shown below is:
\[
\begin{array}{c}
\mathrm{CH}_{3} \\
\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}
\end{array}
\]
A. 4 -methylhex-2-yn-5-ene
B. 3-methylhex-4-yn-1-ene
c. 3 -methylhex- 1 -en- 4 -yne
D. 4-vinyl-2-pentyne


A blue car rounds a circular turn at a
constant speed of \( 30 m / s . \) A grey van rounds the same turn at a constant
speed of \( 15 m / s . \) How does the magnitude of the acceleration of the blue car compare to the magnitude of the acceleration of the grey van?
A. The accelerations of both vehicles are zero, since neither is changing speed
B. The magnitude of the blue car's acceleration is twice the magnitude of the grey van's acceleration
c. The magnitude of the blue car's acceleration is four times the magnitude of the grey van's acceleration
D. The magnitude of each car's acceleration is the same, but is not zero
E. We do not have enough information to determine the relative magnitudes of acceleration for the cars in this questions


Construct a pair of tangents to a cricle of radius \( 3.5 \mathrm{cm} \) from a point \( 3.5 \mathrm{cm} \)
away from the circle.


The function \( f(x)=\frac{\sin x}{x} \) is decreasing
in the interval
\( ^{\mathbf{A}} \cdot\left(-\frac{\pi}{2}, 0\right) \)
B. \( \left(0, \frac{\pi}{2}\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{\pi}{4}, 0\right) \)
D. None of these


What would be expected to happen if:
(a) \( \mathrm{GA}_{3} \) is applied to rice seedlings.
(b) Dividing cells stop differentiating.
(c) A rotten fruit gets mixed with unripe
fruits.
(d) You forget to add cytokinin to the culture medium.


The ratio of 7 th to the \( 3 r d \) term of an
A.P is \( 12: 5 . \) Find the ratio of 13 th to
the \( 4 t h \) term.


Find the average velocity of the train
A . 0
в. \( 80 k m p h \)
c. \( 40 k m p h \)
D. 20kmph


Ram mixes \( 15 \mathrm{kg} \) of sugar purchased with the rate of Rs. 8.00 per \( \mathrm{kg} \) with 25 kg of sugar purchased at the rate of Rs. 10.00 per kg. At what rate per kg should Ram sell the mixture to get a profit of 3 per kg?
A. Rs. 12.25
B . Rs. 11.25
c. Rs. 13.25
D. Rs. 14.25


Replum is present in the ovary of flower of
A. Sun flower
B. Pea
c. Lemon
D. Mustard


The general electronic configuration of block elements is


Choose the correct answer from the
alternatives given.
In normal heart action:
A. right atrium and ventricle contract, followed by the contraction of the left atrium and ventricle
B. two atria contract together, then the two ventricles contract together
C. right atrium and left ventricle contract, followed by the contraction of the left atrium and right ventricle
D. all four chambers of the heart contract and then relax
simultaneously


Show that difference of any two sides of
a triangle is less than to the third side.


A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a
tensile force of \( 400 \mathrm{N} \) is applied to each
end of the wire. What minimum
diameter is required for the wire?? \( \boldsymbol{Y}_{\text {steel}}=\mathbf{2 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \)


A cube is arranged such that its length, breadth, height are along \( X, Y \) and \( Z \)
directions. One of its corners is situated
at the origin. Length of each side of the
cube is \( 25 \mathrm{cm} \). The components of electric field are \( E_{x}=400 \sqrt{2} N / C, E_{y}=0 \) and
\( E_{Z}=0 \) respectively. The flux coming out
of the cube at one end, whose plane is
perpendicular to \( X \) axis, will be:
\( \mathbf{A} \cdot 25 \sqrt{2} N m^{2} / C \)
\( \mathbf{B} \cdot 5 \sqrt{2} N m^{2} / C \)
\( \mathbf{c} \cdot 250 \sqrt{2} N m^{2} / C \)
D. \( 25 \mathrm{Nm}^{2} / \mathrm{C} \)


The sum of the inner and the outer
curved surfaces of a hollow metallic
cylinder is \( 1056 \mathrm{cm}^{2} \) and the volume of
material in it is \( 1056 \mathrm{cm}^{3} \). Find the sum
of its internal and external radii. Given
that the height of the cylinder is \( 21 \mathrm{cm} \)


The hybridisation of nitrogen in nitrate
ion is:
\( \mathbf{A} \cdot s p \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


Four identical plates \( 1,2,3, \) and 4 are
placed parallel to each other at equal
distance as shown in the figure. Plates
1 and 4 are joined together and the
space between 2 and 3 is filled with a
dielectric of dielectric constant \( k=2 \)
The capacitance of the system between
1 and \( 3 \& 2 \) and 4 are \( C_{1} \) and \( C_{2} \)
respectively. The ratio \( C_{1} / C_{2} \) is :
\( \mathbf{A} \cdot 5 \)
\( \overline{3} \)
B.
\( c \cdot \frac{3}{5} \)
D. 5 7


The value of \( \lim _{n \rightarrow \infty} \sqrt{\frac{\mathbf{9}(i-1)}{n}} \cdot \frac{9}{n}=? \)
A \( \cdot \int_{0}^{9} \sqrt{x} d x \)
в. \( \int_{0}^{9} \sqrt{x}^{3} d x \)
\( \mathbf{c} \cdot \int_{0}^{9} \sqrt{9 x} d x \)
D. \( \int_{1}^{9} \sqrt{x} d x \)


For an infinitely dilute aqueous solution, molality will be equal to:
A. formality
B. molarity
c. mole fraction
D. ppm


As the temperature of a transistor
increases,
A. The base-emitter voltage required for a given collector current will decrease
B. The base-emitter voltage required for a given collector current will increase
C. The base-emitter voltage required for a given collector current will remain constant
D. The base-emitter voltage required for a given collector current will be indeterminate


The area bounded by \( y=\sec ^{-1} x, y= \)
\( \operatorname{cosec}^{-1} x \) and the line \( x-1=0 \) is:
\( \mathbf{A} \cdot \ln (3+2 \sqrt{2})-\frac{\pi}{2} \)
В \( \cdot \frac{\pi}{2}+\ln (3+2 \sqrt{2}) \)
\( c \cdot \pi-\ln 3 \)
D . \( \pi+\ln 3 \)


Given above fig. is the bar graph
indicating the marks obtained out of 50 in mathematics paper by 100 students.
Read the bar graph and answer the
following question:
t is decided to distribute work books on
mathematics to the students obtaining
less then 20 marks, giving one
workbook to each of such students. If a
work book costs Rs.5, what sum is
required to buy the work books?


ff \( y=\tan ^{-1}(3 x), \) then find \( \frac{d^{2} y}{d x^{2}} \)


Silk worm : Cocoon :: Wool:?
A. Hair of rabbit
B. Cotton plant
C . Fleece of sheep
D. Jute of hemp


When alkaline earth metals react with
phosphorous, then how many phosphorus atom(s) is/are present in product side?


Lichens are important in the studies on atmospheric pollution because they
A. Can also grow in greatly polluted atmosphere
B. Can readily multiply in polluted atmosphere
C. Are very sensitive to pollutants such as \( S O_{2} \)
D. Efficiently purify the atmosphere


Zinc Blende is concentrated by:
A. chemical separation
B. magnetic speciation
C. froth floatation
D. hydraulic washing


Represent on number line \( \frac{1}{6} \)


A mass of \( 2.0 \mathrm{kg} \) is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and
released the mass executes a simple harmonic motion. The spring constant is \( 200 \mathrm{N} / \mathrm{m} \). What should be the
minimum amplitude of the motion, so
that the mass gets detached from the
pan?
(Take \( \left.g=10 m / s^{2}\right) \)
A. \( 8.0 \mathrm{cm} \)
B. 10.0 \( \mathrm{cm} \)
c. Any values less than \( 12.0 \mathrm{cm} \)
D. 4.0 \( \mathrm{cm} \)


Assertion
In the falling object example, if you include the effect of air resistance
during the fall and see the situation after the object hits the ground and stays there, the total mechanical energy
is not conserved.
Reason
The general law of energy conservation, however, is still applicable but the total mechanical energy is not conserved
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 series of fast moving still pictures
can create an illusion of movement
because.
A. the eye can focus on very rapidly changing pictures
B. eye is quicker than the brain
C. the eye can separate two images only when the interval of separation between them is more than onetenth of a second
D. the optical cortex can see through the rapidly moving images


A soap bubble, having radius of \( 1 \mathrm{mm} \), is blown from a detergent solution having
a surface tension of \( 2.5 \times 10^{-2} N / m \)
The pressure inside the bubble equals at a point \( Z_{0} \) below the free surface of
water in a container. Taking \( \boldsymbol{g}= \)
\( 10 m / s^{2}, \) density of water \( =10^{3} k g / m^{3} \)
the value of \( Z_{0} \) is :
A . \( 100 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c \cdot 1 c m \)
D. \( 0.5 \mathrm{cm} \)


Which of the following is a path function?
A. internal energy
B. enthalpy
c. work
D. entropy


Assertion
no electric current will be present
within a region having uniform and
constant magnetic field.
Reason
Within a region of uniform and constant magnetic field \( \vec{B} \), the path integral of magnetic field \( \oint \vec{B} \cdot \overrightarrow{d l} \) along any closed path is zero. Hence, from Ampere circuital law \( \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I \) (where the
given terms have usual meaning), no
current can be present within a region having a uniform and constant magnetic field
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The magnitude of electric field at different points along the length of the rod is given by
A \( \cdot \frac{V_{o}}{L^{2}}(L-X) \)
B. \( \frac{V_{o}}{(L+X)} \)
c. \( \frac{V_{o}}{L} \)
D. \( \frac{V_{o}}{2 L} \)


STATEMENT-1: Extraction of zinc from
sphalerite ore involves the roasting followed by reduction with coke. STATEMENT-2:Zinc can be
commercially extracted by hydrometallurgy.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


"Alkali metals dissolve in liquid
ammonia to give green coloured solutions which upon standing slowly
liberate \( \boldsymbol{H}_{2} \). The green colour of metalammonia solutions is due to the
presence of solvated electrons."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


The motion of a body is given by the equation \( \frac{d v}{d t}=6-3 v: w \) here \( v \) is in
\( \boldsymbol{m} / \boldsymbol{s} . \) If the body was at rest at \( \boldsymbol{t}=\mathbf{0} \)
(i) the terminal speed is \( 2 m / s \)
(ii) the magnitude of the initial acceleration is \( 6 m / s \)
(iii) the speed varies with time as \( v= \)
\( 2\left(1-e^{-3 t}\right) m / s \)
(iv) The speed is 1 m/s,when the
acceleration is half the initial
\( \mathbf{A} \cdot(i),(i i i) \)
B. \( (i i),(i i i),(i v) \)
c. \( (i),(i i),(i i i) \)
D. Alll


A man stands symmetrically between two large plane mirrors fixed to two adjacent walls of a rectangular room.
The number of images formed are:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


\( \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{B}+\boldsymbol{H} \boldsymbol{C l} \)
\( \boldsymbol{B}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C}+\boldsymbol{H} \boldsymbol{C l} \)
Compound \( (A),(B) \) and \( (C) \) will be
respectively:
A. \( P C l_{5}, P O C l_{3}, H_{3} P O_{3} \)
в. \( P C l_{5}, P O C l_{3}, H_{3} P O_{4} \)
c. \( \operatorname{sOCl}_{2}, \operatorname{POCl}_{3}, H_{3} P O_{3} \)
D. \( P C l_{3}, P O C l_{3}, H_{3} P O_{4} \)


Ignition temperature of flammable substances is
A . high
B. low
c. very high
D. None


Evaluate \( : \int\left(x+\frac{1}{x}\right)^{3} d x, x>0 \)


When a dice is thrown, find the
probability that either an odd number or a multiple of 4 occurs


A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is
defective is.
\( ^{A} \cdot\left(\frac{1}{10}\right)^{5} \)
B. \( \left(\frac{1}{2}\right)^{5} \)
\( ^{\mathbf{c}} \cdot\left(\frac{9}{10}\right) \)
D. \( \left(\frac{9}{10}\right)^{5} \)


In a \( \triangle A B C, \) perpendicular \( A D \) from \( A \) on \( B C \) meets \( B C \) at \( D . \) If \( B D=8 \mathrm{cm} \)
\( D C=2 \mathrm{cm} \) and \( A D=4 \mathrm{cm}, \) then
A. \( \triangle A B C \) is isosceles
B. \( \triangle A B C \) is equilateral
c. \( A C=2 A B \)
D. \( \triangle A B C \) is right angled at \( A \)


Blister copper obtained during
extraction from cuprous oxide is called
so because:
A. it has blister like eruptions due to evolution of gas
B. it has a shining surface like blister
c. it is the most impure form of copper
D. its surface is uneven due to different thickness at different place


Tungsten has work function \( 4.8 e V . \) We
wish to use tungsten as photo-cathode
with a 600 nm wavelength. What shall
we do?
A. Coat tungsten with Cesium
B. Oxide coat tungsten
c. \( C u_{2} O_{2} \) be coated on tungsten
D. None of these


Two adjecnt angles of a parallelogram
are equal measure. Find the measure of each angle.


A line is parallel to \( Y \) -axis and is at a
distance of 5 unit from \( Y \) -axis. Write
the equation of that line.


The coercivity of a magnet is \( 3 x \)
\( 10^{3} A m^{-1} . \) What current should be
passed through a solenoid of length \( 10 \mathrm{cm} \) and number of turns 50 that the
magnet is demagnetized when inserted in it?
A \( .3 A \)
в. \( 6 A \)
c. \( 9 A \)
D. \( 12 A \)


Find the radius of the circle whose
centre is (3,2) and passes through (-5,6)
A \( .4 \sqrt{5} \)
B. \( 2 \sqrt{5} \)
c. \( 4 \sqrt{2} \)
D. None of these


Magnetic lines of force causes
A. The picture on a computer screen
B. Radio reception interference
C. Aurora Borealis
D. V.H.S. films
E. All of these


Lyophilic solutions are:
A. irreversible solutions
B. prepared from inorganic compounds
C. not coagulated by adding electrolytes
D. self stabilizing


Out of two copper spheres of the same
size, \( x \) is hollow while \( y \) is solid. If they
are charged at the same potential, what can be said about the charges on them?
A. Charge on both the spheres is zero
B. Charge on both the spheres is equal
c. sphere \( y \) will have more charge
D. sphere \( x \) will have more charge


If \( f(x)=\frac{1}{(1-x)} \) find \( (f o f o f)(x)=? \)


A parallel plate condenser with oil (dielectric constant 2 ) between the
plates has capacitance \( C . \) If the oil is removed, the capacitance of capacitor becomes:
A. \( \sqrt{2 C} \)
B. 2C
c. \( \frac{c}{\sqrt{2}} \)
D. \( \frac{c}{2} \)


Differentiate between
Blood and Iymph.


What happens when calcium reacts
with water?


Draw the number line and represent the following rational number on it:
\( \frac{-5}{8} \)


A long straight horizontal cable carries a current of \( 2.5 \mathrm{A} \) in the direction \( 10^{\circ} \)
south of west to \( 10^{\circ} \) north of east. The
magnetic meridian of the place happens to be \( 10^{\circ} \) west of the geographical meridian. The earth's magnetic field at the location is \( 0.33 \mathrm{G} \) and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable). (At neutral points, magnetic field due to a currentcarrying cable is equal and opposite to the horizontal component of earth's magnetic field)
A. \( 15.15 \mathrm{mm} \)
B . \( 30.15 \mathrm{mm} \)
c. \( 35.15 \mathrm{mm} \)
D. \( 40.15 \mathrm{mm} \)


Points \( P, Q, R \) and \( S \) divide the line
segment joining the points \( A(1,2) \) and
\( B(6,7) \) in 5 equal parts. Find the
coordinates of the points \( P, Q \) and \( R \)


A motor boat starting from rest on a
lake accelerates in a straight line at
constant rate of \( 3.0 \mathrm{m} / \mathrm{s}^{2} \) for \( 8.0 \mathrm{sec} \)
How far does the boat travel during this time


Find average velocity in the time interval 0 to the time when velocity becomes zero?
A. 113.75 rad\( s^{-1} \)
B. 143.25 rad\( s^{-1} \)
c. \( 162.5 r a d s^{-1} \)
D. none


If \( y=a^{\frac{1}{2} \log _{a} \cos x}, \) find \( \frac{d y}{d x} \)


What is the molecular mass of glucose
\( C_{6} H_{12} O_{6} \) molecule up to 6 significant
figures?
A. 0180.16
B. 180.16
c. 180.1620
D. 180.162


thin shells of uniformly distributed
positive charge \( Q \) and radius \( d \) are
located a distance \( 10 d \) from each other.
A positive point charge \( q \) is placed
inside one of the shells at a distance
\( d / 2 \) from the center, on the line
connecting the centers of the two shells,
as show in the figure. What is the net
force on the charge \( q ? \)
A \( \cdot \frac{Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the left
B. \( \frac{Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the right
c. \( \frac{362 Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the left
D. \( \frac{360 Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the right


Acid hydrolysis of ester in first order reaction and rate constant is given by \( \boldsymbol{k}=\frac{\mathbf{2 . 3 0 3}}{\boldsymbol{t}} \log \frac{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{0}}{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{t}} \) where \( \boldsymbol{V}_{0}, \boldsymbol{V}_{t} \)
and \( V_{\infty} \) are the volume of standard
NaOH required to neutralise acid
present at a given time, if ester is \( 50 \% \) neutralised then:
A. \( V_{\infty}=V_{t} \)
B \( \cdot V_{\infty}=\left(V_{t}-V_{0}\right) \)
\( \mathbf{c} \cdot V_{\infty}=\left(2 V_{t}-V_{0}\right) \)
D. \( V_{\infty}=\left(2 V_{t}+V_{0}\right) \)


\( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( \boldsymbol{N}_{\mathbf{2}}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 N H_{3}(g), \) at \( 298 K \) is \( 5.2 \times 10^{-5} . \) What
is the value of \( K_{c} \) at \( 298 K \), for the
reaction \( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \rightleftharpoons N H_{3}(g) \)


Which of the following process is used to remove impurities from dispersion medium in Ultracentrifugation?
A. Filtration
B. Decantation
c. Sedimentation
D. Any of the above


Which of the following functions represent a simple harmonic motion?
\( \mathbf{A} \cdot \sin \omega t-\cos \omega t \)
B. \( \sin ^{2} \omega t \)
\( \mathbf{c} \cdot \sin \omega t+\sin ^{2} \omega t \)
D. \( \sin \omega t-\sin ^{2} \omega t \)


Define scattering.


Which of the following chemical cause
the thinning of layer P?
A. Carbon monoxide
B. sulphur dioxide
c. chlorofluorocarbons
D. Both A and C


Which of the following graph indicates
direct current?
\( A \)
B.
\( \mathbf{c} \)
\( D \)


A mixture of cement, gravel, coarse sand and water is called:
A. mortar
B. concrete
c. slurry
D. hardner


Which of the following has the strongest H-bond?
A. \( 0-H \ldots . . . \)
B. S-H....0
c. F-H...F
D. F-H...0


A meter bridge is set-up as shown, to
determine an unknown resistance \( \boldsymbol{X} \)
using a standard 10 ohm resistor. The
galvanometer shows null point when
tapping-key is at \( 52 \mathrm{cm} \) mark. The end-
corrections are \( 1 \mathrm{cm} \) and \( 2 \mathrm{cm} \)
respectively for the ends \( A \) and \( B \). The
determined value of \( ^{\prime} \boldsymbol{X}^{\prime} \) is:
A .10 .2 ohm
B. 10.6 ohm
c. 10.8 ohm
D. 11.1 ohm


Find the area of the region bounded by
the curve \( y=x^{2} \) and the line \( y=2 \)


What is the magnitude of force required to newton's produce a pressure of
\( 37500 P a \) in an area of \( 300 c m^{2} ? \)


Fill in the blanks given in list I with
items in list II.


vertices of an ellipse are (0,±10) and its eccentricity \( e=4 / 5 \) then its
equation is
A \( \cdot 90 x^{2}-40 y^{2}=3600 \)
B . \( 80 x^{2}+50 y^{2}=4000 \)
c. \( 36 x^{2}+100 y^{2}=3600 \)
D. \( 100 x^{2}+36 y^{2}=3600 \)


Assertion
A sample of lead (II) bromide, \( P b B r_{2} \)
was placed in a crucible. The ends of two carbon electrodes were put in the
solid and connected to a lamp and
power pack. At first the lamp did not
light, but when the bromide was heated and began to melt, the lamp began to glow. Explain these observations.
Reason
The glowing of lamp tells us that the compound conducts when in molten state in which there are ions which are
free to move. This also suggests that
\( P b B r_{2} \) is ionic.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C . Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following occupies the highest level in the heirarchy of organisation?
A . Organ
B. Cell
c. Tissue
D. Organ system


First link in any food system is green plant because
A. Green plants can synthesize food.
B. They can eat everything
c. Fixed at one place
D. None of the above


The rate of cooling of water is when the difference in the temperature of water and the ambience is large.


Match the following list 1 to list 2


Which one of the following statements regarding helium is incorrect?
A. It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable
B. It is used as a cryogenic agent for carrying out experiments at low temperatures
c. It is used to produce and sustain powerful superconducting magnets
D. It is used in gas-cooled nuclear reactors


Perimeter of a circle is called as:
A . area
B. circumference
c. volume
D. none


The cost of 7 erasers and 5 pencils is Rs
\( \mathbf{5 8} \) and the cost of 5 erasers and 6
pencils is Rs.56. Formulate this problem algebraically and solve it graphically.


At a point very near earth's surface, the acceleration due to gravity is g. What will be the acceleration due to gravity at the same point if the earth suddenly shrinks to half its radius without any
change in its mass?
\( A \cdot 28 \)
B. 48
c. \( g \)
D. 3


A parallel plate air has a capacity of \( 20 \mu F \). what will be the new capacity if a
marble slab of dielectric constant 8 is
introduced between the two plates?


Checking of re-radiation heat by
atmospheric dust, \( O_{3}, O_{2} \) and water vapours is
A. Ozone layer effect
B. Solar effect
c. Radioactive effect
D. Green house effect


The differential equation whose general
solution is \( \boldsymbol{y}=\boldsymbol{A} \cos (\boldsymbol{x}+\boldsymbol{3}), \) where \( \boldsymbol{A} \)
is arbitrary constant is
\( \mathbf{A} \cdot \cot (x+3) y_{1}+y=0 \)
B \cdot \( \tan (x+3) y_{1}+y=0 \)
\( \mathbf{c} \cdot \cot (x+3) y_{1}-y=0 \)
D \cdot \( \tan (x+3) y_{1}-y=0 \)


Find the unknown length \( x \) in the
following figures:-


A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let \( A \) be the event, 'the
number is even', and \( B \) be the event,'the
number is red'. Then \( A \) and \( B \) are
independent events.
A. True
B. False


Assertion
Points \( \boldsymbol{P}(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}), \sin \beta) \) and
\( \boldsymbol{R}(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})), \) where
\( \beta=\frac{\pi}{4}+\frac{\alpha}{2} \) are non-collinear.
Reason
Three given points are non-collinear if they form a triangle of non-zero area.
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 the Reason is correct


A bar magnet of magnetic moment
\( 1.2 A m^{2} \) is placed in the magnetic
meridian with its south pole pointing the north. If a neutral point is found at a
distance of \( 20 \mathrm{cm} \) from the centre of the
magnet, the value of the horizontal
component of the earth's magnetic field is :
A. \( 3 \times 10^{-5} T \)
B. \( 3 \times 10^{-4} T \)
c. \( 3 \times 10^{3} T \)
D. \( 3 \times 10^{-2} T \)


\( " \boldsymbol{N}<\boldsymbol{P}<\boldsymbol{A} \boldsymbol{s}^{\prime \prime} \)
Above order is incorrect for:
A. Electropositivity
B. Covalent radii
c. Size of \( M^{3} \)
D. Acidic nature of \( M_{2} O_{3} \) type oxide


The variance of 5 numbers is \( 10 . \) If each
number is divided by \( 2, \) then the variance of new numbers is
A . 5.5
B . 2.
\( c .5 \)
D. None of these


Integrate the following function with
respect to \( x: \)
\( \int \frac{1}{\left(x^{2}-1\right)} d x \)


A point moves in a straight line under the retardation \( -\mathrm{kv}, \) where \( \mathrm{k} \) is a constant. If the initial velocity is \( u, \) the
distance covered in 't' seconds is?
A \( \cdot \frac{u}{k}\left(1-e^{-k t}\right) \)
B. \( \frac{u}{k}\left(1+e^{-k t}\right) \)
c. \( \frac{u}{k}\left(1-e^{k t}\right) \)
D \( \cdot \frac{u}{k}\left(1+e^{k t}\right) \)


Using substitution method find the value of \( x \) and \( y: \)
\( 4 x+9 y=5 \) and \( -5 x+3 y=8 \)
A. -1 and \( \frac{-2}{5} \)
B. -1 and \( \frac{2}{5} \)
c. -1 and 1
D. 1 and \( \frac{2}{5} \)


Choose the only correct statement from
the following
A. The pressure of a gas is equal to the total kinetic energy of the molecules in a unit volume of the gas.
B. The product of pressure and volume of a gas is always constant.
C. The average kinetic energy of molecules of a gas is proportional to its absolute temperature.
D. The average kinetic energy of molecules of a gas is proportional to the square root of its absolute temperature.


The set of fractions between the natural
numbers 3 and 4 is a :
A. Finite set
B. Null set
c. Infinite set
D. singleton set


A rubber ball is dropped from a height of \( 5 \mathrm{m} \) on a plane. On bouncing it rises to 1.8m. The ball loses its velocity on
bouncing by a factor of
A \( .16 / 25 \)
в. \( 2 / 5 \)
c. \( 3 / 5 \)
D. \( 9 / 25 \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) find \( |\mathbf{2} \boldsymbol{A}| \)


Assertion : The acceleration due to
gravity on the moon is one-sixth that on
the earth.
Reason : The law of gravitation is the
same on both the moon and the earth.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false


A sphere of diameter \( 6 \mathrm{cm} \) is dropped in
a right circular cylindrical vessel partly
filled with water. The diameter of the
cylindrical vessel is \( 12 \mathrm{cm} \). If the sphere is completely submerged in water, by
how much will the level of water rise in
the cylindrical vessel?


Give reason:
\( \left[\boldsymbol{T} \boldsymbol{i}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \) is coloured while
\( \left[S c\left(H_{2} O\right)_{6}\right]^{3+} \) is colourless


Which of the following is true for the inheritance of sex chromosomes in
humans?
A. The gametes from each parent have either an \( x \) or a chromosome.
B. The gamete from the mother has either an \( x \) or a \( y \) chromosome.
c. The gamete from the father has either an \( x \) or a chromosome.
D. The gamete from the father only has an \( x \) chromosome.
E. The gamete from the mother only has a \( Y \) chromosome.


The EAN of Cobalt in complex ion
\( \left\lceil\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right\rceil^{+}: \)
A . 27
B. 36
\( c \cdot 33 \)
D. 35


\( 200 \mathrm{cc} \) of a gas, measured at \( \mathrm{STP} \), has a
mass of 0.268 g. Molecular weight of the gas is:
\( A \cdot 16 \)
B. 2
c. 28
D. 30


Give the classification of aminoacids.


A metal sphere with radius of \( 10 \mathrm{cm} \) is
to be covered with a \( 0.02 \mathrm{cm} \) coating of
silver approximately silver required is
\( \left(\operatorname{in} c m^{3}\right) \)
A \( .2 \pi \)
в. \( 10 \pi \)
\( c .6 \pi \)
D. \( 8 \pi \)


Which of the following vessel carries most of the oxygenated blood?
A. Pulmonary artery
B. Pulmonary vein
c. coronary artery
D. Cerebral artery


Electric field intensity in free space at a
distance ' \( r^{\prime} \) outside the charged
conducting sphere of radius ' \( \boldsymbol{R}^{\prime} \) in
terms of surface charge density '\sigma' is :
A \( \cdot \frac{\sigma}{\epsilon_{0}}\left[\frac{R}{r}\right]^{2} \)
В. \( \frac{\epsilon_{0}}{\sigma}\left[\frac{R}{r}\right]^{2} \)
c. \( \frac{R}{r}\left[\frac{\sigma}{\epsilon_{0}}\right]^{2} \)
D. \( \frac{R}{\sigma}\left[\frac{r}{\epsilon_{0}}\right]^{2} \)


What is the de Broglie wavelength of the electron accelerated through a potential difference of 100 Volt?
A \( . \) १२.२७ \( \AA \)
в. 1.227 ,
c. 0.1227 ,
D. 0.001227 \( \dot{A} \)


If a polynomial \( a z^{3}+4 z^{2}+2 z-4 \) and
\( z^{2}+4 z+a \) leave the same remainder
divide by \( (z-3) . \) Find the value of a.
A . 1
в. \( \frac{-17}{26} \)
c. -1
D. 17


When a current of \( (2.50 \pm 0.5) A \)
flows through a wire, it develops a
potential difference of \( (20 \pm 1) V . \) The
resistance of the wire is :
A. \( (8 \pm 2) \Omega \)
в. \( (10 \pm 3) \Omega \)
c. \( (18 \pm 4) \Omega \)
D. \( (20 \pm 6) \Omega \)


If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 5}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \boldsymbol{B}^{\prime}}\right) \)
equals
A \( \cdot \frac{3}{4} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{1}{4} \)
D.


Given : AB || CD.
If \( \angle 4 \) is an obtuse angle, then \( \angle 5 \) is
A . Acute
B. Right
c. obtuse
D. Straight


The number of positively and negatively charged ions present in \( 1 L \) of \( 0.1 M \) aluminium sulphate solution are:
A \( \cdot 1.2 \times 10^{22}+v e \) ions and \( 1.8 \times 10^{22}-v e \) ions
B . \( 1.2 \times 10^{23}+ \) ve ions and \( 1.8 \times 10^{22}- \) ve ions
c. \( 1.2 \times 10^{23}+ \) ve ions and \( 1.8 \times 10^{23}- \) ve ions
D. \( 1.2 \times 10^{21}+v e \) ions and \( 1.8 \times 10^{21}- \) ve ions


When one mole of each of the following complex is treated with an excess of
\( A g N O_{3} \).which will give maximum
amount of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \) ?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
в. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right) C l_{2}\right] C l \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)


A \( 0.66 \mathrm{kg} \) ball is moving with a speed of \( 100 \mathrm{m} / \mathrm{s} . \) The associated wavelength will
be:
\( \left[h=6.6 \times 10^{-34} \mathrm{J.s}\right] \)
A \( \cdot 6.6 \times 10^{-32} \mathrm{m} \)
B \( \cdot 6.6 \times 10^{-34} \mathrm{m} \)
c. \( 1.0 \times 10^{-35} \mathrm{m} \)
D. \( 1.0 \times 10^{-32} \mathrm{m} \)


Calculate \( 34-98= \)
A .132
B. 64
\( c .-64 \)
D. -132


A. Bakelite is a thermosetting polymer.
R. It can be melted again and again
without any change.
A. Both A and R are correct and R is the correct explanation of the \( A \)
B. Both A and R are correct but R is not the correct explanation of the
C. A is correct but R is incorrect
D. A is incorrect but R is correct


Blood of Periplaneta does not carry
OXygen because
\( \mathbf{A} \cdot O_{2} \) is transported by respiratory tubules
B. Its respiration is anaerobic
C. There is no cells in its blood
D. Periplaneta does not has any blood vessel


What are artificial sweetening agents? Give example


The argument which favours the
particular nature of cathode rays is:
A. they produce fluorescence
B. they travel through vacuum
C. they get deflected by electric and magnetic fields
D. they cast shadows of objects present in their way


Which of these is/are meso?
A. 1 and 2
B. 3 and 4
c. 1 and 4
D. All are Meso


The circuit shown in the figure contains two diodes, each with a forward
resistance of \( 50 \Omega \) and with infinite
backward resistance. If the battery
voltage is \( 6 \mathrm{V} \), the current through the
\( 100-\Omega \) resistance is
A. zer
B. \( 0.02 A \)
c. \( 0.04 A \)
D. \( 0.046 A \)


Which of the following functions are
identity functions?
This question has multiple correct options
\( \mathbf{A} \cdot f: R \rightarrow R, f(x)=x \)
\( \mathbf{B} \cdot g: N \rightarrow Z, g(p)=3 \)
C \( . h: z \rightarrow z, h(y)=y \)
\( \mathbf{D} \cdot g: N \rightarrow N, g(z)=z \)


Glycosidic linkage present between adjacent glucose units of starch or glycogen is generally
A. \( \beta 1 \longrightarrow 4 \)
B . \( \alpha 1 \longrightarrow 4 \)
c. \( \alpha 2 \rightarrow 1 \)
D. \( \beta 2 \longrightarrow 1 \)


Three pieces of cakes of weights \( 4 \frac{1}{2} \) lbs \( \mathbf{6} \frac{\mathbf{3}}{\mathbf{4}} \) lbs and \( \mathbf{7} \frac{\mathbf{1}}{\mathbf{5}} \) lbs respectively are to be
divided into parts of equal weights. Further each must be as heavy as possible. If one such part is served to each guest then what is the maximum number of guests that could be entertained?


Find the consecutive perfect squares
between which the following numbers
lie: 123456


If the atomic weight of oxygen were taken as \( 90, \) then what would be
molecular weight of water?
A . 101.25
в. 104.52
c. 112.5
D. 142.5


Reaction
\[
\begin{array}{l}
\frac{1}{2} N_{2}(g)+O_{2}(g) \leftrightharpoons N O_{2} \\
2 N O_{2}(g) \rightleftharpoons N_{2} O_{4}(g)
\end{array}
\]
Using the above equations, write down
expression for \( \boldsymbol{K} \) of the following
reaction:
\[
N_{2} O_{4}(g) \rightleftharpoons N_{2}(g)+\frac{1}{2} O_{2}(g)
\]
\( \mathbf{A} \cdot K_{1} K_{2} \)
B. \( \frac{K_{2}^{2}}{K_{1}} \)
\( c \)
\[
\frac{1}{K_{2} K_{1}^{2}}
\]
D.
\[
\frac{1}{K_{1}^{2} K_{2}}
\]


The distance between the line \( r=2 \hat{i}- \) \( 2 \hat{j}+3 \hat{k}+\lambda(\hat{i}-\hat{j}+4 \hat{k}) \) and the plane
\( r \cdot(\hat{i}+5 \hat{j}+\hat{k})=5 \) is
A \( \cdot \frac{10}{9} \)
в. \( \frac{10}{3 \sqrt{3}} \)
c. \( \frac{10}{3} \)
D. None of these


Figure shows an equilateral triangle
\( A B C \) of side \( l \) carrying currents as
shown, and placed in a uniform magnetic field \( B \) perpendicular to the
plane of triangle. The magnitude of magnetic force on the triangle is
A . il
B. 3il
\( c .2 i l \)
D. zer


What is the significance of negative electronic energy?


\( \boldsymbol{i}^{242}= \)
\( \mathbf{A} \cdot i \)
B. \( -i \)
c. 1
D. -


The weather forecast in a week has
been summarised as above.
Based on the above information answer
the questions.

Which day has the least temperature?
\begin{tabular}{|l|l|l|l|}
\hline Day & Max. & Min. & Forecast \\
\hline Sun & \( 36^{\circ} \mathrm{C} \) & \( 24^{\circ} \mathrm{C} \) & Sunny and hot \\
Mon & \( 34^{\circ} \mathrm{C} \) & \( 22^{\circ} \mathrm{C} \) & Sunny \\
Tue & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Dry and cloudy \\
Wed & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
Thu & \( 27^{\circ} \mathrm{C} \) & \( 16^{\circ} \mathrm{C} \) & Rain \\
Fri & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Light showers \\
Sat & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
\hline
\end{tabular}
A. Sunday
B. Thursday
c. Saturday
D. Monday


The nucleus of the atom consists of:
A. protons and neutrons
B. protons and electrons
c. neutrons and electrons
D. protons, neutrons and electrons


A thick rope of rubber of density \( 1.5 \times \) \( 10^{3} \mathrm{kg} / \mathrm{m}^{3} \) and Young's modulus \( 5 \times \)
\( 10^{6} \mathrm{N} / \mathrm{m}^{2}, 8 \mathrm{m} \) length is hung from the
ceiling of a room, the increases in its length due to its own weight is :
\( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A \( .9 .6 \times 10^{-2} \mathrm{m} \)
в. \( 19.2 \times 10^{-7} \mathrm{m} \)
c. \( 9.6 \times 10^{-7} \mathrm{m} \)
D. \( 9.6 m \)


\( P M=4 \mathrm{cm} ; Q M=4.5 \mathrm{cm} \)
\( P N=4 \mathrm{cm} ; \mathrm{NR}=4.5 \mathrm{cm} \)


Solve the following pairs of equations.
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4} ; \mathbf{9} \boldsymbol{x}+\mathbf{6} \boldsymbol{y}-\mathbf{1 2}=\mathbf{0} \)
A. Many solution
B. No solution
c. Unique solution
D. None of these


Which term of the following sequences \( \sqrt{3}, 3,3 \sqrt{3}, \dots \) is 729


Assertion
In the process of drying dishes with a towel, the wetting agent is the dish and the drying agent is the towel
Reason
The wetting agent gets wet during the
process.
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


List two advantages of power production by nuclear fusion, over nuclear fission.


The diagram below (Fig.) shows a uniform bar supported at the middle
point \( O . A \) weight of \( 40 g f \) is placed at a
distance \( 40 \mathrm{cm} \) to the left of the point \( O \)
How can you balance the bar with a
weight of \( 80 g f ? \)
A. By placing the weight of \( 80 g f \) at a distance \( 10 \mathrm{cm} \) to the right of the point \( O \)
B. By placing the weight of \( 40 g f \) at a distance \( 20 \mathrm{cm} \) to the right of the point \( O \)
C. By placing the weight of \( 160 g f \) at a distance \( 10 \mathrm{cm} \) to the right of the point \( O \)
D. By placing the weight of \( 80 g f \) at a distance \( 20 \mathrm{cm} \) to the of the point \( O \)


In Youngs double slit experiment, the
slits are \( 2 m m \) apart and are
¡IIluminated with a mixture of two
wavelengths \( \lambda=12000 A^{\circ} \) and \( \lambda= \)
\( 10000 A^{\circ} . \) At what minimum distance
from the common central bright fringe
on a screen \( 2 m \) from the slits will a
bright fringe from one interference
coincide with a bright fringe from the other?
A. \( 3.2 \mathrm{mm} \)
B. \( 6.0 \mathrm{mm} \)
c. \( 7.2 \mathrm{mm} \)
D. \( 9.2 \mathrm{mm} \)


Charge is produced by friction
A. Stationary
B. No
c. Attractive
D. All


Sum of the first \( p, q \) and \( r \) terms of an
A.P. are \( a, b \) and \( c, \) respectively. Prove \( \operatorname{that} \frac{\boldsymbol{a}}{\boldsymbol{p}}(\boldsymbol{q}-\boldsymbol{r})+\frac{\boldsymbol{b}}{\boldsymbol{q}}(\boldsymbol{r}-\boldsymbol{p})+ \)
\( \frac{c}{r}(p-q)=0 \)


The general formula of disaccharides is
A. \( C_{12} H_{22} O_{10} \)
В. \( C_{12} H_{22} O_{12} \)
c. \( C_{12} H_{22} O_{11} \)
D. none of these


In the given figure, what is the force on
the charge \( Q \) kept at \( O \) which is at
the mid point of the line \( A B ? \)
A \( \cdot \frac{2 q Q}{\pi \varepsilon_{0} r^{2}} \) along \( B A \)
B. \( \frac{2 q Q}{\pi \varepsilon_{0} r^{2}} \) along \( A B \)
c. zero
D. \( \frac{q Q}{4 \pi \varepsilon_{0} r^{2}} \)


Find the value(s) of \( k \) for which the
equation \( \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{k} \boldsymbol{x}+\mathbf{1 6}=\mathbf{0} \) has equal
roots.


Find the equation of the line parallel to \( 2 \bar{i}-\bar{j}+2 \bar{k} \) and which passes through
point \( ^{\prime} A^{\prime}(3 \bar{i}+\bar{j}-\bar{k}) . \) if \( P \) is a point on
the line such that \( A P=15 . \) Find the
position vectors of \( \boldsymbol{P} \)


The power radiated by a black body is \( P \)
and it radiates maximum energy around
the wavelength \( \lambda_{0} . \) If the temperature of
the black body is now changed so that it radiates maximum energy around wavelength \( \frac{3}{4} \lambda_{0}, \) power radiated by it will increase by a factor of
\( A \cdot \frac{4}{3} \)
В. \( \frac{16}{9} \)
c. \( \frac{64}{27} \)
D. \( \frac{256}{81} \)


Polyethylene glycols are used in the preparation of which type of detergents?
A. cationic detergents
B. Anioinc detergents
c. Non-ionic detergents
D. Soaps


a person invests rs. 5000 for two year at a certain rate of interest compounded annually at the end of one year this sum amount to rs. 5600 calculate.
(i) the rate of interest per annum


Find the equation of the line in vector and in cartesion form that passes through the point with position vector \( \mathbf{2} \hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) and is in the direction \( \hat{\mathbf{i}}+ \)
\( \mathbf{2} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)


A positive charged particle enters at the middle as shown in the figure with
\( 10^{5} m / s \) will bend:
A. towards 1 A wire
B. upwards the plane of wires.
c. towards 3 A wire.
D. down wards the plane of wires.


Give reasons for the following.
\( a . \) Oxygen is a gas but sulphur is a
solid.
b. \( B i H_{3} \) is the strongest reducing
amongst all hydrides of Group 15 elements.


Excretory organs of Amphioxus are
A. Nephrons
B. Flame cells
c. Nephridia
D. Kidneys


Lanthanides and actinides are
recognised as?
A. s- block element
B. d-block element
c. f-block element
D. p-block element


The acidic behavior of lakes and oceans
can be neutralized by:
A . \( N a O H \)
в. НС l
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( \operatorname{Ca}(O H)_{2} \)


Which sulphur has an open chain \( \boldsymbol{S}_{8} \)
molecule?
A. Rhombic sulphur
B. Monoclinic sulphur
c. Plastic sulphur
D. Roll sulphur


Insert two arithmetic means between
11 and 17
A. 13 and 15
B. 11 and 13
c. 13 and 14
D. 11 and 15


How is systematics relevant to other branches of biology?


The peptide linkage is :
A . amide
B. ether
c. ester
D. anhydride


An atom initially at an energy level \( \boldsymbol{E}= \)
\( -6.52 e V . \) It absorbs a photon of
wavelenght \( 860 n m . \) What is the interna energy of atom after absorbing photon.
A . \( 5.08 e V \)
B. \( 1.44 e V \)
c. \( -1.44 e V \)
D. \( -5.08 e V \)


Three measurements 7.1J, 7.2J and 6.7
are made as experiment and added the result with correct number of
significant figures is
A . 7.1
B . 7.06
c. 7.0
D. 7]


A horizontal plane supports a fixed vertical cylinder of radius \( R \) and a particle is attached to the cylinder by a horizontal thread \( A B \) as shown in
figure. A horizontal velocity \( \boldsymbol{v}_{0} \) is
imparted to the particle, normal to the thread, then during subsequent motion:
A. Angular momentum of particle about \( O \) remain constant
B. Angular momentum of particle about \( B \) remains constant
c. Momentum of particle remains constant
D. Kinetic energy of particle remains constant


The values of the limiting molar
conductivity \( \left(\wedge^{\circ}\right) \) for \( N a C l, H C l \) and NaOAc are 126.4,425.9 and
\( 91.0 S \mathrm{cm}^{2} \) mol \( ^{-1}, \) respectively. For
\( H O A c, \wedge^{\circ} \) in \( S c m^{2} m o l^{-1} \) is:
A. 390.5
B . 299.5
c. 208.5
D. 217.4


Choose the correct answer from the
alternatives given:
Which of the following will not denature a protein?
A. Temperatures above \( 100^{\circ} \mathrm{C} \)
B. Strong acids or strong bases
c. Alcohol
D. Distilled water


Explain the principle of potentiometer.


When a man is standing, rain drops
appear to him falling at \( 60^{\circ} \) from the horizontal from his front side. When he
is travelling at \( 5 k m / h \) on a horizontal
road, they appear to him falling at \( 30^{\circ} \)
from the horizontal from his front side.
The actual speed of the rain in \( k m / h \) is.
A . 3
B. 4
\( c .5 \)
D. 6


Uncertainty in position and momentum are equal. Uncertainty in velocity is:
A \( \cdot \sqrt{h / \pi} \)
B. \( \sqrt{h / 2 \pi} \)
c. \( 1 / 2 m \sqrt{h / \pi} \)
D. None of these


A shopkeeper earns a profit of Re 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock. In a particular month she incurs a loss of Rs. 5 In this period, she sold 45 pens. How many pencils did she sell in this period?


The outer electronic configuration of the element \( M o(Z=42) \) is:
\( \mathbf{A} \cdot 5 s^{2} 4 d^{4} \)
B. \( 5 s^{1} 4 d^{5} \)
c. \( 5 s^{2} 5 p^{4} \)
D. \( 4 s^{2} 3 d^{4} \)


TEL is a compound used as:
\( A \). antibiotic
B. antiswptic
c. antiknocking
D. antioxidant


\( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) solution of a weak acid
\( H A \) has molar conductivity
\( 5 S c m^{2} m o l^{-1} . \) The osmotic pressure of
the resulting solution obtained after
dilution of original solution upto 1 litre at \( 500 \mathrm{K}, \) assuming ideal solution is:
\( \left(G i v e n: \lambda_{m}^{\infty}\left(H^{+}\right)=\right. \)
\( 450 S c m^{2} m o l^{-1}, \lambda_{m}^{\infty}\left(A^{-}\right)= \)
\( \mathbf{5 0} \boldsymbol{S c m}^{2} \boldsymbol{m o l}^{-1}, \boldsymbol{R}= \)
\( \left.0.08 L \text { atm } \operatorname{mole}^{-1} K^{-1}, \sqrt{10}=3.2\right) \)
A. 0.3128 atm
B. 0.4128 atm
c. 0.5128 atm
D. 0.6128 atm


Discuss the continuity of the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\frac{\log (2+x)-\log (2-x)}{\tan x}, \quad \text { for } x \neq 0\right.
\]
at the point \( \boldsymbol{x}=\mathbf{0} \)


State whether true or false.
The recoil of a canon after firing is well explained by Newton's third law of
motion.
A. True
B. False


When all the parallel rays reflected from a mirror are parallel, the reflection is known as:
A . regular reflection
B. irregular reflection
c. diffused reflection
D. none of these


The lanthanide contraction is
responsible for the fact that:
A. zrand Hf have same radius
B. Zrand Zn have the same oxidation state
c. zrand Y have same radius
D. zrand Nb have similar oxidation state


Two different adiabatic parts for the
same gas intersect two isothermals at
\( T_{1} \) and \( T_{2} \) as shown in P-V diagram.
Then the ratio of \( \frac{V_{a}}{V_{b}} \) will be
\( \mathbf{A} \cdot \frac{V_{c}}{V_{d}} \)
B. \( \frac{V_{d}}{V_{c}} \)
\( c \cdot_{\gamma} \frac{V_{d}}{V_{d}} \)
D. \( \frac{1}{\sqrt{V}} \frac{V_{a}}{V_{V}} \)


When chloral hydrate is distilled with sodium hydroxide solution, it forms:
A. acetaldehyde
B. chloral
c. chloroform
D. ethyl chloride


Blue colour of sky is due to:
A. scattering.
B. absorption.
c. reflection.
D. refraction.


If \( y=\frac{\log _{e} x}{x} \) and \( z=\log _{e} x, \) then
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} z^{2}}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} z}= \)
A \( \cdot e^{-} \)
B. \( 2 e^{-2} \)
\( \mathrm{c} \cdot z e^{-} \)
D. \( -e^{-z} \)


State True or False.
Pure water can be used as an electrolyte in the process of electrolysis.
A. True
B. False


Which enzyme induces lysis of fibrinogen to fibrin during fibrinolysis?
A. Plasmin
B. Thrombin
c. Fibrin
D. Trypsin


A thin plano convex lens of focal length
\( f, \) is split into two halves. One of the halves is shifted along the principal
axis as shown. The separation between
an object placed on the axis and its
image is \( 1.8 m \)
The magnification of the image formed
by one of the half lenses is 2 . Find the
focal length of the combination and the separation between the two halves.
\( A \cdot 0.4 m \)
B. \( 0.5 \mathrm{m} \)
c. \( 0.6 \mathrm{m} \)
D. \( 0.7 \mathrm{m} \)


In a polygon, there are 5 right angles and the remaining angles are equal to
\( 195^{\circ} \) each., Find the number of sides in
the polygon.


The covalent and Van der walls radii of
chlorine respectively are:
\( \mathbf{A} \cdot 1.80 A^{\circ} \& 0.99 A^{\circ} \)
B. \( 0.99 A^{\circ} \) \& \( 1.80 A^{\circ} \)
\( \mathbf{C} \cdot 1.80 A^{\circ} \& 1.80 A^{\circ} \)
D. \( 0.99 A^{\circ} \) \& \( 0.99 A^{\circ} \)


Solve:
\( \lim _{h \rightarrow 0} \frac{1}{h}\left[\frac{1}{\cos (x+h)}-\frac{1}{\cos x}\right] \)


The force \( F \) is given in terms of time \( t \) and
displacement \( x \) by the equation \( F=A \) \( \cos B x+C \sin D t . \) The dimensional
formula of D/B is
\( \mathbf{A} \cdot\left[M^{o} L^{o} T^{o}\right] \)
в. \( \left[M^{\circ} L^{\circ} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M^{o} L^{-1} T^{o}\right] \)
D・ \( \left[M^{\circ} L^{1} T^{-1}\right] \)


Hydrolysis of lactose with dilute acid yields:
A. equimolar mixture of D-fructose and D-glucose.
B. equimolar mixture of D-glucose and D-gluctose
c. equimolar mixture of D-glucose and D-fructose
D. equimolar mixture of D-glucose and D-galactose


If the net electric field flux passing through a closed surface is Zero, then the electric field at the surface will be:
\( A \cdot O \)
B. Same at all places
c. depends upon the location of points
D. infinite


Positive of a negative integer is
A. negative
B. positive
c. zero
D. none of these


1, 3 - butadiene and acrylonitrile
undergo co-polymerization to give
\( A \cdot \) Buna \( -S \)
B. Buna - N
c. Buna - A
D. Al


Assertion
The purple colour of \( K M n O_{4} \) is due to
the charge transfer transition.
Reason
The intense colour in most of the
transition metal complexes is due to
\( \boldsymbol{d}-\boldsymbol{d} \) transition.
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


Two skaters have weight in the ratio 4:
5 and are \( 9 \mathrm{m} \) apart, on a smooth
frictionless surface,They pull on a rope stretched between them. The ratio of the
distance covered by them when they meet each other will be
A .5: 4
в. 4: 5
c. 25: 16
D. 16: 25


The particle emitted in the nuclear reaction
\( z^{A}=_{z+1} \mathbf{Y}^{A}+\ldots . . \) will be
A . \( \alpha \) -particle
B . \( \beta^{-} \) -particl
c. \( \beta+ \) -particle
D. Photon


From Rutherford's alpha particle scattering experiment give the experimental evidence for deriving the conclusion that


Sericulture is native of
A. Japan
B. China
c. India
D. Korea


A turn of radius \( 20 m \) is banked for the
vehicles going at a speed of \( 10 m s^{-1} . \) If the coefficient of static friction between
the road and the tyre is \( 0.4, \) what is the
possible speed of a vehicle so that it does not slips down?
(Take \( \left.g=10 m s^{-2}\right) \)
A. \( 50 k / h \)
в. \( 48 k / h \)
c. \( 54 k / h \)
D. \( 10 k / h \)


Two cells of same emf E but different
internal resistances \( r_{1} \) and \( r_{2} \) are
connected in series with an external
resistance \( R \). The potential drop across
the first cell is found to be zero.
The external resistance \( \boldsymbol{R} \) is
A \( \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( r_{2}-r_{1} \)
D. \( r_{1} r_{2} \)


The conjugate acid of \( \boldsymbol{O}^{-2} \) ion is:
A \( . O H^{-} \)
B. \( O H^{+} \)
c. \( H_{2} O \)
D. \( H O_{2}^{-} \)


One growth ring consists of
A. Springwood and early wood
B. only spring wood
c. only autumn woodd
D. spring wood and autumn wood
E. Bryophytes


The normality of a solution of a mixture containing \( \boldsymbol{H} \boldsymbol{C l} \) and \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{N} / \mathbf{5} \)
Twenty millilitres of this solution reacts
with an excess of \( A g N O_{3} \) solution to
give \( 0.287 g \) of silver chloride. The
percentage of \( H C l \) in the mixture by
mass, is \( (A g=108) \)
A . \( 42.69 \% \)
B. \( 57.31 \% \)
c. \( 50 \% \)
D. 25\%


The time taken by the bob of a pendulum to complete one oscillation is called its
A. time period
B. amplitude
c. mass
D. frequency


Solve and graph the inequality. Give
answer in interval notation.
\( 15<4 x+3 \leq 31 \)
A \( \cdot(3,7) \)
в. [3,7)
\( c .(3,7] \)
D・ [3,7]


Given two independence events \( A \) and \( B \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( P(A / B) \)


Define heat transfer due to Radiation.


Which compound is the most soluble in
water?
A. chloroethane
B. Ethanol
c. Ethanal
D. Ethylene glycol


Most harmful pesticide is
\( A \cdot 2,4-D \)
в. \( 2,4,5- \) -
c. DDT
D. PAN


f \( a, b, c, d \) are in continued proportion,
prove that \( (a+d) b+c)-(a+c)(b+d)= \)
\( (b-c)^{2} \)


Two cells, having the same e.m.f are connected in series through an external resistance R. Cells have internal
resistance \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
respectively. When the circuit is closed, the potential difference across the first cell is zero. the value of \( \mathrm{R} \) is
A \( \cdot \frac{r_{1}+r_{2}}{2} \)
B. \( \frac{r_{1}-r_{2}}{2} \)
\( \mathbf{c} \cdot r_{1}+r_{2} \)
D. \( r_{1}-r_{2} \)


A solid sphere of mass \( \mathrm{M} \) and radius \( \mathrm{R} \)
is divided into two unequal parts. The first part has a mass of \( \frac{\mathbf{7} M}{\mathbf{8}} \) and is converted into a uniform disc of radius
\( 2 R . \) The second part is converted into a
uniform solid sphere. Let \( \boldsymbol{I}_{\mathbf{1}} \) be the moment of inertia of the disc about its
axis and \( I_{2} \) be the moment of inertia of
the new sphere about its axis. The ratio
\( \boldsymbol{I}_{1} / \boldsymbol{I}_{2} \) is given by :
A . 185
B. 65
c. 285
D. 140


What is the probability that the wheel
stops at red or pink?
\( \mathbf{A} \)
\( B \)
6
\( c \cdot 3 \)
D. None of these


Each resistance of the circuit shown in
figure is \( r . \) The equivalent resistance
between \( A \) and \( B \) is:
\( A \)
в. \( \frac{r}{4} \)
\( c \cdot \frac{r}{2} \)
D. \( \frac{5 r}{8} \)


If \( 2 a=b, \) the pair of equations \( x+ \)
\( 2 y=2 a-6 b, a x+b y=2 a^{2}-3 b^{2} \)
possess solution(s)
A. No
B. Only one
c. only two
D. An infinite number of slutions


State True or False.
\( N H_{3}, P H_{3} \) and \( A s H_{3} \) have \( s p^{3} \)
hybridised central atom and thus each
had bond angle of \( 109^{\circ} 28^{\prime} \)
A . True
B. False


\( y=2 x^{\sin x}-\left(\sin ^{-1} x\right)^{2} . \) find \( \frac{d y}{d x} \)


The magnetic moment of \( _{41} \mathrm{Nb} \) is found to be \( 5.916 . \) Total no. of unpaired
electron are :
\( A \cdot 6 \)
B. 3
\( c \cdot 5 \)
D.


A pendulum ( positively charged and hinged at some length above the plate) is swinging above a parallel plate (infinitely large and having negative charge),now consider the following statements, (consider gravity)
A. angular momentum about the hinge point of the ball will be max at lowest point
B. electric potential energy will be max at highest point
c. gravitational potential energy will be lowest at highest point
D. none of the above


eac Gopp
\( 0.346 \quad \) Happy Father's Day


Calculate the emf of the following cell at
\( 298 \mathrm{K} \)
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})\left|\boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{0} \cdot \boldsymbol{0} \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \| \boldsymbol{H}^{+}(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{H}_{2}(\boldsymbol{g}) \)
\( \left(\text {Given } \boldsymbol{E}_{\text {cell}}=+\mathbf{0 . 4 4} \boldsymbol{V}\right) \)


Jorge's current hourly wage for working at Denti Smiles is \( \$ 12.00 . \) Jorge was
told that at the beginning of next month, his new hourly wage will be an increase of \( 6 \% \) of his current hourly
wage. What will be Jorge's new hourly wage?
A . \( \$ 12.06 \)
B. \( \$ 12.60 \)
c. \( \$ 12.72 \)
D. \$ 18.00
E . \( \$ 19.20 \)


Adsorption increases with increase in temperature in Physisorption.
A. True
B. False


One of the most abundant extracellular
ions that represents about \( 90 \% \) is
A. Chloride
B. Sodium
c. Calcium
D. Potassium


Explain how the formation of rainbow
occurs.


If a copper rod carries a direct current, the magnetic field associated with the current will be:
A. only inside the rodd
B. only outside the rod
c. both inside and outside the rod
D. neither inside nor outside the rod


Light from two coherent sources of the same amplitude \( A \) and wavelength \( \lambda \) illuminates the screen. The intensity of
the central maximum is \( I_{0} . \) If the
sources were incoherent, the intensity at the same point will be.
A . \( 4 I_{0} \)
в. \( 1 I_{0} \)
c. \( I_{0} \)
D. \( \frac{I_{0}}{2} \)


Which of the following is incorrect
about \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} ? \)
A \( . \) It can be prepared from \( K_{2} C r O_{4} \)
B. It is used in redox titrations
c. It is stable in both acid \& base
D. It is orange in colour


A certain sum amount 12167 in 3 years
at \( 15 \% \) p.a compounded annually. Find
sum


Chemisorption is ............... while physical adsorption is in nature.
A . reversible, reversible
B. irreversible, reversible
c. reversible, irreversible
D. irreversible, irreversible


Calculate the mass of ice required to
lower the temperature of \( 300 g \) of water at \( 40^{\circ} \mathrm{C} \) to water at \( 0^{\circ} \mathrm{C} \). (Specific latent heat of ice \( =336 \mathrm{J} / \mathrm{g}, \) Specific heat capacity of water \( \left.=4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}\right) \)


How can Infrared radiations be harmful
for humans
A. Can cause blindness
B. Can cause skin burns
c. can cause hairfall
D. can cause frostbite


9 volumes of a gaseous mixture contain
an organic compound and oxygen sufficient for its combustion. Burning
the compound yielded 4 volumes of
\( C O_{2}, 6 \) volumes of \( H_{2} O \) and 2 volumes
of \( N_{2}, \) find the molecular formula of the
compound?


involves in the intake of complex material prepared by other organisms.
A. Heterotrophic nutrition
B. Autotrophic nutrition
c. chemotrophic nutrtion
D. Photototrophic nutrition


A force of \( 25 \mathrm{N} \) acts on a body at rest for
\( 0.2 s \) and a force of \( 70 N \) acts for the next
\( 0.1 \mathrm{s} \) in opposite direction. If the final
velocity of the body is \( 5 m s^{-1}, \) the mass
of the body is:
\( A \cdot 1 \mathrm{kg} \)
B. \( 2 \mathrm{kg} \)
c. \( 0.8 \mathrm{kg} \)
D. \( 0.4 \mathrm{kg} \)


The resultant magnetic field at the center of a bar magnet is zero.
A. True
B. False


Find the quotient of \( 100^{100}+50^{50} \)


In the test for the detection of
phosphorous present in an organic compound, which of the following compound is yellow colour or precipitate?
A. Ammonium phosphomolybdate
B. Sodium phosphate
c. phosphoric acid
D. ammonium phosphate


If the angle between incident ray and
normal is \( 30^{\circ} \).what will be the angle of
incidence?
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 150^{\circ} \)


Explain the function of Nervous system.


The process of sending back the light rays into the same medium is called


In which one of the following reagents \( \boldsymbol{O}-\boldsymbol{H} \) bond fission in alcohol can not
take place?
A . Na a
в. \( C H_{3} \) СООН
c. \( C H_{3} M g B r \)
D. \( P C l_{5} \)


Recently (in Aug 2003 ) two new elements have been discovered with
atomic number:
A .113,114
В. 114,115
\( \mathrm{c} .115,116 \)
D. 113,115


Potentiometer wire of length \( 1 \mathrm{m} \) is connected in series with \( 490 \Omega \)
resistance and 2 V battery. If \( 0.2 \mathrm{mV} / \mathrm{cm} \) is the potential gradient, the resistance of the potentiometer wire is
\( A \cdot 4.9 \Omega \)
B. 7.9 \( \Omega \)
\( c \cdot 5.9 \Omega \)
D. \( 6.9 \Omega \)


In simple microscope maximum angular magnification is nearly equal
to:
A .200
B. 10
\( c \cdot 100 \)
D. 1000


Synaptonemal complex is formed during
A. Meiosiss
B. Amitosis
c. Mitosiss
D. cytokinesis


Critical temperature for carbon dioxide
and methane are \( 31.1^{\circ} \mathrm{C} \) and \( -81.9^{\circ} \mathrm{C} \)
respectively. Which of these has stronger intermolecular forces and
why?


Let \( y=e^{\frac{1}{x}} \) then find \( \frac{d^{2} y}{d x^{2}} \)


Show with balanced equations what happens when the following are mixed:
Aqueous solution of potassium chromate and acid.
A \( \cdot 2 C r O_{4}^{2-}+2 H^{+} \rightleftharpoons C r_{2} O_{7}^{2-}+H_{2} O \)
B \( \cdot 2 C r O_{4}^{2-}+10 H^{+} \rightleftharpoons C r_{2} O_{3}^{2-}+5 H_{2} O \)
\( \mathrm{c} \cdot 2 \mathrm{Cr} \mathrm{O}_{4}^{2-}+6 \mathrm{H}^{+} \rightleftharpoons \mathrm{Cr}_{2} \mathrm{O}_{5}^{2-}+3 \mathrm{H}_{2} \mathrm{O} \)
D. None of these


Two drops of the same radius are falling through the air with steady speed v. If the two drops coalesce, what would be
the terminal speed.
\( A \)
B. 2v
\( c \cdot 3 v \)
D. none of these


Assertion
Hydrides of group 13 elements are Lewis acids whereas hydrides of group \( 15-17 \) elements are Lewis bases
Reason
Group 13 hydrides have few electrons
whereas group \( 15-17 \) hydrides have excess electrons which are present as
lone pairs
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


\( (\$) \) \( (\infty) \) \( \$ \) 8


Solve the equation
\[
\begin{array}{l}
\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+ \\
\frac{(x-a)(x-b)}{(c-a)(c-b)}=1
\end{array}
\]


Among mammals, an herbivore has
A. More teeth than carnivore
B. Flatter teeth than carnivore
C. Teeth that are more pointed than carnivore
D. Fever teeth than a carnivore


How many elements will be present in
\( 5^{t h} \) period of the periodic table? Justify
using quantum numbers.


Which one of the following cells can convert chemical energy of \( O_{2} \) and \( H_{2} \)
directly into electrical energy:
A. mercury cell
B. danicell cell
c. fuel cell
D. lead storage cell


First transitional series is present in:
A. third period
B. fifth period
c. fourth period
D. sixth period


How many zones are present in candle flame?
A .2
B. 3
\( c \cdot 4 \)
\( D \)


Each resistor shown is 9 ohms.
When hooked to a 6 -volt battery, which combination would produce 2 watts of
power?
\( A \)
B.
\( c \)
D.


A sample of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) (density
\( 1.787 g c m^{-3} \) ) labelled as \( 86 \% \) by weight. What is the normality of acid?
A . 20
B. 13.6
c. 36.36
D. 15.68


If in the ground state an atom has seven valence electrons, which of the following is the correct electronic configuration of the atom in the ground state?
A \( .3 s^{1} 3 p^{6} \)
В. \( 3 s^{6} 3 p^{\text {। }} \)
c. \( 3 s^{1} 3 p^{4} 3 d^{2} \)
D. \( 3 s^{3} 3 p^{4} 3 d^{1} \)
E \( .3 s^{2} 3 p^{5} \)


The number of \( p \pi-d \pi \) 'pi' bonds
present in \( X e O_{3} \) and \( X e O_{4} \) molecules,
respectively are
\( \mathbf{A} \cdot 3,4 \)
в. 4,2
c. 2,3
D. 3,2


The two electrons have the following set of quantum numbers:
\( \boldsymbol{P}=\mathbf{3}, \mathbf{2},-\mathbf{2},+\frac{\mathbf{1}}{\mathbf{2}} \)
\( \boldsymbol{Q}=\mathbf{3}, \mathbf{0}, \mathbf{0},+\frac{\mathbf{1}}{\mathbf{2}} \)
Which of the following statement is
true?
A. \( P \) and \( Q \) have same energy
B. \( P \) has greater energy than \( Q \)
c. \( P \) has lesser energy than \( Q \)
D. \( P \) and \( Q \) represent same electron


Identify disaccharides among the following:
(a) Stachyose
(b) Lactose
(c) Maltose
(d) Raffinose
A \( . a, b \)
в. \( d, \)
\( c \cdot b, e \)
D. \( b, c \)


What is the producy'P'


The following motion is based on the
law of conservation of angular
momentum
A) rotation of top
B) diving of a diver
C) rotation of ballet dancer on smooth
horizontal surface
D) a solid sphere that rolls down on an inclined plane Identify the wrong statement:
A. In rotating a top, angular momentum is conserved.
B. When a diver dives using a board, angular momentum is conserved.
c. In rotation of a ballet dancer on a smooth horizontal surface, angular momentum is conserved
D. When a solid sphere rolls down an inclined plane angular momentum is conserved.


Effective resistance between \( A \) and \( C \)
is:
A . \( 2 \Omega \)
B. \( 6 \Omega \)
\( c .9 \Omega \)
D. None


Determine the number of electron in the isotope of 'H' (mass no. 2).
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 0 \)
D.


The state of matter in which inter-
particle attraction is weak and inter-
particle space is so large that the particles become free to move randomly in the entire space is known as:
A. solid
B. liquid
c. gas
D. Both A and B


The dead element present in the phloem
is
A. Companion cells
B. Phloem fibres
c. Phloem parenchyma
D. Sieve tubes


The volume of helium is \( 44.8 ~ L \) at:
A \( \cdot 100^{\circ} \mathrm{C} \) and 1 atm
B. \( 0^{\circ} \mathrm{C} \) and 1 atm
c. \( 0^{\circ} \mathrm{C} \) and 0.5 atm
D. \( 100^{\circ} \mathrm{C} \) and 0.5 atm


Complete the following chemical reactions
(b) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l}+\boldsymbol{K} \boldsymbol{C N} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \)
\( (c) C H_{3}-C H=C H_{2}+H I \rightarrow \)
(d) \( C H_{3}-C H_{2}-O H+N a B r+ \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
(a) 0 \( \mathrm{Cl}+\mathrm{CH}_{3}-\mathrm{cl} \) anhydrous \( \mathrm{AlCl}_{3} \)


In warfare smoke screens are prepared
from
A \( . P H_{3} \)
в. \( C a C_{2} \)
\( \mathrm{c} \cdot P_{2} \mathrm{O}_{5} \)
D. \( \operatorname{cocl} \)