A conducting material obeys ohm's law
when
A. The resistivity of material is independent of it magnitude and direction of the applied electric field.
B. The resistivity of material is dependent on the magnitude of the applied electric field
C. When the resistance is dependent on the magnitude of the applied electric field
D. All


When a sphere falling in a viscous fluid attains a terminal velocity, then:
A. the net force acting on the sphere is zero
B. the drag force balances the buoyant force
c. the drag force balances the weight of the sphere
D. the buoyant force balances the weight and drag force


Solve: \( \int_{0}^{\pi / 2} \frac{\sin x d x}{(\sin x+\cos x)^{3}} \)


The state or phase of a given set of matter can change depending on
A. temperature
B. pressure
c. Both a and \( b \)
D. None of above


Find the compound interest on Rs 4000
for \( 2 \frac{1}{2} \) years at \( 10 \% \) per annum
compounded annually


3 mole of gas "X" and 2 moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section, shown as
under
The length of the cylinder is \( 150 \mathrm{cm} \). The gas "X" intermixes with gas "Y" at the point. If the molecular weight of the
gases \( X \) and \( Y \) is 20 and 80 respectively, then what will be the distance of point \( \mathbf{A} \)
from Q?
A. \( 75 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. 37.5
D. \( 90 \mathrm{cm} \)


State and explain Curie's law.


\( \lim _{x \rightarrow 3} \frac{\sqrt{3 x}-3}{\sqrt{2 x-4}-\sqrt{2}} \) is equal to.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)


A student mixes \( 10.0 m L \) of
\( 0.10 M A g N O_{3} \) with excess copper metal. The reaction should produce 0.107 gram of silver; however, the student obtains a mass of 150 grams of silver. Plausible explanations for this yield \( >100 \% \) might include :
I. the student did not subtract the mass of the filter paper before recording
results.
II. the student did not thoroughly dry the sample before massing.
III. the copper metal did not react
completely.
A . I only
B. II only
c. I and II only
D. I and III only
E. I, II, and III


If \( x \) is an odd number, the largest odd number preceding \( x \) is
A . x-
в. x-2
\( c \cdot x-3 \)
D. x-4


High pressure is favourable for those reversible reactions in which there is
decrease in the number of molecules.
If true enter 1 , if false enter 0 .


Which of the following has highest ionic radius:
\( A \cdot F^{-} \)
B . \( B^{3+} \)
\( c \cdot O^{2} \)
D. \( L i^{+} \)


If \( \sum_{r=1}^{n} t_{r}=\frac{n(n+1)(n+2)(n+3)}{8} \)
then \( \sum_{r=1}^{n} \frac{1}{t_{r}} \) equals
A. \( -\left(\frac{1}{(n+1)(n+2)}-\frac{1}{2}\right) \)
B. \( \left(\frac{1}{(n+1)(n+2)}-\frac{1}{2}\right) \)
c. \( \left(\frac{1}{(n+1)(n+2)}+\frac{1}{2}\right) \)
D. \( \left(\frac{1}{(n-1)(n-2)}+\frac{1}{2}\right) \)


Which one of the following compound is not formed in the 'catalytic cracking' of octane?
A. Pentane
B. Butene
c. Propene
D. Hydrogengas


At same temperature and under a
pressure of \( 4 a t m, P C l_{5} \) is \( 10 \% \) dissociation. Calculate the pressure at
which \( P C l_{5} \) will be \( 20 \% \) dissociated
temperature remaining same.


Two satellites of the same mass are
launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is
A. \( -\frac{2 G M m}{r} \)
в. \( -\frac{G M m}{r} \)
c. \( \frac{G M m}{2 r} \)
D. \( \frac{G M m}{4 r} \)


The area of the region bounded by the
curve \( y=2 x-x^{2} \) and \( x \) -axis is
A \( \cdot \frac{2}{3} \) sq. units
B. \( \frac{4}{3} \) sq. units
c. \( \frac{5}{3} \) sq. units
D. \( \frac{8}{3} \) sq. units


Animals having a built-in thermostat to maintain constant body temperature are known as
A. Biothermic
B. Poikilothermic
c. oligothermic
D. Homoeothermic


Obtains Bohr's quantisation condition
for angular momentum of electron orbiting in \( n^{t h} \) hydrogen atom on the
basis of the wave picture of an electron using de Broglie hypothesis.


Evaluate \( \int \frac{\sec ^{2} x}{3+\tan x} d x \)


Let \( A=\{-1,1\} \) then find \( A \times A \)


Metals are usually in
nature
A. soft
c. data insufficient
D. none of above


Describe chromosomal theory of sex determination


Approximately, what is \( \lim _{x \rightarrow \infty} \frac{\sqrt{7} x^{2}+3 x-2}{x^{2}+5} ? \)
A .2 .32
в. 2.43
\( c .2 .54 \)
D. 2.65
E . 2.76


Photosynthetic synthesis of
carbohydrates uses \( C O_{2} \) and
A. Water in the presence of sunlight with the help of chlorophyll
B. Water in the presence of energy
c. Water with the help of chlorophyll
D. Presence of sunlight


Which one of the following reactions of xenon compounds is not feasible?
A \( \cdot 3 X e F_{4}+6 H_{2} O \longrightarrow 2 X e+X e O_{3}+12 H F+1.5 O_{2} \)
B . \( 2 X e F_{2}+2 H_{2} O \rightarrow 2 X e+4 H F+O_{2} \)
\( \mathbf{c} \cdot_{X e F_{6}+R b F} \rightarrow R b\left[X e F_{7}\right] \)
D. \( X e O_{3}+6 H F \rightarrow X e F_{6}+3 H_{2} O \)


Methods used for the management of waste is/are:
A. recycling
B. incineration
c. digesting
D. all of the above


Filicales are classified on the basis of
A. Sori
B. Nature of spores
c. Nature of sporophyll and sporangia
D. Nature of annulus


\( N_{2}(g)+3 H_{2}(g)_{200-300} \frac{773 K}{b a r} 2 N H_{3}(g)+ \)
heat
Which of the following works as a catalyst?
\( \mathbf{A} \cdot A l_{2} O_{3} \)
в. \( K_{2} \),
c. \( F e \)
D. \( V_{2} O_{5} \)


The maximum bowling speed \( (k m / h r) \) of 33 players at a cricket coaching centre is given below:
\[
\begin{array}{llll}
\begin{array}{l}
\text { Bowling } \\
\text { Speed } \\
(\boldsymbol{k m} / \boldsymbol{h r})
\end{array} & \mathbf{8 5}- & \mathbf{1 0 0}- & \mathbf{1 1 5}- \\
\mathbf{1 0 0} & & \mathbf{1 1 5} & \mathbf{1 3 0}
\end{array}
\]
Number
of
players
Find the modal bowling speed (in
\( k m / h r) \) of players


What are effective collisions?
This question has multiple correct options
A. Collisions leading to the transformation of reactants to products
B. formation of activated complex
c. collison between two reactant to decrease the
activation energy
D. collison between two reactant to overcome activation
energy barrier


A graph of volume of hydrogen released
vs time for the reaction between zinc
and dil. \( H C l \) is given. Find the
instantaneous rate of reaction at 40 sec
is :
A. \( \frac{V_{3}-V_{2}}{40} \)
B. \( \frac{V_{2}-V_{1}}{20} \)
c. \( \frac{V_{3}-V_{1}}{40} \)
D. cannot be determined


A spherical planet far out in space has a
\( \operatorname{mass} M_{0} \) and diameter \( D_{0} . \) A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to:
A \( \cdot \frac{G M_{0}}{D_{0}^{2}} \)
в. \( \frac{4 m G M_{0}}{D_{0}^{2}} \)
c. \( \frac{4 G M_{0}}{D_{0}^{2}} \)
D. \( \frac{G m M_{0}}{D_{0}^{2}} \)


The number of unpaired electrons in ferrous ion is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Which of the following is not true?
A. In vulcanisation the rubber becomes harder and
stronger
B. Natural rubber has 'trans' configuration at every double bond
C. Buna-S is a co-polymer of Butene and styrene
D. Natural rubber is 1,4 -polymer of isoprene


Unseasonal rains and cyclones are the
results of:
A. global warming
B. acid rain
c. increase of water pollution
D. increase of \( C O \)


First cell produced on earth is
A. Protobiont
B. Protozoa
c. Metazoa
D. None of the above


\( A, B, C \) and \( D \) summarize the
properties of sulphuric acid depending on whether it is dilute or concentrated.
\( A= \) Typical acid property \( B= \) Non volatile acid
\( C= \) Oxidizing agent
\( D= \) Dehydrating agent.
Choose the property \( (A, B, C \text { or } D) \) depending on which is relevant to each of the following:
(i) Preparation of Hydrogen chloride gas.
(ii) Preparation of Copper sulphate from copper oxide.
(iii) Action of conc. Sulphuric acid on Sulphur.


Maximum DDT is present in birds feeding on
A. Fishes
B. Meat
c. Insects
D. Seeds


In which of the following pairs, both properties are intensive?
A. Pressure, temperature
B. Density, volume
c. Temperature, density
D. Pressure, volume


Two equal charges q of opposite sign are separated by a small distance '2l.' The
electric potential at a point on the
perpendicular bisector of the line joining
the two charges at a distance r is:
\( \mathbf{A} \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r} \)
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{r} \)
c. zero
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{r^{2}} \)


Factorize \( 3(y-2)^{2}-(y-2)-44 \)


Seema is planning a trip to Kashmir this summer. Which of the following clothes should she definitely pack?
A. Denim Jacket
B. Leather pants
c. Woolen sweater
D. cotton shirt


Assertion
In \( S H M, \) acceleration is always
directed towards the mean position.
Reason
\( \ln S H M, \) the body has to stop
momentary at the extreme position and move back to mean position.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following steps during glycolysis is associated with utilization of ATP?
A. Glucose \( \rightarrow \) Glucose- 6 -phosphate
B. Fructose-6-phosphate \( \rightarrow \) Fructose- 1,6 -bisphosphate
c. PEP \( \rightarrow \) Pyruvic acid
D. Both (a) and (b)


Evaluate: \( \int \frac{\cos x+\sin x}{\sqrt{\sin 2 x}} d x \)


A body of mass \( 2 k g \) collides with a wall
with a speed of \( 100 \mathrm{ms}^{-1} \) are rebounds
with the same speed. If the time of
contact is \( 1 / 50 s, \) the force exerted on
the wall is
\( A \cdot 8 N \)
B . \( 2 \times 10^{4} N \)
c. \( 4 N \)
D. \( 10^{4} N \)


Two mirrors meet at right angles. A ray of
light is incident on one of the mirrors at
an angle of 30 degrees as shown in figure.
Find the reflected angle for the reflection
on the second mirror and sketch the
reflected ray.


The rate of reaction that does not
involve gases, is not dependent on:
A. pressure
B. temperature
c. concentration
D. catalyst


The minimum horizontal acceleration of
the container, so that the pressure at
point \( A \) of the container becomes
atmospheric is (the tank is of sufficient
height) ?
\( 4 \frac{2}{3} g \)
B. \( \frac{4}{3} g \)
\( c \cdot \underline{4}_{0} \)
59
D. \( \frac{3}{-g} \)


are rational numbers between \( -\frac{3}{4} \) and \( \frac{1}{2} \)
A \( \cdot \frac{-7}{16}, \frac{-1}{8}, \frac{9}{16} \)
в. \( \frac{-15}{16}, \frac{-1}{8}, \frac{3}{16} \)
c. \( \frac{-7}{16}, \frac{-1}{8}, \frac{3}{16} \)
D. none of the above


Which of the following is a necessary condition for a combustion reaction to
take place?
A. Flame is required
B. Spark is replied.
c. The temperature of the substance should be increased to ignition temperature.
D. Nothing is required


Difference of sums of 998 and -486
from 290 and 732
A . - -510
B. +510
c. - -1022
D. +512


When the current in a coil changes from 2 amp. to 4 amp. in 0.05 sec., an e.m.f. of 8 volt induced in the coil. The coefficient
of self inductance of the coil is
A. 0.1 henry
B. 0.2 henry
c. 0.4 henry
D. 0.8 henry


Which of the following are not
equivalence relations on \( I ? \)
A. \( a R b \) if \( a+b \) is an even integer
B. \( a R b \) if \( a-b \) is an even integer
c. \( a R b \) if \( a<b \)
D. \( a R b \) if \( a=b \)


\( \mathbf{1 5}, \mathbf{1 0}, \mathbf{5}, \dots \dots \dots \) In this A.P., sum of
first 10 terms is


A solid cylinder of mass ' \( m \) ' is kept in
balance position on a fixed incline of
angle \( \alpha=37^{\circ} \) with the help of a thread
fastened to its jacket. The cylinder does not slip. What force \( \boldsymbol{F} \) is required to
keep the cylinder in balance when the
thread is held vertically?
\( \mathbf{A} \cdot m g / 2 \)
в. \( 3 m g / 4 \)
\( \mathrm{c} .3 \mathrm{mg} / 8 \)
D. \( 5 m g / 8 \)


Write balanced chemical equations for the following:
(i) Action of sodium metal on ethanol
(ii) Action of zinc dust on phenol


There is no hydrogen bonding in:
A . acetic acid
B. ammonia
c. ethyl alcohol
D. diethyl ether


A student takes 2 mL acetic acid in a
dry test tube and adds a pinch of sodium hydrogen carbonate to it. He makes the following observations:
I. A colourless and odourless gas evolves with a brisk effervescence.
II. The gas turns lime water milky when
passed through it.
III. The gas burns with an explosion when a burning splinter is brought near ¡t
IV. The gas extinguishes the burning splinter that is brought near it. The correct observations are:
A. ।, , I, and III
B. II, III and IV
c. ॥ा, Iv and ।
D. IV, I and II


A farmer spends \( 30 \% \) of his earning of a month on buying seeds and deposits \( 15 \% \) of his earning in the bank. If he spent Rs 9000 on these two items, then his total earning of the month is
A. \( R s .10 .000 \)
B. \( R s .20,000 \)
c. \( R s .24,000 \)
D. Rs.25, 000


The drug given is used as:
A. Antacid
B. Analgesic
c. Antimicrobia
D. Antiseptic
E. None of the above


The reaction for hydrated copper [II] sulphate is:
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{x} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{b} \boldsymbol{l} \boldsymbol{u} e \boldsymbol{h y} \boldsymbol{d} \boldsymbol{r} \boldsymbol{o u s}) \frac{\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\longrightarrow} \)
\( \boldsymbol{y} \boldsymbol{C u} \boldsymbol{S O}_{4}(\boldsymbol{w} \boldsymbol{h i t e} \text { anhyd.})+\mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
Find \( x \) and \( y \)
A. \( x=5, y=1 \)
В. \( x=5, y=2 \)
c. \( x=2, y=1 \)
D. \( x=2, y=2 \)


A curved road of diameter \( 1.8 \mathrm{km} \) is
banked so that no friction is required at
a speed of \( 30 m / s . \) What is the banking
angle?
A \( \cdot 6 \)
B. 16
\( c \cdot 26 \)
D. \( 0.6^{\circ} \)


Dimensions \( \left[M L^{-1} T^{-1}\right] \) are related to
A. Torque
B. Work
c. Energy
D. coefficient of viscosity


Solve :
\( \left(x^{2}+4 x y\right)+\left(4 y^{2}-9 z^{2}\right) \)


toppr
Q Type your question
\( A \)
\( \mathrm{OH} \quad \mathrm{OCH}_{3} \)
\( X=Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
B.
\( \mathrm{OCH}_{3} \mathrm{OH} \)
\( X=Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
\( c \)
\( \mathrm{OH} \quad \mathrm{OCH}_{3} \)
\( \mathrm{I} \)
\( \mathrm{X}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)
\( \mathrm{OCH}_{3} \mathrm{OH} \)
\( Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
\( D \)
\( \mathrm{OCH}_{3} \)
\( \mathrm{X}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)
\( \mid \)
\( \mathrm{OH} \)
\( \mathrm{OH} \)
\( \mathrm{Y}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)

\( \mathrm{OCH}_{3} \)


The bending of light about corners of an obstacle is called:
A. Dispersion
B. Refraction
c. Deviation
D. Diffraction


The vitamin having metal atom is?
A. Vitamin A
B. Vitamin K
c. Vitamin \( B_{12} \)
D. vitamin C


The shape of ethene molecule is
A. planar
B. tetrahedral
c. bipyramidal
D. None of these


State Parallel axis theorem?


ff \( \boldsymbol{x} \times \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{x} \boldsymbol{y} \) then the value
of \( 9 \times 11 \) is :
A . 93
B. 103
\( c \cdot 113 \)
D. 121


Calculate the specific heat of the material if material of 10 kilograms
raises temperature \( 2^{\circ} C \) when 2000
joules of heat is added.
A \( \cdot 0.01 J / k g \cdot^{\circ} C \)
в. \( 0.2 J / k g \cdot^{\circ} C \)
\( \mathbf{c} \cdot 50 J / k g \cdot^{\circ} C \)
D. \( 100 J / k g \cdot^{\circ} C \)
E \( \cdot 200 J / k g \cdot^{\circ} C \)


If the temperature of a water bath is \( 104^{0} F \) then its value in degree Celsius
scale will be?
\( \mathbf{A} \cdot 35^{0} C \)
В . \( 45^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)


Which of the following statements regarding an electromagnet is NOT true?
A. Insulated wire is wound around it
B. It works only in the presence of electricity
c. It is used in fans and radio


The diagram given represents a stage during cell division. Study the same and answer the question that follow. Name the stage depicted in the diagram.What is the unique feature observed in this stage?


The choice of a reducing agent in a particular case depends on thermodynamic factor. How far do you agree with this statement? Support your opinion with two examples.


Solve the differential equation \( \frac{d y}{d x}+ \)
\( \frac{y}{x}=x^{2} \)
A. \( x=\frac{x^{4}}{4}+C \)
в. \( _{y}=\frac{x^{4}}{4}+C \)
c. \( _{x y}=\frac{x^{4}}{4}+C \)
D. None of these


Which of the following statements are
true for isopentane?
This question has multiple correct options
A \( \cdot \) It has three \( C H_{3} \) groups.
B. It has one \( C H_{2} \) group.
c. It has one \( C H \) group.
D. It has a carbon which is not bonded to hydrogen.


When metal atoms are deposited on
the cathode:
A. the mass of the cathode and anode increases by an equal amount
B. the mass of the cathode decreases and the mass of
the anode increases by an equal amount
c. the mass of the cathode increases and the mass of the
anode decreases by an equal amount
D. the mass of the cathode increases more than the
mass of the anode that decreases


A parallelogram and rhombus are equal in area. The diagonals of the rhombus
measures \( 120 m \) and 44 m. If one of the
side of the parallelogram measures \( 66 m, \) find its corresponding altitude (in
\( \boldsymbol{m}) \)
A . 40
B. 45
c. 48
D. 55


If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature
A . Is doubled
B. Becomes one-fourth
c. Remains constant
D. Become four times


\( \boldsymbol{A} \stackrel{\text {sodalime}}{\longrightarrow} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}} \stackrel{\boldsymbol{C l}_{\boldsymbol{\lambda}}, \boldsymbol{h} \boldsymbol{v}}{\boldsymbol{B}} \)
In this reaction \( A \) and \( B \) are
respectively:
A. Pheno
B. Chlorobenzene
c. Sodium benzoate, Внс
D. \( C_{2} H_{2} \& \) ВНС


The value of the determinant
\( \left|\begin{array}{ccc}1-\alpha & \alpha-\alpha^{2} & \alpha^{2} \\ 1-\beta & \beta-\beta^{2} & \beta^{2} \\ 1-\gamma & \gamma-\gamma^{2} & \gamma^{2}\end{array}\right| \) is equal to
A \( \cdot(\alpha-\beta)(\beta-\gamma)(\alpha-\gamma) \)
В . \( (\alpha-\beta)(\beta-\gamma)(\gamma-\alpha) \)
c. \( (\alpha-\beta)(\beta-\gamma)(\alpha-\gamma)(\alpha+\beta+\gamma) \)
D.


The value of \( \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)+\sin ^{-1}\left(\frac{1}{3}\right) \)
is equal to
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{2 \pi}{3} \)
\( E \)


Consider the following compounds, The correct order towards electrophilic substitution reaction is :
\( A \cdot(\text { iv })>(\text { iii })>(\text { ii })>(i) \)
B. (i)> (ii) > (iii) > (iv)
\( c \cdot(\text { iv })>(\text { iii })>(i)>(\text { ii }) \)
D. (iii) > (iv) > (i) > (ii)


A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 - divisions per milliampere and
voltage sensitivity is 2 divisions per millivolt. In order that
each division reads 1 volt, the resistence in ohms needed to be
connected in series with the coil will be
A . 103
B . 10
\( c .9995 \)
D. 99995


n the following figure, \( X Y \) is parallel to \( B C, A X=9 \mathrm{cm} . X B=4.5 \mathrm{cm} \) and
\( B C=18 \mathrm{cm} \)
What is the value of \( \frac{A Y}{Y C} ? \)


Which of the following are state
property? This question has multiple correct options
A. Internal energy (U)
B. Volume (V)
c. Heat (q)
D. Enthalpy (H)


A tube of uniform cross-sectional area
\( 1 c m^{2} \) is closed at one end with the
semipermeable membrane. a solution of 5 g glucose per 100 mL is placed inside the tube and is dipped in pure
water at \( 27^{\circ} \mathrm{C} \). When equilibrium is established the height developed in a vertical column in cm is \( 1000 x \). (Assume the density of final glucose solution \( 18 / \mathrm{mL} \)
Find the value of \( X \)


The amount of water present in blood plasma is
A . 60\%
B. 70\%
c. 80\%
D. 90\%


Calcium hydroxide react with chlorine to form:
A. bicarbonate
B. bleaching powder
c. baking soda
D. washing soda


The outer electron configuration of Gd
(Atomic No.64) is:
\( \mathbf{A} \cdot 4 \mathrm{f}^{3} 5 \mathrm{d}^{5} 6 \mathrm{s}^{2} \)
B \( \cdot 4 \mathrm{f}^{4} 5 \mathrm{d}^{0} 6 \mathrm{s}^{2} \)
C \( \cdot 4 \mathrm{f}^{2} 5 \mathrm{d}^{4} 6 \mathrm{s}^{2} \)
D. \( 4 \mathrm{f}^{7} 5 \mathrm{d}^{1} 6 \mathrm{s}^{2} \)


Species is a group of organisms that \( \ldots \)
A. cannot inter-breed
B. Live together
c. can inter-breed
D. None of these


Sulphonation differs from most of the electrophilic aromatic substitution reactions with the fact that the reaction
A . is reversible
B. requires Lewis acid as a catalyst
c. is explosive
D. takes place at high temperature


The consolidation \( \& \) exudation are the
terms used when-
A. lungs are filled up with particulate matter
B. lungs are filled up with fluid
c. lungs become spongy
D. lungs become hard


Degree of \( \left[\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=k \frac{d^{2} y}{d x^{2}} \)
is:
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
\( D \)


Which of the following is Iron bacterium?
A. Beggiotoa
B. Geobacillus
c. Thiobacillus
D. None of these


If a line makes an angle of \( \pi / 4 \) with the positive direction of each of \( x \) -axis and
\( \boldsymbol{y} \) -axis, then the angle that the line makes with the positive direction of the \( z \) -axis is
A \( \cdot \frac{\pi}{6} \)
в.
c.
D.


The equation of the line parallel to \( 5 x- \)
\( 12 y+26=0 \) and at a distance of 4
units from it, is
This question has multiple correct options
A. \( 5 x-12 y-26=0 \)
в. \( 5 x-12 y+26=0 \)
c. \( 5 x-12 y-78=0 \)
D. \( 5 x-12 y+78=0 \)


Which one of the following is the primary effect of UV radiation caused due to depletion of ozone layer?
A. Heart attack
B. Skin cancer
c. High fever
D. All of these
E. None of these


The order and power of differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\int \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\sin \boldsymbol{x} \) is
A . 1,3
в. 3,1
c. 1.2
D. 2,1


Determine the magnetic flux through
the smaller loop as a function of \( x \)
A \( \cdot \frac{\mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)
B. \( \frac{\mu_{0} i R^{2} \pi r^{2}}{2 x^{3}} \)
c. \( \frac{2 \mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)
D. \( \frac{\sqrt{2} \mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)


\[
\mathbf{A}=\left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]
\]
The new matrix formed after
interchanging \( 2^{n d} \) and \( 3^{r d} \) rows will be
\( A \)
\[
-\left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]
\]
в.
\[
\left[\begin{array}{lll}
4 & 5 & 6 \\
1 & 2 & 3 \\
7 & 8 & 9
\end{array}\right]
\]
c.
\[
-\left[\begin{array}{lll}
1 & 2 & 3 \\
7 & 8 & 9 \\
4 & 5 & 6
\end{array}\right]
\]
D.
\[
\left[\begin{array}{lll}
1 & 2 & 3 \\
7 & 8 & 9 \\
4 & 5 & 6
\end{array}\right]
\]


Which of the following have state of hybridization of the central atom not same as in the others?
\( A \cdot B \) in \( B F_{3} \)
B. \( \operatorname{oin} H_{3} O^{+} \)
c. \( \mathrm{N} \) in \( N H_{3} \)
D. \( \operatorname{Pin} P C l_{3} \)


In \( \Delta A B C, \) if \( \angle A=50^{\circ} \) and \( \angle B=60^{\circ} \)
then the greatest side is :
\( A \cdot A B \)
B. BC
c. АС
D. cannot say


The chemical treatment of the ore for
concentration is done in the case of :
This question has multiple correct options
A. aluminium
B. silver
c. copper
D. gold


According to Werner's theory of valency
transition metals possesses:
A. only one type of valency
B. two types of valencies
C. three types of valencies
D. four types of valencies


A boy a wagon along a horizontal surface for a distance of 10.0 meters.
The boy applies a force of 15 N straight along the handle while the wagon moves, and the handle makes an angle of 35 degrees with the horizontal.

How much work does the boy do on the wagon?
A. 150 Joules
B. 120 Joules
c. 86 Joules
D. 1.5 Joules
E. 0.67 Joules


Match the following two columns.


\( \mathbf{1}^{3}+\mathbf{1}^{2}+\mathbf{1}+\mathbf{2}^{3}+\mathbf{2}^{2}+\mathbf{2}+\mathbf{3}^{3}+\mathbf{3}^{2}+ \)
\( \mathbf{3}+\ldots+\mathbf{3 n} \) terms \( = \)

\( \mathbf{A} \cdot \frac{n(n+1)\left(n^{2}+12 n+5\right)}{12} \)
\( \mathbf{B} \cdot \frac{n(n+1)\left(3 n^{2}+7 n+8\right)}{12} \)
\( \mathbf{c} \cdot \frac{n(n+1)(n+2)\left(n^{2}+5 n+6\right)}{12} \)
\( \mathbf{D} \cdot \frac{(\mathbf{n}+1)(\mathbf{n}+2)(\mathbf{n}+3)}{4} \)


\( 2.2 \mathrm{g} \) of a compound of phosphorous and sulphur has 1.24 g of \( P \) in it. Its
empirical formula is :
A \( \cdot P_{2} S_{3} \)
в. \( P_{3} S_{2} \)
\( \mathrm{c} \cdot P_{3} S_{4} \)
D . \( P_{4} S_{3} \)


An AC source is connected to a purely resistive circuit. What is true of the
following
A. current leads ahead of voltage in Phase
B. current lags behind voltage in phase
c. current and voltage are in same Phase
D. any of the above may be true depending upon the value of resistance


The electric potential at a point on the equatorial line of an electric dipole is :
A. directly proportional to distance
B. inversely proportional to distance
c. inversely proportional to square of the distance
D. none of these


Which is false for the following reaction? \( \left[\boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3} \boldsymbol{O} \boldsymbol{H}\right]^{+}+ \)
\( \left[\begin{array}{c}\left.\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \longrightarrow\left[\boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right]^{2+}+\end{array}\right. \)
\( \left[\begin{array}{c}\left.\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{O} \boldsymbol{H}\right]^{2+} \\ D\end{array}\right. \)
This question has multiple correct options
\( A . A \) is base and \( B \) is acid
B. \( C \) is conjugate acid of \( A \)
c. \( B \) is conjugate acid of \( D \)
D. \( B \) is conjugate base of \( D \)


Incomplete combustion of fuel such as petrol and diesel gives:
A. nitrogen oxide
B. sulphur dioxide
c. carbon monoxide
D. carbon dioxide


A full bottle of concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) left
uncorked for several days was observed to overflow. This was probably due to
A. dissolution of oxygen from the air
B. temperature changes size of the bottle
c. hygroscopic property of sulphuric acid
D. reaction between the acid and the bottle


Which two gases makes the make the bulk of the atmosphere?


What is rectification? Draw the circuit
diagram of half wave rectifier and explain its working. Show the input ac voltage and output voltage waveforms from the rectifier circuit.


Maxwell's modified form of Ampere's circuital law is
A \( \cdot \oint_{s} \vec{B} \cdot \overrightarrow{d s}=0 \)
в. \( \oint_{s} \vec{B} \cdot \vec{d} l=\mu_{0} I \)
c. \( \oint_{s} \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I+\frac{I}{\varepsilon_{o}} \frac{d q}{d t} \)
D \( \cdot \oint_{s} \vec{B} \cdot \vec{d} \vec{l}=\mu_{0} I+\mu_{0} \varepsilon_{o} \frac{d \phi_{E}}{d t} \)


We can say that the energy of frequency \( \boldsymbol{v} \) is given by \( \boldsymbol{E}=\boldsymbol{h} \boldsymbol{v}, \) where \( \boldsymbol{h} \) is
Planck's constant. The momentum of a photon is \( p=\frac{h}{\lambda} \) where \( \lambda \) is the
wavelength of photon. Then we may conclude that velocity of light is
equal to:
A \( \cdot\left(\frac{E}{P}\right)^{1 / 2} \)
в.
c. Ep
D. \( \left(\frac{E}{P}\right)^{2} \)


Quality factor of series resonance circuit is given by
A \( \cdot \frac{f_{2}-f_{1}}{f_{0}} \)
в. \( f_{2}-f_{1} \)
c. \( \frac{f_{1}-f_{0}}{f_{2}} \)
D. \( \frac{f_{0}}{f_{2}-f_{1}} \)


Define the following terms:
(i) Lyophilic colloid
(ii) Zeta potential
(iii) Associated colloids


The change given below is an example
of :
Hydrogen \( + \) Oxygen \( \stackrel{\text {heat}}{\longrightarrow} \quad \) Water
A. Physical change
B. Chemical change
c. Both A and B
D. Neutralization reaction


When light travels from one medium into another it suffers
A. Reflection
B. Refraction
c. Dispersion
D. None of these


Among the following, the most basic oxide is:
A. \( A l_{2} O_{3} \)
в. \( P_{2} O_{5} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( N a_{2} O \)


What is the energy absorbed during the phase change called?


The distance between the lines \( 4 x+ \)
\( 3 y=11 \) and \( 8 x+6 y=15, \) is
\( A \cdot \frac{7}{2} \)
B. 4
\( c \cdot \frac{7}{10} \)
D. None of these


Which of these are characteristics of an
image formed by a plane mirror? This question has multiple correct options
A. The image is virtual
B. The image is erect
C. The image formed is of the same size as that of the object
D. The image is laterally inverted


Determine \( (8 x)^{x}, \) if \( 9^{x+2}=240+9^{x} \)


It takes time 8 min for light to reach from sun to the earth surface. If speed of
light is taken to be \( 3 \times 10^{8} \mathrm{m} s^{-1}, \) find
the order of magnitude of distance from the sun to the earth in km.
\( \mathbf{A} \cdot 10^{7} k m \)
B . \( 15 \times 10^{8} k m \)
\( \mathbf{c} \cdot 10^{8} k m \)
D. \( 10^{9} k m \)


Assertion
Mass is a measure of inertia of the
body.
Reason
Greater the mass, greater is the force
required to change its state of rest or of
uniform motion.
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


What is peptisation? Give an example


Form the differential equation by eliminating arbitrary constants from the relation \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{\boldsymbol{5} \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{-\boldsymbol{5} \boldsymbol{x}} \)


Assertion
If \( A \) is skew symmetric matrix of order 3 then its determinant should be zero
Reason

If \( A \) is square matrix, then \( d e t A= \)
\( \operatorname{det} A^{\prime}=\operatorname{det}\left(-A^{\prime}\right) \)
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 type of friction is extremely smaller than sliding friction?
A. Kinetic Friction
B. Rolling Friction
c. Static Friction
D. Fluid Friction


At what temperature do the Celsius and
Fahrenheit reading have the same numerical value?


The name " Hydrogen" was given by
A. Cavendish
B. Lavoisier
c. Urey
D. Dalton


Evaluate
\( \int \sin ^{-1} \frac{2 x}{1+x^{2}} d x \)


Sumeet thinks of a number and adds
\( \mathbf{4 0} \)
\( \frac{40}{3} \) to it. He then multiplies the result by
3. The result now obtained is 8 times
the same number he thought of, what is the number?
A . 5
B. 6
c. 8
D. 7


If \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{\pi}, \boldsymbol{\operatorname { t a n } \boldsymbol { x }} \boldsymbol{\operatorname { t a n } \boldsymbol { y }}=\boldsymbol{2}, \tan \boldsymbol{x}+ \)
tany\( + \)tanz\( =6 \) then
This question has multiple correct options
A. \( x=m \pi+\pi / 4 \)
В. \( y=n \pi+\tan ^{-1} 2 \)
\( \mathbf{c} \cdot z=l \pi+\tan ^{-1} 3 \)
D. all are correct \( (l, m, n \varepsilon I) \)


Which one of the following structures
represents the neoprene polymer?
A. \( \operatorname{tg}_{C H}-C H_{2} \tan \)
\( _{C_{B 5}} H_{B} \)
\( \mathbf{B} \cdot\left(C H_{2}-C H=\underset{C l}{C}-C H_{2}\right)_{T} \)
\( c \)
\( D \)


When nitrogen can be formed directly by decomposition of ammonium nitrite, why we start with ammonia chloride in
laboratory?


A nucleotide base present in RNA but absent in DNA is
A . Uraci
B. Adenine
c. cytosine
D. Thymine
E. Guanine


Which hybrid orbitals are used by carbon atoms in the following molecules?
\( (a) C H_{3}-C H_{3} \)
\( (b) C H_{3}-C H=C H_{2} \)
\( (c) C H_{3}-C H_{2}-O H \)
\( (\boldsymbol{d}) \boldsymbol{C H}_{3}-\boldsymbol{C H O} \)
\( (e) C H_{3} C O O H \)


We draw two cards from a deck of
shuffled cards without replacement. Find the probability of getting the second card a queen.
A \( \cdot \frac{1}{13} \)
в. \( \frac{2}{13} \)
\( c \cdot \frac{5}{13} \)
D. None of these


Semiconductor materials like \( S i \) and
\( G e \) are usually purified by:
A. distillation
B. zone refining
c. liquation
D. electrolytic refining


A particle moves with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \) in a circular path. If the speed increases to \( 8 \mathrm{m} / \mathrm{s} \) in the 20 th second
The motion of the particle in the 22 nd second will be
A. Uniform circular motion
B. Non uniform circular motion
c. Linear motion, since the particle flies off from the circular path
D. Non linear motion, since velocity has increased


Ozone layer is harmful when present in and protects life when present
in
A. Troposphere, stratosphere
B. Troposphere, mesosphere
c. Stratosphere, mesosphere
D. Mesosphere, thermosphere


Differentiate between the terms strong electrolyte and weak electrolyte. (sating any two differences)


If a rock is brought from the surface of
the moon
A. its mass will change
B. its weight will change, but not mass
c. both mass and weight will change
D. its mass and weight will remain the same


Statement I: The \( A l^{3+} \) ion needs to be
reduced to form aluminum metal.
Statement II: Reduction is a gain of
electrons.
A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. Statement I is correct, but Statement II is incorrect
D. Statement I is incorrect, but Statement II is correct


The best type of soil for agriculture is
A . Clay
B. Slit
c. Loam
D. sand


If \( \int 2^{2 x} \cdot 2^{x} d x=A \cdot 2^{2^{x}}+c, \) then \( A=? \)
A \( \cdot \frac{1}{\log 2} \)
в. \( \log 2 \)
c. \( (\log 2)^{2} \)
D. \( \frac{1}{(\log 2)^{2}} \)


Heat of atomisation of \( \boldsymbol{N} \boldsymbol{H}_{3} \) and \( \boldsymbol{N}_{2} \boldsymbol{H}_{4} \)
\( \operatorname{are} \boldsymbol{x} \boldsymbol{k} \boldsymbol{c a l} \boldsymbol{m o l}^{-1} \) and \( \boldsymbol{y} \boldsymbol{k} c \boldsymbol{a l} \boldsymbol{m o l}^{-1} \)
respectively. Average bond energy of \( N-N \) bond is:
A \( \frac{3 y-4 x}{3} \) kcal \( m o l^{-1} \)
в. \( \frac{3 y-x}{5} \) kcal \( m o l^{-1} \)
c. \( \frac{2 y-4 x}{4} \) kcal \( m o l^{-1} \)
D. None of these


wavelength:


Enthalpy change for the reaction
\( \mathbf{4} \boldsymbol{H}_{(g)} \rightarrow \mathbf{2} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \) is \( -\mathbf{8 6 9 . 6 k J . T h e} \)
dissociation energy of \( \boldsymbol{H}-\boldsymbol{H} \) bond is?


A rainbow is formed when the air is
completely dry
A . True
B. False


The P-V diagram of path followed by one
mole of perfect gas in a cylindrical container is shown in figure, the work
done when the gas is taken from state \( A \)
to state B is:
\( ^{\mathrm{A}} \cdot_{2 P_{2} V_{1}\left[1-\frac{\sqrt{V}}{\sqrt{V}_{1}}\right]} \)
в. \( 2 P_{1} V_{1}\left[1-\frac{\sqrt{V}_{1}}{\sqrt{V}_{2}}\right] \)
\( c \cdot_{2 P_{2} V_{2}\left[1-\frac{\sqrt{V}}{\sqrt{V}_{2}}\right]} \)
D. \( 2 P_{1} V_{2}\left[1-\frac{\sqrt{V}_{1}}{\sqrt{V}_{2}}\right] \)


Dacron (a polymer) is obtained by the condensation polymerization of:
A. Phenol and formaldehyde
B. Phenol and phthalic acid
c. Terepthalic acid and formaldehyde
D. Dimethyl terephthalate and ethylene glycol


Structure of ethanoic acid is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-C-O H \)
॥
О
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


Find the equivalent capacitance of the
arrangement of three capacitors shown
in figure between points \( X \) and \( Y \)


Find the oxidation number of elements
in each case:
\( C r \) in
\( \boldsymbol{C r} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}, \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r}_{3} \boldsymbol{O}_{10}, \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \) and
\( \left[\boldsymbol{C r} \boldsymbol{O}_{8}\right]^{3-} \)
A. +6,+6,+3,+5
В. +5,+6,+3,+4
\( \mathbf{c} \cdot+4,+6,+2,+5 \)
D. None of the above


f power dissipated in the \( 9 \Omega \) resistor in
the circuit shown is 36 Watt, the
potential difference across the \( 2 \Omega \)
resistor is :
A. 2 volt
3. 4 volt
\( c .8 \) volt
D. 10 volt


Which of the following is correct for acid buffer?
\( [\text { salt }=H A, \text { acid }=A] \)
A \( \cdot p^{K a}=p^{H}-\log \frac{[H A]}{|A|} \)
B・ \( p^{H}=p^{K a}+\log \frac{[H A]}{|A|} \)
c. \( p^{K a}=p^{H}-\log \frac{[A]}{[H A]} \)
D・ \( p^{H}=p^{K a}+\log \frac{[A]}{[H A]} \)


A piece of stone placed on the roof
possesses
A. kinetic energy
B. potential energy
c. thermal energy
D. nuclear energy


How many different four digit numbers can be formed using the digits 1,2,3,4,5,6 when repetition is not
allowed and each number starts with \( 1 ? \)
A . 60
в. 120
c. 140
D. 25


In the given isosceles trapezium ABCD,
\( \boldsymbol{A B} \| \boldsymbol{D C} \) and \( \boldsymbol{A D}=\boldsymbol{B C} \). If \( \angle \boldsymbol{D}= \)
\( 60^{\circ}, A B=18 c m \) and \( A D=12 c m, \) find
the length of DC
A . \( 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 90 \)
D. \( 20^{\circ} \)


Diagnostic feature of insects is
A. Segmented body
B. Chitin in body wall
c. Three pairs of legs
D. one pair compound eyes


Compute the mean for the following
data:
\( \begin{array}{ll}\text { Marks } & \text { No. of students } \\ \text { Less than 10 } & 0 \\ \text { Less than 30 } & 10 \\ \text { Less than 50 } & 25 \\ \text { Less than 70 } & 43 \\ \text { Less than 90 } & 65 \\ \text { Less than 110 } & 87 \\ \text { Less than 130 } & 96 \\ \text { Less than 150 } & 100\end{array} \) mean is 74.80
f true then enter 1 and if false then
enter


Which of the molecule does not exist?
A \( . C l F_{3} \)
в. \( I C l_{3} \)
\( \mathbf{c} \cdot B r F_{3} \)
D. \( C l I_{3} \)


are made up of one kind of
atom which can not be broken into
simpler substances.
A. Compound
B. Molecule
\( c \cdot \log \)
D. Element


The answer of the calculation \( \frac{2.568 \times 5.8}{4.168} \) in significant figures will be:
A . 3.579
B. 3.570
c. 3.57
D. 3.6


A body falling from a height of \( 10 m \)
rebounds from hard floor. If it loses \( 20 \% \)
energy in the impact, then coefficient of restitution is
A . 0.89
B. 0.56
c. 0.23
D. 0.18


Which of the following are lyophilic in
nature?
This question has multiple correct options
A. Gum
B. Sulphur
c. starch
D. Protein


A swimmer can swim \( 2 \mathrm{km} \) in 15
minutes in a lake and in a river he can
swim a distance of \( 4 \mathrm{km} \) in 20 minutes
along the stream. If a paper boat is put in the river, then the distance covered by it in \( 2 \frac{1}{2} 2 \) hours will be
\( \mathbf{A} \cdot 18 \mathrm{km} \)
B. \( 12 \mathrm{km} \)
c. \( 8 \mathrm{km} \)
D. \( 10 \mathrm{km} \)


Arrange the following fibers in the order of increasing strength:
Nylon, Cotton, Wool, Polyester, Silk
A. Silk, Wool, Cotton, Nylon, Polyester
B. Wool, Silk, Cotton, Nylon, Polyester
c. cotton, silk, Wool, Nylon, Polyester
D. Nylon, Cotton, Silk, Wool, Polyester


Find the area of a sector in radians
whose central angle is \( 45^{\circ} \) and radius is
2
A \( \cdot \frac{\pi}{3} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.


In ionic bond formation octet is
completed
A. True
B. False


A game of numbers has cards marked
from \( 11,12,13, \ldots, 40 . \) One card is drawn at random. Find the probability that the number drawn is divisible by 7


Give examples of two functions \( \boldsymbol{f} \)
\( N \rightarrow Z \) and \( g: Z \rightarrow Z \) such that \( g \circ f \)
is injective but \( g \) is not injective.


Lanthanoid elements have:
A. similar lattice and solvation energies but widely different ionization energies
B. similar lattice and ionization energies but widely different solvation energies
C. similar ionization and solvation energies but widely different lattice energies
D. similar lattice, solvation and ionization energies


The number of ordered pair \( (x, y) \) such
that \( 0 \leq x \leq 2 \pi \) and satisfying the inequality \( 2^{\sec ^{2} x} \sqrt{y^{2}-2 y+2} \leq 2 \) is
A .2
B. 3
c. 1
D. None of these


Pyrogallol is used in gas analysis
because its
A. Alkaline solution absorbs oxygen
B. Acidic solution absorbs oxygen
C. Alkaline solution reacts with carbon dioxide
D. Acidic solution absorbs nitrogen


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


Which of the following has the electronic configuration:
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{6} \)
A \( \cdot F e^{2} \)
в. \( C l \)
c. \( K^{\text {t }} \)
D. \( C s \)
E . \( A u \)


A cricket team has 15 members, of
whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least
3 bowlers is
\( A \cdot \frac{7}{13} \)
B. \( \frac{11}{15} \)
c. \( \frac{12}{13} \)
D. None of these.


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


A sewage treatment process in which a portion of the decomposer bacteria present in the waste recycled into the beginning of the process is called as
A. Activated sludge treatment
B. Primary treatment
c. Tertiary treatment
D. cyclic treatment


A physical quantity \( x \) can be dimensionally represented in terms of \( M, L \) and \( T \) is \( x=M^{a} L^{b} T^{c} . \) The
quantity time
A. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c \neq 0 \)
B. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c=0 \)
c. may be dimensionally represented in terms of \( x, M \) and \( L \), irrespective of \( c \)
D. may be dimensionally represented in terms of \( x, M \) and \( L \)


EDTA is used for the estimation of:
\( A \cdot N a^{+} \) and \( K^{+} \) ions
B. CI' and Br" ions
\( c \cdot c u 2^{2+} \) and \( A g^{+} \) ions
D. \( \mathrm{Ca}^{2+} \) and \( \mathrm{Mg}^{2+} \) ions


A moving coil ammeter requires a potential difference of \( 0.4 V \) across it for
full scale deflection. It has fixed shunt
resistance of 0.01 ohm with a coil
circuit resistance of \( \boldsymbol{R}=\mathbf{1} \boldsymbol{k} \) ohm. The
value of shunt required to give full scale deflection when the total current is \( 10 A \)
is equal to
A. 0.02 ohm
B. 0.04 ohm
c. 0.05 ohm
D. 0.06 ohm


A river is flowing from west to east at a speed of 5 meters per minute. A man on
the south bank of the river, capable of
swimming at 10 meters per minute in still waters, wants to swim across the
river in the shortest time, he should
swim in a direction:
A. due north
B. \( 30^{\circ} \) east of north
c. \( 30^{\circ} \) north of west
D. \( 60^{\circ} \) east of north


Vessel are found in
A. All angiosperms and some gymnosperm
B. Most of angiosperms and few gymnosperms
C. All angiosprms, all gymnosperms and some pteridophyta
D. All pteridophyta


The decomposition of dinitrogen monoxide gas occurs in two steps:
\( \operatorname{Step} 1: N_{2} O_{(g)} \rightarrow N_{2(g)}+O_{(g)} \) (slow)
Step \( \mathbf{2}: \mathbf{N}_{\mathbf{2}} \boldsymbol{O}_{(\boldsymbol{g})}+\boldsymbol{O}_{(\boldsymbol{g})} \rightarrow \boldsymbol{N}_{\mathbf{2}(\boldsymbol{g})}+\boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})} \)
(fast)
What is the overall reaction?
A \( \cdot 2 N_{2} O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)} \)
B \( \cdot 2 N_{2} O_{(g)}+O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)} \)
C. \( 2 N_{2} O_{(g)}+O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)}+O_{(g)} \)
D. \( N_{2} O_{(g)} \rightarrow N_{2(g)}+O_{2(g)} \)


Who is considered as ancestor of
modern apes?
A. Dryopithecus
B. Ramapithecus
c. oreopithecus
D. None of the above


The solubility product of \( \boldsymbol{H} \boldsymbol{g}_{2} \mathbf{1}_{2} \) is equal
to
\( \mathbf{A} \cdot\left[H g_{2}^{2+}\right]\left[I^{-}\right] \)
B \( \cdot\left[H g^{2+}\right]\left[I^{-}\right] \)
c. \( \left[H g_{2}^{2+}\right]\left[I^{-}\right]^{2} \)
D \( \cdot\left[H g^{2+}\right]\left[I^{-}\right]^{2} \)


Assertion
Induced potential across a coil and
therefore induced current is always
opposite to the direction of current due
to external source.
Reason
Lenz's law states that induced emf
always opposes the cause due to which it is being produced.
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


Two cells \( A \) and \( B \) of e.m.f \( 2 V \) and \( 1.5 V \)
respectively, are connected as shown in figure through an external resistance
10\Omega. The internal resistance of each cell
is 5\Omega. The potential difference \( V_{A} \) and
\( V_{B} \) across the terminals of the cells \( A \)
and B respectively are.
A \( \cdot V_{A}=2.0 V, V_{B}=1.5 \mathrm{V} \)
B . \( V_{A}=2.12 V, V_{B}=1.375 V \)
C \( . V_{A}=1.875 V, V_{B}=1.625 V \)
D. \( V_{A}=1.875 V, V_{B}=1.375 V \)


The incorrect statement is :
A. Vapour pressure of a liquid always increases by increasing temperature.
B. Vapour pressure onlydepends on temperature and not on the nature of substance.
C. Vapour pressure does not depend on the quantity of the liquid taken and the surface area of the liquid.
D. Vapour pressure is not a colligative property \& is independent of the concentration of the liquid.


The percentage of isomers formed during monobromination of \( 2,3- \) dimethyl butane at room temperature
relative to \( 1,2,3 \mathrm{H} \) atoms to chlorination is \( (1.0: 3.8: 5.0) \)
A . 81\%
B. 56\%
c. 15\%
D. 22\%


Choose the correct option:
A. If only conservative forces act on a particle, the kinetic energy remains constant.
B. If the net force acting on an object is zero, then the object is at rest.
C. If net mechanical work is done on a body, the body must accelerate.
D. If net mechanical work is done on a body, the speed of body remains unchanged.


Refraction of light occurs when
A. Light passes through a narrow opening
B. Light passes into a new transparent material (not head on) in which it travels at a new speed
C. Light strikes the edge of an object
D. Light becomes polarized
E. Light passes through a diffraction grating


The correct statement(s) is/are:
This question has multiple correct options
A. \( B i \) a metal.
B. \( A s \) and \( S b \) are semimetals.
C \( . N_{2} \) is nonmetal but \( P_{4} \) is metal.
D. all the above


The relation between frequency(f) and time period(T) is given by
\( A \cdot f=T \)
B \cdot f \( =\frac{1}{T} \)
\( c \cdot T=f^{2} \)
D. \( T=f^{3} \)


In an experiment the following observations were recorded
\( \boldsymbol{L}=\mathbf{2 . 8 9 0} \) metre
\( \mathbf{M}=\mathbf{3 . 0} \mathbf{k g} \)
\( \ell=0.87 \mathrm{cm} \)
\( \mathbf{D}=\mathbf{0 . 0 4 1} \mathrm{cm} \)
\( \mathbf{g}=\mathbf{9 8 1 c m} / \mathbf{s e c ^ { 2 }} \)
and the formula used for calculatlon of Young's modulus \( (\mathrm{Y}) \) is \( \mathrm{Y}=\frac{\mathrm{MgL}}{\pi \mathrm{r}^{2} l} \)
What is the maximum possible error
expressed in percentage?
A . 6.36\%
B. 4.8\%
c. अ\%
D. 1\%


Smooth E.R. of animal cell does not
synthesize
A. Cholesterol
B. Phospholipid
c. Saturated fatty acid
D. Unsaturated fatty acid


Integrate
\( \int \frac{x}{x^{2}+x+1} d x \)


Construct \( \Delta P Q R, \) such that \( Q R= \)
\( 6.5 c m, \angle P Q R=60^{0} \) and \( P Q-P R= \)
\( 2.5 c m \)


A is a skew symmetric matrix such that \( A^{T} A=I, \) then \( A^{4 n-1}(n \in N) \) is equal
to
A . \( -A^{T} \)
B. \( I \)
\( c .-I \)
D. \( A^{T} \)


The lateral surface of a long straight
solenoid with \( n \) turns per unit
length experiences a pressure of \( \boldsymbol{p}= \) \( \frac{1}{x} \mu_{0} n^{2} I^{2} \) when a current \( I \) flows
through it. Find \( x \)


An aqueous solution contains 0.53 g of
anhydrous \( N a_{2} C O_{3}(\text { Mol. wt. } 106) \) dissolved in \( 100 \mathrm{ml} \) of solution. The
molarity of the solution is:
\( \mathbf{A} \cdot 0.1 M \)
в. \( 0.05 M \)
\( \mathbf{c} \cdot 0.2 M \)
D. \( 0.4 M \)


A particle starts from origin at \( t=0 \) with velocity of \( 15 \hat{i} \) and moves in \( x \) -y plane under the action of force which produce a constant acceleration of \( 15 \hat{i}+20 \hat{j} \)
Find \( y \) -coordinate of particle when \( x \) coordinate is \( 180 \mathrm{m} \)


A broadcasting station transmits waves
of frequency \( 71 \times 10^{4} H z \) with speed of
\( 3 \times 10^{8} m / s . \) The wavelength of the
wave is :
A . \( 418.8 \mathrm{m} \)
B. 324.6 m
c. \( 208.4 \mathrm{m} \)
D. 422.5 m


What is the nature of electric charge?
A . only positive
B. only negative
c. positive and negative both
D. neutral.


Assertion
For a very near to the earth's surface the time period of revolution is given by \( 1 h \) \( 24 m i n \)
Reason
The period of revolution of a satellite depends only upon its height above the earth's surface
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 induction coil works on the
principle of
A. Self-induction
B. Mutual induction
c. Ampere's rule
D. Fleming's right hand rule


Water pollution can be caused due to:
A. chemicals
B. pathogens
c. discoloration
D. all of above


Phenol associates in \( C_{6} H_{6} \) to double
molecules. A solution of 2 g of phenol in 100 g \( C_{2} H_{6} \) has its f.pt. lowered by 0.72
K. \( \boldsymbol{K}_{f} \) for \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}} \) is \( \mathbf{5 . 1 2} \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k} \boldsymbol{g} \)
Percentage degree of association of
phenol is (write the integer at tens place, e.g., if percentage degree of dissociation is \( x y \% \) then answer would
be \( x \) )


A simple method to remove peroxides from ether is to treat them with an
aqueous solution of:
A. \( K I \)
в. КСNS
c. \( N a_{2} S_{2} O_{3} \)
D. \( B r_{2} \)


Which of the following alcohols forms a ketone when oxidized?
A. 1-Propanol
B. Methanol
c. 2-Methyl-2-propanol
D. 2-Propanol


Construct a pair of tangents to a circle
of radius \( 4 \mathrm{cm} \) such that the acute
angle between the tangents is \( 45^{\circ} \)


The potential of a large liquid drop when eight liquid drops are combined is \( 20 V \)
Then the potential of each single drop
was:
A . \( 10 V \)
в. \( 7.5 V \)
\( c .5 V \)
D. 2.5V


A metal sphere A of radius \( r_{1} \) charged
to a potential \( \phi_{1} \) is enveloped by a thin
walled conducting spherical shell B of
radius \( r_{2} \). Then potential \( \phi_{2} \) of the sphere \( A \) after it is connected to the
shell B by a thin conducting wire will be
A \( \cdot \phi_{1} \frac{r_{1}}{r_{2}} \)
В \( \cdot \phi_{1}\left(\frac{r_{2}}{r_{1}}\right) \)
c. \( \phi_{1}\left(1-\frac{r_{2}}{r_{1}}\right) \)
\( \mathbf{D} \cdot \mathbf{q} \phi_{1}\left(\frac{r_{1} r_{2}}{r_{1} r_{2}}\right) \)


If \( f(x) \) is defined in \( [-3,2], \) then find
the domain of definition of \( \boldsymbol{f}([|\boldsymbol{x}|]) \) and
\( \boldsymbol{f}([\mathbf{2} \boldsymbol{x}+\boldsymbol{3}]) \)


Wobble hypothesis was proposed by
A. Holley
B. Nirenberg
c. Khorana
D. Crick


Potassium dichromate can be
converted to potassium chromate by adding:
\( \mathbf{A} \cdot K O H \)
в. Conc.H\( _{2} \)SO\( _{4} \)
c. \( N H_{4} O H \)
D. \( C H_{3} \) СООН


A stone dropped from a height of \( 10 \mathrm{cm} \)
above the top of window \( 80 \mathrm{cm} \) height.
The time taken by the stone to cross the window is \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( \cdot \frac{1}{7} s \)
в. \( \frac{3}{7} s \)
\( c \cdot \frac{2}{7} s \)
D. \( \frac{4}{7} s \)


The best solution to population problem
in India is to
A. Conserve natural resources
B. Increase medical facilities
c. Reduce birth rate
D. Increase food production


Electron-positron pair can be created by \( \gamma \) -rays. In this process the minimum
energy of \( \gamma \) -rays should be :
A. \( 5.0 \mathrm{MeV} \)
в. \( 4.02 \mathrm{MeV} \)
c. \( 15.0 \mathrm{MeV} \)
D. \( 1.02 \mathrm{MeV} \)


When relatively attached groups occupy opposite sides on carbon in an unsaturated hydrocarbon they are called:
A . cis
B. trans
c. neutral
D. none of above


An electric heater which is connected to
a \( 220 \mathrm{V} \) supply line has two resistance
coils. \( A \) and \( B \) of \( 24 \Omega \) resistance each.
these coils can be used separately (one at a time), in series or in parallel.
calculate the current drawn when:
Only one coil A is used
coils \( A \) and \( B \) are used in series


If \( \sqrt{\boldsymbol{y}+\boldsymbol{x}}+\sqrt{\boldsymbol{y}-\boldsymbol{x}}=\boldsymbol{c}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is
equal to
This question has multiple correct options
A \( \cdot \frac{2 x}{c^{2}} \)
B. \( \frac{x}{y+\sqrt{y^{2}-x^{2}}} \)
c. \( \frac{y-\sqrt{y^{2}-x^{2}}}{x} \)
D. \( \frac{c^{2}}{2 y} \)


State one function of each of the
following:
Pleural fluid


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


Davisson and Thomson shared the
Nobel Prize for their experimental discovery of diffraction of electrons by
crystals. True \( =1, \) false \( =0 \)


Construct a differential equation by
eliminating the arbitrary constants \( a, b \) from the equation:
\( \boldsymbol{y}=(\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}) \boldsymbol{e}^{\boldsymbol{x}} \)


Four \( 2 c m \times 2 c m \times 2 c m \) cubes of ice
are taken out from a refrigerator and
are put in \( 200 \mathrm{ml} \) of a drink at \( 10^{\circ} \mathrm{C} \)
(a) Find the temperature of the drink when thermal equilibrium is attained in
it.
(b) If the ice cubs do not do not melt
completely, find the amount melted.
Assume that no heat is lost to the
outside of the capacity. Density of ice
\( =900 k g / m^{3}, \) density of the drink \( = \)
\( 1000 k g / m^{3}, \) specific heat capacity of
the drink \( 4200 \mathrm{J} / \mathrm{kg}-\mathrm{K} \), latent heat of fusion of ice \( 3.4 \times 10^{5} J / k g \)


A charged particle is moving in a uniform magnetic field in a circular
path. The energy of the particle is doubled. If the initial radius of the
circular path was \( R, \) the radius of the new circular path after the energy is doubled will be:
A. \( 0.5 R \)
в. \( \sqrt{2} R \)
\( c .2 R \)
D. \( \frac{R}{\sqrt{2}} \)


The adjoining figure is a rectangle whose diagonals \( A C \) and \( B D \) intersect
at \( O . \) If \( \angle O A B=27^{\circ} \) then find \( \angle O B C \)


A sweet-shop makes gift packet of sweets by combining two special types of sweets \( A \) and \( B \) which weigh \( 7 k g \) Atleast \( 3 k g \) of \( A \) and no more than \( 5 k g \)
of \( B \) should be used. The shop makes a profit of Rs. 15 on \( A \) and \( \operatorname{Rs} .20 \) on \( B \) per
kg. Determine the product mix so as to obtain maximum profit


For silicon, the energy gap at \( 300 K \) is
\( \mathbf{A} \cdot 1.1 W \)
в. \( 1.1 J \)
c. \( 1.1 e V \)
D. None of these


Which of the solution will remain
colourless with phenolphthalein indicator?
A. Soap solution
в. \( C a(O H)_{2} \) solution
c. vinegar solution
D. Baking soda solution


A solid sphere of radius \( \boldsymbol{R} \) has a charge
\( +2 Q . \) A hollow spherical shell of radius
\( 3 R \) placed concentric with the first
sphere has net charge \( -Q . \) If the inner
sphere is earthed, what will be the
charge on it?
A \( \cdot \frac{2 Q}{3} \)
B. \( \frac{-6}{3} \)
c. \( \frac{Q}{3} \)
D. \( \frac{-2 Q}{3} \)


Structure of some important polymers
are given. Which one represents Buna-
S?
\( A \)
\[
\begin{array}{c}
\mathrm{CH}_{3} \\
\left(-\mathrm{CH}_{2}-\mathrm{C}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}}
\end{array}
\]
в.
\[
\begin{array}{c}
\left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \\
\mathrm{C}_{6} \mathrm{H}_{5}
\end{array}
\]
\( c \)
\[
\begin{array}{c}
\left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \\
\mathrm{CN}
\end{array}
\]
\( D \)
\[
\left(-\mathrm{CH}_{2}-\mathrm{C}^{\prime}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}}
\]


Consider the nuclear change \( \mathbf{9 3}^{237} \boldsymbol{X} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{B} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{C} \)
Which of the following statements is
not correct?
A. Mass number of B is 233
B. Atomic number of A is 9
c. \( c \) is an isotope of
D. B is an isobar of A


If \( \int e^{x}(\operatorname{nn} x+x \operatorname{cn} x+1) d x=f(x)+ \)
cwhenf\( (1)=0, \) then \( f(e) \) is equal to
\( A \)
B \( \cdot e^{s} \)
\( \mathbf{c} \cdot e^{s-1} \)
D. \( e^{e+1} \)


Find the median for the following data.
\( \begin{array}{lllll}\text { Height } & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- & \mathbf{2 0}- \\ (\mathrm{ft}) & \mathbf{1 0} & \mathbf{1 5} & \mathbf{2 0} & \mathbf{2 5}\end{array} \)
No. of
trees


If density (D) acceleration (a) and force
(F) are taken as basic quantities,then Time period has dimensions
A \( \cdot \frac{1}{6} \) in \( F \)
B. \( -\frac{1}{6} \) in \( F \)
\( c \cdot-\frac{2}{3} \) in \( F \)
D. All the above are true


A die is thrown twice and the sum of the
numbers appearing is observed to be 7 Find the conditional probability that the
number 3 has appeared at least once.


Prepare the truth table for the following.
\( \sim \boldsymbol{p} \wedge \boldsymbol{q} \)


Two point charges in air at a distance
of \( 20 c m . \) from each other interact with a
certain force. At what distance from
each other should these charges be placed in oil of relative permittivity 5 to obtain the same force of interaction
A. \( 8.94 \times 10^{-2} \mathrm{m} \)
В. \( 0.894 \times 10^{-2} \mathrm{m} \)
\( c \cdot 89.4 \times 10^{-2} m \)
D. \( 8.94 \times 10^{2} m \)


Block A of weight \( 100 \mathrm{N} \) reset on a frictionless inclined plane of slope
angle \( 430^{0} \) as shown in the figure. A
flexible cord attached to A passes over a
frictionless pulley and is connected to
block B of weight W. Find the weight \( \mathbf{W} \) of which the system is in equilibrium.
A . 25 N
в. 50 N
\( c .75 \mathrm{N} \)
D. 100 N


Which of the following contains \( p \pi \)
\( d \pi \) bonds?
A \( . N O_{2} \)
в. \( S O_{3} \)
\( c \cdot s O_{2} \)
D. Both B and C


A convex lens of focal length \( 20 \mathrm{cm} \) and another plano convex lens of focal
length \( 40 \mathrm{cm} \) are placed coaxially (see
fig). The plano convex lens is silvered on plane surface. What should be the
distance d (in cm) so that final image of
the object 'O' is formed on 0 itself?
\( A \cdot 10 \mathrm{cm} \)
B. 40 \( \mathrm{cm} \)
\( c \cdot 20 \mathrm{cm} \)
D. 80 cm


Which among the following solutions is not used in determination of the cell
constant?
\( \mathbf{A} \cdot 10^{-2} M K C l \)
В. \( 10^{-1} M \) КСl
c. \( 1 M K C l \)
D. Saturated \( K C l \)


Which of the following will be most stable diazonium salt \( \boldsymbol{R} \boldsymbol{N}_{2}^{+} \boldsymbol{X}^{-} ? \)
A \( \cdot C H_{3} N_{2}^{+} X^{-} \)
B . \( C_{6} H_{5} N_{2}^{+} X^{-} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{N}_{2}^{+} \mathrm{X}^{-} \)
D. \( C_{6} H_{5} C H_{2} N_{2}^{+} X^{-} \)


Match the following


Find the measure of an angle if its supplement-three times complement
\( =20^{\circ} 30^{\prime} 40^{\prime \prime} \)


During dissolution when a solute is added to the solvent, some solute particles separate out from the solution as a result of crystallization. At the stage of equilibrium, the concentration of solute in the solution at a given
temperature and pressure:
A. increases
B. decreases
c. remains constant
D. keeps changing


The reaction which does not liberate
hydrogen is:
This question has multiple correct options
A. \( A l+N a O H \rightarrow \) conc
B. \( C+N a O H \rightarrow \) molten
\( \mathbf{c} \cdot F_{2}+N a O H \rightarrow c o n c \)
D. \( Z n+N a O H \rightarrow a q \)


If \( A \) and \( B \) are coefficients of \( x^{n} \) in the
expansions of \( (1+x)^{2 n} \) and \( (1+x)^{2 n-1} \)
respectively, then \( \frac{A}{B} \) is equal to
A .4
B . 2
\( c .9 \)
D. 6


Figure shows the strain-stress curve for
a given material. The Young's modulus
of the material is
\( \mathbf{A} \cdot 5 \times 10^{9} N \quad m^{-2} \)
B . \( 5 \times 10^{10} N \quad m^{-2} \)
\( \begin{array}{lll}\text { С. } 7.5 \times 10^{9} N & m^{-2}\end{array} \)
D. \( 7.5 \times 10^{10} N \quad m^{-2} \)


A rectangular metal block has
dimensions \( 3 c m \times 1 c m \times 1 c m . \) The
ratio of the resistance measured
between the two opposite rectangular faces to that measured between the two square forces of the block is:
A . 1: 3
B. 1: 9
c. 3: 1
D. 9: 1


Three of the following pairs of the human skeletal parts are correctly matched with their respective inclusive skeletal category and one pair is not matched. Identify the non-matching pair.
A. Sternum and ribs - Axial skeleton
B. Clavicle and glenoid cavity - Pelvic girdle
c. Humerus and ulna - Appendicular skeleton
D. Malleus and stapes - Ear ossicles


Integrate the following function:
\( e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) \)


Statement 1: Two isotopes of the same
element have the same mass number
Statement 2: Isotopes have the same number of protons.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both Statement 1 and Statement 2 are not correct.


Assertion
The superoxide \( M O_{2} \) contains the
paramagnetic ion \( \boldsymbol{O}_{\mathbf{2}}^{-} \)
Reason
\( O_{2}^{-} \) is stable in presence of large
cations as \( \boldsymbol{K}, \boldsymbol{R} \boldsymbol{b}, \boldsymbol{C} \boldsymbol{s} \)
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. Assertion is incorrect but Reason is correct


Morphine is an important analgesic.
What interactions are involved in
binding the phenol group to the target
binding site?
Alcohol
A. Ionic interactions
B. Hydrogen bonding interactions
c. van der Waals binding interactions
D. The group has no binding role


\( \boldsymbol{P h C H}_{2} \boldsymbol{C H}_{3} \frac{(i) C r O_{2} C l_{2} / C C l_{4}}{(i i) H_{3} O^{+}} \)
\( \boldsymbol{P h C H}_{2} \boldsymbol{C H O} \)
The above reaction is an example of which name reaction?
A. Rossenmund reduction
B. Birch reduction
c. Mendius reduction
D. Etard reduction


A wire suspended from one end carries a sphere at its other end. The elongation in the wire reduces from 2mm to
1.6 \( m m \) on completely immersing the sphere in water. The density of the material of the sphere is
A. \( 3200 \mathrm{kg} / \mathrm{m}^{3} \)
в. \( 800 \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 1250 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 5000 \mathrm{kg} / \mathrm{m}^{3} \)


If . med from the collection
of rational numbers, then they are closed under division.
A .2
B.
\( c \cdot 0 \)
D. -


\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \) then \( \boldsymbol{f} \)
is
A. only one-one
B. only into
c. one-one into
D. not a function


Why sleepers are used below the rails?


An object lying at the equator of the earth will fly off the surface (will feel weightlessness), if the length of the day becomes
\( \mathbf{A} \cdot 1.00 h \)
в. \( 1.41 h \)
c. \( 17.0 h \)
D. 17.0 min


\( p \) is a prime number and \( n<p<2 n . \) If
\( N=^{2 n} C_{n}, \) then
A. \( p \) divides \( N \) completely
B . \( p^{2} \) divides \( N \) completely
c. \( p \) cannot divide \( N \)
D. none of these


Which of the following orbitals are
degenerate?

This question has multiple correct options
\( \mathbf{A} \cdot 4 d_{x y}, 3 d_{y z}, 4 d_{y z}, 4 d_{z 2} \)
B. \( 3 d_{y z}, 4 d_{y z} \)
\( \mathbf{c} \cdot 3 d_{x y}, 3 d_{y z} \)
D. \( 4 d_{d y}, 4 d_{d z}, 4 d_{d z}^{2} \)


Phenol on treatment with \( d i l . H N O_{3} \)
gives two products \( P \) and \( Q . P \) is steam
volatile but \( Q \) is not. \( P \) and \( Q \) are,
respectively:
\( A \)
B.
\( c \)
D.


What is the name of this Acid NaClO?


Consider the charges \( \boldsymbol{q}, \boldsymbol{q} \) and \( -\boldsymbol{q} \) placed at the vertices of an equilateral triangle of each side \( l \). The sum of forces
acting on each charge is
A \( \cdot \frac{q^{2}}{4 \sqrt{2} \pi \varepsilon_{0} l^{2}} \)
в. \( \frac{-q^{2}}{4 \pi \varepsilon_{0} l^{2}} \)
c. \( \frac{q^{2}}{4 \pi \varepsilon_{0} l^{2}} \)
D. zero


Assertion: 1 mole \( O_{3}(\text { ozone })=N \)
molecule of \( O_{3}(\text { ozone })=3 N \) atoms of
\( \boldsymbol{O}(\boldsymbol{o} \boldsymbol{x} \boldsymbol{y} \boldsymbol{g} \boldsymbol{e} \boldsymbol{n})=\boldsymbol{4} \boldsymbol{8} \boldsymbol{g} \)
Reason: A mole is the amount of matter
that contains as many as objects as the number of atoms exactly in 12 g C-12 \( (N \)
Avogadro number)
A. Assertion is correct but Reason is incorrect
B. Assertion is incorrect but Reason is correct
c. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not correct explanation of Assertion


Which of the following is correct?
A. There are 78 neutrons in \( 78 P t^{192} \)
B \( \cdot_{84} P o^{214} \rightarrow_{82} P b^{210}+\beta \)
\( \mathbf{c} \cdot_{92} U^{238} \rightarrow_{90} T h^{234}+_{2} H e^{4} \)
D・ \( _{90} T h^{234} \rightarrow_{91} P a^{234}+_{2} H e^{4} \)


\( \operatorname{Let} f(x)=\cos \left(\tan ^{-1} 2 x\right) \)
\( \sin \left\{\tan ^{-1}\left(\frac{1}{2 x+1}\right)\right\} \) and
\( \boldsymbol{a}=\cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 2 x\right)\right)\right) \) and \( \boldsymbol{b}= \)
\( \cos \left(\frac{\pi}{2}+\cos ^{-1} 2 x\right) \)
The value of \( x \) for which \( f(x)=0 \) is
\( A \cdot-\frac{1}{4} \)
B. \( \frac{1}{4} \)
c. 0
D. \( \frac{1}{2} \)


Account for the following:
(i) \( P C l_{5} \) is more covalent than \( P C l_{3} \)
(ii) Iron on reaction with \( H C l \) forms
\( F e C l_{2} \) and not \( F e C l_{3} \)
(iii) The two \( O-O \) bond lengths in the
ozone molecule are equal.


(-2,-1),(-1,-4) and (-4,-1)


Write any two major reasons for the population explosion in India.


Arrange the oxides of manganese
according to increasing acidic strength.
\( \mathbf{A} \cdot M n O<M n_{3} O_{4}<M n_{2} O_{3}<M n O_{2}<M n_{2} O_{7} \)
B. \( M n_{2} O_{7}<M n O_{2}<M n_{2} O_{3}<M n_{3} O_{4} \)
\( \mathbf{c} \cdot M n O_{2}<M n_{2} O_{7}<M n_{3} O_{4}<M n_{2} O_{3}<M n O \)
D. \( M n_{3} O_{4}<M n_{2} O_{3}<M n_{2} O_{7}<M n O_{2}<M n O \)


A man alternatively tosses a coin and throws a die. The probability of getting a head on the coin before he gets 4 on the
die is
A \( \cdot \frac{6}{7} \)
в. \( \frac{2}{3} \)
\( c \cdot \frac{3}{4} \)
D.


A examination consists of 8 questions in each of which one of the 5
alternatives is the correct one. On
the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternatives with equal probability, the probability that he gets more than one correct answer is equal to five alternatives with equal probability,the probability that he gets more than one correct answer is equal to
A \( \cdot(0.8)^{8} \)
B. \( 3(0.8)^{8} \)
c. \( 1-(0.8)^{8} \)
D. \( 1-3(0.8)^{8} \)


The D.E whose solution is \( y=A \cos x+ \)
\( \sin x \) is:
A \( \cdot \frac{d y}{d x}+y \tan x=\sec x \)
в. \( \frac{d y}{d x}+y \sin x=\cos x \)
c. \( \frac{d y}{d x}+y \sec x=\tan x \)
D. \( \frac{d y}{d x}+y \cot x=\csc x \)


Total number of vertebra in man is
A. 30
B. 33
\( c \cdot 40 \)
D. 35


Name the following:
(a) A chordate animal having flame cells as excretory structures.
(b) Cortical portions projecting between the medullary pyramids in the human kidney.
(c) A loop of capillary running parallel to
the Henle's loop.


The tripeptide hormone present in most living cells is:
A . Glutathione
B. Glutamine
c. oxytocin
D. Ptyalin


\( \boldsymbol{H}_{2}+\boldsymbol{I}_{2}=2 \boldsymbol{H} \boldsymbol{I} . \) What will be the
instantaneous rate of the reaction in
terms of product?
A \( \cdot \frac{1}{2} \frac{d[H I]}{d t} \)
B. \( -\frac{1}{2} \frac{d[H I]}{d t} \)
c. \( \frac{d[H I]}{d t} \)
D. \( -\frac{d[H I]}{d t} \)


Depletion layer consists of:
A. electrons
B. protons
c. mobile ions
D. immobile ions


When in excess, a very dilute aqueous
solution of \( K I \) is added to a very dilute
aqueous solution of silver nitrate, the colloidal particles of silver iodide, associated with the Helmholtz double
layer, are
A \( . A g I: A g^{+}: N O_{3}^{-} \)
B. \( A g I: K^{+}: N O_{3}^{-} \)
c. \( A g I: N O_{3}^{-}: A g^{+} \)
D. \( A g I: I^{-}: K^{+} \)


A string fixed at its both ends vibrates
in 5 loops as shown in the figure
the total number of nodes and antinode
are respectively:
A . 5,6
B. 6,5
\( c .7 .4 \)
D. 4,7


When the speed of electron increases, its specific charge:
A. Increases
B. Decreases
c. Remains unchanged
D. Increases and then decreases


Assertion
Large number of organic compounds
are formed with long carbon-chain.
Reason
Maximum catenation occurs in carbon
atoms.
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


What is the square of the modulus of
the complex number \( 2+3 i \)


Find the power (with sign) of a concave lens of focal length \( 20 \mathrm{cm} \)
A . \( -4 D \)
в. \( -5 D \)
\( c .4 D \)
D. \( 5 D \)


A plot of magnetic flux \( (\phi) \) versus current (I) is shown in the figure, for two
inductors \( A \) and \( B \). Which of the two has
the larger value of self-inductance?


The standard enthalpies of elements in their standard(natural) states are
taken as zero. On basis of this
statement, we can say that the enthalpy of formation of a compound :
A . Is always negative
B. Is always positive
c. May be positive or negative
D. Is never negative


A solution of potassium chloride has no effect on litmus whereas, a solution of
zinc chloride turns the blue litmus red.
Give a reason.


Two positive charges \( Q \) and \( 4 Q \) are placed at points \( A \) and \( B \) respectively where \( \mathrm{B} \) is at a distance 'd' units to the
right of A. The total electric potential due to these charges in minimum at \( \mathrm{P} \) on the line through \( A \) and \( B \), What is (are) the distance(s) of P from A?
A. \( d \) \( \frac{d}{3} \) units to the right of \( A \)
B. \( \frac{d}{3} \) units to the left of
c. \( \frac{d}{5} \) units to the right of
D. d units to the left of A


Find the value of \( x \) so that the points
\( (x,-1),(2,1) \) and (4,5) are collinear.


The circuit has two oppositely connect
ideal diodes in parallel. What is the
current following in the circuit?
A \( .1 .33 A \)
в. 1.71 А
\( c .2 .00 A \)
D. \( 2.31 A \)


Give the likely structure of the polymer
obtained in each of the following
reactions. Also, tell whether these
reactions are examples of chain-
reaction or step-reaction polymers.
(i)
A. Nylon-6, step-reaction polymer
B. Nylon-6, chain-reaction polymer
C. Dacron, step- -reaction polymer
D. Glyptal, chain-reaction polymer


How does \( H_{2} O_{2} \) behave as a bleaching
agent?


Watermelon model of atom was
proposed by :
A. Rutherford
B. Thomson
\( c . \) Bohr
D. Sommerfeld


A \( 15 g \) ball is shot from a spring gun
whose spring has a force constant
\( 600 N m^{-1} . \) The spring is compressed
by \( 5 \mathrm{cm} . \) The greatest possible
horizontal range of the ball for this
compression (Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
\( \mathbf{A} \cdot 6 m \)
B. \( 8 m \)
\( \mathrm{c} .10 \mathrm{m} \)
D. 12 \( m \)


Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{x}^{100}+\boldsymbol{x}^{99}+\boldsymbol{x}^{98}+\ldots+\boldsymbol{x}^{2}+\boldsymbol{x}+\right. \)
\( \mathbf{1} \)


A man usually gets from one corner of a square lot to the opposite corner by walking along two of the sides. Approximately what percent of the distance does he save if he walks along
the diagonal?
A . \( 27 \% \)
B. \( 29 \% \)
\( c .31 \% \)
D. \( 33 \% \)
E . \( 25 \% \)


The value of
\( \frac{(0.31)^{3}-(0.21)^{3}}{0.0961+0.0651+0.0441} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 0 . \)
c. 0.2
D. 0.04


A biconvex lens is made of material of
refractive index 1.5 each of radius of
curvature of lens surface is \( 20 \mathrm{cm} \). The
focal length of lens is:
A. \( 20 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( c \cdot 25 \mathrm{cm} \)
D. 30 cm


An instrument used to measure high
temperature is
A. Pyrheliometer
B. Pyrometer
c. Technometer
D. Pyknometer


Energy released if mass of 2 amu
is converted into energy is :
\begin{tabular}{l}
A. \( 1.5 \times 10^{-10} \mathrm{J} \) \\
\hline
\end{tabular}
В. \( 3 \times 10^{-10} J \)
c. \( 1863 J \)
D. \$\$931.5 IMev\$\$


A lamp rated \( 100 W \) at \( 22 V \) is connected to the main electric supply.
What current is drawn from the supply line if the voltage is \( 220 V \)


High energy bond of ATP are present in between
A . c-c
B. C-O
c. \( c-N \)
D. O-P


A tester is used to check the conduction
of electricity through two liquids, labeled \( A \) and \( B \). It is found that the
bulb of the tester glows brightly for
liquid \( \boldsymbol{A} \) while it glows very dimly for liquid \( B \). You would conclude that:
A. liquid \( A \) is a better conductor than liquid \( B \)
B. liquid \( B \) is a better conductor than liquid \( A \)
c. both liquids are equally conducting
D. conducting properties of liquid cannot be compared in this manner


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
continuous functions, then the value of \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(f(x)+f(-x))(g(x)-g(-x)) d x \)
is equal to
\( A \)
B.
\( c \cdot 1 \)
D. none of these


Prove that \( 2.7^{n}+3.5^{n}-5 \) is divisible
by \( 24, \) for all \( n \in N \)


when and where the ball will meet the
elevator.


Dimensions of impulse are
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
\( \mathbf{B} \cdot\left[M L T^{2}\right] \)
c. \( \left[M T^{-2}\right] \)
D・ \( \left[M L^{-1} T^{-3}\right] \)


Empirical formula of compound is
\( C H_{2} O . \) If is vapour density is \( 90, \) then molecular formula of compound is:


Solve the inequation \( 8-2 x \geq x- \)
\( \mathbf{5} ; \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N} \)


A policeman on duty detects a drop of \( 10 \% \) in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is \( 330 m / s, \) the speed of the car
will be
\( \mathbf{A} \cdot 36.7 m / \)sec
в. \( 17.3 \mathrm{m} / \mathrm{sec} \)
\( \mathbf{c} .25 \mathrm{m} / \mathrm{sec} \)
D. \( 27 \mathrm{m} / \mathrm{sec} \)


Whm \( ^{-2} \) is equal to
\( A \cdot 10^{4} G \)
B . \( 10^{2} \) G
\( c \cdot 10^{-2} \mathrm{G} \)
D. \( 10^{-4} \mathrm{G} \)


The mass of object \( A \) is 5 kg,that of object B is \( 40 \mathrm{kg} \),that of object \( \mathrm{C} \) is 38 kg,and that of object D is 56 kg. Which object has the greatest inertia?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


In a triangle \( \mathrm{ABC}, \angle A=110^{\circ} \) and
\( A B=A C . \) Find \( \angle B \) and \( \angle C \)


What is respiratory quotient (RQ) ? Why RQ in anaerobic respiration is infinite?


If a charge is placed on a conductor having a pointed end, then
A. the charge gets accumulated at the points
B. the charge gets distributed around the conductor
c. the charge collects inside the conductor
D. the charge gets dissipated to the surrounding


The Van't Hoff factor of sulphur solution
is
A . i = 1
B. \( i=1 / 6 \)
c. \( i=1 / 2 \)
D. i =1/8


Before using the clinical thermometer
mercury level should be below:
\( \mathbf{A} \cdot 45^{\circ} C \)
B . \( 35^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 95^{\circ} C \)
D. \( 55^{\circ} \mathrm{C} \)


pH of a neutral solution is:
A. 7
B . >7
\( c \cdot<7 \)
D. none of these


State True or False.
According to Bronsted-Lowry theory, neutralization reaction is the formation
of a conjugate acid base pair.
A. True
B. False


Earliest settlers on barren lands or the
'farmers of nature' are
A. Diatoms
B. Lichens
c. Moss and grasses
D. Ferns


Identify the true statement(s) for
comets:

This question has multiple correct options
A. Those are messengers of disaster
B. Many comets appear after a fixed time interval
C . Occurrance of comets is a natural phenomenon
D. The tail of the comet is always directed towards the
sun


Which is not redox change?
\( \mathbf{A} \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
\( \mathbf{B} \cdot 2 H_{2}+O_{2} \rightarrow 2 H_{2} O \)
\( \mathrm{c} \cdot_{N a}+H_{2} O \rightarrow N a O H+\frac{1}{2} H_{2} \)
D. \( M n C I_{3} \rightarrow M n C I_{2}+\frac{1}{2} C I_{2} \)


Three boxes numbered I, II, III contains
the balls as follows:
\( \begin{array}{llll}\text { White } & \text { Black } & \text { Red } \\ \text { I } & 1 & 2 & 3 \\ \text { II } & 2 & 1 & 1 \\ \text { "II } & 4 & 5 & 3\end{array} \)
One box is randomly selected and a ball is drawn from it. If the ball is red, then
find the probability that it is from box II


A narrow slit \( S \) transmitting light of wavelength \( \lambda \) is placed a distance \( d \)
above a large plane mirror as shown in
fig 29.16 (a). The light coming directly
from the slit and that after reflection
interference coverage at \( \boldsymbol{P} \) on the
screen placed at a distance \( D \) from the
slit. What will be the intensity at a point just above \( O ? \) What will be \( x \) for which
first maxima occurs?


In parasitic food chain, the pyramid of numbers is
A. Upright
B. Inverted
c. Linear
D. Both A and B


Which of the following statement (s) is
/are true?
This question has multiple correct options
A. The lattice structure of diamond and graphite are different.
B. Graphite is an impure form of carbon while diamond is a pure form.
C. Graphite is harder than diamond.
D. Graphite is thermally more stable than diamond.


Which of the following statements
is/are wrong?
This question has multiple correct options
A. Zeolites are hydrated aluminosilicates which can be used as shape-selective catalysts
B. Enzymes show maximum activity when pH is either very low or very high
C. Enzymes shows increasing activity at room temperature \( \left(20^{\circ} C-25^{\circ} C\right) \)
D. Chemically, all enzymes are globular proteins


If \( r, s \) and \( t \) are prime numbers and \( p, q \)
are positive integers such that the LCM of \( p, q \) is \( r^{2} t^{4} s^{2} \) then the number of
ordered pair \( (p, q) \) is
A . 254
B. 252
c. 225
D. 224


A given quantity has both magnitude and direction. Is it necessarily be a vector? Justify.


\( 40 \mathrm{ml} \) of hydrocarbon on combustion gave \( 120 \mathrm{ml} \mathrm{CO}_{2} \) and \( 80 \mathrm{ml} \) water
vapour. The molecular formula of
hydrocarbon is:
A \( \cdot C_{2} H_{6} \)
B. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{4} \)


If \( \bar{a} \) and \( \bar{b} \) include an angle of \( 120^{\circ} \) and their magnitudes are 2 and \( \sqrt{3} \) then \( \bar{a} . \bar{b} \) is
\( A \cdot 3 \)
B. \( -\sqrt{3} \)
\( c \cdot \sqrt{3} \)
D. - 3


A small coin is resting on the bottom of
a beaker filled with a liquid. A ray of
light from the coin travels upto the
surface of the liquid and moves along
its surface (see figure)How fast is the
light travelling in the liquid?
\( \mathbf{A} \cdot 1.2 \times 10^{8} \mathrm{m} / \mathrm{s} \)
B . \( 1.8 \times 10^{8} \mathrm{m} / \mathrm{s} \)
C \( .2 .4 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 3.0 \times 10^{8} \mathrm{m} / \mathrm{s} \)


Which of the following combines with
\( F e(I I) \) ions to form a brown complex?
A \( \cdot N_{2} O \)
B. \( N O \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( N O_{2} \)


Corrosion can be prevented by using


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1}\left(\log _{2}\left(\frac{x^{2}}{2}\right)\right) \) is
A. [-2,-1)\( \cup(1,2] \)
B. (-2,-1]\( \cup[1,2] \)
c. [-2,-1]\( \cup[1,2] \)
D. (-2,-1)\( \cup(1,2) \)


One astronomical unit is the mean
distance between the centre of the
Earth and centre of the
¡) Moon
ii) Sun
iii) Mars


Horizontal force \( \boldsymbol{F} \) to keep the cylinder
in static equilibrium, if it is placed on a
smooth horizontal plane, is
\( A \cdot 7.2 N \)
B. \( 10 N \)
c. \( 15.5 N \)
D. \( 20.4 N \)


State true or false:
In quadrilateral \( A B C D, \) its diagonals \( A C \) and \( B D \) intersect at point \( O, \) such
that \( \frac{\boldsymbol{O C}}{\boldsymbol{O A}}=\frac{\boldsymbol{O D}}{\boldsymbol{O B}}=\frac{1}{3}, \) then
\( \triangle \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \sim \triangle \boldsymbol{O C D} \)
A. True
B. False


sheets having charges \( Q \) and \( 2 Q \) are
placed parallel to each other as shown in Fig. The charge distribution on the
four faces of the two plates is also
shown. The electric field intensities at
three points \( 1,2, \) and 3 are
\( \vec{E}_{1}, \vec{E}_{2}, \) and \( \vec{E}_{3}, \) respectively. Then the magnitudes of \( \overrightarrow{\boldsymbol{E}}_{1}, \overrightarrow{\boldsymbol{E}}_{3} \) and \( \overrightarrow{\boldsymbol{E}}_{2} \) are
respectively (surface area of plates):
\( A \)
\( 0, \frac{Q}{\varepsilon_{0} S}, 0 \)
B. \( \frac{5 Q}{6 \varepsilon_{0} S}, \frac{Q}{2 \varepsilon_{0} S}, 0 \)
c. \( \frac{5 Q}{6 \varepsilon_{0} S}, \frac{Q}{\varepsilon_{0} S}, \frac{Q}{3 \varepsilon_{0} S} \)
D.
\( 0, \frac{Q}{2 \varepsilon_{0} S}, 0 \)


The temperature at which the catalytic activity of the catalyst is maximum, is called:
A . critical temperature
B. room temperature
c. absolute temperature
D. optimum temperature


Let \( z_{1} \) and \( z_{2} \) are two complex numbers
such that \( (1-i) z_{1}=2 z_{2} \) and \( \arg \left(z_{1} z_{2}\right)=\frac{\pi}{2} \) then \( \arg \left(z_{2}\right) \) is equals
to:
A \( \cdot \frac{3 \pi}{8} \)
B. \( \frac{\pi}{8} \)
c. \( \frac{5 \pi}{8} \)
D. \( \frac{-7 \pi}{8} \)


Which of the following molecules does not posses a permanent electric dipole moment?
This question has multiple correct options
A \( . H_{2} \)
в. \( S O_{2} \)
\( c \cdot S O_{3} \)
D. \( C S_{2} \)


The speed of a wave of time period \( T \)
and propagation constant \( \boldsymbol{K} \) is
\( ^{\text {A }} \cdot \frac{2 \pi}{T K} \)
в. \( \frac{T K}{2 \pi} \)
c. \( \frac{1}{T K} \)
D. \( \frac{T}{K} \)


Where are villi? What is their location
and function?


\begin{tabular}{c|ccc}
\( \mathbf{1} \) & \( \mathbf{s i n Q} \) & \( \mathbf{1} \) \\
\( -\mathbf{s i n Q} \) & \( \mathbf{1} \) & \( \mathbf{s i n Q} \) \\
\( \mathbf{- 1} \) & \( -\mathbf{s i n Q} \) & \( \mathbf{1} \)
\end{tabular}


If \( \triangle E \) is the heat of reaction for
\( C_{2} H_{3} O H_{(1)}+3 O_{2(g)} \rightarrow 2 C O_{2(s)}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \mathbf{0}_{(1)} \) at constant volume, the \( \triangle \boldsymbol{H} \)
Heat of reaction at constant pressure) at constant temperature is:
A \( . \triangle H=\triangle E+2 R T \)
B. \( \triangle H=\triangle E-2 R T \)
c. \( \triangle H=\Delta E+R T \)
D. \( \triangle H=\triangle E-R T \)


Prove that:
\( \tan ^{-1}\left(\frac{6 x-8 x^{3}}{1-12 x^{2}}\right) \)
\( \tan ^{-1}\left(\frac{4 x}{1-4 x^{2}}\right)=\tan ^{-1} 2 x ;|2 x|< \)
\( \frac{1}{\sqrt{3}} \)


If phytoplanktons are destroyed in the sea, then
A. No effect will be seen
B. Primary consumers will grow luxuriantly.
c. It will affect the food chain.
D. Algae will get more space to grow


Who proposed the 'signal hypothesis' meant for the biosynthesis of secretory
type of proteins?
A. Baltimore
B. Camillio Golgi
c. Blobel and Sabatini
D. Sheeler and Bianchi


What is peptization? Explain.


An electromagnetic wave of frequency
\( \mathbf{v}=\mathbf{3 . 0} \mathrm{MHz} \) passes from vacuum into a
dielectric medium with permittivity
\( \boldsymbol{\epsilon}=\underline{4} .0 . \) Then:
A. wavelength is doubled and frequency remains unchanged
B. wavelength is doubled and frequency becomes half
C. wavelength is halved and frequency remains unchanged
D. wavelength and frequency both remain unchanged


For any three sets, \( A B \) and \( C, B \backslash(A \cup \)
\( C) \) is:
\( \mathbf{A} \cdot(A \backslash B) \cap(A \backslash C) \)
B . \( (B \backslash A) \cap(B \backslash C) \)
c. \( (B \backslash A) \cap(A \backslash C) \)
D. \( (A \backslash B) \cap(B \backslash C) \)


The relation 'is a subset of in a set of
sets is not an equivalence relation.
Prove.


\( 13.8 g \) of \( N_{2} O_{4} \) was placed in a \( 1 L \)
reaction vessel at \( 400 \mathrm{K} \) and allowed to
attain equilibrium \( N_{2} O_{4}(g) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
The total pressure at equilibrium was found to be 9.15 Bar. Calculate \( K_{c}, K_{p} \) and partial pressure at equilibrium.


The living differentiated cell which have lost capacity to divide can regain capacity of division under certain conditions. This phenomenon is called
A. De-differentiation
B. Differentiation
c. Re-differentiation
D. Regeneration


Each resistance shown in figure is \( 2 \Omega \)
The equivalent resistance between \( \boldsymbol{A} \)
and \( B \) is
\( A \cdot 2 S \)
в. 4 ?
\( c \cdot 85 \)
0.1


Four wires made of same materials are
stretched by the same load. Their dimensions are given below. The one which elongates more is?
A. Wire of length \( 1 \mathrm{m} \) and diameter \( 1 \mathrm{mm} \)
B. Length 2m, diameter 2 mm
c. Length 3m, diameter 3 mm
D. Length 0.5m, diameter 0.5mm


The equation of a plane progressive wave is \( \boldsymbol{y}=\mathbf{0 . 0 2} \sin 8 \boldsymbol{\pi}\left[\boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2 0}}\right] . \) When it
is reflected at a rarer medium, its
amplitude becomes \( 75 \% \) of its previous value. The equation of the reflected wave is
A \( \cdot y=0.02 \sin 8 \pi\left[t-\frac{x}{20}\right. \)
B・ \( y=0.02 \sin 8 \pi\left[t+\frac{x}{20}\right. \)
c. \( y=0.15 \sin 8 \pi\left[t+\frac{x}{20}\right. \)
D. \( y=0.15 \sin 8 \pi\left[t-\frac{x}{20}\right] \)


Choose the correct statement.
A. 'P' waves are slower than 'S' waves.
B. Both'P' and 'S' waves have same speed.
C. 'S' waves are slower than'P' waves.
D. None of the above.


Solve: \( 2 x y d x+\left(x^{2}+2 y^{2}\right) d y=0 \)


\( K_{1} \) and \( K_{2} \) are the velocity constants of the forward and backward reactions.
The equilibrium constant K of the reaction is:
A. \( k_{1} \times k_{2} \)
в. \( k_{1}-k_{2} \)
c. \( \frac{k_{1}}{k_{2}} \)
D. \( \frac{k_{2}}{k_{1}} \)


A ring shaped tube contains two ideal
gases with equal masses and molar
masses \( M_{1}=32 \) and \( M_{2}=28 . \) The
gases are separated by one fixed partition \( P \) and another movable
stopper \( S \) which can move freely
without friction inside the ring. The
angle \( \alpha \) is
\( \mathbf{A} \cdot 182^{\circ} \)
B \( .170^{\circ} \)
\( c \cdot 192^{\circ} \)
D. \( 180^{\circ} \)


The center of pressure of surface subjected to fluid pressure is the point
A. on the surface at which resultant pressure acts
B. on the surface at which gravitational force acts
c. equal to volume of liquid displaced
D. none


An element in period-3 which has zero electron affinity is:
A. neon
B. sulphur
c. sodium
D. argon


A mercury thermometer is transferred from melting ice to hot liquid.The mercury rises to \( 9 / 10 \) distance between
two fixed points. Find the temperature in liquid in Fahrenheit scale
A . 198
в. 194
\( c .190 \)
D. 188


Q Type your question.
\( n=v \) an with its centre al origin.
Current \( I=1 A \) is lead to the sphere in
one of the wires lying (on y-axis) and in the other wire (on x-axis) it is lead away
from the sphere. A uniform and
constant external magnetic field
exists in positive z-direction and has
magnitude \( B_{o}=2 T . \) Then find the
magnitude of magnetic force
(in newtons) on the solid sphere due to
external magnetic field.
\( A \)
B. 4
\( c .5 \)
\( D \)


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{B}-\boldsymbol{D} \)


When \( F e C r_{2} O_{4} \) (chromite) is reduced
with \( A l \)
A \( \cdot C r \) and \( F e_{2} O_{3}, \) are formed
B. Fe and \( C r_{2} O_{3} \) are formed
c. \( F e \) and \( C r \) (ferrochrome) are formed
D. \( F e C r O_{4} \). is formed


If \( \frac{\sin x}{\sin y}=\frac{1}{2}, \frac{\cos x}{\cos y}=\frac{3}{2}, \) where \( x, y \in \)
\( \left(0, \frac{\pi}{2}\right), \) then the value of \( \tan (x+y) \) is
equal to:
A \( \cdot \sqrt{13} \)
B. \( \sqrt{14} \)
c. \( \sqrt{17} \)
D. \( \sqrt{15} \)


Splitting of spectral lines in the presence of electric field is known as:
A. Stark effect
B. Zeeman's effect
c. compton effect
D. Moseley's effect


Identify the odd one out from the
following.
A. Diamond
B. Buckminister fullerene
c. Lampblack
D. Graphite


Energy stored in a stretched spring is gravitational potential energy.
A. True
B. False
c. Ambiguous
D. Data insufficient


The chemical effect produced by an electric current depends on:
A. the nature of electrode
B. the tester
c. the conducting solution
D. none of the above


The highest bond length is \( \boldsymbol{C}-\boldsymbol{H}, \boldsymbol{C}- \)
\( \boldsymbol{O}, \boldsymbol{C}-\boldsymbol{C} \) and \( \boldsymbol{C}=\boldsymbol{C} \) is:
A. \( C-C \)
B. \( C-O \)
c. \( C-H \)
D. \( C=C \)


An athlete is given 180 g of glucose \( \left(C_{6} H_{12} O_{6}\right) \) He utilises \( 50 \% \) of the energy due to internal combustion in
the body.In order to avoid storage of energy in the body.Calculate the mass of water he would need to perspire.Given enthalpy of combustion of glucose is
\( -2800 K J m o l^{-1} \)


The number of six-digit numbers which have sum of their digits as an odd integer, is
A . 45000
B. 450000
c. 97000
D. 970000


Nigrum of one of the species of genus
A. Mangifera
B. Solanum
c. Triricum
D. Pisum


The reason of current flow in \( p-n \)
junction in forward bias is:
A. Drifting of charge carriers
B. Drifting of minority charge carriers
c. Diffussion of charge carriers
D. All of the above


In which of the following phases of Moon we can see the entire half of the moon
surface that is lit?
A. Full Moon
B. New Moon
c. waning Gibbous
D. Last Quarter


Which one of the following compound
contains both ionic and covalent bond?
A \( \cdot \operatorname{si} 0_{2} \)
в. \( B a F_{2} \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( C l_{2} O \)


If 5,7,6 are the sums of the \( x, y \)
intercepts; \( \boldsymbol{y}, \boldsymbol{z} \) intercepts, \( \boldsymbol{z}, \boldsymbol{x} \)
intercepts respectively of a plane then the perpendicular distance from the origin to that plane is
A \( \cdot \frac{144}{61} \)
в. \( \frac{12}{\sqrt{61}} \)
c. \( \frac{\sqrt{61}}{12} \)
D. \( \frac{61}{144} \)


Solve :
\( \int \frac{x}{\sqrt{x+4}} d x \)


Flour, salt, sugar, eggs and baking powder are ingradients for baking a cake, when you mix these ingradients, you get batter. Is batter a mixture or a compound? The batter is put into an oven to bake into a cake. Is the cake a
mixture or a compound? Explain your
answers.


What made the study of cells possible?
A. Discovery of microorganism
B. Division of offsprings
c. Evolution of generation
D. Invention of microscope


If \( \overrightarrow{\boldsymbol{E}}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \widehat{\mathbf{j}}-\mathbf{5} \widehat{k} \) calculate the
electric flux through the surface of area
50 units in \( z-x \) plane.


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


If \( \alpha \) and \( \beta \) differ by an odd multiply on \( \pi / 2 \) prove that the product of the two matrices given below is a null matrix


\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) ; \quad \Delta H=56.9 k J \)
Which of the following will increase the
yield of \( N O_{2} \) of the equilibrium
reaction?
A . Adding \( N_{2} O_{4} \)
B. Heating the reaction container
c. cooling the reaction container
D. Adding a catalyst


Equations with linear expressions in one variable only are called in
one variable.


The ionic strength of solution
containing \( 0.3 \mathrm{N} A l_{2}\left(S O_{4}\right)_{3} \) is
A. 0.75
B . 1.85
c. 3.
D. 1.50


Form the differential equation of the
family of curves represented by \( y^{2}= \)
\( (x-c)^{3} \)


If \( \boldsymbol{A}=\frac{1}{1} \cot ^{-1}\left(\frac{1}{1}\right)+\frac{1}{2} \cot ^{-1}\left(\frac{1}{2}\right)+ \)
\( \frac{1}{3} \cot ^{-1}\left(\frac{1}{3}\right) \) and \( B=1 \cot ^{-1} 1+ \)
\( 2 \cot ^{-1} 2+3 \cot ^{-1} 3 \operatorname{then}|B-A| \) is
equal to \( \frac{a \pi}{b}+\frac{c}{d} \) cot \( ^{-1} 3 \) where
\( a, b, c, d \in N \) and are in their lowest
form then \( a+b+c+d \) equal to


\( \boldsymbol{A B}\|\boldsymbol{C D}\| \boldsymbol{E F} \) and \( \boldsymbol{G H} \| \boldsymbol{D I} \)
\( \angle D I H=95^{\circ} \) then the measure of
\( \angle G C D \) is equal to
\( A \cdot 95 \)
B. \( 105^{\circ} \)
\( c \cdot 90 \)
\( D .85 \)


Find the mean using step deviation
method.
A . 14
B. 13
c. 12
D. 10


A condition of extreme mental and
usually motor excitement, hallucinations and marked
rapid confusion are the symptoms of
A. Wernicke's disease
B. Delirium tremens
c. Jolliffe's encephalopathy
D. Korsakoff's syndrome


For the reaction at \( 298 \mathrm{K}, 2 \mathrm{A}+\mathrm{B} \rightarrow C \)
\( \triangle H=400 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( \triangle \mathrm{S}=0.02 \mathrm{KJ} \)
\( \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{d}^{-1} \)
At what temperature will the reaction
become spontaneous considering \( \triangle \mathrm{H} \) and \( \triangle S \) to be constant over the
temperature range?


Consider the following four statements
(i) - (iv) and select the correct option.
(i) Fish heart contains only oxygenated
blood.
(ii)Closure of A-V valves produces the second heart sound.
(iii) The vascular connection between
the digestive tract and kidney is called hepatic portal system.
(iv) Purkinje fibres are nerve fibres
present in the heart wall.
A. i - F, ii - F, iii - T, iv - F
B. i- F, ii-F, iii - F, iv - T
c. i - \( T, \) ii - \( T, \) iii - \( F \), iv - T
D. i- T, ii - F, iii - T, iv - F


Which of the following doesn't use acetaldehyde as a starting material in its preparation?
A. Ethyl acetate
B. Ethanoic acid
c. Methanoic acid
D. Drugs


\( 5 \mathrm{kg} \) of water at \( 80^{\circ} \mathrm{C} \) is taken in a
bucket of negligible heat capacity, \( 15 \mathrm{kg} \)
of water at \( 20^{\circ} C \) is added to it. What is
the temperature of the mixture?
\( \mathbf{A} \cdot 45^{\circ} C \)
в. \( 65^{\circ} \) С
\( \mathbf{c} \cdot 85^{\circ} C \)
D. \( 35^{\circ} \mathrm{C} \)


If the scalar and vector products of two vector are \( 4 \sqrt{3} \) and 144 respectively, what is the angle between the two
vectors?
A \( \cdot \tan ^{-1}(12 \sqrt{3}) \)
B \( \cdot \tan ^{-1}\left(\frac{38}{\sqrt{3}}\right) \)
c. \( \tan ^{-1}\left(\frac{\sqrt{3}}{12}\right) \)
D. \( \tan ^{-1}(36) \)


Predict the structures of \( \boldsymbol{P H}_{3} \boldsymbol{C l}_{2} \)
A. Trigonal bipyramidal with apical H atoms
C. Trigonal bipyramidal with apical Cl atoms
D. Square pyramidal with apical Cl atom


Q Type your question
\( \boldsymbol{L} \)
(A) Polystyrene, Bakelite,
Teflon, PVC
(B) Polythene, Polystyrene,
Bakelite, PVC
(C) PVC, \( \quad \) Polythene
Polystyrene, Bakelite
(D) PVC, \( \quad \) Teflon
Melamine, Bakelite
Choose your answer from \( A, B, C \) and \( D \)
and enter accordingly.


The two curves \( y=x^{2}-1 \) and \( y= \)
\( 8 x-x^{2}-9 \) at the point (2,3) have
common
A. tangent as \( 4 x-y-5=0 \)
B. tangent as \( x+4 y-14=0 \)
c. normal as \( 4 x+y=11 \)
D. normal as \( x-4 y=10 \)


If total surface area of a cube is
\( 150 \mathrm{cm}^{2}, \) find the edge.


\( \left|\begin{array}{ccc}\mathbf{8} & \mathbf{- 5} & \mathbf{1} \\ \mathbf{5} & \boldsymbol{x} & \mathbf{3} \\ \mathbf{6} & \mathbf{3} & \mathbf{1}\end{array}\right|=\mathbf{2} \) then what is the
value of \( x \) ?
A . 44
B. 55
c. 61
D. 84


If \( \boldsymbol{x}=\mathbf{2} \) and \( \boldsymbol{y}=\mathbf{3}, \) then find the value of \( \left[\frac{1}{x^{x}}+\frac{1}{y^{y}}\right] \)
A \( \cdot \frac{-31}{108} \)
в. \( \frac{31}{108} \)
c. \( \frac{125}{171} \)
D. \( \frac{153}{222} \)


Evaluate \( \int \frac{d x}{\left(a^{2}+x^{2}\right)^{3 / 2}} \)
\( \boldsymbol{I}=\frac{\boldsymbol{x}}{\boldsymbol{a}^{2}\left(\boldsymbol{x}^{2}+\boldsymbol{a}^{2}\right)^{\boldsymbol{K}}}+\boldsymbol{c} \)
What is K?


Evaluate :
\( \sin \left(90^{\circ}-A\right) \sin A-\cos \left(90^{\circ}-\right. \)
\( A) \cos A \)


A square loop of side \( 10 \mathrm{cm} \) and resistance \( 0.5 \Omega \) is placed vertically in the east-west plane. A uniform
magnetic field of \( 0.10 \mathrm{T} \) is set up across the plane in the north-east direction. The magnetic field is decreased to zero
in 0.70 s at a steady rate. The magnitudes of induced emf and current during this time-interval is then
\( A \cdot 1 \mathrm{mV}, 2 \mathrm{mA} \)
B. \( 1 \mathrm{mV}, 1 \mathrm{ma} \)
c. \( 2 \mathrm{mv}, 2 \mathrm{mA} \)
D. \( 2 \mathrm{mV}, 1 \mathrm{mA} \)


Solubility of the alkaline earth's metal sulphates in water decreases in the
sequence:
A. \( S r>C a>M g>B a \)
в. \( B a>M g>S r>C a \)
c. \( M g>C a>S r>B a \)