is used as a unit to measure
the capacity of something.
A. Kilogram
B. Litre
c. Metre
D. None


Calculate the ratio of the speed of sound in neon to that in water vapour at any temperature. Given that molecular
weight of neon gas \( =2.02 \times \)
\( 10^{-2} k g m o l e^{-1} \) and molecular weight of
watervapour \( =1.8 \times 10^{-2} \) kgmole \( ^{-1} \)
A .0 .944
B. 1.944
c. 2.944
D. 3.944


If the total amount of adenine and
thymine in a double-stranded DNA is \( 45 \% \), the amount of guanine in this DNA will be
A . 22.5\%
B . 27.5\%
c. \( 45 \% \)
D. 55\%


If the biquadratic \( x^{4}+a x^{3}+b x^{2}+ \)
\( c x+d=0(a, b, c, d \epsilon R) \) has 4 non real
roots, two with sum \( 3+4 i \) and the other
two with product \( 13+i . \) Find the sum of
the digits of value of ' \( b \)


The curve \( \frac{x^{n}}{a^{n}}+\frac{y^{n}}{b^{n}}=2 \) touches the line \( \frac{x}{a}+\frac{y}{b}=2 \) at the point
A \( .(b, a) \)
в. \( (a, b) \)
c. (1,1)
D \( \cdot\left(\frac{1}{a}, \frac{1}{b}\right) \)


Pure water can be obtain from sea
water by:
A. Centrifugation
B. Plasmolysis
c. Reverse osmosis
D. Sedimentation


The valency of impurity element for making n-type semiconductor is
A . 3
B. 5
\( c \cdot 4 \)
\( D \)


A metallic sphere cools from \( 50^{\circ} \mathrm{C} \) to
\( 40^{\circ} \mathrm{C} \) in 300 seconds. If the room
temperature is \( 20^{\circ} \mathrm{C} \) then its
temperature in the next 5 minutes will
be:
A \( \cdot 30^{\circ} \mathrm{C} \)
B. \( 33.3^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 36^{\circ} C \)
D. \( 38^{\circ} \mathrm{C} \)


In the following solids thermal conductivity is maximum for :
A. copper
B. aluminium
c. gold
D. silver


Define the term 'self-inductance' of a
coil. Write its S.I. unit.


Using appropriate identity, factorise the following:
\( (1) 49 a^{2}+70 a b+25 b^{2} \)
\( (2) 9 a^{2}-30 a b+25 b^{2} \)


Atomic mass unit is abbreviated as
\( A \). atm
B. ama
c. a.m.u.
D. aum


Freshly prepared precipitate sometimes gets converted to colloidal solution by:
A. coagulation
B. electrolysis
c. diffusion
D. peptisation


The colour of a green leaf, when white light passing through a yellow filter is applied on it is:
A . black
B. yellow
\( c \cdot \) red
D. green


Ketones \( \left(\boldsymbol{R}_{1} \boldsymbol{C O} \boldsymbol{R}_{2}\right) ; \boldsymbol{R}_{1}=\boldsymbol{R}_{2}= \) alkyl
group, can be obtained in one step by:


Which chromosome has satellite?
A. Telocentric
B. Metacentric
c. Acrocentric
D. Sub-metacentric


Ozone layer depletion may lead to which of the following harmful effects in
organisms?
A. Skin cancer
B. Cataract
c. Damage to the immune system
D. All of the above


If \( f \) is an increasing and \( g \) is a decreasing function and fog is defined,
then fog will be
A. increasing function
B. decreasing funtion
c. neither increasing nor decreasing
D. None of these


If \( x=3, \) then find the value of the
expression \( \boldsymbol{x}-\mathbf{2} \)


In how many different ways can three
persons \( A, B, C \) having 6,7 and 8 one rupee coins respectively donate \( \boldsymbol{R} \boldsymbol{s} . \mathbf{1 0} \)
collectively?
A . 45
B. 46
c. 47
D. 48


Write the relation for the speed of
electromagnetic waves in terms of the
amplitudes of electric and magnetic fields.


The compressibility of water is \( 4 \times 10^{-5} \)
per unit atmosphere pressure. The
decrease in volume of \( 100 \mathrm{cm}^{3} \) water
under a pressure of 100atm will be
A \( \cdot 0.4 \mathrm{cm}^{3} \)
B. \( 4 \times 10^{-5} \mathrm{cm}^{3} \)
c. \( 0.025 \mathrm{cm}^{3} \)
D. \( 0.04 \mathrm{cm}^{3} \)


For spherical symmetrical charge distribution, variation of electric
potential with distance from centre is
given in diagram. Given that:\( V=\frac{q}{4 \pi \varepsilon_{0} R_{0}} \) for \( r R_{0} \) and \( V=\frac{q}{4 \pi \varepsilon_{0} r} \)
for \( r \geq R_{0} \)
Then which option is incorrect:
A . Total charge within \( 2 R_{0} \) is \( q \)
B. Total electrostatic energy for \( r \leq R_{0} \) is zero
C. At \( r=R_{0} \) electric field is discontinuous
D. There will be no charge anywhere except at \( r=R_{0} \)


A ring is made of a wire having a
resistance \( R_{0}=12 \Omega \). Find the points \( A \)
and \( \mathrm{B} \) as shown in fgure at which a current carrying conductor should be
connected so that the resistance \( R \) of
the sub circuit between these points is
equal to \( \frac{8}{3} \Omega \)
A \( \cdot \frac{l_{1}}{l_{2}}=\frac{3}{8} \)
B \( \cdot \frac{l_{1}}{l_{2}}=\frac{1}{2} \)
\( \mathbf{c} \cdot \frac{l_{1}}{l_{2}}=\frac{5}{8} \)
D. \( \frac{l_{1}}{l_{2}}=\frac{1}{3} \)


The principle involved in the construction of beam balance is :
A. Principle of moments
B. Principle of inertia
c. Principle of superposition
D. Principle of velocity


What is the smallest number by which 1600 is to be divided, so that the quotient is a perfect cube?


Find the mean deviation about the
mean for the following data:
\( \mathbf{3}, \mathbf{6}, \mathbf{1 0}, \mathbf{4}, \mathbf{9}, \mathbf{1 0} \)


Powdered substances are more
effective adsorbents than their
crystalline form because:
A. adsorption is an exothermic process
B. they become inert and do not react with the adsorbate
C. the extent of adsorption increases with increase in surface area of the adsorbent
D. adsorption is more if the size of adsorbent is small.


\( H_{2} O_{2} \) is a weak dibasic acid
If this is true enter 1 , if false enter 0 .


Maximum oxidation state exhibited by
lanthanides is:
\( A \cdot+1 \)
B. +2
\( c \cdot+3 \)
D. +4


What are antifertility drugs? Give an
example.


The value of \( \cos \left(\tan ^{-1} \tan 4\right) \) is
A \( \frac{1}{\sqrt{17}} \)
B. \( -\frac{1}{\sqrt{17}} \)
\( c \cdot \cos 4 \)
D. - cos 4


Evaluate the integral \( \int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x \)
A . \( \pi \)
B . \( \pi / 2 \)
c. \( \pi / 3 \)
D . \( \pi / 4 \)


Let the sequences \( a_{1}, a_{2}, a_{3}, \dots \dots, a_{n}, \dots \)
from an AP. Then \( a_{1}^{2}-a_{2}^{2}+a_{3}^{2}-a_{4}^{2}+ \)
\( \ldots+a_{2 n-1}^{2}-a_{2 n}^{2} \) is equal to
A \( \cdot \frac{n}{2 n-1}\left(a_{1}^{2}-a_{2 n}^{2}\right) \)
B. \( \frac{2 n}{n-1}\left(a_{2 n}^{2}-a_{1}^{2}\right) \)
c. \( \frac{n}{n+1}\left(a_{1}^{2}+a_{2 n}^{2}\right) \)
D. None of these


A strong base can abstract an \( \alpha \) hydrogen from:
A. ketone
B. alkane
c. alkene
D. amine


Two point charges \( +8 q \) and \( -2 q \) are located at \( x=0 \) and \( x=L \) respectively. The location of a point on the \( x \) axis at which the net electric field due to these two
point charge is zero is -
A. 2
B. L/4
\( c \cdot 8 L \)
D. 4 L


\( \frac{-}{8} \)
8
8
8


Osmotic theory for an active absorption
of water was given by
A. Thimann
B. O. Hertwig
c. Atkins and Priestley
D. J. C. Bose


The number of oxygen atoms in 20 gm of sulphur tri-oxide \( S O_{3} \) is the same as
these present in \( x \) gms of Ozone. The atomic mass of sulphur and oxygen are \( 32 \mu \) and \( 16 \mu \) respectively. Find the value of \( \mu .(12 \mathrm{gm}) \)


A dipole consisting of \( +10 n C \) and \( -10 n C \) separated by a distance of \( 2 \mathrm{cm} \) oscillates in an electric filed of strength \( 60,000 \mathrm{Vm}^{-1} . \) The frequency of its
oscillation is (Moment of inertia about the axis of oscillations is \( 3 \times 10^{-10} \mathrm{kgm}^{2} \) ):
A . \( 20.2 \mathrm{Hz} \)
в. \( 25.4 \mathrm{Hz} \)
c. \( 31.38 H z \)
D. \( 37.1 \mathrm{Hz} \)


The remainder obtained when the
polynomial \( \boldsymbol{x}^{4}-\mathbf{3} \boldsymbol{x}^{\mathbf{3}}+\mathbf{9} \boldsymbol{x}^{2}-\mathbf{2 7} \boldsymbol{x}+\mathbf{8 1} \)
is divided by \( (x-3) \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
c. 81
D. 27


The material of a wire has a density of
\( 1.4 \mathrm{g} / \mathrm{cm}^{3} . \) If it is not wetted by a liquid of
surface tension 44 dyne/cm, then the maximum radius of the wire which can
float on the surface of liquid is :
A \( \cdot \frac{10}{28} \mathrm{cm} \)
в. \( \frac{10}{14} \mathrm{cm} \)
c. \( \frac{10}{7} m m \)
D. 0.7 cm


A bent tube is lowered into a water
stream as shown in figure above. The
velocity of the stream relative to the tube is equal to \( v=2.5 m / s . \) The closed
upper end of the tube located at the
height \( h_{0}=12 \mathrm{cm} \) has a small orifice.
The height \( h(\text { in } c m) \) the water jet spurt
is \( 2 \times 10^{x} \). Find \( x \)


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


Given, \( \xi=\{ \) Natural numbers between \( 25 \text { and } 45\} ; A=\{\text { even numbers }\} \) and \( B \)
\( \{\text { multiples of } 3\} \) then \( n(A)+n(B)= \)
\( \boldsymbol{n}(\boldsymbol{A} \cup \boldsymbol{B})+\boldsymbol{n}(\boldsymbol{A} \cap \boldsymbol{B}) . \) If true enter 1 else
0


An example of Liliaceae family is
A. Lupin
B. Soyabean
c. Petunia
D. Tulip


f \( \boldsymbol{m}=-\mathbf{1} \mathbf{9} \) and \( \boldsymbol{n}=\mathbf{2 3}, \) the value of
\( 25 m^{2}+40 m n+16 n^{2} \) is
\( A \cdot 9 \)
в. -9
\( c .1 \)
D. 3


Find the product of \( 3 x^{3} y^{2} \) and \( (2 x-3 y) \)
Also, verify the result for \( \boldsymbol{x}=-\mathbf{1}, \boldsymbol{y}=\mathbf{2} \)


Which one is correct sequence in glycolysis?
A . G 6-P\rightarrow PEP\rightarrow3-PGAL \( \rightarrow \) 3-PGA
B. G 6-P\rightarrow 3-PGAL \( \rightarrow 3 \) -PGA \( \rightarrow \) 3-PEP
c. \( G 6-P \rightarrow P E P \rightarrow 3-P G A \rightarrow 3-P G A L \)
D. G 6-P \( \rightarrow \) 3-PGA \( \rightarrow \) 3-PGAL \( \rightarrow \) 3-PEP


Frequency of oscillation of a body is
6 \( H z \) when force \( F_{1} \) is applied and
\( 8 H z \) when \( F_{2} \) is applied. If both forces
\( F_{1} \& F_{2} \) are applied together then, the frequency of oscillation is :
\( \mathbf{A} \cdot 14 H z \)
в. \( 2 \mathrm{Hz} \)
c. \( 10 H z \)
D. \( 10 \sqrt{2} \mathrm{Hz} \)


An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas (in those same units) in four processes.
Which processes start and end on the same isotherm
\[
\begin{array}{llll}
A & B & C & D \\
5 & 4 & 12 & 6
\end{array}
\]
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


Find the derivative \( x^{3} \)


Which of the following reactions is not used for the preparation of a colloidal solution?
A \( \cdot 2 A u C l_{3}+3 S n C l_{2} \rightarrow 3 S n C l_{4}+2 A u \)
B . \( F e C l_{3}+3 H_{2} O \longrightarrow F e(O H)_{3}+3 H C l \)
\( \mathbf{c} \cdot 2 M g+C O_{2} \rightarrow 2 M g O+C \)
D. \( 2 H_{2} S+2 S O_{2} \rightarrow 2 H_{2} O+3 S \)


A mixture of 2 moles of \( N_{2} \) and 8 moles
of \( H_{2} \) are heated in a 2 lit vessel, till
equilibrium is established. At
equilibrium 0.4 moles of \( N_{2} \) was present. What will be the equilibrium
concentration of \( \boldsymbol{H}_{2} ? \)
\( A \cdot 2 \) mole/lit
B. 4 mole/lit
c. 1.6 mole/lit
D. 1 mole/lit


Which of the following may best be
called aromatic?
\( \mathbf{A} \)
B.
\( \mathbf{C} \)
D.


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.
The propenyl radical, \( \boldsymbol{C H}_{2}=\boldsymbol{C H C H}_{2} \)
is formed in the first propagation step
of the reaction.
Write an equation to show the
formation of \( \boldsymbol{C H}_{2}=\boldsymbol{C H C H}_{2}^{\circ} \) in this
propagation step.


On observing light from three different stars \( P, Q \) and \( R, \) it was found that
intensity of violet colour is maximum in
the spectrum of \( P, \) the intensity of green colour is maximum in the spectrum of
\( \mathrm{R} \) and the intensity of red colour is maximum in the spectrum of Q. If
\( T_{P}, T_{Q} \) and \( T_{R} \) are the respective absolute temperature of \( P, Q \) and \( R, \) then it can be concluded from the above
observations that
\( \mathbf{A} \cdot T_{P}<T_{R}<T_{Q} \)
В \( \cdot T_{P}<T_{Q}<T_{R} \)
\( \mathbf{c} \cdot T_{P}>T_{Q}>T_{R} \)
\( \mathbf{D} \cdot T_{P}>T_{R}>T_{Q} \)


lodoform can be prepared from:
A. isoamyl alcoho
B. \( \alpha \) -phenyl ethanol
c. isobutyl alcohol
D. \( \beta \) -phenyl ethanol


In the adjoining diagram,a wavelength
AB, moving in air is incident on a plane
glass surface XY. Its position CD after
refraction through a glass slab is shown also along with the normals drawn at \( A \)
and D. The refractive index of glass with
respect to air \( (\mu=1) \) will be equal to
A. \( \frac{\sin \theta}{\sin \theta^{\prime}} \)
B. \( \frac{\sin \theta}{\sin \phi^{\prime}} \)
c. \( \frac{\sin \phi^{\prime}}{\sin \theta} \)
\( D \)


In which of the following choices are the noble gases arranged correctly in order of increasing boiling point?
A. \( X e, K r, A r, N e \)
в. \( N e, A r, K r, X e \)
c. \( K r, X e, N e, A r \)
D. \( A r, N e, K r, X e \)


Most primitive members in which roots
are not present is
A. Psilotum
B. Rhynia
c. Lycopodium
D. Selaginella


Q Type your question-
a. \( \boldsymbol{F e}(\boldsymbol{s}) \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-}( \) at anodic
site)
b. \( O_{2}(g)+4 H^{\oplus}(a q)+4 e^{-} \rightarrow 2 H_{2} O(l) \)
(at cathodic site)
c. \( 4 F e^{2+}(a q)+O_{2}(g)+4 H_{2} O(l) \rightarrow \)
\( \mathbf{2} \boldsymbol{F} \boldsymbol{e}_{\mathbf{2}} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{8} \boldsymbol{H}^{\oplus} \)
d. \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{x} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \cdot \boldsymbol{x} \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason
Rusting is accelerated in the presence
of \( N a C l \) and \( C O_{2} \)

Read the above assertion and reason
and choose the correct option regarding
it
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Differentiate the following function with
respect to \( x \) \( 1+3 x \)


In the reaction,
\( \mathbf{3} \boldsymbol{C u} \boldsymbol{O}+\mathbf{2 N H}_{3} \longrightarrow \boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \mathbf{3} C u \)
the change of \( N H_{3} \) to \( N_{2} \) involves:
A . Loss of 6 electrons per mole of \( N_{2} \)
B. Loss of 3 electrons per mole of \( N_{2} \)
c. Gain of 6 electrons per mole of \( N_{2} \)
D. Gain of 3 electrons per mole of \( N_{2} \)


is the electrical
energy produced or consumed per unit
time.


For electron affinity of halogens which of the following is correct?
A. \( B r>F \)
в. \( F>C l \)
c. \( B r<C l \)
\( \mathbf{D} \cdot F>I \)


Match the following. \begin{tabular}{ccc|c}
& List I & & List II \\
\( \mathrm{i} \) & Deforestation & \( \mathrm{a} \) & Urbanization \\
\( \mathrm{ii} \) & Natural cause \( \mathrm{of} \) deforestation & \( \mathrm{b} \) & Cutting of forests \\
iii & Man-made cause of deforestation & \( \mathrm{c} \) & Droughts
\end{tabular}
\( \mathbf{A} \)
\( 1-b \) , \( \|-a,\| I-c \)
\( B \cdot I-a,\|-b,\| I-C \)
\( \mathbf{C} \cdot \mid-\mathrm{c},\|-\mathrm{a},\|-\mathrm{b} \)
D. \( |-b,||-c,|||- \)


Optical isomerism is shown by
octahedral complexes having:
A. Two trans bidentate ligands
B. All mono denatate ligands
c. Two trans monodenatate ligands
D. All the three bidentate ligands


There is a uniform (in spatial districution) magnetic filed B in a circular region of radius \( R \) as shown in
the figure whose magnitude varies uniformly a the rate \( \beta \) w.r.t. time. The emf induced across the ends of a
circular concentric conducting arc of
radius \( R_{1} \) having an agle \( \theta \) as shown
\( \left(<\boldsymbol{O} \boldsymbol{A} \boldsymbol{O}^{\prime}=\boldsymbol{\theta}\right) \) is
\( ^{\mathrm{A}} \cdot \frac{\theta}{2 \pi} R_{1}^{2} \cdot \beta \)
B. \( \frac{\theta}{2} R^{2} \cdot \beta \)
c. \( \frac{\theta}{2 \pi} R^{2} . \).
D. zero


A body is lying on a piston which is executing vertical SHM. Its time period is 2 s. For what value of amplitude, the
body will leave the piston:
\( A \cdot 1 m \)
B. 0.248 m
c. \( 0.428 \mathrm{m} \)
D. \( 0.842 \mathrm{m} \)


Familiar examples of family Liliaceae
are
A. Allium cepa, Aloe vera and Tamarindus indica
B. Saraca indica, Allium cepa and Aloe Vera
C. Allium sativum, Allium cepa and Aloe Vera
D. Tamarindus indica, Allium cepa and Allium sativum


In Carius method for the quantitative
estimation of sulphur. it is estimated
by
A. \( B a S \)
в. \( \mathrm{CaSO}_{4} \)
\( c \cdot B a S O_{4} \)
D. \( B a C l_{2} \)


A \( 60 p F \) capacitor is fully charged by a
\( 20 V \) supply. It is then disconnected
from the supply and is connected to another uncharged \( 60 p F \) capacitor in
parallel. The electrostatic energy that is
lost in this process by the time the charge is redistributed between them is \( (\operatorname{in} n J) \)


The infinity resistance plug in a postoffice box has
A. an airgap only.
B. a resistance coil of infinite resistance.
c. largest resistance available in box.
D. resistance of the coil 5000 \( \Omega \)


Find the values of \( x, y, a \) and \( b \) if \( \left[\begin{array}{cccc}3 x+4 y & 2 & x-2 y \\ a+b & 2 a-b & -1\end{array}\right]= \)


Which one of the following reflex do not include innervation of brain?
A. Spinal reflex
B. Cranial reflex
C. Afferent reflex
D. Efferent reflex


If an object moves towards a plane
mirror with a speed \( \boldsymbol{v}: \)
A. the image moves away from the mirror with a speed \( v \)
B. the image moves away from the mirror with a speed \( 2 v \)
C. the image moves towards the mirror with a speed \( v \)
D. the image moves towards the mirror with a speed \( 2 v \)


Which part of the bulb is an insulator?
\( A \)
B.
\( c \cdot R \)
D.


\( \mathbf{A} \)
\( 0.5 d m^{3} \) flask contains gas \( A \) and 1
\( d m^{3} \) flask contains gas \( B \) at the same temperature. If density of \( \boldsymbol{A}=\mathbf{3} \boldsymbol{g} / \boldsymbol{d} \boldsymbol{m}^{3} \)
and that of \( B=1.5 g / d m^{3} \) and the
molar mass of \( \boldsymbol{A}=\mathbf{1} / \mathbf{2} \) of \( \boldsymbol{B}, \) the ratio
of pressure exerted by gases is:
\( ^{A} \cdot \frac{P_{A}}{P_{B}}=2 \)
в. \( \frac{P_{A}}{P_{B}}=1 \)
c. \( \frac{P_{A}}{P_{B}}=4 \)
D. \( \frac{P_{A}}{P_{B}}=3 \)


toppr 5
Q Type your question
graphs
\( A \)
\( (\mathrm{A}) \)
\( B \)
\( (\mathrm{B}) \)
\( c \)
\( (\mathrm{C}) \)
\( D \)
\( (\mathrm{D}) \)


A chain of length \( l \) and mass \( m \) lies of
the surface of a smooth hemisphere of
radius \( R>1 \) with one end tied to the
top of the hemisphere. Taking base of the hemisphere as reference line, find
the gravitational potential energy of the
chain.


Explain why
(a) Two bodies at different
temperatures \( T_{1} \) and \( T_{2} \) if brought in thermal contact do not necessarily
settle to the mean temperature \( \left(T_{1}+T_{2}\right. \) 12
(b) The coolant in a chemical or a
nuclear plant (i.e. the liquid used to
prevent the different parts of a plant from getting too hot) should have high specific heat
(c) Air pressure in a car tyre increases during driving
(d) The climate of a harbour town is
more temperate than that of a town in a
desert at the same latitude


75 g of water at \( 10^{0} C \) is heated by supplying \( 25200 J \) of heat energy. If the
specific heat of water is \( 4.2 J g^{-10} C^{-1} \)
Calculate the final temperature of
water.


Replacement of chlorine from chlorobenzene to give phenol requires
drastic conditions but chlorine of \( 2,4- \) dinitrochlorobenzene is readily replaced
because:
A. \( N O_{2} \) makes the electron rich ring at ortho and parapositions
B. \( N O_{2} \) withdraws electrons at meta position
c. \( N O_{2} \) donates electrons at meta position
D. \( N O_{2} \) withdraws electrons from ortho- and para position


The coordination of \( P t \) in the complex
\( \operatorname{ion}\left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{2+} \) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Among the following, one statement is not correct when a junction diode is in forward bias
A. the width of depletion region decreases.
B. free electron on n- side will move towards the junction
c. holes on p-side move towards the junction
D. electrons on n-side and holes on p-side will move away from junction.


Which is not a redox reaction?
A. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
в. \( 2 B a O_{+} O_{2} \rightarrow 2 B a O_{2} \)
c. \( 4 K C l O_{3} \rightarrow 4 K C l O_{2}+2 O_{2} \)
D. \( S O_{2}+2 H_{2} S \rightarrow 2 H_{2} O+3 S \)


How will the lowering of temperature affect the chemical equilibrium in the
system \( : 2 N O+O_{2} \rightleftharpoons 2 N O_{2}, \Delta H<0 \)
This question has multiple correct options
A. Relative concentration of products and reactants does not change
B. Relative concentration of products and reactants change
c. Equilibrium is shifted to the lefttt
D. Equilibrium is shifted to the right


An example of chemosynthetic bacteria
is
A. E. coli
B. Sulphur bacteria
c. Nitrobacter
D. Both B and C


\( P b O_{2} \) oxide is:
\( A \). basic
B. acidic
c. neutral
D. amphoteric


The outcome of each of 30 items was observed; 10 items gave an outcome \( \frac{1}{2} \) deach, 10 items gave outcome \( \frac{1}{2} \) each
and the remaining 10 items gave outcome \( \frac{1}{2}+d \) each. If the variance of this outcome data is \( \frac{4}{3} \) then \( |\boldsymbol{d}| \) equals:-
A. 2
B. \( \frac{\sqrt{5}}{2} \)
\( c \cdot \frac{2}{3} \)
D. \( \sqrt{2} \)


Which of the following is not an improper fraction?
\( A \cdot \frac{4}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{7}{11} \)


5 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that all the 5 are hearts is
A \( \cdot \frac{13}{^{52} C_{5}} \)
в.
c.
D. \( \frac{^{13} C_{5}}{^{13} C_{3} \times^{13} C_{4} \times^{13} C_{5}} \)


The value of \( \overline{1}+\overline{1} \) is
\( A \cdot 2 \)
B. 0
\( c .1 \)
D. 10


\( \boldsymbol{A l C l}_{3}(\boldsymbol{a q})+\boldsymbol{N H}_{3}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
Which of the following is one of the products obtained from the reaction above?
A . \( A l N \)
в. \( A l H_{3} \)
c. \( A l \)
D. \( A l\left(N O_{3}\right)_{3} \)
E \( \cdot A l(O H)_{3} \)


Find the odd one. Write down the
common features of others.
(a) Dendrite, Dendron, Axon, Nephron.
(b) Epilepsy, Parkinson disease, Mumps, Alzheimer disease.
(c) Melatonin, Insulin, Glucagon,
Ethylene.


If the direction ratios of two lines are
given by the equations \( 2 l+2 m-n= \)
0 and \( m l+n l+l m=0, \) then the angle
between the two lines is
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


Which one of the following properties is not correct for ozone?
A. It oxidises lead sulphide
B. It oxidises KI
c. It oxidises \( \mathrm{Hg} \)
D. It cannot act as bleaching agent


In the following reaction, \( A \rightarrow B \), rate
constant is \( 1.2 \times 10^{-2} M s^{-1} . \) What is
the concentration of \( B \) after 10 min, if
we start with \( 10 M \) of \( A ? \)
A. 7.2 \( M \)
B. 4.5 M
\( c \cdot 6.7 M \)
D. 7.0 M


A compound has the emperical formula
\( N a_{2} S O_{4} . \) What is its molecular formula?
A. \( N a_{4} S_{2} O_{8} \)
в. \( \operatorname{NaSO}_{4} \)
c. \( N a_{2} S O_{4} \)
D. None


If \( \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right], \) the number of solutions of
the equation, \( \sin 7 x+\sin 4 x+ \)
\( \sin x=0 \) is
A . 3
B. 5
\( c \cdot 6 \)
D. None


Which of the following can cause liver
cancer?
A. \( C H C l_{3} \)
в. \( C C l_{4} \)
c. \( C H_{2} C l_{2} \)
D. \( C_{14} H_{9} C l_{5} \)


The Coefficient of \( x^{53} \) in
\( \sum_{m=0}^{100} C_{m}^{100}(x-3)^{100-m} 2^{m} \) is
\( \mathbf{A} \cdot=-^{100} C_{53} \)
B \( .=-^{101} C_{53} \)
\( \mathbf{C} .=^{101} C_{47} \)
\( \mathbf{D} .=-^{100} C_{47} \)


When a body is negatively charged by
friction, it means
A. the body has acquired excess of electrons
B. the body has acquired excess of protons
C. the body has lost some electrons
D. the body has lost some neutrons


Calculate the ratio of moles of \( 3.6 g \) of
water and \( 4.4 g \) of carbon dioxide.
Atomic mass of \( \boldsymbol{C}=\mathbf{1 2 u}, \boldsymbol{H}= \)
\( \mathbf{1} \boldsymbol{u}, \boldsymbol{O}=\mathbf{1 6} \boldsymbol{u} \)


Solve \( \cos \left[\tan ^{-1}\left[\sin \left(\cot ^{-1} x\right)\right]\right] \)
A \( \cdot \sqrt{\frac{x^{2}+2}{x^{2}+3}} \)
B. \( \sqrt{\frac{x^{2}+2}{x^{2}+1}} \)
c. \( \sqrt{\frac{x^{2}+1}{x^{2}+2}} \)
D. None of these


Which forms interstitial compounds?
A . \( F e \)
в. \( C o \)
c. \( N i \)
D. All


The correct decreasing order of basic strength of the following species is:
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{O} \boldsymbol{H}^{-}, \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \mathbf{A} \cdot N H_{2}^{-}>O H^{-}>N H_{3}>H_{2} O \)
в. \( O H^{-}>N H_{2}^{-}>H_{2} O>N H_{3} \)
C. \( N H_{3}>H_{2} O>N H_{2}^{-}>O H^{-} \)
D. \( H_{2} O>N H_{3}>O H^{-}>N H_{2}^{-} \)


Combination of two Atomic Orbitals
lead to the formation of:
A. two Molecular Orbitals
B. one Molecular Orbitals
c. three Molecular Orbitals
D. four Molecular Orbitals


Write the IUPAC name of the compound.


The colour code of a resistor is brown, black and brown. Then the value of
resistance is
A . \( 10 \Omega \)
в. \( 100 m \Omega \)
c. \( 0.1 k \Omega \)
D. \( 100+5 \% \)


A circular current carrying coil has a radius \( R \). The distance from the centre
of the coil on the axis where the magnetic induction will be \( \frac{1}{8} \) to its value at the centre of the coil, is :
A \( \cdot \frac{R}{\sqrt{3}} \)
в. \( R \sqrt{3} \)
c. \( 2 \sqrt{3} R \)
D. \( \frac{2}{\sqrt{3}} R \)


A function \( f \) is defined by \( f(x)=2 x^{3}- \)
\( \mathbf{3} \boldsymbol{x}, \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \). What is the value of \( \boldsymbol{f}(\boldsymbol{4}) ? \)


Among I-A elements which is the only non-metal?
A. Hydrogen
B. Lithium
c. Sodium
D. Potassium


Chlorine gas obtained above is collected
by the of air.
A. downward displacement
B. upward displacement
c. oxidation
D. reduction


If sum of the first 3 coefficients is 16 in
the expansion \( \left(x+\frac{1}{x^{3}}\right)^{n}, \) then find \( n \)
A . 10
B. 8
\( c .5 \)
D.


\( \operatorname{Let} \boldsymbol{a}_{\boldsymbol{k}}=\boldsymbol{k}\left(^{10} \boldsymbol{C}_{\boldsymbol{k}}\right), \boldsymbol{b}_{\boldsymbol{k}}=(\mathbf{1 0}-\boldsymbol{k})\left(^{10} \boldsymbol{C}_{\boldsymbol{k}}\right) \)
and \( \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{ll}\boldsymbol{a}_{\boldsymbol{k}} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{b}_{\boldsymbol{k}}\end{array}\right] \)
If \( \boldsymbol{A}=\sum_{\boldsymbol{k}=1}^{9} \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{ll}\boldsymbol{a} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{b}\end{array}\right], \) find the value
of \( a+b \)


simplify \( : a^{3}-12 a-16 \)


In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each
section of each class will plant, will be the same as the class, in which they are
studying, e.g., a section of class I will plant 1 tree, a section of class II will
plant 2 trees and so on till Class XII.
There are three sections in each class.
How many trees will be planted by the
students


The length of a rubber cord is \( l_{1} \) metres
when the tension in it is \( 4 N \) and \( l_{2} \)
metres when the tension is \( 5 N \). then the
length in meters when the tension is \( \mathbf{9} N \) is
A \( \cdot 3 l_{2}+4 l_{1} \)
B . \( 3 l_{2}+2 l_{1} \)
\( \mathbf{c} \cdot 5 l_{2}-4 l_{1} \)
D. \( 3 l_{2}-2 l_{1} \)


Which of the following is not Lewis
base?
A. \( A g^{+} \)
в. \( H_{2} \) о
c. \( C N^{-} \)
D. \( R N H_{2} \)


Platelets are a source of
A. Fibrinogen
B. Calcium
c. Thromboplastin
D. Haemoglobin


A physical quantity is measured and the result is expressed as \( n u \) where \( u \) is
the unit used and \( n \) is the numerical
value. If the result is expressed in
various units then
A \( . n \propto \) size of \( u \)
В . \( n \propto u^{2} \)
c. \( n \propto \sqrt{u} \)
D. \( n \propto \frac{1}{u} \)


Match structures given in column I with the type of detergents given in column
II.


What are enzymes? Write in brief the mechanism of enzyme catalysis


Figure shows a conducting loop \( A B C D A \) placed in a uniform magnetic field (strength \( B \) ) perpendicular to its plane. The part \( A B C \) is the (three-
fourth) portion of the square of side Iength \( l \). The part \( A D C \) is a circular arc
of radius \( R \). The points \( A \) and \( C \) are
connected to a battery which supplies a current \( I \) to the circuit. The magnetic force on the loop due to the field \( B \) is :
A . zero
В. \( B I l \)
c. \( 2 B I R \)
D.
\[
\frac{B I l R}{I+R}
\]


A \( 12 k g \) bomb at rest explodes into two
pieces of \( 4 k g \) and \( 8 k g . \) If the momentum
of \( 4 k g \) piece is \( 20 N s, \) the kinetic energy
of the \( 8 k g \) piece is:
A \( .25 J \)
B. \( 20 J \)
c. \( 50 J \)
D. \( 40 J \)


Assertion
Pascal's law is the working principle of
hydraulic lift.
Reason
Pressure \( =\frac{\text {thrust}}{\text {area}} \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


How many additional ATP are used during synthesis of two molecules of hexose sugar in maize than tomato?
A . 12
B . 36
c. 24
D. 8


Simplify the following expressions and evaluate them as directed:
(i) \( x^{2}\left(3-2 x+x^{2}\right) \) for \( x=1 ; x=-1 ; x= \)
\( \frac{2}{3} a n d x=-\frac{1}{2} \)


A copper wire \( 3 \mathrm{m} \) long is stretched to increase its length by \( 0.3 \mathrm{cm} \). Find the lateral strain produced in the wire , if poisson's ratio for copper is 0.25
A. \( 5 \times 10^{-4} \)
B. \( 2.5 \times 10^{-4} \)
c \( .5 \times 10^{-3} \)
D. \( 2.5 \times 10^{-3} \)


A body initially at \( 80^{\circ} \mathrm{C} \) cools to \( 64^{\circ} \mathrm{C} \) in
\( 5 \min \) and \( \operatorname{to} 52^{\circ} C \) in 10 min. The
temperature of the surrounding is
\( A \cdot 26^{\circ} C \)
B. \( 16^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 36^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)


An article was sold at \( 25 \% \) loss. Had the
article been sold for Rs.60 more there
would have been a profit \( 5 \% \). Find the \( \operatorname{cost} \) price of the article.


Draw the structures of the following molecules:
(i) \( N_{2} O_{5} \)
(ii) \( X e F_{2} \)


A wire of density \( \rho \) is stretched between
the clamps at a distance \( L \) apart, while
being subjected to an extension \( l(l<< \)
\( L), Y \) is the Young's modulus of the
wire. The lowest resonant frequency of transverse vibration of the wire is
approximately given by :
A \( \cdot f=\frac{1}{2 L} \sqrt{\frac{Y L}{l \rho}} \)
B. \( f=\frac{1}{2 L} \sqrt{\frac{Y \rho L}{l^{2}}} \)
\( ^{\mathrm{c}} \cdot f=\frac{1}{2 L} \sqrt{\frac{Y l}{L \rho}} \)
D \( f=\frac{1}{2 L} \sqrt{\frac{L \rho}{Y l}} \)


When an additional charge of \( 2 C \) is given to a capacitor, energy stored in it is increased by \( 21 \% \). The original charge of the capacitor is :
A . \( 30 \mathrm{c} \)
B. \( 40 \mathrm{c} \)
c. \( 10 c \)
D. \( 20 \mathrm{c} \)


Which of the following statements is true for a p-n-p transistor when used in an amplifier circuit?
A. Emitter is connected to negative terminal of a battery
B. Base current is always lower than emitter current
c. collector is connected to positive terminal of a battery
D. collector current is always more than the emitter current


Arrange the following species in the correct order of their stability.
\( \boldsymbol{C}_{2}, \boldsymbol{L} \boldsymbol{i}_{2}, \boldsymbol{O}_{2}^{+}, \boldsymbol{H} \boldsymbol{e}_{2}^{+} \)
A \( \cdot L i_{2}<H e_{2}^{+}<O_{2}^{+}<C_{2} \)
B. \( C_{2}<O_{2}^{+}<L i_{2}<H e_{2}^{+} \)
\( \mathbf{c} \cdot H e_{2}^{+}<L i_{2}<C_{2}<O_{2}^{+} \)
D. \( O_{2}^{+}<C_{2}<L i_{2}<H e_{2}^{+} \)
E \( \cdot C_{2}<L i_{2}<H e_{2}^{+}<O_{2}^{+} \)


The IUPAC name of the following
compound is :
A. 3 - Ethyl -2 - methylbut - 3 - ene
B. 2- Ethyl-3 - methyl but-1- -ene
c. 2 - Methyl- - - ethylbut- 3 - ene
D. 3- Methyl- 2 - ethylbut-1-ene


When 0.01 mole of a cobalt complex is treated with excess silver nitrate
solution, 4.305 g silver chloride is precipitated. The formula of the complex is:
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
В . \( \left[C o\left(N H_{3}\right)_{6} C l_{3}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] C l_{2} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] N O_{3} \)


Which substance when used with
butter having butyric acid can cure
acidity?
A . lime water
B. Soda water
c. calcium carbonate
D. lime juice


Find the solution of
\( (3 x+4 y-5)^{2} \frac{d y}{d x}=a^{2} \)
A \( \quad 4 y+\lambda=\frac{2 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
B. \( 2 y+\lambda=\frac{5 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
c. \( \quad 2 y+\lambda=\frac{2 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
D. \( 4 y+\lambda=\frac{5 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)


Q Type your question-
account for this effect we define a
quantity called the Van't Hoff factor
given by :
\[
\boldsymbol{i}=
\]
Actual number of particles in solution Number of formula units initiall
\( i=1 \) (for non-electrolytes)
\( i>1 \) (for non-electrolytes, undergoing dissociation) \( i<1 \) (for solutes, undergoing dissociation)

Answer the following questions:
A solution of benzoic acid is dissolved
in benzene such that it undergoes
molecular association and its molar
mass approaches 244. The benzoic molecules will exist as:
A . Dimer
B. Monomer
C. Tetramer
D. Trimer


What is the total number of p electrons in a single phosphorus atom in its ground state?
\( A \cdot 3 \)
B. 5
\( c .9 \)
D. 15


The cut flowers and vegetables can be kept fresh a long period by this plant hormone
A . Gibberellins
B. Cytokinins
c. Auxins
D. Ethylene
E. 2,4 - dichlorophenoxy acetic acid


Give reasons for the following:
(i) \( Z n^{+2} \) salts are while but \( C u^{2+} \) salts
are blue in colour.
(ii) Fluorine gives only one oxide but chlorine gives a series of oxides.


In a metallic conductor, electric current
is thought to be due to the movement of
A . ions
B. amperes
c. electrons
D. protons


A square loop of side a is rotating about
its diagonal with angular velocity \( \omega \) in
perpendicular magnetic field \( \overline{\boldsymbol{B}}, \) figure It has 10 turns. The e.m.f. induced is?
A. \( B a^{2} \) sinwt
B. \( B a^{2} \)coswt
D. \( 10 B a^{2} \omega \) sinw


In which of the following equilibrium,
\( \boldsymbol{K}_{c} \) and \( \boldsymbol{K}_{\boldsymbol{p}} \) are not equal?
\( \mathbf{A} \cdot 2 C(s)+O_{2}(g) \rightleftharpoons 2 C O(g) \)
B \( \cdot 2 N O(g) \rightleftharpoons N_{2}(g)+O_{2}(g) \)
\( \mathbf{c} \cdot \operatorname{SO}_{2}(g)+N O_{2}(g) \rightleftharpoons S O_{3}(g)+N O(g) \)
D \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)


Show that the relation \( R \) on the \( \operatorname{set} A= \)
\( \{x \in Z ; 0 \leq x \leq 12\}, \) given by \( R= \)
\( \{(a, b): a=b\}, \) is an equivalence
relation.


What are the suitable reagent for
following conversion
\( \mathbf{A} \cdot B r_{2} / F e B r_{3}, K M n O_{4}, H N O_{3} / H_{2} S O_{4} \)
B. \( K M n O_{4}, B r_{2} / F e B r_{3}, H N O_{3} \)
\( \mathbf{c} \cdot H N O_{3}, B r_{2} / F e B r_{3}, K M n O_{4} \)
D. \( H N O_{3}, K M n O_{4}, B r_{2} / F e B r_{3} \)


Light in certain cases may be considered as a stream of particles called photons. Each photon has a linear nomentum \( \frac{h}{\lambda} . \) where \( h \) is the Planck's
constant and \( \lambda \) is the wavelength of the
light.A beam of light of wavelength \( \lambda \) is incident on a plane mirror at an angle of incidence \( \theta \). Calculate the change in
linear momentum of photon as the beam is reflected by the mirror


A copper rod of radius \( 1 \mathrm{cm} \) and length 2
\( \mathrm{cm} \) is drawn into a wire of length \( 18 \mathrm{m} \) of
uniform thickness. Find the thickness
of the wire.


A taxon having cytoplasm, DNA, RNA but no cell wall is
A. Virus
B. Bacterium
c. Mycoplasma
D. cyanobacterium


In the five digit number \( 1 b 6 a 3, \) a is the
greatest single digit perfect cube and twice of it exceeds by \( 7 . \) Then the sum of the number and its cube root is
\( \mathbf{A} \cdot 18700 \)
B. 11862
c. 19710
D. 25320


What type of indicator is phenolphthalein?
A . Acidic
B. Basic
c. Equilibrium (titration)
D. Neutral


\( \int^{-1}(f(x))=x \)


Find the values of \( \cos \theta \) and \( \tan \theta, \) given \( \sin \theta=\frac{8}{17} \) and \( \theta \) is in quadrant 1


\( A B=D C=8 c m, A D=4 c m \) what
should be the length of side \( B C \), if
\( A B C D \) is parallelogram
A. \( 4 c m \)
B. 8 cm
\( \mathbf{c} \cdot 16 c m \)
D. None of the above


Arrange the following compounds in increasing order of boiling point.
\( \begin{array}{ll}\text { Propan-1-ol } & \text { Butan-1-ol } \\ \text { I } & \text { II } \\ \text { Butan-2-ol } & \text { Pentan-1-ol } \\ \text { III } & \text { IV }\end{array} \)
A. \( I<I I I<I I<I V \)
В. \( I I<I I I<I V<I \)
c. \( I I<I V<I I I<V I \)
D. \( I I I<I<I I<I V \)


Which of the following is not an actinoid?
A. Curium (Z = 96)
B. Californium (Z = 98)
c. Uranium ( \( z=92 \) )
D. Terbium (Z = 65)


Write down the Lewis formula or
electron dot formula of the following
compounds.
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4} \)


A radar unit is used to measure speeds
of cars on a motorway. The speeds are normally distributed with a mean of 9
\( \mathrm{km} / \mathrm{hr} \) and a standard deviation of 10
km/hr. What is the probability that a car picked at random is travelling at
more than \( 100 \mathrm{km} / \mathrm{hr} ? \)
A .0 .1698
B. 0.1548
c. 0.1587
D. 0.1236


Two coils of self inductances \( 2 \mathrm{mH} \) and
\( 8 \mathrm{mH} \) are placed so close together that the effective flux in one coil is
completely linked with the other. The mutual inductance between these coils is:
\( A \cdot 10 \mathrm{mH} \)
B. \( 6 \mathrm{mH} \)
\( c \cdot 4 m H \)
D. 16 mH


Which of the following
regarding oscillatory motion is true?
A. Motion of the earth is periodic but not oscillatory because it is not to and fro.
B. Quivering of the string of the musical instrument is an example of oscillatory motion
C. Motion of the earth is periodic and oscillatory motion because it is not to and fro.
D. None of the above


First step in respiration is
A. Aerobic oxidation of pyruvic acid
B. Liberation of \( C O_{2} \)
C . Glycolysis
D. Electron transport system


Let \( A_{n} \) be the area enclosed by the \( n^{t h} \) orbit in a hydrogen atom. The graph of
\( \ln \left(A_{n} / A_{l}\right) \) against \( \ln (n) \)
This question has multiple correct options
A. Will pass through origin
B. Will be a straight line with slope 4
c. will be monotonically increasing nonlinear curve
D. will be circle


Integrate:
\( \int_{0}^{\pi} \frac{d x}{5+3 \cos x} \)


In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. \( \cos \theta=\frac{7}{25} \)


If \( A B=A \) and \( B A=B, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A^{2} B=A^{2} \)
B. \( B^{2} A=B^{2} \)
c. \( A B A=A \)
D. \( B A B=B \)


Humus in soil is necessary for plant
growth because it
A. Increases aeration and water absorption capacity of soil
B. Makes soil compact
C. Makes soil sterile
D. Decreases rate of percolation


Find the degree of the given polynomials. \( m^{3} n^{7}-3 m^{5} n+m n \)


An organic compound of molecular formula \( C_{4} H_{6},(A), \) forms precipitates with ammoniacal silver nitrate and
ammoniacal cuprous chloride.'A' has an isomer'B', one mol of which reacts
with one mol of \( B r_{2} \) to form 1.4 -dibromo-
2-butene. Another isomer of A is 'C', one
mole of \( C \) reacts with only 1 mol. of \( B r_{2} \) to give vicinal dibromide. A,B \& C are
\( A \)
сн \( _{3}- \) сн \( _{2}- \) с \( \equiv c \) н \( _{3} \) апа сн \( _{2}= \) сн \( - \) сн \( = \) си \( _{i} \)
B. \( C H_{3}-C \equiv C-C H_{3} \) and \( C H_{3}-C H=C= \)
\[
C H_{2} ; C H_{3}-C \equiv C-C H_{3}
\]
\( c \)
\[
\left.\left.\right|_{\mathrm{cH}_{2}} ^{\mathrm{cH}_{2}}\right\rangle\left._{\mathrm{c}=\mathrm{cH}_{2} \text { and }}\right|_{\mathrm{cH}_{2}-\mathrm{cH}} ^{\mathrm{cH}_{2}-\mathrm{cH}} ; \mathrm{cH}_{2}=\mathrm{cH}-\mathrm{cH}=\mathrm{cH}_{2}
\]
\( D \)


Arteries of mummies were found to be
well preserved due to
A. Reticular fibres
B. Collagen fibres
c. Elastin fibres
D. Myofibrils


Species formed in experiment (B) is :
A. complex
B. double salt
c. liquid crystal
D. none of these


To observe diffraction, the size of the
obstacle
A. should be \( \lambda / 2 \), where \( \lambda \) is the wavelength.
B. should be of the order of wavelength.
C. has no relation to wavelength.
D. should be much larger than the wavelength.


Ratio of radii of \( \mathrm{K}, \mathrm{L}, \mathrm{M} \) shells of hydrogen atom is :
A. 1: 2: 3
B . \( 1: \frac{1}{4}: \frac{1}{9} \)
c. 1: 4: 9
D. \( 1: \frac{1}{2}: \frac{1}{3} \)


If \( f(x) \) and \( g(x) \) are differentiable
functions for \( 0 \leq x \leq 1 \) such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{6}, \boldsymbol{g}(\mathbf{1})=\mathbf{2} \)
then in the interval \( (\mathbf{0}, \mathbf{1}) \)
\( \mathbf{A} \cdot f^{\prime}(x)=0 \) for all \( x \)
B . \( f^{\prime}(x)=2 g^{\prime}(x) \) for at least one \( x \)
\( \mathbf{C} \cdot f^{\prime}(x)=2 g^{\prime}(x) \) for at most one \( x \)
D. None of these


The height of a parallelogram of area \( 350 c m^{2} \) and base \( 25 \mathrm{cm} \) is
\( A \cdot 12 \mathrm{cm} \)
B. \( 13 \mathrm{cm} \)
c. \( 14 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


In terms of potential difference \( V \)
electric current I, permittivity \( \varepsilon_{0} \)
permeability \( \mu_{0} \) and speed of light \( c, \) the dimensionally correct equation(s) is(are).
This question has multiple correct options
A \( \cdot \mu_{0} I^{2}=\varepsilon_{0} V^{2} \)
В \( \cdot \varepsilon_{0} I=\mu_{0} V \)
c. \( I=\varepsilon_{0} c V \)
D. \( \mu_{0} c l=\varepsilon_{0} V \)


\( y=\tan ^{-1}\left(\frac{1}{x}\right) \) find \( \frac{d y}{d x} \)


Bacteria multiply at a rate proportional to the number present. If the original number \( N \) double in 3 hours, the
number of the bacteria will be \( 4 N \) is (in
hours)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c .5 \)
D.


The total number of electrons present in all the s orbitals, all the p orbitals and all the d orbitals of caesium ion are
respectively:
A. 6,26,10
B. 10,24,20
c. 8,22,24
D. 12, 20, 23


Assume that a shperical randrop evaporates at a rate proportional to its a surface area. if it's radius is originally 3 \( \mathrm{mm}, \) and \( 1 \mathrm{minute} \) later has been
reduced to \( 2 \mathrm{mm} \). Find an expression for the radius of the raindrop at any
time.


If in the expansion of \( (1+x)^{n}, \) the
coefficients of three consecutive terms
are \( 56,70,56, \) then the value of \( n \) and
the position of the terms of these coefficients are given by
A \( \cdot n=8, \) the terms are \( 4^{t h}, 5^{t h}, 6^{t h} \)
B . \( n=7 \), the terms are \( 3^{r d}, 4^{t h}, 5^{t h} \)
C \( \cdot n=8 \), the terms are \( 5^{t h}, 6^{t h}, 7^{t h} \)
D. \( n=7 \), the terms are \( 4^{t h}, 5^{t h}, 6^{t h} \)


The phenomenon of electromagnetic
Induction is :
A. The process of charging a sphere
B. The process of producing magnetic field in a coil
C. The process of producing induced current in a coil whenever there is a relative motion between the coil
and the magnet
D. The process of producing cooling effect


If the position vector \( \vec{a} \) of the point \( (5, n) \) is such that \( |\vec{a}|=13 \), then the
value/values of \( n \) be
\( \mathbf{A} \cdot \pm 8 \)
B. ±12
c. 8 only
D. 12 only


Which of the following compound is
most acidic?
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
c. \( C H \equiv C H \)
D. \( C_{2} H_{5} O H \)


The low solubility of LiF and that of Cs|
in water are respectively due to which of the properties of the alkali metal ions?
A. Higher hydration enthalpy of \( L i^{+} \), higher lattice enthalpy of \( C s^{+} \)
B. Smaller hydration enthalpy of \( L i^{+} \), higher lattice enthalpy of \( C s^{\text {t }} \)
C. smaller lattice enthalpy of \( L i^{+} \), higher hydration enthalpy of \( C s^{+} \)
D. Higher lattice enthalpy of \( L i^{+} \), Smaller hydration enthalpy of \( C s^{\text {t }} \)


The device which produces highly coherent sources is
A. Fresnel biprism
B. Young's double sitt
c. Laser
D. Lloyd's mirror


The cause of shining in diamond is This question has multiple correct options
A. scattering of light
B. refraction of light
c. total internal reflection of light
D. dispersion of light


Soap molecules have two parts - a polar and a non-polar. When soap is added to
water:
A. both parts dissolve in water
B. non-polar part dissolves in water
c. polar part dissolves in water
D. both parts remain undissolved in water and form hydrocarbon layer


Give the IUPAC name of
\( \boldsymbol{C l}_{2} \boldsymbol{C H C H}_{2} \boldsymbol{O H} \)


Which of the following catalyst is used in the conversion of water gas and
hydrogen into methyl alcohol?
\( \mathbf{A} \cdot M n O \)
B. Raney Ni
c. \( F e \)
D. \( Z n O-C r_{2} O_{3} \)


The product \( 864 \times n \) is a perfect cube.
What is the smallest possible value of
\( \boldsymbol{n}^{\prime} ? \)
A . 2
B.
\( c \cdot 4 \)
D. 3


The ratio between the sides of a room is
\( \mathbf{5}: \mathbf{3} . \) The \( \operatorname{cost} \) of white-washing the ceiling of the room at 50 P per square metre is Rs.270 and the cost of papering
the walls at 10 P per square metre is Rs.
48. The height of the room is


Observe the diagram and answer the
questions.
Give a suitable title for the above
diagram.


Let \( A \) be the matrix of order \( 3 \times 3 \) such
that \( |\boldsymbol{A}|=\mathbf{1}, \boldsymbol{B}=\mathbf{2} \boldsymbol{A}^{-1} \) and \( \boldsymbol{C}=\frac{(\boldsymbol{a} d \boldsymbol{j} \boldsymbol{A})}{\sqrt[3]{2}} \)
then the value of \( \left|A B^{2} . C^{3}\right| \) is [Note : \( |A| \) represent determinant value of matrix A.]


Which one of the following is an
environment related disorder with
correct main cause?
A. Black lung disease is found mainly in workers of stone quarries and crushers
B. Blue-baby disease is due to heavy use of nitrogeneous fertilizers.
C. Non-Hodgkin's Iymphoma is found mainly in worker involved in manufacture of neem-based pesticides.
D. Skin cancer occurs mainly in people exposed to benzene and methane.


How many stereoisomers of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}= \)
\( \boldsymbol{C H} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{2} \boldsymbol{C l} \) are
possible ?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Mark the incorrect statement by the
graph of the function \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \)
A. \( f(0)=0 \)
B. \( f(-4)=4 \)
c. \( f(4)=-4 \)
D. The domain of \( f(x) \) is all real numbers


The sum of \( n \) terms of the series \( 1^{2}- \)
\( \mathbf{2}^{2}+\mathbf{3}^{2}-\mathbf{4}^{2}+\mathbf{5}^{2}-\mathbf{6}^{2}+\ldots \) is
This question has multiple correct options
A \( \cdot \frac{-n(n+1)}{2} \) if \( n \) is ever
B. \( \frac{n(n+1)}{2} \) if \( n \) is od
c. \( -n(n+1) \) if \( n \) is even
D. \( \frac{n(n+1)(2 n+1)}{6} \) if \( n \) is odd


What were the reasons for late
discovery of noble gases?

This question has multiple correct options
A. Chemical inertness of lighter noble gases, \( i . e ., \) He, Ne and Ar.
B. rare abundance of comparatively reactive noble gases,
i.e., Kr, Xe and Rn.
C. They were not found in the nature very early, so could not be found.
D. None of the above


Isotopes of an element have:
A. identical chemical properties
B. slightly different physical properties
C . very different half-life
D. all of the above


The movement of Earth around its
axis is called
A. Rotation
B. Translation
c. Revolution
D. Oscillation


Cavendish Experiment to measure \( \boldsymbol{G} \)
uses the concept of
A. Torque
B. Force
c. Force-Torque Equilirium
D. None of these


An inorganic white crystalline compound A has a rock salt structure. A
on reaction with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and
\( M n O_{2}, \) evolves a pungent smelling, greenish - yellow gas B. Compound A gives white ppt. of \( \mathbf{C} \) with \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \)
solution. Compounds \( (A),(B) \) and \( (C) \) will be respectively;
A \( . \) NaCl \( , C l_{2}, \) AgCl
в. \( \operatorname{NaBr}, \operatorname{Br}_{2}, \) Na Вт
c. \( N a C l, C l_{2}, A g_{2} S O_{4} \)
D. \( N a_{z} C O_{3}, C O_{2}, A g_{2} C O_{3} \)


The presence or absence of hydroxyl
group on which carbon atom of sugar differentiates RNA and DNA ?
A . \( 1 s t \)
B. 2nd
\( c .3 r d \)
D. 4 th


Statements
(i) Some chalks are chairs
(ii) Some chairs are tables. Conclusions:
I. Some chalks are tables.
II. Some tables are chalks.
A. Only conclusion lis true
B. Only conclusion II is true
c. Both conclusions I and II are true
D. Neither conclusion I nor conclusion II is true


Which of the following statements is correct regarding rods and cones in the human eye?
A. Cones are sensitive to dim light.
B. Cones are sensitive to bright light.
c. Rods are sensitive to bright light and dim light.
D. Rods can sense colour.


Find the principal value of the following
\( \cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2} \)


State whether given statement is True or False

The majority charge carriers in \( p \) -type semiconductor are electrons.
A . True
B. False


A bag contains 6 red, 4 white and 8 blue balls. If three ball are drawn at random,
find the probability that:
(i) All the three balls are red.
(ii) All the three balls are blue.
\( A \)
(i) \( \frac{5}{204}, \) (ii) \( \frac{7}{102} \)
в.
(i) \( \frac{9}{204}, \) (ii) \( \frac{7}{102} \)
\( c \)
(i) \( \frac{7}{204}, \) (ii) \( \frac{5}{102} \)
D. None of these


Plastic sulphur is orthorhombic
polymorph of \( \boldsymbol{S}_{8} \) molecule
A. True
B. False


A hollow smooth uniform sphere \( \boldsymbol{A} \) of
mass \( m \) rolls without sliding on a
smooth horizontal surface. It collides
elastically and head-on with another
stationary smooth hollow sphere \( \boldsymbol{B} \) of
the same mass mm and same radius.
The ratio of the kinetic energy of \( \boldsymbol{B} \) to that of \( A \) just after the collision is
A . 1: 1
B. 2: 3
\( c \cdot 3: 2 \)
D. None


An organic compound contains \( 90 \% \) carbon and \( 10 \% \) hydrogen by mass. Its empirical formula is:
A. \( C_{2} H_{4} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{3} H_{4} \)


Two forces each of \( 10 \mathrm{N} \) act at an angle
\( 60^{0} \) with each other. The magnitude and direction of the resultant with respect
to one of the vectors is:
A \( \cdot \sqrt{10} \mathrm{N}, 30^{\circ} \)
B . \( 10 \sqrt{3} \mathrm{N}, 30^{\circ} \)
c. \( 20 \mathrm{N}, 120^{\circ} \)
D. \( 10 \sqrt{2} \mathrm{N}, 120^{\circ} \)


If \( g(x)=\frac{5 x-3}{2 x^{2}-11-6}, \) what is the
sum of all the real numbers that are not
in the domain of \( g(x) ? \)
A . -2
B. 0.5
\( c \cdot 2 \)
D. 5.5
E . 6.5


Choose the correct answers from the
alternatives given :
Which process involves chemiosmotic phosphorylation?
A. Krebs cycle
B. Glycolysis
c. Electron transport system
D. Fermentation


The compound which does not lead to
nitrile by substitution with \( N a C N / D M S O \) is:
A. Benzyl chloride
B. Ethyl chloride
c. Isopropyl chloride
D. Chlorobenzene
E. Isobutyl chloride


In Haber's process, the volume of
ammonia relative to the total volume of
reactants at STP is:
A. one fourth
B. one half
c. same
D. three fourth


mole of a gas with \( \gamma=7 / 5 \) is mixed
with 1 mole of a gas with \( \gamma=5 / 3 \) then
the value of \( \gamma \) for resulting mixture is
A . \( 7 / 5 \)
в. \( 2 / 5 \)
c. \( 24 / 16 \)
D. \( 12 / 7 \)


How is Soap industrially
manufactured?


We eat food, which is composed of all
the nutrients like carbohydrates, proteins, fats, vitamins, minerals and water. After digestion, these are absorbed in the form of glucose, amino acids, fatty acids, glycerol etc. What mechanisms are involved in absorption of digested food and water?
A. Diffusion and osmosis respectively
B. Osmosis and diffusion respectively
c. Reverse osmosis and facilitated diffusion respectively
D. None of the above


\( \int \frac{x^{4}}{(x+2)\left(x^{2}+1\right)} d x \)
How to change this improper function to
Rational function.


State whether given statement is True or False

The designation rms means repetitions measured per second.
A. True
B. False


Carnot cycle works with isentropic
compression ratio of 5 bar and isothermal ratio of 2. The volume of air
at beginning of the isothermal expansion is \( 0.3 m^{3} . \) If the temperature
and pressure is limited to \( 550 \mathrm{K} \) and 21 bar, Determine Minimum temperature in the cycle.


n fig., \( C M \) and \( R N \) are respectively
then medians of \( \triangle A B C \) and \( \triangle P Q R \)
prove that:
\( \triangle A M C \sim \triangle P N R \)


When Mg is burnt in air and they are
decomposed by \( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{M} \boldsymbol{g} \boldsymbol{O}, \boldsymbol{M} \boldsymbol{g}_{3} \boldsymbol{N}_{2} \)
changing to \( M g(O H)_{2} \) and \( N H_{3} \). If
true enter 1 , else enter 0


Anaerobic respiration occurs in human
body inside
A. Liver
B. Kidneys
c. Red muscles
D. White muscles


\( \lim _{x \rightarrow 0}\left[\frac{\sin x}{\tan (5 x)} \frac{(1-\cos 4 x)\left(5^{x}-4^{x}\right)}{x^{3}}\right] \)
equals to
A \( \cdot \frac{8}{3} \ell n\left[\frac{5}{2}\right. \)
в. \( \frac{8}{5} \ell n\left[\frac{5}{2}\right. \)
c. \( \frac{8}{5} \ln \left[\frac{5}{4}\right. \)
D. None of these


The IUPAC name of A and B are,
repectively:
A. Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)
B. Tetracyanopotassiumnickelate (II) teterachlorpotassiumnickelate (II)
C. Tetracyanornickel (II), tetrachloronickel (II)
D. Potassium tetracyanonickel (II), potassium tetrachloronickel (II)


Find the area of the shaded region


\( \mathrm{X} \) and \( \mathrm{Y} \) in the below reaction are
and \( _{-}-_{-}- \) respectively
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C O}_{2} \boldsymbol{H}+\boldsymbol{X} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{C}_{6} \boldsymbol{H}_{5}- \)
\( C O C l \frac{H_{2}, P d / B a S O_{4}}{Q u i n o l i n e}> \)
A. \( S O C l_{2} \) and \( C_{6} H_{5} C H O \)
B . \( (C O C l)_{2} \) and \( C_{6} H_{5} C H_{3} \)
c. \( \operatorname{SOCl}_{2} \) and \( C_{6} H_{5} C H_{3} \)
D. \( (C O C l)_{2} \) and \( C_{6} H_{5} C H_{2} O H \)
E \( . S O C l_{2} \) and \( C_{6} H_{5} C H_{2} C l \)


Write the IUPAC name of the following:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}=\boldsymbol{C H}-\stackrel{\mathbb{1}}{\boldsymbol{C}}-\boldsymbol{H} \)


Which one of the following statements
is correct?
A. Lactic acid is an antimicrobial
B. Seconal is an antipyreticc
c. chloroxylenol is a tranquilizer
D. sucralose is an antiseptic


If the focal distance of an end of the
minor axis of any ellipse (referred to its axes as the axes of \( x \) and \( y \)
respectively) is \( k \) and the distance between the foci is \( 2 h, \) then its equation
is:
A \( \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}+h^{2}}=1 \)
в. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}-k^{2}}=1 \)
c. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}-h^{2}}=1 \)
D. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}}=1 \)


Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (Atomic Numbers: \( C r=24 ; M n= \)
\( 25 ; F e=26 ; C o=27) \)
\( \mathbf{A} \cdot\left[F e(C N)_{6}\right]^{3-} \)
B . \( \left[\operatorname{Co}(C N)_{6}\right]^{3} \)
c. \( \left[\operatorname{Cr}(C N)_{6}\right]^{3-} \)
D. \( \left[M n(C N)_{6}\right]^{3} \)


The root mean square velocity of one mole of a monoatomic gas having molar
\( \operatorname{mass} M \) is \( U_{r m s} . \) The relation between
average kinetic energy \( (\boldsymbol{E}) \) of the gas
and \( U_{r m s} \) is :
\( ^{\mathrm{A}} \cdot U_{r m s}=\sqrt{\frac{3 E}{2 M}} \)
В. \( U_{r m s}=\sqrt{\frac{2 E}{3 M}} \)
c. \( \quad v_{r m s}=\sqrt{\frac{2 E}{M}} \)
D. \( U_{r m s}=\sqrt{\frac{E}{3 M}} \)


The radius of a circle is \( 13 \mathrm{cm} \) and the
length of one of its chords is \( 10 \mathrm{cm} \). The distance of the chord from the centre is
A. \( 8 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


The single-bonded metallic radius of sodium is 157 pm. Assume that the increment between radii of different
magnitudes is 60 pm. The ionic radius
\( N a^{+} \) in \( \mathrm{pm} \) is \( (90+x) . \) Find \( x \)


Find the derivative of \( y=\frac{2 x}{1-x^{2}} \)


What do you understand by the term Sonar?


Which of the following contains the least number of molecules?
\( A \cdot 52 g \) of \( N_{2} O_{5} \)
B. 36 g of \( H_{2} \) O
c. 28 g of \( c 0 \)
D. \( 51 \mathrm{g} \mathrm{NH}_{3} \)


The minimum and maximum distances
of a planet revolving around sun are \( r \) and \( R \) If the minimum speed of
planet on its trajectory is \( v_{0}, \) then its
maximum speed will be:
A \( \cdot \frac{v_{0} R}{r} \)
B. \( \frac{v_{0} r}{R} \)
c. \( \frac{v_{0} R^{2}}{r^{2}} \)
D. \( \frac{v_{0} r^{2}}{R^{2}} \)


The radius of a nucleus of an atom
\( (Z=50) \) is \( 9 \times 10^{-10} m \) then potential
on its surface, will be:
A . \( 80 V \)
B. \( 8 k V \)
\( \mathrm{c} .9 \mathrm{V} \)
D. \( 9 k V \)


Let \( A=\{1,2,3\} \) and \( R= \)
\{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3)
then the relation \( R \) and \( A \) is
A. reflexive
B. symmetric
c. transitive
D. equivalence


The number of turns in a coil of wire of
fixed radius is 600 and its self
inductance is 108 mH. The self
inductance of a coil of 500 turns will be
A. 74 mH
B. 75 mH
c. \( 76 \mathrm{mH} \)
D. 77 mH


If in \( \triangle A B C, A \equiv(1,10), \) circumcentre \( \equiv\left(-\frac{1}{3}, \frac{2}{3}\right) \) and orthocentre \( \equiv \)
\( \left(\frac{11}{3}, \frac{4}{3}\right), \) then the coordinates of midpoint of side opposite to \( A \) is
A \( \cdot\left(1,-\frac{11}{3}\right) \)
в. (1,5)
c. (1,-3)
D. (1,6)


Two long and parallel straight wires \( A \) and B are carrying currents of 4 A and 7 A in the same direction are separated by a distance of \( 5 \mathrm{cm} . \) The force acting
on an \( 8 \mathrm{cm} \) section of wire \( \mathrm{A} \) is:
A \( \cdot 3 \times 10^{-6} N \)
B . \( 6 \times 10^{-6} N \)
c. \( 9 \times 10^{-6} N \)
D. \( 12 \times 10^{-6} N \)


Let there be a function \( f(x) \) that is
greater than the cube of \( x \) when
subtracted to the fourth root of the sum
of 2 and square of 2 multiplied with \( x \) Then the function id depicted by
A \( \cdot f(x)<\sqrt[4]{2+4 x^{2}}-x^{3} \)
B . \( f(x)>\sqrt[4]{2+4 x^{2}}-x^{3} \)
C \( \cdot f(x) \geq \sqrt[4]{2+4 x^{2}}-x^{3} \)
D. \( f(x) \leq \sqrt[4]{2+2 x^{2}}-x^{3} \)


Compare the magnetic field produced by a solenoid with that of bar magnet by drawing respective diagrams.


Fructose 1: 6 biphosphate splits into two triose phosphates by enzyme
A. Aldolase
B. Amylase
c. zymase
D. Lipase


Which one of the following pairs
in mismatched-
A. Nuclear power radioactive wastes
B. Solar energy green house effect
C. Fossil fuel burning release of \( C O_{2} \)
D. Biomass burning release of \( C O_{2} \)


Explain aminoacylation of tRNA.


\( \mathbf{N O}_{2} \) can not be obtained by heating:
A. KNO
\( \mathrm{B} \cdot \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \)
c. \( \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} \)
D. \( \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2} \)


Which of the following statement is
correct?
A. First trimester abortions are riskier than the second
trimester.
B. Second trimester abortions are riskier than the first
trimester.
C. Abortions can be carried at any of the stages of pregnancy.
D. None of the above.


How will you prepare the following? Sodium sulphate from sodium chloride


The focal length of a concave lens is \( 2 m \) Then the power of the lens is:
A. 2 dioptre
B. - - dioptre
c. 0.5 dioptre
D. -0.5 dioptre


The following table represents the distance of a car at different instants in
a fixed direction.
Time
\[
1 \quad 2
\]
(s)
Distance \( \quad \) o \( \quad \) 10 \( \quad \) 20 \( \quad \) 30
\( (m) \)
Which of the following is/are true about
its displacement-time graph?
A. Graph will be a straight line inclined towards the time axis
B. Graph will be a straight line parallel to displacement axis
c. Graph will be a straight line parallel to time axis
D. Graph will be a parabolic curve


The oxidation number of phosphorus in
\( \boldsymbol{P O}_{4}^{3-}, \boldsymbol{P}_{4} \boldsymbol{O}_{10} \) and \( \boldsymbol{P}_{2} \boldsymbol{O}_{7}^{4-} \) is:
\( A \cdot+3 \)
\( B \cdot+2 \)
\( c \cdot-3 \)
\( D \cdot+5 \)


The correct statement for significance of mitosis is
A. Equal distribution of chromosomes
B. Restoration of surface-volume ratio
c. Maintenance of nucleoplasmic index
D. All of the above


How do you know the triangle is right
angled?
A. The triangle is right angled when the three sides of a triangle make \( a^{2}+b^{2}=c^{2} \)
B. The triangle is right angled when the three sides of a triangle do not make \( a^{2}+b^{2}=c^{2} \)
C. The triangle is not right angled when the three sides of a triangle make \( a^{2}+b^{2}=c^{2} \)
D. The three sides of a triangle are all same.


Cartesian equation of the plane \( \bar{r}= \) \( (1+\lambda-\mu) \bar{i}+(2-\lambda) \bar{j}+(3-2 \lambda+ \)
\( 2 \mu) \bar{k} \) is :
A \( .2 x+y=5 \)
в. \( 2 x-y=5 \)
c. \( 2 x+z=5 \)
D. \( 2 x-\mathrm{z}=5 \)


Statement \( (\mathrm{A}): C I_{2}+2 N a O H \rightarrow \)
\( N a C I+N a O C I+H_{2} O \) is a
disproportion reaction Statement \( (\mathrm{B}): \boldsymbol{A} \boldsymbol{g}_{(a q)}^{2+}+\boldsymbol{A} \boldsymbol{g}_{(g)} \rightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+} \) is comproportionation reaction Statement \( (\mathrm{C}): 2 \mathrm{Ca} \mathrm{CO}_{3} \stackrel{\Delta}{\longrightarrow} 2 \mathrm{CaO}+ \)
\( 2 C_{2} \) is a combination reaction.
A. All the statement are correct
B. All the statement are incorrect
C. \( A, B \) are correct and \( C \) is incorrect
D. \( A, B \) are incorrect and \( C \) is correct


Simplify:
\( (2 p+3 q+4 r)(9 p-r)+(p+q+r) \)


Ethylidene dichloride is obtained by the reaction of excess of HCl with.
A. Ethylene
B. Acetylene
c. Propane
D. Methane


An aqueous solution of ammonia contains:
A. ammonium ions
B. hydroxy ions
c. both A and B
D. \( H^{+} \) ions


\( \boldsymbol{B}=\boldsymbol{A}+\boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\boldsymbol{A}^{4} \)
If order of \( A \) is 3 then order of \( B \) is
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
D. 9


In a Daniel cell when \( C u \) and \( Z n \)
electrodes are connected current flows
from:
A. \( C u \) to \( Z n \) within the cell
B. \( C u \) to \( Z n \) outside the cell
c. \( Z n \) to \( C u \) outside the cell
D. all of the above


The area (in square units) of the region
bounded by \( \boldsymbol{x}=-\mathbf{1}, \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{1} \)
and \( y=2 x-2 \) is
A . 10
B. 7
\( c \cdot 8 \)
D.


A solid cylinder rolls down an inclined
plane. Its mass is \( 2 k g \) and radius \( 0.1 m \)
If the height of the inclined plane is \( 4 m \) its rotational kinetic energy, when it reaches the foot of the plane is:
A . \( 78.4 \mathrm{J} \)
B. \( 39.2 J \)
c. \( \frac{78.4}{3} \)
D. 19.6 \( J \)


The mean of ten items is 17 and if each
item is increased by 5 then the new mean will be
A . 22
B. 67
c. 17
D. 85


A wire in the shape of an equilateral
triangle encloses an area of \( s \mathrm{cm}^{2} \). If
the same wire is bent to form a circle,
then the area of the circle will be
A \( \cdot \frac{\pi s^{2}}{\pi} \)
B. \( \frac{3 s^{2}}{\pi} \)
\( c \cdot \frac{3 s}{\pi} \)
D. \( \frac{3 s \sqrt{3}}{\pi} \)


Assertion
Neutrons penetrate matter more readily
as compared to protons.
Reason
Neutrons are slightly more massive
than protons.
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


Let \( \bar{a} \) and \( \bar{b} \) be two unit vectors and let \( \theta \)
be angle between them then \( (\bar{a}+\bar{b})^{2}- \) \( (\bar{a}-\bar{b})^{2}= \)
A \( \cdot \cos \theta \)
B . \( 2 \cos \theta \)
\( c \cdot 3 \cos \theta \)
D. \( 4 \cos \theta \)


n-Butylbenzene on oxidation with hot
alkanine \( K M n O_{4} \) gives:
A. Benzoic acid
B. Butanoic acid
c. Benzyl alcohol
D. Benzaldehyde


Which is the main functional group in Acrolein?
A. Aldehyde
B. Alkene
c. Nitrile
D. Ester


The population of a town increases from 10000 to \( 10400 . \) The growth rate is
A . \( 4 \% \)
B. \( 40 \% \)
\( c .2 \% \)
D. \( 20 \% \)


Solve:
\[
x^{2}-21 x+108=0
\]


Consider the following metallurgical
processes.
(i) Heating impure metal with \( \mathrm{CO} \) and distilling the resulting volatile carbonyl (boiling point \( 43^{\circ} C \) ) and finally
decomposing at \( 150^{\circ} \mathrm{C} \) to \( 200^{\circ} \mathrm{C} \) to get
the pure metal
(ii) Heating the sulphide ore in air until a part is converted to oxide and then
further heating in the absence of air to let the oxide react with unchanged
sulphide.
(iii) Electrolysing the molten electrolyte containing approximately equal amounts of the metal chloride and
\( \mathrm{CaCl}_{2} \) to obtain the metal
The process used for obtaining sodium, nickel and copper are, respectively:
A. (i), (ii) and (iii)
B. (ii), (iii) and (i)
c. (iii), (i) and (ii)
D. (ii), (i) and (iii)


\( \boldsymbol{C H C H C l C H C l C H}_{3} \)


The probability that a student will pass
the final examination in both English and Hindi is 0.5 and the probability of passing neither is \( 0.1 . \) If the probability of passing the English examination is \( 0.75, \) what is the probability of passing the Hindi examination?


Fathom is the unit to measure the
A. speed of ship
B. depth of sea
c. distance of the ship
D. speed of cyclone


Which of the following is not a plant product?
A. Hemp
B. Silk
c. cotton
D. Flax


Formation of polyethylene from calcium carbide takes place is follows:
\( \boldsymbol{C a C}_{2}+\mathbf{2 H _ { 2 }} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow+\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}+\boldsymbol{n} \)
The amount of polyethylene obtained from \( 64.0 \mathrm{kg} \) of \( \mathrm{CaC}_{2} \) is:
\( A \cdot 27 \mathrm{kg} \)
в. \( 24 \mathrm{kg} \)
c. \( 22 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)


Find energy of photon of wavelength \( \mathbf{4 0 0 0} \stackrel{\boldsymbol{o}}{\boldsymbol{A}} \)


Thickness of the page on which your are writing is of the order.
A . \( 0.1 \mathrm{cm} \)
B. 0.1 micrometer
c. 0.1 angstrom
D. \( 0.1 \mathrm{mm} \)


A straight line drawn through the common focus \( \mathrm{S}^{\prime} \) of a number of conics
meets them in the points \( P_{1}, P_{2}, \ldots ; \) on
it is taken a point \( Q \) such that the reciprocal of \( \mathrm{SQ} \) is equal to the sum of
the reciprocals of \( S P_{1}, S P_{2}, \ldots \) Prove that the locus of \( Q \) is a conic section
whose focus is \( 0, \) and show that the reciprocal of its latus rectum is equal to
the sum of the reciprocals of the latera
recta of the given conics.


Simplify: \( \left(a^{2} b^{2} c^{3}-a^{2} b^{2} c^{3}+a^{2} b^{2} c^{3}\right) \div \)
\( a^{2} b^{2} c^{3} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \)
D. None of these


\( \boldsymbol{C H}_{3}-\boldsymbol{C H O} \stackrel{\boldsymbol{O H}^{-}}{\longrightarrow} \boldsymbol{A} \)
The IUPAC name of \( \boldsymbol{A} \) is:
A. aldol
B. prop-1-ene-2-ol
c. 4 -hydroxy- 4 -methyl 2 -pentanone
D. 3-Hydroxybutanal


Solve:
\( \lim _{x \rightarrow 2} \frac{x^{2}-4}{\sqrt{3 x-2}-\sqrt{x+2}} \)


Assertion
The heart wood is more durable and
resistant to the attack of the micro
organisms and insects as compared to
the sap wood.
Reason
The heart wood contains organic
compounds like oils, aromatic
substance, gums, resin, tannins and
phenol etc.
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.


Strong electrolytes are those which:
This question has multiple correct options
A. dissolve readily in water
B. conduct electricity in molten state
C. dissociate completely into ions at all concentrations
D. dissociate into ions at high dilution


A domestic electric circuit has a fuse of
5 A. What is the maximum number of
\( \mathbf{1 0 0} W(\mathbf{2 2 0} V) \) bulbs that can be safely used in the circuit?


When two atoms of chlorine combine to
form one molecule of chlorine gas, the energy of molecule:
B. Equal to that of sepatate atommonm
c. Lower than that of separate atoms
D. None of the above


when compound \( \mathbf{C} \) is treated with
\( \boldsymbol{B} \boldsymbol{r}_{2} / \boldsymbol{C} \boldsymbol{C l}_{4} \)
A. a meso dibromide is formed.
B. four stereo-isomers of dibromides are fromed.
C . racemic mixture of dibromides are formed.
D. a pair of enantiomers of dibromides in unequal amount is formed.


Young's modulus of rubber is \( 10^{4} \mathrm{N} / m^{2} \)
and area of cross-section is \( 2 \mathrm{cm}^{2} \). If
force of \( 2 \times 10^{5} \) dyne is applied along
its length, then its final length becomes.
A . \( 3 L \)
B. \( 4 L \)
\( c \cdot 2 L \)
D. None of these


Using identity \( (a+b)^{2}=\left(a^{2}+2 a b+\right. \)
\( b^{2} \) ) Evaluate
(i) \( (609)^{2}\left(\text { ii) }(725)^{2}\right. \)


A moving coil galvanometer has a coil of area \( A \) and number of turns \( N . A \)
magnetic field B is applied on it. The torque acting on it is given by \( \boldsymbol{\tau}=\boldsymbol{k} \boldsymbol{i} \)
where i is current through the coil. If moment of inertia of the coil is I about
the axis of rotation.
If the value of torsional constant if
current \( i_{0} \) produces angular deflection of \( \pi / 2 \) rad is \( C=\frac{x N B A i_{0}}{\pi} . \) Find \( x \)


Four students measure a time interval
that is known to be 1.734 s. The measurement recorded by each student is shown. Which measurement is the
most accurate?
A . 1 s
в. 1.7 s
c. 1.83 s
D. 1.604 s


A plank with a body of mass \( m \) placed
on it starts moving straight up
according to the law \( y=a(1-\cos \omega t) \)
where \( y \) is the displacement from the
initial position, \( \omega=11 \) rad/s. Find the
minimum amplitude of oscillation of the plank at which the body starts falling behind the plank.


Heavy water is used as:
A. drinking water
B. detergent
C. washing water
D. a moderator


Mohan bought a flat worth Rs.10,00,000. He sells it to Rajesh at a profit of \( 10 \% \). If after sometime Rajesh sells it back to Mohan at a \( 10 \% \) loss,
then the amount gain by Mohan is
A. Rs.1, 00,000
в. \( R s .10,00,000 \)
c. \( R s .11,00,000 \)
D. Rs.1,10,000


State whether given statement is True or False

Cooling of a cup of coffee is an example of thermal equilibrium.
A. True
B. False


\( \boldsymbol{I}=\int \sqrt[3]{\boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)


Two identical blocks of metal are at \( 20^{\circ} \)
C and \( 80^{\circ} \mathrm{C}, \) respectively. The specific
heat of the material of the two blocks
increases with temperature. Which of the following is true about the final
temperature \( \mathrm{T}_{f} \) when the two blocks are brought into contact (assuming that no
heat is to the surroundings??
\( \mathbf{A} \cdot \mathbf{T}_{f} \) will be \( 50^{\circ} \mathrm{C} \)
B. \( T_{f} \) will be more than \( 50^{\circ} \) C
\( \mathrm{C} \cdot \mathrm{T}_{f} \) will be less than \( 50^{\circ} \mathrm{C} \)
D. \( T_{f} \) can be either more than or less than \( 50^{\circ} \mathrm{C} \) depending on the precise variation of the specific heat with temperature.


If EAN of a central metal ion \( X^{+2} \) in a
complex is 34 . and atomic number of \( \boldsymbol{X} \)
is \( 28 . \) The number of monodentate
ligands present in complex are:
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D.


What is the compound \( A ? \)
A. Oxalic acid
B. Malonic acid
c. Succinic acid
D. Adipic acid


Two wires carrying equal current \( I \) in opposite directions are placed a distance \( a \) apart. The wires experience a force \( F \) due to the current. The wires are moved to a distance \( \frac{\boldsymbol{a}}{\mathbf{2}} \) If the current in wire one remains the
same, which of the following values of \( \boldsymbol{I}_{2} \) would result in the same force \( \boldsymbol{F} \)
between the wires?
A \( \cdot \frac{1}{4} I \)
B \( \cdot \frac{1}{2} I \)
c. \( I \)
D. 2I
E . \( 4 I \)


A uniform solid cylinder of mass \( 2 k g \)
and radius \( 0.2 m \) is released from the
rest at the top of a semicircular track of
radius \( 0.7 m \) cut in block of mass \( M= \)
\( 3 k g \) as shown. The block is resting on a
smooth horizontal surface and the
cylinder rolls down without slipping. The
distance moved by the block when the cylinder reaches the bottom of the track is:
\( \mathbf{A} \cdot 0.3 m \)
B. \( 0.5 m \)
c. \( 0.7 m \)
D. \( 0.2 m \)


Describe the characteristics of salivary
glands and gastric glands.


Determine \( n \) if \( ^{2 n} C_{3}:^{n} C_{3}=12: 1 \)


If one angle of a linear pair is acute, then its other angle will be
A. obtuse angle
B. Acute angle
c. Right angle
D. None of these


The systematic nomenclature of the
following spiro compound is:
A. 2 -Methyl spiro [3.4] octane
B. 3-Methyl spiro [3.4] octane
C. 6 -Methyl spiro [3.4] octane
D. 7 -Methyl spiro [3.4] octane


Solve :
\( \int_{0}^{\pi} \sin ^{3} x d x \)


Which one of the following forms a colorless solution in aqueous medium?
A \( \cdot C r^{3} \)
в. \( T i^{3} \)
\( c \cdot S c^{3} \)
D. \( V^{3+} \)


Solve the following equation. \( \frac{2}{3} x=\frac{3}{8} x+\frac{7}{12} \)


Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one behind the other should have the same series??
\( \mathbf{A} \cdot 2 \times^{12} C_{6} \times(6 !)^{2} \)
B. 6! x 6!
c. \( 7 ! \times 7 ! \)
D. \( 2 \times 6 ! \)


Find the area of the region enclosed by
the curves \( \boldsymbol{y}=\sin \boldsymbol{\pi} \boldsymbol{x}, \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{x}, \boldsymbol{x}= \)
2


Convert the following ratios to
percentages.
3: 4


Which of the following act as a
stabilizer for the storage of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) ?
A . Alkal
B. Dust
c. urea
D. None of these


Find the values of \( a \) and \( b \) so that the
points \( (\boldsymbol{a}, \boldsymbol{b}, \mathbf{3}),(\mathbf{2}, \mathbf{0},-\mathbf{1}) \) and
(1,-1,-3) are collinear.


Basidiospores are characteristic of
A. Bread mould
B. Mushrooms
c. Aspergillus
D. Yeast


Which is represented by the electric current?
A. Charge per unit volume
B. Charge per unit time
c. charge per unit area
D. Both A.and B


"The sex of a newborn child is a matter
of chance and none of the parents may
be considered responsible for it." Justify this statement with the help of flow chart showing determination of sex of a newborn.


What is the smallest number of squares
that must be added so that the line \( A B \)
becomes a line of symmetry?
\( A \)
B. 2
\( c .5 \)
D.


What happens when Chlorine gas is passed through a hot concentrated
solution of \( N a O H ? \)


Oxidation state of chlorine in compound
\( C \) is:
A. -1
B. +4
\( c \cdot+3 \)
D. +5


The dimensions of energy per unit volumes are the same as those of :
A. work
B. Stress
c. Pressure
D. Modulus


One milligram of matter is converted into energy. The energy released will be
\( \mathbf{A} \cdot 9 \times 10^{6} J \)
B \( .9 \times 10^{8} J \)
c. \( 9 \times 10^{10} J \)
D. \( 9 \times 10^{12} J \)


We usually find matter in and
forms.


The ionization constant and degree of
dissociation of water at \( 25^{\circ} \mathrm{C} \), is:
A \( \cdot 1.8 \times 10^{-9}, 1.8 \times 10^{-16} \)
B . \( 1.8 \times 10^{-16}, 1.8 \times 10^{-9} \)
c. \( 1.8 \times 10^{-12}, 1.8 \times 10^{-14} \)
D. \( 1.8 \times 10^{-14}, 1.8 \times 10^{-12} \)


In a city, three daily newspapers \( A, B, C \) are published. \( 42 \% \) of the people in that city read \( A, 51 \% \) read \( B \) and \( 69 \% \) read \( C .30 \)
\( \% \) read \( A \) and \( B ; 28 \% \) read \( B \) and \( C ; 36 \% \)
read \( A \) and \( C ; 8 \% \) do not read any of the
three newspapers. The percentage of persons who read all the three papers is
A . \( 25 \% \) \%
B. 18\%
c. \( 20 \% \)
D. none of these


Drosophila with \( 2 A+X O \) are
A. Fertile female
B. Infertile female
c. sterile male
D. Intersexes


Relative lowering of vapour pressure is maximum for:
A. \( 0.1 \mathrm{m} \) urea
B. 0.1m Nacı
\( \mathbf{c} \cdot 0.1 m \quad M g C I_{2} \)
D. \( 0.1 m \quad A I_{2}\left(S O_{4}\right)_{3} \)


A good fuel has these qualities:
This question has multiple correct options
A. should have high calorific value
B. should be costly
C. should cause any pollution
D. should be easy to transport


Assertion
An object may fall with a constant
velocity.
Reason
This happens when acceleration of the
object is equal to acceleration due to
gravity
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant \( \boldsymbol{K}_{c} \)
is:
A \( \cdot \Delta G^{o}=R T I n K_{c} \)
в. \( -\Delta G^{o}=R T I n K_{c} \)
c. \( \Delta G=R T I n K_{c} \)
D. \( -\Delta G=R T I n K_{c} \)


Irregular reflection occurs due to:
A. failure of laws of reflection
B. irregularity in reflecting surface
C . irregular light
D. all of these


The value of \( X \) in \( F e(C O)_{2}(N O) x, \) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
D.


There is a number, the second digit of which is smaller than its first digit by 4 and if the number was divided by the
digits sum, the quotient would be \( 7 . \) Can you find the number?
A . 64
B. 46
c. 48
D. 33
E. 84


Write the chemical equation for saponification. Also give the limitations of soap.


Prove that \( 1+3+5+\ldots .+(2 n- \)
1) \( =n^{2} \)


Solve the system of equations \( \boldsymbol{\operatorname { R e }}\left(z^{2}\right)=\mathbf{0},|z|=\mathbf{2} \)


Calculate the uncertainly is the positive of dust particle with mass equal to Img.ln uncertainly in velocity is \( 5.5 \times \) \( \mathbf{1 0}^{-\mathbf{2 0}} \boldsymbol{m} / \boldsymbol{s} \)


Assertion: Two forces \( 7 \mathrm{N} \) and \( 5 \mathrm{N} \) are
acting at a point and their resultant can
be \( 3 N \)
Reason: If two vectors \( \vec{P} \) and \( \vec{Q} \) are
acting at a point their resultant can have a value between \( \vec{P}-\vec{Q} \) to \( \vec{P}+\vec{Q} \).
A. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
c. Assertion is true, but the Reason is false.
D. Assertion is false, but the Reason is true.


Two triangles are ........... if two angles and included side (common to both the
angles) are equal to two angles and included side (common to both angles) of the other triangle.
A. unequal
B. congruent
c. equilateral
D. none of these


Which of the following compounds will give acetic acid with \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} / \boldsymbol{H} \oplus / \boldsymbol{\Delta} ? \)
A \( \cdot C H_{3}-C H O \)
в. \( C H_{3}-C H=C H-C H_{3} \)
c. \( C H_{3}-C=C-C H_{3} \)
D. \( C H_{2} C H_{2} O H \)


A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of
turns were to be quadrupled and the wire radius halved, the electrical power
dissipated would be:
A. Halved
B. The same
c. Doubled
D. Quadrupled


Assertion
\( \mathbf{A} \)
p-njunction with reverse bias can be used as a photo-diode to measure light intensity.
Reason
In a reverse bias condition the current
is small but is more sensitive to
changes in incident light intensity.
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 correct


The marked price of a pair of jeans is
Rs.800. A customer pays \( R s .40 \) as tax for it. Find the rate of tax.


A body is moving up on inclined plane of angle \( \theta \) with an initial kinetic energy \( E \)
The coefficient of friction between the
plane and the body is \( \mu . \) The work done
against friction before the body comes
to rest is:
A \( \cdot \frac{E \cos \theta}{\mu \cos \theta+\sin \theta} \)
B. \( 2 \mu E \cos \theta \)
c. \( \frac{\mu E \cos \theta}{\mu \cos \theta-\sin \theta} \)
D. \( \frac{\mu E \cos \theta}{\mu \cos \theta+\sin \theta} \)


Describe the following.
(i) The role of cryolite in electrometallurgy of aluminium.
(ii) The role of carbon monoxide in the
refining of crude nickel.


Sulfur is used in vulcanisation of
rubbers.
A . True
B. False


Show the vectors \( \vec{A}=2 \hat{i}-3 \hat{j}-\hat{k} \) and \( \vec{B}=-6 \hat{i}+9 \hat{j}+3 \hat{k} \) are parallel.


As observed from the top of a \( 60 \mathrm{m} \) high lighthouse from the sea-level, the angles of depression of two ships are
\( 30^{\circ} \) and \( 45^{\circ} . \) If one ship is exactly behind the other on the same side of the
lighthouse. Find the distance between
the two ships.
A. \( 20 m \)
в. \( 46.5 \mathrm{m} \)
c. \( 54.9 m \)
D. \( 60.1 \mathrm{m} \)


Find the values of \( x \) if \( f(x)=\frac{x}{x^{2}+1} \) is
i) an increasing function
ii) a decreasing function


Assertion
In electrochemical cell, we can not use
KCl in the salt bridge if anodic or
cathodic compartment consists of \( \mathrm{Ag}^{+} \)
or \( P b^{2+} \) ion.
Reason
Salt bridge is employed to maintain the electrical neutrality and to minimize the liquid-liquid junction potential.
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 compound microscope has a magnification 30. The focal length of eyepiece is \( 5 \mathrm{cm} . \) Assuming that the final image is formed at least distance of distinct vision \( (25 \mathrm{cm}) \). Find the
magnification produced by objective.


The species which has its fifth ionisation potential equal to \( 340 \mathrm{V} \) is :
\( A \cdot B^{+} \)
B. \( C^{-} \)
\( c . \) в
D.


A small ball moves toward right with a velocity \( v \). It collides with the wall and
returns back and continues to and fro
motion. If the average speed for first to and fro motion of the ball is \( (2 / 3) v, \) find the coefficient of restitution of impact.


A steel ball moving with a velocity \( \bar{v} \) collides with an identical ball originally at rest. The velocity of the first ball after
the collision is :
A \( \cdot\left(-\frac{1}{2}\right) \bar{v} \)
в. \( -\bar{v} \)
c. \( \bar{v} \)
D. zero


Activity of a radioactive element is \( 10^{3} \) dps. Its half life is 1 sec. After 3 sec its
activity will be \( (d p s= \)
decay per second)
A. 1000 dps
B . 250 dps
\( c .125 \mathrm{dps} \)
D. None of these


Silica gel is utilised for the of the number of gases.
A. adsorption
B. absorption
c. desorption
D. all of the above


Two bodies A and B are said to be in
thermal equilibrium with each other, if
A. heat flows from A to B
B. heat flows from B to A
C. both the bodies lose equal amunts of heat to the atmosphere
D. heat does not flow from either A or B


Give the IUPAC name of the following compounds:
\( \boldsymbol{O H} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)


At an individual level, how can you help reduce air pollution?


To what depth must a rubber ball be taken in deep sea so that its volume is
decreased by \( 0.1 \% \) (Take density of sea water \( 10^{3} k g \quad m^{-3} \)
bulk modulus of rubber \( =9 \times \)
\( \mathbf{1 0}^{8} \mathbf{N m}^{-\mathbf{2}}, \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}} \mathbf{)} \)
\( A .9 m \)
в. 18 т
\( \mathrm{c} .90 \mathrm{m} \)
D. \( 180 m \)


Which of the following occurs when light is reflected from a smooth flat
glass surface, as shown above?
A. The light is somewhat intensified
B. The light is somewhat polarized
C. The light is focused
D. The velocity of the light is reduced
E. The color of the light is shifted toward the blue end of the spectrum.


What numerical value of \( x \) is required to balance the equation below?
\( 2 H_{2} S+x O_{2} \rightarrow 2 S O_{2}+2 H_{2} O \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


Body cavity lined by mesoderm is
A. Coelenteron
B. Blastocoel
c. coelom
D. Pseudocoel


To minimise parallax error, the observer
should place the object:
\( A \cdot \) as near to the scale of the ruler as possible and the eye must be directly above the scale
B. as far to the scale of the ruler as possible and the eye must be directly above the scale
C. as near to the scale of the ruler as possible and the eye must be to the right of the scale
D. as near to the scale of the ruler as possible and the eye must be to the left of the scale


For a cell terminal potential difference is 2.2 volt when circuit is open and
reduces to 1.8 volt when cell is
connected to an external resistance of 5
ohm. What is the internal resistance of
the cell?


Assertion
Element can form different compound.
Reason

Any substance that contains only one
kind of an atom is known as an element.
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


What is the minimum mass of
\( C a C O_{3}(s), \) below which it decomposes completely, required to established equilibrium in a 6.50 litre container for
the reaction:
\( \boldsymbol{C a C O}_{3}(s) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{0 . 0 0 5} \) mole / litre
A. \( 3.25 g \)
в. \( 24.6 g \)
c. \( 40.9 g \)
D. \( 8.0 g \)


Three water samples namely river water, untreated sewage water and secondary effluent discharged from a sewage treatment plant were subjected to BOD test. The samples were labelled
\( A, B \) and \( C ; \) but the laboratory attendant did not note which was which. The BOD
values of the three samples \( A, B \) and \( C \) were recorded as \( 20 m g / L, 8 m g / L \) and \( 400 m g / L, \) respectively. Which sample
of the water is most polluted? Can you assign the correct label to each assuming the river water is relatively clean?


Find the amplitude of \( 1+i \sqrt{3} \)


Volume of \( \boldsymbol{H}_{2} \) produced per minute in
the above reactor is :
A . 23.5
B. 71.8 L
c. 35.2 \( L \)
D. 47.3 L


Which of the following is produced during Krebs cycle?
A . Citric acid
B. Lactic acid
c. Acetyl coenzyme A
D. Acetic acid


If the supplement of an angle is three times its complement, find the angle.


The solubility curve of \( \mathrm{KNO}_{3} \) as a
function of temperature is given above
The amount of \( \mathrm{KNO}_{3} \) that will crystallize
when a saturated solution of \( \mathrm{KNO}_{3} \) in
\( 100 \mathrm{ml} \) of water is cooled from \( 90^{\circ} \mathrm{C} \) to
\( 30^{\circ} \mathrm{C}, \) is
\( A \cdot 16 g \)
B. 100 g
\( c \cdot 56 g \)
D. 160 g


Which of the following set of species do
not have planar structure?
A \( \cdot I_{3}^{-}, C H_{3}, C l O_{3}^{-}, S i F_{6}^{2}- \)
B . \( I_{3}^{+}, I C l_{4}^{-}, A l_{2} C l_{6} . T e C l_{4} \)
c. \( S C l_{2}^{-}, N_{2} O_{5}, S F_{4}, X e O F_{4} \)
D. \( I_{2} C l_{6}, X e F_{2}, B r F_{4}^{-}, X e F_{5}^{-} \)


Which is the smallest of the following fractions?
A \( \cdot \frac{4}{9} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{1}{4} \)


If \( A \) and \( B \) are mutually exclusive
events, then \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c.
D.


The top of a ladder 6 meters long is resting against a vertical wall.Suddenly the ladder begins to slide outwards. At the instant when the foot of the ladder is
4 meters from the wall, it is sliding away at the rate of \( 0.5 \mathrm{m} / \) sec. How fast
is the top sliding downward at this
moment?


Which one of the following statements in regard to the excretion by the human kidneys is correct?
A. Descending limb of loop of Henle is impermeable to water
B. Distal convoluted tubule is incapable of reabsorbing \( N a^{+} \) ions
c. Nearly 99 percent of the glomerular filtrate is reabsorbed by the rental tubules.
D. Ascending limb of loop of Henle is impermeable to electrolytes.


The sequence formed when every term of an arithmetic progression is multiplied or divided by a fixed number is
A. A geometric progression
B. An arithmetic progression
C. Not an arithmetic progression
D. A list of numbers with no pattern


What is self inductance of a coil when a
charge of current from 0 to 2 A in 0.05 second induces an emf of \( 40 \mathrm{V} \) in it?
A . \( 1 \mathrm{H} \)
B. 2H
\( c . \) зн
D. 44


The current in the resistance \( R \) as a
function of time.


The mutual inductance of a pair of coils, each of \( \mathrm{N} \) turn, be M henry. If a current of i ampere in one of the coils is brought to zero in \( t \) second, the emf induced per turn in the other coil, in volt will be
A \( \cdot \frac{M i}{t} \)
в. \( \frac{N M i}{t} \)
c. \( \frac{M N}{i t} \)
D. \( \frac{M^{i}}{N t} \)


If \( ^{15} C_{r}:^{15} C_{r-1}=11: 5 \) find \( r \)


\( x^{2}+(a+b+c) x+a b+b c \)


Find the degree measure of \( \frac{\pi}{8} \)


f \( x \) is a proper fraction, show that \( \frac{\boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}^{2}}-\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{1 - x}^{\mathbf{6}}}+\frac{\boldsymbol{x}^{\mathbf{5}}}{\mathbf{1 - x}^{\mathbf{1 0}}}-\dots \dots \)
\( \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{1}+\boldsymbol{x}^{\mathbf{6}}}+\frac{\boldsymbol{x}^{\mathbf{5}}}{\mathbf{1}+\boldsymbol{x}^{\mathbf{1 0}}}+\dots \)


Two radioactive sources \( A \) and \( B \)
initially contain equal number of radioactive. Source \( \boldsymbol{A} \) has a half-life of
1 hour and source \( B \) has a half-life of
2hours. the ratio of the rate of
disintegration of \( \boldsymbol{A} \) to that of \( \boldsymbol{B} \) is:
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


The roots of the equation \( \sqrt{3 x+1} \) \( \mathbf{1}=\sqrt{\boldsymbol{x}} \) are
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( 0, \)
D. None


Spherical Capacitorlt consists of two
concentric conducting spherical shells
of radii \( a \) and \( b(a<b) . \) The inner shell is
given a charge \( Q \) and outer shell is
given a charge \( Q . \) The potential
difference between the shells is given
by \( \boldsymbol{V}_{\boldsymbol{i}}-\boldsymbol{V}_{\mathbf{0}}=-\int_{\boldsymbol{b}}^{\boldsymbol{a}} \boldsymbol{E} \boldsymbol{d} \boldsymbol{r} \)
\( \Rightarrow V=-\int_{b}^{a} \frac{Q}{4 \pi \varepsilon_{o} r^{2}} d r \)
\( \Rightarrow V=\frac{Q(b-a)}{4 \pi \varepsilon_{o} a b} \)
\( \mathrm{Now}, C=\frac{Q}{V} \Rightarrow C=\frac{4 \pi \varepsilon_{o}}{(b-a)} \)


If all the amines are represented by the
formula \( \boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2}, \) the value of \( \mathrm{R} \) in all
the amines is:
A \( \cdot C_{3} H_{7} \)
в. \( C_{4} H_{9} \)
c. \( C_{5} H_{11}- \)
D. \( C_{2} H_{5} \)


From a circular card sheet of radius 14
\( \mathrm{cm}, \) two circles of radius \( 3.5 \mathrm{cm} \) and \( \mathrm{a} \) rectangle of length \( 3 \mathrm{cm} \) and breadth 1 \( \mathrm{cm} \) are removed.(as shown in the
adjoining figure). Find the area of the emaining sheet. \( \left(\text { Take } \pi=\frac{22}{7}\right) \)


Importance of ecosystem lies in
A . Cycling opmaterials
B. Flow of energy
c. Both A and B
D. None of the above


The slope of velocity-time graph for particle moving with uniform velocity is equal to
A . final velocity
B. initial velocity.
c. zero
D. none the above.


What are the advantage of classifying organisms?


Which weapons among the following, though, would produce far less radioactive fallout than current
designs, although they would release huge numbers of neutrons?
A. Pure fission weapons
B. Boosted fission weapons
c. Pure fusion weapons
D. None of the above


Which of the following species have maximum number of unpaired electrons?
\( A \cdot O_{2} \)
B. \( O_{2}^{\text {t }} \)
\( c \cdot O_{2} \)
D. \( O_{2}^{2} \)


A thin uniform square plate \( A B C D \) of
side \( a \) and mass \( m \) is suspended in a
vertical plane as shown in the figure.
\( A E \) and \( B F \) are two massless
inextensible strings. The line \( A B \) is
horizontal. The tension in \( A E \) just after
\( B F \) is cut will be
A \( \cdot \frac{2 m g}{5} \)
в. \( m g \)
c. \( \frac{2 m g}{7} \)
D. \( \frac{3 m g}{5} \)


Final volume of the system will be
nearly -
\( \mathbf{A} \cdot 6.2 m^{3} \)
B . \( 2.8 m^{3} \)
c. \( 4.5 m^{3} \)
D. \( 1.4 m^{3} \)


Which is a fat-soluble vitamin?
A. Vitamin A
B. Vitamin \( B_{6} \)
c. vitamin c
D. Vitamin \( B_{2} \)


Smoke is a colloidal solution of -
A. gas in solid
B. solid in gas.
c. gas in gas
D. solid in liquid


The heat of reaction for \( \boldsymbol{A}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{A} \boldsymbol{O} \)
is -50 kcal/mol and \( A O+\frac{1}{2} O_{2} \rightarrow A O_{2} \)
is 100 kcal/mol
The heat of reaction (in kcal/mol) for
\( \boldsymbol{A}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{A} \boldsymbol{O}_{2} \) will be:
A . -50
B. +50
c. +100
D. +150


If the atomic number of an element is
\( 58, \) it will be placed in the periodic table
in the:
A . III B gp and \( 6^{\text {th }} \) period
B. IV B gp and \( 6^{\text {th}} \) period
C. \( \mathrm{VB} \) gp and \( 7^{\operatorname{th}} \) period
D. None of the above


The wavelength and frequency of beam of light in water of refractive index \( 4 / 3 \) having wavelength 0.48 micron in air
are
A. \( 0.16 \times 10^{-6} m, 6.25 \times 10^{14} H z \)
В. \( 0.36 \times 10^{-6} m, 6.25 \times 10^{14} H z \)
c. \( 0.36 \times 10^{-6} m, 3.25 \times 10^{14} H z \)
D. \( 0.26 \times 10^{-6} m, 6.25 \times 10^{14} H z \)


Identify the equations involved in
bleaching action of \( \boldsymbol{S O}_{2} \)
A. \( S O_{2}+H_{2} O \rightarrow H_{2} S O_{3} \)
в. \( S O_{2}+O_{2} \rightarrow S O_{3} \)
c. \( S O_{2}+2 H_{2} O \rightarrow H_{2} S O_{4}+2[H] \)
D. \( S O_{3}+H_{2} O \rightarrow H_{2} S O_{4} \)


The drug used for treatment of typhoid
is:
A. Novalgin
B. Quinine
c. chloromycetin
D. Paracetamol


Two systems in mechanical equilibrium will have the same-?
A. Temperatures
B. Pressures
c. chemical potential
D. None of these


Guanine pairs with
A. Adenine
B. Cytosine
c. Thymine
D. None of the above


(a) Write an equation of the reaction of
chlorine with cold and dilute \( N a O H \)
solution.
(b) Explain the reducing nature of
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)


Which of the following represents
calcium chlorate?
A \( \cdot C a C l O_{2} \)
в. \( \operatorname{Ca}\left(C l O_{4}\right)_{2} \)
c. \( C a\left(C l O_{3}\right)_{2} \)
D. \( C a\left(C l O_{2}\right)_{2} \)


There are 45 students in a class and \( \frac{3}{5} \)
of them are boys. How many girls are there in the class?


The diagonals of a quadrilateral are 16 \( \mathrm{cm} \) and \( 13 \mathrm{cm} . \) If they intersect each other at right angles; find the area of the quadrilateral.


Solve the following:
\( 17-(-14) \)


At what moment when the
potentiometer is balanced
A. Current flows only in the primary circuit.
B. Current flows only in the secondary circuit
c. current flows in both primary and secondary circuits.
D. current doesnot flow in any circuit


State the first and second law of
electrolysis.


As oxygen is \( _{--}-_{-}- \) soluble in water
air dissolved in water contains a higher percentage of oxygen \( (30-35 \%) \) than ordinary air \( (21 \%) \)


Which one is not a step polymer?
A. Nylon-6,6
B. Nylon-6
c. Glyptal


The various bulbs and other electrical
appliances in a house are connected
A. In a complicated manner
B. In series
c. In parallel
D. Bulbs in series and others in parallel


Which one of the following statements
is/are correct?
This question has multiple correct options
A. Neutron was discovered by Chadwick.
B. Nuclear filsion was discovered by Hahn and Strassmann
C. Polonium was discovered by Madam Curie
D. Nuclear fusion was discovered by Fermi


The maximum of electrons in \( \mathrm{H} \) atom
that will emit maximum energy is :
\( A \cdot n_{3} \rightarrow n_{1} \)
в. \( n_{4} \rightarrow n_{3} \)
\( \mathrm{c} \cdot \mathrm{n}_{5} \rightarrow \mathrm{n}_{4} \)
\( \mathrm{D} \cdot \mathrm{n}_{6} \rightarrow \mathrm{n}_{5} \)