Write any two applications of interference


Assertion
Scientific notation for the number 100
is expressed as \( 10^{2} \)
Reason
The number \( 10^{2} \) has two significant
figures.
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


Find all zeroes of polynomial \( 3 x^{4}+ \) \( 6 x^{3}-2 x^{2}-10 x-5 \) if two zeroes
\( \operatorname{are} \sqrt{5 / 3} \) and \( -\sqrt{5 / 3} \)


The potential energy of a 1 kg particle free to move along the \( x \) -axis is given by \( V(x)=\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right) J . \) The tota
mechanical energy of the particle 2 J. Then, the maximum speed (in \( \mathrm{m} / \mathrm{s} \) ) is
\( A \cdot 2 \)
B. \( 3 / \sqrt{2} \)
\( c \cdot \sqrt{2} \)
D. \( 1 / \sqrt{2} \)


Which of the reagents listed below could be added to water to make \( 0.1 \mathrm{M} \)
solutions of \( C H_{3} C O O^{\ominus} \) ions?
¡. \( \boldsymbol{C H}_{3} \) COOH
¡i. \( C H_{3} C O O N a \)
A. \( C H_{3} C O O H \) because it is a strong electrolyte
B. \( C H_{3} \) COONa because it is a strong electrolyte
\( \mathrm{c} \cdot C H_{3} C O O H \) because it is a weak electrolyte
D. \( C H_{3} C O O N a \) because it is a weak electrolyte


A stationary wheel starts rotating about its own axis at a constant angular acceleration. If the wheel completes 50 rotations in the first \( 2 s, \) then the number of rotations made by it in the
next \( 2 s \) is:
A . 75
в. 100
c. 125
D. 150


Which of the following statement is
incorrect about the extraction of lead
from galena?
A. Galena is a sulphide ore and therefore, it is concentrated by froth flotation process
B. Self reduction takes place in absence of air.
C. Complete roasting of galena gives PbO which is then reduced by coke or \( \mathrm{CO} \) to give metallic lead.
D. \( F e S i O_{3} \) is obtained as slag.


With the increase in quantum number the energy difference between consecutive energy levels
A. remains constant
B. decreases
c. increases
D. sometimes increases sometimes decreases


Which of the following salts is a strong
electrolyte?
A . \( N a C l \)
в. \( K C l \)
c. \( M g C l_{2} \)
D. All of the above


A steel beam is 5 m long at a
temperature of \( 20^{\circ} \mathrm{C} . \) On a hot day, the
temperature rises to \( 40^{\circ} \mathrm{C} \). What is the
change in the length of the beam due to thermal expansion? Coefficient of linear expansion of stee \( \boldsymbol{\alpha}=\mathbf{1} \cdot \mathbf{2} \times \mathbf{1} \mathbf{0}^{-\mathbf{5}} \boldsymbol{o} \boldsymbol{C}^{-\mathbf{1}} \)


Divide \( 4 x^{3}+3 x^{2}-2 x+8 \) by \( x-2 \)


Select correct statement(s).
A. Across a transition series, there is only a small decrease in atomic radius from one element to another due to very small increase in effective nuclear charge.
B. The rate of decrease in the size across the lanthanide
series is less than the across the first transition series.
c. Both
(a) \&
(b) are correct statements
D. None of the above statement is correct.


How many of the alphabets have more
than 1 line of symmetry?
\[
A B C D E F G H I J K L M N O
\]


Which of the following is true
statement?
A. A is staggered conformation and B is eclipsed conformation
B. B is staggered conformation and A is eclipsed conformation
c. Both are eclipsed conformations.
D. Both are staggered conformations


Which one of the following elements forms compounds that are all coloured?
A. Magnesium
B. Aluminium
c. Iron
D. Chromium


If the last band on the carbon resistor is
absent, then the tolerance is?
A . \( 5 \% \)
B. 20\%
\( c \cdot 10 \% \)
D. \( 15 \% \)


\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \leftrightharpoons \)
A \( \cdot H^{+}+N O_{3}^{2-} \)
B. \( H^{-}+N O_{3}^{+} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{NO}_{3} \)
D. \( H_{3} O^{-}+N O_{3}^{+} \)


If \( \vec{A}=\hat{i}+2 \hat{j}+3 \hat{k} \& \vec{B}=3 \hat{i}-2 \hat{j}+\hat{k} \)
then the area of parallelogram formed with \( \vec{A} \) and \( \vec{B} \) as the sides of the
parallelogram is :
A. \( \sqrt{3} \)
B. \( 8 \sqrt{3} \)
\( c \cdot 64 \)
D.


The mass composition of universe may
be given as \( 90 \% H_{2} \) and \( 10 \% \) He. The
average molecular mass of universe
should be
A .2 .20
B. 2.10
c. 3.80
D. 3.64


Which of the following circular rods (given radius \( r \) and length I), each made of the same material and whose ends
are maintained at the same
temperature will conduct most heat?
A. \( r=r_{0} ; l=l_{0} \)
B . \( r=2 r_{0} ; l=l_{0} \)
c. \( r=r_{0} ; l=2 l_{0} \)
D \( \cdot r=2 r_{0} ; l=2 l_{0} \)


Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) The common name of \( \left(H O O C-C H_{2}-C O O H\right) \) is
malonic acid
B. The common name of is succinic acid is butanedioic acid
C. The IUPAC name of \( \left(C H_{2}=C H-O C O C H_{3}\right) \) is vinyl
acetate
D. The IUPAC name of acrylonitrile is pror-2-enenitrile.


The plane \( 2 x-3 y+z+6=0 \) divides
the line segment joining (2,4,16) and (3,5,-4) in the ratio
A .4: 5
B. 4: 7
c. 2: 1
D. 1: 2


Carbon monoxide emitted by
automobiles prevents transport of oxygen in body due to:
A. its combination with oxygen to form carbon dioxide
B. break down of haemoglobin
c. preventing haemoglobin to form oxyhaemoglobin
D. formation of free radicals in the blood


Give the complete name for \( \boldsymbol{P H B V} \).
How it is useful?


Boiling water is changing into steam. Under this condition, the specific heat
of water is
A. zero
B. one
c. infinite
D. less than one


There is a uniform electrostatic field in
a region. The potential at various points on a small sphere central at \( P \), in the region, is found to vary between the limits \( 589.0 \mathrm{V} \) to \( 589.8 \mathrm{V} \). What is the
potential at a point on the sphere whose
radius vector makes an angle of \( 60^{\circ} \)
with the direction of the field?
A . \( 589.5 \mathrm{v} \)
B. \( 589.2 v \)
c. \( 589.4 \mathrm{v} \)
D. 589.6


Get the algebraic expressions in the
following case using variables, constants and arithmetic operations. One-fourth of the product of numbers p and \( q \)


Tell if the following statement is true or
false. In case give a valid reason for
saying so
\( p: \) If \( x \) and \( y \) are integers such that \( x> \)
\( \boldsymbol{y} \cdot \) then \( -\boldsymbol{x}<-\boldsymbol{y} \)
A. True
B. False


A charged particle is released from rest in a region of steady and uniform electric and magnetic fields where \( \mathrm{E} \| \mathrm{B} \) The particle will follow.
A. circular path
B. Elliptical path
c. Helical path
D. Straight line path


Two different families \( A \) and \( B \) are
blessed with equal number of children.
There are 3 tickets to be distributed
amongst the children of these families so that no child gets more than one
ticket. If the probability that all the tickets go to the children of the family \( B \) is \( \frac{1}{12}, \) then the number of children in
each family is?
A .4
B. 6
\( c .3 \)
\( D \)


Sieve tubes are better suited for
translocation because these
A. Are broad and long
B. Possess bordered pits
c. Possess no end walls
D. Possess a broader lumen and perforated cross walls


Which of the following should be added to \( 9 x^{3}+6 x^{2}+x+2 \) so that the sum is
divisible by \( (3 x+1) ? \)
A . -
B . - -
\( c \cdot-2 \)
D. -


The water table fluctuates:
A. by climatic variations
B. by the amount of precipitation used by vegetation
C. by withdrawing excessive amounts of water from wells
D. all of them


Substrate phosphorylation is the formation of
A. ATP
в. АМР
c. ADP
D. Pyruvic acid


If \( \boldsymbol{A}=\left(\boldsymbol{a}_{\boldsymbol{i} j}\right)_{\mathbf{3} \times \mathbf{3}} \) is a skew symmetric
matrix, then
This question has multiple correct options
\( \mathbf{A} \cdot a_{i i}=0 \forall i \)
B. \( A+A^{T} \) is a null matrix
c. \( |A|=0 \)
D. \( A \) is not invertible


Differentiate with respect to \( x \) :
\( \log (\csc x-\cot x) \)


A ray of light passes through an equilateral prism such that the angle of incidence is equal of emergence and
the later is equal to \( \frac{3}{4} \) th of the angle of the prism. Calculate the angle of deviation.


Bacteria that get their energy by fermentation and oxygen is lethal for them are called:
A. obligate aerobes
B. obligate anaerobes
c. facultative aerobes
D. facultative anaerobes


A electric charge \( 10^{-8} C \) is placed at the
point \( (4 m, 7 m, 2 m) . \) At the point \( (1 m, 3 m, 2 m) \) the electric
A. potential will be \( 18 V \)
B. field has no \( Y \) -component
c. field will be along \( Z \) -axis
D. potential will be \( 1.8 V \)


\( \boldsymbol{f}:(\mathbf{0}, \infty) \rightarrow\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \) be defined as
\( f(x)=\arctan (x) \)
The above function can be classified as
A. injective but not surjective
B. surjective but not injective
c. neither injective nor surjective
D. both injective as well as surjective


The critical density of the \( \operatorname{gas} C O_{2} \) is
\( 0.44 g c m^{-3} \) at a certain temperature. If
\( r \) is the radius of the molecule, \( r^{3} \) in
\( c m^{3} \) is approximately: (N is Avogadro number)
A \( \cdot \frac{25}{\pi N} \)
в. \( \frac{100}{\pi N} \)
c. \( \frac{6.25}{\pi N} \)
D. \( \frac{25}{\pi} \)


Four equal charges, each \( +\boldsymbol{q} \) are placed
at the corners of a square of side \( a \). Then
the coulomb force experienced one charge due to the rest of there is:-
\( ^{\text {A }} \cdot \frac{q^{2}}{k a^{2}}\left[\sqrt{2}+\frac{1}{2}\right] \)
B. \( 3 k q^{2} / a^{2} \)
C \( \cdot 2 \sqrt{2} k q^{2} / a^{2} \)
D. zero


Adsorption theory is applicable for:
A. homogeneous catalysis
B. heterogeneous catalysis
c. autocatalysis
D. induced catalysis


Addition reactions are limited to
chemical compounds that have :
A. multiple bonds
B. single bonds
c. only double bonds
D. only triple bonds


A particle executing SHM has a
maximum speed of \( 0.5 m s^{-1} \) and
maximum acceleration of \( 1 m s^{-2} \)
The angular frequency of oscillation is:
A \( \cdot 2 r a d s^{-1} \)
B . 0.5 rads\( ^{-1} \)
C \( .2 \pi r a d s^{-1} \)
D. \( 0.5 \pi r a d s^{-1} \)


Find the principal values of \( \sin ^{-1}\left(-\frac{1}{\sqrt{2}}\right) \)


Which compound does not gives Cannizaro's reaction:
A. Acetaldehyde
B. Benzaldehyde
c. Formaldehyde
D. None of the above


Ideal solution is formed when its
components:
This question has multiple correct options
A. have zero heat of mixing
B. have zero volume change
c. obey Raoult's law
D. can be converted into gases


If \( \hat{a} \) and \( \hat{b} \) are unit vectors inclined at an
angle \( \theta \), then prove that
\( \cos \frac{\boldsymbol{\theta}}{\mathbf{2}}=\frac{\mathbf{1}}{\mathbf{2}}|\hat{\boldsymbol{a}}+\hat{\boldsymbol{b}}| \)


The expression relating mole fraction of
solute \( \left(\chi_{2}\right) \) and molarity \( (\mathrm{M}) \) of the
solution is (where dis the density of the
solution in \( g L^{-1} \) and \( M w_{1} \) and \( M w_{2} \)
are the molar masses of solvent and
solute, respectively
A \( \cdot x_{2}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)+1000 d} \)
B. \( x_{2}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)+d} \)
c. \( _{x_{2}}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)-1000 d} \)
D. \( _{x_{2}}=\frac{M \times M w_{1}}{M\left(M w_{1}-M w_{2}\right)-d} \)


at the earth's surface is \( 10 m s^{-2} \) and at
the surface of Mars is \( 4.0 m s^{-2} . \) A \( 60 k g \)
passenger goes from the earth to Mars
in a spaceship moving with a constant
velocity. Neglect all other objects in the
sky. Which part of the figure best
represents the weight (net gravitational force) of the passenger as a function of
time?
\( A \cdot A \)
B. \( B \)
\( c \)
\( D \)


Receptors are located in cell membrane.
If true enter 1 , if false enter 0 .


In the complex plane, what is the
distance of \( 4-2 i \) from the origin?
\( A \cdot 2 \)
в. 3.46
c. 4.47
D. 6
E . 12


Calculate the wavelength of an electron moving with a kinetic energy of
\( 18.62 \times 10^{-25} J \)


Find the value of discriminant for
\( \sqrt{3} x^{2}+2 \sqrt{2} x-2 \sqrt{3}=0 \)


Out of the following, select the correct
statements:
This question has multiple correct options
A. refractive index, frequency and deviation are maximum for red colour
B. if there were no atmosphere, the length of the day on the earth would increase
C. for greater value of \( \mu \), the angle of deviation increase
D. if the critical angle for the medium of a prism is \( \theta_{c} \) and the angle of prism is \( A \), there will be no emergent ray when \( A>2 \theta_{c} \)


The figure below shows a variable
resistor in a dimmer switch.
How would you turn the switch to make
the lights: \( (a) \) brighter, and
(b) dimmer? Explain.


Fine beam of light entering through a small hole in a dark room illuminates
the particles in its path. Identify the effect associated with this process.
A. Schottky effect
B. Rutherford effect
c. Tyndall effect
D. Photoelectric effect


Which of the following represents
hydrolysis?
\( \mathbf{A} \cdot \stackrel{\oplus}{N} H_{4}+2 H_{2} O \rightleftharpoons N H_{4} O H+H_{3} O^{\oplus} \)
B. \( \stackrel{\oplus}{N} H_{4}+H_{2} O \rightleftharpoons N H_{3}+H_{3} O^{\oplus} \)
\( \mathrm{c} \cdot H C O_{3}^{\circ}+H_{2} O \rightleftharpoons H_{2} C O_{3}+\stackrel{\ominus}{O} H \)
D. \( H C O_{3}^{\ominus}+H_{2} O \rightleftharpoons C O_{3}^{2-}+H_{3} O^{\oplus} \)


Answer in 40 to 80 words:
What is ecological succession?
Distinguish primary succession from secondary succession.


If the function \( \mathbf{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}\frac{2^{x+2}-16}{4^{x}-16} & \text { for } x \neq 2 \\ \mathbf{A} & x=2\end{array} \) is continuous \right.
at \( \boldsymbol{x}=\mathbf{2}, \) then \( \mathbf{A}= \)
\( A \cdot 2 \)
B.
\( c \cdot \frac{1}{4} \)
D.


The molecular formula of ammonia is
\( N H_{3} . \) Therefore, the number of
hydrogen atoms in 34 g of ammonia will
be:
A. \( 3 \times 6.023 \times 10^{23} \)
В. \( 6.023 \times 10^{23} \)
c. \( 34 \times 6.023 \times 10^{23} \)
D. \( 6 \times 6.023 \times 10^{23} \)


In respiration, pyruvic acid is
A. Formed only when oxygen is available.
B. One of the product of Krebs cycle
c. Broken down into Acetyl Co-A and \( C O_{2} \).
D. A result of protein break down


The order and degree of the differential equation \( \sqrt{\frac{\boldsymbol{d y}}{\boldsymbol{d} \boldsymbol{x}}}-4 \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{7} \boldsymbol{x}=\boldsymbol{0} \) are
A. 1 and \( 1 / 2 \)
B. 2 and 1
c. 1 and 1
D. 1 and 2


What is the final velocity of an electron accelerating through a potential of 1600 \( V, \) if its initial velocity is zero?
A \( .2 .37 \times 10^{9} \mathrm{ms}^{-1} \)
В. \( 4.74 \times 10^{7} \mathrm{ms}^{-1} \)
c. \( 2.37 \times 10^{7} m s^{-1} \)
D. None of these


The name for hydrogen comes from the words which means:
A. water fearer
B. water former
c. gas
D. fire former


Find the angles at which the normal
vector to the plane \( 4 x+8 y+z=5 \) is
inclined to the coordinate axes.


Best neutron moderator is.
A. Beryllium oxide
B. Pure water
c. Graphite
D. Heavy water


A long wire carries a steady current. IT
is bent into a circle of one turn and the
magnetic field at the centre of the coil
is \( B \). It is then bent into a circular loop
of \( n \) turns. The magnetic field at the centre of the coil will be:
\( \mathbf{A} \cdot n B \)
B . \( n^{2} B \)
\( c \cdot 2 n B \)
D. \( 2 n^{2} B \)


Give the IUPAC name of the complex
compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N H}_{\boldsymbol{3}}\right)_{\boldsymbol{4}}\left(\boldsymbol{H}_{\boldsymbol{2}} \boldsymbol{O}\right) \boldsymbol{B r}\right]\left(\boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}\right)_{\boldsymbol{2}} \)
A. Bromoaquotetraaminecobalt(III) nitrate
B. Bromoaquotetraaminocobalt(III) nitrate
C. Bromoaquatetraaminecobalt(III) nitrate
D. Tetraammineaquabromocobalt(III) nitrate


The whole area of the curves \( x= \)
\( a \cos ^{3} t, y=b \sin ^{3} t \) is given by?
A \( \cdot \frac{3}{8} \pi a b \)
в. \( \frac{5}{8} \pi a b \)
c. \( \frac{1}{8} \pi a b \)
D. None of these


\( \boldsymbol{d}_{z^{2}} \) -orbital has:
\( \mathbf{A} \cdot \) a lobe along \( z \) -axis and a ring along \( x y \) -plane.
B. a lobe along \( z \) -axis and a lobe along \( x y \) -plane.
C. a lobe along \( z \) -axis and a ring along \( y z \) -plane.
D. a lobe and a ring along \( z \) -axis.


Evaluate \( \lim _{x \rightarrow 0}\left(\frac{1}{\sin x}-\frac{1}{\tan x}\right) \)


Correct boiling point is:
\( \begin{array}{cc}\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{I} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{B r}\end{array} \)
\( \begin{array}{cc}\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C l} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{F}\end{array} \)
A. \( I V>I I I>I I>I \)
В. \( I I>I I I>I V>I \)
c. \( I>I I>I I I>I V \)
D. \( I V>I I I>I>I I \)


If the solution of the \( C u S O_{4} \) in which
copper rod is immersed in diluted to 10
times, the oxidation electrode potential:
A. increase by 0.030 volt
B. decrease by 0.30 volt
c. increase by 0.059 volt
D. decrease by 0.0059 volt


An object is placed at a distance of \( \boldsymbol{f} / \mathbf{2} \)
from a convex lens. The image will be
A. At one of the foci, virtual and double its size
B. At \( 3 f / 2 \), real and inverted and erect
c. At \( 2 f \), virtual and inverted
D. At \( f \), real and inverted


If vector \( \overrightarrow{\boldsymbol{v}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \) then find their
direction angles.
\( \mathbf{A} \cdot\left(\cos ^{-1} \frac{1}{\sqrt{3}}, \cos ^{-1} \frac{1}{\sqrt{3}}, \cos ^{-1} \frac{1}{\sqrt{3}}\right) \)
B \( \cdot\left(\cos ^{-1}(1), \cos ^{-1}(1), \cos ^{-1}(1)\right) \)
\( ^{c} \cdot\left(\cos ^{-1}(1), \cos ^{-1} \frac{1}{\sqrt{3}}, \cos ^{-1} \frac{1}{\sqrt{3}}\right) \)
D \( \cdot\left(\cos ^{-1} \frac{1}{\sqrt{3}}, \cos ^{-1}(1), \cos ^{-1} \frac{1}{\sqrt{3}}\right) \)


Which of the following has least tendency of catenation?
A. \( C \)
B. \( S \) i
c. \( G e \)
D. \( S n \)


Arrange the following groups in order of decreasing -R (or -M) power.
1) \( \boldsymbol{N} \boldsymbol{O}_{\boldsymbol{2}} \)
2) \( \boldsymbol{S O}_{3} \boldsymbol{H} \)
3) \( C F_{3} \)
4) \( C H O \)
\( A \cdot 1>3>2>4 \)
B. \( 1>2>3>4 \)
\( c \cdot 1>4>3>2 \)
\( D \cdot 4>3>2>1 \)


The boiling point of liquid oxygen is:
\( \mathbf{A} \cdot-156^{\circ} \mathrm{C} \)
B . \( -196^{\circ} \mathrm{C} \)
c. \( -183^{\circ} \mathrm{C} \)
D. \( -173^{\circ} \mathrm{C} \)


Which of the following factors regulate food intake?
A. Body temperature
B. Psychological factors
c. Blood glucose levels
D. All of these


Angular speed and angular frequency
use the same variable \( \omega . \) Are there any
differences in their interpretation. Explain


Two solid rubber balls, A and B having masses 200 and 400 g respectively are moving in opposite directions
with velocity of A equal to \( 0.3 m / s \). After collision the two balls come to rest, then the velocity of B is-
A. \( 0.15 \mathrm{m} / \mathrm{s} \)
в. \( 1.5 \mathrm{m} / \mathrm{s} \)
c. \( -0.15 \mathrm{m} / \mathrm{s} \)
D. None of the above


Calculate the value of \( g \) on the surface
of planet if the planet has \( 1 / 500 \) the mass and \( 1 / 15 \) the radius of the Earth
в. \( 1.6 m / s_{2} \)
\( \mathrm{c} \cdot 2.4 \mathrm{m} / \mathrm{s}_{2} \)
D. \( 4.5 m / s_{2} \)
E \( .7 .1 \mathrm{m} / \mathrm{s}_{2} \)


Calcium oxide is formed as a result of
transfer of \( _{-1-} \) valence electrons
A. one
B. two
c. three
D. four


The primary winding of a transformer
has 100 turns and its secondary winding has 200 turns. The primary is
connected to an ac supply of \( 120 \mathrm{V} \) and the current flowing in it is 10 A. The voltage and the current in the secondary
are
A. \( 240 \vee, 5 A \)
B. 340 V, 7 A
c. \( 290 \vee, 8 A \)
D. 300 V, 9 A


The correct order in which the 0 - 0 bond
length increases in the following is ?
A. \( H_{2} O_{2}<O_{2}<O_{3} \)
в. \( O_{3}<H_{2} O_{2}<O_{2} \)
c. \( O_{2}<O_{3}<H_{2} O_{2} \)
D. \( O_{2}<H_{2} O_{2}<O_{3} \)


Value of all quantum number for 4 th
electron of \( \left(_{16} S\right) \)


Sheet erosion is caused by
A. Sea
B. wind
c. Heavy rains
D. Glaciers


Two coherent light sources each of
wavelength \( \lambda \) are separated by a
distance \( 3 \lambda \). The maximum number of
minima formed on line AB which runs
from \( -\infty \) to \( +\infty \) is


Coulomb's law is applicable only to stationary electric charges.
A. True
B. False


In the manufacture of hydrogen from
water gas \( \left(C O+H_{2}\right), \) which of the
following is correct statement?
A. Hydrogen is isolated by diffusion
B. \( H_{2} \) is removed by occlusion with pd
c. co and \( H_{2} \) are separated based on difference in their densities
D. co is oxidized to \( C O_{2} \) with steam in the presence of a catalyst followed by absorption of \( C O_{2} \) in alkali


Which gas is produced when calcium
nitride \( \left(C a_{3} N_{2}\right) \) is hydrolyzed by water?
A \( . N_{2} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( O_{2} \)


An aluminium wire and steel wire of the
same length and cross section are
joined end to end.The composite wire is hung from a rigid support and a load is suspended from the free end.

The young's modulus of steel is \( 20 / 7 \) times the aluminium. The ratio of
increase of length of steel and aluminium is
A \( .20 / 7 \)
в. \( 400 / 49 \)
\( c \cdot 7 / 20 \)
D. \( 49 / 400 \)


Solve: \( 3 x-5=x-5 \)


Change in internal energy of the gas in the isobaric process is:
A \( .2 .5 \times 10^{4} J \)
В. \( 1.2 \times 10^{6} J \)
c. \( 3 \times 10^{5} J \)
D. \( 0.5 \times 10^{3} J \)


ffunction \( f(x) \) is continuous in interval \( [-2,2], \) find the value of \( (a+b) \)
where \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sin a x}{x}-2, & \text { for }-2 \leq x<0 \\ 2 x+1, & \text { for } 0 \leq x \leq 1 \\ 2 b \sqrt{x^{2}+3}-1, & \text { for } 1<x \leq 2\end{array}\right. \)


Let \( f \) be a real function given by \( f(x)= \) \( \sqrt{x-2} . \) Find the following.
(i) \( \boldsymbol{f} \circ \boldsymbol{f} \)
(ii) \( \boldsymbol{f} \circ \boldsymbol{f} \circ \boldsymbol{f} \)
(iii) \( (f \circ f \circ \)
\( \boldsymbol{f}(\mathbf{3 8}) \)
(iv) \( \boldsymbol{f}^{2} \)
Also, show that \( \boldsymbol{f} \circ \boldsymbol{f} \neq \boldsymbol{f}^{2} \)


Largest amount of fresh water is found
in
A. Lakes and streams
B. Underground
c. Polar ice and glaciers
D. Rivers


A man weighs \( 600 N \) on earth. What
would be his approximate weight on
moon?
A . \( 100 N \)
B. \( 200 N \)
\( c .50 N \)
D. \( 600 N \)


Find the total surface area of cubes
having the following sides.
\( \mathbf{5} c \boldsymbol{m} \)


A wire has resistance of \( 8 \Omega \). If its length is made half by folding, find its resistance after the free ends are
connected to each other


Assertion
A direct current flows through a metallic rod. It produces magnetic field only outside the rod.
Reason
The charge carries flow through whole of
the cross section.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following dissolves in ionic solvents?
A \( \cdot C_{6} H_{6} \)
в. \( C H_{3} O H \)
c. \( C C l_{4} \)
D. \( C_{5} H_{12} \)


The common features of the species
\( N_{2}^{2-}, O_{2} \) and \( N O^{-} \) are:
A. bond order is three and are isoelectronic
B. bond order is two and are isoelectronic
C. bond order is three but are not isoelectronic
D. bond order is two but are not isoelectronic


A man pushes an \( 80 N \) crate a distance
of \( 5.0 m \) upward along a frictionless
slope that makes an angle of \( 30^{\circ} \) with the horizontal. The force he exerts is
parallel to the slope. If the speed of the crate is constant, then the work done by the man is:
A . \( -140 J \)
в. \( 140 J \)
\( c \cdot 200 J \)
D. \( -200 J \)


Find the principal value of the following:
\( \tan ^{-1}(-1) \)


When a substance reacts with water
and breaks into acids and bases the
process is called:
A. dialysiss
B. solvolysis
c. hydrolysis
D. dissolution


A short linear object of length \( b \) lies along the axis of a concave mirror of
focal length \( f \) at a distance \( u \) from the pole of the mirror. The size of the image is approximately equal to:
\( A \)
\[
b\left(\frac{u-f}{f}\right)^{\frac{1}{2}}
\]
в.
\[
b\left(\frac{u-f}{f}\right)
\]
\( c \)
\[
b\left(\frac{f}{u-f}\right)^{\frac{1}{2}}
\]
D.
\[
b\left(\frac{f}{u-f}\right)^{2}
\]


If the outer and inner radii of a ring are
\( 10 \mathrm{cm} \) and \( 8 \mathrm{cm}, \) then its area is nearly
A. 113.443 sq. \( \mathrm{cm} \)
В. 113.343 sq. \( \mathrm{cm} \)
c. 113.243 sq. \( \mathrm{cm} \)
D. 113.143 sq. \( \mathrm{cm} \)


Find the value of \( p, \) if \( p q+12=3 p+ \)
\( p r \) and \( q-r=7 \)
A . -3
B. -4
\( c \cdot \frac{1}{3} \)
D.
E. \( -\frac{6}{5} \)


A rod of mass \( ^{\prime} M^{\prime} \) is subjected to force
\( t^{\prime} \) and \( ^{\prime} 2 f^{\prime} \) at both the ends as shown in
the figure. If young modulus of
its material is ' \( y^{\prime} \) and its length is \( L \)
find total elongation of rod.
A \( \cdot \frac{f l}{2 A y} \)
в. \( \frac{f l}{A y} \)
c. \( \frac{3 f l}{2 A v} \)
D. \( \frac{4 f l}{2 A y} \)


A hydrocarbon \( C_{6} H_{10} \) absorbs only one
molecule of \( \boldsymbol{H}_{2} \) on catalytic hydrogenation. On ozonolysis, the
hydrocarbon yields \( C H O\left(C H_{2}\right)_{4} C H O \)
The hydrocarbon is:
A. cyclohexene
B. 1,5-hexadiene
c. 1,3 -cyclohexadiene
D. 1-methylcyclopentene


Which graph will show equilibrium
condition?
\( A \)
B.
\( c \)
D. None of these


Complete the following ionic equation:
\( \mathbf{3} M n O_{4}^{2-}+4 H^{+} \rightarrow \)


Assertion: pH of water increases with an
increase in temperature
Reason: \( K_{W} \) of water increases with
increase in temperature
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


The masses of three copper wires are in the ratio 1: 2: 3 and their lengths are
in the ratio \( 3: 2: 1 . \) The ratio of their
resistance is:
A. 27: 6: 1
B. 9: 3: 1
\( \mathrm{c} \cdot 6: 3: 2 \)
D. 1: 2: 3


For the gas phase reaction, \( C_{2} H_{4}+ \)
\( \boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6},(\boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 . 7 k c a l}) \)
carried out in a vessel, the equilibrium
concentration of \( C_{2} H_{4} \) can be increased by :

This question has multiple correct options
A. increasing the temperature
B. decreasing the pressure
c. removing some \( H_{2} \)
D. adding some \( C_{2} H_{6} \)


An electron in an atom undergoes transition in such a way that its kinetic energy changes from \( x \) to \( \frac{x}{4}, \) the change in potential energy will be:
A \( \cdot+\frac{3}{2} x \)
B. \( -\frac{3}{8} x \)
\( c \cdot+\frac{3}{4} x \)
D. \( -\frac{3}{4} x \)


Two coaxial coils are very close to each
other and their mutual inductance is 5
\( \mathrm{mH} \). If a current \( 50 \sin 500 r \) is passed in
one of the coils then the peak value of induced e.m.f. in the secondary coil will
be?
A . \( 5000 v \)
в. \( 500 v \)
\( c .150 v \)
D. 125v


Which of the following statement is not
correct?
A. Atomic no.of A,B,C are 40,57,105 respectively
3. Group no of \( A, B, C \) are IV \( B \), III \( B \) and \( V B \) respectively
c. Period no of \( A, B, C \) are 4 th \( , 5 \) th and 6 th respectively
D. \( \mathrm{C} \) is a radioactive element


The energy of an electron in the \( n^{t h} \) Bohr orbit of hydrogen atom is:
A \( \cdot \frac{13.6}{n^{3}} e V \)
В. \( -\frac{13.6}{n^{3}} e V \)
c. \( -\frac{13.6}{n^{2}} e V \)
D. \( -\frac{13.6}{n} e V \)


The given graph shows volume with
time in the source voltage and steady
state current drawn by a series \( \boldsymbol{B} \boldsymbol{L} \boldsymbol{C} \)
circuit:
Which of the following statements
is/are correct?
(a) Current lags the voltage.
(b) Resistance in the circuit is \( 250 \sqrt{\Omega} \)
(c) Reactance in the circuit is \( 250 \Omega \)
(d) Average power dissipation in the
circuit is \( 20 \sqrt{3 \Omega} \)
A. Only a
\( B \cdot a \& b \)
\( c \cdot a, b \& c \)
D. All


IUPAC name for \( \left[C o C l_{2}(e n)_{2}\right]_{2} S O_{4} \) is
A. Dichloridobis(ethylenediamine)cobalt (II) sulphate
B. Dichloridobis(ethylenediamine)cobalt (I) sulphate
C. Dichloridoethylenediaminecobalt (III) sulphate
D. Dichloridobis(ethylenediamine)cobalt (III) sulphate


Metallic character goes on decreasing while going from left to right in a period.
A. True
B. False


Assertion
The endothermic reactions are favoured
at lower temperature and the exothermic reactions are favoured at
higher temperature.
Reason
When a system in equilibrium is disturbed by changing the temperature, it will tend to adjust itself so as to
overcome the effect of the change.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The average molar mass of colloidal particles is determined by:
A. Tyndall effect
B. Osmotic pressure measurement
c. victor Maeyer's method
D. None of the above


Assertion
The gases exert pressure.
Reason
Molecules exert pressure when they
collide with the walls of the container in
which they are taken.
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 function of a vessel is
A. Conduction of food
B. Conduction of water and minerals
c. conduction of hormones
D. All of the.above


An ellipse passes through the point (4,-1) and touches the line \( x+4 y- \)
\( 10=0 . \) Find its equation if its axes
coincide with the coordinate axes.


Which one of the following is laevorotatory?
A. glucose
B. fructose
c. sucrose
D. all the above


In Insulin molecule there are two chains
A and B. "A" contains "X" amino acids \&
"B" contains "Y" amino acids. The values
of \( X \) and \( Y \) are:
A. 21, 31
B. 28, 26
c. 21,30
D. 32, 34


Tomato belongs to genus
A. Solanum
B. Lycopodium
C . Physalis
D. Allium


If \( A^{2}+2 A+10=0 \)
\( A=\left[\begin{array}{lll}1 & 12 & 15 \\ 2 & 10 & 4 \\ 3 & 9 & 5\end{array}\right] \) find \( A^{-1} \)


Dorsiventral leaf is identified by the
presence of
A. Stomata on both the epidermis
B. Stomata mainly present on the lower epidermis
c. No stomata on the epidermis
D. Sunken stomata on the upper epidermis


If the Aufbau principle had not been followed, \( C a(Z=20) \) would have been
placed in the?
A. s-block
B. p-block
c. d-block
D. f-block


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A . an oxiding agent
B. both oxidising and reducing agent
C . reducing agent
D. none of the above


Which of the following pollutants is
released from the emission tubes of
diesel engines?
A. Mercury
B. Aluminium
c. Benzopyrene
D. \( C F C l_{2} \)


The distance between two consecutive
bright bands in a bi-prism experiment is \( 0.32 \mathrm{mm} \) When the red light of wavelength 6400 A is used. by how much will this distance change if the light is substituted by the blue light of wavelength 4800 A with the same
setting?


The chemical equation are balanced to satisfy one of the following laws in chemical reactions. This law is known
as:
A. Law of conservation of momentum.
B. Law of conservation of mass
c. Law of conservation of motion.
D. Law of conservation of magnetism.


Which of the following devices works on the principle of electromagnetic induction?
A. Ammeter
B. Voltmeter
c. Generator
D. Galvanometer


How many solutions does this set include?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 10
c. 20
D. Infinite


Pigeon Pea is
A. Cajanus cajan
B. Vigna unguiculata
C . Phaseolus vulgaris
D. Vigna radiata


Let \( A \) be the set of all points in a plane
and let 0 be the origin. Show that the relation \( \boldsymbol{R}=\{(\boldsymbol{P}, \boldsymbol{Q}): \boldsymbol{P}, \boldsymbol{Q} \in \boldsymbol{A} \) and
\( \boldsymbol{O P}=\boldsymbol{O Q}\} \) is an equivalence relation.


Rise of first primates was in which epoch?


Three charges \( Q, q,-q \) are placed at the vertices of an equilateral triangle. If
the net electric potential energy of the
system is \( 0, \) then \( Q \) is
\( A \cdot-q \)
B. \( q \)
\( c \cdot 0 \)
D. None of the above


Which Newton's law is related to the
Galileo's law of inertia?
A. second
B. First
c. First and second
D. Third


The atmospheric pressure and height of barometer column is \( 10^{5} P_{a} \) and \( 760 \mathrm{mm} \)
respectively on the earth surface. If the barometer is taken to moon then column height will be
A . zero
B. 76 mm
c. \( 126.6 \mathrm{mm} \)
D. 760 mm


If we assume kinetic energy of a proton is equal to energy of the photon, the ratio of de Broglie wave length of proton to photon is proportional to:
A. \( E \)
\( \mathbf{B} \cdot E^{-1 / 2} \)
\( c \cdot E^{1 / 2} \)
D. \( E^{3 / 2} \)


One part of an element A combines with two parts of B (another element). Six parts of element C combine with four
parts of element B. If A and C combines together, the ratio of their masses will
be governed by:
A. law of definite proportions
B. law of multiple proportions
c. law of reciprocal proportions
D. law of conservation of mass


A hemispherical body is placed in a uniform electric field E. What is the flux
linked with the curved surface if the
field is perpendicular to the curved surface at every points as in figure.
A \( \cdot \phi=E 4 \pi R^{2} \)
В. \( \phi=E 2 \pi R^{2} \)
c. \( \phi=E 7 \pi R^{2} \)
D. \( \phi=E 9 \pi R^{2} \)


When an alkyl halide reacts with an alkoxide, the product is?
A. Ether
B. Ester
c. Hydrocarbon
D. Alcohol


Find the mode for the following data:
\[
x
\]
2 and \( \mathbf{5} \) and
Frequency \( \quad 0 \quad 1 \quad 3 \quad 2 \) 1
\( A \cdot 3 \)
B. 5
c. 10
D. 11


Which of the following alloys contain Cu
and Zn?
A. Bronze
B. Brass
c. Gun metal
D. stee


If a fuse is rated as \( 8 \mathrm{A} \), and current
more than 8 A passes through it then
A. it would melt
B. circuit gets broken
\( c . \) both
D. none


If \( \sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}, \) then
the value of \( x \)
\( A \cdot 3 \)
B . 2
c. 1
\( D \)


The contrapositive of \( \sim \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is
\( \mathbf{A} \cdot(q \wedge r) \rightarrow p \)
в. \( (q \rightarrow r) \rightarrow p \)
c. \( (q \vee r) \rightarrow p \)
D. None of these.


What are the postulates of Bohr's mode
of an atom?


In the hierarchy of classification, which group will have the smallest number of
organisms with a maximum number of
characteristics and which group will have the largest number of organism?


The peptide synthesis inside a cell takes place in
A. Ribosomes
B. Chloroplast
c. Mitochondria
D. chromoplast


A conducting loop is held above a
current carrying wire 'PQ' as shown in the figure. Depict the direction of the
current induced in the loop when the current in the wire \( P Q \) is constantly
increasing.


Without actual finding the square of the numbers, find the value of \( 36^{2}-35^{2} \)
A . 70
B. 71
\( c \cdot 72 \)
D. 73


The area of quadrilateral which the straight line cuts off from the given triangle is:
A \( \cdot \frac{3+\tan \theta}{1-\tan \theta} \)
B. \( \frac{3+5 \tan \theta}{1+\tan \theta} \)
c. \( \frac{3+2 \tan \theta}{1+\tan \theta} \)
D. \( \frac{3+\tan \theta}{1+\tan \theta} \)


In which of the following media can nonmechanical waves travel?
B. In vacuum but not in a medium
c. In a medium but not in a vacuum
D. Neither in a medium nor in vacuum


The plot of the variation of potential difference across a combination of
three identical cells in series, versus
current is shown alongside. What is the
emf and internal resistance of each
cell?


Assertion
The wire of a potentiometer should be of uniform area of cross section.
Reason
It satisfies the requirement of the
principle of the potentiometer.
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


Classify the following organisms based on the absence/presence of true coelom (i.e., acoelomate, pseudocoelomate and coelomate) Spongilla, Sea anemone Planaria, Liver fluke, Wuchereria,
Ascaris, Nereis, Earthworm, Scorpion,
Birds, Fishes, Horse.


Action and reaction force acts on:
A. same body
B. different bodies
c. lower body
D. upper body


Which chromium compound in widely used in training of leather?
A. \( C r_{2} O_{3} \)
в. \( C r O_{2} C l_{2} \)
c. \( C r C l_{3} \)
D. \( K_{2} S O_{4} \cdot C r_{2}\left(S O_{4}\right)_{3} .24 H_{2} O \)


Sieve tube is characterized by
A. presence of lignin
B. Absence of cytoplasm
c. presence of pectin
D. Absence of nucleus


If the pH of pure water is \( 7, \) then the
hydrogen ion concentration, \( \left[\boldsymbol{H}^{+}\right] \) in mol
\( \mathbf{L}^{-1} \) will be:
A \( \cdot 10^{-7} \)
7
B. 0
\( c \cdot 7 \)
D. \( 10^{+7} \)


Three charges \( 2 q,-q,-q \) are located at the vertices of an equilateral triangle. At the centre of the triangle :
A. the field is zero but potential is nonzero
B. the field is nonzero but potential is zero
c. both field and potential are zero
D. both field and potential are nonzero


Which of the following do not define
instantaneous reactions?
A. Appearance of a product over a particular time interval
B. Change in the concentration of the products at a particular instant of time
C. Change in the concentration of the reactants at a particular instant of time
D. Reactions completed in fraction of seconds


If a line \( L \) is perpendicular to the line
\( 5 x-y=1, \) and the area of the triangle
formed by the line \( L \) and the coordinate
axes is \( 5, \) then the distance of line \( L \)
from the line \( \boldsymbol{x}+\mathbf{5} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot \frac{7}{\sqrt{5}} \)
в. \( \frac{5}{\sqrt{13}} \)
c. \( \frac{7}{\sqrt{13}} \)
D. \( \frac{5}{\sqrt{7}} \)


Colloidal solutions of gold, prepared by different methods are of different
colours because of:
A. variable valency of gold
B. different concentration of gold particles
C. impurities produced by different methods
D. different diameters of colloidal gold particles


What are the hydrolysis products of
lactose?


Standard form for linear equation in one variable?


Which of the following is not a correct
statement about enthalpy of solution?
A. For most ionic compounds, \( \Delta H_{s o l}^{0} \) is positive and the dissociation process is endothermic.
B. Solubility of most salts increases with increase in temperature
C. If the lattice enthalpy is very high, the dissolution of compound becomes very easy.
D. Enthalpy of solution is determined by the selective values of the lattice enthalpy and hydration enthalpy.


Echo is produced due to:
A. reflection of sound
B. refraction of sound
c. resonance
D. termination of sound


Calculate total resistance, total current
and p.d across \( 7 \Omega \) resistor


Explain the following reactions with
suitable example:
(a) Reimer-Tiemann reaction
(b) Cannizaro reaction
(c) Aldol condensation
(d) Sandmeyer reaction


A charged oil drop is suspended in uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be (take the mass of the charge \( =\mathbf{9 . 9} \times \mathbf{1 0}^{-\mathbf{1 5}} \) and \( \boldsymbol{g}=\mathbf{1 0} \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
B . \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)


Show that \( A(6,4), B(5,-2) \) and \( C(7,-2) \) are
the vertices of an isosceles triangle.
Also, find the length of the median through \( A \)


Which are the correct for fuse wire?
This question has multiple correct options
A. High resistance
B. low resistance.
C . low melting point.
D. high melting point.


An electron in hydrogen atom is excited to 'N' shell. What are the possible
transitions it can undergo ? Compare the energies of transitions.


The phenol-water system has a upper critical solution temperature.
A. True
B. False


Central core of the atom, is called
A . lon
B. Orbit
c. Molecule
D. Nucleus


Cell of Amoeba is
A. Spindle shaped
B. Broad shaped
C. Spherical in shape
D. Indefinite in shape


Draw the graph of \( 2 x+3 y=12 \)


The value of \( (a+2 i)(b-i) \) is
\( \mathbf{A} \cdot a+b-i \)
B. \( a b+2 \)
c. \( a b+(2 b-a) i+2 \)
D. \( a b-2 \)
E \( . a b+(2 b-a) i-2 \)


In which of the following equilibrium
equation, \( \boldsymbol{K}_{\boldsymbol{p}}>\boldsymbol{K}_{\boldsymbol{c}} \)
A \( \cdot 2 S O_{3}(g) \rightleftharpoons 2 S O_{2}(g)+O_{2}(g) \)
B \( \cdot P C l_{3}(g)+C l_{2} \rightleftharpoons P C l_{5}(g) \)
C \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)


Divide :
\( 2 x^{3}-5 x^{2}-3 x b y(x-1) ? \)


Heavy water is used as in
nuclear reactor.
A. controller
B. moderator
c. promoter
D. none of these


Oxidation of NO in air produces:
в. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


Largest mammalian vertebra is
A. Thoracic
B. Sacral
c. Lumbar
D. Cervical


A gas is enclosed in a vessel of volume
\( 1000 \mathrm{cc} \) at a pressure of \( 72.6 \mathrm{cm} \) of Hg. It is being evacuated with the help of a piston pump, which expels \( 10 \% \) gas in each stroke. The pressure after the second stroke will be nearest to
\( A \cdot 60 \mathrm{cm} \)
B. 55 \( \mathrm{cm} \)
\( c \cdot 66 \mathrm{cm} \)
D. 50 cm


If one root of \( x^{2}+a x+8=0 \) is 4 and
the equation \( x^{2}+a x+b=0 \) has equal
roots, then \( b= \)
A . 7
B. 9
\( c .1 \)
D. 3


A microscope consists of an objective of
focal length \( 1.9 \mathrm{cm} \) and eye piece of
focal length 5 cm. The two lenses are
kept at a distance of \( 10.5 \mathrm{cm} . \) If the
image is to be formed at the least distance of distinct vision, the distance
at which the object is to be placed before the objective is:
(Least distance of distinct vision is 25
\( \mathrm{cm} \)
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 2.7 \mathrm{cm} \)
c. \( 21.0 \mathrm{cm} \)
D. \( 4.17 \mathrm{cm} \)


If a triangle \( P Q R \) has been constructed \( \operatorname{taking} Q R=6 \mathrm{cm}, P Q=3 \mathrm{cm} \) and
\( P R=4 \mathrm{cm}, \) then the correct order of
the angle of triangle is
A. \( \angle P<\angle Q<\angle R \)
в. \( \angle P>\angle Q<\angle R \)
с. \( \angle P>\angle Q>\angle R \)
D. \( \angle P<\angle Q>\angle R \)


\( N a C l_{(a q)} \) gives a white precipitate with \( A g N O_{3} \) solution but \( C C l_{4} \) or \( C H C l_{3} \)
does not, because:
A. \( N a C I \) is a covalent compound and forms \( A g C l \) as white ppt
B. \( N a C l \) is an ionic compound and forms \( A g C l \) as white \( p p t \)
c. \( C C l_{4} \) and \( C H C l_{3} \) are ionic compound
D. none of these


Photosynthesis is mainly responsible for the existence of
A. Plants on this earth
B. Animals on this earth
c. Both plants and animals
D. None of these


\( 1 \mathrm{g} \) of \( ^{12} \mathrm{C} \) contains \( 6.022 \times 10^{23} \) atoms
of the isotope.
A. True
B. False


Insulin receptors are.
A. Extrinsic proteins
B. Intrinsic proteins
C . G-proteins
D. Trimeric proteins


From application of thermodynamics on
chemical reaction,
we get \( \Delta G=\Delta G^{0}+R T \ln Q \)
Also \( \Delta G=\Delta H-T \Delta S \)
If \( \Delta G=0, \) reaction is at equilibrium.
If \( \Delta G>0 \) reaction is non-spontaneous
under given condition. \( I f \Delta G<0 \)
reaction is spontaneous under given condition.
Consider the reaction given below. \( \boldsymbol{A}(s) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \quad \boldsymbol{\Delta} \boldsymbol{H}^{0}=\mathbf{1 6 0} \mathrm{KJ} / \mathrm{mol} \)
\( \Delta S^{0}=400 \mathrm{J} / \mathrm{mol}-\mathrm{K} \) at \( 400 \mathrm{K} \)
Which of the following is correct at 400
K?
A. On adding more \( A(s) \), more \( B(g) \) is produced, when \( A(s) \) and \( B(g) \) were in equilibrium
B. The equilibrium constant at \( 400 \mathrm{K} \) can't be found
c. The reaction is at equilibrium at \( 400 \mathrm{K} \) and standard condition
D. The \( \Delta G \) of the reaction is greater than zero, at 400 k and standard condition


What is the value of \( (1+i)^{5}+(1-i)^{5} \)
where \( i=\sqrt{-1} ? \)
A . -8
B. 8
c. \( 8 i \)
D. \( -8 i \)


When objects at different distances are seen by the eye, which of the following remains constant?
A. The focal length of the eye lens
B. The object distance from the eye lens
c. The radii of curvature of the eye lens
D. The image distance from the eye lens


In twenty minutes, the angular displacement of the minute hand of a
wrist watch is
A \( \cdot \frac{\pi}{90} r a d \)
в. \( \frac{\pi}{30} r a d \)
c. \( \frac{\pi}{3} \) rad
D. \( \frac{2 \pi}{3} r a d \)


If a mirror has a focal length of \( -20 \mathrm{cm} \) then it is a
A. Convex mirror
B. Concave mirror
c. Plane mirror
D. None of these


Where among the following metal
complexes the one which exhibits optical activity is: \( (A A= \) bidentate
ligand; \( X= \) monodentate ligand
A \( \cdot \operatorname{cis}-\left[M A_{4} X_{2}\right] \)
B . trans - [M A \( _{4} X_{2} \) ]
c. \( \operatorname{cis}-\left[M(A A)_{2} X_{2}\right] \)
D. \( \operatorname{trans}-\left[M(A A)_{2} X_{2}\right] \)


An event in which all the possible outcomes of the experiments are present is known as event
A. a complement.
B. an experiment
c. a sample space.
D. an exhaustive event.


Match the conversions in List 1 with the
type(s) of reaction(s) given in List 2. Indicate your answer by darkening the appropriate bubbles of the \( 4 \times 4 \) matrix given in the ORS.


The depth of the percolation tank is limited to the \( \ldots \) the height between bed level and full storage level.
A . Half
B. One fourth
c. one third
D. Same


Prove that \( : \frac{\sin A}{\cot A+\operatorname{cossec} A}=2+ \)
\( \frac{\sin A}{\operatorname{Cot} A-\operatorname{cosec} A} \)


\( \int e^{x \sec x} \cdot \sec x(1+x \tan x) d x= \)
A \( \cdot e^{x \sec x}+c \)
B. \( -e^{x \sec x}+c \)
c. \( \frac{1}{e^{x \sec x}}+c \)
D. \( -e^{x \tan x}+c \)


The diagram below shows a cathode ray tube in which the arrow indicates a
beam of charged particles approaching
an electric field between the plates \( A \)
and B. State the approximate voltage \( V_{1} \)
used to heat the filament
A . \( 1.5 \mathrm{v} \)
B. 3
\( c \cdot 6 v \)
D. 12


The second term of a geometric series is 3 and the common ratio is \( \frac{4}{5} . \) Find the sum of first 23 consecutive terms in the
given geometric series


Find the derivative of the following functions from first principle \( (x-1)(x-2) \)


In the given figure shown \( \boldsymbol{P Q R S} \) is a
square and \( S R T \) is an equilateral
triangle then state whether \( \angle Q T R= \)
\( 15^{\circ} \) is true/false.
A. True
B. False


Prove that \( 3 \sqrt{2} \) is irrational


The temperature coefficient of
resistance of wire is \( 12.5 \times 10^{-4} / C^{0} . \) At
\( 300 \mathrm{K} \) the resistance of the wire is 1 ohm.
The temperature at which resistance will be 2 ohm is
\( \mathbf{A} \cdot \) 1154 \( \mathbf{K} \)
B. 1100k
c. \( 1400 \mathrm{K} \)
D. 1127K


f \( f: R \rightarrow R \) be the function defined by
\( f(x)=4 x^{3}+7, \) show that \( f \) is a
bijection.


If 0 is the origin and \( A \) is the point \( (a, b, c), \) then the equation of the plane through \( A \) and at right angles to \( O A \) is
A. \( a(x-a)-b(y-b)-c(z-c)=0 \)
В. \( a(x+a)+b(y+b)+c(z+c)=0 \)
c. \( a(x-a)+b(y-b)+c(z-c)=0 \)
D. None of the above


Let \( A, B \) and \( C \) be the sets such that
\( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{A} \cup \boldsymbol{C} \) and \( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{A} \cap \boldsymbol{C} \)
Show that \( B=C \)


If the galvanometer reading is zero in the gives circuit, the current passing through resistance \( 250 \Omega \) is
A . 0.016 A
B. 0.16 A
\( c \cdot 0.032 \mathrm{A} \)
D. 0.042 A


Induced abortion is
A . IUD
в. мтр
\( c . \) STD
D. None of the above


Illustrate, if possible the following with a rough diagram:
A closed curve that is not a polygon.


The area bounded by the curves \( |\boldsymbol{x}|+ \) \( |y| \geq 1 \) and \( x^{2}+y^{2} \leq 1 \) is
A. 2 sq unit
B. \( \pi \) sq unit
c. \( (\pi-2) \) sq unit
D. None of these


A regular polygon is inscribed in a
circle. If a side subtends an angle of \( 30^{\circ} \)
at the centre, what is the number of its
sides?
A . 10
B. 8
\( c .6 \)
D. 12


For the process, \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \longrightarrow \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}(\boldsymbol{s}) \)
A. \( \Delta H=+v e, \Delta S=+v e \)
B. \( \Delta H=-v e, \Delta S=+v e \)
c. \( \Delta H=+v e, \Delta S=-v e \)
D. \( \Delta H=-v e, \Delta S=-v e \)


The irrigation system shown is:
A. Localized irrigation
B. Surface irrigation
C. Drip irrigation
D. Lateral move irrigation


The mass of a \( _{3}^{7} L i \) nucleus is \( 0.042 u \) less than the sum of the masses of all
its nucleons.What is the binding energy
per nucleon of \( _{3}^{7} \) Li nucleus?
A .23 MeV
в. 46 МеV
\( \mathbf{c} .5 .6 \mathrm{MeV} \)
D. \( 3.9 \mathrm{MeV} \)


If two balls each of mass \( 0.06 \mathrm{kg} \) moving in opposite directions with speed of \( 4 m s^{-4} \) collide and rebound
with same speed, then the impulse imparted to each ball due to other is:
A \( .0 .48 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)
в. 0.53 kg \( m s^{-1} \)
c. \( 0.8 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)
D. \( 0.92 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)


Which logic gate corresponds to the truth table given below.
\( \begin{array}{lll}\text { A } & \text { в } & \text { c } \\ & & \\ \text { 0 } & \text { o } & \text { 1 } \\ \text { 0 } & \text { 1 } & \text { o } \\ \text { 1 } & \text { 0 } & \text { o } \\ \text { 1 } & \text { 1 } & \text { o }\end{array} \)
A. AND
в. NOR
\( c . \) or
D. NAND


Which of the following is NOT the process to obtain Phenol?
A. Cummene-Peroxidation Process
B. Raschig Process
c. Sulfonation Process
D. Solvays Process


Give specific reasons for the following
statements:

Balsam plants wilt during midday even if the soil is well watered.


Determine the power being supplied to the string.


In a single slit diffraction with \( \lambda= \) \( 500 n m \) and a lens of diameter \( 0.1 \mathrm{mm} \)
width of central maxima, obtain on
screen at a distance of \( 1 \mathrm{m} \) will be
\( \mathbf{A} \cdot 5 m m \)
B. \( 1 \mathrm{mm} \)
\( \mathrm{c} .10 \mathrm{mm} \)
D. \( 2.5 m m \)


Which covers the largest number of organisms?
A. Genus
B. Family
c. Phylum
D. class


A string is stretched between fixed points separated by \( 75 \mathrm{cm} \). It is observed to have resonant frequencies
of \( 420 H z \) and \( 315 H z . \) There are no
other resonant frequencies between these two. Then, the lowest resonant
frequency for this string is
A. \( 10.5 ~ H z \)
в. \( 105 \mathrm{Hz} \)
c. \( 1.05 \mathrm{Hz} \)
D. \( 1050 \mathrm{Hz} \)


Consider the reactions:
Identify \( \boldsymbol{A}, \boldsymbol{X}, \boldsymbol{Y} \) and \( \boldsymbol{Z} \)
Silver mirror observe
A \( . A- \) Ethanol, \( X \) - Acetaldehyde, \( Y \) - Butanone, \( Z \) Hydrazone
B. \( A- \) Methoxymethane, \( X \) - Ethanoic acid, \( Y \) -
Acetate ion, \( Z \) - hydrazine
C. \( A- \) Methoxymethane, \( X \) - Ethanol, \( Y \) Ethanoic acid, \( Z \) - Semicarbazide
D. \( A- \) Ethanal, \( X \) - Ethanol, \( Y-B u t-2- \) enal, \( Z \) -
Semicarbazone


Let \( O \) be the origin. We define a relation
between two points \( P \) and \( Q \) in a plane, if \( O P=O Q . \) Show that the relation, so
defined is an equivalence relation.


If an \( A . P \) consists of \( n \) terms with first
term \( a \) and \( n^{t h} \) term \( l \) show that the
sum of the \( m^{t h} \) term from the beginning
and the \( m^{t h} \) term from the ends is \( (a+ \)
\( l \)


Match the compounds (in List I) with the structure (in List II)


Which fish is known as living fossil?
A. Chimaera
B. Latimeria
c. Pristis
D. Harpodon


A particle suspended from a vertical spring oscillates 10 times per second. At the highest point of oscillation, the spring becomes unstretched. Find the speed when the spring is stretched by
\( 0.20 \mathrm{cm} .\left(\text { Take }, g=\pi^{2} m / s^{2}\right) \)
A. \( 110.25 \mathrm{cm} / \mathrm{s} \)
в. \( 12.14 \mathrm{cm} / \mathrm{s} \)
c. \( 15.4 \mathrm{cm} / \mathrm{s} \)
D. \( 16.7 \mathrm{cm} / \mathrm{s} \)


Consider the situation shown in the
figure. The capacitor A has a charge q on it whereas \( \mathrm{B} \) is uncharged. Find the
charge appearing on the capacitor \( \mathrm{B} \) a long time after the switch is closed
A. zero
B. \( q / 2 \)
\( c \cdot q \)
D. \( 2 q \)


A conducting circular loop is placed in a uniform magnetic field, \( B=.025 \) T with its plane perpendicular to the loop The radius of the loop is made to shrink at a
constant rate of \( 1 \mathrm{mms}^{-1} \). The induced
e.m.f. when the radius is \( 2 \mathrm{cm} \), is
\( \mathbf{A} \cdot 2 \pi \mu V \)
в. \( \pi \mu V \)
c. \( \frac{\pi}{2} \mu V \)
D. \( 2 \mu V \)


Mark the correct difference between a
permanent magnet and an electromagnet.
A. Permanent magnet does not require any external electric supply to produce the field. But their magnetic field is normally weaker than that of an electromagnet.
B. Hence, permanent magnets are relatively bulky in size compared to electromagnets.
C. The applications of permanent magnet in the field of engineering are quite limited
D. All


A liquid of refractive index \( n \) is filled in a tank.A plane mirror is kept at the bottom of tank. A point like object P is kept at hieght h from the mirror.An observer observes \( \mathrm{P} \) and image
obtained of \( P \) from the top vertically upward direction.What will be the
distance observed by the observer.
\( A \cdot 2 n h \)
B. 2h/n
c. 2h/-n-
D \( \cdot\left(1+\frac{1}{n}\right) \)


Calculate the diameter of the brass
wire
A \( .2 .1 \times 10^{-4} \mathrm{m} \)
3. \( 4.2 \times 10^{-4} \mathrm{m} \)
c. \( 8.4 \times 10^{-4} \mathrm{m} \)
D. \( 16.8 \times 10^{-4} \mathrm{m} \)


For an organic monoprotic acid solution of concentration \( C_{o} \) mol litre\( ^{-1} \), if \( K_{a} \)
has a value comparable to \( \boldsymbol{K}_{\boldsymbol{w}}, \) show
that the hydronium ion concentration is given by:
\[
\left[\boldsymbol{H}^{+}\right]==\left[\frac{\boldsymbol{K}_{\boldsymbol{w}}}{\left[\boldsymbol{H}^{+}\right]}+\frac{\boldsymbol{K}_{\boldsymbol{a}} \cdot \boldsymbol{C} \boldsymbol{o}}{\left[\boldsymbol{K}_{\boldsymbol{a}}+\boldsymbol{H}^{+}\right]}\right]
\]
\( \mathbf{f}\left[\boldsymbol{H}^{+}\right]=\mathbf{1} \mathbf{0}^{-\mathbf{3}} \boldsymbol{M} \) and \( \boldsymbol{C}_{\boldsymbol{o}}=\mathbf{1 0}^{-\mathbf{1}} \boldsymbol{M} \) in
solution of some organic monoportic acid. According to the above equation,
the order of magnitude of \( K_{a} \) must be \( 10^{-X}, \) the value of \( X \) should be:


The product of \( \left(3 x^{2}-5 x+6\right) \) and
\( -8 x^{3} \) when \( x=0 \) is
A \( \cdot \frac{1}{2} \)
B . 2
\( c \cdot 1 \)
D.


Which of them is a characteristic of
lanthanides?
This question has multiple correct options
A. Dissolve in hot water
B. React with acids
c. React with other non-metals
D. Are non-metals


Differentiate between menarche and
menopause.


The gap between division phase and start of DNA replication is called as
A. Gi phase
B. Ga phase
c. M phase
D. Interkinesis


Fill in the blanks with the correct words:
when a body is in translational motion,
all its parts, move (equal/unequal) distances in a given time.


If in the determinant \( \Delta= \)
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \boldsymbol{c}_{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \boldsymbol{c}_{2} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \boldsymbol{c}_{3}\end{array}\right|, \boldsymbol{A}_{i}, \boldsymbol{B}_{i}, \boldsymbol{C}_{i} \) etc. be the co-
factors of \( a_{i}, b_{i}, c_{i} \) etc., then which of the
following relations is incorrect?
A \( \cdot a_{1} A_{1}+b_{1} B_{1}+c_{1} C_{1}=\Delta \)
B . \( a_{2} A_{2}+b_{2} B_{2}+c_{2} C_{2}=\Delta \)
c. \( a_{3} A_{3}+b_{3} B_{3}+c_{3} C_{3}=\Delta \)
D. \( a_{1} A_{2}+b_{1} B_{2}+c_{1} C_{2}=\Delta \)


Which is most basic fluoride?
A. \( X e F_{6} \)
B. \( X e F_{2} \)
c. \( x e F_{4} \)
D. None is basic, all are acids


If \( \vec{p} \& \vec{s} \) are not perpendicular to each other and \( \vec{r} \times \vec{p}=\vec{q} \times \vec{p} \& \vec{r} . \vec{s}=0 \)
\( \operatorname{then} \vec{r}= \)
A \( \cdot \vec{p} . \vec{s} \)
В \( \cdot \vec{q}+\left(\frac{\vec{q} . \vec{s}}{\vec{p} . \vec{s}}\right) \vec{p} \)
c. \( \vec{q}-\left(\frac{\vec{q} . \vec{s}}{\vec{p} . \vec{s}}\right) \vec{p} \)
D. \( \vec{q}+\mu \vec{p} \) for all scalars \( \mu \)


Among the hydrides given below which are reasonably good acid?
A . \( N H_{3} \)
в. \( H F \)
c. \( H N_{3} \)
D. \( N a H \)


topp
\( Q \) Type your question
wrench, and the length of the wrench ?
\( \operatorname{cockw} \)


Cells of the nervous system that are specialized to provide support arid protection are known as
A. Schwann cells
B. Axons
c. Neurons
D. Neuroglia


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


Two small, identical spheres having \( +\boldsymbol{Q} \)
and \( -Q \) charge are kept at a certain
distance \( F \) force acts between the two
If in the middle of two spheres, another similar sphere having \( +Q \) charge is kept, then it experiences a force in magnitude and direction as
A. Zero having no direction
B. \( 8 F \) towards \( +Q \) charge
c. \( 8 F \) towards \( -Q \) charge
D. \( 4 F \) towards \( +Q \) charge


Electric wires are usually made of copper as they have high resistance.
A. True
B. False


For a common emitter circuit amplifier, the load resistance of the output circuit is 500 times the resistance of the input. circuit. If \( \alpha=0.98, \) then, current gain is
A . 0.98
B. 50
c. 98
D. 49


If \( \mathrm{K} \) for the reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I} \) is
equal to 45.9 at \( 450^{\circ} \mathrm{C} \) and 1 mole of
each \( \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are introduced into a \( \mathbf{1} \)
liter box at same temperature, what will
be the expression for \( \mathrm{K} \) at equilibrium?
A \( \cdot \frac{\left[x^{2}\right]^{2}}{[1-x][1-x]} \)
В. \( \frac{\left[2 x^{2}\right]^{2}}{[1-x][1-x]} \)
c. \( \frac{\left[2 x^{2}\right]^{2}}{[x][x]} \)
D. \( \frac{[1-x][1-x]}{\left[2 x^{2}\right]} \)
E \( \cdot \frac{[1-x][1-x]}{\left[x^{2}\right]^{2}} \)


In a set of reactions of propionic acid yielded a compound \( D \) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \stackrel{S O C l_{2}}{\rightarrow} \boldsymbol{B} \stackrel{N H_{3}}{\longrightarrow} \boldsymbol{C} \frac{\boldsymbol{K O H}}{B r_{2}} \)
\( D \)
The structure of \( D \) would be:
A. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
B. \( C H_{3} C H_{2} C O N H_{2} \)
c. \( C H_{3} C H_{2} N H C H_{3} \)
D. \( C H_{3} C H_{2} N H_{2} \)


What is the role of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in the
given reaction?
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \frac{\operatorname{Conc.H}_{2} \boldsymbol{S O}_{4}}{\longrightarrow} \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. Oxidising agent


Spinal reflex is located in the
A. Nerves
B. Brain
c. Epithelial lining
D. Spinal cord


From methyl alcohol we get:
A. bakelite, a hard plastic
B. the rubber neoprene
C . the plastic perspex
D. sponge rubber


(i) Write down any three difference between Lanthanoid and Actinoid?
(ii) The melting and boiling points of Zy. Cd and Hg are low. Why?
(iii) Draw the structure of manganate
ion.


Number of female flowers found in
cyathium is
A .
B. 2
\( c .3 \)
D. several


A long solenoid of radius 2 cm has 100
turns/cm and is surrounded by a 100
turn coil of radius \( 4 \mathrm{cm} \) having a total
resistance \( 20 \Omega \). If the current changes from \( 5 A \) to \( -5 A \), find the charge through the galvanometer.
A . zero
в. \( 800 \mu \) с
c. \( 400 \mu \) с
D. \( 600 \mu \) C


The equation of a plane which passes through the point of intersection of lines \( \frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}, \) and \( \frac{x-3}{1}= \)
\( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{2}}{\mathbf{3}} \) and at greatest
distance from point (0,0,0) is-
A. \( 4 x+3 y+5 z=25 \)
B. \( 4 x+3 y+5 z=50 \)
c. \( 3 x+4 y+5 z=49 \)
D. \( x+7 y-5 z=2 \)


A current of \( 10 A \) passes through two
very long wires held parallel to each other and separated by a distance of
2m. What is the force per unit length
between them?


Very Short Answer Types:
In which phase of prophase I, crossing over takes place?


If three positive real numbers \( x, y, z \)
satisfy \( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{z}-\boldsymbol{y} \) and \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\boldsymbol{4} \)
then what is the minimum possible
value of \( y ? \)
\( A \cdot 2^{\frac{1}{5}} \)
B. \( 2^{\frac{2}{5}} \)
\( c \cdot 2^{\frac{1}{4}} \)
\( D \cdot 2^{\frac{3}{7}} \)


The oxidation state of the underlined
element in the given compound is:
\( B a_{2} X e O_{2} \)
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
D.


An elevator carrying a charge of \( 0.5 C \) is
moving down with a velocity of \( 5 \times \) \( 10^{3} m s^{-1} . \) The elevator is \( 4 m \) from the
bottom and \( 3 m \) horizontally form \( P \) as
shown in figure. What magnetic field (in
\( \mu T \) ) does it produce at point \( P ? \)


A compound consists of \( 47.8 \% \) zinc and
52.2\% chlorine by mass. The empirical
formula is \( \mathrm{Zn}_{x} \mathrm{Cl}_{y} \) where \( x \) and \( y \) can have the values:
A . 1 and 1
B. 1 and 2
c. 2 and 1
D. 2 and 3 respectively


Imbibition is a
A. Property of solvent
B. Capillary phenomenon
C. Protoplasmic phenomenon
D. Property of solutes


A force \( \overrightarrow{\boldsymbol{F}}=\mathbf{3} \hat{\boldsymbol{i}}+\mathbf{2} \widehat{\boldsymbol{j}}-\boldsymbol{4} \widehat{\boldsymbol{k}} \) is applied at
the point \( (1,-1,2) . \) What is the moment of the force about the point (2,-1,3)\( ? \)
\( \mathbf{A} \cdot \hat{i}+4 \widehat{j}+4 \widehat{k} \)
B. \( 2 \hat{i}+\widehat{j}+2 \widehat{k} \)
c. \( 2 \hat{i}-7 \hat{j}-2 \widehat{k} \)
D . \( 2 \hat{i}+4 \widehat{j}-\widehat{k} \)


Degree of \( \left(\frac{d y}{d x}\right)^{2}+3 \frac{d^{2} y}{d x^{2}}=\sqrt{1+\left(\frac{d y}{d x}\right)^{2}} \)
is:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Differentiate: \( \sin \left(\tan ^{-1} e^{x}\right) \)


A body travels a distance \( s \) in \( t \) seconds.
It starts from rest and ends at rest. In
the first part of the journey, it move with
constant acceleration \( f \) and in the
seconds part with constant retardation
\( r . \) The value of \( t \) given by
\( ^{\mathrm{A}} \cdot_{2 s}\left(\frac{1}{f}+\frac{1}{r}\right) \)
в. \( \frac{2 s}{\frac{1}{f}+\frac{1}{r}} \)
c. \( \sqrt{2 s(f+r)} \)
D. \( \sqrt{2 s\left(\frac{1}{f+r}\right)} \)


Why does solution of chloroform \&
acetone show negative deviation from
Raoult's law?

Illustrate the deviation with the help of diagrams


Few iron nails and screws got mixed
with wood shavings while a carpenter was working with them. How can you help him in getting the nails and screws back from the scrap without wasting his time by searching with his hands?


The integral \( \int_{0}^{\pi} x f(\sin x) d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot \frac{\pi}{2} \int_{0}^{\pi} f(\sin x) d x \)
B \( \cdot \frac{\pi}{4} \int_{0}^{\pi} f(\sin x) d x \)
\( ^{\mathbf{C}} \pi \int_{0}^{\pi / 2} f(\sin x) d x \)
\( ^{\mathrm{D}} \pi \int_{0}^{\pi / 2} f(\cos x) d x \)


The steriochemistry change in
following \( \boldsymbol{S}_{N} \boldsymbol{2} \) is:
A. \( S, S \) changes to \( S, S \)
B. \( R, R \) changes to \( S, R \)
c. \( R, R \) changes to \( R, S \)
D. \( S, S \) changes to \( S, R \)


Find the slope of the straight line passing through the points (3,-2) and (7,2)


A bag contains 4 red balls, 6 blue balls and 3 black balls. A ball is draw at
random from the bag. What is the
probability that the ball drawn is not
blue?
A \( \cdot \frac{6}{13} \)
в. \( \frac{3}{13} \)
\( c \cdot \frac{7}{13} \)
D. None


Obtain the differential equation of linear simple harmonic motion.


A college offers 7 courses in the
morning and 5 in the evening. Find possible number of choices with the
student who want to study one course
in the morning and one in the evening.
A . 35
B. 12
c. 49
D. 25


Which amongst the following element can form amphoteric oxide?
\( \mathbf{A} \cdot M g \)
B. \( N \)
c. \( A l \)
D. \( C \)


The number of lines of symmetry for a
line segment
A. Is infinite
B. One
c. Two
D. None


Which rational expression should be added to \( \frac{x-x^{2}+2}{x\left(x^{2}-1\right)} \) to get \( \frac{x+1}{x^{2}-1} ? \)
A \( \cdot \frac{x}{2} \)
B. \( \frac{2}{x} \)
c. \( 2 x \)
D. \( x^{2} \)


Terminalisation takes place during
A. Pachytene
B. Zygotene
c. Leptotene
D. Diakinesis


Balance the following equations by ion electron method:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2+}+\boldsymbol{S O}_{2}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}^{3+}+ \)
\( \boldsymbol{H} \boldsymbol{S O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)


Find \( (\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}) \cdot(\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{d}}) \) if \( \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{i}}+ \)
\( \overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=2 \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=2 \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}} \)
and \( \overrightarrow{\boldsymbol{d}}=\overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\boldsymbol{2} \overrightarrow{\boldsymbol{k}} \)


Find
\( \boldsymbol{n} \boldsymbol{t h} \) term is the \( \mathbf{A . P} \mathbf{1 3}, \mathbf{8}, \mathbf{3}, \mathbf{2}, \dots . \)


The period of pendulum depends upon
A. mass
B. length
c. amplitude
D. energy


Vector components of the vector with
initial points (2,1) and terminal point (-5,7) are
\( \mathbf{A} \cdot-6 \hat{i}+7 \widehat{j} \)
B. \( -7 \hat{i}+6 \hat{j} \)
c. \( -6 \hat{i}-7 \widehat{j} \)
D. None


In triangle \( A B C, \) right-angled at \( B \), if
\( \tan A=\frac{1}{\sqrt{3}}, \) find the value of:
(i) \( \sin A \cos C+\cos A \sin C \)
(ii) \( \cos A \cos C-\sin A \sin C \)


When light transmitted through the absorbing material after getting dispersed forms dark lines on a
continuous bright background. This kind of spectrum formed is known as
A. Line spectrum
B. Band spectrum
D. Band absorption spectrum


According to Lindeman's 10\% law, what amount of energy will be present at the level of primary consumers if the plants produce 4,000 kcal of energy?
A . 40,000 kcal
B. 4,000 kcal
c. 400 kcal
D. 40 kcal
E. 4kcal


Raunak took 5 moles of carbon atoms in
a container and Krish also took 5 moles
of sodium atoms in another container of
same weight. Whose container is heavier?
A. Krish's container
B. Raunak's container
c. Both the containers are of same weight
D. Cannot be determined


The compound(s) which generate(s) \( N_{2} \) gas upon thermal decomposition below
\( 300^{\circ} \mathrm{C} \) is/are:
This question has multiple correct options
A. \( N H_{4} N O_{3} \)
B. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
c. \( B a\left(N_{3}\right)_{2} \)
D. \( M g_{3} N_{2} \)


Simplify \( \tan ^{-1}\left(\frac{6 x}{1-8 x^{2}}\right) \)
\( A \cdot \tan ^{-1} 2 x+\tan ^{-1} 4 x \)
B. \( \tan ^{-1} 2 x-\tan ^{-1} 4 x \)
c. \( -\tan ^{-1} 2 x-\tan ^{-1} 4 x \)
D. \( 2 \tan ^{-1} 2 x-\tan ^{-1} 4 x \)


Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \) o \( \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})= \)
\( e^{x}, g(x)=\log _{e} x \)


If the mirror has a focal length of +15
\( \mathrm{cm}, \) it is a
A. convex mirror
B. concave mirror
c. plane mirror
D. plano convex mirror


The input characteristics of a transistor
in \( C E \) mode is the graph obtained by
plotting
\( \mathbf{A} \cdot I_{B} \) against \( V_{B E} \) at constant \( V_{C E} \)
B. \( I_{B} \) against \( V_{C E} \) at constant \( V_{B E} \)
C \( \cdot I_{B} \) against \( I_{C} \) at constant \( V_{C E} \)
D. \( I_{V} \) against \( I_{C} \) at constant \( V_{B E} \)


The vascular cambial ring of a dicot
stem is
A. Primary in origin
B. Secondary in origin
c. Embryonic in origin
D. Tertiary in origin
E. Partly primary and partly secondary in origin


How many liters of hard water may
contain \( 60 \mathrm{mg} \) of \( \mathrm{Mg} \mathrm{SO}_{4} \) in order to
have a degree of hardness of 25 ppm?


Q Type your question
temperature (T) is represented then by
\( A \)
\( B \)
\( c \)
\( D \)


Factorise the following: \( y^{6}+32 y^{3}-64 \)
A \( \cdot(y+2)\left(y^{4}-2 y^{3}+8 y^{3}+8 y+16\right) \)
B . \( \left(y^{2}+2 y-4\right)\left(y^{4}-2 y^{3}+8 y^{2}+8 y+16\right) \)
C \( \cdot\left(y^{2}+2 y-4\right)\left(y^{4}-2 y^{3}+8 y^{2}\right) \)
D. \( (y+2)\left(y^{4}-2 y^{3}+8 y^{2}+8 y\right) \)


If the table of atomic masses were
established with the oxygen atom and
assigned value of \( 100, \) then the mass of carbon atom would be, approximately:
A .24
B. 75
c. 50
D. 112


Which of the following is wood alcohol?
A. \( C H_{3} O H \)
в. \( C_{2} H_{5} O H \)
c. 1-Butanol
D. 2-Methyl-1-propanol


Assertion
Although the surfaces of goggle lenses are curved, it does not have any power
Reason
In case of goggle, both the curved surfaces have equal radii of curvature and have center of curvature on the
same side
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


Coordinates of a focus


A compound with molar mass 159 was found to contain \( 39.62 \% \) copper and
20.13\% sulfur. Find the molecular
formula for the compound. \( (\mathrm{Cu}=63 \) \( S=32,0=16) \)


Co-ordination compounds are mostly
formed by:
A. s-block elements
B. p-block elements
c. d-block elements
D. f-block elements


Find the area of a regular hexagon of
side \( 8 \mathrm{cm} \)


Solve \( \tan ^{-1}\left(\tan \frac{2 \pi}{3}\right) \)


n pyrorole- electron density is
maximum on ?
2 and 3
\( 3.3 a n d 4 \)
\( c, 2 a n d 4 \)
\( 2.2 a n d \)


Which of the following is/are correct
A. At least two objects must interact for a force to come into play.
B. Interaction of one object with another object results in a force between the two objects.
c. Interacting forces may be push or pull
D. All


A wheel is made to roll without slipping,
towards right, by pulling a string
wrapped around a coaxial spool as
shown in figure. With what velocity(in
\( \mathrm{m} / \mathrm{s}) \) the string should be pulled so that
the centre of the wheeel moves with a
velocity of \( 3 \mathrm{m} / \mathrm{s} ? \)


A block of mass \( 2 k g \) is free to move along the \( X \) -axis. It is at rest and from
\( t=0 \) onwards it is subjected to a time-
dependent force \( F(t) \) in the \( x \) direction. The force \( F(t) \) varies with \( t \). the kinetic
energy of the block after 4.5 second is?


Which of the following changes occur in diaphragm and intercostal muscles when expiration of air takes place?
A. Internal intercostal muscles relax and diaphragm contracts
B. External intercostal muscles and diaphragm relaxes
c. Internal intercostal muscles contract and diaphragm relax
D. External intercostal muscles and diaphragm contract


The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition elements which shows
highest magnetic moment?
A \( \cdot 3 d^{2} \)
B. \( 3 d^{8} \)
\( c \cdot 3 d^{7} \)
D. \( 3 d^{5} \)


Find the common difference of the A.P.
and write the next two terms:
\( \mathbf{7 5}, \mathbf{6 7}, \mathbf{5 9}, \mathbf{5 1}, \dots . . \)


How many electrons should be removed
from a conductor so that it acquires a positive charge of 3.5 nC?


Oryza sativa belongs to
A. Solanaceae
B. Lilaceae
c. Gramineae
D. Asteraceae


Express the fraction as percentage \( \frac{\mathbf{3}}{\mathbf{8}} \)


Solve the given differential equation. \( \frac{d y}{d x}+\frac{x \sqrt{\left(x^{2}+y^{2}\right)}-y^{2}}{x y}=0 \)
A \( \cdot \sqrt{\left(x^{2}+y^{2}\right)}=x \log k / x \)
B . \( \sqrt{\left(x^{2}+y^{2}\right)}=\log k / x \)
C \( \cdot \sqrt{\left(x^{2}+y^{2}\right)}=x^{2} \log k / x \)
D. none of these


Assertion
In the Rutherford experiment, most of
the \( \alpha \) particles passed without any
deviation through the gold foil.
Reason
The entire positive charge and nearly all
of the mass of an atom is concentrated
in the centre of the atom known as
nucleus.
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


Find the value of \( P \) for the following distribution whose mean is 10
\[
\begin{array}{ccccc}
x_{1} & 5 & 7 & 9 & 11 \\
f_{i} & 4 & 4 & p & 7
\end{array}
\]


In root apoplast path of water transport; the water is transported through
A. cell wall only
B. Cell wall and inter cellular spaces
c. Intercellular spaces
D. Intercellular spaces, cell walls and endodermis


What is a meteorite?
A. A meteor that reaches the surface of Earth
B. Shooting star
C . A constellation
D. A comet


How is rust formed?


Which of the following statements are true and which are false? In each case
give a valid reason for saying so
(i) \( p: \) Each radius of a circle is a chord of the circle
(ii) \( \mathrm{q}: \) The centre of a circle bisects each chord of the circle
(iii) \( r: \) Circle is a particular case of an ellipse
(iv) \( s: \) If \( x \) and \( y \) are integers such that
\( \boldsymbol{x}>\boldsymbol{y} \) then \( -\boldsymbol{x}<-\boldsymbol{y} \)
\( (v) t: \sqrt{11} \) is a rational number


Identify the correct set of electrovalent compounds from the following in which the metal has electrovalency 2 and nonmetal has electrovalency 3
(A) Calcium sulphide
(B) Barium nitride
(C) Magnesium phosphide
(D) Aluminium nitride
(E) Magnesium fluoride
A. \( B \& C \)
в. \( B \& D \)
c. \( C \& D \)
D. \( A, B, C \& E \)


(a) The magnetic field in a region varies
as shown in figure. Calculate the
average induced emf in a conducting
loop of area \( 10^{-3} m^{2} \) placed
perpendicular to the field in each of the
10 \( m s \) intervals shown
(b) In which interval(s), the emf is not
constant? Neglect the behaviour near
the ends of \( 10 \mathrm{ms} \) intervals.


The value of \( \lim _{x \rightarrow 0^{+}} \frac{1}{3 x} \) is
A. \( -\infty \)
B. -
c. 0
\( D \cdot+\infty \)


Photochemical smog consists of an excessive amount of \( X \) in addition to
aldehydes, ketones, PAN etc. \( \boldsymbol{X} \) is :
A. methane
B. ozone
c. carbon dioxide
D. carbon monoxide


A potential barrier V volts exists across a P-N junction. The thickness of the
depletion region is 'd'. An electron with velocity 'v' approaches P-Njunction from N-side. Find the velocity of the electron crossing the junction.


Molar conductivities at infinite dilution
of \( N a C l, H C l \) and \( C H_{3} C O O N a \) are
126.4,425.9 and \( 91.0 \mathrm{Scm}^{2} \) mol \( ^{-1} \)
respectively. Molar conductivity for
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) will be:


How many valence electrons are present in the Lewis structure of \( S O_{2} ? \)
A . 8
B . 10
\( c \cdot 6 \)
D. 12


State whether given statement is True or False

Ventilation is an example of convection current in gases.
A. True
B. False


In a photon-electron collision
A. Only total energy is conserved
B. Only total momentum is conserved
C. Both total energy and total momentum are conserved
D. Both total momentum and total energy are not conserved


If \( g(X)=\frac{x}{[X]} \) for \( X>2 \) then \( \lim _{x \rightarrow 2^{+}} \)
\( \frac{\boldsymbol{g}(\boldsymbol{X})-\boldsymbol{g}(\boldsymbol{2})}{\boldsymbol{X}-\boldsymbol{2}}= \)
A . -
B.
c. \( \frac{1}{2} \)
D.


A circular disc of radius \( \mathrm{R} \) is removed
from a bigger circular disc of radius \( 2 \mathrm{R} \) such that the circumference of the
discs coincide. The centre of mass of
the new disc is \( \alpha R \) from the centre of
the bigger disc. The value of \( \alpha \) is
A. \( 1 / 3 \)
B. \( 1 / 2 \)
c. \( 1 / 6 \)
D. \( 1 / 4 \)


f \( x+y=6 \) and \( 3 x-y=4, \) then \( x-y \)
is equal to:
A . -1
B.
\( c \cdot 2 \)
D.


The boiling points of methane, ethane,
propane and butane are given
compound
\( \begin{array}{ll}\boldsymbol{C H}_{4} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{3}\end{array} \)
boiling \( \quad 112 \quad 185 \) point \( / K \)
Which statement explains the increase in boiling point from methane to
butane?
A. closer packing of molecules results in stronger van der Waals' forces
B. More covalent bonds are present and therefore more energy is required to break the bonds
c. More electrons in the molecules results in stronger van der Waals' forces
D. More hydrogen atoms in the molecules results in stronger hydrogen bonding


\( p^{\delta} \)
\( x \)
\( x \)
\( s \)


Calculate the number of states per
cubic metre of sodium in 3 s band. The
density of sodium is 1013 kgm \( ^{-3} \). How
many of them are empty?


Area bounded by the curve \( y^{2}(2 a- \)
\( x)=x^{3} \) and the line \( x=2 a \), is
A \( .3 \pi a^{2} \)
B. \( \frac{3 \pi a^{2}}{2} \)
c. \( \frac{3 \pi a^{2}}{4} \)
D. \( \frac{\pi a^{2}}{4} \)


Find the integral value of \( x, \) if \( \left|\begin{array}{ccc}\boldsymbol{x}^{2} & \boldsymbol{x} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{2} & \mathbf{1} \\ \boldsymbol{3} & \boldsymbol{1} & \boldsymbol{4}\end{array}\right|=\mathbf{2} \mathbf{8} \)


Diagonal relationship is shown between:
A. \( C \) and \( N \)
B. \( B \) and \( M g \)
c. \( B \) and \( S i \)
D. \( B e \) and \( A l \)


The value of sin
\( \sin \left\{\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{3}\right)\right\} \) is
A .
в.
\( c \cdot-1 \)
D. None of these


Auxospores and hormocysts are
formed respectively, by
A. Some cyanobacteria and many diatoms
B. Several diatoms and a few cyanobacteria
C. Several cyanobacteria and several diatoms
D. Some diatoms and several cyanobacteria


Consider the following statements
(i) Out of two \( -N H_{2} \) groups in semicarbazide only one is involved in formation of semicarbazones.
(ii) Cyclohexane froms cyanohydrin in good yield but \( 2,2,6- \)
trimethylcyclohexanone does not.
(iii) The \( \alpha- \)hydrogens in aldehydes
and ketones are acidic.
A. i and iii
B. ii and iii
c. i and i i
D. i, ii and iii


A bar magnet of magnetic moment
\( 0.4 A m^{2} \) is placed in the magnetic
meridian with its north pole pointing north. A neutral point is obtained at a
distance of \( 10 \mathrm{cm} \) from the centre of the
magnet.If the length of the magnet is
\( 20 \mathrm{cm}, \) then the value of horizontal
component of earth magnetic induction is:
A \( \cdot \sqrt{2} \times 10^{-5} T \)
B. \( \frac{1}{\sqrt{2}} \times 10^{-7} \)
c. \( 2 \times 10^{-7} T \)
D. \( \frac{1}{2} \times 10^{-7} T \)


The equation of circle at center (3,4) and radius 5
A. \( x^{2}+y^{2}-6 x-8 y=0 \)
B . \( x^{2}+y^{2}+3 x+4 y+5=0 \)
C. \( x^{2}+y^{2}+6 x+8 y=0 \)
D. None


\( d \)
\( d \)
\( d \)
\( d \)


\( \Delta C_{p} \) for change \( N_{2}(g)+3 H_{2}(g)= \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \) is:
\( \mathbf{A} \cdot C_{p N H_{3}}-\left(C_{p N_{2}}\right) \)
B . \( 2 C_{p N H_{3}}-\left(C_{p N_{2}}+3 C_{p H_{2}}\right) \)
\( \mathbf{c} \cdot 2 C_{p N H_{3}}-\left(C_{p H_{2}}\right) \)
D \( \cdot 2 C_{p N H_{3}}+\left(C_{p N_{2}}+3 C_{p H_{2}}\right) \)


An unpolarized beam of light is incident on a group of four polarizing sheets,
which are arranged in such a way that the characteristic direction of each
polarizing sheet makes an angle of \( 30^{\circ} \)
with that of the preceding sheet. The fraction of incident unpolarized light transmitted is
A \( \cdot \frac{27}{128} \)
B. \( \frac{128}{27} \)
c. \( \frac{37}{128} \)
D. \( \frac{128}{37} \)


Using postulates of Bohr's theory of hydrogen atom, show that the total energy of electron increases as \( \frac{1}{n^{2}} \)
where \( n \) is the principal quantum number of the atom


An ionic bond \( A^{+} B^{-} \) is most likely to be
formed when:
A. the ionization energy of A is high and the electron affinity of B is low.
B. the ionization energy of A is low and the electron affinity of B is high.
c. the ionization energy of A and the electron affinity of is high
D. the ionization energy of A and the electron affinity of is low.


Find the radius and circumference of a
circle whose area is :
\( 55.44 m^{2} \)


\( \int_{0}^{k} \frac{1}{2+8 x^{2}} d x=\frac{\pi}{16}, \) find the value of \( K \)


A body moves with uniform velocity of \( \boldsymbol{u}=\mathbf{7} \boldsymbol{m} / \boldsymbol{s} \) from \( \boldsymbol{t}=\mathbf{0} \boldsymbol{t o} \boldsymbol{t}=\mathbf{1 . 5 s} . \) It
starts moving with an acceleration of
\( 10 m / s^{2} . \) The distance between \( t= \)
\( \mathbf{0} \) to \( \boldsymbol{t}=\mathbf{3} \boldsymbol{s} \) will be:
A. \( 47.75 \mathrm{m} \)
B. 32.25 m
\( c \cdot 16.75 \mathrm{m} \)
D. 27.50 \( \mathrm{m} \)


Diffrentiate w.r.t \( x: \) \( \boldsymbol{y}=\cos ^{-1}\left[\frac{1-x}{1+x}\right] \)


\( [x] \) is defined as the greatest integer
less than \( x \)
\( \{x\} \) is defined as the least integer greater than \( x \) What is the value of \( [25.8]-\{13.9\} ? \)
A . 13
B. 0.8
c. 11
D. 11.9


Two cards are drawn simultaneously from a well-shuffled deck of 52 cards.
Find the probability distribution of the number of successes, when getting a spade is considered a success.


The integral \( \int_{0}^{a} \frac{g(x)}{f(x)+f(a-x)} d x \)
vanishes, if
A \( \cdot g(x) \) is odd
B. \( f(x)=f(a-x) \)
c. \( g(x)=-g(a-x) \)
D. \( f(a-x)=-g(x) \)


Mark the following statements as true or false
(i) Ordinary hydrogen is a mixture of 75
\( \% \) ortho and \( 25 \% \) para-forms
(ii) All the four atoms of moleculle of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) lie in the same plane.
(iii) Hydrogen peroxide is neutral like
water.
(iv) \( H_{2} O_{2} \) can be prepared from \( B a O_{2} \)
but not from \( M n O_{2} \) and \( P b O_{2} \)
A. \( (i) \) and \( (i v)- \) true \( (i i) \) and \( (i i i)- \) false
B. \( (i) \) and \( (i i)- \) true \( (i v) \) and \( (i i i)- \) false
C. \( (i i i) \) and \( (i v)- \) true \( (i i) \) and \( (i i)- \) false
D. \( (i) \) and \( (i i i)- \) true \( (i i) \) and \( (i v)- \) false


\( g c m s^{-2} \) is also known as
A. newton
B. erg
c. pascal
D. dyne


A system of \( n \) particles is free from any external force. Which of the following is
true for the magnitude of the total momentum of the system?
A. It must be zero
B. It could be non-zero, but it must be constant
c. It could be non-zero, and it might not be constant
D. The answer depends on the nature of the internal forces in the system


The atomic number of the element having magnetic moment equal to \( 1.7 \mathrm{BM} \) in its +2 oxidation state is:
A . 29
B. 25
\( c \cdot 24 \)
D. 30


Which friction comes into play when we
try to move an object at rest?
A. Rolling friction
B. Fluid friction
c. sliding friction
D. Static friction


Degree of polynomial 5 is
\( A \cdot 1 \)
B. 2
\( c \cdot 0 \)
D. Not defined


A biconvex lens of focal length \( 15 \mathrm{cm} \) is in front of a plane mirror. The distance between the lens and the mirror is 10
\( \mathrm{cm} . \mathrm{A} \) small object is kept at a distance of \( 30 \mathrm{cm} \) from the lens. The final image is
A. Virtual and at a distance of \( 16 \mathrm{cm} \) from the mirror
B. Real and at a distance of \( 16 \mathrm{cm} \) from the mirror
c. Virtual and at a distance of \( 20 \mathrm{cm} \) from the mirror
D. Real and at a distance of \( 20 \mathrm{cm} \) from the mirro


At time \( t=0, \) a car moving along a
straight line has a velocity of 16 ms\( ^{-1} \)
It slows down with an acceleration of
-0.5 t \( m s^{-1}, \) where t is in second. Mark
the correct statement(s).
A. The direction of velocity changes at \( t=8 s \)
B. The distance travelled in 4 is approximately \( 58.67 \mathrm{m} \)
C. The distance travelled by the particle in 10 s is 94 m.
D. The speed of particle at \( t=10 \) s is \( 9 m s^{-1} \)


Which of the following is called as a reduction division in the formation of
new cells?
A. Meiosiss
B. Mitosis
c. Cytokinesis
D. None of the above


If vertices of a triangle are represented
by complex numbers \( z, i z, z+i z, \) then
area of triangle is
\( A \cdot|z|^{2} \)
B. \( \frac{1}{2}|z|^{2} \)
c \( \cdot 2|z|^{3} \)
D・ \( 3|z|^{2} \)


Two elements \( A \) and \( B \) have same
number of valence electrons in their
atom have similar:
A. combining capacity
B. chemical properties
c. atomic sizes
D. metallic character


The equations of line \( A B \) and line \( P Q \) are
\( y=-\frac{1}{2} x \) and \( y=2 x \) respectively. Find the
measure of angle \( \angle \mathrm{BOQ} \) which is formed by intersection of line \( A B \) and line PQ. (Point P and point A are in first and second quadrant respectively)
A \( \cdot 60^{\circ} \)
B. \( 150^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 120^{\circ} \)


A ball is thrown vertically upward with a speed of \( 25.0 m / s . \) How high does it rise?
\( \mathbf{A} \cdot 31.9 m \)
в. \( 32 m \)
c. \( 33 m \)
D. 33.9


\( \frac{d^{2} y}{d x^{2}}+3\left(\frac{d y}{d x}\right)^{2}=x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right) \)


A container contains water up to a
height of \( 20 \mathrm{cm} \) and there is a point
source at the centre of the bottom of the
container. A rubber ring of radius \( r \) floats centrally on the water. The ceiling of the room is \( 2.0 m \) above the water
surface.
(a) Find the radius of the
shadow of the ring formed on the ceiling if \( r=15 \mathrm{cm} \)
(b) Find the maximum
value \( r \) for which the shadow of the ring
is formed on the ceiling. Refrective index of water \( =\mathbf{4} / \mathbf{3} \)


3 grams of salt of molecular weight 30
is dissolved in 250 g of water. Find the molality of the solution.(Multiply the answer by 10 )


Carbon, silicon and germanium have
four valence electrons each. At room
temperature the appropriate statement
is
A. The number of free electrons for conduction is significant only in Si and Ge but small in \( \mathrm{C} \)
B. The number of free conduction electrons is significant in C but small si and Ge.
C. The number of free conduction electrons is negligibly small in all the three.
D. The number of free conduction electrons is significant in all the three.


Let \( P(3,2,6) \) be point in space and \( Q \) be appoint on the line \( \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+ \)
\( \mu(-3 \hat{i}+\hat{j}+5 \hat{k}) . \) Then the value of \( \mu \) for which the vector \( \overrightarrow{P Q} \) is parallel to the
plane \( \boldsymbol{x}-\mathbf{4} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{1} \) is
A. \( 1 / 4 \)
B. - 1/4
c. \( 1 / 8 \)
D. \( -1 / 8 \)


If \( \cos \alpha=\frac{3}{5} \) and \( \cos \beta=\frac{5}{13}, \) then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \cos (\alpha+\beta)=\frac{33}{65} \)
B. \( \sin (\alpha+\beta)=\frac{56}{65} \)
c. \( \sin ^{2} \frac{\alpha-\beta}{2}=\frac{1}{65} \)
D \( \cos (\alpha-\beta)=\frac{63}{65} \)


A coil of moving coil galvanometer
twists through \( 90^{\circ} \) when a current of one microampere is passed through it.lf the area of the coil is \( 10^{-4} m^{2} \) and it has
100 turns, calculate the magnetic field of the magnet of the galvanometer.Given \( k=10^{-8} N- \)
\( \boldsymbol{m} / \) degree


In the given figure, \( \triangle A B C \) is an
sosceles triangle in which AB-AC. If
\( B D \perp A C \) and \( C E \perp A B \), prove that
\( \mathrm{BD}=\mathrm{CE} \)


The area of triangle formed by \( (0,0),(0, a) \) and \( (b, 0) \) is \( \ldots \)
\( \mathbf{A} \cdot a b \)
в. \( \frac{a b}{2} \)
c. \( \mid \frac{a b}{2} \)
D. \( |a b| \)


An inductor may store energy in:
A. its electric field
B. its coils
C . its magnetic field
D. both in electric and magnetic fields


A thin circular ring of a mass \( \mathrm{m} \) and radius R is rotating about its axis with a constant angular velocity \( (\mathbf{5} \pm \mathbf{1 . 5}) \mathbf{\Omega} \)
Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The angular velocity of ring is.
A \( \cdot \frac{\omega m}{M+m} \)
в. \( \frac{\omega m}{M+2 m} \)
c. \( \frac{\omega(M+2 m)}{m} \)
D. \( \frac{\omega(m-2 m)}{m+2 M} \)


The most abundant hydrocarbon
pollutant is:
A. Ethane
B. Methane
C. Propane
D. Butane


Statement I : When a clay ball of mass \( \mathrm{m} \) hits normally a wall with speed v and sticks to it, impulse imparted to the ball is 2 mv.
Statement II: Impulse is equal to rate of change of linear momentum with time.


The input of \( A \) and \( B \) for the Boolean
expression \( (\overline{\boldsymbol{A}+\boldsymbol{B}}) \cdot(\overline{\boldsymbol{A} \cdot \boldsymbol{B}})=\mathbf{1} \) is
A . 0,0
в. 0,1
\( c .1,0 \)
D. 1,1


The probability distribution of a random
variable \( X \) is given below:
\[
\begin{array}{lllll}
\mathrm{x}: & 0 & 1 & 2 & 3 \\
\mathrm{P}(\mathrm{x}): & \mathrm{k} & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}
\end{array}
\]
Determine \( \boldsymbol{P}(\boldsymbol{X} \leq \mathbf{2}) \) and \( \boldsymbol{P}(\boldsymbol{X}>\mathbf{2}) \)


What is resonant electrical circuit?
What are its types? Find out an expression for resonant frequency for series L-C-R circuit.


Growth hormones are situated in the
A. Pituitary gland
B. Thyroid gland
c. Adrenal gland
D. Pancreas


What could be the reasons for adopting contraceptive methods?


The boiling point of aldehyde and
ketones depend upon:
A. intermolecular dipole-dipole repulsion
B. intermolecular dipole-dipole attraction.
C. intermolecular induced dipole-dipole attraction.
D. none of these.


\( 5.63 \times 11 \) is equal to
A . 62
B. \( 83 . \overline{93} \)
c. 83.93
D. 83.93


Ethylene is produced by, \( C_{4} H_{8} \stackrel{\Delta}{\longrightarrow} \)
\( 2 C_{2} H_{4} . \) The constant is \( 2.48 \times \)
\( 10^{-4} \)sec\( ^{-1} \). Time in hours (nearest
integer) in which the molar ratio of the
ethylene to cyclobutane in reaction mixture will attain the value of 100
is


What is \( G_{0} \) (quiescent phase) of cell
cycle?


Solve: \( \frac{7}{10}-x=\frac{3}{5} \)


Magnetic moment of \( S c^{2+}= \) Magnetic
moment of \( \boldsymbol{C} \boldsymbol{u}^{2+} \)
If true enter 1 , else enter 0


Write the IUPAC name of the compound.
\[
\begin{array}{c}
\boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \\
\boldsymbol{N H}_{2}
\end{array}
\]


The name of the compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right] \boldsymbol{C l}_{2} \) will be?
A. pentaamminonitrocobalt(II) chloride
B. pentaamminenitrochloridecobaltate(III)
c. pentaamminenitrocobalt(III) chloride
D. pentanitrosoamminechlorocobaltate(III)


For every positive integral value of \( n \)
\( \mathbf{3}^{n}>n^{3} \) when
\( A \cdot n>2 \)
в. \( n \geq 3 \)
c \( . n \geq 4 \)
\( D \cdot n<4 \)


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


Mixture(s) showing positive deviation
from Raoult's law at \( 35^{\circ} \mathrm{C} \) is (are):
This question has multiple correct options
A. Carbon tetrachloride + methanol
B. Carbon disulphide + acetone
c. Benzene + toluene
D. Phenol + aniline


Find the square root of 1764 by the Prime Factorisation Method.


A crucible used in lab to heat solid at
high temperature is made of :
A. sulphur
B. silicon
c. graphite
D. phosphorus


Which element is a transition metal?
A. melting point in \( ^{\circ} C-98 ; \) density in \( g / c m^{3}-1.0 ; \) colour of oxide - white
B. melting point in \( ^{\circ} C-328 ; \) density in \( g / c m^{3}-11.3 ; \) colour of oxide - yellow
C. melting point in \( ^{\circ} C-651 \); density in \( g / c m^{3}-1.7 ; \) colour of oxide - white
D. melting point in \( ^{\circ} C \) - 1240; density in \( g / \mathrm{cm}^{3}-7.4 \) colour of oxide - black


The reduction potential of hydrogen electrode when placed in a buffer solution is found to be -0.413 V. The pH of the buffer is ?


Find the distance between the following
pair of points. (-5,7) and (-1,3)


toppr
Q Type your question
potential difference \( V \) across \( R \) is given
by:
\( A \)
\( B \)
\( c \)
\( D \)


Live wire has \( \ldots \). insulation covering whereas neutral wire has
insulation covering.
\( A \). white and blue
B. red and white
c. red and black
D. black and white


A hollow sphere partly filled with water has moment of inertia \( I \) when it is
rotating about its own axis at an angular velocity \( \omega . \) If its angular velocity
is doubled then its moment of
inertia becomes:
A . Less than \( I \)
B. More than I
c. \( I \)
D. zero


Goodsoil is
A. Which allows the limited amount of water into it
B. Which allows to percolate the water slowly from it
C. Which allows to pass water very quickly from it
D. Which holds whole of water into it


The number of unsuccessful attempts that can be made by a thief to open a number lock having 3 rings in which each rings contains 6 numbers is
A . 205
B. 200
c. 210
D. 215


Human heart is myogenic and it is supplied with sympathetic and vagus nerve branches that are
acceleratory and inhibitory in nature respectively.Which one of the following statement is incorrect w.r.t the heart
beat?
A. In foetal heart the heart rate is \( 140-130 \) beats per minutes
B. Mental status such as depression and grief decrease heart rate
C. An excess of \( C a^{++} \) ion decreases heart beat rate
D. High levels of \( N a^{+} \) and \( K^{+} \) decreases the strength of contraction


Of the following about capacitive
reactance which is correct?
A. The reactance of the capacitor is directly proportional to its ability to store charge
B. Capacitive reactance is inversely proportional to the frequency of the current
C . Capacitive reactance is measured in farad
D. The reactance of a capacitor in an AC circuit is similar to the resistance of a capacitor in a DC circuit


What is the minimum number of
carbon atoms to be present in a carbohydrate?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


Assertion
The external factors that affect
photosynthesis are number, size, age and orientation of leaves, mesophyll cells and chloroplasts and the amount of chlorophyll.
Reason
The internal factors that affect
photosynthesis are availability of
sunlight, temperature \( , C O_{2} \) concentration and water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the reaction \( 2 X+B_{2} H_{6} \rightarrow \)
\( \left[B H_{2} X_{2}\right]^{+}\left[B H_{4}\right]^{-} \) the amine(s) \( X \) is
\( (a r e): \)
This question has multiple correct options
A . \( N H_{3} \)
в. \( C H_{2} N H_{2} \)
c. \( \left(C H_{3}\right)_{2} N H \)
D. \( \left(C H_{3}\right)_{3} N \)


f \( \log _{3} 2, \log _{3}\left(2^{x}-5\right) \) and \( \log _{3}\left(2^{x}-\right. \)
\( 7 / 2) \) are in A.P, then \( x \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 2,3


Write nuclear reaction equations for:
(i) \( \alpha \) - decay of \( _{88}^{226} R a \)
(ii) \( \alpha \)
decay of \( _{94}^{242} P u\left(\text { iii) } \beta^{-} \text {- decay of }_{15}^{32} P\right. \)
(iv) \( \beta^{-} \) - decay of \( _{83}^{210} B i(v) \beta^{+}- \) decay of \( _{6}^{11} C \)
(vi) \( \beta^{+} \) - decay
of \( _{43}^{97} T c\left(\text { vii) Electron capture of } \frac{120}{54} X e\right. \)


Compare \( x \) and \( y \) bond angle from the
above given molecules.
\( \mathbf{A} \cdot x>y \)
В. \( y>x \)
c. \( x=y \)
D. None of these


The amount of energy when a million atoms of iodine are completely
converted into \( I^{-} \) ions in the vapor
state according to the equation, \( \boldsymbol{I}_{(g)}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{I}_{(g)}^{-} \) is \( 4.9 \times 10^{-13} \mathrm{J} . \) What
would be the electron gain enthalpy of
iodine in terms of \( k J \) mol \( ^{-1} \) and \( e V \) per
atom?
\( \mathbf{A} \cdot 295,3.06 \)
в. -295,-3.06
C .439,5.09
D. -356,-7.08


The probability that in a group of \( N \)
people at least two will have the same birthday is
A \( \cdot_{1-\frac{(365) !}{(365)^{N}(365-N) !}} \)
В \( \cdot_{1+\frac{(365) !}{(365)^{N}(365-N) !}} \)
c. \( _{1-} \frac{(365) !}{(365)^{N}(365+N) !} \)
D. None of these


Construct a quadrilateral ABCD with AB \( =4 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm}, \mathrm{CD}=5.6 \mathrm{cm} \mathrm{DA}=5 \mathrm{cm} \)
and \( A C=8 \mathrm{cm} . \) Find also its area.


The Magnus effect is equivalent to:
A . electric field
B. magnetic field.
c. Bernoulli's theorem.
D. magnetic effect of current.


Pyrophosphoric acid is the mixture of :
A. \( \mathrm{H}_{3} \mathrm{PO}_{3}+\mathrm{HPO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4}+\mathrm{H}_{3} \mathrm{PO}_{3} \)
c. \( \mathrm{H}_{3} \mathrm{PO}_{4}+\mathrm{HPO}_{3} \)
D. none of these