An ebonite rod rubbed with fur and a
glass rod rubbed with silk cloth are brought nearer to each other. Then :
A. They will attract each other
B. They will repel each other
C. Nothing will happen to them
D. They will get heated up


Let \( f(x) \) be a real -valued function such that \( f(0)=\frac{1}{2} \) and \( f(x+y)= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \forall \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
then for some real \( a \)
This question has multiple correct options
A. \( f(x) \) is a periodic function
B. \( f(x) \) is a constant function
c. \( f(x)=\frac{1}{2} \)
D. \( f(x)=\frac{\cos x}{2} \)


Which is an example of direct
proportion?
A. More working hours, more earning
B. More speed of car, less time taken
C. More no. of workers, less time taken
D. Less the age of person, more active he is


How many 4 digits numbers can due formed by using the digits 1,2,3,4,5,6,7 if at least one digit is repeated.


The most important center of lymph
formation is
A. Liver
B. Spleen
c. Bone marrow
D. Mucosa of ileum


No current flows between two charged bodies connected together when they have the same:
A. Charge
B. Potential
c. capacitance
D. Resistance


A spherical solid ball of volume \( V \) is
made of a material of density \( \rho_{1} \). It is
falling through a liquid of density
\( \rho_{2}\left(\rho_{2}<\rho_{1}\right) . \) Assume that the liquid
applies a viscous force on the ball
that is proportional to the square of its
speed \( v, \) i.e., \( F_{v i s c o u s}=k v^{2}(k>0) . \) The
terminal speed of the ball is:
A \( \cdot \sqrt{\frac{V g \rho_{1}}{k}} \)
в. \( \frac{V g\left(\rho_{1}-\rho_{2}\right)}{k} \)
c. \( \sqrt{\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}} \)
D. \( \frac{V g \rho_{1}}{k} \)


Find the diameter of a circle whose
circumference is \( 15.7 \mathrm{cm}- \)
A. \( 5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. 4.5 cm


On which one of the factors does the
nature of the thermal radiation depend inside an enclosure?
This question has multiple correct options
A. size of the enclosure
B. temperature
c. nature of the walls
D. color of the walls


Pick up the correct statement about
alkyl halide.
A. They show H-bonding
B. They are soluble in water
C. They are soluble in organic solvents
D. They do not contain any polar bond.


A weak acid HA after treatment with 12
mL of 0.1 M strong base has a pH of \( 5 . \) At the end point, the volume of same base
required is \( 26.6 \mathrm{mL} \). The value of \( K_{a} \) is:
A \( .8 .2 \times 10^{-6} \)
B . \( 6.4 \times 10^{-6} \)
\( \mathbf{c} \cdot 5.3 \times 10^{-5} \)
D. \( 2.4 \times 10^{-6} \)


A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then.
A. compressing the gas isothermally will require more work to be done
B. compressing the gas through adiabatic process will require more work to be done
c. compressing the gas isothermally or adiabatically will require the same amount of work
D. which of the case(whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas


Select the correct order of
electronegativity:
A \( . F>C l>B r>I \)
B. \( N>P>A s \)
\( c . \) both (a) and (b)
\( D S>O>S e \)


Assertion
To overcome electrostatic force of
attraction between electrons and
nucleus, they revolve around the
nucleus
Reason
Mass of the atom is almost due to its
nucleus
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A particle is acted upon by a force whose component's variations with time are shown in diagrams. Then the magnitude of change in momentum
of the particle in 0.1 sec will be
\( ^{\mathbf{A}} \cdot 2 K g \frac{m}{S e c} \)
В. \( 10 \mathrm{Kg} \frac{\mathrm{m}}{\mathrm{Sec}} \)
\( \mathrm{c} \cdot_{12 \mathrm{Kg}} \frac{\mathrm{m}}{\mathrm{Sec}} \)
D. \( 5 \sqrt{2} \mathrm{Kg} \frac{\mathrm{m}}{\mathrm{sec}} \)


The migration of colloidal particles under the influence of an electrical field
is known as:
A. electro-osmosis
B. electrophoresis
c. electrodialysis
D. none


(Allocation problem) A cooperative
society of farmers has 50 hectare of
land to grow two crops \( X \) and \( Y . \) The
profit from crops \( X \) and \( Y \) per hectare
are estimated at \( R s .10,500 \) and

Rs.9, 000 respectively. To control weeds, a liquid herbicide has to be used for
\( \operatorname{crop} s X \) and \( Y \) at rates of 20 litres and
10 litres per hectare. Further, no more than 800 litres of herbicide should be
used in order to protect fish and wildlife using a pond which collects drainage from this land. How much land should
be allocated to each crop so as to maximise the total profit of the society?


\( \ln \) a daniel cell, if \( \boldsymbol{A}\left(\boldsymbol{E}^{o}=-\mathbf{0 . 7 6} \boldsymbol{C}\right) \) and
\( B\left(E^{o}=-2.36 V\right) \) half cells are taken
then:
\( A \cdot B \) acts as anode
B. \( A \) acts as anode
c. \( B \) acts as cathode
D. cannot be predicted


From an external point \( P, \) two tangents
PA and \( P B \) are drawn to the circle with
center \( 0 . \) Prove that OP is the
perpendicular bisector of \( A B \)


Find the value of currents \( l_{1}, l_{2} \) and \( l_{3} \)


In intrinsic semiconductors:
\( \mathbf{A} \cdot n>p \)
В. \( p>n \)
c. \( n=p \)
D. \( n=0 \)


For the velocity-time graph for a body
under uniform retardation
A. retardation is the negative of slope of graph
B. graph is a straight line inclined to the time axis with an obtuse angle
C. graph is a straight line inclined to the time axis with an acute angle
D. Both \( A \& B \)


Consider the following statement:
Both \( L i \) and \( M g \) forms hydrated
chloride.
If true enter \( 1, \) else enter 0


The strongest acid among the following aromatic compound is:
A. o-Nitrophenol
B. p-Chlorophenol
c. p-Nitrophenol
D. m-Nitrophenol


How many isomeric vicinal-dihalides are possible for the compound having molecular formula \( C_{3} H_{6} C l_{2} ? \)
A
B. 2
\( c \cdot 3 \)
D. 4


Add \( 3.8 \times 10^{-6} \) to \( 4.2 \times 10^{-5} \) with due
regard to significant figures.
\begin{tabular}{ll}
A. \( 4.6 \times 10^{-5} \) & 5 \\
\hline
\end{tabular}
в. \( 4.6 \times 10^{-6} \)
c. \( 5.6 \times 10^{-6} \)
D. \( 6.6 \times 10^{-5} \)


\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x}\left(t^{2}+e^{t^{2}}\right)^{\frac{1}{1-\cos t}}}{\left(e^{x}-1\right)} d t \) is equal to
A \( \cdot e^{4} \)
B \( \cdot e^{2} \)
\( c \cdot e^{3} \)
\( D \)


Differentiate \( \frac{1}{3} \tan ^{3} x-\tan x+x \) w.r.t \( x \)


The value of \( 2 \tan ^{-1}(-2) \) is equal to
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(-\frac{4}{5}\right) \)
B. \( -\sin ^{-1}\left(\frac{4}{5}\right) \)
\( \mathbf{C} \cdot \sin ^{-1}\left(\frac{4}{5}\right)-\pi \)
D \( -\cos ^{-1}\left(\frac{4}{5}\right)-\frac{\pi}{2} \)


Fill in the blanks type
Planck's constant has dimensions


Raman Shift' depends on.
A. Incident wavelenght
B. Incident intensity
C . Resolving power of the spectrograph used
D. Molecular energy levels of the scatterer.


Why are all the cells of a multicellular
organism not similar to each other?


n \( \triangle A B C \) and \( \triangle P Q R, \) if \( A B= \) \( 2.5 c m, A C=3.5 c m, B C= \)
\( 4.0 c m, P Q=5 c m, P R=7 c m \) and
\( Q R=8 c m, \) then find whether \( \triangle A B C \)
and \( \triangle P Q R \) are similar or not


\( 34.05 \mathrm{mL} \) of phosphorus vapour weighs
\( 0.0625 \mathrm{g} \) at \( 546^{\circ} \mathrm{C} \) and 1.0 bar pressure. What is the molar mass of phosphorus?


Solve the following equation: \( \frac{\boldsymbol{q}}{\boldsymbol{4}}+\boldsymbol{7}=\mathbf{5} \)


Equal masses of methane and hydrogen are mixed in an empty container at
\( 25^{\circ} \mathrm{C} . \) The fraction of the total pressure
exerted by hydrogen is:
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot \frac{1}{9} \)
D. \( \frac{16}{17} \)


Which of the following phenomena can be used to analyse a beam of light into its component wavelength?
A . Reflection
B. Refraction
c. Polarisation
D. Interference


What is the position of centre of gravity of a rectangular lamina?
A. At the mid point of longer side
B. At the mid point of shorter side
c. At the point of intersection of its diagonals
D. At one of the corners


Solve:
Estimate the mass of the earth, given,
radius of the earth \( =\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)
acceleration due to gravity \( =9.8 m / s^{2} \)
and gravitational constant \( =6.67 \times \)
\( 10^{-11} S . I . \) units.


On stretching a wire, the elastic energy stored per unit volume is
A. \( F l / 2 A L \)
в. \( F A / 2 L \)
c. \( F L / 2 A \)
D. \( F L / 2 \)


Find the equation of the ellipse whose
vertices are (±8,0) and foci are
\( (\pm \mathbf{3}, \mathbf{0}) \)


\( C_{4} H_{8} O_{2} \) represents:
\( A \). an acid only
B. an ester only
c. an ketone only
D. an acid and an ester also


Construct a quadrilateral \( A B C D \) in
which \( A B=B C=3.0 c m, A D= \)
\( C D=5.0 \mathrm{cm} \) and \( \angle A B C=120^{\circ} \)


An atoms contains 15 protons, 15
electrons, and 16 neutrons. Which of the
following combinations of particles is
an isotope of that atom?
\( \begin{array}{llll}\text { Protons } & \text { Electrons } & \text { Neutrons } \\ \text { (A) } & 16 & 16 & 17 \\ \text { (B) } & 15 & 16 & 16 \\ \text { (C) } & 15 & 15 & 15 \\ \text { (D) } & 14 & 15 & 16 \\ \text { (E) } & 14 & 14 & 15\end{array} \)
\( A \)
B.
\( c . \)
\( D \)
\( E \)


The value of \( \sqrt{2}\left(\cos 15^{\circ}-\sin 15^{\circ}\right) \) is
equal to:
A \( \cdot \sqrt{3} \)
B. \( \sqrt{2} \)
c. 1
D. 2
E. \( 2 \sqrt{3} \)


The product of three consecutive natural numbers is divisible by This question has multiple correct options
\( A \cdot 3 \)
B. 8
\( c .6 \)
D. 11


The distance between two point sources
of light is \( 24 \mathrm{cm} \) and a converging lens is kept in between two sources. The object distances of two sources from a converging lens of focal length of \( 9 \mathrm{cm} \) so that the image distances of two
sources are equal
\( A \cdot 12 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \) or \( 18 \mathrm{cm} \)
\( c .18 \mathrm{cm} \) or \( 6 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)


If error in measurement of radium of a
sphere is \( 1 \%, \) what will be the error in
measurement of volume?
A . \( 1 \% \)
B. \( \frac{1}{3} \% \)
\( c .3 \% \)
D. None of these


The equation of the plane passing through the straight line \( \frac{x-1}{2}= \) \( \frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{- 1}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{4}} \) and perpendicular to
the plane \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{1 2} \) is
A. \( 9 x+2 y-5 z+4=0 \)
В. \( 9 x-2 y-5 z+4=0 \)
c. \( 9 x+2 y+5 z+4=0 \)
D. None of these


When orthoboric acid is strongly heated, residue are :
A. meta boric acid
B. boron
\( c . \) both
D. none of these


Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 mA current. The time required to
liberate 0.01 moles of \( H_{2} \) gas at the cathode is
A \( \cdot 9.65 \times 10^{4} s \)
B . \( 19.3 \times 10^{4} s \)
c. \( 28.95 \times 10^{4} s \)
D. \( 38.6 \times 10^{4} s \)


The solution of the differential equation \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{2} \boldsymbol{y}=\boldsymbol{x}^{2}(\boldsymbol{x} \neq \mathbf{0}) \) with \( \boldsymbol{y}(\mathbf{1})=\mathbf{1} \)
is?
A \( \cdot y=\frac{x^{3}}{5}+\frac{1}{5 x^{2}} \)
B. \( y=\frac{4}{5} x^{3}+\frac{1}{5 x^{2}} \)
c. \( y=\frac{3}{4} x^{2}+\frac{1}{4 x^{2}} \)
D. \( y=\frac{x^{2}}{4}+\frac{3}{4 x^{2}} \)


A slide projector gives magnification of
10. If it projects a slide of \( 3 c m \times 2 c m \)
on a screen, the area of image on screen is:
\( \mathbf{A} \cdot 6000 \mathrm{cm}^{2} \)
В. \( 600 \mathrm{cm}^{2} \)
c. \( 3600 \mathrm{cm}^{2} \)
D. \( 12000 \mathrm{cm}^{2} \)


Simplify using commutative and associative property:
\( \left[\frac{2}{5}+\frac{5}{7}+\frac{-12}{5}\right] \)
A \( \cdot-2 \frac{5}{7} \)
B. \( \frac{9}{7} \)
c. \( \frac{-7}{9} \)
D. \( \frac{-9}{7} \)


In the following figure, ABCD to a
trapezium with \( A B \| D C \). If \( A B=9 \mathrm{cm}, D C= \)
\( 18 \mathrm{cm}, \mathrm{CF}=13.5 \mathrm{cm}, \mathrm{AP}=6 \mathrm{cm} \) and
BE=15 cm. Calculate PE
\( A \cdot P E=5.8 \mathrm{cm} \)
3. \( P E=4.8 \mathrm{cm} \)
\( c \cdot P E=2.8 \mathrm{cm} \)
\( P E=3.8 \mathrm{cm} \)


Oxygen gas can be prepared from solid
\( K M n O_{4} \) by
A. treating the solid with \( H_{2} \) gas
B. strongly heating the solid
C . dissolving the solid in dilute \( H_{2} S O_{4} \)
D. dissolving solid in dil HCI


What is a homogeneous solution with intermediate particle size between a solution and a suspension?
A. Element
B. Colloid
c. Solute
D. Pure compound


For a neutral atom, the first ionization energy is equal to its electron affinity.
A. True
B. False


Assertion
Kirchhoff's junction rule can be applied to a junction of several lines or a point in a line.
Reason
When steady current is flowing, there is no accumulation of charges at any junction or at any point in a line.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statements
about blood vessels is true?
A. Arterial walls are generally thicker and contain more elastic tissue than venous walls
B. Blood flows most rapidly through capillaries
C. Blood pressure in arteries is always lower than in veins
D. Venous walls are generally the strongest of all blood vessels and veins may contain valves


Which is the another unit used by
astronomers for measuring distance to other parts of Milky Way Galaxy?
\( A \cdot K m \)
B. Light year
c. Parsec
D. Meter


\( m_{1} \) and diameter \( A O C \) has mass \( m_{2} \)
Here, axis passes through mid-point of
diameter and the axis is perpendicular
to plane \( \boldsymbol{A B C} \)
Here, \( \boldsymbol{A O}=\boldsymbol{O C}=\boldsymbol{R} \). The moment of
inertia of this composite system about
the axis is:
\( \mathbf{A} \cdot \frac{m_{1} R^{2}}{2}+\frac{m_{2} R^{2}}{3} \)
B. \( \frac{m_{1} R^{2}}{2}+\frac{m_{2} R^{2}}{6} \)
\( \mathrm{c} \cdot_{m_{1} R^{2}+} \frac{m_{2} R^{2}}{3} \)
D \( \quad m_{1} R^{2}+\frac{m_{2} R^{2}}{12} \)


Q Type your question
normally on the hypotenuse side is
shown in
\( A \)
B.
\( c \)
\( D \)


Adsorption which arrives because of chemical bond and sometimes high activation energy needed is known as:
A. Physisorption
B. Chemisorption
c. Both physisorption and chemisorption
D. None of the above


A man in a balloon rising vertically with an acceleration of \( 4.9 m / s e c^{2} \) releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is \( (g= \)
\( \mathbf{9 . 8 m} / \boldsymbol{s e c}^{2} \)
A \( .14 .7 m \)
B. \( 19.6 m \)
\( \mathrm{c} .9 .8 \mathrm{m} \)
D. \( 24.5 m \)


The rate of chemical reaction: (except
zero order)
This question has multiple correct options
A. decreases from moment to moment
B. remains constant throughout
C. depends upon the order of reaction
D. none of the above


A hammer of mass 5 kg moving with a speed of \( 2 \mathrm{m} \mathrm{s}^{-1} \) strikes the head of a
nail driving it \( 20 \mathrm{cm} \) into the wall. Find the impulse.
A . \( 10 \mathrm{N} \) s
B. 20 N s
c. 30 N s
D. 40 N s


Solve for \( \boldsymbol{x} \)
\( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{2} & \mathbf{2} \boldsymbol{x}-\mathbf{3} & \mathbf{3} \boldsymbol{x}-\mathbf{4} \\ \boldsymbol{x}-\mathbf{4} & \mathbf{2} \boldsymbol{x}-\mathbf{9} & \mathbf{3} \boldsymbol{x}-\mathbf{1} \mathbf{6} \\ \boldsymbol{x}-\mathbf{8} & \mathbf{2} \boldsymbol{x}-\mathbf{2 7} & \mathbf{3} \boldsymbol{x}-\mathbf{6 4}\end{array}\right|=\mathbf{0} \)
\( A \cdot \frac{7}{4} \)
B. \( \frac{28}{3} \)
\( c \cdot \frac{28}{13} \)
D. \( \frac{14}{0} \)


Choose the correct answers from the
alternatives given Which of the following forms of energy is not correctly matched?
A. Kinetic energy fat molecules
B. Kinetic energy: movement of muscles
c. chemical energy: glucose
D. Potential energy ATP


Verify mean value theorem for the function \( f(x)=x^{2} \) in the interval [2,4]


The difference between the semi
perimeter and the side of a \( \Delta A B C \) arre 8 \( \mathrm{cm}, 7 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. Find the area of the triangle


Which of the following is/are correct for the function \( x \cos \frac{y}{x} ? \)
This question has multiple correct options
A. Not homogenous
B. Homogenous
c. Degree \( =1 \)
D. Degree=2


Find the supplement of the following
angle
\( \mathbf{1 2 0}^{\circ} \)


The velocity of electromagnetic radiation in a medium of permittivity \( \varepsilon_{0} \)
and permeability \( \mu_{0} \) is given by :
A \( \cdot \sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \)
B . \( \sqrt{\mu_{0} \varepsilon_{0}} \)
c. \( \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)
D. \( \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \)


For a gaseous phase reaction, \( \boldsymbol{A}+ \) \( \mathbf{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{A} \boldsymbol{B}_{2} \boldsymbol{K}_{C}=\mathbf{0 . 3 4 7 5} \) litre \( ^{2} \boldsymbol{m o l}^{-2} \)
at \( 200^{\circ} \mathrm{C} \). When 2 mole of \( B \) are mixed
with one mole of \( A \). What total pressure
is required to convert \( 60 \% \) of \( A \) in \( A B_{2} \) ?


On increasing the temperature by \( 10^{0} \mathrm{C} \)
A. number of collisions get doubled
B. value of rate constant does not change
C. energy of activation increases
D. number of fruitful collisions gets doubled


Two squares are chosen from the
squares of an ordinary chess board. It is given that the selected squares do not belong to the same row or column. The probability that they have a side in
common
A \( \cdot \frac{25}{49} \)
в. \( \frac{32}{49} \)
c. \( \frac{1}{18} \)
D.


Which alkyl-halide has maximum
density?
\( \mathbf{A} \cdot C_{3} H_{7} I \)
в. \( C_{2} H_{5} I \)
\( \mathbf{c} \cdot C H_{3} I \)
D. \( C H_{3} B r \)


Solve
\( \int \frac{x^{3}}{x^{3}+1} d x \)


Explain the formation of rainbow.


Two particles move on a circular path (one just inside and the other just
outside) with angular velocities \( \omega \) and
\( 5 \omega \) starting from the same point. Then:
This question has multiple correct options
A \cdot they cross each other at regular intervals of time \( \frac{\pi}{2 \omega} \) when their angular velocities are directed opposite to each other
B. they cross each other at points on the path subtending an angle of \( 60^{\circ} \) at the centre if their angular velocities are directed opposite to each other
C . they cross at intervals of time \( \frac{\pi}{3 \omega} \) if their angular velocities are directed opposite to each other
D. they cross each other at points on the path subtending \( 90^{\circ} \) at the centre if their angular velocities are similar to each other


Assertion
If a conductor is given charge then no
excess inner charge appears.
Reason
Electric field inside conductor is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following options is not a series?
A. -2,-4,-6,-8,-10
0
в. -2,0,2,4,8
c. 1,2,3,4,5
D. All the above


Define intensity of electric field at a
point. Derive an expression for the
electric field intensity due to a point charge.


Which one of these group off elements is also called the halogen family?
A. Group 16
B. Group 18
c. Group 10
D. Group 17


In vitro synthesis of DNA was carried out by
A. Nirenberg
B. Watson and Crick
c. Khorana
D. Kornberg


Find the area of the region bounded by the curve \( a y^{2}=x^{3}, \) the \( y-a x i s \) and
the lines \( y=a \) and \( y=2 a \)


During inspiration, muscles of diaphgram
A. Contracts
B. Expands
c. No effect
D. Coiled like string


\( n \) capacitors each of capacitance \( 2 \mu F \) are connected in parallel and a potential difference of \( 200 \mathrm{V} \) is applied to the
combination. The total charge on all the positive plates is 1 Coulomb then \( n \) is
equal to :
A . 3333
в. 3000
\( c .2500 \)
D. 25


A piece of copper is heated in oven, then dropped into a beaker of water. If a student want to calculate the specific
heat of copper then he must know or measure the value of all of the
quantities below EXCEPT the:
A. mass of the water
B. original temperatures of the copper and the water
c. final (equilibrium) temperature of the copper and the water
D. time taken to achieve equilibrium after the copper is dropped into the water
E. specific heat of the water


What causes friction?
A. The force applied
B. Irregularities on the two surfaces in contact
C. The difference in the weight
D. All of the above


A taxonomic species distinguished on the basis of morphological characters
is
A. Morphospecies
B. Biospecies
c. Linneon
D. Neontological species


Two billiard balls \( A \) and \( B \), each of mass
\( 50 \mathrm{g} \) and moving in opposite directions
with speed of \( 5 m s^{-1} \) each, collide and
rebound with the same speed. The
impulse imparted to each ball is:
A. \( 0.25 \mathrm{Kgms}^{-1} \)
B. \( 0.5 \mathrm{Kgms}^{-1} \)
c. \( 0.1 \mathrm{Kgms}^{-1} \)
D. \( 0.125 \mathrm{Kgms}^{-1} \)


At a certain temperature, only \( 50 \% \) \( H I \)
is dissociated into \( H_{2} \) and \( I_{2} \) at equilibrium. The equilibrium constant is :
A . 1.0
B. 3.0
c. 0.5
D. 0.25


The set of values of \( x \) for which
\( \tan ^{-1} \frac{x}{\sqrt{1-x^{2}}}=\sin ^{-1} x \) holds is
A. \( R \)
в. (-1,1)
\( \mathbf{c} \cdot[0,1] \)
D. [-1,0]


The relation between U,P and V for ideal
gas is \( U=2+3 P V \). What is the adiabatic
coefficient of gas
A . 1.33
B. 1.4
c. 1.5
D. 1.67


An automobile engine absorbs \( 1600 J \) of heat from a hot reservoir and expel
\( 1000 J \) to a cold reservoir in each cycle.
What maximum work is done in each
cycle?
\( \mathbf{A} \cdot 400 J \)
B. \( 500 J \)
c. \( 600 J \)
D. \( 450 J \)


According to the theories of succession,
what will be the result?
A. The lake will get deeper and the trees more numerous
B. The lake will get shallower and the trees will be replaced by grass
c. The lake will dry up
D. The trees will become coniferous types
E. There is no fixed order to the replacement of species


The area bounded by the curves \( y^{2}=4 x \)
and \( x^{2}=4 y \) is :
A \( \cdot \frac{32}{3} \)
B. \( \frac{16}{3} \)
\( c \cdot \frac{8}{3} \)
D.


The amount of work performed to break
a spherical drop of radius 1 mm into millies of equal radius is
\( \left(\boldsymbol{T}=\mathbf{7 . 2} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{N m}^{-\mathbf{1}}\right) \)


Draw a labelled ray diagram of a refractive telescope. Deduce an
expression of magnifiying power of it. Write two main limitations of a
refracting type telescope over a reflecting type telescope.


How many structural isomers are
possible for \( C_{4} H_{10} O ? \) (only alcohol)


If \( \overline{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}-\mathbf{0} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overline{\boldsymbol{c}}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{c}}=\boldsymbol{m} \overline{\boldsymbol{a}}+\boldsymbol{n} \overline{\boldsymbol{b}} \) then \( \boldsymbol{m}+\boldsymbol{n}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. -


If \( A \) is a skew-symmetric matrix and \( n \) is
a positive integer, then \( \boldsymbol{A}^{\boldsymbol{n}} \) is
A. a symmetric matrix
B. skew-symmetric matrix
c. diagonal matrix
D. none of these


Find the value of the polynomial \( 5 x- \)
\( 4 x^{2}+3 \) at \( x=-1,2,-2 \)


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


A full wave rectifier circuit along with
the input and output are shown in the figure. The contribution from the diode
\( \mathbf{1} \) is are
A. \( C \)
в. \( A, C \)
\( c \cdot B \& D \)
D. \( A, B, C, D \)


Presence of large number of alveoli around alveolar ducts opening into bronchioles in mammalian lungs is
A. Inefficient system of ventilation with litle of residual air
B. Inefficient system of ventilation with high percentage of residual air
c. An efficient system of ventilation with no residual air
D. An efficient system of ventilation with little residual air


The relation between magnetic field and current is given by Biot-Savart
law. Illustrate Biot-Savart law with
necessary figure.


State whether true or false:
Unlike charges attract each other
A. True
B. False


Find the magnitude of the electric field strength as a function of the distance \( r \) both inside and outside the ball


In the equilibrium reaction, \( A+B \rightleftharpoons C+ \)
D, the activation energy for the forward
reaction is 25 kcal mole \( ^{-1} \) and that of
the backward reaction is 15 kcal mole \( ^{-1} \)
Which one of the following statements
is correct?
A. The reaction is exothermic
B. The reaction is endothermic
C. The reaction has \( \Delta H \) of 20 kcal mol-
D. Both \( A \) and \( C \)


The chemical formula of marsh gas (methane) is:
A. \( C_{2} H_{6} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{1} \)


The displacement equations of two simple harmonic oscillators are given by \( \boldsymbol{x}_{1}=\boldsymbol{A}_{1} \cos \boldsymbol{\omega} \boldsymbol{t} ; \boldsymbol{x}_{2}=\boldsymbol{A}_{2} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\pi}{6}\right) \)
The phase difference between them is:
\( A \cdot 30 \)
B. 60
\( c \cdot 90 \)
D. \( 120^{\circ} \)


If \( 3+5+7+9+\ldots \) upto \( n \) terms \( =288 \)
then \( n= \)
A . 12
B . 15
c. 16
D. 17


IICII IIIE IdIUWIIIg IEpIESEIIL
physical adsorption?
\( A \)
B.
\( c \)
\( D \)


If \( \boldsymbol{f}(\boldsymbol{x}) \) satisfies the conditions of
Rolle's theorem in [1,2] then \( \int_{1}^{2} f^{\prime}(x) d x \) is equal to
\( A \)
B. 3
\( c \cdot 0 \)
D. none of these


The solution of \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)-\cos ^{-1}\left(\frac{1-b^{2}}{1+b^{2}}\right)= \)
\( 2 \tan ^{-1} x \)
A \( \frac{a-b}{1-a b} \)
B. \( \frac{1+a b}{a-b} \)
c. \( \frac{a b-1}{a+b} \)
D. \( \frac{a-b}{1+a b} \)


The bond dissociation energy needed to form the benzyl radical from toluene is
the formation of the methyl radical from methane.
A. less than
B. greater than
c. equal to
D. greater than or equal to


Pressure depends on distance as, \( \boldsymbol{P}= \) \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \exp \left(-\frac{\boldsymbol{\alpha} \boldsymbol{z}}{\boldsymbol{k} \boldsymbol{\theta}}\right), \) where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are
constants, \( z \) is distance, \( k \) is Boltzman's
constant and \( \theta \) is temperature. The
dimensions of \( \beta \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B \( \cdot\left[M^{-1} L^{-1} T-1\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{2} T^{0}\right] \)
D \cdot \( \left[M^{-1} L^{1} T^{2}\right] \)


The one that is extensively used as a piezoelectric material is :
A. quartz
B. amorphous silica.
c. mica
D. tridymite.


Which of the following can not be
oxidised by \( H_{2} O_{2} ? \)
A. Pbs
в. к।+нс
c. \( N a_{2} S O_{3} \)
D. \( O_{3} \)


OPQR is a square. \( M, N \) are the midpoints of the sides \( P Q \) and \( Q R \)
respectively. If the ratio of the areas of
the square and the \( \triangle O M N \) is \( \lambda: 6 \) then \( \frac{\lambda}{4} \) is equal to
A .2
B. 4
c. 8
D. 16


State whether true or false:
Good conductors have excess of free
electrons.
A. True
B. False


It is difficult for a fireman to hold a
hose pipe which ejects large amounts of water at high velocity due to :
A. Newton's first law
B. Newton's second law
c. Newton's third law
D. Newton's gravitation law


In a series resonant circuit, having L,C,R as its elements, the resonant current is
i. The power dissipated in the circuit at
resonance is
\( \mathbf{A} \cdot i^{2} l \omega \)
B . \( i^{2} R \)
c. zero
\( \mathbf{D} \cdot i^{2} C \omega \)


toppr )
Q Type your question_
watches, etc.
(ii) It consists of zinc-mercury
amalgam as anode and a paste of HgO
and carbon as the cathode.
(iii) The electrolyte is a paste of
\( Z n(O H)_{2} \) and \( K O_{2} \)
(iv) The electrode reactions for the cell
are
At anode: \( Z n(H g)+H_{2} O \rightarrow Z n O_{(s)}+ \)
\( 2 O H^{-}+2 e^{-} \)
At cathode: \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{H} \boldsymbol{g}_{(l)}+2 \boldsymbol{O} \boldsymbol{H} \)
A. (ii) and (iii) only
B. (i) ad (ii) only
C. (i), (iii) and (iv) only
D. (iii) and (iv) only


The median of the observations,
arranged in increasing order is \( 26 . \) Find
the value of \( \boldsymbol{x} . \mathbf{1 0}, \mathbf{1 7}, \mathbf{2 2}, \boldsymbol{x}+\mathbf{2}, \boldsymbol{x}+ \)
4,30,36,40


Assertion (A): Ortho phosphoric acid is
tribasic.

Reason (R): Orthophosphoric acid forms three series of salts
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. (A) is true and (R) is false
D. (A) is false but (R) is true


How many times a wheel of radius 28 cm must rotate to go 352 m?(Take \( \pi= \)
\( \frac{22}{7} \)


If \( z_{1}=2+5 i, z_{2}=3-i \) find \( (a) z_{1} \cdot z_{2} \)
(b) \( z_{1} \times z_{2} \)
\( (c) z_{2} \cdot z_{1} \)
(d) \( z_{2} \times z_{1} \)
(e) acute angle between \( z_{1} \& z_{2} \)
Projection of \( z_{1} \) on \( z_{2} \)
A \( \cdot 1,17,1,17, \cos ^{-1} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
в. \( _{1,-17,1,17, \cos ^{-1}} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
c. \( _{1,17,1,-17, \cos ^{-1}} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
D. \( 1,-17,1,-17, \cos ^{-1} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)


Which of the following is a physical change?
A. Photosynthesis
B. Melting of steel
c. Burning of wood
D. Radioactive decay


If \( \boldsymbol{x}>\boldsymbol{y}>\mathbf{0} \) then find the value of \( \tan ^{-1} \frac{x}{y}+\tan ^{-1}\left[\frac{x+y}{x-y}\right] \)


In the projectile motion, if air resistance is ignored, the horizontal motion is at
A. constant acceleration
B. variable acceleration
C. constant velocity
D. constant retardation


Arrange the three natural radiations in
decreasing order of penetration
A. alpha, beta, and gamma
B. beta, gamma, and alpha
c. gamma, alpha, and beta
D. gamma, beta, and alpha
E. beta, alpha, and gamma


A mixture of three gases P (density
0.90)\( , Q(\text { density } 0.178) \) and \( R( \) density
0.42) is enclosed in a vessel at the
constant temperature. When the equilibrium is established:
A. the gas P will be at the top of the vessel
B. the gas Q will be at the top of the vessel
c. the gas \( R \) will be at the top of the vessel
D. the gases will mix homogeneously throughout the vessel


Give condensed and bond line
structural formula and identify the functional group(s) present, if any, for 2,2,4-Trimethyl pentane.


The value of \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{x}-\boldsymbol{2}-\boldsymbol{x}^{2} \) at \( \boldsymbol{x}= \)
3
\( A \cdot 0 \)
B. - 1
\( c \cdot-2 \)
D. - 3


The value of the Avogadro constant is:
В. \( 6.022 \times 10^{22} \)
c. \( 6.022 \times 10^{23} \)
D. \( 6.022 \times 10^{24} \)


Nitrogen is used in high temperature
thermometer:
This question has multiple correct options
A. to prevent vaporization of mercury
B. to improve conductivity of mercury
C. to maintain mercury in its state
D. to increase the specific heat capacity of mercury


A cube has sides of length \( 1.2 \times \)
\( 10^{-2} m . \) Calculate the volume.
A \( .1 .7 \times 10^{-6} m^{3} \)
В. \( 1.73 \times 10^{-6} m^{3} \)
C. \( 1.70 \times 10^{-6} m^{3} \)
D. \( 1.732 \times 10^{-6} \mathrm{m}^{3} \)


In the following reaction,the product 'R' is \( : \boldsymbol{C a} \boldsymbol{C}_{2} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{P}_{\boldsymbol{t u b e}}^{h o t} \stackrel{i r o n}{\boldsymbol{Q}} \frac{C \boldsymbol{H}_{3} C l}{A \boldsymbol{l} C l_{3}} \boldsymbol{R} \)
A. Chloro benzene
B. benzene
c. toluene
D. anisole


Find the sequence of binding of the
following amino acyl-tRNA complexes during translation of an mRNA transcribed by a DNA segment having the base sequence 3'TACATGGGTCCG5'. Choose the answer showing the correct order of alphabets.
A. P, Q, s,
в. Q, Р, s,
c. Р, \( Q, \) R,
D. Q, P, R,


Smallpox vaccine contains:
A. chemical medicines
B. enzymes
c. killed or dead microorganisms
D. living microorganisms


\( \operatorname{Given}|z|=4 \) and \( A r g z=\frac{5 z}{6}, \) then \( z \) is
A \( \cdot 2 \sqrt{3}+2 i \)
B. \( 2 \sqrt{3}-2 i \)
c. \( -2 \sqrt{3}+2 i \)
D. \( -\sqrt{3}+i \)


The correct balanced equation from the
following is:
A. \( P b O+N H_{3} \rightarrow P b+H_{2} O+N_{2} \)
B. \( P b O+2 N H_{3} \rightarrow P b+H_{2} O+N_{2} \)
c. \( P b O+2 N H_{3} \rightarrow 3 P b+3 H_{2} O+N_{2} \)
D. \( 3 P b O+2 N H_{3} \rightarrow 3 P b+3 H_{2} O+N_{2} \)


Assertion
The energy bands in a solid correspond to the energy levels in an atom.
Reason
An electron in a solid can have only
energies that fall with these energy
bands.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
The excess pressure above atmospheric
pressure is usually called as gauge
pressure.
Reason
Gauge pressure \( =(\text { Total pressure }) \) (atmospheric pressure)
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


Identify which contributes for strengthening of lime mortar structures and contributes for weakening of RCC structures the factor(s)
A. Usage of water containing dissolved salts
B. Addition of lime
C. Absorption of \( C O_{2} \) from atmospheric air
D. Both B and C


The area of a parallelogram is \( 240 \mathrm{cm}^{2} \) and its height is \( 12 \mathrm{cm} . \) The base of the parallelogram is :
A . 24 CM
B. 20 СМ
c. 28 см
D. none of these


Which of the following statements are correct about the functions of
epidermis in
a. Dorsiventral leaf
b. Protection
c. Bears stomata
d. Gaseous exchange through Bulli form cells.
\( A \cdot A \& B \)
B. Only A
c. В \&
D. only


\( (f \circ f)(x) \)


The following is NOT equal to 0 in the
Boolean algebra is
\( \mathbf{A} \cdot \overline{\bar{A} \cdot 0} \)
в. \( A . \bar{A} \)
c. \( A . \)
D. \( \overline{A+\bar{A}} \)


When an impurity is doped into semiconductor, the conductivity of the semiconductor
A . increases
B. decreases
c. remains same
D. becomes zero


Find mode for the following data:
\( \begin{array}{llllll}\mathbf{x} & \mathbf{2}- & \mathbf{4}- & \mathbf{6}- & \mathbf{8}- & \mathbf{1 0} \\ \mathbf{4} & \mathbf{6} & \mathbf{8} & \mathbf{1 0} & \mathbf{1 2} \mathbf{2}\end{array} \)
2 2 1
A . 11
в. 12
c. 13
D. 14


Construct \( \triangle A B C \) in which \( B C= \)
\( \mathbf{7} c \boldsymbol{m}, \angle \boldsymbol{B}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \) and \( \boldsymbol{A} \boldsymbol{B}+\boldsymbol{A} \boldsymbol{C}= \)
\( 12 \mathrm{cm} \)


A \( 20 \Omega \) resistor, \( 1.5 \mathrm{H} \) inductor and \( 35 \mu F \)
capacitors are connected in series with
\( 200 V, 50 H z \) ac supply. Calculate the
impedance of the circuit and also find the current through the circuit?


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


Quadrilateral \( A B C D \) is a square. \( P, Q \)
and \( R \) are the points on \( A B, B C \) and
\( C D \) respectively, such that \( \boldsymbol{A P}= \) \( \boldsymbol{B} \boldsymbol{Q}=\boldsymbol{C} \boldsymbol{R} . \) Hence, If \( \angle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \) is a right
angle, find \( \angle P R Q(\text { in degrees }) \)


Mark, among the following the a cell which does not exhibit pahgocytotic activity
A. Monocytes
B. Neutrophil
c. Basophil
D. Macrophage


Assertion
Fluorine is most electronegative
element.
Reason
Fluorine can form only ionic bond.
A. Both Assertion and Reason are true and Reason is the
correct explanation for Assertion
B. Both Assertion and Reason are true but Reason is not
the correct explanation for Assertion
C. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statement.


Which of the following compound exhibits Hydrogen bonding?
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \) and \( \boldsymbol{C H}_{3} \boldsymbol{S H} \)
A. \( C H_{3} N H_{2} \)
в. \( C H_{3} S H \)
c. Both
D. None


Solve \( : \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 1 0}, \boldsymbol{y}=\boldsymbol{x}+\mathbf{4} \)


\( (x+y)(d x-d y)=d x+d y \)
Solve the above equation.


The furnace which gives the highest
temperature is:
A. Blast furnace
B. Reverberatory furnace
c. Electrical furnace
D. Muffle furnace


Find the locus of a point which moves so that the difference of its distances from
the points, (5,0) and (-5,0) is 2 is:
A \( \cdot \frac{x^{2}}{1}+\frac{y^{2}}{24}=1 \)
B. \( \frac{x^{2}}{24}+\frac{y^{2}}{1}=1 \)
c. \( \frac{x^{2}}{24}-\frac{y^{2}}{2}=1 \)
D. \( \frac{x^{2}}{1}-\frac{y^{2}}{24}=1 \)


From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element which shows diagonal relationship with Mg.


A man pays 8 tax on Re.1. If the total tax
paid by him is Rs.1000, then on how much amount did he pay the tax?
A. Rs.12500
B . Rs.12400
c. Rs.1200
D. Rs.12300


An electric iron is connected to a \( 200 V \)
mains supply and draws a current of \( 4.0 A \) What is the power rating of the iron?
\( \mathbf{A} \cdot 800 W \)
в. \( 50 W \)
c. \( 106 W \)
D. \( 112 W \)


Assertion
If vectors \( a \) and \( c \) are non collinear then
the lines \( r=6 a-c+\lambda(2 c-a) \) and
\( \boldsymbol{r}=\boldsymbol{a}-\boldsymbol{c}+\boldsymbol{\mu}(\boldsymbol{a}+\boldsymbol{3} \boldsymbol{c}) \) are coplanar
Reason
There exist \( \lambda \) and \( \mu \) such that the two
values of \( r \) become same.
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


Bile does not contain any enzyme, but it is essential for digestion.
A. True
B. False


(A) Energy emitted in the transition
\( (5 \rightarrow 2) \) is less than that of \( . \) the
transition \( (2 \rightarrow 1) \) in all hydrogen like
atoms.
(R) The energy difference between 1st
and 2 nd shell is greater than that of any two energy levels provided level (1) is not part of those two energy levels.
A. Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion (A) is true but reason (R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion
(A) is false but reason
(R) is true


Carbon monoxide is naturally produced by oxidation of \( \underline{X}, \) a gas present in swamp area while it can be produced by \( Y \) of fuels containing carbon
A. \( x-C O_{2}, Y= \) complete combustion
B . \( x-C H_{4}, Y= \) incomplete combustion
c. \( x=c, Y= \) oxidation
D. \( x=C H_{4}, Y= \) complete combustion


Based on the figure above, identify the
correct statement (s) from the
following:

This question has multiple correct options
A. At sealevel, the mercury inside the tube stands upto 76
\( \mathrm{cm} \)
B. The pressure exerted inside a liquid is same at all points along the horizontal plane.
C. The vertical height of the liquid column is independent of the shape and size of the tube.
D. The height of the barometric liquid column is independent of nature of liquid used.


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
\( \boldsymbol{y}=\sin \boldsymbol{x} . \cos \boldsymbol{x} \)


\( \frac{5}{2} \)


A body is gently on a conveyor belt moving \( 3 \mathrm{m} / \mathrm{s} \). If \( \mu=0.5 \) how far will the body move relative to the belt befour
coming to rest \( ?\left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
\( A \cdot 0.3 \mathrm{m} \)
B. 0.6 \( m \)
c. \( 0.9 \mathrm{m} \)
D. \( 0.8 \mathrm{m} \)


Which of the following is a strong acid?
A. Sulphuric acid
B. Acetic acid
c. Tartaric acid
D. Lactic acid


Show that the following set of point are collinear?
(2,3,-4),(-1,0,5),(3,4,-7)


The length of a minor arc is \( \frac{2}{9} \) of the circumference of the circle. Write the
measure of the angle subtended by the arc at the centre of the circle.


The depression in freezing point is maximum if the solvent used is:
A. Camphor
B. Naphthalene
c. Benzene
D. water


Among the following one can act as the building blocks for the other gates is
A. NAND and NOR
B. NAND and AND
c. xor and or
D. NOT and OR


Find \( 302 \times 308 \)


Which of the following undergoes diazotization?
A. \( C H_{3} N H_{2} \)
в. \( C_{6} H_{5} N H_{2} \)
c. \( C H_{3} C O N H_{2} \)
D. \( _{C H_{3} N}\left(C H_{3}\right)_{2} \)


Forest fire produces ...... pollution.
A . air
B. water
\( c . \) sea
D. soil


Mercury boils at \( 367^{\circ} \mathrm{C} \). Mercury thermometers are made such that they
can measure temperature up to \( 500^{\circ} \mathrm{C} \) This done by
A. Filling nitrogen gas at high pressure above the mercury column
B. Fillıng oxygen gas at low pressure above the mercury column
c. Filling carbondioxide gas above mercury column
D. None of the above


Balance reaction for preparation
of Ethyl chloride to Ethene is:
A \( \cdot C_{2} H_{5} C l+K O H(\text {alcoholic soln.}) \rightarrow C H_{2}=C H O H+ \)
\( H C l \)
B. \( C_{2} H_{5} C l+K O H(\text {alcoholic soln.}) \rightarrow C H_{3}-C H_{3}+ \)
\( H C l \)
C. \( C_{2} H_{5} C l+K O H \) (alcoholic soln.) \( \rightarrow C H_{2}=C H_{2}+ \) \( H C l \)
D. none of these


In the given figure, \( Q \) is the centre of the
circle and \( P M \) and \( P N \) are tangent
segments to the circle.
If \( m \angle M P N=70^{\circ} \), find \( \angle M Q N \)


When manganese dioxide is treated with \( H C l, \) oxidation state of chlorine on
the product side is:
This question has multiple correct options
A . -1
B. 0
\( c \cdot+1 \)
\( D \cdot+3 \)


The force of gravitation between two
bodies can be zero if the separation
between the bodies becomes
\( A \)
B.
\( c \cdot-1 \)
D. infinity


A speedy rabbit is hopping to the right with a velocity of \( 4.0 \frac{m}{s} \) when it sees a carrot in the distance. The rabbit speeds up its maximum velocity of \( 13 \frac{\mathrm{m}}{\mathrm{s}} \) with a constant acceleration of \( 2.0 \frac{m}{s^{2}} \) rightward. How many seconds does it take the rabbit to speed up from \( 4.0 \frac{m}{s} \) to \( 13 \frac{m}{s} ? \)


The position of a point in time 't' is given by \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}-\boldsymbol{c t}^{2}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{t}+\boldsymbol{b} \boldsymbol{t}^{2} . \) Its
acceleration at time 't' is
A. \( b-c \)
в. \( b+c \)
c. \( 2 b-2 c \)
D. \( 2 \sqrt{b^{2}+c^{2}} \)


Fill in the blanks with appropriate
words. Benzene has a planar structure. All carbon atoms in benzene are \( \underline{\perp} \)
hybridised. The ring structure of benzene was proposed by \( \| . \) It shows \( \underline{\|} \) substitution reactions. It reacts with \( \underline{I V} \)
in presence of aluminium chloride to
form acetophenone.
A \( \cdot I=s p_{2} \) II \( = \) Kekule III\( = \) electrophilic \( I V= \) acetyl chloride
B. \( I=s p I I= \)Dewar III\( = \) nucleophilic \( I V= \) chloromethane
C \( . I=s p_{3} \) II \( = \) Ladenberg III \( = \) electrophilic \( I V= \) chloroethane
D. \( I=s p_{2} \) II \( = \) Baeyer III \( = \) nucleophilic \( I V= \) methylbromide


Choose the correct answer from the
alternatives given. In plants a common symptom caused by deficiencies of \( \mathrm{Ca}, \mathrm{K}, \mathrm{Mg} \) and \( P \) is the:
A. appearance of a dead necrotic area
B. poor development of vasculature
c. bending of the leaf tip
D. formation of carotenes in plenty


Attempt to formulate your 'moral' views on the practice of science. Imagine
yourself stumbling upon a discovery, which has great academic interest but is certain to have nothing but dangerous consequences for the human society. How will you resolve your dilemma?


The Young's modulus of steel is twice that of brass. Two wires of sample
length and of same area of cross section, one of steel and another of
brass are suspended from the same
roof. If we want the lower ends of the
wires to be at the same level, then the
weights added to the steel and brass wires must be in the ratio of:
A. 1: 1
B. 1: 3
c. 2: 1
D. 4: 1


Read the following statements:
(i) The sieve tube elements and
companion cells are connected by pit fields present between their common longitudinal walls.
(ii) Phloem parenchyma is made of elongated non-tapering cylindrical cells that have a scanty cytoplasm.
(iii) Phloem fibers are made of
parenchymatous cells.
(iv) Companion cells help in maintaining the pressure gradient in the sieve tube.
(v) The phloem parenchyma stores food material and other substances like
resins, latex, and mucilage.
How many of the given statements are
correct?
A. Three
в. Two
c. one
D. Four


Among the following, the branched chain polymer is:
A. Polyvinyl chloride
B. Bakelite
c. Low density polythene
D. High density polythene


What are the monomeric repeating
units of Nylon-6 and Nylon-6,6?


Metallic nature increases moving down the group because:
A. nuclear'charge decrease
B. shielding increases
(B) both
\( c \cdot(A) \) and
D. none of these


The feet with two toes forming cloven
hoof is seen in
A . Horse
B. zebra
c. Rhinoceros
D. Elephant
E. Sheep


\( \boldsymbol{C l}_{2} \Leftrightarrow \mathbf{2} \boldsymbol{C l} \)
\( \boldsymbol{C H}_{4}+\boldsymbol{C l} \rightarrow \boldsymbol{C H}_{3}+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{s l o w}) \)
\( \boldsymbol{C H}_{3}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{C l}+\boldsymbol{C l} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C l}+\boldsymbol{C l} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}+\boldsymbol{H} \)
\( \boldsymbol{H}+\boldsymbol{C l} \rightarrow \boldsymbol{H} \boldsymbol{C l} \)
The above mechanism shows the overall
reaction between chlorine gas and methane gas to form dichloromethane gas and hydrogen monochloride gas. The reaction is carried out in the gas
state with no ions being formed during the reaction.

Which of the following statements is not supported by the mechanism?
A. \( C H_{3} C l \) is an intermediate because it is made in step and used in step 4
B. The order of the reaction with respect to \( C H_{4} \) is one since step 2 is the slowest step, making the rate law for step 2: rate \( =k\left[C H_{4}\right][C l] \)
c. The first step is the only equilibrium step in the reaction
D. The overall rate law for the reaction is: rate\( = \) \( k\left[C H_{4}\right]\left[C l_{2}\right] \)


\( \int_{3-\alpha}^{3+\alpha} f(x) d x \) equals, where \( f(3+\beta)= \)
\( f(3-\beta), \beta \in R \)
A. \( _{3} \int_{0}^{\alpha} f(x) d x \)
в. \( 3 \int_{0}^{3} f(x) d x \)
c. \( 3 \int_{\alpha-3}^{\alpha} f(x) d x \)
D. \( 3 \int_{3}^{3+\alpha} f(x) d x \)


Pollution is a change in physical, chemical or biological characters of our land and water that may be:
A. desirable and harmful to humans
B. desirable and useful to humans
c. undesirable and harmful to humans
D. undesirable and useful to humans


Evaluate:
\( \sum_{r=1}^{\infty} \tan ^{-1}\left(\frac{2}{1+(2 r+1)(2 r-1)}\right) \)


Unit of ionic mobility is
\( \mathbf{A} \cdot m^{2} \sec ^{-1} v o l t^{-1} \)
B. \( m \) sec\( ^{-1} \)
\( \mathrm{c} \cdot m \sec ^{-1} \)volt
D. \( m \) sec \( ^{-1} \) volt \( ^{1} \)


Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 2 0}, \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}\right)=\mathbf{0 . 1 5} \)
\( P(A \text { and } B \text { both fail })=0.10 . \) Then
This question has multiple correct options
A. \( P(A / B)=11 / 14 \)
В . \( P(A)=0.7 \)
c. \( P(A \cup B)=0.9 \)
D. \( P(A / B)=1 / 2 \)


The oxidation state of copper changes
when aqueous copper (II) ions react with:
\( (I) N a O H(a q) \)
\( (I I) F e(s) \)
\( (I I I) K I(a q) \)
A. \( I, I I, I I I \)
B. II only
c. \( I I, I I I \)
D. I only


The \( \ldots \). whional number and its
reciprocal is 1
A. sum
B. difference
c. product
D. quotient


If \( x=5+2 \sqrt{6}, \) then the value of
\( \left(\sqrt{\boldsymbol{x}}-\frac{1}{\sqrt{x}}\right)^{2} \)
A \( .4 \sqrt{6} \)
B. 8
c. 16
D. 12
E. None of these


The product formed is a:
A. Carboxylic acia
B. Ketone
c. Alkane
D. Aldehyde


Life cycle of Saccharomyces ludwigiii is
A. Haplobiontic
B. Haplodiplobionitc
C . Diplobiontic
D. All of the above


Find \( \times ? \)
\( 2 x+3=7 \)


Calculate the vapour pressure lowering caused by addition of 50 g of sucrose (molecular mass \( =342 \) ) to 500 g of water if the vapour pressure of pure
water at \( 25^{\circ} \mathrm{C} \) is \( 23.8 \mathrm{mm} \mathrm{Hg} \)


If \( \alpha \) and \( \beta \) are the roots of the equation
\( 375 x^{2}-25 x-2=0, \) then the value of
\( \lim _{n \rightarrow \infty}\left(\sum_{r=1}^{n} \alpha^{r}+\sum_{r=1}^{n} \beta^{r}\right) \) the value of is?
A \( \cdot \frac{29}{248} \)
в. \( \frac{17}{348} \)
c. \( \frac{29}{358} \)
D. \( \frac{11}{34} \)


The first terrestrial plants, to possess vascular tissues, among the following
are
A. Sphagnum \& Selaginella
B. Marchantia \& Funaria
c. selaginella \& Salviniá
D. Funaria \& Equisetum


Identify the favourable conditions for the formation of ionic bond.
A. Low IP value of metal, low EA value of nonmetal
B. High IP value of metal, high EA value of nonmetal
c. Low IP value of metal, high EA value of nonmetal
D. High IP value of metal, low EA value of nonmetal


The structure known as peroxisome is associated with
A. Photosynthesis.
B. Respiration.
c. Photorespiration.
D. Photophosphorylation.


Which of the following is not the reciprocal of \( \left(\frac{2}{3}\right)^{4} ? \)
\( ^{A} \cdot\left(\frac{3}{2}\right)^{4} \)
\( ^{\text {B }}\left(\frac{2}{3}\right)^{-4} \)
\( ^{c}\left(\frac{3}{2}\right)^{-4} \)
D. \( \frac{3^{4}}{4^{2}} \)


\( \boldsymbol{a}^{\boldsymbol{x}}=\boldsymbol{b}, \boldsymbol{b}^{\boldsymbol{y}}=\boldsymbol{c}, \boldsymbol{c}^{\boldsymbol{z}}=\boldsymbol{a} \)
Find the value of \( x, y, z \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. Not valid
c. -1
D.


A telescope gives an (inverted erect) and \( \ldots \ldots . \) (enlarged/diminished) image of a distant object. Choose the correct alternative.
A. Inverted, diminished
B. Inverted, enlarged
c. Erect, diminished
D. Erect, enlarged


The ecosystem services include.
A. Maintenance of biodiversity
B. Pollination of crop
C . Spiritual, cultural and aesthetic values
D. All of these


If the magnitudes of two vectors \( \vec{a} \) and \( \vec{b} \) are equal then which one of the following is correct?
A \( \cdot(\vec{a}+\vec{b}) \) is parallel to \( (\vec{a}-\vec{b}) \)
в. \( (\vec{a}+\vec{b}) \bullet \vec{a}-\vec{b} \)
C . \( (\vec{a}+\vec{b}) \) is perpendicular to \( (\vec{a}-\vec{b}) \)
D. None of the above


A uniform sphere of mass \( M \) and radius \( R \) is placed on a smooth horizontal ground. The angular acceleration of sphere if force \( \boldsymbol{F} \) is
applied on it at a distance \( 7 \frac{R}{5} \) from
ground level is
\( ^{\mathrm{A}} \cdot \frac{F}{2 M R} \)
в. \( \frac{F}{M R} \)
c. \( \frac{F R}{M} \)
D. \( \frac{2 F}{M R} \)


Given:
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) ; K_{1} \)
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g), K_{2} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \boldsymbol{K}_{3} \)
The equilibrium constant for \( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\frac{5}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \) will be:
A. \( K_{1} \)К 2 Кз
B. \( \frac{K_{1} K_{2}}{K_{3}} \)
c. \( \frac{K_{K} K_{3}^{2}}{K_{2}} \)
D. \( \frac{K_{2} K_{3}^{3}}{K_{1}} \)


A hydrocarbon \( \boldsymbol{A}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{10}\right) \) on addition of
\( H B r \) in presence of a peroxide forms
\( \left(C_{5} H_{11} B r\right) B \) which is found to be
resolvable into enantiomers. \( \boldsymbol{A} \) on
addition of \( H B r \) in aqueous medium
produces \( C \) which is an isomer of \( B \) but
can't be resolved. \( \boldsymbol{A} \) on reductive
ozonolysis produced \( \left(C_{4} H_{8} O\right) D \) as one
product. \( D \) on catalytic reduction with
\( N a B H_{4} \) produced \( E\left(C_{4} H_{10} O\right) \) which is
resolvable. \( \boldsymbol{E} \) on dehydration with concentrated sulphuric acid produced
\( F\left(C_{4} H_{8}\right) \) which on ozonolysis followed
by work-up with \( Z n-H_{2} O \) produced
two molecules of ethanol. Identify \( \boldsymbol{A} \) to
\( \boldsymbol{F} \)


A washing machine rated \( 300 W \) is operated for one hour/day. If the cost of a unit is Rs 3.00 then the cost of the
energy to operate a washing machine for the month of March is
A \( . \) Rs 25.60
B . \( R s 27.50 \)
c. \( R s 27.90 \)
D. \( R s 26.90 \)


If a mirror forms a virtual image of a
real object then
A. it must be a convex mirror.
B. it must be concave mirror.
c. it must be a plane mirror.
D. it may be any of the mirrors mentioned above


Find the value of \( x \) if \( 2^{4} \times 2^{5}=\left(2^{3}\right)^{x} \)


Milk is a compound.
A. True
B. False


A certain amount of potassium chlorate on thermal decomposition gives oxygen which is sufficient for the combustion
of ethane. When the products are
cooled, the volume of the gaseous product is \( \mathbf{v} \) ml. Identify the correct sequence of steps for the calculation of the mass of potassium chlorate
(a) Calculation of oxygen required for the combustion of ethane.
(b) Calculation of the amount of the
ethane subjected to combustion from the volume of gaseous product.
(c) Calculation of potassium chlorate which can give the required amount of
oxygen.
(d) Identification of the products of combustion of ethane and the product left after the cooling of products.
\( A \cdot a b c d \)
B. \( d \) b a c
\( c . b \) c a d
\( D \). \( d a c b \)


If \( A \) and \( B \) are two mutually exclusive
events, then
This question has multiple correct options
\( \mathbf{A} \cdot P(A) \leq P(\bar{B}) \)
B \( . P(\bar{A} \cap \bar{B})=P(\bar{A})-P(B) \)
\( \mathbf{c} \cdot P(\bar{A} \cup \bar{B})=0 \)
D . \( P(\bar{A} \cap B)=P(B) \)


Root cells do not play an active role in
the absorption of water in mechanism.
A. Osmotic absorption
B. Non-osmotic absorption
c. Active absorption
D. Passive absorption


If \( \boldsymbol{h}=\mathbf{5}, \boldsymbol{k}=\mathbf{3} \) then find the value of
\( \frac{k^{3}}{9}+\frac{h k}{10} \)


Secondary rainblow in the atmosphere
¡s:
A. the result of polarization and dispersion of light
B. brighter than the primary rainbow
C. due to the phenomenon of double refraction
D. formed with red colour on the top
E. formed due to two reflections in the rain drop


A common emitter transistor amplifier
has a current gain of \( 50 . \) If the load resistance is \( 4 k \Omega, \) and input
resistance is \( 500 \Omega, \) the voltage gain of amplifier is :
A. 100
в. 200
c. 300
D. 400


Short / Long answer type questions. Cell is called an osmotic system.
Explain


The charges of \( 2 \mu c, 4 \mu c \) and \( 6 \mu c \) are
placed at the corner \( A, B \quad \) and
respectively of a square \( A B C D \) of side
\( 0.2 m \) calculate the work done to
transfer a charge of \( 2 \mu c \) from \( D \) to the
center of the square.


Find the value of \( \sin ^{-1}\left[\sin \left(-\frac{17 \pi}{8}\right)\right] \)


Figure shows a surface with smooth
elevated ends PA and QB and a flat
rough surface \( A B \) of length L with variable coefficient of friction at
different positions A particle m is released from rest on surface PA at
height H from the ground The particle
climbs the surface \( \mathrm{BQ} \) once and finally
comes to rest at point A Find the
vertical height raised on surface BQ
\( \mathbf{A} \cdot 2 \mathbf{H} \)
B. H/2
\( c \cdot H \)
D. \( H / 3 \)


Bauxite is concentrated by:
A. Chemical method
B. Roasting
C. Magnetic separation
D. Froth flotation process


Petromyzon belongs to class
A. osteichthyes
B. Chondrichthyes
c. cyclostomata
D. Amphibia


During electroplating by electrolysis,
the article to be electroplated is:
A. Kept immersed in the electrolyte at the bottom.
B. Made the cathode of an electrolytic cell.
C. Made the anode of an electrolytic cell.
D. Made the electrolyte of the electrolytic cell.


The ratio of the radii of the first three
Bohr orbits is:
A .1: 0.5: 0.33
B. 1: 2: 3
c. 1: 4: 9
D. 1: 8: 27


Identify the wrong statement in context of heartwood.
A. It comprises dead elements with highly lignified walls
B. Organic compounds are deposited in it
c. It is highly durable
D. It conducts water and minerals efficiently


Large astronomical telescopes always use as objective
A. Iens
B. mirror
c. combinations of lenses
D. none of the above


If \( \tan \theta=\frac{p}{q} \) then \( \frac{p \sin \theta-q \cos \theta}{p \sin \theta+q \cos \theta}= \)
A. \( \frac{p^{2}-q^{2}}{p^{2}+q^{2}} \)
в. \( \frac{q^{2}-p^{2}}{q^{2}+p^{2}} \)
\( ^{\text {c. }} \cdot \frac{p^{2}+q^{2}}{p^{2}-q^{2}} \)
D.


The ability of an element to catenate is
primarily based on the
A. bond energy of the element to itself
B. bond energy of the element to others
c. mass of element
D. none of the above


When \( C O \) is reacted with ferric oxide
the product obtained is:
\( \mathbf{A} \cdot F e_{3} O_{4} \)
в. \( F e \)
c. ferrous carbonate
D. ferric carbonate


In a \( p \) -type semiconductor germanium
is doped with:
A. Gallium
B. Aluminium
c. Boron
D. All of the above.


Let \( f(x)=x+\frac{1}{2} . \) Then, the number of
real values of \( x \) for which the three
unequal terms \( \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{f}(\mathbf{2} \boldsymbol{x}), \boldsymbol{f}(\boldsymbol{4} \boldsymbol{x}) \) are
in HP is
A . 1
B.
\( c .3 \)
D.


An electron collides with a free
molecule initially in its ground state. The collision leaves the molecule in an
excited state that is metastable and
does not decay to the ground state by radiation. Let \( K \) be the sum of the
initial kinetic energies of the electron and the molecule, the \( \vec{P} \) the sum of their initial momenta. Let \( K^{\prime} \) and \( \vec{P} \)
represent the same physical quantities after the collision. Then.
\( \mathbf{A} \cdot K=K^{\prime}, \vec{P}=\vec{P} \)
B . \( K^{\prime}<K, \vec{P}=\vec{P}^{\prime} \)
C . \( K=K^{\prime}, \vec{P} \neq \vec{P}^{\prime} \)
D . \( K^{\prime} \neq K, \vec{P} \neq \vec{P}^{\prime} \)


If the curve \( x+y=x^{2}(x+1) \) has two
distinct horizontal tangents, then the distance between them is
A \( \cdot \frac{32}{27} \)
в. \( \frac{27}{32} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{22}{27} \)


State Kepler's law of orbit and law of
equal areas.


Using binomial theorem, evaluate \( (96)^{3} \)


Two circular coil 1 and 2 are made from
the same wire but the radius of the 1 st
coil is twice that of the \( 2 n d \) coil. What
potential difference in volts should be applied across them so that the magnetic field at their centres is
the same-
A . 3
B. 4
\( c \cdot 6 \)
D. 2


Photosynthesis in an aquatic plant was
measured by counting the number of
\( O_{2} \) bubbles coming out of the cut end of
the plant. What will happen to \( \boldsymbol{O}_{2} \)
production if you use a pipe blow air
from your mouth into water in the beaker?
A. Air from mouth contains \( O_{2} \) which is being added to
the plant, hence increase in \( O_{2} \) production.
B. Air from mouth contains \( C O_{2} \) which is utilised in
photosynthesis, hence increase in \( O_{2} \) production.
C. Bacteria from mouth will infect plant, hence reduction \( \operatorname{in} O_{2} \) production.
D. Water is already in contact with air, hence air from mouth will have no effect.


Assertion
If the potential difference applied to an electron is made 4 times, the de Broglie
wavelength associated is halved.
Reason
On making potential difference 4 times, velocity is doubled and hence \( d \) is halved.
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 limit of \( \frac{x^{2}-1}{x-1} \) as \( x \) approaches 1 as a limit is
\( \mathbf{A} \cdot \mathbf{0} \)
B. Indeterminate
c. \( x-1 \)
D. 2
\( E \)


The unit of e.m.f. of a cell is:
A. dyne
B. volt
c. ampere
D. joule


Solve \( : \lim _{x \rightarrow 0} \frac{\sin 4 x}{\sin x} \)


Two metallic spheres \( S_{1} \) and \( S_{2} \) are
made of the same material and have
got identical surface finish. The mass of
\( S_{1} \) is thrice that of \( S_{2} \). Both the spheres
are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of
\( S_{1} \) to that of \( S_{2} \) is
\( A \cdot 1 \)
\( \overline{3} \)
в. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{\sqrt{3}}{1} \)
\( D \)
\( \left(\frac{1}{3}\right) \)


A small object is \( 10 \mathrm{cm} \) in front of a plane mirror. A man stands 30 cm from the mirror behind the object and looks at the object's image. He should focus his eyes to see the image at a distance of from himself. (Fill in the blank)
\( A \cdot 25 \mathrm{cm} \)
B. 35 cm
c. \( 45 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


Unwanted material with ore is called as
A. Gangue
B. Rust
c. Slag
D. Silica


Examples of silicate minerals in the crust include:
This question has multiple correct options
A. pyroxene
B. mica
c. amphibole
D. cassertite


The major product of the above reaction
is:
\( \mathbf{A} \)
B.
\( c \)
D.


If \( a^{2}, b^{2}, c^{2} \) are in A.P., then the following are also in A.P. \( \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c}}, \frac{\boldsymbol{b}}{\boldsymbol{c}+\boldsymbol{a}}, \frac{\boldsymbol{c}}{\boldsymbol{a}+\boldsymbol{b}} \)
A. True
B. False


toppr
Q Type your question
19 \( m \) ( )
\( A \)
\( B \)
\( c \)
\( D \)


When two same conducting rod are
kept at different temperature,
A. theirs resistivity will be different
B. their resistivity will be same
c. resistivity doesn't' depend on temperature
D. none of the above


During the adsorption of krypton on activated charcoal at low temperature:
\( \mathbf{A} \cdot \Delta H<0 \) and \( \Delta S>0 \)
B. \( \Delta H>0 \) and \( \Delta S>0 \)
c. \( \Delta H<0 \) and \( \Delta S<0 \)
D. \( \Delta H>0 \) and \( \Delta S<0 \)


If in a binary solution, forces of attraction between like-molecules are
weaker than those prevailing between unlike-molecules, the solution is expected to exhibit ........... deviations from
Raoult's law.
A. negative
B. positive
c. zero
D. none


A glass refractive index 1.5 and radius
\( 10 \mathrm{cm}, \) has a spherical cavity of radius 5
cm concentric with it. A narrow beam of
parallel light is directed into the sphere.Find the final image and its
nature
A . - 25 cm left of \( S_{1} \), virtual
B. 25 cm right of \( S_{4} \), rea
\( \mathbf{c} . \) 15 \( \mathrm{cm} \) left of \( S_{4} \), virtual
D. \( 20 \mathrm{cm} \) right of \( S_{4} \), virtual


Silver and gold are purified with:
A . nitric acid
в. НС l
c. acetic acid
D. sulphuric acid


In library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 meters?


The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field( \( \bar{B} \) ) having magnetic moment \( (\bar{m}) \) will be.
A. - mB, zero
B. mB, zero
c. zero, mB
D. Zero, -mB


Find the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & 1\end{array}\right] \)


Add \( -7 m n+5,12 m n+2,9 m n- \)
\( 8,-2 m n-3 \)


The image of the point (1,2,3) through
the plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}=\boldsymbol{0} \) is
A \( \cdot\left(\frac{-2}{3}, \frac{1}{3}, \frac{-11}{3}\right) \)
в. \( \left(\frac{3}{7},-\frac{6}{7}, \frac{19}{7}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{2}{3}, \frac{1}{3}, \frac{11}{3}\right) \)
D. \( \left(\frac{-2}{3}, \frac{-1}{3}, \frac{11}{3}\right) \)


What are anionic detergents? Give an
example.


The specif heat of a gas:
\( \mathbf{A} \cdot \) Has only two value of \( C_{p} \) and \( C_{v} \)
B. Has a unique value at a given temperature
C. Can have any value between 0 and \( \infty \)
D. Depends upon the mass of the gas


Biomagnification of DDT in aquatic food
chain from 0.003 ppb in water to fish eating birds would be
A. 100 ppm
B. 50 ppm
c. 25 ppm
D. 2 ppm


When the cell has stalled DNA
replication, which check point should be predominantly activated?
A. \( G_{1} / S \)
в. \( G_{2} / G_{0} \)
c. \( G_{2} / M \)
D. \( M \)


Which of the following unicellular algae reproduce by auxospores, have silicified cell wall and store food in the form of
fats, leucosin and chrysolaminarin?
A. Diatoms
B. Yellow green algae
c. Dinoflagellates
D. Euglenoids


The electric potential at a point in free space due to a charge \( Q \) coulomb is \( Q \times 10^{11} V . \) The electric field at that
point is
A \( \cdot 4 \pi \varepsilon_{0} Q \times 10^{22} V / m \)
B . \( 127 \pi \varepsilon_{0} Q \times 10^{20} V / m \)
C. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V / m \)
D . \( 12 \pi \varepsilon_{0} Q \times 10^{22} \mathrm{V} / \mathrm{m} \)


Assertion
Chlorine reacts more rapidly with \( \boldsymbol{H}_{2}, \) in
comparision to \( \boldsymbol{O}_{\mathbf{2}} \)
Reason
\( D-C l \) bond is stronger in comparison
to \( H-C l \) bond
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


\( D_{2} O \) can be obtained by:
This question has multiple correct options
A. repeated distillation
B. exchange process
C. neutron emitting radioactive decay in presence of water
D. exhaustive electrolysis of alkaline water


Conversion of ammonia to nitric acid by the above process giving all conditions is \( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{x} \boldsymbol{O}_{2} \stackrel{\boldsymbol{P} t}{\longrightarrow} \boldsymbol{y} \boldsymbol{N} \boldsymbol{O}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \)
\( \boldsymbol{z} \boldsymbol{N} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{N} \boldsymbol{O} \)
Fiind \( x, y \) and \( z: \)
A. \( x=5, y=4 \) and \( z=3 \)
в. \( x=5, y=2 \) and \( z=4 \)
c. \( x=3, y=4 \) and \( z=5 \)
D. \( x=5, y=2 \) and \( z=3 \)


Consider following complexes:
I: \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \)
\( \|:\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \)
\( \| I:\left[N i(C O)_{4}\right] \)
\( \mid V:\left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
\( \mathbf{V}:\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-} \)
Out of this, select the complexes with
octahedral geometry :
This question has multiple correct options
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
B . \( \left[F e(C N)_{6}\right]^{4} \)
\( \mathbf{c} \cdot\left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
D. \( \left[N i(C N)_{4}\right]^{2-} \)


What is the end product of the above
shown reaction?
\( A \)
B.
\( c \)
D.


Consider the potentiometer circuit arranged as in figure. The
potentiometer wire is \( 600 \mathrm{cm} \) long. At
what distance from the point \( A \) should the jockey touch the wire to get zero deflection in the galvanometer?


Which of the following is correct?
\( A \cdot \sin 1^{\circ}>\sin 1 \)
B. \( \sin 1^{\circ}<\sin 1 \)
\( \mathbf{c} \cdot \sin 1^{\circ}=\sin 1 \)
D. \( \sin 1^{\circ}=\frac{\pi}{180} \sin 1 \)


Which of the following molecular species has unpaired electron(s)?
A. \( N_{2} \)
в. \( F_{2} \)
\( c \cdot O_{2} \)
D. \( o_{2}^{2} \)


Inner mitochondrial membrane allows
the passage of
A. Glucose
B. Pyruvate
c. NADH
D. oxaloacetate


were not given separate place in periodic table.
A. Alkali metalss
B. Isotopes
c. Halogens
D. Non-metals


Which of the following is a favourable factor for cation formation?
A. Low ionisation potential
B. High electron affinity
c. High electronegativity
D. Small atomic size


Two plane wavefronts of light, one
incident on a thin convex lens and
another on the refracting face of a thin prism. After refraction at them, the emerging wavefronts respectively become
A. plane wavefront and plane wavefront
B. plane wavefront and spherical wavefront
c. spherical wavefront and plane wavefront
D. spherical wavefront and spherical wavefront
E . elliptical wavefront and spherical wavefront


If 8.0 g of radioactive isotope has a half life of 10 hours, the half life of 2.0 g of the same substance is :
A. 2.5 hours
B. 5.0 hours
c. 10 hours
D. 40 hours


Linnaeus is associated with
A. Historia Plantarum
B. Origin of species
c. systema Naturae
D. origin of life


The most widely using artificial plant hormone for controlling weed is
A. NAA
B. 2,4-D
\( c \cdot \) ।вА
D. Ethylene


Electrons are charge carriers in conductors.
A . True
B. False


The Lanthanide contraction relates to:
A. oxidation states
B. magnetic state
c. atomic radius
D. valence electrons


Where is the voice box located in the
body?
A. At the upper end of the windpipe
B. At the upper end of the lungs
c. At the lower end of the windpipe
D. In between the oesophagus


Find heat rejected by gas in one
complete cycle


Which of these is not produced by the pituitary gland?
A. FSH
в. мSн
c. oxytocin
D. Prolactin


show that: The modulus and argument
of the complex number \( z_{1}=z^{2}-z, \) if
\( z=\cos \phi+i \sin \phi . \) is
\( \mathbf{2}|\sin \phi / \mathbf{2}|,\left(\frac{\mathbf{3} \boldsymbol{\pi}+\mathbf{3} \boldsymbol{\phi}}{\mathbf{2}}\right) \)


A large tank is filled with water (density
\( \left.=10^{3} k g / m^{3}\right) . \) A small hole is made at
depth \( 10 m \) below water surface. the
range of water issuing out of the hole is
R on ground. What extra pressure must
be applied on the water surface so that
the range becomes \( 2 R(\text { take } 1 a t m= \)
\( 10^{5} P a \) and \( g=10 m / s^{2} \)
A. \( 9 a t m \)
B. \( 4 a t m \)
\( c . \) 5atm
D. 3atm


Solve \( \int \frac{x^{5}}{x^{2}+1} d x \)
A. \( \frac{x^{4}}{4}+\frac{x^{2}}{2}+\tan ^{-1} x+c \)
B. \( \frac{x^{4}}{4}-\frac{x^{2}}{2}+\frac{1}{2} \log \left(x^{2}+1\right)+c \)
C \( \frac{x^{4}}{4}-\frac{x^{3}}{3}+\tan ^{-1} x+c \)
D. \( \frac{x^{4}}{4}+\frac{x^{2}}{2}+\frac{1}{2} \log \left(x^{2}+1\right)+c \)


In a uniform magnetic field of induction
\( B \) a wire in the form of a semicircle of
radius \( r \) rotates about the diameter of
the circle with angular frequency \( \omega . \) the
axis of rotation is perpendicular to the
field. If the total resistance of the circuit
is \( R \) the mean power generated per period of rotation is
A \( \cdot \frac{B \pi r^{2} \omega}{2 R} \)
B. \( \frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R} \)
c. \( \frac{(B \pi r \omega)^{2}}{2 R} \)
D. \( \frac{\left(B \pi r \omega^{2}\right)^{2}}{8 R} \)


1 mole of co-ordinate compound \( C o C l_{3} \)
on reaction with excess AgNCI 143.5 gms of AgCl ppt. Then number of chloride ions satisfying both primary valency and secondary valency are?
A .2
B. 3
c. 1
D.


A steel wire of length \( 4 \mathrm{m} \) and diameters \( 5 \mathrm{mm} \) is stretched by \( 5 \mathrm{kg} \) weight find the change in it's diameter if \( \boldsymbol{y}=\mathbf{0 . 4} \times \)
\( \mathbf{1 0}^{12} \boldsymbol{d} \boldsymbol{y} \boldsymbol{n} e / \boldsymbol{c m}^{2} \) and \( \boldsymbol{\sigma}=\mathbf{0 . 3} \)


Find coefficient of \( a^{3} b^{4} c^{5} \) in the
expansion of \( (b c+c a+a b)^{6} \)


\( 10^{24} \) molecules of solute are dissolved
in \( 10^{25} \) molecules of solvent, the mole
fraction of solute in solution is :
A . 0.09
B. 0.08
c. 0.07
D. 0.9


In the preparation of ammonia gas from ammonium chloride and calcium
hydroxide, the reactants are ground thoroughly. Why?
A.


Check if (0,-2) is a solution of \( 2 x-5 y= \)
10


If \( S(n)=i^{n}+i^{-n}, \) where \( i=\sqrt{-1} \) and
\( n \) is a positive integer, then the total number of distinct values of \( \boldsymbol{S}(\boldsymbol{n}) \) is:
A . 1
B. 2
\( c .3 \)
D. 4


Right atrium of rabbit receives
A. Two anterior vena cava
B. Two posterior vena cava
C. One anterior and one posterior vena cava
D. None of the above


Which of the following has highest
density:
A . \( N e \)
в. \( A r \)
\( \mathrm{c} . \) Не
D. \( x e \)


Anjali saves Rs.1200 every month in a recurring deposit in a bank. If this amount is \( 2 \% \) of her monthly salary, find her monthly salary
A . \( R s .60000 \)
B . Rs.70000
c. \( R s .13000 \)
D. Rs.19000


True statement is:
A. Positive catalyst increases the rate of reaction
B. During the course of the reaction, specific reaction rate remains constant.
C. Rate constant always increases with rise in temperature whether the reaction is endothermic or exothermic.
D. All are correct.


We sit in the room with windows open.
Then
A. Air pressure on the floor of the room equals the atmospheric pressure but the air pressure on the ceiling is eligible
B. Air pressure is nearly the same on the floor, the walls and ceiling
C. Air pressure on the floor equals the weight of the air coloumn inside the room (from floor to the ceiling) per unit area
D. Air pressure on the walls is zero since the weight of air acts downward


Global warming is due to greenhouse effect. The greenhouse gas include:
\( A \cdot C O_{2} \)
B. Oxides of nitrogen
\( c \cdot \) Both a \( \& b \)
D. None of the above


An alpha nucleus of energy \( \frac{1}{2} m v^{2} \) is bombarded onto a heavy nuclear target of charge \( Z e . \) Then the distance of
closest approach for the alpha nucleus will be proportional to
\( \mathbf{A} \cdot v^{2} \)
в. \( 1 / m \)
c. \( 1 / v^{4} \)
D. \( 1 / Z \)


\( \int_{0}^{2 \pi} \frac{x \sin ^{2 n} x}{\sin ^{2 n} x+\cos ^{2 n} x} d x \)
\( \mathbf{A} \cdot \pi^{2} \)
B . \( 2 \pi^{2} \)
\( \mathbf{c} \cdot 4 \pi^{2} \)
D. \( 8 \pi^{2} \)


Towards catalytic hydrogenation, the least reactive compound is:
A \( \cdot C H_{2}=C H_{2} \)
в. \( C H_{3}-C H=C H_{2} \)
c. \( H_{3} C-C H=C H-C H_{3} \)
D. \( \left(C H_{3}\right)_{2} C=C\left(C H_{3}\right)_{2} \)


A train approaching a railway crossing at a speed of \( 180 k m h^{-1} \) sounds a short
whistle at a frequency \( 600 H z \), when it
is \( 400 m \) away from the crossing. The
speed of sound in air is \( 340 m s^{-1} \). The
frequency of the sound heard by a person standing on a road perpendicular to the track at a distance of \( 300 m \) from the crossing is:
\( \mathbf{A} \cdot 680 H z \)
в. \( 480 H z \)
\( c \cdot 40 H z \)
D. \( 50 H z \)


The reaction of Xe with an excess of \( \mathbf{F}_{2} \)
at high pressure and 573 K yields:
A. \( \mathrm{XeF}_{2} \)
в. \( \mathrm{xeF}_{4} \)
c. \( \mathrm{xeF}_{6} \)
D. XeF \( _{3} \)


A ray incident at a point at an angle of
incidence \( 60^{\circ} \) enters a glass sphere of \( \mu=\sqrt{3} \) and is reflected and refracted
at the further surface of the sphere. The angle between the reflected
and refracted rays at this surface is :
A. \( 50^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60 \)
\( D \cdot 40 \)


The gas which we breath out precipitates into milky white.
A. Sodium Chloride solution
B. Calcium Carbonate solution
c. Potassium Permanganate solution
D. Potassium Bicarbonate solution


Write down the characteristic features
of animals mammal?


Evaluate: \( \int \frac{1}{\sin x+\sec x} d x \)


Which types of bonding are present in ammonium carbonate, \( \left(N H_{4}\right)_{2} C O_{3} ? \)
1. lonic
2. Covalent
3. Co-ordinate(dative covalent).
A. 1,2 and 3 are correct
B. 1 and 2 are correct
\( c \cdot 2 \) and 3 are correct
D. 1 is correct


Which among the following are found to be one of the pollutants of air pollution?
A. Chloroflorocarbon
B. Nitrogen
c. Carbon dioxide
D. oxygen


Write the negative (additive inverse) of each of the following:
\( \frac{-16}{13} \)


\( \lim _{x \rightarrow 0} \frac{a^{x}-b^{x}}{e^{x}-1} \)


An aqueous solution of \( 0.1 \mathrm{M} N H_{4} C l \)
will have a pH closer to:
A . \( 9 . \)
B. 8.1
c. 7.
D. 5.1


Which of the following event does not lead into secondary succession?
A. All organisms that existed are lost
B. Where no living organisms ever existed
C. Abandoned crop field
D. Land affected by flood


The standard electrode potential of \( \boldsymbol{C u} \mid \boldsymbol{C u}^{+2} \) is \( -\mathbf{0 . 3 4} \) Volt. At what
concentration of \( C u^{+2} \) ions, electrode
potential will be zero?
A \( \cdot 1.98 \times 10^{-12} M \)
В. \( 2.98 \times 10^{-12} M \)
c. \( 1.49 \times 10^{-12} M \)
D. \( 5.96 \times 10^{-12} M \)


What is the value of \( X \) in the given
chemical formula of crystalline borax,
\( N a_{2}\left[B_{4} O_{5}(O H)_{4}\right] . X H_{2} O ? \)
A. 5
B. 6
\( c \cdot 7 \)
D. 8


Types of forces a fluid exerts are
and


The single-bonded metallic radius of \( N a \) is 157 pm. Give a reasonable estimation of the radii, assuming that the increment between radii of different
magnitudes is 60 pm. the anionic radius of \( N a \) is:
A \( .217 \mathrm{pm} \)
B. 227 pm
c. \( 237 \mathrm{pm} \)
D. 207 pm


Find the sum of odd integers from 1 to
\( \mathbf{2 0 0 1} \)


Differentiate between Vertebrates and
Invertebrates


Dalton's atomic theory was based on:
A. Law of chemical combination
B. Mass theory
c. Periodic table
D. None of the above


A constant potential difference is applied across a resistance. Consider variation of resistance with
temperature. Which graph represents best the variation of power produced in
resistance versus resistance?
A. Straight Line
B. Circle
c. Parabola
D. Hyperbola


Which of the following have highest boiling point?
A. \( C H_{3} C l \)
в. \( C H_{3} C H_{2} C H_{2} C l \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} B r \)
D. \( C H_{3} C H_{2} C H_{2} I \)


A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor
queen?


The surface of the metal is illuminated
with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be \( 1.68 \mathrm{eV} \), the work function of metal is :
A . \( 1.51 \mathrm{eV} \)
B. 1.42 ev
c. 3.0 ev
D. 1.68 ev


A hollow metallic sphere of radius R is given a charge \( Q \). Then, the potential at the centre is
A. zero
в. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{R} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{2}{Q} R \)
D. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{2 R} \)


Which one of the following is the definition of ecosystem?
A. A localised association of seven plants and animals.
B. Different communities of plants, animals and microbes, together with their physicochemical environments
c. Different communities of plants and microbes, plus their physicochemical environments.
D. A community of organisms interacting with one another


In Galapagos islands, Darwin observed variations in structures in
A. Elephants
B. Giraffies
c. Rats
D. Finch birds


Nalorphene \( \left(C_{19} H_{21} N O_{3}\right) \) similar to
morphine, is used to combat
withdrawal symptoms in narcotic uses. Dose of nalorphene generally given is 1.5mg. The mass of \( 1.5 \times 10^{-3} \mathrm{m} \)
aqueous solution required for the above dose is?
A . \( 5.2 \mathrm{g} \)
c. \( 4.6 \mathrm{g} \)
D. \( 1.9 g \)


Electricity is a form of
A. Force
B. Energy
c. Tension
D. Shock


\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{4} & -\mathbf{2} & \mathbf{5}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{l}\mathbf{2} \\ \mathbf{0} \\ \mathbf{3}\end{array}\right], \) then
\( \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{B} \boldsymbol{A})= \)
\( A \cdot\left\{\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right\} \)
\( \mathbf{B} \cdot\left\{\begin{array}{lll}8 & -4 & 10 \\ 0 & 0 & 0 \\ 12 & -6 & 15\end{array}\right\} \)
\( \mathbf{c} \cdot\left\{\begin{array}{ccc}8 & 0 & 12 \\ -4 & 0 & -6 \\ 10 & 0 & 5\end{array}\right\} \)
D. None of the above


Patterns of feeding and digestion in
Protozoa?


A inductance capacitance circuit is in
the state of resonance. if the \( C=0.1 \mu F \)
and \( \boldsymbol{L}=\mathbf{0 . 2 5} \) Henry. Neglecting ohmic resistance of circuit what is the
frequency of oscillations
A. \( 1007 \mathrm{Hz} \)
в. \( 100 \mathrm{Hz} \)
\( \mathrm{c} .109 \mathrm{Hz} \)
D. \( 500 H z \)


Black bodies are:
\( A \cdot \) Good absorbers and bad radiators
B. Good absorbers and good radiators
C. Bad absorbers and good radiators
D. Bad absorbers and bad radiators


Assertion
Smaller the organism higher is the rate of metabolism per gram weight.
Reason
The heart rate of a six month old baby is much higher than that of an old person.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \alpha \) and \( \beta \) are complex conjugates to each other and \( \boldsymbol{\alpha}=-\sqrt{\mathbf{2}}+\boldsymbol{i} \) then find
\( \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}-\boldsymbol{\alpha} \boldsymbol{\beta} \)


When \( 4 V \) DC is connected across an
inductor, current is \( 0.2 A . \) When \( A C \) of
\( 4 V \) is applied the current is \( 0.1 A \) Then self inductance of the coil is:
\( \left[\text { Given } \omega=1000 \text { rads}^{-1}\right] \)
A \( .20 \mathrm{mH} \)
в. \( 40 \mathrm{mH} \)
c. \( 20 \sqrt{3} \mathrm{mH} \)
D. none of these


If \( \sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}, \) then \( x \)
is equal to
A \( \cdot 0, \frac{1}{2} \)
в. \( _{1, \frac{1}{2}} \)
\( c \cdot \frac{1}{2} \)
D.


A convex lens is made of 3 layers of
glass of 3 different materials as in the figure. A point object is placed on its
axis. The number of images of the
object are
\( A \)
B.
\( c .3 \)
\( D \)


An amphibolic pathway is
A. TCA cycle
B. Calvin cycle
c. Terminal oxidation
D. Electron transport chain


A colloidal system having a solid substance as a dispersed phase and a
liquid as a dispersion medium is
classified as:
A. solid sol
B. gel
c. emulsion
D. sol


Which of the following is not a state function?
A. Temperature
B. Density
c. work
D. volume
E . Pressure


In which of the following species the bonds are non-directional?
A \( \cdot N C l_{3} \)
B. \( R b C l \)
c. \( B e C l_{2} \)
D. \( B C l_{3} \)


A body dropped from the top of the tower
covers a distance \( 7 x \) in the last second
of its journey, where \( x \) is the distance covered in first second. How much time
does it take to reach the ground? (in seconds)
A . 3
B. 4
\( c .5 \)
\( D \)


The disease due to inflammation of
vermiform appendix of the digestive system is known as
A. Amoebic dysentery
B. Appendicitis
c. Intestinal cancer
D. Appendectomy


If \( x^{2}+y^{2}=4, \) then \( y \frac{d y}{d x}+x \) is equal to
\( A \cdot 4 \)
B. 0
c. 1
D. -


An electron makes transition from \( \boldsymbol{n}= \)
\( \mathbf{3}, \boldsymbol{n}=\mathbf{1} \) state in a hydrogen atom. The
different possible number of photons that can be emitted is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. 6


\( \int e^{x}(x+1) d x \)


A thin uniform rod of mass \( m \) and
length \( \ell \) is free to rotate about its upper end. When it is at rest it recelves an
impulse \( J \) at its lowest point, normal to
its length. Immediately after impact, This question has multiple correct options
A. The angular momentum of the rod is \( J \ell \)
B. The angular velocity of the rod is \( 3 J / m \ell \)
C. The kinetic energy of the rod is \( 3 J^{2} / 2 m \)
D. The linear velocity of the midpoint of the rod is \( 3 J / 2 M \)


The colour of \( M n O_{4}^{-} \) ion is due to
charge transfer.
If true enter 1 , else enter 0 .


Find the work requires to compress adiabatically \( 1 g \) of air initially at \( N T P \) to half its volume. Density of air at \( N T P=0.001129 g c m^{-3} \) and \( \frac{C_{p}}{C_{v}}=1.4 \)
A . \( 62.64 J \)
в. \( 32.64 J \)
c. \( -32.64 J \)
D. \( -62.64 J \)


Name the stage of mitosis in which chromosomes are arranged on the equator of spindle fibre.
A. Anaphase
B. Metaphase
c. Prophase
D. Telophase


State which of the following solutions contains only ions?
A \( \cdot d i l . H N O_{3} \)
B. Kerosene
c. \( C H_{3} \) СООН
D. Oxalic acid


Find the number of diboromo
derivatives of molecular formula
\( C_{3} H_{6} B r_{2} \) is:
A .4
B . 2
\( c .6 \)
D. 8


The coolant used in the nuclear reactor
is
A . Liquid sodium
B. Cadmium
c. Deuterium
D. Liquid hydrogen


Rusting of iron is a chemical reaction.
The reaction can be termed as:
A. combination reaction
B. addition reaction
c. both (A) and (B)
D. decomposition


Molecular orbital theory could be used to explain the bonding in \( S i F_{6}^{2-} \) and the shape of this ion is octahedral.


Which of the following (s) is/are correct
statement?
This question has multiple correct options
A. The empirical formula of all alkanes is same.
B. The empirical formula of all alkenes is same
C. The empirical formula of all the members of any homologous series is same
D. Two different compound can have the same molecular formula.


Find the value of following determinant. \( \left|\begin{array}{ll}\frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2}\end{array}\right| \)


The order of reactivity of alcohols towards hydrogen halide is :
A \( \cdot \) benzyl\( >3^{0}>2^{0}>1^{0} \)
В. \( 3^{0}> \) benzyl \( >2^{0}>1^{0} \)
c. \( 3^{0}>2^{0}>1^{0}> \) benzyl
D. \( 3^{0}>2^{0}> \) benz \( y l>1^{0} \)


Some physical constants are given in List - I and their dimensional formulae
are given in List - II. Match the following
List - 1
A) Planck's constant
e) \( \left[M L^{-1} T^{-2}\right] \)
B) Gravitational constant
f) \( \left[M L^{1} T^{-1}\right] \)
C) Bulk modulus
g) \( \left[M L^{2} T^{-1}\right] \)
D) Linear momentum
h) \( \left[M^{-1} L^{3} T^{-2}\right] \)
A. A-h, B-g, C-e ,D-f
B. A-f, B-e, C-g, D-h
C. A-g, B-f, C-e, D-h
D. A-g, B-h, C-e, D-f


Solve :
\( \int \frac{d x}{\sqrt{1-x^{2}}}=\sin ^{-1} x+c \)


Discuss the continuity of the function \( f \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x} \neq \mathbf{0} \)


toppr LoGin
Q Type your question
to Rs. \( 50,000 . \) The data about the
number of persons in various
categories is as under:

Monthly \( \quad \) Number of Cars income
(in rupees) 2 More than
30,001
40,000 If 400 50 25
\( 40,001- \)
50,000 \( 100 \quad 300 \) 125
Find the probability that a person
selected at random in the income slab
\( 40,001-50,000 \) have more than 2
cars.
A. 0.125
B. 0.225
c. 0.325
D. None of thesee


What is the work to be done to increase
the velocity of a car from \( 30 \mathrm{km} h^{-1} \) to
\( 60 \mathrm{km} h^{-1} \) If the mass of the car is
\( 1500 k g ? \)


Stage of hydrarch are :
(a) Marsh meadow stage
(b) Reed
swamp stage (c) submerged plant
stage
(d) Phytoplankton stage
(e) Submerged free-floating stage.
Identify the correct sequence:
\( A \cdot d, c, e, b, a \)
B. \( c, e, a, b, d \)
\( c \cdot b, d, c, a, e \)
D. \( d, e, c, b, a \)
E. e, c, b, a, d


Two large, identical and parallel conducting plates have surface \( X \) and \( Y \)
facing each other. The charge per unit
\( \operatorname{area} \) on \( X \) is \( \sigma_{1}, \) and on \( Y \) it is \( \sigma_{2} . \) Then :
A \( \cdot \sigma_{1}=-\sigma_{2} \) in all cases.
B . \( \sigma_{1}=-\sigma_{2} \) only if a charge is given to one plate only
C \( \cdot \sigma_{1}=\sigma_{2}=0 \) if equal charges are given to both the
plates
D. \( \sigma_{1}>\sigma_{2} \) if \( x \) is given more charge than \( Y \)


An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface
of the earth of two earth radii \( (h=2 R \)
where \( R \) is the radius of the earth.
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)
A. 81 pounds
B. 40.5 pounds
c. 18 pounds
D. 54 pounds
E. 0 pounds (astronaut is weightless


Arrange the following steps in correct order in constructing a square whose one diagonal is \( 5 \mathrm{cm} \) Step 1: Let PQ cut AC at 0.
Step 2: Draw a diagonal \( A C=5 c m \) Step 3: Join \( A b, B C, C D \) and DA. Then ABCD is the required square. Step 4: Draw PQ the perpendicular bisector of AC.
Step 5: With 0 as centre and OA radius draw a circle. Let the circle cut QP at
points B and D.
A. 2,1,4,5,3
В. 2,5,4,1,3
c. 2,4,5,1,3
D. 2,4,1,5,3


The number of valence electrons
present in noble gases is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 18
c. 8
\( D \)


The value of \( \lim _{x \rightarrow 0} \frac{\tan 2 x}{\sin 5 x} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{2}{5} \)
\( c \cdot 2 \)
D. 5


Find the height of a cylinder that has a diameter of 10 feet and a surface area
of \( 220 f t^{2} . \) Round your answer to the nearest whole number.
(use \( \pi=22 / 7 \) ).
\( \mathbf{A} \cdot 0.1 \mathrm{ft} \)
в. 3 ft
\( c \cdot 2 f t \)
D. \( 1 \mathrm{ft} \)


\( \int e^{x} \sqrt{1+e^{x}} d x= \)
A \( \cdot\left(1+e^{x}\right)^{\frac{3}{2}}+c \)
B \( \cdot \frac{2}{3}\left(1-e^{x}\right)^{3 / 2}+c \)
\( \mathbf{c} \cdot\left(1-e^{x}\right)^{3 / 2}+c \)
D. \( \frac{2}{3}\left(1+e^{x}\right)^{3 / 2}+c \)


A piece of metal weighs \( 46 \mathrm{g} \) in air. When immersed in a liquid of specific
gravity 1.24 at \( 27^{0} \) it weighs 30 g. When the temperature of the liquid is raised
to \( 42^{0} \) in a liquid of specific gravity 1.20 it weighs \( 30.5 g . \) The coefficient of linear expansion of metal is
A \( .2 .23 \times 10^{-5} /^{0} C \)
B . \( 6.7 \times 10^{-5} /^{0} C \)
c. \( 4.46 \times 10^{-5} /^{0} C \)
D. none of these


happens when two or more waves
overlap.


A particle is an oscillating simple
harmonically with angular frequency \( \omega \)
and amplitude \( A \). It is at a point \( (A) \) at \( a \)
certain instant (shown in the figure). At
this instant, it is moving towards mean
position (B). It takes time \( t \) to reach mean position (B). If the time period of oscillation is \( T, \) the average speed
between \( A \) and \( B \) is :
A. \( \frac{A \sin \omega t}{t} \)
B. \( \frac{A \cos \omega t}{t} \)
c. \( \frac{A \sin \omega t}{T} \)
D. \( A \cos \omega t \)


During winter, an echo is heard
A. sooner than during summer
B. later than during summer
c. can't say
D. Not heard


Which of the following is the best thing to do during heavy lighting?
A. Lying on the ground in an open place
B. Going into the nearest water body
c. staying indoors away from metallic doors or windows
D. standing under a tall tree


One end of a string of length \( L \) and cross-sectional area \( A \) is fixed to a
support and the other end is fixed to a bob of mass \( m \). The bob is revolved in a
horizontal circle of radius \( r \) with an
angular velocity \( \omega \) such that the string makes an angle \( \theta \) with the vertical. The stress in the string is :
A. \( \frac{m g}{A} \)
в. \( \frac{m g}{A}\left(1-\frac{r}{L}\right) \)
c. \( \frac{m g}{A}\left(1+\frac{r}{L}\right) \)
D. none of these


An artifical pacemaker is implanted subcutaneously and connected to the heart in patients
A. Having 90\% blockage of the three main coronary arteries
B. Having a very high blood pressure
c. with i rregularity in the heart rhythm
D. Suffering from arteriosclerosis


Conservation of linear momentum is
equivalent to
A. Newton's first law of motion
B. Newton's second law of motion
c. Newton's third law of motion
D. Newton's law of gravitation


Assertion
Nitrogen does not form \( \boldsymbol{N} \boldsymbol{C} \boldsymbol{I}_{\mathbf{5}} \) or \( \boldsymbol{N} \boldsymbol{F}_{\mathbf{5}} \)
but phosphorus can.
Reason
Nitrogen \( \left(1 s^{2} 2 s^{2} 2 p^{3}\right) \) lacks \( 2 d \) -orbitals
in which electrons of 2 s can be excited
to make five orbitals unpaired. Only
three electrons remain unpaired hence
only \( N X_{3} \) is formed. In case of
\( P\left(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\right), 3 s \) electron can be
excited into \( 3 d \) vacant orbitals thus
making five unoaired electrons, thus
\( P X_{5} \) is possible.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for
\( \boldsymbol{y}=\left(\sin 20 x+a^{2 x}+10\right) \)


\( f(x)=\sin ^{-1}\left[\log _{2}\left(\frac{x^{2}}{2}\right)\right] \) where
denotes the greatest integer function.


Which of the following statements
is/are true?
This question has multiple correct options
A. The standard molar enthalpy of formation of \( C O_{2} \) is equal to the standard molar enthalpy of combustion of carbon (graphite).
B. Molar heat capacity of water in equilibrium with ice at constant pressure is infinity.
C. A reaction is impossible at any temperature if \( \Delta H> \) \( 0, \Delta S<0 \)
D. The heat of neutralization of strong acid and strong base in solution is equal to the \( \Delta H \) of the reaction
\( H_{2} O+H^{+} \rightleftharpoons H_{3} O^{+} \)


A battery of e.m.f \( 15 \mathrm{V} \) and internal resistance 3 ohm is connected to two
resistors of resistances 3 ohm and 6
ohm in series. The current through the battery is
A . 1.25 A
B. 3 A
\( c \cdot 1.5 \mathrm{A} \)
\( D .5 \mathrm{A} \)


If the earth is at one fourth of its present
distance from the sun, the duration of
the year will be
A. Half the present year
B. One eighth of the present year
c. one fourth of the present year
D. One sixth of the present year


The work done by the tension T in the
above process is
A . \( Z \) ero
B . \( T(L-L \cos \theta) \)
c. \( -T L \)
D. \( -T L \sin \theta \)


The time taken by a photoelectron to come Out after the photon strikes is approximately.
\( \mathbf{A} \cdot 10^{-1} s \)
B. \( 10^{-2} s \)
\( \mathbf{c} \cdot 10^{-10} s \)
D. \( 10^{-16} s \)


When 100 J of heat is given to an ideal
gas it expands from \( 200 \mathrm{cm}^{3} \) to \( 400 \mathrm{cm}^{3} \) at a constant pressure of \( 3 \times \)
\( \mathbf{1 0}^{5} \) Pa. Then calculate \( : \boldsymbol{R}= \)
\( \left[\frac{25}{3} J / m o l-k\right] \) The molar heat capacity \( C_{p} \) at constant pressure when
the \( T=400 K \) is
A \( \frac{125}{3} J / m o l-K \)
в. \( \frac{125}{7} J / \) тод \( -K \)
c. \( \frac{125}{9} J / m o l-K \)
D. None of these


Obturator foramen is present in
A. Skull
B. Radio-ulna
c. Pelvic girdle
D. Quadrate


Which of the following is strongest acidic oxide?
\( A \cdot \operatorname{Sb}_{2} O_{3} \)
в. \( \mathrm{P}_{2} \mathrm{O}_{5} \)
\( c \cdot \mathrm{so}_{2} \)
\( \mathrm{D} \cdot \mathrm{s} \mathrm{O}_{3} \)


Prove that
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{rl}
\frac{\boldsymbol{x}^{2}-\boldsymbol{2 5}}{\boldsymbol{x}-\mathbf{5}}, & \boldsymbol{w} \boldsymbol{h} \boldsymbol{e} \boldsymbol{n} \quad \boldsymbol{x} \neq \mathbf{5} \\
\boldsymbol{1 0}, \boldsymbol{w h e n} & \boldsymbol{x}=\mathbf{5}
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{5} \)


The minimum number of carbon atoms
in an alkane having four primary carbon atoms are:
A .4
B. 8
\( c .5 \)
D. 6


Find the sum of all natural numbers
from 1 to 200 which are divisible by 4


For the industrial preparation of nitric acid from ammonia, when ammonia is heated with excess air in presence of a
catalyst, at \( 900^{\circ} \mathrm{C}, \mathrm{NO} \) is obtained. Which line of entry describes the undefined reagents, products and reaction conditions?
A . catalyst at room temperaure \( \left(25^{\circ} \mathrm{C}\right) \) and \( \mathrm{NO}_{2} \)
B. catalyst at room temperature \( \left(25^{\circ} \mathrm{C}\right) \) and \( N_{2} \mathrm{O} \)
C. catalyst hight pressure and \( N O_{2} \)
D. catalyst hight pressure and \( N_{2} O_{3} \)


If the vertex \( =(2,0) \) and the
extremities of the latus rectum are
(3,2) and \( (3,-2), \) then the equation of the parabola is
A \( \cdot y^{2}=2 x-4 \)
B . \( x^{2}=4 y-8 \)
c. \( y^{2}=4 x-8 \)
D. None


Assertion
The water molecules are held together
from root cells to the vascular bundle
because of cohesive force.
Reason
Water does not ascend in the plant because of transpiration pull.
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