In an examination hall there are four
rows of chairs. Each row has 8 chairs
one behind the other. There are two
classes sitting for the examination with
16 students in each class. It is desired
that in each row, all students belong to the same class and that no two
adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?


The integer \( n \) for which \( \lim _{x \rightarrow 0} \frac{(\cos x-1)\left(\cos x-e^{x}\right)}{x^{n}} \) is finite non
zero number is
A . 1
B. 2
\( c .3 \)
\( D \)


A stone thrown upward with a speed 'u' from the top of the tower reaches the ground with a velocity '3u'. The height of
the tower is :-
A \( \cdot \frac{3 u^{2}}{g} \)
в. \( \frac{4 u^{2}}{g} \)
c. \( \frac{6 u^{2}}{g} \)
D. \( \frac{9 u^{2}}{g} \)


Cork cells are impervious due to deposit
of
A. Cutin
B. Lignin
c. suberin
D. Chitin


Which codon does not have tRNA?
A. Start codon
B. Stop codon
c. Aua
D. GGG
E. UUU


Two block of mass \( m_{1} \) and \( m_{2} \) are kept
a part d from each other. What happen to
the magnitude of the force on \( m_{1} \) if the
mass of \( m_{2} \) is doubled?
A. It is quadrupled
B. It is doubleo
c. It remain the same
D. It is halved
E. It is quartered


\( 1.61 \mathrm{gm} \) of \( \mathrm{Na}_{2} \mathrm{SO}_{4} .10 \mathrm{H}_{2} \mathrm{O} \) contains
same number of oxygen atoms as
present in \( x \) gm of \( H_{2} S O_{4} \). The value of
\( x \) is :
A . 1.28
в. 1.38
c. 1.58
D. 1.78


Differences of any two sides of a
triangle is \( \ldots \ldots . . \) than the third side
A. May be less or more
B. More
c. Equal
D. Less


Which of the following occurs in
scattering?
A. Light is reflected back in the original direction.
B. Light is split into its spectrum.
C. Photons in the light wave are absorbed by the particles.
D. Absorption and re-emission of light energy by small particles.


A capacitor is charged using an external battery with a resistance \( x \) in
series. The dashed line shows the
variation of \( l n I \) with respect to time.
If the resistance is changed to \( 2 x, \) the
slope of new graph will be \( ^{\prime} 1 / k^{\prime} \) times of
the old slope. Then the value o \( k \) will be:


If \( a^{2}, b^{2}, c^{2} \) are in A.P. then the following
are also in A.P. True or False? If true
write 1 otherwise write 0 \( \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c}}, \frac{\boldsymbol{b}}{\boldsymbol{c}+\boldsymbol{a}}, \frac{\boldsymbol{c}}{\boldsymbol{a}+\boldsymbol{b}} \)


When drugs attach to allosteric sites on
enzymes, the shapes of active sites radically are affected so that the substrate molecules cannot recognise the active sites.
A. True
B. False


Longitudinal strain is calculated using the formula
A. Change in length/ original length
B. original length/change in length
c. original length \( \times \) change in length
D. original length - change in length


Although a stone and the Earth attract each other with equal force, why do we observe that only the stone falls towards the Earth but not the Earth rising towards the stone? Explain.


An athlete completes half a round of a
circular track of radius, \( \boldsymbol{R} \). Then, the
displacement and distance covered by the athlete are
\( \mathbf{A} \cdot 2 R \) and \( \pi R \)
B. \( \pi R \) and \( 2 R \)
c. \( R \) and \( 2 \pi R \)
D. \( 2 \pi R \) and \( R \)


If one attempts to dissolve lead (II)
oxide in acid, he would choose \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
acid.
If true enter 1 , else enter 0 .


n the following diagram, which particle
has highest \( e / m \) value?
\( A \)
B.
\( c \)
\( D \)


The ratio of magnetic dipole moment of
an electron of charge \( e \) and mass \( m \) in Bohr's orbit in hydrogen atom to its
angular momentum is
A \( \cdot \frac{e}{m} \)
B. \( \frac{m}{e} \)
c. \( \frac{2 m}{e} \)
D. \( \frac{e}{2 m} \)


The structure of compound'X' is:
\( A \)
\[
\mathrm{H}-\underset{\mathrm{O}}{\mathrm{C}}-\mathrm{O}-\mathrm{C}_{2} \mathrm{H}_{5}
\]
B.
\[
\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{C}-\mathrm{O}-\mathrm{C}_{2} \mathrm{H}_{5}
\]
\( c \)
\[
\begin{array}{c}
\mathrm{CH}_{3}-\mathrm{C}-\mathrm{O}-\mathrm{C}_{2} \mathrm{H}_{5} \\
\| \\
\mathrm{O}
\end{array}
\]
\( D \)
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{O}-\underset{\mathrm{O}}{\|}-\mathrm{CH}_{2}-\mathrm{C}_{2} \mathrm{H}_{5}
\]


If a unit vector \( \vec{a} \) makes an angle \( \frac{\pi}{3} \) with \( \hat{i}, \frac{\pi}{4} \) with \( \hat{j} \) and an accute angle \( \theta \) with \( \hat{k}, \) then find \( \theta \) and hence, the
components of \( \overrightarrow{\boldsymbol{a}} \).
A \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}-\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
B \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{-1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
C \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
D \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}-\frac{1}{2} \hat{k} \)


The radius of \( L a^{3+} \) (Atomic number of \( \boldsymbol{L} \boldsymbol{a}=\mathbf{5} \mathbf{7}) \) is \( \mathbf{1 . 0 6} \boldsymbol{A} . \) Which one of the
following given values will be closest to
the radius of \( L u^{3+} \) (Atomic number of
\( \boldsymbol{L} \boldsymbol{u}=\mathbf{7} 1) ? \)
A \( .1 .40 \AA \)
В. 1.06 А
c. \( 0.85 \dot{A} \)
D. 1.60 月


In the figure, if \( \angle q=140 \), what is the
value of \( \angle \boldsymbol{r}-\angle \boldsymbol{p} ? \)
\( A \cdot 0^{\circ} \)
B. \( 10^{\circ} \)
\( c .90^{\circ} \)
D. 130


For the reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \) at a given
temperature the equilibrium amount of
\( C O_{2}(g) \) can be increased by:
A. Adding a suitable catalyst
B. Adding an inertgas
c. Decreasing the volume of container
D. Increasing the amount of \( C O(g) \)


Find the place value of the digit 4 in the following.
\( \mathbf{8 7 4 5 8 3 6} \)


The standard potential for the reaction, \( \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot) \longrightarrow \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
is \( 0.028 V . \) What is the standard free
energy change for this reaction?
A. -3.702 kJ \( m o l^{-1} \)
B. -2.702 kJ \( \mathrm{mol}^{-1} \)
c. -5.702 k \( J \) mol \( ^{-1} \)
D. -4.702 kJ \( \mathrm{mol}^{-1} \)


Divide the polynomial \( p(x) \) by the
polynomial \( g(x) \) and find the quotient and remainder in each of the following:
(i) \( p(x)=x^{3}-3 x^{2}+5 x-3, g(x)= \)
\( x^{2}-2 \)
(ii) \( p(x)=x^{4}-3 x^{2}+4 x+5, g(x)= \)
\( \boldsymbol{x}^{2}+\mathbf{1}-\boldsymbol{x} \)
(iii) \( p(x)=x^{4}-5 x+6, g(x)=2-x^{2} \)


Which of these is a bioindicator?
A. Lichens tracing the presence of pollution
B. Fossil lichens
c. special type of litmus paper
D. None of the above


State whether given statement is True or False

The depletion layer in the p-njunction region is caused by diffusion of carriers.
A. True
B. False


When domestic sewage mixes with
river water
A. Small animals like rats will die after drinking river water.
B. The increased microbial activity releases micro nutrients such as iron
C. The increased microbial activity uses up dissolved oxygen.
D. The river water is still suitable for drinking as impurities are only about \( 0.1 \% \)


The number of solutions of the equation \( \mathbf{1}+\sin \boldsymbol{x} \cdot \sin ^{2} \frac{\boldsymbol{x}}{\mathbf{2}}=\mathbf{0}[-\boldsymbol{\pi}, \boldsymbol{\pi}] \) is
A . zero
B.
\( c \cdot 2 \)
\( D \)


If \( T \) represents the absolute temperature of an ideal gas, the volume coefficient of thermal expansion at constant pressure is proportional to:
A. \( T \)
B \( \cdot T^{2} \)
\( c \cdot 1 / T \)
D. \( 1 / T^{2} \)


What is allotropy? Name allotrops forms of sulphur.


Assertion
An electron cannot exist in the nucleus.
Reason

The de Broglie wavelength of an electron is much smaller than the diameter of
the nucleus.

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


f \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x= \)
\( \frac{f(x)}{x \sin x+\cos x}+\tan x+c, \) then
A \( \cdot f(x)=\frac{x}{\cos x} \)
B. \( f(x)=\frac{\cos x}{x} \)
c. \( f(x)=-\frac{x}{\cos x} \)
D. none of these


If \( a, b, c \) are real and \( b^{2}-4 a c \) is perfect
square then the roots of the equation
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0}, \) will be:
A. Rational \& distinct
B. Real \& equal
C. Irrational \& distanct
D. Imaginary \& distinct


What is absolute refractive index?
A. Refractive index with respect to air
B. Refractive index with respect to vacuum
C. Refractive index with respect to water
D. Refractive index with respect to glass


\( \mathbf{f} \boldsymbol{A}=\left|\begin{array}{cc}\mathbf{2} & \mathbf{0} \\ \mathbf{5} & -\mathbf{3}\end{array}\right| \boldsymbol{B}=\left|\begin{array}{cc}\mathbf{- 2} & \mathbf{1} \\ \mathbf{3} & \mathbf{-} \mathbf{1}\end{array}\right|, \) then
the find the trace of \( \left(A B^{T}\right)^{T} \)
A . 10
B. 12
\( c \cdot 14 \)
D. 16


Given two independence events \( A \) and
\( B, \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Two metallic spheres \( S_{1} \) and \( S_{2} \) are
made of the same material and have
identical surface finish. The mass of \( S_{1} \)
is three times to that of \( S_{2} \). Both
the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of
\( S_{1} \) to that \( S_{2} \) is :
A \( \cdot \frac{1}{3} \)
в. \( \left(\frac{1}{3}\right)^{\frac{1}{3}} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{1} \)


A block is pushed up a rough inclined
plane of \( 45^{\circ} . \) If the time of decent is
twice the time of ascent, the coefficient
of friction is
A. 0.6
B. 0.4
\( c \cdot 0.5 \)
D. 0.25


Assertion
Hydrogen resembles both, alkali metals
as well as halogens.
Reason
Hydrogen forms oxides, halides and sulphides, and exists as diatomic
molecule.
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


f \( a, b, c \) and \( d \) are linearly independent
set of vectors and \( k_{1} a+k_{2} b+k_{3} c+ \)
\( k_{4} d=0, \) then
A. \( k_{1}+k_{2}+k_{3}+k_{4}=0 \)
В. \( k_{1}+k_{3}=k_{2}+k_{4}=0 \)
c. \( k_{1}+k_{2}=k_{3}+k_{4} \)
D. None of the above


Derive an expression for the force per unit length acting on the two straight parallel current carrying conductors. In which condition will this force be
attractive and repulsive? Define the
standard unit of current


Metal solution is negatively charged.
A. True
B. False


A hall has dimensions \( 24 \mathrm{m} \times 8 \mathrm{m} \times 6 \)
m The length of the longest pole which can be accommodated in the hall is
A. \( 26 \mathrm{m} \)
B. 28 m
\( c \cdot 30 m \)
D. 36 m


What is the activation energy for a
reaction if the rate doubles when the
temperature is raised from \( 20^{\circ} \mathrm{C} \) to
\( \mathbf{3 5}^{\circ} \boldsymbol{C} ?\left(\boldsymbol{R}=\mathbf{8 . 1 3 4} \boldsymbol{J} \boldsymbol{m o l}^{-\mathbf{1}} \boldsymbol{K}^{-\mathbf{1}}\right) \)
A \( \cdot 15.1 \mathrm{kJ} \mathrm{mol}^{-1} \)
В. 342 k \( J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 269 k J \mathrm{mol}^{-1} \)
D. 34.7 kJ mol-


Find a cylinder which would have the
greatest volume for the given area \( S \) of
its total surface.


The principal functional group in
aspirin is:
A. Pheny
3. -соон
\( c, \) Ester
DAI


If the difference of two supplementary
angles is \( 40^{0}, \) then the measurement of
the greater angle is:
A \( \cdot 65^{\circ} \)
B . \( 110^{\circ} \)
\( c \cdot 130^{\circ} \)
D. 220


The function of 'buffer solution' is:
A. to increase the pH value in chemical reaction
B. to decrease the pH value on chemical reaction
C. to increase or decrease the pH value of according the need
D. to keep the pH value constante in chemical reaction


The range of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1}{5 \sin x-6} \epsilon[-a,-1 / b] \) Find \( a+b \)


Which of the following is not a branch of physics.?
A. Mechanics
B. Optics
c. cytogenetics
D. Electrodynamics


Differentiate: \( \frac{e^{x}}{\sin x} \)


If \( P(A)=\frac{6}{11}, P(B)=\frac{5}{11} \) and \( P(A \cup \)
\( B)=\frac{7}{11}, \) find \( P(A / B) \)


Two identical copper spheres carrying charges \( +Q \) and \( -9 Q \) separated by a certain distance has attractive force \( F \)
If the spheres are allowed to rouch each
other and moved to distance of
separation 'x'. So that the force between them becomes \( \frac{4 F}{9} \). Then \( X \) is equal to
A. \( d \)
B. \( 2 d \)
\( c \cdot d / 2 \)
D. \( 4 d \)


In a chemical reaction, when 14 g of sodium carbonate reacted with 10 g of acetic acid (ethanoic acid), then it was
observed that, 16.67 g of sodium acetate solution in water and 7.33 g of carbon dioxide were produced. Which law does this depicts?
A. Law of definite proportions
B. Law of conservation of mass
c. Law of constant proportions
D. Avogadro's law


The major product obtained in the
reaction is :
\( A \)
в.
\( c \)
\( D \)


For measuring voltage of any circuit, potentiometer is preferred to voltmeter
because
A. the potentiometer is cheap and easy to handle.
B. calibration in the voltmeter is sometimes wrong
c. the potential draws no current during measurement
D. range of the voltmeter is not as wide as that of the potentiometer


The figure shows three infinite nonconducting plates of charge perpendicular to the plane of the paper with charge per unit area \( +\sigma,+3 \sigma \) and \( -\sigma . \) The ratio of the net
electric field at that point \( A \) to that at point \( \mathrm{B} \) is \( 1 / x \). Find \( x \)


If in a \( \triangle A B C, \cos A=\frac{\sin B}{2 \sin C}, \) then it
is
A. An isosceles triangles
B. An equilateral triangle
C . A right angled triangle
D. None of these


State whether true or false:
The principal focus of a spherical mirror lie midway between the pole and centre of curvature.
A. True
B. False


The number of \( \sigma \) and \( (\pi) \) bonds present
in the sulphuric acid molecule are:
\( \mathbf{A} \cdot 6 \sigma 2 \pi \)
B. \( 6 \sigma \) \( 0 \pi \)
\( \mathbf{c} \cdot 2 \sigma 4 \pi \)
D. \( 2 \sigma 2 \pi \)


A ball of mass \( 0.2 k g \) is thrown against
the wall, the ball strikes the wall
normally with velocity of \( 30 m / s \) sand rebounds with velocity of \( 20 m / s \) Calculate the impulse of the force exerted by the ball on the wall
A . \( 2 N \)
в. \( -10 N \)
\( c .20 N \)
D. \( 40 N \)


Galvanization is applying a coating of
A \( . C r \)
в. \( C u \)
\( c \cdot Z n \)
D. \( P b \)


Outer light coloured region of wood is known as
A. Autumn wood
B. Spring wood
c. Heart wood
D. Sap wood


Solve :
\( \sqrt{2} x^{2}-\sqrt{3} x-3 \sqrt{2} \)


If organisms on the earth start dying, which group of organisms will be the last to die?
A. Monera and Plantae
B. Mycota and Monera
c. Plantae and Protista
D. Animalia and Mycota


Fill in the blank.
In a technical sense a substance with a
elasticity is one that requires a force to
produce a distortion-for example, a steel sphere.
A. high, small
B. high, large
c. low, large
D. low, small


Name the three constituent of an atom
and state their mass and charge of
each. How are they distributed in an atom?


What is glycogenolysis?


If sum of the 20 deviations from the
mean is 100 , then find the mean deviation


A circular track has a circumference of
\( 3140 \mathrm{m} \) with \( \mathrm{AB} \) as one of its diameter
shooter moves from A to B along the circular path with a uniform speed of 10
A. Distance covers by the scooter
B. Displacement of scooters
c. Time taken by the scooter in maching from A to B
D. None of these


The velocity-time graph below
represents the velocity of a toy train as
it moves north and south, with zero
velocity near the middle of the vertical
axis.

During which interval(s) is the toy train
speeding up?
A . A only
B. A and E only
c. \( A, B \) and \( C \) only
D. A and D only
E. \( c \) and D only


Which one is the last electron acceptor
over ETC in oxidative phosphorylation?
A \( . H_{2} \)
B. \( C y t a_{3} \)
c. cyt b
D. \( C O_{2} \)


The \( (\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C}) \cap\left(\boldsymbol{A} \cap \boldsymbol{B}^{C} \cap \boldsymbol{C}^{C}\right)^{C} \cap \)
\( C^{c} \) is equal to
\( \mathbf{A} \cdot B^{C} \cap C^{C} \)
в. \( A \cap C \)
\( c \cdot B \cap C^{c} \)
D. \( C \cap C^{c} \)


\( A B C D \) is a trapezium in which \( A B \| D C \) and its diagonals intersect
each other at the point \( O . \) Show that \( \frac{A O}{B O}=\frac{C O}{D O} \)


MATCH THE COLUMN
\( (C) \)
\( (D) \)
\( (A) \rightarrow p, s(B) \rightarrow p, s(C) \rightarrow q, r(D) \rightarrow r, s \)
\( \mathbf{A} \cdot 1 \)
B. \( 1 .(\mathrm{A}) \rightarrow \mathrm{q}, \mathrm{s}(\mathrm{B}) \rightarrow \mathrm{p}, \mathrm{s}(\mathrm{C}) \rightarrow \mathrm{q}, \mathrm{r}(\mathrm{D}) \rightarrow \mathrm{r}, \mathrm{s} \)
C \( . \) 1. \( (A) \rightarrow p, s(B) \rightarrow q, s(C) \rightarrow p, r(D) \rightarrow r, s \)
D. \( 1 .(A) \rightarrow q, s(B) \rightarrow p, s(C) \rightarrow p, r(D) \rightarrow r, s \)


The equilibrium constant for the
following reaction is \( 1.6 \times 10^{5} \) at \( 1024 \mathrm{K} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
Find the equilibrium pressure of \( \boldsymbol{H}_{2} \) gas if 10.0 bar of HBr is introduced into a
sealed container at \( 1024 \mathrm{K} \)
A \( .2 .8 \times 10^{3} \)
B. \( 5.2 \times 10^{-3} \)
c. \( 2.5 \times 10^{-2} \)
D. \( 2 \times 10^{-3} \)


A toroid of n turns, mean radius R and
cross-sectional radius a carries current
I. It is placed on a horizontal table taken as \( x-y \) plane. Its magnetic moment
\( \bar{M} \) is
A. is non-zero and points in the z-direction by symmetry
B. points along the axis of the toroid \( (\bar{M}=M \phi) \)
c. is zero, otherwise there would be field falling as \( \frac{1}{r^{3}} \) at large distances outside the toroid
D. is pointing radially outwards


A neutral atom of an element has \( 2 \mathrm{K}, 8 \mathrm{L} \)
\( 9 \mathrm{M} \) and \( 2 \mathrm{N} \) electrons
The total number of p-electron are :
\( \mathbf{A} \cdot \mathbf{6} \)
B. 12
c. 18
D. 24


Assertion
Internal forces cannot change linear
momentum.
Reason
Internal forces can change the kinetic
energy of a system.
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


Calcium imide on hydrolysis gives a gas \( B, \) which on oxidation by bleaching powder gives a gas \( C . \) Gas \( C \) on reaction with magnesium gives a compound \( D \), which on hydrolysis again gives a gas \( B \). Hence, \( B, C \) and \( D \) are respectively:
A \( \cdot N H_{3}, N_{2}, M g_{3} N_{2} \)
в. \( N_{2}, N H_{3}, M g N H \)
c. \( N_{2}, N_{2} O_{5}, M g\left(N O_{3}\right)_{2} \)
D. \( N H_{3}, N O_{2}, M g\left(N O_{2}\right)_{2} \)


Find \( n \) if \( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+ \)
\( \sin ^{-1}\left(\frac{16}{65}\right)=\frac{n \pi}{2} \)


Suppose 3 bulbs are selected at random
from a lot. Each bulb is tested and
classified as defective \( (D) \) or non-
defective \( (N) . \) Write the sample space of this experiment?


An article manufactured by a company
consists of two parts \( X \) and \( Y . \) In the
process of manufacture of the part \( \boldsymbol{X} . \mathbf{9} \)
out of 100 parts may be defective.
Similarly 5 out of 100 are likely to be
defective in part \( Y \). Calculate the
probability that the assembled product will not be defective.


Lithopone is mixture of :
A. \( Z n C O_{3}, B a C O_{3} \)
в. \( Z n S, N a_{2} S O_{4} \)
\( \mathrm{c} \cdot Z n S O_{4}, B a S O_{4} \)
D. \( Z n S, \) BaSO\( _{4} \)


A mixture of hydrogen and oxygen contains \( 20 \% \) by mass of hydrogen. What is the total number of molecules
present per gram of the mixture?


Find the binding energy of a body of
mass \( 50 \mathrm{kg} \) at rest on the surface of the
earth.
\( \operatorname{given} G=6.67 \times 10^{-11} N m^{2} / k g^{2} \)
\( \boldsymbol{R}=\mathbf{6 4 0 0 k m}, \boldsymbol{M}=\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 4}} \boldsymbol{k g} \)


The focal lengths of the objective and the eyepiece of an astronomical telescope are \( 20 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. If the final image is formed at a distance of \( 30 \mathrm{cm} \) from the eyepiece, find the separation between the lenses required for distinct vision
A. 32.4 \( \mathrm{cm} \)
B. 42.3 cm
c. \( 24.3 \mathrm{cm} \)
D. 30.24 \( \mathrm{cm} \)


The projection of a directed line segment on the co-ordinate axes are
\( 12,4,3, \) then the direction cosines of
the line are
A \( \cdot \frac{-12}{13}, \frac{-4}{13}, \frac{-3}{13} \)
В. \( \frac{12}{13}, \frac{4}{13}, \frac{3}{13} \)
c. \( \frac{12}{13}, \frac{-4}{13}, \frac{3}{13} \)
D. \( \frac{12}{13}, \frac{4}{13}, \frac{-3}{13} \)


Choose the correct answers from the
alternatives given.
Which one of the following body
structure describes the freshwater
hydra?
A. A swimming medusa with mouth pointing upward
B. A sessile medusa with mouth pointing upward
C. A sessile polyp form with mouth pointing downward
D. A freely moving polyp with mouth pointing upward


In a p-njunction diode, not connected to
any circuit
A. the potential is same everywhere.
B. the p-type side is at a higher potential than the n-type side.
C. there is an electric field at the junction directed from the n-type side to the p-type side.
D. there is an electric field at the junction directed from the p-type side to the n-type side.


If \( A B C D \) is a parallelogram and \( Q \) and \( R \)
are the circumcentres of the triangles \( A B C \) and \( A D C \) respectively, then \( A Q C R \) is always
A. A rectangle
B. A trapezium
c. A rhombus
D. None of these


Is it right to consider the mother responsible for a girl child?


Find the joint equation of the following pair of lines. \( x+2 y-1=0 \) and \( 2 x-3 y+2=0 \)


Which of the following compounds can be purified by steam distillation? This question has multiple correct options
A. Salicylaldehyde
B. Bromobenzene
c. p-Hydroxy benzaldehyde
D. Nitrobenzene


A closed thermally insulated vessel
contains \( 100 g \) of water at \( 0^{\circ} C . \) If the an
from this vessel in rapidly pumped out, intensive evaporation will produce cooling and as a result of this water will
freeze. How much ice will be formed by this method? If latent heat of fusion is
\( 80 c a l / g \) and of evaporation \( 560 c a l / g \)


A die is thrown three times and the sum
of three numbers obtained is \( 15 . \) The
probability of first throw being 6 is:
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)


Derive the expression for the motional
emf induced in a conductor moving in a uniform magnetic field.


Construct a \( \triangle A B C \) with \( A B= \)
\( \mathbf{3} c m, B C=4 c m \) and \( A C=5 c m \) and
find \( \boldsymbol{m} \angle \boldsymbol{A} \boldsymbol{C} \boldsymbol{B}=\boldsymbol{?} \)
A .37
B. 53
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


What is valency? Write valency of
hydrogen.


A ray of light after passing through a medium were spread up into different colours. The phenomenon is called:
A. Total internal reflection
B. Diffraction
c. Dispersion
D. Deviation


\( L i A l H_{4} \) is obtained by reacting an
excess of \( \quad \) with an ethereal
solution of \( \boldsymbol{A} \boldsymbol{l} \boldsymbol{C l}_{3} \)
A. Licl
в. LiН
c. \( L i \)
D. \( L i O H \)


The formula of a carbonyl complex of
cobalt, \( (C O)_{n} C o-C o(C O)_{n}, \) in which
there a single covalent \( C o-C o \) bond
is:
A. \( C o_{2}(C O)_{4} \)
в. \( \operatorname{Co}_{2}(\mathrm{CO})_{6} \)
c. \( \operatorname{Co}_{2}(C O)_{8} \)
D. \( C o_{2}(C O)_{10} \)


In p-type semiconductor major current carriers are:
A. negative ions
B. holes
c. electrons
D. all of these


As we move away from the nucleus, the energy of the electron
A. Increases
B. Decreases
c. Remains same
D. None of these


A sphere of mass m moving with velocity u h its another stationary sphere of same mass. If e is the coefficient of restitution, what is the
ratio of velocities of two spheres after
the collision?
A \( .1: e \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{1+e}{1-e} \)
D. \( 1: e^{2} \)


A person's limbs are swollen and he is suffering from weakness and fatigue. This organ may be damaged in him.
A. Kidney
B. Brain
c. Heart
D. Liver


If kinetic energy' \( K \), velocity' \( v \) ' and
time 'T' are chosen as the fundamental
units, the formula for surface tension \( S \)
\( = \)
\( (A \text { is a constant }) \)
\( ^{\mathbf{A}} \cdot \frac{v^{2} K^{2}}{A K} \)
в. \( \frac{v^{2}}{A K T} \)
c. \( \frac{A K T^{2}}{v^{2}} \)
D. \( \frac{A K}{v^{2} T^{2}} \)


Variance of first 20 natural number is
A \( \frac{133}{4} \)
в. \( \frac{379}{12} \)
\( ^{c} \cdot \frac{133}{2} \)
D. \( \frac{399}{4} \)


Which one of the following possess the minimum boiling point :
A. 1-Pentyne
B. 1-Butyne
c. n-Butane
D. Isobutane


Three identical bulbs are connected in
parallel with a battery. The current drawn from the battery is 6 A. If one of the bulbs gets fused, what will be the total current drawn from the battery?
\( A \cdot 6 A \)
B. 2A
\( c \cdot 4 A \)
D. 5A


Find the equation of the plane which contains the line of intersection of the planes \( \vec{r} \cdot(\hat{i}+2 \widehat{j}+3 \widehat{k})-4= \)
\( \mathbf{0}, \overrightarrow{\boldsymbol{r}} \cdot(2 \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\widehat{\boldsymbol{k}})+\boldsymbol{5}=\boldsymbol{0} \) and which is
perpendicular to the plane \( \vec{r} \cdot(5 \hat{i}+3 \widehat{j}-6 \widehat{k})+8=0 \)


A body is projected with velocity
\( 24 m s^{-1} \) making an angle \( 30^{\circ} \) with the horizontal. The angle made by the direction of the projectile with the horizontal at \( 2 s \) from start is:
A \( \cdot \tan ^{-1} \frac{2}{3 \sqrt{3}} \)
B. \( \tan ^{-1} \frac{1}{3 \sqrt{3}} \)
c. \( \tan ^{-1} \frac{2}{3} \)
D. \( \tan ^{-1} \frac{1}{3} \)


Find the coordinates of the point on the
X-axis which is at distant 5 units from
\( A(4,4) \)


Divide the line segment \( A B=12 \mathrm{cm} \) in
6 equal parts.


Find the measure of the complementary
angle of each of \( 20^{\circ} \)
\( \mathbf{A} \cdot 50^{\circ} \)
B. \( 70^{\circ} \)
\( c \cdot 160^{\circ} \)
D. \( 80^{\circ} \)


Relation between coefficient of static
friction \( \mu_{s} \) and angle of friction is
B \( \cdot \mu_{s}=\cos \theta \)
c. \( \mu_{s}=\tan \theta \)
D. None of these


Find the coordinates of the point \( \boldsymbol{P} \)
which divides line segment \( Q R \)
internally in the ratio \( m: n \) in the
following example:
\( Q \equiv(-5,8), R \equiv(4,-4) \) and \( m: n=2: 1 \)
is (1,0)
If true then enter 1 and if false then
enter 0


Solve the following equations graphically
\[
\begin{array}{l}
\mathbf{2 x}+\boldsymbol{y}=\mathbf{6} \\
\mathbf{2 x - y}+\mathbf{2}=\mathbf{0}
\end{array}
\]


Stereoisomers have different:
A. molecular mass
B. molecular formula
c. structural formula
D. configuration


A particle is acted upon by a force of
constant magnitude which is always perpendicular to the velocity of the
particle, the motion of the particle takes place in a plane. It follows that:
A. Its velocity is constant
B. Its acceleration is constant
C. Its kinetic energy is constant
D. It moves in a straight line


Match the following metals listed in Column I with extraction processes
listed in Column II:


The Sl unit of inductance, henry, can be written as:
A. weber/ampere
B. volt second/ampere
c. joule/ampere \( ^{2} \)
D. all of these


Point out the right statements about the validity of Kirchhoff's junction rule.
A. It is based on conservation of charge
B. Outgoing currents add up and are equal to incoming currents at a junction
C. Bending or reorienting the wire does not change the validity of Kirchhoff's junction rule
D. All of above


For the reaction \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g), \) the forward reaction at constant
temperatureis favoured by:
This question has multiple correct options
A. Introducing an inert gas at constant volume.
B. Introducing chlorine gas at constant volume.
c. Introducing an inert gas at constant pressure.
D. Increasing the volume of the container.


When \( A g N O_{3} \) was treated with \( 5.08 g \) of a sample iron chloride, \( 11.48 g \) pf \( \mathrm{AgCL} \) was formed \( 6.51 g \) of another iron chloride gave \( 17.22 g \) of \( A g C l \) on
treatment with \( A g N O_{3} . \) Show that
these results illustrate the law of
multiplle proportions. [R.A.M. \( A g=108, F e=56 \text { and } C l=35.5] \)


If the light moving in a straight line bends by a small but fixed angle, it may be a case of:
A. reflection
B. refraction
c. dispersion
D. both (a) \& (b)


The thermal dissociation equilibrium of
\( \boldsymbol{C a C O}_{3}(s) \) is studied under different
conditions.
\[
\begin{array}{r}
\boldsymbol{C a C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+ \\
\boldsymbol{C O}_{2}(\boldsymbol{g})
\end{array}
\]
For this equilibrium, the correct statement(s) is (are):
A. \( \Delta H \) is dependent on \( T \)
B. \( K \) is independent of the initial amount of \( C a C O_{3} \)
C. \( K \) is dependent on the pressure of \( C O_{2} \) at a given \( T \)
D. \( \Delta H \) is independent of the catalyst, if any


If \( M \) is the element of the actinoid
series, the degree of complex formation
decrease in the order:
A \( \cdot M^{4+}>M^{3+}>M O_{2}^{2+}>M O_{2}^{+} \)
B . \( M O_{2}^{+}>M O_{2}^{2+}>M^{3+}>M^{4} \)
c. \( M^{4+}>M O_{2}^{2+}>M^{3+}>M O_{2}^{\text {th }} \)
D. \( M O_{2}^{2+}<M O_{2}^{+}<M^{4+}>M^{3+} \)


The kidneys resemble the contractile vacuoles of protozoans in
A. Expelling out excess of water
B. Expelling out glucose
c. Expelling out urea and uric acid
D. Expelling out salts


Find the electric field at \( z<-\mathbf{0 . 5 d} \)
\( \mathbf{A} \cdot E=0 \)
B \( \cdot E=-\frac{\sigma}{\epsilon_{0}} \hat{k} \)
\( \mathbf{c} \cdot E=\frac{\sigma}{\epsilon_{0}} \hat{k} \)
D. \( E=\frac{\sigma}{2 \epsilon_{0}} \hat{k} \)


The effective resistance in between \( \boldsymbol{A} \)
and \( B \) is
Choose answer.
\( A \cdot \frac{R}{1} \Omega \)
B. \( 4 R \Omega \)
\( c . R \Omega \)
D. Zero


A vertical to stands on a horizontal
plane and is surmounted by a vertical flag staff of height 6 meters. At point 0 n the \( p \) angle of elevation of the bottom and the top of the flag staff are respectively \( 30^{\prime} \) and \( 60^{*} \). Find the height of tower-
A. \( 5 \mathrm{m} \)
B. 2.5m
\( c \cdot 10 m \)
D. 7.5m


An electric dipole is placed in an electric field generated by a point charge.
A. The net electric force on the dipole must be zero
B. The net electric force on the dipole may be zero
c. The torque on the dipole due to the field must be zero.
D. The torque on the dipole due to field may be zero


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


The force experienced by a current carrying conductor placed in a magnetic field is largest when magnetic feild,current and length of conducter is more
Type 1 for true and 0 for false


According to Faraday's law of electromagnetic induction:
A. electric field is produced by time varying magnetic flux
B. magnetic field is produced by time varying electric flux
c. magnetic field is associated with a moving charge
D. none of these


Tendons connect
A. A muscle with a muscle
B. A muscle with a bone
C. A bone with another bone
D. A bone with a ligament


Constantan wire is used for making
standard resistance, because it has
A. high melting point.
B. low specific resistance
C . high specific resistance.
D. negligible temperature coefficient of resistance.


Variance of the distribution
\( \mathbf{7 3}, \mathbf{7 7}, \mathbf{8 1}, \mathbf{8 5}, \dots, \mathbf{1 1 3} \) is
A . 10
в. 160
\( c \cdot 161 \)
D. None of these


Prove by mathematical induction that
n. \( 1+(n-1) 2+(n-2) 3+\ldots+2(n-1)+1 . n \)
\( =\frac{n}{6}(n+1)(n+2) \)
A . True
B. False


Identify the chemical which is used to detect leakage of LPG ;
A. Methyl mercaptan
B. Propyl mercaptan
c. Ethyl mercaptan
D. n-butyl mercaptan


Velocity of sound is maximum in
A . solids
B. liquids
c. \( g \)ases
D. ionized gases


Molten \( N a C l \) conducts electricity due
to the presence of:
A. Free molecules
B. Free ions
c. Free electrons
D. Free atoms


Suppose \( x_{1} \& x_{2} \) are the point of
maximum and the point of minimum respectively of the function \( f(x)= \) \( 22 x^{3}-9 a x^{2}+12 a^{2} x+1 \) respectively
then for the equality \( x_{1}^{2}=x_{2} \) to be true
the value of \( ^{\prime} a^{\prime} \) must be
A . 0
в. \( \quad a=\frac{3+\sqrt{5}}{(3-\sqrt{5})} \)
c. \( _{a}=\frac{3+\sqrt{5}}{(3-\sqrt{5})^{2}} \)
D. None of these


If \( \lim _{x \rightarrow 0}(\cos x+a \sin b x)^{\frac{1}{x}}=e^{2} \) then
the possible values of \( ^{\prime} a^{\prime} \&^{\prime} b^{\prime} a r e: \)
This question has multiple correct options
A \( . a=1, b=2 \)
В. \( a=2, b=1 \)
c. \( a=3, b=2 / 3 \)
D. \( a=2 / 3, b=3 \)


In the figure at right, \( A B C D \) is a
parallelogram \( \angle B A O= \)
\( \mathbf{3 0}^{\circ}, \angle \boldsymbol{D A O}=\angle \mathbf{4 5}^{\circ} \) and \( \angle \boldsymbol{C O D}= \)
\( \mathbf{1 0 5}^{\circ} . \) Calculate
\( \angle C B D \)
A \( \cdot 60^{\circ} \)
B. 30
\( c \cdot 20 \)
D. None of these


If \( x \) and \( y \) are sides of two squares such
that \( y=x-x^{2} \). Find the rate of change
of area of second square (side \( y \) ) with respect to area of the first square (side
\( x) \) when \( x=1 \mathrm{cm} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Column - I Column - II
(Metals) (Ores)
A) Tin
1) Calamine
B) Zinc
2) Cassiterite
C) Titanium
3) Cerrusite
D) Lead
4) Rutile
A . A-1, B-2, C-3, D-4
B. A-2, B-1, C-4, D-3
c. \( A-4, A-3, C-2, D-1 \)
D. A-2, B-1, C-3, D-4


Formula for
polygon is \( (\boldsymbol{n}-\mathbf{2}) \times \mathbf{1 8 0}^{\boldsymbol{o}} \)
A. sum of exterior angles
B. sum of interior angles
c. number of edges
D. number of diagonals


A unit vector \( a \) makes an angle \( \frac{\pi}{4} \) with z-axis.. If \( a+i+j \) is a unit vector, then
\( a \) is equal to
A \( \cdot \frac{i}{2}+\frac{j}{2}+\frac{k}{\sqrt{2}} \)
В \( \cdot \frac{i}{2}+\frac{j}{2}-\frac{k}{\sqrt{2}} \)
c. \( -\frac{i}{2}-\frac{j}{2}+\frac{k}{\sqrt{2}} \)
D. None of these


If \( A, B \) are the feet of the perpendiculars
from (2,4,5) to the \( x \) -axis, \( y \) -axis
respectively, then the distance \( A B \) is
A \( .2 \sqrt{5} \)
B. \( \sqrt{29} \)
c. \( \sqrt{41} \)
D. \( 3 \sqrt{5} \)


toppr \( E \)
Q Type your question
\( \operatorname{cooc}_{2} \mathbf{H}_{5} \)
\( A \)
B.
\( c \)
\( D \)


Solve \( \tan \theta+\tan 2 \theta+ \)
\( \sqrt{3} \tan \theta \tan 2 \theta=\sqrt{3} \)
A. \( \theta=\frac{n \pi}{3}+\frac{\pi}{3}, n \in Z \)
в. \( \theta=\frac{n \pi}{3}+\frac{\pi}{6}, n \epsilon Z \)
c. \( \theta=\frac{n \pi}{3}+\frac{\pi}{12}, n \in Z \)
D. \( \theta=\frac{n \pi}{3}+\frac{\pi}{9}, n \in Z \)


Which of the given alkaline earth metal is hardest of all alkaline earth metals?
\( A \cdot \) Mg
B. ca
c. Ве
D. sr


Find the number of words each
consisting of 3 vowels and 3 consonants that can be formed from the letters of
the word Circumference.
A . 22100
B . 40020
c. 32400
D. 64000


Find the nearest integer to the cube root
of 46656


If the acceleration due to gravity at the
surface of the earth is \( g \), the work done
in slowly lifting a body of mass \( m \) from
the earth's surface to a height \( \boldsymbol{R} \) equal to the radius of the earth is
\( ^{\mathrm{A}} \cdot \frac{m g R}{2} \)
в. \( 2 m g R \)
\( \mathrm{c} \cdot m g R \)
D. \( _{m g} \frac{R}{4} \)


The phases of the light wave at \( c, d, e \)
and \( f \) are \( \phi_{c}, \phi_{d}, \phi_{e} \) and \( \phi_{f} \) respectively.
It is given that \( \phi_{c} \neq \phi_{r} \)
\( \mathbf{A} \cdot \phi_{c} \) cannot be equal to \( \phi_{d} \)
B. \( \phi_{d} \) cannot equal to \( \phi_{\mathrm{e}} \)
\( \mathbf{c} \cdot\left(\phi_{d}-\phi_{f}\right) \) is equal to \( \left(\phi_{c}-\phi_{e}\right) \)
\( \mathbf{D} \cdot\left(\phi_{d}-\phi_{c}\right) \) is not equal to \( \left(\phi_{f}-\phi_{e}\right) \)


\( \mathbf{f} \boldsymbol{I}=\int \sin ^{-1}\left(\frac{\mathbf{2} \boldsymbol{x}+\mathbf{2}}{\sqrt{\mathbf{4} \boldsymbol{x}^{2}+\mathbf{8} \boldsymbol{x}+\mathbf{1 3}}}\right) \boldsymbol{d} \boldsymbol{x}= \)
\( (x+1) \tan ^{-1} \frac{2 x+2}{3}-\frac{A}{248} \log \left(4 x^{2}+\right. \)
\( 8 x+13)+C \) then \( A \) is equal to.


Cells are limited in size by the
A. Rate at which substances needed by the cell can enter the cell through its surface
B. Amount of material the cell can collect itself
C. Rate at which the cell can manufacture the genetic information
D. Amount of cell membrane the cell can produce


What is importance of sexual
reproduction in plant?


When a hydrogen atom is raised from
ground energy level to excited energy level, then
A. potential energy increases and kinetic energy decreases
B. kinetic energy increases and potential energy decreases
c. Both KE and PE increase
D. Both KE and PE decrease


Assertion
The \( O^{2-} \) ion and the neon atom have
similar chemical properties because:
Reason
the \( O^{2-} \) ion and the neon atom have the
same number of electrons.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Mention the exact location of the
following:
Islets of Langerhans.


Choose the incorrect formula out of the
four compounds for an elements \( \boldsymbol{X} \)
below:
A. \( X_{2} O_{3} \)
в. \( X_{2}\left(S O_{4}\right)_{3} \)
c. \( X P O_{4} \)
D. \( X_{2} C l_{3} \)


How many total isomeric amines are possible having molecular formula
\( C_{4} H_{11} N \) which gives a bad smelling
compound with \( \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3}+\boldsymbol{K} \boldsymbol{O H} ? \)
A. Five
B. Six
c. seven
D. Eight


Three numbers are in A.P. and their sum
is 21.Find the middle number.


Evaluate the following integral:
\( \int \frac{1}{\sqrt{1+4 x^{2}}} d x \)


Identify the odd term out and explain. Water, mercury, bromine, petrol.


The maleness of a child is determined
by
A. The \( x \) chromosome in the zygote
B. The Y chromosome in zygote
C. The cytoplasm of germ cell which determines the sex
D. Sex is determined by chance


Calculate to find whether the given
triangle is a right angled triangle.
4.10
B. Yes
C. Insufficient data
D. cannot calculate


If \( \boldsymbol{A}=\mathbf{5} \boldsymbol{p}^{2}-\boldsymbol{3} \boldsymbol{q}^{2}+\boldsymbol{r}^{2}, \boldsymbol{B}=-\boldsymbol{2} \boldsymbol{q}^{2}+ \)
\( \boldsymbol{3} \boldsymbol{p}^{2}-\boldsymbol{4} \boldsymbol{r}^{2} \) and \( \boldsymbol{C}=-\boldsymbol{7} \boldsymbol{r}^{2}+\boldsymbol{3} \boldsymbol{p}^{2}+\boldsymbol{2} \boldsymbol{q}^{2} \)
Find \( \boldsymbol{A}+\boldsymbol{B}-\boldsymbol{C} \)


Which of the following items are not bleached by bleaching powder? This question has multiple correct options
A. Straw
B. Silk
c. Ivory
D. None of the above


The figure above represents some of the lower energy levels of the hydrogen atom in simplified form.
If the transition of an electron from \( \boldsymbol{E}_{\mathbf{4}} \)
to \( E_{2} \) were associated with the
emission of blue light, which one of the
following transitions could be
associated with the emission of red
light?
\( \mathbf{A} \cdot E_{4} \) to \( E_{1} \)
B \( . E_{3} \) to \( E_{1} \)
\( \mathbf{c} \cdot E_{3} \) to \( E_{2} \)
D. \( E_{1} \) to \( E_{3} \)


A hammer of mass 5 kg moving with a speed of \( 2 m s^{-1} \) strikes the head of a nail driving it \( 20 \mathrm{cm} \) into the wall. Find the impulse(in N s).
\( A \cdot O \)
B. -100
\( c .-10 \)
D. -10000


The radius of the curved part of the wire is \( R=100 m m, \) the linear parts of the
wire are very long. Find the magnetic induction at the point \( O \) if the wire
carrying a current \( I=8.0 A \) has the
shape shown in figure.
A \( .0 .34 \mu T \)
в. \( 0.11 \mu T \)
c. \( 1.1 \mu T \)
D. \( 34 \mu \) 7


A reaction of hydrogen with which of the following is an example of both reduction and oxidation reactions?
A . \( S \)
в. \( N_{2} \)
\( c \cdot O_{2} \)
D. \( F_{2} \)


Assertion
Natural selection is the outcome of
difference in survival and reproduction among individuals that show variation
in one or more traits.
Reason
Adaptive forms of a given trait tend to become more common, less adaptive
ones become less common or
disappear.
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 number of terms with integral coefficients in the expansion of
\( \left(7^{1 / 3}+5^{1 / 2} \cdot x\right)^{600} \) is
A. 100
B. 50
\( c .101 \)
D. none of these


At what partial pressure, oxygen will have a solubility of \( 0.006 g L^{-1} \) in water
at \( 293 K ? \) Henry's law constant \( \left(K_{H}\right) \) of
\( O_{2} \) in water at \( 303 K \) is \( 46.82 k \) bar.
(Assume the density of the solution to be the same as that of water).


Study the given flowchart and identify
\( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N} \) respectively
*Produced from burning of coal and diesel
**Given off by petrol engines
A. Carbon dioxide, nitrogen oxides, methane, sulphur dioxide
B. Carbon monoxide, methane, sulphur dioxide, nitrogen oxides
C. Methane, carbon monoxide, carbon dioxide, sulphur dioxide
D. Sulphur dioxide, carbon monoxide, methane, nitrogen


A \( 2.00 m \) length of wire carrying \( 3.00 A \) of conventional current southward
through a \( 5.00 T \) magnetic field
directed straight up experience how much force due the field and in what
direction?
A. Amount of Force \( -7.5 N \), Direction of Force - west
B. Amount of Force \( -30.0 N \), Direction of Force - west
c. Amount of Force \( -7.5 N \), Direction of Force - east
D. Amount of Force \( -30.0 \mathrm{N} \), Direction of Force - east
E. Amount of Force \( -3.33 \mathrm{N} \), Direction of Force - north


Let a beam of wavelength \( \lambda \) fall on
parallel reflecting planes with
separation \( d \), then the angle \( \theta \) that the
beam should make with the planes so that reflected beams from successive
planes may interfere constructive
should be (where, \( \boldsymbol{n}=\mathbf{1}, \mathbf{2}, \dots . .) \)
\( ^{\text {A }} \cdot \cos ^{-1}\left(\frac{n \lambda}{2 d}\right) \)
B \( \cdot \sin ^{-1}\left(\frac{n \lambda}{2 d}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{n \lambda}{d}\right) \)
D. \( \tan ^{-1}\left(\frac{n \lambda}{d}\right) \)


\( A B C D \) is a rhombus with \( \angle A B C= \)
\( 56^{\circ}, \) then \( \angle A C B \) will be
A \( .56^{\circ} \)
B. \( 124^{\circ} \)
\( c \cdot 62^{0} \)
D. \( 34^{\circ} \)


The monomers of BUNA-S rubber is:
A. vinyl chloride and sulphur
B. butadiene
C. styrene and butadiene
D. isoprene and butadiene


Assertion
In the formula \( P=\frac{2}{3} E, \) the term \( E \)
represents translational kinetic energy
per unit volume of gas.
Reason
In case of monoatomic gas
translational kinetic energy and total
kinetic energy are equal.
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


Which of the following organisms show
mixotrophic nutrition?
\( A \)
B.
\( c \)
D. Both B and C


Select incorrect statement about
hydrides of group 15 elements:
A. The central atom in the hydride is \( s p^{2} \) hybridised.
B. \( N H_{3} \) readily form \( N H_{4}^{+} \) salts with \( H^{+} ; P H_{4}^{+} \) salts are formed with \( H^{+} \) under anhydrous condition.
C. The tetrahedron is distorted due to repulsion between the lone pair of electrons and the bond pairs.
D. The bond energy of the M-H bond decreases from \( N H_{3} \) to \( B i H_{3} \) because of increase in the size of the element.


In the figure shown ABCDEFGH is a
square conducting frame of side \( 2 m \)
and resistance \( 1 \Omega / m . \) A uniform magnetic field B is applied perpendicular to the plane and pointing
inwards. It increases with time at a
constant rate of \( 10 T / s . \) Then: \( (A B=B C \)
\( =C D=B H=1 m) \)
rhis question has multiple correct options
A. current in DH arm is zero
B. power consumed as heat in the circuit 200 watt
C. heat produced in DH and BF arm is zero
D. current in AG and CB arm is equal and its magnitude \( 5 A \)


The probability that a leap year will have
53 sundays is
\( \mathbf{A} \cdot 1 / 7 \)
в. \( 2 / 7 \)
c. \( 5 / 7 \)
D. \( 6 / 7 \)


The unpaired electrons in \( A l \) and \( S i \) are present in \( 3 p- \) orbital. Which electron
will experience more effective nuclear
charge from the nucleus?


Figure shows a LCR circuit connected
with a dc battery of emf \( \varepsilon \) and internal
resistance \( R \). Initially the capacitor was
uncharged. After a long time:
This question has multiple correct options
A \( \cdot \) current through the inductor is \( \frac{\varepsilon}{8 R} \)
B. charge stored in the capacitor is \( C \frac{^{2}}{4} \)
C. charge stored in the capacitor is \( C \frac{e}{2} \)
D. potential difference across the terminals of battery is
\( \frac{\varepsilon}{4} \)


The standard enthalpy of formation of \( N H_{3} \) is \( -46 k J m o l^{-1} . \) If the enthalpy of
formation of \( \boldsymbol{H}_{2} \) from its atoms is
\( -436 k J m o l^{-1} \) and that of \( N_{2} \) is
\( -712 k J m o l^{-1}, \) the average bond
enthalpy of \( N-H \) bond in \( N H_{3} \) is:
A \( .+1056 k J m o l^{-1} \)
В. \( -1102 k J \) mol \( ^{-1} \)
c. \( -964 k J m o l^{-1} \)
D. \( +352 k J m o l^{-1} \)


Which of the quantum numbers describe shape of electron cloud?
A. Principal quantum number
B. Azimuthal quantum number
c. Magnetic quantum number
D. Spin quantum number


If \( \cos ^{2} 45-\cos ^{2} 30=x \cos 45^{\circ} \sin 45^{\circ} \)
\( \operatorname{then} x= \)
A .2
B. \( \frac{3}{2} \)
\( c \cdot \frac{-1}{2} \)
D. \( \frac{-3}{4} \)


A cockroach has ............... pairs of legs.
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Predict block, group and period of \( \boldsymbol{S b} \)
A. Block-p, Period- \( -5, \) Group- 15
B. Block-p, Period-5, Group-14
c. Block-s, Period- - 5 , Group- 13
D. Block- \( s \), Period-5, Group- 11


Find cofactors of the elements of the \( \operatorname{matrix} \boldsymbol{A}=\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right] \)


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}{[\boldsymbol{x}] \forall \boldsymbol{x} \geq \mathbf{0}} \\ \mathbf{1}+[\boldsymbol{x}] \forall \boldsymbol{x}<\mathbf{0}\end{array}\right. \)
A. \( f(x) \) is a periodic
B. \( f(x) \) is a many one
c. \( f(x) \) is a one-one
D. None of these


Two elements have electronegativity of 1.2 and \( 3.0 . \) Bond formed between them
would be
A. predominantely ionic
B. predominantely covalent
c. co-ordinate bond
D. metallic bond


If \( A \) is a square matrix with \( |A|=8 \)
Find the value of \( \left|\boldsymbol{A} \boldsymbol{A}^{-1}\right| \)


Find the mean deviation about mean for
the following data:
Marks 10 11 obtained
12
No. of students 2
3


A particle moves on the \( x- \) axis. When the particle's acceleration is positive and increasing then
A. Its velocity must be negative
B. It must be slowing down
c. It must be speeding up
D. None of the these


Assertion
Statement-I: Enthalpy of atomization is the heat of reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\mathrm{I}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O} \)
\( (g) \)
Reason
Statement-II : Gaseous molecules are
far apart of each other due to less
attraction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The instantaneous velocity of a body can be measured :-
A. Graphically
B. By speedometer
c. Both of above
D. vectorially


The length \( x \) of an rectangle is
decreasing at the rate \( 2 \mathrm{cm} / \) sec and width y is increasing at the rate of
\( 2 c m / \)sec. When \( x=12 c m \) and \( y= \)
\( 12 c m, \) the rate of change of the area of
the rectangle is \( k c m^{2} / s e c, \) then \( k-9 \) is


Match the complex ions listed in
column-I with the characteristics listed
in column-II using the codes given
below.
ColumnColumn-II
(a)
\[
\left[N i\left(N H_{3}\right)_{6}\right]^{2+}
\]
(p) \( d^{2} s p^{3} \) and diamagnetic
\( (b) \)
\[
\left[C r\left(N H_{3}\right)_{6}\right]^{3+}
\]
(q) \( s p^{3} d^{2} \) and diamagnetic
\( (c) \)
(r) \( s p^{3} d^{2} \) and two unpaired
\[
\left[C o\left(N H_{3}\right)_{6}\right]^{3+}
\]
electrons
\( (d) \)
(s) \( d^{2} s p^{3} \) and three unpaired
\[
\left[Z n\left(N H_{3}\right)_{6}\right]^{2+}
\]
electrons
A. a-r, b-s, c-p, d-q
B. a-s, b-r, c-q, d-p
c. \( a-r, b-s, c-q, d-p \)
D. a-p, b-q, c-r, d-s


State True and False :
If humidity is high in the atmosphere, rate of evaporation is higher.
A. True
B. False


Due to plasmoysis, the plant cell
A. Bursts
B. Swells up
c. Become turgid
D. Become flaccid


Solve :
\[
\boldsymbol{x}^{2}+4 \boldsymbol{x}+\boldsymbol{4}=\mathbf{0}
\]


Evaluate the integral \( \int_{1}^{4}\left(x^{2}-x\right) d x \)


Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown. Construct a \( \triangle A B C \) in which \( B C= \)
\( 6.5 c m, \angle A B C=60^{\circ}, A B=5 \mathrm{cm} \)
Construct a locus of points \( l_{1} \) at a
distance of \( 3.5 \mathrm{cm} \) from \( A . \) Also,
construct a locus of points \( l_{2} \) which is
equidistant from \( A C \) and \( B C . \) Let \( l_{1} \)
intersect \( l_{2} \) in two points \( X \) and \( Y \)
Measure \( \boldsymbol{X} \boldsymbol{Y} \)


On which of the following content of coke, its price depend?
A. Sulphur
B. Ash
c. Nitrogen
D. Both a and


Solve the equation: \( \tan ^{-1} x+ \) \( 2 \cot ^{-1} x=\frac{2 \pi}{3} \)


Which of the following electronic configuration corresponds to the most electropositive character?
A \( \cdot[H e] 2 s^{1} \)
B . \( [H e] 2 s^{2} \)
\( c \cdot[X e] 6 s^{1} \)
D. \( [X e] 6 s^{2} \)


Cell-tissue organisation occurs in
A. Amoeba
B. Hydra
c. Tapeworm
D. Ascaris


A non-uniform thin rod of length \( L \) is placed along \( x- \) axis as such its one of
ends at the origin. The linear mass
density of rod is \( \lambda=\lambda_{0} x . \) The distance
of centre of mass of rod from the origin
is:
A \( . L / 2 \)
B. \( 2 L / 3 \)
c. \( L / 4 \)
D. L/5


A solid body starts rotating about a stationary axis with an angular acceleration \( \boldsymbol{\alpha}=\left(\mathbf{2 . 0} \times \mathbf{1 0}^{-\mathbf{2}}\right) \boldsymbol{t} \boldsymbol{r a d} / \boldsymbol{s}^{2} \)
where \( t \) is in seconds. How soon(in
seconds) after the beginning of rotation will the total acceleration vector of an
arbitrary point of the body form an angle
\( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \) with its velocity vector?


What is nuclear energy?


The reaction quotient \( (Q) \) at
equilibrium is:
\( A \cdot=1 \)
в. \( =K \)
\( c \cdot>K \)
\( \mathrm{D} \cdot<K \)


The sum of two integers is \( -23 . \) If one of
them is 18 , then the other is
A. -14
B. 14
c. 41
D. -41


An object starts \( 5 \mathrm{m} \) from origin and
moves with an initial velocity of \( 5 m s^{-1} \)
and has an acceleration of \( 2 m s^{-2} \). After
10 sec, the object is how far from the origin?
A. \( 150 \mathrm{m} \)
B. 145 \( \mathrm{m} \)
c. \( 155 \mathrm{m} \)
\( D \cdot 55 \mathrm{m} \)


Find the emf and internal resistance of
the equivalent cell between \( A \) and \( B \). put
\[
\begin{array}{l}
\varepsilon_{1}=3 \mathrm{V}, r_{1}=2 \Omega \varepsilon_{2}=2 V, r_{2}=1 \Omega \\
\varepsilon_{3}=6 V, r_{3}=1 \Omega
\end{array}
\]


Which out of following hydrocarbons undergo addition reaction? \( \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{3} \boldsymbol{H}_{6}, \boldsymbol{C}_{2} \boldsymbol{H}_{2} \) and \( \boldsymbol{C} \boldsymbol{H}_{4} \)
A. \( C_{2} H_{6} \) and \( C_{3} H_{8} \)
B. \( C_{3} H_{6} \) and \( C_{2} H_{2} \)
c. \( C H_{4} \) and \( C_{2} H_{6} \)
D. \( C_{3} H_{8} \) and \( C_{2} H_{2} \)


If the voltage applied to a motor is 200
volt and back emf is 160 volt, then the
efficiency of the motor will be :
A. \( 100 \% \)
B. 80\%
c. \( 50 \% \)
D. 25\%


Calculate the overall order of a reaction
which has the rate expression
(a) Rate \( =\boldsymbol{k}[\boldsymbol{A}]^{1 / 2}[\boldsymbol{B}]^{3 / 2} \)
(b) Rate \( =\boldsymbol{k}[\boldsymbol{A}]^{3 / 2}[\boldsymbol{B}]^{-1} \)


In the 'ring test' of \( N O_{3}^{-} \) ion, there is
formation of brown colour ring. What is
its formula?
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{5} N O_{3}\right]^{2} \)
B . \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4} \mathrm{NOSO}_{4}\right]^{2+} \)
c. \( \left[F e\left(H_{2} O\right)_{5} N O\right]^{2+} \)
D. None of these


What should be done if the gas cylinder at your home catches fire?
A. Water should be sprinkled.
B. Sand, soil should be put at it.
c. cylinder should be covered with wet blanket.
D. One should run away


Which of the following statements is a
correct distinction between autotrophs
and heterotrophs?
A. Only heterotrophs need to acquire chemical compounds from the environment
B. Cellular respiration is unique to heterotrophs
C. Only heterotrophs have mitochondria
D. Autotrophs, but not heterotrophs, can nourish themselves beginning with nutrients that are entirely inorganic


Ammonia gas on passing through copper sulphate solution gives deep blue solution.
A. True
B. False


During chemiosmotic synthesis of ATP,
protons diffuse through \( C F_{0} \) channels
that activates ATPase enzyme. As a result, one molecule of ATP is formed
when \( _{\text {一一一一一一一一 }} \) passes through
ATPase.
\( \mathbf{A} \cdot 4 H^{+} \)
в. \( H^{+} \)
\( \mathbf{c} \cdot 2 H^{+} \)
D. \( 6 H^{+} \)


\( 0.54 g \) of an organic compound containing phosphorous gave 0.888 g of
\( M g_{2} P_{2} O_{7} \) by the usual analysis. Calculate the percentage of phosphorous in the compound.
A . 85.4\%
B. 45.88\%
c. २७.२\%
D. 12.8\%


Which quantum number is not related with Schrodinger equation?
A. Principal
B. Azimuthal
c. Magnetic
D. spin


Evaluate \( \int \frac{\boldsymbol{d x}}{\sqrt{(\boldsymbol{x}-\boldsymbol{a})(\boldsymbol{b}-\boldsymbol{x})}} \)
A \( \cdot I=2 \sin ^{-1} \sqrt{\frac{x-a}{(b-a)}}+C \)
в. \( I=2 \cos ^{-1} \sqrt{\frac{x-a}{(b-a)}}+C \)
\( ^{\mathrm{c}} \cdot_{I=\sin ^{-1}} \sqrt{\frac{x-a}{(b-a)}}+C \)
D. \( _{I}=2 \sin ^{-1} \sqrt{\frac{x-b}{(a-b)}}+C \)


\( A \) is \( 25 \% \) older than \( B . \) By what percent is
B younger than A ?


If the net force on an object is zero, then
the object:
A . is in equilibrium
B. is not in equilibrium
c. may or may not be in equilibrium
D. always has zero mass


Which of the following compound is not a vitamin?
A . niacin
B. riboflavin
c. thiamine
D. guanine


A rain drop of mass \( 0.1 g \) is falling with
uniform speed of \( 10 \mathrm{cm} / \mathrm{s} \). What is the net force the drop?
A \( \cdot 10^{-2} N \)
В. \( 10^{-3} N \)
c. \( 2 \times 10^{-3} N \)
D. zero


Two magnetic poles have their strengths
in the ratio \( 3: 2 . \) They are kept at a distance of \( 0.6 \mathrm{m} \) in air and the force of
repulsion is found to be 0.06 dynes. The pole strengths are (in amp. \( m \) )
A . 1.8,1.2
B. 18,12
\( c \cdot 6,4 \)
D. 0.6, 3.6


A ball moving with a moment of \( 15 k g m s^{-1} \) strikes against a wall at \( 60^{\circ} \)
angle and is reflected at the same angle with its initial speed. Find the impulse.


The plant hormone that promote cell
division
A. Abscisic acid
B. Auxins
c. Gibberellins
D. cytokinins


The distillation of bleaching powder and
acetone gives:
A. \( C H C l_{3} \)
B. chloral
c. \( C H_{3} C l \)
D. \( C C l_{4} \)


Represent the following data using suitable graphical representation.
No. of
\[
\begin{array}{llll}
\text { words } & \mathbf{3 0}- & \mathbf{4 0 -} & \mathbf{5 0 -} \\
\text { typed } & \mathbf{3 9} & \mathbf{4 9} & \mathbf{5 9} \\
\text { per } & &
\end{array}
\]
\( \operatorname{minute} \)
No. of typists
15


The image formed by an objective of a compound microscope is
A. virtual and diminished
B. real and diminished
c. real and enlarged
D. virtual and enlarged


Most of the involuntary actions are
controlled by
A. Medulla oblongata
B. Cerebrum
c. Cerebellum
D. Diencephalon


In a carnival ride the passengers travel
in a circle of radius \( 5 \mathrm{m} \), making one complete circle in 4 sec. What is the
acceleration?


Cathode rays are moving between the
poles of a magnet. Due to the effect of magnetic field of magnet:
A. velocity of rays increase
B. velocity of rays decrease
c. rays deflected towards south pole
D. rays deflected in upward direction and perpendicular to the plane of the paper


\( \mathbf{2} \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{5} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{I}_{2}(\boldsymbol{s})+ \)
\( \boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( I_{3}^{-}(a q)+2 S_{2} O_{3}^{2-}(a q) \rightarrow \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
When copper containing alloy of weight \( 0.3175 g \) is dissolved in an acid and an excess of \( K I \) is added, 25 mL of
\( 0.10 M N a_{2} S_{2} O_{3} \) is required, then \( C u \)
present in alloy is
A . \( 20 \% \)
в. \( 40 \% \)
\( c .45 \% \)
D. \( 50 \% \)


Adjacent epithelial cells are held
together by means of
A. Liposomes
B. Glyoxysomes
c. Desmosomes
D. Microsomes


Rishi chakra was a famous ancient
scholar in the field of ?
A. Ayurvedic medicine
B. Homeopathy
c. Alopathy
D. chemistry


Melting point of Aluminium is:
\( \mathbf{A} \cdot 1000^{\circ} \mathrm{C} \)
B . \( 659^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 1500^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)


Sodium extract is heated with
concentrated \( H N O_{3} \) before testing for halogens because:
A. \( A g_{2} S \) and \( A g C N \) are soluble in acidic medium.
B. silver halides are totally insoluble in nitric acid
c. \( S^{2-} \) and \( C N^{-} \), if present, are decomposed by conc. \( H N O_{3} \) and hence do not interfere in the test.
D. \( A g \) reacts faster with halides in acidic medium.


\( \Delta_{f} G^{o} \) at \( 500 K \) for substance 'S' in liquid state and gaseous state are \( +100.7 k c a l \) mol \( ^{-1} \) and
\( +103 k c a l m o l^{-1}, \) respectively
Vapour pressure of liquid 'S' at \( 500 K \)
is approximately equal to: \( (\boldsymbol{R}= \)
\( \left.2 \operatorname{cal} K^{-1} m o l^{-1}\right) \)
A. 100 atm
B. 1 atm
c. 10 atm
D. 0.1 atm


Find the area of a parallelogram with a base of \( 200 \mathrm{cm} \) and height of \( 2.5 \mathrm{cm} \)
в. \( 510 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 520 \mathrm{cm}^{2} \)
D. \( 300 \mathrm{cm}^{2} \)


What is the self inductance of a coil in
which an induced emf of \( 2 V \) is set up,
when the current is changing at the rate
of \( 4 A s^{-1} \)
A . \( 0.5 \mathrm{mH} \)
в. \( 0.05 \mathrm{H} \)
\( c \cdot 2 H \)
D. \( 0.5 H \)


single heart circuit occurs in
A. Fish
B. Frog
c. Reptile
D. Man


The basicity of pyro-phosphoric acid is :
A .4
B. 3
\( c \cdot 2 \)
D. 5


Linear \( \& \) Angular acceleration of a particle is \( 10 \mathrm{m} / \mathrm{sec}^{2} \) and \( 5 \mathrm{rad} / \mathrm{sec}^{2} \)
respectively. What is its from rotational axis :
A . \( 50 m \)
B. \( 1 / 2 m \)
\( c .1 m \)
D. \( 2 m \)


Force between two charges separated by a certain distance in air is \( \mathrm{F} \). If each charge is doubled and the distance
between them is also doubled, force
would be
A. \( F \)
в. \( 2 F \)
\( c \cdot \frac{F}{2} \)
D. \( 3 F \)


A particle executing simple harmonic motion with an amplitude A. The distance travelled by the particle in one time period is
A. zero
B. A
c. 2 A
D. 4A


If \( 2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) is
independent of \( x, \) then
This question has multiple correct options
\( \mathbf{A} \cdot x>1 \)
B. \( x<-1 \)
c. \( 0<x<1 \)
D. \( -1<x<0 \)


A \( 1 k W \) heater is meant to operate at
\( 200 V . \) How much power (in watt) will it
consume if the line voltage drops to
\( 100 V ? \)


number of runs scored by some top
batsmen of the world in one day
international cricket matches:
\begin{tabular}{ll}
Runs scored & No. of batsman \\
\( 3000-4000 \) & 4 \\
\( 4000-5000 \) & 18 \\
\( 5000-6000 \) & 9 \\
\( 6000-7000 \) & 7 \\
\( 7000-8000 \) & 6 \\
\( 8000-9000 \) & 3 \\
\( 9000-10000 \) & 1 \\
\( 10000-11000 \) & 1 \\
\hline
\end{tabular}
Find the mode of the data
A .4608 .695652
B. 4408.695652
c. 4202.695652
D. 4882.69


The wavelength of \( \beta \) -line of the Balmer
series is \( 4815 A \). What is the
wavelength of \( \alpha \) -line of the Balmer
series of the same atom?


(a) Give reasons for the following:
(i) Bond enthalpy of \( F_{2} \) is lower than
that of \( \boldsymbol{C l}_{2} \)
(ii) \( P H_{3} \) has lower boiling point than \( \boldsymbol{N} \boldsymbol{H}_{3} \)
(b) Draw the structures of the following molecules:
(i) \( B r F_{3} \)
(ii) \( \left(\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3}\right)_{3} \)
(iii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)
(a) Account for the following:
(i) Helium is used in diving apparatus.
(ii) Fluorine does not exhibit positive oxidation state.
(iii) Oxygen shows catenation behavior less than sulphur.
(b) Draw the structures of the following molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \)


Glycerol is oxidised by bismuth nitrate to produce:
A . oxalic acid
B. mesooxalic acid
c. glyceric acid
D. glyoxalic acid


In Newland's classification, elements are arranged in an increasing order of their:
A. mass number
B. atomic number
c. atomic weight
D. all of these


The ratio of velocity of sound in hydrogen and oxygen at STP is:
\( \mathbf{A} \cdot 16: 1 \)
B. 8: 1
c. 4: 1
D. 2: 1


Why ethyl mercaptan is added to liquid petroleum gas?


The only element of group 13 which does not form a passive layer on the surface
while dissolving in con. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) but dissolve to form complex is:
A. boron
B. aluminium
\( c . \) both
\( D \cdot \) none


In a group of 50 persons, 14 drink tea
but not coffee and 30 drink tea. Find
how many drink coffee but not tea?


Which technique is used by Mendel for hybridisation?
A. Emasculation
B. Bagging
c. Meristem culture
D. Both A and B


Consider a gravity- free hall in which an experimenter of mass \( 50 \mathrm{kg} \) is resting
on a \( 5 k g \) pillow, \( 8 f t \) above the floor of
the hall. He pushes the pillow down so that it starts falling at a speed of \( 8 f t / s \)
The pillow makes a perfectly elastic
collision with the floor, rebounds and
reaches the experimenter's head. Find the time elapsed in the process.


A remote - sensing satellite of earth revolves in a circular orbit at a height of
\( 0.25 \times 10^{6} \mathrm{m} \) above the surface of earth
If earth's radius is \( 6.38 \times 10^{6} m \) and
\( g=9.8 m s^{-2}, \) then the orbital speed of
the satellite is:
\( \mathbf{A} \cdot 6.67 k m s^{-1} \)
B . \( 7.76 \mathrm{km} \mathrm{s}^{-1} \)
c. \( 8.56 k m s^{-1} \)
D. \( 9.13 \mathrm{km} \mathrm{s}^{-1} \)


A tiny sphere of mass \( m \) and density \( \rho \) is dropped in a tall jar of glycerine of
density \( \sigma . \) When the sphere acquires terminal velocity, the magnitude of the viscous force acting on it is
A. \( \frac{m g \rho}{\sigma} \)
в. \( \frac{m g \sigma}{\rho} \)
c. \( m g\left(1+\frac{\rho}{\sigma}\right) \)
D \( \cdot m g\left(1-\frac{\sigma}{\rho}\right) \)


Q Type your question
Substance Mass(gm) in moles
\( \begin{array}{ll}C H_{3} C O O H & 0.742\end{array} \)
0.0
\( H \)
195
Beaker
The two liquids \( C H_{3} C O O C H_{3} \) and
\( C H C l_{3} \) combine in such away that they
form a single H-bond between each pair of molecules. In an experiment to determine the approximate strength of this bond, samples of the two liquids were mixed in an insulated glass
beaker and the temperature was found to rise by \( 1^{0} C . \) Other data are given in the table.

The approximate strength of the H bond according to the above experiment (in kJ/mole) will be:
A. 0.73
B. 3.6
\( c \cdot 4.9 \)
D. 2.8


Which of the following is the electron
configuration of a transition metal?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{5} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2} \)


Why is it usually difficult to demonstrate respiration in green plants?


Assertion
The kinetic energy, with any reference,
must be positive.
Reason
In the expression for kinetic energy, the
velocity appears with power 2
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 boat is moving with a velocity \( \vec{v}= \) \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}} \) with respect to ground. The
water in the river is moving with a velocity \( \vec{u}=-3 \hat{i}-4 \hat{j} \) with respect to
ground. The relative velocity of boat with
respect to water is :
A \( .6 \hat{i}+8 \hat{j} \)
B.
c. \( 6 \hat{i}-8 \hat{j} \)
D. \( -6 \hat{i}+8 \hat{j} \)


At places, the groundwater is stored between layers of hard rock below the water table. This is known as
A. a reservoir
B. an aquifer
c. a hard water
D. a well water


Linear Acceleration of all the points in
rigid body is-
A. same
B. different
c. may be same may be different
D. none of these


A conductor of uniform resistance (per
unit length) bent in the form of an
equilateral triangle of side a. It is
enclosing on inward magnetic field \( \vec{B}=B_{0} \cos ^{2} \omega t(-\hat{k}) . \) Then
This question has multiple correct options
A \( \cdot \) During \( 0<t<\frac{\pi}{2 \omega} \) an clockwise current is induced in
the coil.
B. During \( 0<t<\frac{\pi}{\omega} \) an anticlockwise current is induced
in the coil
C . During \( \frac{\pi}{2 \omega}<t<\frac{\pi}{\omega} \) an anticlockwise current flows
through it
D. During \( \frac{\pi}{\omega}<t<\frac{3 \pi}{2 \omega} \) a clockwise current flows through
it


The correct statement of third law is:
A. The rate of change of momentum of an object is directly proportional to the applied force
B. For every action there is an equal and opposite reaction
C. An object at rest stays at rest and an object in motion stays in motion unless acted upon by an unbalanced force
D. None of these


The cathode in the central compartment of Castner Kellner cell used for the
manufacture of \( N a O H \) is:
A. Iron
B. Carbon
C. Mercury
D. Steel


The perimeter of a sector of a circle of
radius \( 5.7 m \) is \( 27.2 m . \) Find the area of
the sector.


Write the S.I unit of three fundamental
quantities.


The resistance of the given carbon
resistor is \( \left(2.4 \times 10^{6} \pm\right) 5 \% \Omega . \) What is
the sequence of colours on the strips provided on resistor?


Given, \( \boldsymbol{A}=\{\text { Triangles }\}, \boldsymbol{B}=\{ \)
Isosceles triangles \( \} \) \( C=\{\text { Equilateral triangles }\} . \) State
whether the following statements are correct or incorrect. Give reasons.
\( A \subset B \)


What is formed immediately after
fertilisation?
A. Placenta
B. Foetus
c. Embry
D. zygote


Darwin's finches are the good example
of
A. Convergent evolution
B. Industrial melanism
c. connecting link
D. Adaptive radiation


A unit vector along the incident ray of light is \( \hat{i} \). The unit vector for the
corresponding refracted ray of light is
\( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{n}}, \) a unit vector normal to the
boundary of the medium and directed towards the incident medium. If \( \mu \) is the
refractive index of the medium, then
Snell's law (second law) of refraction is :
\( \mathbf{A} \cdot \hat{i} \times \hat{n}=\mu(\hat{n}+\hat{r}) \)
в. \( \hat{i} \cdot \hat{n}=\mu(\hat{r} \cdot \hat{n}) \)
c. \( \hat{i} \times \hat{n}=\mu(\hat{r} \times \hat{n}) \)
\( \mathbf{D} \cdot \hat{i} \cdot \hat{n}=\mu(\hat{r} \times \hat{n}) \)


A series LCR circuit containing a
resistance of \( 120 \Omega \) has angular resonance frequency \( 4 \times 10^{5} \) rad \( s^{-1} \)
At resonance the voltage across the
resistance and inductance are \( 60 \mathrm{V} \) and
\( 40 \mathrm{V} \) respectively. The angular frequency at which current in the circuit lags the
voltage by \( 45^{0} \) is
A \( \cdot 16 \times 10^{5} \) rad \( s^{-1} \)
B. \( 8 \times 10^{5} \) rad \( s^{-1} \)
C . \( 4 \times 10^{5} \) rad \( s^{-1} \)
D. \( 2 \times 10^{5} \) rad \( s^{-1} \)


In which of the following instruments is the final image virtual? This question has multiple correct options
A. Projector
B. Camera
c. Microscope
D. Telescope


Bond dissociation enthalpies of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( N_{2}(g) \) are \( 436.0 \mathrm{KJ} \) mol \( ^{-1} \) and
\( 941.8 \mathrm{mol}^{-1} \) and enthalpy of formation
of \( N H_{3}(g) \) is \( -46 \mathrm{KJ} \) mol \( ^{-1} . \) What is
enthalpy of atomization of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) ? \)
What is average bond enthalpy of \( N- \)
\( \boldsymbol{H} \) bond?


\( \begin{array}{ll}\text { Item 'I' } & \text { Item 'II' } \\ \text { (compound) } & \text { (reagent) } \\ \text { (A) Lysine } & \text { (P)I-naphthol } \\ \text { (B)Furfural } & \text { (Q)ninhydrin } \\ \text { (C) Benzyl alcohol } & \text { (R) } K M n O_{4} \\ \text { (D)Styrene } & \text { (S)ceric ammonium }\end{array} \)
\( A \)
\( (A) \rightarrow(Q),(B) \rightarrow(P),(C) \rightarrow(S),(D) \rightarrow(R) \)
B. \( (A) \rightarrow(Q),(B) \rightarrow(R),(C) \rightarrow(S),(D) \rightarrow(P) \)
C \( .(A) \rightarrow(Q),(B) \rightarrow(P),(C) \rightarrow(R),(D) \rightarrow(S) \)
D. \( (A) \rightarrow(R),(B) \rightarrow(P),(C) \rightarrow(Q),(D) \rightarrow(S) \)


A modified aerial stem which performs function of photosynthesis, but the modification is actually to reduce the rate of transpiration is
A. Cladode
B. Phylloclade
c. Phyllode
D. Both A and B


\( x^{3}-x-4 \) added to \( x^{4}-x^{3}-x^{2}+ \)
\( x+3 \) to obtain \( x^{4}+x^{2}-1 ? \)
If true then enter 1 and if false then
enter \( \mathbf{0} \)


Which of the following statements is
not correct?
A. Copper liberates hydrogen from acids
B. In its higher oxidation states, manganese forms stable compounds with oxygen and fluorine
C \( . M n^{3-} \) and \( C o^{3+} \) are oxidising agents in aqueous solution.
D. \( T i^{2+} \) and \( C r^{2+} \) are reducing agents in aqueous solution


Which is an example of inverse
proportion?
A. More amount of sweets, more total cost
B. More length of cloth, more cost
C. More expenditure, less saving
D. More height of object, more length of its shadow


Froth floatation:
This question has multiple correct options
A. is a physical method of separating mineral from the gangue
B. is a method to concentrate the ore depending on the difference in wetability of gangue and the ore
C. is used for the sulphide ores
D. is a method in which impurities sink to the bottom


Reaction for the preparation of \( 1^{0} \) amine
is:
A. Hinsberg reaction
B. Hoffman mustard oil reaction
c. Hoffman bromamide reaction
D. Liberman nitroso reaction


Which of the following equations are not
quadratic?
\( \mathbf{A} \cdot x(2 x+3)=x+2 \)
B \( \cdot(x-2)^{2}+1=2 x-3 \)
\( \mathbf{c} \cdot y(8 y+5)=y^{2}+3 \)
D. \( y(2 y+15)=2\left(y^{2}+y+8\right) \)


Turnbull's blue is:
A. ferricyanide
B. ferrous ferrocyanide
C . ferrous cyanide
D. ferrous ferricyanide


Among the following species, identify the isostructural pairs.
\( N F_{3}, N O_{3}^{-}, B F_{3}, H_{3}^{+} O, H N_{3} \)
\( \mathbf{A} \cdot\left[N F_{3}, N O_{3}^{-}\right] \) and \( \left[B F_{3}, H_{3}^{+} O\right] \)
B . \( \left[N F_{3}, H N_{3}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
C \( \cdot\left[N F_{3}, H_{3}^{+} O\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
D. \( \left[N F_{3}, H_{3}^{+} O\right] \) and \( \left[H N_{3}, B F_{3}\right] \)


The figure shows four wire loops, with edge lengths of either I or 21. All four
loops will move through a region of uniform magnetic field \( g \) at the same
constant velocity. In
which loop the emf induced is
maximum:
\( A \)
B. I
c. III
D. IV


Order of magnitude of density of
uranium nucleus is :
\( \left(\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k g}\right) \)
\( \begin{array}{ll}\text { A } \cdot 2 \times 10^{20} & k g / m^{3}\end{array} \)
B . \( 1 \times 10^{10} \mathrm{kg} / \mathrm{m}^{3} \)
C \( \cdot 4 \times 10^{14} \quad k g / m^{3} \)
D. \( 4 \times 10^{11} \quad k g / m^{3} \)


If nth term of an A.P is \( (2 n+1), \) what is
the sum of its first three terms?


The general formula \( C_{n} H_{2 n} O_{2} \) could be
for open chain
A . Diketones
B. Carboxylic acid
\( c . \) Diols
D. Diadehydes


After terminal velocity is reached, the acceleration of a body falling through a viscous fluid is
A. zero
B. equal to g
c. less than \( g \)
D. more than \( g \)


An element \( Z \) has atomic number 16 .
Answer the following questions on \( Z \) :
What kind of a compound is this?


The graph of kinetic energy (K) of a body versus velocity (v) is represented as
A. hyperbola
B. parabola
c. straight line
D. none of these


\( f(a, b, c \) are in G.P., prove taht the following are also
¡) \( a^{3}, b^{3}, c^{3} \)
ii) \( a^{2}+b^{2}, a b+b c+, b^{2}+c^{2} \)


A current \( i \) passes through a wire of length \( L, \) radius \( R \) and resistively \( \rho . \) The rate of heat generated is
A \( \cdot \frac{i \rho L}{\pi r^{2}} \)
В. \( i^{2}\left(\frac{L \rho}{\pi r^{2}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{i^{2} \rho L}{r}\right) \)
D. none of these


What two precautions should be taken
to avoid the overloading of domestic
electric circuits?


If matrix \( \boldsymbol{A}=[\mathbf{1} \mathbf{2} \mathbf{3}], \) then find \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)


Atomic number \( _{-1-}-_{-1} \) by one unit on moving from right to left.
A. increases
B. decreases
c. remains the same
D. None of the above


The equation of an incident wave travelling along +X direction is given by \( y=A \sin (2 t-5 x) . \) This wave gets reflected at a rigid boundary. The change in phase of the wave is
A. \( \pi / 2 \) radians
B. \( \pi \) radians
c. \( \pi / 3 \) radians
D. 2\pi/3 radians


Following is the list of four halides. Select correct sequence of decreasing
order of reactivity for \( \boldsymbol{S}_{N} \) 1 reaction
using the codes given below.
।) \( C_{6} \boldsymbol{H}_{5}-\underset{\mathrm{CH}_{3}}{\boldsymbol{H}}-\boldsymbol{B r} \)
॥) \( C_{6} H_{5}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{B r} \)
\( \| \mathrm{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{I} \)
\[
\boldsymbol{C H}_{3}
\]
IV) \( C_{6} H_{5} \)
\( \boldsymbol{C H}_{2}-\boldsymbol{I} \)
\( A \cdot|||>|>|V>| \mid \)
B. ||| >|> || > IV
D. |> |||> || > IV


The lengths of the perpendicular from
the points \( \left(\boldsymbol{m}^{2}, \boldsymbol{2 m}\right),\left(\boldsymbol{m m}^{\prime}, \boldsymbol{m}+\boldsymbol{m}^{\prime}\right) \)
and \( \left(m^{\prime 2}, 2 m^{\prime}\right) \) to the line \( x+y+1=0 \)
form
\( \cos \alpha+y \sin \alpha+\sin \alpha \tan \alpha=0 \) are in
\( A \). an A.P.
B. a G.P.
c. а н.Р.
D. none of these


What will happen if platelets were absent in the blood?
A. The process of clotting will be affected.
B. Kwashiorkor will be the result
c. RBC will be ruptured.
D. The blood will become more liquid


The horizontal component of the earth's
magnetic field at a place is \( B \) and angle
of dip is \( 60^{\circ} . \) What is the value of vertical component of earth's magnetic field at equator?


Which of the following pairs represent the same rational numbers:
\( \frac{-2}{-3} \) and \( \frac{2}{3} \)


The nuclear spindle
A. Is formed in amitotic division
B. Is formed in mitotic division
C. Is formed in meiotic division
D. Is formed in mitotic and meiotic division


Which of the following ion is
isoelectronic with \( \boldsymbol{O}^{2-} \) ?
This question has multiple correct options
A . \( N^{3-} \)
B. \( N^{\text {t }} \)
\( c \cdot F^{-} \)
D. \( T i^{+} \)


\( \int \frac{1}{(x-1)(x-2)} d x \)


Solve \( \sin \boldsymbol{x}=\frac{1}{2} \)


Find the heat transferred to the
water, when the temperature of a 20 gram sample of water is increased from
\( 10^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} ? \)
A. 400 calories
B. 600 calories
c. 20 calories
D. 200 calories
E. 30 calories


The set of all integral values of \( x \) for
which \( 5 x-1<(x+1)^{2}<7 x-3, \) is
\( A \cdot \phi \)
B . \{1\}
\( c \cdot\{2\} \)
D. \{3\}


Simplify:
\( \frac{8}{9}+\frac{-11}{6} \)


When \( H_{2} O_{2} \) is added to an acidified
solution of \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C} \boldsymbol{r}_{2} \boldsymbol{O}_{7} \)
A. solution turns green due to formation of \( C r_{2} O_{3} \)
B. solution turns yellow due to formation of \( K_{2} \) Cr \( O_{4} \).
c. a deep blue-violet colored compound \( C r O\left(O_{2}\right)_{2} \) is formed
D. solution gives green ppt. of \( \operatorname{Cr}(O H)_{3} \)


How is phosphine prepared using the following reagents?
(a) \( \boldsymbol{H} \boldsymbol{C l} \)
(b) \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(c) Caustic soda


In silica \( \left(S i O_{2}\right), \) each silicon atom is bonded to:
A. two oxygen atoms
B. four oxygen atoms
c. one silicon and two oxygen atoms
D. one silicon and four oxygen atoms


\( F e S O_{4} \) solution mixed with
\( \left(N H_{4}\right)_{2} S O_{4} \) solution in 1: 1 molar
ratio gives the test of \( F e^{2+} \) ion but
\( C u S O_{4} \) solution mixed with aqueous
ammonia in 1: 4 molar ratio does not
give the test of \( C u^{2+} \) ion. Explain why?


If the sides of a parallelogram are \( 2 \hat{i}+ \) \( 4 \hat{j}-5 \hat{k} \) and \( \hat{i}+2 \hat{j}+3 \hat{k}, \) then the unit
vector parallel to one of the diagonals, is
A \( \cdot \frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
B \( \cdot \frac{1}{7}(3 \hat{i}-6 \hat{j}-2 \hat{k}) \)
c \( \cdot \frac{1}{7}(-3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
D \( \cdot \frac{1}{7}(3 \hat{i}+6 \hat{j}+2 \hat{k}) \)


Three different vibrating bodies produce three types of the sounds \( X \), Y and \( Z \) Sounds \( X \) and \( Y \) cannot be hear by a man
having normal range of hearing but sound \( z \) can be heard easily.The sound \( x \) is used to find faults and cracks in
metals.The sound similar to that which is
produced during an earthquake before the main shock wave is generated. Name one device which can produce sound like
\( X \)
A. megaphone
B. sonar
c. bulb horn
D. ear mufflers


If the work done in turning a magnet of
magnetic moment \( M \) by an angle of \( 90^{\circ} \) from the magnetic meridian is n times the corresponding work done to turn it
through an angle of \( 60^{\circ} \), then the value
of \( n \) is
A . 1
B. 2
\( c \cdot \frac{1}{2} \)
D.


Write the given trigonometric expression in its simplest form. \( \tan ^{-1}\left(\frac{3 a^{2} x-x^{3}}{a^{3}-3 a x^{2}}\right), a>0 ; \frac{-a}{\sqrt{3}} \leq \)
\( \boldsymbol{x} \leq \frac{\boldsymbol{a}}{\sqrt{\mathbf{3}}} \)


Which polymer has 'chiral' monomer(s)?
A. \( P H B V \)
B. Nylon 6,6
c. Buna- \( N \)
D. Neoprene


Which of the following is the characteristic of epithelial tissues?
A. They are avascular and innervated.
B. They have a rapid rate of cell division.
c. They have less intercellular spaces.
D. All of the above.


In Erythrina indica and Dolichos lablab, the leaves are
A. Unipinnate
B. Bipinnate
c. Tripinnate
D. Trifoliate


What is called one or more outcomes of
an experiment?
A. Space
B. Experiment
c. sample
D. Event


The angle of banking \( \theta \) for a cyclist taking curve is given by \( \tan \theta=\frac{v^{n}}{r g} \)
where symbols \( (\mathrm{v}= \) speed of the cyclist, \( r= \) radius of the curved path, \( g= \)
acceleration due to gravity) have their usual meanings.Then the value of \( n \) is
equal to
A . 1
B. 3
c. 2
\( D \)


Find \( (l+m)^{2}-(l-m)^{2} \)
A \( .4 l m \)
B. \( 2 l m \)
\( c \cdot 0 \)
\( D \)


The driver of an express train travelling
at a speed of \( v_{1} \) sees on the same track
at distance \( d \) in front of him a goods
train travelling in the same direction at
a speed \( v_{2} \) such that \( v_{1}>v_{2} \)
Immediately he applies brakes to his
express train producing retardation \( a \) to avoid collision. Then
\( ^{\mathbf{A}} \cdot_{a}<\frac{v_{1}^{2}-v_{2}^{2}}{2 d} \)
В. \( _{a<\frac{\left(v_{1}-v_{2}\right)^{2}}{2 d}} \)
c. \( _{a>} \frac{\left(v_{1}-v_{2}\right)^{2}}{2 d} \)
D. \( _{a>} \frac{v_{1}^{2}-v_{2}^{2}}{2 d} \)


Which of the following is a rational number?
\( \mathbf{A} \cdot 3^{29 / 27} .3^{27 / 29} \)
B \( \cdot \sqrt[6]{\left(3^{50 / 51} .3^{52 / 51}\right)^{3}} \)
\( \mathbf{c} \cdot 3^{15 / 6}-3^{7 / 8} \)
D. \( \sqrt[15]{\left(3^{3}\right)^{1 / 5}} \)


A vessel contain \( 2 \mathrm{kg} \) water contained in the vessel. What force liquid will exert
on the base of the vessel?
A. 20
B. 30 N
c. zero
D. 10 N


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


A thin tube of uniform cross-section is
sealed at both ends. It lies horizontally,
the middle \( 5 \mathrm{cm} \) containing mercury and
the two equal ends containing air at the
same pressure \( P_{o} . \) When the tube is held
at an angle \( 60^{\circ} \) with the vertical, the
lengths of the air column above and
below the mercury are 46 and \( 44.5 \mathrm{cm} \)
respectively. The pressure \( P_{o} \) in \( \mathrm{cm} \) of \( \mathrm{Hg} \)
is: (The temperature of the system is left at \( 30 \mathrm{K} \)
A. 80 cm of \( H g \)
B. \( 75.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. 70 cm of \( H g \)
D. 90 cm of \( H g \)


For a crystal, the angle of diffraction (2
\( \theta \) ) is \( 90^{\circ} \) and the second order line has a
d value of \( 2.28 \AA . \) The wavelength \( (\text { in } \AA) \) of X-rays used for Bragg's diffraction is:
A . 1.612
B. 2.00
c. 2.28
D. 4.00


\( \int_{0}^{\pi / 2} \sin 2 x \tan ^{-1}(\sin x) d x= \)
A. \( \frac{\pi}{2}-1 \)
B. \( \frac{\pi}{2}+1 \)
c. \( \frac{3 \pi}{2}+1 \)
D. \( \frac{3 \pi}{2}-1 \)


The two cerebral hemispheres are joined together by
A. Corpora quadrigemina
B. Corpus callosum
c. corpora striata
D. Rhinal fissure


\( f(x)=\frac{\sin 2 x+1}{\sin x-\cos x} \) is discontinuous at
\( \boldsymbol{x}= \)
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{3} \)
c.
D.


Birds can fly because of
A. Feathers
B. wings
c. Hollow bones
D. All of the above


The EMF (in Volts) for the following electrodes are
\( \boldsymbol{P t}, \boldsymbol{H}_{2} \mid \boldsymbol{H} \boldsymbol{C l}\left(\boldsymbol{c}=\mathbf{1 0}^{-4} \boldsymbol{M}\right) \)


The state of hybridization of boron and oxygen atoms in boric acid \( \left(\boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3}\right) \)
respectively are:
A \( \cdot s p^{2} \) and \( s p^{2} \)
B. \( s p^{2} \) and \( s p^{3} \)
c. \( s p^{3} \) and \( s p^{2} \)
D. \( s p^{3} \) and \( s p^{3} \)


Consider the junction diode as ideal The value of current flowing through
\( A B \) is
в. \( 10^{-2} A \)
c. \( 10^{-1} A \)
D. \( 10^{-3} A \)


Three resistances of \( 8 \Omega, 16 \Omega \) and \( 4 \Omega \)
are joined in parallel. If each resistor is
rated \( 0.5 W, \) what is the maximum
voltage that may be applied to the combination?
A . \( 1 V \)
в. \( 1.5 V \)
\( c \cdot 2 V \)
D. 2.5V


Fill in the blanks:
In Duma's method, the nitrogen present in an organic compound is released as
gas.


Sl unit of heat capacity is
A. joule
B. joule/kilogram
C . joule/(kilogram x kelvin)
D. joule/kelvin


In early winter mornings, we can see drops of water on the blades of grass. This is because of :
A. photosynthesis
B. transpiration
c. condensation
D. water cycle


Two wires are pictured below, both
carrying current toward the east. What is the direction of the force exerted by
wire 2 on wire \( 1 ? \)
North
West
A. north
B. south
c. up
D. down
E. east


\( \frac{1}{8}=\frac{-}{2} \)
\( \frac{j}{\delta} \)
\( \delta \)


If two circles intersect at two points, prove that their centres lie on the
perpendicular bisector of the common chord


What will be total energy of electronic which is present in the second excited
state of \( \boldsymbol{H}- \) atom?
A. - 3.4 ev
B . -13.6 ev
c. -122.4 ev
D. -1.51 ev


Soft drinks contains:
A . acetic acid
B. tartaric acid
c. carbonic acid
D. nitric acid


Evaluate: \( \lim _{x \rightarrow-3} \frac{x^{3}+27}{x+3} \)
\( A \cdot 9 \)
B . 27
\( c .-27 \)
\( D \)


The average of first and second number
is 25 more than the average off the
second and third number. Find the
difference between the first and the
third number


The compound having least basic
nature is:
A \( \cdot \) ВіН \( _{3} \)
в. \( \mathrm{NH}_{3} \)
c. \( \mathrm{AsH}_{3} \)
D. \( \operatorname{sb} \mathrm{H}_{3} \)


Find the direction cosines of the vector \( \vec{a}=\hat{i}+\hat{j}-2 \hat{k} \)
\( ^{\mathbf{A}} \cdot\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}}\right) \)
B \( \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{3}}\right) \)
D. None of these


A proton of mass 'm' moving with a
speed \( v(<<c, \) velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If
the speed of the proton is increased to \( \sqrt{2} v, \) what will be time needed to
complete the circular orbit?
A \( \cdot \sqrt{2} T \)
в. T
c. \( \frac{T}{\sqrt{2}} \)
D. \( \frac{T}{2} \)


\( \mathrm{Cu}(s)+\mathrm{NO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) \rightarrow \mathrm{Cu}^{2+}(a q) \)
\( +\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(1) \)
If the above equation is balanced with lowest whole number coefficients, find
the coefficient for \( \mathrm{H}+(\mathrm{aq}) \)
A
B. 2
\( c \cdot 3 \)
D. 4
E. 5


Find the vector equation of the line through \( A(3,4,-7) \) and \( B(6,-1,1) \)


Arrange the following compounds in increasing order of their reactivity in nucleophilic in nucleophili addition
reaction:
(i) Ethanal, propanal, propanone, Butanone.
(ii) Benzaldehyde, \( p- \) Toluahyde, \( p \) Nitrobenzeldehyde, Acetophenone.


In the electronic configuration,
outermost orbit number is considered
as its period number.
A. True
B. False


The equilibrium constant \( \left(K_{c}\right) \) for the
reaction, \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \) at
temperature \( (T) \) is \( 4 \times 10^{-4} \). The value
of \( K_{c} \) for the reaction, \( N O(g) \rightleftharpoons \)
\( \frac{1}{2} N_{2}(g)+O_{2}(g) \) at the same
temperature is:
A .0 .02
В. \( 2.5 \times 10^{2} \)
c. \( 4 \times 10^{-4} \)
D. 50


How many neutrons and electrons are
present in the nuclei of \( _{6}^{13} C_{, 8}^{16} O_{12}^{24} M g_{, 26}^{56} F e \) and \( _{33}^{88} S r ? \)


Cork of commerce obtained from
Quercus is part of
A. Phellem
B. Phellogen
c. Phelloderm
D. All of the above


Find the area of triangle having vertices \( \operatorname{are} \boldsymbol{A}(\mathbf{3}, \mathbf{1}), \boldsymbol{B}(\mathbf{1} \mathbf{2}, \mathbf{2}) \) and \( \boldsymbol{C}(\mathbf{0}, \mathbf{2}) \)
A . 4
B. 6
c. 12
D. 18


Evaluate :
\( \tan \left(2 \tan ^{-1} \frac{1}{5}\right) \)
A \( \cdot \frac{5}{6} \)
в. \( \frac{5}{12} \)
c. \( \frac{7}{12} \)
D. none of these


The angles in a Quadrilateral are \( x, 5 x, 2 x+10, x+80 \) Find \( x \)
A . 30
B . 18
\( c .35 \)
D. 42


Which carbohydrate is used in silvering
of mirrors ?
A. Fructose
B. Glucose
c. sucrose
D. starch


Match the columns:


Solve the differential equation: \( \left(x^{2}+\right. \)
\( \boldsymbol{x} \boldsymbol{y}) \boldsymbol{d} \boldsymbol{y}=\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot k(y-x)^{2}=x e^{-y / x} / x \)
B. \( k(y-x)^{2}=x e^{y / x} \)
C. \( k(x-y)^{2}=x e^{-x / y} / y \)
D. \( k(y-x)=-x e^{y / x} \)


When an object is thrown up from the surface of the earth, the force of gravity:
A. acts in the direction of the motion
B. acts in the opposite direction of the motion
c. remains constant as the body moves up
D. increases as the body moves up


\( 1 \mathrm{s}^{2} 2 \mathrm{s}^{2} 2 \mathrm{p}^{6} \) is the electron configuration
of:
A. nitrogen
B. boron
c. argon
D. neon


In figure, \( P O Q \) is a line. Ray \( O R \) is
perpendicular to line \( P Q . O S \) is another
ray lying between rays \( O P \) and \( O R \) Prove that \( \angle R O S=\frac{1}{2}(\angle Q O S- \)
\( \angle P O S) \)


Find \( \frac{d y}{d x}, \) if \( y=\sqrt{\cos (3 x+1)} \)


Which of the following chemicals is responsible for the depletion of ozone layer in the atmosphere?
A. Sulphur dioxide
B. Nitrous oxide
c. Chlorofluorocarbons
D. Carbon dioxide


The correct IU PAC name of the
following alkane is:
\( \mathbf{A} \cdot 3,6- \) diethyl \( -2- \) methyloctane
B. \( 5- \) isopropyl -3 - ethyloctane
c. \( 3- \) ethyl \( -5- \) isopropyloctane
D. \( 3- \) isopropyl \( -6- \) ethyloctane.


A magnesium ribbon is burnt in oxygen to give a white compound 'X' accompanied by emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to burn and forms a compound 'Y'. Write a balanced chemical equation when 'X' is dissolved in water.
\( \mathbf{A} \cdot 2 M g+O_{2} \rightarrow 2 M g O \)
В. \( 3 M g+N_{2} \rightarrow M g_{3} N_{2} \)
c. \( M g O+H_{2} O \rightarrow M g(O H)_{2} \)
D. \( M g+H_{2} O \rightarrow M g(O H)_{2} \)


Two cells of emf \( E_{1} \) and \( E_{2} \) are to be
compared in a potentiometer \( \left(\boldsymbol{E}_{\mathbf{1}}>\boldsymbol{E}_{2}\right) \)
When be the cells are used in series
correctly, the balancing length obtained is \( 400 \mathrm{cm} . \) When they are used in series
but \( E_{2} \) is connected with reverse
polarities, then find the balancing length obtained is 200 of emf of cells....


The value of \( e / m \) of an electron was
measured by :
A. Millikan
B. J.J. Thomson
c. Dalton
D. Rutherford


Using differentials, find the approximate value of each of the
following up to 3 places of decimal.
(i) \( \sqrt{25.3} \)
(ii) \( \sqrt{49.5} \)
(iii) \( \sqrt{\mathbf{0 . 6}} \)
\( (i v)(0.009)^{\frac{1}{3}} \)
\( (v)(0.999)^{\frac{1}{10}} \)
\( (v i)(15)^{\frac{1}{4}} \)
(vii) \( (26)^{\frac{1}{3}} \)
\( (\text { viii })(255)^{\frac{1}{4}} \)
\( (i x)(82)^{\frac{1}{4}} \)
\( (x)(401)^{\frac{1}{2}} \)
\( (x i)(0.0037)^{\frac{1}{2}} \)


In case of measurement of \( g \), if error in measurement of length of pendulum is \( 2 \%, \) the percentage error in time period is1 \%. The maximum error in
measurement of g is
A . 1 \%
в. 2 \%
c. \( 4 \% \)
D. no error.


How many moles of the iodine remain unreacted at equilibrium?
\( \mathbf{A} \cdot 0.388 \)
B. 0.112
c. 0.25
D. 0.125


The mean free path of molecules of a gas (radius 'r') is inversely proportional
to
A \( \cdot r^{3} \)
В \( \cdot r^{2} \)
\( c \cdot r \)
D. \( \sqrt{r} \)


Classify the following as linear, quadratic and cubic polynomials
\( x-1 \)


A \( -------- \) has only one line of symmetry, two sets of equal sides and only one set of matching angles.


In plants, enzymes are present
A. Only in flowers
B. Only in leaves
C. In all the living cells of plant body
D. Only in parenchyma


Which of the following is not formed
when \( H_{2} S \) reacts with acidic \( K_{2} C r_{2} O_{7} \)
solution?
A \( \cdot C r S O_{4} \)
B. \( C r_{2}\left(S O_{4}\right)_{3} \)
\( c . s \)
D. \( H_{2} O \)


If the orientation of the current loop in a magnetic field is changed then potential energy of loop is also changed.Enter 1 if True and 0 if False.


State Mendeleev's periodic law.


Find the value of \( \cos \left[\frac{\pi}{2}-\sin ^{-1}\left(\frac{1}{3}\right)\right] \)


A junction between the axon of a neuron and dendrites of next one is
A. Synaptic cleft
B. Cell junction
c. synapse
D. Channel


In fig., a cone lies in a uniform electric
field E. Determine the electric flux
entering the cone
A. Flux \( \phi=E A=2 E R h \)
B. Flux \( \phi=E A=7 E R h \)
c. Flux \( \phi=E A=9 E R h \)
D. Flux \( \phi=E A=E R h \)


\( (\boldsymbol{A}+\boldsymbol{A} \boldsymbol{g})+\boldsymbol{Z} \boldsymbol{n} \longrightarrow(\boldsymbol{A}+\boldsymbol{A} \boldsymbol{g}+ \)
\( Z n) \frac{\operatorname{cooling}}{y-\operatorname{layer}} \frac{x-\operatorname{layer}}{y-\ln } \)
x layer - solid alloy y layer - molten metal
Molten metal is purified by:
A. Hall-Heroult process
B. Hoop method
c. Baeyer's process
D. Parkes process


Haematocrit is the ratio of
A. WBC to plasma
B. RBCs to plasma
C . Platelets to plasma
D. Total blood cells to plasma


The transformation ratio of a step up
transformer is :
A. greater than one
B. less than one
C. less than one and some times greater than one
D. greater than one and some times less than one


Arrange the following compounds in increasing order of their boiling points.
\( (i) C H_{3} C H_{2} C H_{2} C H O \)
\( (i i) C H_{3} C H_{2} C H_{2} C H_{2} O H \)
\( (i i i) C_{2} H_{5} O C_{2} H_{5} \)
\( (i v) C H_{3} C H_{2} C H_{2} C H_{3} \)
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i i)>(i)>(i i i)>(i v) \)
c. \( (i v)>(i)>(i i)>(i i i) \)
D. \( (i i i)>(i)>(i i)>(i v) \)


Respiratory intermediate which
undergoes fermentation is generally
A. Glyceraldehyde 3-phosphate
B. 2-phosphoglyceric acid
c. PEP
D. Pyruvic acid


Calculate the scalar product of the following vectors \( \boldsymbol{a}=\mathbf{3} \boldsymbol{i}+\mathbf{2} \boldsymbol{j}+\mathbf{2} \boldsymbol{k} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{b}=\mathbf{1} \mathbf{8} \boldsymbol{i}- \)
\( 22 j-5 k \)


If the Arithmetic mean of
\( 8,6,4, x, 3,6,0 \) is \( 4 ; \) then the value of
\( \boldsymbol{x}= \)
\( A \cdot 7 \)
B. 6
\( c .1 \)
D. 4


If \( \sin A+\cos A=1, \) then \( \sin 2 A \) is
equal to.
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 0 \)
D. \( 1 / 2 \)


f \( \boldsymbol{y}=\boldsymbol{a} \log |\boldsymbol{x}|+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x} \) has its
extremum values at \( x=-1 \) and \( x=2 \)
then the value of \( -2 a b \) is


A plane mirror is placed along the \( x \)
axis facing negative y-axis. The mirror is fixed. A point object is moving with \( 3 \hat{i}+4 \hat{j} \) in front of the plane mirror. The
relative velocity of image with respect
to its object is
\( A \cdot-8 \hat{j} \)
B. \( 8 \hat{j} \)
c. \( 3 \hat{i}-4 \hat{j} \)
D. \( -6 \hat{i} \)


Dry chlorine is not collected over
mercury because:
A. of formation of mercuric chloride
B. of formation of amalgams
c. it is soluble in mercury
D. it is heavier than mercury


Select correct statement about the
product (P) of the reaction:
This question has multiple correct options
A. \( P \) is optically inactive due to internal compensation
B. \( P \) is optically inactive due to the presence of plane of symmetry in the molecule
c. The structure of P can have three optical isomers possible.
D. P can have four possible optical isomers


A certain metallic surface is
illuminated with monochromatic.light of wavelength \( \lambda \) The stopping potential for photo electric .current for this light is \( 3 v \lambda \) if the same surface is
illuminated with light of wavelength 2
\( \lambda \) the stopping potential is \( v_{0} . \) The threshold wavelength for this surface for photo-electric is
A \( .4 \lambda \)
B. \( 5 \lambda \)
c. \( 6 \lambda \)
D. \( 7 \lambda \)


Find the of \( \lambda, \) so that the matrix \( \left[\begin{array}{cc}\mathbf{5}-\boldsymbol{\lambda} & \boldsymbol{\lambda}+\mathbf{1} \\ \mathbf{2} & \mathbf{4}\end{array}\right] \) may be singular


The electron is present in the N shell in H-atom. When energy is lost, spectral line may be observed in \( \ldots \ldots . . \) region.
\( A \). infra-red
B. visible
c. ultra-violet
D. any of these


A slit of width a is illuminated by white light. The first minimum for red light \( (\lambda=6500 A) \) will fall at \( \theta=30 \) when
a will be:
A \( \cdot 3200 \)
В. \( 6.5 \times 10^{-4} \mathrm{mm} \)
c. 1.3 micron
D. \( 2.6 \times 10^{-4} \mathrm{cm} \)


The enzyme recombinase is required in which stage of meiosis?
A. Zygotene
B. Diplotene
c. Diakinesis
D. Pachytene


In the procedure shown above, a
calcium chloride solution is mixed with
a sodium sulfate solution to create the
products shown.Which of the following is illustrated by this activity?
A. Law of conservation of mass
B. Theory of thermal equilibrium
c. Law of conservation of momentum
D. Theory of covalent bonding