A concave lens can form
A. An erect magnified image
B. An erect diminished image
C. An inverted magnified image
D. An inverted diminished image


Evaluate the following integral
\( \int \frac{a}{b+c e^{x}} d x \)


The position vectors of the points \( A, B, C \) are respectively (1,1,1)\( ;(1,-1,2) ;(0,2,-1) \)
Find a unit vector parallel to the plane determined by ABC \& perpendicular to the vector (1,0,1)
A \( \cdot \pm \frac{1}{3 \sqrt{3}}(i+5 j-k) \)
B . \( \pm(i+5 j-k) \)
\( \mathbf{c} \cdot \pm(-i-5 j-k) \)
D \( : \pm \frac{1}{3 \sqrt{3}}(-i-5 j-k) \)


Write the IUPAC names of the given
compounds:


Set up an equation of a tangent to the graph of the following function. \( \boldsymbol{y}=\boldsymbol{3}^{x}+\boldsymbol{3}^{-2 x} \) at the points with
abscissa \( \boldsymbol{x}=\mathbf{1} \)


A man can see distinctly from a distance of \( 0.5 m . \) If he wants to read a
book placed at a distance of \( 25 \mathrm{cm} \), then
what kind of lens should he use??
A. Convex lens with focal length of \( -50 \mathrm{cm} \)
B. Concave lens with focal length of \( -50 c m \)
c. convex lens with focal length of \( 50 \mathrm{cm} \)
D. Concave lens with focal length of \( 50 \mathrm{cm} \)


Write converse, inverse and contrapositive of the following conditional statement:
If an angle is a right angle then its
measure is \( 90^{\circ} \)


Observe the angles shown in the figure
and write the following pair of angles.
(1) Interior alternate angles
(2) Corresponding angles
(3) Interior angles


A body is projected up along the rough inclined plane from the bottom with some velocity. It travels up the incline
and then returns back. If the time of
ascent is \( t_{a} \) and time of descent is \( t_{d} \)
then
\( \mathbf{A} \cdot t_{a}=t_{d} \)
в. \( t_{a}>t_{d} \)
c. \( t_{a}<t_{d} \)
D. Data in-sufficient


Prove that \( \operatorname{at} x=2, \) limits of function
does not exist \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{ccc}x^{2}+x+1 & \text { if } & x \geq \\ n & \text { if } & x<2\end{array}\right\} \)


A bus accelerates uniformly from rest and acquires a speed of \( 75 k m / h r \) in \( 20 s . \) The acceleration of the bus
(rounded off to the nearest integer) is:
A \( \cdot 10 m / s^{2} \)
B . \( 5 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 2 m / s^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)


The foci of the conic section
\( 25 x^{2}+16 y^{2}-150 x=175 \) are
\( A \cdot(0,\pm 3) \)
B \( \cdot(0,\pm 2) \)
c. (3,±3)
D \( \cdot(0,\pm 1) \)


A transverse sinusoidal wave is
generated at one end of a long horizontal string by a bar that moves the end up and down through a distance
by \( 2.0 \mathrm{cm} . \) The motion of bar is continuous and is repeated regularly
125 times per sec. If the distance between adjacent wave crests is
observed to be \( 15.7 \mathrm{cm} \) and the wave
is moving along +ve x-direction, and at \( \boldsymbol{t}=\mathbf{0}, \) the element of the string at \( \boldsymbol{x}=\mathbf{0} \)
is at mean position \( y=0 \) and is
moving downwards, the equation of the
wave is best described by : \( (u s e \pi= \)
\( \mathbf{3 . 1 4}) \)
A \( \cdot y=(1 c m) \sin [(40.0 r a d / m) x-(785 r a d / s) t] \)
B . \( y=(2 c m) \sin [(40.0 r a d / m) x=(785 r a d / s) t] \)
c. \( y=(1 c m) \cos [(40.0 r a d / m) x-(785 r a d / s) t] \)
D. \( y=(2 c m) \cos [(40.0 r a d / m) x-(785 r a d / s) t] \)


Asexual reproduction in fungi takes
place by
A. Endospore
B. Gametangia
c. conidiospore
D. None of the above


Select the correct order of bond angle in
following molecules.
A. \( x<y \)
B. \( y<x \)
c. \( x=y \)
D. None of these


Phosphoric acid \( H_{3} P O_{4} \) can not be neutralised to
A \( \cdot H P O_{4}^{2} \)
в. \( P O_{4}^{3} \)
c. \( H_{2} P O_{4} \)
D. \( H P O_{3}^{2} \)


In Passiflora, the tendrils are
modification of
A. Axillary buds
B. Upper leaflets
c. Whole leaves
D. stipules


\( [(\cos \theta+i \sin \theta)(\cos \theta-i \sin \theta)]^{-1} \)
\( \mathbf{A} \cdot i \)
B.
\( c \cdot-i \)
D. -


Assertion
Evaporation and vapour pressure depends upon available surface area of
solvent at any temperature.
Reason
Larger is surface area of solvent for evaporation more is evaporation.
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


expressed in grams is numerically equal to gram molecular mass of the substance.
A. Molecular mass
B. Atomic mass
c. Formula mass
D. A,


The magnifying power of a telescope is
9. When it is adjusted for parallel rays, the distance between the objective and the eye piece is found to be 20 cm. The
focal length of lenses are
\( \begin{array}{lll}\text { A. } 18 & \text { cm, } 2 & \text { cm }\end{array} \)
\( \begin{array}{lll}\text { В. } 11 & c m, 9 & c m\end{array} \)
\( \begin{array}{lll}\text { c. } 10 & c m, 10 & c m\end{array} \)
D. \( 15 \quad \) cm \( , 5 \) cm


Basal placentation occurs in an ovary which is
A. Unilocular
B. Bilocular
c. Multilocular
D. Lateral


Deuterium is more reactive
than Hydrogen. If this is true enter 1 , if false enter 0 .


Petromyzon is included under
A. Cephalochordata
B. Agnatha
c. Tetrapoda
D. Pisces


The time period of a particle executing SHM is \( 8 s . \) At \( t=0, \) it is at mean
position. If \( A \) is the amplitude of particle, then the distance travelled by particle (in second) is?
A \( \cdot \sqrt{2} A \)
B \( \cdot\left(1-\frac{1}{\sqrt{2}}\right) \)
c. \( 2 A \)
D. \( \frac{A}{\sqrt{2}} \)


When a body of mass \( 1.0 \mathrm{kg} \) is suspended from a certain light spring hanging vertically, its length increases by \( 5 \mathrm{cm} . \) By suspending \( 2.0 \mathrm{kg} \) block to the spring and if the block is pulled through \( 10 \mathrm{cm} \) and released, the
maximum velocity in it in \( m / s \) is
A . 0.5
B. 1
c. 2
D. 4


Find the cube of the following binomial expressions:
\( \frac{3}{x}-\frac{2}{x^{2}} \)


The magnetic field produced by a current-carrying wire at a given point depends on
A. the current passing through it
B. the voltage across it
c. the power through it
D. all


Two bodies of masses \( 10 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities \( 2 \hat{i}-7 \hat{k}+ \) \( 3 \hat{j} m s^{-1} \) and \( -10 \hat{i}+35 \hat{k}-3 \hat{j} m s^{-1} \)
respectively. The velocity of their centre of mass is
A \( \cdot 2 \hat{i} m s^{-1} \)
в. \( 2 \hat{j} \) ms\( ^{-1} \)
\( \mathbf{c} \cdot(2 \hat{j}+2 \hat{k}) m s^{-1} \)
D. \( (2 \hat{i}+2 \hat{j}+2 \hat{k}) m s^{-1} \)


Write short notes on Peptization.


Which of the statements about the
reaction below are incorrect?
\( 2 P b O(s)+C(s) \rightarrow 2 P b(s)+C O_{2}(g) \)
(a) Lead is getting reduced.
(b) Carbon dioxide is getting oxidised
(c) Carbon is getting oxidised.
(d) Lead oxide is getting reduced
A \( \cdot(a) \) and \( (b) \)
B. (a) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. All


Find solution of following inequality, also show it graphically:
\[
\boldsymbol{x}+\mathbf{3} \leq \mathbf{5}, \boldsymbol{x} \in \boldsymbol{N}
\]
\( A \)
\begin{tabular}{rrrrrrrrrr}
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
\end{tabular}
B.
\begin{tabular}{rrrrrr}
\hline & & & & & & \\
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\( \underbrace{\longleftarrow}_{-2}-1 \quad_{0} \quad_{1} \quad_{2} \quad_{1} \)
\( D \)
\begin{tabular}{rrrrrr}
\hline & 1 & 1 & & & 1 \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}


The energy (in \( e V \) ) required to excite an
electron from \( n=2 \) to \( n=4 \) state in
hydrogen atom
\( \mathbf{A} \cdot+2.55 \)
в. -3.4
c. +4.25
D. -0.85


Solve the following equation: If \( 14 y- \) \( 8=13 \) and \( y=\frac{3}{q}, \) then \( q \) is
A . 3
B.
\( c \cdot 2 \)
D.


Find the equations of the lines for which \( \tan \theta=\frac{1}{2}, \) where \( \theta \) is the angle of
inclination of the line and \( x- \) intercept
is 4


The intensity of central fringes in the interference pattern produced by two identical slits is \( I . \) When one of the slits
is closed then the intensity at the same
point is \( I_{o} . \) The relation between the \( I \)
and \( I_{o} \) is
A \( . I=4 I_{0} \)
B . \( I=2 I_{0} \)
c. \( I=I_{o} \)
D. \( I=\frac{I_{o}}{2} \)


Integrate the function : \( \frac{1}{x \sqrt{a x-x^{2}}} \)


Given \( \boldsymbol{x} \in\{\text { integers }\}, \) find the solution \( \operatorname{set} \) of \( :-5 \leq 2 x-3<x+2 \)


A boy who resides near a powerloom has
developed a habit of speaking loudly everywhere. Give a scientific reason.


Statement \( I- \) Zinc and berylium have
electron affinities which are
significantly different from each other.
Statement \( I I- \) Electron affinity is a
measure of the energy used to add an
electron to an atom.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement \( I I \) is false
E. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in 1


\( \frac{\sqrt{0}}{0} \)
0
0
0


A new soft drink bottle is opened, allowing gas to escape into the atmosphere. As the gas escapes, its degree of disorder increases. Identify by which of the following law this can be explained?
A. First law of thermodynamics (conservation of energy)
B. Second law of thermodynamics (law of entropy)
c. Ideal gas law
D. Heat of fusion and heat of vaporization equation
E. Heat engine efficiency


Divide the polynomial \( p(x) \) by the polynomial \( g(x) \) and find the quotient and remainder in each of the following. \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\boldsymbol{3} \quad \boldsymbol{g}(\boldsymbol{x})= \)
\( x^{2}-2 \)


A potted plant was taken in order to prove a factor necessary for photosynthesis. The potted plant was kept in the dark for 24 hours. One of the leaves was covered with black paper in
the centre. The potted plant was then
placed in sunlight for a few hours.
Why was the plant placed in the dark before beginning the experiment?


The dispersed phase and dispersion medium of fog respectively are:
A. solid, liquid
B. liquid, liquid
c. liquid, gas
D. gas, liquid


Buckminster fullerene is:
A. graphite
B. diamond
\( c \cdot c-60 \)
D. quartz


The separation L between the objective
\( f_{o}=0.5 \mathrm{cm} \) ) and the eye piece \( \left(f_{e}=\right. \) \( 5 c m \) )of a compound microscope is 7.0
cm. Where should a small object be placed so that the eye is least strained?
A \( \cdot \frac{1}{2} c m \)
в. \( \frac{3}{2} c m \)
c. \( \frac{2}{3} c m \)
D. \( \frac{1}{3} c m \)


Assertion
Photorespiration is the respiration which occurs during the daytime.
Reason Photorespiration is biochemically different from normal respiration
involving glycolate mechanism.
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


When a current \( I \) is set up in a wire of
radius \( r, \) the drift velocity is \( v_{d} . \) If the
same current is set up through a wire of radius \( 2 r, \) the drift velocity will be
A . \( 4 v_{d} \)
в. \( 2 v_{d} \)
c. \( \frac{v_{d}}{2} \)
D. \( \frac{v_{d}}{4} \)


What amount of power is generated in
that resistance?
\( P=\frac{2 v^{2} B^{2} d^{2} R}{\left(R+\frac{2 \rho d}{S}\right)^{2}} \)
\( P=\frac{2 v^{2} B^{2} d^{2} R}{\left(R+\frac{\rho d}{S}\right)^{2}} \)
\( \mathbf{C} \cdot p=\frac{v^{2} B^{2} d^{2} R}{\left(R+\frac{2 \rho d}{S}\right)^{2}} \)
\( P=\frac{v^{2} B^{2} d^{2} R}{\left(R+\frac{\rho d}{S}\right)^{2}} \)


In the demonstration of stomata on a
leaf peel. The peel should be taken from
A. Freshly-plucked leaf
B. Dry plucked lead
c. Freshly or dry plucked leaf
D. None of the above


Find the value of the determinant
\( \left|\begin{array}{cc}\mathbf{2} \boldsymbol{i} & -\mathbf{3} \boldsymbol{i} \\ \boldsymbol{i}^{3} & -\mathbf{2} \boldsymbol{i}\end{array}\right| \) where \( \boldsymbol{i}=\sqrt{-\boldsymbol{i}} \)


Distribution of energy in the spectrum of a black body can be correctly represented by?
A. Wein's law
B. Stefan's law
c. Planck's law
D. Kirchhoff's law


Pseudoplasmodium is characteristic of
A. Bacteria
B. Acellular slime molds
c. Diatoms
D. Cellular slime molds


\( A \) and \( B \) are fixed points. If \( |P A-P B| \)
is a constant, locus of \( \boldsymbol{P} \) is
A. a parabola
B. an ellipse
c. a hyperbola
D. a circle


What is the minimum energy required to launch a satellite of mass \( \mathrm{m} \) from the
surface of a planet of mass \( \mathrm{M} \) and
radius \( \mathrm{R} \) in a circular orbit at an
altitude of 2R.
\( \mathbf{A} \cdot \frac{5 G m M}{6 R} \)
B. \( \frac{G m M}{2 R} \)
\( \mathbf{c} \cdot \frac{G m M}{3 R} \)
\( \mathbf{D} \cdot \frac{5 G m M}{7 R} \)


If we consider the gravitational force \( F \)
between two objects of masses \( m_{1} \) and
\( m_{2} \) respectively, separated by a distance \( R, \) and we double the distance
between them, what is the new magnitude of the gravitational force between them?
\( A \cdot F / 4 \)
B. F/2
\( c \cdot F \)
D. 2F
E. 4


The correct name of the following
compound is:
A. 2 -hexen- 5 -yne
B. 4-hexen-1-yne
C. 5 -hexyn-2-ene
D. 1-hexyn-4-ene


How many significant figures are present in \( 0.010100 \times 10^{3} ? \)
A. 7
B. 5
\( c \cdot 3 \)
D. 10


If the point \( \left(\boldsymbol{x}_{1}+\boldsymbol{t}\left(\boldsymbol{x}_{2}-\boldsymbol{x}_{1}\right), \boldsymbol{y}_{1}+\right. \)
\( \left.t\left(y_{2}-y_{1}\right)\right) \) divides the join of \( \left(x_{1}, y_{1}\right) \)
and \( \left(x_{2}, y_{2}\right) \) internally, then
A. \( t<0 \)
B. \( 0<t<1 \)
c. \( t>1 \)
D. \( t=1 \)


The mean of \( x, y, z \) is \( y, \) then \( x+z= \)
A \( . y \)
в. \( 3 y \)
c. \( 2 y \)
D. \( 4 y \)


The value of alternating emf in the following circuit will be
A. 220 volt
B. 140 volt
c. 20 volt
D. 100 volt


A ball drops from a height of \( 4802 \mathrm{m} \) Thereafter it bounces every time to a height which is \( 14.28 \% \) less than its previous height. What height will the ball reach on its 4 th bounce \( ? \)


Find the intervals in which the function
\( f \) given by \( f(x)=x^{3}+\frac{1}{x^{3}}, x \neq 0 \) is
(i) increasing
(ii) decreasing.


The number of Four digit numbers formed by using the digits 0,2,4,5 and which are not divisible by \( 5, \) is
A . 10
B. 8
\( c \cdot 6 \)
D. 4


Q Type your question
the center (point \( C \) ) of the equilateral
triangle with charges at the corners?
\( A \)
B.
\( c \)
\( D \)


Which one is not correct about
Freundlich isotherm?
\( n=\frac{1}{\tan \theta} \) at average pressure
\( \mathbf{B} \cdot \theta=45^{\circ} \) at low pressure
\( \mathbf{C} \cdot \theta=45^{\circ} \) at high pressure
\( D \)


\( X \) is a Normally distributed variable
with mean \( =30 \) and standard deviation
\( =4 . \) Find \( P(30<x<35) \)
A . 0.3698
B. 0.3956
c. 0.2134
D. 0.3944


Silt in water remains suspended. It is
removed by sedimentation and filtration. For increasing its sedimentation aluminium sulphates and calcium hydroxide (slaked lime) are added. As a result sticky aluminium hydroxide.
A. Destroys slit particles
B. Attracts the particles of slitt
C. Mixes with slit particles
D. Makes slit particles increases in size and deposit at the bottom


\( \frac{a}{k} \)


Scaly bark occurs in
A. Eucalyptus
B. Betula
c. Psidium
D. Tectona


Fossilization would occur when flora
and fauna are buried by
A. Natural processes
B. Industrial processes
c. Enzymatic process
D. All of the above


Check whether the following is quadratic equation.
\( \boldsymbol{x}^{2}-\mathbf{2} \boldsymbol{x}=(-\mathbf{2})(\boldsymbol{3}-\boldsymbol{x}) \)


Find the range of the following function:
\( f(x)=\frac{|x-4|}{x-4} \)
\( \mathbf{A} \cdot[-1,1] \)
В. \( \left[-\frac{\pi}{2}, \frac{3 \pi}{2}\right] \)
c. \( (-2 \pi, 0] \)
D. \( \left[\frac{-3 \pi}{2}, \frac{\pi}{2}\right. \)


In \( \Delta A B C, A=50^{\circ}, \angle B=60^{\circ} \)
arranging the sides of the triangle in ascending order, we get :
A. \( A B<B C<C A \)
в. \( C A<A B<B C \)
c. \( B C<C A<A B \)
D. \( B C<A B<C A \)


When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law
of conservation of charge.


What is the expression for the maximum height reached by a body thrown vertically upwards with a velocity \( u \) and time of flight \( T \)
A \( \quad h=\frac{g T^{2}}{8} \)
B. \( h=\frac{u^{2}}{2 g} \)
c. Both A \& B
D. None of the above


For a light ray, if the glancing angle of
incidence is \( 30^{\circ}, \) then the angle of
incidence will be
\( A \cdot 30 \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. 150


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


Find the differential coefficient of \( \sin x \)
by first principle.


Which of the following is translated completely?
I. AUG, UGA, UUA, AAG, AAA
II. AUG, AUA, UUG, CCC, UGA
III. \( A G U, U C C, A G A, C U C, U A A \)
IV. AUG, UAC, AGU, AAC, UAG
A. I and II
B. II and IV
c. I and IV
D. II and III


It is observed that the population of a
city increase at the rate of \( 8 \% \) per annum. If the present population of the
city is \( 125000, \) then the population of
the city after 2 years will be
A . 145000
B. 145800
c. 154000
D. 154800


Find the nth term of the A.P.'s:
2, 7, 12, 17,


The hydroxyl ion may be formed by:
This question has multiple correct options
A. acids
B. bases
C. water gaining a hydrogen ion
D. alkali


\( B r F_{5} \) is a:
A. Interhalogen compound
B. Pseudohalogen compound
C. Both the above
D. None of the above


Which of the following reactions is said
to be entropy driven?
A. Endothermic reaction with positive entropy change and high temperature
B. Endothermic reaction with negative entropy change and low temperature
C. Exothermic reaction with positive entropy change and high temperature
D. Exothermic reaction with negative entropy change and low temperature


The image perceived by the brain is:
A. erect and smaller than the object
B. inverted and smaller than the object
c. erect and of same size as the object
D. inverted and of same size as the object


Explain the concept of reaction with no
order.


The focal length of the objective and eye piece of a compound microscope are \( 1 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. An object
is placed at a distance of \( 1.1 \mathrm{cm} \) from objective. If final image is formed by at least distance vision, the magnifying
power is:
\( \mathbf{A} \cdot 60 \)
B. 50
c. 40
D. None of these


Suppose a vertical tunnel is dug along
the diameter of the earth, assumed to
be a sphere of uniform mass density \( \rho \)
If a body of mass \( m \) is thrown in this
tunnel, its acceleration at a distance \( y \)
from the centre is given by:
A.
\[
\frac{4 \pi}{3} G \rho y m
\]
B.
\[
\frac{3}{4} \pi \rho y
\]
\( c \)
\[
\frac{4}{3} \pi \rho y
\]
\( D \)
\[
\frac{4}{3} \pi G \rho y
\]


If the frequency of a sound wave is doubled then the velocity of sound will be
A. zero
B. half
c. double
D. unchanged


The internal and external diameters of a
hollow hemispherical vessel are \( 24 \mathrm{cm} \)
and \( 25 c m, \) respectively. The cost to paint \( 1 \mathrm{cm}^{2} \) surface is \( R s .0 .05 . \) Find the
total cost to paint the vessel all over.
(use \( \left.\pi=\frac{22}{7}\right) \)
A . Rs.2100
B. \( R s .1867 \)
c. \( R s .1245 \)
D. None of the above


Rhizoid containing sporophytic plants are characteristic of
A. Bryopsida
B. Spenopsida
c. cycadophyta
D. Psilopsida


If \( A \) is a square matrix of order \( 3 \times 3 \)
such that \( |\boldsymbol{A}|=\mathbf{5}, \) then find \( |\boldsymbol{4} \boldsymbol{A}| \)


The difference between the C.I. and S.I.
on a sum of money deposited for 4 years at \( 5 \% \) per annum was Rs. \( 15 . \) Find the
sum of the money.
A .667 .74
B. 767.74
c. 867.74
D. 967.74


There are 40 doctors in a surgical department. In how many ways can they be arranged to form the following teams: (a) a surgeon and an assistant;
(b) a surgeon and four assistants?


A charged particle is moved along a magnetic field line.The magnetic force on the particle is
A. opposite to its velocity
B. along its velocity
c. zero
D. perpendicular to its velocity


\( (\boldsymbol{A}+\boldsymbol{B})^{\boldsymbol{T}}= \)
\( A \cdot A+B \)
В. \( A^{T}+B^{T} \)
c. Does not exist
D. (a) or (b)


A lens having focal length \( \boldsymbol{f} \) and
aperture of diameter \( d \) forms an image \( \boldsymbol{d} \)
of intensity \( I . \) Aperture of diameter \( \frac{\mathrm{u}}{2} \) in central region of lens is covered by a
black paper. Focal length of lens and
intensity of image now will be respectively.
A \( \cdot f \) and \( \frac{I}{4} \)
B. \( \frac{3 f}{4} \) and \( \frac{I}{4} \)
c. \( f \) and \( \frac{3 I}{4} \)
D. \( _{f \text { and }} \frac{I}{2} \)


The sum of products of masses and velocities of two moving bodies before and after their collision remains the
same .The law involved here is:
A. Law of conservation of mass
B. Law of conservation of velocity
c. Law of conservation of energy
D. Law of conservation of momentum


Ethyl alcohol is the hydrolysis product of
A \( \cdot C_{2} H_{5} C l \)
в. \( C H_{3} C H O \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{5} M g I \)


Name the type of energy (kinetic energy
\( \boldsymbol{K} \) or potential energy \( \boldsymbol{U} \) ) possessed in the following case.
A piece of stone placed on the roof
A. \( U \)
в. \( K \)
c. \( U \) and \( K \)
D. No energy


Carbon and oxygen combine to form two oxides, carbon monoxide and carbon
dioxide in which the ratio of the weights
of carbon and oxygen is respectively 12 :
16 and \( 12: 32 . \) These figures illustrate the:
A. Law of multiple proportions
B. Law of reciprocal proportions
c. Law of conservation of mass
D. Law of constant proportions


Two blocks of masses \( 10 \mathrm{kg} \) and \( 4 \mathrm{kg} \) and are connected by a spring of negligible mass and placed on a
frictionless horizontal surface. An
impulse gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in the direction of the
lighter block. The velocity of the centre of mass is


The value of relative magnetic
permeability \( \left(\mu_{r}\right) \) for ferromagnetic materials is
A \( \cdot\left(\mu_{r}=1\right) \)
В \( \cdot\left(\mu_{r}>>1\right) \)
c. \( \left(\mu_{r}<1\right) \)
D. \( \left(\mu_{r}>1\right) \)


The area of a rhombus is \( 72 \mathrm{cm}^{2} \) and its
perimeter is \( 32 \mathrm{cm}, \) altitude is
\( A \cdot 8 c m \)
в. 9 ст
\( c .4 \mathrm{cm} \)
D. None of these


A \( 5 \% \) solution of cane sugar is isotonic with \( 0.877 \% \) of \( X . \) The molecular weight of substance X is:
\( \mathbf{A} \cdot 58.98 \)
B. 119.96
\( \mathbf{c} .95 .58 \)
D . 126.98


\( \lim _{n \rightarrow \infty} \frac{n^{p} \sin ^{2}(n !)}{n+1}, 0<p<1, \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \infty \)
c. 1
D. none of these


The value of \( k_{c} \) for the reaction
\( \mathbf{2} \boldsymbol{A} \rightleftharpoons \boldsymbol{B}+\boldsymbol{C} \) is \( 2 \times 10^{-3} \)
At a given time the composition of reaction mixture is \( [A]=[B]=[C]=3 x \)
\( 10^{-4} \) M. In which direction the reaction
will proceed?
A. From left to right
B. From right to left
c. The reaction is at equilibrium
D. First to the right than left


Differentiate the following functions
w.r.t. \( x \)
\( e^{\log (\log x)} \)


A circular road of radius \( 50 \mathrm{m} \) has the
angle of banking equal to \( 30^{\circ} . \) At what speed should a vehicle go on this road so that the friction is not used?
\( \mathbf{A} \cdot 7 m s^{-1} \)
B. \( 17 m s^{-1} \)
\( \mathbf{c} \cdot 22 m s^{-1} \)
D. \( 27 m s^{-1} \)


Calculate the pressure of \( C O_{2} \) gas at 700 K in heterogeneous equilibrium
reaction \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( C O_{2}(g) \) if \( \Delta H \) for this reaction is
\( 130.2 k J \)


The factors that influence the ionisation
energies are :
A. the size of the atom
B. the charge on the nucleus
c. how effectively the inner electron shell screen the nuclear charge
D. all of the above


How will you demonstrate the thermal expansion in a liquid? Describe an experiment.


Which of these elements is not found in
nitrogenous base?
A. Nitrogen
B. Hydrogen
c. carbon
D. Phosphorus


Manasa says, Each angle in any pair of complementary angles is a always
acute. Do you agree? Give reason.


\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{S C} \boldsymbol{N})_{6}\right] \) and
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}(\boldsymbol{S C N})_{4}\right]\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}(\boldsymbol{S C N}\right. \)
are the examples of what type of isomerism?
A. lonisation isomerism
B. Linkage isomerism
c. coordination isomerism
D. Solvate isomerism


Consider a point charge with \( \boldsymbol{q}=\mathbf{1 . 5} \times \)
\( 10^{-8} C . \) Then, the radius of an
equipotential surface having a potential of \( 30 V \) is :
A \( .0 .45 m \)
в. 4.5 т
c. infinite
D. none of the above


Area bounded by the curves \( \boldsymbol{y}= \)
\( e^{x}, y=e^{-x} \) and the straight line \( x=1 \)
is (in sq units)
A \( \cdot_{e+\frac{1}{e}} \)
B. \( e+\frac{1}{e}+2 \)
c. \( _{e+\frac{1}{e}-2} \)
D. \( _{e-\frac{1}{e}+2} \)
E \( e-\frac{1}{e} \)


During the electrolysis of a concentrated brine solution. Calculate
the moles of chlorine gas produced by the passage of \( 4 F \) electricity.


Physical quantities are also known as:
A. Derived quantities
B. Base quantities
c. Professional quantitities
D. Energetic quantities


After how many seconds will the concentration of the reactant in a first
order reaction be halved, if the rate constant is \( 1.155 \times 10^{-3} \) sec \( ^{-1} \) ?
A. 600
B. 100
\( c \cdot 60 \)
D. 10


If the constant forces \( 2 \hat{i}-5 \hat{j}+6 \hat{k} \) and \( -\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) act on a particle due to
which it is displaced from a point \( A(4,-3,-2) \) to a point \( B(6,1,-3) \) then the work done is
A . 15 unit
B. 9 unit
c. -15 unit
D. - 9 unit


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow(-1,1) \) is defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{-\boldsymbol{x}|\boldsymbol{x}|}{\mathbf{1}+\boldsymbol{x}^{2}} \) then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) equals
\( ^{A} \cdot \sqrt{\frac{|x|}{1-|x|}} \)
в. \( \quad-\operatorname{sgn}(x) \sqrt{\frac{|x|}{1-|x|}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{x}{1-x}} \)
D. None of these


Match the name of vitamins in column
with their sources in column II and
mark the appropriate choice.
Column I Column II
(A) Vitamin
\( B_{1} \)
(i) Milk, yeast, cereals
(B) Vitamin
(ii) Meat, fish, egg
\( B_{12} \)
(C) Vitamin
(iii) Carrots, butter, papaya
(D) Vitami
(iv) Citrus fruits, amla, green leafy
\( \mathrm{C} \quad \) vegetables
\( \mathbf{A} \cdot(A) \rightarrow(\text { iii) },(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(\text { ii }) \)
B. \( (A) \rightarrow(\text { ii) },(B) \rightarrow(i),(C) \rightarrow(i \text { i) },(D) \rightarrow(i v) \)
C \( \cdot(A) \rightarrow(\text { iv ) },(B) \rightarrow(\text { iii) },(C) \rightarrow(\text { ii }),(D) \rightarrow(i) \)
D. (A) \( \rightarrow \) (i), (B) \( \rightarrow \) (ii), (C) \( \rightarrow \) (ii), (D) \( \rightarrow \) (iv)


Which of the following is a biodegradable polymer?
A. Polythene
B. Bakelite
c. РнВу
D. PVC


Consider following two reactions:
\( \boldsymbol{A} \longrightarrow \) Product, \( \quad-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}_{1}[\boldsymbol{A}]^{0} \)
\( \boldsymbol{B} \longrightarrow \) Product, \( \quad-\frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}_{2}[\boldsymbol{B}]^{1} \)
\( k_{1} \) and \( k_{2} \) are expressed in terms of
molarity \( \left(\operatorname{mol} L^{-1}\right) \) and time \( (s) \) as:
A \( \cdot s^{-1}, M s^{-1} L^{-} \)
B. \( M s^{-1}, M s^{-1} \)
c. \( s^{-1}, M^{-1} s^{-1} \)
D. \( M s^{-1}, s^{-1} \)


A uniform disc of mass M and radius R
is mounted on an axle supported in friction less bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is:
\( ^{A} \cdot \frac{M R}{2 T} \)
в. \( \frac{2 T}{M R} \)
c. \( \frac{T}{M R} \)
D. \( \frac{M R}{T} \)


Identify the type of isomerism in the following:
Butane and isobutane


If \( A=\left|\begin{array}{cc}0 & 1 \\ 2 & 4\end{array}\right|, B=\left|\begin{array}{cc}-1 & 1 \\ 2 & 2\end{array}\right| \)
\( c=\left|\begin{array}{cc}1 & 0 \\ 1 & 0\end{array}\right|, \) then \( 2 A+3 B-C= \)
A \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 9 & 14\end{array}\right| \)
в. \( \left|\begin{array}{cc}4 & 3 \\ 9 & 10\end{array}\right| \)
с. \( \left|\begin{array}{cc}4 & -5 \\ 9 & 14\end{array}\right| \)
О \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 14 & 9\end{array}\right| \)


If \( |\vec{A}+\vec{B}|=|\vec{A}|=|\vec{B}| \) the angle
between \( A \) and \( B \) will be :-
A \( \cdot 90^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 0^{c} \)
D. \( 60^{\circ} \)


What is meant by periodicity in properties of elements with reference to the periodic table?


The distance between the straight lines
\( 9 x+40 y-50=0,9 x+40 y+32=0 \)
is
\( A \cdot 1 \)
B . 2
\( c \cdot 82 \)
D. 41


In the figure, if \( A B=C D \) and
\( \angle A O B=90^{0} \) find \( \angle C O D \)


The most abundant tissue of the
adenoid tonsils is
A. Epithelium
B. Reticular connective tissue
c. Elastic connective tissue
D. Plasma


Write the scientific name of 'Peat moss'
and mention the division it belongs to


When a plane mirror is placed horizontally on a level ground at a distance of \( 60 \mathrm{m} \) from the front of a
tower, the top of the tower and its image
in the mirror subtend an angle of \( 90^{\circ} \) at the eye. The height of the tower is :
A. \( 30 m \)
в. 60 т
\( \mathrm{c} .90 \mathrm{m} \)
D. \( 120 m \)


The triad of nuclei that is isotonic is :
A \( \cdot \frac{14}{6} C, \frac{15}{7} N, \frac{17}{9} F \)
В \( \cdot \frac{12}{6} C, \frac{74}{7} N, \frac{19}{9} F \)
C \( \cdot \frac{14}{6} C, \frac{14}{7} N, \frac{17}{9} F \)
D \cdot \( _{6}^{14} C, \frac{14}{7} N, \frac{19}{9} F \)


Resistance of a wire at \( 20^{\circ} C \) is \( 20 \Omega \) and
at \( 500^{\circ} \mathrm{C} \) is \( 60 \Omega . \) At what temperature
its resistance is \( 25 \Omega \)
\( \mathbf{A} \cdot 160^{\circ} C \)
B. \( 250^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 100^{\circ} \mathrm{C} \)
D. \( 80^{\circ} \mathrm{C} \)


Calculate and compare the energy released by
(a) Fusion of \( 1.0 \mathrm{kg} \) of hydrogen deep within Sun (b) The fission of \( 1.0 \mathrm{kg} \) of \( ^{235} \mathrm{U} \) in a fission
reactor


A Young's interference experiment is performed with monochromatic light. The separation between the slits is
\( 0.5 m m, \) and the interference pattern on a screen is \( 3.5 m \) away, shows the first
order maximum at \( 3.6 m m \) from the
centre of the pattern. The wavelength is
A \( .515 n m \)
B. \( 315 \mathrm{mm} \)
c. 215 cm
D. \( 15 m \)


Solve:
\( 3 \sin ^{2} x-7 \sin x+2=0 \)


After chronic exposure, the noncarcinogenic effects of PAHs involve
primarily the:
A. pulmonary
B. gastrointestinal
c. renal
D. all of these


Points (1,5),(2,3) and (-2,-11) are
A. Non-collinear
B. Collinear
c. vertices of equilateral triangle
D. Vertices of right angle triangle


Sketch the curve for \( \sin y=\sin x \)


\( \boldsymbol{E}_{\boldsymbol{n}}=-\mathbf{3 1 3 . 6} / \boldsymbol{n}^{2} \boldsymbol{k c a l} / \)mol. If the value
of \( \boldsymbol{E}=-\mathbf{3 4 . 8 4} k c a l / \) mol, to which
value does 'n' correspond?
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
c. 2
D.


The condition that the slope of one of
the lines represented by \( a x^{2}+2 h x y+ \)
\( b y^{2}=0 \) is twice that of the other is
A \( \cdot h^{2}=a b \)
B \( \cdot 2 h^{2}=3 a b \)
D. \( 4 h^{2}=9 a b \)


What is electromagnetic induction? Give an experiment which demonstrate this phenomenon.


Choose the incorrect option: Expansion during heating:
A. occurs only in a solid
B. increases the density of the material
c. decreases the density of the material
D. occurs at the same rate for all liquids and gaseous


Write types of plant succession


The value of \( f(0) \) so that the function \( f(x)=\frac{1-\cos (1-\cos x)}{x^{4}} \) is
continuous everywhere is
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. none of these


Three long wires with same current placed at three corners of an equilateral triangles as shown in figure then the magnetic field at the centre of the
triangle will be (side length of
triangle is a)


Choose the correct answers from the
alternatives given. Which of the following forces pushes
water into the xylem as osmosis moves
water into the root?
A. Water stress
B. Atmospheric pressure
c. Root pressure
D. Transpiration


Compounds \( (C) \) and \( (D) \) are:
\( A \)
\[
\begin{array}{l}
\text { сно } \\
\text { соон }
\end{array}
\]
в.
сно \( _{\text {апа }} \) соон СООН \( ^{\text {СН }} \) он
\( c \)
\[
\begin{array}{l}
\mathrm{COOH} \\
\mathrm{COOH}
\end{array}
\]
D.
\[
\begin{array}{l}
\text { соон соон } \\
\text { соон }^{\text {апа }} \text { СН }_{2} \text { он }
\end{array}
\]


Why is a heater in winter installed near
the floor of room?


The compound used as refrigerant is :
A. Westron
B. Hydrogen peroxide
c. Gammaxane
D. Freon


Name the type of motion in which a body moves along a straight path.
A. Linear motion
B. Rotational motion
c. Brownian motion
D. Circular motion


What are the main functions of a
nucleus?


Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is a first order
reaction. A 16 volume solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
of half-life period 30 minutes is present at the start. When will the solution
become one volume?
A. After 120 minutes
B. After 90 minutes
c. After 60 minutes
D. After 140 minutes


Which of the following are correct?
This question has multiple correct options
A. The product of bulk modulus of elasticity and compressibility is 1
B. A rope 1cm in diameter breaks if the tension in it exceeds \( 500 N \). The maximum tension that may be
given to a similar rope of diameter \( 2 \mathrm{cm} \) is \( 2000 \mathrm{N} \)
C. According to Hooke's law, the ratio of the stress and strain remains constant
D. None of the above


The domain of the functions \( f(x)= \) \( \sqrt{\log \left(2 x-x^{2}\right)} \) is
A \( .(0,2) \)
B. [0,2]
\( c \cdot\{1\} \)
D. none


Biological names are regarded legitimate when
A. They are not illegitimate
B. They are very popular
c. They have their holotypes
D. All of the above


\( \mathrm{R}, \mathrm{S} \) and \( \mathrm{T}, \) respectively are:
\( \mathbf{A} \cdot \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{PCl}_{5} \) and \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
B. \( \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{PCl}_{3} \) and \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
\( \mathrm{c} \cdot \mathrm{OCl}_{2}, \mathrm{PCl}_{3} \) and \( \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( \operatorname{SOCl}_{2}, \mathrm{PCl}_{5} \) and \( \mathrm{H}_{3} \mathrm{PO}_{4} \)


Which of the following will function as
buffer?
This question has multiple correct options
A. \( N a C l+N a O H \)
в. Borax + Boric acid
c. \( N a H_{2} P O_{4}+N a_{2} H P O_{4} \)
D. \( N H_{4} C l+N H_{4} O H \)


\( \ln \) a \( H \) -atom, the \( n \) transition takes
place from \( \boldsymbol{L} \) to \( \boldsymbol{K} \) shell If \( \boldsymbol{R}=\mathbf{1 . 0 8} \times \)
\( 1067 m^{-1}, \) the wave length of the light
emitted is nearly:
A \( \cdot 4400 A^{\circ} \)
B . \( 1250 A^{\circ} \)
c. \( 1650 A^{\circ} \)
D. \( 1850 A^{\circ} \)


The sports boot for soccer and hockey have studs on their soles.Why?


How is the gravitational force of attraction between two bodies affected
if:
(i) Mass of both bodies is doubled
(ii) The distance between them is
halved.


A current is passed through a straight wire. The magnetic field established
around it has its lines of forces:
A . circular
B. parabolic
c. elliptical
D. no fixed shape


The properties of were predicted by Mendeleev before their isolation.
\( A \cdot \) Co and \( N i \)
B. I and Te
c. \( \mathrm{sc} \), Ga and \( \mathrm{Ge} \)
D. Cl, Ar and K


Assertion
When PhCHO is made to react in
\( O D^{\ominus} / D_{2} O \) no \( D \) is incorporated into
the \( C H_{2} \) of \( P h C H_{2} O H, P h C O O^{-} \)
mixture during cannizaro's reaction
Reason
Intermolecular \( \boldsymbol{H}^{\ominus} \) transfer takes place
in the rate determining step, with out getting free in solution
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 correct


A circular disk of moment of inertia \( \boldsymbol{I}_{t} \)
is rotating in a horizontal plane, about
its symmetry axis, with a constant
angular speed \( \omega_{i} . \) Another disk of
moment of inertia \( I_{b} \) is dropped co-
axially onto the rotating disk.Initially
the second disk has zero angular
speed.Eventually both the disks rotate
with a constant angular speed \( \omega_{p} . \) The
energy lost by the initially rotating disc
due to friction is
A \( \cdot \frac{1}{2} \frac{I_{b}^{2}}{\left(I_{t}+I_{b}\right)} \omega_{1}^{2} \)
B. \( \frac{I_{t}^{2}}{2\left(I_{t}+I_{b}\right)} \omega_{1}^{2} \)
c. \( \frac{I_{b}-I_{t}}{\left(I_{t}+I_{b}\right)} \omega_{1}^{2} \)
D. \( \frac{1}{2} \frac{I_{b} I_{t}}{\left(I_{t}+I_{b}\right)} \omega_{1}^{2} \)


The maximum speed of the molecules of a gas in a vessel is \( 400 \mathrm{m} / \mathrm{s} \). If half of the gas leaks out, at constant
temperature, the \( r m s \) speed of the
remaining molecules will be-
A. \( 800 \mathrm{m} / \mathrm{s} \)
B . \( 400 \sqrt{2} \mathrm{m} / \mathrm{s} \)
c. \( 400 \mathrm{m} / \mathrm{s} \)
D. \( 200 \mathrm{m} / \mathrm{s} \)


Which amongst the following options
contains mismatched pair?
A. direct elongation of radical -primary roots
B. root system originating from the stem's base - fibrous roots
C. roots not arising from the radical - stit roots
D. constitution of primary root and its branches - tap root system
E. All are correctly matched.


\( \left|\begin{array}{cc}4 \sin ^{2} \theta & \cos ^{2} \theta \\ 3 \sec ^{2} \theta & \operatorname{cosec}^{2} \theta\end{array}\right|= \)
\( A \cdot 8 \sin ^{2} \theta \cos ^{2} \theta \)
B. \( 4 \sin 2 \theta \cos 2 \theta \)
c.
\( \mathbf{D} \cdot 4 \cos ^{3} \theta-3 \cos \theta \)


Four equal charges \( Q \) are placed at the
removing a charge \( -Q \) from its centr
A . zero
B. \( \frac{\sqrt{2} \mathrm{Q}^{2}}{4 \pi \epsilon_{0} \mathrm{a}} \)
c. \( \frac{\sqrt{2} \mathrm{Q}^{2}}{\pi \epsilon_{0} \mathrm{a}} \)
D. \( \frac{Q^{2}}{2 \pi \epsilon_{0} a} \)


Significance of classification of
periodic table is to
A. predict the blocks of elements
B. predicts the groups of elements
c. both A and B
D. none of these


Assertion
Statement-I: Molar conductivity of a weak electrolyte at infinite dilution cannot be determined experimentally.
Reason

Statement-II : Kohlrausch law help to find the molar conductivity of a weak electrolyte at infinite dilution.
A. statement-l is true, statement-ll is true; Statementis correct explanation for Statement-
B. Statement-lis true, Statement-II is true; Statement-1 is NOT a correct explanation for statement-
c. statement-l is true, statement-ll is false
D. Statement-I is false, Statement-II is true


The tip of the lead pencil is made of:
A. lead
B. graphite
c. zinc
D. charcoal


The roots of the equation \( 2 y^{2}+y- \)
\( \mathbf{2}=\mathbf{0} \) are
A. \( \frac{-1-\sqrt{17}}{2}, \frac{-1-\sqrt{17}}{2} \)
B. \( \frac{-1-\sqrt{17}}{4}, \frac{-1+\sqrt{17}}{4} \)
c. \( -1-\sqrt{17},-1+\sqrt{17} \)
D. None


In a two-step exothermic reaction,
\( \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{3} \boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{D}(\boldsymbol{g}) \)
Steps 1 and 2 are favoured respectively
by:
A. high pressure, high temperature and low pressure, low temperature
B. high pressure, low temperature and low pressure, highh temperature
c. low pressure, high temperature and high pressure,high temperature
D. low pressure, low temperature and high pressure, low temperature


A uniform wire of length \( l \) is bent into
the shape \( V \) as shown in the figure. The
distance of its center of mass from the
vertex \( \boldsymbol{A} \) is \( (\text { in } \boldsymbol{m}) \)
A. \( l / 2 \)
\( B \cdot \frac{1 \sqrt{3}}{1} \)
\( c \cdot \frac{1 \sqrt{3}}{0} \)
D. none of thes


The domain of \( \sin (\cos \theta) \)
A. \( z \)
в. \( R \)
\( c \cdot Q \)
D. \( N \)


\( \mathbf{1 0 0 . 0} \mathrm{mL} \) of a saturated solution of
\( A g_{2} S O_{4} \) is added to \( 250.0 \mathrm{mL} \) of
saturate solution of \( P b C r O_{4} . \) Will any precipitate from and if so what?
Given \( \boldsymbol{K}_{s p} \) for
\( A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}, \) and
\( P b S O_{4} \) are \( 1.4 \times 10^{-5}, 2.4 \times 10^{-12} \)
\( 2.8 \times 10^{-13} \) and \( 1.6 \times 10^{-8} \)
respectively.
A \( \cdot P b C r O_{4} \)
в. \( A g_{2} C r O_{4} \)
\( \mathrm{c} \cdot \mathrm{PbSO}_{4} \)
D. \( A g_{2}, S O_{4} \)


The \( _{\text {- }} \), properties of
isotopes are similar but their
properties are different.
A. chemical, physical
B. physical, chemical
c. mechanical, chemical
D. mechanical, physical


If \( 224 m l \) of triatomic gas has a mass of
\( 1 g \) at \( 273 K \) and 1 at \( m \) pressure, then
the mass of one atom is-
A \( .8 .30 \times 10^{-23} \mathrm{gm} \)
B . \( 2.08 \times 10^{-23} \mathrm{gm} \)
C \( .5 .53 \times 10^{-23} \mathrm{gm} \)
D. \( 6.24 \times 10^{-23} \mathrm{gm} \)


Write short notes on the following.
(a) Fragmentation
(b) Regeneration \( (c) \) Budding


Which is incorrect statement?
A. There are no mesodermal cells in psedocoelomates
B. There is no body cavity in first triploblastic animals
C. There is no second opening in diploblastic animal gut
D. There is no co-ordination between cells of sponges


Numbering of groups as \( 1,2, \ldots \ldots . .18 \) was adopted by IUPAC in:
A . 1986
в. 1906
\( c \cdot 1908 \)
D. 1988


State law of constant properties. Give one example to illustrate this law.


which of the following statements are
true w.r.t. ruthenford's model of an atom
This question has multiple correct options
A. Most of the space inside an atom is empty.
B. The positively changed centre is confined to a very small space inside an atom.
C. negatively charged electrons revolve around nucleus in particular orbits.
D. Atomic mass is evenly distributed throughout the atom


Construct a triangle \( \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) whose
perimeter \( 15 \mathrm{cm} \) and whose base angles
are \( 60^{\circ} \) and \( 70^{\circ} \)


Three identical spheres each of mass 1
kg are placed touching one another with their centres in a straight line. Their
centres are marked as \( A, B, C \) respectively. The distance of centre of
mass of the system from A is.
A \( \cdot \frac{A B+A C}{2} \)
в. \( \frac{A B+B C}{2} \)
c. \( \frac{A C-A B}{3} \)
D. \( \frac{A B+A C}{3} \)


Evaluate using expansion of \( (a+b)^{2} \) or
\( (a-b)^{2}: \)
\( (20.7)^{2} \) is 428.49
If true then enter 1 and if false then
enter 0


The state of equilibrium refers to:
A. State of rest
B. Dynamic state
c. Stationary state
D. State of inertness


Which of these are the characteristics
of wave function \( \mathbf{\Psi} ? \)
This question has multiple correct options
A. \( \Psi \) must be single valued
в. \( \int_{-\infty}^{+\infty} \Psi^{2} d x d y d z=1 \)
c. \( \Psi \) must be finite and continous
D. \( \Psi \) can be discrete


The degree of the polynomial \( x^{2}- \) \( 5 x^{2} y^{3}+30 x^{3} y^{4}-576 x y \) is
\( \mathbf{A} \cdot-576 \)
B. 4
\( c .5 \)
D. 7


If \( \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Pick up the correct statement
A. Charge on surface of inner sphere is non-uniformly distributed
B. Charge on inner surface of outer shell is non-uniformly distributed
C. Charge on outer surface of outer shell is nonuniformly distributed
D. All the above statements are false


In the equation PV=constant, the numerical value of constant depends
upon
a) temperature
b) mass of the
gas
c) system of units used
d) nature of the
gas
\( A \cdot a \& b \)
B. b \&
\( c \cdot c \& d \)
D. all


Write the conjugate of complex number \( \frac{5 i}{7+i} \)


Hot water cools from \( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in
the first 10 minutes and to \( 42^{\circ} C \) in the
next 10 minutes. The temperature of the surroundings is :
A \( \cdot 25^{\circ} \mathrm{C} \)
B . \( 10^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)


If the angles of a triangle are in the ratio \( 1: 2: 7, \) then the triangle is:
A . an acute angled triangle
B. an obtuse angled triangle
c. a right angled triangle
D. a right angled isosceles triangle


In order to stop a car in shortest distance on a horizontal road, one
should:
A. apply the brakes very hard so that the wheels stop rotating
B. apply the brakes hard enough to just prevent slipping
c. pump the brakes (press and release)
D. shut the engine off and not apply brakes.


Give uses of ethanol as fuel. How it
conserves fossil fuel.


What do you mean by dynamic
spherometer?
A. An instrument used to measure radius of curvature
directly
B. An instrument used to measure radius of curvature
more accurately than usual spherometer.
C. An instrument used to measure radius of curvature indirectly
D. None of these


At a place of Earth, the vertical component of Earth's magnetic field is \( \sqrt{3} \) times its horizontal component. The angle of dip at this place is
A .60
B. 30
c. 45
D. 0


Select correct order of sizes of different
species.
\( \mathbf{A} \cdot Z r=H f ; N b=T a ; F e=C o=N i \)
B \( \cdot Z r^{4+}<Z r ; N b^{3+}<T a^{3+}, F e^{3+}<F e^{2+}<F e \)
\( \mathbf{c} \cdot Z r^{4+}=H f^{4+} ; N b^{3+}=T a^{3+} ; F e<C o<N i \)
D. \( Z r^{4+}<H f^{4+} N b^{3+}=T a^{3+}, N i<C u<C o \)


Give reasons for the right and left shift
in the oxygen-hemoglobin dissociation
curve


A ball thrown up vertically returns to the thrower after 6 s. Find
(a) The velocity with which it was
thrown up,
(b) The maximum height it reaches, and
(c) Its position after 4 s.


A current of \( 1 \mathrm{A} \) is flowing along positive x-axis through a straight wire of length \( 0.5 \mathrm{m} \) placed in a region of a magnetic field given by \( \vec{B}=(2 \hat{i}+4 \hat{j}) \) T. The magnitude and the direction of the force experienced by the wire
respectively are:
A \( \cdot \sqrt{18} N, \) along positive z-axis
B. \( \sqrt{20} N \), along positive \( x \) -axis
c. \( 2 N, \) along positive z-axis
D. \( 4 N \), along positive y-axis


A hand watch spring has ............ energy.
A. mechanical
B. kinetic
c. potential
D. kinetic and potential


Observe the given chemical change and answer the following.
i) Identify 'A' and 'B'.
ii) Write the commercial name of
calcium hydroxide.
iii) Identify products 'C' and 'D', when
\( H C l \) is allowed to react with calcium
oxide.
iv) Say whether calcium oxide is acidic or basic.


Find general solution of \( \frac{2 d y}{d x}= \) \( \frac{y(x+1)}{x} \)
\( \mathbf{A} \cdot \log y^{2}=x+\log |x|+k \)
B. \( \log y^{2}=x+\log (x)+k \)
\( \mathbf{c} \cdot \log y=x+\log (x)+k \)
D . \( 2 \log y=x-\log |x|+k \)


Some boys and girls have disproportionate body structure during adolescence. Why?


Which of the following pair of metals is purified by van-Arkel method?
\( \mathbf{A} \cdot Z r \) and \( T i \)
B. \( A g \) and \( A u \)
c. \( N i \) and \( F e \)
D. Ga and In


Assertion: A buffer has a definite pH
value which changes, on keeping it or on diluting it. Reason: A buffer solution is a mixture
consisting of a weak acid and its conjugate base or vice versa.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


\( \int_{0}^{\pi / 4} \frac{\tan ^{3} x}{1+\cos 2 x} d x \)


If action is always equal to
reaction;explain


\( (1,6),(3 .-2) \) and \( (-2, K) \) are collinear
points. What is \( \boldsymbol{K} \) ?
A . -6
B. 2
c. 8
D. 10
E . 18


Who is called as 'father of Indian plant
physiology'?
A. J. C. Bose
B. Calvin
c. R. Mishra
D. K. K. Nanda


Divide :
\( 15 x^{3} y^{3} \) by \( 3 x y^{2} \)


Inductive effects involves:
A. displacement of \( \sigma \) electrons resulting in polarisation
B. displacement of \( \pi \) electrons resulting in polarisation
C. delocalisation of \( \sigma \) electrons
D. delocalisation of \( \pi \) electrons


toppr
Q Type your question
At the point of intersection of \( A l_{2} U_{3} \) and
\( M g O \) curves \( (A), \triangle G^{0} \) becomes zero for
the reaction,
\( \frac{2}{3} A l_{2} O_{3}+2 M g \rightarrow+\frac{4}{3} A l \)
Below this point, magnesium can
reduce alumina. Although
thermodynamically feasible, Al is not
used for reduction of \( M g O \) because:
A. temperature required is very highh
B. the yields of metal is very low
c. the value of \( \triangle G^{0} \) becomes positive
D. magnesium is not used as reducing agent for any


Which will be the third element among
the given elements to complete given Doberiener triad?
(Atomic mass of Be \( 9 ; \) Na \( 23 ; \) Mg \( 24 ; \) si 28; Cl 35; Ca 40) \( \mathrm{Na},_{--}, \mathrm{Cl} \)


Find the equations of the lines for which \( \tan \theta=\frac{1}{3}, \) where \( \theta \) is the angle of
inclination of the line and \( y- \) intercept
is \( \frac{-1}{2} \)


Give a brief account on the
need of classification?


Arum bough a pair of skates at a scale where the distance given was \( 20 \% \). If
the amount he pays is Rs \( 1,600, \) find the
marked price.


True or False
Nitrogen does not form sulphides.


What is the utility of vulcanisation of
rubber? How is vulcanisation carried
out?


Glycerol is added to soap. It functions:
\( A \). as a filler
B. to increase lathering
c. to prevent rapid drying
D. to make soap granules


The decreasing order of the ease of
ionization under acidic conditions of
above alcohols will be
\( A \cdot I>I I I>I I \)
3. \( I>I I>I I I \)
c. \( I I>I I I>I \)
\( . I I>I>I I I \)
\( I \)


A wedge of mass \( 2 \mathrm{m} \) and a cube of
mass \( \mathrm{m} \) are shown in figure. Between cube and wedge, there is no friction. The
minimum coefficient of friction
between wedge and ground so that wedge does not move is


\( \mathrm{m} / \mathrm{s} \) at an angle of \( 60^{\circ}, \) with
the positive \( x \) direction taken along
horizontal. At that instant, an
observer moves past the football in a
car that moves with a constant speed
of \( 11 \mathrm{m} / \mathrm{s} \) in the positive \( \mathrm{x} \) direction. Take
+ve y direction vertically upwards. \( (\boldsymbol{g}= \)
\( \left.10 m / s^{2}\right) \)
ball
Observer
This question has multiple correct options
A. The initial velocity of the ball relative to the observer in the car is \( 11 \sqrt{3} \mathrm{m} / \mathrm{s} \) in the \( +\mathrm{y} \) direction
B. The initial velocity of the ball relative to the observer in the car is \( 17 \mathrm{m} / \mathrm{s} \) at 60 to the \( +x \) direction
c. According to the observer in the car, the ball will follow a path that is straight up and down in the y direction.
D. According to the observer in the car, the ball will follow straight line that is angled (less than 90 ) with respect to the observer.


The width of a rectangle in a histogram
represents of the
class.
A. frequency
B. range
c. class limit
D. upper limit


Match List-I with List-II.
List-I Chemical reaction List-II Name of
process
(1) \( 4 N H_{3}+5 O_{2} \stackrel{800^{\circ} C / P t}{\rightarrow} \)
(a) Contact
\[
4 N O+6 H_{2} O
\]
process
(2) \( 4 H C l+O_{2} \frac{3230^{\circ} C / C u C l_{2}}{450-500^{\circ} / V_{2} O_{5}} \)
(b) Ostwald's
\[
2 C l_{2}+2 H_{2} O
\]
process
(c) Deacon's
(3) \( 2 S O_{2}+O_{2} \rightarrow 2 S O 3 \quad \) process
(d) Haber's
(4) \( 2 N_{2}+3 H_{2} \stackrel{F e+M b}{\rightarrow} 2 N H_{3} \quad \) process
\( \mathbf{A} \cdot 1-a, 2-b, 3-d, 4-c \)
B. \( 1-b, 2-c, 3-a, 4-d \)
C \( .1-a, 2-d, 3-c, 4-b \)
D. \( 1-a, 2-c, 3-b, 4-d \)


For the reaction, \( 2 N O C l(g) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{c} \) at \( \mathbf{4 2 7}^{\circ} \) is \( \boldsymbol{3} \times \)
\( \mathbf{1 0}^{-6} . \) The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) is nearly:
A \( .7 .50 \times 10^{-5} \)
B . \( 2.50 \times 10^{-5} \)
c. \( 2.50 \times 10^{-4} \)
D. \( 1.72 \times 10^{-4} \)


With what angular velocity and in what direction does the turntable rotate?
A. The table rotates anticlockwise (in direction of the mam motion) with angular velocity \( 0.05 r a d / s \)
B. The table rotates clockwise (opposite to the man) with angular velocity \( 0.1 \mathrm{rad} / \mathrm{s} \)
c. The table rotates clockwise (opposite to the man) with angular velocity \( 0.05 r a d / s \)
D. The table rotates anticlockwise (in the direction of the man motion) with angular velocity \( 0.1 \mathrm{rad} / \mathrm{s} \)


Epilepsy can be diagnosed using
A. ECG
B. ultrasound
c. ЕEG
D. x-ray


Add without using number line:
(1) \( 1+(-7) \)
(2) \( (-13)+ \)
(18)
(3) \( (-10)+(19) \)
(4)
\( (-250)+(150) \)
(5) \( (-380)+(-270) \) \( (-217)+(-100) \)


If \( f(x)=3 x-2 \) and \( g(x)= \)
\( \mathbf{7}, \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})]= \)
A . \( 21 x-2 \)
B. 7
c. 19
D. \( 7 x-2 \)
E . 13


Simplify the following expressions:
\( \left(x^{2}-x+1\right)^{2}-\left(x^{2}+x+1\right)^{2} \)


The angle between the vectors \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is?
A \( \cdot \tan ^{-1} \frac{1}{2 \sqrt{2}} \)
в. \( \tan ^{-1} \frac{1}{3} \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
D. \( 90^{\circ} \)


\( \left(\frac{-1}{2}\right)^{2}=\frac{1}{2^{m}} \)


matrix is a square matrix in
which all the elements other than the
principal diagonal elements are zero.
A. scalar
B. null
c. diagonal
D. unit


Select the correct order of first
ionization potential
A. \( N>O_{2} \)
в. \( O_{2}>N \)
\( \mathrm{c} \cdot O_{2} \simeq N \)
D. None of these


The IUPAC name of \( K_{2}\left[N i(C N)_{4}\right] \) and
\( K_{2}\left[N i(C l)_{4}\right] \) are:
A. potassium tetracyanonickelate(II), potassiumtetrachloronickelate(II)
B. tetracyanopotassiumnickelate(II),tetrorachlropotassic
C. tetracyanonickel(II), tetrachlornickel(II)
D. potassium tetracyanonickel(II), potassiumtetrachloronickel(II)


The correct order of activation of
benzene ring towards an electrophile is
\( A \cdot(\mid V)>(|I|)>(\mid I)>(\mid) \)
B. \( (\| I)>(|>>(\mid V)>(||) \)
\( \mathbf{c} \cdot(\|\|)>(|V\rangle>(\mid)>(\|) \)
\( D \cdot(\mid V)>(|| \mid)>(||)>(\mid) \)


The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is:
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{2}{5} \)


A neutron decays to form a proton. Which particle is not involved in the
decay process?
A. Antineutrino
B. Down quark
c. Positron
D. Up quark


Element of group 13:
A. exhibit oxidation state of +3 only
B. form \( M^{+} \) and \( M^{+3} \)
C. exhibit oxidation state of +1 and +3
D. none of these


A bank offers \( 5 \% \) cash back on petrol
purchase up to \( \$ 1500 \) and \( 2 \% \)
on amount spent on petrol thereafter, in
a calendar year. If functions \( g(x) \) and
\( e(x) \) represents cash back earned on
petrol purchases up to \( \$ 1,500 \) and in
excess of \( \$ 1,500, \) respectively, then the sets of functions that could be used to
determine the amount of cash back
earned is
\( \mathbf{A} \cdot g(x)=0.05 x, 0 \leq x<1,500 ; e(x)= \)
\[
0.02(x-1,500), x \geq 1,500
\]
B \cdot \( g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)=0.02 x, x>1,500 \)
C \( \cdot g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)= \)
\[
0.02(x-1,500), x>1,500
\]
D \( \cdot g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)= \)
\[
0.02(1,500-x), x>1,500
\]


Adsorption is a process in which a substance accumulates on the of
the other substance.
A. surface
B. core
c. membrane
D. plasma


If the alloy of metal contains \( 45 \% \) nickel
\( 25 \% \) copper and rest is zinc, then the weight of zinc in 3 kg alloy is


If
\( \log _{10} 2, \log _{10}\left(2^{x}-1\right) \) and \( \log _{10}\left(2^{x}+3\right) \)
be three consecutive terms of an A.P.,
then
\( \mathbf{A} \cdot x=0 \)
B. \( x=1 \)
C \( . x=\log _{2} 5 \)
D. \( x=\log _{10} 2 \)


During the estimation of phosphorous, in the organic compound, which of the following represents final precipitate?
A. \( M g_{3}\left(P O_{4}\right)_{2} \)
B. Magnesium pyrophosphate
c. Magnesium hydrogen phosphate
D. \( P_{4} O_{10} \)


Which of the following oxides is amphoteric in character?
A. \( C a O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( \operatorname{sn} O_{2} \)


\( \boldsymbol{n} \) identical cells, each of internal
resistance \( (r) \) are first connected in
parallel and then connected in series \( \operatorname{across} \) a resistance \( (\boldsymbol{R}) . \) If the
current through \( R \) is same in both the
cases then:
A. \( R=r / 2 \)
в. \( r=R / 2 \)
c. \( R=r \)
\( \mathbf{D} \cdot r=0 \)


What is the pH of a solution made by
mixing \( 100.0 \mathrm{mL} \) of \( 0.10 \mathrm{M} H N O_{3}, 50.0 \)
mL of \( 0.20 \mathrm{HCl} \) and \( 100.0 \mathrm{mL} \) of water?
Assume that the volumes are additive.
A . 2.7
B. 1.10
c. 3.50
D. 1.5


Total kinetic energy of sample of a gas which contains \( 1 \times 10^{22} \) molecules is
\( 24 \times 10^{2} J \) at \( 127^{\circ} C . \) Another sample of
\( \operatorname{gas} \operatorname{at} 27^{\circ} C \) has a total kinetic energy
of \( 48 \times 10^{2} J . \) The number of molecules
in the second sample are:
A. \( 2.67 \times 10^{22} \)
B. \( 1 \times 10^{2} \)
C \( .1 \times 10^{24} \)
D. \( 5.5 \times 10^{21} \)


A cycle tube has volume \( 2000 \mathrm{cm}^{3} \)
Initially the tube is filled to \( 3 / 4 \) th of its
volume by air at pressure of \( 105 N / m^{2} \)
It is to be inflated to a pressure of \( 6 x \) \( 10^{5} N / m^{2} \) under isothermal conditions.
The number of strokes of pump, which
\( \operatorname{gives} 500 c m^{3} \) air in each stroke,
to inflate the tube is
A . 2
B. 12
\( c \cdot 42 \)
D. 1


\( \odot(P, 4 c m) \) is given. Draw a pair of
tangents through \( A \), which is in the
exterior is \( 60^{\circ} . \) Write the construction
steps.


The position \( x \) of a particle varies with time \( (t) \) as \( x=a t^{2}-b t^{3} . \) The
acceleration of the particle will be equal
to zero, at time
A \( \cdot \frac{2 a}{3 b} \)
B. \( \frac{a}{b} \)
c. \( \frac{a}{3 b} \)
D. \( \frac{2 a}{b} \)


Consider the following unbalanced reactions.
\( \boldsymbol{C l}_{2}(\boldsymbol{g})+\boldsymbol{B a}\left(\boldsymbol{O H}_{2}\right) \rightarrow \boldsymbol{X}(\boldsymbol{a q})+\boldsymbol{B a C l}_{2} \)
\( \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{Y}+\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( \boldsymbol{Y} \frac{\boldsymbol{\Delta}}{>\mathbf{3 6 5} \boldsymbol{K}} \boldsymbol{Z}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \) Here, \( \boldsymbol{Y} \) and
\( Z \) are respectively:
A. \( H C l O_{4}, C l O_{2} \)
в. \( H C l O_{3}, C l O_{2} \)
c. \( H C l O_{3}, C l_{2} O_{7} \)
D. \( H C l O_{4}, C l_{2} O_{7} \)


Through an inductance coil of \( \boldsymbol{L}= \)
\( 0.2 H, \) an ac current of 2 ampere is
passed first with frequency \( n_{1} \) and then
with frequency \( n_{2} \). The ratio of the
maximum value of induced emf \( \left(e_{1} / e_{2}\right) \)
in the coil, in the two cases is
A. \( n_{1} / n_{2} \)
в. \( n_{2} / n_{1} \)
c. \( n_{1}^{2} / n_{2}^{2} \)
D \( \cdot n_{2}^{2} / n_{1}^{2} \)


Consider the following statements each with two blanks.
(i) Diaphragm contracts to help in
(1) \( _{--} \) while the contraction of
abdominal muscles helps in (2).
(ii). Vital capacity of trained athletes is
(3) than that of non-athletes
while the vital capacity of non-smokers
is \( -(4)_{-}- \) than that of smokers.
(iii) Alveolar \( \mathrm{PO}_{2} \) is \( ---(5) \) than
the venous \( \mathrm{PO}_{2} \) while arterial \( \mathrm{PO}_{2} \) is
(6) \( _{--} \) than the alveolar \( \mathrm{PO}_{2} \)
Which of the following options gives the correct fill ups for the respective blanks
numbers from (1) to (6) in the above
statements?
A. (1)-expiration,
(2)-inspiration (5)-higher, (6)-lower
B. (3)-higher, (4)-lower, (5)-lower, (6)-higher
c. (1)-inspiration, (2)-forced expiration, (3)-higher, (4)higher
D. (1)-expiration, (2)-forced expiration, (5)-higher, (6) lower


State True or False.
\( \pi \) bond is formed by the colateral overlapping of atomic orbitals.
A. True
B. False


Electrostatic precipitators (ESP) are used to control
A. pesticide pollution
B. air pollution
c. radioactive pollution
D. water pollution


A circuit is shown in diagram. If we put
a conducting wire \( A B \) as shown doted
then current through wire will be
A. Zero
B. 1 amp
\( c .-1 \) amp
D. 3 amp


State true or false:
In nature, all elements during bond formation acquire octet configuration


\( \mathbf{0 . 0 0 0 8 m}=\mathbf{8} \times \mathbf{1 0}^{-\boldsymbol{x}} \boldsymbol{m} . \) Find \( \mathbf{x} \)


A steel wire of length \( 30 \mathrm{cm} \) is stretched ti increase its length by \( 0.2 \mathrm{cm} \). Find the lateral strain in the wire if the poisson's ratio for steel is 0.19:
A . 0.0019
B. 0.0008
c. 0.019
D. 0.008


What is the name of the element having chemical symbol I?
A. lodine
B. Iron
c. Indium
D. Iridium


Which of the following is not a constant polynomial?
A \( \cdot p(x)=3^{3} \)
B \( \cdot p(x)=2^{3} \)
\( \mathbf{c} \cdot p(x)=x^{3} \)
D \( \cdot p(x)=4^{3} \)


A reaction in equilibrium is represented by the following equation:
\( \mathbf{2 A}(s)+\mathbf{3 B}(\boldsymbol{g}) \rightleftharpoons \mathbf{3} \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g})+\boldsymbol{O}_{2} \)
if the pressure on the system is reduced to half of its original value then
A. The amounts of \( C \) and \( D \) increases
B. The amounts of \( C \) and \( D \) decreases
c. The amounts of \( B \) and \( D \) decreases
D. All the amounts remain constant


Find the value of \( x \) from the adjacent
figure


Cyanobacteria (Nostoc) is
A. Oxygenic with nitrogenase
B. Oxygenic without nitrogenase
C. Non-oxygenic with nitrigenase
D. Non-oxygenic without nitrogenase


Assertion
In barrier methods, ovum and sperms
are prevented from physical meetings.
Reason

Barrier methods are used during coitus, to prevent the entry of ejaculated semen into the female reproductive tract
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 density of field lines surrounding any given object reveal information
about the
A. the nature of charge on the source charge.
B. the quantity of charge on the source charge.
c. both A and B
D. it reveals no information


Which one of the following is wrong in
relation to photorespiration?
A. It occurs in chloroplasts
B. It occurs in daytime only
C. It is a characteristic of \( C_{4} \) plants
D. It is a characteristic of \( C_{3} \) plants


Metals heat conductivity depends upon:
A. number of free electrons
B. speed of free electrons
c. how far electrons travel without being bumped into other atoms
D. all of the above


Which of the following molecules are expected to exhibit intermolecular \( \mathrm{H} \) bonding?
: Acetic acid II : \( o \) -nitrophenol Ill: \( m \) -nitrophenol IV: \( o \) -boric acid Select the correct option.
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ।
B. ।, ॥।, IV
c. ।, ॥ा, ।V
D. II, III, IV


The degree of the differential equation \( \left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{3 / 4}=\left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3} \) is:
\( A \)
B.
\( c \cdot 9 \)
\( D \)


Autorhythmicity is a special property of the muscles of the
A. Liver
B. Intestine
c. Heart
D. Kidney


In a balanced equation, \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{x} \boldsymbol{H} \boldsymbol{I} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{y} \boldsymbol{I}_{2}+\boldsymbol{z} \boldsymbol{H}_{2} \boldsymbol{O}, \) the values
of \( x, y \) and \( z \) are respectively:
A. \( x=3, y=5, z=2 \)
в. \( x=4, y=8, z=5 \)
c. \( x=8, y=4, z=4 \)
D. \( x=5, y=3, z=1 \)


A thin plano-convex lens fits exactly into a thin plano-concave lens. Their plane surfaces are \( \mathrm{R} \), for to each other. If the lensps parpenoley of different materials of refractive indices \( \mu_{1} \) and
\( \mu_{2} \) and \( R \) is the radiuts of curvature of
the curved surfaces of the lenses, then the focal length of the combination is:
A \( \frac{R}{\mu_{2}-\mu_{1}} \quad \begin{array}{l}\text { Get } 30 \% \text { scholarship } \\ \text { onanysubscription }\end{array} \) LAST DAY
B. \( \frac{2 R}{\mu_{2}-\mu_{1}} \quad \) use cooe \( \quad \) FathER 30 DAY
C. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \quad \) UPGRADE NOW
D. \( \frac{R}{2-\left(\mu_{1}+\mu_{2}\right)} \quad \) Web \( _{\text {ไingage }}^{\text {povereaby }} \)


An organic compound contains \( 69 \% \) carbon and \( 4.8 \% \) hydrogen, the remainder being oxygen. Calculate the sum of masses (in \( g \) m) of carbon dioxide and water produced when 0.20 \( \mathrm{gm} \) of this compound is subjected to complete combustion. Report your
answer as \( 10 x, \) if \( x \) is the sum of masses
in the nearest integer.


Shape of graph between speed and kinetic energy of the body is:
A. Hyperbola
B. Straight line
c. Parabola
D. circle


Emphysema is a condition resulting
from
A. Cigarette smoking
B. Liquor consumption
c. Drug addiction
D. None of the above


Find the first term and the common
difference of an \( A P, \) if the \( 3^{r d} \) term is 6
and the \( 1^{t h} \) term is 34


Let \( R \) be a relation from \( N \) to \( N \) defined
by \( R=\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} . \) Is
the following statement true for \( (a, b) \in \) \( \boldsymbol{R} \Rightarrow(\boldsymbol{b}, \boldsymbol{a}) \in \boldsymbol{R} ? \)
A. True
B. False


The area of the region bounded by \( y= \)
\( -1, y=2, x=y^{3} \) and \( x=0 \) is
A \( \cdot \frac{17}{4} \) sq. units
B. \( \frac{1}{4} \) sq. units
c. 4 sq. units
D. None of these


Electromeric effect is due to:
A. electronegative elements
B. double bond
C . triple bond
D. all of these


Opening of auricles into ventricles are
guarded by valves.


Value of \( g \) on the surface of earth is
\( 9.8 m / s^{2} . \) Find acceleration due to gravity at depth \( h=\frac{R}{2} \) from the
surface \( (\boldsymbol{R}= \) radius of earth)


Solve the following:
\( \frac{x-8}{5}=\frac{x-12}{9} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


For \( -\frac{\pi}{2}<\theta<\frac{\pi}{2}, \) range of \( f(\theta)= \)
\( \frac{\sin \theta+\sin 2 \theta}{1+\cos \theta+\cos 2 \theta} \) is
A. \( (-\infty, \infty) \)
a
в. (-2,2)
\( c \cdot(0, \infty) \)
D. none of these


Find the value of \( x \) if \( \sin (\arcsin x)= \)
\( \frac{\sqrt{2}}{4} \)
A \( \cdot \frac{\sqrt{2}}{4} \)
B. \( \frac{\sqrt{7}}{7} \)
c. \( \frac{\sqrt{2}}{2} \)
D. \( \frac{2 \sqrt{2}}{3} \)


If the earth shrinks to half of its radius
without changing its mass, the duration of the day will be
A. 48 hours
B. 24 hours
c. 12 hours
D. 6 hours


Is it true that \( y=e^{\log x} \) for all real \( x \)


The dihalides in which halogen atoms
are attached to same carbon atom are
termed as alkylene dihalides


Find a differential equation
corresponding to \( y=a x^{2}+b x \)


The exterior angle of a regular polygon
is \( 24^{\circ} \)
Find the number of sides of this regular polygon.


If the perimeter of rectangular base
\( A B C D \) of a semi-right circular cylinder
is \( 36 \mathrm{m}, \) then the maximum volume of
this semi-cylinder is
\( \mathbf{A} \cdot 36 \pi m^{3} \)
B. \( 96 \pi m^{3} \)
C. \( 108 \pi m^{3} \)
D. \( 54 \pi m^{3} \)


A student traces the path of a ray of
light through a triangular glass prism for different values of angle of incidence. On analyzing the ray diagrams, which one of the following conclusions is he likely to
draw?


The statement 'Acceleration is zero if
and only if the net force is zero' is valid
in
A. Non-inertial frames
B. Inertial frames
C. Both in an inertial frames and non-inertial frames
D. Neither inertial frames nor non-inertial frames


Carbonic acid generally displaces another acid when the acid is heated
with a salt.
A. True
B. False


The reabsorption of water in the tubules of nephrons takes place by
A. Osmosis
B. Simple diffusion
c. Active transport
D. Filtration


If the latus rectum of an ellipse is equal to half of minor axis, find its
eccentricity.


Acetic acid is used for preservation of foods.
A . True
B. False


Find \( \lim _{x \rightarrow 0} f(x), \) where \( f(x)= \)
\( \left\{\begin{array}{ll}\frac{x}{|x|}, & x \neq 0 \\ 0, & x=0\end{array}\right. \)


11
glycolysis has been given below. Select the option which correctly fills up the blanks for \( P, Q, R \) and \( S .\left[' X^{\prime} \) stands for \right.
'nil'].

Steps
\[
\text {Glucose } \rightarrow \text {Glucose }-6-
\]
1. phosphate
Fructose \( -6- \)
2. \( \quad \) phosphate \( \rightarrow \) Fructose \( - \)
\[
\begin{array}{l}
1,6-\text { bisphosphate } \\
1,3-
\end{array}
\]
3
bisphosphoglycericacid \( \rightarrow \)
\[
\begin{array}{l}
\text { orsprospnogiycericacia } \rightarrow \\
3-\text { Phospho - glycericacid } \\
2-
\end{array}
\]
4
Phosphoenolpyruvicacid \( \rightarrow \) Pyruvicacid
A. P-1; Q-X; R-X; S-2
B. P-1; Q-X; R-2; S-X
c. \( P-2 ; Q-1 ; R-X ; S-1 \)
D. P-X; Q-1; R-2; S-X


The ionospheric layer acts as a reflector for the frequency range
\( \mathbf{A} \cdot 1 \mathrm{kHz} \) to \( 10 \mathrm{kHz} \)
B. 3 to 30 МНz
\( c \cdot 3 \) to \( 30 \mathrm{kHz} \)
D. 100 kHz to 1 MHz
\( E . \) 3 GHz to 30 GHz


Read the following statements and answer whether the given statement is true or false.

The induced e.m.f. depends only on the
no of turns of the coil:
A. True
B. False


The relative humidity (in \%) of a certain
city for a September month of 30 days was as follows:
\( \begin{array}{lllll}98.1 & 98.6 & 99.2 & 90.3 & 86.5 \\ 89.2 & 92.3 & 97.1 & 93.5 & 92.7 \\ 96.0 & 92.1 & 84.9 & 90.0 & 95.7\end{array} \)
What is the range of the data?


Is it possible for you to recognize the leaves without seeing them? How?


In which of the following cases, pH is
greater than \( 7 ? \)
A. \( 50 m l \) of \( 0.01 M H C l+50 m l \) of \( 0.1 M \) NaCl
B . \( 50 m l \) of \( 0.1 M H_{2} S O_{4}+50 m l \) of \( 0.2 M \) NaOH
\( \mathrm{c} .50 \mathrm{ml} \) о \( 6.0 .1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+50 \mathrm{ml} \) о \( 0.1 \mathrm{M} \) КОН
D. \( 50 m l \) of \( 0.1 M H N O_{3}+50 m l \) of \( 0.1 M N H_{3} \)


Arrange the following elements in terms of increasing first ionization energy:
\( \boldsymbol{G} \boldsymbol{a}, \boldsymbol{B} \boldsymbol{a}, \boldsymbol{R} \boldsymbol{u}, \boldsymbol{F}, \boldsymbol{N} \)
A. \( B a<R u<G a<N<F \)
в. \( G a<B a<R u<F<N \)
c. \( R u<B a<G a<N<F \)
D. None of the above


Explain the factors responsible for the depletion of water table :


Low temperature is favourable for reactions.
A. exothermic
B. endothermic
\( c . \) both
D. no effect


The value of \( \int_{a}^{b} \frac{\log x}{x} d x \) is
\( \mathbf{A} \cdot \log (a b) \log \left(\frac{b}{a}\right) \)
B \( \cdot \frac{1}{2} \log (a b) \log \left(\frac{b}{a}\right) \)
\( \mathbf{C} \cdot \log \left(a^{2}-b^{2}\right) \)
D. \( (a+b) \log (a+b) \)


System indicated in parentheses by Roman numerals. to name compounds is called as:
A . periodic table
B. stock nomenclature
c. roman nomenclature
D. all of the above


A man runs \( 10 k m \) in 30 min. What is
his speed?
\( \mathbf{A} .5 k m / h \)
в. \( 10 k m / h \)
\( c .15 k m / h \)
D. 20km/h


What is common between the trachea
of rabbit and cockroach?
A. Both startin head region
B. Both are filled with fluid
c. wall in both is strengthened which does not allow to collapse
D. None of the above


A reaction takes place in three steps. The rate constant of the three steps is
\( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \) respectively. The overall rate constant \( \boldsymbol{K}=\frac{\boldsymbol{K}_{\mathbf{1}} \boldsymbol{K}_{\mathbf{3}}}{\boldsymbol{K}_{\mathbf{2}}} . \) If the energy
of activation for the three steps are
40,30 and \( 20 K J \) respectively, then :
This question has multiple correct options
A. overall energy of activation is \( 10 \mathrm{KJ} \)
B. overall energy of activation is \( 30 K J \)
C. the reaction mechanism is \( 2 A \rightleftharpoons A^{*}+A ; A^{*} \frac{K_{3}}{r d s} \)
product and overall order is one
D. the reaction mechanism is \( A \stackrel{K}{\rightarrow} B ; B \stackrel{K}{\longrightarrow} C ; C \stackrel{K_{3}}{\rightarrow} \)
product and overall order is one


\( \boldsymbol{x}>2 \boldsymbol{R} \)
\( \mathbf{A} \cdot \frac{2 G M m^{\prime}}{(x-r)^{2}}+\frac{G m m^{\prime}}{(x+r)^{2}} \)
\( \mathbf{B} \cdot \frac{G M m^{\prime}}{2(x-R)^{2}}+\frac{2 G m m^{\prime}}{(x-r)^{2}} \)
\( \mathbf{C} \cdot \frac{G M m^{\prime}}{(x+R)^{2}}+\frac{G m m^{\prime}}{(x+r)^{2}} \)
D. \( \frac{G M m^{\prime}}{(x-R)^{2}}+\frac{G m m^{\prime}}{(x-r)^{2}} \)


During an experiment, an ideal gas is found to obey a condition \( \frac{\boldsymbol{P}^{2}}{\boldsymbol{\rho}}= \)
constant \( [\rho=\text { density of the gas }] \) The gas is initially at temperature \( T \) pressure \( P \) and density \( \rho . \) The gas expands such that density changes to
\( \frac{\rho}{2} \)
This question has multiple correct options
A. The pressure of the gas changes to \( \sqrt{2} P \)
B. The temperature of the gas changes to \( \sqrt{2} T \)
C. The graph of the above process on the P-T diagram is parabola.
D. The graph of the above process on the P-T diagram is hyperbola.


Mention the names of any two types of fossil fuels.


If you mix 3 litres of 0.5M \( N a C l \) with 9 litres of \( 0.2777 \mathrm{M} N a C l \) what will the
concentration of the final solution be
assuming that volumes are additive?
в. 0.39 м
c. \( 0.5777 \mathrm{M} \)
D. 0.6777 M
E. None of the above


\( \int \frac{2 \sin x}{(3+\sin 2 x)} d x \) is equal to
\( \mathbf{A} \cdot \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{\sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
B. \( \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{2 \sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
C \( \frac{1}{4} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{\sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
D. none of these


Assertion (A): When a ball hits a floor
obliquely and gets reflected after inelastic collision, only the vertical component of its velocity gets changed. Reason (R): During collision the floor
exerts a force on the ball only along the normal but not parallel to the surface
A. Both Assertion
(A) and Reason (R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason (R) are correct but the reason does not give the correct explanation
c. A is true but R is false
D. A is false but R is true


What is the molarity of a solution that has 29.25 grams of NaCl dissolved to make \( 1.5 \mathrm{L} \) of a solution?
A . 19.5 М
B. 3.0 М
c. 1.75 М
D. 0.33 м
E \( .1 .0 \mathrm{M} \)


If \( \boldsymbol{p} \rightarrow(\sim \boldsymbol{p} \vee \boldsymbol{q}) \) is false then the truth
value of \( p \) and \( q \) are respectively
A \( . T, T \)
в. \( T, F \)
c. \( F, T \)
D. \( F, F \)


An electron, proton, deuteron and \( \alpha \) particle enter in a uniform electric field with the same velocity as shown.
The greatest deviation is shown by
A. electron
B. proton
c. deuteron
D. \( \alpha \) - particle


If \( d \) is the \( H C F \) of 56 and \( 72, \) find \( x, y \)
satisfying \( \boldsymbol{d}=\mathbf{5 6 x}+\mathbf{7 2 y} . \) Also, show
that \( x \) and \( y \) are not unique.


Let \( R \) be a relation on the set \( A \) of
ordered pairs of non-zero integers defined by \( (x, y) R(u, v) . \) If \( x v=y u \)
then show that \( R \) is an equivalence
relation.


Which of the following statement(s)
is/are true for the process of anodizing?
A. Anodizing is an electrochemical process
B. It converts the metal surface into a decorative, durable, corrosion-resistant, anodic oxide finish.
C. Aluminum is ideally suited to anodizing, although other nonferrous metals, such as magnesium and titanium, also can be anodized.
D. All of the above


Methyl alcohol is treated with conc HI
and red P. The main product obtained is
?
A. \( C H_{3} O H \)
в. \( C H_{4} \)
c. \( C H_{2} I_{2} \)
D. \( P H_{3} \)


Find the value of \( x \) for which following is
true -
\( \operatorname{sgn}\left(x^{2}-2 x-8\right)=-1 \)


Identity the non-lustrous element.
\( A . \) Bromine
B. lodine
c. Silver
D. Iron


Rayon has properties similar to:
A. wool
B. jute
\( c . \) silk
D. cotton


Iso-octane reacts with oxygen:
A. endothermically
B. exothermically
C . only some activation energy is required
D. doesn't react


The species reduce in the following
reaction is :
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O}_{2} \)
A . \( F e \)
в. \( C O \)
\( c \cdot C O_{2} \)
D. \( F e_{2} O_{3} \)


EtOH The product \( (A) \) in the given
reaction is:


Heat of combustion is the amount of
heat evolved when the number of moles
as represented by the balanced equation have been completely oxidised.lf true enter 1 else
\( A \)


Two equal charges ' \( q \) ' of opposite sign are separated by a small distance 'd'. The electric intensity ' \( E \) ' at a point on the straight line passing through the two charges at a very large distance ' \( r \) ' from the midpoint of two charges is :
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q d}{r^{2}} \)
В. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q d}{r^{2}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q d}{r^{3}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q d}{r^{3}} \)


toppr
Q Type your question
wall consists of teak wood of thickness
\( L_{1} \) and brick of thickness \( \left(L=5 L_{1}\right) \)
sandwitching two layers of an unknown
material with identical thermal
conductivities and thickness. The
thermal conductivity of teak wood is \( \boldsymbol{K}_{\mathbf{1}} \)
and that of brick is \( \left(K_{2}=5 K\right) . \) Heat
conduction through the wall has
reached a steady state with the
temperature of three surfaces being
known. \( \left(T_{1}=, 25^{\circ} C, T_{2}=20^{\circ} C \) and \right.
\( \left.\boldsymbol{T}_{5}=-20^{\circ} \mathrm{C}\right) . \) Find the interface
temperature \( \boldsymbol{T}_{\mathbf{4}} \) and \( \boldsymbol{T}_{\mathbf{3}} \)
A \( \cdot 2.5^{\circ} \)
B \( \cdot 7^{\circ} \)
\( c \cdot 3.5^{\circ} \)
\( D \cdot 9^{\circ} \)


The ability of an ion to bring about coagulation of a given colloid depends
upon:
A. its charge
B. the sign of the charge alone
c. the magnitude of the charge
D. both magnitude and sign of charge


In a Young's Double Slit experiment,
films of thickness \( t_{A} \) and \( t_{B} \) and
refractive indices \( \mu_{A} \) and \( \mu_{B} \) are placed in front of slits \( A \) and \( B \) respectively. If
\( \boldsymbol{\mu}_{A} \boldsymbol{t}_{A}=\boldsymbol{\mu}_{B} \boldsymbol{t}_{B}, \) then the central maxima
\( \operatorname{may} \)
This question has multiple correct options
A. not shift
B. shift forwards A
c. shift towards B
D. None of these


The frequency of oscillation in an
oscillation is
A \( \cdot \frac{\pi}{\omega} \)
в. \( \frac{2 \pi}{\omega} \)
c. \( \frac{\omega}{2 \pi} \)
D. \( \frac{\omega}{\pi} \)


Peptisation is a process in which:
A. precipitation becomes true solution
B. true solution becomes a suspension
C . a colloid gets coagulation
D. a suspension gets converted into a colloid


Rohit purchased a pair of shoes costing
Rs. \( 850 . \) Calculate the total amount to
be paid by him, if the rate of Sales Taxis
\( 6 \% \)


Substance having maximum number of molecules is:
A \( \cdot 44.8 \mathrm{L} \) of \( \mathrm{H}_{2} \) at \( \mathrm{S.T.P.} \)
B. 2 g of \( H e \)
c. \( 16 \mathrm{g} \) of \( C H_{4} \)
D. 33 g of \( C O_{2} \)


\( \frac{d}{d} \)


If \( \sec C \) is \( \frac{m}{2 \sqrt{2}}, \) then \( m \) is:
\( A \)
B
\( c \)


The diameter of a cylinder is \( 0.55 \mathrm{cm} \) its length is \( 1.35 \mathrm{cm} . \) Its volume
is \( c m^{3} \)
A . 0.3240
в. 0.32
c. 0.324
D. 3.2


Name two special characteristics of a
heater coil.


Which tissue is responsible for the transport of nutrients, respiratory gases, metabolites, hormones and
waste products?


In the figure, if line \( l \) has a slope of -2
what is the \( y \) -intercept of \( l \) ?
\( A \cdot 7 \)
B. 8
\( c \)
D. 10


Given are cyclohexanol \( (I), \) acetic acid \( (I I) 2,4,6- \) trinitrophenol \( (I I I) \) and phenol \( (I V) . \) In these the order of decreasing acidic character will be:
A \( , I I I>I I>I V>I \)
\( I \)
В. \( I I>I I I>I>I V \)
c. \( I I>I I I>I V>I \)
D. \( I I I>I V>I I>I \)


1
correctly describes the process of
electrolytic refining?
\( A \)
\( B \)
\( c \)
None of the above


A thunderstorm is generally accompanied by:
A . lightning
B. earthquake
\( c . \) fire
D. mild breeze


At what centigrade temperature will a
given volume of a gas at \( 0^{\circ} \mathrm{C} \) becomes
double if pressure remains constant?
\( \mathbf{A} \cdot 546^{\circ} \mathrm{C} \)
B . \( 200^{\circ} \mathrm{C} \)
\( c \cdot 273^{\circ} \mathrm{C} \)
D. \( 320^{\circ} \mathrm{C} \)


With what considerations in view, a
photodiode is fabricated?

State its working with the help of a suitable diagram.
Even though the current in the forward bias is known to be more than in the
reverse bias, yet the photodiode works in revers bias. What is the reason?


The oxidation number of iodine in \( I F_{5} \) is


If the sign was nailed to the side of a tree \( 5^{\prime} \) above the ground in \( 1997 . \) How high would the sign be in 2007 if the tree grew 4" taller each year?
A. \( 5^{\text {'high }} \)
B. 8'highh
c. 4'8" high
D. 9'4" high


The line \( y=x \) is a tangent at (0,0) to a
circle of radius is \( 1, \) then centre of the
circle is
\( ^{\mathbf{A}} \cdot\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)
B \( \cdot\left(\frac{1}{2 \sqrt{2}}-\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)
D. \( \left(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right) \)


Define molarity.


Find \( \int \frac{2 x}{\left(x^{2}+1\right)\left(x^{4}+4\right)} d x \)


Find the value of \( \int_{0}^{\frac{\pi}{2}} \log (\tan x) d x \)


Which is the smallest unit of time?
A. Second
B. Minute
c. Hour
D. Year


Two equilibria, \( A B \rightleftharpoons A^{+}+B^{-} . \) are
simultaneously maintained in a solution with equilibrium constants,
\( K_{1} \) and \( K_{2} \) respectively. The ratio of
\( \left[\boldsymbol{A}^{+}\right] \) to \( \left[\boldsymbol{A B}_{2}^{-}\right] \) in the solution is:
A. directly proportional to \( \left[B^{-}\right] \)
B . inversely proportional to [ \( B^{-} \)
C. directly proportional to the square of \( \left[B^{-}\right] \)
D. inversely proportional to the square of \( \left[B^{-}\right] \)
E. independent of \( \left[B^{-}\right] \)


\( R H_{2} \) (ion exchange resin) can replace
\( C a^{2+} \) ions in hard water as: \( R H_{2}+ \)
\( C a^{2+} \rightarrow R C a+2 H^{+} \)
If \( 1 L \) of hard water after passing through
\( R H_{2} \) has \( p H=3, \) then hardness in parts
per million of \( C a^{2+} \) is:
A. 80
B. 10
\( c \cdot 40 \)
D. 100


If \( z_{1}, z_{2} \) be two non zero complex
numbers satisfying the equation \( \left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}}+\left(\frac{z_{1}}{z_{2}}\right) \) is
A. zero
B.
c. purely imaginary
D.


If the quadratic equation \( k x^{2}-2 k x+ \)
\( 6=0 \) has equal roots, then find the
value of \( k \)


Assertion
Methane, component of green house gases, contributing to global warming
is about 20 percent.
Reason
Introduction of multi-point fuel
injection engines in automobiles has decreased methane content in the
exhausts.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If true enter 1 , else enter 0
Both \( N \) and \( C l \) has almost same
electronegativity but later is not
involved in \( \boldsymbol{H} \) -bonding.
\( A \cdot 1 \)


Two numbers are in the ratio \( 3: 4 . \) If
their LCM is 180 , find the numbers.


A short linear object of length \( L \) lies on the axis of a spherical mirror of focal length \( f \) at a distance \( u \) from the mirror.
Its image has an axial length \( L \) equal to
\( ^{\mathrm{A}} \cdot\left[\frac{f}{(u-f)}\right]^{1 / 2} \)
\( ^{\mathrm{B}} \cdot\left[\frac{u+f}{(f)}\right]^{1 / 2} \)
\( ^{\mathbf{c}} \cdot\left[\frac{u+f}{(f)}\right]^{2} \)
\( ^{\mathrm{D}} \cdot\left[\frac{f}{(u-f)}\right]^{2} \)


For an \( L C R \) series circuit with an A.C.
source of angular frequency \( \omega, \) which statement is correct?
A \cdot circuit will be capacitive if \( \omega>\frac{1}{\sqrt{L C}} \)
B. circuit will be capacitive if \( \omega=\frac{1}{\sqrt{L C}} \)
c. Power factor of circuit will be unity if capacitive reactance equals inductive reactance
D. current will be leading voltage if \( \omega>\frac{1}{\sqrt{L C}} \)


The degree and order of the differential equation of the family of all those
parabola's whose axis is \( x \) -axis are
respectively.
A \( \cdot 1,2 \)
B. 3,2
c. 2,3
D. 2,


What is the maximum \( p H \) required to
prevent precipitation of \( Z n S \) in a
solution that is \( 0.01 M Z n C l_{2} \) and
saturated with \( 0.1 M H_{2} S ? \)
\( \left[\text { Given: } \boldsymbol{K}_{s p}(\boldsymbol{Z} \boldsymbol{n} \boldsymbol{S})=\mathbf{1 0}^{-\mathbf{2 1}}, \) for \right.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{K} \boldsymbol{a}_{1} \times \boldsymbol{K} \boldsymbol{a}_{2}=\mathbf{1 0}^{-20} \)


The condition that \( \mathbf{f}(\mathbf{x})=\mathbf{x}^{\mathbf{3}}+\mathbf{a x}^{\mathbf{2}}+ \)
\( \mathbf{b x}+\mathbf{c} \) is an increasing function for al
real values of \( \mathbf{x} \) is
A \( \cdot a^{2}<12 b \)
B . a \( ^{2}<3 b \)
\( c \cdot a^{2}<4 b \)
D. \( a^{2}<16 b \)


In a capillary tube, fall of liquid is possible when angle of contact is
A. Acute angle
B. Right angle
c. obtuse angle
D. None of these


Motile sperms are absent in
A. Rhizopus
B. Funaria
c. Fern
D. cycas


Outer limiting layer of mycoplasma is formed of
A . Slime
B. Mucilage
c. Cell wall
D. Cell membrane


State any two difference between
primary rainbow and secondary
rainbow.


Consider the arrangement shown in figure (17-E4). The distance \( D \) is large compared to the separation \( d \) between
the slits
(a) Find the minimum value of
\( d \) so that there is a dark fringe at \( O .(b) \)
Suppose \( d \) has this value. Find the
distance \( x \) at which the bright fringe is formed.
(c) Find the fringe-width.


What conclusion can you draw from the following observations on a resistor
made of alloy manganin?
\( \begin{array}{llll}\begin{array}{l}\text { Current } \\ \text { A }\end{array} & \begin{array}{l}\text { Voltage } \\ \text { V }\end{array} & \begin{array}{l}\text { Current } \\ \text { A }\end{array} & \begin{array}{l}\text { Voltage } \\ \text { v }\end{array} \\ \begin{array}{l}\text { 0.2 } \\ \text { 0.4 }\end{array} & \begin{array}{l}\text { 3.94 } \\ \text { 7.87 }\end{array} & \begin{array}{l}\text { 3.0 } \\ \text { 4.0 }\end{array} & \begin{array}{l}\text { 59.2 } \\ \text { 78.8 }\end{array} \\ \begin{array}{l}\text { 0.6 } \\ \text { 0.8 }\end{array} & \begin{array}{l}\text { 11.8 } \\ \text { 15.7 }\end{array} & \begin{array}{l}\text { 5.0 } \\ \text { 1.0 }\end{array} & \begin{array}{l}\text { 6.0 } \\ \text { 19.7 }\end{array} & \begin{array}{l}\text { 98.6 } \\ \text { 7.0 }\end{array} & \begin{array}{l}\text { 118.5 } \\ \text { 138.2 }\end{array} \\ \begin{array}{ll}\text { 2.0 } & \text { 39.4 } & \text { 8.0 } & \text { 158.0 }\end{array}\end{array} \)


\( x_{10} \)
\( x \)


Show that, if \( \boldsymbol{f}: \boldsymbol{R}-\left\{\frac{\mathbf{7}}{\mathbf{5}}\right\} \rightarrow \boldsymbol{R}-\left\{\frac{\mathbf{3}}{\mathbf{5}}\right\} \)
is defined by \( f(x)=\frac{3 x+4}{5 x-7} \) and \( g: R- \) \( \left\{\frac{3}{5}\right\} \rightarrow R-\left\{\frac{7}{5}\right\} \) is defined by \( g(x)= \)
\( \frac{7 x+4}{5 x-3} \)
then \( \log =l_{A} \) and gof \( =l_{B}, \) where \( l_{A} \) and
\( l_{B} \) are called identity functions on sets
\( A \) and \( B \)


If \( \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\pi / 4 \) then
\( x=? \)


\( \left[M^{-1} L^{3} T^{-2}\right] \) are the dimensions of
A. Acceleration due to gravity
B. Gravitational constant
c. Gravitational force
D. Gravitational potential energy


Lead poisoning in the body can be removed by:
A. EDTA in the form of calcium dihydrogen salt.
B. Cis-platin
c. zeisse's salt
D. DMG


(A) When \( F e(C N)_{2} \) solution is treated with KCN solution, species formed does not give tests of \( F e^{2+} \) and \( C N^{-} \)
(B) When \( K_{2} S O_{4} \) solution is treated
with \( A l_{2}\left(S O_{4}\right)_{3} \) solution, species
formed gives tests of \( \boldsymbol{K}^{+}, \boldsymbol{A l}^{3+} \) and
\( \boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
Species formed in experiment A does
not give test of \( F e^{2+} \) and \( C N^{-} . \) It is due to formation of
A \( \cdot K_{2}\left[F e(C N)_{4}\right] \)
B . \( K_{3}\left[F e(C N)_{5}\right] \)
c. \( K_{3}\left[F e(C N)_{6}\right] \)
D. \( K_{4}\left[F e(C N)_{6}\right] \)


In an endothermic reaction the binding
energies of reactants and products are
\( e_{1}, e_{2} \) respectively, then
B \( \cdot e_{1}=e_{2} \)
\( \mathbf{c} \cdot e_{1}>e_{2} \)
D. \( e_{1} \geq e_{2} \)


Suppose there are two balls of equal mass, shape and size and we apply the equal force on both,suppose \( 5 \mathrm{N} \) but
after when they stop them we see that
one ball covers less distance and ball
covers more, even all are same
(mass,force,shape and size ) Why?


Calculate the number of moles of
hydrogen gas present in \( 0.5 d m^{3} \)
sample of hydrogen gas at a pressure of
\( 101.325 K P a \) and at \( 27^{\circ} C . \) (Write up to
2 decimal places


Two complex numbers are represented by ordered pairs \( z_{1}:(2,4) \& z_{2}:(-4,5) \)
which of the following is real part for
\( \boldsymbol{z}_{1} \times \boldsymbol{z}_{2}=? \)
A . -6
B. -28
\( c \cdot 6 \)
D. None of these


Rusting of iron in the presence of moist oxygen is an oxidation reaction.
A. True
B. False


The reaction that does not define
calcination is:
A \( . Z n C O_{3} \stackrel{\Delta}{\longrightarrow} Z n O+C O_{2} \)
B \( \cdot F e_{2} O_{3} \cdot x H_{2} O \stackrel{\Delta}{\longrightarrow} F e_{2} O_{3}+x H_{2} O \)
\( \mathbf{c} \cdot \mathrm{CaCO}_{3} \cdot \mathrm{MgCO}_{3} \stackrel{\Delta}{\longrightarrow} \mathrm{CaO}+\mathrm{MgO}+2 \mathrm{CO}_{2} \)
D \( \cdot 2 C u_{2} S+3 O_{2} \stackrel{\Delta}{\longrightarrow} 2 C u_{2} O+2 S O_{2} \)


If for a sucrose,elevation in boiling point
is \( 1.0^{\circ} \mathrm{C} \),then what will be the boiling
point of \( N a C l \) solution for same molal concentration?
\( \mathbf{A} \cdot 1.0^{\circ} \mathrm{C} \)
B . \( 2.0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 3.0^{\circ} \mathrm{C} \)
D. \( 4.0^{\circ} \mathrm{C} \)


The top of the atmosphere is about 400
kV with respect to the surface of earth,
corresponding to an electric field that
decreases with altitude. Near the
surface of the earth the field is about
\( 100 \mathrm{V} \mathrm{m}^{-1}, \) but still dont get an electric
shock, as we set out of our houses in to
open because : (assume the house is
free from electric field)
A. Our body is a perfect insulator
B. Our body and ground form an equipotential surface
C. The original equipotential surfaces of open air remain same
D. None of the above


Evaluat the following:
\( \sin ^{-1}(\sin 4) \)


Find the domain of definition of the
following function. \( \boldsymbol{y}=\frac{\sqrt{\mathbf{3} \boldsymbol{x}-\mathbf{7}}}{\sqrt[6]{\boldsymbol{x}+\mathbf{1}}} \)


Choose and write the correct
alternative.
If \( 3 \sin \theta=4 \cos \theta \) then \( \cot \theta=? \)
A \( \cdot \frac{4}{3} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{5}{4} \)


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{D} \)


By using the properties of definite integrals, evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x \)


In the below figure \( A B, C D \) and \( E F \) are
three lines concurrent at \( O \). Find the
value of \( y \)


In the equation \( \boldsymbol{y}= \)
\( \boldsymbol{A} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}_{0}\right) \) the term phase is
defined as:
\( A \cdot \phi_{0} \)
B. \( \phi_{0}-\omega t \)
c. \( k x+\phi_{0} \)
D. \( k x-\omega t-\phi_{0} \)


Which type of isomerism is shown by
But-2-yne and cyclobutene?
A. Ring chain isomerism
B. Chain isomerism
c. Position isomerism
D. Functional isomerism


Which of the following is both neutral and paramagnetic?
A \( \cdot N O_{2} \)
в. \( N O \)
c. \( N_{2} O_{4} \)
D. none of the above


The daniel cell is balanced on \( 125 \mathrm{cm} \)
length of a potentiometer. Now, the cell is short circuited by a resistance of \( 2 \Omega \) and the balance is obtained at \( 100 \mathrm{cm} \)
The internal resistance of the daniel cell
is :
A \( \frac{4}{3} \Omega \)
B. \( 1.5 \Omega \)
c. \( 1.25 \Omega \)
D. \( 0.5 \Omega \)


A resistor of resistance \( R \) is connected
to an ideal battery. If the value of \( \boldsymbol{R} \) is
decreased, the power dissipated in the resistor will
A. Increase
B. Decrease
c. Remains unchanged
D. None of these


The mean deviation of \( a^{3}+b^{3} \) and \( a^{3}- \)
\( b^{3}(\text { when }(a \& b>0) \) is
A \( \cdot a^{3} \)
в. \( b^{3} \)
\( c \cdot 2 a^{3} \)
D. \( 2 b^{3} \)


State True or False.
\( H^{2} \) is more reactive than \( H^{1} \)
A. True
B. False


An element forms two oxides containing respectively 53.33 and 36.36 percent of oxygen. These figures illustrate the law of
A. Conservation of mass
B. Constant proportions
c. Reciprocal proportions
D. Multiple proportions


If \( Z=\cos \theta+i \sin \theta \) find the complex
representation of \( \frac{Z}{1-2 Z} \)


For the reaction of one mole of zinc dust
with one mole of sulphuric acid in a
bomb calorimeter, \( \triangle \boldsymbol{U} \) and \( \boldsymbol{w} \)
corresponds to:
A. \( \triangle U<0, w=0 \)
в. \( \triangle U<0, w<0 \)
c. \( \triangle U>0, w=0 \)
D. \( \triangle U>0, w>0 \)


The following data gives the amount of manure (in thousand tonnes)
manufactured by a company during
some years:
Year \begin{tabular}{lll}
1992 & 1993 & 1994 \\
\hline
\end{tabular}
Manure
(in thousand tonnes
Represent the above data with the help
of a bar graph.


If \( \frac{1}{\boldsymbol{q}+\boldsymbol{r}}, \frac{\mathbf{1}}{\boldsymbol{r}+\boldsymbol{p}} \) and \( \frac{\mathbf{1}}{\boldsymbol{p}+\boldsymbol{q}} \) are in AP
then \( p^{2}, q^{2} \) and \( r^{2} \) are in
\( A \cdot A P \)
в. GP
c. нр
D. AGP


Recycling biodegradable waste into a
nutrient-rich, usable material is often
called as


Simplify \( : \cos Q\left[\begin{array}{cc}\cos Q & \sin Q \\ -\sin Q & \cos Q\end{array}\right]+ \)
\( \sin Q\left[\begin{array}{cc}\sin Q & -\cos Q \\ \cos Q & \sin Q\end{array}\right] \)


ABCD is a parallelogram where
\( \mathbf{A}(\boldsymbol{x}, \boldsymbol{y}), \mathbf{B}(\mathbf{5}, \mathbf{8}), \mathbf{C}(\mathbf{4}, \mathbf{7}) \) and \( \mathbf{D}(\mathbf{2},-\mathbf{4}) \)
Find
(i) the coordinates of \( A \)
(ii) the equation of the diagonal \( B D \)


Evaluate \( \int_{0}^{\pi / 4} \frac{\tan ^{3} x}{1+\cos 2 x} d x \)


A conducting loop in the shape of a right angled isosceles triangle of height
\( 10 \mathrm{cm} \) is kept such that the \( 90^{\circ} \) vertex
is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counter clockwise direction and increased at a constant
rate of \( 10 A s^{-1} . \) Which of the following
statement (s) is (are) true?
This question has multiple correct options
A. There is a repulsive force between the wire and the loo
B. If the loop is rotated at a constant angular speed about the wire, an additional emf of \( \left(\frac{\mu_{0}}{\pi}\right) \) volt is induced in the wire
C . The magnitude of induced emf in the wire is \( \left(\frac{\mu_{0}}{\pi}\right) \) vo
duced current in the wire is in opposite directic to the current along the hypo