An element with the electron
configuration \( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{d}^{7} \boldsymbol{6} \boldsymbol{s}^{2} \) is:
A. an alkaline earth element
B. a transition element
c. an inertgas
D. a rare earth


\( 0.21-H \) inductor and \( a 88-\Omega \) \( \mathbf{A} \)
resistor are connected in series to a
\( 220-V, 50-H z A C \) source. The
current in the circuit and the phase angle between the current and the
source voltage are respectively. Use
\( \boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7} \)
A \( \cdot 2 A, \tan ^{-1} 3 / 4 \)
B. \( 14.4 A, \tan ^{-1} 7 / 8 \)
c. \( 14.4 A, \tan ^{-1} 8 / 7 \)
D. \( 3.28 A, \tan ^{-1} 2 / 11 \)


The common difference for even number
of terms written in symmetrical manner for an arithmetic progression have a common difference of ?
\( A \cdot d \)
B. \( 2 d \)
c. \( 3 d \)
D. \( -2 d \)


\( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2})(\boldsymbol{x}-\boldsymbol{3}), \boldsymbol{x} \in[\mathbf{0}, \boldsymbol{4}] \)
find \( ^{\prime} c^{\prime} \) if \( L M V T \) can be applied.


Find the smallest number by which a given number must be divided to obtain
a perfect cube
81


The angular momentum of electron is \( J \) Its magnetic moment will be
A \( \cdot \frac{m J}{2 e} \)
в. \( \frac{e J}{2 m} \)
c. \( \frac{2 m}{e j} \)
D. \( \frac{e m j}{2} \)


Two balls are thrown with initial
velocities simultaneously at \( t=0 . \) They
will meet at \( t= \)
A. \( \frac{h}{u+u_{1}} \)
в. \( \frac{2 h}{u+u_{1}} \)
c. \( \frac{h}{u-u_{1}} \)
D. \( \frac{2 h}{u-u_{1}} \)


State whether the statement is
true/false
n a quadrilateral \( A B C D, A B+B C+C D+ \)
\( \mathrm{DA}<2(\mathrm{BD}+\mathrm{AC}) \)
A. True
B. False


In Young's double slit experiment, the two equally bright slits are coherent, but of phase difference \( \frac{\pi}{3} . \) If maximum
intensity on the screen is \( I_{o} \), the
intensity at the point on the screen equidistant from the slits is:
A \( \cdot I_{o} \)
в. \( \frac{I_{o}}{2} \)
c. \( \frac{I_{o}}{4} \)
D. \( \frac{3 I_{o}}{4} \)


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{c}-\mathbf{1} \\ \mathbf{2} \\ \mathbf{3}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}-\mathbf{2} & -\mathbf{1} & -\mathbf{4}\end{array}\right] \)
If trace of matrix \( A B \) is -12 , then the
value of \( k \)
\( A \cdot 7 \)
B.
\( c \cdot 2 \)
D. none of these


The correct name for the complex ion
\( \left[\operatorname{CoCl}(O N)(e n)_{2}\right]^{+} \) is :
A. chlorobis(ethylenediamine)nitrito-O-cobaltate (III) ion
B. chlorodiethyldiaminenitrito-O-cobalt (III) ion
C. chloronitrito-O-diethyldiamine cobaltate (III) ion
D. chlorobis(ethylenediamine)nitrito-O-cobalt (III) ion


If \( G \) is the universal gravitation
constant and is the uniform density of a
spherical planet, then,
A. Time period of a planet will be independent of density of the planet
B. The shortest period of rotation of the planet will have very high density
c. The shortest period of rotation of the planet will have very low density
D. The shortest period of rotation of the planet depends on the radius of the planet


Match the names of diseases with the
meanings given. Choose the answer
which gives the correct combination of
the alphabets of the two columns.
\begin{tabular}{llll}
List I & \multicolumn{3}{c} { List II } \\
A. & Jaundice & 1. & Allergic inflammation of nose & Loss of motor functions \\
B. & Stenosis & 2. & Heart valve defect \\
C. & Rhinitis & 3. & Increase in bile pigments in the blood \\
D. & Paralysis & 4. & Septal defect of \\
& & & heart
\end{tabular}
\( \mathbf{A} \)
\( A-3, B-5, C-1, D-2 \)
2
B. A- 4, B-3, C-1, D-2
C. \( A-4, B-3, C-2, D-1 \)
D. \( A-3, B-4, C-1 \)
\( D \)


Give reasons for the following. In the experiment conducted by Faraday the induced electric current was not DC.


ABCD is a quadrilateral; \( P, Q, R \) and \( S \) are
the points of trisection of sides
\( A B, B C, C D \) and DA respectively and are adjacent to A and C; prove thar PQRS is a parallelogram.


A ball is projected from the ground with a speed of \( 20 m / s \) at an angle of 45 with
horizontal. There is a wall of \( 25 m \) height
at a distance of \( 10 m \) from the
projection point. The ball will hit the wal at a height of
\( A \cdot 5 m \)
в. \( 7.5 m \)
c. \( 10 m \)
D. \( 12.5 m \)


A covalent bond is formed by:
A. transfer of electrons.
B. sharing of electrons by only a single atom.
C. sharing of electrons.
D. repulsion of atoms between two atoms.


A heater is designed to operate with a power of \( 1000 W \) on a line of \( 100 V \). It is
connected in combination with
resistance of \( 10 \Omega \) and a resistance \( R \) to
line of \( 100 \mathrm{V} \). The value of \( \mathrm{R} \) so the
entire circuit operates with a power of
\( \mathbf{6 2 5} \boldsymbol{W} \) is
\( A \cdot 5 \Omega \)
В. \( 10 \Omega \)
\( c .15 \Omega \)
D. 20\Omega


A disc rotates about its axis of
symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of \( 1.25 \mathrm{cm} \) from the axis of rotation
remains at rest on the disc. The
coefficient of friction between the coin
and the disc is :
A. 0.5
B. 0.3
\( c . \) о.
D. 0.60


Find the largest number that will divide
\( \mathbf{3 9 8}, \mathbf{4 3 6} \) and \( \mathbf{5 4 2} \) leaving remainders
7,11 and 15 respectively.


During the electrolysis of \( 0.1 \mathrm{M} \) Cu SO solution using copper electrodes, a depletion of \( \left[C u^{2+}\right] \) occurs near the cathode with a corresponding excess near the anode, owing to inefficient stirring of the solution. If the concentrations of \( \left[C u^{2+}\right] \) near the
anode \( \& \) cathode are respectively 0.12 M
\& 0.08 M, calculate the back e.m.f.
developed. Temperature \( =298 \mathrm{K} \)
A . 22 \( \mathrm{mv} \)
B. 5.2 mv
c. \( 29 \mathrm{mv} \)
D. 59 mv


A charged particle \( q \) is shot from a large
distance towards another charged particle \( Q \) which is fixed, with a speed \( v \)
t approaches \( Q \) up to a closest distance \( r \) and then returns. If \( q \) were
given a speed \( 2 v, \) the distance of
approach would be
\( A \)
B. \( 2 r \)
c. \( r / 2 \)
D. \( r / 4 \)


According to the Lux-Flood definition
\( X e F_{6} \) behaves as:
A. an oxidising agent
B. an acid (oxide ion acceptor
\( c . \) a base
D. a reducing agent


Compound 'A' on chlorination gives compound 'B', compound 'B' reacts with alc. KOH gives gas 'C', which decolourizes Baeyer's reagent and ozonolysis of compound 'C' gives only HCHO compound. Then compound 'A' is:
A. \( C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
c. \( C_{4} H_{10} \)
D. \( C_{2} H_{5} C l \)


Increased asthmatic attacks in certain
seasons are related to
A. Hot and humid environment
B. Eating fruits preserved in tin containers
c. Inhalation of seasonal pollen
D. Low temperature


A right angles prism \( \left(45^{\circ}, 90^{\circ}, 45^{\circ}\right) \) of refractive index n has a plate of
refractive index \( \left(n_{1}<n\right) \) cemented to
its diagonal face. The assembly is in air.
A ray is incident on AB. Assuming \( n= \)
1.351, calculate the angle of incidence
(in degrees rounded off to nearest integer) at \( A B \) for which the refracted
ray passes through the diagonal face undeviated


Given 5 line segments of lengths 2,3,4,5,6 units. Then the number of
triangles that can be formed by joining
these lines is
\( \mathbf{A} \cdot^{5} C_{3} \)
B. \( ^{5} C_{3}-3 \)
c. \( ^{5} C_{3}-2 \)
D. \( ^{5} C_{3}-1 \)


Disturbance produced in a material medium due to the vibratory motion of the particles of the medium is called a
A. compression
B. vibration
c. wave
D. rarefaction


Which of the following ores is concentrated by chemical leaching method?
A. Cinnabar
B. Argentite
c. copper pyrites
D. Galena


The principle of controlled chain reaction is used in:
A. atomic energy reactor
B. atom bomb
c. the core of sun
D. artificial radioactivity


How many vertical columns are there in
the modern periodic table and what are they called?


The minimum value of the polynomial.
\( p(x)=3 x^{2}-5 x+2 \)
A \( \cdot-\frac{1}{6} \)
B.
\( c \cdot \frac{1}{12} \)
D. \( -\frac{1}{12} \)


Though India now has a large base in science and technology, which is fast expanding, it is still a long way from realising its potential of becoming a world leader in science. Name some important factors, which in your view
have hindered the advancement
of science in India.


The digits of a positive integer, having three digits are in A.P. and their sum is
15. The number obtained by reversing the digits is 594 less than the original number. Find the number.


If \( \left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right) \) is singular, the value
of \( a \) is
A \( . a=-6 \)
B. \( a=5 \)
c. \( a=-5 \)
\( \mathbf{D} \cdot a=6 \)


Which of the following statements concerning Bohr's model is/are true?
This question has multiple correct options
A. It predicts that probability of electron near nucleus is more
B. Angular momentum of electron in \( H \) atom \( =\frac{n h}{2 \pi} \)
C. It introduces the idea of stationary states
D. It explains line spectrum of hydrogen


Most primary productivity of pond is by
A. Phytoplankton
B. Zooplankton
C. Red algae
D. Floating plants


Why is the of aspartame limited to cold food and soft drinks?


A body starts from rest and acquires a
velocity \( 10 m s^{-1} \) in 2 s. Find the
acceleration.
A \( \cdot 10 m s^{-2} \)
B. \( 20 m s^{-2} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-2} \)
D. \( 40 \mathrm{ms}^{-2} \)


The electron emitted in beta radiation
originates from
A. inner orbits of atoms
B. free electrons existing in nucle
c. decay of a neutron in a nucleus
D. photon escaping from the nucleus


Which base is present in RNA but not in
DNA?
A . Uracil
B. Thymine
c. Guanine
D. Cytosine


Law of conservation of energy is
satisfied because
A. equal loss and gain in intensity is observed
B. all bright fringes are equally bright
C. all dark fringes are of zero brightness
D. the average intensity on screen is equal to the sum of intensities of the two sources.


According to arrhenius, an acid gives:
A . \( H^{+} \) in water
B. \( O H^{-} \) in water
c. Both \( (A) \) and \( (B) \)
D. \( O H^{-} \) in acid medium


Identify the type of set \( \boldsymbol{A}=\{\boldsymbol{x} \mid \boldsymbol{x} \epsilon \boldsymbol{R}, \boldsymbol{2} \leq \boldsymbol{x} \leq \boldsymbol{3}\} \)
A. Finite Set
B. Infinite Set
c. Null set
D. singleton set


Which one of the following is a correct statement?
A. Origin of seed habit can be traced in Pteridophytes
B. Pteridophyte gametophyte has a protonemal and leafy stage
c. In Gymnosperms, female gametophyte is free-living
D. Antheridiophores and Archegoniophores are present in Pteridophytes


The following represent standrard
symbols for transistors.
\( (i) \)
(i)
A. both represent PNP transistors
B. both represent NPN transistors
C. (i) represents PNP transistor while (ii) represent the NPN transistor
D. (i) represents NPN transistor while (ii) represent the PNP transistor


A meristem may be defined as the group of cells which
A. Add to the bulk of the plants
B. Conserve food
c. Divide continuously to give rise to new cells
D. Elongate and add to the group of cells


The average oxidation state of chlorine in bleaching power is :
A . -
B. +1
c. zero
D. - -2 as well as +2


Given below is a diagram showing a
defect of the human eye. Study it and
answer the following question:
Name the type of lens used to correct
the eye defect.


An electron beam is moving between two parallel plates having electric field
\( 1.125 \times 10^{-6} N / m . \) A magnetic field
\( 3 \times 10^{-10} T \) is also applied, so that
beam of electrons do not deflect. The
velocity of the electron is
\( A \cdot 4225 \mathrm{m} / \mathrm{s} \)
B. 3750 m/s
c. \( 2750 \mathrm{m} / \mathrm{s} \)
D. 3200 \( \mathrm{m} / \mathrm{s} \)


The angles which the vector \( \vec{A}=3 \hat{i}+ \) \( 6 \widehat{j}+2 \widehat{k} \) makes with the co-ordinate
axes are:
A \( \cdot \cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{4}{7}, \cos ^{-1} \frac{1}{7} \)
B. \( \cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{6}{7}, \cos ^{-1} \frac{2}{7} \)
C \( \cdot \cos ^{-1} \frac{4}{7}, \cos ^{-1} \frac{5}{7}, \cos ^{-1} \frac{3}{7} \)
D. None of these


Which of the following compound does
not liberate nitrogen with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) ?
A. Carbamide
B. Primary amine
c. Secondary amine
D. Alkanamide


The number of photons required to
release one mole of \( \boldsymbol{O}_{2} \) in
photosynthesis is called as
A. Quantum yield
B. Quantum requirement
c. Red drop
D. Emerson's effect


If \( x^{y}=e^{x-y}, \) then show that \( \frac{d y}{d x}= \) \( \frac{\log \boldsymbol{x}}{(1+\log \boldsymbol{x})^{2}} \)


Subtract the following with the help of
numberline:
\( (-3)-(-2) \)


The specific resistance of a metal wire
is \( 64 \times 10^{-6} \Omega \times c m ., \) the length is 198
\( \mathrm{cm} \) and the resistance is \( 7 \Omega \). The radius
of wire is :-
A. \( 2.4 \mathrm{cm} \)
B. 0.24 cm
c. \( 0.024 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)


A charge \( Q \) is distributed over two
concentric hollow spheres of radii \( r \) and \( R(>r) \) such that the surface densities
are equal. Find the potential at the common centre


A man stands on a rotating platform, with his arms stretched horizontally holding a \( 5 \mathrm{kg} \) weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then
brings his arms close to his body with the distance of each weight from the axis changing from \( 90 \mathrm{cm} \) to \( 20 \mathrm{cm} . \) The moment of inertia of the man together
with the platform may be taken to be
constant and equal to \( 7.6 \mathrm{kg} \mathrm{m}^{2} \).
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?


An electric dipole is placed at the centre
of a sphere. Mark the correct answers:
This question has multiple correct options
A. The flux of the electric field through the sphere is zero.
B. The electric field is zero at every point of the sphere.
C. The electric potential is zero everywhere of the sphere.
D. The electric potential is zero on a circle on the surface.


The oxidation number of Fe in
\( \boldsymbol{K}_{4} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \) is?
\( A \cdot+6 \)
B. +4
\( c \cdot+3 \)
D. +2


Critical mass of \( _{92} U^{235} \) is nuclear fission is :
A. 1 to \( 100 \mathrm{g} \)
B. 100 to \( 1000 \mathrm{mg} \)
c. 1 to \( 100 \mathrm{kg} \)
D. 1 to 100 u


Monocot root differs from dicot root in
having
A. Open vascular bundle
B. Scattered vascular bundle
c. Large pith
D. No pitt


A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statement is corret regarding the behaviour of the solution?
A. The solution formed is an ideal solution
B. The solution is non-ideal, showing positive deviation from Raoults Law
C. The solution is non-ideal, showing negative deviation from Raoults Law.
D. n-heptane shows positive deviation while ethanol shows negative deviation from Raoults Law


In the given graph an ideal gas change its state from A to state \( C \) by two paths ABC and AC. The internal energy of gas
at \( A \) is \( 10 \mathrm{J} \) and the amount of heat
supplied in path AC is 200 J. The
internal energy (in J) of gas at \( \mathrm{C} \) is \( 6 k^{2} \)
What is the value of \( k ? \)


Some magnetic flux is changed from a
coil of resistance \( 10 \Omega \). As a result, an
induced current is developed in it,
which varies with time as shown in the
figure. The magnitude of change in flux
through the coil in webers is:
\( A \)
B. 4
\( c .6 \)
\( D \)


\( n \) drops of water, each of radius \( 2 m m \)
fall through air at a terminal velocity of
\( 8 \mathrm{cm} / \mathrm{s} \). If they coalesce to form a single drop, then the terminal velocity of the combined drop is \( 32 \mathrm{cm} / \mathrm{s} \). The value of
\( n \) is


The reaction given below is interpreted
as:
\( \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{S}(\boldsymbol{s}) \)
A. \( H_{2} S \) is getting oxidized and \( C l_{2} \) is getting reduced
B. \( H_{2} S \) is getting reduced and \( C l_{2} \) is getting oxidized
c. only \( H_{2} S \) is oxidized
D. Both \( H_{2} S \) and \( C l_{2} \) are reduced


metal is a part of hemoglobin
a biomolecule.
A. Aluminium
B. copper
c. Iron
D. Calcium


A body weighing \( 8 g \) when placed in one pan and \( 18 g \) when placed on the other pan of a false balance. If the beam is horizontal when both the pans are
empty, then the true weight of the body is
A . \( 13 g \)
в. \( 9 g \)
c. \( 22 g \)
D. \( 12 g \)


The scientist who first observed
bacteria and protozoa is
A. Antonie Van Leeuwenhoek
B. Robert Hooke
c. Mathias Jacob
D. Robert Brown


\( \left|\begin{array}{lll}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c}\end{array}\right|=\boldsymbol{K}\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \)
\( \operatorname{then} K= \)
\( A \)
B. 2
\( c \)
\( D \)


\( f(x)=\left|\begin{array}{ccc}2 x & x^{2} & x^{3} \\ x^{2}+2 x & 1 & 3 x+1 \\ 2 x & 1-3 x^{2} & 5 x\end{array}\right| \)
then find \( \boldsymbol{f}^{\prime}(\mathbf{1}) \)


The difference between systolic and
diastolic pressure in human is
\( \mathbf{A} \cdot 120 \mathrm{mm} \mathrm{Hg} \)
B. \( 80 \mathrm{mm} \) Hg
c. \( 40 \mathrm{mm} \) Hg
D. \( 200 \mathrm{mm} \) Hg


The compounds which decompose on
passage of an electric current through them are known as:
A. electrolytes
B. non-electrolytes
c. electrolytically compounds
D. non-electrolytically compounds


Which type of fermentation is
accompanied by \( \mathrm{CO}_{2} \) evolution?
A. Alcoholic fermentation
B. Lactic acid fermentation
c. Both A and B
D. None of the above


Methane does not react with chlorine in
dark.
A . True
B. False


At \( 25 C, \) the solubility product values of
\( A g C l \) and \( A g C N S \) are \( 1.7 \times 10^{-10} \) and \( 1.0 \times 10^{-12} \) respectively. When water is
saturated with both solids, calculate
the ratio \( \left[\boldsymbol{C l}^{-}\right] /\left[\boldsymbol{C} \boldsymbol{N} \boldsymbol{S}^{-}\right] \) and also
\( \left[A g^{+}\right] \) in the solution.
A \( \cdot 1.3 \times 10^{2}, 1.7 \times 10^{-5} M \)
В . \( 1.7 \times 10^{2}, 1.308 \times 10^{-5} M \)
C. \( 1.3 \times 10^{4}, 1.308 \times 10^{-4} M \)
D. \( 1.7 \times 10^{3}, 1.67 \times 10^{-6} M \)


If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a} \) \( \overrightarrow{\boldsymbol{b}}=\mathbf{0},(\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{c}}) \cdot(\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}})=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{c}}= \)
\( \lambda \vec{a}+\mu \vec{b}+\omega(\vec{a} \times \vec{b}), \) where \( \lambda, \mu, \omega \) are
scalars then?
A \( \cdot \mu^{2}+\omega^{2}=1 \)
в. \( \lambda-\mu=1 \)
C \( \cdot(\mu+1)^{2}+\mu^{2}+\omega^{2}=1 \)
D. \( \lambda^{2}+\mu^{2}=1 \)


In the first world war, \( 1.1 \times 10^{8} \) kg of
poison gas were fired on the allied forces. If the gas is assumed to be phosgene, how many molecules of the gas correspond to the amount fired on allied forces?
A \( \cdot 1.9 \times 10^{-15} \)
B. \( 6.7 \times 10^{32} \)
c. \( 2.9 \times 10^{-15} \)
D. \( 6.7 \times 10^{29} \)


If \( \boldsymbol{A}(\boldsymbol{6},-\mathbf{7}, \mathbf{0}), \boldsymbol{B}(\mathbf{1 6},-\mathbf{1 9},-\mathbf{4}) \)
\( C(0,3,-6) \) and \( D(2,-5,10) \) are four points in space, then the point of intersection of the lines \( A B \) and \( C D \) is
A \( \cdot(2,1,-1) \)
в. (1,1,2)
D. does not exist as the lines are skew


Show that the product of perpendiculars on the line \( \frac{x}{a} \cos \theta+ \) \( \frac{y}{b} \sin \theta=1 \) from the points
\( (\pm \sqrt{a^{2}-b^{2}}, 0) \) is \( b^{2} \)


Which one of the following substances increase in weight by burning in air?
A. woodd
B. Magnesium
c. Paper
D. candle


The kinetic energy per unit length for a wave on a string is the positional
coordinate
A. True
B. False


Which of the following is not an endocrine gland?
A. Pituitary gland
B. Thyroid gland
c. Pineal gland
D. Salivary gland


\( \boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{x}=? \)
if \( \boldsymbol{x}=\boldsymbol{7} \)


Assertion
In chemisorption, adsorption first increases with temperature and then decreases.
Reason
Heat keeps on providing more and more
activation energy.
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


Measuring vessel to measure volume of irregular shaped solid is
A. Measuring Jar
B. measuring bowl
c. Any of these can be used
D. None


Match the items in column-I with those
in column - II
\begin{tabular}{lllll}
& Column I & & Column II \\
& & & \\
1. & Electric Fuse & A & Chemical Effect \\
\hline 2. & Relay & B & Electric Discharge \\
3. & CFL & C & Magnetic effect \\
4. & Button Cell & D & Heating Effect
\end{tabular} Which of the following shows the correct
matching?
\( A \cdot 1-C, 2-B, 3-A, 4-D \)
B. \( 1-B, 2-A, 3-C, 4-D \)
c. \( 1- \) D, \( 2-c, 3-B, 4-A \)
D. \( 1- \) D, \( 2-B, 3-C, 4-A \)


Coulomb's law is a confirmation
of
A. inverse cube law
B. product law
c. inverse square law
D. None of the above


If \( \vec{a}, \vec{b}, \vec{c} \) are position vectors of the vertices \( A, B, C \) of a triangle \( A B C \)
show that the area of the triangle \( A B C \) is \( \frac{1}{2}[\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}] . \) Also deduc
the condition for collinearity of the
points \( A, B \) and \( C \)


The conversion \( A \rightarrow B \) follows second
order kinetics. Doubling, the concentration of \( \boldsymbol{A} \) will increase the rate
of formation of \( \boldsymbol{B} \) by a factor of:
\( A \cdot 2 \)
B. 4
c. 0.5
D. 0.25


The area enclosed between the curves
\( x^{2}=y \) and \( y^{2}=x \) is equal to
This question has multiple correct options
A \( \cdot \frac{1}{3} \cdot \) sq.unit
B \( \cdot 2 \int_{0}^{1}\left(x-x^{2}\right) d x \)
C \cdot area of the region \( \left\{(x, y): x^{2} \leq y \leq|x|\right\} \)
D. none of the above


n identical cells are joined in series with its two cells \( A \) and \( B \) in the loop with reversed polarities. EMF of each shell is \( \mathrm{E} \) and internal
resistance r. Potential difference across
cell \( A \) or \( B \) is:
A \( \cdot \frac{2 E}{n} \)
В \( \cdot 2 E \mid 1-\frac{1}{n} \)
c. \( \frac{4 E}{n} \)
D. \( 2 E \mid 1-\frac{2}{n} \)


Q Type your question
an apartment are groupea as roılows:
The mean length of the plants is 33.43
years using direct method. Find y in the
table
\( \begin{array}{ll}\text { Age(years) } & \text { Number of people } \\ 0-10 & 10 \\ 10-20 & 15 \\ 20-30 & 26 \\ 30-40 & \mathrm{Y} \\ 40-50 & 23 \\ 50-60 & 16 \\ 60-70 & 3 \\ 70-80 & 1\end{array} \)
A . 23
B . 28
c. 15
\( D \)


Represent the following complex number in trigonometric form:
\( \frac{3}{2}-i \frac{\sqrt{3}}{2} \)


Assertion
Statement 1: When static friction acts,
there is no loss of mechanical energy.
Reason
Statement 2: When kinetic friction acts
between two bodies, there is loss of
mechanical energy.
A. Both Statements1 and 2 are true and Statement 2 is the correct explanation of Statement 1
B. Both Statements 1 and 2 are true, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is true but Statement 2 is false
D. Statement 1 is false but Statement 2 is true


\( p(x)=25 \) is a
polynomial
A. linear
B. quadratic
c. constant
D. cubic


Choose the correct answers from the
alternatives given :
Glycolysis starts and ends m the
A. cytoplasm
B. plasma membrane
c. nucleus
D. mitochondrion


What is the reduction power of the
hydrides of group 14 elements in increases order?


In the Fig. lines \( P Q \) and RS intersect each other at point \( 0 . \) If \( \angle P O R \)
\( \angle R O Q=5: 7, \) Find all the angles


\( 4 r^{3} \) is a quadratic polynomial
A. True
B. False


Draw a circle with the help of a bangle.
Take a point \( \boldsymbol{P} \) outside the circle.

Construct the pair of tangents from this point \( \boldsymbol{P} \) to the circle.


STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured.
Now, the unknown resistance is
put inside an enclosure maintained at a
higher temperature. The null point can be obtained at the same point as before
by decreasing the value of the standard resistance.
STATEMENT-2
Resistance of a metal increases with
increase in temperature.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True


If the speed of rotation of armature coil is increased in an AC generator
A. Magnitude of current increases
B. Frequency of current increases
c. Both 1 and 2
D. Magnitude of current increases, frequency decreases


Evaluate the given integral.
\( \int e^{x}(\sec x(1+\tan x)) d x \)


When diaphragm of man is completely
dome shaped, it shows
A. End of expiration and beginning of inspiration
B. Beginning of expiration and end of inspiration
C. Increased rate of breathing
D. Decreased rate of breathing


Which of the following has the highest molar conductivity under similar conditions?
A. Diamminedichloroplatinum (II)
B. Tetraamminedichlorocobalt (III) Chloride
c. Potassium hexacyanoferrate (II)
D. Hexaaquachromium
(III) chloride


Compound formed by the reaction of furfural with ethanol is:
A. An aldol
B. An acetal
c. A ketal
D. A hemiacetal


If \( a>0 \) and \( z=\frac{(1+i)^{2}}{a-i}, \) has magnitude \( \sqrt{\frac{2}{5}}, \) then \( \bar{z} \) is equal to:
A. \( -\frac{3}{5}-\frac{1}{5} i \)
B. \( -\frac{1}{5}+\frac{3}{5} i \)
c. \( -\frac{1}{5}-\frac{3}{5} i \)
D. \( \frac{1}{5}-\frac{3}{5} i \)


Fill in the blanks: The graph of line \( y+3 \) \( =0 \) is parallel to axis.


If \( \sum_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi, \) then \( \sum_{i=1}^{2 n} x_{i} \) is equal
to
A \( . n \)
B. \( 2 n \)
c. \( \frac{n(n+1)}{2} \)
D. None of these


What are the different ways in which
water gets contaminated?


f \( f: R \rightarrow R \) is defined by \( f(x)= \) \( \left\{\begin{array}{ccc}\frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\mathbf{2}} & \boldsymbol{i f} & \boldsymbol{x} \in \boldsymbol{R}-\{-\mathbf{1},-\mathbf{2}\} \\ -\mathbf{1} & \boldsymbol{i f} & \boldsymbol{x}=-\mathbf{2} \\ \mathbf{0} & \boldsymbol{i f} & \boldsymbol{x}=-\mathbf{1}\end{array}\right. \)
then \( f \) is continuous on the set.
\( A \)
в. \( R-\{-2\} \)
c. \( R-\{-1\} \)
D. \( R-\{-1,-2\} \)


Find the smallest whole number by
which 252 should be divided, so as to
get a perfect square.


Which of the following are true for all
the systems?
A. Will not have definite amount of substance
B. Energy and matter are not be exchanged with surroundings
C. Will have same amount of substance
D. Universe - surroundings


A network of four capacitors of capacity
equal to \( C_{1}=C, C_{2}=2 C, C_{3}=3 C \)
and \( C_{4}=4 C \) are connected to a battery
as shown in the figure. The ratio of the
charges on \( C_{2} \) and \( C_{4} \) is:


What do you understand by the term
wave?


Given \( \tan (\pi \cos \theta)=\cot (\pi \sin \theta) \)
then the value of \( \cos \left(\theta-\frac{1}{4} \pi\right) \) will be
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{1}{3 \sqrt{2}} \)
D. \( \frac{1}{4 \sqrt{2}} \)


A parachutist after bailing out falls \( \mathbf{5 0} \boldsymbol{m} \) without friction. When parachute opens, it decelerates at \( 2 m s^{-2} . \) He
reaches the ground with speed \( 3 m s^{-1} \)
At what height did he bail out?
\( \left(g=9.81 m / s^{2}\right) \)
A. \( 91 m \)
B. 182 m
c. 293 m
D. \( 111 m \)


Which of the following are relevant examples:
A. uniform velocity - A car moving in a straight line
B. variable velocity - A car moving along the periphery of a circle
c. uniform retardation - When brakes are applied to a car moving with constant velocity.
D. All the above


Prussian blue has two types of iron with oxidation number as shown \( \prod_{\boldsymbol{F}}^{\boldsymbol{I I I}}[\stackrel{\boldsymbol{I I}}{\left.\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]}] \)
net charge on Prussian blue is - \( x \). The value of \( x \) is


An electron (mass \( \boldsymbol{m} \) ) with initial
velocity \( \vec{v}=v_{0} \hat{i}+v_{0} \hat{j} \) is an electric
field \( \vec{E}=-E_{0} \hat{k} . \) If \( \lambda_{0} \) is initial de-
Broglie wave length at time \( t \) is given by
\( A \)
\[
\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E^{2} t^{2}}{2 m^{2} v_{0}^{2}}}}
\]
в.
\[
\frac{\lambda_{0} \sqrt{2}}{\sqrt{1+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]
c.
\[
\frac{\lambda_{0}}{\sqrt{2+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]
D.
\[
\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]


Find the value of \( x \) of \( y \) using the information shown in the figure. Find
the measure of \( \angle A B D \) and \( \angle A C D \)


An electrolytic cell is constructed for preparing hydrogen. For an average current of 1 ampere in the circuit, the time required to produced \( 450 m L \) of
hydrogen at NTP is approximately.
A. 30 min
B. 1 hour
c. 2 hours
D. 5 hours


\( 20 \mathrm{ml} \) of methane is completely burnt
using \( 50 \mathrm{ml} \) of oxygen. The volume of the gas left after cooling to room temperature is:
\( A \cdot 80 m \)
B. 40 m
c. \( 60 \mathrm{ml} \)
D. 30 m


Assertion
The force of repulsion between atomic
nucleus and \( \alpha \) -particle varies with distance according to inverse square law.
Reason
Rutherford did \( \alpha \) -particle scattering
experiment.
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


Which among the following reactions is an example of pseudo first order
reaction?
A. Inversion of cane sugar
B. Decomposition of \( H_{2} O_{2} \)
c. Conversion of cyclopropane to propene
D. Decomposition of \( N_{2} O_{5} \)


When water enters in root due to
diffusion, it is termed as
A. Osmosis
B. Endocytosis
c. Active absorption
D. Passive absorption


Two Nicols is oriented with their
principal planes making an angle of \( 60^{\circ} \)
The percentage of incidents unpolarized light which passes through the system are
\( A \cdot 50 \% \)
B. \( 100 \% \)
c. \( 12.5 \% \)
D. 37.5\%


The dehydrogenation of 2-bromo butane with alcoholic KOH gives:
A. only 2 -butene
B. only 1-butene
c. 2-butene as the major product
D. 1- butene as the major product


If \( G \) is centroid of \( \triangle A B C, \) then
A \( \cdot \vec{G}=\vec{a}+\vec{b}+\vec{c} \)
B. \( \vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2} \)
c. \( 3 \vec{G}=\vec{a}+\vec{b}+\vec{c} \)
" \( \quad 3 \vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2} \)


Solve the following pairs of equations by reducing them to a pair of linear
equations:
\( \frac{4}{x}+3 y=14, \frac{3}{x}-4 y=23 \)


The maximum extension of the spring
\( \boldsymbol{x}_{\boldsymbol{m}} \) is
\( A \cdot \frac{m g}{K} \)
в. \( \frac{2 m g}{K} \)
c. \( \frac{3 m g}{K} \)
D. \( \frac{4 m g}{K} \)


A student is weighing an object using a spring balance. The weight and mass of the object are respectively
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A. \( 25 N, \) skg
в. \( 50 N, 5 k g \)
c. \( 25 N, 2.0 k g \)
D. \( 50 N, 2.5 k g \)


A man running on a horizontal road at
\( 8 k m p h \) find that rain is falling vertically. He increases the speed to
\( 12 k m p h \) and find the drops make an
angle \( 30^{\circ} \) with the vertical
A. The speed of rain is \( 8 \sqrt{3} k m p h \)
B. The speed of rain is \( 8 \sqrt{112} k m p h \)
c. speed of rain wrt man is \( 8 k m p h \)
D. Speed of rain wrt man is \( 8 \sqrt{3} k m p h \)


If \( \overrightarrow{P O}+\overrightarrow{O Q}=\overrightarrow{Q O}+\overrightarrow{O R}, \) prove that
the points \( P, Q, R \) are collinear.


A steady current flows in a metallic
conductor of non-uniform cross-section.
The quantity/quantities constant along the length of the conductor is/are.
A. Current, electric field and drift speed
B. Drift speed only
c. current and drift speed
D. Current only


Explain why the given names in the following are wrong. Give the correct name in each case:
1,1,3-trimethyl propane


What are the two properties of carbon which led to the huge number of carbon compounds we see around us?
A . (i) Catenation
(ii) Tetravalency
B. (i) Catenation
(ii) Tri valency
c. (i) Catenation
(ii) Penta valency
D. (i) co valency
(ii) Di valency


If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{k} \sin \boldsymbol{t}+\sin \boldsymbol{k} \boldsymbol{t}), \boldsymbol{y}= \)
\( a(k \cos t+\cos k t), \) then find \( \frac{d^{2} y}{d x^{2}} \) in
terms of t.
A \( \cdot \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k+1}{2} t} \)
в. \( \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k-1}{2} t \cos \frac{k+1}{2} t} \)
c. \( \frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k-1}{2} t} \)
D. \( -\frac{k+1}{4 a k} \frac{1}{\cos ^{3} \frac{k+1}{2} t \cos \frac{k-1}{2} t} \)


Calculate the weight of \( \left(N H_{4}\right)_{2} S O_{4} \) which must be added to \( 500 \mathrm{mL} \) of \( 0.2 \mathrm{M} \)
\( N H_{3} \) to yield a solution of \( \mathrm{pH}=9.35, K_{b} \) for \( \boldsymbol{N} \boldsymbol{H}_{3}=\mathbf{1 . 7 8} \times \mathbf{1 0}^{-\mathbf{5}}(\text { in } \boldsymbol{g} \mathbf{m}) \)
A. 0.4
B. 2
c. 3.52
D. 5.25


Differentiate: \( \log (\log x), x>1 \)


Variation of \( \Delta \boldsymbol{H} \) vs temperature is given by:
A. Kirchhoff's equation
B. Gibbs-Helmholtz equation
c. Clausius-Clapeyron equation
D. Van't Hoff's equation


Name the reagents used in the
following reactions:
(i) Oxidation of a primary alcohol to carboxylic acid.
(ii) Oxidation of a primary alcohol to aldehyde.
(iii) Bromination of phenol to 2,4,6 tribromophenol.
(iv) Benzyl alcohol to benzoic acid.
(v) Dehydration of propan-2-ol to
propene.
(vi) Butan-2-one to butan-2-ol.


If \( f_{1} \) and \( f_{2} \) represent the first and second focal lengths of a single spherical refracting surface of refractive index \( \mu \) then
A \( \cdot f_{1} f_{2}=\mu \)
в. \( \frac{f_{1}}{f_{2}}=-1 \)
\( \mathbf{c} \cdot f_{1}=2 f_{2} \)
D. \( f_{2}=\mu f_{1} \)


A stone is dropped from the top of a cliff It is seem to hit the ground below after
4.2 sec. How high is the cliff?
A. \( 86.44 m \)
B. \( 860 m \)
\( c \cdot 160 m \)
D. 180


Calculate the equilibrium constant at 25 degrees celsius given the Standard
Free Energy value of \( -107.2 \mathrm{kJ} \)
A . - 43.2
B. 43.2
c. \( 6.18 \times 10^{8} \)
D. 1.04
E . \( 6.18 \times 10^{9} \)


In \( N P N \) transistor, \( 10^{10} \) electrons
enters in emitter region in \( 10^{-6} \) sec. If \( 2 \% \) electrons are lost in base region then collector current and current
amplification factor \( (\beta) \) respectively
are
\( A \cdot 1.57 \mathrm{mA}, 49 \)
B. 1.92 \( \mathrm{mA} \), 70
c. \( 2 \mathrm{mA}, 25 \)
D. 2.25 mA, 100


Which one of the following is an
incorrect statement?
\( A \cdot A \) pi bond is formed when a sigma already exists.
B. A pi bond may be formed by the overlapping of p or d orbitals.
C. A pi bond is formed by the overlapping of hybrid orbitals.
D. A pi bond is formed by the lateral overlapping of atomic orbitals.


What is the momentum of a photon if
the wavelength of X-rays is 1 angstrom?


Which of the following gases, in pure form, has a slightly blue colour?
A. Ozone
B. Oxygen
c. Carbon dioxide
D. Hydrogen


In a black box of unknown elements \( (\boldsymbol{L} \) or \( R \) or any other combination), an ac
voltage \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \) is applied
and current in the circuit was found to
be \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin [\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}+(\boldsymbol{\pi} / \mathbf{4})] . \) Then the
unknown elements in the box may be
A. Only capacitor
B. Inductor and resistor both
c. Either capacitor, resistor, inductor or only capacito and resistor
D. only resistor


\( \boldsymbol{I}=\int_{0}^{\pi / 2} \frac{1+2 \cos x}{(2+\cos x)^{2}} d x \)


Kinetic energy of the bob of a simple pendulum is maximum at the extreme left position. State whether true or false.
A. True
B. False


What is the IUPAC name of the given compound?


The area of cross section, length, and density of a piece of metal of atomic
weight 60 are \( 10^{-6} m^{2}, 1 \mathrm{m}, \) and \( 5 \times 10^{3} \)
\( \mathrm{kgm}^{-3}, \) respectively. If every atom
contributes one free electron, find the
drift velocity (in \( \mathrm{mms}^{-1} \) ) of electrons in
the metal when a current of 16 A passes
through it. Avogadro's number is \( N_{A}= \)
\( 6 \times 10^{23} / \) mol and charge on an electron
is \( e=1.6 \times 10^{-19} C \)


Reduce \( \left(\frac{1}{1-4 i}-\frac{2}{1+i}\right)\left(\frac{3-4 i}{5+i}\right) \)
the standard form.


What measures are taken to reduce
fluid friction in aeroplanes?
A. Optimum speed is maintained with respect to the air
B. Metals are choosen in a way to make the aeroplane lighter with smoother surface
C. Streamlined body inspired by birds
D. All of the above


The slope of the tangent at \( (x, y) \) of \( a \) curve passing through the point (2,2) is \( \frac{x}{y}, \) then the equation of the curve is
A \( \cdot x^{2}+y^{2}=4 \)
B . \( x^{2}-y^{2}=4 \)
c. \( x^{2}=y^{2} \)
D. \( x^{2}=y^{2}-4 \)


Which of the following is a polysaccharide?
A. Starch
B. Maltose
c. Lactose
D. Arabinose


I. Agitation and stirring will increase
the rate at which salt dissolves in water
\( I I . \) Increased movement of water
molecules allow sodium ions and
chloride ions to be pulled apart as
shells of hydration are formed.
A. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


Let us consider an equation \( \frac{1}{2} m u^{2}= \) \( m g h, \) where \( m \) is mass of the body, \( v \) its
velocity, \( g \) is the acceleration due to
gravity and \( R \) is the Right. Check whether this equation is dimensionally
correct


Which of the following reactions will not give propane? This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C l \frac{M g / e t h e r}{H_{2} P} \)
в. \( C H_{3} C H_{2} C O C l \frac{C H_{3} M g X}{H_{2} P} \)
c. \( C H_{3} C H=C H_{2} \frac{B_{2} H_{6}}{C H_{3} C O O H} \)
D. \( C H_{3} C H-C H_{3} \stackrel{P / H I}{\longrightarrow} \)
он


The figure shows the variation of internal energy (U) with the pressure (P)
of 2.0 mole gas in cyclic process abcda.
The temperature of the gas at \( c \) and \( d \) are \( 300 \mathrm{K} \) and \( 500 \mathrm{K} \). Calculate the heat
absorbed by the gas during the process.
\( A \cdot 400 \mathrm{R} \ln 2 \)
B. 200 R \( \ln 2 \)
\( c \cdot 100 \mathrm{R} \ln 2 \)
D. 300 R In 2


At \( 10^{0} C, \) the osmotic pressure of urea solution is \( 500 \mathrm{mm} \). The solution is
diluted and the temperature is raised to
\( 25^{0} C, \) so that the osmotic pressure became \( 105.3 \mathrm{mm} . \) The number of times,
the solution diluted is:
A . 6
B. 5
\( c \cdot 4 \)
D. 3


The height of a parallelogram is three-
eights of its base. If the area of the parallelogram is \( 96 \mathrm{cm}^{2} \), find its height
and base.


(a) Draw a labelled diagram of neuromuscular junction.
(b) Compare nervous and hormonal
mechanisms for control and co-
ordination in animals.


The present population of town is 12500 and it is increasing at the rate of \( 8 \% \) per annum. what will be the population of town after two years?
A . 14000
B. 12500
c. 14580
D. 25000


The relation between time \( t \) and
distance \( x \) is \( t=a x^{2}+b x, \) where \( a \) and
\( b \) are constants. The acceleration is:
A \( --2 a v^{3} \)
3 \( ^{-2 a v} \)
B . \( 2 a v^{2} \)
c. \( -2 a v^{2} \)
D. \( 2 b v^{2} \)


Let \( X=\{-3,-2,-1,0,1,2\} \) and \( Y= \)
\( \{x: x \text { is an integer and }-3 \leq x<2\} \)
(i) Is \( X \) a subset of \( Y ? \)
(ii) Is \( Y \) a subset of \( X ? \)


Tritium, \( T \) (an isotope of \( H \) ) combines with fluorine to form weak acid TF,
which ionizes to give Tritium is radioactive and is \( \alpha \beta- \)emitter.
freshly prepared aqueous solution of TF has pT (an equivalent of pH) of 1.5 and freezes at \( -0.372^{\circ} \mathrm{C} . \) If \( 600 \mathrm{ml} \) of
freshly prepared solution were allowed to stand for 24.8 years. Calculate (i) ionization constant of TF. (ii)Number
of lbeta-particles emitted?(Given \( \boldsymbol{K}_{f} \) forwater \( =\mathbf{1 . 8 6 k g m o l} \boldsymbol{K}^{-1}, \boldsymbol{t}_{1 / 2} \) for
tritium \( =12.4 y \) ears
A \( \cdot(i) K_{a}=7.3 \times 10^{-3}(i i) 4.55 \times 10^{22} \)
B . (i)K \( _{a}=7.3 \times 10^{-5}(i i) 4.55 \times 10^{24} \)
C . \( (i) K_{a}=14.3 \times 10^{-3}(i i) 9.1 \times 10^{22} \)
D . (i) \( K_{a}=14.3 \times 10^{-5}(i i) 9.1 \times 10^{24} \)


A semiconductor is doped with a donor
impurity then [more than one option may be correct
This question has multiple correct options
A. the hole concentration increases
B. the hole concentration decreases the electron
concentration increases
C. the electron concentration increases
D. the electron concentration decreases


Match the following and choose the
correct combination from the options
given below.
\begin{tabular}{lll|l}
& Column I & & Column II \\
& (Placentation Types) & & (Represented in ) \\
\hline \( \mathrm{A} \) & Basal & 1 & Dianthus \\
\hline \( \mathrm{B} \) & Free central & 2 & Pea \\
\( \mathrm{C} \) & Parietal & 3 & Lemon \\
\( \mathrm{D} \) & Axile & 4 & Marigold \\
\( \mathrm{E} \) & Marginal & 5 & Argemone
\end{tabular}
\( \mathbf{A} \)
\( A-1, B-2, C-3, D-4, E-5 \)
B. A- 2, B-3, C- 4, D-5, E-1
C. \( A-4, B-1, C-5, D-3, E-2 \)
D. \( A-4, B-3, C-5, D-1, E-2 \)
E. \( A-5, B-4, C-3, D-2, E- \)


A small mass and a thin uniformed rod
each of mass 'm' are positioned along the same straight line as shown. find the forced of gravitational attraction exerted by the rod on the small mass.


If \( t_{5}, t_{10} \) and \( t_{25} \) are \( 5^{t h}, 10^{t h} \) and \( 25^{t h} \)
terms of an AP respectively, then the value of \( \left|\begin{array}{ccc}\boldsymbol{t}_{5} & \boldsymbol{t}_{10} & \boldsymbol{t}_{25} \\ \mathbf{5} & \mathbf{1 0} & \mathbf{2 5} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right| \) is
A . -40
B.
\( c \cdot-1 \)
D. 0
E. 40


Find the square of the following
numbers using the identity \( (a-b)^{2}= \)
\( a^{2}-2 a b+b^{2}: \)
\( \mathbf{9 9} \)


\( \operatorname{Let} g(x)=x^{5} \ln (f(x)) \) where \( f(x) \) is
adifferentiable positive function on
\( (0, \infty) \) satisfying \( f(3)=1 \) and \( f^{\prime}(3)= \)
\( 2 \operatorname{then} g^{\prime}(3) \) is equal to
A . 243
B.
c. 1
D. 486


In a compound microscope the lenses
used are :
A. both convex of same focal length
B. both convex of different focal length
C. both concave of same focal length
D. one convex and one concave of different focal length


What is transpiration?


solve:
\( 4 x+\frac{x-y}{8}=17 \)
\( \mathbf{2} \boldsymbol{y}+\boldsymbol{x}-\frac{\mathbf{5} \boldsymbol{y}+\mathbf{2}}{\mathbf{3}}=\mathbf{2} \)


In the following reactions, \( \boldsymbol{X}, \boldsymbol{Y} \) and \( \boldsymbol{Z} \)
are:
\( \mathbf{A} \cdot X=C H_{3} C l ; Y=a n h y d r o u s A l C l_{3} ; Z=H N O_{3}+ \)
\( H_{2} S O_{4} \)
B \( . X=C H_{3} C O C l ; Y= \) anhydrous \( A l C l_{3} ; Z=H N O_{3}+ \)
\( H_{2} S O_{4} \)
\( \mathbf{c} \cdot X=C H_{3} C l ; Y=c o n c . H_{2} S O_{4} ; Z=H N O_{3}+H_{2} S O_{4} \)
D. \( X=C H_{3} C l ; Y=d i l . H_{2} S O_{4} ; Z=H N O_{3} \)


Which of the hydrated species may
exist?
\( \mathrm{I}: \boldsymbol{H}_{5} \boldsymbol{O}_{2}^{+} \)
\( \|: \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \|: \boldsymbol{H}_{5} \boldsymbol{O}_{2} \)
\( \mathbf{I V}: \boldsymbol{H}_{\mathbf{7}} \boldsymbol{O}_{\mathbf{3}}^{+} \)
A. Il only
B. 1 and I
c. I, Il and IV
D. I. II. III and IV


The products \( X \) and \( Z \) in the following
reaction sequence are
\[
\begin{array}{l}
\| f+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \frac{\mathrm{AlCl}_{3} / \text { ether }}{\text { Heat }} \times \mathrm{x} \\
\qquad \frac{\mathrm{OH}}{\mathrm{O}_{2} / 130^{\circ} \mathrm{C}} \mathrm{Y} \frac{\mathrm{H}^{+} / \mathrm{H}_{2} \mathrm{O}}{\text { Heat }}
\end{array}
\]
A. Isopropylbenzene and acetone
B. Cumene peroxide and acetone
C. Isopropylbenzene and isoproply alcohol
D. Phenol and acetone


If \( r \cdot v \cdot X \sim B\left(n=5, P=\frac{1}{3}\right), \) then
\( P(2<X<4)=\ldots . \)
A. \( \frac{80}{243} \)
B. \( \frac{40}{243} \)
c. \( \frac{40}{343} \)
D. \( \frac{80}{343} \)


Which of the following statements is
not correct about oxidative
decarboxylation?
A. It takes place in mitochondrial matrix
B. Two molecules of NADH are produced by one molecule of pyruvate
C. Pyruvate dehydrogenase is used as catalyst in this reaction
D. Two molecules of NADH are produced by two molecules of pyruvate


A ball is thrown upward with an initial
velocity of \( 100 \mathrm{ms}^{-1} \). After how much
time will it return to the ground.
A. 20
B. 23 s
c. 25 s
D. 40 s


Sum of the interior angles of a regular
polygon is \( 1620^{\circ} . \) How many sides does
this polygon have?


Is hydrogen bonding between dimethyl ether and hydrogen peroxide possible? If yes then how? And if no then why not?


A step-up transformer operates on a \( 230 \mathrm{V} \) line and supplies aload of 2 amp. The ratio of the primary and secondary windings is \( 1: 25 . \) The current in the primary is
\( A \cdot 15 A \)
B. 12.5 A
\( c \cdot 25 A \)
D. 50 A


If pressure of an ideal gas contains in a closed vessel is increased by \( 0.5 \% \) the
increase in temperature is \( 20 \mathrm{k} \) the initial temperature of the gas is
A \( \cdot 27^{\circ} \mathrm{C} \)
B. \( 127^{\circ} \mathrm{C} \)
\( c \cdot 300^{0} c \)
D. \( 400^{\circ} \mathrm{C} \)


Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as if \( \boldsymbol{v}=\boldsymbol{k}\left(\frac{2 y^{2}}{a^{2}}-\frac{y^{3}}{a^{3}}\right) \) If coefficient of
viscosity for water is \( \eta, \) what will be
shear stress between layers of water at
\( y=a \)


Observe the figure and answer the given
questions.
Trance the path from seeds to Hawk


Write the chemical equations to
represent the following reactions. The disproportionation of \( \mathrm{SnO} \) to \( \mathrm{Sn} \) and
\( \operatorname{Sn} O_{2} \) is \( 2 S n O \rightarrow S n+S n O_{2} \)
If true enter 1 , else enter 0


A truck starts from rest and accelerates
uniformly at \( 2.0 m s^{-2} . \) At \( t=10 s, \) a
stone is dropped by a person standing on the top of the truck (6 \( m \) high from the ground). What are the
(a) velocity, and (b) acceleration of the stone at \( t= \)
11 \( s \) ? (Neglect air resistance.)


To divide a line segment in the ratio \( p \) \( \boldsymbol{q}(\boldsymbol{p}, \boldsymbol{q} \text { are integers }) \) a ray \( \boldsymbol{A} \boldsymbol{X} \) is drawn
so that \( \angle B A X \) is an acute angle and
then mark points on ray \( A X \) at equal distances such that the minimum
number of points is:
\( \mathbf{A} \cdot p q \)
В. \( p+q-1 \)
c. \( p+q \)
D. Greater of \( p \) and \( q \)


Which of the following constitutes the genetic material of the cell?
A. Nucleic acids
B. proteins
c. lipids
D. carbohydrates


In figure The sides \( B A \) and \( C A \) have
been produced such that \( \boldsymbol{B A}=\boldsymbol{A D} \)
and \( C A=A E \) prove that segment
\( \boldsymbol{D} \boldsymbol{E} \| \boldsymbol{B C} \)


Calculate \( \Delta H^{o} \) for the reaction between
ethene and water to form ethyl alcohol from the following data
\( \Delta_{c} H^{o} C_{2} H_{5} O H_{(l)}=-1368 k J \)
\( \Delta_{c} H^{o} C_{2} H_{4(g)}=-1410 k J \)
Does the calculated \( \Delta H^{o} \) represent the enthalpy of formation of liquid ethanol?


Which of the following show selective permeability?
A. Cell membrane
B. Cell wall
c. cytoplasm
D. Protoplasm


Cones in Gymnosperm plants are
\( \mathbf{A} \cdot \) Bisexual
B. Unisexual
c. Sterile
D. All of the above.


Two metallic spheres of radii \( 2 \mathrm{cm} \) and
\( 6 \mathrm{cm} \) are given charges \( 3 \times 10^{-2} \mathrm{C} \) and
\( 7 \times 10^{-2} C, \) respectively. If these are
connected by a conducting wire, the final charge on the bigger sphere is
A \( \cdot 7.5 \times 10^{-2} C \)
В. \( 4 \times 10^{-2} \mathrm{C} \)
c. \( 3.5 \times 10^{-2} C \)
D. \( 2 \times 10^{-2} C \)


The radius of a circle is \( 40 \mathrm{cm} \) and the length of perpendicular drawn from its centre to chord is \( 24 \mathrm{cm} . \) The length of
the chord \( A B \) is
A. \( 32 \mathrm{cm} \)
B. 64cm
c. \( 48 \mathrm{cm} \)
D. 24cm


A watch glass containing some powdered substance is placed between the pole
pieces of a magnet. Deep concavity is observed at the center. The substance in
the watch glass is (assume poles are far)
A. iron
B. chromium
c. carbon
D. woodd


Ice skating can be used to demonstrate that when ice is under pressure, its:
A. Melting point remains unchanged
B. Melting point is raised
c. Melting point is lowered
D. coefficient of friction with metal is reduced


The dimensional formula for a physical
quantity \( x \) is \( \left[M^{-1} L^{3} T^{-2}\right] . \) The errors in measuring the quantities \( \mathrm{M}, \mathrm{L} \) and \( \mathrm{T} \) respectively are \( 2 \%, 3 \% \) and4\%. The maximum percentage of error that occurs in measuring the quantity x is
A . 9
B. 10
c. 14
D. 19


Mammals giving rise to immature young ones and nourishing them in a pouch are called as
A. Monotremes
B. Marsupials
c. Primates
D. Carnivores


Photochemical smog is related to pollution of:
A. Soil
B. Air
c. water
D. None of these


When two moles of ethyl chloride react
with two moles of sodium in the
presence of ether what will be formed?
a) 2 moles of ethane
b) 1 moles of ethane
c) 2 moles of butane
d) 1 moles of butane


1 mole of ice at \( 0^{\circ} \mathrm{C} \) and \( 4.6 \mathrm{mm} \) Hg
pressure is converted to water vapour at a constant temperature and pressure.
Find \( \Delta H \) if the latent heat of fusion of
ice is 80 Cal/gm and latent heat of
vaporization of liquid water at \( 0^{\circ} \mathrm{C} \) is
596 Cal per gram and the volume of ice in comparison to that of water (vapour) is neglected.
A. 14.53 Kcal/mol
в. 12.16 Kcal/mol
c. \( 10.22 \mathrm{Kcal} / \mathrm{mol} \)
D. 15.62 Kcal/mol


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{O} \boldsymbol{H} \stackrel{\boldsymbol{C H} C l_{3}+\boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \quad \) Product
About the above reaction the incorrect
statement is:
A. the name of reaction is Riemer teimann's reaction
B. the intermediate in the reaction dichloro carbene
c. the final major product is o-hydroxy benzaldehyde
D. the final major product is benzyl chloride


Chloroform on reduction with zinc dust
and water gives
A. Methyl chloride
B. Dichloro methane
c. chloro methane
D. Methane


What gas is produced when magnesium is made to react with hydrochloric acid?
A. Hydrogen
B. Oxygen
c. Carbon dioxide
D. No gas is produced


Find the oxidation state of bromine in
\( \mathrm{HBrO}_{3} \)
\( A \cdot-3 \)
B . -
\( c \cdot 1 \)
\( D .3 \)
E. 5


A man of mass \( \mathrm{m} \) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
\( W_{\text {gravity}}= \) work done by gravity on the
man
\( W_{\text {friction}}= \) work done by gravity on the
man
\( W_{\text {man }}= \) work done by man Which of the following options is correct regarding the various work done? This question has multiple correct options
\( \mathbf{A} \cdot W_{g r a v i t y}=-m g h \)
B. \( W_{f r i t t i o n}>0 \)
\( \mathbf{c} \cdot W_{m a n}=m g h+\frac{1}{2} m v^{2} \)
D. \( W_{f r i t i o n}=0 \)


When sample of baking soda is strongly ignited in crucible it suffered loss in
weight of \( 3.1 g \) the mass of baking soda
is-
A. \( 16.8 g \)
в. \( 8.4 g \)
c. \( 11.6 g \)
D. \( 4.2 g \)


Explain the term 'drift velocity' of
electrons in a conductor. Hence obtain
the expression for the current through a conductor in terms of 'drift velocity'


It is possible for a body to move in a circular path with uniform speed as
long as it is travelling
A. equal distances in equal interval of time
B. unequal distances in unequal interval of time
c. equal distances in unequal interval of time
D. unequal distances in equal interval of time


The power of a lens is measured in
A. watt
B. horse power
c. dioptre
D. \( m \)


Which of the following equation is dimensionally correct?
A. Pressure = Energy per unit area
B. Pressure = Energy per unit volume
c. Pressure = Force per unit volume
D. Pressure = Momentum per unit volume per unit time


Enlist the number and names of motor
cranial nerves in a human being?


In the Young's double slit experiment
two slits 0.125 mm apart are
illuminated by light of wavelength
\( 4500 A^{\circ} . \) The screen is \( 1 m \) away from
the plane of the slits. Find the separation between second bright fringes on both sides of central maxima.


Do you expect the carbon hydrides of
the type \( \left(C_{n} H_{2 n+2}\right) \) to act as Lewis acid or base? Justify your answer.


Which of the following molecules contains only \( \pi \) bond?
\( \mathbf{A} \cdot B_{2} \)
в. \( C_{2} \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. Both (1) \& (2)


Balance the following equation, when it occurs in basic medium.
\[
\boldsymbol{C l O}_{\boldsymbol{3}}^{-} \longrightarrow \boldsymbol{C l}^{-}
\]
A \( \cdot C l O_{3}^{-}+3 H_{2} O+6 e \rightarrow C l^{-}+6 O H^{-} \)
B . \( C l O_{3}^{-}+3 H_{2} O+5 e \rightarrow C l^{-}+6 O H^{-} \)
c. \( 3 C l O_{3}^{-}+3 H_{2} O+3 e \rightarrow C l^{-}+3 O H \)
D. None of these


Answer the following.
a. What is done to prevent corrosion of
metals?
b. What are the metals that make the
alloys brass and bronze?


The ore of aluminium is :
A . cryolite
B. magnesite
c. carnallite
D. bauxite


Four different radioactive elements are
kept in separate containers. In the beginning the container \( A \) has 200 gatom with half-life of 2 days, \( B \) has 20
g-atom with half-life of 20 days, \( C \) has 2
g-atom with half-life 200 days and \( D \)
has 100 g-atoms with half-life of 10 days. In the beginning the maximum activity exhibited by the container is:
A. \( a \)
B. \( b \)
\( c \)
D. \( d \)


State whether true or false.
If Akhil takes 10 hours and Santosh
takes 12 hours to travel to Chennai from
Hyderabad, then the average velocity of Akhil is more than that of Santosh.
A. True
B. False


Evaluate the following determinant:
\( \left|\begin{array}{ccc}1 & -3 & 2 \\ 4 & -1 & 2 \\ 3 & 5 & 2\end{array}\right| \)


In extrinsic semiconductors:
A. the conduction band and valence band overlap
B. the gap between conduction band and valence band is near about 16 eV
C. the gap between conduction band and valence band is near about \( 1 e V \)
D. the gap between conduction band and valence band will be \( 100 e V \) and more


Which of the following is not a cause of pollution?
A. Afforestation
B. Wars among nations
c. Industrialization
D. Growth of algae in water


A block of mass \( m \) slides down an
inclined wedge of same \( m \) shown in
figure. Friction is absent everywhere Magnitude of acceleration of center of
mass of the block and wedge is
A. zer
B. \( \frac{g \sin ^{2} \theta}{\left(1+\sin ^{2} \theta\right)} \)
c. \( \frac{g \cos ^{2} \theta}{\left(1+\sin ^{2} \theta\right)} \)
D. \( \frac{g \sin \theta}{(1+\cos \theta)} \)


Simplify :-
\( 2 x^{2}-x-3=0 \)


Hess' Law and bond energy data can be used to calculate the enthalpy change of a reaction. Bromoethane
\( C H_{2} C H_{2} B r, \) can be made by reacting ethene with hydrogen bromide.
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H B r} \rightarrow \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
What is the enthalpy change for this
reaction?
A. \( -674 \mathrm{kJ} \mathrm{mol}^{-} \)
B. -64 kJ \( m o l^{-1} \)
c. +186 k \( \mathrm{mol}^{-1} \)
D. +346 k \( \mathrm{mol}^{-1} \)


Priya bought a suitcase for \( 2,730 . \) The
VAT for this item is \( 5 \% \). What was the
price of the suitcase before VAT was
added? Also state how much is the VAT.


Packets of which of the following quantity best describe photons?
A. energy
B. mass
c. volume
D. power
E. waves


Find he point of intersection of \( \mathrm{AB} \) and CD, where
\( \boldsymbol{A}(\boldsymbol{6},-\boldsymbol{7}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{1 6},-\boldsymbol{1 9},-\boldsymbol{4}), \boldsymbol{C}(\boldsymbol{0}, \boldsymbol{3},-\boldsymbol{6}) \)


What is the approximate range of audible sound frequencies for a human
with good hearing?
A. From \( 20 H z \) to \( 2000 H z \)
B. From \( 20 H z \) to \( 20000 H z \)
c. From \( 200 H z \) to \( 20000 H z \)
D. From \( 200 H z \) to \( 200000 H z \)


A gas behaves more closely like an ideal
gas at
A. low pressure and low temperature
B. low pressure and high temperature
c. at all pressure and temperature
D. none of these


Which of the following books is not written by Werner Heisenberg?
A. Breakthrough
B. The Physical Principles of the quantum theory
c. Physics and Philosophy
D. Physics and Beyond


A circular disc of radius \( \boldsymbol{R} \) and
thickness \( \frac{R}{6} \) has moment inertia \( I \) about an axis passing through its
centre perpendicular to its plane. lt is
melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is
A. \( I \)
B. \( \frac{2 I}{8} \)
c. \( \frac{1}{5} \)
D. \( \frac{I}{10} \)


Uncertainty in position is twice the uncertainty in momentum, uncertainty in velocity is
A. \( \sqrt{\frac{h}{\pi}} \)
B. \( \frac{1}{2 m} \sqrt{\frac{b}{\pi}} \)
\( c \cdot \frac{1}{2 m} \sqrt{h} \)
D. \( \frac{1}{2 \sqrt{2 m}} \sqrt{\frac{h}{\pi}} \)


Give two varieties of silk which are
considered as inferior quality to that of mulberry and tasar silk.


\( \frac{3+2 i}{2-5 i}+\frac{3-2 i}{2+5 i} \)


A capacitor of \( 10 \mu F \) charged upto \( 250 \mathrm{V} \) is connected in parallel with another capacitor of \( 5 \mu F \) charged upto \( 100 \mathrm{V} \) The common potential is :
A . 200
B. 300
c. \( 400 \mathrm{v} \)
D. 500


Mahesh bought a leather coat, quoted
at Rs. 12000 for Rs. 30000 after paying the sales tax. Calculate the rate of sales
tax charged.
A. \( 100 \% \)
B. \( 150 \% \)
c. \( 200 \% \)
D. \( 250 \% \)


The imaging drum of a photocopier is positively charged to attract negatively
charged particles of toner. Near the surface of the drum, its electric field
has magnitude \( 1.4 \times 10^{5} N C^{-1} . \) A toner
particle is to be attached to the drum with a force that is 10 times the weight of the particle. Assume toner particles are made of carbon \( _{6}^{12} C \) Find charge to mass ratio of the charged toner particle :
A \( \cdot 7.0 \times 10^{-4} \mathrm{Ckg}^{-1} \)
В. \( 7.0 \times 10^{-3} \mathrm{Ckg}^{-1} \)
C. \( 7.0 \times 10^{-5} \mathrm{Ckg}^{-1} \)
D. \( 7.0 \times 10^{-6} \mathrm{Ckg}^{-1} \)


Which of the following statement is
incorrect about nucleophiles?
a) Nucleophiles have an unshared
electron pair and can make use of this to react with an electron deficient
species
b) The nucleophilicity of an element (an electron donor) generally increases on going down a group in the periodic table
c) A nucleophile is electron-deficient species
d) All good nucleophiles are good bases when we deal across the period


Factorize \( 25 a^{2}-9 b^{2} \)
A \( \cdot(5 a+b)(5 a-3 b) \)
B. \( (a+3 b)(5 a-3 b) \)
c. \( (5 a+3 b)(5 a-3 b) \)
D. \( (5 a-3 b)(5 a+3 b) \)


The average weight of 40 students in a class is 75 kg. By mistake the weights of two students are read as \( 74 \mathrm{kg} \) and 66 kg respectively instead of 66 kg and 54 kg. Find the corrected average weight of the class


For the following reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
If initially \( 25 m L \) of \( H_{2} \) and \( 20 m L \) of \( I_{2} \) are present in a container and at
equilibrium \( 30 m L \) of \( H I \) is formed then calculate equilibrium constant.


Eight point charges (can be assumed
as small spheres uniformly charged
and their centres at the corner of the
cube) having values q each are fixed at
vertices of a cube .The electric flux
through square surface ABCD of the
cube is
A \( \cdot \frac{q}{24 \epsilon_{n}} \)
B. \( \frac{q}{12 \epsilon_{0}} \)
c. \( \frac{q}{6 \epsilon_{0}} \)
D. \( \frac{q}{8 \epsilon_{0}} \)


In which of the following salts, cation does not undergo hydrolysis but anion undergoes hydrolysis?
A. \( B a C O_{3} \)
в. \( C a C l_{2} \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{CO}_{3} \)
D. \( \operatorname{NaNO}_{3} \)


Find the following integral. \( \int e^{x}\left(\sec ^{2} x+\tan x\right) \cdot d x \)


A frog can be levitated in a magnetic field produced by a current in a vertical solenoid placed below the frog. This is possible because the body of the frog behaves as:
A. paramagnetic
B. diamagnetic
c. ferromagnetic
D. antiferromagnetic


Example for a proper fraction is
A \( \cdot \frac{28}{13} \)
в. \( \frac{11}{23} \)
\( c \cdot \frac{16}{9} \)
D. \( \frac{14}{3} \)


Which one of the following statements
is correct?
A. 2 s orbital is spherical with two nodal planes
B. The de Broglie wavelength ( \( \lambda \) ) of a particle of mass 'm' and velocity 'V' is equal to mV/h
C. The principal qantum number (n) indicates the shape of the orbital
D. The electronic configuration of phosphorous is given by [Ne] \( 3 s^{2} 3 p_{x}^{1} 3 p_{y}^{1} 3 p_{z}^{1} \)


Mark the incorrect statement w.r.t cell
division:
A. Ribonuclease suppresses prophase
B. In meiosis-II number of chromosomes as well as amount of DNA is reduced to half
c. When a cell grows its karyoplasmic ratio decreases which leads to cell division
D. Nuclear membrane reappears during telophase


Electricity production from wave energy requires:
A. strong wavess
B. mild waves
c. Either (A) or (B)
D. None of the above


Soil hold water in it, it is called as
A. Soil water
B. Ground water
c. Soil moisture
D. None of the above


If equal volumes of \( \mathrm{BaCl}_{2}(\mathrm{aq}) \) and
NaF(aq) solutions are mixed together, which will give a precipitate? \( \left[K_{s p} \text { of } \operatorname{Ba} F_{2}=1.7 \times 10^{-7}\right] ? \)
B. 0.010M BaCl_and 0.015M NaF
D. 0.020 M BaCl_and 0.002 M Naf


A graph of the output from an A.C.
generator is given. This is given as:
(a) an input to a half wave rectifier
(b) an input to a full wave rectifier Give graphic representations of the outputs in the cases (a) and (b).


The composition of the solution whose normal boiling point is \( T \)
A \( \cdot X_{A}=0.08, X_{B}=0.92 \)
В. \( X_{A}=0.92, X_{B}=0.18 \)
C \( . X_{A}=0.18, X_{B}=0.82 \)
D. None of these


Calculate energy in kcal/mole
necessary to remove an electron in a hydrogen atom in fourth principal quantum number to infinity.


Which of the following are correct about
mixture of two miscible liquids forming
azeotopes?
This question has multiple correct options
A. Has the lowest temperature at which the two liquids can exist in the liquid state
B. Has the lowest temperature attainable at which two liquids forms eutectic mixture
C. Eutectic point has found application to attain low melting point solids which are eutectic mixture
D. Composition of azeotrope and their b.pt. vary with the external pressure


In a coil of area \( 10 \mathrm{cm}^{2} \) and 10 turns
with magnetic field directed perpendicular to the plane and is changing at the rate of \( 10^{4} \) gauss second. The resistance of the coil is 20
\( \Omega . \) The current in the coil will be
A . \( 0.5 A \)
в. \( 5 A \)
c. \( 50 A \)
D. \( 5 \times 10^{8} A \)


The S.I. unit of magnetic field intensity
is :
A. webber
B. Tesla
c. owersted
D. Gauss


Amongst all elements in the periodic table, which element shows maximum catenation?
A. carbon
B. Hydrogen
c. Nitrogen
D. oxygen


Increasing the concentration of an
electrophile in a typical \( S_{N^{2}} \) reaction by
a factor of 3 and the concentration of
the nucleophile by a factor of 3 will change the reaction rate to :
A. increase by a factor of 6
B. increase by a factor of 9
c. decrease by a factor of 3
D. remain about the same


Which one of the following conditions will increase the voltage of the cell represented by the equation? \( \boldsymbol{C u}(s)+\mathbf{2 A g}^{+}(\boldsymbol{a q} .) \rightleftharpoons \boldsymbol{C u}^{2+}(\boldsymbol{a q} .)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
A. Increase in the dimension of \( C u \) electrode
B. Increase in the dimension of \( A g \) electrode
C. Increase in the concentration of \( C u^{2+} \) ion
D. Increase in the concentration of \( A g^{+} \) ion


The amount of heat energy required to
convert 1 kg of ice \( a t-10^{\circ} C \) to water at
\( 100^{\circ} \mathrm{C} \) is \( 7,77,000 \mathrm{J} \). Calculate the specific latent heat of ice. Specific heat capacity of ice \( 2100 J k g^{-1} K^{-1} \), specific heat capacity of water = \( 4200 J k g^{-1} K^{-1} \)
A. \( 3,360 J k g^{-1} \)
B. \( 33,600 J k g^{-1} \)
c. \( 33,60,000 J k g^{-1} \)
D. \( 3,36,000 J k g^{-1} \)


Malonic ester contains an active
methylene group and two hydrogen atoms of active methylene group which
are easily replaced by alkyl and acyl
groups in the presence of a strong base. The carbonation intermediate formed
makes \( S_{N} 2 \) attack on alkyl or acyl
groups. In the sequence of reactions
given above, the final product \( [S] \) is :
\[
[\mathrm{Q}] \stackrel{\mathbf{H}_{3} \mathbf{O}^{+}}{\longrightarrow}[\mathbf{R}] \stackrel{\text { heat }}{\longrightarrow}[\mathrm{s}]
\]
\( \mathbf{A} \cdot C H_{2}=C H-C H_{2}-C H_{2}-C O-C O O H \)
B \( \cdot C H_{2}=C H-C H_{2}-C O-C H_{2}-C O O H \)
c. \( C H_{2}=C H-C H_{2}-C H_{2}-C O O H \)
D. \( C H_{3}-C H=C H-C H_{2}-C O O H \)


Expand \( (\boldsymbol{p}-\boldsymbol{2} \boldsymbol{q}+\boldsymbol{r})^{2} \)
\( \mathbf{A} \cdot p^{2}+4 q^{2}+r^{2}-4 p q-4 q r+2 r p \)
B \( \cdot p^{2}-4 q^{2}+r^{2}-4 p q-4 q r+2 r p \)
C \( \cdot p^{2}+4 q^{2}-r^{2}-4 p q-4 q r+2 r p \)
D. None of these


Figure shows a system of three concentric metal shells \( A, B \) and \( C \) with
radii a, 2a and 3a respectively. Shell B is earthed and shell \( C \) is given a charge \( Q \) Now if shell \( C \) is connected to shell \( A \) then the final charge on the shell B, is
equal to:
A. \( -\frac{3 Q}{4} \)
в. \( -\frac{8 Q}{11} \)
\( c \cdot-\frac{5 Q}{3} \)
D. \( -\frac{3 Q}{7} \)


The determinant
\( \left|\begin{array}{lll}a^{2} & a^{2}-(b-c)^{2} & b c \\ b^{2} & b^{2}-(c-a)^{2} & c a \\ c^{2} & c^{2}-(a-b)^{2} & a b\end{array}\right| \) is divisible by
This question has multiple correct options
\( \mathbf{A} \cdot a+b+c \)
B . \( (a+b)(b+c)(c+a) \)
c. \( a^{2}+b^{2}+c^{2} \)
D. \( (a-b)(b-c)(c-a) \)


Light transmitted by nicol prism is
A. unpolarised
B. plane polarised
c. circular polarised
D. elliptically polarised


\( \ln \Delta \mathrm{ABC}, \overline{X Y} \) is paralled to \( \overline{A C} \) and
divides the triangle into two parts of equal area. Then the \( \frac{A X}{A B} \) equals
A \( \cdot \frac{\sqrt{2}+1}{2} \)
B. \( \frac{2-\sqrt{2}}{2} \)
c. \( \frac{2+\sqrt{2}}{2} \)
D. \( \frac{\sqrt{2}-1}{2} \)


What is the smallest constituent of
matter that retains its chemical
identity?
A. Atom
B. Molecule
\( c \cdot \log \)
D. Radical


If \( A, B \) are two events with
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 5} \)
then find the value of \( \boldsymbol{P}\left(\boldsymbol{A}^{c}\right)+\boldsymbol{P}\left(\boldsymbol{B}^{c}\right) \)


D.E. whose solution is \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)
A \( . x y y_{2}+x y_{1}^{2}=y y_{1} \)
В. \( x y y_{2}+y_{1}=y \)
C \( . x^{2} y_{2}+x y_{1}=y \)
D. \( x^{2} y_{2}+2 x y_{1}=y_{1}^{2} \)


\( \int_{0}^{1} x(1-x)^{4} d x= \)
A . \( 1 / 15 \)
B. 1/30
\( c \cdot-1 / 15 \)
D. 1/60


f \( 1 u=1.492 \times 10^{-a} \) erg; the value of \( a \)
is :


For a given density of the planet, the orbital period of a satellite near the surface of planet of radius \( \boldsymbol{R} \) is
proportional to:
A \( \cdot \frac{1}{2} \)
в. \( \frac{3}{2} \)
c. \( \frac{-1}{2} \)
D. \( R^{0} \)


When lead nitrate is heated, it breaks
down into lead monoxide, nitrogen dioxide and oxygen.
\( 2 P b\left(N O_{3}\right)_{2} \rightarrow 2 P b O+4 N O_{2}+O_{2} \)
The reaction is an example of:
A. combination reaction
B. decomposition reaction
c. double decomposition reaction
D. displacement reaction


An isolated conducting sphere whose radius \( R=1 m \) has a charge \( q=\frac{1}{9} n C \)
The energy density at the surface of the
sphere is:
A \( \cdot \frac{\varepsilon_{0}}{2} J / m^{3} \)
B . \( \varepsilon_{0} J / m^{3} \)
\( \mathbf{c} \cdot 2 \varepsilon_{0} J / m^{3} \)
D. \( \frac{\varepsilon_{0}}{3} J / m^{3} \)


Write each of the following decimals in
words:
\( \mathbf{0 . 4 5 9} \)


Correct balanced equation from the following reactions is:
A. \( N a H C O_{3} \rightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
в. 2 NaHCO \( _{3} \rightarrow 2 \) Na\( _{2} \) CO \( _{3}+H_{2} \) O +3 C \( O_{2} \),
\( \mathrm{c} \cdot 2 \mathrm{NaH} \mathrm{CO}_{3} \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \)
D. \( _{N a H C O_{3} \rightarrow N a_{2} C O_{3}+\frac{1}{2} H_{2} O+C O_{2}} \)


\( \frac{x^{3}+x^{2}+2 x-12}{x-3} \)


\( C_{n} H_{2 n-1} C O O H \) is the general formula
for:
A. saturated fatty acids
B. unsaturated fatty acids
c. simple lipids
D. phospholipids


Which of the following is the anhydride of nitric acid?
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( N_{2} O_{5} \)


The figure shows a uniform isosceles
triangular plate of mass \( M \) and base \( L \)
The angle at the apex is \( 90^{\circ} . \) The apex
lies at the origin and the base is paralle
to the \( x \) -axis. Find the moment of inertia
of the plane about the y-axis.


In which of the following process highest energy is absorbed?
\( \mathbf{A} \cdot C u \rightarrow C u^{+} \)
в. \( B r \rightarrow B r^{-} \)
c. \( I \rightarrow I^{-} \)
D. \( L i \rightarrow L i^{+} \)


Assertion
Energy can be transferred between gaseous molecules during collisions
but \( u_{\mathrm{rms}} \) remains constant.
Reason
The average kinetic energy of gaseous
molecules remains constant as long as
the temperature is constant and
therefore, \( u_{\mathrm{rms}} \) remains unchanged during the collision.
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


Name different types of teeth and their number in and adult human


The cell constant of a conductivity cell
with electrodes of \( 0.5 \mathrm{cm} \times 0.5 \mathrm{cm} \) with a
separation of \( 0.5 \mathrm{cm}, \) is:
A. \( 0.5 \mathrm{cm}^{-1} \)
B. \( 2.0 \mathrm{cm}^{-1} \)
\( c .2 .0 \mathrm{cm} \)
D. \( 2.0 \mathrm{cm}^{-2} \)


Which of the following is not the reason
for the higher \( \boldsymbol{E} \boldsymbol{A}_{1} \) of halogens?
I) High nuclear charge
Il) Larger atomic size
III) Easy to get octet configuration, i.e. \( \boldsymbol{n} \boldsymbol{s}^{2} \boldsymbol{n} \boldsymbol{p}^{6} \)
IV) Half filled p-orbitals
A. I and IV
B. I, II and III
c. Il and IV
D. II and III


The equilibrium constant for the
reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \Leftrightarrow \mathbf{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is \( \boldsymbol{8 1} \)
at a certain temperature. If the
concentrations of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are \( \boldsymbol{3} \)
mole/lit each at equilibrium, the
equilibrium concentration of \( \boldsymbol{H} \boldsymbol{I} \) is:
A. 17 mol/litre
B. 27 mol/litre
c. 34 mol/litre
D. 51 mol/litre


If the position vectors of the points \( \boldsymbol{A}, \boldsymbol{B} \) and \( C \) be \( i+j, i-j \) and \( a i+b j+c k \)
respective;y, then the points \( A, B \) and
\( C \) are collinear if:
A \( . a=b=c=1 \)
B. \( a=1, b \) and \( c \) are arbitrary scalars
C. \( a=b=c=0 \)
0


\( 10 \mathrm{L} \) of hard water required \( 0.56 \mathrm{g} \) of lime (CaO) for removing hardness. Hence, the temporary hardness in ppm
(part per million) of \( C a C O_{3} \) is :
A. 100
в. 200
c. 10
D. 20


Write the IUPAC names of the given
compounds:


The starting material for the manufacture of polyvinyl chloride is obtained by reacting \( \boldsymbol{H} \boldsymbol{C l} \) with:
A. acid chloride
B. acetylene
c. ethyl alcohol
D. ethene


Solve: \( \frac{d y}{d x}=\frac{y+x}{x} \)


Draw the graph for the linear equation given below:
\( \mathbf{2} \boldsymbol{x}-\mathbf{7}=\mathbf{0} \)
Which of the following points lie on this line?
This question has multiple correct options
A. (3.5,0)
в. (3,0)
c. (-2,2)
D. (3.5,2)


IUPAC name of complex \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{A l}\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{4}}\right)_{\boldsymbol{3}}\right] \)
is:
A. potassium alumino-oxalate
B. potassium trioxalatoaluminate (III)
c. potassium aluminium
(III) oxalate
D. potassium trioxalatoaluminate (IV)


If a force of \( 4 N \) is applied on a body of
mass \( 20 k g \), then the work done in \( 3 r d \)
second will be
A \( .1 .2 J \)
в. \( 2 J \)
c. 45
D. 16 \( J \)


Write any three postulates of Kinetic theory of gases.


Which indicator we prefer to use in
iodometric titration?
A. Starch
B. Phenolphthalein
c. 1,10 phenathroline
D. All of the above


The perimeter of a rectangular field is \( \frac{3}{5} \)
km. If the length of the field is twice its
width then find the area of the rectangle
\( \operatorname{in} m^{2} \)


What is the wave number and
wavelength of the first transition in the
Lyman, Balmer and Paschen series in
the atomic spectra of hydrogen?


Stars appears to move from east to
west because
A. all stars move from east to west
B. the earth rotates from west to east
c. the earth rotates from east to west
D. the background of the stars moves from west to east


If \( \boldsymbol{f}=\{(\boldsymbol{6}, \boldsymbol{3}),(\boldsymbol{8}, \boldsymbol{9}),(\boldsymbol{5}, \boldsymbol{3}),(-\mathbf{1}, \boldsymbol{6})\} \)
then the pre-images of 3 are
A. 5 and -1
B. 6 and 8
c. 8 and -1
D. 6 and 5


If \( \boldsymbol{m}\left[\begin{array}{ll}-\mathbf{3} & \mathbf{4}\end{array}\right]+\boldsymbol{n}\left[\begin{array}{ll}\mathbf{4} & -\mathbf{3}\end{array}\right]=\left[\begin{array}{ll}\mathbf{1 0} & -\mathbf{1 1}\end{array}\right] \)
then \( 3 m+7 n= \)
\( A \cdot 3 \)
B. 5
c. 10
\( D \)


The energy of a \( K \) -electron in tungsten is \( -20 k e V \) and of an \( L \) -electrons is
\( -2 k e V . \) The wavelength of \( X \) -rays emitted when there is electronjump from \( \boldsymbol{L} \) to \( \boldsymbol{K} \) shell:
A \( .0 .3443 \AA \)
в. \( 0.6887 \AA \)
c. \( 1.3982 \dot{A} \)
D. 2.78 音


The atomic number of element Unq is:
A . 102
B. 103
\( c \cdot 104 \)
D. 105


ff \( y=\sin ^{-1} x, \) show that
\( \left(1-x^{2}\right) \cdot \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=0 \)


The velocity of sound is \( V_{s} \) in air. If the density of air is increased to 4 times, the new velocity of sound is
A. \( \frac{V_{s}}{2} \)
в. \( \frac{V_{s}}{12} \)
c. \( 12 V_{s} \)
D. \( \frac{3}{2} V_{s}^{2} \)


"The occurrence of one event excludes
the occurrence of another event". In a
random experiment of probability theory, it is called
A. Complementray event
B. Impossible event
c. Mutually exclusive event
D. certain event


Calculate the current strength which
was passed for 15 min to liberated \( 193.11 c m^{3} \) of hydrogen gas at \( 273 K \)
and \( 760 m m \) of \( H g \) pressure during electrolysis of acidulated water


Integrate: \( \frac{3 x^{2}}{x^{6}+1} \)


A transistor is used in the common
emitter mode as an amplifier. Then
This question has multiple correct options
A. the base-emitter junction is forward-biased.
B. the base-emitter junction is reverse-biased.
C. the input signal is connected in series with the voltage applied to bias the base-emitter junction.
D. the input signal is connected in series with the voltage applied to bias the base-collector junction In p-type semiconductor \( n_{h}>n_{e} \)


According to Bohr's theory, the energy in
the \( n^{t h} \) orbit is \( \boldsymbol{E}_{\boldsymbol{n}}= \)
\( \frac{-\mathbf{2 . 1 7 6} \times \mathbf{1 0}^{-\mathbf{1 8}} \times Z^{2}}{\mathbf{n ^ { 2 }}} J . \) The longest
wavelength of light that will be needed to remove an electron from the 3 rd orbit
of \( H e^{+} \) ion is:
A \( \cdot \lambda=2055 A^{\circ} \)
B . \( \lambda=2154 A^{\circ} \)
c. \( \lambda=2164 A^{\circ} \)
D . \( \lambda=2004 A^{\circ} \)


The \( \mathrm{E}^{o} \) for reduction of \( \mathrm{HNO}_{2} \) to \( \mathrm{NO} \) is
\( 0.99 \mathrm{V} \) and \( \mathrm{E}^{\circ} \) for reduction of \( \mathrm{NO}_{3}^{-} \) to
\( \mathrm{HNO}_{2} \) is \( 0.94 \mathrm{V} . \) The equilibrium
constant at \( 25^{\circ} \mathrm{C} \) for the
disproportionation of 3 mole of aqueous
\( \mathrm{HNO}_{2} \) to yield \( \mathrm{NO} \) and \( \mathrm{N} \mathrm{O}_{3}^{-} \) ions is:
A. \( K_{c}=344.64 \)
В. \( K_{c}=336.97 \)
c. \( K_{c}=639.73 \)
D. None of these


Acceleration due to gravity on the moon
is \( 1 / 6 t h \) of the acceleration due to
gravity on the earth. If the ratio of densities of the earth and the moon is
\( 5 / 3, \) then radius on the moon in terms of radius of earth will be


The force on a particle of mass \( 10 g \) is \( (10 \hat{i}+5 \hat{j}) N . \) If it starts from rest, what
would be its position at time \( t=5 s ? \)
A . \( (12500 \hat{i}+6250 \hat{j}) m \)
B. \( (6250 \hat{\imath}+12500 \hat{j}) m \)
c. \( (12500 \hat{i}+12500 \hat{j}) m \)
D. \( (6250 \hat{i}+6250 \hat{j}) m \)


Which of the following characteristics regarding 7 halogens is not correct?
A. lonization energy decreases with increase in atomic number
B. Electronegativity decreases with increase in atomic number
c. Electron affinity decreases with increase in atomic number
D. Enthalpy of fusion increases with increase in atomic number


Benzaldehyde can be prepared by:
A. Etards reaction
B. Aldol condensation
c. Cannizaros reaction
D. Clemmensons reduction


In case of a forced vibration, the
resonance wave becomes very sharp
when the :
A. Damping force is small
B. Restoring force is small
c. Applied periodic force is small
D. Quality factor is small


toppr \( L \)
Q туре your question
potentiometer and measures the corresponding current in the circuit.
The table of data and the resistance vs.
current graph created by the student is shown below.
Based on the experimental data collected by the student, determine the
emf of the battery.
B. 0.5
c. 1.0
D. 2.0
E. 3.0


Blood of earthworm is red because its
haemoglobin is


Which of the following has largest
radius?
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)
B \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{3} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{5} \)


Identify the substances B. If dilute acid
B' which does not normally give hydrogen when reacted with metals but does give a gas when it reacts with
copper.
A . nitric acid
B. hydrochloric acid
c. sulphuric acid
D. none of these


State whether the following statements
are true or false.
Most protozoans are photosynthetic.
A. True
B. False


Polynuclear hydrocarbons are formed by complete combustion of organic materials.
A. True
B. False


Which of the following products have green chemistry approach?
A. Ibuprofen
B. Surfactant
c. Propene
D. All of the above


The eye lens has a focal length of \( 2.5 \mathrm{cm} \)
Find the range of accommodation while
changing the focus from infinity to
\( D=25 \mathrm{cm} \)


Which of the following is first example of class Homo sapiens?
A. Neanderthal
B. Dryopithecus
c. cro Magnon
D. Ramapithecus


How much should the pressure on a
litre of water to be changed to compress it by \( 0.10 \% \) ? (Bulk modulus of water,
\( \left.B=2.2 \times 10^{9} N m^{-2}\right) \)


The value of a machine depreciated by
10\% per year during the first two years and \( 15 \% \) per year during the third year. Express the total depreciation of the
machine, as per cent, during the three
years.


A small block of superdene material
has mass \( 2 \times 10^{24} \) kg. It isn't at a
height \( h<<R \). It falls towards earth.
Find its speed when it is at a height \( h / 2 \)
A \( \cdot \sqrt{\frac{2 g h}{3}} \)
в. \( \sqrt{\frac{3 g h}{4}} \)
c. \( \sqrt{\frac{2 g h}{5}} \)
D. \( \sqrt{\frac{g h}{2}} \)


Express the following derived units in terms of the fundamental units of
length, mass and time.
1) Speed
2) Area
3) Acceleration
4) Density
5) Volume


Define an ecosystem. Draw a block diagram to show the flow of energy in an
ecosystem.


The surface temperature of the sun
which has maximum energy emission at \( 500 \mathrm{nm} \) is \( 6000 \mathrm{K} \). The temperature of a star which has maximum energy emission at \( 400 \mathrm{nm} \) will be
\( \mathbf{A} .8500 K \)
в. \( 4500 K \)
c. \( 7500 K \)
D. \( 6500 K \)


The "lock and key" model of enzyme action illustrates that a particular
enzyme molecule
A. May be destroyed and resynthesized several times
B. Interacts with a specific type of substrate molecul
c. Reacts at identical rates under all conditions
D. Forms a permanent enzyme-substrate complex


Find the next one term of the following
sequence: \( 4,7,10,13, \dots \)


A particle executes \( S H M \) of period
\( 1.2 \mathrm{sec} \) and amplitude \( 8 \mathrm{cm} . \) Find the
time it takes to travel \( 3 \mathrm{cm} \) from the
positive extremity or its oscillation.
\( \left[\cos ^{-1}(5 / 8)=0.9 r a d\right] \)
A. 0.28 sec
B. 0.32 sec
c. 0.17 sec
D. 0.42 sec


The criteria for optical isomerism are:
A. the presence of at least one asymmetric carbon is essential
B. the optical rotation is due to asymmetric carbon
C. non-superimposible mirror image
D. all of the above


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{6} \boldsymbol{x}-\boldsymbol{9}+\boldsymbol{8} \boldsymbol{y}=\mathbf{0} \)


Determine the power consumed in the
circuit in \( \mathbf{w} \)


The circuit diagram shows that
resistors \( 2 \Omega, 4 \Omega \) and \( R \Omega \) connected to
a battery of e.m.f. 2 V and
internal resistance \( 3 \Omega \). A main
current of 0.25 A flows through the
circuit. What is the p.d. across the \( R \Omega \)
and \( 2 \Omega \) resistor?
A. \( 0.25 \vee, 0.5 \mathrm{V} \)
B. 0.25 V, 0.25 V
\( c \cdot 2 v, 1 v \)
D. \( 0.5 \vee, 0.25 \)


Statement 1: In both cases shown in
figures tension in the string will be
same

Statement 2: Tension in the light strings shown is the force with which
its ends are pulled
A. Statement 1 - is true, statement- 2 is true and statement-2 is correct explanation of statement-
B. Statement1- is true, statement- 2 is true and statement-2 is NOT the correct explanation of statement-1
c. Statement 1 - is false, statement- 2 is true
D. Statement 1 - is true, statement- 2 is false


\( 0.284 \mathrm{g} \) of an organic substance gave \( 0.287 \mathrm{g} \) of silver chloride in a Carius estimation of halogen. Find out the percentage of chlorine in the compound. \( (A g=108, C l=35.5) \)
A . \( 35 \% \)
B . 25\%
c. \( 30 \% \)
D . 20\%


Pharynx and middle ear are interconnected by
A. Tympanic canal
B. Eustachian canal
c. cochlear canal
D. Vestibular canal


A negative value for this term indicates
that a reaction process will occur spontaneously.
A. Gibbs Free Energy
B. Entropy
c. Enthalpy
D. Calorimetry


Let \( A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right) \) and \( B= \)
\( \left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right), a, b \in N . \) Then:
A. there exists exactly one B such that \( A B=B A \)
B. there exist exactly infinitely many B's such that \( A B= \) \( B A \)
C. there cannot exist any B such that \( A B=B A \)
D. there exist more than one but finite number of B's such that \( A B=B A \)


\( \frac{e^{-2 \sqrt{x}}-y}{\sqrt{x}} \frac{d x}{d y}=1 \)


The quantity of space occupied by a body is its
A. Area
B. Length
c. volume
D. T.S.A.


f \( M=\{x: x \in N, 1<x \leq 4\} \) and
\( N=\{y: y \in W, y<3\} ; \) find \( : N \times M \)
Also find the number of such ordered
pairs.


Assertion
\( P b I_{4} \) doesn't exist and converts into
\( P b I_{2} \) and \( I_{2} \) spontaneously at room
temperature but \( P b C l_{4} \) needs heating
to convert into \( P b C l_{2} \) and \( C l_{2} \)
Reason
\( P b^{2+} \) is more stable than \( P b^{4+} \) due to
inert pair effect.
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 correct but Reason is not correct.


Elements in the same column/group of the periodic table have similar chemical properties because their atoms have the same
A. number of protons
B. number electrons
c. number of valence electrons
D. atomic mass


The equation of a straight line passing through the point of intersection of \( x- \)
\( \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}+\boldsymbol{y}-\mathbf{5}=\mathbf{0} \) and
perpendicular to one of them, is?
A. \( x+y+3=0 \)
в. \( x-y-3=0 \)
c. \( x-3 y-5=0 \)
D. \( x-3 y+5=0 \)


How many coulombs of electricity are required for the oxidation of one mole of
water to dioxygen?
A \( .9 .65 \times 10^{4} C \)
в. \( 1.93 \times 10^{4} C \)
c. \( 1.93 \times 10^{5} \mathrm{C} \)
D. \( 19.3 \times 10^{5} C \)


The height of 30 boys of a class are
given in the following table :
Height in cm Frequency
\[
\begin{array}{ll}
120-129 & 2 \\
130-139 & 8 \\
140-149 & 10 \\
150-159 & 7 \\
150-159 & 3
\end{array}
\]
If by joining a boy of height \( 140 \mathrm{cm}, \) the median of the heights is changed from
\( M_{1} \) to \( M_{2}, \) then \( M_{1}-M_{2}, \) in cm is
A . \( 0 . \)
B . -0.1
c. 0
D. 0.2


A marketing firm determined that, of
200 households surveyed, 80 used
neither Brand A nor Brand B soap, 60
used only Brand A soap, and for every household that used both brands of
soap, 3 used only Brand B soap. How
many of the 200 households surveyed used both brands of soap?
A . 15
B. 20
c. 30
D. 40
E . 45


Assertion
Rate of nitration is \( C_{6} H_{6} \simeq C_{6} D_{6} \simeq \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{T}_{\boldsymbol{6}} \)
Reason
Formation of intermediate is rate
determining step in nitration of
benzene, not the breaking of \( \boldsymbol{C}-\boldsymbol{H} \) or
\( C-D \) bond
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


In a conjugate pair of reductant and oxidant, the reductant has:
A. lower ox. no
B. higher ox. no
\( c . \) same ox. no
D. either of these


f A.M and H.M between two positive
numbers are 27 and 12 respectively find their G.M.


was launched in the
honour of Kalpana Chawla, a space scientist of Indian origin, who died in mishap in a space vehicle. Fill in the blank.
A. INSAT-3E
B. INSAT-3D
c. INSAT-1A
D. INSAT-IID


Write the expressions \( 5 x^{2}-4-3 x^{2}+ \)
\( 6 x+8+5 x-3 \) in its simplified form
Find its value when \( \boldsymbol{x}=-\mathbf{2} \)


Assertion
Catalytic converters must be used in
cars.
Reason
Catalytic converter helps to reduce the
formation of acid rain.
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


Which of the following is the most stable cycloalkane?
A. Cyclopropane
B. Cyclobutane
c. cyclopentane
D. Cyclohexane


Find the point of local maxima \& local
minima of the function
\( \boldsymbol{f}(\boldsymbol{x})=\sin ^{4} \boldsymbol{x}+\cos ^{4} \boldsymbol{x} \boldsymbol{i n}[\mathbf{0}, \boldsymbol{\pi}] \)


Choose the correct answer among the alternatives given :
Identify the figures of the contraceptives given below and select
the correct option.
A. A - Condom for female, B Implant, C CuT, D- condom for male
B. A Implant, B CuT, C - Condom for female, D - condom for male
c. A - condom for male, B CuT, C Implant, D-condom for female
D. A - condom for male, B Implant, C CuT, D- condom for female


The botanical name of Berseem
(Egyptian clover) is
A. Lens esculenta
B. Crotolaria juncea
c. cyamopsis tetragonoloba
D. Trifolium alexandrinum


In a transverse wave the distance
between a crest and neighbouring trough at the same instant is \( 4.0 \mathrm{cm} \) and the distance between a crest and
trough at the same place is \( 1.0 \mathrm{cm} . \) The next crest appears at the same place after a time interval of 0.4 s. The
maximum speed of the vibrating
particles in the medium is:
A \( \cdot \frac{5 \pi}{2} \mathrm{cm} / \mathrm{s} \)
B. \( 2 \pi c m / s \)
c. \( \frac{\pi}{2} \mathrm{cm} / \mathrm{s} \)
D. \( \frac{3 \pi}{2} \mathrm{cm} / \mathrm{s} \)


State True or False.
The process of heating concentrated ore to a high temperature in excess air is called Roasting.State whether it is true
or false
A. True
B. False


Emulsions of polyvinyl acetate are used
in:
A. polishes
B. latex paints
c. fire works
D. rayons


Chloramine-T is a:
A. disinfectant
B. antiseptic
c. analgesic
D. antipyretic


If there are 120 adenine molecules in a
B-DNA double helical structure showing 20 coils, what is the number of
pyrimidine nucleotides forming three hydrogen bonds in it?
\( A \cdot 80 \)
B. 100
\( c \cdot 120 \)
D. 140


The substance not likely to contain
\( \boldsymbol{C a C O}_{3} \) is :
A. calcined gypsum
B. sea shells
c. dolomite
D. a marble statue


How do you convert bromethane into
diethyl ether? Given the chemical equation of the reaction


An electrovalent bond is formed
between
A. Two electronegative atoms
B. Two metals
c. Electropositive and electronegative atoms
D. Two electropositive atoms


What is the minimum value of \( F \) needed
so that block begins to move upward on frictionless incline plane as shown
A \( \cdot M g \tan \left(\frac{\theta}{2}\right) \)
B. \( M g \cot \left(\frac{\theta}{2}\right) \)
c. \( \frac{M g \sin \theta}{(1+\sin \theta)} \)
D. \( M g \sin \left(\frac{\theta}{2}\right) \)


Evaluate \( \sin \left(\frac{\pi}{6}+\cos ^{-1} \frac{1}{4}\right) \)


The processes involved in Bredig's Arc method is/are:
This question has multiple correct options
A. dispersion
B. condensation
c. vapourisation
D. sublimation


Write the expression of following
statement:
5 is taken from \( y \) we get \( x \)


Which is/are used as ligand in
complexes?
A \( . C N \)
в. \( C O \)
c. Both (A) and (B)
D. None of these


The vapour pressure of a dilute aqueous solution of glucose is \( 750 \mathrm{mm} \) of \( \mathrm{Hg} \) at
\( 373 \mathrm{K} \). Calculate molality.


What is obtained when ammonium
dichromate is heated?
A. Nitrogen
B. Oxygen
c. Ammonia
D. None of the above


The principal value of \( \cos ^{-1}\left(-\sin \frac{7 \pi}{6}\right. \)
\( A \cdot \frac{5 \pi}{3 \pi} \)
B. \( \frac{7 \pi}{6} \)
\( c \cdot \frac{\pi}{3} \)
D. none of these


Which is wrong about \( \boldsymbol{O}_{3} \)
A. It is paramagnetic in nature
B. It has a linear structure
c. It decolourizes acidic \( K M n O_{4} \)
D. All


An equilateral triangle and a square have equal perimeters. If side of the triangle is \( 9.6 \mathrm{cm} ; \) what is the length of
the side of the square?
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 3.2 \mathrm{cm} \)
\( c .5 .2 \mathrm{cm} \)
D. \( 7.2 \mathrm{cm} \)


Which of the following contain both ionic and covalent bonds?
A . \( N a O H \)
в. \( K C N \)
c. \( N a_{2} S O_{4} \)
D. All of these


The length of the shortest face diagonal of a cuboid of dimensions \( 5 \mathrm{cm} \times 4 \mathrm{cm} \times \)
\( 3 \mathrm{cm} \) is \( _{--}-_{-}(\text {in } \mathrm{cm}) \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


Which statements are correct about the
figure given.
This question has multiple correct options
\( A \cdot \) It is sucrose
B. Due to presence of hemi-acetal linkage, it is nonreducing sugar
C. Left side unit is \( \alpha \) -D-Glucose and right side unit is \( \beta \) -D-
Fructose
D. Absence of hemi-acetal linkage


Heating a mixture of \( C u_{2} O \) and \( C u_{2} S \)
will give.
A. \( C u O+C u S \)
в. \( C u+S O_{3} \)
c. \( C u+S O_{2} \)
D. \( C u(O H)_{2}+C u S O_{4} \)


Which of the following will give
Hofmann alkene?

This question has multiple correct options
\( \mathbf{A} \)
B.
\( c \)
D.


An alkyl bromide, \( R B r \) of molecular
weight 151 is the exclusive product of bromination of which hydrocarbon?
A. Dodecane
B. 2, 2 - dimethylpropane
c. 2,2 - dimethylhexane
D. 2,2,3 - trimethylheptane


The longest cell in the animal body is a/an
A. osteocyte
B. Neuron
c. Chromatophore
D. Lymph corpuscle


A particle moves according to the
equation \( \boldsymbol{x}=\mathbf{2} \boldsymbol{t}^{2}-\mathbf{5} \boldsymbol{t}+\boldsymbol{6} . \) The average
velocity in the first \( 3 s \) and velocity at
\( t=3 s \) are repectively
A \( \cdot 1 m s^{-1}, 7 m s^{-1} \)
B. \( 4 m s^{-1}, 3 m s^{-1} \)
\( \mathrm{c} \cdot 2 m s^{-1}, 5 m s^{-1} \)
D. \( 3 m s^{-1}, 7 m s^{-1} \)


The solid angle subtended by the total
surface area of a sphere at the centre is
A . \( 4 \pi \)
в. \( 2 \pi \)
\( c . \pi \)
D. \( 3 \pi \)


If \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\sqrt{\mathbf{6}}, \) then \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


Two parallel and opposite forces each \( \mathbf{5 0 0 0} N \) are applied tangentially to the upper and lower faces of a cubical
metal block of side \( 25 \mathrm{cm} . \) The angle of
shear is then
(The shear modulus of the metal is
\( 80 G P a) \)
A \( \cdot 10^{-4} x a d \)
B \( \cdot 10^{-5} r a d \)
c. \( 10^{-6} \)rad
D. \( 10^{-7} r a d \)


Why +3 oxidation state is stable in
heavier elements of Group 15?


what is the formula of
tetrakis(pyridine) platinum(ii) tetraphenyl borate(iii)


toppr
Q Type your question.
radicals with almost equal ease,
whereas bromine free radicals have a
clear preference for the formation of
tertiary free radicals. So, bromine is
less reactive, and more selective
whereas chlorine is less selective and
more effective.
The relative rate of abstraction of
hydrogen by Br is
\( \begin{array}{c}\mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}^{\circ} \\ \mathbf{( 1 6 0 0})\end{array}>\mathbf{( 8 2 )}^{\circ} \)
The relative rate of abstraction of
hydrogen by Cl is \( \mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}_{\mathbf{1}}^{\circ} \)
\( (\mathbf{5}) \)
2,Bromo-2,5,5 trimethyl hexane(x\%)
What is the value of \( x(\% \) yield of
product) \( ? \)
\( \mathbf{A} \cdot 18 \% \)
B. 82 \%
c. \( 90 \% \)
D. 60 \%


\( M n O_{4}^{2-} \) changes to \( M n O_{2} \) into \( M n O_{4}^{-} \) in acidic medium. Calculate equivalent
weight of \( M n O_{4}^{2-} \)
\( \mathbf{A} \cdot 1 M \)
B. \( \frac{1}{2} M \)
\( c \cdot \frac{3}{2} M \)
D. \( 3 M \)


In Cycas, pollination is by
A. Wind
B. Insect
C. Water
D. Both A and B


f \( p(x)=x+3, \) then \( p(3)+p(-3), \) is equal
to
\( A \cdot 3 \)
B . 2
\( c \cdot 0 \)
D. 6


1 Newton \( =K \) dyne, then what is the
value of \( \boldsymbol{K} \) ?
A . 1
B. \( 10^{2} \)
\( c \cdot 10^{5} \)
D. 10


Haloalkane in the presence of alcoholic
KOH undergoes:
A. elimination
B. polymerisation
c. dimerisation
D. substitution


The value of \( \sqrt{-1} \) is
\( A \cdot 1 \)
B. -
c. \( i \) (iota)
D. none of these


Let \( P(n): n^{2}+n \) is an odd integer. It
is seen that truth of \( P(n) \Rightarrow \) the truth of \( P(n+1) . \) Therefore, \( P(n) \) is true for all
\( A \cdot n>1 \)
B.
\( c \cdot n>2 \)
D. None of these


A circular coil carrying a current I has
radius R and number of turns N. If all
the three, i.e., the current I, radius R and number of turns \( \mathrm{N} \) are doubled, then
magnetic field at its centre becomes.
A. Double
B. Half
c. Four times
D. One fourth


A man of mass \( \mathrm{m} \) is applying a
horizontal force to slide a box of mass
\( \mathrm{m}^{\prime} \) on a rough horizontal surface. It is known that the man does not slide. The
coefficient of friction between the shoes
of the man and the floor is \( \mu \) and
between the box and the floor is \( \mu^{\prime} . \) In
which of the following cases it is certainly not possible to slide the box?


The circum centre of the triangle formed by the points (2,5,1),(1,4,-3) and (-2,7,-3) is
A. (6,0,1)
()
В. (0,6,-1)
c. (-1,6,2)
D. (6,1,-2)


A particle of mass m free to move in the x-y plane is subjected to a force whose
components are \( \boldsymbol{F}_{\boldsymbol{x}}=-\boldsymbol{k} \boldsymbol{y} \) and \( \boldsymbol{F}_{\boldsymbol{y}}= \)
\( -k y, \) where \( k \) is a constant. The particle
is released when \( t=0 \) at the point (2,3) Prove that the subsequent motion is simple harmonic along the straight line
\( 2 y-3 x=0 \)


Find the cube root of the number 514
A . 8.0104
B. 8.1104
\( c \cdot 8.2104 \)
D. 8.3104


The principle behind froth floatation is:
A. preferential wetting of ore and gangue particles.
B. difference is specific gravity of ore and gangue particles.
C. magnetic properties of ore and gangue.
D. electrical properties of gangue particles.