Which of the following graph shows the best relationship of the number of
grams of a solid that are soluble in 100
\( \operatorname{grams} \) of \( H_{2} O \) at varying temperature if
the solubility begins at a small quality and increases at a slow, steady pace as the temperature is increased?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E.


Find the equation of line passing through points
(i) \( (3 \hat{i}+2 \hat{j}-8 \hat{k}),(5,2,-4) \)


If the line \( y=x \sqrt{3}-3 \) cuts the
parabola \( \boldsymbol{y}^{2}=\boldsymbol{x}+\boldsymbol{2} \) at \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) and if
\( A \) be the points \( (\sqrt{3}, 0), \) then \( A P . A Q \) is
A \( \cdot \frac{2}{3}(\sqrt{3}+2) \)
B. \( \frac{4}{3}(\sqrt{3}+2) \)
c. \( \frac{4}{3}(2-\sqrt{3}) \)
D. \( \frac{4}{6-3 \sqrt{3}} \)


The invention which has eased our life
related to field of agriculture is?
A. Thresher
B. Power plant
c. cT scan
D. E learning


Calculate the electric field intensity required to just support a water drop let
of mass \( 10^{-7} k g \) and having a charge of \( +4.0 \times 10^{-13} C \)


Find the least value of \( k \) for which the
function \( x^{2}+k x+1 \) is an increasing
function in the interval \( 1<x<2 \)
A . 1
B. -
\( c \cdot 2 \)
D. -


Find the range and coefficient of range of the following data.
\( \mathbf{5 9}, \mathbf{4 6}, \mathbf{3 0}, \mathbf{2 3}, \mathbf{2 7}, \mathbf{4 0}, \mathbf{5 2}, \mathbf{3 5}, \mathbf{2 9} \)
A . 36,0.44
в. 32,0.44
c. 36,0.84
D. None of these


Two forces simultaneously act on a
particle making an angle \( 120^{\circ} \) with
each other if one of them is reversed the
acceleration of the particle becomes \( \sqrt{3} \) times its initial value. The ratio of the
magnitude of the forces is?
A . 1: 2
B. 1: 1
\( c \cdot 2: 1 \)
D. 1: 3


Write order of dipole moment of
following compounds:
\( (\mathrm{i}) \)
(ii)
(iii)
(v)
\( (\mathbf{v i}) \)
A \( .(i i i)>(i i)>(i)>(i v)>(v)>(v i) \)
B. \( (i i i)>(i)>(i i)=(v i)>(i v)>(v) \)
C. \( (i i)>(i)=(i i i)=(i v)>(v)=(v i) \)
D. \( (i i i)>(i)>(i v)>(v)>(i i)>(v i) \)


Write the product formed in the given
reaction.


The folds of Kerkring are developed in
A. Duodenum
B. Jejunum
c. Ileum
D. Large intestine


A beam of light incident on a convex lens parallel to its principal axis converges at a point on the principal axis. Name the point:
A. First focus
B. Second focus
c. First centre
D. Second centre


IIf \( \mathbf{A}=\left[\begin{array}{ll}\boldsymbol{a} & \mathbf{0} \\ \boldsymbol{a} & \mathbf{0}\end{array}\right], \mathbf{B}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \boldsymbol{b} & \boldsymbol{b}\end{array}\right], \) then
\( \mathbf{A B}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. ВА
c. АВ
D. ABAB


Name the pulmonary disease in which the alveolar surface area involved in gas exchange is drastically reduced due to damage to the alveolar walls.
A. Asthma
B. Pleurisy
c. Emphysema
D. Pneumonia


During fermentation by yeast, alcohol is formed from
A. Proteins
B. Sugars
c. Mucopolysaccharides
D. Fats


Explain how does the OH group
attached to a carbon of benzene
ring activate it towards electrophilic substitution?


Water stored in a tank flows out through
a hole of radius \( 1 \mathrm{mm} \) at a depth \( 10 \mathrm{m} \)
below the surface of water.The rate of
flow of water in \( m^{3} / s \) will be
A \( .4 .4 \times 10^{-5} \)
B. \( 4.4 \times 10^{-4} \)
c. \( 4.4 \times 10^{-3} \)
D. \( 4.4 \times 10^{-2} \)


The figure shows a part of an electric
circuit. The wires \( A B, C D \) and \( E F \) are long
and have identical resistances. The
separation between the neighboring
wires is \( 1.0 \mathrm{cm} \). The wires EA and BF have
negligible resistance and the ammeter
reads 30 A. Calculate the magnetic force
per unit length on \( A B \) and \( C D \)


n fig. \( 2, \) lines \( l_{1} \| l_{2} . \) The value of \( x \) is :
\( A \cdot 70 \)
B. 30
\( c \cdot 40 \)
D. 50


A progressive wave of frequency
\( \mathbf{5 0 0} \boldsymbol{H z} \) is travelling at a speed of
\( 360 m s^{-1} . \) How far are the two points on
it having a phase difference of \( 60^{\circ} \)
A . \( 0.12 \mathrm{m} \)
B. \( 0.36 m \)
c. 0.24 m
D. \( 0.18 m \)


The nervous tissue, which contains
densely packed cells are called as
A. Neurons
B. Nissi's granules
c. Dendrons
D. Axon


Obtain the equation of the line passing through (1,1,2) and (2,1,2) in the vector form.


Which atom contains exactly 15
neutrons?
A \( \cdot P^{32} \) (atomic number \( =17 \) )
B. \( S^{32} \) (atomic number \( =16 \) )
\( \mathrm{c} \cdot O^{15} \) (atomic number \( =8 \)
D. \( N^{15} \) stomic number \( =7 \)


Fishing nets are made of
A. rayon
B. dacron
c. nylon
D. viscose rayon


An object is moving on a circular path of radius \( r \) with constant speed \( v \). The average acceleration of the object, after it has traveled a half rounds, is,
A \( \cdot \frac{2 v^{2}}{\pi r} \)
В. \( \frac{4 v^{2}}{3 \pi r} \)
c. \( \frac{4 v^{2}}{7 \pi r} \)
D. \( \frac{2 v^{2}}{7 \pi r} \)


The cross section of a canal is in the
shape of trapezium. The canal is \( 15 m \)
wide at the top and \( 9 m \) wide at the
bottom. If the area of the cross section
is \( 720 m^{2}, \) then the depth of the canal is
\( \mathbf{A} \cdot 58.4 m \)
B. \( 58.6 m \)
c. \( 58.8 m \)
D. \( 60 m \)


Define lanthanoid contraction. Explain
its effects.


The value of
\( \tan 5^{\circ} \tan 10^{\circ} \tan 15^{\circ} \cdots \tan 85^{\circ} \) is
\( A \cdot 0 \)
B. not defined
\( c \cdot 1 \)
D. -


Oxidation number of the nitrogen atom
in \( H N O_{3} \) is :
A . -
B. +1
\( c \cdot 0 \)
\( D \cdot+4 \)
\( \mathrm{E} \cdot+5 \)


\( \int \frac{\cos 2 x}{\sin x} d x \)


Divide \( \boldsymbol{a}+\boldsymbol{b} \) by \( \boldsymbol{a}^{1 / 3}+\boldsymbol{b}^{1 / 3} \)


Choose the correct answer from the
alternatives given. Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor
A . increases
B. decreases
c. increases or decreases
D. is zero


Which of the following is he chief reason to indicate that proto - cell was probably a fermenter?
A. Fermentation provides the most amount of energy
B. Atmosphere didn't have any oxygen
c. It didn't have any enzymes
D. All of the above


Which of the following is/are state property/properties? This question has multiple correct options
A. Internal energy
B. Volume
c. Heat
D. Enthalpy


\( M n O_{4}^{-} \) is of intense pink colour through Mn is in (+7) oxidation state, it is due to:
A. oxygen gives colour to it it
B. charge transfer when Mn(+7) gives its electron to oxygen and oxidise to Mn (+8) temporarily
c. charge transfer when oxygen gives its electron to Mn (+7) changing in Mn (+6)
D. none is correct explanation


The masses and radii of the earth and
the Moon are \( M_{1}, R_{1} \) and \( M_{2}, R_{2} \)
respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is?
A \( \cdot \sqrt{\frac{2 G\left(M_{1}+M_{2}\right)}{d}} \)
B. \( \sqrt{\frac{4 G\left(M_{1}+M_{2}\right)}{d}} \)
c. \( \sqrt{\frac{4 G M_{1} M_{2}}{d}} \)
D. \( \sqrt{\frac{G\left(M_{1}+M_{2}\right)}{d}} \)


Air resistance is also a form of friction.
A. True
B. False


Find the mean of first five natural
numbers.


Find the 7 th term in the expansion of \( \left(\frac{4 x}{5}+\frac{5}{2 x}\right)^{8} \)


\( A B C D \) is a square of side \( 14 \mathrm{cm} . \) Find
the radius of the circle.


\( \boldsymbol{S}^{2-}+\boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \longrightarrow \)
Complex is having violet/purple coloration(X)
The total number of possible isomers for complex \( X \) is \( \ldots \ldots . . \) provided the
ambident behavior of \( C N^{-} \) is
not considered


Which of the following solids are known to undergo sublimation?
¡. \( C O_{2} \)
ii. \( \boldsymbol{I}_{2} \)
iii. Naphthalene
A. i only
B. ii only
c. i and ii only
D. ii and iii only
E. i, ii and iii


The \( 3^{\prime}-5^{\prime} \) phosphodiester linkages inside a polynucleotide chain serve to join
A. one nucleotide with the another nucleotide
B. One nucleoside with another nucleoside
c. one deoxyribose sugar with another nucleoside
D. One nitrogenous base with pentose sugar


Homo erectus' is the zoological name of
A. Cro-Magnon man
B. Pecking man
C. Nut-cracker man
D. Neanderthal man


Which types of birds were absent on Galapagos islands when they were
surveyed by Darwin?
A. Warblers and wood peckers
B. Carnivores
c. cactus feeding
D. Seed eating


The compressions and rarefactions are
transmitted across the middle ear
through
A. auditory tube
B. ear ossicles
c. cochlea
D. all


Fill in the blanks.
Earth's diameter is roughly times more than
that of the moon.
A. Four
B. Five
\( c . \) six
D. Seven


When a resistor of \( 11 \Omega \) is connected in
series with a electric cell. The current
following in it is \( 0.5 A . \) Instead when a resistor of \( 5 \Omega \) is connected to the same
electric cell in series, the current increases by \( 0.4 A . \) The internal resistance of the cell is
A. \( 1.5 \Omega \)
B. 2\Omega
\( c .2 .5 \Omega \)
D. 3.5\Omega


Order of number of revolution/sec
\( \gamma_{1}, \gamma_{2}, \gamma_{3} \) and \( \gamma_{4} \) for \( I, \) II, III and IV orbits
is:
A \( \cdot \gamma_{1}>\gamma_{2}>\gamma_{3}>\gamma_{4} \)
В \( \cdot \gamma_{4}>\gamma_{3}>\gamma_{2}>\gamma_{1} \)
C \( \cdot \gamma_{1}>\gamma_{2}>\gamma_{4}>\gamma_{3} \)
D. \( \gamma_{2}>\gamma_{3}>\gamma_{4}>\gamma_{1} \)


A diode allows the electric current to
flow, when it is in forward bias, but if it
is in reverse bias it will not allow the
electric current to flow. Why?


The heat needed to turn 1 kg of liquid into gas at its boiling point is known as
A . Latent heat
B. Specific latent heat of vaporization
c. specific latent heat of substance
D. Fermentation


Which of the following is/are paramagnetic in nature? This question has multiple correct options
\( A \cdot O_{2} \)
в. \( O_{2}^{\text {t }} \)
\( c \cdot O_{2} \)
\( D \cdot O_{2}^{2} \)


In Pheretima coelomic fluid contains
A. Dissolved haemoglobin
B. Dissolved RBC
c. Broken WBC
D. Watery plasma


Solution of \( \frac{x}{3}>\frac{x}{2}+1 \) is


Which of the following statements is
not correct for chemisorption and
physisorption?
A. Physical adsorption occurs at a low temperature and chemisorption occurs at high temperatures
B. Magnitude of chemisorption decreases with rise in temperature while physisorption increases with rise in temperature.
C. Chemisorption is irreversible and physisorption is reversible.
D. In physisorption activation energy is low while in chemisorption it is high.


At which phase the moon is nearest to
the sun?
A. New Moon
B. Full Moon
c. First Quater
D. Third Quater


A man in a car at location \( Q \) on a
straight highway is moving with speed
\( \boldsymbol{v} . \) He decides to reach a point \( \boldsymbol{P} \) in a
field at a distance \( \boldsymbol{d} \) from highway
(point \( M) \) as shown in the figure. Speed
of the car in the field is half to that on
the highway. What should be the
distance \( R M, \) so that the time taken to
reach P is minimum?
A \( \cdot \frac{d}{\sqrt{3}} \)
B. \( d \) \( \overline{2} \)
c. \( \frac{d}{\sqrt{2}} \)
D.


\( \int \frac{x}{\sqrt{9+8 x-x^{2}}} d x \) is equal to
A \( \cdot-\sqrt{9+8 x-x^{2}}+4 \sin ^{-1}\left(\frac{x-4}{5}\right)+C \)
B. \( -\sqrt{9+8 x-x^{2}}+4 \cos ^{-1}\left(\frac{x-4}{5}\right)+C \)
c. \( -\sqrt{9+8 x-x^{2}}+4 \cos ^{-1}\left(\frac{x-3}{2}\right)+C \)
D \( \cdot \sqrt{9+8 x-x^{2}}+4 \sin ^{-1}\left(\frac{x-4}{5}\right)+C \)


If \( \sin (\alpha+\beta)=1 \) and \( \sin (\alpha-\beta)=1 / 2 \)
where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{\pi} / 2] \) then
This question has multiple correct options
A \( \cdot \tan (\alpha+2 \beta)=-\sqrt{3} \)
B. \( \tan (2 \alpha+\beta)=-1 / \sqrt{3} \)
\( \mathbf{c} \cdot \tan (\alpha+2 \beta)=\sqrt{3} \)
D. \( \tan (\alpha+2 \beta)=1 / \sqrt{3} \)


ff \( A(-2,1), B(a, 0), C(4, b) \) and \( D(1,2) \)
are the vertices of parallelogram \( A B C D, \) find \( a \) and \( b . \) Hence find the length of it's sides.


Gas \( A \) is formed on the hydrolysis of
calcium cyanamide. The gas can turn moist litmus paper blue and forms a brown precipitate with Nessler's
reagent. The gas, \( \boldsymbol{A} \) is:
A \( \cdot N_{2} \)
B. NO
\( c \cdot N O_{2} \)
D. \( N H_{3} \)


\( \tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]=? \)
\( A \cdot \frac{7}{17} \)
в. \( \frac{-7}{17} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{-7}{12} \)


A convex mirror has a focal length \( f . \mathbf{A} \)
real object is placed at a distance \( f \) in front of it from the pole, produces an
image at:
\( A \cdot \infty \)
B. \( f \)
\( c \cdot \frac{f}{2} \)
D. \( 2 f \)


Explain disinfectants with a suitable example.


Two plane figures are said to be
congruent if they have
A. The same size
B. The same shape
c. The same size and the same shape
D. none


\( A B C D \) is a trapezium in which
\( A B|| C D \) and \( A D=B C . \) Show that
\( \angle A=\angle B \)


Particle acceleration in a travelling longitudinal wave can vary due to
A. change in properties of the medium
B. change in the angular velocity of the wave
c. change in the amplitude of the wave
D. None of these


Considering Ellingham diagram, which of the following metals can be used to reduced alumina?
\( \mathbf{A} \cdot M g \)
в. \( F e \)
c. \( C u \)
D. \( Z n \)


The bonding in ammonium chloride:
A. is covalent only
B. is electrovalent only
C. consists of three covalent nitrogen-hydrogen bonds and an electrovalent bond between the ammonia
molecule and the chlorine atom.
D. consist of four covalent nitrogen-hydrogen bonds and one electrovalent bond between the ammonium ion and chloride ion.


\( \sum_{k}^{i} \)


A body executing S.H.M has a maximum
acceleration equal to \( 48 \mathrm{m} / \mathrm{sec}^{2} \) and maximum velocity equal to \( 12 \mathrm{m} / \mathrm{sec} \)
The amplitude of S.H.M is?
\( A \cdot 3 m \)
B. 3/32 m
c. \( 1024 / 9 \mathrm{m} \)
D. \( 64 / 9 \mathrm{m} \)


The prescribed upper limit concentration of lead in drinking water is about:
\( A \cdot 10 \) ppb
B. 40 ppb
c. 50 pp
D. 60 ppb


For a medium with permitivity \( \epsilon \) and permeability \( \mu, \) the velocity of light is
given by:
\( \mathbf{A} \cdot \sqrt{\mu / \epsilon} \)
B . \( \sqrt{\mu \epsilon} \)
c. \( 1 / \sqrt{\mu \epsilon} \)
D. \( \sqrt{\epsilon / \mu} \)


State True or False:
Addition of \( a-3 b+3,2 a+5 \)
\( \mathbf{3 c}, \mathbf{6 c}-\mathbf{1 5}+\mathbf{6 b} \) is \( \mathbf{3 a}+\mathbf{3 b}+\mathbf{3 c - 7} \)
A. True
B. False


Degree of \( \left[2+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=a \frac{d^{2} y}{d x^{2}} \) is:
\( A \)
B.
\( c \)
\( D \)


Magnetic field at point 'O' due to given current distribution. If 5 A current is
flowing in this system and the diameter of the loop is \( 10 \mathrm{cm} \)
A \( \cdot 2 \times 10^{-5} T, \otimes \)
B \( \cdot 10^{-5} T, \odot \)
\( \mathbf{c} \cdot 10^{-5} T, \otimes \)
D. \( 2 \times 10^{-5} T, \odot \)


ff \( \Delta D E F \equiv \Delta B C A, \) write the part(s) of
\( \Delta B C A \) that correspond to \( \overline{D F} \)


Friction is a that opposite motion?
A. True
B. False


Is 51 a term of the \( A P, 5,8,11,14, \ldots \ldots . . ? \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Which gas can cause acid rain in nearby places and air pollution in downwind areas from the volcanic site?
\( A \cdot S O_{2} \)
в. \( H_{2} S \)
\( c \cdot C O_{2} \)
D. All of the above


Which of the following is not true about
drug receptors?
A. Receptor proteins are embedded in the cell membrane.
B. The chemical known as chemical messengers are received at the binding sites of receptors.
C. The receptors show selectively for one chemical messenger over the other.
D. Receptor protein is decomposed and destroyed after removal of chemical messenger.


Which of the following is not naturally occurring form of water?
A. Solid
B. Liquid
c. vapour
D. Semi-solid


Bleaching powder is soluble in cold water giving a milky solution due to:
A . available chlorine
B. lime present in it
c. calcium carbonate formation
D. the absorption of carbon dioxide from atmospher


\( A(1,3) \) and \( B(7,5) \) are two opposite
vertices of a square. The equation of a side through \( \boldsymbol{A} \) is
A. \( x+2 y-7=0 \)
В. \( x-2 y+5=0 \)
c. \( 2 x+y-5=0 \)
D. None of these


Nucleus is composed of two kinds of
subatomic particles:
A. protons and neutrons
B. electrons and neutrons
c. protons and electrons
D. none of the above


An identical sister chromatids are
present at
I. Beginning of prophase
II. Beginning of metaphase I
III. End of telophase I
A. I only
B. II only
c. ॥ only
D. I and II
E. Il and III


Angles of a triangle are in the ratio 4: 6
5. The triangle is :
A. an acute angles triangle
B. an obtuse angled triangle
c. right angled triangle
D. isosceles triangle


A uniform metre rule balances ho
rizontally on a knife edge placed at the \( 58 c m \) mark when a weigh of \( 29 g f \) is
suspended from one end.
(i)Draw a diagram of the arrangement
(ii)What is the weight of the rule?


The solar heat and light reach the earth
via
A. radiation
B. conduction
c. convection
D. all of these


Draw a circle of radius \( 3 \mathrm{cm} \). Take two
points \( P \) and \( Q \) on one of its extended
on both sides of its centre, each at a distance of \( 7 \mathrm{cm} \) on opposites of its
centre. Draw tangents to the circle from each of these two points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)


Read the following statements and answer as true or false. Graphite is a bad conductor of electricity.
If true enter 1 , else enter 0


What is \( \Delta G^{o} \) for the following reaction?
\( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \rightleftharpoons N H_{3}(g) ; K_{p}= \)
\( 4.42 \times 10^{4} \) at \( 25^{\circ} C \)
\( \begin{array}{lll}\text { A } .-26.5 k J & \text { mol }^{-1}\end{array} \)
B. \( -11.5 k J \) mol \( ^{-1} \)
\( \begin{array}{ll}\text { c. }-2.2 k J & \text { mol }^{-1}\end{array} \)
\( \begin{array}{lll}\text { D. }-0.97 k J & \text { mol }^{-1}\end{array} \)


Complete and name the following
reaction.
\[
c=0 \frac{\mathbf{Z n}-\mathbf{H g}}{\mathbf{H C l}}
\]


Assertion
Water, kept in an open vessel, will quickly evaporate on the surface of the
moon.
Reason
The temperature at the surface of the moon is much higher than boiling point of water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A metallic spoon falls on a metal plate making a huge sound and upon bouncing from the plate, it falls on to the pile of sand below it with no noise being heard. Sound is not heard on sand because
A. Sound is absorbed by sand particles
B. Sound generated by the plate is more than the sand particles
c. Vibration of metal plate is more than sand particles
D. sand does not vibrate


List the relation \( R \) defined by \( R= \)
\( \left\{(a, b): a \leq b^{3}\right\} \) in Roaster form. \( a, b \in \)
\( N \)


Carbon and hydrogen are detected by heating the organic compound with
A. magnesium oxide
B. cupric oxide
c. zinc oxide
D. sulphur dioxide


Student \( A \) and student \( B \) sit in identical
office chairs facing each other, as shown in figure. Student A is heavier than student B. Student A suddenly
pushes with his feet. Which of the
following statements is correct?
A. Both A and B will move in same direction
B. B will move to right while A will not move
c. A will move to right while B will move to let
D. A and B will move in opposite directions


The refining method used when the metal and the impurities have low and
high melting temperatures, respectively, is :
A. zone refining
B. liquation
c. distillation
D. vapour phase refining


The phosphate of a certain metal M is
\( M_{3}\left(P O_{4}\right)_{2} . \) The correct formula of metal sulphate would be:
\( \mathbf{A} \cdot M_{2}\left(S O_{4}\right)_{3} \)
в. \( M S O_{4} \)
c. \( M_{3}\left(S O_{4}\right)_{2} \)
D. \( M_{2} S O_{4} \)


Select the correct statements about
galvanic cells.
This question has multiple correct options
A. Electrons are fed into anode by the oxidation reaction that takes place at the electrode.
B. The anode pushes these electrons into the external circuit and thus, acts as a source of negative charge.
C. The cathode acts as an electron sink and thus, called positive electrode.
D. The algebraic sum of E \( _{O P} \) of anode and E \( _{O P} \) of cathode gives the +ve value for spontaneous process.


Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
What does this experiment tell you
about the factors limiting the rate of
photosynthesis in the regions \( A-B \) and
B-C of curve R?
A. A-B was light intensity and B- C was some other factor (cannot find from available data)
B. A-B was temperature and B- C was light intensity
C. A-B was some other factor (cannot find from available data) and B- C was light intensity
D. None of the above


A person can see objects clearly only upto a maximum distance of \( 60 \mathrm{cm} \). His
eye defect nature of the corrective lens
and its focal length are respectively
A. Myopia, convex, \( 60 \mathrm{cm} \)
B. Myopia, concave, \( 60 \mathrm{cm} \)
c. Hypermetropia, concave, \( 60 \mathrm{cm} \)
D. Contract, convex, \( 60 \mathrm{cm} \)


In \( 50 g m \) alloy of gold and silver. The gold is \( 80 \% \) by weight. How much gold should be mixed to this alloy so that the weight of gold would become \( 95 \% ? \)
A . \( 200 g \) m
в. \( 150 g m \)
c. \( 50 g m \)
D. \( 10 g m \)


TACAAAGGGTTTCAACCC if it is the
sequence of nucleotides in a DNA
strand, they predict the sequence of aminoacids found a protein formed from it.
A. Proline, pherrylalanine, , Iysine, methionine, glycine, valine
B. Methionine, pherrylalanine, glycine, valine, lysine proline
c. Valine, Glycine, proline, lysine, pherrylalanine, methionine
D. Methionine, pherrylalanine, proline, lysine, valine glycine


The spontaneous nature of a reaction is impossible only if:
A. \( \Delta H=+v e, \Delta S=+v e \)
B. \( \Delta H=-v e, \Delta S=-v e \)
c. \( \Delta H=-v e, \Delta S=+v e \)
D. \( \Delta H=+v e, \Delta S=-v e \)


\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{A}+\boldsymbol{A l C l}_{3} \longrightarrow \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O N H}_{2} \)
Here A is:
A. urea
в. \( C l C O N H_{2} \)
c. \( C H_{3} C O N H_{2} \)
D. \( C l C H_{2} C O N H_{2} \)


Two concentric spheres of radii \( R \) and \( r \)
have positive charges \( q_{1} \) and \( q_{2} \) with equal surface charge densities. What is the electric potential at their common centre?
A \( \cdot \frac{\sigma}{\epsilon_{0}}(R+r) \)
в. \( \frac{\sigma}{\epsilon_{0}}(R-r) \)
c. \( \frac{\sigma}{\epsilon_{0}}\left(\frac{1}{R}+\frac{1}{r}\right) \)
D. \( \frac{\sigma}{\epsilon_{0}}\left(\frac{R}{r}\right) \)


STRUCTURED/APPLICATION/SKILL TYPE
Given below are chemical reactions 11 to
5) involving glucose and five other chemical products. \( (A-E) \)

Write the reaction number of the
following:
Anaerobic respiration in animals


In a binomial distribution mean is 4.8
and variance is \( 2.88, \) then the
parameter \( n \) is
A . 8
B. 12
c. 16
D. 20


During the oxidation of \( M n^{2+} \) to
\( M n O_{4}^{-} \) by \( P b O_{2} \) in acid medium, the number of moles of acid consumed per
mole of \( M n^{2+} \) ion is
A .4
B. 1/2
\( c \cdot 2 \)
D. 1/4


The principal amplitude of
\( \left(\sin 40^{\circ}+i \cos 40^{\circ}\right)^{5} \) is
A \( .70^{\circ} \)
B . \( -110^{\circ} \)
\( c \cdot 110 \)
D. \( -70^{\circ} \)


Substances react with each other and
form chemical bonds to:
A. become stable compounds
B. to decrease their energy
C. to increase their energy
D. to form newer compounds


Which material is a best conductor?
A . silver
B. porcelain
c. rubber
D. gold


The pH value of \( 10^{-3} M \) aqueous solution of \( N a C l \) is:
\( A \cdot 7 \)
B. 3
c. 11
D. 14


A cyclotron's oscillator frequency is 10
MHz and the operating magnetic field is \( 0.66 \mathrm{T} . \) If the radius of its dees is \( 60 \mathrm{cm} \)
then the kinetic energy of the proton beam produced by the accelerator is?
\( \mathbf{A} \cdot 9 \mathrm{MeV} \)
B. 10 Mev
c. 7 Mev
D. 11 Mev


Two small identical metal balls \( A \) and \( B \)
radius r are placed apart The distance
between centre of balls is \( a_{0} \) The net
potential of ball \( A \) is \( V_{1} \) and that of \( B \) is
\( V_{2} \) Let \( q_{1} \) and \( q_{2} \) are the charges on balls
A and B respectively Then the charge on
\( A \) and \( B \) are \( \left(\left(g i v e n r<<a_{0}\right)\right) \)
This question has multiple correct options
A \( \cdot q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}-V_{2} r\right)}{a_{0}^{2}-r^{2}} \)
В. \( \quad q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}+V_{2} r\right)}{a_{0}^{2}+r^{2}} \)
\( ^{\mathbf{C}} \cdot_{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{2} a_{0}+V_{1} r\right)}{a_{0}^{2}+r^{2}} \)
D. \( _{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{2} a_{0}-V_{1} r\right)}{a_{0}^{2}-r^{2}} \)


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sqrt{10-\sqrt{x^{4}-21 x^{2}}} \) is
B . \( [\sqrt{-21}, \sqrt{21}] \)
c. [-5,5]
D. \( (-5, \infty) \)


The rate of change of velocity gives acceleration. If the acceleration of a
particle is \( a=3 t^{2} m s^{-2} \) and velocity of
particle at \( t=0 \) is \( 1 m s^{-1}, \) then velocity
of the particle at \( t=2 s \) will be
A \( \cdot 12 m s^{-1} \)
B. \( 13 m s^{-1} \)
\( \mathrm{c} \cdot 11 \mathrm{ms}^{-1} \)
\( \mathbf{D} \cdot 9 m s^{-1} \)


Write structural formula of \( N i(C o)_{4} \)
and \( \boldsymbol{C r}(\boldsymbol{C o})_{\boldsymbol{6}} ? \)


Which is among the greatest contributors to gaseous pollutions that are responsible for acidic rain?
A. Electrical power generation using coal
B. Earthquakes
c. Air pollution
D. All of the above


Convert speed into \( \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \)
\( 25 m / s \)


In the adjoining figure, identify the pair of alternate interior angles.


Some of the batteries have alkaline
electrolytes-
¡) Nickel - cadmium
ii) Mercury battery
iii) Modified Leclanche cell
Cell potential is independent of \( \left[\mathrm{OH}^{-}\right] \) in :
B. ii, ii
c. i, ii, iii
D. iii only


The definite number of water molecules
which enters into a chemical
combination with the substance when
the substance is crystallized from its hot saturated solution is
called
A. crystallization
B. water of crystallization
c. formation of water molecule
D. none of the above


The function \( f \) is defined by \( f(x)= \)
\( (x+3)(x+1) \)
The graph of \( f \) in the \( x y- \) plane is a
parabola.Which of the following
intervals contains the \( x- \) coordinate
of the vertex of the graph of \( f ? ? \)
A. \( -4<x<-3 \)
B. \( -3<x<1 \)
c. \( 1<x<3 \)
D. \( 3<x<4 \)


The ratio in which the join of (1,-2,4)
and (4,2,-1) divided by the \( X-Y \)
plane is
A . 1: 3
B. 3: 1
c. 4: 1
D. 1: 4


An ideal spring is hung vertically from the ceiling. When a \( 2.0 k g \) mass hangs at rest from the spring is extended \( 6.0 \mathrm{cm} \) from its relaxed length.
downward external force is now applied
to the mass to extend the spring an additional 10cm. While the spring is being extended by the force, the work done by the spring is:
A. \( -3.3 J \)
\( J \)
в. 3.3 .5
c. \( -1.67 J \)
D. 3.6 \( J \)


The plates of a parallel plate capacitor
are charged with surface densities \( \sigma_{1} \)
and \( \sigma_{2}\left(\sigma_{1}=\sigma \text { and } \sigma_{2}=-\sigma\right) \)
respectively and placed horizontally. The electric field at points :
This question has multiple correct options
A. inside the region between the plates will be zeroro
B. above the upper plate and below the lower plate will be zero
c. everywhere in space will be zero
D. inside the region between the plates will be uniform and non zero (neglecting other effects)


A uniform string of length \( L \) fixed between the two ends is vibrating in three segments. The wavelength of wave in string is
A \( \cdot \frac{L}{3} \)
в. \( 3 L \)
c. \( \frac{2 L}{3} \)
D. \( \frac{3 L}{2} \)


Study the bar graph and answer the questions. The graph shows the
quantities of different crop production in different states of India.

What is the approximate percentage of
wheat produced by Maharashtra to that of the total crop produced by the state?
Rice \( \square \) Wheat \( \square \) Pulse
A .64 .28
В. 56.6
c. 76.6
D. 86.6


Two persons pull a rope towards themselves. Each person exerts a force
of \( 100 \mathrm{N} \) on the rope. Find the Young
modulus of the material of the rope if it
extends in length by 1cm. (Original length of the rope \( =2 \mathrm{m} \) and the area of
\( \operatorname{cross} \operatorname{section}=2 c m^{2} \)


Which of the following is not an example of symmetrical ether?
A. \( C H_{3}-O-C_{2} H_{5} \)
в. \( C_{2} H_{5}-O-_{\}^{C H}-C H_{2}-C H_{3} \)
c.
\[
C_{2} H_{5}-O-C_{1}^{\prime}-C H_{3}
\]
D. All of them


Observing that \( 1^{3}=1,2^{3}=3+5 \)
\( 3^{3}=7+9+11,4^{3}=13+15+17+19 \)
Find a general formula for the cube of natural number n and prove it by the principle of mathematical induction


While numbering carbon atoms of long carbon chain numbering should be done in such a manner that
substitution gets
A. lowest possible number
B. highest possible number
c. some middle number
D. none of the above


\( (\boldsymbol{k}-\mathbf{1}) \boldsymbol{C}_{(\boldsymbol{k}-\mathbf{1})}+^{\boldsymbol{k}} \boldsymbol{C}_{(\boldsymbol{k}-\mathbf{1})}+^{(\boldsymbol{k}+\mathbf{1})} \boldsymbol{C}_{(\boldsymbol{k}-\mathbf{1})}+ \)
\( +(n+k-2) C_{(k-1)}=? \)
\( \mathbf{A} \cdot(n+k) C_{k} \)
B. \( ^{(n+k+1)} C_{k} \)
\( \mathbf{C} \cdot(n+k) C_{k-1} \)
D. \( (n+k-1) C_{k} \)


Ni is metal but dissolved in \( C O \) gas
due to formation of \( A . A \) decomposes
into metal.
(a)What is \( A \) ?
(b) \( A \) is formed at what temperature
(c) \( A \) decomposes into metal at what
temperature
A \( \cdot(\text { a }) N i(C O)_{4} ;(b) 28^{0} C\left(\text { c) } 230^{0} C\right. \)
B . (a) \( N i(C O)_{4} ;(b) 48^{0} C \) (с) \( 330^{0} C \)
C \( \cdot \) (a) \( N i(C O)_{2} ;(b) 14^{0} C \) (c) \( 230^{0} C \)
D. (a) \( N i\left(C O_{2} ; \text { (b) } 56^{\circ} C \text { (с) } 125^{\circ} C\right. \)


Which of the following is not an essential amionoacid?
A. Trypophen
B. Histidine
c. Proline
D. Threonine


A uniform copper wire carries a current
\( \boldsymbol{i} \) amperes and has \( \boldsymbol{p} \) carriers per metre.
The length of the wire is \( l \) metres and its
cross-section area is s metre. If the
charge on a carrier is \( q \) coulombs, the
drift velocity in \( m s^{-1} \) is given by
\( \mathbf{A} \cdot i / l s q \)
\( \mathbf{B} \cdot i / p s q \)
\( \mathbf{c} \cdot p s q / i \)
\( \mathbf{D} \cdot i / p s l q \)


Assertion
Colloidal solutions exhibits Brownian
motion.
Reason
Brownian motion is responsible for stability of solutions.
Choose the correct option about assertion and reason from the following:
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The line \( \frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1} \)
intersects the curve \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c}^{2}, \boldsymbol{z}=\mathbf{0}, \) if
\( \boldsymbol{c}= \)
A. \( 5 \sqrt{5} \)
B. \( 4 \sqrt{5} \)
c. \( \sqrt{5} \)
D. \( 2 \sqrt{5} \)


What is the site of formation of
glycoxylate from glycolate?


Which of the following is an end product of citric acid cycle?
A . Citric acid
B. Lactic acid
c. Pyruvic acid
D. carbon dioxide


Raoult's law is obeyed by each
constituent of a binary liquid solution
when:
A. the forces of attractions between like molecules are greater than those between unlike molecules
B. the forces of attractions between like molecules are
smaller than those between unlike molecules
C. the forces of attractions between like molecules are identical with those between unlike molecules
D. the volume occupied by unlike molecules are different


Acids and bases are important because
of :
This question has multiple correct options
A. their use in industry
B. their effects on human health
C. their effects on farmer's crops
D. their use in neutralization to form salts


Which term of the A.P.
\( 17,16 \frac{1}{5}, 15 \frac{2}{5}, 14 \frac{3}{5} \dots . \) is first negative
term?


What is the general name of pentanal
\( \left(\boldsymbol{C}_{4} \boldsymbol{H}_{\boldsymbol{g}} \boldsymbol{C H O}\right) ? \)


Evaluate the following definite integrals as limit of sums.
\( \int_{a}^{b} x d x \)
A \( \cdot b^{2}+a^{2} \)
B. \( \frac{b^{2}-a^{2}}{2} \)
c. \( a^{2}-b^{2} \)
D. \( a^{2}+b^{2} \)


Which of the following has \( 2^{n d} I P< \)
\( 1^{s t} \) IP?
A. \( M g \)
в. \( N e \)
\( c . c \)
D. None


A pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected
back with:
A. a phase change of \( 180^{\circ} \) with velocity reversed
B. the same phase as the incident pulse with no reversal of velocity
C. a phase change of \( 180^{\circ} \) with no reversal of velocity
D. the same phase as the incident pulse but with velocity reversed


Classify the pairs of media as denser
and rarer.
A. Air, water
B. Air, glass
C. Water, glass.


In a purely resistive circuit, the current:
A. is always in phase with the applied emf
B. is always out of phase with the applied emf
C. can be in phase or out of phase with the applied emf
D. insufficient information


The number of permutations which can
be formed out of the letters of the word "
SERleS " taking three letters together is :


Solve in
\( R: \frac{10 x}{x^{2}+9} \leq 1 \)


Which of the following compound
processes zero dipole moment?
This question has multiple correct options
A. \( H_{2} O \)
в. \( C H_{3} F \)
c. \( C C l_{4} \)
D. \( B F_{3} \)


Determine whether the following compound statement are true of false:
Delhi is in England and \( 2+2=4 \)
A . True
B. False


During anaphase I of meiosis,
A. Homologous chromosomes separate
B. Non-homologous chromosomes separate
C. Sister chromatide chromosomes separate
D. Non-sister chromatids chromosomes separate


A proton and an alpha particle enter into a uniform magnetic field with the same velocity.The period of rotation of the alpha particle will be
A. four times that of proton
B. two times that of proton
c. three times that of proton
D. same as that of proton


Let \( X \) be the set of all citizens of India.
Elements \( x, y \) in \( X \) are said to be related if the difference of their age is 5 years.
Which one of the following is correct?
A. The relation is an equivalence relation on \( x \).
B. The relation is symmetric but neither reflexive nor transitive
c. The relation is reflexive but neither symmetric nor transitive
D. None of the above


At a Cambridge college, \( 65 \% \) of the maths student come from England. If
there are 240 maths student, How many
are not from England?


Solve the equation:
\( \frac{2 x}{3}=18 \)


Two particles of masses \( 2 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are approaching towards each other with acceleration \( 1 \mathrm{m} / \mathrm{s}^{2} \) and \( 2 \mathrm{m} / \mathrm{s}^{2} \)
respectively, on a smooth horizontal surface. Them find the acceleration of
centre of mass of the system and
direction of acceleration of \( C O M \)


Three identical long solenoids \( P, Q, R \) are connected to each other as shown in
figure. If the magnetic field at the center of \( \boldsymbol{P} \) is \( 2.0 T, \) what would be the
field (in \( T \) ) at the center of \( Q \) ? Assume
that the field due to any solenoid is confined within the volume of that
solenoid only.


Draw the conjugate acid of \( \boldsymbol{H} \boldsymbol{O}^{-} \)


Which of the following is the densest metal on earth?
A. Rhenium
B. Osmium
c. Rhodium
D. Iridium


Largest silk producing state of India is
A. Karnataka
B. Bihar
c. Bengal
D. Assam


The correct name of the compound
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) according to IUPAC
system is:
A. cuprammonium nitrate
B. terrammine copper(II) dinitrate
c. tetrammine copper(II) nitrate
D. tetrammine copper(III) dinitrate


\( f\left|\begin{array}{lll}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\boldsymbol{2} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\boldsymbol{3} & \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{4} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right|=\mathbf{0} \) then show
that \( a, b, c \) are in \( A . P \)


The figure shows two identical paralle plate capacitors connected to a battery
with the switch \( S \) closed. The switch is
now opened and the free space between
the plates of the capacitors is filled with
a dielectric of dielectric constant (or
relative permittivity) 3.Find the ratio of
the total electrostatic energy stored in both capacitors before and after the
introduction of the dielectric.
\( A \cdot \frac{2}{3} \)
B . 5 \( \overline{3} \)
\( c \cdot 3 \)
\( \overline{5} \)
\( D \cdot 3 \)
\( \overline{2} \)


Show by the mathematical induction
that \( \frac{1}{\sin 2 x}+\frac{1}{\sin 4 x}+\frac{1}{\sin 2^{n} x}= \)
\( \cot x-\cot 2^{n} x \)


What will be the compound interest on Rs. 25000 for 3 years at \( 6 \% \) per annum, compounded annually?


The differential equation for a particle of mass \( 2 \mathrm{kg} \) executing \( \mathrm{SHM} \) is \( 2 \frac{d^{2} x}{d t^{2}}+ \)
\( x=0 . \) If amplitude of oscillation is 3
\( \mathrm{cm}, \) then maximum velocity of the particle will be
A. \( 3 \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)
B. \( \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)
c. \( \sqrt{0.5} / 3 \mathrm{cm} / \mathrm{s} \)
D. \( 2 \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)


The process by which smaller molecules combine to give a molecule with a higher molecular weight is known as:
A. condensation
B. polymerisation
c. catenation
D. isomerisation


Which of the following is not a refrigerant?
A. \( C H C l F_{2} \)
в. \( N H_{3} \)
c. Ether
D. \( C_{2} H_{4} \)


a material of bulk modulus B
is surrounded by an incompressible liquid in a cylindrical container. \( \mathbf{A} \) massless piston of area A floats on the surface of the liquid. The magnitude
of fractional change in the radius of the sphere \( \left(\frac{\boldsymbol{d} \boldsymbol{R}}{\boldsymbol{R}}\right) \) when a mass \( \mathrm{M} \) is placed slowly on the piston to compress the liquid is:
A \( \cdot \frac{M g}{3 A B} \)
в. \( \frac{M g}{A B} \)
\( \mathrm{c} \cdot \frac{3 M g}{A B} \)
D. None of these


A compound contains two elements 'X'
and 'Y' in the ratio of \( 50 \% \) each. Atomic
mass of 'X' is 20 and 'Y' is \( 40 . \) What can
be its simplest formula?
A. \( x y \)
в. \( X_{2} Y \)
\( \mathrm{c} \cdot \mathrm{XY}_{2} \)
D. \( X_{2} Y_{3} \)


\( \left.\left(C_{2} H_{5}\right)\right)_{2} C O \frac{H_{3} O^{+}}{C H_{3} M g B r(e x c e s s)} A . A \)
(alcohol) can also be obtained by:
A \( \cdot C H_{3} C H_{2} C H O \frac{H_{3} O^{+}}{C H_{3} M g B r(2 m o l)} \)
в. \( _{\mathrm{II}}^{o} \)
\( C H_{3} C O C_{2} H_{5} \frac{C H_{3} M g B r(2 m o l)}{H_{3} O^{+}} \)
c. \( \quad_{\mathrm{N}}^{o} \mathrm{C}_{\mathrm{H}_{3} \mathrm{CCH}_{3}} \frac{\mathrm{CH}_{3} \mathrm{MgBr}(1 \mathrm{mol})}{\mathrm{H}_{3} \mathrm{O}^{+}} \)
D. both \( B \) and \( C \)


Give possible expressions for the length and breadth of the rectangle whose area is given by
(i) \( 25 a^{2}-35 a+12 \)
(ii) \( 24 x^{2}-15 x \)


For the following concentration cell,to be
spontaneous \( \boldsymbol{P t}\left(\boldsymbol{H}_{2}\right) \boldsymbol{P}_{1} \boldsymbol{a} \boldsymbol{t m} \mid \boldsymbol{H} \boldsymbol{C l} \| \boldsymbol{P t}\left(\boldsymbol{H}_{2}\right), \boldsymbol{P}_{2} \boldsymbol{a} \boldsymbol{t m} \)
Which of the following is correct?
A \( \cdot P_{1}=P_{2} \)
в. \( P_{1}<P_{2} \)
c. \( P_{1}>P_{2} \)
D. Can't be predicted


The number of oxygen atoms surroundings each nitrogen atom in
\( N_{2} O_{5} \) is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Which of the following is a food antioxidant?
A. Butylated hydroxytoluene (ВНТ)
B. Butylated hydroxyanisole (BHA)
c. saccharin
D. Both A and B


When baking soda is mixed with lemon juice, bubbles are formed with the evolution of a gas.What type of change is it? Explain.


The length of the tube of a microscope is \( 10 \mathrm{cm} . \) The lengths of the objective and eye lenses are \( 0.5 \mathrm{cm} \) and \( 1 \mathrm{cm} \)
respectively. The magnifying power of the microscope when the images at far point is about
A. 5
B. 23
\( c \cdot 166 \)
D. 500


Cytokinesis is followed by
\( \mathbf{A} . M \) phase
B. \( G_{1} \) phase
c. \( S \) phase
D. \( G_{2} \) phase


Find the magnetic induction \( B \) on the axis as a function of \( x \)
A \( \cdot B=\frac{1}{2} \mu_{0} n I\left(1-\frac{x}{\sqrt{x^{2}+R^{2}}}\right) \)
в. \( \quad B=\frac{1}{2} \mu_{0} n I\left(2-\frac{x}{\sqrt{x^{2}+R^{2}}}\right) \)
c. \( _{B}=\frac{1}{2} \mu_{0} n I\left(R-\frac{x}{\sqrt{x^{2}+R^{2}}}\right) \)
D. \( B=\frac{1}{2} \mu_{0} n I\left(X-\frac{x}{\sqrt{x^{2}+R^{2}}}\right) \)


If \( * \) represents 5 balloons then number
of symbols to be drawn to represent 60 balloons is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 60
c. 10
D. 12


The density of copper is \( 8.94 m L^{-1} \) Find out the number of coulombs
needed to plate an area \( 10 \times 10 \mathrm{cm}^{2} \) to
a thickness of \( 10^{-2} \mathrm{cm} \) using \( \mathrm{Cu} \) SO
solution as electrolyte. (At. mass of \( \boldsymbol{C u}=\mathbf{6 3 . 6}) \)


Which acid is used in dentistry and orthodontics as an etching solution?
A. Tartaric acid
B. Phosphoric acid
c. carbonic acid
D. Acetic acid


Select the correct I.U.P.A.C name for
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{C o}(\boldsymbol{C O})_{4}\right] \)
A. Sodium tetracarbonylcobalt (-I)
B. Sodium tetracarbonylcobalt (0)
c. Sodium tetracarbonylcobaltate (0)
D. sodium tetracarbonylcobaltate (-I)


Two stones are dropped from the top of a tower at half a second apart. The time after dropping the first stone at which
the distance between the two stones is
\( 20 \mathrm{m} \) is \( \left(g=10 m s^{-2}\right) \)
A \( .4 \mathrm{s} \)
B. 3.75 s
c. 4.25 s
D. 0.53 s


PQ and PR are the tangents to a circle with centre \( O . \) If \( \angle P=\frac{4}{5} \angle O . \) Find
\( \angle Q O R \)
A \( \cdot 90^{\circ} \)
B. \( 80^{\circ} \)
\( c \cdot 110^{\circ} \)
D. None of these


The length of two adjacent sides of a
parallelogram are respectively \( 51 \mathrm{cm} \)
and \( 37 \mathrm{cm} . \) One of its diagonals is
\( 20 \mathrm{cm} . \) Find the area of the
parallelogram.


Stamens attached to petals are
A. Epipetalous
B. Epiphyllous
c. Episepalous
D. All of the above


The final stable community in ecological succession is
A. Seral community
B. Pioneer communiy
c. Ecosere
D. climax community


With the help of a neatly drawn and
labelled diagram, obtain balancing
condition of a Wheatstone bridge.


An infinitely long straight conductor is uniformly charged with charge density \( \lambda \) per meter. The work done to bring a
charge \( q_{0} \) at perpendicular distance \( b \) to
\( a \) perpendicular distance \( a(a<b) \) from
the conductor is :
A. zero
в. \( \frac{q_{0} \lambda}{2 \pi_{0}} \)
c. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log _{0}\left(\frac{b}{a}\right) \)
D. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log _{0}\left(\frac{a}{b}\right) \)


Two coherent point sources \( S_{1} \) and \( S_{2} \) vibrating in phase emit light of wavelength \( \lambda \). The separation between the sources is \( 2 \lambda \). Consider a line
passing through \( S_{2} \) and perpendicular
to the line \( S_{1} S_{2} \). What is the smallest
distance from \( S_{2} \) where a minimum of
intensity occurs?


'The action and reaction both act
simultaneously.' Is this statement true and what is the net force?
A. yes, zero
B. no, zero
c. yes, positive
D. no, negative


A body dropped from the top of a tower reaches the ground in 4 s. Height of the tower is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) ):
A . \( 39.2 m \)
в. \( 44.1 \mathrm{m} \)
c. \( 58.8 m \)
D. \( 78.4 \mathrm{m} \)


The path of the difference between two interfering the waves at a point on the screen \( \frac{\lambda}{8} . \) The ratio of intensity at this point and that of at the central fringe will be
\( \mathbf{A} \cdot 0.853 \)
B. 8.53
c. 85.3
D. 853


Which of the following is not a sugar?
A. Sucrose
B. Glucose
c. Fructose
D. All are sugars


Which of the following salts has the
greatest molar solubility in pure water?
A \( \cdot C a C O_{3} ; K_{s p}=8.7 \times 10^{-9} \)
B. \( C u S ; K_{s p}=8.5 \times 10^{-45} \)
C \( \cdot A g_{2} C O_{3} ; K_{s p}=6.2 \times 10^{-12} \)
D. \( P b\left(I O_{3}\right)_{2} ; K_{s p}=2.6 \times 10^{-13} \)


Mr. Philip invests an amount of Rs.
12200 at the rate of 2 p.c.p.a.for 4 years to obtain a simple interest. Later he invests the principal amount as well as the amount obtained as simple interest
for another 3 years at the same rate of interest. What amount of simple interest will he obtain at the end of the
last 3 years?
A . 1185.84
B. 1285.84
c. 1385.84
D. 1485.84


Which of the following is best scientific method to test presence of water in a liquid?
A . Taste
B. Smell
c. use to litmus paper
D. use of anhydrous \( C u S O_{4} \)


The focal length of the objective and eye lenses of a microscope are \( 1.6 \mathrm{cm} \) and \( 2.5 \mathrm{cm} \) respectively. The distance between the two lenses is \( 21.7 \mathrm{cm} \). If the
final image is formed at infinity, what is the linear magnification?
A . 11
B. 110
\( c \cdot 1 \)
D. 44


A non-conducting ring having charge \( q \) uniformly distributed over its circumference is placed on a rough
horizontal surface. A vertical time
varying magnetic field \( B=4 t^{2} \) is
switched on at time \( t=0 . \) Mass of the
ring is 'm' and radius is R. The ring starts rotating after 2 s. The coefficient of friction between the ring and the table is:
A \( \cdot \frac{4 q m R}{g} \)
в. \( \frac{2 q m R}{g} \)
c. \( \frac{8 q R}{m g} \)
D. \( \frac{q R}{2 m g} \)


A 0.5 molal solution of ethylene glycol in water is used as the coolant in a car. If
the freezing point constant of water is \( 1.86 \mathrm{K} . \mathrm{kg} / \mathrm{mol} \), the mixture will freeze at:
\( \mathbf{A} \cdot 0.93^{0} C \)
B. \( -0.93^{0} C \)
c. \( 1.86^{0} C \)
D. \( -1.86^{0} C \)


Consider a parallel plate capacitor
having charge \( Q \). Then
This question has multiple correct options
A. There is no force acting on plates of the capacitor
B. The electric field at outer side of plates is zero
c. The electric field between the plates of the capacitor is \( \frac{\sigma}{i n_{0}} \)
D. The force between the plates is given by \( \frac{Q^{2}}{2 A \epsilon_{0}} \)


Change in shape of a body caused by the application of stress is called:
A . rigidity
B. elasticity
c. sheer
D. deformation


\( \frac{6 a b-b^{2}+12 a c-2 b c}{b+2 c} \)


Choose the correct statement with
respect of fluids.
A. only gases behave as fluids.
B. Gases and solids behave as fluids.
c. Gases and liquids behave as fluids.
D. None of these.


\( \alpha \) and \( \beta \) - particles emitted when uranium nucleus \( _{92} U^{238} \) decay to \( 82 P b^{214} \) are
A. \( 6-\alpha \) particles and \( 2-\beta \) particles
B. 4 \( \alpha \) - particles and 2 \( \beta \) particles
c. \( 2-\alpha \) particles and \( 6 \beta \) particles
D. 2 \( \alpha \) -particles and 4 \( \beta \) -particles


Which of the following statements are true for hypermetropia?
a. The near point is farther away from
25cm.
b. The image of the object is formed behind the retina.
c. It arises due to decreased power of
accommodation.
d. It can be corrected by diverging lens.
A. b and c
B. c and d
\( c . \) a and \( b \)
D. a and d


Find the \( 10 t h \) term from end for the
\( A . P .3,6,9,12, \dots, 300 \)


How many different types of hybridization are present in the given
compound? \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{3} \)


The dimensional formula of effective
torsional constant of spring is
A \( \cdot M^{1} L^{2} T^{-3} \)
B. \( M^{1} L^{2} T^{-2} A^{-} \)
c. \( M^{1} L^{2} T^{-2} \)
D. \( M^{0} L^{0} T^{0} \)


Which part in the diagram shows band
gap
A.
B. A
\( c . \) в
D. A and C


Young's expt. the ratio of intensity at maxima and minima in the interference
pattern is The \( 25: 9 . \) The ratio of slit
width will be
\( A \cdot 4: 1 \)
B. 2:1
\( c \cdot 16: 1 \)
D. 8: 1


Assertion
Phyllotaxy deals with morphology of
Ieaves
Reason
Foliage denotes all leaves of a plant.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Assuming pool is \( 15 \mathrm{m} \) in length, \( 12 \mathrm{m} \) in breadth and \( 2 m \) in depth. Find the \( \operatorname{cost} \) of cementing the floor and wall at
the rate of \( R s .15 \) per \( s q . m \)


The drift velocity of electrons in a
conducting wire is of the order of
\( 1 m m / s, \) yet the bulb glows very quickly after the switch is put on because
A. the random speed of electrons is very high of the order of \( 10^{-6} \mathrm{m} / \mathrm{s} \)
B. the electrons transfer their energy very quickly through collision.
c. electric field is set up in the wire very quickly, producing a current through each cross section almost intantaneously
D. All the above


Construct a \( \triangle A B C \) in which \( B C= \)
\( 4.5 \mathrm{cm}, \angle B=45^{\circ} \) and \( A B+A C=8 \mathrm{cm} \)
Justify your construction


This desert plant found in Southwestern
United States can survive in the harsh
desert climate by staying dormant. When it rains, it grows new leaves and flowers. On seed maturity, it sheds its leaves and becomes dormant again. Identify the plant.
A. Elephant foot tree
B. Joshua tree
c. ocotillo
D. Saguaro


\( \int_{0}^{\frac{\pi}{4}} \frac{\sin ^{2} x \cdot \cos ^{2} x}{\left(\sin ^{3} x+\cos ^{3} x\right)^{2}} d x=\frac{m}{6} \cdot \) Find \( m \)


Which of the following is not a decomposition reaction?
\( A \cdot \operatorname{cac} 0_{3} \rightarrow \operatorname{cad}+\cos \)
В. \( 2 \mathrm{KClO}_{3} \rightarrow 2 \mathrm{KCl}+3 \mathrm{O}_{2} \)
c. Digestion of food in the body
D. NaOH+HCI \( \rightarrow \) Nacl + Hz


Find total number of stereoisomers for
each compound given below.
\( A \)
B. 13
\( c .16 \)
D. None of these


Let \( \boldsymbol{S}_{\boldsymbol{k}}=\frac{\mathbf{1}+\mathbf{2}+\mathbf{3}+\ldots+\boldsymbol{k}}{\boldsymbol{k}} . \) If \( \boldsymbol{S}_{1}^{2}+ \)
\( S_{2}^{2}++S_{10}^{2}=\frac{5}{12} A \) then \( A \) is equal to
A . 303
в. 283
c. 156
D. 301


A right circular cone has a base radius of \( r \) and a height of \( h . \) If the radius decrease by 20 percent and the height increase by 10 percent, which of the following is the resulting percent change in the volume of the cone?
A . \( 10 \% \) decrease
B. 12\% decrease
c. 18.4\% decrease
D. \( 29.6 \% \) decrease


In case of mechanical wave a particle oscillates and during oscillation its
kinetic energy and potential energy changes.


People working with coal tar (prolonged exposure) suffer from heart diseases.
A. True
B. False


In an A.P., of which a is the first term, if
the sum of the first p terms is zero,
show that the sum of the next q terms is \( -\frac{a(p+q) q}{p-1} \)


Problem associated with nuclear power
plants is
A. Emmission of hazardous waste
B. Disposal of radioactive waste
c. Thermal pollution
D. All of the above


Among \( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \) and \( \boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e} \)
the one with the highest boiling point is:
A. \( H_{2} O \) because of hydrogen bonding interactions
B. \( H_{2} \) Te because of its higher molecular weight
c. \( H_{2} S \) because of hydrogen bonding interactions
D. \( H_{2} \) Se because of its lower molecular weight


State true or false:
Angles forming a linear pair are supplementary.
A. True
B. False


State whether given statement is True or False
The upper standard point of a thermometer is \( 273 \mathrm{K} \)
A. True
B. False


In which of the following molecules, sigma bonds formed by the overlap of
\( s p^{3} d \) and \( p \) -orbitals are present.
A. \( P C l_{5} \)
в. \( C l F_{3} \)
c. \( S b C l_{3} \)
D. \( H C l O_{4} \)


The square of the length of the tangent
from (3,-4) to the circle \( x^{2}+y^{2}- \)
\( 4 x-6 y+3=0 \) is
A . 20
B. 30
\( c \cdot 40 \)
D. 50


Examine if Rolles theorem is applicable to any of the following functions. Can you say some thing about the
converse of Rolles theorem from these
example?
(i) \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \in[\mathbf{5}, \boldsymbol{9}] \)
(ii) \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \in[-\boldsymbol{2}, \boldsymbol{2}] \)
(iii) \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-1 \) for \( \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{2}] \)


If parabolic profile is used for refractive index in the core, what is the name
given to such core?
A. single mode core
B. multi mode core
c. differential mode core
D. curvilinear differential core


Medicine used as an eye lotion is:
A. Silver sol
B. Colloidal gold
c. colloidal antimony
D. Milk of magnesia


What is the value of \( \frac{m^{2}+m n}{m^{2}+n^{2}}+ \) \( \frac{m^{2}-m n}{m^{2}+n^{2}}+\frac{n^{2}+m}{m^{2}+n^{2}}+\frac{n^{2}-m n}{m^{2}+n^{2}} \)
\( A \)
B. 0
\( c \cdot 2 \)
\( D \)


Among
\( \boldsymbol{P b S}, \boldsymbol{C u S}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{S}, \boldsymbol{M n S}, \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}, \boldsymbol{N i S} \)
and \( \operatorname{Sn} S_{2}, \) the total number of black
coloured sulphides are:
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.


The most contributing tautomeric enol
form of \( M e C O C H_{2} C O_{2} E t \) is :
A \( \cdot H_{2} C=C(O H) C H_{2} C O_{2} E t \)
в. \( \operatorname{Me} C(O H)=C H C O_{2} E t \)
c. \( \operatorname{MeCOCH}=C(O H) \) OEt
D. \( H_{2} C=C(O H) C H=C(O H) E t \)


The values of \( p \) and \( q \) for which the
function \( \mathbf{f}(\mathbf{x})= \)
\( \left\{\begin{array}{cl}\frac{\sin (\mathbf{p}+1) \mathbf{x}+\sin \mathbf{x}}{\mathbf{x}} & , \mathbf{x}<\mathbf{0} \\ \mathbf{q} & , \mathbf{x}=\mathbf{0} \\ \frac{\sqrt{\mathbf{x}+\mathbf{x}^{2}}-\sqrt{\mathbf{x}}}{\mathbf{x}^{3 / 2}} & , \mathbf{x}>0\end{array}\right. \)
is continuous for all \( \mathbf{x} \) in \( \mathbf{R} \), are
A \( \cdot p=\frac{1}{2}, q=-\frac{3}{2} \)
B. \( _{\mathrm{p}}=\frac{5}{2}, \mathrm{q}=\frac{1}{2} \)
\( ^{\mathbf{C}} \cdot_{\mathrm{p}}=-\frac{3}{2}, \mathrm{q}=\frac{1}{2} \)
D. \( _{\mathrm{p}}=\frac{1}{2}, \mathrm{q}=\frac{3}{2} \)


Among the following, which do not come
under the category of sewage
treatment?
A. The organic material present in the waste is allowed to undergo microbial oxidation
B. Large size material are filtered through screen
C. The waste water is suitably treated for the removal of phosphate by the coagulation method
D. Degrading the number of toxic organic waste


Which of the following relations is
correct?
A \( \cdot \) Distance \( =\frac{\text {Speed}}{\text {Timed} e e d \text { ed }} \)
B. Distance \( =\frac{\text { Trime }}{\text { speed }} \)
c. Distance = Speed \( \times \) Time
D. Distance = \( \frac{1}{\text { 5peedss } \times \text { ss Time }} \)


a) An ion with mass number 37
possesses one unit of negative charge.
If the ion contains \( 11.1 \% \) more neutrons
than the electrons. Find the symbol of the ion.
b) An electron is in 3d orbitals. Give the
possible values of \( n, \) land \( m_{1} \)
c) What is the maximum number of
emission lines, When the excited
electron of a \( \boldsymbol{H} \) atom in \( \boldsymbol{n}=\boldsymbol{6} \) drops to the ground state?


Which of the following methods of flow of heat is (are) based on gravitational attraction?
A. Conduction
B. Convection
c. Radiation
D. All of these


Resolve into partial fraction \( \frac{x^{3}-3 x-2}{\left(x^{2}+x+1\right)(x+1)^{2}} \)
A \( \cdot \frac{3 x-1}{x^{2}-x+1}+\frac{1}{(x+1)^{2}}-\frac{3}{(x+1)} \)
B. \( \frac{3 x-1}{x^{2}-x+1}+\frac{2}{(x+1)^{2}}-\frac{3}{(x+1)} \)
c. \( \frac{3 x-1}{x^{2}+x+1}+\frac{2}{(x+1)^{2}}-\frac{3}{(x+1)} \)
D. \( \frac{3 x-1}{x^{2}+x+1}+\frac{2}{(x+1)^{2}}+\frac{3}{(x+1)} \)


Which of the following acid is
strongest?
\( \mathbf{A} \cdot H F \)
в. \( H_{2} \) 0
c. \( N H_{3} \)
D. \( C H_{4} \)


\( C N^{-} \) and \( N_{2} \) are isoelectronic. But in
contrast to \( C N^{-}, N_{2} \) is chemically
inert because of:
A. smaller \( N-N \) bond energy
B. I arger \( N-N \) bond energy
c. low inoziation enthalpy
D. none of these


All of the following processes involve a separation of either a mixture into its components or a compound into elements. For each, decide whether the physical process or chemical reaction is required.
a. Sodium metal is obtained from the
substance Sodium chloride.
b. Iron filings are separated from the sand by using a magnet,
c. Sugar crystals are separated from sugar syrup by evaporation of water.
d. Fine crystals of Silver chloride are separated from a suspension of the crystals in water.
e. Copper is produced when Zinc metal is placed in a solution of Copper (II) sulphate, a compound.
A. a, b, c, d, e-physical
B. a, d, b, c, e - chemical
c. b, c, d- physical ; a, e- chemical
D. e a, b - physical ; c, d- chemical


Divide: \( a^{4}+4 b^{4} \) by \( a^{2}+2 a b+b^{2} \)


Do you know many visually challenged persons had great achievements to their credits.Can you identify the one who represented India on Braille problems in UNESCO
A. Manjunath
B. Maria Runyan
c. Lal Advani
D. Ravinder Jair


Q Type your question
against time. Choose a possible option:
4
B.
\( c \)
\( D \)


The sum of the series
\( (2)^{2}+2(4)^{2}+3(6)^{2}+\ldots . \) upto 10
terms is
A . 12100
B. 11300
c. 11200
D. 12300


Which of the following is a proper
sequence?
A. Elastic region, Yielding, Fracture stress, Strain hardening, Necking
B. Elastic region, Yielding, Strain hardening, Necking Fracture stress
C. Elastic region, Strain hardening, Yielding, Necking , Fracture stress
D. Elastic region, Strain hardening, Necking, Yielding, Fracture stress


A \( 10 W \) electric heater is used to heat a
container filled with \( 0.5 \mathrm{kg} \) of water. It is
found that the temperature of water and
the container rises by \( 3 K \) in 15 min. The container is then emptied, dried
and filled with \( 2 k g \) of oil. The same heater now raises the temperature of
container-oil system by \( 2 K \) in 20 min. Assuming that there is no heat loss in the process and the specific heat of water is \( 4200 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \), the specific
heat of oil in the same unit is equal to:
A. \( 1.50 \times 10^{3} \)
В. \( 2.55 \times 10^{3} \)
c. \( 3.00 \times 10^{3} \)
D. \( 5.10 \times 10^{3} \)


State Fleming's right hand rule and give examples. Demonstrate the same with the help of an experiment.


n fig, If \( \Delta A B E \cong \Delta A C D, \) show that
\( \Delta A D E \) is similar to \( \Delta A B C \)


The pH of pure water at \( 25^{\circ} \mathrm{C} \) is close to:
\( A \cdot O \)
B. 7
\( c \cdot 2 \)
D. 9


\( \sin ^{-1}(\sin 3)+\cos ^{-1}(\cos 3)+ \)
\( \tan ^{-1}(\tan 3)= \)


n \( \triangle A B C, \) the bisector \( A D \) of \( \angle A \) is
perpendicular to side \( B C . \) Show that
\( A B=A C \) and \( \triangle A B C \) is isosceles


\( \mathbf{f}\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{7}\end{array}\right]\left[\begin{array}{cc}\mathbf{1} & \mathbf{- 3} \\ -\mathbf{2} & \mathbf{4}\end{array}\right]=\left[\begin{array}{ll}-\mathbf{4} & \mathbf{6} \\ -\mathbf{9} & \boldsymbol{x}\end{array}\right], \) write
the value of \( x \)


The sum of the reciprocals of object distance and image distance is equal to the of a mirror.
A. focal length
B. reciprocal of the focal length
c. radius of curvature
D. reciprocal of the radius of curvature


f a direct current of value \( A \) ampere is
superimposed on an alternating current \( I=b \sin \omega t \) flowing through a wire, what
is the effective (rms) value of the
resulting current in the circuit?


toppr OG
Q Type your question_
-
carried out slowly and reversibly.
Starting at state a, where its volume
and pressure are \( \left(V_{0}, p_{0}\right), \) the gas
undergoes an isothermal expansion
until it reaches state b where its
volume and pressure are \( \left(8 V_{0}, p_{0} / 8\right) . \) In
process \( b \rightarrow c \) the gas is cooled at
constant volume to \( \left(8 V_{0}, p_{0} / 32\right) \)
Process \( c \rightarrow a \) is an adiabatic
compression back to state a.
Select incorrect statement:
This question has multiple correct options
\( \mathbf{A} \cdot a \rightarrow b, \) there is no change in internal energy of gas
B. \( c \rightarrow a \), there is no change in entropy of gas
c. \( b \rightarrow c \), there is no work done by gas
D. \( a \rightarrow b \rightarrow c \rightarrow a \), there is work done by gas in cyclic
process


Write the importance of forests


The equation \( \sqrt{x+4}-\sqrt{x-3}+1=0 \) has:
A. no root
B. one real root
C. one real root and one imaginary root
D. two imaginary roots
E. two real roots


\( \boldsymbol{T}_{\boldsymbol{r}}\left(\boldsymbol{A}+\boldsymbol{B}^{\boldsymbol{T}}+\boldsymbol{3} \boldsymbol{C}\right) \) equals-
(where \( T_{r}(A) \) denotes trace of matrix of
\( A) \)
A . 17
B . 18
c. 20
D. 21


\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}\frac{1-\cos 2 x}{2 x^{2}} & : x \neq 0 \\ k & : x=0\end{array}\right. \)
Then the value of \( k \) for which, \( f(x) \) will
be continuous at \( x=0 \) is
A . 0
B.
\( c \cdot 2 \)
D. none of these


Isotopes are:
A. atoms of same element, having the different atomic number but same mass numbers
B. atoms of same element, having the same atomic number but different mass numbers
C. atoms of different elements with different atomic
numbers, which have the same mass number
D. atoms of different elements with same atomic numbers, which have different mass numbers


A number consist of two digits whose
sum is \( 11 . \) The number formed by reversing the digits is 9 less than the original number. Find the number.


In the middle of the depletion layer of a reverse-biased p-njunction, the
A. electric field is zero
B. potential is maximum
c. electric field is maximum
D. potential is zero


A fair die is tossed. If 2,3 or 5 occurs, the player wins that number of rupees, but if 1,4 or 6 occurs, the player loses that number of rupees. Then find the possible payoffs for the player.


Evaluate the given integral. \( \int \frac{x^{2}-1}{x^{4}+x^{2}+1} d x \)


If 0.03 mol of zinc are added to 0.52 mol
of \( \mathbf{H C l} \), the moles of \( \mathbf{H}_{2} \) formed are:
A . 0.52
B. 0.30
\( c .0 .03 \)
D. 0.60


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{\sqrt{a}}{2}-\frac{1}{2 \sqrt{a}}\right)^{2}\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right) \)


Isotopes of an element contain
A. the same number of protons but different number of
neutrons
B. the same number of neutrons but different number of
protons
C . equal number of protons and electrons
D. equal number of nucleons


According to origin, identify the secondary air pollutant.
\( A \cdot S O_{2} \)
B. Ash
c. Ozone
D. Radioactive compound


Have you ever face shortage of water in
your area? If yes, then what was the
reason for it?


If \( E_{C H_{3} C O O O H \mid C_{2} H_{5} O H}^{\ominus}=0.06 V, \) Then \( E_{c e l l}^{\ominus} \)
of the reaction taking place in alcohol meter is :
\( \mathbf{A} \cdot 1.39 V \)
B. \( 1.27 V \)
c. \( 1.60 V \)
D. \( 1.51 V \)


Match the terms in column I with those
of column II
\( \begin{array}{ll}\text { Column - I } & \text { Column - II } \\ \text { i. Electric fuse } & \text { A. Chemical effect } \\ \text { ii. Relay } & \text { B. Electric discharge } \\ \text { iii. CFL } & \text { C. Magnetic effect } \\ \text { iv. Button cell } & \text { D. Heating effect }\end{array} \)
iii-A, iv-D
\( A \cdot \) i-C, ii-B,
B. i-B, ii-A, iii-C, iv-D
c. i-D, ii-C, iii-B, iv-A
D. i-D, ii-B, iii-C, iv-D


\( \boldsymbol{P}_{\boldsymbol{A}}=\boldsymbol{X}_{\boldsymbol{A}} \boldsymbol{P}_{\boldsymbol{A}} \) and \( \boldsymbol{P}_{\boldsymbol{B}}=\boldsymbol{X}_{\boldsymbol{B}} \boldsymbol{P}_{\boldsymbol{B}} \)
\( \boldsymbol{P}_{\boldsymbol{T}}=\boldsymbol{X}_{\boldsymbol{A}} \boldsymbol{P}_{\boldsymbol{A}}+\boldsymbol{X}_{\boldsymbol{B}} \boldsymbol{P}_{\boldsymbol{B}_{\boldsymbol{B}}} \)
Vapour pressure of mixtures of Benzene \( \left(C_{6} H_{6}\right) \) and toluene \( \left(C_{7} H_{8}\right) \) at \( 50^{\circ} C \) are given by \( \boldsymbol{P}_{M}=\mathbf{1 7 9} \boldsymbol{X}_{\boldsymbol{B}}+\mathbf{9 2} \) where
\( X_{B} \) is mole fraction of \( C_{6} H_{6} \)
What is the vapour pressure of pure liquids?
A \( \cdot P_{B}=92 m m, P_{T}=179 m m \)
B . \( P_{B}=271 \mathrm{mm}, P_{T}=92 \mathrm{mm} \)
c. \( P_{B}=180 m m, P_{T}=91 m m \)
D. None of these


In the following reaction, \( P \) gives two
products \( Q \) and \( R \), each in \( 40 \% \) yield
f the reaction is carried out with
\( 420 m g \) of \( P . \) the reaction yields
\( 108.8 m g \) of \( Q . \) The amount of \( R \)
produced in the reaction is closest to:
A. \( 97.6 \mathrm{mg} \)
B. \( 108.8 \mathrm{mg} \)
c. \( 84.8 \mathrm{mg} \)
D. \( 121.6 \mathrm{mg} \)


Match the reactions of metals with
dilute \( H N O_{3} \) (in column-I) with the
nitrogen compounds (obtained by oxidation/reduction (in column-II).


In a potentiometer the balancing with a
cell is at length of \( 220 \mathrm{cm} . \) On shunting the cell with a resistance of \( 3 \Omega \) balance
length becomes \( 130 \mathrm{cm} \). What is the internal resistance of this cell?
A. \( 4.5 \Omega \)
B. \( 7.8 \Omega \)
\( c \cdot 6.3 \Omega \)
D. \( 2.08 \Omega \)


If \( \boldsymbol{y}=\log \left[\tan \left(\frac{\boldsymbol{\pi}}{\boldsymbol{4}}+\frac{\boldsymbol{x}}{2}\right)\right] \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \cdot \sec x \)
B. \( \sin x \)
c. \( \operatorname{cosec} x \)
D. \( \sec \frac{x}{2} \)


Let \( Q(x) \) denotes the quotient which results from the division of the
polynomial \( x^{5}+3 x^{4}-x^{3}+8 x^{2}-x+ \)
\( 8 \mathrm{by} x^{2}+1 \) The sum of the square of the coefficient of \( Q(x) \) is
A . 36
B. 37
c. 38
D. 39


Close the wrong statement
A. Retardation is vector quantity
B. Acceleration is due to gravity is a vector quantity
C. Average speed is a vector quantity
D. Displacement is a vector quantity


The name of the process is :
\[
\begin{array}{l}
\mathrm{caCO}_{3} \longrightarrow \mathrm{CaO}+\mathrm{CO}_{2} \\
\mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \stackrel{\longrightarrow}{\longrightarrow} \mathrm{NH}_{4} \mathrm{HCO}_{3} \\
\mathrm{NaCl}+\mathrm{NH}_{4} \mathrm{HCO}_{3} \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}+\mathrm{NaHCO}_{3} \\
2 \mathrm{NH}_{4} \mathrm{Cl}+\mathrm{CaO} \longrightarrow \mathrm{CaC}_{2}+2 \mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}
\end{array}
\]
A. solvay
B. lowing
c. salt cake
D. gossage


In general, the resistance to electric
current of a material; in particular, the degree to which a material resists the flow of electricity is called
A. conductivity
B. resistivity
c. conductance
D. none of the above


n the given figure, \( P S=P R . \angle T P S= \)
\( \angle Q P R \) Then \( P T=P Q \)
4 True
3. Fals


An echo will be heard if the minimum
distance between the source of sound
and the obstacle is
A. \( 1 \mathrm{m} \)
B. 10
\( c \cdot 15 m \)
D. 17 m


What is an object, that reflects some
light and transmits some light, called?
A . Coloured
в. ०раяче
c. Diffuse
D. Translucent


A sigma bond forms:
A. when two orbitals directly overlap but there is only one bonding interaction.
B. when two orbitals directly overlap and there are two bonding interaction.
C. when two valence electrons combine into one orbital.
D. when two atoms overlap and the valence electrons bond
E. the creation of an S shaped orbital.


Consider the following population and
year graph, find the slope of the line \( A B \) and using it, find what will be the population in the year \( 2010 ? \)


Find the value of \( n, \) if \( 1+4+7+10+ \)
\( \ldots \) to \( n \) terms \( =\mathbf{5 9 0} \)


Insulin controls the metabolism of -
A. fats
B. Hormones
c. Carbohydrates
D. Proteins


The escape velocity from the earth for a rocket is \( 11.2 \mathrm{km} / \mathrm{s} \) ignoring air resistance. The escape velocity of \( 10 \mathrm{mg} \) grain of sand from the earth will be
\( \mathbf{A} \cdot 0.112 \mathrm{km} / \mathrm{s} \)
B. \( 11.2 \mathrm{km} / \mathrm{s} \)
c. \( 1.12 \mathrm{km} / \mathrm{s} \)
D. \( 0.0112 \mathrm{kms}^{-1} \)


Percentage by weight of 'M' in \( M C l_{3} \) is 20\%. Atomic weight of 'M' is :
A . 26.
B. 13
\( c \cdot 40 \)
D. 10.4


State True or False.
The salt bridge permits movement of charge and mixing of the solution.
A. True
B. False


Which is more metallic: sodium or
aluminium?


Distance of the point \( \boldsymbol{P}(\overrightarrow{\boldsymbol{p}}) \) from the line \( \vec{r}=\vec{a}+\lambda \vec{b} \) is -
A \( \cdot(\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{a}) \cdot \vec{b}) \vec{b}}{|\vec{b}|^{2}} \mid \)
B. \( (\vec{b}-\vec{p})+\frac{((\vec{p}-\vec{a}) \cdot \vec{b}) \vec{b}}{|\vec{b}|^{2}} \mid \)
c. \( \quad\left|(\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{b}) \cdot \vec{b}) \vec{b}}{|\vec{b}|^{2}}\right| \)
D. None of these.


What is the order of magnitude of the
seconds present in a day?


If \( A \) and \( B \) are the variances of the 1 st \( n \)
even numbers and 1st \( n \) odd numbers
respectively then
A \( . A=B \)
в. \( A>B \)
c. \( A<B \)
D. \( A=B+1 \)


The difference between the
circumference and radius of a circle is
\( 30 \pi . \) Find the diameter of circle.
A. \( \frac{30 \pi}{2 \pi-1} \)
в. \( \frac{60 \pi}{2 \pi-1} \)
c. \( \frac{2 \pi-1}{60 \pi} \)
D. None


The mean and standard deviation of a
random variable \( X \) are 10 and 5
respectively. Find.
\( \boldsymbol{E}\left(\left(\frac{\boldsymbol{x}-\mathbf{1 0}}{\mathbf{5}}\right)^{2}\right) \)


Kjeldahl's method cannot be used for estimation of nitrogen in:
(।) \( C_{6} H_{5} C O N H_{2} \)
(II) pyridine
\( (\| I) C_{6} H_{5}-N=N-C_{6} H_{5} \)
\( (\mathrm{IV}) C_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H} \boldsymbol{C O C H}_{3} \)
A . ।, Ill
B. ॥, ॥ Il
c. ॥I, Iv
D. ।, ॥


The indicator which is used to find the
strength of caustic soda solution with the help of oxalic acid is:
A. Methyl orange
B. Phenolphthalein
c. Potassium permanganate
D. None of the above


The lattice energy of \( N a C l \) is \( 788 \mathrm{kJ} \)
mol \( ^{-1} \). This means that 788 kJ of
energy is required:
A. to separate one mole of solid \( N a C l \) into one mole of \( N a_{(g)} \) and one mole of \( C l_{(g)} \) to infinite distance
B. to separate one mole of solid \( N a C l \) into one mole of \( N a_{(g)}^{+} \) and one mole of \( C l^{-}(g) \) to infinite distance
c. to convert one mole of solid \( N a C l \) into one mole of gaseous \( N a C l \)
D. to convert one mole of gaseous \( N a C l \) into one mole of solid \( N a C l \)


For \( a>0, \) all the real roots of the
equation \( \boldsymbol{x}^{2}-\mathbf{3} \boldsymbol{a}|\boldsymbol{x}-\boldsymbol{a}|-\mathbf{7} \boldsymbol{a}^{2}=\mathbf{0} \) are
\( \mathbf{A} \cdot 4 a, 5 a \)
в. \( -4 a, 5 a \)
\( \mathbf{c} .-4 a,-5 a \)
D. \( 4 a,-5 a \)


Let \( \boldsymbol{f}:\{\mathbf{1}, \mathbf{3}, \mathbf{4}\} \rightarrow\{\mathbf{1}, \mathbf{2}, \mathbf{5}\} \) and \( \boldsymbol{g}: \)
\( \{1, \mathbf{2}, \mathbf{5}\} \rightarrow\{1,3\} \) be given \( \boldsymbol{f}= \)
\( \{(\mathbf{1}, \mathbf{2}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{1})\} \) and \( \boldsymbol{g}= \)
\( \{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{3}),(\mathbf{5}, \mathbf{1})\} . \) Write down \( \boldsymbol{g} \boldsymbol{o} \boldsymbol{f} \)


Which of the following is not applicable to the phenomenon of adsorption?
A. \( \triangle H>0 \)
в. \( \triangle G<0 \)
c. \( \Delta S<0 \)
D. \( \triangle H<0 \)


The angle between \( \vec{V}_{1}=\hat{i}+2 \hat{j}+2 \hat{k} \)
and \( \vec{V}_{2}=2 \hat{i}+3 \hat{j}-4 \hat{k} \) is:
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 120^{\circ} \)


An A.C. circuit containing only capacitance, the current:
A . Lags the voltage by \( 90^{\circ} \)
B . Leads the voltage by \( 90^{\circ} \)
c. Remains in phase with voltage
D. Lags the voltage by \( 180^{\circ} \)


\( \frac{\boldsymbol{d}}{d x}\left(e^{\tan x}\right) \)
\( \mathbf{A} \cdot e^{\tan x} \cdot \sec ^{2} x \)
B \( \cdot e^{\cot x} \cdot \sec ^{2} x \)
\( \mathbf{C} \cdot e^{\cos x} \cdot \sec ^{2} x \)
D \( \cdot e^{\sin x} \cdot \sec ^{2} x \)


Polarisation of light was first successfully explained by:
A. corpuscular theory
B. Huygens' wave theory
c. Electromagnetic wave theory
D. Planck's theory


Find the volume of the sphere whose
surface area is \( 9856 \mathrm{cm}^{2} \)


Two particles of masses \( 1 k g \) and \( 2 k g \) are placed at a distance at a distance of
\( 3 m . \) Moment of inertia of the particles about an axis passing through their centre of mass and perpendicular to the
line joining them is \( \left(\operatorname{in} k g-m^{2}\right) \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 8
D. 12


In the given figure, if \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{w}+\boldsymbol{z} \)
then prove that \( A O B \) is a line.


Which is wrong
A. Presence of albumin in urine is albuminaria
B. Presence of glucose in urine is glycosuria
C. Presence of ketose sugar in urine is ketonuria
D. Presence of excess urea in blood is uremia
E. Presence of haemoglobin in nature haemoglobinuria


Shape-selective catalysis is a reaction catalysed by:
A. Zeolites
B. Enzymes
c. Platinum
D. ziegler-Natta catalyst


Equilibrium constants \( \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \) for
the following equilibria are related as:
\( N O(g)+\frac{1}{2} O_{2} \stackrel{K_{1}}{=} N O_{2}(g) \)
\( \mathbf{2} N O_{2}(\boldsymbol{g}) \stackrel{\boldsymbol{K}_{2}}{\rightleftharpoons} \boldsymbol{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( ^{\mathrm{A}} \cdot_{K_{2}}=\frac{1}{K_{1}} \)
B. \( K_{2}=K_{1}^{2} \)
c. \( _{K_{2}=} \frac{K_{1}}{2} \)
D. \( _{K_{2}}=\frac{1}{K_{1}^{2}} \)


A cylinder of height \( 20 \mathrm{m} \) is completely filled with water. The velocity of efflux of water (in \( \mathrm{ms}^{-1} \) ) through a small hole on
the side wall or the cylinder near its bottom is:
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 m/s
c. \( 25.5 \mathrm{m} / \mathrm{s} \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


The radio active isotope of hydrogen is
A. protium
B. deuterium
c. tritium
D. none of these


The angle of rotation symmetry for a shape is \( 60 . \) What is the order of
rotational symmetry?
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. 8


Which of the following triggers the physical changes during the adolescence?
A. Testosterone
B. Estrogen
c. Thyroxine
D. Both A and B


If in solvent, n simple molecules of solute combine to form an associated
molecule, \( x \) is degree of association the
Van't Hoff's factor \( ^{\prime} \boldsymbol{i}^{\prime} \) is equal to:
A \( \cdot \frac{1}{1-n x} \)
в. \( \frac{1-x+n x}{1} \)
c. \( \frac{1-x+\frac{x}{n}}{1} \)
D. \( \frac{x}{\frac{n}{1}-1+x} \)


Assertion: A solution of sodium acetate
and ammonium acetate can act as a
buffer.

Reason: A buffer solution consists of a
mixture of a weak acid and its
conjugate base or vice versa.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


What may be the stable oxidation state
of the transition element with the
following d-electron configuration in the ground state of their atoms:
\( 3 d^{3}, 3 d^{5}, 3 d^{8} \) and \( 3 d^{4} ? \)


Geothermal energy can be best
described as:
A. light energy from Sun.
B. heat energy from rocks inside Earth's surface.
C. heat energy from temperature difference in tides.
D. heat energy from combustion of minerals.


The number of sides of two regular polygons A and B are in ratio 1: 3. If each
interior angle of polygon \( \mathrm{B} \) is \( 168^{\circ} . \) Find each interior angle of polygon \( A \)
A \( .144^{\circ} \)
B. 120
\( c \cdot 72 \)
D. 22.5


Chemical formula of washing soda is:
A. \( N a_{2} C O_{3} \)
в. \( N a_{2} C O_{3} .10 H_{2} O \)
c. \( N a_{2} C O_{3} .5 H_{2} O \)
D. \( N a_{2} S O_{4} .10 H_{2} O \)


\( P \) and \( Q \) are mid point of sides RS \( \& R T \)
respectively of \( \triangle \) RST.
\( \mathrm{PQ}=5 \mathrm{cm}, \mathrm{RS}=\mathrm{RT}=10 \mathrm{cm}, \) then
perimeter of \( \triangle \mathrm{RST} \) is:
A . \( 27.5 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .25 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)


A system is taken from state \( A \) to \( B \)
thought three different paths 1,2 and 3
The work done is maximum in:
A. process 1
B. process 2
c. process 3
D. equal in all process


Moment of inertia of a disc about the
tangent parallel to its plane is \( I \). The moment of inertia of the disc tangent and perpendicular to its plane is
\( ^{\mathrm{A}} \cdot \frac{3 I}{4} \)
в. \( \frac{3 I}{2} \)
c. \( \frac{5 I}{6} \)
D. \( \frac{6 I}{5} \)


A particle is performing linear S.H.M. with period 6 s and amplitude 'a'. The minimum time taken by the particle to travel between two points situated at a distance \( \frac{a}{2} \) on either sides of mean
position is :
A . 1 s
в. 1.5 s
\( c \cdot 3 s \)
D. 6 s


In the treatment of waste water
discharge, which treatment stage involves biological treatment?
A. Primary treatment
B. Secondary treatment
c. Tertiary treatment
D. Reverse osmosis stage


Which of the following liquid pairs will exhibit a positive deviation from
Raoult's law?
A. Water - Hydrochloric acid
B. Cyclohexane - Ethanol
c. Acetone - Chloroform
D. water-Nitric acid


Construct a bisector of an angle.


Find the \( H C F \) of 81 and 237 and
express it as a linear combination of 81
and 237


Statement-I: The point \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \mathbf{6}) \) is the
mirror image of the point \( B(1,3,4) \) in
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Statement-2: The plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
bisects the line segment joining
\( \boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) \) and \( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
A. (1) Statementl is true. Statement-1 is true: Statement
- 2 is a correct explanation for Statement- -
B. (2) Statementl is true, Statement-2 is true: Statement-
9 is not a correct explanation for statement- -
c. (3) Statement-l-lis true, Statement-2 is false.
D. (4) Statementl is false. Statement-2 is true


Magnitude of Seebeck emf between the junctions does not depend on
A. thermocouple
B. temperature of cold junction
c. temperature of hot function
D. neutral temperature


The co-ordination number of zinc in zinc
blende (Zns) is
A. 6
B. 4
\( c \cdot 8 \)
D. 12


One gas bleaches the color of the
flowers by reduction while the other by oxidation. The gases are:
A. co and \( C O_{2} \)
B. \( H_{2} S \) and \( B r_{2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{Cl}_{2} \)
D. \( N H_{3} \) and \( S O_{3} \)


An AC circuit contains a variable
inductor \( L, \) connected in series with a
light bulb of resistance \( R \) as shown
Assume that the resistance of the light bulb is independent of its temperature. Now it is desired to reduce the power of the light bulb to one fourth then
(frequency of ac source is \( \frac{R}{2 \pi L_{0}} \) wher
This question has multiple correct options
A. Power factor of the circuit should be reduced to half
B. Inductance of the circuit should be increased by a factor of \( \sqrt{3} \)
c. Impedance of the circuit should be increased by a factor of 4
D. R.M.S. current in the circuit should be reduced to half


f \( p^{2}=a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta \) then \( \frac{d^{2} p}{d \theta^{2}}+ \)
\( p \) is equal to \( (a \neq b) \)
A \( \cdot \frac{a^{2} b^{2}}{p^{4}} \)
в. \( \frac{a^{2} b^{2}}{p^{2}} \)
c. \( \frac{a b}{p} \)
D. \( \frac{a^{2} b^{2}}{p^{3}} \)


Assertion: Growth involves the
synthesis of protoplasmic as well as a
protoplasmic materials.
Reason: During growth, catabolic
activities are faster than anabolic
activities.
A. Both Assertion and Reason are true and Reason is a correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not a correct explanation of Assertion
C. Assertion is true but Reason is false
D. Both Assertion and Reason are false
E. Assertion is false but reason is true.


Form the differential equation
corresponding to \( \boldsymbol{y}=\boldsymbol{a} \cos (\boldsymbol{n} \boldsymbol{x}+ \)
\( \boldsymbol{b}),(\boldsymbol{a}, \boldsymbol{b}) \)


Can the process of rusting be called combustion? Discuss.


Prove by induction:
\( x^{n}-y^{n} \) is divisible by \( x+y \) when \( n \) is
even


The ratio of nth term of two A.P.s is
\( (14 n-6):(8 n+23), \) then the ratio of
their sum of first \( \mathrm{m} \) terms is
A \( \cdot \frac{4 m+4}{7 m+24} \)
в. \( \frac{7 m+1}{4 m+24} \)
c. \( \frac{7 m+1}{4 m+27} \)
D. \( \frac{28 m-20}{16 m+15} \)


State whether true or false:
A rose appears red in white light as it absorbs red color and reflects all other
colors.
A. True
B. False


dentify i, ii and iii.
A. i-uniport, ii-Antiport, iii-symport
B. i-uniport, ii-symport, iii-Antiport
C. i-Antiport, ii-symport, iii-uniport
D. i-symport, ii-uniport, iii-Antiport


Which among the following is not the example of carbohydrate?
A. Glucose
B. fractose
c. Maltose
D. Nylon


The name of the compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \) is:
A. propanal
B. propanone
c. ethanol
D. ethanal


A zygote which has inherited a \( Y \) chromosome from the father will
develop into
\( A \cdot A \) boy
B. A girl
c. Anyone of the above
D. None of the above


The centre of mass of the disk
undergoes simple harmonic motion
with angular frequency \( \omega \) equal to:
\( A \cdot \sqrt{\frac{k}{M}} \)
3. \( \sqrt{\frac{2 k}{M}} \)
c. \( \sqrt{\frac{2 \mathrm{k}}{3 \mathrm{M}}} \)
D


Which of the following disapproved Thomson's model?
A. The nuclear model of an atom
B. The electron model of an atom
c. The atomic model of an atom
D. None of above


Name the physical quantity whose \( S I \)
unit is \( J / C . \) is it a scalar or a vector
quantity?


toppr
Q Type your question
connected to a large tank of water. The
surface of the water is at a height
above the end of the tap. By considering the dynamics of a thin "cylinder' of water in the stream answer the
following: (ignore any resistance to the
flow and any effects of surface tension,
\( \operatorname{given} \rho_{w} \) density of water)
Which of the following equation expresses the fact that the flow rate at
the tap is the same as at the stream
point with diameter \( D \) and velocity \( v \) (i.e.
D in terms of \( \left.D_{0}, v_{0} \text { and } v \text { will be }\right) \)
A \( \cdot D=\frac{D_{0} v_{0}}{v} \)
B. \( \quad D=\frac{D_{0} v_{0}^{2}}{v^{2}} \)
c. \( D=\frac{D_{0} v}{v_{0}} \)
D. \( D=D_{0} \sqrt{\frac{v_{0}}{v}} \)


In which form, ionic compounds conduct an electric current?
A. Melted
B. Dehydratedd
c. Frozen
D. Solidified


A rectangular coil has 60 turns and its length and width is \( 20 \mathrm{cm} \). and \( 10 \mathrm{cm} \) respectively. The coil rotates at a speed
of 1800 rotation per minute in a
uniform magnetic field of \( 0.5 T \) about its one of the diameter. Calculate
maximum induced emf will be


Let \( P(n) \) be a statement and \( P(n)= \) \( \boldsymbol{P}(\boldsymbol{n}+\mathbf{1}) \forall \boldsymbol{n} \in \boldsymbol{N}, \) then \( \boldsymbol{P}(\boldsymbol{n}) \) is true for
what values of \( n ? \)
A. For all \( n \)
B. For all \( n>1 \)
c. For all \( n>m, m \) being a fixed positive integer
D. Nothing can be said


The angle of deviation when light is
incident at an angle of \( 45^{\circ} \) on one of the refracting faces of an equilateral prism of refractive index 1.414 is
A \( \cdot 40 \)
B. 30
\( c \cdot 45 \)
\( D \cdot 50 \)


If two vertices of a triangle \( A B C \) are \( A(-1,2,4) \) and \( B(2,-3,0), \) and the
centroid is (2,0,2) then the vertex \( C \) has the coordinates
A. (5,1,2)
в. \( \left(1,-\frac{1}{3}, \frac{7}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(3,-\frac{2}{3}, \frac{5}{3}\right) \)
D. none of these


If \( \mathrm{S} \) is the stress and \( \mathrm{Y} \) is Young's modulus of the material of a wire, the
energy stored in the wire per unit volume is :
\( \mathbf{A} \cdot 2 S^{2} Y \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{2 Y}{S^{2}} \)
D. \( \frac{S}{2 Y} \)


A rubber cord catapult has cross-
sectional area \( 25 \mathrm{mm}^{2} \) and initial
length of rubber cord is \( 10 \mathrm{cm} . \) It is stretched to \( 5 \mathrm{cm} \) and then released to
project a missile of mass 5 g. Taking \( \boldsymbol{Y}_{r u b b e r}=\mathbf{5} \times \mathbf{1 0}^{8} \boldsymbol{N} \boldsymbol{m}^{-2}, \) velocity of
projected missile is:
A. \( 20 \mathrm{ms}^{-1} \)
B. \( 100 \mathrm{ms}^{\wedge}(-1) \$ \$ \)
c. \( 250 \mathrm{ms}^{-1} \)
D. \( 200 \mathrm{ms}^{-1} \)


U-proteins and R-proteins are needed in
A. Leptotene
B. Zygotene
c. Pachytene
D. Diplotene


Points (-3,-3),(4,-1),(6,6) and (-1,4)
when joined in the given order form a
A. parallelogram
B. rectangle
c. rhombus
D. square


A transistor is operated in common-
emitter configuration at \( V_{C}=2 V \) such
that a change in the base current from
\( 100 \mu A \) to \( 200 \mu A \) produces a change in the collector current from \( 5 \mathrm{mA} \) to 10
mA. The current gain is :
A . 50
B. 75
\( c \cdot 100 \)
D. 150


Assume that \( a, b, c \) and \( d \) are positive
integers such that \( a^{5}=b^{4}, c^{3}=d^{2} \) and
\( c-a=19 . \) Determine \( d-b \)


Which of the following plants are similar to amphibia animals in requirement of water for fertilisation?
A. Bryophyta
B. Pteridophyta
c. Angiosperm
D. Both A and B


The materials suitable for making electromagnets should have:
A. high retentivity and high coercivity
B. low retentivity and low coercivity
c. high retentivity and low coercivity
D. low retentivity and high coercivity


Product (B) of the reaction is :
\( \|_{\mathbf{C H}-\mathbf{C O}_{2} \mathbf{H}}^{\mathbf{C H}-\mathbf{C O}_{2} \mathbf{H}} \frac{\mathbf{N a O H}}{(\mathbf{t w o ~ m o l e})}>(\mathbf{A}) \frac{\text { electrolysis }}{(\mathbf{B})} \)
\( \mathbf{A} \cdot C H_{3} C H_{3} \)
B \( . H_{2} C=C H_{2} \)
\( \mathbf{c} \cdot H-C \equiv C-H \)
\( \mathbf{D} \cdot C H_{2}=C H-C H=C H_{2} \)


A body is moving with variable
acceleration
(a) along a straight line. The average acceleration of body in
time interval \( t_{1} \) to \( t_{2} \) is


In a glass-tube, there is \( 18 g \) of glucose.
If 0.08 mol of glucose is taken, then glucose left in the glass-tube is:
A. \( 0.10 g \)
в. \( 17.92 g \)
c. 3.60 mol
D. 3.60 \( g \)


In SONAR, we use
A. ultrasonic waves
B. infrasonic waves
c. radio waves
D. audible sound waves


If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a} \cdot \vec{b}=0=\vec{a} \cdot \vec{c} \) and the angle between \( \vec{b} \)
and \( \vec{c} \) is \( \pi / 3, \) then the value to \( |\vec{a} \times \vec{b}-\vec{a} \times \vec{c}| \) is \( ? \)
A. \( 1 / 2 \)
B.
\( c \cdot 2 \)
D. 3


During the primary treatment of sewage, solid particles that settle down are called
\( A \). Flocs
B. Primary sludge
c. Activated sludge
D. Anaerobic sludge


Gases mainly responsible for the greenhouse effect are
A. \( C O_{2} \) and \( c 0 \)
B. \( \operatorname{coand} H_{2} \)
c. \( C O_{2} \) and \( N_{2} O \)
D. \( C O_{2} \) and \( S O_{2} \)


If each side of an equilateral triangle is
8, calculate the length of the altitude.
A . 1.73
B . 2
c. 3.46
D. 4
E . 6.93


\( C H C l_{3} \) is stored in brown-coloured
stoppered bottles filled up to the neck to prevent it from getting:
A. Oxidized
B. Reduced
c. Hydrolysed
D. Decomposed


On the bombardment of Boron with
neutron, an \( \alpha \) - particle is emitted and
product nucleus formed is
\( \mathbf{A} \cdot_{6} C^{12} \)
В \( \cdot_{2} L^{i} \)
\( \mathrm{c} \cdot_{3} L i^{7} \)
D・ \( _{4} B e^{9} \)


\( \int \frac{1}{7} \sin \left(\frac{x}{7}+10\right) d x \) is equal to
\( ^{\mathrm{A}} \cdot \frac{1}{7}^{\cos }\left(\frac{x}{7}+10\right)+C \)
B \( \cdot-\frac{1}{7} \cos \left(\frac{x}{7}+10\right)+C \)
\( ^{\mathbf{c}}-\cos \left(\frac{x}{7}+10\right)+C \)
D \( -7 \cos \left(\frac{x}{7}+10\right)+C \)
E \( \cdot \cos (x+70)+C \)


Which of the following are true for
electrolytic extraction of aluminium?
This question has multiple correct options
A. Cathode material contains graphite
B. Anode material contains graphite
C. Cathode reacts away forming \( C O_{2} \)
D. Anode reacts away forming \( C O_{2} \)


If a capacitor is connected to two
different A.C. generators, then the value of capacitive reactance is:
A. directly proportional to frequency
B. inversely proportional to frequency
C. independent of frequency
D. inversely proportional to the square of frequency


Which of the following compounds shows the same compound as the given
above?
\( A \)
в.
\( c \)
\( D \)


Match the column:
List I list II \( \quad \) List III A) BOD \( \quad \) i) Supernatant
as effluent \( \begin{array}{ll}\text { B) } & \text { ii) Measure of } \\ \text { FLOCS } & \text { Organic Matter }\end{array} \) All \( \| \textrm{ } \)
\( \mathrm{sol} \) SOlids
\( \mathrm{n} \) te carbon \( \begin{array}{l}\text { C) } \\ \text { Primary } \\ \text { sludge }\end{array} \mid \begin{array}{l}\text { iii) Masses of } \\ \text { bacteria } \\ \text { associated with } \\ \text { fungus }\end{array} \) has more
\( \mathbf{A} \cdot A-i i, I V B-i i i, I C-i,\|D-i v,\| I \)
B. A-ii, I B-i, III C-iv, II D-iii, IV
C \( . A \) -i, IV B-iii, II C-iv, I D-ii, III
D. A-ii, III B-ii, IV C-iii, I D-i, II


A block weighing \( 20 \mathrm{N} \) rests on a horizontal surface. The coefficient of
static friction between the block and
surface is 0.4 and the coefficient of
kinetic friction is 0.20 .
a. How much is the friction force exerted
on the block?
b. How much will the friction force be if
a horizontal force \( 5 \mathrm{N} \) is exerted on the
block?
c. What is the minimum force that will
start the block in motion?
d. What is the minimum force that will
keep the block in motion once it has
been started?
e. If the horizontal force is \( 10 \mathrm{N} \), what is
the friction force?


A substance forms zwitter ion, It can
have functional group.
A. \( -\mathrm{NH}_{2},-\mathrm{COOH} \)
в. \( -\mathrm{NH}_{2},-\mathrm{SO}_{3} \mathrm{H} \)
c. Both (A) and (B)
D. None of these


Increase in the concentration of the
toxicant at successive trophic levels is known as
A. Biogeochemical cycling
B. Biomagnification
c. Biodeterioration
D. Biotransformation


When a fruit falls from a tree,
A. only the earth attracts the fruit
B. both the earth and the fruit attract each other
C . only the fruit attracts the earth
D. they repel each other


Equal chords of a circle subtend equal
angle on centre
A . True
B. False


The horizontal component of the earth's magnetic field at a place is \( 3 \times 10^{-4} T \)
and the dip is \( \theta=\tan ^{-1}(4 / 3) . \) A metal
rod of length \( 0.25 \mathrm{m} \) placed in the north south position is moved at a constant speed of \( 10 \mathrm{cm} / \mathrm{s} \) towards the east. The
e.m.f induced in the rod will be:
A. zero
B. \( 1 \mathrm{mV} \)
\( c \cdot 5 m v \)
D. 10 mv


Which of the following is/are most effective uses of phosphorus pentoxide? This question has multiple correct options
A. It is used as dehydrating agent
B. It is used as explosive
c. It is used as hydrogenating agent.
D. It is used as drying agentttt


\( \begin{array}{ccc}(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{a}^{2} & \boldsymbol{a}^{2} \\ \boldsymbol{b}^{2} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{b}^{2} \\ \boldsymbol{c}^{2} & \boldsymbol{c}^{2} & (\boldsymbol{a}+\boldsymbol{b})^{2}\end{array} \mid= \)


The heat of vaporization is very high for
\( ? \)
A . He
B. Ne
c. Ar
D. xe


A moving vehicle on a straight road is an example of -
A. raotatory motion
B. vibratory motion
c. periodic motion
D. rectilinear motion


A dynamo develops \( 0.5 A \) at \( 6 V . \) The energy which is generated in one second is
A. \( 0.083 J \)
\( J \)
B. \( 3 J \)
c. \( 12 J \)
D. none of these


\( \int_{1}^{2} e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x \) equals to
A \( \cdot e\left(\frac{e}{2}-1\right) \)
B. 1
\( c \cdot e(e-1) \)
D. \( \frac{e}{2} \)


A football has lesser inertia than a
stone of the same size because:
A. Football has more air inside than the stone.
B. Football has less air inside than the stone
c. Football has less mass than the stone.
D. Football has more mass than the stone.


Momentum is a measure of quantity of motion.
A . True
B. False


The enhanced growth of water hyacinth
in lakes can be due to
A. Disposal of solid wastes in water bodies
B. Availability of more nutrients to the flora of a water ecosystem
c. Discharge of sewage into water bodies
D. All of the above


For biogas production, besides dung an extensive use of which weed is
recommended in our country
A. Mangifera indica
B. Hydrilla
c. Eichhornia crassipess
D. Solanum


The bob of a pendulum is positively charged. Another identical charge is placed at the point of suspension of the pendulum. The time period of pendulum
A. increases
B. decreases
c. becomes zero
D. remains same


Slime Moulds belong to
A. Fungi
B. Protista
c. Monera
D. Plantae


A thermodynamic process is said to be
reversible if:
A. the process can be turned back such that the system and surroundings return to the original states.
B. the process can be turned back with no change in internal energy of the system.
C. the process can be turned back with a finite heat transfer with the surroundings over a period of time.
D. None of the above.


The area \( (\text { in } s q . \text { units }) \) of the
parallelogram whosed diagonals along the vectors \( 8 \hat{i}-6 \hat{j} \) and \( 3 \hat{i}+4 \hat{j}-12 \hat{k} \)
is:
A . 20
B. 65
\( c .52 \)
D. 26


Explain the working of P-Njunction
diode in forward and reverse biased
mode


\( p K_{a} \) for the acid \( H A \) is \( 6 . \) The value of
\( \boldsymbol{K} \) for the reaction \( \boldsymbol{A}^{-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \) is:
A \( \cdot 1 \times 10^{-6} \)
B. \( 1 \times 10^{8} \)
c. \( 1 \times 10^{-8} \)
D. \( 1 \times 10^{6} \)


When a light ray is reflected repeatedly by a set of parallel plane mirrors, the
intensity of light rays decreases after
some reflections. This is because of
A. Poor reflection from mirrors
B. Absorption of some amount of light by mirrors
c. Dispersion of light when the rays travel through the atmosphere
D. scattering of light by the mirrors


The diameter of a solid disc is \( 0.5 \mathrm{m} \) and
its mass is \( 16 \mathrm{Kg} \). Its angular velocity
increases from zero to 120
rotation/minute in 8 seconds, at what
rate is work done by the torque at the end of 8th second?
A . \( \pi \) Watt \( t \)
B . \( \pi^{2} \) Watt
c. \( \pi^{3} \) Watt
D. \( \pi^{4} \) Watt


The diameter of the wheel of a car is
\( \mathbf{5 6} \) cm. Calculate :
The number of times the wheel will
rotate in travelling through a distance of \( 1.056 k m \)


If \( 2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right), \) prove
that \( \tan \theta+\sqrt{3}=0 \)


The heat released when the requisite amount of ions in the gaseous state combine to give 1 mol of crystal lattice is known as:
A. lattice energy
B. hydration energy
c. formation energy
D. none of the above


Choose the correct answer from the
alternatives given. Which of the following parts of heart receives oxygenated blood returning from lungs?
A. Right ventricle
B. Left atrium
c. Left ventricle
D. Right atrium


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\boldsymbol{x}}{\log \boldsymbol{x}^{2}+\mathbf{1}}\right) \)


The population of a town increase every year at the rate of 25 per thousand. The
present population of the town is
262400.Find Population before one year


An alkane with molecular formula
\( C_{5} H_{12} \) forms only one monochloro
product when heated with \( C l_{2} \). The
I \( \boldsymbol{U} \boldsymbol{A} \boldsymbol{C} \) name of this compound is:
A. \( 1, \) 1-dimethyl propane
B. 1,2-dimethyl propane
c. 2,2-dimethyl propane
D. none of the above


The ratio of maximum to minimum
intensity due to superposition of two waves is \( \frac{49}{9} . \) Then the ratio of the intensity of component waves is :
A \( \cdot \frac{25}{4} \)
в. \( \frac{16}{25} \)
c. \( \frac{4}{49} \)
D. \( \frac{9}{49} \)


The properties of \( \ldots \) are due to the hydrogen ions it produces in aqueous solution.
A . an acid
B. base
c. nuetral
D. none of these


A child pulls a toy bus through a distance of \( 8 \mathrm{m} \) on a smooth horizontal
floor. The string held in the child's hand
makes an angle of \( 60^{\circ} \) with the horizontal surface. If the force applied by the child is 3 N. Calculate the work done by the child in pulling the toy car.


Select the property which is not true for
metals.
A. Metals are good conductors of electricity
B. Metals are malleable and ductile
C. Non-polar covalent compounds are formed from metals
D. Metals have 1,2 or 3 valence electrons


(a) Which solution is used for the
leaching of silver metal in the presence of air in the metallurgy of silver?
(b) Out of 'C' and 'CO', which is a better
reducing agent at the lower temperature range in the blast furnace
to extract iron from the oxide ore?