I. Increase in mass II. Differentiation III.
Increase in number of individuals. IV.
Response to stimuli Which two points are known as the twin characteristics of growth?
A . I and II
B. II and IV
c. II and III
D. I and III


The negation of the statement "2 \( +3= \)
\( 5^{\prime \prime} \) and " \( 8<10^{\prime \prime} \) is
A \( \cdot 2+3 \neq 5 \) and \( 8 \Varangle 10 \)
B. \( 2+3 \) Ineq 5 or \( 8>10 \)
c. \( 2+3 \neq 5 \) or \( 8 \nsupseteq 10 \)
D. None of these


An ultrasonic wave is sent from a ship towards the bottom of the sea. It is
found that the time interval between the
sending and receiving of the wave is 1.6
s. What is the depth of the sea, if the velocity of sound in the seawater is \( 1400 \mathrm{m} / \mathrm{s} ? \)
A. \( 1120 \mathrm{m} \)
B. 560 \( m \)
\( c \cdot 1400 m \)
D. 112 m


Which is / are the material used for
making the fuse wire. This question has multiple correct options
A. copper
B. Glass
c. Silver
D. silicon


Identify 'Z' in the following reaction \( \operatorname{series}, C H_{3} C H_{2} C H_{2} B r \stackrel{N a O H}{\longrightarrow} \)
\( (\boldsymbol{X}) \frac{A l_{2} O_{3}}{\Delta}(\boldsymbol{Y}) \stackrel{\boldsymbol{H O C l}}{\longrightarrow}(\boldsymbol{Z}) \)
\( A \)
Mixture of
в.
\( c \)
D.


Four charges \( +\boldsymbol{Q},-\boldsymbol{Q},+\boldsymbol{Q},-\boldsymbol{Q} \) are
placed at the corners of a square taken order. At the centre of the square
A. \( E=0, V=0 \)
B. \( E=0, V \neq 0 \)
c. \( E \neq 0, V=0 \)
D. \( E \neq 0, V \neq 0 \)


The total revenue in Rupees received
from the sale of \( x \) units of a product
is given by \( \boldsymbol{R}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}^{2}+\mathbf{3 6} \boldsymbol{x}+\mathbf{5} . \) The
marginal revenue, when \( \boldsymbol{x}=\mathbf{1 5} \) is.
A . 116
B. 96
\( c \cdot 90 \)
D. 126


Which of the following metal is the component of crude oil?
A. Scandium
B. Titanium
c. vanadium
D. Manganese


When the frequency of the AC voltage applied to series LCR circuit is gradually increased from a low value, the impedance of the circuit:
A. monotonically increases.
B. first increases and then decreases.
c. first decreases and then increases.
D. monotonically decreases


Consider a circle of radius \( R \). What is
the length of a chord which subtends an
angle \( \theta \) at the centre?
\( ^{\mathrm{A}} \cdot_{2 R \sin \frac{\theta}{2}} \)
B. \( 2 R \sin \theta \)
c. \( _{2 R \tan \frac{\theta}{2}} \)
D. \( 2 R \tan \theta \)


The wavelength of a spectral line for an electronic transition is inversely related
to:
A. the number of electrons undergoing the transition
B. the nuclear charge of the atommmen
c. the difference in the energy of the energy levels involved in the transition
D. the velocity of electron undergoing the transition


A cylınder ot nelght \( n \) thled with water
and is kept on lock of height h/2. The
level of water in the cylinder is kept constant. Four holes numbered 1,2,3
and 4 are at the side of the cylinder and
at height \( 0, \) h/4, h/2 and \( 3 h / 4 \)
respectively. When all four holes are opened together, the hole from which
water will reach farthest distance on
the plane PQ is the hole number.
\( A \)
\( B .2 \)
\( c \cdot 3 \)
D.


Mass of the earth is 81 times the mass
of the moon and distance between the
earth and moon is 60 times the radius
of the earth. If \( R \) is radius of the earth,
then the distance between moon and
the point on the line joining the moon and the earth where the gravitation force becomes zero is
A. 30R
в. 15R
\( c \cdot 6 R \)
D. 5R


Assertion
Strain causes the stress in an elastic
body
Reason
An elastic rubber is more plastic in
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


Acetylene is another name of:
A. ethyne
B. butane
c. hexene
D. propene


The capacity of a closed cylindrical vessel of height \( 1 \mathrm{m} \) is 15.4 litres. How many square meters of metal sheet would be needed to make it?


Draw the conjugate acid of \( C l^{-} \)


The value of \( \sin 27^{\circ}-\cos 27^{\circ} \) is equal to
?;where \( \cos \theta=\frac{\sqrt{5}+1}{4} \)
A. \( -\frac{\sqrt{3-\sqrt{5}}}{2} \)
B. \( -\frac{\sqrt{5-\sqrt{5}}}{2} \)
c. \( \frac{\sqrt{5}-1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3-\sqrt{5}}}{2} \)


n Fig. (i), a metre stick, half of which is
wood and the other half steel is pivoted at the wooden end at \( a \) ' and a Force \( \mathrm{F} \) is
applied to the steel end a. In Fig(ii) the stick is pivoted at the steel end at a and
the same force \( F \) is applied at the wooden end at \( a^{\prime} . \) The angular acceleration
A \( . \) In (i) is greater than in (ii)
B. In (ii) is greater than in (i)
c. Is equal both in (i) and (ii)
D. None of the above


Three condensers each of capacitance 2 \( F, \) are connected in series. The resultant
capacitance will be :
\( A \cdot 6 F \)
B. 5
\( c \cdot 2 / 3 F \)
D. 3/2


Which is the final product obtained by the reaction of a grignard reagent ethyl magnesium bromide with propanone?
A. Pentane-1-ol
B. 2-Methyl-butan-2-ol
c. Pentane-2-ol
D. 3-Methyl-butane-2-ol


What is a linear equation?


The peristome in Funaria consists of at maturity
A. One series of curved narrow triangular teeth, 16 in number
B. One series of curved narrow triangular teeth, 32 in number
C. Two series of curved narrow triangular teeth, 8 teeth in each
D. Two series of curved narrow triangular teeth, 16 teeth in each


Magnetic dipole moment is a vector quantity directed from:
A. south to North pole
B. North to south pole
c. East to west direction
D. west to East direction


Which one of the following energies cannot be possessed by a body at rest?
A. Potential energy
B. Kinetic energy
C. Thermal energy
D. Magnetic energy


Mention the type of reaction to obtain \( \boldsymbol{A} \boldsymbol{u}(\mathbf{s} 0 I) \)
Reaction:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{u} \boldsymbol{C l}_{3}+\mathbf{3} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{u}(\boldsymbol{s} \boldsymbol{o l})+\boldsymbol{3} \boldsymbol{H} \boldsymbol{O O H}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \)
A. Hydrolysis
B. Oxidation
c. Reduction
D. Double decomposition


If \( f(x) \) is continuous function such that
\( \int_{0}^{x} f(t) d t \rightarrow \infty \) as \( x \rightarrow \infty, \) show that
every line \( y=m x \) intersect the curve
\( \boldsymbol{y}^{2}+\int_{0}^{x} \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}=\boldsymbol{a} \) where \( \boldsymbol{a} \in \boldsymbol{R}^{+} \)


The ozone layer: Between 15 and \( 50 \mathrm{km} \)
above the earth is a thin layer of gas called 'ozone'. It protects the earth from most of the sun's harmful ultraviolet
radiation. Too much radiation
causes blindness in animals and skin
cancer in people. In \( 1985, \) scientists discovered a hole in the ozone layer in the Antartica. They have recently discovered a smaller hole over the
arctic. The ozone layer is also becoming thinner over other locations of the earth
too. Scientists believe that over the last
10 years about \( 30 \% \) of the ozone layer has disappeared. This damage is caused by chemicals. Choose the right statement(s) from the following.
A. The greenhouse effect would be more efficient and the temperature of earth would increase.
B. CFCs would result in the depletion of the ozone layer
c. Infrared radiation from the sun would bombard earth
D. Ultraviolet radiation from the sun cannot enter earth


Which of the following have same bond order?
This question has multiple correct options
A \( \cdot H_{2}^{+} \)
в. \( H_{2}^{-} \)
\( c \cdot C l_{2} \)
D. \( H e_{2}^{+} \)


An example of an amorphous from of carbon is
A. diamond
B. graphite
c. fullerene
D. wood charcoal


The above compound on strong heating gives:
\[
\begin{array}{c}
\boldsymbol{o}-\boldsymbol{T} \boldsymbol{s} \\
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{3}
\end{array}
\]
\( A \)
\[
\begin{array}{c}
\mathbf{o} \mathbf{H} \\
\mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{C} \mathbf{H}-\mathbf{C H}_{3} \text { and } \mathbf{C H}_{3}
\end{array}\langle\mathbf{O}\rangle-\mathbf{s} \mathbf{o}_{3} \mathbf{H}
\]
в.
\[
\begin{array}{c}
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{SO}_{3} \mathrm{H} \text { and } \mathrm{CH}_{3}\langle\mathrm{O}\rangle \text { of } \\
\mathrm{CH}_{3}
\end{array}
\]
\( c \)
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \text { and } \mathrm{CH}_{3}\langle\mathrm{O}\rangle-\mathrm{so}_{3} \mathrm{H}
\]
D.
\[
\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3} \text { and } \mathrm{CH}_{3}-\langle\mathrm{O}\rangle-\mathrm{so}_{3} \mathrm{H}
\]


Two bodies \( X \) and \( Y \) are in thermal
equilibrium. Body Y is also at the same temperature as a third body Z. The three
bodies are of different materials and
have different masses. Which
statement must be correct?
A. \( x \) and \( Y \) must have the same heat capacity
B. \( Y \) and \( Z \) have the same internal energy
C. There is no net transfer of energy if \( x \) is placed in thermal contact with z
D. It is not necessary that \( Y \) should be in thermal equilibrium with z


Two masses are connected by a spring as shown in the figure. One of the
masses was given velocity \( v=2 k \) as
shown in figure where \( k \) is the spring
constant. Then maximum extension in
the spring will be? (initially spring is in natural length)
A . 2 m
в. \( m \)
\( \mathrm{c} \cdot \sqrt{2 m k} \)
D. \( \sqrt{3 m k} \)


Which of the following reactions is
impossible?
\( \mathbf{A} \cdot_{2} \mathrm{He}^{4}+_{4} \mathrm{Be}^{9}=_{0} \mathrm{n}^{1}+_{6} \mathrm{C}^{12} \)
\( \mathbf{B} \cdot_{2} \mathrm{He}^{4}+_{7} \mathrm{N}^{14}=_{1} \mathrm{H}^{1}+_{8} \mathrm{O}^{17} \)
\( \mathbf{C} \cdot 4\left(_{1} \mathrm{H}^{1}\right)=_{2} \mathrm{He}^{4}+2\left(_{1} \mathrm{e}^{0}\right) \)
\( \mathbf{D} \cdot_{3} \mathrm{Li}^{4}+_{1} \mathrm{H}^{1}=_{4} \mathrm{Be}^{8} \)


Two vectors \( X \) and \( Y \) are added together.
Which of the following statements
could be true?
I. The resultant magnitude is smaller
than X.
II. The resultant magnitude is larger
than \( Y \)
III. The resultant direction is the same
as either \( X \) or \( Y \)
A. I only
B. II only
C. I and III only
D. II and III only
E . ।, ॥।, and III


The driver of a car traveling at velocity \( v \) suddenly sees a broad wall in front of
him at a distance \( a \). He should
A. break sharply
B. turn sharply
\( c . \) both a and \( b \)
D. none of the above


Find the coordinate of the centre and
radius of the following circle. \( 2 x^{2}+2 y^{2}-3 x+5 y=7 \)


The working of hydraulic brakes is
based on Pascal's law.
A. True
B. False


The potential of hydrogen electrode is
\( -118.5 \mathrm{mV} . \) The \( H^{+} \) concentration of
the solution is:
A . 0.01 M
в. 2 м
\( c \cdot 10^{-4} \) м
D. 1 M


If \( \tan (x+y)+\tan (x-y)=1 \), then
find \( \frac{d y}{d x} \)


Determine the intervals over which the
function is decreasing, increasing, and
constant
A. Increasing \( [3, \infty) ; \) Decreasing \( (-\infty, 3] \)
B. Increasing \( (-\infty, 3] \); Decreasing \( [3, \infty) \)
c. Increasing \( (-\infty, 3] ; \) Decreasing \( (-\infty, 3 \)
D. Increasing [3
\( \infty) ; \) Decreasing \( [3, \infty) \)


Evaluate \( \int_{0}^{\pi / 2} \cos x d x \)


Which of these is not related to energy
efficiency?
A. Useful energy
B. \( k W \)
c. Heat
D. Energy transformation


A uniform rod weighs \( 10 k g \) and with a
load \( 5 k g \) attached to one end, it
balances on a knife edge at \( 2 m \) from
that end. The length of rod is :
A. 10.34 m
B. \( 8.56 m \)
c. \( 6.21 m \)
D. 4.35 m


Two identical containers connected by a
fine capillary tube contain air at N.T.P. if one of those containers is immersed in
pure water, boilling under normal pressure then new pressure is
\( A .76 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 152 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 57 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 87.76 cm of Hg


At puberty stage mammary glands develop inside the breasts.
A. True
B. False


Wave motion is a form of \( _{-} \) travelling in the medium due to the
the particles about their
A. disturbance, periodic, mean
B. disturbance, random, extreme
c. disturbance, periodic, extreme
D. disturbance, random, mean


\( \lim _{x \rightarrow 0^{+}}\left(\left(x^{x^{x}}\right)-x^{x}\right) \) is
A. Equal to 0
B. Equal to 1
c. Equal to - 1
D. Non existent


fin the mixed carbonyl, the other ligand is also pi acceptor, it would compete
with the ligand CO for gaining the metal
\( \boldsymbol{d}_{\pi} \) electron charge. The higher is the extent of back donation in \( \mathrm{CO} \), the lesser
will be the stretching vibration
frequency for \( C \) - 0 bond. If \( P F_{3} \) is better \( \pi \) -acceptor than \( \mathrm{CO} \), then answer the following.

Select the correct order of stretching vibration frequency \( C \) - 0 bond in the following molecules :
A \( \cdot\left[N i(C O)_{4}\right]>\left[N i\left(P F_{3}\right)(C O)_{3}\right] \)
B . \( \left[N i(C O)_{4}\right]<\left[N i(C O)_{3}\left(P F_{3}\right)\right] \)
c. \( \left[N i(C O)_{4}\right]=\left[N i\left(P F_{3}\right)(C O)_{3}\right. \)
D. can not predicted


In a one-dimensional collision between
two particles, their relative velocity is \( \overrightarrow{v_{1}} \) before the collision and \( \overrightarrow{v_{2}} \) after
collision:
A. \( \overrightarrow{v_{1}}=\overrightarrow{v_{2}} \) if the collision is elastic
B. \( \overrightarrow{v_{1}}=-\overrightarrow{v_{2}} \) if the collision is elastic
c. \( |\overrightarrow{v_{2}}|=|\overrightarrow{v_{1}}| \) in all cases
D. \( \overrightarrow{v_{1}}=-k \overrightarrow{v_{2}} \) in all cases, where \( k \geq 1 \)


evaluate :
\[
\boldsymbol{I}=\int \frac{2 x}{x^{2}-60 x+6} d x
\]


Out of 22 non-metal, only liquid nonmetal is:
A. chlorine.
B. bromine.
c. hydrogen.
D. iodine


An electric dipole placed in a non-
uniform electric field experiences:
A. Both a torque and a net force
B. Only a force but no torque
C. Only a torque but no net force
D. No torque and no net force


Simplify:
\( 4 x^{2}-4 x z+6 y z-9 y^{2} \)


State True or False:
The product formed when \( P H_{3} \) reacts
with \( \boldsymbol{O}_{2} \) is \( \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)


Diethyl ether \( C_{4} H_{10} O \), used medically as
an anesthetic, is prepared from ethyl alcohol \( C_{2} H_{5} O H \) in presence of an acid. \( 2 C_{2} H_{5} O H \frac{a c i d}{140^{0}} C_{2} H_{5} O C_{2} H_{5}+H_{2} O \)
Calculate the \( \% \) yield if \( 46 g \) of ethyl alcohol gives \( 30 g \) of ether.


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{7}, \mathbf{0}) \) and foci are
\( (\pm \mathbf{4}, \mathbf{0}) \)


\( 56 g \) of \( N_{2} \) and \( 6 g \) of \( H_{2} \) were kept at
\( 400^{\circ} \mathrm{C} \) in 1 litre vessel. The equilibrium
mixture contained \( 27.54 g \) of \( N H_{3} . \) The
approximate value fro \( K_{c} \) for the above reaction in \( m o l^{2} l i t^{2} \) is:
A . 12
B. 20
\( c .30 \)
D. 40


Standard entropy of \( X_{2}, Y_{2} \) and \( X Y_{3} \) are
60,40 and \( 50 J K^{-1} m o l^{-1} \) respectively. For the reaction: \( \frac{1}{2} X_{2}+\frac{3}{2} Y_{2} \rightarrow X Y_{3}, \Delta H= \)
\( -30 k J \) to be at equilibrium, the
temperature will be:
A. \( 1250 \mathrm{k} \)
B. 500 K
\( c \cdot 1000 k \)
D. \( 750 \mathrm{k} \)


A particle with charge \( q \) is projected successively along the \( x \) and \( y \) axes with same speed v. The force on the particle in these situations are \( \boldsymbol{q} \boldsymbol{v} \boldsymbol{B}(-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \)
and \( q v B(3 \hat{i}) \) respectively. Find the unit vector in direction of \( \vec{B} \)


Let \( a \) be a fixed nonzero complex
number with \( |\boldsymbol{a}|<\mathbf{1} \) and \( \boldsymbol{w}= \)
\( \left(\frac{z-a}{1-\bar{a} z}\right), \) where \( z \) is a complex number. Then,
A. there exists a complex number z with \( |z|<1 \) such that \( |w|>1 \)
B. \( |w|>1 \) for all z such that \( |z|<1 \)
C \( .|w|<1 \) for all \( z \) such that \( |z|<1 \)
D. there exists z such that \( |z|<1 \) and \( |w|=1 \)


If \( \vec{a}=x \hat{i}-y \hat{j} \) and \( \vec{b}=y \hat{i}+x \hat{j}, \mid \vec{a} \times \)
\( \vec{b} \mid=5 \) then locus of \( (x, y) \) is
A. Hyperbola
B. Parabola
c. Ellipse
D. Circle


The increasing order of volatility of
hydrides of the group 16 elements is :
A. \( H_{2} S<H_{2} O<H_{2} S e<H_{2} T e \)
в. \( H_{2} O<H_{2} T e<H_{2} S e<H_{2} S \)
c. \( H_{2} O<H_{2} S<H_{2} S e<H_{2} T e \)
D. none of these


\( \ln \operatorname{an} A \cdot P-10,-6,-2,2, \dots 20 t h \) term
is
A . 66
B. -66
\( c \cdot 77 \)
D. None of these


Write the multiplicate inverse of \( \frac{3}{2} \)


You want to show that \( \Delta A R T \cong \Delta P E N \)
If you have to use SSS criterion, then you need to show RT=?


The oxidising ability of the given anions
follows the order:
A \( \cdot \operatorname{Ti} 0_{4}^{4-}<V O_{4}^{3-}<C r O_{4}^{2-}<M n O_{4} \)
B. \( V O_{4}^{3-}<C r O_{4}^{2-}<M n O_{4}^{-}<T i O_{4}^{4} \)
c. \( C r O_{4}^{2-}<M n O_{4}^{-}<V O_{4}^{3-}<T i O_{4}^{4} \)
D. \( V O_{4}^{3-}<T i O_{4}^{4-}<C r O_{4}^{2-}<M n O_{4} \)


If the bond dissociation energies of
\( X Y_{1} X_{2} \) and \( Y_{2} \) (all diatomic molecules)
are in the ratio of 1: 1: 0.5 and \( \delta_{1} H \) for
the formation of \( X Y \) is \( -200 k J m o l^{-1} \)
The bond dissociation energy of \( \boldsymbol{X}_{2} \) will
be:
A. \( 200 k J ; / m o l \)
в. \( 100 k J / m o l \)
c. \( 800 k J / \) mol
D. 300kJ/mol


Two resistances \( \boldsymbol{R}_{1}=(\mathbf{1 0 0}+\mathbf{3}) \) ohms and \( R_{2}=(200+4) \) ohms are connected in series. What is their
equivalent resistance?


A cable that can support a load of 1000 N is cut into equal parts. the maximum load that can be supported by the either part is:-
A . \( 1000 \mathrm{N} \)
B. 2000 N
c. \( 500 \mathrm{N} \)
D. 250 N


The susceptibility of a paramagnetic substance was found for different
temperatures and a graph of \( \chi \) against
\( \frac{1}{T} \) was plotted. From the graph, it was
found that what \( \chi=0.5, \frac{1}{T}=5 \times \)
\( 10^{-3} / K . \) What is the curie constant for
the substance?
A. \( 50 k \)
B. 75 K
c. \( 100 \mathrm{k} \)
D. 125 K


Which of the following is true of RNA, but not DNA?
A. RNA contains ribose
B. RNA contains adenine, guanine, cytosine and thymine
c. RNA is usually double stranded
D. RNA is produced using complementary base pairing


When a current of 5 A flows in the
primary coil then the flux linked with the secondary coil is 200 weber. The value of coefficient of mutual induction
will be
A . 1000 н
в. 40
c. \( 195 \mathrm{H} \)
D. 205 H


If the area of two similar triangles are equal, then they are
A . equilateral
B. isosceles
c. congruent
D. not congruent


are to proteins as
are to nucleic acids
A. Sugars; lipids
B. Amino acids; hydrogen bonds
C. Sugars, proteins
D. Amino acids, nucleotides


Which of the following birth control methods are associated with the
highest pregnancy rates with typical
use?
A. Cervical cap in nulliparous woman
B. Spermicides
c. symptothermal methodd
D. Two Day method
E. Withdrawal method


Velocity is given by \( v=4 t(1-2 t) \) then find time at which velocity is maximum.
A . \( 0.5 \mathrm{sec} \)
B. \( 0.25 \mathrm{sec} \)
c. \( 0.45 \mathrm{sec} \)
D. \( 1 \mathrm{sec} \)


In case of the circuit arrangement shown below, the equivalent resistance
between \( A \) and \( B \) is:
A. \( 10 \Omega \)
3. \( 2.5 \Omega \)
\( c \cdot \frac{50}{3} s \)
Done of the above


If \( \omega \) is an imaginary cube root of
unity,then the value of \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} \boldsymbol{\omega}^{2} & \boldsymbol{a} \boldsymbol{\omega} \\ \boldsymbol{b} \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\omega}^{2} \\ \boldsymbol{c} \boldsymbol{\omega}^{2} & \boldsymbol{a} \boldsymbol{\omega} & \boldsymbol{c}\end{array}\right|, \) is
\( \mathbf{A} \cdot a^{3}+b^{3}+c^{3} \)
B . \( a^{2} b-b^{2} c \)
\( c \cdot 0 \)
D. \( a^{3} b+b^{3}+3 a b c \)


The diagram which correctly represents the direction of flow of charge carriers
in the forward bias of p-njunction is
\( A \)
в.
c.
D.


On heating lead nitrate the product formed is :
A. \( N o \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)


Inverse of the statement "If the triangle
with side lengths \( a, b, c \) is a right
triangle, then \( a^{2}+b^{2}=c^{2} \)
A \( \cdot \) If \( a^{2}+b^{2} \neq c^{2} \) then the triangle with side lengths \( a, b, c \) is not a right triangle.
B. If \( a^{2}+b^{2}=c^{2} \) then the triangle with side lengths \( a, b, c \) is a right triangle
C. If the triangle with side lengths \( a, b, c \) is a not right triangle, then \( a^{2}+b^{2} \neq c^{2} \)
D. None of the above.


Derive an expression for work done in
sliding body down a rough inclined plane


Equilibrium constant for the given reaction is \( K=10^{20} \) at temperature
\( \mathbf{3 0 0} \boldsymbol{K} \)
\( \boldsymbol{A}(s)+\mathbf{2} \boldsymbol{B}(\boldsymbol{a} \boldsymbol{q} .) \rightleftharpoons \mathbf{2} \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{D}(\boldsymbol{a} \boldsymbol{q} .) \)
\( \boldsymbol{K}=\mathbf{1} \mathbf{0}^{\mathbf{2 0}} \)
The equilibrium concentration of B
starting with a mixture of 1 mol \( / \) lit of A and \( 1 / 3 m o l / l i t \) of \( B \) at \( 300 K \) is
в. \( 2 \times 10^{-1} \)
c. \( 2 \times 10^{-11} \)
D. \( 10^{-10} \)


Find the rational numbers \( a \) and \( b \)
\( \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=a-\sqrt{15} b \)


Fig shows some of the equipotential
surfaces of the magnetic scalar potential
The magnetic field \( B \) at a point in the
region is:
A \( \cdot 2 \times 10^{-3} T \)
B . \( 4 \times 10^{-4} T \)
c. \( 2 \times 10^{-4} T \)
D. \( 4 \times 10^{-3} T \)


A circular loop of radius \( 0.3 \mathrm{cm} \) lies
parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the
smaller loop is on the axis of the bigger drop. The distance between their
centres is \( 15 \mathrm{cm} . \) If a current of \( 10 \mathrm{A} \)
flows through the bigger loop, then the flux linked with smaller loop is
A. \( 9.1 \times 10^{-11} \mathrm{Wb} \)
B. \( 6 \times 10^{-11} \mathrm{Wb} \)
c. \( 3.3 \times 10^{-11} W b \)
D. \( 6.6 \times 10^{-11} \mathrm{Wb} \)


of a reaction cannot be
determined experimentally
A. Order
B. Rate
c. Rate constant
D. Molecularity


Prove that the points (-7,-3),(5,10),(15,8) and (3,-5)
taken in order are the corners of a
parallelogram.


Transform the following expression
\( \frac{\tan \alpha+\tan \beta}{\cot \alpha+\cot \beta}+[\cos (\alpha- \)
\( \boldsymbol{\beta}) \boldsymbol{s e c}(\boldsymbol{\alpha}+\boldsymbol{\beta})+\mathbf{1}]^{-1} \)


The non-metals undergoing disproportionation
are
This question has multiple correct options
\( A \cdot P_{4} \)
в. \( C l_{2} \)
\( c \cdot I_{2} \)
D.


\( \{y: y \) is a point common to any two paral lel lines 3 is \{y:yisapointcommontoanytwoparallel ines \( \} \) a null set
A . True
B. False


The \( 3^{r d} \) term of an A.P. is -40 and \( 13^{t h} \)
term is zero, then \( d \) is equal to :
A . -4
B. 4
c. 0
D. -


Diagrammatically represent the experimental steps in cloning and expressing a human gene (say the gene for growth hormone) in a bacteria like \( E \)
coli?


A particle in uniformly accelerated motion travels \( a, b \) and \( c \) distances in
the \( x^{t h}, y^{t h} \) and \( z^{t h} \) second of it's motion, respectively. Then, value of \( a(y-z)+ \)
\( b(z-x)+c(x-y) \) will be
\( A \)
B. 0
\( c \cdot 2 \)
D. 3


In an n-type semiconductor, the Fermi-
energy level lies:
A. in the forbidden energy gap nearer to the conduction band
B. in the forbidden energy gap nearer to the valence band
C. in the middle of forbidden energy gap
D. outside of the forbidden energy gap


Evaluate the following determinant:
\( \left|\begin{array}{ccc}1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38\end{array}\right| \)


ff \( \boldsymbol{y}=\boldsymbol{x}^{n} \log \boldsymbol{x}+\boldsymbol{x}(\log \boldsymbol{x})^{n}, \) find \( \boldsymbol{d} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot x^{n-1}(1+n \log x)+(\log x)^{n-1}[n+\log x \)
B. \( x^{n}(1+\text { nlog } x)+(\log x)^{n}[n+\log x] \)
C. \( x^{n-1}(1+(n-1) \log x)+(\log x)^{n-1}[n-1+\log x] \)
D. none of these


It two equal chords of a circle intersect within the circle. Prove that the line
joining the point of intersection to the centre makes equal angles with the chords.


If a gas mixture contains 2 moles of \( \boldsymbol{O}_{2} \)
and 4 moles of Ar at temperature \( T \)
then what will be the total energy of the system (neglecting all vibrational modes)
A . 11 RT
B. 15 RT
c. 8 RT
D. RT


Long day plants produces flowers when
they are exposed to
A. Any duration of light
B. Light period longer than a critical day length
C. Light period longer than 12 hrs
D. None of the above


Why do we study the Dispersion
phenomenon using a glass prism and
not a glass slab?
A. Light doesn't undergo any deviation inside a glass slab; so cannot be used to study Disprsion
B. All of the dispersion that takes place at the first interface is exactly reversed at the second parallel surface, 'undoing' the effect of the first interface.
C. Dispersion occurs only in prism and not in glass slab
D. None of the above


Measure of two quantities along with the precision of respective measuring instrument is
\( \boldsymbol{A}=\mathbf{2 . 5 m s}^{-1} \pm \mathbf{0 . 5 m s}^{-1}, \boldsymbol{B}=\mathbf{0 . 1 0 s} \pm \)
\( \mathbf{0 . 0 1 s} \)
The value of \( A B \) will be
\( \mathbf{A} \cdot(0.25 \pm 0.08) m \)
в. \( (0.25 \pm 0.8) m \)
c. \( (0.25 \pm 0.05) m \)
D. \( (0.25 \pm 0.135) m \)


If \( y=e^{x}+\sin x-4 x^{3}, \) find \( \frac{d y}{d x} \)


The longest cell in the body of an animal
is
A. osteocytes
B. Neuron
c. chromatophores
D. Lymph corpuscles


Define hydrogen bond. Is it weaker or stronger than the Van der Waals forces?


Which of the followings prove that plastics do not make food and medicine
toxic?
A. Milk pouches
B. Edible oil container
c. Ice-cream packs
D. All of these


Which of the following are represented by \( P, Q, R \) and \( S \) in the given figure?
\begin{tabular}{|c|c|c|c|}
\hline \( \mathbf{P} \) & \( \mathbf{Q} \) & \( \mathbf{R} \) & \( \mathbf{S} \) \\
\hline & & & \\
& & & \\
& & & \\
& & & \\
& & & \\
\hline
\end{tabular}
A. \( P \) - Diatoms, \( Q \) - Chlamydomonas, R - Spirogyra, \( S \) Volvox
B. P- -Volvox, Q - Chlamydomonas
R - Spirogyra, S Diatoms
c. P- -Volvox, Q - Diatoms, R - Spirogyra, SChlamydomonas
D. P- -Volvox, Q - Chlamydomonas
R - Spirogyra, S Euglena


How is water absorbed by root hairs in
plants? Explain.


Which of the following elements does not show +4 oxidation state?
A \( . Z r \)
в. \( P t \)
c. \( L a \)
D. \( T i \)


By the statement,'survival of the fittest'
Darwin meant that
A. The strongest of all species survives
B. The most intelligent of the species survives
C. The cleverest of the species survives
D. The most adaptable of the species to changes survives


\( \mathrm{If} \mathrm{A}+\mathrm{B}=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 2 & 2 \\ 1 & 1 & 1\end{array}\right] \) and \( A-B= \)
\( \left[\begin{array}{ccc}1 & 4 & 4 \\ 4 & 2 & 0 \\ -1 & -1 & 2\end{array}\right] \)
then prove that \( A=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}0 & -2 & -1 \\ -1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right] \)


Equal charges \( Q \) are placed at the four corners \( A, B, C \) and \( D \) of a square of
length \( a \). The magnitude of the force on
the charge at \( B \) will be
\( ^{\mathrm{A}} \cdot \frac{3 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
В. \( \frac{4 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{k Q^{2}}{a^{2}}\left(\frac{2 \sqrt{2}+1}{2}\right) \)
D \( \cdot\left(2+\frac{1}{\sqrt{2}}\right) \frac{3 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)


In Young's double slit experiment width
sodium vapour lamp of wavelength 589 nm and the slits 0.589 mm apart, the
half angular width of the central maximum is
\( A \cdot \sin ^{-1}(0.01) \)
B. \( \sin ^{-1}(0.0001) \)
\( c \cdot \sin ^{-1}(0.001) \)
D. \( \sin ^{-1}(0.1) \)


Solve the equation using formula. \( 2 x^{2}+\frac{x-1}{5}=0 \)
A \( \cdot x=\frac{-1 \pm \sqrt{10}}{4} \)
B. \( x=\frac{-1 \pm \sqrt{41}}{20} \)
c. \( x=\frac{1 \pm \sqrt{41}}{20} \)
D. \( _{x}=\frac{1 \pm \sqrt{10}}{4} \)


A particular star (assuming it as a black body) has a surface temperature
of about \( 5 \times 10^{4} \) K.The wave length in
nano-meters at which its radiation
becomes maximum is :
\( (b=0.0029 m K) \)
\( A \cdot 48 \)
B. 58
\( c \cdot 60 \)
D. 70


If the heats of formation of \( C_{2} H_{2} \) and
\( C_{6} H_{6} \) are \( 230 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( 85 \mathrm{KJ} \mathrm{mol}^{-1} \)
respectively, the \( \Delta \mathrm{H} \) value for the trimerisation of \( C_{2} \mathrm{H}_{2} \) is:
A . - -605 KJ
B . -205 KJ
c. 205 KJ
D. 605 KJ


Evaluate the left hand limit of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{|\boldsymbol{x}-\mathbf{4}|}{\boldsymbol{x}-\mathbf{4}}, \boldsymbol{x} \neq \mathbf{4} \\ \mathbf{0} \quad, \boldsymbol{x}=\mathbf{4}\end{array}\right. \)


The solubility of \( N a C l \) in water is \( 38 g \)
in \( 100 m L \) at \( 50^{\circ} C \)
I. If \( 50 g \) of salt is added to water, a
dynamic equilibrium will be reached. II. A dissociation equilibrium will
result in \( 50 \% \) of the solute being in the aqueous state and \( 50 \% \) being in the
solid state.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


Satellite performs:
A. weather forcasting
B. telecommunication and remote sensing
C . defense planning
D. all of the above


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


In \( 0.0250, \) number of the digits expressing the significant number is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D.


What is the action of ammonia \( \left[N H_{3}\right. \)
on benzoic acid? Write equation.


\( \lim _{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x} \)


Assertion
Ney York City may submerge due to global warming.
Reason
Due to global warming, glaciers are melting and due to this sea-level will be
certainly increasing which may cause flooding of cities situated at the bank of
the sea. New York is one of them.
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


Two identical particles \( B \) and \( C \) each of
mass \( 50 g \) are connected by a light rod of length \( 30 C M . \) Another particle \( A \) of
same mass moving with a speed \( u= \)
\( 60 C M / s \) strikes \( B, \) in a direction
perpendicular to \( A B, \) and sticks to it.
The whole process takes place on a smooth horizontal plane. Find the
angular velocity \( \omega \) of the system about
its centre of mass, immediately after the impact.


Intensity of central fringe in interference pattern is \( 0.1 W / m^{2} \) then find intensity at a point having path difference \( \lambda / 3 \) on screen from centre
\( \left.\operatorname{in} m W / m^{2}\right): \)
A . 2.5
B. 5
c. 7.5
D. 10


The solution of differential equation \( 2 x \frac{d y}{d x}-y=3 \) represents
A. a straight line
B. an ellipse
c. a parabola
D. circles


The speed of electromagnetic wave in vacuum depends upon the source of radiation. It
A. increases as we move from \( \gamma \) -rays to radio waves
B. decreases as we move from \( \gamma \) -rays to radio waves
c. is same for all of them
D. None of these


Which of the following is oxidised in air?
A. White
в. \( C H_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


The acid in which \( - \) COOH group is
(are) present? This question has multiple correct options
A. ethanoic acid
B. picnic acid
c. lactic acid
D. palmitic acid


Explain the following observations:
(i) Many of the transition elements are known to form interstitial compounds.
(ii) There is a general increase in density from titanium \( (z=22) \) to copper \( (z=29) \)
(iii) The members of the actinoid series
exhibit lager number of oxidation states than the corresponding members of the lanthanoid series.


Express in centimetres.
\( \mathbf{8 9 5 . 4 0 m} \)


The frictional force exerted by fluids is called:
A . lift
B. dragg
c. rolling friction
D. dynamic friction


Assertion
Chemical bonds in organic compounds are covalent in nature.
Reason
Covalent bond is formed by the sharing of electrons in the bonding atoms.
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


Express \( 16 \mathrm{mg} \) mass into equivalent energy in electron volt.


Assertion
Bromine has a higher boiling point than chlorine.
Reason
Bromine has stronger dispersion forces than chlorine.
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


Consider the following reaction:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{P} \boldsymbol{r} \) oduct
Among the following, which one cannot be formed as a product under my conditions?
A. Ethylene
B. Ethyl hydrogen sulphate
c. Acetylene
D. Diethyl ether


Find the value of :
\[
\begin{array}{l}
\cos \left[\frac{\pi}{6}+2 \tan ^{-1}(1)\right]+ \\
\sin \left[3 \sin ^{-1}\left(\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{1}{2}\right)\right]
\end{array}
\]


A car taken a turn along a curved road
of radius \( 40 \mathrm{m} \) and the angle of banking
of the road is \( 45^{\circ} . \) At what maximum
speed can the car be driven so that it may not skid. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A \( \cdot 20 m s^{-1} \)
B. \( 10 \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 1 \mathrm{ms}^{-1} \)


The function of \( F e(O H)_{3} \) in the contact
process is :
A. to detect colloidal impurities
B. to remove moisture
c. to remove dust particles
D. to remove arsenic impurities


Find the fraction of kinetic energy lost when the body of mass \( M \) is jerked into
motion
A \( \cdot \frac{M}{M+m} \)
В. \( \frac{M}{M-m} \)
c. \( \frac{2 M}{M+m} \)
D. \( \frac{M}{2(M+m)} \)


Sound from the outside world reach the
inner ear through:
A. pinna
B. cochlea
c. auditory canal
D. labyrinth


In semiconductor physics, what is meant by an oscillator?


A lift is going up with uniform velocity. When brakes are applied, it slows down. A person in that lift experiences:
A. more weight
B. less weight
c. normal weight
D. zero weight


Q Type your question
charge carried by the cylinder is NOT uniform; the charge density varies with radius according to the equation \( =\frac{A}{r} \)
Which of the following expressions
gives the electric field strength at point
\( P, \) a point that lies inside the cylinder
and is a distance \( r \) from the center of
the cylinder?
\( ^{A} \cdot \frac{A R^{2}}{\epsilon_{n^{2}}^{2}} \)
в. \( \frac{A r}{\epsilon_{0} R} \)
c. \( \frac{A r^{2}}{\epsilon_{6} R^{2}} \)
D. \( \frac{A R}{\epsilon_{0} r} \)
\( E \cdot \underline{A} \)


Two line segments \( A B \) and \( A C \) include an angle of \( 60^{0} \) where \( A B=5 \mathrm{cm} \) and \( A C \)
\( =7 \mathrm{cm} . \) Locate points \( \mathrm{P} \) and \( \mathrm{Q} \) on \( \mathrm{AB} \)
and \( A C, \) respectively such that \( A P=\frac{3}{4} \)
\( A B \) and \( A Q=\frac{1}{4} A C . \) Join \( P \) and \( Q \) and
measure the length PQ.
A. \( 3.25 \mathrm{cm} \)
B. \( 4.25 \mathrm{cm} \)
\( c .5 .25 \mathrm{cm} \)
D. \( 6.25 \mathrm{cm} \)


Hydrochloric acid reacts with a metal 'A'
to form a gas 'B' which burns with a 'pop sound. Sodium hydroxide solution also
reacts with the same metal A on
heating to form the same gas B
Name A \& B
Write chemical reaction of metal \( A \) with
(a) Hydrochloric acid
(b) Sodium hydroxide soln


Two liquids \( A \) and \( B \) are taken in two separate identical containers to the
same height of the column then the pressure exerted by the two liquids in their respective containers is


If order of \( A+B \) is \( n \times n \), then the order
of \( A B \) is
\( \mathbf{A} \cdot n \times n \)
в. \( n \times m \)
\( c \cdot m \times n \)
D. not defined


Assertion
The possible dimension of a matrix
consisting 27 elements is 4
Reason
The number of ways of expressing 27 as a product of two positive integers is 4
A. Both Assertion \& Reason are individually correct \& Reason is correct explanation of Assertion,
B. Both Assertion \& Reason are individually true but Reason is Not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


Calculate the standard deviation of the
following data.
\( \mathbf{1 0}, \mathbf{2 0}, \mathbf{1 5}, \mathbf{8}, \mathbf{3}, \mathbf{4} \)
A . 5.97
в. 59.7
c. 4.97
D. None of these


A convex lens forms image at a distance \( 60 \mathrm{cm} \) from the lens for an
object placed on its principal axis. If one more convex lens is placed in contact with first one then image shifts closer to combination by \( 40 \mathrm{cm} . \) Focal length of second lens in cm is:
A . 20
B. 30
\( c \cdot 40 \)
D. 50


RuBisCo constitutes
A. \( 4 \% \) of the chloroplast protein
B. \( 11 \% \) of the chloroplast protein
C. \( 16 \% \) of the chloroplast protein
D. \( 25 \% \) of the chloroplast protein


A has library has 6 copies of one book, 4 copies of each of three books and single
copies of 8 books. Then number of
arrangements of all the
A \( \cdot \frac{(26) !}{(4 !)^{3} 6 !} \)
В \( \cdot \frac{(26) !}{6 !(4 !)^{4}(6 !)^{3}} \)
c. \( \frac{(26) !}{6 !(4 !)^{2}(6 !)^{3}} \)
D. \( \frac{(26) !}{6 ! ! 4 ! 6 !} \)


Protons move rectilinearly in the region
of space where there are uniform
mutually perpendicular electric and magnetic fields \( \mathrm{E} \) and B.The trajectory
of protons lies in the plane \( x z \) as shown
in the figure and forms an angle \( \theta \) with
X-axis.Find the pitch of the helical
trajectory along which the protons will
move after the electric field is switched
off.


The element which is not common between the compounds called baking
soda and soda ash is:
A. nitrogen
B. hydrogen
c. oxygen
D. sulphur


An aluminium block of \( 2 \mathrm{m} \) mass and an
iron block of \( \mathrm{m} \) mass,each absorbs the
same amount of heat, and both blocks
remain solid. If the specific heat of aluminium is twice the specific heat of iron, then find out the correct
statement?
A. The increase in temperature of the aluminum block is twice the increase in temperature of the iron block
B. The increase in temperature of the aluminum block is four times the increase in temperature of the iron block
c. The increase in temperature of the aluminum block is the same as increase in temperature of the iron block
D. The increase in temperature of the iron block is twice the increase in temperature of the aluminum block
E. The increase in temperature of the iron block is four
block


Assertion
The differential equation of all straight
lines which are at a constant distance \( \boldsymbol{p} \)
from the origin is \( \left(\boldsymbol{y}-\boldsymbol{x} \boldsymbol{y}_{1}\right)^{2}= \)
\( \boldsymbol{p}^{2}\left(\mathbf{1}+\boldsymbol{y}_{1}^{2}\right) \)
Reason
The general equation of any straight line which is at a constant distance \( \boldsymbol{p} \)
from the origin is \( \boldsymbol{x} \cos \boldsymbol{\alpha}+\boldsymbol{y} \sin \boldsymbol{\alpha}=\boldsymbol{p} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A diverging electron beam enters a
region of varying potentials.
Intersection of equispaced
equipotential plane surfaces with the
plane of the paper are shown, with their
potentials mentioned in the figure. If
before entering this region, \( x \) and \( y \)
components of the velocity of electrons \( \operatorname{are} 3 \sqrt{\frac{2 e v}{m}} \) and \( \sqrt{\frac{e v}{m}}, \) respectively, where
\( m \) is the mass of an electron and \( e \) is
the electronic charge, then :
This question has multiple correct options
A. the electron beam is converged
B. the electron beam is diverged
C. the electric field is uniform and is directed towards negative x-axis
D. the electric field is uniform and is directed towards positive x-axis


In which one of the following organisms
excretory organs are correctly stated?
A. Humans- Kidneys, sebaceous glands and tear glands
B. Earthworm- Pharyngeal, integumentary and septal nephridia
C. Cockroach-Malpighian tubules and enter caeca
D. Frog- Kidneys, skin and buccal epithelium


All combustion reactions are oxidation-
reduction reactions.
If true enter 1 , else enter 0 .
\( A \)


Green house effect is increasing due to
A . Increasing \( C O_{2} \) concentration
B. Increasing \( S O_{2} \) concentration
c. Increasing concentration of chlorofluorocarbons
D. Hole in ozone layer


Which among these is the angle of
incidence?
\( A \)
B.
\( c \)
\( D \)


Factorise:
\( 27 a^{2}-75 b^{2} \)
\( \mathbf{A} \cdot(3 a+5 b)(3 a-5 b) \)
B. \( 3(3 a+5 b)(3 a+5 b) \)
\( \mathbf{c} \cdot(3 a+5 b)(a-b) \)
D. \( 3(3 a+5 b)(3 a-5 b) \)


Identify whether \( f(x)=\frac{x^{2}-4}{x-2} \) is
continuous at \( x=2 \) or not


Ultrasonic waves are sent in the sea
from a sonar device attached to a ship. These waves take 0.6 s to travel from the
ship to the bottom of the sea and back to the ship in the form of an echo. What is the depth of the sea? (Speed of sound in water \( =1500 \mathrm{m} / \mathrm{s} \) )
A. \( 450 \mathrm{m} \)
B. 900 \( m \)
c. \( 300 \mathrm{m} \)
D. 600


Hydrochloric acid solution \( A \) and \( B \) have a concentration of \( 0.5 N \) and \( 0.1 N \)
respectively. The volume of solutions \( \boldsymbol{A} \)
and \( B \) required to make 2 litres of
\( \mathbf{0 . 2} \mathbf{N} \mathbf{H} \mathbf{C l} \) are:
A. 0.5 Lof \( A+1.5 \) Lof \( B \)
B. 1.5 Lof \( A+0.5 \) Lof \( B \)
c. 1.0 Lof \( A+1.0 \) Lof \( B \)
D. 0.75 Lof \( A+1.25 \) Lof \( B \)


Nucleic acids are the polymers of
A. Nucleosides
B. Nucleotides
c. Nitrogenous bases
D. sugars


Express the following angles into radian
\( 10^{\circ}, 40^{\circ}, 30^{\circ} \)


Benzene and chloroform are separated by:
A. sublimation
B. filtration
c. distillation
D. crystallization


\( \tan \left(\cot ^{-1} x\right) \) is equal to:
A \( \cdot \frac{\pi}{2}-x \)
B. \( \cot \left(\tan ^{-1} x\right) \)
\( c \cdot \tan x \)
D.


Assertion
A larger dry cell has higher emf.
Reason
The emf of a dry cell is proportional to
its size.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If for hydrogen \( S_{p}-S_{v}=a \) and for
oxygen, \( S_{p}-S_{v}=b \) where \( S_{p} \) and \( S_{v} \)
are specific heat at constant pressure and at constant volume, then
\( \mathbf{A} \cdot a=b \)
в. \( a=16 b \)
c. \( b=16 a \)
D. \( a \) and \( b \) are not pressures


What is the surface area of the given
sphere?
A \( \cdot 9256 \) in \( ^{2} \)
B. 9756 in \( ^{2} \)
c. 615.44 in \( ^{2} \)
D. 9856 in


f a non-zero function \( f \) satisfies the
relation \( f(x+y)+f(x-y)=2 f(x) \cdot f(y) \)
for all \( x, y \) in \( R \) and \( f(0) \neq 0 ; \) then \( f(10)- \)
\( f(-10)= \)
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


Two sinusoidal waves of the same
frequency travel in the same direction
along a string. If \( \boldsymbol{A}_{\mathbf{1}}=\mathbf{3 . 0} \boldsymbol{c m}, \boldsymbol{A}_{\mathbf{2}}= \)
\( 4.0 \mathrm{cm}, \phi_{1}=0, \) and \( \phi_{2}=\pi / 2 \mathrm{rad}, \) what
is the amplitude of the resultant wave?


Identify the missing number in the
given sequence 32,80,200 1250


Which is correct for any kind of
species?
\( \mathbf{A} \cdot\left(E_{2}-E_{1}\right)>\left(E_{3}-E_{2}\right)>\left(E_{4}-E_{3}\right) \)
B \( \cdot\left(E_{2}-E_{1}\right)<\left(E_{3}-E_{2}\right)<\left(E_{4}-E_{3}\right) \)
\( \mathbf{C} \cdot\left(E_{2}-E_{1}\right)=\left(E_{3}-E_{2}\right)=\left(E_{4}-E_{3}\right) \)
D \( \cdot\left(E_{2}-E_{1}\right)=1 / 4\left(E_{3}-E_{2}\right)=1 / 9\left(E_{4}-E_{3}\right) \)


In the Fresnel bi-prism experiment, the refractive index for the bi-prism is \( \mu= \)
\( 3 / 2 \) and fringe width obtained is
\( 0.4 m m . \) If the whole apparatus is immersed as such in water then the
fringe width will become(refractive
index of water is \( 4 / 3 \) ).
\( \mathbf{A} \cdot 0.3 m m \)
B. \( 0.225 \mathrm{mm} \)
\( c .0 .4 m m \)
D. \( 1.2 m m \)


If the volume of the gas is to be increased
by 4 times:
A. temperature and pressure must be doubled
B. at constant \( P \), the temperature must be increased by 4 times
C. at constant \( T \), the pressure must be increased by 4 times
D. it cannot be increased


In the following diagrams, ABCD is a
square and APB is an equilateral triangle. n each case, \( \Delta A P D \cong \Delta B P C \)
State whether the above statement is
true or false.
A. True
B. False


The displacement time graph of a particle executing SHM is shown in
figure. Which of the following
statements is/are true?
This question has multiple correct options
A. The velocity is maximum at t=T/2
B. The acceleration is maximum at t=
c. The force is zero at t=37/4
D. The kinetic energy equals the total oscillation energy at \( t=T / 2 \)


Among the following metals which one has the least metallic character?
\( A \cdot B e \)
в. \( M g \)
\( c . C a \)
D. \( S r \)


Assertion
Liquid exerts pressure on walls of
container
Reason
Molecules of liquid collides
continuously with wall
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The correct stability order of the following resonance structure is:
(।) \( \mathbf{H}_{2} \overline{\mathbf{C}}-\dot{\mathbf{N}} \equiv \mathbf{N} \)
\( (\mathrm{II}) \mathbf{H}_{2} \mathbf{C}=\stackrel{+}{\mathbf{N}}=\overline{\mathbf{N}} \)
\( (\| I) \mathbf{H}_{2} \stackrel{+}{C}-N=\bar{N} \)
\( (\mid V) \mathbf{H}_{2} \overline{\mathbf{C}}-\mathbf{N}=\dot{\mathbf{N}} \)
\( A \cdot(1)>(11)>(1)>(111) \)
B. (I) > (III) > (II) > (IV)
\( c \cdot(11)>(1)>(111)>(1 v) \)
\( D \cdot(\| I)>(I)>(I V)>(I I) \)


Assertion
A piece of ice, with a stone frozen inside
it, floats on water in a beaker. When the
ice melts, the level of water in the
beaker decreases.
Reason
Density of stone is more than of water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A body loses half of its velocity on penetrating \( 6 \mathrm{cm} \) in a wooden block.
How much will it penetrate more before coming to rest?
A. \( 1 ~ c m \)
B. 2 cm
\( \mathrm{c} .3 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)


A body with area \( A \) at a material
temperature \( \boldsymbol{T} \) and emissivity \( \boldsymbol{e}=\mathbf{0 . 6} \) is kept inside a spherical black body. what will be the maximum energy radiated
per second?
\( \mathbf{A} \cdot 0.60 \sigma \mathrm{AT}^{4} \)
B . \( 1.00 \sigma \) AT \( ^{4} \)
c. \( 0.80 \sigma \) АТ \( ^{4} \)
D. \( 0.40 \sigma \) АТ \( ^{4} \)


The projection of the join of the points (3,4,2),(5,1,8) on the line whose d.c's \( \operatorname{are}\left(\frac{2}{7}, \frac{3}{7}, \frac{6}{7}\right) \) is
A. 7
B. \( \frac{31}{71} \)
\( \mathbf{c} \cdot \frac{42}{13} \)
\( D \cdot \frac{38}{138} \)


Four particles, each of mass \( \mathrm{m}, \) are placed at the four corners of a square of side 'a'. Force exerted by this system on another particle of mass \( \mathrm{m} \) placed at the midpoint of a side of square is -
A \( \cdot \frac{16 G m^{2}}{5 \sqrt{5 a^{2}}} \)
в. \( \frac{16 G m^{2}}{5 \sqrt{3 a^{2}}} \)
c. \( \frac{16 G m^{2}}{5 a} \)
D. zero


The earth's magnetic field at the
equator is approximately \( 0.4 G . \) The earth's dipole moment is :
\( \left(\boldsymbol{R}_{e}=\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{\boldsymbol { m }}\right) \)
A \( \cdot 4 \times 10^{2} A m^{2} \)
B . \( 1.05 \times 10^{23} \mathrm{Am}^{2} \)
c. \( 4 \times 10^{-5} \mathrm{Am}^{2} \)
D. \( 1.05 \times 10^{-20} \mathrm{Am}^{2} \)


State True or False:
All seeds have two cotyledons.


What is the unit of electric charge in \( \mathrm{S} \) I system?
A. Coulomb
B. Volt
c. watt
D. Ampere


Evaluate the integral \( \int_{\frac{a}{2}}^{a} \frac{1}{\sqrt{a^{2}-x^{2}}} d x \)
A \( \cdot \frac{\pi}{2} \)
в. \( \pi a \)
c \( . \pi-1 \)
D.


\( \boldsymbol{C l O}_{3}^{-}+\boldsymbol{C l}^{-} \rightarrow \boldsymbol{C l}_{2}+\boldsymbol{C l O}_{2} \)
Which of the following is correct for this reaction:
A. Its a disproportion reaction
B. \( C l \) is both oxidised and reduced
c. \( C l \) is both reducing and oxydising agent
D. All of these


The total number of real tangents that
can be drawn to the ellipse \( 3 x^{2}+ \) \( 5 y^{2}=32 \) and \( 25 x^{2}+9 y^{2}=450 \)
passing through (3,5) is
\( A \cdot 0 \)
B . 2
\( c .3 \)
D.


Which of the following molecules is
most suitable to disperse benzene in
water?
\( A \)
B.
\( c \)
\( D \)


Find out the range for the following
prices of shirts in a shop.
Rupees
150
250
100
500
175
450
300
280
A. Rs. 400
B. Rs. 500
C. Rs. 350
D. Rs. 100


Why does aluminium chloride, \( A l_{2} C l_{6} \)
sublime at the relatively low
temperature of \( 180^{-\circ} \mathrm{C} ? \) 1 The intermolecular forces between the
\( A l_{2} C l_{6} \) molecules are weak.
2 The co-ordinate bonds between
aluminium and chlorine are weak.
3 The covalent bonds between
aluminium and chlorine are weak.
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Which of the following statement is wrong in root-presure concept of ascent of sap?
A. Water can be raised to a height of \( 6^{\prime}-7 \) '.
B. Water moves upward in the absence of shoot.
c. water moves by this force is slow.
D. Root pressure operates in all the plants


Which among the following reactions does not give methyl alcohol?
A. The reaction of ethylene with \( H_{2} S O_{4} \) at \( 80^{\circ} C \)
B. The reaction of water gas with hydrogen at high temperature
c. Alkaline hydrolysis of methyl bromide
D. Both \( A \) and \( B \)


Choose the correct from the alternatives
given Which one of the following organisms is the first to colonise a bare rock?
A . Lichens
B. Mosses
c. Perennial plants
D. Metazoans


A material which is not easily decomposed by natural processes is termed as:
A. biodegradable material
B. non-biodegradable material
c. recycled material
D. natural material


Choose the correct statement(s) from
the given ones.
A. A lewis base is a substance which can donate a pair of electrons.
B. A bronsted base is a substance which can donate a
pair of electrons.
C. A lewis base is a substance which can accept a pair of electrons.
D. A bronsted base is a substance which can accept a pair of electrons.


Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of \( 444 m / s \) in 1.83 seconds, then what is the distance that the sled travels? \( (\text { in } m) \)
\( \mathbf{A} \cdot 406 m \)
в. \( 40 m \)
\( c .46 m \)
D. \( 506 m \)


External fertilization occurs in majority
of
A. Algae
B. Fungi
c. Liverworts
D. Mosses


Given below are the elements and the
type of hydrides formed by them mark the incorrect match
A. Phosphourus-molecular hydride
B. Potassium-lonic hydride
c. Vanadium-Interstitial hydride
D. Nitrogen-Electron-deficient covalent hydride


The minium energy required for the emisson of a metal elctrons is
\( 133.24 \times 10^{-16} J . \) Calculate the cirtical
frequency and the correspoding wavelength of he photon (thesehold wavelength) required to eject the electron?
A light source of wavelength \( \lambda \) illuinates
a metal and ejects photo electrons with
\( (\boldsymbol{K} \boldsymbol{E})_{\max }=\mathbf{1} \boldsymbol{e} \boldsymbol{V} \)
Another light source of wavelength \( \frac{\lambda}{3} \)
ejects photoelectrons from same metal
with \( (\boldsymbol{K} \boldsymbol{E})=\boldsymbol{S} e \boldsymbol{V} \). Find the value of
work function \( (e V) \) of metal.


The crystal field splitting energy CFSE \( \left(\text {In } \Delta_{0} \text {units}\right) \) for \( \left[\text {Co} F_{6}\right]^{3-} \) will be:
A \( .-1.6 \Delta_{0} \)
в. \( -2.4 \Delta_{0} \)
\( c .-0.4 \Delta_{0} \)
D. \( +0.6 \Delta_{0} \)


Let \( S_{n} \) denote the sum of first \( n \) terms
of an \( A P, \) If \( S_{2 n}=3 S_{n} \) then find the
ratio \( \boldsymbol{S}_{\boldsymbol{3} \boldsymbol{n}} / \boldsymbol{S}_{\boldsymbol{n}} \)


If \( \boldsymbol{A}+\boldsymbol{B}=\frac{\boldsymbol{\pi}}{\mathbf{3}} \) and \( \cos \boldsymbol{A}+\cos \boldsymbol{B}=\mathbf{1} \)
then which of the following are true:
This question has multiple correct options
A \( \cdot \cos (A-B)=\frac{1}{3} \)
B. \( \cos (A-B)=-\frac{1}{3} \)
C \( \cdot|\cos A-\cos B|=\sqrt{2 / 3} \)
D. \( |\cos A-\cos B|=\frac{1}{\sqrt{3}} \)


\( \tan 100^{\circ}+\tan 125^{\circ}+ \)
\( \tan 100^{\circ} \tan 125^{\circ} \) is equal to
A . 0
B. \( \frac{1}{2} \)
\( c .-1 \)
D.


For an ideal conductor thermal
resistance is :
A. unity
B. infinity
c. zero
D. 1000


Prove that
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{0}), \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{1}), \boldsymbol{C}(\mathbf{7},-\mathbf{1}, \mathbf{3}) \) are
collinear.


The area bounded by the curves \( x= \)
\( a \cos ^{3} t, y=a \sin ^{3} t \) is
A \( \cdot \frac{3 \pi a^{2}}{8} \)
в. \( \frac{3 \pi a^{2}}{16} \)
c. \( \frac{3 \pi a^{2}}{32} \)
D. None of the above


Find the length of longest chord of the circle if radius is \( 2.9 \mathrm{cm} \) in \( \mathrm{cm} \)


Number of coulombs required to deposit \( 90 g \) of \( A l \) when the electrode
reaction \( A l^{3+}+3 e \rightarrow A l \) is
A \( \cdot 9.65 \times 10^{6} \)
B. \( 8.685 \times 10^{4} \)
c. \( 9.65 \times 10^{4} \)
D. 6.955


Even though both are oxidation processes, combustion and respiration are different in many aspects. Explain those differences.


The charge supplied to a good
conductor always resides:
A. at the supplied position itself
B. on its outer surface
C. inside the body
D. all of the above


If a body is charged by rubbing it, its weight :
A. Remains precisely constant
B. Increase slightly
c. Decrease slightly
D. May increase slightly or may decrease slightly


Liquefaction can be viewed as an extreme deviation from ideal gas
behavior
A. True
B. False


ff \( \left(x_{1}, y_{1}, z_{1}\right) \) and \( B\left(x_{2}, y_{2}, z_{2}\right) \) are
two points such that the direction \( \operatorname{cosines} \) of \( A B \) are \( l, m, n \) then
\( l=\frac{x_{2}-x_{1}}{|A B|}, m=\frac{y_{2}-y_{1}}{|A B|}, n=\frac{z_{2}-z_{1}}{|A B|} \)


Find the area in square meter of a
parallelogram, whose base is \( 140 \mathrm{cm} \) and altitude is \( 20 \mathrm{cm} \)


What are isobars?


i) Match the following graphs with their
corresponding motions.
ii) What is the value of acceleration in
graph B?


A \( 120 m \) long train is moving in a
direction with speed \( 20 m / s . A \) train \( B \) moving with \( 30 m / s \) in the opposite direction and \( 130 \mathrm{m} \) long crosses the
first train in a time of :
\( \mathbf{A} \cdot 5 s \)
в. \( 36 s \)
\( c .38 s \)
D. None of these


Two concentric circular coils of radii
and \( \mathrm{R} \) are placed coaxially with centres coiciding. If \( R \gg r \) then calculate the mutual inductance between the coils.


What do you understand by denaturation of Protein?


Explain \( S N^{1} \) reaction with appropriate
example.


Solve \( \left(\boldsymbol{y}+\mathbf{3} \boldsymbol{x}^{2}\right) \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}=\boldsymbol{x} \)


If the multiplicative inverse of \( \frac{x+1}{x} \) is \( \frac{2}{3}, \) then find \( x \)


Obtain the exponential law of radioactive disintegration. Explain the decay curve.


\( \frac{\cot \theta-\cot 2 \theta}{\cot \theta} \) is equal to
\( \mathbf{A} \cdot \frac{x}{z} \)
\( \mathbf{B} \cdot \frac{y}{z} \)
\( \mathbf{c} \cdot \frac{y}{x} \)
D. \( \frac{x}{y} \)


Assertion (A): With increase of
temperature,elastic property of a substance decreases.

Reason (R) : Elasticity is due to intermolecular forces which decreases
with the increase of intermolecular
distance.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


Animal showing thigmotaxias is
A. Ascaris
B. Taenia
c. Fungia
D. Hydra


Differentiate with respect to \( x e^{x} x^{5} \)
A \( \cdot 5 e^{x} x^{4}+e^{x} x^{5} \)
B. \( 4 e^{x} x^{5}+e^{x} x^{5} \)
\( \mathbf{c} \cdot 5 e^{x} x^{4}+e^{x} x^{4} \)
D. \( 4 e^{x} x^{5}+e^{x} x^{4} \)


Agonists cannot:
This question has multiple correct options
A. inhibit function of receptors
B. mimic natural chemical messengers
C . control body temperature during fever
D. relieve the pain


The magnetic moment of \( \left[M n X_{4}\right]^{2-} \) is 5.9 BM. The geometry of the complex ion
is:
\( (X=\text { monodentate halide ion }) \)
A . tetrahedral
B. square planar
c. both are possible
D. none of these


Two spherical stars \( A \) and \( B \) emit
blackbody radiation. The radius of \( A \) is
400 times that of \( B \) and \( A \) emits \( 10^{4} \)
times the power emitted from \( B \). The ratio \( \left(\frac{\boldsymbol{\lambda}_{\boldsymbol{A}}}{\boldsymbol{\lambda}_{\boldsymbol{B}}}\right) \) of their wavelengths \( \boldsymbol{\lambda}_{\boldsymbol{A}} \)
and \( \lambda_{B} \) at which the peaks occur in their respective radiation curves is


The derivative of \( \tan ^{-1}\left(\frac{\sin x-\cos x}{\sin x+\cos x}\right) \)
with respect to \( \frac{x}{2}, \) where \( \left(x \epsilon\left(0, \frac{\pi}{2}\right)\right) \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{2}{3} \)
c. 1
D.


Using the identity \( (\boldsymbol{a}-\boldsymbol{b})^{2}=\boldsymbol{a}^{2}- \)
\( 2 a b+b^{2} \) compute \( (5 a-4 b)^{2} \)


The centre of mass of system of particles?
A. Coincides with the ca
B. Never Coincides with the CG
c. coincides with the cG in uniform gravitational field
D. None of the above


Which one of these substances will
repress the lac operon?
A. Arabinose
B. Glucose
c. Lactose
D. Tryptopham


Assertion
The various energy bands in a solid may or may not overlap depending on the structure of the solid.
Reason
If they do not overlap then the intervals between them represent energies which the electrons in the solid cannot have.
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


D, \( E \) and \( F \) are the mid-point of sides \( B C \)
CA and \( A B \) of \( \triangle A B C, \) then area \( \triangle A B C \)
area \( \triangle \mathrm{DEF}= \)
A . 4: 1
B. 1: 4
c. 2: 1
D. 4: 3


A photon is a/an
A. Quantum of light
B. Quantum of matter
C. Positively charged paticle
D. Instrument for measuring light intensity


Read the bar graph shown in Fig. and
answer the following questions:
What is the information given by the bar
graph?
Bar graph of the number of commercial banks in India during some years.


A pulley fixed to the ceiling carries a string with bodies of masses \( \mathrm{m} \) and \( 3 \mathrm{m} \) attached to its ends. The masses of the
pulley and the string are negligible, friction is absent. The acceleration of
the centre of mass of the system is
\( \mathbf{A} \cdot-g / 4 \)
в. \( g / 4 \)
c. \( g / 5 \)
\( \mathbf{D} \cdot-g / 5 \)


The value of \( \frac{1}{\operatorname{cosec}^{2} \theta}+\frac{1}{\sec ^{2} \theta} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \sin ^{2} \theta \)
\( \mathbf{D} \cdot \cos ^{2} \theta \)


An experiment involves rolling a pair of dice and recording the numbers that come up describe the following events:
\( A: \) the sum is greater than 8
\( \mathrm{B}: 2 \) occurs on either die
\( \mathrm{C}: \) the sum is at least 7 and a multiple
of 3
Which pairs of these events are mutually exclusive?


If the average kinetic energy of a molecule of a hydrogen gas at \( 300 \mathrm{K} \) is \( \mathrm{E} \) then the average kinetic energy of a molecule of a nitrogen gas at the same temperature is:
A . \( 7 \mathrm{E} \)
в. \( E / 14 \)
\( c .14 E \)
D. \( E / 7 \)
\( E . \)


The mass and sides of a cube given as \( (10 k g \pm 0.1) \) and \( (0.1 m \pm 0.01), \) the
relative error in density is:
A . 0.31
B. 0.5
c. 0.62
D. 0.29


For a reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightarrow \) products
when \( \mathrm{B} \) is taken in excess, then the rate
law expression can be written as:
\( \mathbf{A} \cdot \operatorname{Rate}=K[A]^{1}[B]^{0} \)
B . Rate \( =K[A]^{1}[B]^{2} \)
\( \mathbf{c} . \) Rate \( =K[A][B] \)
D. Rate\( =K[A]^{2}[B]^{1} \)


Which of the following is a highly polar bond?
A \( . O-H \)
в. \( N-H \)
c. \( H-C l \)
D. \( H-F \)


A drop of a solution (volume \( =0.05 m l \) )
contains \( 6 \times 10^{-7} \) mole of \( H^{+} \)
If the rate of disappearance of \( \boldsymbol{H}^{+} \) is
\( 6.0 \times 10^{5} \) mol \( L^{-1} s^{-1} \)
How long will it take for the \( H^{+} \) in the
drop to disappear?
A \( .8 .0 \times 10^{-8} \mathrm{s} \)
B . \( 2.0 \times 10^{-8} \) s
c. \( 6.0 \times 10^{-6} \mathrm{s} \)
D. \( 2.0 \times 10^{-2} \mathrm{s} \)


A rectangular tube of uniform cross section has three liquids of densities
\( \rho_{1}, \rho_{2} \) and \( \rho_{3} . \) Each liquid column has
length I equal to length of sides of the equilateral triangle. Find the length \( x \) of
the liquid of density \( \rho_{1} \) in the horizontal
limb of the tube, if the triangular tube is kept in the vertical plane


The following is a lewis acid?
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( c . F \)
D.


If \( \mathbf{f}(\mathbf{x}) \) is minimum at \( \mathbf{x}=\mathbf{a} \) then
A. There exists \( \delta>0 \) such that \( a-\delta<x<a \Rightarrow f(x)<f(a) \)
B. There exists \( \delta>0 \) such that \( a<x<a+\delta \Rightarrow f(x)>f(a) \)
C. There exists \( \delta>0 \) such that \( a-\delta<x<a+\delta \Rightarrow \)
\( f(x) \geq f(a) \)
D. There exists \( \delta>0 \) such that \( a-\delta<x<a+\delta \Rightarrow \)
\( f(x) \leq f(a) \)


A stationary source emits sound of
frequency \( f_{0}=492 H z . \) The sound is
reflected by a large car approaching the
source with a speed of \( 2 m s^{-1} \). The
reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in \( H z ? \) (Given that the speed of sound in air is \( 330 m s^{-1} \) and the car reflects the sound
at the frequency it has received)


Explain the Junction of bar screens in a wastewater treatment plant.


Why is oil preferred for frying and not
water?


The total of subshells in fourth energy
level of an atom is
A . 4
B. 8
\( c \cdot 16 \)
D. 32


\( \frac{\boldsymbol{\alpha}}{\boldsymbol{t}^{2}}=\boldsymbol{F} \boldsymbol{v}+\frac{\boldsymbol{\beta}}{\boldsymbol{x}^{2}} \)
Find the dimensional formula for \( [\boldsymbol{\alpha}] \)
and \( [\beta] \) using the given equation
(here \( t= \) time, \( F= \) force, \( v= \) velocity, \( x= \) distance)


The nature of electromagnetic wave is:
A. longitudinal
B. longitudinal stationary
c. transverse
D. transverse stationary


The organic compound which when mixed with ethyl alcohol, [ethanol],
makes a spurious is:
A. methanol
B. methanoic acid
c. methanal
D. ethanoic acid


The population of a city increases by
\( 30 \% \) every ytear. If the present population is 338000 , then What was the population of the city two years ago?


If a scalene triangle is cut along its line of symmetry, then the number of triangles so formed is
A . 1
B. 2
\( c .3 \)
D. none of the above


A circular disc of radius 0.2 meter is placed in a uniform magnetic field of \( \frac{1}{\pi} \) \( \boldsymbol{w} \boldsymbol{b} / \boldsymbol{m}^{2} \) in such way that its axis makes an angle of \( 60^{\circ} \) with \( \vec{B} \). The magnetic flux linked with the disc is?
A. 0.08 wb
B. 0.01 wb
\( c .0 .02 \mathrm{wb} \)
D. 0.06 wb


\( \frac{x^{-1}}{x^{-1}+y^{-1}}+\frac{x^{-1}}{x^{-1}-y^{-1}} \) is equal to
A. \( \frac{2 y^{2}}{y^{2}-x^{2}} \)
в. \( \frac{2 x^{2}}{y^{2}-x^{2}} \)
c. \( \frac{2 y^{2}}{y^{2}+x^{2}} \)
D. none


The process of re-emission of absorbed
light in all directions with different intensities by the atom or molecule is called
A. Scattering of light
B. Dispersion of light
c. Reflection of light
D. Refraction of light


If
\( a, b, c \) are distinct non-zero real numbers having the same sign, then prove that \( \cot ^{-1}\left(\frac{a b+1}{a-b}\right)+\cot ^{-1}\left(\frac{b c+1}{b-c}\right)+ \)
\( \cot ^{-1}\left(\frac{c a+1}{c-a}\right)=\pi \quad o r \)


Assertion:In simple harmonic motion A
is the amplitude of oscillation. If \( t_{1} \) be
the time to reach the particle from mean position to \( \frac{A}{\sqrt{2}} \) and \( t_{2} \) the time to reach from \( \frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}} \) to \( \mathbf{A}, \) then \( \boldsymbol{t}_{\mathbf{1}}=\frac{\boldsymbol{t}_{\mathbf{2}}}{\sqrt{\mathbf{2}}} \)
Reason : Equation of motion for the particle starting from mean position is \( \operatorname{given} \operatorname{by} x=A \cos (\omega t) \) and of the
particle starting from extreme position is given by \( \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
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


Describe Kelvins method to determine
the resistance of galvanometer by using meter bridge.


Expand M.T.P.


A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the
liquid and the room is plotted against time. The plot will be very nearly
A. a straight line
B. a circular arc
c. a parabola
D. an ellipse.


\( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}: \Delta H= \)
\( -92 k J \) is Haber s process for
manufacture of \( N H_{3} . \) What is the heat
of formation of \( \boldsymbol{N} \boldsymbol{H}_{3} ?(\text { in } \mathrm{kJ} / \mathrm{mol}) \)


State the following statement is True or False
The area bounded by the circle \( x^{2}+ \) \( \boldsymbol{y}^{2}=\mathbf{1}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{4} \) and the pair of lines
\( \sqrt{3}\left(x^{2}+y^{2}\right)=4 x y, \) is equal to \( \frac{\pi}{2} . \) The
statement is true or false.
A. True
B. False


The hormone which controls the
contraction of uterus after child birth
and also produces lactation in the mammary glands is:
A . Insulin
B. Oxytocin
c. Estrone
D. Estradiol


An electron is released from rest in a
uniform electric field which causes it to
accelerate toward the top of the screen
What is the direction of the electric
field?
A. To the left
B. Toward the top of the screen
c. To the right
D. Toward the bottom of the screen


The compound \( (X) \) is:
\( \mathbf{A} \cdot P h C O O N a \)
B.
\( \mathbf{c} \)
D. \( P h-C H=C H-P h \)


Seed of black pepper is
A. Endospermic
B. Exalbuminous
c. Acotyledonous
D. Perispermic


Evaluate the following limits. \( \lim _{x \rightarrow \sqrt{3}} \frac{x^{4}-9}{x^{2}+4 \sqrt{3} x-15} \)


The correct increasing order of
strengths of following acids is:
\( \mathbf{A} \cdot H_{2} S O_{4}, C H_{3} C O O H, H_{2} C O_{3} \)
B. \( C H_{3} C O O H, H_{2} S O_{4}, H_{2} C O_{3} \)
\( \mathbf{c} \cdot H_{2} C O_{3}, C H_{3} C O O H, H_{2} S O_{4} \)
D. \( C H_{3} C O O H, H_{2} C O_{3}, H_{2} S O_{4} \)


Draw two squares of different sides. Can
you say they are similar? Explain. Find
the ratio of their perimeters and areas. What do you observe?


If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1}{2}(\sqrt{3}+1) \)
B. \( 2(\sqrt{3}-1) \)
c. \( \frac{1}{2}(\sqrt{3}-1) \)
D. none of these


Two unbiased dice are thrown. The
probability that the sum of the numbers appearing on the top face of two dice is
greater than 7 if 4 appear on the top face of the first dice is...
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{12} \)
D.


\( \mathbf{5 0} \boldsymbol{m l}, \mathbf{0 . 6} \boldsymbol{M} \boldsymbol{a q} . \) solution of \( \boldsymbol{B a C l}_{2} \) is
mixed with \( 50 m l, 0.6 M N a_{3} P O_{4} \)
solution at \( 25^{\circ} \mathrm{C} \), then concentration of
\( B a^{2+} \) ions in the solution at \( 25^{\circ} \mathrm{C} \) is:
\( \left(K_{s p} \text { of barium phosphate at } 25^{\circ} C=\right. \) \( \left.2.7 \times 10^{-10}\right) \)
A \( \cdot 1 \times 10^{-3} M \)
В \( \cdot 2 \times 10^{-3} M \)
c. \( 3 \times 10^{-3} M \)
D. \( 3 \times 10^{-2} M \)


Consider \( A \) and \( B \) two square matrices
of same order. Select the correct
alternative.
\( \mathbf{A} \cdot|A B| \) must be greater than \( |A| \)
B. \( \left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] \) is not unit matrix
C \( \cdot|A+B| \) must be greater than \( |A| \)
D. If \( A B=0 \), either \( A \) or \( B \) must be zero matrix


Valency of magnesium and oxygen in MgO is
A. one and one
B. two and two
c. one and two
D. two and one


Asthma is a respiratory disease caused
due to
A. Infection of trachea
B. Infection of lungs
c. Bleeding in pleural cavity
D. Spasm in bronchial muscles


The value of \( \tan \left\{\frac{1}{2} \cos ^{-1}\left(\frac{\sqrt{5}}{3}\right)\right\} \) is
A \( \cdot \frac{3+\sqrt{5}}{2} \)
B. \( 3+\sqrt{5} \)
c. \( \frac{1}{2}(3-\sqrt{5}) \)
D. None of these


Four large parallel identical conducting
plates of area A are arranged as shown
in fig. The charges on each plate are
given in the figure and the separation between the plates is d(d is very small). The surfaces of the plates are numbered (1), (2),
(1)


A moving body weighing \( 400 N \)
possesses \( 500 J \) of kinetic energy. Calculate the velocity with which the
body is moving. \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-1}\right) \)


If \( \frac{25^{x} \times 10^{2 x}}{4^{x}}=5^{8}, \) find \( x \)


Which plant is used for demonstrating plasmolysis in the laboratory?
A. Tropaeolum
B. Impatiens balsam
c. Tradescantia
D. All of the above


A car of mass 500 kg travelling with a speed of \( 20 \mathrm{m} / \mathrm{s} \) stops by applying wakes in 2 seconds. Find :
Force applied by the wakes. Work done by the wakes.


What is the \( 1025^{t h} \) term of the
sequence
\( \mathbf{1}, \mathbf{2}, \mathbf{2}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{8}, \mathbf{?} \)


Find the real values of \( x \) and \( y \) for which
the following equation is satisfied
\[
\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i
\]
A. \( x=3, y=-1 \)
B. \( x=-3, y=-1 \)
c. \( x=3, y=1 \)
D. \( x=-3, y=1 \)


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{3+x}\left(x^{2}-1\right) \) is
A \( \cdot(-3,-1) \cup(1, \infty) \)
B . [-3,-1)\( \cup[1, \infty) \)
c. (-3,-2)\( \cup(-2,-1) \cup(1, \infty) \)
D \( \cdot[-3,-2) \cup(-2,-1) \cup[1, \infty) \)


When a non volatile solute is added to a
pure solvent, the:
A. vapour pressure of the solution becomes lower then that of the pure solvent
B. rate of evaporation of the pure solvent is reduced
C. solute does not effect the rate of condensation
D. rate of the evaporation of the solution is equal to the rate of condensation of the solution at a lower vapour pressure than that in the case of the pure solvent


Which of the following statements is
false?
A. Two different solutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.
B. The osmotic pressure of a solution is given by the equation \( \pi=C R T \) (where \( C \) is the molarity of the
solution)
C. Decreasing order of osmotic pressure for \( 0.01 M \) aqueous solutions of barium chloride, potassium chloride, acetic acid and sucrose is \( B a C l_{2}>K C l> \)
\( C H_{3} C O O H> \) sucrose
D. According to Raout's law the vapour pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution


A particle having a charge of \( 20 \mu C \) and
mass \( 20 \mu g \) moves along a circle of
radius \( 5 \mathrm{cm} \) under the action of a
magnetic field B=0.1 tesla. When the particle is at \( P, \) uniform transverse
electric field is switched on and it is
found that the particle continues along the tangent with a uniform velocity.
Find the electric field :
\( A \cdot 2 V / m \)
B. \( 0.5 \mathrm{V} / \mathrm{m} \)
\( c .5 \mathrm{v} / \mathrm{m} \)
D. \( 1.5 \mathrm{V} / \mathrm{m} \)


A square card of side length \( 1 \mathrm{mm} \) is being seen through a magnifying lens of focal length \( 10 \mathrm{cm} . \) The card is placed at a distance of \( 9 \mathrm{cm} \) from the lens. The apparent area of the card through the lens is
\( \mathbf{A} \cdot 1 \mathrm{cm}^{2} \)
B. \( 0.81 \mathrm{cm}^{2} \)
c. \( 0.27 \mathrm{cm}^{2} \)
D. \( 0.60 \mathrm{cm}^{2} \)


Burning of coal is represented as
\( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \cdot \) The rate of
this reaction is increased by:
A. Decreasing in the concentration of oxygen
B. Powdering the lumps of coal
c. Decreasing the temperature of coal
D. Providing inert atmosphere


Describe laboratory method of preparation of sulphur dioxide giving chemical equations. Give chemical equations of the reactions of sulphur
dioxide with potassium permanganate and lime water


In quantitative inheritance, \( F_{2} \) ratio
obtained in a dihybrid cross is
A .1: 4: 6: 4: 1
B. 15: 1
c. 12: 3:
D. 9 :7


Account for the following.
\( \mathrm{p} K_{a} \) value of 4 -nitrobenzoic acid is
lower than that of benzoic acid.


Meera's mother, in four times as old as
Meera. After 5 years, her mother will be
three times as old as she will be then.
What are their present ages.


The Cahn-Ingold-Prelog stereochemical
designations used for the following
substance are:
\( A \cdot 2 S, 4 R \)
B. \( 2 S, 4 S \)
\( c \cdot 2 R, 4 S \)
D. \( 2 R, 4 R \)


\( \boldsymbol{A O} \rightleftharpoons \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{A}_{2}+\left(\frac{\mathbf{1}}{\mathbf{2}}\right) \boldsymbol{O}_{2} ; \boldsymbol{K}=\mathbf{5} \times \mathbf{1 0}^{\mathbf{5}} \)
\( \boldsymbol{B O} \rightleftharpoons \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{B}_{2}+\left(\frac{\mathbf{1}}{\mathbf{2}}\right) \boldsymbol{O}_{2} ; \boldsymbol{K}=\mathbf{1 . 1 0} \times \)
\( \mathbf{1} \mathbf{0}^{\mathbf{1}} \)
\( \boldsymbol{C O} \rightleftharpoons \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C}_{2}+\left(\frac{\mathbf{1}}{\mathbf{2}}\right) \boldsymbol{O}_{2} ; \boldsymbol{K}=\mathbf{2} . \mathbf{3} \times \mathbf{1 0}^{\mathbf{1 8}} \)
\( \boldsymbol{D} \boldsymbol{O} \rightleftharpoons \frac{1}{2} \boldsymbol{D}_{2}+\left(\frac{1}{2}\right) \boldsymbol{O}_{2} ; \boldsymbol{K}=\mathbf{1 . 4} \times \mathbf{1 0}^{21} \)
Which oxide is most stable?
A \( . A O \)
B. \( B O \)
c. \( C O \)
D. \( D O \)


The mean of five numbers in AP is 89.
The product of first and last terms is
\( 7885 . \) The AM of first, third and fifth term is
\( \mathbf{A} \cdot 83 \)
B. 86
\( c .89 \)
D. 90


A gaseous mixture having 4 mole of \( H_{2} \)
and 6 mole of \( I_{2} \) on heating shows
equilibrium concentration of \( \boldsymbol{H} \boldsymbol{I} \) as \( \boldsymbol{2} \)
mole. If we start with 4 moles of \( H_{2} \) and
9 mole of \( I_{2} \) at the same temperature,
how many mole of \( \boldsymbol{H} \boldsymbol{I} \) will be formed?
Also calculate degree of dissociation of
\( H I \) at this temperature


Two cars each with mass \( M \) are
heading towards each other, one with
velocity \( v_{1}=-2 m / s \) and the other with
\( \boldsymbol{v}_{2}=\mathbf{3} \boldsymbol{m} / \boldsymbol{s} \)
What is the speed of the center of mass of the two-car system?
A \( \cdot \frac{1}{2} m / s \)
в. \( 1 m / s \)
c. \( \frac{3}{2} m / s \)
D. \( \frac{5}{2} m / s \)
E. \( 5 m / s \)


Antoine Henri Becquerel was awarded
the Nobel Prize in 1903 for.
A. Discovering spontaneous radioactivity
B. Diffraction of X-rays
c. Demonstrating the influence of earth's magnetic field on its atmosphere
D. Investigating the absorption of light by crystals


Margarine has the advantage over butter that it can be produced cheaply from vegetable oils. One major process in the production of margarine from vegetable oils involves:
A. hydrogenation of unsaturated esters
B. dehydrogenation of saturated esters
c. polymerization of unsaturated esters
D. polymerization of saturated esters


The extent to which a given measurement agrees with the standard value for that measurement is known
as :
A. Accuracy
B. Precision
c. Accuracy and Precision
D. None of these


Fill in the blanks with appropriate
words.

In meiotic division, prophase lis
completed in five successive stages, viz and


Which of the following is the general electronic configuration in the valence
shell of elements of a group \( -16 ? \)
A \( \cdot n s^{2} n p^{3} \)
В. \( n s^{2} n p^{4} \)
c. \( n s^{2} n p^{6} \)
D. \( n s^{2} n p^{5} \)


Match of the physical quantities given here under having same units and dimensions
Section-A
a)
e) \( \frac{1}{2} \rho\left(v_{2}^{2}-\frac{2}{1}\right) \)
Kinematic viscosity
b) Dynamic lift
\( \eta \)
c) Bernoullis theorer
g) a \( v= \) constant
d) Equation
h) \( p+\frac{1}{2} \rho v^{2}+\rho g h= \)
of continuity \( \quad \) constant
\( A \cdot a-f ; b-e ; c-h ; d-g \)
B. a-f; b-e; c-g; d-h
c. a-g; b-f; c-e; d-h
D. a-h; b-g; c-f; d-e


From Bohr's model radius of the orbit
and energy of the hydrogen atom are
calculated as:
This question has multiple correct options
A. radius of the 1st orbit is \( 0.529 A^{\circ} \)
B. energy of the 1st orbit is \( -13.6 e V \)
C. energy of the 1st orbit is \( -21.72 \times 10^{-19} \mathrm{J} \)
D. radius of the 1st orbit is \( 1.06 A^{\circ} \)


Spore producing plants are
A. I, II and III
B. II, III and IV
c. II and IV
D. III and IV
E. IV only


Given that the equilibrium constant for the reaction \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \)
has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? \( \boldsymbol{S O}_{3(g)} \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2(g)}+\frac{\mathbf{1}}{2} \boldsymbol{O}_{2(g)} \)
B . \( 1.3 \times 10^{-5} \)
c. \( 1.8 \times 10^{-3} \)
D. \( 3.6 \times 10^{-5} \)


A conductor AB of length \( l \) carrying a
current \( i \) is placed perpendicular to a
long straight conductor XY carrying a
current \( I \) as shown. The force on \( A B \) will
be :
A \( \cdot \frac{\mu_{0} l i}{2 \pi} \log 2 \)
B \( \cdot \frac{\mu_{0} l i}{2 \pi} \log 3 \)
c. \( \frac{3 \mu_{0} l i}{2 \pi} \)
D. \( \frac{2 \mu_{0} l i}{3 \pi} \)


Which of the following is an anionic detergent?
A. Glyceryl oleate
B. Sodium stearate
c. sodium lauryl sulphate
D. Cetyltrimethyl ammonium bromide


An acromion process is
characteristically found in the
A. Pectoral girdle of mammals
B. Sperm of mammals
c. Pelvic girdle of mammals
D. skull of frog


A long wire bent as shown in figure
carries current \( I . \) If the radius of the
semicircular portion is \( a \), the magnetic
field at center \( C \) is:
A \( \cdot \frac{\mu_{0} I}{4} \)
B. \( \frac{\mu_{0} I}{4 \pi a} \sqrt{\pi^{2}+4} \)
c. \( \frac{\mu_{0} I}{4 a}+\frac{\mu_{0} I}{4 \pi a} \)
D. \( \frac{\mu_{0} I}{4 \pi a} \sqrt{\pi^{2}-4} \)


Value based questions.
Why does ozone hole form over
Antarctica?


Why is teflon used as a tape for sealing purpose?


An aromatic hydrocarbon has the
molecular formula \( C_{10} H_{14} . \) Upon
oxidation with boiling alkaline \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
followed by acidification, it yields benzene dicarboxylic acid. The total
isomers for \( C_{10} H_{14} \) are:
\( \mathbf{A} \cdot \mathbf{9} \)
B. 8
\( c \cdot 7 \)
D. 6


Write the formula for de Broglie wavelength. An electron is moving with speed of \( 0.5 \times 10^{3} m / s . \) Find the de
Broglie wavelength associated with it.


MN and MQ are tangents from a point \( \mathrm{M} \)
outside the given circle with center \( \boldsymbol{O} \)
If \( \angle N O Q=120^{\circ} \) then which of the
following rlations holds true:
A \( . N Q=M N=M Q \)
в. \( N Q=O M \)
c. \( O Q=O M \)
D. \( O N=M N \)


n given figure \( A B C D \) is a
quadrilateral in which \( P, Q, R \) and \( S \) are
mid-points of the sides. \( A B, B C, C D \)
and \( D A . A C \) is a diagonal. Show that:
(i) \( \boldsymbol{S R} \| \boldsymbol{A C} \) and \( \boldsymbol{S R}=\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{A C} \)
(ii) \( \boldsymbol{P Q}=\boldsymbol{S} \boldsymbol{R} \)
(iii) \( P Q R S \) is a parallelogram


The critical angle of a medium B with
respect another medium A is \( 45^{\circ} \) and
the critical angle of a medium C with
respect the medium B is \( 30^{\circ} . \) The
critical angle of medium \( C \) with respect
to A is :
A. Less than 30
B. Greater than \( 30^{\circ} \)
\( c \cdot 30 \)
D. Cannot be determined


A cricketer catches a ball of mass \( 150 g \) in \( 0.1 s \) moving with speed \( 20 m / s \)
then the experiences force of


A rod of length 1 m and mass 0.5 kg
hinged at one end, is initially hanging vertical. The other end is now raised
slowly until it makes an angle \( 60^{\circ} \) with the vertical. The required work is (use
\( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( \cdot \frac{5}{2} J \)
в. \( \frac{5}{4} J \)
c. \( \frac{17}{8} J \)
D. \( \frac{5 \sqrt{3}}{4} J \)


IUPAC name of \( \mathbf{C C l}_{3} \mathbf{C H}_{2} \mathbf{O H} \)


The population of a town 2 years ago
was \( 2500 . \) Due to migration to cities, it decreases every year at the rate \( 4 \% \) per annum. Find its present population.


In foam extinguisher is
present in the bottle


Which of the following materials is
most similar in its properties to \( M O 3 ? \)
A. Woodd
B. Oiled paper
c. stee
D. Brass


Q Type your question
Nuj \( (2 S, 3 R)-2 \) amino \( -3- \) hydroxybutanoic
acid)?
\( A \)
B.
\( c \)
\( D \)


In Young's double-slit experiment the
spacing between the slits is 'd and wavelength of light used is 6000 A. If the angular width of a fringe formed on a
distant screen is \( 1^{0}, \) then value \( ^{\prime} d^{\prime} \) is :
A . \( 1 m m \)
B. \( 0.05 \mathrm{mm} \)
c. \( 0.03 m m \)
D. \( 0.01 m m \)


Coke is used in preparation of producer gas which is a mixture of:
A. \( C O \) and \( N_{2} \)
в. \( C O \) and \( O_{2} \)
c. \( C O_{2} \) and \( N_{2} \)
D. \( O_{2} \) and \( N_{2} \)


A solution contains \( 0.1 M C l^{-} \) and
\( \mathbf{0 . 0 0 1} \boldsymbol{M} \boldsymbol{C r} \boldsymbol{O}_{4}^{2-} . \) If solid \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) is
gradually added to this solution, which
will precipitate first, \( A g C l \) or \( A g_{2} C r O_{4} \)
? Assume that the addition causes no
change in volume. Given \( \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{M}^{\mathbf{2}} \)
\( \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}=\mathbf{1 . 7 9} \times \mathbf{1 0}^{-\mathbf{1 2}} \boldsymbol{M}^{\mathbf{3}} \)
What percent of \( C l^{-} \) remains in the
solution when \( C r O_{4}^{2-} \) starts precipitating?


Accumulation of food in assimilatory cells results in
A. Increase in the rate of photosynthesis
B. Decrease in the rate of photosynthesis
c. No effect
D. May increase or decrease


\( f(x)=\left\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & x \neq 2 \\ 4 & x=2\end{array} \) discus \right.
continuity at \( \boldsymbol{f}(\boldsymbol{2}) \)


For a given prism \( \theta \) and \( \delta \) are angular dispersion and deviation correct
relation is
\( \mathbf{A} \cdot \theta \propto \delta \)
B \( \cdot \theta \propto \frac{1}{\delta} \)
c. \( \theta \propto \delta^{2} \)
D. \( \theta \alpha \propto \frac{1}{\delta^{2}} \)


\( f(x)=\frac{[x]+1}{\{x\}+1} \) for \( f:\left[0, \frac{5}{2}\right) \rightarrow \)
\( \left[\frac{1}{2}, 3\right), \) where [.] represent the integer
function and \( \{.\} \) represent the fraction
part of \( x \). then which of the following is
true?
A. \( f(x) \) is injective discontinuous function
B. \( f(x) \) is surjective non-differntiable function
\( \mathrm{c} \cdot \min \left(\lim _{x \rightarrow 1^{-}} f(x), \lim _{x \rightarrow 1^{+}} f(x)\right) \)
D. \( \max (x \text { values of point of discontinuity })=f(1) \)


question


The percentage volume of \( C_{3} H_{8} \) in a
mixture of \( C_{3} H_{8}, C H_{4} \) and \( C O \) is 36.5
The volume of \( C O_{2} \) produced when 100
mL of mixture is burnt in excess of \( \boldsymbol{O}_{2} \)
is:
A . \( 273 \mathrm{mL} \)
B. \( 183 \mathrm{mL} \)
\( c .173 \mathrm{mL} \)
D. \( 193 \mathrm{mL} \)


Two resistances \( X \) and \( Y \) in the two gaps
of a meter-bridge gives a null point dividing the wire in the ratio \( 2: 3 . \) If
each resistance is increased by \( 3 \Omega \), the
null point divides the wire in the ratio \( 5: 6, \) calculate the value of \( X \) and \( Y \)


The value of \( \lim _{x \rightarrow \infty} \sqrt{x}(\sqrt{x+c}-\sqrt{x}) \) is
A \( \cdot \frac{c}{2} \)
B. \( \frac{c}{3} \)
\( c \cdot \frac{c}{4} \)
D. none of these


An inorganic compound which on heating first melts, then solidifies and
liberates a gas, is :
A. \( A l_{2} O_{3} \)
B. \( K M n O_{4} \)
\( \mathrm{c} \cdot M n O_{2} \)
D. \( K C l O_{3} \)


\( S O_{2} \) is a more powerful reducing agent
in:
A. acidic medium
B. alkaline medium
c. neutral medium
D. None of these


The ratio of maximum acceleration to
maximum velocity in a simple
harmonic motion \( 10 S^{-1} . A t, t=0 \) the
displacement is \( 5 \mathrm{m} \). What is the maximum acceleration? The initial
phase is \( \frac{\pi}{4} \)
\( \mathbf{A} \cdot 750 \sqrt{2} m / s^{2} \)
B . \( 500 \sqrt{2} \mathrm{m} / \mathrm{s}^{2} \)
c. \( 750 m / s^{2} \)
D. \( 500 m / s^{2} \)


What is the generic name of riboflavin?
A. Vitamin \( B_{1} \)
B. Vitamin \( B_{2} \)
c. Vitamin \( B_{6} \)
D. Vitamin \( B_{3} \)


\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -31.7 k c a l \)
The equilibrium concentration of \( C_{2} H_{4} \) in the following reaction can be increased by:
A. removal of \( C_{2} H_{6} \)
B. addition of \( H_{2} \)
c. increase in temperature
D. increase in pressure


Identify the number of polygons from the given figures?
A . 5
B . 2
\( c \cdot 6 \)
D. 3


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


Write \( I U P A C \) names of the following
compound:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \)


\( \boldsymbol{B} \boldsymbol{e} \boldsymbol{C l}_{2}+\boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{l} \boldsymbol{H}_{4} \longrightarrow \boldsymbol{X}+\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}+ \)
\( \boldsymbol{A l C l}_{3} \)
A. \( X \) is lithium hydride
B. \( X \) is \( B e H_{2} \)
c. \( X \) is \( B e C l_{2} \cdot 2 H_{2} O \)
D. \( X \) is \( L i H \)


Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a
wavelength of \( 32 c m \) and the other of
\( 32.2 \mathrm{cm} . \) The speed of sound in air is
\( 350 m / s \)
\( A .3 H z \)
в. \( 5 H z \)
\( \mathrm{c} .7 \mathrm{Hz} \)
D. \( 2 H z \)


In a triangle \( A B C, \angle A+\angle B=144^{\circ} \) and \( \angle A \)
\( +\angle C=124^{\circ} \)
Calculate each angle of the triangle.
A \( \cdot A=88^{\circ}, B=56^{\circ} \) and \( C=36 \)
B. A \( =78^{\circ}, B=66^{\circ} \) and \( C=36^{\circ} \)
C. \( A=58^{\circ}, B=86^{\circ} \) and \( C=36^{\circ} \)
D. \( A=88^{\circ}, B=26^{\circ} \) and \( C=66^{\circ} \)


The mass of the earth is \( 6 \times 10^{24} \mathrm{kg} \) and
that of the moon is \( 7.4 \times 10^{22} \mathrm{kg} \)
distance between the earth and the
moon be \( 3.84 \times 10^{5} \mathrm{km}, \) calculate the
force exerted by the earth moon. \( (G= \) \( \left.6.7 \times 10^{-11} N m^{2} k g^{-2}\right) \)


For proper ventilation of building, windows must be open near the bottom and top of the walls so as to let pass.
A. In more air
B. In hot air near the roof and cool air out near the bottom
c. out hot air near the roof
D. In cool air near the bottom and hot air out of the roof


You are given two lenses, a converging lens with focal length \( +10 \mathrm{cm} \) and a diverging lens with focal length -20 \( \mathrm{cm} \) Which of the following would produce a real image that is smaller than the object?
A. Placing the object 5 cm from the converging lens
B. Placing the object 15 cm from the converging lens
c. Placing the object 25 cm from the converging lens
D. Placing the object \( 15 \mathrm{cm} \) from the diverging lens


If \( x \) belongs to a set of integers, \( A \) is the
solution set of \( 2(x-1)<3 x-1 \) and \( B \)
is the solution set of \( 4 x-3 \leq 8+x \)
then find \( A \cap B \)
A \( \cdot\{0,1,2\} \)
в. \{1,2,3\}
\( \mathbf{c} \cdot\{0,1,2,3\} \)
D \cdot \{0,2,4\}


A step up transformer is connected on
the primary side to a rechargeable battery which can deliver a large current. If a bulb is connected in the
secondary, then
A. the bulb will glow very bright
B. the bulb will get fused
c. the bulb will glow, but with less brightness
D. the bulb will not glow


The number of integer \( \boldsymbol{x} \) satisfying \( \sin ^{-1}|x-2|+\cos ^{-1}(1-|3-x|)=\frac{\pi}{2} \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
\( D \)


A black smith fixes ring on the rime of
the wooden wheel of a bullock cart the
diameter of the rime and iron ring arc
5.243 and 5.231 resp. at \( 27^{\circ} C \) to what
temp, should the ring be heated. So as to fit the rime of the wheel \( \alpha=1.20 x \)
\( \mathbf{1 0}^{-\mathbf{5}} \)


Which of the following match are incorrect?
(a) Goldschmidt aluminothermite
process \( -C r_{2} O_{3} \)
(b) Mac Arther cyanide process - \( \boldsymbol{F e} \)
(c) Mond process - Ni
(d) Van Arkel process - \( A u \)
A \( \cdot \) a,
B. c, d
\( c \cdot b, d \)
D. a,


Planck's constant has the dimensions
A \( \cdot M L^{3} T^{-1} \)
B . \( M L^{2} T^{-1} \)
\( \mathbf{c} \cdot M L^{6} T^{-1} \)
D. \( M L^{8} T^{-1} \).


Show that \( \mathbf{a} .(\mathbf{b} \times \mathbf{c}) \) is equal in
magnitude to the volume of the
parallelopiped formed on the three
vectors, a, b and c.


A magnetic field of flux density \( 10 T \)
acts normal to a coil of 50 turns having
\( 100 \mathrm{cm}^{2} \) area. The e.m.f. induced if the
coil is removed from magnetic field in
0.1 second is
A . \( 50 V \)
в. \( 60 V \)
c. \( 80 V \)
D. \( 40 V \)


A satellite is projected with a speed \( \sqrt{\frac{5}{6}} \)
times of its escape speed from the earth's surface. The initial speed of the
satellite is parallel to the surface of the earth. The maximum distance of the
satellite from the center of the earth will
be
A. \( 3 R \)
в. \( 6 R \)
\( c .5 R \)
D. None of these


Two identical positive charges are 0.6
meters apart. Which of the following is true about the electric field and
potential at the point which is directly in-between the two?
A. The electric field and potential both are zero
B. The electric field and potential both are positive numbers
C. The electric field is a positive number while the potential is zero
D. The electric field is zero while the potential is a positive number


Which of the following is not correct regarding sexual reproduction?
A. It is usually biparental
B. Gametes are always formed
c. It is a slow process
D. It involves only mitosis


The final image formed by a compound microscope is inverted:
A. True
B. False


Statement-1: Where two vibrating tuning forks having frequencies \( 256 H z \)
and \( 512 H z \) are held near each other,
beats cannot be heard.
Statement-2: The principle of
superposition is valid only if the
frequencies of the oscillations are nearly equal.
A. Both the statements are true and statement- 2 is the correct explanation of statement-
B. Both the statements are true but statement-2 is not
the correct explanation of statement-
c. Statement- 1 is true and statement- 2 is false
D. Statement-1 is false and statement- 2 is true


Write the reaction occurring at the
cathode and anode in \( H_{2} \mathrm{AND} O_{2} \) fuel
cell.


Explain rancidity.


If \( 4 \times 10^{20} e V \) of energy is required to
move a charge of 0.25 coulomb between
two points, the p.d between them is:
A . 256 \( v \)
B. 512 \( v \)
\( c \cdot 123 v \)
D. 215 V


From a point source, if amplitude of
water at a distance 'r' is A, its amplitude at a distance '2r' will be
\( A \cdot A \)
B. 2A
c. A/2
D. A/4


Prove that the points (-3,0),(1,-3) and (4,1) are the vertices of an isosceles right-angled triangle. Find the area of this triangle


Expand each of the following, using suitable identities:
\( (-2 x+3 y+2 z)^{2} \)


Which one of the following statements
is true?
A. A motor works on the principle of electromagnetic induction
B. An electric motor converts mechanical energy into electrical energy
C. AC generator has slip rings while DC generator has a commutator
D. An electric generator converts electrical energy into mechanical energy


The value of \( (i+\sqrt{3})^{100}+ \) \( (i-\sqrt{3})^{100}+2^{100}= \)
A .
B. - -
\( c \cdot 0 \)
D.


An iron block of side \( 50 c m \times 8 c m \times \)
\( 15 c m \) has to be pushed along the floor.
The force required will be minimum
when the surface in contact with
ground is:
A. \( 8 c m \times 15 c m \) surface
B. \( 5 \mathrm{cm} \times 15 \mathrm{cm} \) surface
\( \mathrm{c} .8 \mathrm{cm} \times 5 \mathrm{cm} \) surface
D. force is same for all surfaces


Which one of the following constitutes a group of the isoelectronic species?
A \( \cdot C_{2}^{2-}, O_{2}^{-}, C O, N O \)
B. \( N O^{-}, C_{2}^{2-}, C N^{-}, N_{2} \)
c. \( C N^{-}, N_{2}, C O, C_{2}^{2} \)
D. \( N_{2}, O_{2}^{-}, N O^{-}, C O \)


Application based questions Suggest some habitats in which (a) light intensity or
(b) temperature might be limiting factors in photosynthesis.


The half life of \( R a^{226} \) is 1620 years. Then the number of atoms decay in one second in \( 1 \mathrm{gm} \) of radium:
(Avogadro number \( \left.=\mathbf{6 . 0 2 3} \times \mathbf{1 0}^{\mathbf{2 3}}\right) \)
\( \mathbf{A} \cdot 4 \cdot 23 \times 10^{9} \)
B. \( 3.16 \times 10^{10} \)
c. \( 3.61 \times 10^{10} \)
D. \( 2.16 \times 10^{10} \)


Which of the following acids is
produced by treating \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3} \) with
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) under suitable experimental
conditions?
A. \( H N O_{2} \)
в. \( H_{2} S O_{3} \)
c. \( H N O_{3} \)
D. \( H_{2} S_{2} O_{7} \)


The correct number in the \( 5^{t h} \) decimal
place of the number \( \frac{2}{7}=0 . \overline{285714} \)


From a rifle of mass \( 4 k g, \) a bullet of
mass \( 50 g \) is fired with an initial
velocity of \( 35 m s^{-1} \). Calculate the initia
recoil velocity of the rifle.


The angle between the line \( x+y=3 \) and the line joining the points (1,1) and (-3,4) is
A \( \cdot \tan ^{-1}(7) \)
B \( \cdot \tan ^{-1}(-1 / 7) \)
\( \mathbf{c} \cdot \tan ^{-1}(1 / 7) \)
D. None of these


4 balls are moving in the directions shown. The magnitudes of their momentum are also given in the figure.
Find which two have the same
momentum
A. \( A \) and \( B \)
в. \( C \) and \( D \)
c. \( A \) and \( C \)
D. A and \( D \)


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{a} \)
Given that \( (x+2) \) is a factor of \( f(x) \)
find the value of the constant \( a \)
A . -16
B. 32
\( c .-36 \)
D. 42


In the nuclear reaction given by \( _{2} H e^{4}+_{7} N^{14} \rightarrow_{1} H^{1}+X \) the nucleus
\( x \) is
A. nitrogen of mass 16
B. nitrogen of mass 17
c. oxygen of mass 16
D. oxygen of mass 17


Watson and Crick model of DNA is a
A. \( B \) -form DNA with a spiral length of \( 34 \AA \) and a diameter of \( 20 \dot{A} \)
B. \( A \) -form DNA with a spiral length of 15 and a diameter of \( 20 \AA \)
C. \( Z \) -form DNA with a spiral length of \( 34 \AA \) and a diameter of \( 20 \dot{A} \)
D. \( B \) -form DNA with a spiral length of \( 28 \dot{A} \) and a diameter of \( 14 \dot{A} \)


Evaluate \( \left(17^{2}-8^{2}\right)^{\frac{1}{2}} \)


Which of the following statements is the inverse of "Our pond floods whenever there is a thunderstorm."?
A. If there is a thunderstorm, then our pond floods
B. If we do not get a thunderstorm, then our pond does not flood.
c. If our pond does not flood, then we did not get a thunderstorm
D. None of these


What is \( C_{2} \) Cycle?
A. Glycolate cycle
B. Calvin cycle
c. Krebs cycle
D. TCA cycle