What is the pressure \( 200 \mathrm{m} \) below the surface of the ocean if the sp. gravity of sea water is 1.03: [Atmospheric
pressure \( \left.=1.013 \times 10^{5} N / m^{2}\right] \)
A \( .21 .2 \times 10^{5} N / m^{2} \)
B . \( 20.4 \times 10^{5} N / m^{2} \)
C \( .40 \times 10^{4} N / m^{2} \)
D . \( 21.2 \times 10^{6} N / m^{2} \)


Expansion of a perfect gas into vacuum
is related with:
A. \( \Delta H=0 \)
в. \( q=0 \)
c. \( W=0 \)
D. All the above


How does fish move in water?


A uniform disc is acted by two equal forces of magnitude \( F . \) One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface is nF. If \( r \) be the radius of
the disc, then the value of n would be?
(in \( N) \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. 1.2
c. 2.0
D. 3.2


In \( \triangle A B C, \angle A B C=90^{\circ} \) and BM is the
altitude. If \( A M=16 \) MC Prove that \( A B= \)
\( 4 \mathrm{BC} \)


If \( a=e^{i \alpha}, b=e^{i \beta}, c=e^{i \gamma} \) and \( \cos \alpha+ \)
\( \cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+ \)
\( \sin \gamma, \) then prove the following
\( a+b+c=0 \)


Do you find any relationship between circulatory system and excretory system? What are they?


Assertion
The stress-strain relationship in elastic region need not be linear and can be
non-linear.
Reason
Steel has non linear,profile in elastic
zone
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 thermodynamics cycle takes in heat
energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is 3 times the amount of
work done by the cycle, the efficiency of the cycle is:
A . 0.25
B. 0.33
c. 0.67
D. 0.9


Particle 1 experiences a perfectly elastic
collision with a stationary particle
2. Determine their mass ratio, if after a head-on collision the particles fly apart in the opposite directions with equal
velocities.
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{1}{3} \)
D. 3


Where Chlorophyll II pigments are present in the Chloroplast? What term is used for core of cilium and flagellum?


According to this reaction, ethanol is :
\( 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{Na}-\cdots->2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{ONa}+\mathrm{H}_{2} \)
A. Acidic in nature
B. Basic in anture
c. Amphoteric
D. Neutral


Atomic number of carbon atom is :
\( A \cdot 1 \)
B. 3
\( c \cdot 6 \)
D. 8


Which fuel used injet crafts?
A. Roseneke
B. Keosener
c. Kerosene
D. Rosekene


Which part of cockroach has both exoskeleton and endoskeleton?
A. Head
B. Thorax
c. Abdomen
D. All of the above


If incident ray lies in \( x-y \) plane,
reflected ray lies in \( x-y \) plane, then
the normal will lie in:
A. x-y plane
B. y-z plane
c. x-z plane
D. It does not depend on planes


An small object is kept at \( 18 \mathrm{cm} \) from combination of a convex lens and plane
mirror to get the image on object itself. Now the space between lens and mirror is filled with liquid of refractive index
\( \mu L . \) Now we need to keep the object at
\( 27 \mathrm{cm} \) to get the image on object. Find
\( \mu L \)
\( A \)
B.
\( c \)
2
\( D \)


Bilaterally symmetrical organisms
include
A. Planaria
B. Roundworms
c. Humans
D. Arthropods
E. All of the above


A solution which is \( 10^{-3} M \) each in
\( M n^{2+}, F e^{2+}, Z n^{2+} \) and \( H g^{2+} \) is
treated with \( 10^{-16} M \) sulphide ion. If
\( K_{s p} \) of MnS,FeS,ZnS andHgS are \( 10^{-15}, 10^{-23}, 10^{-20} \) and \( 10^{-54} \)
respectively, which one will precipitate first?
A . Fes
в. Mgs
c. нgs
D. zns


A vehicle moving on a straight road sounds a whistle of frequency \( 256 \mathrm{Hz} \) while nearing a hill with a velocity 10 ms \( -1 . \) The number of beats per second
observed by a person travelling in the vehicle is:
\( \left(V=330 m s^{-1}\right) \)
A. zero
B. 10
\( c \cdot 14 \)
D. 16


If \( A \) is an invertible matrix of order 2
then \( \operatorname{det}\left(A^{-1}\right) \) is equal to
\( \mathbf{A} \cdot \operatorname{det}(A) \)
B. \( \frac{1}{\operatorname{det}(A)} \)
\( c .1 \)
D. 0


Major product X will be:
\( \mathbf{A} \)
\( \mathbf{B} \)
\( \mathbf{c} \)
D.


Find the middle term in the expansion of \( \left(\frac{2 x^{2}}{3}-\frac{3}{2 x}\right)^{12} \)


If \( f(x)= \) \( \left|\begin{array}{ccc}(\mathbf{1}+\mathbf{3} \boldsymbol{x})^{2 \boldsymbol{a}} & (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} & \mathbf{1} \\ \mathbf{1} & (\mathbf{1}+\mathbf{3} \boldsymbol{x})^{2 \boldsymbol{a}} & (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} \\ (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} & \mathbf{1} & (\mathbf{1}+\mathbf{3} \boldsymbol{x})^{\mathbf{2} \boldsymbol{a}}\end{array}\right| \)
then
A. \( f(x) \) has constant term 1
B. constant term is \( 2 a-3 b \)
c. coefficient of \( x \) in \( f(x) \) is zero
D. constant term is \( 2 a+3 b \)


Of the total nephrons,the juxtamedullary nephrons constitute
\( \% \)
A . 15
B. 45 5
\( c \cdot 65 \)
D. 85


Which of the following is a false
statement?
A. Sodium oxide is more basic then magnesium oxide
B. Beryllium oxide is amphoteric.
C. The thermal stability of beryllium carbonate is more than that of calcium carbonate
D. Lithium chloride is deliquescent.


The order of magnitude of 0.00701 is:
A . -
B. - -
\( c \cdot 2 \)
D.


The point (4,0) lie on the line
A. \( y-x=0 \)
В. \( y=0 \)
c. \( x=0 \)
D. \( y+x=0 \)


If an object is placed at a distance of 20cm from the pole of a concave mirror,
the magnification of its real image is 3
If the object is moved away from the mirror by \( 10 \mathrm{cm} \), then the magnification
is -1.
A. True
B. False


In the given square \( P, Q, R, S \) with atomic number is written are
metalloids. About this the 4 statements
are given below. Select the correct
option of the true statements.
(a) Element after square \( P \) is a non-
metal
(b) Square \( R \) represents metalloid
(c) Element just before square \( R \) is a metalloid
\( (d) \) Element just before square \( S \) is a non-metal
\( A \cdot(a),(b) \) and \( (c) \)
в. \( (a),(b) \) and \( (d) \)
c. \( (b) \) and \( (c) \)
D. \( (a),(b),(c) \) and \( (d) \)


How many kinds of cells are found in
islet of Langerhans?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.


A body of mass \( 100 g \) moves at the speed of \( 36 k m / h \). The de-Broglie wavelength related to it is of the order
\( \boldsymbol{m} \)
\( \left(h=6.626 \times 10^{-34} J s\right) \)
A \( \cdot 10^{-24} \)
B . \( 10^{-14} \)
c. \( 10^{-34} \)
the \( 4^{-34} 4 \)
D. \( 10^{-44} \)


Coal is a substance mainly containing carbon also having oxygen, hydrogen, nitrogen and
A. sodium
B. sulphur
c. aluminium
D. chlorine


What is Chain Reaction?
A. Particles released by splitting of atom strikes other uranium atoms and split them.
B. Particles released by expanding of atom strikes other uranium atoms and split them
C. Particles released by contracting of atom strikes other uranium atoms and split them
D. None


Show that the lines whose d.c.s are
given by \( l+m+n=0,2 m n+3 l n- \)
\( 5 l m=0 \) are perpendicular to each
other.


Three simple harmonic motions in the
same direction having the same amplitude a and same period are superposed. If each differs in phase
from the next by \( 45^{\circ}, \) then :
This question has multiple correct options
A. The resultant amplitude is \( (1+\sqrt{2}) a \)
B. The phase of the resultant motion relative to the first is \( 90^{\circ} \)
c. The energy associated with the resulting motion is \( (3+2 \sqrt{2}) \) times the energy associated with any single motion
D. The resulting motion is not simple harmonic


A spectrum is obtained by sending a beam of white light through a prism. \( \mathbf{A} \)
second prism exactly similar to the first
one is placed in an inverted position
with the sides parallel to the first. Now
A. A new spectrum will be formed on the screen with double the number of colours present in the previous spectrum
B. New spectrum will be obtained on the screen with only half the number of colours present in the previous spectrum
C. Previous spectrum will disappear and we will obtain a white light formed by the fusion of the colours
D. A spectrum with same number of colours present in the previous spectrum will be formed but their wave lengths will be increased twice


Substances which allow heat to pass
through them easily are known as
A. Insulators
B. Conductors
c. semi conductors
D. None


The vast surrounding space is called
A . Galaxy
B. Universe
c. Planet
D. None of these


\( \sigma \)
\( \frac{d}{d r} \)


The force of a required to row a boat at velocity is proportional to square of its speed of \( \mathbf{v} \mathrm{km} / \mathrm{h} \) requires \( 4 \mathrm{KW}, \) how many does a seepd of \( 2 \mathrm{V} \mathrm{km} / \mathrm{h} \) required
\( A \cdot 8 \mathrm{kW} \)
B. 16 kw
c. з२кw
D. 76kw


Proton was discovered by:
A. Thomson
B. Rutherford
c. chadwick
D. Goldstein


The incorrectly matched pair, among the following is Molecule Shape
A . \( B r F_{5} \) Trigonal bipyramidal
B. \( S F_{4} \) See saw
c. \( C l F_{3} \) T-shape
D. \( N H_{4}^{+} \) Tetrahedral
E . \( N H_{3} \) Trigonal pyramidal


Name the following compound according to the IUPAC system or nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C H O} \)


\( \lim _{x \rightarrow 0} \frac{1-\cos x}{x \log (1+x)}= \)
A .
B.
c. -1
D.


A wave is represented by the equation \( \boldsymbol{y}=\boldsymbol{A} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}), \) where
\( x \) is in metres and \( t \) is in seconds. What
is the wavelength of this wave travelling in the positive x-direction?
A. \( 0.5 m \)
в. \( 0.2 m \)
c. \( 0.25 m \)
D. \( 0.75 m \)


The diagram shows a section through
the human heart. Which blood vessels
carry blood to and from the lungs?
A. Blood to lungs - 1 , Blood from lungs - 3
B. Blood to lungs - 1, Blood from lungs - 4
C. Blood to lungs - 2, Blood from lungs - 3
D. Blood to lungs - 2, Blood from lungs - 4


\( \boldsymbol{\alpha}-\boldsymbol{s u l p h u r} \leftrightharpoons \boldsymbol{\beta}-\boldsymbol{s u l p h u r} \) is an
example of:
A. physical equilibrium
B. chemical equilibrium
c. irrversible reaction
D. both physical and chemical equilibrium


The split of white light into its constituent colours by a triangular prism is called
A. Dispersion
B. Reflection
c. Refraction
D. Scattering


If \( x=a t^{2}, y=2 a t, \) then \( \frac{d^{2} y}{d x^{2}}= \)
A. \( -\frac{1}{t^{2}} \)
в. \( \frac{1}{2 a t^{3}} \)
c. \( -\frac{1}{t^{3}} \)
D. \( -\frac{1}{2 a t^{3}} \)


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


What is the oxidation number of \( M n \) in
\( M n O_{2} ? \)
\( A \cdot+2 \)
B. +4
\( c \cdot-2 \)
D. -


The slope of velocity-time graph gives
A. acceleration
B. velocity
c. displacement
D. none of these


Green light wavelength \( 5460 \AA \) is incident on an air-glass interface. If the refractive index of glass is \( 1.5, \) the wavelength of light in glass would be \( \left(\boldsymbol{C}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \quad \boldsymbol{m} \boldsymbol{s}^{-\mathbf{1}}\right) \)
A. \( 3640 \AA \)
в. 5460 ,
c. \( 4861 \dot{h} \)
D. None of these


Assertion
The frequencies of incident, reflected and refracted beam of monochromatic
light at the interface of two media are
same
Reason
The incident, reflected, refracted rays are coplanar.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false


State True or False.
\( \alpha \) -particle, when passed through gases, cause large ionisation.
A. True
B. False


The correct statement(s) among the
following is/are:
This question has multiple correct options
A. All \( d \) -orbitals except \( d_{x^{2}} \) have two angular nodes
B. \( d_{x^{2}-y^{2}}, d_{z^{2}} \) lie on the axes
C. The degeneracy of \( p \) -orbitals remains unaffected in the presence of external magnetic field
D. \( d \) -orbitals have 3 -fold degeneracy


Evaluate \( \lim _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2} \) where \( f(x)= \)
\( x^{2}-4 \)
\( A \cdot-1 \)
B. 2
\( c \cdot 0 \)
D. 4


The load voltage is approximately constant when a zener diode is
A. Forward-biased
B. Reverse-biased
c. operating in the breakdown region
D. Unbiased


Two wheels \( A \) and \( B \) are released from
rest from points \( X \) and \( Y \) respectively
on an inclined plane as shown in figure. Which of the following statement(s) is/are incorrect?
This question has multiple correct options
A. Wheel \( B \) takes twice as much time to roll from \( Y \) to \( Z \) than that of wheel \( A \) from \( X \) to \( Z \)
B. At point \( Z \) velocity of wheel \( A \) is four times that of wheel \( B \)
c. Acceleration of the wheel \( A \) is four times that of wheel
\( B \)
D. Both wheel take same time to arrive at point \( Z \).


\( \Delta S_{\text {Total}}=-40 k J / m o l \times K \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{s y s}=\mathbf{2 0 0 0} \boldsymbol{k J} / \boldsymbol{m o l} \)
\( \boldsymbol{T}=\mathbf{4 0 0} \boldsymbol{K} \)
Find out value of \( \Delta S_{\text {system}} \) at equilibrium?
A. \( -35 k J / m o l \times K \)
в. \( -5 k J / m o l \times K \)
c. \( -20 k J / m o l \times K \)
D. \( -10 k J / m o l \times K \)


An asteroid is moving directly towards the centre of the earth. When at a
distance of \( 10 R(R \) is the radius of the
earth) from the earth centre, it has a
speed of \( 12 k m / s . \) Neglecting the effect of the earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is \( 11.2 k m / s \) )? Give your answer to the nearest integer in kilometer/s


The reaction between chloral and
chlorobenzene in \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) yields:
A. chloretone
B. p,p-dichlorodiphenyl trichloroethane
c. o-chlorobenzaldichloride
D. chloralphenylchloride


A body is projected vertically upwards with certain velocity. The magnitude of its displacement in the last second of
its upward motion is...........................
A. \( 2 g \)
в. \( \frac{g}{3} \)
\( c \cdot \frac{g}{2} \)
D. \( \frac{3 g}{2} \)


Which of the following structures has a dipole moment in terms of atom and unbonded electron pair placement from a Lewis Dot structure view?
A \( . I F_{4}^{1} \)
в. \( X e F_{4} \)
\( \mathrm{c} \cdot I F_{4}^{1} \)
D. \( N H_{4}^{1} \)


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


Imagine a new planet having the same density as that of Earth but is 3 times bigger than the Earth in size. If the
acceleration due to gravity on the surface of Earth is \( g \) and that on the surface of the new planet is \( g^{\prime} \), then:
A \( \cdot g^{\prime}=3 g \)
B. \( g^{\prime}=\frac{g}{9} \)
c. \( g^{\prime}=9 g \)
D. \( g^{\prime}=27 g \)


Assertion
\( K, R b \) and \( C s \) form superoxides.
Reason
The stability of the superxides
increases from ' \( K^{\prime} \) to \( ^{\prime} C s^{\prime} \) due to
decrease in lattice energy.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the CSA and TSA of a solid
hemisphere of radius \( 14 \mathrm{cm} \)


Inside a horizontally moving box, an
experimenter finds that when an object
is placed on a smooth horizontal table
and is released, it moves with an
acceleration of \( 10 m s^{-2} . \) In this box, if
1 kg body is suspended with a light string, the tension in the string in equilibrium position. (w.r.t. experimenter) will be (take \( g=10 m s^{-2} \)
A \( \cdot 10 m s^{-2} \)
B . \( 10 \sqrt{2} \mathrm{ms}^{-2} \)
c. \( m s^{-2} \)
D. Zero


A man buys two cricket bats, one for
Rs1360 and the other for Rs1040. He
sells the first bat at a gain of \( 15 \% \) and the second one at a loss of \( 15 \% \). Find his
gain or loss per cent in the whole transaction.


A charged gold leaf electroscope has its leaves apart by certain amount having enclosed air. When the electroscope is subjected to X-rays, then the leaves
A. Further dilate
B. Start oscillating
c. collapse
D. Remain unaltered


If \( x \neq y \) and the sequences \( x, a_{1}, a_{2}, y \)
and \( x, b_{1}, b_{2}, y \) each are in \( A . P ., \) then \( \left(\frac{a_{2}-a_{1}}{b_{2}-b_{1}}\right) \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
c. 1
D.


ff \( x_{1}, x_{2}, x_{3} \) as well as \( y_{1}, y_{2}, y_{3} \) are in
G.P. with same common ratio, then the
points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{Q}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \) and
\( \boldsymbol{R}\left(\boldsymbol{x}_{3}, \boldsymbol{y}_{3}\right) \)
A. lies on a straight line
B. lie on an ellipse
c. lie on a circle
D. are vertices of a triangle


What is EAN? Write it's formula.


If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{2}\end{array}\right|, \) find the value of \( \mathbf{3}|\boldsymbol{A}| \)


Which transition corresponds to series
limits for paschen series?


"Sodium is preferred to be prepared by chemical method over electrolytic method."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


Which of the following options shows bisexual animals only?
A. Amoeba, sponge, leech
B. Sponge, cockroach, Amoeba
c. Earthworm, sponge, leech
D. Tapeworm, earthworm, honeybee


Examine the following functions for continuity.
(i) \( f(x)=x-5 \)
(ii) \( f(x)=\frac{1}{x-5} \)
\( \boldsymbol{x} \neq \mathbf{5} \)
(iii) \( f(x)=\frac{x^{2}-25}{x+5}, x \neq-5 \)
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{5}| \)


Find the values of a and \( b, \) if \( A=B, \) where
\[
\begin{array}{c}
\boldsymbol{A}=\left[\begin{array}{cc}
\boldsymbol{a}+\boldsymbol{4} & \boldsymbol{3} \boldsymbol{b} \\
\boldsymbol{8} & -\boldsymbol{6}
\end{array}\right] \text { and } \boldsymbol{B}= \\
{\left[\begin{array}{cc}
\boldsymbol{2} \boldsymbol{a}+\boldsymbol{2} & \boldsymbol{b}^{2}+\boldsymbol{2} \\
\boldsymbol{8} & \boldsymbol{b}^{2}-\boldsymbol{5} \boldsymbol{b}
\end{array}\right]}
\end{array}
\]


\( f(x)=\left\{\begin{array}{cc}1-\cos x & x \neq 0 \\ x & \\ k & x=0\end{array}\right\} \)
continuous at \( x=0, \) then the value of \( k \)
is:
A . 0
\( B \cdot \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
\( D \cdot-\frac{1}{2} \)


Oxidation number and covalency of
sulphur in \( S_{8} \) molecule respectively are
\( \mathbf{A} \cdot 6 \& 8 \)
B. \( 0 \& 8 \)
c. \( 0 \& 2 \)
D. \( 6 \& 2 \)


Solve the following pair of equations by reducing them to a pair of linear equations:6 \( x+3 y=6 x y, 2 x+4 y= \)
\( 5 x y \)
A. \( x=1, y=1 \)
в. \( x=1, y=2 \)
c. \( x=0, y=1 \)
D. None of these


A gas will approach ideal behavior at:
A. low temperature and low pressure
B. low temperature and high pressure
c. high temperature and low pressure
D. high temperature and high pressure


1 kgwt is equal to
\( \mathbf{A} \cdot 9.8 N \)
B. \( 980 N \)
\( \mathbf{c} .98 N \)
D. none of these


Rancidity can be prevented by This question has multiple correct options
A. adding anti-oxidants
B. packing oily food in nitrogen gas
c. packing oily food in argon gas
D. use of spices


Assertion
Kinetic energy of photoelectrons increases with increase in the
frequency of incident radiation.
Reason
The number of photoelectrons ejected increases with increase in intensity of incident radiation.
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


Can a converging lens produce a virtual image?
A. Yes, only when the object is placed at the focus of the lens.
B. Yes, only when the object is placed at the center of the lens.
C. Yes, when the object is placed inside the focal point.
D. Never


The work done in splitting a drop of water of 1 mm radius into \( 10^{6} \) droplets
is (surface tension of water \( 72 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{3}} \mathbf{N} / \boldsymbol{M}\right) \)
A . \( 5.98 \times 10^{-5} \mathrm{J} \)
В. \( 10.98 \times 10^{-5} J \)
c. \( 16.95 \times 10^{-5} J \)
D. \( 8.95 \times 10^{-5} J \)


The unit of self-inductance in SI system
is


Phenols are prepared from benzene in
the presence of:
A. alum
B. oleum
c. vinegar
D. all of these


The outer membrane that covers brain
is
A. Myelin Sheath
B. Duramater
c. Arachnoid membrane
D. Piamater


After expressing the following as a rational number of the form \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \) \( \frac{-\mathbf{7}}{\mathbf{4}}+\frac{\mathbf{5}}{\mathbf{3}}+\frac{-\mathbf{1}}{\mathbf{2}}+\frac{-\mathbf{5}}{\mathbf{6}}+\mathbf{2}, \) then the
value equivalent to \( p \) is


List-I \( \quad \) List-II If \( r \)
\( (A) \)
, Angular
(1) \( 119.5^{\circ} \)
\( S_{O_{3}} \) anguiar
(B) \( 116.8^{\circ}, \) Angular (2) \( \mathrm{SO}_{2} \) 'Angular A
\( (C) \)
\( \mathrm{H}_{2} \mathrm{O} \)
(3) \( 120^{\circ} \), Trigonal pyramidal of The and dal
\( (D) \)
(4) \( 104.5^{\circ}, \) Angular \( \mathrm{O}_{3} \) \( 104.5^{\circ}, \mathrm{Ar} \) idr The correct match is:
\( A \cdot(A)-3,(B)-1,(C)-4,(D)-2 \)
B. \( (A)-2,(B)-3,(C)-1,(D)-4 \)
C \( \cdot(A)-4,(B)-2,(C)-3,(D)-1 \)
D. \( (A)-1,(B)-2,(C)-4,(D)-3 \)


Which conformer has higher energy in the Sawhorse projection formula of ethane and why?


If \( \sin \theta=\frac{45}{53}, \) find the value of
\( \operatorname{cosec}^{2} \theta-\cot ^{2} \theta \)


Hybridisation involves:
A. Orbitals of same atom with slightly different energies
B. Orbitals of different atoms but with equal energies
C. Orbitals of different atoms with different energies
D. Orbitals of the same atom with exactly equal energies


A very long magnet is placed vertically with one pole on the table. A neutral
point was found at \( 20 \mathrm{cm} \) from the pole. What is the pole strength if the vertical
component of earth's field is \( 0.4 \times \)
\( 10^{-4} W b m^{-2} ? \)
\( \mathbf{A} \cdot 16 A-m \)
в. \( 8 A-m \)
\( \mathrm{c} \cdot 4 A-m \)
D. None of these


A uniform disc of mass \( M \) and radius \( R \)
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull \( T \) is exerted on the cord, the tangential acceleration of a point on the rim is
A \( \cdot \frac{T}{M} \)
в. \( \frac{M}{T} \)
c. \( \frac{2 T}{M} \)
D. \( \frac{M}{2 T} \)


Factorization means, writing an expression as a product of its.....
A. factors
B. multiples
c. нс
D. LCM


Find \( \frac{d y}{d x}, \) if \( x+y=\sin (x-y) \)
A \( \cdot \frac{\cos (x-y)-1}{\cos (x-y)+1} \)
B \( \cdot \frac{\cos (x-y)+1}{\cos (x-y)-1} \)
C \( \frac{\cos (x+y)+1}{\cos (x-y)-1} \)
D. \( \frac{\cos (x+y)-1}{\cos (x-y)+1} \)


The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the \( x \)
axis
A .2
B. 1
\( c .3 \)
D. 4


Distances measured below the
principal axis are taken as
A. Positive
B. Negative
c. None
D. Both


Process in which maximum energy is
released:
A \( \cdot O \rightarrow O^{2} \)
в. \( M g^{+} \rightarrow M g^{2} \)
c. \( C l \rightarrow C l^{-} \)
D. \( F \rightarrow F^{-} \)


A point charge \( \boldsymbol{q}_{1}=+2 \mu C \) is placed at
the origin of co-ordinates. A second
charge, \( q_{2}=-3 \mu C \),is placed on the \( x \)
axis at \( x=100 \mathrm{cm} . \) At what point \( (\mathrm{or} \)
points ) on the \( x \) -axis will the absolute
potential be zero?
A. \( x=40 \mathrm{cm} \) and \( x=-200 \mathrm{cm} \)
в. \( x=40 \) ст опы
c. \( x=-200 c m \) only
D. \( x=80 \) cm only


The image on the retina remains for :
A . \( 20 s \)
B. \( 10 s \)
c. \( \frac{1}{10} s \)
D. \( \frac{1}{16} \)


A solenoid of length \( 0.4 m \) and having
500 turns of wire carries a current of
3 amp. Calculate the torque required to hold a coil (having radius \( 0.02 \mathrm{cm} \)
current \( 2 A \) and turns 50 ) in the middle
of the solenoid with its axis
perpendicular to the axis of the
solenoid. \( \left(\pi^{2}=10\right) \)


The base unit for the length in metric
system is :
A . \( \mathrm{cm} \)
B. \( m \)
\( c \)
D. yd


During cell division in apical meristem nuclear membrane reappears in
A. Interphase
B. Telophase
c. Prophase
D. S phase


In an hydrogen atom, the electron is making \( 6.6 \times 10^{15} \)rps. If the radius of
the orbit is \( 0.53 \times 10^{-10} m, \) then the
equivalent magnetic dipole moment is approximately
\( \mathbf{A} \cdot 10^{-29} A m^{2} \)
B . \( 10^{-27} \mathrm{Am}^{2} \)
c. \( 10^{-23} A m^{2} \)
D. \( 10^{-19} \mathrm{Am}^{2} \)


What will be the critical angle of water
if \( _{a} \mu_{w}=\frac{4}{3} \)
A \( \cdot 42 \)
B . \( 49^{\circ} \)
\( c \cdot 22 \)
D. 1


In which disease, due to narrowing of tracheal passages, alveoli are deprived of oxygen?
A. Asthma
B. Bronchitis
c. Pneumonia
D. Emphysema


From the given traits, which are temporarily acquired traits?
A. Tattoos
B. Blisters
c. organ transplant
D. vaccinations


Name the compound that does not fit
into the formula \( C_{x}\left(H_{2} O\right)_{Y} \) but is a
carbohydrate.


Match the following
1. Horse-shoe
a. Holds the armature in
magnet place
2. Armature
b. Electromagnet
c. Passes electric current to the
3. Spring strip \( \quad \) spring strip
4. Adjusting
d. Fixed to the spring strip screw
\( \mathbf{A} \cdot 1-d, 2-a, 3-c, 4-b \)
B. \( 1-a, 2-c, 3-b, 4-d \)
\( \mathbf{c} \cdot 1-b, 2-d, 3-a, 4-c \)
D. \( 1-c, 2-b, 3-d, 4-a \)


A capacitor of capacity \( 10 \mu F \) is
charged to a potential of \( 10000 \mathrm{V} \) and a
wire is stretched by \( 0.2 m \) by a force of
\( \mathbf{5 0 0 0} N . \) The ration of the potential energies stored in them will be
A . 1
в. 500
c. 0.002
D. 0.0001


A block tied between two identical
springs is in equilibrium. If upper spring is cut, then the acceleration of
the block just after the cut is \( 6 m s^{-2} \)
Now if instead of upper string lower spring is cut, then the acceleration of
the block just after the cut will be
(Take \( \left.g=10 m / s^{2}\right) \)
A \( .1 .25 \mathrm{ms}^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( 2.5 \mathrm{ms}^{-2} \)


Two samples of HI each of 5 g was taken separately in two vessels of volume 5 lit and 10 lit respectively at
\( 27^{\circ} \mathrm{C} . \) The extent of dissociation of \( \mathrm{HI} \)
will be:
A. More in 5 litre vessel
B. More in 10 litre vessel
c. Equal in both vessels
D. Can't be predicted


A stone is projected with a initial velocity at an angle to the horizontal. small piece separates from the stone
before the stone reaches its maximum
height. Then this piece will
A. fall to the ground vertically
B. fly side by side with the parent stone along parabolic path
c. fly horizontally initially and will trace a different parabolic path
D. lag behind the parent stone, increasing the distance from it.


Which among the following have zero
dipole moment?
\( A \cdot \operatorname{cis}-C_{2} H_{2} C l_{2} \)
B. trans- \( C_{2} H_{2} C l_{2} \)
c. \( P C l_{3} \)
D. 2-Pentene


The differential equation of family of coaxial circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{\lambda} \boldsymbol{x}+\boldsymbol{c}=\boldsymbol{0} \) is
A \( \cdot \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}+1=0 \)
B. \( y \cdot \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
\( ^{\mathbf{c}}\left(\frac{d^{2} y}{d x^{2}}\right)+\left(\frac{d y}{d x}\right)^{2}+1=0 \)
D \( \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)


What are the limitations of Mendeleev
periodic table:


Assertion
Threshold wavelength of certain metal
is \( \lambda_{0} . \) Light of wavelength slightly less
than \( \lambda_{0} \) is incident on the plate. It is
found that after some time the
emission of electrons stops
Reason
The ejected electrons experience force
of attraction due to development of
positive.
A. Assertion is incorrect but Reason is correct
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect and Reason is correct explanation for Assertion.


The major product in the following at \( 25^{\circ} \mathrm{C} \) is: \( C H_{3} C O O H^{C H_{3} C H_{2} N H_{2}} \)
\( \mathbf{A} \cdot C H_{3} C O N H C H_{2} C H_{3} \)
B \( \cdot C H_{3} C H=N C H_{2} C H_{3} \)
\( \mathbf{c} \cdot N H_{3}^{+} C H_{2}^{-} C H_{3} \cdot C H_{2} C O O^{-} \)
D. \( C H_{2} C O N=C H C H_{3} \)


True or False
The phenomenon of existence of an element in more than one physical form is called allotropy.
A. True
B. False


The energy needed to remove one electron from unipositive ion is abbreviated as:
\( \mathbf{A} \cdot 1^{s t} I \cdot P \)
B. \( 3^{r d} \) I.P.
\( \mathbf{c} \cdot 2^{n d} I . P \)
D. \( 1^{s t} \) E.A.


In a semiconductor decide, the barrier potential offers opposition to:
This question has multiple correct options
A. Majority charge carries in both regions
B. Minority charge carries in both regions
C. Free electrons in the \( N \) - region
D. Holes in the p - region


The breaking of which of the following
bond is most endothermic?
A \( . F-F \)
в. \( C l- \) Сl
c. \( B r-B r \)
\( \mathbf{D} \cdot I-I \)


Evaluate \( \frac{(-40+80 a)}{8 a} \)


Schizocoelomates and
enterocoelomates are
A. acoelomates
B. invertebrates
c. true coelomates
D. echinoderms only


The valency of impurity element for making p-type semiconductor is
A . 5
B. 3
\( c \cdot 4 \)
\( D \)


Reticulate venation is observed mostly
in
A. Monocot plants
B. Dicot plants
c. Thallophytes
D. Bryophytes


The friction coefficient between the
table and the block shown in the figure is 0.2 . Find the tensions in the two
strings.


Prove that the function \( f(x)=\log _{e} x \) is
increasing on \( (\mathbf{0}, \infty) \)


Normal temperature of a human body is
\( 98.4^{\circ} \mathrm{F} \). Its value in Celsius scale is
\( \mathbf{A} \cdot 32^{\circ} C \)
В. \( 37^{\circ} \mathrm{C} \)
\( c \cdot 28^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)


Is this a negative rational number? \( \frac{-2}{-9} \)


Give four uses of sodium carbonate
(washing soda)


If \( A \) and \( B \) are two events, then which of
the following does not represent the
probability that exactly one of \( A, B \)
occurs is
This question has multiple correct options
\( \mathbf{A} \cdot P(A)+P(B)-P(A \cap B) \)
B \( \cdot P\left(A \cap B^{\prime}\right)+P\left(A^{\prime} \cap B\right) \)
\( \mathbf{c} \cdot P\left(A^{\prime}\right)+P\left(B^{\prime}\right)-2 P\left(A^{\prime} \cap B^{\prime}\right) \)
D \( . P(A)+P(B)-2 P(A \cap B) \)


Which of the following statement is
true?
A. The collenchyma occurs in layers below the epidermis in monocotyledonous plants
B. Sclerenchyma cells are usually dead and without protoplasts.
c. xylem parenchyma cells are living and thin walled and their cell walls are made up of lignin.
D. The companion cells are specialized sclerenchymatous cells.
E. Phloem fibres are generally present in the primary phloem.


\( \triangle U^{\theta} \) of combustion of methane is \( -x \) k
mol \( ^{-1} \). The value of \( \triangle \boldsymbol{H}^{\boldsymbol{\theta}} \) is:
\( \mathbf{A} \cdot=\Delta U^{\theta} \)
в. \( <\Delta U^{\theta} \)
c. zero
\( \mathrm{D} \cdot>\Delta U^{\theta} \)


Which of the following is not a feature of chemical change?
(I) Original substance can be obtained by simple physical methods.
(II) It is a temporary change.
(III) The new substances formed have
properties different from those of the reacting substances.
A . ।, ॥
в. ।, II
c. ॥, ॥।
D. All of the above


Evaluate \( \int_{1}^{3}\left(2 x^{2}+5 x\right) d x \)


Prove that \( 2 \tan ^{-1} \frac{1}{2}-\tan ^{-1} \frac{1}{7}=\frac{\pi}{4} \)
Prove that \( 3 \sin ^{-1} x=\sin ^{-1}(3 x- \)
\( \left.4 x^{3}\right), x \in\left[\frac{-1}{2}, \frac{1}{2}\right] \)


Convert the Ethanol to bromoethane.


The area bounded by the \( x- \) axis, the
curve \( y=f(x) \) and the lines \( x=1 \) and
\( x=b \) is equal to \( (\sqrt{b^{2}+1}-\sqrt{2}) \) for all
\( \boldsymbol{b}>1, \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. \( \sqrt{x-1} \)
B. \( \sqrt{x+1} \)
c. \( \sqrt{x^{2}+1} \)
D. \( \frac{x}{\sqrt{x^{2}+1}} \)


The graph above shows velocity \( v \) Vs
time \( t \) relation for a particle moving in a straight line. Identify which of the
following displacement \( s \) vs. time \( t \)
graph is equivalent to above graph?
A. I only
в. ॥ Il only
c. I and II only
D. II and III only
E . ।, II, and III


In the preparation of alkene from
alcohol using \( A l_{2} O_{3} \) which is effective
factor?
A . Porosity of \( A l_{2} O_{3} \)
B. Temperature
c. concentration
D. surface area of \( A l_{2} O_{3} \)


A box contains 20 cards marked with
numbers 1 to \( 20 . \) One card os drwan
from the box at random. What is the
probability of the following events:
(1) That number on the card is a prime number,
(2) The number on the card is a perfect
square.


Match the following and select the correct answer from codes given below


If (0,0) and \( (3, \sqrt{3}) \) are two vertices of
an equilateral triangle then find third
vertex.


Which of the following acids dissociates to the greatest extent in a
aqueous solution?
A. Trichloroacetic acid
B. Acetic acid
c. chloroacetic acid
D. Dichloroacetic acid


Give one physiological role of nickel


Figure shows three lenses of equal radii of curvature of the curved surfaces. the
ratio of focal lengths of \( \mathrm{P}, \mathrm{Q} \) and \( \mathrm{R} \) is
A .1: 1: 1
B. 1:1:-1
\( c \)
D . - -1:2:-


Find the amount of heat supplied to decrease the volume of an ice water
mixture by \( 1 \mathrm{cm}^{3} \) without any change in
temperature. \( \left(\rho_{\text {ice}}=0.9 \rho_{\text {water}}, L_{\text {ice}}=\right. \)
\( \mathbf{8 0} \) cal \( / \mathbf{g m} \)
A . 360 call
B. 500 call
c. 720 call \( l \)
D. none of these


Electrical conduction in a
semiconductor takes place due to
A. electrons only
B. holes only
c. both electrons and holes
D. neither electrons nor holes


Mars has about \( \left(\frac{1}{10}\right)^{t h} \) as much mass as the Earth and half as a diameter of
earth. The acceleration of failing body on Mars is nearly:
\( \mathbf{A} \cdot 9.8 m s^{-2} \)
B . \( 1.96 \mathrm{ms}^{-2} \)
D. \( 4.9 \mathrm{ms}^{-2} \)


When a dielectric is introduced
between the plates of a condenser, the capacity of condenser:
A . increases
B. decreases
c. remains same
D. none of these


A person travelling from sea level to high altitudes can develop
A. High risk sickness
B. Sea level sickness
c. Altitude sickness
D. All of the above


\( N O \) often acts as a three electron donor
in contrast to most ligands which donate two electrons. What happens
when \( N O \) replaces three \( C O \) in
\( \left[\boldsymbol{F} e(\boldsymbol{C O})_{5}\right] \) and \( \operatorname{six} \boldsymbol{C O} \) in \( \left[\boldsymbol{C r}(\boldsymbol{C O})_{6}\right] ? \)


Among \( N H_{3}, H_{2} O \) and \( H F, \) which
would you expect to have highest magnitude of hydrogen bonding and why?


Boron can be obtained by various
methods but not by
A. Thermal decomposition of \( B_{2} H_{6} \)
B. Pyrolysis of \( B I_{3} \) (van Arkel)
C. Reducing \( B C l_{3} \) with \( H_{2} \)
D. Electrolysis of fused \( B C l_{3} \)


A depolariser used in dry cell batteries
is:
A. ammonium chloride
B. manganese dioxide
c. potassuim hydroxide
D. sodium phosphate


A steel bar \( A B C D 40 c m \) long is made
up of three parts \( A B, B C \) and \( C D, \) as
shown in the figure The rod is subjected
to a pull of \( 25 k N . \) The total extension of
the rod is (Young's modulus for steel
\( 2 \times 10^{11} N m^{-2} \)
\( \mathbf{A} \cdot 0.0637 m m \)
B. \( 0.0647 \mathrm{mm} \)
c. \( 0.0657 m m \)
D. \( 0.0667 m m \)


When applied to law of combining volumes, which of the following is correct about Berzelius hypothesis?
a) it predicts atoms are indivisible
b)it predicts atoms are divisible
c)it is contrary to Dalton's hypothesis
A. Only a
B. Only
c. Both a and \( c \)
D. Both b and c


For a particle in SHM, if the amplitude of the displacement is \( \alpha \) and the
amplitude of velocity is \( v, \) the amplitude of acceleration is
A \( . v \alpha \)
в. \( \frac{v^{2}}{\alpha} \)
c. \( \frac{v^{2}}{2 \alpha} \)
D. \( \underline{v} \)


In triangle \( A B C, M \) is mid-point of \( A B \)
and a straight line through \( \boldsymbol{M} \)
and parallel to \( B C \) cuts \( A C \) in \( N \). Find
the lenghts of \( A N \) and \( M N \) if \( B C=7 \)
\( \mathrm{cm} \) and \( \boldsymbol{A C}=\mathbf{5} \mathrm{cm} \)
A. \( A N=2.5 \mathrm{cm} \) and \( M N=3.5 \mathrm{cm} \)
B. \( A N=1.5 \mathrm{cm} \) and \( M N=3.5 \mathrm{cm} \)
c. \( A N=2.5 \mathrm{cm} \) and \( M N=4.5 \mathrm{cm} \)
D. none of the above


\( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{4} \) and \( \boldsymbol{n}(\boldsymbol{B})=\mathbf{5}: \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B})= \)
\( \mathbf{A} \cdot 20 \)
B. 10
c. 30
D. None of the above


Ground water can be raised by
A. Harvesting water
B. Watershed management
c. Soil erosion
D. Both A and B


Catabolic reactions are exergonic reactions. Justify the statement with
reason.


If the mass of a planet is \( 10 \% \) less than that of the earth and the radius is \( 20 \% \)
greater than that of the earth, the
acceleration due to gravity on the planet will be.
A. \( 5 / 8 \) times that on the surface of the earth
B. \( 3 / 4 \) times that on the surface of the earth
c. \( 1 / 2 \) times that on the surface of the earth
D. \( 9 / 10 \) times that on the surface of the earth


When phenol is distilled with \( Z n \) dust, the main product is :
A. Biphenyl
B. Benzene
c. Benzaldehyde
D. Phenolphthalein


Define stress and explain the types of
stress


Two sides of the parallelogram PQRS
are \( 6 \mathrm{cm} \) and \( 4 \mathrm{cm} . \) The height
corresponding to the base RS is \( 3 \mathrm{cm} \)
Find Area of parallelogram.


Molar heat capacity of water in equilibrium with the ice at constant pressure is
A. zero
B. Infinity
c. \( 40.45 k^{-1} \mathrm{mol}^{-1} \)
D. None


Assertion
In an irreversible process, finite
changes are made; therefore the system is not at equilibrium throughout the
process.
Reason
An ideal constant pressure process that has no internal entropy generation and no friction in its system can be considered as ideal reversible process.
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


When a white light ray falls on a prism, the ray at its first surface suffers:
A. no refraction
B. only dispersion
c. only deviation
D. both deviation and dispersion


Write expressions for \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
following equilibria:
(a) \( 4 N H_{3(g)}+5 O_{2(g)} \rightleftharpoons 4 N O(g)+ \)
\( \mathbf{6} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \)
(b) \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}(\boldsymbol{g})}+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}(\boldsymbol{g}) \)
\( (c) 2 C l_{2(g)}+2 N O_{2(g)} \rightleftharpoons 2 N O_{2} C l_{2(g)} \)


How many cubes each of surface area
\( 24 c m^{2} \) can be made out of a cube of
edge measure \( 1 \mathrm{m} ? \)
A . 165000
B. 125000
c. 180000
D. 155000


Assertion
The equivalent weight of an element is variable.
Reason
The valency of an element is variable.
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


Write a note on economic importance of algae?


If \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & -3 & 0\end{array}\right] \) and \( B=\left[\begin{array}{ccc}3 & 4 & -2 \\ 1 & 0 & 0\end{array}\right] \)
then the order of \( A B^{T} \) is
\( A \cdot 2 \times 3 \)
B. \( 3 \times 3 \)
\( c \cdot 3 \times 2 \)
D. \( 2 \times 2 \)


When a body is placed on a surface, the body exerts a force downwards on the
surface equal to its weight on the surface, but the body does not move because
A. The surface exerts an equal and opposite force on the body normal to the surface.
B. The surface exerts an equal and opposite force on the body parallel to the surface
c. The surface exerts no force on the body
D. The surface exerts an infinite force on the body parallel to the surface


What are fossils? How do fossils provide the guide for evolution?


Classical physics is applicable to the
A. microscopic world
B. macroscopic world
c. both microscopic and macroscopic world
D. cannot say


The de-Broglie wavelength of electron in
\( 3^{r d} \) orbit of \( H e^{+1} \) ion is approximately
\( \mathbf{A} \cdot 2 A^{0} \)
B. \( 3 A^{\circ} \)
c. \( 4 A^{\circ} \)
D. \( 5 A^{\circ} \)


Nephrolepis is a
A. Bryophyte
B. Pteridophyte
C. Gymnosperm
D. Angiosperm


If \( A \) lies between \( 180^{0} \) and \( 270^{0} \) and
\( 12 \tan A=5, \) then find the value of
\( 5 \cot A-13 \sin A+12 \sec A \)


To stop bleeding, \( F e C l_{3} \), is applied
locally because:
A. \( F e C l_{3} \) seals the blood vessels
B. \( F e C l_{3} \) changes the direction of blood flow
\( \mathrm{c} \cdot \mathrm{FeCl}_{3} \) reacts with blood to form a solid substance which seals the blood vessel
D. \( F e C l_{3} \) causes denaturation of proteins present in blood


The half-life of a zero-order reaction is
30 minutes. What is the concentration
of the reactant left after 60 minutes?
A . \( 25 \% \)
B. \( 50 \% \)
c. \( 6.25 \% \)
D. 0


If six persons are at the corners of a regular hexagon of side \( X \) move at a
constant speed \( V . \) Each person
maintains a direction towards the
person at the next corner. The time, the persons will take to meet each other is
A \( \cdot \frac{2 X}{3 V} \)
в. \( \frac{2 X}{V} \)
\( c \cdot \frac{X}{V} \)
D. \( \frac{5 X}{6 V} \)


Assertion
If the velocity time graph of a body moving in a straight line is as shown in the figure, the acceleration of the body
must be constant.
Reason
The rate of change of quantity which is
constant is always 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


The rate of the zero order reaction; \( \boldsymbol{A}+ \)
\( B \rightarrow C \) follows the rate equation:
Rate \( =\boldsymbol{k}[\boldsymbol{A}]^{0}[\boldsymbol{B}]^{0} \)
Then the rate of the reaction is:
A. dependent on the concentration of reactant
B. dependent on the concentration of product
c. independent of concentrations of both reactant and product
D. none of these


What is matter waves? Write any two
characteristics of it.


Which among the following is/are not
correct?
This question has multiple correct options
A. The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides.
B. The areas of two similar triangles are in the ratio of the corresponding altitudes.
C. The ratio of area of two similar triangles are in the ratio of the corresponding medians.
D. If the areas of two similar triangles are equal, then the triangles are congruent


White Phosphorus is generally kept under:
A. Alcohol
B. Water
c. Glycerine
D. Kerosine oil
E. Ether


Which of the following is/ are correct
concerning "The working principle of
LED"?
This question has multiple correct options
A. electrons travel from the n-type to the p-type and holes in the opposite direction
B. n-type silicon has extra electrons to combine with the extra holes of p-type silicon
C. p-type silicon has extra electrons to combine with the extra holes of n-type silicon
D. Both A and C


When processing flower nector into
honeybees extract, a considerable
amount of water gets reduced. How
much flower-nector must be processed to yield \( 1 \mathrm{kg} \) of honey, if nector contains \( 50 \% \) water and the honey obtained from this nector contains \( 15 \% \) water


In the leaching of \( A g_{2} S \) with \( \mathrm{NaCN} \), a
stream of air is also passed. It is
because of:
A. Reversible nature of reaction between \( A g_{2} S \) and NaCN
B. To oxide \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{3} \) and sulphur
c. Both (A) and (B)
D. None of the above


Find \( \boldsymbol{f}^{\prime}(\mathbf{0}) \) for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}+ \)
\( \boldsymbol{a}^{2} \log (\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}) \)
A . - 2a
B. 2a
\( c \cdot-a \)
\( D \)


Write the order and degree of the differential equation \( \boldsymbol{y}=\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{a} \sqrt{1+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}} \)


Solve for \( x \) and
\( \boldsymbol{y} \)
\( \mathbf{2}\left[\begin{array}{cc}\boldsymbol{x} & \mathbf{7} \\ \mathbf{9} & \boldsymbol{y}-\mathbf{5}\end{array}\right]+\left[\begin{array}{cc}\mathbf{6} & -\mathbf{7} \\ \mathbf{4} & \mathbf{5}\end{array}\right]=\left[\begin{array}{cc}\mathbf{1 0} & \mathbf{7} \\ \mathbf{2 2} & \mathbf{1 5}\end{array}\right] \)


List three rules for the linear
combination of atomic orbitals.


What is the hybridization of the carbon atom labeled 3?
\( A \cdot s p \)
B. \( s p^{2} \)
\( c \cdot s p^{3} \)
D. None of the above


A small quantity, mass \( m \), of water at a
temperature \( \theta\left(\text { in }^{\circ} C\right) \) is poured on to a large mass \( M \) of ice which is at its
melting point. If \( c \) is specific heat capacity of water and \( L \) the latent heat
of fusion of ice, then the mass of ice
melted is given by
A \( \cdot \frac{M L}{m c \theta} \)
в. \( \frac{m c \theta}{M L} \)
с. \( \frac{M c \theta}{L} \)
D. \( \frac{m c \theta}{L} \)


\( \int \sin ^{8} x \cos x d x \)


Find the local maxima and local
minima, if any, of the following functions. Find the sum of the local
maximum and the local minimum
values for:
\( g(x)=x^{3}-3 x \)


In order to enter cell cycle a cell must be stimulated from outside. What type of molecule provides this stimulation?
A . cyclin
B. colk
c. cytokines and growth factor
D. tyrosine kinases


What is a mixture?
A. Substance with two or more different particles
B. Substance that is insoluble
c. substance with a single homogenous particle
D. None of above


Prove that the centre of the smallest
circle passing through origin and whose centre lies on \( \boldsymbol{y}=\boldsymbol{x}+\mathbf{1} \) is \( \left(-\frac{\mathbf{1}}{\mathbf{2}}, \frac{\mathbf{1}}{\mathbf{2}}\right) \)


Which of the following quantity remains constant in a uniform circular motion?
A. velocity
B. speedd
c. both velocity and speed
D. none of these


\( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{t} & \boldsymbol{t}+\mathbf{1} \\ \boldsymbol{t}-\mathbf{1} & \boldsymbol{t}\end{array}\right] \) is a matrix such
that \( A A^{T}=I_{2} \) then trace of the matrix
is
A . 2
B. 0
\( c \cdot 4 \)
\( D \)


A radioactive element X decays by the
sequence and with half life given below:
\( \boldsymbol{X} \frac{\boldsymbol{\alpha}}{\mathbf{3 0 m i n}} \boldsymbol{Y} \frac{\mathbf{2} \boldsymbol{\beta}}{\mathbf{2 d a y s}} \boldsymbol{Z} \)
which of the following statements about this system are correct?
A. After two hours, less than \( 10 \% \) of the initial \( x \) is left
B. An intermediate nuclide exists between Y and Z
c. Atomic number of \( x \) and \( z \) are same
D. The mass number of Y is greater than \( x \)


Light moves from air into water. The
light makes an angle of \( 47^{0} \) with the
normal in the air. What angle will it
make with the normal in the water?
The index of refraction for air is 1.00
The index of refraction for water is 1.33
A \( \cdot 47^{\circ} \)
В. \( 77^{\circ} \)
\( c \cdot 43^{\circ} \)
D. 25
E \( .33^{\circ} \)


Superoxides of alkali metals act as
oxidising agents while normal oxides are basic in nature. The oxide which is
paramagnetic in nature due to presence of unpaired electron is :
A. \( N a_{2} O_{2} \)
в. \( K O_{2} \)
\( \mathbf{c} \cdot N a_{2} O \)
D. \( K_{2} O_{2} \)


If \( R \) is relation from a finite \( \operatorname{set} A \)
having \( m \) elements to a finite set \( B \)
having \( n \) elements, then the number of relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
\( A \cdot 2^{m} \)
B . \( 2^{m n}-1 \)
\( c \cdot 2 m n \)
D. \( m^{n} \)


Prove that \( \boldsymbol{f}^{\prime}(\mathbf{1})+\boldsymbol{f}(-1)=-\boldsymbol{f}(\mathbf{0}), \) i
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{5}+\boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{x}-\boldsymbol{3} \)


Read the given statements and select
the correct option:

Statement 1:Backing soda does not
taste sour.

Statement 2 :Bases are sour in taste
while acids are bitter in taste.
A. Both statements 1 and 2 are true statement 2 is correct explanation of statement 1.
B. Both statements 1 and 2 are true both statement 2 is not the correct explanation of statement 1
c. statements 1 is true and statement 2 is false
D. Both statements 1 and 2 are false


If \( \sqrt{\boldsymbol{y}+\boldsymbol{x}}+\sqrt{\boldsymbol{y}-\boldsymbol{x}}=\boldsymbol{c} \text { (where } \boldsymbol{c} \neq \mathbf{0}) \)
then \( \frac{d y}{d x} \) has the value equal to
This question has multiple correct options
A \( \cdot \frac{2 x}{c^{2}} \)
в. \( \frac{x}{y+\sqrt{y^{2}-x^{2}}} \)
c. \( \frac{y-\sqrt{y^{2}-x^{2}}}{x} \)
D. \( \frac{c^{2}}{2 y} \)


What is the amount of work done when
0.5 mole of methane, \( C H_{4(g)}, \) is subjected to combustion at \( 300 \mathrm{K} ? \)
\( \left(\operatorname{given}, R=8.314 J K^{-1} \mathrm{mol}^{-1}\right) \)
в. -4988.5
\( \mathrm{c} \ldots+4988 \mathrm{J} \)
D. +2494.5


Polar covalent compounds dissolve in water due to presence of partial charges on polar covalent compounds.
A. True
B. False


The fusion of chromite ore \( \left(F e C r_{2} O_{4}\right) \)
with \( N a_{2} C O_{3} \) in air gives a yellow
solution upon addition of water. Subsequent treatment with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
produces an orange solution. The yellow and orange colours, respectively, are due to the formation of:
A. \( N a_{2} C r O_{4} \) and \( N a_{2} C r_{2} O_{7} \)
в. \( \operatorname{Cr}(O H)_{3} \) and \( N a_{2} C r_{2} O_{7} \)
c. \( C r_{2}\left(C O_{3}\right)_{3} \) and \( F e_{2}\left(S O_{4}\right)_{3} \)
D. \( \operatorname{Cr}(O H)_{3} \) and \( N a_{2} C r O_{4} \)


\( \operatorname{Let} \sqrt{x}+\sqrt{x+\sqrt{x+\ldots \ldots \infty}} \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \frac{1}{2 y-1} \)
в. \( \frac{x}{x+2 y} \)
c. \( \frac{1}{\sqrt{1+4 x}} \)
D. \( \frac{y}{2 x+y} \)


Assertion
Diffusion is a passive type of transport.
Reason
Osmosis is an active process of
membrane transport.
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 is Shell's law
A. \( n_{1} \) sini \( =n_{2} \) sinr
В \( \cdot n_{1} / n_{2}=\sin r \times \) constant
c. \( n_{2} / n_{1}=\sin r / \sin i \)
D. \( n_{2} \sin i= \) constant


\[
\begin{aligned}
\text { If: } \boldsymbol{f}(\boldsymbol{x})=& \frac{\boldsymbol{x}\left(e^{1 / x}-e^{-1 / x}\right)}{e^{1 / x}+e^{-1 / x}}, \ldots x \neq 0 \\
&=\mathbf{0}, \quad \ldots . . x=0
\end{aligned}
\]
then \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. continuous everywhere but not differentiable at \( x=0 \)
B. continuous and differentiable everywhere
c. discontinuous at \( x=0 \)
D. none of these


Influence of genes in controlling the activity of living organisms is through
A. Vitamins
B. Protein synthesis
c. Photosynthesis
D. Hormones


Which organ in our body is protected by the bones shown in the given picture?
A. Heart
B . Legg
C. Arm
D. Brain


If \( l, m, n \) are three parallel lines and the
transversal \( t_{1} \) and \( t_{2} \) cut the lines \( l, m, n \)
at the points \( A, B, C \) and \( P, O, R \) as
shown in the figure, then
A \( \cdot \frac{A B}{B C}=\frac{P O}{O R} \)
B. \( \frac{A B}{O R}=\frac{B C}{P O} \)
c. \( \frac{A P}{B O}=\frac{B O}{C R} \)
D. \( \frac{A B}{P O}=\frac{A P}{B O} \)


Give the Free amino acids obtained on
the hydrolysis of 'Aspartame'.


Which term of an AP: 2, -1, - 4, .... is
\( -70 ? \)
A . 15 th
B. 18th
c. 25th
D. 30th


The amount of charge which the battery must have been used is:
A \( .9 .88 F \)
в. \( 8.98 F \)
c. \( 8.89 F \)
D. \( 7.88 F \)


The \( (x, y) \) coordinates of the corners of
a square plate are \( (0,0),(L, 0),(L, L) \)
and \( (0, L) . \) The edge of the plate are
clamped and transverse standing
waves are set up in it. If \( u(x, y) \) denotes
the displacement of plate at \( (x, y) \) at some instant of time, the possible expression(s) for \( u \) is (are)
\( \mathbf{A} \cdot a \cos \left(\frac{\pi x}{2 L}\right) \cos \left(\frac{\pi y}{2 L}\right) \)
B. \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{2 \pi y}{L}\right) \)
\( ^{\mathbf{c}} \cdot a \cos \left(\frac{2 \pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
D. none of these


Which one of the following is a possible nuclear reaction?
A \( \cdot \frac{10}{5} B+_{2}^{4} H e \rightarrow_{7}^{13} N+_{1}^{1} H \)
B \( \cdot \frac{23}{13} \mathrm{Na}+_{1}^{1} \mathrm{H} \rightarrow_{20}^{20} \mathrm{Ne}+_{2}^{4} \mathrm{He} \)
C \( \cdot \frac{239}{11} \mathrm{Np} \rightarrow_{94}^{239} \mathrm{Pu}+\beta^{-}+\bar{v} \)
D. \( \frac{11}{7} N+_{1}^{1} H \rightarrow_{6}^{12} C+\beta^{-}+v \)


A body of mass \( 0.4 \mathrm{kg} \) moving with a constant speed of \( 10 \mathrm{m} / \mathrm{s} \) to the north is
subject to a constant force of \( 8 \mathrm{N} \)
direction toward the south for 30 s. Take
the instant the force is applied to be
\( t=0, \) the position of the body at the
time to be \( x=0, \) and predict its
position at \( t=-5 s, 25 s, 100 s \)


How can we explain the reddish
appearance of sun at sunrise
or sunset?
A. Scattering of blue light is more than the scattering of red light
B. Scattering of red light is more than the scattering of blue light
C. Intensity of sun reduces during sunrise and sunset
D. Due to the view angle, it appears blue


Verify Rolle's Theorem for the function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{8}, \boldsymbol{x} \in[-\boldsymbol{4}, \boldsymbol{2}] \)


Complex tissues are not found in
A. Few bryophytes
B. Pteridophytes
c. All gametophytes
D. All spermatophytes


The membrane of a drum vibrates to
produce sound. Similarly the string of a sitar vibrates to produce sound. Based on these two examples answer the following question. Which part of a whistle vibrates to produce sound?
A. Body of whistle
B. Air
c. Mouth of the person
D. All of the above


In refraction of light through a prism,
the light ray:
A. suffers refraction only at one face of the prism
B. emerges out from the prism in a direction parallel to the incident ray
C. bends at both the surfaces of prism towards its base
D. bends at both the surfaces of prism opposite to its base


For three events \( A, B \) and \( C, P \) (exactly one of the events \( A \text { occur })=P \) (exactly
one of the events \( B \text { and } C \text { occur })=P \) (exactly one of the events \( C \) or \( A \) occurs) \( =\mathrm{p} \) and \( \mathrm{P} \) (all the three events occur
simultaneously) \( =p^{2}, \) where \( 0<p< \)
1/2. If the probability of at least one of
the three events \( A, B \) and \( C \) occurs is
\( 11 / 18, \) the value of \( p \) is
A \( \cdot 1 / 6 \)
в. \( 1 / 4 \)
c. \( 1 / 5 \)
D. \( 1 / 3 \)


What is the value of
\[
\begin{array}{l}
\lim _{x \rightarrow \frac{\pi}{2}}[\cos x] ? \\
x
\end{array}
\]


Does the size of the paper change after
making an aeroplane by folding it or by cutting it?


A covalent bond is formed when:
A. combining atoms share the electron pairs
B. combining atoms are attracted by each other
C. the ions of the combining atoms are attracted by electrostatic force of attraction
D. one atom donates a pair of electrons to another atom


Choose the correct labeling
Glyceraldehyde-3-P
\( \mathbf{1}, \mathbf{3} \)
A. a. Ethanol
b. \( C O_{2} \)
c. Acetaldehyde
B. a. \( C O_{2} \)
b. Acetaldehyde
c. Ethanol
\( \mathrm{c} \cdot \) a. \( \mathrm{CO}_{2} \)
b. Ethanol
c. Acetaldehyde
D. a. Ethanol
b. Acetaldehyde
c. \( C O_{2} \)
E. a. Acetaldehyde
b. \( C O_{2} \)
c. Ethanol


The maximum and minimum distance
of a comet from the sun are \( 8 \times 10^{12} m \)
and \( 1.6 \times 10^{12} \) m. If its velocity when
nearest to the sun is \( 60 m / s \), what will
be its velocity in \( m / s \) when it is
farthest:
A . 12
B. 60
\( c \cdot 112 \)
D. 6


The ratio of kinetic energy and the total energy of the electron in the nth
quantum state of Bohr's atomic model of hydrogen atom is
A . -2
B. - 1
\( c \cdot+2 \)
D. +1


Sitar maestro Ravi Shankar is playing sitar on its strings, and you, as a physicist (unfortunately without musical ears!), observed the following oddities.
I. The greater the length of a vibrating string, the smaller its frequency.
II. The greater the tension in the string, the greater is the frequency.
III. The heavier the mass of the string, the smaller the frequency.
IV. The thinner the wire, the higher its frequency. The maestro signalled the following combination as correct one.
A. II, III and IV
B. ।, / I and IV
c. ।, ॥ land III
D. I, II, III and IV


Which of the properties of isotopes of an element is different?
A. First ionisation enthalpy
B. Effective nuclear charge
c. Electron affinity
D. Melting point and boiling point


The first term is 1 in the geometric
sequence \( 1,-3,9,-27, \ldots . . \) What is the
SEVENTH term of the geometric
sequence?
A. -243
B. -30
c. 81
D. 189
\( E .729 \)


The important muscle proteins that help in movement are
A. Actin and myosin
B. Tropomyosin
c. Troponin
D. All of these


Prismatic periscopes use the principle
of :
A. refraction
B. reflection
c. transmission
D. total internal reflection


A train approaching a hill at a speed of \( 40 \mathrm{km} / \mathrm{hr} \) sounds a whistle of frequency \( 600 \mathrm{Hz} \) when it is at a distance of \( 1 \mathrm{km} \)
from a hill. A wind with a speed of 40 \( \mathrm{km} / \mathrm{hr} \) is blowing in the direction of motion of the train. Find the frequency
of the whistle as heard by an observer on the hill.


\( \mathbf{f}(\mathbf{x})=|\mathbf{x}| \) is minimum at \( \mathbf{x}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot-1 \)
D. 2


How does sex determination take place in human beings?


(a) Define electric dipole moment. Is it a
scalar or a vector?
Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surface due to an electric dipole. Locate the points where the potential due to the dipole is
zero.


A car is moving with a speed of \( 30 m / s \)
on a circular track of radius 500 m. Its
speed is increasing at a rate of \( 2.0 \mathrm{m} / \mathrm{s}^{2} \)
Determine the magnitude of its acceleration.


Sum of the series \( \sum_{r=1}^{88}(-1)^{r+1} \frac{1}{\sin ^{2}(r+1)^{\circ}-\sin ^{2} 1^{\circ}} \)
equal to
A \( \cdot \frac{\cot 2^{\circ}}{\sin 2^{\circ}} \)
B. \( \frac{-\cot 2^{\circ}}{\sin 2^{\circ}} \)
c. \( \cot 2^{\circ} \)
D. \( \frac{\cot 2^{\circ}}{\sin ^{2} 2^{\circ}} \)


Short answer
Name any one body part where ciliated epithelium is found in humans? What
is its function?


A rectangular plot is \( 112 \mathrm{m} \) long and \( 6 \mathrm{m} \) broad. It has \( 2 \mathrm{m} \) path all around it on the inside.Find the area of the path and
the cost of constructing it at the rate of
Rs 60 per sq \( m \)


Bring out the Physiological effects of
Auxin.


Which metal can not be extracted by smelting process:
\( A \cdot P b \)
B. Fe
\( c \cdot z n \)
\( D \cdot A \)


If \( 5 f(x)+3 f\left(\frac{1}{x}\right)=x+2 \) and \( y= \)
\( \boldsymbol{x} \boldsymbol{f}(\boldsymbol{x}) \)
\( \operatorname{then} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{n}} \) at \( \boldsymbol{x}=\mathbf{1} \)
A . 14
в. \( \frac{7}{8} \)
c. 1
D.


If \( x=\sin 1, y=\sin 2 ; z=\sin 3 \) then
A. \( x<y<z \)
в. \( x>y>z \)
c. \( y<z<x \)
D. \( z<x<y \)


Which of the function defined below are
one-one function(s)?
This question has multiple correct options
A. \( f(x)=x+1,(x \geq-1) \)
B. \( g(x)=x+\frac{1}{x},(x \geq 0) \)
C \( \cdot h(x)=x^{2}+4 x-5,(x>0) \)
D. \( f(x)=e^{-x},(x \geq 0) \)


How much would a W kg man weigh on the moon in terms of gravitational
units?
A \( \cdot \frac{W}{6} \) kg-wt
B. 6W kg-wt
c. w kg-wt
D. zero


The set of values of \( x \) for which the angle between the vectors \( \vec{a}=x \hat{i}-3 \hat{j}-\hat{k} \) and \( \vec{b}=2 x \hat{i}+x \hat{j}-\hat{k} \) is acute and the
angle between the vector \( \vec{b} \) and the axis of ordinates is obtuse, is:
A. \( 1<x<2 \)
B. \( x>2 \)
c. \( x<1 \)
D. \( x<0 \)


\( \int_{0}^{1} \frac{2 x}{\sqrt{1-x^{4}}} d x \) is equal to?
\( A \)
в. \( \frac{\pi}{2} \)
c. \( 2 \pi \)
D.


Recognize the prism(s) among the
given figures:
\( A . \quad b \) and \( c \)
B. \( c, \) a and \( b \)
c. only b
D. a, b, c, and d


\( \boldsymbol{K}_{c} \) for \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \) is \( \mathbf{1 0} \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} . \) If
a container contains 1,2,3 and 4 mole per litre of \( A, B, C \) and \( D \) respectively
\( \operatorname{at} 25^{\circ} C, \) the reaction shall:
A. Proceed from left to right
B. Proceed from right to left
c. Be at equilibrium
D. None of these


Assertion
Hb reacts with \( O_{2} \) in a way that is
remarkable in comparison to other
chemical reactions.
Reason
Each molecules of iron in Hb can take
two atoms of \( O_{2} \) at its saturation point.
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 man starts repaying a loan as first
installment of Rs. \( 100 . \) If he increases
the installment by Rs 5 every month.
what amount he will pay in the \( 30^{t h} \) installment?


Differentiate the following \( \boldsymbol{w} \cdot \boldsymbol{r} \cdot \boldsymbol{t} \cdot \boldsymbol{x} \)
\( \left(4 x^{2}-7 x+5\right) \cdot \sec x \)


Which of the following is a geometric series?
A \( \cdot 2,4,6,8, \dots \dots \)
B \( \cdot 1 / 2,1,2,4 \ldots \ldots \)
c. \( 1 / 4,1 / 6,1 / 8,1 / 10, \ldots \ldots \)
D・ \( 3,9,18,36, \ldots \)


In the given figure, \( a \) is greater than \( b \) by
two third of a right angle. The values of
\( a \) and \( b \) are
A \( \cdot 100^{\circ}, 80^{\circ} \)
B . \( 105^{\circ}, 75^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ}, 90^{\circ} \)
D. \( 120^{\circ}, 60^{\circ} \)


A copper rod and \( A l \) rod are placed in
conc. \( H N O_{3} \) in separate containers.
Which of the following observations are found after some time?
A. Copper rod and Aluminium rod continue to deteriorate at the same rate
B. Copper rod continues to deteriorate while aluminium rod deteriorates initially then stops
c. There is no deterioration in either copper rod or aluminium rod
D. Aluminium rod continues to deteriorate while copper rod deteriorates initially and then stops


Write an underlying principle of the moving coil galvanometer?


A proton enters a magnetic field of flux density \( 1.5 \mathrm{T} \) velocity of \( 20 \times 10^{2} \mathrm{ms}^{-1} \) at
an angle of \( 30^{\circ} \) with the field. The force on the position is \( \left[e_{p}=1.6 \times 10^{-19} C\right] \)
B . \( 2.403 \times 10^{-12} N \)
c. \( 3 \times 10^{-5} N \)
D. \( 3 \times 10^{-4} N \)


In the diagram, vector \( C \) is equivalent to
B \( . \bar{D}-\bar{A}+\bar{B} \bar{B} \)
c. \( \bar{A}+\bar{B}-\bar{D} \)
\( \mathbf{D} \cdot \bar{D}+\bar{A}-\bar{B} \)


Fuel used in nuclear power plants is:
A. Uranium - 235
B. Plutonium - 235
c. Plutonium - 238
D. Uranium - 238


Which of the following is not an advisable method of contraception?
A. Tubectomy
B. Vasectomy
c. Hysteroctomy
D. condoms


An organism that decomposes remains is most likely to utilize which of the
following modes of nutrition?
A. Parasitic
B. Saprotrophic
c. Ingestion
D. chemosynthesis


An ideal gas is taken through a cyclic thermo dynamical process through four steps. The amounts of heat involved in
steps are
\( Q_{1}=5960 J, Q_{2}=-5585 J, Q_{3}= \)
\( -2980 J, Q_{4}=3645 J ; \) respectively, the
corresponding works involved are
\( \boldsymbol{W}_{\mathbf{1}}=\mathbf{2 2 0 0}, \boldsymbol{W}_{\mathbf{2}}=-\mathbf{8 2 5} \boldsymbol{J}, \boldsymbol{W}_{\mathbf{3}}= \)
\( -1100 J \) and \( W_{4} \) respectively. Find the
value of \( W_{4} \) and efficiency of the cycle
A. 1315 J, 10\%
B. 275 J, 11\%
C. both of them
D. none of these


Prove that \( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{b} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{c}\end{array}\right|= \)
\( \boldsymbol{a b c}\left(\mathbf{1}+\frac{\mathbf{1}}{\boldsymbol{a}}+\frac{\mathbf{1}}{\boldsymbol{b}}+\frac{\mathbf{1}}{\boldsymbol{c}}\right) \)


A virtual image is
A. always magnified
B. always erect
C . always caught on a screen
D. uncapturable on a screen


If \( \tan (x+y)=33 \) and \( x=\tan ^{-1} 3, \) then \( y \)
will be
A. 0.3
B \( \cdot \tan ^{-1}(1.3) \)
\( \mathbf{c} \cdot \tan ^{-1}(0.3) \)
D. \( \tan ^{-1}\left(\frac{1}{18}\right) \)


Comment on the statement that 'Colloid
is not a substance but a state of
substance'.


Obtain the expression for current sensitivity of moving coil galvanometer


Our eyes function similar to a:
A. Convex lens
B. Concave lens
c. cylindrical lens
D. None of these


Find the probability distribution of the number of doublets in three throws of a
pair of dice


Which of the following statements are
correct?
This question has multiple correct options
A. The water drop in vaccum is perfectly spherical.
B. The shape of water drop is distorted due to action of gravity.
C. Soaps and detergents drastically decrease the surface tension of water.
D. As temperature increases, surface tension also increases and becomes maximum at critical
temperature


A tension in wire is \( 40 \mathrm{N} \) and \( 10 \mathrm{m} \) of wire
has a mass of \( 0.01 \mathrm{kg} \). The speed of transverse waves in \( \mathrm{m} / \mathrm{s} \) in the wire is :
A . 200
B. 80
\( c .300 \)
D. 180


The part labelled as 'A' represents the
A. Root
B. Epicotyl
c. Hypocotyl
D. cotyledon
E. Hilum


One can lean further to one side or the
other without creating enough turning force to tip him over. This is because
A. The person has low centre of gravity
B. The person has no centre of gravity
c. The person has high centre of gravity
D. None of the above


If \( a, b \) and \( c \) are in geometric progression, then \( a^{2}, b^{2} \) and \( c^{2} \) are in
progression.
\( A \cdot A P \)
в. GР
c. нр
D. AGP


A new element is produced after
emission of a beta particle with the atomic number:
A. increased by 2
B. decreased by 1
c. decreased by 2
D. increased by


What do you mean by permeability of membrane? Explain with suitable
example.


\( \lim _{\boldsymbol{x} \rightarrow \infty} \sum_{\boldsymbol{r}=1}^{\boldsymbol{n}} \tan ^{-1}\left(\frac{2 r}{1-\boldsymbol{r}^{2}+\boldsymbol{r}^{4}}\right) \) is equal to
\( \mathbf{A} \cdot \pi / 4 \)
B. \( \pi / 2 \)
\( c \cdot \frac{3 \pi}{4} \)
D. None of these


A concave lens of focal length \( 5 \mathrm{cm} \) is used as a simple microscope. The image is formed at the least distance of
distinct vision. Calculate the angular magnification.


Pick out the liquid-in-gas type of mixture from the following.
A. Dissolved carbon dioxide in water
B. Droplets of water in air
C. Oxygen dissolved in water
D. All of the above


Which of the following is a coloured
gas?
A \( \cdot N O_{2} \)
в. \( N_{2} O_{5} \)
c. \( N_{2} O_{4} \)
D. \( N_{2} \),


Give one basic difference between
cytokinesis in plant cells and animal cells.


Mention any two ways in which digested food is utilized by the body.


Find the \( 15^{t h} \) term of the G.P. 3,12,48
\( 192, \ldots \)
A \( \cdot 3 \times 4^{15} \)
B . \( 3 \times 4^{14} \)
\( \mathrm{c} \cdot 3 \times 4^{16} \)
D. \( 3^{15} \)


A ball projected from the ground at a
certain angle has:
A. minimum velocity at the point of projection and maximum velocity at the maximum height
B. maximum velocity at the point of projection and minimum velocity at the maximum height
C. same velocity at any point in its path
D. zero velocity at the maximum height irrespective of the velocity of projection


toppr
Q Type your question
\( 0.1 \mathrm{M} \) starch solution. Dialysis bags
model the selective permeability of cell
membranes and allow very small
molecules, ions and water to pass
through according to the surrounding
concentration gradient.

Starch is too large a molecule to pass
through the dialysis membrane. The
student massed the bags every 5
minutes to monitor the amount of mass
gained or lost by each bag over the
course of 30 minutes. The percent
change in mass for each bag was
calculated and the data were plotted in
the graph:
Which line on the graph would the
student have obtained with the data
from the bag containing a \( 0.1 \mathrm{M} \) starch
solution?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


At what time after throwing does it hit the plateau??
\( \left(g=9.8 m / s^{2}\right) \)
A . \( 0.9 s \)
B. 3.04 \( s \)
\( c \cdot 4 s \)
D. \( 1 s \)


A current source drives a current in a
coil of resistance \( \boldsymbol{R}_{1} \) for a time \( \boldsymbol{t} \). The
same source drives current in another
coil of resistance \( \boldsymbol{R}_{2} \) for same time. If
heat generated is same, find internal resistance of source.
A \( \cdot \frac{R_{1} R_{2}}{R_{1}+R_{2}} \)
в. \( R_{1}+R_{2} \)
c. zero
D. \( \sqrt{R_{1} R_{2}} \)


Solve the following system of equations
\( |\boldsymbol{x}-\mathbf{1}|+|\boldsymbol{y}-\mathbf{2}|=\mathbf{1} \)
\( \boldsymbol{y}=\mathbf{2}-|\boldsymbol{x}-\mathbf{1}| \)
A \( \cdot x=\frac{1}{2}, \frac{5}{2} \) and \( y=\frac{3}{2} \)
B. \( x=\frac{3}{2}, \frac{5}{2} \) and \( y=\frac{7}{2} \)
c. \( x=\frac{5}{2}, \frac{7}{2} \) and \( y=\frac{5}{2} \)
D. \( x=\frac{1}{2}, \frac{3}{2} \) and \( y=\frac{3}{2} \)


Which of the following group contains coloured ions?
1. \( \boldsymbol{C} \boldsymbol{u}^{+} \)
2. \( \boldsymbol{T} \boldsymbol{i}^{4+} \)
3. \( C o^{2+} \)
4. \( \boldsymbol{F} \boldsymbol{e}^{2+} \)
A .1,4
в. 3,4
c. 2,3
D. 1,2


STATEMENT-1
Two cylinders, one hollow (metal) and
the other solid (wood) with the same
mass and identical dimensions
are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the
inclined plane first.
STATEMENT-2
By the principle of conservation of
energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Dilute hydrochloric acid is added to solid sodium carbonate. It is observed
that:
A. no change takes place
B. a loud sound is produced
c. a brisk effervescence occurs
D. the solution turns blue


When water circulates through the water cycle it can be found in the
A. Solid form
B. Liquid form.
c. Gas form.
D. All of the above.


Coronary heart disease is due to
A. Bacterial infection
B. Inflammation of pericardium
c. weakening of the heart valves
D. Insufficient blood supply to the heart muscles


Which of the following \( 0.1 M \) complex compound solutions will have the minimum electrical conductivity?
A. Hexammine platinum (IV) chloride
B. chloropenta ammine platinum (IV) chloride
c. Dichloro tetrammine platinum (IV) chloride
D. Trichloro tetrammine platinum (IV) chloride


Find what straight lines are represented by the following equation and determine the angles between them. \( \boldsymbol{x}^{2}+2 \boldsymbol{x} \boldsymbol{y} \cot \boldsymbol{\theta}+\boldsymbol{y}^{2}=\mathbf{0} \)


A coin is tossed three times, where
(i) \( E: \) head on third toss, \( F: \) heads on
first two tosses
(ii) \( E: \) at least tow heads, \( F: \) at most
two heads
(iii) \( E: \) at most two tails, \( F: \) at least
one tail
Determine \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)
A. 0.42,0.50,0.85
В. 0.50,0.42,0.85
c. 0.85,0.42,0.30
D . .0.42, 0.46, 0.47


The length, breadth and thickness of a block are given by \( l=12 \mathrm{cm}, b=6 \mathrm{cm} \)
and \( t=2.45 \mathrm{cm} . \) The volume of the
block according to the idea of significant figure should be
A \( .2 \times 10^{2} \)
В. \( 2 \times 10^{2} c m^{3} \)
c. \( 1.763 \times 10^{2} c m \)
D. None of these


Assertion
If \( x_{1}>0, i=1,2,3, \dots, 50 \) and \( \sum_{i=1}^{50} x_{i}= \)
\( \mathbf{5 0} \) then minimum value of \( \frac{\mathbf{1}}{\boldsymbol{x}_{\mathbf{1}}}+\frac{\mathbf{1}}{\boldsymbol{x}_{\mathbf{2}}}+ \)
\( +\frac{1}{x_{50}} \) is 50
Reason
\( \boldsymbol{A} \cdot \boldsymbol{M} \geq \boldsymbol{G} \boldsymbol{M} \)
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 volume of \( H C l \) passed through the
solution at \( 25^{\circ} \mathrm{C} \) and 1 atm is:
A. \( 24.46 m L \)
B. \( 2.446 m L \)
c. \( 244.6 m L \)
D. \( 0.2446 m L \)


How is pressure related to force?
A. Directly proportional
B. Inversely proportional
C. Either A or B
D. Neither A nor B


Generators uses the principle of to push electrons through
a wire.
A. electromagnetic induction
B. electromagnetic reduction
c. magnetoelectric conduction
D. electric induction
E. magnetic field contraction


At \( 25^{\circ} \mathrm{C}, \) if 0.001 mol \( L^{-1} \) of a weak acid,
HA is ionized to an extent of \( 1 \%, \) its pH
is?
A . 5
B. 3
c. 6
D. 4


Addition reactions occur in:
This question has multiple correct options
A. alkanes
B. alkenes
C . alkynes
D. All of these


State and explain Biot-Savart Law.


In \( _{\text {十一一一一一一一一一一, }} \) a reaction product is itself a catalyst for that reaction leading to positive feedback.
A. Autocatalysis
B. Catalysis
c. Pressure jump
D. Fast reactions


ff \( \boldsymbol{y}=\mathbf{8} \boldsymbol{x}^{3}-\boldsymbol{6} \mathbf{0} \boldsymbol{x}^{2}+\mathbf{1 4 4} \boldsymbol{x}+\mathbf{2 7} \) is a
strictly decreasing function in the interval
A. (-5,6)
В \( \cdot(-\infty, 2) \)
c. (5,6)
(年. \( 5,6,6) \)
D. \( (3, \infty) \)
E \( .(2,3) \)


Chemical compounds are formed to have constant composition irrespective of their
This question has multiple correct options
A. Method of formation (or) Source
B. Conditions for formation
c. Substances taken for formation
D. Time of formation


A normal eye is not able to see objects
closer than 25 cm because:
A. the focal length of the eye is \( 25 \mathrm{cm} \)
B. the distance of the retina from the eye-lens is \( 25 \mathrm{cm} \)
C. the eye is not able to decrease the distance between the eye-lens and retina beyond a limit
D. the eye is not able to decrease the focal length beyond a limit


A light emitting diode (LED) has a voltage drop of \( 2 \mathrm{V} \) across it and passes a current of 10 mA. When it operates with a \( 6 \mathrm{V} \) battery through a limiting resistor \( R, \) the value of \( R \) is
A . \( 200 \Omega \)
B. 400 \( \Omega \)
c. \( 40 k \Omega \)
D. 4 \( k \Omega \)


In an A.C circuit, a resistance R is
connected in series with an inductance
L. If the phase angle between voltage
and current be \( 45^{0}, \) the value of
inductive reactance will be
A \( \cdot \frac{R}{4} \)
в. \( \frac{R}{2} \)
c. \( R \)
D. \( \frac{R}{3} \)


A parallel plate capacitor of capacitance C consists of two identical plates \( A \) and \( B \). A charge \( q \) is given to plate \( A \) and charge \( -2 q \) is given to plate
B. The space between plates is vacuum. The separation between plates is d. The electric intensity at a point situated between plates is?
A \( \cdot \frac{q}{C d} \)
в. \( \frac{q}{2 C d} \)
c. \( \frac{3 q}{2 C d} \)
D. None of these


What is the order of a reaction which
has a rate expression rate\( = \) \( \boldsymbol{k}[\boldsymbol{A}]^{\frac{3}{2}}[\boldsymbol{B}]^{-1} ? \)
A \( .3 / 2 \)
в. \( 1 / 2 \)
c. 0
D. None of the above


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


A ball of mass 100 g moving with a speed of \( 4 \mathrm{m} / \mathrm{sec} \) strikes a horizontal
surface at an angle of \( 30^{\circ} \) from the
surface. The ball is reflected back with
same speed and same angle of reflection find
(a) The impulse imparted to the ball
(b) change in magnitude of momentum of the ball.


List out any two limitations of Bohr atom model.


Percentage of fresh water in the
hydrosphere is
A . 2.5\%
B. 30\%
c. \( 13 \% \)
D. 33\%


What average speed, most nearly, is required to run a mile \( (1.6 \mathrm{km}) \) in 4 minutes?
A. \( 4.0 \mathrm{m} / \mathrm{s} \)
в. \( 7.0 \mathrm{m} / \mathrm{s} \)
c. \( 40.0 \mathrm{m} / \mathrm{s} \)
D. \( 400.0 \mathrm{m} / \mathrm{s} \)


A car executes a turn of radius \( 22 m \) on
a banked road while travelling at a speed of \( 45 k m / h \). If the height of the outer edge above the inner edge of the road is \( 1.1 m, \) what is the breadth of the
road? \( (\text { in } \boldsymbol{m}) \)
A. 1.745
B. 1.569
c. 1.875
D. 1.236


if \( y^{2}=a x+b x+c, \) then \( y^{3} \frac{d^{2} y}{d x^{2}} \) is
A . a constant
B. a function of \( x \) only
c. a function of \( y \) only
D. a function of \( x \) and \( y \)


Magnetic effect of an electric current was discovered by
A. onm
B. Faraday
c. oersted
D. Ampere


Aqueduct of Sylvius occurs in
A . Heart
B. Eye
c. Brain
D. Ear


Which of the following is called the "Father of Taxonomy"?
A . Aristotle
B. Carolus Linnaeus
c. John Ray
D. Theophrastus


A man is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is
\( 1.39 \times 10^{9} m \) and its mean distance
from the earth is \( 1.5 \times 10^{11} m \), the
diameter of the sun's image on the paper is
A. \( 3.1 \times 10^{-4} \mathrm{m} \)
B . \( 6.5 \times 10^{-5} m \)
c. \( 6.5 \times 10^{-4} m \)
D. \( 9.2 \times 10^{-4} m \)


In which of the following, racemic mixture is obtained on mixing its mirror images in 1: 1 molar ratio?
\( \mathbf{A} \cdot\left[C r(e n)_{3}\right]^{3+} \)
B \( \cdot\left[N i(D M G)_{2}\right] \)
c. \( \operatorname{Cis}-\left[\mathrm{Cu}(\text { Gly })_{2}\right] \)
D. All of the above


Two lamps, one rates \( 100 \mathrm{W} ; 220 \mathrm{V} \), and
the other \( 60 \mathrm{W} ; 220 \mathrm{V} \) are connected in parallel to electric mains supply. Find the current drawn by two bulbs from the line, if the supply voltage is \( 220 \mathrm{V} \)


In a mixture, \( ^{\prime} A^{\prime} \) and ' \( B^{\prime} \) components
show the negative deviations as:
\( \mathbf{A} \cdot \triangle V_{\operatorname{mix}}>0 \)
\( \mathbf{B} \cdot \triangle V_{\operatorname{mix}}<0 \)
C. \( A \) - \( B \) interaction is weaker than \( A-A \) and \( B-B \)
interactions
D. None of the above reasons is correct


\( N_{2} \) and \( H_{2} \) are taken in 1: 3 molar ratio
in a closed vessel to attained the
following equilibrium \( N_{2(g)}+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}(\boldsymbol{g})} \) Find \( \boldsymbol{K}_{\boldsymbol{p}} \) for reaction
if total pressure at equilibrium is 2 P
and \( P_{N_{2}} \) is P/3.
A \( \cdot \frac{1}{3 P^{2}} \)
в. \( \frac{4}{3 P^{2}} \)
c. \( \frac{4 P^{2}}{3} \)
D. none


If \( \boldsymbol{A}=\mathbf{3} \boldsymbol{i}-\mathbf{4} \boldsymbol{j} \) and \( \boldsymbol{B}=-\boldsymbol{i}-\boldsymbol{4} \boldsymbol{j} \)
calculate the direction of \( \boldsymbol{A}-\boldsymbol{B} \)
A. Along positive x axis
B. Along negative x axis
c. Along positive y axis
D. Along negative y axis


For the reaction \( : \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The forward reaction at constant
temperature is favoured by:
This question has multiple correct options
A. introducing chlorine gas at constant volume
B. introducing an inert gas at constant pressure
c. increasing the volume of the container
D. introducing \( P C l_{5} \) at constant volume


(i) How is nitric acid manufactured by
Ostwald process?
(ii) Write down the reaction of Ozone
with black lead sulphide.
(iii) Draw a structure of \( 1 F_{7} \)


If \( y=\sin ^{-1} x \operatorname{th} e n\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}= \)
A \( \cdot-x \frac{d y}{d x} \)
B.
c. \( _{x} \frac{d y}{d x} \)
D. \( x\left(\frac{d y}{d x}\right)^{2} \)


Macroscopic water pollutants include:
A. E. coli bacteria
B. plasticç
c. lead
D. ammonia


The instantaneous value of current at a
given instant is1 \( A \) and peak value of current is \( \frac{5}{3} A . \) The potential difference between \( P \) and \( Q \) at the same instant is
A \( \cdot \frac{23}{3} V \)
B. \( 7 V \)
\( c .3 V \)
D. \( 4 V \)


A stone is released from a hydrogen balloon, going upwards with velocity 12 \( \mathrm{m} / \mathrm{s} . \) When it is at height of \( 65 \mathrm{m} \) from
the ground, time the stone will take to reach the ground is?
A . 5 sec
B. 6 sec
\( c \cdot 7 \sec \)
D. 8 sec


If a ball is thrown vertically upwards and the height 's' reached in time 't' is
given by \( s=22 t-11 t^{2}, \) then the total
distance travelled by the ball is
A. 44 units
B. 33 units
c. 11 units
D. 22 units


A wire when connected to \( 220 \mathrm{V} \) mains
supply has power dissipation \( P_{1} . \) Now
the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this
case is \( P_{2} \). Then \( P_{2}: P_{1} \) is
\( A \)
B. 4
\( c \cdot 2 \)
D. 3


An electric current is the rate of flow of
electric charges and it is measured in Ampere.
A. True
B. False


Conductivity of \( 2.5 \times 10^{-4} \) M methanoic
acid is \( 5.25 \times 10^{-5} S c m^{-1} . \) Calculate it
molar conductivity and degree of dissociation.
\( \left(\text { Given: } \boldsymbol{\lambda}^{0}\left(\boldsymbol{H}^{+}\right)=\right. \)
\( \mathbf{3 4 9 . 5 s} \mathrm{cm}^{2} \) mol \( ^{-1} \) and \( \lambda^{0}\left(\mathrm{HCOO}^{-}\right)= \)
\( \left.50.5 S c m^{2} m o l^{-1}\right) \)


Which of the following liquid pairs shows a positive deviation from Raoult's law?
A. Acetone-chloroform
B. Benzene-methanol
c. water-nitric acid
D. water-hydrochloric acid


\( \mathbf{A} \mathbf{x}=\mathbf{0}, \mathbf{f}(\mathbf{x})=\cos \mathbf{x}-1+\frac{\mathbf{x}^{2}}{\mathbf{2}}-\frac{\mathbf{x}^{\mathbf{3}}}{\mathbf{6}} \)
A. Has a minimum
B. Has a maximum
c. Does not have an extremum
D. Is not defined


Select the correct statement(s).
This question has multiple correct options
A. Passage of sulphur dioxide or of hydrogen sulphide (not in excess) in to a solution of an iodate acidified with dilute hydrochloric acid, liberates iodine
B. Phosphate rock, \( C a_{3}\left(P O_{4}\right)_{2} \) on heating with sand and coke in electric furance at \( 1400-1500^{\circ} \mathrm{C} \) yields
dimeric phosphorus pentaoxide
C. Reaction of \( H_{2} S \) on aqueous solution of sodium sulphite yields sodium thiosulphate
D. Sodium hypophosphite on warming with copper sulphate solution gives red precipitate of copper (I) hydride


When you are in forest during lightning which is safe place?
A. Open field
B. Under tall trees
c. Under short trees
D. None of the above


\( 10 \mathrm{ml} \) of a compound containing 'N' and
'O' is mixed with \( 30 \mathrm{ml} \) of \( \mathrm{H}_{2} \) to
produce \( H_{2} O(\mathrm{l}) \) and \( 10 \mathrm{ml} \) of \( N_{2} \)
(g). Molecular formula of compound if both reactants reacts completely, is:
A. \( N_{2} O \)
в. \( N O_{2} \)
c. \( \quad N_{2} O_{3} \)
D. \( N_{2} O_{5} \)


If \( f(x)=\frac{x^{2}-9}{x^{2}-2 x-3}, x \neq 3 \) is
continuous at \( x=3, \) then which one of
the following is correct?
A. \( f(3)=0 \)
B. \( f(3)=1.5 \)
c. \( f(3)=3 \)
D. \( f(3)=-1.5 \)


Assertion
Water is tested by using blue cobalt
chloride paper.
Reason
Water turns blue cobalt chloride pink
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 meniscus formed by mercury in a
test tube is
A. convex
B. concave
c. no meniscus is formed
D. none of these


Assertion
Reduction of \( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}, \) with \( \mathrm{CO} \) is done
below \( 710^{\circ} \mathrm{C} \)
Reason
\( \Delta G \) is negative at this temperature; thus,process is spontaneous.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Statement-1 is true, statement-2 is true; statement- is a correct explanation for statement- -1.
B. Statement-1 is true, statement-2 is true; statement- is NOT a correct explanation for statement- -2.
c. Statement- 1 is true, statement- 2 is false
D. Statement-1 is false, statement-2 is true


The distance between the points \( \left(\frac{1}{2}, \frac{3}{2}\right) \) and \( \left(\frac{3}{2}, \frac{-1}{2}\right) \) is


A ball is dropped from a great height and the velocity of the ball as a function of time is given \( \boldsymbol{v}=\frac{\boldsymbol{m} \boldsymbol{g}}{\boldsymbol{K}}\left(\boldsymbol{1}-\boldsymbol{e}^{-(\boldsymbol{K} / \boldsymbol{m}) t}\right) \)
where \( m \) is mass of ball, \( K \) is a
constant and \( g \) is the acceleration due to gravity. Then, at a time when \( t \gg \) \( (\boldsymbol{m} / \boldsymbol{K}), \) the velocity of the ball becomes
A. \( v=g t \)
в. \( _{v}=\frac{m g}{K} \)
c. \( v=\frac{m g}{K} \)
D. \( v=0 \)


Solve \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{2} \boldsymbol{y}=\boldsymbol{x}^{2} \log \boldsymbol{x} \)


Express \( \frac{1}{1+\cos 2 \theta+i \sin 2 \theta} \) in the
form of \( a+i b \)


Find \( \frac{d y}{d x} \) if \( y=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^{x}}\right) \)


Estimating the absolute value of the ntegral \( \int_{10}^{19} \frac{\sin x}{1+x^{8}} d x \) we get \( 10^{-m} \).Find
\( \boldsymbol{m} ? \)


A certain network consists of two ideal
and indentical voltage sources in series
and a large number of ideal resistor. The power consumed in one of the resistor is \( 4 W \) when either of the two sources is
active and other is replaced by a short circuit. The power consumed by same resistor when both sources are
simultaneously active would be:
A. 0 or \( 16 W \)
B. \( 4 W \) or \( 8 W \)
\( \mathrm{c} .0 \) or \( 8 \mathrm{W} \)
D. \( 8 W \) or \( 16 W \)


A straight conductor of uniform cross
section carries a current i. Let \( \mathrm{S} \) be the
specific charge on an electron. The momentum of all the free electrons per
unit length of the conductor due to their drift velocity only is
\( ^{A} \cdot \frac{i}{S} \)
B. \( i \) S
\( ^{c} \cdot\left(\frac{i}{S}\right)^{2} \)
D. \( \sqrt{\frac{i}{s}} \)


On mixing equal volumes of acetone and ethanol, what type of deviation from Raoult's law is expected?


If a line passes through the point
\( P(1,2) \) makes an angle of \( 45^{\circ} \) with the x-axis and meets the line \( x+2 y-7= \)
0 in \( Q, \) then \( P Q \) equals-
A. \( \sqrt{3} \)
B. \( \frac{3 \sqrt{2}}{2} \)
\( c \cdot \frac{2 \sqrt{2}}{3} \)
D. \( \sqrt{2} \)


The substances which are attracted
towards a magnet are called
A. metals
B. ferro-magnetic materialss
c. non-metals
D. dia-magnetic materials


Solve \( (\boldsymbol{x} \boldsymbol{y}-\mathbf{1}) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}^{2}=\mathbf{0} \)
A. \( x y+\log x=C \)
в. \( x y+\log y=C \)
c. \( x y-\log y=C \)
D. \( x y-\log x=C \)


If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\{3,5,7\} and \( C=\{2,4\} ; \) find \( :(A- \)
\( \boldsymbol{B}) \times \boldsymbol{C} \)


If \( f(x)=3 x^{2}-5 x-4, \) then \( f(-2 x) \) is
equal to
B . \( -f(x) \)
c. \( 4 f(x) \)
D. \( -4 f(x) \)
E. none of these


Explain the cleansing process of the soap and detergent.


A ray of light is incident on a plane
mirror at an angle of \( 30^{\circ} . \) At what angle
with the horizontal must a plane mirror be placed so that the reflected ray becomes vertically upwards?
\( A \cdot 40^{\circ} \)
B. 20 \( ^{\circ} \)
\( c \cdot 30 \)
D. \( 60^{\circ} \)


f \( x=b-c, y=c-a, z=a-b \) then the value of \( x^{2}-y^{2}+z^{2}+2 x z \) is
\( A \cdot 2 \)
B. -
\( c \cdot 0 \)
D.


The area of the triangle formed by plane \( 2 x+3 y+6 z+9=0 \) with \( y \) -axis, \( z^{-} \)
axis is?(in Sq. units)
A . 9
B. \( \frac{9}{2} \)
\( c \cdot \frac{9}{4} \)
D. None


What is torque?


1)
\( I, \) is placed in a horizontal plane near a
long straight conductor carrying steady
current \( I_{1} \) at a distance \( d \) from the
conductor as shown in figure. The loop
will experience
A. A net repulsive force away from the conductor
B. A net torque acting upward perpendicular to the horizontal plane
c. A net torque acting downward normal to the horizontal plane
D. A net attractive force towards the conductor


The degree of dissociation of \( \boldsymbol{P C l}_{5}(\boldsymbol{\alpha}) \)
obeying the equilibrium \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \)
\( P C l_{3}+C l_{2} \) is related to the
equilibrium pressure by
A \( \cdot \alpha \propto \frac{1}{P^{4}} \)
B. \( \quad \alpha \propto \frac{1}{\sqrt{P}} \)
c. \( \quad \alpha \propto \frac{1}{P^{2}} \)
D. \( \alpha \propto P \)


The weight of an atom of Uranium is 238 amu. Its actual weight is
8
A. \( 1.43 \times 10^{26} \)
B. \( 3.82 \times 10^{-22} \)
c. \( 6.99 \times 10^{-23} \)
D. \( 1.53 \times 10^{-22} \)


A conducting loop in the form of a circle is placed in a uniform magnetic field with its plane perpendicular to the direction of the field. An e.m.f. will be
induced in the loop if This question has multiple correct options
A . I is translated parallel to itself
B. It is rotated about one of its diameters.
c. It is rotated about its own axis which is parallel to the field
D. The loop is deformed from the original shape


From a circle of radius \( 7 \mathrm{cm} \) the largest
possible square is cut and removed Find the area of the remaining portion \( \left(\operatorname{in} \mathrm{cm}^{2}\right) \)
A . 48
B. 50
\( c \cdot 54 \)
D. 56


The distance between the two point
masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) is d. Now, the
distance between them is reduced by two-thirds, Calculate by which factor
new gravitational force would be change?
A. It increases by a factor of 9
B. It increases by a factor of \( \frac{4}{9} \)
c. It increases by a factor of 3
D. It decreases by factor of 9
E. It decreases by a factor of 3


How many geometric isomers are possible in the following coordination
entities?
\( (a)\left[C r(O X)_{3}\right]^{3-} \)
\( (b)\left[C o C l_{3}\left(N H_{3}\right)_{3}\right] \)
\( A \cdot 0,2 \)
B. 2, 0
c. 2,2
D. 4,0


\( M n O_{2}+K O H+O_{2} \stackrel{\Delta}{\rightarrow} \)
\( \mathbf{2 K}_{\mathbf{2}} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} \)
pot manganate
If true enter 1 else 0
\( \mathbf{A} \cdot \mathbf{1} \)


In electromagnetic wave, according to Maxwell, changing electric field gives.
A. Stationary magnetic field
B. conduction current
c. Eddy current
D. Displacement current


Nitric oxide is paramagnetic in :
A . gaseous state.
B. liquid state
c. solid state
D. polymeric state


Fishes die by sewage because
A. Of its bad smell.
B. It replaces food material of fishes.
C. It increases oxygen competition among fishes.
D. \( C O_{2} \) is mixed in large amount in water.


A current of \( 10 \mathrm{A} \) is flowing in a wire of length 1.5 m. When it is placed in a uniform magnetic field of 2 Tesla then a force of \( 15 \mathrm{N} \) acts on it. The angle between the magnetic field and the direction of current flow will be :
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Aqueous solutions of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H} \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \) of identical
concentrations are provided. The pair(s) of solutions which form a buffer upon
mixing are:
This question has multiple correct options
A. \( \mathrm{HNO}_{3} \) and \( \mathrm{CH}_{3} \mathrm{COOH} \)
B. кОН апа СНзСООNa
c. \( \mathrm{HNO}_{3} \) and \( \mathrm{CH}_{3} \mathrm{COONa} \)
D. \( \mathrm{CH}_{3} \mathrm{COOH} \) and \( \mathrm{CH}_{3} \mathrm{COONa} \)


Hard bast (bundle cap) occurs in
A. Sunflower stem
B. Wheat stem
c. Sunflower root
D. None of the above


In outer space there are 10 molecules
per \( \mathrm{cm}^{3} \) on an average and the
temperature there is 3 K. The average
pressure of this light gas is
\( \mathbf{A} \cdot 10^{5} N m^{-2} \)
В. \( 5 \times 10^{-14} \mathrm{Nm}^{-2} \)
c. \( 0.4 \times 10^{-16} N m^{-2} \)
D. \( 4.14 \times 10^{-16} \mathrm{Nm}^{-2} \)


The equation to a straight line referred
to axes inclined at \( 30^{\circ} \) to one another is
\( y=2 x+1 . \) Find its equation referred to
axes inclined at \( 45^{\circ}, \) the origin and axis
of \( x \) being unchanged.


\( f \int \frac{2 e^{5 x}+e^{4 x}-4 e^{3 x}+4 e^{2 x}+2 e^{x}}{\left(e^{2 x}+4\right)\left(e^{2 x}-1\right)^{2}} d x \)
\( =\tan ^{-1}\left(e^{x / 2}\right)-\frac{K}{248\left(e^{2 x}-1\right)}+C \)
then \( K \) is equal to


Simplify \( \left(x^{2}-5\right)(x+5)+25 \)
A \( \cdot x^{2}(x+5)-5(x+5)+15 \)
B . \( x^{2}(x+5)-5(x-5)+25 \)
c. \( x^{2}(x+5)-5(x+5)+25 \)
D. \( x^{2}(x+5)-(x+5)+25 \)


Which of the following is an example of super octet molecule?
A \( \cdot C l F_{3} \)
в. \( P C l_{5} \)
c. \( I F_{7} \)
D. All the three


The commercial salt is purified by
passing:
\( \mathbf{A} \cdot H_{2} S \) gas through an alkaline solution ofsalt
B. HCl gas through a saturated solution of salt
C. \( H_{2} \) gas through a solution of salt
D. \( C I_{2} \) gas through a saturated solution of salt


As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity 'v' in a perpendicular direction from a very long straight conductor a steady conductor carrying a steady current 'I'. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor.
\( A \)
\[
E \propto \frac{1}{t^{2}}
\]
в. \( \quad E \propto \frac{1}{t} \)
c. \( E \propto \ln (t) \)
D.
\[
E \propto \frac{1}{t^{3}}
\]


Statement: The articles made of
thermoplastics can be recycled whereas the articles made of thermosetting plastics cannot be recycled.

State whether the given statement is true or false.
A. True
B. False


The number of sigma bonds in tetra
cyano ethylene is
A. 7
B. 6
\( c \cdot 5 \)
D.


Assertion
Enzymes lower down the activation energy of the reactant molecule to
make its transition into product easier
Reason

Enzymes are highly substrate specific catalysts.
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


Consider the following statements and arrange in the order of true/false as
given in the codes:
\( S_{1}: \ln A B_{2} L_{2} \) type, the \( B A B \) bond angle will always be greater than normal tetrahedral \( (L \) is a lone pair)
\( S_{2}: \) Maleic acid has higher \( K_{a_{1}} \) value than fumaric acid due to
intramolecular hydrogen bonding.
\( S_{3}: \ln C l O_{3}^{-}, N H_{3} \) and \( X e O_{3}, \) the
hybridisation and the number of lone pair(s) on central atoms are same.
\( \mathbf{A} \cdot T T T \)
в. \( F T F \)
c. \( F T T \)
D. \( F F T \)


Three charges \( -q, Q \) and \( -q \) are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio \( \mathrm{Q} \) \( : q \) is
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


The Sl unit of temperature is


\( \int e^{a x} \cdot \sin (b x+c) d x \)


Answer the following question in one word or one sentence or as per exact requirement of the question.

Write the maximum value of \( f(x)= \) \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x}<\mathbf{0} \)


Integrate \( : \int x \sin ^{2} x \)


A stationary body explodes into two
fragments of masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} . \) If momentum of one fragments \( \mathrm{p} \), the minimum energy of explosion is
\( ^{\mathbf{A}} \cdot \frac{p^{2}}{2\left(m_{1}+m_{2}\right)} \)
В. \( \frac{p^{2}}{2 \sqrt{m_{1} m_{2}}} \)
c. \( \frac{p^{2}\left(m_{1}+m_{2}\right)}{4 m_{1} m_{2}} \)
D. \( \frac{p^{2}}{2\left(m_{1}-m_{2}\right)} \)


Two isolated point poles of strength
\( 30 A m^{2} \) and \( 60 A m^{2} \) are placed at a
distance of 0.3 m. The force of repulsion
is:
A \( \cdot 2 \times 10^{-3} N \)
B . \( 2 \times 10^{-4} N \)
C \( .2 \times 10^{5} N \)
D. \( 2 \times 10^{-5} N \)