STATEMENT-1: The order of acidic
character of the given compounds
STATEMENT-2:-I and -R effect of the
group stabilizes the conjugate base decreasing the -ve charge, whereas +1 effect of the group destabilises the conjugate base by intensifying the charge
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Line spectrum is characteristic of:
A . molecules
B. atoms
c. radicals
D. none of the above


Initial speed of the bullet is
A \( .549 m / s \)
B. \( 502 m / s \)
c. \( 475 \mathrm{m} / \mathrm{s} \)
D. \( 624 \mathrm{m} / \mathrm{s} \)


Which type of cloth dries faster in rainy
season?
A. cotton
B. Wool
c. Polyester
D. silk


Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Thickness increases because of air
layer enclosed between the two blankets.
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


The value of \( \sin 20^{\circ} \cdot \sin 40^{\circ} \cdot \sin 80^{\circ} \) is
A. \( \frac{\sqrt{3}}{8} \)
B. \( \frac{1}{8} \)
c. \( \frac{1}{16} \)
D. None of these


If \( x_{1} x_{2} x_{3} \dots x_{n}=1\left(x_{1}>0, i=\right. \)
\( 1,2, \dots . n), \) prove that \( x_{1}+x_{2}+ \)
\( \dots . . x_{n} \geq n(n \geq 2) \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) find \( \boldsymbol{A}^{-1} \) by elementary
transformation


A particle moves in a closed orbit
around the origin, due to a force which
is directed towards the origin. The de Broglie wavelength of the particle varies
cyclically between two values \( \lambda_{1} \) and \( \lambda_{2} \)
with \( \lambda_{1}>\lambda_{2} . \) Which of the following
statement is true?
A. The particle could be moving in an circular orbit with origin as centre
B. The particle could be moving in an parabolic orbit with origin as its focus
C. When the de Broglie wave length is \( \lambda_{1} \), the particle is nearer the origin than when its value is \( \lambda_{2} \)
D. When the de Broglie wavelength is \( \lambda_{2} \), the particle is nearer the origin than when its value is \( \lambda_{1} \)


Assertion
Aquatic species are more comfortable in warm waters than cold waters.
Reason
\( \boldsymbol{K}_{\boldsymbol{H}} \) values for both \( \boldsymbol{N}_{2} \) and \( \boldsymbol{O}_{2} \)
decrease with increase of temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following is the value of \( \cos 170^{0} \cos 10^{0}-\sin 170^{0} \sin 10^{0} ? \)
A . -2
B. - 1
\( c . \)
D.


Solve the following equation using the trial and error method.
\( 11+2 x=19 \)


Tracheids differs from vessels in having
A. Thick wall
B. Bordered pits
c. Discontinuous intercalate wal
D. Spiral thickening


How primary amine is prepared by Hoffmann bromamide degradation reaction? Write equation.


Match the terms to these definitions
Cofactor, coenzyme, holoenzyme, apoenzyme, ligases, lyases, transferases, isozymes, zymogens, competitive inhibitor, non-competitive inhibitor, activation energy ...enzymes which catalyse the linking together of compounds utilising the
energy from ATP


In blood, \( \mathrm{CO}_{2} \) in transported majorly as
A. Sodium carbonate
B. Carboxyhaemoglobin
c. Bicarbonate
D. \( \mathrm{cO}_{2} \) as such


Ordered pair \( (x, y) \) satisfying the
system of simultaneous equation \( \sin ^{-1} x+\sin ^{-1} 2 y=\pi \) and \( \cos ^{-1} x+ \)
\( \cos ^{-1} x^{2}=0 \) is
\( ^{\mathrm{A}} \cdot\left(-1,-\frac{1}{2}\right) \)
B \( \cdot\left(1,-\frac{1}{2}\right) \)
\( ^{c} \cdot\left(-1, \frac{1}{2}\right) \)
D. \( \left(1, \frac{1}{2}\right) \)


Assertion
The strain present in the material after
unloading is called the residual strain or plastic strain and the strain
disappears during unloading is termed as recoverable or elastic strain.
Reason
After yieild point, there is some residual stress left in an material on unloading.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two short electric dipoles are placed as
shown. The energy of electric interaction between these dipoles will be:
\( \mathbf{A} \)
B.
\( \mathbf{c} \cdot \frac{-2 k P_{1} P_{2} \sin \theta}{r^{3}} \)
D.


Both triangles are similar by \( S A S \) similarity rule. Find the ratio by which
they are similar.
A . 1: 3
В. 2: 3
\( c \cdot 1: 4 \)
D. 3: 2


Assertion
Non-striated muscles are said to be
voluntary in nature
Reason
Non-striated muscles can be moved
according to will
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the reason
is not correct explanation of the assertion.
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Find the limits of
\[
\begin{array}{l}
\frac{\sqrt{\boldsymbol{a}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}-\sqrt{\boldsymbol{a}^{2}-\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}}{\sqrt{\boldsymbol{a}+\boldsymbol{x}}-\sqrt{\boldsymbol{a}-\boldsymbol{x}}}, \text { when } \\
\boldsymbol{x}=\mathbf{0}
\end{array}
\]


Which of the following decides the standards for drinking water in Europe?
A. European Environment Protection Agency
B. European Drinking Water Directive
c. European Union Standards
D. European Safe Water Act


\( \int \frac{x+\sin x}{1+\cos x} d x= \)
A \( \cdot x \tan \frac{x}{2}+c \)
B. \( x \cot \frac{x}{2}+c \)
c. \( x \sin \frac{x}{2}+c \)
D. \( x \cos \frac{x}{2}+c \)


What would be the ionisation constant
\( \left(\boldsymbol{K}_{\boldsymbol{a}}\right) \) of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} ? \)
A \( \cdot 2 \times 10^{-5} \)
B \( \cdot 10^{-5} \)
C \( .2 \times 10^{-6} \)
D. \( 5 \times 10^{-6} \)


A wooden plank rests in equilibrium on
two rocks on opposite sides of a narrow
stream. Three forces \( P, Q \) and \( R \) act on
the plank. How are the sizes of the
forces related?
\( \mathbf{A} \cdot \mathbf{P}+\mathbf{Q}=\mathbf{R} \)
B. \( P+R=Q \)
\( \mathbf{c} \cdot \mathrm{P}=\mathrm{Q}=\mathrm{R} \)
D. \( P=Q+R \)


Which type of lenses are used in spectacles for the correction of myopia of the eyes?
A. Convex lenses
B. Concave lenses
c. Both convex and concave lenses
D. None of these


What kind of energy change takes place when a magnet is moved towards a coil having a galvanometer at its ends?
A. Mechanical energy changes to the magnetic energy.
B. Magnetic energy changes to the electrical energy
c. Mechanical energy changes to the electrical energy.
D. None of the above


In the process of electroplating, \( \boldsymbol{m} \boldsymbol{g} \) of silver is deposited when 4 ampere of
current flows for 2 minutes. The amount
(in \( g \) ) of silver deposited by 6 ampere of current flowing for 40 seconds will be:
A. \( 4 m \)
в. \( \frac{m}{2} \)
c. \( \frac{4 m}{3} \)
D. \( 3 m \)


What does \( \psi^{2} \) represents in the quantum model of atom?
A. Density of electron
B. Probability of finding the electron
c. volume of electron
D. Distance of electron from Nucleus


What is the length of \( A B ? \)
\( \mathbf{A} \cdot 8 \mathrm{cm} \)
B. 4.5cm
C. \( 7.35 \mathrm{cm} \)
D. \( 7.30 \mathrm{cm} \)


Write the function of the following part
of human eye. Ciliary muscles.


\( x \) is the multiplicative identity.The
value of \( x \) is
\( A \)
B. 2
\( c \cdot 0 \)
D. None


Zone refining is a method to obtain:
A. very high temperature
B. ultrapure \( A l \)
C. ultrapure metals
D. ultrapure oxides


A body is subjected to strain several times will not obey Hookes law due to
A. Yeild point
B. Permanent state
C. Elastic fatigue
D. Breaking stress


If the displacement of simple pendulum at any time is \( 0.02 m \) and acceleration
is \( 2 m / s^{2}, \) then in this time angular
velocity will be:
\( \mathbf{A} \cdot 100 \mathrm{rad} / \mathrm{s} \)
B. 10 rad/s
c. 1 rad/s
D. \( 0.1 \mathrm{rad} / \mathrm{s} \)


Find the argument of \( -1-i \sqrt{3} \)
A. \( \theta=-2 \pi / 3 \)
В. \( \theta=2 \pi / 3 \)
c. \( \theta=-4 \pi / 3 \)
D. \( \theta=4 \pi / 3 \)


Pin mould reproduces by means of
A . Gametes
B. Spores
c. Seeds
D. Bulbils


If Hund's rule is not followed, magnetic
moment if \( \mathrm{Fe}^{2+} \) is:
\( A \cdot O \)
в. \( \frac{h}{2 \pi} \)
\( c \cdot \frac{3 h}{2 \pi} \)
D. \( \frac{\sqrt{3} h}{4 \pi} \)


When sound travel from air to water
which one of the following remains constant?
A. Time period
B. Frequency
c. velocity
D. wavelength


Two points of a rod move with velocities
\( 3 v \& v \) perpendicular to the rod and in the same direction, separated by a distance 'r'. The angular velocity of rod is :
A \( \cdot \frac{3 v}{r} \)
в. \( \frac{4 v}{r} \)
c. \( \frac{5 v}{r} \)
D. \( \frac{2 v}{r} \)


Sodium is found more useful than
potassium. If true enter 1 ,if false enter 0


The marks scored by two students \( A, B \) in a class are given below.
\( \begin{array}{llllll}\text { A } & 58 & 51 & 60 & 65 & 66\end{array} \)
В 56 87 88 46
Who is more consistent?


A body is sliding down an inclined plane (fixed plane) under its own weight at constant speed.If the inclination of the
plane to the horizontal is \( 30^{\circ} . \) the angle
of friction is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 15^{\circ} \)


Who predicted the existence of electromagnetic waves? Give the wavelength range of electromagnetic
spectrum.


A mobile phone lies along the principal axis of a concave mirror. Show with the
help of suitable diagram, the formation of its image. Explain why magnification is not a uniform?


Safranin stains which of the following elements of the tissue?
A. Starch elements
B. Lignified elements
c. Protein elements
D. Hard bast


\( \left(\frac{1}{64}\right)^{0}+(64)^{\frac{-1}{2}}+(32)^{\frac{4}{5}}-(32)^{\frac{-4}{5}} \) is
equal to
A \( \cdot_{16} \frac{1}{8} \)
в. \( 17 \frac{1}{8} \)
c. \( _{17} \frac{1}{16} \)
D. \( -17 \frac{1}{16} \)


Which of the following statement is not
correct?
A. Fe, Ni, Co form interstetial compound
в. \( C u S O_{4}+C a(O H)_{2} \) is called Bordeaux mixture
c. verdigris is basic copper acetate \( \left[C u\left(C O O C H_{3}\right)_{2} C u(O H)_{2}\right] \)
D. 24 carat gold is an alloy of Au and cu


Simplify: \( \boldsymbol{x}+\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{x} \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( 5 x \)
\( c .6 \)
D. \( 6 x \)


If \( \int_{-2}^{3} f(x) d x=5 \) and
\( \int_{1}^{3}\{2-f(x)\} d x=6 \)
then the value of \( \int_{-2}^{1} f(x) d x \) is?
A . -5
B. 3
c. -7
D. -


A uniform cube is subjected to volume compression. If each side is decreased by \( 1 \% \), then bulk strain is :
A . 0.01
B. 0.06
\( c .0 .02 \)
D. 0.03


Marine protozoans lack contractile vacuole because
A. Their body cannot accommodate it
B. They are hypo osmotic to their environment
c. They are isotonic with their environment
D. osmoregulation is done by cell membrane


From the centre of the earth to the
surface of the earth, the relation between the value of \( g \) and distance \( (r) \) represented as a proportionality, is given by
A \( \cdot g \propto \frac{1}{r^{2}} \)
В . \( g \propto r \)
c. \( g \propto r^{2} \)
D \( \cdot g \propto r^{o} \)


Assertion: There exist two angles of
incidence for the same magnitude of deviation (except minimum deviation)
by a prism kept in the air. Reason: In a prism kept in the air, a ray is incident on the first surface and
emerges out of the second surface. Now
if another ray is incident on second. surface (of the prism) along the
previous emergent ray, then this ray emerges out of the first surface along
the previous incident ray. This principle is called the principle of reversibility of light.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


An inductance, a capacitance and a resistance are connected in series
across a source of alternating voltages. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of
A . \( \pi / 4 \)
B. zero
\( c \)
D. \( \pi / 2 \)


The angle of the sun above the horizon
is 27.5 degrees. Find the approximate length of the shadow of a person who is
4.75 feet tall.
A . 4.75
в. 2.47
c. 4.65
D. 9.12
E . 4.86


When mammary glands of male develop similar to that of female, then this condition is known as:
A. Gonochorism
B. Gynaecomastia
C. Feminism
D. None of the above


1000 small water drops each of radius \( r \)
and charge \( q \) coalesce to form one
spherical drop. The potential of big drop is larger than that of smaller ones by a factor
\( \mathbf{A} \cdot 1000 \)
B. 100
c. 10
D. 1


The ability of the material to deform without breaking is called:
A. Elasticity
B. Plasticity
c. Creep
D. None of these


One way in which the operation of an \( n \) -
\( p-n \) transistor differ from that of a \( p-n-p \)
transistor is that
A. the emitter junction is reverse biased in \( n-p-n \)
B. the emitter junction injects minority carriers into the base region of the \( \mathrm{p}-\mathrm{n}-\mathrm{p} \)
C. the emitter injects holes into the base of the pnp and electrons into the base region of \( n-p-n \)
D. the emitter injects holes into the base of \( n-p-n \)


Which will decay faster if exposed freely?
A. Softwood
B. Heartwood
c. sapwood
D. Wood with lots of fibres


What happens when \( H_{2} S \) gas is passed
into aqueous \( S O_{2} ? \)
A. \( H_{2} S \) is converted into a yellow precipitate of sulphur.
B. \( S O_{2} \) Is converted into yellow precipitate of sulphur.
C. A clear solution of \( H_{2} S O_{4} \) is formed
D. \( S O_{2} \) and \( H_{2} S \) are converted into yellow precipitate


A particle executes SHM with
amplitudes \( 25 \mathrm{cm} \) and period 3 seconds. The minimum time required
for it to move between two points 12.5 \( \mathrm{cm} \) on either side of the mean position
is
A. \( 0.25 \mathrm{sec} \)
B . 0.50 sec
c. \( 0.75 \mathrm{sec} \)
D. \( 1.00 \mathrm{sec} \)


Consider a car moving at a constant speed of \( 14 \mathrm{m} / \mathrm{s} \) around a level circular bend of radius 45 m.The minimum
coefficient of static friction needed
between the car tyres and the road so that the car goes around the bend without skidding is
A. 0.44
B. 1.0
\( c \cdot 0.03 \)
D. 0.31


A parallel plate capacitor has a uniform electric field \( E \) in the space between the
plates. If the distance between the plates is \( d \) and area of each plate is \( A \)
the energy stored in the capacitor is :
A \( \cdot E^{2} A d / \varepsilon_{0} \)
в. \( \frac{1}{2} \varepsilon_{0} E^{2} A d \)
\( \mathbf{c} \cdot \varepsilon_{0} E A d \)
D \( \cdot \frac{1}{2} \varepsilon_{0} E^{2} \)


For all \( \theta \) in \( \left[0, \frac{\pi}{2}\right] \) Prove that
\( \cos (\sin \theta)>\sin (\cos \theta) \)


A trait in an organism is influenced by
A. Paternal DNA only
B. Maternal DNA only
C. Both maternal and paternal DNA
D. Neither by paternal nor by maternal DNA


The observation deck of tall skyscraper \( 370 m \) above the street. Determine the
time required for a penny to free fall from the deck to the street below
\( \mathbf{A} \cdot 8.69 s \)
B. \( 7.69 s \)
\( c .5 .69 \)
D. \( 8.6 s \)


The pair of molecules forming strongest hydrogen bonds are:
A. \( \operatorname{SiH}_{4} \) and \( \operatorname{SiF}_{4} \)
в. \( C H_{3} C O C H_{3} \) and \( C H C l_{3} \)
c. \( C H_{3} C O O H \) and \( H C O O H \)
D. \( H_{2} O \) and \( H_{2} \)


mole \( A_{X} B_{Y} \) when added to \( 1.08 \mathrm{kg} \) of
water, lowers its vapour pressure by 35 torr to 700 torr. If further 1184 g of methanol is added, then the vapour
pressure increase by 37 torr. Consider
only few vapors are formed, and \( \boldsymbol{A}_{\boldsymbol{X}} \boldsymbol{B}_{\boldsymbol{Y}} \)
is a non volatile solute. What is the
value of a if the vapour pressure of pure methanol is \( a \times 10^{2} \) torr.


Solve the given quadratic equation by
factorization method
\( \boldsymbol{x}^{2}-\mathbf{9}=\mathbf{0} \)


The source of stellar energy is
A. Nuclear fission
B. Nuclear fusion
C. Nuclear fission \& fusion
D. Nuclear decay


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}, \) the
value of \( \quad x^{100}+y^{100}+z^{100}- \)
\( \frac{9}{x^{101}+y^{101}+z^{101}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3


Number of sterio isomers are :
\( A \)
B. 6
\( c \cdot 15 \)
\( D \cdot 10 \)


Which of the following reactions
involves oxidation and reduction?
\( \mathbf{A} \cdot N a B r+H C l \rightarrow N a C l+H B r \)
B. \( H B r+A g N O_{3} \rightarrow A g B r+H N O_{3} \)
\( \mathbf{c} \cdot H_{2}+B r_{2} \rightarrow 2 H B r \)
D. \( N a_{2} O+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+H_{2} O \)


A object is placed at \( 30 \mathrm{cm} \) on the principle axis of the convex lens from the lens and an image is formed \( 60 \mathrm{cm} \) from the lens. If focal length of the lens is \( 20 \mathrm{cm} \) then calculate the
magnification.
A . 0.5
B. 0.67
\( c \cdot 1.5 \)
D. 2.0
E. 3.0


An air bubble of radius \( r \) is formed at a
depth \( h \) below the surface of water. The pressure inside the bubble is \( [\boldsymbol{T}= \)
surface tension, \( P_{o}= \) atmospheric pressure, \( \boldsymbol{d}=\text { density of water }] \)
\( ^{\mathrm{A}} \cdot_{P_{o}}=\frac{2 T}{r} \)
в. \( \frac{4 T}{r}+\frac{h}{r} \)
\( ^{\mathrm{c}} P_{o}+h d g+\frac{4 T}{r} \)
D. \( _{P_{o}+h d g}+\frac{2 T}{r} \)


Which Nernst equation is true to find
out the potential of non-standard
electrochemical cell from the following?
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})\left|\boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{x} \boldsymbol{M}) \| \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q} \cdot)\right| \boldsymbol{I}_{2}(\boldsymbol{s})(\boldsymbol{P} \boldsymbol{t}) \)
\( \mathbf{A} \cdot_{E e l l}=E_{c e l l}^{\circ}-\frac{0.592}{n} \log _{10}\left[F e^{2+}\right]\left[I^{-}\right]^{2} \)
B. \( \quad E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0592}{n} \log _{10}\left[\mathrm{Fe}^{2+}\right]\left[I^{-}\right]^{2} \)
\( ^{\mathbf{C}} E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0592}{n} \log _{10}\left[F e^{2+}\right]\left[I^{-}\right] \)
D \( \quad E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0592}{n} \log _{10} \frac{\left[F e^{2+}\right]\left[I^{-}\right]^{2}}{[F e]\left[I_{2}\right]} \)


If 2.5 moles of zinc react with 6.0 moles
of hydrochloric acid react in the
equation \( Z n+2 H C l \rightarrow Z n C l_{2}+H_{2} \)
what is the limiting reactant?
A \( . Z n \)
в. НС l
c. \( H_{2} \)
D. \( Z n C l \)
E . \( Z n H \)


The temperature of liquid hydrogen is
20 \( K \).What is this temperature on the Fahrenheit scale?
A \( \cdot 495.4^{\circ} \mathrm{F} \)
B. \( -423.4^{\circ} \mathrm{F} \)
c. \( -108.56^{\circ} \mathrm{F} \)
D . \( -487.4^{\circ} \mathrm{F} \)


Examine the continuity of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}|\boldsymbol{x}| \cos \frac{1}{x} & , \text { if } \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{0} & , \text { if } \boldsymbol{x}=\mathbf{0}\end{array} \text { at } \boldsymbol{x}=\right. \)
\( \mathbf{n} \)


Which of the following is more basic than aniline?
A. Diphenyl amine
B. Triphenyl Amine
C. p-nitro aniline
D. Benzyl amine


Club moss belongs to
A . Algae
c. Fungi
D. Bryophyta


A certain step-up transformer has 400 turns in the primary winding and 2,000 turns in the secondary winding. The turns ratio is
A . 0.2
B. 0.4
\( c .5 \)
D. 25


Find \( \overrightarrow{A B}, \) if \( A(4,3,4) \) and \( B(2,5,0) \)


Ethanol is converted into ethoxy ethane:
A. by heating excess of ethanol with conc. \( H_{2} S O_{4} \) at \( 140^{\circ} \) \( c \)
B. by heating Ethanol with excess of conc. \( H_{2} S O_{4} \) at 413 \( k \)
C. by treating with conc. \( H_{2} S O_{4} \) at room temperature
D. by treating with conc. \( H_{2} S O_{4} \) at \( 273 \mathrm{K} \)


The phosphorus present in an organic compound of mass 30 g is oxidized to phosphoric acid by heating with fuming nitric acid. The phosphoric acid so
obtained is precipitated as
\( M g N H_{4} P O_{4}, \) which on ignition is
converted into \( M g_{2} P_{2} O_{7} . \) If the
percentage composition of phosphorus present in the sample of the organic compound is 50 percent, find the
approximate mass of \( M g_{2} P_{2} O_{7} \) formed
A . 17 g
B. 25 g
c. \( 10 \mathrm{g} \)
D. None of these


\( S \) and \( T \) are points on sides \( P R \) and \( Q R \)
of \( \triangle P Q R \) such that \( \angle P=\angle R T S . \) Show
that \( \triangle \boldsymbol{R} \boldsymbol{P} \boldsymbol{Q} \sim \triangle \boldsymbol{R} \boldsymbol{T} \boldsymbol{S} \)


From which part of the alimentary canal does chemical digestion begins?
A. Mouth
B. Esophagus
c. Stomach
D. Gall bladder
E. Small intestine


A photon of wavelength 300 nm interacts with a stationary hydrogen atom in ground state. During the interaction, whole energy of the photon is transferred to the electron of the
atom. State which possibility is correct. (consider, Planck's constant \( =4.1 \times \)
\( 10^{-15} e V s, \) velocity of light \( =3 x \)
\( 10^{8} m / s, \) ionisation energy of hydrogen
\( =13.6 \mathrm{eV} \)
A. Electron will be knocked out of the atom
B. Electron will go to any excited state of the atom
C. Electron will go only to first excited state of the atom
D. Electron will keep orbiting on the ground state of the atom


The universal law of gravitation must be applicable to
A. The earth and the moon
B. The planets around the sun
c. Any pair of bodies.
D. The earth and the apple.


Why is soap referred to as salt?
A. It does not contain hydroxide ions
B. It has water of crystallization
C. It is prepared by reacting fatty acid with a strong base
D. All of above


Let \( f \) be a function which is continuous
and differentiable for all real \( x \). If
\( \boldsymbol{f}(\mathbf{2})=-\mathbf{4} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{6} \) for all \( \boldsymbol{x} \in \)
\( [2,4], \) then
\( \mathbf{A} \cdot f(4)<8 \)
B \( \cdot f(4) \geq 8 \)
\( \mathbf{c} \cdot f(4) \geq 12 \)
D. none of these


Solve the equation \( 2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \csc x) \)


Circumference of the first orbit of
hydrogen atom is given by the formula:
\( \left[a_{0}=\frac{h^{2}}{4 \pi^{2} m e^{2}}\right] \)
A \( \cdot \frac{22}{7} a \)
в. \( \frac{\pi a_{0}}{2} \)
c. \( \sqrt{4} \pi a_{0} \)
D. \( \pi a_{0} \)


State whether the following statements are true or false.

To call the leaf and stem of moss as true
leaf and true stem is wrong.
A. True
B. False


Which of the following is correct increasing order of pH of the hydroxide solution of \( \mathrm{T} \), \( \mathrm{P} \) and \( \mathrm{X} \) ?
\( A \cdot T<P<X \)
B. X<P<T
\( c \cdot P<T<x \)
D. P<X <T


Textbooks on science may give you a wrong impression that studying science is dry and all too serious and
that scientists are absent-minded
introverts who never laugh or grin. This image of science and scientists is patently false. Scientists, like anyother group of humans, have their share of humorists, and many have led their
lives with a great sense of fun and adventure, even as they seriously pursued their scientific work. Two great physicists of this genre are Gamow and
Feynman. You will enjoy reading their books listed in the Bibliography.


Identify the correct statement(s) from
the following. This question has multiple correct options
A. The ion having a positive charge on it is known as electro - positive ion.
B. The ion having a negative charge on it is known as electro - negative ion.
C. Simple ion is an ion which contains one or more atoms of the same element.
D. Compound ion is an ion which contains two or more atoms of different elements forming a single unit.


Order of reactivity of halogen acids towards an alcohol is:
A. HCI \( > \) HBr>H I
B. HBr>HI>HCI
c. HI>HBr>HCI
D. HI>HCI>HBr


For joining railway tracks, ferric oxide is reacted with aluminium to produce aluminium oxide and iron. The balanced
chemical equation for the given reaction is \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3(x)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{l}_{(x)} \rightarrow \)
Ferricoxide
\( \begin{array}{cc}\boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{x})} & \boldsymbol{+} \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{x})} \\ \text {Aluminium oxide} & \text {Iron}\end{array} \)
Which of the following substances is oxidized in the given reaction?
A \( \cdot A l_{2} O_{3} \)
в. \( F e_{2} O_{3} \)
\( c . A l \)
D. \( F e \)


A current 10 ampere is maintained in a
conductor of cross-section of \( 10^{-4} m^{2} \) if
the electron density is \( 9 \times 10^{28} m^{-2} \)
what is the drift velocity of free
electrons?


A plane electromagnetic wave of frequency \( 28 M H z \) travels in free space along the positive x-direction. At a particular point in space and time, electric field is \( 9.3 V / m \) along positive y-direction. The magnetic field (in T) at that point is
A \( \cdot 3.1 \times 10^{-8} \) along positive z-direction
B . 3.1 \( \times 10^{-8} \) along negative z-direction
C. \( 3.2 \times 10^{7} \) along positive z-direction
D. 3.2 \( \times 10^{7} \) along negative z-direction


Which of the atomic number represents
s -block elements?
A . 7, 15
B. 3,12
\( c \cdot 6,12 \)
D. 9, 17


Prove using PMI: \( \frac{1}{1.2 .3}+\frac{1}{2.3 .4}+ \)
\( \frac{1}{\mathbf{3 . 4 . 5}}+\ldots+\frac{1}{n(n+1)(n+2)}= \)
\( \frac{n(n+3)}{4(n+1)(n+2)} \)


Differential equation from \( a x^{2}+b y^{2}= \)
\( \mathbf{1} \) is


If you set up the seven overtone on a string fixed at both ends, how many nodes and antinodes are set up in it?
A .6,5
в. 5,4
c. 4,3
D. 3,2


Larger number of oxidation states are
exhibited by the actinoids than those by the lanthanoids, the main reason being:
A. more reactive nature of the actinoids than the lanthanoids
B. 4f orbitals more diffused than the 5 f orbitals
c. more energy difference between 5 5 and \( 6 d \) than between 4 f and 5d orbitals
D. lesser energy difference between 5 and \( 6 d \) than between \( 4 \mathrm{f} \) and \( 5 \mathrm{d} \) orbital


When an electron is moving parallel to
the conductor carrying current as
shown we get
A. region A has strong field
B. region B has weak field
C. region C has strong field
D. electron will move towards conductor


Pancreatic lipase acts upon
A. Glycogen
B. Triglycerides
c. Disaccharides
D. Polypeptides


In an ecosystem, the function of the
producers is to
A. Convert organic compounds into inorganic compounds
B. Trap solar energy and convert it into chemical energy
C. Utilize chemical energy
D. Release energy


The enzyme polynucleotide phosphorylase randomly assembles nucleotides into a polynucleotide phosphorylase to a solution of adenosine triphosphate and guanosine triphosphate, how many types artificial
\( m R N A 3 \) nucleotide codons would be
possible?
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
c. 8
D. 16


Let \( x_{1}, x_{2}, \ldots . . \) be positive integers in
A.P., such that \( x_{1}+x_{2}+x_{3}=12 \) and
\( \boldsymbol{x}_{4}+\boldsymbol{x}_{6}=\mathbf{1 4} . \) Then \( \boldsymbol{x}_{5} \) is
This question has multiple correct options
A. A prime number
B. 11
\( c \cdot 13 \)
D. 7


Rutherford's atomic model does not say
anything about the arrangements of electron in an atom
A. True
B. False


If \( \left(\frac{0.51 \times 10^{-10}}{4}\right) m, \) is the radius of smallest electron orbit in hydrogen like atom, then this atom is
A. H-atom
в. \( H e^{+} \)
\( \mathrm{c} \cdot L i^{2} \)
\( D \cdot B e^{3} \)


Zero group was introduced by :
A. Lother Meyer
B. Mendeleev
c. Ramsay
D. Lockyer


\( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\theta} & -\sin \boldsymbol{\theta} \\ \sin \boldsymbol{\theta} & \cos \boldsymbol{\theta}\end{array}\right] \) and \( \boldsymbol{A B}=\boldsymbol{B A}= \)
\( I, \) then \( B \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{cc}-\cos \theta & \sin \theta \\ \sin \theta & \cos \theta\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-\sin \theta & \cos \theta \\ \cos \theta & \sin \theta\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{cc}\sin \theta & -\cos \theta \\ -\cos \theta & \sin \theta\end{array}\right] \)


A particle with linear momentum of magnitude \( P \) is subjected to a force \( F= \) \( \mathrm{Kt}(\mathrm{k}>0) \) which is directed along the directed of initial momentum. The time
which its liner momentum changes to
\( 3 P \) is :
A \( \cdot \sqrt{\frac{2 P}{K}} \)
в. \( 2 \sqrt{\frac{P}{K}} \)
c. \( \sqrt{\frac{2 K}{P}} \)
D. \( 2 \sqrt{\frac{K}{P}} \)


1-Chlorobutane on reaction with
alcoholic potash gives:
A. 1 -Butene
B. 1-Butanol
c. 2 -Butene
D. 2-Butanol


Eliminate the arbitrary constant and obtain the differential equation satisfied by it
\( \boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}} \)
A \( \cdot y^{\prime}-y=2(1-x) \)
В. \( y^{\prime}-y=2(3-x) \)
c. \( y^{\prime}-y=2(1-3 x) \)
D . \( y^{\prime}-y=3(1-x) \)


The value of Bohr radius for hydrogen
atom is:
A \( .0 .529 \times 10^{-8} \mathrm{cm} \)
B . \( 0.529 \times 10^{-10} \mathrm{cm} \)
c. \( 0.529 \times 10^{-6} \mathrm{cm} \)
D. \( 0.529 \times 10^{-12} \mathrm{cm} \)


How many alphabets need to be there in
a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
A . 10
в. 100
c. 56
D. 26


If \( \left[\sin ^{-1} \cos ^{-1} \sin ^{-1} \tan ^{-1} \theta\right]=1, \) where
[.] denotes the greatest integer function, the \( \theta \) lies in the interval
A. [tan sin cos \( 1, \text { sin tan } \cos \sin 1] \)
B. [sin tan cos \( 1, \text { tan } \sin \cos \sin 1] \)
c. \( [\tan \sin \cos 1, \tan \sin \cos \sin 1] \)
D. None of these


Let \( \boldsymbol{A}=\{\boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}\} . \) Which of the following
is an equivalence relation in \( A \) ?
A \( \cdot R_{1}=\{(p, q),(q, r),(p, r),(p, p)\} \)
B . \( R_{2}=\{(r, q),(r, p),(r, r),(q, q)\} \)
C . \( R_{3}=\{(p, p),(q, q),(r, r),(p, q)\} \)
D. None of these


Wind is blowing west to east along two parallel tracks. Two trains moving with same speed in opposite directions have the relative velocity with respect to wind in the ratio \( 1: 2 . \) The speed of each train
is
A. equal to that of wind
B. double that of wind
c. three times that of wind
D. half that of wind


If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \) then a relation \( \boldsymbol{R}= \)
\( \{(a, b),(b, a),(a, a)\} \) on \( A \) is
A. symmetric and transitive only
B. reflexive and transitive only
c. symmetric only
D. transitive only


If \( f(x) \) is a polynomial of nth degree then \( \int e^{x} f(x) d x= \)
A \( \cdot e^{x}\left[f(x)-f^{\prime}(x)+f^{\prime \prime}(x)-f^{\prime \prime \prime}(x)+\ldots \ldots+(-1)^{n} f^{n}(x)\right] \)
Where \( f^{n}(x) \) denotes nth order derivative of w.r.t. \( x \)
B \cdot \( e^{x}\left[f(x)+f(x)+f^{\prime}(x)+f^{\prime \prime}(x)+\ldots \ldots+(-1)^{n} J^{n}(x)\right] \)
C. \( e^{x}\left[f(x)+f^{\prime}(x)+f^{\prime}(x)+f^{\prime \prime \prime}(x)+\ldots \ldots+(-1)^{n} f^{2 n}(x)\right] \)
D \cdot \( d\left[f(x)+f(x)+f^{\prime}(x)+f^{\prime \prime \prime}(x)+\ldots \ldots+\{-1)^{n} f^{3 n}(x)\right. \)


f points (1,2),(3,5) and \( (0, b) \) are collinear the value of b is
A \( \cdot \frac{1}{2} \)
в. \( \frac{7}{2} \)
\( c \cdot 2 \)
D. -


If we ignore the effect of crossing over, how many different haploid cells arise by meiosis in a diploid cell having \( 2 n=12 ? \)
\( A \cdot 8 \)
B. 16
\( c \cdot 32 \)
D. 64


\( z_{1} \) and \( z_{2} \) are the roots of the equation
\( z^{2}-a z+b=0, \) where \( \left|z_{1}\right|=\left|z_{2}\right|=1 \)
and \( a, b \) are non zero complex numbers, then
This question has multiple correct options
\( \mathbf{A} \cdot|a| \leq 1 \)
B. \( |a| \leq 2 \)
C \( \cdot \arg \left(a^{2}\right)=\arg (b) \)
\( \mathbf{D} \cdot \) arga \( =\arg \left(b^{2}\right) \)


The bond enthalpies of \( \boldsymbol{H}-\boldsymbol{H}, \boldsymbol{C l}-\boldsymbol{C l} \)
and \( H-C l \) are 435,243 and \( 431 \mathrm{kJ} \)
\( m o l^{-1}, \) respectively. The enthalpy of formation of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \) will be:
B. -92 kJ mol \( ^{-1} \)
\( \mathbf{c} \cdot 247 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 770 kJ mol \( ^{-1} \)


Express each of the following without using decimals:
\( \mathbf{3 . 5} \mathrm{cm} \)


Which one is a wrong statement?
A. Brown algae have chlorophyll a and c and fucoxanthin.
B. Archegonia are found in Bryophyta, Pteridophyta and Gymnosperms.
C. Mucor has biflagellate zoospores.
D. Haploid endosperm is typical feature of gymnosperms.


At very close point on the axis of a current carrying circular coil ( \( \boldsymbol{x}<<< \)
\( R \) ) of radius \( ^{\prime} R^{\prime}, \) the value of magnetic
field decreases by a fraction of \( 5 \% \) with respect to centre value. The position of the point from the centre of the coil is :-
A \( \cdot \frac{R}{\sqrt{10}} \)
в. \( \frac{R}{\sqrt{30}} \)
c. \( \frac{R}{\sqrt{50}} \)
D. \( \frac{R}{\sqrt{150}} \)


Let the solubility of an aqueous solution
of \( M g(O H)_{2} \) is \( x \) then its \( K_{s p} \) is
A \( \cdot 4 x^{3} \)
B . \( 108 x^{5} \)
\( \mathbf{c} \cdot 27 x^{4} \)
D. \( 9 x \)


Match the following Location
valve
1) Opening of coronary sinus tricuspid valve
2) The base of pulmonary aorta bicuspid valve
3) The opening of inferior vena cava semilunar valve
4) Bet left atrium and left ventricle
d) thebesian valve
5) Bet right atrium and right ventricle
e) eustachian valves


Choose the correct scientific names of
the following. Bladderwort, sundew, venus flytrap
A. Nepenthes, Dionaea, Drosera
B. Nepenthes, Utricularia, vanda
c. Utricularia, Drosera, Dionaea
D. Dionaea, Trapa, vanda


The following is an example of empty
set:
\( \{x: x \text { is a natural number, } x<8 \) and
simultaneously \( \boldsymbol{x}>\mathbf{1 2}\} \)
A. True
B. False


Seconal, a barbiturate drug, is used as:
A. antihistamine
B. sedative
C. antiseptic
D. antimalerial


The function \( f(x)=\sin ^{-1}(\cos x) \) is :
A. Discontinuous at \( x=0 \)
B. Continuous at \( x=0 \)
c. Differentiable at \( x=0 \)
D. None of these


Draw the electron dot stucture of a
molecule of sulphur which is made up
of eight atoms of sulphur.
\( A \)
B. \( S F_{4} \)
\( c \cdot S_{8} \)
D. None of the above


Find the magnitude of the angular
acceleration of the cone
A \( .3 .3 \mathrm{rad} / \mathrm{s}^{2} \)
B . \( 2.6 \mathrm{rad} / \mathrm{s}^{2} \)
c. 2.3 rad / \( s^{2} \)
D. \( 3.6 \mathrm{rad} / \mathrm{s}^{2} \)


A particle executing SHM takes 4 s to move from one extreme to another
extreme position. Find \( \omega \) of the particle.
A . \( 0.15 \pi \)
B. 0.25 \( \pi \)
c. \( 0.35 \pi \)
D. 0.45 \( \pi \)


ff \( f(x)+f(1-x)=10, \) then the value
of \( \boldsymbol{f}\left(\frac{1}{10}\right)+\boldsymbol{f}\left(\frac{2}{10}\right)+\ldots \ldots \ldots+\boldsymbol{f}\left(\frac{9}{10}\right) \) is
A . 45
B . 50
\( c .90 \)
D. Cannot be determined


sino-atrial node is called as the
pacemaker of our heart. Why?


A basic oxide will be formed by the element:
\( \mathbf{A} \cdot K \)
в. \( S \)
\( c . P \)
D. \( K r \)


Prostaglandin \( E_{1} \) 1 is a compound produced by the body to regulate a variety of processes including blood clotting, fever, pain and inflammation.
How many \( s p^{2} \) hybridised carbon atoms
are present in compound 1?
\( \mathrm{E}_{1} \)
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Symptoms of Lathyrism is/are
A. Bone deformation
B. Muscular dystrophy and paralysis
C. Asphyxia
D. cardiac arrest


A sum of money amounts to \( R s 66,836.70 \) in 2 years at \( 3 \% \) p.a. compound interest sum is


In the reaction \( 4 N H_{3}+5 O_{2} \longrightarrow \)
\( 4 N O+6 H_{2} O, \) when one mole of
ammonia and one mole of oxygen are made to react to completion, then
A . 1.0 mole of \( H_{2} O \) is produced
B. All the oxygen is consumed
c. 1.5 mole of \( N O \) is formed
D. All the ammonia is consumed


\( 20 \% \) of 2 is equal to


Which one of the following is a slime mold?
A. Anabaena
B. Rhizopus
c. Physarum
D. Thiobacillus


To prevent the loss of water, the leaves
of cactus plants are modified into
A. Scaly leaves
B. Tendrils
c. spines
D. Prop roots


A \( 3 p \) -orbital has:
A. two non-spherical nodes.
B. two spherical nodes.
C . one spherical and one non-spherical node.
D. one spherical and two non-spherical nodes.


Conversion of pyruvic acid into ethyl alcohol is facilitated by enzyme(s)
A. Carboxylase
B. Phosphatase
c. Dehydrogenase
D. Decarboxylase and dehydrogenase


\( N H_{4}^{+} \) is iso structural with:
A \( \cdot P C l_{3} \)
в. \( C H_{4} \)
\( \mathrm{c} \cdot B F_{3} \)
D. \( N O_{3} \)


A light spring of force constant \( \boldsymbol{K} \) is
held between two blocks of masses \( m \)
and \( 2 m . \) The two blocks and the spring system rests on a smooth horizontal
floor. Now the blocks are moved towards
each other compressing the spring by \( x \) and then they are suddenly released. The relative velocity between the blocks when the spring attains its natural length will be
\( ^{\mathrm{A}} \cdot(\sqrt{\frac{3 K}{2 m}}) x \)
\( ^{\mathrm{B}} \cdot(\sqrt{\frac{2 K}{3 m}}) x \)
\( ^{c \cdot}(\sqrt{\frac{K}{3 m}}) x \)
\( ^{\mathrm{D} \cdot}(\sqrt{\frac{K}{2 m}}) x \)


Let \( A \) and \( B \) be two finite sets having \( m \)
and \( n \) elements respectively such that \( \boldsymbol{m} \leq \boldsymbol{n} . \) A mapping is selected at random from the set of all mappings from \( A \) to \( B \). The probability that the mapping selected is an injection, is
A. \( \frac{n !}{(n-m) ! m^{n}} \)
в. \( \frac{n !}{(n-m) ! n^{m}} \)
c. \( \frac{m !}{(n-m) ! n^{m}} \)
D. \( \frac{m !}{(n-m) ! m^{n}} \)


Identify the types of rainwater harvesting method.
A. Roof top
B. Run off
c. Dam
D. Both A and B


A lift in which a man is standing, is moving upwards with a speed of \( 10 \mathrm{m} / \mathrm{s} \) The man drops a coin from a height of \( 4.9 m \) and if \( g=9.8 m / s^{2}, \) then the coin
reaches the floor of the lift after a time
A \( \cdot \sqrt{2} s \)
B. \( 1 s \)
c. \( \frac{1}{2} s \)
D. \( \frac{1}{\sqrt{2}} s \)


Compound (X) containing chlorine on treatment with strong ammonia gives a solid Y which is free from chlorine. (Y) analysed as: \( (C)=49.31 \%, H=9.59 \%, \) and
\( \mathrm{N}=19.18 \% \) and reacts with \( \mathrm{Br}_{2} \) and caustic soda to give a basic compound
(Z). \( (z) \) reacts with \( H N O_{2} \) to give ethanol. Suggest structures for \( (X),(Y) \) and \( (z) \)


Match List-I with List-II.


The type of lens present in human eye is
A. Convex lens
B. Concave lens
c. Plano convex lens
D. Plano concave lens


f \( 2 x+3 y=8 \) and \( x y=2, \) find the
value of \( 4 x^{2}+9 y^{2} \)


For the formation of urea, which one of
the following is required along with ammonia?
A. Arginase, \( C O_{2} \) and \( O_{2} \)
B. Arginase, \( C O_{2} \) and water
C. Asparate, \( C O_{2} \) and water
D. Asparate, \( C O_{2} \) and \( O_{2} \)


Chlorobenzene on reaction with acetyl chloride in presence of anhydrous
\( A l C l_{3} \) gives major product of:
A . 2 - chloro acetanilide
B. 2 - chloro acetophenone
c. 3 - chloro acetanilide
D. 4 - chloro acetophenone


Where was the first nuclear explosion by India was carried out?
A. Puskar
B. Narora
c. Pokhran
D. Mumbai


Magnetic filed at point \( ^{\prime} \boldsymbol{P}^{\prime} \) due to both
infinite long current carrying wires is :-
\( ^{A} \cdot \frac{\mu_{0}}{2 \pi} \)
в. \( \frac{5 \mu_{0}}{6 \pi} \)
\( c \cdot \frac{5 \mu_{0}}{6 \pi} \mathrm{c} \)
' \( \frac{\mu_{0}}{2 \pi} \) с


Integrate the following function.
\( \sin x \sin (\cos x) \)


\( H_{3} B O_{3} \) is named as
A. boric acid
B. monobasic and weak bronsted acid
c. dibasic and strong lewis acid
D. tribasic and weak bronsted acid


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A. diamagnetic
B. paramagnetic
c. ferromagnetic
D. none of these


The nth term of a series is given to be \( \frac{3+n}{4}, \) find the sum of 105 term of this series.


Rank in the order of increasing acidic
strength:
A \( . A<B<C \)
в. \( A<C<B \)
c. \( B<A<C \)
D. \( B<C<A \)


A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation(T) of the liquid drop depends on radius \( (r) \) of the drop, density \( (\rho) \) and surface tension(s) of the liquid. Which among the following will be a possible expression for T(where k is a dimensionless constant)?
A \( \cdot k \sqrt{\frac{\rho r}{s}} \)
B. \( k \sqrt{\frac{\rho^{2} r}{s}} \)
\( ^{\mathrm{c}} \cdot \sqrt[k]{\frac{\rho r^{3}}{s}} \)
D. \( k \sqrt{\frac{\rho r^{3}}{s^{2}}} \)


Two particles are moving with velocities \( v_{1} \) and \( v_{2} \). Their relative velocity is the
maximum, when the angle between their velocities is:
A. zero
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D.


Which logic gates is represented by the following combination of logic gates?
A. OR
B. NAND
c. AND
D. NOR


Growth of a shoot or a root involves
A. Cell enlargement
B. Cell division
c. cell differentiation
D. All the above


If \( \lim _{x \rightarrow \frac{\pi}{2}-} \tan x=a \) then \( \frac{1}{a} \) is equal
to


Khilona earned scores of 97,73 and 88
respectively in her first three examinations. If she scored 80 in the
fourth examination, then her average
score will be
A. increased by 1
B. increased by 1.5
c. decreased by 1
D. decreased by 1.5


Which of the following pairs of compounds have central atom with identical hybridization?
A. \( S O_{2} \) and \( S O C l_{2} \)
в. \( X e O_{3} \) and \( X e O_{2} F_{2} \)
c. \( X e F_{4} \) and \( X e O F_{4} \)
D. \( S F_{4} \) and \( X e F_{4} \)


Read the following statements and answer whether the given statement is true or false.

The number of magnetic lines of force passing through a surface is called magnetic flux linked with that surface.
A. True
B. False


Which of the following has the highest
numeric value?
A . 100 Tm
в. \( 1000 \mathrm{Gm} \)
\( \mathbf{c} \cdot 10^{4} \mathrm{mm} \)
\( D \cdot 10^{6} \mathrm{nm} \)


\( K_{c} \) for an equilibrium \( S O_{3} \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is equal to 0.15 at 900
K. The equilibrium constant for the
equation \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3}(g) \) is
A . 6.66
в. 44.4
c. 2.25
D. 0.44


Which of the following has a covalent
bond?
This question has multiple correct options
A \( . \) NaCl
в. \( H_{2} \) О
\( c \cdot O_{2} \)
D. None of these


Phytoplanktons are an important biotic
component of
A. Grassland ecosystem
B. Pond ecosystem
C. Forest ecosystem
D. None of the above


A pale blue liquid which is obtained by reacting equimolar mixture of two
gases at \( -30^{\circ} \mathrm{C} \) is :
A. \( N_{2} O_{3} \)
в. \( N_{2} \),
c. \( N_{2} O_{4} \)
D. \( N_{2} O_{5} \)


Suppose \( f \) and \( g \) both are linear function
with \( f(x)=-2 x+1 \) and \( f(g(x))= \)
\( 6 x-7 \) then slope of line \( y=g(x) \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. -3
\( c \cdot 6 \)
D. - 2


Which of the following represents soap?
A \( \cdot C_{17} H_{35} C O O K \)
в. \( C_{17} H_{35} C O O H \)
\( \mathbf{c} \cdot C_{15} H_{31} C O O H \)
D \( \cdot\left(C_{17} H_{35} C O O\right)_{2} C a \)


At a certain place, horizontal component is \( \sqrt{3} \) times the vertical component. The angle of dip at this place is:
A .
в. \( \pi / 3 \)
c. \( \pi / 6 \)
D. none of these


Stars which appear single to the naked eye but are double when seen through a telescope are
A. novas and supernovas
B. binaries
c. asteroids
D. quasars


Differentiate \( \sin \boldsymbol{h}^{-1}\left(\frac{\mathbf{1}}{\boldsymbol{x}}\right) \) with respect
to \( \boldsymbol{x}(\boldsymbol{x}>\mathbf{0}) \)


The maximum valuue of the expression \( \frac{1}{\sin ^{2} \theta+3 \sin \theta \cos \theta+5 \cos ^{2} \theta} \)


Mr.Abhishak saves Rs.1000 every
month and saves in recurring deposit scheme paying simple interest \( 10 \% \) per annum. In order to receive a total
amount of \( R s .5776, \) how many
installments must be deposits?


If \( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) are positive real
numbers whose product is a fixed number \( c \), then the minimum value of
\( \boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\boldsymbol{a}_{3}+\ldots \ldots+\boldsymbol{a}_{n-1}+\boldsymbol{a}_{n} \) is
A \( \cdot n(c)^{1 / n} \)
B \cdot \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D \cdot \( (n+1)(2 c)^{1 / n} \)


ff \( \left(x^{2}+\frac{1}{x}\right)^{n} \) has exactly one middle term which is equal to \( \alpha . x^{3} \) then the
value of \( (\boldsymbol{\alpha}+\boldsymbol{n}) \) is- \( \quad(\boldsymbol{n} \in \boldsymbol{N}) \)
A . 18
B . 21
c. 24
D. 26


Find the following limit:
\( \lim _{x \rightarrow 1} \frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt[3]{1+x}-\sqrt[3]{1-x}} \)


Animals that feed discontinuously
A. exhibit extremely rapid digestion
B. must have digestive tracts that permit storage
C . are able to avoid predators by limiting their feeding time
D. both (b) and (c)


Magnification produced by a convex mirror is always:
A. equal to 1
B. less than
c. more than 1
D. zero


Trochophore larva occurs in
A. Annelida and porifera
B. Coelenterata and annelida
C. Mollusca and coelenterata
D. Annelida and mollusca


Mercury in the presence of ozone is
oxidised to mercuric oxide.

If the given statement is true enter 1 else enter 0
A. True
B. False


The redox potential of \( \boldsymbol{F e}^{\mathbf{3}+} \mid \boldsymbol{F e}^{\mathbf{2}+} \)
electrode at \( \mathrm{pH}=4 \) is:
A. \( 0.8 \mathrm{v} \)
B. 0.5
c. \( 0.2 v \)
D. 0.1


For a transformer, the turns ratio is 3 and its efficiency is \( 0.75 . \) The current flowing in the primary coil is \( 2 A \) and the
voltage applied to it is \( 100 \mathrm{V} \). Then the
voltage and the current flowing in the secondary coil are
respectively.
A. \( 150 V, 1.5 A \)
B . \( 300 V, 0.5 A \)
c. \( 300 V, 1.5 A \)
D. \( 150 V, 0.5 A \)


List conditions under which
combustion can take place.


The velocity (v) of a particle that moves in the positive x-direction varies with its position (x) as shown in the figure.
The acceleration of the particle at \( x=5 \)
\( \mathrm{m} \) is nearly:
A \( \cdot 10 \mathrm{ms}^{-2} \)
В. \( 9.4 \mathrm{ms}^{-2} \)
\( c \cdot 7 \cdot 4 m s^{-2} \)
D. \( -1.25 \mathrm{ms}^{-2} \)


The differential equation obtained by eliminating arbitrary constants from \( \boldsymbol{y}=\boldsymbol{a} \cdot \boldsymbol{e}^{b \boldsymbol{x}}, \) is
A \( \cdot y \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=0 \)
B. \( y \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0 \)
c. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)^{2}=0 \)
D. \( y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)


The reaction of aqueous \( K M n O_{4} \) with
\( H_{2} O_{2} \) in acidic conditions gives:
\( A \cdot M n^{4+} \) and \( O_{2} \)
B. \( M n^{2+} \) and \( O_{2} \)
c. \( M n^{2+} \) and \( O_{3} \)
D. \( M n^{4+} \) and \( M n O_{2} \)


The general formula of carbohydrates is:
A \( \cdot C_{n} H_{2 n+1} O \)
в. \( C_{n} H_{2 n} O \)
\( \mathbf{c} \cdot C_{n}\left(H_{2} O\right)_{n} \)
D. \( C_{n}\left(H_{2} O\right)_{2 n} \)


Assertion
Selaginella and Salvinia are homosporous
Reason
Similar kind of spores are produced in Selaginella and Salvinia.
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


Among the following orbital bonds, the angle is minimum between :
A \( \cdot s p^{3} \) bonds.
B . \( p_{x} \) and \( p_{y} \)
c. \( H-O-H \) in water
D. \( s p \) bonds


If calcium of weight \( x \) g, carbon \( y \) g and oxygen \( z \) g, are present in 1.5 g of calcium carbonate and if a sample of calcium carbonate from another source contains the following percentage composition: \( \boldsymbol{C a}=\mathbf{4 0 . 0 \%}, \boldsymbol{C}=\mathbf{1 2 . 0 \%} \)
and \( O=48.0 \% \), then find the value of
\( x, y \) and \( z . \) (The law of constant composition holds true.)
в. \( x=0.4, y=0.18, z=0.62 \)
c. \( x=0.6, y=0.2, z=0.70 \)
D. None of the above


Rainfall patterns depend on
A. The underground water table
B. The number of water bodies in an area
C. The density pattern of human population in an area
D. The prevailing season in an area.


How are the areas study of evolution
and classification interlinked?


In a transistor,
A. both emitter and the collector are equally doped
B. base is more heavily doped than collector
C. collector is more heavily doped than the emitter
D. the base is made very thin and is lightly doped


Two positive point charges are of \( 12 C \) and \( 8 C \) are \( 10 \mathrm{cm} \) apart from each other
The work done in bringing them \( 4 c m \) closer is
A . \( 5.8 J \)
в. \( 13 e V \)
c. \( 5.8 e V \)
D. \( 13 J \)


7 white balls and 3 black balls are
randomly placed in a row. The probability that no two black balls are placed adjacently equals
A \( \cdot \frac{1}{2} \)
в. \( \frac{7}{15} \)
c. \( \frac{2}{15} \)
D.


Drawing of ductile metals into thin wires results in:
A. increase in molecular separation
B. increase in stress in the metal
c. reducton of cross-sectional area
D. all of these


In the above figure both RISK and CLUE
are parallelograms. Find the value of \( x \)


Prove the following using the principle
of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( 1+3+3^{2}+\ldots \ldots . .+3^{n-1}=\frac{\left(3^{n}-1\right)}{2} \)


\( N X \) is produced by the following step of reactions:
\( \boldsymbol{M}+\boldsymbol{X}_{2} \longrightarrow \boldsymbol{M} \boldsymbol{X}_{2} \)
\( \mathbf{3} \boldsymbol{M} \boldsymbol{X}_{\mathbf{2}}+\boldsymbol{X}_{\mathbf{2}} \longrightarrow \boldsymbol{M}_{\mathbf{3}} \boldsymbol{X}_{\mathbf{8}} \)
\( M_{3} X_{8}+N_{2} C O_{3} \longrightarrow N X+C O_{2}+ \)
\( \boldsymbol{M}_{3} \boldsymbol{O}_{4} \)
How much \( M \) (metal) is consumed to
produce \( 206 g m \) of \( N X ? \) (Take atomic weight of \( \boldsymbol{M}=\mathbf{5 6}, \boldsymbol{N}= \)
\( \mathbf{2 3}, \mathbf{X}=\mathbf{8 0}) \)
\( \mathbf{A} \cdot 42 g m \)
в. \( 336 g m \)
c. \( \frac{14}{3} g m \)
D \( \cdot \frac{7}{4}^{g m} \)


Water is filled to a height \( \boldsymbol{H} \) behind \( \boldsymbol{a} \)
dam of width \( w . \) The resultant force on
dam is:
A. \( p g w H^{2} \)
В \( \cdot \frac{1}{2} p g w H^{2} \)
c. \( 2 p g w H^{2} \)
D. \( 4 p g w H^{2} \)


In Thomson's experiment, a magnetic field of induction \( 10^{-2} w b / m^{2} \) is used
For an undeflected beam of cathode
rays, a Potential Difference of \( 500 V \) is
applied between the plates which are \( 0.5 c m \) apart. Then the velocity of the cathode ray beam is \( \mathrm{m} / \mathrm{s} \)
A \( \cdot 4 \times 10^{7} \)
B . \( 2 \times 10^{7} \)
c. \( 2 \times 10^{8} \)
D. \( 10^{7} \)


In a Fraunhofer diffraction at single slit of width d with incident light of
wavelength \( 5500 A^{0} \), the first minimum
is observed at angle \( 30^{0} . \) The first secondary maximum is observed at an
angle \( \theta= \)
A \( \cdot \sin ^{-1}\left[\frac{1}{\sqrt{2}}\right] \)
B. \( \sin ^{-1}\left[\frac{1}{4}\right] \)
\( \mathbf{c} \cdot \sin ^{-1}\left[\frac{3}{4}\right] \)
D. \( \sin ^{-1}\left[\frac{\sqrt{3}}{2}\right] \)


A toy car with charge \( q \) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \( \vec{E} \). Due to the force \( \boldsymbol{q} \overrightarrow{\boldsymbol{E}} \), its
velocity increases from 0 to 6 m/s in
one second duration. At that instant the
direction of the field is reversed. The car
continues to move for two more seconds
under the influence of this field. The
average velocity and the average speed
of the toy car between 0 to 3 seconds
are respectively
A \( .2 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
B. \( 1 \mathrm{m} / \mathrm{s}, 3.5 \mathrm{m} / \mathrm{s} \)
c. \( 1 \mathrm{m} / \mathrm{s}, 3 \mathrm{m} / \mathrm{s} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}, 3 \mathrm{m} / \mathrm{s} \)


Let \( 0<\alpha<\frac{\pi}{2} \) be a fixed angle. If \( P= \)
\( (\cos \theta, \sin \theta) \) and \( Q=(\cos (\alpha- \)
\( \boldsymbol{\theta}), \sin (\boldsymbol{\alpha}-\boldsymbol{\theta})) \) then \( \boldsymbol{Q} \) is obtained from
\( P \) by
A. clockwise rotation around the origin through an angle
B. anticlockwise rotation around the origin through an angle \( \alpha \)
c. reflection in the line through origin with slope \( \tan \alpha \)
D. reflection in the line through the origin with slope \( \tan (\alpha / 2) \)


Area of the region bounded by \( \boldsymbol{x}=\mid \boldsymbol{y}+ \)
\( 4 \mid \) and \( x \) axis is sq. units
A .4
B. 8
\( c \cdot 16 \)
D. 32


If image is real and inverted, mangification will be:
A . two
B. negative
c. one
D. zero


The surface of a planet is found to be uniformly charged. When a particle of
mass \( m \) and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range \( L \). A particle
of mass \( m \) and charge \( q \) with the same initial conditions has a range \( \frac{L}{2} \). The range of particle of mass \( m \) and charge \( 2 q \)
with the same initial conditions is :
A. \( L \)
в. \( \frac{L}{2} \)
c. \( \frac{L}{3} \)
D. \( \frac{L}{4} \)


Prove that the centre of a circle
touching two intersecting lines lies on the angle bisector of the lines.


If a ball is projected with a velocity equal to \( 1 / 4 \) th of the escape velocity from the surface of the earth. the height it will attain is \( _{-} \).
Radius of Earth]
A \( \cdot \frac{R}{4} \)
в. \( \frac{R}{32} \)
c. \( 4 R \)
D. \( \frac{R}{16} \)


When a colloidal solution is viewed from
the direction at right angles of the light beam, the path of the beam is
illuminated due to scattering of light. In the given figure (A) and (B) are:
A . A - Tyndall cone, B - Scattered light
B. A - Scattered light, B - Tyndall cone
C. A - Tyndall cone, B - Blind spot
D. A - Tyndall effect.
B - Tyndall cone


A healthy person eats a very highprotein diet.What will be the effect on
the person's urine?
A. It will contain amino acids.
B. It will contain glucose.
c. It will contain more urea
D. It will contain more water.


Assertion
Pure water obtained from different
sources such as river, well, spring, sea etc. always contain hydrogen and oxygen combined in the ratio 1: 8 by
mass.
Reason
A chemical compound always contains elements combined together in same proportion by mass, it was discovered by French chemist, Joseph Proust (1799)
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


If \( \theta_{1}, \theta_{2}, \theta_{3}, \ldots . \theta_{n} \) are in \( A . P ., \) then
\( \frac{\sin \theta_{1}+\sin _{2}+\ldots+\sin \theta_{n}}{\cos \theta_{1}+\cos \theta_{2}+.+\cos \theta_{n}}= \)
\( A \cdot 0 \)
B \( \cdot \tan \left(\theta_{1}+\theta_{n}\right) \)
c. \( \tan \left(\frac{\theta_{1}+\theta_{n}}{2}\right) \)
D. \( \tan \left(\frac{\theta_{n}-\theta_{1}}{2}\right) \)


Metals which have a low melting point are refined by liquation.
A. True
B. False


On the Cartesian plane, \( Q \) is the
midpoint of the straight line \( \boldsymbol{P} \boldsymbol{R} \)
Find the values of \( x \) and \( y \)
A \( . x=3, y=2 \)
B. \( x=4, y=2 \)
c. \( x=4, y=3 \frac{1}{2} \)
D. \( x=8, y=3 \)


The echo will be heard if the orginal
sound reflected by an obstacle reaches our ears after
A . 10 sec
B. 5 sec
c. 1 sec
D. 0.1 sec


The cell reaction for the given cell is spontaneous if:
\( \boldsymbol{P t}\left|\boldsymbol{C l}_{2}\left(\boldsymbol{P}_{1} \boldsymbol{a} \boldsymbol{t m}\right)\right| \boldsymbol{C l}^{-}(\boldsymbol{1} \boldsymbol{M}) \mid \boldsymbol{C l}_{2}\left(\boldsymbol{P}_{2} \boldsymbol{a}\right. \)
A \( \cdot P_{1}>P_{2} \)
в. \( P_{1}<P_{2} \)
c. \( P_{1}=P_{2} \)
D. \( P_{1}=1 \) at \( m \)


Two electrochemical cells are
assembled in which following reactions
occur.
\( \boldsymbol{V}^{2+}+\boldsymbol{V} \boldsymbol{O}^{2+}+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{2} \boldsymbol{V}^{3+}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} ; \quad \boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 6 1 6} \boldsymbol{V} \)
\( \boldsymbol{V}^{3+}+\boldsymbol{A} \boldsymbol{g}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{V} \boldsymbol{O}_{2}+\boldsymbol{4} \boldsymbol{H}^{+}+ \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) ; \boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 4 3 9} \boldsymbol{V} \)
\( E^{o} \) for half reaction, \( V^{3+}+e \rightarrow V^{2+} \) is :
Given that \( \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}=\boldsymbol{0 . 7 9 9} \boldsymbol{V} \)
A. \( -0.256 v \)
B . - 0.216 V
c. \( -0.346 v \)
D. None of these


5th period element with no electrons in
5th orbit is:
A. Pd
B. Pt
c. \( \mathrm{Ni} \)
D. zn


In a given area, insects live by making burrows in the bark of a tree. These
insects are fed upon by a population of birds in the same area. The most correct
explanation for the increase in the beak size of the bird population is
A. Increased fitness of the birds, leading to speciation
B. Decreased fitness of the insects, allowing the birds to catch them more easily
c. Increased fitness of large-beaked birds, leading to evolution
D. Decreased fitness of small-beaked birds, leading to speciation
E. Random mutation and genetic recombination


Write the formula of the
potassiumtetracyanonickel(0).


ff \( A=\left[\begin{array}{ccc}-1 & 0 & 0 \\ 0 & x & 0 \\ 0 & 0 & m\end{array}\right] \) is a scalar matrix
then \( \boldsymbol{x}+\boldsymbol{m}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot-2 \)
D. -3


Which of the following functions correctly represent the travelling wave equation for finite values of \( x \) and \( t \)
A \( \cdot y=x^{2}-t^{2} \)
B \( \cdot y=\cos x^{2} \sin t \)
c. \( y=\log \left(x^{2}-t^{2}\right)-\log (x-t) \)
D・ \( y=e^{2 x} \sin t \)


1 kg of a sample of water contains 222
\( \mathrm{mg} \) of \( \mathrm{CaCl}_{2} \) and \( 219 \mathrm{mg} \) of
\( M g\left(H C O_{3}\right)_{2} . \) Its permanent hardness and temporary hardness in ppm are respectively:
A .200,200
B . 200,150
c. 200,300
D. 150,220


Maximum number of electrons in a sub
shell is given by:
A \( \cdot(2 l+1) \)
B. \( 2(2 l+1) \)
\( \mathbf{c} \cdot(2 l+1)^{2} \)
D. \( 2(2 l+1)^{2} \)


A son inherits an \( X \) chromosome from
A. Mother
B. Father
c. Both A and B
D. Grandparents


Match the Column-I with Column-II.


If \( \boldsymbol{A}=\left|\begin{array}{cc}\mathbf{5} & \boldsymbol{x}-\mathbf{2} \\ \mathbf{2} \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\mathbf{1}\end{array}\right| \) is symmetric
\( \operatorname{then} x= \)
A .4
B. 5
c. -5
D. -


Which of the squares must be shaded
so that the dotted line AB becomes the
line of symmetry?
\( A \)
B. \( I I \)
c. \( I I I \)
D. \( I V \)


A body is given translational velocity and kept on a surface that has sufficient friction. Then:
A. Body will move forward before pure rolling
B. Body will move backward before pure rolling
c. Body will start pure rolling immediately
D. None of these


have 4 to 8 electrons
in the outermost shell.
A. Non-metals
B. Metalss
c. Metalloids
D. Transition elements


\( \int x^{5} d x \)


The denominator of a fraction is greater
than its numerator by \( 7 . \) If 4 is added to both its numerator and denominator,
then it becomes \( \frac{1}{2} . \) Find the fraction.
A \( \cdot \frac{1}{6} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{3}{10} \)
D. 6 \( \overline{7} \)


\( 32 g \) of oxygen and \( 3 g \) of hydrogen are mixed and kept in a vessel at 760 mm
pressure and \( 0^{\circ} \mathrm{C} \). The total volume occupied by the mixture will be nearly:
A . 22.4 litre
B. 11.2 litre
c. 44.8 litre
D. 56 litre


\( \left(2 m^{2}-3 m+10\right) \div(m-5) \)


The force between two parallel conductors, each of length \( 50 \mathrm{cm} \) and
distant \( 20 \mathrm{cm} \) apart is \( 100 \mathrm{N} \). If the current in one conductor is double that
in another one then the values will
respectively be(Given \( \left.\mu_{0}=4 \pi \times 10^{-7}\right) \)
B. \( 50 A \) and \( 100 A \)
c. \( 10 A \) and \( 20 A \)
D. \( 5 A \) and \( 10 A \)


Peptidyl transferase plays an important role during protein synthesis. What is true about this enzyme?
A. It is proteinaceous
B. It is RNA as catalyst
c. It helps in peptide bond formation
D. Both B and C


Match the integrals of \( f(x) \) if


A train of length \( 100 m \) travelling at \( 20 m / s \) overtakes another of length
\( 200 m \) travelling at \( 10 m / s . \) The time taken by the first train to pass the second train is
A . \( 30 s \)
в. \( 50 s \)
\( c \cdot 10 s \)
D. \( 40 s \)


The correct order of ionization energies
of \( \boldsymbol{F}^{-}, \boldsymbol{C l}^{-} \boldsymbol{F} \) and \( \boldsymbol{C l} \) is:
A \( \cdot C l<F<C l^{-}<F^{-} \)
B . \( C l^{-}<F^{-}<C l<F \)
c. \( F^{-}<C l^{-}<C l<F \)
D. \( C l^{-}<C l<F^{-}<F \)


Negative deviation from Raoult's law is observed in which one of the following binary liquid mixtures?
A. Ethanol and acetone
B. Benzene and toluene
c. Acetone and chloroform
D. Chloroethane and bromoethane


toppr
Q Type your question
the graph shown on the right above.
What will be the average current that
flows through the coil during time T?
A \( \cdot V_{0} T / 2 L \)
\( (\mathrm{A}) \)
в. \( V_{0} T / 6 L \)
\( (\mathrm{B}) \)
\( \mathbf{c} \cdot 3 V_{0} T / 2 L \)
\( (C) \)
D. \( V_{0} T / L \)
\( (\mathrm{D}) \)


Without actual finding the square of the numbers, find the value of \( 120^{2}-119^{2} \)
A . 239
в. 240
\( c \cdot 238 \)
D. 237


Assertion
Rainy clouds appear dark from below.
Reason

There is not sufficient light which can
be scattered by these clouds.
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


There are two non conducting spheres
having uniform volume charge
densities \( \rho \) and \( -\rho . \) Both spheres have
equal radius R. The spheres are now laid
down such that they overlap as shown in the figure. The electric field \( \overrightarrow{\boldsymbol{E}} \) in the
overlap region is :
A. non uniform
B. zero
c. \( \frac{\rho}{3 \epsilon_{0}} \vec{d} \)


In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other. Then,
in the interference pattern.
A. The intensities of both the maxima and the minima increase
B. The intensity of the maxima increases and the minima has zero intensity
c. The intensity of the maxima decrease and that of the minima increases
D. The intensity of the maxima decreases and the minima has zero intensity


A boy is \( 1.8 m \) tall and can see his
image in a plane mirror fixed on a wall.
His eyes are \( 1.6 m \) from the floor level
The minimum length of the mirror to see his full image is-
A \( .0 .9 m \)
B. \( 0.85 m \)
\( c .0 .8 m \)
D. Can't be determined


The length of an elastic string is \( a \) metre when the longitudinal tension is \( 4 \mathrm{N} \) and \( b \) metre when the longitudinal
tension is 5 N. The length of the string in metre when longitudinal tension is \( 9 N \) is :
\( \mathbf{A} \cdot a-b \)
B. \( 5 b-4 a \)
c. \( 2 b-\frac{1}{4} a \)
D. \( 4 a-3 b \)


A uniform solid cylinder is given a linear
velocity and angular velocity, so that it rolls without sliding up the incline. Out
of the four points \( A, B, C \) and centre of mass, about which point its angular
momentum will be conserved?
(A and \( C \) are taken at appropriate distance)
\( A \cdot \) Point \( A \)
B. Point B
C. Point \( C \)
D. Centre of mass


\( \cot ^{-1} 9+\operatorname{cosec}^{-1} \frac{\sqrt{41}}{4}=? \)
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{3 \pi}{4} \)


The velocity of a particle is \( \overrightarrow{\boldsymbol{v}}=\mathbf{6} \hat{\mathbf{i}}+ \)
\( 2 \hat{j}-2 \hat{k} . \) The component of the velocity parallel to vector \( \vec{a}=\hat{i}+\hat{j}+\hat{k} \) is :-
\( \mathbf{A} \cdot 6 \hat{i}+2 \hat{j}+2 \hat{k} \)
B . \( 2 \hat{i}+2 \hat{j}+2 \hat{k} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( 6 \hat{i}+2 \hat{j}-2 \hat{k} \)


Assertion
The \( 5^{t h} \) period of periodic table contains 18 elements not 32
Reason
\( \mathbf{n}=\mathbf{5}, \ell=\mathbf{0}, 1,2, \) 3. The order in which the
energy of available orbitals \( 4 \mathrm{d}, 5 \mathrm{s} \) and
\( 5 p \) increases is \( 5 s<4 d<5 p \) and the total number of orbitals available are 9
and thus 18 electrons can be
accommodated.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A family which was named after its
inflorescence is
A. Poaceae (graminae)
B. Malvaceae
c. Apiaceae (Umbelliferae)
D. Moraceae


In the esterification of an organic acid R-COOH by alcohol R'OH, O of acid is isotopic. \( \boldsymbol{R}-\stackrel{\mathbb{N}}{\boldsymbol{C}}-\stackrel{\mathbf{1 8}}{\boldsymbol{O} \boldsymbol{H}}+\boldsymbol{R}^{\prime}-\boldsymbol{O}-\boldsymbol{H} \rightarrow \boldsymbol{R}- \)
\( \stackrel{0}{C}-O R^{\prime}+H_{2} O \)
Which of the following statement is correct?
A. 18 p is in ester
B. 18 O is in water
\( c \cdot 18 O \) is in both
\( D \cdot 18 O \) is in none


Which one of the following changes may occur due to desertification?
A. Decrease in atmosphere temperature
B. Increase in water holding capacity of soil
c. Increased chances of foods
D. Conversion of fertile land into a desert


A particle stars from rest covers a distance of x with constant acceleration
then move with constant velocity and
cover distance \( 2 x \) then after come to
rest will constant retardation with cover
distance of \( 3 x, \) then ratio of \( V_{\max } / V_{\text {avg }} \)
will be
\( A \cdot 3: 5 \)
B. 5: 3
c. 7:
D. 5:


Consider the following statements
A) Linear momentum of a system of
particles is zero
B) Kinetic energy of a system of particles is zero Then
A. A does not imply B \& B does not imply A
B. A implies B and B does not imply A
c. A does not imply B but B implies A
D. A implies B and B implies A


If the roots of the equation \( 5 x^{2}-7 x+ \)
\( k=0 \) are mutually reciprocal then \( k= \)
A . 5
B. 2
\( c \cdot \frac{1}{5} \)
D. None of these


Find the inverse of the following matrices by the adjoining method
\[
\left[\begin{array}{lll}
1 & 2 & 3 \\
0 & 2 & 4 \\
0 & 0 & 5
\end{array}\right]
\]


Expand \( (1-2 x)^{5} \)


Let \( \boldsymbol{f}: \mathbb{R} \rightarrow(0,1) \) be a continuous
function. Then, which of the following function(s) has (have) the value zero at
some point in the interval (0,1)\( ? \) This question has multiple correct options
\( \mathbf{A} \cdot f(x)+\int_{0}^{\frac{\pi}{2}} f(t) \sin t d t \)
B . \( e^{x}-\int_{0}^{x} f(t) \sin t d t \)
C \( \cdot x-\int_{0}^{\frac{\pi}{2}-x} f(t) \cos t d t \)
D. \( x^{9}-f(x) \)


If the midpoints of the line segment joining the points \( P(6, b-2) \) and (-2,4) is \( (2,-3), \) find the value of \( b \)


Find an angle \( \theta, 0<\theta<\frac{\pi}{2}, \) which
increases twice as fast as its sine.
A \( .60^{\circ} \)
B. \( 120^{\circ} \)
\( c .90^{\circ} \)
D. \( 45^{\circ} \)


The continuous movement of a fluid
when heated is called:
A. convectional current
B. conduction current
c. electric current
D. magnetic current


State true or false:
Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
A. True
B. False


The potential across a 25.0 microfarad capacitor is \( 5.0 V . \) What is the charge on
the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. We cannot determine the charge on the capacitorwith the given information


Which of the following is s-
butylphenylvinyl methane?
\( A \)
\( B \)
\( c \)
\( D \)


An atom contains eleven protons. State
its atomic number and the number of
electrons it contains.
\( A \cdot 12,12 \)
B. 12,11
c. 11,11
D. 12, 13


If \( A \) and \( B \) are two square matrices such that \( B=-A^{-1} B A, \) then
\( (A+B)^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)


A rod of mass \( m \) and length \( l \) is
connected with a light rod of length \( l \)
The composite rod is made to rotate with angular velocity \( \omega \) is shown in the
figure. Find the total kinetic energy.


When the power delivered by a 100 volt battery is 40 watts, the equivalent resistance of the circuit is:
A. 100 ohms
B. 250 ohms
c. 300 ohms
D. 350 ohms


Which letter corresponds to the total
change in energy for the overal
reaction?
\( A \)
B. B
\( c \cdot c \)
0.0
\( E \)


Number of \( s p \) carbons in the molecule
\( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2} \) is:


Which gas is liberated when an acid
reacts with metal?


Construct the following Quadrilateral of
given measures.
In Quadrilateral MORE: \( \ell(M O)= \)
\( \mathbf{5 . 8} \boldsymbol{c m}, \ell(\boldsymbol{O} \boldsymbol{R})=\mathbf{4 . 4} \boldsymbol{c m}, \boldsymbol{m} \angle \boldsymbol{M}= \)
\( \mathbf{5 8}^{\circ}, \boldsymbol{m} \angle \boldsymbol{O}=\mathbf{1 0 5}^{\circ}, \boldsymbol{m} \angle \boldsymbol{R}=\mathbf{9 0}^{\circ} \mathbf{?} \)


The solubility product of sparingly soluble salt \( A g_{2} C r O_{4} \) is \( 4 \times 10^{-12} \). The
molar solubility of the salt is
\( 10^{-x} \) mol \( / L ? \) What is the value of \( x ? \)


The mean deviation of a frequency dist. is equal to
A \( \frac{\sum d_{i}}{\sum f_{i}} \)
в. \( \frac{\sum\left|d_{i}\right|}{\sum f_{i}} \)
\( c \cdot \frac{\sum f_{i} d_{i}}{\sum f_{i}} \)
D \( \cdot \frac{\sum f_{i}\left|d_{i}\right|}{\sum f_{i}} \)


A body moving along a circular path may have
A. A constant speed
B. A constant velocity
c. No tangential velocity
D. No radial acceleration


The phenomenon of diffraction can be treated as interference phenomenon if the number of coherent sources is
A. one
B. two
c. zero
D. infinity


Area bounded by the curve \( y=x^{3}, \) the
x-axis and the ordinates \( x=-2 \) and
\( x=1 \) is :


In resting stage, binding sites for myosin on actin filaments are masked by
A. Troponin
B. Light meromyosin
c. Heavy meromyosin
D. Calcium ions


Which of the following carbohydrates is not a monosaccharide?
A. Glucose
B. Fructose
c. Galactose
D. sucrose


As dilution of the solution increases
then the conductivity of solution
A. increases
B. decreases
c. remain unchanged
D. none of the above


Given
\( \boldsymbol{S}_{(s)}+\boldsymbol{O}_{2(g)} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2(g)} ; \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\mathbf{2 9 8 . 2 k J} \)
\( \boldsymbol{S} \boldsymbol{O}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3(g)} ; \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -98.7 k J \)
\( \boldsymbol{S O}_{\boldsymbol{3}(\boldsymbol{g})}+\boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -130.2 k J \)
\( \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -287.3 k J \)
The enthalpy of formation of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) will
be :
\( \mathbf{A} \cdot-814.4 k J \)
В. \( +320.5 k J \)
c. \( -650.3 k J \)
D . \( -933.7 k J \)


How many total distinct terms are there
in the expansion of \( (x+y+z+t)^{10} \)


An Arithmetic progression consists of 20 terms of which 4 th term is 16 and the
last term is \( 208 . \) Find the 15 th term
A . 146
B. 147
\( c \cdot 148 \)
D. 149


Solve the following inequality and show it graphically:
\( -2<x+3<5, x \in Z \)
\( A \)
в.
\( c \)
D.


Ectoparasite of shark is
A. Herdmania
B. Balanoglossus.
c. Amphioxus
D. Petromyzon


For the reaction
\[
\boldsymbol{P C l}_{3(g)}+\boldsymbol{C l}_{2(g)} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5(g)}
\]
the value of \( \boldsymbol{K}_{c} \) at \( 250^{\circ} \mathrm{C} \) is \( 26 . \) The
value of \( K_{p} \) a this temperature will be
A . 0.61
B. 0.57
c. 0.83
D. 0.46


\( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{7}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{4} \\ -\mathbf{1} & \mathbf{7}\end{array}\right] \boldsymbol{C}= \)
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ \mathbf{- 1} & \mathbf{4}\end{array}\right] \)
find \( \boldsymbol{A} \boldsymbol{C}+\boldsymbol{B}^{2}-\mathbf{1 0 C} \)


A coin is rolled n times. If the probability of getting head at least once is greater than \( 90 \% \) then the minimum value of \( n \)
is?
A .4
B. 3
\( c .5 \)
\( D \)


A light bulb uses energy at a rate of 25.0 Watts. If the current through light bulb is 2.00 A. What is the resistance of the
bulb?
A. 6.25 ohms
B. 12.5 ohms
c. 0.0800 ohms
D. 50.0 ohms
E. 100.0 ohms


If \( \left|\frac{z-5 i}{z+5 i}\right|=1, \) prove that \( z \) is real.


State True or False.
All living organisms contain carbon-14.
A. True
B. False


Identify the error(s) in the orbital notation diagram for oxygen in the in
the image \( a \)
a. \( \prod_{1 \mathrm{s}} \frac{|\uparrow \downarrow|}{2 \mathrm{s}} \frac{|\uparrow| \downarrow|\uparrow|}{2 \mathrm{p}} \)
\( \frac{\sqrt{11}}{1 \mathrm{s}} \frac{\sqrt{11}}{2 \mathrm{s}} \frac{\sqrt{\mathrm{t}} \uparrow 1}{2 \mathrm{p}} \)
e. \( \frac{\sqrt{\uparrow} \mid}{1 s} \)
\[
\frac{|\uparrow| \uparrow|\uparrow|}{2 p}
\]
This question has multiple correct options
A. The electrons are not drawn with the appropriate spins
B. This is not a picture of oxygen. It is nitrogen
c. The electrons are not filled out according to Aufbau's's Principle
D. The electrons are not filled out according to Hund's Rule


Physical chemistry is the branch of chemistry which deals with the study of
A. physical aspects of chemical reactions
B. qualitative and quantitative analysis of chemical substances
c. interaction of light with the chemical substances
D. None of these


Action spectrum of photosynthesis was discovered in 1883 by
A. Engelmann
B. Calvin
c. Arnon
D. Hill


Degree of the polynomial \( 4 x^{4}+0 x^{3}+ \)
\( \mathbf{0} \boldsymbol{x}^{\boldsymbol{5}}+\mathbf{5} \boldsymbol{x}+\mathbf{7} \) is
A . 4
B. 5
\( c \cdot 3 \)
D.


Which of the following has the tendency to act as an oxidizing agent?
A \( \cdot C e^{4} \)
B . \( S m^{2+} \)
\( c \cdot L u^{3} \)
D. \( G d^{3} \)


The ore that is concentrated by the froth floatation process is:
A. chalcopyrites
B. cryolite
c. cuprite
D. calamine


The fraction of atoms of radioactive
element that decays in 6 days is \( 7 / 8 \) The fraction that decays in 10 days will
be :
A. \( 77 / 80 \)
B. \( 71 / 80 \)
c. \( 31 / 32 \)
D. \( 15 / 16 \)


The value of \( K_{c}=4.24 \) at \( 800 K \) for the
reaction
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Calculate equilibrium concentrations of
\( C O_{2}, H_{2}, C O \) and \( H_{2} O \) at \( 800 K, \) if only
\( C O \) and \( H_{2} O \) are present initially at concentration of \( 0.10 M \) each?


In the reaction, \( A+B \rightarrow \) Products, if \( B \)
is taken in excess, then it is an example
of :
A. second order reaction
B. zero order reaction
c. fractional order reaction
D. first order reaction


The grandparents and parents of twoyear old girl are playing with her in a room. A sound source produces a \( 28 k H z \) sound. Who in the room is most
likely to hear the sound?
A. Grandparent
B. Little girl
c. Both
D. None of them


The number of atoms in \( 67.2 \mathrm{L} \) of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
\( (g) \) at \( S T P \) is:
\( A \cdot 9 N_{A} \)
B . \( 12 N_{A} \)
c. \( 3 N_{A} \)
D. \( 4 N_{A} \)


In thermodynamics process pressure of a fixed mass of gas is changed in such
a manner that the gas releases \( 30 J \) of heat and \( 18 J \) of work was done on the
gas. If the initial energy of the gas was
\( 60 J \) then, the final internal energy will
be:
в. 48 Л
\( c .72 J \)
D. 965


What is the distance of points \( \boldsymbol{A}(\mathbf{5},-\mathbf{7}) \)
from \( y \) -axis.


The DNA molecules of each
chromosome replicates in
A. Gi phase
B. \( G_{2} \) phase
c. s phase
D. Mitotic phase


For any two complex numbers \( z_{1}, z_{2} \) and any two real numbers a, b show that
\( \left|\boldsymbol{a} \boldsymbol{z}_{1}-\boldsymbol{b} \boldsymbol{z}_{2}\right|^{2}+\left|\boldsymbol{b} \boldsymbol{z}_{1}+\boldsymbol{a} \boldsymbol{z}_{2}\right|^{2}= \)
\( \left(a^{2}+b^{2}\right)\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)


Phenol is more acidic than:
\( A \)
B.
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. Both (A) and (C)


Loss of haemoglobin can be controlled
by
A. Platelets
в. RВС
c. wвс
D. None of the above


In photosynthetic electron transport system, Mn ions are associated with
A. \( C F_{0}-C F_{1} \) complex
B. \( \mathrm{cyt} b_{6}- \) Cyt f complex
c. oxygen evolving complex
D. Plastoquinone.


Hysteresis loops for two magnetic
materials \( A \) and \( B \) are given below:
These materials are used to make
magnets for electric generators, transformer core and electromagnet
core. Then it is proper to use:
A. A for electric generators and transformers
B. A for electromagnets and B for electric generators
c. A for transformer and B for electric generators
D. B for electromagnets and transformers


If the lift starts moving up with a uniform speed of \( 5 m s^{-1} \) and the girl again throws the ball up with the same speed, how long does the ball take to
return to her hands?
A \( . .5 s \)
B. \( 1.0 s \)
c. \( 1.5 s \)
D. 2.0


Both growth and differentiation in
higher plants are open. Comment.


One end of a uniform rod of mass \( \boldsymbol{M} \)
and cross-sectional area \( \boldsymbol{A} \) is
suspended from the other end. The stress at the mid-point of the rod will be
A \( \cdot \frac{2 M g}{A} \)
в. \( \frac{3 M g}{2 A} \)
c. \( \frac{M g}{A} \)
D. zero


An arbitrary shaped closed coil is made of a wire of length L and a current ampere is flowing in it. If the plane of the coil is perpendicular to magnitude field \( \vec{B}, \) the force on the coil is?
A. zero
B . IBL
c. 2 IBL
D. \( \frac{1}{2}^{18 L} \)


Given two vectors \( \vec{A}=3 \hat{i}+4 \hat{j} \) and \( \vec{B}=\hat{i}+\hat{i} . \theta \) is the angle between \( \vec{A} \) and
\( \vec{B} \). Which of the following statements is/are correct?
\( ^{\mathbf{A}} \cdot|\vec{A}| \cos \theta\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \) is the component of \( \vec{A} \) along \( \vec{B} \)
B \( \cdot|\vec{A}| \sin \theta\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \) is the component of \( \vec{A} \) perpendicular
to \( \bar{b} \)
\( ^{\mathrm{c}}|\vec{A}| \cos \theta\left(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\right) \) is the component of \( \vec{A} \) along \( \vec{B} \)
D. All of the above


Of the following, which is a greenhouse gas?
A. Nitrogen dioxide
B. Sulphur dioxide
c. Carbon dioxide
D. Carbon monoxide


Zener diode is used for
A. amplification
B. rectification
C. stabilisation
D. all of the above


In the discharge tube as the density of atom increases, the intensity spectral
lines
A. Decreases continuously
B. Increases continuously
c. Remains constant
D. None of these


Solve the equation
\( |x+1|-|x|+3|x-1|-2|x-2|=x+2 \)


If each permutation of the digits
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6} \) are listed in the increasing
order of magnitude, then \( 289^{t h} \) term will
be
A . 361452
B. 321546
c. 321456
D. 341256


What is NCSR?
A. National Commission for Space Research
B. National Committee for Space Research
C. National Commission for Space Reaction
D. National Commission for Space Reading


\( 4 \sin 90^{0}=? \)


\( \frac{x^{2}+3 x+5}{(x+1)(x+2)(x+3)}= \)
\( \frac{\boldsymbol{A}}{(\boldsymbol{x}+\mathbf{1})}+\frac{\boldsymbol{B}}{(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})}+ \)
\( \frac{c}{(x+1)(x+2)(x+3)} \) then ascending
order of \( A, B, C \) is
\( A \cdot B, A, C \)
B. A, B, C
c. \( c, A, B \)
D. B, C, A


A conducting loop carrying a current
is placed in a uniform magnetic field
acting perpendicular to the plane of the coil shown in figure. the loop will have a tendency to
A. contract
B. expand
c. move towards positive X-axis
D. move towards positive Y-axis


An electron accelerated by a potential
difference \( V=1.0 k V \) moves in a
uniform magnetic field at an angle \( \boldsymbol{\alpha}= \)
\( 30^{\circ} \) to the vector \( B \) whose modulus is
\( B=29 \) mT.Find the pitch of the helical
trajectory of the electron.
\( A \cdot 1 m \)
B. \( 1 \mathrm{cm} \)
\( c \cdot 2 m \)
D. \( 2 \mathrm{cm} \)


Write the IUPAC name of the compound
is:


If \( A=\{1,2,3,4\}, \) then the number of
subsets of \( A \) that contain the element 2
but not \( 3, \) is
A . 16
B. 4
c. 8
D. 24


Assertion
The common name of Exocetus is flying
fish.
Reason
Exocetus has wing like pectoral fins.
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 best method to reduce random error
is
A. To change the instrument used for the measurement
B. To take help of experienced observer
C. To repeat the experiment many times and to take the average results
D. None of the above


If \( \int \frac{\cos 4 x+1}{\cot x-\tan x} d x=A \cos 4 x+B \)
where \( A \& B \) are constants, then
A \( . A=-1 / 4 \& B \) may have any value
B. \( A=-1 / 8 \& B \) may have any value
c. \( A=-1 / 2 \& B=-1 / 4 \)
D. \( A=B=1 / 2 \)


Prove that \( (-1) \times(-1)=1 \)


For which of the following dependence of
drift velocity \( v_{d} \) on electric field E is Ohm's law obeyed?
A \( \cdot v_{d} \propto E \)
B . \( v_{d}= \) constant
\( \mathbf{c} \cdot v_{d} \propto \sqrt{E} \)
D \( \cdot v_{d} \propto E^{2} \)


Which of the following is the most
sonorous metal?
A. Gold
B. Platinum
C. Mercury
D. Silver


Which of the following statements is
false?
A. Kirchhoff's second law represents energy conservation.
B. Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.
C. In a balanced Wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed.
D. A rheostat can be used as a potential divider.


For how many hours did the maximum
number of students watch TV?
A \( .7-8 \)
B . \( 8-9 \)
\( \mathbf{c} \cdot 4-5 \)
D. \( 9-10 \)


A ray of light passes through four transparent media with refractive
indices \( \mu_{1}, \mu_{2}, \mu_{3} \) and \( \mu_{4} \) as shown in the
figure. The surfaces of all media are
parallel. If the emergent ray CD is parallel to the incident ray AB, we must
have:
A \( \cdot \mu_{1}=\mu_{2} \)
в. \( \mu_{2}=\mu_{3} \)
\( \mathbf{c} \cdot \mu_{3}=\mu_{4} \)
D. \( \mu_{4}=\mu_{1} \)


Which of the following has coenzyme
activity?
A. Nicotinamide
B. Purine
c. Pyrimidine
D. Both B and C


Eroded soils are
A. Devoid of plant nutrients
B. Richer in plant nutrients
C. Unaltered in plant nutrients
D. Fit for agriculture


If the degree of \( 12 x^{3} y^{8} z^{n} \) is \( 14, \) then
\( \boldsymbol{n}= \)


The points \( \boldsymbol{A}(\mathbf{1}, \mathbf{2},-\mathbf{1}), \boldsymbol{B}(\mathbf{2}, \mathbf{5},-\mathbf{2}), \boldsymbol{C}(\mathbf{4}, \mathbf{4},-\mathbf{3}) \)
and \( D(3,1,-2) \) are
A. collinear
B. vertices of a rectangle
c. vertices of a square
D. vertices of a rhombus


Rakesh purchased a TV for 5000 and paid 250 for its transportation. If he sold
the TV for \( 5075, \) find his profit or loss
percentage.


Write one main use of Zener diode.


A man on a moving cart, facing the direction of motion throws a ball
straight up with respect to himself. Which of the following statements is(are) correct?
This question has multiple correct options
A. The ball will always return to him
B. The ball will never return to him.
c. The ball will return to him if the cart moves with a constant velocity
D. The ball will fall behind him if the cart moves with some acceleration


The force \( F \) acting on a particle moving
in a straight line is shown below. What is the work done by the force on the particle in the 1st metre of the trajectory?
\( A \cdot 5 J \)
В. \( 10 J \)
\( c .15 J \)
D. 2.5 5


What will be the octane number of best
fuel?
A. 80
B. 81
\( c \cdot 82 \)
D. 83


If the line \( 3 x-4 y=\lambda \) cuts the circle
\( x^{2}+y^{2}-4 x-8 y-5=0 \) in two
points then limits of \( \lambda \) are
A . [-35,15]
В . (-35,15)
c. (-35,10)
D. (-35,15]


What is rectification? Explain the working of a full-wave rectifier with a diagram. What is a zener diode? How
will a zener diode be connected in a
circuit generally?


Four rod each of mass \( \mathrm{m} \) from a square
length of diagonal b rotates about its
diagonal. Its moment of inertia is:-


A particle is projected at an angle \( \theta \)
from ground with speed \( u\left(g=10 m / s^{2}\right) \)
then which of the following is true? This question has multiple correct options
A \( \cdot \) If \( u=10 m / s \) and \( \theta=30^{\circ}, \) then time of flight will be 1
\( \sec \)
B . If \( u=10 \sqrt{3} m / s \) and \( \theta=60^{\circ} \), then time of flight will be \( 3 \sec \)
C . If \( u=10 \sqrt{3} m / s \) and \( \theta=60^{\circ} \), then after 2 sec velocity
becomes perpendicular to initial velocity
D. If \( u=10 m / s \) and \( \theta=30^{\circ} \), then velocity never becomes
perpendicular to intial velocity during its flight


If \( P(x, y, x) \) is a point on the line
segment joining \( Q(2,2,4) \) and \( R(3,5,6) \) such that the projection of \( O P \) on the axis are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in the
ratio
A . 1: 2
B. 3: 2
\( c \cdot 2: 3 \)
D. 1: 3


How is sex determination happen in
birds and honeybees?


The fluoride of \( x e n o n \) with zero dipole
moment is :
This question has multiple correct options
A \( \cdot \mathrm{xeF}_{6} \)
в. \( \mathrm{xeO}_{3} \)
c. \( \mathrm{xeF}_{4} \)
D. XeF \( _{2} \)


Which of the following is paramagnetic
in nature?
A. \( N_{2} O_{4} \)
is
в. \( N_{2} \)
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


What were the limitations of
Dobereiner's classification?


A LASER is a source of very intense, monochromatic, and unidirectional
beam oflight. These properties of a laser light can be exploited to measure long distances.The distance of the Moon
from the Earth has been already
determined very preciselyusing a laser as a source of light. A laser light beamed at the Moon takes 2.56 s
to return after reflection at the Moons
surface. How much is the radius of the
lunar orbit around the Earth?


Which of the following do not form
oxides easily?

This question has multiple correct options
A. Platinum
B. Aluminium
c. Sodium
D. Silver


Correct sequence of stages in evolution
of Modern Man/Homo sapiens sapiens is
A. Australopithecus, Neanderthal Man, Cro-Magnon Man, Homo erectus, Modern Man
B. Australopithecus, Homo erectus, Neanderthal Man, Cro-Magnon Man, Modern Man
C. Neanderthal Man, Australopithecus, Cro-Magnon Man, Homo erectus, Modern Man
D. Homo erectus, Australopithecus, Neanderthal Man, Cro-Magnon Man, Modern Man


How much work is required to slowly
move a \( 1 \mu C \) charge from \( E \) to D?
A \( \cdot 2 \times 10^{-5} J \)
B . \( -2 \times 10^{-5} J \)
C \( \cdot 4 \times 10^{-5} J \)
D. \( -4 \times 10^{-5} J \)


The solubility of a substance is 40 to 50
C such that at same temperature its solution contains 5 g of it in 10 gof water
A . True
B. False
c. Nither
D. Either


When we pluck the wire of a sitar, the waves produced in the air
are
A. longitudinal
B. transverse
c. sometimes longitudinal and sometimes transverse
D. electromagnetic


\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2}-\underset{\boldsymbol{O}}{\|}-\boldsymbol{C} \boldsymbol{H}_{3} \frac{N a N \boldsymbol{O}_{2}}{\boldsymbol{H} C l} \)
Major product of this reaction is:
\( \mathbf{A} . \)
\( C H_{3} C H-C_{1} H-C-C H_{3} \)
\( N O \)
B.
\[
C H_{3}-C H_{2}-C-C H=N-O H
\]
\( c \)
\( C H_{3}-\underset{N-O H}{C}-\stackrel{0}{N}-C H_{3} \)
D. \( C H_{3}-C H_{2}-\underset{N-O H}{\|}-C H_{3} \)


Assertion
Saline water is not given to patients with hypertension.
Reason
Saline water can cause vomiting and may drop blood pressure suddenly causing cardiac arrest.
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


What will happen when an electron jumps from an excited energy state to a
more stable energy state in a hydrogen
atom?
A. Electromagnetic radiation is emitted by the atom
B. Electromagnetic radiation is absorbed by the atom
C. The atom becomes a positively charged ion
D. The atom becomes a negatively charged ion
E. The atom undergoes nuclear decay


Derive the expression for of K.E. of mass \( m \) moving with velocity \( (v) \)


All practical mirrors absorb a little fraction of light incident on it. Due to this, when a ray of light is reflected repeatedly by a set of parallel plane mirrors, the intensity of the ray, after a few reflections, becomes:
A. more than that of the incident ray
B. less than that of the incident ray
c. same as that of the incident ray
D. equal to zero


The fossil fuels include:
A. Uranium
B. Soil
c. Natural gas
D. Plants


Assertion
if \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|+|\boldsymbol{x}-\mathbf{4}|+|\boldsymbol{x}-\mathbf{6}| \)
an identify function for \( 4<x<6 \)
Reason
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) is an
identify function
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 value of median of
\( \begin{array}{llll}\text { Income } & & & & \\ & 1000 & 1100 & 1200 & 1300\end{array} \) No. of
persons \( \quad 14 \quad 26 \quad 21 \)
\( A \cdot 1300 \)
B. 1200
c. 1250
D. 1150


A swimmer wants to cross a \( 200 m \) wide
river which is flowing at a speed of \( 2 m / s . \) The velocity of the swimmer with respect to river is \( 1 \mathrm{m} / \mathrm{s} \). How far from
the point directly opposite to the starting point does the swimmer reach
the opposite bank?
\( \mathbf{A} \cdot 200 m \)
B. \( 400 m \)
\( c .600 m \)
D. \( 800 m \)


Let \( \bar{x}, M \) and \( \sigma^{2} \) be respectively the
mean mode and variance of \( n \)
observations \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots . ., \boldsymbol{x}_{\boldsymbol{n}} \) and \( \boldsymbol{d}_{\boldsymbol{i}}= \)
\( -\boldsymbol{x}_{1}-\boldsymbol{a}, \boldsymbol{i}=1,2, \ldots . ., \boldsymbol{n}, \) where a is any
number.
Statement I : Variance of \( \boldsymbol{d}_{1}, \boldsymbol{d}_{1}, \ldots . ., \boldsymbol{d}_{n} \) is
\( \sigma^{2} \)
Statement II : Mean and mode of
\( \boldsymbol{d}_{1}, \boldsymbol{d}_{2}, \dots, \boldsymbol{d}_{n} \) are \( -\overline{\boldsymbol{x}}-\boldsymbol{a} \) and \( -\boldsymbol{M}-\boldsymbol{a} \)
respectively
A. Statement I and Statement II are both false
B. Statement I and Statement II are both true
c. Statement I is true and Statement II is false
D. Statement I is false and Statement II is true


A point object is placed in air at a
distance of \( 40 \mathrm{cm} \) from a concave
refracting surface of refractive index
1.5 If the radius of curvature of the
surface is \( 20 \mathrm{cm}, \) then the position of the image is-


If \( e^{x}+e^{y}=e^{x+y}, \) show that \( \frac{d y}{d x}= \)
\( -e^{y-x} \)


The temperature at which a liquid is converted into vapour (gas) is called boiling point.
A. True
B. False


If 1.0 mol of \( N O \) is mixed with 1.0 mol
of \( O_{2} \) as given in the following reaction
then the number of moles of \( N O_{2} \)
produced is
\( \mathbf{2} N O(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A. 0.5
B.
\( c \cdot 2 \)
D. 1.5


Name two hormones secreted by the
anterior lobe of pituitary gland.


How many numbers can be formed from
the digits 1,3,5,9 if repetition of digits is not allowed?


Which of the following complex is most stable among the folowing?
\( \mathbf{A} \cdot N a_{3}\left[F e\left(C_{2} O_{4}\right)_{3}\right. \)
B \( \cdot\left[C O\left(N H_{3}\right)_{6}\right]^{+3} \)
\( \mathbf{c} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
D. \( N a_{3}\left[\text {CoF}_{6}\right] \)


The major fraction of \( C O_{2} \) released
during cellular respiration is transported by the blood to the lung capillaries
A. In combination with haemoglobin
B. As free \( C O_{2} \)
c. As carbonic acid or \( H_{2} C O_{3} \)
D. In the form of bicarbonate ions


A Cylindrical vessel of cross-sectional
area \( 1000 \mathrm{cm}^{2} \), is fitted with a
frictionless piston of mass \( 10 \mathrm{kg} \), and
filled with water completely. A small hole of cross-sectional area \( 10 m m^{2} \) is
opened at a point \( 50 \mathrm{cm} \) deep from the lower surface of the piston. The velocity of effluent from the hole will be
A. \( 10.5 \mathrm{m} / \mathrm{s} \)
B. 3.4 m/s
c. \( 0.8 \mathrm{m} / \mathrm{s} \)
D. \( 0.2 \mathrm{m} / \mathrm{s} \)


For the given combination of gates, if the logic states of inputs \( A, B, C \) are as
follows \( \boldsymbol{A}=\boldsymbol{B}=\boldsymbol{C}=\mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{B}= \)
\( 1, C=0 \) then the logic states of output
D are
\( A \cdot 0,0 \)
B. 0,1
c. 1,0
D. 1,1


The multiplicative inverse of \( \frac{-4}{11} \) is
A \( \cdot \frac{-11}{4} \)
в. \( \frac{-4}{11} \)
c. \( \frac{11}{4} \)
D. \( \frac{4}{11} \)


Balance the following chemical equation.
\( Z n+A g N O_{3} \rightarrow Z n\left(N O_{3}\right)_{2}+A g \)


Find the sum given.
\( 34+32+30+\ldots+10 \)


Solve the following equation:
\( \sin x-\sin 2 x+\sin 5 x+\sin 8 x= \)
\( \mathbf{0} \)


If one diagonal of a square is along the
line \( x=2 y \) and one of its vertices is
\( (3,0), \) then its sides through this vertex are given by the equations
A. \( y-3 x+9=0,3 y+x-3=0 \)
B. \( y+3 x+9=0,3 y+x-3=0 \)
c. \( y+3 x+9=0,3 y-x+3=0 \)
D. \( y-3 x+3=0,3 y+x+9=0 \)


\( Z n O, T i O_{2} \) and \( V_{2} O_{5} \) are oxides of \( d \) block elements. If all of three are
amphoteric enter \( 1, \) else enter 0


Find the discriminant of the equation and the nature of roots. Also find the
roots.
\( 6 x^{2}+x-2=0 \)
A \( \cdot D=49, \) Real and distinct roots: \( \frac{1}{5}, \frac{-2}{3} \)
B. \( D=39 \), Real and distinct roots: \( \frac{1}{2}, \frac{-2}{3} \)
C. \( D=49 \), Real and distinct roots: \( \frac{1}{3}, \frac{-7}{3} \)
D. \( D=49 \), Real and distinct roots: \( \frac{1}{2}, \frac{-2}{3} \)


The run of cyanamide \( N H_{2} C N \) with dioxygen was carried out in a bomb
calorie meter and \( \Delta u \) was found to be
\( -742.7 k J / m o l \)
Calculate the enthalpy for the reaction at \( 298 \mathrm{K} \)
\( N H_{2} C N(s)+\frac{3}{2} O_{2} \rightarrow N_{2}+C O_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


In the given food chain, suppose the amount of energy at fourth trophic level is \( 5 \mathrm{kJ} \), what will be the energy available at the producer level?Grass Grasshopper- - Frog - Snake - - Hawk
A . 5 kJ
B. 50 kJ
c. \( 500 \mathrm{kJ} \)
D. 5000 k J


A body starts from rest and travels a
distance \( x \) with uniform acceleration,
then it travels a distance \( 2 x \) with
uniform speed, finally it travels a distance \( 3 x \) with uniform retardation
and comes to rest. If the complete motion of the particle is along a straight line, then the ratio of its average velocity to maximum velocity is
A \( \cdot 2 / 5 \)
B. \( 3 / 5 \)
\( c \cdot 4 / 5 \)
D. 6/7


Assertion
The bond angle of \( P B r_{3} \) is greater than
\( P H_{3} \) but the bond angle of \( N B r_{3} \) is
lesser than \( \boldsymbol{N} \boldsymbol{H}_{3} \)
Reason
Electronegativity of \( P \) -atom is less than
that of \( N \) -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. Assertion is incorrect but Reason is correct


What is molecular orbital theory? with the help of energy level in homo nuclear diatomic orbitals arranfe the following series increasing order \( O_{2}^{2-}, O_{2}^{-}, O_{2}, O_{2}^{+} \)


If \( \boldsymbol{b}>\boldsymbol{a} \) and \( \boldsymbol{I}=\int_{a}^{b} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{(\boldsymbol{x}-\boldsymbol{a})(\boldsymbol{b}-\boldsymbol{x})}} \)
then \( I \) equals
A . \( \pi / 2 \)
в. \( \pi \)
\( \mathrm{c} \cdot 3 \pi / 2 \)
D . 2 \( \pi \)


In alcoholic fermentation, two
molecules of glucose produce ethano
and \( \mathrm{CO}_{2} \) respectively
\( A \cdot 2+2 \)
B. \( 3+3 \)
\( c \cdot 4+4 \)
\( D \cdot 6+6 \)