Fruit bearing plants are
A. Gymnosperms
B. Dicotyledons
c. Angiosperms
D. spermatophytes


The distance between the line \( \vec{r}=2 \vec{i}- \) \( \mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}}+\boldsymbol{\lambda}(\overrightarrow{\boldsymbol{i}}-\overrightarrow{\boldsymbol{j}}+\boldsymbol{4} \overrightarrow{\boldsymbol{k}}) \) and the plane
\( \vec{r} \cdot(\vec{i}+5 \vec{j}+\vec{k})=5 \) is
A \( \cdot \frac{10}{3 \sqrt{3}} \)
в. \( \frac{10}{9} \)
c. \( \frac{10}{3} \)
D.


\( \lim _{x \rightarrow \pi / 4}\left(\frac{1-\tan x}{1-\sqrt{2} \sin x}\right) \) is equal to
A.
B.
\( c \cdot-2 \)
D.


The radius of a cylinder is increasing at the rate of \( 5 \mathrm{cm} / \mathrm{min} \) so that its volume
is constant. When its radius is \( 5 \mathrm{cm} \) and
height is \( 3 \mathrm{cm}, \) then the rate of decreasing of its height is
\( \mathbf{A} \cdot 6 \mathrm{cm} / \mathrm{min} \)
B. \( 3 \mathrm{cm} / \mathrm{min} \)
c. \( 4 \mathrm{cm} / \mathrm{min} \)
\( \mathbf{D} \cdot 5 \mathrm{cm} / \mathrm{min} \)
E . \( 2 \mathrm{cm} / \mathrm{min} \)


Which of the following points lie above X-axis
\( \boldsymbol{a}) \boldsymbol{A}(-\boldsymbol{3}, \boldsymbol{5}) \)
\( \boldsymbol{b}) \boldsymbol{B}(\boldsymbol{5},-1) \)
\( c) C(0,2) \)
\( \boldsymbol{d}) \boldsymbol{D}(\boldsymbol{0}, \boldsymbol{2}) \)
\( e) E(5,1) \)
\( \boldsymbol{f}) \boldsymbol{F}(\boldsymbol{3}, \mathbf{1}) \)


Which of the following statement is
incorrect?
A. Fangs are certain specialised teeth attached to maxillary bones in poisonous snakes.
B. Niacin is also known as pellagra preventing vitamin
c. choleretic are substances which increases secretion of
HCI from stomach
D. Hormone villikinin is released from intestinal villi


Agonists can:
This question has multiple correct options
A. inhibit function of receptors
B. mimic natural chemical messengers
C . help transfer of message to receptors
D. inhibit the catalytic activity of the enzyme


The equation of tangent to the curve \( y=b e^{-x / a} \) where it cuts the \( y \) -axis is
A \( \cdot \frac{x}{a}+\frac{y}{b}=1 \)
B. \( \frac{x}{a}+\frac{y}{b}=-1 \)
c. \( \frac{x}{a}-\frac{y}{b}=1 \)
D. none of these


A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively, this region of space may not have
A. \( E=0, B=0 \)
B. \( E=0, B \neq 0 \)
c. \( E \neq 0, B=0 \)
D. \( E \neq 0, B \neq 0 \)


What will be the pressure in dyne \( \mathrm{cm}^{-2} \) due to a water column of height
\( 12.5 c m ?\left(g=980 c m s^{-2}\right) \) (density of
water \( 10^{3} k g m^{-3} \) ).


Statement I: A molecule of ethyne is
linear.
Because
Statement II: The carbon atoms in
ethyne are sp hybridized.
A. True, True CE
B. True, True
c. True, False
D. False, True
E. False, False


Which of the following is solid?
A. Rubber band
B. Sugar
c. sponge
D. All of the above


Which of the following indicates that a potato is a conductor of electricity?
A. Greenish blue spot on potato around one wire.
B. Greenish blue spot on potato around both wires.
c. Blue color spot on potato around one wire.
D. Blue color spot on potato around both wires


A battery of emf 2 volt and internal resistance 0.1 ohm is being charged
with a current of 5 ampere. The
potential difference between the two terminals of the batteries is
A \( .2 V \)
в. \( 0.5 V \)
\( c .1 .5 V \)
D. 2.5V


Fill in the blanks:
A current carrying solenoid when freely suspended, it always rests in direction.
A. north-south
B. vertical
c. east-west
D. a direction inclined to north-south


Classify the following polynomials as monomials, binomials and trinomials:
\( 3 x^{2}, 3 x+2, x^{2}-4 x+2, x^{5}-7, x^{2}+ \)
\( \mathbf{3} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}, \boldsymbol{s}^{2}+\boldsymbol{3} \boldsymbol{s} \boldsymbol{t}-\boldsymbol{2} \boldsymbol{t}^{2}, \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+ \)
\( z x, a^{2} b+b^{2} c, 2 l+2 m \)


\( \operatorname{Let} g(x)=\lim _{n \rightarrow \infty} \frac{x^{n} f(x)+h(x)+1}{2 x^{n}+3 x+3}, x^{1} 1 \)
and \( g(1)=\lim _{x \rightarrow 1} \frac{\sin ^{2}\left(\pi \cdot 2^{x}\right)}{\ln \left(\sec \left(\pi \cdot 2^{x}\right)\right)} \) be a
continuous function at \( x=1, \) find the
value of \( 4 g(1)+2 f(1)-h(1) . \) Assume
that \( f(x) \) and \( h(x) \) are continuous at
\( \boldsymbol{x}=\mathbf{1} \)


\( \int_{0}^{\pi / 2} \sin x \cos x d x \)


Explain the relative rate of \( E 2 \) reaction of the given compounds.
A. \( I I I<I<I I \)
В. \( I<I I<I I I \)
c. \( I I I<I I<I \)
D. None of these


Nuclei A and B convert into a stable
nucleus C. Nucleus A is converted into C
by emitting \( 2 \alpha- \) particles and \( 3 \beta- \) particles. Nucleus B is converted into \( C \) by emitting one \( \alpha- \) particle and \( 5 \beta- \)
particles. At time \( t=0, \) nuclei of A are
\( 4 N_{0} \) and nuclei of \( B \) are \( N_{0} . \) Initially,
number of nuclei of \( C \) are zero. Half-life
of \( A \) (into conversion of \( C \) ) is 1 min and
that of \( \mathrm{B} \) is 2 min. Find the time (in
minutes) at which rate of disintegration of \( A \) and \( B \) are equal


Which of the following are a group of protists?
A. Euglena, Dinoflagellates and Yeast
B. Amoeba, Paramecium, Hydra
c. Euglena, Paramaecium, Mushroom
D. Amoeba, Paramaecium and Dinoflagellates


If \( A r g\left(\frac{z+1}{z-1}\right)=\frac{\pi}{6}, \) then find the locus of
\( \mathbf{z} \)


Lady's finger belongs to family of
A. Malvaceae
B. Cruciferae
c. compositae
D. None of the above


A ball of mass \( 2 k g \) is connected to a
string of length \( 1 m \) and made to move
in a horizontal circle on a smooth
frictionless table with a constant speed
of \( 2 m / s . \) The other end of the string is connected to a fixed peg on the table. Find the magnitude of the average impulse exerted by the string on the
ball in half a revolution:
A. 0
в. \( 8 N-s \)
c. \( 4 N-s \)
D. \( 2 \sqrt{2} N-s \)


Among the following, one statement is not correct when a junction diode is in forward bias
A. the width of depletion region decreases.
B. free electron on n- side will move towards the junction
c. holes on p-side move towards the junction
D. electrons on n-side and holes on p-side will move away from junction.


Cytokinins are present in greater concentration in young fruits and seeds.
A. True
B. False


In the following figure, the circle
centered at \( N \) has a radius of \( 4 . \) What is
the area of the shaded region?
\( A \cdot 3 \pi \)
B. \( 6 \pi \)
\( c .9 \pi \)
D. \( 12 \pi \)
E . \( 16 \pi \)


Represent the following complex number in trigonometric form:
\( 3-4 i \)


Evaluate the given integral.
\( \int \frac{1}{x^{4}-1} d x \)


A solution of \( N a_{2} S_{2} O_{3} \) is saturated iodometrically against 0.334 g of pure \( K B r O_{3}\left(\text { converted to } B r^{-}\right) \) requiring 40
\( \mathrm{ml} . \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \) solution. What is the
molarity of \( N a S_{2} O_{3} \) solution? (Molar
mass of \( \boldsymbol{K} \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}=\mathbf{1 6 7} \) g \( \boldsymbol{m o l}^{-1} \) )


\( A B \) and \( C D \) are two slabs. The
medium between the slabs has
refractive index 2 . Find the minimum
angle of incidence (in degrees) at \( Q \) so
that the ray is totally reflected by both
the slabs


If \( f(x)=\int_{0}^{x} t \sin t d t, \) then \( f^{\prime}(x) \) is
A \( \cdot \cos x+x \sin x \)
B. \( x \sin x \)
c. \( x \cos x \)
\( \mathbf{D} \cdot \sin x+x \cos x \)


In the figure given below, \( D E \| B C \). If
\( \boldsymbol{A D}=\boldsymbol{p} \mathrm{cm}, \boldsymbol{D B}=\boldsymbol{p}-\boldsymbol{2} \mathrm{cm}, \boldsymbol{A} \boldsymbol{E}= \)
\( p-1 \mathrm{cm}, \) then find the value of \( \mathrm{p} \)
\( A \)
B.
c. None
\( D \)


Blood contains:
A. positively charged particles
B. negatively charged particles
C . neutral particles
D. negatively as well as positively charged colloids


Rutherford Model could not explain:
A. maxwell's theory of elctrodynamics
B. line spectra of atom
C. both \( A \) and \( B \)
D. None of these


The membrane attached to the hair of
sensory cells of organ of Corti is
A. Basilar
B. Tectorial
C. Reissner
D. None of the above


n Fig., a circle touches all the four side
of a quadrilateral \( A B C D \) whose sides
\( A B=6 c m, B C=7 c m \) and \( C D= \)
\( 4 \mathrm{cm} . \) Find \( \boldsymbol{A D} \)
\( A \cdot 2 c m \)
B. 5 cm
\( c .3 c m \)
D. \( 4 \mathrm{cm} \)


The expectation of the number of heads in 15 tosses of a coin is \( \frac{x}{2} . \) The value of
\( x \) is


Which of the following has longest \( C-0 \)
bond length? (Free C-O bond length is Co is \( 1.128 \dot{A}) \)
\( \mathbf{A} \cdot N i(C O)_{4} \)
B . \( \left[N i(C O)_{3}\right]^{+} \)
\( \mathrm{c} \cdot\left[\mathrm{Fe}(\mathrm{CO})_{4}\right]^{2-} \)
D・ \( \left[\mathrm{Mn}(\mathrm{C} O)_{6}\right]^{+} \)


The circuit has two oppositively
connected ideal diodes in parallel. What
is the current flowing in the circuit?
\( \mathbf{A} \cdot 1.71 A \)
B . \( 2.00 A \)
c. \( 2.31 A \)
D. \( 1.33 A \)


How many moles are there in \( 1 m^{3} \) of
any gas at NTP?
A . 22.4
в. 24.4
c. 44.8
D. 44.6


A rigid body consists of a \( 3 k g \) mass
connected to a \( 2 k g \) by a massless rod.
The \( 3 k g \) mass is located at \( r_{1}=2 i+ \)
\( 5 j m, \) and the \( 2 k g \) mass at \( r_{2}=4 i+ \)
\( 2 j m . \) Find the length of the rod and the
coordinates of the centre of mass.


Which of the following diazonium salt is
relatively stable at \( 0-5^{0} C ? \)
A. \( \left.C H_{3}-N \equiv N\right\}^{\oplus} C l^{-} \)
В \( \left.\cdot\left(C H_{3}\right)_{2} C H-N \equiv N\right\} \oplus C l^{-} \)
c. \( \left.C_{6} H_{5}-N \equiv N\right\}^{\oplus} C l^{-} \)
D \( \left.\cdot\left(C H_{3}\right)_{3} C-N \equiv N\right\}^{\oplus} C l \)


State Kirchhoff's rules. Explain briefly how these rules are justified.


toppr
Q Type your question
energy KE and time t is correctly
represented by
4
\( B \)
\( c \)
\( D \)


Write short notes.
Biodiversity


Solve.
\( 4 x-4=5+x \)


High boiling fluorescent fraction of coal
tar causes asthma.
A . True
B. False


A marble block of mass \( 2 \mathrm{kg} \) lying on ice
when given a velocity of \( 6 m s^{-1} \) is stopped by friction in 10 s. Then the coefficient of friction is ( Take \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A . 0.06
B. 0.03
\( c \cdot 0.04 \)
D. 0.01


From top of a building a ball is dropped
while another is projected horizontally
at the same time. (a)Which ball will
strike the ground first? (b)Which ball
will strikes the ground with more speed?


In bimolecular reaction, the steric
factor \( P \) was experimentally
determined to be \( 4.5 . \) The correct
option(s) among the following is (are):
This question has multiple correct options
A. the activation energy of the reaction is unaffected by the value of the steric factor
B. experimentally determined value of frequency factor is higher than that predicted by Arrheneius equation
C . since \( P=4.5 \), the reaction will not proceed unless an
effective catalyst is used
D. tThe value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally


If \( \frac{2 x^{2}+3 x+4}{(x-1)\left(x^{2}+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^{2}+2} \)
Then the value of \( B \) is equal to
A . 3
B. -
\( c \cdot-2 \)
D.


Instrument used to measure
earthquake is known as:
A. Typanic graph
B. Seismograph
c. Quake graph
D. Quake meter


Assertion
Bluish colour predominates in a clear
sky, since blue has a shorter wavelength and is scattered strongly.
Reason
Blue has the shortest wavelength among all colours.
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


Choose the correct answer from the
alternatives given
The lymph consists of:
A . plasma
B. leucocytes
c. plasma and leucocytes
D. plasma and erythrocytes


Find the inductance \( L \) of a solenoid of
length I whose windings are made of material of density D and resistivity \( \rho \) The winding resistance is \( \mathrm{R} \) :
A \( \cdot \frac{\mu_{0}}{4 \pi l} \cdot \frac{R_{m}}{\rho D} \)
в. \( \frac{\mu_{0}}{4 \pi R} \cdot \frac{l_{m}}{\rho D} \)
c. \( \frac{\mu_{0}}{4 \pi l} \cdot \frac{R^{2} m}{\rho D} \)
D. \( \frac{\mu_{0}}{2 \pi R} \cdot \frac{l_{m}}{\rho D} \)


The correct sequence of match for List-
from List-II is:
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ A) \mathrm{O}_{2} & 1 \text { ) Monoatomic } \\ B \text { Po } & 2 \text { ) Bent molecule } \\ C / \mathrm{S}_{8} & \text { 3) Paramagnetic } \\ D) \mathrm{O}_{3} & \text { 4) Puckered ring }\end{array} \)
B. A-3, B-1, C-4, D-2
c. \( A-4, B-2, C-3, D-1 \)
D. A-2, B-4, C-1, D-3


Three samples of the same gas \( A, B \) and
\( \boldsymbol{C}(\gamma=\mathbf{3} / \mathbf{2}) \) have initially equal
volume. Now the volume of each sample is doubled. The process is adiabatic for A, isobaric for \( \mathrm{B} \) and isothermal for \( \mathrm{C} \). If
the final pressures are equal for all the three samples, the ratio of their initial
pressures is:
A \( \cdot 2 \sqrt{2}: 2: 1 \)
B \( \cdot 2 \sqrt{2}: 1: 2 \)
c. \( \sqrt{2}: 1: 2 \)
D. \( 2: 1: \sqrt{2} \)


\( \mathbf{y}=\sin \mathbf{x}, \boldsymbol{y}_{n}=\frac{\boldsymbol{d}^{n}(\sin \boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}^{n}} \)
\( \operatorname{then}\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{y}_{1} & \boldsymbol{y}_{2} \\ \boldsymbol{y}_{3} & \boldsymbol{y}_{4} & \boldsymbol{y}_{5} \\ \boldsymbol{y}_{6} & \boldsymbol{y}_{7} & \boldsymbol{y}_{8}\end{array}\right|=? \)
\( A \cdot-\sin x \)
B.
\( c \cdot \sin x \)
D. \( \cos \)


Which of the following is formed during photorespiration?
A. Sugar
B. Phosphoglycolate
c. NADPH
D. ATP
E. Oxaloacetate


The surface fibres of commercial use
are obtained from
A. Gossypium
B. Agave
c. Helianthus
D. Solanum


A string of length \( 100 \mathrm{cm} \) and mass
\( 0.5 g m \) is streched with a force of \( 20 N \)
It is pulled at a distance of \( 12.5 \mathrm{cm} \) from one end. The frequency of the note emitted by it is
A . \( 100 \mathrm{Hz} \)
в. \( 200 H z \)
c. \( 400 H z \)
D. \( 800 H z \)


A car moving along a circular path of radius R with uniform speed covers an
angle \( \theta \) during a given time t. What is
its average velocity?
A \( \cdot \frac{2 R \sin (\theta / 2)}{t} \)
B. \( \frac{2 R \cos (\theta / 2)}{t} \)
c. \( \frac{2 R \sin (\theta)}{t} \)
D. \( \frac{R \sin (\theta / 2)}{t} \)


Two equilateral triangles with side \( 4 \mathrm{cm} \)
and \( 6 \mathrm{cm} \) are \( _{--}-_{-} \) triangles.
A. similar
B. congruent
c. both
D. none of these


All of the following are components that
make up an ecosystem except
A. Biodiversity
B. Climate
c. Demography
D. Energy flow
E. Nutrient cycling


Atomic mass of an element is not
necessarily a whole number becuase:
A. it contains electrons, protons and neutrons
B. it exists in all tropic forms
c. it contains isotopes
D. atoms are no longer indivisible


State whether given statement is True or False
The \( p \) -n type junction can act as a semiconductor diode
A. True
B. False


The function of glucagon hormone is
A. To increase glycogenesis.
B. To decrease blood sugar level.
C. To release glucose from liver cells and glycogenolysis promotion.
D. To increase the absorption of glucose and fatty acids through cell.


Displacement of ball with respect to ground during its flight would be
A . \( 16.25 \mathrm{m} \)
B. 8.76 m
c. \( 20.24 \mathrm{m} \)
D. 30.56 \( m \)


Two metallic blocks \( P \) and \( Q \) of masses
in ratio 2: 1 are given same amount of
heat. If their temperature rise by same amount, what is the ratio of their
specific heat capacities?
A .1: 2
B . 2: 1
c. 1: 3
D. 3: 1


In the preparation of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) we get \( \mathrm{NO} \)
gas by catalytic oxidation of ammonia. The moles of NO produced by the
oxidation of two moles of \( N H_{3} \) will be :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


Find the area of the sector of circle
which substands an angle of \( 150^{\circ} \) at the centre, if the radius of the circle is \( 6 \mathrm{cm} \)


Which one of the following diseases is caused due to ozone depletion on
human?
A. Huntington's chorea
B. Small pox
c. Plague
D. Erythemia


Answer in one word:
Which hormone regulates the sugar level in the blood?


The value of \( \int_{0}^{1} \tan ^{-1}\left(\frac{2 x-1}{1+x-x^{2}}\right) d x \)
is
A .
B.
\( c \cdot-1 \)
D.


Evaluate using expansion of \( (a+b)^{2} \) or
\( (a-b)^{2}: \)
\( (92)^{2} \)
A. 8444
B. 8464
c. 8474
D. 8414


The number of ways in which 6 men can be arranged in a row, so that three particular men are consecutive, is
A \( .4 ! \times 3 ! \)
в. \( 4 ! \)
c. \( 3 ! \times 3 ! \)
D. none of these


ff \( \left(\frac{1+i \sqrt{3}}{1-i \sqrt{3}}\right)^{n} \) is an integer, then \( n \) is
\( A \)
B. 2
\( c .3 \)
D.


What is the oxidation number of
lithium in \( \boldsymbol{L} \) i \( C l \) ?
\( A \cdot+3 \)
B. -
\( c \cdot+1 \)
D. 0


Cellular part of lymph contains
A. Only Leukocytes
B. Water
c. Proteins
D. All of the above


A ball is thrown up vertically after going to a certain height, it returns to the
ground, then its potential energy is maximum.
A. When it goes up
B. When it comes down
c. At maximum height
D. Data Insufficient


The fangs of python which pulled out
can
A. Not come again
B. Come,again with half the length
c. come again with same length
D. come again with double length


\( Q \) Type your question


Write the decimal forms of \( \frac{1}{3} \) and \( \frac{1}{9} \)


toppr b
Q Type your question
1.
v. The source of sound is capable of giving varied frequencies in the range
of \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2}\left(\text { where } \boldsymbol{v}_{2}>\boldsymbol{v}_{1}\right) . \) If \( n \) is an
integer then frequency for maximum intensity is given by?
A \( \cdot \frac{n v}{f} \)
B. \( \frac{n v}{r(\pi-2)} \)
c. \( \frac{n v}{\pi r} \)
D. \( \frac{n v}{(r-2) \pi} \)


Light energy is propagated in the form
of particles having wave nature. Justify this statement using Quantum theory of light.


Regarding vision in cockroach, which is
incorrect?
A. Total image is formed in the compound eye
B. Apposition image, mosaic vision
C. Retinulae in immediately below the vitrellae and crystalline cone, surrounded by retinal pigment sheath
D. All of these


mole of gas \( A B \) dissociates to an
extent of \( 10 \% \) at \( 127^{0} C \) according to
\( A B \rightleftharpoons A+B \) occupies a volume of
\( 4 \times 10^{4} \) ml. Find the total pressure at
this temp, assuming ideal gas behaviour.


The number of molecules of methane
ore present in 5.6 litres of methane at NTP is \( x \times 10^{23} . \) What is the value of \( x ? \)


Two springs of force constants \( \mathbf{1 0 0 0} N / \boldsymbol{m} \) and \( \mathbf{2 0 0 0} \boldsymbol{N} / \boldsymbol{m} \) are
stretched by same force. The ratio of their respective potential energies is
A .2: 1
B. 1: 2
c. 4: 1
D. 1: 4


The arithmetic mean of the following
data is \( 25, \) find the value of \( k \)
35 \( \begin{array}{llll}\boldsymbol{x}_{\boldsymbol{i}}: & \boldsymbol{5} & \boldsymbol{1} \boldsymbol{5} & \boldsymbol{2} \boldsymbol{5}\end{array} \)
\( \begin{array}{llll}f_{i:} & 3 & k & 3 & 6\end{array} \)


Which gas dissolves in \( H_{2} S O_{4} \) to give
oleum?
\( A \cdot S O_{2} \)
в. \( H_{2} S \)
\( c \cdot S_{2} O \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


Which of the following is a fundamental
unit?
A. Ampere
B. Newton
c. volt
D. onm


The coefficient of three consecutive
terms in the expansion of \( (1+a)^{n} \) are
in ratio 1: 7: 21 , then find the value of
\( \boldsymbol{n} \)


Two glucose solutions are mixed of \( 1 M \)
and \( 2 M \) respectively in equal volume ratio then the new molarity will be:
\( \mathbf{A} \cdot 1.4 M \)
в. \( 1.25 M \)
c. \( 1.5 M \)
D. \( 1.27 M \)


Solve by matrix method \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}= \)
\( \mathbf{2}, \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\boldsymbol{z}=-\mathbf{1}, \boldsymbol{x}-\boldsymbol{y}-\boldsymbol{z}=-\mathbf{2} \)


When a chemical reaction takes place, during the course of the reaction the rate of reaction?
A. Keeps on increasing with time
B. Remains constant with time
c. Keeps on decreasing with time
D. Shows irregular trend with time


The force between two charges in different media are different because.
B. Different media have different viscosities
c. Different media have different densities
D. Different media have different permeabilities


A charge of \( 20 \mu C \) produces an electric
field. Two points are \( 10 \mathrm{cm} \) and \( 5 \mathrm{cm} \)
away from this charge. Find the values of potentials at these points and also find the amount of work done to take an
electron from one point to the other


\( \mathbf{f} \boldsymbol{A}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{1} \\ \mathbf{0} & \mathbf{2} & -\mathbf{3} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right| \) and \( \boldsymbol{B}=(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \)
and \( C=5 A, \) then \( \frac{|a d j B|}{|C|} \) is?
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. -1
D.


Let \( P \) be the set of points inside the
square, \( Q \) be the set of points inside the triangle and \( R \) be the set of points
inside the circle. If the triangle and circle intersect each other and are
contained in the square then,
This question has multiple correct options
A. \( P \cap Q \cap R \neq \phi \)
в. \( P \cup Q \cup R=R \)
c. \( P \cup Q \cup R=P \)
D. \( P \cup Q=R \cup P \)


If \( \bar{P} Q \) is a chord of a circle with centre \( O \)
and \( P R \) is a tangent to the circle at \( P \)
then \( \angle P O Q= \)
A. \( 4 \angle R P Q \)
B. \( 3 \angle R P Q \)
c. \( 2 \angle R P Q \)
D. \( \angle R P Q \)


Maximum change in \( p H \) is observed
when 50 of \( 1 M K O H \) solution is
added to
A . 25 ml. of \( 2.5 N \) HCl
B. \( 50 \mathrm{ml} \) of \( 1 \mathrm{N} \) HCl
c. \( 30 \mathrm{ml} \) of \( 2 \mathrm{N} \) HCl
D. \( 50 \mathrm{ml} \) distilled water


The coefficient of \( 1 / x \) in the expansion of
\( (1+x)^{n}(1+1 / x)^{n} \) is
A. \( \frac{n !}{(n-1) !(n+1) !} \)
B. \( \frac{2 n !}{(n-1) !(n+1) !} \)
c. \( \frac{2 n !}{(2 n-1) !(2 n+1) !} \)
D. none of these


Assertion
Argon does not react.
Reason
Noble gases have complete octet so
they dont have tendency to pair with
other elements and they show zero
valency.
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.


\( \int_{1}^{4} \frac{\mathbf{x} \mathbf{d x}}{\sqrt{\mathbf{2 + 4 x}}}= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3}{\sqrt{2}} \)


Q Type your question
with time according to the equation
\( \boldsymbol{x}=\mathbf{4}-\mathbf{2} \boldsymbol{t}+\boldsymbol{t}^{2} . \) The speed of the
particle will vary with time as
\( A \)
B.
\( c \)
\( D \)


I. When an electric current runs
through a sealed tube that contains a
very low pressure of hydrogen gas, four different colors of light are produced, red, blue-green, blue-violet, and violet.
II. Energy added to the electrons
causes them to transition from lower
energy levels to higher energy levels. As the electrons return to the lower energy levels they were originally located in, photons of light are emitted.
A. Statement I is true, Statement II is true
B. Statement \( I \) is true, Statement \( I I \) is false
c. Statement \( I \) is false, statement \( I I \) is true
D. Statement \( I \) is false, Statement \( I I \) is false


Find the value of \( \sin ^{-1}\left(\sin \frac{3 \pi}{5}\right) \)


Which of the following is a wrong statement for physisorption?
A. It is a reversible reaction
B. Reaction required an energy of activation.
c. The value of adsorption enthalpy is low.
D. It generally occurs at a low temperature.


In an experiment set up for the measurement of EMF of a half cell using reference electrode and a salt bridge, when the salt bridge is removed, the voltage:
A. Does not change
B. Increase to maximum
c. Decreases to half the value
D. Drops to zero


Find the mean deviation about median
for the following data.
\begin{tabular}{lllll}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \mathbf{2 0}- \) & \( \mathbf{3 0 -} \) & \( \mathbf{4 0 -} \) & \( \mathbf{5 0 -} \) \\
\( \mathbf{3 0} \) & \( \mathbf{4 0} \) & \( \mathbf{5 0} \) & \( \mathbf{6 0} \)
\end{tabular}
18


In a triple bond, there is sharing of:
A. 3 electrons
B. 4 electrons
c. 6 electrons
D. none of these


What weight of zinc will get deposited?
A . 65.3 g
B. 0.33 mg
c. 0.438 g
D. 42.3 \( g \)


(i) Water in lakes and ponds do not freeze at once in cold countries. Give a
reason in support of your answer.
(iii) What is the principle of
Calorimetry?
(iiii) Name the law on which this
principle is based.
\( (i v) \) State the effect of an increase of impurities on the melting point of ice.


Which is not a Lindane?
\( A \cdot 6,6,6 \)
в. Внс
c. Gammaxene
D. Benzene


A permanent magnet moving coil gives full scale deflection at \( 40 \mathrm{mV} \) potential difference and 8 mA current. What will
be the required series resistance when it is used as voltmeter of range \( 0200 \mathrm{V} ? \)
A . 19556 ohm
B. 20163 ohm
\( c \cdot 23884 \) ohm
D. 24995 ohm


Show that no triangular number can be
of the form \( 3 n-1 \)


More soil erosion occurs where there is
A. No rainfall
B. Low rainfall
C. High rainfail
D. None of the above


What is the pressure on a swimmer 20
\( \mathrm{m} \) below the surface of water:
\( A \cdot 1 \) atm
B. 2 atm
\( c \cdot 3 \operatorname{atm} \)
D. 4 atm


A current passes through a resistor. If \( \mathrm{K} \)
and \( \mathrm{K}_{2} \) represent the average kinetic
energy of the conduction electrons and
the metal ions respectively then
\( \mathbf{A} \cdot K_{1}<K_{2} \)
B \( . K_{1}=K_{2} \)
\( \mathbf{c} \cdot K_{1}>K_{2} \)
D. Any of these three may occur


Choose the correct options regarding a
galvanometer.
This question has multiple correct options
A. It measures current
B. It is marked with positive and negative polarity
C. The deflection in the galvanometer is proportional to the current
D. Zero is marked at the middle of instrument


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


A lens has power of, -25 D. What is the focal length and nature of the lens?


One of the following areas is an example of secondary succession if succession takes place in / an
A. Abandoned farm land
B. Newly cooled larva
c. New created pond
D. Bare rock


Assertion
The Brownian movement is due to the
bombardment of collodial particles by the molecules of dispersion medium which are in the constant motion like
molecules in a gas.
Reason
Brownian movement provides a visible proof of the random kinetic motion of molecules in a liquid.
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


\( \mathbf{X} \mathbf{e} \mathbf{F}_{4} \) on partial hydrolysis produces
A. \( \mathrm{XeF}_{4} \)
в. \( \mathrm{XeF}_{5} \)
c. \( \mathrm{xeOF}_{2} \)
D. \( \mathrm{xeO}_{3} \)


The mole fraction of \( A \) in \( 10 \%(w / w) \) aq. solution of glucose is:
A . 0.18
B. 0.011
\( c .0 . \)
D. 0.017


A is known to speak truth 5 out of 7
times. What is the probability that \( \boldsymbol{A} \)
reports that it is a 7 when a die is
thrown?


Microscopes are used for magnification:
A. True
B. False


Write the energy conversion that takes place in a hydropower plant.


Find the equation of the plane passing through the points
\( (\mathbf{1}, \mathbf{1}, \mathbf{1}),(\mathbf{3},-\mathbf{1}, \mathbf{2}),(-\mathbf{3}, \mathbf{5},-\mathbf{4}) \)


Average distance of the earth from the
sun is \( L_{1} . \) If one year of the earth \( =D \)
days, one year of another planet whose
average distance from the sun is \( L_{2} \) will
be
\( ^{\mathrm{A}} \cdot_{D}\left(\frac{L_{2}}{L_{1}}\right)^{1 / 2} \) days
B. \( \quad D\left(\frac{L_{2}}{L_{1}}\right)^{3 / 2} \) days
\( ^{\mathbf{C}} \cdot_{D}\left(\frac{L_{2}}{L_{1}}\right)^{2 / 3} \) days
D. \( D\left(\frac{L_{L}}{L_{1}}\right) \) days


Which of the following orbit is impossible for an electron according to Bohr's theory?
A \( \cdot m v r=\frac{h}{2 \pi} \)
B. \( m v r=\frac{3 h}{4 \pi} \)
c. \( _{m v r}=\frac{2 h}{\pi} \)
D. \( m v r=\frac{4 h}{2 \pi} \)


Foliose lichen is
A. Cladonia
B. Glomus
c. Usnea
D. Parmelia


Tangent \( 0 A \) and \( O B \) are drawn for
\( O(0,0) \) to the circle \( (x-1)^{2}+(y- \)
1) \( ^{2}=1 \)
Equation of the circumcircle of triangle
OAB is
A \( \cdot x^{2}+y^{2}+x+y=0 \)
B . \( x^{2}+y^{2}-x+y=0 \)
c. \( x^{2}+y^{2}+x-y=0 \)
D. \( x^{2}+y^{2}-x-y=0 \)


When NaCl is added to the reaction
mixture of an oil and caustic soda, the
soap is thrown out because
A. \( N a C l \) is an ionic compound
B. Soap is insoluble in the presence of chloride ions
C. The solubility product of \( N a C l \) decreases in the presence of soap
D. The solubility product of the soap is exceeded due to the increased concentration of \( N a^{+} \) ions


Assertion
Nitrogen and oxygen are the main
components in the atmosphere but do not react to form oxides of nitrogen
Reason

The reaction between nitrogen and
oxygen requires high temperature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The value of \( \sin 105^{0} \) is
A \( \cdot \frac{\sqrt{3}-1}{2 \sqrt{2}-1} \)
B. \( \frac{\sqrt{3}-1}{\sqrt{2}-1} \)
c. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}+1}{\sqrt{2}} \)


Andy is 27 years older than Ted, who is
38 years younger than Amy. In how many years will Andy be the same age as Amy is now?
A . 11
B. 12
c. 13
D. 10


A body ties to a string of length \( \boldsymbol{L} \) is
revolved in a vertical circle with
minimum velocity, when the body
reaches the upper most point the string
breaks and the body moves under the influence of the gravitational field of
earth along a parabolic path. The
horizontal range \( A C \) of the body will be:
A \( . x=L \)
B. \( x=2 L \)
C \( . x=2 \sqrt{2 L} \)
\( \mathbf{D} \cdot x=\sqrt{2 L} \)


Which is most optimum site for EAS
(Electrophilic Aromatic Substitution) in
the given compound?


A determinant of second order is made
with the elements 0 and \( 1 . \) Find the
number of determinants with non-
negative values.


The waste products produced in man, which need excretion are
A. Carbon dioxide
B. Urea and salts
c. Excess of water
D. All of the above


Choose the correct answers from the
alternatives given Which of the following live in habitats much like those of the early Earth?
A. Protozoans
B. Eubacteria
c. Archaebacteria
D. cyanobacteria


A students scores 40 marks in an
examination and fails by 26 marks If the passing percentage is 33 then find the maximum marks in the
examination


While mixing sugar with water, the level
of water does not increase because
A. matter has large particles which destroy water particles
B. tiny particles of sugar adjust among the space between tiny particles of water
C. tiny particles of sugar destroy large particles of water
D. none of above


Choose the correct reason(s) for the
stability of the Iyophoic colloidal
particles.

This question has multiple correct options
A. Preferential adsorption of ions on their surface from the solution.
B. Preferential adsorption of solvent on their surface from the solution.
C. Attraction between different particles having opposite charges on their surface.
D. Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles.


The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.


In the preparation of amorphous silicon,
HF acid is used to remove:
A. \( M g \)
в. \( \operatorname{si} 0_{2} \)
\( c . s i \)
D. None


If \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0} \) then what is the value
of \( \frac{x^{2}}{y z}+\frac{y^{2}}{z x}+\frac{z^{2}}{x y} ? \)
A \( \cdot(x y z)^{2} \)
B. \( x^{2}+y^{2}+z^{2} \)
c. 9
D. 3


At NTP, 10 litre of hydrogen sulphide gas reacted with 10 litre of sulphur dioxide gas. The volume of gas, after the reaction is complete, would be:
A. 5 litre
B. 10 litre
c. 15 litre
D. 20 litre


Find the inverse of matrices by
elementary row transformation.


Which one of the following statements is not true regarding thermal radiations?
A. All bodies emit thermal radiation at all temperatures
B. They are electromagnetic in nature
C. They travel in straight line with a velocity of \( 3 \times 10^{8} \) \( \mathrm{m} / \mathrm{s} \) in free space
D. They cannot be reflected by mirrors


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}2 x^{2} & \text { if } \boldsymbol{x} \text { is rational } \\ 0 & \text { if } \boldsymbol{x} \text { is irrational } \boldsymbol{l}\end{array}\right. \)
then
A. \( f \) is continuous on \( \mathrm{R} \)
B. \( f \) is not continuous except at \( x=0 \)
C \( . f \) is differentiable only at one point
D. \( f \) is continuous at infinitely many points of \( \mathrm{R} \)


If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})-\boldsymbol{x} \boldsymbol{y} \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \lim _{\boldsymbol{h} \rightarrow \mathbf{0}} \frac{\boldsymbol{f}(\boldsymbol{h})}{\boldsymbol{h}}=\mathbf{3}, \) then the
area bounded by the curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \)
and \( \boldsymbol{y}=\boldsymbol{x}^{2} \) is:
A . 1
B. 2
\( c \cdot 3 \)
D. 4


The inequality \( \sin ^{-1} x>\cos ^{-1} x \) vholds
for
A. all values of \( x \)
B \( \cdot x \in\left(0, \frac{1}{\sqrt{2}}\right) \)
\( ^{c} \cdot_{x \in\left(\frac{1}{\sqrt{2}}, 1\right)} \)
D. no value of \( x \)


Three charges \( Q,+q \) and \( +q \) are placed
at the vertices of a right angle triangle (isosceles triangle) as shown. If the net electrostatic potential energy of the
configuration is zero, value of \( Q \) is:
A \( \cdot \frac{+q}{2+\sqrt{2}} \)
B. \( \frac{-q}{2+\sqrt{2}} \)
c. \( \frac{+2 q}{2+\sqrt{2}} \)
D. \( \frac{-2 q}{2+\sqrt{2}} \)


Which one is resistant to vegetable and
mineral oils?
A. Neoprene
B. Glyptal
c. Nitrile rubber
D. Both B and C


n fig. \( \mathbf{7 . 8}, \boldsymbol{O A}=\boldsymbol{O B} \) and \( \boldsymbol{O D}=\boldsymbol{O C} \)
Show that (i) \( \Delta A O D \cong \Delta B O C \) and (ii)
\( \boldsymbol{A} \boldsymbol{D} \| \boldsymbol{B} \boldsymbol{C} \)


Assertion
Moles of KMnO4 required for oxidation of Fe2 in acidic and basic medium will
be different.
Reason
Final oxidation state to which M will be
reduced will be different in case of
acidic and basic medium.
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


Define the following terms:
1) Spectrum of action of antibiotic
2) Narrow specturm antibiotics
3) limited spectrum antibiotics


Position of P is
A. Interior of curve
B. Exterior of curve
c. on the curve
D. can not be said


Hybridization on carbon in carbonion \( \stackrel{\Theta}{C} H_{3} \) is:
\( A \cdot s p^{3} \)
B. \( s p^{3} d^{2} \)
\( c \cdot s p^{2} \)
D. \( s p^{3} d \)


Assertion
In the Contact process, vanadium
pentoxide is preferred to platinum during the catalytic oxidation of sulphur dioxide.
Reason
Vanadium pentoxide is cheaper and
easily available as compared to platinum
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


Evaluate \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{(\boldsymbol{x}-\mathbf{2})^{7 / 8}(\boldsymbol{x}+\mathbf{3})^{9 / 8}} \)
A \( \cdot \underline{8}\left(\frac{x-2}{x+3}\right)^{1 / 8}+c \)
в. \( \frac{8}{3}\left(\frac{x-2}{x+3}\right)^{1 / 8}+c \)
c. \( \frac{8}{5}\left(\frac{x+2}{x+3}\right)^{1 / 8}+c \)
D. \( \frac{3}{8}\left(\frac{x+2}{x+3}\right)^{1 / 8}+c \)


The number of solid spheres, each of diametres \( 6 \mathrm{cm}, \) that could be moulded to form a solid metal cylinder of height \( 45 \mathrm{cm} \) and diameter \( 4 \mathrm{cm} \) is
\( A \cdot 3 \)
B. 4
\( c .5 \)
\( D \)


The area bounded by the curves \( y= \)
\( x(x-3)^{2} \) and \( y=x \) is (in sq.units):
A . 28
B. 32
\( c \cdot 4 \)
D. 8


An auto charges Rs. 15 for first kilometer and Rs. 8 each for each
subsequent kilometer. For a total
distance of \( ^{\prime} x^{\prime} k m \) an amount of Rs. \( ^{\prime} y^{\prime} \)
is said.

Write the linear equation representing this information
A \( . y=8 x+7 \)
В. \( y=8 x-7 \)
c. \( y=8 x+15 \)
D. None of these


Given that the standard reduction
potentials for \( M^{+} / M \) and \( N^{+} / N \)
electrodes at \( 298 K \) are \( 0.52 V \) and
\( 0.25 V \) respectively. Which of the following is correct in respect of the following electrochemical cell?
\( \boldsymbol{M}\left|\boldsymbol{M}^{+} \| \boldsymbol{N}^{+}\right| \boldsymbol{N} \)
A. The overall cell reaction is a spontaneous reaction
B. The standard EMF of the cell is \( -0.27 V \)
c. The standard EMF of the cell is \( 0.77 V \)
D. The standard EMF of the cell is \( -0.77 V \)
E. The standard EMF of the cell is \( 0.27 V \)


Given that:
\( \boldsymbol{C}(\text {graphite})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} \cdot \boldsymbol{7} \boldsymbol{k} \boldsymbol{J} \)
Calculate the quantity of graphite (in
\( \mathrm{gm} \) ) that must be burnt to evolve
\( 5000 k J \) of heat.
A. 152.8
B. 15.2
c. 200
D. None of these


A stationary light, smooth pulley can rotate without friction about a fixed
horizontal axis. A light rope passes over
the pulley. One end of the rope supports
a ladder with man and the other end
supports a counterweight of mass \( \mathrm{M} \)
Mass of the man is m. Initially, the
centre of mass of the counterweight is
at a height h from that of man as shown
in figure.

If the man starts to climb up the ladder
slowly, calculate work done by him to
reach his centre of mass in level with
that of the counterweight


Statement I: Ice is denser than water in
the liquid phase.
Because
Statement II: In water, hydrogen bonds can form between the positively charged \( \mathrm{H} \) atom on one water molecule and the slightly negatively charged 0 atom on a nearby water molecule
\( \mathbf{A} \cdot \) false, true
B. true, false
c. false, false
D. true, true, correct explanation
E. true, true, not correct explanation


Match the following.


Plates move towards each other in :
A. divergent boundaryy
B. tensional boundary
c. conservative boundary
D. compression boundary


Match the following Columns I, II with III.
\begin{tabular}{lll}
Column I (Common name) & Column II (Roman numerical designation) & Column III (Activation product) \\
A. & & \\
Prothrombin & 1.1 & (i) Convertin \\
B. & & \\
Proconvertin & 2. \( \mathrm{V} \) & (ii) Fibrin \\
Cibrinogen & 3. II & (iii) \\
D. & & Thrombin \\
Proaccelerin & 4. VII & (iv) \\
\hline
\end{tabular}
\( A \)
A- 3- (iii), B- 4- (i), C-1- (ii), D- 2- (iv)
B. D- 4- (ii), B- 3- (iii) C- 2- (iv), A- - 1- (i)
c. \( c-3- \) (iii), A- \( 4- \) (ii), B- \( 1- \) (iv), D- \( 2- \) (i)
D. A- 3- (iii),C- 4- (i), D- 2- (ii), B- 1- (iv)


For which of the following reactions
\( k_{310} / k_{300} \) would be maximum?
A \( \cdot A+B \rightarrow C ; E_{a}=50 k J \)
в. \( X+Y \rightarrow Z ; E_{a}=40 k J \)
c. \( P+Q \rightarrow R ; E_{a}=60 k J \)
D. \( E+F \rightarrow G ; E_{a}=100 k J \)


In a stationary wave:
A. Strain is maximum at antinodes
B. Strain is minimum at nodes
C. Strain is maximum at nodes
D. Amplitude is zero at all points


Which of the following is an example of
uniform circular motion?
A. The planet Pluto in its wandering about the sun
B. The swing of a pendulum between the turning points
C. A bug sitting still at the centre of a playing 50 rpm record
D. The weights on the rim of a car tire as the car slowly accelerates


Blood consists of two parts, a liquid part
and a cellular part. Name these parts and briefly write about them.


Write electronic configurations of the elements (number in the brackets
indicate atomic numbers) potassium \( (\mathbf{1 9}) \)


What of the following statements is
correct?
A. Benzene hexachloride is non-biodegradable pollutant.
B. Anthropogenic air pollutants are natural in origin.
C. Carbon monoxide is a primary air pollutant.
D. \( \mathrm{SO}_{2} \) causes brown air effect during traffic congestion
in cities.


Match the two sets
\( \mathbf{A} \)
I- D, II- A, III- B, IV- C
B. I- A, II- B, III-C, IV-D
\( \mathbf{C} \cdot \mid-\mathrm{B},\|-\mathrm{A},\| \mathrm{I}-\mathrm{D}, \mathrm{IV}-\mathrm{C} \)
D. \( |-A,| I-D,|I|-C, \mid V-B \)


Which term of the \( A P 4,9,14,19, \dots \) is
\( \mathbf{1 0 9} ? \)
\( \mathbf{A} \cdot 14^{t h} \)
B. \( 18^{\text {th }} \)
\( c \cdot 22^{n d} \)
D. \( 16^{\text {th }} \)


If \( \vec{A}=2 i+3 j \) and \( \vec{B}=2 \hat{j}+3 \hat{k} \) the
component of \( \bar{B} \) along \( \bar{A} \) is
A. 6
B. 1/6
\( c \cdot 6 / 13 \)
D. \( \frac{6}{\sqrt{13}} \)


STATEMENT-1: Magnesium can be prepared by the electrolysis of aq.
\( M g C l_{2} \)
STATEMENT-2: The reduction potential
of \( M g^{2+} \) is much lower than that of \( H^{+} \)
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


A student plots graph from his readings on the determination of Young's modulus of a metal wire but forgets to
put the labels (figure). The quantities
on \( X \) and \( Y \) -axes respectively may be
This question has multiple correct options
A. weight hung and length increased
B. stress applied and length increased
c. stress applied and strain developed
D. length increased and the weight hung


A uniform slab of dimension \( 10 \mathrm{cm} \times \)
\( 10 \mathrm{cm} \times 1 \mathrm{cm} \) is kept between two heat
reservoirs at temperatures \( 10^{0} C \) and \( 90^{0} C \)
The larger surface areas touch the reservoirs. The thermal conductivity of
the material is \( 0.80 W / m-^{0} C . \) Find the
amount of heat flowing through the slab per second.


How do alveoli help in gas exchange?


Zeolites are used as catalyst in :
A. petrochemical industries during cracking
B. the preparation of \( H_{2} S O_{4} \)
c. the hydrolysis of ester
D. all of the above


Applying the principal of mathematical
induction of prove that
\[
\frac{2 \sin \theta}{\cos \theta+3 \cos \theta}+\frac{2 \sin \theta}{\cos \theta+5 \cos \theta}+
\]
\( \frac{2 \sin \theta}{\cos \theta+\cos (2 n+1) \theta} \)
\[
=\tan (n+1) \theta-\tan \theta
\]


In the given figure \( D C=C B=4 \mathrm{cm} \)
and \( A E=2 \mathrm{cm} . \) Calculate the area of
shaded portion, if \( D C \| A B \)
\( 4 \cdot 8 c m^{2} \)
3. \( 8.44 \mathrm{cm}^{2} \)
\( \therefore 7 \mathrm{cm}^{2} \)
) \( 7.44 \mathrm{cm}^{2} \)


Calculate the change in the
gravitational potential energy of the
skier between \( A \) and \( B \) :
A \( \cdot 1.8 \times 10^{4} J \)
B . \( 3.6 \times 10^{2} J \)
c. \( 3.6 \times 10^{4} J \)
D \( .1 .8 \times 10^{2} J \)


An identity function is a?
A. Many to many function
B. One to One function
C. Many to one function
D. None


The sum of the digits of a two-digit number is \( 12 . \) The number obtained by interchanging the two digits exceeds
the given number by \( 18 . \) Find the
number.
A . 57
B. 42
\( c \cdot 69 \)
D. 84


The diagram show the energy levels for
an electron in a certain atom. Which
transition shown represents the
emission of a photon with the most
energy?
\( A \)
B. III
\( c \)
2.


When temperature of \( \operatorname{gas} \) is \( 20^{\circ} \mathrm{C} \) and pressure is changed from \( P_{1}=1.01 \times 10^{5} \)
Pa to \( P_{2}=1.165 \times 10^{5} \) Pa then the volume
changed by \( 10 \% \). the bulk modulus is:
A \( .1 .55 \times 10^{5} P a \)
В. \( 0.155 \times 10^{5} P a \)
c. \( 15.5 \times 10^{5} P a \)
D. \( 155 \times 10^{5} P a \)


Find the \( 12^{t h}, 24^{t h} \) and \( n t h \) term of the
A.P. given by \( 9,13,17,21,25, \dots \)


Moth repellents are:
\( A \)
B. perchloroethane
\( c \)
D. all of the above


Total vapour pressure of mixture of 1 mole of \( \boldsymbol{A}\left(\boldsymbol{P}_{A}^{0}=\mathbf{1 5 0 m m}\right) \) and 2 mole of
B \( \left(P_{B}^{0}=240 m m\right) \) is \( 200 m m . \) In this
case:
A. There is a positive deviation from Raoult's law
B. There is a negative deviation from Raoult's law
c. There is no deviation from Raoult's law
D. Molecular masses of A \& B are also required for calculating deviation


In Homo habilis, 'habilis' refers to
A. Wandering species
B. Ancient man
c. Modern man
D. Tool maker


Mention a drug which can act both as an analgesic as well as an antipyretic. Name an artificial sweetening agent.


Pure water is a
of electricity.
A. good
B. badd
c. semi
D. very good


Name any two characteristics of light explained by Huygens wave theory?


Which of the following will show "Tyndal effect"?
This question has multiple correct options
A. Salt solution
B. Milk
c. copper sulphate solution
D. starch solution


Find the ratio of the boiling point of water and melting point of water in Kelvin scale (up to three decimal places)
\( \mathbf{A} \cdot 1.233 \)
B. 1.366
c. 1.433
D. 1.566


The solubility product expression for silver (I) sulfide, using x to represent the molar concentration of silver (I) and y to represent the molar concentration of sulfide, is formulated as
A \( . x y \)
B . \( x^{2} y \)
c. \( x y^{2} \)
D. \( x^{2} y^{2} \)
E \( \cdot x y^{3} \)


Which one among the following is a transition element that occurs when the
inner \( 3 d \) orbitals is partially filled
\( A \cdot F e \)
B. Au
c. Na
D. Ar
E.


Although much \( C O_{2} \) is carried in blood,
yet blood does not become acidic,
because
A. \( C O_{2} \) is absorbed by the leukocytes
B. \( C O_{2} \) combines with water to form \( H_{2} C O_{3} \) which is
neutralised by \( N a_{2} C O_{3} \)
c. \( C O_{2} \) transport and blood buffers play an important role in it
D. it is continuously diffused through the tissues and is not allowed to accumulate


State Second Law of Thermodynamics. How is heat engine different from a refrigerator?


SnO is called an amphoteric oxide.
Give an explanation for it.


The activation energy for most of the
reaction is approximately \( 50 \mathrm{kJ} \) mol \( ^{-1} \)
The rate for temperature coefficient for
such reaction will be:
\( \mathbf{A} \cdot \approx 2 \)
в. \( \approx 3 \)
\( c \cdot<1 \)
\( D \ldots 4 \)


A silver electrode is immersed in
saturated \( A g_{2} S O_{4}(a q .) . \) The potential
difference between silver and the
standard hydrogen electrode is found to
be \( 0.711 V . \) Determine \( K_{s p}\left(A g_{2} S O_{4}\right) \)
\( \left(\text { Given, } \boldsymbol{E}_{A \boldsymbol{g}^{+} / A \boldsymbol{g}}^{\circ}=\mathbf{0 . 7 9 9} \boldsymbol{V}\right) \)


A person sitting in a speeding train is at rest with respect to -
A. trees
B. fields
c. buildings
D. other passengers


Find the angle in radian though which a
pendulum swings if its length is \( 75 \mathrm{cm} \) and the tip describes an arc of length
(i) \( 10 \mathrm{cm} \)
(ii) \( 15 \mathrm{cm} \)
(iii) \( 21 \mathrm{cm} \)


The value of \( 2 \cos ^{-1} x \) is:
\( A \cdot \cos ^{-1}\left(2 x^{2}+1\right) \)
B. \( \cos ^{-1} \frac{2 x}{1+x^{2}} \)
C \( \cos ^{-1}\left(2 x^{2}-1\right) \)
D. \( \tan ^{-1} \frac{2 x}{1-x^{2}} \)


If volume of the hemispherical pond \( = \) \( 523.908 m^{3}, \) maximum depth (radius)
\( =\boldsymbol{r} \boldsymbol{m} \)
Volume of a hemisphere \( =\frac{2}{3} \pi r^{3} \)


n triangle \( A B C, A B=A C ; B E \perp A C \)
and \( C F \perp A B \)
State whether following statement is
true or false
\( \boldsymbol{A F}=\boldsymbol{A E} \)
A. True
3. False


Find \( \lim _{x \rightarrow 2^{+}} f(x), \) where \( f(x)= \)
\( \left\{\begin{array}{ll}4 x+9, & x<2 \\ x+5, & x>2\end{array}\right. \)


Calculate the wavelength of radiation
emitted when electron in a
hydrogen atom jumps from \( n=\infty \) to
\( \boldsymbol{n}=\mathbf{1} \)


The rms value of the electric field of the
light coming from sun is \( 720 \mathrm{N} C^{-1} \). The
average total energy density of the electromagnetic wave is
в. \( 4.5810^{-6} \mathrm{Jm}^{-3} \)
c. \( 6.3710^{-9} \mathrm{Jm}^{-3} \)
D. \( 81.3510^{-12} \mathrm{Jm}^{-3} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{0} \\ \mathbf{1} & \mathbf{4} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] . \) Show that \( \boldsymbol{A}^{\mathbf{2}} \)
\[
\mathbf{7 A}+\mathbf{1 0}=\mathbf{0}
\]


By which process can we separate camphor from ammonium chloride?
A. Filtration
B. Sublimation
c. Dissolution and evaporation
D. Distillation


In a figure \( \boldsymbol{A B} \| \boldsymbol{C D} \angle=\mathbf{3 5}^{\circ} \) and
\( \angle Q R D=135^{\circ} \) find \( \angle P Q R \)


A ball thrown in vertical upward
direction attains maximum height of 16 \( m \). At what height would its velocity be half of its initial velocity?


Deuterio hydrate of magnesium sulphate contains how many molecules of heavy water?
\( A \cdot 2 D_{2} O \)
B. \( 3 D_{2} \) O
\( \mathrm{c} \cdot 10 \mathrm{D}_{2} \mathrm{O} \)
D. \( 7 D_{2} O \)


Find the co-ordinates of the point from
which tangents drawn to the circle \( x^{2}+y^{2}-6 x-8 y+3=0 \) such that the
mid point of its chord of contact is (1,1)


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right], \boldsymbol{i}, \boldsymbol{j}=1,2 \) where \( \boldsymbol{a}_{i j} \) is
defined as \( a_{i j}=i^{2}+j^{2} \) then write the
sum of the elements of the matrix \( \boldsymbol{A} \)


A histrogram consists of
A. sectors
B. rectangles
\( c . \) triangle
D. squares


What is the need for the Kelvin scale of
temperature?


The correct stability order for \( N_{2} \) and its given ions is:
A \( \cdot N_{2}>N_{2}^{+}>N_{2}^{-}>N_{2}^{2-} \)
B . \( N_{2}^{-}>N_{2}^{+}>N_{2}>N_{2}^{2} \)
C \( \cdot N_{2}^{+}>N_{2}^{-}>N_{2}>N_{2}^{2-} \)
D. \( N_{2}>N_{2}^{+}=N_{2}^{-}>N_{2}^{2} \)


Enzymes required for phosphorylation are located in \( \ldots \). chloroplast.
A. Peristromium
B. Plastidome
c. stroma
D. Quantosome


Which is the lightest gas?
A. \( N_{2} \)
в. не
\( c \cdot O_{2} \)
D. \( H_{2} \)


Consider a satellite moving in a circular orbit around Earth. If \( \mathrm{K} \) and \( \mathrm{V} \) denote its
kinetic energy and potential energy respectively, then(Choose the convention, where \( V=0 \text { as } r \rightarrow \infty) \)
A \( . K=V \)
в. \( K=2 V \)
\( \mathbf{c} \cdot V=2 K \)
D. \( K=-2 V \)
E . \( V=-2 K \)


By the action of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
phosphorus changes to :
A. phosphorus acid
B. orthophosphoric acid
c. metaphosphoric acid
D. pyrophosphoric acid


On adding \( 2 \mathrm{mL} \) acetic acid to \( 2 \mathrm{mL} \) of water in a test tube, it was observed that:


Assertion
Farther the image greater is the
magnification.
Reason
Magnification is equal to the ratio of the
distance of the object and that of the
image.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Statement- \( I: \) chloropropane has higher boiling point than chlorethane.
Reason
Statement- \( I I \) I haloalkanes are polar
molecules.
A. (A) Statement-I is true, Statement-II is true Statement-II is correct explanation for Statement-I
B. (B) Statement-I is true, Statement-II is true Statement-II is NOT a correct explanation for Statement-I.
c. (c) Statement-I is true, statement-II is false.
D. (D) Statement-I is false, Statement-II is true.


The population explosion in India has led to fragmentation of land holdings leading to creation of more small and marginal farmers.
A . True
B. False


When an object is placed on the principal axis of a convex lens at two different positions, it produces the images with magnification +2 and -4 respectively. How many times more away from the lens the image will be formed in the second position as compared to the first position?
\( A \cdot 2 \)
B. 4
\( c \cdot 5 \)
D. 10


The most suitable method of separation of 1: 1 mixture of ortho and para-
nitrophenols is:
A. steam distillation
B. sublimation
c. chromatography
D. crystallisation


Q Type your question
placed near a long straight current-
carrying wire. The dimensions are
shown in the figure. The lone wire lies in
the plane of the loop. The current in the
long wire varies as \( \boldsymbol{I}=\boldsymbol{I}_{\mathbf{0}}(\boldsymbol{t}) . \) The
mutual inductance of the pair is
A \( \cdot \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{2 a+l}{l}\right) \)
B. \( \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{2 a-l}{l}\right) \)
c. \( \frac{2 \mu_{0} a}{2 \pi} \ln \left(\frac{a+l}{l}\right) \)
D. \( \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{a+l}{l}\right) \)


Regarding open organ pipe, which of following is correct?
A. Both ends are pressure antinodes
B. Both ends are displacement nodes
c. Both ends are pressure nodes
D. Both (1)and (2)


If the force applied on a particle is zero then the quantities which are conserved are
A. Only momentum
c. Momentum and angular momentum
D. only potential energy


The equation of the common normal at the point of contact of the curves \( x^{2}=y \)
and \( x^{2}+y^{2}-8 y=0 \)
A \( . x=y \)
B. \( x=0 \)
\( \mathbf{c} \cdot y=0 \)
D. \( x+y=0 \)


Assertion
A current continues to flow in
superconducting coil even after switch
is off.
Reason
Superconducting coils show Meissner effect
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 reagents do not give oxygen as one of the product during oxidation with ozone?
This question has multiple correct options
A. \( H g \)
в. \( S O_{2} \)
c. \( \operatorname{sn} C l_{2} / H C l \)
D. \( H_{2} \).


The equation of the hyperbola whose foci are the foci of the ellipse \( \frac{x^{2}}{25}+ \) \( \frac{\boldsymbol{y}^{2}}{\mathbf{9}}=1 \) and the eccentricity is \( \mathbf{2}, \) is


For a chess tournament 13 people were
selected for quarter finals. Each person plays two matches with the other. How
many matches have been held in the whole tournament?
A .144
в. 156
\( c .185 \)
D. 116


Choose the correct options:
This question has multiple correct options
A. Remainder obtained on dividing \( p(x)=x^{3}+1 \) by \( (x+ \)
1) is 0
B. \( x=1 \) and \( x=2 \) are zeroes of polynomial \( P(x)= \)
\( 5 x^{5}-20 x^{4}+5 x^{3}+50 x^{2}-20 x-40 \)
C \( \cdot 6 x^{7}-5 x^{4}+2 x+3 \) is a polynomial of degree 7
D. \( x+1 \) and \( 2 x-3 \) are factors of \( 2 x^{3}-9 x^{2}+x+12 \)


The highest value of \( e / m \) of anode rays has been observed when the discharge tube is filled with:
A. nitrogen
B. oxygen
c. hydrogen
D. helium


If a \( \triangle A B C, \) the bisectors \( \angle B \) and \( \angle C \)
intersect at \( O . \) Prove that \( \angle B O C= \)
\( \mathbf{9 0}^{\circ}+\frac{\mathbf{1}}{\mathbf{2}} \angle \boldsymbol{A} \)


Which is the correct order of bond
energy of single, double and triple bonds between carbon atoms?
A. \( C-C>C=C>C \equiv C \)
в. \( C=C>C \equiv C>C-C \)
c. \( C \equiv C>C-C>C=C \)
D. \( C \equiv C>C=C>C-C \)
\( C \)


Which of the following will have the molecular shape of a triangle bipyramid?
A \( . P F_{3} C l_{2} \)
в. \( I F_{5} \)
\( \mathbf{c} \cdot B r F_{5} \)
D. \( S b F_{2}^{2} \)


A discrete random variable \( X, \) can take
all possible integer values from 1 to \( K \)
each with a probability \( 1 / K . \) Its mean is
\( \mathbf{A} \cdot K \)
в. \( K+1 \)
c. \( K / 2 \)
D. \( K / 4 \)


Out of given atoms which atoms has highest energy of 2 s-subshell ?
A .
B. Li
c. Na
D. All have same


Heparin is a
A. Protein
B. Lipid
c. Enzyme
D. Mucopolysaccharide


If \( |z-2+i| \leq 2 \), then find the greatest
value of \( |z| \)


Which of the following are examples of transparent material?
A . Glass
B. water
c. Plastic
D. All of these


Verify:
\( (a+b)^{2}-(a-b)^{2}=4 a b, \) for \( a= \)
\( \mathbf{4}, \boldsymbol{b}=\mathbf{3} \)


Argon is a:
A. ionic compound
B. noble gas
C . polar covalent compound
D. nonpolar covalent compound
E. metallic substance


The substance that helps to friction are called lubricants.
A. increase
B. decrease
c. create
D. eliminate


Which one of the following oxides is soluble in water?
A. zinc oxide
B. Calcium oxide
c. Ferric oxide
D. Ferrous oxide


Why \( H F \) is a weak acid while \( H C l \) is a
strong acid?
A \( . H F \) produces very few \( H^{+} \) ions in water
B. \( H C l \) dissociates completely to produce many \( H^{+} \) ions in water
\( c . \) Both \( A \) and \( B \)
D. None of the above


For the given Question (1,2,3) consider the following reaction. Which halogen will give the best yield of a single monohalogenation product?
A. \( F_{2} \)
в. \( C l_{2} \)
\( \mathbf{c} \cdot B r_{2} \)
D. \( I_{2} \)


\( \lim _{\mathbf{n} \rightarrow \infty} \sum_{\mathbf{r}=\mathbf{1}}^{\mathbf{n}} \frac{\mathbf{1}}{\mathbf{n}} \mathbf{e}^{\mathbf{r} / \mathbf{n}} \mathbf{i} \mathbf{s} \)
\( \mathbf{A} \cdot \mathbf{e} \)
B. e -1
\( c \cdot 1-e \)
D. e +1


Two particles on a wave having wavelength \( 2 \mathrm{m} \) are at the distances of 5
\( \mathrm{m} \) and \( 9 \mathrm{m} \) respectively from origin. The phase difference between the particles
is
A \( \cdot \frac{\pi}{2} \) rad
B. \( \pi \) rad
\( c \cdot 2 \pi \) rad
D. \( 4 \pi \) rad


The oxidation number of chlorine in
KCIO is:
\( A \cdot+1 \)
\( B .+3 \)
\( c \cdot+5 \)
\( D \cdot+7 \)


Two celestial bodies are separated by
some distance. If the mass of any one of the point like bodies is doubled while
the mass of other is halved then how far
should they be taken so that the gravitational force between them becomes one-fourth?


A triangle has vertices at \( (\mathbf{6}, \mathbf{7}),(\mathbf{2},-\mathbf{9}) \)
and \( (-4,1) . \) Find the slope of its sides.
A \( \cdot \frac{11}{7},-13,-\frac{1}{4} \)
в. \( \frac{11}{7}, 13,-\frac{1}{4} \)
c. \( \frac{11}{7},-13, \frac{1}{4} \)
D. None of these


In \( , \) excess minority carriers recombine with majority carriers near the p-njunction.
A. Photodiode
B. Light Emitting Diode
c. solar cells
D. zener diode


\( \int_{0}^{\pi} \frac{x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} d x \)


The angular width of the central maximum in a single slit diffraction
pattern is \( 60^{\circ} . \) The width of the slit is 1
\( \mu \mathrm{m} . \) The slit is illuminated by
monochromatic plane waves. If another slit of same width is made near it,
Young's fringes can be observed on a
screen placed at a distance \( 50 \mathrm{cm} \) from the slits. If the observed fringe width is
1cm, what is slit separation distance? (i.e., distance between the centres of each slit.)
A. \( 75 \mu \) m
B. \( 100 \mu \) m
c. \( 25 \mu \) m
D. \( 50 \mu \) m


Common example of red algae is
A. Porphyra
B. Batrachospermum
c. Ectocarpus
D. both (a) and (b)


Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{c}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1 \\
\operatorname{atan}^{-1}\left(\sqrt{\frac{a-b}{a+b}} \tan \frac{\theta}{2}\right)= \\
\cos ^{-1} \frac{a \cos \theta+b}{a+b \cos \theta}
\end{array}
\]


The vector \( \vec{A}=\vec{i}+\vec{j} \) where \( \vec{i}, \vec{j} \) are unit vectors along \( X \) and \( Y \) axes respectively makes an angle of with \( X \)
axis.
\( A \cdot 0^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 60 \)
D. \( 90^{\circ} \)


In which of the following cells, the potential difference between the
terminals of a cell exceeds its emf.
(a)
(b)
(No current)
\( (\mathbf{d}) \)
\( (c) \)
\( A \)
B. \( b \)
\( c \)
D. \( d \)


The equivalent resistance between \( A \)
and B is
\( A \cdot R \)
в. \( \frac{R}{2} \)
\( c .2 R \)
D. None of these


At low temperatures ................... type of thermometer is used.
A. mercury thermometer
B. water thermometer
c. alcohol thermometer
D. thermometers cannot be used


An aqueous solution of a metal salt \( (X) \)
reacts with carbon dioxide to give a water soluble compound (Y) which on heating gives the starting metal salt back Y when present in water does not produce lather with soap. The compounds \( X \) and \( Y \), respectively are
A. \( C a C O_{3} \) and \( C a\left(H C O_{3}\right)_{2} \)
в. \( M g\left(H C O_{3}\right)_{2} \) and \( M g C O_{3} \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( C a C O_{3} \)
D. \( M g C O_{3} \) and \( M g\left(H C O_{3}\right)_{2} \)


Which of the following statements is/are correct?
I. \( B_{2} O_{3} \) is an acidic oxide
Il. \( G a_{2} O_{3} \) and \( A l_{2} O_{3} \) are amphoteric
oxides.
III. \( l n_{2} O_{3} \) and \( t l_{2} O_{3} \) are basic oxides.
A . ।, ॥।, ॥।
B. ।, ॥
c. ॥, ॥ा
D. I, III


Answer the following question in one
word or one sentence or as per exact requirement of the question.

Write the minimum value of \( f(x)= \) \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)


The correct order of boiling point for
primary \( (1), \) secondary (2) and tertiary
(3) alcohols is:
\( \mathbf{A} \cdot 1>2>3 \)
В. \( 3>2>1 \)
c. \( 2>1>3 \)
D. \( 2>3>1 \)


If the mean of \( x \) and \( \frac{1}{x} \) is \( M, \) then the mean of \( x^{3} \) and \( \frac{1}{x^{3}} \)
A \( \cdot \frac{M\left(M^{2}-3\right)}{2} \)
В. \( M\left(4 M^{2}-3\right) \)
\( c \cdot M^{3} \)
D. \( M^{3}+3 \)


What is carbon cycle?


An ellipse has its centre at (1,-1) and semi-major axis \( =8 \) and it passes
through the point \( (1,3) . \) The equation of the ellipse is
A \( \cdot \frac{(x+1)^{2}}{64}+\frac{(y+1)^{2}}{16}=1 \)
в. \( \frac{(x-1)^{2}}{64}+\frac{(y+1)^{2}}{16}=1 \)
c. \( \frac{(x-1)^{2}}{16}+\frac{(y+1)^{2}}{64}=1 \)
D. \( \frac{(x+1)^{2}}{64}+\frac{(y-1)^{2}}{16}=1 \)


When n number identical cell of emf E is
connected in series, the net emf of the
system will be
\( A \cdot E \)
B. Eln
\( c \cdot n E \)
D. \( (n+1) E \)


If \( \boldsymbol{A}=-\mathbf{1 2 5} \boldsymbol{m}^{\mathbf{6}} \boldsymbol{n}^{2} \boldsymbol{x}, \boldsymbol{B}=\boldsymbol{6} \boldsymbol{m}^{2} \boldsymbol{n} \boldsymbol{x}, \boldsymbol{C}= \)
\( -\boldsymbol{6} \boldsymbol{4} \boldsymbol{m}^{6} \boldsymbol{n}^{2} \boldsymbol{x} \) and \( \boldsymbol{D}=\boldsymbol{8} \boldsymbol{m}^{2} \boldsymbol{n} \boldsymbol{x} \), then
\( (\boldsymbol{A} \div \boldsymbol{B})+(\boldsymbol{C} \div \boldsymbol{D}) \) is \( _{-}-\ldots- \) - -


The SD of the data 6,5,9,13,12,8,10 is
A \( \cdot \sqrt{\frac{52}{7}} \)
B. \( \frac{52}{7} \)
c. \( \sqrt{6} \)
D. 6


Which of the following will be the angles of a triangle?
A \( \cdot 35^{\circ}, 45^{\circ}, 90^{\circ} \)
B . \( 26^{\circ}, 58^{\circ}, 96^{\circ} \)
\( \mathbf{c} \cdot 38^{\circ}, 56^{\circ}, 96^{\circ} \)
D . \( 30^{\circ}, 55^{\circ}, 90^{\circ} \)


If the transformation \( z=\log \tan \left(\frac{x}{2}\right) \)
reduces the differential equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\cos \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{4} \boldsymbol{y} \operatorname{cosec}^{2} \boldsymbol{x}=\mathbf{0} \) int
\( \frac{d^{2} y}{d x^{2}}+A y=0 \) then the value of \( A \) is


Solve : \( \int x e^{x} \sin x d x \)


Core condition for state of equilibrium in principle of moment is:
A. Distance between two objects in a beam balance should be same
B. Resultant of force should be zero
c. weight of both the object on beam balance should be same
D. Tension should be equal on both sides


Find the derivative of
\( f(x)=\left(x^{2}-5\right)\left(x^{3}-2 x+3\right) \)


According to Rutherford's atomic model entire mass of the atom is concentrated
at the
A . electron
B. nucleus
c. proton
D. none of these


The uncertainty in momentum of a
particle is \( 3.31 \times 10^{-2} \mathrm{Kg} \) msec \( ^{-1} \)
Calculate uncertainty in its position.
A. \( 6.4 \times 10^{-33} m \)
m
В. \( 1.6 \times 10^{-33} m \)
c. \( 3.2 \times 10^{-33} m \)
D. \( 5 \times 10^{-33} m \)
E \( .2 .5 \times 10^{-33} m \)


An aircraft having a wingspan of \( 20.48 m \) flies due north at a speed of
\( 40 m s^{-1} . \) If the vertical component of earth's magnetic field at the place is \( 2 \times 10^{-5} T, \) calculate the emf induced
between the ends of the wings.


The pair of amphoteric hydroxides is:
A. \( A l(O H)_{3}, L i O H \)
B. \( B e(O H)_{2}, M g(O H)_{2} \)
c. \( B(O H)_{3}, B e(O H)_{2} \)
D. \( B e(O H)_{2}, Z n(O H) \)


Which of the following processes is unsuitable for softening water possessing temporary hardness?
A. Adding calcium hydroxide
B. Filtration
c. Boiling
D. Distillation


Name the apparatus used to measure the heat absorbed or released by a
reaction.
A. Centrifuge
B. Barometer
c. Balance
D. Calorimeter
E. Battery


A unit vector \( \vec{a} \) makes angles \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with \( \hat{i} \) and \( \hat{j} \) respectively and an acute angle \( \theta \) with \( \hat{k} \). Find the angle \( \theta \) and
components of \( \overrightarrow{\boldsymbol{a}} \)


A sphere of mass m moving with
constant velocity u, collides with another stationary sphere of same mass. If e is the coefficient of
restitution, the ratio of the final velocities of the first and second sphere
is
A \( \cdot \frac{1+e}{1-e} \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{e}{1-e} \)
D. \( \frac{1+e}{e} \)


Diethyl ether is mostly used in solvent
extraction due to all of the following
reasons except:
A. Its solvation capacity is very high
B. being inert, it does not react with most organic compound
C. there are two lone pairs in it, therefore it acts as a strong nucleophile
D. its boiling point is low, therefore, it can be easily separated by distillation


5 pencils and 7 pens together cost Rs.
\( 50, \) whereas 7 pencils and 5 pens
together cost Rs. \( 46 . \) Find the cost of one
pencil and that of one pen by graphical
method.
A. cost of one pencil \( =\mathrm{Rs} .2 \) and that of one pen \( =\mathrm{Rs} .4 \)
B. cost of one pencil \( =\mathrm{Rs} .3 \) and that of one pen \( =\mathrm{Rs} . \)
C. \( \operatorname{cost} \) of one pencil \( =\operatorname{Rs} .5 \) and that of one pen \( =\operatorname{Rs} .6 \)
D. cost of one pencil \( = \) Rs. 2 and that of one pen \( = \) Rs. 6


Compressed Natural Gas (CNG) is
A. Propane
B. Methane
c. Ethane
D. Butane


The output of the given circuit in the
figure.
A. would be zero at all times
B. would be like a half-wave rectifier with positive cycles in output
C. would be like a half -wave rectifier with negative cycles in output
D. would be like that of a full wave rectifier


Assertion
A liquid will flow faster and more
smoothly from a sealed can when two
holes are punched in the can than when
one hole is punched.
Reason
The flow becomes streamlined with two
holes rather than with one hole.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the area of \( \triangle P Q R \) whose vertices \( \operatorname{are} \boldsymbol{P}(\mathbf{2}, \mathbf{1}), \boldsymbol{Q}(\mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{R}(\mathbf{5}, \mathbf{2}) \)


From a well shuffied pack of cards one
card is drawn at random. The
probability that the card drawn is an
ace is
A \( \cdot \frac{1}{13} \)
в. \( \frac{1}{14} \)
c. \( \frac{3}{52} \)
D. \( \frac{1}{26} \)


A diatomic ideal gas initially at 273 k is given 100 cal heat due to which system did \( 209 \mathrm{J} \) work Molar heat capacity
\( \left(C_{m}\right) \) of gas for the process is :
A \( \cdot \frac{3}{2} \) R
B \( \cdot \frac{5}{2} \) R
\( c \cdot \frac{5}{4} R \)
D. 5 R


\( \mathbf{1 0 0} \mathrm{mL} \) of \( \mathbf{0 . 2} \mathrm{N} \) HCl is added to \( \mathbf{1 0 0} \mathrm{mL} \)
of \( 0.18 \mathrm{N} \). NaOH and the whole volume is
made one litre. The pH of the resulting solution is:
A . 1.2
в. 2.7
c. 3.9
D. 4


Which one of the following animals can hear infrasound?
A. rhinoceros
B. bat
\( c \cdot \operatorname{dog} \)
D. honey bee


Number of paramagnetic molecules
from the following are:
\( \boldsymbol{C N}^{-}, \boldsymbol{N O}, \boldsymbol{O}_{2}^{2-}, \boldsymbol{O}_{2}, \boldsymbol{N} \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{-}, \boldsymbol{B}_{2}, \boldsymbol{C}_{2}, \boldsymbol{l} \)


The earth's satellite is moving round the earth in a circular orbit. Which of the
following are true regarding the satellite?
1. Its speed is constant
2. Its velocity is constant
3. Its angular momentum is constant
4. Its gravitational pull is balanced by the centrifugal force
A. 1,3 and 4
B. 2,3 and 4
c. 1,2 and 3
D. 1,2 and 4


Two identical flutes produce fundamental notes of frequency \( 300 H z \)
at \( 27^{\circ} \mathrm{C} \). If the temperature in the air in
one of the flutes is increased to \( 31^{\circ} C \)
the number of beats heard per second will be:
A . 3
B. 2
\( c \cdot 1 \)
D.


Three identical specimens of a magnetic materials nickel, antimony and aluminium are kept in a nonuniform magnetic field. Draw the modification in the field line in each
case. Justify your answer.


The fact about tyndall effect is
A. the diameter of dispersed particles is much smaller than the wave length of light used
B. refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude
C. it is shown by true solution
D. All of the above


Atoms \( A, B, C \) occur in the same period and have one, six and seven valence
electrons respectively. The electronic structure of the
compound formed between \( B \) and \( C: \)
\( A \)
в.
\( c \)
D.


Fill in the blank
The common water pump works on the
principle that atmosphere exerts
A. Torceilian
B. pressure
c. sea level
D. none


A triangle has sides of length 13,30 and
\( 37 . \) If the radius of the inscribed circle is
\( \frac{p}{q}(\text { where } p \text { and } q \text { are coprime }) \),then the value of \( \boldsymbol{q}^{\boldsymbol{p}+\mathbf{3}} \) is
A . 2048
в. 4096
c. 1024
D. 512


Find the sum of first eight multiples of
three.


Assertion
In interference, all the fringes are of
same width.
Reason
In interference, fringe width is independent of the position of fringe.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Given \( 2 N O_{(g)}+O_{2(g)} \rightarrow 2 N O_{2(g)} ; \) rate
\( =\mathbf{k}[\boldsymbol{N} \boldsymbol{O}]^{2}\left[\boldsymbol{O}_{2}\right]^{1} . \) By how many times does
the rate of the reaction change when the volume of the reaction vessel is reduced
to \( 1 / 3 \) rd of its original volume? Will there be any change in the order of the reaction?


For transistor action which of the
following statements is correct?
This question has multiple correct options
A. Base, emitter and collector regions should have similar size and doping concentration.
B. The base region must be very thin and lightly doped.
C. The emitter junction is forward biased and collector junction is reverse biased.
D. Both emitter junction and collection junction are forward biased.


The sum of first 20 odd natural number
is :
A . 100
в. 210
c. 400
D. 420


If \( a-\frac{1}{a}=5 ; \) find \( a^{2}+\frac{1}{a^{2}}-3 a+\frac{3}{a} \)
A . 10
B. 14
\( c \cdot 6 \)
D. 12


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{C l})-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
and \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C}(\boldsymbol{C l})\left(\boldsymbol{C H}_{3}\right)- \)
\( C H_{3} \) are both positional and chain
isomerism of each other.
A. True
B. False


The dimensional formula of \( \frac{1}{2} \mu_{0} H^{2}\left(\mu_{0}\right. \) Permeability of free space and \( \mathrm{H} \) magnetic field intensity) is:
A \( \cdot M L T^{-1} \)
B. \( M L^{2} T^{-2} \)
c. \( M L^{-1} T^{-2} \)
D. \( M L^{2} T^{-1} \)


Taxonomic system based only on the traits, that reflect the order in time in
which branches arose in phylogenetic tree is called as
A. Phylogeny
B. Cladistics
c. classical evolutionary taxonomy
D. Phenetics


The boiling point of aldehyde and
ketones are:
A. higher than those of alcohols of similar molecular
masses
B. lower than those of alcohols of similar molecular
masses
C. similar to the alcohols of similar molecular masses
D. similar to the alcohol of different molecular mass


A swimming pool was sufficiently
alkaline so that \( \mathrm{CO}_{2} \) absorbed from the
air produced in the pool a solution
which \( 2 \times 10^{-4} M \) in \( C O_{3}^{2-} M . \) If the
pool water was originally \( 4 \times 10^{-3} M \) in
\( M g^{2+}, 6 \times 10^{-4} M \) in \( C a^{2+} \) and \( 8 x \)
\( 10^{-7} M \) in \( F e^{2+}, \) then a precipitate
should form of:
\( \left(\boldsymbol{K}_{s p} \text { for } \boldsymbol{C a} \boldsymbol{C O}_{3}, \boldsymbol{M} \boldsymbol{g} \boldsymbol{C O}_{3}, \boldsymbol{F e} \boldsymbol{C O}_{3} \) are \right.
\( \mathbf{2 . 8} \times \mathbf{1 0}^{-\mathbf{9}}, \mathbf{3 . 5} \times \mathbf{1 0}^{-\mathbf{8}}, \mathbf{3}, \mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 1}} \)
respectively
A . only \( M g C O_{3} \)
B . only \( C a C O_{3} \)
c. only \( F e C O_{3} \)
D. only \( M g C O_{3} \) and \( F e C O_{3} \)
E. \( M g C O_{3}, C a C O_{3} \) and \( F e C O_{3} \)


The correct order of acidity is:
\( \mathbf{A} \cdot C H F_{3}>C H C l_{3}>C H B r_{3}>C H I_{3} \)
B \( \cdot C H I_{3}>C H B r_{3}>C H C l_{3}>C H F_{3} \)
\( \mathbf{c} \cdot C H C l_{3}>C H F_{3}>C H B r_{3}>C H I_{3} \)
D. \( C H I_{3}>C H B r_{3}>C H F_{3}>C H C l_{3} \)


Which of the following statement is
incorrect?
A. Reducing power in aqueous solution is maximum for lithium metal.
B. Electron affinity order \( O^{+}>O>O^{-}>O^{2-} \)
C. Order of oxidation number of oxygen \( O_{3}>K O_{2}> \)
\( B a O_{2}>K_{2} O \)
D. \( p H \) of aqueous solution \( L i C l>B e C l_{2}>M g C l_{2}> \)
\( A l C l_{3} \)


Let \( \triangle A B C \sim \triangle D E F \) and their areas
be \( 64 \mathrm{cm}^{2} \) and \( 121 \mathrm{cm}^{2} \) respectively. If
\( \boldsymbol{E F}=\mathbf{1 5 . 4} \boldsymbol{c m}, \) find \( \boldsymbol{B C} \)


Enthalpy change equal internal energy
change when
This question has multiple correct options
A. all the reactants and products are in solution
B. reaction is carried out in a closed vessel
C. number of moles of gaseous reactants and that of products is equal
D. reaction is carried out at constant pressure


When waves of same intensity from two coherent sources reach a point with
zero path difference the resultant intensity is \( K \) when the above path difference is \( \lambda / 4 \) the intensity becomes:
\( A \cdot K \)
в. \( \frac{K}{2} \)
c. \( \frac{K}{4} \)
D. \( \frac{K}{8} \)


Braille system is traditionally written
with:
A. White Paper
B. Black Paper
c. Embossed Paper
D. Typed Paper


Which of the following is the least reactive metal?
A. Aluminium
B. Iron
c. Platinum
D. Calcium


All the elements of the same group have similar \( _{\text {一一一一一一一一 }} \) properties.


When phenol is treated with \( C H C l_{3} \)
and \( N a O H, \) the product formed is:
A. Benzaldehyde
B. Salicylaldehyde
c. Salicylic acid
D. Benzoic acid


\( \int_{0}^{2} 3 x+2 d x \)


Portuguese man of war is
A. Pennatula
B. corallium
c. Physalia
D. obelia


If \( \boldsymbol{a}=\frac{-1+\sqrt{3 i}}{2}, \boldsymbol{b}=\frac{-1-\sqrt{3 i}}{2} \) then show
that \( a^{2}=b \) and \( b^{2}=a \)


Solve the equation \( \sin ^{-1}(3 x)=-\frac{1}{3} \pi \)
giving the solution in an exact form.


The total number of isomers for \( C_{4} H_{8} \) is
A. 5
B. 6
c. 7
D. 8


Name the following triangle in two different ways.(you mayjudge the nature of the angle by observation)


What should be the ratio of area of
cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of \( 15 N \) can be obtained at
each of its brake shoe by exerting a
force of \( 0.5 N \) on the pedal?
\( \mathbf{A} \cdot 1: 60 \)
B. 1: 30
c. 1: 15
D. 1: 45


If \( \overline{\boldsymbol{F}} \) is the force and \( \bar{r} \) is the radius
vector, then the torque is :
A \( \cdot \bar{r} \times \bar{F} \)
в. \( \bar{r} \bar{F} \)
c. \( |\bar{r}| .|\bar{F}| \)
D \( \cdot \frac{|\bar{r}|}{|\bar{F}|} \)


Write three properties of ferromagnetic
materials.


Write the chemistry of recharging lead storage battery highlighting all the materials that are evolved during recharging.


The most reactive form of phosphorus is
A. red phosphorus
B. yellow phosphorus
c. violet phosphorus
D. black phosphorus


Calculate the [OH] of
\( \left[\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{H}_{3}\right]^{\oplus} \) and \( \left[\boldsymbol{H}_{3} \boldsymbol{N}-\right. \)
\( \left.C_{2} H_{4} N H_{3}\right]^{2+} \) in 0.15 M ethylene
diamine (aq) if
\( N H_{2} C_{2} H_{4} N H_{2}+H_{2} O \rightleftharpoons \)
\( N H_{2} C_{2} H_{4} \stackrel{\oplus}{N} H_{3}+\stackrel{\ominus}{O} H\left(K_{1}=8.5 \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{5}}\right) \)
\( N H_{2} C_{2} H_{4} \stackrel{\oplus}{N} H_{3}+H_{2} O \rightleftharpoons \)
\( \left[\boldsymbol{N} \boldsymbol{H}_{3} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{H}_{3}\right]^{2+}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H}\left(\boldsymbol{K}_{2}=\right. \)
\( \left.2.7 \times 10^{-8}\right) \)
\( \begin{array}{lll}\text { A. Case } 1: 3.57 \times 10^{-3} M & \text { Case } \|: 2.7 \times 10^{-8} M=K_{b a}\end{array} \)
B. Casel: \( 4.57 \times 10^{-3} M \quad \) Case \( \|: 3.7 \times 10^{-8} M=K_{h} \)
C. Casel: \( 5.57 \times 10^{-3} M \quad \) Case \( \|: 4.7 \times 10^{-8} M=K_{h} \)
D. Case I: \( 6.57 \times 10^{-3} M \quad \) Case \( \|: 5.7 \times 10^{-8} M=K_{h} \)


If \( S \) is the circumcentre, \( O \) is the
orthocenter of \( \triangle \boldsymbol{A B C} \), then \( \boldsymbol{S A}+ \)
\( \boldsymbol{S B}+\boldsymbol{S C}= \)
A. \( S O \)
B. 2SO
\( c . O S \)
D. \( 20 S \)


Glycerol is:
A. \( 1,3- \) dihydroxy propane
B. \( 2,3- \) dihydroxy propanone
c. \( 2,3- \) dihydroxy propane
D. \( 1,2,3- \) Propane triol


A door of length \( 2 m \) and breadth 1 m is fitted in a wall. The length of the wall is \( 4.5 m \) and breadth is \( 3.6 . \) Find the cost
of white washing the wall, if the rate of
white washing the wall is \( R s 20 \) per \( m^{2} \)


I.P. of sodium is 5.14 eV then I.P. of
potassium will be :
A. equal to sodium
B. 5.68 ev
c. 4.34 ev
D. 10.28 ev


What is the degree of the given
monomial \( -11 y^{2} z^{2} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c \cdot 4 \)
D.


The distance between an object and its real image produced by a converging lens is \( 0.72 \mathrm{m} \). The magnification is 2
What will be the magnification when the object is moved by 0.04 m towards the lens?
A .2
B. 4
\( c .3 \)
\( D \)


When light falls on a given plate at
angle of incidence of \( 60^{\circ}, \) the reflected
and refracted rays are found to be
normal to each other. The refractive
index of the material of the plate is then
A . 0.866
B. 1.5
\( c \cdot 1.732 \)
D. 2


The human eye part which can be used again and again for forming different images is called:
A . iris
B. pupil
c. cornea
D. retina


(a) Write the necessary conditions for the phenomenon of total internal
reflection to occur.
(b) Write the relation between the
refractive index and critical angle for a given pair of optical media.


A certain reaction occurs in the
following steps.
(i) \( C l_{(g)}+O_{3(g)} \rightarrow C l O_{(g)}+O_{2(g)} \)
(ii) \( C l O_{(g)}+O_{(g)} \rightarrow C l_{g}+O_{2(g)} \)
What is the molecularity of each of the elementary steps?


How is acid-base balance maintained in
human body.


What is the rate of the reaction for
\( \mathbf{2 A} \rightarrow \boldsymbol{B} ? \)
\( ^{\mathrm{A}} \cdot-\frac{1}{2}\left[\frac{d[A]}{d t}\right] \)
в. \( -\frac{d[A]}{d t} \)
c. \( -\frac{d[B]}{d t} \)
D. \( +\frac{d[A]}{d t} \)


The
in


Oxygen has a sweet odour.
A. True
B. False


A cylinder of height \( h \) is filled with water and is kept on a block of height h/2. The level of water in the cylinder is kept
constant. Four holes numbered 1,2,3 and 4 are at the side of the cylinder and at heights \( 0, h / 4, h / 2 \) and \( 3 h / 4 \) respectively.When all four holes are opened together, the hole from which water will reach farthest distance is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


A purse contains 2 silver and 4 copper
coins. \( A \) second purse contains 4 silver
and 3 copper coins. If a coin is pulled at random from one of the two purses,
what is the probability that it is a silver \( \operatorname{coin} \)


Conductivity of \( 0.00241 \mathrm{M} \) acetic acid is \( \mathbf{7} . \mathbf{8} 9 \mathbf{6} \times \mathbf{1 0}^{-5} \mathbf{S} \mathbf{c m}^{-1} . \) Calculate its
molar conductivity. If \( \lambda_{m}^{o} \) for acetic acid is \( 390.5 S c m^{2} \) mol \( ^{-1} . \) what is its
degree of dissociation?


Find out elongation in a rod Given :
\( Y=2 \times 1011 \mathrm{N} / \mathrm{m} 2, \mathrm{p}=104 \mathrm{kg} / \mathrm{m} 3 \mathrm{Y}=2 \times 1011 \mathrm{N} / \mathrm{m} \)
\( 2, p=104 \mathrm{kg} / \mathrm{m} 3 \)
\( A .9 m n \)
в. \( 10 m m \)
\( c .18 m m \)
D. \( 3 m m \)


If \( z=3-4 i, \) then \( z^{4}-3 z^{3}+3 z^{2}+ \)
\( 99 z-95 \) is equal to
A . 5
B. 6
\( c .-5 \)
D. - 4


In view of the signs of \( \Delta_{r} G^{o} \) for the
following reactions,
\( P b O_{2}+P b \rightarrow 2 P b O, \Delta_{r} G^{o}<0 \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{S} \boldsymbol{n} \rightarrow 2 \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}, \boldsymbol{\Delta}_{r} \boldsymbol{G}^{o}>\mathbf{0} \)
Which oxidation states are more
characteristic for lead and tin?
A. For lead \( +4, \) for tin +2
B. For lead +2 , for tin +2
c. For lead \( +4, \) for tin +4
D. For lead \( +2, \) for tin +4


One mole of an organic compound requires 0.5 moles of oxygen to produce a carboxylic acid. The compound may
be:
A. alcohol
B. ether
c. ketone
D. aldehyde


Pick out the mixture from the following.
A. water
B. Oxygen
c. Carbon dioxide
D. Air


Amniotes include
A. Fishes, reptiles and amphibians
B. Amphibians, birds and reptiles
C. Birds, reptiles and mammals
D. Amphibians, reptiles and mammals


A quarter disc of radius \( R \) and mass \( m \)
is rotating about the axis \( O O^{\prime} \)
(perpendicular to the plane of the disc)
as shown. Rotational kinetic energy of
the quarter disc is
\( A \)
в.
c. \( \frac{1}{8} m R^{2} \omega^{2} \)
\( D \)


\( K_{2} C r_{2} O_{7} \) react with hydrazine to form
product. The oxidation state of \( C r \) in the
product will be:
\( A \cdot+4 \)
B. +3
\( c .+5 \)
D. +2


What is the effect on chemical and
physical properties of water when temperature is changed?
A. Chemical properties of water remain same but the physical state changes with change in temperature
B. Chemical properties of water change with change in temperature but physical properties remain same
C. There is no effect on chemical or physical properties of water when temperature is changed
D. Both chemical and physical properties of water change with change in temperature


Assertion
Cyclopentadienyl anion is aromatic in
nature.
Reason
Cyclopentadienyl anion has \( \operatorname{six} \pi \)
electrons.
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 is a true statement for the acids of phosphorus:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} ? \)
A. The order of their acidic strength is \( H_{3} P O_{4}> \) \( H_{3} P O_{3}>H_{3} P O_{2} \)
B. All of them are reducing in nature.
c. All of them are tribasic acids
D. The geometry of phosphorus is tetrahedral in all the three


(B) and (C) are:
A \( \cdot C a O, C a(O H)_{2} \)
в. \( C a(O H)_{2}, C a C O_{3} \)
c. \( \operatorname{CaCO}_{3}, \operatorname{Ca}(O H)_{2} \)
D. \( C a(O H)_{2}, C a O \)


Choose an incorrect statement.
\( \mathbf{A} \cdot \operatorname{In} C O_{2} \) molecule both \( \pi \) -bond's plane are
perpendicular of each other
B. \( C O_{2} \) is gas while \( S i O_{2} \) is solid
C \( \cdot \ln P_{4} \) molecule there are total six \( P-P \) linkage
D. In \( S_{8} \) molecule there are 16 lone pairs while in \( P_{4} \) molecule there are 8 lone pairs


connected in a circuit as shown in
figure. The galvanometer is kept
undeflected always. Here \( A B=l . \) When
the switch \( S \) is connected to point \( S_{1} \)
\( B P=x_{1} \) and when the switch \( S \) is
connected to point \( S_{2}, B P=x_{2} . \) Here
the ratio of emf's of the two batteries,
i.e., \( \varepsilon_{1} / \varepsilon_{2} \) equal/s:
\( \mathbf{A} \cdot x_{1} / x_{2} \)
B. \( x_{2} / x_{1} \)
c. \( \frac{\left(l-x_{1}\right)}{\left(l-x_{2}\right)} \)
D. \( \frac{\left(l-x_{2}\right)}{\left(l-x_{1}\right)} \)


A body is \( 1.8 m \) tall can see his image in a plane mirror fixed on a wall. His eyes
are \( 1.6 m \) from the floor level. The
minimum length of the mirror to see his full image is
A. \( 0.9 m \)
B. \( 0.85 m \)
\( c .0 .8 m \)
D. can't be determined


Why is the red colour used as a sign of
danger?


Two independent events are always mutually exclusive, If this is true enter
1, else enter 0
A. True
B. False


Which of the following will react with sodium metal?
A. Ethanol
B. Ethanal
c. Ethene
D. Ethane


Represent \( \frac{7}{4} \) on the number line.


\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { Compound } & \text { Uses }\end{array} \)


Consider the following anions.
When attached to \( s p^{3-} \) hybridized
carbon, their leaving group ability in nucleophilic substitution reactions
decreases in the order.
(II)
A. \( I>I I>I I I>I V \)
В. \( I>I I>I V>I I I \)
c. \( \quad I V>I>I I>I I I \)
D. \( I V>I I I>I I>I \)


Select correct statement for 50ml 0.1M
\( \boldsymbol{H}_{2} \boldsymbol{A}(\boldsymbol{a} \boldsymbol{q} .) \) solution
\( \boldsymbol{K}_{\boldsymbol{a}_{1}}=\mathbf{1 0}^{-\mathbf{5}} ; \boldsymbol{K}_{\boldsymbol{a} \mathbf{2}}=\mathbf{1 0}^{-\mathbf{8}} \)
\( \mathbf{A} \cdot\left[H^{+}\right]=2\left[A^{2-}\right] \)
B. pH of 0.1M \( H_{2} A \) solution is 3
C. In above \( H_{2} A \) solution when 5 milimoles of NaHA are added then pH increases by 2 units
D. 50ml of 0.1M NaOH required to neutralised completely 50ml of 0.1M \( H_{2} A \) solution


A small object of mass \( m \) is attached to a light string which passes through a hollow tube. The tube is hold by one hand and the string by the other. The object is set into rotation in a circle of
radius \( R \) and velocity \( v \). The string is
then pulled down, shortening the radius of path to \( r . \) What is conserved?
A. Angular momentum
B. Linear momentum
c. Kinetic energy
D. None of these


ABCD is a rectangle. If \( A B P \) and \( B C Q \) are
equilateral triangle, \( \angle P B Q=\dots \)
A \( \cdot 65 \)
B. 75
\( c \cdot 60 \)
D. \( 90^{\circ} \)


A steel wire of length \( 2 \mathrm{m} \) is hanging from a rigid horizontal support. How much energy is stored in it when a load
of 5 kg is suspended on it? If the load is
increased to 10 kg then by how much the energy stored will increase? \( (Y= \)
\( 2 \times 10^{11} N / m^{2}, \) area of cross-section \( = \)
\( \left.10^{-6} m^{2}\right) \)


Find variance for the following data:
\( \begin{array}{lllll}\text { Wages } & \begin{array}{l}125- \\ 175\end{array} & \begin{array}{l}\text { 175- } \\ 225\end{array} & \begin{array}{l}\text { 225- } \\ 275\end{array} & \begin{array}{l}\text { 275- } \\ 325\end{array}\end{array} \)
workers 2 १९ 14
A . 7935.69
в. 7935.56
c. 7835.89
D. 7835.16


Find the value of limit
\( \lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .-3 \)
D.


Solve graphically the linear inequalities \( 2 x+3 y \leq 7, x+2 y \leq 4 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
If \( z=6 x+5 y \) is the objective function
find its maximum value.


A rectangular coil having 60 turns and area of \( 0.4 m^{2} \) is held at right angles to a uniform magnetic field of flux density
\( \mathbf{5} \times \mathbf{1 0}^{-5} \mathbf{T} . \) Calculate the magnetic flux
passing through it.


A man starts from \( O \) moves 500 m turns
by \( 60^{\circ} \) and moves \( 500 m \) again turns by
\( 60^{\circ} \) and moves \( 500 m \) and so on. Find
the displacement after
\( (i) 5 \) th turn \( ,(i i) \) 3rd turn.
A . \( -500 m, 1000 m \)
в. \( 500 m, 500 \sqrt{3} m \)
c. \( 1000 m, 500 \sqrt{3} m \)
D. none of these


If \( \mathbf{A}=(-\mathbf{1}, \mathbf{6}, \mathbf{6}), \mathbf{B}=(-\mathbf{4}, \mathbf{9}, \mathbf{6}), \mathbf{G}= \)
\( \frac{1}{3}(-5,22,22) \) and \( G \) is the centroid of
the \( \Delta A B C \) then the name of the
triangle \( \mathbf{A B C} \) is
A. an isosceles triangle
B. a right angled triangle
c. an equilateral triangle
D. a right-angled isosceles triangle


How many pairs of contrasting characters in pea were chosen by
Mendel?
A . 3
B. 5
\( c \cdot 7 \)
D.


\( |f| z_{1}|=2,| z_{2}|=3,| z_{3} \mid=4 \) and \( \mid z_{1}+ \)
\( z_{2}+z_{3} \mid=5, \) then \( \mid 4 z_{2} z_{3}+9 z_{3} z_{1}+ \)
\( \mathbf{1 6 z}_{1 \mathbf{z}_{2}} \mid= \)
A . 20
B. 24
\( c \cdot 48 \)
D. 120


What is a motion?


Which of the following oxides is most
acidic?
A. \( A l_{2} O_{3} \)
в. \( \operatorname{si} 0_{2} \)
c. \( P_{2} O_{5} \)
D. \( S O_{3} \)


To know the resistance \( G \) of a
galvanometer by half deflection method,
a battery of emf \( V_{E} \) and resistance \( R \) is
used to deflect the galvanometer by
angle \( \theta . \) If a shunt of resistance \( S \) is
needed to get half deflection the \( G, R \) and \( S \) are related by the equation:
A. \( S(R+G)=R G \)
B. \( 2 S(R+G)=R G \)
\( \mathrm{c} \cdot 2 G=S \)
D. \( 2 S=G \)


If matrices \( A \) and \( B \) anticommute then
\( \mathbf{A} \cdot A B=B A \)
B. \( A B=-B A \)
c \( \cdot(A B)=(B A)^{-1} \)
D. None of these


Find the 7 th term from the end in the
expansion of \( \left(2 x^{2}-\frac{3}{2 x}\right)^{8} \)


\( \boldsymbol{I} \boldsymbol{f} \quad \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \quad \) then
A. \( \frac{d y}{d x} \) doesn't exist at \( x=1 \)
B. \( \frac{d y}{d x}=0 \quad \) when \( \quad x=1 \)
c. \( \frac{d y}{d x}=\frac{1}{2} \quad \) when \( \quad x=e \)
D. None of these


The work done to rotate the electric dipole
from the equilibrium position by \( 180^{0} \) is :
A. \( 3 \times 10^{-23} J \)
В. \( 6 \times 10^{-23} J \)
c. \( 12 \times 10^{-23} J \)
D. Zero


Which of the following forms unstable
diazonium ion when treated with
\( N a N O_{2} \) in aqueous \( H C l ? \)
A. p-nitrotoluene
B. ethylamine
c. N,N-dimethyl aniline
D. All of the above


A weakly damped harmonic oscillator is executing resonant oscillations. The phase difference between the oscillator
and the external periodic force is:
A. zero
B . \( \pi / 4 \)
c. \( \pi / 2 \)
\( D \)


\( \int_{0}^{1} \frac{d x}{x \sqrt{x}} \)
\( \mathbf{A} \cdot 2 \)
B . -2
\( \mathbf{c} \cdot 1 \)
D. 3


Raffinose on hydrolysis does not give :
A. Glucose
B. Ribose
c. Fructose
D. Galactose


Divide 18 into 2 parts such that their product is 81
A. 9,-9
в. 3,27
c. \( 9, \frac{1}{9} \)
D. 9,9


What happen with the rate of the reaction when the frequency and the number of effective collisions between
reacting particles increases?
A. Increases
B. Decreases
c. Remains the same
D. Approaches zero
E. None of the above


The function of counter current
mechanism is performed by
I. Gills
II. Kidneys
III. Intestines
IV. Lungs
A. I and III only
B. Il and IV only y
c. ।, ॥, and IV
D. I, II, III, and IV


Assertion
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{3}^{+}-\boldsymbol{C H}_{3} \boldsymbol{N H}_{2} \) is a conjugate
acid base pair.
Reason
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}, \boldsymbol{O} \boldsymbol{H}^{-} \) is a conjugate acid base
pair.
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 amount of oxygen transported by a litre of oxygenated blood to tissues of a person undergoing severe exercise will
be
A . \( 150 \mathrm{ml} \)
B. \( 200 m l \)
\( c .15 m l \)
D. \( 5 m l \)


Where and when was the world's first oil
well dugo?
\( A \cdot \) in 1959 AD in Pennsylvania (USA).
B. in 1859 AD in Pennsylvania (USA).
C. in 1849 AD in Pennsylvania (USA).
D. in 1989 AD in Pennsylvania (USA)


The straight line which is parallel to \( x \) axis and crosses the curve \( y=\sqrt{x} \) at an
angle of \( 45^{0} \) is
A \( \cdot x=\frac{1}{4} \)
в. \( y=\frac{1}{4} \)
c. \( y=\frac{1}{2} \)
D. \( x=\frac{1}{2} \)


Two resistance thermometers are
made, one of the platinum wire and the other of germanium wire. The resistance of both the thermometers
are equal at room temperatures. Now the two resistance wires are connected
to a battery. The two resistance wire
are heated to \( 100^{\circ} \mathrm{C} \). The potential drop
in the two resistance is measured.
Which of the following statements is
correct?
A. The potential drop across the platinum wire is equal to the potential drop across the germanium wire
B. The potential drop across platinum wire is greater than that across germanium
C. The potential drop across the platinum wire is less than that across germanium
D. The nature of the potential drop can be ascertained unless the magnitude of the current is known


\( \boldsymbol{C} \cdot \boldsymbol{P}=\boldsymbol{R} \boldsymbol{s} .16000, \boldsymbol{S} \cdot \boldsymbol{P}=\boldsymbol{R} \boldsymbol{s} .18500, \boldsymbol{x} \% \)
\( =\frac{x}{100}, \) Profit \( \% \)
A . \( 25 \% \) \%
в. \( _{15} \frac{1}{4} \% \)
c. \( 25 \frac{1}{8} \% \)
D. \( _{15} \frac{5}{8} \% \)


The following acids have been arranged in order of decreasing acid strength. Identify the correct order \( \mathrm{ClOH}(\mathrm{l}) \) \( \mathrm{BrOH}(\mathrm{II}), \mathrm{IOH}(\mathrm{III}) \)
B. ॥>1>111
\( c \cdot\|\mid>\|>1 \)


In a primary coil \( 5 A \) current is flowing
on 220 volts. If the secondary coil produces \( 2200 V \) voltage. Then the
ratio of number of turns in secondary coil and primary coil will be
\( \mathbf{A} \cdot 1: 10 \)
B. 10: 1
c. 1: 1
D. 11: 1


soil holds plenty of air.
A. Sandy
B. Clayey
c. silt
D. Both B and C


At room temperature \( \left(27.0^{\circ} \mathrm{C}\right) \) the
resistance of a heating element is \( 100 \Omega \) What is the temperature of the element if the resistance is found to be
\( 117 \Omega, \) given that the temperature coefficient of the material of the
resistor is \( 1.70 \times 10^{-4} C^{-1} \)


The general value of \( \theta \) satisfying the equation \( \sin ^{2} \theta-3 \cos \theta+\frac{3}{4}=0 \)
A \( \cdot 2 n \pi \pm \frac{\pi}{3} \)
В \( \cdot 2 n \pi \pm \frac{\pi}{6} \)
\( \mathbf{c} \cdot 2 n \pi \pm \frac{\pi}{4} \)
D. None


Sound waves travel at \( 350 m s^{-1} \)
through warm air and at \( 3500 m s^{-1} \)
through brass. The wavelength of a
\( \mathbf{7 0 0} \boldsymbol{H} z \) acoustic wave as it enters
brass from warm air:
A. decrease by a factor 10
B. increase by a factor 20
c. increase by a factor 10
D. decrease by a factor 20


HOCl\( (a q) \) is the molecule that kills bacteria wen chlorine is added to water
The following reaction produces this
molecule
\( \boldsymbol{C l}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \boldsymbol{H} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
Which statement about this reaction is
correct?
A. Chlorine is both oxidised and reduced
B. Chlorine is oxidised but not reduced
c. Hydrogen is both oxidised and reduced
D. Hydrogen is oxidised but not reduced


Position-time graph is shown, which is
a semicircle from \( t=2 \) to \( t=8 \) sec.
Find time \( t \) at which the instantaneous
velocity, is equal to average velocity
over first \( t \) seconds
A . \( 4.8 \mathrm{sec} \)
B. 3.2 sec
\( c .2 .4 \mathrm{sec} \)
D. 5 sec


If element with principal quantum
number \( n>4 \) were not allowed in
nature, the number of possible elements would be
\( \mathbf{A} \cdot 60 \)
B. 32
\( c \cdot 4 \)
D. 64