Tanvi bought ten food items from the supermarket, which are wheat, bananas, mushrooms, onions, Porphyra(Laver), Kelps, pine seeds, Sphagnum moss, lady's fingers and potatoes. Based on hierarchical classification, how many different phyla/divisions do these items belong
to?
\( A .3 \)
B. 4
\( c .5 \)
D. 6


\( M g^{2+}, A l^{3+} \) have identical:
A. configuration
B. atoms
\( c . \) ions
D. molecules


Choose the correct answer from the
alternatives given Which of the following are components of blood?
A. Plasma
B. Blood cells and platelets
c. Gases and other dissolved substances
D. All of the above


The primary ventral cell give rises to
A. Jacket
B. Tapetum
c. oosphere
D. Oospore


A progressive wave is represented as \( \boldsymbol{y}=\mathbf{0 . 2} \cos \boldsymbol{\pi}\left(\mathbf{0 . 0 4 t}+\mathbf{0 . 2 x}-\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \) where
distance is expressed in cm and time in second. What will be the minimum
distance between two particles having
the phase difference of \( \frac{\pi}{2} ? \)
A. \( 4 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. 12.5 cm


Which of the following statements are
correct about Nylon - 6, 6 ?
This question has multiple correct options
A. Nylon fibers have higher tensile strength than teylene fibres.
B. Nylon fibers have lower tensile strength than terylene fibres.
C. In nylon, there is strong intermolecular H-bonding, while in terylene there is weak dipole-dipole interaction.
D. In nylon, there is weak dipole-dipole interaction, while in terylene there is strong intermolecular H-bonding.


State the property that is used in each of the following statements?
If \( \angle \mathbf{4}=\angle \mathbf{5}=\mathbf{1 8 0}^{\circ} \) then \( \boldsymbol{a} \| \boldsymbol{b} \)


The liquid is allowed to flow into a tube
of truncated cone shape. Identify the correct statement from the following.
A. The speed is high at the wider end and high at the narrow end
B. The speed is low at the wider end and high at the narrow end
c. The speed is same at both ends in a stream line flow.
D. The liquid flows with uniform velocity in the tube


A candle flame \( 3 \mathrm{cm} \) high is placed at a distance of \( 3 \mathrm{m} \) from a wall.how far from
the wall must a concave mirror be
placed so that it may form \( 9 \mathrm{cm} \) high image of the flame on the same wall? Also find the focal length of the mirror.


Gonadotropic hormone is
A. FSH
B. LH
c. LTH
D. FSH, LH


The secondary wall material suberin deposited on the walls of
A. Phellogen and Phelloderm
B. Epidermis of stem and Endodermis of root
c. Pericycle of stem and Endodermis of root
D. Phellem of stem and Endodermis of root


The ratio of acceleration due to gravity
at a depth \( h \) below the surface of earth
and at a height \( h \) above the surface for
\( \boldsymbol{h}<<\boldsymbol{R} \)
A. is constant
B. increases linearly with h.
c. varies parabolically with h.
D. decreases.


\( 0.124 g m \) of an organic compound containing phosphorus gave \( 0.222 g m \)
of \( M g_{2} P_{2} O_{7} \) the usual analysis.
Calculate the percentage of phosphorous in the compound. \( (M g= \)
\( \mathbf{2 4}, \boldsymbol{P}=\mathbf{3 1}) \)
A .25
в. 15
\( c .62 \)
D. 50


Identify the correct pair of statements.
(1) Lutein is an oxygenated hydrocarbon.
(II) Inhibition of bacteroid respiration by oxygen is referred to as 'Warburg effect'.
(III) Triplet code 'UAA' is called 'Amber'.
(IV) Delay of senescence by cytokinins is known as 'Richmond-Lang effect'.
A \( .(\text { II }), \) (III)
B. (I), (IV)
c. \( (1),(\text { III }) \)
D. (II), (IV)


Filteration takes place in
A. Malpighian corpuscles
B. Bowman's capsule
c. Glomerulus
D. collecting tubule


\( \int \frac{x^{2}}{\sqrt{1-x^{6}}} d x=\frac{1}{k} \sin ^{-1}\left(x^{k}\right)+C . \) what


Object placed \( \ldots \) lens or mirror give infinite magnification
A. At focus
B. At infinite distance
c. Between \( F_{1} \) and \( 2 F_{1} \)
D. At \( 2 F_{1} \)


When an electron moves in a circular
path around a stationary nucleus
charge at the center:

This question has multiple correct options
A. the acceleration of the electron changes
B. the velocity of the electron changes
c. electrostatic force due to the nucleus at the electron changes
D. none of these


Find the magnitude of two vectors \( \vec{a} \) and
\( \vec{b}, \) having the same magnitude and such
that the angle between them is \( 60^{\circ} \) and their scalar product is \( \frac{1}{2} \)
A \( .-1,-1 \)
в. 1,1
c. -2,-2
D. 2,2


Verify that \( y^{2}=4 a(x+a) \) is a solution
of the differential equation
\( \boldsymbol{y}\left\{1-\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}\right\}=\boldsymbol{2} \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


The water stored in a
reservoir possesses:
A. Kinetic energy
B. Muscular energy
c. Potential energy
D. Magnetic energy


If the distance of the point \( P(4,3,5) \) from the Y-axis is \( \lambda \), then the value of
\( 7 \lambda^{2} \) is
A .287
B. \( 7 \sqrt{41} \)
c. 63
D. 21


Assertion
Elementary phosphorus exists in three principal allotropic forms, i.e., white (or yellow), red (or violet) and black.
Reason
Of the three forms, white phosphorus is the most important and most reactive.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The most common ore of iron is
A. calamine
B. hematite
c. zinc blende
D. copper pyrite


Starting from rest, a body slides down a 45 degrees inclined plane in twice the time it takes to slide down the same
distance in the absence of friction. The
coefficient of friction between the body
and the inclined plane is:
A . 0.33
B. 0.25
c. 0.75
D. 0.80


Which one of the following is Zeise's
salt?
\( A \)
\( \left[\left(C_{2} H_{2}\right)_{2} F e\right] \)
в. \( \left(P h_{3} P\right)_{3} \) Rh\( C l \)
c. \( \left[\left(C_{6} H_{6}\right)_{2} C r\right] \)
D \( \cdot K\left[P t C l_{3} . C_{2} H_{4}\right] \)


If \( a \sin ^{2} \theta+b \cos ^{2} \theta=c, \) then \( \tan ^{2} \theta= \)
A \( \cdot \frac{b-c}{a-c} \)
в \( \cdot \frac{c-b}{a-c} \)
c. \( \frac{a-c}{b-c} \)
D. \( \frac{a-c}{c-b} \)


The angle of incidence on a plane mirror
is \( 45^{\circ}, \) then the angle of reflection will
be
A . 35
B . 45
\( \mathrm{c} \cdot 135^{\circ} \)
D. 145


Which of the following would be expected to be most highly ionised in water?
A \( \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COO} \)
в. \( \mathrm{CH}_{3} \mathrm{CH} \mathrm{ClCH}_{2} \mathrm{COOH} \)
\( \mathbf{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CCl}_{2} \mathrm{COOH} \)
D. \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH} \mathrm{ClCOOH} \)


The range of \( a r c \sin x+a r c \cos x+ \)
\( \arctan x \) is


Which of the following number of lone
pair at central atom zero?
\( X e O_{3}, X e O_{2} F_{2}, X e O_{4}, X e O_{3} F_{2}, B a_{2} X \)
A . 2
B. 3
\( c \cdot 4 \)
D. zero


The pole strength of \( 12 \mathrm{cm} \) long bar magnet is \( 20 \mathrm{A} \) m. The magnetic induction at a point \( 10 \mathrm{cm} \) away from the centre of the magnet on its axial line is \( \left[\frac{\boldsymbol{\mu}_{\boldsymbol{o}}}{\boldsymbol{4} \boldsymbol{\pi}}=\mathbf{1 0}^{-\boldsymbol{7}} \boldsymbol{H} \boldsymbol{m}^{-1}\right] \)
A \( .1 .17 \times 10^{-3} \mathrm{T} \)
В. \( 2.20 \times 10^{-3} \mathrm{T} \)
c. \( 1.17 \times 10^{-2} \mathrm{T} \)
D. \( 2.20 \times 10^{-2} \mathrm{T} \)


To make a tea, a tourist puts into a
kettle 2 kg of ice at a temperature of \( 0^{\circ} \)
C. What quantity of heat is required to transform the ice into boiling water at
\( 100^{\circ} \mathrm{C} \) temperature?


Given that for the reaction,
\( A g\left(N H_{3}\right)_{2}^{+} \rightleftharpoons A g^{+}+2 N H_{3}, \quad K_{c}= \)
\( 6.2 \times 10^{-8} \) and \( K_{s p} \) of \( A g C l=1.8 \times \)
\( 10^{-10} \) at \( 298 K . \) The concentration of the
complex ion in \( 1.0 ~ M \) aqueous ammonia is:
A. \( 0.0539 M \)
B. \( 0.0589 M \)
c. \( 0.0639 M \)
D. None of these


Biotic potential refers to
A. Increase of population under optimum environmental conditions
B. Increase of population under given conditions
C. Increase of population under natural conditions
D. Increase of population under climatic conditions


\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right] \) is 60\% ionized.
What will be its van't Hoff factor?
A . 1.4
B. 2.4
c. 3.4
D. 4.4


Calculate the wavelength of the first number of Balmer series of hydrogen spectrum (R for hydrogen \( =1.09678 \times 10 \) \( \left.7 m^{-1}\right) \)
A \( \cdot 2188 \times 10^{-10} \mathrm{m} \)
B. 656 \( \times 10^{-10} \mathrm{m} \)
c. \( 6564 \times 10^{-10} \mathrm{m} \)
D. None of these


Give reasons as to why one cannot hear the sound produced by other sources on
the moon.
A. no presence of a medium for propagation
B. the radiations from the sun destroy all the sound waves created
c. sound only propagates on the earth
D. none of these


Does the composition of nucleus changes, if it emits \( \gamma \) -radiation?
A . yes
B. no
c. may be
D. cant say


By the addition of \( \mathrm{CO} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \) on ethene, the following is obtained:
A. Propanoic acid
B. Propanal
c. २Propenoic acid
D. None of the above


For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material
whose refractive index lies between:
\begin{tabular}{ll}
B. 1 & and \( \sqrt{2} \) \\
\hline
\end{tabular}
\( \begin{array}{lll}c \cdot \sqrt{3} & \text {and} & 2\end{array} \)
\( \begin{array}{lll}\text { D. } \sqrt{5} & \text { and } 2\end{array} \)


Find the real and imaginary parts of \( \frac{4+2 i}{1+2 i} \)


What is meant by amplification? Draw a simple circuit of \( n \) -p-n common emitter
transistor amplifier. On the basis of band theory, distinguish between conductor, insulator and semi-
conductor.


If \( \boldsymbol{y}+\sin \boldsymbol{y}=\cos \boldsymbol{x}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


The apparent flattening of the sun at sunset and sunrise is due to
A. refraction
B. diffraction
c. total internal reflection
D. interference
E. polarization


Which of the following reactions is/are disproportionation reaction(s)?
This question has multiple correct options
A \( \cdot C l_{2}+2 \stackrel{\ominus}{O} H \rightarrow C l^{\ominus}+C l O^{\ominus}+H_{2} O \)
в. \( 2 H C u C l_{2} \rightarrow C u+C u^{2+}+4 C l^{\ominus}+2 H^{\oplus} \)
c. \( _{H C H O}+\stackrel{\ominus}{O H} \longrightarrow C H_{3} O H+H C O O^{\circ} \)
D. \( M g C O_{3} \rightarrow M g O+C O_{2} \)


A cube of \( 4 \mathrm{cm} \) has been painted on its surface in such a way that two opposite surfaces have been painted blue and
two adjacent surfaces have been painted red Two remaining surfaces have been left unpainted Now the cube is cut into smaller cubes of sides \( 1 \mathrm{cm} \)
each

How many cubes will have at least blue
colour on its surface?
A. 20
B. 8
\( c \cdot 24 \)
D. 32


The refractive index of the core of an
optical fibre is \( \mu_{2} \) and that of the
cladding is \( \mu_{1} . \) The angle of incidence on the face of the core so that the light ray just under goes total internal reflection at the cladding is:
A \( \cdot \sin ^{-1}\left(\frac{\mu_{1}}{\mu_{2}}\right) \)
B. \( \sin ^{-1} \sqrt{\mu_{2}^{2}-\mu_{1}^{2}} \)
c. \( \sin ^{-1} \sqrt{\mu_{2}-\mu_{1}} \)
D. \( \sin ^{-1} \sqrt{\mu_{1}^{2}+\mu_{2}^{2}} \)


For the sustained interference of light,
the necessary condition is that the two sources should
A. have constant phase difference only
B. be narrow
c. be close to each other
D. of same amplitude with constant phase difference


Hookes Laws is used in the
determination of
A. Weight of a body
B. Density of a body
c. volume of body
D. None of these


The dipolemoment of the given system is:
A. \( \sqrt{3} q l \) along perpendicular bisector of \( q-q \) line
B. \( 2 q l \) along perpendicular bisector of \( q-q \) line
C \( \cdot q l \sqrt{2} \) along perpendicular bisector of \( q-q \) line
D. 0


Which of them are atomic models?
Thomsons plum puddling model
Rutherfords nuclear model
Bohrs model
Sommerfelds model
\( A \cdot i \& \) i
B. i, ii \& iii
c. ii, ii \& iv
D. All of these


Assertion
In a small segment of string carrying sinusoidal wave, total energy is conserved if system is isolated.
Reason

Every small part moves in SHM.
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


Explain avalanche breakdown in a diode and zener breakdown in a zener diode


The angle between two diagonals of a cube is.
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
c. \( \cos ^{-1}\left(\frac{1}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)


For the binary operation \( \times_{10} \) on \( \operatorname{set} S= \)
\( \{1,3,7,9\}, \) find the inverse of 3


The size of an object as perceived by a human eye depends primarily on the
A. Actual size of the object
B. Distance of the object from eye
c. Aperture of the pupil
D. Size of the image formed on the retina


Which of the following is the wrong
statement?
A. Ozone is paramagnetic gas.
B. The two oxygen-oxygen bond length in ozone are identical.
\( \mathrm{c} \cdot O_{3} \) molecule is bent.
D. Ozone is violet-black in solid state


Which of the following statement(s) is/are true?
This question has multiple correct options
A. All reactions are oxidation and reduction reactions.
B. Oxidising agent is itself reduced.
c. oxidation and reduction always go side by side
D. Oxidation number during reduction decreases.


In the figure the position time graph of a particle of mass \( 0.1 \mathrm{kg} \) is shown. Find
the impulse at \( t=4 \sec : \)
A. \( 0.2 \mathrm{kgcms}^{-1} \)
в. \( -0.2 \mathrm{kgcms}^{-1} \)
c. \( 0.1 \mathrm{kg} \mathrm{cms}^{-} \)
D. - \( 0.4 \mathrm{kgcms}^{-} \)


For the following equilibrium \( 2 F e(s)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{3}}(\boldsymbol{s})+ \)
\( \mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}), \boldsymbol{K}_{c}=\mathbf{2 7 .} \) Hence ratio of molar
concentration of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) is:
\( A \cdot 3 \)
B.
\( c \cdot 9 \)
D. 27


\( \Delta G^{\circ} \) vs \( T \) plot in Ellingham diagram slopes downward for the reaction:
\( ^{\mathrm{A}} \cdot_{M g}+\frac{1}{2} O_{2} \rightarrow M g O \)
в. \( _{2 A g}+\frac{1}{2} O_{2} \longrightarrow A g_{2} O \)
\( ^{\mathrm{c}} \cdot c+\frac{1}{2} O_{2} \rightarrow C O \)
\( ^{\mathrm{D}} \cdot_{C O}+\frac{1}{2} O_{2} \rightarrow C O_{2} \)


Al is obtained by the electrolysis of
fused mixture of \( A l_{2} O_{3} \) and \( N a_{2} A l F_{6} . \) If
true enter 1 else 0


The perpendicular drawn to the surface of the mirror at the point of incidence
is known as:
A. reflected ray
B. refracted ray
c. incident ray
D. normal ray


What osmotic pressure would the 1.25 molal sucrose solution exhibit at \( 25^{\circ} \mathrm{C} \) ?
(The density of this solution is 1.34 \( g / m L \)
\( \mathbf{A} \cdot 28.70 \mathrm{atm} \)
B. 30.22 atm
c. 21.72 atm
D. 24.55 atm


\( \int \frac{2 x+\sin 2 x}{1+\cos 2 x} d x \)
\( A \cdot x \cot x \)
B. \( x \tan x \)
c. \( x^{2} \tan x \)
D. \( x \)


If the mass of a body is \( 12.1 \mathrm{g} \) and its density is \( 2.2 \mathrm{g} / \mathrm{cc}, \) its volume is.
\( \mathbf{A} \cdot 5.5 \mathrm{cm}^{3} \)
B. 8 сс
c. 11 сс
D. 55 сс


Assertion
Sulphur on reaction with HCl produces
sulphur monochloride.
Reason
Sulphur undeigoes displacement reaction with acid.
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


Assertion
A normal human eye can clearly see all the objects at the different distance.
Reason

The human eye has the capacity to suitably adjust the focal length of its
lens to a certain extent
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


When a rubber-bank is stretched by a distance \( x, \) it exerts a restoring force of magnitude \( F=a x+b x^{2} \) where \( a \) and \( b \)
are constants. The work done in
stretching the unstretched rubber band
by \( \boldsymbol{L} \) is:
\( ^{\mathrm{A}} \cdot \frac{a L^{2}}{2}+\frac{b L^{3}}{3} \)
\( ^{\mathrm{B}} \cdot \frac{1}{2}\left(\frac{a L^{2}}{2}+\frac{b L^{3}}{3}\right) \)
\( \mathbf{c} \cdot a L^{2}+b L^{3} \)
D. \( \frac{1}{2}\left(a L^{2}+b L^{3}\right) \)


\( H_{2} S, \) a toxic gas with rotten egg like smell, is used for the qualitative
analysis. If the solubility of \( H_{2} S \) in water at STP is \( 0.195 \mathrm{m} \), Calculate Henry's law constant.
A. 282.0 bar
B. 324.8 bar
c. 462.9 bar
D. 534.8 bar


An object of mass \( \mathrm{m} \) rests on a plane
inclined at an angle of \( \theta . \) What is the
maximum value for the coefficient
of static friction at which the object will slide down the incline?
A \( . \sin \theta-\cos \theta \)
B. \( \cos \theta-\sin \theta \)
c. mgsint
D. \( \sin \theta / \cos \theta \)
E. \( \sin \theta+\cos \theta \)


State whether the following statements
are true or false.
In the conversion of pyruvic acid to acetyl coenzyme \( A, \) pyruvic acid is reduced.
A. True
B. False


In \( \triangle A B C, \) bisector of \( \angle A \) and \( \angle B \)
intersect at point \( O . \) If \( \angle C=70^{\circ} \) what
is the value of \( \angle A O B ? \)


Verify :
\( \mathbf{1 7} \times(\mathbf{9}+(-\mathbf{3}))=(\mathbf{1 7} \times \mathbf{9})+(\mathbf{1 7} \times \)
(-3))


The value of \( \int_{0}^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) d x \)
is equal to
A \( \cdot \frac{\pi}{2} \)
B. \( -\frac{\pi}{2} \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. \( -\frac{\pi}{\sqrt{2}} \)


Circular arc of radius \( 7 \mathrm{cm} \) has been
drawn with vertex \( A \) of an equilateral
triangle \( A B C \) of side \( 14 \mathrm{cm} \) at center Find the area of shaded region.


The voltage at \( B \) in the figure is :
\( A \cdot 5.3 V \)
В. \( 5.7 V \)
\( c .6 .3 V \)
D. \( 6 V \)


The order and degree of the differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3 / 2}=\boldsymbol{y} \) are
respectively
A . 1,1
в. 1,2
\( \mathrm{c} .1,3 \)
D. 2,
E .2,2


What is the half life of a radioactive
substance if it has a count rate of 500
counts/sec and 62.5 counts/sec two
hours later?
A . 10 min
B. 20 min
c. 30 min
D. 40 min
E. 50 min


Which of the following is initiation codon?
A . AUGGGGGGGGG \( . \) GGGGG
B. AUU
c. UAG
D. uvu


When a body moves along a circular path,its direction of speed
A. remains constant
B. keep changing continuosly
c. may change sometime
D. cant be predicted


Assertion
The solubility of Ammonium chloride increases with increase in temperature
Reason In case of substances whose solubility increases with increase in temperature is due to the dissolution process being endothermic.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The coefficient of restitution of a
perfectly elastic collision is :
A .
B. 0
\( c \cdot \infty \)
D. -


Sunken stomata are found in leaves of
A. Trifolium
B. Lemna
c. Nerium
D. Lilium


Pascal is the SI unit of
A . weight
B. thrust
c. pressure
D. temperaure


When copper is heated with
conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) it produces :
A \( \cdot C u\left(N O_{3}\right)_{2} \) and \( N O_{2} \)
B . \( C u\left(N O_{3}\right)_{2} \) and \( N O \)
c. \( C u\left(N O_{3}\right)_{2}, N O \) and \( N O_{2} \)
D. \( C u\left(N O_{3}\right)_{2} \) and \( N_{2} \)


Two thin films of the same material but
different thickness are separated by air Monochromatic light in incident on the first film. When viewed normally from
the point \( A \), the second film appears
dark.
From point \( B \), on normal viewing
A. the first film will appear bright
B. the first film will appear dark
c. the second film will appear bright
D. the second film will appear dark


Arrange the following compound in order of decreasing acidic strength.


The actinoids showing +7 oxidation
state are:
A. \( U, N p \)
в. \( P u, A m \)
c. \( N p, P u \)
D. \( A m, C m \)


Find the de Broglie wavelength of
electrons moving with a speed of \( 7 \times \) \( 10^{6} m s^{-1} \)


In the network shown in figure, the
equivalent resistance between points \( X \) and Y will be
\( A \)
в. \( \frac{r}{2} \)
\( c \cdot 2 r \)
D. \( \frac{r}{3} \)


Assertion
Mean free path of a gas molecules varies inversely as density of the gas.
Reason
Mean free path varies inversely as
pressure of the gas.
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


An electron of stationary hydrogen atom jumps from 4 th energy level to ground level. The velocity that the photon acquired as a result of electron transition will be (h = Planck's constant,
\( \mathrm{R}= \) Rydberg's constant, \( \mathrm{m}= \) mass of photon)
A \( \cdot \frac{9 R h}{16 m} \)
в. \( \frac{11 h R}{16 m} \)
c. \( \frac{13 h R}{16 m} \)
D. \( \frac{15 h R}{16 m} \)


The resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) are joined in parallel and a current is passed so that the amount of heat liberated is \( \boldsymbol{H}_{1} \) and
\( H_{2} \) respectively. The ratio \( \frac{H_{1}}{H_{2}} \) has the
value
A \( \cdot \frac{R_{2}}{R_{1}} \)
в. \( \frac{R_{1}}{R_{2}} \)
c. \( \frac{R_{1}^{2}}{R_{2}^{2}} \)
D. \( \frac{R_{2}^{2}}{R_{1}^{2}} \)


Let \( T \) be the set of all triangles in the
Euclidean plane, and let a relation \( R \) on \( T \) be defined as \( a R b, \) if \( a \) is congruent to
\( b \) for all \( a, b \in T . \) Then, \( R \) is
A. reflexive but not symmetric
B. transitive but not symmetric
c. equivalence
D. none of these


Express the complex number \( \frac{2+i}{3-4 i} \) in
\( a+i b \) form.


Number of electrons constituting \( 1 C \)
electric charge is
A \( \cdot 6.25 \times 10^{18} \) electrons
B. \( 1.6 \times 10^{-19} \) electrons
C. \( 6.25 \times 10^{-19} \) electrons
D. \( 1.6 \times 10^{-18} \) electrons


Kinetic energy of a body depends on its:
A. Position
B. Velocity
c. shape
D. colour


Which one of the following can produce maximum induced e.m.f.?
A. 50 ampere DC
B. 50 ampere 50 Hz AC
c. 50 ampere 500 нz
D. 100 ampere DC


Effect of day length duration on plant development/flowering is
A. Chemotropism
B. Phototropism
c. Photoperiodism
D. Photonasty


Evaluate the following limits. \( \lim _{x \rightarrow 3} \frac{x^{2}-4 x+3}{x^{2}-2 x-3} \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{3} \)
D.


Find the angle between the vectors \( \hat{i}- \) \( 2 \hat{j}+3 \hat{k} \) and \( 3 \hat{i}-2 \hat{j}+\hat{k} \)


Two bulbs, one of \( 200 \mathrm{W} \) and the other of
\( 100 \mathrm{W}, \) are connected in series with a
100V battery which has no internal
resistance. Then
A. the current passing through the 200 W bulb is more than that through the 100 w bulb
B. the power dissipation in the 200 W bulb is more than that in the 100 W bulb
c. the voltage drop across the 200 W bulbs is more than that across the \( 100 \mathrm{W} \) bulb
D. the power dissipation in the 100 W bulb is more than that in the \( 200 \mathrm{w} \) bulb


\( X^{\prime} \) litres of carbon monoxide is present
at \( S T P . \) It is completely oxidized to
\( C O_{2} . \) The volume of \( C O_{2} \) formed is
11.207 litres at \( S T P . \) What is the value
of \( ^{\prime} \boldsymbol{X}^{\prime} \) in litres?
A . 22.414
B. 11.207
c. 5.6035
D. 44.828


Evaluate \( \int \frac{a^{\sqrt{x}}}{\sqrt{x}} d x \)
A \( \cdot \frac{2 a^{\sqrt{x}}}{\log a}+c \)
B. \( \frac{\log a}{a^{\sqrt{x}}}+c \)
C \( \cdot 2 a^{\sqrt{x}} \log a+c \)
D. \( a^{\sqrt{x}} \log _{a} e+c \)


Which is a unit vector?
A. \( (\cos \alpha, 2 \sin \alpha) \)
B. \( (\sin \alpha, \cos \alpha) \)
c. (1,-1)
D. \( (2 \cos \alpha, \sin \alpha) \)


\( \underbrace{\bar{L}}_{k} \)


Differentiate the following function with
respect to \( x \) \( \sin ^{2} x \)
\( A \cdot \cos x \)
B. \( \sin 2 x \)
\( \mathbf{c} \cdot \sin 3 x \)
D. \( \sin ^{2} x \cos x \)


What is the study of the modern theory of the strong forces between quarks?
A. Quantum chromodynamics
B. Quantum electromagnetism
c. Quantum electrodynamics
D. Quantum astronomy


Find the value of \( f \) in \( \frac{1}{f}=\frac{1}{u}+\frac{1}{v}, \) when
\( \boldsymbol{u}=\mathbf{1 5} \) and \( \boldsymbol{v}=\mathbf{1 0} \)
A . -6
в. \( \frac{1}{6} \)
\( c \cdot 6 \)
D. \( -\frac{1}{6} \)


Which is the correct method of
synthesising acetamide from acetone?
A \( \cdot C H_{3} C O C H_{3} \stackrel{P d / B a S O_{4}}{\longrightarrow} C H_{3} C H O \stackrel{N H_{3}}{\longrightarrow} \)
\( C H_{3} C H_{2} N H_{2} \stackrel{H_{2} O}{\longrightarrow} C H_{3} C O N H_{2} \)
в. \( C H_{3} C O C H_{3} \frac{I_{2}}{N a O H} C H_{3} C O O N a \frac{H^{+}}{N H_{3}} \)
\( C H_{3} C O O N H_{4} \stackrel{\Delta}{\longrightarrow} C H_{3} C O N H_{2} \)
c. \( C H_{3} C O C H_{3} \stackrel{C r O_{3}}{\longrightarrow} C H_{3} C O O H \stackrel{N H_{3}}{\longrightarrow} C H_{3} C O N H_{2} \)
D. \( C H_{3} C O C H_{3} \frac{I_{2}}{_{N a O H}} C H_{3} C O O H \stackrel{H C l}{\longrightarrow} \)
\( C H_{3} C O C l \stackrel{N H_{3}^{3}}{\longrightarrow} C H_{3} C O N H_{2} \)


The reaction between \( X \) and \( Y \), forms
compound \( Z . X \) loses an electron and \( Y \)
gains an electron which of the following properties is NOT shown by \( Z \) ?
A. Has high melting point
B. Has low melting point
c. conducts electricity in moltenstate
D. Occurs as solid


Electromeric effect:
A. comes into play at the demand of attacking reagent
B. involves the displacement of electrons in a sigma bond
C. comes into play in the molecule when at least one atom has unshared pair of electrons
D. involves the distortion of electron cloud.


Find the equations of the lines for which \( \tan \theta=\frac{3}{5}, \) where \( \theta \) is the angle of
inclination of the line and \( x- \) intercept
is -8


Find the value of the polynomial \( 5 x- \)
\( 4 x^{4}+3 \) at
\( \boldsymbol{x}=\mathbf{0} \)


\( H_{2} O_{2} \) is decomposed to \( H_{2} O \) and \( O, \) in
the following sequence of reactions:
\( \mathbf{I} \boldsymbol{H}_{2} \boldsymbol{O}_{2(\boldsymbol{a q})}+\boldsymbol{I}_{(\boldsymbol{a} q)}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+\boldsymbol{I} \boldsymbol{O}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \)
ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2(a q)}+\boldsymbol{I}_{(a q)}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{I} \boldsymbol{O}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \)
(a) Write the chemical equation for the overall reaction.
(b) Identify the species that acts as a
catalyst.
(c) Identify the intermediate.


\( 50 m L \) of \( 2 N \) acetic acid mixed with
\( 10 m L \) of \( 1 N \) sodium acetate solution
will have an approximate \( \boldsymbol{p} \boldsymbol{H} \) of \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\right. \)
\( \left.10^{-5}\right) \)
A . 4
B. 5
\( c .6 \)
D.


The mode of coelom formation
in Hemichordata are
A. Enterocoelus
B. Pseudocoelous
c. Schizcoelous
D. All of the above


Which metal is in ores such
as orpiment, realgar etc?
A. phosphorous
B. arsenic
c. nitrogen
D. bismuth


Heated calcium sulphate with half a water of crystallization is commonly called as:
A. washing soda
B. plaster of paris
c. naushadar salt
D. bleaching powder


The table shows Paula's scores in a
revision test out of \( 20 . \) Find the median
score for the subject.

Maths Science History Geography
12
A. Maths
B. English
c. science
D. French


Does Euclid' fifth postulate imply the existence of parallel lines? Explain
A. True
B. False


Which of the following has highest dipole moment?
A. \( C H_{3} C l \)
в. \( C H_{3} F \)
c. \( C H_{3} B r \)
D. \( C H_{3} l \)


toppr \( t \)
Q Type your question
\( \mathbf{A} \)
B. Diagram B
\( c \)
D.
\( E \)


\( \ln \) an A.P. the first term is 2 and the sum
of the first five terms is one fourth of the
next five terms. Show that 20 th term is
-112


Fifth term of \( \frac{1}{16}, \frac{1}{8}, \frac{1}{4} \dots \dots \) is
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot c \)
\( D \)


The total number of possible isomers for square-planar
\( \left[\boldsymbol{P t}(\boldsymbol{C l})\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})\right]^{2-} \) is:
A . 16
B. 12
\( c \cdot 8 \)
D. 24


If \( A \) and \( B \) are two independent events such that \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2} \) and \( \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{1}}{\mathbf{5}} \)
then
A \( \cdot P(A \cup B)=\frac{3}{5} \)
в. \( P\left(\frac{A}{B}\right)=\frac{1}{2} \)
\( ^{c} \cdot p\left(\frac{A}{A \cup B}\right)=\frac{5}{6} \)
\( ^{\mathrm{D}} \cdot_{P}\left(\frac{A}{\bar{A}} \stackrel{\cap}{\longrightarrow} \overline{\bar{B}}\right)=0 \)


The polyhydroxy aldehydes are called:
A. proteins
B. fats
c. carbohydrates
D. vitamins


\( x^{2} \sqrt{1-x^{2}} d x= \)
A \( \cdot \frac{1}{8} \arcsin x-\frac{1}{8} x\left(1-2 x^{2}\right) \sqrt{1-x^{2}}+C \)
B \( \cdot \frac{1}{8} \arcsin x+\frac{1}{8} x\left(1-2 x^{2}\right) \sqrt{1+x^{2}}+C \)
C \( \cdot \frac{1}{8} \arcsin x+\frac{1}{8} x\left(1-x^{2}\right) \sqrt{1-x^{2}}+C \)
D. None of these


The IUPAC name of the compound
formed when natural rubber is
subjected to ozonolysis is
A. 3-oxopentanal
B. 5-formyl-2-pentanone
c. 4 -oxopentanal
D. 4-formyl-2-pentanone


Chitin is composed of
A. Protein and carbohydrates
B. Carbohydrates and mannose
C. Fatty acids and carbohydrates
D. Polysaccharides rich mannose


Which of the following is/are Iyophobic colloids?
This question has multiple correct options
A. Blood
B. Starch
c. Gelatin
D. Gold


Construct a triangle \( A B C \) in which
\( B C=7 c m, \angle B=75^{\circ} \) and \( A B+ \)
\( A D=13 \mathrm{cm} \)


A large spherical planet of radius \( \mathrm{R} \) made of a material of density d, has a spherical cavity of radius R/2,with centre of cavity a distance R/2 from the
centre other planet. Find the gravitational force one small mass \( \mathrm{m} \) at
the centre of the cavity.
A. 2 RGmd/3
B. RGmd/3
c. 2RGmd
D. 4 RGmd/3


Unusually high boiling point of water is result of
A. Intermolecular hydrogen bonding
B. Intramolecular hydrogen bonding
c. Both intra and inter molecular hydrogen bonding
D. High specific heat


Determine whether \( (x+1) \) is a factor of
the polynomial:
\( 6 x^{4}+7 x^{3}-5 x-4 \)


Write Faraday's laws of electro magnetic induction.


What can you say about the angle of deviation in such a situation?
A. Angle of deviation is minimum.
B. Angle of deviation is maximum.
c. Angle of deviation is constant.
D. None of the above


The source of pyridoxine is:
A. cereals
B. meat
c. yeast
D. all of the above


If the diagonal \( \boldsymbol{A C} \) of a parallelogram
\( A B C D \) bisects \( \angle A, \) Show that \( A B E D \)
is a rhombus.


Find the height of the building which is on moon without using any measuring device ?(you can use stopwatch)
A \( \cdot h=\frac{1}{12} g t^{2} \)
B. \( h=\frac{1}{24} g t^{2} \)
c. \( _{h}=\frac{1}{30} g t^{2} \)
D. \( h=\frac{1}{42} g t^{2} \)


Inertia is
A. a property of matter
B. a type of force
C. the speed of an object
D. none of the above


\( \mathbf{A} \)
\( 24 V \) battery having internal resistor of \( X \Omega \) is connected to a \( 4 \Omega \) resistor,
causing a current of \( 5 A \). Find out the
value of \( \boldsymbol{X} \) ?
\( \mathbf{A} \cdot 0 W \)
B. \( 0.8 W \)
c. \( 0.4 W \)
D. \( 1.6 W \)
E . \( 1.2 W \)


The material used for permanent
magnet has:
A. low retentivity, high coercivity
B. high retentivity, low coercivity
c. high retentivity, high coercivity
D. low retentivity, , low coercivity


What is sexual and asexual
reproduction. Explain with example.


Total no of lines in Lyman series of \( \mathrm{H} \) spectrum will be (where \( n= \) no.of orbits)
\( A \cdot n \)
B. \( n(n-1) / 2 \)
\( c \cdot n-2 \)
\( D \cdot n(n+1) \)


Assertion
While measuring the thermal conductivity of liquid experimentally, the upper layer is kept hot and the lower
layer is kept cold.
Reason
This avoids heating of liquid by
convection.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \left(1+x^{2}\right) y_{1}=x(1-y), y(0)=\frac{4}{3} \)
then \( y(\sqrt{8})-\frac{1}{9} \) is


In the circular lawn, there is a \( 16 \mathrm{m} \) long path in the form of a chord. If the path is \( 6 \mathrm{m} \) away from the centre of the lawn, then the radius of the circular lawn is
A. \( 16 \mathrm{m} \)
B. \( 6 \mathrm{m} \)
c. \( 10 \mathrm{m} \)
D. 8 m


Rearrange the following compounds in the increasing order of their boiling points:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H O}, \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{O} \boldsymbol{H}, \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{3} \)


A flower bed is made in the shape of sector of a circle. \( 20 m \) of wire is
available to make a fence for the flower
bed. Find the radius of the circle so that
area of the flower bed is maximum.


Electric current is passed through a straight conductor passing through the centre of a piece of cupboard. Some iron filings are sprinkled on the cardboard and tapped. How will the iron filings
spread out around the conductor?
A. settle as parallel lines
B. settle as circles
c. settle at one point
D. do not acquire any regular pattern


For vectors \( \vec{a} \& \vec{b} . \) Prove that \( |\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}|^{2}=|\overrightarrow{\boldsymbol{a}}|^{2}|\overrightarrow{\boldsymbol{b}}|^{2}-|\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}|^{2} \)


Write a note on phyllotaxy.


A piece of copper having a rectangular cross-section of \( 15.2 m m \times 19.1 m m \) is
pulled in tension with \( 44,500 N \) force, producing only elastic deformation.Calculate the resulting strain? Shear modulus of elasticity of
copper is \( 42 \times 10^{9} N / m^{2} \)


What is the function of pericardial fluid and where is it found?


Find the value of the polynomial \( 4 x^{2}- \)
\( \mathbf{5} \boldsymbol{x}+\mathbf{3}, \) when \( \boldsymbol{x}=\mathbf{0} \)


PQRS is a isosceles trapezium with
\( \boldsymbol{P Q} \| \boldsymbol{R S}, \) if \( \mathrm{P}=\mathbf{6 0}, \) then \( \mathrm{Q} \) equals to
A . 120
B . 30
\( c .60 \)
D. 150


Oxygen is filled in a closed metal jar of volume \( 1.0 \times 10^{-3} m^{3} \) at a pressure of
\( 1.5 \times 10^{5} \) Pa and temperature \( 400 K \)
The jar has a small leak in it. The
atmospheric pressure is \( 1.0 \times 10^{5} \mathrm{Pa} \)
and the atmospheric temperature is \( 300 K . \) Find the mass of the gas that
leaks out by the time the pressure and the temperature inside the jar equalize with the surrounding.


Electromeric effect in an organic
compound is
A. Temporary effect
B. Permanent effect
c. Temporary-permanent effect
D. None of these


Facilitated diffusion involves the
movement of
A. Small, charged and polar molecules with the help of ATP
B. Small, neutral and nonpolar molecules with the help of ATP
c. Small, neutral and nonpolar molecules without an ATP requirement.
D. Small, charged and polar molecules without an ATP requirement.


A uniform rod of length \( ^{\prime} L^{\prime} \) and density
\( \rho^{\prime} \) is being pulled along a smooth floor
with horizontal acceleration \( \alpha \) as shown
in the figure. The magnitude of the stress at the transverse cross-section
through the mid-point of the rod is
A \( \frac{\rho l \alpha}{4} \)
в. \( 4 \rho l \) d
\( c \cdot 2 \rho l \)
D. \( \frac{\rho l \alpha}{2} \)


Explain the preparation of carboxylic
acids from Grignard reagent. Give
equation.


Minimum components needed for an
ecosystem to survive are
A. Producers and primary consumers
B. Producers and primary carnivores
C. Producers and decomposers
D. Primary consumers and decomposers


The given arranged sequence on the basis of their increasing atomic masses represents which law of classification of elements?
\( \boldsymbol{F}, \boldsymbol{N} \boldsymbol{a}, \boldsymbol{M} \boldsymbol{g}, \boldsymbol{A l}, \boldsymbol{S} \boldsymbol{i}, \boldsymbol{P}, \boldsymbol{S}, \boldsymbol{C l} \& \boldsymbol{K} \)
A. Modern table
B. Newton's law
c. Newland's law of octaves
D. Mendeleev's periodic table


Write in about 1000 words a fiction
piece based on your speculation on the science and technology of the twentysecond century.


Number of terms free from radical sign in the expansion of \( \left(1+3^{1 / 3}+7^{1 / 2}\right)^{10} \)
is
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


The electric field in a region is radially
out ward with magnitude \( \boldsymbol{E}=\boldsymbol{A} \boldsymbol{r} \). Find
the charge contained in a sphere of
radius \( 20 c m . \) Given \( A=100 V m^{-2} \)


Enlist the type of non-genetic RNA. What
is a gene responsible for expression of a
trait called?


\( \frac{1}{n} \sum_{i=1}^{n} f^{-1}\left(x_{i}\right)=f\left(\frac{1}{n} \sum_{i=1}^{n} x_{i}\right) \)


Draw a neat labelled energy level diagram of the Hydrogen atom.


If there exists a geometric progression containing 27,8 and 12 as three of its terms (not necessarily consecutive) then no. of progressions possible are
A . 1
B . 2
c. infinite
D. None of these


Additional of \( B r_{2} \) to trans- 2 - butene
would give a product which is :
A . achiral
B. racemic
c. meso
D. optically active


In a normal man to help the transport of
\( O_{2} \) and \( C O_{2} \) properly, the blood is
A. Slightly alkaline
B. Slightly acidic
c. strongly alkaline
D. Strongly acidic


The source of folic acid is:
A. yeast
B. spinach leaf
C. liver of ox
D. all of the above


Very pure hydrogen \( (99.9 \%) \) can be made by 'which of the following processes?
A. Reaction of methane with steam
B. Mixing natural hydrocarbons of high molecular weight
c. Elecrolysis of water
D. Reaction of salt like hydrides with water


The distance between an object and a divergent lens is \( m \) times the focal
length of the lens. The linear magnification produced by the lens is
A . \( m \)
в. \( \frac{1}{m} \)
c. \( m+1 \)
D. \( \frac{1}{m+1} \)


Compared with the gametophytes of the bryophytes, the gametophytes of vascular plants tend to be
A. Smaller but to have larger sex organs
B. Larger but to have smaller sex organs
c. Larger and to have larger sex organs
D. Smaller and to have smaller sex orqans


The metal used as a catalyst in
the hydrogenation of oil is:
A. sodium
B. nickel
c. mercury
D. manganese


Write the principal value of \( \tan ^{-1}(1)+ \) \( \cos ^{-1}\left(-\frac{1}{2}\right) \)


From below which is the example of insulators.
A. Metallic elements
B. Non Metallic elements
c. graphite
D. acqueous solution of salt


Which one of the following is not a reducing agent?
A \( . H_{2} S \)
в. \( H_{2} T e \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{Se} \)
D. \( H_{2} O \)


Which of the following layer has more minerals?
A. A-Horizon
B. B-Horizon
c. C-Horizon
D. Both A and C


Water treatment plants should be installed in all
A. desert
B. residential
c. industrial
D. none of the above


The VAT (Value Added Tax) paid by the
shopkeeper.
A . \( R s .40 \)
B. \( R s .50 \)
c. \( R s .60 \)
D. \( R s .70 \)


If \( f(x)=x+\log x \) find \( f^{\prime}(x) \)


The back wall of an aquarium is a
mirror that is \( 30 \mathrm{cm} \) away from the front
wall. The sides of the tank are negligibly thin. A fish is swimming midway between the front and back walls.
a. An image of the fish appears behind the mirror. How far does this image appear to be from the front wall of the
aquarium?
b. Would the refractive index of the
liquid have to be larger or smaller in order for the image of the fish to appear in front of the mirror, rather than behind it? Find the limiting value of this refractive index. Initially, water is there in aquarium having a refractive index
\( 4 / 3 \)


The coefficient of \( t^{4} \) in the expansion of
\( \left(1+t^{2}\right)^{3} \)
\( A \)
B. 3
\( c \cdot-3 \)
D. -


To sharpen the blade of a knife by rubbing it against a surface, which of the following will be most suitable?
A. stone
B. plastic block
C. wooden block
D. glass block


The most suitable material to be used
as the core of an electromagnet is
A. Iron
B. steel
c. copper
D. Aluminium


Vibrations of period 0.25 s propagate along a straight line at a velocity of 48 \( \mathrm{cm} / \mathrm{s} . \) One second after the emergence of vibrations at the initial point, displacement of the point, \( 47 \mathrm{cm} \) from it is found to be \( 3 \mathrm{cm} \). Then,
A. amplitude of vibrations is 6 cm
B. amplitude of vibrations is \( 3 \sqrt{2} c m \).
c. amplitude of vibrations is 3 \( \mathrm{cm} \)
D. None of the above


Derive the conservation of linear
momentum


A small air bubble within a glass sphere
of radius \( 20 m m \) and \( n=1.54 \) appears
to be 10 mm below the surface, when
looked along the diameter containing the bubble. Find the real depth of the
bubble along the line of sight.


A shopkeeper sells sugar in such a way that the selling price of 950 gm is the same as the cost price of one kg. Find his gain \%.
\( \mathbf{A} \cdot 5.26 \% \)
в. \( 7.8 \% \)
c. \( 6.26 \% \)
D. none of these


If ' \( \omega^{\prime} \) is a complex cube root of unity,then \( \omega\left(\frac{1}{3}+\frac{2}{9}+\frac{4}{27} \dots \infty\right) \)
\( \omega\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32} \dots \infty\right)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot \omega \)
D.


Sum of any two sides of a triangle is than the third side.
A. Greater
B. Lesser
c. Equal
D. May be greater or lesser


A plane sound wave passes from medium 1 into medium \( 2 . \) The speed of
sound in medium 1 is \( 200 \mathrm{m} / \mathrm{s} \) and in
medium 2 is \( 100 \mathrm{m} / \mathrm{s} \). The ratio of
amplitude of the transmitted wave to that of incident wave is
A. \( \frac{3}{4} \)
в. \( \frac{4}{5} \)
c. \( \frac{5}{6} \)
D. \( \frac{2}{3} \)


The Bronsted acid which gives the weakest conjugate base is:
\( \mathbf{A} \cdot H F \)
в. \( H_{2} \).
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. HCl


Reagents used for oxidation of carbon
compounds are:
A . acidified \( K_{2} C r_{2} O_{7} \)
B. alkaline \( K M n O_{4} \)
c. both \( A \) and \( B \)
D. none of these


Solve graphically, the following pairs of equations:
\( 2 x+y=23 \)
\( 4 x-y=19 \)
A. \( x=1, y=4 \)
B. \( x=9, y=2 \)
c. \( x=5, y=0 \)
D. \( x=7, y=9 \)


The standard enthalpy of formation of ammonia gas is
Given \( : N_{2} H_{4}(g) \rightarrow 2 N H_{3}(g) \)
\( \Delta H_{r}^{\circ}=-40 k J / m o l \) and
\( \Delta \boldsymbol{H}_{f}^{\circ}\left[\boldsymbol{N}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})\right]=-120 k \boldsymbol{J} / \boldsymbol{m o l} \)
A . - 60
B . -180
\( c \cdot 40 \)
D. - 80


Which one is not correctly matched?
A. Azotobacter- Nitrogen fixation
B. Streptococcus thermophilus - Yogurt
c. chlorobium - Photosynthesis
D. Streptomyces rimosus - Chloromycetin


Let \( E^{e} \) denotes the complement of an
event \( E . \) If \( E, F, G \) are pairwise
independent events with \( P(G)>0 \) and
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F} \cap \boldsymbol{G})=\mathbf{0 .} \) Then, \( \boldsymbol{P}\left(\boldsymbol{E}^{e} \cap \boldsymbol{F}^{e} \mid \boldsymbol{G}\right) \)
equals
\( \mathbf{A} \cdot P\left(E^{e}\right)+P\left(F^{e}\right) \)
B . \( P\left(E^{e}\right)-P\left(F^{e}\right) \)
\( \mathbf{c} \cdot P\left(E^{e}\right)-P(F) \)
D. \( P(E)-P\left(F^{e}\right. \)


Argon was discovered by:
A. Rayleigh
B. Ramsay
C. Both (A) and (B)
D. Frankland and Lockeyer


Which of the process is not the irreversible process?
A. The free expansion of gas
B. When a vessel is heated its base is warmer than other
parts
C. The quasi-static isothermal expansion of ideal gas in cylinder fitted with frictionless piston
D. Diffusion of gas from cylinder


The energy of a photon is given as
\( 3.03 \times 10^{-19} \) J/atom. The wavelength of
the photon is :
\( A \cdot 6.56 \mathrm{nm} \)
B. 65.6 nm
c. \( 0.656 \mathrm{nm} \)
D. 656 nm


Two isothermals are shown in figure at
temperature \( T_{1} \) and \( T_{2} . \) Which of the
following relations is correct?
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
\( c \cdot T_{1}=T_{2} \)
\( T_{1}=(1 / 2) T_{2} \)


A test-tube contains a colourless
solution of potassium iodide. The presence of iodine can be tested by:
A. adding a few drops of blue litmus solution
B. adding a few drops of copper sulphate solution
c. passing carbon dioxide gas through the solution
D. passing chlorine gas through the solution


Depletion of ozone layer is due to
A. Oxides of nitrogen
B. Oxides of carbon
c. Oxides of sulphur
D. None of the above


The first experiment on radioactivity was done with the element


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}}+\int_{0}^{1}\left(\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{t} \boldsymbol{e}^{-\boldsymbol{x}}\right) \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t} \)
then prove that \( f(x)=\frac{2(e-1)}{4 e-2 e^{2}} \cdot e^{x}+ \)
\( \frac{e-1}{4-2 e} \cdot e^{-x} \)


ype you
the reaction between \( A l C l_{3} \) and
\( \boldsymbol{C H}_{3} \boldsymbol{O C H}_{3} ? \)
\( A \)
в.
\( c \)
\( D \)


The correct set of quantum numbers for \( t \)
he last electron of \( N a^{+} \) is :
\( \mathbf{A} \cdot 3,0,0,-\frac{1}{2} \)
B. \( 3,1,0,+\frac{1}{2} \)
\( \mathbf{c} \cdot 3,1,1,+\frac{1}{2} \)
D. \( 2,1,0,-\frac{1}{2} \)


The temperature at which the reading of Fahrenheit thermometer will be double
that of a Centigrade thermometer is:
A \( \cdot 160^{\circ} \mathrm{C} \)
B. \( 180^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 32^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)


Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{x}^{2}+ \)
\( 100 x+5 \sin x, \) then \( f(x) \) is bijective.
Reason
\( \mathbf{3} \boldsymbol{x}^{\mathbf{2}}+\mathbf{2} \boldsymbol{x}+\mathbf{9 5}>\mathbf{0} \boldsymbol{x} \in \boldsymbol{R} \)
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


Calculate the following limits. If \( \lim _{x \rightarrow-2 / 3} \frac{6 x^{2}-5 x-6}{3 x^{2}-x-2} \) is k.Find \( 5 k \)


\( A B C D \) is a rectangular and \( P, Q, R \)
and \( S \) are mid points of the sides \( A B, B C, C D \) and \( D A \) respectively. Show that the quadrilateral \( P Q R S \) is a
rhombus.


Which of the following does not have the same dimensions as the Henry?
A. \( \frac{\text { joule }}{(\text { ampere })^{2}} \)
B. \( \frac{\text { tesla }-m^{2}}{(\text { ampere })^{2}} \)
c. ohm-second
D. \( \frac{1}{\text { Farad-second }} \)


\( B e^{+3} \) and a proton are accelerated by the same potential,their de-Broglie wavelengths have the ratio:
(Assume mass of proton = mass of
neutron)
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. 1: 4
c. 1: 1
D. \( 1: 3 \sqrt{3} \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], \boldsymbol{n} \in \boldsymbol{N}, \) then \( \boldsymbol{A}^{4 n} \) equals
\( A \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)


A ball is bouncing elastically with a
speed \( 1 \mathrm{m} / \mathrm{s} \) between walls of a railway
compartment of size \( 10 m \) in a direction
perpendicular to walls. The train is
moving at a constant velocity of \( 10 \mathrm{m} / \mathrm{s} \)
parallel to the direction of motion of the ball. As seen from the ground.
This question has multiple correct options
A. The direction of motion of the ball changes every 10
B. Speed of ball changes every 10
C. Average speed of ball over any 20 interval is fixed.
D. The acceleration of ball is the same as from the train


The IUPAC name for
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
A. 2-methyl butyl alcohol
B. 2-methyl butanol - 1
c. Pent-1-ene-3-ol
D. 2- methyl butanol and - 2- ol


Two polaroids \( A \) and \( B \) are kept with
their transmission axis at an angle \( \theta \)
with respect to one another. If the
transmitted intensity of light is \( \boldsymbol{I}_{t}= \)
\( 0.75 I_{0}, \) where \( I_{0} \) is the intensity of light
incident on the system, then \( \theta \) is:
A \( \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A sphere of mass \( 50 k g \) is attached by a
second sphere of mass \( 90 \mathrm{kg} \) with a
force equal to a weight of \( 0.5 m g \) and
their centres are \( 20 \mathrm{cm} \) apart.
The gravitational constant is.
A \( .4 .2 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{2} \)
B. \( 6.23 \times 10^{-15} \mathrm{Nm}^{2} \mathrm{kg}^{2} \)
c. \( 3.3 \times 10^{-11} N m^{2} k g^{2} \)
D. \( 4.4 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{2} \)


Q Type your question
appropriate choice.
Column I 11
\( (A) \)
\[
\begin{array}{l}
\left.3 M g_{(} s\right)+ \\
N_{2(g)} \stackrel{\Delta}{\longrightarrow} \quad(i) \quad \text { Displacement }
\end{array}
\]
\( N_{2}(g) \longrightarrow \)
\( M g_{3} N_{2(s)} \)
\[
\begin{array}{l}
\left.N a H_{(} s\right)+ \\
\left.H_{2} O_{(} l\right) \rightarrow
\end{array}
\]
\( (B) \)
\[
N a O H_{(a q)}+
\]
\( (i i) \)
Decomposition
\( H_{2(g)} \)
\[
3 C l O_{(a q)}^{-} \rightarrow
\]
\( (C) \)
\( 2 C l_{(a q)}^{-}+ \) \( (i i i) \) Combination
\( \mathrm{ClO}^{-}_{(a q)} \)
\[
2 K C l O_{3(s)} \rightarrow
\]
\( (D) \)
\( \left.2 K C l_{(} s\right)+ \) \( (i v) \) Disproportiona
\( 3 O_{2(g)} \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i i),(C) \rightarrow(i i), D \rightarrow(i v) \)
B \( .(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i), D \rightarrow(i) \)
\( \mathbf{c} \cdot(A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i i i), D \rightarrow(i v) \)
\( \mathbf{D} \cdot(A) \rightarrow(i i i),(B) \rightarrow(i),(C) \rightarrow(i v), D \rightarrow(i i) \)


Prove that the area of a circular path of
uniform width \( h \) surrounding a circular region of radius \( r \) is \( \pi h(2 r+h) \)


Table


Using specific charge Thomson could find isotopes. Name another method with which isotopes could be separated.
A. Mass spectrometer
B. Millikan's method
c. Superconductivity transition
D. Mossbaur effect


The function \( \boldsymbol{f} \) satisfying \( \frac{\boldsymbol{f}(\boldsymbol{b})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \neq \boldsymbol{f}^{\prime}(\boldsymbol{x}) \) for any \( \boldsymbol{x} \in(\boldsymbol{a}, \boldsymbol{b}) \)
is :
A \( \cdot f(x)=x^{1 / 3}, a=-1, b=1 \)
B. \( f(x)=1 / x ; a=1, b=4 \)
C . \( f(x)=x|x| ; a=-1, b=1 \)
D. None of these


\( \ln \Delta A B C, \angle C=90^{\circ}, \) then the value of
\( \cos ^{2} A+\cos ^{2} B \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot \frac{1}{2} \)
D. \( \frac{\sqrt{3}}{2} \)


Choose the group showing position isomerism:
(b)
\( (c) C H_{2}=C H-C H_{2} O H \)
(d)
\( (\mathbf{e}) \)
\( A \cdot b \) and \( e \)
B. b and c
\( \mathbf{C} \cdot \) a and \( d \)
D. \( a, b, c \) and \( e \)


Stomatal index 'I' is equal to (where \( \mathrm{S}= \) number of stomata per unit area and \( \boldsymbol{E}= \) number of epidermal
cells in the same unit area)
\( A \cdot \frac{s}{E-s} \)
B. \( \frac{s}{E+s} \)
\( \mathbf{c} \cdot \frac{E}{S+S} \)
D. \( \frac{E+S}{E} \)


The angle between the lines \( r \cos (\theta- \)
\( \boldsymbol{\alpha})=\boldsymbol{p}, \boldsymbol{r} \sin (\boldsymbol{\theta}-\boldsymbol{\alpha})=\boldsymbol{q} \) is
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{\pi}{2} \)
D. \( \frac{5 \pi}{12} \)


Stability order of following carbocation
A. \( i>i i> \) ii \( i>i v \)
в. \( i v> \) ii \( i>i> \) il \( i \)
\( \mathbf{c} . i v>i>i i i>i i \)
D. \( i i i>i v>i i>i \)


The motion described by the string of a violin is
A. Vibratory motion
B. Oscillatory motion
c. circulatory motion
D. Linear Motion


The unit of rate of reaction varies with
order of reaction.
A . True
B. False


A planet in its elliptical orbit has the
farthest distance from the sun(r, \( ) \)
equal to three times its nearest
distance from the sun(r \( _{2} \) ). Will the
orbital speed of the planet be different
at those points?
A. Orbital velocity at nearest point will be twice that at farthest point
B. orbital velocity at nearest point will be thrice that at farthest point
c. orbital velocity at farthest point will be thrice that at nearest point
D. orbital velocity will be same, since no other force acts on the planet


If \( \vec{r} \times \vec{b}=\vec{c} \times \vec{b} \& \vec{r}, \vec{a}=0 \) where
\( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}-\boldsymbol{k}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) then \( \overrightarrow{\boldsymbol{r}} \)
A \( \cdot 2(\hat{i}-\hat{j}+\hat{k}) \)
B \( \cdot 2(\hat{i}+\hat{j}-\hat{k}) \)
c. \( 2(-\hat{i}+\hat{j}+\hat{k}) \)
D. \( 2(\hat{i}+\hat{j}+\hat{k}) \)


Solve the following differential equation \( \frac{d y}{d x}=1-\cos x \)


A beam of light gets reflected from a plane mirror and a real image is formed The incident beam should be
A. Parallel
B. convergent
c. Divergent
D. Plane mirror cannot form a real image


Percentage of sodium sulphate
\( \left(N a_{2} S O_{3}\right) \) in hydrated salt is \( 50 . \) Hence, molecular formula of hydrated salt is
\( N a_{2} S_{2} O_{3} \cdot 7 H_{2} O \)
If true enter 1 , else enter 0


Verify Rolle's theorem for the following
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{9}, \boldsymbol{x} \varepsilon[\mathbf{1}, \boldsymbol{4}] \)


The lewis structure of the product that is formed.


The formula proposed by Newton for velocity of sound in air is based on
process.


A variable triangle is inscribed in a circle of radius \( \mathrm{R} \). If the rate of change of
side is \( R \) times the rate of change of the opposite angle, then that angle is
\( \mathbf{A} \cdot \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( \pi / 2 \)


The sum of the series \( 1+2.2+3.2^{2}+ \)
\( 4.2^{3}+5.2^{4}+.+100.2^{99} \) is \( ? \)
B. \( 100.2^{100}+1 \)
c. \( \$ \$ 99.2^{\lambda}[100] \$ \$ \)
D. \( 99.2^{100}+1 \)


Rahim takes out all the hearts from the
cards. What is the probability of Picking out an ace from the remaining
pack.


A p-n photodiode is manufactured from
a semiconductor with gap of \( 3.1 \mathrm{eV} \) Which of the following wavelengths can be detected by it?
\( A \cdot 4000 \hat{A} \)
в. 3900 ,
\( c \cdot 4200 \hat{A} \)
D. Both (1) \& (2)


If the range of \( f(x)=\sin ^{-1} x+ \)
\( \tan ^{-1} x+\cos ^{-1} x \) is
\( =\left[\frac{\pi}{a}, \frac{b \pi}{c}\right] \)
Find the value of \( a+b+c \)
A. 7
B. 8
c. 10
D. 11


In what ratio does the point \( P(p,-1) \) divide the line segment joining the points \( A(1,-3) \) and \( B(6,2) ? \) Hence, find the value of \( \mathrm{p} \)


Give IUPAC name of the given
compound
A. 1,3,3 -Trimethylcyclohex- 1 -ene
B. 1,1,3 -Trimethylcyclohex- -1 -ene
c. 1,3,3 -Trimethylcyclohex- 2 -ene
D. None of these


Solve the equation for \( x: \sin ^{-1} \frac{5}{x}+ \) \( \sin ^{-1} \frac{12}{x}=\frac{\pi}{2}, x \neq 0 \)


depends on mass and kind of material of the body.


If the lines \( y=3 x+1 \) and \( 2 y=x+3 \)
are equally inclined to the line \( y= \)
\( m x+4 . \) Find the values of \( m \)


Which of the following statements is
correct?
A. The maximum number of unpaired electrons in a subshell is equal to \( 2 l+1 \)
B. The maximum value of magnetic moment for an atom with \( l=2 \) subshell is 3.9
C. The total spin of \( 3 d^{6} \) configuration is 3.
D. Both A and B


In mitosis, the spindle is
A. Bipolar
B. Multipolar
c. Apolar
D. Random


Show that the frictional error in the \( n^{t h} \)
power of a quantity is equal to n times the fractional error in the quantity itself
State the general rule for evaluating the error in a combined calculation.


The figure shows schematic field lines
resulting from interaction between
A . two positive charges
B. two negative charges
c. a positive and a negative charge
D. None of these


Which of the following elements
involves gradual filling of \( 5 f \) -level?
A. Lanthanoids
B. Actinoids
c. Transition metals
D. Coinage metals


A sound source is moving towards stationary listener with \( \frac{1}{10} \) th of the speed of sound. The ratio of apparent to real frequency is:
\( ^{\mathrm{A}} \cdot\left(\frac{9}{10}\right)^{2} \)
в. \( \frac{10}{9} \)
c. \( \frac{11}{10} \)
D \( \cdot\left(\frac{11}{10}\right)^{2} \)


A quadratc function in x has the value
10 when \( x=1 \) and has minimum value 1
when \( x=-2 \) the function is
\( A \cdot 2 x^{2}+3 x+5 \)
B. \( 3 x^{2}+2 x+5 \)
c. \( x^{2}+3 x+6 \)
D. \( x^{2}+4 x+5 \)


Match the following two columns.
Column I Column I


Substituting \( x=-3 \) in
\( x^{2}-5 x+4 \)
A . -2
B . 28
\( c \cdot 2 \)
D. -1


\( 0.12 \mathrm{g} \) of an organic compound containing phosphorous gave 0.22 g of
\( M g_{2} P_{2} O_{7} \) by usual analysis. Calculate
the percentage of the phosphorous in the organic compound.
A. \( 48.5 \% \)
B . \( 51.2 \% \)
c. \( 63.9 \% \)
D. \( 69.2 \% \)


There is a mistake in each of the
following ray diagrams given as Fig. 16.9
\( a, b, \) and \( c . \) Make the necessary correction \( (s) \)


A closely wound, circular coil with
radius \( 2.40 \mathrm{cm} \) has 800 turns. The
distance \( x \) from the centre of the coil,
along the axis, at which the magnetic field is half of its value at the centre, is
\( 184 \times 10^{-x} m . \) Find the value of \( x \)


Which one is the correct food chain?
A. Eagle \( \rightarrow \) Snake \( \rightarrow \) Grasshopper \( \rightarrow \) Grass \( \rightarrow \) Frog
B. Frog \( \rightarrow \) Snake \( \rightarrow \) Eagle \( \rightarrow \) Grasshopper \( \rightarrow \) Grass
C. Grasshopper \( \rightarrow \) Grass \( \rightarrow \) Snake \( \rightarrow \) Frog \( \rightarrow \) Eagle
D. Grass \( \rightarrow \) Grasshopper \( \rightarrow \) Frog \( \rightarrow \) Snake \( \rightarrow \) Eagle


Which one of the following type of groups will produce an oxime on reaction with \( N H_{2} O H ? \)
A. \( R C O O H \)
в. \( R C H O \)
с. \( R C O O C H_{3} \)
D. \( R C O N H C H_{3} \)


A compound containing \( C a, C, N \) and \( S \) was subjected to quantitative analysis and formula mass determination. A 0.25 g of this compound was mixed with \( N a_{2} C a C O_{3} \)
to convert all \( C a \) into 0.16 g \( C a C O_{3} . A \) \( 0.115 \mathrm{gm} \) sample of compound was carried through a series of reactions until all its \( S \) was changed into \( S O_{4}^{2-} \)
and precipitated as 0.344 g of \( B a S O_{4} . \) A 0.712 g sample was processed to liberated all of its \( N \) as \( N H_{3} \) and 0.155
g \( N H_{3} \) was obtained. The formula mass was found to be \( 156 . \) Determine
the empirical and molecular formula of the compound.


A fair coin is tossed \( 2 n \) times. The
probability of getting as many heads in
the first \( n \) tosses as in the last \( n \) is
A \( \cdot \frac{2 n_{C_{n}}}{2^{2 n}} \)
B. \( \frac{2 n_{C_{n-1}}}{2^{n}} \)
c. \( \frac{n}{2^{n}} \)
D. \( \frac{n^{2}}{2^{n}} \)


Write the mechanism of the reaction:
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H} \boldsymbol{X} \rightarrow \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{X} \)


A ray reflected successively form to p[lane mirrors inclined at a certain angle undergoes a deviation of \( 300^{0} \)
Then the no. of images observable is?
A . 11
B . 15
c. 12
D. 20


Direction cosines of the line \( \frac{x+2}{2}= \)
\( \frac{2 y-5}{3}, z=-1 \) are
A \( \cdot \frac{4}{5}, \frac{3}{5}, 0 \)
B. \( \frac{3}{5^{\prime}}, \frac{4}{5^{\prime}} \frac{1}{5} \)
c. \( \quad-\frac{3}{5}, \frac{4}{5}, 0 \)
D. \( \frac{4}{5},-\frac{2}{5}, \frac{1}{5} \)


Coordinate bond is formed in:
A . \( N a C l \)
в. \( N H_{4} C l \)
\( c \cdot C l_{2} \)
D. \( B C l_{3} \)


The number of side in pentagon are
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
D. 8


Which one of the following processes is/are not used, for the manufacture of
calcium?
This question has multiple correct options
A. Reduction of CaO with carbon
B. Reduction of CaO with hydrogen
c. Electrolysis of a mixture of an hydrous \( C a C l_{2} \)
D. Electrolysis of molten \( C a(O H)_{2} \)


Three years ago, a High School started charging an admission fee for volleyball
games to raise money for new sports. The initial price was \( \$ 2 \) per person, now school raised this price of admission to \( \$ 2.50 \) this year. Assuming this trend continues, which of the following equations can be used to described the \( \operatorname{cost} \) of admission \( (c), y \) years after the school began charging for admission to games?
A. \( c=6 y+2 \)
B \( \cdot c=\frac{y}{6}+2.5 \)
\( \mathbf{c} \cdot c=\frac{y}{6}+2 \)
D. \( c=\frac{y}{2}+6 \)


Let \( \boldsymbol{f}(\boldsymbol{a}, \boldsymbol{b})= \)
\( \int_{a}^{b}\left(x^{2}-4 x+3\right) d x,(b>a) \) then
A \( \cdot f(a, 3) \) is least when \( a=1 \)
B . \( f(4, b) \) is an increasing function \( \forall b \geq 4 \)
C \( \cdot f(0, b) \) is least for \( b=2 \)
\( \mathrm{D} \cdot \min \{f(a, b)\}=-\frac{4}{3} \forall a, b \in R \)


If in the formula \( \boldsymbol{X}=\mathbf{3} \boldsymbol{Y} \boldsymbol{Z}^{2}, \) the
dimensions of \( X \) and \( Z \) are those of the
capacitance and magnetic induction, then the dimensions of Y are:
A . \( M^{-3} L^{-2} T^{8} A^{4} \)
B. \( M^{-3} L^{-2} T^{4} A^{4} \)
\( \mathbf{c} \cdot M^{-3} L^{-2} T^{-4} A^{-4} \)
D. \( M^{-3} V^{-2} T^{-8} A^{-4} \)


Evaluate \( \int \frac{1}{\left(e^{x}-1\right)} d x \)


A force of \( 5 N \) is applied on a \( 20 k g \) mass at rest. the work done in the third
second is:-
A \( \cdot \frac{25}{8} J \)
в. \( \frac{25}{4} J \)
c. \( 12 J \)
D. 25J


Which one of the following ionic species will not impart color to an aqueous solution?
A \( \cdot T i^{4} \)
в. \( C u^{+} \)
c. \( z n^{2+} \)
D. \( C r^{3} \)


Magnifying glass forms
A. Real Image
B. Virtual Image
c. Both A and B
D. Neither A nor B


Myxomycetes are
A. Saprobes or parasites, having mycelium, asexual reproduction by fragmentation.
B. Slimy mass of multinucleate protoplasm, having pseudopodia like structures for engulfing food, reproduction through fragmentation or zoospores
C. Prokaryotic organisms, cellular or acellular, saprobes or autotrophic, reproduce by binary fission
D. Eukaryotic, single-celled or filamentous, saprobes or autotrophic, asexual reproduction by division of haploid individuals, sexual reproduction by fusion of two cells or their nuclei.


At some temperature and under a
pressure of 4 atm, \( P C l_{5} \) is \( 10 \% \) dissociated. Calculate the pressure at
which \( P C l_{5} \) will be \( 20 \% \) dissociated,
temperature remaining same.
\( A \cdot 0.97 \) atm
B. 0.34 atm
C. 1.43 atm
D. 1.67 atm


Find the coefficient of range for the given data
\( \mathbf{5 9}, \mathbf{4 6}, \mathbf{3 0}, \mathbf{2 3}, \mathbf{2 7}, \mathbf{4 0}, \mathbf{5 2}, \mathbf{3 5}, \mathbf{2 9} \)
A . 0.46
B. 0.44
\( c .0 .56 \)
D. 0.124


A block of mass of a \( 2 k g \) with
dimensions \( 5 c m \times 20 c m \times 10 c m \)
respectively. The ratio of minimum to
maximum pressure it exerts on the change in orientation is:
A . 1: 1
B. 1: 2
c. 1: 4
D. 4: 1


Describe types of asexual reproduction


What is the self inductance of a
straight conductor?


Fill in the blanks.
(i) The additive identity of the integers is P.
(ii) The integer which is 8 less than -24 is \( \underline{Q}_{-} \)
(iii) Every integer less than zero is \( R \)
\( P \quad Q \quad R \)
\( \begin{array}{lll}A \cdot O & -32 & \text { negative }\end{array} \)
B. \( 1-32 \) positive
c. \( 0-16 \) negative
D. 1 -32 negative


Fill in the Blank:
Two units Area:
(a)
\( (b) \)


Three lines \( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{q} \boldsymbol{y}+\boldsymbol{r}=\mathbf{0}, \boldsymbol{q} \boldsymbol{x}+\boldsymbol{r} \boldsymbol{y}+ \)
\( \boldsymbol{p}=\mathbf{0} \) and \( \boldsymbol{r} \boldsymbol{x}+\boldsymbol{p} \boldsymbol{y}+\boldsymbol{q}=\mathbf{0} \) are
concurrent if
This question has multiple correct options
A \( . p+q+r=0 \)
B . \( p^{2}+q^{2}+r^{2}=p r+q r+p q \)
c. \( p^{3}+q^{3}+r^{3}=3 p q r \)
D. none of these


Which among the following is not a planar molecule?
A \( \cdot B C l_{3} \)
B. \( C_{2} H_{4} \)
c. \( S F_{4} \)
D. \( H_{2} O \)


\( \ln \) an oscillating \( L C \) circuit the
maximum charge on the capacitor is \( Q \)
The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
\( \mathbf{A} \cdot Q / 2 \)
в. \( Q / \sqrt{3} \)
c. \( Q / \sqrt{2} \)
D. \( Q \)


Below is given frequency distribution of driving speed (in kms/hour) of a vehicle of 400 college students.
Speed 20
in \( \begin{array}{llll}\operatorname{lm} s / h r) & -30 & 40 & 50 & 60 \\ & 40 & 50 & 60\end{array} \)
No. of \( \quad 6 \quad \) 80 \( \quad 156 \quad 98 \) students

Find modal driving speed of college students.
A. \( 41.67 \mathrm{kms} / \) hour
B. \( 45.67 \mathrm{kms} / \) hour
c. \( 49.67 \mathrm{kms} / \) hour
D. \( 53.67 \mathrm{kms} / \) hour


A vertical steel post of diameter \( 25 \mathrm{cm} \)
and length \( 2.5 m \) supports a weight of
\( 8000 k g . \) Find the change in length
produced. (Given \( \left.\boldsymbol{Y}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{P a}\right) \)
\( A \cdot 2.1 \mathrm{cm} \)
B. 0.21 \( \mathrm{cm} \)
c. \( 0.21 \mathrm{mm} \)
D. 0.021 mm


A force acts on a body of mass \( 3 \mathrm{kg} \) such that its velocity changes from \( 4 \mathrm{m} \)
\( s^{-1} \) to \( 10 \mathrm{m} s^{-1} . \) Calculate the change in
the momentum of the body.
A \( \cdot 2 \mathrm{kg} \mathrm{m} s^{-1} \)
B. 14 kg m s \( ^{-1} \)
c. \( 18 \mathrm{kg} \mathrm{m} s^{-1} \)
D. \( 42 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)


The graph of \( y=6 \) is a line:
A. parallel to \( x \) -axis \& at a distance of 6 units from the
\( x- \) axis
B. parallel to \( y \) -axis at a distance of 6 units from the origin
c. making an intercept 6 on the \( x \) -axis
D. making an intercept 6 on both the axes.


Match the following:
Column I
A. \( \mu=\tan i_{p} \)
P. Snell's law
B. \( \mu=\frac{1}{\sin i_{c}} \)
Q. Brewster's law
C. \( \mu=\frac{\sin i}{\sin r} \)
R. Prism
D. \( \mu= \)
\( \frac{\sin \left(\frac{A+D_{m}}{2}\right)}{\sin \frac{A}{2}} \begin{array}{l}\text { S. Total internal } \\ \text { reflection }\end{array} \)


Which of the following represents the important proteins required for our body?
A. Enzymes
B. Hormones
c. Antibodies
D. All of the above


Which type of cell division occurs in the gonads?
A. Mitosis only
B. Meiosiss
c. Both A and B
D. Amitosis and meiosis


A rectangular coil of wire of 500 turns of
area \( 10 \times 5 c m^{2} \) carries a current of \( 2 A \)
in a magnetic field of induction \( 2 \times \)
\( 10^{-3} T . \) If the plane of the coil is parallel
to the field. The torque on the coil is (in
\( N m) \)
A . 0.1
B. 0.01
c. 0.001
D.


Find the coordinates of the foci, the
vertices the eccentricity and the length
of latus rectum of the hyperbola \( 9 y^{2}- \) \( 4 x^{2}=36 \)


The velocity of a body of rest mass \( m_{o} \) is \( \frac{\sqrt{3}}{2} c(\text { where } c \) is the velocity of light in vacuum). The mass of this body is :
\( ^{\mathbf{A}} \cdot\left(\frac{\sqrt{3}}{2}\right) m_{o} \)
B \( \cdot\left(\frac{1}{2}\right) m_{o} \)
\( \mathrm{c} \cdot 3 m_{0} \)
D. \( 2 m_{o} \)


Liquation method is used to refine which of the following crude metal?
A . Silver
B. Leadd
C. Mercury
D. copper


The inductor in a \( L-C \) oscillation has
a maximum potential difference of \( 16 V \) across the inductor of \( 3 m H \) and
maximum energy of \( 160 \mu J . \) The value
of capacitor in \( L-C \) circuit is :
\( \mathbf{A} \cdot 0.8 \mu F \)
B. \( 0.625 \mu F \)
c. \( 1.6 \mu F \)
D. \( 1.25 \mu F \)


The nitrate (A) can be confirmed by
flame test.

The colour imparted by the salt to the flame is :
A . yellow
B. green
c. blue
D. red


Which metal will be suitable for a
photoelectric cell using light of wavelength \( 4000 A \) The work functions of sodium and copper are respectively 2eV and \( 4 e v \)
A. Sodium
B. Copper
c. Both
D. None of these


The pressure and temperature of \( 4 d m^{3} \) of carbon dioxide gas are doubled. Then volume of carbon dioxide would be :
\( \mathbf{A} \cdot 2 d m^{3} \)
B. \( 3 d m^{3} \)
\( \mathbf{c} \cdot 4 d m^{3} \)
D. \( 8 d m^{3} \)


\( \lim _{x \rightarrow \infty}\left(\frac{x^{2}+5 x+3}{x^{2}+x+3}\right)^{1 / x} \)
A \( \cdot e^{4} \)
B. \( e^{2} \)
\( c \cdot e^{3} \)
\( D \)


A diode is connected to the output of a transformer as shown in the figure given below. Analyse the figure.
a) Draw a time-voltage graph for the current obtained across AB.
b) What is the function of the diode in
the circuit?


The length of the chord \( x+y=3 \)
intercepted by the circle \( x^{2}+y^{2}- \)
\( 2 x-2 y-2=0 \) is
A \( \cdot \frac{7}{2} \)
B. \( \frac{3 \sqrt{3}}{2} \)
c. \( \sqrt{14} \)
D. \( \frac{\sqrt{7}}{2} \)


If the magnitude of mass is 1 kg that of time is 1 minute and that of
acceleration due to gravity is \( 10 \mathrm{ms}^{-2} \) the magnitude of energy injoule
A \( .3 .6 \times 10^{5} \)
В. \( 3.6 \times 10^{-5} \)
c. \( 3.6 \times 10^{2} \)
D. 10


Three coins are tossed. Describe two
events \( A \) and \( B \) which are mutually
exclusive but not exhaustive.


A balloon vendor has 2 red,3 blue and 4
green balloons. He wants to choose one
of them at random to give it to Pranali. What is the probability of the event that Pranali gets:
(i) a red balloon
(ii) a blue balloon
(iii) a green balloon.


Equation of SHM is \( x=10 \sin 10 \pi t . \) Then the time period is, \( x \) is in \( \mathrm{cm} \) and \( \mathrm{t} \) is in
\( \sec \)
\( A \cdot 10 \pi \)
B. 0.2 sec
c. \( 0.1 \mathrm{sec} \)
D. 2 sec


Following 10 observations are arranges in ascending order as follows. \( \mathbf{2}, \mathbf{3}, \mathbf{5}, \mathbf{9}, \boldsymbol{x}+\mathbf{1}, \boldsymbol{x}+\mathbf{3}, \mathbf{1 4}, \mathbf{1 6}, \mathbf{1 9}, \mathbf{2 0} \)
If the median of the data is 11 , find the
value of \( x \)


One would come across the terms
isotactic, syndiotactic and atactic in connection with the chemistry of
A. Polymers
B. Dyes
c. crystals
D. Textiles


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}\} \)
Find \( \boldsymbol{A}-\boldsymbol{B} \) and \( \boldsymbol{B}-\boldsymbol{A} \)


To find out degree of freedom, the correct expression is :
A \( \cdot f=\frac{2}{\gamma-1} \)
B. \( f=\frac{\gamma+1}{2} \)
\( ^{\mathbf{C}} f=\frac{2}{\gamma+1} \)
D. \( f=\frac{1}{\gamma+1} \)


Negative soil pollution is:
A. reduction in soil productivity due to erosion and over
use
B. reduction in soil productivity due to addition of pesticides and industrial wastes
C. converting fertile land into barren land by dumping ash, sludge and garbase
D. none of the above


If mean \( =(3 \text { median }-\text { mode }) x, \) then
the value of \( x \) is
A . 1
B. 2
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{2} \)


Which of the following species exhibits diamagnetic behaviour?
A . \( N O \)
в. \( O_{2}^{2} \)
\( c \cdot O_{2}^{+} \)
D. \( O_{2} \)


If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{5}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{5}, \boldsymbol{6}\}, \) then
\( (\boldsymbol{A}-\boldsymbol{B}) \times(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A \( \cdot\{(3,2),(3,3),(3,5)\} \)
B - \{(3,2),(3,5),(3,6)\}
c. \{(3,2),(3,5)\}
D. none of these


A molecule is reduced means it:
A. loses electron.
B. gains proton
c. loses proton and electrons
D. gains electron.


For cell reaction \( : Z n+C u^{2+} \rightarrow Z n^{2}+ \)
\( C u \) cell representation is:
A \( \cdot Z n\left|Z n^{2+} \| C u^{2+}\right| C u \)
в. \( C u\left|C u^{2+} \| Z n^{2+}\right| Z n \)
c. \( C u\left|Z n^{2+}\right||Z n| C u^{2+} \)
D. \( C u^{2+}\left|Z n \| Z n^{2+}\right| C u \)


A body of mass \( 5 k g \) is acted upon by
two perpendicular forces of \( 8 N \) and \( 6 N \) find the magnitude of acceleration?
A \( \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
в. \( 3 m / s^{2} \)
\( \mathrm{c} \cdot 4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 2 m / s^{2} \)


Four parts of 24 are in A.P. such that the
product of extremes is to product of
means is 7: 15 then four parts are
A. \( \frac{3}{2}, \frac{9}{2}, \frac{15}{2}, \frac{21}{2} \)
B. \( \frac{11}{2}, \frac{13}{2}, 9 \)
C. \( \frac{5}{2}, \frac{15}{2}, \frac{9}{2}, \frac{21}{2} \)
D. \( \frac{21}{2}, \frac{9}{2}, \frac{15}{2}, \frac{5}{2} \)


All resistors in the circuit have the
same resistance, \( \boldsymbol{R}, \) and the battery is
having a constant voltage \( \boldsymbol{V} \) Find out power dissipated by resistor \( \boldsymbol{f} \) Given that the power dissipated by
resistor \( e \) is \( P: \)
A \( \frac{P}{6} \)
в. \( \frac{P}{3} \)
c. \( \frac{P}{2} \)
D. \( P \)
E . \( 2 P \)


Which among the following molecules
have \( s p^{3} d \) hybridisation with one lone pair of electrons on the central atom?
(i) \( \boldsymbol{S} \boldsymbol{F}_{4}\left(\text { ii) }\left[\boldsymbol{P C I}_{4}\right]^{+}\left(\text {iii) } \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{2} \boldsymbol{F}_{2}(\text { iv })\right.\right. \)
ClOF \( _{3} \)
A . (i), (ii) and (iii) only
B. (i), (iii) and (iv) only
c. (i) and (ii) only
D. (iii) and (iv) only


Eutrophication means
A. Toxication of water by fertilisers
B. Decrease in the growth of algae
C. Increase in the fertility of the soil
D. All of the above


Two objects have the same mass and are located near each other at a
distance (r). If the mass of one of the
objects is doubled and the mass of the other object is tripled, Find out the
change in gravitational attraction between them?
A. Decrease by \( 1 / 6 \)
B. Decrease by \( 2 / 3 \)
c. Increase by \( 3 / 2 \)
D. Increase by 5
E. Increase by 6


The population of Hyderabad was 68,09,000 in the year 2011 . If it increases at the rate of \( 4.7 \% \) per annum.
What will be the population at the end of the year 2015


The maximum speed of a car on a road turn of radius \( 30 m, \) if the coefficient of
friction between the tyres and the road
is \( 0.4, \) will be
\( \mathbf{A} .9 .84 \mathrm{m} / \mathrm{s} \)
в. \( 10.84 \mathrm{m} / \mathrm{s} \)
c. \( 7.84 \mathrm{m} / \mathrm{s} \)
D. \( 5.84 \mathrm{m} / \mathrm{s} \)


Asexual reproduction in ascomycetous fungi takes place by :
A. Gametangia
B. Conidiophore
c. Exospores
D. Endospores


The hammer hits the gong because
A. It has electric charge
B. It displays the spring effect
D. All of the above


If \( \boldsymbol{x}=\boldsymbol{y} \cos \frac{\boldsymbol{2} \boldsymbol{\pi}}{\boldsymbol{3}}=\boldsymbol{z} \cos \frac{\boldsymbol{4} \boldsymbol{\pi}}{\boldsymbol{3}}, \) then \( \boldsymbol{x} \boldsymbol{y}+ \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
A . -1
B. 0
c. 1
D. 2


Pollution of water
due to agricultural operations can be minimized by using:
A . pesticides
B. fertilizers
c. all of the above
D. none of the above


Evaluate
\( \lim _{x \rightarrow 0} \frac{\sqrt[k]{1+x}-1}{x}(\mathrm{K} \) is a positive
integer \( ) \)
\( A \cdot K \)
B. - -
c. \( \frac{1}{K} \)
D. \( -\frac{1}{K} \)


How many carbon atoms are present in citric acid?
\( A \cdot 8 \)
B. 6
c. 10
\( D \)


When an electric cell drives current
through load resistance, its back emf,
A. Supports the original emf
B. opposes the original emf
c. supports if internal resistance is low
D. Opposes if load resistance is large


Prove that \( \sum_{r=0}^{n} 3^{r n} C_{r}=4^{n} \)


Lassaigne extract is acidified with acetic acid and then lead acetate
solution is added. It forms black
precipitate of :
A . \( P b S \)
в. \( C H_{3} \) СОО Na
\( c \cdot P b S O_{4} \)
D. \( P b O \)


If the side of cube is \( 2 \mathrm{m} \), then surface
area of cube is
\( \mathbf{A} \cdot 24 m^{2} \)
B. \( 124 \mathrm{m}^{2} \)
\( c \cdot 24 m \)
D. \( 124 \mathrm{m} \)


Generally natural gas is associated with the following
A . oil fields
B. coal fields
\( c . \) a and \( b \)
D. minerals


The direction cosines of a line whose
equations are \( \frac{x-1}{2}=\frac{y+3}{4}=\frac{z-2}{-3} \)
A \( \cdot \frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}} \)
В \( \cdot \frac{2}{\sqrt{29}}, \frac{4}{\sqrt{29}}, \frac{-3}{\sqrt{29}} \)
c. \( \frac{1}{\sqrt{29}}, \frac{-3}{\sqrt{29}}, \frac{2}{\sqrt{29}} \)
D. 2,4,-3


Work-energy theorem is valid in the
presence of
A. All types of forces
B. Internal force only
c. conservative forces only
D. Non-conservative forces only


A car of mas sm starts moving so that its velocity varies according to the law \( \boldsymbol{v}=\boldsymbol{\beta} \sqrt{\boldsymbol{s}} \) where \( \boldsymbol{\beta} \) is a constant, ands is
the distance covered. The total work
performed by all the forces which are acting on the car during the first t seconds after the beginning of motion
is
A \( \cdot m \beta^{4} t^{2} / 8 \)
B \( \cdot m \beta^{2} t^{4} / 8 \)
\( \mathbf{c} \cdot m \beta^{4} t^{2} / 4 \)
D \( \cdot m \beta^{2} t^{4} / 4 \)


A triangle \( A B C \) can be constructed in
which \( \angle B=60^{\circ}, \angle C=45^{\circ} \) and \( A B+B C \)
\( +A C=11 \mathrm{cm} . \) Is this Statement true?
A . True
B. False


Differentiate the function with respect
to \( \boldsymbol{x} \)
\( f(x)=x^{2 / 3}+7 e^{x}-\frac{5}{x}+7 \tan x \)


The angle of incidence for an equilateral prism of refractive index so that the ray is parallel to the base inside the prism is
A \( .30^{\circ} \)
B . \( 20^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 45^{\circ} \)
\( E \cdot 75^{\circ} \)


What is the current I for the circuit
shown in the figure?
\( A \cdot 3 A \)
в. \( 1 A \)
\( c .-5 h \)
D. \( 5 A \)


A drum of kerosene oil is \( \frac{3}{4} \) full. When
30 litres of oil are drawn from it, it is \( \frac{7}{12} \) full. Find the capacity of the drum?
A. 120 litres
B. 140 litres
c. 180 litres
D. 240 litres


Give the reasons for the following: In front of an ambulance the word is
written as
зэиАлувмА


\( \int_{0}^{\pi} \frac{d x}{1+2^{\tan x}}= \)
\( A \cdot O \)
B . \( \pi / 4 \)
c. \( \pi / 2 \)
D.


Plexiglass, also known as PMMA is a
polymenr of:
A. methyl acrylate
B. methyl methacrylate
c. acrylic acid
D. none of these


Find the values of \( a \) and \( b \) if
\( (3 a-2, b+3)=(2 a-1,3) \)


"Carrageenan" is obtained from
A. Chondrus crispus
B. Laminaria
c. Gelidium
D. Macrocystis


Assertion
Smaller drops of liquid resist deforming forces better than the larger drops.
Reason

Excess pressure inside a drop is directly proportional to its surface 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. Both Assertion and Reason are incorrect


After two or three years of secondary growth, the cortex in dicot roots
A. Remains intact
B. Is completely sloughed away
c. Is largely lost
D. Is converted into cork


Which one of the following substances is a good oxidising agent?
A. coke
B. water
c. Hydrogen peroxide
D. sulphur dioxide


A device based on multiple reflection
used as hearing aid.
A. bulb horn
B. ear trumpet
c. megaphone
D. all


If the \( p^{t h}, q^{t h} \) and \( r^{t h} \) term of a G.P. are
a,b,c respectively, then \( a^{q-r} \cdot b^{r-p} \cdot c^{p-q} \)
is equal to
A.
B.
\( c \cdot a b c \)
D. par


In the electrolytic refining of a metal \( M \) what would you take as the anode, the cathode and the electrolyte?


Use Euclid's division algorithm to find the H.C.F. of 196 and 38318


What is the oxidation state of \( F e \) in the
product formed when acidified potassium ferrocyanide is treated with
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
\( A \cdot+2 \)
B. +6
\( c \cdot+1 \)
D. +3


Two samples were weighed using different balance and the following data were obtained.
Sample \( \# 1=3.719 \) grams Sample \( \# 2=0.42 \) gram The total mass of the samples should be reported as:
A. 4 grams
B. 4.1 grams
c. 4.139 grams
D. 4.14 grams
E. 4.140 grams


Which of the following statements is
not correct?
A. In a chemical change, color of the object may change.
B. In a chemical change, heat will always be released.
C. A chemical change always involves a physical change.
D. Rusting of iron becomes faster when humidity is high.


The capacitive reactance in an \( A C \) circuit is
A. effective resistance due to capacity
B. effective wattage
c. effective voltage
D. None of these


Arrange the following types of
interactions in order of increasing
stability (covalent, van der Waals' force,
hydrogen bonding).
A. Hydrogen bonding < covalent < van der Waals' force
B. Covalent \( < \) hydrogen bonding \( < \) van der Waals' force
C. Hydrogen \( < \) Van der Waals' force < covalent bonding
D. Van der Waals' force < hydrogen bonding < covalent


Explain the alpha and beta decay in radioactivity


Solve: \( \left(x^{2}+1\right)^{5} \sin 4 x \)


A person has a \( 18 \mathrm{cm} \) wide face and his
two eyes are separated by \( 8 \mathrm{cm} . \) Find the minimum width of a mirror required for the person to view is face laterally is
A. \( 9 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)


A force \( F=\left(3 x^{2}+2 x-7\right) N \) acts on a
\( 2 k g \) body as a result of which the body gets displaced from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\mathbf{5} \boldsymbol{m} \)
The work done by the force will be:
A . \( 5 . J \)
B. \( 70 J \)
\( \mathrm{c} .115 \mathrm{J} \)
D. \( 270 J \)


An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in
equilibrium the volume of the gas \( V_{0} \)
and its pressure is \( P_{0} \). The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{M V_{0}}{A \gamma P_{0}}} \)
c. \( \frac{1}{2 \pi} \frac{V_{0} M P_{0}}{A^{2}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{A^{2} \gamma P_{0}}{M V_{0}}} \)


Describe in brief the function of ribs
and diaphragm in breathing.


Oswald Tippo included how many divisions in sub-kingdom thallophyta?
A. 20 divisions
B. 10 divisions
c. 7 divisions
D. 2 divisions


In Mendeleev's periodic table, the gap
was not left for one of the following elements. This element is:
A. potassium
B. beryllium
c. germanium
D. scandium


If \( f(x)=\frac{3 x^{2}+a x+a+1}{x^{2}+x-2}, \) then which
of the following can be correct? This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exists \( \Rightarrow a=-2 \)
B. \( \lim _{x \rightarrow-2} f(x) \) exists \( \Rightarrow a=13 \)
\( \mathbf{c} \cdot \lim _{x \rightarrow 1} f(x)=\frac{4}{3} \)
D. \( \lim _{x \rightarrow-2} f(x)=-\frac{1}{3} \)


\( \mathbf{1} N=Z k g f \) (approx.), then what is the
value of \( Z \) ?
A . \( 0 . \)
B.
\( c \cdot 10 \)
D.


Bond order for \( C O \) is :


An urn contains 5 red marbles, 4 black
marbles and 3 white marbles. Then the number of ways in which 4 marbles can
be drawn so that the most three of them
are red is


Triangle \( A B C \) is similar to triangle
PQR. Find \( P Q \)


The angle between the lines \( 3 x+y- \)
\( \mathbf{7}=\mathbf{0} \) and \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{9}=\mathbf{0} \) is
A \( \cdot \frac{\pi}{3} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.


On complete hydrogenation, natural rubber produces:
A. ethylene-propylene copolymer
B. vulcanized rubber
c. polypropylene
D. polybutylene


The joint between the human skull bones is
A. Hinge joint
B. Immovable joint
c. cartilaginous joint
D. synovial joint


What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of \( 2.0 \times 10^{5} N m^{-2} \) from
the following data? Density of kerosene \( =800 \mathrm{kg} \mathrm{m}^{-3} \) and speed of sound in kerosene \( =1330 \mathrm{ms}^{-1} \)
\( A \cdot 0.97 \mathrm{cm}^{-3} \)
B. \( 0.66 \mathrm{cm}^{-3} \)
c. \( 0.15 \mathrm{cm}^{-3} \)
D. \( 0.59 \mathrm{cm}^{-3} \)


Assertion
During rapid pumping of air in tyres, air inside the tyre is hotter than
atmospheric air.
Reason
Adiabatic process occurs at very high
rate
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


Find determinant of \( \left|\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{2} \\ \mathbf{2} & \mathbf{1} & \mathbf{0} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right| \)


Find the equation of the parabola that satisfies the following conditions:
Vertex \( (\mathbf{0}, \mathbf{0}) ; \) focus \( (\mathbf{3}, \mathbf{0}) \)


Determine the current drawn from 12
supply with internal resist \( 0.5 \Omega \) by
infinite network. Each resistor has \( 1 \Omega \)
resistance
\( A \cdot 3 A \)
3. 2.7A
\( c .3 .7 A \)
D. 4.2 A


When aqueous solution of cupric bromide is electrolyzed the product obtained at cathode will be
A. \( C u \)
в. \( H_{2} \)
c. \( B 4_{2} \)
D. \( O_{2} \)


State and explain Gay Lussac's law of combining volumes


What is 'depletion region' in a semi conductor diode?


Let the function \( \boldsymbol{f}: \boldsymbol{R}-\{-\boldsymbol{b}\} \rightarrow \boldsymbol{R} \)
\{1\} be defined by \( f(x)=\frac{x+a}{x+b}, a \neq b \)
then
A. \( f \) is one-one but not onto
B. \( f \) is onto but not one-one
c. \( f \) is both one-one and onto
D. None of these


A single conservative force \( F(x) \) acts on a \( 1.0 k g \) particle that moves along the \( x- \) axis.The potential energy U(x) is given
by \( U(x)=20+(x-2)^{2} \) where \( x \) is in
meters.At \( x=5.0 m, \) the particle has a
kinetic energy of 20 J. What is the
mechanical energy of the system?


Give the structural formulae and IUPAC
names of the following compounds:
(a) Formaldehyde
(b) Acetone.


Name of the chemical responsible for destructive of the ozone layer. Start the main chemical from these chemicals
which is responsible for more then \( 80 \% \) onzen depletion. Start the man -made applications which make of the
chemical


The differential equation of the family of circles with fixed radius 5 units and
centre on the line \( y=2 \) is given by:
A \( \cdot(y-2)^{2} y^{\prime 2}=25-(y-2)^{2} \)
B . \( (x-2)^{2} y^{\prime 2}=25+(y-2)^{2} \)
c. \( (x-2) y^{\prime 2}=25-(y-2)^{2} \)
D . \( (y-2) y^{\prime 2}=25-(y-2)^{2} \)


A point mass \( \mathrm{m} \) is placed inside a spherical shell of radius \( \mathrm{R} \) and mass \( \mathrm{M} \)
at a distance \( R / 2 \) from the centre of the shell. The gravitational force exerted by the shell on the point mass is?
\( ^{\mathbf{A}} \cdot \frac{G M m}{R^{2}} \)
В. \( -\frac{G M m}{R^{2}} \)
c. zero
D. \( _{4} \frac{G M m}{R^{2}} \)


If \( f(x)=\int \frac{\left(x^{2}+\sin ^{2} x\right)}{1+x^{2}} \sec ^{2} x d x \) and
\( f(0)=0 \) then \( f(1) \) is equal to
A \( \cdot 1-\frac{\pi}{4} \)
B. \( \frac{\pi}{4}-1 \)
c. \( \tan 1-\frac{\pi}{4} \)
D. \( \frac{\pi}{4}-\tan 1 \)


At constant temperature, the kinetic
energy of a gas is independent on
l. pressure
II. Volume
III. Density
A . ।, ॥
в. ॥, III
\( c \cdot \) ।, ॥
D. I, II, III


Which of the following properties of atom could be explained correctly by Thomson model of atom?
A. Overall neutrality of atom.
B. Spectra of hydrogen atom.
c. Position of electrons, photons and neutrons in atom.
D. Stability of atom.


The algebraic expression for \( \tan \left(\sin ^{-1} \cos \tan ^{-1} \frac{x}{2}\right) \) is
A \( \cdot \frac{2}{x} \)
в. \( \frac{x}{2} \)
\( c \cdot \frac{1}{x} \)
D. \( \frac{2}{|x|} \)


In a potentiometer experiment, the
balancing length with a cell in the
secondary circuit is found to be \( 480 \mathrm{cm} \)
When a resistor of 8 ohm is connected
in parallel to the cell, the balancing length is found to be \( 420 \mathrm{cm} . \) The internal resistance of the cell is :
A . \( 1.14 \Omega \)
B. 2\Omega
c. \( 4.12 \Omega \)
D. \( 56 \Omega \)


Find out the current through \( 2 \Omega \) resistor
in the circuit shown in figure.
\( A, 2,5 A \)
B. 5 A
c. 1.25 A
D. 2 A


in \( 1 L \) saturated solution of
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\left[\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l})=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 0}}\right] \)
\( \mathbf{0 . 1} \) mol of
\( \boldsymbol{C u} \boldsymbol{C l}\left[\boldsymbol{K}_{s p}(\boldsymbol{C u C l})=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{6}}\right] \)
added. The resultant concentration of
\( A g^{+} \) in the solution is \( 1.6 \times 10^{-x} \). The
value of \( x \) is:


An object \( 4.0 \mathrm{cm} \) in size, is placed 25.0 \( \mathrm{cm} \) in front of a concave mirror of focal
length \( 15.0 \mathrm{cm} \)
(i) At what distance from the mirror
should a screen be placed in order to obtain a sharp image?
(ii) Find the size of the image.
(iii) Draw a ray diagram to show the formation of image in this case.


Non-proteinaceous enzyme that acts as a catalyst for the formation of peptide bond is
OR
"All enzymes are proteins." This statement is now modified because an
apparent exception to this biological truth is
A. Spliceosome
B. Ribozyme
c. RNA polymerase


Holotype is the specimen
A. Synonym of paratype
B. Synonym for neotype
c. synonym for lectotype
D. Used by author of the name designated by him as the nomenclature type


Which of these contains the carbonyl
group?
A. ketones
B. aldehydes
c. carboxylic Acids
D. all of these


Assuming that about 20 MeV of energy is released per fusion reaction \( _{1} H^{2}+1 \)
\( \boldsymbol{H}^{2} \rightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{4}+\boldsymbol{E}+ \) other particles, then
the mass of \( _{1} H^{2} \) consumed per day in a
fusion reactor of power 1 megawatt will approximately be
A . \( 0.001 \mathrm{g} \)
B. 18
c. \( 10.0 \mathrm{g} \)
D. 1000


Derive an expression for the capacitance of a parallel plate
capacitor.


Which of the following is responsible for glittering of diamond.
A . Interference
B. Diffraction
c. Total internal reflation
D. Refraction


Find the volume of a 0.2 molar solution
of sodium hydroxide, which is used to neutralize 40 liters of a 0.3 molar
hydrochloric acid solution.
A. 10 liters
B. 20 liters
c. 40 liters
D. 60 liters
E. 120 liters


Find the middle term(s) in the
expansion of :
\( \left(3 x-\frac{x^{3}}{6}\right)^{9} \)
A \( \cdot \frac{189}{8} x^{15},-\frac{21}{16} x^{17} \)
В \( \cdot \frac{189}{8} x^{17},-\frac{21}{16} x^{19} \)
C. \( \frac{189}{7} x^{15},-\frac{23}{13} x^{19} \)
D. None of thes


\( \boldsymbol{I}=\int \frac{1}{\sqrt{2 x^{2}+3 x+8}} d x \)


Explain the carbon-cycle in nature.


Let \( A B C D \) is a square with sides of
unit length.Points E and F are taken on
\( \operatorname{sides} A B \) and \( A D \) respectively so that
\( A E=A F \).Let \( P \) be a point inside the
\( \square A B C D \)
Let a line passing through point \( \boldsymbol{A} \) divides the square \( \square A B C D \) into two
parts so that area of one portion is double the other, then the length of portion of line inside the square is
A. \( \frac{\sqrt{10}}{3} \)
B. \( \frac{\sqrt{13}}{3} \)
c. \( \frac{\sqrt{11}}{3} \)
D. \( \frac{2}{\sqrt{3}} \)


A conducting circular loop is placed in a uniform magnetic field, \( B=.025 \) T with its plane perpendicular to the loop. The
radius of the loop is made to shrink at a
constant rate of \( 1 \mathrm{mm} \) s1. The induced
e.m.f. when the radius is \( 2 \mathrm{cm} \), is
\( A \cdot 2 \mu V \)
в. \( 2 \pi \mu V \)
\( c . \pi \mu V \)
D \( \cdot \frac{\pi}{2} \mu V \)


An element which is an essential
constituent of all organic compounds
belongs to :
A. group 1
B. group 14
c. group 15
D. group 16


The value of form factor in case of half
wave rectifier is:
A . 1.11
в. 1.57
c. 1.27
D. 0.48


Which of the following species are stabilized by removal of electron? This question has multiple correct options
A . \( N O \)
в. \( O_{2} \)
c. \( F_{2} \)
D. \( C N \)


Self inductance of a long solenoid
depends upon following(s)This question has multiple correct options
A. number of turns
B. radius of solenoid
c. length of solenoid
D. none of these


What does the path of an object look
like when it is in uniform motion?
A. Straight line
B. Zig-Zag
c. curved line
D. cicular


Which of the following fossil man was expert in making tools and weapons?
A. Java ape-man
B. Peking man
c. African man
D. Cro-Magnon man


Mark the correct match.
A. Good reflectors of sound - Tiles, Marble slabs.
B. Bad reflectors of sound - Thick curtains, thick carpets.
C. Good absorbers of sound - Holed cardboard.
D. All


Q Type your question
11
the latter in the pair represents the set
of characters present in Casuarina.
Study the following table:
Unisexual
flowers Chala
entry
\( (i) \)
Modified
aerial stem develop acropetally tube
(ii)
(iii) \begin{tabular}{l|l|l}
& Pedicels of & \\
& the & Presen \\
Flowers & all flowers & of \\
achlamydeous & are of & false \\
& same & whorl \\
& length & \\
Cohesion of & Centrifugal & Male \\
bracts & opening of & flowers \\
forming & flower & many \\
a cup & & \\
& & Termin \\
Flower & & part \\
formation on & Presence of & of the \\
one side in a & rachilla & pedunc \\
spiral manner & & is \\
& & flower \\
& &
\end{tabular} \( v \)
(iv
A. Both (ii) and (iii)
B. Both (i) and (ii)
C. Both (iv) and (iii)
D. Both (iii) and (i)


Soil formed after leaching and rich in \( A \) and Fe is
A. Alluvial
B. Podosol
c. Laterite
D. None of the above


Which has maximum number of
atoms?
A. 24 g of \( C \) (12)
B. \( 56 \mathrm{g} \) of Fe (56)
c. 27 g of Al (27)
D. \( 108 \mathrm{g} \) of \( \mathrm{Ag}(108) \)


Osmotic theory for active absorption of
water was given by
A. Thimann
B. O. Hertig
c. Atkins and Priestly
D. J. C. Bose


Which of the following does exist?
A. \( H F O_{2} \)
в. \( H C l O_{2} \)
\( \mathrm{c} . H B r O_{2} \)
D. \( H I O_{2} \)


Hydridization of anionic part of \( \boldsymbol{X} \) is:
\( A \cdot s p^{2} \)
B . \( s p^{3} \)
\( \mathrm{c} \cdot s p^{3} d \)
D. \( s p^{3} d^{2} \)


The missing value in \( \frac{2}{3} \times \frac{5}{6}=\dots . . \times \frac{2}{3} \)
is
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{5}{6} \)
D.


State any one property which is common to all electromagnetic waves.


The area of an ellipse is \( 8 \pi \) sq. units. Its distance between the foci is \( 4 \sqrt{3} \), then
\( \mathbf{e}= \)
\( \mathbf{A} \cdot \sin 30^{\circ} \)
B. \( \sin 45^{\circ} \)
c. \( \sin 60^{\circ} \)
\( \mathbf{D} \cdot \sin 75^{\circ} \)


Ethyl chloride on reduction with \( L i A l H_{4} \)
gives compound \( x \) as important
product. \( x \) on chlorination with one mole
of \( C l_{2} \) in the presence of light at
ordinary temperature gives \( y \). What is \( y \)
\( ? \)
A. \( C H_{3} C l \)
в. \( C H_{2} C l_{2} \)
\( \mathbf{c} \cdot C_{2} H_{5} C l \)
\( \mathrm{D} \cdot C_{2} H_{4} C l_{2} \)


Which term of the AP.20, \( 17,14, \ldots \ldots . \) is
the
first negative term?
A. 8th
B. 6th
c. 9 th
D. 7th


Assertion
The lowest attainable temperature is
absolute zero,i.e.,0 \( K=-273.15^{\circ} \mathrm{C} \)
Reason
Size of each degree on Kelvin scale is same as that on Celsius scale.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Direction cosines of \( Y \) -axis are


Even through the magnitudes at action
force and reaction force are equal and
their direction are opposite, their effects do not get cancelled,


The melting point of a material with low binding energy is:
A . high
B. low
c. infinity
D. negative


For linear motion, acceleration \( \times \) time \( = \)
A . speedd
B. change in speed
c. initial speed
D. final speed


Zeroes of polynomial \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+ \)
2 are
This question has multiple correct options
\( A \cdot 3 \)
B.
\( c \cdot 4 \)
D. 2


Sai is ordering new shelving units for
his store. Each unit is 7 feet in length and extends from floor to ceiling. Sai's store has 119 feet of wall space that
includes 21 feet of windows along the
walls. If the shelving units cannot be placed in front of the windows, which of the following inequalities includes all possible values of \( r, \) the number of shelving units that Sai could use?
A \( \cdot r \leq \frac{119-21}{7} \)
B. \( r \geq \frac{119+21}{7} \)
c. \( r \leq 119-21+7 r \)
D. \( r \geq 119+21-7 r \)
\( r \)