A cube of side \( 10 \mathrm{cm} \) encloses a charge
of \( 0.1 \mu C \) at its centre.What is the
number of lines of force through each
face of the cube
A \( \cdot 1.13 \times 10^{11} \)
В. \( 1.13 \times 10^{6} \)
c. \( 1.13 \times 10^{23} \)
D. 1883


Assertion
Inspiration occurs when there is a negative pressure in the lungs with respect to the atmospheric pressure.
Reason
During inspiration, a decrease in pulmonary volume increases the intrapulmonary pressure than atmospheric pressure which forces the air from
outside to move into the lungs.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the following circuit, the switch is
closed at \( t=0 . \) Find the currents
\( i_{1}, i_{2}, i_{3} \) and \( d i_{3} / d t \) at \( t=0 \) and \( a t t= \)
\( \infty . \) Initially, all currents are zero


A solution containing
0.1 mole of naphthalene and 0.9 mole of benzene is cooled out until some benzene freezes
out. The solution is then decanted off
from the solid and warmed up to \( 353 \mathrm{K} \) where its vapour pressure was found to
be 670 torr. The freezing point and boiling point of benzene are \( 278.5 \mathrm{K} \) and
\( 353 \mathrm{K} \) respectively and its enthalpy of fusion is \( 10.67 \mathrm{kJ} \) mol \( ^{-1} \). Calculate the
depression in freezing point for original solution to the nearest integer. Assume ideal behaviour


Find the value of \( \frac{d y}{d x} \) at \( \theta=\frac{\pi}{4} \) if \( x= \) \( \boldsymbol{a} e^{\theta}(\sin \theta-\cos \theta) \) and \( y=a e^{\theta}(\sin \theta+ \)
\( \cos \theta) \)


Critical elements are
A. Na, K and ca
B. N, P and Mg
c. \( N, \) P and \( \kappa \)
D. Mn, B and Mo


The sum of an infinitely decreasing
geometric progression is equal to 4 and the sum of the cubes of its terms is
equal to \( 192 . \) Find the first term and the
common ratio of the progression.


What is Misch metal? Give its
composition and uses.


Two wires carrying current in opposite
directions are placed a distance \( a \)
apart Which of the following will cause the greatest increase in the magnitude of the force between the wires?
A. Doubling the current in one wire.
B. Doubling the current in both wires.
c. Doubling the distance between the wires to \( 2 a \)
D. Decreasing the distance between the wires to
E. Running the currents in the same direction


Electromagnets are made of soft iron
because soft iron has
A. high susceptibility and low retentivity
B. low susceptibility and high retentivitty
c. low susceptibility and low retentivity
D. high susceptibility and high retentivity


IUPAC name of \( N a_{3}\left[C o\left(N O_{2}\right)_{6}\right] \) is
A. sodium hexanitrocobaltate (III)
B. sodium cobaltnitrate
C. trisodium hexanitrocobalt
D. hexanitrocobalt (III) trisodium complex


Determine the distance from (5,10) to
the line \( x-y=0 \)
A . 3.86
в. 3.54
c. 3.68
D. 3.72
E. none of these


Some of the most profound statements
on the nature of science have come
from Albert Einstein, one of the greatest
scientists of all time. What do you think did Einstein mean when he said : "The
most incomprehensible thing about the world is that it is comprehensible"?


When ethyl alcohol and acetic acid mixed together in equimolecular proportions, equilibrium is attained when two-third of the acid and alcohol
are consumed. The equilibrium constant of the reaction will be:
A . 0.4
B. 4
c. 40
D. 0.04


If the mass of electron is \( 9.11 \times 10^{-31} \)
kg. Planck's constant is \( 6.626 \times 10^{-34} \)
J-s and uncertainty in position is \( 0.1 A \) then uncertainty in velocity is?
A \( \cdot 5.79 \times 10^{8} \mathrm{m} / \mathrm{s} \)
В. \( 5.79 \times 10^{5} \mathrm{m} / \mathrm{s} \)
c. \( 5.79 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 5.79 \times 10^{7} \mathrm{m} / \mathrm{s} \)


Electricity at rest is called
A. Dynamic Electricity
B. Static Electricity
C. Both (a) and (b)
D. None of these


Number of waves made by the pion when orbiting in third excitation state
are
\( A \cdot 3 \)
B. 6
\( c \cdot 3 z^{2} \)
\( D \cdot 4 z^{2} \)


The area under the velocity-time graph
between any two instant \( t=t_{1} \) and \( t= \)
\( t_{2} \) gives the displacement covered in
time \( \delta t=t_{2}-t_{1} . \) This is true:
A. only if the particle moves with a uniform velocity
B. only if the particle moves with a uniform acceleration
c. only if the particle moves with an acceleration increasing at a uniform rate
D. in all cases irrespective of whether the motion is one of uniform velocity, or of uniform acceleration or of variable acceleration


The thermodynamic efficiency of cell is given by:
A. \( \Delta H / \Delta G \)
в. \( \frac{n F E}{\Delta G} \)
c. \( \frac{-n F E}{\Delta H} \)
D \( \cdot n F E^{\ominus} \)


The colloidal system consisting of a liquid adsorbate in a solid adsorbent is termed as:
A . Aerosol
B. Foam
c. Emulsion
D. Gel


The size of \( N b \) is very similar to:
A. \( L a \)
в. \( H f \)
c. \( T a \)
D. \( W \)


Which of the following takes place in
discharge process at anode?
\( \mathbf{A} \cdot P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+2 H_{2} O \)
B \( \cdot P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \)
\( \mathbf{c} \cdot P b S O_{4}+2 e^{-} \rightarrow P b+S O_{4}^{2} \)
\( \mathbf{D} \cdot P b S O_{4}+4 H_{2} O \rightarrow P b O_{2}+8 H^{+}+S O_{4}^{2-}+2 e^{-} \)


A spherical rock weighs \( 1000 N \) on a
certain planet. The planet is a billion times as massive as the rock and has a
radius that is a billion times as great as that of the rock's radius.

How much force does the rock exert on
the planet?
A. A thousand-billion Newtons
B. A thousand-billion-billion Newtons
c. A thousand billionths of a Newton
D. A thousand billion-billionths of a Newton
E. A thousand Newtons


Form the differential equation
corresponding to \( y=c x-2 c^{2} \) where \( c \)
is a parameter


If no force acts on a body it will
A. change shape
B. move with increased speed
C. either remain in rest or move with uniform speed
D. break up


The magnification of an object placed in front of a convex lens of focal length
\( 20 \mathrm{cm} \) is \( +2 . \) To obtain a magnification
of \( -2, \) the object has to be moved a distance equal to:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


The distance between an object and its real image formed by a convex lens
cannot be
A. greater than \( 2 f \)
B. less than \( 2 f \)
c. greater than \( 4 f \)
D. less than \( 4 f \)


\( \boldsymbol{X} \) has three children in his family. Probability of atleast two girls in the family is....
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{4} \)


A ball of mass \( m \) and radius \( r \) is
released in a viscous liquid. The density of the liquid is negligible compared to that of the ball.The value of its terminal
velocity is proportional to:
A \( \cdot \frac{1}{r} \) only
в. \( \frac{m}{r} \)
c. \( \sqrt{\frac{m}{r}} \)
D. m only


The free energy of the formation of \( ^{\prime} N O^{\prime} \)
is \( 78 k J / m o l \) at the temperature of an
automobile engine \( (1000 K) . \) What is
the \( K_{C} \) equilibrium constant for this
reaction at \( 1000 K \)
\( \frac{1}{2} N_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons N O(g) \)
A . \( 8.4 \times 10^{-5} \)
В. \( 7.1 \times 10^{-9} \)
c. \( 4.2 \times 10^{-10} \)
D. \( 1.7 \times 10^{-19} \)


What is the angle of incidence for an
equilateral prism of refractive index \( \sqrt{\mathbf{3}} \) so that the ray is parallel to the base inside the prism?
\( A \cdot 30 \)
B . 45
\( c \cdot 60 \)
D. Either \( 30^{\circ} \) or 60


Which one of the following is a scalar quantity?
A. Displacement
B. Velocity
c. Acceleration
D. Linear momentum
E. Kinetic energy


The correct sequence of linkage among N of base, \( C \) of sugar and \( P \) of phosphate in adenosine-5'triphosphate is:
A. C-P-N-P-P
B. N-P-C-P-P-P
c. p-c-N-p-p
D. P-P-P-C-N


There are four different white balls and
four different black balls. The number of
ways that balls can be arranged in a row so that white and black balls are placed alternately is
\( A \cdot(4 !)^{2} \)
B. \( 2(8 !)^{2} \)
\( c \cdot 4 \)
\( D \cdot(4 !)^{3} \)


An electron in hydrogen atom stays in 2nd orbit for \( 10^{-8} \). How many, revolutions will it make till it jumps to the ground state?


Assertion
\( X e F_{6} \) can be used as an oxidising
agent.
Reason
Oxidation state of \( \mathrm{Xe} \) in \( X e F_{6} \) is +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 true but Reason is false
D. Assertion is false but Reason is true


Given \( A=\hat{i}+2 \hat{j}-3 \hat{k} . \) When a vector
\( B \) is added to \( A, \) we get a unit vector
along \( x \) -axis. Then \( B \) is
\( \mathbf{A} \cdot-2 \hat{j}+3 \hat{k} \)
В. \( -1 \hat{i}-2 \hat{j} \)
c. \( -1 \hat{i}+3 \hat{k} \)
D. 2 \( \hat{j}-3 \hat{k} \)


Given the velocity-time graph. How can
it be used to find the distance of the
body in a given time.
A. The total area under velocity-time graph
B. The net area under velocity-time graph
c. slope of velocity-time graph
D. negative slope of velocity-time graph


Myelin sheath has layers of fat and
protein
A. Upto 100
B. 10-20
c. Two each
D. one each


Factory A Factory B
No. of wage earners 250 200
Average daily wage Rs. २.०० Rs. 2.50
The average of daily wages for the
earners of the two factories combined is
A. Rs. 2.12
B. Rs. 2.06
C. Rs. 2.20
D. Rs. 2.22


Which nomeclature system is employed for naming plants:
A. Vernacular
B. Binomial
c. Monomial
D. Polynomial


Which one of the following is true?
\( \mathbf{A} \cdot \tan x>1 ; 45<x<90^{\circ} \)
B. \( \sin x>\frac{1}{2} ; 0^{\circ}<x<30^{\circ} \)
\( ^{\mathbf{C}} \cos x>\frac{1}{2} ; 60^{\circ}<x<90^{\circ} \)
D. \( \sin x=\cos x \) for some value of \( x ; 30^{\circ}<x<45^{\circ} \)


Bleaching action of \( C a O C l_{2} \) is due to
This question has multiple correct options
A. Nascent oxygen
в. \( C a \)
c. \( C l \)
D. \( H C l \)


How do the following properties vary in a Period and in a Group?
(A) Atomic radius
(B) Ionization energy
(C) Electronegativity
(D) Electropositivity


Why does \( H^{+} \) always get associated
with other atoms or molecules?
A. lonisation enthalpy of hydrogen resembles that of alkali metals.
B. Its reactivity is similar to halogens.
c. It resembles both alkali metals and halogens.
D. Loss of an electron from hydrogen atom results in a nucleus of very small size as compared to other atoms or ions. Due to small size it cannot exist freely


Aluminium and copper are extracted from their oxide and sulphide ores
respectively. Which of the following is
correct?
I. Copper is extracted by the auto reduction of copper oxide by copper sulphide.
II. Aluminium cannot be obtained by
chemical reduction due to its strong
affinity for oxygen.
III. In electrometallurgy of \( A l \), graphite is used as cathode to avoid reoxidation
of \( A l \) into \( A l_{2} O_{3} \) by preventing
formation of \( \boldsymbol{O}_{2} \)
IV. Sulphide ores of copper are difficult
to be reduced than the oxide ores.
A. \( I, I I, I V \)
B. II and III
c. \( I I I \)
D. II and \( I V \)


\( \boldsymbol{n} \in \boldsymbol{N},\left(\frac{1+i}{\sqrt{2}}\right)^{8 n}+\left(\frac{1-i}{\sqrt{2}}\right)^{8 n}= \)
\( A \)
B.
\( c \)
D. -


Two springs have their force constants
\( K_{1} \) and \( K_{2} . \) Both are stretched till their
elastic energies are equal. If the
stretching forces are \( F_{1} \) and \( F_{2} \) then
\( F_{1}: F_{2} \) is equal to
A \( \cdot K_{1}: K_{2} \)
в. \( K_{2}: K_{1} \)
c. \( \sqrt{K_{1}}: \sqrt{K_{2}} \)
D. \( K_{1}^{2}=K_{2}^{2} \)


Given that \( \boldsymbol{X} \sim \boldsymbol{B}(\boldsymbol{n}=\mathbf{1 0}, \boldsymbol{p}) . \) If
\( \boldsymbol{E}(\boldsymbol{X})=\mathbf{8}, \) then the value of \( \boldsymbol{p} \) is
A . 0.6
в. 0.7
c. 0.8
D. 0.4


State the cause of the apparent motion of the sun from east to west.


The ratio of coefficient of \( x^{3} \) and \( x^{4} \) in
expansion \( (1+x)^{12} \) is:
\( A \cdot \frac{4}{9} \)
B . \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.


A compound of vanadium possesses a
magnetic moment of 1.73 BM. The oxidation state of vanadium in this
compounds is :
A
B. 2
\( c \cdot 4 \)
D. can not be predicted


The velocity of the electron in the first orbit of H-atom as compared to the velocity of light is:
A \( \cdot \frac{1}{10} t h \)
B. \( \frac{1}{100} t h \)
c. \( \frac{1}{1000} \) th
D. None of the above


The power (in diopters) of an equiconvex lens with radii of curvature
of \( 10 \mathrm{cm} \) and refractive index of \( 1.6 \mathrm{is} \)
A. -12
B. +12
\( c .+1.2 \)
D. \( -1 / 2 \)


Three binders and four notebooks cost a
total if \( \$ 4.32 . \) One binder and five note-
books cost \( \$ 3.97 . \) What is the cost of
one notebook?
A . 0.50
B. 0.69
c. 0.72
D. 0.79


According to Werner's theory the primary valency and secondary valency in complex \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} \) is
respectively:
\( A \cdot 3,3 \)
B. 3,6
\( c \cdot 6,3 \)
\( D \cdot 4,2 \)


Potentiometer measures the potential difference more accurately than a voltmeter because:
A. it has a wire of high resistance
B. it has a wire of low resistance
c. it does not draw current from external circuit
D. it draws a heavy current from external circuit


If every particle of fluid has irregular flow, then flow is said to be
A. laminar flow
B. turbulent flow
C. fluid flow
D. both \( A \) and \( B \)


Four identical charges of charge \( q \) are
placed at the corners of a square of
sides r as shown above. Find the
magnitude of the net force acting on a
charge of magnitude \( 2 q \) placed in the
center of the square.
\( \mathbf{A} \cdot \mathbf{0} \)
\( \mathbf{B} \cdot \frac{2 k q^{2}}{r^{2}} \)
\( \mathbf{c} \cdot \frac{4 k q^{2}}{r^{2}} \)
D. \( \frac{16 k q^{2}}{r^{2}} \)
E \( \cdot \frac{\text { g } 2 k q^{2}}{r^{2}} \)


A straight wire of finite length carrying
current I subtends an angle of \( 60^{\circ} \) at
point \( P \) as shown. The magnetic field at
P is:
\( ^{\mathrm{A}} \cdot \frac{\mu_{0} I}{2 \sqrt{3} \pi x} \)
B. \( \frac{\mu_{0} I}{2 \pi x} \)
c. \( \frac{\sqrt{3} \mu_{0} I}{2 \pi x} \)
D. \( \frac{\mu_{0} I}{3 \sqrt{3} \pi x} \)


The rate reaction is measured either by
an increase in the amount of
products or by the decrease in the amount of reactants per unit interval of time.
A. True
B. False


If a coin is tossed, then the probability
that a head turns up is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D. \( \frac{1}{6} \)


Mirage is an example of


Check whether the given equation is a
quadratic equation or not. \( x^{2}+2 \sqrt{x}-3 \)
A. True
B. False


The number of boys and girls in a class are in the ratio \( 7: 5 . \) The number of boys
is 8 more than the number of girls. What is the total class strength?
\( \mathbf{A} \cdot 48 \)
B. 47
c. 46
D. 45


Coagulation value of the electrolytes
\( A l C l_{3} \) and \( N a C l \) for \( A s_{2} S_{3} \) sol are
0.093 and 52 repectively. How many
times \( A l C l_{3} \) has greater coagulating
power than \( N a C l ? \)
A . 930
в. 520
\( c .560 \)
D. None of these


What fraction of the assimilated energy
is used in respiration by the herbivores?
A. 10 percent
B. 60 percent
c. 30 percent
D. 80 percent


Identify the wrong statement for long
form of periodic table.
A. It reflects the sequence of filling the electrons in the order of energy levels \( \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N} \)
B. It helps to predict the stable valence states of the elements
C. It reflects trends in physical and chemical properties of the elements
D. It helps to predict the relative ionicity of the bond between any two elements


Which of the following does not participate in Carbylamine reaction?
A. Aniline
B. Chloroform
c. Ethanal
D. кон


The repeating unit of PTFE
is
A. \( C l_{2} C H-C H_{3} \)
в. \( F_{2} C=C F_{2} \)
\( \mathbf{c} \cdot F_{3} C-C F_{3} \)
D. \( F C l C=C F_{2} \)


Find two fractions having 7 and 9 for their denominators, and such that their sum is \( 1 \frac{10}{63} \)


If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{2}}, \) then what is \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\boldsymbol{\pi} \)
equal to?
\( \mathbf{A} \cdot(1+\pi) e^{\pi^{2}} \)
В . \( 2 \pi e^{\pi^{2}} \)
\( \mathbf{c} \cdot 2 e^{\pi^{2}}^{2} \)
D \cdot \( e^{\pi^{2}} \)


(i) Why does the Sun appear red at
sunrise?
(iii) Name the subjective property of
light related to its wavelength.


The molecular interactions responsible for hydrogen bonding in HF:
A. ion induced dipole
B. dipole dipole
c. dipole induced dipole
D. none


The reagents \( X \) and \( Y \) are respectively:
A \( \cdot X=C H_{3} C O C l / A l C l_{3}, Y=K M n O_{4} / O H^{\Theta} / \Delta \)
(acidification)
B. \( X=C H_{3} C H_{2} C l / A l C l_{3}, Y=C r O_{3} / H^{+} / \Delta \)
C. \( X=C H_{3} C O C l / A l C l_{3}, Y=I_{2} / N a O H, \) (acidification)
D. \( X=K M n O_{4} / O H^{\Theta} / \Delta, \) (acidification), \( Y= \)
\( C H_{3} C H_{2} C l / A l C l_{3} \)


Find the slope of a line passing through the following points:
\( \left(a t_{1}^{2}, 2 a t_{1}\right) \) and \( \left(a t_{2}^{2}, 2 a t_{2}\right) \)
A. \( \frac{2}{t_{2}-t_{1}} \)
в. \( \frac{2}{t_{2}+t_{1}} \)
c. \( \frac{1}{t_{2}+t_{1}} \)
D. None of these


Line segment \( A B \) is parallel to another
ine-segment \( C D, O \) is the midpoint of
AD.Show that \( \triangle A O B \cong \triangle D O C \)


\( \frac{0}{\frac{0}{6}} \)


Equal masses of \( S_{2}, S_{4} \) and \( S_{8} \) are
taken. Highest number of free species are present in:
A. \( S_{2} \)
в. \( S_{4} \)
\( \mathrm{c} \cdot S_{8} \)
D. all have same number of molecule


The value of \( \frac{\overline{\mathbf{5}}}{\mathbf{5}} \) is
\( A \cdot \frac{2}{25} \)
B. \( \frac{10}{5} \)
\( c \cdot \frac{2}{5} \)
D. None of the above


In the following figure the current
through \( 4 \Omega \) resistor is
\( 4 \cdot 1.4 \mathrm{A} \)
B. \( 0.4 \mathrm{A} \)
\( c \cdot 1.0 A \)
D. 0.7


National Forest Policy of India has recommended (i) forest cover for the plains and (ii) for the hills.
\( A \cdot \) (i) 33\% (ii) 67\%
B. (i) 67\% (ii) 33\%
c. (i) 50\% (ii) 50\%
D. (i) 40\% (ii) 60\%


The compound which gives off oxygen on moderate heating is :
A. Cupric oxide
B. Mercuric oxide
c. zinc oxide
D. Aluminium oxide


The sides \( A B, B C, C A \) of a triangle \( A B C \) have 3,4 and 5 interior points
respectively on them. The number of triangles that can be constructed using these points as vertices is
A . 205
в. 210
c. 315
D. 216


Derive an expression for the intensity of magnetic field on broad side on position due to a bar magnet.


Which of the following is a transcription factor produced by a regulatory gene?
A. A promoter
B. An operon
c. A cofactor
D. A repressor


Green-house gases are
A. Absorbers of long wave radiations from earth.
B. Transparent to both solar radiation and long wave radiation from earth.
C. Absorbers of solar radiation for warming the atmosphere of earth.
D. Transparent to emissions from earth for passage into
outer space.


In the reaction of phenol with \( \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3} \)
and aqueous \( N a O H, \) the electrophile attacking the ring is:
A. \( C H C l_{3} \)
в. \( C H C l_{2} \)
\( \mathbf{c} \cdot: C C l_{2} \)
D. \( C O C l_{2} \)


Jaundice is due to
A. Excessive intake of curcuma
B. Excessive intake of Sugar
c. Pork
D. Contaminated water


Biochemical reactions are carried out
by enzymes
A. By decreasing the energy of the reactants
B. By increasing the activation energy of the reaction
C. By decreasing the activation energy of the reaction
D. By increasing the energy of the products of the reaction
E. By decreasing the energy of the products of the reaction


Two coherent sources of intensity ratio
9: 4 produce interference. The intensity
ratio of maxima and minima of the
interference pattern is:
\( \mathbf{A} \cdot 13: 5 \)
B. 5: 1
c. 25: 1
D. 3: 2


Two particles \( A \) and \( B \) have de-Broglie's wavelengths \( 30 A \) and \( 20 A, \) combined to form a particle C. Momentum is conserved in this process. The possible de-Broglie's wavelength of C is :
(the motion is one dimensional)
A \( \cdot 12 \AA \)
в. 20 ,
\( c .10 \hat{A} \)
D. 22 a


A polymer of prop- 2 -ene nitrile is called:
A. Saran
B. Orlon
c. Dacron
D. Tereylene


Right sequence in increasing
magnitude is:
A. decade, second, week, nanosecond
B. nanosecond, week, second, decade
c. nanosecond, second, week, decade
D. nanosecond, decade, second, week


The equation \( _{-}-_{-}-_{-}--_{-}- \) and \( 2 x+ \)
\( 2=0 \) have the same solution.
A \( . x-1=0 \)
B . \( x+1=0 \)
c. \( x-2=0 \)
D. \( x+2=0 \)


Chief components of Hill's reaction used in Blackman's reaction are
A. ATP and NAD
B. ADP and NADP
c. ATP and \( N A D P H_{2} \)
D. All of the above


The laws governing the movement of celestial bodies are studied under the
branch of physics called
A. spintronics
B. astrophysics
c. nuclear physics
D. nano physics


Consider the time interval \( t=2.0 s \) to
\( \boldsymbol{t}=\mathbf{4} . \mathbf{0} \boldsymbol{s} \)
The magnetic field is perpendicular to
the plane of the loop.


Which of the following \( 3^{\circ} \) alcohols does
propyl ester give during reaction with
Et MgBr?
\( A \)
B.
\( c \)
\( D \)


composite tube as shown in the Figure
14.24. The radius of the semicircular
portion of the tube is \( r . \) The speed of
sound in air is \( v . \) The source of sound is
capable of giving sound of varied
frequency. If \( n \) is an integer then frequency for maximum intensity is given by:
\( \mathbf{A} \cdot n v / r \)
в. \( n v / r(\pi-2) \)
c. \( n v / \pi r r \)
D. \( n v / \pi(r-2) \)


If \( 0 \leq x \leq \pi \) and \( 81^{\sin ^{2} x}+81^{\cos ^{2} x}=30 \)
then \( x \) is equal to:
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{2} \)
c.
D. \( \frac{3 \pi}{4} \)


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


In breathing movements, air volume can be estimated by
A. stethoscope
B. hygrometer
c. sphygmomanometer
D. spirometer


Solve \( \int_{0}^{1}|\boldsymbol{x}| \boldsymbol{d} \boldsymbol{x} \)


Viscosity of a liquid arises due to strong intermolecular forces existing between the molecules. Stronger the intermolecular forces, greater is the viscosity. Name the intermolecular forces
existing in the following liquids: Water and glycerine
A. Hydrogen bonding
B. London forces
c. vander waal 's forces
D. Steric repulsion


Select the incorrect option regarding digestion and absorption of substances in different parts of digestive system.
A. In large intestine, absorption of water, some minerals and drugs take place
B. Absorption of water, simple sugars and alcohol takes place in stomach
c. Small intestine is the principal organ for absorption of nutrients
D. The digestion is completed in large intestine


frictionless surface of an inclined plane,
as shown in the figure. The angle of the
incline suddenly changes from \( 60^{\circ} \) and
\( 30^{\circ} \) at point \( B \)
The block is initially at rest at \( \boldsymbol{A} \)
Assume that collisions between the
block and the incline are totally
inelastic. The speed of the block at point
\( B \) immediately after it strikes the
second incline is
\( \mathbf{A} \cdot \sqrt{60} m / s \)
B. \( \sqrt{45} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot \sqrt{30} m / s \)
D. \( \sqrt{15} \mathrm{m} / \mathrm{s} \)


The mode of the distribution
\begin{tabular}{lccccc}
Marks & 4 & 5 & 6 & 7 & 8 \\
No. of students & 6 & 7 & 10 & 8 & 3 \\
\hline
\end{tabular}
A. 5
B. 6
\( c \cdot 8 \)
D. 10


A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined as
\( f(x)=x^{3}+4 . \) Is it a bijection or not? In
case it is a bijection, then find \( \boldsymbol{f}^{-1}(\mathbf{3}) \)


How many sets had more even than
negative numbers?

Negative and Even Number Distributions
DNegative Numbers DEven Numbers
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D .3 \)


Match the column I with column II and
choose the correct option.
\( \begin{array}{llll}\text { Column I } & & \text { Column II } \\ \begin{array}{l}\text { Synaptonemal } \\ \text { complex }\end{array} & \text { 1) } & \text { Zygotene } \\ \text { b) } & \begin{array}{l}\text { Recombination } \\ \text { nodules }\end{array} & \text { 2) } & \text { Pachytene } \\ \text { c) } & \begin{array}{l}\text { Activation of } \\ \text { recombinase } \\ \text { enzyme }\end{array} & \text { 3) } & \text { Diplotene } \\ \text { d) } & \begin{array}{l}\text { Termination of } \\ \text { chiasmata }\end{array} & \text { 4) } & \text { Diakinesis }\end{array} \)
\( A \cdot a-1, b-2, c-3, d-4 \)
\( B \cdot a-1, b-2, c-4, d-3 \)
\( c \cdot a-1, b-4, c-2, d-3 \)
\( D \cdot a-1, b-3, c-2, d-4 \)


If \( ^{n} C_{6}:^{n-3} C_{3}=33: 4, \) find \( n \)


Magnetic flux through a circuit of
resistance \( 20 \Omega \) is changed from 20 Wb to \( 40 \mathrm{Wb} \) in \( 5 \mathrm{ms} \). Charge passed through the circuit during this time is
A . \( 1 \mathrm{c} \)
B. 2
c. zero
D. \( 0.5 \mathrm{c} \)


Which of the following substances undergo(s) disproportionation reactions under basic medium?
This question has multiple correct options
A. \( F_{2} \)
в. \( P_{4} \)
\( \mathrm{c} \cdot S_{8} \)
D. \( B r_{2} \)


ICBN is
A. International Code of Botanical Naming
B. International Code of Botanical Nomenclature
C. International Class of Botanical Nomenclature
D. International Classification of Botanical
Nomenclature


describe briefly any one way of
inducing e.m.f.


Let 'a' be a positive constant number.
Consider two curves \( C_{1}: y=e^{x}, C_{2} \)
\( y=e^{a-x} . \) Let \( S \) be the area of the part
surrounded by \( C_{1}, C_{2} \) and the \( y \) -axis,
then
A \( \cdot \lim _{a \rightarrow \infty} S=1 \)
B. \( \lim _{a \rightarrow 0} \frac{S}{a^{2}}=\frac{1}{4} \)
C. Range of \( \operatorname{sis}(0, \infty) \)
D. S(a) is neither odd nor even


Molar mass of \( C_{2} H_{6}(\text { in } g) \) is :


The group or radical derived by removal
of one hydrogen atom of an alkyne is known as alkynyl radical.
A. True
B. False


Statement 1: An element that has an
electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3} 4 s^{2} \) is a transition
element.
Statement 2: The transition elements
from scandium to zinc are filling the \( 3 d \)
orbitals.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


Which of the following can be used to
prove that \( \Delta A B C \cong \Delta S R T ? \)
\( A \cdot A S A \)
B. SAS
C . RHS
D. AAA


For a given reaction, pressure of catalyst reduces the energy of
activation by 2 kcal at \( 27^{0} C . \) The rate of reaction will be increased by:
A. 20 times
B. 14 times
c. 28 times
D. 2 times


On the earth, a Sumo of \( 420 \mathrm{kg} \) is checking his reading on a spring balance. To have the same reading of spring balance on the moon, how many Sumos of mass \( 420 \mathrm{kg} \) each should stand on it. Explain. \( \left(g=30 \mathrm{m} \mathrm{s}^{-2}\right) \)
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D.


A capacitor of capacitance \( 10, \mathrm{f} \) is charged to a potential of \( 100 \mathrm{V} \) Now connecting it in parallel with an uncharged capacitor, the resultant potential difference becomes 40 volt.The capacitance of this capacitor is
A \( .2 .5, \mathrm{F} \)
в. \( 5, \) F
\( c .10, F \)
D. \( 15, \) F


Solve: \( 6 \leq-3(2 x-4)<12 \)


A fixed volume of iron is drawn into a
wire of length \( L \). The extension \( x \) produced in the wire by a constant force
\( F . F \) is proportional to
A \( \cdot \frac{1}{L^{2}} \)
в. \( \frac{1}{L} \)
c. \( L^{2} \)
D. \( L \)


Choose the correct statement with
respect to the vapour pressure of a liquid among the following.
A. Increases linearly with increasing temperature.
B. Increases non-linearly with increasing temperature.
c. Decreases linearly with increasing temperature
D. Decreases non-linearly with increasing temperature.


\( \boldsymbol{n} \) is an integer. The largest integer \( \boldsymbol{m} \)
such that \( n^{m}+1 \) divides \( 1+n+n^{2}+ \)
\( \dots . . n^{127}, \) is
A . 127
B. 63
c. 64
D. 32


You have a bag of cotton and an iron bar
each indicating a mass of \( 100 k g \) when measured on a weighing machine. In reality, one is heavier than the other Can you say which one is heavier and why?


Write formulae for all the isomers of the
following. Designate pairs of enantiomers and achiral compounds where they exist.
1-Bromo-4-chlorocyclohexane


The electric field at a point is
A. always continuous
B. continuous if there is no charge at that point
C. discontinuous if there is a charge at that point
D. both
(b) and
(c) are correct


Write the Quadratic equation to find two consecutive odd positive integers, whose product is 323


Answer the following question in one word or one sentence or as per exact requirement of the question.
If \( \boldsymbol{x}<\mathbf{2}, \) then write the value of \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\sqrt{\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4}}) \)


The vertical columns in Mendeleev's
table were called:
A. verticals
B. periods
c. columns
D. groups


A reaction \( A+B \rightarrow C+D \) is found to have a
positive entropy change. The reaction will be :
A. possible at high temperature
B. possible only at low temperature
C. not possible at any temperature
D. possible at any temperature


What is the value of \( p_{1} \) and \( m_{2} ? \)
\( \begin{array}{lll}\mathrm{m}(\mathrm{kg}) & \mathrm{v}(\mathrm{m} / \mathrm{s}) & \mathrm{p}=\mathrm{mv}(\mathrm{kgm} / \mathrm{s}) \\ 85 & 60 & p_{1} \\ m_{2} & 2.5 & 6.25\end{array} \)
\( A \cdot 5100,2.5 \)
B. 5.1 , 2.5
c. 2500,
D. 55, 2.6


Calculate the current through the given
circuit. (The diodes are ideal)
\( 4.6 \mathrm{A} \)
B. 12 A
\( c \cdot 1 A \)
2


If a triplet on template DNA is AAA, what will be the anticodon on tRNA
A. UUU
B. AAA
c. \( \pi T \)
D. AUGGGGGGGGGG


In the homologous series of alkane, the boiling point increases with:
A. increase in volume
B. decrease in mass
c. increase in mass
D. decrease in number of atoms


On hydrolysis, \( X e F_{4} \) produces:
This question has multiple correct options
A. \( X e F_{6} \)
в. \( X e O_{3} \)
\( c \cdot X e O \)
D. \( x e \)


Fill in the blanks.
The stroke of a heat engine in which outlet valve opens is


A solid cylinder rolls without slipping on
an inclined plane inclined at an angle \( \theta \) Find the linear acceleration of the
cylinder. Mass of the cylinder is \( M \)
A \( \cdot a=\frac{1}{3} g \sin \theta \)
B. \( a=\frac{2}{3} g \sin \theta \)
c. \( _{a=\frac{1}{3}} g \cos \theta \)
D. \( a=\frac{2}{3} g \cos \theta \)


The number of distinct terms in \( (a+ \)
\( \boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d}+\boldsymbol{e})^{3} \) is
A . 35
B . 38
\( c \cdot 42 \)
D. 45


A dicot leaf having parallel venation is
A. Eryngium
B. Zizyphus
c. Ricinus
D. cassia


Leguminous plants have their roots modified into
A. Fibrous roots
B. Stilt roots
c. Nodulated roots
D. Prop roots


If in \( \triangle A B C \) and \( \triangle E D A \)
\( B C \perp A B, A E \perp A B \) and \( D E \perp A C \) then
\( D E \cdot B C=A D \cdot A B \)
A. True
B. False


SONAR is
A. SOund Navigation And Ranging
B. SOund Nullyfying And Ranging
C. SOund Navigation with Amplitude and Ranging
D. None


The flux linked with a coil at any instant
\( \mathrm{t}^{\prime} \) is given by \( \phi=10 t^{2}-50 t+250 . \) The
induced emf at \( t=3 s \) is
A . -190
B. -10 V
\( c \cdot 10 v \)
D. 190 V


Which of the following is the strongest
base?
\( A \)
в.
\( c \)
D.


Two adjacent sides of a parallelogram are \( 34 \mathrm{cm} \) and \( 20 \mathrm{cm} . \) One of its
diagonals is \( 42 \mathrm{cm} . \) Then the area of the parallelogram is
\( \mathbf{A} \cdot 612 \mathrm{sq.cm} \)
B. 672 sq.cm
c. 784 sq.cm
D. 796 sq.cm


Which one of the following conditions of the zygotic cell will produce a normal human female child?
A. Only heterologous X chromosome
B. One \( x \) and one \( Y \) chromosome
c. Two homologous \( x \) chromosome
D. Only one Y chromosome


The incorrect statement among the
following is :
\( \mathbf{A} \cdot C_{60} \) is an allotropic form of carbon
B. \( O_{3} \) is an allotropic form of oxygen
\( \mathrm{C} \cdot S_{8} \) is the only allotropic form of sulphur
D. Red phosphorus is more stable in air than white phosphorus


Assertion
The size and shape of the rigid body remains unaffected under the effect of
external forces.
Reason
The distance between two particles remains constant in a rigid body
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In a purely resistive circuit:
A . current lags behind the voltage by \( 90^{\circ} \)
B. current leads the voltage by \( 90^{\circ} \)
C . current can lag or lead the voltage by \( 90^{\circ} \)
D. current is in phase with the voltage


An aluminium container of mass 100
\( \mathrm{gm} \) contains \( 200 \mathrm{gm} \) of ice at \( -20^{0} \mathrm{C} \) Heat is added to the systeam at the rate of 100 cal/s. Find the temperature of the system after 4 minutes (specific heat of ice \( =0.5 \) and \( L=80 \) cal/gm, specific heat of \( \left.A l=0.2 c a l / g m^{0} C\right) \)


For each \( n \epsilon N, \) then \( 3^{2 n+1}+1 \) is
divisible by -
\( A \cdot 2 \)
B. 3
\( c \cdot 7 \)
D. None of these


Match the column I with column II with respect to applications of properties of colloids in different fields and mark the
appropriate choice.
Column I Column I
(A) Coagulation
(i) Colloidal medicines
(B) Adsorption
(ii) Photographic films
(C) Electrophoresis
(iii) Sewage disposal
(D) Emulsions
(iv) Smoke precipitator
B. (A) \( \rightarrow \) (ii), (B) \( \rightarrow \) (iii), \( (c) \rightarrow(i),(D) \rightarrow( \) iv )
c. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow( \text { ii) } \)
D. \( (A) \rightarrow(\text { i) },(B) \rightarrow(\text { iv) },(C) \rightarrow(\text { iii) },(D) \rightarrow( \text { ii) } \)


A rigid body rotates about a stationary
axis according to the law \( \boldsymbol{\theta}=\boldsymbol{a t}-\boldsymbol{b} \boldsymbol{t}^{3} \)
awhere \( a=6 \frac{r a d}{s} \) and \( b=2 \frac{r a d}{s^{3}} . \) Then
mean value of angular velocity ( \( \omega \) ) over
the interval \( t=0 \) and the moment when
it comes to rest is:
A \( .4 \mathrm{rad} / \mathrm{s} \)
B. 3 rad /
c. 8 rad \( / s \)
D. 6 rad \( / \) s


Insufficient light causes while powerful light can cause
A. damage to retina, headaches and eye strain
B. headache and eye strain, damage to retina
c. eye strain, formation of multiple image
D. damage to retina, healing to retina


Resin and turpentine are products of
A. Teak
B. Oak
c. Eucalyptus
D. Pine


The co-ordinates of a moving particle at
any time \( t \) are given by \( \alpha t^{3} \) and \( y=\beta t^{3} \)
The speed of the particle at time is given by
A \( \cdot 3 t \sqrt{\alpha^{2}+\beta^{2}} \)
B . \( 3 t^{2} \sqrt{\alpha^{2}+\beta^{2}} \)
c. \( 3 t \sqrt{\alpha^{2}+\beta^{2}} \)
D. \( \sqrt{\alpha^{2}+\beta^{2}} \)


If the roots of cubic equation \( a x^{3}+ \)
\( b x^{2}+c x+d=0 \) are in G.P., then
В \( \cdot c a^{3}=b d^{3} \)
\( \mathbf{c} \cdot a^{3} b=c^{3} d \)
D. \( a b^{3}-c d^{3} \)


Evaluate the following limit:
\( \lim _{x \rightarrow 0} \frac{\sqrt{(1+\sin x)}-\sqrt{(1-\sin x)}}{x} \)


Find the following squares by using the identity \( \left(\frac{2 a}{3 b}+\frac{3 b}{2 a}\right)^{2} \)


Assertion
STATEMENT-1: 2,2-dimethylpropanal
undergoes cannizzaro reaction with
concentrated \( N \) a \( O H \)
Reason
STATEMENT-2: Cannizzaro reaction is a
disproportionation reaction.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


A person places his ear at the end of a long steel pipe. He hears two distinct sounds at an interval of 0.5 s when
another person hammers at the other end of the pipe. If the speed of the sound in metal and air are \( 3630 \mathrm{ms}^{-1} \) and 330
\( \mathrm{m} s^{-1} \) respectively, then the distance between the two persons is
A. \( 90.75 \mathrm{m} \)
в. 181.5 \( \mathrm{m} \)
c. \( 363 \mathrm{m} \)
D. 1650 \( \mathrm{m} \)


\( \lim _{x \rightarrow 0} \frac{\int_{0}^{t^{2}} \cos t^{2} d t}{x \sin x} \) is equal to:
\( A \cdot-1 \)
B. +1
\( c \cdot 2 \)
\( D \ldots-2 \)


Lateral line organs occur in
A. Fishes
B. Fishes and amphibian larvae
C . Cartilaginous fishes and amphibian larvae
D. Fishes and larvae of other vertebrates


Let \( n \) be a positive integer. Then
\( (i)^{4 n+1}+(-i)^{4 n+5}= \)
\( A \)
в. 2
\( c \)
D. \( -i \)


Evaluate the following integrals:
\( \int \sec ^{4} 2 x d x \)


In the figure a potential of \( +1200 \mathrm{V} \) is
given to point \( A \) and point \( B \) is
earthed,what is the potential at the
point
A . \( 100 \mathrm{V} \)
B. 200
c. \( 400 \mathrm{v} \)
D. 600 v


If \( x^{2}+y^{2}=t-\frac{1}{t} \) and \( x^{4}+y^{4}=t^{2}+ \)
\( \frac{1}{t^{2}}, \) then prove that \( \frac{d y}{d x}=\frac{1}{x^{3} y} \)


Snow blindness is caused due to
A. Ozone hole
B. Nuclear winter
c. Acid rain
D. Green house effect


Explain how Alcohols of lower molecular mass are soluble in water.


Two small particles of equal masses
start moving in opposite directions
from a point \( A \) in a horizontal circular
orbit. Their tangential velocities are \( \boldsymbol{v} \)
and \( 2 v \) respectively, as shown in the
figure. Between collisions, the particles
move with constant speeds. After making how many elastic collisions, other than that at \( A \), these two
particles will again reach the point \( A \) ?
A . 4
B. 3
\( c \cdot 2 \)
D.


The total height of 10 identical coins each of thickness \( 0.5 \mathrm{cm} \) placed one over the other will be \( 50 \mathrm{mm} \)
A. True
B. False


Find the number of diagonals of a
polygon of 16 sides.


What is a semi conductor diode or
junction diode?


In the third group of qualitative
analysis, the precipatitating reagent is
\( N H_{4} C l / N H_{4} O H . \) The function of
\( N H_{4} C l \) is to
A. increase the ionisation of \( N H_{4} O H \)
B. supress the ionisation of \( N H_{4} O H \)
C. convert the ions of group third into their respective chlorides
D. stabilise the hydroxides of group III cations


A ball of weight \( \mathrm{W} \) is supported on a
vertical jet of water. If the stream of
water flowing from the nozzle has a
diameter \( D \) and velocity \( u, \) determine the value of H. Assume that no loss of
energy takes place


A gaseous compound A reacts by three independent first-order processes (as shown in the figure) with rate constant
\( 2 \times 10^{3}, 3 \times 10^{3} \) and \( 1.93 \times 10^{3} \) sec \( ^{1} \)
for products \( \mathrm{B}, \mathrm{C} \) and \( \mathrm{D} \) respectively. If
initially pure \( A \) was taken in a closed
container with \( P=8 a t m, \) then the
partial pressure of \( \mathrm{B}(\text { in atm }) \) after 100 sec from the start of experiment:
\( \mathbf{A} \cdot 0.288 \)
B. 0.577
c. 1.154
D. noneofthese


A bar magnet of pole strength \( 20 A-m \)
is cut into four equal parts breadth wise. Consider the following statements
A) Length becomes \( 1 / 4^{t h}, \) pole strength will be same. Intensity of magnetisation
will be same
B) Length becomes \( 1 / 4^{t h}, \) pole strength
will be \( 1 / 4^{t h} . \) Intensity of magnetisation
also becomes \( 1 / 4^{t h} \)
A . A is correct
B. B is correct
c. Both A and B are correct
D. Both A and B are false


In a series of \( 2 n \) observations, half of
them equal \( a \) and remaining half
equation \( -a . \) If the standard deviation of the observations is \( 2, \) then \( |a| \) equals:
A \( \cdot \frac{1}{n} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \frac{\sqrt{2}}{n} \)


When hydrogen sulphide is reacted with sulphur dioxide, the product obtained is:
A. Flower of sulphur
B. colloidal sulphur
c. milk of sulphur
D. none of these


Mark the statement which is an
advantage of hydel energy.
A. Water availability is free of cost.
B. construction of dams is an easy task
c. Both A and B
D. None of the above


A \( 200 H z \) wave with amplitude 1 mm
travels on a long string of linear mass of density \( 6 g m^{-1} \) kept under a tension of
\( 60 N . \) The average power transmitted across a given point in the string is
A. \( 0.53 \mathrm{W} \)
Wh
в. \( 0.83 \mathrm{W} \)
c. \( 0.47 W \)
D. \( 0.89 W \)


A student has to focus his compound
microscope to observe a prepared slide
showing different stages of binary fission in Amoeba. The steps he is likely to follow are listed below in a haphazard
manner:
. Adjust the diaphragm and the mirror of the microscope so that sufficient light may enter to illuminate the slide.
Il. Fix the slide on the stage carefully.
III. Adjust the microscope to high power and focus.
IV. Adjust the microscope to low power and focus.

The correct sequence of the above steps
to observe the slide under
themicroscope is
A . ।,॥,।V, ॥॥
B. ॥,,|V,III
c. ॥,ा॥,।,॥
D. I,IV,II,II


In gymnosperms, pollination is exclusively by
A. Animals
B. Wind
c. water
D. Insects


XY sex chromosomes were discovered
by
A. Gregor Johann Mendel
B. M.J.D. White
c. Nettie Stevens
D. Robert Brown


If \( \cos \alpha, \cos \beta \) and \( \cos \gamma \) are direction
cosines of a vector, then they satisfy which of the following? Prove it.
A \( \cdot \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=0 \)
B . \( \cos ^{2} \alpha+\cos ^{2} \beta=\cos ^{2} \gamma \)
c. \( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=-1 \)
D. \( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)


Which of the following gives ethyl alcohol by the action of methyl magnesium halide followed by hydrolysis?
A. Formaldehyde
B. Acetaldehyde
c. Acetic acid
D. Methyl alcohol


Alanine forms Zwitter ion which exists
as
\( A \)
\( C H_{3} C^{\text {ему }} H C O O^{-} \) in acidic medium
в. \( C H_{3} C^{\text {емуз }} H C O O H \) in a medium of \( p H=4 \)
c. \( C H_{3} C H C O O^{-} \)
Niz
in a medium of \( p H=1 \)
D. \( C H_{3} C H C O O^{-} \) in a medium of \( p H=2 \)


The image formed by a plane mirror is generally inverted. State whether true or false.
A. True
B. False


Calculate the mole fraction of benzene
in solution containing \( 30 \% \) by mass in
\( \boldsymbol{C C l}_{4} ? \)


Time in which the vibrating particle completes one vibration is called the time period. Explain.


Among the following pairs of ions, the lower oxidation state in aqueous solution is more stable than the other
in
A \( \cdot T i^{+}, T i^{3+} \)
в. \( C u^{+}, C u^{2+} \)
c. \( C r^{2+}, C r^{3+} \)
D. \( V^{2+}, V O^{2+} \)


Differentiate between primary and secondary valencies?


Assertion
If \( z=i+2 i^{2}+3 i^{3}+\ldots \ldots \ldots \ldots+32 i^{32} \)
then \( z, \bar{z}, z \& \bar{z} \) forms the vertices of
square on argand plane.
Reason
\( z, \bar{z}, z, \bar{z} \) are situated at the same
distance from the origin on argand
plane.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A horizontal overhead power line is at a height of \( 5 ~ m \) from the ground and carries a current of \( 100 A \) from east to
west. The magnetic field directly below it on the ground is
A \( \cdot 2.5 \times 10^{-6} T \) eastward
B . \( 4 \times 10^{-6} T \) eastward
c. \( 5 \times 10^{6} \) southward
D. \( 2 \times 10^{-6} \) westward


A particle of mass \( 10 g \) is placed in potential field, given by \( V=\left(50 x^{2}+\right. \)
100) erg/g. What will be frequency of
oscillation of particle?


A man weighing \( 60 \mathrm{kg} \) lifts a body of mass 15 kg to the top of a building 10 m high in 3 minutes. His efficiency is
A . \( 20 \% \)
B. \( 10 \% \)
\( c .30 \% \)
D. \( 40 \% \)


Consider the following hydration reaction
The correct statement regarding the above reaction is (are)
\[
\langle f\rangle_{-} \mathrm{cH}=\mathrm{CD}_{2}+\operatorname{dil} . \mathrm{H}_{2} \mathrm{SO}_{4} \stackrel{\text { Heat }}{\longrightarrow} \text { Alcohol }(\mathrm{s})
\]
This question has multiple correct options
A. The product is a racemic mixture
B. The unreacted alkenes retain all deuterium atoms
c. A pure enantiomer of product is formed
D. The unreacted alkene will have some deuterium replaced by hydrogen


Light wave of frequency \( 4 \times 10^{14} \mathrm{Hz} \)
passes through a medium. The wave
length in the medium is \( \lambda=5 \times 10^{-7} \)
m. The refractive index of the medium
is:
\( A \cdot 2 / 3 \)
B. \( 4 / 3 \)
\( c \cdot 3 / 2 \)
D. 1.414


The organisms shown in figure can be
grouped into two separate groups
based on their mode of nutrition
Which of the following options is correct
regarding this?
A. \( P \) is an autotroph whereas \( Q \), \( R \) and \( S \) are heterotrophs.
B. P show intracellular digestion while \( Q \), R and S show extracellular digestion.
C. \( P \) and \( Q \) are autotrophs while \( R \) and \( S \) are heterotrophs.
D. P shows intracellular digestion while \( Q \), R and S show extracellular digestion.


\( \int\left\{\frac{(\log x-1)}{1+(\log x)^{2}}\right\}^{2} d x \) is equals to?
A. \( \frac{\log x}{(\log x)^{2}+1}+C \)
в. \( \frac{x}{x^{2}+1}+C \)
c. \( \frac{x e^{x}}{1+x^{2}}+C \)
D. \( \frac{x}{(\log x)^{2}+1}+C \)


A solid conducting sphere having a
charge \( Q \) is surrounded by an
uncharged concentric conducting
hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer surface of the hollow shell be \( V \). If the
shell is not given a charge of \( -3 Q \), the
new potential difference between the
same two surfaces is:
\( \mathbf{A} \cdot V \)
B. \( 2 V \)
c. \( 4 V \)
\( \mathbf{D} \cdot-2 V \)


In chromite ore, the oxidation number of
iron, and chromium are respectively.
\( A \cdot+3,+2 \)
\( B \cdot+3,+6 \)
\( c \cdot+2,+6 \)
\( D \cdot+2,+3 \)


Match the items in List 1 and with those
in List 2


If \( |z|=3, \) then \( \frac{9+z}{1+\bar{z}} \) equals
\( A \)
B.
\( c \cdot 3 z \)
D. \( z+\bar{z} \)


\( \frac{(x+1)^{2}}{x^{3}+x}=\frac{A}{x}+\frac{B x+C}{x^{2}+1} \Rightarrow \)
\( \sin ^{-1}\left[\frac{A}{C}\right]= \)
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
\( D \cdot \frac{\pi}{2} \)


The contrapositive of the statement 'If am not feeling well, then I will go to the
doctor' is:
A. If I am feeling well, then I will not go to the doctor
B. If / will go to the doctor, then I am felling well
c. If 1 will not go to the doctor, then I am feeling well
D. If I will go to the doctor, then I am not feeling well


Two moles of \( O_{2} \) gas is collected over
water at \( 400 \mathrm{K} \) temperature in 2
litre vessel. If the pressure of dry \( O_{2} \) gas is 32.20 bar then find the vapour pressure of water under the same
conditions.


The binary mixture of a particular composition in both liquid and vapour state is known as a/an azeotropic mixture.
If true enter 1 , if false enter 0 .


Ratio of energy of photon of wavelength \( 3000 A \) and \( 6000 A \) is :
A . 3: 1
B . 2: 1
c. 1: 2
D. 1: 3


Two moles of a perfect gas undergo the following process:
(a) A reversible isobaric expansion from
\( (1 \operatorname{atm} \operatorname{to} 20 L) \) to \( (1 \operatorname{atm} \operatorname{to~} 40 L) \)
(b) A reversible isochoric change of
state from \( (1 \text { atm to } 40 L) \) to \( (0.5 \) atm to
\( 40 L) \)
(c) A reversible isothermal
compression from \( (0.5 \text { at } m \text { to } 40 L) \) to
\( 1 \text { atm to } 20 L) \)
(i) Sketch with labels each of the
process on the same P-V diagram.
(ii) Calculate the total work \( (w) \) and the
total change \( (q) \) involved in the above
process
(iii) What will be the value of
\( \Delta U, \Delta H, \Delta S \) for the overall process?


A block of mass \( 1 k g \) is free to move
along the \( X \) -axis. It is at rest and from
time \( t=0 \) onwards it is subjected to a
time-dependent force \( F(t) \) in the \( X \)
direction. The force \( F(t) \) varies with \( t \) as shown in figure. The kinetic energy of
the block at \( t=4 s \) is
A \( .1 . \)
B. \( 2 J \)
\( c .3 J \)
D. \( 0 . \)


When a capacitor of value 200 uf
charged to \( 200 \mathrm{V} \) is discharge separately through resistance of 2 ohms and 8 ohms, then heat produced
in joule will respectively be:


Rhombic sulphur is insoluble in carbon disulphide
A. True
B. False


A perpendicular at the end of the radius of a circle is
A. diameter
B. tangent
c. chord
D. anyline


The Gibbs energy change for a reversible reaction at equilibrium is:
A . zero
B. small positive
c. small negative
D. large positive


In the phenomena of diffraction of light, when blue light is used in the experiment in spite of red light, then
A. fringes will become narrower
B. fringes will become broader
c. no change in fringe width
D. None of these


\( y= \)
\( y \)
\( y \)
\( y \)


A large quantity of fluid is filtered every day by the nephrons in the kidneys, only about \( 1 \% \) of it is excreted as urine. The
remaining \( 99 \% \) of the filtrate
A. Gets collected in the renal pelvis
B. Is lost as sweat.
c. Is stored in the urinary bladder.
D. Is reabsorbed into the blood


In A.C. circuit in which inductance and
capacitance are joined in series, current is found to be maximum when
the value of inductance is \( 0.5 H \) and the
value of capacitance is \( 8 \mu F \). The angular frequency of applied alternating voltage will be
A. \( 400 \mathrm{Hz} \)
в. 500 на
c. \( 4000 \mathrm{Hz} \)
D. 5000 Hz


Bauxite, the ore of aluminium, is purified by which process?
A. Hoope's process
B. Hall's process
c. Mond's process
D. Liquation process


It pructur
\( A \)
\( B \)
\( c \)
\( D \)


Discuss the continuity of the following function at the indicated point(s):
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{\boldsymbol{2}|\boldsymbol{x}|+\boldsymbol{x}^{2}}{\boldsymbol{x}}, & \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{0}, & \boldsymbol{x}=\mathbf{0}\end{array}, \text { at } \boldsymbol{x}=\mathbf{0}\right. \)


toppr
Q Type your question
capacitor \( C \) as shown in the figure.
Magnetic field \( B \) is into the plane.
Consider the following statements:
(i) Current in loop \( \boldsymbol{A} \boldsymbol{E} \boldsymbol{F} \boldsymbol{B} \boldsymbol{A} \) is
anticlockwise.
(ii) Current in loop \( \boldsymbol{A} \boldsymbol{E} \boldsymbol{F} \boldsymbol{B} \boldsymbol{A} \) is
clockwise
(iii) Current through the capacitor is
zero.
(iv) Energy stored in the capacitor is
\( \frac{1}{2} C B^{2} L^{2} V^{2} \)
Which if the following options is
correct?
A. Statements (i) and (iii) are correct
B. Statements (ii) and (iv) are correct
c. Statements (i), (iii) and (iv) are correct
D. None of these


Glyptal (alkyd resins) are polyesters of acids and polyhydric alcohols. They are used in the manufacture of:
A. printing inks
B. paints and lacqures
c. rubber and tyres
D. nail polish


Channel proteins allow ions that would not normally pass through the cell membrane to go through the channel What properties of the proteins are responsible for this?
A. The channels are often composed of charged or polar \( R \) groups.
B. The channels are often composed of hydrophobic \( R \) group
\( c . a \) and \( b \)
D. None of these


What are saprophytes? Give two examples


A galvanometer of resistance \( 50 \Omega \) is
connected to a battery of \( 3 V \) along with a resistance of \( 2950 \Omega \) in series. A full-
scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be equal
to
A . \( 5050 \Omega \)
B. \( 5550 \Omega \)
c. \( 6050 \Omega \)
D. \( 4450 \Omega \)


Raunak took 5 moles of carbon atoms in
a container and Krish also took 5 moles of sodium atoms in another container of
same weight. Whose container has more number of atoms?
A. Raunak
B. Krish
c. Both have same
D. None of these


If the following matter waves travel with equal velocity, the longest wavelength is that of a/an:
A . electron
B. proton
c. neutron
D. particle


Which of the following halides is least stable and has doubtful existence?
A. \( C C l_{4} \)
в. \( G e I_{4} \)
\( \mathrm{c} \cdot \operatorname{SnI}_{4} \)
D. \( P b I_{4} \)


If \( A=\left[\begin{array}{cc}-3 & 5 \\ 5 & 0 \\ -7 & 4\end{array}\right] \) and \( B=\left[\begin{array}{ccc}3 & -5 & 7 \\ -5 & 0 & -4\end{array}\right] \)
then find \( \boldsymbol{A}+\boldsymbol{B}^{\boldsymbol{T}} \)
\( A \cdot 0 \)
в. \( 2 B \)
\( c \cdot 2 A^{T} \)
D. \( 2 B^{T} \)


The equation of the plane through the
intersection of \( p_{1} \& p_{2} \) containing the
point (1,1,2) is
A. \( 5 x-6 y+4 z=4 \)
в. \( 5 x+6 y-4 z=3 \)
c. \( 3 x-2 y+4 z=9 \)
D. Nonoe of these


Two masses \( m_{1}=10 \mathrm{kg} \) and \( m_{2}= \)
\( 5 k g \) are connected by an ideal string as
shown in the figure. The coefficient of
friction between \( m_{1} \) and the surface is
\( \mu=0.2 . \) Assuming that the system is
released from rest. The velocity of
blocks when \( m_{2} \) has descended by \( 4 m \)
is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. \( 4 \mathrm{m} / \mathrm{s} \)
в. \( 8 \mathrm{m} / \mathrm{s} \)
c. \( 2 m / s \)
D. \( 12 \mathrm{m} / \mathrm{s} \)


Which acid is produced in our stomach? What happens if there is an
excess of acid in the
stomach? How can its effect be cured?


A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
Plank is pulled to right by a constant force \( F, \) If sphere does not slip over the
plank:
This question has multiple correct options
A. both have same acceleration
B. acceleration of centre of sphere is less then that of the plank
C. work done by friction acting on the sphere is equal to its total KE
D. total KE of the system is equal to work done by the force \( F \)


A point on \( P-V \) diagram represents
A. the condition of a system
c. work done in a cyclic process
D. a thermodynamic process


The work function of metal is in the
range of \( 2 e V \) to \( 5 e V \). Find which of the
following wavelength of light cannot be used for photoelectric effect:
(Consider, Plank constant \( =\mathbf{4} \times \)
\( 10^{-15} e V s, \) velocity of light \( =3 x \)
\( \left.\mathbf{1 0}^{\mathbf{7}} \boldsymbol{m} / \boldsymbol{s}\right) \)
A. 510 nm
B. 650 nm
\( c .400 \mathrm{nm} \)
D. 570 nm


The correct sequence of thermal
stability of the following carbonates is:
A. \( B a C O_{3}<C a C O_{3}<S r C O_{3}<M g C O_{3} \)
в. \( M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)
c. \( B a C O_{3}<S r C O_{3}<C a C O_{3}<M g C O_{3} \)
D. \( M g C O_{3}<S r C O_{3}<C a C O_{3}<B a C O_{3} \)


Which of the following does not result in an increase in entropy?
A. Rusting of iron
B. Conversion of ice to water
c. crystallisation of sucrose from solution
D. Sublimation of camphor


According to Bohr theory, the electronic
energy of hydrogen atom in the \( n \) th Bohr orbit is given by,
\[
\boldsymbol{E}_{\boldsymbol{n}}=-\frac{\boldsymbol{2} \mathbf{1} . \boldsymbol{7} \boldsymbol{6} \times \mathbf{1 0}^{-19}}{\boldsymbol{n}^{2}} \boldsymbol{J}
\]
Calculate the longest wavelength of light that will be needed to remove an electron from the 2 nd orbit of \( L i^{2+} \) ion.


Two particles of masses \( m \) and \( M \) are
initially at rest at an infinite distance
apart. They move towards each other
and gain speeds due to gravitational attraction. Find their speeds when the separation between the masses becomes equal to \( d \)


The electronic configuration of a
transition element ' \( X^{\prime} \) in +3 oxidation
state is \( [A r] 3 d^{5} . \) What is its atomic
number?
A .24
B . 25
\( c \cdot 26 \)
D. 27


A square of side \( 16 \mathrm{cm} \) is reduced by a scale factor 0.5 Find the area of the
image
A \( \cdot 16 \mathrm{cm}^{2} \)
В. \( 32 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 64 c m^{2} \)
D. \( 1024 \mathrm{cm}^{2} \)


The correct increasing order of the acidic strength of acids, butyric acid (I),
\( 2- \) chlorobutyric acid \( (\|), 3 \) chlorobutyric acid (III) and 2, 2dichlorobutyric acid (IV) is :
\( A \cdot|<||<|||<\mid V \)
B. III <II IV <1
c. \( |<|||<||<\mid V \)
D. \|\|\( <1<\|<\mathbb{V} \)
E. IV \( <\|1<\|<1 \)


Find the profit per cent or loss per cent made, when the S.P. of 15 identical
articles is equal to the C.P. of 20 articles.
A ' profit \( =33 \frac{1}{3} \% \)
B. Profit \( =23 \frac{1}{2} \% \)
c. profit \( =23 \frac{1}{3} \% \)
D. \( \operatorname{Loss}=31 \frac{1}{8} \% \)


Amit deposited 150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the
maturity value of his deposits, if the rate of interest is \( 8 \% \) per annum and interest is calculated at the end of every
month


Refer to the Periodic table and
identify the halogen element in the fifth
period among following.
A . \( I \)
в. \( C l \)
\( c . B r \)
D. None of these


Electric lines of force are:
A. Exist everywhere
B. Exist only in the immediate vicinity of electric charges
C. Exist only when both positive and negative charges are near one another
D. Are imaginary


Which of the following sequences of
taxa in the animal kingdom is correct?
A. Kingdom \( \rightarrow \) Phylum \( \rightarrow \) Class \( \rightarrow \) Order \( \rightarrow \) Family \( \rightarrow \)
Species\( \rightarrow \)Genus
B. Kingdom \( \rightarrow \) Phylum \( \rightarrow \) Class \( \rightarrow \) Order \( \rightarrow \) Family \( \rightarrow \) Genus \( \rightarrow \) Species
c. Kingdom\( \rightarrow \)Phylum\( \rightarrow \)Class\( \rightarrow \)Family\( \rightarrow \)Order\( \rightarrow \)
Genus \( \rightarrow \) Species
D. Phylum \( \rightarrow \) Kingdom \( \rightarrow \) Class \( \rightarrow \) family \( \rightarrow \) Order \( \rightarrow \) Genus \( \rightarrow \) Species


Given two independent events \( A, B \)
such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6} \)
Determine
\( \boldsymbol{P}(\boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{n} \boldsymbol{o} \boldsymbol{B} \boldsymbol{B}) \)


Rain is falling vertically. A man running on the the road keeps his umbrella
tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them
keep their umbrella vertical to avid the
vertical sun-rays. Explain.


What weight of \( C a C O_{3} \) must be decomposed to produce the sufficient quantity of carbon dioxide to convert
21.2 \( \mathrm{kg} \) of \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) completely into
\( N a H C O_{3} \)
[Atomic mass \( N a=23, C a=40] \)
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \mathbf{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3}+\boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3} \)
\( A \cdot 100 \mathrm{kg} \)
B. 20 kg
c. \( 120 \mathrm{kg} \)
D. 30 kg


A sphere of radius \( R \) has a volume
density of charge \( \rho=k r, \) where \( r \) is the
distance from the centre of the sphere
and \( k \) is constant. The magnitude of the
electric field which exits at the surface
of the sphere is given by:
\( \left(\varepsilon_{0}=\text { permittivity of free space }\right) \)
A \( \cdot \frac{4 \pi k R^{2}}{3 \varepsilon_{0}} \)
B. \( \frac{k R}{3 \varepsilon_{0}} \)
c. \( \frac{4 \pi k R}{\varepsilon_{0}} \)
D. \( \frac{k R^{2}}{4 \varepsilon_{0}} \)


Given: \( \boldsymbol{x}, \boldsymbol{y} \) and \( \boldsymbol{z} \) are integers and
\( \mathbf{3}^{x+5}=\mathbf{2 7}^{y+1}, \) then \( \boldsymbol{x} \) is even
A. True
B. False


The coefficient of restitution e for a
perfectly inelastic collision is:
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \alpha \)
\( D \)


Each of the following ion contains
vanadium in +5 oxidation state except:
A. \( V O_{2}^{\text {th }} \)
B. \( V(O H)_{4}^{+} \)
c. \( V O^{2+} \)
D \( \cdot\left[V O_{3} O H\right]^{2} \)


No matter how far you stand from a mirror, your image always appears erect. Then the mirror among the following is likely to be:
A. a plane mirror
B. a concave mirror
c. any type of mirror
D. none of the above


Dimerization of benzoic acid occurs in
benzene solution, then the relation
between van't Hoff factor \( i \) and amount
of association \( x \) is:
A \( \cdot i=(1-x) \)
B . \( i=(1+x) \)
c. \( i=\left(1-\frac{x}{2}\right) \)
D. \( i=\left(1+\frac{x}{2}\right) \)


Based on modern classification of
periodic table atomic number increases on moving from in
periodic table.
A . left to right
B. right to left
c. straight
D. none of these


\( f(-A) \) and \( C B \) are congruent, \( A C=12 \)
then find \( B C \).
4. 12
3.10
\( c \)
2.2


Following alkanes are wrongly named. Write their correct IUPAC names
(i) 2-Ethylbutane
(ii) \( 4- \) Methylpentane
(iii) 3,5 -Dimethylhexane
(iv) 5 -Ethyl-4
methylheptane
(v) 2,3 -Dimethyl-3 ethylpentane
(vi) 3 -Methyl-4 isopropylheptane (vii) 4-Ethyl-5-secbutyInonane


Calculate the wave number of the fourth
line of Balmer series.


A body takes time \( t \) to reach the bottom
of an inclined plane of angle \( \theta \) will the horizontal. if the plane made rough, time takes now is \( 2 t . \) The coefficient of
frcition of the rough surface is
A \( \cdot \frac{3}{4} \tan \theta \)
B. \( \frac{1}{2} \tan \theta \)
c. \( \frac{2}{5} \tan \theta \)
D. \( \frac{1}{4} \tan \theta \)


Which of the following will have the largest size in water?
\( \mathbf{A} \cdot R b^{-} \)
В. \( N a^{+} \)
\( c \cdot K^{+} \)
D. \( L i^{+} \)


Find the domain and range of each of the following real value functions:
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}-1} \)


A square and a rectangular plot of land have same perimeter. If the square is of side \( 40 m \) and rectangle is of length 5 decameter. Then area of rectangle is
A \( \cdot 1500 m^{2} \)
В. \( 1600 m^{2} \)
c. \( 200 m^{2} \)
D. \( 150 m^{2} \)


The wrong unit conversion among the
following is
\( \mathbf{A} \cdot 1 \) angstrom \( =10^{-10} m \)
B. 1 fermi \( =10^{-15} \mathrm{m} \)
C \( . \) 1 light year \( =9.46 \times 10^{15} \mathrm{m} \)
D. 1 astronomical unit \( =1.496 \times 10^{-11} \mathrm{m} \)


Freon 12 is prepared from:
A. \( C C l_{4} \)
в. \( C H_{2} C l_{2} \)
c. \( C H C l_{3} \)
D. \( \operatorname{cocl}_{2} \)


The gradient or slope of the distancetime graph at any point gives
A. Acceleration
B. Displacement
c. velocity
D. Time


To separate a mixture of
monosaccharides, you would use:
A. Centrifuge
B. Chromatograph
c. Mass spectrometer
D. Electrolytic cell
E. Dialysis


Insert 20 AM between 2 and 86 .Then find
first mean.


Find the integrating factor of the
differential equation \( \left(\frac{e^{-2 \sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}}\right) \frac{d x}{d y}=1 \)


The biggest star in the night sky is
A. Rigel
B. sirius
c. Proxima centauri
D. Betelgeuse


\( \underbrace{\frac{-}{6}} \)


During photorespiration oxygen consuming reaction(s) occur in
A. Stroma of chloroplasts \& peroxisomes
B. Stroma of Chloroplasts
C. Grana of chloroplast and peroxisomes
D. Stroma of chloroplasts and mitochondria


If \( \cos \theta=\frac{1}{3}, \) then \( \tan \theta= \)
\begin{tabular}{l}
A \( \cdot 2 \sqrt{2} \) \\
\hline
\end{tabular}
B. 2
\( c \cdot \sqrt{2} \)
D. None of above


Electric field inside the capacitor is 100 \( \mathrm{V} / \mathrm{m} \) and dielectric constant \( =5.5 \)
What is the polarization?


If there are two de-Broglie waves formed in an orbit of H-atom then the energy of
electron in that orbit is.
A. \( -3.4 e V \)
B. \( -13.6 e V \)
c. \( -9.06 e V \)
D. \( 1.51 \mathrm{eV} \)


The frequency of a light wave in a material is \( 2 \times 10^{14} H z \) and wavelength is 5000 A. The refractive index of
material will be :
A . 1.50
B. 3.00
\( c .1 .33 \)
D. 1.40


In a DNA molecule, the phosphate group is attached to \( _{--} \) carbon of the sugar
residue of its own nucleotide
and \( _{-1-1} \) carbon of the sugar
residue of the next nucleotide
by bonds.
A. 5 ', 3 ', phosphodiester
B. 5', 3', glycosidic
c. 3 ', 5', phosphodiester
D. 3', 5', glycosidic


For the function \( f(x)=e^{x}, a=0, b=1 \)
the value of \( c \) in mean value theorem
will be
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log (e-1) \)
\( c \cdot \log x \)
\( D \)


A balloon gets negatively charged by
rubbing ceilings of a wall.
A. This implies that the wall is positively charged.
B. This implies that the wall is negatively charged.
C. This does not imply that the wall is positively charged.
D. None of these


Power required to drive a centrifugal pump is directly proportional to of its impeller.
A. Cube of diameter
B. Fourth power of diameter
c. square of diameter
D. Diameter


A balloon is rising vertically up with a velocity of \( 29 \mathrm{ms}^{-1} . \) A stone is dropped
from it and it reaches the ground in 10 s. The height of the balloon when the stone
was dropped from it is: \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} \boldsymbol{s}^{-1}\right) \)
\( \mathbf{A} \cdot 400 \mathrm{m} \)
B. \( 150 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. 200m


Assertion
Statement-I : boiling point of alkyl halide increases with increase in
molecular weight.
Because
Reason
Statement-II : boiling point of alkyl halides are in the order \( R I>R B r> \)
\( \boldsymbol{R} \boldsymbol{C l}>\boldsymbol{R} \boldsymbol{F} \)
A. (A) Statement-I is true, Statement-II is true Statement-II is correct explanation for Statement-I
B. (B) Statement-I is true, Statement-II is true Statement-II is NOT a correct explanation for Statement-I.
c. (c) Statement-I is true, Statement-II is false
D. (D) Statement-I is false, Statement-II is true


Describe location, structure and
function of the nervous tissue.


A 0.001 molal solution of
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{4}\right] \) in water has a freezing
point depression of \( 0.0054^{0} C . \) If \( K_{f} \) for water is \( 1.80, \) the correct formulation of
the above molecule is:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{3}\right] C l \)
B . \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \)
c. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{3} \)
D \( \cdot\left[P t\left(N H_{3}\right)_{4} C l_{4}\right] \)


Membrane bound Krebs cycle enzyme is
A. Fumarase
B. Cis-aconitase
c. succinic dehydrogenase
D. Malate dehydrogenase


A satellite is moving very close to a planet of density \( 8 \times 10^{3} k g m^{-3} . \) If \( G= \)
\( 6.67 \times 10^{-11} N m^{2} k g^{-2}, \) then the time
period of the satellite is nearly.
A. \( 420 s \)
B. \( 4200 s \)
c. 1 hour
D. 1 day


A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 \( c m . \) If the bowl is filled with soup to a
height of \( 4 c m, \) then find the quantity of soup to be prepared daily in the hospital
to serve 250 patients.
A. 38.5 litres
B . 3.5 litres
c. 8.5 litres
D. None of these


A city has 20000 residents. Its population grows at the rate of \( 10 \% \) per annum, what will be its total population
after 5 years?


A resistance of \( \mathrm{R} \Omega \) draws current from
a potentiometer as shown in the figure.
The potentiometer has a total
resistance \( R_{0} \Omega . \) A voltage \( V \) is supplied
to the potentiometer. Derive an
expression for the voltage across \( \mathrm{R} \) when the sliding contact is in the
middle of the potentiometer.


Write uses of melamine plastic.


The discrete spectral lines of line
spectra occur when excitation of electrons takes place in
A. Solids
B. Liquids
c. Gases
D. Plastics
E. All of these


Find two solutions for each of the
following equations:
\( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \)


\( \Delta A P B \) is similar to \( \Delta C P D \)
State whether the above statement is
true or false.


What creates a colorful pattern through light entering the other end of Kaleidoscope?
A. Refraction from mirrors
B. Reflection from mirrors
c. Diffraction from mirrors
D. Deviation from mirrors


Solve \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}-\sin \boldsymbol{\theta}), \boldsymbol{y}=\boldsymbol{a}(\mathbf{1}+\cos \boldsymbol{\theta}) \)
find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} ? \)


Mixture can be of
\( \mathbf{A} \)
\( B \)
c. Both (a) and (b)
D. None of these


Write the definition of electric potential. Calculate the electric potential due to a point charge \( Q \) at a distance \( r \) from it. Draw a graph between electric potential Vand distance r for a point charge \( Q \)


Leaves of Nelumbo plant are
A. Epistomatic
B. Hypostomatic
c. Amphistomatic
D. None of the above


Which of the following is a noble gas?
A. \( H e \)
в. \( N_{2} \)
c. \( H_{2} \)
D. \( O_{2} \)


Choose the correct answers from the
alternatives given :
In certain organisms and under certain conditions, which of the following can be used as an energy alternative to glucose
A. fatty acids
B. glycerol
c. amino acids
D. all of these


Elements \( X, Y \) and \( Z \) have atomic numbers 19,37 and 55 respectively. Which of the following statements are true about them?
A. Their ionization potential would increase with increasing atomic number
B. Y would have an ionization potential between those of \( x \) and \( z \)
c. z would have the highest ionization potential
D. \( \mathrm{r} \) would have the highest ionization potential


The value of \( ^{10} \boldsymbol{C}_{1}+^{10} \boldsymbol{C}_{2}+^{10} \boldsymbol{C}_{3}+\ldots+ \)
\( ^{10} \mathrm{C}_{9} \) is
A \( .2^{10} \)
B . \( 2^{11} \)
\( c \cdot 2^{10}-2 \)
D. \( 2^{10}-1 \)


Prove the following identities :
\[
\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2 c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}
\end{array} \mid=
\]
\( \mathbf{2}(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)


If the function
\( f(x)=\frac{15^{x}-3^{x}-5^{x}+1}{x \tan x}, x \neq 0 \)
continuous at \( x=0, \) then find \( f(0) \)


If \( \vec{a}=2 \hat{i}+l \hat{j}-3 \hat{k} \) and \( \vec{b}=4 \hat{i}-3 \hat{j}- \)
\( 2 \hat{k} \) are perpendicular to each other then
find the value of scalar \( \lambda \)


Value of v for which particle hit vertical
walls \( n \) times is \( \left(x n+\frac{5}{2}\right) \mathrm{m} / \mathrm{s} \) and
finally hit the point \( A \) which is the centre point between the two vertical walls (all collison are elastic) Find \( x \)
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


If \( \boldsymbol{S}=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2}}+\frac{\mathbf{1}}{\mathbf{4}}+\frac{\mathbf{1}}{\mathbf{8}}+\frac{\mathbf{1}}{\mathbf{1 6}}+\frac{\mathbf{1}}{\mathbf{3 2}}+ \)
\( \dots \infty \)
then, the sum of the given series is 2
A. True
B. False


How many constitutional isomer of \( C_{7} H_{15} C l \) will form in the radical chain
chlorination of 2,4 -dimethylpentane?
A. 7
B. 6
\( c .5 \)
D. 3


How can an electromagnet be made stronger?
A. Add more coils of wire.
B. Add an iron core.
c. Increase the voltage.
D. All of these answers are correct


The solution set of \( |\boldsymbol{3}-\boldsymbol{x}|=\boldsymbol{a} \) is?
A \( \cdot\{3-a, 3+a\} \) for \( a \geq 0 \) and \( \phi \) for \( a<0 \)
В. \( [3-a, 3+a] \)
\( c \cdot \phi \)
D. None of these


Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}=14 \)
Hence find the value of \( k, \) if \( y=k x-2 \)
A \( \cdot x=4, y=1 \) and \( k=\frac{2}{3} \)
в. \( x=5, y=3 \) and \( k=\frac{3}{5} \)
c. \( _{x}=3, y=2 \) and \( k=\frac{4}{3} \)
D. \( x=1, y=2 \) and \( k=\frac{9}{2} \)


Find the modulus and the argument of the complex number \( z=-\sqrt{3}+i \)


Short / Long type answer type
questions. Draw a simple diagrammatic sketch of
the internal structure of human heart.
Label the different chambers and the
valves.


Locate the points representing the complex number for which \( \log _{1 / 2} \frac{|z-1|+4}{|z-1|-2}>1 \)


Phenyl magnesium bromide reacting
with t-Butyl alcohol gives:
A. \( P h-O H \)
в. \( P h-H \)
\( c \)
\( D \)


The solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\tan \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)+\frac{\boldsymbol{y}}{\boldsymbol{x}} \) is:
A \( \cdot \cos \left(\frac{y}{x}\right)=c x \)
B. \( \sin \left(\frac{y}{x}\right)=c x \)
\( \mathbf{c} \cdot \cos \left(\frac{y}{x}\right)=c y \)
D \( \cdot \sin \left(\frac{y}{x}\right)=c y \)


Bond lengths which are present in diamond is:
A. \( 234 \mathrm{pm} \)
B. 154 pm
\( c . \) 900 pm
D. 600 pm


Which of the following statements is
not true?
A. Silk is a protein
B. Polyurethane foams are used for making pillows
C. HDPE is prepared by Ziegler Natta polymerization
D. Viscose fabric is not made from cellulose


Let \( m \) and \( n(m<n) \) be the roots of the
equation \( \boldsymbol{x}^{2}-\mathbf{1 6 x}+\mathbf{3 9}=\mathbf{0 .} \) If four
terms \( p, q, r \) and \( s \) are inserted between
\( m \) and \( n \) form an \( A P, \) then what is the
value of \( \boldsymbol{p}+\boldsymbol{q}+\boldsymbol{r}+\boldsymbol{s} ? \)
A . 29
B. 30
\( c \cdot 32 \)
D. 35


A square box of water has a small hole
located in one of the bottom corners.
When the box is full and sitting on a level surface, complete opening of the hole results in a flow of water with a
speed \( v_{0}, \) as shown in fig. When the box
is still half empty, it is tilted by \( 45^{\circ} \) so
that the hole is at the lowest point. Now the water will flow out with a speed of:
A \( \cdot v_{0} \)
B. \( v_{0} \cdot 2 \)
c. \( \frac{v_{0}}{\sqrt{2}} \)
D. \( \frac{v_{0}}{\sqrt[4]{2}} \)


(a) State the names of two elements
that produce nuclear energy.
(b) What are high and low tides?


The heat of combustion of benzene at
\( 27^{\circ} \mathrm{C} \) found by bomb calorimeter i.e. for
the reaction \( C_{6} H_{6(l)}+7 \frac{1}{2} O_{2(g)} \rightarrow \)
\( \mathbf{6} C O_{2(g)}+\mathbf{3} H_{2} O_{(l)} \) is 780 K.Cal \( m o l^{-1} \)
The heat evolved on burning 39 g of benzene in an open vessel will be
A. 390 K.Cal I
B. 780.9 K.Cal
c. 390.45 K.Cal
D. 780 K.Cal


The total energy of the electron of \( \boldsymbol{H} \) atom in the second quantum state is
\( -\boldsymbol{E}_{2} . \) The total energy of the \( \boldsymbol{H} \boldsymbol{e}^{+} \) atom in the third quantum state is:
\( ^{\mathrm{A}} \cdot-\left(\frac{3}{2}\right) E_{2} \)
в. \( -\left(\frac{2}{3}\right) E_{2} \)
c. \( -\left(\frac{4}{9}\right) E_{2} \)
D. \( -\left(\frac{16}{9}\right) E_{2} \)


Solve the following inequalities. \( \log _{1 / 2}\left(x^{2}+2 x+4\right)>-2 \)


A body of mass \( 2 k g \) slides down a plane
inclined at an angle of \( 30^{\circ} \) with horizontal. The co-efficient of friction between the body and the plane is \( \sqrt{\frac{3}{2}} \) What force must be applied on the body so that it moves down without
acceleration?
A. \( 11 N \)
в. \( 14.7 \sqrt{2} N \)
c. zero
D. None of these


Does the following series form an \( \boldsymbol{A P} \) ?
\( 0.2,0.22,0.222,0.2222, \ldots . \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


A hollow insulated conduction sphere is
given a positive charge of \( 10 \mu C . \) What
will be the electric field at the centre of
the sphere if its radius is 2 metres?
A. zero
в. \( 5 \mu C m^{-2} \)
\( c \cdot 20 \mu C m^{-2} \)
D. \( 8 \mu C m^{-2} \)


Find the area between the \( x \) -axis and
the curve \( y=\sin x \) from \( x=0 \) to \( x=2 \pi \)


An object of mass \( m \) is released from
rest from the top of a smooth inclined
plane of height \( h \). Its speed at the
bottom of the plane is proportional to:
\( \mathbf{A} \cdot m^{0} \)
в. \( m \)
\( c \cdot m^{2} \)
D. \( m^{-1} \)


Can you say, whether the compound in
the attached image numbered as 9 is \( \mathrm{E} \)
or \( Z \) isomer?
\( \mathbf{1 0} \)
A. E isomer
B. Z isomer
\( c \cdot \) Both
D. None of these


Equipotential surfaces are shown in fig,
then the electric field strength will be
A . \( 100 \mathrm{Vm}-1 \) along \( \mathrm{X} \) -axis
B. \( 100 \mathrm{Vm}-1 \) along \( \mathrm{Y} \) -axis
c. \( 200 \mathrm{Vm}-1 \) at an angle \( 120^{\circ} \) wirh \( \mathrm{x} \) -axis
D. 50 Vm-1 at an angle \( 180^{\circ} \) wirh \( x \) -axis


Find the arguments of \( z_{1}=5+ \)
\( \mathbf{5} i, z_{2}=-4+4 i, z_{3}=-3-3 i \) and
\( z_{4}=2-2 i, \) where \( i=\sqrt{-1} \)


A ray of light enters a medium of
refractive index \( \mu_{m} . \) It is observed that
the angle of refraction is half the angle of incidence. Then, the angle of incidence will be :
\( \mathbf{A} \cdot \cos ^{-1} \mu \)
B \( \cdot 2 \cos ^{-1} \frac{\mu}{2} \)
\( c \cdot 2 \cos ^{-1} \mu \)
D. \( \cos ^{-1} \frac{\mu}{3} \)


Can white light produce interference?
What is the nature?


A sphere of mass \( m_{1} \) in motion hits
directly another sphere of mass \( m_{2} \) at
rest and sticks to it, the total kinetic
energy after collision is \( 2 / 3 \) of their total
K.E before the collision. Find the ratio
\( \boldsymbol{m}_{1}: \boldsymbol{m}_{2} \)


Which one of the following is an amphoteric oxide?
A \( \cdot M n_{2} O_{7} \)
в. \( C r O \)
\( \mathrm{c} \cdot V_{2} \mathrm{O}_{4} \)
D. \( C r_{2} O_{3} \)
E. \( V_{2} O_{3} \)


If the temperature of a Black body increases by \( 50 \% \) then amount of radiation emmitted by it in a given time interval will
A. Increase by \( 800 \% \)
B. Increase by 400\%
c. Increase by 200\%
D. Increase by 1600\%


If there are ' \( n \) ' arithmetic means
between \( a \) and \( b \), then the common
difference \( (\boldsymbol{d})= \)
A \( \cdot \frac{a-b}{n+1} \)
в. \( \frac{b-a}{n+1} \)
c. \( \frac{a+b}{n-1} \)
D. \( \frac{b-a}{n-1} \)


Toxic agents present in food, which interfere with thyroxine synthesis lead to the development of
A . Goitre
B. Thyrotoxicosis
c. Diabetes
D. Cretinism


The electrical charge on a colloidal particle is indicated by :
A. Brownian movement
B. electrophoresis
c. ultra microscope
D. molecular sieves


The following compounds are:
A. geometrical isomers
B. positional isomers
c. optical isomers
D. functional group isomers


The compound which gets dissolved in
water is :
A. \( C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
c. \( C_{2} H_{2} \)
D. \( C_{2} H_{5} O H \)
E \( \cdot C_{3} H_{8} \)


Which one of the following can more readily donate the lone pair?
A . \( \mathrm{NH}_{3} \)
в. \( \mathrm{PH}_{3} \)
c. \( \mathrm{AsH}_{3} \)
D. \( \operatorname{BiH}_{3} \)


The product of two vectors \( \vec{A} \) and \( \vec{B} \) may
be:
This question has multiple correct options
\( \mathbf{A} \cdot \geq A B \)
в. \( \leq A B \)
c. \( <A B \)
D. zero


A uniform rod of mass \( 15 k g \) is held
stationary with the help of a light string as shown in fig. \( \boldsymbol{L}=\mathbf{5} \boldsymbol{m}, \) angle between
rod and ground is \( 37^{0} . \) The tension in the
string is :
A . \( 150 N \)
B. \( 225 N \)
c. \( 100 N \)
D. None of these


Which of the following is incorrect
about compound microscope?
A. It consists of two convex lenses
B. The objective has smaller focal length than the eyepiece
C. The objective forms a real magnified image
D. The final image is real and much magnified


\( \int_{0}^{\pi / 2} \frac{\sin 8 x \log (\cot x) d x}{\cos 2 x} \)


\( E \) value for the cell reaction
\( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+}(\mathbf{0 . 0 0 1 M}) \| \boldsymbol{C u}^{2+}(\mathbf{0 . 1 m})\right| \boldsymbol{C u} \)
\( ^{\mathrm{A}} \cdot \frac{R T}{F} i n(0.01) \)
в. \( -\frac{R T}{F} \) in (0.1)
c. \( +\frac{R T}{F} i n(0.01) \)
D. \( \frac{R T}{F} \) in (0.1)


Stopping Potential is:


Two charges are placed a certain
distance apart. A metallic sheet is placed between them. What will happen to the force between the charges?
A. Increase
B. Decrease
c. No change
D. either 'a' or 'b


The modal class of the given frequency distribution is
\( \begin{array}{llll}\text { Marks } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { Obtained } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}\end{array} \)
7 35 Cumulative
Frequency 27
A . \( 10-20 \)
в. \( 30-40 \)
\( c \cdot 20-30 \)
D. \( 40-50 \)


Boojho has learnt that non-metals on beating with a hammer are generally broken into pieces. Which of the
following is a non-metal?
A. Iron nail
B. Aluminium wire
c. copper plate
D. Piece of coal


The coefficient of y in the expansion of \( \left(y^{2}+\frac{c}{y}\right)^{5} \) is
A . 20c
B. 10c
\( c \cdot 10 c^{3} \)
D. \( 20 c^{2} \)


The front and side view are same in
which figure?
A. rectangle
B. square
c. triangular pyramid
D. rhombus


Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve


The stress required to double the length of a wire of Young's modulus \( \boldsymbol{E} \) is :
A \( .2 E \)
в. \( E \)
c. \( E / 2 \)
D. \( 3 E \)


Area of the circle \( (x-2)^{2}+(y-3)^{2}= \)
32 which lies below the line \( y=x+1 \) is \( \int_{-2}^{6}[(x+1)+\sqrt{32-(x-2)^{2}}+3] d x \)


\( A \) and \( B \) are two gases. A is identified
with the glass rod dipped in \( N H_{3} \) and \( B \) is identified with the glass rod dipped
in \( H C l . \) Then \( A \) and \( B \) are :
A. \( \mathrm{HCl}, \mathrm{NO}_{2} \)
в. \( \mathrm{HCl}, \mathrm{NH}_{3} \)
c. \( \mathrm{NH}_{3}, \mathrm{HCl} \)
D. \( \mathrm{NH}_{3}, \mathrm{SO}_{2} \)


\( \frac{\text {Charge}}{\text {Time}}=\dots \)
A. Voltage
B. current
c. Potential
D. work done


The value of the resistor, \( \boldsymbol{R}_{S}, \) needed in
the DC voltage regulator circuit shown
here, equals
A \( \cdot \frac{\left(V_{i}+V_{L}\right)}{(n+1) I_{L}} \)
B. \( \frac{\left(V_{i}-V_{L}\right)}{n I_{L}} \)
c. \( \frac{\left(V_{i}+V_{L}\right)}{n I_{L}} \)
D. \( \frac{\left(V_{i}-V_{L}\right)}{(n+1) I_{L}} \)


Two samples of radioactive substances
initially contain equal number of atoms
Their half life times are respectively 2 hours and 4 hours. The ratio of their
disintegration rates after 12 hours is :
A .1: 4
B. 1: 8
c. 3: 4
D. 2: 3


The approximate value of \( (1.0002)^{3000} \) is
A . 1.2
B. 1.4
c. 1.6
D. 1.8


Assertion
\( H N O_{3} \) is stronger acid than \( H N O_{2} \)
Reason
\( \ln H N O_{3} \) there are two nitrogen to
oxygen bonds where as in \( H N O_{2} \) there
is only one.
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


If \( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{2} \\ \mathbf{1} & \mathbf{5}\end{array}\right] \)
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{X}=\mathbf{0}, \) then the matrix \( \boldsymbol{X} \) is
A. \( \left[\begin{array}{ll}1 & 2 \\ 7 & 13\end{array}\right] \)
B. \( \left[\begin{array}{cc}-1 & 2 \\ 7 & -13\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & -2 \\ 7 & 13\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & -2 \\ -7 & -13\end{array}\right] \)


Write the reaction involved in lead
storage battery


Which of the following is/are example(s) of isobars?
A. \( 11 . N a^{23} \) and \( 12 \mathrm{Mg}^{24} \)
\( ^{4} \)
B . \( _{19} K^{39} \) and \( _{20} A r^{40} \)
\( \mathbf{c} \cdot_{18} A r^{40} \) and \( _{20} C a^{40} \)
D・ \( _{17} C l^{35} \) and \( _{17} C l^{37} \)


fe is the eccentricity of the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{25}=1 \) and \( e_{2} \) is the eccentricity
of the hyperbola passing through the foci of the ellipse and \( e_{1} e_{2}=1, \) then equation of the hyperbola is
\( \stackrel{\mathbf{A}}{*} \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 \)
в. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=-1 \)
c. \( \frac{x^{2}}{9}-\frac{y^{2}}{25}=1 \)
D. \( \frac{x^{2}}{25}-\frac{y^{2}}{9}=1 \)


Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.


\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{C l} \) is an octahedral
coordination compound. Draw the diagram which indicate the splitting of 'd' orbitals in tetrahedral field.


According to Bentham and Hooker, polypetalous and epigynous flowers should be placed under the
A. Thalamiflorae
B. Calyciflorae
c. Disciflorae
D. Heteromerae


Light of wavelength \( 5000 \dot{A} \) and intensity \( 3.96 \times 10^{-3} W / c m^{2} \) is
incident on the surface of a
photosensitive material. If 1 percent of incident photons only emit
photoelectrons, then the number of electrons emitted per unit area from the surface will be
A \( \cdot 10^{16} \)
B. \( 10^{18} \)
\( c \cdot 10^{20} \)
D. \( 10^{2} \)


A sample of 0.25 g of organic compound was treated according to Kjeldahl's method. The ammonia evolved was
absorbed in \( 25 \mathrm{ml} \) of \( 0.25 \mathrm{M} H_{2} C O_{4} \). The
residual acid required \( 60 \mathrm{mL} \) of \( 0.25 \mathrm{M} \) solution of NaOH for neutralisation. Find
the percentage composition of nitrogen in the compound.


is the material remaining after the removal of pyridine and other distillates from coal tar
\( A \). Pitch
B. Stalk
c. Lignite
D. None of above


to detect small alternating currents. Which of the diagrams shows how a
diode could be connected in order to
make conversion?
\( A \)
B.
\( c \)
D.


IUPAC name of \( \beta \) - Chloro- \( \alpha \) - methyl
butyric acid:
A. 3 -Chloro-2 methyl-butanoic acid
B. 2-chloro-3-methyl Butanoic acid
C. 2 -chloro-3- methyl-Butan-4-acid
D. 3-chloro-isopentanoic acid


Ratio of solubilities of \( \operatorname{gases} N_{2} \& O_{2} \)
in water from air at \( 25^{\circ} \& 1 \) atm will be
if air is \( 20 \% \) by volume of \( O_{2} \) and \( 80 \% \) by
volume of \( \boldsymbol{N}_{2} \)
\[
\begin{aligned}
\operatorname{Given} &: \boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{N}_{2}\right)=\boldsymbol{2} \times \mathbf{1 0}^{4} \boldsymbol{a t m} \\
\boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{O}_{2}\right) &=\mathbf{1 0}^{4} \boldsymbol{a t m}
\end{aligned}
\]
A . 8: 1
B. 1: 8
\( c \cdot 1: 2 \)
D. 2: 1


Which type of fibres mainly occur in phloem?
A. Libriform
B. Fibre tracheids
c. Sclereids
D. wood fibres


\( \ln \) an a.c. circuit \( V \) and \( I \) are given by
\( \boldsymbol{V}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) \boldsymbol{v o l t s} \) and \( \boldsymbol{I}= \)
\( \mathbf{1 0 0} \sin (\mathbf{1 0 0} t+\boldsymbol{\pi} / \mathbf{3}) \boldsymbol{m} \boldsymbol{A} . \) The power
dissipated in the circuit is
A \( \cdot 10^{4} \) watt
B. 10 watt
c. 2.5 watt
D. 5.0 watt


The mass of the Jupiter is \( 1.9 \times 10^{27} k g \)
and that of the sun is \( 1.99 \times 10^{38} k g \).
The mean distance of the Jupiter from the sun is \( 7.8 \times 10^{11} \) m. Speed of the
Jupiter is (assuming that Jupiter moves in a circular orbit around the sun)
A \( \cdot 1.304 \times 10^{4} \mathrm{m} / \mathrm{sec} \)
в. \( 13.04 \times 10^{4} \mathrm{m} / \mathrm{sec} \)
c. \( 1.304 \times 10^{6} \mathrm{m} / \mathrm{sec} \)
D. \( 1.304 \times 10^{2} \mathrm{m} / \mathrm{sec} \)


The D.E of simple harmonic motion
whose solution is given by \( \boldsymbol{x}= \) \( A \cos (n t+\alpha) \) is
A \( \cdot \frac{d^{2} x}{d t^{2}}+n x=0 \)
B. \( \frac{d^{2} x}{d t^{2}}+n^{2} x=0 \)
c. \( \frac{d^{2} x}{d t^{2}}-n^{2} x=0 \)
D. \( \frac{d^{2} x}{d t^{2}}+\frac{1}{n^{2}} x=0 \)


A common emitter amplifier has a voltage gain of \( 50, \) an input impedance of \( 100 \Omega \) and an output impedance of 200\Omega. The power gain of the amplifier is:-
A . 100
B. 500
\( c \cdot 1000 \)
D. 1250


A \( 8 \mathrm{m} \) long string of rubber, having density \( 1.5 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} \) and young's
modulus \( 5 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \) is suspended
from the ceiling of a room. The increase in its length due to its own weight
will be \( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A. \( 9.6 \times 10^{-2} \mathrm{m} \)
В. \( 19.2 \times 10^{-5} \mathrm{m} \)
c. \( 9.6 \times 10^{-3} \mathrm{m} \)
D. \( 9.6 \mathrm{m} \)


Among the following species, the \( \boldsymbol{H}- \) \( \boldsymbol{X}-\boldsymbol{H} \) angle \( (\boldsymbol{X}=\boldsymbol{B}, \boldsymbol{N} \text { or } \boldsymbol{P}) \) follows
the order:
A \( \cdot P H_{3}<N H_{3}<N H_{4}^{+}<B F_{3} \)
B. \( N H_{3}<P H_{3}<N H_{4}^{+}<B F_{3} \)
C. \( B F_{3}<P H_{3}<N H_{4}^{+}<B F_{3} \)
D. \( B F_{3}<N H_{4}^{+}<N H_{4}^{+}<B F_{3} \)


Choose incorrect stability order:
\( \left.\mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+}<C u(e n)_{2}\right]^{2+}<[C u(\text {trien})]^{2+} \)
B. \( \left[F e\left(H_{2} O\right)_{6}\right]^{3+}<\left[F e\left(N O_{2}\right)_{6}\right]^{3+}<\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Rh}\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Ir}\left(H_{2} O\right)_{6}\right]^{3+} \)
\( \mathbf{D} \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{1+}<\left[C r\left(N H_{3}\right)_{6}\right]^{2+}<\left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)


Which of the following has least band
gap energy at \( 273 K \)
A . Insb
B. InAs
\( c \cdot \ln P \)
D. Gasb


The equilibrium expression, \( \boldsymbol{K}=\left[\boldsymbol{C O}_{2}\right] \)
represents the reaction:
A. \( C(s)+O_{2}(g) \rightleftharpoons C O_{2}(g) \)
B. \( C O(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons C O_{2}(g) \)
c. \( \operatorname{CaCO}_{3}(s) \rightleftharpoons C a O(s)+C O_{2}(g) \)
D. \( C O_{2}(g) \rightleftharpoons C(s)+O_{2}(g) \)
E \( \cdot \operatorname{CaO}(s)+C O_{2}(g) \rightleftharpoons \operatorname{CaCO}_{3}(s) \)


If \( A \) and \( B \) are two Mutually Exclusive events in a sample space S such that
\( \boldsymbol{P}(\boldsymbol{B})=2 \boldsymbol{P}(\boldsymbol{A}) \) and \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{S} \) then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. 5


Which of the following arrangements does not represent the correct order of
the property stated against it? This question has multiple correct options
A \( \cdot N i^{2+}<C o^{2+}<F e^{2+}<M n^{2+}: \) lonic size
B . \( C o^{3+}<F e^{3+}<C r^{3+}<S c^{3+}: \) Stability in aqueous solution
c. \( S c<T i<C r<M n \) : Number of oxidation states
D. \( V^{2+}<C r^{2+}<M n^{2+}<F e^{2+}: \) Paramagnetic
behaviour


The variance of 20 observations is \( 5 . \) If
each observation is multiplied by 2 then what is the new variance of the
resulting observations?
A . 5
B. 10
c. 20
D. 40


Which of the following element and its hydride gives same product on treatment with water?
\( \mathbf{A} \cdot R b \)
в. \( A l \)
c. мgмg
D. All


The \( P^{H} \) of \( 0.001 \mathrm{M} C H_{3} C O O H ? \)
\( A \cdot 3 \)
B. 1
c. Between 3 and 7
D. 7


How much approx aluminium in g can
be produced by a current of 94 A flowing through a Hall-Heroult cell for 1.00 h? (If the answer is \( \left.X, \text { then write } \frac{X}{8}\right) \)


The ratio of moments of inertia of two
solid spheres of same mass but densities in the ratio 1: 8 is:
A . 1: 4
B . 4: 1
c. 2: 1
D. 8: 1


A cylinder of same height and radius is placed on the top of a hemisphere. Find
the curved surface area in \( c m^{2} \) of the
shape if the length of the shape be
\( \mathbf{7} \boldsymbol{c m} \)


The enthalpy change of which reaction
corresponds to \( \Delta H_{f}^{o} \) for \( N a_{2} C O_{3} \) at \( 298 K ? \)
A \( \cdot \operatorname{Na(s)}+C(s)+\frac{3}{2} O_{2}(g) \rightarrow N a_{2} C O_{3}(s) \)
в. \( N a_{2} O(s)+C O_{2}(g) \rightarrow N a_{2} C O_{3}(s) \)
c. \( 2 N a^{+}(a q .)+C O_{3}^{2-}(a q .) \rightarrow N a_{2} C O_{3}(s) \)
D \( \cdot 2 N a^{+}(a q)+2 O H^{-}(a q .)+C O_{2}(a q .) \longrightarrow N a_{2} C O_{3}(s)+ \)
\( H_{2} O \)


A solenoid of 500 turns, diameter \( 20 c m \)
and resistance \( 2 \Omega \) is rotated about its
vertical diameter through \( \pi \) radian in
\( 1 / 4 \) s, when a horizontal field of \( 3 x \)
\( 10^{-5} T \) acts normal to its plane. Find the
emf induced and current thereof


Identify the correct reason for higher
boiling point of \( I C l \) than \( B r_{2} \)
A . higher molecular weight of \( I C l \) than \( B r_{2} \)
B. presence of dipole - dipole forces in \( I C l \)
c. presence of vanderwaals forces in \( I C l \)
D. None of these


Spore producing body of a cellular slime mould is
A. Pseudoplasmodium
B. Plasmodium
c. sporangium
D. Sporophore


A powdered mixture of \( K C l O_{3} \) is
heated in presence of \( M n O_{2} \) to prepare oxygen in the laboratory because:
A. this gives pure oxygen
B. \( M n O_{2} \) liberates oxygen in presence of \( K C l O_{3} \)
c. it is cheaply obtained
D. oxygen is liberated at lower temperature


What is a Fermi energy level? What is its position in case of an intrinsic semiconductor?


Find \( n \) if:
\[
\mid \begin{array}{ccc}
1+a^{2}-b^{2} & 2 a b & -2 b \\
2 a b & 1-a^{2}+b^{2} & 2 a \\
2 b & -2 a & 1-a^{2}-b^{2}
\end{array}
\]
\( \left(1+a^{2}+b^{2}\right)^{n} \)


Peroxisome is associated with.
A. Photorespiration.
B. Photosynthesis.
c. Photoperiodism.
D. Phototropism.


The \( X-Z \) plane separates two media
\( A \) and \( B \) of refractive indices \( \mu_{A}=1.5 \)
and \( \mu_{B}=2 . \) A ray of light travels from
\( A \) to \( B \), its direction in two media are
given by unit vectors. \( \hat{\boldsymbol{u}}_{\boldsymbol{A}}=\boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \hat{\boldsymbol{j}} \) and
\( \hat{\boldsymbol{u}}_{B}=\boldsymbol{c} \hat{\boldsymbol{i}}+\boldsymbol{d} \hat{\boldsymbol{j}} \) respectively, then :
\( ^{A} \cdot \frac{a}{c}=\frac{4}{3} \)
B. \( \frac{a}{c}=\frac{3}{4} \)
c. \( \frac{b}{d}=\frac{4}{3} \)
D. \( \frac{b}{d}=\frac{3}{4} \)


Assertion
Eddy currents in conductors of non-zero resistivity generate heat as well as electromagnetic forces.
Reason
Current is always associated with heat
and electromagnetic forces
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 of the following represent the number 300,000,000
\( A \cdot 3 \times 10^{6} \)
B . \( 3 \times 10^{7} \)
\( c \cdot 3 \times 10^{8} \)
D. \( 3 \times 10^{9} \)
E . \( 3 \times 10^{-9} \)


Nobel gases were included in Mendeleev's periodic table in the:
A. 1 st group
B. 7th group
c. 8 th group
D. none of these


Write a short note on:
1. Armature coil
2. Brushes
3. Commutator
4. Direct current


Given \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{[\{|\boldsymbol{x}|\}] \boldsymbol{e}^{\boldsymbol{x}^{2}}\{[\boldsymbol{x}+\{\boldsymbol{x}\}]\}}_{\left(\frac{1}{\boldsymbol{e}^{x^{2}}-1}\right)} \boldsymbol{s} \boldsymbol{g n}(\sin \boldsymbol{x}) \\ \boldsymbol{0} \quad \text { for } \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
Where \( \{x\} \) is the fractional part
function; \( [x] \) is the step up function and
\( \operatorname{sgn}(x) \) is the signum function of \( x \) then,
\( \boldsymbol{f}(\boldsymbol{x}) \)
A. Is continuous at \( x=0 \)
B. Is discontinuous at \( x=0 \)
C. Has a removable discontinuity at \( x=0 \)
D. Has in irremovable disconitnuity at \( x=0 \)


An element \( X \) has a valency \( 3 . \) Write the formula of its oxide?


The number of possible open chain (acyclic) isomeric compounds for
molecular formula \( C_{5} H_{10} \) would be
\( A \cdot 8 \)
B. 7
\( c \cdot 6 \)
D. 5


Prove using vectors : If the diagonals of a parallelogram are equal in length, then it is a rectangle.


In hydrogen economy, energy required for automobiles or electrical energy is obtained from the reaction between
and oxygen.
A. hydrogen
B. oxygen
c. silver
D. none of these


The Molecular weight of Mohr's salt is
392. Its equivalent weight when it is
oxidized by \( K M n O_{4} \mathrm{KMnO} 4, \) in acidic medium is:
A . 392
B. 196
\( c \cdot 130.6 \)
D. 78.5


The middle point of the mirror is called
A . pole
B. centre of sphere
c. centre of curvature
D. none of these


Binary acid of sulphur is


Bioassay for auxin is
A. Avena curvature test
B. Green leaf test
C. Dwarf maize test
D. Cell division test


\( x^{2} \)
\( d x \)
\( d x \)


A projectile is launched vertically upward. It explodes into two pieces at the top point of its trajectory. One piece has twice the mass of the other.
Immediately after the explosion,
the more massive piece has
kinetic energy \( \boldsymbol{E} \). What is the total
kinetic energy of both pieces immediately after the explosion?
\( \mathbf{A} \cdot 1.5 E \)
B. \( 2 E \)
\( c .3 E \)
D. not enough information to answer
E. Answer required


Charge \( q \) is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f \( \mathrm{Hz} \) The magnitude of magnetic induction at the center of the ring is
\( \mathbf{A} \cdot \underset{2 \pi \Omega}{\operatorname{maf}} \)
B. \( \frac{\text {иоя}}{2 R} \)
c. \( \frac{\mu q}{2 f R} \)
D. \( \frac{\mu_{\text {Ho }}}{2 \pi / R_{R}} \)


A thin rod of length \( d / 3 \) is placed along the principal axis of a concave mirror of
focal length \( =d \) such that its image,
which is real and elongated,just touches the rod. Find the length of the
image?


Reversible adsorption is:
A. chemical adsorption
B. physical adsorption
\( c \). both
D. none


Without expanding, show that the value of each of the following determinants is
zero:
\( \left|\begin{array}{ccc}a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z\end{array}\right| \)