The vapour if an aqueous solution of glucose is \( 750 m m \) of \( \mathrm{Hg} \) at \( 373 \mathrm{K} \) Calculate molality of the solution?
A. 0.523 mol/kg
в. 0.617 mol / \( / k g \)
c. 0.731 mol \( / \mathrm{kg} \)
D. 0.836 mol / \( / k g \)


\( A+2 B=4 C . \) The rate of appearance of
\( C \) at a time \( t \) is \( 1.5 x \)
\( 10^{-3} \) mol \( L^{-1} \) sec \( ^{-1} \). What will be the
instantaneous rate of the reaction?
A \( .6 .0 \times 10^{-3} \)
В. \( 1.5 \times 10^{-3} \)
c. \( 0.675 \times 10^{-3} \)
D. \( 0.375 \times 10^{-3} \)


The K.E. of a body is increased most by doubling its :
A. mass
B. weigth
c. speed
D. P.E


The domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\tan \pi[x]}{1+\sin \pi[x]+\left[x^{2}\right]} \) is (where [.] denotes
greatest integer function)
A. \( (0, \infty) \)
в. \( R \)
\( c \cdot(-\infty, 0) \)
D. \( z \)


Chemistry is sometimes called as:
A. Biological Science
B. Central Science
c. Biochemistry
D. Both A and C


Write the name of lightest element


Which amongst the following can lose 2 electrons to acquire the configuration of argon?
A. \( N \)
в. \( M g \)
\( c . C a \)
D. \( B e \)


Calculate the mean deviation for the
following data about median.
\( \begin{array}{lllll}\text { Class } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- \\ \text { interval } & \mathbf{4} & \mathbf{9} & \mathbf{1 4} & \mathbf{1 9}\end{array} \)
Frequency \( \quad 11 \quad 12 \) 17
A. 10.22
в. 7.57
c. 5.55
D. 8.45


A chemical A is used for the preparation of washing soda to recover ammonia.
When \( C O_{2} \) is bubbled through an aqueous solution of \( A, \) the solution turns milky. It is used in white washing due to disinfectant nature. What is the
chemical formula of \( A \) ?
A \( \cdot C a\left(H C O_{3}\right)_{2} \)
в. \( C a O O \)
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( C a C O_{3} \)


Write formula of the following
compound:
(i) dichloridobis (ethylene diamine) cobalt (III) ion.
(ii)
sodiumethylenediaminetetraacetatonic kelate (II)
(iii) hexaammineplatinum (IV) chloride


Expand the following expression in
ascending powers of \( x \) as far as \( x^{3} \) \( \frac{1+2 x}{1-x-x^{2}} \)


The sum of the \( 4^{t h} \) and \( 8^{t h} \) terms of an
AP is 24 and the sum of the \( 6^{t h} \) and \( 10^{t h} \)
terms is \( 44 . \) Find the first three terms of
the AP.


The value of \( 16-|-7|-|11-22| \) is
equal to
A . 56
B. - -
\( c \cdot 39 \)
D. 26


At a certain height above the earth surface the gravitational acceleration is \( 4 \% \) of its value at the surface of the
earth find the height above the earth surface:


A particle is moving in a horizontal circle with constant speed. It has
constant
A. Velocity
B. Acceleration
c. Kinetic energy
D. Displacement


STATEMENT 1: In a \( \Delta A B C, a, b, c \) denotes lengths of the sides and \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|=\mathbf{0} \) then the triangle is
equilateral triangle.
STATEMENT 2: Sum of three non-
negative numbers \( =0 \Rightarrow \) each number
is zero.
A. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement-
B. Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true


A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1 A. What is
the uncertainty involved in the measurement of its velocity? \( (h=6.626 \)
\( \times 10^{-34} \mathrm{Js}, \) mass of electron \( =9.1 \)
\( \times 10^{-31} \mathrm{kg} \)


In a series LCR circuit with an AC
source, \( \boldsymbol{R}=\mathbf{3 0 0} \boldsymbol{\Omega}, \boldsymbol{C}=\mathbf{2 0} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{L}= \)
10 henry \( \epsilon_{\text {max }}=50 V \) and \( v= \)
\( \mathbf{5 0} / \boldsymbol{\pi} \boldsymbol{H z} . \) Find
(a) the \( r m s \) current in the circuit.
(b) the \( r m s \) potential differences
across the capacitor, the resistor and the inductor, Note that the sum of the
rms potential difference across the
three elements is greater than the \( r m s \) voltage of the source.


Given a reactangular ground is \( 90 m \) long and \( 32 m \) broad. In the middle of the
ground there is a circular thank of
radius 14 metres. Find the cost of
turfing the remaining portion at the
rate of \( R s .2 .50 \) per square meter.
A. \( R s .5660 \)
в. \( R s .4295 \)
c. \( R s .552 \)
D. \( R s .6250 \)


The half life of radium is 1600 years. The
time \( 1 g m \) of radium take to reduce to
\( 0.125 g m \) is:
A. 4800 years
B. 4500years
c. 5000 years
D. 4750 years


The de-Broglie wavelength associated with a proton changes by \( 0.25 \% \) if its
momentum is changed by \( P_{o} \). The initial momentum of proton is
A \( \cdot 100 P_{o} \)
в. \( 400 P_{o} \)
\( c \cdot P_{o} / 400 \)
D. \( P_{o} \)


The particle that possesses half integral spin is
A. Photon
B. Pion
c. Proton
D. K-meson


The value of \( x \) where \( x>0 \)
\( \tan \left(\sec ^{-1} \frac{1}{x}\right)=\sin \left(\tan ^{-1} 2\right) \) is
A \( \cdot \sqrt{5} \)
в. \( \frac{\sqrt{5}}{3} \)
c.
D.


Tyloses occur in
A. Secondary xylem
B. Secondary phloem
c. Callus tissue
D. Cork cells


In the following pressure-volume
diagram, the isochoric, isothermal and
isobaric parts, respectively, are
A. \( B A, A D, D C \)
в. \( C B, B A, D C \)
c. \( A B, B C, C D \)
D. \( C D, D A, A B \)


The digestive enzymes secreted in the food vacuole helps in
A. Locomotion
B. Engulfment of food particle
c. Digestion of complex food material into simpler ones
D. None of the above


Oxidative phosphorylation is the
formation of
A. NADPH \( _{2} \) in respiration
B. ATP in respiration
c. NADPH \( _{2} \) in photosynthesis
D. ATP in photosynthesis


Assertion
In a meter bridge experiment, null point for an unknown resistance is put inside
an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
Reason Resistance of metal increases with
increase in temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The following equilibrium exists in aqueous solution:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C H}_{3} \boldsymbol{C O O} \)
If dilute \( H C l \) is added:
A. The equilibrium constant will increase
B. The equilibrium constant will decrease
c. Acetate ion concentration will increase
D. Acetate ion concentration will decrease


Four charges \( 1 \mathrm{mc}, 2 \mathrm{mc}, 3 \mathrm{mc}, \ldots 6 \mathrm{mc} \)
are placed on at corner of a square of
side \( 1 \mathrm{m} . \) The square lies in \( \mathrm{XY} \) plane with its centre at origin
A. The electric potential at origin at origin
B. The electric potential is zero every where along \( x \) axis
c. The electric potential is not zero along z-axis
D. The electric potential is zero along Z- axis for any orientation of square in \( \mathrm{XY} \) plane


Let \( \vec{a}=x^{2} \hat{i}+2 \hat{j}-2 \hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k} \)
and \( \vec{c}=x^{2} \hat{i}+5 \hat{j}-4 \hat{k} \) be three vectors.
Find the values of \( x \) for which the angle between \( \vec{a} \) and \( \vec{b} \) is acute and the angle between \( \vec{b} \) and \( \vec{c} \) is obtuse.
A \( \cdot(-3,-2) \cup(2,3) \)
B . (-3,-1)\( \cup(1,3) \)
c. (-3,-1)\( \cap(1,3) \)
D. (-3,-2)\( \cap(2,3) \)


Sodium is obtained by the electrolysis of:
A. an aqueous solution of sodium chloride
B. an aqueous solution of sodium hydroxide
c. fused sodium chloride
D. fused sodium sulphate


If \( a, b, x, y \) be real numbers such that
\( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}=\mathbf{8} \mathbf{1}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1 2} \mathbf{1} \) and \( \boldsymbol{a} \boldsymbol{x}+ \)
\( \boldsymbol{b} \boldsymbol{y}=\mathbf{9} \boldsymbol{9} \), then find the set of all possible
values of \( a y-b x \)
A \( \cdot\left(0, \frac{9}{11}\right] \)
в. \( \left(0, \frac{9}{11}\right) \)
\( c \cdot\{0\} \)
D. \( \left[\frac{9}{11}, \infty\right) \)


As the train starts moving; a man sitting inside leans backwards because
of :
A. Inertia of rest
B. Inertia of motion
c. Moment of inertia
D. conservation of mass


What will be the value of Van't Hoff
factor for ethanoic acid in benzene?


Find out \( \mathrm{B} \) in the given process.
A \( \cdot \operatorname{Na}\left[A l(O H)_{4}\right. \)
в. \( N a O H \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( A l_{2} O_{3} \)


The functions of the reflectors in
nuclear power plant is that:
A . It reflects the neutrons that are escaping from the case
B. It reflects the radiation escaping the case of the reactor
c. Both (1) and (2)
D. It accelerates the reaction


15 circular plates, each of radius \( 7 \mathrm{cm} \)
and thickness \( 3 \mathrm{cm} \) are placed one above the another to form a cylindrical solid. Find the volume of the cylinder so formed


Water is flowing through a pipe of uniform cross-section under constant
pressure. At some place the pipe becomes narrow, the pressure of water at this place:
A. increases
B. decreases
c. remains unchanged
D. depends on several factors


Rectilinear motion of light in a medium is caused due to:
A. high frequency
B. short wavelength
c. velocity of light
D. uniform refractive index of the medium


Potential gradient along AB is
\( \mathbf{A} \cdot 1 / 5 \mathrm{Vm}^{-1} \)
B. 2/5 Vm \( ^{-1} \)
c. \( 3 / 5 \mathrm{Vm}^{-1} \)
D. \( 4 / 5 \mathrm{Vm}^{-1} \)


The surface area of a cuboid is
\( 4150 \mathrm{cm}^{2} . \) If its length and breadth are
\( 35 \mathrm{cm} \) and \( 25 \mathrm{cm} \) respectively, find its height.


To examine the function \( f(x)=2 x^{3}- \)
\( 15 x^{2}+36 x+10 \) for maxima and
minima, if any. Also find the maximum and minimum value.


How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?
A .7920
в. 330
c. 14640
D. 419430


The least distance of distinct vision is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 30 c m \)


Which of the following is a common characteristic of a covalent compound?
A. High melting point
B. Conducts electricity when it is in the molten state
c. consists of molecules
D. Always soluble in water


State if the given statement is True or False

Derivative of \( y=\cos x \) with respect to \( x \)
is \( \sin x \)
A. True
B. False


A motor of \( 50 ~ W \) runs for 20 hrs. How
many 'units' ( \( k W h \) ) of electrical energy are consumed?
\( \mathbf{A} .5 \mathrm{kWh} \)
в. \( 2 k W h \)
\( c \cdot 1 k W h \)
D. \( 2.5 \mathrm{kWh} \)


State True or False.
If \( \frac{e^{y}}{e^{x}}=x y, \) then \( y^{\prime}=\frac{2-\log x}{(1-\log x)^{2}} \)
A. True
B. False


In apple type of stomata
A. Stomata are present only on the upper surface of leaf
B. Stomata are present only on the lower surface of leaf
C. Stomata are present on both surface of leaf
D. Stomata are vestigial


The stationary wave, \( \boldsymbol{y}= \) \( 2 a(\sin k x \cos \omega t), \) in a closed organ pipe
is the result of the superposition of
\( \boldsymbol{y}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \) and:
A. \( y=-a \cos (\omega t+k x) \)
B. \( y=a \cos (\omega t+k x) \)
c. \( y=a \sin (\omega t-k x) \)
D. \( y=-a \sin (\omega t+k x) \)


Assertion
Law of conservation of mass holds good
for nuclear reactions.
Reason
Law states that mass can be neither
created nor destroyed in a chemical
reaction.
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


Which of the following pairs of ions are isoelectronic and isostructural?
\( A \cdot S O_{3}^{2-}, N O_{3}^{-} \)
B . \( \mathrm{ClO}_{3}^{-}, \mathrm{CO}_{3}^{2} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3} \)
D. \( C l O_{3}^{-}, S O_{3}^{2} \)


Assertion: For a charged particle moving from point \( P \) to point \( Q, \) the net work done by an electrostatic field on the particle is independent of the path connecting point \( P \) to point \( Q \) Reason: The net work done by a
conservative force on an object moving along a closed loop is zero.
A. If both Assertion arid Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Rea not the correct explanation of Assertion.
c. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.


For a uniformly accelerated motion, the average acceleration is equal to
A. unity
B. negative
c. zero
D. uniform acceleration


Assertion: \( p H \) value of \( H C N \) solution
decreases when \( N a C N \) is added to it
Reason: \( N a C N \) provides a common ion
\( C N^{\ominus} \) to \( H C N \)
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
E. Both Assertion and Reason are incorrect


A turn of radius \( 20 \mathrm{m} \) is banked for the
vehicles going at a speed of \( 36 k m h^{-1} \) If the coefficient of static friction
between the road and the tyre is 0.4
what are the possible speed of a vehicle so that it neither slips down nor skids
up?


A rectangular loop with a slide wire of
length \( l \) is kept in a uniform magnetic
field as shown in figure (a). The
resistance of slider is \( \boldsymbol{R} \). Neglecting self
inductance of the loop find the current
in the connector during its motion with
a velocity \( \boldsymbol{v} \)
\( (b) \)
A \( \cdot \frac{B l v}{R_{1}+R_{2}+R} \)
B. \( \frac{B l v\left(R_{1}+R_{2}\right)}{R\left(R_{1}+R_{2}\right)} \)
c. \( \frac{B l v\left(R_{1}+R_{2}\right)}{R R_{1}+R R_{2}+R_{1} R_{2}} \)
D \( \cdot \operatorname{Blv}\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right) \)


Draw structure and write geometry of
\( \boldsymbol{P C l}_{3} \) and \( \boldsymbol{P C l}_{5} \)


The internal cellular energy reserve in autotrophs is
A . Glycogen
B. Protein
c. starch
D. Fatty acid


Assertion
The extent to which a dissolved
substance can act as an acid or base
depends largely on the solvent.
Reason
The solute only shows acidicproperties if its proton donating ability exceed that of the solvent
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


A stone is dropped from a tower. It was
found that it covered a distance of \( 45 m \)
during its last second of the fall.
Calculate the time of the fall and the
height of the tower? \( \left(g=10 m s^{-2}\right) \)
\( A \cdot 5 s, 45 m \)
B . \( 10 s, 90 m \)
\( \mathbf{c} .5 s, 125 m \)
D. \( 10 s, 100 m \)


Prove that the points (7,-9) and (11,3)
lie on a circle with centre at the origin.
Also its equation.


A solution of \( (R)-2- \) iodobutane,
\( [\alpha]=15.9^{\circ} \) in acetone is treated with
radioactive iodied, until 1.0\% of
iodobutane contain radioactive iodine, the specific rotation of recovered
iodobutane is found to be \( -15.58^{\circ} \) which statement is correct about above information?
This question has multiple correct options
A. It has optical purity \( 96 \% \)
B. \% of R in solution is \( 99 \% \)
c. Racemic mixture is \( 2 \% \)
D. Final solution is dextrorotatory


If the line \( l x+m y+n=0 \) touches the
parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a} \boldsymbol{x}, \) prove that \( \boldsymbol{l} \boldsymbol{n}= \)
\( \boldsymbol{a} \boldsymbol{m}^{2} \)


The least value of \( 5^{\sin x-1}+5^{-\sin x-1} \) is
A . 10
в. \( \frac{5}{2} \)
\( c \cdot \frac{2}{5} \)
D.


Permanent hardness of water may be
removed by the addition of:
A. sodium carbonate
B. alum
c. potassium permanganate
D. lime


Name the type : A flying insect
A. Random motion (Irregular motion)
B. Circular motion
C. Rolling motion
D. Purely translation motion


A police party is moving in a jeep at a
constant speed \( v \). They saw a thief at a
distance \( x \) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant
acceleration \( a \). Which of the following relations is true if the police is able to catch the thief?
A \( \cdot v^{2}<a x \)
В. \( v^{2}<2 a x \)
c. \( v^{2}>2 \) ах
D. \( v^{2}=a x \)


A vertical wire carrying current in the downward direction is placed in a horizontal magnetic field directed northwards. The direction of the force on
the wire is
A. Eastward
c. Upwards
D. Westward


Find the direction cosines of the line
which is perpendicular to the lines which direction cosines proportional to
1,-2,-2 and 0,2,1


Arrange the following in an ascending
order. \( -4,2,0,-\frac{5}{4}, 2.17,-3.7, \frac{22}{7}, 8 \)
A \( \cdot-4,-3.7,-\frac{5}{4}, 0,2,2.17, \frac{22}{7}, 8 \)
в. \( _{-4,0,-\frac{5}{4},-3.7,2,2.17, \frac{22}{7}, 8} \)
c. \( _{-4,-3.7,-\frac{5}{4}, 2,0,2.17, \frac{22}{7}, 8} \)
D. \( -4,-3.7,-\frac{5}{4}, 2.17,2,0, \frac{22}{7}, 8 \)


The least stable hydride of 15 th group elements is
A \( . N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( B i H_{3} \)


A current loop consists of two identical
semicircular parts each of radius \( \mathrm{R} \), one
lying in the \( x \) -y plane and the other in \( x-z \)
plane. If the current in the loop is i. The
resultant magnetic field due to the two
semicircular parts at their common
centre is
A \( \cdot \frac{\mu_{0} i}{2 \sqrt{2} R} \)
B. \( \frac{\mu_{0} i}{2 R} \)
c. \( \frac{\mu_{0} i}{4 R} \)
D. \( \frac{\mu_{0} i}{\sqrt{2} R} \)


The ionization potential \( \left(I_{1}\right) \) of nitrogen \( (Z=7) \) is more than oxygen \( (Z=8) \)
This is explained by :
A. Hunds rule
B. Excitation rule
c. Pauli principle
D. Aufbau principle


Any given statement in the List I can
have correct matching with one or more statement(s) given in the List II. Match the entries in the List I with entries in
the List II.


Select the correct statement
regarding hydrides of \( L i \) and \( B e \)
\( \mathbf{A} \cdot \operatorname{Both} L i H \) and \( B e H_{2} \) are ionic.
B. \( L i H \) is ionic while \( B e H_{2} \) is covalent.
C . Both \( L i H \) and \( B e H_{2} \) are covalent.
D. \( L i H \) is covalent while \( B e H_{2} \) is ionic.


In the given arrangement, the loop is moved with constant velocity v in a
uniform magnetic field B in a restricted region of width a. The time for which the
emf is induced in the circuit is?
A \( \cdot \frac{2 b}{v} \)
B. \( \frac{2 a}{v} \)
c. \( \frac{(a+b)}{v} \)
D. \( \frac{2(a-b)}{v} \)


Are the magnetic field lines closed?
Explain.


Preventive measures of constipation is
A. High fibre diet
B. Vaccination
c. Antacids
D. None of the above


Evaluate the following:
\( \tan ^{-1}(\tan 12) \)


Why does the boundary between liquid phase and gaseous phase disappear on heating a liquid upto? Critical temperature in a closed vessel?


How many molecules of oxygen are used during the glycolysis of one glucose molecule?
\( A \cdot 2 \)
B. 32
\( c \cdot 38 \)
D. zero


If both \( x+1 \) and \( x-1 \) are factors of \( a x^{3}+ \)
\( x^{2}-2 x+b, \) find the values of a and \( b \)


Evaluate \( \int \frac{x^{2}}{x\left(1+x^{2}\right)} d x \)


Rivers on meeting with oceans form
1. estuaries
2. swamps
3. deltas
4. none of the above
Choose the correct option.


On a slinky, which of the following is
produced?
A. A longitudinal wave but not a transverse wave
B. A transverse wave but not a longitudinal wave
C. A longitudinal wave as well as a transverse wave
D. Neither a longitudinal nor a transverse wave


What is Heterogeneous catalysis? Give an example.


Fill in the blank:
In \( 1752, \) scientist Benjamin Franklin showed that lightning and spark from our clothes are \( _{-}-_{-}- \) - phenomena
A. same
B. different
c. simultaneous
D. none of these


For a general gaseous reaction of the type \( R \rightarrow P \), if the initial concentration
of \( \boldsymbol{R} \) is doubled, half-life of the reaction
is also doubled, the order of that
reaction is:
A .
B.
\( c \cdot 2 \)
D. 3


Draw the graph of straight line \( y= \)
\( -2 x+3 . \) Use graph to find the
intercept on \( y \) -axis.
A . 3
B . 2
c. 0
D.


If a nuclues \( z^{A} \) emits \( 9 \alpha \) and \( 5 \beta \) particles, then the ratio of the total protons and neutrons in the final nucles is
A \( \cdot \frac{(Z-13)}{(A-36)} \)
в. \( \frac{(Z-13)}{(A-Z-13)} \)
c. \( \frac{(Z-18)}{(A-36)} \)
D. \( \frac{(Z-13)}{(A-Z-23)} \)


Which of the following is a unisexual animal?
A. Tiger
B. Earthworm
c. Leech
D. Snail


Mark the correct option in impure
spectrum:
A. order of colours is revers
B. Order of colours is irregular
c. colours are overlapped
D. no colours is present


1 calorie \( = \)
A. amount of heat energy required to transform \( 1 \mathrm{kg} \) of ice into water at \( 0^{\circ} \mathrm{C} \)
B. amount of heat energy required to raise the temperature of \( 1 k g \) of water through \( 1^{\circ} C \)
C. amount of heat required to raise the temperature of \( 1 g \) of water through \( 1^{\circ} \mathrm{C} \)
D. quantity of work done at atmospheric pressure


Which of the following halides undergoes hydrolysis?
A. \( \mathrm{PF}_{3} \)
B. NF
\( c \cdot \mathrm{N} \mathrm{Cl}_{3} \)
D. PF \( _{5} \)


A body has a relative density of \( x \) with
respect to water at \( 25^{\circ} \mathrm{C} \). What is the
effect on the relative density of the body
with respect to water at \( 50^{\circ} \mathrm{C} ? \)
A. It increases
B. It decreases
c. No effect.
D. Depends on the time of heating


A substance 'A decomposes in solution following the first order kinetics. Flask contains I L of 1 M solution of A and flask
II contains \( 100 \mathrm{mL} \) of \( 0.6 \mathrm{M} \) solution
After \( 8 \mathrm{hr} \), the concentration, of \( \mathrm{A} \) in flask I becomes 0.25 M. What will be the
time for concentration of \( A \) in flask II to
become 0.3 M?
A. \( 0.4 \mathrm{hr} \)
B. 2.4 hr
c. \( 4.0 \mathrm{hr} \)
D. Unpredictable as rate constant is not given


A uniform wire of resistance \( 50 \Omega \) is cut
into five equal parts. These parts are now connected in parallel. Then the equivalent resistance of the combination is:
A . \( 2 \Omega \)
B. \( 12 \Omega \)
\( \mathbf{c} \cdot 250 \Omega \)
D. \( 6250 \Omega \)


State Huygens' principle.


A wire of cross section \( A \) is stretched
horizontally between two clamps
located \( 2 l m \) apart. A weight \( W k g \) is suspended from the mid-point of the wire.If the Young's modulus of the
material is \( Y, \) the value of extension \( x \)
is
\( ^{\mathrm{A}} \cdot\left(\frac{W l}{Y A}\right)^{1 / 3} \)
\( \mathbf{B} \cdot\left(\frac{Y A}{W I}\right)^{1 / 3} \)
c. \( \frac{1}{l}\left(\frac{W l}{Y A}\right)^{2 / 3} \)
\( ^{\mathrm{D}} \cdot\left(\frac{W}{Y A}\right)^{2 / 3} \)


An n-p-n transistor conducts when
A. both collector and emitter are positive with respect to the base.
B. collector is positive and emitter is negative with respect to the base.
C . collector is positive and emitter is at same potential as the base.
D. both collector and emitter are negative with respect to the base.


Read the assertion and reason carefully
to mark the correct option out of the
options given below:
Assertion: When radius of orbit of a
satellite is made 4 times, its time period becomes 8 times. Reason : Greater the height above the surface of earth, greater is the time period of revolution.
A. If both assertion and reason are true and the
reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason
is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true


If two events \( A \) and \( B \) are such that
\( P(A)>0 \) and \( P(B)=1, \) then \( P \) is equal to
A \( \cdot_{1-P}\left(\frac{A}{B}\right) \)
в. \( _{1-P}\left(\frac{A^{\prime}}{B}\right) \)
\( ^{c} \cdot_{1-P}\left(\frac{A \cup B}{B^{\prime}}\right) \)
D. \( P\left(\frac{A}{B^{\prime}}\right) \)


A long straight wire carrying current \( I \) is bent at its mid-point to form an angle
of \( 45^{\circ} . \) The field at point \( P \) as shown in
the figure is
A \( \cdot \frac{\mu_{0} I}{4 \pi R}(\sqrt{2}-1) \)
в. \( \frac{\mu_{0} I}{4 \pi R}(\sqrt{2}+1) \)
с. \( \frac{\mu_{0} I}{4 \sqrt{2} \pi R}(\sqrt{2}+1) \)
D. \( \frac{\mu_{0} I}{4 \sqrt{2} \pi R}(\sqrt{2}-1) \)


Assertion : The crown fires are most
destructive as they burn the tree top.
Reason: Due to crown fire the
temperature of that area may rise upto
\( 7000 C \)
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


Solve : \( (a+b)(a-b) \)


The exploding star is called
A. super nova
B. black hole
C . pulsar
D. none of these


We are required to form different words with the help of the letters of the word
INTEGER. Let m1 be the number of words
in which I and \( \mathrm{N} \) are never together and \( \mathrm{m} 2 \) be the number of words which begin with I and end with \( \mathrm{R} \), then \( \mathrm{m} 1 / \mathrm{m} \) 2 is
given by:
A .42
B. 30
\( c \cdot 6 \)
D. 1/30


State true or false:
Is it possible to have a polygon whose
sum of interior angles is \( 540^{\circ} ? \)
A. True
B. False


Jet plane works on the principal of conservation of
A. mass
B. energy
c. linear momentum
D. angular momentum


If \( a, b, c, d \) are real and no two of them
are simultaneously zero, then the equation \( \left(x^{2}+a x-3 b\right)\left(x^{2}-c x+\right. \)
b) \( \left(x^{2}-d x+2 b\right)=0 \) has
A. at least two real roots
B. at least four real roots
c. all roots real
D. at least two imaginary roots


Write the name, the structure and the
magnetic behavior of each of the
following complexes:
(i) \( \left(\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right) \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \)
(ii) \( \left(\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
(iii) \( \boldsymbol{N} \boldsymbol{i}(\boldsymbol{C O})_{4} \)


Assertion
Statement \( -1: P O F_{3} \) exist but \( N O F_{3} \)
does not exist.
Reason
Statement - 2 : 'P' can form five bonds by
expanding its octet while 'N' can not expand its octet to form five bonds.
A. Statement-1 is true, statement- - 2 is true and statement - 2 is correct explanation for statement-1
B. Statement-1 is true, statement - 2 is true and statement - 2 is NOT the correct explanation for statement - 1.
c. statement- 1 is true, statement- 2 is false.
D. Statement- -1 is false, statement - 2 is true


Which of the following qualities are best suited for handling a cooking
utensil?
A. high specific heat and low thermal conductivity
B. high specific heat and high thermal conductivity
c. low specific heat and low thermal conductivity
D. low specific heat and high thermal conductivity


A disc of radius \( R \) is rolling without sliding on a horizontal surface with a velocity of center of mass \( v \) and angular
velocity \( \omega \) in a uniform magnetic field \( B \) which is perpendicular to the plane of
the disc as shown in figure. \( O \) is the
center of the disc and \( P, Q, R \) and \( S \) are
the four points on the disc. Which of the
following statements is true?
This question has multiple correct options
A. Due to translation, induced emf across \( P S=B v r \)
B. Due to rotation, induced emf across \( Q S=0 \)
c. Due to translation, induced emf across \( R O=0 \)
D. Due to rotation, induced emf across \( O Q=B v r \)


In the following figure,' \( P^{\prime} \) is point
equidistance from two lines \( ^{\prime} l^{\prime} \) and \( ^{\prime} m^{\prime} \)
intersecting at point \( ^{\prime} A^{\prime} . \) Show that the
line \( A P \) bisect the angle between them.


If \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) where \( [.] \) is the greatest
integer function, and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( x\left(1-x^{2}\right)\left(4-x^{2}\right), \) then \( g[f(x)] \) is
A. discontinuous at all integer
B. continuous at all integer
c. continuous at \( x=0,\pm 1,\pm 2 \)
D. discontinuous at \( x=0,\pm 1,\pm 2 \)


Convert given percents to decimal fractions and also to fractions in
simplest forms:
\( 5 \% \)


Suppose \( A \) and \( B \) are independent events with \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7} \)
.Then compute:
a) \( P(A \cap B) \)
b) \( P(A \cup B) \)
\( \mathbf{c}) \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)
d) \( P\left(A^{c} \cap B^{c}\right) \)


L - shaped chromosomes are called as
A. Sex chromosome
B. Acrocentric
c. Telocentric
D. Sub-metacentric


Derive the integrated rate equation for expressing the rate constant of a first order:
\( \boldsymbol{R} \rightarrow \boldsymbol{P} \)


The value of
\( \lim _{x \rightarrow \infty}\left\{\frac{x}{x+\frac{\sqrt[3]{x}}{x+\frac{\sqrt[3]{x}}{x+\sqrt[3]{x}}} \cdots}\right\} \)
\( A \)
B
\( c \)
\( D \)


A circular current loop of magnetic moment M is in an arbitrary orientation in an external magnetic field \( \bar{B} \). The work done to rotate the loop by 30 about an axis perpendicular to its plane is:
\( A . M B \)
в. \( \sqrt{3} \frac{M B}{2} \)
c. \( \frac{M B}{2} \)
D. zero


What is the angle of incidence when the incident ray is normal to the interface or boundary separating two media?
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 45^{\circ} \)


Quantisation of charge implies:
A. charge cannot be destroyed
B. charge exists on particles
C. there is a minimum permissible charge on a particle
D. charge, which is a fraction of a charge on an electron is not possible


A metal rod \( A \) of length \( \ell_{0} \) expands by
\( \Delta \ell \) when its temperature is raised by
\( 100^{\circ} \mathrm{C} . \) Another rod \( B \) of different metal
of length \( 2 \ell_{0} \) expands by \( \Delta \ell / 2 \) for same
rise in temperature. A third rod \( C \) of
length \( 3 \ell_{0} \) is made up of pieces of rods
\( A \) and \( B \) placed end to end expands by \( 2 \Delta \ell \) on heating through 100 K.The length of each portion of the composite rod is:
A \( \cdot \frac{5}{3} \ell_{0}, \frac{4}{3} \ell_{0} \)
B. \( \ell_{0}, 2 \ell_{0} \)
c. \( \frac{3 \ell_{0}}{2}, \frac{3 \ell_{0}}{2} \)
D \( \cdot \frac{2}{3} \ell_{0}, \frac{7}{3} \ell_{0} \)


When light passes through a medium that consists of scatters such as water
vapour, dust particles, which colour of light experiences highest scattering?
A . Violet
в. Red
c. Yellow
D. Orange


If \( \Delta \boldsymbol{H}_{\text {vaporisation}} \) of substance \( \boldsymbol{X}(l) \)
(molar mass \( : 30 g / \text { mol }) \) is \( 300 J / g \) at its boiling point \( 300 K \), then molar
entropy change for reversible condensation process is:
A. \( 30 J / \) mol. \( K \)
В \( .-300 J / \) mol. \( K \)
c. \( -30 J / \) mol. \( . \)
D. None of these


A solution of \( X Y(100 \% \) ionised has osmotic pressure equal to four times
the osmotic pressure of \( 0.01 \mathrm{MBaCl}_{2} \) 100\% ionised ). Find the molarity of \( \boldsymbol{X} \boldsymbol{Y} \)
A \( \cdot 6 \times 10^{-2} M \)
В. \( 3 \times 10^{-2} M \)
c. \( 4 \times 10^{-2} M \)
D. \( 12 \times 10^{-2} M \)


Which of the following are isomers?
B. PGAL and DHAP
c. Glucose and Fructose
D. All of these


\( \left|\begin{array}{cc}\mathbf{1} & \log _{\boldsymbol{b}} \boldsymbol{a} \\ \log _{\boldsymbol{a}} \boldsymbol{b} & \mathbf{1}\end{array}\right|= \)
A \( . a b \)
B. ba
\( c \cdot a b \)
\( D \)


The rate of \( S_{N} 2 \) reaction is maximum
when the solvent is:
A. \( C H_{3} O H \)
в. \( H_{2} \) о
c. DMSO
D. Benzene


\( 540 g \) ice at \( 0^{\circ} \mathrm{C} \) is mixed with \( 540 g \) of
water at \( 80^{\circ} \mathrm{C} \). The final temperature of mixture is
\( \mathbf{A} \cdot 0^{\circ} C \)
B . \( 40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 80^{\circ} \mathrm{C} \)
D. less than \( 0^{\circ} \mathrm{C} \)


True or False.
Duralimin - \( (A I=95 \%, C u=4 \%, M n= \)
\( 0.5 \%, \mathrm{Mg}=0.5 \% \)


Evaluate \( \int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x \)


In which of the following vertebrate groups, heart does not pump oxygenated blood to different parts of the body?
A. Pisces and amphibians
B. Amphibians and reptiles
c. Amphibians only
D. Pisces only


Which of the following is true of
oxidation-reduction reactions?
A. The reducing agent is reduced at the cathode.
B. The oxidizing agent is oxidized at the anode.
C. The oxidizing agent is reduced at the cathode.
D. The reducing agent is oxidized at the cathode.


A parallel-plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by \( Q_{0}, V_{0}, E_{0} \) and \( U_{0} \) respectively. \( A \) dielectric slab is now introduced to fill
the space between the plates with battery still in connection. The corresponding quantities now given by Q, \( V \), E and \( U \) are related with previous
ones as:
This question has multiple correct options
A. \( V>V_{0} \)
в. \( U>U_{0} \)
c. \( Q>Q_{0} \)
D. \( E>E_{0} \)


The frequency of a fork is 500 Hz. The
velocity of sound in air is \( 350 \mathrm{ms}^{-1} \). The
distance through which sound travels
by the time the fork makes 125 vibrations is
\( \mathbf{A} \cdot 87.5 m \)
B. \( 700 m \)
c. \( 1400 m \)
D. \( 1.75 m \)


The two lines \( \boldsymbol{x}=\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}, \boldsymbol{z}=\boldsymbol{p} \boldsymbol{y}+\boldsymbol{q} \)
and \( \boldsymbol{x}=\boldsymbol{m}^{\prime} \boldsymbol{y}+\boldsymbol{n}^{\prime}, \boldsymbol{z}=\boldsymbol{p}^{\prime} \boldsymbol{y}+\boldsymbol{q}^{\prime} \) are
perpendicular to each other, if
\( \mathbf{A} \cdot m m^{\prime}+p p^{\prime}=1 \)
В \( \cdot \frac{m}{m^{\prime}}+\frac{p}{p^{\prime}}=-1 \)
c. \( \frac{m}{m^{\prime}}+\frac{p}{p^{\prime}}=1 \)
D. \( m m^{\prime}+p p^{\prime}=-1 \)


The equation of motion of a body falling under gravity is given by \( \frac{d v}{d t}=g- \) \( \frac{\boldsymbol{g}}{\boldsymbol{\lambda}^{2}} \boldsymbol{v}^{2} . \) Distance travelled as a function
of time is given by?. Give at \( \boldsymbol{v}=\mathbf{0}, \boldsymbol{t}=\mathbf{0} \)
A \( \cdot x=\frac{\lambda^{2}}{g} \log \sinh \left(\frac{g t}{\lambda}\right) \)
B. \( x=\frac{\lambda}{g} \log \cos h\left(\frac{g t}{\lambda^{2}}\right) \)
\( ^{\mathbf{C}} x=\frac{\lambda^{2}}{g} \log \sec h\left(\frac{g t}{\lambda}\right) \)
D \( x=\frac{\lambda^{2}}{g} \log \cos h\left(\frac{g t}{\lambda}\right) \)


In normal blood pressure \( 120 / 80 \) the denominator indicates \( \ldots \ldots . . . . . \) pressure.
A. Systolic
B. Diastolic
c. Both A and B
D. None of the above


Which of the following does not support the wave nature of light?
A . Interference
B. Diffraction
c. Polarisation
D. Photoelectric effect.


A beam of light containing two wavelengths \( 5200 A \) and \( 6500 A \) is used in Young's experiment to obtain interference fringes. What is the least distance from the central maximum on
the screen where the bright fringes due to both wavelengths concide? (Given distance between slits is 2 \( \mathrm{mm} \) and
distance of screen from slits is 120
\( \mathrm{mm} \)
A. \( 0.156 \mathrm{mm} \)
B. \( 0.312 \mathrm{mm} \)
\( c .0 .78 \mathrm{mm} \)
D. \( 1.1 \mathrm{mm} \)


If \( \boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{W}: \boldsymbol{5}<\boldsymbol{x}<\mathbf{1 0}\}, \boldsymbol{B}= \)
\( \{\mathbf{3}, \boldsymbol{4}, \mathbf{5}, \boldsymbol{6}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\boldsymbol{x}=\boldsymbol{2} \boldsymbol{n} ; \boldsymbol{n} \in \boldsymbol{N} \)
and \( \boldsymbol{n} \leq \mathbf{4}\}, \) Find \( :(\boldsymbol{A} \cap \boldsymbol{B}) \cup(\boldsymbol{A} \cap \boldsymbol{C}) \)


Complete the sentence by using the
correct words given in the brackets:
\( A_{-}-_{-}-_{-}-_{-} \) (generator \( / \) transformer/motor/transducer) is a
source of electricity that generates large amount of electricity in a power house.
A. Motor
B. Generator
c. Transducer
D. Transformer


When \( C u S O_{4} \) is added to a solution of
ammonia?
A. Freezing point is lowered
B. Freezing point is raised
c. Boiling point is raised
D. Both (1) and (2)


The adjacent sides of a parallelogram
are \( 8 m \) and 5 m. The distance between
the longer sides is 4 m. What is the
distance between the shorter sides?
\( \mathbf{A} \cdot 6.4 m \)
B. \( 6 m \)
c. \( 8.6 m \)
D. None of these


Nucleophilic addition reaction will be
most favoured in:
A \( \cdot C H_{3}-C H_{2}-C H_{2} C-C H_{3} \)
В \( \cdot\left(C H_{3}\right)_{2} C=O \)
c. \( C H_{3} C H_{2} C H O \)
D. \( C H_{3} C H O \)


When a bicycle travels on a rough surface, its speed,
A. increases
B. decreases
c. remains the same
D. none of these


In the given figure find the value of
\( \angle A O C \)
\( \mathbf{A} \cdot 130^{\circ} \)
B. \( 140^{\circ} \)
\( \mathbf{c} \cdot 150^{\circ} \)
D. \( 160^{\circ} \)


Which of the following will have
maximum electron affinity?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \) ff \( y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+ \)
\( \sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right), 0<x<1, \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{4}}{\boldsymbol{1}+\boldsymbol{x}^{2}} \)


In identical mercury droplets charged to the same potential \( V \) coalesce to form a single bigger drop. The potential of the new drop will be:
A \( \cdot \frac{V}{n} \)
в. \( n V \)
c. \( N V^{2} \)
D. \( \frac{2}{n^{3} V} \)


Calculate the heat of formation of
methane, given that heat of formation of water \( = \)
\( -286 k J \quad m o l^{-1} \)
heat of combustion of methane \( = \)
\( -890 k J \quad m o l^{-1} \)
heat of combustion of carbon \( = \)
\( -393.5 k J \quad m o l^{-1} \)
A \( .75 .5 ~ k J ~ m o l- \)
-
В. \( -75.5 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. \( -55.5 ~ k J \) mol \( ^{-1} \)
D. \( 55.5 ~ k J \) mol \( ^{-1} \)


If \( z_{1} \) and \( z_{2} \) be complex numbers such that \( z_{1}+i(\overline{z_{2}})=0 \) and \( \arg \left(\overline{z_{1}} z_{2}\right)=\frac{\pi}{3} \)
Then, \( \arg (\overline{z_{1}}) \) is equal to
A \( \cdot \frac{\pi}{3} \)
B. \( \pi \)
c.
D. \( \frac{5 \pi}{12} \)
E \( \cdot \frac{5 \pi}{6} \)


According to Werner's theory of
coordination compounds:
A. primary valency is ionisable
B. secondary valency is ionisable
C . primary and secondary valencies are ionisable
D. neither primary nor secondary valency is ionisable


\( \frac{6}{8} \)


The value of \( f(0) \) so that the function \( f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \) is continuous at
each point in its domain, is equal to
A . 2
в. \( \frac{1}{3} \)
c. \( \frac{2}{3} \)
D. \( \frac{-1}{3} \)


Formation of \( N_{2} H_{4} \) is an exothermic
reaction but the combination is an
endothermic reaction.
A. True
B. False


What will happen if the reverberation
time in a big hall is too long?
A. Sound will persist for some time in the hall
B. The reflection may become an echo.
C. Multiple reflection may occur
D. All the above will happen


A body is dropped from certain height H. If the ratio of the distances travelled by
it in \( (n-3) \) seconds to \( (n-3)^{r d} \) second
is \( \left.4: 3, \text { find } H . \text { (Take } g=10 \mathrm{m} s^{-2}\right) \)
A. \( 75 \mathrm{m} \)
B. 100 \( m \)
c. \( 125 \mathrm{m} \)
D. 150 \( m \)


Explain why the intensity of light
coming out of a polaroid does not change irrespective of the orientation of
the pass axis of the polaroid.


Uniform linear motion is a/an
motion while uniform
circular motion is a/an
motion.
A . accelerated, non accelerated
B. non accelerated, accelerated
c. deviated, retarded
D. uniform, retarded


Male and female cockroaches can be
distinguished externally through
A. Anal styles in male
B. Anal corsi in female
c. Anal style and antennae in females
D. Both A and C


The frequency of a tuning fork is \( 256 H z . \) The velocity of sound in air is
\( 344 m s^{-1} . \) The distance travelled (in
metres) by the sound during the time in which the tuning fork completes 32 vibrations is:
A . 21
B. 43
c. 86
D. 129


Find the radius of a circle whose
diameter has endpoints (-3,-2) and \( (7, \)
8)
A. 5
B. \( 5 \sqrt{2} \)
\( c \cdot(2,3) \)
D. \( \sqrt{52} \)
E. none of these


Choose the correct statement:
A. All bodies repel each other in this universe
B. Our earth does not behave like a magnet
C. Acceleration due to gravity is \( 8.9 \mathrm{m} / \mathrm{s}^{2} \)
D. All bodies fall at the same rate in vacuum


Which of the following reactions will
produce the highest yield of single
product, ignore stereoisomer?
\( A \)
B.
\( c \)
D.


If \( \frac{a}{8}+\frac{a}{4}=6, \) the value of \( a \) is
A . 122
B. -16
c. 16
D.


If \( n^{t h} \) term of AP is \( t_{n}=4 n+1 . \) Find
mean of first 10 terms.
A . 85
B. 95
\( c \cdot 23 \)
D. 7.5


If the conjugate of \( (x+i y)(1-2 i) \) is
\( 1+i, \) then
This question has multiple correct options
A \( \cdot x-i y=\frac{1+i}{1-2 i} \)
B. \( x+i y=\frac{1-i}{1-2 i} \)
c. \( _{y}=\frac{1}{5} \)
D. \( x=-\frac{1}{5} \)


The visible part of electromagnetic
spectrum lies in between
A. \( x \) -ray and ultra-violet
B. Ultra violet and infra red
C. Infra red and microwave
D. X-ray and infra red


In the given figure, \( \angle A O B=90^{\circ} \) and
\( C O D \) is a straight line. The values of \( x \)
and \( y \) are respectively.
A \( \cdot 25^{\circ} \) and \( 15^{\circ} \)
B \( \cdot 20^{\circ} \) and \( 30^{\circ} \)
\( \mathbf{c} \cdot 15^{\circ} \) and \( 45^{\circ} \)
D. \( 10^{\circ} \) and \( 60^{\circ} \)


The number of nodal planes in each \( \boldsymbol{p} \)
orbital
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


The connective tissue known as
middleman is
A . Lymph
B. Blood
c. Serum
D. Bone


Shape of \( D C l_{4}^{-} \) is:
\( A \cdot \) see-saw
B. perfect tetrahedral
c. square planar
D. none of these


Which of the following is not an allylic
halide?
A. 4-Bromopent-2-ene
B. 3-Bromo-2-methylbut-1-ene
c. 1 -Bromobut-2-ene
D. 4-Bromobut-1-ene


If the tangent to the curve, \( y=x^{3}+ \)
\( a x-b \) at the point (1,-5) is
perpendicular to the line, \( -\boldsymbol{x}+\boldsymbol{y}+ \)
\( 4=0, \) then which one of the following
points lies on the curve?
A. (-2,2)
)
в. (2,-2)
c. (2,-1)
D. (-2,1)


An alpha nucleus of energy \( \frac{1}{2} m v^{2} e V \)
bombards a heavy nuclear target of
charge \( Z e . \) Then the distance of closest
approach for the alpha nucleus will be proportional to
This question has multiple correct options
A \( \frac{1}{Z e} \)
B \( \cdot v^{2} \)
c. \( \frac{1}{m} \)
D. \( \frac{1}{v^{2}} \)


The ionisation of strong electrolytes in acetic acid compared to that in water is
A. weak
B. Strong
c. Medium
D. No ionisation


How many lines in the spectrum will be observed when electrons return from 7
th shell to 2nd shell?
A . 13
B. 14
c. 15
D. 16


A biochemical reaction triggers the expansion of 2.5 mol of an ideal gas
reversibly, coming to rest an equalized
pressure of \( 58 k P a \) at \( 37^{\circ} C . \) If the initial volume was 55.5 litres, then the
work that is done by the system in this process was approximate:
A . \( 4466 \mathrm{J} \)
в. \( -4466 J \)
c. \( -40030 J \)
D. 3600 J


Consider a uniform spherical charge
distribution of radius \( R_{1} \) centred at the
origin \( 0 . \) In this distribution, a spherical
cavity of radius \( R_{2}, \) centre at \( P \) with
distance \( \boldsymbol{O P}=\boldsymbol{\alpha}=\boldsymbol{R}_{1}-\boldsymbol{R}_{2} \) is made. If
the electric field inside the cavity at position \( \vec{r} \) is \( \vec{E}(\vec{r}), \) then the correct
statement(s) is (are)
A \( \cdot \vec{E} \) is uniform, its magnitude is independent of \( R_{2} \) but
its direction depends on \( \vec{r} \)
B. \( \vec{E} \) is uniform, its magnitude is depends on \( R_{2} \) and its direction depends on \( \vec{r} \)
C. \( \vec{E} \) is uniform, its magnitude is independent of \( \alpha \) but its direction depends on \( \vec{\alpha} \)
D. \( \vec{E} \) is uniform and both its magnitude and direction depend on \( \vec{\alpha} \)


Why reactions of higher order are
unknown?


How many electrons in an atom may
have the following quantum numbers:
\( \boldsymbol{n}=\mathbf{4}, \boldsymbol{m}_{s}=-\frac{\mathbf{1}}{\mathbf{2}} \)
A \( \cdot 14 \)
B. 16
c. 32
D. 20


The incident intensity on a horizontal surface at sea level from the sun is
about \( 1 k W m^{-2} . \) Assuming that 50 per cent of this intensity is reflected and 50 per cent is absorbed, determine the
radiation pressure on this horizontal surface (in pascals).
A \( .8 .2 \times 10^{-2} \)
В . \( 5 \times 10^{-6} \)
c. \( 3 \times 10^{-5} \)
D. \( 6 \times 10^{-5} \)


According to Faraday's law, the total charge induced in a conductor that is moved in a magnetic field depends upon
A. Initial magnetic flux
B. Final magnetic flux
c. Rate of change of magnetic flux
D. change in magnetic flux


Space between two concentric spheres
of radii \( r_{1} \) and \( r_{2}, \) such that \( r_{1}<r_{2}, \) is
filled with a material of resistivity \( \rho \)
Find the resistance between inner and
outer surface of the material.
A \( \cdot \frac{r_{1}}{r_{2}} \frac{\rho}{2} \)
В. \( \frac{r_{2}-r_{1}}{r_{r} r_{2}} \frac{\rho}{4 \pi} \)
c. \( \frac{r_{1} r_{2}}{r_{2}-r_{1}} \frac{\rho}{4 \pi} \)
D. None of these


The angle between the two tangents from the origin to the circle \( (x-7)^{2}+ \)
\( (y+1)^{2}=25 \) equals-
\( ^{A} \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{4} \)
D. None of these.


If \( \left(\frac{1+i}{1-i}\right)^{x}=1, \) then
A. \( x=2 n \), where \( n \) is any positive integer
B. \( x=4 n+1 \), where \( n \) is any positive integer
C. \( x=2 n+1, \) where \( n \) is any positive integer
D. \( x=4 n \), where \( n \) is any positive integer


Which among the following best describes the orbital overlap in
a molecule of :
\( \boldsymbol{H}-\underset{H}{_{H}}=\underset{H}{\boldsymbol{I}}-\boldsymbol{H} \)
i. s to s
ii. s to \( \mathrm{p} \)
iii. \( s p^{2} \) to \( s p^{2} \)
A. i only
B. ii only
c. i and iii only
D. ii and iii only
E. i, ii and iii


How is \( C l_{2} \) prepared using \( K M n O_{4} \)


The mean score of 1000 students for an
examination is 34 and standard
deviation is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) Determine the limits of the marks of
the central \( 70 \% \) of the candidates
\( \{P[0<z<0.25]=0.0987 ; P[0<z< \)
1.63 \( ]=\mathbf{0 . 4 4 8 4} ; P[\mathbf{0}<\boldsymbol{z}<\mathbf{1 . 0 4}]= \)
\( \mathbf{0 . 3 5}\} \)


Galvanizing is a process of coating iron with a metal to prevent it from rusting. The metal is:
A . tin
B. zinç
c. copper
D. silver


Let \( f(x) \) be the function part of the integral part, the find \( f(0) \) \( \int \frac{e^{x}\left(x^{3}+x+1\right)}{\left(x^{2}+1\right)^{3 / 2}} d x \)


Calculate the sum of the series \( 1+3+ \)
\( \mathbf{5}+\mathbf{7}+\ldots . \mathbf{2} n-\mathbf{1} \)


Find the equation of line passing through the points (3,2) and (-1,3) by using determinants.


A horizontal wind is blowing with a velocity \( v \) towards north-east. A man starts running towards north with
acceleration \( a \). The time after which
man will feel the wind blowing towards east is
A \( \cdot \frac{v}{a} \)
B. \( \frac{\sqrt{2} v}{a} \)
c. \( \frac{v}{\sqrt{2} a} \)
D. \( \frac{2 v}{a} \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sec ^{2} \boldsymbol{x}+\operatorname{cosec}^{2} \boldsymbol{x}\right)= \)
\( \mathbf{A} \cdot-4 \sec x \cdot \tan x \cdot \cos e c x \cdot \cot x \)
B. \( 4 \sec x \cdot \cos \) ec \( x \)
c. \( 2 \sec x \cdot \tan x-2 \cos e c x \cdot \cot x \)
D. \( 2 \sec ^{2} \cdot \tan x-2 \operatorname{cosec}^{2} x \cdot \cot x \)


Determine the matrix \( A \), when
\( \boldsymbol{A}=\mathbf{4}\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ -\mathbf{1} & -\mathbf{2} & -\mathbf{3} \\ \mathbf{4} & \mathbf{2} & \mathbf{6}\end{array}\right]+\mathbf{2}\left[\begin{array}{ccc}\mathbf{5} & \mathbf{4} & \mathbf{1} \\ \mathbf{3} & \mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{8} & \mathbf{2}\end{array}\right] \)


In the year 2012 , it was estimated that
there were 36.4 crore Internet users
worldwide. In the next ten years, that number will be increased by \( 125 \% \) Estimate the number of Internet users
worldwide in 2022


An electron moving along a horizontal line with respect to the observer and
towards the north. Due to each
magnetic field, it deflects towards the east then position observer:
A . In NHS
B. In SHS
c. At Equator
D. None


The power obtained in a reactor using
\( U^{235} \) disintegration is \( 1000 k W . \) The
mass decay of \( U^{235} \) per hour is :
A. 10 microgram
B. 20 microgram
c. 40 microgram
D. 1 microgram


What are the functions of three regions
of a transistor?


The electrical circuit used to get
smooth D.C output from a rectifier circuit is called:
\( \mathbf{A} \). Filter
B. Oscillator
c. \( \operatorname{cogic} \) gates
D. Amplifier


A nuclear reaction is given as
\( \boldsymbol{p}+^{15} \boldsymbol{N} \rightarrow_{Z}^{A} \boldsymbol{X}+\boldsymbol{n} \)
Find the \( Q \) value of the reaction


What is the role of collectors in froth
flotation process?


Among the given compounds, the most susceptible to nucleophilic attack at the carbonyl group is:
A. \( C H_{3} C O O C H_{3} \)
в. \( C H_{3} C O N H_{2} \)
с. \( C H_{3} \) СООСОСН\( _{3} \)
D. \( C H_{3} C O C l \)


List two function of lymphatic system?


An ideal gas goes from state \( A \) to state
B via three different processes as
indicated in the P-V diagram. If
\( Q_{1}, Q_{2}, Q_{3} \) indicate the heat absorbed
by the gas along the three processes
and \( \Delta U_{1}, \Delta U_{2}, \Delta U_{3} \) indicate the
change in internal energy along the
three processes respectively, then,
\( \mathbf{A} \cdot Q_{3}>Q_{2}>Q_{1} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
B \( \cdot Q_{1}=Q_{2}=Q_{3} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
\( \mathbf{c} \cdot Q_{1}>Q_{2}>Q_{3} \) and \( \Delta U_{1}=\Delta U_{2}=\Delta U_{3} \)
D \( \cdot Q_{3}>Q_{2}>Q_{1} \) and \( \Delta U_{1}>\Delta U_{2}>\Delta U_{3} \)


Kilowatt hour (kWh) represents the unit
of
A. Power
B. Impulse
c. Momemtum
D. Energy


The configuration \( 1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1} \) shows
the :
A. ground state of the fluorine atom
B. excited state of the fluorine atom
c. excited state of the neon atom
D. excited state of \( 0_{2}^{-} \) ion


The conditions for the combination of
atomic orbitals to form molecular
orbitals are stated below. Mark the
incorrect condition mentioned here.
A. The combining atomic orbitals must have nearly same energy
B. The combining atomic orbitals must overlap to maximum extent
c. combining atomic orbitals must have same symmetry about the molecular axis.
D. Pi ( \( \pi \) ) molecular orbitals are symmetrical around the bond axis


The probability of getting a number greater than 2 or an even number in a single throw of a fair die is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D.


What is resonance circuit? An
alternating current circuit consenting L-C-R is connected to a A.C.
voltage source in series. Determine:
A. Resultant voltage
B. Impedance
c. Resonance frequency
D. None of these above


In a pea plant, wrinkling of seeds is due to nonformation of starch, because of the absence of
A. Amylase
B. Invertase
c. Branching enzyme
D. Diastase


Arrange the following compounds in the increasing order of their acid strength:
p-cresol, p-nitrophenol, phenol


Consider the following molecules:
(।) \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\( (\|) \boldsymbol{H}_{2} \boldsymbol{S} \)
\( (\| I) \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \)
\( (\mid V) H_{2} T e \)
Arrange these molecules in increasing order of bond angle.
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I<I I<I V<I I I \)
D. \( I I<I V<I I I<I \)


One end of a wire \( 2 m \) long and \( 0.2 c m^{2} \)
in cross section is fixed to a ceiling and a load of \( 4.8 k g \) is attached to its free
end. The elongation in the wire in mm is
(if \( y=2.0 \times 10^{11} \mathrm{N} . \mathrm{m}^{-2}, \mathrm{g}=10 \mathrm{ms}^{-2} \) )
A. \( 2.4 \times 10^{-5} \)
B. 2.4
c. 0.024
D. 0.0024


Assertion
Receptors are crucial to boy's
communication process.
Reason
Receptors are proteins.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \) where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \)
\( \mathbf{A} \cdot i \)
B . \( i-1 \)
\( c \cdot-i \)
D.


give any four characteristic properties of transition elements?


The mean deviation from mean of
observations \( 5,10,15,20, \dots .85 \) is
A. 43.71
B. 21.17
\( c .38 .7 \)
D. None of these


PQ and PR are the tangents to a circle with centre \( O . \) If \( \angle P=\frac{4}{5} \angle O . \) Find
\( \angle Q P R \)
A \( \cdot 100^{\circ} \)
B. \( 180^{\circ} \)
\( c .80^{\circ} \)
D. None of these


Let \( a=i+2 j+3 k \) and \( b=3 i+j . \) Find
the unit vector in the direction of \( a+b \)


The order of the matrix \( \left[\begin{array}{c}-1 \\ 3 \\ 4\end{array}\right] \) is :
\( \mathbf{A} \cdot 1 \times 3 \)
B. \( 3 \times 1 \)
c. \( 1 \times 1 \)
D. \( 3 \times 3 \)


The IUPAC name of \( \boldsymbol{K}_{3} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \) is:
A. potassium hexacyanoferrate(II)
B. potassium hexacyanoferrate(III)
c. potassium hexacyanoiron(II)
D. tripotassium hexacyanoiron(II)


Carbon monoxide is acidic, basic or neutal oxide? Also write the balanced
equation to prepare it.


If we apply mean value theorem for
\( \boldsymbol{f}(\boldsymbol{x})=\log \boldsymbol{x} \boldsymbol{x} \in[\mathbf{1}, \mathbf{2}], \) then the value of
\( c \) is
A \( \cdot \sqrt{3} \)
B. \( \log _{e} 2 \)
\( \mathbf{c} \cdot \log _{2} e \)
D.


Transverse nature of light was confirmed by the phenomenon of the
A. refraction of light
B. diffraction of light
c. dispersion of light
D. polarization of light.


How does ammonia react with a
solution of \( C u^{2+} ? \)


If \( \cos ^{-1}\left(\frac{x}{2}\right)+\cos ^{-1}\left(\frac{y}{3}\right)=\theta, \) if \( 9 x^{2}- \)
\( 12 x y \cos \theta+4 y^{2}=m \sin ^{2} \theta . \) Find \( m . \)


If one triose phosphate completely oxidized inside the prokaryotic cell, then the net gain of ATP of energy is equal to
A . 5 ATP
B. 4 АТР
c. 20 АтР
D. 19 ATP


When \( a \) is real number then \( (z+ \)
\( \boldsymbol{a})(\overline{\boldsymbol{z}}+\boldsymbol{a})= \)
A. \( |z-a| \)
B. \( z^{2}+a^{2} \)
c. \( |z+a|^{2} \)
D. \( z^{2}-a^{2} \)


Normal temperature of the human body is ?
\( \mathbf{A} \cdot 40^{\circ} F \)
B . \( 40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 37^{\circ} C \)
D. \( 37^{\circ} F \)


State whether the following statement
is True or False.

Prime numbers do not have any factors.
A. True
B. False


Write the IUPAC name of the given
compound.


Which among the following element has largest atomic size?
A.
B.
c. As
D. sb


The value of \( a \) for which the function \( f(x)=a \sin x+\left(\frac{1}{3}\right) \sin 3 x \) has an
extremum at \( x=\frac{\pi}{3} \) is
A .
B. -
c. 0
\( D \)


The nth triangular number is defined to
be the sum of the first \( n \) positive
integers. For example, the \( 4^{t h} \) triangular
number is \( 1+2+3+4=10 . \) In the
first 100 terms of the sequence
1,3,6,10,15,21,28 of triangular
numbers, how many are divisible by \( 7 ? \)


In this method, a low melting metal like tin can be made to flow on a sloping surface. In this way it is separated from
higher melting impurities. The method
is known as:
A. distillation
B. vapour phase refining
c. liquation
D. zone refining


The volume of a gas at \( 0^{\circ} \mathrm{C} \) and \( 760 \mathrm{mm} \) pressure is \( 22.4 \mathrm{cc} \). Find the no. of
molecules present in this volume.


Duct of Bellini opens on
A. Ureter
B. Renal papilla
c. Duodenum
D. Distal convoluted tubule


Identify the similarity between isotopes of the same element.
A. They have the same particles in the nucleus
B. They have the same number of neutrons
C. They are equally abundant in nature
D. They have the same number of protons
E. They have the same mass.


An inductor of \( 30 \mathrm{mH} \) is connected to a
\( 220 \mathrm{V}, 100 \mathrm{Hz} \) ac source. The inductive
reactance is then
A . \( 10.58 \Omega \)
в. \( 12.64 \Omega \)
c. \( 18.85 \Omega \)
D. 22.67\Omega


Radio waves with frequencies higher than television signals are
A. ultrasonic waves
B. sound waves
c. light waves
D. microwaves


The angular momentum of an electron present in the excited state of Hydrogen is \( \frac{1.5 h}{\pi} . \) The electron is present in:
A. third orbit
B. second orbit
c. fourth orbit
D. fifth orbit


When a forward bias is applied to \( \mathrm{p}-\mathrm{n} \) junction it:
A. Raises the potential barrier.
B. Reduces the majority carrier current to zero.
c. Lowers the potential barrier.
D. None of the above


Exocoetus is a \( _{-1-}-_{-1}-_{\text {type of }} \)
fish.
A. Bony
B. Semi-bony
c. cartilaginous
D. None of these


Simplify: \( (\boldsymbol{p}-\boldsymbol{q})^{2}+\mathbf{4} \boldsymbol{p} \boldsymbol{q} \)
A \( \cdot p^{2}-q^{2} \)
в. \( (p+q)^{2} \)
c. \( (2 p-q)^{2} \)
D. \( (2 p-2 q)^{2} \)


Electrons can revolve around the
nucleus at any radial distance from the
nucleus.
A. True
B. False


Water takes longer time to boil than
alcohol because water has :
A. a higher specific heat capacity
B. a smaller molecular weight
c. a lower specific heat capacity
D. polar covalent bonds
E . a larger molecular weight


\( A \sigma \) bonded molecule \( M X_{3} \) is \( T- \)
shaped. The number of non-bonding pairs of electrons (on central atom) is
\( A \cdot 0 \)
B. 2
c. 1
D. can be predicated only if atomic number of \( M \) is known


The kinetic energy (in keV) of the alpha particle when the nucleus \( _{84}^{210} P O \) at rest undergoes alpha decay, is
A. 5314
B. 5422
c. 570
D. 5818


Match the hormones and its source.
(A) \( s \) Somatostatin
(1) \( \quad \) Pineal gland
(B) Melatonin
(2) Corpus luteum
(C) Aldosterone
(3) Placenta
(D) Progesterone
(4)
Adrenal cortex
(E) \( \mathrm{HCG} \)
(5)
Islets of
Langerhans
(6) \( \quad \) Adenohypophys
A. (A)- (5), (B)- (1), (C)- (6), (D)- (3), (E)- (2)
B. \( (A)-(1),(B)-(2),(C)-(4),(D)-(3),(E)-(5) \)
C. \( (A)-(2),(B)-(6),(C)-(4),(D)-(5),(E)-(3) \)
D. \( (A)-(5),(B)-(1),(C)-(4),(D)-(2),(E)-(3) \)
E. \( (A)-(1),(B)-(3),(C)-(4),(D)-(2),(E)-(5) \)


Very Short Type Question How is ozone important for us?


Bakelite is formed by:
A. polymerization of phenol and formaldehyde
B. polymerization of alcohol and acetaldehyde
C. condensation of phenol and formaldehyde
D. condensation of phenol and acetaldehyde


A sphere of mass \( \mathrm{m} \) and radius \( \mathrm{R} \) rests
on sufficiently rough inclined plane in equilibrium as shown in the figure. Find
the tension in the string.


A horizontal board of negligible mass supports a mass weighing \( 20 N \) at a
distance of \( 2 m \) from the point \( A \)
Calculate the weight which must be
placed at point \( B \), which is \( 5 m \) from
point \( A, \) in order to keep the board in
rotational equilibrium?
A. \( 4 N \)
B. \( 8 N \)
\( c .10 N \)
D. \( 40 N \)
E. \( 60 N \)


Which of the following pairs represent the same rational number?
This question has multiple correct options
A \( \cdot \frac{-7}{21} \) and \( \frac{3}{9} \)
B. \( \frac{-16}{20} \) and \( \frac{20}{-25} \)
c. \( \frac{-2}{-3} \) and \( \frac{2}{3} \)
D. \( \frac{-1}{3} \) and \( \frac{2}{9} \)


Assertion
If \( \boldsymbol{f}, \boldsymbol{g} \) and \( \boldsymbol{h} \) be continuous function on
\( [0, a] \) such that \( f(x)=f(a-x) \)
\( g(x)=-g(a-x) \) and \( 3 h(x)-4 h(a- \)
\( \boldsymbol{x})=\mathbf{5}, \) then \( \int_{0}^{\boldsymbol{a}} \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{h}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)
Reason \( \int_{0}^{a} f(x) g(x) d x=0 \)
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


In a sinusoidal wave the time required
for a particular point to move from
maximum displacement is 0.17 sec then the frequency of wave is
A. \( 1.47 H z \)
в. \( 0.36 \mathrm{Hz} \)
\( \mathrm{c} .2 .94 \mathrm{Hz} \)
D. \( 2.48 H z \)


Find the area of the figure bounded by the following curves
Find all values of a for which the
inequality \( \int_{0}^{a} x d x \leqslant a+4 \) is
satisfied.


Middle man of the body is
A. Plasma
B. Lymph
c. wвс
D. RBC


Solve \( \boldsymbol{x}=\frac{\mathbf{4}}{\mathbf{5}}(\boldsymbol{x}+\mathbf{1 0}) \)


Inferior ovary, syngenesious anther and cypsela fruit are found in
A . Liliaceae
B. Cruciferae
c. Solanaceae
D. compositae


The correct sequence of taxa in the animal kingdom is
A. Kingdom, phylum, class, order, family, species and genus
B. Kingdom, phylum, class, order, family, genus and species
C. Kingdom, phylum, class, family, order, species and genus
D. Phylum, kingdom, class, family, order, genus and species


The lower layer of the atmosphere is known as
A. Mesosphere
B. Ionosphere
c. Troposphere
D. Stratosphere


\( L n^{3+}( \) trivalent lanthanides ions) have
\( E C \)
A \( \cdot[X e] 4 f^{1} \) to \( [X e] 4 F^{14} \)
B . \( [X e] 4 d^{1} 4 f^{1} \) to \( [X e] 4 d^{1} 4 F^{14} \)
\( \mathbf{c} \cdot[X e] 4 d^{2} 4 f^{0} \) to \( [X e] 4 d^{1} 4 F^{1} \)
D \( \cdot[X e] 4 f^{0} \) to \( [X e] 4 F^{1} \)


The mass of hydrogen molecule us \( 3.32 x \) \( 10^{-27} \) kg.If \( 10^{23} \) hydrogen molecules
strike per second at \( 2 \mathrm{cm}^{2} \) area of a rigid
wall at an angle \( 45^{0} \) from the normal and
rebound back with speed of \( 1000 \mathrm{m} / \mathrm{s} \)
then the pressure exerted on the wall is
A. 2 Pascal
B. 2.34 \times 10 \( ^{3} \) Pascal
c. \( 0.23 \times 10^{3} \) Pascal
D. 23.4 x 10 \( ^{3} \) Pascal


A rubber ball of mass \( 4 \mathrm{kg} \) has the same diameter as a plastic ball of mass 0.5
kg. Both the balls are dropped simultaneously from the roof of a building.When they are \( 8 \mathrm{m} \) above the ground,they have the same
A. Kinetic energy
B. Potential energy
c. Momentum
D. Acceleration


Assertion
The images formed by total internal reflections are much brighter than those formed by mirrors or lenses
Reason

There is no loss of intensity in total
internal reflection.
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


Which of the following are isoelectronic species?
(i) \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
(ii) \( \boldsymbol{C} \boldsymbol{H}_{3}^{+} \)
(iii) \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}}^{-} \)
(iv) \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}}^{+} \)
Choose the correct answer from the
codes given below:
A \( \cdot(i),(i i),(i i i) \)
B. (i),(iii), (iv)
C . \( (i),(i i),(i v) \)
D. \( (i i),(i i i) \)
E. None of these


Which of the following is a medicine?
A. Penicillin
B. Heroin
c. cannabis
D. LSD


Identify the following structures which are presnt in dioptrical region of the ommatidium of cockroach.
A. Vitrellae, retinulea, rhabdome
B. crystalline cone, retinulae, rhobdome
c. Lenticular cells, rhabdome, rhabdomeres
D. Lenticular cells, vitrellae, crystalline cone


The example of heteropolar sol is?
A. Starch sol in water
B. Rubber sol in water
C. Protein sol in water
D. Sulphur sol


IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \) is-
A. Ethoxymethane
B. 1-methoxyethane
c. Methylethyl ether
D. Ethylmethyl ether


A chord of length \( 30 \mathrm{cm} \) is drawn at a
distance of \( 8 \mathrm{cm} \) from the centre of
a circle. The radius of the circle (in cm.)
is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
c. \( 18 \mathrm{cm} \)
D. \( 17 \mathrm{cm} \)


Water is leaking from a conical funne
at the rate of \( 5 \mathrm{cm}^{5} / \) sec. If the radius of
base of funnel is \( 10 \mathrm{cm} \) and the altitude
is \( 20 \mathrm{cm} . \) Find the rate at which water
level is dropping when it is \( 10 \mathrm{cm} \) from
the top.


Define refraction


The displacement \( x \) of a particle moving in one dimension under the action of a
constant force is related to time \( t \) by the
equation \( t=\sqrt{x}+3, \) where \( x \) is in
meter and \( t \) is in second. Find the
displacement of the particle when its velocity is zero.


When the ink fountain pen leaks on
high altitude:
A. pressure of air is more outside than inside the ink pen
B. pressure of air is less outside than inside the pen
C. the density of ink on high altitude decreases
D. none of these


The nuclei of tritium \( \left(H^{3}\right) \) atom would contain neutrons equal to:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


The two lenses of an achromatic
doublet should have:
A. Equal powers
B. Equal dispersive powers
C. Equal ratio of their power and dispersive power
D. Sum of the product of their powers and dispersive power equal to zero


Find the approximate value of mode for the following data:
\( \begin{array}{lllll}\text { Class } & 7- & 14- & 21- & 28 \\ \text { interval } & 14 & 21 & 28 & 35\end{array} \)
Frequency 4 3
A . 30
B. 32
c. 31
D. 35


Find the length of the side of a square whose area is 441 sq.m.


If \( \Delta=\left|\begin{array}{lll}\mathbf{5} & \mathbf{3} & \mathbf{8} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right|, \) white the cofactor of
the element \( a_{32} \)


Mean deviations of the series \( a, a+ \) \( \boldsymbol{d}, \boldsymbol{a}+\mathbf{2} \boldsymbol{d}, \ldots, \boldsymbol{a}+\boldsymbol{2 n} \boldsymbol{d} \) from its mean is
A \( \cdot \frac{n(n+1) d}{(2 n+1)} \)
в. \( \frac{n d}{2 n+1} \)
c. \( \frac{(n+1) d}{2 n+1} \)
D. \( \frac{(2 n+1) d}{n(n+1)} \)


Formation of \( C a O \) by Born-Haber cycle
involves which of the following
processes?
A. Sublimation of \( C a \)
B. Ionization of \( C a \) to \( C a^{+2} \)
C. Homolytic Bond dissociation of \( O_{2} \)
D. Electron Affinity of \( O \) to \( O^{2-} \)
E. All of these


Which of the following is/are Absolute Temperature Scale(s)? This question has multiple correct options
A. Kelvin Scale
B. Rankine Scale
c. celsius scale
D. Fahrenheit Scale


4 cards are chosen from a pack of 52
playing cards? In how many of these two are red cards
and two are black cards.


The charge on \( A s_{2} S_{3} \) sol is due to the
adsorption of :
A . \( H^{+} \)
B. \( O H^{-} \)
\( c \cdot O_{2} \)
\( D \cdot S^{2} \)


Tautomerism is exhibited by :
A \( \cdot C_{6} H_{5}-C H=C H-O H \)
B.
\( c \)
D. None of the above.


Why does Mathura refinery pose problems to the TajMahal?


If \( N \) is the number of turns in a circular
coil then the value of self inductance
varies as
A . \( N^{0} \)
в. \( N \)
\( c \cdot N^{2} \)
D. \( N^{-2} \)


When electric current is passed through acidified water for 1930 s, \( 1120 \mathrm{mL} \), of \( H_{2} \)
gas is collected (at STP) at the cathode.
What is the current passed in amperes?
A . 0.05
B. 0.50
\( c . \) 5.
D. 50


A beam of light passes from air into a substance \( X \). If the angle of incident be
\( 72^{\circ} \) and the angle of refraction be \( 40^{\circ} \)
calculate the refractive index of
substance \( X \). (Given: \( \sin 72^{\circ}=0.951 \)
and \( \left.\sin 40^{\circ}=0.642\right) \)


\( \left[N i(C O)_{4}\right]>\left[C o(C O)_{4}\right]^{-}>\left[F e(C O)_{4}\right]^{2-} \)
is the correct order with respect to M-C \( \pi \)
bond. Where \( \mathrm{M}=\mathrm{Ni}, \mathrm{Fe} \), and \( \mathrm{Co} \)
A . True
B. False


Bleaching powder loses oxygen in the
presence of
A . calcium chloride
B. cobalt chloride
c. sodium chloride
D. none of the above


A non-metal which is a good conductor
of electricity is:
A. graphite
B. hydrogen
c. sodium
D. mercury


Fill in the blanks:
According to Newton, different colors of light are due to the difference in of the corpuscles.
A. mass
B. nature
c. shape
D. size


Area of the region bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}^{2} \) and \( \boldsymbol{y}=\boldsymbol{s e c}^{-1}\left[\boldsymbol{s i n}^{2} \boldsymbol{x}\right] \) (where \( [.] \)
denotes the greatest integer function) is
A \( \cdot \frac{\pi}{3} \sqrt{\pi} \)
В. \( \frac{2 \pi \sqrt{\pi}}{3} \)
c. \( \frac{4 \pi \sqrt{\pi}}{3} \)
D. \( \frac{6 \pi \sqrt{\pi}}{3} \)
E \( \cdot \frac{3 \pi \sqrt{\pi}}{2} \)


Pure \( S i \) at \( 500 K \) has equal number of
electron \( \left(\boldsymbol{n}_{e}\right) \) and hole \( \left(\boldsymbol{n}_{\boldsymbol{h}}\right) \)
concentration of \( 1.5 \times 10^{16} m^{-3} \)
Doping by indium increases \( n_{h} \) to \( 4.5 \times \)
\( 10^{22} m^{-3} . \) The doped semiconductor is
of
A \( \cdot n \) -type with electron concentration \( n_{e}=5 \times 10^{22} \mathrm{m}^{-3} \)
B . p-type with electron concentration \( n_{e}=2.5 \times 10^{10} \mathrm{m}^{-3} \)
C . \( n \) -type with electron concentration \( n_{e}=2.5 \times 10^{23} \mathrm{m}^{-3} \)
D. \( p \) -type having electron concentrations \( n_{e}=5 \times \) \( 10^{9} m^{-3} \)


Find the value of \( 1+i^{2}+i^{4}+i^{6}+\ldots+ \)
\( i^{2 n} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
c. 0
D. it cannot be determined


Total area under velocity-time graph
give us the :
A. acceleration
B. velocity
c. time
D. distance


It is given that a thermodynamic
system changes from state \( A \) to state \( B \) and then back to state A. It is given that the process is reversible. Choose the
correct statements.
A. The states occurring between A to B are the same as states occurring between B to A.
B. The states occurring between A to B may be different from the states occurring between B to A
c. The energy required for transition from state \( A \) to state B is same as the energy required for the transition from state B to state A
D. The states occurring between A to B cannot be measured


Which of the following is an initiation codon?
A . AUGGGGGGGGG \( . \) GGGGG
B. UAG
c. UGA
D. UAA


Photosynthetic protists having trichocysts are
A. Dinophyceae
B. Ciliates
c. Bacillariophyceae
D. Euglenophyceae.


The top of an insulated cylindrical container is covered by a disc having emissivity \( 0.6, \) conductivity
\( 0.167 W K^{-1} m^{-1} \) and thickness \( 1 \mathrm{cm} \)
The temperature is maintained by circulating oil.
(a) Find the radiation loss to the
surroundings in \( J m^{-2} s^{-1} \) if
temperature of the upper surface of the
disc is \( 127^{\circ} \mathrm{C} \) and temperature of
surroundings is \( 27^{\circ} \mathrm{C} \)
(b) Also find the temperature of the circulating oil. Neglect the heat loss due
to convection.


Assertion
Statement-I: Lead, tin and bismuth are purified by liquation method.
Reason
Statement- -II : Lead, tin and bismuth
have low m.p. as compared to impurities.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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 term best describes why a low molecular weight compound could have an unusually high melting point, high boiling point and low vapor pressure?
A. Dipole-dipole attraction
B. Hydrogen bonding
c. van der Waals forces
D. covalent bond


Find four rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \)


The end points of a body diagonal of a rectangular parallelepiped whose faces are parallel to the coordinate planes are
(2,3,5) and \( (5,7,10) . \) The lengths of its sides are
A. 5,7,3
B. 6,5,3
c. 3,6,2
D. 3,4,5


Explain the bleaching action of ozone.


A diamagnmetic material in a
magnetic field moves:
A. Perpendicular to the field.
B. From weaker to the stronger parts of the field.
C. From stronger to the weaker parts of the field.
D. In none of the above directions.


For the reaction \( 4 N H_{3}+5 O_{2} \rightarrow \)
\( 4 N O+6 H_{2} O, \) if the rate of
disappearance of \( N H_{3} \) is \( 3.6 \times \)
\( 10^{-3} \) mol \( L^{-1} s^{-1}, \) what is the rate of
formation of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
A \( \cdot 5.4 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
B. \( 3.6 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
D. \( 0.6 \times 10^{-4} \) mol \( L^{-1} s^{-1} \)


Which of the following is/are use(s) of aluminium?
A. It is used in paints
B. It is used for packaging
c. It is used to make electrical wires
D. All of the above


If the spinning speed of the earth is
decreased, then the weight of the body
at the poles.
A. does not change
B. Decresing
c. incresing
D. may increase and decrease


Sub-shell electronic configuration of elements \( P, Q \) and \( R \) is given
\( [P, Q \text { and } R \text { are imaginary symbols }] \) \( P=1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
\( Q=1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
\( \mathrm{R}=1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} 4 s^{2} 3 d^{1} \)
(a) One of these electronic
configurations given above is wrong. Which is the element?
(b) Out of \( P, Q \) and \( R \) which has the highest electronegativity?
(c) Can \( P \) and \( Q \) join to form an ionic compound? Justify your answer


A conducting sphere of radius \( \mathrm{R} \) is given a charge \( Q . \) The electric potential and the electric field at the centre of the
sphere respectively are :
A \( \cdot \) zero and \( \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)
в. \( \frac{Q}{4 \pi \epsilon_{0} R} \) and zerc
c. \( \frac{Q}{4 \pi \epsilon_{6} R} \) and \( \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)
D. Both are zero


The application of Doppler effect of microwave among the following is
A. Ultrasound scanner
B. Echocardiography
c. Tracking of artificial satellites
D. Determining velocity of submarine


State whether the following number is
rational, If rational then enter 1 and if
false then enter 0
\( (2+\sqrt{2})^{2} \)


Spirit of salt is the other name of :
A. hydrochloric acid
B. sulphuric acid
C. nitric acid
D. hydroiodic acid


A function of time given by
\( (\sin \omega t-\cos \omega t) \) represents
A. simple harmonic motion
B. non-periodic motion
c. periodic but not simple harmonic motion
D. oscillatory but not simple harmonic motion


The laughing gas is:
A. \( N_{2} O_{4} \)
в. \( N O \)
\( c \cdot N_{2} O \)
D. \( N_{2} O_{5} \)


Sulphur is soluble in:
A. Carbon disulphide
B. Bromine
c. Heavy water
D. Distilled water


Permanent hardness of water is due to
the presence of the chlorides and sulphates of Ca, Mg and Fe. If this is true enter 1 , if false enter 0 .


A \( 2.0 m \) diameter propeller is rotating at
\( 2500 r p m \)
Which of the following values best represents the tangential velocity of the tip of the propeller blade?
A \( .262 m / s \)
в. \( 524 m / s \)
c. \( 1,050 m / s \)
D. \( 15,700 \mathrm{m} / \mathrm{s} \)
E . \( 2500 \mathrm{m} / \mathrm{s} \)


Reptiles were dominant during
period.
A. Permian
B. Cretaceous
c. Canubran
D. Oligocene


If \( \boldsymbol{A} \cap \boldsymbol{B}^{\prime}=\boldsymbol{\phi}, \) then show that \( \boldsymbol{A}=\boldsymbol{A} \cap \)
\( B \) and hence show that \( A \sqsubseteq B \)


A glass full of hot milk is poured on the table . It begins to cool gradually. Which of the following is incorrect?
A. The rate of cooling is constant till milk attains the temperature of the surrounding
B. The temperature of milk falls of exponentially
c. While cooling there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surrounding and that is why it cools.
D. All three phenomenon,conduction,convection and radiation are responsible for the loss of heat from milk to the surroundings


The structural formula of organic
molecules is:
A. structural formulae represents number of atoms of the constituent elements.
B. structural formulae represents exact arrangement of atoms of different elements
C. structural formulae represents exact arrangement of functional group of different elements
D. Both A and B


Which of the following is not a property of electric lines of force?
A. Lines of force start from positive charge and terminate at negative charge
B. Lines of force always intersect
c. The tangent to a line of force at any point gives the direction of the electric field(E) at that point
D. The number of lines per unit area, through a plane at right angles to the lines, is proportional to the magnitude of elctric field(E)


Which product is formed when 3
methylpentane-1,3,4-triol is heated under reflux with an excess of acidified
potassium dichromate(VI)?
A \( \cdot H O_{2} C C H_{2} C\left(C H_{3}\right)(O H) C O C H_{3} \)
в. \( H O_{2} C C H_{2} C O C(O H)\left(C H_{3}\right)_{2} \)
c. \( O H C C H_{2} C\left(C H_{3}\right)(O H) C O C H_{3} \)
D. \( H O_{2} C C H_{2} C O\left(C H_{3}\right) C O C H_{3} \)


How would you name the following compounds?
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)


\( \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ} \) is equal to?
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{7}{8} \)


Hydrogen undergoes both reduction and oxidation when reacted with:
A.
в. \( N_{2} \)
\( c \cdot O_{2} \)
\( D \cdot F_{2} \)


Two gases A\&B having same pressure \( P \)
volume \( V \) and absolute temperature T are
mixed. If the mixture has volume and
temperature as \( \vee \& \) T respectively then
the pressure of mixture is
\( A \cdot 2 P \)
B.
\( c \cdot P / 2 \)
D. \( 4 P \)


Both the strings shown in the figure are
made of same material and have the
same cross-section. The pulleys are
light. The wave speed of a transverse
wave in the string \( A B \) is \( v_{1} \) and in \( C D \) it
is \( \boldsymbol{v}_{2} \) The \( \boldsymbol{v}_{1} / \boldsymbol{v}_{2} \) is
\( A \)
B. 2
\( c \cdot \sqrt{2} \)
D. \( \frac{1}{\sqrt{2}} \)


During discharging of lead-storage acid battery following reaction takes place:
\( \boldsymbol{P b}(s)+\boldsymbol{P b O}_{2}(s)+2 \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
\( 2 P b S O_{4}(s)+2 H_{2} O \)
If 2.5 amp of current is drawn for 965
minutes, \( H_{2} S O_{4} \) consumed is:
A. 0.75 mol
B. 3.00 mol
c. 1.50 mol
D. 4.50 mol


A specialized structure in intestine that helps in absorption is
A. Alveoli
B. Villi
c. Bowman's capsule
D. Salivary glands
E. Pyloric sphincter


The air pollution caused by the internal combustion engine vehicles can be reduced by using:
A. CNG gas
B. LPG
c. petrol
D. either (a) or (b).


Two bodies, one held \( 30 \mathrm{cm} \) directly above the other, are released
simultaneously and allowed to fall freely under gravity. After 2 s their relative separation will be :
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
\( c .30 \mathrm{cm} \)
D. zero


Give one example (equation) of a homogeneously catalysed reaction and name the catalyst.


Find the velocity of a body of mass \( 100 g \)
having a kinetic energy of \( 20 J \)


Maximum covalency shown by sulphur is:
A .2
B. 4
\( c .6 \)
D. none


Find the modal age of 100 residents of a colony from the following data:
Age in yrs (more 10
20 \( \quad 30 \) than o equal
to)
No. of 00
persons


Evaluate \( \lim _{n \rightarrow \infty}\left[\frac{1}{(n+1)(n+2)}+\frac{1}{(n+2)(n+4)}\right. \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{C}} \) for
\( A(g) \rightleftharpoons B(g) \) is 1.1
Which gas has a molar concentration greater than 1?
A. Both [A] and [B] > 1
B. only [A]
c. only [B]
D. Neither [A] or [B]


Which of the following has highest dipole moment?
A \( . N H_{3} \)
в. \( P H_{3} \)
\( \mathrm{c} \cdot \operatorname{SbH}_{3} \)
D. \( A s H_{3} \)


Two particles of masses \( m_{1} \) and \( m_{2} \) initially at rest at infinite distance from each other, move under the action of
mutual gravitational pull. Show that at any instant their relative velocity of approach is \( \sqrt{2 G\left(m_{1}+m_{2}\right) / R, \text { where }} \) \( \mathrm{R} \) is their separation at that instant.


(a) Why do diabetic persons require
artificial sweetening agents?
(b) Write the name of a food
preservative. How does it preserve food?
(c) Give the name and formula of a
cationic detergent.


For the cell
\( \boldsymbol{P t}, \boldsymbol{H}_{2}(\boldsymbol{g}) \mid \boldsymbol{2} \boldsymbol{M} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O N} \boldsymbol{H}_{4} \| \mathbf{2} M \boldsymbol{n} \)
20
\( \operatorname{atm} \quad 0.2 \operatorname{atm} \)
Given \( : \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{C H}_{3} \boldsymbol{C O O H}\right)=\mathbf{4 . 7 4} \) and
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}}\left(\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}\right)=\mathbf{4 . 7 4} \)
EMF of the cell in millivolt is: (Given
\( \left.\frac{2.303 R T}{F}=0.059\right) \)


If the foot of the perpendicular from
(0,0,0) to a plane is \( P(1,2,2) . \) Then, the equation of the plane is
A. \( -x+2 y+8 z-9=0 \)
B. \( x+2 y+2 z-9=0 \)
c. \( x+y+z-5=0 \)
D. \( x+2 y-3 z+3=0 \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of function \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{3}}+\frac{\mathbf{1}}{\mathbf{2}} \log \boldsymbol{x} \)
A \( \cdot 2 . e^{x^{3}} x^{2}+\frac{1}{2 x} \)
B. \( e^{x^{3}} x^{2}+\frac{1}{2 x} \)
c. \( 3 . e^{x^{3}} x^{2}+\frac{1}{2 x} \)
D. \( 3 . e^{x^{3}} x^{2}+\frac{1}{x} \)


The cellular structure which disappear during mitosis is
A. Plasma membrane
B. Nuclear membrane
c. Mitochondria
D. Nuclear membrane and nucleolus


Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\mathbf{1})=\mathbf{1} \)
and \( \boldsymbol{f}(\mathbf{1})=\mathbf{2} \boldsymbol{f}(\mathbf{2})+\mathbf{3} \boldsymbol{f}(\mathbf{3})+\ldots+ \)
\( \boldsymbol{n} \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{n}(\boldsymbol{n}+1) \boldsymbol{f}(\boldsymbol{n}), \) for all
\( \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N}, \boldsymbol{n} \geq 2, \) where \( \boldsymbol{N} \) is the set of
natural numbers and \( R \) is the set of real
numbers. Then the value of \( \boldsymbol{f}(\mathbf{5 0 0}) \) is
A. 1000
в. 500
c. \( 1 / 500 \)
D. \( 1 / 1000 \)


Find the greatest and the least values of the following functions. Fin the extrema of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( 2 x \sin 2 x+\cos 2 x-\sqrt{3} \) on the
interval \( [-\boldsymbol{\pi} / 2, \mathbf{3} \boldsymbol{\pi} / \mathbf{8}] \)


In hydrogen atom the electron is
making \( 6.6 \times 10^{15} \) rev/s around the
nucleus of radius 0.53 A. The magnetic field produced at the centre of the orbit is nearly
A. \( 0.12 W b / m^{2} \)
в. \( 1.2 \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 12 W b / m^{2} \)
D. \( 120 W b / m^{2} \)


The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is:
A . 2: 1
B. \( \sqrt{5}: \sqrt{6} \)
c. 2: 3
D. \( 1: \sqrt{2} \)


Find the perimeter of the triangles
whose vertices have the following coordinates \( (\mathbf{3}, \mathbf{1 0}),(\mathbf{5}, \mathbf{2}),(\mathbf{1 4}, \mathbf{1 2}) \)


Assertion
Transperent soaps are made by
dissolving soaps in ethanol
Reason
Ethanol makes things invisible.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
The points (1,1)\( \&(-1,-1) \) lie on the
same side of the line \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
Reason
The algebraic perpendicular distances from the given points to the line have
same sign
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The reaction of \( \mathbf{P}_{4} \) with \( X \) leads
selectively to \( \mathbf{P}_{4} \mathbf{O}_{6} \). The \( \mathbf{X} \) is:
A . Dry \( \mathrm{O}_{2} \)
B. A mixture of \( \mathrm{O}_{2} \) and \( \mathrm{N}_{2} \)
c. Moist \( \mathrm{O}_{2} \)
D. \( \mathrm{O}_{2} \) in the presence of aqueous \( \mathrm{NaOH} \)


The value of \( X \) such that \( -\frac{3}{8} \) and \( \frac{X}{-24} \) are equivalent rational numbers is
A .64
B. -64
c. -9
D.


The energy of a photon is calculated by:
A. \( E=h v \)
в. \( h=E v \)
\( c \cdot h=\frac{v}{E} \)
D. \( \quad E=\frac{h}{v} \)


The value of \( ^{n-1} C_{r-2}+^{n-1} C_{r-1} \) is
A. \( ^{n-2} C_{r} \)
B. \( ^{n-1} C_{r} \)
c. \( ^{n+1} C_{r} \)
D. \( ^{n} C_{r-1} \)


The rate constant of a reaction is \( 1.5 \times \)
\( 10^{7} s^{-1} \) at \( 50^{\circ} C \) and \( 4.5 \times 10^{7} s^{-1} \) at
\( 100^{\circ} \mathrm{C} . \) Calculate the Arrhenius
parameter \( \boldsymbol{A} \) and \( \boldsymbol{E}_{\boldsymbol{a}} \)


The drug which is used to cure diseases
caused by microbes or microorganisms is called as an:
\( A \). antibiotic
B. antimicrobial
c. antifungal
D. none of these


The eccentricity of the hyperbola \( x y=4 \)
is
\( A \cdot 2 \)
B. \( \sqrt{2} \)
\( c \cdot \frac{3}{2} \)
D. \( \sqrt{3} \)


Atomic radius of which element has the
least value in \( 2^{n d} \) period?
A. Hydrogen
B. Florine
c. Neon
D. Helium


In optical instruments, the lenses are
used to form images by :
A. Reflection
B. Refraction
c. Dispersion
D. Scattering


Reproduction is essential for living organisms in order to
A. Keep the individual organism alive
B. Fulfiill their energy requirement
c. Maintain growth
D. continue the species generation after generation


Find the area of the region enclosed between the two circles \( x^{2}+y^{2}=1 \& \)
\( (x-1)^{2}+y^{2}=1 \)
A \( \cdot \frac{\pi}{6}-\frac{\sqrt{3}}{2} \) squnits
B. \( \frac{\pi}{3}-\frac{\sqrt{3}}{2} \) sq.units
c. \( \frac{\pi}{6}-\frac{\sqrt{3}}{4} \) sq.units
D. \( \frac{\pi}{3}-\frac{\sqrt{3}}{4} \) sq.units


In a nuclear reaction some mass
converts into energy. In this reaction total B.E of reactants when compared with that of products is:
A. always greater
B. always less
c. either greater or less
D. always equal


Which of the above synthetic scheme
can be used to prepare the oct-2,7dione?
A. React acetylene with \( N a N H_{2} / N H_{3} \); add half of an equivalent of 1,4-dibromobutane; then add \( H_{2} O / H_{2} S O_{4} / H g S O_{4} \)
B. React 1,6-octadiene with \( O_{3} \) followed by \( Z n \) -acetic acid
C . React 1,2-dimethylcyclohexene with \( K M n O_{4} / H^{+} \)
D. Both (a) and (c) may work.


A thin \( 1 \mathrm{m} \) long rod has a radius of 5
mm.1 A force of 50 \( \pi k N \) is applied at
one end to determine its Young's modulus. Assume that the force is
exactly known. If the least count in the measurement of all lengths is \( 0.01 \mathrm{mm} \) which of the following statements is false?
A. The maximum value of \( Y \) that can be determined is \( 10^{14} N / m^{2} \)
B. \( \frac{\Delta Y}{Y} \) gets minimum contribution. from the uncertainty in the length.
c. \( \frac{\Delta Y}{Y} \) gets its maximum contribution from the uncertainty in strain
D. The figure of merit is the largest for the length of the rod


The given figure shows a graph
representing reaction rate versus
substrate concentration. The last part of
the curve shows the plateau formation
because
A. A noncompetitive inhibitor is present
B. A competitive inhibitor is present
C. All the substrate has been converted to product
D. The active site is saturated with substrate


Find the continuity of \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{x}-|\boldsymbol{x}|} \)
for \( \boldsymbol{x}>\mathbf{0} \)


At \( 60^{\circ} C \), pure water has \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right]= \)
\( 10^{-6.7} \) mol / lit.What is the value of \( K_{W} \)
\( a t 60^{\circ} C:- \)
A \( \cdot 10^{-6} \)
B. \( 10^{-12} \)
c. \( 10^{-67} \)
D. \( 10^{-13.4} \)


Two circular coils \( P \) and \( Q \) are made
from similar wire but radius of \( Q \) is
twice that of \( P \). Relation between the
values of potential difference across them so that the magnetic induction at their centers may be the
same is :
\( \mathbf{A} \cdot V_{Q}=2 V_{P} \)
B. \( V_{Q}=3 V_{P} \)
\( \mathbf{c} \cdot V_{Q}=4 V_{P} \)
D. \( v_{Q}=\frac{1}{4} V_{P} \)


Evaluate the Given limit:
\( \lim _{x \rightarrow 2} \frac{3 x^{2}-x-10}{x^{2}-4} \)


A feature common to both \( A C \) and \( D C \)
generator is
A. Split rings
B. Electrical energy is converted to mechanical energy
c. slip rings
D. Mechanical energy is converted to electrical energy


Two oxides of Nitrogen, \( N O \) and \( N O_{2} \)
react together at \( 253 K \) and form a compound Nitrogen \( X . X \) reacts with water to yield another compound of Nitrogen Y. The shape of the anion of \( Y \) molecule is:
A. Tetrahedral
B. Triangular planar
c. Square planar
D. Pyramidal


In Lassaigne's test, the organic compound is fused with sodium metal
as to:
A. hydrolyse the compound
B. form a sodium derivative
c. convert nitrogen, sulphur or halogens if present into soluble ionic sodium compound
D. burn the compound


Figure shows a capillary rise \( h . \) If air is
blown through the horizontal tube in the
direction as shown then rise in capillary
tube will be
\( \mathbf{A} \cdot=h \)
B. \( >h \)
\( c \cdot<h \)
D. zer


Atomic number 64 will have electronic
configuration:
\( \mathbf{A} \cdot[X e]_{54} 6 s^{2} 4 f^{3} \)
В \( \cdot[X e]_{54} 6 s^{2} 4 f^{7} 5 d^{1} \)
\( \mathbf{c} \cdot[X e]_{54} 4 f^{10} \)
\( \mathbf{D} \cdot[X e]_{54} 6 s^{2} 4 f^{7} 5 p^{1} \)


What are antibiotics ? Give example.


Which one of the following methods, does not give the solution?
A. Electrophoresis
B. Peptisation
c. Electrodispersion
D. Solvent exchange


1,3,5,7- Octatetraene contains \( \underline{X} \boldsymbol{\sigma}- \)
bonds and \( \underline{Y} \pi- \) bonds. \( X \) and \( Y \) are:
A .23,4
B. 17,4
\( \mathbf{c} \cdot 18,5 \)
D. 33, 2


Number of acidic hydrogen
in Hypophosphorus acid are :


Rectangle ABCD is the image of rectangle ABCD after which of the following rotations?
A . A \( 90^{\circ} \) clockwise rotation about the origin
B. A \( 90^{\circ} \) clockwise rotation about the point (1,1)
C. A \( 90^{\circ} \) counterclockwise rotation about the point (1,1)
D. A \( 90^{\circ} \) clockwise rotation about the point (2,1)


In Kjeldahl method to estimate nitrogen, the compound is heated with
conc. \( H_{2} S O_{4} \) in presence
of
A. \( \operatorname{CaSO}_{4} \)
B. \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( C u S O_{4} \)
D. \( P_{2} O_{5} \)


Assertion
Third law of thermodynamics is
confined to pure crystalline solids.
Reason
Theoretical arguments and practical
evidence have shown that entropy of
solutions and super cooled liquids is
not zero at \( 0 \mathrm{K} \)
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 is the correct symbol for manganese?
A.
в. ма
\( c . \) мп
D. Mg


If the volume of a sphere is \( 4851 c m^{3} \)
then its surface area is
\( \mathbf{A} \cdot 1385 \mathrm{cm}^{2} \)
В . \( 1386 \mathrm{cm}^{2} \)
c. \( 1486 \mathrm{cm}^{2} \)
D. \( 1390 \mathrm{cm}^{2} \)


One mega volts is equal to
\( \mathbf{A} \cdot 10^{3} V \)
В. \( 10^{4} V \)
\( \mathbf{c} \cdot 10^{5} V \)
D. \( 10^{6} V \)


Which of the following statements is
not correct about the structure of \( \boldsymbol{P C l}_{5} \)
\( ? \)
A . \( P C l_{5} \) has a trigonal bipyramidal structure
B. Three equatorial P-CI bonds are equivalent
c. The two axial bonds are different and longer than equatorial bonds
D. Equatorial bond pairs suffer more repulsion than that of the axial bond pairs


The enzyme which has EC number 4.2.1.7
is assigned to which of the following classes of enzyme?
A. Hydrolases
B. Lyases
c. Isomerases
D. Ligases


Both the organic compounds A and B can release hydrogen with Na. Only compound A can form a salt with NaOH,
whereas B cannot.When A reacts with B
in the presence of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) a pleasant smelling compound is formed. The pair of compounds \( A \) and \( B \) can be respectively:
A \( \cdot C_{2} H_{5} O H \) and \( C_{2} H_{2} \)
в. \( C H_{3} C O O H \) and \( C_{2} H_{2} \)
c. \( C H_{3} C O O H \) and \( C_{2} H_{5} O H \)
D. \( C_{2} H_{5} O H \) and \( C H_{3} C O O H \)


What is the correct structure of \( 3- \)
Bromoprop-1-ene?
\( \mathbf{A} \cdot C H_{3}-C B r=C H_{2} \)
B \( . B r-C H=C=C H_{2} \)
\( \mathbf{c} \cdot B r-C H_{2}=C H-C H_{2} \)
\( \mathbf{D} \cdot B r-C H_{2}-C H=C H_{2} \)


If the volume of a solid sphere is
\( 7241 \frac{1}{4} c u . c m, \) then find its radius. \( \left(\text { Take } \pi=\frac{22}{7}\right) \)


Phosphine is not obtained, when:
A. red phosphorous us heated with \( N a O H \)
B. white phosphorous is heated with \( N a O H \)
C \( \cdot C a_{3} P_{2} \) reacts with water
D. phosphorous trioxide is boiled with water


Assertion
In meter bridge experiment, a high resistance is always connected in
series with a galvanometer.
Reason
As resistance increases current
through the circuit increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the value of \( \frac{i^{6}+i^{7}+i^{8}+i^{9}}{i^{2}+i^{3}} \)
\( A \cdot 0 \)
B.
\( c .-1 \)
D. None


If \( \sqrt{3} \) is static friction coefficient, what
is the angle of inclination of incline at which the body will start sliding?
A \( .90^{\circ} \)
B . \( 60^{\circ} \)
c. 45
D. 30


If \( g \) is the acceleration due to gravity at
the Earths, surface, the gain of the potential energy of an object of mass \( \mathrm{m} \)
raised from the surface of the Earth to
height equal to the radius \( \mathrm{R} \) of the Earth
is :
A \( \cdot \frac{m g R}{4} \)
в. \( \frac{m g R}{2} \)
\( \mathrm{c} \cdot m g R \)
D. \( 2 m g R \)


The geometric series 3,6,12,24,48 has
common ratio, \( r \) as
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Motion of charges is noting but :
A . Electric current
B. magnetic effect
c. heating effect
D. all of the above


A person walk up a stalled \( 15 \mathrm{m} \) long
escalator in 90 s. When standing on the same escalator, now moving, the person is carried up in 60 s. How much time would it take that person to walk up the moving escalator? Does the answer depend on the length of the escalator?
A. 36 s, Yes
B. 30s, Yes
\( c .36 s, \) No
D. 30s, No


Which of the following compounds is
most acidic?
A \( . H_{2} O \)
в. \( H_{2} S \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{Se} \)
D. \( H_{2} T e \)


What function does a condenser
perform,in heat pumps?
A. Condenser performs the most important function of cooling the room.
B. Condenser performs the most important function of heating the room.
C. Condenser performs the most important function of freezing outside the room
D. Condenser performs the most important function of heating the atmosphere


One reversible heat engine operates
between \( 1600 \mathrm{K} \) and \( T_{2} \mathrm{K}, \) and another reversible heat engine operates
between \( T_{2} \) K and 400 K. If both the
engines have the same heat input and
output, then the temperature \( T_{2} \) must
be equal to:
A. 600
B. 800
\( c \cdot 650 \)
D. 675


The critical constant \( P_{C} \& T_{C} \) for
methane are 45 atm and 189 K. The
correct statement is-(Single option correct
\( \begin{array}{ll}\text { A. } V_{C}=1.2 & L \\ \end{array} \)
В. \( b=0.8 \quad L / m o l \)
c. \( V_{C}=2.4 \quad L \)
D. \( b=0.04 \quad L / m o l \)


A particle of mass \( \mathrm{M} \) and charge \( \mathrm{Q} \) moving with velocity \( \vec{v} \) describe a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is
\( ^{\mathbf{A}} \cdot\left(\frac{M v^{2}}{R}\right)^{2 \pi R} \)
в. zero
с. \( B Q 2 \pi R \)
D. \( B Q v 2 \pi R \)


A sphere of mass \( m \) is moving with a velocity \( (4 \hat{i}-\hat{j}) m / s \) hits a frictionless and rebounds with a velocity \( (\hat{\mathbf{i}}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) The coefficient of restitution
between the sphere and the surface is :
A \( \cdot 2 / 5 \)
в. \( 4 / 9 \)
c. \( 9 / 16 \)
D. \( 4 / 25 \)


Calculate the change in pH of one litre of buffer solution containing 0.10 mole
each of \( N H_{3} \& N H_{4} C l \) upon addition
of,
(i) 0.02 mole of dissolved gaseous \( H C l \) (ii) 0.02 mole of dissolved \( N a O H \)
Assume no change in solution volume. \( \left(\boldsymbol{K}_{\boldsymbol{b}} \boldsymbol{f} \boldsymbol{o r} \boldsymbol{N} \boldsymbol{H}_{3}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}\right) \)
A \( .4 .57,4.92 \)
B. 4.25,4.57
c. 4.83,4.64
D. 3.25,3.9