The order of calorific values of fuel
gases is:
A. Carburetted water gas > Producer gas
Semi water gas
B. Carburetted water gas \( > \) Semi water gas
Producer gas
C. Producer gas \( > \) Semi water gas \( > \)
Carburetted water gas
D. Semi water gas > Producer gas
Carburetted water gas


f \( 2 x+y=14 \) and \( x y=6, \) Find the
value of \( 4 x^{2}+y^{2} \)


Match the items of column I and
column II
\begin{tabular}{ccc|c}
& Column I & & Column II \\
\( a \) & Auxin & \( p \) & \( G A_{3} \) \\
\( b \) & Gibberellin & \( q \) & Indole Acetic Acid \\
\( c \) & Cytokinin & \( r \) & Abscisic Acid \\
\( d \) & Dormin & \( s \) & Acetic acid \\
& & \( t \) & Zeatin
\end{tabular}
\( A \)
\( a-q, b-r, c-p, d-t \)
B. \( a-q, b-s, c-p, d-t \)
c. \( a-q, b-p, c-t, d-r \)
D. \( a-q, b-t, c-p, d-r \)


In helicoid cyme, the lateral flowers arise
A. on the same side
B. On alternate sides
c. In all the directions
D. From a common point


For a particle executing simple
harmonic motion, the displacement x is given by \( \boldsymbol{x}= \) Acoswt. Identify the graph
which represents the variation of
potential energy (U) as a function of
time \( t \) and displacement \( x \)
A . ।, II
B. ॥, ॥॥
\( c \cdot 1,1 v \)
D. II, IV


Evaluate \( \int_{0}^{1} e^{2-3 x} d x \) as a limit of a
sum


\( y=8 \)
\( y=4 \)
\( y \)


Which one of the following is called as horsetail?
A. Lycopodium
B. Marsilea
c. Equisetum
D. Selaginella


On dissolving moderate amount of sodium metal in liquid ammonia at low
temperature, which of the following
does not occur?
A. Blue coloured solution is obtained
B. Sodium ions are formed in solution
C. Liquid ammonia becomes a good conductor of electricity
D. Liquid ammonia remains diamagnetic.


Filum terminale is attached to
A. Epithalamus
B. First segment of coccyx
C. Cerebral ventricles
D. Medulla oblongata


A uniform cube of mass \( m \) and side \( a \) is
resting in equilibrium on a rough \( 45^{\circ} \)
inclined surface. The distance of the
point of application of normal reaction measured from the lower edge of the
cube is:
A . zero
B. \( \frac{a}{2} \)
c. \( \frac{a}{\sqrt{2}} \)
D. \( \frac{a}{4} \)


Product \( A \) and \( B \) formed in the
following reactions are respectively


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

The magnitude of induced current can be increased by increasing the number of turns in coil.
A. True
B. False


The torque of force \( \overrightarrow{\boldsymbol{F}}=\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \)
newton acting at a point \( \vec{r}=3 \hat{i}+2 \hat{j}+ \) \( 3 \hat{k} \) metre about is:
A. \( 6 \hat{i}-6 \hat{j}+12 \hat{k} N-m \)
B . \( -6 \hat{i}+6 \hat{j}-12 \hat{k} N-m \)
c. \( 17 \hat{i}-6 \hat{j}-13 \hat{k} N-m \)
D. \( -17 \hat{i}+6 \hat{j}+13 \hat{k} N-m \)


Which of the following statements
regarding enzyme inhibition is correct -
A. Competitive inhibition is seen when a substrate competes with an enzyme for binding to an inhibitor protein
B. Non-competitive inhibitors often bind to the enzyme irreversibly
C. Competitive inhibition is seen when the substrate and the inhibitor compete for the active site on the enzyme
D. Non-competitive inhibition of an enzyme can be overcome by adding large amount of substrate


Discuss the special properties of ferromagnetic materials.


Find the angle between the planes
whose vector equations are \( \vec{r} \cdot(2 \hat{i}+2 \hat{j}-3 \hat{k})=5 \) and
\( \vec{r} \cdot(3 \hat{i}-3 \hat{j}+5 \hat{k})=3 \)


If we apply Euclid"s division algorithm
for \( 20,8, \) then the correct answer will be
\( \mathbf{A} \cdot 20=8 \times 2+4 \)
В. \( 20=8 \times 4+0 \)
c. \( 20=8 \times 3+3 \)
D. none of the above


Three particle \( A, B, C \) mass \( m, 2 m \& m \)
are connected with the cup of massless
rod of length I. Rod can rotate freely
about c. Sys. released from rest when
rod almost vertical. \( A \& B \) start moving
in opposite direction. Find
displacement of \( C \) when it list the ground.


A parallel plate air capacitor has
capacity \( ^{\prime} C^{\prime} \) farad, potential \( ^{\prime} V^{\prime} \) volt
and energy' \( E^{\prime} \) joule. When the gap
between the plates is completely filled
with dielectric.
\( A . \) Both \( V \) and \( E \) increase
B. Both \( V \) and \( E \) decrease
c. \( V \) decreases, \( E \) increases
D. \( V \) increases, \( E \) decreases


In the end of manufacturing of cement which powder is mixed with the
clinkers.
A. Gypsum powder
B. Magnesium powder
c. Alumina powder
D. None of the above


A mixture of two or more miscible
liquids, for which the difference in the boiling points is less than 25 K can be separated by the process called:
A. fractional distillation
B. sedimentation
c. decantation
D. filtration


Under which of the following conditions is the law \( p V=R T \) obeyed most
closely by a real gas?
A. High pressure and high temperature
B. Low pressure and low temperature
c. Low pressure and high temperature
D. High pressure and low temperature


If \( n_{1}, n_{2}, n_{3} \) be the frequency of the segments of a stretched string, then the frequency \( n \) of the string itself in terms
of \( n_{1}, n_{2} \) and \( n_{3} \) is
A. \( \frac{\left(n_{1} n_{2}+n_{2} n_{3}+n_{1} n_{3}\right)}{n_{1} n_{2} n_{3}} \)
B. \( \frac{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{3} \mathrm{n}_{1}\right)}{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}} \)
c. \( \frac{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}}{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{3} \mathrm{n}_{1}\right)} \)
D. \( \frac{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}}{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{2} \mathrm{n}_{3}+\mathrm{n}_{3} \mathrm{n}_{1}\right)} \)


Calcium oxychloride is a :
A . Double salt
B. Acid salt
c. Mixed salt
D. Basic salt


How many buses are there for Suryapet from Hyderabad?
\( \mathbf{A} \cdot \mathbf{7} \)
B. 17
c. 12
D. 15


In Penicillium, the asexual reproduction takes place by
A. ascospores
B. aplanospores
c. sporangiospores
D. conidiospores


Evaluate: \( \int \frac{\sin ^{2} x}{\cos ^{4} x} d x \)
A \( \cdot \frac{1}{2} \tan ^{2} x+c \)
B \( \cdot \frac{1}{2} \cot ^{2} x+c \)
c. \( \frac{1}{3} \cot ^{3} x+c \)
D. \( \frac{1}{3} \tan ^{3} x+c \)


At \( 25^{\circ} \mathrm{C}, \) the solubility product of
\( M g(O H)_{2} \) is \( 1.0 \times 10^{-11} . \) At which \( p H \)
will \( \mathrm{Mg}^{2+} \) ions start precipitating in
the form of \( \mathrm{Mg}(\mathrm{OH})_{2} \) from a solution of
\( 0.001 \mathrm{M} \mathrm{Mg}^{2+} \) ions?
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 8


Which of the following step of regeneration stops the bleeding at the site of amputation?
A. Wound closure
B. Redifferentiation
c. Dedifferentiation
D. Blastema formation


What is the value of \( (\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}) \cdot(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}-B^{2} \)
c. \( A^{2}+B^{2}+2 A B \)
D. None of these


A wire is stretched \( 1 \mathrm{mm} \) by a force of 1
kN. How far would a wire of the same
material and length but of four times that diameter he stretched by the same force?
\( ^{\mathbf{A}} \cdot \frac{1}{2} \mathrm{mm} \)
в. \( \frac{1}{4} \mathrm{mm} \)
c. \( \frac{1}{8} \mathrm{mm} \)
D. \( \frac{1}{16} \mathrm{mm} \)


A convex refracting surface of radius of
curvature \( 20 \mathrm{cm} \) separates two media of refractive indices \( 4 / 3 \) and \( 1.60 . \) An
object is placed in the first medium \( (\mu=4 / 3) \) at a distance of \( 200 \mathrm{cm} \) from
the refracting surface. The position of
the image formed is
A . \( 120 \mathrm{cm} \)
B. 240 cm
\( c .100 \mathrm{cm} \)
D. 60 cm


The melting point of amino acids are higher than the corresponding haloacids because?
A. amino acids exist as zwitter ions resulting in strong dipole-dipole attraction
B. amino acids are optically active
C. due to higher molecular mass of \( -N H_{2} \) group molecular mass of amino acids is higher
D. they interact with water more than halo-acids and have salt like structure


An LCR series circuit contains \( \boldsymbol{L}=\mathbf{8} \boldsymbol{H} \)
\( \mathrm{C}=0.5 \mu \mathrm{F} \) and \( \mathrm{R}=100 \Omega \).The resonant
frequency of the circuit is
\( ^{\mathrm{A}} \cdot \frac{100}{\pi} H z \)
в. \( \frac{500}{\pi} H z \)
c. \( \frac{250}{\pi} H z \)
D. \( \frac{125}{\pi} H z \)


State whether true or false.
The sum of the interior angles of a
quadrilateral is \( 350^{\circ} \)
A. True
B. False


Sum \( : \frac{3}{1^{2} \cdot 2^{2}}+\frac{5}{2^{2} \cdot 3^{2}}+\frac{7}{3^{2} \cdot 4^{2}}+\dots \dots \)
terms


The angle made by the vector \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+ \)
\( 3 \hat{j} \) with \( y \) -axis is:
A \( \cdot \tan ^{-1}\left(\frac{3}{2}\right) \)
B. \( \tan ^{-1}\left(\frac{2}{3}\right) \)
c. \( \sin ^{-1}\left(\frac{2}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{3}{2}\right) \)


If a body is taken up to a height of \( 1600 \mathrm{km} \) from the earth's surface, then the percentage loss of gravitational force acting on that body will be -
(Radius of earth \( R_{e}=6400 \mathrm{km} \) ).
A . 50\%
B. 36\%
c. 25\%
D. 10\%


Can a concave lens form an image of size two times that of the object?
A. Yes
B. No
c. sometimes
D. None of these


The plane passing through the point (-2,-2,2) and containng the line joining the points (1,1,1)\( \&(, 1,-1,2) \) makes intercept of length \( a, b, c \) an aes
of \( x, y, z \) respectively then This question has multiple correct options
A \( . a=3 b \)
B . \( a+b+c=12 \)
c. No. of ways to distribute \( (3 b+6 c) \) alike objects among \( \frac{a}{2} \) boys \( =^{19} C_{4} \)
D \( \tan \left(\frac{\pi(b+c)}{2 a}\right)=1 \)


After how many seconds will the
concentration of a reactant in a
reaction is halved in a first
order reaction, if the rate constant is
\( 6.93 \times 10^{-3} s e c^{-1} \)
A \( \cdot 10^{4} \)
B. 100
\( c \cdot 10^{3} \)
D. 10


A skull excavated from a place had large zygomatic arches, 2 pairs of large incisors, 2 pairs of premolars following a gap and 3 pairs of large molars. The foramen magnum was direction posterior. This skull belongs to a
A. Predatory mammal with bipedal locomotion
B. Predaceous dinosaur with bipedal locomotion
c. herbivorous mammal with Quadrupedal locomotion
D. Herbivorous dinosaur with Quadrupedal locomotion


\( \frac{1}{4}+\frac{3}{6}=\frac{x}{8} \)


The diagram shows experiments involving the rusting of iron. The following results were suggested. 1 In tube \( P \), the iron nails rust.
2 In tube \( Q \), the iron nails do not rust.
3 In tube \( R \), the iron nails do not rust.
Which results are correct?
A . 1 and 2 only
B. 1 and 3 only
c. 2 and 3 only
D. 1,2 and 3


If \( I=\int \frac{(x+1)^{2}}{\sqrt{x^{2}+1}} d x, \) then 2 l equals
A \( \cdot(x+4) \sqrt{x^{2}+1}+\log (x+\sqrt{x^{2}+1})+C \)
B. \( x \sqrt{x^{2}+1}+2 \log (x+\sqrt{x^{2}+1})+C \)
c. \( x \sqrt{x^{2}+1}+\log (x+\sqrt{x^{2}+1})+C \)
D. \( (x-3) \sqrt{x^{2}+1}+\log (x+\sqrt{x^{2}+1})+C \)


The figure shows a particle ( carrying change \( +q \) ) at the origin. A uniform magnetic field is directed into the plane of the paper. The particle can be projected only in the plane of paper and along positive or negative \( x \) -or \( y \) -axis. The particle moves with constant speed and has to hit target located in the third quadrant. There are two direction of projections, which can make it possible, these are then
\( A \cdot+x \) and \( +y \)
B. \( +x \) and \( -y \)
\( c .-x \) and \( +y \)
D. - x and - y


A gold leaf electroscope is given a positive charge so that its leaves diverge. How is the divergence of leaves affected, when a positively charged rod is brought near its disc?
A. Divergence increases
B. Divergence decreases
c. Divergence remains same
D. can't say


Which among the following is an example of coelenterata?
A. Sycon
B. Hydra
c. tapeworm
D. Leech


If there is an error of \( 2 \% \) in measuring the length of a simple pendulum, then percentage error in its period is
A . \( 1 \% \)
B. 2\%
\( c .3 \% \)
D. \( 4 \% \)


Fill in the blanks.
is the fastest mode
of transfer of heat.


A hollow sphere is held suspended. Sand is now poured into it in stages. The centre of gravity of the sphere with the sand
A. Rises continuously
B. Remains unchanged in the process
c. Firstr rises and then falls to the original position
D. First falls and then rises to the original position


Which of the following is the property of
a group?
A. The elements in the same group have similar outer electronic configuration.
B. Their atomic size increases on moving down the group
C. Their melting and boiling points changes in a regular manner
D. All of the above


A boy is running along the circumference of a stadium with
constant speed. Which of the following is changing in this case?
A. Centripetal force acting on the boy
B. Distance covered per unit time
c. Direction in which the boy is running
D. Magnitude of acceleration


The line \( A x+B y+C=0 \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\boldsymbol{0} \) in \( \boldsymbol{P} \)
and \( Q \)
The line \( \boldsymbol{A}^{\prime} \boldsymbol{x}+\boldsymbol{B}^{\prime} \boldsymbol{y}+\boldsymbol{C}^{\prime}=\mathbf{0} \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y}+\boldsymbol{c}^{\prime}=\mathbf{0} \) in \( \boldsymbol{R} \)
and \( S \).
If \( P, Q, R, S \) are concyclic, then show
that
\( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{a}^{\prime} & \boldsymbol{b}-\boldsymbol{b}^{\prime} & \boldsymbol{c}-\boldsymbol{c}^{\prime} \\ \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} \\ \boldsymbol{A}^{\prime} & \boldsymbol{B}^{\prime} & \boldsymbol{C}^{\prime}\end{array}\right|=\mathbf{0} \)


Air filled capacitor of capacitance \( 2 \mu \boldsymbol{F} \)
is filled with three dielectric material of
dielectric constants \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4}, \boldsymbol{K}_{\mathbf{2}}= \)
4 and \( K_{3}=6 \) as shown in the figure.
The new capacitance of the capacitors
is
\( \mathbf{A} \cdot 50 \mu F \)
в. \( 2 \mu F \)
\( c \cdot 20 \mu F \)
D. \( 10 \mu F \)


In case of monocots, hypodermis is
A. Collenchymatous
B. Parenchymatous
c. Sclerenchymatous
D. Both A and B


A solid sphere is projected up along an inclined plane from its bottom with a
velocity \( 2.8 m s^{-1} \) so that it rolls upward.
If the inclined plane makes an angle of
\( 30^{\circ} \) with the horizontal, the sphere can
roll to a maximum height of : (Take \( \boldsymbol{g}= \)
\( \left.10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 0.35 m \)
B. \( 0.55 m \)
\( c .0 .7 m \)
D. \( 0.84 m \)


Nonpolar intramolecular and
intermolecular bonds are present in:
A. \( C C l_{4} \)
в. \( C O \)
c. \( H F \)
D. \( H C l \)
E . \( F_{2} \)


State true or false:
The more is the temperature difference of hot and cold body more slowly the heat flows from it into the cold body
A. True
B. False


Two cars are moving with same velocity
of \( 30 k m h^{-1} \) maintaining a distance of
5 km between them. Speed of third car
moving in the opposite direction and meeting the two cars at an interval of
\( 240 s \) is
\( \mathbf{A} \cdot 45 \mathrm{km} h^{-1} \)
B. \( 30 \mathrm{km} \mathrm{h}^{-1} \)
c. \( 55 \mathrm{km} \) h \( ^{-1} \)
D. \( 35 \mathrm{km} h^{-1} \)


The general solution of the equation
\( \sin x+\cos x=1 \) is
A \( \cdot x=2 n \pi+\frac{\pi}{2}, n=0,\pm 1,\pm 2 \)
B \( \cdot x=n \pi+\left((-1)^{n}+1\right) \frac{\pi}{4}, n=0,\pm 1,\pm 2 \)
C \( x=n \pi+\left((-1)^{n}-1\right) \frac{\pi}{4}, n=0,\pm 1,\pm 2 \)
D. \( x=2 n \pi, n=0,\pm 1,\pm 2 \)


A ball of mass 'm' is projected from the
ground with a speed 'u' at an angle ' \( \alpha \) with the horizontal. The magnitude of
the change in momentum of the ball over a time interval from begining till it strikes the ground again is
A \( \cdot \frac{m u \sin \alpha}{2} \)
B. \( 2 m u \cos \alpha \)
c. \( \frac{m u \cos \alpha}{2} \)
D. \( 2 m u \sin \alpha \)


What would be the electron dot
structure of a molecule of sulphur
which is made up of eight atoms of sulphur?


In the figure below. PQR is a right-
angle triangle right angled at \( Q . X Y \) is
parallel to \( \boldsymbol{Q} \boldsymbol{R} . \boldsymbol{P} \boldsymbol{Q}=\boldsymbol{6} \mathrm{cm}, \boldsymbol{P Y}=\mathbf{4} \mathrm{cm} \)
and \( P X: X Q=1: 2 . \) Calculate the
lengths of \( \boldsymbol{P R} \) and \( \boldsymbol{Q} \boldsymbol{R} \)
A. \( P R=12 \mathrm{cm} ; Q R=10.392 \mathrm{cm} \)
B. \( P R=13 \mathrm{cm} ; Q R=11.392 \mathrm{cm} \)
c. \( P R=11 \mathrm{cm} ; Q R=12.392 \mathrm{cm} \)
D. none of the above


A person drives the paddle ball by moving his finger up and down at a certain frequency. In this example he is causing
A. a damped vibration
B. a forced vibration
c. a mechanical vibration
D. a transnational vinration


A body undergoing \( S H M \) about the
origin has its equation is given by \( \boldsymbol{x}= \) \( 0.2 \cos 5 \pi t . \) Find its average speed in
\( \boldsymbol{m} / \boldsymbol{s} \) from \( \boldsymbol{t}=\mathbf{0} \) to \( \boldsymbol{t}=\mathbf{0 . 7} \boldsymbol{s e c} \)


Which of the following compound is expected to have the highest boiling point?
\( \boldsymbol{P H}_{3}, \boldsymbol{N} \boldsymbol{H}_{3},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \)
A \( \cdot N H_{3} \)
B. \( \left(C H_{3}\right)_{3} N \)
с. \( P H_{3} \)
D. None of these


Jacobson's organ is related
to
A. Taste
B. Sight
c. Touch
D. olfaction/Smell


Consider the following equation, \( \frac{d y}{d x}+ \) \( \boldsymbol{P}(\boldsymbol{x}) \boldsymbol{y}=\boldsymbol{Q}(\boldsymbol{x}) \)
(i) If two particular solutions of given equation \( u(x) \) and \( v(x) \) are known, find the general solution of the same equation in terms of \( u(x) \) and \( v(x) \)
(ii) If \( \alpha \) and \( \beta \) are constants such that
the linear combinations \( \boldsymbol{\alpha} \cdot \boldsymbol{u}(\boldsymbol{x})+\boldsymbol{\beta} \)
\( v(x) \) is a solution of the given equation,
find the relation between \( \alpha \) and \( \beta \)
(iii) If \( \boldsymbol{w}(\boldsymbol{x}) \) is the third particular
solution different from \( u(x) \) and \( v(x) \) then find the ratio \( \frac{\boldsymbol{v}(\boldsymbol{x})-\boldsymbol{u}(\boldsymbol{x})}{\boldsymbol{w}(\boldsymbol{x})-\boldsymbol{u}(\boldsymbol{x})} \)


Define the term solution. How many
types of solutions are formed? Write
briefly about each type with an example.


In the manufacture of nitric acid by
Ostwald's process, a dehydrating agent is used to convert
\( 68 \% \) by mass of \( H N O_{3} \) to \( 98 \% \) by mass
of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)


Fill in the blanks with appropriate
words.

Azeotropic mixtures boil without change in their \( _{\text {一一一一一一一. }} \) Azeotropic mixtures exist in solutions showing
or deviations.
solutions do not form
azeotropic. van't Hoff factor for an
electrolyte is than 1
A. colour, positive, negative, non-ideal, greater
B. properties, positive, negative, ideal, smaller
c. boiling point, positive, negative, non-ideal, lesser
D. composition, positive, negative, ideal, greater


A steam engine delivers \( 5.4 \times 10^{8} \) Jof
work per minute and services \( 3.6 \times 10^{9} \)
Jof heat per minute from its boiler
What is the efficiency of the engine? How much heat is wasted per minute?


8
5
is most stable?
\( A \)
B.
\( c \)
\( D \)


A capacitors has square plates each of
side \( l \) making an angle a with each
other as shown in the figure. Then, for
small value of a the capacitance \( C \) is
given by :
\( ^{\mathbf{A}} \cdot \frac{\epsilon_{0} I^{2}}{d}\left(1-\frac{a l}{2 d}\right) \)
В \( \cdot \frac{\epsilon_{0} I^{2}}{2 d}\left(1-\frac{a l}{d}\right) \)
c. \( \frac{\epsilon_{0} I^{2}}{d}\left(1-\frac{a l}{d}\right) \)
D \( \cdot \frac{\epsilon_{0} I^{2}}{2 d}\left(1+\frac{a l}{d}\right) \)


In an a.c. circuit, the instantaneous
e.m.f. and current are given by \( e= \) \( \mathbf{1 0 0} \sin \mathbf{3 0} t, \boldsymbol{i}=\mathbf{2 0} \sin \left(\mathbf{3 0} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{\mathbf{4}}\right) . \) In one
cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively.
A \( \cdot \frac{50}{\sqrt{2}}, 0 \)
в. 50,0
c. 50,10
D. \( \frac{1000}{\sqrt{2}}, 10 \)


Which of the following quantities is not affected by a magnetic field?
A. Stationary charge
B. Moving charge
c. change in magnetic flux
D. Current flowing in a conductor


A solid metal sphere of surface area \( \boldsymbol{S}_{1} \)
is melted and recast into a number of
smaller spheres. \( S_{2} \) is the sum of the surface areas of all the smaller spheres.
Then
A. \( S_{1}>S_{2} \)
в. \( S_{2}>S_{1} \)
c. \( S_{1}=S_{2} \)
D. \( S_{1}>S_{2} \) only if all the smaller spheres of equal radii


The transistor are usually made of
A. metal oxides with high temperature coefficient of resistivity.
B. metals with high temperature coefficient of resistivity.
C. metals with low temperature coefficient of resistivity.
D. semiconducting materials having low temperature coefficient of resistivity.


Show that the latus rectum of the
parabola \( \left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)=(\boldsymbol{b} \boldsymbol{x}+ \)
\( a y-a b)^{2} \) is \( 2 a b \div \sqrt{a^{2}+b^{2}} \)


A particle of mass \( m \) is oscillating with amplitude \( A \) and angular frequency \( \omega \) its average energy in one time period is
?
A \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. zero


Which of the protozoan is considered as a connecting link between plants and animals?
A. Entamoeba
B. Paramoecium
c. Euglena
D. Monocystis


A body of mass 'm' is raised from the surface of earth to a point which is at a height \( 5 R \) from the surface of the earth.
The change in PE is
A. \( 5 \mathrm{mgR} \)
в. \( \frac{2 m g R}{3} \)
c. \( \frac{4}{5} m g r \)
D. \( \frac{5 m g R}{6} \)


Which of the following substances is a Bronsted-Lowry acid?
A . \( N a O H \)
в. \( C H_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( H_{2} O \)


Why is the base of a cooking pan generally made thick?


What cross-sections do you get when you cut a candle horizontally?
A. Rectangle
B. Square
c. circle
D. Triangle


\( \operatorname{Let} \overrightarrow{\boldsymbol{A}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\boldsymbol{4} \hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{C}}= \)
\( \mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{2} \hat{k} . \) Then the ratio in which \( \boldsymbol{C} \)
divides \( A B \) is
A . 3: 4
B. 1: 3
c. 1: 2
D. 1: 1


topp
Q Type your question
spherical shell with inner radius \( c \) and
outer radius \( d \) (as shown in Fig). The
inner shell has total charge \( +2 q \) and the
outer shell has charge \( +4 q \). Calculate
the electric field in terms of \( q \) and the
distance \( r \) from the common centre of
the two shells for:
\( a<r<b \)
A. zero
в. \( \frac{1}{4 \pi \varepsilon_{8}} \frac{2 q}{r^{2}} \)
C. \( -\frac{1}{4 \pi \varepsilon_{0}} \frac{6 q}{r^{2}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}} \)


If \( A B C \) and DEF are similar triangles
such that \( \angle A=47^{\circ} \) and \( \angle B=83^{\circ} \)
then \( \angle \boldsymbol{F} \) is
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 70^{\circ} \)
\( c .50^{\circ} \)
D. \( 100^{\circ} \)


Water is not used as a dielectric
between the plates of a capacitor because its.
A. Dielectric constant is very low
B. Dielectric strength is very low
c. Dielectric constant is very highh
D. Dielectric strength is very large


If a sub-shell is denoted as \( 2 p \) then its magnetic quantum number values are
A . - 3, -2, - -
B. - -1, 0, + 1
\( c .-2,-1,0 \)
D. 0, 1, 2


When a circle is cut into eighths, those
sectors are called as,
A. Sextants
B. Quadrants
c. octants
D. None of these


The resistance of two electrolytes \( X \) and
Y were found to be 45 and 100
respectively when equal volumes
of both the solutions were taken in the
same cell in two different experiments.
If equal volumes of these solutions are mixed in the same cell, what will be the
conductance of the mixture?
\( A \cdot 0.032 \mathrm{mho} \)
B. 0.048 mho
c. 0.026 mho
D. 0.016 mho


A uniform steel rod of length 1 m and
area of cross section \( 20 \mathrm{cm}^{2} \) is hanging
from a fixed support. Find the increase in the length of the rod. \( \left(Y_{\text {steel}}=2.0 \times\right. \)
\( \mathbf{1 0}^{11} \boldsymbol{N m}^{-2}, \boldsymbol{\rho}_{\text {steel}}=\mathbf{7 . 8 5} \times \)
\( \left.10^{3} K g m^{-3}\right) \)
A \( .1 .923 \times 10^{-5} \mathrm{cm} \)
В. \( 2.923 \times 10^{-5} \mathrm{cm} \)
c. \( 1 . .123 \times 10^{-5} \mathrm{cm} \)
D. \( 3.123 \times 10^{-5} \mathrm{cm} \)


On electrolysis, water splits into
A. positively charged hydrogen ions and negatively charged oxygen ions.
B. negatively charged hydrogen ions and positively charged oxygen ions
C. hydrogen and oxygen atoms having positive and negative charges respectively.
D. hydrogen and oxygen atoms having negative and positive charges respectively.


The maximum number of electrons \( K \)
shell can accommodate are
\( A \cdot 2 \)
B. 4
\( c .6 \)
D.


Which is the volatile covalent liquid at
\( 25^{\circ} \mathrm{C} \) and 1 atm \( ? \)
\( A \cdot N_{2} \)
B. KI
\( c \cdot c c l_{4} \)
D. AgNO
E \( . \mathrm{caCO}_{3} \)


The electronic configurations of three elements \( X, Y \) and \( Z \) are given below. Which of the following is correct? \( x: 2,8 \)
\( Y: 2,8,7 \)
\( Z: 2,8,2 \)
A. \( x \) is a metal
B. Y is a metal
c. \( z \) is a non-metal
D. Y is a non-metal and \( z \) is a metal


The oxidation state of boron in
potassium tetrafluoroborate is:
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
\( D \cdot-3 \)


The only non-metal which is liquid at
ordinary temperature is \( B r_{2} \)
A. True
B. False


Which of the following complex/ion has highest C-O bond length?
\( \mathbf{A} \cdot\left[V(C O)_{6}\right]^{-} \)
в. \( F e(C O)_{5} \)
c. \( N i(C O)_{4} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)


The total number of antibonding
electrons in \( N_{2} \) and \( O_{2} \) molecules
respectively is:
\( A \cdot 6,8 \)
в. 5,8
c. 4,8
D. 4,6


The IUPAC name of the following compound biphenyl
A. True
B. False


Different states of same substance are
due to the difference in
A. temperature
B. pressure
c. either temperature or pressure
D. none of the above


Define specific heat capacity of a substance. Mention its unit.


I : Some alpha particles shot at a thin
metal foil are reflected back toward the
source.
II : Alpha particles shot at thin metal foil sometimes approach the nuclei of the metal atoms head-on and arc thus
repelled.


Find the number of all onto functions
from the set \( A=\{1,2,3, \ldots n\} \) to itself


Kamal and Monika appeared for an
interview for two vacancies. The
probability of Kamal's selection is \( \frac{1}{3} \) and that of Monika's selection is \( \frac{1}{5} . \) Find the probability that at least one of them will be selected.


In a p-njunction photo cell, the value of
the photo electromotive force produced
by monochromatic light is proportional
to
A. the barrier voltage at the p-njunction.
B. the intensity of the light falling on the cell.
C. the frequency of the light falling on the cell.
D. the voltage applied at the p-n junction.


A small metal sphere of radius \( a \) is
falling with a velocity \( v \) through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid
is \( \eta \), then the sphere encounters an opposing force of:
A \( \cdot 6 \pi \eta a^{2} v \)
в. \( \frac{6 \eta v}{\pi a} \)
c. \( 6 \pi \eta a v \)
D. \( \frac{\pi \eta v}{6 a^{3} v} \)


Identify the correct statement about nomenclature of alkylidene dihalides.
A. Dihaloalkanes in which two halogen atoms of the same type are present on the same carbon atom are called alkylidene dihalides.
B. In common naming system these are called as alkylene dihalides
c. In the IUPAC system, the locants for the two halogen atoms are prefixed to the name of dihaloalkane.
D. Both \( A \) and \( C \)


If \( a, b, c, p, q, r \) are three non-zero complex number such that \( \frac{p}{a}+\frac{q}{b}+ \) \( \frac{r}{c}=1+i \) and \( \frac{a}{p}+\frac{b}{q}+\frac{c}{r}=0, \) then
value of \( \frac{p^{2}}{a^{2}}+\frac{q^{2}}{b^{2}}+\frac{r^{2}}{c^{2}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 2 i \)
D. \( -2 i \)


If \( \bar{x}, \bar{y}, \bar{z} \) are mutually perpendicular vectors of eqaul magnitude, then find the measure of an angle that \( \bar{x}+\bar{y}+\bar{z} \)
makes with any of the three vectors.


A room is \( 3 \mathrm{m} \) high and \( 5 \mathrm{m} \) long. A man is standing in front of one of the walls 1 \( \mathrm{m} \) from the wall. A mirror is to be
installed on the wall. Find the height (minimum) of the mirror so that complete image of the wall behind him
is seen.
A . \( 1.5 \mathrm{m} \)
B. \( 1 \mathrm{m} \)
\( c \cdot 2 m \)
D. \( 0.5 \mathrm{m} \)


The output of the given combination of gates is equivalent to:
A. NAND
B. OR
\( c . \) AND
D. NOR


Less amount of energy is required to
remove s' electron than 'p' electron.
A. True
B. False


If \( \mathbf{A} \) and \( \mathbf{B} \) are two events such that \( P(\mathbf{A} \cup B) \geq \frac{3}{4} \) and \( \frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8} \)
then
This question has multiple correct options
A \( \cdot \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) \leq \frac{11}{8} \)
в.
c. \( \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) \geq \frac{7}{8} \)
D. \( \mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \geq \frac{1}{8} \)


KEPLER'S LAWS
A planet revolves around the sun in an
elliptical orbit. If \( v_{p} \) and \( v_{a} \) are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by
A. \( \frac{v_{p}}{v_{n}} \)
в. \( \frac{v_{a}-v_{p}}{v_{a}+v_{p}} \)
c. \( \frac{v_{p}+v_{a}}{v_{p}-v_{a}} \)
D. \( \frac{v_{p}-v_{a}}{v_{p}+v_{a}} \)


The band gap for a pure semiconductor is \( 2.1 e V . \) The maximum wavelength of a
photon which is able to create a hole-
electron pair is nearly:
A. \( 600 n m \)
B. 590 nm
c. 400 n \( m \)
D. 200nm


Fill in the blank.
The electric potential \( V \) at any point \( x, y, z \) (all in meters) in space is given
by \( V=4 x^{2} \) volts. The electric field at
the point \( (1 m, 0,2 m) \) is \( _{-----} V / m \)


Which of the following is true regarding the absorption mechanism of carbohydrates in the intestine?
A. Glucose is absorbed passively
B. Galactose is absorbed passively
c. Fructose is transported actively
D. Glucose and galactose are transported actively


Which of the following amino acid is neutral?
A. Aspartic acid
B. Glycine
c. Lysine
D. Arginine


The range of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{4-x^{2}}+\sqrt{x^{2}-1} \) is
A \( \cdot[\sqrt{3}, \sqrt{7}] \)
B \( \cdot[\sqrt{3}, \sqrt{5}] \)
c. \( [\sqrt{2}, \sqrt{3}] \)
D. \( [\sqrt{3}, \sqrt{6}] \)


What is a codon? How many codons serve as stop (non-sense) codons and
how many as initiating codons?


The proportion of nucleotides in a given acid are : adenine 18\%, Guanine 30\%,
Cytosine42 \% and Uracil 10 \%. Name the
nucleic acid and mention the number of
strands in it.


Identical charges \( (-q) \) are placed at
each corner of a cube of side b then
E.P.E. of charge \( (+\boldsymbol{q}) \) which is placed at the centre of the cube will be:
\( ^{\mathbf{A}} \cdot \frac{-4 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
B. \( \frac{-8 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
c. \( \frac{-4 q^{2}}{\sqrt{3} \pi \epsilon_{0} b} \)
D. \( \frac{8 \sqrt{2} q^{2}}{4 \pi \epsilon_{0} b} \)


In pyramid of food, the producers
occupy
A. The base
B. Position near the base
c. Apex
D. Position near apex


Consider a transparent hemisphere \( (n=2) \) in front of which a small object
is placed in air \( (n=1) \) as shown.
Consider a ray starting from \( \boldsymbol{O} \) which strikes the spherical surface at grazing
incidence \( (\boldsymbol{i}=\mathbf{9 0 ^ { \circ }}) . \) Taking \( \boldsymbol{x}=\boldsymbol{R}, \) what
will be the angle (from normal) at which
the ray may emerge from the plane
surface.
\( \mathbf{A} \cdot 90 \)
В. \( 0^{\circ} \)
\( c .30 \)
\( D \cdot 60 \)


Photocatalysis of effluents is carried out with the help of
A. Polymeric adsorbents
B. Titanium dioxide
c. Resins
D. UV radiations


Distinguish between the phenomenon of interference and diffraction of light.


A flat curve on a highway has a radius
of curvature 400 m. A car goes around a
curve at a speed of \( 32 m / s . \) What is the minimum value of coefficient of friction
that will prevent the car from sliding? \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \boldsymbol{)} \)


Which material is most suitable to
make the front-view glass of a car?
A. \( M O 6 \)
в. \( M O 3 \)
c. \( M O 1 \)
D. \( M O 4 \)


Which one of the following group of
codons is called as degenerate codons?
A. UAA, UAG and UGA
B. GUA, GUG, GCA and GCG
C . UUC, UUG, CCU, CAA and CUG
D. UUA and UUG, CUU, CUC and CUG
E . AAC, AAG, GAC and CGG


f a plane passes through the point (1,1,1) and is perpendicular to the line \( \frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4} \) then its
perpendicular distance from the origin is
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{7}{5} \)
D.


Which of the following reduction
processes are correct? This question has multiple correct options
A \( \cdot F e_{2} O_{3}+C^{\text {Reduction}} F e \)
B . \( Z n O+C \stackrel{\text {Reduction}}{\longrightarrow} \) Zn
\( \mathrm{c} \cdot \operatorname{Sn} \mathrm{O}_{2}+C^{\text {Redution}} S n \)
D \( \cdot P b O+C \stackrel{\text {Reduction}}{\rightarrow} P b \)


The formula of hydride of nitrogen that
is acidic in nature is:
A \( . N H_{3} \)
в. \( N_{3} H \)
c. \( N_{2} H_{4} \)
D. \( N H_{2} O H \)


Assertion
Consider the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x} \)
and \( \boldsymbol{g}(\boldsymbol{x})=-|\boldsymbol{x}| \)
The composite function \( \boldsymbol{F}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) \) is not derivable at \( \boldsymbol{x}=\mathbf{0} \)
Reason
\( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{+}\right)=\mathbf{2} \) and \( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{-}\right)=-\mathbf{2} \)
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


toppr
Q Type your question
particle.
\( \mathbf{A} \)
\( B \)
\( C \)
\( D \)
E


A vernier calipers have \( 1 \mathrm{mm} \) marks on the main scale. It has 20 equal divisions on the vernier scale
which matches with 16 main scale
divisions. For this vernier calipers, the
least count is :
\( A \cdot 0.02 \mathrm{mm} \)
B. 0.05 mm
\( c .0 .1 \mathrm{mm} \)
D. 0.2 mm


Consider a circular coil of wire carrying
constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane contains the circular coil and excluding the circular coil area is
given by \( \mathbf{\Phi}_{\mathbf{i}} . \) The magnetic flux through
the area of the circular coil area is given
by \( \mathbf{\Phi}_{\mathbf{0}} \)
Which of the following options is
correct?
\( \mathbf{A} \cdot \Phi_{\mathrm{i}}<\Phi_{0} \)
\( \mathbf{B} \cdot \Phi_{\mathrm{i}}=\Phi_{0} \)
\( \mathbf{c} \cdot \Phi_{\mathrm{i}}>\Phi_{0} \)
\( \mathbf{D} \cdot \Phi_{\mathrm{i}}=-\Phi_{0} \)


The diagonals \( A C \) and \( B D \) of a
parallelogram \( A B C D \) intersect each
other at the point \( O \)
If \( \angle D A C=32^{\circ} \) and \( \angle A O B=70^{\circ}, \) then
\( \angle D B C \) is equal to?
A \( \cdot 24^{\circ} \)
B. \( 86^{\circ} \)
\( c \cdot 38^{\circ} \)
\( D \cdot 32^{\circ} \)


The angle between the lines \( x \cos \alpha+ \)
\( \boldsymbol{y} \sin \boldsymbol{\alpha}=\boldsymbol{p}_{1} \) and \( \boldsymbol{x} \cos \boldsymbol{\beta}+\boldsymbol{y} \sin \beta=\boldsymbol{p}_{2} \)
where \( \boldsymbol{\alpha}>\boldsymbol{\beta} \) is
\( \mathbf{A} \cdot \alpha+\beta \)
B. \( \alpha-\beta \)
\( c \cdot \alpha \beta \)
D. \( 2 \alpha-\beta \)


Anomalous pair in Mendeleev's periodic
table is:
A. \( L i, N a \)
в. \( M g, \) Аl
c. \( C o, N i \)
D. \( B e, B \)


The work function of a substance is
4.0eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A . \( 5400 A^{\circ} \)
в. \( 4000 A^{\circ} \)
c. \( 3100 A^{\circ} \)
D. 2200A \( ^{\text {0 }} \)


Ozone on reaction with one of the
following reagents uses all three oxygen atoms for oxidation. The reagent is:
\( A \cdot S O_{2} \)
B. \( S n C l_{2} \) in presence of HCl
c. \( C H_{2}=C H_{2} \)
D. All


The given diagram shows a hill with four labelled positions \( \mathrm{W}, \mathrm{X}, \mathrm{Y} \) and \( \mathrm{Z} \) When a ball is rolled down the hill, then
from which position will it finish rolling
with the greatest speed?
A. Position \( \mathrm{w} \)
B. Position \( x \)
c. Position Y
D. Position z


Let 'gh' and 'g \( _{d} \) ' be the acceleration due
to gravity at height 'h' above the earth's
surface and at depth ' \( d \) below the
earth's surface respectively. IF \( \boldsymbol{g}_{\boldsymbol{h}}=\boldsymbol{g}_{\boldsymbol{d}} \)
then the relation between 'h' and ' \( d \) is
\( \mathbf{A} \cdot d=h \)
B. \( d=\frac{h}{2} \)
\( c \cdot d=\frac{h}{4} \)
D. \( d=2 h \)


The direction ratios of the joining \( A(1,2,1) \) and (2,1,2) are
A .3,3,3
B. -1,1,-1
c. 3,1,3
D. \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)


Assertion
Simple distillation can help in separating a mixture of propan-1-ol
(boiling point \( 97^{\circ} \mathrm{C} \) ) and propanone
(boiling point \( 56^{\circ} C \) )
Reason
Liquids with a difference of more than
\( 20^{\circ} \mathrm{C} \) in their boiling points can be
separated by simple distillation.
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


Deduce an expression for the effective
capacitance of capacitors of \( C_{1}, C_{2} \) and
\( C_{3} \) connected in series


Let lines \( A B \) and \( C D \) intersect at \( O \)
If \( \angle A O C+\angle B O E=70^{\circ} \) and
\( \angle B O D=40^{\circ}, \) find \( \angle B O E \)


pH of the buffer containing \( 0.6 g \) of
acetic acid and \( 8.2 g \) of sodium acetate
in 1 litre of water is: \( \left(p K_{a} \) of acetic acid \right.
\( =4.5) \)
A . 7.5
в. 4.5
c. 5.5
D. 6.5


Two kg of a monoatomic gas is at a pressure of \( 4 \times 10^{4} N / m^{2} . \) The density
of the gas is \( 8 k g / m^{3} . \) What is the order
of energy of the gas due to its thermal motion?
A \( \cdot 10^{3} J \)
\( J \)
В. \( 10^{5} J \)
\( c \cdot 10^{6} J \)
D. \( 10^{4} J \)


Which of the following is correct IUPAC
name of any complex compound?
A. Tris(acetylacetonato)iron(III)chloride
B. Hexachloroplatinum(IV)tetraammine dicyano platinate(IV)
C. Ammine bromochloro methylamine platinum(II)
D. cis-dichloro (ethylenediamine) platinum (II)


In transformer, power of secondary
A. less than primary coil
B. more than primary coil
C. more in step up and less in step primary coil
D. same in both primary and secondary coil


Formation of nitric oxide from nitrogen and oxygen is a reaction.
A. combination
B. combustion
c. calcination
D. roasting


Let \( \boldsymbol{A}=\{1,2\} \) and \( \boldsymbol{B}=\{3,4\} . \) Write
\( A \times B \) and find how many subsets will
\( A \times B \) have? List them.


After scattering, the light moves in:
A. the same direction as the original light ray.
B. opposite to the original direction of the light ray
c. all directions
D. the direction of the shortest path.


Two spheres having same radius and mass are suspended by two strings of equal length from the same point in such a way that their surfaces touch
each other. On depositing charge \( 2 \times \) \( 10^{-6} C \) on them they repel each other in
such a way that in equilibrium the angle between their strings becomes
\( 60^{\circ} . \) If the distance from the point of
suspension to the centre of the sphere is \( 10 \mathrm{cm} . \) Find the mass of each sphere.
\( \left(\boldsymbol{K}=\mathbf{9} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{S} \boldsymbol{I} \quad \text { and } \quad \boldsymbol{g}=\mathbf{1 0 m s}^{-1}\right) \)
A. \( 0.6235 k g \)
в. \( 0.3117 k g \)
c. \( 0.1559 k g \)
D. \( 1.2468 k g \)


Find \( \mathbf{k} \) if \( \frac{\mathbf{1}}{\mathbf{6} !}+\frac{\mathbf{1}}{\mathbf{7} !}=\frac{\boldsymbol{k}}{\mathbf{8} !} \)


Excretory products of mammals are useful to plants. Which of the following is not a part of such secretions?
A. Carbon dioxide
B. Mineral salts
c. Bile pigments
D. urea


A cuboid has volume \( \boldsymbol{V}=\mathbf{1} \times \mathbf{2 l} \times \mathbf{3 l} \)
where 1 is the length of one side. If the
relative percentage error in the
measurement of \( l \) is \( 1 \% \), then the
relative percentage error in measurement of \( V \) is
\( \mathbf{A} \cdot 18 \% \)
B. \( 6 \% \)
c. \( 3 \% \)
D. 1\%


Which pair of products would result from the acid cleavage of phenyl propyl ether with excess concentrated \( \boldsymbol{H} \boldsymbol{B r} \) ?
A. Phenol and 1-propanol
B. Bromobenzene and 1-propanol
c. Bromobenzene and 1-bromopropane
D. Phenol and 1-bromopropane


A point \( Q \) at a distance 3 from the point \( P(1,1,1) \) lying on the line joining the points \( \boldsymbol{A}(\mathbf{0},-\mathbf{1}, \mathbf{3}) \) and \( \boldsymbol{P}, \) has the
coordinates
This question has multiple correct options
A \( \cdot(2,3,-1) \)
В. (4,7,-5)
D. (-2,-5,7)


What are poikilothermic animals?


If the irrigation water contains dissolved salts, is
particularly suitable.
A. surface irrigation
B. drip irrigation
c. sprinkler irrigation
D. localized irrigation


The adjacent sides of a parallelogram \( \operatorname{are} 2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( \hat{i}+2 \hat{j}+3 \hat{k} \) then
the unit vector parallel to a diagonal is
A \( \cdot \frac{-\bar{i}-2 \bar{j}+8 \bar{k}}{\sqrt{69}} \)
в. \( \frac{3 \bar{i}+6 \bar{j}-2 \bar{k}}{7} \)
c. \( \frac{\bar{i}+2 \bar{j}-8 \bar{k}}{\sqrt{69}} \)
D. All the above


For the wave shown in figure, the
wavelength of the wave is:
\( \mathbf{A} \cdot 0.4 m \)
B. \( 0.2 m \)
\( \mathbf{c} .0 .16 m \)
D. \( 0.8 m \)


The diameter of a solid disc is \( 0.5 \mathrm{m} \)
and its mass is \( 16 \mathrm{Kg} \). What torque will increase its angular velocity from zero to 120 rotation/minute in 8
seconds?
A \( \cdot \frac{\pi}{4} N / m \)
в. \( \frac{\pi}{2} N / m \)
c. \( \frac{\pi}{3} N / m \)
D. \( \pi N / m \)


An ideal monoatomic gas is carried
around the cycle ABCDA as shown in the
fig. The efficiency of the gas cycle is
A \( \frac{4}{21} \)
в. \( \frac{2}{21} \)
c. \( \frac{4}{31} \)
D. \( \frac{2}{31} \)


The law of limiting factor for photosynthesis was given by
A . R. Hill
B. Krebs
c. Calvin
D. Blackman


In a semiconductor, acceptor impurity is :
A. Antimony
B. Indium
c. Phosphorous
D. Arsenic


Three lenses in contact have a
combined focal length of \( 12 \mathrm{cm} \). When the third lens is removed the combined
focal length becomes \( 60 \mathrm{cm} \). The third
lens is :
A. a converging lens of focal length 30 cm
B. a converging lens of focal length 60 cm
c. a diverging lens of focal length 30 cm
D. a diverging lens of focal length 60 cm


On the basis of the characteristics
given below, name the phylum or class:
Presence of vertibral column, hairy skin and oviparous in nature


The monocotyledonous seed consists of one large and shield shaped cotyledon known as
A. Aleurone layer
B. Scutellum
c. coleoptile
D. Hilum
E. Coleorhiza


Fill in the blank:
To locate Sirius with the help of Orion, an imaginary line is to be drawn towards
A. South
B. North
c. west
D. East


Out of the following matrices, choose that matrix which is a scalar matrix.
\( A \cdot\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)
В. \( \left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0 \\ 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)


f \( a, b, c \) are real number, then find the
intervals in which \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\begin{array}{ccc}
\boldsymbol{x}+\boldsymbol{a}^{2} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a c} \\
\boldsymbol{a b} & \boldsymbol{x}+\boldsymbol{b}^{2} & \boldsymbol{b c} \\
\boldsymbol{a c} & \boldsymbol{b c} & \boldsymbol{x}+\boldsymbol{c}^{2}
\end{array} \mid
\]
increasing or decreasing


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}\left(\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}\right), \boldsymbol{x}>1 \)
Then
A. \( f(x) \leq 1 \)
B. \( 1<f(x) \leq 2 \)
c. \( 2<f(x) \leq 3 \)
D. \( f(x)>3 \)


Pressure of real gas is less than the pressure of ideal gas because:
A. No. of collisions increases
B. Definite shape of molecul
c. K.E. of molecule increases
D. Inter molecular forces


State the number of unpaired electrons
in \( N i^{2+}: \)
\( A \cdot O \)
B. 2
\( c \cdot 4 \)
D. 8


Find the value of the following.
\( \sin 26^{\circ} \)


Which one of the following structural
formula of two organic compounds is correctly identified along with its
related function?
A. B- uracil a component of DNA
B. A- triglyceride major source of energy
c. A- lecithin a component of cell membrane
D. B- adenine a nucleotide that makes up nucleic acid


In a crossed field, the magnetic field
induction is \( 2.0 T \) and electric field
intensity is \( 20 \times 10^{3} V / m . \) At which
velocity the electron will travel in a straight line without the effect of electric and magnetic fields?
A \( \cdot \frac{20}{16} \times 10^{3} \mathrm{ms}^{-1} \)
B. \( 10 \times 10^{3} \mathrm{ms}^{-1} \)
c. \( 20 \times 10^{3} \mathrm{ms}^{-1} \)
D. \( 40 \times 10^{3} \mathrm{ms}^{-} \)


The reaction between \( N O \) and \( C l_{2} \) takes place in the following two steps:
\( \boldsymbol{I} \cdot \boldsymbol{N} \boldsymbol{O}+\boldsymbol{C l}_{2}_{k_{2} \atop f a t}^{k_{1}} \boldsymbol{N O C l}_{2} \)
II. \( N O C l_{2}+N O \frac{k_{3}}{s l o w} \geq 2 N O C l \)
The rate law of overall reaction, \( 2 N O+ \)
\( C l_{2} \longrightarrow 2 N O C l, \) can be given by:
A \( \cdot \) Rate \( =k[N O]^{2}\left[C l_{2}\right] \)
B・Rate \( =k[N O]\left[C l_{2}\right] \)
c. Rate \( =k[N O C l][N O \)
D・Rate \( =k[N O]\left[C l_{2}\right]^{2} \)


Distinguish between interference and diffraction.


The average half-cycle value of a sine
wave with a \( 40 V \) peak is
A . \( 25.48 V \)
B . \( 6.37 V \)
c. \( 14.14 V \)
D. \( 50.96 V \)


If the \( 4^{t h} \) and \( 7^{t h} \) term of a G.P. are 54
and 1458 respectively, then find its
¡) Common ratio
ii) \( 6^{t h} \) term


are examples of isobars.
\( \mathbf{A} \cdot_{14} S i^{31},_{15} P^{32} \)
\( \mathbf{B} \cdot_{6} C^{13},_{7} N^{13} \)
\( \mathbf{C} \cdot_{7} N^{14},_{7} N^{15} \)
D. None of the above


Tangents PA and PB drawn to \( x^{2}+y^{2}= \)
9 from any arbitrary point 'P' on the line \( x+y=25 . \) Locus of midpoint of chord
AB is
A \( \cdot 25\left(x^{2}+y^{2}\right)=9(x+y) \)
B . \( 25\left(x^{2}+y^{2}\right)=3(x+y) \)
C. \( 5\left(x^{2}+y^{2}\right)=3(x+y) \)
D. None of these


Two hail stones with radii in the ratio of
1:2 fall from a great height through the atmosphere. Then their terminal
velocities are in the ratio of:
A .1: 2
B . 2: 1
\( c \cdot 1: 4 \)
D. 4: 1


China wares are wrapped in straw or
paper before packing. This is the application of concept of :
A. Impulse
B. Momentum
c. Acceleration
D. Force


The resultant of two vectors acting at an
angle of \( 150^{\circ} \) is of magnitude 10 units and is perpendicular to one of the vectors. The magnitude of the other vector is :
A \( \cdot \frac{20}{\sqrt{3}} N \)
в. \( 10 \sqrt{3} \) N
\( c \cdot 20 N \)
D. \( 20 \sqrt{3} N \)


The inert gas which cannot be adsorbed over activated coconut charcoal?
A . Ne
B. Ar
c. не
D. \( \mathrm{Kr} \)


If \( 0.4 \hat{i}+0.7 \widehat{j}+c \hat{k} \) is a unit vector, then
the value of \( c \) is:
A \( \cdot \sqrt{0.67} \)
the 0.66
B. \( \sqrt{0.12} \)
c. \( \sqrt{1.44} \)
D. \( \sqrt{0.35} \)


jacks can be categorized based on which types of forces from below
A. Mechanical and hydraulic
B. Mechanical and kinetic
c. Kinetic and potential
D. Hydraulic and rotational


A cross done between a homozygous recessive and a heterozygous plant is called as
A. Monohybrid cross
B. Dihybrid cross
c. Test cross
D. Back cross


For two events \( A \) and \( B \) with \( P(B) \neq 1 \)
prove that \( \boldsymbol{P}\left(\boldsymbol{A} \mid \boldsymbol{B}^{\prime}\right)= \)
\( \frac{\boldsymbol{P}(\boldsymbol{A})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{1-\boldsymbol{P}(\boldsymbol{B})} \)


Give IUPAC name of the given
compound:
A. 1 -ethyl-2-methylcyclohexene
B. 1-ethyl-3-methylcyclohexane
C. 1 -methyl-3-ethylcyclohexane
D. 1 -ethyl-3-methycyclohexene


Match the theories given with the names of scientists. Choose the answer
which gives the correct combination of
the alphabets.
Names of Names of theories \( \quad \) scientists
A. Relay pump theory
p. Schleiden
B. Cohesion tension theory
q. Sir J.C. Bose
C. Mass flow theory Godlewski
D. Pulsation theory
s. Dixon and Jolly
t. Ernst Munch
A \( \cdot \) A- \( q, \) B- \( p, C-t, D-r \)
B. A-r, B- q, C- t, D- q
c. \( A-s, B-r, C-p, D-q \)
D. A- r, B- s, C- t, D- q


The torque equation for a pendulum bob
making an angle \( \theta \) with the vertical is
given by
\( \mathbf{A} \cdot d^{2} \theta / d t^{2}=-(g / L) \cos \theta \)
B \( \cdot d^{2} \theta / d t^{2}=-(g / L) \sin \theta \)
\( \mathbf{c} \cdot d^{2} \theta / d t^{2}=-(g / L)^{2} \sin \theta \)
D. \( \left.d^{2} \theta / d t^{2}=-\sqrt{(} g / L\right) \sin \theta \)


Read the following \( (A-D) \) :-
A. RBCs are the most abundant of all the
cells in blood.
B. A healthy adult man has no an
average 5 Billions to 5.5 Billions of RBCs
\( m m^{-3} \) of blood
C.RBCs are formed in liver in the adults.
D.RBCs are devoid of nucleus in most of
the mammals and are biconcave in
shape. How many of the above statement are incorrect?
\( A \cdot 4 \)
в. 3
\( c \cdot 2 \)
D. 1


In the above figure, \( \boldsymbol{E}_{1} \) to \( \boldsymbol{E}_{6} \) represent
some of the energy levels of an electron in the hydrogen atom. Which one of the following transitions produces a photon of wavelength in the ultra-violet region of the electromagnetic spectrum?
\( e V \)
\( 85 \mathrm{eV} \)
A \( . E_{2}-E_{1} \)
в. \( E_{3}-E_{2} \)
\( \mathbf{c} \cdot E_{4}-E_{3} \)
D. \( E_{6}-E_{4} \)


Derive the condition for balance of a
Wheatstone's bridge using Kirchhoff's rules.


Which of the following is not an interstitial compound?
A. Tic
B. VN
\( c \cdot v B \)
D. sic


Th - 230 undergoes a series of
radioactive decay processes resulting
in \( B i-214 \) being the final product.
What was the sequence of the
processes that occurred?
\( \mathbf{A} \cdot \alpha, \alpha, \alpha, g, \beta \)
в. \( \alpha, \alpha, \alpha, \alpha, \beta \)
\( \mathbf{c} \cdot \alpha, \alpha, \beta, \beta \)
\( \mathbf{D} \cdot \alpha, \beta, \beta, \beta, \gamma \)


Stem of Opuntia is
A. Phyllode
B. Phylloclade
c. cladode
D. Bulbil


On complete hydrogenation, natural rubber produces:
A. ethylene-propylene copolymer
B. vulcanised rubber
c. polypropylene
D. polybutylene


Why must electrostatic field at the surface of a charged conductor be
normal to the surface at every point? Give reason.


Which of the following statement is
incorrect for \( \boldsymbol{P} \boldsymbol{C l}_{5} \) ?
A. Its three P-CI bond lengths are equal
B. It involves \( s p^{3} d \) hybridization
c. It has linear geometry
D. Its shape is trigonal bipyramidal


Oxygen gas is a Supporter of combustion and keeps the burning splinter glowing.
A. True
B. False


If \( \Delta G^{o} \) for the reaction given below is
\( 1.7 k J ; \) the equilibrium constant of the reaction,
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \) at \( 25^{\circ} C, \) is:
A . 0.5
B . 2.
\( c .3 .9 \)
D. 24.0


If a plant cell is placed in deionised
water, the water potential of that cell
becomes
A. More positive because pressure potential becomes more positive
B. More positive because pressure potential becomes more negative
C. More negative because pressure potential becomes more negative
D. Less negative because pressure potential becomes more positive


When the nucleus of an electrically neutral atom undergoes a radioactive decay process, it will remain neutral after the decay if the process
is
A. an \( \alpha \) -decay
B. a \( \beta \) -decay
c. a \( \gamma \) -decay
D. a K-capture process


Tension in the string in the mean position of an oscillating pendulum is:
A. Same as tension when it is not oscillating
B. Depend upon the time speedd
c. Less than tension when it is not oscillating
D. More than tension when it is not oscillating


Fill in the blanks with appropriate
words.

The yellow colour of urine is due to


A lake receiving nutrients would be
A. oligotrophic
B. Eutrophic
\( c . \operatorname{sink} \)
D. Rich in fossils


In the dissociation of HI, 20\% of HI is dissociated at equilibrium. Calculate
\( \boldsymbol{K}_{\boldsymbol{p}} \) for
\( \mathrm{HI}(\mathrm{g}) \leftrightharpoons \frac{1}{2} H_{2}(g)+\frac{1}{2} I_{2}(g) \)
A . 1.25
B. 0.125
c. 12.5
D. 0.0125


In an LCR circuit the potential
difference between the terminal of the
inductance is \( 60 V \), between the
terminals of the capacitor is \( 30 V \) and
that between the terminals of the
resistance is \( 40 \mathrm{V} \). The supply voltage
will be equal to:
\( \mathbf{A} \cdot 130 V \)
в. \( 10 V \)
\( c .50 V \)
D. \( 70 V \)


Given that \( P \) is a point on a wheel rolling on a horizontal ground. The radius of the wheel is \( R \). Initially if the point \( P \) is
in contact with the ground, the wheel rolls through half revolution. What is the displacement of point \( P ? \)
B. \( R \sqrt{\pi^{2}+4} \)
\( c . \pi R \)
D. \( 2 \pi R \)


If the second I.P of calcium is 275.12
kcals \( m o l^{-1}, \) then, the equation that
represents this ionization can
be written as:
A \( \cdot C a_{(S)}^{+} \rightarrow C a_{(S)}^{3+}+2 e^{-}-275.12 \) kcals
B. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{3+}+2 e^{-}+275.12 \) kcals
c. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{2++}+e^{-}+275.12 \) kcals
D. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{2+1}+e^{-}-275.12 \) kcals


If we consider molecules of an ideal gas
in a box with a frictionless piston and
now the box is heated and piston moves
slowly outwards then:
A. the force on piston is due to molecular collision with piston
B. the molecules collide with piston and return back with same speed
c. the molecular collision with piston is inelastic
D. both (a) and
(b) are correct


The hydraulic press is used in the extraction of oil from oil-seeds.
A. True
B. False


\( = \)
\( d_{c} \)
\( d \sigma \)


\( B F_{3} \) and \( N F_{3} \) both molecules are
covalent, but \( B F_{3} \) is non-polar and \( N F_{3} \)
is polar. Its reason is:
A. in uncombined state boron is metal and nitrogen is gas
B. \( B-F \) bond has no dipole moment whereas \( N-F \) bond has dipole moment.
C. The size of boron atom is smaller than nitrogen
D. \( B F_{3} \) is planar whereas \( N F_{3} \) is pyramidal


During the electrolysis of the aqueous solution of copper sulphate using Pt electrodes, the reaction taking place at
anode electrode is:
A \( \cdot C u^{2+}+2 e^{-} \rightarrow C u \)
в. \( C u \rightarrow C u^{2+}+2 e^{-} \)
\( \mathbf{c} \cdot 2 H_{2} O \rightarrow 4 H^{+}+O_{2}+4 e^{-} \)
" \( \quad H_{2} O+e^{-} \rightarrow O H^{-}+\frac{1}{2} H_{2} \)


When a coin is tossed in an experiment, the result is either a head or a tail. A
head is given a point value of 1 and \( a \) tail is given a point value of \( -1 . \) If the sum of the point values after 50 tosses
is \( 14, \) how many of the tosses must
have resulted in heads?
A . 14
B. 18
c. 32
D. 36
E. 39


Weight of iodine required to oxidise
\( 500 m L N a_{2} S_{2} O_{3} \) solution, is
\( \mathbf{A} \cdot 6.35 g \)
в. \( 63.5 g \)
c. \( 127 g \)
D. \( 254 g \)


State the following statement is True or
False
If Shelly does not like John, then the truth value of the statement "Shelly likes Mike and she likes John" is True
A. True
B. False


What is the common difference of an
A.P. in which \( a_{24}-a_{17}=-28 ? \)


Draw the graph for the linear equation \( 3 y+5=0 \) and select the correct
option:
A. The line is parallel to the \( x \) -axis and passes through \( \left(0,-\frac{5}{3}\right) \)
B. The line is parallel to the \( y \) -axis and passes through \( \left(0,-\frac{5}{3}\right) \)
c. The line is parallel to the \( x \) -axis and passes through \( \left(0, \frac{5}{3}\right) \)
D. The line is parallel to the \( y \) -axis and passes through \( \left(0, \frac{5}{3}\right) \)


\( A, B, C \) are three events for which
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{C})= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=\mathbf{0 . 3} \)
and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0 . 2 .} \) If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \)
\( C) \geq 0.85 \) then the interval of values of
\( \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C}) \) is
В. [0.55,0.7]
D. none of these


Nitrogen, \( N_{2}, \) is the most abundant gas
in the Earth's atmosphere and is very
unreactive
State why \( N_{2} \) is very unreactive.


n given figure \( A B C D \) is a trapezium in
which \( A B \| C D \) and \( A D=B C . \) Show
that
(i) \( \angle \boldsymbol{A}=\angle \boldsymbol{B} \)
(ii) \( \angle C=\angle D \)
(iii) \( \triangle A B C \cong \triangle B A D \)
(iv) diagonal \( A C=\operatorname{diagonal~} B D \)


We should not use plurals when we write the unit in words.
A. True
B. False


If \( \int f(x) d x=\frac{3}{55} \sqrt[3]{\tan ^{5} x}\left(5 \tan ^{2} x+\right. \)
11) \( +C \) then \( f(x) \) is equal to
This question has multiple correct options
A \( \cdot \sqrt[3]{\sin ^{2} x \cos ^{-14} x} \)
B. \( \sqrt[3]{\tan ^{2} x\left(1+\tan ^{2} x\right)^{6}} \)
c. \( \sqrt[3]{\cos ^{2} x \sin ^{-14} x} \)
D. \( \frac{7}{3} \sqrt[3]{\sin ^{2} x \cos ^{-14} x} \)


Give first the step you will use to separate the variable and then solve the
equations \( \frac{3 p}{10}=6 \)


If \( \lim _{x \rightarrow 0}\left(\frac{\sin 2 x}{x^{3}}+a+\frac{b}{x^{2}}\right)=0 \) then
the value of \( 3 a+b \) is
A . 2
B. -2
\( c \cdot-1 \)
D.


Solve for \( x \) :
\( \tan ^{-1} x=\frac{1}{2} \cot ^{-1} x \)


During photorespiration, in which of the following NAD is reduced?
A. Mitochondria and peroxisome
B. Chloroplast and peroxisome
c. chloroplast and mitochondria
D. Mitochondria


A \( 60 \mathrm{kg} \) man pushes a \( 40 \mathrm{kg} \) man by a
force of \( 60 N . \) The \( 40 \mathrm{kg} \) man has
pushed the other man with a force of:
A \( .40 N \)
B. 0
\( c .60 N \)
D. 20 N


In this ladder, symbols of elements are jumbled up. Rearrange these symbols of elements in the increasing order of their atomic number in the periodic table
\( \mathrm{Ca} \)
B. H, He, Li, B, Be, C, N, O, F, Ne, Na, Mg, Al, S, P, Si, CI, Ar, K \( \mathrm{c} \)
c. H, He, Li, Be, B, C, N, O, F, Na, Ne, Mg, Al, S, P, s, Cl, Ar, K. \( \mathrm{Ca} \)
D. H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, si, P, s, cl, Ar. \( c \)


A tank with a small orifice contains oil
on top of water. It is immersed in a large
tank of the same oil. Water flows
through the hole. Assuming the level of
oil outside the tank above orifice does
not change. a. What is the velocity of
this flow initially? b. When the flow
stops, what would be the position of the
oil-water interface in the tank?
Determine the time at which the flow
stops? Density of oil \( =\mathbf{8 0 0} k g / m^{3} \)


Which of the following is a monounsaturated hydrocarbon, i.e. the compound that contains one carbon -
carbon double bond?
A \( \cdot C_{3} H_{6} \)
в. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C_{5} H_{8} \)


The 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred from one plate to another?
\( \mathbf{A} \cdot 1.1 \times 10^{9} \)
B . \( 6.7 \times 10^{9} \)
\( \mathrm{c} \cdot 4 \times 10^{19} \)
D . \( 5 \times 10^{19} \)


\( \left[\begin{array}{lll}0 & 0 & 0\end{array}\right] \) is an example of
A. Scalar matrix
B. Diagonal matrix
c. Identity matrix
D. Null matrix


Two parallel straight conductors, in which current is flowing in the same direction, attract each other. The cause
of it is
A. magnetic force between the two
B. electric force between the two
c. potential difference between the two
D. mutual induction between the two


The reduction of acetamide gives:
A. \( C H_{3} C H_{2} N H_{2} \)
в. \( \left(C H_{3}\right)_{2} C H N H_{2} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{3} C N H_{2} \)
D. \( \left(C H_{3} C H_{2}\right)_{2} N H \)


Cyanosis is
A. Lack of oxygen in body fluids.
B. Difficult or heavy breathing.
C. Excess of carbon dixode in the body fluids.
D. Skin turning blue due to excessive amount of deoxygenated haemoglobin in the skin blood vessels.


Diamond and graphite are the covalent compounds of carbon element (C).
A. True
B. False


If the straight line \( x \cos \alpha+y \sin \alpha= \)
\( p \) touches the curve \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \) then
prove that \( \boldsymbol{a}^{2} \cos ^{2} \boldsymbol{\alpha}+\boldsymbol{b}^{2} \sin ^{2} \boldsymbol{\alpha}=\boldsymbol{p}^{2} \)


The electronic configuration of \( \boldsymbol{H} e \) is 2
and that of oxygen is


If \( A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right] \) and \( \left|A^{3}\right|=125 \) then \( \alpha \) is
\( \mathbf{A} \cdot \pm 1 \)
B. =2
\( c .\pm 3 \)
D. ±5


Which of the following way of reading is
good for eyes?
A. Reading the book too close to eyes
B. Reading the book by keeping it too far from eyes
C. Keeping the book at normal distance of vision
D. All are true


If \( \boldsymbol{y}=e^{m x}+e^{-m x}, \) then prove that
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\boldsymbol{m}^{2} \boldsymbol{y} \)


\( \{g, h\} \) are the elements of
A \( \cdot(\text { A } \cup \text { B }) \)
\( 3 \cdot(A \cap B) \)
e (A\cupB)
A \( (A \cap B) \)


Find the volume of a sphere whose
surface area is 154 square \( \mathrm{cm} \)


\( 0.2864 g \) of \( C u \) was deposited on
passage of a current of 0.5 ampere for 30 minutes through a solution of
copper sulphate. What is the electrochemical equivalent of copper?


\( P V=n R T \) holds good for
a) Isobaric process
b) Isochoric
process
c) Isothermal process
d) Adiabatic
process
\( A \cdot a \& b \)
B. a,b \&
\( c \cdot a, b \& d \)
D. all


A die of six faces marked with the
integers 1,2,3,4,5,6 one on each face Is thrown twice in succession what is
the total number of outcomes thus
obtained?


Write the balanced equation for the
following:Bromoethane and an aqueous solution
of sodium hydroxide.
A. \( C_{2} H_{5} B r+N a O H \rightarrow C_{2} H_{6} \)
в. \( C_{2} H_{5} B r+N a O H \rightarrow C_{2} H_{5} O H \)
c. \( C_{2} H_{5} B r+N a O H \rightarrow C_{2} H_{4} O \)
D. \( C_{2} H_{5} B r+N a O H \rightarrow C_{2} H_{2} O \)


In which of the following subject the dead space is highest?
A. Old man
B. Old woman
c. Young man
D. Young woman


What is the number density of donor atoms which must be added to a pure
germanium semiconductor to produce an N-type semiconductor of
conductivity \( 6.4 X 10^{2} \) oh \( m^{-1} m^{-1} \) ? The mobility of electrons in N-type germanium is \( 4 X 10^{-1} m^{2} V^{-1} s^{-1} \)
Neglect contribution of holes to conductivity.
A \( \cdot 10^{20} m^{-3} \)
B. \( 10^{21} m^{-3} \)
\( \mathrm{c} \cdot 10^{22} \mathrm{m}^{-3} \)
D. \( 10^{23} \) s \( ^{-3} \)


Arrange the following compounds in increasing order of their boiling points.
(a)
(b) \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} \)
\( (c) \)
\( \mathbf{A} \cdot(b)<(a)<(c) \)
B. \( (a)<(b)<(c) \)
C \( .(c)<(a)<(b) \)
D. \( (c)<(b)<(a) \)


f the matrix \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{6} & \boldsymbol{x} & \mathbf{2} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{- 1 0} & \mathbf{5} & \mathbf{2}\end{array}\right] \) is
singular matrix. Find the value of \( x \)


The osmotic pressure of solution increases if:
A. temperature is decreased
B. concentration is decreased
c. number of solute molecules are increased
D. volume is increased


One mole of magnesium nitride on the reaction with an excess of water gives:
A. one mole of ammonia
B. one mole of nitric acid
c. two moles of ammonia
D. two moles of nitric acid


Moment of inertia of a uniform disc of
mass \( m \) about an axis \( x=a \) is \( m k^{2} \)
where \( k \) is the radius of gyration. What
is its moment of inertia about an axis
\( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \)
A \( \cdot m k^{2}-m a^{2}+m(a+b)^{2} \)
B \( \cdot m k^{2}+m \frac{(a+b)^{2}}{2} \)
c. \( m k^{2}+m \frac{b^{2}}{2} \)
D. \( m k^{2}+m b^{2} \)


Match the columns
\( \begin{array}{ll}\text { A } & \text { B } \\ \text { i) } h \text { image }=h \text { object } & \text { a) } M<1 \\ \text { ii) } h \text { image }>h \text { object } & \text { b) } M>1 \\ \text { iii) } h \text { image }<h \text { object } & \text { c) } M=1\end{array} \)
\( \mathbf{A} \cdot i-a, i i-c, i i i-b \)
B \( . i-b, i i-a, i i i-c \)
\( \mathbf{c} \cdot i-c, i i-b, i i i-a \)
D. \( i-a, i i-b, i i i-c \)


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


\( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+3 \mathrm{H}_{2} \mathrm{S}+8 \mathrm{H}^{+} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}+ \)
3S.
If true enter 1 else 0
\( A \)


The breathing cycle is rhythmic whereas, exchange of gases is a continuous process. Justify this statement.


Which is not correct for Earthworm
A. It walks with a speed of \( 25 \mathrm{cm} / \mathrm{min} \)
B. It can remain without oxygen for 630 hrs
C. Life span is 3.510 years
D. Setae easily dissolve in KOH


State whether true or false:
All the elements having one electron in their outermost shell are metals.
A. True
B. False


A person carrying a whistle emitting
continuously a note of \( 272 H z \) is running towards a reflecting surface with a speed of \( 18 k m / \)hour. speed of
sound in air is \( 45 m / s . \) The number of
beats heard by him is:
A . 4
B. 6
\( c \cdot 8 \)
\( D \cdot 3 \)


Give reasons.
\( \boldsymbol{E}^{o} \) value for \( \boldsymbol{M} \boldsymbol{n}^{3+} / \boldsymbol{M} \boldsymbol{n}^{2+} \) couple is
much more positive than that for \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} / \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \)


A steel wire of length \( L \) and area of cross-section A shrinks by \( \Delta l \) during
night. Find the tension developed at
night if Young's modulus is \( Y \) and wire is clamped at both ends
A. \( \frac{A Y L}{\Delta l} \)
в. \( A Y L \)
c. \( A Y \Delta l \)
D. \( \frac{A Y \Delta l}{L} \)


calculate \( \Delta G_{f}^{\ominus} \) of the reaction:
\( \boldsymbol{A} \boldsymbol{g}^{\oplus}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C l}^{\ominus}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \)
Given \( : \Delta G^{\ominus_{A g C l}}=-109 k J m o l^{-1} \)
\( \Delta G_{\left(C l^{\ominus}\right)}^{\ominus}=-129 k J m o l^{-1} \)
\( \Delta G_{\left(A g^{\oplus)}\right.}^{\ominus}=-77 k J m o l^{-1} \)
в. \( -57 k J \) mol\( ^{-} \)
c. \( 57 k J \) mol \( ^{-1} \)
D. \( 97 k J \) mol \( ^{-1} \)


An inductor with an inductance of
\( 3.00 H \) and a resistance of \( 7.00 \Omega \) is
connected to the terminals of a battery
with an emf of \( 12.0 \mathrm{V} \) and negligible
internal resistance. Find the initial rate
of increase of current in the circuit.


A certain compound when burnt gave three oxides. The first turned lime water
milky, the second turned cobalt chloride
paper pink and the third formed an
aqueous solution of pH 3 nearly. The elements present in the compound are:
\( \mathbf{A} \cdot C, S, O \)
B. \( C, H, N a \)
c. \( C, H, S \)
D. \( C, H, C a \)


The derivative of \( f(x)=\sin ^{2} 2 x \)


Three bodies of the same material and
having masses \( \mathrm{m}, \mathrm{m} \) and \( 3 \mathrm{m} \) are at
temperatures \( 45^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \) and \( 60^{\circ} \mathrm{C} \)
respectively. If the bodies are brought in thermal contact, the final temperature
will be.
A \( \cdot 45^{\circ} \mathrm{C} \)
В. \( 54^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 52^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)


Which one of the following is true about Bulk Modulus of elasticity?
A. It is the ratio of compressive stress to volumetric strain
B. It is the ratio of compressive stress to linear strain
c. It is the ratio of tensile stress to volumetric strain
D. It is the ratio of tensile stress to linear strain


The length of a rectangle is \( 3 \mathrm{cm} \) more than its width and area is \( 54 \mathrm{cm}^{2} \). Find
the perimeter of the rectangle.
\( \mathbf{A} \cdot 25 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 35 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


Factorise the following:
\( 2 x^{2}-7 x-15 \)
A \( .(x+3)(x+4) \)
В. \( (2 x+3)(x+5) \)
c. \( (2 x+3)(x-5) \)
D. \( (x-2)(x-8) \)


A candidate scored \( 25 \% \) marks and
failed by 30 marks and another candidate scored \( 50 \% \) marks and got 20 marks more than the minimum
marks required to pass. Find the maximum marks and the passing mark.


How many atom(s) of \( B e C l_{2} \) lie in the
same plane?


What is the basic formula for starch?
\( \mathbf{A} \cdot\left(C_{6} H_{12} O_{6}\right)_{n} \)
В \( \cdot\left(C_{6} H_{10} O_{5}\right)_{n} \)
\( \mathrm{c} \cdot\left(C_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) \)
D \( \cdot\left(C_{6} H_{12} O_{4}\right)_{n} \)


According to modern atomic theory
atoms of argon and calcium have same
atomic weight, these are known as:
A. Isobars
B. Isotopes
c. None of these
D. Both a and


The distance between the parallel planes given by the equations, \( \vec{r} .(2 \hat{i}- \) \( \mathbf{2} \hat{\mathbf{j}}+\hat{\boldsymbol{k}})+\mathbf{3}=\mathbf{0} \) and \( \vec{r} \cdot(\mathbf{4} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}})+\mathbf{5}=\mathbf{0} \) is -
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 1 / 6 \)


Copper and Carbon wires are connected in series and the combined resistor is
kept at \( 0^{\circ} \mathrm{C} \). Assuming the combined resistance does not vary with
temperature, the ratio of the resistances of Carbon and Copper wires
at \( 0^{\circ} C \) is:
(Temperature coefficients of resistivity of Copper and Carbon respectively are \( \left.4 \times 10^{-3} /^{\circ} C \text { and }-0.5 \times 10^{-3} /^{\circ} C\right) \)
\( A \)
в. 6
\( c \cdot 2 \)
\( D \)


Who among the following scientist was awarded the Nobel Prize in 1961 for
tracing the path of carbon in photosynthesis?
A. Huber
B. Calvin
c. Hatch
D. Rubin


\( \underbrace{\frac{k}{k}} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & \mathbf{1}\end{array}\right] \) then \( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A})=? \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}1 & -2 \\ -2 & 1\end{array}\right] \)
в. \( \left[\begin{array}{cc}2 & 1 \\ 1 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & -2 \\ -2 & -1\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & 2 \\ 2 & -1\end{array}\right] \)


A lines makes angles \( \frac{\boldsymbol{\alpha}}{2}, \frac{\boldsymbol{\beta}}{2}, \frac{\gamma}{2} \) with
positive direction of coordinate axes, then \( \cos \alpha+\cos \beta+\cos \gamma \) is equal to
A . -1
B. 1
\( c \cdot 2 \)
D. 3


Solve :
\( \int \frac{x+4}{x^{3}+3 x^{2}-10 x} d x \)
A \( \cdot \frac{2}{5} \ln |x|-\frac{3}{7} \ln |x-2|+\frac{1}{35} \ln |x+5|+c \)
B. \( -\frac{2}{5} \ln |x|+\frac{3}{7} \ln |x-2|-\frac{1}{35} \ln |x+5|+c \)
c. \( \frac{2}{5} \ln |x|+\frac{3}{7} \ln |x-2|+\frac{1}{35} \ln |x+5|+c \)
D. \( -\frac{2}{5} \ln |x|-\frac{3}{7} \ln |x-2|-\frac{1}{35} \ln |x+5|+c \)


Find the highest common factor of the
monomial.
\( 6 a^{2} b^{2} c \) and \( 27 a b c^{3} \)


The apparent depth of water in a
cylindrical water tank of diameter \( 2 R \)
\( \mathrm{cm} \) is reducing at the rate of \( x \mathrm{cm} / \mathrm{min} \)
when water is being drained out at a
constant rate. The amount of water
drained in \( c c / \) minute is: \( \left(n_{1}=\right. \)
refractive index of air, \( n_{2}= \) refractive
index of water)
A \( \cdot \frac{x \pi R^{2} n_{1}}{n_{2}} \)
В \( \cdot \frac{x \pi R^{2} n_{2}}{n_{1}} \)
\( \mathbf{c} \cdot \frac{2 \pi R n_{1}}{n_{2}} \)
D. \( \pi R^{2} x \)


Which of the following is an endothermic
reaction?
\( \mathbf{A} \cdot 2 H_{2}+O_{2} \rightarrow 2 H_{2} O \)
\( \mathbf{B} \cdot C_{(g r a p h i t e)}+H_{2} O_{\rightarrow} C O_{(g)}+H_{2(g)} \)
\( \mathbf{c} \cdot 2 N a O H+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
D. \( C_{2} H_{5} O H+3 O_{2} \rightarrow 2 C O_{2}+3 H_{2} O \)


Two dice are thrown The events \( A, B \)
and \( C \) are as follows:
A : getting an even number on the first die
B : getting an odd number on the first die
C : getting the sum of the numbers on the dice \( \leq 5 \)
Describe the events
(i) \( A^{\prime} \)
(ii) not \( \boldsymbol{B} \)
(iii) \( \boldsymbol{A} \) or \( \boldsymbol{B} \)
(iv) \( A \) and \( B \)
(v) \( A \) but not \( C \)
(vi) \( B \) or \( C \)
(vii) \( B \) and \( C \)
(viii) \( \boldsymbol{A} \cap \boldsymbol{B}^{\prime} \cap \boldsymbol{C}^{\prime} \)


In the following \( I \) refers to current and
other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:
A \( \cdot M L^{-3} T^{-3} I^{2} \)
B. \( M^{-1} L^{-3} T^{3} I^{2} \)
c. \( M^{-1} L^{3} T^{3} I \)
D. \( M^{-1} L^{-3} T^{3} I \)


\( \tan ^{-1}\left(\tan \frac{2 \pi}{3}\right)= \)
A \( \cdot \frac{\pi}{3} \)
B \( \cdot \frac{2 \pi}{3} \)
c. \( -\frac{\pi}{3} \)
D. \( -\frac{2 \pi}{3} \)


The magnetic field of a solenoid carrying a current is similar to that of a
B. bar magnet
c. toroid
D. none


The value of Planck's constant is
\( 6.63 \times 10^{-34} J-s . \) The velocity of light
is \( 3 \times 10^{8} m / \) sec. Which value is closest
to the wavelength in nanometer of a
quantum of light with frequency of \( 8 \times \) \( 10^{15} s e c^{-1} ? \)
A \( .5 \times 10^{-18} \)
B . \( 4 \times 10^{1} \)
\( c \cdot 3 \times 10^{7} \)
D. \( 2 \times 10^{-25} \)


The shaded region is represented by the
inequation:
A \( . y \geq x \)
В . \( y \geq-x \)
c \( \cdot y \geq|x| \)
D・ \( y \leq|x| \)


A ray of light fall normally on the face of a glass prism \( (n=1,5) . \) Find the angle of prism, if the rayjust fails to emerge from the second surface.


Assertion
The given equation \( \boldsymbol{x}=\boldsymbol{x}_{0}+\boldsymbol{u}_{0} \boldsymbol{t}+ \)
\( \frac{1}{2} a t^{2} \) is dimensionally correct, where
is the distance travelled by a particle in
time \( t, \) initial position \( x_{0}, \) initial velocity
\( u_{0} \) and uniform acceleration a is along the direction of motion
Reason
Dimensional analysis can be used for checking the dimensional consistency or homogeneity of the equation.
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 oxalic acid is acted upon by sulphuric acid, some products are formed. Oxidation state of carbon in the
product/s formed is/are:
This question has multiple correct options
A. 0
B. +2
\( c \cdot+4 \)
D. - 4


Which one of the following is best catalyst for the reaction shown below? \( C H_{3}\left(C H_{2}\right)_{8} C H_{2} B r \frac{K C N}{b e n z e n e} C H_{3}\left(C H_{2}\right) \)
\( A \)
в.
\( c \)
D.


A conveyor belt is moving horizontally with a uniform velocity of \( 2 \mathrm{m} / \mathrm{sec} \) Material is dropped at one end at the rate of \( 5 \mathrm{kg} \)./sec. and discharge at the other end. Neglecting the friction, the force required to move the belt is (N).
A . 10
B . 15
c. 20
D. 40


A hydrogen atom emits a photon corresponding to an electron transition from \( n=5 \) to \( n=1 . \) The recoil speed of
hydrogen atom is almost
\( \mathbf{A} \cdot 10^{-4} m s^{-1} \)
B. \( 2 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 4 m s^{-1} \)
D. \( 8 \times 10^{2} m s^{-1} \)


What is the dimensional formula of
resistance?
\( \mathbf{A} \cdot\left[M^{-1} L^{-2} T^{4} A^{-2}\right] \)
В \( \cdot\left[M L^{2} T^{-5} A^{-3}\right] \)
C \( \cdot\left[M^{-1} L^{-2} T^{4} A^{2}\right] \)
D. None of these


What do you call the angle of inclination
of the axis of the magnetic needle to the horizontal plane when suspended freely
\( ? \)
A. Angle of inclination
B. Angle of variation
c. Angle of declination
D. None of the above


\( \operatorname{det}\left\{\begin{array}{lll}18 & 40 & 89 \\ 40 & 89 & 198 \\ 89 & 198 & 440\end{array}\right\}= \)
A . -8
B. -
\( c .-1 \)
\( D \)


Use Euclid's division algorithm to find
the HCF of:
(i) 135 and 225
(ii) 196 and 38220 (iii)
867 and \( 255 . \) Enter the highest HCF amongst the following.


Let \( A \) be a set containing \( n \) elements. \( A \) subset \( P \) of the set \( A \) is chosen at
random.The set A is reconstructed by replacing the elements of \( P \) and
another subset \( Q \) of \( A \) is chosen at
random. The probability that \( \boldsymbol{P} \cap \boldsymbol{Q} \)
contains exactly \( m(m<n) \) elements is
\( ^{A} \cdot \frac{3^{n \cdot m} \cdot m^{n}}{^{n}} \)
В. \( \frac{n_{C_{m}} \times 3^{m}}{4^{n}} \)
c. \( \frac{n_{m_{m} \times 3^{n . m}}}{4^{n}} \)
D. None of these


Select wrong option among the following.
A. Tetravalency and catenation are two characteristic features of carbon which give rise to large number of compounds.
B. Silicon forms compounds with hydrogen which have chains of up to seven or eight atoms.
C. All carbon compounds are studied under organic chemistry.
D. Carbon forms very strong bond with other atoms because of its small size.


Explain the formation of a chemical
bond.


f \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}, \) prove that
\( \frac{2 x}{1-x^{2}}+\frac{2 y}{1-y^{2}}+\frac{2 z}{1-z^{2}}= \)
\( \frac{2 x}{1-x^{2}} \frac{2 y}{1-y^{2}} \frac{2 z}{1-z^{2}} \)


Which of the following compounds is an
imine?
\( A \)
\( B \)
\( c \)
D.


The number of integral terms in the expansion of \( (2 \sqrt{5}+\sqrt[66]{7})^{642} \)
A. 105
B. 107
\( c .321 \)
D. 108


Modulus of Elasticity is dimensionally equivalent to:
A. Stress
B. Surface tension
c. Strain
D. coefficient of viscosity


Write scientific name of any two plant
and any two animals?


Which of the following cannot be used for the preparation of iodoform?
A. Acetone
B. Methanol
c. Ethanol
D. Acetaldehyde


If a coin is tossed by a boy in a moving train and it falls behind him, then the motion of the train is
A. Uniform
B. Accelerated
C. Retarded
D. Along a circular track


\( A 5 \times 5 \times 5 \) cube is formed by using1 \( x \)
\( 1 \times 1 \) cubes if we add another layer of
\( \operatorname{such} 1 \times 1 \times 1 \) cube in the \( 5 \times 5 \times 5 \)
cube What will be the number of \( 1 \times \)
\( 1 \times 1 \) cubes in the newly formed cube?
A .216
в. 343
c. 294
D. 264


Which wave will have larger energy:
A. High frequency
B. Large amplitude
c. Both A and B
D. None of the above


\( H_{2} O_{2} \) used in rocket has the
concentration:
A . \( 50 \% \)
B. \( 70 \% \)
\( c .30 \% \)
D. \( 90 \% \)


The longest stage of meiosis is
A. Zygotene
B. Diplotene
c. Pachytene
D. Diakinesis


The function \( y=\frac{2-x^{2}}{x^{4}} \) takes on
equal values at the end-points of the interval \( [-1,1] . \) Is Rolle's theorem valid in
this interval?


Find the value of \( f(0) \) so that the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( 8\left(\frac{1-\cos ^{2} x+\sin ^{2} x}{x^{2}}\right), x \neq 0 \) is
continuous


Which of the following methods is/are correct for the synthesis of :
A. \( \mathrm{PhBr} \frac{(1) \mathrm{Li}(2) \mathrm{CuII}(3) \mathrm{Pr} \mathrm{COC}}{(4) 2 \mathrm{n}-\mathrm{Hg} / \mathrm{HCl}} \)
B. \( \mathrm{PhCOPr} \quad \) Zn-Hg/HCl
\( c \)
\( \mathrm{PhCOPr} \frac{\mathrm{NH}_{2} \mathrm{NH}_{2}}{_{\mathrm{OH}, \Delta}^{\circ}} \)
\( D \)


Fill in the blanks:
The of water is defined as the
constant temperature at which water changes to steam.
A. melting point
B. boiling point
c. saturation point
D. all of the above


What is psuedo first order reaction? Give an example.


If the projection of \( \vec{a} \) on \( \vec{b} \) and the projection of \( \vec{b} \) on \( \vec{a} \) are equal then the angle between \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) is
\( A \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{2 \pi}{3} \)


The area of rhombus is \( 119 \mathrm{cm}^{2} \) and its
perimeter is \( 56 \mathrm{cm} . \) Find its height.


When the current through the electromagnet of a relay reaches a particular value
A. It breaks the circuit
B. It open the circuit by pulling in an iron contact
c. It closes the circuit by pulling in an iron contact
D. Both A or C


From the two allotropes of sulphur, Rhombic sulphur and Monoclinic sulphur, which is more stable?
A. Rhombic
B. Monoclinic
c. Both are equally stable
D. None


Find the potential energy of an electric dipole (length \( 4 \mathrm{cm} \) ) each experiences a torque of \( 4 \sqrt{3} \mathrm{Nm} \) placed in a from
electric field angle \( 60^{\circ} q=1+n c \)


Which of the following is the most
stable state when two atoms come
closer to each other to form a molecule?
A. When the bond is formed, the energy is minimum
B. When the atoms touch each other, the energy is zero
C. When the atoms are isolated, the energy is minimum
D. None of these


In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the centre. Identical charges are placed at \( (n-1) \) corners. At the centre, the magnitude of intensity is \( \mathrm{E} \) and the potential is V.The ratio V/E is
\( A \cdot r n \)
B. \( r(n-1) \)
\( c \cdot(n-1) / r \)
\( D \cdot r(n-1) / n \)


If \( \frac{a-b}{b-c}=\frac{a}{b}, \) then \( a, b, c \) are in
\( A \cdot G P \)
в. нР
\( c \cdot A P \)
D. sp


A body with moment of inertia \( 3 K g m^{2} \) is
at rest. A torque of \( 6 N m \) applied on it rotates the body for 20 seconds. The angular displacement of the body is
A. 800 radians
B. 600 radians
c. 400 radians
D. 200 radians


Due to an impulse, the change in the momentum of a body is \( 1.8 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} . \) If the duration of the impulse is \( 0.2 \mathrm{s} \) then what is the force produced in it?
\( A \cdot 9 N \)
B. 8 N
\( c \cdot 7 N \)
\( D \cdot 6 N \)


A line parallel to the base of a triangle cuts the triangle into two regions of equal area. This line also cuts the altitude into two parts. Find the ratio of the two parts of the altitude.
A . 1: 1
B. 1: 2
c. \( 1: \sqrt{2} \)
D. \( 1:(\sqrt{2}+1) \)


Assertion
Swimming is possible due to third law
of motion
Reason
Rebounding of rubber ball takes place
due to third law of motion.
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


Parthenogenesis is the development of
A. Fruit without hormones
B. Fruit without fertilisation
c. Egg without fertilisation
D. Embryo without fertilisation


What is Primordial Soup?


Write balanced chemical equations to show:

The behavior of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) as an acid when
it reacts with Magnesium.


Integrate \( \int_{2}^{3}\left(2 x^{2}+1\right) d x \)


An important postulate of Dalton's
atomic theory is:
A. an atom contains electrons, protons and neutrons
B. atom can neither be created nor destroyed nor divisible
C. all the atoms of an element are not identical
D. all the elements are available in nature in the form of
atoms


The process of photosynthetic photophosphorylation was described by
A. Blackman
в. ні||
c. Arnon
D. Benson


The chordate which has teeth on tongue
belongs to
A. Protochordates
B. Pisces
c. Frog
D. Lamprey


The rate law for a reaction between
substances \( A \) and \( B \) is given by Rate\( = \)
\( \boldsymbol{k}[\boldsymbol{A}]^{n}[\boldsymbol{B}]^{m} \) On doubling the
concentration of \( A \) and halving the concentration of \( \mathrm{B} \), the ratio of the new
rate to the earlier rate of reaction will
be:
\( A \cdot m+n \)
B. n-m
\( c \cdot 2^{n-m} \)
D. \( \frac{1}{2^{m+n}} \)


The second most abundant metal
present in the crust of the earth is :
A. \( C a \)
в. \( A l \)
c. \( C u \)
D. \( F e \)


If both the wires are pulled for the same extension, then:
A. \( W_{A}>W_{B} \)
в. \( W_{A}<W_{B} \)
\( \mathbf{c} \cdot T_{A}<T_{B} \)
D \( \cdot Y_{A}<Y_{B} \)


An A.C. of \( 50 \mathrm{Hz} \) and \( 1 \mathrm{A} \) peak value flows
in primary coil transformer whose mutual inductance is \( 1.5 \mathrm{H} \). Then peak
value of induced emf in the secondary coil is:
A. \( 150 v \)
B. \( 150 \pi v \)
c. \( 300 \vee \)
D. 200 V


What is the refractive index of a prism
whose angle \( A=60^{\circ} \) and angle of
minimum deviation \( \boldsymbol{d}_{\boldsymbol{m}}=\boldsymbol{3} \boldsymbol{0}^{\boldsymbol{o}} \) ?
A \( \cdot \sqrt{2} \)
в. \( \frac{1}{\sqrt{2}} \)
c. 1
D. \( \frac{1}{\sqrt{3}} \)


\( \overrightarrow{\boldsymbol{E}} \times \overrightarrow{\boldsymbol{B}} \) equals to


\( \frac{8}{8} \)


What is the function of a non-sense
codon?
A. To release polypeptide chain from tRNA.
B. To form an unspecified amino acid.
C. To terminate the message of a gene controlled protein synthesis.
D. To convert a sense DNA into non sense DNA.


Which increases average
kinetic energy?
A. An increase in the reaction concentration
B. An increase in temperature
c. A decrease in pressure
D. Catalysis
E \( . p H \)


Which of the following is false about food chain?
A. Grazing food chain is major conduit of energy for aquatic ecosystem.
B. In terrestrial ecosystem, large fraction of energy flows through detritus food chain
C. Primary consumers belong to first trophic level
D. Detritus food chain begins with dead organic matter.
E. Cockroaches and crows are omnivores


Simplify \( 3 x(4 x-5)+3 \) and find its
value for \( (\mathrm{i}) x=3 \)
(ii) \( x=\frac{1}{2} \)


If the position vector of a point \( \boldsymbol{R} \) which divides the line segment joining points \( P(\hat{i}+2 \hat{j}+\hat{k}) \) and \( Q(-\hat{i}+\hat{j}+\hat{k}) \) in the
ratio 2: 1 internally is \( -\frac{1}{3} \hat{i}+\frac{a}{3} \hat{j}+\hat{k} \)
What is the value of \( a ? \)


What is menstruation?
A. Its a women disease recurring every month.
B. Its a normal reproductive process in mature females.
C. When fertilization does not occur, the released egg, and the thickened lining of the uterus along with its blood vessels are shed off
D. Both B and C.


Potassium permanganate is:
A. purple solution
B. brown-orange liquid
C. green gas
D. silver-gray liquid
E . yellow-orange when burned in a flame


The condition which cannot be detected
by ECG is
A. Blockage of coronary artery
B. Gastric ulcer
c. Defect of heart valve
D. Angina


Perpendicular distance between \( 2 x+ \) \( 2 y-z+1=0 \) and \( 2 x+2 y-x+4= \)
0 is


Vector sum of two vectors holds the
A. multiplicative property
B. distributive property
c. associative property
D. commutative property


If \( 0<A<\frac{\pi}{6} \) then \( A(\csc A) \) is:
\( A \cdot<\frac{\pi}{3} \)
в. \( >\frac{\pi}{3} \)
\( c \cdot=\frac{\pi}{3} \)
D. \( =\frac{\pi}{6} \)


A heat engine receives 150 Joules of
heat energy and performs 70 Joules of work. If heat loss in the surrounding is zero. Find out by what value does the internal energy of the system change?
A . \( 0 . J \)
B. \( 40 J \)
c. \( 80 J \)
D. \( 120 J \)
E . \( 150 J \)


The pH of solution in a cell : Reference
electrode \( \| \boldsymbol{H}_{3} \boldsymbol{O}^{+}(?) \boldsymbol{H}_{2} \mid \boldsymbol{P} \boldsymbol{t} \) can be
determined by using the formula \( \boldsymbol{p} \boldsymbol{H}= \) \( -\frac{\left[\boldsymbol{E}_{\text {cell}}+\boldsymbol{E}_{\text {ref}}\right]}{\mathbf{0 . 0 5 9}} . \) However, the use of
hydrogen electrode to determine pH is usually ignored. Which are the correct facts about this observation?
This question has multiple correct options
A. The use of H-electrode hinders in the establishment of the equilibrium at the surface and the electrode no Ionger behaves reversibly
B. The use of H-electrode is usually restricted if solution contains reducible materials
c. The use of H-electrode is usually restricted as it is easily poisoned
D. The use of quinhydrone electrode as electrode is usually preferred as reference electrode \( \left|H_{3} O^{+}, Q, Q H_{2}\right| A u \)


Among the following, elastomers are:
This question has multiple correct options
A. Natural rubber
B. Low sulphur rubber
c. Buna-s
D. ButyI rubber


The distance between two rails of
railway track is \( 1.6 \mathrm{m} \) along a curve of radius \( 800 \mathrm{m} . \) The outer rail is raised
above the inner rail by \( 10 \mathrm{cm} . \) With what maximum speed can a train be safely driven along the curve
A . 22.2 \( \mathrm{m} / \mathrm{sec} \)
B. 12.2 \( \mathrm{m} / \mathrm{sec} \)
c. \( 42.2 \mathrm{m} / \mathrm{sec} \)
D. \( 90.9 \mathrm{m} / \mathrm{sec} \)


Find the value of \( K \) for which the points
(7,-2),(5,1) and \( (3, K) \) are collinear.


A lift of mass \( 100 \mathrm{kg} \) starts moving from
rests in the upward direction. Fig shows
the variation if speed of the lift, \( \boldsymbol{T}_{1}, \boldsymbol{T}_{2} \)
and \( T_{3} \) stand for tension in the rope
form zero to two seconds, two to six
seconds, six to seven seconds
respectively then:
A \( \cdot T_{1}: T_{2}: T_{3}:: 1: 1: 1 \)
B. \( T_{1}: T_{2}: T_{3}:: 6: 5: 3 \)
\( \mathbf{c} \cdot T_{1}: T_{2}: T_{3}:: 3: 5: 6 \)
D. \( T_{1}: T_{2}: T_{3}:: 6: 5: 6 \)


\( \operatorname{If}\left(1+3 x+3 x^{2}\right)^{20}=a_{0}+a_{1} x+ \)
\( \boldsymbol{a}_{2} \boldsymbol{x}^{2}+\boldsymbol{a}_{3} \boldsymbol{x}^{3}+\boldsymbol{a}_{4} \boldsymbol{x}^{4}+\boldsymbol{a}_{5} \boldsymbol{x}^{5}+\ldots \ldots+ \)
\( a_{40} x^{40}, \) then find the value of \( 2 a_{2}- \)
\( 6 a_{3}+12 a_{4}-20 a_{5} \dots \dots+1560 a_{40} \)
A . 3450
B. 3350
\( c .3540 \)
D. 2150


Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to
displacement current.


You have been provided with three testtubes. One of them contains distilled
water and the other two contain an
acidic solution and a basic solution
respectively.


A difference of \( 1^{\circ} \mathrm{C} \) is as the
difference of \( 1 K \)


Silver is extracted from \( A g_{2} S \) by
A. fusing it with KCl and electrolyzing the melt
B. reducing it with Zinc
c. treating with sodium cyanide followed by zinc
D. rosting it and reducing the resultant product by smelting


The earth retains its atmosphere
because
A. the value of the escape is less than the average kinetic of atmospheric molecules.
B. the value of the escape is more than the average kinetic of atmospheric molecules
c. the earth rotates
D. the earth is spherical


Heart of frog differs from that of rabbit by presence of
A. sinus venosus
B. Four chambers
c. Mitral valve
D. Two aortae


Animals, plants and bacteria are
A. biotic component
B. abiotic component
c. renewable component
D. non-renewable component.


A sphere rolling on a horizontal rough
surface collides elastically with a
smooth vertical wall, as shown in
Figure. State which of the following statements is true or false.

After collision the friction the linear
force acts on the sphere such that it decreases the linear speed and
increases the angular speed.


Construct a triangle \( P Q R \), whose
perimeter is \( 22 \mathrm{cm} \) and whose sides are
in the ratio \( 2: 4: 5 . \) Measure the sides
of the triangle.
A .5,7,10
в. 4,8,10
c. 5,8,9
D. None of these


The Van't Hoff equation is :
A \( \cdot \Delta G^{\circ}=R T l o g_{e} K_{p} \)
в. \( -\Delta G^{\circ}= \) RTloge \( K_{p} \)
\( \mathbf{c} \cdot \Delta G^{\circ}=R T^{2} l n K_{p} \)
D. None of the above


Two particles having position vectors \( \overrightarrow{\boldsymbol{r}}=(\mathbf{3} \overrightarrow{\boldsymbol{i}}+\mathbf{5} \boldsymbol{j}) \boldsymbol{m} \) and \( \overrightarrow{\boldsymbol{r}}_{2}=(-\mathbf{5} \boldsymbol{i}+\boldsymbol{3} \boldsymbol{j}) \boldsymbol{m} \)
are moving with velocities \( \overrightarrow{\boldsymbol{V}}_{1}=(\mathbf{4} \hat{\mathbf{i}}- \)
\( 4 \hat{j}) m s^{-1} \) and \( \vec{V}_{2}=(a \hat{i}-3 \hat{j}) m s^{-1} . \) If
they collide after 2 seconds, the value
of \( a \) is
\( A \cdot-2 \)
B . -4
\( c \cdot-6 \)
\( D .-8 \)


Let \( A=\{0,1,2,3,4\}, B=\{1,-2,3,4,5,6\} \)
and \( C=\{2,4,6,7\} \)
(i) Show that \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \cup \)
\( \boldsymbol{B}) \cap(\boldsymbol{A} \cup \boldsymbol{C}) \)
(ii) Verify this relation using Venn diagram.


Identify which of the following energy
released when a large nucleus splits
into smaller nuclei.
A. nuclear energy
B. thermal energy
c. radiant energy
D. sound
E. potential energy


If \( N_{1}, N_{2}, N_{3}, \dots \) are the number of
molecules with molecular masses
\( M_{1}, M_{2}, M_{3}, \ldots \) respectively, then
mass average molar mass is expressed
as :
\( ^{\mathbf{A}} \cdot \frac{\sum N i M i^{2}}{\sum N i M i} \)
в. \( \frac{\sum N i M i}{\sum N i} \)
c. \( \frac{\sum M i^{2}}{\sum N i} \)
D. \( \frac{\sum N i M i}{\sum M i} \)


The focal length of an equiconcave lens is \( \frac{3}{4} \) times of radius of curvature of its surfaces. Find the refractive index of the
material of the lens. Under what
condition will this lens behave as a
converging lens?


Variance of the first 11 natural numbers
is:
A \( \cdot \sqrt{5} \)
B. \( \sqrt{10} \)
\( c \cdot 5 \sqrt{2} \)
D. 10


If \( \cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac{x}{m}, x \in \)
\( \left(0, \frac{\pi}{4}\right) \).Find \( m \)


The change in the value of \( g \) at a height
\( h \) above the surface of the earth is the
same as at a depth d below the surface of the earth.When both \( h \) and \( d \) are
much smaller than the radius of
earth,then which one of the following is
true?
A \( . a=h / 2 \)
В. \( d=3 h / 2 \)
c. \( d=2 h \)
\( \mathbf{D} \cdot h=d \)


The following are the formulae for three compounds 2,3 -dichorobutane written
in non-eclipsed conformations. In each
instance, tell which compounds are enanatiomers and which are meso:
\( \mathbf{a} \)
A. (a) and (c) are enantiomers;(b) is meso
B. (a) and
(b) are enantiomers;(c) is meso
\( c \cdot(b) \) and
(c) are enantiomers;(c) is meso
D. none of these


According to Bohr's theory, the time averaged magnetic field at the centre (i.e nucleus) of a bydrogen atom due to the motion of electrons in the \( n^{t h} \) orbit
is propotional to : \( (n= \) principal quantum number)
\( \mathbf{A} \cdot n^{-3} \)
B . \( n^{-4} \)
\( c \cdot n^{-5} \)
D. \( n^{-2} \)


A plano-convex lens fits exactly into a plano-concave lens. Their plane
surfaces are parallel to each other. If the lenses are made of different material of
refractive indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is the
radius of curvature of the curved
surface of the lenses, then focal length
of the combination is :
A \( \cdot \frac{R}{\mu_{1}-\mu_{2}} \)
В. \( \frac{2 R}{\mu_{2}-\mu_{1}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{2-\left(\mu_{1}+\mu_{2}\right)} \)


Factorize:
\( a^{2}-(2 a+3 b)^{2} \)
\( \mathbf{A} \cdot-3(a+b)(a+3 b) \)
B \( \cdot 3(a+b)(a+3 b) \)
\( \mathbf{c} \cdot-3(a-b)(a-3 b) \)
D. \( 3(a+b)(a-3 b) \)


ff \( \left[\begin{array}{cc}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\gamma} & -\boldsymbol{\alpha}\end{array}\right] \) is square root of \( \boldsymbol{I}_{2}, \) then \( \boldsymbol{\alpha} \)
\( \beta \) and \( \gamma \) will satisfy the relation
A. \( 1+\alpha^{2}+\beta \gamma=0 \)
В. \( 1-\alpha^{2}+\beta \gamma=0 \)
C \( \cdot 1+\alpha^{2}-\beta \gamma=0 \)
D. \( -1+\alpha^{2}+\beta \gamma=0 \)


In a dicotyledonous stem, the sequence of tissues from the outside to the inside
is
A. Phellem, Pericycle, Endodermis, Phloem
B. Phellem, Phloem, Endodermis, Pericycle
C. Phellem, Endodermis, Pericycle, Phloem
D. Pericyle, Phellem, Endodermis, Phloem


Which of the following properties shows that light is a transverse wave?
A. Reflection
B. Interference
c. Diffraction
D. Polarization


Ribozyme is
A. RNA with enzyme activity
B. RNA without sugar
C. RNA without phosphate
D. RNA with extra phosphate


The area of cross-section of the two
arms of a hydraulic press are \( 1 \mathrm{cm}^{2} \) and
\( 10 \mathrm{cm}^{2} \) respectively (figure). A force of \( 50 \mathrm{N} \) is applied on the water in the thicker arm. What force should be
applied on the water in the thinner arm
so that the water may remain
in equilibrium?
A. 5 N
B. 10 N
\( c \cdot 25 N \)
D. 50 N


What is the pollutant produced from
industries and chemical factories?
A. Sediments
B. Radioactive substances
c. Toxic heavy metals
D. organic wastes


What is A?
\[
\begin{array}{c}
\text { ОН } \\
\mathbf{A}+\mathbf{H C N} \rightarrow \mathbf{C H}_{3} \mathbf{C H C N}
\end{array} \stackrel{\text { нзо+ }}{\longrightarrow} \text { ме }^{\text {ОН }}
\]


Which of the following statements is
correct about halogens?
A. they are all capable of exhibiting more than one oxidation states
B. they are all diatomic and form diatomic ions
C. they are all diatomic and form univalent ions
D. they are all reducing agents


16 divides \( n^{4}+4 n^{2}+11, \) if \( n \) is an odd
integer.
A. True
B. False


The constant \( k \) in Coulomb's law
depends upon
A. nature of medium
B. system of units
c. intensity of charge
D. both (a) and (b)