One atom of an element \( X \) has a mass of
\( 9.123 \times 10^{-23} g . \) There is only one
isotope of \( X . \) The element \( X \) is :
A. Chlorine
B. Chromium
c. Magnesium
D. Manganese


The time period of periodic motion is
calculated using
A. Number of metres covered in 1 sec
B. Number of 90 degree turns covered in 1 sec
C. Number of oscillations per sec
D. Number of hairpin bends particle covers in 1 sec


In the soap micelles:
A. the ionic end of soap is on the surface of the cluster while the carbon chain is in the interior of the cluster
B. ionic end of soap is in the interior of the cluster and the carbon chain is out of the cluster
c. both ionic and carbon chain are in the interior of the
cluster
D. both ionic end and carbon chain are on the exterior of
the cluster


A particle is moving along a circular
path of radius \( 5 m \) with a uniform speed
\( 5 m s^{-1} . \) What is the magnitude of average acceleration during the interval in which particle completes half revolution?


The transportation of food in phloem is
A. Basipetal
B. Acropetal
c. Both A and B
D. None of the above


To find the n-factor in the following chemical changes.
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4} \)


The S.I. unit of magnetic pole strength is
A \( . A . m^{2} \)
B. \( A . m^{-1} \)
c. A.m
D. \( A / m^{2} \)


Who postulated that electrons revolve in orbits around the nucleus?
A. Bohr model
B. deBroglie's wave hypothesis
c. Heisenberg's uncertainty principle
D. Quantum
E. Atomic theory


In a trapezium \( A B C D \) with \( A B \| C D \)
the given that \( A D \) is not parallel to \( B C \) Is \( \triangle A B C \cong \triangle A D C ? \) Give reasons


Which of them is CORRECT statement
for \( N\left(C H_{2} C H_{2} N H_{2}\right)_{3} \) and
\( N\left(C H_{2} C O O\right)_{3}^{3-} ? \)
A. Both are tetradentate
B. Both has four donor site but act as tridentate
C. \( N\left(C H_{2} C H_{2} N H_{2}\right)_{3} \) is tetradentate but \( N\left(C H_{2} C O O\right)_{3}^{3} \) is tridentate
D. \( N\left(C H_{2} C H_{2} N H_{2}\right)_{3} \) is tridentate but \( N\left(C H_{2} C O O\right)_{3}^{3-} \) is tetradentate


An object is placed at \( 40 \mathrm{cm} \) from the optic centre of a convex lens on its
principal axis. if the focal length of the lens is \( 24 \mathrm{cm} \), find how far from the lens
the screen should be placed to obtain a well-defined image.
A . \( 48 \mathrm{cm} \)
B. 38 cm
\( c .50 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


The electric field intensity at a point \( \boldsymbol{P} \)
due to point charge \( q \) kept at point \( Q \) is
\( 24 N C^{-1} \) and the electric potential at
point is \( 12 J C^{-1} . \) The order of
magnitude of charge \( q \) is
A \( \cdot 10^{-6} C \)
B. \( 10^{-7} C \)
\( \mathbf{c} \cdot 10^{-10} C \)
D. \( 10^{-9} C \)


Lungs ventilation movements is due to
A. costal muscle and diaphragm
B. costal muscle
C. Diaphragm
D. Wall of the lungs


The major product of the following
reaction is:
\( A \)
\( B \)
\( c \)
\( D \)


Which one of the following ionic species will impart colour to an aqueous
solution?
\( A \cdot s c^{+3} \)
B. \( c d^{+2} \)
\( c \cdot z n^{+2} \)
\( D \cdot \operatorname{cr}^{+3} \)


The terminal velocity \( V \) of a spherical
ball of lead of radius \( R \) falling through a
viscous liquid varies with \( \boldsymbol{R} \) such that:
A \( \cdot \frac{V}{R}= \) constant
B. \( V R= \) constant
c. \( V= \) constant
D. \( \frac{V}{R^{2}}= \) constant


Three lines \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\mathbf{7}=\mathbf{0}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{3}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{4}=\mathbf{0} \) form \( \mathbf{3} \) sides
of two squares then equation of
remaining side of these squares is
A. \( 2 x+y+14=0 \)
В. \( 2 x-y-14=0 \)
c. \( 2 x-y+6=0 \)
D. \( 2 x-y+14=0 \)


Calculate the power of an electric bulb which consumes 2400 Jin a minute
\( A \cdot 80 w \)
B. 120 W
\( c \cdot 60 w \)
D. \( 40 \mathrm{w} \)


In which of the following change entropy decreases?
A. Crystallisation of sucrose from solution
B. Dissolving sucrose in water
c. Melting of ice
D. Vaporisation of camphor


A man moves \( 4 m \) along east direction,
then \( 3 m \) along north direction, after
that he climbs a pole to a height of \( 12 m \) Find the distance covered by him and his displacement.


In a reaction \( A+B \rightarrow \) products, the rate
of reaction is doubled when the
concentration of \( A \) is doubled and \( B \) is
kept constant and the rate of the
reaction is increased by 8 times when the concentrations of both \( A \) and \( B \) are
doubled, thus overall order of the
reaction is:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Why are plastics difficult to biodegrade?
A. They are not environment friendly
B. Burning process is slow
c. They release lot of poisonous fumes
D. All of above


Show that each of the relation \( R \) in the
\( \operatorname{set} A=\{x \in Z: 0 \leq x \leq 12\}, \) given by
(i) \( \boldsymbol{R}= \)
\( \{(a, b):|a-b| \text { is a multiple of } 4\} \)
(ii) \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}=\boldsymbol{b}\} \)
is an equivalence relation. Find the set of all elements related to 1 in each case.


Which one of the following pairs is not of a contrasting character?
A. Tall and dwarf
B. Axial and terminal
c. Green and yellow
D. Round and light


If
\( \int \frac{d x}{\sqrt[3]{\cos ^{12} x+3 \cos ^{10} x+3 \cos ^{8} x+\cos ^{6}}} \)
then \( f(x) \) is
A. Bounded \& periodic
B. Bounded \& aperiodic
c. Unbounded \& periodic
D. Unbounded \& aperiodic


\( \boldsymbol{C}(\text {diamond})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C H}_{4}(\boldsymbol{g}) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
\( \mathbf{c} \cdot \Delta H<\Delta U \)
D. None of these


Solve: \( -(x-2)+4>-3 x+10 \)


The magnets shown here will
A. Attract each other
B. Repel each other
c. Pull each other
D. cannot say


The shape of the top surface of a table is
trapezium. Find its area if its parallel
sides are 1 m and \( 1.2 m \) and the
perpendicular distance between them
is \( 0.8 m \)
A \( \cdot 0.88 m^{2} \)
B \( .0 .8 m^{2} \)
\( \mathbf{c} \cdot 8.8 m^{2} \)
D. \( 0.88 \mathrm{cm}^{2} \)


If the largest cube that can be carved
out from a gold sphere has a thermal capacity of 'K' units, what would be the thermal capacity of the sphere?


The self inductance of a straight conductor is.
A. zero
B. Infinity
c. Very large
D. Very small


11 mangocs are bought for Rs. 10 and mangoes are sold for Rs. 11 Find the gain
(or) loss per cent
A. 21\% gain
B. 11\% gain
c. \( 21 \% \) loss
D. 11\% loss


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}, \) verify
conditions of the mean value theorem
satisfied for \( \boldsymbol{a}=\mathbf{1}, \boldsymbol{b}=\mathbf{3} . \) Find \( \boldsymbol{c} \boldsymbol{\epsilon}(\mathbf{1}, \boldsymbol{3}) \)
such that \( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\frac{\boldsymbol{f}(\boldsymbol{3})-\boldsymbol{f}(1)}{\boldsymbol{3}-1} \)
\( A \cdot 2 \)
B.
\( c .3 \)
D.


Rh antibody formed in Rh -ve mother during Rh incompatibility and develops Erythroblastosis fetalis is?
A. Universal Ab
B. Secretory Ag
c. surface Ag
D. Allergic Ab


The number of oxygen atoms in 0.50 mole
of \( K H S O_{4} \) is :
A \( .1 .2 \times 10^{23} \)
B . \( 2.4 \times 10^{23} \)
c. \( 3.0 \times 10^{23} \)
D . \( 1.2 \times 10^{24} \)
E \( .2 .4 \times 10^{24} \)


Find solution of following inequality
also show it graphically.
\[
\boldsymbol{x}+\mathbf{3}<\mathbf{5}, \boldsymbol{x} \in \boldsymbol{R}
\]
\( A \)
\begin{tabular}{lllllllll}
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
\end{tabular}
B.
\( c \)
\begin{tabular}{llllll}
\hline & & & & & & \\
-2 & -1 & 0 & 1 & 2 & 3 \\
\hline & & & & & & \\
& & & & & & \\
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
D. \begin{tabular}{cccccc}
\hline & 1 & & & & \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}


At Curie temperature the ferromagnetic materials get converted into.
A. non-magnetic material
B. para magnetic material.
c. dia magnetic material.
D. all of the above.


Two interfering waves have the same wavelength, frequency, and amplitude. They are traveling in the same direction
but are \( 90^{\circ} \) out of phase. Compared to the individual waves, the resultant wave
will have the same.
A. amplitude and velocity but different wavelength
B. amplitude and wavelength but different velocity
c. wavelength and velocity but different amplitude
D. amplitude and frequency but different velocity


18 g glucose \( \left(C_{6} H_{12} O_{6}\right) \) is added to 178.2 \( g \) water. The vapor pressure of water (in torr) for this aqueous solution
is:
A . 76.0
B. 752.4
c. 759.0
D. 7.6


Find the increase in pressure required to decrease volume of mercury by \( 0.001 \% \). (Bulk modulus of mercury \( = \)
\( \left.2.8 \times 10^{10} N / m^{2}\right) \)


A metal plate of thickness half the
separation between the capacitor plates of capacitance \( C \) is inserted. The new
capacitance is:
A .
B. \( \frac{c}{2} \)
c. zero
D. 2C


The use of chemicals for treatment of
diseases is called:
A. chemotherapy
B. physiotherapy
c. antiotherpy
D. polytherapy


Which one of the following has the same
dimension as that of time, if \( \boldsymbol{R} \) is
resistance, \( L \) inductance and \( C \) is
capacitance?
A \( . R C \)
B . \( \sqrt{L C} \)
c. \( \frac{L}{R} \)
D. All of the above


A long magnet is cut into two equal parts such that the length of each half
is same as that of original magnet. If the period of original magnet is \( T, \) then
the period of new magnet is :
A. \( T \)
в. \( T / 2 \)
c. \( T / 4 \)
D. \( 2 T \)


lime-knots of slime moulds are
A. Swarm cells
B. Spore
c. capillitia
D. Fruit bodies


The correct statement among the following is:

This question has multiple correct options
A. the first ionization potential of \( A \) l is less than the first ionization potential of Mg
B. the second ionization potential of Mg is greater than the second ionization potential of \( \mathrm{Na} \)
C. the first ionization potential of Na is less than the first ionization potential of Mg
D. the third ionization potential of Mg is greater than the third ionization potential of Al


When light is going from vacuum to another medium, then the value of refractive index is called:
A. Relative refractive index
B. Absolute refractive index
c. critical angle
D. None


The narrowest hysterisis loop is for
A . cobalt stee
B. almico
c. soft magnetic material
D. stainless steel


If a source emitting waves of frequency
\( f \) moves towards an observer with a
velocity \( \frac{v}{4} \) and the observer moves away
from the source with a velocity \( \boldsymbol{v} / \boldsymbol{6}, \) the
apparent frequency as heard by the observer will be \( (v= \) velocity of sound)
A \( \cdot \frac{14}{15} \)
B. \( \frac{14}{9} \)
c. \( \frac{10}{9} \)
D. \( \frac{2}{3} f \)


Solve:
\( 4 x-58=-8-6 x \)


\( A, B \) and \( C \) are the three forces each of
magnitude \( 4 N \) acting in the plane of
paper as shown in Fig. The point \( O \) lies
in the same plane. Which force has the
greatest moment about \( O \) ?
A . \( A \)
в. \( B \)
\( c . c \)
D. all of the above


Which of the following terms is not
correct for hydrogen?
A. Its molecule is diatomic
B. It exists both as \( H^{+} \) and \( H^{-} \) in different chemical
compounds
C. It is the only species which has no neutrons in the nucleus
D. Heavy water is unstable because hydrogen is substituted by its isotope deuterium


Sulphuric acid is strong dehydrating agent. Give a chemical reaction in which the above property is exploited.
A \( \cdot C_{6} H_{12} O_{6} \rightarrow 6 C+6 H_{2} O \)
в. \( H_{2} S O_{4} \rightarrow S O_{3}+H_{2} O \)
c. \( H_{2} S O_{4}+P \rightarrow H_{3} P O_{4}+S O_{2}+H_{2} O \)
D. \( H_{2} S O_{4}+N a O H \rightarrow N a H S O_{4}+H_{2} O \)


An urn contains 5 red and 2 black balls.
Two balls are randomly drawn. Let \( \boldsymbol{X} \) represent the number of black balls. What are the possible values of \( X ? \) Is
\( X \) a random variable ?
\( \mathbf{A} \cdot 0,1,2 \)
в. 3,5,7
c. 7,7,8
D. 1,5,7


Correct order of \( 1^{s t} \) IP among following elements Be, B, C, N, O is:
\( A \cdot B<B e<C<0<N \)
B. \( B<B e<C<N<0 \)
\( c \cdot B e<B<C<N<0 \)
\( D \cdot B e<B<C<0<N \)


The first term of an arithmetic
progression \( a_{1}, a_{2}, a_{3}_{-}-_{-}-_{-} \) is equal to unity then the value of the common
difference of the progression if \( a_{1} a_{3}+ \)
\( a_{2} a_{3} \) is minimum, is
A. \( -5 / 4 \)
B. - \( 5 / 2 \)
\( c \cdot 4 \)
D. None of these


Find the square root of each of the
following by prime factorization:
\( \mathbf{1 9 0 9 6 9} \)


A light is incident normally on a mirror. The value of angle of reflection will
be
\( \mathbf{A} \cdot 90 \)
B . 45
\( c \cdot 0^{c} \)
D. 135


For the wave \( \boldsymbol{y}=5 \sin 30 \pi[t- \)
\( (x / 240)] \) is in seconds. Find the
wavelength(in \( \mathrm{cm} \) ).


Compute the heat added (in Joules)
A . 199800
B. 0
c. 200000
D. 200200


A current of \( 1 A \) flows through a copper
wire. The number of electrons passing through any cross-section of the wire in
1.6 \( \sec \) is (charge of a electrons \( =1.6 \times \)
\( \left.10^{-19} C\right) \)
\( \mathbf{A} \cdot 10^{19} \)
B. \( 10^{2} \)
\( c \cdot 10^{25} \)
D. \( 10^{28} \)


\[
\text { If } f(x)=\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}}, x \neq 2
\]
\( =k, x=2 \) is continuous at \( x=2 \)
find the value of k.


Find the direction cosines of the sides
of the triangles whose vertices are (3,5,-4),(-1,1,2) and (-5,-5,-2)


What is formed if a mixture of powdered
iron and sulphur is heated in a test
tube?
A. An element
B. A mixture
c. A compound
D. None of the above


Chlorine gas oxidises the following:
A. sodium sulphate
B. sodium chloride
c. potassium bromide
D. potassium sulphate


The correct order of increasing acidic
strength is:
A. Phenol \( < \) Ethanol \( < \) Chloroacetic acid \( < \) Acetic acid
B. Ethanol \( < \) Phenol \( < \) Chloroacetic acid \( < \) Acetic acid
C. Ethanol \( < \) Phenol \( < \) Acetic acid \( < \) Chloroacetic acid
D. Chloroacetic acid \( < \) Acetic acid \( < \) Phenol \( < \) Ethanol


If the half-life period of a radioactive substance is 0.693 years, what is its decay constant?
A. 0.2 year \( ^{-1} \)
B. 0.1 year \( ^{-1} \)
c. 0.5 year \( ^{-1} \)
D. 1 year \( ^{-1} \)


How many of the following organisms have nuclear membrane? Mycoplasma, Blue - green algae, Fungi, Bacillus, Yeast, Purple photosynthetic bacteria, E.coli, Chlamydomonas
\( A \cdot 4 \)
B. 3
\( c \cdot 5 \)
D.


The ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) passes
through the point (-3,1) and has the eccentricity \( \sqrt{\frac{2}{5}} . \) Then the major axis of the ellipse has the length:
\( ^{A} \cdot 4 \sqrt{\frac{2}{5}} \)
B. \( 8 \sqrt{\frac{2}{3}} \)
\( ^{c} \cdot 4 \sqrt{\frac{2}{3}} \)
D. \( 8 \sqrt{\frac{2}{5}} \)


Who formulated the Zeroth law of
thermodynamics?
A. Ralph Fowler
B. James Maxwell
c. Rudolf Clausius
D. william Thomson


Write a rational number between 7 and
87


Name the three main classes of
Bryophyta


Prove that \( x^{2}+y^{2}=9 \) where \( z=x+ \)
\( i y \) and \( |z+6|=|2 z+3| \)


Carbon dioxide gas turns limewater
milky.
A . True
B. False


Which allotropic form of phosphorus
has discrete tetrahedral \( P_{4} \) molecules


\( \mathbf{\Lambda}_{\infty} \) of propionic acid cannot be
determined experimentally because:
A. conductance at high concentration cannot be determined
B. conductance at low concentration cannot be determined
c. conductance a thigh pressure cannot be determined
D. all of the above


A circle that has its center at the origin and passes through (-8,-6) will also pass through the point
B. (4,7)
c. (7,7)
(年. \( (7,7)) \)
D. \( (9, \sqrt{19}) \)


The separation between the plates of a charged parallel plate capacitor is increased. The force between the plates
A. increases
B. decreases
c. remains same
D. first increases then decreases


The melting point of mercury is:
A \( .38 .8^{\circ} \mathrm{C} \)
B . \( -38.8^{\circ} \mathrm{C} \)
c. \( 4250^{\circ} \mathrm{C} \)
D. \( 452^{\circ} \mathrm{C} \)


Hydrolysis of sucrose gives:
A. Glucose and Galactose
B. Maltose and Glucose
c. Galactose and Fructose
D. None of the above


Due to which forces physisorption
arises?


Ethyl alcohol fermentation can be
observed in
A. Rhizopus
B. Lactobacillus
c. Mesophyll cell


Find the slope of the line joining the points (-4,1) and (-5,2)


A field in the form of a parallelogram
has an area of \( 432 m^{2} . \) Find the length
of its diagonal on which the perpendiculars drawn from two vertices
on either side of it are \( 12 m \) long.


Cathode rays
A. Are the atoms moving toward the cathode
B. Are electromagnetic waves
C. Are negative ions travelling from cathode to anode
D. Are electrons emitted by cathode and travelling towards anode


Two algae which produce agar-agar are
A. Nostoc and Anabaena
B. Volvox and Vaucheria
C. Gracilaria and Gelidium
D. Harveyella and Porphyra


If \( f(x)=\frac{1}{\sqrt{x-5}}, \) then find the domain
and range of \( \boldsymbol{f}(\boldsymbol{x}) \)


The differential equation of all parabolas having their axis of symmetry with the axis of \( x \) is?
A \( \cdot \quad y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
B. \( \quad y \frac{d^{2} x}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
\( \mathbf{c} \cdot y=2 x \frac{d y}{d x} \)
D. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)=0 \)


Direction of nerve impulse is reversed in nerve with.
A. Axo-axonic
B. Axo-dendritic
c. Both A and B
D. None of the above


A tuning fork is in resonance with a sonometer wire. The same tuning fork produces 3 beats in \( 2 s \) when the tension in the wire is increased by \( 2 \% \) The frequency of wire before increasing tension is:
A . \( 100 \mathrm{Hz} \)
в. \( 150 \mathrm{Hz} \)
c. \( 200 H z \)
D. 300 H


Assertion
\( (\sqrt{2}-1)^{n} \) can be expressed as \( \sqrt{N} \) \( \sqrt{N-1} \) for \( \forall N>1 \) and \( n \in N \)
Reason
\( (\sqrt{2}-1)^{n} \) can be written in the form \( \boldsymbol{\alpha}+\boldsymbol{\beta} \sqrt{\boldsymbol{2}} \forall, \boldsymbol{\alpha}, \boldsymbol{\beta} \) are integers \& n is a
positive integer.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion,
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion,
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true.


The combination of \( N_{2} \) and \( H_{2} \) in the
presence of \( F e \) as a catalyst is an
example of heterogeneous catalysts.
A . True
B. False


The equivalent capacitance between \( A \)
and B are:


The polarizing angle of glass is \( 57^{\circ} . A \) ray of light which is incident at this
angle will have an angle of refraction as
A . 25
B. 33
\( c \cdot 42^{\circ} \)
D. \( 38^{\circ} \)


Two wires \( A \) and \( B \) of radius \( 2 r \) and \( r \)
respectively are joined and a force \( \boldsymbol{F} \) is
applied at the end. The length of each
wire is \( L . \) Their Youngs modulus are \( Y \)
and \( 2 Y \) respectively. Find the net elongation.


If the equilibrium constants of the
reacrions \( 2 A \rightarrow B \) and \( B \rightarrow 2 A \) are \( K_{1} \)
and \( K_{2} \) respectively, than:
A \( . K_{2}=2 K_{2} \)
в. \( _{K_{1}=} \frac{1}{K_{2}} \)
C \( . K_{2}=\left(K_{1}\right)^{2} \)
D. \( _{K_{2}}=\frac{1}{K_{2}^{2}} \)


State whether the following statement
is True or False.

Boojho stands at A just on the side of a
plane mirror as shown in fig. He sees himself in the mirror.
A. True
B. False


In passing through a boundary, refraction will not take place if This question has multiple correct options
A. light is incident normally on the boundary
B. the indices of refraction of the two media are same
c. the boundary is not visible
D. angle of incidence exceeds the critical angle


Let \( \mathbf{A B C} \) be a triangle and let \( \mathbf{D}, \mathbf{E} \) be the midpoints of the sides \( \mathbf{A B}, \mathbf{A C} \) respectively,then \( \hat{B} E+\hat{D} C= \)
\( \mathbf{A} \cdot \) ВС
в. \( \frac{1}{2} \hat{B C} \)
c. \( \frac{3}{2} \hat{B C} \)
D. \( \frac{3}{4} \) for


Mass and percentage by weight do not change with temperature.
A. True
B. False


In the given diagram, a line of force of a particular force field is shown. Out of
the
following options, it can never
represent

This question has multiple correct options
A . an electrostatic field
B. a magnetostatic field
c. a gravitational field of a mass at rest
D. an induced electric field


The difference between \( (\boldsymbol{n}+\boldsymbol{2})^{t h} \) Bohr
radius and \( n^{t h} \) Bohr radius is equal to
the \( (n-2)^{t h} \) Bohr radius. The value of \( n \)
is:


Respiration oxidizes
A. Glucose
B. Carbon
C. Nitrogen
D. None of the above


In a cylindrical space uniform electric field varies with respect to time with rate \( (d E / d t) . P \) is a point at a distance
\( r \) from the axis of the space. Deduce the
expression for the magnetic field at \( P \)


Find the surface area of a sphere of
radius: \( 10.5 \mathrm{cm}\left(\text { in } c m^{2}\right) \)


If an angle is eight times its complementary angle, then the measurement of the angle is:
A \( .90^{\circ} \)
B . 20
\( c .80 \)
D. 160


The electric flux through a certain area of dielectric is \( 8.76 \times 10^{3} t^{4} \). The
displacement current through the area
is \( 12.9 p A \) at \( t=26.1 m s . \) Find the
dielectric constant of the material.
A \( .2 \times 10^{-8} \)
B. \( 4 \times 10^{-8} \)
c. \( 8 \times 10^{-8} \)
D. \( 2 \times 10^{-7} \)


\( 5 \mathrm{ml} \) of water was taken in a test tube
and a china dish respectively. these
samples were then kept under different conditions as below:
a) Both the samples are kept under a fan.
b) Both the samples are kept inside a
cupboard.


Among which the magnetic susceptibility does not depend on the temperature?
A. Dia-magnetism
B. Para-magnetism
c. Ferro-magnetism
D. Ferrite


Most common oxidation state of Ce
(Cerium) are:
\( A \cdot+3,+4 \)
\( B \cdot+2,+3 \)
\( c \cdot+2,+4 \)
\( D \cdot+3,+5 \)


The equation \( \frac{x^{2}}{10-\lambda}+\frac{y^{2}}{6-\lambda}=1 \)
represents This question has multiple correct options
A. a hyperbola if \( \lambda<6 \)
B. an ellipse if \( \lambda>6 \)
c. a hyperbola if \( 6<\lambda<10 \)
D. an ellipse if \( 0<\lambda<6 \)


The mass of a ball is \( 1.76 k g . \) The mass
of 25 such balls is
A. \( 440.00 \mathrm{kg} \)
в. \( 44.40 k g \)
c. \( 44.0 k g \)
D. 44.00kg


Out of the following the one that undergoes reaction with \( 50 \% \) NaOH solution to give corresponding alcohol
and acid is:
A. phenol
B. benzaldehyde
c. butanol
D. benzoic acid


Newton's ring pattern in reflected
system, viewed under white light
consists of
A. Equally spaced bright and dark bands with central dark spot
B. Equally spaced bright and dark bands with central white spot
C. A few coloured rings with central dark spot
D. A few coloured rings with central white spot


Which of the following trait is controlled by dominant autosomal genes?
A. Polydactyly
B. Huntingtons chorea
c. PTC (phenylthiocarbamide) tasting
D. All of the above


State, whether the following statement
is True or False:
Neohydrocarbons contain a tertiary carbon atom.


A circle with center (3,8) contains the point \( (2,-1) . \) Another point on the circle is:
в. (4,17)
c. (5,-9)
D. (7,15)
E . (9,6)


\( \operatorname{Let} f(x)=\max \left\{3, x^{2}, \frac{1}{x^{2}}\right\} \) for \( \frac{1}{2} \leq \)
\( x \leq 2 . \) Then the value of the integral
\( \int_{1 / 2}^{2} f(x) d x \) is?
A \( \cdot \frac{11}{3} \)
в. \( \frac{13}{3} \)
c. \( \frac{14}{3} \)
D. \( \frac{16}{3} \)


Nucleic acids were discovered by
A. Watson and Crick
B. Khorana
c. wilkins
D. Miescher


Which one of the following statements
for order of reaction is not correct?
A. Order can be determined experimentally
B. Order of reaction is equal to sum of powers of concentration terms in differential rate law
c. It is not affected by the stoichiometric coefficient of the reactants
D. Order cannot be fractional


The direction shown in figure of
convection current is correct.
A. The direction in warmer water is correct but in cooler
water is incorrect
B. The direction in warmer water is incorrect but in cooler
water is correct
C. Both the direction in warmer water and in cooler water
are correct
D. None of the above


Out of 8 ascospores formed in
Neurospora, the arrangement is \( 2 a: \)
\( 4 A: 2 a \) showing.
A. No crossing over
B. Some meiosis
c. Second generation division
D. First generation division


The aqueous solution of \( \mathrm{NCl}_{3} \) can be
used as:
This question has multiple correct options
A. Chlorinating agent
B. Bleaching agent
c. Reducing agent
D. Explosive


If the tangent at any point on the curve \( x^{4}+y^{4}=c^{4} \) cuts off intercepts \( a \) and \( b \)
on the coordinate axes, the value of
\( \boldsymbol{a}^{-\mathbf{4} / \mathbf{3}}+\boldsymbol{b}^{-\mathbf{4} / \mathbf{3}} \) is
A \( \cdot c^{-4 / 3} \)
B \( \cdot c^{-1 / 2} \)
c. \( c^{1 / 2} \)
D. \( c^{4 / 3} \)


The ratio of wavelengths of photons emitted when hydrogen atom de-excites from third excited state to second
excited state an then de-excites form
seconds excited state to first excited
state is
A \( \cdot \frac{7}{20} \)
в. \( \frac{20}{7} \)
\( c .5 \)
D. 20


\( (\boldsymbol{A}) \)
\( (C) \stackrel{H_{3} O^{\oplus}}{\longrightarrow}(D) \)
Which statements are correct about the
reaction of maltose?
This question has multiple correct options
A. Product \( (C) \) is:
B. Product \( (C) \) is
c. Product \( (D) \) are
D. Products \( (D) \) are 2 mol \( \alpha \) - and \( \beta \) -D-glucose


\( \underbrace{j}_{m} \)


Let the number of elements of the sets
\( A \) and \( B \) be \( p \) and \( q \) respectively. Then
the number of relations from the set \( \boldsymbol{A} \)
to the set \( B \) is
\( \mathbf{A} \cdot 2^{p+q} \)
B. \( 2^{p q} \)
c. \( p+q \)
\( \mathbf{D} \cdot p q \)


Solve \( : \frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}= \)


The mole fraction of \( N_{2} O \) In a mixture of \( N_{2} O \) and \( N O \) is \( \frac{1}{3} . \) The mole fraction
of \( N O \) in a mixture of \( N O \) and \( N O_{2} \) is
3. The two mixtures are mixed in 3: 4
\( \overline{\mathbf{4}} \)
molar ratio. the mole fraction of \( N O_{2} \) in
the resulting mixture is:


\( \ln \) a \( \mathrm{G} . \mathrm{P}, ., \mathrm{T}_{2}+\mathrm{T}_{5}=216 \) and \( \boldsymbol{T}_{4}: \boldsymbol{T}_{6}= \)
1: 4 and all terms are integers, then its
first term is:
A . 16
B. 14
c. 12
D. 15


Calculate the amount of heat energy
required to raise the temperature of 1
kg of iron from \( 20^{\circ} C \) to \( 100^{\circ} \) C. \( c= \) \( 483 J k g^{-1} K^{-1} \)
A. 35674
B. 48266 J
c. \( 38640 \mathrm{J} \)
D. 56446 J


Find the circumference of the circles
with the following radius:(Take \( \pi=\frac{22}{7} \) )
\( \mathbf{1 4 c m} \)


\( 6.02 \times 10^{20} \) molecules of urea are
present in \( 100 \mathrm{mL} \) of its solution. The
molarity of urea solution is :
A . \( 0 . \)
B. 0.01
c. 0.02
D. 0.001


Temporary hardness of water can be removed by adding:
A . \( N a O H \)
в. \( N a_{2} C O_{3} \)
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( M g C l_{2} \)


Area of parallelogram \( A B C D=60 c m^{2} \)
then find the area of parallelogram
ABEF
\( A \cdot 30 \mathrm{cm}^{2} \)
B. \( 60 \mathrm{cm}^{2} \)
\( c \cdot 40 c m^{2} \)
None of the above


Mention the target gland for corticotrophin (ACTH) hormone.


For \( L i^{2+}, \) when an electron falls from a
higher orbit to \( n \) th orbit, all the three types of lines, i.e., Lyman, Balmer and Paschen was found in the spectrum.
Here, the value of ' \( n \) ' will be
A . 1
B . 2
\( c .3 \)
D.


A remote-sensing satellite of earth revolves in a circular orbit at a height of
\( 0.25 \times 10^{5} \mathrm{m} \) above the surface of earth
If earth's radius is \( 6.38 \times 10^{6} \mathrm{m} \) and
\( \boldsymbol{g}=\mathbf{9 . 8} \quad \boldsymbol{m} \boldsymbol{s}^{-2}, \) then the orbital speed
of the satellite is
A \( .6 .67 \mathrm{Kms}^{1} \)
B. \( 7.92 \mathrm{Kms}^{1} \)
c. \( 8.56 \mathrm{Kms}^{1} \)
D. \( 9.13 \mathrm{Kms}^{1} \)


Which of the following elements will form acidic oxide?
This question has multiple correct options
A. Na a
в. \( s \)
\( c . \) мв
D. P


The \( p K_{a} \) values of four carboxylic acids
are given below. Identify the weakest carboxylic acid.
A . 4.89
B. 1.28
c. 4.76
D. 2.56


What is lymph? Explain its constitution


Why are cholorofluorocarbons supposed to be responsible for depletion of ozone
layer? Explain.


Assertion
If linear momentum of a particle is constant, then its angular momentum about any axis will also remain
constant.
Reason
Linear momentum remain constant, if \( \vec{F}_{n e t}=0 \) and angular momentum remains constant if \( \overrightarrow{\boldsymbol{T}}_{\boldsymbol{n e t}}=\mathbf{0} \)
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion
B. Both Assertion and Reason are true, Reason is not the correct explanation of Assertion
C. Assertion is true, but the Reason is false
D. Assertion is false but the Reason is true


If the above process is repeated for all other compositions of mixture of \( \mathrm{C} \) and
B. If all the points where vapours start converting into liquid are connected and all the points where vapours get
completely converted into liquid are connected then obtained graph will look
like
\( A \)
B. b-
\( c \cdot c \)
\( D \cdot d \)


If a magnet is dropped along the axial line of a horizontally held copper ring, then the acceleration of the magnet
while it passing through the ring will
A. Less than that due to gravity
B. Equal to that due to gravity
c. More than that due to gravity
D. Depend on the size of the ring and magnet


\( \boldsymbol{I} \boldsymbol{f} \boldsymbol{I}=\int \boldsymbol{x} \sqrt{\frac{x^{2}+1}{x^{2}-1}} \boldsymbol{d} \boldsymbol{x}, \) then I equals
A \( \cdot \frac{1}{2} \sqrt{x^{4}-1}+\frac{1}{2} \sqrt{x^{4}+1}+c \)
B - \( \frac{1}{2} \sqrt{x^{4}-1}+\frac{1}{2} \operatorname{tn}\left(x^{2}+\sqrt{x^{4}-1}\right)+c \)
c. \( \sqrt{x^{4}-1}+\sin ^{-1}\left(x^{2}\right)+c \)
D. \( \sqrt{x^{4}-1}+2 \sin ^{-1}\left(x^{2}\right)+c \)


Let \( A \) and \( B \) be two nonsingular square
matrices, \( A^{T} \) and \( B^{T} \) are the transpose
matrices \( A \) and \( B \), respectively, then which of the following are correct? This question has multiple correct options
A \( \cdot \mathrm{B}^{T} \) AB is symmetric matrix if \( \mathrm{A} \) is symmetric
B. B \( ^{T} \) AB is symmetric matrix if \( B \) is symmetric
C. \( \mathrm{B}^{T} \) AB is skew-symmetric matrix for every matrix \( \mathrm{A} \)
D. \( B^{T} \) AB is skew-symmetric matrix if A is skewsymmetric


Alka spend \( 90 \% \) of the amount sent to
her and saves Rs. 120 per month. Find the amount sent to her per month.


f \( ^{24} C_{x}=^{24} C_{2 x+3}, \) find \( x \)


The coordinate of vertices of triangles are given. Identify the types of triangles (3,-3)(3,5)(11,-3)


\( C O_{2} \) gas below \( 31.2^{\circ} C \) is called as:
A \( \cdot C O_{2} \) vapours
B. \( C O_{2} \) gas
c. \( C O_{2} \) liquid
D. none of these


When 1 mole of \( N_{2} \) and 1 mole of \( H_{2} \) is
enclosed in \( 3 L \) vessel and the reaction
is allowed to attain equilibrium .it is found that at equilibrium there is 'x'
mole of \( \boldsymbol{H}_{2} \) The number of moles of
\( N H_{3} \) formed would be?
\( A \cdot \frac{2 x}{3} \)
B. \( \frac{2(1+x)}{3} \)
c. \( \frac{2(1-x)}{3} \)
D. \( \frac{(1+x)}{2} \)


Which one of the following is present in the renal pyramid
A. Peritubular capillary
B. convoluted tubules
c. collecting ducts
D. Both A and C


(i) Which one of the following is a polysaccharide:
Starch, Maltose, Fructose, Glucose
(ii) What is the difference between native protein and denatured protein?
(iii) Write the name of the vitamin
responsible for the coagulation of blood.


How many \( C O_{2} \) will releave in the
following reaction


Select the mis-matched pair.
A. Rudolf Virchow - Omnis cellula-e-zcellula
B. Robert Brown - Discovered the nucleus
C. Leeuwenhoek - First described a live cell
D. Schwann and Schleiden - Modified and gave final shape to cell theory


8 players compete in a tournament, every one plays everyone else just once. The winner of a game gets \( 1, \) the loser 0 or each gets \( \frac{1}{2} \) if the game is drawn. The
final result is that every one gets a different score and the player playing placing second gets the same as the total of four bottom players.The total
score of all the players is
A .28
в. 21
\( c \cdot 20 \)
D. 22


The reaction \( N_{2} O_{5} \quad\left(\text { In } \quad C C l_{4}\right) \rightarrow \)
\( 2 N O_{2}+1 / 2 \quad O_{2}(g) \) is first order in
\( N_{2} O_{5} \) with rate constant \( 6.2 \times \)
\( 10^{-4} S^{-1} . \) What is the value of rate of
reaction when \( \left[\boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{5}}\right]= \)
\( \begin{array}{lll}\mathbf{1 . 2 5} & \text { mole } & \boldsymbol{L}^{-1}\end{array} \)
\( \begin{array}{ll}\text { A } \cdot 7.75 \times 10^{-4} & L^{-1} S^{-1}\end{array} \)
B. \( 6.35 \times 10^{-3} \quad L^{-1} S^{-1} \)
\( \begin{array}{ll}\text { C. } 5.15 \times 10^{-5} & L^{-1} S^{-1}\end{array} \)
D. 3.85 \times 10 \( ^{-4} \quad L^{-1} S^{-1} \)


\( 1 \mathrm{cc} \) of \( 0.1 \mathrm{N} H C l \) is added to \( 999 \mathrm{cc} \)
solution of \( N a C l . \) The \( p H \) of the
resulting solution will be:
A. 7
B. 3
\( c \cdot 4 \)
D.


Androgens are
A. female sex hormone
B. non steriod
C . plant hormone
D. male sex hormones


A convex mirror of radius of curvature
\( 20 \mathrm{cm} \) forms an image which is half the size of the object.How far is the object from the mirror?
A. \( 5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c .-30 \mathrm{cm} \)
D. 12.5 cm


How much heat energy is released when
\( 5.0 g \) water at \( 42^{\circ} C \) changes into ice at
\( 0^{\circ} \mathrm{C} ? \) Take specific heat capacity of
water \( =4.2 J g^{-1}, \) specific latent heat of
fusion of ice \( =336 J g^{-1} \)
\( \mathbf{A} \cdot 21 J \)
B. \( 4200 J \)
c. \( 42 J \)
D . 2562 \( J \)


State the law of Radioactive
disintegration


Carrier protein helps in
A. Transport of ions across the membrane
B. Passive ions absorption
C. Water absorption
D. Vaporization


If \( y=\tan ^{-1}\left(\frac{1}{1+x+x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{x^{2}+3 x+2}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{x^{2}+5 x+6}\right)+\ldots+ \) upto \( n \)
terms then \( \frac{d y}{d x} \) at \( x=0 \) and \( n=1 \) is
equal to
A \( \frac{1}{2} d \)
B. \( -\frac{1}{2} \)
\( c \)
\( D \)


According to Rutherford's \( \alpha \) -scattering
experiment, which of the following is
the INCORRECT conclusion?
A. There is a large space between the nucleus of the atom and the electrons
B. The electrons orbit the nucleus of the atom.
C . The nucleus is positively charged.
D. The atom is neutral.
E. Electrons can change orbits when they absorb or emit energy.


The electric potential due to an infinite sheet of positive charge density \( \sigma \) at a point located at a perpendicular distance \( Z \) from the sheet is (Assume
\( V_{0} \) to be the potential at the surface of sheet):
A. \( V_{0} \)
в. \( _{V_{0}-\frac{\sigma Z}{\epsilon_{0}}} \)
\( ^{\mathbf{c}} \cdot_{V_{0}}+\frac{\sigma Z}{2 \epsilon_{0}} \)
D. \( _{V_{0}-} \frac{\sigma Z}{2 \epsilon_{0}} \)


The temperature coefficient of the rate of a reaction is \( 2.3 . \) How many times will the rate of the reaction increase if
the temperature is raised by \( 25 K ? \) \( (8.02 t i m e s) \)


Find the cube root of each of the
following numbers by prime factorisation method:
13824
A . 14
B . 24
\( c .34 \)
D. 44


In the given figure, we have \( A C \perp C D, B C \perp C D \) and \( D A=D B \)
then \( C A=C B \).
A. True
B. False


Acetic acid formed during hydrolysis of
ester acts as an induced catalyst.
A. True
B. False


The rest energy of an electron is
\( \mathbf{A} \cdot 510 K e V \)
B. \( 931 \mathrm{KeV} \)
c. \( 510 M e V \)
D. \( 931 \mathrm{MeV} \)


Number of DNA molecules in a
metaphase chromosome is
A. Many
B. Three
c. one
D. Two


Suppose that you tum on the heater in your room and all of the lights in your room go out. Give a possible reason why the lights went out.


Assertion
At some given instant \( I_{1} \) and \( I_{2} \) both are
\( \mathbf{2} \boldsymbol{A} \) each. Then \( \boldsymbol{I} \) at this instant should
be zero.
Reason
There is a phase difference of \( \pi \) between
\( I_{1} \) and \( I_{2} \) functions
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 boy can throw a stone up to a
maximum height of \( 10 m . \) The maximum horizontal distance up to
which the boy can throw the same stone up to will be
A \( .20 \sqrt{2} m \)
the
B. 10
c. \( 10 \sqrt{2} \)
(
D. 20 \( m \)


Order of magnitude of density of
Uranium nucleous is: \( \left[\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right] \)
A \( \cdot 10^{20} \mathrm{kgm}^{3} \)
В . \( 10^{17} \mathrm{kgm}^{3} \)
\( \mathbf{c} \cdot 10^{14} \mathrm{kgm}^{3} \)
D. \( 10^{11} \mathrm{kgm}^{3} \)


The induced emf produced when a magnet is inserted into a coil does not
depend upon:
A. The number of turns in the coil
B. The resistance of the coil
D. All the above


A glass plate is partly dipped vertically in the mercury and angle contact is measured. If the plate is inclined, then the angle of contact will
A. Increase
B. Decrease
c. Remain unchanged
D. Increase or decrease


In each of the following figure \( A B \| C D \) Find the value of \( x \) in each case


(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium
with speed of light in vacuum.
(b) The refractive indices of water and
glass with respect to air are \( 4 / 3 \) and \( 3 / 2 \) respectively. If the speed of light in
glass is \( 2 \times 10^{8} m s^{-1}, \) find the speed of
light in (i) air, (ii) water.


Solve the following pair of linear equations by cross miltiplication
method
\( 0.3 x+0.4 y=2.5 \) and \( 0.5 x-0.3 y= \)
\( \mathbf{0 . 3} \)
A. \( x=-3 \) and \( y=4 \)
в. \( x=3 \) and \( y=4 \)
c. \( x=4 \) and \( y=-4 \)
D. None of these


When \( M_{1} \) gram of ice at \( -10^{0} C \)
(specific heat \( =\mathbf{0 . 5} \) calg\( ^{10} \boldsymbol{C}^{-1} \) ) is
added to \( M_{2} \) gram of water at \( 50^{\circ} C \) finally no ice is left and the water is at
\( 0^{o} C . \) The value of latent heat of ice, in
cal \( g^{-1} \) is:
\( ^{\mathrm{A}} \cdot \frac{5 M_{1}}{M_{2}}-50 \)
в. \( \frac{5 M_{2}}{M_{1}} \)
c. \( \frac{50 M_{2}}{M_{1}}-5 \)
D. \( \frac{5 M_{2}}{M_{1}}-5 \)


Examples of few compounds in a particular oxidation state are given Mark the example which is not correct.
A. Phosphorus in + 1 oxidation state - \( H_{3} P O_{2} \)
B. Chlorine in +7 oxidation state - \( H C l O \)
c. Chromium in +6 oxidation state \( -C r O_{2} C l_{2} \)
D. Carbon in 0 oxidation state \( -C_{12} H_{22} O_{1} \)


Find the sum of the following AP
\( 1,3,5,7 \dots \dots \dots \dots .199 \)


Assertion
On a rainy day it is difficult to drive a
car or bus at high speed.
Reason
The value of coefficient of friction is
lowered due to wetting of the surface.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two aeroplanes \( I \) and \( I I \) bomb a target
in succession. The probability of \( \boldsymbol{I} \) and
\( I I \) scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
B. 0.14
c. 0.32
D. 0.7


A hydrogen-like atom has ground state
binding energy \( 122.4 e V . \) Then This question has multiple correct options
A. its atomic number is 3
B. an electron with 90 eV can excite it to a higher state
c. an 80 eV electron can excite it to a higher state
D. an electron of \( 8.2 \mathrm{eV} \) and a photon of \( 91.8 \mathrm{eV} \) emitted when a 100 eV electron interacts with it


(i) If area \( (\triangle A B C)=16 \mathrm{cm}^{2}, \) area \( (\triangle \)
\( \mathrm{DEF}=25 \mathrm{cm}^{2} \) and \( \mathrm{BC}=2.3 \mathrm{cm}, \) find EF.
(ii) If area \( (\triangle A B C)=9 c m^{2}, \operatorname{area}(\triangle D E F) \)
\( =64 \mathrm{cm}^{2} \) and \( \mathrm{DE}=5.1 \mathrm{cm}, \) find \( \mathrm{AB} \)
(iii) If \( A C=19 \mathrm{cm} \) and \( \mathrm{DF}=8 \mathrm{cm}, \) ratio of
the area of two triangles.
(iv) If area \( (\triangle A B C)=36 \mathrm{cm}^{2}, \) area \( (\triangle \)
DEF) \( =64 \mathrm{cm}^{2} \) and \( \mathrm{DE}=6.2 \mathrm{cm}, \) find \( \mathrm{AB} \)
(v) If \( A B=1.2 \mathrm{cm} \) and \( \mathrm{DE}=1.4 \) find the ratio
of the areas of triangle \( A B C \) and DEF.


Gaurav was participating in a marathon. Just when he was nearing the finishing line. He started running even
faster. However, when he was about to reach the finishing line, he suffered a severe muscle cramp in his leg. He could not run and affected the race. Subhash, his friend immediately reached out to him and massaged the affected area, relieving some pain.
(a) Which process in the human body provides most of the energy to humans for activities such as running of marathon?
(b) Which substance gets accumulated in the leg muscles of Gaurav., that cause muscle cramps?
(c) What values were shown by Subhash in this situation? (write any one value)


A small uncharged metallic sphere is positioned exactly at a point midway between two equal and opposite point charges separated by very small distance. If the spheres is slightly displaced towards the positive charge and released, then
This question has multiple correct options
A. It will oscillate about it's original position.
B. It will move further towards the positive charge.
c. Its potential energy will decrease and kinetic energy will increase
D. The total energy remains constant but is non-zero


ABCD is a parallelogram, AD is produced to E so that DE = DC and ED
produced meets AB produced in F. Prove that \( \mathrm{BF}=\mathrm{BC} \)


The standard electrode potential \( \left(\boldsymbol{E}^{\ominus}\right) \) for \( \boldsymbol{O C l}^{-} \mid \boldsymbol{C l}^{-} \) and \( \boldsymbol{C l}^{-} \mid \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C l}_{2} \)
respectively are \( 0.94 \mathrm{V} \) and \( -1.36 \mathrm{V} \). The
\( \boldsymbol{E}^{\ominus} \) value of \( \boldsymbol{O} \boldsymbol{C l}^{-} \mid \frac{\boldsymbol{1}}{\boldsymbol{2}} \boldsymbol{C l}_{2} \) will be:
A. \( -0.42 \mathrm{v} \)
в. \( -2.20 \mathrm{v} \)
c. \( 0.52 \mathrm{v} \)
D . 1.04


Let the equation of the plane which contains the line \( \boldsymbol{x}=\frac{\boldsymbol{y}-\boldsymbol{3}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{3}} \)
and which is perpendicular to the plane \( 2 x+7 y-3 z=1 . \) be \( k x-m y-z+ \)
\( \boldsymbol{p}=\mathbf{0} . \) Find \( \boldsymbol{p}-\boldsymbol{k}-\boldsymbol{m} ? \)


Which of the following maintains constant sugar level in blood?
A. Gibberlins
B. Insulin
c. Glucogen
D. Estrone


A group of 10 observations has mean 5 and \( S . D .2 \sqrt{6} \) another group of 20 observations has mean 5 and \( \mathrm{S.D.} 3 \sqrt{2} \)
then the S.D. of combined group of 30 observations is
A \( \cdot \sqrt{5} \)
B. \( 2 \sqrt{5} \)
\( c \cdot 3 \sqrt{5} \)
D. none of these


Write about selective harvesting.


How much work is done in raising a stone of mass \( 5 \mathrm{kg} \) and relative density
3 lying at the bed of a lake through
height of 3 meter? (Take \( g=10 m s^{-2} \) ):
A . 25 J
B. 100
c. 75 J
D. none


The final velocity of a body starts from rest and moving with an acceleration
\( 2 m s^{-2} \) and covering a distance of \( 10 \mathrm{m} \)
is \( m s^{-1} \)
A \( \cdot \sqrt{98} \)
в. \( \sqrt{40} \)
\( c \cdot \sqrt{20} \)
D. \( \sqrt{12} \)


\( \boldsymbol{y}=\boldsymbol{c o t}^{-1} \frac{\boldsymbol{2} \boldsymbol{x}}{1-\boldsymbol{x}^{2}}, \boldsymbol{x} \neq \pm \mathbf{1} \)


Scientific study of diversity of organisms and their evolutionary relationshipd is called
A. systematics
B. Anatomy
c. Morphology
D. Taxonomy


Assertion
Energy can not be given to a system without giving it momentum.
Reason
If kinetic energy is given to a body it
means it has acquired momentum.
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


Assertion
Only one in 20000 of alpha particles deflected in Rutherford's experiment.
Reason

Most of the space in the atom is empty.
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


\( N H_{3} \) has much higher boiling point
than \( P H_{3} \) because:
A. \( N H_{3} \) has much higher molecular mass
B. \( N H_{3} \) forms hydrogen bonds
c. \( N H_{3} \) contains ionic bonds while \( P H_{3} \) contains covalent bonds
D. \( N H_{3} \) undergoes umbrella inversion.


The ventricles of the brain are filled with
A. Cerebro-spinal fluid
B. Lymph
c. Blood
D. Amniotic fluid


The graph shows position as a function of time for two trains \( A \) and \( B \) running on parallel tracks. For times greater
than \( t=0, \) which of the following
statement is true?
A. At time \( t_{B} \), both trains have the same velocity
B. Both trains speed up all the time
\( c . \) Both trains may have the same velocity at some time earlier than \( t_{B} \)
D. Graph indicates that both trains have the same acceleration at a give


Critical count of platelet is
A \( \cdot 40,000 / \mathrm{mm}^{3} \)
B. 1 lac \( / \mathrm{mm}^{3} \)
c. \( 2 \operatorname{lac} / \mathrm{mm}^{3} \)
D. 4 lac / \( \mathrm{mm}^{3} \)


The method of zone refining of metals
is based on the principle of:
A. greater mobility of the pure metal than that of impurity
B. higher melting point of the impurity than that of the pure metal
C. greater noble character of the solid metal than that of the impurity
D. greater solubility of the impurity in the molten state than in the solid state


Two elements combine to form one
compound in a displacement reaction.
A. True
B. False


mol of \( [A g] A g^{\oplus} \) sol is coagulated by
This question has multiple correct options
A. 1 mol of \( K I \)
B. \( 500 \mathrm{mL} \) of \( 1 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4} \)
c. \( 300 \mathrm{mL} \) of \( 1 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4} \) solution
D. 1 mol of \( A g I \)


How many structural isomers of \( \boldsymbol{C}_{\mathbf{9}} \boldsymbol{H}_{\mathbf{1} \mathbf{8}} \)
that have a six membered ring and
trisubstituted?
A . 3
B. 4
\( c .5 \)
D. 6


Find the roots of the equation \( x \) \( \frac{1}{3 x}=\frac{1}{6},(x \neq 0) \)


The first transition state in the overall
exothermic addition of HBr to propane
resembles the
intermediate (carbocation). Choose the
best phrase to complete the following
statement
The second transition states (for
addition of \( B r^{-} \) to the carbocation):
A. resembles the final product
B. resembles the 2-propyl cation
c. resembles propene
D. has all carbons almost entirely sp \( ^{3} \) hybridized


Current \( I_{o} \) flows through the solenoid of length \( L \) having \( N \) number of turns when
its connected to DC. A charged particle is projected along the axis of the solenoid
with a speed \( v_{0}, \) then the force on the
charged particle in the solenoid is:
A. Becomes zero
B. Remains same
c. Decreases
D. Increases


An intense stream of water of cross
section area A strikes a wall at an angle \( \theta \) with the normal to the wall and
returns back elastically. If the density of
water is \( \rho \) and its velocity is \( v \), then the force exerted on the wall will be :
A \( \cdot 2 A v^{2} \)
В. \( 2 A v^{2} \rho \)
c. \( 2 A v^{2} \rho \cos \theta \)
D \( \cdot 2 A v^{2} \rho \sin \theta \)


A particle is moving with a constant speed \( v \) in a circle of radius \( R \). What is
the magnitude of average acceleration after half revolution?
\( ^{\text {A }} \cdot \frac{v^{2}}{2 R} \)
в. \( \frac{2 v^{2}}{\pi R} \)
c. \( \frac{v^{2}}{R} \)
D. \( \frac{v^{2}}{\pi R} \)


State True or False:
Addition of \( 5 a+3 b, a-2 b, 3 a+5 b \) is
\( 9 a+6 b \)
A. True
B. False


\( \boldsymbol{C H} \boldsymbol{C l}_{3}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{H} \boldsymbol{C O O} \)
Intermediate of this reaction can be:
A. \( C C l_{3} \)
в. \( C C l_{2} \)
c. both of these
D. none of these


n given figure, IF \( \angle A=\angle C \), then prove
that \( \triangle A O B \sim \triangle C O D \)


Which of the following pair consists of only network solid?
A. \( \operatorname{si} 0_{2}, \mathrm{CO}_{2} \)
B . Graphite, \( S O_{2} \)
\( \mathrm{c} \cdot P_{4} O_{10}, P_{4} \mathrm{O}_{6} \)
D. Diamond, \( S i O_{2} \)


Vibrations, whose amplitudes of oscillations decrease with time are
called
\( A \). Free vibrations
B. Forced vibrations
c. Damped vibrations
D. None of these


The amount of chlorine evolved by
passing 2 A of current in an aqueous solution of \( N a C l \) for 30 minutes is:
A. 2.648
в. \( 1.32 \mathrm{g} \)
c. \( 3.62 g \)
D. \( 4.22 \mathrm{g} \)


A person sells 36 oranges per rupee and suffers a loss of \( 4 \% \) Find how
many oranges should be sold per rupee to have a gain of \( 8 \% \)
A . 32
B. 40
c. 30
D . 28


\( \cos \boldsymbol{x} \cdot \log (\cos \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( . \sin x \log (\cos x)-\log (\cos x)+c \)
B. \( \sin x \log (\cos x)+\sec x+c \)
c. \( \sin x \log (\cos x)-\sin x+\log |\sec x+\tan x|+c \)
D. \( \sin x \log (\cos x)-\sec x+c \)


Which of the following free radicals is the most stable?
A. primary
B. methy
c. secondary
D. tertiary


Write structural formulae of the organic
compounds \( ^{\prime} \boldsymbol{A}^{\prime},^{\prime} \boldsymbol{B}^{\prime},^{\prime} \boldsymbol{C}^{\prime} \) and \( ^{\prime} \boldsymbol{D}^{\prime} \) in the
following sequence of reaction. \( \boldsymbol{A}^{\prime}+\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B} \boldsymbol{r} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \frac{c o n c . \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{1}} \)
\( ^{\prime} \boldsymbol{B}^{\prime} \stackrel{\boldsymbol{B} \boldsymbol{r}_{2}}{\longrightarrow}^{\prime} \boldsymbol{C}^{\prime} \stackrel{\text {alc.} \boldsymbol{K O H}}{\longrightarrow} \boldsymbol{D}^{\prime} \)


The side of a rhombus in \( 5 \mathrm{cm} \). If the
length of one diagonal of the rhombus is
\( 8 \mathrm{cm}, \) then find the length of the other diagonal.


In the reaction \( 2 P(g)+Q(g) \rightleftharpoons \)
\( 3 R(g)+S(g) . \) If 2 moles each of \( P \) and
\( Q \) is taken initially in a 1 litre flask. At equilibrium which of the following is
true?
\( \mathbf{A} \cdot[P]<[Q] \)
B \( \cdot[P]=[Q] \)
\( \mathbf{c} \cdot[Q]=[R] \)
D. None of these


Which one is included under ecosystem
services?
A. Protection of soil
B. Conservation and purification of water
c. Climate control
D. All of the above


The framework elements of the plants
are
A. Magnesium, copper and iron
B. Copper, carbon and oxygen
c. Manganese, calcium and nitrogen
D. Carbon, hydrogen and oxygen


Find the de-Broglie wavelength of an electron with kinetic energy of \( 120 e V \)
\( \mathbf{A} \cdot 95 p m \)
в. \( 102 \mathrm{pm} \)
c. 112 pm
D. \( 124 \mathrm{pm} \)


000
0
0
\( \infty \)
00


A dam of water reservoir is built thicker
at bottom than at the top because
A. pressure of water is very large at the bottom due to its large depth
B. water is likely to have more density at the bottom due to its large depth
c. quantity of the water at the bottom is very large
D. none of the above


\( \ln \) an A.P., prove that \( \boldsymbol{d}=\boldsymbol{S}_{\boldsymbol{n}}-\boldsymbol{2} \boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{1}}+ \)
\( \boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{2}} \)


Clamp connections occur in :
A . Algae
B. Fungi
c. Bryophytes
D. Pteridophytes


In answering the above questions, which law has been used? \( [\mathrm{C}=12, \mathrm{N}=14 \) \( 0=16] \)
A. Avogadro's law
B. Mass balance
c. Equilibrium
D. All of the above


The corecivity of a small magnet where the ferromagnet gets demagnetized is
\( 3 \times 10^{3} A m^{-1} . \) The current required to
be passed in a solenoid of length \( 10 \mathrm{cm} \)
and number of turns \( 100, \) so that the magnet gets demagnetized when inside the solenoid is:
\( A \cdot 3 A \)
в. \( 6 A \)
\( c .30 m A \)
D. \( 60 m A \)


Sulfuric acid can be produced in the laboratory by burning sulfur in air and dissolving the gas produced in
\( \mathbf{a} \)
A. hydrochloric acid solution
B. sulphur trioxide solution
c. hydrogen peroxide solution
D. copper sulphate solution


Choose the correct answer from the
following
This question has multiple correct options
\( A \cdot \) An area of one square centimetre is \( 10^{4} \) times greater
than one square metre
B. 1 hour 18 min is equal to 3618 seconds.
C. Sl unit of volume is cubic metres.
D. Metre is the standard unit to measure length


Which of the following is an amphoteric oxide?
A. \( S O_{3} \)
в. \( M g O \)
c. \( A l_{2} O_{3} \)
D. \( P_{4} O_{10} \)


Which of the method used for the
concentration of sulfide ores?
A. froth floatation
B. smelting
c. magnetic separation
D. gravity separation


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{g}^{\prime}(1)+\boldsymbol{g}^{\prime \prime}(2) \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(1) \cdot \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{f}^{\prime}(\boldsymbol{x})+\boldsymbol{f}^{\prime \prime}(\boldsymbol{x}) \) then
This question has multiple correct options
A \( \cdot f^{\prime}(1)+f^{\prime}(2)=0 \)
B . \( g^{\prime}(2)=g^{\prime}(1) \)
c. \( g^{\prime \prime}(2)+f^{\prime \prime}(3)=6 \)
D. none of these


The accuracy in the measurement of
speed of light measured as \( 3.00 \times \) \( 10^{8} m / s \) is :
A. \( 30 \% \)
B. \( \frac{1}{3} \% \)
c. \( 3 \% \)
D. \( \frac{1}{30} \% \)


The volume of hollow sphere is
A \( \cdot \frac{4}{3} \pi \quad\left(R^{3}-r^{3}\right) c m^{3} \)
B・\frac{2 } { 3 } \pi \( \quad\left(R^{3}-r^{3}\right) c m^{3} \)
\( \mathbf{c} \cdot \frac{1}{2} \pi \quad\left(R^{3}-r^{3}\right) c m^{3} \)


A ball which is at rest is dropped from height \( h \) metre. As it bounces off the
floor, its speed is \( 80 \% \) of what it was just before touching the ground. The ball will then rise to nearly a height.
\( \mathbf{A} \cdot 0.94 h \)
B. \( 0.74 h \)
c. \( 0.64 h \)
D. \( 0.84 h \)


Rods of carbon and copper are hammered simultaneously. Which property of carbon is responsible for carbon rod breaking down into pieces?
A. Ductility
B. Malleability
c. Elasticity
D. Brittle


Group 16 element are called:
A. Carbon family
B. Chalcogen family
c. Halogen family
D. Nitrogen family


Which of the following will react violently with water to form a base?
A. Chlorine
B. cobalt
c. Calcium
D. Aluminum
E. Potassium


A fixed container of height \( ^{\prime} \boldsymbol{H}^{\prime} \) with
large cross-sectional area \( ^{\prime} A^{\prime} \) is
completely filled with water. orifice of
cross-sectional area \( ^{\prime} a^{\prime} \) are made, one
at the bottom and the other on the vertical wall container at a distance
\( H / 2 \) from the top of the container. Find
the time taken by the water level of a
height of \( \boldsymbol{H} / \mathbf{2} \) to get reduced to ground level.


Solution of differential equation \( \frac{d y}{d x}+ \) \( \frac{\boldsymbol{y}}{\mathbf{1}+\boldsymbol{x}^{2}}=\frac{e^{t a n^{-1} \boldsymbol{x}}}{1+\boldsymbol{x}^{2}} \) is
A \( \quad y=\frac{e^{\tan ^{-1} x}}{2}+c \)
B. \( y=\frac{e^{2 t a n^{-1} x}}{2}+c \)
c. \( y=\frac{e^{\tan ^{-1} x}}{2}+c e^{-\tan ^{-1} x} \)
D. \( y=e^{\tan ^{-1} x}+c \)


The electric field in a region of space is given by \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}+\boldsymbol{2} \boldsymbol{E}_{\boldsymbol{o}} \hat{\boldsymbol{j}} \) where \( \boldsymbol{E}_{\boldsymbol{o}}= \)
\( \mathbf{1 0 0} N / C . \) The flux of this field through a
circular surface of radius \( 0.02 \mathrm{m} \)
parallel to the \( Y \) -Z plane is nearly:
A \( \cdot 0.125 \mathrm{Nm}^{2} / \mathrm{C} \)
B . \( 0.02 \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 0.005 \mathrm{Nm}^{2} / \mathrm{C} \)
D. \( 3.14 \mathrm{Nm}^{2} / \mathrm{C} \)


Which pair of sub-shell has same energy for above described exceptional element under rule (a)?
\( A \cdot 1 s, 2 s \)
B. 2s, 2p
\( c \cdot 3 d, 4 p \)
\( D \cdot 5 p, 4 s \)


The \( p H(p H \) at the isoelectric point) of
the given amino acid is :
A . 3.22
B. 6.96
\( c .5 .93 \)
D. 8.05


The discovery of neutron was made on the basis of conservation principle of
A. momentum
B. momentum and energy
c. charge
D. charge and energy


The graph shows how the amount of digested food in the blood leaving the
small intestine changed after a student ate a meal. Explain.


A beaker contains 40 g of water at \( 20^{\circ} \mathrm{C} \) Now 50 g of ice is put into the beaker. The resulting temperature will be
\( \mathbf{A} \cdot-7^{\circ} C \)
B . \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 10^{\circ} \mathrm{C} \)
D. \( 1.5^{\circ} \mathrm{C} \)


What is the importance of pectoral and pelvic girdle?


Name the following hormones -
(1) Produced by cortex of Adrenal
(2) Produced by medulla of Adrenal.


\( x=0.500 \mathrm{m}, y=0.500 \mathrm{m}, \mathrm{z}=0 \)


Write the formula of the following complexes. Tris (ethylene diammine) cobalt (II) sulphate


A condenser and a \( 30 \Omega \) resistance are
connected in series. When they are
connected to 120 V A.C. source then the
current flowing in the circuit is 1A The
p.d. across the ends of the condenser
will be nearly
\( A \cdot 1 v \)
B. 116 \( v \)
c. zero
D. 220


Growth curve of higher animals is
A. J-shaped
B. R-shaped
c. I-shaped
D. S-shaped


Total no. of compound which are not
possible? \( \boldsymbol{P} \boldsymbol{C} \boldsymbol{I}_{5}, \boldsymbol{N} \boldsymbol{C} \boldsymbol{I}_{5}, \boldsymbol{O} \boldsymbol{F}_{4}, \boldsymbol{O} \boldsymbol{F}_{2}, \boldsymbol{S} \boldsymbol{F}_{4} \)
\( \boldsymbol{S} \boldsymbol{F}_{6}, \boldsymbol{P H}_{5}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{H}_{4}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}, \boldsymbol{I} \boldsymbol{F}_{7}, \boldsymbol{I} \boldsymbol{H}_{5} \)
\( \boldsymbol{P B r}_{6}^{-}, \boldsymbol{C l F}_{3} \)


What is self inductance? Establish
expression for self inductance of a long Solenoid.


The number of solutions of \( z^{2}+|z|=0 \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. Infinite


Volkmann canal interconnect
A. Bone marrow
B. \( 3^{r d} \) and \( 4^{t h} \) ventricle of brain
C. Central canals and \( 4^{t h} \) ventricle
D. Haversian canals


\( \int \frac{e^{x}}{\sqrt{5-4 e^{x}+e^{2 x}}} d x \)
\( \mathbf{A} \cdot \cos ^{-1}\left(\frac{e^{x}+2}{3}\right)+c \)
\( \mathbf{B} \cdot \cos ^{-1}\left(\frac{e^{x}-3}{2}\right)+c \)
\( \mathbf{C} \cdot \sin ^{-1}\left(\frac{e^{x}+2}{3}\right)+c \)
\( \mathbf{D} \cdot \sin ^{-1}\left(\frac{e^{x}-3}{2}\right)+c \)


What is the hybridization state of
carbon number 2 and 3 in the following
compound \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \)
A. sp and \( s p^{2} \)
B. \( s p^{2} \) and \( s p \)
\( \mathbf{c} \cdot s p^{3} \) and \( s p \)
D. \( s p \) and \( s p \)


The IUPAC name of the insecticide
lindane is:
A. dichlorodiphenyltrichloroethane
B. benzene hexachloride
c. hexachloran
D. 1,2,3.4,5,6 -hexachlorocyclohexane


The set onto which the derivative of the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\log \boldsymbol{x}-1) \) maps the
ray \( [1, \infty) \) is \( ? \)
A. \( [1, \infty) \)
(n)
в. \( (10, \infty) \)
\( c \cdot[0, \infty) \)
D. (0,0)


Two particle starting from a point on a circle of radius \( 4 \mathrm{m} \) in horizontal plane move along the circle with constant
speed of \( 4 \mathrm{ms}^{-1} \) and \( 6 \mathrm{ms}^{-1} \)
respectively in opposite direction.The paticles will collide with each other after a time of
A . \( 3.0 s \)
в. \( 2.5 s \)
\( c .2 .0 s \)
D. \( 1.5 s \)


In the Venn diagram, \( \boldsymbol{\xi}=\boldsymbol{F} \cup \boldsymbol{G} \cup \boldsymbol{H} \)
The shaded region in the diagram
represents set
\( A \cdot(F \cap H)^{\prime} \cup G \)
в. \( (F \cup H) \cap G \)
c. \( G \cup(F \cap H) \)
D. \( G \cap(F \cup H) \)


Solve the following equations and verify
your answers:
\( \frac{2-y}{y+7}=\frac{3}{5} \)


The speed of car is \( 45 k m p h \)
Find the time taken to it to travel
\( \mathbf{9 0 0 k m} \)


Direction ratio of two lines are \( l_{1}, \boldsymbol{m}_{1}, \boldsymbol{n}_{1} \)
and \( l_{2}, m_{2}, n_{2} \) then direction ratios of the line perpendicular to both the lines
are
A \( . l_{1}-l_{2}, m_{1}-m_{2}, n_{1}-n_{2} \)
в. \( l_{1}+l_{2}, m_{1}+m_{2}, n_{1}+n_{2} \)
c. \( m_{1} n_{2}-n_{1} m_{2}, n_{1} l_{2}-n_{2} l_{1}, l_{1} m_{2}-m_{1} l_{2} \)
D. \( m_{1} n_{2}-n_{1} m_{2}, n_{1} l_{2}-n_{1} l_{1}, l_{1} m_{2}-m_{1} l_{2} \)


Write the cell reaction and calculate \( \boldsymbol{E}^{o} \)
cell of the following electrochemical
cell:
\( \boldsymbol{A} \boldsymbol{l}\left|\boldsymbol{A} \boldsymbol{l}^{3+} \| \boldsymbol{Z} \boldsymbol{n}^{2+}\right| \boldsymbol{Z} \boldsymbol{n} \)
\( (\boldsymbol{s})(\boldsymbol{a q} \cdot) \)
\[
\begin{array}{c}
(\mathbf{1} \boldsymbol{M})(\mathbf{1} \boldsymbol{M}) \\
\boldsymbol{E}_{\boldsymbol{A} l}^{o}=-\mathbf{1 . 6 6 V} \\
\boldsymbol{E}_{Z n}^{o}=-\mathbf{0 . 7 6 V}
\end{array}
\]


The \( K_{s p} \) value for \( G d(O H)_{3} \) is \( 2.8 \times \) \( 10^{-23}, \) the \( p H \) at which \( G d(O H)_{3} \)
begins to precipitate is:
A . 6.08
B. 5.08
c. 8.47
D. 4.08


Express the vector \( \vec{a}=5 \hat{i}+5 \hat{k} \) as sum
of two vector such that one is parallel to the \( \vec{b}=3 \hat{i}+\hat{k} \) and other is
perpendicular to \( \vec{b} \)


A cracker at rest explodes into a large number of parts. What happens to the center of mass of the system?
A. It describes a straight line
B. It describes a parabola
c. It continues to be at the same point at which it existed before explosion
D. Nature of the path described cannot be predicted


The correct variation of resistance \( \boldsymbol{R} \)
with frequency \( f \) is given by
\( A \)
в.
c.
D.


Let \( S=x^{2}+y^{2}+2 g x+2 f y+c=0 \)
be a given circle. Then the locus of the foot of the perpendicular drawn from the origin upon any chords of \( S \) which
subtends right angle at the origin is:
A \( \cdot x^{2}+y^{2}+g x+f y+c / 2=0 \)
B . \( x^{2}+y^{2}=g \)
c. \( x^{2}+y^{2}=f \)
D. \( x^{2}+y^{2}+g=0 \)


Which of the following has zero spin and angular momentum?
\( A \cdot_{20}^{40} C a \)
в. \( _{1}^{3} H \)
\( \mathbf{c} \cdot \frac{i 4}{6} C \)
D \( \cdot \frac{37}{17} C l \)


Silver glance or argentite is
the
A. Sulphide ore of silver
B. Carbonate ore of silver
c. Halide ore of silver
D. silicate ore of silver


State similarities and differences
between the laboratory thermometer
and the clinical thermometer.


A sample of \( A g C l \) was treated with 5
\( \mathrm{mL} \) of \( 1.5 M N a_{2} C O_{3} \) solution to give
\( A g_{2} C O_{3} . \) The remaining solution
contained \( 0.0026 g \) of \( C l^{-} \) per litre. The
solubility product of \( A g C l \) is \( \left(\boldsymbol{K}_{\boldsymbol{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C O}_{3}\right)}=\boldsymbol{8 . 2} \times \mathbf{1 0}^{-12}\right) \)
A \( \cdot K_{s p}=1.63 \times 10^{-10} M^{2} \)
B. \( K_{s p}=1.71 \times 10^{-10} M^{2} \)
C . \( K_{s p}=1.82 \times 10^{-10} M^{2} \)
D. None of these


Which of the following contains same number of atoms as in 2.4 g of carbon? This question has multiple correct options
A. 0.1 moles of oxygen
B. 2.8 g of nitrogen
c. \( 2 g \) of hydrogen
D. 35.5 g of chlorine


If \( n(A)+n(B)=m, \) then the number
of possible bijections from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
\( \mathbf{A} \cdot\left(\frac{m}{2}\right) ! \)
в. \( m^{2} \)
\( c . m ! \)
D. \( 2 m \)


Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of
introducing a new product is 0.7 and
the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.


If the vectors \( a=\left(c \log _{2} x\right) \hat{i}-6 \hat{j}+3 \hat{k} \)
and \( b=\left(\log _{2} x\right) \hat{i}+2 \hat{j}+\left(2 c \log _{2} x\right) \hat{k} \)
make an obtuse angle for any \( \boldsymbol{x} \in \)
\( (0, \infty), \) then \( c \) belongs to
\( \mathbf{A} \cdot(-\infty, 0) \)
в. \( \left(-\infty,-\frac{4}{3}\right) \)
c. \( \left(-\frac{4}{3}, 0\right) \)
D. \( \left(-\frac{4}{3}, \infty\right) \)


Which of the following are formed by
xenon?
A \( \cdot \mathrm{xeF}_{7} \)
B. \( \mathrm{XeF}_{4} \)
c. \( \mathrm{xeF}_{5} \)
D. XeF \( _{3} \)


An equilateral triangle frame PQR of
mass \( \mathrm{M} \) and side a is kept under the
influence of magnetic force due to inward perpendicular magnetic field B and gravitational field as shown in the
figure.The magnitude and direction of current in the frame so that the frame
remains at rest is
\( A \)
\[
I=\frac{2 M g}{a B} ; \text { anticlockwise }
\]
в.
\[
I=\frac{2 M g}{a B} ; \text { clockwise }
\]
\( c \)
\[
I=\frac{M g}{a B} ; \text {anticlockwise}
\]
\( D \)
\[
I=\frac{M g}{a B} ; \text { clockwise }
\]


This holds a sample of barium iodide,
\( B a I_{2}, \) together:
A. hydrogen bonding
B. ionic bonding
c. metallic bonding
D. nonpolar covalent bonding
E. polar covalent bonding


If the median of the observation \( \frac{x}{5}, x, \frac{x}{4}, \frac{x}{2} \) and \( \frac{x}{3} \) is \( 8, \) then \( x= \)
\( \boldsymbol{x}>0 \)
\( A \cdot 2 \)
B. 4
c. 24
D. 16


Select the correct alternative.
When Zn changes to \( Z n^{+2} \)
it
A. looses 2 electrons
B. looses 1 electron
c. gains 1 electron
D. gains 2 electrons


The value of
\( \int_{1}^{2}[\boldsymbol{f}\{\boldsymbol{g}(\boldsymbol{x})\}]^{-1} \cdot \boldsymbol{f}^{\prime}\{\boldsymbol{g}(\boldsymbol{x})\} \cdot \boldsymbol{g}^{\prime}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \)
where \( g(1)=g(2), \) is equal to?
A . 1
B . 2
c. 0
D. none of these


Find the values of \( x, y \) and \( z \) if \( \left[\begin{array}{lll}\boldsymbol{x} & \mathbf{5} & \mathbf{4} \\ \mathbf{5} & \mathbf{9} & \mathbf{1}\end{array}\right]=\left[\begin{array}{lll}\mathbf{3} & \mathbf{5} & \boldsymbol{z} \\ \mathbf{5} & \boldsymbol{y} & \mathbf{1}\end{array}\right] \)


A stone drop from height 'h' reaches at earth surface in 1 sec. If the same stone
is taken to moon and dropped freely from height \( h, \) then it will reach the surface of moon in \( \ldots \ldots \) sec
A \( \cdot \sqrt{6} \sec \)
B. \( 9 s e c \)
\( c .3 s e c \)
D. 6 sec


A bag contains \( 100 A \times 4 \) sheets. The
weight of an \( A \times 4 . \) Sheet is \( 0.01 m g \) and weight of empty bag is \( 6.00 g m \)
Find weight of bag alone with all \( \boldsymbol{A} \times \mathbf{4} \)
sheets.


The standard deviation \( \sigma \) of the first \( N \)
natural numbers can be obtained using which one of the following formula?
\( ^{\mathrm{A}} \cdot_{\sigma}=\frac{N^{2}-1}{12} \)
B. \( \sigma=\sqrt{\frac{N^{2}-1}{12}} \)
c. \( _{\sigma}=\sqrt{\frac{N-1}{12}} \)
D. \( _{\sigma}=\sqrt{\frac{N^{2}-1}{6 N}} \)


toppr
Q Type your question.
point of time direction of magnetic field
is reversed then which of the following path is/are possible for the charged
particle. Here \( \boldsymbol{v}_{0} \) and \( \boldsymbol{B}_{0} \) are positive
constants.
\( A \)
в.
\( c \)
D. None of the abç


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


Which statement is not correct?
A. Physical adsorption is due to van der Waals forces.
B. Physical adsorption decreases at high temperature and low pressure
C . Physical adsorption is reversible.
D. Adsorption energy for chemical adsorption is generally lesser than that for physical adsorption.


Thickness of a pencil measured by using a screw gauge (least count. \( 001 \mathrm{cm} \) ) comes out to be \( 0.802 \mathrm{cm} \). The
percentage error in the measurement is
A . \( 0.125 \% \)
B . \( 2.43 \% \)
c. \( 4.12 \% \)
D. 2.14\%


The sac fungi belongs to
A. Ascomycetes
B. Basidiomycetes
C . Phycomycetes
D. Deuteromycetes


Units of instantaneous rate of reaction
is equal to :
A. an overall rate of reaction
B. an average rate of reaction
c. Both \( A \) and \( B \)
D. unitless


Which of the following is an emulsifier?
A . oil
B. Soap
c. solvent
D. KCI


In which of the following energy of \( 2 s \) orbital is minimum.
A . \( L i \)
в. \( N a \)
\( c . K \)
D. \( H \)


The height \( h_{m} \) at which the hole should
be punched so that the liquid travels
the maximum distance is
A. \( \frac{2 H}{3} \)
в. \( \frac{3 H}{8} \)
c. \( \frac{4 H}{3} \)
\( D \cdot \frac{5 H}{3} \)


If
\( 11\left[^{n-1} c_{3}\right]=24\left[^{n} C_{2}\right], \) then the value
of n is
A . 12
B. 1
\( c \cdot 10 \)
D. 13


At a given instant, four particle having
masses and acceleration as shown in
the figure lie at vertices of a square.
Acceleration of the center of mass of the
system is:
A \( \cdot \frac{1}{5}(\hat{i}+\hat{j}) \)
B \( \cdot \frac{1}{5}(\hat{j}-\hat{i}) \)
c. \( \frac{1}{5}(\hat{i}-\hat{j}) \)
D. \( -\frac{1}{5}(\hat{i}+\hat{j}) \)


The rain water that falls on a roof of area
\( 6160 m^{2} \) is collected in a cylindrical tank of diameter \( 14 \mathrm{m} \) and height \( 10 \mathrm{m} \) and thus the tank is completely filled. Find the height of rain water on the roof.


Metal that exist in liquid state at room temperature is :
A. mercury
B. silver
c. palladium
D. platinum


Find the value of \( x \) if \( \frac{x}{4}+\frac{1}{2}=4 \)


There are some passengers inside a stationary railway compartment. The
centre of mass of the compartment
itself (without the passengers) is \( C_{1} \)
while the centre of mass of the
compartment plus passengers' system
is \( C_{2} \). If the passengers move about
inside the compartment then
A \( . \) both \( C_{1} \) and \( C_{2} \) will move with respect to the ground
B. neither \( C_{1} \) nor \( C_{2} \) will be stationary with respect to the ground
C. \( C_{1} \) will move but \( C_{2} \) will be stationary with respect to the ground
D. \( C_{2} \) will move but \( C_{1} \) will be stationary with respect to the ground


Complex compound
\( \left[\boldsymbol{C o}(\boldsymbol{S C N})_{2}\left(\boldsymbol{N H}_{3}\right)_{4}\right] \boldsymbol{C l} \) exhibits :
This question has multiple correct options
A. ionization isomerism
B. geometrical isomerism
c. optical isomerism
D. linkage isomerism


Among \( \boldsymbol{C a} \boldsymbol{H}_{2}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{N a H} \) and \( \boldsymbol{B}_{2} \boldsymbol{H}_{6} \)
which are covalent hydrides?
\( \mathbf{A} \cdot N H_{3} \) and \( B_{2} H_{6} \)
в. \( N a H \) and \( C a H_{2} \)
c. \( N a H \) and \( N H_{3} \)
D. \( C a H_{2} \) and \( B_{2} H_{6} \)


Which of the following species combine
to form ferrocene?
A \( \cdot F e^{3+} \) and two molecules of cyclopentadiene
B. Fe and two \( C_{5} H_{6} \) molecules
C \( \cdot F e^{2+} \) ion and two cyclopentadienyl ions
D. \( F e^{2+} \) and two \( C_{5} H_{6} \) molecules.


Distinguish between aerobic respiration and fermentation.


The length of a thin wire require to
manufacture a solenoid of length \( l= \) \( 100 \mathrm{cm} \) and inductance \( L=1 m H, \) if
the solenoid's cross-sectional diameter
is considerably less than its length is:
A. \( 1 k m \)
в. \( 0.10 \mathrm{km} \)
c. \( 0.010 \mathrm{km} \)
D. \( 10 \mathrm{km} \)


When Magnesium is burnt in air, a
white ash remain as left over. What is
this?
\( \mathbf{A} \cdot M g O_{2} \)
в. \( M g O \)
c. \( M g \)
D. \( M g_{3} O \)


Clauiceps is a member of
A. Ascomycetes
B. Basidiomycetes
c. zygomycetes
D. Phycomycetes


Find the slope of line \( l \), which is the
perpendicular bisector of the line segment with endpoints (2,0) and (0,-2)
A . 2
B.
c. 0
D. -
E. -2


The metal ion involved in the stomatal
regulation is
A. Iron
B. Magnesium
c. zinc
D. Potassium


Which statement is false regarding nucleic acids?
A. Base pairing occurs between purine and pyrimidine
B. The two nucleotide chains in DNA have opposite polarity
c. Guanine : cytosine bonding involves the formation of two hydrogen bonds
D. A hydrogen-bonded base pairs in a DNA double helix forms an approximately planar structure


The coefficients of self induction of two
coils are \( L_{1}=8 \mathrm{mH} \) and \( L_{2}=2 \mathrm{mH} \)
respectively. The current rises in the two
coils at the same rate. The power given
to the two coils at any instant is same. The ratio of energies stored in the coils
will be:
A. \( \frac{W_{1}}{W_{2}}=4 \)
B. \( \frac{W_{1}}{W_{2}}=\frac{1}{4} \)
\( \mathbf{c} \cdot \frac{W_{1}}{W_{2}}=\frac{3}{4} \)
D. \( \frac{W_{1}}{W_{2}}=\frac{4}{3} \)


Of the following, the anhydride of nitric acid is:
A \( \cdot N_{2} O \)
B. \( N O \)
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


\( \lim _{x \rightarrow \sqrt{2}} \frac{x^{2}-2}{x^{2}+\sqrt{2 x}-4} \)


Work out the following divisions:
\( \left(5 x^{3}-4 x^{2}+3 x\right) \div(2 x) \)


Three players play a total of 9 games. In each game, one person wins and the other two lose; the winner gets 2 points and the losers lose 1 each. The number
of ways in which they can play all the 9 games and finish each with a zero score
is
\( \mathbf{A} \cdot 84 \)
B. 1680
c. 7056
D.


State Faraday's law of electromagnetic induction. Apply the law to obtain an expression for the induced emf in a conducting rod of length \( a \) rotating about its one end with angular velocity
\( \omega \) in uniform magnetic field B.


Basic strength of the given compound is in order of:
(i) \( \boldsymbol{C H}_{3} \overline{\boldsymbol{C}} \boldsymbol{H}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{C}=\stackrel{\Theta}{\boldsymbol{C}} \boldsymbol{H} \) and
(iii) \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}^{\ominus} \)
A \( .(i i)>(i)>(i i i) \)
B. \( (i i i)>(i i i)>(i) \)
c. \( (i)>(i i i)>(i i) \)
D. \( (i)>(i i)>(i i i) \)


\( \sin A=\frac{4}{5}, A \) being an acute angle. Find
the value of \( 2 \tan A+3 \sec A+ \)
\( 4 \sec A \cdot \csc A \)


How will you convert phenol to phenolpthalein?


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 2 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 8} \)
\( P(B)=0.25 \)


The correct order of bond
angle(smallest first) in \( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{B} \boldsymbol{F}_{3} \)
and \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{4} \) is:
A. \( H_{2} S<N H_{3}<B F_{3}<S i H_{4} \)
B. \( N H_{3}<H_{2} S<S i H_{4}<B F_{3} \)
c. \( H_{2} S<N H_{3}<S i H_{4}<B F_{3} \)
D. \( H_{2} S<S i H_{4}<N H_{3}<B F_{3} \)


The Sl unit of resistance is :
A. Newton
B. ohm
c. watt
D. Joule


\( \ln \) a \( S_{N} 2 \) substitution reaction of the type \( \boldsymbol{R}-\boldsymbol{B r}+\boldsymbol{C l}^{-} \stackrel{D M \boldsymbol{F}}{\rightarrow} \boldsymbol{R}-\boldsymbol{C l}+ \)
\( B r^{-} \) Which one of the following has the
highest relative rate?
\( A \)
(1)
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3}-C H_{2}-C H_{2} B r \)
D.
(4)
\[
\begin{array}{c}
\mathrm{cH}_{3}-\mathrm{cH}-\mathrm{cH}_{2} \mathrm{Br} \\
\mathrm{CH}_{3}
\end{array}
\]


Which of the following is not a method for the disposal of hazardous wastes?
A. Isv
B. Landfills
c. Deep-will injection
D. Surface impoundments


If \( f(x)=\frac{\sin 3 x}{\sin x}, x \neq 0 \) is continuous
\[
=\boldsymbol{K}, \boldsymbol{x}=\mathbf{0}
\]
function, then \( \boldsymbol{K}= \)
A .
B. 3
\( c \cdot \frac{1}{3} \)
D.


Hydrolysis of trichloro methane with aq KOH gives finally:
A. methanol
B. chloral
c. acetylene
D. potassium formate


The point on the curve \( y^{2}=8 x \) for
which the abscissa and ordinate
change at the same rate is.
A \( \cdot(4,2) \)
в. (-4,2)
\( c \cdot(2,4) \)
D. (-2,-4)


If a random variable \( X \) takes value 0 and
1 with respective probabilities \( \frac{2}{3} \) and \( \frac{1}{3} \) then the expected value of \( X \) is
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
c. 0
D.


A bread gives a boy of mass \( 40 k g \) an
energy of \( 21 k J . \) If the efficiency is \( 28 \% \) then the height can be climbed by him using this energy is
\( \mathbf{A} \cdot 22 \cdot 5 m \)
в. \( 14.7 m \)
\( c .5 m \)
D. \( 10 m \)


Anthracite is an ore of Fe?
A. True
B. False


The first cloned sheep is called
A . Dolly
B. Polly
c. Molly
D. Holly


A plane wavefront \( A_{1} B_{1} \) is incident at a
boundary \( A_{1} B_{2} \) as shown. It takes time
\( \tau \) for the wavefront to travel from \( B_{1} \) to
\( B_{2} . \) Speeds of propagation of light in
medium 1 and 2 are \( v_{1} \) and \( v_{2} \)
respectively and \( v_{2}>v_{1} . \) For the total
internal reflection of wavefront.
\( \mathbf{A} \cdot v_{1} \tau>A_{1} B_{2} \)
B . \( v_{2} \tau>A_{1} B_{2} \)
c. \( v_{1} \tau<A_{1} B_{2} \)
D. \( v_{2} \tau<A_{1} B_{2} \)


An automobile, travelling at \( 40 \mathrm{km} / \mathrm{h} \) Can be stopped at a distance of \( 40 \mathrm{m} \) by applying brakes. If the same automobile is travelling at \( 120 \mathrm{km} / \mathrm{h} \), the minimum stopping distance in meter, is(assume no skidding)
\( \mathbf{A} \cdot 270 \mathrm{m} \)
B. \( 160 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. 360m


The total number of injective mappings from a set with \( m \) elements to a set
with \( n \) elements, \( m \leq n \), is
\( \mathbf{A} \cdot m^{n} \)
B . \( n^{\text {m }} \)
c. \( \frac{n !}{(n-m) !} \)
D. \( n ! \)


State whether given statement is True or False :

Mud houses are hot in summer and cold
in winter.
A. True
B. False


Which is no intensive property?
A. boiling point
B. refractive index
c. molarity
D. volume


A molecule of Stachyose contains how many carbon atoms?
A. 6
B. 12
\( c \cdot 18 \)
D. 24


\( \mathbf{f} \boldsymbol{\omega}=\frac{Z}{\bar{Z}}, \) then \( |\boldsymbol{\omega}|= \)


Cathode rays contain:
A. neutrons
B. protons
c. electrons
D. mesons


Which metal is used to make
ferromagnets?
A. Iron
B. cobalt
c. Nickel
D. All of these


Which of the following is one of the ten most endangered river in the world?
A. Ganga
B. Yamuna
c. Mahanadi
D. Krishna


The thickness of a micron is :
B. \( 10^{-6} \mathrm{m} \)
\( \mathrm{c} \cdot 10^{-9} \mathrm{m} \)
D. \( 10^{-12} \) m


If \( \sin x+\sin ^{2} x=1, \) then \( \cos ^{2} x+\cos ^{4} x \)
is :
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


\( S O_{2} \) does not acts as:
A. bleaching agent
B. oxidising agent
c. reducing agent
D. dehydrating agent


Which type of vascular bundles are found in monocot stem?
A. Collateral, open, endarch
B. Radial, open, diarch
c. Radial, open, mesarch
D. Collateral, closed, endarch


The volume (in ml) of oxygen liberated
at STP when \( 100 \mathrm{ml} \) of \( 15 \mathrm{V} \mathrm{H}_{2} \mathrm{O}_{2} \)
decomposes is:
A . 150
в. 300
c. 3000
D. 1500


Which of the following compounds has the lowest boiling point?
A. 2-propanamine
B. ethylmethylamine
c. 1-propanamine
D. N,N-dimethylmethanamine


Calculate the ground state Q value of the induced fission reaction in the
equation
\( \boldsymbol{n}+_{\mathbf{9 2}}^{235} \boldsymbol{U} \rightarrow_{\mathbf{9 2}}^{236} \boldsymbol{U}^{*} \rightarrow_{40}^{99} \boldsymbol{Z} \boldsymbol{e}+_{52}^{134} \boldsymbol{T} \boldsymbol{e}+ \)
\( \mathbf{3} n \)
if the neutron is thermal. A thermal
neutron is in the thermal equilibrium with its environment; it has an average kinetic energy given by (3/2) kT. Given:
\( \$ \$ m(n)=1.0087 \) amu,
\( \mathrm{M}(\wedge\{235\} \cup)=235.0439 \) amu,
\( M(\wedge\{99\} Z r)=98.916 \)
amu \( \mathrm{M}(\wedge\{134\} \mathrm{Te})=133.9115 \) amu \( \$ \$ \)


If the base sequence in DNA is \( 5^{\prime} \) AAAA
\( 3^{\prime} \) then the bases sequence in mRNA is
A . 5' UUUU 3
B. 3' UUUU 5'
C . 5' AAAA 3'
D. 3' गागा 5'


For 'invert sugar', the correct
statement(s) is (are)
(Given : specific rotations of \( (+)- \)
sucrose,
\( (+) \) -maltose, \( L-(-) \) -glucose and
L-(+)-fructose in aqueous solution are
\( +66^{0},+140^{0},-52^{0} \) and \( 92^{0} \)
respectively
A. 'invert sugar' is prepared by acid catalyzed hydrolysis of maltose
B. 'invert sugar' is an eqimolar mixture of D-(+)-glucose and D-(-)-fructose
C . specific rotation of 'invert sugar' is \( -20^{\circ} \)
D. on reaction with \( B r_{2} \) water, 'invert sugar' forms saccharic acid as one of the products


The temperature at which the domain
structure gets destroyed and ferromagnetic substance is converted into paramagnetic substance is called
as
A. Domain
B. Curie Temperature
c. Rowland
D. Magnetic Field Intensity


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{B} \times \boldsymbol{A}= \)
\{(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)\}
If true enter 1 , or else enter 0 .


State with reasons, it is possible or impossible for an object to have :
Zero distance covered and may have non zero displacement


Differentiate \( \frac{x}{\sin x} \) with respect to \( x \)
A \( \frac{\sin x+x \cos x}{\sin ^{2} x} \)
B. \( \frac{\sin x-x \cos x}{\sin ^{2} x} \)
\( \frac{\cos x+x \cos x}{\sin x} \)
D. \( \frac{\cos x-x \sin x}{\sin x} \)


The ratio of number of moles of
\( K M n O_{4} \) and \( K_{2} C r_{2} O_{7} \) required to
oxidise \( 0.1 \mathrm{mol} \mathrm{Sn}^{+4} \) in acidic medium:
A .6: 5
B. 5: 6
c. 1: 2
D. 2: 1


Dry air was drawn through bulbs containing a solution of 40 grams of
urea in 300 grams of water, then through bulbs containing pure water at the same temperature and finally through a tube in which pumice
moistened with strong \( H_{2} S O_{4} \) was kept. The water bulbs lost
\( 0.0870 g r a m s \) and the sulphuric acid
tube gained 2.036 grams. Calculate the
molecular weight of urea.
A. \( \quad M=26.9 \)
В. \( \quad M=46.8 \)
c. \( \quad M=53.8 \)
D. \( M=93.6 \)


The geometry of \( N i(C O)_{4} \) and
\( \left[N i\left(P P h_{3}\right)_{2} C l_{2}\right] \) are:
A. both square planar
B. tetrahedral and square planar
c. both tetrahedral
D. square planar and tetrahedral


Find correct for both DNA and RNA
A . Ability to replicate
B. similar sugar
c. similar bases
D. Polymeric nucleotides


A man of 50 kg mass is standing in a gravity free space at a height of \( 10 \mathrm{m} \) above the floor. He throws a stone of 0.5
kg mass downwards with a speed 2 \( \mathrm{m} / \mathrm{s} . \) When the stone reaches the
floor,the distance of the man above the floor will be
\( A \cdot 9.9 \mathrm{m} \)
B. \( 10.1 \mathrm{m} \)
\( c \cdot 10 m \)
D. 20 \( m \)


Which of the following statement is
correct?
This question has multiple correct options
A. Froth flotation method can only be used for sulphide
ore
B. Tin stone consists of wolframite as non-magnetic impurity
C. In cyanide process for the extraction of silver, Zn is used as leaching agent
D. Bessemerization process is used in the extraction of copper from copper pyrite


Statement I: \( C H C l_{3} \) is stored in
transparent bottles.
Statement II: \( C H C l_{3} \) is oxidised in air.
A. Statement I \& Statement II are correct and statement is the correct explanation of statement
B. Statement I \& Statement II are correct and statement is not the correct explanation of statement!
c. statement lis correct and Statement II is wrong
D. Statement I is wrong and Statement II is correct


State Avogadro's law?


In figure, write all pairs of adjacent
angles and all the linear pairs.


For the reaction \( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
equilibrium mixture contains \( N O_{2} \) at
\( \boldsymbol{P}=\mathbf{1 . 1} \boldsymbol{a} \boldsymbol{t m} \& \boldsymbol{N}_{2} \boldsymbol{O}_{4} \) at \( \boldsymbol{P}=\mathbf{0 . 2 8 a t m} \)
at \( 350 \mathrm{K} \). The volume of the container is
doubled. Calculate the equilibrium pressures of the two gases when the system reaches new equilibrium:
A \( \cdot P_{N O_{2}}=0.32 a t m, P_{N_{2}} o_{4}=0.095 a t m \)
B . \( P_{N O_{2}}=0.64 a t m, P_{N_{2}} o_{4}=0.049 a t m \)
C. \( P_{N O_{2}}=0.64 a t m, P_{N_{2}} o_{4}=0.05 a t m \)
D. \( P_{N O_{2}}=0.32 a t m, P_{N_{2}} o_{4}=0.049 a t m \)


How much heat is required to raise the
temperature of \( 150 g \) of iron from \( 20^{\circ} \mathrm{C} \)
to \( 25^{\circ} C ? \)
A . \( 350 J \)
в. \( 345 J \)
\( c .360 J \)
D. \( 330 J \)


If \( S \) is the set containing values of \( x \)
satisfying \( [\boldsymbol{x}]^{2}-\mathbf{5}[\boldsymbol{x}]+\boldsymbol{6} \leq \mathbf{0}, \) where \( [\boldsymbol{x} \)
denotes greatest integer function then \( S \) contains :
в. (2,4]
c. [2,3]
D. [2,4]


Which of the following is planar?
A. \( X e O_{4} \)
в. \( X e O_{3} F \)
c. \( X e O_{2} F_{2} \)
D. \( X e F_{4} \)


On passing a current through a molten aluminium chloride for some time
produced 11.28 lit of \( C l_{2} \) at \( \mathrm{NTP} \) at anode.
The quantity of aluminium deposited at
cathode is:
A. 27grams
B. 18gram
c. \( \operatorname{ggram} \)
D. 36 gram


Using integration, find the area of the triangle \( P Q R, \) whose vertices are at
\( \boldsymbol{P}(\mathbf{2}, \mathbf{5}), \boldsymbol{Q}(\mathbf{4}, \mathbf{7}) \) and \( \boldsymbol{R}(\mathbf{6}, \mathbf{2}) \)


Haldol is a tranquilizer
A. True
B. False


Sl unit of permittivity is:
\( \mathbf{A} \cdot F m^{-1} \)
В. \( N m^{2} C^{-2} \)
c. \( N m^{2} C^{-1} \)
D. \( A m^{-1} \)


Earth has no gravitational force:
A. True
B. False
\( c . \) Both
D. None


The correct statement for \( d \) -block
element is:

This question has multiple correct options
A. It shows magnetic property
B. It has variable valency
C. It has tendency of formation of colored ions
D. It has complete \( d \) -orbitals


A function
\( f:[3,7) \rightarrow R \) is defined as
follows
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x<7\end{array}\right. \)
Find \( \boldsymbol{f}(-\mathbf{2})-\boldsymbol{f}(\mathbf{4}) \)


Assertion
Small leaflets are present on the
phyllode of Parkinsonia aculeata
Reason

Phyllode does not bear leaves and
flowers
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Two wires of the same material and
length but diameter in the ratio 1: 2 are
stretched by the same load. The ratio of
elastic potential energy per unit volume for the two wires is:
A . 1: 1
B . 2: 1
c. 4: 1
D. 16: 1


A number exceeds by 40 when added by \( 20 \% \) of itself. The number is
A. 800
в. 100
c. 200
D. 320


Most abundant fibrous protein in the human body is:
A. collagen
B. keratin
c. elastin
D. myosin


The time period of a sound wave from a piano is \( 1.18 \times 10^{-3} s . \) Find its
frequency
\( \mathbf{A} \cdot 847.45 H z \)
в. \( 800 H z \)
\( \mathbf{c} .935 .55 H z \)
D. \( 1000 H z \)


A transformer has 50 turns in primary and 100 turns in secondary. If the primary is connected to 220 V d.c.
supply, then the voltage across the secondary will be :
A . \( 440 \mathrm{V} \)
B. 220
\( c \cdot 110 v \)
D. o v


A perfect cube does not end with two
zeros
A. True
B. False
c. Ambiguous
D. Data insufficient


At \( 25^{\circ} C, \) the total pressure of an ideal solution obtained by mixing 3 mole of \( A \) and 2 mole of \( \mathrm{B} \), is 184 torr. What is the
vapour pressure (in torr) of pure \( \mathrm{B} \) at the same temperature (Vapour pressure of
pure \( A \) at \( 25^{\circ} C \) is 200 torr.)?
A . 180
B. 160
\( c \cdot 16 \)
D. 100


\( \left\{\begin{array}{l}2 \pi \\ 0 \\ 1\end{array}\right. \)
\( a^{n / 2}\{\emptyset \)
\( \left[\begin{array}{l}y^{\prime \prime} \\ 0\end{array}\right\} \)
\( \left\{\begin{array}{l}y_{1} \\ \Delta\end{array}\right\} \)


The emission spectra of atoms in the gaseous phase do not show a continuous spread of wavelength from red to violet, rather they emit light only at specific wavelengths with dark
spaces between them. Such spectra is/are called:
A. line spectra
B. atomic spectra
c. both \( (A) \) and \( (B) \)
D. none of these


If \( 2 x+\frac{1}{3 x}=5 \) then the value of
\( \frac{5 x}{6 x^{2}+20 x+1} \) is
A \( \cdot \frac{3}{7} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{1}{7} \)
D.


\( 25.0 \mathrm{mL} \) of \( 1.0 \mathrm{M} \mathrm{HCl} \) is combined with
\( 35.0 \mathrm{mL} \) of \( 0.5 \mathrm{M} \) NaOH. The initial
temperature of the solutions is \( 25^{\circ} C \) the density of the solution is \( 1.0 \mathrm{g} / \mathrm{mL} \) the specific heat capacity of the
solution is \( 4.184 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C} \), the reaction is
completed in an insulated coffee cup,
and the standard enthalpy of reaction
for \( \boldsymbol{H}_{(\boldsymbol{a q})}^{+}+\boldsymbol{O H}_{(\boldsymbol{a q})}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(1)} \) is - 56
kJ/mol. What is the final temperature of the solution?
\( \mathbf{A} \cdot 28.9^{\circ} C \)
B. \( 30.1^{\circ} \mathrm{C} \)
c. \( 32.8^{\circ} \mathrm{C} \)
D. none of the above


The sides of a right triangle are 9,12 and \( 15 \mathrm{cm} \) long. Find the sum of the squares of the medians.
A. \( 327.5 \mathrm{cm} \)
B . \( 332.5 \mathrm{cm} \)
c. \( 337.5 \mathrm{cm} \)
D. \( 322.5 \mathrm{cm} \)


The factors, which influence the
conductance of solutions:

This question has multiple correct options
A. solute-solute interaction
B. solute-solvent interaction
c. temperature
D. solvent-solvent interaction


The largest sphere is curved out of cube
of side \( 14 c m \). Find surface area of
sphere


If any positive' even integer is of the form \( 4 q \) or \( 4 q+2, \) then \( q \) belongs to:
A. whole number
B. rational number
c. real number
D. none of these


Which is the following is/are correct for Iyophilic sols?
This question has multiple correct options
A . Its surface tension is lower than that of \( 4 H_{2} O \)
B. Its viscosity is higher than that of water.
c. Its surface tension is higher than that of water.
D. Its viscosity is equal to that of water.


The \( V-I \) graph for a conductor at
temperature \( T_{1} \) and \( T_{2} \) are as shown in
figure. The term \( \left(\boldsymbol{T}_{\mathbf{2}}-\boldsymbol{T}_{\mathbf{1}}\right) \) is
proportional to:
\( \mathbf{A} \cdot \cos 2 \theta \)
B. \( \sin 2 \theta \)
\( c \cdot \cot 2 \theta \)
D. \( \tan 2 \theta \)


Heterotrophic plants which feed on other plants and decaying matter are
A. Orchids.
B. Jasmines.
c. conifers.
D. cedar plants


If \( f^{\prime}(x)=g(x)(x-a)^{2}, \) where \( g(a) \neq 0 \)
and \( g \) is continuous at \( x=a \) then
This question has multiple correct options
A. \( f \) is increasing near a if \( g(a)>0 \)
B. \( f \) is increasing near a if \( g(a)<0 \)
c. \( f \) is decreasing near a if \( g(a)>0 \)
D. \( f \) is decreasing near a if \( g(a)<0 \)


What is the length of the sheet, 2 meter
wide, required for making an open tank \( 15 \mathrm{m} \) long, \( 10 \mathrm{m} \) wide and \( 5 \mathrm{m} \) deep?


Assertion
Consider the points \( A, B \) and \( C \) The vector sum, \( \overrightarrow{\boldsymbol{A B}}+\overrightarrow{\boldsymbol{B C}}+\overrightarrow{\boldsymbol{C A}}=\overrightarrow{\mathbf{0}} \)
Reason
\( A, B \) and \( C \) form the vertices of a
triangle.
A. Assertion and Reason are correct and the Reason is the correct explanation for the Assertion
B. Assertion and Reason are correct but the Reason is not the correct explanation for the Assertion
c. Assertion is correct while the Reason is incorrect
D. Assertion is incorrect while the Reason is correct


is the most stable form
of sulphur.
A. Rhombic sulphur
B. Plastic sulphur
c. Monoclinic sulphur
D. Needle shaped sulphur


Who described role of natural selection
in speciation?
A. Orator F. Cook
B. Charles Robert Darwin
c. J.B.S Haldane
D. None of these


In the complexes \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+},\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{3-},\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)\right. \)
and \( \left[\boldsymbol{F} e \boldsymbol{C l}_{6}\right]^{3-}, \) more stability is shown
by :
\( \mathbf{A} \cdot\left[F e C l_{6}\right]^{3-} \)
B . \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right]^{3}\right. \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3+} \)
D. \( \left[F e(C N)_{6}\right]^{3-} \)


What is soap? Describe its preparation.


The solution of the equation \( \sin ^{-1}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\boldsymbol{x}+\boldsymbol{y} \) is
A \( \cdot \tan (x+y)+\sec (x+y)=x+C \)
B \cdot \( \tan (x+y)-\sec (x+y)=x+C \)
C \( \cdot \tan (x+y)+\sec (x+y)+x+C=0 \)
D. None of the above


Which one of the following is not an assumption of kinetic theory of gases?
A. The volume occupied by the molecules of the gas is negligible
B. The force of attraction between the molecules is negligible
c. The collision between the molecules are elastic
D. All molecules have same speedd


Find whether the lines drawn through the two pairs of points are parallel or perpendicular \( (\boldsymbol{3}, \boldsymbol{3}),(\boldsymbol{4}, \boldsymbol{6}) \) and
(4,1),(6,7)


If the matrix \( A \) is both symmetric and
skew symmetric, then
A. \( A \) is a diagonal matrix
B. \( A \) is a zero matrix
c. \( A \) is a square matrix
D. None of these


In the following sequence of reaction:
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \frac{\boldsymbol{K O H}(\boldsymbol{a l} \boldsymbol{c})}{(\boldsymbol{A})} \stackrel{\boldsymbol{H B r}}{\longrightarrow} \)
\( (B) \frac{K O H(a q)}{(C)} \)


What is control and coordination?


In the following sets of reactants which two sets exhibit the amphoteric
character of \( \boldsymbol{A l}_{2} \boldsymbol{O}_{3} \cdot \boldsymbol{x} \boldsymbol{H}_{2} \boldsymbol{O} ? \)
\( \operatorname{set} 1: A l_{2} O_{3} \cdot x H_{2} O(s) \) and \( O H^{-}(a q) \)
\( \operatorname{set} 2: A l_{2} O_{3} \cdot x H_{2} O(s) \) and \( H_{2} O(l) \)
\( \operatorname{set} 3: A l_{2} O_{3} \cdot x H_{2} O(s) \) and \( H^{+}(a q) \)
\( \operatorname{set} 4: A l_{2} O_{3} \cdot x H_{2} O(s) \) and \( N H_{3}(a q) \)
A . 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 4
D. 3 and 4


Give reasons for the following
Valves are present in veins but not in
arteries


\( \cos ^{-1}\left(\cos \left(\frac{-17 \pi}{5}\right)\right) \) is equal to
A. \( -\frac{17 \pi}{5} \)
в. \( \frac{3 \pi}{5} \)
\( c \cdot \frac{2 \pi}{5} \)
D. none of these


Find the amplitude of -4


The following real numbers have decimal expansions as given below. In each case, decide whether they are
rational or not. If they are rational or not. If they are rational, and of them \( \frac{p}{q}, \) what can you say about the prime factors of \( q \)
\( ? \)
¡) 43.123456789
¡i) 0.120120012000120000....
iii) \( 43 . \overline{123456789} \)


Aeration process change the odour of wastewater
A . True
B. False


Evaluate the integral \( \int_{0}^{\infty} e^{-2 x} \cdot \sin 5 x d x \)
A \( \cdot \frac{-2}{29} \)
в. \( \frac{2}{29} \)
c. \( \frac{5}{29} \)
D. \( \frac{7}{25} \)


Vibrations in a body produces sound. How do you prove it?


Assertion
LiCl is predominantly a covalent
compound.
Reason
Electronegativity difference between \( L i \)
and \( C l \) is too small.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A boy pushes a wall with a force of \( 10 N \)
towards east. What force is exerted by
the wall on the boy?
A. \( 10 N \) towards east
B. \( 10 N \) towards west
c. \( 10 N \) towards north
D. \( 10 N \) towards south.


\( A B C D \) is a parallelogram and \( B P C \) is a triangle with \( P \) falling on \( A D . \) If the
area of parallelogram \( A B C D=26 \mathrm{cm}^{2} \)
find the area of triangle \( \boldsymbol{B} \boldsymbol{P} \boldsymbol{C} \)


Find the equation of a straight line:
with slope \( -1 / 3 \) and \( y- \) intercept -4


A body moving along the ground with a velocity of \( 14 m / s \) comes to rest due to
friction after travelling a distance of 50cm Determine the coefficient of
friction between the body and the
ground \( g=9.8 m / s^{2} \)


Which of the following acids is
monobasic?
A. Hypophosphorous acid \( \left(H_{3} P O_{2}\right) \)
B. Orthophosphoric acid \( \left(H_{3} P O_{4}\right) \)
C. Pyrophosphoric acid \( \left(H_{4} P_{2} O_{7}\right) \)
D. Hypophosphoric acid \( \left(H_{4} P_{2} O_{6}\right) \)


If \( P \) is a \( 3 \times 3 \) matrix such that \( P^{T}= \)
\( 2 P+I \) where \( P^{T} \) is the transpose of \( P \)
and lis the \( 3 \times 3 \) identify matrix, then there exists a column matrix \( \boldsymbol{X}= \) \( \left[\begin{array}{l}x \\ y \\ z\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \) such that
\( ^{\mathbf{A}} \cdot \operatorname{IX}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
B. PX = X
\( c \cdot \) Рх \( =2 x \)
D. PX = - x