The phenomenon of photoperiodism in plants was discovered by
A. Garner and Allard
B. Wolff and Mendel
c. Thiman and Skoog
D. Hendricks and Borthwick


If \( m=^{n} \mathrm{C}_{2}, \) then \( ^{m} \mathrm{C}_{2} \) equals
\( \mathbf{A} \cdot^{n+1} \mathbf{C}_{4} \)
B. \( 3 x^{n+1} \mathrm{C}_{4} \)
\( \mathrm{c} \cdot^{n} \mathrm{C}_{4} \)
D. \( n+1 \mathrm{C}_{3} \)


Algal blooms impart a distinct colour to
water due to
A. Their pigments
B. Excretion of coloured substances
C. Formation of coloured chemicals in water facilitated
by physiological degradation of algae
D. Absorption of light by algal cell wall


Classification of organisms based on evolutionary as well as genetic relationship is known as
A. Biosystematics
B. Phenetics
c. Numerical taxonomy
D. Cladistics


An isomer of ethanol is:
A. methanol
B. dimethyl ether
\( c . \) acetone
D. diethyl ether


An electron in a hydrogen atom in its ground state absorbs energy equal to the ionization energy of \( L i^{+2} . \) The wavelength of the emitted electron is:
A. \( 3.32 \times 10^{-10} \mathrm{m} \)
в. 1.17 А
c. \( 2.32 \times 10^{-9} \mathrm{nm} \)
D. 3.33 pm


If percentage of cytosine is \( 18 \%, \) what will be the percentage of adenine?
A . 32\%
B. 64\%
c. 36\%
D. 23\%


The rate of a chemical reaction doubles
for every \( 10^{\circ} \mathrm{C} \) rise in temperature. If the
temp is increased by \( 60^{\circ} \mathrm{C} \) the rate of reaction increases by:
A. 20 times
B. 32 times
c. 64 times
D. 128 times


Use the formula \( \lambda_{m} T=0.29 \mathrm{cm} \mathrm{K} \) to
obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?


The displacement current flows in the
dielectric of a capacitor when the potential difference across its plates
A. becomes zero
B. has assumed a constant value
c. is increasing with time
D. is decreasing with time


Which of the following list of numbers
does form an AP?
A. \( 2,4,8,16, \dots \)
В \( \cdot 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots \)
c. \( 0.2,0.22,0.222,0.2222, \ldots \)
D. \( 1,3,9,27, \ldots \)


The centre of mass of a body:
A. lies always at the geometrical centre
B. lies always inside the body
C. lies always outside the body
D. may lie within or outside the body


Ammonia acts as a:
A . reducing agent
B. oxidising agent
C . bleaching agent
D. both \( A \) and \( c \)


The metals undergoing disproportionation are
A. sn
B. Na
\( c \cdot c u \)
D. \( c a \)


Find the domain of the function defined
\( \operatorname{as} f(x)=\frac{x+1}{2 x+3} \)
A \( \cdot x_{\epsilon} \mathrm{R}-\left\{\frac{3}{2}\right\} \)
B. \( _{x \in \mathrm{R}-\left\{\frac{-3}{2}\right\}} \)
\( c . x \epsilon \) R
D. \( _{x \in \mathrm{R}-\left\{\frac{2}{3}\right\}} \)


If \( p K_{b} \) for fluoride ion at 25 is 10.83 , the
ionisation constant of hydrofluoric acid
in water at this temperature is :
A \( \cdot 1.74 \times 10^{-5} \)
В. \( 3.52 \times 10^{-3} \)
c. \( 6.75 \times 10^{-4} \)
D. \( 5.38 \times 10^{-2} \)


A train is moving from south to north with a velocity of \( 90 \mathrm{km} / \mathrm{h} \). The vertical component of earth's
magnetic induction is \( 0.4 \times \) \( 10^{-4} W b / m^{2} . \) If the distance between
the two rails is \( 1 m, \) what is the induced
e.m.f. in its axle?
A. \( 1 m V \)
B. \( 0.1 m V \)
\( \mathrm{c} .10 \mathrm{mV} \)
D. \( 100 m V \)


The given figure shows the velocity-time
graph of an object. Find the acceleration
during the last \( 15 s \)
\( \mathbf{A} \cdot-2 m / s^{2} \)
B \( \cdot-4 m / s^{2} \)
\( \mathrm{C} \cdot-8 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{D} \cdot-16 m / s^{2} \)


\( \frac{d}{d x}\left(\log _{3} x\right) \)


A simple pendulum with bob of mass \( m \) and conducting wire of length L swings
under gravity through an angle \( 2 \theta \). The
earth's magnetic field component in the direction perpendicular to swing is B. The maximum potential difference
induced across the pendulum is?


The sum of the oxidation numbers of all
the atoms in a neutral molecule is
equal to:
A. zero
B. one
c. three
D. four


Give any two examples of forces in case
of push.


Decarboxylation of benzoic acid with soda lime gives:
A. benzene
B. Sodium bicarbonate
c. sodium benzoate
D. both A and B


A study found that children with lightcoloured eyes are likely to have parents with light-coloured eyes. On this basis, can we say anything about whether the light eye colour trait is dominant or recessive? Why or why not?


The wheels of an airplane are set into rotation just before landing so that the wheels do not slip on the ground. If the airplane is travelling in the east direction, what should be the direction of angular velocity vector of the wheels?
A. East
B. west
c. south
D. North


The value of \( \boldsymbol{f}(\mathbf{0}) \) so that \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\sqrt{1+x}-\sqrt[3]{1+x}}{x} \) is continuous is
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{4} \)
c. \( \frac{1}{3} \)
D. -


Study the bar graph representing the
number of persons in various age groups in a town shown in Fig. Observe the bar graph and answer the following
questions:
Whether the population in general increases, decreases or remains
constant with the increase in the age-
group


When mass is enclosed in a system and none is allowed in or out, it's
will never change.
A. quality
B. quantity
c. temperature
D. shape


Solve:
\( \frac{d y}{d x}=x^{2}(x-2), \) given \( y=2 \) where
\( \boldsymbol{x}=\mathbf{0} \)


Every elementary event associated with a random experiment has probability


If the rate of change of area of a square plate is equal to that of the rate of change of its perimeter, then length of the side is
A. 1 unit
B. 2 units
c. 3 units
D. 4 units


Solve the initial value problem:
\( \boldsymbol{d} \boldsymbol{y}=\boldsymbol{e}^{2 \boldsymbol{x}+\boldsymbol{y}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{y}(\boldsymbol{0})=\boldsymbol{0} \)


\( A B, B C \) and \( C D \) are the three consecutive
sides of a regular polygon. If \( \angle B A C= \)
\( 15^{\circ} . \) Find each interior angle of the
polygon.
A \( .147^{\circ} \)
B. 162
\( c \cdot 150 \)
D. \( 140^{\circ} \)


The magnetic moment \( (\mu) \) of a revolving electron around the nucleus varies with
principal quantum number \( n \) as :
A. \( \mu \propto 1 / n \)
В \( \cdot \mu \propto 1 / n^{2} \)
c. \( \mu \propto n \)
D. \( \mu \propto n^{2} \)


The theory of evolution indicates that
A. Man evolved from monkeys
B. Monkeys evolved.from man
C. Man evolved from Dinosaurs
D. Man and apes had a common ancestor


The value of \( x \) satisfying the equation
\( -3(x+6)=24 ? \)


Which one of the following bonds has the highest average bond energy?
A. \( S=O \)
в. \( C \equiv C \)
\( \mathbf{c} \cdot C \equiv N \)
D. \( N \equiv N \)


Work done in converting 18 of ice at \( -10 \mathrm{C} \) into steam at \( 100 \mathrm{C} \) is
A. 3.04 KJ
B. 6.05 KJ
c. о.721 к
D. 0.616 KJ


At a certain time of the day, a man 6
feet tall, casts his shadow 8 feet long. Find the length of the shadow cast by a
building 45 feet high, at the same time
which is next to the man


Consider the reaction:
\[
\begin{array}{l}
\boldsymbol{C l}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{S}(\boldsymbol{s})+ \\
\boldsymbol{2} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})
\end{array}
\]
The rate equation for this reaction is
rate \( =\boldsymbol{k}\left[\boldsymbol{C l}_{2}\right]\left[\boldsymbol{H}_{2} \boldsymbol{S}\right] \)
Which of these mechanisms is /are
consistant with this rate equation?
\( (\mathbf{A}) \boldsymbol{C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \rightarrow \boldsymbol{H}^{+}+\boldsymbol{C l}^{-}+\boldsymbol{C l}^{+}+ \)
\( \boldsymbol{H} \boldsymbol{S}^{-} \quad(\text { slow }) \)
\[
\boldsymbol{C l}^{+}+\boldsymbol{H} \boldsymbol{S}^{-} \rightarrow \boldsymbol{H}^{+}+\boldsymbol{C l}^{-}+\boldsymbol{S}
\]
(fast)
(B) \( \boldsymbol{H}_{2} \boldsymbol{S} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{S}^{-} \)
(fast equilibrium)
\[
\boldsymbol{C l}_{2}+\boldsymbol{H} \boldsymbol{S}^{-} \rightarrow \boldsymbol{2} \boldsymbol{C l}^{-}+\boldsymbol{H}^{+}+\boldsymbol{S}
\]
(slow)
A. B only
B. Both A and B
C. Neither A nor B
D. A only


An \( \alpha- \) particle having energy \( 10 M e V \) collides with a nucleus of atomic
number 50.Then distance of closet
approach will be
A \( \cdot 14.4 \times 10^{-16} m \)
в. \( 1.7 \times 10^{-7} \mathrm{m} \)
c. \( 1.5 \times 10^{-12} m \)
D. \( 14.4 \times 10^{-15} \mathrm{m} \)


A current \( I \) flows in a long single-layer
solenoid with cross-sectional radius \( \boldsymbol{R} \)
The number of turns per unit length of
the solenoid equals \( n \). If the limiting current at which the winding
may rupture if the tensile strength of
the wire is equal to \( \boldsymbol{F}_{\text {lim }} \) is \( \boldsymbol{I}_{\text {lim }}= \) \( \sqrt{\frac{x F_{l i m}}{\mu_{0} n R}} . \) Find \( x \)


A train covered a certain distance at a
uniform speed. If the train would have been \( 10 \mathrm{km} / \mathrm{h} \) faster, it would have
taken 2 hours less than the scheduled
time. And, if the train were slower by 10 \( \mathrm{km} / \mathrm{h} ; \) it would have taken 3 hours more
than the scheduled time. Find the
distance covered by the train.


A helium nucleus makes a full rotation
in a circle of radius \( 0.8 m \) in 2 sec. The
value of the magnetic field induction \( \boldsymbol{B} \)
in tesla at the centre of circle will be
A \( \cdot 2 \times 10^{-19} \mu_{0} \)
B . \( 10^{-19} / \mu_{0} \)
\( \mathbf{c} \cdot 10^{-19} \varphi_{0} \)
D. \( 2 \times 10^{-20} / \mu_{0} \)


For PN junction, the intensity of electric field is \( 1 \times 10^{6} \mathrm{V} / \mathrm{m} \) and the width of
depletion region is 5000 A. The value of
potential barrier=
V.
A . 0.05
B. 0.005
\( c .0 .5 \)
D. 5


A circular park has a path of uniform width around it. The difference between
outer and inner circumference of the
circular path is \( 132 m \). Its width is: Take \( \left(\boldsymbol{\pi}=\frac{22}{7}\right) \)
\( A \cdot 22 m \)
B. \( 20 m \)
\( \mathbf{c} \cdot 21 m \)
\( \mathbf{D} \cdot 24 m \)


The energy gap between the valence
band and the condition band for a
material is \( 6 \mathrm{eV} \). The material is?
A. an insulator
B. a metal
c. an intrinsic semiconductor
D. a superconductor


thingy hanging from a spring. The system was set vibrating by pulling the
thingy down below its equilibrium position and then letting it go from
rest. If the initial displacement is
doubled what happens to the maximum
kinetic energy of the thing?
A. It is unchanged.
B. It is doubled
c. It is increased by a factor of \( 4 . \)
D. We can't tell from the information provided


Choose the correct statement from the
following This question has multiple correct options
A. Electric current is a scalar quantity
B. Charge carriers in metals are ions
c. The area of current - time graph gives charge
D. A charge in motion produces both electric and magnetic field


Which of the following fish is jawless?
A. Chondrichthyes
B. osteichthyes
c. cyclostomata
D. Amphibia


Choose the incorrect relation on the
basis of Bohr's theory.
A \( \cdot \) velocity of electron \( \propto \frac{1}{n} \)
B. Frequency of revolution \( \propto \frac{1}{n^{3}} \)
c. Radius of orbit \( \propto n^{2} Z \)
D. Force on electron \( \propto \frac{1}{n^{4}} \)


Graph ( \( i v \) ) is represented by which
equation?
\( (i) \)
(i)
(iii)
(iv)
A \( \cdot y=2 x \)
B. \( y+x=2 \)
\( \mathbf{c} \cdot y=2+x \)
D. \( x=y+22 \)


Define and understand the following
terms:
(i) Phylum
(ii) Class
(iii) Family (iv) Order (v) Genus


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{2 5}-\boldsymbol{x}^{2}} \) on \( [-\mathbf{3}, \boldsymbol{4}] \)


How can the following conversions be brought about :
Benzene to phenol.


A steering wheel of diameter \( 0.5 m \) is rotated anti-clockwise by applying two
forces each of magnitude \( 5 N \). Calculate the moment of couple applied:
A. \( 5 N m \)
в. \( 25 N m \)
\( c .50 N m \)
D. \( 2.5 N \) m


The inverse of a diagonal matrix is a :
This question has multiple correct options
A. Symmetric matrix
B. Skew-symmetric matrix
c. Diagonal matrix
D. None of the above


If \( \boldsymbol{A}=\tan ^{-1}\left(\frac{\boldsymbol{x} \sqrt{\mathbf{3}}}{\mathbf{2 K}-\boldsymbol{x}}\right) \) and \( \boldsymbol{B}= \)
\( \tan ^{-1}\left(\frac{2 x-K}{K \sqrt{3}}\right), \) then the value of
\( A-B \) is
\( A \)
B. 45
\( c .60 \)
D. 30


For a group of 200 candidates, the mean and \( S . D . \) were found to be 40 and 15
respectively. Late on it was found that
the score 43 was misread as \( 34 . \) Find
the correct mean and correct \( S . D . \)


The correct order of dipole moment is :
A. \( C H_{4}<N F_{3}<N H_{3}<H_{2} O \)
B. \( N F_{3}<C H_{4}<N H_{3}<H_{2} O \)
c. \( N H_{3}<N F_{3}<C H_{4}<H_{2} O \)
D. \( H_{2} O<N H_{3}<N F_{3}<C H_{4} \)


Let \( \rho \) be a relation defined on \( N, \) the set
of natural numbers, as
\( \boldsymbol{\rho}=\{(\boldsymbol{x}, \boldsymbol{y}) \in \boldsymbol{N} \times \boldsymbol{N}: \mathbf{2} \boldsymbol{x}+\boldsymbol{y}=\mathbf{4 1}\} \)
then
A. \( \rho \) is an equivalence relation
B. \( \rho \) is only reflexive relation
c. \( \rho \) is only symmetric relation
D. \( \rho \) is not transitive


At present Pooja is 21 years younger to her mother. 6 years from now, Pooja will be half her mother's age then. How old is Pooja's mother at present?
A. 36 years
B. 40 years
c. 42 years
D. 45 years


A body covers \( 10 \mathrm{m} \) in the seconds
second and \( 25 \mathrm{m} \) in fifth second of its
motion. If the motion is uniformly accelerated, how far will it go in the seventh second?


The shape of \( S C l_{2} \) molecule is:
A. linear
B. triangular
c. angular
D. pyramidal


A metallic square loop is moving in its
own plane with velocity \( v \) in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric
field is induced
\( A \). in AD, but not in BC
B. in BC, but not in AD
c. neither AD nor BC
D. in both AD and BC


In the screw gauge, the screw should be
moved in the same direction to avoid
which of the following error?
A . Zero error
B. Parallel error
c. Backlash error
D. Index error


Construct following quadrilaterals
(i) Quadrilateral \( L I F T \)
\( \boldsymbol{L} \boldsymbol{I}=\boldsymbol{4} \boldsymbol{c m} \)
\( \boldsymbol{I} \boldsymbol{F}=\mathbf{3} \boldsymbol{c m} \)
\( \boldsymbol{T} \boldsymbol{L}=\mathbf{2 . 5} \boldsymbol{c m} \)
\( \boldsymbol{L} \boldsymbol{F}=\mathbf{4 . 5} \boldsymbol{c m} \)
\( \boldsymbol{I} \boldsymbol{T}=\boldsymbol{4} \boldsymbol{c m} \)
(ii) Quadrilateral \( G O L D \)
\( \boldsymbol{O} \boldsymbol{L}=\mathbf{7 . 5} \boldsymbol{c m} \)
\( G L=6 \mathrm{cm} \)
\( G D=6 \mathrm{cm} \)
\( \boldsymbol{L} \boldsymbol{D}=\mathbf{5} \boldsymbol{c m} \)
\( O D=10 \mathrm{cm} \)
(iii) Rhombus \( B E N D \)
\( \boldsymbol{B} \boldsymbol{N}=\mathbf{5} . \boldsymbol{6} \boldsymbol{c m} \)
\( D E=6.5 \mathrm{cm} \)


Among the following compounds, which one has maximum boiling point?
A. n-butyl alcohol
B. n-butyraldehdye
c. diethyl ether
D. Butanoic acid


What extinguishes a fire most quickly?
A. Cold water
B. Boiling water
c. Hot water
D. Ice


The number of structural alcoholic
isomers for \( C_{4} H_{10} O \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


An elevator is moving up with \( 2.5 m s^{-1} \)
A bolt in the elevator ceiling 3 m above the elevator falls. How long (in seconds)
does it take for the bolt to fall on the
floor of the elevator?
A . 0.73
в. 0.71
c. 0.56
D. 1.06


Q Type your question
Clapeyron equation describes this
relationship. The Clausius-Clapeyron equation is :
\( \ln \left(P_{v a p o u r}\right)=-\frac{\Delta H_{v a p o u r}}{R}\left[\frac{1}{T}\right]+C \)
According to the graph, at high temperatures, which substance has
the greatest vapour pressure?
\( A \cdot w \)
B. \( x \)
\( c \)
\( D \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C} \) MgBr can be prepared by
the reaction of
A. \( C H_{3}-C \equiv C-B r \) with \( M g B r_{2} \)
B . \( C H_{3}-C \equiv C H \) with \( M g B_{2} \)
c. \( C H_{2}-C \equiv C H \) with KBr and Mg metal
D. \( C H_{3}-C \equiv C H \) with \( C H_{3} M g B r \)


Ores contain a large amount of impurities, which is called as:
A . ore
B. gangue
c. dust
D. particulate


toppr
Q Type your question
'8
center of the sphere according to the equation \( =C r . \) The diagram also shows
the cross-section of a Gaussian sphere
of radius \( a \) that is concentric with the
charged sphere

Which of the following expresses the
charge enclosed in the Gaussian
sphere?
\( ^{\mathrm{A}} \cdot \frac{2}{3}^{\pi} C a^{3} \)
в \( \cdot \frac{4}{3} \pi C a^{4} \)
c \( \cdot \frac{1}{4} \pi C a^{4} \)
D \( \cdot \pi C a^{4} \)
E \( \frac{4}{15} \pi C a \)


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined on \( [-2,2], \) and is
given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}-1,-2 \leq x \leq 0 \\ x-1,0 \leq x \leq 2\end{array} \text { and } g(x)=\right. \)
\( \boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})|, \) then find \( \boldsymbol{g}(\boldsymbol{x}) \)


Semi water gas is:
A. water gas + producer gas
B. water gas \( +C O_{2} \)
C . producer gas \( +C O_{2} \)
D. producer gas + Coal gas


The number of the terms of a geometric progression is even. The sum of all terms of the progression is thrice as large as the sum of its odd terms. Find
the common ratio of the progression.


The radius of a spherical soap bubble is increasing at the rate of \( 0.2 \mathrm{cm} / \mathrm{sec} \) Find the rate of increase of its surface
area, when the radius is \( 7 \mathrm{cm} \)


Find the modulus, argument and the principal argument of the complex numbers.
\( (\tan 1-i)^{2} \)
A. Modulus\( =\sec ^{2} 1, \operatorname{Arg}(z)=2 n \pi+(2- \)
\( \pi \) ), Principal \( \operatorname{Arg}(z)=(2-\pi) \)
B. Modulus = \( \operatorname{cosec}^{2} 1, \) Arg\( (z)=2 n \pi-(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(-2-\pi) \)
C. Modulus\( =\sec ^{2} 1, \operatorname{Arg}(z)=2 n \pi-(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(-2-\pi) \)
D. Modulus \( =\operatorname{cosec}^{2} 1, \) Arg\( (z)=2 n \pi+(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(2-\pi) \)


When phenol is treated with bromine
water, the product formed is :
A. \( o \) -Bromo phenol
B. \( p \) - Bromo phenol
c. \( m \) -Bromo phenol
D. 2,4,6 -Tribromo phenol


OPQR is a square, \( M \) and \( N \) are the
middle points of the sides \( P Q \) and \( Q R \)
respectively. This question has multiple correct options
A. ratio of the areas of quadriateral \( O M N R \) and the square is 5: 8
B. ratio of the areas of the \( \Delta M Q N \) and \( \Delta O M N \) is 1: 3
C. ratio of the areas of the \( \Delta O P M \) and \( \Delta O R N \) is 1: 1
D. ratio of the areas of quadriateral \( O M Q N \) and the square is 1: 2


An example for a function which is a
relation, (Domain-R, Codomain-R) is:
This question has multiple correct options
A \( \cdot y=x \)
В. \( y=x-1 \)
c. \( y=x^{2} \)
D. none of these


is the basic unit of life.
A. Cell
B. Tissue
c. system
D. Organism


In the figure \( l / / m \) and \( p \) is a
transversal, find the value of \( x, \) giving
necessary reasons.


\( \left(3 x^{2}-2 x\right) \div x \)
\( A \cdot 3 x \)
B. \( 3 x-2 \)
c. \( 3 x+2 \)
D. None


A ball hits a wall with a velocity of 30
\( m / s \) and re bounces with same velocity
What is change in its velocity.


Consider the algebraic equation:
\( 3 x^{3} y-4 x^{2} y^{2}+\frac{1}{2} x y^{2}-5 x \) How many
terms are there in the equation? List all the terms.What is the numerical coefficient of the term \( \frac{1}{2} x y^{2} ? \)


Two elements A and B have the
following configuration: \( \boldsymbol{A}: \mathbf{2}, \mathbf{7} ; \boldsymbol{B} \)
\( 2,8,7 . \) Both of them belong to:
A. the same group and are chemically similar
B. different groups but are chemically similar
C. the same group but are chemically dissimilar
D. the same period and are chemically similar


Divide the polynomial by monomial:
\( 3 x^{5}-4 x^{4}+3 x^{3}+2 x ; x^{2}-3 \)
A \( \cdot\left(x^{2}-3\right)\left(3 x^{3}-4 x^{2}+12 x-12\right)+38 x-36 \)
B . \( \left(x^{2}-3\right)\left(x^{3}-4 x^{2}+2 x-2\right)+3 x-6 \)
C. \( \left(2 x^{2}-7\right)\left(3 x^{3}+4 x^{2}+x-1\right)+47 x-109 \)
D. \( \left(2 x^{2}+7\right)\left(3 x^{3}-4 x^{2}+12 x-12\right)+38 x-36 \)


A ray of light is normally incident on one face of an equilateral glass prism. What is the angle of incidence on the first
face of the prism?
\( \mathbf{A} \cdot 0^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


The inductive reactance of a coil is
\( 2500 \Omega . \) On increasing its selfinductance three times, the
new inductive reactance will be
A. \( 7500 \Omega \)
B. 2500 \Omega
c. \( 1225 \Omega \)
D. zero


A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the
radius of the balloon is increasing when the radius is \( 15 \mathrm{cm} \)


An endothermic reaction which
proceeds with decrease in volume will give maximum yield of the products at high \( \boldsymbol{P} \) and high \( \boldsymbol{T} \)
If true enter \( 1, \) if false enter 0


\( A \) and \( B \) are two objects with mass 6 kg and 34 kg respectively. Then,
A. A has more inertia than \( B \)
B. B has more inertia than A
c. A and B both have same inertia
D. None of the above statements is true


Who speculated for the first time the presence of organ forming substances in the plant now called as hormones?
A. Darwin
B. went
c. Yabuta
D. sachs


For which one of the following reactions
will \( \boldsymbol{K}_{\boldsymbol{C}}=\boldsymbol{K}_{\boldsymbol{P}} \)
A \( \cdot C O(g)+2 H_{2}(g) \rightleftharpoons C H_{3} O H(g) \)
в. \( Z n O(s)+C O(g) \rightleftharpoons Z n(s)+C O_{2}(g) \)
\( \mathrm{c} \cdot 2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) \)
D. \( \operatorname{COCl}_{2}(g) \rightleftharpoons \operatorname{CO}(g)+C l_{2}(g) \)


In aerial mapping a camera uses a lens with a \( 100 \mathrm{cm} \) focal length. The height
at which the airplane must fly, so that
the photograph of a \( 1 k m \) long strip on the ground fits exactly on the \( 20 \mathrm{cm} \) long filmstrip of the camera, is
A . \( 200 \mathrm{km} \)
B. \( 20 \mathrm{km} \)
\( c .5 k m \)
D. \( 1 \mathrm{km} \)


If
\( [x] \) denotes the integral part of \( x, \) then
\( \lim _{x \rightarrow \infty} \frac{1}{n^{3}}\left(\sum_{k=1}^{n}\left[k^{2} x\right]\right) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{x}{2} \)
c. \( \frac{x}{3} \)
D. \( \frac{x}{6} \)


Divide \( 4 x^{2} y^{2}(6 x-24) \div 4 x y(x-4) \)
\( \mathbf{A} \cdot 6 x y \)
B. \( 4 x y \)
c. \( x-4 \)
D. \( x y(x-4) \)


Draw front view of the diagram.


If \( \alpha, \beta \) be straight lines in a plane, then
check \( R_{1} \) and \( R_{2} \) for being reflexive,
symmetric and transitive \( \boldsymbol{\alpha} \boldsymbol{R}_{1} \boldsymbol{\beta} \boldsymbol{i} \boldsymbol{f} \boldsymbol{\alpha} \perp \)
\( \boldsymbol{\beta} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{\alpha} \boldsymbol{R}_{2} \boldsymbol{\beta} \boldsymbol{i} \boldsymbol{f} \boldsymbol{\alpha} \)


Imole of \( 50 \% \) pure \( C a C_{2} \) on hydrolysis followed by passing through red hot copper tube. How many moles of benzene is formed?
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{6} \)
D. \( \frac{1}{8} \)


Highest covalent character is found in which of the following?
A. \( C a F_{2} \)
в. \( C a C l_{2} \)
\( \mathrm{c} \cdot \mathrm{CaI}_{2} \)
D. \( C a B r_{2} \)


Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{5} \times \)
\( 10^{3} \hat{i} N / C, \) find the flux of this field
through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( y \) -z plane. What could be the flux through the
same square if the plane makes \( 30^{\circ} \)
angle with the \( x \) -axis?


The frequencies below \( 20 \mathrm{Hz} \) are known
as sounds.


A metal sphere of radius \( r \) and specific heat \( \mathrm{S} \) is rotated about an axis passing through its centre at a speed of \( n \) rotations per second. It is suddenly stopped and \( 50 \% \) of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is?
A \( \cdot \frac{2}{5} \frac{\pi^{2} n^{2} r^{2}}{S} \)
C \( \cdot \frac{7}{8} \pi r^{2} n^{2} S \)
D・ \( 5\left[\frac{r n x}{[145]}\right]^{2} \)


An engine can pump 40,000 liters of water to the vertical height of 35 meters in 5 minutes. Calculate the
gravitational potential energy of water at given height.


Waves inside a gas are
A. Longitudinal
B. Transverse
C . Partly longitudinal, partly transverse.
D. None of these


Identify the incorrect statement related
to \( P C l_{5} \) from the following:
A. Three equitorial \( P-C l \) bonds makes an angle of \( 120^{\circ} \) with each other
B. Two axial \( P-C l \) bonds make an angle of \( 180^{\circ} \) with each other
c. Axial \( P-C l \) bonds are longer than equatorial \( P-C l \) bonds
D. \( P C l_{5} \) molecules is non reactive


If \( \operatorname{cosec}^{-1}(\operatorname{cosec}(x)) \) and
\( \operatorname{cosec}\left(\operatorname{cosec}^{-1}(x)\right) \) are equal functions,
then the maximum range of value of \( x \)
is
A \( \cdot\left[-\frac{\pi}{2},-1\right] \cup\left[1, \frac{\pi}{2}\right] \)
в. \( \left(-\frac{\pi}{2},-1\right) \cup\left(1, \frac{\pi}{2}\right) \)
c. \( (-\infty,-1] \cup[1, \infty) \)
D. \( (-\infty,-1) \cup(1, \infty) \)


To make the following reduction process
spontaneous, temperature should be:
\( Z n O+C \longrightarrow Z n+C O \)
A \( \cdot 1000^{\circ} \mathrm{C} \)
В. \( >1000^{\circ} \mathrm{C} \)
\( c \cdot<500^{\circ} C \)
D. \( <1000^{\circ} \mathrm{C} \)


A boy can jump to a height \( h \) from ground on earth. What should be the
radius of a sphere of density \( \delta \) such that on jumping on it, he escapes out of the gravitational field of the sphere?
A. \( \sqrt{\frac{4 \pi G \delta}{3 g h}} \)
B. \( \sqrt{\frac{4 \pi g h}{3 G \delta}} \)
c. \( \sqrt{\frac{3 g h}{4 \pi G \delta}} \)
D. \( \sqrt{\frac{3 G \delta}{4 \pi g h}} \)


Ethanol reacts with sodium and forms
two products. These are:
A. sodium ethanoate and hydrogen
B. sodium ethanoate and oxygen
c. sodium ethoxide and hydrogen
D. sodium ethoxide and oxygen


\( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{2} & \boldsymbol{x} \\ \mathbf{4} & \mathbf{3}\end{array}\right|=\mathbf{0} \) find the value of \( \mathbf{x} \)


Find the value of
\( \frac{\sqrt{1+\sin 2 A}+\sqrt{1-\sin 2 A}}{\sqrt{1+\sin 2 A}-\sqrt{1-\sin 2 A}} \) when
\( |\tan A|<1 \) and \( |A| \) is acute
\( \mathbf{A} \cdot \tan A \)
B. \( -\tan A \)
\( c \cdot \cot A \)
D. - cot \( A \)


Given \( 3 x-4 y=7 \) and \( x+c y=13 \) for what value of "c" will the two equation not have a solution?
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot-4 \)
D. \( \frac{-4}{3} \)


If \( \omega \) is a cube root of unity, then \( (3+ \) \( \left.\mathbf{5} \boldsymbol{\omega}+\mathbf{3} \boldsymbol{\omega}^{2}\right)^{2}+\left(\mathbf{3}+\mathbf{3} \boldsymbol{\omega}+\mathbf{5} \boldsymbol{\omega}^{2}\right)^{2} \) is equal
to
A . 4
B.
\( c \cdot-4 \)
D. None of these


A transparent cube contains a small air bubble. Its apparent is \( 2 \mathrm{cm} \) when seen
through one face and \( 5 \mathrm{cm} \) when seen through other face. If the refractive
index of the material of the cube is 1.5
the real length of the edge of cube must
be
A. \( 7 \mathrm{cm} \)
B. \( 7.5 \mathrm{cm} \)
c. \( 10.5 \mathrm{cm} \)
D. \( \frac{14}{3} \mathrm{cm} \)


Assertion
Work-energy theorem can be applied for
non-inertial frames also.
Reason
Earth is a non-inertial frame.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A body of mass \( 50 \mathrm{kg} \) revolves in a circle of diameter \( 0.40 \mathrm{m}, \) making 500 revolutions per minute. Calculate linear
velocity and centripetal acceleration


Proteins are:
A. Polyamides
B. Polyesters
C . Polyhydric alcohols
D. Polycarboxylic acids


Cells appear like pipeline arranged in co ntinuous pattern below the cambium u nder microscope
It could be \( _{----} \) type cell.
A. xylem vessel
B. Parenchyma
c. collenchyma
D. Sclerenchyma


Three particles of mass \( 1 k g, 2 k g \) and
\( 3 k g \) are placed at the corners \( A, B \) and
\( C \) respectively of an equilateral triangle
\( A B C \) of edge 1 m. Find the distance of their centre of mass from \( \boldsymbol{A} \)


Addition of \( B r_{2} \) to cis-2-hexene gives
racemic mixture, even though attack of the bromide ion on unsymmetrical bromonium ion intermediate is not
equally likely at both carbons. The reason for the racemic product are:
A. the reaction is reversible, after a while both enantiomers are produced in equal amount
B. the bromonium ion formed has a plane of symmetry
c. two enantiomeric bromonium ions are formed in equal amounts
D. four different stereo isomers are formed, but all in equal amount


if \( A=\left[\begin{array}{cc}2 & 3 \\ 5 & -7\end{array}\right] \) then \( \quad\left(A^{1}\right)^{2}= \)
A. \( \left[\begin{array}{ccc}5 & -7 & 12 \\ 1 & 4 & 22\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}1 & 17 \\ 1 & -4 \\ 0 & 2\end{array}\right] \)
c. \( \left[\begin{array}{cc}-19 & -25 \\ -15 & 64\end{array}\right] \)
D. \( \left[\begin{array}{cc}19 & -25 \\ -15 & 64\end{array}\right] \)


Find the angles of inclination of straight lines whose slopes are \( \sqrt{\mathbf{3}} \)


Given two vectors \( \vec{A}=\hat{i}-2 \hat{j}-3 \hat{k} \) and \( \vec{B}=4 \hat{i}-2 \hat{j}+6 \hat{k}, \) the angle made by
\( (\vec{A}+\vec{B}) \) with \( x \) -axis is:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Choose the alternative which closely resembles the mirror image of the given
combination.
\( \mathbf{1 9 6 5} \) I NDOPAK
(1) \( \mathrm{XAGOG} \) И I ट9 96 .
(3) XAGOG I I ¿Q dI
(4) XAGOG I I èdel
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


"She moves at a constant speed in a constant direction." Rephrase the same
sentence in fewer words using concepts related to motion.


Write the importance of DNA.


Evaluate \( : \int \frac{d x}{1+\cos a \cos x} \)


All of the following have a tetrahedral
shape except :
\( \mathbf{A} \cdot S O_{4}^{2-} \)
в. \( X e F_{4} \)
\( c \cdot C l O_{4}^{-} \)
D. \( X e O_{4} \)


Find what straight lines are represented by the following equation and determine the angles between them. \( \boldsymbol{y}^{3}-\boldsymbol{x} \boldsymbol{y}^{2}-\mathbf{1 4} \boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{2 4} \boldsymbol{x}^{3}=\mathbf{0} \)


Find total work done on the block as it
moves by \( 4 m \) as shown


ff \( p^{2}=a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta \) then Prove
That:
\( \boldsymbol{P}+\frac{\boldsymbol{d}^{2} \boldsymbol{p}}{\boldsymbol{d} \boldsymbol{\theta}^{2}}=\frac{\boldsymbol{a}^{2} \boldsymbol{b}^{2}}{\boldsymbol{p}^{3}} \)


Select the correct statement about:
\( A g F, C a F_{2}, B e F_{2}, M g F_{2} \)
A \( \cdot \) AgF and \( B e F_{2} \) are soluble, and \( C a F_{2} \) and \( M g F_{2} \) are insoluble in water.
B. AgF is soluble, others insoluble
c. \( \mathrm{AgF} \) is insoluble, others are soluble.
D. All are insoluble


Assertion
Sucrose is a reducing sugar and
exhibits mutarotation.
Reason
Sucrose is a disaccharide consisting of
glucose and fructose units.
A. Statements A and R are true and \( \mathrm{R} \) is the correct
explanation of \( A \)
B. Statements A and R are true and R is not the correct explanation of \( A \)
C. Statements A is true and R is false.
D. Statements A is false and R is true.


Above reaction is known as:
A. Wurtz reaction
B. Wurtz fitting reaction
C . Fitting reaction
D. Kolbe electrolysis


The pressure exerted by solids is a little different from that of fluids as in the
case of solids, due to
A. Tight interactions of atoms/ molecules
B. Loose interactions of atoms/ molecules
c. Medium interactions of atoms/ molecules
D. This statement is incorrect


The rotation of the Earth having radius \( \mathrm{R} \) about its axis speed upto a value
such that a man at latitude angle \( 60^{\circ} \)
feels weightless. The duration of the day in such case will be.
\( ^{\mathrm{A}} \cdot_{8 \pi} \sqrt{\frac{R}{g}} \)
в. \( 8 \pi \sqrt{\frac{g}{R}} \)
\( ^{c} \cdot \sqrt{\frac{R}{g}} \)
D. \( 4 \pi \sqrt{\frac{g}{R}} \)


Which of the following biomolecules contain non-transition metal ion?
A. Vitamin \( B_{12} \)
B. Chlorophyll
c. Haemoglobin
D. Insulin


The number of amino acids found in
proteins that a human body can
synthesise is?
A . 20
B. 25
\( c \cdot 11 \)
D. 100


If two sides of a right triangle are respectively equal to other two sides of a right triangle, then the two triangles are congruent. If true enter 1 else 0


Draw electron dot representation for the formation of Sodium oxide.


Of the 1000 inhabitants of a town, \( 60 \% \) are males of which \( 20 \% \) are literate. If
among all the inhabitants, \( 25 \% \) are
literate, then what percent of the females of the town are literate?
A . 22.5
в. 27.5
c. 32.5
D. 37.5


Approximate value of \( \tan ^{-1}(0.999) \) is
A . 0.7847
B. 0.748
c. 0.787
D. 0.847


If \( A(x) \) and \( B(x) \) be two polynomials
and \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{A}\left(\boldsymbol{x}^{3}\right)+\boldsymbol{x} \boldsymbol{B}\left(\boldsymbol{x}^{3}\right) . \) If \( \boldsymbol{f}(\boldsymbol{x}) \) is
divisible by \( x^{2}+x+1 \) then show that it
is divisible by \( x-1 \) also.


The prices of table and chair are in the
ratio of \( 25: 6 . \) If table costs Rs. 950
more than chair, then cost of two chairs
is
A . Rs. 300
B. Rs. 600
c. Rs. 900
D. Rs. 1200


The output of an OR gate is connected to both the inputs of a NAND gate. The combination will serve as:
A. AND gate
B. NOT gate
c. NAND gate
D. NOR gate


For which of the following electrolytic
solution \( \wedge_{m} \) and \( \wedge_{e} \) are equal?
A. \( B a C l_{2} \)
в. \( K C l \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( \operatorname{CaCl}_{2} \)


For the given A.P. 5,10,15,20 Find the common difference (d).


Which of the following is correctly matched with no exception in regard to plant classification?
A. Family - Poaceae - ae
B. Division - Pteridophyta - phyta
c. Class - Bryopsida - sida
D. Genus - Solanum - um


Which of the following species are oxidised and reduced in the following (unbalanced) reaction?
\( \boldsymbol{C}+\boldsymbol{Z} \boldsymbol{n} \boldsymbol{O} \longrightarrow \boldsymbol{Z} \boldsymbol{n}+\boldsymbol{C O} \)
A. zno Reduced ; c Oxidizedd
B. c Reduced ; zno Oxidizedd
c. Neither of them reduced or oxidized
D. None of the above


Very short answer type.
Mark the odd one in each series.
salivary gland, thyroid gland, gastric gland, tear gland


A mass of \( 4 \mathrm{kg} \) rest on the horizontal
plane. The plane is gradually inclined
until at an anger of \( \theta=15^{\circ} \) with the
horizontal, The mass just begin the block \& the surface


Which one of the above compounds is
not aromatic?
\( A \)
B. i i
\( c \)
\( D \cdot \) iv


The near point of a hypermetropic eye is
1m. Assume that near point of the
normal eye is \( 25 \mathrm{cm} . \) The power of the lens required to correct this defect will be \( \ldots \ldots(+\mathbf{3},-\mathbf{3}) \) dioptre


\( 2 \frac{3}{11}+1 \frac{3}{77} \)


Which of the following reactions show
the process of smelting?
\( \mathbf{A} \cdot 2 P b O+P b S \rightarrow 3 P b+S O_{2} \)
B \( \cdot 2 \operatorname{Na}\left[A u(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[Z n(C N)_{4}\right]+2 A u \)
\( \mathbf{c} \cdot P b O+C \rightarrow P b+C O \)
D. \( 2 H g S+3 O_{2} \rightarrow 2 H g O+2 S O_{2} \)


What is the heat of formation of \( C_{6} H_{6} \)
give that the heat of combustion of Benzene, carbon and Hydrogen are
-782,-94 and \( -68 K \) respectvely
A. +14 K.Cal
в. -14 К.Са
c. +28 K.Cal
D . -28 K.Cal


In the circuit shown in figure heat
developed across \( 2 \Omega, 4 \Omega \) and \( 3 \Omega \)
resistances are in the ratio of
A .2: 4: 3
в. 8: 4: 12
\( c \cdot 4: 8: 27 \)
D. 8: 4: 27


If the \( 4^{t h} \) and \( 7^{t h} \) terms of a G.P. are 54
and 1458 respectively, find the G.P.


If a displacement-time graph of an object is a straight line parallel to the time axis, the object is
A. stationary
B. moving away from the reference point
c. moving towards the reference point
D. moving with an infinite velocity


The human eye forms the image of an
object at its


The limit of \( \left\{\frac{1}{x} \sqrt{1-x}-\sqrt{1+\frac{1}{x^{2}}}\right\} \) as
\( \boldsymbol{x} \rightarrow \mathbf{0} \)
A. Does not exist
B . Is equal to \( \frac{1}{2} \)
c. Is equal to 0
D. Is equal to


The terms of an infinitely decreasing
G.P. in which all the terms are positive, the first term is 4 and the difference between the third and fifth term is \( \frac{32}{81} \) then find the common ratio.


Find how long the cylinder will move with sliding.
A \( \cdot t=\frac{\omega_{0} R}{3 k g} \)
В. \( t=\frac{\omega_{0} R}{6 k g} \)
c. \( _{t=2} \frac{\omega_{0} R}{3 k g} \)
D. \( t=2 \frac{\omega_{0} R}{6 k g} \)


State True or False.
The redox reaction involved in galvanic
cell is a non-spontaneous process.
A. True
B. False


What is the place value of 5 in 65.45


Middle vascular coat that darkens the
eye chamber and prevents refraction by absorbing the light rays is:
A. Choroid
B. Sclera
c. Retina
D. cornea


Portland cement consists essentially of compounds of
A . lime (calcium oxide, \( C a O \) )
B. silica (silicon dioxide, \( S i O_{2} \) )
c. alumina (aluminum oxide, \( A l_{2} O_{3} \) )
D. all of them


A ball of mass \( m \) moving with velocity \( v \) collides with another ball of mass \( 2 m \)
and sticks to it. The velocity of the final system is:
\( \mathbf{A} \cdot v / 3 \)
B. \( v / 2 \)
c. \( 2 v \)
D. 3v


\( \sin ^{-1} \mathbf{6} \boldsymbol{x}+\boldsymbol{\operatorname { s i n }}^{-1} \boldsymbol{6} \sqrt{\mathbf{3}} \boldsymbol{x}=-\boldsymbol{\pi} / 2 \) if \( \mathbf{x} \) is
equal to
A . - \( -1 / 12 \)
B. 1/6
\( c \cdot 1 / 12 \)
D. -1/6


In a town of 10000 families, it was found
that \( 40 \% \) families buy a newspaper \( A \) \( 20 \% \) families buy newspaper \( B \) and \( 10 \% \) families buy newspaper C. 5\% families buy both \( A \) and \( B, 3 \% \) buy \( B \) and \( C \) and 4\% buy A and C. If 2\% families buy all the three newspapers, then the number of families which buy A only.
A . 3300
в. 3500
\( c .3600 \)
D. 3700


\( P H_{3} \) is a weaker base than \( N H_{3} \)
A. True
B. False


Why do we require artificial sweetening
agents?


A rectangular coil of a moving coil galvanometer contains 100 turns, each
having area \( 15 c m^{2} . \) It is suspended in
the radial magnetic field \( 0.03 \mathrm{T} \). The twist constant of suspension fibre is
\( 15 \times 10^{-10} \mathrm{N}-\mathrm{m} / \) degree. Calculate the sensitivity of the moving coil galvanometer.


Let \( n(\cup)=700, n(A)=400, n(B)=300, n(A \cap \)
\( \mathrm{B})=300 . \) Then \( \left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)= \)
A . 300
B. 400
\( c . \) 350
D. 250


Observe the given figure and answer the
questions given below.
Which fraction would you expect to
produce most radioactively-labelled protein if labelled amino acids were
added? Give a reason for your answer


In which type of passive transport simple diffusion or facilitated diffusion.
A carrier protein is required for transport across the membrane.


The amount of heat required to convert 1 g of ice (specific 0.5 cal at \( g^{-1 o} C^{-1} \) ) at
\( -10^{0} C \) to steam at \( 100^{\circ} \mathrm{C} \)
is
Given: Latent heat of ice is \( 80 \mathrm{Cal} / \mathrm{gm} \)
Latent heat of steam is \( 540 \mathrm{Cal} / \mathrm{gm} \) Specific heat of water is \( 1 C a l / g m / C] \)
A . 725 cal
B. 636 cal
c. 716 cal
D. None of these


Construct triangle \( \boldsymbol{A B C} \) in which
\( B C=3.4 c m, A B-A C=1.5 c m \) and
\( \angle B=45^{\circ} \)


The addition of 1 equivalent of \( D C l \) to
1, 3- cyclohexadiene generates a mixture of products. Find out the total
no. of products.


The value of \( \int\left(x e^{\ell n \sin x}-\cos x\right) d x \) is
equal to:
\( \mathbf{A} \cdot x \cos x+C \)
B. \( \sin x-x \cos +C \)
c. \( -e^{e n x} \cos x+C \)
\( \mathbf{D} \cdot \sin x+x \cos x+C \)


Which of the following statement is correct for the attainment of stable
electronic configuration in case of magnesium atom?
A. Magnesium atom attains stable electronic configuration of nearest noble gas-Neon
B. Magnesium atom attains stable electronic configuration by losing two electrons from its valence shel
c. Magnesium atom becomes positively charged magnesium ion after attaining stable electronic configuration
D. All of the above


If the bond energies of \( \boldsymbol{H}-\boldsymbol{H}, \boldsymbol{B} \boldsymbol{r}- \)
Br and \( H-B r \) are 433,192 and 364
kJ mol \( ^{-1} \) respectively. Then \( \Delta H^{o} \) for the
reaction \( \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})}+\boldsymbol{B} \boldsymbol{r}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(\boldsymbol{g})} \) is :
B. +103 k
\( c .+261 k \)
D. -103kJ


Ratio of the currents \( I_{1} \) and \( I_{2} \) flowing
through the circular and straight parts
is
A \( \cdot \frac{\sqrt{3}}{2 \pi} \)
B. \( \frac{2 \sqrt{3}}{5} \)
\( c \cdot \frac{3 \sqrt{3}}{2 \pi} \)
D. \( \frac{3 \sqrt{3}}{2 \sqrt{2} \pi} \)


Consider the following statements:
(i) Soft iron conducts electricity
(ii) Soft iron is magnetic material
(iii) Soft iron is used for magnetic
permanent magnets
(iv) Soft iron is used as electro magnet
A. (i) and (ii) are correct
B. (i) and (iii) are correct
c. (ii) and (iv) are correct
D. (i), (ii) and (iv) are correct


Find the area of square whose one pair of the opposite vertices are (3,4) and \( (5, \)
6)


Which of the following method(s) does work for the preparation of secondary amine?
A \( \cdot R_{3} N \frac{(i) B r-C N}{(i i) H_{3} O^{+}} ? \)
\( (i i i) \Delta \)
c. \( R N C \frac{N l / H_{2}}{\Delta} ? \)
D. All of these


Two tall buildings are \( 80 m \) apart. The velocity with which a ball should be thrown horizontally from a window \( 95 m \) above the ground in one building so that it will enter a window 15 m above the
ground in the second building is : \( (g= \)
\( \left.10 m / s^{2}\right) \)
A. \( 15 \mathrm{m} / \mathrm{s} \)
B. \( 5 m / s \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. 20 \( m / s \)


In connection with circulatory system,
valves are present
A. Not only in heart and blood vessels of vertebrates and invertebrates but in vertebrate lymphatics as well
B. Vertebrate heart only
C . Vertebrate and invertebrate hearts only
D. Vertebrate hearts, invertebrate hearts and their blood vessels


The value of \( \sec \left[\tan ^{-1} \frac{b+a}{b-a}-\tan ^{-1} \frac{a}{b}\right] \) is
\( A \)
B. \( \sqrt{2} \)
\( c \cdot 4 \)
D.


A body has a weight of \( 10 k g \) on the
surface of the Earth. What will be its
mass and weight when taken to the centre of the Earth?
A. \( 10 \mathrm{kg} \), zero
B. zero, zero
c. \( 10 \mathrm{kg}, 10 \mathrm{g} \)
D. zero, \( 10 g \)


A particle starts travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment
when particle complete half the circular track, is:
\( \mathbf{A} \cdot \tan ^{-1}(2 \pi) \)
B. \( \tan ^{-1}(\pi) \)
\( \mathbf{c} \cdot \tan ^{-1}(3 \pi) \)
D. \( \tan ^{-1}(2) \)


A car moving at \( 40 \mathrm{km} / \mathrm{h} \) is to be stopped by applying brakes in the next 4.0m. If the car weighs 2000 kg what average force must be applied on it?


If \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\mathbf{3} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) are vectors
satisfying \( \boldsymbol{\alpha} \overrightarrow{\boldsymbol{a}}+\boldsymbol{\beta} \overrightarrow{\boldsymbol{b}}+\boldsymbol{\gamma} \overrightarrow{\boldsymbol{c}}=-\boldsymbol{3}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}), \) then the
ordered triplet \( (\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}) \) is
В . (-2,-1,1)
c. (-2,1,1)
D. (2,1,1)


Which of the following is correct for the efficiency of a heat engine:
A \( \cdot \eta=\frac{W}{Q_{1}} \)
в. \( \eta=\frac{W}{Q_{2}-Q_{1}} \)
c. \( _{\eta}=\frac{W}{Q_{2}} \)
D. \( \eta=\frac{Q_{2}}{Q_{1}} \)


Kirchhoff's rules are very useful for analysis of electrical circuits. State Kirchhoff's junction rules.


Cleaning of dust from carpet is due to
A. Inertia of motion
B. Inertia of rest
c. Inertia of direction
D. Momentum


The reaction: \( O C l^{-}+I^{-} \stackrel{O H^{-}}{\longrightarrow} O I^{-}+ \)
\( C l^{-} \) takes place in following steps:
(i) \( O C l^{-}+H_{2} O \stackrel{K_{1}}{\kappa_{2}} H O C l+O H^{-} \)
(fast)
(ii) \( I^{-}+H O C l \stackrel{K_{3}}{\longrightarrow} H O l+C l^{-} \) (slow)
\( \left(\text { iii) } O H^{-}+H O I_{K_{2}^{\prime}}^{K_{1}^{\prime}} H_{2} O+O I^{-}(\text {fast })\right. \)
The rate of expression in terms of rate of
consumption of \( I^{-} \) is :
A \( \cdot \frac{-d I}{d t}=K \cdot \frac{[O C l] \mid I}{\int_{O H} \mid}^{-} \)
B. \( \frac{d I \text { - }}{d t}=K \cdot \frac{[O C l][I]}{[O H]^{2}} \)
c. \( \frac{d I}{d t}=K \cdot \frac{(O C l)^{2} I}{[\rho H]} \)
D. None of these


The values of the Henry's law constant
of \( A r, C O_{2}, C H_{4} \) and \( O_{2} \) in water at
\( 25^{0} C \) are 40.30,1.67,0.41 and
\( 34.86 k b a r, \) respectively. The order of
their solubility in water at the same
temperature and pressure is:
A. \( A r>O_{2}>C O_{2}>C H_{4} \)
в. \( C H_{4}>C O_{2}>A r>O_{2} \)
c. \( C H_{4}>C O_{2}>O_{2}>A r \)
D. \( A r>C H_{4}>O_{2}>C O_{2} \)


Micelles are used in
A. detergents
B. petroleum recovery
C. magnetic separation
D. all of these


Which of the following is the correct sequence of three steps in the sexual cycle of fungi?
A. Karyogamy, plasmogamy and meiosis
B. Meiosis, plasmogamy and karyogamy
c. Plasmogamy, karyogamy and meiosis
D. Meiosis, karyogamy and plasmogamy


Verify whether the points (1,5),(2,3) ,and (-2,-1) are collinear or not.


In the arrangement shown above, a
block of mass \( 2700 \mathrm{kg} \) is in equilibrium
on applying a force F. The value of force
\( \mathrm{F} ?\left(d_{l i q u i d}=0.75 g c m^{-3} i s\right) \)
A . \( 147 N \)
B. \( 1755.18 N \)
c. \( 153 N \)
D. \( 918 N \)


Water harvesting is done by
processes.
A. rainwater
B. groundwater
c. both A and B
D. atmospheric water


A body has a positive charge of \( 8 x \) \( 10^{-19} \mathrm{C} . \) It has :
A. an excess of 5 electrons
B. a deficiency of 5 electrons
c. an excess of 8 electrons
D. a deficiency of 8 electrons


Magnetic induction produced at the centre of a circular loop carrying
current is \( B . \) The magnetic moment of
the loop of radius \( \boldsymbol{R} \) is
\( \left(\mu_{0}=\text { permeability of free space }\right) \)
\( ^{\mathrm{A}} \cdot \frac{B R^{3}}{2 \pi \mu_{0}} \)
в. \( \frac{2 \pi B R^{3}}{\mu_{0}} \)
c. \( \frac{B R^{2}}{2 \pi \mu_{0}} \)
D. \( \frac{2 \pi B R^{2}}{\mu_{0}} \)


The larva which is hatch from eggs of silk moth is called:
A. Caterpillar
B. Silkworm
c. Both A and B
D. Butterfly


Atomic number of a halogen element in the fourth period is \( 35 . \) If true enter 1 else enter 0


In representative elements the
ionization energy values generally
decrease smoothly down the group. But
in boron group the values show an
erratic trend. This is mainly due to:
A. increase in metallic nature down the group
B. inert pair effect in the heavier elements of the group
c. d-block contraction and lanthanide contraction affecting the values of later elements due to poor shielding by d and f electrons
D. the different type of packing in their crystalline structure


The preserved traces of all living organisms are called as fossils.
A. True
B. False


The value of \( n \stackrel{l i m}{\longrightarrow} \)
\( \infty \frac{1 . n+2 .(n-1)+3 .(n-2)+\ldots+n}{1^{2}+2^{2}+\ldots+n^{2}} \)
is
A .
B. - -
\( c \cdot \frac{1}{\sqrt{2}} \)
D.


Consider the statement, if \( n \) is divisible
by 30 then \( n \) is divisible by 2,3 and by 5 Which of the following statements is equivalent to this statement??
A. If \( n \) is not divisible by 30 then \( n \) is divisible by 2 or divisible by 3 or divisible by 5
B. If \( n \) is not divisible by 30 then \( n \) is not divisible by 2 or not divisible by 3 or not divisible by 5
c. If \( n \) is divisible by 2 and divisible by 3 and divisible by 5 then \( n \) is divisible by 30
D. If \( n \) is not divisible by 2 or not divisible by 3 or not divisible by 5 then \( n \) is not divisible by 30


The number of ordered pairs \( (\boldsymbol{m}, \boldsymbol{n}) \)
where \( \boldsymbol{m}, \boldsymbol{n} \in\{1,2,3, \ldots, 50\}, \) such
that \( 6^{m}+9^{n} \) is a multiple of 5 is
A . 1250
B. 2500
\( c .625 \)
D. 500


What replacement is required to
convert an AC generator to DC generator
?
A. Armature with coil
c. Slip rings with split rings
D. All of the above


If a raw egg and a boiled egg are spinned together with same angular velocity on the horizontal surface then
which one will stops first?
A. boiled egg
B. raw egg
c. Both egg will stop simultaneously
D. Cannot be ascertained


Assertion
If \( a, b, c \) each greater than zero are in
A.P. then minimum value of \( b=4 \) if
\( a b c=64 \)
Reason
\( \boldsymbol{A} \cdot \boldsymbol{M} \geq \boldsymbol{G} \cdot \boldsymbol{M} \)
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 age of the wood if only \( \frac{1}{16} t h \) part of original \( C^{14} \) is present in its piece is
\( T \) of \( C^{14} \) is 5,580 years
A. 5580 years
B. 11,160 years
c. 22320 years
D. 16740 years


The ratio in which \( \bar{i}+2 \bar{j}+3 \bar{k} \) divides the join of \( -2 \bar{i}+3 \bar{j}+5 \bar{k} \) and \( 7 \bar{i}-\bar{k} \) is
\( \mathbf{A} \cdot-3: 2 \)
B. 1: 2
\( c \cdot 2: 3 \)
D. -4: 3


kg of iron and 1 kg of cotton are allowed
to fall from the roof top of a building simultaneously. Which one do you think will reach the ground first. Justify your answer.


In the following equilibrium:
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
when 5 mole of each are taken and
temperature is kept at \( 298 K \), the total
pressure was found to be 20 bar.
given: \( \Delta G_{f}^{o} N O_{2}=100 k J, G_{f}^{o} N_{2} O_{4}= \)
\( \mathbf{5 0 k J} \)
(i) Find \( \Delta G \) of the reaction at \( 298 K \)
(ii) Find the direction of the reaction.


Let \( n \) be a fixed positive integer. Define
a relation \( R \) on \( Z \) as follows:
\( (a, b) \in R \Leftrightarrow n \) divides \( a-b \)
Show that \( R \) is an equivalence relation
on \( Z \)


Which of the following will not increase voltage in a simple generator?
A. Increasing the number of turns in armature coil
B. Winding the coil on a soft armature
c. Increasing the size of the gap in which the armature turns
D. Increasing the speed of rotation.


Give the function of Saliva in digestion.


A sum of Rs.15, 000 is invested for 3 years at \( 13 \% \) per annum Simple interest. Calculate the interest for the
third year.
A . 1850
в. 1950
c. 1550
D. 2050


A wheel having a diameter of 3 m starts
from rest and accelerates uniformly to an angular velocity of 210 r.p.m.in 5 seconds. Angular acceleration of the wheel is
A \( \cdot 4.4 \pi \frac{r a d}{s^{2}} \)
В. \( _{3.3 \pi} \frac{r a d}{s^{2}} \)
c. \( _{2.2 \pi} \frac{r a d}{s^{2}} \)
D. \( _{1.1 \pi} \frac{r a d}{s^{2}} \)


\( A+B \rightleftharpoons 2 C+D \)
II. \( 2 C+D \rightleftharpoons A+B \)
If the equilibrium constant for the reaction represented by equation I above is \( 4.0 \times 10^{-2} . \) What is the value
of the equilibrium constant for the
reaction represented by equation II?
\( \mathbf{A} \cdot 16 \times 10^{-4} \)
В. \( 4.0 \times 10^{-2} \)
c. \( \frac{1}{4.0} \)
D. \( \frac{1}{4.0 \times 10^{-2}} \)
E \( .4 .0 \times 10^{2} \)


Who proposed induced fit theory?


The IUPAC name of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}(\boldsymbol{C H O}) \boldsymbol{C H}_{2} \boldsymbol{C} \)
is:
A. 2-sec-butylbutanal
B. 2,3-diethylbutanal
c. 2-Ethyl-3-methyl-pentanal
D. 3-methyl-2-ethylpentanal


A lead sphere of mass \( 20 k g \) has the same diameter as an aluminium
sphere of mass \( 72 k g \). The spheres are simultaneously dropped from a tower.
When they are \( 10 m \) from the ground, they have identical (neglect air resistance):
A. kinetic energy
B. potential energy
c. momentum
D. acceleration


f \( \boldsymbol{y}=\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\sqrt{\mathbf{1}-\boldsymbol{x}^{2}}}+ \)
\( \sin \left(2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right), \) then find \( \frac{d y}{d x} \) for
\( \boldsymbol{x} \in(-1,1) \)


An oxide of iron from the following is:
A. mud
B. dust
c. rust
D. none of these


Q Type your question-
car has a constant speed corresponding
to a normal acceleration of \( 8 m / s^{2} \) The
tracks abcde and \( 2 C 3 \) are semicircular
track while tracks \( 1-2 \) and \( 3-4 \) are
straight track Point \( a \) and point 1 are
the starting point of race and point 4 and point e are finishing point of race
and point 4 and point \( e \) are finishing
point of the race Choose the correct
statements
A \( \cdot \) Car A wins the race with time difference \( \frac{14+3}{3} s \)
B. car A wins the race with time difference \( \frac{14-3}{3} \)
C car B wins the race with time difference \( \frac{14+3}{3} s \)
D. car B wins with the race with time difference \( \frac{14-3}{3} s \)


Three successive measurements in an
experiment gave value 10.9,11.4042 and 11.42 the correct way of reporting
the average value is:
A. 11.2080
B. 11.21
c. 11.2
D. 11


An AC source of angular frequency \( \omega \) is
fed across a resistor \( r \) and a capacitor
\( C \) in series. The current registered is \( I \) If now the frequency of source is changed to \( \omega / 3 \) (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio
of reactance to resistance at the
original frequency \( \omega \)
A \( \cdot \sqrt{\frac{3}{5}} \)
B. \( \sqrt{\frac{2}{5}} \)
c. \( \sqrt{\frac{1}{5}} \)
D. \( \sqrt{\frac{4}{5}} \)


With what velocity should \( \alpha \) - Particle
travel towards the neucleus of a Cu
atom so as to arrive at a distance of
\( 10^{-13} m \)


\( \frac{\sqrt{x}}{\frac{x}{x}} \)


\( \mathbf{3}+\mathbf{3 3}+\mathbf{3 3 3}+\ldots . .+\mathbf{n} \) terms.


A drying agent is not suitable for removing the water vapor from a sample of gas with which the drying agent reacts chemically. Which of the following gases can properly be dried by means of \( N a O H ? \)
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
\( c . H B r \)
D. \( O_{2} \)
E . \( H C l \)


At \( 0^{\circ} \) and 760 mm Hg pressure, a gas
occupies a volume of \( 100 \mathrm{cm}^{3} \). Kelvin
temperature of the gas is increased by one-fifth and the pressure is increased one and a half times. Calculate the final
volume of the gas
\( A \cdot 80 \)
B. 90
\( c \cdot 100 \)
D. 129


Which of the following compounds have
delocalized electrons?
\( A \)
B.
\( c \)
\( \mathbf{D} \cdot C H_{3} C H_{2} C H_{2} O C H=C H C H_{3} \)


Identify the first component of an ordered pair (2,1)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot-1 \)
\( D \)


\( \operatorname{can} \frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}} \) be the direction
cosines of any directed line?
A. Yes
B. No
c. cannot say
D. None of these


The thermal capacity of 10 gm of the substance is 8 calories. Then its
specific heat is.
A. 0.8
в. 1.25
c. 0.4
D. \( 0 . \)


Which of the following crop is not grown in clayey soil?
A. Wheat
B. Gram
c. Paddy
D. cotton


Assertion
La'should be the \( f \) -block element
according to Aufbau principle.
Reason
57 th electron exceptionally enters into
the \( 5 d \) -orbital.

Read the above assertion and reason
and choose the correct option regarding
¡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. Assertion is incorrect but Reason are incorrect


Fill in the blank.
Pressure is inversely proportional to
A . force
B. mass
c. area
D. none of the above


Height of the cliff is
\( A \cdot 20 m \)
B. 10 \( m \)
\( c \cdot 15 m \)
D. 30 \( m \)


Name the process by which you receive heat from sun.
A. thermal radiation
B. conduction
c. convention
D. none of these


What is likely to be principal quantum number for a circular orbit of diameter
\( 20 \mathrm{nm} \) of the hydrogen atom, if we assume Bohr orbit be the same as that
represented by the principal quantum number?
A . 10
B. 14
c. 12
D. 16


Each interior angle of a \( n \) -sided
regular polygon is \( 162^{\circ} . \) Find the interior
angle of another polygon with \( 2 n \) sides.
A . \( 155^{\circ} \)
B . \( 160^{\circ} \)
\( c \cdot 171 \)
D. one of the above


Destructive interference of two waves
travelling in a medium occurs when the crest of one wave lines up with the
of another wave
A. trough
B. amplitude
c. crest
D. frequency
E. wavelength


Fill in the blanks with approriate words. Specialized muscular tissue forming a network which conducts impulses from pacemaker down throughout the
auricles and ventricles of vertebrate
heart is known as............fibres.


Let \( R \) be a relation defined as \( a R b \) if
\( 1+a b>0, \) then the relation \( R \) is:
A. Reflexive and symmetriç
B. Symmetric but not reflexive
c. Transitive
D. Equivalence


\( X e F_{2} \) on hydrolysis gives:
A. \( X e O_{3} \)
в. \( X_{e O} \)
\( c \cdot X e \)
D. \( X e O_{2} \)


Find the value of wave number \( \bar{v} \) in
terms of Rydberg's constant, when transition of electron takes place between two levels of \( H e^{+} \) ion whose
sum is 4 and difference is 2
\( ^{A} \cdot \frac{8 R}{9} \)
в. \( \frac{32 R}{9} \)
c. \( \frac{3 R}{4} \)
D. None of these


An important requirement of
fermentation is
A. Oxygen
B. Zymase
c. \( \mathrm{Fe} \)
\( D \cdot c O_{2} \)


One litre of Helium gas at a pressure of 76
\( \mathrm{cm}-\mathrm{Hg} \) and temperature \( 27^{0} \mathrm{C} \) is heated till its pressure and volume are doubled. The final temperature attained by the gas is
A \( \cdot 900^{0} \mathrm{C} \)
B . \( 927^{\circ} \mathrm{C} \)
c. \( 627^{\circ} \mathrm{C} \)
D. 327 \( ^{0} \mathrm{c} \)


How many unpaired electrons are there
in the electronic structure for \( C u^{+} \) ion?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D. none of these


If \( \frac{\sin ^{3} \theta-\cos ^{3} \theta}{\sin \theta-\cos \theta}-\frac{\cos \theta}{\sqrt{1+\cot ^{2} \theta}}- \)
\( 2 \tan \theta \cot \theta=-1, \theta \in[0,2 \pi], \) then
A \( \cdot \theta \in\left(0, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4}\right\} \)
в. \( _{\theta} \in\left(\frac{\pi}{2}, \pi\right)-\left\{\frac{3 \pi}{4}\right\} \)
c. \( _{\theta \in\left(\pi, \frac{3 \pi}{2}\right)-\left\{\frac{5 \pi}{4}\right\}} \)
D. \( \theta \in(0, \pi)-\left\{\frac{\pi}{4}, \frac{\pi}{2}\right\} \)


The work done during the process when
1 mole of gas is allowed to expand freely into the vacuum is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. positive
c. negative
D. either of these


An ion is an atom with an electric
charge due to a loss or gain of an electron.
Which of the following is the electron configuration of a ground state of the most common alkali metal ion?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} \)
B. \( 1 s^{2} 2 s^{\text {। }} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} s s^{2} 3 p^{6} 3 d \)


All of the following are physiologic effects of acute renal failure, except
A. Edema
B. Hypertension
c. Acidosis
D. Immediate death


Define electric resistance of a
conductor.


with an angular frequency \( \omega \) with one
end hinged at the centre and the other
end at the circumference of a circular
metallic ring of radius \( R, \) about an axis
passing through the centre and
perpendicular to the plane of the
ring.There is a magnetic field B, perpendicular to the plane of the ring. The emf induced between the centre
and the metallic ring is
A. \( B \) sinwt
\( ^{\mathbf{B}} \cdot \frac{B R^{2} \omega}{2} \)
\( \mathbf{c} \cdot 2 B R^{2} \omega \)
D. \( B R^{2} \omega \)


The number of aromatic isomers
possible for \( C_{7} H_{8} O \) are:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


A cube of side \( l \) is placed in a uniform electric field \( E \hat{i} \). Then the net flux
through the cube is:
A. 0
B . \( l^{2} E \)
\( \mathbf{c} \cdot 4 l^{2} E \)
D. \( 6 l^{2} E \)


Given are some of the stages of the hydrarch.
A. Marsh-meadow stage
B. Reed-swamp stage
C. Submerged plant stage
D. Phytoplankton stage
E. Free floating plant stage
Select the option that represents the correct sequence of these stages.
\( A \cdot D \rightarrow C \rightarrow E \rightarrow B \rightarrow A \)
B \( \cdot \mathrm{C} \rightarrow \mathrm{E} \rightarrow \mathrm{A} \rightarrow \mathrm{B} \rightarrow \) D
\( c \cdot B \rightarrow D \rightarrow C \rightarrow A \rightarrow E \)
D. D \( \rightarrow E \rightarrow C \rightarrow B \rightarrow A \)


State whether True or False:
The angle through which cyclist should bend will be greater for the sharper
curve
A. True
B. False


Coal gas contains:
A. hydrogen
B. carbon monooxide
c. methane
D. all of the above


Which of the following has maximum number of zero values appear in the curve plotted between \( \psi^{2} \) (probability of finding electron) versus radius?
A \( .3 p \)
B. \( 4 d \)
c. \( 5 p \)
D. \( 4 f \)


Find the magnitude of the vector which starts at the point \( 2 \hat{i}+\hat{j}-3 \hat{k} \) and ends at \( 4 \hat{i}-\hat{j}-\hat{k} \)


The primary of a transformer has 40
turns and works on 100 volt and 100
watt. Then the number of turns in the
secondary to step up voltage to \( 400 \mathrm{V} \) and the current in the secondary and primary will be
A. \( 260,0.25 \mathrm{A}, 2 \mathrm{A} \)
B. 160, 0.25A, 1A
c. \( 360,0.55 \mathrm{A}, \) 1А
D. None of these


The table shows the number of books on
each number of subjects. Find the
median.
Subject \( \quad 2 \quad 3 \quad 5 \quad 6 \) 3
50 \begin{tabular}{l|c|c|c|}
number f books & 20 & 39 & 10 \\
\hline
\end{tabular} 20
\( A \cdot 2 \)
B. 3
c. 5
\( D \)


IP values of an element 'X' are 104 kJ,
\( 200 \mathrm{kJ}, 420 \mathrm{kJ}, 2825 \mathrm{kJ} \) per mole
Identify the group to which the element
belongs ?
A . \( I A \)
в. \( I I A \)
c. \( I I I A \)
D. \( I V A \)


An electron in ground state absorbs 1.5 times as much energy required to escape from H atom. The wavelength
of electron emitted in \( A^{\circ} \) is :
A . 4.21
B. 4.71
c. 3.52
D. 3.71


Two moles of helium gas undergo a
cyclic process as shown in figure.
Assuming the gas to be ideal. The net
work done by the gas is:
A. 200 R \( \ln 2 \)
B. 100 R \( \ln 2 \)
\( c \cdot 300 R \ln 2 \)
D. 400 R \( \ln 2 \)


State whether true or false.
A concave mirror always forms a real image.
A. True
B. False


\( \lim _{x \rightarrow 2} \frac{x^{2}+5 x+6}{2 x^{2}-3 x} \)
A . 10
B. \( \infty \)
\( c \cdot 2 \)
D.


When the temperature changes, the
operating point is shifted due to
A. Change in \( I_{C B O} \)
B. Change in \( V_{C C} \)
C. Change in the values of circuit resistance
D. None of the above


A starts business with Rs 3500 and
after 5 months B joins with \( A \) as his
partner After a year the profit is divided in the ratio 2: 3 What is B's contribution
in the capital?
A. Rs 7500
B. Rs 8000
c. \( R s 8500 \)
D. Rs 9000


A number when divided by 156 gives
29 as remainder. If the same number is
divided by \( 13, \) what will be the remainder?
A .4
B. 3
c. 5
D. 6


When light shines on a \( \boldsymbol{p}-\boldsymbol{n} \) junction
diode, the current \( (I) v s . \) voltage \( (V) \) is observed as in the figure below:
In which quadrant(s) does the diode generate power, so that it can be used
as a solar cell?
A . Quad 1 only
c. Quad 4 only
D. Quad 1 and 4 onl


Allyl chloride can be produced by many different methods. The most common
method is chlorination of propene which proceeds via a free-radical substitution mechanism.

Allyl chloride can also be formed by the following substitution reaction.
Suggest the identity of reagent \( \boldsymbol{X} \)


Complete the correlation. Silk worm: Cocoon : :Wool:
A. Hair of rabbitt
B. Cotton plant
c. Fleece of sheep
D. Jute of hemp


Two classrooms A and B having capacity of 25 and \( (n-25) \) seats
respectively. \( A_{n} \) denotes the number of
possible seating arrangements of room
\( A^{\prime}, \) when 'n' students are to be seated
in these rooms, starting from room \( ^{\prime} \boldsymbol{A}^{\prime} \) which is to be filled up to its capacity. If \( \boldsymbol{A}_{n}-\boldsymbol{A}_{n-1}=\mathbf{2 5 !}\left(^{49} \boldsymbol{C}_{25}\right) \) then 'n' equals:
A . 50
B . 48
c. 49
D. 51


(a) A student wants to use two \( p-n \)
junction diodes to convert alternating current into direct current. Draw the
labelled circuit diagram she would use and explain how it works.
(b) Give the truth table and circuit
symbol for NAND gate.


Two identical solid copper spheres of
radius \( R \) are placed in contact with each other. The gravitational attraction between them is proportional to
\( \mathbf{A} \cdot R^{2} \)
B. \( R^{-2} \)
\( c \cdot R^{-4} \)
D. \( R^{4} \)


Value Based Questions
Which of the following statements is associated with A. prophase, B. meraphase, \( C . \) anaphasc, \( D \). telophase and E. interphase of mitosis? Chromosomes are thickest and
shortest.


State whether true or false.
The weight of a body on the surface of the moon is \( \frac{1}{6} t h \) of that on the earth's surface. It is because acceleration due
to gravity on the surface of the moon is six times that on the surface of the
earth.
A. True
B. False


If the gas 'X' behaves ideally, then the
pressure \( P \) of \( \operatorname{gas} \) at \( 27^{\circ} C \) is :
\( \mathbf{A} \cdot 12.32 \mathrm{atm} \)
B. 24.63 atm
c. 1 atm
D. 6.15 atm


A magnifier lens focusses a beam of light on a sheet of paper for 5 secs and the paper starts burning. The process described here is
A. Concentrated light produces heat
B. Light energy is converted in to heat energy
c. Photons heating the paper
D. Electrons heating the paper


The ionization energy of hydrogen atom
is \( 13.6 e V . \) Hydrogen atoms in the ground state are excited by electromagnetic radiation of energy
12.1 \( e V \). How many spectral lines will be emitted by the hydrogen atoms?
A. one
B. two
c. three
D. four


Assertion:
\( 3 d_{z^{2}} \) orbital is spherically symmetrical.
Reason:
\( 3 d_{z^{2}} \) orbital is the only d-orbital which is spherical in shape.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


Given, standard electrode potentials,
\[
\begin{array}{l}
\boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}, \boldsymbol{E}^{o}=-\mathbf{0 . 4 4 0 V} \\
\boldsymbol{F e}^{-} \rightarrow \boldsymbol{F e}, \boldsymbol{E}^{\boldsymbol{o}}=-\mathbf{0 . 0 3 6} \mathbf{v}
\end{array}
\]
The standard electrode potential \( \left(E^{o}\right) \)
for \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} \) is:
A. \( +0.771 \mathrm{V} \)
В. \( -0.771 V \)
c. \( +0.404 V \)
D. \( -0.417 V \)


Two horizontal plates charged with \( +q \)
and \( -q \) charges are having an area of \( A \) A charged drop of oil is suspended in equilibrium position between the plates, then the charge on the oil drop will be :
A. \( m g / 4 \)
в. \( m g / A \)
\( \mathbf{c} \cdot m g \varepsilon_{0} A / q \)
D. \( m \varepsilon_{0} A / q \)


Find the principle value of \( \cos ^{-1}\left[\cos \left(\frac{7 \pi}{3}\right)\right] \)


When sugar is acted upon by conc. sulphuric acid, the product formed is:
A. ethyl alcohol
B. methyl alcohol
c. black mass carbon
D. carbon dioxide


Assuming that the junction diode is ideal, the current in the arrangement shown in figure is?
\( A .30 \mathrm{mA} \)
B. \( 40 \mathrm{mA} \)
c. \( 20 \mathrm{mA} \)
D. \( 10 \mathrm{mA} \)


Which term in the expansion of \( \left(\frac{x}{3}-\frac{2}{x^{2}}\right)^{10} \) contains \( x^{4} ? \)
\( A \)
B. 3
\( c \cdot 4 \)
D.


Interfasicular cambium is a
A. Primary meristematic tissue
B. Primordial meristem
c. Type of protoderm
D. Secondary meristematic tissue


The osmotic pressure of a dilute solution is given by :
A. \( P=P_{0} \times N_{1} \)
B . \( \pi V=n R T \)
c. \( \Delta P=P_{0} N_{2} \)
D. \( \frac{\Delta P}{P^{o}}=\frac{P^{o}-P_{S}}{P^{o}} \)


A ball is dropped from height \( \boldsymbol{H} \) on to a horizontal surface. If the coefficient of
restitution is \( e, \) then the total time after
which it comes to rest is
A. \( \sqrt{\frac{2 H}{g}}\left(\frac{1-e}{1+e}\right) \)
B. \( \sqrt{\frac{2 H}{g}}\left(\frac{1+e}{1-e}\right) \)
\( ^{\mathbf{c}} \cdot \sqrt{\frac{2 H}{g}}\left(\frac{1+e^{2}}{1-e^{2}}\right) \)
D. \( \sqrt{\frac{2 H}{g}}\left(\frac{1-e^{2}}{1+e^{2}}\right) \)


When the liquid is getting converted into solid, then what is the latent heat
involved?


If a A.P. \( \& \) an H.P. have the same first
term, the same last term \& the same
number of terms; then the product of
the \( r^{t h} \) term from the beginning in one
series \( \& \) the \( r^{t h} \) term from the end in
the other is independent of \( r \)
If true enter 1 else enter 0


If each edge of a cube is increased by \( 50 \% \) then the percentage increase in the surface area is
A . 50
B. 125
\( c \cdot \) 150
D. 300


Number of elements presents in the fifth period of periodic table is
A . 32
B. 10
c. 18
\( D \)


Azoic dyeing is a technique in which an insoluble ........................ compound dye is produced directly onto the fiber.
A . azo
B. sulphur containingg
c. carbonyl
D. carboxylic acid


A password for a computer system
requires exactly 6 characters. Each
character can be either one of the 26
letters from \( A \) to \( Z \) or one of the ten
digits from 0 to \( 9 . \) The first character
must be a letter and the last character
must be a digit. How many different possible passwords are there?
A \( \cdot \) Less than \( 10^{7} \)
B. Between \( 10^{7} \) and \( 10^{8} \)
C . Between \( 10^{8} \) and \( 10^{9} \)
D. Between \( 10^{9} \) and \( 10^{10} \)
E. More than \( 10^{10} \)


The cost price of 20 articles is the same as the selling price of \( x \) articles. If the profit is \( 25 \%, \) then the value of \( x \) is:
A . 15
B . 16
c. 18
D. 25


The site of initial digestion of
carbohydrates is
\( A \cdot A \)
3. \( c \)
\( c \cdot D \)
\( D \cdot F \)
E . H.


What are allotropes? Write the names of allotropes of phosphorus.


Find the velocity of a wave whose
frequency is \( 60 \mathrm{Hz} \) and wavelength is 20
\( \mathrm{m} \)


What transition the hydrogen spectrum would have the same wavelength as the Balmer transition \( n=4 \) to \( n=2 \) of
\( \boldsymbol{H} \boldsymbol{e}^{+} \) spectrum?
A \( \cdot n_{1}=3, n_{2}=6 \)
в. \( n_{1}=2, n_{2}=4 \)
c. \( n_{1}=1, n_{2}=2 \)
D \( \cdot n_{1}=1, n_{2}=4 \)


Choose the substance that
shows sublimation.
A. Naphthalene
B. Toluene
c. Kerosene
D. water


Match column I with column II.


Why is AMBULANCE written laterally
inverted on an Ambulance van?
A. It gathers more attention since it is laterally inverted.
B. Vehicle in front sees a laterally inverted image and perceives it correctly, hence giving side to the ambulance van.
C. Vehicle in front sees a virtually erect image and perceives it correctly, hence giving side to the ambulance van.
D. None of the above.


A circle of radius 7 is tangent to the
lines of an angle \( 60^{\circ} . \) is larger circle of
radius \( r \) is tangent to same lines as
well as given circle, then value of \( r \) is:
\begin{tabular}{l}
A \( .7 \sqrt{3} \) \\
\hline
\end{tabular}
B. \( \frac{28}{\sqrt{3}} \)
\( c \cdot 21 \)
D. 14


Find the square root of the following number by the prime factorisation method. \( \mathbf{6} \frac{\mathbf{1}}{\mathbf{4}} \)


Gradient of a line perpendicular to the
line \( 3 x-2 y=5 \) is
\( A \cdot \frac{-2}{3} \)
B.
\( c \cdot-\frac{3}{2} \)
\( D \cdot-\frac{5}{2} \)


was the first to discover
that lightning is electric discharge.
A. Thomas Alva Edison
B. Nicolas Tesla
c. Benjamin Franklin
D. Isaac Newton


One vertex of the equilateral triangle with centroid at the origin and one side
as \( \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{2}=\mathbf{0} \) is?
A \( \cdot(-1,-1) \)
в. (2,2)
c. (-2,-2)
D. None of these


A compound contains \( 38.8 \% C, 16 \% H \)
and \( 45.2 \% N . \) The formula of the
compound would be:
A. \( C H_{3} N H_{2} \)
в. \( C_{2} H_{5} C N \)
c. \( C H_{3} C N \)
D. \( C H_{2}\left(N H_{2}\right)_{2} \)


The nerve cell has branches that
develop during cell specialisation. These branches help the nerve cell to
perform which of the following functions?
A. Communication with other cells
B. Moving from one location to the other
c. Storing extra DNA
D. Exerting force on non-nervous tissue


A body of mass 2 kg is thrown up vertically with a KE of 490 J. If the acceleration due to gravity is \( 9.8 m s^{-2} \) the height at which the KE of the body becomes half of the original value is:
\( A \cdot 50 \mathrm{m} \)
B. 25 \( \mathrm{m} \)
c. \( 12.5 \mathrm{m} \)
D. \( 10 \mathrm{m} \)


A body of mass \( 20 \mathrm{kg} \) is at rest. A force of \( 5 \mathrm{N} \) applied on it. Calculate the work done in the first second


Thermal decomposition of alkanes in the absence of air is called
1) cracking
2) oxidation
3) combustion
4) hydrogenation


Urea-formaldehyde glues are also called
as \( -------- \) glues
A. urea-acetone
B. urea-ketone
c. urea-methanal
D. all of the above


Let \( a, b \) be two distinct roots of a polynomial \( f(x) \). Then there exists at least one root lying between a and b of the polynomial
A \( . f(x) \)
B. \( f^{\prime}(x) \)
c. \( f^{\prime \prime}(x) \)
D. \( f^{\prime \prime \prime}(x) \)


a. Draw the given diagram and label the
following in the diagram.
¡) Incident ray
ii) Refracted ray
iii) Emergent ray
iv) Angle of refraction
v) Angle of deviation
vi) Angle of emergence
b. The retractive index of diamond is
2.42. What is the meaning of this
statement in relation to the speed of
light?


\( \% \) composition requires of the
compound:
A. molar mass
B. temperature
c. atmospheric pressure
D. both a and


An immersion heater is rated \( 836 W . \) It
should heat \( 1 l \) of water from \( 20^{0} C \) to \( 40^{0} \)
\( \mathrm{C} \) in about:
A. \( 200 s \)
B. \( 100 s \)
\( \mathbf{c} .836 s \)
D. \( 418 s \)


Construct a \( \triangle P Q R \) in which \( Q R= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{P Q}=\mathbf{4 . 4} \boldsymbol{c m} \) and \( \boldsymbol{P} \boldsymbol{R}=\mathbf{5 . 3} \boldsymbol{c m} \)
Draw the bisector of \( \angle P \)


In an LC circuit the capacitor has
maximum charge qo. The value of \( \left(\frac{d I}{d t}\right)_{\max } \)
A \( \cdot \frac{q_{0}}{L C} \)
в. \( \frac{q_{0}}{\sqrt{L C}} \)
c. \( \frac{q_{0}}{L C}-1 \)
D. \( \frac{q_{0}}{L C}+1 \)


An electrical cable of copper has just one wire of radius \( 9 \mathrm{mm} \). Its resistance
is \( 5 \Omega .6 \) different well-insulated copper wires each of radius \( 3 \mathrm{mm} \) replace this single copper wire of the cable. The total resistance of the cable will now be
equal to
A . \( 7.5 \Omega \)
B. \( 45 \Omega \)
c. \( 90 \Omega \)
D. 270\Omega


The dimensions of an atom are of the
order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why then is the electrostatic field inside a conductor
zero?


When sodium is treated with sufficient
oxygen/air, the product obtained is:
This question has multiple correct options
A. \( N a_{2} O \)
в. \( N a_{2} O_{2} \)
\( \mathrm{c} \cdot \mathrm{NaO}_{2} \)
D. \( N a O \)


For a critical study of secondary growth in plants, which one of the following pairs is suitable?
A. Sugarcan and sunflower
B. Teak and pine
c. Deodar and fern
D. Wheat and maiden hair fern


Write the set of values of \( a \) for which
\( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x}+\boldsymbol{a}^{2} \boldsymbol{x}+\boldsymbol{b} \) is strictly
increasing on \( \boldsymbol{R} \)


The solubility of \( N_{2} \) in water is \( 2.2 \times \) \( 10^{-4} g \) in \( 100 g \) of \( H_{2} O \) at \( 20^{\circ} C \) when
the pressure of \( N_{2} \) over the solution is
1.2 atm.

Calculate the solubility at \( 20^{\circ} \mathrm{C} \) when
the pressure of \( N_{2} \) over the solution is
\( \mathbf{1 0} \) at \( \boldsymbol{m} \)
A \( \cdot 1.25 \times 10^{-3} g / 100 g \mathrm{H}_{2} \mathrm{O} \)
B . \( 1.49 \times 10^{-3} g / 100 g H_{2} O \)
c. \( 2.56 \times 10^{-3} g / 100 g H_{2} O \)
D. \( 1.83 \times 10^{-3} g / 100 g H_{2} O \)


Determine the domain and range of the relation R defined by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{x}+\mathbf{5}) \)
\( \boldsymbol{x} \in\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}\} \)


Find the value of \( \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18} \)


A point object is placed on the principal axis of the convex lens of focal length
\( 20 \mathrm{cm} \) at a distance \( 40 \mathrm{cm} \) to the left on
it. The diameter of the lens is \( 10 \mathrm{cm} \). If
the eye is placed 60cm to the right of the lens at a distance h below the
principal axis, then max value of 'h' to
see the image is
A . \( 1.5 \mathrm{cm} \)
B. 2.5 \( \mathrm{cm} \)
c. \( 3 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


Two particle performed simple harmonic motion of same frequency an
about same mean position. Their
amplitude is same and is equal to \( \boldsymbol{A} \)
and their time period is \( T . \) If at \( t=0 \)
separation is maximum and is \( A \), their separation at \( t=\frac{T}{12} \) is:-
A \( \cdot \quad A \frac{\sqrt{3}}{2} \)
B. \( A \)
c. \( \frac{A}{\sqrt{2}} \)
D. \( \frac{A}{2} \)


A short electric dipole moment \( \vec{p} \) is
placed at a distance \( r \) from the centre
of a solid metallic sphere of radius \( a(< \)
\( <r) \) as shown in the figure. The
electric field intensity at the centre of
sphere \( C \) due to induced charge on the
sphere is :
A. zero
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 p}{r^{3}} \) along \( C O \)
\( ^{\mathbf{C}} \frac{1}{4 \pi \varepsilon_{0}} \frac{2 p}{r^{3}} \) along \( O C \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{p}{r^{3}} \) along \( C O \)


Two students \( P \) and \( Q \) perform an experiment to verify Ohm's law for a conductor with resistance R. They use a current source and a voltmeter with
least counts of \( 0.1 \mathrm{mA} \) and \( 0.1 \mathrm{mV} \)
respectively. The plots of the variation of voltage drop(V) across R with current(i)
for both are shown. the statement which
is most likely to be correct is?
A. P has only random error(s)
B. Q has only systematic error(s)
c. \( Q \) has both random and systematic errors
D. P has both random and systematic errors


If \( \cos A=\frac{\sqrt{3}}{2}, \) then \( \tan 3 A= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c. 1
\( D \cdot \alpha \)


Assertion
Rectified spirit can be further purified by adding a dehydrating agent.
Reason
Addition of \( H_{2} S O_{4} \) to \( 96 \% \) ethyl alcohol
gives \( 100 \% \) ethyl alcohol
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following units denotes the dimension \( \frac{M L^{2}}{Q^{2}} \) where \( Q \) denotes the electric charge?
A \( \cdot W b / m^{2} \)
в. henry\( (H) \)
c. \( H / m^{2} \)
D. weber \( (W b) \)


Benzaldehyde undergoes reaction due to
of \( \alpha \) -hydrogen atom.
A. Cannizzaro' presence
B. Cannizzaro; absence
c. Henry's; absence
D. Henry's; presence


Cambium is absent in
A. Pteridophytes
B. Gymnosperms
c. Angiosperms
D. Pteridophytes and Gymnosperms


Why does the reactivity of nitrogen differ from phosphorus?


\( x \)
a small block is projected along it's
length with velocity \( v \) towards front.
Coefficient of restitution for each
collision is \( e . \) The cart rests on a smooth
ground and can move freely. The time
taken by block to come to rest w.r.t. cart
is :
A \( \cdot \frac{e d}{(1-e) v} \)
B. \( \frac{e d}{(1+e) v} \)
\( c \cdot d \)
\( \bar{e} \)
D. infinite


If \( A \) and \( B \) be two complex numbers satisfying \( \frac{\boldsymbol{A}}{\boldsymbol{B}}+\frac{\boldsymbol{B}}{\boldsymbol{A}}=1 . \) Then the two
points represented by A and B and the origin form the vertices of
A. An equilateral triangle
B. An isosceles triangle which is not equilateral
c. An isosceles triangle which is not right angled
D. A right angled triangle


Carbohydrates such as glucose,
fructose and sucrose are sweet in taste.
But, starch has bland taste though it is a carbohydrate. How do you account for this?


A block of mass \( m \) containing a net positive charges \( q \) is placed on a smooth horizontal table which
terminates in a ventricles wall as shown
in figure \( (29 . E 2) . \) The distance of the
block from the wall is \( d . \) A horizontal
electric field \( E \) towards right is
switched on. Assuming elastic collisions ( if any) find the time periods of the resulting oscillatory motion. Is it a simple harmonic motion?


On Heating hydrazoic acid form
A . \( N H_{3} \)
B. \( N_{2}+N H_{3} \)
c. \( N_{2} H_{4}+N H_{3} \)
D. \( H_{2}+3 N_{2} \)


In a Vander waals interaction: \( \boldsymbol{U}= \)
\( \boldsymbol{U}_{0}\left[\left(\frac{\boldsymbol{R}_{0}}{\boldsymbol{r}}\right)^{12}-\boldsymbol{2}\left(\frac{\boldsymbol{R}_{0}}{\boldsymbol{r}}\right)^{6}\right] \)
A small displacement x is given from
equilibrium position \( r=R_{0} . \) Find the
approximate PE function.
A \( \cdot \frac{36 U_{0}}{R_{0}^{2}} x^{2}-U_{0} \)
в. \( \frac{24 U_{0}}{R_{0}} x-U_{0} \)
c. \( \frac{96 U_{0}}{R_{0}^{2}}-U_{0} \)
D. none of these


Liquid pressure is measured using a
A. barometer
B. manometer
c. sphigmomanometer
D. thermometer


Evaluate :
\( \int \frac{x^{5}}{x^{2}+9} d x \)


At the centre of the earth, the value of \( g \)
becomes
A . zero
B. unity
c. infinity
D. none of these


(a) Give one example of redox reaction.
(b) Draw the labelled diagram of electrolytic decomposition of water


Assertion
Consider the function \( \boldsymbol{F}(\boldsymbol{x})= \) \( \int \frac{x}{(x-1)\left(x^{2}+1\right)} d x \)
STATEMENT-1 : \( \boldsymbol{F}(\boldsymbol{x}) \) is discontinuous at
\( \boldsymbol{x}=\mathbf{1} \)
Reason
STATEMENT-2 : Integrand of \( \boldsymbol{F}(\boldsymbol{x}) \) is discontinuous at \( x=1 \)
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


The pressure of a gas filled in a closed vessel increases by \( 0.4 \% . \) When
temperature is increases by \( 1^{\circ} \mathrm{C} \) the initial temperature of the gas is
\( A \cdot 250^{\circ} \mathrm{C} \)
B. 250 K
c. \( 250^{\circ} \mathrm{F} \)
D. 2500 \( ^{\circ} \)


Choose the correct relation between \( u, v \)
and \( r \) for a spherical mirror:
A \( \cdot r=\frac{2 u v}{u+v} \)
B. \( r=\frac{2}{u+v} \)
c. \( r=\frac{2(u+v)}{(u v)} \)
D. \( r=\frac{u v}{u+v} \)


The vector equation of the plane which is at a distance of \( \frac{3}{\sqrt{14}} \) from the origin and the normal from the origin is \( 2 \hat{i}- \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( . \vec{r} .(2 \hat{i}-3 \hat{j}+\hat{k})=3 \)
B . \( \vec{r} .(\hat{i}+\hat{j}+\hat{k})=9 \)
c. \( \vec{r} .(\hat{i}+2 \hat{j})=3 \)
D. \( \vec{r} .(2 \hat{i}+\hat{k})=3 \)


Which of the following has the highest molar conductivity in solution?
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{6}\right] C l_{4} \)
в. \( \left[P t\left(N H_{3}\right)_{5} C l\right] C l_{3} \)
\( \mathbf{c} \cdot\left[\operatorname{Pt}\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \)
D \( \cdot\left[\operatorname{Pt}\left(N H_{3}\right)_{3} C l_{3}\right] C l \)


Find the first 3 terms of a G.P. if \( a=4 \)
and \( r=2 \)


Generally, non-metals are not conductors of electricity. Which of the following is a good conductor of electricity?
A. Diamond
B. Graphite
c. sulphur
D. Fullerene


The amino acid containing mercaptan unit is:
A. leucine
B. glutamine
c. cysteine
D. lysine


A constant volume gas thermometer
works on:
A. Archimedes' principle
B. Pascal's law
c. Boyle's law
D. charles' Law


\( \operatorname{Let} A=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right| \) and suppose that
det. \( (A)=2 \) then the det.(B) equals, where \( \boldsymbol{B}=\left|\begin{array}{ccc}\mathbf{4} \boldsymbol{x} & \mathbf{2} \boldsymbol{a} & -\boldsymbol{p} \\ \mathbf{4} \boldsymbol{y} & \mathbf{2} \boldsymbol{b} & -\boldsymbol{q} \\ \boldsymbol{4} \boldsymbol{z} & \boldsymbol{2} \boldsymbol{c} & -\boldsymbol{t}\end{array}\right| \)
A. \( \operatorname{det}(B)=-2 \)
B. \( \operatorname{det}(B)=-8 \)
c. \( \operatorname{det}(B)=-16 \)
D. \( \operatorname{det}(B)=8 \)


In an atom, the differentiating electron
enters into 7 s sub shell. The number of
incomplete shells in the atom could be:
A . 1
B . 2
\( c .3 \)
D.


Point out the correct decreasing order of
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) values of following amines:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H}_{3} \)
\( \left(C_{2} H_{5}\right)_{2} N H \) and \( C_{6} H_{5} N H_{2} \)
\( \mathbf{A} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N H_{2}>C_{6} H_{5} N H C H_{3}> \)
\( C_{6} H_{5} N H_{2} \)
B. \( \left(C_{2} H_{5}\right)_{2} N H>C_{6} H_{5} N H C H_{3}>C_{6} H_{5} N H_{2}> \)
\( C_{2} H_{5} N H_{2} \)
c. \( C_{6} H_{5} N H_{2}>C_{6} H_{5} N H C H_{3}>C_{2} H_{5} N H_{2}> \)
\( \left(C_{2} H_{5}\right)_{2} N H \)
D. \( C_{2} H_{5} N H_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{6} H_{5} N H C H_{3}> \)
\( C_{6} H_{5} N H_{2} \)


Four point charges \( Q, q, Q \) and \( q \) are
placed at the corners of a square of side
\( a^{\prime} \) as shown in the figure.
Find the
(a) resultant electric force on a charge
\( Q, \) and
(b) potential energy of this system.


Let \( \bar{z}, \bar{w} \) be complex numbers such that
\( z+w \) purely imaginary and \( z-w \) is
purely real
\( \mathbf{A} \cdot z=w \)
в. \( z=-w \)
\( \mathbf{c} \cdot z=\bar{w} \)
D. \( z=-\bar{w} \)


During concentration of \( _{--}-_{-}- \) ores by froth floatation process potassium ethy xanthate is added.
A. sulphide
B. carbonate
c. halide
D. amide


An example of nuclear fusion reaction
is :
A \( \cdot \frac{2033}{90} \mathrm{Th}+\frac{1}{0} \mathrm{n} \rightarrow \frac{23^{3} \mathrm{Th}}{ } \)
B \( \cdot \frac{27}{13} \mathrm{AI}+\frac{4}{2} \mathrm{He} \rightarrow \frac{30}{15} \mathrm{P}+\frac{1}{0} \mathrm{n} \)
\( \mathbf{c} \cdot_{2}^{3} \mathrm{He}+_{2}^{3} \mathrm{He} \rightarrow_{2}^{4} \mathrm{He}+2_{1}^{1} \mathrm{H} \)
D \( \cdot \frac{239}{92} \mathrm{U} \rightarrow_{93}^{239} \mathrm{Np}+_{-1}^{0} \mathrm{e} \)


A pin which is \( 2 \mathrm{cm} \) long is placed at a distance of \( 16 \mathrm{cm} \) from a convex lens.
Assuming it to be perpendicular to the principal axis, find the position of the image if the focal length of the lens is 12
\( \mathrm{cm} \)
A . \( 48 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. None of these


Let \( A=\{1,2,3,4,5\}, B=N \) and \( f: A \rightarrow \)
\( B \) be defined by \( f(x)=x^{2} \)
Find the range of \( f \). Identify the type of function.


Find the angle of incidence and angle of
reflection from the diagram.
A \( \cdot 45^{\circ}, 40^{\circ} \)
B . \( 55^{\circ}, 55^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ}, 60^{\circ} \)
D. \( 30^{\circ}, 30^{\circ} \)


A man stands in between two cliffs and
fires a gun. He hears two successive echoes after 3 sec and 5 sec. What is the distance between two cliffs? (speed of sound \( =330 \quad m s^{-1} \)


\( A B C D \) is a parallelogram and \( A P \) and
\( C Q \) are perpendiculars from vertices \( A \)
and \( C \) on diagonal
BD( see Fig.). Show that \( \mathbf{A P}=\mathbf{C Q} \)


Explain syngas in detail.


What is this distance between the lens
and the screen called?


A metallic ring is attached to the wall of the room.When the north pole of magnet is brought near the ring, the induced current in the ring is:
A . zero
B. in clockwise direction
c. in anti-clockwise direction
D. infinite


The pH of a neutral water is \( 6.5 . \) Then
the temperature of water:
\( A \cdot \operatorname{ls} 25^{\circ} C \)
B. Is more than \( 25^{\circ} \mathrm{C} \)
c. Is less than \( 25^{\circ} \mathrm{C} \)
D. can be more or less than \( 25^{\circ} \mathrm{C} \)
E. Cannot be predicted


Describe the method for the purification of colloidal sol containing excess amount of electrolytes with diagram:


At \( 1400 K, K_{c}=2.5 \times 10^{-3} \) for reaction
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{S}_{2}(\boldsymbol{g})+ \)
\( 4 H_{2}(g) . \) At \( 10.0 L \) reaction vessel at
\( 1400 \mathrm{K} \) contains 2.00 mole of \( \mathrm{CH}_{4}, 3.0 \)
mol of \( \mathrm{CS}_{2}, 3.0 \) mole of \( \mathrm{H}_{2} \) and 4.0 mole
of \( \mathrm{H}_{2} \mathrm{S} \). Then
A. this reaction is at equilibrium with above concentrations
B. the reaction will proceed in forward direction to reach equilibrium
c. the reaction will proceed in backward direction to each equilibrium
D. the information is insufficient to decide the direction of progress of reaction


Write chemical reaction for the
following conversion. Cumene to phenol


The parallel combination of two air filled parallel plate capacitors of capacitance \( \mathrm{C} \) and \( \mathrm{NC} \) is connected to a battery of
voltage, \( V \). When the capacitors are fully charged, the battery is removed and after that a dielectric material of
dielectric constant \( \mathrm{K} \) is placed between the two plates of the first capacitor. The new potential difference of the combined system is?
A \( \cdot \frac{V}{K+n} \)
в. \( V \)
c. \( \frac{(n+1) V}{(K+n)} \)
D. \( \frac{n V}{K+n} \)


The water content of soil is defined as
the ratio of
A. Volume of water to volume of voids in soil
B. Volume of water to volume of given soil
C. Weight of water to weight of solids of given mass of soil
D. Weight of water to weight of air in voids


Express the matrix \( \left[\begin{array}{ccc}\mathbf{3} & -\mathbf{2} & \mathbf{- 4} \\ \mathbf{3} & -\mathbf{2} & -\mathbf{5} \\ -\mathbf{1} & \mathbf{1} & \mathbf{2}\end{array}\right] \) as
the sum of a symmetric and skew-
symmetric matrix


Current in circuit, which makes bulb
glow or heats up the wire, is:
A. motion of charges
B. motion of atoms
c. motion of molecules
D. none of the above


Out of the complexes \( \left.\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right)\right]^{3+} \)
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-},\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \) and
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C l})_{6}\right]^{3-}, \) the most stable one is:
\( \left.\left.^{\mathbf{A}} \cdot_{[F e}\left(H_{2} O\right)_{6}\right)\right]^{3+} \)
B. \( \left[F e(C N)_{6}\right]^{3-} \)
\( c \)
\( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \)
\( D \)
\( \left[F e(C l)_{6}\right]^{3-} \)


Which of the following gives, on ozonolysis, both aldehydes and
ketones?
A. \( M e_{2} C=C H M e \)
В. \( M e_{2} C=C M e_{2} \)
\( \mathbf{c} \cdot \operatorname{meCH}_{2}-C(M e)=C M e_{2} \)
D. \( \operatorname{Me} C H(M e)-C H=C H M e \)


\( A B C \) is a triangle right angled at \( C . A \) line through the mid-point \( M \) of
hypotenuse \( A B \) and parallel to \( B C \)
intersects \( A C \) and \( D . \) Show that
(i) \( D \) is the mid-point of \( A C \)
(ii) \( M B \perp A C \)
(iii) \( \boldsymbol{C M}=\boldsymbol{M} \boldsymbol{A}=\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{A} \boldsymbol{B} \)


\( \int \frac{1-x^{7}}{x\left(1+x^{7}\right)} d x \) equals
A \( \quad \ln |x|+\frac{2}{7} \ln \left|1+x^{7}\right|+c \)
B \( \cdot \ln |x|+\frac{2}{4} \ln \left|1-x^{7}\right|+c \)
C \( \quad \ln |x|-\frac{2}{7} \ln \left|1+x^{7}\right|+c \)
D. \( -\ln |x|+\frac{2}{4} \ln \left|1-x^{7}\right|+c \)


The range of clinical thermometer is
A \( .37^{\circ} \mathrm{C} \) to \( 42^{\circ} \mathrm{C} \)
B \( \cdot 95^{\circ} F \) to \( 110^{\circ} F \)
\( \mathbf{c} \cdot 90^{\circ} F \) to \( 112^{\circ} F \)
D. \( 95^{\circ} C \) to \( 104^{\circ} C \)


Study the following lists. List-
List-II
(A) Corynebacterium glutamicum
(I) Flexibility in shape
(B) Halobacterium
(II) Mineralisation
(C) Cristispira
(III) Lysine
(D) Bacillus mycoides
(IV) Gas vacuoles
(V) Parasite on bacteria
The correct match is
\( A \cdot(A)-(V),(B)-(11),(C)-(111),(D)-(1 V) \)
B. (A)-(III), (B)- (IV), (C)-(I), (D)- (II)
\( c \cdot(A)-(11),(B)-(V),(C)-(1 V),(D)-(1) \)


Solve \( \left(2 x-10 y^{3}\right) \frac{d y}{d x}+y=0 \)
A \( \cdot x=-2 y^{3}+c y^{-2} \)
B . \( x=2 y^{3}+c y^{-2} \)
c. \( x=2 y^{3}+c y^{2} \)
D. None of these


A stone dropped from the top of a tower travels \( 15 \mathrm{m} \) in the last second of its
motion. If \( g=10 m s^{-2} \) then the time of
fall is
\( \mathbf{A} \cdot 2 s \)
в. \( 2.5 s \)
c. \( 5 s \)
D. \( 3 s \)


Quantum number \( (n=3) \) has:
A. s, p electrons
B. s, p, d, electrons
c. s electrons
D. s,p,d,f electrons


A train \( 100 \mathrm{m} \) long travelling at \( 40 \mathrm{m} / \mathrm{s} \) starts overtaking another train \( 200 \mathrm{m} \) long travelling at \( 30 \mathrm{m} / \mathrm{s} \). The time taken by the first train to pass the second train completely is:
A. 30
B. 40
\( c .50 \mathrm{s} \)
D. 60 s


The RNA and DNA differ in having different
A. Type of pentose sugar
B. Type of Phosphates
c. Type of Nitrogen base
D. Both A and C


What are artificial sweetening agents? Give example.


\( \boldsymbol{H} \boldsymbol{C l O}, \boldsymbol{H} \boldsymbol{C l O}_{2}, \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{3}, \boldsymbol{H} \boldsymbol{C l O}_{4} \)
Arrange the given compound in order of increasing acidic strength


Which of the following is not true for electromagnetic waves?
A. They transport energy.
B. They have momentum.
C. They travel at different speeds in air depending on their frequency.
D. They travel at different speeds in medium depending on their frequency.


A charge q of mass m starting from rest is allowed to move between two points having a potential difference of V volts. What is the final velocity of the charge?


The formation of phenol from benzene diazonium chloride is a
A. Hydrolysis reaction
B. pyrolysis reaction
c. Photosynthesis reaction
D. combustion raection


A copper rod of length \( L \) and radius \( r \) is suspended from the ceiling by one of its ends. What will be elongation of the rod due to its own weight when \( \rho \) and \( Y \) are
the density and Young's modulus of the copper respectively?
\( ^{\text {A } \cdot \frac{\rho^{2} g L^{2}}{2 Y}} \)
\( ^{\mathrm{B}} \cdot \frac{\rho g L^{2}}{2 Y} \)
c. \( \frac{\rho^{2} g^{2} L^{2}}{2 Y} \)
D. \( \frac{\rho g L}{2 Y} \)


\( \boldsymbol{x} \boldsymbol{N a O H}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \rightarrow \boldsymbol{N a}_{2} \boldsymbol{S O}_{4}+ \)
\( \boldsymbol{y} \boldsymbol{H}_{2} \boldsymbol{O} . \) Balance the given chemical
equation and find the value of \( x \) and \( y \)
A .2,1
в. 2,2
c. 2,3
D. 1,2


The maximum value of \( a^{2} b^{3} c^{4} \) subject
\( \operatorname{to} a+b+c=18 \) is
\( \mathbf{A} \cdot 4^{2} 6^{3} 8^{4} \)
В \( \cdot 4^{3} 6^{2} 8^{4} \)
c. \( 4^{4} 6^{2} 8^{3} \)
D \( \cdot 4^{2} 6^{4} 8^{3} \)


State true or false:
46656 is a perfect cube.
A. True
B. False


Which of the following is incorrect?
A. If the wave is longitudinal, it must be a mechanical wave
B. If the wave is mechanical, it may OR may not be a transverse wave
C. Mechanical waves cannot propagate in vacuum
D. 'Diffraction' helps us to distinguish between sound wave and light wave


The function \( f(x)=x(x+3) e^{-(1 / 2) x} \)
satisfies the condition of Rolle's
theorem in \( [-3,0] . \) The value of \( c \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. -2
D. - 3


Meiosis II fails after completion of meiosis I. This phenomenon
A. Beachymeiosis
B. Dinomitosis
c. Karyokinesis
D. Noni


Calculate the shortest and longest
wavelengths of Balmer series of
hydrogen atom. Given \( \boldsymbol{R}=\mathbf{1 . 0 9 7} \times \)
\( 10^{7} m^{-1} \)


Mark the incorrect statement
A. Sound can be produced by beating an object irrespective of whether there are vibrations or not.
B. The sound of a tabla normally has a lower pitch than the sound of a violin.
C. A short flute will produce sound of lower pitch than a long flute.
D. All of the above


Identify the incorrectly matched pair.
A. Pair of skeletal parts - Sternum and ribs
Category - Axial skeleton
B. Pair of skeletal parts - Clavicle and glenoid cavity
Category - Pelvic girdle
C. Pair of skeletal parts - Humerus and ulna
Category - Appendicular skeleton
D. Pair of skeletal parts - Malleus and stapes
Category - Ear ossicles


An electric fuse used in households
works on which principle of
A. Joule's heating
B. Coulomb's law
c. Maxwell's law
D. Ohm's law