Which of the following statement is not
correct regarding cathode rays?
A. Cathode rays originate from the cathoge
B. charge and mass of the particles constituting cathode rays depends upon the nature of the gas
C. Charge and mass of the particles present does not depend the material of the cathode
D. The ratio charge/mass of the particles is much greater than that of anode rays.


The greatest value of \( |z+1| \) if \( |z+4| \leq \)
3 is
A . 4
B. 5
\( c \cdot 6 \)
D. None of these


In vacuum, heat is transferred by
A. conduction
B. convection
c. radiation
D. all the above three


Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.


The time, in which a force of \( 2 \mathrm{N} \) produces a change in momentum of \( 0.4 k g m s^{-1} \) in a body whose mass is 1
kg is:
A. \( 0.2 \mathrm{s} \)
B. 0.02 \( s \)
\( c .0 .5 \mathrm{s} \)
D. \( 0.05 \mathrm{s} \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}a \sin ^{2 n} x & \text { for } x \geq 0 \text { and } \\ b \cos ^{2 m} x-1 & \text { for } x<0 \text { and }\end{array}\right. \)
\( n \rightarrow \infty \)
\( m \rightarrow \infty \)
then -
A \( \cdot f\left(0^{-}\right) \neq f\left(0^{+}\right. \)
в. \( f\left(0^{+}\right) \neq f(0) \)
c. \( f\left(0^{-}\right)=f(0) \)
D. fis continuous at \( x=0 \)


Which one is an antibiotic?
A. Aspirin
B. Chloramphenicol
c. chloroquin
D. Madribon


Ranitidine is also called as:
A. zinetaç
B. Cimetidine
c. Pepsin
D. Histamine


Unpolarized light of intensity \( I \) is incident on a system of two polarizes, \( A \)
followed by \( B \). The intensity of emergent light is \( I / 2 . \) If a third polarizer \( C \) is placed between \( A \) and \( B \), the intensity
of emergent light is reduced to \( I / 3 . \) The
angle between the polarizers \( A \) and \( C \) is
\( \theta . \) Then
\( ^{\mathrm{A}} \cdot \cos \theta=\left(\frac{2}{3}\right)^{1 / 4} \)
в. \( \cos \theta=\left(\frac{1}{3}\right)^{1 / 4} \)
\( ^{\mathrm{c}} \cos \theta=\left(\frac{1}{3}\right)^{1 / 2} \)
Des \( \theta=\left(\frac{2}{3}\right)^{1 / 2} \)


Find the solution of
(i) \( 10 \cos ^{3} x-16 \cos x=3 \cos 2 x+3, \) in
the interval \( [-\boldsymbol{\pi}, \boldsymbol{\pi}] \)
\( (i i) 2(\cos x+\cos 2 x)+\sin 2 x(1+ \)
\( 2 \cos x)=2 \sin x \) in the interval \( [-\pi, \pi] \)


A dip circle is at right angle to the magnetic meridian. The apparent dip angle is
A. \( 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


For the strong electrolytes NaOH, NaCl
and \( B a C l_{2}, \) the molar ionic
conductances at infinite dilution are
\( 248 \times 10^{-4}, 126.5 \times 10^{-4} \) and \( 280.0 x \)
\( 10^{-4} \mathrm{s} m^{2} m o l^{-1}, \) respectively. Calculate \( \wedge_{m}^{0} \) for \( B a(O H)_{2} \)


Flourobenzene \( \left(C_{6} H_{5} F\right) \) can be
synthesised in the laboratory:
A. by heating phenol with \( H F \) and \( K F \)
B. from aniline by diazotisation followed by heating the diazonium salt with \( H B F_{4} \)
C. by direct fluorination of benzene with \( F_{2} \) gas
D. by reacting \( P h B r \) with \( N a F \) solution


A wire of length \( 1.0 \mathrm{m} \) and radius \( 10^{-3} \)
\( \mathrm{m} \) is carrying a heavy current and is assumed to radiate as a black body. At
equilibrium its temperature is \( 900 K \)
while that of the surrounding is \( 300 K \) The resistivity of the material of wire at \( 300 K \) is \( \pi^{2} \times 10^{-8} \Omega . m . \) Its
temperature coefficient of resistance is
\( 7.8 \times 10^{-3} /^{0} C . \) Then current in wire will
be (Assume resistivity is linear function of temp.)
\( A \cdot 12 A \)
B. 24 A
c. 36 A
D. 48 A


Find fringe width and number of
possible maxima on the screen \( \boldsymbol{E} \)
A. \( 1.1 m m, 8 \)
B. \( 1.1 m m, 9 \)
c. \( 0.8 m m, 8 \)
D. \( 0.9 m m, 9 \)


Dry \( N_{2} \) was passed successively
through a solution of solute \( A_{2} B \) in
water at \( 27^{\circ} C \) and then through pure
water. The loss in mass of solution was
\( 2.5 \mathrm{g} \) and that of pure water was \( 0.04 \mathrm{g} \) Find the degree of dissociation of salt
\( A_{2} B \) when solution of \( A_{2} B \) has same concentration as \( 1.86 \% \) (mass/vol)
solution of urea at \( 27^{\circ} C . \) Assume
molarity is equal to molality. Divide answer by 10 and write the nearest integer.


Select correct about \( \boldsymbol{A l}\left(\boldsymbol{B} \boldsymbol{H}_{4}\right)_{3} \)
A. all three tetrahydride borate form two hydrogen bridges
B. two \( B H_{4}^{\Theta} \) form 2 hydrogen bridges and one form one hydrogen bridge
\( \mathrm{C} \cdot \) one \( B H_{4}^{\Theta} \) form 2 hydrogen bridge and two form one hydrogen bridge
D. \( B \) form only \( 2 c-2 e \) bond


A thin converging lens is formed with
one surface convex and the other plane. Does the position of image depend on whether the convex surface or the plane surface faces the object?


If a charge \( q \) is placed at the centre of the line joining two equal charges \( Q \) such that the system is in equilibrium
then the value of \( q \) is :
A \( . Q / 2 \)
в. \( -Q / 2 \)
c. \( Q / 4 \)
D. \( -Q / 4 \)


Find the arithmetic mean of the series:
\( \mathbf{1}, \mathbf{3}, \mathbf{5} \dots \dots \dots \dots(\mathbf{2 n}-\mathbf{1}) \)
\( A \cdot n \)
B. \( 2 n \)
\( c \cdot \frac{n}{2} \)
D. \( n-1 \)


Construct the following angles using
set-squares: \( 150^{\circ} \)


If
A, B are supplementary angles then \( \cos ^{2} A+\sin ^{2} B= \)
A . 10
B.
\( c \cdot 2 \)
D.


Find the measure of interior angle. Also name the polygon.


A diet is to contain at least 80 units of
vitamin \( A \) and 100 units of minerals.
Two foods \( F_{1} \) and \( F_{2} \) are available. Food
\( F_{1} \operatorname{costs} \) Rs. 4 per unit food and \( F_{2} s \)
costs Rs.6 per unit. One unit of food \( \boldsymbol{F}_{1} \)
contains 3 units of vitamin \( A \) and 4
units of minerals. One unit of food \( \boldsymbol{F}_{2} \)
contains 6 units of vitamin \( A \) and 3
units of minerals. Formulate this as a
linear programming problem. Find the minimum cost for diet that consists of
mixture of these two foods and also
meets the mineral nutritional
requirements?


The IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C O O H} \) is:
A. but-2-ene-1-oic acid
B. but-1-ene-1-oic acid
c. but-2-ene-1-carboxylic acid
D. propene-1-carboxylic acid


The slope and the y-intercept of the given line, \( 2 x-3 y=7 \) are respectively
A \( \cdot \frac{3}{2}, \frac{-3}{7} \)
B. \( \frac{2}{3}, \frac{-7}{3} \)
\( c \cdot \frac{3}{2}, \frac{3}{7} \)
D. \( \frac{2}{3}, \frac{7}{3} \)


Dimensional methods provide three major advantages in verification, derivation and changing the system of units. Any empirical formula that is derived based on this method has to be
verified and proportionality constants
found by experimental means. The presence or absence of certain factors -
non dimensional constants or variables
cannot be identified by this method. So every dimensionally correct relation
cannot be taken as perfectly correct. The energy of an SHM is dependent on mass \( m \), frequency \( f \), and amplitude \( A \) of oscillation. The relation is
\( \mathbf{A} \cdot M f / A^{2} \)
B. \( M f A^{-2} \)
\( \mathbf{c} \cdot M f^{2} A^{-2} \)
\( \mathbf{D} \cdot M f^{2} A^{2} \)


Find: \( \int \frac{\left(x^{4}-x\right)^{4}}{x^{3}} d x \)


Chemical combination involves:
A. Combination of two atoms.
B. Combination of only same type of elements.
C. Combination of only same type of compounds
D. Combination of any two or more elements or compounds.


Write down de Broglie's relation and explain the terms therein.


In the following reaction:
\( \boldsymbol{C r}(\boldsymbol{O H})_{3}+(\boldsymbol{O H})^{-}+\boldsymbol{I O}_{3}^{-} \rightarrow \)
\( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{I}^{-} \)
A \( \cdot I O_{3}^{-} \) is oxidising agent
B. \( \operatorname{Cr}(O H)_{3} \) is oxidised
c. \( 6 e^{-} \) are being taken per \( I \) atom
D. All of the above are correct


\( \ln (46)^{13} \) unit digit is 6


If \( \overrightarrow{\boldsymbol{a}}=2 \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{3} \hat{\boldsymbol{i}}-\boldsymbol{4} \hat{\boldsymbol{j}}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}-\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}} \) then the projection
of \( \vec{a}+\vec{b} \) on \( \vec{c} \) is
A \( \cdot \frac{17}{3} \)
в.
\( c \cdot \frac{4}{3} \)
D. \( \frac{17}{\sqrt{43}} \)


\( \begin{array}{ccc}\boldsymbol{A} & \boldsymbol{B} & \boldsymbol{Q} \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
The truth table is given above for which of the following gates is correct
A. NAND gate
B. OR gate
c. AND gate
D. NOT gate


Two light waves are represented by \( \boldsymbol{y}_{1}=\mathbf{3} \sin \omega t \) and \( \boldsymbol{y}_{2}=\mathbf{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \)
The resultant amplitude due to interference will be
A \( \cdot \sqrt{21} \)
B. \( \sqrt{26} \)
c. \( \sqrt{37} \)
D. \( \sqrt{41} \)


Assertion
Physisorption of a gas adsorbed at low temperature may change into chemisorption at a high temperature.
Reason

Usually low pressure is also favourable
for chemisorption.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Consider a capacitor-charging circuit.
Let \( Q_{1} \) be the charge given to the capacitor in a time interval of \( 10 m s \)
and \( Q_{2} \) be the charge given in the next time interval of 10 ms. Let \( 10 \mu C \) charge be deposited in a time interval \( t_{1} \) and
the next \( 10 \mu C \) charge is deposited in
the next time interval \( t_{2} \)
A. \( Q_{1}>Q_{2}, t_{1}>t_{2} \)
в. \( Q_{1}>Q_{2}, t_{1}<t_{2} \)
c. \( Q_{1}<Q_{2}, t_{1}>t_{2} \)
D. \( Q_{1}<Q_{2}, t_{1}<t_{2} \)


A body A of mass M falling vertically downwards under gravity breaks into two part; a body \( B \) of mass \( \frac{M}{3} \) and \( a \) body \( C \) of mass \( \frac{2}{3} \) M. The COM of bodies B and \( C \) taken together shifts compared to that of body A towards:
A. depends on height of breaking
B. does not shift.
\( c . \) body c.
D. body B


In a two step pulley arrangement meant
for a load \( \mathrm{W} \), the ratio between force \( \mathrm{P} \)
and \( W \) in equilibrium position, when
radii of pulleys are \( r_{1} \) and \( r_{2} \)
A \( \cdot \frac{r_{2}}{r_{1}-r_{2}} \)
B. \( \frac{r_{1}-r_{2}}{r_{2}} \)
c. \( \frac{r_{1}}{r_{2}-r_{1}} \)
D. \( \frac{r_{2}-r_{1}}{r_{1}} \)


Which of the following is/are pyrimidine derivatives?
1.Cytosine 2. Adenine 3. Uracil 4. Thymine
A. 1 and 4 only
B. 2 and 3 only
c. 1 and 3 only
D. 1, 3 and 4 only


A path \( 2 m \) wide surrounds a circular
pond of diameter \( 40 m \). How many cubic
metres of gravel are required to grave the path to a depth of \( 20 \mathrm{cm} \) ?


Derived units can be defined in terms of
one or two of all the fundamental units
in them.
A. True
B. False


Choose the pair of complementary angles.
A \( \cdot 30^{\circ}, 150^{\circ} \)
B. \( 76^{\circ}, 14^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 65^{\circ} \)
D. \( 120^{\circ}, 30^{\circ} \)


For a bowling ball, how far apart are the
center of gravity and center of mass?
A. They are at almost exactly the same location.
B. They are at opposite sides of the object.
C. They are both at the surface of the object.
D. They mean the same thing, so they're at the same location, as always.
E. None of the other answers is correct.


The given figure shows a parallelogram
\( A B C D \) with area \( 324 s q . c m . P \) is a
point in \( A B \) such that \( A P: P B=1: 2 \)
Find:the ratio \( O P: O D \)
4: 3
в. 2:
\( c \cdot 1: 4 \)
D. 4: 3


\( 1.35 \mathrm{gm} X \) element is completely converted to 1.88 gm compound \( X O \)
What is the atomic weight of \( X ? \)
A . 20.32
B. 40.64
c. 16.25
D. 56.10


The oscillator frequency of a cyclotron is 10 MHz what should be the operating magnetic field accelerating proton?
A . 0.156 न
B. 0.256 T
c. 0.356 न
D. 0.656 T


In the diagram shown
A \( \cdot \mu^{1}=\mu \)
B . \( \mu^{1}<\mu \)
c. \( \mu^{1}>\mu \)
\( \mathbf{D} \cdot \mu^{1} \geq \mu \)


Cicer arietinum is
A. Bengal Gram
B. Black Gram
C. Green Gram
D. Dew Gram


\( _{11} N a^{22} \) and \( _{10} N e^{22} \) are
A. Isotopes
B. Isomers
c. Isotones
D. Isobars


The formula unit mass of \( C a_{3}\left(P O_{4}\right)_{2} \) is
A . 360
в. 240
c. 118
D. 310


The attempt for classifying elements by plotting the atomic masses of elements against the atomic volumes was made
by:
A. Dobereiner
B. Newlands
c. Lother Meyer
D. Mendeleev


\( \mathbf{3} C_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{P} \boldsymbol{C l}_{3} \rightarrow \mathbf{3} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}+\boldsymbol{X} \)
Where \( X \) is an oxyacid of phosphorus.
\( \boldsymbol{X} \) is:
A \( . H_{3} P O_{4} \)
в. \( H_{3} P O_{3} \)
c. \( H_{3} P O_{2} \)
D. \( H P O \)


A truck of mass \( 500 k g \) moves from the
rest at the top of a section of track
\( 400 m \) long and \( 30 m \) high, as shown. The
frictional force acting on the truck is
\( 250 N \) throughout its journey.

What is the final speed of the truck?
A \( \cdot 14 \mathrm{ms}^{-1} \)
В \( \cdot 24 m s^{-1} \)
\( \mathrm{c} \cdot 31 \mathrm{ms}^{-1} \)
D. \( 190 \mathrm{ms}^{-1} \)


A thin rod of negligible mass and crosssectional area \( 4 \times 10^{-6} m^{2}, \) suspended
vertically from one end, has a length of
\( 0.5 \mathrm{m} \) at \( 100^{\circ} \mathrm{C} . \) The rod is cooled to \( 0^{\circ} \mathrm{C} \)
Young's modulus \( =10^{11} \mathrm{Nm}^{-2} \)
coefficient of linear expansion \( =10^{-5} \mathrm{K} \)
-1 and \( g=10 m s^{-2} . \) The total energy
stored in the rod is :
A. 0.15
J 5.1 .1 .5
в. \( 0.2 \mathrm{J} \)
c. \( 0.3 J \)
D. \( 0.4 J \)


A fuse wire of radius \( 0.1 \mathrm{mm} \) melts when
a current in A of 10 A is passed through
it. Find the current at which a fuse wire
of \( 0.12 \mathrm{mm} \) will melt.


From the electronic configuration of the given elements \( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N}, \) which
one has the highest ionization potential?
\( \mathbf{A} \cdot M=[N e] 3 s^{2} 3 p^{2} \)
B . \( L=[N e] 3 s^{2} 3 p^{3} \)
C \( \cdot K=[N e] 3 s^{2} 3 p^{1} \)
D \cdot \( N=[A r] 3 d^{10}, 4 s^{2} 4 p^{3} \)


The molecular mass of organic acid was determined by the study of its barium salt \( 4.290 \mathrm{g} \) of salt was quantitatively converted to the free acid by the
reaction with \( 21.64 \mathrm{ml} \) of 0.477
\( M H_{2} S O_{4} . \) The barium salt was found to
have two moles of water of hydration per \( B a^{2+} \) ion and acid is monobasic. What
is the molecular weight of anhydrous acid?
A . 130
B . 142
\( c \cdot 100 \)
D. 110


Choose the correct answers from the
alternatives given :
The greatest contributor of electrons to
the electron transport system is
A. oxygen
B. transition reaction
c. glycolysis
D. Krebs cycle


Solve \( \lim _{x \rightarrow a} \frac{\sqrt{1+a x}-\sqrt{1-a x}}{x} \)


The equilibrium established when
\( H g C l_{2} \) is shaken with an excess of \( H g \)
is:
\( \mathbf{A} \cdot H g^{2+}+H g \rightleftharpoons 2 H g^{+} \)
B. \( H g^{2+}+H g_{(l)} \rightleftharpoons H g_{2}^{2+} \)
C. \( H g+2 H g^{2+} \rightleftharpoons H g^{2+}+2 H g^{+} \)
D. no equilibrium is established


In a certain shop, which stocks four types of caps, there are \( \frac{1}{3} \) as many red caps as blue and \( \frac{1}{2} \) as many green caps
as red caps. There are equal number of
green caps and yellow caps. If there are
42 blue caps, then what percent of the total caps in the shop are blue?
A. \( 70 \% \)
в. \( 28 \% \)
c. \( 60 \% \)
D. \( 14 \% \)


If \( x^{2}+\frac{1}{x^{2}}=A \) and \( x-\frac{1}{x}=B, \) then least value of \( \frac{\mathbf{A}}{B} \) is
A .2
B. \( \sqrt{2} \)
\( c \cdot-\sqrt{2} \)
D. \( 2 \sqrt{2} \)


Out of the rational numbers
\( \frac{5}{-11}, \frac{5}{-12}, \frac{5}{-17}, \) which is the greatest?
A \( \cdot \frac{-5}{11} \)
в. \( \frac{5}{-12} \)
\( c \cdot \frac{-5}{17} \)
D. Cannot be compared


Evaluate the following limit \( \lim _{x \rightarrow 0} \frac{(1+x)^{6}-1}{x} \)


Explain how the human ear works.


The osmotic pressure of equimolar
solutions of
a) \( A l_{2}\left(S O_{4}\right)_{3}, \) b) \( K C l \) and
c) sugar will be:
\( \mathbf{A} \cdot b>a>c \)
В . \( a>b>c \)
\( \mathbf{c} . c>b>a \)
\( \mathbf{D} \cdot b>c>a \)


Which of the following complex can not exhibit geometrical isomerism:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{2} C l N O_{2}\right] \)
B・ \( \quad\left[P t(g l y)_{2}\right] \)
\( \mathbf{c} \cdot\left[C u(e n)_{2}\right]^{+} \)
D. \( \left[P t\left(H_{2} O\right)\left(N H_{3}\right) B r C l\right. \)


Which of the following statement is/are
correct?
This question has multiple correct options
A. lonic compounds undergo ionization
B. All covalent compounds undergo ionization
C. Only polar covalent compounds undergo ionization
D. Ionic compounds undergo dissociation


A wheel of radius \( 10 \mathrm{cm} \) can rotate freely
about an axis passing through its centre. A force \( 20 N \) acts tangentially at
the rim of wheel. If moment of inertia of
wheel is \( 0.5 k g m^{2}, \) its
angular acceleration is:
A \( \cdot 2 \) rad/s^
B . \( 2.5 \mathrm{rad} / \mathrm{s}^{2} \)
C. 4 rad/s\( ^{2} \)
D. 5 rad/s\( ^{2} \)


"It is more important to have beauty in the equations of physics than to have them agree with experiments." The great British physicist P. A. M. Dirac held this view.Criticize this statement.
Look out for some other equations and results, which strike you beautiful


A spherical ball of salt is dissolving in water in such a manner that the rate of
decrease of the volume at any instant is
proportional to the surface. The radius is decreasing at a constant rate.
A. True
B. False


Geometry and lone pairs of electrons in
\( X e O F_{4} \) molecule is
A. Square planar,
B. Square pyramidal,
c. Trigonal bipyramidal, 2
D. Distorted octahedraon,


The diagram shows the change \( x \) in the length of a thin uniform wire caused by the application of stress \( F \) at two
different temperatures \( T_{1} \) and \( T_{2} . \) The
variations shown suggest that:
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
c. \( T_{1}=T_{2} \)
D. None of these


Which one of the following is ' \( d \) -block element?
A. \( G d \)
в. \( H s \)
c. \( E s \)
D. \( C s \)


The magnetic field inside the coils of a
toroid of radius \( R \) and \( N \) turns with a
current of \( \boldsymbol{I} \boldsymbol{A} \) is given by
A \( \cdot B=\frac{\mu_{o} N I}{4 \pi R} \)
в. \( B=\frac{\mu_{o} N I}{2 \pi R} \)
C \( . B=\mu_{o} N I \)
D. None of these


Combination of notes that produced jarring effect on the ear is called
A. discord
B. harmony
c. noise
D. melody


To construct a convex quadrilateral,
which of the following cases is not
correct?
A. When the lengths of four sides and one diagonal are given
B. When the lengths of three sides and the two diagonals are given
C. When the lengths of four sides and one angle are given
D. When the lengths of two sides and two included angles are given


When a hydrogen atom is raised from the ground state to an excited state.
A. Both K.E. and P.E. increase
B. Both K.E. and P.E. decrease
c. The P.E. decreases and K.E. increases
D. The P.E. increases and K.E. decreases


Which one has (a) Tissue level
organisation,
(b) Organ level organisation?
A. Tissue level organisation- Hydra, Organ level organisation - Liver fluke
B. Tissue level organisation - Liver fluke, Organ level organisation - Hydra
c. Tissue level organisation - Centipede, Organ level organisation - Earthworm
D. Tissue level organisation - Earthworm, organ level organisation - Centipede


If two lenses are placed in contact, the combination has power equal to
A. Algebraic sum of power of two lenses
B. Division of power of two lenses
c. Multiplication of power of two lenses
D. Subtraction of power of two lenses


What is the shape of the equipotential surface for the line charge?
A. Sphere
B. cylinder
c. will depend upon the type of charge.
D. can't say.


Assertion
The ratio of speeds of cation and anions of an electrolyte under same potential gradient is \( 2: 3, \) the fall in concentration around anodic and cathodic solution
will be in the ratio 1: 1 during the passage of current.
Reason
The number of ions discharged at either
electrode during electrolysis in independent of their relative speed.
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 reversible reaction \( A \rightleftharpoons C \) takes
place in two steps \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} \)
which are also equilibrium steps. If the equilibrium constants of the two steps
are \( K_{1} \) and \( K_{2} \) respectively, the overall equilibrium constant \( \boldsymbol{K} \) is equal to:
\( ^{\text {A }} \cdot \frac{K_{1}}{K_{2}} \)
в. \( \frac{K_{2}}{K_{1}} \)
\( \mathbf{c} \cdot K_{1} \times K_{2} \)
D. \( K_{1}-K_{2} \)


The pressure of gas in a metal cylinder
is 4 atmospheres at \( 27 C, \) then the
pressure at \( 54 C: \) (in atmosphere)
A . 4.36
B. 8
\( c .3 \)
D. \( 400 / 109 \)


Formulate the equations for the above problem. \( (x \text { and } y \text { are the number of units of } A \)
and \( B \) manufactured in a day
respectively)
A. \( 15 x+5 y \leq 10 ; 24 x+14 y \geq 1000 \)
B. \( 15 x+5 y \leq 600 ; 24 x+14 y \geq 1000 \)
c. \( 5 x+15 y \leq 600 ; 24 x+14 y \geq 1000 \)
D. \( 5 x+15 y \leq 10 ; 24 x+14 y \geq 1000 \)


Which of the following polymers does not involve cross linkages?
A. Bakelite
B. Melamine
c. Polythene
D. Vulcanized rubber


A parallel plate capacitor has plates
with area \( A \& \) separation \( d . A \) battery charges the plates to a potential
difference of \( V_{0} . \) The battery is then
disconnected \& a di-electric slab of
constant \( K \& \) thickness \( d \) is
introduced. Calculate the positive work done by the system (capacitor \( + \) slab) on the man who introduces the slab.


If \( c \) is the concentration of \( n \) moles of a
gas at pressure \( P \) and temperature \( T \)
then for the ideal gas reaction. the rate of reaction can be given by :
A \( \cdot-\frac{d[A]}{d t} \)
B. \( -\frac{1}{R T} \frac{d P}{d t} \)
c. \( -\frac{1}{\nu} \frac{d n}{d t} \)
D. either of these


Plants are able to produce fruits with the help of insects as they are
A. Help in aestivation
B. Help in pollination
c. Help to overcome dormancy
D. None of the above


Find the product of \( \left(\frac{1}{2} m-\frac{1}{3}\right)\left(\frac{1}{2} m+\right. \)
\( \left.\frac{1}{3}\right)\left(\frac{1}{4} m^{2}+\frac{1}{9}\right) \)


When two bodies approach each other
with different uniform speeds, the distance between them decreases by
\( 120 m \) per every 1 min. If they move in
the same direction, the distance between them increases by
\( 90 m \) per every 1 min. The speeds of the
bodies are respectively.
A \( .2 m / s, 0.5 m / s \)
B. \( 3 m / s, 2 m / s \)
c. \( 1.75 m / s, 0.25 m / s \)
D. \( 2.5 m / s, 0.5 m / s \)


A uniformly charged ring of radius \( R \) is
rotated about its axis with constant
linear speed \( v \) of each of it's particles.
The ratio of electric field to magnetic
field at a point \( \boldsymbol{P} \) on the axis of the ring
at a distant \( x=R \) from the centre of
the ring is :
\( (c \text { is speed of light }) \)
A \( \frac{c^{2}}{v} \)
в. \( \frac{v^{2}}{c} \)
c. \( \frac{c}{v} \)
\( D \cdot \underline{v} \)


Which one of the followings is/are an
example of homogeneous catalysis? This question has multiple correct options
A. Formation of \( S O_{3} \) in the chamber process
B. Formation of \( S O_{3} \) in the contact process
c. Hydrolysis of an ester in the presence of acid.
D. Decomposition of \( K C l O_{3} \) in the presence of \( M n O_{2} \)


Who wrote the famous book 'Origin of species'?
A . Lamarck
B. Darwin
c. De Vries
D. Mendel


Which is not true statement?
A. -carbon of -amino acid is asymmetric
B. all proteins are found in L-form.
C. human body can synthesize all proteins they need.
D. at \( p H=7 \) both amino and carboxylic groups exist in ionised form.


\( a, b, c, d, e \) are in \( A . P . \) Prove the
following results \( \boldsymbol{a}-\boldsymbol{2} \boldsymbol{b}+\boldsymbol{c}=\mathbf{0} \)


In which graph, frequency is represented by the area of each rectangle?
A. bar
B. pie
c. line
D. histogram


Two identical trains take 3 sec to pass
one another when going in the opposite direction but only 2.5 sec if the speed of
one is increased by \( 50 \% \). The time one would take to pass the other when going in the same direction at their original speed is
A \( .10 \mathrm{sec} \)
B. 12 sec
c. 15 sec
D. 18 sec


ngiven figure, \( \frac{A O}{O C}=\frac{B O}{O D}=\frac{1}{2} \) and
\( A B=5 \mathrm{cm} . \) Find the value of DC.


A ball is let fall from a height \( h_{0} \). It makes \( n \) collisions with the earth. After
\( n \) collisions it rebounds with a velocity
\( v_{n} \) ' and the ball rises to a height \( h_{n} \) then coefficient of restitution is given
by:
\( ^{\mathbf{A}} \cdot_{e}=\left[\frac{h_{n}}{h_{0}}\right]^{1 / 2 n} \)
\( ^{\mathrm{B}} e=\left[\frac{h_{0}}{h_{n}}\right]^{1 / 2 n} \)
c. \( _{e}=\frac{1}{n} \sqrt{\frac{h_{n}}{h_{0}}} \)
D. \( _{e}=\frac{1}{n} \sqrt{\frac{h_{0}}{h_{n}}} \)


Which of the following will exhibit
aromatic character?
\( A \cdot 1, \) II
В. III, IV
c. ॥, IV
D. II, III


Three different vibrating bodies produce
three types of sounds \( X, Y \) and \( Z . \) Sounds \( \mathrm{X} \) and \( \mathrm{Y} \) cannot be heared by a man
having normal range of hearing but sound \( Z \) can be heard easily. The sound \( X \)
is used in for monitoring nuclear
reactor.The sound similar to that which is
produced during an earthquake before
the main shock wave is generated. What type of sounds are (i) \( \mathrm{X} \) (ii) \( \mathrm{Y} \), and (iii) \( \mathrm{Z} \) ?
A. \( x \) -infrasound
Y-ultrasound
Z- audible sound
B. X-audible sound
Y-infrasound
z-ultrasound
c. X-ultrasound
Y-infrasound
Z-audible sound
D. X-infrasound
Y-audible sound
Z-audible sound


A person drinks 200 g of \( 3 \% \) glucose solution (molecular wt. \( =180 \) ) after
aerobic exercise. The number of carbon
atoms consumed by him is :
\( \begin{array}{ll}\text { A } & \text { . } 3.01 \times 10^{2}\end{array} \)
В. \( 1.0 \times 10^{22} \)
C. \( 2.01 \times 10^{22} \)
D. \( 1.20 \times 10^{23} \)


Carbohydrates contains carbon, hydrogen, and oxygen molecules.
A. True
B. False


What causes winds?


How much time will have elapsed?
A \( .1 .42 \times 10^{-8} \mathrm{s} \)
B . \( 2.84 \times 10^{-8} \mathrm{s} \)
c. \( 3.84 \times 10^{-8} \mathrm{s} \)
D. \( 5.68 \times 10^{-8} \mathrm{s} \)


The interference phenomenon can take place
A. in transverse wave
B. in longitudinal wave
c. in electromagnetic waves
D. in all waves


\( \int e^{a x} \cdot \sin (b x+c) d x \)


Dobereiner was able to identify triads from the elements
known at that time.


A potential difference of \( 20 \mathrm{V} \) is needed to make a current of \( 0.05 \mathrm{A} \) flow through a resistor. What potential difference is needed to make a current of \( 300 \mathrm{mA} \)
flow through the same resistor?
A. \( 60 v \)
B. 1200
c. \( 40 v \)
D. 150V


The resistance of a galvanometer is 50 ohm and the maximum current which
can be passed through it is \( 0.002 A \) What resistance must be connected to
it in order to convert it into an ammeter
of range \( 0-0.5 A ? \)
A. 0.2 onm
B. 0.002 ohm
c. 0.02 ohm
D. 0.5 ohm


If \( x_{1}, x_{2}, \dots . . x_{n} \) are \( n \) values of a variable
\( X \) and \( y_{1}, y_{2}, \dots . y_{n} \) are \( n \) values of \( a \)
variable \( \boldsymbol{Y} \) such that \( \boldsymbol{y}_{i}= \)
\( \frac{\boldsymbol{x}_{i}-\boldsymbol{a}}{\boldsymbol{h}} ; \quad \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \ldots . ., \boldsymbol{n}, \) then
A. \( \operatorname{Var}(Y)=\operatorname{Var}(X) \)
B. \( \operatorname{Var}(X)=h^{2} \operatorname{Var}(Y) \)
C \( . \operatorname{Var}(Y)=h^{2} \operatorname{Var}(X) \)
D. \( \operatorname{Var}(X)=h^{2} \operatorname{Var}(Y)+a \)


If a ball is thrown upwards from the
Surface of earth:
A. The earth remains stationary while the ball moves upwards
B. The ball remains stationary while the earth moves downwards
C. The ball and earth both moves towards each other
D. The ball and earth both move away from each other


State True or False.
The cell voltage is a quantitative measure of the driving force of the cell
reaction.
A. True
B. False


The order of stability of metal oxides is
\( \mathbf{A} \cdot A l_{2} O_{3}<M g O<F e_{2} O_{3}<C r_{2} O_{3} \)
B. \( C r_{2} O_{3}<M g O<A l_{2} O_{3}<F e_{2} O_{3} \)
\( \mathbf{c} \cdot F e_{2} O_{3}<C r_{2} O_{3}<A l_{2} O_{3}<M g O \)
D. \( F e_{2} O_{3}<A l_{2} O_{3}<C r_{2} O_{3}<M g O \)


A \( 0.1 ~ M \) aqueous solution of a weak
acid is \( 2 \% \) ionized. If the ionic product
of water is \( 1 \times 10^{-14}, \) the \( \left[O H^{-}\right] \) is:
A \( \cdot 5 \times 10^{-12} \mathrm{M} \)
В. \( 2 \times 10^{-3} \) М
c. \( 1 \times 0^{-14} \mathrm{M} \)
D. none of these


The Gaussian surface for calculating the electric field due to a charge
distribution is
A. any closed surface around the charge distribution
B. any surface near the charge distribution
c. a spherical surface
D. a closed surface at a every point of which electric field has a normal component which is zero or a fixed value


The domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{x-2-2 \sqrt{x-3}}- \)
\( \sqrt{x-2+2 \sqrt{x-3}}, \) is
A \( .[3,5] \)
в. (3,5)
\( c \cdot[5, \infty) \)
\( D \cdot[3, \infty) \)


The underground storage structure in Gladiolus is
A. Corm
B. Bulb
c. Rhizome
D. Stem tuber


Compost is being used for all of the following except:
A. landfill cover
B. landscaping
c. low grade fertilizers
D. agricultural field


Assertion
Drift velocity of electrons is
independent of time.
Reason
Electrons are accelerated in the
presence of electric field.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the diagonals of a rhombus are \( 24 \mathrm{dm} \) and \( 10 \mathrm{dm}, \) then the perimeter of the rhombus will be
A. \( 68 \mathrm{dm} \)
B. 60 dm
\( c .52 \mathrm{dm} \)
D. 50 dm


Find the velocities of the point \( \boldsymbol{A} \)
A. \( 10.0 \mathrm{cm} / \mathrm{s} \)
в. \( 7.21 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 5 c m / s \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)


Which of the following reaction occur when urea is added to soil as a fertilizer?
A. \( N H_{2} C O N H_{2} \longrightarrow H N C O+N H_{3} \)
B. \( N H_{2} C O N H_{2}+H_{2} O \longrightarrow 2 N H_{3}+C O_{2} \)
c. \( 2 N H_{2} C O N H_{2} \longrightarrow H_{2} N C O N H C O N H_{2}+N H_{3} \)
D. Both 1 and 2


If \( \mu_{r} \) be the relative permeability and \( \varepsilon_{r} \) be the relative dielectric constant of a
medium, its refractive index is:
\( ^{A} \cdot \frac{1}{\sqrt{\mu_{r} \epsilon_{r}}} \)
в. \( \frac{1}{\mu_{t} \epsilon_{r}} \)
c. \( \sqrt{\mu_{r} \epsilon_{r}} \)
D. \( \mu_{r} \epsilon_{r} \)


Explain the digestion of proteins in small intestine?


Write the name of alternative path of
oxidation of glucose.


The strongest bond is present in:
A. \( B r_{2} \)
В. \( I_{2} \)
\( c \cdot C l_{2} \)
D. \( F_{2} \)


The work function of the following metals is given: \( N a=2.75 e V, K= \)
\( \mathbf{2 . 3} e V, M o=4.17 e V \) and \( N i= \)
\( 5.15 e V . \) Which of these metals will not
undergo photoelectric emission for
radiation of wavelength \( 3300 A \) from a
laser source placed 1 m away from these metals? What happens if the
laser source is brought closer and
placed \( 50 \mathrm{cm} \) away?


Write the correct alternatives:
In the Wilfley table method, the particles of gangue are separated by \( \dots \dots \dots \)
A. Magnetic
B. Froth floatation
c. Hydraulic
D. Gravitational


The reaction,
\[
\begin{array}{c}
(\mathbf{1} / \mathbf{2}) \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{l}(\boldsymbol{s})= \\
\boldsymbol{H}+(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{l}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \text { occurs in }
\end{array}
\]
the galvanic cell
The correct cell representation is given
by
\( \mathbf{A} \cdot A g|A g C l(s)| K C l(s o l n .)\left|A g N O_{3}(s o l n .)\right| A g \)
B \( \cdot P t\left|H_{2}(g)\right| H C l(\text {soln.}) \mid A g N O_{3}(\text {soln.}) \mid A g \)
\( \mathbf{c} \cdot P t\left|H_{2}(g)\right| H C l(s o l n .)|A g C l(s)| A g(s) \)
D \( \cdot P t\left|H_{2}(g)\right| K C l(s o l n .)|A g C l(s)| A g \)


Distance between two very long parallel wires is \( 0.2 m . \) Electric currents of \( 4 A \) in
one wire and \( 6 A \) in the other wire are
passing in the same direction. Find the position of a point on the perpendicular line joinig the two wires at which the magnetic field intensity is zero.


The centre of the ellipse \( 4 x^{2}+y^{2}- \)
\( 8 x+4 y-8=0 \) is
A \( .(0,2) \)
в. (2,-1)
c. (2,1)
()
D. (1,2)


Add the expressions in each of the following.
i) \( 2 l+3 m-6 n+4 p, 3 l-5 m+ \)
\( 16 n-4 p, 12 l-6 m-4 n-2 p a n d l- \)
\( 2 m+3 n-4 p \)
ii) \( 7 x^{3}+3 x+9,-2 x^{3}-3 x^{2}- \)
\( 15,3 x^{3}-6 x^{2}+4 x-6 a n d 12 x^{2}-6 \)
iii) \( 5 a^{2}-7 a b+9 b^{2}, 4 a^{2}-2 b^{2}- \)
\( 9 a b-6,4-3 b^{2}+2 a b+ \)
\( 6 a^{2} \) and \( 12 a b-3 a^{2}-9 b^{2} \)


Match the columns.


The entropy change(cal/mol) for vaporisation of water if latent heat of vaporisation for water is 540 cal/g
\( \left(\operatorname{Given} K_{b} \text { for } H_{2} O=0.51 K / \text {molality}\right) \)
is (write answer to the nearest integer
after dividing entropy change by 5 )


In which of the following systems will the radius of the first orbit \( (n=1) \) be
minimum?
A. Doubly ionized lithium
B. singly ionized helium
c. Deuterium atom
D. Hydrogen atom


A ball of mass m makes perfectly elastic head-on collision with a ball of mass nm which is initially at rest. Show
that the fractional transfer of energy by the first ball is \( 4 n /(1+n)^{2} . \) Deduce the
value of \( n \) for which the transfer is
maximum.


Explain Saponification of oil/fats with equation.


Which of the following is a basic oxide?
A \( . C a O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( N_{2} \) O


A vessel \( A \) has volume \( V \) and vessel \( B \)
has volume \( 2 V \) Both contain some
water which has a constant volume.The
pressure in the space above water is \( p_{a} \)
for vessel \( \boldsymbol{A} \) and \( \boldsymbol{p}_{\boldsymbol{b}} \) for vessel \( \boldsymbol{B} \) ?
A \( \cdot p_{a}=p_{b} \)
в. \( p_{a}=2 p_{b} \)
\( \mathbf{c} \cdot p_{b}=2 p_{a} \)
\( \mathbf{D} \cdot p_{b}=4 p_{a} \)


Most energetic radiations and fluorescence are properties of
A. Gamma rays
B. UV Rays
c. Infrared Rays
D. Radio waves


If \( D, E, F \) are the mid-points of the sides \( B C, C A \) and \( A B \) respectively of \( \triangle A B C, \) prove that \( B D E F \) is a parallelogram whose area is half to that
of \( \triangle A B C . \) Show that \( a r(\triangle D E F)= \) \( \frac{1}{4} a r(\triangle A B C) \)


Fossil of Neanderthal Man was first
discovered in
A . 1856
в. 1868
\( c \cdot 1924 \)
D. 1994


Speed of efflux is
A \( \cdot \sqrt{3 g h} \)
в. \( \sqrt{2 g h} \)
\( c \cdot \sqrt{g h} \)
D. \( \frac{1}{2} \sqrt{2 g h} \)


If \( \boldsymbol{R} \) divides the line segment joining \( P(2,3,4) \) and \( Q(4,5,6) \) in the ratio
\( -3: 2, \) then the parameter which
represent \( \boldsymbol{R} \) is
\( A \cdot 3 \)
B . 2
\( c . \)
D. -


If the vector \( 6 \hat{i}-3 \hat{j}-6 \hat{k} \) is decomposed into vectors parallel and perpendicular to the vector \( \hat{i}+\hat{j}+\hat{k} \)
then the vectors are
A \( .-(\hat{i}+\hat{j}+\hat{k}) \& 7 \hat{i}-2 \hat{j}-5 \hat{k} \)
B. \( -2(\hat{i}+\hat{j}+\hat{k}) \& 8 \hat{i}-\hat{j}-4 \hat{k} \)
\( \mathbf{c} \cdot+2(\hat{i}+\hat{j}+\hat{k}) \& 8 \hat{i}-\hat{j}-4 \hat{k} \)
D. none


What is the importance of Monsoon
winds?
A. They lower the temperature of areas where temperature is usually high.
B. They bring rain and play important role in water cycle.
C. They clear up the sky and make atmosphere sunny.
D. None of the above


Very small animals are rarely found in
polar regions because
A. small animals have a larger surface area relative to their volume, so they lose body heat very fast when it is cold outside
B. small animals have a smaller surface area relative to
their volume, so they lose body heat very fast when it iis cold outsiide
C. small body volume makes internal heat production very difficult
D. none of these


A sensitive magnetic instrument can be
shielded very effectively from outside
magnetic fields by placing it inside a box
of:
A. wood
B. plastic
C. metal of high conductivity
D. soft iron of high permeability


The strongest acid among the following is:
A. \( H_{2} S O_{4} \)
в. \( H_{2} \) Se \( O_{4} \)
c. \( H_{2} T e O_{4} \)
D. \( H_{2} P o O_{4} \)


\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
According to above reaction, the Hydrocyanic acid dissociates, find the
acid dissociation constant for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) ?
\( ^{\mathbf{A}} \cdot \frac{\left[H^{+}\right]\left[C N^{-}\right]}{[H C N]} \)
в. \( \left[H^{+}\right]\left[C N^{-}\right][H C N] \)
c. \( \frac{[H C N]}{\left[H^{+}\right]\left[C N^{-}\right]} \)
D. \( \frac{\left[H^{+}\right]}{[H C N]\left[C N^{-}\right]} \)
E \( \frac{1}{[H C N]\left[H^{+}\right]\left[C N^{-}\right]} \)


In the reaction \( 2 N O_{(g)}+2 H_{2_{(g)}} \rightarrow \)
\( N_{2_{(g)}}+2 H_{2} O, \) if initial concentration of
hydrogen is kept constant and the concentration of NO is doubled, the rate
of reaction increases by 4 times. This shows that rate is directly proportional
to
A. catalyst
B. concentration of nitric oxide
c. concentration of Hydrogen
D. concentration of water


Isomer \( (I I I) \) on monochlorination gives
three products. The isomer \( (\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)
is
\( A \)
B.
\( c \)
D.


Assertion
A solution of sucrose in water is
dextrorotatory while on hydrolysis in presence of little hydrochloric acid, becomes laevorotatory.
Reason
Sucrose on hydrolysis give unequal amounts of glucose and fructose as result of which change in sign of rotation observed.
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


Fill in the blank:
The quotient when a rational number is
divided by its additive inverse is


\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \mathbf{7} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{4} & \mathbf{5}\end{array}\right] \)
\( \operatorname{Tr}(A B)=\lambda \operatorname{Tr}(\mathrm{A}) . \operatorname{Tr}(\mathrm{B}), \) then \( \lambda= \)
\( A \)
B. 0
\( c \cdot \frac{6}{5} \)
\( \frac{20}{27} \)


Fill in the blank:
A boy blinks his right eye. Mirror image of the boy blinks its \( _{-}-_{-}-_{-}- \) eye
A. both
B. right
c. none
D. left


Half the internuclear distance between
two atoms bonded by a single covalent
bond.
If true enter 1 , else enter 0


Catterpillar, Snake, Owl Frog, Green
leaves.


If the magnetizing field on a ferromagnetic material is increased, its permeability
A . Decreased
B. Increased
c. Is unaffected
D. May be increased or decreased


Two half-cells have potentials -0.44 and 0.799 volt respectively. These two are coupled to make a galvanic cell. Which of the following will be true?
A. Electrode of half-cell potential \( -0.44 \mathrm{V} \) V will act as anode
B. Electrode of half-cell potential -0.44 V will act as cathode
c. Electrode of half-cell potential \( 0.799 \mathrm{V} \) will act as anode
D. Electrode of half-cell potential \( -0.44 \mathrm{V} \) will act as a positive terminal


Open circuit voltage of a source is 7.86 V and its short circuit current is 9.25 A. Find the current when an external
resistance of \( 2.4 \Omega \) is connected
A . \( 1.4 \mathrm{A} \)
B. 1.82A
c. 2.01A
D. 2.4A


Assertion
Sensitive electrical instruments should
not be placed in the vicinity of an electromagnet.
Reason
Electromagnet can damage the instruments.
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


Graphite powder is used in machines to
A. enhance friction
B. enhance profit
c. reduce friction
D. reduce efficiency


The arrangement of leaves on a branch
is
A. Phyllode
B. Phyllotaxy
c. Phylloclade
D. Phloem


A body of mass \( 2 \mathrm{kg} \) is at rest. A force of \( 4 \hat{i}+3 \hat{j}-5 \hat{k} \) N acts on it and displaces through \( 2 \hat{i}+\hat{j}+2 \hat{k} \) m. The velocity acquired by the body is:
A \( \cdot 0 \mathrm{ms}^{-1} \)
B. \( 1 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


The enthalpy change for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}) \) is:
The bond energies are, \( \boldsymbol{H}-\boldsymbol{H}= \)
\( \mathbf{1 0 3}, \boldsymbol{C}-\boldsymbol{H}=\mathbf{9 9}, \boldsymbol{C}-\boldsymbol{C}=\mathbf{8 0} \) and
\( \boldsymbol{C}=\boldsymbol{C}=\mathbf{1 4 5} \boldsymbol{K} \boldsymbol{c a l} \boldsymbol{m o l}^{-1} \)
A. -10 Kcalmol\( ^{-1} \)
B. +10 K calmol\( ^{-1} \)
C. -30 K calmol\( ^{-1} \)
D. +30 Kcalmol-\( ^{-1} \)


5th term of an AP is 26 and 10 th term is
51. The 15 th term is :
A . 60
B. 76
\( c .55 \)
D. 72


In the following figure, \( M \) is midpoint of
BC of a parallelogram ABCD. DM intersects the diagonal \( A C \) at \( P \) and
AB produced at E. Then
\( \mathbf{A} \cdot P E=3 P D \)
B. \( P E=2 P D \)
c. \( P E=P D \)
\( D . P E=4 P D \)


What are polar and non polar dielectric
give one example each other ?Define dielectric constants.


How are electrons involved in the
formation of a covalent compound


\( \left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 15^{\circ} & \cos 15^{\circ}\end{array}\right|=? \)
A . 1
B.
c. \( \frac{\sqrt{3}}{2} \)
D. none of these


What is the value of \( x \) for the following
equations: \( x-5 y=10 \) and \( x+y=4 ? \)
(Use cross multiplication method)
\( \mathbf{A} \cdot x=5 \)
B. \( x=4 \)
c. \( x=3 \)
D. \( x=2 \)


Light waves exhibit polarization but sound waves do not exhibit polarization because they are not:
A. longitudinal
B. coherent
c. dispersive
D. transverse
E. refractive


The empirical formula of stannous fluoride, a compound added to tooth
paste to protect teeth against tooth
decay is \( S n F_{2}, \) if its mass per cent
composition is \( 24.25 \% F, 75.75 \% \) Sn.
If true enter 1 , else enter 0 .


The number of point of intersection of the two curves \( y=2 \sin x \) and \( y= \)
\( 5 x^{2}+2 x+3 \) is \( ? \)
\( A \cdot \infty \)
B. 0
c. 1
D. less than two


A person standing in a moving bus falls backwards when bus suddenly starts moving in forward direction. This happens due to


If \( a^{2}, b^{2}, c^{2} \) are in A.P. then show that \( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \) are also in A.P.


The IUPAC name of the following
compound is:
A. 4 Bromo -3 - Cyanophenol
B. 2 - Bromo - 5 - hydroxybenzonitrile
C. 2 - Cyano - 4 - hydroxybromobenzene
D. 6 - Bromo - 3 - hydroxybenzonitrile


Find \( \boldsymbol{x} \)
\( -(x-3)+4<5-2 x \)


The basicity is highest for which of the following acids
A. Phosphorus acid
B. Metaphosphoric acid
c. ortho phosphoric acid
D. Hypo phosphorus acid


Argument and modulus of \( \frac{1+i^{2013}}{1-i} \) are respectively
A \( \cdot \frac{-\pi}{2} \) and 1
в. \( \frac{\pi}{2} \) and \( \sqrt{2} \)
c. 0 and \( \sqrt{2} \)
D \( \cdot \frac{\pi}{2} \) and 1


Explain how equal genetic contribution
of male and female parents is ensured
in the progeny.


A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the
ratio \( \frac{\mid \text {displacement} \mid}{\text {distance}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{2}{7} \)
D. \( \frac{7}{11} \)


In isothermal expansion the pressure is
determined by :
A. temperature only
B. compressibility only
C. both temperature and compressibility
D. latent heat


The number of tetrads present in pachytene and Metaphase-I of Allium cepa respectively
A. 16 and 8
B. 16 and 16
\( c .8 \) and 8
D. 16 and 32


Which of the following functions is always increasing?
\( \mathbf{A} \cdot x+\sin 2 x \)
B. \( x-\sin 2 x \)
c. \( 2 x+\sin 3 x \)
\( \mathbf{D} \cdot 2 x-\sin x \)


A virtual image larger than the object can be produced by a
A. concave lens
B. Concave mirror
c. convex mirror
D. Plane mirror


In an annual ring, the light coloured part
is
A. Heart wood
B. Sapwood
c. Early wood
D. Late wood


The variable plane \( (2 \lambda+1) x+ \)
\( (3-\lambda) y+z=4 \) always passes
through the line
A \( \cdot \frac{x}{0}=\frac{y}{0}=\frac{x+4}{1} \)
в. \( \frac{x}{1}=\frac{y}{2}=\frac{z}{-3} \)
c. \( \frac{x}{1}=\frac{y}{2}=\frac{z-4}{-7} \)
D. none of these


Which of the following is a fibrous protein?
A. Haemoglobin
B. Albumin
c. Keratin
D. Insulin


Give any three oxidation reactions of
Ozone \( \left(O_{3}\right) \) with chemical equations.


\( 14 \mathrm{g} \) of element \( \mathrm{X} \) combine with \( 16 \mathrm{g} \) of oxygen. On the basis of this information, which of the following is a correct statement?
A. The element \( x \) could have an atomic weight of 7 and its oxide is \( x 0 \)
B. The element \( x \) could have an atomic weight of 14 and its oxide is \( X_{2} O \)
c. The element \( x \) could have an atomic weight of 7 and its oxide is \( X_{2} O \)
D. The element \( x \) could have an atomic weight of 16 and its oxide is \( X_{2} O \)


Which scale is used to measure the
magnitude of earthquake?
A. Kelvin
B. Parcal
c. celsius
D. Richter


Which of the following represents a bronsted acid-base reaction?
\( \mathbf{A} \cdot 3 O_{2}(g) \rightleftharpoons 2 O_{3}(g) \)
B. \( O H^{-}+H_{3} O^{+} \rightleftharpoons 2 H_{2} O \)
\( \mathbf{c} \cdot B a C l_{2} \cdot 2 H_{2} O(s) \triangleq B a C l_{2}(s)+2 H_{2} O(g) \)
\( \mathbf{D} \cdot C a^{2+}+C O_{3}^{2-} \rightarrow C a C O_{3}(s) \)
\( \mathbf{E} \cdot F e+C u^{2+} \rightleftharpoons F e^{2+}+C u \)


An ideal gas whose adiabatic exponent is \( \gamma \) is expanded so that the amount of heat transferred to the gas is equal to the decrease of its internal energy. Molar heat capacity of the gas for this
process is
A \( \cdot \frac{R}{1-\gamma} \)
B. \( \frac{R}{\gamma-1} \)
c. \( R \)
D. \( \frac{n}{2} \)


Find the sum of the number of terms in
the geometric progressions in \( 0.15,0.015,0.0015, \dots 20 \)


Expand: \( (x y+8)(x y-8) \)


What is the mass of :
(a) 0.2 mole of oxygen atoms?
(b) 0.5 mole of water molecules?


Which of the following are correct for
insulators?
A. The valence band is partially filled with electrons.
B. The conduction band is partially filled with electrons.
C. The conduction band is partially filled with electrons and valence band is empty.
D. The conduction band is empty and the valence band is filled with electrons.


The catalyst used in making \( H_{2} S O_{4} \) in
contact process is :
A \( \cdot V_{2} O_{5} \)
в. \( F e_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( C r O_{3} \)


Squaring a given number is a
A. relation in some set
B. relation
c. unary operation
D. binary operation


For moon its mass is \( \frac{1}{81} \) of earth's mass
and its diameter is \( \frac{1}{3.7} \) of earth's
diameter. If acceleration due to gravity of earth surface is \( 9.8 m / s^{2}, \) then at moon its value is
A \( \cdot 2.86 m / s^{2} \)
B . \( 1.65 m / s^{2} \)
\( \mathbf{c} \cdot 8.65 m / s^{2} \)
D. \( 5.16 m / s^{2} \)


State True or False.
For a solution of \( A l C l_{3} \) in water, the Van't Hoff factor (i) is greater than 1
A. True
B. False


Which among the following are essential chemical components of
many coenzymes?
A. Nucleic acids
B. Carbohydrates
c. Vitamins
D. Proteins


Which of the following compound gives \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) by the addition of \( \boldsymbol{H}_{2} \boldsymbol{O} ? \)
A \( \cdot C O\left(N H_{2}\right)_{2} \cdot H_{2} O_{2} \)
в. \( N a_{2} H P O_{4} . H_{2} O_{2} \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot H_{2} O_{2} \)
D. All of the above


A particle is moving with velocity \( \vec{v}= \) \( \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}} \) and it produces an electric field at that point equal to \( 2 \hat{k} \), find the magnetic field at that point (all) quantities are in Sl units)
A \( \cdot(6 \hat{i}-2 \hat{j}) \mu_{0} \varepsilon_{0} \)
B . \( (6 \hat{i}+2 \hat{j}) \mu_{0} \varepsilon_{0} \)
c. zero
D. cannot be determined from the given data


Explain in detail the processes involved in the production of pig iron and steel.


Give Reasons
A frequency polygon can be drawn with the help of a Histogram.


When 4.0 A of current is passed through a \( 1.0 \mathrm{L}, 0.10 \mathrm{M} F e^{3+}(a q) \) solution for 1.0
hour, it is partly reduced to \( \mathrm{Fe}(\mathrm{s}) \) and partly of \( \boldsymbol{F e}^{2+}(\boldsymbol{a q}) \). The correct statements(s) is/are:
This question has multiple correct options
A. 0.10 mol of electrons are required to convert all \( F e^{3} \)
to \( F e^{2+} \)
B. 0.025 mol of Fe(s) will be deposited.
c. 0.075 mol of iron remains as \( F e^{2+} \)
D. 0.050 mol of iron remains as \( F e^{2+} \)


Calculate the total power of 2 fans, if each of them draws a current of \( 5 A \) at a
p.d of \( 200 V \)
A . \( 2000 \omega \)
в. \( 1000 V \)
\( c .250 \omega \)
D. 2


Find 9 rational numbers between 2 and
3
\( \mathbf{A} \cdot 2<2.1<2.2<3.3<2.4<\ldots<2.9<3 \)
B . \( 2<4.1<2.2<2.3<2.4<\ldots<2.9<3 \)
c. \( 2<2.1<2.2<2.3<2.4<\ldots<2.9<3 \)
D. \( 2<2.1<2.2<2.3<2.4<\ldots<0.9<3 \)


\( 10^{-3} W \) of \( 5000 A \) light is directed on a
photoelectric cell. If the current in the cell is \( 0.16 \mu A \), the percentage of incident photons which produce photoelectrons, is
A . \( 40 \% \)
B . 0.04\%
c. 20\%
D. 10\%


Out of the elements marked \( A, B, C, D, E \)
\( \mathrm{F}, \mathrm{G} \) and \( \mathrm{H} \) which form superoxides?
This question has multiple correct options
\( A \cdot A \)
B. B
\( c . c \)
\( D \cdot D \)
E.
\( F . F \)
\( G \)


What will be the ionisation constant of
formic acid if its \( 0.01 \mathrm{M} \) solution is
\( 14.5 \% \) ionised?
A \( \cdot 2.1 \times 10^{-4} \)
в. 14.5
c. 0.145
D. \( 1.45 \times 10^{-4} \)


Immediately after the right string is
cut, what is the linear acceleration
of the middle of the rod?


Assertion
Dust particles generally settle down
gradually in a closed room.
Reason
The terminal velocity is inversely proportional to the square of their radii.
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


The standard reduction potential of a \( A g C l / A g \) electrode is \( 0.2 V \) and that of
a silver electrode \( \left(\boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}\right) \) is \( \mathbf{0 . 7 9} \boldsymbol{V} \)
The maximum amount of \( A g C l \) that
can dissolve in \( 10^{6} \) L of a \( 0.1 M A g N O_{3} \)
solution is:
A. \( 0.5 \mathrm{mmol} \)
в. \( 1.0 \mathrm{mmol} \)
c. \( 2.0 \mathrm{mmol} \)
D. \( 2.5 \mathrm{mmol} \)


A nine year old boy is \( 120 \mathrm{cm} \) tall. If the
present height of the boy is \( 75 \% \) of his full height calculate


State True or False:
On subtracting \( a-b-2 c \) from \( 4 a+ \)
\( 6 b-2 c, \) the answer is \( 3 a+7 b \)
A. True
B. False


In which of the following cases the net force is not equal to zero?
A. A kite.skillfully held stationary in the sky
B. A ball falling feely from a height
c. A helicopter hovering above the ground
D. A cork floating on the surface of water


The value of \( k \) when the distance
between the points \( (3, k) \) and (4,1) is \( \sqrt{10} \) is
A . \( 30 r 4 \)
B. \( -4 o r-2 \)
c. \( -4 o r 2 \)
D. \( 4 o r-2 \)


Which of the following halides is not correct according to the name and classification?
A \( \cdot C H_{3} C H_{2} C\left(C H_{3}\right)_{2} C H_{2} I-1 \) -lodo- 2,2 -dimethylbutane Primary haloallkane
B. \( \left(C H_{3}\right)_{2} C H C H(C l) C H_{3} \) - 2-Chloro-3-methylbutane, Secondary haloalkane
C. \( C H_{3} C(C l)\left(C_{2} H_{5}\right) C H_{2} C H_{3} \) - 2-Chloro-2-ethylbutane Secondary haloalkane
D. \( C H_{3} \)
\( C H_{3}-C H_{2}-C H-C H-C H_{2}-C H_{3} \quad \) 3-Chloro
4- - methylhexane secondary haloalkane


\( \lim _{x \rightarrow 0} \frac{1-\cos ^{2} x}{x \sin x \cos x} \) is equal to
A . 1
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{2} \)
D.


Solve: \( \int \frac{\sqrt{1+x^{2}}}{x^{4}} d x \)


Which of the following acids, listed with
their ionization constant at \( 25^{\circ} C \), is the
strongest?
A . Nitrous acid \( \left(H N O_{2}\right) K_{i}=4.5 \times 10^{-4} \)
B. Formic acid \( \left(H C H O_{2}\right) K_{i}=1.8 \times 10^{-4} \)
C . Benzoic acid \( \left(H C_{7} H_{5} O_{2}\right) K_{i}=6.3 \times 10^{-5} \)
D. Acetic acid \( \left(H C_{2} H_{3} O_{2}\right) K_{i}=1.8 \times 10^{-5} \)
E . Hydrocyanic acid (H \( C N \) ) \( K_{i}=4.0 \times 10^{-10} \)


Identify the substance underlined, in each of the following cases:
An organic compound containing COOH functional group.


Among the following compounds, which one is a disinfectant?
A. Phenol
B. p-Xylene
c. chloromethylbenzene
D. Morphine


Assertion
For practical purposes, the earth is
used as a reference at zero potential in
electrical circuits.
Reason
The electric potential of a sphere of
radius \( R \) with charge \( Q \) uniformly distributed on the surface is given by
\( \frac{Q}{4 \pi \varepsilon_{0} R} \)
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 and Reason are correct


If \( A=\left[\begin{array}{cc}-8 & 5 \\ 2 & 4\end{array}\right] \) satisfies the equation \( x^{2}+4 x-p=0, \) then \( p= \)
A . 64
B. 42
\( c . \) 36
D. 24


Which is the correct relationship
between wavelength and momentum of particles?


Evaluate :
\( \lim _{x \rightarrow \infty} x^{2}(\sqrt{\frac{x+2}{x}}-\sqrt[3]{\frac{x+3}{x}}) \)


Assertion
The regulation of RBC production is accomplished by FSH
Reason Erythropoietin, hormone circulates to red bone marrow where it increases
stem cell mitosis and speed up
development of RBCs
A. If both the assertion and the reason are true and the reason is correct explanation of the assertion
B. If both the assertion and the reason are true but the reason is not correct explanation of the assertion
c. If the assertion is false but the reason is true
D. If both the assertion and reason are false


The equation of the plane, which bisects the line joining the points (1,2,3) and (3,4,5) at right angles is?
A. \( x+y+z=0 \)
B. \( x+y-z=9 \)
c. \( x+y+z=9 \)
D. \( x+y-z+9=0 \)


The triplet on coding strand of DNA is ATG. What would be the required anticodon on corresponding tRNA during translation?
A. UAA
B. UAG
c. UGA
D. UACC


A curve drawn at constant pressure is called an isobar and shows relationship
between:
A \( \cdot V \) and \( \frac{1}{T} \)
B. \( V T \) and \( V \)
c. \( T \) and \( V \)
D. \( \quad P \) and \( \frac{1}{V} \)


Explain how to human ear works.


The smog is essentially caused by the
presence of
\( A \cdot O_{2} \) and \( O_{3} \)
B. \( O_{2} \) and \( N_{2} \)
c. Oxide of sulphur and Nitrogen
D. \( O_{3} \) and \( N_{2} \)


If K.E. of an electron, \( \alpha \) -particle and a proton are represented by
\( \boldsymbol{E}_{1}, \boldsymbol{E}_{2} \) and \( \boldsymbol{E}_{3} \) respectively, (provided all these have same de Broglie wavelength) then:
A. \( E_{1}=E_{2}=E_{3} \)
B . \( E_{1}>E_{2}>E_{3} \)
c. \( E_{1}>E_{3}>E_{2} \)
D. \( E_{2}>E_{3}>E_{1} \)


When a hydrogen atom is raised from
the ground state to and excited state
A. P.E increases and K.E decreases
B. P.E decreases and K.E increases
c. Both energy (K.E and P.E) increases
D. Both K.E and P.E decreases


What do you mean by resonance in
\( L C R \) series circuit? Write the formula
for resonant frequency.


\( \alpha=\frac{F v^{2}}{\beta^{2}} \log _{e}\left(\frac{2 \pi \beta}{v^{2}}\right) \) where \( F= \) force
= velocity
Find the dimensions of \( \alpha \) and \( \beta \)


In L-D converter pure oxygen is used for
oxidation while in Bessemer process air is used for the same purpose. Which of these is better and why?
A. nitrogen in air makes the steel brittle
B. nitrogen away from lot of heat
\( c \cdot \) both 1 and 2
D. none of these


\( \mathbf{0 . 2 x + 0 . 1 y}=\mathbf{2 5} \)
\( \mathbf{2 ( x - 2 ) - 1 . 6 y}=\mathbf{1 1 6} \)


An electric dipole as shown is free to
move and rotate.lt will
A. Rotate clock - wise and move to the left
B. Rotate anti clock wise and move to the right
C. Rotate clock wise and move to the right
D. Rotate anticlockwise and move to the left


Find the area of the trapezium ABCD in which \( A B \| D C, A B=18 \mathrm{cm}, \angle B=\angle C= \)
\( 90^{\circ}, C D=12 \mathrm{cm} \) and \( A D=10 \mathrm{cm} \)


If the sum of \( n \) terms of an A.P. is \( 3 n^{2}+ \)
\( 5 n \) and its \( m^{t h} \) term is \( 164 . \) Find the
value of \( m \)


A man walks \( 20 \mathrm{m} \) at an angle of \( 60^{\circ} \) east of north. How far towards north has
he traveled?
A . \( 10 m \)
в. 20m
\( \mathrm{c} \cdot 10 \sqrt{3} m \)
D. \( 10 / \sqrt{3} m \)


Which of the following element forms
\( \boldsymbol{p}_{\boldsymbol{\pi}}-\boldsymbol{p}_{\boldsymbol{\pi}} \) bond with itself?
A. Se
B. Te
\( c \cdot N \)
D. P


Which of the following is not oxidized by
\( \boldsymbol{O}_{3} ? \)
A. KI
в. \( F e S O_{4} \)
c. \( K M n O_{4} \)
D. \( K_{2} M n O_{4} \)


State whether true or false.
The image formed in a plane mirror is formed as far behind the mirror as the
object is in front of it.
A. True
B. False


Which of the following examples exhibits zero displacement with non-
zero distance?
A. A runner running one round on a circular track
B. A cyclist riding on a straight road
c. A aeroplane cruising in air
D. None of these


Divide:
0.03 by 100


Which of the following pairs of
compound are positional isomers?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-C-C H_{3} \) and \( C H_{3}-C H_{2}- \)
\( C H_{3}-C H_{2}-C H_{2}-\underset{O}{C}_{O}-C H_{3} \)
\( C-C H_{2}-C H_{3} \)
\( _{O} \)
\( \| \)
B. \( C H_{3}-C H_{2}-C H_{2}-C-C H_{3} \) and \( C H_{3}-C H- \)
\[
\begin{aligned}_{\|} &_{C H_{3}} \end{aligned}
\]
\( C H_{2}-C H O \)
\( \mathbf{c} \cdot C H_{3}-C H_{2}-C O-C H_{2}-C H_{3} \) and \( \left(C H_{3}\right)_{2}-C H \)
\( C H_{2}-C H O \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C H O \) and \( C H_{3}- \)
\( C H_{2}-C H_{2}-\stackrel{\|}{C}-C H_{3} \)


The functional group present in the final
product is :
A. \( O H \)
в. СООН
\( c . C H O \)
D. None of the above


Planar structure is shown by:
\( \mathbf{A} \cdot C O_{3}^{2-} \)
в. \( B C l_{3} \)
\( \mathbf{c} \cdot N\left(S i H_{3}\right) \)
D. All of these


f \( p=2-a \) then prove that \( a^{3}+6 a p+ \)
\( \boldsymbol{p}^{3}-\boldsymbol{8}=\boldsymbol{0} \)


The rate constant for forward and
backward reaction of hydrolysis of ester are \( 1.1 \times 10^{-2} \) and \( 1.5 \times 10^{-3} \) per
minute respectively
Equilibrium constant for the reaction is
\( C H_{3} C O O C_{2} H_{5}+H_{2} O \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \)
A .4 .33
B. 5.33
\( c \cdot 6.33 \)
D. 7.33


A cell of e.m.f. \( \mathrm{E} \) and internal resistance
is connected in series with an external
resistance nr then the ratio of the
terminal potential difference to E.M.F. is
A \( \cdot 1 / n \)
B. \( 1 / n+1 \)
\( c \cdot n / n+1 \)
D. \( n+1 / n \)


At equimolar concentrations of \( \boldsymbol{F} \boldsymbol{e}^{2+} \)
and \( F e^{3+}, \) what must \( \left[A g^{+}\right] \) be so that
the voltage of the galvanic cell made
from the \( \left(A g^{+} \mid A g\right) \) and \( \left(F e^{3+} \mid F e^{2+}\right) \) electrodes equals zero? \( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{A} \boldsymbol{g}^{+} \rightleftharpoons \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{A} \boldsymbol{g} \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{o} \mid \boldsymbol{A} \boldsymbol{g}}^{o}=\boldsymbol{0 . 7 9 9 1} ; \boldsymbol{E}_{\boldsymbol{F e}^{3+} \mid \boldsymbol{F} e^{2-}}=\mathbf{0 . 7 7 1} \)
A .0 .34
B. 0.44
c. 0.47
D. 0.61


Frame the given statement into a mathematical expression: "Thrice of a number increased by 150 ."
A. \( 150-x \)
B. \( 3 x-150 \)
c. \( 3 x+150 \)
D. None of these


A curve has equation \( \boldsymbol{y}=(2 x-1)^{-1}+ \)
\( 2 x . x \neq \frac{1}{2} \)
Find \( \frac{d y}{d x} \) and \( \frac{d^{2} y}{d x^{2}} \)


The working principle of a ball point pen is:
A. Bernoullis theorem
B. Surface tension
c. Gravity
D. Viscosity


A capacitor of capacitance \( \boldsymbol{C}=\mathbf{1 5 p} \boldsymbol{F} \)
is charged with voltage \( V=500 V . \) The
electric field inside the capacitor with
dielectric is \( 10^{6} V / m \) and the area of the plate is \( 10^{-4} m^{2}, \) then the dielectric
constant of the medium is : \( \left(\varepsilon_{0}=\right. \)
\( 8.85 \times 10^{-12} \) in S.l.units
A. 12.47
B. 8.47
c. 10.85
D. 14.85


Passengers standing in a bus are thrown outwards when the bus takes a
sudden turn, Because of:
A. Outward pull on them
B. Inertia
c. change in momentum
D. change in acceleration


If a magnetic field \( B \) points in the
positive x direction, what is the magnitude of the emf developed in the
wire when \( B \) increases at the rate of \( 3 m \)
\( \boldsymbol{T} \boldsymbol{s}^{-1} ? \)


During puberty, the testes of boys ....... in size.
A. Enlarges
B. Shortens
c. Lengthens
D. Thickens


A bomb explodes on the moon. How long will it take for the sound to reach the
earth?
A. \( 1 d a y \)
B. \( 1000 s \)
\( c .10 s \)
D. None of these


A current of \( 2.0 \mathrm{A} \) is passed for 5 hours through a molten metal salt deposits 22.2 \( g \) of metal (At. mass: 177 u). The oxidation states of the metal in metal
salt is:
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)


Breathing rate ............. during physical exercise.
A. Increases
B. Decreases
c. Remains same
D. None of the above


A body of mass \( 40 \mathrm{kg} \) resting on rough horizontal surface is subjected to a
force \( P \) which is just enough to start the
motion of the body. If \( \mu_{s}=5, \mu_{k}= \)
\( \mathbf{0 . 4}, \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}, \) and the force \( P \) is
continuously applied on the body, then the acceleration of the body is?
A. zero
B . \( 1 m / s^{2} \)
\( \mathrm{c} \cdot 2 m / s^{2} \)
D. \( 2.4 m / s^{2} \)


Differentiate between gaseous and
sedimentary cycles.


\( 200 \mathrm{g} \) of hot water at \( 80^{0} \mathrm{C} \) is added to
300 g of cold water at \( 10^{0} \) C. Neglecting the heat taken by the container, calculate the final temperature of the
mixture of water. Specific heat
capacity of water \( =4200 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)


What are the products formed when ammonia reacts with excess chlorine?
A. \( \mathrm{N}_{2} \) and \( \mathrm{NCl}_{3} \)
B. NCls and HCl
c. \( \mathrm{N}_{2} \) and \( \mathrm{NH}_{4} \mathrm{Cl} \)
D. \( \mathrm{N}_{2} \) and \( \mathrm{HCl} \)


(a) Explain giving reasons, the basic difference in converting a galvanometer into
(i) a voltmeter and (ii) an ammeter
(b) Two long straight parallel
conductors carrying steady currents \( I_{1} \)
and \( I_{2} \) are separated by a distance \( ^{\prime} d^{\prime} \) Explain briefly, with the help of a suitable diagram, how the magnetic field due to one conductor acts on the
other. Hence deduce the expression for
the force acting between the two conductors. Mention the nature of this
force.


Suppose that the potential energy of a hypothetical atom consisting of a proton and an electron is given by \( \mathrm{U}=- \)
\( \mathrm{Ke}^{2} / 3 \mathrm{r}^{3} . \) Then if Bhor's postulates are applied to this atom, then the radius of
the \( n^{t h} \) orbit will be proportional to:
\( A \cdot n^{2} \)
\( B \cdot 1 / n^{2} \)
\( c \cdot n^{3} \)
\( D \cdot 1 / n^{3} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\boldsymbol{e}^{\sqrt{\boldsymbol{x}}} \)


\( C O_{2} \) gas along with solid \( (Y) \) is obtained when sodium salt \( (X) \) is
heated. \( (X) \) is again obtained when
\( C O_{2} \) gas is passed into aqueous solution of \( (\boldsymbol{Y}) \cdot(\boldsymbol{X}) \) and \( (\boldsymbol{Y}) \)
respectively are:
A \( . N a_{2} C O_{3} \) and \( N a_{2} O \)
в. \( N a_{2} C O_{3} \) and \( N a O H \)
c. \( N a H C O_{3} \) and \( N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3} \) and \( N a H C O_{3} \)


Why is the speed of sound different in
different media?


Choose the correct answers from the
alternatives given :
Transcription involves
A. synthesizing the protein on the ribosome
B. transferring information contained in the DNA to mRNA
c. joining amino acids by peptide bonds
D. transferring information from the mRNA to tRNA


Dr.
F. Went noted that if coleoptile tips were removed and placed on agar for
one hour, the agar would produce a bending when placed on one side of a freshly cut coleoptile stumps. Of what significance is this experiment.
A. It is basis of quantitative determination of small amounts of growth promoting substances
B. It supports the hypothesis that IAA is auxin
c. It demonstrated polar movement of auxins
D. It made possible the isolation and exact identification of auxin


Find the derivatives of \( x \cos x \)


In an angiospermic plant, endosperm is formed due to fertilization of secondary nucleus but it is absent in some of the
seeds viz. pea, bean, phaseolus (moong) etc. It is due to lack of
A. Certain enzymes
B. Dicotyledonous hormone
c. Growth hormone
D. None of the above


If the base of a parallelogram is \( (x+4) \)
altitude to the base is \( (x-3) \) and the
area is \( \left(x^{2}-4\right), \) then what is the actual
area equal to?
A. 60 sq units
B. 45 sq units
c. 77 sq units
D. 96 sq units


\( \boldsymbol{C C l}_{3} \boldsymbol{C H}(\boldsymbol{O H})_{2} \) is stable. It's
extraordinary stability is due to the presence of:
A. two \( O H \) groups on the same carbon
B. hydrogen bonding with \( C l \)
c. \( -C H O \) group present
D. all of the above


Primary alkyl halide \( C_{4} H_{9} B r \)
\( (a) \)
reacted with alcoholic KOH to give compound (b). Compound (b) is reacted with \( H B r \) to give (c) which is an isomer of (a). When (a) is reacted with sodium
metal it gives compound (d), \( C_{8} H_{18} \) which is different from the compound formed when n-butyl bromide is reacted with sodium. Give the structural
formula of (a) and write the equations for all the reactions.


Find out most correct statement.
A. In pteridophytes there is a connection between the main sporophytic plant and prothallus
B. In homosporous pteridophytes gametophyte is monoecious
C. Life cycle of pteridophyte is haplo-dilontic type
D. cones are formed in all pteridophytes


The points on the curve \( 12 y=x^{3} \) whose
ordinate and abscissa change at the
same rate, are
A \( \cdot(-2,-2 / 3),(2,2 / 3) \)
в. \( (-2,2 / 3),(2 / 3,2) \)
c. \( (-2,-2 / 3) \) only
D. \( (2 / 3,2) \) only


Identify the correct labels of \( A, B \) and \( C \)
in the following graph from the options
given below:
Ref. image
Root mean square speed \( \left(V_{r m s}\right) ; \) most
probable speed \( \left(V_{m p}\right) ; \) Average speed
\( \left(V_{a v}\right) \)
A \( \cdot A-V_{m p} ; B-V_{a v} ; C-V_{r m s} \)
B . \( A-V_{m p} ; B-V_{r m s} ; C-V_{a v} \)
c. \( A-V_{a v} ; B-V_{r m s} ; C-V_{m p} \)
D. \( A-V_{r m s} ; B-V_{m p} ; C-V_{a v} \)


Describe the important characteristics
of gymnosperms?


If \( f(x) \) be a quadratic polynomial such
that \( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=-\mathbf{3} \) and
\( \boldsymbol{f}^{\prime \prime}(\mathbf{0})=\mathbf{4} \)
then \( \int_{-1}^{1} f(x) d x \) is equal to
A . -3
в. \( 16 / 3 \)
c. 0
D. none of these


\( 56 \mathrm{g} \) of nitrogen and \( 96 \mathrm{g} \) of oxygen are mixed isothermally and at a total pressure of 10 atm. The partial pressures of oxygen and nitrogen (in atm) are \( _{\text {- - }} \) -respectively
\( A \cdot 4,6 \)
B. 5,5
c. 2,8
\( D \cdot 6,4 \)


If the K.E. of a body is increased by \( 300 \% \) its momentum will increase by
A. \( 100 \% \)
B. \( 150 \% \)
c. \( \sqrt{300 \%} \)
D. \( 175 \% \)


The ionization energy of the hydrogen atom is \( 13.6 e V . \) The potential energy of
the eletron in \( n=2 \) state of hydrogen
atom is
A. \( +3.4 e V \)
в. -3.4eV
\( \mathrm{c} .+6.8 \mathrm{eV} \)
D. - \( 6.8 e V \)


Pressure is also measured in
A. Joule
B. mm of Hg
c. mm of Ag
D. Metre


his question has multiple correct options
4
\( B \)
\( c \)
\( D \)


ABCDE...... is part of a polygon which has
interior angles of \( 160^{0} . \) CDLM is a
Square.
Find the value of \( x \) and \( y \) respectively.
A. 70,105
B. 70,150
c. 105,70
D. 150,70


If \( A=\tan ^{-1} \frac{1}{7} \) and \( B=\tan ^{-1} \frac{1}{3} \) then
This question has multiple correct options
A \( \cdot \cos 2 A=\frac{24}{25} \)
B. \( \cos 2 B=\frac{4}{5} \)
c. \( \cos 2 A=\sin 4 B \)
D. \( \tan 2 B=\frac{3}{4} \)


Which of the following is not a quadratic equation?
A \( \cdot x^{2}+6 y+2 \)
B. \( (x-2)+(x+2)^{2}+3 \)
c. \( (3 x-2)^{3}+\frac{1}{2} x-4 \)
D. \( 3 x^{2}-6 x+\frac{1}{2} \)


The odourless, poisonous gas mixed with smoke that arises from burning coal is:
A. carbon monoxide
B. nitrogen
c. carbon dioxide
D. methane


Find the mean deviation about mean for
the following data:
\[
\text { Score }(\boldsymbol{x}) \quad \boldsymbol{6} \quad \boldsymbol{2 0}
\]
18
Frequen
\[
2
\]
11
\( (f) \)


When you open a soft drink bottle, the
bubbles oozes through the opening. The bottle contains gas which is highly compressed. Guess the gas.
A. Dry ice
B. Carbon dioxide
c. oxygen
D. Nitrogen


The correct relation relating the potential energy U and \( r \) between two atoms is
A \( \cdot U_{(r)}=\frac{A}{r^{12}}+\frac{B}{r^{6}} \)
B. \( U_{(r)}=\frac{A}{r^{12}}-\frac{B}{r^{6}} \)
c. \( U_{(r)}=\frac{A}{r^{6}}-\frac{B}{r^{12}} \)
D. \( -U_{(r)}=\frac{K}{r^{2}} \)


Skin of reptiles is characterised by
A. Sweat gland
B. Oil gland
c. Hair
D. Scales


A person of \( 40 \mathrm{kg} \) is managing to be at rest between 2 vertical walls by
pressing one wall \( A \) by his hands and feet and \( \mathrm{B} \) with his back as shown in fie
The coeff. of friction between his body
and the wall is 0.8 . The normal force
exerted by the person is
\( \left(g-10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 250 N \)
B. \( 290 N \)
\( c \cdot 100 N \)
D. \( 106 N \)


The electronic configuration of neon is:
\( \mathbf{A} \cdot 1 \mathbf{s}^{2} 2 \mathbf{s}^{2} 2 \mathbf{p}^{6} \)
B. \( 1 \mathrm{s}^{2} \)
\( c \cdot 2 s^{2} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{2} \)


Depression of freezing point of which of the following solutions does represent the cryoscopic constant of water?
A. \( 6 \% \) by mass of urea in aqueous solution.
B. 100 g of aqueous solution containing 18 g of glucose.
c. 59 g of aqueous solution containing 9 g of glucose.
D. 1 M \( K C l \) solution in water.


Assertion
Zoological parks are the places where wild animals are kept in protected environments under human care and
which enable use to learn about their
food habits and behaviour.
Reason
Adequate arrangements for the treatment, medication, regular check up and pathological investigations are absolutely necessary to be made for the health, care and upkeep of the animals.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the following circuit the output \( Y \)
becomes zero for the input
combinations:
\( A \cdot A=1, B=0, C=0 \)
B. \( A=0, B=1, C=1 \)
C. \( A=0, B=0, C=0 \)
D. \( A=1, B=1, C=0 \)


Alluvial soils in India are
A. Found in desert
B. Least fertile
c. Very rare
D. Most extensive soils


Which of the following is true for a system whose equilibrium constant is
relatively small?
A. It will take a short time to reach equilibrium.
B. It will take a long time to reach equilibrium.
c. The equilibrium lies to the left.t
D. The equilibrium lies to the right
E. It requires a higher concentration of reactants to reach equilibrium.


State whether the following statements are true or false. Give reasons for your
answers.
For any real number \( \boldsymbol{x}, \boldsymbol{x}^{2} \geq \mathbf{0} \)
A. True
B. False


List the salient features of double helix
structure of DNA.


Components which have small value of K have affinity for :
A. stationary phase
B. solution
c. mobile phase
D. no phase


\( \frac{\frac{10}{e}}{x} \) \( \alpha \)
\( \overbrace{\infty} \)


In long sightedness image is formed-
A. On Retina
B. Infront of Retina
c. Behind Retina
D. on blind spot


Magnetic lines of force always cross
each other. Is the given statement true or false? Justify.


Which of the following was not explained by Bohr's atomic model
A. Splitting of spectral lines in Magnetic field
B. Splitting of spectral lines in electric field
C. Bohr model could not explain the uncertainty principle of Heisenberg.
D. All of the above


The number of gram molecules of hydrogen liberated by the passage of 1 Faraday of electricity through hydrogen ion solution is
A . 0.5
в. 1.0
\( c .0 .2 \)
D. 4.0


Consider the following reaction.
\[
\left.\right|_{\mathbf{C H O}} ^{\mathbf{C H O}}+\left.\mathbf{O H}^{-} \longrightarrow\right|_{\mathbf{C H}_{2} \mathbf{O H}} ^{\mathbf{O O}^{-}}
\]
A. It is not a disproportionation reaction
B. It is intramolecular redox reaction
C. \( O H^{-} \) is reducing as well as oxidising agent
D. \( (C H O)_{2} \) is a reducing as well as oxidising agent


If equal volume of following solutions are mixed, precipitation of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{I}_{2}\left(\boldsymbol{K}_{s p}=\mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{2 6}}\right) \) will not
occur only with:
A \( \cdot 10^{-4} M H g_{2}^{2+}+10^{-11} M I^{-} \)
B . \( 10^{-5} M \) H \( g_{2}^{2+}+10^{-10} M I^{-} \)
\( \mathbf{c} \cdot 10^{-11} M H g_{2}^{2+}+10^{-7} M I^{-} \)
D. \( 10^{-6} M H g_{2}^{2+}+10^{-9} M I^{-} \)


A triangle cannot have more than right angle(s).
A. one
B. two
c. three
D. zero


Answer the following questions:
1. Define instantaneous rate of reaction.
2. Explain pseudo first-order reaction with suitable example.


In the process of earthing, how does charges get discharged to Earth?
A. Through some conductor
B. Directly to the Earth
c. Through transformer
D. None of the above


A shopkeeper sells an article at its marked price (Rs. 7,500 ) and charges sales-tax at the rate of \( 12 \% \) from the
customer. If the shopkeeper pays a VAT of Rs. \( 180 ; \) calculate the price (inclusive
of tax) paid by the shopkeeper.


An iron rod of length \( 2 m \) and cross-
sectional area of \( 50 \mathrm{mm}^{2} \) stretched by
\( 0.5 m m, \) when a mass of \( 250 k g \) is hung from its lower end. Young's modulus of iron rod is
A \( \cdot 19.6 \times 10^{20} N / m^{2} \)
В. \( 19.6 \times 10^{18} \mathrm{N} / \mathrm{m}^{2} \)
C. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{15} N / m^{2} \)


A convex mirror always produces:
A. an erect, virtual image of diminished size
B. an erect, real image of diminished size
C . an erect, real and enlarged size
D. a virtual, erect and enlarged size


From below which of them are used in
electrostatic experiments and demonstrations?
A. conductors
B. Insulators
c. Semi conductors
D. None


Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitudes \( A=3.00 \) and \( B=3.00 . \) Their vector product is \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}=-\mathbf{5 . 0 0 \hat { k }}+\mathbf{2 . 0 0 \hat { \mathbf { i } }} \)
What is the angle between \( \vec{A} \) and \( \vec{B} \) ?
\( ^{\mathrm{A}} \cdot \sin ^{-1}\left[\frac{\sqrt{29}}{9}\right] \)
\( ^{\mathrm{B}} \cdot_{\cos ^{-1}}\left[\frac{\sqrt{29}}{9}\right] \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left[\frac{\sqrt{29}}{10}\right] \)
D. \( \sin ^{-1}\left[\frac{\sqrt{29}}{19}\right] \)


Express the following complex numbers
in the form \( r(\cos \theta+i \sin \theta) \)
\( 1+i \tan \alpha \)


What are vaccines? Who developed the
first vaccine?


The source is at some distance from an
obstacle. Distance between obstacle
and the point of observation is \( b \) and
wavelength of light is \( \lambda \). The distance of
\( \boldsymbol{n}^{t h} \) Fresnel Zone from the point
of observation is :
A \( \cdot \frac{b n \lambda}{2} \)
в. \( _{b-} \frac{n \lambda}{2} \)
c. \( _{b+\frac{n \lambda}{2}} \)
D. \( b-n \lambda \)


The time in which a force of \( 2 N \)
produces a change in momentum of \( 0.4 k g m s^{-1} \) in the body is
A . \( 0.2 s \)
в. 0.02
c. \( 0.5 s \)
D. \( 0.05 s \)


The fragrance of flowers can be felt as soon as one enters the room because of:
A. condensation
B. fusion
c. diffusion
D. solidification


\( \operatorname{Let} g(x)= \)
\( \left\{\begin{array}{ll}2(x+1), & -\infty<x \leq-1 \\ \sqrt{1-x^{2}}, & -1<x<1 \\ |x+1|, & 1 \leq x<\infty\end{array} \) then \right.
A \( \cdot g(x) \) is discontinuous at exactly three points
B . \( g(x) \) is continuous in \( (-\infty, 1] \)
C \( \cdot g(x) \) is continuous in \( [1, \infty) \)
D. \( g(x) \) has finite type of discontinuity at \( x=1, \) but continuous at \( x=-1 \)


What prevents backflow of blood inside the heart during contraction?
A. Valves in heart
B. Thick muscular walls of ventricles
c. Thin walls of atria
D. All of the above


Edible oil is not allowed to stand for a
long time in an iron or tin container
Give reasons.


For the moon to cease to remain the
earth's satellite its orbital velocity has to increase by a factor of
\( A \cdot 2 \)
B. \( \sqrt{2} \)
\( c \cdot 1 \sqrt{2} \)
D. \( \sqrt{3} \)


f \( f(x)=\sqrt{1+\cos ^{2}\left(x^{2}\right)}, \) then \( f^{\prime}(x) \) is?


Astragalus and calcaneum are part of
A. Fore limb
B. Hind limb
c. scapula
D. Clavicle


The Sl unit of momentum is :
A \( \cdot k g m s^{-1} \)
в. \( k g m s^{-2} \)
c. \( k g m s^{2} \)
D. \( k g m^{-1} s^{-1} \)


Find the value of \( k \) for which the
quadratic equation \( (k-2) x^{2}+ \)
\( 2(2 k-3) x+5 k-6=0 \) has equal
roots
\( A \)
B. 3
c. A and B both
D. none of these


Fill in the blank.
Five point charges, each of value \( +\boldsymbol{q} \boldsymbol{C} \) are placed on five vertices of a regular hexagon of side \( L \) m. The magnitude of the force on the point charge of value \( -q C \) placed at the centre of the
hexagon is \( N \)


Assertion
Consider \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. \)
\( \cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right. \)
Statement-1: Domain of \( f(x) \) is a
singleton.
Reason
Statement-2: Range of the function \( \boldsymbol{f}(\boldsymbol{x}) \)
is a singleton.
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1.
c. Statement- lis true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true


The velocity of an electron in the first
Bohr orbit of a hydrogen atom is:
A . \( 3.08 \times 10^{6} \mathrm{m} / \mathrm{s} \)
B. \( 2.18 \times 10^{6} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 2.78 \times 10^{6} m / s \)
D. none of these


The derivative of \( f(\tan x) \) with respect
\( \operatorname{tog}(\sec x) \) at \( \quad x=\frac{\pi}{4}, \) where \( f^{\prime}(1)= \)
\( \mathbf{2} ; \quad \boldsymbol{g}^{\prime}(\sqrt{\mathbf{2}})=\mathbf{4} \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
c. 1
D.


What happens to ferromagnetic substance heated above Curie
temperature?


Sewage is waste water released by:
A. homes
B. industries, hospitals
C. offices and other users
D. all of the above


mrs Razdan wants to use tiles of length
\( 20 \mathrm{cm} \) and breadth \( 10 \mathrm{cm} \) to cover the
floor of hger balcony shown in the figure.What is the area of the balcony? How many tiles does she neeed to buy \( (1 s q m=10,000 s q c m) ? \)


In a hypothetical star,two carbon nuclei fuse to form magnesium.The reaction is:(take :1amu \( \left.=\mathbf{9 3 1} \text { Me } \boldsymbol{V} / \mathbf{c}^{\mathbf{2}}\right) \)
\( ^{12} \boldsymbol{C}+^{12} \boldsymbol{C} \rightarrow^{24} \boldsymbol{M} \boldsymbol{g} \)
The energy released per carbon nuclei
is: (Mass of \( \left.^{24} M g=23.985 a m u\right) \)
A. 13.965 MeV
В. 11.12 Ме \( V \)
c. 6.982 MeV
D. 10.12 MeV


When the free ends of a tester are
dipped into a solution, the magnetic needle shows deflection.
A. True
B. False
c. Ambiguous
D. Data insufficient


A barometer made of very narrow tube
is placed at normal temperature and pressure. The coefficient of volume
expansion of mercury is 0.00018 per \( ^{\circ} C \) and that of the tube is negligible. The temperature of mercury in the
barometer is now raised by \( 1^{\circ} \mathrm{C} \), but the
temperature of the atmosphere does
not change. Then the mercury height in the tube remains unchanged.
A. True
B. False


Relation between amino acids and
proteins is similar to the one present
between
A. nucleotides and nucleic acids
B. RNA and DNA
c. glucose and fructose
D. all of the above


Find the time required to liberate 1 litre
of \( \boldsymbol{H}_{2} \) at \( \mathrm{STP} \) in an electrolytic cell
operating at 5 A.
A . 19 min
B. 24 min
c. 29 min
D. 14.5 min


Industrially, ammonia is obtained by direct combination between nitrogen and hydrogen. The formation of ammonia is promoted at:
\( A \cdot 1000 \) atm
B. 200 atm
\( c .25 \) atm
D. 1 atm


Maxwell's corrections to Ampere's law
was required when the later was
extended to:
A. a static situation
B. a non-static situation
c. a semi-static situation
D. a quasi-static situation


After reflection from a concave mirror, a
plane wave front becomes
A. Cylindrical
B. Spherical
c. Remains planar
D. None of the above


What is the volume of a cube whose
surface area is \( 150 m^{2} ? \)
A \( \cdot 25 m^{3} \)
в. \( 100 m^{3} \)
c. \( 125 m^{3} \)
D. \( 1000 m^{3} \)


The IUPAC name of the following molecule is:
A. 5,6 -Dimethylhept-2-ene
B. 2, 3-dimethylhept-5-ene
c. 5,6 -dimethylhept-3-ene
D. 5-isopropylhex-2-ene


Fermentation products of yeast are
\( \mathbf{A} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{C} \mathrm{O}_{2} \)
B. Methyl alcohol \( +\mathrm{CO}_{2} \)
C. Methyl alcohol + Water
D. Ethyl alcohol \( +\mathrm{CO}_{2} \)


The correct order of the strength of \( \boldsymbol{H}- \) bonds is:
A. \( H . . F>H . . O>H \ldots N \)
в. \( H . . N>H . . O>H \ldots . \)
c. \( H . . O>H . . N>H \dots F \)
D. \( H . . F>H . . N>H . . . O \)


How many inner and outer hair cells
does a normal human ear possess?
A . 25000
B. 30000
c. 27000
D. 50000


Find \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\mathbf{2} \boldsymbol{x}-\boldsymbol{x}^{2}}} \)


The wall of heart is made up of
A. Epicardium
B. Myocardium
c. Endocardium
D. All of the above


A point moves in a straight line so that its displacement \( x \) metre at a time \( t \) second is such that \( t=\left(x^{2}-1\right)^{1 / 2} \). Its
acceleration in \( m / s^{2} \) at time \( t \) second
is:
A \( \cdot \frac{1}{x-1} \)
в. \( \frac{1}{x^{3}} \)
c. \( \frac{-t}{x^{2}-1} \)
D. \( \frac{t}{x^{2}-1} \)


What is the conductivity of a
semiconductor if electron density \( = \)
\( 5 \times 10^{12} / c m^{3} \) and hole density \( =8 \times \)
\( \mathbf{1 0}^{13} / \mathbf{c m}^{3}\left(\boldsymbol{\mu}_{e}=\mathbf{2 . 3 m}^{2} \boldsymbol{V}^{-1} \boldsymbol{s}^{-1}, \boldsymbol{\mu}_{\boldsymbol{h}}=\right. \)
\( \left.0.01 m^{2} V^{-1} s^{-1}\right) \)
\( \mathbf{A} \cdot 5.634 \)
B. 1.968
c. 3.421
D. 8.964


Which of the following is a suitable example for illustrating the law of conservation of mass?
(Atomic mass of \( \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{H}=\mathbf{1} \)
g/mole)
A. 18 g of water is formed by the combination of \( 16 \mathrm{g} \) oxygen with 2 g of hydrogen
B. 18 g of water in liquid state is obtained by heating 18 g of ice
c. 18 g of water is completely converted into vapour state on heating
D. \( 18 \mathrm{g} \) of water freezes at \( 4^{\circ} \mathrm{C} \) to give same mass of ice


The third ionization energy amongst \( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B} e, \boldsymbol{B} \) and \( \boldsymbol{C} \) is lowest for
A . \( L i \)
в. \( B e \)
\( c . B \)
D. \( C \)


\( \left(x^{2}+y^{2}\right) d x+2 x y d y=0 \)
Solve the above equation.
A \( \cdot x\left(x^{2}+3 y^{2}\right)=c \)
B. \( x\left(3 x^{2}+y^{2}\right)=c \)
C \( \cdot y\left(3 x^{2}+y^{2}\right)=c \)
D. \( y\left(x^{2}+3 y^{2}\right)=c \)


Find the rate of change of the area of a
circular disc with respect to its
circumference, when the radius is 3
\( \mathrm{cm} .\left(\text { incm }^{2}\right) \)


The type of flow in which there is a
regular gradient of velocity in going from one layer to the next is called
laminar flow.
If true enter \( 1, \) for false enter 0


A partical having mass 10 g oscillates according to the equation \( \boldsymbol{x}= \) \( (2.0 c m) \sin \left[\left(100 s^{-1}\right) t+\frac{6}{\pi}\right] . \) Find
(a) the amplitude, the time period and
the force constant
(b) the position, the velocity and the
acceleration at \( t=0 \)


Integrate:
\( \int \frac{\boldsymbol{v}}{1-\boldsymbol{v}}= \)


The force on a hemisphere of radius 1
\( \mathrm{cm} \) if a parallel beam of monochromatic light of wavelength 500 nm. falls on it with an intensity of \( 0.5 \mathrm{W} / \mathrm{cm}^{2}, \) striking the curved surface in a direction which
is perpendicular to the flat face of the hemisphere is:
(Assume the collisions to be perfectly inelastic)
A. \( 5.2 \times 10^{-13} N \)
В. \( 5.2 \times 10^{-12} N \)
\( \mathrm{c} \cdot 5.22 \times 10^{-9} \mathrm{N} \)
D. 0 n


Find the set of values of \( b \) for which
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{b}(\boldsymbol{x}+\cos \boldsymbol{x})+\boldsymbol{4} \) is decreasing
on \( \boldsymbol{R} \)


Short / Long Answer Type Questions:
When and where does meiotic division
take place in cells? What is the significance of this type of cell division in the animals life?


A metallic rod of length \( l \) is hinged at
the point \( M \) and is rotating about an axis perpendicular to the plane of paper
with a constant angular velocity \( \omega . A \) uniform magnetic field of intensity \( B \) is acting in the region (as shown in the figure) parallel to the plane of paper. The potential difference between the
points \( \boldsymbol{M} \) and \( \boldsymbol{N} \)
A. is always zero
B. varies between \( \frac{1}{2} B \omega l^{2} \) to 0
\( ^{\mathbf{C}} \cdot_{\text {is always }} \frac{1}{2} B \omega l^{2} \)
D. is always \( B \omega l^{2} \)


Give the characteristics of magnetic
field lines.


Plants with joined stem and hollow
internodes are known as
A. Culms
B. Scape
c. Ephemerals
D. Lianas


Total no. of electron in \( N a \) having \( n \times \)
\( \ell=0 \) is :
\( \mathbf{A} \cdot \mathbf{5} \)
B. 2
\( c \cdot 6 \)
D. 8


\( \sum_{k=1}^{k} \)


f \( y=\tan ^{-1}\left[\frac{5 \cos x-12 \sin x}{12 \cos x+5 \sin x}\right] \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot-2 \)
D.


The graph of \( f(x) \) is shown above in the
\( x y \) -plane. The points \( (0,3),(5 b, b) \) and
\( (10 b,-b) \) are on the line described by
\( f(x) . \) If \( b \) is a positive constant, find the
coordinates of point \( C \)
\( \mathbf{A} \cdot(5,1) \)
B. (10,-1)
c. (15,-0.5)
(15, \( -0.5) \)
D. (20,-2)


Secretion of which hormone is
stimulated by strong acid in stomach and intestine?


Liquid ammonia or liquid sulphur dioxide are used in:
A. Refrigerators
B. Air conditioners
c. washing machines
D. Inverters


Three coins are tossed simultaneously:
\( P \) is the event of getting at least two
heads.
\( Q \) is the event of getting no heads.
\( R \) is the event of getting heads on second coin. Which of the following pairs is mutually exclusive?
This question has multiple correct options
A. \( Q, R \)
в. \( Q, P \)
c. \( P, R \)
D. None of these


Butylated hydroxy toluene is used in:
A. preventing oxidative rancidity of fats
B. preserving food grains
c. killing bacteria on living tissues
D. reducing stress and anxiety


How is silver extracted from argentite?


In the figure, \( \boldsymbol{O} \) is the point of
intersection of two chords \( A B \) and \( C D \)
such that \( O B=O D \), then triangles
\( O A C \) and \( O D B \) are:
A. Equilateral but not similar
B. Isosceles but not similar
c. Equilateral and similar
D. Isosceles and similar


A frog is levitated in magnetic field
produced by current in a vertical solenoid below the frog is:
A. Diamagnetic
B. Paramagnetic
c. Ferromagnetic
D. non-magnetic


For the reaction of sodium with water,
the balanced equation using the smallest whole numbers has which of
the following coefficients?
।. 1
II. 2
||I. 3
Select the correct option.
A . I only
B. III only
c. I and II only
D. II and III only
E. I, II and III


A motorist drives north for 35.0 minutes
at \( 85.0 k m / h \) and then stop for 15.0
minutes. He next continues north, travelling \( 130 \mathrm{km} \) in 2.00 hours. What is his total displacement:
\( \mathbf{A} \cdot 85 k m \)
B. \( 179.6 \mathrm{km} \)
c. \( 20 \mathrm{km} \)
D. \( 140 \mathrm{km} \)


Assertion
Atoms can neither be created nor
destroyed.
Reason
Under similar condition of temperature
and pressure, equal volume of gases
does not contain equal number of
atoms.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An object is placed at distance of \( 64 \mathrm{cm} \)
from a white screen. By placing a convex
lens at a distance of \( 32 c m \) from the
object, it is found that a distinct image of the object is formed on the screen. Calculate the focal length of the lens?


The correct set of quantum numbers for the unpaired electron of a chlorine atom is:
A \( \cdot 2,0,0,+\frac{1}{2} \)
в. \( _{2,1,-1,+\frac{1}{2}} \)
c. \( _{3,1,1, \pm} \frac{1}{2} \)
D. \( _{3,0,0, \pm} \underline{1} \)


Fill in the blank:
A group of a few stars, whose arrangement can be compared to the figure of some kind of animal or any other known thing, is called a
A. Nabula
B. constellation
c. Pluto
D. Stellar


Find equivalent resistance between \( \mathbf{X} \)
and \( Y \)
\( A \)
B. R/L
\( c \cdot 2 R \)
5. 5


Acetone is used:
A. for extraction of essential oils
B. as a constituent of liquid nail polish
C. both A and B
D. none of these


For every pair of continuous functions
\( \boldsymbol{f}, \boldsymbol{g}:[\mathbf{0}, \mathbf{1}] \rightarrow \boldsymbol{R} \) such that max
\( \{\boldsymbol{f}(\boldsymbol{x}): \boldsymbol{x} \in[\mathbf{0}, \mathbf{1}]\}= \)
\( \max \{g(x): x \in[0,1]\}, \) the correct
statement (s) is (are)
A \( \cdot(f(c))^{2}+3 f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
B \( \cdot(f(c))^{2}+f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
\( (f(c))^{2}+3 f(c)=(g(c))^{2}+g(c) \) for some \( c \in[0,1] \)
D \( \cdot(f(c))^{2}=(g(c))^{2} \) for some \( c \in[0,1] \)


A particle is falling freely under gravity from rest. In first \( t \) second it covers
distance \( x_{1} \) and in the next \( t \) second it
covers distance \( x_{2}, \) then \( t \) is given by:
A. \( \sqrt{\frac{x_{2}-x_{1}}{g}} \)
в. \( \sqrt{\frac{x_{2}+x_{1}}{2 g}} \)
c. \( \sqrt{\frac{\left(x_{2}-x_{1}\right)}{2 g}} \)
D. \( \sqrt{\frac{\left(x_{2}+x_{1}\right)}{g}} \)


If \( A=\{1,2,3,4,5,6,7,8\} \) and \( B=\{1,3,5 \)
73, then find \( A-B \) and \( A \cap B \)
\( A \cdot\{3,5\} \) and \{2,4,6\}
B. \{2,4,6) and (1,5\}
c. \{2,4,6,7\} and (1,3,5,6)
D. \{2,4,6,8\} and \{1,3,5,7\}


The anematic flagellum is found in
A. Peranema
B. Polytoma
c. cryptomonas
D. Urceolus


If the S.D. of a set of observations is 8
and if each observation is divided by -2 the S.D. of the new set of observations
will be
A . -4
B. -8
\( c .8 \)
\( D \)


Explain dipole-dipole interaction with suitable example.


Solve the system \( : \mathbf{6} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}=-\mathbf{3}, \boldsymbol{y}= \)
\( -2 x-7 \)
A. (-2,4)
()
в. (-1,2)
c \( .(-8,9) \)
D. (-7,8)


The genotype of offspring formed from Tt \( x \) tt will be
A. \( \pi \) and tt
B. Tt and tt
c. only tt
D. only TT


Find the distance between the points whose position vectors are given as follows \( \mathbf{4} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\mathbf{6} \hat{\boldsymbol{k}},-\mathbf{2} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
A . \( \sqrt{65} \)
B. \( \sqrt{69} \)
c. 13
D. none of these


A jet of water is projected at an angle
\( \theta=45^{\circ} \) with horizontal from point \( A \)
which is situated at a distance \( x=O A \)
\( =(a) 1 / 2 m,(b) 2 m \) from a vertical wall.
If the speed of projection is \( v_{0}= \)
\( \sqrt{10} m s^{-1}, \) find point \( P \) of striking of
the water jet with the vertical wall.


The pitch angle of deflection between
two successive base pairs in DNA double helix is
A \( \cdot 20^{\circ} \)
B. \( 34^{\circ} \)
\( c \cdot 36^{\circ} \)
D. \( 360^{\circ} \)


What are soaps and detergents?


Phosphorus has oxidation state of +3 in:
A. phosphorus acid
B. orthophosphoric acid
c. metaphosphoric acid
D. pyrophosphoric acid


Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?
A. A coenzyme
B. A hormone
c. An enzyme
D. An antibiotic


What is emulsion? How are emulsions
classified? Give example?


The number with which when 82 is
multiplied product remains the same.
\( \mathbf{A} \cdot 82 \)
B. 0
c. \( \frac{1}{82} \)
D.


A cell of emf 5 V can supply a total energy of \( 9000 \mathrm{J}, \) then the total charge that can be obtained from the cell would
be
A . 180
B. 18000
c. 1800
D. 18


If \( A \) and \( B \) are any two events such that \( P(A)=\frac{2}{5} \) and \( P(A \cap B)=\frac{3}{20}, \) then
the condition probability, \( \boldsymbol{P}\left(\boldsymbol{A} \mid \boldsymbol{A}^{\prime} \cup\right. \)
\( \left.B^{\prime}\right) \), where \( A^{\prime} \) denotes the complement
of \( A, \) is equal to:
A \( \cdot \frac{5}{17} \)
в. \( \frac{11}{20} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{8}{17} \)


Match the column.
List -
\( \| \)
A) Rayon Cationic Polymerisation
B) Glass
Organic Polymers
C) Polystyrene Inorganic polymers
D) Polyisoprene Anionic polymerisation
A. \( A-2, B-3, C-4, D-1 \)
в. \( A-3, B-2, C-4, D-1 \)
c. \( A-2, B-1, C-3, D-4 \)
D. \( A-2, B-3, C-1, D-4 \)


Which of the following is a redox
reaction:
A \( \cdot 2 \operatorname{Na}\left[A g(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[\operatorname{Zn}(C N)_{4}\right]+2 A g \)
в. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
c. \( N_{2} O_{5}+H_{2} O \rightarrow 2 H N O_{3} \)
D. \( A g N O_{3}+K I \longrightarrow A g I+K N O_{3} \)


n the figure \( D \) and \( E \) are the mid-
points of sides \( A B \) and \( A C \) respectively
of \( \Delta A B C . \) Find \( \angle E D B \)
A \( .110^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 70 \)
\( D \cdot 80 \)


Find the domain of the following function. \( y=\sqrt{-4 x^{2}+4 x+3} \)


The full name of'SONAR'is.
A. Sonography and Research
B. Solar Navigation and Research
C. Sound Navigation and Ranging
D. Sound Navigation and Research


Let \( p \) be a nonsingular matrix, and \( I+ \)
\( \boldsymbol{p}+\boldsymbol{p}^{2}+\ldots . .+\boldsymbol{p}^{n}=\mathbf{0}, \) then find \( \boldsymbol{p}^{-1} \)
A . \( I \)
B . \( p^{n+1} \)
c. \( p^{n} \)
D \( \cdot\left(p^{n+1}-I\right)(p-I) \)


If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi \)
then the value of \( x y+y z+z x \) is
A . -3
B.
\( c .3 \)
D. none of these


A mixture of \( a \) mol of \( C_{3} H_{8} \) and \( b \) mol of
\( C_{2} H_{4} \) was kept is a container of \( V \) L
which exerts a pressure of 4.93 atm at temperature T. Mixture was burnt in
presence of \( O_{2} \) to convert \( C_{3} H_{8} \) and
\( C_{2} H_{4} \) into \( C O_{2} \) in the container at the
same temperature. The pressure of gases after the reaction and attaining the thermal equilibrium with atmosphere at temperature T was
found to be 11.08 atm.

The mole fraction of \( C_{3} H_{8} \) in the
mixture is :
A .0 .25
в. 0.75
\( c \cdot 0.45 \)
D. 0.55


A mass slides down an inclined plane and reaches the bottom with a velocity
\( v . \) If the same mass is in the form of a
disc and rolls down the same inclined
plane, what will be its velocity at the bottom?
A \( . v \)
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \sqrt{2} v \)
D. \( \frac{v}{\sqrt{2}} \)


Substances react with each other and
form chemical bonds to:
A. become stable compounds
B. to decrease their energy
C. to increase their energy
D. to form newer compounds