Which of the following leaves no residue
on heating?
\( A \cdot P b\left(N O_{3}\right)_{2} \)
B. \( \mathrm{NH}_{4} \mathrm{NO}_{3} \)
\( c \cdot \operatorname{cu}\left(N O_{3}\right)_{2} \)
D. NaNO


In the equation \( y=A \sin \left[k t-\frac{x}{\lambda}\right], \) the dimensional formula for \( k \) is
A \( \cdot M^{0} L^{0} T^{-1} \)
B . \( M^{0} L^{0} T^{0} \)
c. \( M^{0} L T^{0} \)
D. \( M L^{0} T^{0} \)


tissue is the protective tissue in animal body.
A. Epithelial
B. Endothelial
c. Both A and B
D. None of the above


Evaluate the following definite integral:
\( \int_{4}^{9} \frac{\sqrt{x}}{\left(30-x^{3 / 2}\right)^{2}} d x \)


Among the following, the only secondary pollutant is:
\( A \cdot S O_{2} \)
в. \( C O \)
\( c \cdot O_{3} \)
D. \( N O \)


Evaluate \( \int_{0}^{2}\left(x^{2}+2 x+1\right) d x \)


\( \mathrm{n}\left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-}, \) the isomerism shown
is :
A. ligand
B. optical
c. geometrical
D. ionisation


If \( (2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0 \) and
\( \boldsymbol{y}(\mathbf{0})=\mathbf{1}, \) then \( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) is equal to:
A \( \cdot \frac{1}{3} \)
в. \( -\frac{2}{3} \)
\( c \cdot-\frac{1}{3} \)
D.


Match compounds given in (X) with their uses in \( (Y): \)
\( X \)
A. \( \mathrm{Na}_{2} \mathrm{CO}_{3} \)
I glass
B. \( \mathrm{Na}_{2} \mathrm{SO}_{3} \)
II bleach
C. \( \mathrm{NaOH} \)
III \( \mathrm{SO}_{2} \) absorber
D. NaOCI
IV detergent
A . A-IV, B-I, C-III, D-II
B. A-I, B-III, C-IV, D-1 ||
c. A-II, B-IV, C-I, D-III
D. A-III, B-II, C-IV, D-1


If the earth stops rotating.then the value of acceleration due to gravity at a latitude \( 45^{\circ} \) will increases by


The building block of proteins are:
A. \( \alpha \) -hydroxy acid
B. \( \alpha \) -amino acid
c. \( \beta \) - hydroxy acid
D. \( \beta \) - amino acid


A loosely wound helix made of stiff wire is mounted vertically with the lower end just touching a dish of mercury when a current from the battery is started in
the coil through the mercury
A. the wire oscillates
B. the wire continues making contact
c. the wire breaks contact just when the current is passed
D. the mercury will expand by heating due to passage of current


If
\( a, b \) and \( c \) are three positive real numbers, then the minimum value of the expression \( \frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c} \)
is:
A .
B . 2
\( c \cdot 3 \)
D.


Which scientist proposed the concept of atomic mass?
A. Avogadro
B. Gay Lussac
c. Prout
D. Dalton


A loop shown in the figure is immersed
in the varying magnetic field \( B=B_{0} t \)
directed into the page. If the total
resistance of the loop is \( R \), then the
direction and magnitude of induced current in the inner circle is :
\( ^{\mathrm{A}} \cdot_{\mathrm{clockwise}} \frac{B_{0}\left(\pi a^{2}-b^{2}\right)}{R} \)
B. anticlockwise \( \frac{B_{0}\left(\pi a^{2}+b^{2}\right)}{R} \)
c. \( _{\text {clockwise }} \frac{B_{0}\left(\pi a^{2}+4 b^{2}\right)}{R} \)
" clockwise \( \frac{B_{0}\left(4 b^{2}-\pi a^{2}\right)}{R} \)


When a voltage source that is inducing voltage into a large number of coils is disconnected, and a switch that is in
series with the coils of wire is also
opened, a spark is observed to jump across the switch terminals as the
switch begins to open up. Identify the cause of this spark?
A. Free electrons from the voltage source
B. Free electrons from the coils of wire
c. collapse of the magnetic field in the coils
D. Secondary electron flow from the source
E. Stored voltage in the coils of wire


An optically active compound A upon acid catalysed hydrolysis yield two
optically active compound B and \( C \) by pseudo first order kinetics. The observed rotation of the mixture after
20 min was \( 20^{\circ} \) while after completion
of the reaction it was \( -20^{\circ} . \) If optical
rotation per mole of \( A, B \& C \) are \( 60^{\circ}, 40^{\circ} \)
\( \&-80^{\circ} . \) Calculate half life of the
reaction.
A. 20 min
B. 24 min
c. 28 min
D. 32 min


Which of the following statements are true about acid rain?
(i) Acid rain is harmful to some plants and animals.
(ii) Acid rain mainly comprises the sulphuric acid and nitric acid
(iii) Acid rain helps farmers to produce
more crops.
(iv) Acid rain corrodes buildings and
statues.
A \( \cdot \) (i) and (ii)
B. (i) and (iii)
\( c \cdot \) (i), (iii) and (iv)
D. (i), (ii) and (iv)


toppr
Q Type your question-
magnetic field shows that the atoms
must have magnetic moment. However,
the moment cannot be due to the orbital
angular momentum since \( \varphi=0 . \) Hence
one must assume existence of intrinsic
angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produces angular momentum equal to \( s=\sqrt{s(s+1)} \frac{h}{2 \pi} \)
where \( s=+\frac{1}{2} \)
Total spin of an atom \( =+\frac{n}{2} o r-\frac{n}{2} \)
where \( n \) is the number of unpaired
electron
The Substance which contain species
with unpaired electrons in their orbitals
behave as paramagnetic substances.
The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom \( \boldsymbol{\mu}=\sqrt{\boldsymbol{s}(\boldsymbol{s}+\mathbf{1})} \frac{e h}{2 \pi \boldsymbol{m} c}=\sqrt{\frac{n}{2}\left(\frac{n}{2}+1\right)} \frac{e h}{2 \pi m c} \)
\( s=\frac{n}{2} \)
\( \boldsymbol{\mu}_{s}=\sqrt{\boldsymbol{n}(\boldsymbol{n}+\mathbf{2})} \mathbf{B} . \mathbf{M} \)
n-number of upaired electrons
1.B.M. (Bohr magneton) \( =\frac{e h}{4 \pi m c} \)
f magnetic moment is zero the substance is di-magnetic.
Which of the following ion has highest magnetic moment?
A \( \cdot F e^{2} \)
в. \( M n^{2} \)
\( c \)
D. \( V 3+ \)


A die is thrown. Find the probability of getting an odd number


Name the functional group of the given compound.
A. Aldehydic group
B . Alcoholic group
c. Ketonic group
D. Carboxylic group


The emf induced between \( M \) and \( Q \) if
the potential between \( P \) and \( Q \) is \( 100 V \)
\( M \) is midpoint of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
A . \( 25 V \)
в. \( 50 V \)
\( c .75 V \)
D. \( 100 V \)


\( 252 \mathrm{gm} \) of oxalic acid with molecular
formula \( C_{2} H_{2} O_{4} \cdot 2 H_{2} O \) dissolve in
water to form \( 250 \mathrm{ml} \). of the solution. Its
molarity will be:
A . 16 м
B. 8 M
c. 32 м
D. 24 M


Which of the following does not apply to
ascomycetes?
A. Mycelium is coenocytic and aseptate.
B. Commonly known as sac fungi
C. Asexual spores called conidia are produced exogenously.
D. Sexual spores called ascospores are produced endogenously.
E. They are saprophytic, decomposers, parasitic or coprophilous.


Two particles \( A \) and \( B \) are moving with constant velocities \( v_{1}=\hat{j} \) and \( v_{2}=2 \hat{i} \) respectively \( A \) is at \( c o \) -ordinates (0,0) and B is at (-4,0) . the angular velocity of B with respect to \( A \) at \( t=2 s \) is (all
physical quantities are in Sl units)
A \( \cdot \frac{1}{2} r a d / s \)
B. \( 2 r a d / s \)
c. \( 4 r a d / s \)
D. \( 1 r a d / s \)


The electric field at point Pjust outside the outer surface of a hollow spherical conductor of inner radius \( 10 \mathrm{cm} \) and
outer radius \( 20 \mathrm{cm} \) has magnitude 450 \( \mathrm{N} / \mathrm{C} \) and is directed outward. When an
unknown point charge \( Q \) is placed at the center of the sphere, the electric field at point \( P \) is still pointing outward but is now \( 180 \mathrm{N} / \mathrm{C} \). What is the value of
charge Q?
A . 4.5 nc
в. 1.5 nc
\( c .-1.5 \mathrm{nc} \)
D. -1.2 nc


The rate of a reaction increases four
fold when the concentration of reactant
is increased 16 times. If the rate of
reaction is \( 4 \times 10^{-6} \) mol \( L^{-1} s^{-1} \) when
the concentration of the reactant is
\( 4 \times 10^{-4} \) mol \( L^{-1} . \) The rate constant of
the reaction will be:
B. \( 1 \times 10^{-2} \mathrm{s}^{-1} \)
C . \( 2 \times 10^{-4} \mathrm{mol}^{-1 / 2} \mathrm{L}^{1 / 2} \mathrm{s}^{-1} \)
D. 25 mol-1 L min \( ^{-1} \)


Match the List I with List 2.


The correct order of increasing dissociation constant of the following compounds is:
\( A \cdot\|<I V<I<\| \)
B. IV < III < I <I
c. \( |V<\|<\mid<\| \)
D. IV <I<II<III


Acetyl chloride cannot be obtained from
acetic acid with
A \( \cdot P C l_{3} \)
в. \( P C l_{5} \)
c. \( \operatorname{sOCl}_{2} \)
D. \( S_{2} C l_{2} \)


What is molecular formula for 3 - Ethyl 2, 3 - dimethyl pentane


If the ratio of the corresponding sides of two similar triangles is 2: 3 then the ratio of their corresponding altitude is
A. 3: 5
B. 16: 81
\( c \cdot 4: 9 \)
D. 2:3


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\tan ^{-1} \frac{\mathbf{1}+\boldsymbol{x}^{2}}{\boldsymbol{x}}\right\}= \)
A . 0
B.
\( c \cdot \frac{1}{2} \)
\( D \)


Four pieces each of length \( l \) of a
conducting rod are joined as shown in the figure. The rod is placed in a downward magnetic field B. If the rod is
moved towards right with a uniform
velocity \( v, \) then the induced emf across the two ends of the rod is
\( A \). Blv
B. 4 Blv
C \( \cdot 2 \) Blv \( \sin (\theta / 2) \)
D \cdot 2 Blv (1+ sin\theta/2)


Integrate the following w.r.t. \( x \) \( \frac{1}{2 x+3} \)


The curve whose subtangent is twice the abscissa of the point of contact and passing through (1,2) is
A \( \cdot y^{2}=4 x \)
B \( \cdot y^{2}=-4 x \)
c. \( x^{2}=4 y \)
D. \( x^{2}=-4 y \)


The filament of a bulb takes a current
\( 100 \mathrm{mA} \) when potential difference across it is \( 0.2 \mathrm{V} \). When the potential difference across it becomes \( 1.0 \mathrm{V} \), the
current becomes 400 mA. Calculate the
resistance of filament in each case and
account for the difference.
\( A \cdot 2,2.5 \)
B. 3, 3.5
\( c \cdot 4,0 \)
D. 5,


write down the formulae of given compound tetra amine zinc(II) nitrate


Some hydrogen-like atom in ground state absorb \( n \) photons having the same energy and on de-excitation, it
emits exactly \( n \) photons. Then the energy of absorbed photon may be:
This question has multiple correct options
A. \( 91.8 e V \)
B. \( 40.8 e V \)
c. \( 48.4 e V \)
D. \( 54.4 e V \)


Assuming the water resistance to be negligible, find the horizontal
component of the force with which the man acted on the raft during the
motion.
\( ^{\mathrm{A}} \cdot_{F}=-\frac{2 m M}{M+m} \frac{d v^{\prime}}{d t} \)
\( ^{\mathrm{B}} \cdot_{F}=\frac{2 m M}{M+m} \frac{d v^{\prime}}{d t} \)
c. \( _{F}=\frac{m M}{M+m} \frac{d v^{\prime}}{d t} \)
D. \( F=-\frac{m M}{M+m} \frac{d v^{\prime}}{d t} \)


How many terms of the geometric progression \( 1+4+16+64+\dots \dots \)
must be added to get sum equal to
\( \mathbf{5 6 4 1} ? \)


A certain series resonant circuit has a
bandwidth of \( 2 k H z . \) If the existing coil
is replaced with one having a higher value of \( Q, \) the bandwidth will
A. Increase
B. Remain the same
c. Decrease
D. Be less selective


Mark the following rational numbers on
number line.
\( \frac{4}{5} \)


\( \int \cot ^{2} x d x= \)


The magnetic field of a solenoid can be increased by
A. adding more loops per metre
B. increasing the current
c. putting an iron core inside the coil to make an electromagnet
D. All of the above


The electronic configuration with the highest ionization enthalpy is:
A \( \cdot[N e] 3 s^{2} 3 p^{1} \)
B \( \cdot[A r] 3 d^{10} 4 s^{2} 4 p^{3} \)
\( \mathbf{c} \cdot[N e] 3 s^{2} 3 p^{3} \)
D. \( [N e] 3 s^{2} 3 p^{2} \)


At the initial moment three points \( A, B \)
and \( C \) are on a horizontal straight line
at equal distances from one another.
Point \( A \) begins to move vertically
upward with constant velocity \( v \) and
point \( C \) vertically downward without
any initial velocity at constant acceleration \( a \). Assuming the point
begin to move simultaneously, then comment on the motion of the B such
that centre of mass of the
system doesn't move.
A \( \cdot \) acceleration \( \frac{1}{2} a \) downwards and initial velocity \( \frac{1}{2} v \) upwards
B. retardation \( \frac{1}{2} a \) and initial velocity \( \frac{1}{2} v \) both upwards
c. zero acceleration and initial velocity
D. acceleration \( \frac{1}{2} a \) and initial velocity \( \frac{1}{2} v \) both downwards


Which of the following molecule is
paramagnetic?
A. Chlorine
B. Nitrogen
c. oxygen
D. Hydrogen


Find the value of \( \boldsymbol{T} \times \mathbf{1 0}^{\mathbf{1 7}} \) where \( \boldsymbol{T} \) is
the orbital period of the electron?


In how many different ways can the letter of the word FINANCE be arranged?
A . 5040
в. 2040
\( c .2520 \)
D. 4080
E. None of these


The equation of plane containing the lines \( \vec{\gamma}=\vec{\alpha}+\overrightarrow{\lambda \beta} \) and \( \vec{\gamma}=\vec{\beta}+\mu \vec{\alpha} \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}\vec{\gamma} & \vec{\alpha} & \vec{\beta}\end{array}\right]=\vec{\alpha} \cdot \vec{\beta} \)
B \( \cdot\left[\begin{array}{lll}\vec{\gamma} & \vec{\alpha} & \vec{\beta}\end{array}\right]=0 \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}\vec{\alpha} & \vec{\beta} & \vec{\gamma}\end{array}\right]=\vec{\alpha} \cdot \vec{\beta} \)
D. None of these


The full moon night is called:
A. Purnima
B. Amavasya
c. Both (A) and (B)
D. None of them


When a wire is subjected to a force along its length, its length increases by \( 0.4 \% \) and its radius decreases by \( 0.2 \% \)
Then the Poisons ratio of the material of
the wire is
A . 0.8
B. 0.5
\( c .0 .2 \)
D. \( 0 . \)


Which of the following is a cubic polynomial?
A. \( x^{3}+3 x^{2}-4 x+3 \)
B. \( x^{2}+4 x-7 \)
\( c \cdot 3 x^{2}+4 \)
D. \( 3\left(x^{2}+x+1\right) \)


NOR gate is the series combination of
A. NOT gate followed by OR gate.
B. OR gate followed by NOT gate.
C. AND gate followed by OR gate.
D. OR gate followed by AND gate.


Figure
(a) below shows a Wheatstone
bridge in which \( P, Q, R, S \) are fixed
resistances, G is a galvanometer, and B
is a battery. For this particular case the galvanometer shows zero deflection.
Now, only the positions of B and G are interchanged, as shown in figure (b).
The new deflection of the galvanometer.
A. Is to the left
B. Is to the right
c. Is zero
D. Depends on the values of P, Q, R, s


Discuss briefly the following:
(a) Greenhouse gases
(b) Catalytic converter
(c) Ultraviolet B


To find a point \( \boldsymbol{P} \) on the line segment
\( A B=6 \mathrm{cm}, \) such that \( A P: A B=2: 5 \)
in which ratio does the line segment
\( A B \) is divided by \( P ? \)


The sum of any number of consecutive cubes beginning with 1 is always a:
A. perfect square
B. perfect cube
c. odd number
D. even number


Boiling point of an organic compound is \( 310 K . \) Its enthalpy of vaporisation per mole \( \Delta_{v a p} H \) is \( 27.9 k J m o l^{-1} . \) If the
entropy of vaporisation \( \Delta_{v a p} S \) of organic compound is \( X \) then find out the value of \( X \)
A \( \cdot X=0.09 k J K^{-1} m o l^{-1} \)
B. \( X=-0.09 k J K^{-1} m o l^{-1} \)
c. \( X=0.18 k J K^{-1} m o l^{-1} \)
D. None of these


A charge of magnitude \( Q \) is placed at
the origin. A second charge of
magnitude \( 2 Q \) is placed at the position \( \boldsymbol{x}=\boldsymbol{d} \) along the \( \mathbf{x} \) -axis.

Other than infinitely far away, at what position on the \( x \) -axis will a positive test charge experience a zero net force?
A \( x=\frac{d}{\sqrt{2}} \)
B. \( x=\frac{d}{2 \sqrt{2}} \)
c. \( x=\frac{d}{3} \)
D. \( x=\frac{d}{1+\sqrt{2}} \)
E. At no position other than infinitely far away will the positive test charge experience zero net force


State true or false of the following. If a and b are natural numbers and \( a< \)
\( b, \) than there is a natural number c such
that \( a<c<b \)
A. True
B. False


To induce formation of organs in a
callus it is necessary to provide
A. Growth hormones
B. water
c. Soil
D. Antibiotics


Three rods of identical cross-sectional
area are made from the same metal and form the sides of an isosceles triangle
\( A B C, \) right-angled at \( B . \) The points \( A \)
and \( B \) are maintained at temperatures \( T \) and \( (\sqrt{2}) T, \) respectively. In the steady
state, the temperature of the point is \( T_{c} \) Assuming that only heat conduction
takes place, \( \boldsymbol{T}_{c} / \boldsymbol{T} \) is
\( ^{A} \cdot \frac{1}{2(\sqrt{2}-1)} \)
в. \( \frac{3}{\sqrt{2}+1} \)
c. \( \frac{1}{\sqrt{3}(\sqrt{2}-1)} \)
D. \( \frac{1}{\sqrt{2}+1} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) when \( \boldsymbol{y}=(\boldsymbol{1}+\boldsymbol{x})\left(\boldsymbol{1}+\boldsymbol{x}^{2}\right)(\boldsymbol{1}+ \)
\( \left.\boldsymbol{x}^{4}\right)\left(\boldsymbol{1}+\boldsymbol{x}^{6}\right) \)


The most effective method of
magnetisation is
A. single touch method
B. Double touch method
c. Electrical method
D. All the above


Sum of infinity the following series:
\( \mathbf{3}+\mathbf{5} \cdot \frac{\mathbf{1}}{\mathbf{4}}+\mathbf{7} \cdot \frac{\mathbf{1}}{\mathbf{4}^{2}}+\dots \dots \)


A capillary tube is dipped in water vertically.Water rises to a height of 10mm. The tube is now tilted and makes
an angle \( 60^{\circ} \) with vertical.Now water
rises to a height of:
\( A \cdot 10 \mathrm{mm} \)
B. \( 5 \mathrm{mm} \)
c. \( 20 \mathrm{mm} \)
D. 40 mm


Cane sugar on hydrolysis gives:
A. glucose and galactose
B. glucose and fructose
c. glucose only
D. fructose only


Evaluate the integral \( \int_{0}^{\pi} x \sin ^{5} x \cos ^{6} x d x=? \)
A \( \cdot \frac{5 \pi}{16} \)
в. \( \frac{35 \pi}{128} \)
c. \( \frac{5 \pi}{8} \)
D. \( \frac{8 \pi}{693} \)


Simplify \( \frac{1}{177} \cdot 11 \frac{1}{17} \)


The energy bands are present only when
the substance is present in the solid
state.
A. True
B. False


Of the following acids, the one that is strongest is :
A. \( H B r O_{4} \)
в. НОС l
c. \( H N O_{2} \)
D. \( H_{3} P O_{3} \)


Which of the following structures helps in the release of excretory gases like carbon dioxide, in plants?
A. Root hair
B. Stomata
c. Lenticels
D. None of the above


An astronomical telescope has focal lengths \( 100 \& 10 \mathrm{cm} \) of objective and eyepiece lens respectively when final image is formed at least distance of
distinct vision,magnification power of telescope will be,
A . -15
B. -14
\( c .-17 \)
D. -19


In the given figure AE is bisector of
\( \angle B A C \) and of \( \angle B D C . \) show that
\( \Delta A B D \cong A C D \) and hence \( B D=C D \)


If the papers of 4 students can be
checked by any one of the seven teachers, then the probability that all the four papers are checked by exactly two teachers is
A \( \cdot \frac{6}{49} \)
B. \( \frac{2}{7} \)
c. \( \frac{32}{343} \)
D. \( \frac{2}{343} \)


The radius of gyration of a uniform rod of length \( l \) and mass \( M \) about an axis
passing through its centre and perpendicular to its length is:
A \( \cdot \frac{l^{2}}{12} \)
в. \( \frac{l}{2 \sqrt{3}} \)
\( c \cdot \frac{l}{2} \)
D. \( \frac{l}{\sqrt{2}} \)


A solution of sugar in which some more sugar could be dissolved without
changing its temperature is called a/an
A. unsaturated solution
B. saturated solution
c. solid solution
D. true solution


On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on Rs.
9,430 for 10 years, both at the rate of 5
per cent per annum?


A point on the line \( y=x \) whose
perpendicular distance from the line \( \frac{x}{4}+\frac{y}{3}=1 \) is 4 has the coordinates
This question has multiple correct options
\( \mathbf{A} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right) \)
B \( \cdot\left(\frac{32}{7}, \frac{32}{7}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{3}{2}, \frac{3}{2}\right) \)
D. none of these


In Krebs cycle, malate hands over hydrogen to
\( A \cdot N A D^{+} \)
B. FAD
c. FMN
D. Oxaloacetate


Very short answer type.
How does the segmentation of an annelid worm differ from the repeating units of the body of a tapeworm?


Which of the following is used in the manufacture of ethanol?
A \( \cdot C_{2} H_{6} \)
B. \( C_{2} H_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C_{2} H_{4} \)


Which of the following is rightly matched?
A. Mammalia - Human beings
B. Mollusca - Centipede
c. Pisces - silver fish
D. Echinoderm - Echidna


Define angle of repose. Deduce its relation with coefficient of limiting
friction.


In which of the following reactions, products are not correctly matched in:
A \( \cdot R M g X+C O_{2} \frac{(i) C O_{2}}{(i) H \oplus} \) Carboxylic acio
B . \( R M g X+C_{2} H_{5} O H \rightarrow \) Alkane
c. \( R M g X+C H_{3} C H_{2} C l \rightarrow \) Alkene
D.
\[
\operatorname{RMgX}+\text { cl } \widehat{\operatorname{lth} e r}
\]


In the quadrilateral \( A B C D \), the diagonals \( A C \) and \( B D \) are equal and
perpendicular to each other. What type of a quadrilateral is \( A B C D ? \)
A. A square
B. A parallelogram
c. A rectangle
D. A trapezium


A bucket tied to a string is lowered at a constant acceleration of \( g / 4 . \) If the mass of the bucket is \( M \) and is lowered
by a distance \( d \), the work done by the string will be (assume the string to be massless
A. \( 1 / 4 M g d \)
в. \( -4 / 3 \) М \( g d \)
c. \( -3 / 4 M g d \)
D. \( 4 / 3 M g d \)


Which of the following is an isoelectronic pair?
A \( \cdot K^{+}, C l^{-} \)
В. \( N a^{+}, C l^{-} \)
\( \mathbf{c} \cdot N a^{+}, H e \)
D. \( H^{+}, X e \)


What type of mirror is used in automobiles to viewing of back side?


Which of the following processes does not occur at the interface of phases?
A. Crystallisation
B. Heterogeneous catalysis
c. Homogeneous catalysis
D. corrosion


A car is moving towards a hill cliff. The driver sounds a horn of frequency f. The reflected sound heard by the driver has frequency \( 2 f \) if \( v \) the velocity of sound, then the velocity of the car, in units will
be


The parameter irrelevant for an electric
fuse wire is
A. its radius.
B. its specific resistance
c. current flowing through it.
D. its length.


Iron is not protected from rusting by:
A. galvanization
B. electroplating with \( N i \) or \( C r \)
C. heating the iron to redness in steam
D. treating it with \( H_{3} P O_{4} \)


At a particular position the velocity of a particle in SHM with amplitude a is \( \frac{\sqrt{3}}{2} \) that at its mean position. In this position, its displacement is:
A \( \cdot \frac{a}{2} \)
в. \( \sqrt{3} \frac{a}{2} \frac{a}{2} \)
\( c \cdot a \sqrt{2} \)
D. \( \sqrt{2 a} \)


Most abundant, harmful and universal
waste product of metabolism is
A. Uric acid
в. \( H_{2} \)
\( c \cdot C O_{2} \)
D. None of the above


Which of the following is/are the properties of sols? This question has multiple correct options
A. Adsorption
B. Tyndall effect
c. Flocculation
D. Paramagnetism


When hydrogen peroxide is treated with
a cold acidified \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}} \) solution
containing ether, blue colour is obtained. This is due to:
A. perchromic acid
B. potassium chromate
c. chromium sulphate
D. chromium trioxide


Which one of the following relations on \( \mathbf{Z} \) is equivalence relation?
A \( . x R_{1} y \Leftrightarrow|x|=|y| \)
В. \( x R_{2} y \Leftrightarrow x \geq y \)
c. \( x R_{3} y \Leftrightarrow \frac{x}{y} \)
D. \( x R_{4} y \Leftrightarrow x<y \)


In both dialysis and osmosis which particles do not pass thorugh the semipermeable membrane?
A. water
B. Small molecules
c. Colloids
D. All of the above


If \( \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi \) then
prove that:
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z} \)


The living jawless vertebrates belong to the class
A. Ostracoderms
B. cyclostomes
c. Placoderms
D. Chondrichthyes


Seismic waves that vibrate
perpendicular to the direction of their
path.
A. Spread on the surface of the earth
B. Travel through the solid as well as other parts of the earth
C. Travel through the solid parts of the earth only
D. None of the above


A vehicle travels half the distance L with
speed \( V_{1} \) and the other half with speed
with \( \mathrm{V}_{2} \) what is the average speed?


Solve the following differential equation
\( \frac{d y}{d x}+1=\sin x \)


Construct \( \triangle A B C \) with \( B C=7.5 \mathrm{cm} \),
\( A C=5 \mathrm{cm} \) and \( m \angle C=60^{\circ} . \)


Recently (in 2003) element with atomic
number 110 has been named by IUPAC
as:
A. \( H s \)
в. \( M t \)
\( c . D s \)
D. \( S g \)


In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the
common ratio of this progression equals
A \( \cdot \frac{1}{2}(1-\sqrt{5}) \)
B \( \cdot \frac{1}{2} \sqrt{5} \)
c. \( \frac{1}{5} \sqrt{2} \)
D. \( \frac{1}{2}(\sqrt{5}-1) \)


Which of the following molecule/molecules will be have zero
dipole moment?
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{C} \boldsymbol{O}_{2}, \boldsymbol{C} \boldsymbol{C l}_{4}, \boldsymbol{C H} \boldsymbol{C l}_{3}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{B} \boldsymbol{F}_{3}, \boldsymbol{B} \)


What is the value for \( \Delta H \) for the
reaction \( N_{2} O_{4} \rightarrow 2 N O_{2} ? 2 N O_{2} \rightarrow \)
\( N_{2}+2 O_{2} \quad \Delta H=-16.2 k c a l \)
\( N_{2}+2 O_{2} \rightarrow N_{2} O_{4} \quad \Delta H= \)
\( +2.31 k c a l \)
A . +13.89 kcal
B . +18.51 kcal
c. +37.42 kcal
D. -13.89 kcal
E . -18.51 kcal


The lighting circuit is used for running:
A. devices which draw small current
B. devices which draw large current
C. devices which do not draw current
D. devices which are weightless


If \( m \) is the mass of silver deposited at
the cathode by \( 2 A \) current flowing for
\( 25 m i n \) through a silver voltameter, then
the mass deposited by \( 1.5 A \) current flowing for \( 600 s \) is
A .
в. \( 3 m \)
\( \mathrm{c} .0 .3 \mathrm{m} \)
D. None


A gas mixture contain \( 1 g H_{2} \) and \( 1 g H_{e} \) temperature of gas mixture is
increased from \( 0^{\circ} \) to \( 100^{\circ} C \) at isobaric
process. Then find given heat of gas mixture
\( \left[\gamma_{H e}=\mathbf{5} / 3, \gamma_{H e}=\mathbf{7} / \mathbf{5}, R=2 c a l / m o l\right. \)
A . 124 call
в. 327 cal
c. 218 cal
D. 475 cal


Nylon is obtained by:
A. treating wood pulp
B. solidifying water
C. mixing coal, air and water
D. mixing chemicals


The type of epithelium seen in the walls
of blood vessels is
A. Squamous epithelium
B. Columnar epithelium
c. ciliated epithelium
D. Cuboidal epithelium
E. Compound epithelium


What will be the absolute value of \( a \), for which point \( P\left(\frac{a}{2}, 2\right) \) is the mid-point of the line segment joining the point
\( Q(-5,4) \) and \( R(-1,0) \)


Solve \( y=\tan ^{-1}\left(\frac{\cos x}{1-\sin x}\right) \)


Longitudinal waves travels faster in
which medium:
A . liquids
B. gases
c. solids
D. vacuum


Distinguish between Diamond and
Graphite.


The value of \( \sin ^{-1}\left(\cos \left(\cos ^{-1}(\cos x)+\right.\right. \)
\( \left.\sin ^{-1}(\sin x)\right), \) where \( x \epsilon\left(\frac{\pi}{2}, \pi\right), \) is
equal to
A \( \cdot \frac{\pi}{2} \)
в. \( -\pi \)
\( c \)
D. \( -\frac{\pi}{2} \)


The difference between \( C . I . \& S . I . \) on
Rs. 700 in 2 years at \( 5 \% \) per annum is :
A . Rs. 10
в. Rs.
c. Rs. 1.75
D. Rs. 2.5


A system consists of a uniformly charged sphere of radius \( \boldsymbol{R} \) and \( \mathbf{a} \) surrounding medium filled by a charge
with the volume density \( \rho=\frac{\alpha}{r}, \) where
\( \alpha \) is a positive constant and \( r \) is the
distance from the centre of the sphere.
Find the charge of the sphere for which the electric field intensity \( \boldsymbol{E} \) outside the
sphere is independent of \( \boldsymbol{R} \)
\( ^{\mathrm{A}} \cdot \frac{\alpha}{2 \varepsilon_{0}} \)
в. \( \frac{2}{\alpha \varepsilon_{0}} \)
\( c \cdot 2 \pi \alpha R^{2} \)
D. None of these


A car starts from rest and is uniformly
accelerated to a speed of \( 30 \mathrm{m} / \mathrm{s} \) in \( 6 \mathrm{s} \)
What is the distance travelled by the
car?
\( A \cdot 5 \) n
B. 30
\( c \cdot 90 \)
D. \( 180 \mathrm{m} \)


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


Haemodialysis is connected with
A . Liver
B. Spleen
c. Stomach
D. Kidney


Uses of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) are:
This question has multiple correct options
A. rocket fuel with hydrazine
B. oxidising agent
C. removing hardness of water
D. turn hair blonde/gold


The quantity of heat required to raise the temperature of unit mass of a given
body through \( 1^{\circ} C \) is known as


Calculate the pressure exerted by a man weighing 85 kg standing on a piece of tile. The dimensions of his feet
are \( 30.2 \mathrm{cm} \times 15 \mathrm{cm} \)
A. \( 20,825 \mathrm{N} / \mathrm{m}^{2} \)
В. \( 2,458 N / m^{2} \)
c. \( 21,754 N / m^{2} \)
D. \( 28,456 N / m^{2} \)


Which of the following is the most basic oxide?
в. \( B i_{2} O_{3} \)
\( \mathrm{c} \cdot \operatorname{Se} \mathrm{O}_{2} \)
D. \( A l_{2} O_{3} \)


Some heat is provided to a body to raise
its temperature by \( 25^{\circ} \mathrm{C} \). What will be
the corresponding rise in temperature of the body as shown on the kelvin scale?


The vectors \( \hat{i}-2 x \hat{j}-3 y \hat{k} \) and \( \hat{i}+ \) \( 3 x \hat{j}+2 y \hat{k} \) are orthogonal to each other.
Then the locus of the point \( (x, y) \) is
A. Hyperbola
B. Ellipse
c. Parabola
D. circle


Electrical wires have a coating of an insulated material. The material
generally used is :
A. sulphur
B. graphite
c. PVC
D. None of the above


Write the principal values of the
following: \( \sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{1}{2}\right) \)


What is the major \( X \) -ray emitted by the sample?
A \( . K_{\alpha} \)
в. \( K_{\beta} \)
c. \( K_{\gamma} \)
D. \( K_{\delta} \)


In a party, 70 guests were to be served tea or coffee after dinner. There were 52
guests who preferred tea while 37 preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?
A . 15
B . 18
c. 19
D. 33


Use synthetic division to find the quotient \( Q \) and remainder \( R \) when
dividing \( f(x)=x^{2}+2 x+3 \) by \( x-i \)
\( i=\sqrt{(}-1) \) the imaginary unit)


Which of the following is an occupational respiratory disorder?
A. Botulism
B. Anthracis
c. Emphysema
D. silicosis


Which of the following choices shows the ground state electron configuration of an ion of a halogen?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 2 d^{10} 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1} \)


In response to increased returns of
venous blood in the heart,
hormone is secreted from
A. ADH from kidney
B. ANF from heart
c. Epinephrine from adrenal medulla
D. Nor-adrenaline from adrenal medulla


A ratio station transmists musical
programme at \( 220 \mathrm{m} \) wavelength and \( 1200 \mathrm{Hz} \) frequency. Calculate the velocity of radio waves.
A. \( 346 \mathrm{km} / \mathrm{sec} \)
B. 264 km/sec
c. \( 442 \mathrm{km} / \mathrm{sec} \)
D. \( 468 \mathrm{km} / \mathrm{sec} \)


Energy of H- atom in the ground state is \( -13.6, \) Hence energy in the second excited state is:
A . -6.8ev
B. - 3.4ev
c. -1.51ev
D. -4.3ev


Intensity of refracted ray of light will be than that of the incident
light. Fill in the blank.
A . Less
B. Greater
c. Both
D. None


What is the essential difference
between the working of a nuclear reactor and that of a fission bomb?


Bombyx mori belongs to which of the following class?
A. Insecta
B. Chilopoda
c. Arachnida
D. crustacea


Boats and aeroplanes are \( \ldots \ldots . . . . . . . . \) so as
to reduce fluid friction.fill in the blank.
A. large
B. broader
c. streamlined
D. bigger


The permanent magnetic moment of
the atoms of a material is not zero. The
material :
A. must be paramagnetic
B. must be diamagnetic
c. must be ferromagnetic
D. may be paramagnetic


Two coaxial solenoids of different radii
carry current I in the same direction. Let \( \vec{F}_{1} \) be the magnetic force on the inner solenoid due to the outer one and \( \vec{F}_{2} \) be
the magnetic force on the outer
solenoid due to the inner one. Then
\( A \cdot \vec{F}_{1}=\vec{F}_{2}=0 \)
B . \( \vec{F}_{1} \) is radially inwards and \( \vec{F}_{2} \) is radially outwards
C \( \cdot \vec{F}_{1} \) is radially inwards \( \vec{F}_{2}=0 \)
D. \( \vec{F}_{1} \) radially outwards and \( \vec{F}_{2}=0 \)


Which of the following is a linear polynomial?
A \( \cdot 4 x^{2}+5 \)
B. \( x+9 \)
c. \( x^{4}+x^{3}+x^{2}+1 \)
D. None of the above


A village with a population of 400 requires 150 I water per head per day. It has a tank measuring \( 20 \mathrm{m} \times 15 \mathrm{m} \times 6 \)
\( \mathrm{m} \) If the tank is full then how many days
will the water last?
A. 20 days
B. 18 days
c. 10 days
D. 30 days


Based upon M.O. theory state reason for the paramagnetic characater of \( \boldsymbol{C} \boldsymbol{N} \)
the diamagnetic character of \( C N \), the
stability of \( C N \) and calculate their respective bond orders.
A \( \cdot_{2} \frac{1}{2}, 2 \)
в. \( _{2 \frac{1}{2}, 3} \)
c. \( _{1 \frac{1}{2}, 3} \)
D. \( _{1} \frac{1}{2}, 2 \)


Identify the order in which the spin only magnetic moment (in BM) increases for the following four ions:
(।) \( \boldsymbol{F} \boldsymbol{e}^{2+}(\|) \boldsymbol{T} \boldsymbol{i}^{2+}(\| \boldsymbol{l}) \boldsymbol{C} \boldsymbol{u}^{2+}(\mid V) \boldsymbol{V}^{2+} \)
A \( . I, I I, I V, I I I \)
в. \( I V, I, I I, I I I \)
с. \( I I I, I V, I, I I \)
D. III, II, IV,


The average degree of freedom per molecule for a gas is \( 6 . \) The gas performs \( 25 \mathrm{J} \) of work when it expands
at constant pressure. The heat absorbed by the gas is
A . 75 J
B. 100
c. 150 J
D. 125 J


Two charge of \( +25 \times 10^{-9} \mathrm{C} \) and
\( -25 \times 10^{-9} \mathrm{C} \) are placed \( 6 \mathrm{m} \) apart.
Find the electric field intensity ratio at point \( 4 \mathrm{m} \) from the centre of the electric dipole
(i) on axial line
(ii) on equatorial line


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\frac{\boldsymbol{x}^{2}}{\left(1+\boldsymbol{x}^{2}\right)}+\frac{\boldsymbol{x}^{2}}{\left(1+\boldsymbol{x}^{2}\right)^{2}}+ \)
\( +\frac{x^{2}}{\left(1+x^{2}\right)^{n}}+\ldots . \) then at \( x=0 \)
A \( \cdot f(x) \) has no limit
B . \( f(x) \) is discontinuous
C . \( f(x) \) is continuous but not differentiable
D \cdot \( f(x) \) is differentiable


Biogas contains \( \% \) methane.
A. 75-85\%
в. 50-75\%
c. \( 80-90 \% \)
D. 35-55\%


Zinc, not copper, is used for the recovery
of metallic silver from the complex
\( \left[A g(C N)_{2}\right]^{-}, \) explain
A. zinc is more reducing and cheaper than copper.
B. Zinc is less reducing and cheaper than copper.
c. zinc is more reducing and higher than copper.
D. None of these


Explain the terms with suitable
examples:
(i) Alcosol
(ii) Aerosol
(iii) Hydrosol


A galvanometer in a circuit:
A. measures current
B. measures voltage
C. measures emf
D. indicates flow of current


n the circuit shown in the figure, the
ammeter reading is:
\( A \cdot 0.8 A \)
B. 1.2 A
\( c \cdot 2 A \)
D. \( 0.4 \mathrm{A} \)


Neutrons are present in all atoms except?
A . не
B.
\( c \cdot H \)
D. Ne


In the figure, if linel \( \| \) m. What is the
value of \( x \)


An astronaut in outer space will observe
sky as
A. White
B. Black
c. Blue
D. Red


A student has obtained an image of a
well-illuminated distant object on
a screen to determine the focal length,
\( F_{1} \) of the given spherical mirror. The teacher then gave him another
mirror of focal length, \( F_{2} \) and asked
him to obtain a focused image of the
same object on the same screen. The student found that in order to focus
the same object using the second mirror, he has to move the
mirror away from the screen. From this observation it may be concluded that both the spherical mirrors given to the student were (select the correct
option)
A. Concave and \( F_{1}<F_{2} \)
B. Concave and \( F_{1}>F_{2} \)
C. Convex and \( F_{1}<F_{2} \)
D. Convex and \( F_{1}>F_{2} \)


Which one of the following is used in the preparation of cellulose nitrate?
A. \( K N O_{3} \)
в. \( H N O_{3} \)
c. \( K N O_{2} \)
D. \( H N O_{2} \)


\( 2 P b S+3 O_{2} \longrightarrow A+2 S O_{2} \)
The name of \( A \) is :
A. litharge
B. galena
c. sesquioxide
D. none of these


Choose the correct answer from the
alternatives given
Most commonly used bleaching agent
is
A. alcohol
B. carbon dioxide
c. chlorine
D. sodium chloride


A piece of paper appears to be attracted to a charged ebonite rod, even before they touch (see fig.). The charge at A is :
A. positive
B. negative
c. no charge
D. may be positive or negative


In a photo-diode,
A. photocurrent is proportional to incident light intensity
B. photocurrent is inversely proportional to incident light intensity
C. photocurrent is independent of the incident light intensity
D. incident light intensity is proportional to the photocurrent


If the initial speed of the cars is \( x \mathrm{m} / \mathrm{s} \)
find \( 2 x \)


What is Microscope? Describe the simple microscope.


Arrange the following compounds in increasing order of boiling points:
\( \mathrm{I}: C H_{3} C l \quad \|: C H_{2} C l_{2} \)
\( \left\|: \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3} \quad \quad\right\| \boldsymbol{V}: \boldsymbol{C} \boldsymbol{l}_{4} \)
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I I<I V<I<I I I \)
D. \( I V<I I<I<I I I \)


Given that \( \vec{a} \cdot \vec{b}=0 \) and \( \vec{a} \times \vec{b}=\overrightarrow{0} \)
What can you conclude about the vectors \( \vec{a} \) and \( \vec{b} ? \)


When a metal wire is stretched by a load, the fractional change in its volume \( \Delta V / V \) is proportional to?
\( ^{\mathrm{A}} \cdot-\frac{\Delta l}{l} \)
\( ^{\mathrm{B}}\left(\frac{\Delta l}{l}\right)^{2} \)
c. \( \sqrt{\Delta l / l} \)
D. None of these


The pendulum of a clock is made of brass. If the clock keeps correct time at \( 20^{\circ} \mathrm{C} \). Calculate how many seconds per
day will it loose at \( 35^{\circ} \mathrm{C} \) ( \( \alpha \) for brass = \( \left.2 \times 10^{-5 o} C\right) \)
A . 12.96
B. 1.29 s
c. \( 129.6 \mathrm{s} \)
D. 8.64


Particle is moving rectilinearly at \( t=0 \) such that the velocity changes with time as \( v=t^{2}-t ; \) find interval of time
where the particle retards.


Solve:
\( \int \frac{4 x+6}{2 x^{2}+5 x+3} d x \)


A uniform bar of length \( 6 a \) and mass \( 8 m \) lies on a smooth horizontal table
Two point masses \( m \) and \( 2 m \) moving in opposite direction in the same
horizontal plane with speed \( 2 v \) and \( v \)
respectively. strike the bar and stick to
the bar after the collision. Calculate:
The angular velocity of the centre of mass after collision.


Find the remainder when the polynomial
\( 4 y^{3}-3 y^{2}-5 y+1 \) is divided by \( 2 y+3 \)


The number of stationary points of \( \mathbf{f}(\mathbf{x})=\cos \mathbf{x} \) in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) are
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


How do we hear: Match the parts of a
human ear with their functions:
Match the columns:


A wire as a parabola \( y=4 x^{2} \) is located
in a uniform magnetic field of inductance B perpendicular to the XY plane. At t=0 a connection starts
translation wise from the parabola apex
with constant acceleration \( \alpha \). The
induced emf in the loop, thus formed, as a function of y is:
A \( e=\sqrt{2 \alpha} \cdot B y \)
\( y \)
в. \( e=B y \sqrt{\frac{\alpha}{2}} \)
c. \( e=\frac{B y \sqrt{a}}{2 \sqrt{2}} \)
D. \( e=\frac{B y \sqrt{\alpha}}{4} \)


If \( z_{1} \) and \( z_{2} \) two complex numbers satisfying the equation \( \left|\frac{z_{1}+i z_{2}}{z_{1} i z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}} \) is a
A . purely real
B. of unit modulus
c. purely imaginary
D. none of these


Two cubes, one silver and one iron, have the same mass and temperature. A quantity Q of heat is removed from each cube which of the following properties do not causes the final temperature of the cubes to be different?
This question has multiple correct options
A. Density
B. Specific heat capacity
c. volume
D. Mass


Assertion
Propyne is more reactive than propene
towards electrophilic addition of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
Reason

Propyne has greator electron density avaliable for electrophile due to two pibonds, therefore more electrophilic
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following has pseudo inert gas configuration?
A . \( N a^{\text {t }} \)
в. \( C u^{+} \)
\( c \cdot K^{+} \)
\( D \cdot S^{2} \)


\( 10 \mathrm{mt} \) of hydrogen combine with \( 5 \mathrm{mL} \) of oxygen to yield water. When \( 200 \mathrm{mL} \) of
hydrogen at NTP are passed over heated Cu0, the Cu0 loses 0.144 g of its mass. Do these mulls correspond to the law of constant proportions?


Acids in the rain react with the calcium
compounds in the stones to create:
A. sulphuric acid
B. calcium hydroxide
c. gypsum
D. All of the above


Find the derivative of \( \frac{x}{(x-1)} \)


If \( P=\{a, b, c\} \) and \( Q=\{b, c, d\} ; \) find number of elements in \( (\boldsymbol{P} \cap \boldsymbol{Q}) \times \boldsymbol{P} \)


From the figure, identify a point in the
exterior.


Formation of \( \boldsymbol{O}^{-} \) is exothermic,
whereas formation of \( \boldsymbol{O}^{2-} \) is
endothermic. Explain.


Which of the following pairs of elements cannot form an alloy?
A. zn, Cu
в. Fe, Hg
c. Fe,


The chemical name of vitamin \( B_{12} \) is:
A. Calciferol
B. Tocopherol
c. Pyridoxine
D. Cyanocobalamine


Name the compound.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)


Antimicrobials are effective on which
kind of organisms?
A. Bacteria
B. Viruses
c. Fungi
D. all of these


The isothermal elasticity of a medium
is \( E_{i} \) and the adiabatic elasticity is \( E_{a} \)
The velocity of the sound in the medium is proportional to:
A \( \cdot \sqrt{E_{i}} \)
в. \( E_{a} \)
\( \mathrm{c} \cdot \sqrt{E_{a}} \)
D. \( E_{i} \)


Atomic radius goes on decreasing while going from left to right in a period


If the net external force on a body is zero, its acceleration:
A. must be equal to zero
B. may be equal to zero
c. must be non-zero
D. must be equal to \( g \)


The total number of ways in which 5
balls of different colours can be
distributed among 3 persons so that each person gets at least on ball is


Total internal reflection occurs when
\( A \cdot i=0 \)
B. i>ic
\( c . \) i=ic
D. All


reaction is (are):
Consider the following reaction
This question has multiple correct options
\( \mathbf{A} \)
(a) Under thermodynamic control is
formed as major product,
\( B \)
(b) Under kinetic condition is Formed as
major product
\( \mathbf{C} \)
formed under thermodynamic
D. Under thermodynamic control a pair of diastereomers are formed


The graph of the equation \( y^{2}+z^{2}=0 \)
in three dimensional space is
A. x- axis
B. y- axis
c. z- axis
D. yz-plane


\( \frac{1-\sin A}{\cos A} \) is equal to
\( A \cdot \frac{\cos A}{1+\sin A} \)
B. \( \frac{\sin A}{1-\cos A} \)
c. \( \frac{\tan A}{1+\tan A} \)
D. \( \frac{\tan A}{1+\cos A} \)


\( \sqrt{1+\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}=\left(2+\frac{d y}{d x}\right)^{1 / 3} \)
Find it's order and degree.
A .2,3
в. 2,9
\( c \cdot 2,6 \)
D. 2,2


The bond of \( H g-C l \) is more ionic in
\( H g C l_{2} \) than that in \( H g_{2} C l_{2} \)
A. True
B. False


The method of measuring distance to stars beyond 100 light-years is
A. Capheid variable stars
B. Heid variable stars
c. Lowheid variable stars
D. None


A red colour in air has wavelength 760
nm when light passes through water of refractive index \( \left(n=\frac{4}{3}\right), \) wavelength
becomes 570 nm.(wavelength of yellow colour in air is 570 nm.Then colour of
red light in water is
A. Red
B. Green
c. Yellow
D. Blue


The mean deviation of the numbers 1,2
3,4,5 is
A. 0
B. 1.2
\( c \cdot 2 \)
D. 1.4


Find the mean derivation from the mean
for the following data
\[
\begin{array}{ccccc}
x_{1} & 2 & 5 & 6 & 8 \\
y_{1} & 2 & 8 & 10 & 7
\end{array}
\]


Tangents are drawn from (4,4) to the \( \operatorname{circle} x^{2}+y^{2}-2 x-2 y-7=0 \)
meet the circle at \( A \) and \( B \). The length
of the chord \( A B \) is
A \( \cdot 2 \sqrt{3} \)
3
B. \( 3 \sqrt{2} \)
c. \( 2 \sqrt{6} \)
D. \( 6 \sqrt{2} \)


If the position vectors of \( A, B, C, D \) are \( \vec{a}, \vec{b} \cdot 2 \vec{a}+3 \vec{b}, \vec{a}-2 \vec{b} \) respectively, then
\( \overrightarrow{\boldsymbol{A C}}, \overrightarrow{\boldsymbol{D B}}, \overrightarrow{\boldsymbol{B A}}, \overrightarrow{\boldsymbol{D A}} \) are?
A \( \cdot \vec{a}+3 \vec{b}, 3 \vec{b}-\vec{a}, \vec{a}-\vec{b}, 2 \vec{b} \vec{b} \)
B . \( 2 \vec{b}, \vec{b}-2 \vec{a}, 3 \vec{b}+\vec{a}, \vec{b}-\vec{a} \)
c. \( \vec{a}-3 \vec{b}, 3 \vec{b}-\vec{a}, \vec{a}+\vec{b}, 2 \vec{b} \)
D. \( -2 \vec{b}, \vec{b}-2 \vec{a}, 3 \vec{b}-\vec{a}, \vec{b}-\vec{a} \)


\( N H_{3}+O_{2} \longrightarrow(B) \) (brown fumes)
Identify the compound B.
A . \( N O \)
в. \( N O_{2} \)
\( c \cdot N O_{3} \)
D. \( H N O_{2} \)


For which of the following processes is the relation \( d Q=d U \) true ?
A. isobaric
B. isochoric
c. isothermal
D. adiabatic


Let \( f(x) \) be a continuous function
whose range is \( [2,6.5] . \) If \( h(x)= \)
\( \left[\frac{\cos x+f(x)}{\lambda}\right], \lambda \in N, \) be continuous
where [.] denotes the greatest integer function, then the least value of \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
\( c \cdot 8 \)
D. None of these


Which cell of the following will measure standard electrode potential of copper electrode?
A \( \cdot P t_{(s)}\left|H_{2}(g, 0.1 b a r)\right| H^{+}(a q, 1 M) \| C u^{2+}(a q, 1 M) \mid C u \)
B . \( P t_{(s)}\left|H_{2}(g, 1 b a r)\right| H^{+}(a q, 1 M)|| C u^{2+}(a q, 2 M) \mid C u \)
C \( \cdot P t_{(s)}\left|H_{2}(g, 1 b a r)\right| H^{+}(a q, 1 M)|| C u^{2+}(a q, 1 M) \mid C u \)
D. \( P t_{(s)}\left|H_{2}(g, 1 b a r)\right| H^{+}(a q, 0.1 M)|| C u^{2+}(a q, 1 M) \mid C u \)


For what values of \( k, \) the roots of the
quadratic equation \( (\boldsymbol{k}+\mathbf{4}) \boldsymbol{x}^{2}+(\boldsymbol{k}+ \)
1) \( x+1=0 \) are equal?


If \( A \) is a \( 3 X 3 \) non-singular matrix such
that \( \boldsymbol{A} \boldsymbol{A}^{\prime}=\boldsymbol{A}^{\prime} \boldsymbol{A} \) and \( \boldsymbol{B}=\boldsymbol{A}^{-1} \boldsymbol{A}^{\prime}, \) then
\( B B^{\prime} \) equals to
\( \mathbf{A} \cdot 1+B \)
B. \( I \)
c. \( B^{-1} \)
D. \( \left(B^{-1}\right)^{\prime} \)


A magnesium ion has a net positive charge while the magnesium atom has
\( A \)
+2
B. +1
c. no charge
D. -


The dimension of mass is zero in which
of the following physical quantities?
A. Gravitational potential
B. Latent heat
c. specific heat capcity
D. All of the above


Evaluate: \( \int \frac{(x(\pi+49))^{15 / 7}}{\pi^{2}\left(x^{\pi}+7\right)} d x \)


Center of mass of 3 particle \( 10 k g, 20 k g \) and \( 30 k g \) is at \( (0,0,0,) . \) Where shoud a
particle of mass \( 40 k g \) be placed so that the combination centre of mass will be at
(3,3,3)
A. (0,0,0)
)
в. (7.5,7.5,7.5)
c. (1,2,3)
D. (4,4,4)


Give analytical treatment of YDSE
interference bands and hence obtain
the expression for fringe width.


What weights of \( P_{4} O_{6} \) and \( P_{4} O_{10} \) will be produced by the combustion of 31 g of
\( P_{4} \) with \( 32 g \) of oxygen leaving no \( P_{4} \) and
\( O_{2} ? \)
A. 2.75 g, 219.5 \( g \)
B. 27.5 \( g \), 35.5 \( g \)
c. 55 g, \( 71 g \)
D. 17.5 \( g \), 190.5 \( g \)


Anthers represent
A. Male gametophytes
B. Male sporophylls
C . Spermatogonia
D. Female gametophytes


Assertion
Bacterial cell wall is characterised by
having mucopolysaccharidies.
Reason
Acetylmuramic acid is an example of mucopolysaccharide.
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.


Parathyroid hormone (PTH):
A. stimulates the release of calcium by the kidneys
B. stops the absorption of calcium from the intestine
C. causes blood calcium level to decrease
D. causes blood phosphate level to decrease


The Earth's crust plates moves
brushing past each other or collide. It
causes:
A . landslides
B. volcanic eruption
c. earthquake
D. none of the above


Deoxygenated blood
A. Flows to lungs from the left side of the heart.
B. Flows to lungs from the right side of the heart.
C. Flows to right side of the heart from the lungs.
D. Flows to left side of the heart from the.lungs.


The cost price of 12 candles is equal to
the selling price of 15 candles. Find the
loss percent?


A homozygous tall plant (T) bearing red
coloured (R) flowers is crossed with a
homozygous dwarf
(t) plant bearing white (r) flowers.
What is the phenotypic ratio obtained in
\( F_{2} \) generation?


A uniform ladder of mass \( 10 g \) leans against a smooth vertical wall making
an angle of \( 53^{\circ} \) with it. the other end rests on a rough horizontal floor. Find
the normal force and the frictionless
force that the floor exerts on the ladder.


sleep. He classifies sleep activity in four stages: 1,2,3 and \( 4 . \) Stage 3 is the only stage considered to be deep sleep. Ajay goes to clinic for sleeping brainwashes analyzed. Doctor
monitored the person's brainwashes in \( 15- \) minute intervals, for 8 continuous
hours, and categorized them into one of the four stages. The graph above shows this study. fone \( 15- \) minute time period is chosen at random, then the probability that the patient was in deep sleep during that time is \( \frac{a}{b}, \) where \( a, b \) are co-primes. What is the value of \( a+b ? \)


The molecular formula of sucrose is
A. \( C_{10} H_{22} O_{11} \)
B. \( C_{12} H_{22} O_{11} \)
c. \( C_{13} H_{22} O_{11} \)
D. \( C_{12} H_{22} O_{10} \)


Classify the following reaction in one of the reaction type.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r}+\boldsymbol{H O}^{-} \rightarrow \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{B r} \)


State True or False.
The presence of double bonds in rubber
molecules influence their structure and
reactivity
A. True
B. False


Which type of an image is formed by a plane mirror?
A . Real \& inverted
B. Real \& erect
c. virtual \& erect
D. Virtual \& inverted


A stone weight \( 100 \mathrm{N} \) on the surface of the earth. The ratio of its weight at a height of half the radius of the earth to
its weight at a depth of half the radius of the earth will be approximately
A. 3.6
B. 2.2
\( c \cdot 1.8 \)
D. None of these


If \( \vec{A} \times \vec{B}=\vec{B} \times \vec{A}, \) then the angle between \( \vec{A} \) and \( \vec{B} \) is
A . \( \pi \)
в.
\( c \cdot \frac{\pi}{2} \)
D.


Balance the following equations.
(i) \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{K} \boldsymbol{C l}+ \)
\( M n C l_{2}+H_{2} O+C l_{2} \)
(ii) \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{N} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)


Assertion
Air is a good conductor of heat
Reason
It's molecules are in close contact with
each other
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The electric field for \( \boldsymbol{R}_{1}<\boldsymbol{r}<\boldsymbol{R}_{2} \) is
\( \operatorname{given} \operatorname{by} \boldsymbol{E}=\frac{Q}{\boldsymbol{X} \boldsymbol{\pi} \varepsilon_{0} r^{2}}\left[\frac{r^{3}-\boldsymbol{R}_{1}^{3}}{R_{2}^{3}-\boldsymbol{R}_{1}^{3}}\right] . \) Find \( \mathbf{X} ? \)


The radius of the circle \( x^{2}+y^{2}+x+ \)
\( c=0 \) passing through the origin is
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
c. 1
D. 2


Family \( y=A x+A^{4} \) of curves is
represented by the differential equation of degree.
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
D.


How much work they do in just holding it ?
A. 250 J
B. 2500 J
c. 0 J
D. 625 J


Complete combustion of alkene require sufficient :
A. oxygen
B. hydrogen
c. nitrogen
D. sulphur


The product(s) formed when \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) reacts with disodium hydrogen
phosphate is:
A \( \cdot P_{2} O_{5} \cdot N a_{3} P O_{4} \)
в. \( N a_{2} H P O_{4} . H_{2} O_{2} \)
c. \( \operatorname{NaH}_{2} P O_{4}, H_{2} O \)
D. \( N a_{2} H P O_{4} \cdot H_{2} O \)


Endosperm in Gymnosperm is
A. Haploid
B. Diploid
c. Triploid
D. All of the above


A glass sphere of radius \( 15 \mathrm{cm} \) has a
small bubble \( 6 \mathrm{cm} \) from it centre. The
bubble is viewed along a diameter of
the sphere from the side o which it lies. How far from the surface will it appear
to be if the refractive index of glass is
\( \mathbf{1 . 5} ? \)


Minerals having Fe is :
A. Magnetite
B. Pyrites
c. spathic iron
D. All of these


An inclined plane making an angle \( 30^{\circ} \)
with the horizontal is placed in a uniform horizontal electric field of
\( 100 V m^{-1} . \) A particle of mass \( 1 k g \) and
charge \( 0.01 C \) is allowed to slide down
from rest from the top of the inclined plane. If the coefficient of friction is 0.2
the particle reaches the bottom of the
inclined plane in 1 second. Then the length of the inclined plane is (Acceleration due to gravity \( =10 m s^{-2} \) )
A \( .1 .150 m \)
в. \( 1.323 m \)
c. \( 1.151 m \)
D. \( 1.172 m \)


n Fig. 0 is the centre of the circle such
that \( \angle A O C=130^{\circ}, \) then \( \angle A B C= \)
A \( \cdot 130 \)
B. 115
\( c \cdot 65 \)
D. 165


A gas undergoes change in its state
from state \( A \) to state \( B \), via three
different paths as shown in the figure.
Select the correct alternative(s)
This question has multiple correct options
A. Change in internal energy in all the three paths is
equa
B. In all the three paths heat is absorbed by the gas
C. Heat absorbed / released by the gas is maximum in path (1)
D. Temperature of the gas first increases and then decreases continuously in path (1)


The \( 3^{\prime}-5^{\prime} \) phosphodiester linkages inside a polynucleotide chain serve to join
A. One nitrogenous base with pentose sugar
B. One DNA strand with the other DNA strand
c. one nucleoside with another nucleoside
D. One nucleotide with another nucleotide


For making an electromagnet the best material to be used is
A. stainless steel
B. silver
c. soft iron
D. nickel


If elements with principal quantum
number \( n>4 \) were not allowed in
nature, the number of possible elements would have been
A . 32
B. 60
c. 18
\( D \)


\( \boldsymbol{O H} \quad \boldsymbol{H}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{H} \quad \boldsymbol{C}_{\boldsymbol{H}}=\underset{\boldsymbol{H}}{\boldsymbol{C}} \)
(1)
\( (\mathbf{3}) \)
The structures of four molecules are
shown.

Which molecules belong to the same homologous series?
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 4
D. 3 and 4


Products formed are:
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{B} \boldsymbol{H}_{4}+\boldsymbol{I}_{2} \stackrel{\text {Polyether}}{\longrightarrow} \)
A. \( H I, N a l \) and \( H_{2} \)
в. \( B_{2} H_{6}, \) Nal and \( H I \)
c. \( B_{2} H_{6}, \) Nal and \( H_{2} \)
D. \( H_{3} B O_{3}+H_{2} \)


The speed of the earth is highest when
it is
A. Farthest from the sun
B. Nearest to the sun
c. Passing through the month of September
D. None of the above


Solve \( \int_{2}^{-13} \frac{d x}{\sqrt[5]{(3-x)^{4}}} \)
A \( \cdot-5(\sqrt[5]{16}-1) \)
B \( \cdot 5(\sqrt[3]{16}-1) \)
\( \mathbf{c} \cdot-5(\sqrt[5]{16}+1) \)
D. None of these


Low levels of adrenal cortex hormones
result in :
A. Addison disease
B. Cushing syndrome
c. tetany
D. goiter


The number of degrees of freedom for each atom of a monoatomic gas is :
\( A \cdot 3 \)
B. 5
\( c \cdot 6 \)
\( D \)


What is the role of auxin?
A. Prevents abscission of leaves and fruits
B. Promotes abscission of leaves and fruits
c. Promotes stomatal closure
D. Promotes dormancy


A uniform solid cylinder of mass \( 5 k g \)
and radius \( 30 \mathrm{cm}, \) and free to rotate about its axis, receives an angular
impulse of \( 3 k g m^{2} s^{-1} \) initially followed
by a similar impulse after every 4 s.
What is the angular speed of the cylinder \( 30 s \) after the initial impulse?
The cylinder is at rest initially.
A. 100
в. 200
c. 300
D. 500


The number of different wavelengths that is possible to be observed in the
spectrum from a hydrogen sample if the
atoms are excited to third excited state
is:
A . 3
B. 4
c. 5
D. 6


Find the value of unknown \( x \) in the
following diagram.


Order is placed between
A. Kingdom and Phyla
B. Kingdom and Class
C . Class and Family
D. Genus and Species


The current flowing through the resistor
in a series LCR a.c. circuit, is \( \boldsymbol{I}=\varepsilon / \boldsymbol{R} \)
Now the inductor and capacitor are
connected in parallel and joined in series with the resistor as shown in
figure. The current in the circuit is now.
(Symbols have their usual meaning)
A . equal to I
B. more than I
c. less than 1
D. zero


Consider the charge configuration and
a spherical Gaussian surface as shown
in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be?
\( \mathbf{A} \cdot \) Due to \( q_{2} \)
B. Only due to the positive charges
c. Due to all the charges
D. Due to \( +q_{1} \) and \( -q \)


1g of ice at \( 0^{0} \mathrm{C} \) is mixed \( 1 \mathrm{g} \) of steam at
\( 100^{0} \mathrm{C} . \) The mass of water formed is
A. \( 0.33 \mathrm{g} \)
в. 18
c. 0.1338
D. \( 13.3 \mathrm{g} \)


Assertion
Anhydrous sulphuric acid has very high viscosity.
Reason
\( H- \) bonding makes it viscous.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The equilibrium constant for the
reaction: \( 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons 2 S O_{3(g)} \) is
5. If the equilibrium constant mixture
contains equal moles of \( S O_{3} \) and \( S O_{2} \)
the equilibrium partial pressure of \( \boldsymbol{O}_{2} \) gas is:
A. 0.2 atm
B. 2 atm
c. 0.02 atm
D. 0.04 atm


The heat of formation of \( C O_{2} \) is
\( -96 k c a l . \) The amount of carbon which
on burning will evolve 1000 kcal is:
A . 12.63 g
в. 17.95 g
\( c \cdot 126.38 \)
D. 179.5 \( g \)


Factorise:
\( 4 x^{2}+9 y^{2}+25 z^{2}+12 x y+30 y z+ \)
\( 20 z x \)


You must have seen tarnished copper
vessels being cleaned with lemon or
tamarind juice. Explain why these sour substances are effective in cleaning the
vessels.


Degree of \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\mathbf{3} \boldsymbol{y}=\boldsymbol{x}^{2} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 2
\( c .3 \)
D.


Caprolactam is used for the manufacture of:
A. terylene
B. nylon - 6,6
c. nylon - 6
D. teflon


\( \operatorname{Let} P \equiv(a, b), Q \equiv(c, d) \) and \( 0<a<b< \)
\( \mathbf{c}<\mathrm{d} \boldsymbol{L} \equiv(\boldsymbol{a}, \mathbf{0}), \boldsymbol{M} \equiv(\boldsymbol{c}, \mathbf{0}), \mathbf{R} \) lies on \( \mathbf{x} \)
axis such that PR + RQ is minimum
then \( R \) divides \( L M \)
A. internally in the ratio a :
B. internally in the ratio b:
c. internally in the ratio b: \( d \)
D. internally in the ratio c : d


Growth curve indicates
A. A growth parameter at various intervals
B. Absolute growth
C. Absolute increase
D. None of the above


Lymph plays an important role in protecting immune system of the body Justify this statement.


What is not true regarding free radical
polymerisation of propene?
A. Without proper control, atactic polypropylene is formed
B. Use of Ziegler-Natta catalyst results in isotactic polypropylene
C. During polymerisation, a linear unbranched, crystalline polymer is usually obtained
D. During polymerisation, a secondary free radical is produced in every step


Two independent monohybrid crosses were carried out involving a tall pea plant with a dwarf pea plant. In the first cross, the offspring population had equal number of tall and dwarf plants, whereas in the second cross it was
different. Work out the crosses, and explain giving reasons for the difference in the offspring populations.


The radius of a soap bubble is r. The surface tension of soap solution is \( \mathrm{S} \)
Keeping temperature constant, the radius of the soap bubble is
doubled, the energy necessary for this will be :
A \( \cdot 24 \pi r^{2} S \)
B. \( 8 \pi r^{2} S \)
\( \mathrm{c} \cdot 12 \pi r^{2} S \)
D. \( 16 \pi r^{2} S \)


Evaluate the following definate integral:
\( \int_{0}^{2} 3 x+2 d x \)


Magnetic monopoles are arranged as shown. The resultant magnetic
induction at point ' \( q^{\prime} \) is:
A \( \cdot \frac{\mu_{0}}{4 \pi} \frac{m}{r^{2}} \frac{3}{2} \)
В. \( \frac{\mu_{0}}{4 \pi} \frac{m}{r^{2}} \frac{1}{4} \)
\( \mathbf{C} \cdot \frac{\mu_{0}}{4 \pi} \frac{m}{r^{2}} \frac{3}{4} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{m^{2}}{r^{2}} \frac{3}{8} \)


If \( a_{1}, a_{2}, a_{3} \dots \) are in A.P.with common
difference 'd',then
\( \tan \left\{\tan ^{-1}\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right)+\right. \)
is equal to
A \( \cdot \frac{(n-1) d}{a_{1}+a_{n}} \)
B \( \cdot \frac{(n-1) d}{1+a a_{n}} \)
c. \( \frac{(n-1) d}{1+a a a_{n}} \)
D. \( \frac{a_{n}-a_{1}}{a_{n}+a_{1}} \)


Find the current flows through a copper wire of length \( 0.2 \mathrm{m}, \) area of crosssection \( 1 m m^{2}, \) when connected to a
battery of \( 4 \mathrm{V} \). Given that electron
mobility is \( 4.5 \times 10^{-6} m^{2} s^{-1} \) and
charge on an electron is \( 1.6 \times 10^{-19} C \)
The number density of electron in copper wire is \( 8.5 \times 10^{2} 8 m^{3} \)


\( A B C D \) is a rhombus such that
\( \angle A D B=50^{\circ}, \) then what is the
measure of \( \angle A C B ? \)


A ball of mass \( 100 \mathrm{g} \) is moving with a velocity of \( 10 \mathrm{m} s^{-1} . \) The force of the
blow by the bat acts for 0.01 seconds. What is the force exerted on the ball by the bat if the ball retraces its path with same speed?
A. \( 100 \mathrm{N} \)
B. 200 N
c. 300 N
D. 400 N


Determine the value of \( x \) in the figure
given below
A . \( 40^{\circ} \)
B. 75
\( \mathbf{c} \cdot 65^{\circ} \)
D. 105


The basis for measuring thermodynamic property of temperature is given by
A. zeroth law of Thermodynamics
B. First law of Thermodynamics
c. second law of Thermodynamics
D. Third law of Thermodynamics


Choose the correct answer.
Sound can travel through
A. Gases only
B. Solids only
c. Liquids only
D. solids, liquids and gases


On strong heating, 3.64 g of a silver salt of an organic dibasic acid yield 2.16 g of silver. If the weight percentage of carbon in it is 8 times the weight
percentage of hydrogen and one-half the weight percentage of oxygen, then the molecular formula of the acid is:
[Atomic weight of \( \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8}] \)
A \( \cdot C_{4} H_{6} O_{4} \)
в. \( C_{4} H_{6} O_{6} \)
\( \mathrm{c} \cdot C_{2} H_{6} \mathrm{O}_{2} \)
D. \( C_{5} H_{10} O_{5} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{1} \\ \mathbf{0} & -\mathbf{2} & \mathbf{4}\end{array}\right], \boldsymbol{I}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right] \)
and
\( \boldsymbol{A}^{-1}=\frac{1}{\boldsymbol{6}}\left(\boldsymbol{A}^{2}+\boldsymbol{\alpha} \boldsymbol{A}+\boldsymbol{\beta} \boldsymbol{I}\right), \) find \( \boldsymbol{\beta} / \mathbf{1 1} \)


An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm
and a temperature of \( 27^{\circ} \mathrm{C} \). After some
oxygen is withdrawn from the cylinder
the gauge pressure drops to 11 atm and
its temperature drops to \( 17^{\circ} \mathrm{C} \)

Estimate the mass of oxygen taken out of the cylinder. \( \left(R=8.31 J m o l^{-1} K^{-1}, \) molecular \right.
mass of \( \boldsymbol{O}_{2}=\boldsymbol{3} \boldsymbol{2} \boldsymbol{u} \)


Electrons in.......... shell are called valence
electrons.


Which of following was not explained by Rutherford?
A. Arrangement of electrons around the nucleus
B. Arrangement of protons
c. Arrangement of nuetrons
D. None of the above


Solubility product of \( B a S O_{4} \) in water
\( 57^{\circ} \mathrm{C} \) is:
A . \( 5 \times 10^{-19} \)
В. \( 3.125 \times 10^{-13} \)
\( \mathrm{c} .5 .625 \times 10^{-13} \)
D. \( 2.25 \times 10^{-12} \)


Alkali metals (M) dissolve in liquid
\( N H_{3} \) to give:
A \( \cdot M N H_{2} \)
в. \( M H \)
C \( \cdot\left[M\left(N H_{3}\right)_{x}\right]^{+}+\left[e\left(N H_{3}\right)_{y}\right] \)
D. \( M_{3} N \)


\( P Q \) is an infinite current carrying
conductor. \( A B \) and \( C D \) are smooth
conducting rods on which a conductor
\( E F \) moves with constant velocity \( v \) as
shown. The force needed to maintain
constant speed to \( \boldsymbol{E} \boldsymbol{F} \) is
\( ^{\mathbf{A}} \cdot \frac{1}{v R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(b)}{(a)}\right]^{2} \)
\( ^{\mathrm{B}} \cdot \frac{v}{R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(a)}{(b)}\right]^{2} \)
\( ^{\mathrm{c}} \cdot \frac{v}{R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(b)}{(a)}\right]^{2} \)
D. None of these


Circulatory system also performs the function of homeostasis.
A. True
B. False


Two blocks of masses 400 g and 200 g are connected through a light string going over a pulley which is free to rotate about is axis. The pulley has a moment of inertia \( 1.6 \times 10^{-4} k g-m^{2} \)
and a radius \( 2.0 \mathrm{cm} . \) Find the speed of the blocks at this instant.


If the length of second's pendulum is increased by \( 2 \% \), how many seconds it will lose per day.
A . 3927s
B. 3727s
c. 3427 s
D. 864s


Which of the following bacteria is utilized in gobar gas plant?
A. Methanogens
B. Nitrifying bacteria
c. Ammonifying bacteria
D. Denitrifying bacteria


What is the functional groups in the following molecules?
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)


Give an example of the motion of a body moving with a constant speed, but with a variable velocity. Draw a diagram to represent such a motion.


An area of soil is thoroughly wefted and allowed to drain until capillary movement of water stopped. The water contents of the soil will give an estimate of its
A. Capillary water
B. Storage water
c. Field capacity
D. Gravitational water


In
Fig., line \( n \) is a transversal to lines \( l \)
and
\( \boldsymbol{m} . \) Identify the following:
Angle alternate to \( \angle P Q R \) and angle
corresponding to angles \( \angle R Q F \) and
angle alternate to \( \angle P Q E \) in Fig.


Three metal rods made of copper,
aluminium and brass, each \( 20 \mathrm{cm} \) long
and \( 4 \mathrm{cm} \) in diameter, are maintained
at 100 and \( 0^{\circ} \mathrm{C} \) respectively. Assume
that the thermal conductivity of copper
is twice that of aluminium and four
times that of brass. The approximately
equilibrium temperatures of the copper
-aluminium and aluminium - brass
junctions are respectively.
A \( \cdot 68^{\circ} \mathrm{C} \) and \( 75^{\circ} \mathrm{C} \)
B. \( 75^{\circ} \mathrm{C} \) and \( 68^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 57^{\circ} \mathrm{C} \) and \( 86^{\circ} \mathrm{C} \)
D. \( 86^{\circ} \mathrm{C} \) and \( 57^{\circ} \mathrm{C} \)


Aqueous solution of ammonia consists of :
A \( \cdot H^{+} \) only
B. \( H^{-} \) only
\( \mathbf{c} \cdot N H_{4}^{+} \) only
D. \( N H_{4}^{+} \) and \( O H^{-} \)


A bullet traveling with a velocity of \( 16 m / s \) penetrates a tree trunk and
comes to rest in 0.4 m. Find the time
taken during the retardation.


Evaluate: \( \int_{0}^{\frac{\pi}{4}}\left(\tan ^{4} x+\tan ^{2} x\right) d x \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( 1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 4 \)


Concentrated \( H N O_{3} \) reacts with iodine
to give :
A . \( H I \)
в. \( H O I \)
\( \mathbf{c} \cdot H O I O_{2} \)
D. НОПО\( _{3} \)


The vapour pressure of a solution containing 2 g of an electrolyte BA in 100 g water which dissociates in one
\( B^{+} \) and one \( A^{-} \) ion in water is \( 751 \mathrm{mm} \)
at \( 100^{\circ} \mathrm{C} . \) Percentage degree of
ionisation of BA if its molar mass is 56
g \( m o l^{-1} \) (write answer after dividing
degree of dissociation by 80 to the nearest integer) is


Which one of the following statements
is correct?
A. Th Standard deviation for a given distribution is the square of the variance.
B. The standard deviation for a given distribution is the square root of the variance.
C. The standard deviation for a given distribution is equal to the variance.
D. The standard deviation for a given distribution is half of the variance.


Identify the correct lewis symbol from the following:
\( A \)
\( \cdot C \cdot \)
в. \( \cdot \dot{O} \)
c.
\[
B
\]
D. \( \dot{\mathbf{N}} \)


Gastric juice contains 0.03 moles \( H C l \)
of per liter. If a person produces \( 2.5 \mathrm{L} \) of gastric juice per day. How many antacid tablets each containing \( 400 \mathrm{mg} \) of
\( A l(O H)_{3} \) are needed to neutralize all the \( H C l \) produced in one day?


The variance of a constant is
A. Constant
B. zero
c. Number itself
D. None


Assertion
Dissociation takes place in ionic
compound
Reason
It involves separation of ions that are
held together by electrostatics force
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


Metaphase chromosome appears to be longitudinally divided into two identical parts known as
This question has multiple correct options
A. Sister chromosomes
B. Satellites
c. Daughter chromosomes
D. sister chromatids


If the equilibrium constant of the reaction of weak acid \( \boldsymbol{H} \boldsymbol{A} \) with a strong
base is \( 10^{9} \), then the \( p H \) of \( 0.1 M N a A \)
solution will be:


Who found that organic matter is synthesised with the help of solar energy?
A . Hill
B. Van Steil
c. Mayer
D. Bayer


Evaluate \( : \int \frac{1}{\sqrt{x^{3}}} d x \)


Prove that: \( \sum \sin ^{4} \frac{r \pi}{16}=\frac{3}{2}, r= \)
1,3,5,7


A planet of mass \( M \) moves around the
Sun along an ellipse so that its minimum distance from the Sun is
equal to \( r \) and the maximum distance
to
\( R \) Making use of Kepler's laws, find
its period of revolution around the Sun.


The total number of \( \boldsymbol{H}_{2} \boldsymbol{O} \) molecules
present in the balanced chemical
reaction is :
\( M n O_{4}^{\ominus}+F e^{2+} \longrightarrow M n^{2+}+F e^{3+}( \) in
alkaline medium)


Radius of a nucleus is proportional to:
A. \( A \)
B. \( A^{1 / 3} \)
c. \( A^{2} \)
D. \( A^{2 / 3} \)


The weather department has predicted that a thunderstorm is likely to occur on
a certain day. Suppose you have to go
out on that day. Would you carry an umbrella? Explain.


toppr
Q Type your question
'Igure. Ine coemcıent \( \mu \) Is insurırcıent
to start pure rolling. The sphere slides a
length \( \ell \) on the incline from rest and its
kinetic energy becomes K. Then, the work done by friction will be
A. \( -\mu \) mglcos \( \theta \)
в. \( -m g \ell \sin \theta+K \)
\( c \)
\( D \)


In a class consisting of 100 students, 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students knowing both Hindi and English is:
A. 5
B. 10
c. 15
D. 20


For a biased die the probabilities for the different faces to turn up are given
below:
The die is tossed and you are told that either face one or face two turned up.
Then the probability that it is face one
is.
Faces:
Probabilities: \( \quad \) 0.1 \( \quad \) 0.32 \( \quad \) 0.21
A. \( 1 / 6 \)
в. \( 1 / 10 \)
c. \( 5 / 49 \)
D. \( 5 / 21 \)


5 mole of oxygen are heated at constant
volume from \( 10^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \). What will be
the change in the internal energy of gas? The molar heat of oxygen at
constant pressure, \( C_{P}=7.03 \mathrm{cal} \)
\( m o l^{-1} d e g^{-1} \) and \( R= \)
\( 8.31 J \) mol\( ^{-1} d e g^{-1} \)


Select the correct option:
Read the given statements.
I. Fructose is the sweetest sugar.
ii. Glycine is the simplest amino acid.
iii. Lactose is a disaccharide composed
of one molecule each of glucose and
galactose.
iv. Cellulose is an unbranched chain of
glucose molecules linked by \( \beta 1,4 \) glycosidic bond. Which of the given statements are
correct?
A \( \cdot \) (i) and (ii)
B. (iii) and (iv)
c. (i), (ii) and (iii)
D. (i), (ii), (iii) and (iv)


Cellulose, protein and starch are classified as:
A. natural polymers
B. aldehydes
c. esters
D. synthetic polymers


For the reaction,
\( \mathrm{C}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} \)
Which of the following option is correct?
\( \mathbf{A} \cdot \Delta \mathbf{H}>\Delta \mathbf{E} \)
B. \( \Delta \mathrm{H}<\Delta \mathrm{E} \)
c. \( \Delta H=\Delta E \)
D. \( \Delta H=0 \)


Which of the following is not true about
Laboratory thermometers?
A. Laboratory thermometers are used to measure temperatures with a high degree of precision.
B. Laboratory thermometers are used to measure body temperature
C. Range of laboratory thermometer is -10C to 110C
D. Laboratory thermometers are designed for lab purposes such as checking boiling point, freezing point etc.


The following questions are based on the preparation of ammonia gas in the laboratory:
Explain why ammonium nitrate is not used in the preparation of ammonia?


How much work would be required to move a proton from the negative to the positive plate?
A. \( -3.6 \times 10^{-18} J \)
в. \( 3.6 \times 10^{-19} \mathrm{J} \)
c. \( 3.6 \times 10^{-18} \mathrm{J} \)
D. \( -3.6 \times 10^{-19} \mathrm{J} \)


Maximum number number of electron
that may be present on a \( 4 f \) -orbital is:
\( A \cdot 2 \)
B. 4
c. 7
D. 14


If \( (\sqrt{3}-i)^{n}=2^{n}, n \in N, \) then \( n \) is a
multiple of
\( \mathbf{A} \cdot \mathbf{6} \)
B. 10
\( c .9 \)
D. 12


What is a biodegradable polymer? Give an example of a biodegradable aliphatic polyester.


If horizontal and vertical components of the earth's magnetic field are equal at a certain place, then the angle of the dip at that place will be
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 0^{\circ} \)


Assertion
Two bodies at the same temperature may contain different amounts of heat
Reason
Two bodies may require different
amounts of heat to maintain or acquire
same temperature
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 gas which exists in three allotropic
forms \( \alpha, \beta \) and \( \gamma \) is :
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
\( c \cdot C O_{2} \)
D. \( N H_{3} \)


Heavy hydrogen is used:
A. in filling balloons
B. in studying reaction mechanism
C. in calculating heat of formation
D. as oxidizing agent


Describe how ozone present in the atmosphere is important for sustaining life on earth?


If the distance between two unlike poles
is doubled then the force of attraction
between them becomes \( _{--}-_{-}- \) times
its original value
A . 0.25
B. 0.5
c. 0.125
D. 2


Find elasticity of supply when price
increases by 20 per cent and quantity increases from 100 to 250 units of the
commodity.


Calculate the solubility of AgCl in \( 0.2 \mathrm{M} \)
\( -N H_{3} \) solution
Given : Ksp of \( \mathrm{AgCl}=2 \times 10, \mathrm{Kf} \) of \( A g\left(N H_{3}\right) 2^{+}=8 \times 10^{6} \)


The complimentary base pairing in RNA molecules is seen between uracil and
A. Thymine
B. Guanine
c. cytosine
D. Adenine
E. Uracil


State True or False :
More we increase the temperature, more is the thermal expansion of solids.
A. True
B. False


The following table shows the age distribution of cases of a certain
disease reported during a year in a particular city.
\( \begin{array}{lllll}\text { Age } & 5- & 15- & 25- & 35- \\ \text { in } & 14 & 24 & 34 & 44 \\ \text { years } & & & \end{array} \)
No. of 6
11
Obtain the mean, median and mode of
the above data.


Excessive thirst leading to increased consumption of water is
A. Polyurea
B. Glycemia
c. Polyphagia
D. Polydipsia


When benzene sulphuric acid and \( p \)
nitrophenol are treated with \( N a H C O_{3} \)
the gases released, respectively are:
A. \( S O_{2}, N O_{2} \)
в. \( S O_{2}, N O \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}, \mathrm{CO}_{2} \)
D. \( C O_{2}, C O_{2} \)


Which one of the following is not a characteristic feature of the sub-
phylum Vertebrata?
A. Dorsal tubular nerve cord
B. Ventral muscular heart
c. Presence of notochord in the adult
D. Presence of kidneys
E. Two pairs of lateral appendages, fins or limbs


Let \( (a b c=8, a, b, c \geq 0) \) and the real
valued function \( f(x)=b c(a x-1)^{2}+ \)
\( c a(b x-1)^{2}+a b(c x-1)^{2} \) has
minimum value at \( x=\frac{1}{2}, \) then the
value of \( \boldsymbol{a}^{16}+\boldsymbol{b}^{17}+\boldsymbol{c}^{16} \)
A \( \cdot 2^{15} \)
B . \( 2^{16} \)
\( c \cdot 2^{17} \)
D. \( 2^{18} \)


If the turns ratio of a transformer is 2
and the impedance of primary coil is 250 W then the impedance of secondary coil will be
A . \( 1000 \Omega \)
B. 500 \( \Omega \)
\( c \cdot 250 \Omega \)
D. 125 \( \Omega \)


Viroids have a
A. \( d s R N A \) enclosed by a protein coat
B. \( d s D N A \) not enclosed by a protein coat
C. ssRNA enclosed by a protein coat
D. ssRNA not enclosed by a protein coat


A man having a height \( 6 m, \) wants to see his full height in mirror. He observes an image of \( 2 m \) height standing erect, then the type of mirror used is?
A. Concave
B. convex
c. Plane
D. None of these


Differentiate between
FSH and LH


f \( A, B, C \) are three events show that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C})=\boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})+ \)
\( \boldsymbol{P}(\boldsymbol{C})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})-\boldsymbol{P}(\boldsymbol{b} \cap \boldsymbol{C})- \)
\( \boldsymbol{P}(\boldsymbol{C} \cap \boldsymbol{A})+\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C}) \)


Emulsions of polyvinyl acetate are used in?
A. Polishes
B. Firecrackers
c. crayons
D. Latex paints


The ratio of the radii of planets \( A \) and \( B \)
is \( K_{1} \) and ratio of accelerations due to
gravity on them is \( K_{2} \) The ratio of escape velocities from them will be:
A. \( K_{1} K_{2} \)
B. \( \sqrt{K_{1} K_{2}} \)
c. \( \sqrt{\frac{K_{1}}{K_{2}}} \)
D. \( \sqrt{\frac{K_{2}}{K_{1}}} \)


The mass of an electron is \( 9.11 \times \)
\( 10^{-31} k g . \) How many electrons would 1
milligram make?


If \( (\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin \theta) \)
\( (\cos n \theta+i \sin n \theta)=1, \) then the value
of \( \boldsymbol{\theta} \) is
A \( \cdot \frac{2 m \pi}{n(n+1)} \)
B. \( 4 m \pi \)
c. \( \frac{4 m \pi}{n(n+1)} \)
D. \( \frac{m \pi}{n(n+1)} \)


Which of the following is a chemical change?
A. Boiling of eggs
B. Evaporation of water
c. Precipitation of snow
D. Melting of wax


Boojho stands at A just on the side of a plane mirror as shown in Fig.. Can he see himself in the mirror? Also can he
see the image of objects situated at \( P \)
Q and R?
\( A(B \text { oojho }) \cdot P \quad . Q \)


Five balls, numbered 1 to \( 5, \) are suspended using separate threads. Pairs (1,2),(2,4),(4,1)
show electrostatic attraction, while pairs (2,3) and (4,5) show repulsion therefore ball 1 must be:
A. Positively charged
B. Negatively chargedd
c. Neutral
D. Made of metal


Which coloured light scatters least by fog and smoke?
A. Green
B. Yellow
c. Blue
D. Red


The moment of inertia of a non-uniform
semicircular wire having mass \( m \) and
radius \( r \) about a line perpendicular to
the plane of the wire through the centre is
\( \mathbf{A} \cdot m r^{2} \)
B. \( \frac{1}{2} m r^{2} \)
c. \( \frac{1}{4} m r^{2} \)
D. \( \frac{2}{5}^{m r^{2}} \)


Show that the function \( \boldsymbol{f}: \mathbb{R} \rightarrow \)
\( \{x \in \mathbb{R}:-1<x<1\} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|}, \boldsymbol{x} \in \mathbb{R} \)
is one to one and onto function.


The values of \( a \) and \( b \) such that the
function defined as \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}a x^{2}-b, & |x|<1 \\ -1 /|x|, & |x| \geq 1\end{array} \) is differentiable are \right.
\( ? \)
A \( \cdot a=1, b=-1 \)
1
B. \( a=\frac{1}{2}, b=\frac{1}{2} \)
c. \( _{a=\frac{1}{2}, b=\frac{3}{2}} \)
D. \( a=\frac{3}{2}, b=\frac{3}{2} \)


In the circuit shown, the potential
difference across the \( 3 \mu F \) capacitor is
\( \mathrm{V}, \) and the equivalent capacitance
between \( A \) and \( B \) is \( C_{A B} \)

This question has multiple correct options
\( \mathbf{A} \cdot C_{A B}=4 \mu F \)
в. \( c_{A B}=\frac{18}{11} \mu F \)
c. \( v=20 \)
D. \( V=40 \)


Why are most carbon compounds poor conductors of electricity? Write the name and structure of a saturated
compound in which the carbon atoms
are arranged in a ring. Give the number of single bonds present in this
compound.


What is the angle of the prism for which there will be no emergent ray from the prism if \( C \) is the critical angle \( ? \)
A . 2
B. less than 2C
c. more than 2 C
D. None of these


Complete the following sentences by selecting the correct option.
(A) Inspiratory capacity (IC) = (i) + IRV
(B) \( (i i)=T V+I R V+E R V \)
(C) Functional residual capacity \( (\mathrm{FRC})= \) ERV \( +(\text { iii }) \)
A. (ii)Vital capacity (ii) Tidal volume (iii)Residual volume
B. (i)Expiratory capacity
(ii) Residual volume (iii) Inspiratory reserve volume
c. (i)Tidal volume (ii) Vital capacity (iii) Residual volume
D. (i)Tidal volume (ii) Total lung capacity (iii) Expiratory capacity


Weakest interactions are involved in:
A. dative bond
B. metallic bond
c. hydrogen bond
D. vander waals forces


A truck and a car are moving on a smooth, level road such that the K.E.
associated with them is the same.
Brakes are applied to both of them simultaneously. Which one will cover a greater distance before it stops?
A . car
B. truck
c. the same distance
D. nothing can be decided


A rectangle and a parallelogram are on
the same base and between the same
parallels. If the area of the rectangle is \( 50 c m^{2}, \) then what is the area of the
parallelogram?
\( \mathbf{A} \cdot 20 \mathrm{cm}^{2} \)
B. \( 60 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 30 c m^{2} \)
D. \( 50 c m^{2} \)


The graph between displacement and
time in a motion along straight is
detached below. Which interval
indicates that no force is acting on the
particle?
\( A \cdot R S \)
B. PQ
c. PQ and OP
D. op


A motor cyclist at a speed of \( 5 \mathrm{m} / \mathrm{s} \) is describing a circle of radius \( 25 \mathrm{m} \). Find his inclination with vertical. What is the
value of coefficient of friction between
type and ground?


The correct order of acid strength of the
following substituted phenols in water
at \( 28^{\circ} C \) is:
A. p-nitrophenol<p-fluorophenol<p-chlorophenol
B. p-chlorophenol
D. p-fluorophenol<p-nitrophenol<p-chlorophenol
October 15, 2019
Q omuttam venkateshwarlu
(8) Share Save


The ratio of modulus of rigidity to bulk modulus for a Poisson's ratio of 0.25
would be
A. \( 2 / 3 \)
в. \( 2 / 5 \)
\( c .3 / 5 \)
D. 1.0


\( \ln L_{-} C \) oscillation, maximum charge on
capacitor is \( Q_{0} . \) The current in the
circuit, when \( 50 \% \) energy is electrical
and \( 50 \% \) is magnetic is
A \( \cdot \frac{Q_{0}}{\sqrt{L C}} \)
B. \( \frac{Q_{0}^{2}}{\sqrt{L C}} \)
с. \( \frac{Q_{0}}{2 \sqrt{L C}} \)
D. \( \frac{Q_{0}}{\sqrt{2 L C}} \)


Three vectors \( \vec{A}, \vec{B}, \vec{C} \) satisfy the relation \( \vec{A} \cdot \vec{B}=0 \) and \( \vec{A} \cdot \vec{C}=0 . \) The
vector \( \vec{A} \) is parallel to
A \( \cdot \vec{B} \)
в. \( \vec{c} \)
c. \( \vec{B} \cdot \vec{C} \)
D . \( \vec{B} \times \vec{C} \)


If \( x \& y \) are in direct proportion and if \( \boldsymbol{x}=\mathbf{2 0} \) at proportionality constant \( =\mathbf{4} \)
find \( y \)
A .2
B. 3
\( c \cdot 4 \)
D. 5


Which is incorrect about \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. Reducing agent
B. Dehydrating agent
c. sulphonating agent
D. Highly viscous


Which of the following is the enantiomer of the following compound?
A . \( I \)
B. II
c. \( I I I \)
D. It doesn't have a non-superimposable enantiomer


How far was the automobile behind the
truck initially?


In following cell reaction
\( M g(s)+2 A g^{+}(0.001 M) \rightarrow \)
\( M g^{2+}(0.20 M)+2 A g(s) \)
Calculate \( E_{\text {cell}} \) for the reaction \( \left[E^{o}=\right. \) \( \left.\mathbf{3 . 1 7} \boldsymbol{V}, \frac{\mathbf{2 . 3 0} \boldsymbol{R} \boldsymbol{T}}{\boldsymbol{F}}=\mathbf{0 . 0 5 4}\right] \)
\( A \cdot 2.63 V \)
B. 3.01V
c. \( 3.33 v \)
D. 3.51V


Two sinusoidal waves with same
wavelengths and amplitudes travel in opposite directions along a string with a speed \( 10 \mathrm{m} s^{-1} . \) If the minimum time
interval between two instant when the
string is flat is \( 0.5 s, \) the wavelength of the waves is?
A \( .25 \mathrm{m} \)
в. 20
\( c .15 \mathrm{m} \)
D. 10


In the depletion region of an unbiased \( \mathrm{P} \)
Njunction diode there are


why is not water used as a barometeric
liquid. Give two reasons.


Artificial silk is a
A . polypeptide
B. polysaccharide
c. polythene
D. polyvinyl chloride


The period of growth is generally divided into-


During a radioactive decay, which of the following statements is false
A. atomic mass number cannot increase
B. atomic number may increase
c. atomic number may decrease
D. atomic number will remain unchanged


\( x^{2}+\frac{1}{x^{2}}=6 \)
Find
(i) \( x^{3}-\frac{1}{x^{3}} \)
(i) \( x^{6}+\frac{1}{x^{6}} \)


A piece of wood was found to have
\( ^{14} C /^{12} C \) ratio 0.6 times that in a living
plant. Calculate the period when the plant died. (Half life of \( ^{14} C=5760 \)
years)


Market value (in rupees) of a share through a week is changing as 3672,3657,3673,3673,3665,3668
Find the arithmetic mean of the marks
value of the share


The intensity of magnetic induction at the center of a circular coil carrying a current is \( B \). If the number of turns and
radius are doubled, the intensity of
magnetic induction at the center with the same current will be
A \( .2 B \)
в. \( 4 B \)
\( c . B \)
D. \( 0.5 B \)


Draw the structure of the following compound:
Hex-2-en-4-ynoic acid


Given real numbers \( b \) and \( c \) such that
the product of 3 and \( c \) is \( b \). Which of the
following expressions represents, in terms of \( b \), the sum of \( c \) and \( 3 ? \)
A. \( b+3 \)
B. \( 3 b+3 \)
\( c \cdot 3(b+3) \)
D. \( \frac{b+3}{3} \)
E \( \frac{b}{3}+3 \)


Most of the vertebrates have jaws with teeth. The mode of arrangement of teeth
on the jaws is called dentition.
The various types of teeth seen in mammals are incisors (I) canines (C)
premolars (P) and molars(M). They are used for biting, tearing, chewing and grinding respectively. Canines, the tearing teeth are welldeveloped in carnivores and illdeveloped or absent in herbivores.
Now answer the following:
(i) In frogs, all the teeth in the upper jaw look alike, whereas in human beings
they are different. The type of dentition in man can be called
(a) Homodont
(b) Isodont \( (c) \)
Heterodont
(d) Acrodont
(ii) The dental formula of a mammal is
written as ICPM=2023/1023. The teeth
missing in it are
(a) incisors
(b) canines
(c) premolars
(d) molars


The number of lines of symmetry in a scalene triangle is
A. 0
B.
\( c \cdot 2 \)
\( D \)


The percentage of an element \( M \) is 53 percentage in its oxide of molecular
formula \( M_{2} O_{3} \). Its atomic mass is
about:
A . 45
B. 9
\( c \cdot 18 \)
D. 38
E. 27


Statement-1: The resistivity of
a semiconductor decreases with
increases of temperature
Statement-2: In a conducting solid, the rate of collision between free electrons
and ions increases with the increase of
temperature
A. Statement-1 is true and Statement-2 is correct explanation for Statement-
B. Statement-1 is true and Statement-2 is NOT the correct explanation for Statement-
c. Statement- 1 is true, Statement- 2 is false
D. Statement-1 is false, Statement-2 is true


An artificial satellite moving in a
circular orbit around the earth has a
total (kinetic \( + \) potential ) energy \( \frac{\boldsymbol{E}_{0}}{\boldsymbol{4}} \)
Its potential energy is
A \( \cdot \frac{E_{0}}{4} \)
в. \( \frac{E_{0}}{2} \)
c. \( \frac{E_{0}}{8} \)
D. \( E_{0} \)


The direction of which of the following vectors is along the line of axis of
rotation?
A. Angular velocity, angular acceleration only
B. Angular velocity, angular momenturm only
c. Angular velocity, angular acceleration, angular momentum only
D. Angular velocity, angular acceleration, angular momentum and torque


Which one of the following is an example of a lung-fish?
A. Scoliodon
B. Coelacanth
c. Labeo
D. Protopterus


State whether the following statements are true of false. Justify.
(i) For an arbitrary binary operation \( * \) on as \( \operatorname{set} N, a * a=a \forall a \epsilon N \)
(ii) If \( * \) is a commutative binary
operation on \( N, \) then \( a *(b * c)=(c * \)
\( b) * a \)
A. True
B. False


Which of the following methods is based on the principle of the difference in the wetting properties of the ore and
gangue particles with water and oil?
A. Magnetic separation
B. Froth floatation process
c. Hydraulic washing
D. None of these


The fuel used in nuclear power plants is
A. U-235
B. U-238
c. \( \cup-236 \)
D. None of the above


Isoelectronic species have same number of electrons.
A. True
B. False


Solve \( \lim _{x \rightarrow a} \frac{x^{2}-(a+1) x+a}{x^{3}-a^{3}} \)
A \( \cdot \frac{a-2}{a^{2}} \)
в. \( \frac{a-1}{3 a^{2}} \)
c. \( \frac{a+1}{3 a^{2}} \)
D. None of these


For an amplitude modulated wave, the maximum amplitude is found to be 10 while the minimum amplitude is found
to be \( 2 v \). Determine the modulation
index \( \mu \)


Which of the following is dry and permanent bleaching agent?
A. \( O_{3} \)
B. Moist \( S O_{2} \)
c. \( H_{2} O_{2} \)
D. \( C l_{2} \) water


There is a cuboid of dimensions \( l \times b \times \)
\( h \) and thermal capacity 'K' units. On
doubling the dimensions of the cuboid. Find the thermal capacity.


The angles of triangle are in ratio 1: 3:
5 find the angles
\( \mathbf{A} \cdot 20,60,100 \)
в. 30,60,90
c. 45,60,75
D. 50,60,70


How will you identify \( S O_{2}^{2-} \) in presence
of \( \boldsymbol{C O}_{3}^{2-} \) ?
A. by odour.
B. color change
c. PH measurement.
D. weight measurement.


In the figure, if lines \( P Q \) and \( R S \)
intersect at point \( T, \) such that
\( \angle P R T=40^{\circ}, \angle R P T=95^{\circ} \) and
\( \angle T S Q=75^{\circ}, \) find \( \angle S Q T \)


Find the derivative of \( \sin (x+1), \) with
respect to \( x, \) from first principle.


0
6
0
6


Standard electrode potential of cell
\( \boldsymbol{H}_{2}\left|\boldsymbol{H}^{+} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \) is :
A. \( 0.8 \mathrm{v} \)
в. \( -0.8 V \)
c. \( -1.2 V \)
D. \( 1.2 V \)


Which is an intensive property?
A. Volume
B. Mass
C. Refractive index
D. weight


Let ' \( n^{\prime} \) be the number of elements in
the domain set of the function \( f(x)= \) \( \left|\ln \sqrt{x^{2}+4 x} C_{2 x^{2}+3}\right| \)
and ' \( Y^{\prime} \) be the global maximum value
of \( \boldsymbol{f}(\boldsymbol{x}), \text { then }[\boldsymbol{n}+[\boldsymbol{Y}]] \text { is .... (where }]= \)
Greatest Integer Function).


A particle starts \( S . H . M . \) from the
mean position. Its amplitude is \( A \) and
time period is \( T . \) At the time when its speed is half of the maximum speed, its displacement \( y \) is :
A \( \cdot \frac{A}{2} \)
B. \( \frac{A}{\sqrt{2}} \)
c. \( \frac{A \sqrt{3}}{2} \)
D. \( \frac{2 A}{\sqrt{3}} \)


Which of the following is wrong?
A. PMMA is called plexiglass
B. PTFE is called teflon
C. SBR is natural rubber
D. LDPE is called low density polythene


\( 2.1 g \) of \( F e \) combines with \( S \) evolving \( 3.77 k J . \) The heat of formation of \( F e S \) in
\( k J / m o l \) is:
A. -3.77
B . -1.79
c. -100.5
D. None of these


The distance between the circumcentre
and the ortho centre of the triangle formed by the points (2,1,5),(3,2,3) and (4,0,4) is
A \( \cdot \sqrt{6} \)
B. \( \frac{\sqrt{6}}{2} \)
c. \( 2 \sqrt{6} \)
D.


In which compound among the following, carbon has a zero oxidation
state?
A \( . C H_{4} \)
в. \( C H_{3} C l \)
c. \( C H_{2} C l_{2} \)
D. \( C C l_{4} \)


Two identical bricks of length \( L \) are
piled one on top of the other on a table
as shown in the figure. The maximum
distance \( S \) the top brick can overhang
the table with the system still balanced
is :
A \( \cdot \frac{1}{2} L \)
в. \( \frac{2}{3} L \)
c. \( \frac{3}{4} L \)
D. \( \frac{7}{8} L \)


Which of the following quantities are independent of the choice of zero
potential or zero potential energy? This question has multiple correct options
A. Potential at a point
B. Potential difference between two points.
c. Potential energy of a two charge system.
D. change in potential energy of a two charge system.


If \( x \epsilon N, \) then range of function \( f(x)= \) \( \frac{16-x}{20-3 x} C_{x-1} \) is
A. [1,15]
В \( \cdot_{14} C_{4}, \frac{^{10} C_{5}}{2} \)
c. \( ^{11} C_{4} \)
\( \mathbf{D} \cdot[5,15 \)


Assertion
D-Fructose is used for sweetening cold
drinks but not in hot ones
Reason
The sweet form is fructopyranose; on increasing temperature causes a shift
in the pyranose \( \rightleftharpoons \) furanose equilibrium towards the less sweet furanose form
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the properties are suitable for a cooking utensil? This question has multiple correct options
A. High specific heat
B. Low specific heat
c. High conductivity
D. Low conductivity


In presence of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q} .) ; \boldsymbol{H}_{2} \boldsymbol{S} \) gas
results the precipitation of group- 2
cations but not of group- 4 cations during qualitative analysis. It is due to:
A. Lower concentration of \( S^{2-} \)
B. Higher concentration of \( S^{2} \)
C. Lower concentration of \( H^{+} \)
D. Higher concentration of \( H^{+} \)


Find the complement of the angle :
\( \frac{1}{4} \) of a right angle
\( \mathbf{A} \cdot 67 \cdot 5^{\circ} \)
B \( .57 \cdot 5^{\circ} \)
\( \mathbf{c} \cdot 37 \cdot 5^{\circ} \)
D. none of the above


\( f(x)=x^{2}-2 \sqrt{2} x+1 . \) Then find the
value of \( \boldsymbol{p}(\boldsymbol{2} \sqrt{\boldsymbol{2}}) \)


A uniform long rope is suspended from the roof. A transverse wave pulse is produced at its lower end. As the wave travels upward along the suspended rope, then the
1) velocity of wave increases
2) wavelength of wave increases
3) frequency of wave remains constant
A. only 1 and 2 are true
B. only 2 and 3 are true
c. only 1 and 3 are true
D. 1,2 and 3 all are true


Given is mechanism of Beckmann
rearrangement.

Rate determining step in Beckmann
rearrangement:
A . \( I \)
B. \( I I \)
c. \( I I I \)
D. \( I V \)


The nondirectional orbital has ....... value
of azimuthal quantum number.
A. 0
B.
\( c \cdot-1 \)
\( D \cdot+1 / 2 \)


0.5 mole of \( H_{2} S O_{4} \) is mixed with 0.2
mole of \( \boldsymbol{C a}(\boldsymbol{O H})_{2} . \) The maximum
number of moles of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \) formed is:
A. 0.2
B. 0.5
\( c \cdot 0.4 \)
D. 1.5


When \( M n O_{2} \) is fused with KOH in the
presence of air, a coloured compound is formed, the product and its colour is :
A \( \cdot K_{2} M n O_{4}, \) dark green
B. \( K M n O_{4} \), purple
c. \( M n_{2} O_{3} \), brown
D. \( M n_{3} O_{4} \), black.


Which of the following is amphoteric in \( n \)
ature?
A \( . H C l O_{4} \)
в. \( N a O H \)
\( \mathbf{c} \cdot Z n(O H)_{2} \)
D. None of these


Two waves are represented by \( x_{1}= \) \( A \sin \left(\omega t+\frac{\pi}{6}\right) \) and \( x_{2}=A \cos \omega t \) then
the phase difference between them is :
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \pi \)


If the hypotenuse of a right angled triangle is \( 41 \mathrm{cm} \) and the area of the
triangle is 180 sq \( c m \), then the
difference between the lengths of the triangle must be
\( \mathbf{A} \cdot 22 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c \cdot 27 \mathrm{cm} \)
D. \( 31 \mathrm{cm} \)


Find the unit vectors orthogonal to both
(2,3,5) and (2,-1,4)


Which of the following applications reveal that nitrogen is inert? This question has multiple correct options
A. Tinned food products
B. Making of fertilizers
c. Refrigerantt
D. Electric bulbs


The inflorescence in cauliflower is
A. Compound corymb
B. Corymb
c. Umbel
D. catkin


A scientist wants to raise the
temperature of \( 0.1 \mathrm{Kg} \) sample of glass
from \( -45^{0} C \) to \( 15^{0} C . \) How much heat
energy is required to raise the temperature? (SHC of glass
\( \left.\boldsymbol{8} \boldsymbol{J} / \boldsymbol{K} \boldsymbol{g} /^{o} \boldsymbol{C}\right) \)


If the angle of incidence increases
gradually then angle of refraction also
A . increases
B. decreases
c. remains Same
D. none


A ball is thrown vertically upwards from the top of a tower with an initial velocity
of \( 19.6 m s^{-1} . \) The ball reaches the
ground after \( 5 s . \) Calculate \( :(i) \) the height of the tower, (ii) the velocity of ball on
reaching the ground. Take \( g=9.8 m s^{-2} \)
A . \( (i) 24.5 m,(i i) 29.4 m s^{-1} \)
B . (i)24.5m, (ii)19.4 m s \( ^{-1} \)
C \( \cdot(i) 24.5 m,(i i) 28 m s^{-1} \)
D. \( (i) 25 m,(i i) 29.4 \mathrm{m} s^{-1} \)