\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be such that
\( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|^{2} \leq|\boldsymbol{x}-\boldsymbol{y}|^{3} \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \)
\( R \) then the value of \( f^{\prime}(x) \) is
A \( \cdot f(x) \)
B. constant possibly different from zero
c. \( (f(x))^{2} \)
D.


In a plane perpendicular to the magnetic meridian the dip needle will
remain :
A. Vertical
B. Horizontal
C. At an angle of \( 45^{\circ} \) from horizontal
D. At an angle of \( 60^{\circ} \) from vertical


It has been observed that the ratio of the
molar heat of vaporization of liquid and its normal boiling point is approximately same for most of the liquids (called Trouton's rule). Which of the following does not follow this rule?
A. \( C_{6} H_{6} \)
в. \( C_{6} H_{14} \)
c. \( C C l_{4} \)
D. \( N H_{3} \)


Write the equation for the laboratory preparation of Copper sulphate from copper using sulfuric acid.


If the coefficient of linear expansion of glass is 0.000009 , the coefficient of cubical expansion of glass is :
A . 0.0000027
B. 0.000027
c. 0.00027
D. 0.000018


According to drop model of nucleus which of the following cannot be explained?
A. Fission
B. Fusion
D. All of these


Find the smallest number by which the following number must be divided to obtain a perfect cube 704
A . 1
B. 12
\( c \cdot 14 \)
D. 15


Find the odd one out:
A. Electrodialysis
B. Ion exchange chromatography
C. Reverse osmosis
D. Electrostatic precipitator


The difference between pressure and
stress is
A. pressure and stress have different units
B. pressure and stress have different dimensions
C. Force cannot be determined using stress, but in pressure it can be done
D. Pressured is applied to a body, while stress is induced


Which of the following cyanohydrins on hydrolysis give an optically active acid giving iodoform reaction?
A. Acetone cyanohydrin
B. Propionaldehyde cyanohydrin
c. Acetaldehyde cyanohydrin
D. Formaldehyde cyanohydrin


Dihydrogen reacts with dioxygen \( \left(O_{2}\right) \) to form water. Write the name and formula of the product when the isotope of hydrogen which has one proton and one neutron in its nucleus is treated
with oxygen. Will the reactivity of both the isotopes be the same towards
oxygen? Justify your answer.


If \( a=\frac{1}{3-2 \sqrt{2}}, b=\frac{1}{3+2 \sqrt{2}}, \) then the
value of \( a^{3}+b^{3} \) is
A \( \cdot 194 \)
в. 196
\( c \cdot 198 \)
D. 200


In the given figure, \( A, B, C, D, E \) and \( F \)
represent some stages of hydrosere.
Select the correct statement regarding
these.
A. Hydrilla and Potamogeton occur in stage \( A \); Nymphaea and Nelumbo occur in stage B
B. Phragmites and Typha occur in stage \( C ; \) Carex and Cyperus occur in stage \( \mathrm{D} \)
C. Aluns and Populus occur in stage \( \mathrm{E} \); Acer and Quercus occur in stage \( F \)
D. All of these


Correct order of Acidic strength:
\( A \). iii \( > \) ii \( >i> \) iv
B. i> iii > ii > iv
c. iv \( >i> \) ii \( > \) iii
D. iii \( > \) iv \( >i> \) ii i


The speed of a falling body increases continuously. This is because:
A. No force acts on it
B. It is very light
c. Air exerts a frictional force along the direction of motion
D. The earth attracts it


What is a hydrogen bond?
A. An attraction between a slightly positive hydrogen on one molecule and a slightly negative atom on another molecule.
B. An attraction between a slightly negative hydrogen on one molecule and a slightly positive atom on another molecule.
C. A very weak force within an atom.
D. A weak attraction between the carbon and hydrogen within a molecule.
E. An attraction between a slightly negative hydrogen on one molecule and a slightly positive atom on the same molecule.


Does a substance that heats up quickly
have a high or a low specific heat
capacity?


Match the following.
\( \begin{array}{llll}\text { Sr.no } & \text { Column -I } & \text { Sr.no } & \text { Column -II } \\ \text { A. } & \text { Testosterone } & 1 . & \begin{array}{l}\text { Sexual } \\ \text { contraction } \\ \text { in male }\end{array} \\ \text { B. } & \begin{array}{l}\text { Atrial } \\ \text { natriuretic } \\ \text { factor }\end{array} & \text { 2. } & \begin{array}{l}\text { Decrease in } \\ \text { blood } \\ \text { pressure }\end{array} & \begin{array}{l}\text { Decrease in } \\ \text { liver } \\ \text { glycogen } \\ \text { content }\end{array} & \begin{array}{l}\text { Increases } \\ \text { in } \\ \text { heartbeat }\end{array} & \text { 3. } \\ \text { C. } & \text { Glucagon } & & & \\ \text { D. } & \text { Epinephrine } & \text { 4. } & & \\ & & & \end{array} \)
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-1, B-3, C-2, D-4
C. \( A-3, B-4, C-1, D-2 \)
D. A-3, B-4, C-2, D-1


The height of water in a capillary tube of
radius \( 2 c m \) is \( 4 c m . \) What should be the
radius of capillary, if the water rises to \( 8 c m \) in tube?
A . \( 1 c m \)
B. \( 2 c m \)
\( c .3 c m \)
D. \( 4 c m \)


Tubeless tyres are co-polymers of isoprene and :
A. neoprene
B. silicons
c. isobutylene
D. PAN


The cube of a two digit number may have seven or more digits.
A. True
B. False
c. Insufficient Data
D. None of these


To draw a pair of tangents to a circle which are inclined to each other at an
angle \( 35^{\circ}, \) it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
A . \( 105^{\circ} \)
B. 70
c. \( 145^{\circ} \)
D. \( 150^{\circ} \)


The rainbow and the rainbow-like
colours seen on a thin film of oil on a
water surface are two phenomenon.
They are:
A. Similar in nature and both are due to interference of light
B. Different in nature and rainbow is due to interference of light, while colour of this film is due to diffraction
C. Similar in nature and both are due to refraction of light
D. Different in nature and rainbow is due to refraction, while colour of thin film is dues to interference of light


If \( \tan (A+B)=1, \) and \( \cos (A-B)= \)
\( \frac{\sqrt{3}}{2}, 0^{o}<A+B<90^{\circ} \) and \( A>B ; \) find
\( A \) and \( B \)


Which of the following carboxylic acids undergoes decarboxylation easily?
A. \( C_{6} H_{5} \) СОСН\( _{2} \) СООН
в. \( C_{6} H_{5} \) СОСООН
c. \( C_{6} H_{5} C H-\underset{O H}{_{O H}} \) С ООН
D. \( C_{6} H_{5} \) СНСООН
\( N H_{2} \)


A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \( 15 \mathrm{cm} \) from the lens. If the lens is removed, the point where the rays meet will move \( 5 \mathrm{cm} \) closer to the mounting
that holds. Find the focal length \( (\text { in } \mathrm{cm}) \) of the lens without sign.


Which of the following bodies has the largest kinetic energy?
A. Mass \( 3 M \) and speed \( V \)
B. Mass \( 3 M \) and speed \( 2 V \)
c. Mass \( 2 M \) and speed \( 3 V \)
D. Mass \( M \) and speed \( 4 V \)


Longitudinal waves cannot travel
through
A. Vacuum
B. Solids
c. Liquids
D. Gases


Of the students in a school in a school, it is known that \( 30 \% \) have \( 100 \% \)
attendance and \( 70 \% \) students are
irregular. Previous year results report that \( 70 \% \) of all students who have \( 100 \% \)
attendance attain A grade and \( 10 \% \)
irregular students attain A grade in
their annual examination. At the end of
the year,one student is chosen at
random from the school and he was
found to have an A grade,what is the probability that the student has \( 100 \% \) attendance?


If \( \theta \) is the angle between \( \bar{a} \) and \( \bar{b} \), then \( \frac{|\bar{a} \times \bar{b}|}{\bar{a} \cdot \bar{b}} \) equals
A \( \cdot \tan \theta \)
B. - \( \tan \theta \)
\( c \cdot \cot \theta \)
D. - cot \( \theta \)


A copper wire of length \( 2.2 \mathrm{m} \) and a stee
wire of length \( 1.6 \mathrm{m} \). both of diameter 3.0
\( \mathrm{mm}, \) are connected end to end.When
stretched by a load, the net elongation is found to be \( 0.70 \mathrm{mm} . \) Obtain the load
applied.


Solve: \( \cos ^{2} x-2 \cos x=4 \sin x- \)
\( \sin 2 x, 0 \leq x \leq \pi \)


Pitch of a note depends on its
A. Wavelength
B. Frequency
\( c . \) Both
D. None


Out of the following which has no charge?
A. \( \alpha \) -rays
B. \( \beta \) -rays
c. \( \gamma \) -rays
D. cathode rays


A point \( (\alpha, \beta) \) lies on a circle \( x^{2}+y^{2}= \)
1, then locus of the point \( (3 \alpha+2 \beta) \) is a
/ an.
A. Straight line
B. Ellipse
c. Parabola
D. None of these


Which one of the following statements
is correct?
A. Neurons regulate endocrine activity, but not vice verse
B. Endocrine glands regulate neural activity, and nervous system regulates endocrine glands
C. Neither hormones control neural activity nor the neurons control endocrine activity
D. Endocrine glands regulate neural activity, but not vice versa


Name one source each of D.C and A.C.


The upper end of a wire of radius \( 4 m m \)
and length \( 100 \mathrm{cm} \) is clamped and its other end is twisted through an angle of
30. The angle of shear is:
A . 12
в. 1.2
c. 0.12
D. 0.012


The potential energy of a simple harmonic oscillator of mass \( 2 \mathrm{kg} \) in its mean position is 5 J. If its totalenergy is
\( 9 \mathrm{J} \) and its amplitude is \( 0.01 \mathrm{m}, \) its time period would be
A. \( \pi / 10 \) sec
B . \( \pi / 20 \mathrm{sec} \)
c. \( \pi / 50 \) sec
D. \( \pi / 100 \) sec


\[
\begin{array}{c}
\begin{array}{c}
O \\
C
\end{array}-H \\
H-C_{1}^{\prime} O-H \\
H
\end{array}
\]
Write oxidation No. of each \( C \) atom.


When chlorine gas is passed through an aqueous solution of a potassium halide in the presence of chloroform, a violet
coloration is obtained. On passing more
of chlorine water, the violet color is
disappeared and the solution becomes
colorless. This test confirms the
presence of in aqueous solution.
A. chlorine
B. fluorine
c. bromine
D. iodine


Two wire of same radius and length are subjected to the same load, One wire is of steel and the other is copper. If

Young's modulus of steel is twice that of copper, then the ratio of elastic energy stored per unit volume of steel to that of
copper wire is
A .2: 1
B. 1: 2
\( c \cdot 1: 4 \)
D. 4: 1


Kirchoffs law of junctions is also called the law of conservation of:
A. Energy
B. charge
c. Momentum
D. Angular momentum


When four hydrogen nuclei fuse
together to form a helium nucleus, then
in this process
A. energy is absorbed
B. energy is liberated
c. absorption and liberation of energy depends upon the temperature.
D. energy is neither liberated nor absorbed


\( \cos ^{2} 42^{\circ}-\sin ^{2} 48^{\circ} \)


In the solid state \( P C l_{5} \) exists as:
A \( \cdot\left[P C l_{4}\right]^{-} \) and \( \left[P C l_{6}\right]^{+} \) ions
B. covalent \( P C l_{5} \) molecules only
\( \mathbf{c} \cdot\left[P C l_{4}\right]^{+} \) and \( \left[P C l_{6}\right]^{-} \) ions
D. covalent \( P_{2} C l_{10} \) molecules only


Two plane mirrors are inclined at an
angle \( \theta . \) A ray of light is reflected from the first mirror and is then incident on
the second mirror from which it is again
reflected. What is deviation of incident
ray?
A \( \cdot 360^{\circ}+2 \theta \)
В. \( 360^{\circ}-\theta \)
\( \mathbf{c} \cdot 360^{\circ}-2 \theta \)
D. \( 360^{\circ}+\theta \)


A committee of 4 students is selected
at random from a group consisting of 8 boys and 4 girls. Given that there is at least one girl in the committee, the
probability that there are exactly 2 girls in the committee is
A \( \cdot \frac{168}{4558} \)
B. \( \frac{85}{99} \)
\( \mathbf{c} \cdot \frac{_{5}}{165} \)
D. \( \frac{14}{999} \)


If \( y=\left(\cos ^{-1} x\right)^{2}, \) prove that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-2=0 . \) Hence find \( y_{2} \)
when \( \boldsymbol{x}=\mathbf{0} \)


In which position \( (A, B, C, \text { or } D) \) of
second charge, the flux of the electric
field through the hemisphere remains uncharged? Explain.


Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is prevented by adding:
A. \( N a O H \)
в. \( M n O_{2} \)
c. acetanilide
D. carbon powder


Which of the following is a factor of the
polynomial \( -2 x^{2}+7 x-6 ? \)
A. \( -2 x-3 \)
B. \( 2 x+2 \)
c. \( x-6 \)
D. \( 2 x-2 \)
E . \( -2 x+3 \)


Which of the following is not correctly
matched with its uses?
A. Methanol: As a solvent for paints, varnishes etc.
B. Ethanol: For denaturing spirit, in manufacture of formaldehyde.
C. Ethers: To provide inert medium for chemical reactions, as anaesthetic.
D. All are correctly matched.


If no net force acts on an object, then the velocity of the object:
A. remains same
B. becomes zero
c. increases
D. decreases


List the events that reduce the
biological oxygen demand (BOD) of a primary effluent during sewage
treatment.


Do you think a cell can be called an
organism? Justify


Find the sum of \( \frac{5}{6} \) and \( \frac{11}{13}, \frac{4}{7} \) and \( \frac{-3}{5} \) \( \frac{-7}{4} \) and \( \frac{-3}{7}: \)


When \( C O_{2} \) is bubbled through a solution of barium peroxide in water
then:
A. carbonic acid is formed
B. \( O_{2} \) is released
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \) is formed
D. no reaction occurs


Which of the following factors increase the magnitude of deflection of cathode rays in discharge tube?
A. More charge on the particles
B. Greater interaction with the electric or magnetic field
c. Lesser mass of the particle
D. All of the above


The classification of Linnaeus was
mainly based on
A. Sepals
B. Stem
c. Petals
D. Stamens


Largest ovule in plant kingdom are found in
A . Pinus
B. Cycas
c. Thuja
D. Gnetum


A particle of mass ' \( m^{\prime} \) and charge \( ^{\prime} q^{\prime} \) is accelerated through a potential
difference of \( ^{\prime} V^{\prime} \) volt. Its energy is...
A \( . q V \)
в. \( m q V \)
c. \( \left(\frac{q}{m}\right) v \)
D. \( \frac{q}{m V} \)


Amongs the following which are
correctly matched:

This question has multiple correct options
A. Meta boric acid : \( H B O_{2} \)
B. Mangnaic acid : \( H M n O_{4} \)
C . Xenic acid : \( H_{2} X e O_{4} \)
D. Dithionic acid : \( H_{2} S_{2} O_{6} \)


Why is the freezing chest (or cooling unit) in a refrigerator fitted near the top?


An artillery machine consistently shoots its shells with the same muzzle
speed, so that the maximum range of each shell is \( R \). To hit a target which is
\( \boldsymbol{R} \)
at a distance \( \frac{i c}{2} \) from the gun and at the same level, the elevation angle of the gun should be
A \( \cdot 15^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 60^{\circ} \)


Which one of the following ionic species will impart colour to an aqueous solution?
\( \mathbf{A} \cdot T i^{4} \)
в. \( C u^{+} \)
c. \( Z n^{2+} \)
D. \( C r^{3} \)


Which of the following is a hydrophobic colloidal sol?
A. Barium sulphate sol
B. Arsenious sulphide sol
c. starch sol
D. Silver iodide sol.


(a) What type of battery is the lead storage battery? Write the anode and the cathode reactions and the overal
reaction occurring in a lead storage battery when current is drawn from it.
(b) In the button cell, widely used in watches, the following reaction taken place.
\( Z n(s)+A g_{2} O(s)+H_{2} O(l) \rightarrow \)
\( Z N^{2+}(a q)+2\left(A g(s)+2 O H^{-}(a q)\right. \)
Determine \( E^{o} \) and \( \Delta G^{o} \) for the reaction
(given: \( \boldsymbol{E}_{\boldsymbol{\beta} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}=+\boldsymbol{0 . 8 0} \boldsymbol{V}, \boldsymbol{E}_{Z n^{2+} / Z n}^{o}= \)
\( -0.76 V) \)


Calculate the equilibrium constant for the reaction:
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C u} \boldsymbol{S O}_{4} \rightleftharpoons \boldsymbol{F} \boldsymbol{e} \boldsymbol{S O}_{4}+\boldsymbol{C u} \)
Given, \( \boldsymbol{E}_{\boldsymbol{F e} / \boldsymbol{F e}}^{\boldsymbol{o}}=\mathbf{0 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{C u} / \boldsymbol{C u}^{2+}}^{\boldsymbol{o}}= \)
\( -0.337 V \)


A ball is thrown vertically downwards from a height of \( 20 \mathrm{m} \) with an initial
velocity \( v_{0} . \) It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same
height. The initial velocity \( v_{0} \) is (Take
\( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \mathbf{)} \)
A \( \cdot 10 m s^{-1} \)
B. \( 14 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-1} \)
D. \( 28 m s^{-1} \)


Meiosis occurs in organisms during
A. Sexual reproduction
B. Vegetative reproduction
c. Both sexual and vegetative reproduction
D. None of the above


Meiosis and mitosis differ from each
other because in meiosis
A. The four nuclei formed are not similar to parental ones
B. Homologous chromosomes pair exchange parts
C. Number of chromosomes gets halved
D. All of the above


Assertion : Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in
which the later motion occurs.

Reason: Simple harmonic motion is a uniform motion.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


The range of the function \( \Delta=f(|x|) \) is-
A \( \cdot[0,1] \)
в. [0,1)
c. (0,1]
D. None of these


A man of length \( h \) requires a mirror, to
see his own complete image of length at
least equal to:
\( A \cdot \frac{h}{4} \)
B. \( \frac{h}{3} \)
\( c \cdot \frac{h}{2} \)
D. \( h \)


Two point charges \( +9 q \) and \( +q \) are kept \( 16 \mathrm{cm} \) apart. Where should a third charge \( Q \) be placed between them so that the system remains in equilibrium
\( ? \)
A. \( 24 \mathrm{cm} \) from \( +9 q \)
в. \( 12 \mathrm{cm} \) from \( +9 q \)
c. 24 cm from \( +q \)
D. \( 12 \mathrm{cm} \) from \( +q \)


If \( \tan x=-\frac{3}{4}, \frac{3 \pi}{2}<x<2 \pi, \) then find
\( \cos 2 x \)


The isotopes present in naturally occurring uranium are
\( (i) U-235 \)
\( (i i) U-236 \)
\( (i i i) U-238 \)
\( (i v) U-232 \)
A \( .(i) \) and \( (i i i) \)
B. \( (i) \) and \( (i i) \)
c. \( (i i) \) and \( (i i i) \)
D. (iv) and (ii)


What should be added to \( \frac{1}{x}, \) to make it
equal to \( x ? \)
A. \( \frac{x^{2}-x}{x^{2}} \)
в. \( \frac{x}{x^{2}-1} \)
c. \( \frac{x^{2}+1}{x} \)
D. \( \frac{x^{2}-1}{x} \)


Chemical equilibria is (I) in nature. It occurs in (2)
reactions only. At equilibria, all (3) properties becomes constant. Chemical equilibrium gets affected by change in temperature, pressure, concentration, volume etc but
is not altered by addition of
(4) \( -\dots-\dots-\dots \)
two types (5) and
homogeneous equilibria.
A. (1) dynamic
(2) reversible (3) observable (4) catalyst
(5) homogeneous
B. (1) static
(2) irreversible
(4) reactants
(3) observable
(5) heterogeneous
c. (1) dynamic
(2) irreversible
(3) observable (4) reactants
(5) homogeneous
D. (1) dynamic
(2) reversible
(3) observable
(4) catalyst
(5) heterogeneous


Differentiate
\( -3 x^{2} \cdot\left(\sin 2 x^{3}\right)\left\{\cos \left[\cos ^{2}\left(x^{3}\right)\right]\right\} \)


Diacetone alcohol is also known as
A. 4 -hydroxy butyraldehyde
B. 4 -Hydroxy- 4 -methyl-2-pentanone
c. but-2-en-1-al
D. butan- 2,4 -dione


Rusting of an iron nail is
reaction.
A. Combination
B. displacement
c. decomposition
D. double displacement


The heat of combustion of carbon
(graphite) is not equal to that of carbon(diamond).lf true enter 1 else o
\( A \)


The process of formation of colloidal gel
from calcium silicate and aluminates
is:
A. endothermic
B. exothermic
c. reversible
D. both \( B \) and \( C \)


Rate of effusion of a gas is volume of gas escaping per second. If the statement is true, enter 1 if false
enter 0


The gases which are absorbed by alkaline pyrogallol and carbon tetrachloride are
respectively
A. \( O_{3}, C H_{4} \)
в. \( O_{2}, O_{3} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}, \mathrm{CH}_{4} \)
D. \( N_{2} O_{4}, O_{3} \)


A man of mass \( M \) is standing on a plank kept in a box. the plank and box
as a whole has mass \( \boldsymbol{m} . \) A light string
passing over a fixed smooth pulley
connects the man and box. If the box
remains stationary, find the tension in
the force exerted by the man on the plank.


Three one dimensional mechanical
waves in an elastic medium is given as
and
\( \boldsymbol{y}_{1}=\mathbf{3} \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
\( \boldsymbol{y}_{2}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}+\boldsymbol{\pi}) \)
\( \boldsymbol{y}_{3}=2 \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{k} \boldsymbol{x}) \)
are superimposed with each other. The
maximum displacement amplitude of the medium particle would be
\( A \cdot 4 A \)
B. 3A
c. \( 2 A \)
D. A


Check whether the value given in the brackets is a solution to the given equation or not:
\( \boldsymbol{n}+\mathbf{5}=\mathbf{1 9} \quad(\boldsymbol{n}=\mathbf{1}) \)


In old age, problems like indigestion, constipation and gases are caused because of
A. Number of taste buds decreases
B. Amount of digestive juices decreases
c. Muscular strength reduces
D. All of the above


f \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)+\sin ^{-1}\left(\frac{2 b}{1+a^{2}}\right)= \)
\( 2 \tan ^{-1} x, \) then \( x \) is equal to
A \( \frac{a-b}{1+a b} \)
в. \( \frac{b}{1+a b} \)
c. \( \frac{b}{1-a b} \)
D. \( \frac{a+b}{1-a b} \)


D.E. of family of parabolas symmetrical
about the X-axis is
A \( \cdot y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
B. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)^{2}=0 \)
\( ^{\mathbf{C}}-y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=1 \)
D. \( y^{2} \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=1 \)


The last reactive chlorine is present in:
A. Methyl chloride
B. Allyl chloride
c. Ethyl chloride
D. vinyl chloride


When the terminals of a cell of e.m.f. \( 1.5 v \)
are connected to an ammeter of
resistance \( 4 \Omega, \) the ammeter read 0.30
amp. which of the following statements
is/are correct?
This question has multiple correct options
A. The cell is non-ideal
B. If a \( 4 \Omega \) resistor is also connected across terminals of the cell, the ammeter will read 0.50 amp.
c. If a \( 4 \Omega \) resistor is also connected across terminals of the cell, one-third of the electrical power generated will dissipate as heat within the cell
D. If a voltmeter of resistance \( 4 \Omega \) is used to measure potential difference between terminals of the cell, it will read \( 1.2 \mathrm{v} \)


Which among the following is likely to have the highest levels of DDT
deposition in its body?
A. sea gull
B. Phytoplankton
c. Eel
D. crab


The reagent used in dumas method is:
This question has multiple correct options
A. ferrous acid
B. cuprous oxide
c. ferric oxide
D. cupric oxide


In a spinning top, axis moves around the vertical through its point of contact with the ground sweeping out a cone. This movement of the axis of the top
around the vertical is known as
A. rotation
B. translation
c. procession
D. rolling


Two points \( A \) and \( B \) are located in diametrically opposite directions of a
point charge of \( +2 \mu \mathrm{C} \) at distances \( 2 \mathrm{m} \) and \( 1 \mathrm{m} \) respectively from it. The potential difference between \( A \) and \( B \) is
A. \( 3 \times 10^{3} \vee \)
В. \( 6 \times 10^{4} \mathrm{V} \)
\( \mathbf{c} \cdot-9 \times 10^{3} \mathbf{v} \)
D. \( -3 \times 10^{3} \mathrm{v} \)


Statement - 1
Two vessels \( A \) and \( B \) are connected to
each other by a stopcock. Vessel \( A \)
contains a gas at \( 0^{\circ} \mathrm{C} \) and 1 atmosphere pressure and vessel B is evacuated. The
two vessels are thermally insulated from the surroundings. If the stopcock is suddenly opened, there will be no change in the internal energy of the gas.
Statement - 2
No transfer of heat energy takes place between the system and the surroundings.
A \( \cdot 1) \) Statement - - lis true, Statement - \( \| \) is true; statement
- I is a correct explanation for statement- -
B. 2) Statement - - lis true, statement - - ll is true statement - II is NOT a correct explanation for statement - -
c. 3 statement - 1 is true, statement- - \( \| \) is false
D. 4 statement - - lis false, statement - - II is true


In any triangle, the side opposite to the larger (greater) angle is longer
A. True
B. False


Assertion (A):In Lyman series of Hspectra, the maximum wavelength of
lines is \( 121.56 \mathrm{nm} \)
Reason (R): Wavelength is maximum when the transition is from the very
next level.
A. Both A and R are true and R is the true explanation of
B. Both A and R are true, but R is not the correct explanation of A
c. A is true, but R is false
D. R is true, but A is false


The axis bearing flowers in a spikelet is called?
A. Rachilla
B. Peduncle
c. Receptacle
D. Scape


Name the temperature above which the
formation of micelles takes place. What type of semiconductor is obtained when silicon is doped with arsenic?


Octet rule is not valid for which of the
following molecule?
A. \( C O_{2} \)
в. \( H_{2} \) о
\( c \cdot O_{2} \)
D. \( C O \)


The order of the differentiable equation
associated with the primitive \( \boldsymbol{y}= \)
\( C_{1}+C_{2} e^{x}+C_{3} e^{-2 x+C_{4}} \) where
\( C_{1}, C_{2}, C_{3}, C_{4} \) are arbitrary constants,
is
A . 3
B. 4
\( c \cdot 2 \)
D. None of these


Which of the following coordination compounds will give precipitate with an
aqueous solution of \( A g N O_{3} ? \)
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
B \( \cdot\left[C r\left(N H_{3}\right)_{3}\right] C l_{3} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{4}\right] S O_{4} \)
D. \( N a_{3}\left[C r(C N)_{6}\right] \)


Currents flowing in each of the following
circuits \( A \) and \( B \) respectively are
\( A \cdot 1 A, 2 A \)
B. 2 A, 1 A
\( c \cdot 4 A, 2 A \)
D. 2 A, 4 A


Two balls initially moving in same
direction with speed \( 10 m s^{-1} \) and
\( 5 m s^{-1} \) make a head-on collision. After
collision, they move with speed \( 4 m s^{-1} \)
and \( 6 m s^{-1} \) in the same direction. Coefficient of restitution of collision is :
A . 0.2
B. 0.4
\( c \cdot 0.6 \)
D. 0.8


If \( 4^{x}-4^{x-1}=24, \) then \( (2 x)^{x} \) equals
A . 25
в. 125
\( c \cdot \sqrt{5} \)
\( \mathbf{D} \cdot 25 \sqrt{5} \)


A force of \( 10 \mathrm{N} \) acts on a body for 3
microsecond \( (\mu \mathrm{s}) . \) If mass of the body is \( 6 \mathrm{g} \), calculate the change of velocity.
\( \mathbf{A} \cdot 26 \times 10^{-2} m s^{-1} \)
B . \( 16 \times 10^{-3} \mathrm{m} \mathrm{s}^{-1} \)
C \( .5 \times 10^{-3} \mathrm{m} \mathrm{s}^{-1} \)
D. \( 36 \times 10^{-2} \mathrm{m} \mathrm{s}^{-1} \)


If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated with it would become:
A. Two times
B. Half
c. One fourth
D. Four times


Which of the following triatomic
molecules does not exist?
A. \( C O_{2} \)
в. \( C S_{2} \)
c. \( C S e_{2} \)
D. \( C T e_{2} \)


The temperature, to which a gas must be cooled before it can be liquified by pressure alone, is known as its
A. Saturation point
B. Freezing point
c. Liquification temperature
D. critical temperature


The IUPAC name of
\( \left[\boldsymbol{P t C l}\left(\boldsymbol{N H}_{2} \boldsymbol{C H}_{3}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \boldsymbol{C l} \) is :
A. diamminechloro(methylamine)platinum(II)chloride
B. (dimethylamine)chlorodiamminoplatinum(II)chloride
C. bis(ammine)chloro(methylamine)platinate(II)chloride
D. diaminechloro(mehylamine)platinum(II)chloride


Protein synthesis in an animal cell
takes place
A. Only in the cytoplasm
B. In the cytoplasm as well as in mitochondria
C. In the nucleolus as well as in the cytoplasm
D. Only on ribose attached to nucleus


Type of flame produced by a fuel depends upon
A. calorific value
B. amount of oxygen
c. type of fuel and its chemical composition
D. all of the above


Among the following compounds, which one has maximum boiling point?
A. Propionic acid
B. Ethyl methyl ketone
c. n- butyraldehyde
D. n-pentane


Match the Column-I with Column-II.
Column-I
(i) Depolarisation of
(a) P-wave
(ii) Repolarisation of
(b) QRS complex \( \quad \) ventricles
(iii) Coronary
(c) T-wave
(d) Reduction in the size
(iv) Depolarisation of of T-wave atria
(v) Repolarisation of atria
Select the correct option.
A. (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
B. (a)-(iv), (b)-(i), (c)-(ii), (d)-(v)
\( c \cdot(a)-(i i),(b)-(i),(c)-(v),(d)-(i i i) \)
D. (a)-(ii), (b)-(iii), (c)-(v), (d)-(iv)


Why adolescence is also called
teenage?


The degree of freedom of a three atomic
molecule can not be \( 5 . \) true \( =1, \) false \( =0 \)


Describe physiology of digestion in detail.


If the \( 14^{t h} \) term of an arithmetic series
is 6 and \( 6^{t h} \) term is \( 14, \) then what is the
\( 95^{t h} \) term?
A . -75
B. 75
c. 80
D. - 80


Archegoniate plant belongs to
A. Bryophyta, pteridophyta, gymnosperms, angiosperms
B. Thallophyta, bryophyta, pteridophyta
C. Bryophyta, pteridophyta, angiosperm
D. Bryophyta, pteridophyta, gymnosperm


A ball falls from a height of \( 10 \mathrm{m} . \) On rebounding, it loses \( 30 \% \) energy. The ball goes upto a height of
\( A \cdot 5 m \)
B. 7 \( m \)
\( c \cdot 6 m \)
D. 8 m


13 chambered heart is found in
A. Cockroach
B. Frog
c. Human
D. Fish


If the equilibrium constant of the reaction of weak acid \( \boldsymbol{H} \boldsymbol{A} \) with strong
base is \( 10^{9} \), then \( \mathrm{pH} \) in \( 0.1 M \) NaA is:
A . 5
B. 9
\( c \cdot 7 \)
D.


Match the column \( I \) and \( I I \)


STATEMENT-1: According to kinetic
theory of gases the internal energy of a given sample of an ideal gas is only kinetic.
STATEMENT-2: The ideal gas molecules
exert force on each other only when they
collide.
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


The galvanometer resistance is \( 30 \Omega \) and it is connected to 2 V battery along with a resistance \( 2000 \Omega \) in series. \( A \)
full scale deflection of 25 divisions is
obtained. In order to reduce this
deflection to 20 divisions, the resistance in series should be
A. 2507 \( \Omega \)
в. 2320 \( \Omega \)
c. \( 2180 \Omega \)
D. 2210 \( \Omega \)


Using differential, find the approximate value of the following:
\( \sqrt{401} \)


Give reasons:
On the basis of \( E^{\circ} \) values, \( O_{2} \) gas
should be liberated at anode but it is
\( C l_{2} \) gas which is liberated in the
electrolysis of aqueous NaCl.


One of the difference between blood and
lymph is that
A. Blood has RBCs and WBCs while lymph has Iymphocytes.
B. Blood has RBCs while lymph has no wBCs
c. Blood has WBCs while lymph has RBCs.
D. Blood has dissolved organic salts while lymph has no such inorganic salt.


Which of the following statements regarding the gravitational attraction between man and the earth are correct?
1. The man and the earth pull each other with the same force
2. The earth pulls the man with more
force than the man pulling the earth
3. The acceleration of the man due to
the earth's pull is more than that of the
earth due to the man's pull
4. The accelerations of the man and the
earth are the same
\( A \cdot 2 \) and 3
B. 1 and 4
c. 1 and 3
D. 2 and 4


Hybridisation of silicon atom in silica is
\( A \cdot s p \)
B. \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


The escape velocity for the earth is 11.2 \( \mathrm{km} / \mathrm{s} . \) The mass of another planet 100 times mass of earth and its radius is 4
times radius of the earth. The escape
velocity for the planet is
\( A \cdot 280 \mathrm{km} / \mathrm{s} \)
в. 56.0 km/s
c. \( 112 \mathrm{km} / \mathrm{s} \)
D. 24 km/s


A factory has three machines \( A, B \) and \( C \) which produce 100,200 and 300 items of a particular type daily. The machines produce \( 2 \%, 3 \% \) and \( 5 \% \) defective items respectively. One day when the production was over, an item was picked up randomly and it was found to be defective. Find the probability that it was produced by machine \( A \)


If \( \sin ^{-1} x=\frac{\pi}{5}, \) for some \( x \in(-1,1) \)
then find the value of \( \cos ^{-1} x \)


a) Draw labelled diagram of Standard Hydrogen Electrode (SHE).

Write its half cell reaction of \( \boldsymbol{E}^{o} \) value
b) Calculate \( \triangle r G^{\ominus} \) for the following
reaction:
\( \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{a q})}^{+\mathbf{2}}+\boldsymbol{A} \boldsymbol{g}_{(\boldsymbol{a q})}^{+} \rightarrow \boldsymbol{F e}_{(\boldsymbol{a q})}^{+\mathbf{3}}+\boldsymbol{A} \boldsymbol{g}_{(s)} \)
\( \left(\text { Given }: \boldsymbol{E}_{\text {Cell }}^{0}=+\mathbf{0 . 0 3} \boldsymbol{V}, \boldsymbol{F}=\mathbf{9 6 5 0 0} \boldsymbol{C}\right) \)


An \( \alpha- \) particle passes through a
potential difference of \( 2 \times 10^{6} V \) and
then it becomes incident on a silver foil.
The charge number of silver is \( 47 . \) The energy of incident particles will be (in joules)
A \( .5 \times 10^{-12} \)
B. \( 6.4 \times 10^{-13} \)
c. \( 5.8 \times 10^{-14} \)
D. \( 9.1 \times 10^{-15} \)


What is wattles current?


Warming ammonium sulphate with sodium hydroxide solution gives:
A. ammonia
B. chlorine
c. nitrogen
D. none of these


Which of the following is a Lewis acid?
A. \( B\left(C H_{3}\right)_{3} \)
в. Nah
c. \( N F_{3} \)
D. \( P H_{3} \)


If the angle between two tangents drawn from an external point \( P \) to a
circle of radius a and a center \( O \), is \( 60^{\circ} \)
then find the length of \( O P \)


can removes over \( 99 \% \)
particulate matter present in exhaust from a thermal power plant.


Show that rate of change of
momentum = mass ltimes
acceleration.Under what condition does
this relation hold


\( \left|\begin{array}{ccc}1 & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a}(\boldsymbol{b}+\boldsymbol{c}) \\ \mathbf{1} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{a}) \\ \boldsymbol{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{c}(\boldsymbol{a}+\boldsymbol{b})\end{array}\right|= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot a b c \)
D. \( a b+b c+c a \)


Cohesive force of water is due to
A. 0 -bonds
B. OH - bonds
C. S-bonds
D. H-bonds


Alcohols containing only up to
carbon atoms
are completely miscible with water
A . 10
B. 3
\( c \cdot 8 \)
D. 14


In the given circuit diagram the ratio of
potential difference across 3 ohm and 4
ohm resistance is \( \frac{3}{4} . \) The unknown
resistance \( \boldsymbol{R} \) is:-
A. 8.0 ohm
B. 2.0 ohm
\( c .4 .5 \) ohm
D. 7.0 ohm


Assertion
The variance of first \( n \) natural numbers
is \( \frac{n^{2}-1}{6} \)
Reason
The sum of the first \( n \) odd natural
numbers is \( n^{2} \) and the sum of squares
of first \( n \) odd natural numbers is
\( \frac{n}{3}\left(4 n^{2}-1\right) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A thin horizontal disc of radius
\( \mathrm{R}=10 \mathrm{cm} \mathrm{R}=10 \mathrm{cm} \) is located within a
cylindrical cavity filled with oil whose
viscosity is \( \eta=0.08 P(\text { fig }) . \) The
clearance between the disc and the
horizontal planes of the cavity is equal
to \( h=1 \) mm. Find the power developed
by the angular velocity \( \omega=60 \) rad/s.
The end effects are to be neglected.
\( \mathbf{A} \cdot 8 W \)
В. \( 9 W \)
\( c \cdot 10 W \)
\( \mathbf{D} \cdot 19 W \)


Grass stem elongates by the activity of
A. Secondary meristem
B. Intercalary meristem
C. Apical meristem
D. Primary meristem


Which of the following generations of a monohybrid cross shows that all the individuals are same?
A. Parental
B. \( F_{1} \)
\( c \cdot F_{2} \)
\( D \cdot F_{3} \)
\( E \cdot F_{4} \)


If \( \Delta_{1}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) and \( \boldsymbol{\Delta}_{2}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right| \) then
\( \Delta_{2} \Delta_{1} \) is equal to
\( \mathbf{A} \cdot a c \)
B. \( b d \)
c. \( (b-a)(d-c) \)
D. none of these


Which among the following is an effect of population explosion in India?
A. Pressure on agricultural sector
B. Rising unemployment
c. Environmental degradation
D. All of the above


Two blocks \( A \) and \( B \) of mass \( m_{A}=10 k g \)
and \( m_{B}=20 k g \) are place on rough
horizontal surface. The blocks are
connected with a string. If the coefficient of friction between block \( A \)
and ground is \( \mu_{A}=0.9 \) and between
block B and ground is \( \mu_{B}=0.3, \) find the
tension in the string in situation as
shown in Fig. Forces \( 120 \mathrm{N} \) and \( 100 \mathrm{N} \)
start acting when system is at rest?


The displacement-time graph for the two particles \( A \) and \( B \) are straight lines inclined at angles of \( 30^{0} \) and \( 45^{0} \) with the time axis. What is the ratio of
velocities \( \boldsymbol{v}_{\boldsymbol{A}} \cdot \boldsymbol{v}_{\boldsymbol{B}} ? \)
A \( \cdot 1: 3^{\wedge} 1 / 2 \)
B. 311/2:
\( c \cdot 1: \)
D. none


Use Euclid's division algorithm to find
the H.C.F. of 6265 and 76254


In the figure the arrow head segments
are parallel then find the value of \( x \) and
\( y \)


If \( A=\left[\begin{array}{cr}2 & 5 a \\ -3 & 1\end{array}\right] \) and \( A \) doesn't have multiplicative inverse then find \( \mathbf{A} \)


If the roots of the quadratic equation
\( x^{2}+6 x+b=0 \) are real and distinct
and they differ by atmost 4 then the least value of \( b \) is
A . 5
B. 6
\( c \cdot 7 \)
D. 8


According to the quantum mechanics, correct statements concerning the
electron in the hydrogen atom include
which of the following?
I. It moves in a definite orbit around the
nucleus.
II. It is associated with definite energy
levels.
III lit occupies a fixed position in space with reference to the nucleus
A. \( I \) only
B. II only
C. \( I \) and \( I I I \) only
D. II and III only
E. \( I, I I \) and \( I I I \)


Units of physical quantities can be expressed in terms of fundamental units and such units are called:
A. Fundamental units
B. Derived units
c. Both a and
D. None of the above


A charge \( Q \) is placed inside the sphere of radius \( a \) then electric potential (magnitude) at the surface of the sphere will be, (symbols have their usual meaning)
\( ^{A} \cdot \frac{K Q}{a} \)
в. \( \frac{2 K Q}{a} \)
c. \( \frac{1}{\frac{2}{a}} \)
D.


at very low pressure?
\( A \)
\( B \)
\( c \)
\( D \)


A capillary tube is dipped in water vertically. It is long enough for the water to rise to the maximum height
h in the tube. The length of portion immersed in water is \( 1<\mathrm{h} \). The lower end
of the tube is closed and then the tube
is taken out and opened again. Will all the water flow out of tube? Explain.


Calculate the area enclosed by a circle
of radius \( 0.56 \mathrm{m} \) to the correct number
of significant figures.


State whether the given statement is True or False:

Cow-dung, crop residue, garbage and sewage are decomposed in the absence of oxygen to produce bio-gas.
A. True
B. False


If \( \boldsymbol{x}=\mathbf{2}, \boldsymbol{x}=\mathbf{0} \) are roots of the
polynomials \( f(x)=2 x^{3}-5 x^{2}+a x+ \)
\( b, \) then find the values of \( a \) and \( b \)
A \( \cdot a=2, b=0 \)
В. \( a=7, b=0 \)
c. \( a=3, b=0 \)
D. \( a=1, b=0 \)


If two chords of lengths \( 2 a \) each, of a
circle of radius \( R, \) intersect each other
at right angles then the distance of their point of intersection from the
centre of the circle is
A \( \cdot 2 \sqrt{R^{2}-a^{2}} \)
the \( \sqrt{R^{2}-a^{2}} \)
B . \( \sqrt{2\left(R^{2}-a^{2}\right)} \)
c. \( 4 \sqrt{\left(R^{2}-a^{2}\right)} \)
D \( \cdot 2\left(R^{2}-a^{2}\right) \)


For the same two projectiles, after \( 3 s \) from the initial launch, what will be the
difference between the two projectiles
speeds? The previous problem's text:
A projectile is fired 30.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{1}\right|=\mathbf{4 0 m} / \boldsymbol{s} \)
and a second one 60.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{2}\right|=\mathbf{3 0 m} / \boldsymbol{S} \)
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air
resistance and that they are fired from the same spot, and that each moves independent of the outer projectile. Take \( \boldsymbol{g}=\mathbf{9 . 8 1 m} / \boldsymbol{s}^{2} \)
A. \( 10 \mathrm{m} / \mathrm{s} \)
B. \( 15.4 m / s \)
c. \( 20.5 m / s \)
D. \( 30.0 \mathrm{m} / \mathrm{s} \)
E . \( 35.9 \mathrm{m} / \mathrm{s} \)


A ray of light travels from ethanol into air. If the angle of incidence of the ray at
the boundary is \( 30^{\circ} \) and the refractive
index of ethanol is \( 1.36, \) what is the
angle of refraction of the ray as it
emerges out of ethanol?


The differential equation of a free falling body is governed by the DE \( v \frac{d v}{d x}= \) \( -c x-b v^{2} \).where \( v \) and \( x \) are velocity
and displacement respectively. The velocity of the body is given by the equation \( v^{2}=\frac{c}{2 b^{2}}\left(1-e^{-2 b x}\right)-\frac{c x}{b} \)
A. True
B. False


In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
A \( \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
\( E \cdot 75^{\circ} \)


If a random variable X takes values
\( (-1)^{k} 2^{k} / k ; k=1,2,3, \dots . \) with
probabilities \( \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{k})=\frac{\mathbf{1}}{\mathbf{2}^{k}} \) then
\( E(X)= \)
A \( . \log 2 \)
в. \( \log e \)
c. \( \log \left(\frac{1}{2}\right) \)
D. \( \log \left(\frac{1}{4}\right) \)


A dishonest milkman professes to sell
his milk at cost price but he mixes it
with water and thereby gains \( 20 \% . \) The percentage of water in the mixture is
A . \( 4 \% \)
B . \( 16.66 \% \)
c. \( 20 \% \)
D. \( 25 \% \)


The indicator which shows colour
change in the entire pH range is
A. phenolphthalein
B. methyl orange
c. universal indicator
D. thymol blue


In Fraunhofer diffraction experiment, \( \boldsymbol{L} \)
is the distance between screen and the
obstacle, \( b \) is the size of obstacle and \( A \)
is wavelength of incident light. The general condition for the applicability of Fraunhofer diffraction is
\( ^{\mathrm{A}} \cdot \frac{b^{2}}{L \lambda} \gg 1 \)
B. \( \frac{b^{2}}{L \lambda}=1 \)
c. \( \frac{b^{2}}{L \lambda} \ll 1 \)
D. \( \frac{b^{2}}{L \lambda} \neq 1 \)


A solution is prepared by dissolving \( 5.64 \mathrm{g} \) of glucose in \( 60 \mathrm{g} \) of water. Calculate the molality of the
solution.
A. \( 0.281 \mathrm{m} \)
B. 1.21 \( \mathrm{m} \)
\( c \cdot 1.044 \mathrm{m} \)
D. 0.522 \( \mathrm{m} \)


How many nodal planes are present in \( \delta \) bonding molecular orbital?


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


What do you mean by 'Reflection of light'? State the laws of reflection.


If 8 is a root of the equation \( x^{2}-10 x+ \)
\( k=0, \) then the value of \( k \) is :
A . 2
B. 8
\( c .-8 \)
D. 16


The equation of the plane containing the line \( \frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1} \)
and the point (0,7,-7) is
A. \( x+y+z=0 \)
в. \( x+y+z=2 \)
c. \( x+y+z=1 \)
D. None of these


Hofmann's bromamide reaction is to
convert:
A. acid to alcohol
B. alcohol to acid
c. amide to amine
D. amine to amide


Which of the following species does not
show aromaticity?
\( \mathbf{A} \)
B.
\( c \)
D.


The number of molecules in \( 22.4 \mathrm{cm}^{3} \) of
nitrogen gas at STP is
A \( .6 .023 \times 10^{20} \)
В. \( 6.023 \times 10^{23} \)
c. \( 22.4 \times 10^{20} \)
D. \( 22.4 \times 10^{23} \)


Which of the following structure of a molecule is expected to have three bond pairs and one loan pair of electrons?
A . Octahedral
B. Trigonal planar
c. Pyramidal
D. Tetrahedral


Find \( V_{b a} \) if \( 12 J \) of work has to be done
against an electric field to take a
charge of \( 10^{-2} C \) from \( a \) to \( b \)
A . \( 1000 V \)
B. 1200V
c. \( 1100 V \)
D. 2400V


A battery has four cells in parallel, each has an e.m.f \( 1.5 V \) and internal
resistance \( 0.8 \Omega . \) The current delivered
by it to a load of \( 2.8 \Omega \) is
A. \( 0.2 A \)
B. 0.4A
c. \( 0.5 \mathrm{A} \)
D. \( 0.6 A \)


Which molecule has no unshared
electron pairs?
A. \( H_{2} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( C O_{2} \)
E. \( N H_{3} \)


What is the IUPAC name of the following
compound?
A. 3,4-Dimethyl-1-pentene-3-01
B. Isopropyl-3-methyl vinyl carbinol
c. 2,3-Dimethyl-4-pentene-3-ol
D. None of the above


A man sells an article at a profit of \( 25 \% \)
If he had bought it at \( 20 \% \) less and sold
it for \( R s .38 .75 \) less, he would have
gained \( 30 \% \). Find the cost price of the article.


Find the fundamental frequency and the next three frequencies that could cause a standing-wave pattern on a string that is \( 30.0 \mathrm{m} \) long, has a mass per unit length of \( 9.00 \times 10^{-3} k g / m \) and is
stretched to a tension of \( 20.0 \mathrm{N} \)


Describe the structure of the common
form of ice.


Dehydration of formic acid gives:
A. \( O_{2} \)
в. \( H_{2} \)
\( c \cdot c o \)
D. none of these


When a few drops of dilute hydrochloric acid are added to silver nitrate solution,
then what product will be formed?


Evaluate: \( \lim _{x \rightarrow 0} x^{2} \)


A body has a charge of one coulomb. The
number of excess (or lesser) electrons
on it from its normal state will be :
\( A \cdot \infty \)
B . \( 1.6 \times 10^{-19} \)
\( \mathbf{c} \cdot 1.6 \times 10^{19} \)
D. \( 6.25 \times 10^{18} \)


A small planet is revolving around a very massive star in a circular orbit of
radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to \( R^{-5 / 2}, \) then \( T \) would be proportional to
A \( \cdot R^{3 / 2} \)
B. \( R^{3 / 5} \)
c. \( R^{7 / 2} \)
D. \( R^{7 / 4} \)


An Evoked Potential Studies (EPS) enables us to
A. Evaluate different sensory functions
B. Detect clinically silent tensions
c. Study hearing and vision in children
D. All of the above


A cross section at the midpoint of the middle piece of a human sperm will
show
A. Centriole, mitochondria and \( 9+2 \) arrangement of microtubules
B. Centriole and mitochondria
c. Mitochondria and \( 9+2 \) arrangement of microtubules
D. 9+2 arrangement of microtubules only


An element \( X \) belongs to group III-A and 4 th period in the periodic table. Find out
the atomic numbers of \( X \) and the
element which is placed just below \( \boldsymbol{X} \) in the periodic table.


A thin uniform rod of length \( L \) is bent at
its midpoint as shown in the figure. The distance of the center of mass from the
point \( ^{\prime} \boldsymbol{O}^{\prime} \) is
A \( \cdot \frac{L}{2} \cos \frac{\theta}{2} \)
B. \( \frac{L}{4} \sin \frac{\theta}{2} \)
c. \( \frac{L}{4} \cos \frac{\theta}{2} \)
D. \( \frac{L}{2} \sin \frac{\theta}{2} \)


The rate of is more than the
rate of \( _{--}-_{--} \) in the daytime in the
case of green plants.


What do you mean by magnetic flux?


Causes of air pollution are:
i. Exhaust from automobiles
ii. Exhaust from factories and power
plant
iii. CFCs
iv. Polythene
\( A \). i, ii, ii i
B. ii, iii, iv
c. iii, iv,
D. i, ii in


Which is the strongest base among the
following?
\( \mathbf{A} \cdot L a(O H)_{3} \)
В. \( L u(O H)_{3} \)
\( \mathbf{c} \cdot \operatorname{Ce}(O H)_{3} \)
D. \( Y b(O H)_{3} \)


Three candidates, Ajay, Bijoy \& Chandu contested an election and received
1800,3300 and 3900 votes respectively. What percent of the total votes did get?


f \( x=\tan \left(\frac{1}{a} \log y\right), \) prove that \( (1+ \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}+2 x \frac{d y}{d x}-a 0 \)


Which one of the following substances is a mixture?
A. water
B. copper
c. Seawater
D. salt


If \( y_{1}(x) \) is a solution of the differential equation \( \frac{d y}{d x}+f(x) y=0, \) then \( a \) solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{y}=\boldsymbol{r}(\boldsymbol{x}) \) is
A \( \cdot \frac{1}{y(x)} \int y_{1}(x) r(x) d x \)
B. \( y_{1}(x) \int \frac{r(x)}{y_{1}(x)} d x \)
c. \( f r(x) y_{1}(x) d x \)
D. None of these


There are 2 red and 2 yellow flowers in a
basket. A child picks up at random three flowers. What is the probability of picking up both the yellow flowers?


\( 20 \mathrm{ml} \) of \( 0.2 \mathrm{M} H C N \) mix with \( 10 \mathrm{ml} \) of
0.2 M \( N a O H, \) then calculate \( p H \) of resulting mixture, \( p K a \) value of \( H C N \)
is \( 5:- \)
A . 6
B. 7.5
\( c .5 \)
D. 11


The hole in a p-type semiconductor is
A. an electron deficiency
B. an electron excess
c. an atom deficiency
D. positive ion


An \( \alpha- \) particle passes through a
potential difference of \( 2 \times 10^{6} V \) and
then it becomes incident on a silver foil.
The charge number of silver is 47. The
distance of closest approach of the particle to the nucleus will be:
A. \( 6.4 \times 10^{-13} \mathrm{m} \)
B. \( 4.3 \times 10^{-13} \mathrm{m} \)
c. \( 2.1 \times 10^{-13} m \)
D. \( 3.76 \times 10^{-15} \mathrm{m} \)


Calculate the area of cross section of a
wire of length \( 2 m, \) resistance \( 46 \Omega \) and
resistivity \( 1.84 \times 10^{-6} \Omega m \)


Velocity of particle moving along a
straight line at any time \( t \) is given by \( v=\cos \left(\frac{\pi}{3} t\right) . \) The distance travelled by the particle in the first two seconds is equal to
A \( \cdot \frac{\sqrt{3}}{2 \pi} \)
B. \( \frac{3 \sqrt{3}}{2 \pi} \)
\( c \cdot \frac{3 \sqrt{3}}{\pi} \)
D. zero


A particle of mass \( 0.3 \mathrm{kg} \) is subjected to a force \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) with \( \mathbf{k}=15 \mathrm{N} / \mathrm{m} . \) What
will be its initial acceleration if it is
released from a point \( x=20 \mathrm{cm} ? \)


When an impurity is doped into an intrinsic semiconductor, the
conductivity of the semiconductor
A . increases
B. decreases
c. remains the same
D. becomes zero


A charge \( +10^{-9} C \) is located at the origin in free space and another charge
\( Q \) at \( (2,0,0) . \) If the \( X \) -component of the electric field at (3,1,1) is zero, calculate the value of \( Q . \) Is \( Y- \) component zero at (3,1,1)\( ? \)


Which hydride among the following is strongest reducing agent?
A. \( A s H_{3} \)
в. \( B i H_{3} \)
c. \( P H_{3} \)
D. \( S b H_{3} \)


Select the correct statement:
This question has multiple correct options
A. The value of compressibility factor \( ^{\prime} Z^{\prime} \) for \( H_{2} \) gas is greater than one at room temperature and pressure
B. The real gas behaves as an ideal gas at Boyle's temperature.
C. For a real gas following van der Waals' equation of state, the expression of critical temperature is \( \frac{8 a}{27 R . b} \)
D. At low pressure, the compressibility factor \( ^{\prime} Z^{\prime}=1+ \)
\( \frac{P . b}{R T} \) for a van der Waals' gas


If \( \int \sin ^{-1} x \cos ^{-1} x d x= \)
\( \boldsymbol{f}^{-1}(\boldsymbol{x})\left[\frac{\boldsymbol{\pi}}{2} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{f}^{-1}(\boldsymbol{x})-\boldsymbol{2} \sqrt{1-\boldsymbol{x}^{2}}\right] \frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
\( 2 x+C, \) then
A \( \cdot f(x)=\sin x \)
B . \( f(x)=\cos x \)
c. \( f(x)=\tan x \)
D. None of these


Simplify the expression: \( t^{2}-59 t+ \)
\( 54-82 t^{2}+60 t \)
\( \mathbf{A} \cdot-26 t^{2} \)
B . \( -26 t^{6} \)
c. \( -81 t^{4}+t^{2}+54 \)
D. \( -81 t^{2}+t+54 \)


Under which of the following conditions is the relation,
\( \Delta H=\Delta U+P \Delta V \) valid for closed
system?
A. constant pressure
B. Constant temperature
c. constant temperature and pressure
D. constant temperature, pressure and composition


A lamp consumes only \( 50 \% \) of maximum power applied in an AC circuit. What will be the phase difference between applied voltage and circuit current?
A \( \cdot \frac{\pi}{3} r a d \)
B. \( \frac{\pi}{6} r a d \)
c. \( \frac{\pi}{4} r a d \)
D. \( \frac{\pi}{2} r a d \)


Assertion
When radius of a circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason
Magnetic moment depends on the area of the loop.
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


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \log _{\boldsymbol{b}} \boldsymbol{a} \\ \log _{\boldsymbol{a}} \boldsymbol{b} & \mathbf{1}\end{array}\right] \) then \( |\boldsymbol{A}| \) is equal
to
A. 0
B \( \cdot \log _{a} b \)
\( c \cdot-1 \)
\( \mathbf{D} \cdot \log _{b} a \)


The ratio of the energies of the hydrogen atom in its first to second excited state
is
A \( \cdot 1 / 4 \)
в. \( 4 / 9 \)
c. \( 9 / 4 \)
D.


The redox reaction involving the reducing power of hydrogen sulphide is:
\[
\begin{array}{c}
\boldsymbol{S}+\mathbf{2} \boldsymbol{H}^{+}+\mathbf{2} \boldsymbol{e}^{-} \rightarrow \\
\boldsymbol{H}_{2} \boldsymbol{S}, \quad \boldsymbol{E}_{\boldsymbol{S} / \boldsymbol{H}_{2} \boldsymbol{S}}^{\circ}=+\mathbf{0 . 1 4} \boldsymbol{V}
\end{array}
\]
Two other half equations are:
\[
\boldsymbol{F} e^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} \quad \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}^{\mathrm{O}}=
\]
\[
\begin{array}{l}
+\mathbf{0 . 7 7} V \\
B r_{2}+2 e^{-} \rightarrow 2 B r^{-} \quad E_{B r_{2} / B r^{-}}^{0}=
\end{array}
\]
\( \mathbf{1 . 0 7} V \)
Under standard conditions, hydrogen sulphide reacts with iron \( (I I I) \) ions If this statement is true enter 1 , else
enter 0


Global warming is due to the increase
of:
A. methane and nitrous oxide in atmosphere
B. methane and \( C O_{2} \) in atmosphere
c. methane and \( O_{3} \) in atomsphere
D. methane and co in atmosphere


Solve:
\( x^{11} \div x^{15} \)


The isothermal diagram of a gas at
three different temperatures \( T_{1}, T_{2} \)
and \( T_{3} \), is shown in the given figure.
Then
A \( \cdot T_{1}<T_{2}<T_{3} \)
в. \( T_{1}<T_{2}>T_{3} \)
c. \( T_{1}>T_{2}>T_{3} \)
\( \Omega_{1}>T_{2}<T_{3} \)


Show dimensionally that the expression, \( \boldsymbol{Y}=\frac{\boldsymbol{M} \boldsymbol{g} \boldsymbol{L}}{\boldsymbol{\pi} \boldsymbol{r}^{2} \boldsymbol{l}} \) is
dimensionally correct, where Y is Young's modulus of the material of wire,
Lis length of wire, Mg is the weight applied on the wire and I is the increase in the length of the wire.


The area of a triangle is computed using the formula \( S=\frac{1}{2} b c \sin A . \) If the relative errors made in measuring b, \( c \) and calculating \( \mathrm{S} \) are respectively 0.02
0.01 and 0.13 the approximate error in \( A \) when \( A=\pi / 6 \) is
A . 0.05 radians
B. 0.01 radians
c. 0.05 degree
D. 0.01 degree


The compound \( Y \) is:
A. 1,3 - dichloro benzene
B. benzyl chloride
\( \mathrm{C} \cdot 1,3,5- \) trichloro benzene
D. mixture of 1,2 and 1,4 dichlorobenzene


A process employed for the concentration of sulphide ore is:
A. froth floatation
B. gravity separation
c. froth separation
D. gravity floatation


Find diameter \( \& \) circumference with
radius \( 7.7 \mathrm{cm} \)


The compound will show
A. geometrical isomerism
B. optical isomerism
C. geometrical and optical isomerism
D. neither geometrical nor optical isomerism


Find the number of triangles whose vertices are at the vertices of an
octagon but none of whose sides happen to come from the octagon.


State whether true or false.
A ray of light which emerges after bouncing off the surface of a mirror is called an incident ray.
A. True
B. False


The largest planet of the solar system is
A. Jupiter
B. Mars
c. Neptune
D. None of the above


Commonly used heating element are
made of:
A. Iron
B. Manganese
c. Nichrome
D. Platinum


The expression for de Broglie wavelength is :
A \( \cdot p=\frac{h}{\lambda} \)
в. \( p=\frac{h}{2 \lambda} \)
c. \( _{p}=\frac{2 \pi}{h \lambda} \)
D. \( p=\frac{2 \pi}{\lambda} \)


Find the equation of a straight line:
with slope -2 and intersecting the \( x- \)
axis at a distance of 3 units to the left
of origin.


The equation of a travelling wave is given by \( \boldsymbol{y}=\mathbf{1 0} \cos \left[\frac{\boldsymbol{\pi} \boldsymbol{t}}{\mathbf{3}}+\boldsymbol{\alpha}\right] . \) If the
displacement is \( 10 \mathrm{cm} \) at \( t=0, \) then the
total phase at \( t=1.5 s \) will be
A \( \cdot\left(\frac{2 \pi}{3}\right) r a d \)
в. \( (2 \pi) \) rad
c. \( \left(\frac{\pi}{3}\right) r a d \)
D. \( \left(\frac{2 \pi}{6}\right) r a d \)


A thin prism angle \( 3^{\circ} \) deviates a ray of
light through \( 2^{\circ} \) while passing through
it find the refractive index of the
material of the prism?


Electricians wear rubber gloves
because:
A. it is soft
B. it is water proof
c. it is an insulator
D. it is inexpensive


A box contains 1 red and 3 identica
white balls. Two balls are drawn at
random in succession without
replacement. Write the sample space for this experiment.


The equations of the line of intersection
of the planes \( x+y+z=2 \) and \( 3 x- \)
\( \boldsymbol{y}+\mathbf{2} z=\mathbf{5} \) in symmetric form are
A \( \frac{x-\frac{7}{4}}{4}=\frac{y-\frac{1}{4}}{-1}=\frac{z}{-3} \)
B. \( \quad \frac{x}{3}=\frac{y+\frac{1}{3}}{1}=\frac{z-\frac{7}{4}}{-4} \)
c. \( \frac{x}{1}=\frac{3 y+1}{1}=\frac{3 z-7}{-4} \)
D. none of these


\( \int \frac{(x+3) e^{x}}{(x+4)^{2}} d x= \)


Soaps are:
A. sodium or potassium salts of higher fatty acid
B. esters of higher fatty acids
C . glycerides of fatty acids
D. hydrides of fatty acids


Solve \( \cos (\sin \theta)=\sin (\cos \theta) \)


Divide and write the quotient and
remainder.
(a) \( \left(y^{2}+10 y+24\right) \div(y+4) \)
(b) \( \left(p^{2}+7 p-5\right) \div(p+3) \)


The IUPAC name of the given compound
is :
A. 3 -Phenyl-4-methylhexene
B. 3-Phenyl-4-methylhexane
c. 3 -Phenyl- -4-methylhex-2-ene
D. 4 -methyl- - -phenylhexene


State Snells law.
Calculate the velocity of light in a glass block of refractive index 1.5
(Velocity of light in air \( \left.=3 \times 10^{8} m s^{-1}\right) \)


The type of hybridization in \( B \) of \( B_{2} H_{6} \)
is:
\( A \cdot s p^{2} \)
B . \( s p^{3} \)
\( c \cdot s p \)
D. \( d s p^{2} \)


Two triangles are similar, if their corresponding angles of two triangles areequal and corresponding sides are in the same ratio. Is it true?
A. Yes
B. Not of same size
c. Not sure
D. cannot be possible


A horizontal rod of \( 0.200 \mathrm{m} \) long is mounted on a balance and carries a
current. At the location of the rod a
uniform horizontal magnetic field has magnitude \( 0.067 \mathrm{T} \) and direction perpendicular to the rod.The magnetic
force on the rod is measured by the balance and is found to be 0.13 N. The
current is \( 970 \times 10^{-x} \) A. Find \( x \)


A child is sitting on a swing. Its minimum and maximum heights from
the ground are \( 0.75 m \) and \( 2 m \) respectively, its maximum speed will be:
A. \( 5 m / s \)
в. \( 8 m / s \)
c. \( 10 m / s \)
D. \( 15 \mathrm{m} / \mathrm{s} \)


If you set up the seventh harmonic on a string fixed at both ends, how many nodes and antinodes are set up in it.
\( A \cdot 8,7 \)
в. 7,7
c. 8,9
D. 9,8


A parallelepiped is formed by planes
drawn through the point \( P(6,8,10) \) and
\( Q(3,4,8) \) parallel to the coordinate
planes. Find the length of edges and edges and diagonals of the
parallelepiped.


The Rydberg constant for Hydrogen is \( 1.097 \times 10^{7} m^{-1} . \) Calculate the short
wavelength limit of Lyman series.


Two circular coils can be arranged in
any of the three situations shown in the
figure. Their mutual inductance will be
A. maximum in situation \( (a) \)
B. maximum in situation \( (b) \)
C. maximum in situation \( (c) \)
D. the same in all situations


Find the maximum or minimum value
of the quadratic expression \( 2 x-7- \)
\( 5 x^{2} \)


Photoelectric effect supports the
quantum nature of light because
This question has multiple correct options
A. There is minimum frequency of light below which no photoelectrons are emitted
B. The maximum KE of photoelectrons depends only on the frequency of light and not on its intensity
C. Even when the metal surface is faintly illuminated by light of wavelength less than the threshold wavelength, the photoelectrons leave the surface immediately
D. Electric charge of photoelectrons is quantized


If \( \cos \alpha+\cos \beta+\cos \gamma=0=\sin \alpha+ \)
\( \sin \beta+\sin \gamma \) then \( \cos 2 \alpha+\cos 2 \beta+ \)
\( \cos 2 \gamma \) equals
A. \( 2 \cos (\alpha+\beta+\gamma) \)
B. \( \cos 2(\alpha+\beta+\gamma) \)
\( c \cdot 0 \)
D.


To determine whether a water solution
of \( N a_{2} S_{2} O_{3} \) at room temperature is
supersaturated, one can :
A. heat the solution to its boiling point
B. add water to the solution
c. add a crystal of \( N a_{2} S_{2} O_{3} \) to the solution
D. acidify the solution
E. cool the solution to its freezing point


When the current in the inductor has
half its maximum value, what is the charge on the capacitor?
A \( \cdot 1.33 \times 10^{6} C \)
B. \( 9.33 \times 10^{-6} C \)
\( \mathbf{c} \cdot 4.33 \times 10^{-6} C \)
D. \( 7.33 \times 10^{6} C \)


Which of the following compound has maximum number of primary H-atoms?
A \( . C H_{4} \)
в. \( C H_{3}-C H_{2}-C H_{3} \)
D. \( C\left(C H_{3}\right)_{4} \)


Two electric charges \( q \) and \( -2 q \) are placed at a distance 3a apart. The locus of points in the plane of the charges where the field potential is zero is:
A. straight line
B. circle
c. ellipse
D. hyperbola


An electron of mass \( M_{e}, \) initially at rest moves through a certain distance in a uniform electric field in time \( t_{1} . A \)
proton of mass \( M_{p} \) also intially at rest,
takes time \( t_{2} \) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio \( t_{2} / t_{1} \) is nearly equal to:
A . 1
в. \( \sqrt{\frac{M_{p}}{M_{e}}} \)
c. \( \sqrt{\frac{M_{e}}{M_{p}}} \)
D. 1836


The sum of the cubes of three
consecutive natural numbers is
divisible by
A. 7
B. 9
\( c \cdot 25 \)
D. 26


Two diametrically opposite points of a metal ring are connected to terminals of
the left gap of meter bridge. In the right gap, resistance of \( 15 \Omega \) is introduced. If
the null point is obtained at a distance
of \( 40 \mathrm{cm} \) from the left end, find
resistance of the wire that is bent in the
shape of the ring.


If 1 is a zero of the polynomial \( p(x)= \)
\( a x^{2}-3(a-1) x-1, \) then find the
value of \( \boldsymbol{a} \)


Spectrum of sunlight is an example for
A. Band emission spectrum
B. Line absorption spectrummmmm
c. continuous emission spectrumm
D. continuous absorption spectrum


Which one of the following pairs is not
correctly matched?
A. Recombinant DNA - DNA formed by the joining of segments of DNA from different sources
B. Purine - Nitrogenous bases cytosine, thymine and uracil
C. ATP - The principal energy carrying compound in the cell
D. r-RNA - RNA molecules found in ribosomes


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


\( \int \frac{d x}{x^{2}+2 x+2}=f(x)+c \Longrightarrow f(x)= \)
A \( \cdot \tan ^{-1}(x+1) \)
B. \( 2 \tan ^{-1}(x+1) \)
c. \( -\tan ^{-1}(x+1) \)
D. \( 3 \tan ^{-1}(x+1) \)


Which component obtained from the refining of petroleum is used as a solvent in petrochemicals?
A. Tar
B. Kerosene
c. Naphtha
D. Petroleum coke


What is the value of \( \sqrt[3]{-8}-\sqrt[3]{-216} ? \)
A . -8
B. -4
\( c \cdot 4 \)
D.


Under which of the following conditions is the relation,
\( \triangle \boldsymbol{H}=\triangle \boldsymbol{U}+\boldsymbol{P} \triangle \boldsymbol{V} \) valid for a closed
system?
A. constant pressure
B. Constant temperature
c. constant temperature and pressure
D. constant temperature, pressure and composition


Air is not visible because it:
\( \mathbf{A} \cdot \) is nearly a perfectly transparent substance
B. neither absorbs nor reflects light
C. transmits whole of light
D. follows all of the above


Represent the following mixed infinite decimal periodic fractions as common
fractions:
\( \left(\frac{\boldsymbol{P}^{3 / 2}+\boldsymbol{q}^{3 / 2}}{\boldsymbol{p}-\boldsymbol{q}}-\frac{\boldsymbol{p}-\boldsymbol{q}}{\boldsymbol{P}^{1 / 2}+\boldsymbol{q}^{1 / 2}}\right)\left(\sqrt{\boldsymbol{p} \boldsymbol{q}} \frac{\sqrt{\boldsymbol{p}}}{\boldsymbol{p}}\right. \)


Soft drinks bottles and baby feeding bottles are generally made up of
A. polyester
B. polyurethane
c. polystyrene
D. polyamide


If \( a>0 \) and \( z|z|+a z+2 a=0, \) then \( z \)
must be
A. purely imaginary
B. a positive real number
c. a negative real number
D. having positive imaginary part


In which case of a moving body, force is not needed?
A. To increase the speed of the body
B. To decrease the momentum of the body
c. To change the direction of motion
D. To keep the body in uniform velocity


We can cook pulses easily in hard water
A. True
B. False


\( \left(4 l^{5}-6 l^{4}+8 l^{3}\right) \div 2 l^{2} \)
A \( \cdot\left(2 l^{2}-3 l+4\right) \)
B \( \cdot l\left(2 l^{2}-3 l+4\right) \)
c. \( l\left(2 l^{2}-3 l+3\right) \)
D. None


A line coming from point (3,4) is
reflected on a point A of x-axis and it
passes through point (1,8) then
coordinate of point A is
A \( \cdot(7 / 3,0) \)
В \( \cdot(5,0) \)
C \( \cdot(29 / 3,0) \)
D \cdot \( (9 / 2,0) \)


The disk has a weight of \( 100 \mathrm{N} \) and rolls without slipping on the horizontal surface as it oscillates about its
equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the
equation which describes its oscillatory motion when it is released.
A \( \cdot \theta=-0.2 \cos (16.16 t) \)
B \( \cdot \theta=0.2 \cos (16.16 t) \)
c. \( \theta=-0.4 \cos (16.16 t) \)


The equation of plane passing through (-1,0,-1) parallel to \( x z \) plane is
В. \( y=0 \)
c. \( -x-z=0 \)
D. None of the above


Derive following equations for a uniformly accelerated motion where the symbols have their usual meanings:
\( \boldsymbol{v}=\boldsymbol{u}+\boldsymbol{a} \boldsymbol{t} \)


If \( \lim _{x \rightarrow 0^{+}} \frac{2}{x^{1 / 5}}=a \) then \( \frac{1}{a} \) is equal
to


\( \mathbf{1} \boldsymbol{g} \boldsymbol{f}= \)
A. 980 dyne
B. 98 dyne
c. 9.8 dyne
D. 0.98 dyne


The measure of the external angle of a
regular octagon is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 6 \)
c. \( \pi / 8 \)
D. \( \pi / 12 \)


Write the chemical reaction of
chloroform with the following:
(i)Silver powder
(ii)Concentrate \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
(iii)Acetone
(iv)Alkaline Solution of phenol


If (-4,0),(0,3),(0,-3) are the vertices
of a triangle, then find the shape of the triangle.
A. isosceles
B. equilateral
c. scalene
D. None of these


Electric Fuse wire is working on principle.
A. control of voltage in circuit
B. chemical effect of electric current
C. control of current in circuit
D. heating effect of electric current


gas turns colourless nitrogen monoxide into brown fumes of
nitrogen dioxide.


The potential difference between points A and B of adjoining figure is :
0
A. \( 2 / 3 V \)
B. \( 8 / 9 V \)
c. \( 4 / 3 V \)
D. \( 2 V \)


A beam of light of wavelength 600 nm from a distant source falls on a single
slit \( 1.00 m m \) wide and the resulting
diffraction pattern is observed on a
screen 2 m away. The distance between
the first dark fringe on either side of the central maxima is :
A \( .1 .2 \mathrm{cm} \)
B. \( 1.2 \mathrm{mm} \)
\( c .2 .4 m m \)
D. \( 4.8 \mathrm{mm} \)


For the reaction: \( 2 H I \rightarrow H_{2}+I_{2} \). the
expression \( \frac{-1}{2} \frac{d(H I)}{d t} \) represents:
A. the rate of formation of \( H I \)
B. the rate of disappearance of \( H I \)
c. the instantaneous rate of the reaction
D. the average rate of reaction


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \mid \begin{array}{ccc}\sin x+\sin 2 x+\sin 3 x & \sin 2 x & \sin 3 x \\ 3+4 \sin x & 3 & 4 \sin x \\ 1+\sin x & \sin x & 1\end{array} \)
then the value of \( \int_{0}^{\frac{\pi}{2}} f(x) d x, \) is
A . 3
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{3} \)
D.


Prove that :
\( 3 \cos ^{-1} x=\cos ^{-1}\left(4 x^{3}-3 x\right) \)


Write an expression for the kinetic energy of an object.


If the charge \( +Q \) is now at the centre of
a cube of side \( 2 l \), what is the total flux
emerging from all the six faces of the
closed surface?
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{Q}{2 \epsilon_{0}} \)
c. \( \frac{Q}{4 \epsilon_{0}} \)
D. \( \frac{Q}{6 \epsilon_{0}} \)


Assertion
Unreacted \( A g N O_{3} \) of photographic plate is removed by \( N a_{2} S_{2} O_{3} \) (hypo)
Reason
\( N a_{3}\left[A g\left(S_{2} O_{3}\right)_{2}\right] \) is soluble complex.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


A charged oil drop falls with terminal
velocity \( V_{0} \) in the absence of electric
field. An electric field 'E' keeps it stationary. The drop acquires additional charge \( q \) and starts moving
upwards with velocity \( V_{0} . \) The initia
charge on the drop was
\( A \cdot 49 \)
B. 29
\( c \cdot q \)
D. \( 9 / 2 \)


A resistor \( R \) is connected to a cell of
emf \( e \) and internal resistance \( r \)
Potential difference across the resistor
\( \boldsymbol{R} \) is found to be \( \boldsymbol{V} . \) State the relation
between \( e, V, R \) and \( r \)


The term hormone was first introduced
by
A. Gobind khorana
B. Baylers and Starling
c. James waston
D. Giulio natta


Find \( \theta \) when
\( \sin \theta+\operatorname{cosec} \theta=1 \)


A line passes through the origin and makes an angle of \( \pi / 4 \) with the line
\( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} . \) Then
This question has multiple correct options
A. Equation of the line is \( x=0 \)
B. The equation of the line is \( y=0 \)
C. The point of intersection of the line with the given line \( s(-1,0) \)
D. The point of intersection of the line with the given line is (0,1)


If a maximum cube carved out from a
gold sphere has thermal capacity of 'K' units, what would be the thermal capacity of the sphere?


\( \operatorname{Matrix} \boldsymbol{A}_{\boldsymbol{r}}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{r}-\mathbf{1} \\ -\mathbf{2} & \mathbf{1}\end{array}\right] ; \boldsymbol{r}= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots . . \) If \( \sum_{r=\mathbf{1}}^{\mathbf{1 0 0}}\left|\boldsymbol{A}_{\boldsymbol{r}}\right|=(\sqrt{\mathbf{1 0}})^{\boldsymbol{k}}, \) then
\( \boldsymbol{K}=\ldots . . ;\left(\left|\boldsymbol{A}_{\boldsymbol{r}}\right|=\operatorname{det}\left(\boldsymbol{A}_{\boldsymbol{r}}\right)\right) \)
A .2
B. 6
\( c \cdot 4 \)
\( D \)


The man who has won Nobel Prize twice
in physics is
A. Einstein
B. Bardeen
c. Heisenberg
D. Faraday


Choose the 0 DD one out of the following terms given and name the CATEGORY to which the others belong:
Phosphate, RNA, Sugar, Nitrogenous base.


Which among the following is the commercial unit of electric power?
A. volt
B. Watt
c. Ampere
D. Kwh


What is Physics?


All of the following symptoms are found in jaundice except
A. Disorders of hepato-billary system
B. Abnormal secretion of pancreatic and gastric juices
c. Bile duct obstruction
D. Anaemia


n the given circuit, the potential
difference across \( 3 \mu F \) capacitor will
be:
A. \( 12 V \)
B. \( 10 V \)
\( c .6 V \)
D. \( 4 V \)


Find the sum of all multiples of 5 lying between 101 and 999


When a straight wire is moved up and down rapidly between two poles of a horseshoe magnet then is
produced in the wire.
A. magnetic field
B. magnetic current
c. electric current
D. none


A shopkeeper bought two TV sets at Rs 10,000 each.He sold one at a profit \( 10 \% \) and the other at a loss of \( 10 \% \). Find
whether he made an overall profit or loss.


Radiations of two photon's energy, twice and ten times the work function of
metal are incident on the metal surface
successively. The ratio of maximum velocities of photoelectrons emitted in two cases is:
A . 1: 2
B. 1:3
\( c \cdot 1: 4 \)
D. 1:


State whether the following statement
is true or false:

Plants do not respire whereas animals
do.
A. True
B. False


Solve:
\( (-20)-(13) \)


Atomic mass number is same as
A. atomic number
B. mass number
c. formula mass number
D. valency


Neurogenic heart is characteristic of
A. Humans
B. Lower invertebrates
c. Rat
D. Rabbit


The magnetic field inside a solenoid carrying current.
A. is the same at all points
B. is zero at all points
c. becomes zero at its north pole
D. becomes zero at its south pole


Note the following.
An insect whose mouth parts are biting and chewing type in the larval condition and siphoning type in the adult which gives an economically important substance during another yet stage of
its development This insect is
A. Anopheles
B. Laccifer
c. Bombyx
D. Apis


Mass number is
A. the sum of the total number of protons and neutrons present in the nucleus of an atom.
B. the electrons present in the outermost shell of an
atom.
C. an atom of each element having a definite combining capacity.
D. the total number of protons present in the nucleus of an atom.


A parallel beam of monochromatic light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At
the first minimum of the diffraction
pattern, the phase difference between the rays coming from the two edges of the slit is :
A. zero
в. \( \frac{\pi}{2} \)
\( c \)
D. \( 2 \pi \)


A process that occurs without loss or
gain of heat is
A. Coriolis effect
B. Eustatic effect
c. Adiabatic
D. All the above


Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulation
agent for \( \boldsymbol{S b}_{2} \boldsymbol{S}_{3} \) sol is:
\( \mathbf{A} \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
c. \( _{A l_{2}}\left(S O_{4}\right)_{3} \)
D. \( N H_{4} C l \)


For the differential equation \( x \frac{d y}{d x}- \) \( \boldsymbol{y}=\sqrt{\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)}, \) show that its solution
is \( y+\sqrt{\left(x^{2}+y^{2}\right)}=k x^{2} \)


f \( \tan C \) is \( \frac{3}{m}, \) then \( m \) is
4
3
\( c \cdot 3 \)
\( D \)


Compound \( S C l_{6} \) can be prepared.
If true enter 1 , else enter 0 .


Maximum biodiversity is found in
A. Tropical rain forests
B. Temperate rain forests
c. Mangrove vegetation
D. Tundra


A mixture of formic acid and oxalic acid
is heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \). The gas
produced is collected and treated with OH solution whereby the volume decreases by \( \frac{1}{6} \) th. The molar ratio of the two acids (formic acid/oxalic acid) is
\( \boldsymbol{x}: \boldsymbol{y} . \) The value of \( (\boldsymbol{x}+\boldsymbol{y}) \) is :


Select the group which shares the
maximum number of common
characters.
A. Two species of a genus.
B. Two genera of a family
c. Two individuals of same species.
D. Two genera of two families


\( \mathbf{f} \mathbf{f}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{3} & -\mathbf{2}\end{array}\right] \) then \( \mathbf{A}^{\mathbf{5}}= \)
\( A \cdot I \)
в. \( A \)
\( c .-A \)
D. \( A^{2} \)


What is meant by an acetal? Give an example of reaction(with mechanism) showing its formation.


The probability of \( A= \) Probability of \( B= \) Probability of \( \mathrm{C}=\frac{1}{4} \)
\( \boldsymbol{P}(\boldsymbol{A}) \cap \boldsymbol{P}(\boldsymbol{B}) \cap \boldsymbol{P}(\boldsymbol{C})=\mathbf{0} . \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C})= \)
0 and \( P(A \cap C)=\frac{1}{8} . P(A \cap B)=0 \) the
probability that atleast one of the events \( A, B, C \) exists is?
A \( \cdot \frac{5}{8} \)
в. \( \frac{37}{64} \)
\( c \cdot \frac{3}{4} \)
\( D \)


What is the oxidation state of chlorine
in hypochlorous acid?
\( A \cdot+1 \)
B. +3
\( c .+5 \)
\( D \cdot+7 \)


Chemical equilibrium is
in nature.
A. static
B. dynamic
\( c . \) fast
D. both \( B \) and \( C \)


Which of the following length measurements is most precise and why?
a. \( 2.0 \mathrm{cm} \)
b. \( 2.00 c m \)
c. \( 2.000 \mathrm{cm} \)


Which of the following complex ion is expected to absorb light in the visible
region?
\( \mathbf{A} \cdot\left[T i(e n)_{3}\right]^{4+} \)
B \( \cdot\left[S c\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{3+} \)
c. \( \left[C r O_{4}\right]^{2} \)
D \cdot \( \left[Z n(C N)_{2}\right]^{2} \)


Which of the following activities increase the concentration of carbon
dioxide in the atmosphere?
(i) Deforestation
(ii) Combustion of fuel
(iii) Over hunting
A. Deforestation
B. combustion of fuel
c. over hunting
D. Both A and B


Which of the following phenomenon is a pplicable to the process shown in the
figure?
A. Absorption
B. Adsorption
c. coagulation
D. Emulsification


f a satellite is revolving around a planet of mass \( \mathrm{M} \) in an elliptical orbit of semimajor axis a. Show that the orbital speed of the satellite when it is at a distance r from the focus will be given by \( \boldsymbol{v}^{2}=\boldsymbol{G} \boldsymbol{M}\left[\frac{\boldsymbol{2}}{\boldsymbol{r}}-\frac{\mathbf{1}}{\boldsymbol{a}}\right] \)


If the perimeter of one face of a cube is
\( 20 \mathrm{cm}, \) then its surface area is
A \( \cdot 120 \mathrm{cm}^{2} \)
в. \( 150 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 125 \mathrm{cm}^{2} \)
D. \( 400 \mathrm{cm}^{2} \)


For what value of \( \mathrm{k} \), does the equation \( \left[k x^{2}+(2 k+6) x+16=0\right] \) have equal
roots?
A. 1 and 9
B. -9 and -1
c. -1 and 9
D. -1 and -9


Is inclusion of a subset in another, in
the context of a universal set, an
equivalence relation in the family of subsets of the sets? Justify your
answer


\( 3^{r d} \) term of a G.P. is 27 and its \( 6^{t h} \) term
is \( 729 . \) Find the product of its first and \( \mathbf{7}^{t h} \) terms.


Find expected value \( (\mu) \) variance \( \left(6^{-12}\right) \)
and \( \mathrm{S.D}(\sim) \) for the following probability
distribute.
\( x \) 2 3
\( P(x) \quad 0.4 \quad 0.3 \quad 0.2 \) o.


Match the terms of column I correctly
with the phrases given in column II.


n the given figure \( A B C \) is a triangle. If \( \frac{A D}{A B}=\frac{A E}{A C}, \) then prove that DE II BC


Given \( \boldsymbol{X}-\boldsymbol{B}(\boldsymbol{n}, \boldsymbol{p}) \)
If \( n=10 \) and \( p=0.4, \) find \( E(X) \) and
\( \operatorname{Var}(\boldsymbol{X}) \)


Which one of following have highest frequency?
A . radio waves.
B. infrared.
c. ultraviolet.
D. gamma rays


When a vibrating tuning fork is placed on a table, a large sound is heard. This
is due to
A. forced vibrations
B. resonance
c. beats
D. reflection


Which of the following has the characteristics of a good fuel?
A. coke
B. Butane
c. coal
D. Kerosene


A freely suspended magnetic needle will always come to rest in which direction?
A. north-east direction
B. north-west direction
c. north-south direction
D. south-west direction


If \( \int \frac{\sec x-\tan x}{\sqrt{\sin ^{2} x-\sin x}} d x=k \ln \mid f(x)+ \)
\( \sqrt{2} \sqrt{\tan x(\tan x-\sec x)} \mid+c, \) where \( c \)
is arbitrary constant and \( k \) is a fixed
constant, then
This question has multiple correct options
A. \( k=\sqrt{2} \)
в. \( k=\frac{1}{\sqrt{2}} \)
c. \( f(x)=\tan x-\sec x \)
D. \( f(x)=\sqrt{\tan x+\sec x} \)


The number of electrons required to balance the following equation is:
\( N O_{3}^{-}+4 H^{+}+e^{-} \rightarrow 2 H_{2} O+N O \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c .3 \)
D. 2


Let \( S \) be the set of all real values of \( \lambda \)
such that a plane passing through the points \( \left(-\lambda^{2}, 1,1\right),\left(1,-\lambda^{2}, 1\right) \) and
\( \left(1,1,-\lambda^{2}\right) \) also passes through the point \( (-1,-1,1) . \) Then \( S \) is equal to:
A \( \cdot(\sqrt{3}) \)
B. \( \{\sqrt{3}-\sqrt{3}\} \)
\begin{tabular}{l}
c. \{1,-1\} \\
\hline
\end{tabular}
D. \{3,-3\}


The swelling of 'gel' when placed in water is called:
A. gelation
B. imbibition
c. thixotropy
D. synersis


If \( P_{a t m}=0 \mathrm{mm} \mathrm{Hg} \) and \( P_{a l v}=-2 \mathrm{mm} \mathrm{Hg} \)
then
A. it is the end of the normal inspiration and there is no airflow
B. it is the end of the normal expiration and there is no airflow
C. transpulmonary pressure \( \left(P_{t p}\right) \) is \( -2 \mathrm{mm} \) Hg
D. air is flowing into the lungs


Electrons from succinate in Kreb's cycle are picked by
A. FMN of first complex of ETC
B. FMN of second complex ETC
c. FAD of I complex of ETC
D. FAD of II complex ETC


Explain the following with one-one example
(i) Antiseptic
(ii) Antacid
(iii) Sulpha drug
(iv) Antifertility
(v) Antipyretic.


A ball is released from height along the
slope and move along a circular track of radius \( R \) without falling vertically downwards Show that \( h=\frac{5}{2} R \)


What is the speed of propagation of
transverse wave in the wire?


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


Which of the following is correct statement regarding \( N\left(C H_{3}\right)_{3} \) and
\( N\left(S i H_{3}\right)_{3} ? \)
A \( \cdot N\left(S i H_{3}\right)_{3} \) is planar and more basic than \( N\left(C H_{3}\right)_{3} \)
B. \( N\left(S i H_{3}\right) \) ) is planar and less basic than \( N\left(C H_{3}\right) \) 3
C. \( N\left(C H_{3}\right)_{3} \) is planar and more basic than \( N\left(S i H_{3}\right)_{3} \)
D. \( N\left(C H_{3}\right)_{3} \) is pyramidal and less basic than \( N\left(S i H_{3}\right)_{3} \)


A lot contains 20 articles. The
probability that the lot contains exactly 2 defective articles is 0.4 and the
probability that the lot contains exactly 3 defective articles is \( 0.6 . \) Articles are
drawn from the lot at random one by one without replacement and tested till all the defective articles are found. The
probability that the testing procedure ends at the twelfth testing \( \frac{100-k}{1900} \) Find the value of \( k \)


If \( \left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}=a^{2} \)
\( \left(x_{2}-x_{3}\right)^{2}+\left(y_{2}-y_{3}\right)^{2}=b^{2} \)
\( \left(x_{3}-x_{1}\right)^{2}+\left(y_{3}-y_{1}\right)^{2}=c^{2} \) and
\( k\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \mathbf{1}\end{array}\right|=(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})(\boldsymbol{b}+\boldsymbol{c}- \)
\( a)(c+a-b) \times(a+b-c), \) then the
value of \( k \) is
\( A \)
в. 2
\( c \)
D. none of these


A uniform rod \( A B \) of mass \( 2 k g \) is
hinged at one end \( A \). The rod is kept in
the horizontal position by a massless
string tied to point \( B \). Find the reaction
of the hinge \( (\text { in } N) \) on end \( A \) of the rod at the instant when string is cut.
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot 6 \)
в. 40
\( c \cdot 15 \)
D.


Statements \( (A, B, C, D) \) in column I have
to be matched with statements \( (p, q, r, s) \)
in column II.
\( \mathbf{A} \)
\( A-q, B-t, C-p, D-r \)
B. A-r, B- t, C- p, D- q
C. \( A-t, B-p, C-r, D-q \)
D. \( A-r, B-t, C-q, D- \)


How is the sex of the baby determined?
A. Sex chromosomes of mother
B. Sex chromosomes of father
C. 'X' chromosome of unfertilised egg
D. All 23 pairs of chromosomes


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(\frac{\sin ^{m} x}{\sin ^{n} x}\right)^{m+n} \cdot\left(\frac{\sin ^{n} x}{\sin ^{p} x}\right)^{n+p} \cdot\left(\frac{\sin ^{p} x}{\sin ^{m} x}\right) \)
then \( f^{\prime}(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( \mathbf{c} \cdot \cos ^{m+n+p} x \)
D. None of these


Octet rule is not valid for the molecule:
A \( \cdot C O_{2} \)
в. \( H_{2} O \)
\( c \cdot O_{2} \)
D. \( C O \)


Normal to the curve \( x^{2}=4 y \) which
passes through the point \( (\mathbf{1}, \mathbf{2}) \)
A. \( x+y=3 \)
в. \( x-y=3 \)
c. \( 2 x+y=4 \)
D. \( x+2 y=5 \)


toppr \( \mathbf{G} \)
Q Type your question
the plates
As some of the oil evaporates, the
droplet loses mass and starts to
accelerate. Its charge remains constant.
In which direction does the droplet
accelerate, and which change needs to
be made to the separation of the plates in order to stop this acceleration?
separation of the direction of
acceleration
downwards
downwards
upwards decrease
D upwards increase
\( A \cdot A \)
B. B
\( c \cdot c \)
D. D


\( \boldsymbol{R}_{3}= \)
\{(1,1),(1,3),(3,5),(3,7),(5,7)\}
Is it a mapping?


Explain the industrial preparation of ammonia by Haber's process. Also, write two physical properties of ammonia.


Give the number of neutrons in an atom
of the isotope \( _{47}^{107} A g \)
A . 59
B. 60
\( c .61 \)
D. 58


Which are general property of Bronsted
acids?
This question has multiple correct options
A. They turn litmus red
B. They react with alkalies
c. They burn the skin
D. They contain \( H \) -atom replaceable with metal


Fill in the blanks
The eye lens can change its focal length
due to working of
muscles.


A piece of magnesium ribbon was heated to redness in nitrogen gas and then dropped into water. The gas
evolved is:
A \( . N H_{3} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


A hypothetical radioactive nucleus decays according to the following series \( \mathrm{z}_{2} \boldsymbol{A}^{180} \underline{\boldsymbol{\alpha}} \boldsymbol{A}_{1} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{A}_{2} \underline{\boldsymbol{\alpha}} \boldsymbol{A}_{3} \underline{\boldsymbol{\Upsilon}} \boldsymbol{A}_{4} \)
If the mass number and atomic number
of A are respectively 180 and 72 . then the atomic number and mass number
of A will respectively be:
\( \mathbf{A} \cdot 69,171 \)
B. 70,172
c. 68,172
D. 69,172


A thin convex lens made of glass of \( \mu= \) 1.5 has refracting surfaces of radii of curvature \( 10 \mathrm{cm} \) each. The left space of lens contains air and the right space is filled with water of refractive index \( \frac{4}{3} \cdot A \) parallel beam of light is incident on it. The position of the image is :
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c \cdot 24 c m \)
D. \( 10 \mathrm{cm} \)


Assertion
A current carrying conductor experiences a force in a magnetic field.
Reason
The net charge on a current carrying
conductor is zero.
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


Lenz's law is a consequence of the law of conservation of
A. charge
B. mass
c. energy
D. momentum


\( \mathbf{A} \)
\& B are sharp shooters whose probabilities of hitting a target are \( \frac{\mathbf{9}}{\mathbf{1 0}} \)
\( \& \frac{14}{15} \) respectively. If it is knownthat exactly one of them has hit the target, then the probability that it was hit by \( A \) is equal to
A \( \cdot \frac{24}{55} \)
в. \( \frac{27}{55} \)
c. \( \frac{9}{23} \)
D. \( \frac{10}{23} \)


Oxidation state of +1 for phosphorous is
found in :
A \( . \mathrm{H}_{3} \mathrm{PO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)


Which one of the following is not an essential micronutrient for plants?
A. Sodium
B. zinç
c. Boron
D. copper


If a body of mass \( 5 g \) initially at rest is acted upon by a force of 50 dynes for \( 3 s \)
Then the impulse will be
A \( \cdot 0.98 \times 10^{-3} N s \)
В. \( 1.5 \times 10^{-3} N s \)
c. \( 2.0 \times 10^{-3} N s \)
D. 2.5 \( \times 10^{-3} \mathrm{Ns} \)


What is the role of a plane mirror and a glass sheet in a solar cooker?


The demand of different shirt sizes, as
obtained by a survey, is given. Calculate
the Mode.
Size
\( 38 \quad 39 \)
Number of
persons(wearin it)


R.Q. of malic acid is
\( A \cdot 0.7 \)
B. 1
\( c \cdot 1.33 \)
D. 4


Matter waves are waves associated
with
A. photons
B. electrons
c. matter
D. neutrons


The equilibrium constant for the reaction
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\boldsymbol{a q})+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H}(\boldsymbol{a q}) \Leftrightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \) is 16
The initial concentration of each of
\( C H_{3} C O O H \) and \( C_{2} H_{5} O H \) is two (mole/lit). What is the concentration of
\( C H_{3} C O O C_{2} H_{5} \) at equilibrium in moles / lit?
A. 0.9
B. 0.6
\( c \cdot 1.6 \)
D. 0.7


Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582
marks out of 600 marks. Who scored
percentage is better?


Figure shows a small magnetised
needle \( P \) placed at a point \( O . \) The arrow
shows the direction of its magnetic
moment. The other arrows show
different positions (and orientations of
the magnetic moment) of another
identical magnetised needle \( Q \)
In which configuration the system is not in equilibrium?


On increasing the applied potential difference in X-ray tube This question has multiple correct options
A. The intensity of emitted radiation increases.
B. The minimum wavelength of emitted radiation increases
c. The intensity of emitted radiation remains unchanged.
D. The minimum wavelength of emitted radiation decreases


The value of \( \lim _{x \rightarrow 0} \frac{x}{5}\left[\frac{x}{2}\right] \) (where \( [.] \)
denotes the greatest integer function) is
A \( \cdot \frac{2}{5} \)
в. \( -\frac{2}{5} \)
c. 0
\( D \cdot \infty \)


State which of the following are finite
sets.
\( (i)\{x: x \in N\} \) and \( (x-1)(x-2)=0 \)
\( (i i)\{x: x \in N\} \) and \( x \) is prime.
\( (i i)\{x: x \in N\} \) and \( x \) is odd
A . (i) only
B. \( (i),(i i) \) and \( (i i i) \)
c. \( (i) \) and \( (i i) \)
D. (ii) and (iii)


Order of increasing basic strength.
\( (\|) \)
A \( . I>I I>I I I \)
B. \( I I>I I I>I \)
c. \( I>I I I>I I \)
D. \( I I I>I I>I \)


Suppose in a clinical thermometer, the
difference between first and second
bigger marks is \( 1^{\circ} \) and there are 5
small divisions between them
then each small division refers to the
difference in scale of:
\( \mathbf{A} \cdot 0.1^{\circ} C \)
B. \( 0.2^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.3^{\circ} \mathrm{C} \)
D. \( 0.4^{\circ} \mathrm{C} \)


If \( A \) is a square matrix of order 5 and
\( \left.9 A^{-1}=4 A^{T} \text { then ladj (adj }(\operatorname{adj} A)\right) \)
(where \( A^{-T} \) and adj \( (A) \) denotes the inverse, transpose and adjoint of matrix A respectively) contains: \( (\log 3= \)
\( \mathbf{0 . 4 7 7}, \log \mathbf{2}=\mathbf{0 . 3 0 3}) \)
A. 56 digits
B. 60 digits
c. 58 digits
D. 53 digits


Assertion
\( \mathbf{S}_{2} \boldsymbol{O}_{\mathbf{7}}^{\mathbf{2}-} \)
\( \& C r_{2} O_{7}^{2-} \) both exist.
Reason
Both have same valence electrons.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A large cylindrical tank has a hole of area \( A \) at its bottom and water is
poured into the tank through a tube of cross-sectional area \( \boldsymbol{A} \) ejecting water at
the speed \( v \). Which of the following is
true?
A. Water level in tank keeps on rising.
B. No water can be stored in the tank
c. water level will rise to a height \( \frac{v^{2}}{2 g} \) and then stop.
D. The water level will be oscillating.


The smallest unit of classification is
known as
A. species
B. De condole
c. Linnaeus
D. Mayr


Define non-benzenoid aromatic
compound with example.


Animal charcoal is used to remove
moisture
A . True
B. False


Describe Bohr's model of the atom.


\( \mathbf{X} \) and \( \mathrm{Y} \) are large, parallel conducting plates close to each other. Each face
has an area A. X is given a charge Q.Y is without any charge. Point \( A, B \) and \( C \) are as shown in the figure. Which statement is wrong.
A . The field at B is \( \frac{Q}{2 \frac{6}{80 A}} \)
B. The field at B is \( \frac{Q}{6 \mathrm{c} A} \)
C. The fields at \( A, B \) and \( C \) are of the same magnitude.
D. The fields at A and C are of the same magnitude, but in opposite directions


In a series L-C circuit, if \( L=10^{-3} \mathrm{H} \) and
\( C=3 \times 10^{-7} F \) is connected to a
\( 100 V-50 H z \) a.c. source, the
impedance of the circuit is
A \( \cdot \frac{10^{5}}{3 \pi}-10 \pi \)
В. \( 0.1 \pi-3 \times 10^{-5} \pi \)
\( ^{\mathbf{C}} \cdot \frac{10^{5}}{3 \pi}-\frac{\pi}{10} \)
D. None of these


Give a balanced reaction in which
ammonia is oxidised by a metal oxide.
A \( .4 N H_{3}+3 C u O \rightarrow 2 N_{2}+3 H_{2} O+3 C u \)
B. \( 2 N H_{3}+4 C u O \rightarrow N_{2}+3 H_{2} O+4 C u \)
\( \mathrm{c} \cdot 2 N H_{3}+C u O \rightarrow N_{2}+3 H_{2} O+C u \)
D. \( 2 N H_{3}+3 C u O \rightarrow N_{2}+3 H_{2} O+3 C u \)


Fill in the blanks.
A body is projected upward. Up to the maximum height, the time taken will be
greater to travel (first
half/second half)


2-chloro-2-methylpentane on reaction with sodium methoxide in
methanol yields:
(a)
(b)
\( (c) \)
A \( . a \) and \( c \)
B. \( c \) only
\( c . a \) and \( b \)
D. all of these


Find the equation of the plane in scalar product form \( \hat{r}=(2 \hat{i}+\hat{k})+\lambda \hat{i}+ \)
\( \mu(\hat{i}+2 \hat{j}-3 \hat{k}) \)


If DNA was made of 6 nucleotides
instead of \( 4, \) what are the total number of triplet codons possible?
A .24
B . 18
\( c .64 \)
D. 216


A long solenoid having 200 turns per \( \mathrm{cm} \) carries a current of \( 1.5 a m p . \) At the centre of it is placed a coil of 100 turns
of cross-sectional are \( 3.14 \times 10^{-4} m^{2} \)
having its axis parallel to the field produced by the solenoid. When the direction of current in the solenoid is
reversed within 0.05 sec, the induced
e.m.f. in the coil is
A. \( 0.48 V \)
в. \( 0.048 V \)
\( \begin{array}{ll}.0 .0048 V & V \\ V V & 0.088\end{array} \)
D. \( 48 V \)


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) given by
\( f(x)=x^{3}-1 \) is
A. A one-one function
B. An onto function
c. A bijection
D. Neither one-one nor onto


What does the exponential factor
represent?
A. The total number of reactants in a reaction.
B. The amount of energy needed to start a chemical reaction.
C. The fraction of reactants that have approached the activation energy hill and made it over per number of attempts.
D. The fraction of reaction energy given off per unit of time.
E. The fraction of products that have approached the activation energy hill and made it over per number of attempts.


By mistake a clerk, calculate the simple interest on principle for 5 months at \( 6.5 \% \) p.a. instead of 6 months at
\( 5.5 \% \) p.a. If the error in calculation was
Rs.25.40. The original sum of principle
was:


\( P Q R S \) is a parallelogram \( P M \) is the
altitude on base \( S R . S N \) is the altitude
on base \( Q R \) If \( S R=8.2 \mathrm{m}, P M=4.8 \)
\( \mathrm{m} \) and \( S N=6 \mathrm{m} \). Find \( P S \)


The statement \( P(n) " 1 \times 1 !+2 \times 2 !+ \)
\( \mathbf{3} \times \mathbf{3} !+\ldots+\boldsymbol{n} \times \boldsymbol{n} !=(\boldsymbol{n}+\mathbf{1}) ! \mathbf{1} " \)
A. True for all \( n>1 \)
B. Not true for any \( n \)
c. True for all \( n \epsilon N \)
D. None of these


Two trains \( A \) and \( B \) of length 400 m each are moving on two parallel tracks with uniform speed of
\( 20 \mathrm{m} / \mathrm{s} \) in the same direction. with \( \mathrm{A} \)
ahead of \( \mathrm{B} \), driver of \( \mathrm{B} \) accelerates at
\( 1 m / s^{2} \) in order to overtrake. if after 50 sec, the guard of B just brushes past driver of \( A, \) what was original distance between drivers of the trains?
A. \( 450 m \)
В. \( 1250 m \)
\( \mathbf{c} .850 m \)
D. 1650m


If \( S \) is any set, then the family of all the
subsets of \( S \) is called the power set of \( S \) and it is denoted by \( P(S) . \) Power set of a
given set is always non-empty. If \( A \) has n elements, then \( P(A) \) has?


The first term of an A.P. is 5 and its
common difference is \( -3 . \) Find the \( 11^{t h} \)
term of an A.P.


A invested Rs 5000 in a business. After
4 months B joined him by investing Rs \( 4800 . \) After a further of 2 months, \( C \)
joined them with Rs \( 5200 . \) If after the end of year, they earned a total profit if Rs \( 14,400, \) then what is the difference
between the shares of \( A \) and \( B ? \)


\( 200 V \) A.C is applied at the ends of an LCR circuit. The circuit consists of an
inductive reactance \( \boldsymbol{X}_{\boldsymbol{L}}=\mathbf{5 0 \Omega} \)
capacitive reactance \( X_{C}=50 \Omega \) and ohmic resistance \( R=10 \Omega \). Calculate
the impedance of the circuit and also
potential difference across \( L \) and \( R \)
What will be the potential difference
across L-C?


When crystals of washing soda are left
open in air, they lose:
A. nine molecules of water of crystallisation
B. five molecules of water of crystallisation
C. three molecules of water of crystallisation
D. ten molecules of water of crystallisation


Suppose \( \vec{V}_{1}=\hat{i}+\hat{j}-2 \hat{k}, \vec{V}_{2}=\hat{i}- \)
\( \mathbf{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{V}}_{3}=-2 \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) are three
vectors. Let \( \vec{V} \) be a vector such that it
can be expressed as a linear combination of \( \vec{V}_{1} \) and \( \vec{V}_{2} . \) Also \( \vec{V} \vec{V}_{3}= \)
0 and the projection of the vector \( \vec{V} \) on \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is \( \boldsymbol{6} \sqrt{\boldsymbol{3}} . \) If \( \overrightarrow{\boldsymbol{V}}=\boldsymbol{\lambda}(\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}- \)
4 \( \hat{k} \) ) then find the absolute value of \( \lambda \)


If the d.rs of \( O A \) and \( O B \) are 1,-1,-1
and \( 2,-1,1, \) then the d.cs of the line perpendicular to both \( \boldsymbol{O} \boldsymbol{A} \) and \( \boldsymbol{O B} \) are
в. -2,-3,1
c. \( \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
D. \( \frac{2}{\sqrt{41}}, \frac{3}{\sqrt{41}}, \frac{-1}{\sqrt{41}} \)