For preparing a buffer solution of \( \mathrm{pH}= \) 7.0, which buffer system you will
choose:
A \( \cdot H_{2} P O_{4}, H_{2} P O_{4}^{-} \)
B . \( H_{2} P O_{4}^{-}, H P O_{4}^{2-} \)
\( \mathbf{c} \cdot H P O_{4}^{2-}, P O_{4}^{3} \)
D. \( H_{3} P O_{4}, P O_{4}^{3-} \)


A man with blood group AB' marries a woman with \( 0^{\prime} \) blood group. In this
situation
A. The blood groups of their children will be the same as that of the mother
B. The blood group of the children differs from both the
parents
C. While \( 50 \% \) of children will have father's blood group, the remaining will have mother's blood group
D. None of the above


If for a reaction \( k_{c}=1 \) then \( \Delta G^{\circ} \)
\( = \)
A . 1.987
B. 4.184
\( c \cdot 0 \)
D.


Name the region beyond the red end of
the spectrum.
A. Ultra red
B. infra red
c. dark red
D. light red


Solve:
\( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3} \)


A graph drawn using vertical bars is called
A. Bar graph
B. Line graph
c. Pictograph
D. Pie graph


\( \frac{2}{5} \) of total students in a class have opted
Maths.Find the percentage of students
opting Maths
A \( \cdot \frac{2}{5} \times 100 \)
В. \( \frac{5}{2} \times 100 \)
\( \mathbf{c} \cdot \frac{2}{5} \times \frac{1}{100} \)
D. \( \frac{5}{2} \times \frac{1}{100} \)


If \( \int \frac{d x}{x^{2}+a x+1}=f(g(x))+c, \) then
This question has multiple correct options
A \( \cdot f(x) \) is inverse trigonometric function for \( |a|>2 \)
B . \( f(x) \) is logarithmic function for \( |a|<2 \)
C . \( g(x) \) is quadratic function for \( |a|>2 \)
D \( \cdot f(x) \) is logarithmic function for \( |a|>2 \)


In a clockwise system:
\( \mathbf{A} \cdot \hat{k} \times \hat{j}=\hat{i} \)
\( \mathbf{B} \cdot \hat{i} \cdot \hat{i}=0 \)
c. \( \hat{j} \times \hat{j}=\hat{i} \)
D. \( \hat{k} \cdot \hat{j}=1 \)


Which of the following vertebrates were
the first to evolve a three chambered
heart for proper distribution of oxygen
in the body?
A. Fishes
B. Reptiles
c. Amphibians
D. Birds
E. Mammals


At a place, the value of 'g' is less by \( 1 \% \) than its value on the surface of the Earth (Radius of Earth, \( \boldsymbol{R}=\mathbf{6 4 0 0 k m} \) ).
The place is:
A. \( 64 \mathrm{km} \) below the surface of the earth
B. \( 64 \mathrm{km} \) above the surface of the earth
c. \( 30 \mathrm{km} \) above the surface of the earth
D. 32 km below the surface of the earth


The Sl unit of inductance, the henry, can
be written as :
This question has multiple correct options
A. weber / ampere
B. volt second / ampere
C . joule / ampere \( ^{2} \)
D. ohm second


The mole fraction of water in \( 98 \% \) (w/w)
\( H_{2} S O_{4} \) solution is :
A . \( 0 . \)
B. 0.9
\( c \cdot 0.8 \)
D. 0.02


Assertion
Peak value of current in \( \boldsymbol{A} \boldsymbol{C} \) through a
resistance of \( 10 \Omega \) is \( 2 A \). Then power
consumed by the resistance should be \( \mathbf{2 0} \boldsymbol{W} \)
Reason
Power in \( \boldsymbol{A C} \) is \( \boldsymbol{P}=\boldsymbol{I}_{r m s}^{2} \boldsymbol{R} \)
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


Fill in the blanks.
Rhombic sulphur is
allotropic form of sulphur.


When there is no external torque acting on a body moving in an elliptical path, which of the following quantities remains constant?
A. Kinetic energy
B. potential energy
c. Linear momentum
D. Angular momentum


The area of the curved surface of a
sphere is \( 5544 m^{2} \). Find the radius of
the sphere
A. 12 m
в. \( 20 \mathrm{m} \)
\( c .22 \mathrm{m} \)
D. \( 21 \mathrm{m} \)


The vapour pressure two pure liquids, \( A \) and \( \mathrm{B} \) that form an ideal solution are
300 and 800 torr respectively, at
temperature T.A mixture of the vapour of \( A \) and \( B \) for which the mole fraction of
\( A \) is 0.25 is slowly compressed at temperature T. Calculate
(a) the
composition of the first drop of the
condensate.
Upto two decimal places and multilply the answer by 100


Degree of the polynomial \( \left(x^{3}-2\right)\left(x^{2}+\right. \)
11) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 5
\( c .3 \)
D.


Which of the following metal is
sometimes found native in nature?
A. Aluminium
B. Copper
c. sodium
D. Magnesium


What are the electronic configuration of
\( N a^{+} \) and \( C l^{-} \) ions?
\( \mathbf{A} \cdot N a^{+}=2,8,2 \) and \( C l^{-}=2,8,7 \)
B. \( N a^{+}=2,8 \) and \( C l^{-}=2,8,8 \)
\( \mathbf{C} \cdot N a^{+}=2,8,2 \) and \( C l^{-}=2,8,6 \)
D. \( N a^{+}=2,8 \) and \( C l^{-}=2,8,7 \)


Find time period of \( \mathrm{SHM}=? \)


A particle of mass \( 12 \mathrm{kg} \) is acted upon
by a force \( \boldsymbol{f}=\left(\mathbf{1 0 0}-\mathbf{2 x}^{\mathbf{2}}\right) \) when \( \boldsymbol{f} \) is in
newton and \( x \) is in metre. Calculate the
wrok done by this force in moving the particle \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=-\mathbf{1 0 m} . \) What will
be the speed at \( x=10 m \) if it starts
from rest.


A jet of water with area of cross-section
\( 3 c m^{2} \) strikes a wall at an angle \( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)
to the normal and be rebounds
elastically from the wall with the same speed. If the speed of water in the jet is \( 12 \mathrm{m} / \mathrm{s}, \) then the force acting on the wall
is
A . \( 4.31 N \)
В. \( 4.32 \times 10^{-2} N \)
c. \( 4.32 \times 10^{-3} N \)
D. 43.2N


The perimeter of a rhombus is \( 46 \mathrm{cm} . \) If
the height of the rhombus is \( 8 \mathrm{cm} \); find
its area.


A coil of cross-sectional area \( \boldsymbol{A} \) having
\( \boldsymbol{n} \) turns is placed in a uniform magnetic
field \( B \). When it is rotated with an
angular velocity \( \omega, \) the maximum e.m.f.
induced in the coil will be
\( \mathbf{A} \cdot n B A \omega \)
В \( \cdot \frac{3}{2} n B A \omega \)
\( c .3 n B A \omega \)
D. \( \frac{1}{2} n B A \)


The equation for the solubility product
constant of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4} \) is:
A \( \cdot K_{s p}=\left[A g^{2+}\right] \cdot\left[C r O^{2-}\right] \)
B . \( K_{s p}=\left[A g^{+}\right]^{2} \cdot\left[C r^{6+}\right] \cdot\left[O_{4}^{8-}\right] \)
C \( \cdot K_{s p}=\left[A g^{+}\right] \cdot\left[C r^{6+}\right] \cdot\left[O_{4}^{8-}\right. \)
D. \( K_{s p}=\left[A g^{+}\right]^{2} \cdot\left[C r O_{4}^{2-}\right] \)


What are the characteristic properties of fuse wire?


A blackbox (BB) which may contain a
combination of electrical circuit
elements (resistor capacitor or
inductor) is connected with other
external circuit elements as shown
below in the figure (a).After the switch(s) is closed at time \( t=0, \) the
current (I) as a function of time (t) is
shown in the figure (b).
From this we can infer that the blackbox
contains
A. A resistor and a capacitor in series.
B. A resistor and a capacitor in parallel.
c. A resistor and an inductor in series
D. A resistor and an inductorin parallel.


A cylindrical pencil of diameter \( 1.2 \mathrm{cm} \) has one of its ends sharped into a
conical shape of height \( 1.4 \mathrm{cm} . \) The volume of the material removed is (in
\( \mathbf{A} \cdot 4 \cdot 224 \)
B. 1.056
c. 10.56
D. 42.24


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{4}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{5}\} \) and \( \boldsymbol{C}= \)
\( \{2,5\}, \) then \( (A-B) \times(B-C)= \)
A \( \cdot\{(1,2),(1,5),(2,5)\} \)
В \( \cdot\{\{1,4\}\} \)
\( \mathbf{c} \cdot(1,4) \)
D・ \{(1,2)\}


Why \( B i^{3+} \) more stable than \( B i^{+5} ? \)
A. Due to inert pair effect
B. Due to inert gas electronic configuration
c. Due to half filled configuration
D. Due to lanthanide Contraction


\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{2} \\ \mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}-\mathbf{1} & \mathbf{3} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}-\mathbf{3} \\ \boldsymbol{x}^{\mathbf{2}}+\mathbf{2} \boldsymbol{x}+\mathbf{3} & \mathbf{2} \boldsymbol{x}-\mathbf{1} & \mathbf{2} \boldsymbol{x}-\mathbf{1}\end{array}\right|= \)
\( A x-12, \) then the value of \( A \) is
\( A \cdot 12 \)
в. 24
\( c .-12 \)
\( D .-24 \)


Ecesis is
A. Establishment of a plant in a new place
B. A condition of equilibrium
C . Climax
D. Invasion of a number of plants


Select the correct statement(s).
This question has multiple correct options
A. When the lead-silver alloy is rich in silver, lead is removed by the cupellation process.
B. When the lead-silver alloy is rich in lead, silver is removed by Parke's or Pattinson's process
C. Zinc forms an alloy with lead from which lead is separated.
D. zinc forms an alloy with silver from which zinc is separated by distillation.


Water is flowing steadily through a horizontal tube of non-uniform cross-
section.If the pressure of water is \( 4 \times \) \( 10^{4} N / m m^{2} \) at a point when cross
section is \( 0.02 m^{2} \) velocity of flow is
\( 2 \mathrm{m} / \mathrm{s} \) what is pressure at a point where \( \operatorname{cross} \) section reduces to \( 0.01 m^{2} \)
A \( \cdot 1.4 \times 10^{4} N m^{2} \)
B. \( 3.4 \times 10^{4} N m^{2} \)
c. \( 2.4 \times 10^{-4} N m^{2} \)
D. none of these


In LED visible light is produced by
A. Gallium phosphide
B. Gallium arsenide
c. Germanium phosphide
D. silicon phosphide


The reference electrode is made from
which of the following?
A. \( Z n C l_{2} \)
в. \( C u S O_{4} \)
c. \( H g_{2} C l_{2} \)
D. \( H g C l_{2} \)


Find the measure of each angle of a parallelogram, one its angle is 30 less than twice the smaller angle.


From the given electrolytes, indicate which one will bring about the coagulation of a gold sol quickest and in the least of molar concentration?
A \( . \) NaCl
B . \( M g S O_{4} \)
\( ^{\mathrm{c}} \cdot_{A l_{2}}\left(S O_{4}\right)_{3} \)
D. \( K_{4}\left[F e(C N)_{6}\right] \)


The angles \( A, B, C, D \) in the
parallelogram ABCD are
\( \mathbf{A} \cdot 90^{\circ}, 90^{\circ}, 90^{\circ}, 90^{\circ} \)
В \( \cdot 90^{\circ}, 45^{\circ}, 30^{\circ}, 15^{\circ} \)
c. \( 30^{\circ}, 60^{\circ}, 20^{\circ}, 40^{\circ} \)
D. \( 90^{\circ}, 45^{\circ}, 15^{\circ}, 20^{\circ} \)


\( \mathbf{2} \boldsymbol{H}+\boldsymbol{C u O} \rightarrow \boldsymbol{X}+\boldsymbol{Y} \)
The compound \( X \) and \( Y \) are:
A. \( H_{2} O, C u \)
в. \( H_{2}, \) Си \( O \)
\( c . \) both \( A \) and \( B \)
D. none of the above


A tunnel is dug along a diameter of the
earth. If \( M_{e} \) and \( R_{e} \) are the mass and
radius, respectively, of the earth, then
the force on a particle of mass \( m \) placed in the tunnel at a distance \( r \) from the
centre is :
\( ^{\mathbf{A}} \cdot \frac{G M_{e} m}{R_{e}^{3}} r \)
в. \( \frac{G M_{e} m}{R_{s}^{3} r} \)
c. \( \frac{G M_{e} m R_{e}^{3}}{r} \)
\( ^{\mathrm{D}} \cdot \frac{G M_{e} m}{R^{2}} \)


The equation of a standing wave produced on a string fixed at both ends is
\( \boldsymbol{y}=\mathbf{0 . 4} \sin [\mathbf{0 . 3 1 4 x}] \cos [\mathbf{6 0 0} \boldsymbol{\pi} \boldsymbol{t}] \) where \( \boldsymbol{x} \)
and \( y \) are in \( c m \) and \( t \) in seconds. The
smallest possible length of the string is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


Assertion
If \( a>0 \) and \( b^{2}-4 a c<0, \) then the value of the integral \( \int \frac{d x}{a x^{2}+b x+c} \) will be of the type \( \mu \tan ^{-1} \frac{x+A}{B}+C \)
where \( A, B, C, \mu \) are constants.
Reason
If \( a>0, b^{2}-4 a c<0, \) then \( a x^{2}+b x+ \)
\( C \) can be written as sum of two squares.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A dip of needle shows a dip of \( \delta \) when placed in magnetic meridian. Now, the vertical plane in which the needle
moves is rotated by an angle \( \alpha\left(<90^{0}\right) \)
from the place of the magnetic meridian. With what angle the needle
will dip
\( A \cdot<\delta \)
B. \( >\delta \)
\( c .=\delta \)
D. cant be determined


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


Which of the following is true regarding
an \( N e \) atom with a mass number of 20
and an \( O^{2-} \) ion with a mass number of
\( 16 ? \)
A. They contain the same number of protons.
B. They contain the same number of neutrons.
C. They contain the same number of protons plus neutrons.
D. They are isoelectronic.


What is the minimum interior angle in
degrees possible for a regular polygon?
A . 45
B. 55
c. 60
D. 65


Define functional group. Write any four organic functional groups with their formula?


In the brown ring complex, the oxidation state of iron is:


Total number of stereo isomers of
\( \left[\boldsymbol{C o}(\boldsymbol{a} \boldsymbol{c a c})_{2} \boldsymbol{B r} \boldsymbol{C l}\right]^{-} \) are:
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
D.


a concave mirror is shown by \( \boldsymbol{P} \boldsymbol{Q} \) while
directions in which the ray would travel
after reflection is shown by four rays
marked 1,2,3 and 4

Which of the four rays correctly shows
the direction of reflected ray?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


The reactivities of methanol (I), \( 1- \)
propanol (II), 2 - butanol (III) and 2 methyl-2- propanol (IV) towards sodium
metal follow the order:
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. ।>IV> || > ||
D. IV > || > || > |


The probability that a person will get an electric contract is \( \frac{2}{5} \) and the probability that he will not get plumbing contract is \( \frac{4}{7} . \) If the probability of getting at least one contract is \( \frac{2}{3}, \) what is the probability that he will get both?


\( \int_{0}^{16} \frac{d x}{\sqrt{x+9}-\sqrt{x}}= \)
A . 10
B. 12
\( c \cdot 14 \)
D. 16


A magnetising field of 1500 A \( m^{-1} \)
produces flux of \( 2.4 \times 10^{-5} \) weber in a
iron bar of the cross-sectional area of
\( 0.5 c m^{2} . \) The permeability of the iron bar is?
A . 245
в. 250
c. 252
D. 255 55


Which of the following drugs are
analgesic?

This question has multiple correct options
A. Sulphaguanidine
B. Paludrine
c. Analgin
D. lodex


\( A B \) and \( C D \) are two parallel chords of a circle of radius \( 3 \mathrm{cm} . \) If \( A B=4 \mathrm{cms} \)
and \( C D=5 \mathrm{cm} . \) Then the distance
between them (in \( \mathrm{cm} \) ) is
A \( \cdot \frac{\sqrt{5}}{2}+\sqrt{11} \)
B. \( \sqrt{5}+\sqrt{11} \)
\( ^{c} \cdot \sqrt{5}+\frac{\sqrt{11}}{2} \)
D. \( \sqrt{2}+\frac{\sqrt{11}}{\sqrt{5}} \)


I. Under standard conditions the states
of the elemental forms of the halogens are: iodine-solid, bromine-liquid,
chlorine-gas, fluorine-gas.
II. Diatomic halogen molecules exhibit dispersion forces and increase in mass moving down through the family.
A. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


If \( A \) and \( B \) are two events, then which of
the following does not represent the
probability of at most one of \( A, B \) occurs.
\( \mathbf{A} \cdot 1-P(A \cap B) \)
B . \( P(\bar{A})-P(\bar{B})+-P(\bar{A}+\bar{B}) \)
\( \mathbf{c} \cdot P(\bar{A})+P(\bar{B})+-P(\bar{A} \cap \bar{B}) \)
\( \mathbf{D} \cdot P(A \cap \bar{B})+P(\bar{A} \cap \bar{B})-P(\bar{A} \cap \bar{B}) \)


(i) Name the kind of vibrations.
(ii) Give one example of such vibrations
(iii) Why is the amplitude of vibrations
gradually decreasing?
(iv) What happens to the vibrations of the body after some time?


Assertion
A bag contains \( n+1 \) coins. It is known
that one of these coins has a head on
both sides while the other coins are fair.
One coins is selected at random and
tossed. If head turns up, the probability that the selected coin was fair, is \( \frac{n}{n+2} \)
Reason

If an event \( A \) occurs with two mutually
exclusive and exhaustive events \( \boldsymbol{E}_{1} \) and
\( E_{2}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{E}_{\boldsymbol{i}}}{\boldsymbol{A}}\right)= \)
\( \frac{\boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{i}}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{i}}\right)}{\boldsymbol{P}\left(\boldsymbol{E}_{1}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{1}}\right)+\boldsymbol{P}\left(\boldsymbol{E}_{2}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{2}}\right)}, \boldsymbol{i}= \)
\( \mathbf{1}, \mathbf{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The standard enthalpies of formation of
\( C O_{2(g)}, \) and \( H C O O H(I) \) are
\( -393.7 k J / m o l \) and \( -409.2 k J / m o l \)
respectively This question has multiple correct options
A. \( -393.7 k J / \) mol is the enthalpy change for the reaction \( C_{(s)}+O_{2(g)} \rightarrow C O_{2(g)} \)
B. The enthalpy change for the reaction \( C O_{2(g)}+ \) \( H_{2(g)} \rightarrow H C O O H_{(I)} \) would be \( -15.5 k J / m o l \)
c. The enthalpy chage for the reaction \( H_{2} O+C O \rightarrow \) \( H C O O H \) is \( -409.2 k J / m o l \)
D. The enthalpy change for the reaction \( H_{2(g)}+ \) \( C O_{2(g)} \longrightarrow H_{2} O_{(I)}+C O_{(g)} \) is \( -409.2 k J / m o l \)


The diagram below represents the simplified pathway of the circulation of
blood. Study the same and answer the
questions that follow:
State the function of blood
vessels labelled 5 and 8


Why is atomic mass of chlorine taken
as \( 35.5 u \) and not a whole number like
\( 35 u \) or \( 36 u ? \) Explain.


Write down 5 difference between N-type and P-type semiconductors.


A coin is released inside a lift at a
height of \( 2 \mathrm{m} \) from the floor of the lift. The height of the lift is 10 m. The lift is
moving with an acceleration of \( 9 m / s^{2} \) downwards. The time after which the
coin will strike the lift is :
\( A \cdot 4 s \)
B. 2 s
c. \( \frac{4}{\sqrt{21}} s \)
D. \( \frac{2}{\sqrt{11}} s \)


State whether true or false:
IUPAC name of the complex \( \left[N i C l_{4}\right]^{2-} \) is Tetrachloronickelate(II) ion.


Helium is the most abundant Noble
gas in the universe

If this is true enter 1 , if false enter 0 .


A spherical mirror is a :
A. reflecting elliptical surface
B. reflecting spherical surface
C. reflecting parabolic surface
D. flat reflecting surface


Total number of valence electrons in the
molecules \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \)
is


A charged oil drop falls with terminal
velocity \( v_{0} \) in the absence of electric
field. An electric field E keeps it stationary. The drop acquires additonal charge \( q \) and starts moving upwards with velocity \( v_{0} . \) The initial charge on
the drop was
\( A \cdot 4 q \)
B. 2a
\( c \cdot q \)
D. \( \frac{q}{2} \)


\( A \)
\( 0.1(\mathrm{M}) \) solution of an acid HA of density \( 1.01 \mathrm{gm} / \mathrm{ml} \) is taken in a beaker. The molec ular mass of HA is \( 300 \mathrm{g} / \mathrm{mol} \) The freezing point of solution is
\( 0.2087^{\circ} \mathrm{C} . \) For \( \mathrm{H}_{2} \mathrm{O}, \quad K_{f}=1.86 \mathrm{K} / \mathrm{m} \)
What is the degree of dissociation of HA i
n its \( 0.1(\mathrm{M}) \) aqueous solution (in percentage) ?
A . \( 10 \% \)
B. 20\%
c. \( 25 \% \)
D. \( 55.56 \% \)


Find \( \int \sqrt{1+\cos 2 x} d x \)


Divide the given shape in a Horizontal
symmetry (into 2 trapeziums)
(iii) into 2 trapeziums


Displacement \( (x) \) of a particle is related to time \( (t) \) as \( x=a t+b t^{2}+c t^{3} \) where
\( a, b \) and \( c \) are constants of motion. The velocity of the particle when its acceleration is zero, is given by:
A. \( _{a+\frac{b^{2}}{c}} \)
в. \( _{a-} \frac{b^{2}}{3 c} \)
c. \( _{a}+\frac{b^{2}}{3 c} \)
D. \( _{a-\frac{b^{2}}{4 c}} \)


Statement I: Metals are good
conductors of electricity
Statement II: In \( M_{2} \), they are held
together by ionic bonds
A. Both statement 1 and statement 2 are correct and statement 2 is the correct explanation for statement 1
B. Both statement 1 and statement 2 are correct but statement 2 is NOT the correct explanation for statement 1
c. Statement 1 is correct but statement 2 is incorrect
D. Statement 1 is incorrect but statement 2 is correct
E. Both statement 1 and statement 2 are incorrect


The ratio of densities of two substances
is 2: 3 and that of specific heats is 1: 2 The ratio of thermal capacities per unit volume is
A \( \cdot 1: 2 \)
B. 2:1
\( c \cdot 1: 3 \)
D. 3:


A geometric series consists of four terms and has a positive common ratio.
The sum of the first two terms is 9 and
sum of the last two terms is \( 36 . \) Find the
series


Given: \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{i}-\mathbf{2} \boldsymbol{j}, \overrightarrow{\boldsymbol{B}}=\mathbf{2} \hat{\mathbf{i}}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \overrightarrow{\boldsymbol{C}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
Find component of vector \( \overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}} \) along:
(i) x-axis
(ii) \( \overrightarrow{\boldsymbol{C}} \)
A \( \cdot 3 ; \frac{1}{\sqrt{2}} \)
в. \( 2 ; \frac{1}{\sqrt{3}} \)
c. \( _{3 ; \frac{1}{\sqrt{3}}} \)
D. \( 2 ; \frac{1}{\sqrt{2}} \)


The value of a machine depreciates every year by \( 5 \% \). If the present value of the machine be Rs. \( 100,000, \) what will be its value after two years?
A . Rs. 100,050
B. Rs. 90,250
c. Rs. 99,250
D. Rs. 99,000


The hydration of ionic compounds involves:
A. evolution of heat
B. weakening of attractive forces
c. dissociation into ions
D. all of these


An ideal gas is heated in a container that has a fixed volume. Identify which of the following will increase as a result of this heating?
I. The pressure against the walls of the container
Il. The average kinetic energy of the gas
molecules
III. The number of moles of gas in the
container
A. I only
B. I and II only
c. II and III only
D. II only
E . III only


Highly pure metal can be obtained by zone refining.
A . True
B. False


Two identical circular loops of \( A \& B \) of metal wire are lying on a table without touching each other. Loop A carries a current which increases with time. In
response, the loop B:
A. Remains stationary
B. Is attracted by the loop \( A \)
C. Is repelled by the loop \( A \)
D. Rotates about its CM, with CM fixed


Uphill transport i.e., movement of substances from their lower
concentration to their higher concentration occurs in
A. Simple diffusion
B. Facilitated diffusion
c. Active transport
D. Both B and C


A transparent material which is thicker in the middle and thinner at the edges
is called:
A. Concave lens
B. Convex lens
c. Plano-concave lens
D. Convexo-concave lens


The advantage(s) of using \( O_{2} \) rather than air in the steel industry is (are):
\( (I) \) There is a faster conversion, so a
given plant can produce more in day
\( (I I) \) Larger quantities can be handled
\( (I I I) \) It gives a pure product, and the surface is free from nitrides.
A. I only
B. II and III only
c. \( I I \) only
D. \( I, I I \) and \( I I I \)


A ruby laser produces radiations of wavelengths, \( 662.6 \mathrm{nm} \) in pulse
duration are \( 10^{-6} \) s. If the laser produces
\( 0.39 \mathrm{J} \) of energy per pulse, how many photons are produced in each pulse?
A \( \cdot 1.3 \times 10^{9} \)
B . \( 1.3 \times 10^{18} \)
c. \( 1.3 \times 10^{27} \)
D. \( 3.9 \times 10^{18} \)


In the rhythm method of birth control, the couple abstain from intercourse
A. One day before and after ovulation
B. Two days before and after ovulation
c. Three days before and after ovulation
D. One week days before and after ovulation


The rate constant of a chemical
reaction at a very high temperature will
approach:
A. Arrhenius frequency factor divided by the ideal gas constant
B. Activation energy
C. Arrhenius frequency factor
D. Activation energy divided by the ideal gas constant


Because most of the amino acids
are represented by more than one codons, the genetic code is said to be
A. Deaminated
B. Comma less
c. Degenerate
D. Overlapping


You soak seeds of bean and observe
them after \( 2-3 \) days. what will be your observations?


Colloids are purified by:
A. Precipitation
B. Coagulation
c. Dialysis
D. Filtration


\( \ln \Delta A B C, \) a \( \sin (B-C)+b \sin (C- \)
\( A)+c \sin (A-B)= \)
\( A \)
B. \( a+b+c \)
c. \( a^{2}+b^{2}+c^{2} \)
D \( \cdot 2\left(a^{2}+b^{2}+c^{2}\right) \)


Integrate the rational function: \( \frac{1}{x^{2}-9} \)


Sound waves can't be Polaroids.
Explain:


Assertion
Moment of inertia is always constant.
Reason

Angular moment is conserved that is
why moment of inertia is constant.
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


Solve:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}+\boldsymbol{y}-\mathbf{1}} \) when \( \boldsymbol{y}=\frac{\mathbf{1}}{\mathbf{3}} \) at \( \boldsymbol{x}=\frac{\mathbf{2}}{\mathbf{3}} \)


If \( 0<x \leq \frac{\pi}{2}, \) then \( (\sin x+\operatorname{cosec} x) \) is
greater than or equal to
A . 0
B.
\( c \cdot 2 \)
D. None of these


One of the two events must happen. Given that the chance of one is two-
third of the other, find the odds in favour of the other.


Which of the following statements are
correct?
A. There are two types of addition reaction: polar addition and non-polar addition
B. There are two types of polar addition : electrophilic and nucleophilic addition
C. There are two types of non-polar addition: free radical addition and cycloaddition
D. All of the above


In the expansion of \( (1+x)^{n}, \) the \( 5^{t h} \)
term is 4 times the \( 4^{t h} \) term and the \( 4^{t h} \)
term is 6 times the \( 3^{r d} \) term. than \( n= \)
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 12


With what speed in miles/hour \( 1 m / s=2.23 m i / h \) ) must an object be
thrown to reach a height of \( 91.5 m \) (equivalent to one football field)? Assume negligible air resistance.
A. \( 94.4 \mathrm{mi} / \mathrm{h} \)
в. \( 84.4 \mathrm{mi} / \mathrm{h} \)
c. \( 74.4 \mathrm{mi} / \mathrm{h} \)
D. \( 94 m i / h \)


Balance the following equation.
\( \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot 2 I O_{4}^{-}+14 I^{-}+16 H^{+} \rightarrow 8 I_{2}+8 H_{2} O \)
B . \( 2 I O_{4}^{-}+14 I^{-}+4 H^{+} \rightarrow 3 I_{2}+8 H_{2} O \)
c. \( I O_{4}^{-}+7 I^{-}+8 H^{+} \rightarrow 4 I_{2}+4 H_{2} O \)
D. None of these


Complete reduction of archegonium is observed in
A. Gnetum
B. Cycas
c. Ginkgo
D. Pinus


\( \sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} \frac{1}{2}\right)\right] \) is equal
to
A \( \cdot \frac{3 \sqrt{7}}{8} \)
B. \( \frac{5 \sqrt{7}}{8} \)
\( c \cdot \frac{5 \sqrt{7}}{2} \)
D. \( \frac{3 \sqrt{7}}{2} \)


Lanthanide ions show
A. magnetic properties
B. coloured ion formation
c. lanthanide
D. All of the above


Heaviest atom among the following is:
A. uranium
B. Ieadd
c. mercury
D. radium


Which of the following is the requirement for active absorption?
A. Evolution of heat
B. Availability of light and heat
c. Presence of light
D. Availability of energy


Which of the following is not a
chalcogen?
A. \( O \)
B. \( S \)
\( c . S e \)
D. \( P \)


Which one of these is not an oviparous animal?
A. Human
B. Crocodile
c. Hen
D. crow


What is the oxidation state of the
underlined atoms in \( \left[\underline{C r}(\boldsymbol{C N})_{6}\right]^{3-} \) ? (answer is modulus of oxidation state)


What is the magnetic moment of the atom due to the motion of the electron?


Say Yes or No. Is it important that offsprings from the same parent should have common traits?
A. No
B. Yes
c. мaybe
D. None of the above


The value of \( \int \frac{d t}{t^{2}+2 x t+1}\left(x^{2}>1\right) \) is...
\( ^{\mathrm{A}} \cdot \frac{1}{2 \sqrt{\left(x^{2}-1\right)}} \log \frac{t+x-\sqrt{x^{2}-1}}{t+x+\sqrt{\left(x^{2}+1\right)}} \)
B. \( \frac{1}{2 \sqrt{\left(x^{2}-1\right)}} \log \frac{t+x-\sqrt{x^{2}-1}}{t+x+\sqrt{\left(x^{2}-1\right)}}+c \)
c. \( \frac{1}{2 \sqrt{\left(x^{2}+1\right)}} \log \frac{t+x-\sqrt{x^{2}+1}}{t+x+\sqrt{\left(x^{2}+1\right)}} \)
D. \( \frac{1}{2 \sqrt{\left(x^{2}+1\right)}} \log \frac{t+x-\sqrt{x^{2}+1}}{t+x+\sqrt{\left(x^{2}-1\right)}}+c \)


Four wires are made from the same
metal.
Which wire has the lowest resistance?
A. Length of wire / \( \mathrm{cm}-20 \), Diameter of wire / \( \mathrm{mm}-0.20 \)
B. Length of wire / \( \mathrm{cm}-20 \), Diameter of wire / \( \mathrm{mm}-0.40 \)
C. Length of wire / \( \mathrm{cm}-40 \), Diameter of wire / \( \mathrm{mm}-0.20 \)
D. Length of wire / \( \mathrm{cm}-40 \), Diameter of wire / \( \mathrm{mm}-0.40 \)


A metal .......... hydrogen in the activity series gives hydrogen with \( \ldots \ldots . . . \) acid or acid.
This question has multiple correct options
A . above
B. below
c. dilute hydrochloric acid
D. concentrated hydrochloric
E. dilute sulphuric
\( F \). none of the above


Trivial name of 2,3 -dihydroxy butanedioic acid is-
A. Malic acid
B. Tartaric acid
c. citric acid
D. Lactic acid


A stone is dropped into a quiet lake and
waves move in a circle at a speed of 3.5 \( \mathrm{cm} / \mathrm{sec} . \) At the instant when the radius
of the circular wave is \( 7.5 \mathrm{cm}, \) how fast is the enclosed area increasing?


Which of the following process is used in the extractive metallugy of magnesium?
A. Fused salt electrolysis
B. Self reduction
c. Aqueous solution electrolysis
D. Thermite process


Which of the following oxide of nitrogen
is ionic?
A. NO
в. \( N_{2} O_{3} \)
c. \( N_{2} O_{5} \)
D. \( N O_{2} \)


The refractive index of a medium:
\( \mathbf{A} \cdot \) is defined with respect to another medium
B. is an absolute constant for a medium
C. depends on the frequency of the light in the medium
D. is more for higher intensity of light ray


Assertion
The differential equation of the family of
curves represented by \( \boldsymbol{y}=\left(\boldsymbol{a}+\boldsymbol{b} e^{c}\right) \boldsymbol{x} \)
is \( x \frac{d y}{d x}-y=0, \) where \( a, b \) and \( c \) are
constant.
Reason
In general, a differential equation of \( n \) th
order is obtained on eliminating \( n \) arbitrary constants.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The lining of the stomach is protected
by
A. Hydrochloric acid
B. Mucous
c. Digestive juicies
D. None of the above


Find \( n \) if the given value of \( x \) is the \( n \) th
term of the given A.P.
\( 25,50,75,100, \dots \dots ; x=1000 \)


A long solenoid with 40 turns per \( \mathrm{cm} \)
carries a current of \( 1 A . \) The magnetic
energy stored per unit volume is
\( \boldsymbol{J} / \boldsymbol{m}^{3} \)
A . \( 3.2 \pi \)
B. \( 32 \pi \)
c. \( 1.6 \pi \)
D. \( 6.4 \pi \)


Liquid ethanol can be separated from a mixture of ethanol and water by:
A. Chromatography
B. Fractional distillation
c. centrifugation
D. All of above


Show that LHS=RHS i.e. \( \frac{2}{9} \times 3=\frac{2}{9} \times \) \( \frac{3}{1}=\frac{2 \times 3}{9 \times 1}=\frac{6}{9}=\frac{2}{3} \)


Equal masses of \( \mathrm{N}_{2} \) and \( \mathrm{O}_{2} \) gases are filled in vessels \( A \) and \( B \). The volume of
vessel B is double of A. The ratio of
pressure in vessel \( A \) and \( B \) will be
A . 16: 7
B. 16: 14
c. 32: 7
D. 32 : 28


An electron beam is moving from left to right of the observer and magnetic field is acting vertically upwards. The direction of force acting on electron is
A. towards the observer
B. away from the observer
c. downwards
D. upwards


Which among the following is a significant feature of the India's
population?
A. High rural population
B. Low death rate
c. Low gender ratio
D. All of the above


connected by a string going over
clamped light smooth pulley as shown
in figure. The system is released from
rest. The larger mass is stropped for a
moment \( 1.0 s \) after the system is set in
motion. Find the time elapsed before the
string is tight again.
\( \mathbf{A} \cdot \frac{1}{3} s \)
B . \( 1 s \)
c. \( 2 s \)
D. \( 3 s \)


Short / Long Answer Types:
What is meant by respiratory quotient
(RQ)? When will the value of RQ be 1 and when will it be less than 1?


If the standard deviation of the values
2,4,6,8 is \( 2.33, \) then the standard
deviation of the values 4,6,8,10 is
\( \mathbf{A} \cdot \mathbf{0} \)
в. 2.58
c. 4.66
D. None of these


Define Antioxidants.


Which of the following produces hydrolith with dihydrogen?
\( A \cdot \) Mg
в. А।
\( c \cdot c u \)
D. \( c \)


If the frequency of a wave is doubled,
then its wavelength
A. Becomes doubled
B. Remains same
c. Becomes half of the original
D. None of these


In nucleic acids, the sequence is:
A. phosphate-sugar-base
B. sugar-acid-phosphate
c. sugar-base-phosphate
D. base-phosphate-sugar


Mucosa forms rugae in the?
A. Small intestine
B. Large intestine
c. Oesophagus
D. Stomach


The eyeball is approximately spherical in shape. What is the diameter of a
normal human eyeball?
A. Approximately 2.3 cm
B. Approximately 4.3 cm
c. Approximately 5.3 cm
D. None of the above


Arrange the following.
(i) \( C a H_{2}, B e H_{2} \) and \( T i H_{2} \) in order of
increasing electrical conductance.
(ii) \( L i H, N a H \) and \( C s H \) in order of increasing ionic character.
(iii) \( \boldsymbol{H}-\boldsymbol{H}, \boldsymbol{D}-\boldsymbol{D} \) and \( \boldsymbol{F}-\boldsymbol{F} \) in order
of increasing bond dissociation
enthalpy.
(iv) \( N a H, M g H_{2} \) and \( H_{2} O \) in order of increasing reducing property.


The value of
\( \left(497 e^{-2}\right) \lim _{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{1 / x} \)


If the terminal speed of a sphere of gold (density \( \left.=19.5 k g / m^{3}\right) \) is \( 0.2 m / s \) in a
viscous liquid (density \( \left.=1.5 k g / m^{3}\right) \)
find the terminal speed of a sphere of silver (density \( =10.5 k g / m^{3} \) ) of the
same size in the same liquid
A. \( 0.4 m / s \)
в. \( 0.133 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)


Calculate the volume of \( \mathrm{CO}_{2} \) formed at
STP when 2.32 g of zinc carbonate decomposes with no further loss in weight.
A . \( 0.205 l \)
B. 0.41 l
c. \( 0.82 l \)
D. 1.23 \( l \)


The sound waves which cannot be heard
by a human ear are called.
A. Ultrasonic sounds
B. Infrasonic sounds
c. Extraordinary sounds
D. Both (a) and (c)


If \( \oint_{s} \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s}=\boldsymbol{0} \) over surface, then
A. the electric field inside the surface and on it is zero
B. the electric field inside the surface is necessarily uniform
C . all charges must necessarily be outside the surface
D. all of these


The number of real solutions of the
equation \( \sin \left(e^{x}\right)=2018^{x}+2018^{-x} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinitely many


What is one unit of household electrical
energy in J?
в. \( 3600 J \)
c. \( 0.6 \times 10^{3} J \)
D. \( 3.6 \times 10^{6} J \)


Which of the following cell does not secrete hormone?
A. Kupffer cell
B. Leydig cell
c. Lutein cell
D. Parafollicular cells of thyroid


State True or False.
The s orbital is spherical in shape.
A. True
B. False


f \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined
by \( f(x)=2 x+3, g(x)=x^{2}+7, \) what
are the values of \( \boldsymbol{x} \) for which \( \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})]= \)
\( \mathbf{2 5} ? \)
\( A \cdot \pm 1 \)
B. ±2
\( c .\pm 3 \)
\( \mathrm{D} \cdot \pm 4 \)


A light ray from air is incident \( ( \) as
shown in figure \( ) \) at one end of a glass
fibre (refractive index, \( \mu=1.5 \) ) making
an incidence angle of \( 60^{\circ} \) on the lateral
surface, so that it undergoes a total
internal reflection. How much time
would it take to traverse the straight
fiber of length 1 km?
A. \( 3.33 \mu s \)
B. \( 6.67 \mu s \)
\( c .5 .77 \mu s \)
D. \( 3.85 \mu s \)


Let \( f(x)=x \) and \( g(x)=|x| \) for all \( x \in R \)
The function \( \phi(x) \) given that \( \phi(x) \geq 0 \)
satisfying \( (\phi(x) f(x))^{2}+ \)
\( (\phi(x) g(x))^{2}=x^{4} \) is.
This question has multiple correct options
A \( . \phi(x)=x, x \in[0, \infty) \)
B. \( \phi(x)=x, x \in R \)
c. \( \phi(x)=-x, x \in(-\infty, 0] \)
D. \( \phi(x)=x+|x|, x \in R \)


\( \boldsymbol{l} \boldsymbol{t}_{n \rightarrow \infty}\left[\frac{\mathbf{1}}{\boldsymbol{n a}}+\frac{\mathbf{1}}{\boldsymbol{n a}+\mathbf{1}} \frac{\mathbf{1}}{\boldsymbol{n a}+\mathbf{2}} \cdots \cdots+\frac{\mathbf{1}}{\boldsymbol{n b}}\right] \)
\( ^{\mathrm{A}} \cdot \log \left(\frac{b}{a}\right) \)
B. \( \log \left(\frac{a}{b}\right) \)
\( c \cdot \log a \)
D. \( \log b \)


If \( z_{0}=\frac{1-i}{2}, \) then
\( \left(\mathbf{1}+\boldsymbol{z}_{0}\right)\left(\mathbf{1}+\boldsymbol{z}_{\mathbf{0}}^{\mathbf{2}^{1}}\right)\left(\mathbf{1}+\boldsymbol{z}_{\mathbf{0}}^{\mathbf{2}^{2}}\right) \ldots \ldots \ldots(\mathbf{1}+ \)
must be
A \( \cdot(1-i)\left(1+\frac{1}{2^{2^{n}}}\right) \) for \( n>1 \)
B. \( (1-i)\left(1-\frac{1}{2^{2^{n}}}\right) \) for \( n> \)
c. \( \frac{1+i}{2} \) for \( n>1 \)
D. \( (1-i)\left(1-\frac{1}{2^{2 n+1}}\right) \) for \( n>1 \)


\( f(x)\left(x+\frac{1}{x}\right)=x^{2}+\frac{1}{x^{2}}, \) find \( f\left(x^{3}\right) \)


Find the area of a rhombus whose
diagonals are \( 12 \mathrm{cm} \) and \( 13 \mathrm{cm} \)


Two light wires made up of the same material (Young Modulus, Y) have
length \( L \) each and radii \( R \) and \( 2 R \) respectively, They are joined together and suspended from a rigid
support. Now a weight \( W \) attached to
the free end of the joint wire as shown in the figure. Find the elastic potential energy stored in the system due to the
extension of the wire


Find the value of \( x \) in given figure if
\( \boldsymbol{A B} \| \boldsymbol{C D} \)
\( x \) is the exterior angle of \( \angle P Q R \)
A \( .275^{\circ} \)
B . \( 280^{\circ} \)
\( \mathbf{c} \cdot 285^{\circ} \)
D. \( 295^{\circ} \)


Why is it said animals are a cause for
soil erosion?
A. As they walk on it
B. As they freely graze and spoil the soil by their hoofs
c. As they spoil the soil by grazing itself
D. None of the above


All the five digit numbers that can be formed using the digits 1,2,3,4,5 without repetition, are arranged in the decreasing order of magnitude. The rank of the number 34215 is
A . 58
B. 62
c. 96
D. 128


Proton donor is:
A. arrhenius acid
B. arrhenius base
C. lewis acid
D. lewis base
E. bronsted-lowry acid


Prove that:
\( |\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}| \)


Three masses \( 2 \mathrm{kg}, 3 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are lying at the corners of an equilateral triangle of side a. The \( x \) coordinate of
the centre of mass is :
\( ^{A} \cdot \frac{7}{12} a \)
\( B \cdot \frac{5}{2} a \)
\( \frac{7 \sqrt{2}}{9} a \)
D


Derive an expression for potential and kinetic energy of an electron in any orbit of a hydrogen atom according to Bohr's atomic model.


The population of a village is \( 6250 . \) It is found that the rate of increase in
population is \( 8 \% \) per annum. Find the
population after 2 years.


Given that \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x} \boldsymbol{g}(\boldsymbol{x})}{|\boldsymbol{x}|}, \boldsymbol{g}(\mathbf{0})= \)
\( \boldsymbol{g}^{\prime}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f} \) is continuous at \( \boldsymbol{x}=\mathbf{0} \)
the value of \( f^{\prime}(0) \) is


Accessory sexual characters first appear in
A. Childhood
B. Puberty
c. Fetus
D. Adulthood


Which of the following is coated as a thin layer on the inner side of non-stick
pans?
A. Bakelite
B. PVC
c. Teflon
D. Polypropylene


If masses of two point objects are tripled and distance between them is doubled,then gravitational force of attraction between them will
A. Increase by 225\%
B. Decrease by 56\%
c. Increase by 125\%
D. Decrease by 144\%


Stat law of conservation of charges?


Iron has \( _{-}-_{-}-_{-}- \) isotopes


Assertion
The mobility of \( N a^{\oplus} \) is lower than that
of \( \boldsymbol{K}^{\oplus} \) ion
Reason
The ionic mobility depends upon the effective radius of the ion.
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


Apex beat is felt on
A. Lungs
B. Right side of chest
C. Left side of chest
D. Centre of chest


How can you find critical angle of water? Explain your steps briefly.


Which term of the geometric sequence,
(i) \( 5,2, \frac{4}{5}, \frac{8}{25}, \dots, \) is \( \frac{128}{15625} ? \)
(ii) \( 1,2,4,8, \dots, \) is \( 1024 ? \)


\( f\left(\frac{1}{2 i^{2}}\right)=t, \) then \( \tan t \) equals


Two positive charges \( \boldsymbol{q}_{1}=20 C \) and
\( q_{2}=6 C \) are separated by diameter of
3 \( m \). Then what is the force produced by
them?
\( A \cdot 80 N \)
B. \( 53.3 N \)
\( c .56 N \)
D. \( 72.5 N \)


The oxo-acids of \( P_{2} O_{5} \) are
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3}, \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
A. True
B. False


Evaluate: \( \int_{0}^{\pi / 4} \sec ^{7} \theta \sin ^{3} \theta d \theta= \)
A \( \cdot \frac{1}{12} \)
в. \( \frac{3}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{7}{12} \)


Sprouting of potato can be prevented in storage by
A. Maleic hydrazide
B. Gibberellins
c. Indole acetic acid
D. cytokinins


Which oxide of nitrogen is obtained on
heating ammonium nitrate at \( 250^{\circ} \mathrm{C} \) ?
A. Nitric oxide
B. Nitrous oxide
c. Nitrogen dioxide
D. Dinitrogen tetraoxide


The divisor when the quotient, dividend
and the remainder are respectively 547,171282 and 71 is equal to
A . 333
в. 323
c. 313
D. 303


Given ordered pairs :(5,4),(5,5),(5,6) \( (6,4),(6,5),(6,6),(6,7),(8,4),(8,5),(8, \)
6), (8,8)
Use these ordered pairs to find the following relation:
\( R_{4}= \) "is greater than"


If \( \boldsymbol{A}=(\mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}), \boldsymbol{B}=(\mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( B-C \)
A \( \cdot\{4,6\} \)
в. \{4,6,8\}
c. \{6,8,10\}
D. \{8,10\}


Evaluate \( (\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}+\sqrt{2})^{6} ? \)


On introducing a catalyst at \( 500 K \), the rate of a first order reaction increases
by 1.718 times. The activation energy in
the presence of a catalyst is \( 6.05 k J \) \( m o l^{-1} . \) The slope of the plot of
\( \ln k\left(\sec ^{-1}\right) \) against \( 1 / T \) in the absence
of catalyst is:
A . +1
B. - 1
c. +1000
D. -1000


Show that the points \( \boldsymbol{A}(\mathbf{0}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{3}) \) and \( \boldsymbol{C}(\mathbf{1},-\mathbf{3}, \mathbf{1}) \)
are vertices of an isosceles right-angled triangle.


The laws of electromagnetic induction have been used in the construction of a
A. galvanometer
B. voltmeter
c. electric motor
D. electric generator


In the space shown a non-uniform
magnetic field \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0}(\boldsymbol{1}+\boldsymbol{x})(-\boldsymbol{k}) \)
tesla is present. A closed loop of small resistance, placed in the \( x \) -y plane is
given velocity \( V_{0} . \) The force due to
magnetic field on the loop is
A. zer
B. along + x direction
C. along \( -x \) direction
D. along +y direction
E. none of these


\( A n^{3+} \) (trivalent actinoid ions) have
configuration
A \( .5 f^{0} \) to \( 5 f^{14} \)
B. \( 5 f^{1} \) to \( 5 f^{14} \)
\( \mathbf{c} \cdot 5 f^{2} \) to \( 5 f^{1} \)
D. \( 5 f^{0} \) to \( 5 f^{13} \)


The adjacent diagram shows a coil would around a soft iron bar XY. How
can the strength of the electromagnet
be increased?
A. Increasing the current in the circuit
B. Increasing the number of turns of the coil
\( c . \) both \( a \) and \( b \)
D. None of these


Construct a triangle with sides \( 4 \mathrm{cm}, 5 \) \( \mathrm{cm} \) and \( 7 \mathrm{cm} \) and then another triangle whose sides are \( \frac{3}{4} \) of the corresponding sides of the first triangle.


A transverse wave passes through a string with the equation \( \boldsymbol{y}= \)
\( 10 \sin \pi(0.02 x-2 t) \) where \( x \) is in
metres and \( t \) in seconds. The maximum
velocity of the particle in wave motion is
A \( \cdot 63 m s^{-1} \)
B. \( 78 \mathrm{ms}^{-1} \)
c. \( 100 m s^{-1} \)
D. \( 121 \mathrm{ms}^{-1} \)


Identify the largest angle of the triangle.
\( A \)
в.
\( c \)
\( D \)


An urn contains one black ball and one
green ball. A second urn contains one
white and one green ball. One ball is drawn at random from each urn. What is
the probability that both balls are of
same colour?
A . \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 2 / 3 \)


Due to refraction,
A. Image in the plane mirror is clear
B. Polished black surfaces shine
C. speed of light is constant in all mediums
D. A glass sphere appears attractive


Assertion
Electromagnetic radiations exert
pressure.
Reason
Electromagnetic-waves carry both momentum and energy.
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


\( \lim _{y \rightarrow 1}\left(\frac{1}{y^{2}-1}-\frac{2}{y^{4}-1}\right)= \)
\( A \)
2
B. 3
\( c \cdot \frac{1}{4} \)
\( D \)


The sequence of a reflex arc is
A. Receptor \( \rightarrow \) Sensory neuron \( \rightarrow \) Motor neuron \( \rightarrow \) Effector \( \rightarrow \) Response
B. Effector \( \rightarrow \) Sensory neuron \( \rightarrow \) Motor neuron \( \rightarrow \) Receptor \( \rightarrow \) Response
C. Effector \( \rightarrow \) Motor Neuron \( \rightarrow \) Interneuron \( \rightarrow \) Receptor \( \rightarrow \) Response
D. Receptor \( \rightarrow \) Motor neuron \( \rightarrow \) Sensory neuron \( \rightarrow \) Effector \( \rightarrow \) Response


The element which catches fire at \( 30^{0} C \)
and stored under water
A. \( C a \)
в. \( N a \)
\( c . P \)
D. \( Z n \)


ABCD is a trapezium in which \( \boldsymbol{A B} \| \) \( \boldsymbol{D} \boldsymbol{C}, \boldsymbol{A B}=\mathbf{5 0} \mathrm{cm}, \boldsymbol{D} \boldsymbol{C}=\mathbf{3 0} \mathrm{cm} . \) If \( \boldsymbol{X} \)
and \( Y \) are respectively the mid-points
of \( A D \) and \( B C, \) prove that
\( \boldsymbol{a} \boldsymbol{r}(\operatorname{trap} \cdot \boldsymbol{D} \boldsymbol{C} \boldsymbol{Y} \boldsymbol{X})= \)
\( \frac{\mathbf{7}}{\mathbf{9}} \boldsymbol{a} \boldsymbol{r}(\operatorname{trap} . \boldsymbol{X} \boldsymbol{Y} \boldsymbol{B} \boldsymbol{A}) \)


The energy released on burning coal, oil, wood or gas is:
A. kinetic energy
B. heat energy
c. light energy
D. solar energy


Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are (0,-1),(2,1) and \( (0,3) . \) Write the ratio of the area fo the given triangle to the area of the new triangle.


During upward motion of a body projected vertically upward, the angle
between velocity and 'g' is \( 90^{\circ} \)
A. True
B. False


Prefix is a part of IUPAC name which appear after the word root.
A. True
B. False


Mass of the one atom of the element \( X \)
is \( 1.66 \times 10^{-26} \) g. Number of atoms in 1
g of the element is:
A \( \cdot 1.66 \times 10^{-26} \)
B . \( 1.66 \times 10^{25} \)
c. \( 1.66 \times 10^{-24} x N o \)
D. \( 6.024 \times 10^{25} \)


a) For concave mirror focal length is taken as
b) For convex mirror, radius of curvature
is taken as
A \( . a= \)positive, \( b= \) negative
B. \( a= \) negative, \( b= \) positive
c. \( a= \) positive \( , b= \) positive
D. \( a= \) negative, \( b= \) negative


Translucent materials allow
amount of light to pass through.
A . entire
B. some
c. very less
D. no


Which of the following is symmetrical about its diagonals?
A. Square
B. Rectangle
c. Parallelogram
D. None of these


Find the depth of a lake at which
density of water is \( 1 \% \) greater than at
the surface. Given compressibility \( K= \) \( 50 \times 10^{-6} / \) atm


The element placed with cerium, in the table formed by Newlands' was:
A . actinium
B. lanthanum
c. lawrencium
D. zirconium


Two metallic spheres of radii \( 2 \mathrm{cm} \) and
\( 6 \mathrm{cm} \) are given charge \( 3 \times 10^{-2} \mathrm{C} \) and
\( 7 \times 10^{-2} C, \) respectively. If these are
connected by a conducting wire, the final charge on the bigger sphere is


State whether true or false.
Weight of a body remains constant anywhere in the universe.
A. True
B. False


Which of the following statements is incorrect about Dolly, the clone?
A. Dolly was developed from a cell taken from the mammary gland of Scottish blackface ewe and an unfertilized egg obtained from Finn Dorsett sheep
B. The egg produced by the fusion was implanted into Scottish blackface ewe
C. Dolly was identical to Fin Dorsett sheep and was called its done
D. None of these


Periodic Table(Abbreviated): The
element that will react in a 1: 1 ratio
with (D) is:
\begin{tabular}{|c|c|c|c|c|c|}
\hline \( \mathbf{z}_{\mathbf{L i}} \) & & & & & \( \mathbf{( D )} \) & \( \mathbf{1 0} \) \\
\hline & \( \mathbf{( A )} \) & & & & \( \mathbf{( C )} \) & & \\
\hline \( \mathbf{( B )} \) & \( \mathbf{2 0} \) & & & & & \\
\hline
\end{tabular}
B.
\( r \)
D


What is the correct order of acidity in
the given compounds?
A. \( I<I I<I I I \)
В. \( I I I<I<I I \)
c. \( I I<I<I I I \)
D. III \( <I I<I \)


Explain why the following are made of thermosetting plastics.
(a) Saucepan handles
(b) Electric plugs/switches/plug boards


Match the enzymes with their
respective substrates and choose the
right one among options given.
Column II
Dipeptides \begin{tabular}{c|c|c}
& Column I \\
\hline A. & Lipase \\
\hline B. & Nuclease \\
\hline C. & Carboxypeptidase \\
D. & Dipeptidases \\
\hline
\end{tabular} Fats Nucleic
acids Proteins,
peptones
and
proteoses
A. A-(ii), B-(iii), C-(i), D-(iv)
B. A-(iii), B-(iv), C-(ii), D-(i)
C. A-(iii), B-(i), C-(iv), D-(ii)
D. A-(ii), B-(iii), C-(iv), D-(i)


The table below gives the distance, \( d \)
feet, the cart was from a reference point
at 1 second intervals while it moves
from \( t=0 \) seconds to \( t=5 \) seconds.
\[
\begin{array}{cccccc}
t & 0 & 1 & 2 & 3 & 4 \\
d & 14 & 20 & 26 & 32 & 38 \\
88 & & & & \\
& & & & \\
& 20 & 26 & 32 & 38 & 38 & 3
\end{array}
\]
Find the correct relationship between \( d \)
and \( t \)
A. \( d=t+14 \)
B. \( d=6 t+8 \)
c. \( d=6 t+14 \)
D. \( d=14 t+6 \)
E \( . d=34 t \)


Few polymers are matched with their
uses. Point out the wrong match.
A. Polyester - Fabric, tyre cords, safety belts
B. Nylon 6 - Ropes, tyre cords, fabrics
C. Bakelite - Packaging industry, lubricant
D. Teflon- Oil seals, gaskets, non-stick utensils


How many sub-atomic particles are present in ana- particle used in
Rutherford's scattering experiment?
A. Protons - 4, Neutrons - 0, Electrons - 0
B. Protons - 2, Neutrons - 0, Electron - 2
c. Protons - 2, Neutron - 2, Electron - 0
D. Protons - 2, Neutron - 2, Electron - 1


A substance cools from \( 75^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \)
in \( T_{1} \) minute, from \( 70^{\circ} C \) to \( 65^{\circ} C \) in \( T_{2} \)
minute and from \( 65^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in \( T_{3} \)
minute, then
A \( \cdot T_{1}=T_{2}=T_{3} \)
в. \( T_{1}<T_{2}<T_{3} \)
c. \( T_{1}>T_{2}>T_{3} \)
D. \( T_{1}<T_{2}>T_{3} \)


\( A B C \) is an isosceles triangle with
vertex at \( A \) and \( P \) is any point inside
the triangle. If the rectangle contained by perpendicular from \( \boldsymbol{P} \) to sides \( \boldsymbol{A B} \) and \( A C \) is equal to square of the perpendicular from \( \boldsymbol{P} \) to base \( \boldsymbol{B} \boldsymbol{C}, \) then prove that the locus of \( \boldsymbol{P} \) is a circle.


Pressure varies inversely with area \( (A) \) provided the thrust is same.
A. True
B. False


Abida and Ramesh were doing an experiment in which water was to be
heated in a beaker. Abida kept the beaker near the wick in the yellow part of the candle flame. Ramesh kept the
beaker in the outermost part of the
flame. Whose water will get heated in a shorter time?


Factorise the expression and divide them as directed.
\( \left(5 p^{2}-25 p+20\right) \div(p-1) \)


Calculate the percent composition of
carbon in \( C_{6} H_{12} O_{6} \)
A . \( 50 \% \)
B. \( 40 \% \)
c. \( 35.3 \% \)
D . 22.1\%


The IUPAC name of the given compound
is:
A . 1-hydroxycyclohex-4-en-3-one
B. 1-hydroxycyclohex-3-en-5-one
c. 3-hydroxycyclohex-5-en-1-one
D. 5-hydroxycyclohex-2-en-1-one


The major air pollutant is:
A. \( C O \)
B. oxides of nitrogen
\( c . \) soot
D. oxides of sulphur


Monocot stem has
A. Bicollateral closed vascular bundles
B. Bicollateral open vascular bundles
C. Collateral open vascular bundles
D. Collateral closed vascular bundles


Movement of snake is helped by
A. Muscles
B. Head
c. Tail
D. Reduced ribs


In a dry cell
A. Chemical energy is converted into heat
B. Electrical energy is converted into electrical energy
C . Chemical energy is converted into electrical energy
D. Chemical energy is constant


Show graphically the given system of equations
\( 2 x+4 y=10 \) and \( 3 x+6 y=12 \) has no
solution.


The diameters of the internal and
external surfaces of a hollow spherical
shell are \( 6 \mathrm{cm} \) and \( 10 \mathrm{cm} \) respectively. If
it is melted and recast into a solid
cylinder of diameter \( 14 c m, \) find the
height of the cylinder.


In a transistor, the base is
A. a conductor of low resistance
B. a conductor of high resistance
C. an insulator
D. an extrinsic semiconductor


Assertion
The mobilities of the alkali metal ions
in aqueous solutions are: \( \boldsymbol{L} \boldsymbol{i}^{+}< \)
\( \boldsymbol{N} \boldsymbol{a}^{+}<\boldsymbol{K}^{+}<\boldsymbol{R} \boldsymbol{b}^{+}<\boldsymbol{C} \boldsymbol{s}^{+} \)
Reason
Greater the charge, smaller the radius, larger the hydration and thus heavier (hydrated) ion slower.
Read the above assertion and reason and
choose the correct statement regarding
it.
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


Glisson's capsules are present in
A . Liver
B. Lung
c. Kidney
D. Stomach


\( \boldsymbol{C H}_{2} \boldsymbol{O H C H O H C H}_{2} \boldsymbol{O H} \) is glycerol.
It doesn't contain
alcoholic group.
A . \( 1^{\circ} \)
B . \( 2^{\text {? }} \)
\( c \cdot 3^{0} \)
D. both \( 1^{0} \& 2^{0} \)


Balance the following equations by ion electron method:
\( \boldsymbol{I}_{2}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)


Europium belongs to:
A. \( s \) -block
B. \( p \) -block
c. \( d \) -block
D. \( f \) -block


In this question, there are four items, three of which are alike by some means while the other one is out of the class.
Identify that element among the
following four.
(1) Mercury
(2) Bromine
(3) Chlorine
(4) Carbon


In the series LCR circuit, the voltmeter
and ammeter readings are respectively.
\( \mathbf{A} \cdot V=250 V, I=4 A \)
B. \( V=150 V, I=2 A \)
C . \( V=1000 V, I=5 A \)
D. \( V=100 V, I=2 A \)


Two plane mirrors are inclined to each
other with their reflecting faces making acute angle. A light ray is incident on one plane mirror. The total deviation
after two successive reflections is
This question has multiple correct options
A. independent of the initial angle of incidence
B. independent of the angle between the mirrors
c. dependent on the initial angle of incidence
D. dependent on the angle between the mirrors


What product(s) is (are) expected during electrolysis of aqueous solution of potassium propanoate? This question has multiple correct options
A. Butane
B. Ethyl ethanoate
c. Ethyl propanoate
D. (снзсо) 0 - о (осснз)


If you go on increasing the stretching force on a wire in a guitar, its frequency
A. Increases
B. Decreases
c. Remains unchanged
D. None of the above


Find the centre and radius of the circle
\( 2 x^{2}+2 y^{2}=3 x-5 y+7 \)


A small disk being pulled by a constant
horizontal force \( F \) on an inclined plane
moves with a constant velocity v as
shown in the figure. The angle of inclination of the plane from the
horizontal is \( \alpha \) and angle between the
velocity vector and the force vector is \( \beta \)
Find the coefficient of kinetic friction
between the disk and the plane.


Which class of protozoa is totally parasitic?
A. Flagellata
B. Sporozoa
c. Rhizopda
D. Ciliate


An electron of mass \( m \) and a photon
have same energy \( E . \) The ratio of de-
Broglie wavelength associated with them is:
\( \stackrel{\mathbf{A}}{_{c}}\left(\frac{E}{2 m}\right)^{\frac{1}{2}} \)
B. \( \quad\left(\frac{E}{2 m}\right)^{\frac{1}{2}} \)
\( c \cdot(2 m E)^{\frac{1}{2}} \)
\( \stackrel{1}{c}\left(\frac{2 m}{E}\right)^{\frac{1}{2}} \)
\( (c \) being velocity of light)


Sum of certain number of terms of the series \( \frac{2}{9},-\frac{1}{3}, \frac{1}{2}, \dots \) is \( \frac{55}{72} . \) Find the
number.


A bullet moving with a uniform velocity stops suddenly after hitting target. Let whole mass melts be \( m \), specific heat
be \( S, \) initial temperature be \( 25^{\circ} C \)
melting point be \( 475^{\circ} C \), and the latent
heat be \( L . \) Then \( v \) is given by


toppr OGII
Q Type your question
\( +y^{\prime}=4 \) where \( x \) and \( y \) are in meters.
wire frame \( A_{1} A_{2} A_{4} A_{3} A_{1} \) is placed in
the magnetic field as shown. Segment \( \mathbf{A} \)
\( A_{2} \) and \( A_{3} A_{4} \) are identical
quarter circles parallel to each other
with axis along z-axis.The induced
current flowing in the wire frame is
equal to : (The total length of the loop of
wire frame is \( 10 \mathrm{m}, \) radius of arc \( \mathrm{A}_{3} \mathrm{A}_{4} \)
and arc \( A_{1} A_{2} \) is \( 1 \mathrm{m} \) each and resistance
per unit length is \( 1 \Omega / m \) ):
\( A \cdot \) zero
В. \( \frac{B_{0} \pi}{10} \)
c. \( \frac{B_{0} \pi}{5} \)
D. \( \frac{B_{0} \pi}{20} \)


\( * \) is said to be commutative in \( \boldsymbol{A} \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{A} \)
A \( . a+b=b+a \)
B. \( a * b=b * a \)
c. \( a-b=b-a \)
\( a \)
D. \( a * b \neq b * a \)


Find the cubes of the following
numbers:
\( \mathbf{3 0 2} \)


If \( r \) be the ratio of the roots of the
equation \( a x^{2}+b x+c=0, \) then \( \frac{(r+1)^{2}}{r}= \)
A \( \cdot \frac{a^{2}}{b c} \)
в. \( \frac{b^{2}}{c a} \)
c. \( \frac{c^{2}}{a b} \)
D. None of these


Which is(are) correct statements about
the role of a catalyst in a reaction?
A. It is reactant in a rate-determining step and then a product of some subsequent step.
B. It provides an alternate mechanism with a lower energy of activation.
C. It increases the rate of chemical reaction but does not
itself undergo a permanent change during the course of the reaction.
D. Enzyme catalysts are protein molecules.
E. All of the above.


The IUPAC name of \( C_{6} H_{5} \) COCl is :
A. Benzoyl chloride
B. Benzene chloro ketone
c. Benzene carbonyl chloride
D. chlorophenyl ketone


Which are true statements among the
following?
(1) \( P H_{5} \) and \( B i C l_{5} \) do not exist
(2) \( p, d \) bonds are present in \( S O_{2} \)
(3) Electrons travel with the speed of
light
(4) \( S e F_{4} \) and \( C H_{4} \) have same shape
(5) \( I_{3}^{+} \) has bent geometry
A \( \cdot 1,3 \)
B. 1,2,5
\( c \cdot 1,3,5 \)
D. 1,2,4


An electric bulb is rated \( 220 \mathrm{V} \) and \( 100 \mathrm{W} \)
When it is operated on 110 V, the power consumed will be :
A . \( 100 \mathrm{w} \)
B. 75w
\( c . \) sow
D. 25W


Adding and constant difference
between the terms is called
A. sequence
B. constant
c. term
D. series


A square planar complex is formed by hybridization of which atomic orbitals?
A \( . s, p_{x}, p_{y}, d_{y z} \)
В. \( s, p_{x}, p_{y}, d_{x^{2}-y^{2}} \)
c. \( s, p_{x}, p_{y}, d_{z^{2}} \)
D. \( s, p_{y}, p_{x}, d_{x y} \)


Which group elements of the modern periodic table were placed along with alkali metals in Mendeleeff table?
\( A \cdot 1 B \)
B. ॥ в
\( c \cdot \| A \)
D. IA


A compound \( X \), of boron reacts with
\( N H_{3} \) on heating to give another
compound \( Y \) which is called inorganic
benzene. The compound \( X \) can be
prepared by treating \( B F_{3} \) with lithium
aluminum hydride. The compounds \( \boldsymbol{X} \)
and \( Y \) are represented by formula:
\( \mathbf{A} \cdot B_{2} H_{6}, B_{3} N_{3} H_{6} \)
в. \( B_{2} O_{3}, B_{3} N_{3} H_{6} \)
c. \( B F_{3}, B_{3} N_{3} H_{6} \)
D. \( B_{3} N_{3} H_{6}, B_{2} H_{6} \)


In which pair second ion is more stable than first?
A. (i) and (ii)
B. (ii) and (iii)
c. (ii) and (iv)
D. (iii) and (iv)


Two long parallel wires are a distance 2 a apart, as shown. Point P is in the plane of the wires and a distance a from wire
X. When there is a current lin wire \( X \)
and no current in wire \( Y \), the magnitude
of the magnetic field at \( P \) is \( B_{0} . \) When
there are equal currents lin the same direction in both wires, the magnitude of the magnetic field at P is?
A. \( \frac{2 B_{0}}{3} \)
в. \( B_{0} \)
c. \( \frac{10 B_{0}}{9} \)
D. \( \frac{4 B}{3} \)


The inductance of a resistanceless coil
is 0.5 henry. In the coil, the value of alternating current is \( 0.2 \mathrm{A} \) whose frequency is 50 Hz. The reactance of circuit is
\( A \cdot 15.7 \Omega \)
в. \( 157 \Omega \)
c. \( 1.57 \Omega \)
D. 757\Omega


The transfer characteristics of a
transistor means a plot of
A. input voltage versus input current
B. output voltage versus output current
c. input voltage versus output voltage
D. input current versus output current


Which allotrogic form of phosphorus
has discrete tetrahedral \( \mathrm{P}_{4} \) Molecule?
How is Phosphine prepared in the laboratory? Give the equation.


Find the sum of place value of last 3
places in the sum of first '10' terms of : 4 \( +44+444+\dots \)


A gas is filled in a container at pressure
\( P_{0} . \) If the mass of molecules is halved
and their rms speed is doubled, then the resultant pressure would be.
\( \mathbf{A} \cdot 2 P_{0} \)
в. \( 4 P_{0} \)
c. \( \frac{P_{0}}{4} \)
D. \( \frac{P_{0}}{2} \)


The bond in semiconductors is :
A. covalent
B. ionic
c. metallic
D. hydrogen


\( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{4}, \mathbf{5}, \mathbf{7}), \boldsymbol{C}= \)
\( (-4,3,-6), D=(2, k, 2) \) are four
points. If the lines \( A B \) and \( C D \) are
parallel, then \( k= \)
\( A \cdot 0 \)
в. -9
\( c .9 \)
D. 2


The expression wherever defined simplifies to
\( \frac{\cos ^{3}\left(\frac{\pi}{2}+x\right) \cot (3 \pi+3) \sec (x-3 \pi) c}{\tan ^{2}(x-\pi) \sin (x-2 \pi)} \)


The equilibrium constant \( \left(\boldsymbol{K}_{c}\right) \) for the
reaction, \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \) at
room temperature \( \boldsymbol{T} \) is \( \boldsymbol{4} \times \mathbf{1 0}^{-4} \). The
value of \( \boldsymbol{K}_{c} \) for \( \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{N}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) \) at the same \( T \) is:
A .0 .02
B . 50
C \( .4 \times 10^{-4} \)
D. \( 2.5 \times 10^{-2} \)


If \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \) such that \( |\vec{a}|=3,|\vec{b}|= \)
\( \mathbf{5} \) and \( |\overrightarrow{\boldsymbol{c}}|=\mathbf{7} \)
What is \( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \) equal to.
A . -83
B. \( \frac{-83}{2} \)
c. 75
D. \( \frac{-75}{2} \)


In a good auditorium the reverberation time is
A. 0.17 v/A
B. \( >0.17 \) V/A
c. \( <0.17 \) V/A
D. none of these


A particle executes SHM on a straight line path. The amplitude of oscillation is \( 2 \mathrm{cm} . \) When the displacement of the
particle from the mean position is \( 1 \mathrm{cm} \) the numerical value of the magnitude of
acceleration is equal to the numerical
value of the magnitude of the velocity.
The frequency of SHM is:
\( A \cdot 2 \pi \sqrt{3} \)
B. \( \frac{2 \pi}{\sqrt{3}} \)
\( c \cdot \frac{\sqrt{3}}{2 \pi} \)
D. \( \frac{1}{2 \pi \sqrt{3}} \)


What is the heat produced by a \( 552 \Omega \) resistance in 5 seconds when
connected to a 3 V battery?


The metabolism of cell decreases
during prophase again increases during which of the following phase?
A. Telophase
B. Anaphase
c. Metaphase
D. Gi phase


A ray of light is incident normally on the first refracting face of the isosceles
prism of refracting angle A. The ray of light comes out at grazing emergence. If one half of the prism (shaded position) is knocked off, the same ray will:
A \( \cdot \) emerge at an angle of emergence \( \sin ^{-1}\left(\frac{1}{2} \sec A / 2\right) \)
B. not emerge out of the prism
C. emerge at an angle of emergence \( \sin ^{-1}\left(\frac{1}{2} \sec A / 4\right) \)
D. None of these


The value of \( (-3)^{0}-(-3)^{3}- \)
\( (-3)^{-1}+(-3)^{4}-(-3)^{-2} \) is
A \( \cdot_{109} \frac{2}{9} \)
в. \( _{109} \frac{9}{2} \)
\( c .109 \)
D. None of these


Which of the bicarbonates does not
exist in solid state?
A. \( N a H C O_{3} \)
в. \( K H C O_{3} \)
c. \( \operatorname{Ca}\left(H C O_{3}\right)_{2} \)
D. \( R b H C O_{3} \)


Rhombic sulphur is .......................... allotropic
form of sulphur.
A. crystalline
B. liquid
c. gaseous
D. Both A and C


A simple pendulum is taken to \( 64 K m \) above the earth's surface. It's time
period will :
A. increase by \( 1 \% \)
B. decrease by 1\%
c. increase by 2\%
D. decrease by 2\%


The phenomenon of converting colloidal solution into suspension is known as:
A. coagulation
B. flocculation
c. Both A and B
D. none of the above


Solve: \( \int \frac{1}{\sqrt{1-e^{2 x}}} d x \)


Copper of fixed volume 'V' is drawn into
wire of length 'I'. When this wire is
subjected to a constant force 'F', the
extension produced in the wire is \( ^{\prime} \Delta l^{\prime} \) Which of the following graph is a straight line?
A \( \cdot \Delta l v s \frac{1}{l} \)
B. \( \Delta l v s l^{2} \)
c. \( \Delta l v s \frac{1}{l^{2}} \)
D. \( \Delta l \) vs \( l \)


If \( \boldsymbol{x}=\boldsymbol{a} \cos \boldsymbol{\theta} ; \boldsymbol{y}=\boldsymbol{b} \sin \theta, \) then find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)


Green house effect is related to
A. Increased growth of green algae
B. Global warming
C. Cultivation of vegetables in houses
D. Development of terrace gardens


In the reaction \( 2 A g+2 H_{2} S O_{4} \rightarrow \)
\( A g_{2} S O_{4}+2 H_{2} O+S O_{2} \) sulphuric acid
acts as:
A. an oxidising agent
B. a reducing agent
c. a catalyst
D. an acid as well as oxidant


Find the area bounded by the curve \( y= \)
\( x^{2}+x+1 \) and tangent to it at (1,3)
from \( \boldsymbol{x}=-\mathbf{1} \) to \( \boldsymbol{x}=\mathbf{1} \)
A \( \cdot \frac{2}{3} \)
в. \( \frac{5}{3} \)
c. \( -\frac{2}{3} \)
D. \( \frac{1}{3} \)


The photograph of a house occupies an
area of \( 1.75 \mathrm{cm}^{2} \) on a \( 35 \mathrm{mm} \) slide. The
slide is projected on to a screen, and the area of the house on the screen is
\( 1.55 m^{2} . \) What is the linear
magnification of the projector-screen
arrangement.


The area of a rectangular park is 3100
\( m^{2} \) and its breadth is 50 m. The value of
4 times Its perimeter is


The energy released (exothermic) or
adsorbed (endothermic) in a chemical
reaction is a result of:
A. loss of energy.
B. gain of energy.
C. energy transfer between atoms and their environment
D. None of the above


A current of 9.95 amperes flowing for 10 minutes, deposits \( 3 g \) of metal. An equivalent weight of the metal is:
A . 12.5
B. 18.5
c. 21.5
D. 48.5


Write chemical reactions to justify that hydrogen peroxide can function as an oxidising as well as reducing agent


Due to \( \gamma \) decay, what is the effect on
neutron and proton numbers?
A. Both remains constant
B. Proton number increase but neutron number decreases
c. Proton number decreases and neutron increases
D. None of these


The base pairs of DNA are correctly shown as
\( A \cdot A \equiv T \) and \( C=G \)
\( B \cdot A=T \) and \( C=G \)
c. \( A=T \) and \( C \equiv G \)
D. \( A \equiv T \) and \( C \equiv G \)


According to Maxwell's hypothesis, a changing electric field gives rise to
A. an electromagnetic force
B. electric displacement current
c. magnetic field
D. pressure gradient


A carnot engine works as a refrigerator
in between \( 250 \mathrm{K} \) and \( 300 \mathrm{K} \). If it
acquires 750 calories from heat source
at low temperature, then what is the
heat generated at higher temperature. (in calories)?


Calculate the moment of inertia of a
ring having mass \( M, \) radius \( R \) and
having uniform mass distribution
about an axis passing through the centre of the ring and perpendicular to
the plane of the ring
(mass elements


Total energy of an electron in an atom is
A. less than zero
B. more than zero
c. may be less or more than zero
D. none of the above


Consider the reaction \( : 2 C O(g)+ \)
\( O_{2}(g) \rightleftharpoons 2 C O_{2}(g)+H e a t \)
Under what conditions shift is
undeterminable?

This question has multiple correct options
A. addition of \( O_{2} \) and decrease in volume
B. Addition of \( C O \) and removal of \( C O_{2} \) at constant volume
c. Increase in temperature and decrease in volume.
D. Addition of \( C O \) and increase in temperature at constant volume


When a body slides down from an inclined plane, Work is said to be done because of gravity. State whether given statement is True/
False?
A. True
B. False


For what value of \( x, \) is the matrix \( A= \)
\( \left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & -\mathbf{2} \\ -\mathbf{1} & \mathbf{0} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{- 3} & \mathbf{0}\end{array}\right] \) a skew-symmetric
matrix?


Avogadro's number is NOT equal to:
A. the number of atoms in 11.2 L of \( O_{2} \) at STP
B. the number of atoms in 1 mole of \( H e \) at STP
C. the number of electrons in 96,500 coulombs
D. the number of \( S O_{4}^{2-} \) ions in 1 L of 0.5 M sulphuric acid


Meiosis takes place in
A. Meiocyte
B. conidia
c. Gemmule
D. Megaspore


Find the inclination of the line \( ( \) in degrees ) whose slope is \( \frac{\mathbf{1}}{\sqrt{\mathbf{3}}} \)


Sweat is reddish in
A. Hippopotamus
B. Elephant
C. Rhino
D. Musk deer


If \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
then find a unit vector along \( (\vec{A}-\vec{B}) \)


Identify the factor that distinguishes each element from every other element in the periodic table ?
A. The number of protons in the nucleus
B. The number of neutrons in the nucleus
c. The number of electrons about the nucleus
D. The total mass of the nucleus (protons plus neutrons)
E. Its position in the periodic table


Who proposed cAMP mediated 'Cascade model' of enzyme regulation?
A. Fischer
B. Sutherland
c. Sumner
D. Koshland


\( \int x \sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}} d x \) is equal to
A \( \cdot \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+C \)
B \( \cdot \frac{a^{2}}{2} \tan ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+C \)
C \( \cdot \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{3}{2} \sqrt{a^{2}-x^{2}}+C \)
D \( \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{2}-x^{2}}+C \)


Find the area of the region \( \{(x, y) \)
\( \left.\boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{2}\right\} \)
\( \mathbf{A} \cdot \pi-2 \)
B. \( \pi-1 \)
c. \( 2 \pi-2 \)
D. \( 4 \pi-2 \)


Nitrogen (I) oxide is produced by:
A. Thermal decomposition of Ammonium Nitrate
B. Decomposition of \( N O_{2} \)
C. By the decomposition \( N a N O_{2} \)
D. By the interaction of Hydroxyl amine and Nitrous acid


\( \boldsymbol{I}=\int \log [\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}] \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot x \log [x+\sqrt{x^{2}+a^{2}}]-\sqrt{x^{2}+a^{2}} \)
B \( \cdot x \log [x+\sqrt{x^{2}+a^{2}}]+x^{2}+a^{2} \)
C \( x \log [x+\sqrt{x^{2}+a^{2}}]+\sqrt{x^{2}+a^{2}} \)
D. \( x \log [x+\sqrt{x^{2}+a^{2}}]-x^{2}+a^{2} \)


A particle of mass \( \mathrm{M} \) is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the
centre will be :
\( A \cdot \frac{G M}{a} \)
B. \( \frac{2 G M}{a} \)
\( \mathrm{c} \cdot \frac{3 G M}{a} \)
D. \( \frac{4 G M}{a} \)


On heating, lead nitrate forms oxides of nitrogen and lead. The oxides formed
are
A. \( N_{2} O, P b O \)
в. \( N O_{2}, P b O \)
c. \( N O, P b O \)
D. \( N O, P b O_{2} \)


What is name of the compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{O H} ? \)
A. 2-methylbutanol
B. 3-methylbutanol
c. 2-methylpentanol
D. Pentanol


Which of the following is known as invert soap?
A. Pentaeryth ritol monostearate
B. Sodium stearyl sulphate
c. Trimethlsteary ammonium bromide
D. Ethoxylated nonyphenol


The quantity of \( A \) and \( B \) in one day for which profit will be maximum is:
A .25,30
B. 30,25
c. 25,25
D. 30,30


The current gain of a transistor in a
Common base arrangement is \( 0.98 . \) The Change in collector current
corresponding to a change of \( 5 m A \) in emitter current is :
\( \mathbf{A} \cdot 0.1 m A \)
B. \( 0.2 m A \)
c. \( 4.9 m A \)
D. \( 9.2 m A \)


Which one of the following pairs is
mismatched?
A. Fossil fuel burning - release of \( C O_{2} \)
B. Nuclear power - radioactive wastes
C. Solar energy - Greenhouse effect
D. Biomass burning - release of \( C O_{2} \)


Match the list -I with list - II.
List-
List - II
A) Hess law is not applicable for
1) is not a state function
B) All combustion reactions are
2) Heat of dilution
C) Work
3) Exothermic
D) Difference between two integral
4) Nuclear reaction
heats of solutions
A . A-1, B-2, C-3, D-4
B. A-4, B-3, C-1, D-2
c. \( A-3, B-2, C-4, D-1 \)
D. A-2, B-1, C-4, D-3


In solid state, Boric acid has which type of interaction between layers?
A. Hydrogen bonding
B. Van der Walls' force
c. covalent bond
D. None of these


The level of water in a tank is \( 5 \mathrm{m} \) high.
hole of area of cross section \( 1 \mathrm{cm}^{2} \) is
made at the bottom of the tank. The rate
of leakage of water from the hole in \( \boldsymbol{m}^{3} \boldsymbol{s}^{-1} \) is \( \left(\boldsymbol{g}=10 \mathrm{ms}^{-2}\right) \)
A \( \cdot 10^{-3} \)
B . \( 10^{-4} \)
c. 10
D. \( 10^{-2} \)


Solved:
\( \sqrt[3]{64} \)


Mention practical importance of Zener
diode in a laboratory.


Buffer solution is prepared by mixing:
A. Strong acid + its salt of strong base
B. Weak acid + its salt of strong base.
c. Strong acid + its salt of weak base
D. None of the above


The amplitude of a damped oscillator decreases to 0.9 times its original
magnitude is \( 5 s . \) In another \( 10 s \) it will
decrease to \( \alpha \) times its original
magnitude, where \( \alpha \) equals.
A . 0.81
B. 0.729
c. 0.6
D. 0.7


Iron is extracted from iron oxide using
carbon monoxide as shown.
iron oxide \( + \) carbon monoxide \( \rightarrow \) iron \( + \)
carbon dioxide
Which statement is correct?
A. Carbon monoxide is oxidised to carbon dioxide
B. Carbon monoxide is reduced to carbon dioxide
C. Iron is oxidised to iron oxide
D. Iron oxide is oxidised to iron


There exist two triangles such that there five parts ( i.e. three angles and two sides) are congruent to each other but yet the triangles are not congruent?
A . True
B. False


Homologous have the same:
A. empirical formulae
B. molecular formulae
C . chemical properties
D. physical properties


Evaluate the following definite integral.
\( \int_{2}^{3} \frac{x}{x^{2}+1} d x \)


In nomenclature
A. Both genus and species are printed italics
B. Genus and species are always of the same name
C. Both in genus and species the first letter is capital
D. Genus is written after the species


A cylindrical tube of radius \( 12 \mathrm{cm} \)
contains water upto a depth of \( 20 \mathrm{cm} . \) A spherical iron ball is dropped into the tube and thus the level of water is
raised by \( 6.75 \mathrm{cm} . \) The radius of the ball
is
A . \( 4.5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .7 .25 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


The technique by which "Dolly" the sheep obtained is termed as
A. Cloning by zygote transfer
B. Cloning by nuclear transfer
c. Cloning without the help of gametes
D. Cloning by tissue culture of somatic cells


If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{-3} \) then \( \boldsymbol{y}= \)
A \( \cdot \frac{-1}{2 x^{2}}+c \)
B \( \cdot \frac{-x^{-4}}{4}+c \)
c. \( \frac{2}{x^{2}}+c \)
D. \( \frac{x^{-2}}{2}+c \)


The resistivity of a wire varies with
A . length
B. cross-section
c. mass
D. material


if \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \mathbf{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right|=\mathbf{0} \) then
A. \( a \) is a cube root of 1
B. \( b \) is a cube root of 1
c. \( \frac{a}{b} \) is a cube root of 1
D. \( \frac{a}{b} \) is a cube root of -1


Directions ratio of two lines are \( 3,-2, k \)
and \( -2, k, 4 . \) Find \( k \) if the lines are perpendicular to each other.


The displacement-time graph of a moving particle is shown.The
instantaneous velocity of the particle is
negative at the point :-
\( A \)
B.
\( c \cdot c \)
\( D \)


A planet of mass \( M \) has uniform
density in a spherical volume of radius
\( R \) Calculate the work done by the
external agent to de-assemble the planet in eight identical spherical part against gravitational pull amongst its constitute particle.


If \( a, b, c \in+R \) such that \( \lambda a b c \) is the
minimum value of \( a\left(b^{2}+c^{2}\right)+b\left(c^{2}+\right. \)
\( \left.a^{2}\right)+c\left(a^{2}+b^{2}\right), \) then \( \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D. None of the above


Which of the following does not obey 18 electron rule?
\( \mathbf{A} \cdot C r(C O)_{6} \)
в. \( F e(C O)_{5} \)
c. \( V(C O)_{6} \)
D. \( M n_{2}(C O)_{10} \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin \{[\boldsymbol{x}+\mathbf{5}]+\{\boldsymbol{x}-\{\boldsymbol{x}-\{\boldsymbol{x}\}\}\}\} \) for
\( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{4}}\right) \) is invertible, where \( \{.\} \)
and [.] represent fractional part and greatest integer functions respectively,
then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) is
This question has multiple correct options
\( \mathbf{A} \cdot \sin ^{-1} x \)
в. \( \frac{\pi}{2}-\cos ^{-1} x \)
\( c \cdot \sin ^{-1}\{x\} \)
D \( \cdot \cos ^{-1}\{x\} \)


It is warmer to have two thin blankets
than to have single thick blanket
because:
A. Thick blankets cannot give more warmth
B. Two blankets allow more heat to pass through them
c. Air between the two blankets is a good conductor of heat
D. Air between the thin blankets does not allow heat to pass through it since it is a bad conductor


A machine gun fires a bullet of mass \( 65 g \) with a velocity of \( 1300 m / s \). The man holding it can exert a maximum
force of \( 169 N \) on the gun. The number of
bullets he can fire per second will be
A . 1
B. 2
\( c .3 \)
D. 4


Which of the following bond is formed during the condensation of
monosaccharides?
A. Covalent bond
B. Glycosidic bond
c. Peptide bond
D. lonic bond


Complementary cells of lenticels develop from
A. Phellem
B. Phelloderm
c. Endodermis
D. Phellogen


Why do we need to classify drugs in
different ways?


The rate equation for the hydrolysis of an ester in the presence of \( N a O H \) is given as, \( r a t e=k[\text { ester }][N a O H] . \) If the
concentration of \( N a O H \) is increased
by 100 times than that of ester, the order of the reaction will be:
A.
B. 2
\( c \cdot 0 \)
D. 3


Number of cytochrome molecules
required for the transfer of \( 2 e^{-} \) in ETS is
A. 2
B. 4
\( c \cdot 1 \)
D. 10


The circuit given below represents which of the logical operations?
\( A \cdot A N D \)
в. NOT
\( c . \) ов
D. NOR


The equation of line perpendicular to \( \boldsymbol{x}=\boldsymbol{c} \) is
\( \mathbf{A} \cdot y=d \)
B. \( x=d \)
c. \( x=0 \)
D. None of these


Show that the equations to the straight
lines passing through the point (3,-2) and inclined at \( 60^{\circ} \) to the line \( \sqrt{3} x+ \) \( \boldsymbol{y}=1 \) are \( \boldsymbol{y}+\boldsymbol{2}=\boldsymbol{0} \) and \( \boldsymbol{y}-\sqrt{\mathbf{3}} \boldsymbol{x}+ \)
\( \mathbf{2}+\mathbf{3} \sqrt{\mathbf{3}}=\mathbf{0} \)


Metal M and chlorine combine in
different proportions to form two
compounds \( A \) and \( B \). The mass ratio \( M: \) Cl is 0.895: 1 in \( A \) and 1.791: 1 in \( B . \) What
law of chemical combination is
¡Ilustrated?


Rank the order of the magnitude of the momenta of the four objects pictured below, greatest first.
Masses are shown inside the
boundaries of the objects. Velocities are shown with the red arrows with the corresponding values.
A. Blue and yellow tie, green and purple and orange tie
B. Purple and orange tie, blue, yellow, green
c. Blue, purple and orange tie, green, yellow
D. Green and purple tie, orange, blue and yellow tie
E. Green, purple, and orange tie, blue and yellow tie


Let \( S_{1}, S_{2}, S_{3}, \dots \) be squares such that
for each \( n \geq 1 ; \) the length of a side of \( S_{n} \)
equals the length of a diagonal of \( S_{n+1} \)
If the length of a side of \( S_{1} \) is \( 10 \mathrm{cm} \) then for which of the following values of
\( n \) is the area of \( S_{n} \) less than 1 sq.cm? This question has multiple correct options
\( A \cdot 7 \)
B. 8
c. 9
D. 10


Sugar is
A. an element
B. a mixture
C . a compound
D. none of the above


A ball starts rolling on a horizontal surface with an initial velocity of \( 1 \mathrm{m} / \mathrm{s} \) Due to friction, its velocity decreases at the rate of \( 0.1 m / s^{2}, \) How much time will it take for the ball to stop?
A . \( 1 \mathrm{s} \)
B. 100 s
\( c \cdot 10 s \)
D. 0.1 s


The atom of largest size is:
A .
B. At
\( c \)
D. Be


A 4 kg mass is resting on a horizontal
surface. for this surface \( \mu_{8}=0.6 \) and \( \mu_{k}= \)
0.2. force required to move the body with \( 5 m s^{-2} \) acceleration is \( \left(g=10 m s^{-2}\right) \)
A. 20
B. 24 N
\( c .25 \mathrm{N} \)
D. 32 N


Let \( A \) and \( B \) be independent events with \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})=0.5 . \) Then find:
(i) \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}) \)
(ii) \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A}) \)
\( (\text { iii) } \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
(iv) \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


The substance added to chloroform as
a preservative is:
A. \( C O C l_{2} \)
в. \( A g N O_{3} \)
\( \mathbf{c} \cdot C_{2} H_{5} O H \)
D. \( \left(C_{2} H_{5}\right)_{2} C O_{3} \)


Clitellum of Pheretima is thick girdle
that is
A. Nonglandular around \( 14^{t h}-16^{t h} \) segments
B. Glandular around \( 14^{t h}-16^{t h} \) segments
C. Glandular around \( 16^{t h}-18^{t h} \) segments
D. Nonglandular around 16 \( ^{t h}-18^{t h} \) segnments


Select correct combination of
statements for Lymph.
(i) It helps to maintain fluid balance of the body.
(ii) It is contained in Iymphatic vessels and lymphatic organs in mammals.
(iii) It is derived from tissue fluid.
(iv) It contains less antibodies than
plasma.
(v) It flows in both directions.
(vi) It helps to conserve proteins and remove bacteria.
A. i, ii, iii, v
B. ii, iii, iv, vi
c. i, iv, v, vi
D. iii, iv, v, vi


\( \lim _{x \rightarrow 1} \frac{\sqrt{1-\cos 2(x-1)}}{x-1} \)
A. exists and it equals \( \sqrt{2} \)
B. exists and it equals \( -\sqrt{2} \)
c. does not exist because \( x-1 \rightarrow 0 \)
D. does not exist because left hand limit is not equal to right hand linitt


The real values of \( a \) for which the
quadratic equation \( 2 x^{2}-\left(a^{3}+8 a-\right. \)
1) \( x+a^{2}-4 a=0 \) possesses roots of opposite signs are given by :
\( \mathbf{A} \cdot a>6 \)
B . \( a>9 \)
c. \( 0<a<4 \)
D. \( a<0 \)


An example of secondary battery cell is:
A. Edison Alkaline cell
B. Daniel cell.
c. Lachanche cell.
D. Bunsen cell.


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1 0} & \mathbf{0} \\ \mathbf{4} & \mathbf{1 0}\end{array}\right], \) then find \( |\boldsymbol{A}| \)


If the magnitude of intensity of electric
field at a distance \( x \) on axial line and at
a distance \( y \) on equational line on a given dipole are equal, then \( x: y \) is ?


Fog is a colloidal solution of:
A. liquid particles dispersed in a gas
B. gaseous particles dispersed in a liquid
C. solid particles dispersed in a liquid
D. solid particles dispersed in a gas


The development of offspring from any part of the body is called-
A. Asexual reproduction.
B. Sexual reproduction.
c. vegetative reproduction
D. All the above


A ball is dropped from height hon the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is :
A \( \cdot \frac{h}{e^{2 n}} \)
B. \( \frac{e^{2 n}}{h} \)
\( c \cdot h e^{2 n} \)
D. \( h e^{n} \)


Write the name of monomer unit of
polymer used in non-stick surface
coated utensils.


Evaluate the following limits. \( \lim _{x \rightarrow 2}\left(\frac{1}{x-2}-\frac{4}{x^{3}-2 x^{2}}\right) \)


Magnetic lines of force are:
A. continuous
B. discontinuous
c. some times continuous and some times discontinuous
D. nothing can be said


Discharge of centrifugal pump is
A. inversely proportional to diameter of its impeller
B. inversely proportional to diameter \( ^{2} \) of its impeller
C. directly proportional to (diameter)2 of its impeller
D. directly proportional to diameter of its impeller


Let 'n' Arithmetic Means and 'n'
Harmonic Means are inserted between
two positive number'a' and 'b'. If sum of all Arithmetic Means is equal to sum of
reciprocal all Harmonic means, then product of number is
\( A \)
B. 2
\( c \cdot \frac{1}{2} \)
D. 3


Two point masses, m each carrying charges - \( q \) and \( +q \) are attached to the ends of a massless rigid non-
conducting wire of length 'L'. When this
arrangement is placed in a uniform electric field, then it deflects through an
angle \( \theta . \) The minimum time needed by
rod to align itself along the field is:
A \( \cdot 2 \pi \sqrt{\frac{m L}{q E}} \)
В. \( \frac{\pi}{2} \sqrt{\frac{m L}{2 q E}} \)
\( ^{\mathbf{C}} \cdot \pi \sqrt{\frac{2 m L}{q E}} \)
D \( \cdot 2 \pi \sqrt{\frac{3 m L}{q E}} \)


In the arrangement shown in figure
above, a weight \( A \) possesses mass \( m \), a
pulley \( B \) possesses mass \( M \). Also
known are the moment of inertia \( I \) of
the pulley relative to its axis and the
radii of the pulley \( R \) and \( 2 R \) The mass
of the threads is negligible. If the acceleration of the weight \( \boldsymbol{A} \) after the
system is set free is \( \boldsymbol{w}= \)
find the value of \( b \)


In an intrinsic semiconductor, the
density of conduction electrons is \( \mathbf{7 . 0 7} \times \mathbf{1 0}^{\mathbf{1 5}} \mathbf{m}^{-3} . \) When it is doped with
indium, the density of holes becomes \( 5 \times 10^{22} m^{-3} . \) Find the density of
conduction electrons in doped
semiconductor
A. \( Z \) ero
В. \( 1 \times 10^{9} m^{-3} \)
c. \( 7 \times 10^{15} m^{-3} \)
D. \( 5 \times 10^{22} m^{-3} \)


Assertio
A block of mass \( m \) starts moving on a
rough horizontal surface with a velocity
\( v . \) It stops due to friction between the
block and the surface after moving through a certain distance. The surface
is now tilted to an angle of \( 30^{\circ} \) with the horizontal and the same block is made
to go up on the surface with the same
initial velocity \( v \). The decrease in the
mechanical energy in the second situation is smaller than that in the
first situation.
Reason
The coefficient of friction between the
block and the surface decreases with
the increase in the angle of inclination.
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 will be the prefix in the following compound? HOOC \( -\boldsymbol{C H}_{2} \)
\( \boldsymbol{H O O C}-\boldsymbol{C H}-\boldsymbol{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C O O H} \)
A. methycarboxy
B. carboxymethyl
c. carboxyethyl
D. ethylcarboxy


In the coordinate plane, a circle has center (2,-3) and passes through the point \( (5,0), \) What is the area of the circle?
\( A \cdot 3 \pi \)
B. \( 3 \sqrt{2} \pi \)
c. \( 3 \sqrt{3} \pi \)
D. \( 9 \pi \)
E . \( 18 \pi \)


What are antibiotics? Give two
examples.


When a wave travels from one medium
to another, the quantity which will not change is its
A. Amplitude
B. Velocity
c. Frequency
D. Intensity


Eliminating \( a, b, c \) from \( x=\frac{a}{b-c}, y= \)
\( \frac{b}{c-a}, z=\frac{c}{a-b} \) we get
\( \mathbf{A} \cdot\left|\begin{array}{lll}1 & -x & x \\ 1 & -y & y \\ 1 & -z & z\end{array}\right|=0 \)
B. \( \left|\begin{array}{ccc}1 & -x & x \\ 1 & 1 & -y \\ 1 & z & 1\end{array}\right|=0 \)
c. \( \left|\begin{array}{ccc}1 & -x & x \\ y & 1 & -y \\ -z & z & 1\end{array}\right|=0 \)
D. none of these


The reactivity of \( \mathrm{Cu}, \mathrm{Ag} \) and \( \mathrm{Au} \) decreases in the order:
A. \( C u>A g>A u \)
в. \( A u>A g>C u \)
c. \( A g>A u>C u \)
D. \( A g>C u>A u \)


A progressive wave of frequency \( 500 H z \) is travelling with a speed of \( 330 m / s \) in air. The distance between the two points which have a phase
difference of \( 30^{\circ} \) is:
A . \( 0.11 m \)
в. 0.055 т
c. \( 0.22 m \)
D. 0.025 m


For a reaction \( : A+B \rightarrow \) Products, the
rate of the reaction at various
concentrations are given below:
Expt
[А] \( \quad \) [В] rate (mol Io \( \left.d m^{-3} s^{-1}\right) \)
\( \begin{array}{lll}\text { 0.2 } & \text { 0.2 } & \text { 2. }\end{array} \)
\( 0.2 \quad 0.4 \)
\( \begin{array}{ll}0.4 & 36\end{array} \)
The rate law for the above reaction is :
A \( \cdot r=K[A]^{2}[B] \)
B . \( r=K[A][B]^{2} \)
c . \( r=K[A]^{3}[B] \)
D . \( r=K[A]^{2}[B]^{2} \)


If the points \( (0,1,-2),(3, \lambda,-1) \) and \( (\mu,-3,-4) \) are collinear, the point on the same line is
в. (1,-1,-2)
c. (5,-3,4)
D. (0,0,0)


Find the direction angles of vector \( -8 \hat{i}+3 \hat{j}+2 \hat{k} \)
A \( \cdot 156^{\circ}, 70^{\circ}, 77^{\circ} \)
В. \( 155^{\circ}, 72^{\circ}, 80^{\circ} \)
c. \( 145^{\circ}, 83^{\circ}, 74^{\circ} \)
D. \( 150^{\circ}, 76^{\circ}, 83^{\circ} \)


Which nitrogen trihalide is least basic?
A . \( N F_{3} \)
в. \( N C l_{3} \)
c. \( N B r_{3} \)
D. \( N I_{3} \)


Choose the correct answer from the
alternatives givens. Which of the following tissues has closely linked cells and one free
surface?
A. Epithelial
B. Connective
c. Nervous
D. Muscle


The equation of tangent at those points where the curve \( y=x^{2}-3 x+2 \) meets
\( x \) -axis are
A. \( x-y+2=0, x-y-1=0 \)
в. \( x+y-1=0, x-y-2=0 \)
c. \( x-y-1=0, x-y=0 \)
D. \( x-y=0, x+y=0 \)


Two plates are placed at a separation of \( 2 \mathrm{cm} . \) An electron placed at the perryferry of one plate reaches the second plate in 2 microsecond. Calculate the inner charge density of the surface assuming the case of infinite plate.
A . \( 0.505 \times 10^{-12} \mathrm{Cm}^{-2} \)
В. \( 0.15 \times 10^{-12} \mathrm{Cm}^{-2} \)
c. \( 1.01 \times 10^{-12} \mathrm{Cm}^{-2} \)
D. \( 0.505 \times 10^{-11} \mathrm{Cm}^{-2} \)


Assertion (A): The roots of \( (x-a)(x- \)
\( b)+(x-b)(x-c)+(x-c)(x-a)= \)
0 are real
Reason (R): A quadratic equation with non-negative discriminant has real
roots
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of \( (A) \)
\( c \cdot(A) \) is true but (R) is false
D. (A) is false but (R) is true


Seven spheres of equal radii are made by melting a silver-cuboid of
dimensions \( 8 \mathrm{cm} \times \times 11 \mathrm{cm} \times 9 \mathrm{cm} . \) Find
the radius of a silver sphere (in \( \mathrm{cm} \) ).


\( (p \wedge \sim q) \wedge(\sim p \wedge q) \) is a:
A. A tautology
B. A contradiction
C. Both a tautology and a contradiction
D. Neither a tautology nor a contradiction


Where is bile produced? Which component of the food does it help to
digest?


Most advanced gymnosperm belongs to
A . Cycadales
B. Coniferales
c. Gnetales
D. cycadofillicales


A solenoid is \( 2.0 \mathrm{m} \) long and \( 3.0 \mathrm{cm} \) in diameter. It has 5 layers of winding of 1000 turns each and carries a current of
5.0 A. What is the magnetic field at its centre?
A \( \cdot 1.5 \times 10^{-3} T \)
в. \( 1.5 \times 10^{-2} T \)
c. \( 1.5 \times 10^{-4} T \)
D. \( 2.5 \times 10^{-2} T \)


The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic
field change, is
A \( \cdot \frac{B R}{4} \)
в. \( \frac{B R}{2} \)
c. \( B R \)
D. \( 2 B R \)


A boat full of rocks is at rest, if some
rocks are thrown out from it towards left.
What would happen to the boat?
A. Boat will not move
B. Boat will also move towards left
C. Boat will move towards right
D. Cant say


Select the correct statement -
A. When ATP is synthesised directly from metabolites, it is substrate level phosphorylation.
B. In Krebs' cycle, citrate undergoes 2 decarboxylations and 4 dehydrogenations.
C. Krebs' cycle is an amphibolic process
D. All of these


When do we say sound travels in a medium?
A. When the medium travels.
B. When the particles of the medium travel.
c. When the source travels
D. When the disturbance travels


\( \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\left(\boldsymbol{a}^{2}+\boldsymbol{a}-\boldsymbol{6}\right)=\mathbf{0} \)


State Newland's law of octaves.


The material suitable for making electromagnets should have
A. High retentivity and high coercivity
B. Low retentivity and low coercivity
c. High retentivity and low coercivity
D. Low retentivity and high coercivity


The value of \( \lim _{n \rightarrow \infty} \Sigma_{1}^{n} \cos \left(\frac{\pi}{2}+\frac{\pi i}{2 n}\right) \frac{\pi}{2 n}=? \)
A \( \cdot \int_{\frac{\pi}{2}}^{\pi} \cos x \)
B. \( \int_{\frac{\pi}{2}}^{\pi} \cos x \)
\( ^{\mathrm{c}} \cdot \int_{\frac{\pi}{2}}^{2 \pi} \cos x \)
D. \( \int_{\frac{\pi}{2}}^{5 \pi} \cos x \)


In a physical balance working on the principle of moments, when \( 5 \mathrm{mg} \) weight is placed on the left plan, the beam becomes horizontal. Both the
empty pans of the balance are of equal mass. Which of the following statements is correct?
A. Both the arms are of same length.
B. Every object that is weighed using this balance appears lighter than its actual weight
c. Left arm is longer than the right arm.
D. Left arm is shorter than the right arm.


Which of the following statements
is/are true?
This question has multiple correct options
A. It is impossible to satisfy the octet rule for all atoms in \( X e F_{2} \)
B. \( M g S O_{4} \) is soluble in water because hydration energy of \( M g S O_{4} \) is higher in comparison to its lattice energy.
C. The bond in \( N O^{+} \) should be stronger than the bond in
\( N O^{-} \)
D. For ozone molecule, one oxygen-oxygen bond is stronger than the other oxygen-oxygen bond.


Diaspore, germanite and gallite have:
A. boron
B. aluminium
c. gallium
D. indium


Differentiate the following w.r.t. \( x \)
\( \log \left(\cos e^{x}\right) \)


A square matrix A has 9 elements. What is the possible order of \( A ? \)
\( \mathbf{A} \cdot 1 \times 9 \)
B. \( 9 \times 9 \)
c. \( 3 \times 3 \)
D. \( 2 \times 7 \)


According to the ideal gas law, what is the approximate volume that will be occupied by 0.5 mole of an ideal gas at
\( 30^{\circ} \mathrm{C} \) and 3 atm pressure (gas constant \( \boldsymbol{R}=\mathbf{0 . 0 8 2 1} \boldsymbol{L} . \boldsymbol{a t m} /(\boldsymbol{m o l . K})) ? \)
A. Less than 1 L
в. 5 L
\( c .10 L \)
D. 15 L


Which of the following represents the
best reagent(s) for the electrophilic
nitration of benzene?
A \( \cdot N O_{2} \)
B. \( H N O_{2} \)
\( c \cdot H N O_{3} \)
D. \( H_{2} S O_{4} / H N O_{3} \)


No matter how far you stand from a mirror, your image always appears erect. The mirror is likely to be:
A. Plane
B. Concave
c. Both A and B
D. None


If \( a=1 \) and \( r=\frac{2}{3}, \) find \( (a) T_{n} \) (b) \( T_{4} \)


If a half cell \( \boldsymbol{X} \mid \boldsymbol{X}^{2+}(\mathbf{0 . 1} \boldsymbol{M}) \)
is connected to another half cell
\( \boldsymbol{Y} \mid \boldsymbol{Y}^{2+}(\mathbf{1} . \mathbf{0} \boldsymbol{M}) \) by means of \( \mathbf{a} \)
salt bridge and an external circuit at
\( 25^{\circ} C, \) the cell voltage would be:
\( \mathbf{A} \cdot 0.06 V \)
B. \( 0.12 V \)
c. \( 0.62 V \)
D. \( 0.72 V \)


An organic liquid vaporizes at a temperature its boiling point in steam distillation.
A. above
B. below
c. equal to
D. none of the above


Which of the following corresponds to longest wavelength electronic transition?
A. \( n=3 \) to \( n=1 \)
B. \( n=3 \) to \( n=2 \)
c. \( n=4 \) to \( n=1 \)
D. \( n=4 \) to \( n=2 \)


What will be the frequency of an alternating current, if its direction changes after every 0.05 s?
A. \( 5 \mathrm{Hz} \)
в. 10нz
\( c \cdot 50 H z \)
D. онz