The loop shown moves with a velocity \( v \)
in a uniform magnetic field of
magnitude \( B \), directed into the paper. The potential difference between points
\( P \) and \( Q \) is \( e . \) Then
This question has multiple correct options
B. \( e=B l v \)
C. \( P \) is positive with respect to \( Q \)
D. \( Q \) is positive with respect to \( P \)


Assertion
The bar magnet falling vertically along
the axis of the horizontal coil will be
having acceleration less than \( g \)
Reason
Clockwise current induced in the coil.
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


An object is seen first in red light and
then in violet light through a simple microscope. In which case is the magnification larger?


What is the oxidation state of Co in the
complex \( \left[\text { Co} C l_{2}(e n)_{2}\right]^{+} ? \)
[Note: Ethylenediamine \( (e n)=H_{2} N- \)
\( \left.\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{N} \boldsymbol{H}_{2}\right] \)


The process of separation of racemic modifications into d and I enantiomers
is called :
A. Resolution
B. Dehydration
c. Revolution
D. Dehydrohalogenation


\( A B \| \overrightarrow{C D} \) in the following figure. \( \overline{X Y} \) is
the transversal. If \( m \angle P Q A=140^{\circ}, \) find
the measure of remaining angles:


The two above shown structures are
related as:
and
A. enantiomers
B. diastereomers
c. constitutional isomers
D. conformational isomers


Pappus is modification of
A. Bracts
B. corolla
c. calyx
D. All of the above


Assertion
Nitrogen-fixing enzyme in legume root nodules function at low oxygen
concentration.
Reason
Low oxygen concentration is provided by leghaemoglobin.
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


How will you weight the sun that estimates its mass? The mean orbital
radius of the earth around the sun is


elevated ends and a flat central part as shown in the Figure below. The flat portion BC has a length \( l=3.0 m . \) The
curved portions of the track are
frictionless. For the flat part the
coefficient of kinetic friction is \( \mu_{k}= \)
\( 0.20, \) the particle is released at point \( A \)
which is at height \( h=1.5 m \) above the
flat part of the track. Where does the
particle finally comes to rest?
B. The particle comes to rest at \( \frac{1}{4} \) th distance from the point B of the flat part.
C. The particle comes to rest at \( \frac{3}{4} \) th distance from the
point B of the flat part.
D. The particle comes to rest at point


Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a paralle plate capacitor. A small spherical metallic ball is suspended by a long insulated thread such that it hangs
freely in the center of the two metallic plates. The ball, which is uncharged, is taken slowly towards the positively charged plate and is made to touch that
plate. Then the ball will :
A. stick to the positively charged plate
B. come back to its original position and will remain there
c. oscillate between the two plates touching each plate in turn
D. oscillate between the two plates without touch them


If \( \bar{z}_{1}=a \hat{i}+b \hat{j} \) and \( \bar{z}_{2}=c \hat{i}+d \hat{j} \) are two
vectors in \( \hat{i} \) and \( \hat{j} \) system where \( \left|\bar{z}_{1}\right|= \)
\( \left|\bar{z}_{2}\right|=r \) and \( \bar{z}_{1} \cdot \bar{z}_{2}=0, \) then \( \bar{\omega}_{1}=a \hat{i}+ \)
\( c \hat{j} \) and \( \bar{\omega}_{2}=b \hat{i}+d \hat{j} \) satisfy
\( \mathbf{A} \cdot\left|\bar{\omega}_{1}\right|=r \)
В \( \cdot\left|\bar{\omega}_{2}\right| \neq r \)
\begin{tabular}{l}
c. \( \bar{\omega}_{1}, \bar{\omega}_{2}=0 \) \\
\hline
\end{tabular}
D. None of these


\( \operatorname{Let} \boldsymbol{f}=\{(1, \boldsymbol{a}),(\boldsymbol{2}, \boldsymbol{c}),(\boldsymbol{4}, \boldsymbol{d}),(\boldsymbol{3}, \boldsymbol{b})\} \) and
\( \boldsymbol{g}^{-1}=\{(\boldsymbol{2}, \boldsymbol{a}),(\boldsymbol{4}, \boldsymbol{b}),(1, c),(\boldsymbol{3}, \boldsymbol{d})\}, \) then
show that \( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})^{-1}=\boldsymbol{f}^{-1} \boldsymbol{o g}^{-1} \)


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}(\mathbf{1}+\boldsymbol{a} \cos \boldsymbol{x})-\boldsymbol{b} \sin \boldsymbol{x}}{\boldsymbol{x}^{3}}, \boldsymbol{x} \neq \mathbf{0} \) and
\( f(0)=1 . \) The value of \( a \) and \( b \) so that \( f \)
is a continuous function are-
A \( \cdot \frac{5}{2}, \frac{3}{2} \)
В. \( \frac{5}{2},-\frac{3}{2} \)
c. \( -\frac{5}{2},-\frac{3}{2} \)
D. None of these


The correct geometry and hybridization
for \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) are :
A . trigonal planar, \( s p^{3} d^{3} \)
B. square planar, \( s p^{3} d^{2} \)
c. octahedral, \( s p^{3} d^{2} \)
D. trigonal bipyramidal, \( s p^{3} d \)


Write any two methods of preparation of phenol. Give their corresponding equations.


What is the role of fuse, used in series
with any electrical appliance? Why should a fuse with defined rating not be replaced by one with a larger rating?


Assertion
The isothermal curves intersect each
other at a certain point
Reason
The isothermal change takes place slowly so, the isothermal curves have
very little slope.
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. Reason is correct but Assertion is incorrect
D. Both Assertion and Reason are incorrect


The value of \( \int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\sin ^{4} x+\cos ^{4} x} d x \) is
A \( \cdot \pi^{2} / 8 \)
B . \( \pi^{2} / 16 \)
c. \( 3 \pi^{2} / 4 \)
D. \( \pi^{2} / 2 \)


If \( \sin (A+B)=1 \) and \( \cos (A-B)= \)
\( \frac{\sqrt{3}}{2} . \) then find the minimum positive
value of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
A \( \cdot 60^{\circ}, 30^{\circ} \)
\( ^{\circ} 0^{\circ} \)
B . \( 75^{\circ}, 15^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ}, 60^{\circ} \)
D. \( 45^{\circ}, 45^{\circ} \)


The separation between two masses is reduced to half. How is the magnitude of gravitational force between them affected?
A. Force will become four times
B. Force will remains same
c. Force will become twice
D. Force will become eight times


Aqueous solution of ammonium
sulphate:
A. turns blue litmus to red
B. turns red litmus to blue
c. bleaches litmus
D. has no action on litmus


Which of the following logic gates is an universal gate?
A. or
в. NOT
c. AND
D. NAND


How many glucose molecules are required for the formation of 52 pyruvic acid molecules at the end of glycolysis?
A . 52
B. 46
\( c \cdot 32 \)
D. 26


The graph (2) tells us that:
A. equilibrium is never achieved
B. equilibrium is achieved after the concentration reactants and products become equal
C. equilibrium is achieved before the concentration reactants and products become equal
D. none of the above


Prove that:
\[
\cos 20^{\circ}+\cos 100^{\circ}+\cos 140^{\circ}=0
\]


\( \boldsymbol{p} \boldsymbol{\pi}-\boldsymbol{p} \boldsymbol{\pi} \) multiple bonding between
nitrogen atoms is present in:
A. hyponitrous acid
B. nitrous acid
c. nitric acid
D. all of these


The force between the plates of a parallel
plate capacitor of capacitance \( C \) and distance of separation of the plates \( d \) with a potential difference \( V \) between the
plates, is:
\( ^{\text {A }} \cdot \frac{C V^{2}}{2 d} \)
B. \( \frac{C^{2} V^{2}}{2 d^{2}} \)
c. \( \frac{C^{2} V^{2}}{d^{2}} \)
D. \( \frac{V^{2} d}{C} \)


The mole fraction of solute in \( 10 \% \) (w/w)
aqueous NaOH solution is:
A . 0.1
B. 0.05
c. 0.0476
D. 0.075


In anaphase, a metacentric
chromosome appears in which of the following?
A. I shaped
B. J shaped
c. \( \mathrm{v} \) shaped
D. L shaped


Let 'o' be a binary operation on the set
\( Q_{0} \) of all non-zero rational numbers defined by \( a o b=\frac{a b}{2}, \) for all \( a, b \in Q_{0} \)
Find the identity element in \( Q_{0} \)


If \( \boldsymbol{x}+\boldsymbol{y}=\tan ^{-1} \boldsymbol{y} \) and \( \boldsymbol{y}^{\prime \prime}=\boldsymbol{f}(\boldsymbol{y}) \boldsymbol{y}^{\prime} \) then
\( \boldsymbol{f}(\boldsymbol{y})= \)
A \( \cdot \frac{1}{y\left(1+y^{2}\right)} \)
В. \( \frac{3}{y\left(1+y^{2}\right)} \)
c. \( \frac{2}{y\left(1+y^{2}\right)} \)
D. \( \frac{-2}{y\left(1+y^{2}\right)} \)


Which of the following statements is
true?
A. The satellite \( A \) has a shorter period than the satellite \( B \)
B. The satellite \( B \) has a shorter period than the satellite \( A \)
C. The two satellites must have the same period
D. The two satellites must have the same linear speed
E. The two satellites must have the same period and the same linear speed


If the radius of a sphere is doubled, then its volume is increase by
\( \mathbf{A} \cdot 100 \% \)
B. 200\%
\( c .700 \% \)
D. \( 800 \% \)


A parallel plate capacitor is charged
and then the battery is disconnected, When the plates of the capacitor are brought closer, then This question has multiple correct options
A. energy stored in the capacitor decreases
B. the potential difference between the plates decreases
c. the capacitance increases
D. the electric field between the plates decreases


Prove that the function \( f(x)=[x] \) is not
continuous at \( \boldsymbol{x}=\mathbf{0} . \) Where \( [\boldsymbol{x}] \) is the
greatest integer function.


The force with which water molecules
are held together in xylem is
A. Imbibition pressure
B. Osmotic pressure
c. Adhesion force
D. cohesion force


Which of the following statement is true for graphite?
(a) In graphite, each carbon atom is bonded to four other carbon atoms.
(b) Graphite is very hard.
(c) It is a good conductor of electricity.
(d) It is bad conductor of electricity.
\( A \cdot a, b \) and \( d \)
B. only c
\( c . \) a and d
D. a and c


What is activation energy?


The thermal stability of alkaline earth
metal carbonates-
\( M g C O_{3}, C a C O_{3}, S r C O_{3} \) and \( B a C O_{3} \)
follows the order:
A. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
в. \( C a C O_{3}>S r C O_{3}>M g C O_{3}>B a C O_{3} \)
с. \( M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
D. \( B a C O_{3}>S r C O_{3}>M g C O_{3}>C a C O_{3} \)


Img of matter convert into energy will give
A. 90 joul
B. \( 9 \times 10^{3} \) joule
c. \( 9 \times 10^{5} \) joule
D. \( 9 \times 10^{10} \) joule


The word Argon
means
A . Noble
B. Now
c. strange
D. Lazy


Write the equation occurring at anode
in lead battery.


Three charges \( +4 q, Q \) and \( q \) are placed in a straight line of length I at points at distances \( 0,1 / 2, \) and I respectively. What should be \( Q \) in order to make the
net force on q to be zero?
\( A \cdot-q \)
B. -29
\( c \cdot-\frac{q}{2} \)
D. 49


An iron rod of length \( 2 \mathrm{m} \) and cross sectional area of \( 50 \mathrm{mm}^{2} \) stretched by
0.5mm, when a mass of 250 kgis hung from its lower end. Young's modulus of
iron rod is
\( \mathbf{A} \cdot 19.6 \times 10^{20} N / m^{2} \)
B . \( 19.6 \times 10^{18} N / m^{2} \)
C \( \cdot 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{15} N / m^{2} \)


Acromegaly is due to hypersecretion of hormone from
A. Neurohypophysis
B. Adenohypophysis
c. Pars intermedialis
D. Cells of Leydig


A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different
arrangements can the dolphins swim?
A .24
B. 36
\( c .30 \)
D. 18


Biological control during sewage treatment is observed in
A. Aerating tanks
B. Settling tanks
c. Anaerobic sludge digesters
D. Primary treatment


A physical quantity of the dimensions of mass that can be formed out of \( c, G \) and \( \frac{e^{2}}{8 \pi \varepsilon_{0}} \) is \( (c \text { is velocity of light, } G \) is
universal constant of gravitation and \( e \)
is charge, \( \left.\varepsilon_{0} \text { is electrical permittivity }\right) \)
\( ^{\mathbf{A}} \cdot\left[G \frac{e^{2}}{8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)
\( ^{\mathbf{B}} \cdot_{c^{0}}\left[\frac{G e^{2}}{8 \pi \varepsilon_{0}}\right]^{2} \)
\( c \cdot\left[\frac{e^{2}}{G 8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)
\( c^{0}\left[\frac{G e^{2}}{8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)


If \( \frac{\cos (\theta-\alpha)}{\sin (\theta+\alpha)}=\frac{m+1}{m-1}, \) then \( m \) is equal
to
A \( \cdot \tan \left(\frac{\pi}{4}-\theta\right) \tan \left(\frac{\pi}{4}-\alpha\right) \)
B. \( \tan \left(\frac{\pi}{4}-\theta\right) \tan \left(\frac{\pi}{4}+\alpha\right) \)
c. \( \tan \left(\frac{\pi}{4}+\theta\right) \tan \left(\frac{\pi}{4}+\alpha\right) \)
D. \( \tan \left(\frac{\pi}{4}+\theta\right) \tan \left(\frac{\pi}{4}-\alpha\right) \)


Here \( \boldsymbol{X} \) is


Evaluate \( \cos \left[\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)+\frac{\pi}{6}\right] \)


Write balanced chemical equations for the reduction reaction of lead (II) oxide
by carbon.


Water has maximum density at
A. Room temperature
B. \( 4^{\circ} \mathrm{C} \)
\( c \cdot 0^{o} C \)
D. \( -4^{\circ} C \)


ff \( \Delta=\left|\begin{array}{lll}a r g z_{1} & a r g z_{2} & a r g z_{3} \\ a r g z_{2} & a r g z_{3} & a r g z_{1} \\ a r g z_{3} & a r g z_{1} & a r g z_{2}\end{array}\right|, \) the \( , \Delta \)
is divided by:
A \( \cdot \arg \left(z_{1}+z_{2}+z_{3}\right) \)
B \( \cdot \arg \left(z_{1} \cdot z_{2} \cdot z_{3}\right) \)
C \( \cdot\left(a r g z_{1}+a r g z_{2}+\arg z_{3}\right) \)
D. N.O.T


Suppose the exact charge neutrality does not hold in a world and the electron
has a charge \( 1 \% \) less in magnitude
than the proton. Calculate the Coulomb
force acting between two blocks of iron each of mass \( 1 k g \) separated by a distance of 1 m. The number of protons
in an iron atom \( =26 \) and \( 58 k g \) of iron
contains \( 6 \times 10^{26} \) atoms.


Draw the graph of \( I_{r m s} \rightarrow \omega \) for an A.C.
L-C-R series circuit and hence explain
Q-factor.


Find the cube root of the following number by prime factorisation method 175616


Which acid is present in the stinging hair of nettle leafs?


is a self adjusting force.
A. Magnetic Force
B. Electrostatic Force
C. Frictional Force
D. All


Let \( R \) be the set of all real numbers and
\( \boldsymbol{f}:[-1,1] \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}x \sin \frac{1}{x} ; \quad x \neq 0 \\ 0 ; \quad x=0\end{array}\right. \)
A . \( f \) satisfies the conditions of Rolle's theorem on [-1,1]
B. \( f \) satisfies the conditions of Lagrange's mean value theorem on [-1,1]
C. \( f \) satisfies the conditions of Rolle's theorem on [0,1]
D. \( f \) satisfies the conditions of Lagrange's mean value
theorem on [0,1]


Heart beat is accelerated by
A. Sympathetic nerves and noradrenaline
B. Cranial nerves and adrenaline
C. Cranial nerves and acetylcholine
D. Sympathetic nerves and acetylcholine


Assertion
\( N_{2} O \) is represented by \( (i) N=N=O \)
and
\( (i i) N \equiv N \rightarrow O \) but later is more
stable.
Reason
The form
(ii) shows resonance.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The enthalpy of solution of anhydrous
\( C u S O_{4} \) is \( -16 k C a l \) and that of
\( \mathrm{CuSO}_{4} \cdot \mathrm{5H}_{2} \mathrm{O} \) is \( 3 \mathrm{kCal} \). Calculate \( \Delta \boldsymbol{H} \)
for the following reaction at \( 500 K \) and
constant pressure.


In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come
together?


Which of the following is a \( 1^{\circ} \) amine?
A \( \cdot\left(C H_{3}\right)_{3} C N H_{2} \)
в. \( C_{6} H_{5} N H C H_{3} \)
\( \mathbf{c} \cdot_{C H_{3} N H C H}\left(C H_{3}\right)_{2} \)
D. \( \left(C H_{3} C H_{2}\right)_{2} N C H_{3} \)


An object \( A \) of mass \( 1 k g \) is projected vertically upward with a speed of \( 20 m / s . \) At the same moment another object \( B \) of mass \( 3 k g, \) which is initially
above the object \( A \), is dropped from a
height \( h=20 m . \) The two point like
objects \( (A \text { and } B) \) collide and stick to
each other. The kinetic energy is \( \boldsymbol{K} \) (in \( \boldsymbol{J} \)
of the combined mass just after collision, find the value of \( \boldsymbol{K} / \mathbf{2 5} \)


\( 99 \% \) of a first - order reaction was
completed in 32 min When will \( 99.9 \% \) of
the reaction complete?
A. 50 Min
B. 46Min
c. 49 Min
D. 48Min


The diameter of a solid disc is \( 0.5 m \) and
its mass is \( 16 k g \)

What torque is required to increase its angular velocity about an axis perpendicular to its plane from zero to 120 rotations/minute in 8 seconds?
\( ^{\mathbf{A}} \cdot \frac{\pi}{4} N / m \)
в. \( \frac{\pi}{2} N / m \)
c. \( \pi N / m \)
D. \( 2 \pi N / m \)


The reactance of a \( 2.00 \mu F \) capacitor at a frequency of \( 50.0 H z \) is \( \frac{x}{10} k \Omega . \) Find \( x \)


Calculate net work done by the gas.


Integrate :\( \int \frac{d x}{x(x+1)} \)


The reciprocals of all the terms of a geometric progression form a progression.
\( A \cdot A P \)
в. нР
c. ศ
D. AGP


Which of the following sulphides when heated strongly in air gives the corresponding metal without undergoing separate reduction of oxide?
A \( \cdot C u_{2} S \)
в. FeS
с. Нg S
D. \( Z n S \)


How many times will he hear a
minimum in sound intensity?


Solve for \( x \) :
\( \frac{2}{\sqrt{x}}+\frac{8}{\sqrt{y}}=2 \)
\( \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \)


Which of the following statements is
incorrect about the trends in periodic
properties in the periodic table ?
A. Metallic character increases from Li to Cs
B. The acidity of oxides increases from left to right in a period
C. Noble gases have the highest electron affinity among all the elements in the periodic table
D. Ionisation energy of aluminium is lower than that of magnesium


Show that in an ideal toroid the
magnetic field outside the toroid at any point in the open space is zero.


What is an orbital? How is it different
from Bohr's orbit?


The Joules heating effect for an electric heater in \( A . C \) and in D.C. circuit is
A. Equal
B. nearly Equal
c. not equal
D. opposite


Find the oxidation number of \( \mathrm{P} \) in \( \boldsymbol{P} \boldsymbol{H}_{4}^{+} \)


Which of the following(s) is/are correct
statements?
This question has multiple correct options
A. Hardy Schulz rule is related to coagulation
B. Brownian movement and Tyndall effect are shown by colloids
c. When liquid is dispersed in liquid, it is called gel.
D. Gold number is a measure of protective power of lyophillic colloid


State the kind of triangle in the
adjoining figure.


If the equation \( \sin ^{-1}\left(x^{2}+x+1\right)+ \)
\( \cos ^{-1}(\lambda x+1)=\frac{\pi}{2} \) has exactly two
solutions for \( \lambda \epsilon[a, b) \) then the value of
\( (a+b) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Tritium is obtained by:
A. Nuclear reactions
B. Passing steam over heated \( C \)
C. Action of \( N a O H \) on \( ^{\prime} A l^{\prime} \)
D. Action of \( H_{2} S O_{4} \) on \( ^{\prime} Z n^{\prime} \)


Prove that induction that
\( \sin x+\sin 3 x+\dots+\sin (2 n-1) x= \)
\( \frac{\sin ^{2} n x}{\sin x} \)


The letters of the word COCHIN are
permuted and all the permutations are arranged in an alphabetical order as in
an English dictionary. The number of words that appear before the word COCHIN is
A . 360
B. 192
\( c \cdot 96 \)
D. 48


Find \( \boldsymbol{F}(\boldsymbol{x}) \) from the \( \operatorname{given} \boldsymbol{F}^{\prime}(\boldsymbol{x}) \)
\( \boldsymbol{F}^{\prime}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}+\mathbf{1} \) and \( \boldsymbol{F}(-1)=\mathbf{2} \)


An iron wire is immersed in a solution
containing \( Z n S O_{4} \) and \( N i S O_{4} . \) Predict giving reasons which of the following reactions is likely to proceed?
(i) Iron reduces \( Z n^{2+} \) ions
(ii) Iron
reduces \( N i^{2+} \) ions.
Given: \( \boldsymbol{E}_{\boldsymbol{Z} n^{2+} / \boldsymbol{Z} \boldsymbol{n}}= \)
-0.76 volt; \( E_{F e^{2+} / F e}^{\circ}=-0.44 \) volt and
\( \boldsymbol{E}_{N i^{2+} / N i}^{\circ}=-\mathbf{0 . 2 5} \) volt.


Increasing electropositive character:
\( \boldsymbol{A l}<\boldsymbol{M} \boldsymbol{g}<\boldsymbol{N} \boldsymbol{a} \)
If true enter 1 , else enter 0 .
\( A \)


According to the collision theory, most molecular collisions do not lead to a
reaction. Which of the following is(are) necessary for collisions to successfully
lead to the reaction?
This question has multiple correct options
A. The total kinetic energy of the collision must be greater than some minimum value
B. A catalyst must be present at the collision.
c. The colliding particles must be properly oriented in space when they collide.
D. None of the above


Nichrome and copper wire of same
length and same radius are connected in series. Current \( I \) is passed through
them. Which wire gets heated up more? Justify your answer.


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


According to Hooke's law of elasticity, if stress is increased, then the ratio of
stress to strain :
A. becomes zero
B. remains constant
c. decreases
D. increases


In Dumas method for estimation of
nitrogen \( 0.30 g \) of an organic compound gave \( 50 m l \) of nitrogen collected at \( 300 K \) and 715 mm of \( H g \) pressure.
What is the percentage composition of nitrogen in the compound if aqueous tension at \( 300 K \) is 15 mm of \( H g ? \)
A . \( 15.23 \% \)
B. \( 17.46 \% \)
c. \( 19.23 \% \)
D . 22\%


A good characteristic of fuel is that it:
A. leaves more ash
B. leaves no ash
c. is highly expensive
D. none of the above


The graph of \( x=5 \) is perpendicular to
A. x-axis
B. y-axis
c. Line \( y=x \)
D. Line \( y=-x \)


One curie is equal to
A \( .3 .7 \times 10^{10} \) disintegration / sec
B. \( 3.2 \times 10^{8} \) disintegration/sec
c. \( 2.8 \times 10^{10} \) disintegration / sec
D. None of these


Give an example of motion in which
average speed is not zero, but the
average velocity is zero.
A. A car moving with an average speed returns to the initial position
B. A car at rest
c. A car with non zero displacement.
D. All of the above.


A small hole is made at the button of a
symmetrical jar as shown in figure.
liquid is filled into the jar upto a certain
height. The rate of descension of liquid
is independent of the level of liquid in
the jar. Then the surface of jar is a
surface of revolution of the curve
\( \mathbf{A} \cdot y=k x^{4} \)
\( \mathbf{B} \cdot y=k x^{2} \)
\( \mathbf{c} \cdot y=k x^{3} \)
D. \( y=k x^{5} \)


Derive the expression for the self
inductance of a long solenoid of cross
sectional area \( A \) and length \( l \), having \( n \)
turns per unit length.


For the gas phase reaction,
\[
\mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3} ; \quad \boldsymbol{\Delta} \boldsymbol{H}=
\]
\( -x \)
carried out in a vessel, the equilibrium
concentration of \( S O_{2} \) can be increased
by :
This question has multiple correct options
A. increasing the temperature.
B. decreasing the pressure.
c. removing some oxygen.
D. none of the above


Ausralopithecus and Homo erectus both had erect posture. But why Homo erectus is considered more advanced? Give
atleast three such differentiating points to illustrate your answer.


Find the value of \( x \) which satisfy equation \( \cos \left(2 \sin ^{-1} x\right)=\frac{1}{3} \)
A \( \cdot x=\frac{1}{\sqrt{5}} \) and \( x=\frac{-1}{\sqrt{5}} \)
B . \( x=\frac{1}{\sqrt{3}} \) and \( x=\frac{-1}{\sqrt{3}} \)
c. \( x=\frac{1}{\sqrt{2}} \) and \( x=\frac{-1}{\sqrt{2}} \)
D. None of these


Which of the above metal oxide has
the minimum thermal decomposition
temperature?
Cad
O
\( 3 . \) Fed
\( c \cdot Z r O_{2} \)
D. \( M q \)


Value of \( 2^{2} \times(-3)^{2} \times 2^{2} \times(-4)^{2} \) is
A .2034
в. 2403
\( c .2304 \)
D. None of these


A trolley is moving horizontally with a velocity of \( v \) m/s w.r.t. earth. A man
starts running in the direction of
motion of trolley from one end of trolley
with a velocity \( 1.5 v \) m/ \( s \) w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running
with a velocity of1.5 \( \boldsymbol{v} \boldsymbol{m} / \boldsymbol{s} \) w.r.t. trolley
in the backward direction. If the length
of the trolley is \( \mathrm{L} \), then the displacement
of the man with respect to earth,
measured as a function of time, will
attain a maximum value of
A \( \cdot \frac{4}{3} L \)
B. \( \frac{2}{3} L \)
c. \( \frac{5 L}{3} \)
D. \( 1.5 L \)


To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{3}{5} \) of that of \( \Delta A B C, \) a ray \( B X \) is drawn at acute
angle with \( B C \). How many minimum no
of points should be marked on \( B X ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


If forest disappear
A. The amount of \( C O_{2} \) in air decrease
B. The amount of \( O_{2} \) in air will increases
C. The amount of \( C O_{2} \) in air increases
D. The Amount of nitrogen in air will increase


A \( 100 m \) train is moving North at a
speed of \( 16 m s^{-1} . \) A bird flying at 4
\( m s^{-1} \) towards South crosses the train
in
A . \( 5 s \)
в. \( 10 s \)
\( c \cdot 12 s \)
D. 20


A wave equation which gives the displacement along the y-direction is given by \( \boldsymbol{y}=\mathbf{1 0} \sin (\mathbf{6 0} t+\mathbf{2} \boldsymbol{x}) \) where \( \boldsymbol{x} \)
and \( y \) are in metres and \( t \) is time in
seconds. This represents a wave This question has multiple correct options
A. travelling with a velocity of \( 30 \mathrm{m} / \mathrm{s} \) in the negative \( x- \) direction
B. of wavelength \( \pi \mathrm{m} \)
c. of frequency \( \frac{30}{\pi} H \)
D. of amplitude \( 10 m \)


The apes are usually
A. Insectivorous
B. Carnivorous
C . Herbivorous
D. Omnivorous


Let \( A \) be a square matrix, all of whose entries are integers. Then, which one of the following is true?
\( \mathbf{A} \cdot \) If \( \operatorname{det}(A)=\pm 1, \) then \( A^{-1} \) need not exist
B . If \( \operatorname{det}(A)=\pm 1 \), then \( A^{-1} \) exists but all its entries ar not necessarily integers
C \( \cdot \) If \( \operatorname{det}(A) \neq\pm 1, \) then \( A^{-1} \) exists and all its entries are non-integers
D. If \( \operatorname{det}(A)=\pm 1 \), then \( A^{-1} \) exists and all its entries are integers


Select the correct option:
Identify \( A, B, C, D \) and \( E \) in the given flow
chart showing Z-scheme of light
reaction
\( \mathbf{A} \cdot A-P_{700} ; \mathrm{B}-H^{+} \) acceptor; \( \mathrm{C}-e^{-} \) acceptor; \( \mathrm{D}-P_{680} ; \mathrm{E} \)
\( N A D P^{+} \)
B. A-Photo -system I ; B- \( e^{-} \) acceptor; C- \( e^{-} \) transport
system; D-Photo system II; E- NADPH
C. A-Photo-system II; B- \( H^{+} \) acceptor; \( \mathrm{C}-e^{-} \) acceptor; \( \mathrm{D} \) -
\( P_{700} ; \) E- NADPH.
D. A-Photo-system II; B- \( e^{-} \) acceptor; \( C-e^{-} \) transport
system; D- photo-system I; E- NADPH.


An element A (atomic weight \( =12 \) ) and
B (atomic weight \( =35.5 \) ) combines to
form a compound X. If 4 mol of B
combines with 1 mol of \( A \) to give 1 mol
of X. The weight of 1 mol of \( X \) would be :
A. \( 47.5 \mathrm{g} \)
B. 74.0 g
c. \( 154.0 \mathrm{g} \)
D. 148.8 g


Balance the following in basic medium:
\( \boldsymbol{A s O}_{3}^{3+}+\boldsymbol{M n O}_{4}^{-} \rightarrow \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{M n O}_{2} \)
A \( \cdot 3 A s O_{3}^{3+}+2 M n O_{4}^{-}+H_{2} O \rightarrow 3 A s O_{4}^{3-}+2 M n O_{2}+ \)
\( 2 O H^{-} \)
B. \( 3 A s O_{3}^{3+}+2 M n O_{4}^{-}+4 H_{2} O \rightarrow 3 A s O_{4}^{3-}+3 M n O_{2}+ \)
\( 2 O H^{-} \)
\( \mathrm{c} \cdot 3 A s O_{3}^{3+}+4 M n O_{4}^{-}+3 H_{2} O \rightarrow 3 A s O_{4}^{3-}+2 M n O_{2}+ \)
\( 4 O H^{-} \)
D. None of these


An arrow is placed at a distance of 25 \( \mathrm{cm} \) from a diverging mirror of focal length \( 20 \mathrm{cm} . \) Find the image distance.
A . \( 12.1 \mathrm{cm} \)
B. \( 13.1 \mathrm{cm} \)
\( c .11 .1 c m \)
D. \( 14.2 \mathrm{cm} \)


Name three good conductors of heat


Calculate the number of molecules in a
drop of water weighing \( 0.05 \mathrm{gm} \)


What happens when methane reacts with chlorine?


What do you mean by oxidation and
reduction?


The bond between two identical non
metallic atoms has a pair of electrons:
A. unequally shared among the two atoms.
B. equally shared among two atoms
c. equal transfer of electrons from one atom to another
D. shared by only one atom.


Solve \( -\mathbf{7}(\mathbf{2}+\boldsymbol{x})=\mathbf{8} \mathbf{7} \)


Match the terms to these definitions.
Centromere, centrosome, chromatin, hromosome, spindle, cell cycle, karyot ype, meiosis, mitosis, sister chromatids, interphase, metaphase The period from the end of one division of a, cell to the end of the next
division.


Representative elements belong to:
A. \( s \) -and \( p \) - block
B. \( d- \) block
c. \( d \) and f block
D. \( f \) - block


Which one of the following is least
chemically reactive?
\( A \cdot A r \)
B.
\( c \cdot s \)
D. Ti
E.


\( C_{6} H_{5} C l \frac{N a O H}{\text {High temperature and pressure}} \)
\( \boldsymbol{A} \stackrel{\boldsymbol{H C l}}{\longrightarrow} \boldsymbol{B} \)
Identify \( A \) and \( B \) in the above reaction.


Dipole moment of \( C O \) is very small
\( (0.1 D) \) (in-spite of the larger difference in electronegativity between \( C \text { and } O) \) and negative end of the dipole lies near
the less electronegative \( C \) -atom. It is
due to:
A. occupation of anti-bonding molecular orbitals
B. occupation of empty \( d \) - orbitals
c. occupation of lone-pairs
D. occupation of the lone pairs as well as empty \( d- \) orbitals


Which of the following has no conjugate
base?
A. Oxide ion
B. Hydroxide ion
c. Hydrogen peroxide ion
D. Hydrogen sulphate ion


Given that \( \prod_{n=1}^{n} \cos \frac{x}{2^{n}}=\frac{\sin x}{2^{n} \sin \left(\frac{x}{2^{n}}\right)} \)
and \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{c}
\lim _{n \rightarrow \infty} \sum_{n=1}^{n} \frac{1}{2^{n}} \tan \left(\frac{x}{2^{n}}\right), \quad x \in(0, \\
\frac{2}{\pi}
\end{array}\right.
\]
Then which one of the following is true?
A. \( f(x) \) has non-removable discontinuity of finite type at
\[
x=\frac{\pi}{2}
\]
B.
\( f(x) \) has removable discontinuity at \( x=\frac{\pi}{2} \)
C \( \quad f(x) \) is continuous at \( x=\frac{\pi}{2} \)
D. \( f(x) \) has non-removable discontinuity of infinite type at \( x=\frac{\pi}{2} \)


Arrange benzoic acid, 4-methyl benzoic
acid and 4 -nitrobenzoic acid in
increasing order of their acidic
strength.


If point (3,0) lies on the graph of the
equation \( 2 x+b y=k, \) then the value of
\( k^{\prime} \) is :
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
\( c \cdot 2 \)
D.


Name the following compound according to the IUPAC system or
nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H O} \)


What happens when two straws are individually rubbed with separate sheets of paper and are brought near to each other?
A. The straws attract each other
B. The straws repel each other
c. The straws remain indifferent of each other
D. Either A or B


Two forces of \( 10 \mathrm{N} \) and6 \( \mathrm{N} \) act upon a
body. The direction of the forces are
unknown.the resultant force on the body
may be
A . 15 N
B. 3 N
c. 17
D. 2 N


Number of nephrons of a kidney is equal
to
A. Sum of Bowmans capsules and glomeruli
B. Sum of Bowmans capsules and malpighian corpuscles
C. Double the number of Bowmans capsule
D. Equal to number of Bowmans capsules


The domain of the real valued sine
function \( f(x)=2 \sin (x-1) \) is
\( (-\infty, \infty) \). If true enter 1 else 0


Which compound has lowest melting
point?
A. Ethane
B. Ethene
c. Ethyne
D. All have approximately equal melting points.


A unit vector which make \( 45^{0} \) with
vector \( 2 i+2 j-k \) and angle of \( 60^{0} \) with
vector \( \boldsymbol{j}-\boldsymbol{k} \) is
A. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} k \)
в. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} j \)
c. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} j+\frac{1}{\sqrt{2}} j \)
D. none of the above


Mesophyll is differentiated into
palisade and spongy tissue in
A. Some monocot leaves
B. All dorsiventral leaves
c. All monocot leaves
D. All isobilateral leaves


The geomatric mean of 4,6,8
A \( \cdot 2 \sqrt[3]{6} \)
B. \( \sqrt{24} \)
\( c \cdot 6 \sqrt{2} \)
D. \( 4 \sqrt[3]{3} \)


In finding the electric field using Gauss law the formula \( |\overrightarrow{\boldsymbol{E}}|=\frac{\boldsymbol{q}_{e n c}}{\in_{\mathbf{0}}|\boldsymbol{A}|} \) is
applicable. In the formula \( \in_{0} \) is
permittivity of free space, \( \boldsymbol{A} \) is the area
of Gaussian surface and \( q_{e n c} \) is charge enclosed by the Gaussian surface. This
equation can be used in which of the
following situation?
A. For any choice of Gaussian surface.
B. Only when the Gaussian surface is an equipotential surface and \( |\vec{E}| \) is constant on the surface.
C. Only when \( |\vec{E}|= \) constant on the surface
D. Only when the Gaussian surface is an equipotential surface.


Solve the following pair of equations:
\( \frac{a}{x}-\frac{b}{y}=0 \)
\( \frac{a b^{2}}{x}+\frac{a^{2} b}{y}=a^{2}+b^{2} \)
A. \( x=a b \) and \( y=b \)
B. \( x=a \) and \( y=b \)
c. \( x=b \) and \( y=a \)
D. \( x=b-a \) and \( y=a b \)


The consumers are
A. All plants
B. All animals
c. All microbes
D. All living things


A vehicle starts from rest and moves at
uniform acceleration such that its
velocity increases by \( 3 m s^{-1} \) per every second. If diameter of wheel of that vehicle is \( 60 \mathrm{cm}, \) the angular acceleration of wheel is:
A .5 rads\( ^{-2} \)
B. 10 rads\( ^{-2} \)
C .15 rads\( ^{-2} \)
D. 20 rads \( ^{-2} \)


If \( T_{r} \) denotes the \( r^{t h} \) term in the
expansion of \( \left(x+\frac{1}{x}\right)^{23}, \) then
\( \mathbf{A} \cdot T_{12}=T_{13} \)
В . \( x^{2} . T_{13}=T_{12} \)
c. \( x^{2} . T_{12}=T_{13} \)
D. \( T_{12}+T_{13}=25 \)


Which of the given statements is INCORRECT about glycogen?
A. It is a straight chain polymer similar to amylose
B. only \( \alpha- \) linkages are present in the molecule
c. It is present in animal cells.
D. It is present in some yeast and fungi


Solve
\( \boldsymbol{x}-\boldsymbol{4}=\boldsymbol{9} \)


Select the correct matches.
(a) Nitrosomonas - nitrite to nitrate
(b) Thiobacillus - denitrification
(c) Nostoc - free-living nitrogen fixer
(d) Azotobacter - anaerobic nitrogen fixer
A. a and
B. b and c
\( c . \) a and \( c \)
D. c and d
E. b and d


The energy of an electron in the first
Bohr's orbit of a hydrogen atom is \( 2.18 \times 10^{-18} J . \) Its energy in the second
orbit will be:
A. \( -1.09 \times 10^{-18} \mathrm{J} \)
B . \( -4.36 \times 10^{-18} J \)
c. \( -5.45 \times 10^{-19} \mathrm{J} \)
D. \( -8.72 \times 10^{-18} \mathrm{J} \)


Two spheres of radius \( 5 \mathrm{cm} \) and \( 10 \mathrm{cm} \) both charged to \( 120 \mu C \), are joined by a metal wire and then metal wire is
removed. What is the charge on each after removal of the wire?
\( \mathbf{A} \cdot 120 \mu C, 120 \mu C \)
в. \( 80 \mu C, 160 \mu C \)
c. \( 100 \mu C, 140 \mu C \)
D. None of these


Cavitation is a special application property exhibited only by:
A. Ultrasonics
B. Electromagnetic waves
c. Audible sound
D. Infrasonics


Give the IUPAC names of the following compounds:
¡) \( \boldsymbol{C H}_{3} \boldsymbol{C H}(\boldsymbol{C l}) \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
ii) \( C H F_{2} C B r C l F \)
iii) \( C l C H_{2} C \equiv C C H_{2} B r \)
iv) \( \left(C C l_{3}\right)_{3} C C l \)
v) \( \boldsymbol{C H}_{3} \boldsymbol{C}\left(\boldsymbol{p}-\boldsymbol{C l} \boldsymbol{C}_{6} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
vi) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C H}=\boldsymbol{C C l C}_{6} \boldsymbol{H}_{4} \boldsymbol{I}-\boldsymbol{p} \)


Area bounded by curve \( y=x^{2} \) and \( y= \)
\( 2-x^{2} \) is \( ? \)
A \( \cdot \frac{8}{3} \) sq units
B. \( \frac{3}{8} \) sq units
c. \( \frac{3}{2} \) sq units
D. None of these


The redox reaction among the following
is :
\( \mathbf{A} \cdot \) reaction of \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3} \) with \( \mathrm{AgNO}_{3} \)
B. formation of ozone from atmospheric oxygen in the presence of sunlight
C. combination of dinitrogen with dioxygen at \( 2000 K \)
D. reaction of \( H_{2} S O_{4} \) with \( N a O H \)


Differentiate the given function w.r.t. \( x \) \( \frac{\cos x}{\log x}, x>0 \)


Ordinary hydrogen at room temperature is a mixture of
\( \mathbf{A} \cdot 75 \% o-\mathrm{Hydrogen}+25 \% p \) -Hydrogen
B. \( 25 \% \) o-Hydrogen \( +75 \% \) p-Hydrogen
\( \mathbf{c} .50 \% o \) -Hydrogen \( +50 \% p \) -Hydrogen
D. \( 1 \% \) o-Hydrogen \( +99 \% \) p-Hydrogen


The potential difference between the fixed charged layer and the diffused layer having opposite charge is called?
A. Colloidal potential
B. Zeta potential
c. Electrostatic potential
D. None of these


In Kranz anatomy, the bundle sheath
cells have
A. Thin walls, many intercellular space and no chloroplast
B. Thick walls, no intercellular spaces and large number of chloroplasts
c. Thin walls, no intercellular spaces and several chloroplasts
D. Thick walls, many intercellular space and few chloroplasts


If the closest distance of approach for
an \( \alpha \) particle when it is radiated upon an element of atomic no.40, is \( 10^{-14} m \)
then find the initial \( K E \) of the \( \alpha \)
particles.


An acidic buffer solution can be
prepared by mixing the solutions of:
A. Sodium acetate and acetic acid
B. Ammonium chloride and ammonium hydroxide
c. sulphuric acid and sodium hydroxide
D. sodiu chlmoride and sodium hydroxide


Roundworms are found to live in which
sort of environment?
A. Almost any
B. Hot
c. Extremely cold
D. sunny


The \( \boldsymbol{H}-\boldsymbol{C}-\boldsymbol{H}, \boldsymbol{H}-\boldsymbol{N}-\boldsymbol{H}, \) and
\( H-O-H \) bond angles (in degrees) in
methane, ammonia and water are
respectively, closest to.
A. 109.5,104.5,107.1
в. 109.5,107.1,104.5
c. 104.5,107.1,104.5
D. 107.1,104.5,109.5


If \( A \) satisfies the equation \( x^{3}-5 x^{2}+ \)
\( 4 x+\lambda=0, \) then \( A^{-1} \) exists if
A. \( \lambda \neq 1 \)
B. \( \lambda \neq 2 \)
c. \( \lambda \neq-1 \)
D. \( \lambda \neq 0 \)


The magnetic field generated along the axis of a solenoid is proportional to:
A. its length
B. square of current flowing in it
c. number of turns per unit length in it
D. reciprocal of its radius


Measure of one angle of linear pair is given. Find the measure of another
angle:
\( \mathbf{2 0}^{\circ} \)


The ratio of speeds of sound in hydrogen gas and oxygen gas at same temperature will be
A . 8: 1
в. 4: 1
\( \mathrm{c} \cdot 1: 8 \)
D. 1: 4


In a compound of \( X e, F \) and 0
\[
\begin{array}{l}
X e=60.4 \%(131.3) \\
F=17.5 \%(19.0)
\end{array}
\]
Thus, number of oxygen atoms is 3 if true enter 1 , else enter 0 .
\( A \)


When sound waves travels from air to
water, which of the following parameters remains constant?
A. Wavelength
B. Velocity
c. Frequency
D. Phase


Determine domain of \( \frac{\sqrt{4-x^{2}}}{\sin ^{-1}(2-x)} \)
A \( .(4,5) \)
B. [1,2]
c. both a and \( b \)
D. none of the above


An unbiased coin is tossed. if the result
is a head, a pair of unbiased dice is rolled \& the number obtained by adding the numbers on the two faces is noted. If
the result is a tail, a card from a well
shuffled pack of eleven cards numbered \( 2,3,4, \dots, 12 \) is picked \( \& \) the number on the card is noted. What is the
probability that the noted number is
either 7 or \( 8 ? \)
A. 0.24
в. 0.27
\( c .0 .3 \)
D. 0.31


How is 4 -methylpent-3-en-2-one obtained from propan-e-one?


The amount of energy required to remove an electron from ground sate of
\( H e^{+} \) ion is:
A. -54.4 ev
B . -13.6 ev
c. -24.4 ev
D. -34 ev


Find the value(s) of k such that the term
independent of \( x \) in \( \left(3 x^{2}+\frac{k}{2 x}\right)^{6} \) is 135
\( A \cdot \pm 2 \)
B. ±1
\( c .\pm 3 \)
D. ±4


Given the limiting molar conductivity
as:
\( A_{m}^{\infty}(H C l)=126.4 \Omega^{-1} c m^{2} m o l^{-1} \)
\( A_{m}^{\infty}(N a C l)=425.9 \Omega^{-1} c m^{2} m o l^{-1} \)
\( A_{m}^{\infty}\left(C H_{3} C O O N a\right)= \)
\( 91 \Omega^{-1} c m^{2} m o l^{-1} \)
The molar conductivity at infinite
dilution of acetic acid
\( \left(i n \Omega^{-1} c m^{2} m o l^{-1}\right) \) will be:
\( \mathbf{A} \cdot 481.5 \)
B. 390.5
\( \mathbf{c} \cdot 299.5 \)
D . 516.9


How many balls each of radius \( 1 \mathrm{cm} \)
can be made from a copper sphere whose radius is \( 8 \mathrm{cm} ? \)


You are sitting in a room in which uniform magnetic field is present in vertically downward direction. When an
electron is projected in horizontal direction, it will be moving in circular path with constant speed
A. clockwise in vertical plane
B. clockwise in horizontal plane
c. anticlockwise in vertical plane
D. anticlockwise in horizontal plane


Which of the following sets of examples and geometry of the compounds is not correct?
A . Octahedral - \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3} \)
B. Square planar - \( \left[N i(C N)_{4}\right]^{2-},\left[C u\left(N H_{3}\right)_{4}\right]^{2} \)
C. Tetrahedral- \( \left[N i(C O)_{4}\right],\left[Z n C l_{4}\right]^{2} \)
D. Trigonal bipyramidal - [Fe \( \left.\left(N H_{3}\right)_{6}\right]^{2+},\left[C u C l_{4}\right]^{2-} \)


Assertion
Atomic number is a more fundamental
property of an element than its atomic
mass.
Reason
Atomic number is equal to number of
protons in an atom.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Differentiate the following functions
with respect to \( x \) \( \sin ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\},-1<x<1 \)


The electric field in the dielectric slab
is:
A \( \cdot \frac{V}{K d} \)
B. \( \frac{K V}{d} \)
c. \( \frac{V}{d} \)
D. \( \frac{K V}{t} \)


A \( 10 k W \) drilling machine is used to drill a bore in a small aluminium block
of mass \( 8 k g . \) Find the rise in
temperature of the block in 2.5 minutes,assuming \( 50 \% \) power is used up in heating the machine itself or lost to the surroundings.
(Specific heat of aluminium= \( \left.0.91 J g^{-1 o} C^{-1}\right) \)
\( \mathbf{A} \cdot 100^{\circ} C \)
в. \( 103^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 150^{\circ} \mathrm{C} \)
D. \( 155^{\circ} \mathrm{C} \)


The value of rotational K.E. at
temperature T of one gram molecules of a diatomic gas will be-


If same quantity of electricity is passed
through three electrolytic cells
containing \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3}, \) and
\( \boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{3}, \) then:
This question has multiple correct options
A. the amount of iron deposited in \( F e S O_{4} \) and \( F e_{2}\left(S O_{4}\right)_{3} \) are equal
B. the amount of iron deposited in \( F e S O_{4} \) is 1.5 times of the amount of iron deposited in \( F e\left(N O_{3}\right)_{3} \)
C. the amount of iron deposited in \( F e\left(S O_{4}\right)_{3} \) and
\( F e\left(N O_{3}\right)_{3} \) are equal
D. the same amount of gas is evolved in all three cases of the anode.


The maximum slope of the curve \( \mathbf{y}= \) \( -x^{3}+3 x^{2}+9 x-27 \) is
\( A \)
B. 12
\( c \cdot 6 \)
D.


A particle of mass \( M \) at rest decays
into two particles of masses \( m_{1} \) and \( m_{2} \)
having non-zero velocities. The ratio of the de-Brogile wavelengths of the particles, \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}} \) is:
A. \( \frac{m_{1}}{m_{2}} \)
в. \( \frac{m_{2}}{m_{1}} \)
\( c \cdot 1: 1 \)
D. \( \sqrt{\frac{m_{2}}{m_{1}}} \)


What is the value of \( X \) and \( Y ? \) Report
your answer as \( (X Y) \)


Surface of lyophilic sols is:
A. equal to that of solvent
B. less than that of solvent
c. more than that of solvent
D. cannot be predicted


A tetrapeptide has \( - \) COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary
structures) with \( N H_{2} \) group attached
to a chiral centre is :
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D \cdot 2 \)


Solve \( \lim _{x \rightarrow-2} \frac{\left(\frac{1}{x}+\frac{1}{2}\right)}{x+2} \)


Which of the following is Not an advantage of having two eyes?
A. It gives a wider field view
B. The ability to detect faint objects is enhanced with two detectors instead of one
c. It gives the ability to interpret the closeness of an object
D. It gives the eye higher protection from dust and pollution.


Chemical compounds which conduct electricity in the fused or in aqueous solution state and undergo chemical decomposition due to the flow of
current through it are known as:
A. electrolytes
B. non-electrolytes
c. weak electrolytes
D. all of the above


Explanation and types of Mitosis and Meiosis with the help of diagram.


Boron has two isotopes, \( 10 B \) and \( ^{11} B \) whose relative abundances are \( 20 \% \) and
\( 80 \% \) respectively. Atomic weight of boron is:
A . 10
B. 11
c. 10.5
D. 10.8


An alternating voltage of \( 220 V, 50 H z \) frequency is applied across a capacitor of capacitance \( 2 \mu F \). The impedence of
the circuit is:
A \( \frac{\pi}{5000} \)
в. \( \frac{1000}{\pi} \)
\( c .500 \pi \)
D. \( \frac{5000}{\pi} \)


Prove that \( \left|\begin{array}{ccc}\boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} \\ \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} \\ \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2}\end{array}\right| \) is
divisible by \( (x+y+z), \) and hence find
the quotient
OR
Using elementary transformations, find the inverse of the matrix \( \boldsymbol{A}= \) \( \left(\begin{array}{lll}8 & 4 & 3 \\ 2 & 1 & 1 \\ 1 & 2 & 2\end{array}\right) \) and use it to solve the
following system of linear equations:
\( 8 x+4 y+3 z=19 \)
\( 2 x+y+z=5 \)
\( x+2 y+2 z=7 \)


What is the velocity of the cart just after the first collision?
A \( \cdot \frac{-m v_{0}}{m+M} \)
в. \( \frac{M v_{0}}{m+M} \)
c. \( \frac{M-m}{M+m} v_{0} \)
D. \( \frac{2 M}{m+M} v_{0} \)


Obtain the relation between the
magnitude of linear acceleration and angular acceleration in circular motion.


The work done in rotating a bar magnet
of magnetic moment \( M \) from its unstable equilibrium position to its stable equilibrium position in a uniform magnetic field \( B \) is
\( \mathbf{A} \cdot 2 M B \)
в. \( M B \)
c. \( -M B \)
D. \( -2 M B \)


In the commercial extraction of iron,
roasting is adopted because:
This question has multiple correct options
A. it removes impurities of \( S, A s \), and \( S b \) in the form of their elemental vapor
B. it prevents slag formation by \( F e_{2} O_{3} \)
C. it prevents slag formation by \( \mathrm{FeO} \)
D. limonite is converted into its anhydrous form


Find the equation of the parabola with
vertex (0,0) and focus at (-3,0)


The electric potential \( V \) at any point
\( (x, y, z) \) in space is given by \( V=3 x^{2} \)
where \( x, y, z \) are all in metre. The
electric field at the point \( (1 m, 0,2 m) \) is
A \( \cdot 6 V m^{-1} \) along negative \( x \) -axis
B. \( 6 V m^{-1} \) along positive \( x \) -axis
C. \( 12 \mathrm{Vm}^{-1} \) along negative \( x \) -axis
D. \( 12 \mathrm{Vm}^{-1} \) along positive \( x \) -axis
E. \( 8 \mathrm{Vm}^{-1} \) along negative \( x \) -axis


A drop of alcohol is introduced into the
vaccum space of mercury barometer completely evaporates and then slightly lowers the height of the barometer. If the barometer tube is raised from this
position, the height of the barometer will
A. fall
B. rise
C. remains stationery
D. falls first and then rises


Five identical conducting plates, 1.2,3,4 and 5 are fixed parallel plates equidistant from each other (see
figure). A conductor connects plates 2
and 5 while another conductor joins 1
and 3. The junction of 1 and 3 and the plate 4 are connected to a source of
constant emf \( V_{o} \). Find the effective
capacitance of the system between the terminals of source where \( d \) is the
distance between any two successive
plates


Magnifying power of simple microscope is \( 6, \) when image is formed at distance of distinct vision, the focal length of simple microscope is :
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 4.16 \mathrm{cm} \)


A heavy seesaw (i.e., not massless) is out of balance. A light girl sits on the
end that is tilted downward, and a heavy
body sits on the other side so that the
seesaw now balances. If they both move
forward so that they are one-half their original distance from the pivot point (the fulcrum) what will happen to the
seesaw?
A. The side the body is sitting on will tilt downward
B. The side the girl is sitting on will once again tilt downward
C. Nothing; the seesaw will still be balanced.
D. It is impossible to say without knowing the masses and the distances.


If \( A \) and \( B \) are two events such that
\( P(A)=\frac{3}{8}, P(B)=\frac{5}{8} \) and
\( P(A \cup B)=\frac{3}{4}, \) then \( P(A \cap \bar{B})= \)
\( A \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{1}{8} \)
D.


Which type of molecules form micelles?
A. Polar molecules
B. Non-polar molecules
c. surfactant molecules
D. Any of these


A gravitational field is present in a
region. A point mass is shifted from \( \boldsymbol{A} \)
to \( B, \) along different paths shown in the
figure. If \( W_{1}, W_{2} \) and \( W_{3} \) represent the
work done by gravitational force for
respective paths, then
\( \mathbf{A} \cdot W_{1}=W_{2}=W_{3} \)
В. \( W_{1}>W_{2}>W_{3} \)
c. \( W_{1}>W_{3}>W_{2} \)
D. none of these


The quality factor of an AC circuit is related to bandwidth as
A. inversely proportional
B. directly proportional
c. directly proportional to log
D. inversely proportional to log


Identify the incorrect statement.
A. Orbitals of a subshell have same value of \( (n+l) \) but
the orbitals having same \( (n+l) \) value may not belong
to the same subshell
B. The orbital having value of \( l=2 \) will have 2 orientations in space
C. \( 3 p \) and \( 3 d \) orbitals have directional character
D. Orbits in Bohr's model are two dimensional in nature
E. All are correct


The velocity-time graph given shows the motion of a cyclist. Its velocity is given
by
A \( \cdot 20 m s^{-1} \)
B. \( 22.5 m s^{-1} \)
\( \mathrm{c} \cdot 19 \mathrm{ms}^{-1} \)
D. \( 21 m s^{-1} \)


State the law of conservation of
momentum and derive related
expression.


Assertion
Statement- \( 1: C u F e S_{2} \) is concentrated
by froath floatation method.
Reason
Statement-II: \( C u F e S_{2} \) is main ore of
copper.
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


High concentrations of carbon
monoxide \( (C O): \)
A. reduces capacity of blood transport
B. reduces capacity of oxygen transportation through blood in body
C. is caused due to incomplete fossil decay
D. is caused due to smog formation


The printed price of an article is Rs. 900 but the retailer gets a discount of \( 40 \% \) He sells the article for Rs. 900. Retailers'
gain per cent is.
A . 40
B. 60
c. \( 66 \frac{2}{3} \)
D. \( 68 \frac{1}{3} \)


IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{B r} \) is:
A. 1-Bromopentane
B. 2-Methyl-4-bromobutane
c. 1-Bromo-3-methylbutane
D. 2-Methyl-3-bromobutane


Find \( (5 \sqrt{3}+3 \sqrt{2}) \Delta \) where
\( \Delta=\left|\begin{array}{ccc}\sqrt{13}+\sqrt{3} & \sqrt{5} & 2 \sqrt{5} \\ \sqrt{15}+\sqrt{26} & \sqrt{10} & 5 \\ 3+\sqrt{65} & 5 & \sqrt{15}\end{array}\right| \)


How many terms of the A.P. \( 1,4,7, \ldots \)
are needed to make the sum \( 51 ? \)


Oxidation number of \( C l \) in \( C a O C l_{2} \)
(bleaching powder) is:
A . zero, since it contains \( C l_{2} \)
B. -1 , since it contains \( C l^{-} \)
c. \( -1, \) since it contains \( C l O^{-} \)
D. +1 and -1 since it contains \( C l O^{-} \) and \( C l^{-} \)


Water is a
A. acidic
B. neutral
c. basic
D. amphoteric


The pneumotaxic center of rabbit is located in the
A. Brain
B. Heart
c. Medulla
D. Lungs


Asha lifts a doll from the floor and
places it on a table. If the weight of the doll is known, what else does one need
to know in order to calculate the work
Asha has done on the doll?
A. The time required
B. Height of the table
c. Mass of the doll
D. cost of the doll or the table


Significance of mitosis is in
A. Occurrence in every tissue of body
B. Increasing cellular mass
C. Swift division
D. Producing cells genetically similar to parent cell


The drug used as an antidepressant is :
A. Luminal
B. Phenelzine
c. Mescaline
D. Sulphadiazine


A fan is making 600 rpm. If it makes \( 1200 r p m, \) what is the increase in its angular velocity?
\( \mathbf{A} \cdot 10 \pi r a d s^{-1} \)
B. \( 20 \pi \) rads\( ^{-1} \)
c. \( 60 \pi \) rads\( ^{-1} \)
D. \( 40 \pi \) rads\( ^{-1} \)


The electric current flowing through the
circuit varies directly with the value of unknown resistance.


Which of the following is correct regarding Ellingham diagram?
A \( \cdot \) It is plot of \( \Delta G_{f} \) per mole of metal versus temperature
B. Reduction of a metal oxide is difficult if the metal formed is in liquid state at the temperature of reduction
c. Plot is a straight line except when some change in phase.
D. Ellingham diagram deals with both the feasibility as well as the rate of the reduction process


If \( A \) and \( B \) are two independent events such that \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2} \) and \( \boldsymbol{P}(\boldsymbol{B})=\frac{1}{5} \)
then
This question has multiple correct options
A \( \cdot P(A \cup B)=\frac{3}{5} \)
в. \( P(A / B)=\frac{1}{2} \)
c. \( P(A / A \cup B)=\frac{5}{6} \)
D \cdot \( P\left(A \cap B / A^{\prime} \cup B^{\prime}\right)=0 \)


(a) What is Lanthanoid contraction?
(b) What are Interstitial compounds? Give an example.
(c) Calculate the 'Spin only' magnetic moment of \( M_{(a q)}^{2+} \) ion \( (Z=29) \)


The latent hear of vaporization of water
is \( 2240 J . \) If the work done in the process
of vaporization of \( 1 g \) is \( 168 J \), then increase in internal energy is:
\( \mathbf{A} \cdot 1940 J \)
в. \( 2072 J \)
c. \( 2240 J \)
D. 2408J


\( A^{\prime} s \) height is more than \( B^{\prime} s \) height by
\( 20 \% . \) By what percent is \( B^{\prime} s \) height less
then \( A^{\prime} s \) height ?


Write each of the following decimals in
words:
\( \mathbf{9 . 0 0 4} \)


Which of the following statements are
correct?
(i) When a fruit develops from the inflorescence, it is composite.
(ii) Mesocarp is the edible part in apple.
(iii) Gynobasic style is seen in Ocimum.
(iv) Hypanthodium is a special type of inflorescence found in Euphorbia species.
A. (i) and (iv) are correct
B. (i) and (iii) are correct
C \( . \) (i) and (ii) are correct
D. (ii), (iii) and (iv) are correct
E. (ii) and (iv) are correct


Assertion
Width of the beam is increased in going from in air to water.
Reason
Rays of light diverge when they go from one medium to another.
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


Latent heat of vaporization of water is 538 cal/g. During the conversion of 1 g of water to steam, if the external work
done is \( 168 \mathrm{J} \), the increase in internal
energy is:
A . 638 call \( l \)
B. 538 саг \( l \)
c. 498 call \( l \)
D. 80 cal


Which of the following is technique used to measure the heat of a reaction?
A. Gibbs Free Energy
B. Entropy
c. Enthalpy
D. Calorimetry


The formation of \( C a O \) from lime stone
is favoured by:
A. adding flux
B. removing \( C O_{2} \)
c. adding methyl
D. adding \( C a \)


Two identical pulses move in opposite directions with same uniform speeds on a stretched string. The width and kinetic energy of each pulse is \( L \) and \( k \)
respectively. At the instant they completely overlap, the kinetic energy of
the width \( L \) of the string where they
overlap is
\( A \cdot k \)
B. \( 2 k \)
c. \( 4 k \)
D. \( 8 k \)


Beta particles are essentially:
A. neutrons
B. protons
c. electrons
D. helium nuclei


At a particular temperature, the vapour pressures of two liquids \( A \) and \( B \) are respectively 120 and 180 mm of
mercury. If 2 moles of \( A \) and 3 moles of
Bare mixed to form an ideal solution,
the vapour pressure of the solution at the same temperature will be (in mm of
mercury) :
A . 156
в. 145
\( c .150 \)
D. 108


An electron with kinetic energy \( \boldsymbol{E} \boldsymbol{e} \boldsymbol{V} \)
collides with a hydrogen atom in the ground state. The collision will be elastic
A. for all values of \( E \)
B. for \( E<10.2 e V \)
c. for \( E<13.6 e V \)
D. only for \( E<3.4 e V \)


If aabb is a four digit number and also a perfect square then the value of \( a+b \) is
A . 12
B. 11
c. 10
D. 9


Evaluate:
\( \int x \cos ^{3} x d x \)


A horizontal force of \( 1 g \) w\( t \). is applied
on a mass of \( 9.8 ~ k g \) placed on a smooth
surface. The acceleration produced is:
\( \mathbf{A} \cdot 1 m s^{-2} \)
B. \( \frac{1}{9.8} m s^{-2} \)
c. \( 9.8 \mathrm{ms}^{-2} \)
D. \( 10^{-3} \mathrm{ms}^{-2} \)


1 weber is equivalent of
A \( \cdot 10^{-8} \) Maxwell
1
B . \( 10^{12} \) Maxwell
c. \( 10^{8} \) Maxwel
D. \( 10^{4} \) Maxwell


In aqueous solution, the proton exists
as a (acid/base)


Given figure shows measuring cylinder \( \left(\text { in } c m^{3}\right) \) before and after the immersion
of an irregular solid object. The volume
of the object is
A \( \cdot \) 82 \( c m^{3} \)
B. \( 12 \mathrm{cm}^{3} \)
c. \( 30 \mathrm{cm}^{3} \)
\( \mathrm{D} \cdot 18 \mathrm{cm}^{3} \)


From a batch of 100 items of which 20
are defective, exactly two items are chosen, one at a time, without
replacement. Calculate the probabilities that the second item chosen is defective
A \( \cdot \frac{2}{5} \)
в. \( \frac{19}{100} \)
\( c \cdot \frac{1}{5} \)
D. none of these


Bond length is more in:
A. \( H-H \)
B. D - D
c. \( T-T \)
D. same in All


The ratio of the value of any colligative
property for \( B a C l_{2} \) solution to that for
urea solution under similar condition
is:
A .2
B. 3
\( c \)
\( D \)


In a pure capacitive circuit if the frequency of ac source is doubled, then its capacitive reactance will be
A. remains same
B. doubled
c. halved
D. zero


The value of the Avogadro constant is :
В. \( 6.022 \times 10^{22} \)
c. \( 60.22 \times 10^{24} \)
D. \( 6.022 \times 10^{23} \)


A box of mass \( 8 \mathrm{kg} \) is placed on a rough
inclined plane of inclined \( \theta \). Its downward motion can be prevented by applying an upward pully \( F \) and it can be made to slide upwards by applying a force \( 2 \mathrm{F} \). The coefficient of friction
between the box and the inclined plane
is
\( \mathbf{A} \cdot(\tan \theta) / 3 \)
B. \( \tan \theta \)
\( \mathbf{c} \cdot(\tan \theta) / 2 \)
D. \( 2 \tan \theta \)


The most important gas which leads to acidification is:
A. hydrochloric acid
B. sulphur dioxide
c. sulphurous acid
D. hydrogen peroxide


If numerator and denominator of a
proper fractions are increased by the same quantity, then the resulting fraction is then
A. always greater than the original fraction
B. always less than the original fraction
c. always equal to the original fraction
D. none of these


A number is added to \( 15 . \) The new
number is multiplied by 3 to give 60 Find the number.


When 100 g of ethylene polymerises entirely to polyethene, the weight of polyethene formed as per the equation:
\( \boldsymbol{n}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \rightarrow-\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right)_{n}- \) is:
A \( \cdot \frac{n}{2} g \)
B. 1009
c. \( \frac{100}{n} \mathrm{g} \)
D. \( 100 n \) g


Assertion: At high temperature, a ferromagnet becomes a paramagnet. Reason: The ferromagnetic property depends on temperature
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false


Addition reaction to alkenens and
alkynes are called as:
A. polymerisation
B. saturation
c. unsaturation
D. catalyzation


In the method using the transformers,
assume that the ratio of the number of
turns in the primary to that in the secondary in the step-up transformer is \( 1: 10 . \) If the power to the consumers has to be supplied at \( 200 \mathrm{V} \), the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is
\( A \cdot 200: 1 \)
B. 150:1
c. 100: 1
D. 50:


The kinetic energy of \( N \) molecules of \( O_{2} \)
is \( x \) joule at \( -123^{\circ} \mathrm{C} \). Another sample
of \( O_{2} \) at \( 27^{\circ} C \) has a kinetic energy of \( 2 x \)
The later sample contains
molecules of \( \boldsymbol{O}_{2} \)
A. \( N \)
B. \( N / 2 \)
\( c \cdot 2 N \)
D. 3N


An electric toaster draws \( 8 A \) current in
a \( 220 V \) circuit. It is used for \( 2 h r . \) What
is the cost of operating the toaster if the
\( \operatorname{cost} \) of electrical energy is
Rs. \( 4.5 / k W h ? \)
A. \( R s .9 .50 \)
B. Rs. 25.50
c. \( R s .14 .84 \)
D. Rs. 15.84


The first and last terms of an A.P of \( n \)
terms is 1,31 respectively. The ratio of \( 8^{t h} \) term and \( (n-2)^{t h} \) term is \( 5: 9, \) the
value of \( n \) is:
\( A \cdot 14 \)
B. 15
\( c \cdot 16 \)
D. 13


Molar heat capacity of a gas does not depend on
A. Its temperature
B. Its molecular weight
c. Its atomicity
D. The conditions under which heat is supplied


I. When iron reacts with oxygen an iron oxide compound with the formula of
\( F e_{2} O_{3} \) can be formed
II. Iron atoms form cations with a
charge of +3 by losing 3 electrons and
oxygen atoms gain 2 electrons to form
an anion with a -2 charge.
A. Statement \( I \) is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in 1
B. Statement I is true, Statement II is false
c. Statement I is false, statement II is true
D. Statement I is false, Statement II is false


\( \lim _{x \rightarrow 3} \frac{x-3}{\sqrt{x-2}-\sqrt{4-x}} \) equals to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{1}{4} \)
D. none of these


The normal boiling point of liquid
hydrogen is \( -253^{\circ} \mathrm{C} \). What is the corresponding temperature on absolute scale?
A . \( 22 K \)
в. \( 20 K \)
c. \( 274 K \)
D. \( -20 K \)


The preparation of ammonia by Haber's process is an exothermic reaction. If the
preparation follows the following
temperature pressure relationship for
its \% yield. Then the temperatures
\( T_{1}, T_{2} \) and \( T_{3}, \) the correct option is:
A \( \cdot T_{3}>T_{2}>T_{1} \)
В \( \cdot T_{1}>T_{2}>T_{3} \)
\( \mathbf{c} \cdot T_{1}=T_{2}=T_{3} \)
D. Nothing can be predicted


Number of \( P_{2} \) and \( P_{3} \) viewers.


Select the correct I.U.P.A.C. name for the
following complex:
This question has multiple correct options
A. di bromidoplatinum(II)bis- - \( \mu \) -(dimethylthioether)
dibromidoplatinum(II)
B. bisf \( \mu \) (dimethylthioether)dibromidoplatinum(II))
C. bis- \( \mu \) -dimethylthioethertetrabromidodiplatinum(II)
D. bis-f.L-dimethylthioethertetrabromidodiplatinate(II)


Using Gauss's theorem determine the electric field due to a uniformly charged sphere shell at a point which is


Find the probability of scoring a total of more than \( 7, \) when two dice are thrown
A \( .5 / 12 \)
B. \( 5 / 18 \)
\( c .5 / 6 \)
D. \( 5 / 24 \)


Assertion
If both \( \Delta H^{0} \) and \( \Delta S^{0} \) are positive then
reaction will be spontaneous at high temperature.
Reason
All processes with positive entropy change are spontaneous.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The concentration of carbon dioxide
beyond which it fails to accelerate the photosynthesis is known as
A. Saturation point.
B. Compensation point.
c. Both A and B
D. None of the above


Under what soil condition do you think a
farmer would treat the soil of his fields with quick lime (calcium oxide) or
slaked lime (calcium hydroxide) or chalk (calcium carbonate)?


The number of electrons having \( n+ \)
\( s=2.5 \) in sulphide ion is:
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 2


Assertion
Every vibrating body is a source of
Sound.
Reason
All sounds are audible.
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


By selling a watch for \( R s 1260 \) a person gains \( 5 \% \). Find the cost price of the
watch.


In meiosis I, the centromere undergoes
A. No division
B. Division between prophase and metaphase
C. Division between anaphase and interphase
D. Division but the daughter chromosomes do not separate


With the help of two suitable example, explain why certain experiences and traits earned by people during their lifetime are not passed on to their nest
generations.When can such traits be passed on?


Find the remainder using remainder theorem, when:
\( 2 x^{3}-4 x^{2}+7 x+6 \) is divided by \( x-2 \)


State three points of differences between a real image and a virtual image.


The product \( C \) is (according to the image shown)
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


There is a point charge q located at the centre of a cube. What is the electric
flux of this point charge, through a face of the cube?
A \( \cdot \frac{q}{\epsilon_{0}} \)
в. \( \frac{q}{6 \epsilon_{0}} \)
c. \( \frac{q}{3 \epsilon_{0}} \)
D. It will depend on the size of the cube


\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \stackrel{\Delta}{\longrightarrow}(\boldsymbol{X})+\boldsymbol{P} \boldsymbol{H}_{3} \) is :
A. Dehydration reaction
B. Oxidation reaction
c. Dispropportionation reaction
D. Dephosphorelation reaction


Write value of the 'least distance of
distinct vision' for a young adult with normal vision.


Two particles \( P \) and \( Q \) move in a
straight line \( A B \) towards each other. \( P \)
starts from \( \boldsymbol{A} \) with velocity \( \boldsymbol{u}_{1}, \) and an
acceleration \( a_{1}, Q \) starts from \( B \) with
velocity \( u_{2} \) and acceleration \( a_{2} \). They
pass each other at the midpoint of \( \boldsymbol{A B} \)
and arrive at the other ends of \( A B \) with
equal velocities This question has multiple correct options
A \( \cdot \) They meet at midpoint at time \( t=\frac{2\left(u_{2}-u_{1}\right)}{a_{1}-a_{2}} \)
B. The length of path specified i.e. \( A B \) is \( l= \) \( \frac{4\left(u_{2}-u_{1}\right)\left(a_{1} u_{2}-a_{2} u_{1}\right)}{\left(a_{1}-a_{2}\right)^{2}} \)
C. They reach the other ends of \( A B \) with equal velocities if
\( \left(u_{2}+u_{1}\right)\left(a_{1}-a_{2}\right)=8\left(a_{1} u_{2}-a_{2} u_{1}\right) \)
D. They reach the other ends of \( A B \) with equal velocities if
\( \left(u_{2}-u_{1}\right)\left(a_{1}+a_{2}\right)=8\left(a_{2} u_{1}-a_{1} u_{2}\right) \)


Check whether the relation \( \boldsymbol{R} \) in \( \boldsymbol{R} \)
defined by \( R=\left\{(a, b): a \leq b^{3}\right\} \) is
reflexive, symmetric or transitive.


A medicine is known to be \( 75 \% \) effective
to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is curved by this medicine?
A \( \cdot \frac{1}{1024} \)
в. \( \frac{243}{1024} \)
c. \( \frac{1023}{1024} \)
D. \( \frac{781}{1024} \)


Check if 0 is a term of the \( A P: 31,28,25 \)


A decomposition reaction taking place
due to passage of electric current is
called


Thirty-two player ranked 1 to 32 are play knockout tournament. Assume that in
every match between any two players
the better ranked player wins, the
probability that ranked 1 and ranked 2 players are winner and runner up
respectively is \( p \), then the value of \( [2 / p] \)
is, where [.] represents the greatest integer function.


Density and Molar Mass of Gaseous
Substances


If the perpendicular distance of a point
\( P \) from the \( X \) -axis is 5 units and the
foot of the perpendicular lies on the
negative direction of \( X \) -axis, then the
point \( \boldsymbol{P} \) has
A. \( X \) -coordinate \( =-5 \)
B. Y-coordinate = - 5
c. \( Y \) -coordinate \( =-5 \) only
D. \( Y \) -coordinate \( =5 \) or -5


The body plan in which the alimentary canal has a single opening is known as
A . Cell aggregate body plan
B. Blind sac body plan
c. Tube within tube plan
D. All of the above


There are no compounds of He and Ne.
If true enter 1 , else enter 0


The unit of zero order rate constant is:
A . litre mol" \( \sec ^{-1} \)
B. mol liitre \( ^{-1} \)sec\( ^{-1} \)
\( \mathbf{c} \cdot \sec ^{-1} \)
D. litre^ sec-


Assertion
Weight of solid in air is \( \mathrm{W} \) and in water is \( T=\frac{2 W}{3} \) Then relative density of
solid is 3.0
Reason
Relative density of any solid is given by \( R D=\frac{\text { Weight in air }}{\text { Change in weight in water }} \)
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


War gas is:
A. chloretone
B. ethyl carbonate
C. chloropicrin
D. methylene chloride


Two spheres of same size one of mass \( 2 k g \) and another of mass \( 4 k g \) are
dropped simultaneously from the top of Qutab Minar (height \( =\mathbf{7} 2 \boldsymbol{m} \) ). When
they are \( 1 m \) above the ground, the two
spheres have the same:
A. momentum
B. kinetic energy
c. potential energy
D. acceleration


The range of the wavelength of audible sound that travels with a velocity of 330 \( m s^{-1} a t 0^{\circ} C \) is \( 16.5 m-16.5 m m \)
A. True
B. False


Name the Scientist who stated that
matter can be converted into energy


Which statement describes positive
ions?
A. Positive ions have more electrons than neutrons
B. Positive ions have more protons than neutrons
C. Positive ions have more electrons than protons
D. Positive ions have more protons than electrons


\( f^{35} C_{n+7}=^{35} C_{4 n-2}, \) then the value of \( n \)
is
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


Pericardial fluid present between?
A. Fibrous pericardium \& Parietal layer
B. Parietal layer and visceral layer
C. Visceral layer \& epicardium
D. Myocardium \& Endocardium


Factories \( : 2 x y+2 y+3 x+3 \)


If the total surface area of a solid
hemisphere is \( 462 \mathrm{cm}^{2} \), find its volume. \( \left[\text { take } \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)


Evaluate the definite integral:
\( \int_{0}^{\pi / 2} \sin x d x \)


(a) Draw a labelled diagram of an
electric generator. Explain its construction and working in brief.
(b) Write down any two characteristics of magnetic field lines of a bar magnet.


A dielectric slab of thickness \( 6 \mathrm{cm} \) is
placed between the plates of a parallel plate capacitor. If the distance between
plates is reduced by \( 4 c m, \) the capacity of the capacitor remains the same. Find the dielectric constant of the medium.
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 3


Iron is in +2 oxidation state in:
This question has multiple correct options
\( \mathbf{A} \cdot N a_{2}\left[F e(C N)_{5} N O\right] \)
\( \mathbf{B} \cdot\left[F e\left(H_{2} O\right)_{5} N O\right] S O_{4} \)
\( \mathbf{c} \cdot K_{3}\left[F e(C N)_{6}\right] \)
\( \mathbf{D} \cdot K_{4}\left[F e(C N)_{6}\right] \)


Two blocks of masses \( 10 \mathrm{kg} \) and \( 4 \mathrm{kg} \)
are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/ \( s \) to the heavier block
in the direction of the lighter block, The velocity of the centre of mass is:
A. \( 30 \mathrm{m} / \mathrm{s} \)
в. 20 \( m / s \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


Derivative of \( 2 \tan x-7 \sec x \) with
respect to \( x \) is:
\( \mathbf{A} \cdot 2 \sec x+7 \tan x \)
B. \( \sec x(2 \sec x+\tan x) \)
c. \( 2 \sec ^{2} x+\sec x \). tan \( x \)
D. \( \sec x(2 \sec x-7 \tan x) \)


Non-combustible hydride is:
A . \( N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( S b H_{3} \)


Fill in the blanks
is the most
stable form of sulphur.


The outer capsule of drugs is made up
of a polymer of:
A. glycolic acid and lactic acid
B. glycine and caproic acid
C. salicylic acid and p-aminobenzoic acid
D. 3 -hydroxybutanoic acid and 3 -hydroxypentanoic acid


The principal of nitrogenous excretory
compound in humans is synthesised
A. in kidneys but eliminated mostly through liver
B. as well as eliminated by kidneys
C. in liver and also eliminated by the same through bile
D. in the liver, but eliminated mostly through kidneys.


Assuming ideal behaviour, calculate the work done when 1.6 mole of water
evaporates at \( 373 \mathrm{K} \) against the atmospheric pressure of 1 atm.
A . 29.67 J
B. 48.8 J
c. 21.2 J
D. none of these


Which of the following statement is
correct?
A. Dilution increases the extent of deviation of ideality
B. Dilution has no effect on deviation
c. Dilution decreases the extent of deviation from ideality
D. More concentrated the solution is, lesser will be the deviation


Which shows the highest lattice energy?
A. \( R b F \)
в. \( C s F \)
\( c . N a F \)
D. \( K F \)


At what change in temperature will the resistance of a copper wire become three times its value at \( 0^{0} C ? \) [Temperature coefficient of resistance for copper \( \left.4 \times 10^{-3}\right]: \)
A \( .400^{\circ} \mathrm{C} \)
B. 450 \( ^{0} C \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)


A current of 5 amperes is passed
through \( \mathrm{AlCl}_{3} \) solution for 15 minutes using Pt electrodes, when 0.504 g of \( A l \) is produced. What is the molar mass of Al?


There exist uniform magnetic and electric fields of magnitudes \( 1 T \) and \( \mathbf{1} \boldsymbol{V} / \boldsymbol{m}, \) respectively, along positive \( \boldsymbol{y}- \)
axis. A charged particle of mass \( 1 k g \) and charge \( 1 C \) is having velocity 1 \( m / s \) along \( x \) -axis and is at origin at \( \boldsymbol{t}=\mathbf{0} . \) Then, the coordinates of the
particle at time \( \pi s \) will be
A. (0,1,2)\( m \)
в. \( \left(0,-\pi^{2},-2\right) m \)
c. \( \left(2, \pi^{2} / 2,2\right) m \)
D・ \( \left(0, \pi^{2} / 2,2\right) m \)


One ohm is equal to
\( \mathbf{A} \cdot 10^{6} M \Omega \)
B \( \cdot 10^{9} M \Omega \)
\( \mathbf{c} \cdot 10^{-6} M \Omega \)
D. none of these


What are the different types of adventitious root modifications?


The elasticity of various materials is controlled by its
A. Ultimate tensile stress
B. Stress at yield point
c. Stress at elastic limit
D. Tensile stress


An electric field \( \vec{E}-\vec{i} A x \) exists in the
space, where \( A=V / m^{2} \). take the
potential at \( (10 m, 20 m) \) to be zero. Find the potential at the origin.


\( \mathbf{8}^{214} \boldsymbol{B} \boldsymbol{i} \quad \boldsymbol{\alpha}-e m i s s i o n \quad \boldsymbol{A} \quad \boldsymbol{\beta}-e m i s s i o \boldsymbol{n} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{\beta}-\text {emission}}{\longrightarrow} \boldsymbol{C} \quad \boldsymbol{\beta}- \)emission
\( \boldsymbol{D} \stackrel{\boldsymbol{\alpha}-\boldsymbol{e} \boldsymbol{m} i \boldsymbol{s} \boldsymbol{s} i \boldsymbol{o} \boldsymbol{n}}{\boldsymbol{}} \boldsymbol{E} \)
\( E^{\prime} \) is an element of stable nucleus.
What is the element' \( ' E \) '?
\( \mathbf{A} \cdot_{81}^{207} T l \)
B. 206
82 \( \mathrm{Pb} \)
C \( \cdot 206 \)
80 \( \mathrm{Hg} \)
D. 206
79


An isotope of helium is represented by the symbol \( _{2}^{3} H e . \) How many protons, neutrons and electrons are there in an
atom of the isotope?
A. 1 proton, 2 neutrons, 1 electron
B. 1 proton, 3 neutrons, 2 electrons
C. 2 protons, 1 neutron, 2 electrons
D. 2 protons, 3 neutrons, 2 electrons


Identify the wrong statement with
reference to UV rays.
A. UV-A is more harmful to animals than UV-B.
B. UV radiation falls in the range between \( 100-300 \mathrm{nm} \) wavelength.
C. UV radiation is classified into three categories.
D. UV radiation kills microorganisms.


which an electron in hydrogen atom
jumps from the third excited state to the ground state


The ratio of the energy of a photon of \( 2000 A \) wavelength radiation to that of \( 4000 A \) radiation is:
A \( \cdot \frac{1}{4} \)
B. 4
\( c \cdot \frac{1}{2} \)
D. 2


The difference of \( \Delta H-\Delta U \) for the
given reaction is \( \Delta n_{g} R T . \) The value of
\( \Delta n_{g} \) is
\( C_{6} H_{12} O_{6(s)}+6 O_{2(g)} \longrightarrow+6 C O_{2(g)}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}_{(\boldsymbol{v})} \)


A block of mass \( 2 k g \) is moving with a velocity of \( 2 \hat{i}-\hat{j}+3 \hat{k} m / s . \) Find the
magnitude and direction of momentum of the block with the \( x- \) axis.
A \( \cdot_{2 \sqrt{14}} \operatorname{kg} m / s, \tan ^{-1}(\sqrt{\frac{5}{7}}) \)
B. \( _{2 \sqrt{7}} k g m / s, \tan ^{-1}(\sqrt{\frac{2}{7}}) \)
c. \( _{2 \sqrt{14}} k g m / s, \tan ^{-1}(\sqrt{\frac{2}{7}}) \)
D. \( 2 \sqrt{9} \) kg \( m / s, \tan ^{-1}(\sqrt{\frac{3}{7}}) \)


A lightning conductor consists of
A. several sharp metal spiked connected to a thick copper strip.
B. a metal plate buried deep inside the ground connected to the ground end of copper strip.
C. a conductor fixed on top of the building.
D. all of the above


Many cells function properly and divide
mitotically even though they do not have
A. Plasma membrane
B. Cytoskeleton
c. Mitochondria
D. Plastids


An inclined plane of length \( 5.60 m \)
making an angle of \( 45^{\circ} \) with the horizontal is placed in an uniform electric field \( \boldsymbol{E}=\mathbf{1 0 0} \boldsymbol{V m}^{-1} . \) A particle
of mass \( 1 k g \) and charge \( 10^{-2} C \) is allowed to slide down from rest position
from maximum height of slope. If the
coefficient of friction is \( 0.1, \) the time
taken by the particle to reach the bottom is
\( \mathbf{A} \cdot 1 s \)
B. \( 1.41 s \)
c. \( 2 s \)
D. None of these


The lead marked with the arrow is the
A . collector
B. base
c. emitter
D. cor


Solve \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{2} \boldsymbol{y}}{\boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{x}} \)


\( A \) body at \( 80^{\circ} C \) cools down to \( 64^{\circ} \mathrm{C} \) in 5
minutes; and in 10 minutes it cools
down to \( 52^{\circ} C . \) What will be its
temperature after 20 minutes? What is the temperature of the environment?


On comparing the emf's \( E_{1} \) and
\( \boldsymbol{E}_{2}\left(\boldsymbol{E}_{1}>\boldsymbol{E}_{2}\right) \) of two cells by a
potentiometer, the balancing lengths
come out to be \( l_{1} \) and \( l_{2} \) respectively,
then
A \( \cdot l_{1}<l_{2} \)
В. \( l_{1}-l_{2} \)
c. \( l_{1}>l_{2} \)
D. none of the above


\( \mathbf{0 . 3}+\mathbf{0 . 0 3 + 0 . 0 0 3 + 0 . 0 0 0 3}+\ldots \ldots . \) to
terms.


Calculate the mode for the following
data:
\begin{tabular}{lllll}
Score & 14 & 16 & 18 & 20 \\
Frequency & 2 & 4 & 4 & 8 \\
\hline
\end{tabular}
A . 14
B . 16
c. 18
D. 2


If a car at rest accelerates uniformly to a speed of \( 144 \mathrm{km} / \mathrm{h} \) in 20 second, it covres a distance of :-
A . \( 20 m \)
B. \( 400 m \)
c. \( 1440 m \)
D. 2980 \( m \)


One electron is present in the outer most shell of the atom of an element \( X \)
What would be the nature and value of
charge on the ion formed if this electron is removed from the outer most shell?
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)


The correct value of dip angle at a place
is \( 45^{\circ} . \) If the dip circle is rotated by \( 45^{\circ} \) out of the meridian, then the tangent of the angle of apparent dip at the place is
A . 1
B. \( 1 / 2 \)
c. \( 1 / \sqrt{2} \)
D. \( \sqrt{2} \)


Empirical formula of an ingredient in
buffering tablets that has the per cent composition \( \boldsymbol{C}: \mathbf{1 4} . \mathbf{2 5} \%, \boldsymbol{O} \)
\( \mathbf{5 6 . 9 3 \%}, \boldsymbol{M g}: \mathbf{2 8 . 8 3 \%} \) by mass is
\( \boldsymbol{C O}_{3} \boldsymbol{M} \boldsymbol{g} \)
If true enter 1 , else enter 0 .


A student answers a multiple choice question with 5 alternatives, of which
exactly one is correct. The probability that he knows the correct answer is
\( \boldsymbol{p}, \boldsymbol{0}<\boldsymbol{p}<1 . \) If he does not know the
correct answer, he randomly ticks one answer. Given that he has answered the
question correctly, the probability that he did not tick the answer randomly, is
A. \( \frac{3 p}{4 p+3} \)
в. \( \frac{5 p}{3 p+2} \)
c. \( \frac{5 p}{4 p+1} \)
D. \( \frac{4 p}{3 p+1} \)


Which of the following waves is udsed in sonography?
A. Radio waves
B. X-rays
c. Ultrasonic waves
D. Gamma rays


Consider the following \( \boldsymbol{E}^{0} \) values:
\( \boldsymbol{E}_{\boldsymbol{F} \boldsymbol{e}^{3+} / \boldsymbol{F} e^{2+}}^{\boldsymbol{0}}=\boldsymbol{0 . 7 7 V} \)
\( E_{S n^{2+} / S n}^{0}=-0.14 V \)
Under standard conditions the potential
for the reaction, is:
\( \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{S} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q}) \)
A . \( 0.91 \mathrm{V} \)
B. 1.40V
c. \( 1.68 v \)
D. 0.63v


Amount of zinc deposited when \( 3.01 \times \)
\( 10^{20} \) electrons pass through \( Z n S O_{4} \)
solution is:
A . \( 16.35 g \)
B . \( 16.375 \times 10^{-3} g \)
c. \( 32.7 \times 10^{-3} g \)
D. 32.7g


Ropes of nylon and polyester are commonly used in cranes and elevators.
A. True
B. False


If the variance of the first \( n \) natural
numbers is 10 and the variance of the
first \( m \) even natural numbers is 16
then \( m+n \) is equal to


The convex surface of a thin concavo-
convex lens of glass of refractive index
1.5 has a radius of curvature \( 20 \mathrm{cm} . \) The
concave surface has a radius of
curvature \( 60 \mathrm{cm} . \) The convex side is
silvered and placed on a horizontal
surface.
(i) Where should a pin be placed on the optical axis such that its image is
formed at the same place?
(ii) If the concave part is filled with
water of refractive index \( 4 / 3, \) find the distance through which the pin should
be moved so that the image of the pin again coincidence with the pin.


Plant growth-promoting rhizobacteria, Pseudomonas produce which chelate iron and make it
unavailable to harmful fungi for potato, sugarbeet and radish.
A. Nutrilite
B. NPK with Anabaena
c. Biopoesticide rich in Nostoc
D. siderophore


Domain of the function \( \log \left|x^{2}-9\right| \) is
A. \( R \)
B. \( R-[-3,3] \)
c. \( R-\{-3,3\} \)
D. None of these


The objective and eyepiece of an astronomical telescope are doubled convex lenses with refractive index 1.5
When the telescope is adjusted to infinity, the separation between the two lenses is \( 16 \mathrm{cm} \). If the space between
the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses is:
A. \( 8 \mathrm{cm} \)
в. 16 ст
\( c \cdot 24 c m \)
D. 32 ст


Climax vegetation of a region is generally
A. Xerophytic
B. Hydrophytic
c. Mesophytic
D. Depends upon the climate


Which of the following is not present in
Water?
A. Antimony
B. Arsenic
c. Benzene
D. Bismuth


The standard e.m.f. of the following cell
is \( 0.463 \mathrm{V} \)
\( \boldsymbol{C} \boldsymbol{u}\left|\boldsymbol{C} \boldsymbol{u}^{++} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \)
\( (s)^{\prime}(I M)^{\prime}(I M)^{\prime}(s) \)
If the standard potential of Ag electrode
is \( 0.800 \mathrm{V} \), what is the standard
potential of Cu electrode?


A small disc \( A \) is placed on an inclined
plane forming an angle \( \alpha \) with the
horizontal (shown in figure above) and
is imparted an initial velocity \( v_{0} \). Find
how the velocity of the disc depends on
the angle \( \varphi \) if the friction coefficient
\( k=\tan \alpha \) and at the initial moment
\( \varphi_{0}=\frac{\pi}{2} \)
A \( \cdot v=\frac{v_{0}}{1+2 \cos \varphi} \)
в. \( v=\frac{v_{0}}{1-2 \cos \varphi} \)
c. \( v=\frac{v_{0}}{1+\cos \varphi} \)
D. \( v=\frac{v_{0}}{1-\cos \varphi} \)


Explain the principle and working of
Nuclear Reactor with the help of a
labelled diagram.


\( 510 \mathrm{mg} \) of a liquid on vapourisation in Victor Mayer's apparatus displaces 67.2 cc of dry air (at NTP). The molecular weight (in g/mol) of the liquid is :
A . 130
B. 17
c. 1700
D. 170


The focal length of the eye lens
increases when eye muscles:
A. are relaxed and lens becomes thinner.
B. contract and lens becomes thicker.
C. are relaxed and lens becomes thicker.
D. contract and lens becomes thinner.


Which of the following are examples of multiple reflections of sound?
A. Stethoscope
B. Sound board
c. Megaphone
D. All of the above


What is the pressure drop (in \( \mathrm{mm} \) Hg) in the blood as it passes through a capillary \( 1 \mathrm{mm} \) long and \( 2 \mu m \) in radius if the speed of the blood through the centre of the capillary is \( 0.66 \mathrm{mm} / \mathrm{s} \) ? (The viscosity of whole blood is \( 4 \times \) \( 10^{-3} \) poise


Find the volume of a sphere whose radius is \( 7 \mathrm{cm} \)
A. \( _{1437} \frac{1}{3} c m^{3} \)
в. \( _{1437} \frac{1}{4} c m^{3} \)
c. \( _{1437} \frac{2}{3} c m^{3} \)
D. \( _{1437} \frac{1}{2} c m^{3} \)


The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of \( \sqrt{3 g l} \). Find the angle rotated by the string before it becomes slack.


Number of solutions of the equation \( [y+ \) \( [y]]=2 \cos x \) is
(where \( y=(1 / 3)[\sin x+[\sin x+[\sin x]]] \)
and []\( =\text { greatest integer function }) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \cdot \infty \)


Assertion
Isomers can be homologues.
Reason

Homologues can be isomers.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


The presence of nucleus in an atom is
determined by Rutherford \( \boldsymbol{\alpha}-\boldsymbol{r} \boldsymbol{a} \boldsymbol{y} \)
scattering experiment.
A. True
B. False


The distance travelled by a body in the nth second is given by the expression \( (2+3 n) . \) Find the initial velocity and
acceleration. Also, find its velocity at
the end of 2 seconds.


Which of these steps in krebs' cycle indicates substrate level
phosphorylation?
A. Conversion of succunic acid to a-ketoglutaric acid
B. Conversion of succunic acid to malic acid
c. conversion of succunyl CoA to succunic acid
D. Conversion of malic acid to oxaloacetic acid


Evaluate the following definite integral:
\( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


Final setting time of cement should not be more than:
A. 1 hour
B. 2 hours
c. 5 hours
D. 10 hours


Find inclination (in degrees) of a line perpendicular to y-axis.


Detergents are more efficient than soaps in cleaning, yet you have to limit the use of detergents because:
A. they are costly
B. they are not ecofriendly
c. their production cost is high
D. they produce scum in hard water


A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of
incidence \( 45^{\circ} . \) The ray undergoes total internal reflection. The possible value of
refractive index of the medium
with respect to air is
A \( \cdot 1.245 \)
B. 1.324
\( c \cdot 1.414 \)
D. 1.524


\( f(x)=\frac{3 x^{2}+a x+a+1}{x^{2}+x-2}, \) then which
of the following can be correct? This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exists \( \Rightarrow a=-2 \)
B. \( \lim _{x \rightarrow-2} f(x) \) exists \( \Rightarrow a=13 \)
C if the limit exists, lim \( f(x)=\frac{4}{3} \)
D. If the limit exists, \( \lim _{x \rightarrow-2} f(x)=-\frac{1}{3} \)


The forelimbs and hindlimbs movement
is caused by
A. Striated muscle
B. Unstriated muscles
c. cardiac muscles
D. None of these


Which of the following is not one of the prime health risks associated with
greater UV radiation due to the
depletion of stratospheric ozone?
A. Increased liver cancer
B. Increased skin cancer
c. Reduced immune systemmm
D. Damage to eyes


The reactive species in chlorine bleach
is:
A. \( C l_{2} O \)
в. \( O C l^{-} \)
c. \( C l O_{2} \)
D. \( H C l \)


Find the Odd one among : 23,13,34,25 56,51
A . 23
B. 13
\( c \cdot 34 \)
D. 51


If \( \vec{a}+2 \vec{b}, 2 \vec{a}+\vec{b} \) be the position vectors
of the points \( A \) and \( B \), then the position
vector of the point \( C \) which divides \( A B \)
internally in the ratio 2: 1 is
A \( \cdot \frac{5 \vec{a}-4 \vec{b}}{3} \)
в. \( \frac{5 \vec{a}+4 \vec{b}}{3} \)
c. \( \frac{5 \vec{a}-2 \vec{b}}{3} \)
D. \( \frac{5 \vec{a}+2 \vec{b}}{3} \)


Assertion
Nitrogenous matter produces ammonia.
Reason
Mammals excrete urea and
birds,reptiles produce uric acid which is a metabolite of amino acids
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 \( A \) and \( B \) have \( n \) elements in common,
then the number of elements common
to \( A \times B \) and \( B \times A \) is
A \( . n \)
B. \( 2 n \)
\( c \cdot n^{2} \)
D.


Sum of two numbers is 6 times their
geometric mean, show that numbers are in the ratio \( (3+2 \sqrt{2}):(3-2 \sqrt{2}) \)


A maxima or minima obtained in the
temperature composition curve of a mixture of two liquids indicates:
A. an azeotropic mixture
B. an eutectic formation
c. that the liquids are immiscible with one another
D. that the liquids are partially miscible at the maximumm or minimum


Assertion: The resistance offered by an inductor in a d.c circuit is always
constant.
Reason : The resistance of inductor in
steady state is non-zero.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements


Assertion
With \( B r_{2}-H_{2} O, \) phenol give \( s 2,4,6 \)
tribromophenol but with \( B r-C S_{2}, \) it
gives 4 -bromophenol as the major
product.
Reason
In water ionization of phenol is
enhanced but in \( C S_{2}, \) it is greatly
suppressed.
Read the above assertion and reason
and choose the correct option regarding
it.
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


For \( \boldsymbol{z}=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then for \( \boldsymbol{e}^{|\boldsymbol{z}|} \)
A \( \cdot e^{|x|} \leq e^{|z|} \)
B \( \cdot e^{x} \geq e^{|z|} \)
\( \mathbf{c} \cdot e^{|x|}=e^{|z|} \)
D. none of these


If \( \int \frac{e^{x}\left(2-x^{2}\right)}{(1-x) \sqrt{1-x^{2}}} d x= \)
\( \mu e^{x}\left(\frac{1+x}{1-x}\right)^{\lambda}+C, \) then \( 2(\lambda+\mu) \) is
equal to
\( A \)
B.
\( c \cdot 2 \)
D. 3


A car starting from a speed of \( 12 \mathrm{m} / \mathrm{s} \) slows to \( 6 \mathrm{m} / \mathrm{s} \) in a time of \( 3 \mathrm{s} \). Calculate the average acceleration of the car? [Unless otherwise mention, use \( \boldsymbol{g}= \) \( \left.10 m / s^{2} \text { and neglect air resistance }\right] \)
A \( \cdot 2 m / s^{2} \)
B . \( 4 m / s^{2} \)
\( \mathrm{c} \cdot 3 \mathrm{m} / \mathrm{s}^{2} \)
D. \( -2 m / s^{2} \)
E \( .-4 m / s^{2} \)


In a step-down transformer, the number
of turns in
A. primary are less.
B. primary are more.
c. primary and secondary are equal.
D. secondary are infinite.


Rational number \( \frac{-18}{5} \) lies between consecutive integers
\( A \cdot-2 \) and -3
B. -3 and -4
c. -4 and -5
D. -5 and -6


If \( \tan \theta+\tan 4 \theta+\tan 7 \theta= \)
\( \tan \theta \tan 4 \theta \tan 7 \theta, \) then \( \theta= \)
A \( \cdot \frac{n \pi}{4} \)
в. \( \frac{n \pi}{7} \)
c. \( \frac{n \pi}{12} \)
D. \( n \pi \)


Write electronic configurations of the
\( \boldsymbol{H} e \)


Straight chain silicones are prepared by hydrolysis by:
A \( \cdot R_{2} S i C l_{2} \)
в. \( R_{3} \) SiCl
c. \( R S i C l_{3} \)
D. \( R_{2} \) Si


Stomata are not found in
A . Algae
B. Mosses
c. Ferns
D. Liverworts


A ball is projected horizontally from the
top of a tower with a velocity \( v_{0} \). It will be
moving at an angle of \( 60^{\circ} \) with the horizontal after time -
A. \( \frac{v_{0}}{\sqrt{3} g_{g}} \)
B. \( \frac{\sqrt{3} v_{0}}{g} \)
c. \( \frac{v_{0}}{g} \)
D. \( \frac{v_{0}}{2 g g g g g g_{0}} \)


A thin wire has a length of \( 21.7 \mathrm{cm} \) and
radius 0.46 mm. The volume of the wire
to correct significant figures is :
A \( .1 .4 \mathrm{cm}^{3} \)
B. \( 0.14 \mathrm{cm}^{3} \)
c. \( 0.14 \mathrm{mm}^{3} \)
D. None of these


\( \boldsymbol{A}-\boldsymbol{B}= \)
\( \mathbf{A} \cdot A \cup(A \cap B) \)
В . \( B-A \)
\( \mathbf{c} \cdot A-(A \cap B) \)
\( \mathbf{D} \cdot A^{\prime} \cap B \)


The phenomenon of producing an emf in a circuit whenever the magnetic flux linked with a coil changes is
A. Electro-magnetic induction
B. Inducing current
c. Inducing voltage
D. change in current


The convection current continues till
the entire medium acquires the
density
A. Different
B. Same
c. Both
D. None


Formation of ozone hole is maximum
over
A. India
B. Australia
c. Antarctica
D. Europe


In given figure, \( P B \) and \( Q \) a are perpendiculars to segment AB. If PO=5 \( \mathrm{cm}, \mathrm{Q} \mathrm{O}=7 \mathrm{cm} \) and Area \( \triangle \boldsymbol{P O B}= \)
\( 150 c m^{2} \) find the area of \( \triangle Q O A \)


A string fixed at both ends, oscillate in
\( 4^{t h} \) harmonic. The displacement of a particle of string is given as:
\( \boldsymbol{Y}=\boldsymbol{2} \boldsymbol{A} \sin (\boldsymbol{5} \boldsymbol{\pi} \boldsymbol{x}) \cos (\boldsymbol{1} \boldsymbol{0} \boldsymbol{0} \boldsymbol{\pi} \boldsymbol{t}) . \) Then find
the length of the string?
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. 100 ст
\( \mathbf{c} .60 \mathrm{cm} \)
D. \( 120 \mathrm{cm} \)


How is a nail able to pierce the surface
of wood?


\( \boldsymbol{C O}_{2}: \boldsymbol{N} \boldsymbol{A} \boldsymbol{D} \boldsymbol{P} \boldsymbol{H}_{2}: \boldsymbol{A} \boldsymbol{T} \boldsymbol{P} \) ratio for \( \boldsymbol{C}_{3} \)
plants is
A. 1: 2: 3
B. 1: 2: 4
\( \mathrm{c} \cdot 1: 3: 6 \)
D. 1: 5: 10


Which of the following statements is
not correct?
A. For a zero order reaction, \( t_{1 / 2} \) is proportional to initial concentration
B. The relationship of variation of rate constant with temperature is given by \( \log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right] \)
C. The unit of rate constant for a reaction is \( m o l^{1-n} L^{n-1} s^{-1} \) where \( n \) is order of the reaction
D. The unit of rate of reaction changes with order of reaction


\( I_{3}^{-} \) is formed when \( I_{2} \) combines with \( I^{-} \)
"I \( _{2} \) behaves as a Lewis base."

Answer whether the above statement is
true or false. If true enter 1 , else 0


\( (\triangle \boldsymbol{H}-\triangle \boldsymbol{E}) \) is maximum at a given
temperature in case of:
\( \mathbf{A} \cdot P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)
B. \( C a C O_{3}(s) \rightarrow C a O_{3}(s)+C O_{2}(g) \)
\( \mathbf{c} \cdot N H_{4} H S(s) \rightarrow N H_{3}(g)+H_{2} S(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) \)


If \( \boldsymbol{P}(\boldsymbol{B})=\frac{\boldsymbol{3}}{\boldsymbol{4}}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \overline{\boldsymbol{C}})=\frac{1}{3} \) and
\( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B} \cap \overline{\boldsymbol{C}})=\frac{1}{3} \operatorname{then} \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C}) \) is
A \( \cdot \frac{1}{12} \)
B.
c. \( \frac{1}{15} \)
\( D \)


A body starts from the rest with uniform acceleration. If its displacement in the
3rd seconds and 7th second are \( x_{1} \) and
\( \boldsymbol{x}_{2}, \) then:
A. \( 13 x_{1}=5 x_{2} \)
В. \( 5 x_{1}=13 x_{2} \)
c. \( 3 x_{1}=7 x_{2} \)
D. \( 7 x_{1}=3 x_{2} \)