Two masses of \( 40 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are
connected by a weightless string
passing over a friction less pulley as
shown in the figure. The acceleration of
the system would be:
B. \( 0.8 \mathrm{ms}^{-2} \)
\( c \cdot 0.7 m s^{-2} \)
D. \( 0.5 \mathrm{ms}^{-2} \)


Prove that \( 4-3 \sqrt{2} \) is an irrational


Write the names of the monomers of the
following polymers:
(a) Bakelite
(b) Nylon - 6,6


Third period of the periodic table contains the following number elements:
\( A \cdot 2 \)
B. 18
\( c \cdot 8 \)
D. 32


Light waves producing interference have their amplitudes in the ratio 3: 2 The intensity ratio maximum and minimum of interference fringes is :
A . 36:
B. 9: 4
c. 25:
D. 6:


Balance the following redox reaction in
basic medium:
\( M n O_{4}^{-}+N O_{2}^{-} \longrightarrow M n O_{2}+N O_{3}^{-} \)
A \( \cdot 2 M n O_{4}^{-}+3 N O_{2}^{-}+H_{2} O \longrightarrow 2 M n O_{2}+3 N O_{3}^{-}+ \)
\( 2 O H^{-} \)
B . \( 2 M n O_{4}^{-}+4 N O_{2}^{-}+H_{2} O \longrightarrow M n O_{2}+3 N O_{3}^{-}+ \)
\( 5 O H^{-} \)
\( \mathrm{c} \cdot 2 \mathrm{Mn} \mathrm{O}_{4}^{-}+5 \mathrm{NO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{MnO}_{2}+3 \mathrm{NO}_{3}^{-}+ \)
\( 5 O H^{-} \)
D. None of these


Regardless of its electron configuration it must always be paramagnetic when it's a single, neutrally charged atom. Which of the following is this?
A. Carbon
B. Nitrogen
c. oxygen
D. Neon
E. Argon


Two bodies of different masses are
dropped from height of \( 16 m \) and \( 25 m \) respectively. The ratio ofthe times taken by them is
A \( \cdot \frac{25}{16} \)
в. \( \frac{16}{21} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{4}{5} \)


If two balls of some mass are dropped from the same height, would they fall down at the same time?


A sphere is rotating between two tough
inclined walls as shown in figure.

Coefficient of friction between each wall
and the sphere is \( 1 / 3 . \) If \( f_{1} \) and \( f_{2} \) be the
friction forces at \( P \) and \( Q . \) Then \( \frac{f_{1}}{f_{2}} \) is:
A \( \cdot \frac{4}{\sqrt{3}}+1 \)
B. \( \frac{1}{\sqrt{3}}+2 \)
c. \( \frac{4}{2}+\sqrt{3} \)
D. \( 1+2 \sqrt{3} \)


Two dice are thrown at a time, find the
probability that the sum obtained is
less than 6
\( A \cdot \frac{2}{9} \)
B. \( \frac{1}{4} \)
c. \( \frac{5}{18} \)
D. \( \frac{1}{3} \)


Two point white dots are \( 1 \mathrm{mm} \) apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at
which these dots can be resolved by the eye? [Take wave length of light =500 nm]
A . \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. None of these


Enzymes also act as a catalyst in biological process.
A. True
B. False


The diagram shows the change of phase of a substance on a temperature-time
graph. What is the boiling point of the substance?
\( \mathbf{A} \cdot t_{1}^{\circ} C \)
B . \( t_{2}^{\circ} C \)
c. \( t_{3} \circ C \)
D. \( t_{4}^{\circ} C \)


Derivate \( e^{\sqrt{2 x+1}} \) where \( x=12 \) w.r.t. \( x \)


Curd contains acid.
A. ascorbic
B. tartaric
c. lactic
D. acetic acid


Find a particular solution of the differential equation \( (x+1) \frac{d y}{d x}= \)
\( 2 e^{-y}-1, \) given that \( y=0 \) when \( x=0 \)


The domain of the function \( f(x)= \) \( \sqrt{\sec ^{-1}\left\{\frac{1-|x|}{2}\right\}} \)
A \( \cdot(-\infty,-3] \cup[3,+\infty) \)
B. \( [3,+\infty) \)
\( c . \Phi \)
D. \( R \)


Given the following standard molar enthalpies:
\( \Delta \boldsymbol{H}_{f}^{o} \) of \( \boldsymbol{C H}_{3} \boldsymbol{C N}(\boldsymbol{g})=\mathbf{8 8 k J} / \boldsymbol{m o l} \)
\( \Delta H_{f}^{o} \) of \( C_{2} H_{6}=-84 k J / m o l \)
\( \Delta \boldsymbol{H}_{\text {sublimation}}^{o} \) of \( \boldsymbol{C}(\boldsymbol{g} \boldsymbol{r})=\mathbf{7 1 7 k J} / \boldsymbol{m o l} \)
bond dissociation energy of \( N_{2}(g) \) and
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \) are \( \boldsymbol{9} \boldsymbol{4} \boldsymbol{6} \) and \( \boldsymbol{4} \boldsymbol{3} \boldsymbol{6} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m} \boldsymbol{o} \boldsymbol{l} \)
respectively, \( \boldsymbol{B} \cdot \boldsymbol{E}(\boldsymbol{C}-\boldsymbol{H})= \)
\( 410 k J / \) mol. Determine \( C-C \) and
\( C \equiv N \) bond energies respectively.
\( \mathbf{A} \cdot 366 k J / m o l ; 1095 k J / m o l \)
B. \( 366 k J / m o l ; 877 k J / m o l \)
c. \( 877 k J / m o l ; 366 k J / m o l \)
D. \( 877 k J / m o l ; 1095 k J / m o l \)


\( \gamma \) -rays has least penetrating power.
A. True
B. False


Which one of the following is not true?
\( \mathbf{A} \cdot A \backslash B=A \cap B^{\prime} \)
в. \( A \backslash B=A \cap B \)
C \( . A \backslash B=(A \cup B) \cap B^{\prime} \)
D. \( A \backslash B=(A \cup B) \backslash B \)


One litre of water weighs 1 kg. How many cubic millimetres of water will
weigh 0.1 gram?
\( \mathbf{A} \cdot 100 \) cubic \( \mathrm{mm} \)
B. 150 cubic mm.
c. 90 cubic \( \mathrm{mm} \)
D. 80 cubic mm.


For an isomerization \( \boldsymbol{X}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{Y}(\boldsymbol{g}), \) the
temperature dependency of equilibrium constant is given by :
\( \mathbf{n}=2-\frac{\mathbf{1 0 0 0}}{\mathbf{T}} \)
The value of \( \Delta_{r} S^{o} \) at \( 300 K \) is :
\( \mathbf{A} \cdot 2 R \)
в. \( \frac{2}{R} \)
c. \( 1000 R \)
D. None of these


A solid ball of radius \( R \) has a charge
density p given by \( \boldsymbol{p}=\boldsymbol{p}_{0}(\mathbf{1}-\boldsymbol{r} / \boldsymbol{R}) \) for
\( \mathbf{0} \leq \boldsymbol{r} \leq \boldsymbol{R} . \) The electric field outside the
ball is:
A \( \cdot \frac{p_{0} R^{3}}{\epsilon_{\sigma} r^{2}} \)
в. \( \frac{p_{0} R^{3}}{12 \epsilon_{0} r^{2}} \)
c. \( \frac{4 p_{0} R^{3}}{3 \epsilon_{0} r^{2}} \)
D. \( \cdot \frac{3 p_{0} R^{3}}{4 \epsilon_{0} r^{2}} \)


\( \int \frac{[\log (\log \boldsymbol{x})]^{\boldsymbol{m}}}{\boldsymbol{x} \log \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \frac{[\log (\log (x))]^{m+1}}{m+1}+c \)
B. \( \frac{[\log (\log (x))]^{m}}{m}+c \)
c. \( \frac{[\log (\log (x))]^{m+1}}{m}+c \)
D. \( \frac{[\log (\log (x))]^{m}}{m+1}+c \)


Enzyme renin is secreted by
A. Cells of stomach
B. Cells of intestine
C. The cortical cells of kidney
D. The cells of juxtaglomerular apparatus of kidney


At which point is the centre of gravity
situated in: A circular lamina.
A. At the centre of radius
B. At the centre of semi circular lamina
c. At the centre of circular lamina
D. can not say


An alternating voltage of 260 volt and \( \omega \) \( =100 \) radian/second, is applied in an
LCR
series circuit where \( \mathrm{L}=0.01 \mathrm{H}, \mathrm{C}=4 \times \)
\( 10^{-4} F \) and \( R=10 \Omega . \) the power supplied
by the source is:
A. 1000 w
в. 6760 w
\( c . \) 3380 \( w \)
D. 3000


In the direct current:
A. The direction of current is always positive
B. The direction of current is always negtive
C. The direction of current changes constantly
D. The direction of current is always in the same direction


Two sound speakers are driven in phase by an audio amplifier at frequency \( 600 H z . \) The speed of sound is \( 340 m / s \)
The speakers are on the \( y \) -axis, one at \( \boldsymbol{y}=+\mathbf{1 . 0 m} \) and the other at \( \boldsymbol{y}= \)
\( -1.0 m . \) A listener begins at \( y=0 \) and
walks along a line parallel to the \( y \) -axis
at a very large distance \( x \) away. How
many maxima can she possibly hear if she keeps walking in the same direction?


Acceleration is maximum at which
point on the graph?
\( \mathbf{A} \)
B
\( c \)
\( D \)
\( E \)


Select the incorrect statement from the
following:
A \( \cdot H^{+} \) can as \( H_{9} O_{4}^{+} \) in water
B. \( H_{2} \) is thermally stable
C. lonization of \( C H_{3} \mathrm{COOH} \) is slower than that of \( C H_{3} \)
COOD
D. Kinetic isotopic effect is observed when there is retardation in the rate if \( H_{2} O \) is replaced by \( D_{2} O \)


Prove: (+3)\( [+(-7)=(-4) \)


The correct order of energy of orbitals in
octahedral complex is:
A \( \cdot d_{x^{2}-y^{2}}=d_{z^{2}}>d_{x y}=d_{y z} \)
В . \( d_{z^{2}}>d_{x y}>d_{x^{2}-y} \)
c. \( d_{z^{2}}=d_{x y}>d_{x^{2}-y^{2}} \)
D. \( d_{x^{2}-y^{2}}>d_{x y}>d_{y z} \)


The product of acid hydrolysis of \( \mathrm{P} \) and
Q can be distinguished by:
A. Lucas Reagent
B. 2,4-DNP
C. Fehling's Solution
\( \mathrm{D} \cdot \mathrm{NaHSO}_{3} \)


Which of these ions are involved in
muscle contraction?
A. \( C a^{2+} \) and \( M g^{2+} \)
B. \( C a^{2+} \) and \( N a^{+} \)
c. \( N a^{+} \) and \( K^{+} \)
D. \( M g^{2+} \) and \( K^{+} \)


A bag contains 6 balls. Two balls are
drawn and found to be red. The
probability that five balls in the bag are red
A \( \cdot \frac{5}{6} \)
в. \( \frac{12}{17} \)
\( c \cdot \frac{1}{3} \)
D.


The fungus that grows on bread is known
as
A. Bread mould
B. Yeast
c. Bacteria
D. All of the above


The reflecting surface is given by \( y= \) \( \frac{10 L}{\pi} \sin \frac{\pi x}{5 L} . \) The co-ordinates of the
point where a horizontal ray becomes vertical after reflection is:
A \( \cdot \frac{5 L}{3}, \frac{5 \sqrt{3} L}{\pi} \)
B. \( \frac{5 \sqrt{3} L}{\pi}, \frac{5 L}{3} \)
c. \( \frac{5 L}{\sqrt{3}}, \frac{\pi L}{5} \)
D. \( \frac{\pi L}{5}, \frac{5 L}{\sqrt{3}} \)


The energy levels of a certain atom for
1st, 2nd and 3rd levels are \( \mathrm{E}, 4 \mathrm{E}_{1 \rightarrow 3} \) and
2E respectively. A photon of wavelength
\( \lambda \) is emitted for a transition \( 3 \rightarrow 1 \)
What will be the wavelength of emissions for transition \( 2 \rightarrow 1: \)
\( A \cdot \lambda / 3 \)
в. \( 4 \lambda / 3 \)
c. \( 3 \lambda / 4 \)
D. \( 3 \lambda \)


The weakest acid among the following
is
A. \( C H_{3} \) СООН
в. \( C H_{3} C H_{2} C O O H \)
c. \( \left(C H_{3}\right)_{2} \) СНСООН
D. \( \left(C H_{3}\right)_{3} C C O O H \)


The density of water in \( k g m^{-3} \) is :
A. 1000
в. 100
c. 10,000
D. 4000


Frictional force is more between which
type of surfaces?
A. Smooth
B. Rough
c. Both A and B
D. None of the above


Which of the following is not a part of
moss capsule?
A. Operculum
B. Peristome
c. Annulus
D. Protonema


If the value of an equilibrium constant
for a particular reaction is \( 1.6 \times 10^{12} \)
then at equilibrium the system will contain:
A. mostly products
B. similar amounts of reactants and products
c. all reactants
D. mostly reactants


A wave represented by \( \boldsymbol{y}= \) \( 100 \sin (a x+b t) \) is reflected from a
dense plane at the origin. If \( 36 \% \) of energy is lost and rest of the energy is reflected, then the equation of the
reflected wave will be
A \( . y=-8.1 \sin (a x-b t) \)
B. \( y=8.1 \sin (a x+b t) \)
c. \( y=-80 \sin (a x-b t) \)
D. \( y=-10 \sin (a x-b t) \)


If \( \sin \alpha+\sin \beta+\sin \gamma=0=\cos \alpha+ \)
\( \cos \beta+\cos \gamma \) then \( \sin ^{2} \alpha+\sin ^{2} \beta+ \)
\( \sin ^{2} \gamma= \)
A. \( -\frac{3}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{2}{3} \)
D. none of these


In crushing can experiment, the
vaccum inside the can causes
pressure
A. Increase
B. Decrease
c. No change
D. All


At \( 100^{\circ} \mathrm{C}, \) resistance of a conducting
coil is \( 4.2 \Omega . \) If the temperature
coefficient of resistance is \( 0.004^{\circ} \mathrm{C} \)
what will be the resistance of \( 0^{\circ} \mathrm{C} \) ? (in
ohm
\( A \cdot 3 \)
B. 5
\( c \cdot 4 \)
D. 3.5


Calculate the following limits. \( \lim _{x \rightarrow 3} \frac{x^{2}-5 x+6}{x-3} \)


Evaluate \( \int_{-\pi}^{\pi} \frac{2 x(1+\sin x)}{1+\cos ^{2} x} d x \)


Let \( \boldsymbol{J}, \boldsymbol{g}:\lfloor-\mathbf{1}, \boldsymbol{2}\rfloor \rightarrow \boldsymbol{K} \) be continuous
functions which are twice differential
on the interval \( (-1,2) . \) Let the values of
\( f \) and \( g \) at the points -1,0 and 2 be as given in the following table:
\( f(x)=\left\{\begin{array}{l}3 ; x=-1 \\ 6 ; x=0 \quad \text { and } g(x)= \\ 0 ; x=2\end{array}\right. \)
\( \left\{\begin{array}{l}0 ; x=-1 \\ 1 ; x=0 \\ 0 ; x=-1\end{array}\right. \)
In each of the intervals (-1,0) and
\( (0,2), \) the function \( (f-3 g)^{\prime \prime} \) never
vanishes. Then the correct statement(s)
is (are)
This question has multiple correct options
A \( \cdot f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly three solutions in (-1,0)\( \cup(0,2) \)
B. \( f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly one solutions in (-1,0)
C \( \cdot f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly one solutions in (0,2)
D. \( f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly two solutions in (-1,0) and exactly two solutions in (0,2)


Give the chemical equation for th following. Piece of calcium is dropped in water


A rope of length \( L \) and mass \( M \) is being
pulled on a rough horizontal floor by a
constant horizontal force \( \boldsymbol{F}=\boldsymbol{m} \boldsymbol{g} \). The
force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is \( 0.5 . \) Then, tension at the midway of the rope is:
A. \( \frac{M g}{4} \)
в. \( \frac{3 M g}{4} \)
c. \( \frac{M g}{8} \)
D. \( \frac{M g}{2} \)


In a given square \( A B C D, \) if the area of triangle \( A B D \) is \( 36 \mathrm{cm}^{2}, \) find
(i) the area of triangle \( B C D ; \) (ii) the
area of the square \( A B C D \)


The sum of the following series \( 1+6+ \) \( \frac{\mathbf{9}\left(\mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}\right)}{\mathbf{7}}+ \)
\( \frac{12\left(1^{2}+2^{2}+3^{2}+4^{2}\right)}{9}+ \)
\( \frac{15\left(1^{2}+2^{2}+\ldots+5^{2}\right)}{11}+\ldots . \) up to 15
terms is:
A . 7820
в. 7830
c. 7520
D. 7510


Two elements A and B have 3 and 4
shells respectively and the ratio of valence electrons is \( 1: 2 . \) When these two
metals are dropped in water in separate containers, what observations do you find? Justify your observation and write
periodic property.


In which of the following pairs the angle of dispersion will we maximum?
A. Yellow and green
B. Red and blue
c. Green and red
D. Blue and orange


Braille system is used for:
A. reading
B. writing
c. both reading and writing
D. hearing


Draw the structure of the following compound:
3-Bromo-4-phenylpentanoic acid


Which of the following statements is
not correct about the characteristics of
cathode rays?
A. They starts from the cathode and move towards the anode
B. They travel in straight line in the absence of an external electrical or magnetic field
C. Characteristics of cathode rays do not depend upon the material of electrodes in cathode ray tube
D. characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube


\( A B \) is a straight line and \( O \) is a pont
lying on \( A B . A \) line \( O C \) is drawn from \( O \)
such that \( \angle C O A=36^{\circ} . O D \) is a line
within \( \angle C O A \) such that \( \angle D O A=\frac{1}{3} \) \( \angle C O A \). If \( O E \) is a line within the \( \angle B O C \)
\( \angle B O E=\frac{1}{4} \angle B O C, \) then \( \angle D O E \) must
be:
A \( \cdot 60^{\circ} \)
В \( \cdot 132^{\circ} \)
\( c \cdot 144^{\circ} \)
D. \( 108^{\circ} \)


Which change in the system will drive
equilibrium to the left in the following reaction?
\( N_{2} O_{5}(g)=N O_{2}(g)+N O_{3}(g) \)
A. Increase the volume
B. Increase the pressure
c. Decrease the amount of \( N O_{3} \)
D. Increase the amount of \( N_{2} O_{5} \)


Three cubes whose edges measure
\( 3 c m, 4 c m \) and \( 5 c m \) respectively are
used to form a single cube. Find its edge. Also, find the surface area of the new cube.


An alternating voltage is represented as \( E=20 \sin 300 t . \) The average value of
voltage over one cycle will be?
A. zero
B. 10 volt
c. \( 20 \sqrt{2} \) volt
D. \( \frac{20}{\sqrt{2}} \) volt


The \( C r O_{3} \) on reaction with \( H C l \) and
NaOH(aq) gives, respectively:
A \( \cdot C r O_{2} C l_{2}, C r O_{4}^{2} \)
B. \( \operatorname{Cr}(O H)_{2}, C r O_{4}^{2} \)
c. \( C l_{2}, C r_{2} O_{7}^{2-} \)
D. \( C l_{2}, C r(O H)_{3} \)


If \( I=\int_{0}^{\pi} \frac{d x}{5+3 \cos x} \) then \( I \) equals
\( A \)
в. \( 2 \pi / 3 \)
c. \( \pi / 4 \)
D. 2\pi/\sqrt \sqrt


Which of the following is incorrect?
A. \( O_{2} \) is weaker oxidant than \( O_{3} \)
B. \( O_{2} \) has small bond length than \( O_{3} \)
c. Both \( O_{2} \) and \( O_{3} \) are paramagnetic
D. \( O_{3} \) is angular in shape


Select the correct statements.
a. There is asymmetry between converting work to heat and converting heat to work.
b. No process is possible in which the sole result is the absorption of heat
from a reservoir and its complete
conversion into work.
c. For every chemical reaction at
equilibrium, standard change in Gibbs
free energy is zero.
At constant temperature and pressure, chemical reactions are
spontaneous in the direction of
decreasing Gibbs energy. This question has multiple correct options
A. Statement a
B. Statement b
c. statement c
D. Statement d


The centre of curvature of a ..... mirror is
behind it.
A. convex
B. Concave
c. convex or concave
D. None of these


Two identical \( 5 \mathrm{kg} \) blocks are moving
with same speed of \( 2 m s^{-1} \) towards
each other along a frictionless
horizontal surface. The two blocks
collide, stick together, and come to rest. Consider the two blocks as a system
The work done by external and internal forces are respectively,
\( A \cdot 0,0 \)
B. 0, 20J
c. 0,-20
D. 20J, -20J


Which pair of compounds would make
an NPK fertiliser?
A. Ammonium sulfate and potassium phosphate
B. Calcium hydroxide and ammonium nitrate
C. Calcium phosphate and potassium chloride
D. Palcium phosphate and potassium chloride


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


The property that corresponds to the
order
\( \mathbf{H I}>\mathbf{H B r}>\mathbf{H C l}>\mathbf{H F} \)
A. Thermal stability
B. Reducing power
c. lonic character
D. Bond strength


The current produced in a closed coil, where magnetic lines of force rapidly change within it is called:
A. direct current
B. alternating current
c. induced current
D. none of these


What do you understand by ppm?
A. Parts per million
B. Particles per million
C. Parts and particles per million
D. None of the above


How many sulphur atoms in \( N a_{2} S_{4} O_{6} \)
have zero oxidation state?


Tertiary butyl amine is a:
A \( \cdot 1^{\circ} \) amine
B . \( 2^{\circ} \) amine
\( \mathbf{c} \cdot 3^{\circ} \) amine
D. quaternary salt


The structural feature which
distinguishes proline from other
natural \( \alpha \) -amino acids is that:
A. it is optically inactive
B. it contains aromatic group
c. it contains two amino groups
D. it is secondary amine


The EMF of the cell :
\( \boldsymbol{P t}, \boldsymbol{H}_{2}(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\left|\boldsymbol{H}^{\oplus}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\right| \boldsymbol{A} \boldsymbol{g} \) is
0.27 and \( 0.26 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \) and \( 35^{\circ} \mathrm{C} \)
respectively. The posituve value of heat of the reaction occurring inside the cell
\( \operatorname{at} 25^{\circ} C\left(i n k J K^{-1}\right) \) is: \( ( \) write your
answer to nearest integer)


A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary
particle of mass m. They are in contact for a short time T. Their force of
interaction increases from zero to \( F_{0} \)
linearly in time \( \frac{T}{2} \) and decreases inearly to zero in further time \( \frac{T}{2} \) (shown in figure)
The magnitude of \( F_{0} \) is :
A . \( m u / 2 T \)
в. \( m u / T \)
\( \mathrm{c} .2 \mathrm{mu} / \mathrm{T} \)
D. None of these


Match the following, regarding nature of the oxides.
\( \begin{array}{ll}\text { Column - - } & \text { Column-II } \\ \text { a. } N_{2} O & \text { (i) Basic } \\ \text { b. Bao } & \text { (ii) Amphoteric } \\ \text { c. } A s_{2} O_{3} & \text { (iii) Acidic } \\ \text { d. } C l_{2} O_{7} & \text { (iv) Neutral }\end{array} \)
\( A \)
\( a(\text { ii) }, b(i), c(\text { iii) }, d(i \text { iv }) \)
B. a (iv), b(i), c(iii), d(ii)
c. \( a(\text { iv) }, b(i), c(i \text { i) }, d( \text { iii) } \)
\( \mathbf{D} \cdot \mathbf{a}(\mathbf{i} \mathbf{i}), \mathbf{b}(\mathbf{i}), \mathbf{c}(\mathbf{i} \mathbf{v}), \mathrm{d}(\text { iii }) \)


A point charge \( +q \) is placed at the centre of a cube of side \( L \). The electric
flux emerging from the cube is
A \( \cdot \frac{q}{\varepsilon_{0}} \)
B. Zero
c. \( \frac{6 q L^{2}}{\varepsilon_{0}} \)
D. \( \frac{q}{6 L^{2} \varepsilon_{0}} \)


Define congruent chords.


The smallest ketone and its next
homologue are reacted with \( N H_{2} O H \)
to form:
A. two different oxime
B. four different oxime
C. three different oxime
D. optically active oxime


The relation between displacement \( x \)
and time \( t \) for a body of mass \( 2 K g \) moving under the action of a force is given by \( x=\frac{t^{3}}{3}, \) where \( x \) is in meter and
\( t \) in second, calculate the work done by
the body in first 2 seconds.


A solid metal cube of edge length \( 2 \mathrm{cm} \)
is moving in a positive \( y \) direction at a constant speed of \( 6 m / s . \) There is a
uniform magnetic field of \( 0.1 T \) in the
positive \( z- \) direction. The potential
difference between the two faces of the
cube perpendicular to the \( x- \) axis, is:
\( \mathbf{A} \cdot 6 m V \)
B. \( 1 \mathrm{mV} \)
c. \( 12 \mathrm{mV} \)
D. \( 2 m V \)


Which ligand is expected to be
bidentate?
A. \( C_{2} O_{4}^{2} \)
в. \( C H_{3} C \equiv N \)
\( c \cdot B r^{-} \)
D. \( C H_{3} N H_{2} \)


Count total number of S.F. in \( 1.60 \times \)
\( \mathbf{1 0}^{-19} \)
\( A \cdot 3 \)
B. 5
\( c \cdot 2^{-} \)
D. 22


If true enter 1 , else enter 0 .
When \( C l_{2} \) gas is passed into a mixture
containing \( B r^{-} \) and \( I^{-} \) and \( C H C l_{3}, I_{2} \)
(violet) first apears in \( C H C l_{3} \) layer.


Given below are five groups of five terms in each. Arrange the terms in each group in their proper sequence.
I.Renal Pelvis, Urethra, Ureter Kidney
Urinary Bladder
ii. Sodium ions move into the axon,
Repolarisation. Polarisation, Stimulus, Depolarisation
iii. ATP is produced, guard cells photosynthesise during the day guard cells become more turgid. guard cells become hypertonic, Potassium ions are actively pumped into the guard cells iv Efferent ducts, Network of ducts,
Seminiferous tubules. Urethra, Vas
deferens v. Response, Effector Brain or Spinal Cord, Receptor Stimulus


Hence, \( \Delta A D C \) and \( \Delta B A C \) are similar.
If the above statement is true then
mention answer as 1 , else mention 0 if
false


For given complex \( \left[N i\left(P P h_{3}\right)_{2} C l_{2}\right] \)
mention
(i) IUPAC Name
(ii) Central metal ion
(iii) Ligands
(iv) Coordination number
(v) Nature of the complex


Let \( \boldsymbol{A}=\{1,2,3\} . \) Which of the following
is not an equivalence relation on A?
A \( \cdot\{(1,1),(2,2),(3,3)\} \)
B - \{(1,1),(2,2),(3,3),(1,2),(2,1)\}
C \( \cdot\{(1,1),(2,2),(3,3),(2,3),(3,2)\} \)
D \cdot \{(1,1),(2,1)\}


Q Type your question
be :
\( \mathbf{A} \)
B.
\( c \)
D.


A sample of peanut oil weighing 2 added to \( 25 \mathrm{mL} \) of \( 0.40 \mathrm{M} \) KOH. After
saponification is complete, \( 8.5 \mathrm{mL} \) of
\( 0.28 \mathrm{M} H_{2} S O_{4} \) is needed to neutralize
excess of KOH. The saponification number of peanut oil is: (Saponification number is defined as the milligrams of
KOH consumed by 1 g of oil
A . 146.72
в. 223.44
c. 98.9
D. none of these


Most acidic and basic oxides in \( 2 n d \)
period elements are formed by which compound?


The mean deviation from mean of the
observation \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots . . \boldsymbol{a}+ \)
2nd is
A \( \cdot \frac{n(n+1) d^{2}}{3} \)
в. \( \frac{n(n+1)}{2} d^{2} \)
c. \( _{a+\frac{n(n+1) d^{2}}{2}} \)
D. \( \frac{n(n+1) d}{(2 n+1)} \)


If \( a, b, c \) are the roots of the equation
\( \boldsymbol{x}^{3}+\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}+\boldsymbol{r}=\boldsymbol{0}, \) form the
equation whose roots are \( a-\frac{1}{b c}, b-\frac{1}{c a}, c-\frac{1}{a b} \)


The value of Curie temperature for \( N i \) is
nearly
\( \mathbf{A} \cdot 631 K \)
B. \( 770 K \)
\( \mathbf{c} .890 K \)
D. \( 1100 K \)


Which of the following will give maximum number of isomers?
A. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] \)
в. \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{c} \cdot_{\left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right]} \)
D. \( \left[C r(S C N)_{2}\left(N H_{3}\right)_{4}\right]^{2+} \)


The metal which is soft?
A. \( N a \)
в. \( P b \)
c. \( A l \)
D. \( C u \)


If error in measuring the edge of a cube is \( k \% \) then the percentage error in
estimating its volume is
\( A \cdot k \)
B. \( 3 k \)
\( c \cdot \frac{k}{3} \)
D. none of these


A geyser heats water flowing at the rate of 4 litre per minutes from \( 30 \mathrm{C} \) to \( 85 \mathrm{C} \) If the geyser operates on gas burner then the amount of heat used per
minute is :
A \( \cdot 9.24 \times 10^{5} \) j
В. \( 6.24 \times 10^{7} \),
D. \( 6.24 \times 10^{5} \) j


List all of the subsets of the set
\( \{a, b, c, d\} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \)


Find the value of \( x, y \) and \( z \) in the
adjoining figure.
\( \mathbf{A} \cdot x=160, y=60, z=80 \)
B . \( x=60, y=80, z=40 \)
C \( . x=80, y=60, z=140 \)
D. \( x=140, y=80, z=60 \)


Three point charges \( q \) are placed at three vertices of an equilateral triangle of side a. The magnitude of electric force on any charge due to the other two is equal to \( \frac{\sqrt{x}}{4 \pi \varepsilon_{0}}\left(\frac{q}{a}\right)^{2} \) where \( x \) is:


Critical temperature of \( C O_{2} \) is \( 31.2^{\circ} C \)
In summer, the room temperature is
\( 40^{\circ} \mathrm{C}: \)
A. \( C O_{2} \) cannot be liquefied
B. Can be liquefied with increase of pressure
c. can be liquefied with decrease of pressure
D. can be liquefied if temperature of \( C O_{2} \) is decreased below 31.2


If mass \( \mathrm{M} \) is split into two parts, \( \mathrm{m} \) and \( (M-m) \) which are then separated by a
certain distance. What ratio of \( \mathrm{m} / \mathrm{M} \)
maximizes the gravitational force between the two parts.
A . \( 1 / 3 \)
B. \( 1 / 2 \)
c. \( 1 / 4 \)
D. \( 1 / 5 \)


The reaction \( C_{6} \boldsymbol{H}_{6}+\boldsymbol{C H}_{3} \frac{A l C l_{3}}{\text {anhydrous}} \)
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C} \boldsymbol{H}_{3} \) is:
A. Friedel-Crafts alkylation
B. addition reaction
C . Friedel-Crafts acylation
D. Friedel -Craft's benzylation


Assertion
Diamonds are known for their
spectacular brilliance, but diamonds found in nature rarely exhibit the
brilliance.
Reason
By cutting the diamond suitably,
multiple total internal reflections can
be made to occur.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( A \) is a singular matrix, then adj \( A \) is
A. non- singular
B. singular
c. symmetric
D. not defined


Coal can be used as a main source for:
A. water
B. air
c. energy
D. soil


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


Which of the following numbers are not perfect cubes?
(i) 128
(ii) 100
(iii) 64
(iv) 125
\( \mathbf{7 2} \quad(\mathbf{v i}) \mathbf{6 2 5} \)


Consider the following list of reagents:
Acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}, \) alkaline
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{O}_{2}, \boldsymbol{C l}_{2}, \boldsymbol{O}_{2}, \boldsymbol{F e C l} \)
and \( N a_{2} S_{2} O_{3} . \) The total number of
reagents that can oxidise aqueous iodide to iodine is:


Phosphorus trichloride reacts with phosphorus acid to give pyrophosphoric acid.
A. True
B. False


Which of the following statement is
correct?
\( \mathbf{A} \cdot E_{\text {cell}} \) and \( \triangle_{r} G \) of cell reaction both are extensive
properties
B. \( E_{\text {cell}} \) and \( \triangle_{r} G \) of cell reaction both are intensive
properties
C. \( E_{\text {cell}} \) in the intensive property while \( \triangle_{r} G \) of cell reaction is an extensive property.
D. \( E_{\text {cell}} \) in the intensive property while \( \triangle_{r} G \) of cell reaction is an intensive property.


Solve: \( \frac{d}{d x} x \sin ^{2} x \)


In a tug of war, the team that exerts a
larger tangential force on the ground wins, winning team not moving. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. Which of the following work is negative?
A. work by the ground on the winning team.
B. work done by string on the winning team.
c. work by ground on the losing team.
D. total external work on the two teams.


The wave nature of the electron was
verified using
A. Photo electric effect
B. Compton effect
c. The phenomenon of X-ray emission
D. Diffraction of electron by a crystal


What is called secondary or lateral
meristem?


\( \int \frac{1}{\sin ^{2} x+\sin 2 x} d x \)
A. \( \frac{1}{2} \log \frac{\tan x}{\tan x+2} \)
B. \( -\frac{1}{2} \log \frac{\tan x}{\tan x+2} \)
c. \( \frac{1}{2} \log \frac{\tan x}{\tan x-2} \)
D. \( \log \frac{\tan x}{\tan x+2} \)


Which of the following equations corresponds to the definition of
enthalpy of formation at \( 298 K ? \)
A \( \cdot C(\text { graphite })+2 H_{2}(g)+\frac{1}{2} O_{2}(g) \longrightarrow C H_{3} O H(l) \)
B \( \cdot 2 C(\text { graphite })+4 H_{2}(g)+O_{2}(g) \longrightarrow 2 C H_{3} O H(l) \)
c. \( C(\text { diamond })+2 H_{2}(g)+\frac{1}{2} O_{2}(g) \longrightarrow C H_{3} O H(l) \)
D. \( C(\text { graphite })+2 H_{2}(g)+\frac{1}{2} O_{2}(l) \longrightarrow C H_{3} O H(g) \)


f \( \tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)= \)
4
Find \( \boldsymbol{x} \)


The lowering of activation energy by
catalyst is due to:
A. formation of adsorbed activated complex and to provide new pathway to reaction
B. adsorption is always exothermic
C. the adsorbed activated complex possesses lower energy level than simple activated complex
D. all of the above


Which of the following is the smallest unit?
A. millimetre
B. angstrom
c. fermi
D. metre


On treatment with cold water, an
element (A) reacts readily liberating a colorless, odorless gas \( (\mathrm{B}) \) and \( \mathrm{a} \) solution (C). Lithium is reacted with (B)
yielding a solid product (D) which effervescence with water to give a
strongly basic solution (E). When \( C O_{2} \) gas is bubbled through the solution \( (\mathrm{C}) \) a white ppt (F) is formed but this redissolved forming solution (G) when
more \( C O_{2} \) is passed. The precipitate (F) effervesced when moistened with conc.
\( H C l \) and give deep red coloration to the
Bunsen burner flame.(F) on heating
with an excess of carbon at \( 2000^{\circ} \mathrm{C} \)
give (H). Metal (A) may be:
\( A \cdot B e \)
B. \( c a \)
\( c \cdot s r \)
D. Ba


Jacob bought a scooter for a certain
sum of money. He spent \( 10 \% \) of the cost on repairs and sold the scooter for a
profit of Rs. 1100. How much did he spend on repairs if he made a profit of \( 20 \% \)
A . Rs. 400
B. Rs. 440
c. Rs. 500
D. Rs. 550


\( P-V \) diagram of an ideal gas for a
process \( A B C \) is as shown in the figure. If the total heat absorbed or released by
the gas during the process \( A B C \) is
\( \operatorname{given} \operatorname{by} \boldsymbol{H}=-\boldsymbol{x} \boldsymbol{P}_{0} \boldsymbol{V}_{0}, \) what is the
value of \( x \) ?


When rate of change of current in a circuit is unity, the induced emf is
equal to
A. total flux linked with the coil.
B. induced charge.
c. number of turns in the circle.
D. coefficient of self induction


Nature of valves in the heart is
A. Membraneous
B. Muscular
c. Tendinous
D. Ligamentous


How is reproduction in hydra different from that in amoeba?
A. Hydra reproduces by budding, amoeba reproduces by binary fission.
B. Hydra reproduces by binary fission, amoeba reproduces by budding.
C. Hydra reproduces by sexual reproduction, amoeba reproduces by asexual reproduction.
D. None of the above.


A simple harmonic oscillator has a period \( T \) and energy E. The amplitude of the oscillator is doubles. Choose the
correct answer.
A. Period and energy get doubled
B. Period gets doubled while energy remains the same.
c. Energy gets doubled while period remains the same
D. Period remains the same and energy becomes four times


A ring of charge with radius of \( 0.5 \mathrm{m} \)
has \( 0.02 \mathrm{m} \) gap. If the ring carries a charge of \( +1 C, \) the field at the centre is:
A \( \cdot 2.31 \times 10^{4} N / C \)
B . \( 2.31 \times 10^{8} N / C \)
c. \( 1.6 \times 10^{4} N / C \)
D. \( 1.6 \times 10^{8} N / C \)


What is nutrition? Explain with
diagram the process of nutrition in Amoeba.


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \frac{\boldsymbol{O}_{3}}{\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{S}} ? \)
Products obtained at the end of the
reaction when given compound is subjected to ozonolysis are:
A. acetaldehyde
B. propanaldehyde
c. acetone, acetaldehyde
D. acetone, formaldehyde


For the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
doubling the concentration of both the reactants increases the reaction rate 8
times an ddoubling the concentration of only \( B \) simply dubles the reaction rate.
Find the rate law for the above equation.


Which biological process is responsible for the appearance of these plants in a burned area?
A. Evolution by natural selection
B. Succession
c. Mutation
D. Eutrophication
E. Recombination


What is the reason for a region of a lake turned into a dead zone?
A. Eutrophication
B. Acid rain
c. washed off fertilizers in the lake
D. All of the above


Assertion
Histones are basic proteins of major importance in packaging of eukaryotic DNA. DNA and histones comprise chromatin forming the bulk of
eukaryotic chromosome.
Reason
Histones are of five major types: \( \mathrm{H} 1 \) H2A, H2B, H3 and H4.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{4}, \mathbf{9}, \mathbf{1 6}, \mathbf{2 5}, \dots\} \) and \( \boldsymbol{B}= \)
\( \left\{\boldsymbol{x} \mid \boldsymbol{x}=\boldsymbol{n}^{2}, \boldsymbol{n} \in \boldsymbol{N}\right\}, \) then
A \( . A=B \)
в. \( A \neq B \)
c. \( A \subset B \)
D. \( B \subset A \)


If the kinetic energy of a particle is increased by 16 times, the percentage change in the de Broglie wavelength of the particle is:
A . 25\%
B. 75\%
c. 60\%
D. 50\%


Which of the following is true regarding a bucket of boiling water and a cup of boiling water.
I.The temperature of the two is the
same.

II.The heat content of the two is the
same
III. The bucket of water contains more
heat and is therefore hotter
A . Ionly
B. II only
c. I and III only
D. II and III only
E . I, II and III only


When o-xylene is oxidised with alkaline
\( K M n O_{4}, \) the product is
A. Terephthalic acid
B. Phthalic acid
c. Benzoic acid
D. Salicylic acid


How many carbon atoms are present in a molecule of propene?
A . 4
B.
\( c \cdot 3 \)
D. 2
E. 7


A parallel plate capacitor (fig.) made of circular plates each of radius \( \boldsymbol{R}= \) \( 6.0 \mathrm{cm} \) has a capacitance \( C=100 \mu \mathrm{F} \)
The capacitor is connected to a \( 230 V \) ac supply with a (angular) frequency of
300 rad \( s^{-1} \)
Is the conduction current equal to the
displacement current?


Sea is the greatest source of halogens.
Comment.


Sodium dissolves in liquid ammonia giving a blue coloured solution. Enter 1 if the statement is True or 0 if
statement is False.


The initial and final temperatures of a
liquid are measured to be \( 67.7+0.2^{0} C \)
and \( 76.3+0.3^{0} C \)
Calculate the rise in temperature with error limits.
A \( \cdot 8.6 \pm 0.5^{\circ} \mathrm{C} \)
B \( .9 \pm 0.5^{0} C \)
\( \mathbf{c} \cdot 16 \pm 0.5^{0} C \)
D. \( 2.6 \pm 0.5^{\circ} \mathrm{C} \)


A ball is released from the top of a tower
of height h meters. It takes T seconds to reach the ground. What is the position of the ball in \( \frac{T}{3} \) seconds?
A \( \cdot \frac{h}{9} \) metres from the ground
B. \( \frac{7 h}{9} \) metres from the ground
c. \( \frac{8 h}{9} \) metres from the grounds
D. \( \frac{17 h}{18} \) metres from the ground


The interference of light was first demonstrated experimentally by
A. sir Isaac Newton
B. Michelson
c. Fraunhoffer
D. Thomas Young


Compound (C) is
Solid \( (\mathrm{B}) \)
Contains \( 67.8 \% \) of \( \mathrm{Br} \) )
One mono \( \ll \) Nitration
nitro compound
in. Compound (C) [Isomer of (A)] Compound (D)
(Contains \( 76,4 \% \) of \( B \) f)
\[
\begin{array}{l}
\text { One mono } \leftarrow \text { Nitration } \\
\text { nitro compound }
\end{array}
\]


The normal boiling of water is \( 373 K \) Vapour pressure of water at temperature \( \boldsymbol{T} \) is \( 19 \mathrm{mm} \) Hg. If enthalpy of evaporation is \( 40.67 k J / m o l, \) then
temperature \( \boldsymbol{T} \) would be:
(Use \( \log 2=\mathbf{0 . 3}, \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \mathbf{)} \)


The pressure of a given mass of gas at
constant volume varies with temperature
\( a S \)
A \( \cdot \frac{1}{T^{2}} \)
в. \( \frac{1}{T} \)
c. \( \frac{1}{T^{3}} \)
D. \( T \)


Let \( M \) and \( N \) be two \( 3 \times 3 \) non-singular
skew-symmetric matrices such that
\( M N=N M . \) If \( P^{T} \) denotes the
transpose of \( P, \) then
\( M^{2} N^{2}\left(M^{T} N\right)^{-1}\left(M N^{-1}\right)^{T} \) is equal to
A \( . M^{2} \)
B. \( -N^{2} \)
c. \( -M^{2} \)
D. \( M N \)


In \( _{-1}-\ldots_{\text {eactants are }} \)
continuously supplied energy which can be withdrawn indefinately until outside supply of reactant is maintained. These
cells are more efficient than
conventional batteries and moreover,
these are eco-friendly.
A . fuel
B. galvanic
C. primary
D. secondary


For the refraction of light through a
prism
A. For every angle of deviation there are two angles of incidence.
B. The light travelling inside an equilateral prism is necessarily parallel to the base when prism is set for minimum deviation.
C. There are two angles of incidence for maximum deviation.
D. Angle of minimum deviation will increase if refractive index of prism is increased keeping the outside medium unchanged if \( \mu_{p}>\mu_{s} \)


Fill in the blanks:
The reflecting surface of a spherical mirror may be curved


Evaluate
\( \lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^{2}}\right)\left(1+\frac{2^{2}}{n^{2}}\right)\left(1+\frac{3^{2}}{n^{2}}\right)\right. \)
A \( \cdot\left(\frac{\pi-4}{2}\right) \)
в. \( _{2 e}\left(\frac{\pi-2}{2}\right) \)
c. \( _{2 e}\left(\frac{\pi-4}{4}\right) \)
D. \( _{2 e}\left(\frac{\pi-4}{3}\right) \)


The tension force between two block is:
A \( .10 N \)
\( B \cdot \frac{8}{3} N \)
\( c .8 N \)
D. zero


The oxides of nitrogen which show neither acidic nor basic properties are :
A. \( N O, N_{2} O_{3} \)
B. \( N_{2} O, N O \)
c. \( N O, N_{2} O_{4} \)
D. \( N_{2} O, N_{2} O_{4} \)


A boy of mass \( M \) stands on a platform
of radius \( R \) capable to rotate freely
about its axis. The moment of inertia of
the platform is \( I . \) The system is at rest.
The friend of the boy throws a ball of mass \( m \) with a velocity \( v \) horizontally. The boy on the platform catches it. Find the angular velocity of the system in the
process.
A \( \cdot \frac{m v R}{(M+m) R^{2}} \)
в. \( \frac{m v}{I+M R^{2}} \)
c. \( \frac{m v R}{I+m R^{2}} \)
D. \( \frac{m v R}{I+(M+m) R^{2}} \)


There are 4 balls of different colours \( \& 4 \)
boxes of colours same as those of the
balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is:
A . 9
B . 30
c. 20
D. None


Which covers the largest number of
organisms?
A. Genus
B. Family
c. Phylum
D. class
E. order


The oxidation state of the most
electronegative element in the products
of the reaction between \( B a O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) are
A. 0 and -1
B. -1 and -2
c. -2 and 0
D. -2 and +1


A light rod of length \( 2.00 m \) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross section
\( 10^{-3} m^{2} \) and the other is of brass of
cross-section \( 2 \times 10^{-3} m^{2} . \) Find out the
position along the rod at which a weight may be hung to produce.(Youngs modulus for steel is \( 2 \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \) and for
brass is \( 10^{11} \mathrm{N} / \mathrm{m}^{2} \) )
a) equal stress in both wires
b) equal strains on both wires
A. \( 1.33 m, 1 m \)
в. \( 1 m, 1.33 m \)
c. \( 1.5 m, 1.33 m \)
D. \( 1.33 m, 1.5 m \)


If the equations of the hypotenuse and a side of a right-angled isosceles triangle be \( \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}=\mathbf{1} \) and \( \boldsymbol{x}=\boldsymbol{k} \) respectively
then
This question has multiple correct options
\( \mathbf{A} \cdot m=1 \)
в. \( m=k \)
c. \( m=-1 \)
D. \( m+k=0 \)


The commonest disaccharide has the
molecular formula
A. \( C_{10} H_{18} O_{19} \)
В . \( C_{10} \mathrm{H}_{20} \mathrm{O}_{10} \)
c. \( C_{11} H_{22} O_{11} \)
D. \( C_{12} H_{22} O_{11} \)


On addition of \( A g N O_{3} \) to \( N a C l \) white
precipitate occurs:
A. instantaneously
B. with a measurable speed
c. slowly
D. none of the above


Anthracene can be electrolytically
oxidised to anthraquinone. What mass of anthraquinone can be
produced by the passage of 1 ampere current for an hour at \( 100 \% \) efficiency?
A . \( 3.654 g \)
В. \( 2 g \)
c. \( 12 g \)
D. \( 1.2932 g \)


How many optically inactive isomers
\( \operatorname{are} \) present in \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C H}(\boldsymbol{O H})- \)
\( \boldsymbol{C H}(\boldsymbol{O H})-\boldsymbol{C O O H} ? \)
A .
B. 2
\( c \)
D. 3


A circle and a squre have the same
perimeter. Then:
A. there areas are equal
B. the area of the circle is the greater
C. the area of the square is the greater
D. the area of the circle is \( x \) times the area of the square
E. none of these


Hydroponic is a technique of growing
A. Submerged plants
B. Free floating aquatic plants
C . Terrestrial plants in sand
D. Terrestrial plants in water containing nutrients


Find the distance of image from convex
ens.
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. 20cm
\( c .4 \mathrm{cm} \)
D. None of these


The following three objects (1) a metal
tray,
(2) a block of wood,and (3) a
wooden cap are left in a closed room
overnight. Next day the temperature of
each is recorded as \( T_{1}, T_{2} \) and \( T_{3} \)
respectively. The likely situation is
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{3}>T_{2}>T_{1} \)
c. \( T_{3}=T_{2}>T_{1} \)
D. \( T_{3}>T_{2}=T_{1} \)


Dryopithecus occurred about
\( A \cdot 2.5 \times 10^{6} \) years back
B. \( 25 \times 10^{6} \) years back
\( \mathbf{C} \cdot 50 \times 10^{6} \) years back
D. \( 75 \times 10^{6} \) years back


Assertion
The properties of phosphorus should be closer to those of sulfur than to those of
nitrogen.
Reason
Phosphorus and nitrogen are in the same row of the periodic table.
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


Calculate the median for the following
data
\( \begin{array}{lllll}\text { class } & 1- & 6- & 11- & 16- \\ \text { interval } & 5 & 10 & 15 & 20\end{array} \)
Frequency 1
18
25


Period number and group number of "Tantalum" (Z -73) are respectively:
A. 5,7
B. 6, 13
\( c \cdot 6,5 \)
D. None of these


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then number of
elements in \( A \) are
A .4
B. 3
\( c \cdot 2 \)
D. None of these


The path difference produced by two
waves is \( 3.75 \mu m \) and the wavelength is \( \mathbf{5 0 0 0} \boldsymbol{A} . \) The point is
A. Uncertain
B. Dark
c. Partially bright
D. Bright


Solve
\( \frac{5}{6} x+\frac{3}{8} x=2+\frac{1}{3} x \)


Find the radius of the circle which
passes through the origin, (0,4) and (4,0)
A. \( \sqrt{8} \)
B. 4
c. 16
D. \( \sqrt{36} \)


Solid ammonium carbamate,
\( N H_{4} C O_{2} N H_{2}(s), \) dissociates into
ammonia and carbon dioxide, when it
evaporates as shown by:
\( N H_{4} C O_{2} N H_{2}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( C O_{2}(g) . \) At \( 25^{\circ} C, \) the total pressure of
the gases in equilibrium with the solid
is 0.116 atm. If 0.1 atm of \( C O_{2} \) is introduced after equilibrium is reached,
then:
This question has multiple correct options
A. the final pressure of \( C O_{2} \) will be less than 0.1 atm
B. the final pressure of \( C O_{2} \) will be more than 0.1 atm
c. the pressure of \( N H_{3} \) will decrease due to addition of \( C O_{2} \)
D. the pressure of \( N H_{3} \) will increase due to addition of \( C O_{2} \)


If \( C \) is the value of the capacitance of a capacitor filled with a given dielectric and \( a \) is the capacitance of an identical capacitor in a vacuum, the dielectric constant, symbolized by the Greek letter kappa,, is simply expressed as
A \( \cdot \frac{C}{a} \)
B. \( \frac{a}{C} \)
c. \( C \times a \)
D. None


In our houses, we receive AC current at
a voltage of with a
frequency of


By adding a non-volatile salute into a solution vapour pressure is reduces.


If they are A.P. find the common
difference, 2,4,6,8


Position of the bromine in the product
structure is:


Two-third of a number is greater than
one-third of the number by 3. Find the
number


\( \int_{2}^{3} \frac{(x+2)^{2}}{2 x^{2}-10 x+53} d x \) is equal to
\( A \cdot 2 \)
B.
\( c \cdot 1 / 2 \)
D. \( 5 / 2 \)


If \( f(x)=\frac{1}{(1-x)} \) then \( (\text { fofof })(x)=? \)
A \( \cdot \frac{1}{(1-3 x)} \)
в. \( \frac{x}{(1+3 x)} \)
c. \( x \)
D. None of these


Assertion (A): The hydrides of VA group elements are good reducing agents.
Reason \( (\mathrm{R}): N H_{3} \) is a weak reducing
agent among the hydrides of VA group.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
\( c . \) (A) is true and
(R) is false
D. (A) is false but (R) is true


The mass to charge ratio for \( \mathbf{A}^{+} \) ions is \( 1.97 \times 10^{-7} \mathrm{kg} \mathrm{C}^{-1} . \) calculate the mass
of A atom


The opening between the right atrium and the right ventricle is guarded by the
valve named
A. Bicuspid valve
B. Tricuspid valve
c. Mitral valve
D. Semilunar valve


lonisation constant of \( \boldsymbol{C H}_{3} \) COOH is
\( 1.7 \times 10^{-5} \) and concentration of \( H^{+} \)
ions is \( 3.4 \times 10^{-4} \). Then find out initial
concentration of \( \boldsymbol{C H}_{3} \) COOH molecule.
A. \( 3.4 \times 10^{-4} \)
В. \( 3.4 \times 10^{-3} \)
c. \( 6.8 \times 10^{-4} \)


Cruciform corolla is found in
A. Sunflower
B. China-rose
c. Radish
D. Pea


The change in pressure will not affect the equilibrium constant for:
A \( \cdot N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
B . \( P C l_{5}(s) \rightleftharpoons P C l_{3}(s)+C l_{2}(g) \)
C. \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
D. all of the above


Q Type your question
illustrated in Fig.
Ball \( X \) has an initial velocity of
\( 3.0 m s^{-1} \) in a direction along line \( A B \)
Ball \( Y \) has a mass of \( 2.5 k g \) and an
initial velocity of \( 9.6 m s^{-1} \) in a
direction at an angle of \( 60^{\circ} \) to line \( A B \)
The two balls collide at point \( B \). The
balls stick together and then trave along the horizontal surface in a
direction at right-angles to the line \( \boldsymbol{A B} \)
as shown in Fig.

Calculate the common speed \( V \) of the
two balls after the collision


If \( m \) and \( p \) are positive \( (m \geq p) \) and
\( \boldsymbol{\Delta}(\boldsymbol{m}, \boldsymbol{p})= \)
\( \left|\begin{array}{ccc}m & C_{p} & m \\ m+1 & C_{p} \\ m+2 & m+1 & C_{p+1} & m+1 \\ m_{p} & m+2 & m_{p+2} \\ & & m+2\end{array}\right| \) and
\( m_{\boldsymbol{p}}=\mathbf{0} \) if \( \mathbf{m}<\mathbf{p}, \) then
This question has multiple correct options
A \( . \Delta(2,1) / \Delta(1,0)=4 \)
B. \( \Delta(4,3) / \Delta(3,2)=2 \)
\( \mathbf{c} \cdot \Delta(4,3) / \Delta(2,1)=5 \)
D. \( \Delta(4,3) / \Delta(1,0)=10 \)


Which one of the following method is a commonly used method for destruction of colloid?
A. Dialysiss
B. Condensation
C . Filteration by animal membrane
D. By adding electrolyte


Which one is mineral of manganese?
A . Magnesite
B. Malachite
c. Magnetite
D. Pyrolusite


Value of \( c \) of Lagranges mean theorem for
\[
\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}+\boldsymbol{x}^{\mathbf{3}} \text { if } \boldsymbol{x} \leq \mathbf{1}
\]
\( =3 x \) if \( x>1 \) on [-1,2] is
\( A \cdot \pm \frac{\sqrt{5}}{3} \)
B. \( \pm \frac{\sqrt{3}}{2} \)
\( c \cdot \pm \frac{\sqrt{2}}{5} \)
\( D \cdot \pm \frac{3}{\sqrt{5}} \)


The word mole was introduce by
in
A. Avogadro, 1897
B. Dalton, 1896
c. wilhelm ostwald, 1896
D. Proust, 1897


Sketch the graph \( y=|x-5| . \) Evaluate \( \int_{0}^{1}|x-5| d x . \) What does this value of the integral represent on the graph?


A converging lens of focal length \( 10 \mathrm{cm} \) forms an image two times magnified image. Calculate position (s) of the object.


If \( n=m_{2}, \) then the value of \( ^{n} C_{2} \) is
given by
\( \mathbf{A} \cdot m+1 C_{4} \)
В . \( m-1 C_{4} \)
c. \( m+2 C_{4} \)
D. None of these


\( \left|\begin{array}{cc}\mathbf{0} & \boldsymbol{a}-\boldsymbol{b} \\ -\boldsymbol{a} \mathbf{0}-\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} \mathbf{0}\end{array}\right|=\mathbf{0} \)


The antiderivative of \( \frac{x+\left(\cos ^{-1} 3 x\right)^{2}}{\sqrt{1-9 x^{2}}} \) is
A \( \cdot C-\frac{1}{9}\left[\sqrt{1-9 x^{2}}+\left(\cos ^{-1} 3 x\right)^{3}\right] \)
B. \( C+\frac{1}{9}\left[\sqrt{1-9 x^{2}}+\left(\cos ^{-1} 3 x\right)^{2}\right. \)
c. \( c-\frac{1}{3}\left[\left(1-9 x^{2}\right)^{3 / 2}+\left(\cos ^{-1} 3 x\right)^{3}\right. \)
D. none of these


The credit for preparing the first organic compounds in the laboratory went to:
A. Berzellius
B. Wohler
c. Kolbe
D. Berthelot


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \) is an
example of :
A. primary alkyl halide
B. secondary alkyl halide
C. tertiary alkyl halide
D. none of these


In the crystal field of the complex
\( \left[\boldsymbol{F} e(\boldsymbol{C l})(\boldsymbol{C} \boldsymbol{N})_{4}(\boldsymbol{O})_{2}\right)^{4-}, \) the electronic
configuration of metal is found to be \( t_{2 g}^{6} \) \( e_{g}^{0}, \) then which of the following is/are true about this complex ion? This question has multiple correct options
A. It is paramagnetic complex
B. 0 - 0 bond length will be more than found in \( O_{2} \) molecule
c. Its IUPAC name will be chlorotetracyanosuperoxidoferrate (II) ion
D. It will show geometrical as well as optical isomerism


If the volume and surface area of a
sphere are numerically the same, then its diameter is
A. 6 units
B. 8 units
c. 10 units
D. 12 units


Which of these choices is not a family of elements?
A. Halogen
B. Metal
c. Inert Gas
D. Fire extinguishers


The types of energies generated from
sea are:
A. Renewable and Non Conventional source of energy
B. Non Renewable and Non Conventional source of
energy
C. Renewable and Conventional source of energy
D. Non Renewable and Conventional source of energy


The melting point of pure ice is \( 0^{\circ} C \)
A . True
B. False


Express in centimetres.
\( \mathbf{5 0 0 . 0 0 m} \)


Which one of the following complexes is not expected to exhibit isomerism?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \)
B \( \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{2} C l_{2}\right] \)
D. \( \left[N i(e n)_{3}\right]^{2+} \)


A solid uniform ball of volume \( V \) floats
on the interface of two immiscible
liquids (see the figure). The specific
gravity of the upper liquid is \( \rho_{1} \) and that
of lower one is \( \rho_{2} \) and the specific
gravity of ball is \( \rho\left(\rho_{1}<\rho<\rho_{2}\right) \). The
fraction of the volume of the ball in the
upper liquid is
\( A \cdot \frac{\rho_{2}}{\rho_{1}} \)
в.
c. \( \frac{\rho-\rho_{1}}{\rho_{2}-\rho_{1}} \)
D. \( \frac{\rho_{1}}{\rho_{2}} \)


Which of the following relations are functions from \( A=\{1,4,9,16\} \) to \( B=\{-1 \) \( \mathrm{~ 2 , ~ - 3 , ~ - 4 , ~ 5 , ~ 6 ~ \} . ~ I n ~ c a s e ~ o f ~ a ~ f u n c t i o n , ~ w r i t e ~} \)
down its range.
\( f_{1}=\{(1,-1),(4,2),(9,-3),(16,-4)\} \)


A solid sphere and a hollow sphere of
the same mass have the same M.I.
about their respective diameters. The ratio of their radii will be:-
A .1: 2
B. \( \sqrt{3}: \sqrt{5} \)
c. \( \sqrt{5}: \sqrt{2} \)
D. 5: 4


Which of the following statements is/are correct about work?
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} \) a certain reference frame, \( W_{\text {pseudo force}}+ \)
\( W_{\text {conservattive force}}+W_{\text {non-conservattive force}}+ \)
\( W_{\text {other forces}}=\Delta K \)
B. Work done by friction is always negative.
C. Work done by a force is defined as the dot product of the force and the displacement of the point of application of force.
D. Work done by conservative force in moving a body from \( A \) to \( B= \) potential energy of the body at \( A \) potential energy of the body at B


surface absorbs more heat than
any other surface under identical
conditions.
A. White \& Shiny
B. White \& Rough
c. Black \& Rough
D. Yellow \& Shiny


At high temperature, nitrogen combines
with \( C a C_{2} \) to give:
A. calcium cyanide
B. calcium cyanamide
c. calcium carbonate
D. calcium nitride


Let \( \boldsymbol{f}(\boldsymbol{x})=\operatorname{cosec}^{-1}\left[1+\sin ^{2} \boldsymbol{x}\right], \) where
[.] denotes the greatest integer function
Then \( f(x) \) equals;
\( ^{A} \cdot\left\{\frac{\pi}{2}\right\} \)
В \( \cdot\left\{\frac{\pi}{2}, \operatorname{cosec}^{-1} 2\right\} \)
c. \( \left\{\operatorname{cosec}^{-1} 2\right\} \)
D. none of these


The first ionisation potential in electron volts of nitrogen and oxygen atoms are, respectively, given by :
A. 14.6,13.6
B. 13.6, 14.6
c. 13.6,13.6
D. 14.6,14.6


Choose the correct option for following
statement.

Subtraction of rational numbers is not
commutative.
A. True
B. False
c. Cannot be determined
D. None of these


Heating rubber with sulphur is known
as:
A. galvanization
B. bessemerisation
c. vulcanization
D. sulphonation


Assertion(A): The temperature in
the stratosphere increases with
altitude.
Reason(R): Ozone present absorbs
ultraviolet radiation which is converted
into heat.
Choose the correct option from the
following:
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
C. Assertion is true and Reason is false
D. Assertion is false and Reason is true


A quantity of \( P C l_{5} \) was heated in a 10
litre vessel at \( 250^{\circ} \mathrm{C} \)
\( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P C l}_{3(g)}+\boldsymbol{C l}_{2(g)} \)
At equilibrium, the vessel contains \( 0 . \)
mole of \( \boldsymbol{P} \boldsymbol{C l}_{5}, \) 0.2 mole of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) and 0.2
mole of \( C l_{2} . \) The equilibrium constant is
A. 0.02
B. 0.05
\( c \cdot 0.04 \)
D. 0.025


A ball falls from a height of \( 5 \mathrm{m} \) and strikes the roof of a lift. If at the time of
the collision, lift is moving in the upward direction with a velocity of 1 \( \mathrm{m} / \mathrm{s}, \) then the velocity with which the
ball rebounds after the collision will be
\( (e=1): \)
A \( .11 \mathrm{m} / \mathrm{s} \)
B. \( 12 \mathrm{m} / \mathrm{s} \)
c. \( 13 \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


A particle executes SHM with a time period of 4 s. At what instant of time, will the displacement of the particle be equal to the velocity of the particle
\( A \cdot 4 s \)
B. 1 s
\( c \cdot 8 s \)
D. Displacement and velocity cannot be equal at any instant


Find the slope of the line passing through the following points \( M(4,0) \) and \( Q(-3,-2) \)
A \( \cdot \frac{2}{7} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{8}{5} \)


A magnifying glass is what kind of lens, and where do where should I place the
lens relative to the object to see an image larger than the object and rightside-up? ("F" stands for the focal length of the lens.)


Which statement is incorrect?
A. Mast cells and basophils secrete histamine and heparin.
B. Mast cells are long lived, basophils are short lived.
C. Mast cells are smaller than basophils with a bilobed nucleus.
D. Mast cells are relatively sessile, basophils are mobile.


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{O}+\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C H}= \)
\( O^{H} \stackrel{O^{\theta}, \Delta}{\rightarrow} \) mixture of aldols
\( (z)= \) total number of aldols including stereoisomers.
Report your answer as \( (z-5) \)


In the given \( \Delta A B C, \) if \( A B=A C \) and
\( B D=D C, \) then \( \angle A D C= \)
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 120^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


Image formed by plane mirror is
A. real and erect
B. virtual and erect
c. real
D. virtual


If the points \( (x, y,-3),(2,0,-1) \) and (4,2,3) lies on a straight line, then what are the values of \( x \) and \( y \) respectively?
A. 1,-1
в. -1,1
c. 0,2
D. 3,4


Microwaves from a transmitter are
directed normally toward a plane reflector. A detector moves along the normal to the reflector. Between
positions of 14 successive maxima the
detector travels a distance 0.14 m. The
frequency of the transmitter is \( (c= \) \( 3 \times 10^{8} m s^{-1} \)
A. \( 1.5 \times 10^{10} \mathrm{Hz} \)
в. \( 10^{10} \mathrm{Hz} \)
c. \( 3 \times 10^{10} H z \)
D. \( 6 \times 10^{10} \mathrm{Hz} \)


Simplify
\( (a+b)(c-d)+(a-b)(c+d) \)


Calculate the molality of a \( 1 \mathrm{M} \) solution of sodium nitrate. The density of the
solution is \( 1.25 g c m^{-3} \)
A . 0.66 mol \( k g^{-1} \)
B. 0.86 mol \( k g^{-} \)
c. 0.46 mol \( k g^{-1} \)
D. None of these


I.F of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{x} \sin 2 \boldsymbol{y}=\boldsymbol{x}^{3} \cos ^{2} \boldsymbol{y} \) is:
A. \( \tan y \)
B. \( e^{\tan y} \)
\( \mathbf{c} \cdot e^{\sin } \)
D. \( e^{x} \)


In the following figure, \( A B C D \) and
PORS are two parallelograms such
that \( \angle D=120^{\circ} \) and \( \angle Q=70^{\circ} . \) Find the
value of \( \boldsymbol{x} \)


On a photosensitive material, when frequency of incident radiation is increased by \( 30 \% \) kinetic energy of emitted photo electrons increases from
\( 0.4 e V \) to \( 0.9 e V . \) The work function of
the surface is :
A. \( 1 e V \)
B. 1.267 eV
c. \( 1.4 e V \)
D. 1.8 eV


The middle colour in sunlight spectrum
is
A . red
B. green
c. blue
D. orange


How many of the following is/are not obtained as one of the hydrolysis
products of \( X e F_{2} \) with water?
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3}, \boldsymbol{X} \boldsymbol{e}, \boldsymbol{H} \boldsymbol{F}, \boldsymbol{O}_{2} \)
A.
B. 3
\( c \cdot 4 \)
D.


Eight drops of a liquid of density \( \rho \) and
each radius a are falling through air with a constant velocity \( 3.75 \mathrm{cm} s^{-1} \)
when the eight drops coalesce to from a single drop the terminal velocity of the
new drop will be
A. \( 2.4 \times 10^{-2} \mathrm{ms}^{-1} \)
В. \( 15 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 0.75 \times 10^{-2} \mathrm{ms}^{-1} \)
D. \( 25 \times 10^{-2} \mathrm{ms}^{-1} \)


In an earth satellite moving in a circular orbit, a piece of metal weighing \( 16 g \) (on the earth) is weighed by a spring balance while the metal is suspended in water. If the relative density of the
metal is \( 8, \) what weight will be
recorded?
A. \( -2 g \)
B. zero
\( c \cdot 2 g \)
D. 14 g


Let \( \mathbf{f}(\mathbf{x}) \) be differentiable on the interval
\( (0, \infty) \) such that \( f(1)=1, \) and \( \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1 \)
for each \( \mathbf{x}>0 . \) Then \( \mathbf{f}(\mathbf{x}) \) is
A \( \frac{1}{3 \mathrm{x}}+\frac{2 \mathrm{x}^{2}}{3} \)
B. \( -\frac{1}{3 x}+\frac{4 x^{2}}{3} \)
c. \( -\frac{1}{x}+\frac{2}{x^{2}} \)
\( D \cdot \underline{1} \)


Out of list 1 , select the cation which has
less polarizing power than \( C a^{2+} \) and from list II, select the anion having more polarisability:
List \( \mathrm{I}: M g^{2+}, S c^{3+}, K^{+} \)
List II: \( \boldsymbol{O}^{2-}, \boldsymbol{C l}^{-}, \boldsymbol{P}^{3-} \)
\( \mathbf{A} \cdot M g^{2+}, O^{2+} \)
B. \( K^{+}, P^{3-} \)
\( \mathbf{c} \cdot S c^{3+}, P^{3-} \)
D. \( M g^{2+}, C l^{-} \)


The value of \( 36^{\circ} \) in radians is
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{2 \pi}{5} \)
c.
D. \( 3 \pi \)


Out of 35 students participating in a debate 10 are girls The probability that the winner is a boy will be
A \( \cdot \frac{3}{7} \)
B.
c. \( \frac{1}{7} \)
D. \( \frac{2}{7} \)


A box contains 100 tickets numbered
\( 1,2, \dots .100 . \) Two tickets are chosen at
random. It is given that the minimum number on the two chosen tickets is not
more than \( 10 . \) The maximum number on
them is 5 with probability.
A.
в.
c. \( \frac{1}{90} \)
D.


Q Type your question
The compound A is:
\( A \)
3
\( c \)
\( D \)


In a parallelogram \( A B C D, \) the side \( D C \)
is produced to \( E \) and \( \angle B C E=105^{\circ} \)
Calculate \( \angle A, \angle B, \angle C, \) and \( \angle D \)


Two bodies of masses \( m_{1} \) and \( m_{2} \) are
separated by a distance \( R \). The distance
of the centre of mass of the bodies from
the mass \( m_{1} \) is
A \( \cdot \frac{m_{2} R}{m_{1}+m_{2}} \)
В. \( \frac{m_{1} R}{m_{1}+m_{2}} \)
c. \( \frac{m_{1} m_{2}}{m_{1}+m_{2}} R \)
D. \( \frac{m_{1}+m_{2}}{m_{1}} R \)


Puberty occurs in females at the age of
A . \( 8-10 \) years
B. 11- 14 years
c. \( 15-17 \) years
D. 18 - 20 years


Mr bajaj every morning walks 3 rounds of circular field having \( 100 \mathrm{m} \) as radius.
What is the total distance covered by him?
A. \( 2000 \pi m \)
в. \( 900 \pi m \)
c. \( 600 \pi m \)
D. \( 1500 \pi m \)


A salt of sulphurous acid is called:
A. sulphate
B. sulphurite
c. sulphite
D. sulphide


Determine the pressure required to reduce the given volume of water by \( 2 \% \) Bulk modulus of water is \( 2.2 \times \)
\( 10^{4} N m^{-2} \)
A \( \cdot 4.4 \times 10^{7} \mathrm{Nm}^{-2} \)
В. \( 2.2 \times 10^{7} N m^{-2} \)
c. \( 3.3 \times 10^{7} \mathrm{Nm}^{-2} \)
D. \( 1.1 \times 10^{7} N m^{-2} \)


If \( \boldsymbol{y}=\boldsymbol{e}^{2 x}(\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}), \) show that \( \boldsymbol{y}_{2} \)
\( \mathbf{4} \boldsymbol{y}_{1}+\mathbf{4} \boldsymbol{y}=\mathbf{0} \)


Which type of the following heart valves are generally damaged?
A. Tricuspid valve
B. Eustachian valve
c. Bicuspid valve
D. Aortic semilunar valves


In which of the following solvents, KI has highest solubility? The dielectric
constant \( (\epsilon) \) of each liquid is given in
parentheses.
A \( \cdot C_{6} H_{6}(\epsilon=0) \)
B. \( \left(C H_{3}\right)_{2} C O(\epsilon=21) \)
c. \( C H_{3} O H(\epsilon=32) \)
D. \( C C l_{4}(\epsilon=0) \)


The factors of \( 63 x^{2}-448 \) is
A. \( 9(7 x+8)(7 x-8) \)
B. \( 7(3 x+8)^{2} \)
c. \( 7(3 x+8)(3 x-8) \)
D. \( 9(7 x-8)^{2} \)


How many \( S-S \) linkage(s) is/are
present in \( \boldsymbol{H}_{2} \boldsymbol{S}_{4} \boldsymbol{O}_{6} ? \)


An octahedral complex is formed when hybrid orbitals of the following type are involved:
\( A \cdot s p^{3} \)
B. \( d s p^{2} \)
c. \( d^{2} s p^{3} \)
D. \( s p^{2} d^{2} \)


Using properties of determinants, find
the following:
\( \left|\begin{array}{ccc}\boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{\gamma} \\ \boldsymbol{\alpha}^{2} & \boldsymbol{\beta}^{2} & \boldsymbol{\gamma}^{2} \\ \boldsymbol{\beta}+\boldsymbol{\gamma} & \boldsymbol{\gamma}+\boldsymbol{\alpha} & \boldsymbol{\alpha}+\boldsymbol{\beta}\end{array}\right| \)
A \( \cdot(\alpha+\beta)(\beta+\gamma)(\gamma-\alpha)(\alpha+\beta+\gamma) \)
B . \( (\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)(\alpha+\beta+\gamma) \)
c.
D. None of these


Imagine an atom made up of a proton and a hypothetical particle of double
the mass of the electron but having the same charge as the electron. Apply the Bohr atomic model and consider all
possible transitions of this hypothetical particle to the first excited level. The largest wavelength photon that will be emitted has wavelength \( \lambda \) (given in
terms of the Rydberg constant \( R \) for the hydrogen atom) is equal to:
A \( \frac{9}{5 R} \)
в. \( \frac{36}{5 R} \)
c. \( \frac{18}{5 R} \)
D.


Which of the following is correct regarding evolution of mankind?
A. Homo erectus was preceded by Homo habitue
B. Australopithecus lived in Australia.
c. Neanderthal Man and Cro-Magnon man lived together
D. None of the above


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}, \) if
\( \boldsymbol{x}>2 ; \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}-\boldsymbol{2} \) if \( \boldsymbol{x} \leq 2 \) then \( \boldsymbol{f} \) is
A. an identity function
B. one one
c. onto
D. one one and onto


Breakdown voltage is
A. voltage at which dielectric behaves as conductor
B. voltage at which molecules starts flowing inside the dielectric freely Which of the following is correct regarding above case,
A. Both \( B, A \) are correct
B. \( B \) is correct
c. \( A \) is correct
D. None of the above is correct


Find the sum of first 10 terms of the
arithmetic series if \( a_{1}=25 \) and \( a_{10}= \)
\( \mathbf{1 0 0} \)
A. 300
в. 320
\( c .625 \)
D. 312


At sea level, the atmospheric pressure is \( 1.04 \times 10^{5} \) Pa. Assuming \( g= \)
\( 10 m s^{-2} \) and density of air to be uniform
and equal to \( 1.3 k g m^{-3}, \) find the height of the atmosphere
\( A \cdot 8000 \mathrm{km} \)
B. 8000 \( \mathrm{mm} \)
c. \( 8000 \mathrm{cm} \)
D. 8000 \( \mathrm{m} \)


The following is a example of empty set:
Set of all even natural numbers
divisible by 5
A . True
B. False


Compared to blood our Iymph has
A. More RBCs and less WBCs
B. No plasma
C. Plasma without proteins
D. More WBCs and no RBCs


Volume of a liquid when compressed by additional pressure of \( 10^{5} N / m^{2} \) is 196
cc and when compressed by a pressure of \( 1.5 \times 10^{5} N / m^{2}, \) the volume is \( 194 c c \)
The bulk modulus of the liquid is:
A \( \cdot 10^{5} N / m^{2} \)
B . \( 1.5 \times 10^{6} \)
c. \( 5 \times 10^{5} N / m^{2} \)
D. \( 5 \times 10^{6} N / m^{2} \)


Which term of the \( \boldsymbol{A P}: 88,84,80, \ldots \ldots \) is
zero?


Which of the following vessels contains oxygenated blood?
A. Hepatic veins
B. Pulmonary vein
c. Hypophyseal portal vein
D. Renal vein


Which one is not correct about
Freundlich isotherm?
A \( n=\frac{1}{\tan \theta} \) at average pressure
B . \( \theta=45^{\circ} \) at low pressure
C \( \cdot \theta=45^{\circ} \) at high pressure
D. None of these


Which of the following number lines represents only natural numbers?
\( A \)
\( \begin{array}{lllllllllll}\nwarrow & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array} \)
B.
\( c \)
D.
\( \frac{1}{10} \frac{2}{10} \frac{3}{10} \frac{4}{10} \frac{5}{10} \frac{6}{10} \frac{7}{10} \frac{8}{10} \frac{9}{10} \frac{10}{10} \)


Give the IUPAC name of the following
compound.


Find an angle \( \theta, 0<\theta<\frac{\pi}{2}, \) which
increases twice as fast as its sine.


In the spring-ball model of intermolecular forces, the balls
represent \( _{\text {一一一一一一 }} \) and springs
represent
A. atoms, inter atomic forces
B. nuclei, nuclear forces
c. masses, gravitational forces
D. none of the above


An object is placed \( 30 \mathrm{cm} \) away from a convex lens of focal length \( 10 \mathrm{cm} \) and a
sharp image is formed on a screen. Now
a concave lens is placed in contact with the convex lens. The screen now has to
be moved by \( 45 \mathrm{cm} \) to get a sharp image again. The magnitude of focal length of the concave len is (in cm)
A . 72
B. 60
c. 36
D. 20


If \( \left[\cot ^{-1} x\right]+\left[\cos ^{-1} x\right]=0, \) where [
denotes the greatest integer function, then the complete set of values of \( x \) is
A \( .(\cos 1,1] \)
B. \( (\cos 1,-\cos 1) \)
c. \( (\cot 1,1] \)
D. none of these


an axis passing through the centroid
and perpendicular to plane of the
triangle PQR.


Carbon in the form of \( \ldots \ldots . . . . . . . . . . . \) can be
used in preparation of pencil.
A. graphite
B. dry ice
\( c . \) both a and \( b \)
D. none of the above


The ratio of radii of first orbit of
hydrogen atom and the second orbit of singly ionised helium atom will be
A . 1: 2
B . 4: 1
c. 1: 4
D. 8: 1


How much energy is given off when \( 22 g \)
of \( C_{3} H_{8} \) burns?
The heat of combustion for \( C_{3} H_{8} \) is
\( \mathbf{2}, \mathbf{2 2 0} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
A \( .2242 k J \)
в. \( 1110 k J \)
c. \( 2220 k J \)
D. \( 1500 k J \)


Statement 1: Conc \( \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \) is a low
volatility and viscos nature acid. Statement2: It is due to Hydrogen
bonding.
A. Statement 1 and 2 are correct and 2 is correct explanation of 1
B. Statement 1 and 2 are correct and 2 is not correct explanation of 1
c. statement 1 is correct and 2 is not correct
D. Statement 1 is not correct and 2 is correct.


Copper sulphate dissolves in ammonia
due to the formation of:
\( \mathbf{A} \cdot C u_{2} O \)
B \( \cdot\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
\( \mathbf{c} \cdot\left[C u\left(N H_{3}\right)_{4}\right] O H \)
D. \( \left[C u\left(H_{2} O\right)_{4}\right] S O_{4} \)


Which of the following is dominant trait in pea?
A. Wrinkled seed
B. White flower
c. Dwarf plant
D. Green podd


Which carboxylic acid \( (B) \) (Equivalent
weight \( \left.=52 g m e q^{-1}\right) \) loses \( C O_{2}, \) which
on heating gives an acid \( (\boldsymbol{C}) \)
(Equivalent weight \( =\mathbf{6 0} \) gm \( e q^{-1} \) )?
A \( \cdot R=C H_{3} \)
\[
\begin{array}{l}
C=C H_{3} C O O H \\
N . E .(E w)=52 \mathrm{gm} \mathrm{eq}^{-1}
\end{array}
\]
В. \( R=C H_{3} \)
\[
C=C H_{3}-C H_{2}-C O O H
\]
\[
\text { N.E. }(E w)=52 \text { gm } e q^{-1}
\]
\( \mathbf{c} \cdot R=C H_{3} \)
\[
\begin{array}{l}
C=C O O H \\
N \cdot E \cdot(E w)=52 \mathrm{gm} \mathrm{eq}^{-1}
\end{array}
\]
D. None of these


\( \lim _{x \rightarrow 3}\left(x^{2}-9\right)\left[\frac{1}{x+3}+\frac{1}{x-3}\right] \)


A pendulum clock keeps correct time at
\( 20^{\circ} \mathrm{C} . \) The correction to be made during
summer per day where the average
temperature is \( 40^{\circ} C,\left(\alpha=10^{-5} /^{\circ} C\right) \)
will be:
A. 5.64 sec
B. 6.64 sec
c. 7.64 sec
D. 8.64 sec


Compound (B) and (C) are:
\( A \)
(B)
B.
(B)
\( c \)
(B)
\( (\mathbf{C}) \)
D.
(B)
\( (\mathbf{C}) \)


In the reaction sequence, \( (X) \) is:
A. cyclohexanone
B. caprolactum
\( \mathbf{c} \cdot H O\left(C H_{2}\right)_{6} N H_{2} \)
D. hexamethylene disocyanate


Integrate the function \( \sqrt{x^{2}+4 x-5} \)


If the time taken. by a hot body to cool
from \( 50^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) is 10 min when the
surrounding temperature is \( 25^{\circ} \mathrm{C} \), then
the time taken for it to cool from \( 40^{\circ} \mathrm{C} \)
to \( 30^{\circ} C \) when the surrounding
temperature is \( 15^{\circ} \mathrm{C} \), is
A. 40 min
B. 10 min
c. \( 4 \min \)
D. 15 min
E. 20 min


A ray of light is incident on a plane
mirror and the angle of incident is \( 25^{\circ} \)
What is the angle of reflection?
A. 0
B. \( 50^{\circ} \)
\( c .90^{\circ} \)
D. \( 25^{\circ} \)


An AC circuit containing \( 80 m H \)
inductor and a \( 60 \mu F \) capacitor is in series with \( 15 \Omega \) resistance. They are
connected to \( 230 V, 50 H z \) AC supply
What is the total average power absorbed by the circuit?
A . zero
B. 5 watt
c. 40 watt
D. 10 watt


To from a super saturated solution of salt one must:
A. cool slowly
B. cool rapidly
c. add some salt to cold solution
D. use a clear vesse


The hydrated salt of \( N a_{2} C O_{3} . . x H_{2} O \)
undergoes \( 63 \% \) loss in mass on heating
and become anhydrous. The value of \( x \)
is:
\( A \cdot 3 \)
B. 5
c. 7
D. 10


A road is 8 m wide. Its radius of
curvature is \( 40 \mathrm{m} \). The outer edge is
above the lower edge by distance of 1.2 \( m . \) The most suited velocity on the
road is nearly:
\( \mathbf{A} \cdot 5.7 m s^{-1} \)
B. \( 8 m s^{-1} \)
c. \( 36.1 \mathrm{ms}^{-1} \)
D. \( 9.7 \mathrm{ms}^{-1} \)


If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) is surjective then
A. no two elements of \( A \) have the same image in \( B \)
B. every element of \( A \) has an image in \( B \)
C. every element of \( B \) has at least one pre-image in \( A \)
D. \( A \) and \( B \) are finite non empty sets


The probability that \( A \) can solve a problem is \( \frac{2}{3} \) and that \( B \) can solve is \( \frac{3}{4} \) If both of them attempt the problem. What is probability that the problem act solved?
A \( \cdot \frac{11}{12} \)
в. \( \frac{7}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{9}{12} \)


A pole of height 20 ft has a shadow of length \( 11.55 \mathrm{ft} \) at a particular instant of
time. Find the angle of elevation (in degree) of the sun at this point of time.
\( \mathbf{A} \cdot 90 \)
B. 60
\( c \cdot 30^{\circ} \)
D. 45


Solve the differential equation: \( \frac{\boldsymbol{d} z}{\boldsymbol{d} \boldsymbol{x}}+ \) \( \frac{z}{x} \log z=\frac{z}{x^{2}}(\log z)^{2} \)
A \( \cdot \frac{1}{-x \log z}=\frac{1}{2 x^{2}}-c \)
в. \( \frac{1}{x \log z}=\frac{1}{2 x^{-2}}-c \)
c. \( \frac{1}{x \log z}=\frac{-1}{2 x^{2}}-c \)
D. \( \frac{1}{x \log z}=\frac{1}{2 x^{2}}-c \)


An ecosystem includes
A. All living organisms
B. Non-living objects
C. Both living organisms and non - living objects
D. Sometimes living organisms and sometimes non living objects


Which one of the following is not a physical property of water?
A. Water has low specific heat capacity
B. It expands on cooling
c. It is odorless and tasteless
D. The boiling point of water is \( 100^{\circ} \mathrm{C} \)


An ion \( M^{2+}, \) forms the complexes
\( \left[M\left(H_{2} O\right)_{6}\right]^{2+},\left[M(e n)_{3}\right]^{2+} \) and
\( \left[M B r_{6}\right]^{4-} . \) The colour of the complexes
will be
respectively.
A. green, blue and red
B. blue, red and green
c. green, red and blue
D. red, blue and green


\( \boldsymbol{L}_{1}: \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{4}} \)
\( L_{2}: \frac{x-2}{3}=\frac{y-4}{2}=\frac{z-5}{5} \) be two
given lines, point P lies on \( L_{1} \) and Q lies
on \( L_{2} \) then distance between \( P \) and \( Q \)
can be
This question has multiple correct options
A \( \cdot \frac{1}{3} \)
B.
c. 15
D. 30


Show that there are two values of time
for which a projectile is at the same height. Also show mathematically that the sum of these two times is equal to
the time of flight.


A stone is thrown vertically upward with
an initial velocity \( V_{0} . \) The distance
traveled in time \( 4 v_{0} / 3 g \) is
\( ^{A} \cdot \frac{2 v_{0}^{2}}{g} \)
в. \( \frac{v_{0}^{2}}{2 g g g} \)
\( ^{\mathrm{c}} \cdot \frac{4 v_{0}^{2}}{9 g} \)
D. \( \frac{5 v_{0}^{2}}{9 g} \)


is a point at which crossing over has taken place between homologous chromosomes.
A. Chiasmata
B. Synaptonemal complex
c. centromeres
D. Protein axes


Among I-A elements, which element is
gas at room temperature?
A. Hydrogen
B. Lithium
c. Sodium
D. Potassium


\( \mathbf{N} i(p y)_{4}\left(C l O_{4}\right)_{2} \) exists in a yellow
diamagnetic form containing the cation
\( \left[N i(p y)_{4}\right]^{2+} \) and \( C l O_{4}^{-} \) icons, and in a blue paramagnetic form containing
\( \operatorname{trans}\left[N i(p y)_{4}\left(C l O_{4}\right)_{2}\right] \) molecules in
which oxygen atoms form the \( \mathrm{Cl} \mathrm{O}_{4} \)
icons completed the octahedral coordination of the metal ion. The
hybridisation of nickel in the yellow \( \& \) blue complexes respectively are:
A \( \cdot s p^{3} \) and \( d^{2} s p^{3} \)
B. \( d s p^{2} \) and \( d^{2} s p^{3} \)
C \( \cdot d s p^{2} \) and \( s p^{3} d^{2} \)
D. \( s p^{3} \) and \( s p^{3} d^{2} \)


Rajiv bought a horse for Rs. 20000 and sold it for Rs. 25000 . Check if Rajiv made profit or loss in this transaction Find the profit or loss per cent.


Construct a \( \triangle A B C \) in which \( B C= \)
\( \mathbf{7} \boldsymbol{c m} \angle \boldsymbol{B}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \boldsymbol{\&} \boldsymbol{A} \boldsymbol{B}+\boldsymbol{A C}=\mathbf{1 3} \boldsymbol{c m} \)


Human ear is divided into:
A. external ear
B. middle ear
c. inner ear
D. all


If \( z=\left(\frac{\sqrt{3}}{2}+i \frac{1}{2}\right)^{5}+\left(\frac{\sqrt{3}}{2}-i \frac{1}{2}\right)^{5} \)
then \( \operatorname{lm}(z)= \)


A 50 V d.c power supply is used to charge a battery of eight lead
accumulators, each of emf \( 2 \mathrm{V} \) and
internal resistance \( 1 / 8 \Omega \). The charging current also runs a motor connected in
series with the battery. The resistance of the motor is \( 5 \Omega \) and the steady current supply is 4 A. The chemical power stored in the battery is
\( A \cdot 64 \mathrm{W} \)
B. 96 \( w \)
\( c \cdot 16 w \)
D. 50 w


Assume that the chances of a patient having a heart attack are \( 40 \% \). It is also assumed that a meditation and yoga
course reduce the risk of heart attack
by \( 30 \% \) and the prescription of certain drugs reduces its chances by \( 25 \% \). At a time a patient can choose any one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?


When temperature decreases, oxy-Hb curve becomes
A. more steep
B. straight
c. parabola
D. none of these.


In a small town, the number of water pumps, concrete houses and roads increased. The water table of that
place will:
A. get lower
B. get higher
c. remain unaffected
D. none of these


Fill in the blanks
Nitrogen on reaction with hot calcium
forms


A parallel plate capacitor is filled by a di-electric whose relative permitivity varies with the applied voltage according to the law \( =\alpha V \), where \( \alpha=1 \)
per volt. The same (but containing no dielectric) capacitor charged to a voltage \( V=156 \) volt is connected in parallel to
the first "non-linear" uncharged capacitor. Determine the final voltage (in volts) \( V_{f} \) across the capacitors.


How is sound produced and how is it transmitted and heard by us?


At some instant, a radioactive sample
\( \boldsymbol{S}_{1} \) having an activity \( 5 \mu C i \) has twice the number of nuclei as another sample
\( S_{2} \) which has an activity of \( 10 \mu C \) i. The
half lives of \( S_{1} \) and \( S_{2} \) are
A. 20 years and 5 years, respectively
B. 20 years and 10 years, respectively
c. 10 year each
D. 5 year each


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \frac{\boldsymbol{H C l}}{\boldsymbol{Z n C l}_{2}} \)
Product
Find the correct statement.
This question has multiple correct options
A. Reaction is \( S_{N} 1 \), if higher concentration of \( Z n C l_{2} \) is used
B. Reaction is \( S_{N} 2 \), if higher concentration of \( Z n C l_{2} \) is used
c. Rearranged the product if higher concentration of \( Z n C l_{2} \) is used.
D. All of the above


Assume that the decomposition of
\( H N O_{3} \) can be represented by the following equation
\( 4 H N O_{3}(g) \rightleftharpoons 4 N O_{2}(g)+ \)
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
The reaction approaches equilibrium at \( 400 K \) temperature and 30 atm pressure. At equilibrium partial
pressure of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is \( \boldsymbol{2} \) atm.
Calculate \( \boldsymbol{K}_{c} \) in \( (\boldsymbol{m} \boldsymbol{o l} / \boldsymbol{L})^{3} \) at \( \boldsymbol{4} \boldsymbol{0} \boldsymbol{0} \boldsymbol{K} \)
\( (\text { Use }: \boldsymbol{R}=\mathbf{0 . 0 8 a t m}-\boldsymbol{L} / \boldsymbol{m o l}-\boldsymbol{K}) \)
\( A \cdot 4 \)
B. 8
\( c \cdot 16 \)
D. 32


\( A B C D \) is a rectangle and \( P, Q, R \) and \( s \)
are mid-points of the side \( A B, B C, C D \)
and DA respectively. Show that the quadrilateral PQRS is a rhombus.


Find the value of \( x \) and \( y \) using elimination method:
\( 2 x+3 y=-6 \) and \( b x+2 y=-10 \)
A \( \cdot\left(2, \frac{-2}{3}\right) \)
B \( \cdot\left(-2, \frac{2}{3}\right) \)
c. \( \left(2, \frac{2}{3}\right) \)
D. \( \left(-2, \frac{-2}{3}\right) \)


Find the mode of the following distribution
Marks in Mathemati
45
Number of
15
students


(i) With reference to structural
variability and chemical reactivity, write the difference between
lanthanoids and actinoids.
(ii) Name a member of the lanthanoid series which is well known to exhibit +4 oxidation state
(iii) Complete the following equation:
\[
M n O_{4}^{-}+8 H^{+}+5 e^{-} \rightarrow
\]
(iv) Out of \( M n^{3+} \) and \( C r^{3+}, \) which is
more paramagnetic and why? (atomic number : \( M n=25, C r=24) \)


Two triodes having amplification factors 30 and 21 and plate resistances
\( 5 k \Omega \) and \( 4 k \Omega \) respectively are connected in parallel. The composite amplification factor of the system is
A . 25
B . 50
c. 75
D. 100


Column II gives approximate values of
magnetic field due to source given
in column I


Evaluate the following limits. \( \lim _{x \rightarrow 0} 9 \)


Mark the correct alternative of the
following. \( f(x)=1+2 \sin x+3 \cos ^{2} x, 0 \leq x \leq \)
\( \frac{2 \pi}{3} \) is?
A. Minimum at \( x=\pi / 2 \)
B . Maximum at \( x=\sin ^{-1}(1 / \sqrt{3}) \)
c. Minimum at \( x=\pi / 6 \)
D. Maximum at \( \sin ^{-1}(1 / 6) \)


Intermediate compound formed in the
depletion of \( \boldsymbol{O}_{3} \) layer by
chlorofluorocarbons is:
\( \mathbf{A} \cdot O_{2}, F_{2} \)
в. ОС l
c. \( O F_{2} \)
D. \( C l_{2} O \)


For the complex ion \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-}, \) state:
(i) the type of hybridisation.
(ii) the magnetic behaviour
(iii) the oxidation number of the central
metal atom.


Draw the curve represented by \( \sqrt{x}+ \) \( \sqrt{\boldsymbol{y}}=\mathbf{1} \)


The degree of dissociation of \( N_{2} O_{4} \) into
\( N O_{2} \) at 1.5 atmosphere and \( 40^{\circ} C \) is
0.25. Calculate its \( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \boldsymbol{4} \boldsymbol{0}^{\circ} \boldsymbol{C} \)
A. \( K_{p}=0.4 \)
в. \( K_{p}=0.8 \)
\( \mathbf{c} \cdot K_{p}=0.2 \)
D. \( K_{p}=0.6 \)


If \( \lambda_{0} \) is the de Broglie wavelength for a proton accelerated through a potential difference of \( 100 \mathrm{V}, \) the de Broglie
wavelength for \( \alpha \) -particle accelerated through the same potential difference is
A \( \cdot 2 \sqrt{2} \lambda_{0} \)
B. \( \frac{\lambda_{0}}{2} \)
\( c \cdot \frac{\lambda_{0}}{2 \sqrt{2}} \)
D. \( \frac{\lambda_{0}}{\sqrt{2}} \)


In a 0.25 -liter tube dissociation of 4
moles of NO is took place. If its degree of
dissociation is \( 10 \% . \) The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) for
reaction \( 2 N O \rightleftharpoons N_{2}+O_{2} \) is:
A \( \cdot \frac{1}{(18)^{2}} \)
в. \( \frac{1}{(8)^{2}} \)
c. \( \frac{1}{(16)} \)
D. \( \frac{1}{(32)} \)


A closed vessel contains 8 g of oxygen and 7 g of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suiColumn absorbent the pressure of the remaining gas (in atm) will be:
\( A \cdot 2 \)
B. 10
\( c \cdot 4 \)
\( D .5 \)


\( \operatorname{Solve}\left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{p}-\boldsymbol{q} & \boldsymbol{p}-\boldsymbol{r} \\ \boldsymbol{q}-\boldsymbol{p} & \boldsymbol{0} & \boldsymbol{q}-\boldsymbol{r} \\ \boldsymbol{r}-\boldsymbol{p} & \boldsymbol{r}-\boldsymbol{q} & \boldsymbol{0}\end{array}\right|= \)
\( \mathbf{A} \cdot p+q+r \)
в. \( p q+q r+r p \)
\( c \cdot c \)
D. \( p^{2}+q^{2}+r^{2} \)


The current i in the circuit (see figure)
is :
\( A \cdot \frac{1}{A 5} \)
\( B \cdot \frac{1}{15} A \)
\( c \cdot \frac{1}{10} A \)
\( D \cdot \underline{1} \)


A coil of insulating wire is connected to battery. If it is moved towards a galvanometer then its point gets
deflected because
A. the coil behaves like a magnettet
B. induced current is produced in the coil
C. the number of turns in the galvanometer coil remains constant
D. none of the above


A body of mass \( m \) is taken from earth's surface to q a height equal to radius of earth. the change in potential will be
A . \( m g \)
B. \( \frac{1}{2} m g R \)
c. \( 2 m g R \)
D. \( \frac{1}{4} m g R \)


In Brownian movement or motion, the paths of the particle are
A . linear
c. uncertain
D. curvedd


The radiations suffers maximum
deflection in a magnetic field is:
A. \( \alpha \) -particles
B. \( \beta \) -particles
c. \( x \) -rays
D. \( \gamma \) -radiations


Match the following
¡.
a. Back surface of eye where image is Cornea formed
ii. Pupil
b. Coloured part of eye
iii.
c. Membrane that refracts light and Retina protects the eye
¡V. Iris
d. Transparent opening of eye.Light passes through it
\( A \cdot \) i-c ,ii-d,iii-a,iv-b
B. i-a,ii-c,iii-b,iv-d
C . i-d,ii-a,iii-b,iv-c
D. i-b,ii-c,iii-d,iv-a


State whether following statement is
true or false.

By using the principle of mathematical induction we can proove that
\( \boldsymbol{n}(\boldsymbol{n}+1)(\boldsymbol{n}+\mathbf{5}) \) is a multiple of \( \boldsymbol{3} \)
A. True
B. False


Find the angle that the vector \( \vec{A}=2 \hat{i}+ \) \( 3 \hat{j}-\hat{k} \) makes with y-axis.
A \( \cdot \theta=\cos ^{-1}\left(\frac{3}{\sqrt{14}}\right) \)
B. \( \theta=\cos ^{-1}\left(\frac{2}{\sqrt{14}}\right) \)
\( ^{\mathrm{c}} \cdot_{\theta}=\cos ^{-1}\left(\frac{3}{\sqrt{16}}\right) \)
D. \( \theta=\cos ^{-1}\left(\frac{3}{\sqrt{28}}\right) \)


Range of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\sec ^{2} x-\tan x}{\sec ^{2} x+\tan x}-\frac{\pi}{2}<x<\frac{\pi}{2}, \) is
\( A \cdot R \)
в. \( R-\left(\frac{1}{3}, 3\right) \)
c. \( \left[\frac{1}{3}, 3\right] \)
D. \( \left[-1, \frac{5}{3}\right. \)


If 0 is the origin and \( A_{n} \) is the point
with coordinates \( (\boldsymbol{n}, \boldsymbol{n}+\mathbf{1}) \) then
\( \left(O A_{1}\right)^{2}+\left(O A_{2}\right)^{2}+\ldots+\left(O A_{7}\right)^{2} \) is
equal to


Special character of coelenterates is
A. Polymorphism
B. Nematocysts
c. Flame cells
D. Hermaphroditism


Photochemical smog affects plants by
A. Bleaching of leaves and excess production of pigments
B. Shedding of foliage and increase of transpiration
C. Decolourising and curling of leaves
D. Degradation of chlorophyll by ozone


Classify the following function \( \boldsymbol{f}(\boldsymbol{x}) \)
defined in \( R \rightarrow R \) as injective,
surjective, both or none
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{1} \mathbf{1} \boldsymbol{x}+\boldsymbol{6} \)
A. Surjective but not injective
B. Injective but not surjective
c. Neither injective nor surjective
D. Both injective and surjective


Name the following:
The property possessed by metals by which they can be beaten into sheets.


lonization Energy \( (\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m} \boldsymbol{o l}) \)
First
\[
896
\]
Secon
\[
1,752
\]
Third
\[
14,807
\]
Fourth
\[
17,948
\]
The table above shows the first four
ionization energies of an element. This element is located in which group of the
periodic table?
A. Group 1
B. Group 2
C . Group 3
D. Group 4


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


How will you prepare the following compounds from benzene? You may use any inorganic reagent and any organic reagent having not more than one carbon atom:
(i) Methyl benzoate
(ii) \( m \)
Nitrobenzoic acid
(iii) p-Nitrobenzoic acid
Phenylacetic acid
(v) p-Nitrobenzaldehyde.


\( \int \frac{x^{2}-1}{x^{4}+x^{2}+1} d x \) is equal to
A \( \cdot \log \left(x^{4}+x^{2}+1\right)+c \)
B. \( \log \frac{x^{2}-x+1}{x^{2}+x+1}+c \)
\( ^{\mathrm{C}} \cdot \frac{1}{2}^{\log \frac{x^{2}-x+1}{x^{2}+x+1}}+c \)
D. \( \frac{1}{2} \log \frac{x^{2}+x+1}{x^{2}-x+1}+c \)


Various steps of human nutrition are in
the order
A. Ingestion, egestion, digestion, absorption and assimilation
B. Ingestion, egestion, assimilation, absorption and assimilation
c. Ingestion, assimilation, digestion, absorption and egestion
D. Ingestion, digestion, absorption, assimilation and egestion


A car driver going at a speed \( \mathbf{v} \) suddenly
find a wide wall at a distance.
(coefficient of friction is \( \mu \) )
A. If the apply breaks, he will come to rest after a distance \( \frac{v^{2}}{2 \mu g} \)
B. If he turn the cart in a circle to avoid hitting, then radius of the circle is \( \frac{v^{2}}{\mu g} \)
C. It is better to apply breaks rather than to turn the vehicle in a circle
D. It is better to turn the vehicle in a circle than to apply brakes


\( Z n \) Amalgam is prepared by the
electrolysis of aqueous \( Z n C l_{2} \) using \( H g \) cathode \( (9 \mathrm{gm}) . \) How much current
should be passed through \( Z n C l_{2} \) solution for 1000 seconds to prepare a
\( Z n \) amalgam with \( 25 \% Z n \) by weight ? \( (Z n \text { atomic weight }=65.4) \)
A . \( 5.6 \mathrm{A} \)
в. 7.2 A
\( c \cdot 8.85 A \)
D. 11.2 A


On hydrolysis of sodium carbonate, the reaction takes place between?
A \( . N a^{+} \) and water
B. \( N a^{+} \) and \( O H^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \) and water
D. \( C O_{3}^{2-} \) and \( H^{+} \)


Two identical cylindrical vessels with their bases at the same level; contain
liquid of density \( \rho . \) The area of both is \( S \) but the height of liquid in one vessel is \( h_{1} \) and in other \( h_{2} . \) The work done when both cylinders are connected, by gravity in equalising levels is:
A \( \cdot \frac{1}{4} g \rho S\left(h_{2}-h_{1}\right)^{2} \)
в. \( g \rho S\left(h_{2}-h_{1}\right)^{2} \)
c. \( g \rho S\left(h_{2}-h_{1}\right) \)
D. \( \frac{1}{4} g \rho S\left(h_{2}-h_{1}\right) \)


The heat generated in a circuit is given
by \( Q=I^{2} R t, \) where I is current, \( \mathrm{R} \) is
resistance and t is time. If the
percentage errors in measuring I, R and \( t \) are \( 2 \%, 1 \% \) and1 \( \%, \) respectively, then the maximum error in measuring heat will be
A . \( 2 \% \)
B. \( 3 \% \)
c. \( 4 \% \)
D. \( 6 \% \)


Biennials are
A. Plants, which remain vegetative in first growing season but produce flowers in the next season.
B. Plants producing flowers twice in their lifecycle.
C. Plants, which flower many times.
D. Plants finishing their lifecycle in one season only.


The length of a brass scale is \( 1 m \) at
\( 301 K . \) If the coefficient of linear
expansion is \( 18 \times 10^{-6} / K, \) what is its
new length at \( 341 K ? \)


Given the arrangement of charge below and the point \( P, \) what do we know for sure?
The distance between adjacent charges is the same for all and the same as the
distance from the nearest charges to
point \( P \)
\( \left(\begin{array}{ll}1.0 & c\end{array}\right) \quad\left(\begin{array}{ll}1.0 & c\end{array}\right) \quad \) op
A. The electric potential at point \( P \) is positive.
B. The electric potential at point \( P \) is negative.
c. The electric potential at point \( P \) is directed down and to the right.
D. The electric potential at point P is directed up and to the left
E. The electric potential at point P is zero.


The graph between two temperature
scales \( A \) and \( B \) is shown in figure.
Between upper fixed point and lower
fixed point, there are 150 equal
divisions on scale \( A \) and 100 on scale \( B \)
The relationship for conversion between the two scales in given by:
A \( \cdot \frac{t_{A}-180}{100}=\frac{t_{B}}{150} \)
в. \( \frac{t_{A}-30}{150}=\frac{t_{B}}{100} \)
c. \( \frac{t_{B}-180}{150}=\frac{t_{A}}{100} \)
D. \( \frac{t_{B}-40}{100}=\frac{t_{A}}{180} \)


The phase difference between the two
simple harmonic oscillations, \( \boldsymbol{y}_{1}= \) \( \frac{1}{2} \sin \omega t+\left(\frac{\sqrt{3}}{2}\right) \cos \omega t \) and \( y_{2}= \)
\( \sin \omega t+\cos \omega t \) is
A \( \cdot \frac{\pi}{6} \)
B. \( -\frac{\pi}{6} \)
c. \( \frac{\pi}{12} \)
D. \( \frac{7 \pi}{12} \)


The water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop
at that instant? (Take \( \left.g=10 m s^{-2}\right) \)


Name the lens.


When a radioactive nucleus emits a \( \beta \) particular, the proton- neutron ratio
A . decreases
B. increases
c. remains same
D. first decreases and increases


A man slides down a snow covered hill
along a curved path and falls \( 20 \mathrm{m} \) below his initial position. The velocity in \( \mathrm{m} / \mathrm{sec} \) with which he finally strikes the
ground is? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s e c}^{2}\right) \)
A . 20
в. 400
c. 200
D. 40


The given diagram represents:
Total enthalpy of reactants
Total enthalpy of products
A. Enthalpy diagram for endothermic reaction
B. Enthalpy diagram for exothermic reaction
C. Enthalpy diagram for reversible reaction
D. Enthalpy diagram for non-spontaneous reaction


The self ionisation constant for pure
formic acid. \( \boldsymbol{K}= \)
\( \left[\boldsymbol{H} \boldsymbol{C O O H}_{2}^{+}\right]\left[\boldsymbol{H} \boldsymbol{C O O}^{-}\right] \) has been
estimated as \( 10^{-6} \) at room
temperature. The percentage of formic
acid molecules in pure formic acid are converted to formate ion is \( 0.00 X \% \). The
density of formic acid is \( 1.22 g / c m^{3} \) Value of \( X \) is:


Gas \( (X) \) turns lime water milky. Gas \( (X) \)
also turns acidied \( K_{2} C r_{2} O_{7} \) green. \( (X) \) is :
A \( . C O \)
в. \( C O_{2} \)
\( c \cdot s O_{2} \)
D. none of these


Large nearly empty, colourless cells present on the upper surface of grass leaf are
A. Accessory cells
B. Bulliform cells
c. Palisade parenchyma
D. Spongy parenchyma
E. Passage cells


The velocity of electromagnetic wave is
parallel to:
\( \mathbf{A} \cdot \vec{B} \times \vec{E} \)
в. \( \vec{E} \times \vec{B} \)
\( c \cdot \vec{E} \)
D. \( \vec{B} \)


Draw a \( \triangle A B C, \) right - angled at \( B \) such that \( A B=3 c m, B C=4 \) cm. Now
construct a \( \triangle P B Q \) similar to \( \Delta A B C \) each of whose side is \( \frac{7}{5} \) times the
corresponding side of \( \Delta A B C \)


A letter is known to have come from
either \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{A} \boldsymbol{R} \) or
CALCUTTA. On the envelope just two consecutive letters \( \boldsymbol{T} \boldsymbol{A} \) are visible. The
probability that the letter has come
from \( C \) ALCUTTA is
A \( \cdot \frac{4}{11} \)
B. \( \frac{1}{3} \)
c. \( \frac{5}{11} \)
D. \( \frac{4}{7} \)


In which of the following molecule, the number of possible \( \angle X A X \) angles is maximum in the anionic part of their
solid state? \( [\boldsymbol{A}: \text { Central atom, } \boldsymbol{X} \)
surrounding atom]
A. \( P B r_{5} \)
в. \( N_{2} O_{5} \)
c. \( P C l_{5} \)
D. \( C l_{2} O_{6} \)


Compare and contrast bio-mass and hydro electricity as sources of energy.


Which of the following Kepler's laws is also known as harmonic law?
A. First law
B. Second law
c. Third law
D. None of these


Assertion
The weight of an object changes from
place to place but not mass.
Reason
The weight of the object is independent
of the value of \( \mathfrak{g} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Give reasons:
When a body falls freely to the ground,
its motion has a uniform acceleration.


A coil of insulated wire is connected to a
battery. If it is taken to a galvanometer, its pointer is deflected, because
A. induced current is produced in the galvanometer coil
B. the coil acts like a magnet
c. the number of turns in the coil of the galvanometer are changed
D. none of the above


Can you store copper sulphate solutions
in a zinc pot?


Q Type your question
charges along the \( x-, y- \) and z-axes,
respectively. The charge density, i.e.,
charge per unit length of each wire is \( \lambda: \)
A \( \cdot \frac{\lambda}{3 \pi \varepsilon_{0} a}(\hat{i}+\hat{j}+\widehat{k}) \)
В \( \cdot \frac{\lambda}{2 \pi \varepsilon_{0} a}(\hat{i}+\hat{j}+\widehat{k}) \)
c. \( \frac{\lambda}{2 \sqrt{2} \pi \varepsilon_{0} a}(\hat{i}+\widehat{j}+\widehat{k}) \)
D. \( \frac{\sqrt{2} \lambda}{(\hat{i}+\hat{j}+\widehat{k})} \)


The de Broglie wavelength of an electron
accelerated by an electric field of \( V \) volt is given by:
A \( \cdot \lambda=\frac{1.23}{\sqrt{m}} \)
в. \( \lambda=\frac{1.23 m}{\sqrt{h}} m \)
c. \( \lambda=\frac{1.23}{\sqrt{V}} n m \)
D. \( \lambda=\frac{1.23}{V} \)


A particle moves along the parabolic
path \( y=a x^{2} \) in such a way that the \( y- \)
component of the velocity remains constant, say \( c . \) The \( x \) and \( y \) coordinates
are in meters. Then acceleration of the
particle at \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m} \) is:
\( \mathbf{A} \cdot a c \hat{k} \)
B \( \cdot 2 a c^{2} \hat{j} \)
c. \( -\frac{c^{2}}{4 a^{2}} \)
D. \( -\frac{c}{2 a} \hat{i} \)