How much heat energy should be added to the gaseous mixture consisting of one gram of hydrogen and one gram
helium to raise its temperature from
\( 0^{\circ} C \) to \( 50^{\circ} C \)
(a) at constant volume and
(b) at constant pressure, assuming both the gases to be ideal \( \boldsymbol{R}=\boldsymbol{2} \boldsymbol{c a l} / \boldsymbol{m o l}-\boldsymbol{K}, \boldsymbol{\gamma}_{\boldsymbol{H}_{2}}=\mathbf{1 . 4 1} \)
\( \gamma_{H_{e}}=1.67 \)


\( 30 \% \) passenger from train got down at
station \( A, 70 \% \) of the remaining got
down at station \( B \), If there are still 1050
passenger in the train, how many passenger were there before station \( \boldsymbol{A} \) provided no one boarded the train at station \( A \) and \( B ? \)


Find the least number by which 384
must be divided to make it a perfect
square


Haloarenes react with halogens in the presence of ferric salt as catalyst to give ortho and para dichloro benzene. Which of the following products predominates in ortho and para isomers in this case?
A. ortho-dichlorobenzene
B. Para-dichlorobenzene
c. Meta-dichlorobenzene
D. A and c both


Can the centre of gravity be situated outside the material of the body?
A. Yes
B. No
c. can't say
D. None


If \( R \) is universal gas constant, the amount of heat needed to raise the
temperature of 2 moles of an ideal
monoatomic gas from 273 \( K \) to 373 \( K \) when no work is done
\( \mathbf{A} \cdot 100 R \)
в. \( 150 R \)
c. \( 300 R \)
D. \( 500 R \)


a) Write the chemical equation to prepare sulphur dioxide from industrial
method?
b) What happens when \( S O_{2} \) is pass
through water?
c) Write reaction showing reducing property of sulphur dioxide?
d) Draw a labeled diagram showing ring structure of rhombic sulphur?


Solve for \( x \) and \( y, \) if \( \left(\begin{array}{l}x^{2} \\ y^{2}\end{array}\right)+3\left(\begin{array}{c}2 x \\ -y\end{array}\right)= \)
\( \left(\begin{array}{c}-\mathbf{9} \\ \mathbf{4}\end{array}\right) \)


A policeman blows a whistle with a frequency of \( 500 H z . \) A car approaches
him with a velocity of \( 15 ~ m s^{-1} \). The change in frequency as heard by the driver of the car as he passes the policeman is (Given, speed of sound in air is \( 300 m s^{-1} \)
\( \mathbf{A} \cdot 25 H z \)
в. \( 50 H z \)
c. \( 100 H z \)
D. \( 150 H z \)


If a complex number z satisfies the equation \( z+\sqrt{\mathbf{2}}|z+\mathbf{1}|+\mathbf{i}=\mathbf{0}, \) where
\( \boldsymbol{i}=\sqrt{-\mathbf{1}}, \) then \( |\boldsymbol{z}| \) is equal to.
A .
B. 2
\( c \cdot \sqrt{3} \)
D. \( \sqrt{5} \)


In an experiment, 10 L of air (containing
\( O_{3} \) ) at 1 atm and \( 27^{\circ} C \) was passed through an alkaline KI solution. After
neutralisation, free iodine requires 1.5
\( \mathrm{mL} \) of \( 0.01 N \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \) solution. The
molar percentage of \( \boldsymbol{O}_{3} \) in air is \( \boldsymbol{y} \times \)
\( 10^{-4 \%} . \) Here \( y \) is (in nearest integer):


Larva of Bombyx mori is
A . Caterpillar
B. Trochophore
c. Nymph
D. cocoon


Fill in the blank:
The 3 middle stars in Orion represent
the
A. belt of the bear
B. belt of the hunter
c. tail of the bear
D. stick of the hunter


A parallel beam of light falls on a solid
transparent sphere. Which of the
following options is/are correct?
A. If the beam is thick, then whole beam can be focussed
at \( A \)
B. The whole beam can be focussed at A only if the beam is thin enough
c. If the beam is thin, then the beam can't be focussed
before A
D. None of these


An electric dipole is placed in a non
uniform electric field increasing along the
\( + \)ve direction of \( \mathrm{X} \) - axis. The dipole
moves along and rotates
A. \( +v e \) direction of \( X \) - axis, clockwise
B. - ve direction of \( X \) - axis, clockwise
c. \( +v e \) direction of \( X \) - axis, anti clockwise
D. - ve direction of \( X \) - axis, anti clockwise


The alkali metals are in which group of the periodic table?
A. Group
B. Group 2
c. Group 3
D. Group 4


A saturated solution of iodine in water
contains \( 0.33 I_{2} / L . \) More than this can
dissolve in a \( K I \) solution because of the
following equilibrium : \( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \left.\boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})\right] \rightleftharpoons \boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q}) \cdot \mathbf{A} \mathbf{0} \cdot \mathbf{1} \mathbf{0} \boldsymbol{N} \boldsymbol{K} \boldsymbol{I} \)
solution \( \left(0.10 M I^{-}\right) \) actually dissolves \( 12.5 g \) of iodine \( / L, \) most of which is
converted to \( I_{3}^{-} . \) Assuming that the
concentration of \( \boldsymbol{I}_{2} \) in all saturated
solutions is the same, calculate the equilibrium constant for the above reaction. What is the effect of adding
water to a clear saturated of \( I_{2} \) in the
\( K I \) solution?


Given, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\tan 4 x \times \cos 3 x & x \neq 0 \\ x & x=0\end{array} . \text { If } f \) is \right.
continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \boldsymbol{k}= \)
\( A \cdot 0 \)
B. 4
c. \( \frac{4}{3} \)
D.


The number of subsets of the \( \operatorname{set} A= \)
\( \left\{a_{1}, a_{2}, \dots \dots \dots a_{n}\right\} \) which contain even
number of elements is
A \( \cdot 2^{n-1} \)
B . \( 2^{n}-1 \)
c. \( 2^{n}-2 \)
D \( \cdot 2^{n} \)


The fundamental particles present in equal numbers in neutral atoms
(atomic number \( 71) \)
are
A. protons and electrons
B. neutrons and electrons
c. protons and neutrons
D. protons and positrons


Find the slope of a non-vertical line
\( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\mathbf{0} \)


Pressure exerted by \( 76 \mathrm{cm} \) high column of mercury is equal to
pressure.
A. 1 atmospheric
B. 2 atmospheric
c. 3 atmospheric
D. 4 atmospheric


If the key in the arrangement is taken out (the circuit is made open)
and magnetic field lines are drawn over the horizontal plane \( A B C D, \) the lines are:
A. concentric circles
B. elliptical in shape
c. straight lines parallel to each other
D. concentric circles near the point 0 but of elliptical shapes as we go away from it


Which is not correct in case of \( B e \) and
\( A l ? \)
A. Both are rendered passive by conc. \( H N O_{3} \)
B. Carbides of both give methane on hydrolysis
C. Both give hydroxides which are basic
D. Both give covalent chlorides


The fourth term of a geometric progression exceeds the second term by
24 and the sum of the second and the
third term is \( 6 . \) Find the progression.


Which gas is released by improper or incomplete combustion and are generally emitted from vehicles?
\( A \cdot S O_{2} \)
в. \( C O \)
c. \( N O \)
D. \( C O_{2} \)


The isomer(s) of diethylether is/are:
This question has multiple correct options
A. methyl-n-propylether
B. butan-1-ol
c. butan-2-ol
D. butanal


A series \( L C R \) circuit has an inductance
of \( 100 m H, \) a capacitor \( 0.1 \mu F \) and a
resistance of \( 200 \Omega \). Find the impedance
at resonance and the resonant
frequency.


DDT residues are rapidly passed through food chain as DDT is
A. water solubl
B. Moderately toxic
c. Liposoluble
D. Nontoxic to aquatic animals


Let \( I_{A} \) and \( I_{B} \) be moments of inertia of \( a \)
body about two axes \( A \) and \( B \)
respectively. The axis \( A \) passes through
the centre of mass of the body but \( B \)
does not
A \( \cdot I_{A}<I_{B} \)
B. If \( I_{A}<I_{B} \)
C. If the axes are parallel, \( I_{A}<I_{B} \)
D. If the axes are not parallel, then \( I \geq I_{B} \)


The linear momentum \( P \) of a particle
varies with time as follow \( \boldsymbol{P}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}^{2} \)
Where \( a \) and \( b \) are constants. The net
force acting on the particle is:
A. Proportional to \( t \)
B. Proportional to \( t^{2} \)
c. zero
D. constant


The shear modulus is also known as
A. bulk modulus
B. Young's modulus
c. modulus of rigidity
D. Poisson's ratio


State whether given statement is True or False

Buildings have wide foundations so
that they exert less force on the ground
or Earth.
A. True
B. False


Main function of phorphyrin pigment present in earthworm
A. Help in respiration
B. Helps in reproduction
c. Makes the worm beautiful
D. Protection from adverse effects of sun


\( \sim(\boldsymbol{p} \wedge \boldsymbol{q}) \equiv \)
\( \mathbf{A} \cdot \sim p \vee \sim q \)
в. \( p \vee \sim q \)
\( \mathrm{c} \cdot \sim p \vee q \)
D. None


What are the benefits of using mechanical barriers during sexual act?
A. Prevention of infection
B. Contraception
c. Both A and B
D. None of these


Tanya wants to fix wooden planks on the
floor of a room for her pets. The room is
\( 13 m \) long and \( 10 m \) broad. Find the cost
of fixing the planks at the rate of \( R s 500 \)
per square meter.


Oxygen is reduced to water in
A. Fermentation
B. Calvin cycle.
c. Electron transport
D. Krebs cycle.


When a glass prism of refracting angle
\( 60^{\circ} \) is immersed in a liquid its angle of
minimum deviation is \( 30^{\circ} . \) The critical
angle of glass with respect to the liquid medium is:
A \( \cdot 42^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
\( D \cdot 52^{\circ} \)


The reason for quick hotness of sand
more than the bank side water in a river
is:
A. Specific heat of water is more than sand
B. Specific heat of water is less than sand
c. specific heat of water is equal than sand
D. Due to local conditions


In an examination there are three
multiple choice questions and each question has 4 choices. Number of ways
in which a student can fail to get all answer correct is?
A . 11
B. 12
c. 27
D. 63


The trivalent ion having largest size is
A. Ti
B. zr
\( c . \) нf
D. La


In a moving coil galvanometer, the deflection of the coil \( \theta \) is related to the
electric current \( i \) by the relation
A. \( i \propto \tan \theta \)
В \( . i \propto \theta \)
\( \mathbf{c} \cdot i \propto \theta^{2} \)
\( D \cdot i \propto \sqrt{\theta} \)


For the reaction; \( F e C O_{3(s)} \longrightarrow \) \( \boldsymbol{F e O}_{(s)}+\boldsymbol{C O}_{2}(\boldsymbol{g}), \boldsymbol{\Delta H}=\mathbf{8 2 . 8} \boldsymbol{k J} \) at
\( 25^{0} C . \) What is \( \Delta U \) at \( 25^{0} C ? \)
A . \( 82.8 k J \)
в. \( 80.32 k J \)
c. \( -2394.77 k J \)
D. \( 85.28 k J \)


Ultraviolet light absorbed by nucleic acids is at
\( \mathbf{A} \cdot 26 n m \)
B. \( 75 n m \)
\( c .260 n m \)
D. 1500 nm


Which of the following two metals will
melt at body temperature \( \left(377^{\circ} C\right) ? \) Gallium, Magnesium, Caesium. Aluminium


Most harmful type of environmental pollutants are
A. Human organic wastes
B. Natural nutrients in excess
c. waste animal feed
D. Non-biodegradable chemicals


Name the factors which can increase
the rate of evaporation.


Which of the following is satisfied by an ideal solution?
A. Formation of an azeotropic mixture
В. \( \Delta S_{m i x}=0 \)
c. Raoult's law is obeyed under particular set of conditions only
D. \( \triangle H_{m i x}=0 \)


Find the value of \( x \) if
\( \sin \left\{\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right\}=1 \)


If universal set \( \boldsymbol{\xi}= \)
\( \{a, b, c, d, e, f, g, h\}, A= \)
\( \{b, c, d, e, f\}, B=\{a, b, c, g, h\} \) and
\( C=\{c, d, e, f, g\}, \) then find \( B-A \)
\( \mathbf{A} \cdot\{b, c, e, f\} \)
в. \( \{a, b, f, h\} \)
\( c \cdot\{a, g, h\} \)
D. \( \{a, c, e, g\} \)


Value of Henry's constant \( \boldsymbol{K}_{\boldsymbol{H}} \) ?
A. increases with increase in temperature
B. decreases with increase in temperature
c. remains constant
D. first increases then decreases


Which salt shows maximum osmotic
pressure in its \( 1 \mathrm{m} \) solution.
A \( . A g N O_{3} \)
в. \( N a_{2} S O_{4} \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{3} P O_{4} \)
D. \( M g C l_{2} \)


Surekha took a loan from yusuf at the rate of \( 6 \% \) per annum SI. She returned
Rs. 7,000 to yusuf after 2 years. Find the amount she took as loan.


A cube of side 'a' has a charge \( q \) placed
at each of its eight corneres. The potential at the centre of the cube due
to all the charges is :
A \( \cdot \frac{16 q}{4 \pi \varepsilon_{0} a \sqrt{3}} \)
в. \( \frac{16 q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
D. \( \frac{q}{4 \pi \varepsilon_{0} a \sqrt{3}} \)


Pile of plates can be used to produce completely polarised light due to :
A. Reflection
B. Refraction
c. Double refraction
D. A and B


Which of the following number sentences best describes the problem
shown on the number line?
A. \( -2+(-4) \)
B. \( -5+3 \)
c. \( 5+(-3) \)
D. \( -4+2 \)


Which one of the following is not correct order of boiling points of the alkyl/aryl halides?
A. \( C H C l_{3}>C H_{2} C l_{2} \)
B. \( C H_{3}\left(C H_{2}\right)_{3} C l>C H_{3}\left(C H_{2}\right)_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C C l>\left(C H_{3}\right)_{2} C H C H_{2} C l \)
D. \( C H_{3}\left(C H_{2}\right)_{3} C l>C H_{3} C H_{2} C H C l C H_{3} \)


In
fig., \( L \) is a converging lens of focal length \( 10 c m \) and \( M \) is a concave mirror
of radius of curvature \( 20 \mathrm{cm} . \) A point
object \( \boldsymbol{O} \) is placed in front of the lens at
a distance of \( 15 \mathrm{cm} . A B \) and \( C D \) are
optical axes of the lens and mirror, respectively. Find the distance of the final image formed by this system from the optical center of the lens. The distance between \( C D \) and \( A B \) is \( 1 c m \).


Show that the area of the triangle
contained between the vectors a and b
is one half of the magnitude of \( a \times b \)


Seed develops from


Ramesh tries to pull a box placed on a smooth table.He now places the box on an array of pencils,observe the amount
of force used in both the cases.ls it
easier to move the box with the pencils or without them.


The primary and secondary coils of a
transformer
have 50 and 1500 turns respectively. If
the
magnetic flux linked with the primary coil is
given by \( \phi=\phi_{0}+4 t, \) where \( \phi \) is in
webers, tis
time in seconds and \( \phi_{0} \) is a constant,
the output voltage across the secondary coil is:
A. 30 volts
B. 90 volts
c. 120 volts
D. 220 volts


A potentiometer wire of length \( L \) and a
resistance \( r \) are connected in series
with a battery of e.m.f. \( \boldsymbol{E}_{0} \) and \( \mathbf{a} \)
resistance \( r_{1} . \) An unknown e.m.f. \( \boldsymbol{E} \) is
balanced at a length \( l \) of the
potentiometer wire. The e.m.f. \( \boldsymbol{E} \) will be
given by:
A \( \cdot \frac{L E_{0} r}{\left(r+r_{1}\right) l} \)
в. \( \frac{L E_{0} r}{l r_{1}} \)
\( \mathbf{c} \cdot \frac{E_{0} r}{\left(r+r_{1}\right)} \cdot \frac{l}{L} \)
D. \( \frac{E_{0} l}{L} \)


The frequency of damped vibrations remains same but the amplitude decreases gradually.
A. True
B. False
c. Nither
D. Either


A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from
each bag, then the probability that one ball is white and one ball is black is
A \( \cdot \frac{5}{24} \)
в. \( \frac{13}{24} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{2}{3} \)


The opposing force that is caused due
to relative motion between two surfaces
in contact is celled


Each metaphasic plate in heterotypic division of meiosis contains half the
number of diploid set of chromosomes.


Find the breadth of the rectangle whose length is \( 70 \mathrm{cm} \) and perimeter \( 200 \mathrm{cm} \)


Very short answer type:
What is double fertilization?


0.3780 g of an organic chloro compound gave 0.5740 g of silver chloride in Carius estimation. Calculate the
percentage of chlorine present in the compound.


\( \frac{e^{x} \sin x-\cos x}{e^{x} \cos x+\sin x}=0 \)


The triangle \( A B C \) is defined by the vertices \( \boldsymbol{A}=(\mathbf{0}, \mathbf{7}, \mathbf{1 0}), \boldsymbol{B}=(-\mathbf{1}, \mathbf{6}, \mathbf{6}) \)
and \( C=(-4,9,6) . \) Let \( D \) be the foot of the attitude from \( B \) to the side \( A C \) then
\( B D \) is
A \( . \bar{i}+2 \bar{j}+2 \bar{k} \)
B. \( -\bar{i}+2 \bar{j}+2 \bar{k} \)
c. \( \bar{i}+2 \bar{j}-2 \bar{k} \)
D. \( \bar{i}-2 \bar{j}+2 \bar{k} \)


Placenta of a flower is a tissue that
A. Forms pollen grains
B. Attaches stamens with corolla/ sepals/ tepals
c. Bears ovule
D. Bears corolla


If \( a, b, c \) are non-coplanar vectors, then
which of the following points are collinear whose position vectors are given by :
This question has multiple correct options
A. \( a-2 b+3 c, 2 a+3 b-4 c,-7 b+10 c \)
в. \( 3 a-4 b+3 c,-4 a+5 b-6 c, 4 a-7 b+6 c \)
c. \( 2 a+5 b-4 c, a+4 b-3 c, 4 a+7 b-6 c \)
D. \( 6 a-b-2 c, 2 a+3 b+2 c,-a-9 b+7 c \)


An air bubble of radius \( 1.0 \mathrm{cm} \) rises
with a constant speed of 3.5 mm/s
through a liquid of density \( 1.75 \times \) \( 10^{3} k g / m^{3} . \) The coefficient of viscosity
of the liquid is: (Neglect the density of
air)
A \( \cdot 109 \mathrm{Ns} / \mathrm{m}^{2} \)
В. \( 10.9 \mathrm{Ns} / \mathrm{m}^{2} \)
c. \( 1.09 \mathrm{Ns} / \mathrm{m}^{2} \)
D. \( 0.109 \mathrm{Ns} / \mathrm{m}^{2} \)


State whether the following statement
is true or false:
The velocity of light is different in different media.


The part of plant used for asexual reproduction is called as
A. Reproductive partt
B. Vegetative part
c. seeds
D. Flowers


In Searle's exp to find Young's modulus, the diameter of wire is measured as \( \mathrm{D}= \) \( 0.05 \mathrm{cm}, \) length of wire is \( \mathrm{L}=125 \mathrm{cm}, \) and when a weight, \( m=20.0 \mathrm{kg} \) is put, extension in wire was found to be 0.100
cm. Find maximum permissible error in young's modulus (Y).
A . 43 \%
в. 6.3\%
c. \( 0.63 \% \)
D. 630\%


Balance the following redox reaction in basic medium.
\( \boldsymbol{C l}_{2}+\boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{O H}^{-} \longrightarrow \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{C l}^{-} \)
A \( \cdot C l_{2}+I O_{3}^{-}+3 O H^{-} \rightarrow I O_{4}^{-}+5 C l^{-}+H_{2} O \)
B. \( C l_{2}+I O_{3}^{-}+2 O H^{-} \rightarrow I O_{4}^{-}+2 C l^{-}+H_{2} O \)
c. \( C l_{2}+2 I O_{3}^{-}+2 O H^{-} \rightarrow I O_{4}^{-}+5 C l^{-}+H_{2} O \)
D. None of the above


Find \( p, q, r \) and \( s, \) if \( \left[\begin{array}{cc}\boldsymbol{p}+\boldsymbol{4} & \boldsymbol{2} \boldsymbol{q}-\boldsymbol{7} \\ \boldsymbol{s}-\boldsymbol{3} & \boldsymbol{r}+\boldsymbol{2} \boldsymbol{s}\end{array}\right]=\left[\begin{array}{cc}\boldsymbol{6} & -\boldsymbol{3} \\ \boldsymbol{2} & \boldsymbol{1} \boldsymbol{4}\end{array}\right] \)


Average can be used
A. only in unity
B. when combined with other average
\( c \cdot \) Both a \& b
D. None of the above


Assertion
Perspiration fro human body helps in
cooling the body.
Reason
A thin layer of water on the skin
enhances its emissivity.
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 enclosure of volume 3 litre contains
16g of oxygen, 7g of nitrogen and 11g of
carbondioxide at \( 27^{\circ} \mathrm{C} \). The pressure
exerted by the mixture is approximately
A. 9 atmosphere
B. 8.3 atmosphere
c. 3 atmosphere
D. 1 atmosphere


Which of the following is an example of plastic deformation?
A. stretching a rubber band
B. stretching saltwater taffy
c. none
D. both


Which of the following constitutes the best substrate during the acidic
hydrolysis of amides?
\( A \)
в.
\( c \)
D.


Which is true for excretion in humans
A. Glucose and amino acids are reabsorbed in PCT by simple diffusion
B. DCT is impermeable to water
C. On the average, \( 25-30 \) gm of urea is excreted per day
D. Maximum reabsorption occurs in loop of Henle


Give an example of a metal purified by
Mond process.


Laws of refraction to hold good:
A. one medium has to be air
B. one medium has to be glass
C. one medium has to be solid
D. two media should have different optical densities


The facts that are true among the
following are:

This question has multiple correct options
A. The electron affinity of oxygen is less than that of \( s \) but greater than that of Se
B. For Polonium, +4 oxidation state is more stable than
+6 state
C. S-S-S bond angle is \( 60^{\circ} \) in \( S_{8} \) ring
D. Dissociation constant is minimum for \( H_{2} O \) among
the hydrides of 16 th group elements.


Which of the following is used as artificial kidney in kidney failure patients?
\( \mathbf{A} \). Filter
B. Angiogram
c. Dialysis
D. Ventilation


Leaves of many grasses are capable of folding and unfolding because they
A. Are very thin
B. Are isobilateral
c. Have specialised bulliform cells
D. Have parallel vascular bundles


The secondary suffix, '-one' indicates
the following functional group in the compound.
A. -coon
в.
c.
D. - он


If the same element is forming oxides in different oxidation states, then, which
of the following statement is incorrect? This question has multiple correct options
A. Oxide will be neutral in nature in which element is in its highest oxidation state
B. Oxide will be highly acidic in nature in which element is in its highest oxidation state
c. oxide will be amphoteric in nature in which element is in its highest oxidation state
D. oxide will be highly basic in nature in which element is in its highest oxidation state


The intercepts made by the line \( x- \) \( 2 y=6 \) on the \( Y \) -axis is b.Find \( b \)


State the laws of reflection.


If \( g_{E} \) and \( g_{M} \) are the accelerations due
to gravity on the surfaces of the Earth and the Moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the Moon/ electronic charge on the Earth) to be:
A . 1
B.
\( \mathbf{c} \cdot g_{E} / g_{M} \)
D. \( g_{M} / g_{E} \)


Good fuel is:
A. Readily available
B. Cheap
C. Burn easily in air
D. All of these


Let \( \boldsymbol{P} \) be an \( \boldsymbol{m} \times \boldsymbol{m} \) matrix such that
\( \boldsymbol{P}^{2}=\boldsymbol{P} . \) Then \( (\boldsymbol{I}+\boldsymbol{P})^{n} \) equals.
\( \mathbf{A} \cdot I+P \)
B. \( I+n P \)
c. \( I+2^{n} P \)
D. \( I+\left(2^{n}-1\right) P \)


During the formation of \( M g C l_{2} \) by Born Haber cycle, which of the following
occurs?
A . lonisation of \( M g \) to \( M g^{+2} \)
B. Bond dissociation of \( C l_{2} \)
c. Sublimation of \( M g \)
D. Electron gained by \( C l \)
E. All of these


Choose the correct alternative:
(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
(b) Alloys usually have much (lower/higher) temperature coefficients
of resistance than pure metals.
(c) The resistivity of the alloy manganin is nearly independent of increases rapidly with increase of
temperature
(d) The resistivity of a typical insulator
(e.g., amber) is greater than that of a metal by a factor of the order of \( \left.\mathbf{1 0}^{\mathbf{2 2}} / \mathbf{1 0}^{\mathbf{3}}\right) \)


and \( C_{2} H_{5}-O-N=O \) are example
of:
A. Functional isomerism
B. tautomers
C. position isomers
D. metamers


For the conic \( 9 x^{2}-16 y^{2}+18 x+ \)
\( 32 y-151=0, \) find \( e \)
A \( \cdot \frac{5}{4} \)
в. \( \frac{4}{5} \)
\( c \cdot \frac{1}{2} \)
D. None of these


Find the incorrect statements related to
the rainbow:
A. The rainbow is formed in the same direction to the
position of the sun
B. When the light rays undergo dispersion and total internal reflection, the water droplets present in atmosphere forms rainbow
C. A rainbow is formed in the shape of circle
D. When light rays undergo one internal reflection and two refractions produce primary rainbow whereas two internal reflections and two refractions produce secondary rainbow


Find the new position of the balance point when \( 5 \omega \) resistor is changed by 4
\( \omega \) resistor
A. \( 26.5 \mathrm{cm} \)
B. 52 \( \mathrm{cm} \)
c. 67.2 \( \mathrm{cm} \)
D. \( 83.3 \mathrm{cm} \)


The heat developed in a resistor \( \boldsymbol{R}_{1} \) connected to a cell is equal to the heat developed when it is connected to
another resistance, \( \boldsymbol{R}_{2} \) replacing \( \boldsymbol{R}_{1} \) for the same time. The internal resistance
of the cell will be
A. \( \frac{R_{1}+R_{2}}{2} \)
в. \( \frac{R_{1} R_{2}}{2\left(R_{1}+R_{2}\right)} \)
c. \( \frac{R_{1} R_{2}}{R_{1}+R_{2}} \)
D. \( \sqrt{R_{1} R_{2}} \)


Differentiate: \( \boldsymbol{y}=\sin ^{-1}\left(\frac{1-\boldsymbol{x}^{2}}{\mathbf{1}+\boldsymbol{x}^{2}}\right), \mathbf{0}< \)
\( \boldsymbol{x}<\mathbf{1} \)


Resistance of a metallic conductor
depends on
A. Its length
B. Its area of cross section
c. Temperature
D. All the above


Charges always reside of the
charged conducting object.
\( A \). in the bulk
B. on the surface
c. Both A and B
D. Neither A nor B


The numerical ratio of displacement to distance covered is always:
A. Less than one
B. Equal to one
c. Equal to or less than one
D. Equal to or greater than one


Plastic used to preserve yogurts is replaced with a polymer called polylactic acid is an example of
A. green chemistry
B. waste management
c. green revolution
D. none of above


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


Which of the following is considered most advanced amongst the
pteridophyte?
A . Quillworts
B. Scouring rushes
c. Ferns
D. club mosses


If \( a, b, c \) are vectors such that \( a+b+ \)
\( \boldsymbol{c}=\mathbf{0} \) and \( |\boldsymbol{a}|=\mathbf{7},|\boldsymbol{b}|=\mathbf{5},|\boldsymbol{c}|=\mathbf{3}, \) then
the angle between \( c \) and \( b \) is
A \( \cdot \frac{\pi}{3} \)
в.
c.
D.


In violin there is part which is used to adjust the string for getting right pitch. What is the name of that part?
A. Tunning peg
B. Volute
c. Finger board
D. Neck


An integer is chosen at random between
1 and \( 100 . \) Find the probability that it is divisible by 8 is \( \frac{m}{25} . \) Find \( m \)


\( \mathbf{f} \mathbf{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{b} & \boldsymbol{a}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{cc}\boldsymbol{c} & \boldsymbol{d} \\ -\boldsymbol{d} & \boldsymbol{c}\end{array}\right] \) show
that \( A \) product \( B \) commute
i. e. \( A B=B A \) also verify that \( |\boldsymbol{A B}|=|\boldsymbol{A}| \cdot|\boldsymbol{B}| \)


Explain the industrial method of preparation of bleaching powder with a neat diagram.


A liquid is being converted into vapours at its boiling point the specific heat of the liquid at this temperature will be.
A. zero
B. Infinite
c. Positive
D. Negative


Assertion
The relation \( \frac{x}{m}=k \cdot p^{1 / n} \) is known as Freundlich adsorption isotherm, where
\( x \) is the mass of gas adsorbed by \( m \)
grams of adsorbate, \( \boldsymbol{p} \) is the
equilibrium pressure, \( k \) and \( n \) are
constants for given system and
temperature
Reason
When several substances have the
same value of \( \frac{1}{n}, \) the lines by which their adsorption isotherms can be
represented will meet at a point.
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.


Let \( \boldsymbol{R}=\boldsymbol{g} \boldsymbol{S}-\mathbf{4} . \) When \( \boldsymbol{S}=\mathbf{8}, \boldsymbol{R}=\mathbf{1 6} \)
When \( S=10, R \) is equal to
A . 11
B. 14
c. 20
D. 21
E. None of these


Among the following gaseous elements with atomic numbers, which will have
grater rate of diffusion?
\( A \cdot Z=7 \)
B . \( Z=8 \)
c. \( Z=10 \)
D. \( Z=17 \)


Which postulates of Dalton's atomic theory can explain the Law of definite proportion?
A. All matter is made of very tiny particles called atoms.
B. Atoms of a given element are identical in mass and chemical properties
c. Atoms are indivisible particles and cannot be created nor destroyed.
D. The relative number and kind of atoms in a given compound remain constant


\( A 2 k g \) copper block is heated to \( 500^{\circ} \mathrm{C} \) and then it is placed on a large block of
ice at \( 0^{\circ} \mathrm{C} \). If the specific heat capacity of copper is \( 400 \mathrm{J} / \mathrm{kg} / \mathrm{C} \) and latent heat of water is \( 3.5 \times 10^{5} J / k g . \) The amount
of ice that can melt is:
\( A \cdot 7 / 8 \mathrm{kg} \)
B. 7/5 kg
c. \( 8 / 7 \mathrm{kg} \)
\( D \cdot 5 / 7 \mathrm{kg} \)


An electric dipole consists of charges
\( \pm 2.0 \times 10^{-8} C \) separated by a distance
of \( 2.0 \times 10^{-3} m \). It is placed near a
long line charge of linear charge density \( 4.0 \times 10^{-4} C \quad m^{-1} \) as shown in the
figure, such that the negative charge is
at a distance of \( 2.0 \mathrm{cm} \) from the line
charge. The force acting on the dipole
will be
A. \( 7.2 N \) towards the line charge
B. \( 6.6 N \) away from the line charge
c. \( 0.6 N \) away from the line charge
D. \( 0.6 N \) towards the line charge


Find the second order derivatives of
\( \sin (\log x) \)


Slowest reaction among the following under identical conditions is:
A \( \cdot N a O H+H C l \rightarrow N a C l+H_{2} O \)
B. \( H^{+}+O H^{-} \rightarrow H_{2} O \)
\( \mathrm{c} \cdot 2 \mathrm{N} \mathrm{O}+\mathrm{O}_{2} \rightarrow 2 \mathrm{N} \mathrm{O}_{2} \)
D. \( C H_{4}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \)


In the density measurement of a cube, the mass an edge length are measured
as \( (\mathbf{1 0 . 0 0} \pm \mathbf{0 . 1 0}) k g \) and
\( (0.10 \pm 0.01) m, \) respectively. The error
in the measurement of density:
\( \mathbf{A} \cdot 0.10 k g / m^{3} \)
в. \( 0.31 k g / m^{3} \)
\( \mathbf{c} \cdot 0.07 k g / m^{3} \)
D. \( 0.01 k g / m^{3} \)
E. No answer


Gas particles vibrate about
A. their mean positions
B. any direction
c. both of above
D. none of these


The velocity of the wind over the surface
of the wing of an aeroplane is \( 80 \mathrm{ms}^{-1} \)
and under the wing \( 60 \mathrm{ms}^{-1} \). If the area
of the wing is \( 4 \mathrm{m}^{2} \), the dynamic lift experienced by the wing is [ density of \( \left.\operatorname{air}=1.3 \mathrm{kg} . \mathrm{m}^{-3}\right] \)
A. 3640 N
в. 7280 N
c. \( 14560 \mathrm{N} \)
D. 72800 N


Which type of bond forms on the transfer of electrons?
A. Ionic Bond
B. Metallic Bond
c. Hydrogen Bond
D. covalent bond


Prove that \( \sin 60^{\circ} . \cos 30^{\circ}- \)
\( \cos 60^{\circ} \cdot \sin 30^{\circ}=\sin 30^{\circ} \)


For a metallic conductor, what is the
relation between current density \( (j) \) conductivity \( (\sigma) \) and electric field
Intensity \( E ? \)


Two complementary angles differ by \( 10^{\circ} \) Find the angles


The least distance of distinct vision for
a young adult with normal vision is
about
A. \( 1 \mathrm{m} \)
B. 2.5 \( m \)
c. \( 0.25 \mathrm{m} \)
D. 25 m


The correct statements among
\( (a) \operatorname{to}(d) \)
regarding \( \mathrm{H}_{2} \) as a fuel are :
(a) It produces less pollutant than petrol.
(b) A cylinder of compressed dihydrogen weighs \( \sim 30 \) times more than a petrol
tank producing the same amount of
energy.
(c) Dihydrogen is stored in tanks of
metal alloys like \( N a N i_{5} \)
(d) On combustion, values of energy
released per gram of liquid dihydrogen and LPG are 50 and \( 142 \mathrm{kJ} \), respectively
\( A \). b and donly
B. a, b and conly
\( c . \) b, cand donly
D. a and c only


Why is an electromagnet more
advantageous?
A. It produces a strong magnetic field
B. The magnitude of the magnetic field can be easily changed
C. Reversing the current changes the polarity of the magnet
D. All of the above


Phenol reacts with alkali to give:
A . salt
B. water
c. both \( A \) and \( B \)
D. complex compound


(a) Using Bohr's postulates, obtain the expression for total energy of the electron in the \( n^{t h} \) orbit of hydrogen
atom.
(b) What is the significance of negative \( \operatorname{sign} \) in the expression for the energy?
(c) Draw the energy level diagram showing how the line spectra corresponding to Paschen series occur due to transition between energy levels.


Assertion
In the titration of \( N a_{2} C O_{3} \) with \( H C l \)
using methyl orange indicator, the volume required at the equivalence
point is twice that of the acid required using phenolphthalein indicator.
Reason
Two mole of \( H C l \) are required for the
complete neutralization of one mole of
\( N a_{2} C O_{3} \)
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct


Macromolecule, most diverse in cell to control physiological and chemical properties is?
A. Nucleic acid
B. Protein
c. Glycogen
D. oligosaccharide


The position of both, an electron and a range of helium atom is known within
1.0 \( n m . \) Further the momentum of the
electron is known within a range of \( \mathbf{5 . 0} \times \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g} \mathbf{m s}^{-1} . \) The minimum
uncertainty in the measurement of the
momentum of the helium atom is:
A. \( 50 \mathrm{kg} \mathrm{ms}^{-1} \)
B. \( 80 \mathrm{kg} \mathrm{ms}^{-1} \)
c. \( 80 \times 10^{-26} \) kg \( m s^{-1} \)
D. \( 5 \times 10^{-26} \mathrm{kg} \mathrm{ms}^{-1} \)


Calculate the quantity of heat required to convert \( 1.5 \mathrm{kg} \) of ice at \( 100^{\circ} \mathrm{C} \) to water
\( \operatorname{at} 15^{\circ} C .\left(L_{i c e}=3.34 \times\right. \)
\( \mathbf{1 0}^{\mathbf{5}} \boldsymbol{J} \quad \boldsymbol{k} \boldsymbol{g}^{-\mathbf{1}}, \boldsymbol{C}_{\boldsymbol{w} a t e r}= \)
\( \begin{array}{llll}\mathbf{4 1 8 0} & \boldsymbol{J} & \boldsymbol{k g}^{-1} & ^{\circ} \boldsymbol{C}^{-1} \mathbf{)}\end{array} \)
\( \begin{array}{llll}\text { A } \cdot 5.85 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { В. } 5.95 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { C } \cdot 3.95 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { D. } 4.95 & \times & 10^{5} & J\end{array} \)


Find the distance between the point (7,2,4) and the plane determined by
the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{5},-\mathbf{3}), \boldsymbol{B}(-\mathbf{2},-\mathbf{3}, \mathbf{5}) \)
and (5,3,-3)


A bird flies in a circle on a horizontal
plane. An observer stands at a point on the ground. Suppose \( 60^{\circ} \) and \( 30^{\circ} \) are the maximum and the minimum angles
of elevation of the bird and that they
occur when the bird is at the points \( \mathrm{P} \) and \( Q \) respectively on its path. Let \( \theta \) be the angle of elevation of the bird when it is a point on the are of the circle exactly midway between \( P \) and \( Q \). Find the numerical value of \( \tan ^{2} \theta \) (Assume that
the observer is not inside the vertical
projection of the path of the bird).


The drawing below shows a cell whose diplod chromosome number is four. this cell is in
A. Metaphase
B. Anaphase of mitosis
c. First anaphase of meiosis
D. Second anaphase of meiosis


An inductive coil has a resistance of 100
\( \Omega . \) When an \( A C \) signal of frequency 1000 \( \mathrm{Hz} \) is applied to the coil, the voltage
leads the current by \( 45^{\circ} . \) The inductance of the coil is
A \( \cdot \frac{1}{100 \pi} \) #
в. \( \frac{1}{20 \pi} \) н
c. \( \frac{1}{40 \pi} \) н
D. \( \frac{1}{60 \pi} \) н


Which one of the following has the regular tetrahedral structure?
A \( \cdot \mathrm{xeF}_{4} \)
в. \( \mathrm{SF}_{4} \)
\( \mathrm{c} \cdot \mathrm{BF}_{4}^{-} \)
D. None of the above


Compound eyes are found in
\( A \cdot F \operatorname{rog} \)
B. Earthworm
c. cockroach
D. Roundworm


Five identical cubes each of mass \( m \)
are on a straight line with two adjacent faces in contact on a horizontal surface
as shown in the figure. Suppose the surface is frictionless and a constant
force \( \boldsymbol{P} \) is applied from left to right to the end face of \( A ; \) which of the following statements are correct?
\( \mathbf{P} \rightarrow \)\begin{tabular}{|l|l|l|l|l|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{C} \) & \( \mathbf{D} \) & \( \mathbf{E} \) \\
\hline
\end{tabular}
A the acceleration of the system is \( \frac{5 P}{m} \)
B. the resultant force acting on each cube is \( \frac{P}{5} \)
c. the force exerted on D due to C is \( \frac{2 P}{5} \)
D. the acceleration of the cube \( D \) is \( \frac{P}{5} \) m


What is oxygen dissociation curve? List the factors which result in causing this
curve


Which of the following pairs of compounds of carbon will undergo combustion as well as addition
reactions?
A. \( C H_{4} \) and \( C_{2} H_{6} \)
в. \( C_{2} H_{6} O \) and \( C_{3} H_{8} \) O
c. \( C_{2} H_{4} O_{2} \) and \( C_{3} H_{6} O \)
D. \( C_{2} H_{2} \) and \( C_{3} H_{6} \)


What are the differences between DNA
and RNA?


A woman has an \( X \) linked condition on
one of her \( \mathrm{X} \) chromosomes. This chromosome can be inherited by
A. only grandchildren
B. Only daughter
c. Both sons and daughters
D. Only sons


\( 2- \) pentanone and \( 3- \) pentanone are:
A. Chain isomers
B. Tautomers
C. Metamers
D. Positional isomers


There are two opposing views about origin of modern man. According to one view, Homo erectus in Asia was ancestor
of modern man. A study of variations of DNA, however suggested African origin of modern man.
What kind of observation of DNA
variations could suggest this?
A. Greater variation in Asia than in Africa
B. Greater variation in Africa than in Asia
c. similar variation in Africa and Aisa
D. Variation only in Asia and no variation in Africa


A particle is in motion along a curve \( 12 y-x^{3} . \) The rate of change of its
ordinate exceeds that of abscissa in
This question has multiple correct options
A \( .-2<x<2 \)
B. \( x=\pm 2 \)
c. \( x<-2 \)
D. \( x>2 \)


Dipole moment of is 1.5 D. The dipole
moment of is
\( \mathbf{A} \cdot 1.5 D \)
B. \( 2.25 D \)
c. \( 1 D \)
D. \( 3 D \)


The hybridization of iodine in \( \mathbf{I F}_{5} \) is :
\( A \cdot s p^{3} d \)
B \( \cdot \operatorname{sp}^{3} \mathrm{d}^{2} \)
\( \mathbf{c} \cdot \mathbf{s p}^{3} \mathrm{d}^{3} \)
\( D \cdot s p^{3} \)


From the given compounds, \( X \) is the
number of compounds which are acidic
in water.
\( C a O, S O_{2}, S O_{3}, F e_{2} O_{3}, C l_{2} O_{7}, C O_{2} \)
Find the value of \( \boldsymbol{X} \)


When an object is placed \( 20 \mathrm{cm} \) from a complex lens then a real image is formed \( 30 \mathrm{cm} \) from the lens. Where
should the object be placed so that a real image of the same size is formed
by the lens.
A. object should be placed \( 24 \mathrm{cm} \) from the lens.
B. object should be placed \( 34 \mathrm{cm} \) from the lens.
c. object should be placed 14 cm from the lens.
D. object should be placed 30 cm from the lens


State whether the given statement is
True or False :

Lightning conductor always develops the opposite charges as is the charge in
the clouds.
A. True
B. False


lonic interactions are stronger than covalent bonds.
A. True
B. False


If \( A \) is a square matrix of order 3 and \( |\boldsymbol{A}|=4 . \) Find the value of \( |\mathbf{2 A}| \)


Which of the following is a negative rational number:
A \( \cdot \frac{-15}{25} \)
B.
\( c \cdot \frac{3}{5} \)
\( D \cdot \frac{-3}{-5} \)


The percentage of marks obtained by the
students in a class of 50 are given below.
Find the mode for the following data.
Marks \( \begin{array}{lll}\mathbf{4 0}- & \mathbf{5 0}- & \mathbf{6 0}- \\ \mathbf{5 0} & \mathbf{6 0} & \mathbf{7 0}\end{array} \)
\( (\%) \)
Number
of 6
12
14
horses
A .62 .5
B. 63.5
c. 64.5
D. 65.5


Extraction of gold (Au) involves the formation of complex ions \( X \) and \( Y \) Gold ore \( \frac{\text { Roasting }}{C N^{-}, H_{2} O, O_{2}} H O^{-}+X \stackrel{Z n}{\longrightarrow} \)
\( \boldsymbol{Y}+\boldsymbol{A} \boldsymbol{u} \)
X and Y respectively are :
A \( \cdot A u(C N)_{2}^{-} \) and \( Z n(C N)_{4}^{2} \)
B . \( A u(C N)_{4}^{3-} \) and \( Z n(C N)_{4}^{2} \)
c. \( A u(C N)_{3}^{-} \) and \( Z n(C N)_{6}^{4} \)
D. \( A u(C N)_{4}^{-} \) and \( Z n(C N)_{3} \)


The name of the compound \( C_{6} H_{5}- \)
\( C H_{2}-C \equiv C H \) is 3 -phenyl-1-propyne.
A. True
B. False


Let \( I \) be the purchase value of an equipment and \( v(t) \) is the value after it has been used for \( t \) years. the value \( v(t) \) depreciates at a rate \( \frac{\boldsymbol{d v}(\boldsymbol{t})}{\boldsymbol{d t}}=-\boldsymbol{k}(\boldsymbol{T}- \)
\( t) \) where \( k>0 \) is a constant and \( T \) is
the total life in years then the scrap
value \( v(T) \) of the equipment is
A \( \cdot I-\frac{k T^{2}}{2} \)
B. \( _{I-\frac{k(T-t)^{2}}{2}} \)
\( \mathbf{c} \cdot e^{-k T} \)
D. \( T^{2}-\frac{1}{T} \)


Evaluate \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}), \) if \( \boldsymbol{2} \boldsymbol{P}(\boldsymbol{A})= \)
\( \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{5}}{13} \) and \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\frac{2}{\mathbf{5}} \)


Paneth cells are found in
A . Liver
B. Stomach
c. Intestine
D. Kidney


What is meant by unidentate, didentate and ambidentate ligands? Give two examples for each.


An electric dipole when placed in a uniform electric field will have minimum
potential energy, if the angle between dipole moment and electric field is
A . zero
B. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( \frac{3 \pi}{2} \)


\( A \) is a \( 3 \times 3 \) diagonal matrix having integral entries such that \( \operatorname{det}(A)=120 \)
number of such matrices is \( 10 n \), then
\( \boldsymbol{n} \) is
A . 36
B . 38
\( c \cdot 34 \)
D. 30


Which of the following helps the soil to prevent the flood?
A. Forest
B. Animals
c. Fishes
D. None of the above


Assertion
A wire bent into an irregular shape with
the points \( P \) and \( Q \) fixed. If a current
passed through the wire, then the area
enclosed by the irregular portion of the wire increases.
Reason
Opposite currents carrying wires repel
each other.
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 major product (ester) of the
following reaction is?
A. A single stereoisomer (optically active)
B. A mixture of diastereomers (both optically active)
c. A racemic mixture (optically inactive)
D. A mixture of four stereoisomers (two racemic mixtures


What is the weight of a man whose mass is \( 80 \mathrm{kg} ? \)
A. \( 8.1 \mathrm{N} \)
B. 70.2 N
c. \( 80 \mathrm{N} \)
D. 89.8 N
E. 784 N


A \( 300 \Omega \) resistor is connected in series
with a \( 0.800 H \) inductor. The voltage
across the resistor as a function of time
is \( V_{R}=(2.50 V) \cos [(950 r a d / s) t] \)
Determine the inductive reactance of
the inductor.


Prove the following identities:
\( \sin 3 x+\sin 2 x-\sin x= \)
\( 4 \sin x \cos \frac{x}{2} \cos \frac{3 x}{2} \)


Match the following items in column I with column II and choose the correct
answer.

Column I
A. Arsenic
1. Minamata
disease
B. Nitrate
2. Itai-itai
C. Mercury
3. Blue-baby syndrome
D. Cadmium
4. Skeletal
fluorosis
E. Fluoride
5. Black-foot
disease
A \( \cdot A-2, B-3, C-5, D-1, E-4 \)
B. A- 5, B- - 3, С-1, D- 2, E- 4
c. \( A-3, B-4, C-5, D-1, B-2 \)
D. A- 5, B- 4, C- 3, D-2, B-1
E. A- 2, B- 5, C- 4, D- 3, E-1


The unitless quantity is:
A. velocity gradient
B. pressure gradiant
C. displacement gradient
D. force gradient


A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity ( \( \omega \) )of the
disc varies with the number of rotations
\( (n) \) made by the disc after starting from
rest as \( \omega=h n^{1 / x} \) then \( x \) is : \( (K \) is
constant)


Find the integral of \( \int\left(2 x^{2}-3 \sin x+\right. \) \( \mathbf{5} \sqrt{\boldsymbol{x}}) \boldsymbol{d} \boldsymbol{x} \)


\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\mathbf{1} / \boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \boldsymbol{\Delta} \boldsymbol{H}_{298}^{o}= \)
\( \mathbf{9 8 . 3 2 k J / m o l e , \Delta S _ { 2 9 8 } ^ { o }}= \)
\( \mathbf{9 5 . 0 J} / \boldsymbol{K} / \) mole
Find the \( K_{p} \) for this above reaction at
298K:
B. \( K_{P}=5.34 \times 10^{-13} a t m^{1 / 2} \)
c. \( K_{P}=3.7 \times 10^{-13} a t m^{1 / 2} \)
D. \( K_{P}=3.7 \times 10^{-14} \mathrm{atm}^{1 / 2} \)


If the sides \( A B, B C, C D \) and \( D A \) of a trapezium ABCD measure \( 10 \mathrm{cm}, 20 \mathrm{cm} \)
\( 18 \mathrm{cm} \) and \( 16 \mathrm{cm} \) respectively then find the length of the longer diagonal given
that \( A B \) is parallel to \( C D \)
A \( . \sqrt{760} \mathrm{cm} \)
В. \( \sqrt{231} \mathrm{cm} \)
\( c \cdot \sqrt{54} c m \)
D. \( \sqrt{930} \mathrm{cm} \)


What is electrometallurgy?


The projection of a line segment joining
the points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1},\right) \) and
\( Q\left(x_{1}, y_{1}, z_{1},\right) \) on another line whose
DC's are \( l, m, n \) is given by This question has multiple correct options
A \( \cdot l\left(x_{1}+x_{2}\right)+m\left(y_{2}+y_{2}\right)+n\left(z_{1}+z_{2}\right) \)
B. \( 2\left[\frac{\left(l x_{2}+m y_{2}+n z_{2}\right)}{2}-\frac{\left(l x_{1}+m y_{1}+n z_{1}\right)}{2}\right. \)
c. \( l\left(x_{2}-x_{1}\right)+m\left(y_{2}-y_{1}\right)+n\left(z_{2}-z_{1}\right) \)
D. \( \frac{x_{2}-x_{1}}{l}+\frac{y_{2}-y_{1}}{m}+\frac{z_{2}-z_{1}}{n} \)


Q Type your question
1
\( A \)
11
B.
(2)
\( c \)
\( D \)
(4)


state-wise teacher-student ratio in
higher secondary schools of India. Find
the mode and mean of this data.
Interpret, the two measures.
A. \( M o d e=43.6 \) and Mean\( =21 . \)
and \( M e a n=24 . \)
B. Mode\( =39.6 \)
c. Mode\( =35.6 \) and Mean \( =27.2 \)
D. \( M o d e=30.6 \) and Mean


A cricketer draws his hands backwards
to catch the ball, because
A. by increasing the time in which he stops the ball, he reduces the force on his hands
B. by increasing the distance, he allows the ball to travel a greater distance for more runs
C. it is an art to catch the ball
D. it is a rule in cricket


Which of the following brings
oxygenated blood into left atrium in
heart?
A. Superior venacava
B. Inferior venacava
c. Pulmonary artery
D. Pulmonary vein


Side \( A B \) and \( B C \) and median \( A D \) of a
triangle \( A B C \) are respectively
proportional to sides \( P Q \) and \( Q R \) and
median \( P M \) of \( P Q R \) Show that
\( A B C \sim P Q R \)


Deuteriated solvents are used to
conduct NMR.
If this is true enter 1 , if false enter 0 .


1: Primary waves can travel in all
directions in an ether
2: Secondary waves can travel only in backward in an ether
A \( . \) 1 is true, 2 is false
B. Both 1 and 2 are true
c. 1 is false, 2 is true
D. Both 1 and 2 are false


Assertion
Strain is a unitless quantity.
Reason

Strain is equivalent to force
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following energy changes
occur in galvanic cell?
A. Electrical energy \( \rightarrow \) Chemical Energy
B. Chemical Energy \( \rightarrow \) Electrical Energy
C. Chemical Energy \( \rightarrow \) Internal Energy
D. Internal Energy \( \rightarrow \) Electrical Energy


\( \lim _{x \rightarrow \infty} x^{3 / 2}(\sqrt{x^{3}+1}-\sqrt{x^{3}-1})= \)
A . -1
B. 0
\( c \cdot \frac{1}{2} \)
\( D \)


Velocity of sound in air is \( 340 \mathrm{m} / \mathrm{s} \)
Sound waves of wavelength \( 0.01 \mathrm{m} \) from a vibrating body reach your ear through air. Will you be able to hear the sound? Justify your answer.


In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the
centre. Identical charges are placed at \( (n-1) \) corners. At the centre, the
intensity is \( \boldsymbol{E} \) and the potential is \( \boldsymbol{V} \)
The ratio \( V / E \) has magnitude.
\( \mathbf{A} \cdot r n \)
в. \( r(n-1) \)
\( c \cdot r \)
D. \( r(-1) / n \)


What is the relation between \( T \) and \( V \) of
gas in this process?
A \( \cdot T \cdot V^{2(\gamma-1)}= \) constant
B. \( T \cdot V^{\gamma-1}= \)constant
c. \( T \cdot V^{\gamma-1 v^{2}}= \) constant
D. \( T \cdot V^{\gamma}= \) constant


Scientific names of potato and tomato plants are
A. Potato- Solanum tuberosum- Solanaceae
B. Tomato- Lycopersicum esculentum- - Solanaceae
c. Potato- Ocimum sanctum- Lamiaceae
D. Both A and B


Explain the terms
(i) bonding molecular orbitals,
(ii) antibonding molecular orbitals,
(iii) non-bonding molecular orbitals.


Which of the following expression is that of a simple harmonic progressive
wave?
A. \( A \sin (\omega t-k x) \)
B. \( A \sin \omega t \)
c. \( A \sin \omega t \cos k x \)
D. \( A \cos k x \)


The load versus elongation graph for four wires of the same material and
same length is shown in the figure.
The thinnest wire is represented by the
ine
\( A \cdot O A \)
B. OB
\( c \cdot 0 c \)
D. o


State whether true or false.
The time taken by a body which is falling freely from a height h to reach the ground is equal to \( \sqrt{\frac{2 h}{g}} \)
A. True
B. False


Atmospheric pollutants formed by human activities constitute of the total
of
A . \( 95 \% \)
B. \( 75 \% \)
\( c .25 \% \)
D. \( 0.05 \% \)


If \( x \) takes negative permissible value,
then \( \sin ^{-1} x= \)
B. \( -\cos ^{-1} \sqrt{1-x^{2}} \)
\( \mathrm{c} \cdot \cos ^{-1} \sqrt{x^{2}-1} \)
D・ \( \pi-\cos ^{-1} \sqrt{1-x^{2}} \)


In a certain store, the profit is \( 320 \% \) of the cost. If the cost increases by \( 25 \% \)
but the selling price remains constant, approximately what percentage of the selling price is the profit?


Root cap has no role in water absorption because
A. It has no direct connection with the vascular system
B. It has no cells containing chloroplasts.
c. It has no root hairs
D. It has loosely arranged cells.


How can you identify the three types of
mirrors without touching them? Give
reasons.


The nucleus finally formed in fusion of protons in proton-proton cycle is that of
A. Heavy hydrogen
B. Carbon
c. Helium
D. Lithium


The process of coating of zinc over iron
is known as
A. Calcination
B. Metallurgy
c. Tinning
D. Galvanisation


Three solid spheres each of mass \( P \) and
radius \( Q \) are arranged as shown in
figure. The moment inertia of the
arrangement about \( Y Y^{\prime} \) axis will be
\( ^{A} \cdot \frac{7}{2} P Q^{2} \)
B. \( \frac{2}{7} P Q^{2} \)
c. \( \frac{2}{5} P Q^{2} \)
D. \( \frac{5}{2} P Q \)


Thickness of very thin films can be found by the technique of
A. Dispersion
B. Interference
c. polarization
D. Diffraction


\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \frac{C a(\boldsymbol{O H})_{2}}{\boldsymbol{\Delta}} \boldsymbol{A} \frac{\boldsymbol{C a}(\boldsymbol{O O C H})_{2}}{\boldsymbol{\lambda}} \)
\( \boldsymbol{B} \stackrel{N H_{2} O \boldsymbol{H}}{\longrightarrow} \boldsymbol{C} \)
Identify the ' \( C^{\prime \prime} \) in the given series
\( \stackrel{\mathrm{H}_{3} \mathrm{C}}{\mathrm{H}_{3} \mathrm{C}} \mathrm{C}=\mathrm{NOH} \)
в. \( C H_{3} C H=N O H \)
\( \mathbf{c} \cdot H_{2} C=N O H \)
D. \( C H_{3} C H_{2} C H=N O H \)


If two particles of masses \( m_{1} \) and \( m_{2} \)
move with velocities \( v_{1} \) and \( v_{2} \) towards
each other on a smooth horizontal
plane, what is the velocity of their
centre of mass.?
A \( \cdot V=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}} \)
B. \( V=\frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}+m_{2}} \)
\( \mathbf{c} \cdot V=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}-m_{2}} \)
D. \( V=\frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}-m_{2}} \)


The velocity-time graph of a body is
given in figure. The maximum
acceleration in \( \boldsymbol{m} \boldsymbol{s}^{-2} \) is:
4
\( B \)
\( c \)
D


In a region of uniform electric field of
intensity \( \boldsymbol{E}, \) an electron of mass \( \boldsymbol{m}_{e} \) is relased from rest. The distance travelled
by the electron in a time \( t \) is:
\( ^{\mathbf{A}} \cdot \frac{2 m_{e} t^{2}}{e} \)
B. \( \frac{e E t^{2}}{2 m_{e}} \)
\( ^{\mathbf{c}} \cdot \frac{m_{e} g t^{2}}{e E} \)
D. \( \frac{2 E t^{2}}{e m_{c}} \)


The graph illustrates the data obtained
from reactions of an enzyme with its specific substrate at various
temperatures and at pH 6 Based on the data, what would be the
result if the experiment is carried out at
\( \mathbf{5}^{\circ} \boldsymbol{C} ? \)
A. No prediction would be valid
B. An amount of product equal to that at \( 20^{\circ} \mathrm{C} \) would be formed
c. An amount of product equal to that at the optimum temperature would be formed
D. An amount of product equal to that at \( 60^{\circ} \mathrm{C} \) would be formed
E. Little or no product would be formed


From the following options, choose the option with which perfect answer does not ends with
A . 5
B. 4
\( c \cdot 0 \)
D. None of the above


A semicircle loop \( P Q \) of radius \( ^{\prime} R^{\prime} \) is
moved with velocity \( ^{\prime} v^{\prime} \) in transverse
magnetic field as shown in figure. The
value of induced emf. at the end of loop
is :-


A body is under the action of two equal and oppositely directed forces and the body is rotating with constant non-zero angular acceleration. Which of the following cannot be the separation between the lines of action of the
forces?
A. \( 1 m \)
в. \( 0.4 m \)
c. \( 0.25 m \)
D. zero


Assertion
\( \ln S O_{2}, \) the bond angle is \( 119^{\circ} \) whereas
in \( S O_{3}, \) the bond angle is \( 120^{\circ} \)
Reason
\( \boldsymbol{S} \) atom in both \( \boldsymbol{S O}_{2} \) and \( \boldsymbol{S O}_{3} \) is \( \boldsymbol{s} \boldsymbol{p}^{2} \)
hybridized.
A. If both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion.
B. If both assertion and reason are CORRECT, but reason
is NOT THE CORRECT explanation of the assertion.
C. If assertion is CORRECT, but reason is INCORRECT
D. If assertion is INCORRECT, but reason is CORRECT.


What is the difference in the oxidation
numbers of the two types of sulphur
\( \operatorname{atomsin} N a_{2} S_{4} O_{6} ? \)


Find \( a \) for which \( f(x)=a(x+\sin x)+ \)
\( a \) is increasing on \( \boldsymbol{R} \)


If \( f(x)=x^{3}-3 \) and \( g(x)=7 x^{5}, \) what
is the approximate value of \( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{3} . \boldsymbol{9})) ? \)
A . 389.23
в. 938.32
c. 4261.48
D. 11086.57
E . 14257.91


Construct tangents to a circle of radius
\( 4 \mathrm{cm} \) at \( Q \) and \( R, \) from a point \( P \) on the
concentric circle of radius \( 6 \mathrm{cm} \)


Which of the following complex species is not expected to exhibit optical isomerism?
\( \mathbf{A} \cdot\left[\operatorname{Co}(e n)\left(N H_{3}\right)_{2} C l_{2}\right]^{+} \)
B. \( \left[\mathrm{Co}(e n)_{3}\right]^{3+} \)
c. \( \left[\operatorname{Co}(e n)_{2} C l_{2}\right]^{+} \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)


\( A \) began a business with Rs. \( 85,000 . \) He
was joined afterwards by \( B \) with Rs.
\( 42,500 . \) For how much period does \( B \) join, if the profits at the end of the year are divided in the ratio of \( 3: 1 ? \)
A. 4 months
B. 5 months
c. 6 months
D. 8 months


If a car is to travel with a speed v along the frictionless, banked circular track of
radius \( r, \) the required angle of banking so that the car does skid is
A \( \cdot \theta=\tan ^{-1}\left(\frac{v^{2}}{r g}\right) \)
B . \( \theta=\tan ^{-1}\left(\frac{v}{r g}\right) \)
c. \( \theta=\tan ^{-1}\left(\frac{\pi^{2}}{v g}\right) \)
D \( \cdot \theta=\tan ^{-1}\left(\frac{v^{2}}{2-g}\right) \)


If acceleration \( (A), \operatorname{mass}(M), \) velocity
\( V \) ), time \( (T) \) are the fundamental units,
then the dimensions of height will be
A \( \cdot V T^{-1} M^{2} \)
в. \( A M T^{-1} \)
c. \( A^{-1} M^{3} V^{-1} \)
D. \( A T^{2} \)


Amoeba sticks to substratum by means
of
A. Rough surface
B. Plasmalemma
c. Protein
D. None of the above


5 kilomoles of oxygen is heated at
constant pressure. The temperature of the oxygen gas is increased from \( 295 \mathrm{K} \) to 305 K. If the molar heat capacity of oxygen at constant pressure is 6.994 kcal/kmole K. The amount of heat
absorbed in kcal,
A . 249.7
B. 44
c. 349.7
D. 539.7


Differentiate between macro and micro
element.


Subtract the sum of \( 865 \&-493 \) from
the sum of \( -380 \& 675 \)


Using Biot-Savart's law, obtain an expression for magnetic field at a distance \( r \) metre from an infinitely long
wire carrying a current of \( i \) ampere.


The HCF of 256,442 and 940 is
\( A \cdot 2 \)
B. 14
\( c \cdot 142 \)
D. none


Find the zeros of the quadratic
polynomial \( x^{2}+7 x+12, \) and verify the
relation between the zeros and its
coefficients.


The process of warming of earth by sun
is
A. Conduction
B. Convertion
c. Radiation
D. None


In lac operon, structural gene 'Z' synthesizes
A. \( \beta \) - galactosidase
B. Galactosidase permease
c. Galactosidase transacetylase
D. None of the above


If \( ^{n} p_{4}=20 \times^{n} p_{2} \) then find the value \( n \)
\( A \cdot 7 \)
B. 5
\( c \cdot 6 \)
D. 4


What are reducing sugars?


\( \sin ^{-1}|\sin x|=\sqrt{\sin ^{-1}|\sin x|} \) then \( x \neq ? \)


A resistor has resistance R. When the
potential difference across the resistor
is \( V \), the current in
the resistor is I. The power dissipated in
the resistor is P. Work W is done when
charge \( Q \) flows through the resistor. What is not a valid relationship between
these variables?
\( \mathbf{A} \cdot I=\frac{P}{V} \)
В \( \cdot Q=\frac{W}{V} \)
C \( \cdot R=\frac{P}{I^{2}} \)
D \( \cdot R=\frac{V}{P} \)


Which among the following elements has the largest atomic radii?
A. \( N a \)
в. \( M g \)
c. \( K \)
D. \( C a \)


Energy of all molecules of a monatomic
gas having a volume \( V \) and pressure \( P \) is \( \frac{3}{2} P V . \) The total translational kinetic energy of all molecules of a diatomic
gas at the same volume and pressure is
A \( \cdot \frac{1}{2} P V \)
в. \( \frac{3}{2} P V \)
c. \( \frac{5}{2} P V \)
D. 3 PV


Concentration of \( A g^{+} \) ions in a
saturated solution of \( A g_{2} C r O_{4} \) at \( 20^{\circ} \mathrm{C} \)
is \( 1.5 \times 10^{-4} \) mol \( L^{-1}, \) At \( 20^{0} C, \) the
solubility product of \( A g_{2} C r O_{4} \) is:
A. \( 5.6 \times 10^{-12} \)
B . \( 1.68 \times 10^{-10} \)
c. \( 5.6 \times 10^{-11} \)
D. \( 1.68 \times 10^{-11} \)


Derivative of \( (x+3)^{2}(x+4)^{3}(x+5)^{4} \)
\( \boldsymbol{w} \cdot \boldsymbol{r} \cdot \operatorname{to} \boldsymbol{x} \) is
A \( \cdot(x+3)(x+4)(x+5)^{2}\left(9 x^{2}+70 x+133\right) \)
B \cdot \( (x+3)(x+4)^{2}(x+5)^{3}\left(9 x^{2}+70 x+133\right) \)
C \( \cdot(x+3)(x+4)^{2}(x+5)\left(9 x^{2}-70 x-133\right) \)
D. none of these


Why most of the mountain climbers
carry oxygen cylinder with them
A. Because as height increases,air pressure increases
B. Because as height increases,air pressure decreases
c. At high altitudes,breathing capacity increases
D. None


Find the principal value:
\( \tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right) \)


Weightlessness in a satellite is experienced because
A . of inertia
B. the gravitational force acting on the satellite is zero
c. of centre of gravity
D. centrifugal acceleration negates the acceleration due to gravity


Pyruvic acid is formed during
A. Krebs cycle
B. Glycolysis.
c. ornithine cycle.
D. Calvin cycle.


A password consists of two letters of alphabet followed by three digits chosen from 0 to \( 9 . \) Repeats are allowed. How many different possible passwords are allowed
A .492804
B. 650000
c. 676000
D. 1757600


The mass of \( P_{4} O_{10} \) produced, if 440 g of \( P_{4} S_{3} \) is mixed with \( 384 g m \) of \( O_{2}, \) is:
\( \boldsymbol{P}_{4} \boldsymbol{S}_{3}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{P}_{4} \boldsymbol{O}_{10}+\boldsymbol{S} \boldsymbol{O}_{2} \)
\( A .568 g m \)
в. \( 426 \mathrm{gm} \)
c. \( 284 g m \)
D. \( 396 g m \)


Which of the following figure represents damped harmonic motion


Reaction of \( \boldsymbol{O}_{2} \) is faster with \( \boldsymbol{C} \boldsymbol{a} \) or \( \boldsymbol{M} \boldsymbol{g} \) ?
\( \mathbf{A} \cdot M g \)
в. \( C a \)
c. Equally react
D. Do not react


Let \( A B C \) is a right angled triangle in which \( A B=3 \mathrm{cm} \) and \( \mathrm{BC}=4 \mathrm{cm} \) and
\( \angle A B C=90^{\circ} . \) The three charges +15,+12
and -20 esu are placed on A, B and C respectively. The force acting on B will be
A. zero
B. 25 dyne
c. 30 dyne
D. 150 dyne


Three charges \( -q_{1},+q_{2} \) and \( -q_{3} \) are placed
as shown in the figure. The \( x \) -component
of the force on \( -q_{1} \) is proportional to:
A \( \cdot \frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \cos \theta \)
B \( \cdot \frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \sin \theta \)
C \( \cdot \frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \cos \theta \)
D. \( \frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \sin \theta \)


The two aqueous solutions; \( \boldsymbol{A}\left(\boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}\right) \)
and \( \boldsymbol{B}(\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}) \) were electrolysed using
Pt electrodes. The pH of the resulting solutions will :
A. increase in A and decrease in B
B. decrease in both
c. increase in both
D. decrease in A and increase in B


Consider the following two statement-
[A] Linear momentum of a system of
particle is zero
[B] kinetic energy of a system of
particles is zero. Then
A. A does not imply B but B implies A
B. A implies B and B implies A
c. A does not imply B \& B does not imply A
D. A implies B but B does not imply A


Which of the following hormone, is responsible for the growth of animals?
A . Auxin
B. Insulin
c. Adrenaline
D. Somatotropin


The uncertainty in position and velocity of the particle are \( 0.1 n m \) and \( 5.27 \times \)
\( 10^{-24} m s^{-1} \) respectively then find the
mass of the particle \( (\boldsymbol{h}=\mathbf{6 . 6 2 5} \times \) \( 10^{-34} J s^{-1} \)


If the perimeter of a circle is \( 132 \mathrm{cm} \)
find its area.
A. 1356 sq. \( \mathrm{cm} \)
B. 1386 sq. \( \mathrm{cm} \)
c. 1340 sq. \( \mathrm{cm} \)
D. 1436 sq. \( \mathrm{cm} \)


Which of the following is best conductor of electricity?
A. copper
B. Gold
c. Platinum
D. Silver


A parallel plate capacitor is first charged and then isolated, and a dielectric slab is
introduced between the plates. The quantity that remains unchanged is:
A. charge \( Q \)
B. potential \( V \)
c. capacity \( C \)
D. energy \( U \)


\( \mathbf{P} \mathrm{Cl}_{3} \) is prepared by the action of \( \mathbf{C l}_{2} \)
on:
\( \mathbf{A} \cdot \mathrm{P}_{2} \mathrm{O}_{3} \)
в. \( \mathrm{P}_{2} \mathrm{O}_{5} \)
c. white \( \mathrm{P} \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{3} \)


The height of a cylinder is equal to the radius. If an error of \( \alpha \% \) is made in the
height, then percentage error in its volume is
A . \( \alpha \% \)
в. \( 2 \alpha \) \%
\( c .3 \alpha \% \)
D. none of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & -\mathbf{3} \\ \mathbf{4} & \mathbf{1}\end{array}\right], \) then adjoint of matrix
\( A \) is
A. \( \left[\begin{array}{cc}1 & 3 \\ -4 & 2\end{array}\right] \)
В. \( \left[\begin{array}{cc}1 & -3 \\ -4 & 2\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & 3 \\ 4 & -2\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & -3 \\ -4 & 2\end{array}\right] \)


Find the phase difference between a
particle at \( 1^{s t} \) crest and a particle at \( 4^{t h} \)
crest.


\( O_{2}^{2-} \) is the symbol of ion. (2003)
A . oxide
B. super oxide
c. peroxide
D. monoxide


Which element has an oxide that is
used as a food preservative?
A. Helium
B. Hydrogen
c. Iron
D. Sulfur


How many ATP molecules could maximally be generated from one molecule of glucose if the complete
oxidation of one mole of glucose to \( C O_{2} \)
and \( H_{2} O \) yields 686 kcal and the useful chemical energy available in the high energy phosphate bonds of one mole of ATP is 12 kcal?
A. Fifty-seven
B. One
c. Two
D. Thirty


Heat of \( 30 k c a l \) is supplied to a system
and \( 4200 J \) of external work is done on
the system so that its volume
decreases at constant pressure. What
is the change in its internal energy. \( = \) \( (J=4200 J / k c a l) \)
A \( \cdot 1.302 \times 10^{5} \mathrm{J} \)
J. \( 1.302 \times 10^{2} \)
в. \( 2.302 \times 10^{5} \mathrm{J} \)
c. \( 3.302 \times 10^{5} J \)
D. \( 4.302 \times 10^{5} \mathrm{J} \)


An aqueous solution is 1.00 molal in \( \mathrm{Kl} \)
Which change will cause the vapour
pressure of the solution to increase?
A. Addition of Nacı
B. Addition of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \)
c. Addition of 1.00 molal KI
D. Addition of water


The letters of the word "INDEPENDENCE"
are arranged in all possible ways. The number of words in which the 'D's
do not come together is
A \( \cdot \frac{10 !}{4 ! 3 !} \)
B. \( \frac{10 !}{4 ! 3 !} \frac{10}{2 !} \)
c. \( \frac{10 !}{4 ! 3 !}^{10} P_{2} \)
D. \( \frac{10 !}{4 ! 3 !} \frac{11}{2 !} \)


The amount of usable energy remains
constant as it is passed from one trophic level to another.
A. True
B. False
c. Either
D. Neither


Which of the following is an example of nuclear fusion reaction?
\( \mathbf{A} \cdot \underset{90}{233} T H+_{0}^{1} n \rightarrow_{90}^{234} T H \)
B . \( _{48}^{13} \mathrm{Cd}+_{0}^{1} n \rightarrow_{48}^{114} \mathrm{Cd}+\gamma-\mathrm{ray} \)
\( \mathbf{c} \cdot_{i H}^{3} H+_{1}^{1} H \rightarrow_{2}^{4} H e \)
D \( \cdot \frac{239}{92} U \rightarrow_{93}^{239} N p+_{-1}^{0} e \)


About centre \( \boldsymbol{O} \)
\( \mathbf{A} \cdot 4 N m \) (clockwise)
B. \( 4 N m \) (anti clockwise)
c. \( 2 N m \) (clockwise)
D. \( 2 N m \) (anti clockwise)


The stability of a Lyophobic colloid is
due to:
A. adsorption of covalent molecules on the colloid
B. the size of the particles
c. the charge on the particles
D. tyndall effect


Write short on the functions of the
testis.


The formula of the complex, tris(ethylenediamine) cobalt (iii) sulphate is:
A \( \cdot\left[\operatorname{Co}(e n)_{2} S O_{4}\right] \)
в. \( \left[\operatorname{Co}(e n)_{3} S O_{4}\right] \)
\( c \cdot\left[C o(e n)_{3}\right]_{2}\left(S O_{4}\right)_{3} \)
D. \( \left[C o(e n)_{3}\right]_{2} S O_{4} \)


A point object is placed mid-way between two plane mirrors at distance
'a' apart. The plane mirror forms an infinite number of images due to multiple reflections. The distance
between the first two images formed behind any mirror is:
\( A \)
B. \( 2 a \)
c. \( a / 2 \)
D. \( 4 a \)


Find the A.P. if the 6 th term of the A.P.is
19 and the 16 th term is 15 more than
the 11 th term.


A bullet mass \( m \) is fired at a certain
angle q with the vertical. The bullet is returned to ground in time. The total change of momentum is equal to then :
\( A \cdot m g / 2 \)
B. mgt
c. \( 2 \mathrm{mgt} \)
D. mg


A student has problem in reading as he is unable to contract his
A. Suspensory ligament
B. Ciliary muscles
c. Pupil
D. Iriss


For which of the following processes, total entropy of universe increases.
This question has multiple correct options
A. Melting one mole of ice to water at \( 0^{\circ} \mathrm{C} \)
B. Freezing one mole of water to ice at \( 0^{\circ} \mathrm{C} \)
C. Freezing one mole of water to ice at \( -10^{\circ} \mathrm{C} \)
D. Melting one mole of ice at \( 10^{\circ} \mathrm{C} \) into water


Which place in India is called "The
Golden Mine of Liverworts"?
A. Eastern Himalayas
B. Western Himalayas
c. western Ghats
D. Eastern Ghats
E. Sundarbans


A random variable \( X \) has its range \( X= \)
\{3,2,1\} with the probabilities, \( \frac{1}{2}, \frac{1}{3} \) and \( \frac{1}{6} \) respectively. The mean
value of \( X \) is
A \( \cdot \frac{5}{3} \)
B. \( \frac{7}{3} \)
\( c .3 \)
\( D \)


A material has Poisson's ratio 0.3 .ff a
uniform rod of its suffers a longitudinal
strain of \( 3 \times 10^{-3}, \) what will be the
percentage increase in volume?


Fructose reduces fehling's solution due
to the presence of:
A. hydroxy group.
B. aldehyde group.
c. ketone group
D. \( \alpha \) -hydroxyketone group


An antipyretic is:
A. Quinine
B. Paracetamol
C . Luminal
D. Piperazine


Choose the Correct answer from
alternative given. Wavefront is the locus of all points, where the particles of the medium vibrate with the same
A . phase
B. amplitude
c. frequency
D. period


Show that the relation \( R \) defined in the
\( \operatorname{set} A \) of all polygons as \( R=\left\{\left(P_{1}, P_{2}\right):\right. \)
\( P_{1} \) and \( P_{2} \) have same number of sides
\}\( , \) is an equivalence relation. What is the set of all elements in \( A \) related to
the right angle triangle \( T \) with sides 3,4
and \( 5 ? \)


Statement: Plastics which get deformed
easily on heating and can be bent easily are known as thermoplastics.
State whether the given statement is
true or false.
A. True
B. False


Fill in the blanks with appropriate
words.
Digestive system consists of Gl tract,


Assertion
Work done by friction on a body sliding
down an inclined plane is negative
Reason
Work done is greater than zero, if angle between force and displacement is
acute or both are in same direction
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A uniform rod of mass \( \mathrm{m} \) and length Lis held at rest by a force \( F \) applied at it's end as shown in the vertical plane. The ground is sufficiently rough. Find
(a) Force \( F \)
(b) Normal reaction exerted by the
ground
(c) Frictional force exerted by the ground (magnitude and dirtection)


Vermi-processing toilet is beneficial
because
A. It reduces the diseases.
B. It increases soil fertility.
c. Both A and B.
D. It reduces electricity.


What is meant by power of a lens?
Define its SI unit.

You have two lenses \( A \) and \( B \) of focal lengths \( +10 \mathrm{cm} \) and \( -10 \mathrm{cm}, \) respectively. State the nature and power of each lens. Which of the two lenses will form a
virtual and magnified image of an object placed \( 8 \mathrm{cm} \) from the lens? Draw
a ray diagram to justify your answer.


Define fertilization and write the list of
events occuring in human fertilization.


Graphite is an example of:
A . ionic solid
B. covalent solid
c. van der Waals solid
D. metallic solid


The atomic number of chlorine is \( 17 . \) Its
electronic configuration is:
A . \( \mathrm{K}, \mathrm{L}, \mathrm{M} \)
2,10,5
B. K, L, M
2, 8,
c. к, L, м
7,8,2
D. K, L, M
5,10,2


Under what condition the van't Hoff
factor is greater than one?


Which of the following exist?
This question has multiple correct options
\( \mathbf{A} \cdot I C l_{3} \)
\( \mathbf{B} \cdot C l F_{3} \)
\( \mathbf{C} \cdot I F_{7} \)
\( \mathbf{D} \cdot B r F_{3} \)


Find the approximate value of \( \boldsymbol{f}(\mathbf{2 . 0 1}) \)
where \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\mathbf{2} \)


If a conductor carrying current is kept in the magnetic field, the magnitude of force on the electric conductor will be
maximum when :
A. The conductor makes an angle of \( 30^{\circ} \) with the magnetic field
B. The conductor makes an angle of \( 60^{\circ} \) with the magnetic field
c. The conductor makes an angle of \( 90^{\circ} \) with the magnetic field
D. The conductor makes an angle of \( 45^{\circ} \) with the magnetic field


Find the locus of a point whose co-
ordinates are given by \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}^{2}, \boldsymbol{y}=\boldsymbol{2} \boldsymbol{a} \boldsymbol{t} \)
Where 't' is a parameter


Two probability distributions of the discrete random variable \( X \) and \( Y \) are
given below.
\( \boldsymbol{X} \quad \mathbf{0} \) 3 \( \mathbf{2} \)
\( P(X) \quad \frac{1}{5} \quad \frac{2}{5} \quad \frac{1}{5} \quad \frac{1}{5} \)
\[
\begin{array}{ccccc}
\boldsymbol{Y} & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} \\
P(Y) & \frac{1}{5} & \frac{3}{10} & \frac{2}{5} & \frac{1}{10}
\end{array}
\]
Then
A.
\[
E\left(Y^{2}\right)=2 E(X)
\]
B.
\[
E\left(Y^{2}\right)=E(X)
\]
\( \mathbf{c} \cdot E(Y)=E(X) \)
\( D \)
\[
E\left(X^{2}\right)=2 E(Y)
\]


The value of
\( \begin{array}{|ccc|}1 & \cos \alpha-\sin \alpha & \cos \alpha+\sin \alpha \\ 1 & \cos \beta-\sin \beta & \cos \beta+\sin \beta \\ 1 & \cos \gamma-\sin \gamma & \cos \gamma+\sin \gamma\end{array} \mid \)
A. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)
B. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)
\( \mathbf{c} \cdot\left|\begin{array}{lll}\cos \alpha & \cos \beta & 1 \\ \cos \beta & \cos \gamma & 1 \\ \cos \gamma & \cos \alpha & 1\end{array}\right| \)
D. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)


(a) Differentiate \( \boldsymbol{y}=\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \) with
respect to \( \boldsymbol{x}, \mathbf{0}<\boldsymbol{x}<\mathbf{1} \)
(b) Differentiate \( x^{x}-2^{\sin x} \) with respect
to \( x \)


A mixture of two immiscible liquids
nitrobenzene and water boiling at \( 99^{\circ} C \) has a partial pressure of water \( 733 \mathrm{mm} \) and of nitrobenzene \( 27 \mathrm{mm} \). The ratio of
masses of water and nitrobenzene in
mixture is :


Simpllify \( : 2 x^{2}+5 x-1+8 x+x^{2}+ \)
\( 7-6 x+3-3 x^{2} \)


If an electron jumps from orbit \( A \) to
orbit \( B \) it loses energy while when it jumps from \( C \) to \( B \) it gains energy.
Arrange the orbits in the increasing order of distance from the nucleus.
A. \( A<B<C \)
B. \( C<A<B \)
c. \( C<B<A \)
D. \( A<C<B \)


Assertion
Sulphuric acid is more viscous than
water.
Reason
Concentrated sulpuric acid has a great affinity for water.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statement


A \( 60 \mathrm{kg} \) man goes around the earth in a satellite. In the satellite, his weight will
be
A. 60 N
B. \( 60 \mathrm{kg} \)
c. 600 N
D. zero


Four identical hollow cylindrical columns of mild steel support a big
structure of mass 50,000 kg. The inner and outer radii of each column are 30
and \( 60 \mathrm{cm} \) respectively. Assuming the load distribution to be uniform,
calculate the compressional strain of each column.


An analyser examines two adjacent
plane-polarised beams A and B whose planes of vibration are mutually perpendicular. In one position of the analyser, beam B shows zero intensity.
From this position, a rotation of \( 30^{\circ} \)
shows the two beams as matched in
intensity. The intensity ratio I_(A \( \} / I_{-}\{B\} \) of the two beams is
A \( \cdot \sqrt{3} \)
B. \( 1 / 3 \)
c. \( 1 / \sqrt{2} \)


mole of \( A(g) \) is heated to \( 300^{\circ} C \) in closed one litre vessel till the following equilibrium is reached: \( \boldsymbol{A}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{B}(\boldsymbol{g}) \)
The equilibrium constant for
the reaction at \( 300^{\circ} \mathrm{C} \) is \( 4 . \) What is the
concentration of \( \mathrm{B}\left(\text { in } \operatorname{mol} . l i t^{-1}\right) \) at
equilibrium?
A . 0.2
B. 0.6
\( c \cdot 0.8 \)
D. 0.1


Choose the correct option:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is a
acid,
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) is a
acid and
\( H_{3} P O_{2} \) is a
acid
A. dibasic, tribasic, monobasic
B. tribasic, monobasic, dibasic
c. monobasic, dibasic, tribasic
D. tribasic, dibasic, monobasic


We come to a conclusion, that plastics are bad conductors of electricity from the following. This question has multiple correct options
A. Refrigerators and freezers have a plastic foam core
B. Electrical wires have a plastic covering
c. cooking pans have plastic handles
D. we use to prepare parachutes


The wave front due to a source situated
at infinity is :
A. spherical
B. cylindrical
c. planar
D. none of these


To reach the left side of heart the blood
must pass through
A. sinus venosus
B. Kidneys
c. Liver
D. Lungs


A charge of \( +2 \mu C \) is placed at \( x=0 \) and a charge of \( -32 \mu C \) at \( x=60 \mathrm{cm} . \) Athird
charge - \( Q \) be placed on the \( x \) -axis such that it experiences no force. The distance of the point from \( +2 \mu C \) is (in \( (m) \)
\( A \cdot 30 \)
B. 20
c. 15
D. 10


Which of the following sets of elements has strongest tendency to form anions?
A. \( A s, S e, B r \)
в. \( P, S, C l \)
c. \( N, O, F \)
D. \( S b, T e, I \)


Very short answer type.
A chordate animal having flame cells as
excretory structures.


If a line \( A B \) makes an angle \( \theta \) with \( O X \)
and is at a distance of \( p \) units from the
origin, then the equation of \( A B \) is
A \( . x \sin \theta-y \cos \theta=p \)
B. \( x \cos \theta+y \sin \theta=p \)
\( \mathbf{c} . x \sin \theta+y \cos \theta=p \)
D. \( x \cos \theta-y \sin \theta=p \)


Which solution would have a \( \boldsymbol{p} \boldsymbol{H} \)
greater than \( 7.0 ? \)
A. \( 1.0 M \) HCl
в. \( 0.5 M \) NH\( _{4} \) С \( l \) l
c. \( 0.1 M K C N \)
D. \( 1.0 M H_{2} S O_{4} \)
E. \( 0.25 M \) НС \( N \)


Find the condition tht the curves \( 2 x= \)
\( y^{2} \) and \( 2 x y=k \) intersect orthogonally.


In an ac circuit the instantaneous
values of current and applied voltage
are respectively \( i= \)
\( 2(A m p) \sin \left(250 \pi s^{-1}\right) t \) and \( \epsilon= \)
\( (10 V) \sin \left[\left(250 \pi s^{-1}\right) t+\frac{\pi}{3}\right] . \) Find the
power drawn from the source at \( t= \)
\( \frac{2}{3} m s \)


Beryllium gives a compound \( \boldsymbol{X} \) with the
following percentage composition: \( \boldsymbol{B} \boldsymbol{e}- \)
\( 6.1 \%, N-37.8 \%, C l-48 \%, H-8.1 \% \)
Molecular weight of \( \boldsymbol{X} \) is 148 g \( \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
and that of \( B e \) is \( 9 g \) mol\( ^{-1} \). The
molecular formula of the compound is:
A. \( B e N_{4} C l_{l} H_{12} \)
в. \( B e N_{2} C l H_{6} \)
c. \( B e N_{4} C l_{2} H_{6} \)
D. \( B e N_{4} C l H_{8} \)


In the combustion of \( 2.0 \mathrm{gm} \) of methane 25 kcal heat is liberated, heat of
combustion of methane would be
A. 100 kcal
B. 200 kcal
c. 300 kcal
D. 400 kcal


When a glass rod is rubbed with a piece
of silk cloth the rod
\( A \cdot \) and the cloth both acquire positive charge
B. becomes positively charged while the cloth has a negative charge
\( \mathrm{C} \). and the cloth both acquire negative charge
D. becomes negatively charged while the cloth has a positive charge


When a die is thrown, list the outcomes
of an event of getting:
a number lesser than 5
A .1,2,3,4
B. 1,2,3
c. 3,4,5
D. 4,5


opp
Q Type your question
3
\( c \)
\( D \)


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


If \( z \) lies on the curve \( a r g(z+i)=\frac{\pi}{4} \)
then minimum value of \( |z+4-3 i|+ \)
\( |z-4+3 i| \) is


\( 10 \% \) of urea is isotonic with \( 6 \% \) solution
of a non-volatile solute \( X . \) What is the
molecular mass of solute \( \boldsymbol{X} \) ?
A \( \cdot 6 g \) mol \( ^{-1} \)
B. \( 60 g \) mol \( ^{-1} \)
c. \( 36 g \) mol \( ^{-1} \)
D. \( 32 g \) mol \( ^{-1} \)


\( (m x-n y)(m x-n y)= \)
A \( \cdot m^{2} x^{2}+2 m x n y-n^{2} y^{2} \)
B \( \cdot m^{2} x^{2}-2 m x n y-n^{2} y^{2} \)
C \( \cdot m^{2} x^{2}-2 m x n y+n^{2} y^{2} \)
D. \( m^{2} x^{2}+2 m x n y+n^{2} y^{2} \)


Strongest reducing agent is:
\( A \cdot K \)
в. мв
\( c . \) Both
D. None


Choose the odd one out in each of the
following groups of four items each:
Trachea, Bronchus, Alveolus, Diaphragm


Find the speed of A after all collisions
end.
A \( \cdot \frac{V}{8} \)
B. \( \frac{V}{4} \)
c. \( \frac{3 V}{8} \)
D. \( 2 V \)


Carl von Linne was involved with which
of the following branches of science?
A. Morphology
B. Taxonomy
c. Physiology
D. Medicine


The planes \( 2 x-y+4 z=5 \) and \( 5 x- \)
\( 2.5 y+10 z=6 \) are
A. Parallel
B. Perpendicular
c. Intersect
D. intersect \( x \) axis


A man of mass \( 80 \mathrm{kg} \) is riding on a trolley of mass \( 40 \mathrm{kg} \) which is rolling along a level surface at a speed of 2 \( \mathrm{m} / \mathrm{s} . \) He jumps off the back of the trolley so that his speed relative to the ground is:


If a sphere and a cube have the same
surface area, then the ratio of the
diameter of sphere to edge of the cube is
A. \( \sqrt{6}: \sqrt{\pi} \)
(年) \( \sqrt{\pi} \). \( \pi \)
B. \( \sqrt{\pi}: \sqrt{6} \)
c. 2: 1
D. 1: 2


Solve \( 7 x^{2}-5 x-3=0 \)


Find the value of: \( \sin \left(2 \tan ^{-1} \frac{1}{4}\right)+ \)
\( \cos \left(\tan ^{-1} 2 \sqrt{2}\right) \)


In a cyclotrimetaphosphoric acid molecule, how many single and double bonds are present?
A. 3 double bonds; 9 single bonds
B. 6 double bonds; 6 single bonds
c. 3 double bonds; 12 single bonds
D. Zero double bonds; 12 single bonds


State the principle of moving coil galvanometer?


Digestion of food in human starts from
A. Duodenum
B. Small intestine
c. Mouth
D. Large intestine.


A certain sum of money becomes three
times of itself in 20 years at simple
interest. In how many years does it
become double of itself at the same
rate?
A. 8 years
B. 10 years
c. 12 years
D. 14 years


Which of the following is not a compound?
A. Sugar
B. Ozone
c. Benzene
D. salt


How many triangles are there in the
following figure?
4.10
B . 24
\( c \cdot 22 \)
D. 20


Compute the median for the following cumulative frequency distribution:
\( \begin{array}{lllll}\text { Less } & \text { Less } & \text { Less } & \text { Less } & \text { Less } \\ \text { than } & \text { than } & \text { than } & \text { than } & \text { than } \\ 20 & 30 & 40 & 50 & 60\end{array} \)
१६ 30


and \( m \) are two parallel lines intersect
by another pair of parallel lines \( p \) and \( q \) Show that \( \Delta A B C \cong \Delta C D A \)


How much heat would be required to
convert 14 kg of ice at \( 0^{\circ} \mathrm{C} \) into water of
\( \mathbf{0}^{\circ} \mathbf{C} \) ?
A . 4704 J
в. 4704 k
c. 336 J
D. 336 kJ


In Young's interference experiment, the central bright fringe can be identified
due to the fact that it
A. has greater intensity than other fringes which are bright
B. is wider than the other bright fringes
c. is narrower than the other bright fringes
D. can be obtained by using white light instead of monochromatic light


Which among the following belong to same phyla?
A. Physalia, obelia, Pleurobrachia - Coelenterata
B. Bombyx, Palaemon, Limulus - Arthropoda
c. star fish, jelly fish, sea urchin - Echinodermata
D. cuttle fish, devil fish, Patella - Mollusca


Which one is correctly matched
A. Tears - Excretion of salts
B. Sweat - Thermoregulation
C. Saliva - Testing food
D. Statolith - Sexual attraction


Silica dissolves readily in:
A . HF
в. нс
c. нвт
D. \( H N O_{3} \)


Which row describes isotopes of the
same element?
A. Number of protons - different, number of neutrons different
B. Number of protons - different, number of neutrons -
same
C. Number of protons - same, number of neutrons different
D. Number of protons - same, number of neutrons - same


Bohr's theory is not applicable for:
A . \( H \)
B . \( L i^{2} \)
\( \mathrm{c} \cdot H^{+} \)
D. \( B e^{3} \)


Two trains start a distance of \( 2000 m \)
apart. Train one is moving with a constant speed of \( 30 m / s \) directly
towards train 2 which starts from rest
and accelerates with a constant acceleration of \( 5 m / s^{2} \) directly towards train 1. When do the trains meet?
\( \mathbf{A} \cdot 22.9 s \)
в. \( 34.9 s \)
\( c .30 s \)
D. \( 40 s \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{0} \\ -\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0}\end{array}\right], \) Show that
\( \boldsymbol{A}^{2}=\boldsymbol{A}^{-1} \)


\( \mathbf{A} \)
1.05 \( m \) having negligible mass is
supported at its ends by two wires
of steel (wire \( A \) ) and aluminium (wire \( B \)
of equal lengths as shown in Fig. The cross-sectional areas of wires \( A \) and \( B \)
are \( 1.0 m m^{2} \) and \( 2.0 m m^{2}, \) respectively
At what point along the rod should a
mass \( m \) be suspended in order
to produce
(a) Equal stress in \( A \) and \( B \) and
(b) Equal strains in \( A \) and \( B \) ?


\( \left(6 x^{2}-5 y\right)^{2} \) Find square by identity


The first organic compound synthesised in the laboratory from its elements.
A. Urea
B. Methane
c. Ethylene
D. Acetic acid


The two sides of a right-angled triangle are \( \boldsymbol{x}, \boldsymbol{x}+\mathbf{1} \) and hypotenuse, the longest
side is \( \sqrt{1} 3 . \) Find the area of the
triangle.
A \( \cdot 1 \mathrm{m}^{2} \)
B. \( 2 \mathrm{m}^{2} \)
\( c \cdot 3 m^{2} \)
D. \( 4 \mathrm{m}^{2} \)


(t)-Sucrose has a specific rotation of \( +66.5, \) while \( D-(+) \) -glucose and D-(-)fructose have specific rotations of +52.5
and -92.4 respectively. After complete hydrolysis of (+)-sucrose by dilute acid, what will be the specific rotation of the hydrolysis product, called invert sugar [a 1: 1 mixture of \( D \) - \( (+) \) -glucose and \( D \) (-)-fructose] ?
\( A \cdot-39.9 \)
в. -72.4
\( c .-19.9 \)
D. -34.9


A particle of mass \( m \) is attached to
three springs \( A, B \) and \( C \) of equal force
constants \( k \) as shown in figure. If the
particle is pushed slightly against the
spring \( C \) and released, the time period
of oscillation is
A \( \cdot 2 \pi \sqrt{\frac{m}{k}} \)
В \( \cdot 2 \pi \sqrt{\frac{m}{2 k}} \)
c. \( 2 \pi \sqrt{\frac{m}{3 k}} \)
D. \( 2 \pi \sqrt{\frac{3 m}{k}} \)


A particle of mass \( m \) is located in a one dimensional potential field where potential energy is given by \( U(x)=A(1- \) \( \cos p x), \) where \( A \) and \( p \) are constants. The period of small oscillations of the particle
A \( \cdot 2 \pi \sqrt{\frac{m}{A p^{2}}} \)
в. \( \pi \sqrt{\frac{m}{A P}} \)
c. \( \pi \sqrt{\frac{m}{A}} \)
D. \( \left(\frac{1}{2 \pi}\right) \sqrt{\frac{A p}{m}} \)


A mass \( m, \) which is attached to a
spring with constant \( k, \) oscillates on a
horizontal table, with amplitude \( A . \) At
an instant when the spring is stretched by \( \sqrt{3} A / 2, \) a second mass \( m \) is dropped
vertically onto the original mass and immediately sticks to it. What is the amplitude of the resulting motion?
A \( \cdot \frac{\sqrt{3}}{2} A \)
B. \( \sqrt{\frac{7}{8}} A \)
c. \( \sqrt{\frac{13}{16}} A \)
D. \( \sqrt{\frac{2}{3}} A \)


One mole of an ideal gas undergoes a process \( P=\frac{P_{o}}{1+\left(\frac{V}{V_{o}}\right)^{2}}, \) where \( P_{o} \) and
\( V_{o} \) are constants. Find the temperature
of the gas when \( V=V_{o} \)
A \( \cdot \frac{P_{o} V_{o}}{R} \)
в. \( \frac{2 P_{o} V_{o}}{3 R} \)
c. \( \frac{2 P_{o} V_{o}}{R} \)
D. \( \frac{P_{o} V_{o}}{2 R} \)


The best method to separate the mixture of ortho and para-nitrophenol
\( (1: 1) \) is:
A. vaporization
B. color spectrum
c. distillation
D. crystallization


Which of the following statement is
correct?
A. Cathode is negative terminal both in galvanic and electrolytic cells
B. Anode is positive terminal both in galvaniv and electrolytic cells
C. Cathode is negative terminal in an electrolytic cell whereas anode is negative terminal in a galvanic cell
D. Anode is negative terminal in an electrolytic cell whereas cathode is positive terminal in galvanic cell


Water in its pure form is a:
A. good conductor of heat
B. bad conductor of electricity
c. good conductor of electricity
D. none of these


A particle is dropped from top of tower During its motion its covers \( \frac{9}{25} \) part of height of tower in last 1 sec . then height
of tower?
\( \mathbf{A} \cdot 100 m \)
B. \( 125 m \)
c. \( 175 m \)
D. \( 123 m \)


During a planned manoeuvre in a space flight, a free-floating astronaut \( A \) pushes another free floating astronaut
B, the mass of A being greater than that of B. Then, the magnitude of the force
exerted by astronaut A on astronaut B is:
A. equal to zero
B. equal to the force exerted by B on A
c. greater than the force exerted by B on A
D. less than the force exerted by B on A


Of the ions \( A g^{+}, C o^{+2} \) and \( T i^{+4} \) which
one will be coloured in aqueous
solution?


In which of the following pair(s), is/are the stronger bond found in the first
species? This question has multiple correct options
A. \( O_{2}^{-}, O_{2} \)
в. \( N_{2}, O_{2}^{+} \)
c. \( N O^{+}, N O \)
D. \( O_{2}^{-}, O_{2}^{2+} \)


Diacidic base among the following is :
A. Ammonia
B. Hydroxyl amine
c. Hydrazine
D. Hydrazoic acid


Find the value of \( k \) for which the
quadratic equation \( (3 k+1) x^{2}+ \)
\( 2(k+1) x+1=0, \) has equal roots. Also
find these roots.


The first member of the Balmer series of
hydrogen atom has wavelength of \( 6561 A \). The wavelength of the second member of the Balmer series (in \( n m \) ) is


Genus Homo was identified during epoch.
A. Eocene
B. Palaeocene
c. oligocene
D. Pleistocene


The average transnational KE of N2 molecules at NTP is-
\( \mathbf{A} \cdot 0.15 J \)
в. 0.036 .5
c. \( 0.032 J \)
D. \( 152 J \)


If \( \alpha, \beta \) are roots of the equation \( x^{2}+ \) \( \mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{a}}=(\boldsymbol{\alpha}+\boldsymbol{\beta}) \hat{\mathbf{i}}+ \)
\( \boldsymbol{\alpha} \boldsymbol{\beta} \hat{\boldsymbol{j}} \overrightarrow{\boldsymbol{b}}=\boldsymbol{\alpha} \boldsymbol{\beta} \hat{\boldsymbol{i}}+(\boldsymbol{\alpha}+\boldsymbol{\beta}) \hat{\boldsymbol{j}}+\left(\boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}\right) \hat{\boldsymbol{k}} \)
\( \operatorname{then} \vec{a} \times \vec{b}= \)
A \( . \hat{i}+12 \hat{j}+12 \hat{k} \)
B . \( -30 \hat{i}+12 \hat{j}-4 \hat{k} \)
c. \( -30 \hat{i}-12 \hat{j}-21 \hat{k} \)
D. \( \hat{i}-12 \hat{j}+29 \hat{k} \)


The diagrams below show regions of equipotentials. A positive charge is moved from \( A \) to \( b \) in each diagram.
A. Maximum work is required to move \( q \) in figure (b)
B. Maximum work is required to move \( q \) in figure(c)
\( \mathrm{c} . \) In all the cases the work done is the same
D. Minimum work is required to move \( q \) in figure(a)


The displacement-time equation of a
straight line motion is \( \boldsymbol{x}=\mathbf{4} \boldsymbol{t}-\mathbf{5} \boldsymbol{t}^{2}+ \)
\( 3 t^{3}-4 t^{4} . \) The velocity at \( t=2 \sec \) is
A. - -86 units
B. +26 units
c. -12 units
D. +16 units


When the angle of reflection is \( 40^{\circ}, \) then
the angle between normal and the
mirror will be
A .40
B. \( 90^{\circ} \)
\( c \cdot 45 \)
D. \( 60^{\circ} \)


Slit 1 of Young's double-slit experiment is wider than slit \( 2, \) so that the light
from slits are given as \( A_{1}=A_{0} \sin \omega t \) and \( A_{2}=A_{0} \sin \left(\omega t+\frac{\pi}{3}\right) . \) The
resultant amplitude and intensity, at a point where the path difference between them is zero, are \( A \) and \( I \) respectively.
Then
This question has multiple correct options
A \( \cdot A=\sqrt{3} A_{0} \)
B \( \cdot A=4 A_{0} \)
\( \mathbf{c} \cdot I \propto 16 A_{0}^{2} \)
D. \( I \propto 3 A_{0}^{2} \)


A uniform metallic rod rotates about its
perpendicular bisector with constant angular speed. If it is heated uniformly
to raise its temperature slightly:
A. its speed of rotation increases
B. its speed of rotation decreases
c. its speed of rotation remains same
D. its speed increases because its moments of inertia increases


How is dacron obtained from ethylene
glycol and terephthalic acid?


Acid rain is produced by:
A. excessive release of CO in air
B. excessive release of \( S O_{2} \) and \( H_{2} S \) in air
C . excessive release of \( N O_{2} \) and \( S O_{2} \) in air
D. excessive release of \( N H_{3} \) and \( C O_{2} \) in air


A rectangular block of wood has
dimensions \( 24 \mathrm{cm} \) by \( 8 \mathrm{cm} \) by \( 7 \mathrm{cm} . \) It is cut up into children's bricks.
Each brick is a cube of side \( 3 \mathrm{cm} \)
Find the volume of wood that is left.


Why is plastic used in covering of electrical appliances?
A. Good conductors of heat and electricity
B. Durable
c. Poor conductors of heat and electricity
D. None of above


Seedless nonvascular plants are
A. Angiosperm
B. Gymnosperm
c. Pteridophyte
D. Bryophytes


Which of the following engines is more
efficient?
A. Heat utilised - 80 kilojoules, work done - 32 kilojoules
B. Heat utilised - 60 kilojoules, work done - 12 kilojoules
C. Heat utilised - 50 kilojoules, work done - 25 kilojoules
D. Heat utilised - 90 kilojoules, work done - 27 kilojoules


Three photons coming from emission spectra of hydrogen sample are picked
up. Their energies are \( 12.1 e V, 10.2 e V \)
and \( 1.9 e V . \) These photons must come
from
A. a single atom
B. two atoms
c. three atom
D. either two atoms or three atoms


The harmonic conjugate of (2,3,4) with respect to the points (3,-2,2) and (6,-17,-4) is
\( ^{\mathbf{A}} \cdot\left(\frac{18}{5},-5, \frac{4}{5}\right) \)
в. (11,-16,2)
c. \( \left(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right) \)
D. (0,0,0)


If there were no atmosphere around the earth, the temperature of the earth will
A. Increase
B. Decrease
c. Increase during day and decrease during night
D. Remain unaffected


If \( x^{3}-\frac{1}{x^{3}}=14, \) then \( x-\frac{1}{x}= \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D.


Choose the schematic diagram, which
properly represents pulmonary
circulation in human.
A \( \cdot \) Right ventricle \( \frac{\text { Deoxygenated }}{\text { blood }} \) Lungs \( \frac{\text { Oxygenated }}{\text { blood }} \) Left auricle
B. Right ventricle \( \frac{\text { Oxygenated }}{\text { blood }} \) Lungs \( \frac{\text { Deoxygenated }}{\text { bood }} \) Left auricle
C. Left ventricle \( \frac{\text { Oxygenated }}{\text { blood }} \) Lungs \( \frac{\text { Deoxygenated }}{\text { blood }} \) Right ventricle
D. Left auricle \( \frac{\text { Oxygenated }}{\text { blood }} \) Lungs \( \frac{\text { Deoxygenated }}{\text { blood }} \) Right ventricle


If \( A^{\prime} \cup B=U, \) then show that \( A \subset B \)


Which of the following is a true fish?
A . Flying fish
B. Cuttle fish
c. silver fish
D. Jelly fish


Mirror formula is valid for:
A. Convex mirror
B. Concave mirror
c. Both A and B
D. For lenses and mirrors


A voltmeter is always connected in parallel in the experiment to determine the resistance of a given wire using
ohm's law because it has
A. high resistance.
B. low resistance
c. sensitive device
D. non sensitive device.


Which food substance is absorbed
during digestion?
A. Carbohydrates
B. Proteins
c. Vitamins
D. Fats


Find the derivative of the following functions: \( 3 \cot x+5 \cos e c x \)


A particle with mass 2.0 mg and charge \( 3.0 \mu C \) is in a region with uniform electric field of \( (\mathbf{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{N} / \boldsymbol{C} \). The
acceleration of the particle will be:
A \( \cdot(3 \hat{i}+4 \hat{j}) m / s^{2} \)
B \( \cdot(1.5 \hat{i}+2 \hat{j}) m / s^{2} \)
\( \mathbf{c} \cdot(4.5 \hat{i}+6 \hat{j}) m / s^{2} \)
D. \( (2 \hat{i}+3 \hat{j}) m / s^{2} \)


The adjacent sides of a parallelogram 21 \( \mathrm{cm} \) and \( 28 \mathrm{cm} . \) If its one diagonal is 35 \( \mathrm{cm} ; \) find the area of the parallelogram.


Which of the following isomerization reactions is/are of the first order?
This question has multiple correct options
A. Cyclopropane \( \rightarrow \) Propane
B. cis-But-2-ene \( \rightarrow \) Trans-but-2-ene
c. vinyl allyl ether \( \rightarrow \) Pent-4-enal
D. \( C H_{4} N C \rightarrow C H_{3} C N \)


\( \lim _{x \rightarrow 0} \frac{1}{x} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 2 \)
D. \( 1 / 2 \)


HOF is the only known molecule that contains only the elements hydrogen, oxygen and fluorine. Pure \( H F \) is a colourless liquid at \( 273 K \)
The liquid contains \( H F \) molecules
that have strong hydrogen bonds between them.

Draw a fully labelled diagram to suggest how a hydrogen bond can form between two \( H F \) molecules.


In the figure shown, angle of repose is
\( 45^{0} . \) Find the force of friction, net force
and acceleration of the block when:
\( \boldsymbol{\theta}=\boldsymbol{3} \boldsymbol{0}^{0} \)
2)1) \( \boldsymbol{\theta}=\mathbf{4 5}^{\mathbf{0}} \)
3)1) \( \boldsymbol{\theta}=\mathbf{6 0}^{\mathbf{0}} \)


Add the following algebraic expression using both horizontal and vertical methods. Did you get the same answer
with both methods
\( x^{2}-2 x y+3 y^{2} ; 5 y^{2}+3 x y-6 x^{2} \)


Find truth value of compound
statement 'All natural number are even
or odd"


If the population of a country doubles in
60 years, in how many years will it be triple under the assumption that the rate of increase is proportional to the number of inhabitants?
\( [\text { Given: } \log 2=0.6912 \text { and } \log 3= \)
1.0986.


Growth rate in childhood is controlled by
A. Thymosin
B. Thyroxine
c. Progesterone
D. Oestrogen


Which inert gas haves highest boiling point?
A . \( x_{e} \)
B. Ar
c. \( \mathrm{kr} \)
D. He
E. Answer required


Which of the following is correct order of the evolutionary history of man?
A. Peking man, Homo sapiens, Neanderthal man, CroMagnon man
B. Peking man, Neanderthal man, Heidelberg man, CroMagnon man
c. Peking man, Heidelberg man, Neanderthal man
Cro-Magnon man
D. Peking man, Neanderthal man, Homo sapiens, Heidelberg -man


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


Statement 1: Excited tungsten atoms will give off light energy. Statement 2: As the excited electrons
return to their ground state, they emit energy in the form of light.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Write the hybridization and draw the
shape of following \( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{S} \boldsymbol{F}_{6}, \boldsymbol{P} \boldsymbol{C l}_{5} \)


\( f(x)=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{n}{n^{2}+k^{2} x^{2}}, x>0 \) is
equal to
\( \mathbf{A} \cdot x \tan ^{-1}(x) \)
B \( \cdot \tan ^{-1}(x) \)
c. \( \frac{\tan ^{-1}(x)}{x} \)
D. none of the above