STATEMENT-1: A Solenoid tend to
contract (along its length) when a current is passed through it. STATEMENT-2: If current in two coaxial
circular rings of equal radii is in same sense( as seen by an observer on axis away from both the rings), the rings
attract each other. Further the given current carrying rings attract each other because parallel current attracts.
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


\( m \) onto a spring of spring constant 800
N/m as shown in the figure. A frictional
force equivalent to 0.4 kgwt acts on the
body. The speed of the body just before
striking the spring will be (Take \( \boldsymbol{g}= \)
\( \left.10 m / s^{2}\right) \)
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 m/s
\( c \cdot 3 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)


The solution of \( (s e c \boldsymbol{\theta}+1)=(2+ \) \( \sqrt{3}) \tan \theta(0<\theta<2 \pi) \) are
\( \mathbf{A} \cdot \pi / 6, \pi \)
в. \( \pi / 3, \pi / 4 \)
c. \( \pi / 6,2 \pi / 3 \)
D. none of these


Find the value of \( \mathrm{k}, \) If \( x, 2 x+k, 3 x+5 \) are
consecutive terms in A.P.


Solve \( : \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\sin \boldsymbol{3} \boldsymbol{x})=? \)


Using the principle of mathematical induction prove that \( 2+4+6+\ldots+ \)
\( \mathbf{2} \boldsymbol{n}=\boldsymbol{n}^{2}+\boldsymbol{n} \)


Find the area of the region bounded by
\( \boldsymbol{a}) \boldsymbol{y}=\sin \boldsymbol{x}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{\pi} \)


The major products obtained during ozonolysis of \( 2,3- \) dimethyl -1
butene and subsequent reductions with
\( Z n \) and \( H_{2} O \) are :
A. Methanoic acid and \( 2- \) methyl -2 - butanone
B. Methanal and \( 3- \) methyl -2 - butanone
C. Methanol and \( 2,2- \) dimethyl -3 - butanone
D. Methanoic acid and \( 2- \) methyl -3 - butanone


Assertion
Alkyl benzene is not prepared by Friedel Craft's alkylation of benzene.
Reason
Alkyl halides are less reactive than acyl halides.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


In a modified \( Y D S \) the two slits \( S_{3} \) and
\( S_{4} \) are placed in front of the slits \( S_{1} \) and
\( S_{2}, \) calculate the ratio of \( m a x^{m} \)
intensity to minimum intensity produced in the screen if


Consider the distribution of speeds of
molecules as shown in figure Which is
correct ordering for speeds?
A \( . V_{r m s}<V_{a v g}<V_{m p} \)
B. \( V_{r m s}<V_{m p}<V_{a v g} \)
\( \mathbf{C} \cdot V_{a v g}<V_{r m s}<V_{m p} \)
\( \mathbf{D} \cdot V_{m p}<V_{a v g}<V_{r m s} \)


The bisectors of opposite angles are parallel to each other


Find the deff equation \( \left(x^{2}+y^{2}\right) d x \)
\( 2 x y d y=0 \)


Which of the following is not formed from procambium?
A. Xylem
B. Phloem
c. Intra-fascicular cambium
D. Inter-fascicular cambium


For the probability distribution given by \begin{tabular}{cc|c|c|c}
\( \boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}} \) & \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{2} \) \\
\( \boldsymbol{P} \) & \( \frac{\mathbf{2 5}}{\mathbf{3 6}} \) & \( \mathbf{5} \) & \( \mathbf{1} \) \\
\( \mathbf{1 8} \) & \( \mathbf{3 6} \) & the standard
\end{tabular}
deviation \( (\sigma) \) is?
A \( \cdot \sqrt{\frac{1}{3}} \)
B. \( \frac{1}{3} \sqrt{\frac{5}{2}} \)
c. \( \sqrt{\frac{5}{36}} \)
D. None of the above


If \( \theta \leq x \leq \pi ; \) then the area bounded by
the curve \( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}+\sin \boldsymbol{x} \) is
A . 2
B. 4
\( c \cdot 2 \pi \)
D. \( 4 \pi \)


Except blood, the cells of connective
tissue secrete certain substances that
act as matrix. These substances are
A. Conjugated proteins
B. signalling molecules
c. cholesterol
D. Modified polysaccharides


World biodiversity day is
A \( \cdot 22^{n d} \) April
B. \( 16^{\text {th }} \) September
c. \( 5^{t h} \) June
D. \( 22^{2 d} \) may


Describe the principle and use of
SON \( A R \) and \( R A D A R \)


Match the items in List I with the
correct choice in List II.


What is the rate of change of
capacitance with temperature if the
capacity of capacitor is \( \mathrm{C} \) ?
\( A \cdot C\left(2 \alpha_{1}-\alpha_{2}\right) \)
B. \( c\left(\alpha_{1}-\alpha_{2}\right) \)
\( c \cdot c\left(\alpha_{1}-2 \alpha_{2}\right) \)
D. \( \frac{C\left(\alpha_{1}-\alpha_{2}\right)}{2} \)


What is the formula of Chloral?
A \( . C H C l_{3} \)
в. \( C C l_{3} \) СОСН\( _{3} \)
c \( \cdot C C l_{3} C H O \)
D. \( \operatorname{cocl}_{2} \)


Find the mean deviation about the
median of the following data:
\( \mathbf{1 1}, \mathbf{3}, \mathbf{8}, \mathbf{7}, \mathbf{5}, \mathbf{1 4}, \mathbf{1 0}, \mathbf{2}, \mathbf{9} \)
A . 2.8
B. 3
\( c .3 .3 \)
D. 2.9


Mammals have biconcave RBC. The
physiological use for it is
A. To decrease the surface area
B. To increase the surface area
c. To be packed like coins
D. None of the above


A voltmeter of resistance \( 998 \Omega \) is
connected across a cell of emf \( 2 \mathrm{V} \) and
internal resistance 2\Omega. The potential difference across the voltmeter is?
\( \mathbf{A} \cdot 1.99 \mathrm{v} \)
B. 3.5v
c. \( 5 v \)
D. \( 6 v \)


The minerals are the
compounds of metal with sulphur.


figure. The system is released from rest
and the block of mass 1 kg is found to
have a speed \( 0.3 m / s \) after it has
descended through a distance of 1 m.
The coefficient of kinetic friction
between the block and the table is (All
pulleys are massless and smooth and
strings are inextensible and light
acceleration due to gravity \( =10 m / s^{2} . \) ):
A . 0.12
B. 0.5
\( c .0 . \)
D. 0.15


State whether the following statements
are true or false with reasons.

Elastic forces are strictly conservative only when Hooke's law is obeyed.
A. True
B. False


A motorcyclist drives from \( A \) to \( B \) with a
uniform speed of \( 30 \mathrm{km} \mathrm{h}^{-1} \) and returns
with a speed of \( 20 \mathrm{km} \mathrm{h}^{-1} \). Find his
average speed.


The position of a particle is given by \( \vec{r} \) \( =3 t \hat{i}+2 t^{2} \hat{j}+5 \hat{k}, \) where \( t \) is in seconds and the coefficients have the proper
units for \( r \) to be in metres. The direction
of velocity of the particle at \( t=1 \) s is:
\( A \cdot 53^{\circ} \) with \( x \) -axis
B. 37 \( ^{\circ} \) with \( x \) -axis
c. \( 30^{\circ} \) with \( y \) -axis
D. \( 60^{\circ} \) with \( y \) -axis


\( \$ \$ x|,+|, \) i \( \left|s q r t x^{\wedge}\right|, 4\left|,+, x^{\wedge} 2\right|,+\mid, 1 \$ \$ \)


Which condition zygotic cell will form normal human female child?
A. \( x x \) chromosomes
B. Y-chromosome
c. x-chromosome
D. xy chromosomes


Cellulose contains so many \( O H \) groups, it is insoluble in
A . water
B. banzene
c. both \( A \) and \( B \)
D. none of these


What will be the effect on the
centripetal acceleration, if both the
speed and the radius of the circular path of the body are doubled?


Assertion
The zeroth law of thermodynamics was known before law I of thermodynamics.
Reason
The zeroth law concerning thermal
equilibrium was appeared after three
laws (I, II and III) of termodynamics and
thus was named as zeroth law.
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 particle moves on the \( X \) -axis
according to the equation \( \boldsymbol{x}= \)
\( x_{0} \sin ^{2} \omega t . \) The motion is simple
harmonic.
A. with amplitude \( x_{0} \)
B. with amplitude \( 2 x_{0} \)
c. with time period \( \frac{2 \pi}{\omega} \)
D. with time period \( \frac{\pi}{\omega} \)


The increasing concentration of a substance, such as a toxic chemical, in
the tissues of tolerant organisms at successively higher levels in a food chain, is known as biological magnification. Enter 1 for True and 2 for
False.


Find the equation of the ellipse whose
foci are (0,±3) and length of the minor
axis is 16


If there is change of angular momentum from \( 1 J \) to \( 5 J \) in 5 second
Then the torque is
A \( \cdot \frac{3 J}{5} \)
в. \( \frac{4 J}{5} \)
c. \( \frac{5 J}{4} \)
D. none of these


What is the common name of methyl alcohol?
A. wine
B. Wood spirit
c. Dilute acid
D. None of the above


The main cause of avalanche
breakdown is
A. collision by ionisation
B. high doping.
c. recombination of electrons and holes.
D. low doping.


If \( f(x)=a x^{2}+b x+c \) satisfies the
identity \( f(x+1)-f(x)=8 x+3 \) for
all \( x \in R . \) Then \( (a, b)= \)
A. (2,1)
(i)
в. (4,-1)
c. (-1,4)
D. (-1,1)


Which of the following is the weakest force?
A. Nuclear force
B. Gravitational force
c. Electromagnetic force
D. None of these


The differential equation of all vertical lines in a plane is?
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
B. \( \frac{d^{2} x}{d y^{2}}=0 \)
c. \( \frac{d y}{d x}=0 \)
D. \( \frac{d x}{d y}=0 \)


A hoop rolls without slipping on a horizontal ground having centre of
mass speed \( v_{0} . \) The speed of a particle \( P \) on the circumference of the hoop at
angle \( \boldsymbol{\theta} \) is?


If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right], \) then the value of
\( |\boldsymbol{A}||\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}| \) is \( \boldsymbol{a}^{\boldsymbol{k}} \)
What is k?


Three wires of length \( l_{1}, l_{2}, l_{3} \) form a
triangle surmounted by another
circular wire, If \( l_{3} \) is the diameter and
\( l_{3}=2 l_{1}, \) then the angle between \( l_{1} \) and
\( l_{3} \) will be
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


In a metre bridge the null point is found
at a distance of \( 40 \mathrm{cm} \) from \( \mathrm{A} \). If \( \mathrm{a} \)
resistance of \( 12 \Omega \) is connected in
parallel with \( ^{\prime} S^{\prime}, \) the null point occurs
at \( 50 \mathrm{cm} \) from \( \mathrm{A} \). determine value of \( ^{\prime} \boldsymbol{R}^{\prime} \)
and ' \( \boldsymbol{S}^{\prime} \)


Isotopes have similar:
A. physical properties
B. chemical properties
c. mass numbers
D. number of neutrons


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) then \( \left|\begin{array}{lll}\boldsymbol{p}^{2} \boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{p} \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{p c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) is
equal to
A \( . p \Delta \)
B . \( p^{2} \Delta \)
c. \( p^{3} \Delta \)
D. \( 2 p \Delta \)


Very short answer type. Where are cytokinins synthesised in
plants? Mention any two functions of cytokinins.


Two boys are standing at the ends \( A \) and
B of a ground where \( A B=a \). The boy at \( B \)
starts running in a direction
perpendicular to AB with velocity \( v_{1} . \) The
boy at A starts running simultaneously with velocity \( \mathbf{v} \) and catches the other in
a time \( t, \) where \( t \) is?
A \( \cdot \frac{a}{\sqrt{v^{2}+v_{1}^{2}}} \)
B. \( \frac{a}{v+v_{1}} \)
C. \( \frac{a}{v-v_{1}} \)
D. \( \sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}} \)


A unit positive charge is moved along
the circumference of a circle due to the
attraction of a \( -100 \mathrm{C} \) charge at the centre of the circle. Then the work done
in the process is
A. negative work of 100 J
B. positive work of 100 J
c. zero
D. \( \frac{Q .1}{4 \pi \epsilon_{0} r} \)


\( \operatorname{Let} F(x)=f(x) g(x) h(x) \) for all real \( x \)
where \( \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x}), \boldsymbol{h}(\boldsymbol{x}) \) are
differentiable functions. At some point \( \boldsymbol{x}_{0}, \) if \( \boldsymbol{F}^{\prime}\left(\boldsymbol{x}_{0}\right)=\mathbf{2 1} \boldsymbol{F}\left(\boldsymbol{x}_{0}\right), \boldsymbol{f}^{\prime}\left(\boldsymbol{x}_{0}\right)= \)
\( 4 f\left(x_{0}\right), g^{\prime}\left(x_{0}\right)=-7 g\left(x_{0}\right) \) and
\( h^{\prime}\left(x_{0}\right)=\lambda h\left(x_{0}\right), \) then \( \lambda= \)
A . 12
B. -12
\( c \cdot 24 \)
D. -24


The frequencies below \( 20 \mathrm{Hz} \) are known as infrasonic sounds.
A . True
B. False


Conversion of green tomatoes into red
form involves
A. Formation of chromoplasts from chloroplasts
B. Destruction of chloroplasts and development of chromoplasts from leucoplasts
C. Formation of chromoplasts from proplastids
D. All of the above


A rectangular loop is placed near a current carrying straight wire as shown in figure. If the loop is rotated about an axis passing through one of its sides, find the direction of induced current in
the loop.


An amount of 18 g glucose corresponds
to
A. 1.8 mole
B. 1 mole
c. 0.18 mole
D. 0.1 mole


A particle starts from rest from the top
of an inclined plane and reaches the
bottom most point again at rest. If the
coefficient of friction on some part of
the inclined plane is \( 3 \tan \theta \) and the remaining portion is smooth, the ratio of the length of the rough part is \( \frac{4}{x} \) times the length of the smooth part. Then, \( x \) is \( (\theta \text { is the plane angle }) \)


Which of the following statements is correct regarding the propagation of light of different colors of white light in air?
A. Red light moves fastest
B. Blue light moves faster than green light
c. All the colours of the white light move with the same speed
D. Yellow light moves with the mean speed as that of the red and the violet light


Two elements 'P' and 'Q' combine to form
a compound. Atomic mass of 'P' is 12 and 'Q' is 16. Percentage of 'P' in the
compound is 27.3. What will be the empirical formula of the compound?
A \( \cdot P_{2} Q_{2} \)
B. PQ
\( c \cdot P_{2} Q \)
D. \( P Q_{2} \)


A compound contains \( 10^{-2 \%} \) of
phosphorus. If the atomic mass of P is
\( 31, \) then the molecular mass of the
compound having one phosphorous atom per molecule is:
A \( .3 .1 \times 10^{5} \)
B. 3.1
c. 31
D. None of these


When we hit a thin plastic ruler firmly
on a bench:
A. the free end of the ruler vibrates and produces sound
B. the end held by hand vibrates and produces sound
C . even after it stops vibrating it continues to produce sound
D. none of the above occur


The number of unpaired electrons in a
chromic ion \( \left.C r^{+3} \text {(atomic number } 24\right) \)
is:
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D.


A boy sitting on the top most berth in the compartment of a train which is
just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about \( 2 \mathrm{m} \)
The apple will fall
A. In the hand of his brother
B. Slightly away from the hand of his brother in the direction of the motion of the train
c. Slightly away from the hands of his brother in the direction opposite to the direction of the motion of the train
D. None of these


The order of size of nucleus and Bohr's
radius of an atom respectively are:
\( \mathbf{A} \cdot 10^{-14} m, 10^{-10} m \)
В. \( 10^{-10} m, 10^{-8} m \)
c. \( 10^{-20} m, 10^{-16} m \)
D. \( 10^{-8} m, 10^{-6} m \)


Plot the point (5,0) on a graph paper.


A step down transformer reduces \( 220 V \)
to \( 110 V . \) The primary and secondary
current are 5 and 9 amperes
respectively. The efficiency of transformer is
A . \( 20 \% \)
B . 4\%
c. \( 90 \% \)
D. 100\%


Which one is most ionic:
A \( \cdot P_{2} O_{5} \)
B. \( C r O_{3} \)
c. \( M n O \)
D. \( M n_{2} O_{7} \)


The area of the plane region bounded by the curves \( x+2 y^{2}=0 \) and \( x+3 y^{2}= \)
\( \mathbf{1} \)
A \( \cdot \frac{4}{3} \)
B.
\( c \cdot \frac{2}{3} \)
D.


Convert into mole
\( 12 g \) of \( O_{2} \) gas \( 20 g \) of water
\( 22 g \) of \( C O_{2} \)
\( 52 g \) of helium


a body is rotating nonuniformly about a vetical axis fixed is an intertial frame.
The resultant force on a particle of the
body not on the axis is
A. Vetical
B. horizontal and skew with the axis
c. horizontal and intersection the axis
D. None of these


If \( \hat{a}, \hat{b}, \hat{c} \) are unit vectors such that \( \hat{a} \cdot \hat{b}=0=\hat{a} \cdot \hat{c} \) and the angle between \( \hat{b} \)
and \( \hat{c} \) is \( \pi / 3, \) then the value of \( |\hat{\boldsymbol{a}} \times \hat{\boldsymbol{b}}-\hat{\boldsymbol{a}} \times \hat{\boldsymbol{c}}| \)
A . \( 1 / 2 \)
B. 1
\( c \cdot 2 \)
D. none of these


Integrate the Rational Function \( \int \frac{2 x}{x\left(x^{2}+1\right)} d x \)


Some word/ words are missing in the following statements. You are required
to rewrite the statements in the correct
form using the appropriate word/ words:
Magneisum reacts with nitric acid to liberate hydrogen gas.


If \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2} \boldsymbol{y}, \boldsymbol{x}-\mathbf{2} \boldsymbol{y})=\boldsymbol{x} \boldsymbol{y}, \) then \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}) \)
is equal to
A \( \cdot \frac{1}{4} x y \)
B. \( \frac{1}{4}\left(x^{2}-y^{2}\right) \)
c. \( \frac{1}{8}\left(x^{2}-y^{2}\right) \)
D. \( \frac{1}{2}\left(x^{2}+y^{2}\right) \)


Utilization of \( \boldsymbol{O}_{2} \) by the cells to derive energy from nutrients for performing various activities and resultant release
of \( C O_{2} \) as by-produced is called This question has multiple correct options
A. Breathing
B. Cellular respiration
c. Pulmonary ventilation
D. Fermentation


In a circuit \( \mathrm{L}, \mathrm{C} \) and \( \mathrm{R} \) are connected in
series with an alternating voltage source of frequency v. The current leads
the voltage by \( 45^{0} . \) The value of \( C \) is
A \( \cdot \frac{1}{\pi v(2 \pi v L-R)} \)
B . \( \frac{1}{2 \pi v(2 \pi u L-R)} \)
c. \( \frac{1}{\pi v(2 \pi v L+R)} \)
D. \( \frac{1}{2 \pi v(2 \pi v L+R)} \)


During the cycle
A. work done by the gas is about \( 55 J \) and heat absorbed by the gas is also about \( 55 J \)
B. work done by the gas is about \( 42 J \) and heat rejected by the gas is \( 60 J \)
C. work done on the gas is \( 60 J \) and heat rejected by the \( \operatorname{gas} \) is also \( 60 J \)
D. work done on the gas is \( 60 J \) and heat absorbed by the gas is also about \( 60 J \)


Which is the most stable conformation
of ethane?
A. Eclipsed
B. Skew
c. staggered
D. All are equally stable


Why Noble gases are usually have large atomic size in the period?


A market research group conducted a survey of 2,000 consumers and reported that 1720 consumers liked
product \( P_{1} \) and 1,4500 consumers liked
product \( P_{2} . \) What is the least number that must have liked both the products.


How many different numbers of two
digits can be formed with the digits
1,2,3,4,5,6 no digits being repeated?


Succession is
A. Deforestation to obtain barren lands
B. Series of physical changes involved in colonising a bare area
C. Series of biological changes involved in colonizing an unoccupied area
D. Both B and C


Not more than one fuses.


Mark correct statement
for grunge flower
A. Palea is a bracteole
B. Ovary has 2 styles
c. Awn is present on paleo
D. Tetrarmerous


A \( 1 \mathrm{kg} \) ball is suspended in a uniform electric field with the help of a string fixed to a point. The ball is given a charge \( \sqrt{5} \) coulomb and the string
makes an angle \( 37^{0} \) with the vertical in
the equilibrium position. In the equilibrium position the tension is double the weight of the ball. Find the magnitude of the electric field in \( \mathrm{N} / \mathrm{C} \)
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D. 5


The \( p H \) of boiling water is \( 6.4 . \) This
implies that boiling water is:
B. slightly acidic
c. neutral
D. amphoteric


Which of the following conversions is
correct?
\( A \cdot 1 a t m=1.01 \times 10^{4} \mathrm{Pa} \)
B. \( 1 \mathrm{mm} \) of \( \mathrm{Hg}=133 \mathrm{Pa} \)
c. 1 bar \( =10^{7} \) Pa
D. 1 torr \( =10^{2} \) Pa


Prove that the Greatest integer function \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) given by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) is neither
one-one nor onto, where \( [x] \) denotes the
greatest integer less than or equal to \( x \)


The straight lines \( 7 x+y+1=0 \) and
\( 7 x+y-9=0 \) are tangents to the
same circle.Then the area of this circle
is


Stability of tetrabromides follows the
order:
A. \( \operatorname{SeBr}_{4}<\operatorname{Te} B r_{4}<\operatorname{PoBr}_{4} \)
B. \( \operatorname{SeBr}_{4}<\operatorname{PoBr}_{4}<\operatorname{TeBr} \)
\( \mathrm{c} \cdot \operatorname{PoBr}_{4}<\operatorname{Te} \mathrm{Br}_{4}<\operatorname{SeBr}_{4} \)
D. None of the these


The tetrabromide of 16th group element that is most stable is :
A. \( S B r_{4} \)
в. \( \operatorname{SeBr}_{4} \)
c. \( T e B r_{4} \)
D. \( \operatorname{PoBr}_{4} \)


Which of the following statements is
false?
A. The breakdown of most of biomacromolecules occurs in duodenum.
B. Simple substances (digested foods) are absorbed in the jejunum and ileum.
C. Significant digestive activity occurs in large intestine.
D. Undigested and unabsorbed substances are passed on to the large intestine.


Which of the following nuclei is unstable?
\( \mathbf{A} \cdot_{5} B^{10} \)
B. \( _{4} B e^{10} \)
\( \mathrm{c} \cdot_{7} N^{14} \)
\( \mathrm{D} \cdot_{8} \mathrm{O}^{1} \)


What initiatives were taken for
reducing vehicular air pollution in Delhi? Has air quality improved in Delhi?


There is more deviation in the behaviour
of a gas from the ideal gas equation \( \boldsymbol{P V}=\boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
A. At high temperature and low pressure
B. At low temperature and high pressure
C. At high temperature and high pressure
D. At low temperature and low pressure


The correct order of boiling point is:
\( \mathbf{A} \cdot H F>H I>H B r>H C l \)
B \( . H F>H B r>H I>H C l \)
\( \mathbf{c} . H C l>H B r>H I>H F \)
D. \( H C l>H I>H B r>H F \)


A metal, M forms chlorides in its +2 and +4 oxidation states. Which of the
following statements about these chlorides is correct?
A \( \cdot M C l_{2} \) is more ionic than \( M C l_{4} \)
B. \( M C l_{2} \) is more easily hydrolysed than \( M C l \)
c. \( M C l_{2} \) is more volatile than \( M C l_{4} \)
D. \( M C l_{2} \) is more soluble in anhydrous ethanol than \( M C l \)


An infinite cylinder of radius \( r_{0} \) carrying
linear charge density \( \lambda \). The equation of the equipotential surface for this
cylinder is
\( \mathbf{A} \cdot r=r_{0} e^{\pi \varepsilon_{0}\left[V(r)+V\left(r_{0}\right)\right] \lambda} \)
B . \( r=r_{0} e^{2 \pi \varepsilon_{0}}\left[V(r)-V\left(r_{0}\right)\right] \lambda^{2} \)
C . \( r=r_{0} e^{-2 \pi \varepsilon_{0}}\left[V(r)-V\left(r_{0}\right)\right] / \lambda \)
D. \( r=r_{0} e^{-2 \pi \varepsilon_{0}\left\lfloor V(r)-V\left(r_{0}\right) \backslash \lambda\right.} \)


Let \( n \) be a positive integer such that
\( \left(1+x+x^{2}\right)^{n}=a_{0}+a_{1} x+a_{2} x^{2}+ \)
\( \ldots+a_{2 n} x^{2 n}, \) then \( a_{r}= \)
В \( \cdot a_{2 n} ; 0 \leq r \leq 2 n \)
D. None of these


A bulb uses 5000 J of energy in 10 s calculate its power.
A. \( 50 J / \) s
B. 500w
\( c .5 w \)
D. 600 J/s


A string vibrates in 4 segments to a frequency of 400 Hz. What frequency will cause it to vibrate into 7 segments?
A. \( 700 H z \)
в. \( 500 H z \)
c. \( 400 \mathrm{Hz} \)
D. \( 100 H z \)


Assertion : Electric lines of force never
cross each other.
Reason: Electric field at a point superimpose to give one resultant electric field.
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false


A bar magnet is demagnetized by inserting it inside a solenoid of length \( 0.2 m, 100 t u r a s, \) and carrying a current
of \( 5.2 A . \) The coercivity of the bar
magnet is:
A. \( 1200 A / m \)
в. \( 2600 A / m \)
c. \( 5200 A / j m \)
D. \( 285 A / m \)


The sum of the series \( 1+\frac{1.3}{6}+\frac{1.3 .5}{6.8}+ \)
\( \ldots \infty \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \infty \)
D.


The heats of adsorption \( (\text { in } k J / m o l) \) in
physisorption or physical adsorption lie
in the range of:
A. \( 40-400 \)
B . \( 40-100 \)
c. \( 10-40 \)
D. \( 200-400 \)


A kid enjoying the rotatory ride which is
rotating with angular speed equals to
3.14 rad/s. Find out the period of
revolution for this ride?
\( A \)
B \( \cdot \frac{1}{2} s \)
c. 2 rev / \( s \)
D. 2s
E. 4 s


Assertion
Isotopes of an element can be separated by using a mass spectrometer.
Reason
Separation of isotopes is possible because of difference in electron
number of isotopes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


When \( 2 x^{2}-a x+7 \) and \( a x^{2}+7 x+12 \)
are divided by \( (x-3) \) and \( (x+1) \) respectively, the remainder is same. Find the value of a.
\( \mathbf{A} \cdot a=7 \)
B. \( a=14 \)
c. \( a=21 \)
\( \mathbf{D} \cdot a=5 \)


Write any four solution of the equation
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{2} \)


A body at an unknown temperature is placed in a room which is held at a
constant temperature of \( 30^{0} F . \) If after
10 minutes the temperature of the body
is \( 0^{0} F \) and after 20 minutes the
temperature of the body is \( 15^{0} F, \) find the unknown initial temperature.
A . -50
B. -20
c. -40
D. -30


A number lock on a suitcase has 3
wheels each labeled with 10 digits from
0 to \( 9 . \) If the opening of the lock is a particular sequence of three digits with
no repeats, how many such sequences will be possible?


Define reflex arc and its component.


Calculate the work done in increasing
the radius of a soap bubble in air from
\( 1 \mathrm{cm} \) to \( 2 \mathrm{cm} . \) The surface tension of
soap solution is 30 dyne \( / \) cm. \( (\pi= \)
3.142)


What is the unit of relative density?
A. \( g c m^{-3} \)
B. \( k g m^{-3} \)
c. \( m^{3} k g^{-1} \)
D. no unit


toppr
Q Type your question
radicals with almost equal ease,
whereas bromine free radicals have a
clear preference for the formation of tertiary free radicals. So, bromine is
less reactive, and more selective
whereas chlorine is less selective and
more effective
The relative rate of abstraction of
hydrogen by Br is \( \begin{array}{c}\mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}^{\circ} \\ \mathbf{( 1 6 0 0})\end{array}>\left(\begin{array}{c}\mathbf{8 2} \\ \mathbf{1}\end{array}\right) \)
The relative rate of abstraction of
hydrogen by Cl is \( \mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}^{\circ} \)
\( (\mathbf{5}) \)
G. How many dichloro products (including stereoisomers) will be
formed when \( R-2- \) chloropentane
reacts with \( C l_{2} \) in presence of UV
radiation?
A . 5
B. 6
c. 7
D. 8


A composite light containing yellow, blue and orange colours is passed through a prism. Which colour bends
the most?


Which of the following is not an electromagnetic wave?
A. Radio waves
B. X-rays
c. Earthquake P-waves
D. Gamma rays


The mass defect for helium nucleus is
0.0304 a.m.u. The binding energy per
nucleon of helium nucleus is
\( \mathbf{A} \cdot 28.3 \mathrm{MeV} \)
в. \( 7.075 \mathrm{MeV} \)
\( \mathbf{c} .9 .31 \mathrm{MeV} \)
D. \( 200 \mathrm{MeV} \)


Find the values of \( x \), if \( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)


A body dropped from the top of the tower covers a distance \( 7 x \) in the last second
of its journey, where \( x \) is the distance
covered in first second. How much time
does it takes to reach the ground?
A . \( 3 s \)
B. \( 4 s \)
\( c .5 s \)
D. \( 6 s \)


Artists use KALEIDOSCOPE for
A. Entertaining themselves
B. Getting ideas for new patterns
c. Discovering new properties of light
D. None of these


In the electric field of an point charge \( q \)
a certain charge is carried from point \( \mathbf{A} \)
to \( \mathrm{B}, \mathrm{C}, \mathrm{D} \) and \( \mathrm{E} \). Then the work done
during movement along each path is:
A. least along the path AB
B. least along the path AD
C. zero along any one of the path \( A B, A C, A D \) and \( A E \)
D. least along AE


\( \int \frac{\sin ^{2} x \cos ^{2} x}{\left(\sin ^{3} x+\cos ^{3} x\right)^{2}} \)


Assertion
Pressure applied to an enclosed fluid is transmitted undiminished to every
portion of the fluid and the walls of the
containing vessel.
Reason
Fluids cannot distribute the external
pressure equally to all portions.
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 probabilities that student will
receive \( A, B, C \) or \( D \) grade are
0.40,0.35,0.15 and 0.10 respectively Find the probability that a student will recive
i) not an A grade
ii) B or \( \mathrm{C} \) grade
iii) at most \( C \) grade


A particle in linear SHM performs \( 30 s c / s e c . \) Its velocity is \( 0.120 m / s \) when it passes through the middle of its path. The length of path is
A. \( 0.012 \mathrm{cm} \)
B. \( 3.2 \mathrm{cm} \)
c. \( 0.04 c m \)
D. \( 1.2 \mathrm{cm} \)


A coin is placed \( 10 \mathrm{cm} \) in front of a concave mirror. The mirror produces a real image that has diameter 4 times that of the coin. What is the image distance.


Acceleration-time graph of a particle
executing SHM is as shown in the
figure. Select the correct alternative(s)
This question has multiple correct options
A. Displacement of particle at 1 is negative
B. Velocity of particle at 2 is positive
C. Potential energy of particle at 3 is maximum
D. Speed of particle at 4 is decreasing


A ray makes angles \( \frac{\pi}{3}, \frac{\pi}{3} \) with \( \overrightarrow{O X} \) and \( \boldsymbol{O Y} \) respectively. Find the angle made by it with \( \overrightarrow{O Z} \)


The rate of change of magnetic flux density through a circular coil of area 10
\( \mathrm{m} \) and number of turns 100 is \( 10^{3} \mathrm{Wb} / \mathrm{m} \)
2 /s. The value of induced emf will be
\( A \cdot 10^{-2} v \)
B. \( 10^{-3} v \)
\( c \cdot 10 v \)
\( D \cdot 10^{6} v \)


The correct statement(s) about the
compound \( \boldsymbol{H}_{3} \boldsymbol{C}(\boldsymbol{H} \boldsymbol{O}) \boldsymbol{H} \boldsymbol{C}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3}(\boldsymbol{X}) \) is(are):
This question has multiple correct options
A. The total number of stereoisomers possible for \( X \) is 6
B. The number of diastereomers possible for \( X \) is 3
c. If the stereochemistry about the double bond in \( X \) is trans, the number of enantiomers possible for \( X \) is 4
D. If the stereochemistry about the double bond in \( X \) is cis, the number of enantiomers possible for \( X \) is 2


In sweet pea, the tendrils are
modification of
A. Stem branches
B. Leaflets
c. stipules
D. None of the above


Write the smallest equivalence relation
on the \( \operatorname{set} A=\{1,2,3\} \)


How long after the block leaves the free
end of the spring does it come to rest.
A .3 .33 sec
B. 2.3 sec
\( c .3 .53 \mathrm{sec} \)
D. 3.6 sec


Loranthus is a
A. Commensal
B. Epiphyte
C. Parasite
D. Symbiont


Solve the following equation:
\( 7 x-5=2 x \)


Explain hybridization of central atom in
\( : I F_{7} \)


A family is going to a theme park having \( t \) members in the family. Each ticket costs \( \$ 80, \) and the number of
tickets needs to be bought can be
calculated from the expression \( t^{2}- \)
\( 4 t-90=6 \) when \( t>0 . \) What is the
total cost of the theme park tickets that
the family paid?
A. \( \$ 640 \)
B. \( \$ 800 \)
c. \( \$ 960 \)
D. \( \$ 1,120 \)


We consider the radiation emitted by the human body, which of the following statements is true?
A. The radiation is emitted only during the day.
B. The radiation is emitted during the summers and absorbed during the winters
C. The radiation emitted lies in the ultraviolet region and hence is not visible
D. The radiation emitted is in the infrared region


Output emf in a dynamo is generated on
A. Magnettet
B. Armature coil
c. slip rings
D. Carbon brushes


A point object is kept at a distance of
\( 60 \mathrm{cm} \) from the combination of
two identical thin prisms (prism angle =
\( 4^{0} \& \) refractive index \( =1.5 \) ) as shown
in figure. If distance between the two images formed by the combination is \( \frac{x \pi}{3} \mathrm{cm} \) approximately, then \( x \) is:


\( \sqrt{ }\rceil \)
\( \Gamma \)
\begin{tabular}{r}
\( \pi \) \\
\hline
\end{tabular}


Nitrogen waste product of Amoeba is
A. Ammonia
B. Urea
c. Uric acid
D. None of the above


If \( A=\{1,3,5,7\} \) and \( B=\{1,2,3,4,5,6,7, \)
83, then the number of one-to-one functions from A into B is
A \( \cdot 1340 \)
B. 1860
\( c \cdot 1430 \)
D. 1880
E . 1680


Using Principle of mathematical
induction prove that \( 6^{n}-1 \) divisible by
\( \mathbf{5} \)


Differentiate \( e^{x}+e^{-x} \) with respect to \( x \)


Sound waves are passing through two
routes-one in straight path and the other along a semicircular path of
radius \( r \) and are again combined into
one pipe and superposed as shown in
the figure. If the velocity of sound waves
in the pipe is \( v, \) then frequencies of
resultant waves of maximum
amplitude will be integral multiples of:
\( A \)
в. \( \frac{v}{r(\pi-1)} \)
c. \( \frac{2 v}{r(\pi-1)} \)
D. \( \frac{v}{r(\pi+1)} \)


Our palms get warmed up when rubbed together. This is because of:
A. kinetic energy
B. friction
c. electrostatic force
D. all of the above


Common name of Fungia is
A. Mushroom coral
B. Red coral
C. Brain coral
D. Organ pipe coral


Short / Long answer type questions. Why annual rings are comparatively well marked in plants growing in hilly areas than those in coastal areas?


A body of mass \( m \) falls from rest
through a height \( h \) under gravitation acceleration \( g \) and is then brought to rest by penetrating through a depth \( d \) into some sand. The average
deceleration of the body during penetration into sand is
A \( \frac{g h^{2}}{d^{2}} \)
в. \( \frac{g h^{2}}{2 d^{2}} \)
c. \( \frac{g h}{d} \)
D. \( \frac{g d}{h} \)


If \( \boldsymbol{A}=\{1,2,4,5\} \) and \( B=\{a, b\} \) Find
the total number of relations from \( A \) to
\( \boldsymbol{B} \)


Cane sugar on hydrolysis gives:
A. glucose only
B. glucose and maltose
C . glucose and fructose
D. glucose and lactose


Lacteal present in the villi of the small intestine
A. Help to absorb fatty acids and glycerol
B. Secrete enzymes for digestion
c. secrete hormones
D. Help to absorb proteins


The minimum value of \( x \log x \) is equal
to.
\( A \)
B. \( \frac{1}{e} \)
\( c \cdot-\frac{1}{e} \)
\( D \cdot 2 \)


A fuse wire is always connected to the
A. earth wire
B. neutral wire
C. live wire
D. none of these


Which of the following is the most chemically reactive?
A \( . L i \)
в. \( N a \)
c. \( K \)
D. \( R b \)
ह. \( C s \)


If \( I \) is the centre of a circle inscribed in
a triangle \( A B C, \) then \( |\overline{B C}| \overline{I A}+ \) \( |\overline{C A}| \overline{I B}+|\overline{A B}| \overline{I C} \) is
A. \( \overline{0} \)
в. \( \overline{I A}+\overline{I B}+\overline{I C} \)
c. \( \frac{\overline{I A}+\overline{I B}+\overline{I C}}{3} \)
D. \( \frac{\overline{I A}+\overline{I B}+\overline{I C}}{2} \)


If you raise your right hand in front of a plane mirror, what will you see in it?
A. You have raised your right hand
B. You have raised your left hand
c. You have lowered your right hand
D. You have lowered your left hand


The teeth present after the age of 8 -12 is called as
A. Milk teeth
B. Temporary teeth
c. Permanent teeth
D. Both A and C


At constant temperature and constant
pressure, the heat of the reaction is equal
to:
\( A \cdot \Delta E \)
в. \( \Delta H \)
\( c \cdot \Delta P \)
D. \( \Delta V \)


If \( \{x\} \) denotes fractional part of \( x, \) then \( \lim _{x \rightarrow 1} \frac{x \sin \{x\}}{x-1}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. 1
D. does not exist


The value of \( \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)
A \( \cdot 3 \times 10^{6} m / s \)
В. \( 3 \times 10^{8} m / s \)
c. \( 3 \times 10^{4} m / s \)
D. 332m/s


Chords \( M N \) and \( R S \) of a circle
intersect at \( \boldsymbol{P} \) outside the circle If
\( \boldsymbol{P N}=\mathbf{3} \boldsymbol{c m}, \boldsymbol{M} \boldsymbol{N}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{P} \boldsymbol{R}=\boldsymbol{2} \boldsymbol{c m} \)
then the value of \( S R \) is equal to
\( \mathbf{A} \cdot 5 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Bleaching powder is a:
A. double salt
B. complex salt
c. mixed salt
D. normal salt


A man sold two chairs at Rs. 492 each.
On one, he gained \( 20 \% \) and on the other, he lost \( 20 \% \). Find his net gain \( \% \) or loss \( \% \) in the whole transaction.


\( \mathbf{f} \boldsymbol{y}=\sin ^{-1}(\mathbf{3} \boldsymbol{x})+\mathbf{s} \mathbf{e} \mathbf{c}^{-1}\left(\frac{\mathbf{1}}{\mathbf{3} \boldsymbol{x}}\right), \) find \( \frac{\boldsymbol{d} \mathbf{2}}{\boldsymbol{d}} \)


\( 1.22 \mathrm{g} \) of a monobasic acid is dissolved in 100 g of benzene. The boiling point of the solution increases by \( 0.13^{\circ} \mathrm{C} \) with respect to pure benzene. Find the
molecular mass of aid in benzene
solvent (in \( u \) ). Report your answer after dividing it by 100 and Round it off to the
nearest integer. \( \left(K_{b} \text { of benzene }=2.6 \mathrm{K}\right. \)
\( \mathrm{kg} \mathrm{mol}^{-1} \) ).


Calculate the velocity of an electron placed in the third orbit of hydrogen atom. Also calculate the number of
revolutions per second that this electron mkaes around the nucleus.


If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{t}-\sin \boldsymbol{t}), \boldsymbol{y}=\boldsymbol{a}(1+\cos \boldsymbol{t}) \) then
find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)


The induced EMF in loop at time \( t= \)
\( 2 \pi / \omega \) is :
\( A \cdot O \)
B. \( \frac{B_{0} \pi \omega R^{2}}{2} \)
\( \mathbf{c} \cdot B_{0} \pi \omega R^{2} \)
D. \( -\frac{B_{0} \pi \omega R^{2}}{2} \)


Rutherford's alpha particle scattering experiment eventually led to the conclusion that:
A. mass and energy are related
B. electrons occupy space around the nucleus
c. neutrons are buried deep in the nucleus
D. the point of impact with matter can be precisely determined


The Bulk of Ethanol, Mercury and water are given as 0.9,25 and 2.2 respectively in units of \( 10^{8} N m^{-2} \). For a given value
of pressure, the fractional compression in volume is \( \triangle V / V . \) Which of the
following statements about \( \triangle \boldsymbol{V} / \boldsymbol{V} \) for
these three liquids is correct?
A. Mercury > Ethanol > Water
B. Ethanol> Mercury > Water
c. water> Ethanol > Mercury
D. Ethanol> Water> Mercury


Let
\( f(x)=\left|\begin{array}{ccc}\sec ^{2} x & 1 & 1 \\ \cos ^{2} x & \cos ^{2} x & \operatorname{cosec}^{2} x \\ 1 & \cos ^{2} x & \cot ^{2} x\end{array}\right| \)
then


Solve \( : \boldsymbol{x}^{2} \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\left(\boldsymbol{x}^{3}+\boldsymbol{y}^{3}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


In which of the following cases, is the
work done maximum?
\( A \)
B.
\( \mathbf{c} \)
D.


A given amount of gas is heated until both its pressure and volume are doubled. If initial temperature is \( 27^{0} \mathrm{C} \), its
final temperature is
\( A \cdot 300 K \)
B. 600 K
\( c \cdot 1200 k \)
D. 900K


For a certain reaction the rate law is
rate \( =k[C]^{3 / 2} . \) If the rate of the reaction
is \( 0.020 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \) when \( [C]=1.0 \mathrm{M} \)
what is the rate when \( [C]=0.60 \mathrm{M} ? \)
\begin{tabular}{l}
A \( \cdot 0.0093 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \) \\
\hline
\end{tabular}
B. \( 0.012 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \)
c. 0.033 mol \( L^{-1} s^{-1} \)
D. \( 0.040 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \)


An object mass \( 10 \mathrm{kg} \) falls from rest through a vertical distance of \( 10 \mathrm{m} \) and acquires a velocity of \( 10 \mathrm{m} / \mathrm{s} \). The work done by the push of air on the object is \( \left(g=10 m / s^{2}\right) \)
A. 500 J
B . -500 J
c. 250
D . -250J


Which of the following will have the maximum dipole moment?
A. \( C H_{3} F \)
в. \( C H_{3} C l \)
\( \mathrm{c} \cdot C H_{3} B r \)
D. \( C H_{3} I \)


another in 2 hours time, its speed
during the motion is shown in graph above. The maximum acceleration
during the journey and distance covered during the time interval from
0.75 hour to 1.00 hour are
\( \mathbf{A} \cdot 60 \mathrm{kmhr}^{-2}, 100 \mathrm{km} \)
B. \( 160 \mathrm{kmhr}^{-2}, 10 \mathrm{km} \)
\( \mathbf{C} \cdot 10 \mathrm{kmhr}^{-2}, 10 \mathrm{km} \)
D. \( 260 \mathrm{kmhr}^{-2}, 1 \mathrm{km} \)


Find all solution of the equation. \( \frac{(\mathbf{2}|\boldsymbol{x}|-\mathbf{3})^{2}-|\boldsymbol{x}|-\mathbf{6}}{\mathbf{4} \boldsymbol{x}+\mathbf{1}}=\mathbf{0}, \) which
belong to the domain of definition of the
function \( \boldsymbol{y}=(2 \boldsymbol{x}+\mathbf{1}) /\left(\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{6}\right) \)


Check whether \( \boldsymbol{x}^{2}+\frac{1}{2} \boldsymbol{x}=\mathbf{0} \) is
a quadratic equation.


State the following statement is True or
False

Standard deviation is the measure of dispersion
A. True
B. False


Which water pollutant is incorrectly paired with the source?
A. Oil spill- ship
B. Pesticide - -Oil palm plantation
c. Sewage-Large factory
D. Nitrate - Farm


With a neat labelled diagram, explain the formation of image in a simple microscope.


Which one of the following halogen compounds is difficult to be hydrolysed
by \( S_{N} 1 \) mechanism?
A. Tertiary butyl chloride
B. Isopropyl chloride
c. Benzyl chloride
D. Chlorobenzene
E. Allyl chloride


The distance formula between two
points \( A\left(x_{1}, y_{1}\right) \) and \( B\left(x_{2}, y_{2}\right) \) is given by
A \( \cdot\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2} \)
B . \( \left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2} \)
c. \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
D. None of the above


At which phase of the cell cycle, DNA polymerase activity is at its highest?
A. Gap 1 (GI)
B. Mitotic (M)
c. synthetic (s)
D. Gap 2 (G2)


Which of the following involves reduction?
A. conversion of an anion to atom
B. conversion of a cation to atom
c. both these
D. none of these


Sea anemone belongs to which of the following phylum?
A. Protozoa
B. Poriferara
c. coelenterata
D. Echinodermata


Two perpendicular lines are intersecting at \( (4,3) . \) One meeting coordinate axis at \( (4,0), \) find the
coordinates of the intersection of other
line with the cordinate axes.
A \( .(0,3) \)
B. (1,3)
D. None of these


Which of the following are used as Control Rods:
a) Boron rods
b) Cadmium rods
c) Copper rods
A . a is correct
B. b is correct
c. c is correct
D. a,b are correct


A capacitor of capacitance \( 2 \mu F \) is
charged to a voltage of \( 6 \mathrm{V} \). The charge
on its plates is:
A . \( 1.2 \times 10^{-5} C \)
B . \( 3 \times 10^{-6} C \)
c. \( \frac{1}{3} \times 10^{-6} C \)
D. \( \frac{1}{12} \times 10^{-6} \mathrm{C} \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{1} \)
then the values of \( \boldsymbol{f}^{-}(\mathbf{1 7}) \) and \( \boldsymbol{f}^{-}(-\mathbf{3}) \)
respectively are
\( \mathbf{A} \cdot \phi,\{4,-4\} \)
B \( \cdot\{3,-3\}, \phi \)
\( \mathbf{c} \cdot \phi,\{3,-3\} \)
\( \mathbf{D} \cdot\{4,-4\}, \phi \)


Find the factors of the following expression:
\( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y} \)
This question has multiple correct options
\( \mathbf{A} \cdot(a+b) \)
в. \( (a-b) \)
c. \( (x+y) \)
D. \( (x-y) \)


The vertical forces that the ground
exerts on a stationary van are shown.
The van is \( 2.50 \mathrm{m} \) long with the wheels
at a distance of \( 0.600 \mathrm{m} \) from the front
of the van and \( 0.400 \mathrm{m} \) from the rear of
the van.

What is the horizontal distance of the
van's centre of gravity from the front of the van?
A. \( 0.540 \mathrm{m} \)
B. 0.960 m
c. \( 1.14 \mathrm{m} \)
D. \( 1.36 \mathrm{m} \)


A constant force \( F \) acts on a particle of
mass \( 1 \mathrm{kg} \) moving with a velocity \( v, \) for
one second. The distance moved in that
time is :
A . 0
в. \( \frac{F}{2} \)
c. \( 2 F \)
D. \( \frac{v}{2} \)
E \( \cdot v+\frac{F}{2} \)


If \( z_{1}, z_{2}, \varepsilon C \) are such that \( \left|z_{1}+z_{2}\right|^{2}= \)
\( \left|z_{1}\right|^{2}+\left|z_{2}\right|^{2} \) then \( \frac{z_{1}}{z_{2}} \) is
A . zero
B. purely real
c. purely imaginary
D. complex


The extent of charge of lead
accumulator is determined by:
\( \mathbf{A} \cdot \) amount of \( P b S O_{4} \) in the battery
B. amount of \( P b O_{2} \) in the battery
C . specific gravity of \( H_{2} S O_{4} \) of the battery
D. amount of \( P b \) in the battery


\( \int x^{2} \tan ^{-1} x d x \)
A. \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{6} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
B. \( \frac{x^{3}}{3} \tan ^{-1} x+\frac{1}{6} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
C \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{3} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
D. \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{6} x^{2}+\frac{1}{3} \log \left(x^{2}+1\right) \)


A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to
the rock.
A. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite
B. As the rock cannot generate its own force, it will slow down
c. Gravity will pull the rock towards earth
D. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity
E. As the rock is smaller than the satellite, its inertia will pull it further away from earth


What are the precautions to be taken by the people who are working in radiation laboratories?


How many chamber are present in human heart?
A . 2
B. 3
\( c \cdot 4 \)
\( D \)


In cell representation, oxidation half cell is represented on the:
A. Ieft hand side
B. right hand side
c. salt bridge
D. none of the above


Match the polymers given in column
with monomers in column II and mark
the appropriate choice.
\( \rightarrow(\text { iv }) \)
(B) (ii) (iii)
\( A \cdot(A) \)
\( - \)
\( (C) \rightarrow(i),(D) \) \( \rightarrow \)
B. (iii) \( \rightarrow(\text { iv }) \) \( \rightarrow \) (ii) \( (A) \rightarrow(i) \) (B) \( \rightarrow \)
\( (C) \)
(D)
\( c \)
\( (A) \rightarrow(i v) \)
(B) \( \rightarrow \) (i)
\( (C) \rightarrow(i i),(D) \) \( \rightarrow \) (iii)
\( D \cdot(A) \)
\( \rightarrow \) (ii)
\( \mathrm{R} \)
v)
C) \( \rightarrow \) (iii)
\( (D) \rightarrow(i) \)


An angiosperm lacking vessels is
A. Trochodendron
B. Acacia
c. salix
D. Dendrocalamus


What is the value of mode for the
following data:
\( \begin{array}{ll}\text { Class interval } & \text { Frequency } \\ 350-369 & 15 \\ 370-389 & 27 \\ 390-409 & 31 \\ 410-429 & 19 \\ 430-449 & 13 \\ 450-469 & 6\end{array} \)
\( A . \quad 390 \)
B . 394.50
\( c .394 \)
D. 400


Internal energy of \( n_{1} \) moles of \( H_{2} \) at
temperature \( \boldsymbol{T} \) is equal to the internal
energy of \( n_{2} \) moles of He at temperature
27. Then the ratio \( \frac{\boldsymbol{n}_{1}}{\boldsymbol{n}_{2}} \) is
A . \( 3 / 5 \)
B. 2/3
\( c \cdot 6 / 5 \)
D. 3/7


Image seen by a periscope is:
A. Iaterally inverted
B. Iongitudinally inverted
c. both \( A \) and \( B \)
D. neither A nor B


Nerve cord of Cockroach is
A. Dorsal and single
B. Dorsal and double
C. Ventral and single
D. Ventral and double


The expenditure (in 10 crores of rupees) on health by the Government of India during the various five year plans is shown below:
Plans:
\( I I \quad I I I \)
Expenditure on health in 10 crores 23
of rupees
Construct a bar graph to represent the
above data.


(a) Give the postulates of Werner's theory of co-ordination compounds.
(b) Differentiate between chemical
reactions and nuclear reactions.


Column-I
(A) Tyrosine
(P)Essential amino acids
(B) Serin
(Q) Ceric Ammonium Nitrate
\( (\mathrm{C}) \)
Tryptophane
(R) Neutral \( F e C l_{3} \)
(S) Carbaylamine Test -
(D) Proline \( \quad \) Negative.
Select the correct set of answer.
\( A \cdot A-R, B-Q, C-P, D-S \)
B. A-Q, B-R, C-S, D-P
C. \( A-R, B-P, C-Q, D-S \)
D. A-S, B-Q, C-P, D-R


Total number \( 1^{\circ} \) and \( 3^{\circ} \) alcohols
possible for \( C_{5} H_{11} O H ? \)


Sum the following series to n terms and o infinity \( \frac{1}{1.3 .5}+\frac{1}{3.5 .7}+\frac{1}{5.7 .9}+\ldots . \)


A force of \( 10 \mathrm{N} \) is applied on an object at
rest of mass \( 2 \mathrm{kg} \) placed on a smooth
surface. The kinetic energy after 5 s is
\( J \)
A . 124.6
в. 625
c. 312.5
D. 683.8


\( \ln \) a \( \Delta A B C, E \) and \( F \) are the mid-points
of \( A C \) and \( A B \) respectively. The altitude
AP to BC intersects FE at Q. Prove that
\( \boldsymbol{A} \boldsymbol{Q}=\boldsymbol{Q} \boldsymbol{P} \)


Order of magnitude of density of
Uranium nucleus is, \( \left[\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right] \)
\( \mathbf{A} \cdot 10^{20} k g / m^{3} \)
B . \( 10^{17} \mathrm{kg} / \mathrm{m}^{3} \)
C. \( 10^{14} \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 10^{11} \mathrm{kg} / \mathrm{m}^{3} \)


The structure of the compound with
molecular formula \( C_{6} H_{12} \) that has only primary and secondary H atoms is:
A. 1-Methyl cyclo-pentane
B. 1,1-Dimethyl cyclobutane
c. cyclohexane
D. 2-Methyl pent-2-ene


If \( A \) and \( B \) be two events such that
\( P(A)=\frac{1}{4}, P(B)=\frac{1}{3} \) and \( P(A \cup B)= \)
\( \frac{1}{2} \) then show that \( A \) and \( B \) are
independence events


Number of solution of equation \( \left|\sin ^{-1} x-\cos ^{-1} x\right|=x+2 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Valency of carbon in ethylene is


Discuss briefly giving an example in
each case the role
of coordination compound medicinal chemistry.


Write the common difference of an A.P.
whose \( n^{t h} \) terms is \( 3 n+5 \)


Dry ice is:
A. ice cube
B. sodium chioride
C . liquid nitrogen
D. solid carbon dioxide


Mention any one skeletal difference
between ape and man.


A diastema:
A. Is a gap between two teeth
B. Appears due to the absence of canine teeth in herbivores
C. May occur in humans
D. Is related to more than one option given above


Find the value of \( x \) if \( \left|\begin{array}{ccc}3 & 5 & x \\ 2 & 4 & 1 \\ -1 & 2 & 3\end{array}\right|=0 \)


Which one of the following statement is
correct?
A. Chest expands because air enters into the lungs.
B. Air enters into the lungs because chest expands.
C. The muscles of the diaphragm contracts because air enters into the lungs.
D. All of the above statements are correct.


The sequence of cell organelles during
photorespiration is
A. Chloroplast - Golgi bodies - Mitochondria
B. Chloroplast - Rough endoplasmic reticulum Dictyosomes
C. Chloroplast-Peroxisomes-Mitochondria
D. Chloroplast - Vacuole - Peroxisome


In any discrete series (when all the value are not same) the relationship between M.D. about mean and S.D. is
\( A \cdot M \cdot D=S \cdot D \)
в. \( M . D .> \) S.D.
c. \( M . D .<S . D \)
D. \( M . D . \leq S . D . \)


Find the value of following polynomial
by taking \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{y}=\mathbf{3} \)
\( \boldsymbol{y}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \)
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 11


Fill in the blanks with appropriate
words.
The jelly-like fluid protoplasmic matrix
which surrounds the nucleus
and constitutes the true internal milieu
of the cell is called


The differential equation of all
parabolas with axis parallel to the axis
of \( \boldsymbol{y} \) is:
A \( \cdot y_{2}=2 y_{1} \)
в. \( y_{3}=2 y_{1} \)
c. \( y_{2}^{3}=y_{1} \)
D. none of these


For a cell terminal potential difference is \( 2.2 \mathrm{V} \) when circuit is open and
reduces to \( 1.8 \mathrm{V} \) when cell is
connected to a resistance of \( \boldsymbol{R}=\mathbf{5} \Omega \)
then determine internal resistance of
cell is :-
A \( \cdot \frac{10}{9} \Omega \)
в. \( \frac{9}{10} \Omega \)
c. \( \frac{11}{9} \Omega \)
D. \( \frac{5}{9} \Omega \)


Cytochromes are concerned with which of the following processes?
A. Protein synthesis
B. Cellular digestion
c. Cell division
D. cellular respiration


Calculate the average molecular kinetic
energy :
(a) per kilomole,
(b) per kilogram,
of oxygen at \( 27^{\circ} \mathrm{C} \)
\( (R=8320 J / K m o l e K, \) Avogadro's
number \( =\mathbf{6 . 0 3} \times \)
\( 10^{26} \) molecules \( / \) Kmole


Divide the following polynomial \( p(x) p(x) \) by the polynomial \( S(x) 5(x) \)
\( \boldsymbol{P}(\boldsymbol{x})=\frac{2}{3} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\boldsymbol{6}, \boldsymbol{S}(\boldsymbol{x})=\boldsymbol{x}+\boldsymbol{6} \)


A \( 5 \% \) solution of cane sugar is isotonic with \( 0.877 \% \) solution of \( X . \) Calculate
the molecular mass of \( X \), if the
molecular mass of cane sugar is 342 g/mol.
A \( .60 \mathrm{g} / \mathrm{mol} \)
B. \( 120 \mathrm{g} / \mathrm{mol} \)
c. 78 g/mol
D. 30 g/mol


When a magnet M is pushed in and out
of a circular coil \( C \) connected to a very
sensitive galvanometer \( G \) as shown in
the figure with frequency f then which of
the following holds true?
A. constant deflection will be observed in the galvanometer.
B. visible small variation will be observed in the galvanometer if \( f \) is about 50 Hz
c. oscillation in the deflection will be seen clearly when \( f=1 \) or \( 2 \mathrm{Hz} \)
D. no variation in the deflection will be seen even when \( f=1 \) or 2 Hz.


A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of \( 10 \mathrm{m} \) from
the foot of the tower. The initial velocity
of the body is \( \left(g=10 m s^{-2}\right) \)
A \( .2 .5 \mathrm{ms}^{-1} \)
B. \( 5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 20 m s^{-1} \)


Choose the correct answers from the
alternatives given
The presence of mesoderm
A. restricts the development of a coelom
B. is associated with the organ level of organization
\( \mathbf{c} . \) is associated with the development of muscles
D. both (b) and (c)


When a beam of white light parallel to the principal axis is refracted through a convex lens, then the rays converge to the principal axis. If a screen is placed at a sufficient distance from the focus-
point perpendicular to the principal axis then the image on the screen will be
A. A sharp white point
B. A sharp violet point or red point
c. A circular spot whose edges are violet and central portion red
D. A circular spot whose edges are red and central portion violet


Blood pressure and heart beat is regulated by
A . Insulin
B. Adrenalin
c. optic nerve
D. Growth hormone


Write the IUPAC name of above
compound.


Aqueous solution of nickel sulphate on treating with pyridine and then adding a solution of sodium nitrate gives dark
blue crystals of:
\( \mathbf{A} \cdot\left[N i(p y)_{4}\right] S O_{4} \)
B \( \cdot\left[N i(p y)_{2}\left(N O_{2}\right)_{2}\right. \)
c. \( \left[N i(p y)_{4}\left(N O_{2}\right)_{2}\right. \)
D. \( \left[N i(p y)_{3}\left(N O_{2}\right)\right]_{2} S O_{4} \)


The greenhouse effect is useful
because:
A. it reduces water pollution
B. it increases normal temperature of earth
c. keeps the temperatures on our planet mild and suitable for living things
D. reduces greenhouse gases


An aqueous solution of \( 0.24 M \) aniline
\( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{4} . \mathbf{1 6 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \) ) is mixed with
Na \( O H \) solution to maintain anilinium
ion concentration to \( 1 \times 10^{-8} M \)

The \( p O H \) of \( N a O H \) solution used was:


The bond length of \( C-O \) bond in
carbon monoxide is \( 1.128 \$ \$\{ \) buildrel \( \mathrm{~ I l c i r c ~ l o v e r ~ \{ m a t h r m \{ A \} \} \$ \$ . ~ T h e ~} \)
\( C-O \) bond in \( F e(C O)_{5} \) is:


Driving a car on a highway with windows open reduce the speed. This is
due to:
A. air resistance
B. mechanical defect
c. bad driving
D. none of these


The statement that is not correct is :
A. Van der Waals constant 'a' measures extent of
intermolecular attractive forces for real gases
B. Boyle point depends on the nature of real gas
C . compressibility factor measures the deviation of real gas from ideal behaviour
D. critical temperature is the lowest temperature at which liquefaction of a gas first occurs


A beam of light \( A O \) is incidents on a glass slab \( (\mu=1.54) \) in a direction as
shown, in the Fig. The reflected ray \( O B \)
is passed through a Nicol prism. On rotating the Nicol prism we observe the
A. the intensity is reduced to zero and remains zero
B. the intensity reduces somewhat and rise again
c. there is no change in intensity
D. the intensity is gradually to reduces to zero and then again it increases


Define one watt:
A. one joule per second
B. one second per joule
C . ten joules per second
D. voltage divided by current
E. resistance multiplied by voltage


Activation energy of a reaction is:
A. the energy released during the reaction.
B. the energy evolved when activated complex is formed.
C . additional amount of energy needed by the reactants to overcome the potential barrier of reaction.
D. the energy needed to form one mole of the product.


A physical quantity consists of a :
A. analogical magnitude
B. numerical magnitude
c. alphabetical magnitude
D. symbolic magnitude


Image is formed at that point where
A . At least two rays of light meet
B. Where three rays of light meet
c. Where two rays of light appear to meet
D. B and C


The quantity of heat required to change the temperature of \( 1 \mathrm{kg} \) of a substance
by \( 1^{\circ} \mathrm{C} \) is called its :
A. specific heat
B. Latent heat
c. Total energy
D. Heat of fusion


A dairy produces a 500 -gram pack of butter in the shape of a cylinder. The radius of the circular end of the pack is \( 3.9 \mathrm{cm} . \) and the length of the pack is 10.5 cm. The volume of the pack of the butter
is \( x \mathrm{cm}^{3} . \) The 500 gm pack is redesigned. It is now produced in the shape of a cuboid with a square end of side \( 6.5 \mathrm{cm} . \) The length of the redesigned pack f butter is y cm. Now
choose the correct options. This question has multiple correct options
A. \( x=405 \)
в. \( y=11.9 \)
c. \( x=502 \)
D. \( y=13.9 \)


What are fuel cells? How are they
different from Galvanic cells? Give the
construction of hydrogen-oxygen fuel cells.


Given two independence events \( A \) and
\( B \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)


All rhombuses are parallelogram.
A. True
B. False


In how many ways can the letters of the word 'PERMUTATIONS' be arranged if the
(i) words start with \( P \) and ends with \( S \)
and
(ii) Vowels are all together.


The total energy of the electron in the first excited state of hydrogen is
\( -3.4 e V . \) What is the kinetic energy of
the electron in this state?
A. +1.7 eV
B. +3.4 eV
c. \( +6.8 \mathrm{eV} \)
D. \( -13.4 \mathrm{eV} \)


Ms. Kyle deposits an amount of Rs.
15400 to obtain a simple interest at the rate of \( 12.5 \% \) for 4 years. What total
amount will Ms. Kyle get at the end of 4
years?
A . 13100
B . 23100
c. 33100
D. 43100


In forced oscillation of a particle the amplitude is maximum for a frequency
\( \omega_{1} \) of force, while the energy is
maximum for a frequency \( \omega_{2} \) of the force, then:
A. \( \omega_{1}=\omega_{2} \)
В. \( \omega_{1}>\omega_{2} \)
C. \( \omega_{1}<\omega_{2} \) when damping is small and \( \omega_{1}>\omega_{2} \) when damping is large
D. \( \omega_{1}<\omega_{2} \)


The acid present in curd/sour milk is:
A . acetic acid
B. formic acid
c. lactic acid
D. hydrochloric acid


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{x}(\cos x) \) is
A \( \cdot\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\{1\} \)
в. \( \left(\frac{\pi}{2}, \frac{\pi}{2}\right)-\{1\} \)
c. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
D. \( \left(0, \frac{\pi}{2}\right)-\{1\} \)


If \( (3 p+q, p-q)=(p-q, 3 p+q) \)
then:
A. \( p=q=0 \)
B \( . p=q \)
c. \( p=2 q \)
D. \( p+q=0 \)


A closed vessel is maintained at a
constant temperature. It is first evacuated and then vapour is injected into it continuously. The pressure of the vapour in the vessel is:
A. increases continuously
B. first increases and then remains constant
c. first increases and then decreases
D. none of the above


Under the same conditions, two gases have the same number of molecules.
They must
A. be noble gases
B. have equal volumes
c. have a volume of \( 22.4 \mathrm{dm}^{3} \) each
D. have an equal number of atoms


Cycloalkanes are isomeric with:
A. alkadienes
B. alkynes
c. aromatic compounds
D. olefins


Le Chatelier principle is
A. reaction of a system to maintain equilibrium
B. feedback
C . cybernetics
D. carrying capacity


Find \( F(x) \) from the \( \operatorname{given} F^{\prime}(x) \) \( F^{\prime}(x)=2 \sin 5 x+3 \cos (x / 2) \) which is
zero for \( \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{3} \)


Body cavity lined by mesoderm is called
as
A. Coelenteron
B. Pseudocoel
c. coelom
D. Blastocoel


Which of the following is not a series?
\( A \cdot A P \)
в. GР
C. Fibonacci pattern
D. None of the above


Which of the following phenomenon occurs when we open a bottle of perfume and its smell spreads in the entire room with in a short time?
A. Evaporation
B. Sublimation
C . Diffusion
D. Decantation


In the adjacent figure, ABC is a triangle
in which \( \angle B=50^{\circ} \) and \( \angle C=70^{\circ} \)
Sides \( A B \) and \( A C \) are produced. If ' \( z^{\prime} \) is
the measure of the angle between the
bisectors of the exterior angles of
formed, then find 'z'.


A bookseller buys 220 books at \( R s 25 \)
each. He sold than at a loss of \( 5 \% \) Find
the selling price of each books


In balancing the half reaction, \( S_{2} O_{3}^{2-} \rightarrow S(s), \) the number of electrons
that must be added on the left is :


In figure, name each linear pair and
each pair of vertically opposite angles


Rice takes longest time to cook
A. at sea level
B. at shimla
C. at Mount Everest
D. in a submarine \( 100 \mathrm{m} \) below the surface of sea


A point positive charge of \( Q \) ' unit is moved round another positive charge of \( \mathrm{Q} \) unit on a circular path. If the radius of the circle is \( r, \) the work done on the charge \( Q \)
in making one complete revolution is:
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} r} \)
в. \( \frac{Q Q^{\prime}}{4 \pi \epsilon_{0} r} \)
c. \( \frac{Q^{\prime}}{4 \pi \epsilon_{0} r} \)
D. 0


projected with a velocity \( v_{0} \) towards a
circular region having a uniform
magnetic field \( B \) perpendicular and
into the plane of paper from point \( \boldsymbol{P} \) as
shown in the figure. \( \boldsymbol{R} \) is the radius and
O is the center of the circular region. If
the line \( O P \) makes an angle \( \theta \) with the
direction of \( v_{0} \) then the value of \( v_{0} \) so
that particle passes through \( \boldsymbol{O} \) is
A \( \cdot \frac{q B R}{m \sin \theta} \)
B. \( \frac{q B R}{2 m \sin \theta} \)
c. \( \frac{2 q B R}{m \sin \theta} \)
D. \( \frac{3 q B R}{2 m \sin \theta} \)


A car moving with a speed of \( 40 \mathrm{km} / \mathrm{h} \) can be stopped by applying brakes at least after \( 2 \mathrm{m} \). If the same car is moving with a speed of \( 80 \mathrm{km} / \mathrm{h} \), what is the minimum stopping distance?
\( A \cdot 8 c m \)
B. \( 6 m \)
\( c .4 m \)
D. \( 2.6 m \)


Rutherford's alpha ( \( \alpha \) ) particle scattering experiment resulted in discovery of:
A . electron
B. proton
c. nucleus in the atom
D. atomic mass


The de Broglie wavelength of an electron having 80 eV of energy is nearly \( \left(1 e V=1.6 \times 10^{-19} J, \) Mass of electron \right.
\( =9 \times 10^{-31} k g \)
Planck's constant \( =\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)
(nearly)
A . \( 140 A^{\circ} \)
B. 0.14 \( A^{0} \)
\( \mathbf{c} \cdot 14 A^{0} \)
D. 1.4 \( A^{0} \)


\( F e^{2+} \) is oxidised by \( M n O_{4}^{-} \) or \( C r_{2} O_{7}^{2-} \) in acidic medium. What is new
oxidation number of Fe?
\( A \cdot+3 \)
B. +1
\( c \cdot+2 \)
D. +4


A constant potential difference is applied between the ends of the wire. If
the length of the wire is elongated 4 times, then the drift velocity of electrons will be:
A. increases 4 times
B. decreases 4 times
c. increases 2 times
D. decreases 2 times


The least abundant element of IV A
group is :
A .
B. si
\( c \cdot \) Ge
D. Pb


In the given velocity time graph, the net
displacement of the object in time interval 0 to 8 s is
\( 4.20 \mathrm{m} \)
B. \( 10 \mathrm{m} \)
\( c .-20 \mathrm{m} \)
D. zer


The sum of mass of all the atoms in a
molecule is known as:
A. molecular mass
B. atomic mass
c. atomic weight
D. None of above


Blood pressure of a person is measured by


Which of the following best describes the field due to a magnet?
A. The region where its effects are felt
B. The two regions close to its poles
c. The region between its poles
D. The region where it aligns itself along the north-south direction


Simplify \( 4 x-(3 y-x+2 z) \)


Define the following terms giving an example of each:
(i) Associated colloids
(ii) Lyophilic sol
(iii) Adsorption


An amount of 2 moles \( K C l O_{3} \) is
decomposed completely to produce \( \boldsymbol{O}_{2} \)
gas. How many moles of butane, \( C_{4} H_{2} \)
can be burnt completely by the \( O_{2} \) gas
produced?
A . 0.6
B. 1.0
\( c .2 .0 \)
D. 3.0


Which of the following ions would have the minimum coagulating value for sol obtained on peptizing \( \boldsymbol{S n}(\boldsymbol{O} \boldsymbol{H})_{4} \) by
little \( N a O H \) solution?
A \( \cdot C l \)
B. \( S O_{4}^{2-} \)
\( c \cdot K^{+} \)
D. \( B a^{2+} \)


To a \( 10 \mathrm{mL}, 1 M \) aqueous solution of
\( B r_{2} \) and excess of \( N a O H \) is added so
that all \( B r_{2} \) is disproportional to \( B r^{-} \)
and \( B r O_{3}^{-} . \) The resulting solution is
free from \( B r^{-} \) by extraction and excess
of \( \boldsymbol{O H}^{-} \) is neutralised by acidifying the solution. The resulting solution is sufficient to react with \( 2 g \) of impure \( \boldsymbol{C a} \boldsymbol{C}_{2} \boldsymbol{O}_{4}(\boldsymbol{M}=\mathbf{1 2 8} \boldsymbol{g} / \boldsymbol{m o l}) \) sample
The \% purity of oxalate sample is
A. \( 85.3 \% \)
в. \( 12.5 \% \)
\( \mathbf{c} .90 \% \)
D. \( 64 \% \)


A colourless paramagnetic gas among the following is :
A. Nitric Oxide
B. Nitrous Oxide
c. Nitrogen dioxide
D. Dinitrogen trioxide


A red cart starts from rest at the top of a
ramp and coasts down the ramp with a constant acceleration. A blue motor car
starts at the top of the same ramp
directly beside the red cart. The blue motor car moves down the ramp with a
constant speed.
When the red cart catches up to the blue car, how does the speed of the red cart compare with the speed of the blue
car?
A. The red cart is moving at the same speed as the blue car
B. The red cart is moving slightly faster than the blue car
c. The red cart is moving more slowly than the blue car
D. The red cart is moving twice as fast as the blue car


Protective layer of ozone in the atmosphere exists in which layer?
A. Troposphere
B. Lonosphere
c. Stratosphere
D. Atmosphere


Dalton's theory of same element have same mass and properties was proved wrong with the invention of
A. molecules
B. isotopes
c. neutrons
D. compounds


State true or false:
If \( x \) is a positive integer or a solution to \( x+3>4, \) then \( x>0 \) and \( x>\frac{1}{2} \)
A . True
B. False


The energy of the electron in \( 3 r d \) orbital is less than that in \( 4 s \) -orbital.
A. True
B. False


\( \frac{w}{L} \)


If 1 mole of ethyl alcohol in 1,000 grams of water depresses the freezing point by
\( 1.86^{\circ} \mathrm{C}, \) what will be the freezing point
of a solution of 1 mole of ethyl alcohol in
\( \mathbf{5 0 0} \) grams of water?
A \( .-0.93^{\circ} \mathrm{C} \)
В. \( -1.86^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-2.79^{\circ} \mathrm{C} \)
D. \( -3.72^{\circ} \mathrm{C} \)
E . \( -5.58^{\circ} \mathrm{C} \)


A ray of light is incident normally on one
of the faces of a prism of apex angle \( 30^{\circ} \) and refractive index \( \sqrt{2} . \) The angle of
deviation of the ray is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 15^{\circ} \)
D. \( 90^{\circ} \)


There are 7 defective items in a sample
of 35 items. Find the probability that an item chosen at random is non-defective.


The hybridisation of atomic orbitals of
\( N \) in \( N O_{2}^{+}, N O_{3}^{-} \) and \( N H_{4}^{+} \) are respectively:
A \( \cdot s p, s p^{2}, s p^{3} \)
В \( . s p, s p^{3}, s p^{2} \)
\( \mathbf{c} \cdot s p^{2}, s p, s p^{3} \)
D. \( s p^{2}, s p^{3}, s p \)


\( \mathbf{A} \mathbf{7} \mathbf{5} \mathbf{0} \boldsymbol{H} \boldsymbol{z}, \mathbf{2 0} \boldsymbol{V} \) source is connected to
a resistance of \( 100 \Omega, \) an inductance of
\( 0.1803 H \) and a capacitance of \( 10 \mu F \)
all in series. The time in which the
resistance (thermal capacity \( \left.=2 J /^{0} C\right) \)
will get heated by \( 10^{0} C \) is
A . 348 s
B. 328 s
c. 248 s
D. 228


Two similar balls, each of mass \( \mathrm{m} \) and
charge \( q, \) are hung from a common point by two silk threads, each of length
I. Prove that separation between the balls is \( \boldsymbol{x}=\left[\frac{\boldsymbol{q}^{2} \boldsymbol{l}}{2 \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{m} \boldsymbol{g}}\right]^{1 / 3}, \) if \( \boldsymbol{\theta} \) is small.
Find the rate da/dt with which the charge should leak off each sphere if the velocity of approach varies as \( \boldsymbol{v}= \) \( a / \sqrt{x}, \) where a is a constant


Find the incorrect match
\( \begin{array}{lll}\text { । } & \text { II } & \text { III } \\ \text { i. Crab } & \text { Sacculina } & \begin{array}{l}\text { Interaction } \\ ++\end{array} \\ \begin{array}{l}\text { ii. Human } \\ \text { being }\end{array} & \text { Mosquito } & \begin{array}{l}\text { Interaction } \\ -+\end{array} \\ \begin{array}{l}\text { iii. Sea } \\ \text { anemone }\end{array} & \begin{array}{l}\text { Hermit } \\ \text { crab }\end{array} & \begin{array}{l}\text { Interaction } \\ ++\end{array}\end{array} \)
A . i. only
B. ii. and iii.
c. iii. and
D. ii. only


Choose the correct identification for the
given stage of succession and is preceded by which stage respectively?
Submerged free floating plant stage
A. Marsh-meadow, Reed-swamp
B. Submerged free floating, Read-swamp
c. Submerged plant, Scrub stage
D. Phytoplankton, Marsh-meadow


form
conducts electricity.
A. diamond
B. graphite
c. coal
D. petroleum


When the light is incident at the polarizing angle on transparent medium, then the completely polarized light is
A. refracted light
B. reflected light
c. refracted and reflected light
D. neither reflected nor refracted light


Select the incorrect statement.
A. Male fruit fly is heterogametic
B. In male grasshoppers \( 50 \% \) of sperms have no sexchromosome
C. In domesticated fowls, sex of progeny depends on the type of sperm rather than egg
D. Human males have one of their sex-chromosome
much shorter than the other


Prove that the distance s metres, which
a body falling from rest covers in time
seconds is 4.9 times the square of the time t.


Reactance of a coil is \( 157 \Omega \). On
connecting the coil across a source of frequency \( 100 H z \), the current lags
behind e.m.f. by \( 45^{\circ} . \) The inductance of
the coil is
A \( .0 .25 H \)
в. \( 0.5 H \)
\( c .4 H \)
D. \( 314 H \)


Number of oxygen molecules required during glycolysis of one glucose molecule is
A . 38
B. 36
\( c \cdot 2 \)
D. zero


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


If \( \boldsymbol{A} \) is \( (2,4,5), \) and \( B \) is (-7,-2,8) then which of the following is collinear with \( A \) and \( B \) is
A \( .(1,2,6) \)
В. (2,-1,6)
c. (-1,2,6)
D. (2,6,-1)


If an alternating current \( \boldsymbol{i}=\boldsymbol{i}_{m} \sin \omega \boldsymbol{t} \) is
flowing through a capacitor then
voltage drop \( \Delta V_{C} \) across capacitor \( C \)
will be?
A \( \cdot-\frac{i_{m}}{\omega C} \sin \omega t \)
в. \( -\frac{i_{m}}{\omega C} \cos \omega t \)
c. \( -\frac{i_{m}}{\omega C}\left(\sin \omega t+\frac{\pi}{4}\right) \)
D. \( \frac{i_{m}}{\omega C}\left(\sin \omega t-\frac{\pi}{4}\right) \)


1 L of a hydrogen weighs as much as 1 L
of \( C O_{2} . \) The molecular formula of the
hydrocarbon is :
A \( \cdot C_{3} H_{8} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{3} H_{6} \)


The rate constant of a first order
reaction is \( 1.54 \times 10^{-3} \) sec \( ^{-1} \). Calculate
its half life period.


Number of critical points of the function \( f(x)=(x-2)^{\frac{2}{3}}(2 x+1) \) is equal to


What is meant by depletion of ozone layers? What are its causes?


Which ion has the least value of
theoritical magnetic moment?
A \( \cdot C r^{3} \)
в. \( C o^{3} \)
\( c \cdot T i^{3} \)
D. \( V^{3+} \)


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a \( 2 \times 2 \) matrix such that
\( a_{i j}=i+2 j, \) then find \( A \)


Radius of the circle that passes through
origin and touches the parabola \( \boldsymbol{y}^{2}= \)
\( 4 a x \) at the point \( (a, 2 a) \) is
A \( \cdot \frac{5}{\sqrt{2}} a \)
В. \( 2 \sqrt{2} a \)
c. \( \sqrt{\frac{5}{2} a} \)
D. \( \frac{3}{\sqrt{2}} a \)


Which of the following is combustible?
A. Oxygen
B. Carbon dioxide
c. Hydrogen
D. All of these


Specific heat of substance at m.pt. (or
b.pt. or for isothermal process) and specific heat of a substance during adiabatic change respectively are
\( A \cdot 0,0 \)
B. \( 0, \infty \)
\( c \cdot \infty, 0 \)
\( D \cdot \infty, \infty \)


Why do fireflies glow at night?
A. Fireflies contain an organic compound.
B. Chemical reaction involves emission of visible light.
C. Fireflies produce two chemicals which mix with each other and oxygen.
D. All of the above.


Assertion
Assertion: Higher order ionization constants \( \left(\boldsymbol{K}_{a_{2}}, \boldsymbol{K}_{a_{3}}\right) \) are smaller than
the lower order ionization constant \( \boldsymbol{K}_{\boldsymbol{a}_{\mathbf{1}}} \) of polyprotic acid.
Reason
Reason: Polyprotic acid solutions contain a mixture of acids.
A. If both the assertion and reason are true and reason is the correct explanation of assertion
B. If both the assertion and reason are true but reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


\( \operatorname{Let} \boldsymbol{S}= \)
\( \left\{\frac{a^{2}+b^{2}+c^{2}}{a b+b c+c a}: a, b, c \epsilon R, a b+b c+c a\right. \)
where \( R \) is the set of real numbers. Then S equals.
A \( \cdot(-\infty,-1] \cup[1, \infty) \)
В . \( (-\infty, 0) \cup(0, \infty) \)
c. \( (-\infty,-1] \cup[2, \infty) \)
D \( \cdot(-\infty,-2] \cup[1, \infty) \)


Engulfing of food in solid or fluid state
is
A. Saprozoic nutrition
B. Parasitic nutrition
c. Saprophytic nutrition
D. Holozoic nutrition


Why is be solubility of \( N a C l \) in water
\( 311 g l^{-1} N \) but is zero in benzene?


n Fig. \( 14.2, \) there is a histogram
depicting daily wages of workers in a
factory. Construct the frequency
distribution table.
A. 145
B . 142
c. 148
D. 146


In triangle \( A B C, \angle A=\angle B=52^{\circ}, \) write
the name of its largest side.
\( A \cdot A B \)
B. BC
\( c \cdot c A \)
D. None of these


Which of the following is an important function attributed to lysosomes?
A. Bone restoration
B. Reabsorption in kidney and urinary bladder
c. scavenging of worn out cells
D. All of the above


In the above figure, \( D \) and \( E \) are the
mid-points of the sides \( A C \) and \( B C \)
respectively of \( \triangle A B C . \) If
\( \boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{B} \boldsymbol{E} \boldsymbol{D})=12 \boldsymbol{c m}^{2}, \) then
\( \boldsymbol{a} \boldsymbol{r}(\boldsymbol{A} \boldsymbol{B} \boldsymbol{E} \boldsymbol{D})= \)
\( \mathbf{A} \cdot 36 \mathrm{cm}^{2} \)
B. \( 48 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 24 \mathrm{cm}^{2} \)
D. None of these


Draw the resonance structures for
\( C H_{3} C H=C H C^{+} H_{2} . \) Show the electron
shift using curved-arrow notation.


Find out the total current flowing in the circuit as shown in above figure?
\( A \cdot 4 A \)
B. 3A
c. \( 2 A \)
D. \( \frac{4}{3} \)
\( E \)


If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right) \) and \( A^{3}-6 A^{2}+ \)
\( 7 A+k I^{3}=0, \) find \( k \)


Value of \( \boldsymbol{H} \) on earth's surface is
A. \( 0.32 G \)
в. \( 0.32 T \)
c. \( 0.32 \times 10^{-4} G \)
D. \( 0.32 \times 10^{-5} T \)


A photon of wavelength \( 4 \times 10^{-7} m \)
strike on metal surface,the work
function of the metal being \( 2.13 e V \)
\( \left(1 e V=1.6020 \times 10^{-19} J\right) \) calculate the
velocity of the photoelectron in \( n \times \) \( 10^{5} m s^{-1} \)


The direction ratios of the line, given by the planes \( x-y+z-5=0, x-3 y-6=0 \)
are
A \( .(3,1,-2) \)
в. (2,-4,1)
c. (1,-1,1)
D. (0,2,1)


Damage to thymus in a child may lead
to
A. Loss of cell mediated immunity
B. A reduction in the haemoglobin content in blood
C. A reduction in the amount of plasma proteins
D. Loss of antibody mediated immunity


In the preparation of sodium carbonate, which of the following is used as raw material?
A. Slaked lime
B. Quick lime
c. lime stone
D. Sodium hydroxide


The structure of DNA is
A. Linear
B. Double helix
C. single helix
D. Triple helix


The ionisation energy of isotopes of an element will be:
A. same
B. different
c. dependent on atomic masses
D. dependent on the number of neutrons present in the nucleus


A rocket works on the
A. first law of motion
B. second law of motion
C. third law of motion
D. law of conservation of energy


Solve the following differential
equations:
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}+\boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}-\boldsymbol{y} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \ln \left(x^{2}+y^{2}\right)=2 \tan ^{-1}\left(\frac{y}{x}\right)+c \)
B \cdot \( \ln (x+y)^{2}=2 \tan ^{-1}\left(\frac{y}{x}\right)+c \)
c. \( \ln \left(x^{2}+y^{2}\right)=2 \tan ^{-1}\left(\frac{x}{y}\right)+c \)
D \( \cdot \ln (x+y)^{2}=2 \tan ^{-1}\left(\frac{x}{y}\right)+c \)


Assertion
\( \boldsymbol{H}_{2} \boldsymbol{O} \) is the only hydride of group -16 which is liquid at ordinary temperature.
Reason

In ice, each oxygen atom is surrounded by two convalent bonds and two
hydrogen bonding.
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 solubility of metal halides depends on their nature, lattice enthalpy and hydration enthalpy of the individual ions. Amongst fluorides of alkali metals, the lowest solubility of LiF in water is due to:
A. ionic nature of lithium fluoride
B. high lattice enthalpy
c. high hydration enthalpy for lithium ion
D. low ionisation enthalpy of lithium atom


The IUPAC name of the given compound
is :
A. \( 4- \) ethyl \( -3- \) propylehex -1 -ene
B. \( 3- \) ethyl -4 -ethenylheptane
c. \( 3- \) ethyl- \( 4- \) propylehex \( -5- \) ene
D. 3 -ethyl(1-propyl)hex-1-ene


Which is a naturally occuring polymer?
A. Polythene
B. PVC
c. Acetic acid
D. Protein


The metal liberated into the
environment through exhaust fumes of motor vehicles is:
A. \( H g \)
в. \( A \) s
\( c . P b \)
D. \( N O_{2} \)


Diameter of DNA double helix is
\( A \cdot 34 A^{0} \)
B . 20 \( A^{0} \)
c. \( 3.4 A^{\circ} \)
D. 340 \( A^{\circ} \)


Atomic mass of \( _{6}^{13} C \) is 13.00335 amu and its mass number is \( 13.0 . \) If amu \( = \)
\( 931 \mathrm{MeV}, \) the binding energy of the
neutrons present in the nucleus is
A. \( 0.24 \mathrm{MeV} \)
B . \( 1.44 \mathrm{MeV} \)
c. \( 1.68 \mathrm{MeV} \)
D. 3.12 Mev


A beam of monochromatic blue light of wavelength \( 4200 A \) in air travels in water of refractive index \( 4 / 3 . \) Its wavelength in water will be
в. \( 5800 \dot{A} \)
c. \( 4150 \hat{h} \)
D. 3150 ,


Hair shampoos belong to which class of synthetic detergent?
A. Anionic
B. Cationic
c. Neutral
D. None of these


Indicate which nitrogen compound amongst the following would undergo Hofmann reaction (i.e., reaction with
\( \left.B r_{2}, \text { and strong } K O H\right) \) to furnish the
primary amine \( \left(\boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2}\right) \)
A. \( R C O N H C H_{3} \)
в. \( R C O O N H_{4} \)
\( \mathbf{c} \cdot R C O N H_{2} \)
D. \( R-C O-N H O H \)


The daily sale of milk (in litres) in a
ration shop for eight days is as follows\( \mathbf{6 0}, \mathbf{4 0}, \mathbf{1 0}, \mathbf{4 0}, \mathbf{4}, \mathbf{7 0}, \mathbf{3 0} \) and \( \mathbf{1 0} . \) The
average daily sale is-
A . 40
B. 33
\( c .64 \)
D. 24


A particle of mass \( 2 \mathrm{kg} \) moving with a velocity of \( 3 \mathrm{m} / \mathrm{s} \) is acted upon by a force which changes its direction of
motion by an angle of \( 90^{\circ} \) without changing its speed. What is the magnitude of impulse experienced by the particle?
\( A \cdot 6 N \)
B. 2 N s
c. \( 3 \sqrt{2} \) N s
D. \( 6 \sqrt{2} \) N s


What is 'Chipko movement'? Why should we conserve forest?


A dealer sold a motorcycle at a loss of \( 10 \% \). If he had sold it for Rs 4500 more,
he would have made a profit of \( 5 \% \). Find the selling price of the motorcycle.


Find the square root of 298116 using
long division method.
A . 546
в. 123
c. 234
D. 564


The critical mass of a fissionable
material is
A. \( 0.1 \mathrm{kg} \)
B. the minimum mass needed for chain reaction
C. the rest mass equivalent to 1020 joules
D. \( 0.5 \mathrm{kg} \)


Main component (quantity wise) of urine is.
A. Urea
B. Sodium
c. water
D. Creatine


Let \( \boldsymbol{f}:[\mathbf{0}, \mathbf{1}] \rightarrow \boldsymbol{R} \) be a continuous
function then the maximum value of \( \int_{0}^{1} f(x) \cdot x^{2} d x-\int_{0}^{1} x \cdot(f(x))^{2} d x \) for all
such function(s) is
\( A \cdot \frac{1}{8} \)
B. \( \frac{1}{20} \)
c. \( \frac{1}{12} \)
D. \( \frac{1}{16} \)


Which one is correct about the concept regarding the number of particles in a
mole.
A. Avogadro's number
в. \( P_{1} V_{1}=P_{2} V_{2} \)
c. \( V_{1} T_{2}=V_{2} T_{1} \)
D. Dalton's Theory
E. Gay-Lussac's Law


Two objects \( A \) and \( B \) are thrown upwards simultaneously with the same speed. The mass of \( A \) is greater than the mass
of
B. Suppose the air exerts a constant and equal force of resistance on the two
bodies.Which object will go high?


A tennis ball has a mass of 57 g and a diameter of \( 7 \mathrm{cm} . \) Find the moment of
inertia about its diameter. Assume the
ball is a thin spherical shell:
A . \( 4.65 \times 10^{-5} \)
В. \( 9.65 \times 10^{-5} \)
c. \( 4.65 \times 10^{-3} \)
D. \( 9.65 \times 10^{-3} \)


\( M, M_{n} \) and \( M_{p} \) denotes the masses of
a nucleus of \( z X^{A}, \) a neutron, and a
proton respectively. If the nucleus is separated into its individual protons and neutrons then,
A \( \cdot M=(A-Z) M_{n}+Z M_{p} \)
B. \( M=Z M_{n}+(A-Z) M_{p} \)
C. \( M>(A-Z) M_{n}+Z M_{p} \)
D. \( M<(A-Z) M_{n}+Z M_{p} \)


Find the points on the X-axis which are at a distance of \( 2 \sqrt{5} \) from the point
\( (7,-4) . \) How many such points are there?


State True or False.
Corrosion of motor cars is the major problem in the winter, when salt is spread on road to melt ice and snow
A. True
B. False


The correct order according to acidic
nature is:
A. \( C H_{3} O H<C H_{3} S H<C H_{3} N H_{2} \)
в. \( C H_{3} N H_{2}<C H_{3} O H<C H_{3} S H \)
\( \mathbf{c} \cdot C H_{3} S H<C H_{3} O H<C H_{3} N H_{2} \)
D. none of these


Given the perimeter of rhombus is 40 \( \mathrm{cm} \) and one diagonal is \( 12 \mathrm{cm} \). The length of second diagonal is
A . \( 19 \mathrm{cm} \)
B. 18 \( \mathrm{cm} \)
\( c \cdot 17 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


If \( \vec{a} \) and \( \vec{b} \) are the vectors determined by
two adjacent sides of regular hexagon, then vector \( \boldsymbol{E} \boldsymbol{F} \) is
A \( \cdot(\vec{a}+\vec{b}) \)
B . \( (\vec{a}-\vec{b}) \)
\( c \cdot 2 \vec{a} \vec{a} \vec{a} \)
\( D \cdot 2 \vec{b} \)


A point light source are located at \( P_{1} \) as shown in the figure in which all sides of the polygon are equal. The intensity of illumination at \( P_{2} \) is \( 8 \frac{W}{m^{2}}, \) what will be
the intensity of illumination at \( P_{3} \)
A \( \cdot 3 \sqrt{3} \frac{W}{m^{2}} \)
в. \( 6 \frac{W}{m^{2}} \)
с. \( _{8^{2}} \frac{W}{^{2}} \)
D. \( \sqrt{3} \frac{w}{m^{2}} \)


Evaluate \( \boldsymbol{x} \stackrel{\lim }{\boldsymbol{a}} \frac{\boldsymbol{x}^{\boldsymbol{7}}-\boldsymbol{a} \boldsymbol{7}}{\boldsymbol{x}-\boldsymbol{a}} \)


A ray reflected successively from two plane mirrors inclined at a certain
angle \( 90^{\circ} \) undergoes a deviation of \( 300^{\circ} \) The number of images observable are:
A . 10
B. 11
c. 12
D. 14


A constant horizontal \( 4.0 N \) force acts
on a \( 300 g \) cart on a horizontal track as
the cart moves through a distance of \( 43.0 \mathrm{cm} . \) The cart decelerates as a
result.
What was the work performed on the cart by the force?
в. \( -1.27 J \)
c. \( 1.27 J \)
D. \( 1.72 J \)
E. None of the above


Assertion
On plotting the length of the root against time, a linear curve is obtained.
Reason
An elongating root exemplifies arithmetic growth.
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 number of solutions of
\( \sin ^{-1}\left(1+b+b^{2}+\cdots \infty\right)+ \)
\( \cos ^{-1}\left(a-\frac{a^{2}}{3}+\frac{a^{2}}{9} \cdots \infty\right)=\frac{\pi}{2} \) is
\( A \)
B. 2
\( c .3 \)
\( D \)


An element \( X \) decays into element \( Z \) by
two-step process.
\[
\begin{array}{l}
\boldsymbol{X} \longrightarrow \boldsymbol{Y}+_{2}^{4} \boldsymbol{H} \boldsymbol{e} \\
\boldsymbol{Y} \longrightarrow Z+2 \bar{e} \text { then }
\end{array}
\]
\( A \cdot X \) and \( Z \) are isobars
B. \( X \) and \( Y \) are isotopes
c. \( X \) and \( Z \) are isotones
D. \( X \) and \( Z \) are isotopes


A film of water is formed between two
straight parallel wires of length \( 10 \mathrm{cm} \)
each, separated by \( 0.5 \mathrm{cm} . \) If their separation is to be increased by 1 m \( m \) while still maintaining their parallelism, how much work will have to
be done? \( \left[\boldsymbol{T}=\mathbf{7 . 2} \times \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{N} / \boldsymbol{m}\right] \)


A tank with a small hole at the bottom has been filled with water and kerosene
(specific gravity 0.8 ). The height of water is \( 3 m \) and that of kerosene \( 2 m \)
When the hole opened the velocity of
fluid coming out from it is nearly: (take \( g=10 m s^{-2} \) and density of water
\( \left.10^{3} k g m^{-3}\right) \)
A \( \cdot 9.6 \mathrm{ms}^{-1} \)
B . \( 8.5 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 7.6 m s^{-1} \)
D. \( 10.7 \mathrm{ms}^{-1} \)


A mass \( m_{1} \) with initial speed \( v_{0} \) in the
positive \( x \) -direction collides with a
\( \operatorname{mass} \boldsymbol{m}_{2}=2 \boldsymbol{m}_{1} \) which is initially at
rest at the origin, as shown in figure.
After the collision \( m_{1} \) moves off with
speed \( \boldsymbol{v}_{1}=\boldsymbol{v}_{0} / 2 \) in the negative \( \boldsymbol{y} \)
direction, and \( m_{2} \) moves off with speed
\( v_{2} \) at angle \( \theta . \) Determine \( \tan \theta, \) and find
\( v_{2} \) in terms of \( v_{0} \)


Which of the following compounds is covalent?
A \( . H_{2} \)
в. \( C a O \)
c. \( K C l \)
D. \( N a_{a} S \)


\( B e^{+3} \) and a proton are accelerated
same potential their Debroglic wavelength have the ratio?


Q Type your question.
is earthed. \( C \) is the common center of \( A \)
and \( B . \) Study the following statements.
Which of the following statements are
correct?

The potential at a distance \( r \) from \( C \) where \( a \leq r \leq b, i s \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q}{r}\right) \)
i. The potential difference between \( A \) and
\( B \) is \( \frac{1}{4 \pi \varepsilon_{0}} Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
iii. The potential at a distance \( r \) from \( C \) where \( a \leq r \leq b, i s \frac{1}{4 \pi \varepsilon_{0}} Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
A. Only (i) and (ii)
B. Only (ii) and (iii)
c. only (i) and (iii)
Dhe above


State True or False.
A solution of ethyl alcohol and water shows positive deviation from Raoult's
law.
A. True
B. False


In the equations below, \( A, B, \omega \) and \( \phi \) are
constants; \( y \) and \( t \) are variables; \( t \)
represents time. Only one of the following equations does not represent SHM. Which one is that?
A. \( y= \) Asinwt
B. \( y= \) Bcoswt
c. \( y= \) Asinwt \( +B \) coswt
D. \( y= \) Asinwt \( +B \cos (2 \omega t) \)


Which term of the G.P.: \( 2,2 \sqrt{2}, 4, \dots \) is
\( 128 ? \)


State two essential features of a
geostationary satellite.


Why are NOR gates considered as
universal gates?


What number of mature egg cells are produced as a result of meiosis in humans?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
\( E \)


The G.M. of n positive terms \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots . . . \boldsymbol{x}_{n} \)
is
в. \( \frac{1}{n}\left(x_{1} \times x_{2} \times \ldots . . \times x_{n}\right) \)
C. \( \left(x_{1} \times x_{2} \times \ldots . \times x_{n}\right)^{1 / n} \)
D. none of these


Raney nickel, which is used as a
catalyst, is obtained:
A. by grinding solid nickel
B. by treating nickelaluminium alloy with dilute \( N a O H \)
C. by treating nickelaluminium alloy with dilute \( H C l \)
D. by heating nickel tetracarbonyl


\( 0 \% \)
000
\( \sigma_{i}^{i-\alpha} \)
\( @^{i 0} \)


In Venn diagram given:
\( \mathbf{A} \cdot A \cup B=0 \)
В \( . A \cup B=\mu \)
\( \mathbf{c} \cdot A \cap B=\mu \)
D. \( A \cap B=\phi \)


When an azeotropic mixture is distilled,
its composition remains unchanged If true enter \( 1, \) if false enter 0


Rain appears to fall vertically to a man
walking at \( 3 k m h^{-1}, \) but when he changes his speed to double, the rain
appears to fall at \( 45^{\circ} \) with vertical

Study the following statements and find which of them are correct.
i. Velocity of rain is \( 2 \sqrt{3} k m h^{-1} \)
ii. The angle of fall of rain (with vertical) is \( \boldsymbol{\theta}=\tan ^{-1}\left(\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}\right) \)
iii. The angle of fall of rain (with vertical) is \( \boldsymbol{\theta}=\sin ^{-1}\left(\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}\right) \)
iv. Velocity of rain is \( 3 \sqrt{2} k m h^{-1} \)
A. Statement (i) and (ii) are correct
B. Statement (i) and (iii) are correct
c. statement
(iii) and (iv) are correct
D. statement (ii) and (iv) are correct


A particle \( A \) moves in one direction
along a given trajectory with a
tangential acceleration \( \omega_{\tau}=a \tau, \) where
\( \vec{a} \) is a constant vector coinciding in direction with the \( x \) axis as shown in
figure above, and \( \vec{\tau} \) is a unit vector coinciding in direction with the
velocity vector at a given point. Find how the velocity of the particle depends on \( x \) provided that its velocity is negligible at the point \( \boldsymbol{x}=\mathbf{0} \)


If true then enter 1 and if false then
enter 0

Can two acute angles form a linear pair?


All statements are true about ferns
except
A. The gametophyte is larger than the sporophyte.
B. The sori give rise to the gametophytes.
C. Eggs are fertilized by sperm in the archeogonia.
D. Ferns possess vascular tissue for the transport of water and minerals.
E. Male gametes depend on water for fertilization.


Which of the following microbe is used as an insecticide?
A. Protozoa
B. Fungi
c. virus
D. None of the above


Who named the negatively charged
particles present in cathode rays as electrons?
A. J.J. Thomson
B. Stoney
c. Goldstein
D. None of these


Find the constant after subtracting from \( x^{4}+4 x^{2}-3 x+7 \) to get \( 3 x^{3}- \)
\( x^{2}+2 x+1 ? \)


Verify the Rolle's theorem for the following functions:
\( f(x)=x^{4}-1 \) on the interval [-1,1]
A. True
B. False


In conventional light sources:
A. different atoms emit radiation at different times
B. there is no phase relation between the emitted photons
C. different atoms emit photon in different direction
D. all of the above


A vision problem that happens when light is focussed in front of the retina is:
A. Farsightedness
B. Nearsightedness
c. colour deficiency
D. None of these


Find the median for the following data
given below:
\( \begin{array}{lllll}\text { Class } & 0- & 2- & 4- & 6 \\ \text { interval } & 2 & 4 & 6 & 8\end{array} \)
Frequencies 3. 2 3
A . 5.3
в. 5.4
c. 5.1
D. 5.6


Short / long answer type questions. Briefly describe how the atmospheric air is drawn into lungs.


Given: \( z_{1}+z_{2}+z_{3}=A ; z_{1}+z_{2} w+ \)
\( z_{3} w^{2}=B ; z_{1}+z_{2} w^{2}+z_{3} w=C \) where
\( \boldsymbol{w} \) is cube rott of unity
Prove: \( |\boldsymbol{A}|^{2}+|\boldsymbol{B}|^{2}+|\boldsymbol{C}|^{2}= \)
\( \left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}+\left|z_{3}\right|^{2}\right) \)


Two vectors of equal magnitude have a resultant equal to either of them. Then, the angle between them will be \( 2 \pi / 3 \)
radians. The angle in degrees is:
A \( .30^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 60 \)
D. \( 45^{\circ} \)


A hydrogen bomb is a
\( A . \) A hydrogen bomb is a
B. uncontrolled nuclear fision
c. uncontrolled nuclear fusion
D. controlled nuclear fusion


\( (-12) \times(-3) \times(+4) \times(-6)= \)
A \( .-144 \)
B . -908
\( c \cdot+864 \)
D. - 864


Prove that \( (A B)(A B)^{-1}=1 \)


Area of a parallelogram is \( 400 \mathrm{cm}^{2} \) and its height is \( 16 \mathrm{cm} . \) Find its base.


Find the distance between the points
(2,1) and (3,2)


Gases begin to conduct electricity at
low pressure because
A. the lectrons in atoms can move freely at low pressures
B. atoms break up into electrons and protons.
C. colliding electrons can acquire higher kinetic energy due to increased mean free path leading to ionization of atoms.
D. at low pressure gases turn into plasma.


Compound \( A\left(C_{7} H_{15} B r\right) \) is not \( a \)
primary alkyl bromide. It yield a single alkene (compound B) on being heated with sodium ethoxide in ethanol.
Hydrogenation of compound B yield
\( 2,4- \) dimethylpentane. Identify
compounds \( A \) and \( B \)
A. 3-Bromo-2,4-dimethylpentane and 2,4-Dimethylpent2-ene
B. 2-bromo-2,4-dimethylhexane and 2,4-dimethylhex-2ene
c. 3-bromo-2,4-dimethylhexane and 2,3-dimethylhex-2ene
D. None of these


Two vectors of magnitude 3 units and 4 units respectively. What should be the
angle between them if the magnitude of the resultant is 5 units?
A \( .180^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 160^{\circ} \)


The solution of \( \frac{d y}{d x}=|x| \) is :
A \( \cdot y=\frac{x|x|}{2}+c \)
В . \( y=\frac{|x|}{2}+c \)
C・ \( y=\frac{x^{2}}{2}+c \)
D・ \( y=\frac{x^{3}}{2}+c \)


Which among the following are the consequences of ozone depletion?
A. Entry of UV-rays in earth's atmosphere
B. Various skin troubles like skin cancer
c. cataract
D. All of the above


Classify the following substances under
three headings.
Strong electrolytes, Weak electrolytes


A constant voltage is applied between the two ends of a uniform metallic wire.
Some heat is developed in it. The heat developed is doubled if This question has multiple correct options
A. radius is halved
B. length is halved
c. the radius of the wire is doubled
D. the length of the wire is doubled


Compare paramagnetism and ferro magnetism. Give examples of each.


Express the linear equation in the form \( a x+b y+c=0 \) and indicate the value
of \( a, b \) and \( c \) in each case:
\( x-\frac{y}{5}-10=0 \)


Look at leaves of the same plant on the shady side and compare it with the
leaves on the sunny side or compare the potted plants kept in the sunlight with those in the shade. Which of them has
leaves that are darker green? Why?


A plastic circular disc of radius \( R \) is
placed on a thin oil film, spread over a flat horizontal surface. The torque
required to spin the disc about its central vertical axis with a constant
angular velocity is proportional to
\( \mathbf{A} \cdot R^{2} \)
B . \( R^{3} \)
\( c \cdot R^{4} \)
D. \( R^{6} \)


Two masses \( A \) and \( B \) are moving in the same straight line, A moves with a
uniform velocity of \( 11 m / \)sec\( , B \) starts from rest at the instant when it is 52.5
metres ahead of \( A \), and moves with a
uniform acceleration \( 1 \mathrm{m} / \mathrm{sec}^{2} \). When
will \( A \) catch \( B ? \) Explain the reason for
two answers?


The value of \( x \) in \( K A l\left(S O_{4}\right)_{x} \cdot 12 H_{2} O \)
is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


The upper stratosphere consisting of
the ozone layer protects us from the sun's radiation that falls in the
wavelength region of:
A. \( 600-750 \mathrm{nm} \)
B. \( 0.8-1.5 \mathrm{nm} \)
\( c .400-550 \mathrm{nm} \)
\( m \)
D. 200 - 315 nm


If the decay constants of two elements
are in 1: 2 ratio, their half lives are in
the ratio:
A . 1: 2
B \( \cdot 1^{2}: 2^{2} \)
c. 2: 1
D. 4: 1