If \( C \) and \( D \) are two events such that
\( C \subset D \) and \( P(D) \neq 0, \) then the correct
statement among the following is
\( \mathbf{A} \cdot P(C \mid D)<P(C) \)
\( ^{\mathbf{B}} P(C \mid D)=\frac{P(D)}{P(C)} \)
c. \( P(C \mid D)=P(C) \)
D. \( P(C \mid D) \geq P(C) \)


The Sl unit of solid angle is
A. radians
B. steradians
c. degrees
D. All of the above


A spherical air bubble in water will act
A. Convex lens
B. Concave lens
c. Plane glass plate
D. Plano-concave lens


Assertion
Diamagnetism is universal, it is
present in all materials.
Reason
Field due to induced magnetic moment is opposite to the magnetising field.
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 first diffraction minima due to a
single slit diffraction is at \( \theta=30^{\circ} \) for a
light of wavelength 5000 A. The width of the slit is:
\( \mathbf{A} \cdot 5 \times 10^{-5} \mathrm{cm} \)
В. \( 10 \times 10^{-5} \mathrm{cm} \)
c. \( 2.5 \times 10^{-5} \mathrm{cm} \)
D. \( 1.25 \times 10^{-5} \mathrm{cm} \)


Function \( \frac{e^{2 x}-1}{e^{2 x}+1} \) is
A. increasing
B. decreasing
c. neither increasing nor decreasing
D. none of these


An unarmoured dinoflagellate is
A. Ceratium
B. Noctiluca
c. Gonyaulax
D. Both B and C


Which one of the following is the correct characteristic of the caterpillars?
A. All caterpillars are insectivorous
B. Caterpillars are known to be voracious feeders
c. caterpillars are not considered agricultural pests
D. None of the caterpillars are nocturnal


If \( \vec{a}=\hat{i}+\hat{j}-\hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+2 \hat{k} \& \)
\( \vec{c}=-\hat{i}+2 \hat{j}-\hat{k}, \) find a unit vectors normal to the vectors \( \vec{a}+\vec{b} \) and \( \vec{b}+\vec{c} \).
\( ^{\mathbf{A}} \cdot \frac{-\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{40}} \)
B. \( \frac{-\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)
c. \( \frac{\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)
D. \( \frac{-\hat{i}+2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)


Assertion
For stabilization of an emulsion, a third component called emulsifying agent is usually added.
Reason
Emulsions of oil in water are unstable
and sometimes they separate into two layers on standing.
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


At rotational equilibrium, the sum of
clockwise moments equals to the sum
of anti-clockwise moments.
A. True
B. False


Magnetic moment of \( F e^{3+} \) ions \( \sqrt{35} \)
BM. Determine number of unpaired electrons.


Show that \( \sin ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)= \)
\( \tan ^{-1}\left(\frac{63}{16}\right) \)


Number of pi bonds in cyclic structure
of \( \boldsymbol{S}_{3} \boldsymbol{O}_{9} \) is:


If \( _{5} \mathrm{B}^{11} \) converts into \( _{6} \mathrm{C}^{11}, \) then the
particle emitted in this process will be
A. electron
B. proton
C. neutron
D. positron


In increasing order of boiling point :
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H}, \quad\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H}, \quad \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H} \)


One cannot see through fog because:
A. fog absorbs light
B. light is scattered away by the droplets in fog
C. light suffers total internal reflection at the droplets in fog
D. the refractive index of fog is infinity


When \( N_{2} O_{5} \) is heated at temp. \( T, \) it
dissociates as \( N_{2} O_{5} \rightleftharpoons N_{2} O_{3}+ \)
\( O_{2}, K_{c}=2.5 . \) At the same time
\( N_{2} O_{3} \rightleftharpoons N_{2} O+O_{2} \). If initially 4.0
moles of \( N_{2} O_{5} \) are taken in 1.0 litre
flask and allowed to attain equilibrium,
concentration of \( O_{2} \) was formed to be
2.5 M. Equilibrium concentration of
\( N_{2} O \) is:
A .1 .0
в. 1.5
\( c \cdot 2.166 \)
D. 0.334


Evaluate:-
\( \left(\frac{2}{7}\right)^{2} \times\left(\frac{7}{2}\right)^{-3} \div\left\{\left(\frac{7}{5}\right)^{-2}\right\}^{-4} \)


f \( a \neq b \neq c \) such that
\( \left|\begin{array}{ccc}\boldsymbol{a}^{3}-\mathbf{1} & \boldsymbol{b}^{\mathbf{3}}-\mathbf{1} & \boldsymbol{c}^{\mathbf{3}}-\mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{\mathbf{2}} & \boldsymbol{b}^{\mathbf{2}} & \boldsymbol{c}^{\mathbf{2}}\end{array}\right|=\mathbf{0} \) ther
A \( . a b+b c+c a=0 \)
B . \( a+b+c=0 \)
\( c \cdot a b c=1 \)
D. \( a+b+c=1 \)


Main factor which limits the rate
of photosynthesis on a clear day is
A. Chlorophyll.
B. Light.
c. \( C O_{2} \)
D. water


When a cylinder is spinned and placed
somewhere on surface of a rough inclined planes as shown then after
release.
A. The cylinder may continue to accelerate down and never be in pure rolling
B. The cylinder may accelerate up for some time then retard and come down in pure rolling
C. The cylinder may accelerate down continuously and pure rolling will start after some time
D. Friction will act on cylinder in upward direction initially and later it will be downward direction


A hollow smooth uniform sphere \( A \) of mass m rolls without sliding on a smooth horizontal surface. It collides
head on elastically with another stationary smooth solid sphere \( B \) of the same mass \( \mathrm{m} \) and same radius. The
ratio of kinetic energy of \( B \) to that of \( A \) just after the collision is :
\( A \cdot 1: 1 \)
в. 2: 3
\( c .3: 2 \)
D. 4: 3


According to Darwinism,
fossils of organisms found in south America resemble most
to the fossils of
A. North America
B. Africa
C. Australia
D. Both A and B


For the transformer shown in figure if
the primary to secondary turns ratio is 1
10, the voltage across the terminals of the secondary coil-will be :
A. Zero
B. 1 volt
c. 10 volt
D. 100 volt


Some elements in \( p \) -block shows
allotropy.
(a) What are the allotropic forms of
sulphur?
(b) (i) How will you manufacture
Sulphuric Acid by contact process?
(ii) What are inter halogen
compounds?


Acceleration of particle moving rectilinearly is \( a=4-2 x \) (where \( x \) is
position in meter and \( a \) in \( m s^{-2} \) ). It is at
instantaneous rest at \( x=0 . \) At what
position \( x \) (in meter) will the particle again come to instantaneous rest?


The rate constant of a reaction does not
depend upon:
A. temperature
B. activation energy
c. catalyst
D. concentration of reactants and products


Explain Mond's process used for refining of nickel.


Core of electromagnets are made of ferromagnetic material which has:
A. High permeability and Low retentivity
B. High permeability and High retentivity
c. Low permeability and High retentivity
D. Low permeability and Low retentivitty


From the given examples, form the pair of isotopes and the pair of isobars:
\( 18 A r^{40},_{17} C l^{35},_{20} C a^{40},_{17} C l^{37} \)


The correct arrangement of following
acids of phosphorus in the increasing
order of oxidation state of phosphorous
¡S:
A. hypophosphorous acid < orthophosphorous acid pyrophosphoric acid
B. hypophoshporous acid < pyrophosphoric acid \( < \) orthophosphorous acid
C. pyrophosphoric acid < hypophosphrous acid orthophosphorous acid
D. pyrophosphoric aicd < orthophosphorous acid hypophosphorous acid


\( \boldsymbol{H}_{2}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
The rate law is \( \frac{d x}{d t}=k\left[H_{2}\right]^{1 / 2}\left[B r_{2}\right]^{1 / 2}: \)
On increasing the concentration of \( B r_{2} \)
four times, by how much times the rate of reaction will change?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


If the vertical component of earth's magnetic field at a place is \( \sqrt{3} \) times the horizontal component, then the value of dip at that place is
A .60
B . 45
c. 30
D. \( 15^{\circ} \)


\( A \) and \( B \) are isotopes. \( B \) and \( C \) are isobars. All three are radioactive.
A. \( A, B \) and \( C \) must belong to the same element
B. \( A, B \) and \( C \) may belong to the same element
c. It is possible that \( A \) will change to \( B \) through a radioactive-decay process
D. It is possible that \( B \) will change to \( C \) through a radio active -decay process


In which reaction \( S O_{2} \) is oxidized?
A . Acidified \( K M n O_{4} \)
B. Acidified \( K_{2} C r_{2} O_{7} \)
c. Acidified \( C_{2} H_{5} O H \)
D. \( H_{2} S_{S} \)


A particle moves along a parabolic path \( \boldsymbol{x}=\boldsymbol{y}^{2}+\boldsymbol{y}+1 \) in such a way that the \( y \)
component of the velocity vector remain \( 4 m s^{-1} \) during the motion. The magnitude of the acceleration of the prtile is
\( \mathbf{A} \cdot 4 m s^{-2} \)
B \( \cdot m s^{-2} \)
\( \mathrm{c} \cdot 32 m s^{-2} \)
D. \( 50 m s^{2} \)


The capacitors of three capacities are in
the ratio \( 1: 2: 3 . \) Their equivalent capacity when connected in parallel is \( \frac{60}{11} \mu F \) more
than that when connected in series. The
individual capacities are :
\( A \cdot 4,6,7 \)
B. 1,2,3
c. 2,3,4
D. 1,3,6


Four particles each of mass \( \boldsymbol{m} \) are
placed at the corners of a square of side length \( l \). The radius of gyration of the system about an axis perpendicular to the square and passing through its
center is:
A \( \frac{l}{\sqrt{2}} \)
B. \( \frac{l}{2} \)
c. \( l \)
D. \( (\sqrt{2}) l \)


Evalaute \( :\left[i^{18}+\left(\frac{1}{i}\right)^{25}\right]^{3} \)


\( \cos ^{3} \theta+\cos ^{3}\left(120^{\circ}+\theta\right)+\cos ^{3}\left(120^{\circ}-\right. \)
\( \boldsymbol{\theta})= \)
\( A \cdot \frac{3}{4} \sin 3 \theta \)
B . \( \frac{3}{4} \cos 3 \theta \)
\( \mathrm{c} \cdot \frac{3}{4} \tan 3 \theta \)
D. \( \frac{3}{4} \cot 3 \theta \)


Assertion
When current through a bulb decreases by \( 0.5 \%, \) the glow of bulb decreases by
\( 1 \% \)
Reason
Glow (Power) which is directly proportional to square of current.
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 incorrect


There is no atmosphere on moon. Therefore,
A. no sound can be heard
B. sound can be easily heard
c. sound is sometimes heard
D. all the above statements are correct


Integral of \( \frac{\left(4 x^{2}-2 \sqrt{x}\right)}{x}+\frac{1}{1+x^{2}}- \)
5 \( \operatorname{cosec}^{2} x \) is


Which of the following statements are
correct?
1. On the application of an electric field, the particles of Iyophobic sol may move either direction or not move at all.
2. The surface tension of Iyophobic sols is similar to that of the dispersion medium.
3. Electro-osmosis is the movement of
the particles of dispersion medium under the influence of an electric field.
A. 1,2 and 3
B. 1 and 3
c. 2 and 3
D. 1 and 2


Equal masses of oil and water are given equal amounts of heat. Then which of the following statement is true?
A. Temperature rise in oil is less than temperature rise in water.
B. Temperature rise in oil is more than temperature rise in water.
c. Temperature rise in oil is equal to the temperature rise in water
D. None of these


An incident ray makes an angle of \( 90^{\circ} \) with the mirror surface. The angle of reflection for this ray is:
A \( .90^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 45^{\circ} \)


\( P \) is a variable point in the square formed by the lines \( \boldsymbol{x}=\pm \mathbf{1} \) and \( \boldsymbol{y}=\pm \mathbf{1} \)
P moves such. that its distance from
the origin is loss than its distance from
any side of square. The area traced by the point \( P \) is
A \( \cdot \frac{4}{3}(4 \sqrt{2}+1) \)
B . \( \frac{4}{3}(4 \sqrt{2}-1) \)
c. \( \frac{4}{3}(4 \sqrt{2}-3) \)
D - \( \frac{4}{3}(4 \sqrt{2}-5) \)


For \( n \) being natural number, if \( ^{2 n} C_{r}= \) \( ^{2 n} C_{r+2}, \) find \( r \)
A \( . n \)
B. \( n-1 \)
\( \mathbf{c} \cdot n-2 \)
D. \( n-3 \)


State Coulomb's law of force in
electrostatics.


The action of concentrated sulphuric
acid on urea \( \left(N H_{2} C O N H_{2}\right) \) results in
the production of a white crystalline solid \( X \) of formula \( H_{3} N O_{3} S . \) This is a
monobasic acid. On treatment with
sodium nitrate and dilute hydrochloride
acid at \( 0^{\circ} \mathrm{C}, \) it liberates 1 mole of \( N_{2} \) per
mol of \( X \) and on addition of aqueous
barium chloride, the resulting solution
yields 1 mole of \( B a S O_{4} \) per mole of \( X \) taken
Deduce the structure of \( \boldsymbol{X} \)


Define the term
dielectric constant. Give its S.l.unit.


\( \lim _{x \rightarrow 1+} \frac{\sqrt{x-1}}{\sqrt{x^{2}-1}+\sqrt{x^{3}-1}} \)


A card is drawn at random from a pack
of 52 cards. Find the probability that the card drawn is a black king.


The IUPAC name of:
A. 2 -methyl-3-bromo hexanal
B. 3-bromo-2-methyl butanal
c. 2 -bromo-3-bromo butanal
D. 3-bromo-2-methyl pentanal


What volume of air (containing \( 20 \% O_{2} \) by volume) will be required to burn
completely \( 10 \mathrm{cm}^{3} \) each of methane and
acetylene
\( \boldsymbol{C H}_{4}+\mathbf{2 O}_{2} \longrightarrow \boldsymbol{C} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( 2 C_{2} H_{2}+5 O_{2} \longrightarrow 4 C O_{2}+2 H_{2} O \)


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


The electronic configuration of four atoms are given in brackets:
\( \mathrm{L}:\left(1 s^{2} 2 s^{2} 2 p^{1}\right) \)
\( \mathrm{M}(: \)
\( \left.1 s^{2} 2 s^{2} 2 p^{5}\right) \)
\( Q:\left(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1}\right) \)
\( 1 s^{2} 2 s^{2} 2 p^{2} \)
The element that would most readily
form a diatomic molecule is :
A. \( Q \)
в. м
c.
D.


Fill in the blanks:
The phenomenon of change in the of light when it passes from one transparent medium to another is
refraction.
A . speedd
B. direction
\( c \cdot \operatorname{both} A \& B \)
D. None of the above


Lanthanide are:
A. 14 element in the sixth period (atomic no. \( =90 \) to 103 ) that are filling \( 4 f \) -sublevel
B. 14 element in the seventh period (atomic no. \( =90 \) to
103) that are filling 5f-sublevel
C. 14 element in the sixth period (atomic no. \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel
D. 14 element in the seventh period (atomic no. \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel


The boiling point of \( D_{2} O \) is greater than
\( H_{2} O . \) It is because:
A \( . D_{2} O \) has lower \( K_{w} \) value
B. \( D_{2} O \) has a lower dielectric constant
\( \mathrm{c} \cdot D_{2} O \) is a associated liquid
D. the molecular weight of \( D_{2} O \) is greater than \( H_{2} O \)


Find the value of \( m \) for which \( 5^{m} \div \)
\( 5^{-3}=5^{5} \)


If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Draw the electron-dot structure for
ethyne. A mixture of ethyne and oxygen is burnt for welding. In your opinion, why cannot we use a mixture of ethyne and air for this purpose?


In Friedel craft alkylation of benzene with methyl chloride, the catalyst used
is:
A. Anhydrous \( A l C l_{3} \)
B. Conc. sulphuric acid
c. Dilute sulphuric acid
D. Anhydrous \( Z n C l_{2} \)


If \( \cos ^{-1}\left(4 x^{3}-3 x\right)=2 \pi-3 \cos ^{-1} x \)
then \( x \) lies in interval
A \( \cdot\left[-1,-\frac{1}{2}\right] \)
в. \( |x|<\frac{1}{2} \)
\( \mathbf{c} \cdot\left[\frac{1}{2}, 1\right. \)
D. None of these


One gram of water on evaporation at atmospheric pressure forms \( 1671 \mathrm{cm}^{3} \) of steam. The heat of vaporisation at this pressure is 540 cal \( / \) gm. The increase in internal energy is
A . 250 call
в. 500 cal
c. 1000 cal
D. 1500call


Find the length of a chord which is at a
distance of \( 4 \mathrm{cm} \) from the centre of a
circle whose radius is \( 5 \mathrm{cm} \)


What is the angle of reflection, if the
raye of light is incident normally on a plane mirror?
\( \mathbf{A} \cdot 0^{\circ} \)
В. \( 90^{\circ} \)
c. will not be reflected
D. None of these


A hydrocarbon contains \( 75 \% \) of carbon It's empirical formula is
A \( \cdot C H_{4} \)
B. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{2} H_{2} \)


\( \int \frac{\cos x}{\sin ^{2} x \cdot(\sin x+\cos x)} d x \) is equal to
\( \mathbf{A} \cdot \log \left|\frac{1+\tan x}{\tan x}\right|-\cot x+C \)
\( ^{\mathbf{B}} \cdot \log \left|\frac{1+\tan x}{\tan x}\right|+C \)
\( ^{\mathbf{C}} \log \left|\frac{1+\tan x}{\tan x}\right|-\tan x+C \)
D \( \cdot \log \left|\frac{1+\tan x}{\tan x}\right|+\cot x+C \)


m/s strikes a hard wall at an angle of
\( 30^{\circ} \) with the wall. It is reflected with the
same speed and at the same angle. If the ball is in contact with the wall for
0.25 seconds, the average force acting on the wall is?
A . \( 48 \mathrm{N} \)
B. 25N
c. \( 12 \mathrm{N} \)
D. 96N


Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behavior is that graphite :
A. has molecules of variable molecular masses like polymers
B. has carbon atoms arranged in large plated of rings of strongly bonded carbon atoms with weak inter plate bonds
C. is a non-crystalline substance.
D. is an allotropic form of diamond


Taxable income of Smt. Rekha (age 45 years) is Rs. 6,50,000 for the financial year \( 2012-13 . \) Compute the income
tax she will have to pay for \( 2012-13 \)


A homogeneous block of mass \( m \), width
\( b \) and height \( h \) is resting on a rough
horizontal surface. A horizontal force \( \boldsymbol{F} \)
is applied to it, which makes it to move
with a constant velocity. The coefficient
of friction between block and surface is
\( \mu . \) Find the greatest height at which
force \( \boldsymbol{F} \) may be applied to slide the
block without tipping over.
\( ^{A} \cdot \frac{b}{2 \mu} \)
B. \( \frac{2 b}{\mu} \)
\( c \cdot b \)
\( \bar{\mu} \)
\( \frac{2 \sqrt{2} b}{\mu} \)


Which of the following has the maximum penetrating power?
\( A \cdot \alpha- \) Jarticle
B. Proton
c. \( \gamma \) - particle
D. Positron


A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and
another point \( Q \) lies to the west at the same distance the magnetic field at \( \mathrm{P} \)
is :
A. greater than at \( Q \)
B. same as at \( Q \)
c. less than at \( Q \)
D. greater or less than at Q depending upon the strength of current


Two identical charged spheres are suspended by strings of equal lengths.
The strings make an angle of \( 30^{\circ} \) with each other. When suspended in a liquid of density \( 0.8 g c m^{-3} \) the angle remains
the same. If density of the material of the sphere is \( 1.6 g c m^{-3}, \) the dielectric constant of the liquid is
A . 1
B. 4
\( c \cdot 3 \)
D.


The velocity of a car increases from
\( 54 k m / h \) to \( 72 k m / h . \) If the mass of the
car is \( 1500 k g, \) find the work done to increase the velocity.
A . \( 27000 J \)
в. \( 131250 J \)
c. \( 0 . \)
D. \( 1500 J \)


Prove:
\( 2 \tan ^{-1}\left(\sqrt{\frac{a-b}{a+b}} \tan \frac{\theta}{2}\right)=\cos ^{-1} \)
\( \left(\frac{a \cos \theta+b}{a+b \cos \theta}\right) \)


A string of length 12 is bent first into a square PQRS and then into an isosceles
triangle PQT by keeping the side PQ of
the square as base then area of the
Square PQRS: area of the triangle PQT=
\( ? \)


In a certain region of space, electric field is along z-direction throughout The magnitude of electric field is, however, not constant but increases
uniformly along the positive z-direction, at the rate of \( 10^{5} N C^{-1} \) per metre. What
is the torque experienced by a system having a total dipole moment equal to \( 10^{-7} \mathrm{C}-\mathrm{m} \) in the negative z-direction?
A. 2 N-m
B. 3 N-m
c. \( 4 \mathrm{N}-\mathrm{m} \)
D. zero


The output of a 2 -input OR gate is zero only when its
A. both inputs are 0 .
B. either input is 1.
c. both inputs are 1
D. either input is 0


Which of the following is factorization of \( \left(-56 m n p^{2}+7 m n p\right) \)
A. \( 7 m n p(-8 p+1) \)
в. \( 7 m n p(8 p+1) \)
\( \mathrm{c} .7 m n p(8 p-1) \)
D. None of these


Branching among angiosperms is due
to
A. Lateral buds
B. Apical buds
c. Deciduous buds
D. Dormant bud


A proton moving with a velocity of \( 1.25 \times 10^{5} \mathrm{m} / \mathrm{s} \) collides with a
stationary helium atom. The velocity of proton after collision is
\( \mathbf{A} \cdot 0.75 \times 10^{5} m s^{-1} \)
B . \( 7.5 \times 10^{5} \mathrm{ms}^{-1} \)
c. \( -7.5 \times 10^{5} \mathrm{ms}^{-1} \)
D. \( 0 m s^{-1} \)


Assertion
Reduction potential of \( M n(+3 t o+2) \) is more positive than \( \boldsymbol{F e}(+\boldsymbol{3} \text { to }+\mathbf{2} \) ).
Reason
lonisation potential of \( M n \) is more than
that of \( F e \)
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


\( v- \) I graphs of a nichrome wire at three
different temperatures \( t_{1}, t_{2} \) and \( t_{3} \) are
shown in the figure. What inference can be drawn from the figure?
This question has multiple correct options
A. Resistance of nichrome wire at \( t_{1} \) is greater than
resistance at \( t_{2} \) and \( t_{3} \)
B . \( t_{1}<t_{2} \) and \( t_{2}<t_{3} \)
c. \( t_{1}<t_{2} \) and \( t_{3}<t_{2} \)
D. Resistance of nichrome wire \( t_{3} \) is greater than
resistance at \( t_{3} \) and \( t_{2} \)


dinitrogen and dioxygen react together
to form different compounds:
Mass of Mass of
dinitrogen
(i)
\[
148
\]
(ii)
\[
148
\]
(iii) \( \quad 28 g \)
(iv)
\[
28 g
\]
\( 80 g \)
(a) Which law of chemical combination
is obeyed by the above experimental data? Give its statement.
(b) Fill in the blanks in the following
conversions:
(i) \( 1 \mathrm{km}= \)
\[
m m=
\]
pm
(ii) \( 1 \mathrm{mg}= \)
\[
-\mathrm{kg}=
\]
(iii) \( 1 \mathrm{mL}= \)
\( \boldsymbol{d} \boldsymbol{m}^{3} \)


If \( \boldsymbol{u}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2} \)
\( \operatorname{then} x \frac{\partial^{2} u}{\partial x \partial y}+y \frac{\partial^{2} u}{\partial y^{2}}=? \)
\( \mathbf{A} \cdot 2(h x+b y) \)
B. \( 2(h x-b y) \)
c. \( 2(b x+h y) \)
D. \( 2(b x-h y) \)


Differentiate between
gravitational water and capillary water


\( \frac{\sin 70^{0}+\cos 40^{0}}{\cos 70^{0}+\sin 40^{0}}= \)


Assertion: The S-S-S bond angle in \( S_{8} \)
molecule is \( 105^{\circ} \)
Reason \( : S_{8} \) has V-shape.
A. If both assertion and reason are true and the reason is correct explanation of the assertion
B. If both assertion and reason are true but reason is not correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


A leaf insect looks like leaves and polar
bear living in snowy regions has white fur on its skin. Although these animals are very different from each other, what
is the one way in which they are similar?
A. They use their bodies to attack enemies
B. They use their bodies to confuse enemies
c. They use their bodies to prepare food
D. They migrate to long distances to protect themselves from enemies.


One light year is equal to
A. 3.26 parsec
B . \( 3.26 \mathrm{km} \)
c. 3.26 AU
D. \( \frac{1}{3.26} \) parsec


Differentiate: \( \sin ^{2} 3 x \cdot \tan ^{3} 2 x \)


Decreasing order of reactivity of \( \boldsymbol{F}_{2} \)
\( C l F \) and \( C l F_{3} \) is :
A. \( C l F_{3}>C l F>F_{2} \)
в. \( C l F>C l F_{3}>F_{2} \)
c. \( C l F_{3}>F_{2}>C l F \)
D. \( F_{2}>C l F>C l F_{3} \)


A packet of 10 CD's contains 4 defected. The CD's are selected at random, one by one, examined and are not replaced. The probability that 7 th \( C D \) is the last defective is
A \( \cdot \frac{2}{21} \)
B. \( \frac{4}{9} \)
c. \( \frac{7}{27} \)
D. None of these


A block 'A' of mass \( 4 k g \) is kept on ground. The coefficient of friction
between the block and the ground is 0.8 The external force of magnitude \( 30 N \) is applied parallel to the ground. The resultant force exerted by the ground on the block is: \( \left(g=10 m s^{-2}\right) \)
A . \( 40 N \)
в. \( 30 N \)
c. zero
D. \( 50 N \)


is toxic substance getting mixed with ground water.
A. Endosulfan
B. Sodium bicarbonate
c. Hydrogen sulphide
D. None of the above


Find the integral curve of the differential equation, \( x(1-x \ln y) \cdot \frac{d y}{d x}+y=0 \) which passes
hrough \( \left(1, \frac{1}{e}\right), \) then \( (2+\ln y) x \) is:
A . 1
B. 2
c. 0
D. None of these


Give three factors on which solubility of solids depends.


Aqueous solution of \( H_{2} S \) and \( S O_{2} \) when mixed together yield:
A. Sulphur and water
B. Sulphur trioxide and water
c. Hydrogen peroxide and sulphur
D. Hydrogen and sulphuric acid


Two rods \( A \) and \( B \). each of equal length
but different materials are suspended from a common support as shown in the figure. The roads \( A \) and \( B \) can support a
maximum load of \( W_{1}=600 \mathrm{N} \) and \( W_{2}= \) \( 6000 \mathrm{N}, \) respectively. If their cross-
sectional areas are \( A_{1}=10 m m^{2} \) and \( A_{2} \)
\( =1000 m m^{2}, \) respectively, then identify the stronger material.


A current of 9.65 A is passed through an aqueous solution of \( N a C l \) using suitable electrodes for 1000 sec. Given
that 1 faraday equals 96500 coulombs
the amount of \( N a O H(\text { mol wt. } 40) \)
formed on electrolysis is:
A . 2.0 g
B. 8.0 g
c. \( 4.0 \mathrm{g} \)
D. \( 1.0 \mathrm{g} \)


There are two hollow spheres made of different materials, one with double the
radius and one fourth wall thickness of
the other are filled with ice. If the time
taken for melting the ice completely in larger sphere is 25 minutes and that for
smaller sphere is 16 minutes, the ratio of the thermal conductivity of the larger sphere to the smaller sphere is :
A . 4: 5
B. 5: 4
\( c \cdot 25: 8 \)
D. 8: 25


What are clones?


Exposed Electric doorbell can be
damaged by
A. Mechanical damage
B. High Electric currents
c. Humidity
D. All of the above


Fo matrices \( A, B \)
\( \boldsymbol{\alpha}(\boldsymbol{A}+\boldsymbol{B})= \)
A. \( \alpha A+\alpha B \)
B . \( \alpha^{2} A+\alpha^{2} B \)
c. \( \sqrt{\alpha} A+\sqrt{\alpha} B \)
D. none


Find \( \int \frac{\sin x}{\sin 4 x} d x \)


Who proposed the planetary model of the atom?
A. John Dalton (early 1800's)
B. Ernest Rutherford (1911)
c. Niels Bohr (1913)
D. Joseph John Thomas (1897)


At an instant a watch shows time 2: 35
when seen through the mirror, what time will be appeared?


The comparison of an unknown quantity
with a known constant quantity is known as:
A. Unit
B. Scale
c. Magnitude
D. Measurement


Which of the following is a unit for intensity of light?
A. candle power
B. Lux
c. Both A \& B
D. None of the above


Pure clay is not suitable for plant growth because
A. It is chemically inert
B. It is chemically active
c. It forms a solid non penetrable mass
D. All of the above


Combustion of hydrogen in a fuel cell at
\( 300 K J \) is represented as \( 2 H_{2}(g)+ \)
\( O_{2}(g) \rightarrow 2 H_{2} O(g) . \) If \( \Delta H \) and \( \Delta G \) are
\( -241.60 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( -228.40 \mathrm{KJ} \mathrm{mol}^{-1} \)
of \( H_{2} O \) respectively, then the value of
\( \Delta S \) for the above process is
A . 4.4
B . -88」
c. \( +88 J \)
D. -44


The reaction of Benzenediazoinum
chloride with aniline yields yellow dye. The name of the yellow dye is
A . p-Hydroxyazobenzene
B. p-Aminoazobenzene
c. p-Nitroazobenzene
D. o-Nitroazobenzene


A charged particle \( A \) of charge \( q=2 C \)
has velocity \( \boldsymbol{v}=\mathbf{1 0 0} \boldsymbol{m} / \boldsymbol{s} . \) When it
passes through point \( A \) and has
velocity in the direction shown, the strength of magnetic field at point \( B \)
due to this moving charge is \( (r=2 m) \)
A \( .2 .5 \mu T \)
B. \( 5.0 \mu T \)
c. \( 2.0 \mu T \)
D. none of these


Which of the following are added to soap to impart antiseptic properties?
A. Bithionol
B. Luminal
c. veronal
D. chloral


The solution of natural rubber in
benzene is an example of:
A. Iyophobic colloids
B. macromolecular colloid
c. multimolecular colloid
D. associated colloid


Assertion
Lead, tin and bismuth are purified by liquation method.
Reason
Lead, tin and bismuth have low m.p. as
compared to impurities.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.


Which of the following are correct statements about white phosphorus
\( \left(P_{4}\right) ? \)
This question has multiple correct options
A. Each P atom has one lone pair of electrons in a
molecules of \( P_{4} \)
B. It has tetrahedral structure with \( 109^{\circ} 28^{\prime} \) bond angle.
C. There are six P-P linkages in a molecule of \( P_{4} \)
D. It undergoes dispropartionation on reaction with alkalies.


Which one is the correct graph for arithmetic growth?
\( A \)
в.
\( c \)
D.


Find the number of four digit numbers
that are divisible by 15 and formed with the digits 0,1,2,3,4,5 when repetition
is not allowed.
A . 25
B. 34
c. 40
D. 55


Find the values of the unknown \( x \) and \( y \)
in the following diagram


If \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) is such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}- \)
11 then \( f \) is
A. injective but not surjective
B. surjective but not injective
c. bijective
D. neither injective nor surjective


If \( \boldsymbol{m} \sin \boldsymbol{\theta}=\boldsymbol{n} \sin (\boldsymbol{\theta}+\boldsymbol{2} \boldsymbol{\alpha}), \) then
\( \tan (\boldsymbol{\theta}+\boldsymbol{\alpha}) \cdot \cot \boldsymbol{\alpha} \) equal to
A. \( \frac{1-n}{1+n} \)
в. \( \frac{m+n}{m-n} \)
c. \( \frac{m-n}{m+n} \)
D. \( \frac{1+n}{1-n} \)


Which of the following is not a water pollutant?
A. Metal nitrates
B. Sewage
c. oxygen
D. Human excreta


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) exhibits:
This question has multiple correct options
A. Emulsifying properties
B. Hardness Removal properties
C . Reducing properties
D. Bleaching property


Oxidation number of three elements
\( A, B \) and \( C \) are +2,+3 and -2 respectively. What is the formula of the compound formed from these three elements?
A. \( A_{2} B C_{3} \)
в. \( A B_{2} C_{4} \)
\( \mathrm{c} \cdot A_{3} B C_{3} \)
D. \( A_{2} B_{2} C_{4} \)


Green light is incident at the polarising angle on a certain transparent medium.
The angle of refraction is \( 30^{\circ} . \) Find
(i) polarising angle, and
(ii) refractive index of the medium.


When a certain amount of ethylene was
burnt, \( 622 \mathrm{kJ} \) heat was evolved. If heat of
combustion of ethylene is 1411 kJ, the
volume of \( \boldsymbol{O}_{2} \) that entered into the
reaction is:
A \( .296 .5 \mathrm{mL} \)
B . 29.62 L
c. \( 6226 \times 22.4 \) 느
D. 22.4 mL


The ease of formation of free radicals
follows the order:
A \( \cdot 3^{\circ}>2^{\circ}>1^{\circ}>\dot{C} H_{3} \)
в. \( \dot{C H}_{3}>1^{\circ}>2^{\circ}>3^{\circ} \)
c. \( 1^{\circ}>2^{\circ}>3^{\circ}>\dot{C} H \)
D \( \cdot 2^{\circ}>1^{\circ}>3^{\circ}>\dot{C} H_{3} \)


When a resistor of \( 2 \Omega \) is connected
across the terminals of a battery a current of \( 2 A \) is found to flow. When a
second resistor of \( 8 \Omega \) is connected in
series with the first, the current is
reduced to \( 1 A . \) The emf and internal
resistance of the battery are
A \( .12 \%, 4 \Omega \)
B. 10V, 2\Omega
\( c \cdot 16 v, 6 \Omega \)
D. 16V, 4\Omega


Which of the following are homosporous?
B. Salvinia, Lycopodiummm
c. selaginella, Salvinia
D. Lycopodium, Equisetum


If \( a=\cos 3 \) and \( b=\sin 8 \) then:
\( \mathbf{A} \cdot a>0, b>0 \)
B. \( a b<0 \)
\( \mathbf{c} \cdot a>b \)
D. \( a b>0 \)


For the reaction at \( 25^{\circ} C, X_{2} O_{4(l)} \longrightarrow \)
\( \mathbf{2} \boldsymbol{X} \boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \)
\( \Delta H=2.1 k c a l \) and \( \Delta S=20 c a l \quad K^{-1} \)
The reaction would be:
A. spontaneous
B. non-spontaneous
c. at equilibrium
D. unpredictable


A fine spectrum is splitting of a
spectrum into closely spaced lines.
A. True
B. False


In which one of the following, the male and female gametophytes don't have free-living independent existence?
A. Pteris
B. Funaria
c. Polytrichum
D. cedrus


Whenever the surfaces in contact, tend
to move or move with respect to each
other, the force of friction comes into
play:
A. only if the objects are solid.
B. only if one of the two objects is liquid
C. only if one of the two objects is gaseous.
D. irrespective of whether the objects are solid, liquid or gaseous.


Two radio active elements \( X \) and \( Y \) have
half lives of 50 minutes and 100
minutes respectively. Samples of \( X \) and initially contain equal number of atoms. After 200 minutes, the ratio
of number of atoms of X unchanged to that of Y is
A .4
B . 2
c. \( 1 / 2 \)
D. \( 1 / 4 \)


A double-slit arrangement produces interference fringes for sodium light \( (\lambda=589 n m) \) that hae an angular
separation of \( 3.50 \times 0^{-3} \)rad. For what
wavelength would the angular separation be \( 10 \% \) greater?
\( \mathbf{A} .527 n m \)
B. \( 648 n m \)
\( \mathrm{c} .722 \mathrm{nm} \)
D. \( 449 n m \)


Which is the elementary quantum of energy?
A. Photon
B. Electron
c. Proton
D. Neutron


(a) What are different losses in
transformer, suggest steps to minimise
the losses in transformer.
(b) State principle and explain the working of transformer


Write the general formula of zwitter ionic form of an amino acid.


How is chlorine prepared in the laboratory? Explain how it reacts with the following along equations
(a) Hot, conc. NaOH
(b) \( N H_{3}(\text { Excess }) \)
\( (c) N a_{2} S_{2} O_{3} \)


An observer \( A \) and a charge \( Q \) are fixed
in a stationary frame \( F_{1} \). an observer \( \mathrm{B} \)
is fixed in a frame \( F_{2}, \) which is moving
with respect to \( \boldsymbol{F}_{1}: \)
This question has multiple correct options
A. both A and B will observe electric fields
B. both A and B will observe magnetic fields
C. neither A nor B will observe magnetic fields
D. B will observe a magnetic field, but A will not


Assume \( \pi=\frac{22}{7}, \) unless stated
otherwise.
Find the volume of a sphere whose
radius is
(i) \( 7 \mathrm{cm} \)
(ii) \( 0.63 \mathrm{m} \)


A closed container is fully insulated
from outside. One half of it is filled with
an ideal gas \( \mathrm{X} \) separated by a plate \( \mathrm{P} \) from the other half \( Y \) which contains a
vacuum as shown in figure. When 0 is removed \( , X \) moves into \( Y \). Which of the
following statements is correct
\begin{tabular}{|c|c|}
\hline\( X \) & \( Y \) \\
gas & vacuum \\
& \( p \) \\
\hline
\end{tabular}
A. No work is done by \( x \)
B. \( x \) decreases in temperature
c. \( x \) increases in internal energy
D. \( x \) doubles in pressure


Which of the following type of movement are seen in human body?
A. Amoeboid
B. Ciliary
C. Flagellar
D. Muscular
\( A \cdot A, b \) and \( c \)
B. \( A, b \) and \( d \)
C. \( A, \) c and \( d \)
D. \( A, b, \) c and \( d \)


The ratio of the size of the image to the
size of the object is known as:
A. the focal plane
B. the transformation ratio
c. the efficiency
D. the magnification ratio


If the arithmetic mean between \( a \) and \( b \)
is twice as great as the geometric mean, show that \( a: b=2+\sqrt{3}: 2- \)
\( \sqrt{3} \)


During secondary growth in a dicot root, cork cambium is formed by the activity of
A. cortex
B. hypodermis
c. pericycle
D. epidermis


n the circuit diagram given below, find:
(A) total resistance of the circuit
(B) total current flowing in the circuit
and
(C) the potential difference across \( \boldsymbol{R}_{1} \)


A ring consisting of two parts \( A D B \) and
\( A C B \) of same conductivity k carries an amount of heat H. The ADB part is now
replaced with another metal keeping
the temperatures \( T_{1} \) and \( T_{2} \) constant. The heat carried increases to 2 H. What
should be the conductivity of the new
ADB part? Given \( \frac{A C B}{A D B}=3 \)
A \( \cdot \frac{7}{3} k \)
B. 2k
c. \( \frac{5}{2} k \)
\( D . \) 3k


Form the differential equation by
eliminating the arbitrary constant \( a \) from the relation \( (x-a)^{2}+y^{2}=1 \)


What is meant by electric flux? Write its
S.I. unit and dimensional formula.


A shopkeeper sold sarees at Rs 266 each after giving \( 5 \% \) discount on labelled price. Had he not given the discount, he would have earned a profit of \( 12 \% \) on the cost price. what was the cost price of each saree ?
This question has multiple correct options
A. Rs 240
B. Rs 260
c. Rs 280
D. Date indepequate
E. None of these


Assertion
Cellulose is not digested by human beings
Reason
Cellulose is a polymer of \( \beta \) -D-glucose
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


In the synthesis of sodium carbonate by solvay (or ammonia-soda) process, the recovery of ammonia is done by treating
\( N H_{4} C l \) with \( C a(O H)_{2} . \) The by-product obtained in this process is:
A. \( C a C l_{2} \)
в. \( N a C l \)
c. \( N a O H \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


Prove that the following functions are
increasing on \( \boldsymbol{R} \)
(i) \( f(x)=3 x^{5}+40 x^{3}+240 x \)
(ii) \( f(x)=4 x^{3}-18 x^{2}+27 x-27 \)


Calculate the oxidation no. of sulphur in
\( \boldsymbol{H}_{2} \underline{\boldsymbol{S}}_{4} \boldsymbol{O}_{\boldsymbol{6}} \)


Which of the following properties of the elements chlorine,bromine and iodine increase with increasing atomic number?

This question has multiple correct options
A. lonization energy
B. Ionic radius
C. Bond energy of the molecule \( X_{2} \)
D. Enthalpy of vaporization


In the following figure, ray PA is
tangent to the circle at \( A \) and \( P B C \) is a
secant. If \( A P=15, B P=10, \) then find \( B C \)


The different in \( \Delta H \) and \( \Delta E \) for the
combustion of methane at \( 27^{\circ} \mathrm{C} \) would
be:
A . 2578 J/mol
B. 2493 J/mol
c. 3256 J/mol
D. none of these


More than \( 70 \% \) of worlds fresh water is
contained in
A. Polarice
B. Antarctica
c. Green land
D. Glaciers and mountains


What is the magnitude of the gravitational force between the earth and a \( 1 \mathrm{kg} \) object on its surface? (Mass
of the earth is \( 6 \times 10^{24} \) kg and radius of
the earth is \( \left.6.4 \times 10^{6}\right) \)


In case of a liquid,
A. only bulk modulus is defined
B. only bulk and Young's modulus are defined
C. only bulk and shear modulus are defined
D. Young's modulus is defined but shear modulus is not defined


Two spherical bodies of mass \( M \) and
\( 5 M \) and radii \( R \) and \( 2 R \) respectively are
released in free space with initial separation between their centres equal
to \( 12 R \) If they attract each other due to
gravitational force only, then the distance covered by the smaller body just before collision is
A . \( 2.5 R \)
в. \( 4.5 R \)
\( c .7 .5 R \)
D. \( 1.5 R \)


Rainwater harvesting is collecting \& storing rainwater, which includes activities aimed at:
A. harvesting surface water
B. groundwater
c. prevention of losses through evaporation and seepage
D. all of the above


In the series \( S c(Z=21) \) to \( Z n(Z=30) \) the enthalpy of atomisation of which element is least?
A. Sç
в. мп
c. \( c u \)
D. zn


In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential, and points outside have negative potential. A positive charge, which is free to move, is placed
inside S.
A. It will remain in equilibrium
B. It can move inside s, but is cannot cross
c. It must cross \( S \) at some time.
D. It may move, but will ultimately return to its starting point


If the coefficients of \( x \) and \( x^{2} \) in the
expansion of \( (1+x)^{m}(1-x)^{n} \) are 3
and -6 respectively. Find the values of
\( m \) and \( n \)


Oxygen is more electronegative than
sulphur, yet \( H_{2} S \) is acidic while \( H_{2} O \) in
neutral. This is because
A. water is a highly associated compound
B. \( H-S \) bond is weaker than \( H-O \) bond
c. \( H_{2} S \) is a gas while \( H_{2} O \) is a liqiud
D. the molecular weight of \( H_{2} S \) is more than that of \( H_{2} O \)


Suggest synthesise for:
\( ^{32} \boldsymbol{P H}_{3}, \boldsymbol{H}_{3}^{32} \boldsymbol{P O}_{3} \) from \( \boldsymbol{C a}_{3}\left(^{32} \boldsymbol{P O}_{4}\right)_{2} \)


A block of mass \( m \) is pulled along a
circular are by means of a constant
horizontal force \( \boldsymbol{F} \) as shown. Work done
by this force in pulling the block from \( \boldsymbol{A} \)
to \( B \) is-
A \( \frac{F R}{2} \)
в. \( F R \)
c. \( \frac{\sqrt{3}}{2} F R \)
D. \( m g R \)


In reversible reactions concentration of:
A. reactants decreases with time at equilibrium
B. products increases with time at equilibrium
C. reactants decreases and then increases with time at equilibrium
D. reactants and products are constant at equilibrium


Match List 1 with List 2 :


Equal currents are passing through two very long and straight parallel wires in the same direction. They will
A. repel each other
B. attract each other
c. lean towards each other
D. neither attract nor repel each other


If the resultant force on a system of
particles is non-zero, then:
A. The linear momentum of the system must increase
B. The velocity of the centre of mass of the system must change.
C. The distance of the centre of mass may remain constant from a fixed point.
D. Kinetic energy of all particles must either increase simultaneously or decrease simultaneously.


\( A \) and \( B \) are two independent events of
an experiment .if \( \boldsymbol{P}(\boldsymbol{n} \boldsymbol{o} \boldsymbol{t} \boldsymbol{B})= \)
\( \mathbf{0 . 6 5}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 8 5}, \) find \( \boldsymbol{P}(\boldsymbol{A}) \)


The phenomenon when a reaction influences the rate of other reaction is
1. homogenous catalysis
2. heterogeneous catalysis
3. induced catalysis
4. competitive catalysis


Which of the following statements is
correct for any thermodynamic system?
A. The internal energy changes in all processes
B. Internal energy and entropy are state functions
C. The change in entropy can never be zero
D. The work done in an adiabatic process is always zero


Assertion
It is harder to open and shut a door if we
apply force near the hinge
Reason
Torque is maximum if force is applied at the hinge of the door
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


At \( 80^{0} \mathrm{C}, \) the vapour pressure of pure liquid \( A \) is \( 250 m m \) of \( H g \) and that of pure liquid B is \( 1000 \mathrm{mm} \) of Hg. If a
solution of \( A \) and \( B \) boils at \( 80^{\circ} \mathrm{C} \) and 1
atm pressure, the amount of A in the
mixture is : \( (1 a t m=760 m m H g) \)
A . 50 mole percent
B. 52 mole percent
c. 32 mole percent
D. 48 mole percent


To obtain maximum intensity of magnetic field at a point the angle between position vector of point and small elements of length of the conductor is
A. 0
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D.


The quantity of electricity required to deposit 1.15 g of sodium from molten \( \mathrm{NaCl}(\mathrm{Na}=23, \mathrm{Cl}=35.5) \) is :
\( A \cdot 1 F \)
в. 0.5 F
c. \( 0.05 \mathrm{F} \)
D. 1.5 F


By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial:
\( \boldsymbol{x}^{4}+\mathbf{1} ; \boldsymbol{x}-\mathbf{1} \)
A \( \cdot x^{3}+x^{2}+x+1,3 \)
B. \( x^{3}+x^{2}+x+1,1 \)
c. \( x^{3}+x^{2}+x+1,5 \)
D. \( x^{3}+x^{2}+x+1,2 \)


Find the differential equation of all the
ellipse whose center at origin and axis are along the coordinate axis.


A sequence of numbers such that the quotient of any two successive members of the sequence is a constant
called the common ratio of the
sequence is known as:
A. geometric series
B. arithmetic progression
c. harmonic sequence
D. geometric sequence


Ultimate source of hydroelectricity is
the
A. thermal energy
B. solar energy
c. hydrothermal energy
D. wind energy


Prokaryotic cells are ............ organism.


Which of the following metals is used in ceramic applications? This question has multiple correct options
A. Cerium
B. Neodymium
c. Praseodymium
D. None of these


One angle of a six-sided polygon is \( 140^{\circ} \)
and the other angles are equal. Find the measure of each equal angle.
\( \mathbf{A} \cdot 116^{\circ} \)
B . \( 130^{\circ} \)
c. \( 120^{\circ} \)
D. \( 110^{\circ} \)


List I
A) Salt bridge
Reduction
B) Standard hydrogen electrode 2 )
Oxidation
C) Cathode
3) Reference
electrode
D) Anode
4) \( \mathrm{KCl}, \mathrm{KNO}_{3} \)
\( (\text { or }) \mathrm{NH}_{4} \mathrm{NO}_{3} \)
The correct match is :
A. 3421
B. 4 312
c. 4321
D. 1234


Which of the following organisms reproduce asexually?
A. Archaebacteria
B. Protists
c. Rats
D. Both A and B


Evaluate \( \lim _{x \rightarrow-2^{+}} \frac{x^{2}-1}{2 x+4} \)


The position vector of a particle \( \vec{R} \) as a function of time is given by:
\( \overrightarrow{\boldsymbol{R}}=\boldsymbol{4} \sin (2 \pi t) \hat{\hat{i}}+4 \cos (2 \pi t) \hat{j} \)
where \( R \) is in meters, \( t \) is in seconds
and \( \hat{i} \) and \( \hat{j} \) denote unit vectors along \( x \) and y- directions, respectively. Which one of the following statements is wrong for the motion of particle?
A. Path of the particle is a circle of radius \( 4 \mathrm{m} \)
B. Acceleration vector is along \( -\vec{R} \).
C. Magnitude of acceleration vector is \( \frac{v^{2}}{R} \), where \( v \) is th velocity of particle
D. Magnitude of the velocity of particle is \( 8 \mathrm{m} / \mathrm{s} \)


The total number of stereoisomers of
\( \left(\boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2}\right)_{3} \boldsymbol{C H} \) is:
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. 5


A solid object when seen from one side
looks the same when viewed from the
top. Which of these shapes could it be?
\( A \)
B.
\( c \)
D.


Which of following metal is extracted by electrometallurgical method-
This question has multiple correct options
A. \( C u \)
в. \( F e \)
\( c . N a \)
D. \( A g \)


Mass number is denoted by:
\( A \cdot D \)
B. s
\( c \cdot A \)
D. z


Choose the correct answer from the
alternatives given in the brackets. An electric current through a metallic
conductor produces around it.
A . heat
B . light
c. magnetic field
D. mechanical force


The products \( (Y) \) and \( (Z) \) are
respectively:
\[
\mathrm{NH}_{3}+\mathrm{Cl}_{2}(\mathrm{excess}) \rightarrow \text { Exlosive substance }(\mathrm{X})
\]
\( \mathbf{A} \cdot N H_{3} \) and \( C l_{2} \)
\( B . N_{2} \) and \( C l_{2} \)
\( \mathbf{C} \cdot N H_{2}-N H_{2} \) and \( C l_{2} \)
D. \( H N=N H \) and \( C l_{2} \)


Assertion
The equation \( \boldsymbol{f}(\boldsymbol{x})\left(\boldsymbol{f}^{\prime \prime}(\boldsymbol{x})\right)^{2}+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}^{\prime}(\boldsymbol{x}) \boldsymbol{f}^{\prime \prime \prime}(\boldsymbol{x})+\left(\boldsymbol{f}^{\prime}(\boldsymbol{x})\right)^{2} \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})= \)
0 has atleast 5 real roots
Reason
The equation \( f(x)=0 \) has atleast 3
real distinct roots
\& if \( f(x)=0 \) has \( k \)
real distinct roots, then \( f^{\prime}(x)=0 \) has
atleast k-1 distinct roots.
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


According to the Lewis acid-base
concept:
A. species in which the central atom has completed octet can not act as an acid
B. negatively charged ions are acids
C. molecule in which a central atom has vacant d-
orbitals available acts as an acid
D. all positively charged ions are bases


Flg can maintain community structure during food scarcity in tropical deciduous forest these are act as:
A. Exotic species
B. Pioneer species
c. Edge species
D. Key stone species


Find the value of \( \sin ^{-1} x+\sin ^{-1} \frac{1}{x}+ \)
\( \cos ^{-1} x+\cos ^{-1} \frac{1}{x} \)
A. \( -\pi \)
в. \( +\pi \)
\( c .-2 \pi \)
D. \( +2 \pi \)


Describe a Pyrometer.


Define sure event.


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)


Three numbers whose sum is 15 are in
A.P. If 1,4,19 be added to them
respectively, then they are, in \( G . P . \) Find
the numbers.


Most carbon dioxide in blood is in the
form of
A. carbon dioxide
B. carbonic acid
c. carbon monoxide
D. hydrogencarbonate


A steel cylindrical rod of length \( l \) and
radius \( r \) is suspended by its end from the ceiling. Find the elastic deformation
energy \( U \) of the rod.
A \( \cdot U=\frac{1}{6} \pi r^{2} \rho^{2} g^{2} \frac{l^{3}}{E} \)
B. \( U=\frac{5}{6} \pi r^{2} \rho^{2} g^{2} \frac{l^{3}}{E} \)
\( ^{\mathrm{C}} U=\frac{1}{6} \pi r^{2} \rho^{2} g^{2} \frac{2 l^{3}}{E} \)
D. \( U=\frac{5}{6} \pi r^{2} \rho^{2} g^{2} \frac{2 l^{3}}{E} \)


Estimate the cell potential of a Daniel cell having \( 1.0 M Z n^{++} \) and originally having \( 1.0 M C u^{++} \) after sufficient
\( N H_{3} \) has been added to the cathode
compartment to make \( N H_{3} \)
concentration \( 2.0 M \) at equilibrium.
\( \operatorname{Given} \boldsymbol{K}_{f} \) for \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+}=\mathbf{1} \times \)
\( 10^{12}, E^{o} \) for the reaction, \( Z n+ \)
\( \boldsymbol{C u}^{2+} \longrightarrow Z \boldsymbol{n}^{2+}+\boldsymbol{C u} \quad \mathbf{1 . 1} \boldsymbol{V} \) (Take
\( \frac{\mathbf{2 . 3 0 3} \boldsymbol{R} \boldsymbol{T}}{\boldsymbol{F}}=\mathbf{0 . 0 6} \log \mathbf{6 . 2 5}=\mathbf{0 . 8} \mathbf{)} \)


Laminaria and Fucus belongs to
A. Chlorophyceae
B. Rhodophyceae
c. Phaeophyceae
D. Cyanophyceae


Find the cube root of 5832


Hard, lignified, thick, walled, long and pointed cells in plants are
A. Parenchyma
B. Sclerenchymatous fibre
c. collenchyma
D. Sclereids


The chemical formula of tear gas is:
A \( \cdot C O C l_{2} \)
в. \( C_{10} H_{5} \) Сl \( N_{2} \)
\( c \cdot C l_{2} \)
D. \( P h C O C H_{2} C l \)


A charge of \( +2 Q \) resides inside of a conducting sphere with a hollow center If the net charge on the conducting
sphere is \( +5 Q, \) what is the amount of charge on the outer surface of the
conducting sphere?
\( A \cdot 2 Q \)
в. \( 3 Q \)
\( c .5 Q \)
D. \( 7 Q \)


The acid strength of active methylene group in given compounds decreases
as:
(a) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \)
(b) \( C H_{3} C O C H_{2} C O C H_{3} \)
(c) \( C_{2} H_{5} O O C C H_{2} C O O C_{2} H_{5} \)
\( \mathbf{A} \cdot a>b>c \)
В . \( c>a>b \)
\( \mathbf{c} \cdot a>c>b \)
D. \( b>a>c \)


Residual air mostly occurs in
A. Alveoli
B. Bronchus
c. Nostnls
D. Trachea


There are two old wells in the area where
Punita lives. Her grandmother says that about fifteen-twenty years ago there was water in these wells. The wells
could have dried up because:
Water is being pumped up from under the ground with the help of electric
motors.
The lakes in which rainwater used to
collect are no longer there.
The soil around trees and parks is now covered with cement.
Is there some other reason for this?
Explain


Heavy water is obtained by?
A. boiling water
B. heatiing \( H_{2} O_{2} \)
C. Prolonged electrolysis of \( H_{2} O \)
D. All of these


The area of the region bounded by the
curve \( \boldsymbol{x}=\boldsymbol{y}^{2}-\boldsymbol{2} \) and \( \boldsymbol{x}=\boldsymbol{y} \) is
A \( \cdot \frac{9}{4} \)
B. 9
c. \( \frac{9}{2} \)
D.


Derive the relation between half life and
rate constant for a first order reaction.


Sl unit of the angular velocity is
\( A \cdot m / s \)
B. rad
\( c \cdot \operatorname{rad} / \mathrm{s} \)
D. m/rad


Which of the following will not act as a tranquilizer?
A. Equanil
B. Analgin
c. Meprobamate
D. chlordiazepoxide


\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{B} \boldsymbol{a}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
Whai is \( K_{s p} \) for above reaction?
\( \mathbf{A} \cdot\left[B a^{2+}\right]\left[S O_{4}^{2-}\right] \)
\( ^{\mathbf{B} \cdot} \frac{\left[B a^{2+}\right]\left[S O_{4}^{2-}\right]}{B a S O_{4}} \)
\( ^{\mathrm{c}} \cdot \frac{\left[B a^{2+}\right]\left[S O_{4}^{2-}\right]}{\left[B a S O_{4}\right]} \)
D. None


Which of the following is correct
regarding mechanical passivity?
A. Visible metal oxide film is formed
B. Visible metal oxide film prevents dissociation of metal
C. Fe, Mn and Pb exhibit mechanical passivity
D. All the above


Calculate number of photons passing
through a ring of unit area in unit time
if light of intensity \( 100 W m^{2} \) and of
wavelength \( 400 n m \) is falling normally on the ring.


Mean life of a radioactive sample is 100
s. Then its half-life(in minutes) is.
A. 0.693
B.
\( c \cdot 10^{-4} \)
D. 1.155


Which of the following has the highest specific heat?
A. water
B. Mercury
c. Kerosene
D. copper


Which of the following layer of soil is called as zone of leaching?
A. \( A_{0} \)
B. \( A_{00} \)
c. \( A_{2} \)
D. \( A_{1} \)


tRNA has the function of
A. Transcription
B. Carrier for attaching amino acids over mRNA template
c. Transferring information to mRNA
D. Carrying genetic code to cytoplasm


The centre, vertex, focus of a conic are
\( (0,0),(0,5),(0,6) . \) Its length of latus rectum is
A \( \cdot \frac{11}{5} \)
в. \( \frac{7}{5} \)
c. \( \frac{14}{5} \)
D. \( \frac{22}{5} \)


A number which is assigned to each
atom or ion in a compound which explains its degree of oxidation is called:
A. oxidation degree
B. oxidation number
c. oxidation state
D. both \( B \) and \( C \)


What is the concentration of \( A g^{+} \) in a
solution made by dissolving both
\( A g_{2} C r O_{4} \) and \( A g_{2} C_{2} O_{4} \) until
saturation is reached with respect to
both salts?
\( \left[\boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)=\boldsymbol{2} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{1 1}}, \boldsymbol{K}_{\boldsymbol{s p}}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}\right)=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 2}}\right] \)
A \( \cdot 2.80 \times 10^{-4} \)
B . \( 7.6 \times 10^{-5} \)
c. \( 6.63 \times 10^{-6} \)
D. \( 3.52 \times 10^{-4} \)


On plotting a graph between substrate concentration and time, a scientist found a sigmoid curve. The enzyme is
A. Allosteric
B. Apoenzyme
c. Mono enzyme
D. Isozyme


Which of the following metabolites enter the TCA cycle during glucose oxidation?
A. Oxaloacetic acid
B. Pyruvic acid
c. Acetyl CoA
D. Malic acid


A haploid cell doesn't undergo
A. Mitosis
B. Meiosis
c. ATP production
D. DNA replication
E. Transcription


A pair of fair dice is thrown independently three times. The probability of getting a score of exactly
9 twice is-
A \( \cdot \frac{1}{729} \)
в. \( \frac{8}{9} \)
c. \( \frac{8}{729} \)
D. \( \frac{8}{243} \)


Which of the following has same number of protons?
A. Isobars
B. Isotropes
c. Isotopes
D. Isotones


Three coins are tossed. Describe
two events \( A \) and \( B \) which are mutually
exclusive.


Which of the following is known as artificial silk?
A. Rayon
B. Nylon
c. Polyester
D. Acrylic


Which of the following is not a metalloid?
A. Silicon
B. Germanium
c. Arsenic
D. Beryllium


What is the molarity of \( H C l \) in a solution prepared by dissolving \( 5.5 \mathrm{g} \) \( H C l \) in 200 g ethanol if the density of the solution is 0.79 g/ mL?
A . 0.58 M
B. 0.21
c. 0.93 M
D. 1.7 м


The combined equation of the three sides of a triangle is
\( \left(x^{2}-y^{2}\right)(2 x+3 y-6) . \) If the point
\( (0, a) \) lies in the interior of this triangle
then
A \( .-2<\alpha<0 \)
B. \( -2<\alpha<2 \)
c. \( 0<\alpha<2 \)
D. \( \alpha \geq 2 \)


Factorize the following
\( x^{2}-2 x-99 \)
A. \( (x+9)(x-11) \)
В. \( (x-9)(x-11) \)
c. \( (x+9)(x+11) \)
D. None of these


Differentiate between regular and
irregular reflection.


Select correct statement(s).
This question has multiple correct options
A. Nickel (II) compounds tend to be thermodynamically more stable than platinum (II)
B. Platinum (IV) compounds are relatively more stable than nickel (IV) compounds
\( \mathbf{C} \cdot K_{2} P t^{I V} C l_{6} \) exists
D. \( K_{2} N i^{I V} C l_{6} \) exists


The area of a circular playground is
\( 22176 m^{2} . \) Find the cost of fencing at the
rate of \( R s .50 \) per \( m \)


Vessels are found in
A. Ephedra
B. All gymnosperms
c. Funaria
D. None of the above


A man sees a small stationary fish deep in a very clear lake and shoots it accurately. He will
A . hit
B. miss
c. hit but fish will not die
D. may hit or miss depending on the bullet


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


When 4 -pentene-1-ol is treated with aqueous bromide, a cyclic bromosubstituted ether is formed
rather than expected bromohydrine. Select the explanation that best
account for the result.
A. The ether is the result of a hydride shift in the initially formed carbocation
B. The ether is formed in the intramolecular nucleophilic attack on the initially formed bromonium ion
C. The reaction is initiated by the deprotonation of the \( O H \) group
D. The initially formed bromonium ion undergoes an alkene shift to form new \( C-O \) bond


Complete the given statement, the
strength of an electromagnet can be:
A. increased by adding a ferromagnetic core
B. decreased by adding turns of wire to the coil
C. increased by reducing the current through the wire
D. increased by adding an aluminum core
E. decreased by adding more layers of wire to the coil


The sun delivers \( 10^{3} W m^{-2} \) of
electromagnetic flux on the earth's surface. The total power that is incident
on a roof of dimensions \( 6 m \times 30 m \) is
A . \( 1.8 \times 10^{5} \mathrm{W} \)
В. \( 7.2 \times 10^{5} \mathrm{W} \)
\( \mathbf{c} \cdot 0.9 \times 10^{5} W \)
D. \( 4.5 \times 10^{5} \mathrm{W} \)


Find the distance between the origin
and the point (5,12)


The internal energy of a perfect gas depends on:
A. Pressure
B. Temperature
c. volume
D. specific heat


How can the following conversation be brought about:
Propanoic acid to ethylamine.


Prove that \( \frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left[\frac{\pi}{2}+x\right]}= \)
\( \cot ^{2} x \)


Let the function \( f \) be defined by \( f(x)= \) \( 5 x-2 a, \) where \( a \) is a constant. If
\( \boldsymbol{f}(\mathbf{1 0})+\boldsymbol{f}(\mathbf{5})=\mathbf{5 5}, \) what is the value of
\( \boldsymbol{a} ? \)
A . -
B. 0
\( c \cdot 5 \)
D. 10
E. 20


Molten \( A l C l_{3} \) is electrolysed with the current of 0.5 empere to produced 27 g
Al. Number of Farady used are:
\( A \cdot 3 \)
B. 5
\( c .6 \)
D. None of these


cost of 2 articles are ratio 3: 2 On the
first there is \( 40 \% \) loss on the second
\( 30 \% \) gain. What is overall percentage of loss?
A . 12\%
B. 30\%
c. \( 40 \% \)
D. 10\%


Find the time in which Rs. 2,000 will amount to Rs. 2,330 at \( 11 \% \) p.a.


Cholecystokinin involves in
A. controlling growth
B. Controlling stress
c. controlling appetite
D. None of the above


Pruning of plants promotes branching because the axillary buds get sensitized to
A. Ethylene
B. Gibberellin
c. cytokinin
D. Indole acetic acid


Which of the following are polyhalogen compounds?
A. Dichloromethane
B. Chloroform
c. Tetrachloromethane
D. All of the above


Which family outer shell configuration
is \( n s^{2} n p^{5} ? \)
A. Alkali metals
B. Alkali earth metalss
c. chalcogen family
D. Halogen family


What does the equation \( \frac{x^{2}}{r-1}- \) \( \frac{y^{2}}{1+r}=1, r>1, \) represents


\( \mathrm{f}\left[\begin{array}{l}\mathbf{4} \\ \mathbf{1} \\ \mathbf{3}\end{array}\right] \boldsymbol{A}=\left[\begin{array}{lll}-\mathbf{4} & \mathbf{8} & \mathbf{4} \\ -\mathbf{1} & \mathbf{2} & \mathbf{1} \\ -\mathbf{3} & \mathbf{6} & \mathbf{3}\end{array}\right], \) if \( \boldsymbol{A}= \)
\( \boldsymbol{a} \quad \boldsymbol{b} \quad \boldsymbol{c}] \)
Find \( a+b+c \)


In dim light:
A. rods are sensitive but cones are not
B. cones are sensitive but rods are not
C. both rods and cones are sensitive
D. neither rods nor cones are sensitive


A glass tumbler containing ice shows droplets of water on the outer surface
because
A. The outer surface of the tumbler shows hygroscopic effect
B. Water from inside oozes out through the wall of the tumbler
c. The moisture in the air on coming in contact with the cold surface of the tumbler condenses in the form of droplets of water
D. (A) and (B)


Densities of diamond and graphite are
\( 3.5 \mathrm{g} / \mathrm{mL} \) and \( 2.3 \mathrm{g} / \mathrm{mL} \)
\( \boldsymbol{C}(\text {diamond}) \rightleftharpoons \boldsymbol{C}(\text {graphite}) \)
\( \boldsymbol{\Delta}_{r} \boldsymbol{H}=-\mathbf{1 . 9} \mathbf{k J} / \mathrm{mole} \)
Favourable conditions for formation of
diamond are:
A. high pressure and low pressure
B. low pressure and high temperature
c. high pressure and high temperature
D. low pressure and low temperature


Choose the answer below that
accurately describes the correct
molecular shape for the molecule
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4} \)
A. Tetrahedral
B. Trigonal pyramidal
c. Trigonal bipyramidal
D. Square pyramidal


Assertion
The maximum stress value below which
the strain is fully recoverable is called the elastic limit.
Reason
All materials are elastic to some extent
but the degree varies.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the ratio of diameters, lengths and
Young's moduli of steel and brass wires
shown in the figure are \( p, q \) and \( r \)
respectively. Then the corresponding ratio of increase in their lengths would
be:
A \( \frac{3 q}{5 n^{2} r} \)
в. \( \frac{5 q}{3 p^{2}} \)
c. \( \frac{3 q}{5 p r} \)
D. \( \frac{5 q}{p r} \)


Evaluate: \( \lim _{x \rightarrow 20} \frac{\sqrt{x+5}+5}{\sqrt{x+5}-5} \)
\( A \)
B. 2
\( c \cdot 4 \)
D. \( \infty \)


Which of the following is used for punching holes in metals:
A. Hydraulic brakes
B. Hydraulic jack
c. Hydraulic press
D. All


Light is incident on a polarizer with
intensity \( I_{0} . \) A second prism called
analyser is kept at a angle of \( 15^{\circ}, \) from the first polarizer then the intensity of final emergent light will be?


In split genes, the coding sequences are called as
A. Introns
B. Operons
c. Exons
D. Cistrons


Assertion
A capacitor blocks direct current in the
steady state.
Reason
The capacitive reactance of the capacitor is inversely proportional to
frequency f of the source of e.m.f...
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


Weight of diamonds are measured
in
A . aunce
в. \( \mathrm{kg} \)
c. carats
D. pounds


What is the purpose of using coke?
A. Reducing agent
B. Oxidising agent
c. both A and B
D. none of the above


In which case(s) does carbocation
formed after protonation undergo resonance?

This question has multiple correct options
\( A \)
\( (A) \)
в.
(B)
\( c \)
\( (c) \)
\( D \)
\( (D) \)


Which of the following quantities is scalar?
A. Dipole moment
B. Electric force
c. Electric field intensity
D. Electric potential


Give two point of difference between a step-up transformer and a step-down transformer?


Which liquid metal is used for making thermometers?
A. Mercury
B. Bromine
c. lodine
D. Cadmium


The electronic configuration of \( _{59} P r \) (Praseodymium) is?
A \( \cdot\left[_{54} X e\right] 4 f^{2} 5 d^{1} 6 s^{2} \)
B . \( \left[_{54} X e\right] 4 f^{1} 5 d^{2} 6 s^{2} \)
c. \( \left[_{54} X e\right] 4 f^{3} 6 s^{2} \)
D・ \( \left[_{54} X e\right] 4 f^{3} 5 d^{2} \)


If in Millikan's oil drop experiment charges on drops are found to be
\( 8 \mu C, 12 \mu C, 20 \mu C, \) then quanta of quanta of charge is :-
\( A \cdot 8 \mu C \)
в. \( 4 \mu C C \)
c. \( 20 \mu C \)
D. \( 12 \mu C \)


if \( ^{2017} c_{0}+^{2017} c_{1}+^{2017} c_{2}+ \)
\( \ldots+^{2017} c_{1008}=\lambda^{2}(\lambda>0), \) then
remainder when \( \lambda \) is divided by 33 is
\( A \cdot 8 \)
B. 13
\( c \cdot 17 \)
D. 25


Consider the given statements:
I. Maltose is also known as malt sugar.
II. Sucrose is also known as cane sugar.
III. Lactose is also known as grape
sugar.
IV. Starch is also known as amylum.
The correct statement(s) is/are:
\( A \cdot \) ।, ॥ and IV
B. I, II and III
c. ॥, ॥ा and IV
D. All


Find the value of \( k \) for which the
following system of equations has no solution:
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{k} \boldsymbol{y}=\mathbf{1 1} \)
\( 5 x-7 y=5 \)


Construct the graphs of the following
functions.
\( \boldsymbol{y}=\mathbf{1} /|\boldsymbol{x}| \)


(a) Name any two places where it is essential to install electrostatic
precipitators to do so?
(b) Mention one limitation of
electrostatic precipitator


The movement of the dispersion
medium in an electric field when the
dispersed particles are prevented from moving is called:
A. cataphoresis
B. electrophoresis
c. electro-osmosis
D. brownian movement


Let \( F_{1} \) be the set all of parallelograms, \( F_{2} \)
be the set of the rectangles, \( F_{3} \) be the
set of rhombuses, \( F_{4} \) be the set of
squares \( F_{5} \) be the set of trapezium in a
plane then \( F_{1}= \)
A. \( F_{2} \cap F_{3} \)
B. \( F_{2} \cup F_{3} \cup F_{4} \)
c. \( F_{3} \cup F_{4} \cup F_{5} \)
D. \( F_{3} \cap F_{1} \)


Ionic compounds are
A . crystalline
B. highly soluble in water
C. hard and rigid
D. All of the above


Assertion
In projectile motion at any two positions \( \frac{\overrightarrow{\boldsymbol{v}}_{2}-\overrightarrow{\boldsymbol{v}}_{1}}{\boldsymbol{t}_{2}-\boldsymbol{t}_{1}} \) always remains constant.
Reason
The given quantity is average
acceleration, which should remain
constant as acceleration is constant
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion is incorrect but Reason is correct


Find the ratio in which the line segment
joining the points (4,8,10) and (6,10,-8) is divided by the \( Y Z- \) plane


If \( \vec{V}=3 \hat{i}+4 \hat{j} \) then, with what scalar 'C must it be multiplied so that \( C|\overrightarrow{\boldsymbol{V}}|= \)
\( \mathbf{7 . 5}: \)
A . 0.5
B . 2.
c. 1.5
D. 3.5


Number of chambers in the heart of
cockroach is
A. 5
B. 9
\( c \cdot 13 \)
D. 16


Diagram shows an electron gun inside
cathode ray tube. Label the screen with
the letter \( S \).


If a force \( 10 \hat{i}+15 \hat{j}+25 \hat{k} \) acts on a
system and gives an acceleration \( 2 \hat{\mathbf{i}}+ \) \( 3 \hat{j}-5 \hat{k} \) to the centre of mass of the
system, the mass of the system is
A . 5 units
B. \( \sqrt{38} \)units
c. \( 5 \sqrt{38} \) units
D. Given data is not correct


The wave number of first line of Balmer
series of hydrogen atom is \( 15200 \mathrm{cm}^{-1} \) What is the wave number of first line of
Balmer series of \( L i^{2+} \) ion.
A. \( 15200 \mathrm{cm}^{-1} \)
В. \( 136800 m^{-1} \)
c. \( 76000 \mathrm{cm}^{-1} \)
D. \( 13680 \mathrm{cm}^{-1} \)


In Rutherford's \( \alpha \) -particle scattering
experiment, a very small fraction of \( \alpha \)
particles were deflected by \( 180^{\circ} . \) What did the conclude from this observation?
A. All the positive charge and mass of the atom occupy very little space.
B. Most of the space inside the atom is empty
c. All the positive charge and mass of the atom were concentrated in a very small volume.
D. Both A and B


Which of the following heavenly bodies is different from others?
A. Ursa Major
B. Ursa Minor
c. Alpha Centauri
D. Scorpio


Find the equation of the following curve in cartesian form \( \boldsymbol{x}=-\mathbf{1}+\mathbf{2} \sin \boldsymbol{\theta}, \boldsymbol{y}= \)
\( 1+2 \cos \theta . \) find the centre and radius
of circle.


There is a regular bus service between
towns \( A \) and \( B, \) with a bus leaving towns A and B every \( \boldsymbol{T} \) minutes. A cyclist
moving with a speed of \( 20 k m h^{-1} \) in the direction \( A \) to \( B \) notices that a bus goes
past him every 18 minutes in the direction of his travel and every
6 mins in the opposite direction. What is the speed with which buses travel between towns \( A \) and \( B ? \) (Assume the
speeds to be constant.)
\( \mathbf{A} \cdot 30 k m h^{-1} \)
В. \( 40 k m h^{-1} \)
\( \mathrm{c} \cdot 50 k m h^{-1} \)
D. \( 60 k m h^{-1} \)


The purity of a solute collected between two times t1 and t2 during chromatographic separation is :
A. amount of solvent eluted + amount of impurity eluted
B. amount of solute eluted / amount of impurity eluted
c. amount of solvent eluted / amount of impurity eluted
D. amount of solute eluted - amount of impurity eluted


Write the formula of compound \( \boldsymbol{A} \)
formed.


During adverse season, therophytes survive as
A. Bulbs
B. Corms
c. Rhizomes
D. seed


Which of the following is true for RBCs?
A. They have no nucleus.
B. They are replaced in the liver.
C. They are outnumbered by white blood cells in the circulatory system.
D. They are made in the spleen.
E. They are the sites of rapid protein synthesis.


The oxide that \( \operatorname{gives} H_{2} O_{2} \) on treatment with a dilute acid is :
A \( \cdot P b O_{2} \)
в. \( N a_{2} O_{2} \)
\( \mathrm{c} \cdot M n O_{2} \)
D. \( B a O_{2} \)


A long solenoid of radius \( R \) carries a time (t)-dependent current \( \boldsymbol{I}(\boldsymbol{t})= \)
\( \boldsymbol{I}_{0} \boldsymbol{t}(\mathbf{1}-\boldsymbol{t}) \cdot \mathbf{A} \) ring of radius \( 2 \boldsymbol{R} \) is placed
coaxially near its middle. During the
time interval \( 0 \leq t \leq 1, \) the induced
current \( \left(I_{R}\right) \) and the induced
\( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F}\left(\boldsymbol{V}_{\boldsymbol{R}}\right) \) in the ring change as:
\( \mathbf{A} \cdot \) At \( t=0.5 \) direction of \( I_{R} \) reverses and \( V_{R} \) is zero.
B. Direction if \( I_{R} \) remains unchanged and \( V_{R} \) is zero at \( t=0.25 \)
C . At \( t=0.25 \) direction of \( I_{R} \) reverses and \( V_{R} \) is maximum.
D. Direction of \( I_{R} \) remains unchanged and \( V_{R} \) is maximum at \( t=0.5 \)


A solid sphere of radius \( R \) made of
material of bulk modulus \( \boldsymbol{K} \), is
surrounded by a liquid in a cylindrical container. A massless piston of area \( \boldsymbol{A} \) floats on the surface of liquid. When a mass \( m \) is placed on the piston to compress the liquid, the fractional
change in the radius of the sphere \( \boldsymbol{\delta} \boldsymbol{R} / \boldsymbol{R} \) is :
A. \( m g / A K \)
в. \( m g / 3 A K \)
c. \( m g / A \)
D. \( m g / 3 A R \)


A hollow sphere of radius \( 2 \mathrm{cm} \) is attached to an \( 18 \mathrm{cm} \) long thread to
make a pendulum. Find the time period of oscillation of this pendulum. How does it differ from the time period calculated using the formula for a
simple pendulum?


Which formula is used to calculate the
coefficient of viscosity of a given liquid in the laboratory (symbols have their usual meanings)?
A \( \cdot_{\eta}=\frac{9}{2}(\rho-\sigma) g \frac{r^{2}}{v} \)
в. \( \frac{2}{9}(\rho-\sigma) g \frac{r^{2}}{v} \)
\( ^{\mathrm{c}} \cdot \frac{2}{9}(\rho-\sigma) g \frac{r^{2}}{v g} \)
\( ^{\mathrm{D}} \cdot \frac{2}{9}(\rho-\sigma) g \frac{v g}{r^{2}} \)


Mineral requirement is studied through hydroponics which is related to growing plants in
A. Soil
B. Air
c. solution
D. Ponds


The steel wire can withstand a load up
to \( 2940 \mathrm{N} \). A load of \( 150 \mathrm{kg} \) is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position so that the wire does not break
A . 30
B. 60
\( c .80 \)
D. \( 85^{\circ} \)


Q Type your question-
The diagram shows the ride (yellow) and the girl (red) as viewed from above at the instant the ride is stopped. The
curved arrow shows the direction of the
rotation of the ride before it was
stopped.
Which arrow shows the direction of the
girl's velocity at the instant she flies off
the ride?
\( A \)
B.
\( c \)
D.
三


Find the number of arrangements ofthe letters of the word

INDEPENDENCE.In how many of
these arrangements so the words start
with \( \boldsymbol{P} \)


o Prove: \( -\frac{\boldsymbol{A} \boldsymbol{M}}{\boldsymbol{A B}}=\frac{\boldsymbol{A} \boldsymbol{N}}{\boldsymbol{A D}} \)


The ratio in which the area bounded by
the curves \( y^{2}=4 x \) and \( x^{2}=4 y \)
is divided by the line \( x=1 \) is
A. 64: 49
B. 15: 34
c. 15: 49
D. None o fthese


In Young's double slits experiment, if the separation between the slits is halved, and the distance between the
slits and the screen is doubled, then the fringe width compared to the original one will be?
A. Unchanged
B. Halved
c. Doubled
D. Quadrupled
E. Fringes will disappear


At \( 298 \mathrm{K} \), the standard reduce
potentials are \( 1.51 \mathrm{V} \) for \( \mathrm{MnO}_{4}^{-}, 1.36 \mathrm{V} \) for \( \boldsymbol{C l} \boldsymbol{l}_{2} \mid \boldsymbol{C l}^{-}, 1.07 \mathrm{V} \) for \( \boldsymbol{B} \boldsymbol{r}_{2} \mid \boldsymbol{B r}^{-}, 0.54 \mathrm{V} \) for
\( I_{2} \mid I^{-} . \) At \( p H=3, \) permangnate is expected to oxidize:
\( \left(\frac{R T}{F}=0.059\right) \)
A \( . C l^{-} \) and \( B r^{-} \)
B. \( B r^{-} \) and \( I^{-} \)
c. \( I^{-} \) only
D. \( C l^{-}, B r^{-} \) and \( I^{-} \)


A monoatomic gas expands isobarically. The percentage of heat supplied that increases the thermal energy and that involved in doing work for expansion is
A .40: 60
B. 60: 40
c. 50: 50
D. none of these


Which point belongs to the region
represented by \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{0} ? \)
This question has multiple correct options
A. (4,5)
(年) (4,5)
в. (-7,9)
c. (7,-9)
D. (8,-12)


Twenty seven identical mercury drops each charged to \( 10 V \), are allowed to form
a big drop. The potential of the big drop is
A . \( 90 V \)
в. \( 9 V \)
\( c .900 V \)
D. \( 270 V \)


If \( 1+\sin x+\sin ^{2} x+\sin ^{3} x+\ldots \infty \) is
equal to \( 4+2 \sqrt{3}, 0<x<\pi, \) then \( x \) is
equal to
\( ^{A} \cdot \frac{\pi}{6} \)
в.
c. \( \frac{\pi}{3} \) or \( \frac{\pi}{6} \)
D. \( \frac{\pi}{3} \) or \( \frac{2 \pi}{3} \)


Assertion
\( 1 M \) solution of \( K C l \) has greater
osmotic pressure than \( 1 M \) solution of
glucose at the same temperature.
Reason
In solution \( K C l \) dissociates to produce more number of particles.
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 block of mass \( m \) is connected to
another block of mass \( M \) by a spring (massless) of spring constant \( k . \) The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force \( \boldsymbol{F} \) starts acting on the
block of mass \( M \) to pull it. Find the
force on the block of mass \( m \)
\( A \cdot \frac{m F}{M} \)
в. \( \frac{(M+m) F}{m} \)
c. \( \frac{m F}{(m+M)} \)
D. \( \frac{M F}{(m+M)} \)


A block of mass' \( m^{\prime} \) is kept on the
ground as shown in figure. Which of the
following statements is/are correct of
action-reaction force pair?
This question has multiple correct options
A. Normal force can never be a reactive force
B. Weight of the body is not a part of action reaction pair
c. Forces act on different bodies
D. None of these


A transformer with primary to secondary turns ratio of \( 1: 2, \) is connected to an alternator of voltage \( 200 \mathrm{V} . \) A current of \( 4 \mathrm{A} \) is flowing through the primary coil. Assuming that the transformer has no losses, the
secondary voltage and current are respectively:
\( A \cdot 100 \vee, 8 A \)
B. \( 400 \vee, 8 A \)
c. \( 400 \vee, 2 \mathrm{A} \)
D. \( 100 \vee, 2 A \)


Statement: \( S O_{2} \) and \( C O_{2} \) both turns
lime water milky.

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


Find the inclinations of the axes so that
the following equations may represent circles, and in each case find the radius
and centre;
\( \boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}-2 \boldsymbol{g} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}=\mathbf{0} \)


Sub-mucosal layer of stomach consists
of
A. Nerves, Blood vessels and Lymphatic vessels
B. Lymphatic vessels, Oxyntic cell, Blood vessels and Glands
C . Zymogen cell, Nerve, Glands, Blood vessels and Lymphatic vessels
D. Blood vessels, Lymphatic vessels, Nerve and Hepatic cells


Find the mean deviation from the mean
of the following data, using step deviation method.
\( \begin{array}{lllll}\text { Marks } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array}\end{array} \)
No. of
students 5


A metal cube of side \( 10 \mathrm{cm} \) is subjected
to a shearing stress of \( 10^{4} N m^{-2} \). The modulus of rigidity if the top of the cube is displaced by \( 0.05 \mathrm{cm} \) with respect to its bottom is
A . \( 2 \times 10^{6} \mathrm{Nm}^{-2} \)
B. \( 10^{5} N m^{-2} \)
c. \( 1 \times 10^{7} N m^{-2} \)
D. \( 4 \times 10^{5} \mathrm{Nm}^{-2} \)


Fraunhoffer lines in the Sun's spectrum
are present because
A. Vapours of certain elements present in the atmosphere absorb certain colours
B. The temperature of the Sun is very high
c. The sun does emit certain light
D. Certain elements present in the Sun interfere


Draw a neat labelled diagram of a parallel plate capacitor completely filled with dielectric.


In periodic table, the period number
indicates the number of:
A. neutrons
B. protons
c. electrons
D. none of the above


Assertion
Dumas method is more applicable to nitrogen containing organic compounds than Kjeldahl's method.
Reason
Kjeldahl's method does not give satisfactory results for compounds in which \( \mathrm{N} \) is linked to 0 atom.
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


One root of the equation \( \cos x-x+ \)
\( \frac{1}{2}=0 \) lies in the interval?
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
В. \( \left(-\frac{\pi}{2}, 0\right) \)
c. \( \left(-\frac{\pi}{2}, \pi\right) \)
D. \( \left(\pi, \frac{3 \pi}{2}\right) \)


Length of DNA with 23 base pairs is
A . \( 78.4 \mathrm{A}^{\circ} \)
B. 78.2 A \( ^{\text {о }} \)
\( \mathbf{c} \cdot 78 \mathrm{A}^{\circ} \)
D. 74.8 A


If \( a x^{3}+b x^{2}+c \) is divided by \( (x-3) \)
then the remainder is:
A. \( -27 a+9 b+c \)
B . \( -27 a-9 b \)
c. \( 27 a+9 b+c \)
D. \( 27 a+9 b \)
E \( .-27 a+9 b \)


When two bodies collide elastically then the quantity conserved is:
A. kinetic energy
B. mometum
c. both
D. none


Write the place value of 3 in the following decimal numbers.
\( \mathbf{9 0 . 3 0} \)
place value is \( \frac{\mathbf{3}}{\mathbf{1 0}} \)
A. True
B. False


Which of the following system of equations has unique solution?
A. \( 3 x+y=2,6 x+2 y=3 \)
в. \( 2 x-5 y=3,6 x-15 y=9 \)
c. \( x-2 y=3,3 x-2 y=1 \)
D. \( 2 x+3 y=4,4 x+6 y=8 \)


If the probability of defective bolts is
\( 0.1, \) find the mean and standard
deviation for the distribution of
defective bolts in a total of 500 bolts.


The area of the floor of a room is \( 15 m^{2} .1 \)
its height is \( 4 m \), then the volume of the
air contained in the room is
A. \( 60 d m^{3} \)
в. \( 600 d m^{3} \)
\( \mathbf{c} \cdot 6000 x m^{3} \)
D. \( 60000 d m^{3} \)


Rank the indicated bonds in each
compounds in order of increasing bond
strength:
A. \( 1<2<3 \)
B. \( 3<1<2 \)
c. \( 1<3<2 \)
D. \( 2<3<1 \)


Enzymes provide active sites for holding the substrate molecules through a variety of interactions like:
This question has multiple correct options
A. ionic bonding
B. metallic bonding
c. hydrogen bonding
D. covalent bonding


Which of the following is a poor
electrolyte?
A. A hydrochloric acid solution
B. A sodium hydroxide solution
C. A vinegar solution
D. A sodium chloride solution
E. Molten sodium chloride


Which of the following is used to dissolve argentite ore?
A \( \cdot \operatorname{Na}\left[\operatorname{Ag}(C N)_{2}\right] \)
в. \( N a C N \)
c. \( N a C l \)
D. HCl


Write Lewis's electron dot formula of
water \( \left(\boldsymbol{H}_{2} \boldsymbol{O}\right) \)


He was a professor of mathematics at St. Petersburg University, Prof. of anatomy and physics at the University of Groningen, and prof. of physics, anatomy and botany at the University of Basle. But he is most famous for what is
known as 'Bernouilli's theorem'. Name
the outstanding mathematician- of a
well-known Swiss family.
A. Johann Bernouill
B. Jacob Bernouilli
c. Danial Bernouill
D. None of these


Assertion
Molar conductivity increases with
decrease in concentration.
Reason
Conductivity always decreases with
decrease in concentration.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Solve \( \int \frac{x^{2}}{x+1} d x \)


A plane wave front falls on a convex lens
The emergent wave front:
A. converges to a point
B. diverges from a point
c. does not suffer any refraction
D. may or may not converge at point


Four wires \( P, Q, R \) and \( S \) of same
materials have diameters and
stretching forces as shown
below. Arrange their strains in the
decreasing order.
\( \begin{array}{lll}\text { Wire } & \text { Diameter } & \text { Stretching force } \\ \mathrm{P} & 2 \mathrm{mm} & 10 \mathrm{N} \\ \mathrm{Q} & 1 \mathrm{mm} & 20 \mathrm{N} \\ \mathrm{R} & 4 \mathrm{mm} & 30 \mathrm{N} \\ \mathrm{S} & 3 \mathrm{mm} & 40 \mathrm{N}\end{array} \)
\( A \)
\( \mathrm{Q}, \mathrm{S}, \mathrm{P}, \mathrm{R} \)
B. R,P,S,Q
\( \mathbf{c} . \) P,Q,R,S
D. \( P, R, Q, S \)


A metal ball of mass \( 2 k g \) moving with velocity of \( 36 k m / h \) has a head on collision with a stationary ball of mass 3kg. If after the collision the two balls moves together, the loss in kinetic energy due to collision is (in J)
A . 140
в. 100
c. 60
D. 40


Which of the following will result in the
formation of an ether?
This question has multiple correct options
A \( \cdot\left(C H_{3}\right)_{3} C \bar{O} \stackrel{+}{N} a+C H_{3} C H_{2} B r \longrightarrow \)
В \( \cdot\left(C H_{3}\right)_{3} C B r+C_{2} H_{5} \bar{O} \dot{N} a \longrightarrow \)
c. \( C_{6} H_{5} \) ONa \( +C H_{3} B r \longrightarrow \)
D. \( C_{6} H_{5} B r+C H_{3} \bar{O}_{N a} \rightarrow \)


If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} d x, \) then
\( \frac{1}{I_{2}+I_{4}} \frac{1}{I_{3}+I_{5}} \frac{1}{I_{4}+I_{6}} \) is:
A. A.P
B. G.P.
c. н.P.
D. None of these


What is the relationship between the
two terminal \( \boldsymbol{H}_{2} \boldsymbol{C}= \) groups in a cumulene containing three consecutive double bonds? \( \left(\boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2}\right) \)
A. They are in the perpendicular plane
B. They are in same plane
c. They are in two planes at \( 120^{\circ} \)
D. They are in two planes at \( 109^{\circ} \)


Who was the first scientist to propose a
model for the structure of an atom?
A. J.J. Thomson
B. Dalton
c. Ernest Rutherford
D. E. Goldstein


ff \( A=\left|\begin{array}{ccc}\boldsymbol{4} & \boldsymbol{k} & \boldsymbol{k} \\ \mathbf{0} & \boldsymbol{k} & \boldsymbol{k} \\ \mathbf{0} & \boldsymbol{0} & \boldsymbol{k}\end{array}\right| \) and \( \operatorname{det}(\boldsymbol{A})=\mathbf{2 5 6} \)
then \( |\boldsymbol{k}| \) equals
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


Carbon monoxide can kill a person
because of it's extremely high affinity for
A. haemoglobin
B. phytochrome
c. cytochrome
D. none of these.


Assertion
Inertia is the property by virtue of which the body is unable to change by itself, its state of rest or motion and its
direction of motion.
Reason
The bodies do not change their state
unless acted upon by an unbalanced external 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


The bending of light ray after passing through a medium is commonly known
as:
\( A \). refraction
B. scattering
c. reflection
D. interference


A stone is swinging in a horizontal circle of diameter \( 0.8 ~ m \) at 30 rev / min. A distant light causes a shadow of the stone on a nearly wall. The amplitude and period of the SHM for the shadow of the stone are:
A. \( 0.4 m, 4 s \)
B. \( 0.2 m, 2 s \)
c. \( 0.4 m, 2 s \)
D. \( 0.8 m, 2 s \)


Assertion
lonisation potential increases with
increase in nuclear charge of the
elements.
Reason
lonization energies increase moving from left to right across a period.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{I}_{1}=\int_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} \boldsymbol{x}}{1+\cos ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
\( I_{2}=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+\sin ^{2} x} d x \)
\( I_{3}=\int_{0}^{\frac{\pi}{2}} \frac{1+2 \cos ^{2} x \sin ^{2} x}{4+2 \cos ^{2} x \sin ^{2} x} d x, \) then
A \( \cdot I_{1}=I_{2}>I_{3} \)
В . \( I_{3}>I_{1}=I_{2} \)
\( \mathbf{c} \cdot I_{1}=I_{2}=I_{3} \)
D. None of these


Consider a uniformly charged sphere that has a total charge of \( Q \) that has a
radius of \( R \). What is the electrostatic
potential difference, \( \Delta V \), between the
centre of the sphere and the surface of
the sphere?
A \( \cdot \frac{4 k_{e} q}{R} \)
в. \( \frac{2 k_{e} q}{R} \)
c. \( \frac{k_{e} q}{R} \)
D. \( \frac{k_{e q}}{2 R_{q}} \)


A body of mass \( M \) (figure shown above)
with a small disc of mass \( m \) placed on it rests on a smooth horizontal plane. The disc is set in motion in the
horizontal direction with velocity \( v . \) The
height (relative to the initial level) to
which the disc rise after breaking off
the body \( M \) is given as \( h= \) \( \frac{M v^{2}}{x g(M+m)} . \) The friction is assumed to
be absent. Find ' \( x \) '.


The work done in carrying 20 coulomb charge through a distance of \( 5 \mathrm{m} \) is \( 2 J \)
The potential difference between these
two points will be:
\( \mathbf{A} \cdot 2 \times 10^{-1} V \)
B. \( 1 \times 10^{-2} V \)
c. \( 2 \times 10^{-2} V \)
D. \( 1 \times 10^{-1} V \)


Which of the following is more basic than aniline?
A. Diphenylamine
B. Triphenylamine
c. p-nitroaniline
D. Benzylamine


Find the cube root of 512


rove: \( \left|\begin{array}{ccc}-\cos \alpha & \sin \beta & 0 \\ 0 & -\sin \alpha & \cos \alpha \\ \sin \alpha & 0 & -\sin \beta\end{array}\right|=0 \)


The angle of incidence at which
reflected light is totally polarized for
reflection from air to glass (refractive
index \( n \) ), is:
\( A \cdot \sin ^{-1} \)
B. \( \sin ^{-1}(1 / \mathrm{n}) \)
\( c \cdot \tan ^{-1}(1 / \mathrm{n}) \)
D. \( \tan ^{-1}(n) \)


Calculate the standard deviation of the
following data
\( \boldsymbol{x} \quad \boldsymbol{3} \quad \boldsymbol{8} \quad \mathbf{1 3} \quad \mathbf{1 7} \quad \boldsymbol{2 3} \)
\( \begin{array}{llllll}f & 7 & 10 & 15 & 10 & 8\end{array} \)


The two rails of a railways track, insulated from each other and the
ground, are connected to a milli voltmeter. What is the reading of the milli voltmeter when a train travels at a
speed of \( 20 \mathrm{ms}^{-1} \) along the track, given that the vertical component of the
earth's magnetic field is \( 0.2 \times 10^{-4} \) \( \mathrm{Wbm}^{-2} \) and the rails are separated by 1
\( \mathrm{m} ? \)
A. 4 mv
B. \( 0.4 \mathrm{mv} \)
c. \( 80 \mathrm{mv} \)
D. 10 mv


The most commonly used thermometric substance is
A. water
B. alcohol
c. mercury
D. steam


A body travels \( 200 \mathrm{cm} \) in the first 2 s
and \( 220 \mathrm{cm} \) in the next 4 s with deceleration. The velocity of the body at the end of the seventh second is
A. \( 5 \mathrm{cm} / \mathrm{s} \)
в. \( 10 \mathrm{cm} / \mathrm{s} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} / \mathrm{s} \)
D. 20cm/s


10ml of \( N H_{4} C l, 20 \mathrm{ml} \) of \( N / 2 H_{2} S O_{4} \)
and \( 30 \mathrm{ml} \) of \( N / 3 H N O_{3} \) are mixed together and volume made to one litre.
Normality of resulting solution is:
A. \( 30 N / 100 \)
в. \( N / 10 \)
c. \( N / 20 \)
D. \( N / 40 \)


Let \( \triangle \boldsymbol{a}=\left|\begin{array}{ccc}\boldsymbol{a}-\mathbf{1} & \boldsymbol{n} & \boldsymbol{6} \\ (\boldsymbol{a}-\mathbf{1})^{2} & \boldsymbol{2} \boldsymbol{n}^{2} & \boldsymbol{4} \boldsymbol{n}-\boldsymbol{2} \\ (\boldsymbol{a}-\mathbf{1})^{3} & \boldsymbol{3} \boldsymbol{n}^{3} & \boldsymbol{3} \boldsymbol{n}^{2}-\boldsymbol{3} \boldsymbol{n}\end{array}\right| \)
Then \( \sum_{a-1}^{n} \triangle a \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
В \( \cdot(a-1) \sum n^{2} \)
c. \( (a-1) n \sum n \)
D. None of these


Why are the leaves attacked by aphids often feel sticky?


If \( \boldsymbol{x}=\frac{\mathbf{4} \boldsymbol{a} \boldsymbol{b}}{\boldsymbol{a}+\boldsymbol{b}}, \) where \( \boldsymbol{a} \neq \boldsymbol{b} \neq \mathbf{0}, \) then the
value of \( \frac{x+2 a}{x-2 a}+\frac{x+2 b}{x-2 b} \) is
(Assume that everything is defined) This question has multiple correct options
A. Independent of \( a \)
B. Independent of \( b \)
c. Independent of \( x \)
D. None of these


Which of the following element is formed as a result of transfer of one
valence electron?
A. Sodium chloride
B. Calcium oxide
c. Magnesium chloride
D. All of the above


The number of bacteria, measured in thousands, in a culture is modeled by the equation \( b(t)=\frac{380 e^{2.3 l t}}{175+e^{3.2 l t}}, \) where
\( t \) is the number of days since the culture was formed. According to this model, the culture can support a maximum population of
A . 217
в. 205
\( c .380 \)
D. 760
\( E \cdot \alpha \)


What percent of 150 is \( 96 ? \)


Make the correct pairs for the following
given \( \mathrm{X} \) and \( \mathrm{Y} . \mathrm{X} \) contains substance
and Y has method of manufacture:
\[
x
\]
1. Extraction of Sulphur \( \quad \) p. Contact process
2. Production of Nitric acid
q. Frasch method
3. Production of Sulphuric \( \quad \) r. Haber's process acid
4. Production of Ammonia \( \quad \) s. Ostwald's gas \( \quad \) process
A \( \cdot(1-s),(2-r),(3-q),(4-p) \)
B. \( (1-r),(2-q),(3-s),(4-p) \)
C \( .(1-q),(2-s),(3-p),(4-r) \)
D. \( (1-s),(2-q),(3-r),(4-p) \)


n the given figure, \( \triangle A B C \) is an equilateral triangle and \( \square A W X B \) and
\( \square A Y Z C \) are two squares. The value of \( \frac{1}{10}(\angle Z X A) \) is:


Which of the following has highest calorific value?
A. Animal fat
B. Hydrogengas
c. Gasoline
D. coal


Amongst element \( X(2,8,6) \) and \( Y \) \( (2,8,8), \) which is more reactive and why?
A. \( x \) because it is a metal
B. Y because it is non metal
c. \( x \) because it has 6 valence electrons
D. Y because it is gas


What kind of lens would form an erect
and magnified image?


How electromagnetic waves are produced?


The pressure applied from all directions
on a cube is \( p . \) How much its
temperatures should be raised to maintain the original volume? The
volume elasticity of the cube is \( \beta \) and
the coefficient of volume expansion is \( \alpha \)
A \( \cdot \frac{p}{\alpha \beta} \)
B. \( \frac{p \alpha}{\beta} \)
\( c \cdot \frac{p \beta}{\alpha} \)
D. \( \frac{\alpha \beta}{p} \)


carried out?
(i) Propene to propan-1-ol
(ii) Ethanol to but-1-yne
(iii) \( 1- \) Bromopropane to 2 -bromopropane
(iv) Toluene to benzyl alcohol
(v) Benzene to 4-bromonitrobenzene
(vi) Benzyl alcohol to 2phenylethanoic acid
(vii) Ethanol to propanenitrile (viii) Aniline to chlorobenzene
(ix) 2 -Chlorobutane to \( 3,4- \)
dimethylhexane
(x) 2-Methyl-1propene to 2-chloro-2-methylpropane
(xi) Ethyl chloride to propanoic acid
(xii) But-1-ene to n-butyliodide
(xiii) 2-Chloropropane to 1-propanol
(xiv) Isopropyl alcohol to iodoform
(xv) Chlorobenzene to p-nitrophenol
(xvi) 2-Bromopropane to 1bromopropane
(xvii) Chloroethane to butane
(xviii) Benzene to diphenyl
(xix) tert-Butyl bromide to isobuty| bromide \( (x x) \) Aniline to
phenylisocyanide


In the 5 band color resistor,which color
bands are considered as significant
digits?
A. First band only
B. First three bands
c. First two bands
D. Last band


Most of the cell organelles are derived from
A. Nucleus
B. Endoplasmic reticulum
c. Mitochondria
D. chloroplast


\( \frac{d}{d x}\left(\tan ^{-1} \frac{\cos x-\sin x}{\cos x+\sin x}\right) \)
\( A \)
B. -
\( c \cdot 1 \)
D.


Name the latest theory of fundamental physics in which the basic entity is a one-dimensional object as against the zero-dimensional' points representing the elementary particles.
A. String theory
B. Supersymmetry
c. symmetry
D. superstring theory


Light with an energy flux of \( 20 \mathrm{W} / \mathrm{cm}^{2} \) falls on a non-reflecting surface at normal incidence. If the surface has
an area of \( 30 \mathrm{cm}^{2} \), the total
momentum delivered (for complete
absorption) during 30 minutes is :
A \( .3 .6 \times 10^{-3} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 3.3 \times 10^{-8} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 10.8 \times 10^{4} \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 1.08 \times 10^{7} \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Binomial nomenclature means writing
the name of plant / animal in two words,
which designate
A. Genus and species
B. Species and variety
c. order and family
D. Family and genus


The value of \( \int \sqrt{2}\left(\frac{\sin x}{\sin \left(x-\frac{\pi}{4}\right)}\right) d x \)
is
\( ^{\mathbf{A}} \cdot_{x-\log }\left|\sin \left(x-\frac{\pi}{4}\right)\right|+c \)
B. \( x+\log \left|\cos \left(x-\frac{\pi}{4}\right)\right|+c \)
\( ^{\mathbf{C}} x-\log \left|\cos \left(x-\frac{\pi}{4}\right)\right|+c \)
D. \( x+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+c \)


The sales tax on a refrigerator at the rate of \( 9 \% \) is \( 1,170 . \) Find the actual sale price.


A first order reaction is \( 50 \% \) complete in 25 minutes. Calculate the time for \( 80 \% \)
completion of the reaction.


Match the items in column I with
column II and choose the correct option
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { A. } & \text { Binary fission } & \text { 1. } & \text { Algae } \\ \text { B. } & \text { Zoospore } & \text { 2. } & \text { Amoeba } \\ \text { c. } & \text { Conidium } & \text { 3. } & \text { Hydra } \\ \text { D. } & \text { Budding } & \text { 4. } & \text { Penicillium } \\ \text { E. } & \text { Gemmules } & \text { 5. } & \text { Sponge }\end{array} \)
\( A \)
\( A-1, B-4, C-5, D-3 \)
B. A - 2, B-1,C - 4, D-3, E-5
c. \( A-1, B-4, C-3, D-2, E-5 \)
D. A - 4. - 1. C - 3. D


The solution to the differential equation \( (x+1) \frac{d y}{d x}-y=e^{3 x}(x+1)^{2} \) is
A \( \cdot y=(x+1) e^{3 x}+c \)
B. \( 3 y=(x+1)+e^{3 x}+c \)
c. \( \frac{3 y}{x+1}=e^{3 x}+c \)
D. \( y e^{-3 x}=3(x+1)+c \)


The distance between the poles of a horse shoe magnet is \( 0.1 \mathrm{m} \) and its pole strength is \( 0.01 \mathrm{A} \) -m. The induction of magnetic field at a point mid way between the poles will be :
A. zero
В. \( 2 \times 10^{-5} T \)
C \( .4 \times 10^{-6} T \)
D. \( 8 \times 10^{-7} T \)


Intersecting point of \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6}, \boldsymbol{x}- \)
\( \boldsymbol{y}=\boldsymbol{4} \) is


Work done in turning dipole through an angle 60 is
A. zero
в. \( p E / 4 \)
c. \( p E \)
D. \( p E / 2 \)


A uniform disc of mass \( m \) and radius \( R \)
is rotating with angular velocity \( \omega \) on a smooth horizontal surface. Another
identical disc is moving translationally
with velocity \( v \) as shown. When they
touch each other, they stick together.
The angular velocity of centre of mass of
the system after contact will be
A. Zero
B.
c. \( \frac{v}{R} \)
D. \( \frac{\omega}{2^{2}} \)


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{\sqrt{5 x-4}-\sqrt{x}}{x^{3}-1} \)
A \( \cdot \frac{2}{5} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. None of these


When a particle executing SHM
oscillates with a frequency' \( \omega^{\prime}, \) then the kinetic energy of the particle
A. Changes periodically with a frequency of ' \( \omega^{\prime} \)
B. Changes periodically with a frequency of '2 \( \omega \) '
C . changes periodically with a frequency of \( ^{\prime} \frac{\omega}{2} \)
D. Remains constant