The electric current in a wire may be
calculated using the equation \( \boldsymbol{I}= \)
Anvq.

Which statement is not correct?
A. \( n \) is the number of charge carriers per unit volume of the wire
B. nA is the number of charge carriers per unit length of the wire
c. q is the charge of each charge carrier
D. v is the velocity of each charge carrier


Find the mass percentages (mass \%) of Na, H, C, and O in sodium hydrogen
carbonate.
A. 30,20,45,5
B. 28,1,14,57
c. 24,23,12,1
D. None of above


Which of the following combination will form an electrovalent bond?
A \( . P \) and \( C l \)
B. \( N H_{3} \) and \( B F_{3} \)
c. \( H \) and \( C a \)
D. \( H \) and \( S \)


A ring and a disc are initially at rest, side by side, at the top of an inclined
plane which makes an angle \( 60^{\circ} \) with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is \( \frac{(2-\sqrt{3})}{\sqrt{10} s}, \) then the height of the top of the inclined plane, in meters.
is \( _{-1} \). Take \( g=10 m s^{-2} \)


Find the approximate value of
\( (0.009)^{1 / 3} \)
\( \mathbf{A} \cdot 0.208 \)
B. 0.108
c. 0.205
D. 0.204


The probability that a person will get an electric contract is \( \frac{2}{5} \) and the
probability that he will not get plumbing contract is \( \frac{4}{7} . \) If the probability of getting at least one contract is \( \frac{2}{3}, \) then the probability that he will get both is \( \frac{17}{105} \)
A. True
B. False


Select the correct statement regarding
activated sludge formed during
secondary sewage treatment.
A. A small part of it is rapidly pumped back from sedimentation to aeration tank.
B. It absorbs pathogenic bacteria present in waste water while sinking to the bottom of the settling tank.
C. A major part of it Is anaerobically digested.
D. Both
(a) and (c)


Two blocks \( A \) and \( B \) each of 20 kg lying on a frictionless table are connected by
a light string. The system is pulled horizontally with an acceleration of
\( 2 m s^{-2} \) by a force \( F \) on \( B . \) The tension in the string will be:
A. \( 10 N \)
в. \( 40 N \)
c. \( 100 N \)
D. \( 120 N \)


In a p-njunction the depletion region is \( 400 n m \) wide and electric field of \( 5 \times \)
\( 10^{5} V m^{-1} \) exists in it. The minimum
energy of a conduction electron, which can diffuse from n-side to the p-side is:
A . \( 4 e V \)
в. \( 5 e V \)
c. \( 0.4 e V \)
D. \( 0.2 e V \)


Two measurements of a cylinder are varying in such a way that the volume is kept constant. If the rates of change of the radius \( (r) \) and height \( (h) \) are equal in magnitude but opposite in sign, then
A \( . r=2 h \)
B . \( h=2 r \)
c. \( h=r \)
D. \( h=4 r \)


If
\( A B \) is a chord of a circle with centre \( O \)
and \( P \) is a point on \( A B \) such that \( B P=4 P A, O P=5 \mathrm{cm} \) and the radius
of the circle is \( 7 \mathrm{cm} \), find the value of \( (\sqrt{6} \times A B) \)


Find the maximum and minimum
values, if any, without using derivatives of the following function \( \boldsymbol{f}(\boldsymbol{x})=-|\boldsymbol{x}+1|+\boldsymbol{3} \) on \( \boldsymbol{R} \)


According to Newton's formula, the speed of sound in air at STP is:
(Take the mass of 1 mole of are is \( 29 \times \)
\( \left.10^{-3} k g\right) \)
\( \mathbf{A} \cdot 250 m s^{-1} \)
B . \( 260 \mathrm{m} \mathrm{s}^{-1} \)
c. \( 270 m s^{-1} \)
D. \( 280 \mathrm{m} \mathrm{s}^{-1} \)


Match the following:
Table - 1
(a) Minimum current will flow through
(b) Maximum current will flow through
(c) Maximum power will be generated across
(d) Minimum power will be generated across
\( \mathbf{A} \cdot a-p ; b-p ; c-q ; d-r \)
B \( . a-r ; b-r ; c-p ; d-s \)
\( \mathbf{c} \cdot a-q ; b-p ; c-r ; d-q \)
D. \( a-s ; b-s ; c-r ; d-q \)


All the following IUPAC names are correct except :
A. 1-chloro-1-ethoxypropane
B. 1-amino-1-ethoxypropane
c. 1-ethoxypropan-2-01
D. 1-ethoxypropan-1-amine


For undergoing glycolysis, glucose requires priming with the help of how
many ATP?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Dry \( S O_{2} \) does not bleach dry flowers
because:
A. nascent hydrogen responsible for bleaching is produced only in presence of moisture
B. water is the actual reducing agent responsible for bleaching
C. water is_stronger acid than \( S O_{2} \)
D. the \( O H^{-} \) ions produced by water cause bleaching


In silicosis the silica particles can be
seen
A. As needle shaped crystal by light microscopy
B. As needle shaped crystals under polarized light
C. As maltese cross shaped crystal by light microscopy
D. As maltese cross shaped crystals under polarized light


The lanthanide contraction is
responsible for the fact that
A. zrand Y have about the same radius
B. Zrand Nb have similar oxidation state
c. zrand Hf have about the same radius
D. zrand zn have similar oxidation state


Type your question
\( \mathbf{H} \)
4
3
\( c \)
\( D \)


Spot the odd one out from the following structures with reference to the male reproductive system.
A. Rete testis
B. Epididymis
c. vasa efferentia
D. Isthmus


Find the bar graph and state why?


The lymph differs from the blood in having
A. More RBC less WBC
B. Less RBC more WBC
c. No RBC less WBC
D. No RBC more WBC


Two fixed charges \( A \) and \( B \) of \( 5 \mu C \) each
are separated by a distance of \( 6 \mathrm{m} . \mathrm{C} \) is the mid point of the line joining A and B. A charge 'Q' of \( -5 \mu C \) is shot perpendicular to the line joining A and B
through \( C \) with a kinetic energy of 0.06
J. The charge 'Q' comes to rest at a point
D. The distance CD is?


\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}+\boldsymbol{C} \)
Time \( t \)
Total pressure of \( (\boldsymbol{B}+\boldsymbol{C}) \quad \boldsymbol{P}_{2} \)
Find equilibrium constant \( k \)
A \( \cdot k=\frac{1}{t} \ln \frac{P_{3}}{2\left(P_{3}-P_{2}\right)} \)
в. \( _{k=\frac{1}{t} l n \frac{P_{2}}{2\left(P_{3}-P_{2}\right)}} \)
c. \( k=\frac{1}{t} \ln \frac{P_{3}}{2\left(P_{3}+P_{2}\right)} \)
D. None of these


How many primary amines are possible
with the formula \( C_{4} H_{11} N ? \)
A.
B. 2
\( c \cdot 3 \)
D. 4


At which height above earth's surface
value of \( ^{\prime} g^{\prime} \) is same as in a mine \( 100 k m \)
deep.


\( 200 g \) of a certain metal at \( 83^{\circ} \mathrm{C} \) is
immersed in \( 300 g \) of water at \( 30^{\circ} \mathrm{C} \). The
final temperature is \( 33^{\circ} \mathrm{C} \). Calculate the specific heat capacity of the metal. Assume that the specific heat capacity of water is \( 4.2 J g^{-1} K^{-1} \)
A \( \cdot 0.378 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
B. \( 0.578 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
C. \( 0.778 \mathrm{Jg}^{-1} \mathrm{K}^{-1} \)
D. None of the above


Two north poles of pole strengths \( 4 A- \)
\( m \) and \( 16 A-m \) are separated by a
distance of \( 20 \mathrm{cm} . \) The position of the neutral point from \( 4 A-m \) pole is :
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 6.67 \mathrm{cm} \)


A \( 68 n m \) length double stranded DNA
has 24 adenine nucleotices. What must
be the number of guanine nucleotides?
\( \mathbf{A} \cdot 48 \)
B. 72
c. 76
D. 176


A sample of water from a large swimming pool has a resistance of \( 9200 \Omega \) at 25 of NaCl wear dissolved in
the pool, which was throughly stirred. A sample of this solution gave a resistance at \( 7600 \Omega \). calculate the
volume of water in the pool
Given: Molar conductor of NaCl at that
concentration is \( 126.5 \Omega^{-1} c m^{2} m o l^{-1} \)
and molar conductivity of KCl at \( 0.02 \mathrm{M} \) is \( 138 \Omega^{-1} c m^{2} \) mol \( ^{-1} \) and resist is 85
\( \Omega^{-1} \)


A cell supplies a current of \( 0.9 A \)
through a \( 2 \Omega \) resistor and a current of \( 0.3 A \) through a \( 7 \Omega \) resistor. The
internal resistance of the cell is :-
\( \mathbf{A} \cdot 1.0 \Omega \)
B. \( 0.5 \Omega \)
c. \( 2.0 \Omega \)
D. \( 1.2 \Omega \)


Construct the circuit symbol of Zener
diode


A mixture of all isomers of pentane is allowed to react with chlorine
radicals(produced by photochemical
cleavage of \( C l_{2} \) ). How many different isomeric alkyl radicals can form by hydrogen abstraction in the following? Pentane\( (\text {all isomers})+\boldsymbol{C l}^{\bullet} \longrightarrow \)
Pentyl radicals (all isomers) \( + \) HCl
A. 5
B. 6
\( c \cdot 7 \)
D. 8


Who contributed to the research
process on fermentation?
A. Johannes Miller
B. Matthias Jakob
c. Robert Brown
D. Schwann Theodor


A sound wave is travelling in a medium
in which the velocity is \( v \). It is incident in the second medium in which the velocity of the wave is \( 2 v \). What should
be the minimum angle of incidence in the first medium, so that the wave fails to cross the surface of separation of the two media?
A \( \cdot 60^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 15^{\circ} \)


Solve the following equations. \( 7^{x+2}-\frac{1}{7} \cdot 7^{x+1}-14 \cdot 7^{x-1}+2 \cdot 7^{x}=49 \)


Which of the following statements is
correct regarding the universal
gravitational constant G?
A. G has same value in all systems of units.
B. The value of G is same everywhere in the universe
c. The value of G was first experimentally determined by Johannes Kepler.
D. G is a vector quantity


Energy required to develop proton
gradient during respiration comes from
A. Oxidation process of \( N A D H \)
B. Oxidation-reduction process of \( C O_{2} \) and \( N A D H \) respectively
C. From heat energy developed during respiration
D. Oxidation-reduction process of \( N A D P H \) and \( O_{2} \) respectively


Specific heat capacity of substance \( \boldsymbol{A} \)
is \( 3.8 J g^{-1} K^{-1} \) whereas the Specific
heat capacity of substance \( B \) is
\( \mathbf{0 . 4} \boldsymbol{J} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
(i) Which of the two is a good conductor of heat?
(ii) How is one led to the above
conclusion?
(iii) If substances \( A \) and \( B \) are liquids then which one would be more useful in
car radiators?


What quantities are conserved in this
collision?
A. Linear and angular momentum, but not kinetic energy
B. Linear momentum only
C. Angular momentum only
D. Linear momentum, angular momentum and kinetic energy


Calculate the current (in mA) required to deposit \( 0.195 g \) of platinum metal in
5.0 hours from a solution of \( \left[\boldsymbol{P t} C l_{6}\right]^{2-} \) (Atomic weight: \( \boldsymbol{C r}=\mathbf{5 2 . 0} \) )
A . 310
B. 31
c. 21.44
D. 5.36


When bromate salt are reacted with
fluorine in alkaline solution,which salt
is formed?
A. Bromide
B. Bromous
c. Hypobromous
D. Perbromate


Transistors used for making NOT
gate.why?


An ideal thermometer should have
A. Small heat capacity
B. Large heat capacity
c. Medium heat capacity
D. Variable heat capacity


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}- \)
2 then \( (f o f)(x)+2= \)
A \( . f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( -f(x) \)


If the function \( f(x)=x^{4}-62 x^{2}+a x+ \)
9 is maximum at \( x=1 \), then the value
of a is


If the product of the first four consecutive terms of a G.P is 256 and if
the common ratio is 4 and the first term
is positive, then its \( 3^{r d} \) term is
\( A \cdot 8 \)
B. \( \frac{1}{16} \)
c. \( \frac{1}{32} \)
D. 16


A person is suffering from myopia. Then
A. he can not see anything.
B. he cannot see distant objects clearly.
c. he can see only distant objects
D. he can not see nearly objects.


If the system is in equilibrium \( \left(\cos 53^{0}=\right. \)
\( \mathbf{3} / \mathbf{5}), \) then the value of \( ^{\prime} \boldsymbol{P}^{\prime} \) is
\( \mathbf{A} \cdot 16 N \)
B. \( 4 N \)
\( \mathbf{c} \cdot \sqrt{208} N \)
D. \( \sqrt{232} N \)


If \( \sin ^{-1} a+\sin ^{-1} b+\sin ^{-1} c=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{2})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \operatorname{then} \boldsymbol{a}^{f(\boldsymbol{2})}+ \)
\( \boldsymbol{b}^{f(4)}+\boldsymbol{c}^{f(\boldsymbol{6})}-\frac{\boldsymbol{3}\left(\boldsymbol{a}^{f(\boldsymbol{2})} \cdot \boldsymbol{b}^{\boldsymbol{f}(4)} \cdot \boldsymbol{c}^{\boldsymbol{f}(\boldsymbol{6})}\right)}{\boldsymbol{a}^{\boldsymbol{f}(\boldsymbol{2})}+\boldsymbol{b}^{\boldsymbol{f}(4)}+\boldsymbol{c}^{\boldsymbol{f}(\boldsymbol{6})}} \)
equals
\( A \cdot 2 \)
в.
\( c \cdot 6 \)
D.


A square plate of edge d and a circular disc of diameter dare placed touching
each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination,
assuming same mass per unit area for
the two plates.


For given A.P. \( -\frac{1}{2},-\frac{3}{2}, \frac{1}{2},-\frac{3}{2}, . . \) find the
common difference.
A . -1
B. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
\( D \)


Anabolism is
A. Endergonic process
B. Exergonic process
C. Bidirectional process
D. Destructive process


Sl unit of \( g \) i.e. the acceleration due to
gravity is
A \( \cdot m^{2} / s \)
B. \( m / s^{2} \)
\( \mathrm{c} \cdot s / m^{2} \)
D. \( m / s \)


Two identical flutes produce
fundamental notes of frequency \( 300 \mathrm{Hz} \)
at \( 27^{\circ} \mathrm{C} . \) If the temperature of the air in
one flute is increased to \( 31^{\circ} \mathrm{C} \)
the number of beats heard per second will be :
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Obtain the condition for bridge balance in Wheatstone's bridge.


The degree of the differential equation
\( \boldsymbol{x}=\mathbf{1}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\mathbf{1}}{\mathbf{2 !}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+ \)
\( \frac{1}{3 !}\left(\frac{d y}{d x}\right)^{3}+\dots \dots \) is?
\( A \cdot 3 \)
B.
c. Not defined
D. None of these


Prove that \( n^{3}+3 n^{2}+5 n+3 \) is
divisible by 3 for any natural \( n \)


The height (in \( \mathrm{cm} \) ) of 50 students in a particular class are given. Find the median.
\( \begin{array}{lll}\mathbf{1 5 6} & \mathbf{1 5 5} & \mathbf{1 5 4}\end{array} \) Height
(in \( \mathrm{cm} \) )
Numbe of studen


If \( \boldsymbol{A} \) is a skew symmetric matrix of even order then \( \operatorname{det}(A) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B \( . \neq 0 \)
c. non zero perfect square
D. None of these


\( \mathbf{2} S \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these


The set of all points of continuity of \( f o \) fo\( f, \) where \( f(x)=\operatorname{sgn} x \) is
A \( . R \sim\{0\} \)
в. \( R \sim\{1,0,1\} \)
c. \( R \sim\{-1,1\} \)
D. none of these


Head-to-tail addition is not preferred in?
A \( \cdot C H_{2}=C H C l \)
в. \( C H_{2}=C H C N \)
\( c \)
\( D \)


\( A B C D \) is a trapezium in which
\( A B|| C D \) and \( A D=B C, \) then show
that \( \angle C=\angle D \)


The enzyme of yeast which converts glucose into ethyl alcohol is called as
A. Diastase
B. Invertase
c. zymase
D. Maltase


Assertion
The variance of first \( n \) even natural
numbers is \( \frac{n^{2}-1}{4} \)
Reason
The sum of first \( n \) natural even
numbers is \( n(n+1) \) and the sum of
squares of first \( n \) natural numbers is \( \frac{n(n+1)(2 n+1)}{6} \)
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


\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{5} & \mathbf{2} \\ \mathbf{7} & \mathbf{3}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{- 1} & \mathbf{1}\end{array}\right) \)
verify that \( (\boldsymbol{A B})^{\boldsymbol{T}}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)


A monochromatic light of wavelength \( 589 \mathrm{nm} \) is incident from air on a water
surface, what are the wavelength, frequency and speed is of refracted light? the refractive index of water is
1.33.


in plant cell and in
mannalian cells are non-nucleated in
mature stages.
A. Tracheids, osteocytes
B. Sieve tubes, RBC
c. Companion cells, RBC
D. Parenchyma, bone marrow


The divers have to wear specially designed air filled suits for their
protection while diving deep under the
sea.


The area of the parallelogram constructed on the vectors \( \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{p}}+ \) \( \mathbf{3} \overrightarrow{\boldsymbol{q}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{3} \overrightarrow{\boldsymbol{p}}+\overrightarrow{\boldsymbol{q}} \) where \( \overrightarrow{\boldsymbol{p}}, \overrightarrow{\boldsymbol{q}} \) are
unit vectors enclosing an angle of \( 30^{\circ} \) is
A . 4
B. \( \frac{7}{2} \)
\( c \cdot \frac{3}{2} \)
D. None of these


Read the following bar graph and answer the following question:
Which state is the largest producer of
rice?


Breaking stress of a material is \( 2 \times \) \( 10^{8} N / m^{2} . \) What maximum length of
the wire of this material can be so that the wire does not break my own weight? [Density of material \( =\mathbf{5} \times \mathbf{1 0}^{\mathbf{3}} \mathbf{k g} / \mathbf{m}^{\mathbf{3}} \mathbf{]} \)
A. \( 1 k m \)
B. \( 2 \mathrm{km} \)
\( c .3 k m \)
D. \( 4 k m \)


The length I, breadth b, and thickness t of a block of wood were measured with
the help of a measuring scale. The results with permissible errors (in cm )
are
\( l=15.12+_{0} .01, b=10.15+0 \)
\( .01, \) andt \( =5.28+0.01 \)
The percentage error in volume up to proper significant figures is
A. \( 0.28 \% \)
B. \( 0.35 \% \)
c. \( 0.48 \% \)
D. \( 0.64 \% \)


Aldehydes other than formaldehyde react with Grignard's reagent to give addition products which on hydrolysis give:
A. tertiary alcohols
B. secondary alcohols
c. primary alcohols
D. carboxylic acids


Benzene and naphthalene form an ideal
solution at room temperature. For this process, the true statement(s) is(are):
This question has multiple correct options
A. \( \Delta G \) is positive
B . \( \Delta S_{\text {system}} \) is positive
C. \( \Delta S_{\text {surroundings}}=0 \)
D. \( \Delta H=0 \)


Construct a scalene triangle \( \boldsymbol{A B C} \)
given base \( A B=3 c m, \) base angle \( = \)
\( 90^{\circ} \) and sum of the lengths \( B C+ \)
\( \boldsymbol{A C}=\mathbf{9} \boldsymbol{c m} \)


Which of the following metals cannot give flame tests?
\( A \cdot B e \)
B. Na a
\( c \cdot k \)
D. ca


Short / Long answer type questions. How does the absorption of nutrients take place? Discuss the role of blood and lymph vessels


Nitrogen dioxide is released by
heating-
\( \mathbf{A} \cdot P b\left(N O_{3}\right)_{2} \)
в. \( K N O_{3} \)
c. \( N a N O_{2} \)
D. \( N H_{4} N O_{3} \)


A conducting rod \( P Q \) of length \( l=2 m \)
is moving at a speed of \( 2 m s^{-1} \) making
an angle of \( 30^{\circ} \) with its length.
uniform magnetic field \( B=2 T \) exists
in a direction perpendicular to the plane of motion. Then
\( \mathbf{A} \cdot V_{P}-V_{Q}=8 V \)
B. \( V_{P}-V_{Q}=4 V \)
C \( . V_{Q}-V_{P}=8 V \)
\( \mathbf{D} \cdot V_{Q}-V_{P}=4 V \)


A person in lift which ascends up with
acceleration \( 10 \mathrm{m} / \mathrm{s}^{2} \) drops a stone
from a height 10 m. The time of descent
is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . \( 1 s \)
B . \( 2 s \)
c. \( 1.5 s \)
D. \( 0.5 s \)


Amount of \( C u \) deposited from
\( \boldsymbol{C u} \boldsymbol{S O}_{4}(\boldsymbol{a q}) \) when 5 amp current is
passed for 965 seconds through it, is \( \boldsymbol{C u}=\mathbf{6 3 . 5 g m o l}^{-1} \mathbf{)} \)
A . \( 1.6 g \)
B. \( 3.2 g \)
c. \( 1.45 g \)
D. \( 2.9 g \)


The energy levels of an atom of a certain
element are shown in the given figure 5
Which one of the transitions \( A, B, C, D \) or
E will result in the emission of photons
of electromagnetic radiation of wavelength 618.75 nm?
Support your answer with mathematical calculations.


If the plane \( 7 x+11 y+13 z=3003 \)
meets the axes in \( A, B, C, \) then the
centroid of \( \Delta A B C \) is
A. (143,91,77)
В. (143,77,91)
c. (91,143,77)
D. (143,66,91)


A buys an old bicycle for Rs. 162 and
spends Rs. 18 on its repairs. He then
sells the bicycle for Rs. 207 ; find his gain or loss as percent.
A. Gain = 15\%
B. Gain = 20\%
\( c \cdot \cos s=12 \% \)
D. \( \operatorname{Loss}=19 \% \)


A weightless rod is acted on by upward parallel forces of \( 2 N \) and \( 4 N \) on ends \( A \)
and \( B \) respectively. The total length of
the rod \( A B=3 m . \) To keep the rod in
equilibrium a force of \( 6 N \) should act in
the following manner:
A. Downwards at any point between \( A \) and \( B \).
B. Downwards at mid point of \( A B \).
c. Downwards at a point \( C \) such that \( A C=1 m \).
D. Downwards at a point \( C \) such that \( B C=1 m \).


Rutherford's atomic model could not
explain the stability of atom. How do you account for this?


The radius of two metallic sphere \( A \) and
\( B \) are \( r_{1} \) and \( r_{2} \) respectively \( \left(r_{1}>r_{2}\right) \)
They are connected by a thin wire and the system is given a certain charge. The charge will be greater
A. Equal to both
B. Zero on both
c. on the surface of sphere \( A \)
D. On the surface of sphere \( B \)


Why do people prefer to use copper bottom vessels for cooking?


Find the electric field inside the shell at
a distance \( r \) from the centre.
\( \mathbf{A} \cdot E=0 \)
в. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
c. \( _{E}=\frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
D. \( \quad E=\frac{Q}{4 \pi \epsilon_{6}(a-r)^{2}} \)


Density is:
A. mass per time
B. mass per weight
C. mass per volume
D. mass per atomic weight


Find the wavelength of the most energetic photons in this series.
A . \( 1800 \AA \)
в. 1500 А
c. \( 1300 \AA \)
D. 1650 A


Find the value of \( \cos \left(\sec ^{-1} x+\right. \)
\( \left.\csc ^{-1} x\right),|x| \geq 1 \)


A potential difference of \( 20 \mathrm{KV} \) is applied across an X-ray tube. Find the minimum wavelength of X-ray generated.


A thin film with index of refraction 1.50
coats a glass lens with index of
refraction \( 1.80 . \) What is the minimum
thickness of the film that will strongly
reflect light with wavelength 600 nm?
A . \( 150 \mathrm{nm} \)
B. \( 200 n m \)
c. 300 nm
D. \( 450 n m \)


Very short answer type. Name a symbiotic bacterium.


How many rational numbers are there
between \( -\frac{3}{2} \) and 0 with denominator as
1?


Which of the following represents
correct statement(s)?
A. Salt can be obtained by the evaporation of sea water.
B. The salt obtained during crystallisation is pure and its crystals are large.
C. After crystallisation, the shape of the crystals can be seen clearly.
D. Large crystals of pure substances cannot be formed from their solutions.


Ventricles of brain are lined by the cells known as
A. Ependymal cells
B. Nerve cells
c. Neuroglia
D. Schwann's cells


In the following strong acid and strong alkaine base is-
(a) Acetic Acid or Hydrochloric Acid
(b) Sodium hydroxide or calcium hydroxide


Figs belong to
A. Keystone species as they show animal dependent pollination.
B. Keystone species as they produce food and provide protection to animals during the lean period.
C . Critical link species as they form connecting link between trees and herbs.
D. Critical link species as they establish essential links for absorbing nutrients from the soil and organic residues.


Which of the following is phenol?
A. Cresol
B. Catechol
c. Resorcinol
D. All of these


Find the principal value of:
\( \tan ^{-1} \sqrt{3}-\sec ^{-1}(-2) \)


How much energy has been lost during these four oscillations?
A . 0.31
B. 0.41
c. 0.51
D. 0.39


Find the area of both the segments of a
Circle of radius \( 43 \mathrm{cm} \) with central angle \( 120^{\circ} .\left[\text { Given, } \sin 120^{\circ}=\frac{\sqrt{3}}{2} a n d \sqrt{3}=\right. \)
1.73]


Apply the Imitsto given expression
\( \lim _{x \rightarrow 0}(((x+1)(x+2)(x+3)(x+4)) \)


Find the arithmetic mean of the sales
per day in a fair price shop in a week rs10000, rs10250, rs10790, rs9865.
rs15350, rs10110


State the working principle of potentiometer. Explain with the help of circuit diagram how the emf of two primary cells are compared by using the potentiometer


Two magnetic poles each of magnetic pole strength \( 16 \mathrm{A} \mathrm{m} \) are placed at a distance of \( 2 \mathrm{m} \) apart. Find magnetic force acting on each pole.
A \( \cdot 4 \times 10^{-7} N \)
B . \( 16 \times 10^{-7} N \)
c. \( 32 \times 10^{-7} N \)
D. \( 64 \times 10^{-7} N \)


\( H_{2} O_{2} \) has greater reactivity in basic medium. It is because bases catalyze
the decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
A. True
B. False


A covalent bond is formed by:
A. transfer of electrons
B. sharing of electrons by only a single atom
C. sharing of electrons
D. repulsions of atoms between two atoms


Assertion
Ethane is a gas while ethyl alcohol is a liquid.
Reason
Ethyl alcohol has greater molecular
mass than ethane.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which series have highest energy in hydrogen spectrum?
A. Balmer
c. Pfund
D. Lyman


How are the macroscopic properties
classified ?


Assertion
Statement \( 1: \cos 1<\sin 1(\text { in } \text {radians}) \)
Reason
Statement 2: cosine x decreases but
sine \( x \) increases for \( x \in\left(0, \frac{\pi}{2}\right) \)
A. Both the statements are TRUE and STATEMENT 2 is the
correct explanation of STATEMENT 1
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.


The physical state of water is liquid at which of the following temperatures?
\( A \cdot 25^{\circ} C \)
B. \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 100^{\circ} c \)
D. none of these


Which term describes the mass of
\( 6.022 \times 10^{23} \) representative particles?
A. Molar mass
B. Avogadro's number
c. Empirical formula
D. Molecular formula


In case of sodium chloride, the
chemical bond is formed by:
A. the transfer of valence electrons
B. the sharing of electrons
c. donation of electrons
D. both \( A \) and \( B \)


Write the logic symbol and truth table of NAND gate.


The escape velocity from the earth is 11
\( \mathrm{km} s^{-1} . \) The escape velocity from a planet having twice the mass and twice
the radius will be :
A . \( (11 \times \sqrt{12}) k m s^{-1} \)
B. \( 11 k m s^{-1} \)
c. \( \frac{11}{2} k m s^{-1} \)
D. \( (11 \times \sqrt{2}) k m s^{-1} \)


What is the specific latent heat of the
metal?
A \( \cdot 1000 \) J \( g^{-1} \)
B. \( 500 \mathrm{Jg}^{-1} \)
c. 1500 J \( g^{-1} \)
D. None of the above


The addition of which metal into liquid
\( N H_{3} \) leads to the formation of a blue
solution:
This question has multiple correct options
A \( . L i \)
в. \( S r \)
c. \( C s \)
D. \( B a \)


Which of the following statement(s) is
(are) true about heart?
A. The left atrium receives oxygenated blood from different parts of the body, while right atrium receives deoxygenated blood from lungs.
B. The left ventricle pumps oxygenated blood to different body parts, while right ventricle pumps deoxygenated blood to lungs.
C. The left atrium transfers oxygenated blood to the right ventricle, which sends it to different body parts.
D. The right atrium receives oxygenated blood from different parts of the body, while left ventricle pumps oxygenated blood to different parts of the body.


Which of the following statements are
incorrect?
This question has multiple correct options
A. For coagulation of \( A s_{2} S_{3} \) sol, tve ions are effective
B. For coagulation of aluminium hydroxide sol, \( B a^{2+} \)
ions are more effective than \( N a^{+} \)
C. Cellulose solution is an example of multimolecular colloid system
D. Colloidal sol of metals such as gold, silver etc. are prepared by Bredig's arc method


Select the incorrect statement
regarding the given reaction.
\( \boldsymbol{R} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \frac{\boldsymbol{P d}-\boldsymbol{B a S O}_{4}}{\boldsymbol{\lambda}} \boldsymbol{R C H O}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
A. \( P d \) acts as a positive catalyst.
B. It is Rosenmund reaction
c. \( B a S O_{4} \) acts as poison for \( P d \)
D. \( B a S O_{4} \) acts as promoter for \( P d \).


\( 500 m L \) of a sample of water required
19.6 mg of \( K_{2} C r_{2} O_{7} \) for the oxidation
of dissolved organic matter in it in the
presence of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) The \( \boldsymbol{C O D} \) of water
sample is:
A. 3.2 ppm
в. 7.2 ррт
\( \mathrm{c} .6 .4 \mathrm{ppm} \)
D. \( 4.6 \mathrm{ppm} \)


The component of vector \( 3 \hat{i}+4 \hat{j} \) along vector \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \) is
A \( \cdot \frac{1}{2}(\hat{j}+\hat{i}) \)
B \( \cdot \frac{3}{2}(\hat{j}+\hat{i}) \)
c. \( \frac{5}{2}(\hat{j}+\hat{i}) \)
D. \( \frac{7}{2}(\hat{j}+\hat{i}) \)


An animal which has notochord
throughout its life is
A. Fish
B. Birdd
c. snake
D. Amphioxus


Fill up the following with suitable terms.
(i) Activation energy \( = \) Threshold
energy -
(ii) Half-life period of zero order reaction
\( = \)
(iii) Average rate of reaction \( = \)
(iv) Instantaneous rate of reaction \( = \)
A \( \cdot \) potential energy, \( \frac{0.693}{k}, \frac{d x}{d t}, \frac{\Delta[A]}{\Delta t} \)
B. Energy of reactants, \( \frac{1}{k}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)
C. Energy of reaction, \( \frac{\log k}{t}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)
Derage kinetic energy of reactants, \( \frac{a}{2 k}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)


Two bodies of equal weights are kept at
heights \( h \) and 1.5 respectively. The ratio of their potential energy is
A .3: 2
B. 1: 1
\( c \cdot 2: 3 \)
D. 3: 4


Mixture of chloroxylenol and terpineol
acts as:
A. antiseptic
B. antipyretic
c. antibiotic
D. analgesic


The correct statement for the following
reaction is:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{N} \boldsymbol{H}_{4}^{+} \)
A. the state of hybridisation changes
B. bond angle increases
C. \( N H_{3} \) act as a Lewis acid
D. regular geometry changes


For the Daniel cell involving the cell reaction \( Z n_{(s)}+C u_{(a q)}^{+2} \rightleftharpoons \)
\( Z n^{+2}_{(a q)}+C u_{(s)} \) the standard free
energies of formation of \( Z n_{(s)}, C u_{(s)} \) \( C u_{(a q)}^{+2} \) and \( Z n_{(a q)}^{+2} \) are 0,0,64.4
KJ/Mole and -154.0 KJ/Mole,
respectively. Calculate the standard
EMF of the cell?
A. 2.13 Volts
B. 1.13 Volts
c. \( 2.26 \mathrm{Volts} \)
D. 3.42Volts


Pressure at a point in a fluid is directly proportional to This question has multiple correct options
A. depth of the point from the surface
B. density of the fluid
c. acceleration due to gravity
D. the area of cross section


In how many ways can four people, each
throwing a dice once, make a sum of \( 6 ? \)
\( \mathbf{A} \cdot^{9} C_{2} \)
в. \( ^{10} C_{3} \)
\( \mathbf{c} \cdot^{8} C_{3} \)
D. \( ^{9} C_{3} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H} \boldsymbol{C H O} \frac{O \boldsymbol{H}^{-}}{A l d o l} \boldsymbol{A}, \boldsymbol{A} \) is?
A \( \cdot C H_{3}(C H=C H)_{3} C H O \)
B . \( C H_{3} C H_{2} C H_{2}(C H=C H)_{2} C H O \)
c. \( C H_{3}\left(C H_{2} C H_{2}\right) C H=C H-C H O \)
D. None of the above is correct


Mechanical waves are generated, when
the disturbance is
A. generated in vacuum and propagates in the space.
B. generated in elastic mediums and propagates in the space
C. generated by photons and propagates in space.
D. generated by electrons and propagates in the space.


The given figure shows a solid formed of
a solid cube of side \( 40 \mathrm{cm} \) and a solid
cylinder of radius \( 20 \mathrm{cm} \) and height 50 \( \mathrm{cm} \) attached to the cubes as shown.
Find the volume and the total surface
area of the whole solid [Take \( \boldsymbol{\pi}=\mathbf{3 . 1 4}] \)
A \( \cdot 122700 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
B. \( 126800 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
c. \( 148900 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
D. \( 148800 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)


Which of the following is the correct
order of decreasing \( S_{N} 2 \) reactivity?
A \( . R C H_{2} X>R_{3} C X>R_{2} C H X \)
в. \( R C H_{2} X>R_{2} C H X>R_{3} C X \)
c. \( R_{3} C X>R_{2} C H X>R C H_{2} X \)
D. \( R_{2} C H X>R_{3} C X>R C H_{2} X \)


The process of obtaining wool is:
A. shearing, sorting, scouring and dyeing
B. shearing, scouring, sorting and dyeing
C . scouring, sorting, shearing and dyeing
D. sorting, scouring, shearing and dyeing


A long straight conductor carrying a
current lies along the axis of a ring. The
conductor will exert a force on the ring if
the ring
A. carries a current
B. has uniformly distributed charge
C. has nonumiformly distributed charge
D. none of these


The approximate value of \( f(x)=x^{3}+ \)
\( 5 x^{2}-7 x+9=0 \) at \( x=1.1 \) is
A . 8.6
B. 8.5
\( c .8 .4 \)
D. 8.3


No reaction occurs in which of the
following equations?
This question has multiple correct options
\( \mathbf{A} \cdot I^{\ominus}+F e^{2+} \longrightarrow \)
B . \( F_{2}+2 N a C l \longrightarrow \)
\( \mathbf{c} \cdot C l_{2}+2 N a F \longrightarrow \)
D \( \cdot I_{2}+2 N a B r \longrightarrow \)


Multicostate divergent reticulate venation is seen in \( \ldots \). Ieaf.
A. Zizyphus
B. Bamboo
c. castor
D. Mango


A quantity of \( 1.4 g \) of a hydrocarbon gives \( 1.8 g \) water on complete combustion. The empirical formula of hydrocarbon is :
A \( . C H \)
в. \( C H_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \)
D. \( C H_{4} \)


Ligulate/strap-shaped corolla occurs in sunflower in
A. Disc florets
B. Immature florets
c. Ray florets
D. Both ray and disc florets


For the following compounds, the correct statement(s) with respect to
nucleophilic substitution reactions is
\( (\operatorname{are}) \)
This question has multiple correct options
\( \mathbf{A} \cdot \) I and III follow \( S_{N} 1 \) mechanism
B. Compound IV undergoes inversion of configuration
C. I and II follow \( S_{N} 2 \) mechanism
D. The order of reactivity for I, III and IV is: \( I V>I>I I I \)


Gita arranges some mirrors in group- 1
and group- 2 according to the magnification, type of image and size of image from the following data.
Sr. Group-1 \( \quad \) Group- 2
No.
\( <1 \) and \( \quad \) Real, inverted and
(1) \( \quad \) nocative \( \quad \) small negative
\( >1 \) and \( \quad \) Real, inverted and
(2) \( \quad \) positive \( \quad \) enlarged
\( >1 \) and \( \quad \) Virtual, erect and
(3)\( \quad \) negative \( \quad \) enlarged
\( <1 \) and Virtual, erect and
positive \( \quad \) small
For which of the pairs from the group 1
and 2 you disagree.
A. 1 and 3
B. 2 and 3
c. 3 and 4
D. 1 and 2


Assertion: In O/W emulsion, soap is
mixed
Reason: Soap reduces surface tension
A. If both assertion and reason are true and reason is the
correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.


Value of Current i in the following
circuit is :-
A . 13 A
B. 12 A
\( c \cdot 9 A \)
D. None of these


Which of the following expression
of concentration of a solution
is independent of temperature?
A. Molarity
B. Normality
c. Formality
D. Molality


The electric field for \( r>R_{2} \) is given by
\( \boldsymbol{E}=\frac{1}{\boldsymbol{X} \boldsymbol{\pi} \varepsilon_{0}} \frac{Q}{r^{2}} . \) Find \( \mathbf{X} ? \)


The rate of a reaction doubles when its
temperature changes from \( 300 K \) to
\( 310 K . \) Activation energy of such a
reaction will be : \( (\boldsymbol{R}= \)
\( \left.8.314 J K^{-1} m o 1^{-1} \text {and } \log 2=0.301\right) \)
A \( .48 .6 \mathrm{kJmol}^{-1} \)
B. 58.5 kJmol\( ^{-1} \)
\( \mathbf{c} \cdot 60.5 k J m o l^{-1} \)
D. \( 53.6 \mathrm{kJmol}^{-1} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{1} \\ \mathbf{0} & \mathbf{2} & -\mathbf{3} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left(\boldsymbol{a d} \boldsymbol{j}_{\boldsymbol{j}}\right. \)
and \( C=5 A, \) then \( \frac{|a d j \quad B|}{|C|} \) is equal to
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
\( c \)
\( D \)


\( \lim _{n \rightarrow \infty} \sum_{n=1}^{20} \cos ^{2 n}(x-10) \) is equal to
\( A \)
B.
\( c \cdot 19 \)
D. 20


if the coefficient of the middle term in
the expansion of \( (1+x)^{2 n+2} \) and \( p \) and
the coefficients of middle terms in the
expansion of \( (1+x)^{2 n+1} \) are \( q \) and \( r \)
then
A \( . p+q=r \)
в. \( p+r=q \)
c. \( p=q+r \)
D. \( p+q+r=0 \)


Mark the correct option
A. When a force is applied on a soft object,it changes the size and shape of the object.
B. A force can increase the speed of a moving object
C. If applied force acts on a body in the direction of motion,the speed of the body will increase
D. All


A current \( l \) is flowing in a straight
conductor of length \( L \). The magnetic
induction at a point on its axis at a
distance \( \frac{L}{4} \) from its centre will be
A . zero
в. \( \frac{\mu_{0} l}{2 \pi L} \)
c. \( \frac{\mu_{0} l}{\sqrt{2} L} \)
D. \( \frac{4 \mu_{0} l}{\sqrt{5} \pi L} \)


A bomb blasts on the Moon. Its sound
reaches the Earth
A. after 10 minutes
B. after 24 hours and 10 minutes
c. after 3.7 minutes.
D. cannot reach.


The alkyne which will react with
\( K M n O_{4} \) to give pyruvic acid is:
A. ethyne
B. propyne
c. butyne
D. 2-pentyne


Assertion
\( H C l \rightarrow H^{+}+C l^{-} \) is an ionization
Reason
The electron is initially shared between both atoms, thus the dissociation event
into ions involves the transfer of an
electron from one atom to the other.
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


Give an example of a relation. which is
reflexive and symmetric and Transitive


The number of resonating structures of allyl radical is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Which was the first metal used?
A. Iron
B. copper
c. zinc
D. Gold


Heat energy for its propagation essentially requires:
A. no medium
B. gaseous medium
c. solid medium
D. liquid medium


Temperature coefficient of resistance ' \( \alpha \)
and resistivity \( \rho \) of a potentiometer
wire must be:
A. high and low
B. low and highh
c. low and low
D. high and high


On a friction less surface, a ball of mass
\( m \) moving at a speed \( v \) makes a headon collision with an identical ball at
rest. The kinetic energy of the balls after the collision is \( \frac{3}{4} t h \) of the original. Find the coefficient of restitution?
A \( \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{5}} \)


The nearest point on the line \( 3 x-4 y= \)
25 from the origin is :
A \( \cdot(-4,5) \)
В \( \cdot(3,-4) \)
\( \mathbf{c} \cdot(3,4) \)
D \( \cdot(3,5) \)


A sample of 0.50 g of an organic compound was treated according to Kjeldahls method. The ammonia evolved was absorbed in \( 50 \mathrm{ml} \) of \( 0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \)
The residual acid required \( 60 \mathrm{mL} \) of 0.5 M solution of NaOH for neutralisation.
Find the percentage composition of nitrogen in the compound.


Hasan buys two kinds of cloth material for school uniforms, shirt material that
\( \operatorname{costs} \) hom Rs 50 per metre and trouser
material that costs him Rs 90 per
metre.for every 3 meters of shirt
material he buys 2 meters of the trouser
material. he sells the material at \( 12 \% \)
and \( 10 \% \) profit respectively. his total sale is Rs 36,600 . how much trouser material did he buy?


The cambium located in between xylem
and phloem in dicot stem is
A. Interfascicular
B. Intrafascicular
c. Both A and B
D. None of the above


The commonly used safety fuse wire is
made of
A. copper
B. lead
c. nickel
D. an alloy of tin and lead


When PNjunction os forward biased the current in junction
A. increases
B. decreases
c. Remains same
D. None of these


Monochromatic light of wave length \( 667 \mathrm{nm} \) is produced by a helium neon laser. The power emitted is \( 9 \mathrm{mW} \). The
number of photons arriving per second on the average at a target irradiated by this beam is
A \( \cdot 3 \times 10^{16} \)
В . \( 3 \times 10^{19} \)
\( \mathrm{c} \cdot 9 \times 10^{15} \)
D. \( 9 \times 10^{17} \)


In case of a planet revolving around the sun, the angle between the gravitational force and the radial vector is
A. zero
B. 90
c. 180
D. 45


A radioactive isotope of radium placed in the second group in the periodic table emits one \( \alpha \) -particle and one \( \beta \)
particle. The new element formed is in the \( _{-}-\ldots_{-}-_{\text {roup. }} \)
A . first
B. second
c. third
D. fourth


The part of IUPAC name which indicates
saturation or unsaturation is:
A. root word
B. primary suffix
c. secondary suffix
D. prefix


Formalin \( 40 \% \) indicates:
A. \( 40 \% \) water, \( 6 \% \) formaldehyde
B. \( 40 \% \) water, \( 60 \% \) formaldehyde
C. \( 60 \% \) water, \( 40 \% \) formaldehyde
D. \( 4 \% \) water, \( 69 \% \) formaldehyde


A ray of light from denser medium strikes a rarer medium at an angle of
incidence i. The reflected and refracted
rays make an angle of \( 90^{\circ} \) with each other. Angle of reflection and refraction
are r \( \& r^{1} . \) The critical angle is
a) \( \sin ^{-1}(\tan r) \)
b) \( \sin ^{-1}(\cot r) \)
c) \( \sin ^{-1}\left(\tan r^{1}\right) \)
d) \( \sin ^{-1}\left(\cot r^{1}\right) \)
A. only a is correct
B. only b is correct
c. a and b are correct
D. a and d are correct


Fill in the-blanks with suitable terms
given below:
(Fast, Leaves, Stomata, Closed,
Transpiration, Humid) The leaves have more \( \ldots \). on their lower
surface.


The wavelength of first line of Balmer
spectrum of hydrogen will be:
в. \( 4101 \hat{A} \)
\( c .6569 \hat{A} \)
D. \( 4861 A \)


The relative molecular masses of
hydrogen, nitrogen, oxygen and chlorine are \( X \) times of their relative atomic
masses. Identify \( \mathbf{X} \)
A. Same
B. Double
c. Triple
D. Half


The compound \( C_{8} H_{18} \) forms single
product on monohalogenation. The
IUPAC name of \( \boldsymbol{C}_{\mathbf{8}} \boldsymbol{H}_{\mathbf{1 8}} \) is :
A. 2,2,3,3 - tetramethylbutane
B. 2,3- dimethyl hexane
c. n-octane
D. 2,3,4 - trimethyl pentane


n given figure triangle \( \mathrm{ABCCCC} \)
circumscribes the circle with center 0
and radius \( 2 \mathrm{cm} \)
Area of \( \Delta A B C \) is \( 16 \mathrm{cm}^{2} \). find \( \mathrm{AB} \)
\( 5 \mathrm{cm} \)
\( 6 c \)
\( 7 \mathrm{cm} \)


The \( x \) -component of the resultant of several vectors :-
(a) Is equal to the sum of the \( x \) components of the vectors
(b) May be smaller than the sum of the magnitudes of the vectors
(c) May be greater than the sum of the
magnitudes of the vectors
(d) May be equal to the sum of the magnitudes of the vectors
\( A \cdot a, c, d \)
B. \( a, b, c \)
\( c \cdot a, b, d \)
D. b, c, d


\( \left|\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right| \) then
\( \mathbf{A} \cdot \Delta=0 \)
B. \( \Delta \in(0, \infty) \)
c. \( \Delta \in[-1,2] \)
D. \( \Delta \in[2,4] \)


Hormone that promotes growth of lateral buds/has negative effect on apical dominance is
A. Cytokinin
B. Gibberellin
c. Auxin
D. Both B and C


In which of the following species the angle around the central atom is
exactly equal to \( 109^{\circ} 28^{\prime} ? \)

This question has multiple correct options
\( \mathbf{A} \cdot S F_{4} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot 1 \mathrm{NH}_{4}^{+} \)
D. None of the above


Virtual Image is always erect. Is
statement True or False?
A. True
B. False


Assertion
If \( \boldsymbol{r}_{\boldsymbol{x} \boldsymbol{y}} \) i.e. \( \boldsymbol{r}(\boldsymbol{x}, \boldsymbol{y})=\mathbf{0 . 2 5}, \boldsymbol{\sigma}_{\boldsymbol{x}}=\mathbf{0 . 1}, \boldsymbol{\sigma}_{\boldsymbol{y}}= \)
\( 4, \) then \( b_{y x}=10 \)
Reason
\( \boldsymbol{b}_{\boldsymbol{y} \boldsymbol{x}}=\boldsymbol{r} \frac{\boldsymbol{\sigma}_{\boldsymbol{y}}}{\boldsymbol{\sigma}_{\boldsymbol{x}}} \)
A. Both Assertion \&. Reason are individually true \& Reason is correct explanation of Assertion,
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
c. Assertion is true Reason is false.
D. Assertion is false Reason is true.


The length of a rectangle is \( \left(\frac{3}{4}\right)^{t h} \) of its breadth. If its perimeter is \( 126 \mathrm{m} \), then its area will be
A . \( 972 m^{2} \)
B. \( 640 m^{2} \)
\( c \cdot 840 m^{2} \)
D. 954 \( m^{2} \)


Match the sites in list I with the
processes in list II and choose the
correct combination from the options.
\( A \cdot A-4, B-3, C-2, D-1 \)
B. \( A-1, B-2, C-4, D-3 \)
c. \( A-2, B-3, C-4, D-1 \)
D. \( A-3, B-4, C-1, D-2 \)


If \( \boldsymbol{x}=\sqrt{\frac{1-\boldsymbol{t}^{2}}{1+\boldsymbol{t}^{2}}} \) and \( \boldsymbol{y}= \)
\( \frac{\sqrt{1+t^{2}}-\sqrt{1-t^{2}}}{\sqrt{1+t^{2}}+\sqrt{1-t^{2}}}, \) then the value of
\( \frac{d^{2} y}{d x^{2}} \) at \( t=0 \) is given by
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{-1}{4} \)
D. \( \frac{1}{4} \)


Which of the following is a representation of Gay-Lussac's law?
A \( \cdot P_{1} T_{1}=P_{2} T_{2} \)
B . \( P_{1} T_{2}=P_{2} T_{1} \)
c. \( P_{1} V_{1}=P_{2} V_{2} \)
D. \( V_{1} T_{2}=V_{2} T_{1} \)


\( (+13)-(+12) \) is equal to
\( A \cdot+1 \)
\( B \cdot+13 \)
\( c \cdot-1 \)
D. None of these


Myelin sheath is derived from
A . Neuroglial cells
B. Schwann cells
c. Nerve cells
D. All of these


Acetylene is mixed with oxygen and burned to produce:
A. a hot flame for cutting steel
B. carbon ash for fertilizers
c. acetaldehyde
D. heat for the manufacture of nuclear-grade materia


When a coordination compound
\( C O C l_{3} .6 N H_{3} \) is mixed with \( A g N O_{3}, 3 \)
moles of AgCl are prepitated per mole of the compound. write
i) structure formula of the complex.
ii) IUPAC name of the complex.


Which of the following has \( +R \) (resonance) effect?
\( \mathbf{A} \cdot-C N \)
в. \( -C H O \)
\( \mathrm{c} \cdot-N H_{2} \)
D. \( -N O_{2} \)


If \( \boldsymbol{A}=\left[\begin{array}{cr}\mathbf{2} & \mathbf{3} \\ -\mathbf{1} & \mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{1} \\ \mathbf{4} & -\mathbf{2}\end{array}\right] \)
then find \( \boldsymbol{A}-\boldsymbol{B} \)


\( \int x \cdot e^{x^{2}} d x= \)
A \( \cdot e^{x^{2}}+c \)
B. \( \frac{1}{2} e^{x^{2}}+c \)
\( \mathbf{C} \cdot-e^{x^{2}}+c \)
D. \( \frac{1}{7} e^{x^{2}}+c \)


Speed of sound wave in a given medium
is
A. Directly proportional to its frequency
B. Inversely proportional to its frequency
C. Directly proportional to the square of frequency
D. Independent of its frequency


The correct order of volalitity is:
\( \mathbf{A} \cdot N H_{3}<H_{2} O \)
B. p-nitro phenol < o-nitro phenol
\( \mathbf{c} \cdot C H_{3} O H>C H_{3}-O-C H_{3} \)
D. \( H F>H C l \)


Given that the equilibrium constant for
the reaction, \( 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons \)
\( 2 S O_{3(g)} \) has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?
\( \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{g})} \rightleftharpoons \quad \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{1} / \boldsymbol{2} \boldsymbol{O}_{2(\boldsymbol{g})} \)
A \( .3 .6 \times 10^{-3} \)
в. \( 6.0 \times 10^{-2} \)
c. \( 1.3 \times 10^{-5} \)
D. \( 2.2 \times 10^{-4} \)


Which one of the following contains copper besides iron?
A. cytochrome
B. Cytochrome oxidase
c. Plastoquinone
D. cytochrome \( c_{1} \)


The disinfecting action of \( C l_{2} \) is due to :
A. Oxidation
B. Reduction
c. Bleaching
D. Dehydrating


During the estimation of phosphorous, 10 g of an organic compound gave 6.73 g
of \( M g_{2} P_{2} O_{7} . \) What is the percentage of phosphorous in the organic compound?
A . 10
B. 20
\( c . \) 30
\( D \cdot 40 \)


Two numbers are selected at random
from integers 1 through \( 9 . \) If the sum is even, find the probability that both the
numbers are odd.


Three men have 6 different trousers, 5
different shirts and 4 different caps.
Number of different ways in which they
can wear them is


A mass \( m \) is placed at point \( P \) lies on the axis of a ring of mass \( \mathrm{M} \) and radius
\( R \) at a distance \( R \) from its centre. The
gravitational force on mass \( \mathrm{m} \) is then
\( ^{\mathbf{A}} \cdot \frac{G M m}{\sqrt{2} R^{2}} \)
в. \( \frac{G M m}{2 R^{2}} \)
c. \( \frac{G M m}{2 \sqrt{2} R^{2}} \)
D. \( \frac{G M m}{4 R^{2}} \)


What is the value of \( i^{i} \)
Where \( i=\sqrt{-1} \)


Compare the structures of oxides of
sulphur.


The largest gene in man is
A. Dystrophin
B. Insulin gene
C. Beta globin gene of haemoglobin
D. Tumor suppressor gene
E . Oncogene


The intensity of the light coming from
one of the sites in a Young's double slit
experiment in the intensity from the
other slit. Determine the ratio of the
maximum intensity to the minimum intensity in the interference fringe
pattern observed.


Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotized and heated with
cuprous bromide. The reaction mixture
formed contains:
A. Mixture of o- and p- bromoanilines
B. Mixture of o- and m- bromotoluenes
c. Mixture of o- and p- bromotoluenes
D. Mixture of o- and p- dibromobenzenes


Objects with the same type of charges attract each other.
A . True
B. False


If the function \( f(x)=\frac{\log x-1}{x-e}, \) for
\( x \neq e \) is continuous at \( x=e, \) then find
\( \boldsymbol{f}(\boldsymbol{e}) \)


A uniform magnetic field B is set up along the positive \( x \) -axis. A particle of charge 'q' and mass 'm' moving with a velocity v enters the field at the origin in \( X-Y \) plane such that it has velocity
components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation


A satellite of mass m revolves around
the earth of radius \( R \) at a height \( x \) from its surface. If \( g \) is the acceleration due
to gravity on the surface of the earth, the orbital speed of the satellite is
\( \mathbf{A} \cdot g x \)
B. \( \sqrt{\frac{g R^{2}}{R+x}} \)
c. \( \frac{g R^{2}}{R+x} \)
D. \( \frac{g R}{R-x} \)


The negation of the statement \( (\boldsymbol{p} \rightarrow \)
\( \boldsymbol{q}) \wedge \boldsymbol{r} \) is
\( \mathbf{A} \cdot p \wedge \sim q \vee \sim r \)
В \( .(\sim p \wedge q) \wedge(\sim r) \)
c. \( (p \wedge \sim q) \wedge(r) \)
D. \( (p \wedge \sim q) \wedge(\sim r) \)


The Biot Savart's Law in vector form is
\( ^{\mathrm{A}} \cdot_{\overline{\delta B}}=\frac{\mu_{0}}{4 \pi} \frac{d l(\vec{l} \times \vec{r})}{r^{3}} \)
B・ \( _{\overline{\delta B}}=\frac{\mu_{0}}{4 \pi} \frac{I(\bar{d} l \times \vec{r})}{r^{3}} \)
\( ^{\mathbf{C}} \cdot \frac{\mu_{0}}{\delta B}=\frac{I(\vec{r} \times \overrightarrow{d l})}{4 \pi} \frac{r^{3}}{ } \)
D \( \cdot \frac{ }{\delta B}=\frac{\mu_{0}}{4 \pi} \frac{I(\vec{d} l \times \vec{r})}{r^{2}} \)


Calculate the kinetic energy of 10 gram
of Argon molecules at \( 127^{\circ} \mathrm{C} \) [Universal gas constant \( \boldsymbol{R}= \) \( 8320 J / \) mol \( K . \) Atomic weight of Argon
\( =\mathbf{4 0} k \boldsymbol{g} / \boldsymbol{m o l}] \)


A moving coil galvanometer has a coil of area \( A \) and number of turns \( N . A \)
magnetic field B is applied on it. The
torque acting on it is given by \( \boldsymbol{\tau}=\boldsymbol{k} \boldsymbol{i} \)
where i is current through the coil. If moment of inertia of the coil is I about
the axis of rotation.
If the value of k in terms of
galvanometer parameters \( (\mathrm{N}, \mathrm{B}, \mathrm{A}) \) is given by \( k=x \times N B A \). Find \( x \)


A number is selected at random from
the first 1,000 natural numbers. What is the probability that the number so
selected would be a multiple of 7 or \( 11 ? \)
A . 0.25
B. 0.32
c. 0.23
D. 0.33


In a World Cup final match against Srilanka, for six times Sachin Tendulkar
hits a six out of 30 balls he plays. What is the probability that in a given throw the ball does not hit a six?
A \( \cdot \frac{1}{4} \)
B.
\( c \cdot \frac{4}{5} \)
D. \( \frac{3}{4} \)


In a hostel, \( 60 \% \) of the students read
Hindi newspaper, \( 40 \% \) read English
newspaper and \( 20 \% \) read both Hindi and English newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English
newspapers.
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)


Assertion
In Rutherfourd's \( \alpha \) -particle scattering
experiment, most of the \( \alpha \) -particles
were deflected by nearly \( 18^{0} \)
Reason
The positive charge of the atom is spread throughout the atom that repelled and deflected the positively charged \( \alpha \) -particles.
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


f \( l, m, n \) are \( p^{t h}, q^{t h}, r^{t h} \) terms of \( G . P . \) al positive, then \( \left|\begin{array}{lll}\log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1\end{array}\right| \) equals
A . -
B. 2
\( c \)
\( D \)


The working of a generator is based
upon the
A. magnetic effect of current
B. heating effect of current
c. chemical effect of current
D. electromagnetic induction


\( \sqrt{3} \) percent of \( 2 \sqrt{12} \) is equal to
A . 12
в. \( 6 \sqrt{12} \)
c. \( \frac{3}{25} \)
D. \( \frac{6}{25} \)
E \( \cdot \frac{3 \sqrt{12}}{25} \)


Let \( a, b, c \) be such that \( b(a+c) \neq 0 \) \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{a}+\mathbf{1} & \boldsymbol{a}-\mathbf{1} \\ -\boldsymbol{b} & \boldsymbol{b}+\mathbf{1} & \boldsymbol{b}-\mathbf{1} \\ \boldsymbol{c} & \boldsymbol{c}-\mathbf{1} & \boldsymbol{c}+\mathbf{1}\end{array}\right|+ \)
\( \left|\begin{array}{ccc}\boldsymbol{a}+\mathbf{1} & \boldsymbol{b}+\mathbf{1} & \boldsymbol{c}-\mathbf{1} \\ \boldsymbol{a}-\mathbf{1} & \boldsymbol{b}-\mathbf{1} & \boldsymbol{c}+\mathbf{1} \\ (-\mathbf{1})^{n+\mathbf{2}} \boldsymbol{a} & (-\mathbf{1})^{n+\mathbf{1}} \boldsymbol{b} & (-\mathbf{1})^{n} \boldsymbol{c}\end{array}\right|=\mathbf{0} \)
then the value of \( n \) is
A. Any integer
B. zero
c. Any even integer
D. Any odd integer


A cylindrical cistern whose diameter is
\( 21 c m \) is partly filled with water. If a
rectangular block of iron \( 14 \mathrm{cm} \) in length, \( 11 c m \) in breadth and \( 12 c m \) in thickness if wholly immersed in water, by how many centimetres will the water level rise? \( \left(\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)


Assertion
Acceleration due to gravity at a place on earth remains constant for all objects
Reason
Acceleration due to gravity doesn't depend on the mass of the object but
only on mass of earth
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


Following reaction can take place in both direction \( A \stackrel{k_{1}}{_{k_{2}}} B, \) It is given that for the forward reaction:
\( [\mathrm{B}] \)
Rate
\( 0.01 M \quad 1 \times 10^{-2} M s^{-1} \)
\( 0.02 M \quad 2 \times 10^{-2} M s^{-1} \)
Hence, net reaction rate of B is:
Rate
\( \mathbf{A} \cdot k_{1} \)
\( \mathbf{B} \cdot k_{1}-k_{2} \)
\( \mathbf{c} \cdot k_{1}[A]-k_{2} \)
D. none of these


The tension of a stretched string is increases by \( 44 \% \). In order to keep its frequency of vibration same its length must be increased by.
A . \( 10 \% \)
B. 20\%
c. \( 15 \% \)
D. \( 25 \% \)


The emf of a genetator is 12 V and its internal resistance is 1 K\( \Omega .0 \mathrm{m} \)
measuring its emf with a voltmeter of \( 5 K \Omega \) the reading will be:-
A . \( 10 v \)
B. 10 milli v
c. 1 milliv
\( D \cdot 1 v \)


Consider the following statements:
(a) In leguminous plants, leaf base becomes swollen, called pulvinus.
(b) The fleshy leaves of onion and garlic
store food
(c) In Alstonia, leaves show alternate
phyllotaxy.
(d) The lamina in Australian acacia
become green and synthesize food.
Of the above statements.
A \( \cdot(b) \) and
(d) are correct
B. (a) and
(c) are correct
c. (a) and (b) are correct
D. (b) and
(c) are correct
E . (a) and
(d) are correct


\( |\mathbf{f}| z-i R e(z)|=| z-\operatorname{Im}(z) \mid \)
then prove that \( z \) lies on the bisectors of the quadrants.


When the equilibrium is attained, the concentration of each of the reactants
and products becomes equal.
A. True
B. False


The process by which a mixture of sodium chloride and ammonium
chloride can be separated, is called
A. sublimation
B. chromatography
c. evaporation
D. distillation


If \( M_{O} \) is the mass of an oxygen isotope
\( \mathrm{s} \boldsymbol{O}^{17}, \boldsymbol{M}_{\boldsymbol{p}} \) and \( \boldsymbol{M}_{\boldsymbol{n}} \) are the masses of a
proton and a neutron, respectively, the
nuclear binding energy of the isotope is
A. \( M_{O} c^{2} \)
B. \( \left(M_{O}-17 M_{n}\right) c^{2} \)
\( \mathbf{c} \cdot\left(M_{O}-8 M_{p}\right) c^{2} \)
D. \( \left(8 M_{p}+9 M_{n}-M_{O}\right) c^{2} \)


For making cake, baking powder is taken. If at home your mother uses baking soda instead of baking powder
in cake, how will it affect the taste of the
cake?
A. Bitter in taste
B. Sour in taste
c. salty in taste
D. sweet in taste


Choose the correct answers from the
alternatives given :
Chromosomes are in their most
extended form during:
A. interphase
B. anaphase
c. metaphase
D. prophase


Two bulbs, one of \( 200 \mathrm{W} \) and the other of
\( 100 \mathrm{W}, \) are connected in series with a
\( 100 \mathrm{V} \) battery which has no internal
resistance. Then
A. The current passing through the 200 W bulb is more than that through the 100 w bulb
B. The power dissipation in the 200 W bulb is more than that In the 100 w bulb
C. The voltage drop across the 200W bulb is more than that across the 100 w bulb
D. The power dissipation In the 100 W bulb is more than that in the 200 w bulb


What is the other name
(a) myopia (b) hypermetropia?


If due to some injury the chordae tendineae of the tricuspid valve of the human heart is partially non-functional,
what will be the immediate effect?
A. The flow of blood into the pulmonary artery will be reduced
B. The flow of blood into the aorta will be slowed down
c. The pacemaker will stop working
D. The blood will tend to flow back into the left atrium


ABCD is a trapezium with \( A B \) and \( C D \) parallel. If \( \mathrm{AB}=\mathbf{6}, \mathrm{BC}=\mathbf{5}, \mathrm{CD}=\mathbf{3}, \mathrm{DA}=\mathbf{4} \)
\( A=90^{\circ} \) the area of \( A B C D \) is?
A .27
B. 12
c. 18
D. 15


Find the probability that a number selected at random from the numbers 3
\( 4,5, \dots, 25 \) is prime


A compound of \( X e \) and \( F \) is found to
have \( 53.5 \% \) of \( X e . \) What is oxidation
number of \( X e \) in this compound?
A . -4
B. 0
\( c \cdot+4 \)
D. +6


Assertion (A): Stress is restoring force per unit area.

Reason (R) : Interatomic forces in solids
are responsible for the property of
elasticity
A. Both Assertion and Reason are true and the reason is correct explanation of the assertion
B. Both Assertion and Reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the Reason is false
D. Assertion is false, but the reason is true


Reproduction, unlike other life processes, is not essential to maintain the life of an individual organism.
A. True
B. False


Check the commutativity and associativity of the following binary operation:
\( *^{\prime} \) on \( Q \) defined by \( a * b=a b+1 \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Q} \)


Define empirical probability


\( 4 g \) of \( C O_{2} \) and 2.27 litre of \( H_{2} \) at \( S T P \)
(273.15 K and 1 atm pressure) are mixed
in a container. The total number of
molecules present in the container will be:
В. \( 6.022 \times 10^{23} \)
D. \( 12.044 \times 10^{2} \)


The correct statement is :
A. leaching of bauxite using concentrated \( N a O H \) solution gives sodium aluminate and sodium silicate
B. The blistered appearance of copper during the metallurgical process is due to the evolution of \( C O_{2} \)
C . pig iron is obtained from cast iron
D. the Hall-Heroult process is used for the prodeuction of aluminium and iron.


During the propagation of wave motion,
A. there is transfer of energy from one particle to another without any actual transfer of the particles of the medium.
B. there is transfer of energy from one particle to another with transfer of the particles of the medium.
C. there is no transfer of energy from one particle to another
D. None of these.


A massless spring of natural length of \( 0.5 m \) and spring constant \( 50 N / m \) has one end fixed and the other end
attached to a mass of 250 g. The spring mass system is on a smooth floor. The mass is pulled until the length of the
spring is 0.6 and then released from rest. The kinetic energy of the mass when the length of the spring is \( 0.5 m \) is
A. \( 0.25 J \)
B. \( 2.25 J \)
c. \( 6.25 J \)
D. \( 9 . J \)


Hydrogen resembles:
A. alkali metals
B. halogens
C. both \( A \) and \( B \)
D. none of the above


Two coherent sources of different
intensities sends wave which interferes.
The ratio of maximum intensity to the
minimum intensity is 25. The intensities of the sources are in the
ratio
\( \mathbf{A} \cdot 25: 1 \)
B. 5: 1
\( \mathrm{c} .9: 4 \)
D. 625: 1


Most of the \( \alpha \) -particles passed straight through the gold foil. This proved the existence of \( _{-} \) in an atom.
A. electrons
B. nucleus
c. Empty space
D. positive charge


The number of alkenyl groups possible
(structural isomers) from \( C_{4} H_{7}- \) are:
\( A \cdot 7 \)
B. 5
\( c .3 \)
D.


If \( \Delta A B C \equiv \Delta F E D \) under the
correspondence \( A B C \leftrightarrow F E D, \) write all the corresponding congruent parts of the triangles.


Prove that: \( \sin ^{2} A \cos ^{2} B- \)
\( \cos ^{2} A \sin ^{2} B=\sin ^{2} A-\sin ^{2} B \)


A radioactive nucleus emits an \( \alpha \)
particle and a neutron simultaneously with speed but in opposite direction in order to form a stable nuclei. If the
speed of emitted particles is \( v \) and \( A \) is
the mass number of radioactive
nucleus, then speed of stable nucleus is:
A. \( \frac{3 v}{A-5} \)
B. \( \frac{2 v}{A-5} \)
c. \( \frac{4 v}{A-5} \)
D. \( \frac{2 v}{A+5} \)


Which of the following is the range of temperature recorded by a laboratory thermometer?
A \( \cdot 0^{\circ} C \) to \( 100^{\circ} \mathrm{C} \)
B . \( -10^{\circ} \mathrm{C} \) to \( 110^{\circ} \mathrm{C} \)
c. \( 30^{\circ} C \) to \( 120^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \) to \( 145^{\circ} \mathrm{C} \)


Evaluate \( : \lim _{x \rightarrow-2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2} \)


Check the commutativity and associativity of the following binary
operation:
\( ' *^{\prime} \) on \( Z a * b=a-b \) for all \( a, b \in Z \)


\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{4} \boldsymbol{I}_{2}+\boldsymbol{3} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \rightarrow \boldsymbol{X}+ \)
\( \boldsymbol{H} \boldsymbol{C O O N} \boldsymbol{a}+\mathbf{5} \boldsymbol{N a I}+\mathbf{3} \boldsymbol{C O}_{2}+\mathbf{2 H}_{2} \boldsymbol{O} \)
In the above reaction \( ^{\prime} X^{\prime} \) is :
A. Di iodo methane
B. Tri iodo methane
c. lodo methane
D. Tetra iodo methane


An object free falls \( 15 m \) from the top of
a ladder. Select the graph that best
describes the following quantities during the fall. The momentum of the object
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
\( E \)


Secondary amines can be prepared by:
A. reduction of nitro compounds
B. reduction of amides
c. reduction of isonitriles
D. reduction of nitriles


A string vibrates according to equation
\( y=\sin \frac{\pi x}{3} \cos 40 \pi t . \) The potential
energy of the string will be zero at times
\( ^{A} \cdot \frac{1}{20} s \) and \( \frac{1}{40} s \)
B. \( \frac{1}{40} s \) and \( \frac{1}{80} s \)
\( ^{\mathrm{c}} \cdot \frac{1}{80} s \) and \( \frac{3}{80} s \)
D. \( \frac{1}{40} s \) and \( \frac{3}{40} s \)


Assertion: Specific heat of a body is
always more than its thermal capacity
Reason : Thermal capacity is the heat required for raising temperature of unit mass of the body through unit degree.
A. Both assertion and reason are correct and reason is the correct explanation of the assertion.
B. Both assertion and reason are correct, but reason is not the correct explanation of the assertion.
c. Assertion is correct but reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both assertion and reason is incorrect


Which of the following is not a physical
property?
A. Density
B. Temperature
c. Boiling point
D. Color
E. Flammability


Arrange the following in the order of increasing oxidation number of
nitrogen: \( N H_{3}, N_{3} H, N_{2} O, N O, N_{2} O_{5} \)


Maximum intercellular substance is
found in
A. Connective tissue
B. Nervous tissue
c. Muscular tissue
D. Epithelial tissue


Assertion \( : \int \frac{1}{\sqrt{x^{2}+2 x+10}} d x= \)
\( \sinh ^{-1} \frac{x+1}{3}+c \)
Reason : \( \operatorname{If} \boldsymbol{a}>\mathbf{0}, \boldsymbol{b}^{2}-\mathbf{4} \boldsymbol{a} \boldsymbol{c}<\mathbf{0}, \) then
\( \int \frac{d x}{\sqrt{a x^{2}+b x+c}}= \)
\( \frac{1}{\sqrt{a}} \sinh ^{-1}\left(\frac{2 a x+b}{\sqrt{4 a c-b^{2}}}\right)+k \)
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true but R is not correct explanation of
\( c . \) A is true but \( R \) is false
D. A is false but R is true


A cell balances against a length of
\( 200 \mathrm{cm} \) on a potentiometer wire, when it
is shunted by a resistance of 8\Omega. The balancing length reduces by \( 40 \mathrm{cm} \)
when it is shunted by a resistance of \( 4 \Omega \) Calculate the balancing length when the cell is in open circuit. Also calculate
the internal resistance of the cell.


A bullet moving at \( 20 m / \) sec. It strikes a wooden plank and penetrates \( 4 \mathrm{cm} \) before coming to stop. The time taken to stop is:
A. 0.004 sec
в. 0.016 sec
c. 0.008 sec
D. 0.002 sec


The S.D. of the following frequency distribution is
\( \begin{array}{lllll}\text { Class } & 0- & 10 & 20- & 30- \\ & 10 & 20 & 30 & 40\end{array} \)
\( f_{i} \)
A . 7.8
B. 9
c. 8.1
D. 0.9


Write the name of any one natural
method of contraceptive.


The length of half wave dipole at \( 15 \mathrm{MHz} \) is?
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. None of these


Express the following matrices as the sum of a symmetric and a skew symmetric matrix :
\( \left[\begin{array}{ccc}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right] \)


The gravitational potential due to earth at infinite distance from it is zero. Let
the gravitational potential at a point \( \boldsymbol{P} \) be \( -5 J k g^{-1} . \) Suppose, we arbitrarily assume the gravitational potential at infinity to be \( +10 J k g^{-1} \), then the gravitational potential at \( \boldsymbol{P} \) will be
\( \mathbf{A} \cdot-5 J k g^{-1} \)
\( \mathbf{B} \cdot+5 J k g^{-1} \)
c. \( -15 J k g^{-1} \)
\( \mathbf{D} \cdot+15 J k g^{-1} \)


According to the kinetic theory of gases:
This question has multiple correct options
A. Pressure of a gas is due to collisions of molecules with each other
B. Kinetic energy is proportional to square root of the temperature
C. Pressure of a gas is due to collisions of molecules against the sides of the container
D. There is no force of attraction between gas molecules


Unit of mobility:
A. \( C s k g \)
B . \( m^{2} V^{-1} s^{-1} \)
c. \( \operatorname{cskg}^{-1} \)
D. \( m^{2} V^{-1} s \)


Two symmetrical dice are thrown at a time. If the sum of points on them is 7 the chance that one of them will show a
face with 2 points is
A \( \cdot \frac{1}{8} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.


A sample of HCl is placed in an electric
field of \( 2.5 \times 10^{4} N C^{-1} . \) The dipole
moment of HCl is \( 3.4 \times 10^{-30} \mathrm{Cm} \). Find
the maximum torque that can act on a
molecule.
A \( \cdot 7.6 \times 10^{-26} \mathrm{Nm} \)
В. \( 4.3 \times 10^{-26} \mathrm{Nm} \)
c. \( 6.5 \times 10^{-26} \mathrm{Nm} \)
D. \( 8.5 \times 10^{-26} \mathrm{Nm} \)


A coil in the shape of an equilateral triangles of side I is suspended between the pole pieces of a permanent magnet such that \( \mathrm{B} \) is in plane of the coil. If due to a current i in the triangle, a torque \( \tau \) acts on it, the side I of the triangle is :
\( ^{\mathrm{A}} \cdot \frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2} \)
в. \( \frac{2}{3}\left(\frac{\tau}{B i}\right) \)
\( ^{c} \cdot\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2} \)
D. \( \frac{1}{\sqrt{3}} \frac{\tau}{B i} \)


If \( A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\} \). Find \( A \times \)
\( (B \cap C) \)


Two plane mirrors are inclined at \( 70^{0} . \) A
ray incident on one mirror at an angle \( \theta \) after reflection falls on the second
mirror and is reflected from there
parallel to the first mirror \( \boldsymbol{\theta} \) is
A \( .50^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 30^{0} \)
D. 55


\( \int \frac{x d x}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)} \)


Match the compounds in column I with
their
characteristic(s)/test(s)/reaction(s)/re agent(s)/stereochemistry/isomer(s) given in column II. Matching can be one or more than one.


In which of the following functions is Rolle's theorem applicable
A \( , \quad f(x)=\left\{\begin{array}{l}x, 0 \leq x<1 \\ 0, x=1\end{array} \text { on }[0,1]\right. \)
в. \( \quad f(x)=\left\{\begin{array}{l}\frac{\sin x}{x},-\pi \leq x<0 \\ 0, x=0\end{array} \text { on }[-\pi, 0]\right. \)
c. \( f(x)=\frac{x^{2}-x-6}{x-1} \) on [-2,3]
D \( \quad f(x)=\left\{\begin{array}{l}\frac{x^{3}-2 x^{2}-5 x+6}{x-1}, \text { if } x \neq 1 \\ -6, \text { if } x=1\end{array}\right. \)


In the primary rainbow, what is the order in which colours are observed?
A. Violet innermost and red outermost
B. Red innermost and violet outermost
c. Violet, blue, red, yellow
D. Haphazard


A sonar device on a submarine sends
out a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is \( 3625 \mathrm{m} \)
\( A \cdot 1450 \mathrm{m} / \mathrm{s} \)
B. 1650 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 1350 \mathrm{m} / \mathrm{s} \)
D. \( 967 \mathrm{m} / \mathrm{s} \)


Which of the following sequence of
explanation is appropriate for explaining the reason for the periodicity of reducing property in a period or
group?
(a) Tendency to undergo oxidation decreases in a period and increases in a
group.
(b) In a period ionization energy increases and in a group it decreases.
(c) In a period the atomic size
decreases and in a group it increases.
(d) The elements present in the left side of the periodic table have strong reducing property.
\( A \cdot \cos a \)
B. c d b a
\( c \cdot d c a b \)
D. \( d \) b a c


Name the parts of the ovary which give
rise to:
Seed


A particle having initial velocity
moves with a constant acceleration a
for a time \( t . \) Evaluate it for \( \boldsymbol{u}= \)
\( \mathbf{5 m} / \boldsymbol{s}, \boldsymbol{a}=\mathbf{2 m} / \boldsymbol{s} \) and \( \boldsymbol{t}=\mathbf{1 0 s} \)


Which of the reactants act as oxidant or
reductant if any:
\( \boldsymbol{C a}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C l}_{2} \)
A \( \cdot C l_{2} \)
в. \( C a \)
c. Both of these
D. None of these


In an experiment with 15 observations the following results were available \( \sum x^{2}=2830, \quad \sum x=170 . \) One
observation that was 20 was found
wrong and was replaced by the correct value \( 30 . \) The corrected variance is
A . 8.33
B. 78.00
c. 188.66
D. 177.33


f \( x, y \) are rational numbers such that
\( (x+2 y)+(x-3 y) \sqrt{6}= \)
\( (x-y-2) \sqrt{5}+(2 x+y-2), \) then
A \( . x+y=6 \)
В. \( x+y=5 \)
c. \( x+y=4 \)
D. \( x+y=3 \)


A vibrating string of certain length \( \ell \) under a tension \( T \) resonates with a
mode corresponding to the first overtone (third harmonic) of an air column of length \( 75 \mathrm{cm} \) inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be \( 340 \mathrm{m} / \mathrm{s}, \) the frequency nof the tuning fork in \( \mathrm{Hz} \) is
\( A \cdot 344 \)
в. ззб
\( c . \) 117.
D. 109.


Which of the following electron transition in hydrogen atom will require the largest amount of energy?
A. from \( n=1 \) to \( n=2 \)
B. from \( n=2 \) to \( n=3 \)
\( c . \) from \( n=\infty \) to \( n=1 \)
D. from \( n=3 \) to \( n=5 \)


If \( \vec{a}=i+2 j+k, \vec{b}=i-j+k \) and \( \vec{c}= \)
\( i+j-k . \) A vector in the plane of \( \vec{a} \) and \( \vec{b} \) whose projection on \( \vec{c} \) is \( 1 / \sqrt{3}, \) is
A \( .4 i-j+4 k \)
в. \( 3 i+j-3 k \)
c. \( 2 i+j-2 k \)
D. \( 4 i+j-4 k \)


Q Type your question
situation.
Only atmospheric pressure is exerted on
I. the exposed mercury surface in the right side of the tube.
II. The gas pressure is greater than atmospheric pressure.
III. The difference in the height of mercury levels is equal to the pressure of the gas
A. II only
B. III only
C. I and II only
D. I and III only
E. I, II and III


Which of the following units can be used to represent solubility?
\( \mathbf{A} \cdot \mathbf{g} \)
B. mol
c. \( m o l / L \)
\( \mathbf{D} \cdot m L / s \)


The reaction \( \boldsymbol{A} \boldsymbol{g}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}(s) \rightarrow \)
\( 2 A g^{+}(a q) \) is an example of
This question has multiple correct options
A. disproportionation
B. proportionation
c. comproportionation
D. symproportionation


More reactive hydride of the \( \mathbf{V} \) group :
A. \( \mathrm{NH}_{3} \)
в. РНз
\( \mathrm{c} \cdot \mathrm{sbH}_{3} \)
D. AsH \( _{3} \)


The side of a cube \( 4 \mathrm{cm} \). Its area is
A . 16 sq. \( \mathrm{cm} \)
B. 64 sq. cm
c. 12 sq. \( \mathrm{cm} \)
D. None of these


Assertion
Alkyl halides are colourless when pure.
Reason
Bromides and lodides develop colour
when exposed to light.
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 energy stored in water formed from
ice is:
This question has multiple correct options
A. Latent heat of fusion of ice
B. \( 80 c a l^{-1} \)
c. Latent heat of boiling
D. Latent heat of fusion of water


A square park has each side of \( 100 m \)
At each corner of the park, there is a
flower bed in the form of a quadrant of
radius \( 14 m \) as shown in figure. Find the
area of the remaining part of the park. \( \left[\text { Use } \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
A \( \cdot 12843 m^{2} \)
B. \( 11284 m^{2} \)
\( \mathrm{c} \cdot 9384 m^{2} \)
D. \( 7382 m^{2} \)


Why are shockers used in scooters and
cars? Explain.
A. decreases friction
B. Increase the time of impact
c. increases friction
D. decorative


(a) Write a note on Rosenmund
reduction.
(b) Why is fluoroacetic acid more acidic than chloroacetic acid?
(c) Draw the resonating structures of carboxylate ion.


The Bohr's model could successfully
explain.
A. The stability of the atom
B. The atomic spectra of hydrogen atom.
C. The calculation of energy of the electron in a particular orbit of hydrogen atom.
D. All the above


The enthalpy change when 1 mol of graphite is converted into diamond is known as the enthalpy of transition. If
true enter 1 else 0
A.


Find the non-zero roots of the equation \( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} & \boldsymbol{c}\end{array}\right|=0 \)


Who first proposed the light as electromagnetic wave?
A. Thomas Young
B. Max planck
c. James Clerk Maxwell
D. Albert Einstein


A line d.c's proportional to (2,1,2)
meets each of the lines \( \boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z} \)
and \( x+a=2 y=2 z . \) Then the
coordinates of each of the points of
intersection are given by
A . \( (3 a, 2 a, 3 a) ;(a, a, 2 a) \)
в. \( (3 a, 2 a, 3 a) ;(a, a, a) \)
C. \( (3 a, 3 a, 3 a) ;(a, a, a) \)
D. \( (2 a, 3 a, 3 a) ;(2 a, a, a) \)


The equation \( \boldsymbol{y}=\mathbf{4}+\mathbf{2} \sin (\mathbf{6} \boldsymbol{t}-\mathbf{3} \boldsymbol{x}) \)
represents a wave motion with amplitude of
A. 6 units
B. 2units
c. 20 units
D. 8 units


Spermatozoid of Cycas is
A. Biflagellate
B. Nonflagellate
C . Uniflagellate
D. Multiciliated


If \( i^{2}=-1, \) then \( 4+i, \) and \( 4-i \) are
roots of which of the following equations?
A. \( x^{2}+8 x-17=0 \)
B. \( x^{2}-8 x+17=0 \)
c. \( x^{2}-8 x-17=0 \)
D. \( x^{2}+10 x-8=0 \)
E . \( x^{2}-8 x+8=0 \)


If the volume of a cube is \( 512 \mathrm{cm}^{3} \), then
find the length of an edge of the cube


The graph of two conductors of same
materials connected in series justify (i)
which one has more resistance
(ii)Which one will produce more heat?


Heating of a wheel on applying brakes is due to the relation
\( ^{\mathrm{A}} \cdot_{P} \propto \frac{1}{V} \)
в. \( P \propto T \)
\( c . W \propto Q \)
D. \( V \propto T \)


Which of the following functions represent a travelling wave?
A \( \cdot(x-v t)^{2} \)
B \cdot \( \operatorname{Ln}(x+v t) \)
\( \mathbf{C} \cdot e^{-(x-\pi)^{2}} \)
D. \( \frac{1}{x+v t} \)


The area bounded by \( \boldsymbol{y}=\mathbf{2}- \) \( |2-x|, y=\frac{3}{|x|} \) is
\( ^{\text {A } \cdot \frac{5-4 \ln 2}{3} . \text { sq.unit }} \)
B. \( \frac{2-\ln 3}{2} . \) sq.unit
c. \( \frac{4-3 \ln 3}{2} \). sq.unit
D. none of these


The molecular formula of the first
member of alkenynes and its name is
given by the set:
A \( \cdot C_{3} H_{2}, \) Alkene
B. \( C_{5} H_{6} \), Pent-1-en-3-yne
C. \( C_{6} H_{8} \), Hex-1-en-5-yne
D. \( C_{4} H_{4}, \) But-1-en-3-yne


Which of the following is the side view
of the prism?
A. Square
B. Rectangle
c. Circle
D. Triangle


When \( 100 m l \) of \( 0.06 m \mathrm{Fe}\left(N O_{3}\right)_{3}, 50 m l \)
of \( 0.2 m l F e C l_{3} \) and \( 100 m l \) of
\( 0.26 m m g\left(N O_{3}\right)_{2} \) are mixed, then
calculate molarity of reaction in final solution.


Oxidation of one molecule of glucose in aerobic respiration results in the production of
A. 36 ATP molecules.
B. 38 ATP molecules
c. 3 ATP molecules
D. Both A or B.


If \( n=^{m} C_{2}, \) then the value of \( ^{n} C_{2} \) is
given by
A. \( ^{m+1} C_{4} \)
в. \( ^{m-1} C_{4} \)
c. \( ^{m+2} C_{4} \)
D. \( 3 .^{m+1} C_{4} \)


In order that a relation \( R \) defined on a
non-empty set \( A \) is an equivalence
relation
It is sufficient, if \( \boldsymbol{R} \)
A . is reflexive
B. is symmetric
\( \mathbf{c} \). is transitive
D. possesses all the above three properties.


Which chamber is the first to receive
oxygenated blood from the lungs in the figure given below?
\( A \cdot w \)
B.
\( c \)
\( D \)


A particle is projected vertically upwards and it reaches the maximum height H in time T seconds. The height of the particle at any time t will be
A \( \cdot g(t-T)^{2} \)
B \( \cdot H-\frac{1}{2} g(t-T)^{2} \)
c. \( \frac{1}{2} g(t-T)^{2} \)
D. \( H-g(t-T)^{2} \)


toppr
Q Type your question
production to improve the subsequent hardening of concrete. The elevated temperature during the production of cement may lead to the formation of unwanted hemihydrate
\( C a S O_{4} \cdot \frac{1}{2} H_{2} O \) according to reaction
\( \operatorname{CaSO}_{4} \cdot 2 H_{2} O(s) \rightarrow C a S O_{4} \)
\( \frac{1}{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\frac{3}{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
The \( \Delta_{f} H^{\ominus} \) of \( C a S O_{4} \)
\( 2 H_{2} O(s), C a S O_{4} \frac{1}{2} H_{2} O(s), H_{2} O(g) \)
\( \operatorname{are}-2021.0 k J m o l^{-1} \)
\( -1575.0 k J m o l^{-1} \) and \( -241.8 k J m o l^{-1} \)
respectively. The respective values of their standard entropies are 194.0 130.0 and \( 188.0 J K^{-1} m o l^{-1} \)
\( \boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}= \)
\( 0.0831 L b a r m o l^{-1} K^{-1} \)
Answer the follwoing questions on the basis of above information.

The value of equilibrium constant for
reaction is:
A. 0
B.
\( c \)
\( D \)


Laughing gas is prepared by heating:
A. \( N H_{4} C l+N a N O_{3} \)
в. \( N H_{4} C l \)
c. \( \left(N H_{4}\right)_{2} S O_{2} \)
D. \( N H_{4} N O_{3} \)


In \( \triangle P Q R, N \) is a point on \( P R \) such that \( Q N \perp P R \) If \( P N \times N R=Q N^{2}, \) prove
that \( \angle P Q R=90^{\circ} \)


Fossils are dated now by
A. Stratigraphic position
B. Amount of calcium residue
C. Association with other animals
D. Radioactive carbon contents


Four vertices of a tetrahedron are
(0,0,0),(4,0,0),(0,-8,0) and
\( (0,0,12), \) Its centroid has the coordinates
A \( \cdot\left(\frac{4}{3},-\frac{8}{3}, 4\right) \)
В. (2,-4,6)
c. (1,-2,3)
a 5
D. none of these


The molarity of \( H_{2} S O_{4} \) is \( 18 M . \) Its
density is \( 1.8 g m L^{-1} . \) Hence, molality is :
\( A \cdot 36 m \)
B. 200 \( \mathrm{m} \)
c. \( 500 \mathrm{m} \)
D. \( 18 \mathrm{m} \)


Figure shows a square current-carrying
loop \( A B C D \) of side \( 2 m \) and current
\( \boldsymbol{I}=\frac{1}{2} \boldsymbol{A} . \) The magnetic moment \( \overrightarrow{\boldsymbol{M}} \) of
the loop is:
A \( \cdot(\hat{i}-\sqrt{3} \hat{k}) A-m^{2} \)
\( \mathbf{B} \cdot(\hat{j}-\hat{k}) A-m^{2} \)
c. \( (\sqrt{3} \hat{i}-\hat{k}) A-m^{2} \)
D. \( (\hat{i}-\hat{k}) A-m^{2} \)


Is 51 a term of the \( A P 5,8,11,14, \ldots ? \)


Give four rational numbers equivalent
to:
\( \frac{5}{-3} \)


Draw structures of \( N H_{3}, P C l_{5}, P C l_{3} \)


ff \( \frac{x^{3}}{(x-a)(x-b)(x-c)}=1+ \)
\( \frac{\boldsymbol{A}}{\boldsymbol{x}-\boldsymbol{a}}+\frac{\boldsymbol{B}}{\boldsymbol{x}-\boldsymbol{b}}+\frac{\boldsymbol{C}}{\boldsymbol{x}-\boldsymbol{c}} \) then \( \mathbf{A}= \)
A \( \cdot \frac{a^{3}}{(c-b)(c-a)} \)
в. \( \frac{a^{3}}{(b-c)(b-a)} \)
c. \( \frac{a^{3}}{(a-b)(a-c)} \)
D.


Semiconductors are generally made up of which substance?
A. silicon
B. Carbon
c. Phosphorus
D. Boron


Multiple Answer Question
According to Bohr, when electronjumps
from one shell to another:
This question has multiple correct options
A. if it gains energy, it moves away from the nucleus
B. when it gains energy it moves towards the nucleus
C. it emits energy in the form of radiations when it moves from higher energy level to lower energy level
D. it always gains energy in the form of light


Assertion
The transfer of electrons from zinc to
copper takes place through metal wire connecting the two rods.
Reason
Electricity from solution in one beaker to other flows by migration of ions through the salt bridge.
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


A bar made of material whose Young's
modulus is equal to \( E \) and Poisson's
ratio to \( \mu \) is subjected to the
hydrostatic pressure \( p \). Find the relationship between the
compressibility \( \beta \) and the
elastic constants \( \boldsymbol{E} \) and \( \boldsymbol{\mu} \)
\( ^{\mathbf{A}} \cdot_{\beta}=(1-2 \mu) \frac{3}{E} \)
B. \( \beta=(1-3 \mu) \frac{2}{E} \)
\( ^{\mathbf{c}} \cdot_{\beta}=(1+2 \mu) \frac{E}{3} \)
D \( \mu=(1-2 \beta) \frac{3}{E} \)


Assertion
HCl doesn't used to acidify a \( K M n O_{4} \) solutions in volumetric estimations of
\( \boldsymbol{F} \boldsymbol{e}^{2+} \) or \( \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \)
Reason
\( K M n O_{4} \) oxidizes HCl to \( C l_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A community which starts succession in a habitat is
A. Pioneer Community
B. Seral Community
c. Biotic Community
D. Ecosere


A lamp post stands on a horizontal plane. From a point situated at a distance \( 150 \mathrm{m} \) from its foot, the angle
of elevation of the top is \( 30^{\circ} . \) What is the
height of the lamp post?
A . \( 50 m \)
в. \( 50 \sqrt{3} m \)
c. \( \frac{50}{\sqrt{3}} m \)
D. \( 100 m \)


A truck is moving with the speed of
\( 20 m / s \) and having a momentum of \( 12,000 k g m / s . \) Find out the mass of
the truck?
A. \( 240,000 k g \)
в. 6,000 kg
c. \( 1,200 k g \)
D. \( 600 k g \)
E . \( 120 k g \)


Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with:
(i) 7 sides
(ii) 10 sides
(iii) 250 sides


Which of the following points is equidistant from (3,2) and (-5,-2)\( ? \)
в. (0,-2)
D. (2,-2)


The reduction potential of an electrode can be increased by:
A. increasing the area of the electrode
B. decreasing the temperature
c. increasing the temperature
D. decreasing the concentration of metal ions


When two bodies at different
temperatures are placed in thermal
contact with each other, heat flows from
the body at a higher temperature until they both acquire the same temperature. Assuming that there is no loss of heat to the surroundings, then:
A. The heat gained by the hotter body will be equal to the heat lost by the colder body
B. The heat gained by the hotter body will be less than the heat lost by the colder body
c. The heat gained by the hotter body will be greater than the heat lost by the colder body
D. The heat lost by the hotter body will be equal to the heat gained by the colder body


If \( X, Y \) are independent then \( S D(X- \)
\( \boldsymbol{Y}) \) is:
\( \mathbf{A} \cdot S D(X)-S D(Y) \)
в. \( S D(X)+S D(Y) \)
c. \( \sqrt{S D(X)+S D(Y)} \)
D. None of these


The electronic configuration of \( G d^{2+} \) is (atomic number of \( G d \text { is } 64) \)
\( \mathbf{A} \cdot[X e] 4 f^{8} \)
\( \mathbf{B} \cdot[X e] 4 f^{7} \)
\( \mathbf{c} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
D \( \cdot[X e] 4 f^{7} 5 d^{1} \)


Find the area of the triangle formed by the line \( y=2 x+4 \) and coordinate
axes


\( \ln \operatorname{an} A P a=5, d=3, a_{n}=50 \) find \( n \)
and \( \boldsymbol{S}_{n} \)


Assertion
The electrical conductivity of a gas
increases when \( X \) -rays or \( \gamma \) -rays pass through it
Reason
lonization in the gas is produced by \( x \)
rays or \( \gamma- \) rays
A. Assertion is True and Reason is True; Reason is a correct explanation of Assertion
B. Assertion is True and Reason is True but Reason is not a correct explanation of Assertion
c. Assertion is True and Reason is False
D. Assertion is False and Reason is True


Define coefficient of mutual induction.
If in the primary coil of a transformer, the current decreases from \( 0.8 A \) to
\( 0.2 A \) in 4 milliseconds, calculate the
induced e.m.f in the secondary coil. Mutual inductance is \( 1.76 H \)


One solid sphere and disc of same
radius are falling along an inclined plane without slipping. One reaches
earlier than the other due to
A. Different radius of gyration
B. Different sizes
c. Different friction
D. Different moment of inertia


When an electronjumps from \( n_{1} \) th orbit
to \( n_{2} \) th orbit then the formula for energy
radiated out is
A \( . E_{1}-E_{2}=h v \)
в. \( E_{2}-E_{1}=h v \)
c. \( h v=\frac{E_{1}+E_{2}}{2} \)
D. \( h v=\frac{E_{1}}{E_{2}} \)


Solve the following differential equation \( \frac{d y}{d x}=x^{2} \)


Reflection can occur on :
A. transparent surfaces
B. glass
c. opaque surfaces
D. a and


How many grams of sucrose must be
added to \( 320 g \) of water to lower the
vapour pressure by \( 1.5 m m H g \) at \( 25^{\circ} C \)
\( ? \)
(Given: The vapour pressure of water at
\( 25^{\circ} \mathrm{C} \) is \( 23.8 \mathrm{mm} \) Hg and molar mass
of sucrose is \( 324.3 g / m o l \) )
A. \( 21.5 g \)
в. \( 140 g \)
c. \( 363.36 g \)
D. \( 160.12 g \)


Three uniform sphere, each having mass \( m \) and radius \( r, \) are kept in such a way that each touches the other two.
The magnitude of the gravitational force on any sphere due to the other two is
A \( \cdot \frac{G m^{2}}{r^{2}} \)
в. \( \frac{G m^{2}}{4 r^{2}} \)
c. \( \frac{\sqrt{3} G m^{2}}{4 r^{2}} \)
D. \( \frac{\sqrt{3} G m^{2}}{r^{2}} \)


A positive charge and a negative charge are held in place and initially form a
dipole. Then a uncharged conducting bar is placed in between them.

How is the force between the charges
affected?
A. The force increases.
B. The force is unaffected.
c. The force decreases.
D. The answer cannot be determined.


Two circles of radii \( 10 \mathrm{cm} \) and \( 8 \mathrm{cm} \)
intersects each other and the length of
the common chord is \( 12 \mathrm{cm} \), find the
distance between their centers.
A. \( 2 \mathrm{cm} \)
в. \( (8+2 \sqrt{7}) \) ст
\( c .8 \mathrm{cm} \)
D. \( 2 \sqrt{7} \) cm


Which are heavier than dry air?
This question has multiple correct options
A. Moist air
в. \( S O_{2} \)
\( c \cdot C l_{2} \)
D. \( O_{2} \)


Chemically, cytokinins are related to
A. Carotenoid
B. Terpenes
c. Aminopurines
D. Indole


Find \( 20^{t h} \) term from the end of an A.P
\( \mathbf{3}, \mathbf{7}, \mathbf{1 1}, \dots \dots \dots \dots \mathbf{. 4 0 7} \)


The atomic radii of cerium and
promethium are quite similar because
A. they belong to the same period in periodic table
B. they have similar electronic configuration
C. f-orbitals have poor shielding effect
D. nuclear charge is higher on cerium than promethium


Which of the following statements
about ethylmethylamine is true?
This question has multiple correct options
A. It is a dialkylamine.
B. It is a tertiary amine.
C. Its IUPAC name is N-methylaminoethane.
D. Its IUPAC name is N-ethylaminomethane.


How to find atomic mass of any
element, explain.


Basal placentation occurs in
A. Poaceae
B. Solanaceae
c. Malvaceae
D. Liliaceae


A gas expands from 1.5 to 6.5 L against a
constant pressure of 0.5 atm and during
this process the gas also absorbs \( 100 \mathrm{J} \) of heat. The change in the internal energy of
the gas is:
A. 153.3 J
в. 353.3 J
c. -153.3 J
D. -353.3 J


How many bricks, each measuring
\( 25 c m \times 12.5 c m \times 7.5 c m \) will be
needed to construct a wall \( 15 \mathrm{m} \) long,
1.8 \( m \) high and \( 37.5 \mathrm{cm} \) thick?
A. 4400
B. 4660
\( c .4320 \)
D. 4575


A converging lens of focal length 6.25 \( \mathrm{cm} \) is used as a magnifying glass. If near point of the observer is \( 25 \mathrm{cm} \) from the eye and the lens is held close to the eye, then the magnification is :
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D. 10


At low temperatures \( _{\text {thpe }} \) of thermometer is used.
A. mercury thermometer
B. water thermometer
c. alcohol thermometer
D. thermometers cannot be used


Name of the simplest hydrocarbon is


Find the centre of the circle passing through (6,-6),(3,-7) and (3,3)


A person, exerting a steady force of
\( 200 N, \) pushes a box of mass \( 50 k g \)
across a flat wooden floor. If the box
does not move while he pushes. Find out
the coefficient of kinetic friction
between the box and the floor?
A . 0.2
B. 0.4
c. 0.5
D. 0.6
E . 0.8


Find \( : \int \frac{(2 x-5) e^{2 x}}{(2 x-3)^{3}} d x \)


Out of 7 consonants and 4 vowels, words
are formed each having 3 consonants
and 2 vowels. The number of such words
that can be formed is
A . 210
B. 25200
c. 2520
D. 302400


Name the following part from the adjacent figure where 'O' is the center of
the circle.
\( \boldsymbol{A O} \)


What is the minimum value of force ( in following two cases ) required to pull a block of mass \( \mathrm{m} \) on a horizontal surface
having coefficient of friction \( \mu \) ? Also
find the angle this force makes with the horizontal.


A student noted the number of cars
passing through a spot on a road for
100 periods each of 3 minutes and summarised it in the table given below.
Find the mode of the data
Number \( \begin{array}{ll}0- & 10 \\ 10 & 2\end{array} \) 30 of cars \( \begin{array}{ll}10- & 2 \\ 20 & 3\end{array} \) \( 20- \)
30 40
Frequency 14


Match list I with list II and choose the
correct answer.
\( \begin{array}{lllll} & \text { List } 1 & & \text { List II } \\ \text { (A) } & \text { Hypothalamus } & \text { (1) } & \begin{array}{l}\text { Sperm } \\ \text { lysine }\end{array} \\ \text { (B) } & \text { Acrosome } & \text { (2) } & \text { Estrogen } \\ \text { (C) } & \begin{array}{l}\text { Graafian } \\ \text { follicle }\end{array} & \text { (3) } & \text { Relaxin } \\ \text { (D) } & \text { Leydig cells } & \text { (4) } & \text { GnRH } \\ \text { (E) } & \text { Parturition } & \text { (5) } & \text { Testosterone }\end{array} \)
\( A \)
(A)- (4), (B)- (1), (C)- (2), (D)- (3), (E)- (5)
B. \( (A)-(2),(B)-(1),(C)-(4),(D)-(3),(E)-(5) \)
\( c \)
(A)- (2), (B)- (1), (C)- (5), (D)- (4), (E)- (3)
D.
\( E \cdot(A)-(5),(B)-(1),(C)-C \)
(3) \( D_{D} \) (2)
(E)- (4)


Prove that \( \boldsymbol{x}^{4}+\boldsymbol{4}=(\boldsymbol{x}+\mathbf{1}+\boldsymbol{i})(\boldsymbol{x}+ \)
\( \mathbf{1}-\boldsymbol{i})(\boldsymbol{x}-\mathbf{1}+\boldsymbol{i})(\boldsymbol{x}-\mathbf{1}-\boldsymbol{i}) \)


Calculate the molarity of each of the
ions in a solution when 3.0 litre of \( 4.0 \mathrm{M} \)
NaCl and 4.0 litre of \( 2.0 \mathrm{M} \) CaCl\( _{2} \) are
mixed and diluted to 10 litre.


The velocity of the wave
\( \mathbf{A} \cdot 80 \mathrm{cm} / \mathrm{sec} \)
B. \( 112 \mathrm{cm} / \mathrm{sec} \)
c. \( 120 \mathrm{cm} / \mathrm{sec} \)
D. \( 140 \mathrm{cm} / \mathrm{sec} \)


Atomic mass of chlorine atom is
A . 35.
B. 16
c. 32
D. 24


The rate at which a body radiates heat depends on-
A. its temperature
B. its colour
c. its nature (dull or shiny)
D. all of these


Which one of the following has the maximum number of \( \boldsymbol{P}-\boldsymbol{O H} \) bonds?
A \( . H_{3} P O_{2} \)
в. \( H_{3} P O_{4} \)
c. \( H_{3} P O_{3} \)
D. \( H_{4} P_{2} O_{5} \)
E \( . H_{4} P_{2} O_{6} \)


It is safer to use mobile and cordless
phone during lightning because?
A. They are wireless
B. Less chances of getting in contact with lightning
c. Both a \( \& \mathrm{b} \)
D. None of the above


Simplify the multiplication of complex numbers: \( (\boldsymbol{x}, \boldsymbol{y}) \times(\mathbf{1}, \mathbf{0}) \)
A. \( (-x,-y) \)
в. \( (y, x) \)
c. \( (x, y) \)
D. None of these


A stone is thrown upwards with a
velocity \( v \) from the top of a tower. It
reaches the ground with a velocity \( 3 v \) What is the height of the tower?
A \( \cdot \frac{2 v^{2}}{g} \)
B. \( \frac{3 v^{2}}{g} \)
c. \( \frac{4 v^{2}}{g} \)
D. \( \frac{6 v^{2}}{g} \)


The following flow diagram represents the manufacturing of sodium
carbonate?
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{O}_{2} \longrightarrow \)
\( \left(N H_{4}\right)_{2} C O_{3}(a q) \stackrel{(a)}{\longrightarrow} N H_{4} H C O_{3} \stackrel{(b)}{\longrightarrow} \)
\( \boldsymbol{N} \boldsymbol{a} \boldsymbol{H} \boldsymbol{C O}_{3}+(\boldsymbol{c}) \)
\( \downarrow(d) \)
\( N a_{2} C O_{3}+C O_{2}+H_{2} O \)
Which of the following option describes the underlined reagents, products and reaction conditions?
A \( \cdot \) (a) - Carbon dioxide, \( (b)-N a C l,(c)-N H_{4} C l, \) (d) - Heat
B. (a) - Carbon dioxide, (b) - \( N a C l \), (c) \( -N H_{4} C l \), (d) Catalyst
c. (a) - Higher tempt., (b) - \( N a C l \), (c) \( -N H-4 C l \), (d) Heat
D. (a) - Higher pressure, (b) - \( N a C l \), (c) \( -N H_{4} C l \), (d) Catalyst


A ball is thrown with a velocity \( v_{0} \) and it
returns to the spot of throw. Plot \( \boldsymbol{v}-\boldsymbol{t} \)
and \( \boldsymbol{v}-\boldsymbol{x} \) graphs.


If \( P \) is a point \( (x, y) \) on the line \( y=-3 x \)
such that \( \boldsymbol{P} \) and \( \boldsymbol{Q}(\boldsymbol{3}, \boldsymbol{4}) \) are on opposite
side of the line \( 3 x-4 y=8, \) then:
A \( \cdot x>\frac{8}{5}, y<\frac{-8}{15} \)
В. \( x>\frac{8}{15}, y<-\frac{8}{5} \)
c. \( x=\frac{8}{15}, y=\frac{-8}{5} \)
D. \( x=2, y=-2 \)


The COM of body in pure rotation does-
A. translation
B. rotation
C. remain steady
D. none of these


The statements regarding preparations of ammonia is/are :
(i) Raw materials in cyanamide process are limestone, coke and nitrogen gas.
(ii) On heating nitrogen gas and \( \boldsymbol{C a}(\boldsymbol{O H})_{2}, \boldsymbol{N} \boldsymbol{H}_{3} \) is formed
(iii) In Haber's process \( 100 \% \) yield of
\( N H_{3} \) is possible at \( 500^{\circ} C \) and 250 atm
A. all are correct
B. i and ii
\( c \)
D. i and iii


If aqueous solution of \( A l_{2}\left(S O_{4}\right)_{3} \) is
mixed with \( N a_{2} C O_{3} \) which of the
following will be one the products?
A \( \cdot A l_{2}\left(C O_{3}\right)_{3} \)
В \( \cdot A l(O H)_{3} \)
c. \( _{A l}\left(H C O_{3}\right)_{3} \)
D. \( _{N a A l_{2}}\left(C O_{3}\right)_{2} \)


Four equal charges \( +Q \) are placed at the four corners of a body of side \( a \) each. Work done in removing a charge \( -\boldsymbol{Q} \) from its centre to infinity is
A. zero
В. \( \frac{\sqrt{2} Q^{2}}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{\sqrt{2} Q^{2}}{\pi \varepsilon_{0} a} \)
\( ^{\mathrm{D}} \cdot \frac{Q^{2}}{2 \pi \varepsilon_{0} a} \)