To measure a small resistance \( \sim \)
\( 10^{-5} \Omega, \) one should used
A. Wheatstone bridge
B. Postoffice box
c. wein's bridge
D. Carrey Foster bridge


Which of the following form/s an ideal solution?
This question has multiple correct options
A. Ethyl bromide + ethyl iodide
B. Ethyl alcohol + water
c. chloroform + benzene
D. Benzene + toluene


Compare Biot-Savart law with Coulomb's law for electrostatic field.


Charge \( Q \) taken from the battery of 12 V in
the circuit is :
\( \mathbf{A} \cdot 72 \mu C \)
B. \( 36 \mu C \)
\( c \cdot 156 \mu C \)
D. \( 20 \mu C \)


Assertion
In rate law, unlike in the expression for
equilibrium constants, the exponents for concentrations do not necessarily match the stoichiometric coefficients.
Reason
t is the mechanism and not the
balanced chemical equation for the overall change that governs the reaction
rate
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following do not have linear shape?
A. Mercurous chloride
B. Acteylene
c. Carbon dioxide
D. Methane


Identify the balanced chemical reaction
of chlorine with respect to reactant \( D \)
A \( \cdot F e+C l_{2} \rightarrow F e C l_{3} \)
в. \( 2 F e+3 C l_{2} \rightarrow 2 F e C l_{3} \)
\( \mathrm{c} \cdot 2 \mathrm{Fe}+6 \mathrm{Cl}_{2} \rightarrow 2 \mathrm{FeCl} \)
D. \( F e+C l_{2} \longrightarrow F e C l_{3}+F e C l_{2} \)


The two plate \( X \) and \( Y \) of a parallel-
plates capacitor of capacitance \( \mathbf{C} \) are
given a charge of amount Q each. \( X \) is
now joined to the positive terminal and
y to the negative terminal of a cell of
emf \( \varepsilon=Q / C \)
This question has multiple correct options
A. Charge of amount Q will flow from the positive terminal to the negative terminal of the cell through the capacitor.
B. The total charge on the plate \( X \) will be \( 2 Q \)
C. The total charge on the plate Y will be zero.
D. The cell will supply \( C \varepsilon^{2} \) amount of energy.


The amplitude of two interfering waves are \( a \) and \( 2 a \) respectively. The resultant amplitude in constructive interference
will be
\( \mathbf{A} \cdot 5 a \)
B. \( a \)
\( c \cdot 3 a \)
D. \( 2 a \)


Explain daniel cell with cell diagram, representation and process taking place in the cell.


One of the following is an incorrect
statement, point it out?
A. Permanent hardness can be removed by boiling water.
B. Hardness of water effects soap consumption.
C. Temporary hardness is due to bicarbonates of \( C a \) and \( M g \)
D. Permanent hardness is due to the soluble \( S O_{4}^{2-}, C l^{-} \) of \( C a \) and \( M g \)


How is the e.m.f. across primary and
secondary coils of a transformer related
with the number of turns of coil in
them?


Which is correct in normal humans
A. pH of urine is around 8
B. \( 20-30 \) mg of urea is excreted per day
C. Ketone bodies in urine indicate diabetes mellitus
D. Glycosuria is treated with hemodialysis


Choose the correct answer from the
alternatives given The valve between the left atrium and
left ventricle is:
A. bicuspid (mitral) valve
B. aortic semilunar valve
c. tricuspid valve
D. sinoatrial valve


Chemical kinetics a branch of
physical chemistry deals with:
A. structure of molecules
B. heat changes in a reaction
c. physical changes in a reaction
D. rate of reactions


Construct \( \triangle L M N \) in which base
\( M N=7 \mathrm{cm}, \angle L M N=75^{\circ} \) and
\( \boldsymbol{L} \boldsymbol{M}+\boldsymbol{L} \boldsymbol{N}=\mathbf{9} \boldsymbol{c m} \)


Acid anhydride on reaction with primary amine give:
A. Amide
B. Imide
c. Secondary amine
D. Imine


A wall clock has a \( 5 \mathrm{cm} \) long minute
hand. The average velocity of the tip of the hand reaching 06.00 hrs. to 18.30 hrs. is
A \( .2 .2 \times 10^{-4} \mathrm{cm} / \mathrm{s} \)
B. \( 1.2 \times 10^{-4} \mathrm{cm} / \mathrm{s} \)
C . \( 5.6 \times 10^{-4} \mathrm{cm} / \mathrm{s} \)
D. \( 3.2 \times 10^{-4} \mathrm{cm} / \mathrm{s} \)


Equilibrium constant, \( K_{c} \) for the
reaction, \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} ; \) at
\( 500 K \) is \( 0.061 l i t r e^{2} m o l e^{-2} . A t \)
particular time, the analysis shows that composition of the reaction mixture is 3.00 mol litre\( ^{-1}, N^{2}, 2.00 \) mol litre\( ^{-1} \boldsymbol{I} \)
and 0.500 mol litre \( ^{-1} N H_{3} \). Is the
reaction at equilibrium? If not, in which
direction does the reaction tend to
proceed to reach equilibrium?


The solution of \( \mathrm{SO}_{2} \) in water is known
as:
A. sulphuric acid
B. sulphurous acid
c. hydrosulphuric acid
D. thiosulphurous acid


\( \boldsymbol{p} \Rightarrow \boldsymbol{p} \vee \boldsymbol{q} \) is a


\( \sin \theta=\frac{3}{5}, \operatorname{cosec} \theta=? \)


Peroxy linkage is present in:
A. Caros acid
B. Pyrosulphuric acid
c. Sulphurous ac
D. Dithionic acid


(a) A person cannot see nearby objects, then write name of eye defect. Write name of lens used to correct this eye
defect.
(b) In brief define 'Tyndall effect'.


\( \ln a \Delta A B C, \cos B \cdot \cos C+ \)
\( \sin B \cdot \sin C \cdot \sin ^{2} A=1 . \) Then the
triangle is
A. right - angled isosceles
B. isosceles whose equal angles are greater then \( \pi / 4 \)
c. equilateral
D. none of these


Which has the highest pH?
A. \( C H_{3} \) СООК
в. \( N a_{2} C O_{3} \)
c. \( N H_{4} C l \)
D. \( \operatorname{NaNO}_{3} \)


\( H_{2} S O_{4} \) acts as dehydrating agent


A steel wire of diameter \( d=1.0 \) mm is
stretched horizontally between two clamps located at the distance \( l= \) \( 2.0 m \) from each other. A weight of mass
\( \boldsymbol{m}=\mathbf{0 . 2 5} \boldsymbol{k g} \) is suspended from the
midpoint \( O \) of the wire. What will the
resulting descent of the point \( O \) be in millimetres?E=2 \( \times 10^{11} N / m^{2} \)


Reaction of alkyl halide with metallic sodium in presence of dry ether solution is called:
A. Friedel-crafts reaction
B. Sandmeyers reaction
c. Wurtz reaction
D. Gabriels reaction


Choose the odd one out from given
option.
A. Renin
B. ANF
c. АDH
D. Aldosterone


A proton is fired from very far away towards a nucleus with charge \( Q=120 \mathrm{e} \) where e is the electronic charge. It makes a closest approach of \( 10 \mathrm{fm} \) to the nucleus. The de Broglie wavelength (in units of \( \mathrm{fm} \) ) of the proton at its start is :
(take the proton mass, \( \boldsymbol{m}_{\boldsymbol{p}}=(\mathbf{5} / \mathbf{3}) \times \)
\( 10^{-27} k g \) and
\( \boldsymbol{h} / \boldsymbol{e}=\mathbf{4 . 2} \times \mathbf{1 0}^{-15} \boldsymbol{J} . \boldsymbol{s} / \boldsymbol{C} ; \frac{1}{4 \pi \epsilon_{0}}=\mathbf{9} \times \)
\( \left.\mathbf{1 0}^{9} \boldsymbol{m} / \boldsymbol{F} ; \mathbf{1} \boldsymbol{f} \boldsymbol{m}=\mathbf{1 0}^{-\mathbf{1 5}} \boldsymbol{m}\right) \)
\( A \cdot 7 f m \)
B. 8 fm
\( c .9 f m \)
D. \( 10 \mathrm{fm} \)


\( \left.\boldsymbol{R}-\stackrel{\boldsymbol{O}}{\boldsymbol{C}}-\boldsymbol{C l} \frac{\boldsymbol{N} \boldsymbol{a} \boldsymbol{N}_{3}}{\boldsymbol{c o n c .} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}\right\rangle_{\boldsymbol{C H}_{3}-\boldsymbol{C l}(\mathbf{1} \text { eqv } \boldsymbol{t} .)} \)
\( \boldsymbol{P} \quad \) Hence, Product \( (\boldsymbol{P}) \) is:
(Major product)
\( \mathbf{A} \cdot R-N H_{2} \)
\( \mathbf{B} \cdot R-N H-C H_{3} \)
C.
\[
R-C-N H-C H_{3}
\]
D.
\[
R-N H-C-C H_{3}
\]


The maximum number of dectrons in
\( Z n \) is :
A . 10
B. 0
\( c \cdot 2 \)
D. 6


An e.m.f. of 5 millivolt is induced in a
coil when in a nearby placed another coil, the current changes by 5 ampere in
0.1 second. The coefficient of mutual
induction between the two coils will be :
A. 1 Henry
B. 0.1 Henry
c. 0.1 millihenry
D. 0.001 millihenry


Calculate the mean deviation for the
data given here:
\( \begin{array}{llll}\text { class } & 0- & 10- & 20- \\ \text { interval } & 10 & 20 & 30\end{array} \)
3 3 5 Frequency


Two plants can be conclusively said to belong to the same species if they
A. Can reproduce freely with each other and form seeds
B. Have more than 90 percent similar genes
C. Look similar and possess identical secondary metabolites
D. Have same number of chromosomes


Complete the given \( S_{N} 2 \) reactions
Comment on stereochemistry.


State True or False.
According to principle of calorimetry heat absorbed by cold bodies is equal to heat released by hot bodies.
A. True
B. False


Molecules are different from
compounds.
A. True
B. False


For \( a n A, P, \frac{1}{3}, \frac{4}{3}, \frac{7}{3}, \frac{10}{3} \dots \dots \dots, \) Find \( T_{18} \)
For \( a n A, P, 3,9,15,21 \dots \dots \dots, \) Find \( S_{10^{\circ}} \)


Assertion
Silver metal does not show any change
when it is placed in HCl solution.
Reason
Silver metal does not react with dilute
HCI
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 bird flies to and fro between two cars
which move with velocities \( v_{1} \) and \( v_{2} \). If
the speed of the bird is \( v_{3} \) and the initial
distance of separation between them is
d, find the total distance covered by the
bird till the cars meet.


A man got a \( 10 \% \) increase in his salary. If his new salary is Rs. \( 1,54,000, \) find his original salary.


For the reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
the unit of \( \boldsymbol{K}_{c} \)
A. litre/mole
B. mol/litre
c. \( \left(\text {mol litre}^{-1} \text {) }^{-1}\right. \)
D \cdot (litre mole \( ^{-1} \) ) \( ^{2} \)


How does ammonia react with solution
of Cu?


The van's Hoff factor for 0.1 molar
\( B a\left(N O_{3}\right)_{2} \) solutions is \( 2.74 . \) Its degree of dissociation is:
A . 0.74
в. 0.87
c. 0.91
D. 1.0


Explain why is oil preferred over water for frying?


State the effect on the divergence of the leaves of a gold leaf electroscope on bringing a negatively charged rod near it if the electroscope is positively
charged:
A. Divergence decreases
B. Divergence increases
c. Divergence remains same
D. can't say


Four speakers will address a meeting where speaker \( Q \) will always speak after
P. Then, the number of ways in which the order of speakers can be prepared is
A . 256
в. 128
c. 24
D. 12


In the pelvic girdle of man \( A, B, C, D \) and
E respectively represents
A. A-Pubis, B-Acetabulum, C-llium, D-Ischium, E-Pubic symphysis
B. A-llium, B-Acetabulum, C-Pubis, D-Ischium, E-Pubic
symphysis
C. A-lschium, B-Acetabulum, C-Pubis, D-llium, E-Pubic symphysis
D. A-llium, B-Pubis, C-Acetabulum, D-Pubic symphysis E-lschium
E. A-llium, B-Acetabulum, C-Pubic symphysis, D-Ischium, E-Pubis


At \( 25^{\circ} C, K_{p} \) for the reaction:
\( N_{2} O_{4}(g) \leftrightharpoons 2 N O_{2}(g) \)
has a value of 0.14 atm. Calculate the
value of \( K_{c} \) in which the concentrations
are measured in mol \( \boldsymbol{L}^{-1} \)


What is maximum Reylonds number for
laminar flow?
A . 500
B. 4000
\( c .2000 \)
D. 8000


Which of the following is an auxin?
A . Maleic acid
B. Abscisic acid
c. Pyruvuc acid
D. Indole acetic acid


A point charge of value \( 10^{-7} C \) is
situated at the centre of cube of \( 1 \boldsymbol{m} \)
side. The electric flux through its total
surface area is:
A. \( 113 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
в. \( 11.3 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
C. \( 1.13 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
D. none of these


Potential at the point of a pointed
conductor is greater than the other points on surface:
A. True
B. False


If the maximum velocity of a particle in
SHM is \( v_{0}, \) then its velocity at half the amplitude from position of rest will be :
A \( \cdot v_{0} / 2 \)
B. \( v_{0} \)
c. \( v_{o} \sqrt{3} / 2 \)
D . \( v_{0} \sqrt{3} / 4 \)


The current \( I \) and voltage \( V \) graphs for a
given metallic wire at two different
temperatures \( T_{1} \) and \( T_{2} \) are shown in
the figure. It is concluded that :
A \( \cdot T_{1}>T_{2} \)
В. \( T_{1}<T_{2} \)
\( \mathbf{c} \cdot T_{1}=T_{2} \)
D. \( T_{1}=2 T_{2} \)


The probability that a leap year will have
only 52 Sundays is
A \( \cdot \frac{4}{7} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{6}{7} \)
D.


The order of magnitude of 147 is
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


What is water harvesting? How can this technique help in the conservation of
water?


A small, conducting circular loop is placed inside a long solenoid carrying a current. The plane of the loop contains
the axis of the solenoid. If the current in
the solenoid is varied. The current
induced in the loop is
A. clockwise
B. anti-clockwise
c. zero
D. clockwise or anti-clockwise depending on whether the resistance is increased or decreased


The area of the plane region bounded by the curves \( x+2 y^{2}=0 \) and \( x+3 y^{2}= \)
\( \mathbf{1} \) is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{3} \)
D.


Distinguish clearly between distance and displacement of a projectile.


n given figure \( \angle P Q R=100^{\circ}, \) where
\( P, Q \) and \( R \) are points on a circle with
centre \( O . \) Then, \( \angle O P R \) is
\( A \cdot 20 \)
B. 10
\( c \cdot 30^{\circ} \)
D. 40


What will happen after heating a
mixture of copper and concentrated nitric acid?


Lowering in vapour pressure is highest
for:
A. \( 0.2 m \) urea
B. \( 0.1 m \) glucose
c. \( 0.1 m \) M \( g S O_{4} \)
D. \( 0.1 m B a C l_{2} \)


If \( g \) is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass \( \boldsymbol{m} \)
raised from the surface of the earth to a
height equal to the radius \( R \) of the earth
is
A. \( 2 m g R \)
в. \( \frac{1}{2} m g R \)
c. \( \frac{1}{4} m g R \)
D. \( m g R \)


I The ideal gas law does not hold under low temperatures and high pressure.
II : Interactions between particles cannot be neglected under these conditions.
A . I is true, II is true
B. I is true, II is false
c. I is false, ll is false
D. I is false, Il is true


\( \sum_{i=3}^{\infty} \)


Cathode rays travel in
A. waves
B. packets
c. straight lines
D. alternative waves


Assertion
Assertion: When a light wave travels
from a rarer to a denser medium, its
speed decreases. The decrease in speed
imply a reduction in energy carried by the light wave.
Reason
Reason: The energy of a wave is inversely proportional to velocity of
wave
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


Generation of non-conventional energy
produces air pollution.
A. True
B. False


A particle executes SHM on a straight line. At two positions it's velocity \( u \) and \( \boldsymbol{v} \) while acceleration, \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
respectively \( [\beta>\alpha>0] . \) the distance
between the these two positions is
A \( \cdot \frac{u^{2}+v^{2}}{\alpha+\beta} \)
в. \( \frac{u^{2}-v^{2}}{\alpha+\beta} \)
c. \( \frac{u^{2}-v^{2}}{\beta-\alpha} \)
D. \( \frac{u^{2}+v^{2}}{\beta-\alpha} \)


Correct order of molecular weight is
A. DNA <rRNA<tRNAA
B. DNA <mRNA <rRNA
\( c . \) tRNA \( < \) mRNA \( < \) DNA
D. tRNA \( < \) DNA \( < \) mRNA


Statement I : Deuterium and hydrogen
are different elements.

Statement II: They have the different numbers of protons in each
A. Statement I is True, Statement II is True and statement I is correct explanation of statements
B. Statement I is True, Statement II is True and statement II is NOT correct explanation of statements
c. Statement I is True, Statement II is False
D. Statement I is False, Statement II is True
E. Statement I is False, Statement II is False


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
(i) \( \left[\begin{array}{cc}\mathbf{3} & \mathbf{5} \\ \mathbf{1} & -\mathbf{1}\end{array}\right] \)
(ii) \( \left[\begin{array}{ccc}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right] \)
(iii) \( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{3} & -\mathbf{1} \\ -\mathbf{2}-\mathbf{2} & \mathbf{1} \\ -\mathbf{4}-\mathbf{5} & \mathbf{2}\end{array}\right] \)
(iv) \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{5} \\ -\mathbf{1} & \mathbf{2}\end{array}\right] \)


\( m-15+25-15-15=20, \) then
\( m=? \)


The colloidal sol found effective in the
treatment of eye disease is:
A. colloidal sulphur
B. colloidal antimony
c. colloidal silver
D. colloidal gold


If \( \boldsymbol{A}=\{1,2,3,4\}, B=\{1,2,3,5,6\} \)
then find
(i) \( \boldsymbol{A} \cap \boldsymbol{B}, \) (ii) \( \boldsymbol{B} \cap \boldsymbol{A} \)
, (iii) \( \boldsymbol{A}-\boldsymbol{B} \), (iv)
\( \boldsymbol{B}-\boldsymbol{A} \)
What do you observe?


The momentum acquired by all free electrons in a wire a length I when a
current of i amp starts to flow is
A \( \cdot \frac{m i l}{e} \)
B. \( \frac{m e l}{i} \)
\( c . m i l \)
D. mie


Among seven pairs of traits studied by Mendel, the number of traits related to
flower, pod and seed were
A \( . \) 2, 2, 2
B. 2, 2, 1
\( c \cdot 1,2,2 \)
D. 1,1,2


In which of the following cell, salt bridge is not needed?
This question has multiple correct options
A \( \cdot P b\left|P b S O_{4}(s) \| H_{2} S O_{4}\right| P b O_{2} \mid P b \)
в. \( C d|C d O(s)| K O H(a q)\left|N i O_{2}(s)\right| N i \)
c. \( F e(s)|F e O(s)|\left|K O H(a q)-N i_{2} O_{3}(s)\right| N i \)
D. \( Z n\left|Z n S O_{4}\right| C u S O_{4} \mid C u \)


Jiah is doing an experiment in her math class. She flips four coins in the air. What is most likely to happen?
A. Two of the coins will be heads and two will be tails
B. Three of the coins will be heads and one will be tail
c. All four coins will be heads
D. None of the coins will be heads


Find the unit vectors perpendicular to
each of the following pairs of vectors:
\( \vec{i}+\vec{j}+\vec{k} \) and \( \vec{i}+\overrightarrow{2} j-\vec{k} \)
\( \mathbf{A} \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 1 / \sqrt{14} \)
B \( \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 2 / \sqrt{14} \)
C \( \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 2 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 1 / \sqrt{14} \)
\( \mathbf{D} \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 3 / \sqrt{14} \)


The scientific name of mango is written as Mangifera indica L. Pickup the correct statement about the
significance of letter 'L'.
A. Letter'L' singnifies Latin language.
B. The name is reverse with indica preceding Mangifera.
c. Letter 'L' signifies the taxonomist, Linnaeus
D. Letter 'L' is superfluous


An organic compound of mass 0.39
gave \( 50 \mathrm{ml} \) nitrogen at \( 27^{0} \mathrm{C} \) and \( 715 \mathrm{mm} \)
pressure. The \( \% \) of nitrogen in the compound is:
A. 17.83
B. 50
\( c \cdot 25 \)
D. 20


Which of the following is the best example of law of conservation of
mass?
A. \( 12 \mathrm{gm} \) of carbon combines with \( 32 \mathrm{gm} \) of oxygen to form \( 44 \mathrm{gm} \) of \( \mathrm{CO}_{2} \)
B. When 72 gm of carbon is heated in vacuum and no change in mass takes place
c. The weight of a piece of platinum is the same before and after heating in air
D. None of these


If the intensity of electric field at a distance \( x \) from the centre in axial
position of small electric dipole is equal
to the intensity at a distance \( y \) in
equatorial position, then
\( \mathbf{A} \cdot x=y \)
в. \( x=y / 2 \)
C \( . y=x / 2^{2 / 3} \)
D. \( y=x / 2^{1 / 3} \)


If two events \( A \) and \( B \) are such that
\( P(\bar{A})=\frac{3}{10}, P(B)=\frac{2}{5} \) and \( P(A \cap \)
\( \bar{B})=\frac{1}{2}, \operatorname{then} P\left(\frac{B}{A \cup \bar{B}}\right) \) is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D.


The distance between the X-axis and
the point (3,12,5) is
A. 3
B. 13
\( c \cdot 14 \)
D. 12
E. 5


Which one of the following statements regarding Henry's law is not correct?
A. The value of \( K_{H} \) increases with the function of the nature of the gas
B. Higher the value of \( K_{H} \) at a given pressure, higher is the solubility of the gas in the liquids
C. The partial of the gas in vapour phase is proportional to the mole fraction of the gas in the solution
D. Different gases have different \( K_{H} \) (Henry's law constant) values at the same temperature


f \( x, y, z \) be rational numbers such that \( x \) > y and z \( <y \) then
\( A \cdot z>x \)
B. z<x
\( c \cdot y<z \)
D. y > x


Write only equation for the reactions for preparation of glucose from sugar and starch.


If \( (\boldsymbol{w}-\overline{\boldsymbol{w}} \boldsymbol{z}) /(1-\boldsymbol{z}) \) is purely real where
\( \boldsymbol{w}=\boldsymbol{\alpha}+\boldsymbol{i} \boldsymbol{\beta}, \boldsymbol{\beta} \neq \mathbf{0} \) and \( \boldsymbol{z} \neq \mathbf{1}, \) then set
of the values of \( z \) is
\( \mathbf{A} \cdot z:|z|=1 \)
B . \( z: z=\bar{z} \)
c. \( z: z \neq 1 \)
D \( \cdot z:|z|=1, z \neq 1 \)


Which choice shows the answer to the
following mathematical operation with the correct number of significant
figures? \( 4.51 \times 10^{5}+3.6 \times 10^{3} \)
A \( .4 .55 \times 10^{5} \)
В. \( 8.11 \times 10^{5} \)
c. \( 4.546 \times 10^{5} \)
D. \( 8.11 \times 10^{8} \)
E . \( 4.5 \times 10^{5} \)


A particle of mass \( 0.3 \mathrm{kg} \) is subjected to a force \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) with \( \boldsymbol{k}=\mathbf{1 5} \boldsymbol{N} / \boldsymbol{m} \)
What will be its initial acceleration if it
is released from a point \( 20 \mathrm{cm} \) away
from the origin?


The element which exists in the liquid
state is:
A. bromine
B. mercury
c. gallium
D. all of these


A bullet on penetrating \( 30 \mathrm{cm} \) into its target loses its velocity by \( 50 \% . \) What additional distance will it penetrate
into the target before it comes to rest?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


What must be added to \( f(x)=4 x^{4}+ \)
\( 2 x^{3}+2 x^{2}+x-1 \) so that the resulting
polynomial is divisible by \( g(x)=x^{2}+ \)
\( 2 x-3 \)
A. \( -61 x+65 \)
в. \( 2 x-15 \)
c. \( -15 x+2 \)
D. None of these


Study of history of life forms on earth is known as
A. Evolutionary biology
B. Morphology
c. Physiology
D. Biogenesis


Which equation is the most appropriate to calculate the energy of activation, if the rate of reaction is doubled by
increasing temperature from \( \boldsymbol{T}_{1} \boldsymbol{K} \) to \( T_{2} K ? \)
\( ^{\mathbf{A}} \cdot \log _{10}\left(\frac{k_{1}}{k_{2}}\right)=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
B. \( \log _{10}\left(\frac{k_{2}}{k_{1}}\right)=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
\( ^{\mathbf{C}} \cdot \log _{10} \frac{1}{2}=\frac{E_{a}}{2.303}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
D \( \cdot \log _{10} 2=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)


Pick out the isoelectronic structures of
the following
\( \begin{array}{lll}\text { I. } C H^{3+} & \text { II. } \boldsymbol{H}_{3}^{+} & \text {III. } \boldsymbol{N} \boldsymbol{H}_{3}\end{array} \)
A. II, ,II and IV
B. I and II
c. Ill and IV
D. I and III


Construct a quadrilateral \( A B C D, \) when
Angle \( \boldsymbol{A}=\mathbf{9 0}^{\circ} \boldsymbol{A B}=\mathbf{4 . 6} \mathrm{cm}, \boldsymbol{B D}=\mathbf{6 . 4} \)
\( \mathrm{cm}, A C=6 \mathrm{cm} \) and \( C D=4.2 \mathrm{cm} \)


n the figure (1) given below, AB I CR and LM | QR Prove that \( \frac{\boldsymbol{B} \boldsymbol{M}}{\boldsymbol{M} \boldsymbol{C}}=\frac{\boldsymbol{A} \boldsymbol{L}}{\boldsymbol{L} \boldsymbol{Q}} \)


The pair of equations \( 5 x-15 y=8 \) and \( 3 x-9 y=\frac{24}{5} \) has
A. One solution
B. Two solutions
c. Infinitely many solutions
D. No solution


Total number of 6 -digit number in which
only and all the five digits 1,3,5,7 and 9 appear, is :
A \( \cdot \frac{1}{2}(6 !) \)
B. \( 5^{\text {f }} \)
c. \( \frac{5}{2}(6 !) \)
D. \( 6 ! \)


In the figure, \( A \) and \( B \) are two adiabatic
curves for two different gases. Then \( \mathbf{A} \)
and B correspond to:
A. Ar and He respectively
B. He and \( H_{2} \) respectively
\( \mathrm{c} \cdot \mathrm{O}_{2} \) and \( \mathrm{H}_{2} \) respectively
D. \( H_{2} \) and He respectively


Two sound speakers are driven in phase by an audio amplifier at frequency \( 600 H z . \) The speed of sound is \( 340 m / s \)
The speakers are on the \( y \) -axis, one at \( \boldsymbol{y}=+1.0 \boldsymbol{m} \) and the other at \( \boldsymbol{y}= \)
\( -1.0 m . \) A listener begins at \( y=0 \) and
walks along a line parallel to the \( y \) -axis at a very large distance \( x \) away. At what
angle \( \theta^{o} \) (between the line from the origin to the listener at the \( x \) -axis will
she first hear a minimum sound
intensity?


Sum of internal angles of a triangle equals to
\( \mathbf{A} \cdot 135^{\circ} \)
B. \( 180^{\circ} \)
c. \( 270^{\circ} \)
D. \( 360^{\circ} \)


Two spheres have their surface areas in
the ratio \( 4: 9 . \) Their volumes are in the
ratio \( \boldsymbol{m}: \boldsymbol{n} . \) Find \( \boldsymbol{m}+\boldsymbol{n} \)


Which of the following statements
is/are correct, when a mixture of \( N a C l \)
and \( K_{2} C r_{2} O_{7} \) is gently warmed with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
This question has multiple correct options
A. Deep red vapors are evolved
B. The vapors when passed into \( N a O H \) solution give a yellow solution of \( N a_{2} C r O_{4} \)
c. chlorine gas is evolved.
D. Chromyl chloride is formed.


A mixture of 2 moles \( C O \) and 1 mole \( O_{2} \)
in a closed vessel is ignited to convert
CO into \( C O_{2} \). Then
\( \mathbf{A} \cdot \Delta H=\Delta E \)
в. \( \Delta H>\Delta E \)
c. \( \Delta H<\Delta E \)
D. none of the above


More \( \mathrm{CO}_{2} \) is evolved than the volume
of oxygen consumed when the respiratory substrate is
A. Fat
B. Sucrose
c. Glucose
D. organic acid


Which of the following pairs of
semiconductor devices and the
materials used don't match?
A. Solar cell : \( C u I n S e_{2} \) as absorber and \( C d S \) as collector
B. LED:GaAs and AlGaAs
c. optical fibre : Vitreous high silica glass doped with germanium
D. Semiconductor Laser: NdYAG


Assertion
The plot of atomic number \( (y \text { -axis) } v s \)
number of neutrons \( (x- \) axis ) for stable
nuclei shows a curvature towards \( x- \)
axis from the line of \( 45^{\circ} \) slope as the
atomic number is increased.
Reason
Proton-proton electrostatic repulsion begins to overcome attractive forces involving proton and neutrons in heavier nucleides.
A. \( S \) is correct but \( E \) is wrong
B. \( S \) is wrong but \( E \) is correct
c. Both \( S \) and \( E \) are correct and \( E \) is correct explanation of \( S \)
D. Both \( S \) and \( E \) are correct but \( E \) is not correct explanation of \( S \)


Using graph paper, (take \( 2 \mathrm{cm}=1 \) unit on both axis), plot \( \boldsymbol{A}(-\mathbf{4}, \mathbf{2}) \) and \( \boldsymbol{B}(\mathbf{2}, \mathbf{4}) \)
\( A^{\prime} \) is the image of \( A \) when reflected in
the \( y \) -axis. Plot it on the graph paper
and write the coordinates of \( A^{\prime} . B^{\prime} \) is
the image of \( B \) when reflected about the
line \( A A^{\prime} . \) Join \( A-B-A^{\prime}-B^{\prime} \) and
name the quadrilateral


lce begins to separate at \( -0.744^{\circ} \mathrm{C} \) from a solution containing 2.4 g of nonvolatile, non-electrolyte in 100 g water. Calculate the molar mass of solute, \( \boldsymbol{K}_{\boldsymbol{f}} \)
for \( \boldsymbol{H}_{2} \boldsymbol{O} \) is \( 1.86 \mathrm{K} \) mol\( ^{-1} \boldsymbol{k} \boldsymbol{g} \). Assume
mass of solvent is equal to mass of solution. Answer in g/mol.(Enter the answer as \( \frac{M a s s}{10} \) ).


Which has a higher melting point between \( 1,3- \) dichlorobenzene and
1, 4-dichlorobenzene?
A. 1,3 -dichlorobenzene
B. 1,4-dichlorobenzene
c. Both have same melting point
D. None of these


\( \int \frac{\left(x^{3}+8\right)(x-1)}{x^{2}-2 x+4} d x \)


If \( A \) and \( B \) are two mutually exclusive
events in a sample space \( S \) such that \( \boldsymbol{P}(\boldsymbol{B})=2 \boldsymbol{P}(\boldsymbol{A}) \) and \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{S} \) then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.


Some statements about heavy water
are given below:
(a) Heavy water is used as a moderator in nuclear reactions
(b) Heavy water is more associated
than ordinary water
(c) Heavy water is more effective solvent than ordinary water Select correct statements:
A. \( (a),(b) \) and \( (c) \)
\( c \)
B. \( (b) \) and \( (c) \)
c. \( (a) \) and \( (c) \)
D. \( (a) \) and \( (b) \)


What is the value of \( \frac{\sin ^{2} 30^{0}}{\cos ^{2} 30^{0}}+ \)
\( \frac{\cos ^{2} 30^{0}}{\sin ^{2} 30^{0}} ? \)


20 persons were invited to a party. In how many ways can they be seated in a round table such that two particular persons sit on either side of the host?
A . 18
в. \( 16 ! \)
c. \( 2 \times 18 \)
D. none of these


Which one of the following is the oldest use of earthworm?
A. Bait for catching fish
B. Source of manure
c. Food of poultry
D. Medicine for gout


An electrochemical cell consists of?
A. A cathode, anode, electrolyte, wire and two compartments.
B. Cathode, anode, and wire
C. Two compartments that conduct electricity.
D. A positive and negative side.
E. A cathode and an anode.


Find the value of the complex number
\( \left(i^{25}\right)^{3} \)


How many of the following is the
matter?
Chair, Air, Heat, Smell, Sound, Almonds, Thought and Cold drink.
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


Find out \( E: \)
\( \mathbf{A} \cdot N a_{3} G e F_{6} \)
\( \mathbf{B} \cdot N a_{3} A l F_{6} \)
\( \mathbf{C} \cdot A l_{2} O_{3} \)
D. none of these


In the above reaction the attack of a
nucleophile would be from which side:
\( \mathbf{3} \)
\( \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\boldsymbol{C}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C l} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \boldsymbol{C} \boldsymbol{H}_{3}- \)
\( \boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{O} \boldsymbol{H} \)
\( \boldsymbol{C} \boldsymbol{H}_{3} \)
A. on the front side of \( C l \) and \( C_{1} \) carbon
B. on \( C_{2} \)
C. on the rear side of Cl and \( C_{1} \) carbon
D. on \( C_{3} \) carbon


Find the distance covered by a particle
during the interval \( t=0 \) to \( t=20 \) s for
which the speed-time graph is shown in
figure.
A . 200 \( \mathrm{m} \)
B. 400 \( m \)
c. \( 100 \mathrm{m} \)
D. 300 \( \mathrm{m} \)


Find the equations of the lines for which \( \tan \theta=\frac{1}{4}, \) where \( \theta \) is the angle of
inclination of the line and \( y- \) intercept
is \( \frac{-3}{2} \)


In which of the following is \( \Delta H_{h}^{\circ} \) the
maximum ?
\( \mathbf{A} \cdot H_{2} C=C H_{2} \)
в. \( H_{2} C=C=C H_{2} \)
c.
D.


Given below are assertion and reason.
Point out if both are true with reason
being correct explanation (A), both true but reason is not correct explanation
(B), assertion true but reason wrong (C)
and both wrong (D), Assertion. Vascular cambium is
considered as lateral meristem.
Reason. It gives rise to lateral shoots.
\( A \cdot A \)
B. B
\( c \cdot c \)
D. D


All of the following statement about feedback inhibition of enzyme is true, with an exception of
A. It is exerted through allosteric effects
B. It is directed at the enzyme that catalyzes the first committed step in a branch of a pathway
c. It affects the rate of reaction, not the concentration of enzyme
D. It acts very slowly


The IUPAC name of the well known
terpene camphor having the structure
is:
A. 6 -oxo-1,2,2-trimethylbicyclo[2.2.1]heptane
B. 1,7,7-trimethyl bicyclo[2.2.1]heptane-2-one
C. 1,5,5 -trimethyl bicyclo[2.1.1]hexane-2-one
D. 1,7,7 -trimethyl bicyclo[2.1.2]heptane-2-one


Assertion
Free chlorine is the Oxidising agent in aqua regia.
Reason It is present in high concentration as compared to nitric acid. Nitric acid reacts with HCl to form nitrosyl chloride
NOCI,chlorine and water
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


For two structures namely \( S_{1} \) with \( n_{1}= \) \( \sqrt{45 / 4} \) and \( n_{2}=3 / 2, \) and \( S_{2} \) with \( n_{1}= \)
\( 8 / 5 \) and \( n_{2}=7 / 5 \) and taking the refractive index of water to be \( 4 / 3 \) and
that of air to be \( 1, \) the correct option is
are
This question has multiple correct options
A. NA of \( S_{1} \) immersed in water is the same as that of \( S_{2} \)
immersed in a liquid of refractive index \( \frac{16}{3 \sqrt{15}} \)
B. NA of \( S_{1} \) immersed in liquid of refractive index \( \frac{6}{\sqrt{15}} \)
same as that of \( S_{2} \) immersed in water
C. NA of \( S_{1} \) placed in air is the same as that of \( S_{2} \)
immersed in a liquid of refractive index \( \frac{4}{\sqrt{15}} \)
D. NA of \( S_{1} \) placed in the air is the same as that of \( S_{2} \) placed in water


Write down the number of significant figures in \( 12.00 \mathrm{N} \)
A. four
B. three
c. two
D. one


A right angled tube is fixed horizontally on a horizontal surface and an ideal
liquid of density p is flowing into the
tube at the rate of \( Q=4 m^{3} / s \) Cross
sectional area of the tube at intake and
outlet positions are \( A=2 m^{2} \) and \( S= \)
\( 1 m^{2} \) respectively. The magnitude of net
force exerted by liquid on the tube is (Given that the value of atmospheric
pressure \( \left.P_{o}=4 p N / m^{2}\right) \)
\( \mathbf{A} \cdot 3 \sqrt{12} p \)
B. \( 4 \sqrt{41} p \)
c. \( 5 \sqrt{21} p \)
D. None of there


The sum of first six terms of an
arithmetic progression is \( 42 . \) The ratio of its \( 10^{t h} \) term and \( 30^{t h} \) term is 1: 3
Calculate the first and the thirteenth
term of A.P.


fray \( O S \) stand on a line \( P O Q \). Ray \( O R \)
and ray \( \boldsymbol{O} \boldsymbol{T} \) are angle bisectors of
\( \angle P O S \) and \( \angle S O Q \) respectively. If
\( \angle P O S=x, \) find \( \angle R O T \)


Figure shows a disc of mass \( \mathrm{M} \) and radius R hinged at the centre. A small ball of mass \( \frac{M}{2} \) is attached to point \( P \)
with a thread of length \( 2 R \) and held at
rest at position shown. Now, the ball is released to fall under gravity. With what
angular speed does the disc start
turning when the string becomes taut?
A \( \cdot \sqrt{\frac{g}{R}} \)
в. \( \sqrt{\frac{g}{2 R}} \)
\( c \cdot \sqrt{\frac{R}{q}} \)
D. \( \sqrt{\frac{2 g}{R}} \)


supports combustion.
A. Sodium bicarbonate
B. Hydrogen
c. Carbon dioxide
D. None of these


The synthesis of ATP from ADP and inorganic phosphate is a(n) reaction that is coupled to
a reaction known as
A. Endergonic; Chemiosmosis
B. Exergonic; Chemiosmosis
c. Chemical; ATP synthase
D. Chemiosmotic; ATP synthase


Show that \( \triangle A B C, \) where
\( \boldsymbol{A}(-\mathbf{2}, \mathbf{0}), \boldsymbol{B}(\mathbf{2}, \mathbf{0}), \boldsymbol{C}(\mathbf{0}, \mathbf{2}) \) and \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \)
where \( \boldsymbol{P}(-\mathbf{4}, \mathbf{0}), \boldsymbol{Q}(\mathbf{4}, \mathbf{0}), \boldsymbol{R}(\mathbf{0}, \mathbf{4}) \) are
similar.


The opening of the urinary bladder is
A. Nephron
B. Ureter
c. Urethra
D. Nephridia


Pithecanthropus erectus fossil was found
\( \mathbf{n} \)
A. China
B. Japan
c. Java
D. Texas


The cylindrical shape of alkynes is due
to:
\( \mathbf{A} \cdot \) three \( \sigma C-C \) bonds
B. three \( \pi C-C \) bonds
C. two \( \sigma C-C \) and two \( \pi C-C \) bonds
D. one \( \sigma C-C \) and two \( \pi C-C \) bonds


Gametes are never hybrid'. This
statement is law of
A. Dominance
B. Independent assortment
c. Segregation
D. Random fertilization


An oil drop of radius r carrying a charge q' remains stationary in the presence of electric field of intensity E. If the density of oil is \( \rho, \) then
\( ^{\mathbf{A}} \cdot E=\frac{4}{3} \pi r^{3} \rho g q \)
B. \( \quad E=\frac{4}{3} \pi r^{3} \rho g \)
c. \( _{E}=\frac{4}{3} \pi r^{3} \rho g / q \)
D. \( E=\frac{4}{3} \pi r^{3} \rho / g^{3} \)


The absolute charge of the electron
is
A \( \cdot 1.1 \times 10^{11} \mathrm{C} \)
B . \( 1.6 \times 10^{14} \mathrm{C} \)
c. \( 1.6 \times 10^{-19} \mathrm{c} \)
D. \( 6.0 \times 10^{-21} \mathrm{c} \)


Choose the correct answers from the
alternatives given
Pteridophytcs differ from bryophytes in having:
A. motile male gametes
B. alternation of generations
c. antheridia
D. vascular tissue


A concave mirror has a radius of
curvature \( 2 \mathrm{m} . \) The light from a distance source is incident on the mirror. The
distance of the image of the source
from the mirror is:
\( \mathbf{A} \cdot 0.5 m \)
B. \( 1 m \)
c. \( 1.5 m \)
D. \( 2 m \)


State whether given statement is True or False

During the night, land cools faster than
sea.
A. True
B. False


A block of mass \( 12 \mathrm{Kg} \) is attached to a
string wrapped around a wheel of
radius \( 10 \mathrm{cm} . \) The acceleration of the
block moving down an inclined plane is
measured as \( 2 m / s^{2} . \) The tension in the string is :
A . \( 24.5 N \)
B. \( 68.7 N \)
c. \( 23.4 N \)
D. \( 46.8 N \)


The area of the region bounded by the
curves \( \boldsymbol{y}=\mathbf{2}^{x}, \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\mathbf{2} \)
is
A \( \cdot \frac{3}{\log 2}-\frac{4}{3} \)
в. \( \frac{3}{\log 2}-\frac{4}{9} \)
c. \( \frac{3}{2}-\frac{\log 2}{9} \)
D. None of these


Prove that \( \frac{(2 n !)}{n !}=2^{n}(1.3 .5 \dots .(2 n-1)) \)


Prothallial cells in pollen of Cycas are
found to be
A. one
B. Two
c. Three
D. Four


Write short note on sex determination
in humans.


The displacement time graph for the
particles \( A \) and \( B \) are straight lines inclined at angles 30 degree and 40 degree with the time axis. What is the ratio of the velocities of \( A \) and \( B ? \)


Using binomial theorem find the value of \( (102)^{3} \)


Ajay had purchased a second hand scooter for Rs. 18000 and spent Rs 1800
for repairs. After 1 year he wanted to sell the scooter. At what price should he sell
it to gain \( \frac{\mathbf{1 0 0}}{\mathbf{9}} \%, \) if \( \frac{\mathbf{1 0 0}}{\mathbf{1 1}} \% \) is to be
deducted at the end of every year on
account of depreciation?
A. Rs. 18000
B. Rs. 19800
c. Rs. 20000
D. Rs. 22500


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


A two-digit number is formed with the
digits 2,5 and \( 7, \) where repetition of digits is not allowed. Find the probability that the number so formed
is a square number


\( f(x) \) is a function defined on the set of
Real Numbers \( \boldsymbol{f}(\mathbf{1})=\mathbf{1} \)

Also, \( f(x+5) \geq f(x)+5 \) for all \( x \epsilon R \)
and \( f(x+1) \leq f(x)+1 \)
If \( , g(x)=(f(x))^{2}-f(x) \)
This question has multiple correct options
A \( \cdot g(2019)>(2019)^{2} \)
B . \( g(2019)<(2019)^{2} \)
C \( \cdot g(2019)=(2019)^{2} \)
D. \( g(2019)=2019 \times 2018 \)


Which of the following is(are) the the product(s) in the above reaction?
A. 2 -chloroacetophenone
B. 4-chloroacetophenone
c. 3 -chloroacetophenone
D. Both A and


Give reason: Birds puff up their
feathers in winter
A. so that they can trap more air
B. so that can develop charge
c. cant say
D. so that friction reduces


A man of mass \( 62 \mathrm{kg} \) is standing on a stationary boat of mass 238 kg. The man is carrying a sphere of mass \( 0.5 \mathrm{kg} \) in his hands. If the man throws the
sphere horizontally with a velocity of
\( 12 m s-1, \) find the velocity with which the boat will move (in magnitude)
A \( .0 .02 m s^{-1} \)
B. \( 0.5 m s^{-1} \)
C. \( 0.04 m s^{-1} \)
D. \( 0.06 m s^{-1} \)


List I and List II contains four entries
each. Entries of Column I are to be
matched some entries of List II. One or
more than one entries of List I may
match with the same entry of List II. List I lists the partial derivatives and List II lists the thermodynamic variable.


Consider a fuel cell supplied with 1 mol
of \( H_{2} \) gas and 10 moles of \( O_{2} \) gas. If fuel
cell is operated at 96.3 m \( A \) current, how long will it deliver power? (Assume \( 1 F=96500 C / \)mol of
electrons)
\( \mathbf{A} \cdot 1 \times 10^{6} s \)
B . \( 0.5 \times 10^{6} s \)
C \( .2 \times 10^{6} s \)
D. \( 4 \times 10^{6} s \)
E . \( 5 \times 10^{6} \)


In a triangle \( P Q R, L \) and \( M \) are two points
on the base \( Q R, \) such that \( \angle L P Q= \)
\( \angle Q R P \) and \( \angle R P M=\angle R Q P . \) Prove
that
\( \boldsymbol{P Q}^{2}=\boldsymbol{Q} \boldsymbol{R} \times \boldsymbol{Q} \boldsymbol{L} \)


Assertion
If the earth suddenly stops rotating about its axis, the n acceleration due to gravity will become the same at all
places.
Reason
The value of acceleration due to gravity is independent of rotation of the earth.
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


In which of the following plant, the fruit is a drupe, seed coat is thin, embryo is inconspicuous and endosperm is edible?
A. Groundnut
B. Wheat
c. Apple
D. coconut


A body falls freely from rest. It cover as much distance in the last second of its
motion as covered in the first three
second. The body has fallen for a time of
A . \( 3 s \)
B . \( 5 s \)
c. \( 7 s \)
D. \( 9 s \)


\( X e F_{2} \) reacts with \( P F_{5} \) to give:
A. \( X e F_{6} \)
\( \mathbf{B} \cdot[X e F]^{+}\left[P F_{6}\right]^{-} \)
c. \( x e F_{4} \)
\( \mathbf{D} \cdot\left[P F_{4}\right]^{+}\left[X e F_{3}\right]^{-} \)


An electromagnetic wave radiates outwards from a dipole antenna, with
\( E_{0} \) as the amplitude of its electric field
vector. The electric field \( E_{0} \) which
transports significant energy from the source falls off as
A \( \cdot \frac{1}{r^{3}} \)
B. \( \frac{1}{r^{2}} \)
\( c \cdot \frac{1}{r} \)
D. remains constant


A marble of mass \( x \) and diameter \( 2 r \) is
gently released a tall cylinder containing honey.If the marble displaces mass \( \$ \$ y(\langle 1, x) \) of the liquid then the terminal velocity is proportional to
A. \( (x+y) \)
в. \( (x-y) \)
c. \( \left(\frac{x+y}{r}\right) \)
D. \( \left(\frac{x-y}{r}\right) \)


Solve \( : 2 x+5 x=0 \)


If the mother is \( R h^{-v e} \) and father is
\( R h^{+v e}, \) which of the following \( R h^{+v e} \)
child is normally not affected?
A. First
B. second
c. Male child
D. Female child


What is the quotient when \( \left(x^{3}+8\right) \) is
divided by \( \left(x^{2}-2 x+4\right) ? \)
\( \mathbf{A} \cdot x-2 \)
B. \( x+2 \)
c. \( x+1 \)
D. \( x-1 \)


A woman bought 50 dozen eggs at Rs 16 a dozen. Out of these, 20 eggs
were found to be broken. She sold the
remaining egg at \( R s 1.50 \) per egg. Find her gain or loss per cent.


For long distance transmission, the AC
is stepped up because at high voltage, the transmission is
A. faster
B. economical
c. undamped
D. less dangerous


A die is rolled, find the probability that an odd numbers is obtained.
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{7}{2} \)
D. \( \frac{6}{3} \)


Thin threads are tightly wound on the ends of a uniform solid cylinder of mass
m. The free ends of the threads are
attached to the ceiling of an elevator car. The car starts going up with an
acceleration \( \overrightarrow{\boldsymbol{w}}_{\mathbf{0}} \)
Find the acceleration \( \vec{w}^{\prime} \) of the cylinder
relative to the car:
A \( \cdot \vec{w}^{\prime}=\frac{2}{3}\left(g-\vec{w}_{0}\right) \)
B \( \cdot \vec{w}^{\prime}=\frac{3}{2}\left(g-\vec{w}_{0}\right) \)
c. \( \vec{w}^{\prime}=2 \frac{3}{2}\left(g-\vec{w}_{0}\right) \)
D・ \( \vec{w}^{\prime}=2 \frac{2}{3}\left(g-\vec{w}_{0}\right) \)


Match the reactions in column I with
the molar ratio of their respective oxidants and reductant in column II.


Closing both the eyes when a torch light is flashed on one eye is a part of
A. Reflex action
B. Chemotropism
c. Hormonal control
D. None of these


Cells of the pancreas is not digested by their own enzymes because
A. Enzymes are secreted in inactive form
B. Cells are lined by mucous membrane
c. Enzymes are released only when needed
D. None of the above


Three angles of a seven sided polygon
are \( 132^{\circ} \) each and the remaining four
angles are equal. Find the value of each equal angle.
A .125
B. \( 156^{\circ} \)
\( c \cdot 126^{\circ} \)
D. \( 130^{\circ} \)


All alkali metals dissolve in anhydrous liquid ammonia to give a blue color solution. It is the ammoniated electron
which is responsible for the blue color of the solution, and the electrical conductivity is due to ammoniated
cation, \( \left[M\left(N H_{3}\right)_{x}\right]^{+} \) as well as the
ammoniated electron, \( \left[e\left(N H_{3}\right)_{y}\right]^{-} \) values of \( x \) and \( y \) depend on the extent of
solvation by \( N H_{3} . \) Dilute solutions are
paramagnetic due to free ammoniated electrons.
What happens if alkali metals are allowed to react with concentrated
liquid ammonia?
A. Paramagnetic character of solvated electrons is retained.
B. Solvated electrons associate to form electron-pairs and paramagnetic character decreases
c. Reducing character is increased.
D. Reducing character is not affected.


The focal length of a glass slab of
refractive index 1.5 is
A . Infinite
B. Zero
c. Unity
D. None of these


Which one of the following hormones is not found in plants?
A. \( 2,4- \) D
B. IAA
c. Gibberellin
D. None of the above


State whether given statement is True or False.

The motion described by wire of sitar is a vibratory motion
A. True
B. False


Which of the following is not an actinoid?
A. Carium\( (Z=96) \)
B. Californium(Z = 98)
c. Uranium\( (Z=92) \)
D. Terbium( \( Z=65 \) )


Expand:
\( \left(\frac{2}{x}-\frac{x}{2}\right)^{5} \)


Obdiplostemonous condition is that in which the stamens are in two whorls
and
A. Outer whorl is fused to inner whorl.
B. Outer whorl is opposite to petals.
c. Inner whorl is opposite to petals.
D. Both, inner as well as outer whorls are opposite to petals


Two waves \( A \) and \( B \) have wavelength
\( 0.01 A^{\circ} \) and \( 9000 A^{\circ} \) respectively. Name
the two waves.
A. A-gamma, B-infrared
B. A-gamma, B-ultraviolet
c. A-ultraviolet, B-infrared
D. A-gamma, B-X rays


The general molecular formula for
disaccharide is:
A. \( C_{12} H_{22} O_{11} \)
B. \( C_{10} H_{20} O_{10} \)
c. \( C_{12} H_{20} O_{10} \)
D. \( C_{12} H_{22} O_{10} \)


Energy ol electron varies wIIn acormcc
number as the following curve/line:
\( A \)
B.
\( c \)
D.


4th period in periodic table, ends with krypton.
A . True
B. False


Among the following, the INCORRECT statement about colloids is:
A. They can scatter light
B. They are larger than small molecules and have high molar mass
c. The range of diameters of colloidal particles is between 1 and \( 1000 n m \)
D. The osmotic pressure of a colloidal solution is of higher order than the true solution at the same concentration


The rate constant for two parallel
reactions were found to be \( 1.0 \times \)
\( 10^{-2} d m^{3} m o l^{-1} s^{-1} \) and \( 3.0 \times 10^{-2} d m^{3} \)
\( m o l^{-1} s^{-1} . \) If the corresponding energies
of activation of the parallel
reactions are \( 60.0 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( 70.0 \mathrm{KJ} \)
mol \( ^{-1} \) respectively, then what is the apparent overall energy of activation?
B. 65.0 KJ \( m o l^{-1} \)
c. 67.5 к \( \operatorname{mol}^{-1} \)
D. 100.0 K」 \( m o l^{-} \)


A triangle \( A B C \) is placed so that the
midpoints of its sides are on the \( \boldsymbol{x}, \boldsymbol{y} \)
and \( z \) axes respectively. Lengths of the
intercepts made by the plane containing the triangle on these axes
\( \operatorname{are} \) respectively \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \) then
the coordinates of the centroid of the
triangle \( A B C \) are
A \( \cdot\left(-\frac{\alpha}{3}, \frac{\beta}{3}, \frac{\gamma}{3}\right) \)
В \( \cdot\left(\frac{\alpha}{3},-\frac{\beta}{3}, \frac{\gamma}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{\alpha}{3}, \frac{\beta}{3},-\frac{\gamma}{3}\right) \)
D \( \cdot\left(\frac{\alpha}{3}, \frac{\beta}{3}, \frac{\gamma}{3}\right) \)


The resistance of wire is \( 20 \Omega \). The wire
is stretched to three time its length. Then the resistance will now be
\( \mathbf{A} \cdot 6.67 \Omega \)
B. \( 60 \Omega \)
c. \( 120 \Omega \)
D. \( 180 \Omega \)


A radioactive sample decays by \( 63 \% \) of its initial value in \( 10 s . \) It would have
decayed by \( 50 \% \) of its initial value in
\( \mathbf{A} \cdot 7 s \)
в. 14 s
c. \( 0.7 s \)
D. \( 1.4 s \)


The reaction that is responsible for the
primary fixation of \( C O_{2} \) is catalysed by
A. \( R u B P \) carboxylase
B. \( P E P \) carboxylase
c. \( R u B P \) carboxylase and \( P E P \) carboxylase
D. \( P G A \) synthase


If \( A_{n} \) is the area bounded by \( y= \)
\( \left(1-x^{2}\right)^{n} \) and coordinate axes, \( n \) is in
set of natural numbers, then
A. \( A_{n}=A_{n-1} \)
В. \( A_{n}<A_{n-1} \)
C \( . A_{n}>A_{n-1} \)
D. \( A_{n}=2 A_{n-1} \)


The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne: The
bromoalkane and alkyne respectively
are:
A \( \cdot B r C H_{2} C H_{2} C H_{2} C H_{2} C H_{3} \) and \( C H_{3} C H_{2} C=C H \)
B. \( B r C H_{2} C H_{2} C H_{3} \) and \( C H_{3} C H_{2} C H_{2} C=C H \)
C. \( B r C H_{2} C H_{2} C H_{2} C H_{2} C H_{3} \) and \( C H_{3} C=C H \)
D. \( B r C H_{2} C H_{2} C H_{2} C H_{3} \) and \( C H_{3} C H_{2} C=C H \)


Integrate the function \( \left(\sin ^{-1} x\right)^{2} \)


Select the correct statement(s) about
ether.
This question has multiple correct options
A. Symmetrical ethers have zero dipole moment.
B. Unsymmetrical ethers don't have zero dipole moment.
C. Ethers have lower boiling point as compared to alcohols.
D. There extent of H-bonding in ethers are comparable to that in alcohols.


The time taken by the current to rise to 0.63 of its maximum value in a d.C
circuit containing inductance \( (\boldsymbol{L}) \) and
resistance \( (\boldsymbol{R}) \) depends on
A. \( L \) only
B. \( R \) only
c. \( \frac{L}{R} \) only
D. \( L R \) only


Which of the following is/are correct for lyophillic sols?
This question has multiple correct options
A . Its surface tension is lower than that of \( H_{2} O \)
B. Its viscosity is higher than that of water.
c. Its surface tension is higher than that of water.
D. Its viscosity is equal to that of water.


Give the balanced equation to prepare sulphur dioxide. Which type of oxide is sulphur dioxide?


If the points with position vectors \( 60 \hat{i}+ \) \( \mathbf{3} \hat{\mathbf{j}}, \mathbf{4 0} \hat{\mathbf{i}}-\mathbf{8} \hat{\mathbf{j}} \) and \( \boldsymbol{a} \hat{\mathbf{i}}-\mathbf{5 2} j \) are collinear
then \( a=? \)
A . -40
B. -20
c. 20
D. 40


Evaluate:
\( \left(y^{3}-216\right) \div(y-6) \)


A long solenoid carrying a current
produces a magnetic field B along its axis. If the current is doubled and the
number of turns per cm is halved, the new value of the magnetic field is
\( A \cdot B / 2 \)
B. B
\( c \cdot 2 B \)
D. 4 B


Polyester is a natural fiber.
A. True
B. False


The magnetic field of a given length of wire carrying a current for a single turn cicular coil at center is \( \mathrm{B} \), then its value
for two turns for the same wire when
same current passing through it is
A \( \cdot \frac{B}{4} \)
в. \( \frac{B}{2} \)
\( c .2 B \)
D. \( 4 B \)


State whether True or False.
Factorization of \( 54 a^{2} b^{2}-6 \) is \( 6(3 a b+ \)
1) \( (3 a b-1) \)
A. True
B. False


What is a genetic code?


A sinusoidal voltage \( V=200 \sin 314 t \) is
applied to a \( 10 \Omega \) resistor. Find power dissipated as heat.
\( \mathbf{A} .500 W \)
в. \( 1000 \mathrm{W} \)
c. \( 2000 W \)
D. 3000W


Assertion: Copper sulphate solution can be stored in a zinc vessel.
Reason: \( \boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{\ominus}= \)
\( \mathbf{0 . 3 4} \boldsymbol{V}, \boldsymbol{E}_{Z n^{2+} \mid \mathbf{Z} n}^{\ominus}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{\oplus} \mid A \boldsymbol{g}}^{\ominus}=\mathbf{0 . 8 0} \boldsymbol{V} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


What are the changes observed at the transition temperature in
superconductors?


In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along - \( \hat{y} \) )?
A. \( (I I I)(i i)(P) \)
B . \( (I I)(i i i)(Q) \)
c. \( (I V)(i i)(S) \)
D. \( (I I I)(i i)(R) \)


A conductor \( A B C D E F, \) shaped as
shown, carries a current i. It is placed in
the \( x y \) plane with the ends \( A \) and \( E \) on
the \( x \) -axis. A uniform magnetic field of
magnitude \( B \) exists in the region. The
force acting on it will be :
This question has multiple correct options
A. zero, if \( B \) is in the \( x \) -direction
B. \( \lambda B i \) in the \( z \) -direction, if \( B \) is in the \( y \) -direction
C. \( \lambda B i \) in the negative \( y \) -direction, if \( B \) is in the \( z- \) direction
D. \( 2 a B i \), if \( B \) is in the \( x \) -direction


For the circuit shown in the fig., the
current through the inductor is \( 0.9 A \)
while the current through the condenser
is \( 0.4 A . \) Then
A. current drawn from generator \( I=1.13 A \)
B. \( \omega=1 /(1.5 L C) \)
\( \mathbf{c} \cdot I=0.5 A \)
D. \( I=0.6 A \)


The non-zero vectors \( \bar{a}, \bar{b} \) and \( \bar{c} \) are related \( \bar{a}=8 \bar{b} \) and \( \bar{c}=-7 \bar{b} . \) Then the
angle between \( \bar{a} \) and \( \bar{c} \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D. \( \pi \)


In a metre bridge, the balancing point obtained at \( 40 \mathrm{cm} . \) If a resistance equa
that in the left gap is shunted across it
the new balancing point.
\( A \cdot 20 \mathrm{cm} \)
B. 25 cm
c. \( 30 \mathrm{cm} \)
D. 15 \( \mathrm{cm} \)


\( \boldsymbol{L} \boldsymbol{t}_{\boldsymbol{x} \rightarrow \mathbf{0}}=\frac{\sqrt{\mathbf{1}+\mathbf{x}}-\sqrt{\mathbf{1}+\mathbf{x}^{2}}}{\sqrt{\mathbf{1 - x}^{2}}-\sqrt{\mathbf{1 - x}}}= \)
\( A \)
B. -
\( c \cdot 0 \)
\( D \)


Sulfide ores are usually dressed by the
process.
A. sieve process
B. froth floatation
c. magnetic floatation
D. none of these


What type of sound waves can
propagate in solids?
A. Longitudinal only
B. Transverse Only
C. Both longitudinal and transverse
D. Non mechanical waves only


Write the IUPAC names of the given
compounds:
\[
\equiv>-
\]


\( 60 \mathrm{cc} \) of a liquid of relative density 1.4 is mixed with \( 40 \mathrm{cc} \) of another liquid of relative density 0.8. The density of the resulting mixture will be
A. \( 1.16 \mathrm{g} / \mathrm{cc} \)
B. 2.26 g/cc
c. \( 11.6 \mathrm{g} / \mathrm{cc} \)
D. 116 g/cc


A rigid body is a body in which
A. the distance between any two given points remains constant till an external forces exerted on it.
B. the distance between any two given points changes with time regardless of external forces exerted on it.
C. the distance between any two given points remains constant in time regardless of external forces exerted on it.
D. the distance between any two given points changes with time until external forces exerted on it.


Science fiction films often show battles
between spaceships. Four friends were arguing what would someone in space hear if an enemy spaceship exploded? Rekha said, 'they would hear a big explosion. Renu saud,'they will not hear anything as there is no medium for sound to
travel, but they can see the explosion. Ramesh said, 'yes, they will not hear
anything and they will not be able to see the explosion. Raghav said,'the explosion produces sound of frequency above \( 20,000 \mathrm{Hz} \) hence we cannot hear it.'
Who is correct?
A. Rekha
B. Renu
C. Ramesh
D. Raghav


The intensity of principal maxima in the
single slit diffraction pattern is \( I_{o} \) ?
What will be the intensity when slit width is doubled?
A \( .2 I_{0} \)
в. \( 4 I_{0} \)
c. \( I_{o} \)
D. \( \frac{I_{0}}{2} \)


The minimum force required to move a body of mass m vertically upward is
\( \mathbf{A} \cdot \mathbf{m g} \)
B. mg/2
C. more that \( 2 \mathrm{mg} \)
D. more than mg


In a permutit, the calcium and magnesium ions of hard water are exchanged by:
A \( \cdot C O_{3}^{2-} \) and \( H C O_{3}- \) ions of permutit
B. \( N a^{+} \) ions of permutit
c. \( A l^{3+} \) ions of permutit
D. \( S i^{4+} \) ions of permutiti


Potential energy is classified into which
two energy?
A. Gravitational and Elastic Potential Energy
B. Kinetic and Elastic Potential Energy
c. Mechanical and Elastic Potential Energy
D. None


The units of force, velocity and energy are 100 dyne, \( 10 \mathrm{cms}^{-1} \) and 500 erg respectively. The units of mass, length and time are:
\( A \cdot 5 g, 5 \mathrm{cm}, 5 \mathrm{s} \)
B. 5 g, \( 5 \mathrm{cm}, 0.5 \) s
c. \( 0.5 \mathrm{g}, 5 \mathrm{cm}, 5 \mathrm{s} \)
D. 5 g, \( 0.5 \mathrm{cm}, 5 \mathrm{s} \)


In photosynthesis, the energy is
transferred in
A. One energy step
B. Small energy steps
c. Large energy steps
D. All of the above


Name any one heterocrine gland?


Find the measure of the angle between two lines if their direction cosines
\( \ell, \boldsymbol{m}, \boldsymbol{n} \) satisfy \( \ell+\boldsymbol{m}-\boldsymbol{n}=\mathbf{0}, \ell^{2}+ \)
\( \boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)


If sum of \( n \) terms of an A.P.is given by
\( \boldsymbol{S}_{n}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{n}+\boldsymbol{c} \boldsymbol{n}^{2} \) where \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are
independent of \( n, \) then This question has multiple correct options
\( \mathbf{A} \cdot a=0 \)
B. Common difference of A.P. must be 2b.
c. Common difference of A.P. must be 2 c
D. All above


A metal rod of length \( 10 \mathrm{cm} \) and a rectangular cross section of \( 1 \mathrm{cm} \times \frac{1}{2} \) \( \mathrm{Cm} \) is connected to a battery across opposite faces. The resistance will be.
A. Maximum when the battery is connected cross \( 1 \mathrm{cm} \) \( \times \frac{1}{2} \mathrm{cm} \) faces
B. Maximum when the battery is connected across \( 10 \mathrm{cm} \) \( \times 1 \mathrm{cm} \) faces
c. Maximum when the battery is connected across \( 10 \mathrm{cm} \) \( \times \frac{1}{2} \mathrm{cm} \) faces
D. Same irrespective of the three faces


There are three sets of animals \( C, D \) and
E. What type of symmetry is shown by
each?
A. C- - Bilateral symmetry, D- Radial symmetry, E- No symmetry
B. C- Radial symmetry, D- Bilateral symmetry, E- No symmetry
c. c- Bilateral symmetry, D- No symmetry, E- Radial symmetry
D. C- No symmetry, D- Radial symmetry, E- Bilateral symmetry


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


Which of the following circuit type is
based upon time or clock pulse?
A. Combinational circuit
B. Sequential circuit
c. Full adder
D. None of these


1 g-atom of nitrogen represents:
A \( \cdot 6.02 \times 10^{23} \mathrm{N}_{2} \) molecules
B . \( 22.4 L \) of \( N_{2} \) at \( S . T . P \)
c. \( 11.2 L \) and \( N_{2} \) at \( S . T . P . \)
D. \( 28 g \) of nitrogen


\( f\left(2 x+\frac{y}{8}, 2 x-\frac{y}{8}\right)=x y, \) then show
that \( \boldsymbol{f}(\boldsymbol{m}, \boldsymbol{n})+\boldsymbol{f}(\boldsymbol{n}, \boldsymbol{m})=\mathbf{0} \)


What is the final product \( ^{\prime} C^{\prime} \) in the following reaction? \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \stackrel{\boldsymbol{H C N}}{\longrightarrow} \boldsymbol{A}^{\prime} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}^{+}}{\longrightarrow} \)
\( ' \boldsymbol{B}^{\prime} \frac{\text {sodalime}}{\longrightarrow} \boldsymbol{C}^{\prime} \)
A. Propane
B. Propanol
c. Ethanol
D. Propanoic acid


toppr
Q Type your question
the following:
4
B.
\( c \)
\( D \)


\( \int \frac{x^{3}-1}{x^{3}+x} d x \) equal to
\( \mathbf{A} \cdot x-\log x+\log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
B. \( x-\log x+\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
c. \( x+\log x+\frac{1}{2} \log \left(x^{2}+1\right)+\tan ^{-1} x+c \)
D. \( x+\log x-\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)


What is the IUPAC name for \( C H_{3} C H O ? \)
A . Acetal
B. Methanal
c. Ethanal
D. Acetaldehyde


IUPAC name of the following compound
is :
A. 6 -ethyl-1,4, 6-octanetrioic acid
B. 5-Ethyl -hexane-1, 3, 6-tricarboxylic acid
C. 3-ethyl-5-carboxyoctanedioic acid
D. 4-carboxy-6-ethyloctanedioic acid


In nucleic acids, the sequence is
A. Phosphate base sugar
B. Sugar phosphate base
C. Phosphate-sugar base
D. Base phosphate sugar


Find the order and degree, if defined of
the differential equation
\( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{3}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+\sin \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{1}=\mathbf{0} \)


The area of a parallelogram is \( y \mathrm{cm}^{2} \) and its height is \( h \) cm. The base of
another parallelogram is \( x \) cm more
than the base of the first parallelogram
and its area is twice the area of the first.
Find, in terms of \( y, h \) and \( x, \) the expression for the height of the second
parallelogram.
A \( \frac{h y}{y h-x} \)
B. \( \frac{y}{y-x h} \)
c. \( \frac{2 h y}{y+x h} \)
D. None of these


A uniform sphere of mass \( \mathrm{M} \) and radius
\( \mathrm{R} \) is surrounded by a concentric spherical shell of same mass but
radius \( 2 \mathrm{R} . \) A point mass \( \mathrm{m} \) is kept at a distance \( x(>R) \) in the region bounded by spheres as shown in the figure. The net
gravitational force on the particle is
A \( \cdot \frac{\operatorname{CMm}}{\frac{\pi^{2}}{n}} \)
B. \( \frac{G M m}{R^{3}} \)
\( c \cdot \frac{G(M+m)}{x^{2}} \)
D. zer


Maximum change in oxidation number
of nitrogen is


Derive an expression for electric field intensity due to an electric dipole at a point on its axial line.


Which of the following actions can be grouped as pull:
a. Moving a loaded cart
b. Applying brakes while driving car
c. Drawing a bucket of water from a well
A. Only a
B. a and
\( c . \) b and \( c \)
D. a and c


The shape of stress vs strain graph within elastic limit is :
A. parabolic
B. curve
c. straight line
D. ellipse


Diazonium salts of aliphatic amines are more stable than
those of aromatic amines.
If this is true enter 1 , if false enter 0 .


What happens to the following after
fertilization?
Ovules


The thermal radiations are similar to :
A . x-rays
B. cathode rays
c. \( \alpha \) - rays
D. \( \gamma \) - rays


In AC circuit having only capacitor, the
current
A \( \cdot \) Leads the voltage by \( \frac{\pi}{2} \) in phase
B \cdot Lags behind the voltage by \( \frac{\pi}{2} \) in phase
C. Leads the voltage by \( \pi \) in phase
D. Lags behind the voltage by \( \pi \) in phase


Useful buffer range of weak acid
\( \boldsymbol{H} \boldsymbol{A}\left(\boldsymbol{K}_{a}=\mathbf{1 0}^{-5}\right) \) is:
\( \mathbf{A} \cdot 5 \) to 7
B. 4 to 6
c. 3 to 5
D. none of these


If range of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1} x+2 \tan ^{-1} x+x^{2}+4 x+1 \) is
\( [p, q], \) then the value of \( (p+q) \) is


\( \boldsymbol{A}(\boldsymbol{p}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{4}, \boldsymbol{0}), \boldsymbol{C}(\boldsymbol{5}, \boldsymbol{6}) \) and \( \boldsymbol{D}(1, \boldsymbol{4}) \) are
the vertices of a quadrilateral \( A B C D . \) If
\( \angle A D C \) is obtuse, the maximum
integral value of \( p \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Draw neat labelled diagram of a cross
section of an artery and a vein


If \( A_{1}, A_{2}, \dots, A_{100} \) are sets such that \( \boldsymbol{n}\left(\boldsymbol{A}_{\boldsymbol{i}}\right)=\boldsymbol{i}+\boldsymbol{2}, \boldsymbol{A}_{1} \subset \boldsymbol{A}_{2} \subset \boldsymbol{A}_{3} \ldots \ldots . . \boldsymbol{A}_{100} \)
and \( \bigcap_{i=3}^{100} A_{i}=A, \) then \( n(A)= \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


Four forces are acting on a body. if the body doesn't change its position or shape, the forces:
A. must be of equal magnitude
B. must be parallel \& opposite
c. must add up to zero when taken as vectors
D. must be in a single line


The relationship between rate constant and half-life for first order reaction is:
A \( \cdot t_{1 / 2}=\frac{0.693}{k} \)
B. \( _{k=\frac{-t_{1 / 2}}{0.693}} \)
c. \( t_{1 / 2}=0.693 k \)
D \( t_{1 / 2}=\frac{k}{0.693} \)


Arrange the following compounds in increasing order of boiling points. Propan-1-ol, butan-1-ol, butan-2-ol, pentan-1-ol
A. Propan-1-ol, butan-2-ol, butan-1-ol, pentan-1-ol
B. Propan-1-ol, butan-1-ol,butan-2-ol, pentan-1-o
c. Pentan-1-ol, butan-2-ol, butan-1-ol, propan-1-ol
D. Pentan-1-ol, butan-1-01, butan-2-ol, propan-1-o


Which of the following statement is
incorrect?
\( \mathbf{A} \cdot R M S \) velocity depends on the molecular weight of the gas
B. \( R M S \) velocity depends on temperature of the gas
C . \( R M S \) velocity depends on the number of molecules present in unit volume
D. \( R M S \) velocity is greater than average velocity and most probable velocity.


The equipotential surface of an electric
dipole is:
A. A sphere whose centre coincides with the centre of the electric dipole
B. A plane surface inclined at an angle of \( 45^{\circ} \) with the axis of the electric dipole
C. A plane surface passing through the centre of the electric dipole and perpendicular to the axis of the electric dipole
D. Any plane surface parallel to the axis of the electric dipole


Find the direction cosines of a line that
pass through the point \( \boldsymbol{P}(\mathbf{1}, \mathbf{4}, \boldsymbol{6}) \) and
\( Q(5,1,11) \) and is so directed that it
make an acute angle with the positive direction of \( \boldsymbol{y}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \)


Ine elastıc collısıon between two
bodies, A and B, can be considered
using the following model. A and B are
free to move along a common line without friction. When their distance is
greater than \( d=1 \mathrm{m}, \) the interacting
force is zero; when their distance is less
than \( d, \) a constant repulsive \( F=6 N \) is
present. The mass of body \( A \) is \( m_{A}=1 \mathrm{kg} \)
and it is initially at rest; the mass of
body \( \mathrm{B} \) is \( m_{B}=3 \mathrm{kg} \) and it is
approaching body A head-on with a
speed \( v_{o}=2 \mathrm{m} / \mathrm{s} \). Find the minimum
distance between \( A \) and \( B \)
A. \( 0.25 \mathrm{m} \)
B. \( 0.50 \mathrm{m} \)
c. \( 0.75 \mathrm{m} \)
D. \( 2 \mathrm{m} \)


State whether True or False.
Divide: \( x^{2}+3 x-54 \) by \( x-6, \) then the
answer is \( x+9 \)
A. True
B. False


Write he name of any one doped semiconductor used for making light emitting diode (LED)


ff \( \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\boldsymbol{r}-\mathbf{1} & \boldsymbol{n} & \boldsymbol{6} \\ (\boldsymbol{r}-\mathbf{1})^{2} & \boldsymbol{2} \boldsymbol{n}^{2} & \boldsymbol{4} \boldsymbol{n}-\boldsymbol{2} \\ (\boldsymbol{r}-\mathbf{1})^{3} & \boldsymbol{3} \boldsymbol{n}^{3} & \boldsymbol{3} \boldsymbol{n}^{2}-\boldsymbol{3} \boldsymbol{n}\end{array}\right| \)
then \( \sum_{r=1}^{n} D_{r}= \)
\( A \)
B.
c. \( \frac{n(n-1)}{2}-r^{2} \)
D. \( 2 n-n^{2} \)


If the areas of two similar triangles are equal, then they are
A . equilateral
B. isosceles
c. congruent
D. not congruent


Explain why \( N H_{3} \) is basic while \( B i H_{3} \) is only feebly basic.


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}+\boldsymbol{a} & ; \quad \boldsymbol{x}<0 \\ |\boldsymbol{x}-1| & ; \quad \boldsymbol{x} \geq 0\end{array}\right. \)
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}+\mathbf{1} & ; \text { if } \boldsymbol{x}<\mathbf{0} \\ (\boldsymbol{x}-\mathbf{1})^{2}+\boldsymbol{b} ; \boldsymbol{x} \geq \mathbf{0}\end{array}\right. \)
fgof is continuous \( (a>0), \) then
A \( . a=2, b=0 \)
В. \( a=2, b=1 \)
c. \( a=1, b=0 \)
D. \( a=1, b=1 \)


The population of a town increased from
\( \mathbf{1 7 5 0 0 0} \) to 262500 in a decade. The
average percent increase of population
per year is?
A. 33.33\%
B. 5\%
c. \( 6 \% \)
D . 8.75\%


Express the following as a fraction and simplify:
\( \mathbf{2 . 4 5} \)
A \( \cdot \frac{49}{20} \)
в. \( \frac{20}{49} \)
c. \( \frac{19}{20} \)
D. \( \frac{20}{19} \)


Mulberry, munga, oak and tussar are all the four varieties of silk are present in a single country. The country is
A. China
B. India
c. Japan
D. Korea


At certain temperature radius of an air
bubble is doubled when it comes to the
top from bottom of a mercury column of height H if the pressure is:
A. 5.5
B. 10.64
c. 12.45
D. 15


The phenomena which is not explained by Huygen's construction of the
wavefront
A. reflection
B. diffraction
c. refraction
D. origin of spectrata


Write the name of two metals which are
used in maximum composition in mischmetal?


Slope of the line passing through the
points \( \boldsymbol{P}(1,-1) \) and \( \boldsymbol{Q}(-2,5) \) is
\( A \cdot 2 \)
B. 6
c. -2
D. - 3


\( B e F_{2} \) has zero dipole moment where as
\( H_{2} O \) has a dipole moment because:
A. water is linear
B. \( H_{2} O \) is bent
C. \( F \) is more electronegative than \( O \)
D. hydrogen bonding is present in \( H_{2} O \)


A particle of mass \( 1 \mathrm{kg} \) is placed at a distance of \( 4 \mathrm{m} \) from the centre and on
the axis of a uniform ring of mass \( 5 \mathrm{kg} \)
and radius 3m. The work done to
increase the distance of the particle from \( 4 \mathrm{m} \) to \( \sqrt{3} m \) is.
A \( \cdot \frac{G}{3} J \)
в. \( \frac{G}{4} J \)
c. \( \frac{G}{5} J \)
D. \( \frac{G}{6} J \)


The sum of nn is equal to
A \( \cdot \frac{1}{4} n(n+1)(n+2) \)
B. \( \frac{1}{4} n(n+1)(n+2)(n+3) \)
c \( \cdot \frac{1}{2} n(n+1)(n+2)(n+3) \)
D. None of these


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


What would be the stoichiometric
coefficient of hydrochloric acid in the following equation?
\( \boldsymbol{C l}_{2}+_{--} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow_{--} \boldsymbol{H} \boldsymbol{C l}+_{-} \)
\( \boldsymbol{H} \boldsymbol{C l O}_{3} \)
\( A \)
B. 3
\( c \cdot 5 \)
D. 10


A car travelling \( 20 m / s \) enters into a
unbanked curve with a radius of \( 25 m \)
If the coefficient of friction between the
tires and the road is \( 0.75, \) what is the
magnitude of the change in velocity of the car if the car is going to stay in its lane?
\( \mathbf{A} \cdot \Delta v=3.20 m / s \)
B. \( \Delta v=6.40 m / s \)
c. \( \Delta v=12.8 m / s \)
D. \( \Delta v=13.6 \mathrm{m} / \mathrm{s} \)
E \( . \Delta v=26.4 m / s \)


Choose the correct statement from the
following
This question has multiple correct options
A. Woollen clothes keep the body warm in winter as air is the bad conductor of heat
B. Shining surfaces are good reflectors of heat
C. Heat radiations travel with speed of light
D. The Sl unit of coefficient of cubical expansion is \( K^{-1} \)


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{1} \) on \( [\mathbf{2}, \boldsymbol{3}] \)


The area of the triangle formed by the
three complex numbers \( 1+i, i-1,2 i \)
in the Argand diagram is:
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \sqrt{2} \)
D. 2


Which of the following aqueous solutions has the highest boiling point?
A \( .0 .1 \mathrm{M} \) К \( \mathrm{NO}_{3} \)
В. \( 0.1 \mathrm{M} \) Na \( _{3} \mathrm{PO}_{4} \)
c. \( 0.1 \mathrm{M} \) ВаСг
D. \( 0.1 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4} \)


The \( \beta \) of a transistor is \( 74 . \) It is connected in common base configuration. If the emitter current is
\( 5 m A, \) the collector current is
(approximately)
A. \( 0.45 \mathrm{mA} \)
B. \( 4.93 \mathrm{mA} \)
\( \mathbf{c} .370 \mathrm{mA} \)
D. \( 5 m A \)


The growth of plants differs from growth of animals in being
A. Localised
B. Diffused
c. Localised and diffused
D. None of the above


If \( ^{\prime} R^{\prime} \) is the radius of the earth, then the
height at which the weight of a body becomes \( \frac{1}{4} \) of its weight on the surface of the earth is:
A \( .2 . R \)
в. \( R \)
c. \( \frac{3 R}{8} \)
D. \( \frac{R}{4} \)


If \( F_{g} \) and \( F_{e} \) are gravitational and electrostatic forces between two
electrons at a distance \( 0.1 m \) then
\( \boldsymbol{F}_{\boldsymbol{g}} / \boldsymbol{F}_{e} \) is in the order of
A \( \cdot 10^{43} \)
B . \( 10^{-43} \)
\( \mathbf{c} \cdot 10^{35} \)
D. \( 10^{-35} \)


Assume that the chances of a patient
having a heart attack is \( 40 \% \). Assuming that a mediation and yoga course
reduces the risk of heart attack by \( 30 \% \) and prescription of certain drug reduces its chance by \( 25 \% \). At a time a patient can choose any one of the two options with equal possibilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of mediation and yoga. Interpret the result and state which of the above
stated methods is more beneficial for
the patient.


Destructive distillation of wood in the
laboratory will result in the formation of
A. Ethanol
B. Methane
c. Methanol
D. Butane


Find the value of \( \frac{\cos A-\sin A+1}{\cos A+\sin A-1}- \)
\( (\operatorname{cosec} A+\cot A) \)


Mendel studied seven contrasting characters for his breeding experiment with a pea. Which of the following characters he did not use?
A. Pod shape
B. Leaf shape
c. Plant height
D. Pod colour


Choose the correct statement.
A. weight is a vector quantity
B. the weight of a body in interplanetary space is maximum
C. weight increases with height from the earth surface
D. \( 1 N=1 k g \times 1 m / s \)


The third stage of demographic transition is characterised with low
growth rate of population due to decline in both birth as well as the death rate.
A. True
B. False


Calculate the longest wavelength in \( \boldsymbol{A} \) \( \left(1 \dot{A}=10^{-10} m\right) \) in the Balmer series of singly ionized helium \( H e^{+} . \) Select the
correct answer. lgnore the nuclear
motion in your calculation.
в. \( 1641.1 \dot{A} \)
\( c .6569 \hat{A} \)
D. \( 3249 \dot{h} \)


Ultimate products of hydrolysis of protein in:
A . aniline
B. aliphatic acid
c. amino acid
D. aromatic acid


Borax is actually made of two tetrahedral and two triangular units joined together and should be
written as \( : N a_{2}\left[B_{4} O_{5}(O H)_{4}\right] .8 H_{2} O \)
Consider the following statements about borax:
1. Each boron atom has four B-O bonds
2. EAch boron atom has three B-O bonds
3. Two boron atoms have four B-O bonds
while other two have three B-O bonds
4. Each boron atom has one-OH groups
Select correct statement(s)-
A \( \cdot 1,2 \)
B. 2,3
\( c \cdot 3,4 \)
D. 1, 3


A body of mass 'm' is raised from the surface of the earth to a height 'nR' (Rradius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
B \( \cdot\left(\frac{n-1}{n}\right) m g R \)
c. \( \frac{m g R}{n} \)
D. \( \frac{m g R}{(n-1)} \)


Statement I: \( _{6}^{14} C \) and \( _{6}^{12} C \) are isomers of the element carbon.

Statement II: Isomers contain the same
number of protons but a different number of neutrons
A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. Statement I is correct, but Statement II is incorrect
D. Both Statement I and Statement II are incorrect


If \( \tan ^{-1} x+\tan ^{-1} y=\frac{2 \pi}{3}, \) then
\( \cot ^{-1} x+\cot ^{-1} y \) is equal to
\( ^{A} \cdot \frac{\pi}{2} \)
в.
c.
D. \( \frac{\sqrt{3}}{2} \)
E . \( \pi \)


In the given figure, 0 is the centre of the
circle and \( \angle A B C=36^{\circ} . \) The measure
of \( \angle A O C \) is :
\( A \cdot 36 \)
B. 72
\( c \cdot 144 \)
\( D \cdot 18 \)


Heavy water \( \left(D_{2} O\right) \) freezes at:
\( \mathbf{A} \cdot 0^{\circ} C \)
в. \( -3.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.8^{\circ} \mathrm{C} \)
D. \( 3.82^{\circ} \mathrm{C} \)


A block of metal weighing 2 kg is resting on africtionless plane. It is struck by a jet releasing waterat a rate of \( 1 \mathrm{kg} / \mathrm{s} \) with a speed of \( 5 \mathrm{m} / \mathrm{s} \)
Theinitial acceleration of the block will
be :-


How many unit cubes were removed
from the solid on the left to obtain the
solid on the right?
\( A \)
\( B \)
\( c .5 \)
D. 6


\( \int \frac{\boldsymbol{x}+\sqrt[3]{\boldsymbol{x}^{2}}+\sqrt[6]{\boldsymbol{x}}}{\boldsymbol{x}(1+\sqrt[3]{\boldsymbol{x}})} \boldsymbol{d} \boldsymbol{x} \) is equal to
A \( \cdot \frac{3}{2} x^{2 / 3}+6 \tan ^{-1} x^{1 / 6}+c \)
B. \( \frac{3}{2} x^{2 / 3}-6 \tan ^{-1} x^{1 / 6}+c \)
c. \( -\frac{3}{2} x^{2 / 3}+6 \tan ^{-1} x^{1 / 6}+c \)
D. None of these


What to you understand by free
vibrations of a body?


\( \int \sqrt[3]{x} d x \)


A solution of \( X S O_{4} \) is electrolyed. When a constant current of 2.0 amperes is applied for 800 minutes, \( 4.5 g \) of the unknown metal X is deposited. Identify the unknown metal, X.
A. \( C d \)
в. \( B e \)
c. \( M g \)
D. \( C u \)


Compute the derivative of \( 6 x^{100}- \)
\( \boldsymbol{x}^{\boldsymbol{5} \boldsymbol{5}}+\boldsymbol{x} \)


At a height \( h \) above the surface of earth, the change in value of \( g \) is same as that
at a depth \( x \) below the surface on the
earth. Both \( x \) and \( h \) are very small in comparison to the radius of the earth. Then
\( \mathbf{A} \cdot x=h \)
B. \( x=2 h \)
c. \( 2 x=h \)
D. \( x=h^{2} \)


If two unit vectors \( \bar{a} \) and \( \bar{b} \) are inclined
at an angle \( 2 \theta(0<\theta<\pi) \) and \( \mid \bar{a}- \)
\( \vec{b} \mid \leq 1, \) then \( \theta \in \)
A \( \cdot\left[0, \frac{\pi}{6}\right) \)
в. \( \left[0, \frac{\pi}{3}\right] \cup\left[\frac{2 \pi}{3}, \pi\right] \)
\( ^{\mathrm{c}} \cdot\left[0, \frac{\pi}{6}\right] \cup\left[\frac{5 \pi}{6}, \pi\right] \)
D.


Which series shows molecules in order
of increasing bond angle?
A \( \cdot C H_{4}<B F_{3}<N H_{3} \)
в. \( H_{2} O<C O_{2}<B F_{3} \)
\( \mathrm{c} . N H_{3}<C H_{4}<\mathrm{CO}_{2} \)
D. \( N H_{3}<C H_{4}<H_{2} O \)


The displacement of a particle in S.H.M.
is indicated by equation \( \boldsymbol{y}= \)
\( 10 \sin (20 t+\Omega / 3) \) where \( y \) is in
metres. The value of time period of vibration will be (in seconds):
A . \( 10 / \pi \)
в. \( \pi / 10 \)
c. \( 2 \pi / 10 \)
D. \( 10 / \pi 2 \)


Which of the following elements does not forms stable diatomic molecules:
A . \( I \)
в. \( P \)
\( c . N \)
D.


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


If \( 0<\cos ^{-1} x<1 \) and \( 1+ \)
\( \sin \left(\cos ^{-1} x\right)+\sin ^{2}\left(\cos ^{-1} x\right)+ \)
\( \sin ^{3}\left(\cos ^{-1} x\right)+\ldots x=2 \) then the value
of \( 12 x^{2} \) is


When sodium is heated in moist air, the ultimate product obtained is:
A. \( N a_{2} O \)
в. маОН
c. \( N a_{2} C O_{3} \)
D. \( N a_{2} O_{2} \)


Two weak acid solutions \( H A_{1} \) and \( H A_{2} \)
each with the same concentration and
having pKa values 3 and 5 are placed in contact with hydrogen electrode \( (1 \mathrm{atm} \) \( 25^{0} C \) ) and are interconnected through a salt bridge. Find emf of the cell.
A \( .+0.059 \mathrm{V} \)
B. 0.059
c. \( 0.0295 \mathrm{v} \)
D. 0.118 V


If there is deficiency of surfactant the disease is
A. Emphysema
B. Respiratory distress syndrome
c. Bronchitis
D. All of the above


A ring rolls without slipping on the
ground. Its centre \( C \) moves with a
constant speed \( u . P \) is any point on the
ring. The speed of \( P \) with respect to the
ground is \( \boldsymbol{v} \) This question has multiple correct options
A \( .0 \leq v \leq 2 u \)
B. \( v=u \), if \( C P \) is horizontal
c. \( v=u \), if \( C P \) makes and angle of \( 30^{\circ} \) with horizontal and \( P \) is below the horizontal level of \( C \)
D. \( v=\sqrt{2} u \), if \( C P \) is horizontal


The most commonly used themometric substance is
A. water
B. alcohol
c. mercury
D. none of these


Growth rings are either absent or are not sharply demarcated in
A. Temperate deciduous trees
B. Tropical evergreen trees
c. Temperate hot regions
D. Tropical deciduous trees


If \( z \) is a nonzero complex number then \( \left|\frac{|\bar{z}|^{2}}{z \bar{z}}\right| \) is equal to
This question has multiple correct options
A \( \cdot \mid \frac{z}{z} \)
B.
c. \( \mid z \)
D. none of these


How will you convert Acetonitrile to
ethanol?


If \( \Delta A B C \cong \Delta X Y Z, \) which of the
following statements is incorrect?
\( \mathbf{A} \cdot \angle A=\angle X \)
В. \( \angle B=\angle Z \)
c. \( A B=X Y \)
\( \mathbf{D} \cdot B C=Y Z \)


For chemisorption,which is wrong?
A. It forms multimolecular layers on adsorbate
B. Irreversible
C. Surface compounds are formed
D. It required activation energy


If \( f(x)=\left\{\begin{array}{ll}x^{2} & \text { for } 0 \leq x \leq 1 \\ \sqrt{x} & \text { for } 1 \leq x \leq 2\end{array} \) then \right.
\( \int_{0}^{2} f(x) d x= \)
A \( \cdot(1 / 3)(4 \sqrt{2}+1) \)
B. \( (1 / 3)(4 \sqrt{2}-1) \)
c. \( (1 / 3)(2 \sqrt{2}-1) \)
(年) \( (1 / 3)(2 \sqrt{2}-1)(\sqrt{2}-1) \)
D. \( (1 / 2)(3 \sqrt{2}-1) \)


Units of the properties measured are given. Which of the properties has not been matched correctly?
A. Molar conductance \( =\mathrm{S} m^{2} m o l^{-1} \)
B. Cell constant \( =m^{-1} \)
C. Specific conductance \( =\mathrm{S} m^{2} \)
D. Equivalent conductance \( =\operatorname{Sm}^{2}(g e q)^{-1} \)


What are cationic detergents? Give an
example.


In the nitration of benzene with a
mixture of concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) the active species involved is :
A \( . N O_{3}^{-} \)
в. \( N O_{2} \)
\( \mathbf{c} \cdot N O_{2}^{-} \)
D. \( N O_{2}^{\text {th }} \)


Sparking occurs when a load is switched off because the circuit has
high :
A . resistance
B. inductance
c. capacitance
D. impedance


For any two independent events \( \boldsymbol{E}_{1} \) and
\( \boldsymbol{E}_{2}, \boldsymbol{P}\left\{\left(\boldsymbol{E}_{1} \cup \boldsymbol{E}_{2}\right) \cap(\overline{\boldsymbol{E}_{1}}) \cap(\overline{\boldsymbol{E}_{2}})\right\} \) is
\( A \cdot \leq \frac{1}{4} \)
B. \( >\frac{1}{4} \)
\( c \cdot \geq \frac{1}{2} \)
D. None of these


opo
yo


f \( A(2,1,3), B(2,-3,4), C(-1,2,7) \) are the
three points ; find a point D such that \( |\overrightarrow{A B}|=\frac{1}{2}|\overrightarrow{C D}| \) and \( A B|| C D \)


Select the incorrect option regarding following plot.
A. Minimum possible angular node will be zero
B. It is for \( n-1-1=0 \)
c. wave function does not depend on angle \( \theta \) and \( \phi \)
D. It gives probability of finding the electron at a point at distance r from the nucleus


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


The reaction of chlorine with \( C O \) in the
presence of sunlight gives:
A \( . C O C l_{2} \)
в. \( C O_{2} C l_{2} \)
c. НОС l
D. \( H_{2} C l_{2} O_{2} \)


An electrolyte \( A \) gives 3 ions and \( B \) is a non- electrolyte. If \( 0.1 ~ M \) solution of \( B \)
produces an osmotic pressure \( P, \) then \( 0.05 M \) solution of \( A \) will produce an osmotic pressure, assuming that the electrolyte is completely ionised:
A . \( 1.5 P \)
в. \( P \)
\( c .0 .5 P \)
D. \( 0.75 P \)


Ampere rule is used to determine:
A. direction of current
B. direction of magnetic field
c. direction of motion of the conductor
D. magnitude of current


What is meant by forward bias and reverse bias of a diode? Indicate in a
figure.


Evaluate: \( \int_{2}^{3} \frac{x d x}{x^{2}+1} \)


Metals are generally malleable in
character and can be hammered into
sheet
A. True
B. False


Assertion
According to Newton's third law, the sum of action and reaction forces on a
body is equal to zero.
Reason
The action and reaction forces act on
different bodies.
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


Voltage in the secondary coil of a transformer does not depend upon:
A. frequency of the source
B. voltage in the primary coil
c. ratio of number of turns in the two coils
\( D . \) both \( (b) \) and \( (c) \)


An isolated conductor of any shape has a net charge of \( +15 \mu C \). Inside the conductor is a cavity within which is a point-charge of \( +3.0 \mu C . \) What is the charge on the cavity wall and on the outer surface of the conductor?


The relationship between force and
position is shown in the figure (in one
dimensional case). Work done by the
force in displacing a body from \( x=1 \mathrm{cm} \)
to \( x=5 c m \) is :
A. 700 erg
B. 70 erg
c. 60 erg
D. 20 erg


Brunner's glands are present in the
A. Stomach
B. Pancreas
c. Small intestine
D. oesophagus


Increasing basic properties of
\( T i O_{2}, Z r O_{2} \) and \( H f O_{2} \) are in order:
A. \( T i O_{2}<Z r O_{2}<H f O_{2} \)
в. \( H f O_{2}<Z r O_{2}<T i O_{2} \)
c. \( H f O_{2}<T i O_{2}<Z r O_{2} \)
D. \( Z r O_{2}<T i O_{2}<H f O_{2} \)


State the following statement is true or
false

We can construct a quadrilateral if the measurement of four sides and one
diagonal are given.
A. True
B. False


Sporophyte in Nephrolepis is and
the spores are.
A. Diploid, haploid
B. Haploid, haploid
c. Haploid, diploid
D. Diploid, diploid


\( \Delta U^{\circ} \) of combustion of methane is \( -X \)
\( k J \) mol \( ^{-1} \). The value of \( \Delta H^{o} \) is:
\( A \cdot=\Delta U^{o} \)
В \( \cdot>\Delta U^{\circ} \)
\( \mathrm{c} \cdot<\Delta U^{\circ} \)
\( \mathrm{D} \cdot=0 \)


A cold soft drink is kept on the balance. When the cap is open, then the weight:
A. increases
B. decreases
c. first increases then decreases
D. remains same


A high energy photon collides elastically with a charged particle (usually an electron)., The photon "bounces away" with less energy (a longer wavelength) The process described here is known as
A. Compton scattering
B. The photoelectric effect
c. x-ray production
D. Annihilation
E. Quantum tunneling


All colloidal dispersions have
A. Very high osmotic pressure
B. Low osmotic pressure
c. No osmotic pressure
D. High osmotic pressure


Cards marked with numbers 4 to 99 are
placed in a box and mixed thoughtly. One card is drawn from this box. Find
the probability that the number on the card is a perfect square between 91 and
\( \mathbf{9 9} \)


Ratio of transverse to axial strain is
A. Toricelli ratio
B. Poisson's ratio
c. Stoke's ratio
D. Bernoulli's ratio


Which of the following is not an actinide?
A. Uranium
B. Curiummmmmumm
c. Californium
D. Erbium


Electronic configuration of deuterium is
A \( \cdot 1 s^{2} \)
B. \( 1 s^{\text {। }} \)
c. \( 1 s^{2} 2 s^{\text {। }} \)
D. \( 1 s^{2} 2 s^{2} \)


The line represented by the equation \( \boldsymbol{y}=-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{6} \) is the perpendicular
bisector of the line segment AB. If A has the coordinates \( (7,2), \) what are the
coordinates for B ?
A. (3,0)
(年) (3,0),(0,0)
в. (4,0)
c. (6,2)
(年. \( 6,2,2,6) \)
D. (5,6)


A grocer bought 15 sweets at \( \mathrm{Rs} 72 . \mathrm{He} \)
sold them at a gain Rs \( 18 . \) Find his profit
\( \% \). Also, find the selling price of 20
sweets


The chiasmata are formed as a result
of
A. Exchange of parts of paired homologus chromosome.
B. Exchange of part of unpaired non-homologus chromosome.
C. Duplication of parts of paired homologus o chromosome.
D. Loss of parts of unpaired non-homologus chromosome.


Study the lists and find the correct
match
(a)
(b) \( \begin{array}{lll}\text { I } & & \text { II } \\ \text { BOD } & \text { (i) } & \text { Treatment of sewage } \\ \text { KVIC } & \text { (ii) } & \begin{array}{l}\text { Measure of organic } \\ \text { matter in water }\end{array} \\ \text { LAB } & \text { (iii) } & \begin{array}{l}\text { Biological methods } \\ \text { for controlling plant } \\ \text { diseases }\end{array} \\ \text { STPS } & \text { (iv) } & \text { Increases vitamin B }_{12} \\ & \text { (v) } & \text { Production of biogas }\end{array} \)
(c)
(d)
b-iii, c-ii, d-v
\( A \cdot a-i v \)
b-ii, c-iii, d-i
B. a-v,
c. a-ii, b-i, c-iv, d-v
D. a-ii, b-v, c-iv, d-i


To measure the-roughness of the surface of a material, which of the following microscope is preferred for better result output?
A. Compound microscope
B. Electron microscope
c. Atomic force microscope
D. None of the above


The rest mass of a photon is
A. zero
B . \( 1.6 \times 10^{-19} \mathrm{kg} \)
c. \( 3.1 \times 10^{-30} \mathrm{kg} \)
D. \( 9.1 \times 10^{-31} \mathrm{kg} \)


The position of a particle as a function
of time is described by relation \( \boldsymbol{x}= \)
\( 3 t-3 t^{2}+t^{3} \) where the quantities are
expressed in S.I. units. If mass of the particle be \( 10 \mathrm{kg} \), the work done in first
three seconds is
A . 10
B. 30 J
c. \( 300 J \)
D. 675 J


If \( A \) is a \( 3 \times 3 \) matrix and \( \operatorname{det}(3 A)= \)
\( \boldsymbol{k}\{\boldsymbol{d e t}(\boldsymbol{A})\}, \boldsymbol{k}= \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 6
c. 1
D. 27


A rigid body can be hinged about any point in the \( x \) -axis. When it is hinged
such that the hinge is at \( x, \) the moment
of inertia is given by \( \boldsymbol{I}=\mathbf{2} \boldsymbol{x}^{2}-\mathbf{1} \mathbf{2} \boldsymbol{x}+ \)
\( \mathbf{2 7} \) the \( \mathbf{x} \) -coordinate of centre of mass is:
A \( . x=2 \)
B. \( x=0 \)
c. \( x=1 \)
D. \( x=3 \)


Write the differences between.
(a) Blood and Lymph
(b) Open and closed system of
circulation
(c) Systole and diastole
(d) P- wave and T- wave


In cyclotron the gyro radius is:
A. proportional to momentum
B. proportional to energy
C. inversely proportional to momentum
D. inversely proportional to energy


Show diagramatically the behavior of magnetic field lines in the presence of
(i) paramagnetic and
(ii) diamagnetic substances. How does one explain this distinguishing feature.


On the set \( N \) of all natural numbers
define the relation \( R \) by \( a R b \) if and only
if the G.C.D. of \( a \) and \( b \) is 2 . Then \( R \) is:
A. Reflexive, but not symmetrica
B. Symmetric only
C. Reflexive and transitive
D. Reflexive, symmetric and transitive


Determine the average life \( U^{238} \) having
\( t_{1 / 2}=140 \) days.


The acceleration due to gravity
A. Has the same value everywhere in space
B. Has the same value everywhere on the earth
C. varies with the latitude on the earth
D. is greater on the moon due to its smaller diameter


If \( \int e^{x}(1+x) \sec ^{2}\left(x e^{x}\right) d x=f(x)+c \)
then \( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \cos \left(x e^{x}\right) \)
B. \( \sin \left(x e^{x}\right) \)
c. \( 2 \tan ^{-1}(x) \)
D. \( \tan \left(x e^{x}\right) \)


Which of the following will be the most
effective in the coagulation of \( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{3} \)
sol?
в. \( B a C l_{2} \)
c. Nacı
D. ксм


Which of the following oxides is
nuetral?
A . \( c o \)
в. \( S n O_{2} \)
\( c \cdot z n 0 \)
D. \( \operatorname{si} 0_{2} \)


Diatoms do not decay easily because
A. They have siliceous walls
B. Their body is impervious to water
c. They are chitinous
D. They are abundant in saline soil


Which of the following is incorrect for physisorption?
A . Reversible
B. Increases with increase in temperature
c. Low heat of adsorption
D. Increases with increase in surface area


The volume of \( 8 \mathrm{g} \) of \( \mathrm{O}_{2} \) at STP is:
A . 22.4 L
B. 11.2 느
\( c .5 .6 \)
D. 2.24 L


Distilled water is clean and pure water, but unfit for human consumption.
A. True
B. False


A resistance of \( \boldsymbol{R} \) draws the current
form of the potentiometer. The
potentiometer wire, \( A B, \) has a total
resistance of \( \boldsymbol{R}_{0} . \) A voltage \( \boldsymbol{V} \) is
supplied to the perpendicular. Derive an
expression for the voltage across \( \boldsymbol{R} \)
when the sliding contact is in the middle of potentiometer wire.


The specific conductance of \( 0.1 N K C l \) solution at \( 23^{\circ} C \) is 0.012 oh \( m^{-1} c m^{-1} \)
The resistance of cell containing the solution at the same temperature was
found to be 55 ohm. The cell constant
will be:
A \( \cdot 0.142 \mathrm{cm}^{-1} \)
B. \( 0.66 \mathrm{cm}^{-1} \)
D. \( 1.12 \mathrm{cm}^{-1} \)


Assertion
Cyclic pathway of photophosphorylation first appeared in some eubacterial
species.
Reason
Oxygen started accumulating in the atmosphere after the non-cyclic pathway of photosynthesis evolved.
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


\( \operatorname{Given} \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{0}) ; \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{2}) \)
\( C(2,-2,4) \) and \( D(-1,1,-1) \) which of
the following points neither lie on \( \boldsymbol{A B} \)
nor on \( C D ? \)
A \( .(2,2,4) \)
В. (2,-2,4)
c. (2,0,1)
D. (0,-2,-1)


For a prism of refracting angle \( A \) and refractive index 2 . Assume rays are
incident at all angles of incidence \( 0^{\circ} \leq \)
\( i \leq 90^{\circ} . \) Ignore partial reflection


Which of the following is a female sex hormone?
A. Estrone
B. Testosterone
c. cortisone
D. Thyroxine


An infinitely long straight non-magnetic conducting wire of radius a carries a \( d c \)
current I. The magnetic field \( B \), at a distance \( r(r<a) \) from axis of the wire
is:
A \( \cdot \frac{\mu_{0} I}{2 \pi a} \)
в. \( \frac{\mu_{0} I r}{2 \pi a^{2}} \)
c. \( \frac{2 \mu_{0} I r}{\pi a^{2}} \)
D. \( \frac{\mu_{0} I r^{2}}{2 \pi a^{3}} \)


Outermost shells of two elements \( X \) and
Y have one and six electrons
respectively. If they combine, what will be expected formula of the compound?


Find the maximum value of \( |z| \) when \( \left|z-\frac{3}{z}\right|=2, \) where \( z \) being a complex
number.
A \( .1+\sqrt{3} \)
B. 3
\( c \cdot 1+\sqrt{2} \)
D.


The minimum coefficient of friction
\( \mu_{\min } \) between a thin homogeneous rod
and a floor at which a person can slowly lift the rod from the floor without
slippage to the vertical position, applying to it a force perpendicular to it is \( \frac{1}{x \sqrt{x}} . \) Find the value of \( x \)


Classify \( D=\left\{x \mid x=2^{n}, n \in N\right\} \) as
'finite' or 'infinite'.
A . Infinite
B. Finite
c. Data insufficient
D. None of these


What is the problem faced while using alitame as artificial sweetener?
A. It decomposes when added to the food items.
B. It provides a huge number of calories to the food
c. It is difficult to control the sweetness of food while using it
D. It increases the volume of the contents to a large extent


Which of the following elements has the least non-metallic character?
A. Fluorine
B. Chlorine
c. Bromine
D. lodine


A meteor of mass \( M \) breaks up into two
parts. The mass of one part is \( m \). For a
given separation \( r \) the mutual
gravitational force between the two parts will be maximum if
A. \( m=(M / 2) \)
в. \( m=(M / 3) \)
c. \( _{m}=\frac{M}{\sqrt{2}} \)
D. \( _{m}=\frac{M}{2 \sqrt{2}} \)


The enzyme which combines with a
nonprotein prosthetic group to form a functional enzyme is called
A. Apoenzyme
B. Holoenzyme
c. coenzyme
D. Proenzyme


If \( \left(x+\frac{1}{x}\right)=6, \) fiind the vaue of
(i) \( \left(x-\frac{1}{x}\right)(i i)\left(x^{2}+\frac{1}{x^{2}}\right) \)


Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket?


Ravi and Kumar are working on as assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar
takes 5 hours to type 40 pages. How much time will they take, working together on two difference computers to
type an assignment of 110 pages?
A. 7 hours 30 minutes
B. 8 hours
c. 8 hours 15 minutes
D. 8 hours 25 minutes


Solve the simultaneous equations:
\( \frac{1}{x}+\frac{1}{y}=12, \frac{3}{x}-\frac{2}{y}=1 \)


Standing waves are formed on a string
when interference occurs between two
waves having
A. The same amplitude travelling in the same direction with no phase difference between them
B. The same amplitude, travelling in the opposite direction with no phase difference between them
C. Different amplitudes travelling in the same direction
D. Different amplitudes travelling in the opposite direction


An element X belongs I, II, III or V groups. Its oxide reacts with water to produce highly acidic solution the element \( x \)
belongs to :
A. I groups
B. II group
c. III group
D. v group


Two major requirements for preparation of ammonia are
A. Low temperature and high pressure
B. Low temperature and present pressure
C. High temperature and low pressure
D. High temperature and high pressure


The focal length of an equiconvex lens
in air is equal to either of its radii of
curvature. the refractive index of a
material of the lens is:
A . 1.2
B. 1.25
\( c .1 .5 \)
D. 1.8


Calculate the work done to rise a body of \( 30 \mathrm{kg} \) to a height of \( 50 \mathrm{m}\left(\mathrm{g}=10 \mathrm{m} \mathrm{s}^{-2}\right) \)
(in kJ)
A . 100
B.
c. 15
D. 0.5


Evaluate the following
\( \left(i^{77}+i^{70}+i^{87}+i^{414}\right)^{3} \)