If the line \( x=\alpha \) divides the area of
region \( \boldsymbol{R}= \)
\( \left\{(x, y) \in R^{2}: x^{3} \leq y \leq x, 0 \leq x \leq 1\right\} \)
into two equal parts, then This question has multiple correct options
A \( \cdot 2 \alpha^{4}-4 \alpha^{2}+1=0 \)
B. \( \alpha^{4}+4 \alpha^{2}-1=0 \)
c. \( _{0<\alpha \leq \frac{1}{2}} \)
D. \( \frac{1}{2}<\alpha<1 \)


A particle has potential energy dependent on its position on the \( x \) axis,
represented by the function \( U(x)= \)
\( e^{2 x}+1 \) for all real values of \( x \) where
\( U(x) \) and \( x \) are given in standard units.
The force it feels at position \( x=1 \) is
closest to
A. \( 7.39 N \)
B. \( 8.39 N \)
c. \( -8.39 N \)
D. \( 14.8 N \)
E. \( -14.8 N \)


\( \frac{\sin i}{\sin r}= \) constant. This is
A. Newton's law
B. Snell's law
c. Both
D. None


The incorrect statement is:
A. all the collisions between reactant molecules do not lead to a chemical change
B. a zero order reaction proceeds at a constant rate independent of concentration or time
C. fast reactions have low activation energies
D. in a first order reaction, the reaction ideally takes finite time to be completed


When an air bubble moves up from the
bottom of a lake
a) velocity decreases and becomes zero
b) acceleration increases and becomes
zero
c) velocity increases and becomes
constant
d) acceleration decreases and becomes
zero
\( A \cdot a, d \) are correct
B. a, b are correct
c. \( c, \) d are correct
D. c is correct


If the quotient obtained on dividing
\( x^{4}+10 x^{3}+35 x^{2}+50 x+29 \) by \( (x+ \)
4) is \( x^{3}-a x^{2}+b x+6 \) then find \( a \) and
b. Also find the remainder


\( (x, y) \) and \( (p, q) \) are two ordered pairs.
Find the values of \( x \) and \( p, \) if \( (3 x- \)
\( \mathbf{1}, \mathbf{9})=(\mathbf{1 1}, \boldsymbol{p}+\mathbf{2}) \)
A. \( x=4, p=9 \)
В. \( x=6, p=7 \)
c. \( x=4, p=5 \)
D. \( x=4, p=7 \)


Similarity between fish and tadpole is
A . Legs
B. Fins
c. Lateral line
D. Scales


Modern vacuum pumps can evacuate a
vessel down to a pressure of \( 4.0 \times \) \( 10^{-15} a t m . \) at room temperature (300
K). Taking \( \boldsymbol{R}= \)
\( 8.3 K J^{-1} \) mole \( ^{-1}, 1 a t m=10^{5} \) Pa and
\( N_{\text {Avogradro}}=6 \times 10^{23} \)mole\( ^{-1}, \) the mean
distance between molecules of gas in an evacuated vessel will be of the order
of
A. \( 0.2 \mu m \)
B. \( 0.2 \mathrm{mm} \)
c. \( 0.2 \mathrm{cm} \)
D. 0.2 nm


\( x=5, y=2 \) is a solution of the linear
equation
A \( .5 x+y=7 \)
в. \( 5 x+2 y=7 \)
c. \( x+y=7 \)
D. \( x+2 y=7 \)


If \( \boldsymbol{x} \cos \boldsymbol{\alpha}+\boldsymbol{y} \sin \boldsymbol{\alpha}=\boldsymbol{x} \cos \boldsymbol{\beta}+ \)
\( \boldsymbol{y} \sin \beta=2 a(0<\alpha, \beta \pi / 2), \) then
This question has multiple correct options
A \( \cdot \cos \alpha+\cos \beta=\frac{4 a x}{x^{2}+y^{2}} \)
B. \( \cos \alpha \cos \beta=\frac{4 a^{2}-y^{2}}{x^{2}+y^{2}} \)
c. \( \sin \alpha+\sin \beta=\frac{4 a y}{x^{2}+y^{2}} \)
D \( \sin \alpha \sin \beta=\frac{4 a^{2}-x^{2}}{x^{2}+y^{2}} \)


What is the sum of all 5 digit numbers which can be formed with digits 0,1,2
3, 4 without repetition
A. 2599980
B. 2679980
c. 2544980
D. 2609980


An organic compound containing \( - \) COOH functional group is called:
A. aldehyde
B. ketone
c. amide
D. carboxylic acid


Choose the correct answer from the
alternatives given. The amplitude of an electromagnetic wave in vaccum is doubled with no
other changes made to the wave. As a result of this doubling of the amplitude, which of the following statement is
correct?
A. The frequency of the wave changes only
B. The wave length of the wave changes only
c. The speed of the wave propagation changes only
D. None of the above is correct


For the equilibrium at \( 298 \mathrm{K} \) \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) ; G_{N_{2}}^{\ominus}_{O_{4}}= \)
\( 100 k J m o l^{-1} \) and \( G_{N O_{2}}^{\ominus}=50 k J m o l^{-1} \)
If 5 mol of \( N_{2} O_{4} \) and 2 moles of \( N O_{2} \) are taken initially in one litre container
than which statement are correct
This question has multiple correct options
A. reaction proceeds in forward direction
B . \( K_{c}=1 \)
c. \( \Delta G=-0.55 k J, \Delta G^{\ominus}=0 \)
D. At equilibrium \( \left[N_{2} O_{4}\right]=4.84 M \) and \( \left[N O_{2}\right]=0.212 M \)


Identify the incorrect statement
A. The \( S-S-S \) bond angles in the \( S_{8} \) and \( S_{6} \) rings are
the same
B. Rhombic and monoclinic sulphur have \( S_{8} \) molecules
\( \mathrm{C} \cdot S_{2} \) is paramagnetic like oxygen
D. \( S_{8} \) ring has a crown shape


When the reactor shuts down why does
it require cooling?
A. To cool the reactor from chain reaction
B. To cool the reactor from fission reaction
c. Both (1) and (2)
D. None of these


In the given figure three lines \( \overrightarrow{A B}, \overrightarrow{C D} \)
and \( \widehat{E F} \) intersecting at \( 0 . \) Find the values of \( x, y \) and \( z \) it is being given
that \( \boldsymbol{x}: \boldsymbol{y}: \boldsymbol{z}=\boldsymbol{2}: \boldsymbol{3}: \boldsymbol{5} \)


The differential equation by eliminating \( A \) and \( B \) from \( y=A x^{3}+B x^{2} \) is
\( ^{\mathbf{A}} \cdot_{x^{2}}\left(\frac{d^{2} y}{d x^{2}}\right)+4 x\left(\frac{d y}{d x}\right)+6 y=0 \)
в. \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-4 x\left(\frac{d y}{d x}\right)-6 y=0 \)
c. \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-4 x\left(\frac{d y}{d x}\right)+6 y=0 \)
D \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-5 x\left(\frac{d y}{d x}\right)+6 y=0 \)


Select the correct option:Fermentation
is represented by the equation
\( \mathbf{A} \cdot C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+6 H_{2} O+686 K c a l \)
B \( \cdot C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+59 K c a l \)
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \frac{\text {Light}}{\text {Chlorophyll}} C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
D. \( 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)


Find the derivative of \( e^{x}+e^{y}=e^{x+y} \)
\( \mathbf{A} \cdot-e^{x-y} y^{y} \)
B . \( e^{x-y} \)
\( \mathbf{c} \cdot-e^{y-x} \)
D. \( e^{y-x} \)


By suspending a mass of \( 0.50 \mathrm{kg} \), a spring is stretched by \( 8.20 \mathrm{m} . \) If a mass of \( 0.25 \mathrm{kg} \) is suspended, then its period of oscillation will be:
(Take \( g=10 m s^{-2} \) )
A . 0.137 s
B. 0.328 s
c. 0.628 s
D. 1.000


List the coordinates of the vertices of
the larger shape


A smooth rubber cord of length \( l \) whose
coefficient of elasticity is \( k \) is
suspended by one end from the point \( \boldsymbol{O} \) (figure shown above). The other end is fitted with a catch \( B . \) A small sleeve \( A \)
of mass \( m \) starts falling from the point
O. Neglecting the masses of the thread and the catch, find the
maximum elongation of the cord.


How many different words can be
formed from the letters of the word
GANESHPURI when:
The letter \( P \) and \( I \) respectively occupy
the first and last places.


A man standing on the edge of a cliff throws a stone straight up with initia speed \( u \) and then throws another stone
straight down with same initial speed \( u \)
from the same position. Find the ratio of speeds, the stones would have attained
when they hit the ground at the base of the cliff?
A . 2: 1
B. 1: 2
c. 1: 1
D. 3: 1


Prove: \( \tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)= \)
\( \frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x,-\frac{1}{\sqrt{2}} \leq x \leq 1 \)
[Hint: \( p u t x=\cos 2 \theta] \)


Explain the importance of fossils in organic evolution.


Checking of radiating heat by
atmospheric dust, \( 0_{3}, \mathrm{CO}_{2} \) and water vapours is
A. Greenhouse effect
B. Solar effect
c. Ozone layer effect
D. Radioactive effect


In damped vibrations, as time progresses, amplitude of oscillation
A. decreases
B. increases
c. Remains same
D. Data insufficient


A ball falling in a lake of depth \( 200 \mathrm{m} \) shows \( 0.1 \% \) decrease in its volume at
the bottom. What is the Bulk modulus
of the ball material? (Take density of water \( =1000 \mathrm{kg} / \mathrm{m}^{3} \) ):
A \( \cdot 19.6 \times 10^{8} N / m^{2} \)
В. \( 19.6 \times 10^{-10} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{-8} N / m^{2} \)


A solid sphere of radius \( R \) has a charge
\( +2 Q . \) A hollow spherical shell of radius
\( 3 R \) placed concentric with the first
sphere has net charge - \( Q \). Calculate
the potential difference between the
spheres:
\( ^{A} \cdot \frac{Q}{3 \pi \varepsilon_{0} R} \)
в. \( \frac{2 Q}{3 \pi \varepsilon_{\Omega} R} \)
c. \( \frac{3 Q}{\pi \varepsilon_{0} R} \)
\( D \)


As waves propagate through a medium,
they transport energy. We can easily
demonstrate this by
This question has multiple correct options
A. hanging an object on a stretched string and then sending a pulse down the string
B. throwing a stone into a pond
C . compressing a spring and releasing it.
D. None of these.


Which of the following is not a function of Iymph?
A. Supplies oxygen and prevents spreading of infections
B. Returns proteins to the bloodd
c. Absorbs vitamins and minerals
D. None of the above


When a body is placed on a surface, the body exerts a force downwards
A. Move then the weight of the body
B. Less than the weight of the body
c. Equal to its weight on the surface
D. All


A system of \( 100 k g \) mass undergoes a process in which its specific entropy
increases from \( 0.3 k J g^{-1} K^{-1} \) to
\( 0.4 k J g^{-1} K^{-1} . \) At the same time, the entropy of the surrounding decreases from \( 80 k J K^{-1} \) to \( 75 k J K^{-1} . \) Find the
\( (\Delta S)_{\text {universe}} \) in \( k J K^{-1} \)


A storage cell is charged by 5 amp d.c. for 18 hours.lts strength after charging will be
\( \mathbf{A} \cdot 18 A H \)
в. \( 5 A H \)
c. \( 90 A H \)
D. \( 15 A H \)


The given figure illustrates the changes in lung volume during the process of breathing.The change from II to III
indicates the
A. movement of diaphragm away from the lungs
B. expansion of the thoracic cavity
c. movement of air out of the lungs
D. expansion of ribs.


In N-type semiconductors, holes are:
A. majority carriers
B. minority carriers
\( c . \) absent
D. none of these


The wave motion of electron in a Bohr's
orbit of hydrogen is as shown in
diagram. The potential energy of
electron in the given orbit of hydrogen
atom is:
A \( .-3.4 \mathrm{eV} \)
B. +3.4 ev
\( \mathbf{c} .-3.02 \mathrm{eV} \)
D. -1.51 ev


What makes the boiling point of water abnormally high as compared to similar compounds?
A. Van der Waals forces
B. Hydrogen bonding
c. Polar covalent bonding
D. Dipole insulation


\( P \) is a point moving with constant speed \( 10 m / s \) such that its velocity
vector always maintains an angle \( 60^{\circ} \)
with line \( O P \) as shown in figure \( (O \) is a fixed point in space). The initial distance between \( O \) and \( P \) is \( 100 m \).
After what time shall \( P \) reach \( O \)
A . \( 10 s \)
B. \( 15 s \)
c. \( 20 s \)
D. \( 20 \sqrt{3} s \)


A gas cylinder containing cooking gas
can withstand a pressure of 14.9 atm. The pressure guage of the cylinder
indicates 12 atm at \( 27^{\circ} \mathrm{C} \). Due to
sudden fire in the building, its temperature stats rising. At what temperature cylinder will explode?


Biotic community along with its interacting physical environment comprises
A. Phytosociology
B. Phytogeography
c. Ecosystem
D. Ecology


\( \underbrace{k} \)


Where do you found ligament in our body?


Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-\left(1-2 a^{2}\right) x+\left(1-2 a^{2}\right)=0 . \) Under
what condition does the given equation have real roots.
A \( \cdot a^{2}<\frac{1}{2} \)
B. \( a^{2}>\frac{1}{2} \)
\( c \cdot a^{2} \leq \frac{1}{2} \)
D. \( a^{2} \geq \frac{1}{2} \)


The most efficient precursor of ethylene
is
A. Adenine
B. Thiocarbarnate
c. zeatin
D. Methionine


Find the acceleration of the moon with
respect to the earth from the following
data:
Distance between the earth and the
moon \( =3.85 \times 10^{5} \) and the time taken
by the moon to complete one revolution around the earth \( =27.3 \) days.


If a point lies at a distance \( ^{\prime} x^{\prime} \) from the
mid point of the dipole, the electric potential at this point is proportional to
A \( \cdot \frac{1}{x^{2}} \)
B. \( \frac{1}{x^{3}} \)
c. \( \frac{1}{x^{4}} \)
D. \( \frac{1}{x^{3 / 2}} \)


Which of the following is the pribnow
box?
A . 5' TATAAT 3
B. 5' TAATTAT 3
c. \( 5^{\text {' }} \) AATAAT \( 3^{\text {' }} \)
D. 5' ATATTA 3'


\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{5}), \boldsymbol{B}(\mathbf{5}, \mathbf{7}, \mathbf{9}) \) and \( \boldsymbol{C}(\mathbf{3}, \mathbf{2},-\mathbf{1}) \) are
given three points \( A \) unit Vector normal
to the plane of the triangle \( A B C \)
A \( \cdot \frac{15 \bar{i}+16 \bar{j}-5 \bar{k}}{\sqrt{506}} \)
B. \( \frac{-15 \bar{i}+16 \bar{j}-5 \bar{k}}{\sqrt{506}} \)
c. \( \frac{-15 \bar{i}+16 \bar{j}+5 \bar{k}}{\sqrt{506}} \)
D. \( \frac{\bar{i}+\bar{j}+\bar{k}}{\sqrt{506}} \)


A point charge \( q \) is placed at \( O \) as shown in the figure. Is \( V_{P}-V_{Q} \) positive or negative when a)
\[
\boldsymbol{q}>\mathbf{0} \text { b) } \boldsymbol{q}<\mathbf{0} ?
\]
Justify your answer.


Explain the use of P-N junction diode as
full wave rectifier on the basis of the
following points.
(i) Labelled circuit diagram
(ii) Working method
(iii) Graph between input and output potential with the variation of time.


Assertion
A mixture of o- nitrophenol and \( p \) nitrophenol can be separated by steam distillation.
Reason
p-nitrophenol is steam volatile whereas o-nitrophenol is not steam volatile.
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 power rating of an electric motor
that draws a current of \( 3.75 A \), when
operated at \( 200 V \), is nearly
\( \mathbf{A} \cdot 54 W \)
в. \( 1 h p \)
c. \( 500 W \)
D. \( 800 W \)


If \( \frac{3}{2}+y^{3}=3 a x y, \) then find \( \frac{d y}{d x} \)


toppr
-oGıN
Q Type your question_
Help him by completing the following
table.
Number of spokes 10
Angle between pair of consecutive
spokes (in degrees)
(i) Are the number of spokes and the
angles formed between the pairs of
consecutive spokes in inverse
proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with
15 spokes
(iii) How many spokes would be needed, if the angle between a pair of
consecutive spokes is \( 40 ? \)


Name the waves which are used in
'SONAR' to find the depth of a sea. State
one property of waves for their use.


For a cell, a graph is plotted between the potential difference \( V \) across the
terminals of the cell and the current \( I \)
drawn from the cell (see Figure). The
emf and the internal resistance of the
cell are \( E \) and \( r, \) respectively. Then :
A \( . E=2 V, r=0.5 \Omega \)
B. \( E=2 V, r=0.4 \Omega \)
c. \( E>2 V, r=0.5 \Omega \)
D. \( E>2 V, r=0.4 \Omega \)


Two long current carrying thin wires, both with current \( I \), are held by
insulating threads of length \( L \) and are in equilibrium as shown in the figure, with threads making an angle ' \( \boldsymbol{\theta}^{\prime} \) with
the vertical. If wires have mass \( \lambda \) per
unit length then the value of \( I \) is \( :(g= \)
gravitational acceleration)
A \( \cdot 2 \sqrt{\frac{\pi g L}{\mu_{0}} \tan \theta} \)
B. \( 2 \sin \theta \sqrt{\frac{\pi \lambda g L}{\mu_{0} \cos \theta}} \)
c. \( \sin \theta \sqrt{\frac{\pi \lambda g L}{\mu_{0} \cos \theta}} \)
D. \( \sqrt{\frac{\pi \lambda g L}{\mu_{0}}} \tan \theta \)


The amplitude of a particle in SHM is \( 5 \mathrm{cms} \) and its time period is \( \pi . \) At a displacement of \( 3 \mathrm{cm} \) from its mean
position the velocity in cm/sec will be:
\( A \cdot 8 \)
B. 12
\( c \cdot 2 \)
D. 16


The fraction \( \frac{x}{y} \) is altered by decreasing
\( x \) by 25 per cent and increasing \( y \) by 25 percent. The new fraction is what
percent less than the original?
A . 35
B. 40
\( c \cdot 42 \)
D. 45


Under 3 atm, 12.5 litre of a gas weighs
15 gm. What will be the average speed of gaseous molecules?
A \( \cdot 8.028 \times 10^{4} \mathrm{cm} / \mathrm{sec} \)
B. \( 6.028 \times 10^{2} \mathrm{cm} / \mathrm{sec} \)
c. \( 8.028 \times 10^{5} \mathrm{cm} / \mathrm{sec} \)
D. \( 6.028 \times 10^{4} \mathrm{cm} / \mathrm{sec} \)


Force vs Elongation graph of a wire is shown in the figure for two different
temperatures \( \boldsymbol{T}_{1} \& \boldsymbol{T}_{2}, \) then
A \( \cdot T_{1}=T_{2} \)
В \( \cdot T_{1}<T_{2} \)
\( c \cdot T_{1}>T_{2} \)
D. cannot be predicted


A bicycle can go up a gentle incline with
constant speed where the frictional force of ground pushing the rear whee
is \( F_{2}=4 N . \) With what force \( F_{1} \) must
the chain pull on the socket wheel if
\( R_{1}=5 \mathrm{cm} \) and \( R_{2}=30 \mathrm{cm} ? \)
\( A \cdot 4 N \)
В. 24 .
\( c .140 N \)
D. \( \frac{35}{4} \) N


On squared paper copy the triangle in
the following figure. In a given case
draw the line (s) of symmetry if any
identify the type of the triangle.


A trapezium has its non parallel sides congruent, then its opposite angles are
A. congruent
B. supplementary
c. complementary
D. None of these


force that is transmitted
through a string, rope, cable etc. When it is pulled by forces acting from opposite ends.
A. Normal reaction
B. Tension
c. Gravitation
D. All


The three cardinal points related to photosynthesis was proposed by
A. Blackman
B. Sachs
c. Roger slack
D. None of the above


Function of ciliary muscles is
A. To contract pupil when one move in sunlight
B. To keep valve in position
C . To rotate eye ball
D. To change shape of lens


A volume of gaseous hydrocarbon was exploded with an excess of oxygen. The
observed contraction was \( 2.5 V \), and on
treatment, with potash, there was a
further contraction of \( 2 V . \) What is the
molecular formula of the hydrocarbon?
A. \( C_{2} H_{6} \)
в. \( C_{3} H_{6} \)
c. \( C_{6} H_{10} \)
D. \( C_{2} H_{4} \)


Nephrons are connected with
A. Respiratory system
B. Nervous system
C. Circulatory system
D. Excretory system


Two forces each of \( 5 N \) act vertically upwards and downwards respectively
on the two ends of a uniform metre rule
which is placed at its mid-point as shown in the diagram. Determine the magnitude of the resultant moment of
these forces about the midpoint


An unnumbered wall clock shows time
\( 04: 25: 37, \) where ist term represents
hours, 2nd represents minutes and the last term represents seconds. What time will its image in a plane mirror show
\( \mathbf{A} \cdot 08: 35: 23 \)
B. \( 0 .: 35: 23 \)
c. 07: 35: 23
D. none of these


Which of the following oxide(s) of iron would be obtained on prolonged reaction of iron with steam?
A. FeO
в. \( F e_{2} O_{3} \)
\( \mathbf{c} \cdot F e_{3} O_{4} \)
D. \( F e_{2} O_{3} \) and \( F e_{3} O_{4} \)


MSH produced by the pars intermedia of pituitary causes in lower vertebrates
A. Darkening of skin
B. Light colouration of skin
c. Both A and B
D. None of the above


If \( f(x) \) be such that \( f(x)=\max \)
\( \left\{|2-x|, 2-x^{3}\right\}, \) then
This question has multiple correct options
A continuous \( \forall x \in R \)
\[
f(x) \text { is continuous } x \in R
\]
B. \( f(x) \) is differentiable \( \forall x \in R \)
c. \( f(x) \) is non-differentiable at one point only
D. \( f(x) \) is non-differentiable at 4 points only


A diode is connected in a circuit as
shown in the figure. The correct
statement related to this figure is?


Assertion
Bending a wire does not effect electrical
resistance
Reason
Resistance of wire is proportional to
resistivity of material
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


If carbon dioxide is withdrawn from the
biosphere, which organism would first experience negative effects?
A. Primary consumers
B. Producers
c. Secondary consumers
D. Tertiary consumers


At what speed does heat radiation travel? What path does it follow?


Explain the term lattice energy as applied to an ionic solid. Calculate the lattic energy of caesium chloride using the following data:
\[
\operatorname{Cs}(s) \rightarrow \operatorname{Cs}(g) \quad \Delta H=+79.9 \mathrm{kJ} \mathrm{mol}^{-1}
\]
\[
\begin{array}{ll}
\mathrm{Cs}(\mathrm{g}) \rightarrow \mathrm{Cs}^{-}(8) & \Delta H=+37+.05 \mathrm{kJ} \mathrm{mol}^{-1} \\
\mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{C} \mid(\mathrm{g}) & \Delta H=+241.84 \mathrm{kJ} \mathrm{mol}^{-1}
\end{array}
\]
\[
\mathrm{Cl}(\mathrm{g})+\mathrm{e} \rightarrow \mathrm{Cl}^{-}(\mathrm{g}) \quad \Delta H=-397.90 \mathrm{kJ} \mathrm{mol}^{-1}
\]
\[
\mathrm{Cs}(\mathrm{s})+\frac{1}{2} \mathrm{Cl}_{2} \rightarrow \mathrm{CsCl}(\mathrm{s}) \quad \Delta H=-623.00 \mathrm{kJ} \mathrm{mol}^{-1}
\]


Diameter of the largest sphere which can be carved out from a cube of side \( x \)
\( \mathrm{cm} \) is equal to This question has multiple correct options
A. one third of sum of all edges
B. One twelfth of sum of all edges
c. one half of sum of length of diagonals
D. \( \frac{1}{\sqrt{3}} \) times of length of any diagonal


A conductor behave as a super
conductor
A. Above critical temperature
B. At critical temperature
c. \( \operatorname{At} 100^{\circ} C \)
D. At boiling point of that metal


The curve amongst the family of curves, represented by the differential
equation, \( \left(x^{2}-y^{2}\right) d x+2 x y d y=0 \)
which passes through (1,1) is :
A. A circle with centre on the y-axis
B. A circle with centre on the x-axis
c. An ellipse with major axis along the y-axis
D. A hyperbola with transverse axis along the x-axis


The distance of the sun form the earth
is \( 1.5 \times 10^{11} \) and its diameter is \( 1.40 \times \)
\( 10^{9} m . \) The diameter of the image of the
sun formed by a lens of focal length \( 1 \boldsymbol{m} \)
is nearly:
A \( \cdot 1 \times 10^{-4} m \)
в. \( 1 \times 10^{-3} \mathrm{m} \)
c. \( 1 \times 10^{-2} m \)
D. \( 100 m \)


Days and nights are caused by
A. rotation of the Earth
B. revolution of the Earth
C. both rotation and revolution of the Earth
D. neither rotation nor revolution of the Earth


Two long conductors, separated by a
distance \( d \) carry currents \( I_{1} \) and \( I_{2} \) in
the same direction. They exert a force \( \boldsymbol{F} \)
on each other. Now the current in one of
them is increased to two times and
its direction is reversed. The distance is
also increased to \( 3 d \). The new value of
the force between them is:
\( \mathbf{A} \cdot-2 F \)
В. \( \frac{F}{3} \)
c. \( \frac{-2 F}{3} \)
D. \( \frac{-F}{3} \)


A particle is dropped from the top of the tower. During its motion it covers \( 9 / 25 \)
th part of the tower in the last one sec.
Find the height of the tower.


An excess of \( A g N O_{3} \) is added to
\( 100 m L \) of a \( 0.01 M \) solution of
dichlorotetraaquachromium (III) chloride. The number of moles of \( A g C l \) precipitated would be:
A. 0.001
B. 0.002
c. 0.003
D. 0.01


Match the columns
A. A-2, B-5, C-4, D-3, E-1
B. \( A-1, B-2, C-3, D-4, E-5 \)
c. \( A-3, B-4, C-5 \) \( D-1 \) \( E-2 \)
D. \( A-4, B-5, C-2, D-1 \)
1.E


Given that force \( F \) is given by, \( \boldsymbol{F}= \)
\( \boldsymbol{P t}^{-1}+\boldsymbol{Q} \boldsymbol{t}, \) where \( t \) is the time. The unit
of \( P \) is same as that of
A. velocity
B. acceleration
c. displacement
D. momentum


Assertion
Glycerol is purified by distillation under
reduced pressure.
Reason
Method of distillation under reduced
pressure is used to purify liquids having very high boiling points and those, which decompose at or below their boiling point.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Referring the figure given below, for \( \Delta P Q R \) and \( \Delta X Y Z, P Q=Y Z, Q R= \)
\( \boldsymbol{X} \boldsymbol{Z} \) and \( \angle \boldsymbol{Q}=\angle \boldsymbol{Z} . \) The value of \( \angle \boldsymbol{P} \) is
A \( \cdot 42^{\circ} \)
B . \( 75^{\circ} \)
\( c \cdot 63^{\circ} \)
D. cannot be determine


product (c)is.
\( A \)
B.
\( c \)
\( D \)


Use dimensional analysis to convertt 4.30 days to seconds. (Hint: Don't forget about the significant figures)
A. 258 seconds
B. 929,000 seconds
c. 15,500 seconds
D. 372,000 seconds
E. 6,190 seconds


Why is it essential to wash the
precipitate with water before estimating it quantitatively?


Which of the following phenomena does not come under macroscopic domain?
A. Phenomena at laboratory scales
B. Phenomena at terrestrial scales
c. Molecular and nuclear phenomena
D. Phenomena at astronomical scales


Pashmina a type of wool is obtained
from:
A . camel
B. goat
c. sheep
D. artificially


The focal length of a thin biconvex lens
is \( 20 \mathrm{cm} \). When an object is moved from
a distance of \( 25 \mathrm{cm} \) in front of it to \( \mathbf{5 0} \mathrm{cm}, \) the magnification of its image
changes from \( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{60} . \) The ratio
\( \boldsymbol{m}_{25} / \boldsymbol{m}_{50} \) is


Through a solution of \( C u S O_{4}, \) a current
of 3 amperes was passed for 2 hours. At cathode, \( 3 g \) of \( C u^{2+} \) ions were discharged. The current efficiency is :
[At. wt. of \( \boldsymbol{C u}=\mathbf{6 3 . 5} \) ]
A . \( 33.3 \% \)
B . \( 42.2 \% \) \%
c. \( 48.7 \% \)
D . 54.4 \%


\( \mathrm{ff} \mathbf{A}=\left[\begin{array}{lll}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \quad \) and
\( A B=I_{3}, \quad \) then \( \quad x+ \)
\( \boldsymbol{y} \quad \boldsymbol{i s} \quad \boldsymbol{e q u a l} \quad \boldsymbol{t o} \)


Two numbers are such that their sum
multiplied by the sum of their squares is 5500 and their difference multiplied
by the difference of the squares is 352 Then the numbers are?
A. Prime numbers only
B. Odd positive integers
c. Prime but not odd
D. odd but not prime


The minors and cofactors of -4 and 9 in
determinant \( \left|\begin{array}{ccc}-1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9\end{array}\right| \) are
respectively
A. 42,\( 42 ; 3,3 \)
В. -42,\( 42 ;-3,-3 \)
c. 42,\( -42 ; 3,-3 \)
D. 42,3: 42,3


f \( z=a+i b \) is a complex number such
that \( z=(a+i b)^{2} \) then
show that \( x^{2}+y^{2}=\left(a^{2}+b^{2}\right)^{2} \)


The pairs \( \bar{a}, \bar{b} \) and \( \bar{c}, \bar{d} \) each determine a plane. Then the planes are parallel if \( (\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \times(\overline{\boldsymbol{b}} \times \overline{\boldsymbol{d}})= \)
\( \mathbf{0} 2)(\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \cdot(\overline{\boldsymbol{b}} \times \overline{\boldsymbol{d}})=\mathbf{0} \)
\( (\bar{a} \times \bar{b}) \times(\bar{c} \times \bar{d})= \)
\( \mathbf{0} 4)(\bar{a} \times \bar{b}) \cdot(\bar{c} \times \bar{d})=0 \)


No net force acts on a rectangular coil
carrying a steady current when suspended freely in a uniform magnetic field.
A. True
B. False


Work function is the energy required
A. To excite an atom
B. To produce X-rays
C. To eject an electron just out of the surface
D. To explode the atom


A solid weights \( 500 \mathrm{N} \). Calculate the pressure extended by solid on surface if the area of contact is \( 100 \mathrm{cm} \) square.


2-Pentanol can be converted to 2-ethoxy
pentane by two paths. In path I, \( \boldsymbol{H}^{\oplus} \) is abstracted from 2-pentanol to form the
nucleophile while in path II, \( \boldsymbol{H}^{\oplus} \) is abstracted from ethanol. What is true
about the configuration at chiral \( C \) of 2
pentanol?
A. Retained in both paths
B. Retained in path I and Inverted in path I
c. Inverted in path I and Retained in path।
D. Inverted in both paths


A wire extends by 'I' on the application of load 'mg'. Then, the energy stored in it is :
A \( . m g l \)
в. \( \frac{m g l}{2} \)
\( c \cdot \frac{m g}{l} \)
D \( \cdot m g l^{2} \)


Given are three positive integers \( a, b \)
and \( c . \) Their greatest common divisor is
\( D ; \) their least common multiple is \( M \) Then, which two of the following statements are true?
(1) The product \( M D \) cannot be less
than abc
(2) The product \( M D \) cannot be greater
than abc
(3) \( M D \) equals \( a b c \) if and only if \( a, b, c \) are each prime
(4) \( M D \) equals \( a b c \) if and only if \( a, b, c \) are relatively prime in pairs (This means: no two have a common
factor greater than \( 1 . \)
\( \mathbf{A} \cdot 1,2 \)
в. 1,3
c. 1,4
D. 2,3
E .2,4


ff \( f(x+y)=f(x y) \) for all \( x, y, \in R, \) and
\( \boldsymbol{f}(\mathbf{2 0 0 3})=\mathbf{2 0 0 3}, \) then \( \boldsymbol{f}(\mathbf{2 0 0 0}) \) equals
A . 2003
B.
c. -2003
D. none of these


Synthetic soaps are superior to ordinary
Soaps because:
A. they are cheap
B. they need not boiling water to wash
C. they can be used even in hard water
D. all of the above


State whether the following sentence is always true, always false or ambiguous. Justify your answer. Makarasankranthi falls on a Friday.


\( \mathrm{CaCl}_{2} \) is preferred over \( \mathrm{NaCl} \) for clearing ice on roads on particularly in very cold countries. This is because:
A \( \cdot C a C l_{2} \) is not soluble in \( H_{2} O \) than \( N a C l \)
B . \( C a C l_{2} \) is hygroscopic but \( N a C l \) is not
c. eutectic mixture of \( C a C l_{2} / H_{2} O \) freezes at \( -55^{\circ} C \) while that of \( N a C l / H_{2} O \) freezes at \( -18^{\circ} C \)
D. \( N a C l \) makes the road slippery but \( C a C l_{2} \) does not


The following expression is a rational number. Find its value. \( \sqrt[3]{\mathbf{6} \sqrt{\mathbf{3}}+\mathbf{1 0}}-\sqrt[3]{\mathbf{6} \sqrt{\mathbf{3}}-\mathbf{1 0}} \)


The probability of electrons to be found
in the conduction band of an intrinsic
semiconductor at a finite temperature
A. decreases exponentially with increasing band gap
B. increases exponentially with increasing band gap
c. decreases with increasing temperature
D. is independent of the temperature and the band gap


A rectangular block is heated from \( 0^{\circ} C \)
to \( 100^{\circ} C \).
The percentage increase in its length is
\( 0.2 \% \).The percentage increase in its volume is:
A. \( 0.6 \% \)
B. \( 0.10 \% \)
\( c .0 .2 \% \)
D. \( 0.4 \% \)


Assertion
Chemicals added to foods for
increasing their life are called preservatives.
Reason
Natural sweeteners like sucrose and
artificial sweeteners like saccharin are
commonly used as food preservatives.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A particle of mass \( m \) moves on a straight line with its velocity varying with the distance travelled according to the equation \( \boldsymbol{v}=\boldsymbol{\alpha} \sqrt{\boldsymbol{x}}, \) where a is a
constant. Find the total work done by all the forces during a displacement from
\( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\boldsymbol{d} \)
A \( \cdot \frac{1}{2} m a^{2} b \)
B. \( \frac{1}{4} m a^{2} b \)
\( c \cdot m a^{2} b \)
D. \( 2 m a^{2} b \)


Write two distinguishing feature of nuclear forces.


Flash-lights make use of
A. convex lenses
B. concave lenses
c. both convex and concave lenses
D. no lenses at all


Assertion
\( C O \) is toxic.
Reason
CO forms complex with haemoglobin in the blood, and this complex is more stable than oxy-haemoglobin.
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 colour and state of phosphorus pentoxide is :
A. white crystalline solid
B. white amorphous liquid
c. blue crystalline
D. blue colour liquid


There are \( _{\text {- }-\text { - }-\text { - }} \) isotopes of hydrogen
A. 0
B.
\( c \cdot 2 \)
D.


Thickest cell wall is seen in ........ cell.
A. Sclerenchyma
B. Parenchyma
c. collenchyma
D. Both A and B


Among noble gases, only xenon reacts with fluorine to form stable xenon
fluorides, this is because xenon:
A. has the highest ionisation enthalpy
B. has the lowest ionisation enthalpy
c. has the highest heat of vapourisation
D. is the most readily available noble gas


In the set up shown, the two slits \( S_{1} \) and
\( S_{2} \) are not equidistant from the slit
S. The central fringe at 0 is then
A. always bright
B. always dark
C. either dark or bright depending on the position of
D. neither dark nor bright


\( F_{p p}, F_{n n} \) and \( F_{n p} \) are the nuclear forces
between proton-proton, neutron-neutron and neutron-proton respectively. Then relation between them is
\( \mathbf{A} \cdot F_{p p}=F_{n n} \neq F_{n p} \)
B . \( F_{p p} \neq F_{n n}=F_{n p} \)
\( \mathbf{c} \cdot F_{p p}=F_{n n}=F_{n p} \)
D \( \cdot F_{p p} \neq F_{n n} \neq F_{n p} \)


Sulphur molecule is:
A. diatomic
B. triatomic
c. tetraatomic
D. octa-atomic


In our society women are blamed for producing a female child. Choose the correct answer for sex determination in
humans due to
A. Some defect like aspermia in mann
B. Genetic make up of particular sperm which fertilizes the egg
c. Genetic make up of egg
D. Some defect in reproductive system of women


150 metre long train takes 10 seconds to pass a man who is going in the same
direction at the speed of \( 2 \mathrm{km} / \mathrm{hr} \). What is the speed of the train?
\( \mathbf{A} \cdot 52 \mathrm{km} / \mathrm{hr} \)
B. \( 56 \mathrm{km} / \mathrm{hr} \)
\( \mathbf{c} .84 \mathrm{km} / \mathrm{hr} \)
D. Data inadequate


State true or false:
The complex numbers \( \boldsymbol{z}=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) which
satisfy the equation \( \left|\frac{z-5 i}{z+5 i}\right|=1 \) lie on
the axis of \( Y \)


Reservoirs, lakes, ponds, rivers and
canals contains how much percentage of fresh water?
A . 77.2 \%
B. 22.4 \%
c. \( 0.36 \% \)
D. 30.3 \%


Find the components along the coordinate axes of the position vector of each of the following point:
\( \boldsymbol{R}(-\mathbf{1 1},-\mathbf{9}) \)


What are the properties of a metal? This question has multiple correct options
A. Malleable
B. Ductile
c. Form acidic oxides
D. conductor


The magnification of an object placed in front of a convex lens of focal length 20 \( \mathrm{cm} \) is is \( +2 . \) To obtain a magnification of
\( -2, \) The object has to be moved a distance equal to:
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


The element with atomic number 111
might belong to which of the following group?
A. Chromium
B. Scandium
c. copper
D. Titanium


If the system of equations of \( 3 x-2 y+ \)
\( \boldsymbol{z}=\mathbf{0}, \boldsymbol{k} \boldsymbol{x}-\mathbf{1 4} \boldsymbol{y}+\mathbf{1 5 z}=\mathbf{0}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{3} z=\mathbf{0} \) has non trivial solution then \( \boldsymbol{k}= \)
A . 29
B . 26
\( c \cdot 23 \)
D. 19


Which of the following device is used to measure the optical activity?
A. Manometer
B. Barometer
c. Polarimeter
D. Hygrometer


If ordered pair \( (a, b) \) is given as (-2,0)
then \( a= \)
A . -2
B. 0
\( c \cdot 2 \)
D. None of the above


When light is refracted, which of the following does not change?
A. Wavelength
B. Frequency
c. velocity
D. Amplitude


A chair is bought by a trader for Rs. 7,200 at \( 20 \% \) discount on its marked
price. If he sells it at \( 16 \% \) discount on its marked price, find the profit percent made in the whole transaction.


In which one of the following reactions
does ozone act as a reducing agent?
A. \( B a O_{2}+O_{3} \rightarrow B a O+2 O_{2} \)
в. \( 2 H C l+O_{3} \rightarrow C l_{2}+H_{2} O+O_{2} \)
c. \( P b S+4 O_{3} \rightarrow P b S O_{4}+4 O_{2} \)
D. \( 2 K I+O_{3}+H_{2} O \rightarrow 2 K O H+I_{2}+O_{2} \)


A certain simple harmonic vibrator of
mass \( 0.1 k g \) has a total energy of \( 10 J \)
.Its displacement from the mean
position is \( 1 \mathrm{cm} \) when it has equal
kinetic and potential energies. The amplitude \( A \) and frequency \( n \) of
vibration of the vibrator are
\( ^{\mathbf{A}} \cdot A=\sqrt{2} c m, n=\frac{500}{\pi} H z \)
B. \( A=\sqrt{2} c m, n=\frac{1000}{\pi} H z \)
\( ^{\mathbf{C}} \cdot A=\frac{1}{\sqrt{2}} c m, n=\frac{500}{\pi} H z \)
D. \( A=\frac{1}{\sqrt{2}} c m, n=\frac{1000}{\pi} H z \)


Select the mismatched pair.
A. Gibberellic acid - Increases yield of sugarcane
B. Cytokinin - Promotes apical dominance
C. Ethylene - Sprouting of potato tuber
D. Abscisic acid - Inhibits seed germination


The disjunction of the statements, "lt is raining; The sun is shining" is
A. It is raining and the sun is shining
B. It is raining or the sun is shining
c. It is raining and the sun is not shining
D. It is not raining or the sun is not shining


The unit of molar conductivity is
A \( \cdot \operatorname{scm}^{2} s^{-1} \)
B . \( \mathrm{S} l^{2} \mathrm{mol}^{-1} \)
c. \( \operatorname{scm}^{2} m o l^{-1} \)
D. None of these


Find the radii of curvature of a convexo -
concave convergent lens made of glass with refractive index \( n=1.5 \) having
focal length of \( 24 \mathrm{cm} . \) One of the radii of
curvature is double the other


Use Euclid's division algorithm to find
the HCF of 135 and 225


(9,2),(5,-1) and (7,-5) are the vertices of the triangle. Find its area.
A . 10
B. 1
c. 12
D. 13


The binary compounds of metallic or non metallic elements with oxygen are called oxides.
A. True
B. False


In the expansion of \( \left(\boldsymbol{a} \sqrt{\boldsymbol{a}}+\frac{\mathbf{1}}{\boldsymbol{a}^{4}}\right)^{\boldsymbol{n}} \), the
coefficient in the second term exceeds
by 44 the coefficient in the first term. Find \( n \)
A . 20
B . 25
\( c .35 \)
D. 45


Hydrogen at the moment of its generation is generally called:
A. molecular hydrogen
B. nascent hydrogen
c. atomic hydrogen
D. protium


An electric dipole is held in a uniform electric field
(i) Using diagram show that it does not undergo any translatory motion,
(ii) derive an expression for torque acting on it.


The moment of inertia of a uniform
circular disc of radius 'R' and mass 'M'
about an axis touching the disc at its diameter and normal to the disc is:
\( A \cdot M R^{2} \)
B . \( \frac{2}{5} \mathrm{MR}^{2} \)
\( \mathbf{c} \cdot \frac{3}{2} \mathbf{M} \mathbf{R}^{2} \)
D. \( \frac{1}{2} \mathrm{MR}^{2} \)


Find the change in internal energy in
joule when \( 10 g \) of air heated from \( 30^{\circ} C \) to \( 40^{\circ} \mathrm{C} \)
\( \left(c_{v}=\mathbf{0 . 1 7 2} k c a l / k g / K J=\right. \)
\( 4200 J / k c a l) \)
\begin{tabular}{l}
A \( .62 .24 \mathrm{J} \) \\
\hline
\end{tabular}
в. 72.24
\( \mathrm{c} .52 .24 \mathrm{J} \)
D. \( 82.24 \mathrm{J} \)


Two bars of masses \( m_{1} \) and \( m_{2} \)
connected by a weightless spring of stiffness \( \kappa \) (figure shown above) rest on a smooth horizontal plane. Bar 2 is
shifted a small distance \( x \) to the left
and then released. If the velocity of the centre of inertia of the system after bar
breaks off the wall is given as \( v_{c m}= \)
\( \frac{s x \sqrt{m_{2} k}}{\left(m_{1}+m_{2}\right)} . \) Find \( s \)


Can friction ever be eliminated?
A. Yes
B. No
c. Sometimes
D. Depends on the object in regard


The height of a cuboid is \( 18 \mathrm{m} \). Its length is 3 times its height and 2 times its width. Find the surface area of the
cuboid.
\( \mathbf{A} \cdot 5280 m^{2} \)
В. \( 5832 m^{2} \)
c. \( 5313 m^{2} \)
D. \( 5188 m^{2} \)


If the reaction equation is \( n A+m B \leftrightarrow \)
\( x C+y D \)
What is the equilibrium equation?
A \( \cdot K=[C]^{x}[D]^{y} /[A]^{n}[B]^{m} \)
B . \( K=[A]^{n}[B]^{m} /[C]^{x}[D]^{y} \)
C . \( K=[A]^{n}[B]^{m} /[A]^{n}[B]^{m} \)
D. \( K=[C]^{x}[A]^{y} /[A]^{n}[D]^{m} \)
E . \( K=[C][D] /[A][B] \)


The lift of an air plane is based on
A. Torricelli's theorem
B. Bernoulli's theorem
c. Law of gravitation
D. conservation of .linear momentum


The number of triangles with any three of the length 1,4,6 and \( 8 \mathrm{cm} \) as sides is:
A . 4
B. 2
c. 1
\( D \)


The difference in the length of a mean
solar day and a sidereal day is about
A. 1 minute
B. 4 minute
c. 15 minute
D. 56 minute


When \( \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{y}=\mathbf{5}, \) by how much
does the value of \( 3 x^{2}-2 y \) exceed the
value of \( 2 x^{2}-3 y ? \)
A . 4
в. 14
c. 19
D. 20
\( E \cdot 50 \)


An "Anti-symmetric" relation need not be reflexive relation: give an example.


When \( N H_{4} C l \) is added to \( N H_{4} O H \)
solution, the dissociation of ammonium hydroxide is reduced. It is due to:
A. common ion effect
B. hydrolysis
c. oxidation
D. reduction


Explain why (or how):
(a) in a sound wave, a displacement node is a pressure antinode and vice
versa,
(b) bats can ascertain distances
directions, nature and sizes of the
obstacles without any "eyes"
(c) a violin note and sitar note may have
the same frequency, yet we can distinguish between the two notes,
(d) solids can support both longitudinal and transverse waves, but only
longitudinal waves can propagate in gases, and
(e) the shape of a pulse gets distorted during propagation in a dispersive medium.


A capacitor of capacitance \( C \) is charged
to a potential difference \( V \) from a cell and then disconnected from it. A charge
\( +Q \) is now given to its positive plate. The potential difference across the capacitor is now
A. \( V \)
B. \( V+\frac{Q}{C} \)
c. \( _{V}+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C}, \) if \( Q<C V \)


The ray diagram shown below is
introduced to show how a concave
mirror forms an image of an object
a) Identify the mistake and draw the
correct ray diagram
b) Write the justifications for your
corrections.


The compounds used in plastic industry and polymer industry respectively are :
A. Vinyl acetate \& Vinylcyanide
B. Vinyl cyanide \& Vinyl acetate
C. Acrylonitrile \& Ethylidene
D. Ethylidene cyanide \& Vinyl cyanide


The correct order of increasing basic nature of the following base is:
5
\( A \cdot 2<5<1<3<4 \)
B. \( 5<2<1<3<4 \)
\( c \cdot 2<5<1<4<3 \)
D. \( 5<2<1<4<3 \)


The P-T graph for the given mass of an
ideal gas is shown in figure. Then the
volume
A . increases
B. decreases
c. remains constant
D. data insufficient


How burning of fossil fuels leads to
increase in global warming?


If the first seven children born to a
particular pair of parents are all males, what is the probability that the eighth
child will also be a male?
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot \frac{1}{8} \)
D. \( \frac{1}{16} \)


If \( A=\{1,2\}, B=\{3,4\}, \) then \( A \times B= \)
B. \{(1,1),(2,2),(3,3),(4,4)\}
c. \{(4,1),(3,1),(4,2),(3,2)\}
D. All the above


A carbon resistor is shown in the figure.
Using colour code, write the value of the
resistance.


Arrange the following acids in
decreasing order of \( \left[\boldsymbol{H}^{+}\right] \) conc.
\( \mathrm{cH}_{2}=\mathrm{cHCH}_{2}-\mathrm{cooH} \quad \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{coot} \)
(II
A \( . I>I I>I I I \)
В. \( I I>I I I>I \)
c. \( I I>I>I I I \)
D. \( I I I>I I>I \)


Among the four compounds (i) acetone,
(ii) propanol, (iiii) methyl acetate and
(iv) propionic acid, the two that are isomeric are
A. methyl acetate and acetone
B. methyl acetate and propanol
c. propionic acid and methyl acetate
D. propionic acid and acetone


Find the value of \( \boldsymbol{x}+\boldsymbol{y} \) if \( \left[\begin{array}{cc}\boldsymbol{x} & \mathbf{7} \\ \mathbf{9} & \boldsymbol{y}-\mathbf{5}\end{array}\right]+\left[\begin{array}{cc}\mathbf{6} & -\mathbf{7} \\ \mathbf{4} & \mathbf{5}\end{array}\right]=\left[\begin{array}{cc}\mathbf{1 0} & \mathbf{7} \\ \mathbf{2 2} & \mathbf{1 5}\end{array}\right] \)


At which parts of our body can we bend?
A. Knee
B. Elbow
c. Neck
D. All of the above


Seven different coins are to be divided
amongst three persons. If no two of the persons receive the same number of
coins but each receives at least one
coin \( \& \) none is left over, then the
number of ways in which the division
may be made is


Match the scientists and their
contribution given in the columns.
Scientists \( \quad \) Contribution
A. Pasteur
p. Beer and butter milk are products of fermentation by yeast
B. Hansen \( \quad \) q. Diastase
C. Payen and \( \quad \) r. Purified rennet
Perso
D. \( \quad \) s. Streptomycin Waksman
\( A \cdot A-p, B-q, C-r, D-s \)
B. A - p, B - r, C - q, D - s
C. \( A-p, B-s, C-r, D-q \)
D. \( A-s, B-r, C-q, D-p \)


Let \( R \) be the equivalence relation in the
\( \operatorname{set} A=0,1,2,3,4,5 \) given by \( R= \)
\( (a, b): 2 \) divides \( (a-b) . \) Write the
equivalence class [0].


The \( V-I \) graph for a conductor at
temperature \( T_{1} \) and \( T_{2} \) are shown in fig.
\( \left(T_{2}-T_{1}\right) \) is proportional to
A \( . \cos 2 \theta \)
B. \( \sin 2 \theta \)
c. \( \cot 2 \theta \)
D. \( \operatorname{Tan} 2 \theta \)


Which of the following makes water a very essential element for growth of plant?
A. Turgidity of cells helps in extension growth
B. Water provides the medium for enzymatic activities
c. Cell enlargement
D. All of the above


Figure shows a parallel beam of monochromatic light incident on a convex spherical surface, radius of
curvature \( \boldsymbol{R}=\mathbf{3} \mathbf{0} \mathrm{cm}, \) which separates
glass(refractive index \( =1.6 \) ) from air.
Find the position of the image formed due to refraction of light at this single
spherical surface


A fair coin is tossed 100 times. The
probability of getting tails an odd number of times is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
c. \( \frac{1}{8} \)
D. \( \frac{3}{8} \)


An \( s p^{3} \) hybrid orbital contains:
A . \( 1 / 4 \) s-character
B. 1/2 s-character
c. \( 2 / 3 \) s-character
D. 3/4 s-character


Four identical cubes are joined end to
end to form a cuboid. If the total surface
area of the resulting cuboid is \( 648 \mathrm{cm}^{2} \)
find the length of edge of each cube. Also, find the ratio between the surface area of resulting cuboid and the surface
area of a cube.
A. \( 9 \mathrm{cm} \) and 3: 1
B. 2 cm and 3: 1
c. \( 6 \mathrm{cm} \) and 3: 1
D. \( 3 \mathrm{cm} \) and 3: 1


The moles of \( B a\left(N O_{3}\right)_{2} \) which on
dissolving in 12 moles of water lowers the vapour pressure of water to \( 80 \% \) are


Gelatin is often used as an ingredient in
the manufacture of ice-cream. The
reason for this is :
A. to prevent the formation of a colloid.
B. to stabilize the colloid and prevent crystal growth.
c. to cause the mixture to solidify
D. to improve the flavour.


The tarnishing of silver ornaments in the atmosphere is due to the formation
of:
\( \mathbf{A} \cdot A g_{2} O, A g_{2} S \)
B. \( A g N O_{3}, A g_{2} S \)
c. \( A g O H, A g_{2} C O_{3} \)
D. \( A g \)


Sulfuric acid is produced from sulfur, oxygen and water via
A. oiling process
B. contact process
c. vitroling process
D. none of the above


Assertion
Electric filed of a dipole can't be found using only Gauss law. (i.e. without using superposition principle)
Reason
Gauss law is valid only for symmetrical charge distribution
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


If \( a, b, c \) are in A.P., then \( \frac{1}{\sqrt{b}+\sqrt{c}}, \frac{1}{\sqrt{c}+\sqrt{a}}, \frac{1}{\sqrt{a}+\sqrt{b}} \) are in
A. \( A . P \)
в. G.Р.
c. \( H . P \)
D. None of these


What will happen if one kidney is removed from the body of a human
being?
A. Death due to poisoning
B. Uremia and death
c. Stoppage of urination
D. The person will survive


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


Solve:
\( 8 l^{3}-36 l^{2} m+54 l m^{2}-27 m^{3} \)


\( C_{6} H_{6} \frac{H N O_{3}}{H_{2} S O_{4}} A \frac{B r_{2}}{F e B r_{3}} B, \) Find the final
product B.


An organic compound has \( C \) and \( H \) percentage in the ratio 6: 1 by mass
and \( \mathrm{C} \) and 0 percentage in the ratio 3: 4
by mass. The compound is:
A. \( H C H O \)
в. \( C H_{3} O H \)
c. \( C H_{3} C H_{2} \) ОН
D. \( (C O O H)_{2} \)


Sodium carbonate is used to:
A. preserve pickles, fish
B. baking industry
c. manufacture borax
D. all of above


What will be the length of eukaryotic
DNA segment having 10 pairs of nucleotides?


If \( \frac{\mathbf{x}^{4}+\mathbf{2 4 x}^{2}+\mathbf{2 8}}{\left(\mathbf{x}^{\mathbf{2}}+\mathbf{1}\right)^{\mathbf{3}}} \)
\( =\frac{\mathbf{A} \mathbf{x}+\mathbf{B}}{\mathbf{x}^{2}+\mathbf{1}}+\frac{\mathbf{C} \mathbf{x}+\mathbf{D}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{2}}+\frac{\mathbf{E} \mathbf{x}+\mathbf{F}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)^{3}} \)
then \( \boldsymbol{A}= \)
\( A \)
B. -
c.
\( D \)


The ends of a diagonal of a square are (2,-3) and \( (-1,1) . \) Another vertex of the square can be
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{-3}{2},-\frac{5}{2}\right) \)
в. \( \left(\frac{5}{2}, \frac{1}{2}\right) \)
\( ^{c} \cdot\left(\frac{1}{2}, \frac{5}{2}\right) \)
D. none of these


Find \( x, \) if the angles of a triangle have
measures \( \left(x+40^{0}\right),\left(2 x+20^{0}\right) \) and \( 3 x \)
also state which type of triangle is this.
A . \( x=60^{\circ} \) and Equilateral triangle
B. \( x=20^{\circ} \) and Scalene triangle
C . \( x=20^{\circ} \) and Equilateral triangle
D. \( x=40^{\circ} \) and Scalene triangle


A small metal ball of mass 'm' is
dropped in a liquid contained in a vessel, attains a terminal velocity 'v'. If a metal ball of same metarial but of mass
\( 8 \mathrm{m}^{\prime} \) is dropped in same liquid, then the terminal velocity will be:
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( 8 V \)


\( \boldsymbol{x}+\mathbf{1} \leq \mathbf{7}, \) where \( \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{1,2,3,4,5,6,7\} \)
в. \{1,2,3,4,5,6\}
c. Data insufficient
D. None of these


Which of the following statement best
describe torque?
A. is the vector product of force and lever arm length.
B. is a scalar and has no direction associated with it
C. is always equal to force.
D. is always greater for shorter lever arms.
E. must always equal zero


For a given value of the degree of dissociation \( (\alpha), \) which of the following
have correct van't Hoff factor?
This question has multiple correct options
A. \( N a C l ; i=2+\alpha \)
в. \( C a\left(N O_{3}\right)_{2} ; i=1+2 \alpha \)
c. \( K_{4}\left[\left(F e(C N)_{6}\right] ; i=1+4 \alpha\right. \)
D. \( \left(N H_{4}\right)_{3} P O_{4} ; i=3+\alpha \)


A car moving on a straight road covers
the one third of the total distance with
\( 20 \mathrm{Km} / \mathrm{h} \) and the rest with \( 60 \mathrm{Km} / \mathrm{h} \)
.The average speed is


A vessel has \( 6 g \) of hydrogen at pressure \( P \) and temperature \( 500 K . A \) small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is \( \boldsymbol{P} / 2 \) and temperature falls to \( 300 \mathrm{K} ? \)
\( A \cdot 28 \)
B. 3g
\( c \cdot 4 g \)
D. 18


Derivation of second equation of motion
is:
\( \mathbf{A} \cdot d \theta=w d 2 t \)
B \( . d \theta=w d t \)
\( \mathbf{c} \cdot d \theta=w d 3 t \)
\( \mathbf{D} \cdot d \theta=w d t^{2} \)


Write the differences between static
electricity and electric current.


What does the mass number of an atom
represent?
A. Only the number of protons
B. The number of protons and neutrons
c. The number of protons and electrons
D. Only the number of neutrons


The molar mass of \( N_{2} O \) as well as \( C O_{2} \)
is \( 44 g m o l^{-1} . A t 25^{o} C \) and 1 atm
pressure, \( 1 \mathrm{L} N_{2} \mathrm{O} \) contains \( \mathrm{n} \) molecules
of gas. The number of \( C O_{2} \) molecules in
2 L under same conditions will be:
\( A \)
B. \( 2 n \)
\( c \cdot \frac{n}{2} \)
\( D \cdot \frac{n}{n} \)


\( I_{2} \) produced, when ozone reacts with
moist \( K I \), is used to convert \( C_{2} H_{5} O H \)
to \( C I_{3} C H O . \) The number of moles of
ozone required to convert 1 mol of
\( C_{2} H_{5} O H \) into \( C I_{3} C H O \) is :
A . 1
B . 2
\( c \cdot 4 \)
D. 3


Arrange following according to boiling point
\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{5} \boldsymbol{H}_{12} \)


The velocity \( v \) versus \( t \) graph of a body in
a straight line is as shown in Fig. The
displacement of the body in five
seconds is
\( A \cdot 2 m \)
B. \( 3 m \)
\( c .4 m \)
D. 5 m


Wisdom tooth appears in a human being, when age is between
A. 4 to 8 years
B. 10 to 14 years
\( c . \) 17 to 30 years
D. 30 to 40 years


How do plants change their shape?
A. By photosynthesis
B. By changing amount of water
C. By using minerals from the soil
D. All of the above


A distinct monocot character shown by the flowers of Liliaceae is
A. Hypogynous flowers
B. Actinomorphic flowers
c. Trimerous flowers
D. Bisexual flowers


Obturator foramen is found in
A. Frog's pelvic girdlel
B. Frog's pectoral girdle
c. Rabbit's pelvic girdle
D. Rabbit's pectoral girdle


Match the column I with II and column I
and mark the appropriate choice.
Column I

İ
Uncertainty of an
(i)
(A) \( \quad \) object
(B) Bohr's radius of an
(ii) \( \frac{h}{4 \pi m} \) orbit
Angular
(C) momentum of an
(iii) \( \frac{h}{m v} \) electron
(D) de Broglie
(iv) \( n \cdot \frac{h}{2 \pi} \) wavelength
A \( \cdot(A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(i i) \)
в. \( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
C. \( (A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i i) \)
D. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)


The equivalent inductance of two inductor is \( 2.4 m H \) when connected in
parallel and \( 10 m H \) when connected in
series. The difference between two
inductance is (neglecting mutual induction between coils)
\( \mathbf{A} \cdot 3 m H \)
в. \( 2 m H \)
\( \mathrm{c} .4 \mathrm{mH} \)
D. \( 16 m H \)


Assertion
\( \mid \mathfrak{f}^{6} \boldsymbol{C}_{\boldsymbol{n}}+\boldsymbol{2} \cdot^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+1}+^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+\boldsymbol{2}}>^{\boldsymbol{8}} \boldsymbol{C}_{\boldsymbol{3}} \) then
the quadratic equations whose roots \( \operatorname{are} \alpha, \beta \) and \( \alpha^{n-1}, \beta^{n-1} \) (for least value
of
n) have two common roots.
Reason
Equation \( a x^{2}+b c+c=0 \) and \( a^{1} x^{2}+ \)
\( b^{1} x+c^{1}=0 \) have two roots common
\( \operatorname{then}\left(b c^{1}-b^{1} c\right)\left(a b^{1}-a^{1} b\right)=\left(c a^{1}-\right. \)
\( \left.\boldsymbol{c}^{1} \boldsymbol{a}\right)^{2} \)
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


Effective nuclear charge \( \left(Z^{*}\right) \) can be
calculated by using the formula:
\( \mathbf{A} \cdot Z^{*}=Z-S \)
B . \( Z^{*}=Z+S \)
c. \( Z^{*}=S-Z \)
D. \( Z=Z^{*}-S \)


Find the order of the differential
equation:
\( \log \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\boldsymbol{x} \)


Find the first term and the difference of
an arithmetic progression if the sum of its first five even terms is equal to 15
and the sum of the first three terms is
equal to (3)


Vitamin \( C \) is an organic acid known as:
A. ascorbic acid
B. citrus acid
c. glycolic acid
D. acetic acid


Assertion
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision
Reason
Principle of conservation of momentum holds true for all kinds of collision
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


andiscilicia du
consists of two identical uniform solid
cylinders, each of mass \( m, \) on which two
light threads are wound symmetrically.
The friction in the axle of the upper
cylinder is assumed to be absent. If the
tension of each thread in the process of motion is \( \boldsymbol{T}=\frac{\boldsymbol{m} \boldsymbol{g}}{\boldsymbol{x}}, \) then the value of \( \boldsymbol{x} \)
is :
A . 10
B. 20
c. 15
\( D \)


Choose the correct statement
B. \( \alpha: \beta: \gamma:: 2: 3: 1 \)
c. \( \alpha: \beta: \gamma:: 3: 1: 1 \)
D. \( \alpha: \beta: \gamma:: 1: 2: 3 \)


A student uses a magnetic compass to
perform a laboratory experiment in the Northern Hemisphere. She then carries the same magnetic compass with her to the Southern Hemisphere, taking care not to damage the compass in any way. When she reaches her destination at the equivalent latitude and longitude in the Southern Hemisphere, she prepares to perform the same laboratory experiment. The student looks at the compass before performing the experiment to see if the compass needle has changed. How has the compass changed?
A. The compass needle points \( 90^{\circ} \) to the left of the expected direction
B. The compass needle points \( 90^{\circ} \) to the right of the expected direction
c. The compass needle slowly rotates in a counter clockwise direction
D. The compass needle slowly rotates in a clockwis tion
as been no he co


The ionisation potential of isotopes of
an element will be:
A. same
B. different
c. dependent on atomic masses
D. dependent on the number of neutrons present in the nucleus


Evaluate \( \sqrt{11 \sqrt{11 \sqrt{11 \sqrt{11 \dots \dots \infty}}}} \)


For each given solid, identify the top view, front view and side view.


Which of the following will best give
resorcinol (1,3-dihydroxy benzene)?
\( A \)
B.
\( c \)
\( D \)


In the following reaction Phenol\( \stackrel{Z n d u s t}{\rightarrow} X \frac{C H_{3} C l}{a n h . A l c l_{3}} \)
\( \boldsymbol{Y}^{\boldsymbol{a l k} \cdot \boldsymbol{K} \underline{M n} \boldsymbol{O}_{4} / \triangle} \boldsymbol{Z} \)
The product \( Z \) is:
A. toulene
B. benzaldehyde
c. benzoic acid
D. benzene


Assertion
In order to reduce sliding friction, lubricants are used.
Reason Lubrication changes the conditions of rubbing, replacing the sliding friction by rolling friction, there by reducing the force of friction.
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 principle value of
\( \operatorname{cosec}^{-1}(-\sqrt{2}) \)


In Kolbe's reaction with phenol as the
reactant, the number of \( O \) atoms in the
final product is:


The increasing order of reactivity among group 1 element is \( L i<N a< \)
\( R b<C s, \) whereas that among group 17
element is \( F>C I>B r>I . \) Explain?


Emulsion can be destroyed by:
This question has multiple correct options
\( A \). the addition of emulsifier which tends to form another
emulsion
B. electrophoresis with high potential
C. freezing
D. all


Derive relationship between H and U.


The process of introducing impurities in small quantities into an intrinsic semiconductor is called Doping.
A. True
B. False


Area of \( \Delta A B C \) is
A. 45 squares units
B. 55 squares units
c. 65 squares units
D. none of these


Which property of water is used by plants for taking minerals from the soil?
I) Water can form aqueous solutions.
Il) Water can dissolve a wide variety of
substances
\( A \)
B. I
\( c \cdot 1,1 \)
D. none of the above


A simple harmonic motion has an amplitude \( A \) and time period \( T . \) Find the time required by it to travel directly from \( \boldsymbol{x}=\boldsymbol{A} \) to \( \boldsymbol{x}=\boldsymbol{A} / \mathbf{2} \)


Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+\ldots+\mathbf{3}^{n-1}=\frac{\left(\mathbf{3}^{n}-\mathbf{1}\right)}{\mathbf{2}} \)


If the function \( u=f(x) \) is continuous at
the point \( x=a \) and the
function \( y=g(u) \) is continuous at the
point \( u=f(a), \) then the
composite function \( \boldsymbol{y}=(\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( g(f(x)) \) is
A. continuous at the point \( x=f(a) \)
B. continuous at the point \( x=a \)
c. discontinuous at the point \( x=a \)
D. continuous at the point \( x=g(a) \)


Specify the co-ordination geometry
around and hybridization of \( N \) and \( B \)
\( \operatorname{atom} \operatorname{in} \mathbf{a} 1: 1 \) complex of \( B F_{3} \) and
\( \boldsymbol{N} \boldsymbol{H}_{3}: \)
\( \mathbf{A} \cdot N: \) tetrahedral, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)
B. \( N: \) pyramidal, \( s p^{3} ; B \) : pyramidal, \( s p^{3} \)
C \( . N: \) pyramidal, \( s p^{3} ; B: \) planar, \( s p^{3} \)
D. \( N: \) pyramidal, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)


The van der Waal's parameters for
\( \operatorname{gases} A, B, C \) and \( D \) are:
\begin{tabular}{lll}
Gas & \( a \) \( \left(l i t r e^{2} a t m / m o l^{2}\right) \) & \( b(l i t r e / m o l \) ) \\
\( A \) & 4.0 & 0.027 \\
\( B \) & 8.0 & 0.030 \\
\( C \) & 6.0 & 0.032 \\
\( D \) & 12.0 & 0.027 \\
\hline
\end{tabular} Which one of these gases has the
highest critical temperature?
\( \mathbf{A} \cdot A \)
\( \mathbf{B} \cdot B \)
\( c \cdot C \)
D. \( D \)


The mass of particle executing S.H.M is gm.lf its periodic time is \( \pi \) seconds,
the value of force constant is:-
A. 4 dynes/cm
B. \( 4 \mathrm{N} / \mathrm{cm} \)
\( c \cdot 4 N / m \)
D. 4 dynes/m


Two molecules indicated below are
capable to intramolecular H-bonding. Which is likely to form more stable
hydrogen bonds?
\( A \)
B. II
C. Both are equally capable
D. Cannot be predicted


The third term from the end in the
expansion of \( \left(\frac{4 x}{3 y}-\frac{3 y}{2 x}\right)^{9} \) is
A \( \cdot \) s \( _{C_{7}} \frac{3^{5}}{2} \frac{y^{5}}{x^{5}} \)
В. \( -_{-9} \sigma_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{5}} \)
c. \( _{9} C_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{3}} \)
D. none of these


In the above figure, 0 is the centre of the
circle. The angle \( C B D \) is equal to
\( A \cdot 25 \)
B. 50
\( c \cdot 40^{\circ} \)
D. 130


If the roots of a quadratic expression
\( a x^{2}+b x+c \) are complex, then
A \( \cdot b^{2}<4 a c \)
В. \( b^{2}>4 a c \)
c. \( b^{2}=4 a c \)
\( \mathbf{D} \cdot a=0 \)


During glycolysis, the compounds PGAL and DHAP are formed from fructose 1,6
diphosphate by
A . Cleavage.
B. Isomerisation.
c. Phosphorylation.
D. Condensation


In a process 701 J of heat is absorbed by a system and 394 J of work is done by system. What is the change in internal energy for the process?


Explain the following terms giving one
example for each:
(i) Micelles
(ii) Aerosol


What are emulsions? What are their
different types? Give examples of each
type


In a trapezium. ABCD, \( \angle A D C=110^{\circ} \)
Find \( \angle \boldsymbol{A} \)
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c .70^{\circ} \)
D. \( 80^{\circ} \)


If \( \frac{(x+1)^{2}}{x^{3}+x}=\frac{A}{x}+\frac{B x+C}{x^{2}+1}, \) then
\( \sin ^{-1} A+\tan ^{-1} B+\sec ^{-1} C= \)
A \( \cdot \frac{\pi}{2} \)
B.
\( c \cdot c \)
D. \( \frac{5 \pi}{6} \)


Three point charges \( +\boldsymbol{q},+\mathbf{2} \boldsymbol{q} \) and \( -\mathbf{4 q} \)
where \( \boldsymbol{q}=\mathbf{0 . 1} \boldsymbol{\mu} \boldsymbol{C}, \) are placed at the
vertices of an equilateral triangle of
side \( 10 \mathrm{cm} \) as shown in figure. The potential energy of the system is
A \( \cdot 3 \times 10^{-3} J \)
В. \( -3 \times 10^{-3} J \)
\( \mathbf{c} \cdot 9 \times 10^{-3} J \)
\( \mathbf{D} \cdot-9 \times 10^{-3} \mathbf{J} \)


Which of the following statements concerning Lanthanide elements is false?
A. All Lanthanides are highly dense metals
B. Most characteristic oxidation state of Lanthanide elements is +3
C. The ionic radii of trivalent Lanthanides steadily increase with increase in the atomic number
D. Lanthanoids are separated from one another by ion exchange methods


Draw the graph of the linear equations
\( 4 x-3 y+4=0 \) and \( 4 x+3 y-20=0 \)
Find the area bounded by these lines and x-axis.


All x satisfying the inequality
\( \left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+10>0, \) lie in
the interval:-
A \( \cdot(-\infty, \cot 5) \cup(\cot 4, \cot 2) \)
B. (cot \( 5, \) cot 4 ) \( \$ \$ \)
c. \( (\cot 2, \infty) \)
D. \( (-\infty, \cot 2) \cup(\cot 5, \infty) \)


If the following ion is coloured enter 1
else enter 0
\( N i^{2+} \)


Select the correct order of lattice
energy.

This question has multiple correct options
\( \mathbf{A} \cdot L i F<L i B r<L i I \)
B. \( L i C l>L i B r>L i I \)
C \( . L i C l>N a C l>K C l \)
D. \( B e C O_{3}<M g C O_{3}<S r C O_{3}<B a C O_{3} \)


A block of wood mass \( 5 k g \) is placed on a
plane making an angle \( 30^{\circ} \) with the horizontal. If the coefficient of friction
between the surface of contact of the
body and the plane is \( 0.5 . \) What force is required to keep the body sliding down with uniform velocity?
A. \( 1.6 N \)
B. \( 4.8 N \)
\( c \cdot 6.4 N \)
D. \( 3.35 N \)


In the vulcanization of rubber:
A. sulphur reacts to form a new compound
B. sulphur cross-links are introduced
c. sulphur forms a very thin protective layer over rubber
D. All of the above


There are n identical capacitors, which are connected in parallel to a potential
difference \( V . \) These capacitors are then reconnected, in series. The potential difference between the extreme ends is:
A . zero
в. \( n V \)
c. \( (n-1) V \)
D. none of the above


A circular loop of radius \( 2 \mathrm{cm} \), is placed in a time varying magnetic field with rate of \( 2 T / \)sec. Then induced electric
field in this loop will be:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 0.002 \mathrm{V} / \mathrm{m} \)
c. \( 0.01 V / m \)
D. \( 2 V / m \)


Use Lagrange's Mean Value Theorem to
determine a point on the curve \( y= \) \( \sqrt{x-2} \) at the tangent is parallel to the
chord joining the points (2,0) and (3,1)


Most abundant bacteria are


The geometry of \( N i(C O)_{4} \) and
\( N i\left(P P h_{3}\right)_{2} C l_{2} \) are:
A. both square planar
B. tetrahedral and square planar, respectively
c. both tetrahedral
D. square planar and tetrahedral, respectively


With the usual notations, check if the
following equation \( S_{t}=u+\frac{1}{2} a(2 t-1) \)
is dimensionally correct or not.


Let \( p, q \in\{1,2,3,4\} . \) The number of
equation of the form \( p x^{2}+q x+1=0 \)
having real roots, is
A . 15
B. 9
c. 8
D. 7


Evaluating the following:
\( (1+2 \sqrt{x})^{5}+(1-2 \sqrt{x})^{5} \)
A \( \cdot 2\left(1+40 x^{2}+80 x\right) \)
B. \( 2\left(1-40 x+81 x^{2}\right) \)
c. \( 2\left(1+40 x+80 x^{2}\right) \)
D. None of these


In the third period of the periodic table,the element having smallest size is :
A. \( N a \)
в. \( A r \)
c. \( C l \)
D. \( s i \)


Rosenmund reduction is used for
the preparation of
A. carboxylic acid
B. aldehydes
c. esters
D. alcohols


Which of the following molecules has the smallest dissociation energy?
A \( \cdot L i_{2} \)
в. \( N a_{2} \)
c. \( K_{2} \)
D. \( C s_{2} \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 2} & \mathbf{3} \\ -\mathbf{4} & \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} \\ \mathbf{2} & \mathbf{1}\end{array}\right] \)
Check commutativity of the two matrices


What is common to the following? Motion of the propeller of a flying helicopter, the minute hand of a watch,
the tape of cassette recorder.
A. All are example of translatory motion
B. All are examples of oscillatory motion
c. All are examples of rotatory motion
D. All are examples of periodic motion


Two distinct chords drawn from the
point \( (p, q) \) on the circle \( x^{2}+y^{2}= \)
\( p x+q y \) are bisected at the \( x \) -axis.
Then
A \( \cdot|p|=|q| \)
B \( \cdot p^{2}=8 q^{2} \)
\( \mathbf{c} \cdot p^{2}<8 q^{2} \)
D \( \cdot p^{2}>8 q^{2} \)


The \( I U P A C \) name for the complex
\( \left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Cl}_{2} \) is:
A. pentaamminenitrito-N-cobalt(III) chloride
B. nitrito-N-pentaamminecobalt(III) chloride
C . pentaamminenitrito-N-cobalt(II) chloride
D. pentaamminenitrito-N-cobalt(I) chloride


The first remarkable human fossil was
that of H.habilis/H. africanus.


What are hydrocarbons? Give one
example.


Find the number of terms in each of the
following AP's
\( 7,13,19, \dots 205 \)
A. 20 terms
B. 28 terms
c. 34 terms
D. 40 terms


If \( p^{2}-6 p+7 \) is divided by \( (p-1) \) the
remainder will be
A. positive
B. zero
c. negative
D. none of these


Why has it been difficult to study the
chemistry of radon?


The minimum number of carbon atoms
an alkane should contain in order to
exhibit optical activity is :
A. 5
B. 6
\( c \cdot 7 \)
D. 8


In Earthworm, cocoon is formed by
A. Epidermal muscles
B. Setae
c. cuticle
D. Clitellum


A rectangular coil of 200 turns and area
\( 100 \mathrm{cm}^{2} \) is kept perpendicular to a
uniform magnetic field of induction
\( 0.25 T . \) If the field is reversed
in direction in 0.01 second, the average induced emf in the coil is :
A \( \cdot 10^{6} V \)
B . \( 10^{4} V \)
\( \mathbf{c} \cdot 10^{2} V \)
D. zero


\( \boldsymbol{R}-\boldsymbol{O H} \stackrel{\boldsymbol{P B r}_{3}}{\boldsymbol{A}} \)
\( \boldsymbol{B} \frac{\text {Grignard reaction}}{\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O}} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{O}}{\boldsymbol{N}} \boldsymbol{D} \)
What are \( A, B, C \) and \( D \) are
respectively?
\( \mathbf{A} \cdot R-B r, R-M g-B r, R-C H_{2}-O-M g-B r, R- \)
\( C H_{2} C H_{2}-O H \)
B . \( R-B r, R-M g-B r, R-C H_{2}-O-C H_{2}-M g- \)
\( B r, R-C H_{2} C H_{2}-O H \)
c. \( R-B r, R-M g-B r, R-C H_{2}-C H_{2}-O-M g- \)
\( B r, R-C H_{2} C H_{2}-O H \)
D. \( R-B r, R-M g-B r, R-C H_{2}-C H_{2}-O-M g- \)
\( B r, R-C H_{2} O H \)


Assertion
In a terrestrial ecosystem, detritus food chain is a major conduit for energy flow.
Reason

Solar energy is direct source of energy
supply in detritus food chain.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \frac{\mathbf{3} \boldsymbol{x}+\mathbf{4}}{\boldsymbol{x}^{2}-\mathbf{3} \boldsymbol{x}+\mathbf{2}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}-\frac{\boldsymbol{B}}{\boldsymbol{x}-\mathbf{1}}, \) then
\( (A, B)= \)
A. (7,10)
()
B. (10,7)
c. (10,-7)
D. (-10,7)


Suppose, the acceleration due ot gravity
at the earth's surface is \( 10 m s^{-2} \) and at
the surface of Mars it is \( 4.0 m s^{-2} . A 60 \)
kg passenger goes from the Earth to the
Mars in a spaceship moving with a
constant velocity. Neglect all other
objects in the sky. Which part of figure
bests represents the weight (net
gravitational force) of the passenger as
a function of time?
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
\( D . D \)


In a cricket match, a batswoman hits a
boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.


How are the following compounds
prepared? Benzaldehyde from benzene.


Bernoulli's principle is based on the law of conservation of :
A. Mass
B. Momentum
c. Energy
D. None of these


Consider the reaction:
\( \mathbf{4} N \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{5}}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta}_{\boldsymbol{r}} \boldsymbol{H}= \)
\( -111 k J \)
If \( N_{2} O_{5(s)} \) is formed instead of \( N_{2} O_{5}(g) \)
in the above reaction, then \( \Delta_{r} H \) value
will be:
[Given, \( \Delta \boldsymbol{H} \) of sublimation for \( \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{5}} \) is
\( \left.\mathbf{5 4} k J m o l^{-1}\right] \)
A \( .+54 k J \)
B . \( +219 k J \)
c. \( -219 k J \)
D. \( -165 k J \)


Let the opposite angular points of a square be (3,4) and \( (1,-1) . \) Find the coordinates of the remaining angular points.


\( A, B, C \) are three sets such that \( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{2}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{C})=\boldsymbol{4}, \) If \( \boldsymbol{P}(\boldsymbol{x}) \)
denotes power set of \( \boldsymbol{X}, \boldsymbol{k}= \) \( \frac{\boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{C})))}{\boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{A}))) \times \boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{B})))} \).then find
the Sum of digits of \( k \)


An orbital with \( l=0 \) is Symmetrical
about the :
A. \( x- \) axisonly
B. \( y- \) axisonly
c. \( z- \) axisonly
D. nucleus


Assertion
When a gun is fired, the bullet moves forward (action). The gun recoils backward (reaction)
Reason
Driving a nail into a wooden block without holding the block is difficult.
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


As a body moves from the equator to the poles, the value of \( g \) experienced by the body
A . decreases
B. increases
c. remains unchanged
D. first decreases then increases


Solve: \( \boldsymbol{x}^{2} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{y}(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)
A \( \cdot y-2 x=k x^{2} y \)
B . \( y+2 x=k x^{2} y \)
c. \( 2 y+x=k x y^{2} \)
D. \( 2 y-x=k x y^{2} \)


\( C u^{+}(a q) \) is unstable in solution and
undergoes simultaneous oxidation and
reduction, according to the reaction \( \mathbf{2} C u^{+}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C u}(s) \)
Choose correct \( E \) for above reaction if
\( \boldsymbol{E}_{C u^{2+} / C u}=\mathbf{0 . 3 4} \boldsymbol{V} \) and \( \boldsymbol{E}_{c u^{2+} / \boldsymbol{C u}^{+}}= \)
\( \mathbf{0 . 1 5} \boldsymbol{V} \)
A. \( -0.38 V \)
в. \( +0.49 V \)
\( \mathrm{c} \ldots+0.38 \mathrm{V} \)
D. - \( 0.19 V \)


(a) Three point charges \( q,-4 q \) and \( 2 q \) are placed at the vertices of an
equilateral triangle \( A B C \) of side \( ^{\prime} l^{\prime} \) as
shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the
charge \( \boldsymbol{q} \)
(b) Find out the amount of the work done to separate the charges at infinite
distance.


Ozone belongs to which groups of the periodic table?
A. IV
B.
\( c \cdot v \)
D. vı


If the variance of the series of the form
\( 5 x_{1}+7 \) is 225
then standard deviation of the series of
the form
\( 7 x_{1}+5 \) is
A .21
B. 44
c. 484
D. 22


The resistance of a bulb filament is
\( 100 \Omega \) at a temperature of \( 100^{\circ} \mathrm{C} \). If its temperature coefficient of resistance
be 0.005 per \( ^{o} C, \) its resistance will
become \( 200 \Omega \) at a temperature of :
\( \mathbf{A} \cdot 200^{\circ} C \)
B. \( 300^{\circ} \mathrm{C} \)
c. \( 400^{\circ} \mathrm{C} \)
D. \( 500^{\circ} \mathrm{C} \)


The marks secured by 400 students in a Mathematics test were normally distributed with mean \( 65 . \) If 120
students got marks above 85 , the number of students securing marks between 45 and 65 is
A . 120
B . 20
c. 80
D. 160


Make n the subject of formula:
\( N=90\left(2-\frac{4}{n}\right) \) Find \( n, \) if \( N=108 \)
A \( \cdot n=\frac{360}{180+N} ; n=4 \)
в. \( n=\frac{180}{180-N} ; n=3 \)
c. \( n=\frac{360}{180-N} ; n=5 \)
D. none of the above


Solve:
\( \lim _{\boldsymbol{\theta} \rightarrow \boldsymbol{\pi}} \frac{\boldsymbol{\pi}-\boldsymbol{\theta}}{\sqrt{\cos \theta+1}} \)


The dry cell of E.M.F \( 12 V \), is connected
in series to a \( 3 \Omega \) and a \( 6 \Omega \) resistor
Calculate the total power supplied by
the dry cell.
\( \mathbf{A} .9 W \)
B. \( 72 \mathrm{W} \)
c. \( 16 W \)
D. \( 2 W \)


\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{(\sqrt{\mathbf{1}+\boldsymbol{x}^{2}}-\boldsymbol{x})^{n}}(\boldsymbol{n} \neq \pm \mathbf{1})= \)
\( \frac{1}{2}\left(\frac{z^{n+1}}{n+1}+\frac{z^{n-1}}{n-1}\right)+O \)
where
A. \( z=x-\sqrt{1+x^{2}} \)
B. \( z=\sqrt{1+x^{2}}-x \)
c. \( z=x+\sqrt{1+x^{2}} \)
D. \( z=x-\sqrt{1-x^{2}} \)


In which of the following, the growing point ends in a flower?
A. Raceme
B. Verticillaster
c. catkin
D. Spike


In the equation \( y=A \sin (\omega-K x) \)
obtain the dimensional formula of \( \omega \)
and K.Given \( x \) is distance and \( t \) is time.


What are Forward and Reverse bias
conditions of a Diode?


A 10 watt electric heater is used to heat
a container filled with 0.5 kg of water. It
is found that the temperature of water
and the container rises by \( 3^{\circ} \mathrm{K} \) in 15 minutes. The contain \( r \) is then emptied,
dried and filled with 2 kg of oil. The same heater now raises the
temperature of container-oil system by \( 2^{o} \mathrm{K} \) in 20 minutes. Assuming that there is no heat loss in the process and the specific heat of water as 4200 \( J k g^{-1} K^{-1}, \) the specific heat of oil in the same unit is equal to
A \( \cdot 1.50 \times 10^{3} \)
B. \( 2.55 \times 10^{3} \)
c. \( 3.00 \times 10^{3} \)
D. \( 5.10 \times 10^{3} \)


State True or False :
Convection is not possible in vacuum.
A. True
B. False


\( \lim _{x \rightarrow 3} x^{2}-3 x+1 \)


Assertion
Kepler's second law can be understood by conservation of angular momentum principle.
Reason
Kepler's second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as \( (\boldsymbol{d A} / \boldsymbol{d t})=\left(\boldsymbol{r}^{2} \boldsymbol{\omega}\right) / 2 \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two isomers \( (\boldsymbol{I} \boldsymbol{V}) \) and \( (\boldsymbol{V}) \) on
monochlorination give four products.
The isomers \( (\boldsymbol{I} \boldsymbol{V}) \) and \( (\boldsymbol{V}) \) are:
\( \mathbf{A} \)
B.
\( c \)
and
D.


Acetaldehyde on reaction with Grignard reagent and subsequent hydrolysis yields:
A. tertiary alcohol
B. primary alcohol
c. secondary alcohol
D. both primary and secondary alcohol


For the given cell \( \boldsymbol{P t}_{D_{2} \mid D^{+}} \| \boldsymbol{H}^{+}|\boldsymbol{P t}| \boldsymbol{H}_{2} \)
if \( \boldsymbol{E}_{D_{2} \mid D^{\oplus}=0.003 V}^{\ominus}, \) what will be the ratio of \( D^{\oplus} \) and \( H^{\oplus} \) at \( 25^{\circ} C \) when he
reaction: \( D_{2}+2 H^{\oplus} \rightarrow 2 D^{\oplus}+H_{2} \)
attains equilibrium:
A .1 .34
B . 1.24
c. 1.124
D. 1.45


Find the principal value of \( \sec ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


The value of \( \sqrt{99} \times \sqrt{396} \) is :
A .208
в. 198
\( c \cdot 254 \)
D. None of these


What is free fall?
A. It is the acceleration experienced due to gravity only.
B. When an object falls under the effect of gravity alone.
C. Both A and B
D. Neither A nor B


Measures of opposite angles of
parallelogram are \( (3 x-2)^{\circ} \) and \( (50- \)
\( x)^{\circ} . \) Find the measure of its other
angles.
A . 143
в. 153
\( c \cdot 163 \)
D. 173


Assertion
Gauss law holds good only to those
closed surfaces which is enclosing non-
zero electric charge.
Reason
The electric flux through a closed surface is unaltered due to the
presence of outside charge.
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 incorrect


An aqueous solution of hydrogen sulphide and sulphur dioxide when mixed together yield:
A. sulphur and water
B. hydrogen peroxideand sulphur
c. sulphur trioxide and water
D. hydrogen and sulphurous acid


How much blood is pumped to the brain in 1 minute?
A. \( 450 \mathrm{ml} \)
B. 750 m1
\( c \cdot 1000 \mathrm{m} \)
D. 2500 ml


For uranium nucleus how does its mass
vary with volume?
\( A \cdot m \propto V \)
B. \( m \propto 1 \) IN
\( c \cdot m \propto \)
\( D \cdot m \propto V^{2} \)


Charges +50,+20,+30 and -100 nano coulomb are placed at the four corners of a square of side \( 5 \sqrt{2} \mathrm{cm} . \) The potential at
the intersection of diagonals is :
A \( \cdot 1.8 \sqrt{2} \times 10^{4} V \)
\( V \)
B. \( 3.6 \times 10^{4} V \)
c. \( 1.8 \times 10^{4} V \)
D. Zero


If the primitive of \( \frac{x^{5}+x^{4}-8}{x^{3}-4 x} \) is \( \frac{x^{3}}{3}+ \) \( \frac{\boldsymbol{x}^{2}}{2}+\boldsymbol{A} \boldsymbol{x}+|\log \boldsymbol{f}(\boldsymbol{x})|+C \) then
This question has multiple correct options
\( \mathbf{A} \cdot A=1 \)
\( \mathbf{B} \cdot A=4 \)
\( \mathbf{C} \cdot f(x)=x^{2}(x-2)^{5}(x+2)^{-3} \)
D. \( f(x)=x^{2}(x-2)^{3}(x+2)^{-2} \)


State whether following statements are
true or false
Statement-1: The only circle having
radius \( \sqrt{10} \) and a diameter along line
\( 2 x+y=5 \) is \( x^{2}+y^{2}-6 x+2 y=0 \)
Statement-2: The line \( 2 x+y=5 \) is a
normal to the circle \( x^{2}+y^{2}-6 x+ \)
\( 2 y=0 \)
A. Statement- 1 is false, statement- 2 is true.
B. Statement-1 is true,statement-2 is true and statement 2 is NOT the correct explanation for statement-1.
c. Statement-1 is true, statement-2 is false.
D. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-


Why is CNG a cleaner fuel?
A. No particulate emission
B. Releases very less amounts of sulphur and nitrogen oxides
C. No emission of ash
D. All of the above


What is the correct structure of \( 1,2- \)
Dichloropropane?
A. \( C H_{3}-C H C l-C H C l_{2} \)
в. \( C H_{3}-C H C l-C H_{2} C l \)
\( \mathrm{c} \cdot C H_{3}-C C l_{2}-C H_{3} \)
D. \( C H_{3}-C H_{2}-C H C l_{2} \)


Find the sum the infinite G.P.:
\( \frac{2}{3}-\frac{4}{9}+\frac{8}{27}-\frac{16}{21}+\dots \dots \)
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
c. \( \frac{19}{27} \)
D. 8


An electric dipole consists of two opposite charges each of magnitude
\( 1.6 \times 10^{-19} \) coulomb at separation
1 Armstrong. The diploe moment is:
A \( \cdot 1.6 \times 10^{-19} c-m \)
В. \( 1.6 \times 10^{-29} c-m \)
c. \( 3.2 \times 10^{-29} c-m \)
D. \( 3.2 \times 10^{-19} \mathrm{C}-\mathrm{m} \)


In the figure 0 is the centre of the circle. The tangents at \( \mathrm{B} \) and \( \mathrm{D} \) intersect each other at point P. If AB is parallel to CD and \( \angle A B C=55^{\circ} \) Find (i) \( \angle B O D \) (ii)
\( \angle B P D \)


The common impurity present in
bauxite is:
\( \mathbf{A} \cdot F e_{2} O_{3} \)
в. \( A l_{2} O_{3} . H_{2} O \)
c. \( A l C l_{3} . A I_{2} O_{3} \)
D. \( M g C l_{2} . C a C l_{2} \)


Show that the expression of the time period \( T \) of a simple pendulum of length
\( l \) given by \( T=2 \pi \sqrt{\frac{l}{g}} \) is dimensionally
correct.
A. As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct
B. The dimension of LHS and RHS are not same
c. It cannot be solved
D. None of these


How many employees get to work in less
than 60 minutes?
A . 10
B. 5
\( c .15 \)
D. 20


Which oxyacid of sulphur contains \( \boldsymbol{S}- \)
\( \boldsymbol{S} \) single bond?
A. Oleum
B. Marshall's acid
c. Dithionic acid
D. Thisolphuric acid


In a circular current-carrying conductor,
if the current flows in the clockwise
direction, the magnetic field direction
is
A. Parallel to the coil towards the observer
B. Perpendicular to the plane of the coil away from the observer
C. Perpendicular to the plane of the coil towards the observer
D. Parallel to the plane of the coil away from the observer


Phenol in presence of sodium hydroxide reacts with chloroform to form
salicyladehyde. The reaction is known
as:
A. Kolbe's reaction
B. Reimer-Tiemann reaction
c. stephen reaction
D. Etard reaction


Cloud or fog is a colloidal system in which the dispersed phase and the dispersion medium are:
A. gas, liquid
B. liquid, gas
c. liquid, liquid
D. solid, solid


If \( \sin ^{2} \theta+5 \cos ^{2} \theta=4, \) then find \( \theta \) and
hence prove that \( \sec \theta+\operatorname{cosec} \theta=2+ \)
\( \frac{2}{\sqrt{3}} \)


In deriving the speed of sound in air, Newton assumed that the wave travels
in
A. Adiabatic condition
B. Isothermal condition
c. Isobaric condition
D. Isoclinic condition


Ten rational numbers between \( \frac{-2}{5} \) and \( \frac{1}{2} \)
\( \operatorname{are} \frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0 \ldots, \frac{1}{20}, \frac{2}{20} \)
If true then enter 1 and if false then
enter \( \mathbf{0} \)


\( P Q R S \) is a parallelogram. From the
information given in the figure, find the
values of \( x \) and \( y \)


Figure shows an Amperian path
\( A B C D A \). Part \( A B C \) is in verical plane
PSTU while part \( C D A \) is in horizontal
plane \( P Q R S \). Direction of circulation along the path is shown by an arrow
near point \( B \) and \( D \) \( \oint \vec{B} \cdot d \vec{l} \) for this path according to
Ampere's law will be:
\( \mathbf{A} \cdot\left(I_{1}-I_{2}+I_{3}\right) \mu_{0} \)
B・ \( \left(-I_{1}+I_{2}\right) \mu_{0} \)
\( \mathrm{c} \cdot I_{3} \mu_{0} \)
\( \mathbf{D} \cdot\left(I_{1}+I_{2}\right) \mu_{0} \)


Differentiate w.r.t \( \boldsymbol{x} \)
\( e^{x} \cos ^{3} x \sin ^{2} x \)


By the principle of interference, condition for constructive
interference in terms of the path
difference?
A \( \cdot n^{-1} \lambda \)
B. \( n \lambda \)
c. \( n \lambda^{2} \)
\( \mathbf{D} \cdot n \lambda^{4} \)


Select the odd one out w.r.t. the type of reflection of incident light (wood, steel, silver, mirror, graphite)
A. mirror
B. woodd
c. silver
D. steel


\( \ln \) a \( H_{2}-O_{2} \) fuel cell. \( 6.72 L \) of
hydrogen at NTP reacts in 15 minutes, the average current produced in amperes is:
A. 64.3 amp
B. 643.3 amp
c. 6.43 amp
D. 0.643 amp


f a heterozygous tall pea plant is selfpollinated, what will be the heterozygous: homozygous proportion of the progenies?
A . 1: 3
B. 1:
\( c .3: \)
D. 1: 2


The most significant sources of water
pollution
A. waste water from domestic and industrial processes
B. agricultural process
c. oil spillage
D. all of the above


How many electron will constitute \( 32 \mathrm{C} \)
of charge?
A \( .2 \times 10^{19} \)
B . \( 2 \times 10^{18} \)
\( \mathrm{c} \cdot 2 \times 10^{17} \)
D. \( 2 \times 10^{20} \)


Die \( A \) has 4 red and 2 white faces
whereas die \( B \) has 2 red and 4 white
faces. A coin is flipped once. If it shows a head, the game continues by throwing die \( A, \) if it shows tail, then die \( B \) is to be
used. If the probability that die \( A \) is used is \( \frac{64}{66} \) where it is given that red turns up every time in first \( n \) throws,
then \( n \) is


Fill in the blanks with approriate words. Elements required by plants in relatively large amounts are ........... and in very small amounts are


The atomic number of three elements
\( A, B \) and \( C \) are \( a, a+1 \) and \( a+2 \)
respectively. If \( C \) is an alkali metal, then
the nature of bonding in the compound of \( A \) and \( C \) is
A. co-ordinate
B. covalent
c. ionic
D. metallic


Presence of magnesium chloride in water makes it temporary hard.
A. True
B. False


What we say when a body remains in one position for a long time?
A. Motion
B. Rest
c. Stationary
D. None of the above


Nomenclature is governed by certain universal rules.Which one of the
following is contrary to the rules of
nomenclature?
A. Biological names can be written in any language.
B. The first word in a biological name represents the genus name and the second is a specific epithet
C. The names are written in Latin and are italicised.
D. When written by hand, the names are to be underlined.


Laboratory thermometers have a range
of \( -10^{\circ} C \) to \( \$ \$ \)
\( \$ \$^{\circ} \mathrm{C} \)


In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be
A . 100\%
B . 200\%
c. 50\%
D. 25\%


Choose the correct answer from the
allternatives given. What is the name of the structures
which help the mandibles and function as accessory jaws?
A. Maxillae
B. Galea
c. Lacinia
D. Labial palp


Carbon dioxide is used in the
production of three carbon sugar by which of the following method?
A. Photosystem-I
B. Photosystem-II
c. Electron transport chain
D. Calvin cycle
E . citric acid cycle


The value of universal gravitational
constant \( G \) is-
A. \( 6.67 \times 10^{-11} \frac{N m^{2}}{k g} \)
в. \( 6.67 \times 10^{-11} \frac{N m^{2}}{k g^{2}} \)
c. \( 66.7 \times 10^{-11} \frac{N m^{2}}{k g^{2}} \)
D. \( _{66.7} \times 10^{-11} \frac{N m^{2}}{k g} \)


Which of the following is an important source of light for us?
A. sun
B. Stars
c. Jupiter
D. Venus


If the vectors \( 2 \vec{a}-\vec{b}+\vec{c}, \vec{a}+2 \vec{b}- \)
\( \overrightarrow{3} c, 3 \vec{a}+m \vec{b}+5 \vec{c} \) are linearly
dependent, then \( \boldsymbol{m}= \)
\( A \cdot 2 \)
B. -
\( c \cdot 4 \)
D. -4


Circles are drawn on chords of the
rectangular hyperbola \( \boldsymbol{x} \boldsymbol{y}=\mathbf{4} \) parallel to the line \( y=x \) as diameters.All such
circles pass through two fixed points whose coordinates are
This question has multiple correct options
\( \mathbf{A} \cdot(2,2) \)
B \( \cdot(2,-2) \)
c. (-2,2)
D. (-2,-2)


\( P \) and \( Q \) are the mid points of the sides
\( C A \) and \( C B \) respectively of a triangle
\( A B C, \) right angled at \( C . \) Then, find the
value of \( 4\left(A Q^{2}+B P^{2}\right) \)
\( A \cdot 5 A B^{2} \)
B . \( 3 A B^{2} \).
c. \( 2 A B^{2} \)
\( \mathrm{D} \cdot 4 A B^{2} \)


\( f\left(\begin{array}{ccc}-1 & -3 & -3 \\ 3 & 1 & -3 \\ 3 & -3 & 1\end{array}\right] \) then adj \( (A) \) is
A.
\[
=4\left[\begin{array}{ccc}-2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & 3 & 2\end{array}\right]
\]
B. \( \quad\left[\begin{array}{ccc}-2 & 3 & 3 \\ 3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right] \)
C.
\[
=4\left[\begin{array}{ccc}-2 & -3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right]
\]
D.
\[
=4\left[\begin{array}{ccc}-2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right]
\]


A calcite crystal is placed over a dot on
a piece of paper and rotated. On seeing through the calcite, one will see :
A. one dot
B. Two stationary dots
c. Two rotating dots
D. One dot rotating about the other


\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}3 x-8 & \text { if } x \leq 5 \\ 2 k & \text { if } x>5\end{array}\right. \)
continuous, find \( k \)
\( A \cdot \frac{2}{7} \)
B. 3 \( \overline{7} \)
\( c \cdot \frac{4}{7} \)
D.


The angle between the two vectors \( \vec{A}= \) \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}+\mathbf{5} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\boldsymbol{j}}-\mathbf{5} \hat{\boldsymbol{k}} \) is :
A \( .60^{\circ} \)
B . \( 0^{\circ} \)
\( c .90^{\circ} \)
D. None of these


Which of the following oxo-acids of sulphur has more than one oxidation
state of
oxygen?
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S_{2} O_{4} \)
c. \( H_{2} S_{2} O_{6} \)
D. \( H_{2} S_{2} O_{8} \)


For a reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \) Products, it is
observed that doubling the concentration of \( B \) caused the reaction
rate to increase four times, but
doubling the concentration of \( A \) has no effect on the rate of reaction. The rate
equation is therefore:
A \( \cdot \) rate \( =K[A]^{2} \)
B . rate = \( K[B]^{2} \)
c. rate \( =K[A][B] \)
D. rate = \( K[A] \)


Triangle \( A B C \) is angled at \( A . A D \) is
drawn perpendicular to \( B C . \) If \( A B= \) \( 10 \mathrm{cm}, A C=12 \mathrm{cm}, \) find the area of
\( \triangle A B C . \) Also find the length of \( A D \)


Five ordinary dies are rolled at random and the sum of numbers shown is 16
What is the probability that the number
shown on each is any one from 2,3,4 or
\( \mathbf{5} ? \)
A \( \cdot \frac{9}{49} \)
B. \( \frac{3}{49} \)
c. \( \frac{2}{49} \)
D. None of these


Identify \( X \) in the reaction.
\( \boldsymbol{C H} \boldsymbol{C l}_{3} \frac{\boldsymbol{S b F}_{3}}{H \boldsymbol{F}} \boldsymbol{C H} \boldsymbol{F}_{2} \boldsymbol{C l}^{\underline{1070} \boldsymbol{K}}(\boldsymbol{X})+ \)
\( \mathbf{2} \boldsymbol{H} \boldsymbol{C l} \)
\( \mathbf{A} \cdot F_{2} C=C F_{2} \)
в. \( C l F C=C F C l \)
c. \( F_{2} C=C F C l \)
D. \( F_{2} C=C C l_{2} \)


Which of the following instruments make use of principle of moments
during operation?
A . Ruler
B. Vernier calipers
c. spring balance
D. Simple balance


When a lead storage battery is
discharged:
A. \( S O_{2} \) is evolved
B. lead sulphate is consumed
\( \mathrm{c} \). lead is formed
D. sulphuric acid is consumed


The two long polynucleotide chains of DNA are held together by
A. Hydrogen bonds
B. Covalent bonds
c. Metallic bonds
D. lonic bonds
E. Polar covalent bonds


A particle executes \( \boldsymbol{S H} \boldsymbol{M} \) on a line
\( 8 c m \) long. Its \( K . E \) and \( P . E \) will be equal
when its distance from the mean
position is:
A. \( 4 \mathrm{cm} \)
B. 2 cm
\( \mathrm{c} \cdot 2 \sqrt{2} \mathrm{cm} \)
D. \( \sqrt{2} \) cm


A plant that prepares its own food is
A. Autotroph
B. Parasite
c. Epiphyte
D. Saprophyte


Find the smallest number by which 243 must be multiplied to make it a perfect
cube.
A . 1
B. 2
\( c .3 \)
D. 4


In the leaching of \( A g_{2} S \) with \( N a C N, \) a
stream of air is also passed. It is
because of:
A. Reversible nature of reaction between \( A g_{2} S \) and NaCN
B. To oxidise \( N a_{2} S \) into \( N a_{2} S O_{4} \)
c. Both (A) and (B)
D. None of the above


Find the chance of throwing more than
15 in one throw with 3 dice.


Magnetic force required to demagnetize the material
A. retainity
B. coercivity
c. energy loss
D. hysteresis


What is the speed at the top?
A \( \frac{E}{B} \)
в. \( \frac{E}{2 \text { }} \)
c. \( \frac{2 E}{B} \)
D. \( \frac{B}{2 E} \)


A reversible galvanic cell is connected to an external battery. If the EMF of the battery is less than the EMF of the galvanic cell, then the current:
A. will not pass through the circuit
B. will flow from the battery to the galvanic cell
c. will flow from the galvanic cell to the battery
D. can flow in any direction


The reaction does not proceed in the
forward direction \( f \Delta G \) is
A. Positive
B. Negative
c. zero
D. None of these


An automobile engine absorbs \( 1600 J \) of heat from a hot reservoir and expel
\( 1000 J \) to a cold reservoir in each cycle.
What is the power output of engine if it
operates at 200 cycle per minute?
\( \mathbf{A} \cdot 3 H P \)
B. \( 4 \mathrm{HP} \)
c. 2.7 НР
D. 3.7 НР


An equation of a plane containing the
lines \( r=a_{1}+t b_{1} \) and \( r=a_{2}+t b_{2} \)
where \( \left[\boldsymbol{a}_{2}-\boldsymbol{a}_{1}, \boldsymbol{b}_{1}, \boldsymbol{b}_{2}\right]=\boldsymbol{0} \) is
A \( \cdot\left[r-a_{1}, b_{1}, b_{2}\right]=0 \)
B . \( \left[r-a_{2}, b_{1}, b_{2}\right]=0 \)
c. \( \left[r-a_{2}, a_{1}, b_{2}\right]=0 \)
D . \( \left[r-a, a_{2}, b_{2}\right]=0 \)


Which one of these is viviparous?
A . Turtle
B. Running birds
c. Rabbit and whale
D. Bony fish


In the method using the transformers, assume that the ratio of the number of
turns in the primary to that in the secondary in the step-up transformers
is \( 1: 10 . \) If the power to the consumers
has to be supplied at \( 200 V, \) the ratio of the number of turns in primary to that in the secondary in the step-down transformer is
B. 150: 1
c. 100: 1
D. 50: 1


Examples of non-conductors include
A. sulphur
B. phosphorus.
c. wood
D. all of these.


The figure shows a mechanical set-up.
What mechanism is reflected by this
schematic?
A. Sliding mechanism
B. Rotation mechanism
C. Slide-crank mechanism
D. Rolling mechanism


\( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{\boldsymbol{Z}} \)
\( \boldsymbol{P}(\boldsymbol{B})=\frac{1}{\boldsymbol{4}} \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\frac{1}{\mathbf{5}} \)
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=? \)


Number of NADH produced during breakdown of one molecule of glucose to 1: 3 diphosphoglycerate stage is
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D.


In the lunch, you ate boiled green
vegetables, a piece of cooked meat, one boiled egg and a sugar candy. Which
one of these foods may have been digested first?
A. Boiled green vegetables
B. The piece of cooked meat
c. Boiled egg
D. sugarcandy


Find the area of the region enclosed by
the curves \( \boldsymbol{y}=\mathbf{4} \boldsymbol{x}-\boldsymbol{x}^{2}, \boldsymbol{y}=\mathbf{5}-\mathbf{2} \boldsymbol{x} \)


n exponential form \( 729=3^{a}, \) what is
the value of \( a ? \)


Find the multiplicative inverse of the complex numbers given the following:
\( \sqrt{5}+3 i \)


Find the maximum value of \( \sqrt{3} \sin x+ \)
\( \cos x \)