Three boys rahul, raju, and ravi stand at
three places and clap their hands
simultaneously. Calculate the time between the clap and the echo of the clap of each body. Infer how can the
time between the clap and echo of the
clap varied. Velocity of sound in air is
\( \mathbf{3 3 0} \quad \boldsymbol{m s}^{-1} \)


\( f(x)=2 x^{2}+3 x+4 \) in the interval [1
2] if \( f^{\prime}(c)=f(1) \) then \( c=\frac{a}{2} \) Find \( a \)


An electric bulb is rated \( 200 V-100 W \)
Find the resistance of the bulb.


The family of elements to which sodium belongs is :
A. alkali metalss
B. alkaline earth metals
c. halogens
D. inert gases


The intercepts made by the line \( x+ \)
\( 5 y=3 \) on the \( X \) -axis is a.Find \( a \)


Which of the following is the right
derivation for Ampere-Maxwell law?
A \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+4 \pi \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{d t} \)
B \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+3 \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{i d t} \)
\( ^{\mathbf{C}} \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+\mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{d t} \)
D \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+\frac{\mu_{0}}{\varepsilon_{0}} \frac{d \phi_{E}}{d t} \)


A plant hormone used for inducing morphogenesis in plant tissue culture
is
A. Ethylene
B. Gibberellin
c. cytokinin
D. Abscisic acid


To reduce the momentum of a given body to half its original value then the
velocity must be
A. reduced to half
B. reduced to one-third
c. doubled
D. remain same


The law of the multiple proportion was proposed by:
A. Dalton
B. Dulong
c. Petit
D. Lavoisier


In order to increase the angular
magnification of a simple microscope, one should increase
A. The object size
B. The aperture of the lens
c. The focal length of the lens
D. The power of the lens


f \( 3 x+8=17 \) find the value of \( x \)


From below what are the properties of
concave mirrors?
A. Converging mirrors and form real and inverted image in front of the mirror
B. Diverging mirrors and form virtual and upright image behind the mirror.
C. Converging mirrors and form virtual and inverted image in front of the mirror.
D. Diverging mirrors and form real and inverted image in front of the mirror.


In a business venture a man can make
a profit of Rs. \( 2000 /- \) with probability of 0.4 or have a loss of Rs. \( 1000 /- \) with probability 0.6. His expected profit is
A. Rs. \( 800 /- \)
B. Rs. \( 600 /- \)
c. Rs. \( 200 /- \)
D. Rs. 400/-


Assertion
In the extraction of \( A g, \) complex
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) is reacted with \( \boldsymbol{Z} \boldsymbol{n} \)
Reason
\( Z n \) is d-block transition metal.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct


The rate of reaction w.r.t reactants is
indicated by a negative sign
A. True
B. False


The unit of power of lens is
A . Metre
B. Centimeter
c. Diopter
D. \( M^{-1} \)


reflexive, symmetric and transitive.
This question has multiple correct options
\( A \cdot R_{3}=\{(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)\} \)
\( \mathbf{B} \cdot R_{3}= \)
\( \{(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(4, \)
\( \mathbf{c} \cdot R_{3}=\{(1,1),(2,2),(3,3),(4,4)\} \)
D. none of these


The mean and the standard deviation of
a group of 20 items was found to be 40 and 15 respectively. While checking it
was found that an item 43 was wrongly written as \( 53 . \) Calculate the correct
mean and standard deviation.


Assertion
Let \( \boldsymbol{f}:[\mathbf{8} \boldsymbol{\pi}, \mathbf{9} \boldsymbol{\pi}] \rightarrow[-\mathbf{1}, \mathbf{1}], \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{\operatorname { c o s } \boldsymbol { x }} \)
then
Statement-1: \( \boldsymbol{f}^{-1}(-1)=\mathbf{9} \boldsymbol{\pi} \) because
Reason
Statement-2 : \( \boldsymbol{f}^{-1}(\boldsymbol{x})=\mathbf{1 0} \boldsymbol{\pi}- \)
\( \cos ^{-1} x \forall x \infty[-1,1] \)
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true


Dehiscence of sporangia of fern occurs through
A. Annulus
B. Stomium
c. Elaters
D. sori


Multiple Answer Question
In Rutherford's model of atom:
This question has multiple correct options
A. atom is a planetary model
B. electrons never loose nor gain energy
C. electron revolve around nucleus with high velocities to counter balance the forces of electrostatic forces of
attraction between protons and electrons
D. electrons do not move at all


Find \( X, \) if \( Y=\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right] \) and \( 2 X+Y= \)
\( \left[\begin{array}{cc}1 & 0 \\ -3 & 2\end{array}\right] \)


To measure the field \( B \) between the
poles of an electromagnet, a small test loop of area \( 1 \mathrm{cm}^{2} \), resistance \( 10 \Omega \) and 20 turns is pulled out of it. A galvanometer shows that a total charge of \( 2 \mu C \) passed through the loop. The
value of \( B \) is
A . \( 0.001 T \)
в. \( 0.01 T \)
\( c .0 .17 \)
D. \( 1.0 T \)


Branch of chemistry deals with structure of matter, the energy changes and theories, laws and principles that
explain the transfer motion of matter for one form to another is known as:
A. Physical chemistry
B. Inorganic chemistry
c. organic chemistry
D. Analytical chemistry


Write a note on trends in the following properties of groups 16 elements
i) Density
ii) Melting and Boiling points


Rate of dissipation of Joule's heat in resistance per unit volume is (symbols have usual meaning)
A \( \cdot \sigma E \)
в. \( \sigma J \)
\( c . J E \)
D. None


A function \( \boldsymbol{f}:[-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined
as follows
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x<7\end{array}\right. \)
(i) \( \boldsymbol{f}(\mathbf{5})+\boldsymbol{f}(\boldsymbol{6}) \)
(ii) \( \boldsymbol{f}(\mathbf{1})-\boldsymbol{f}(\mathbf{3}) \)
(iii) \( \boldsymbol{f}(-\mathbf{2})-\boldsymbol{f}(-\mathbf{4}) \)
(iv) \( \frac{\boldsymbol{f}(\mathbf{3})+\boldsymbol{f}(\mathbf{1})}{\mathbf{2} \boldsymbol{f}(\boldsymbol{6})-\boldsymbol{f}(\mathbf{1})} \)


Three cubes of sides \( 3 \mathrm{cm}, 4 \mathrm{cm}, \) and 5
\( \mathrm{cm} \) respectively are melted and recasted into a larger cube What is the
side of the cube so formed?
A . \( 12 \mathrm{cm} \)
B. \( 9 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Alcohols can be identified by the
reaction with sodium.
A. True
B. False


\( \operatorname{Let} \boldsymbol{A}+\mathbf{2} \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{0} \\ \mathbf{6} & -\mathbf{3} & \mathbf{3} \\ \mathbf{- 5} & \mathbf{3} & \mathbf{1}\end{array}\right] \) and
\( \mathbf{2} \boldsymbol{A}-\boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{2} & -\mathbf{1} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{2}\end{array}\right] \) then Det
\( \operatorname{Tr}(A)-\operatorname{Tr}(B)) \) has the value equal to
\( A \)
B.
\( c \)
\( D \)


Which chamber of the heart receives
deoxygenated blood from the body?


Two bodies are thrown simultaneously from a tower with same initial velocity \( v_{0} \)
one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is
\( \mathbf{A} \cdot 2 v_{0} t+\frac{1}{2} g t^{2} \)
B. \( 2 v_{0} \)
C. \( v_{0} t+\frac{1}{2} g t^{2} \)
D. \( v_{0} \)


Which reaction is this?
\( 4 F e+3 O_{2}+3 H_{2} O \rightarrow 2 F e_{2} O_{3} \rightarrow \)
\( 3 H_{2} O \)


How many spectral lines are observed in spectra of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
A .2
B. 4
\( c \cdot 6 \)
D.


Keeping the length of the conductor constant, if the radius of the conductor is doubled, then its resistance becomes
A. Double
B. Quadrupled
c. Half
D. Four times less


Geometrical isomerism is shown by:
\( A \)
B.
\( c \)
D


A point mass \( m_{0} \) is placed at a distance \( \boldsymbol{R} \)
\( \frac{n}{3} \) from the centre of a spherical shell of mass \( M \) and radius \( R \). The
gravitational force on the point mass
\( \boldsymbol{m}_{0} \) is:
\( ^{\mathrm{A}} \cdot \frac{9 G M m_{0}}{R^{2}} \)
в. \( \frac{G M m_{0}}{R^{2}} \)
c. zero
D. \( \frac{4 G M m_{0}}{R^{2}} \)


On Monday morning Mr. Smith had a certain amount of money that he planned to spend during the week. On each subsequent morning, he had one fourth the amount of the previous
morning. On Saturday morning, 5 days later, he had \( \$ 1 . \) How many dollars did
Mr. Smith originally start with on Monday morning?(Disregard the \( \$ \operatorname{sign} \)
when gridding your answer.


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y} \cos \boldsymbol{x}=\boldsymbol{y}^{\boldsymbol{n}} \sin \boldsymbol{2} \boldsymbol{x} \)
\( \mathbf{A} \cdot \frac{1}{y^{n+1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} \)
B. \( \frac{1}{y^{n-1}}=2 \sin x+\frac{2}{1-n}+c e^{(n-1) \sin x} x \)
C \( \frac{1}{y^{n-1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} x \)
D. \( \frac{-1}{y^{n-1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} x \)


A stationary particle of mass \( \boldsymbol{m}= \)
\( 1.5 k g \) is acted upon by a variable force.
The variation of force with respect to
displacement is plotted in fig. What is the maximum speed attained
by the particle and at what time is it
attained?


The trees growth in deserts will
A. Show alternate rings of xylem and sclerenchyma
B. Show distinct annual rings
C. Not show distinct annual rings
D. Have only conjunctive tissue and phloem formed by the activity of cambium


\( 40 \% \) mixture of 0.2 mole of \( N_{2} \) and
0.6 mole of \( H_{2} \) react to give \( N H_{3} \)
according to the equation \( \boldsymbol{N}_{2}(\boldsymbol{g})+ \) \( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}), \) at constant
temperature and pressure. Then the ratio of the final volume to the initial
volume of gases is:
A . 4: 5
B. 5: 4
c. 7: 10
D. 8: 5


A ray of light travels from a denser to a rarer medium then, the ray:
A. doesn't bend at all
B. bends towards the normal
c. bends away from the normal
D. goes along the normal


Explain ferromagnetism on the basis of domain theory?


A mild steel wire of length \( 1.0 \mathrm{m} \) and
cross-sectional area \( 0.50 \times 10^{-2} \mathrm{cm}^{2} \)
is stretched, well within its elastic
limit, horizontally between two pillars. A mass of \( 100 \mathrm{g} \) is suspended from the mid-point of the wire. Calculate the depression at the mid-point.


Kupffer's cells are
A. Phagocytic
B. Actin
c. Myosin
D. Fibrin


A ray of light is incident normally on a plane glass slab. What will be the angle of refraction?
A \( \cdot 90^{\circ} \)
B. \( 180^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 0^{\circ} \)


Suboxide of Rb has the formula:
\( \mathbf{A} \cdot R b O_{2} \)
в. \( R b O_{3} \)
\( \mathrm{c} \cdot R b_{2} O_{2} \)
D. \( R b_{6} O \)


Can the following groups of elements be classified as Dobereiner's triad:
(a) \( \mathrm{Na}, \mathrm{Si}, \mathrm{Cl} \)
(b) Be, Mg, Ca
Justify the answer in each case.
[Atomic mass of \( \boldsymbol{B e}-\mathbf{9} ; \boldsymbol{N} \boldsymbol{a}- \)
\( \mathbf{2 3} ; \boldsymbol{M} \boldsymbol{g}-\mathbf{2 4} ; \boldsymbol{S} \boldsymbol{i}-\mathbf{2 8} ; \boldsymbol{C l}-\mathbf{3 5} ; \boldsymbol{C} \boldsymbol{a}- \)
40]


Which one of the following pairs of animals comprises 'Jaw less fishes'?
A. Guppies and hag fishes
B. Lampreys and eels
c. Mackerals and Rohu
D. Lampreys and hag fishes


The power of a convex lens of focal length 2 metre will be:
A \( .+0.5 D \)
в. \( +5 D \)
\( \mathrm{c} \cdot+50 D \)
D. - 5D


A divergent series:
A. The infinite sequence of the partial sums of the series does not have a finite limit.
B. \( 2+4+6+8+\ldots . . \)
C. Both A and B are correct
D. Only A is correct


A semiconductor has an electron
concentration of \( 8 \times 10^{13} \) per \( c m^{3} \) and \( a \)
hole concentration of \( 5 \times 10^{12} \) per \( c m^{3} \)
The electron mobility is \( 25000 c m^{2} V^{-1} s^{-1} \) and the hole mobility
is \( 100 \mathrm{cm}^{2} V^{-1} s^{-1} . \) Then
A. The semiconductor is \( n \) -type
B. The conductivity is 320 \( \mathrm{m} \) mho \( \mathrm{cm}^{-1} \)
c. Both (a) and (b)
D. None of the above


Four point charges \( -\mathrm{Q},-\mathrm{q}, 2 \mathrm{q} \) and \( 2 \mathrm{Q} \) are placed, one at each corner of the square The relation between \( Q \) and \( q \) fo which
the potential at the centre of the square is zero, is
A. \( Q=q \)
B. \( Q=\frac{1}{q} \)
c. \( Q=-q \)
D. \( Q=-\frac{1}{q} \)


n mutual induction
A: when current in one coil increases, induced current in neighbouring coil flows in the opposite direction
B: When current in one coil decreases,
induced current in neighbouring coil flows in the opposite direction
A. A is true, B is false
B. A and B are false
c. A and B are true
D. A is false, B is true


Outer covering of cartilage is known as:
A. perichondrium
B. periosteum
c. endosteum
D. peritoneum


The second cranial nerve is
A. Optic
B. Trigeminal
c. olfactory
D. Abducens


The values of Planck's constant is
\( 6.63 \times 10^{-34} J s . \) The velocity of light is
\( 3.0 \times 10^{8} m s^{-1} . \) Which value is closest
to the wavelength in nanometres of a quantum of light which frequency of
\( 8 \times 10^{15} s^{-1} ? \)
\( \mathbf{A} \cdot 5 \times 10^{-18} \)
B. \( 4 \times 10^{1} \)
\( c \cdot 3 \times 10^{7} \)
D. \( 2 \times 10^{-25} \)


Factorize \( : \boldsymbol{y}^{2}+\mathbf{1 0 0} \boldsymbol{y} \)
A. \( y(y+100) \)
B . \( y^{2}(y+100) \)
c. \( y\left(y^{2}+100\right) \)
D. none of these


Name the reducing agent in the following:
\( \mathbf{3} M n O_{2}+4 A l \rightarrow 3 M n+2 A l_{2} O_{3} \)
\( \mathbf{A} \cdot M n \)
B. \( A l \)
\( \mathrm{c} \cdot M n O_{2} \)
D. \( A l_{2} O_{3} \)


Assertion
A mixture of nitrogen and carbon dioxide can be distinguished by passing it through lime water.
Reason
Nitrogen does not turn lime water milky
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{A} \times \boldsymbol{B}=\{(\boldsymbol{a}, \boldsymbol{x}),(\boldsymbol{a}, \boldsymbol{y}),(\boldsymbol{b}, \boldsymbol{x}),(\boldsymbol{b}, \boldsymbol{y})\} \)
Find \( A \) and \( B \)


Explain the following terms with one
example each.
(a) Corrosion
(b) Rancidity


Statement 1: The stem tubers are the
swollen ends of specialized underground stem branches, which help in vegetative propagation of the plant. Statement 2: Solanum tuberosum is an
example of a stem tuber which stores inulin as the main reserve food
material.
A. Both statement 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statement 1 and 2 are incorrect


How does \( H_{2} O_{2} \) reacts with \( K_{2} C r_{2} O_{7} \)
in acidic medium in ether cold
conditions?


The amount of heat energy released when a fuel burns completely is called calorific value.
A. True
B. False
c. Nither
D. Either


In Milikan's oil drop experiment, an oil
drop of radius \( r \) and charge \( q \) is held in equilibrium between the plates of a charged parallel plate capacitor when
the potential difference is \( V . \) To keep a
drop of radius \( 2 r \) and with a charge \( 2 q \)
in equilibrium between the plates the
potential difference \( \boldsymbol{V} \) required is :
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( 8 V \)


The probability of student \( A \) passing an examination is \( 2 / 9 \) and of students, \( B \) passing is \( 5 / 9 . \) Assuming the two events: \( A \) passes'. \( B \) passes' as independent, find the probability of only
\( B \) passing the examination


Elements \( 0, \) S, Se and Te are commonly known as:
A. Halogens
B. Rare earth elements
c. chalcogens
D. Pnictogens


A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with constant angular velocity \( \omega . \) Two objects each of mass \( m \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by:
A \( \cdot \frac{(M+2 m) \omega}{2 m} \)
в. \( \frac{2 M \omega}{M+2 m} \)
c. \( \frac{(M+2 m) \omega}{M} \)
D. \( \frac{M \omega}{M+2 m} \)


Bleaching powder loses by the action of dilute
acids in excess.
A . oxygen
B. calcium
c. chlorine
D. water


Given below are the steps for extraction
of copper from its ore. The balance reaction involved in reduction of
copper(l) oxide with copper(l) sulphide is given in the reaction below.
\[
\mathbf{2} C u_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S} \stackrel{\text {Heat}}{\longrightarrow} \boldsymbol{6} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2}
\]
This reaction is known as:
A. auto-reduction
B. catalytic- reduction
c. acid reduction
D. none of these


Two identical metallic spheres are
given charges \( +q \) and \( -q \) respectively
now:
A. Both sphere have equal masses
B. The positively charged sphere has a mass smaller than the negatively charged sphere
C. The change in their masses depends on the magnitude of \( q \)
D. Both (A) \& (C)


The graph shows the variation in
displacement with time for an object
moving with simple harmonic motion. What is the maximum
acceleration of the object?
A . 10
B. 0.99
\( c .0 .44 \)
D. none of the above


A body of weight \( 50 N \) placed on a
horizontal surface is just moved by a
force of \( 28.2 N . \) The frictional force and
the normal reaction are
A \( .10 N, 15 N \)
B. \( 20 N, 30 N \)
\( c \cdot 2 N, 3 N \)
D. \( 5 N, 6 N \)


If a magnet is suspended at an angle \( 30^{\circ} \)
to the magnetic meridian, the dip needle
makes an angle of \( 60^{\circ} \) with the horizontal
The true value of dip is :
A \( \cdot \tan ^{-1}(2 / 3) \)
B \( \cdot \tan ^{-1}(3 / 2) \)
c. \( \tan ^{-1}(3) \)
D. \( \tan ^{-1}(2) \)


The radius of a sphere is measured to be \( (4.0+2.0) \mathrm{cm} \) the maximum
percentage error in the measurement of
the volume of the sphere is
A . \( 10 \% \)
B. 15 \%
c. \( 20 \% \)
D. 25 \%


Very short answer type.
Name two catecholamines produced by adrenal medulla.


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{1} \\ \mathbf{0} & -\mathbf{2} & \mathbf{4}\end{array}\right], \mathbf{6} \boldsymbol{A}^{-\mathbf{1}}=\boldsymbol{A}^{\mathbf{2}}+ \)
\( c A+d I, \) then \( (c, d) \) is equal to
A \( \cdot(-6,11) \)
в. (-11,6)
c. (11,6)
\( D \)


Which of the following pairs constitute isotones?
A \( \cdot \frac{i 3}{6} \mathrm{C} \) and \( \frac{14}{6} \mathrm{C} \)
B . \( _{6}^{13} C \) and \( \frac{14}{7} N \)
C \( \cdot \frac{44}{7} N \) and \( _{9}^{19} F \)
D. \( \frac{14}{7} N \) and \( \frac{15}{7} N \)


Consider the following statements with reference to criterion/criteria used in
the classification of plants in the engler and Prantl's system.
a. The families were arranged according to the increasing complexity of flower
and fruit.
b. In flowering plants absence of perianth was considered as a primitive character
c. Monocots were considered to be more
primitive than dicots
d. Unisexual flowers were derived from
bisexual flowers.
Which of the statements given are
correct?
A. 1 and 2
B. 1 and 4
C .1,2 and 3
D. 2,3 and 4


In the lac operon, the structural genes
are switched off when repressor binds
to the
A. Operator
B. Promoter
c. Regulator
D. Inducer
E. Allolactose


If the function \( f \) defined on \( \left(\frac{\pi}{6}, \frac{\pi}{3}\right) \) b \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{\sqrt{\mathbf{2}} \cos \boldsymbol{x}-\mathbf{1}}{\cot \boldsymbol{x}-\mathbf{1}}, & \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \\ \boldsymbol{k}, & \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\end{array}\right. \)
continuous, then \( k \) is equal to?
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{\sqrt{2}} \)
\( D \)


Which names are associated with
PMMA?
A. Melmac
B. Acrilan
c. saran
D. Acrylite


\( \lim _{n \rightarrow \infty} \frac{(2 n-1)(3 n+5)}{(n-1)(3 n+1)}= \)
A . 2
B. \( \infty \)
\( c \cdot 0 \)
D. None of these


Three identical bars \( A, B \) and \( C \) are
made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as
follows:
Make the correspondence of these bars with their material being diamagnetic
\( (D), \) ferromagnetic \( (\boldsymbol{F}) \) and paramagnetic \( (\boldsymbol{P}) \)
A. \( A \leftrightarrow F, B \leftrightarrow P, C \leftrightarrow D \)
в. \( A \leftrightarrow P, B \leftrightarrow F, C \leftrightarrow D \)
c. \( A \leftrightarrow D, B \leftrightarrow P, C \leftrightarrow F \)
D. \( A \leftrightarrow F, B \leftrightarrow D, C \leftrightarrow P \)


A projectile is fired with a velocity at
right angle \( \theta \) to the slope which is
inclined at an angle \( \theta \) with the horizontal. The expression for the range \( \boldsymbol{R} \) along the incline is:
\( ^{\mathbf{A}} \cdot \frac{2 v^{2}}{g} \sec \theta \)
B \( \cdot \frac{2 v^{2}}{g} \tan \theta \)
\( ^{\mathrm{c}} \cdot \frac{2 v^{2}}{g} \sec \theta \tan \theta \)
D \( \cdot \frac{2 v^{2}}{g} \tan ^{2} \theta \)


In a period, elements are arranged
strictly in a sequence of:
A. decreasing charge in the nucleus
B. increasing charge in the nucleus
C. constant charge in the nucleus
D. equal charge in the nucleus


Brown algae is characterised by the presence of
A. Phycocyanin
B. Phycoerythrin
c. Fucoxanthin
D. Haematochrome


Prove that \( \left(x^{2}+y^{2}\right)^{4}=\left(x^{4}-6 x^{2} y^{2}+\right. \)
\( \left.y^{4}\right)^{2}+\left(4 x^{3} y-4 x y^{3}\right)^{2} \)


Prove the converse of the mid-point theorem following the guidelines given below: Consider a triangle \( A B C \) with \( D \) as the mid-point of \( A B . \) Draw \( D E \| B C \)
to intersect \( A C \) in \( E . \) Let \( E_{1} \) be the mid-
point of \( A C . \) Use mid-point theorem to
\( \operatorname{get} D E_{1} \| B C \) and \( D E_{1}=B C / 2 \)
Conclude \( E=E_{1} \) and hence \( E \) is the
mid-point of \( \boldsymbol{A C} \)


If the density of methanol is \( 0.793 \mathrm{kg} L^{-1}, \) what is its volume
needed for making 2.5 L of its 0.25 M
solution?


Write down the letters of the word
PHYSICS as seen in a plane mirror held perpendicular to the plane of the
paper


Velocity of a particle of mass \( 2 \mathrm{Kg} \) varies with time \( t \) according to the equation \( \boldsymbol{v}=(\mathbf{2} \boldsymbol{t} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \mathrm{m} / \mathrm{s} . \) Here \( \mathrm{t} \) is in seconds.
Find the impulse imparted to the particle in the time interval from \( t=0 \) to \( t=2 s \)


A car travels \( 40 \mathrm{km} \mathrm{s} \) in 30 mins. If the
speed of bus remains same, how far can
it travel in 3 hrs?
A. \( 120 \mathrm{km} \)
B. \( 80 \mathrm{km} \)
\( c .240 k m \)
D. None of these


What is the order of mobilities of the
alkali metal ions in aqueous solution?
\( \mathbf{A} \cdot L i^{+}>N a^{+}>K^{+}>C s^{+}>R b^{+} \)
B. \( N a^{+}<L i^{+}<K^{+}<R b^{+}<C s^{+} \)
c. \( L i^{+}>K^{+}>N a^{+}>R b^{+}>C s^{+} \)
D. \( L i^{+}<N a^{+}<K^{+}<R b^{+}<C s^{+} \)


What will be the half-life of the first
order reaction for which the value of
rate constant is \( 200 s^{-1} ? \)
A . \( 3.46 \times 10^{-2} s \)
B. \( 3.46 \times 10^{-3} s \)
c. \( 4.26 \times 10^{-2} s \)
D. \( 4.26 \times 10^{-3} s \)


The current \( I_{1}(\text { in } A) \) flowing through \( 1 \Omega \)
resistor in the above circuit is :
A . 0.25
B. 0.2
\( c .0 .5 \)
D. 0.4


\( \ln \triangle D E F, \) Line PQ \( \| \) side EF. Find DP.
\( \boldsymbol{D} \boldsymbol{Q}=\mathbf{1 . 8} \mathrm{cm}, \boldsymbol{Q} \boldsymbol{F}=\mathbf{5} . \boldsymbol{4} \mathrm{cm}, \boldsymbol{E} \boldsymbol{P}=\mathbf{7 . 2} \)
\( \mathrm{cm} \)
A \( .2 .4 \mathrm{cm} \)
B. \( 4.2 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
D. \( 1.8 \mathrm{cm} \)


The magnetic field at the centre of a circular loop of area \( A \) is \( B \). The
magnetic moment of the loop is
A \( \cdot \frac{B A^{2}}{\mu_{0} \pi} \)
B. \( \frac{B A \sqrt{A}}{\mu} \)
\( ^{\mathrm{c}} \cdot \frac{B A \sqrt{A}}{\mu_{0} \pi} \)
D. \( \frac{2 B A \sqrt{A}}{\mu_{0} \sqrt{\pi}} \)


A number \( a \) is called a perfect cube if
there exists a natural number \( b \) such
that
A. \( a=b \times b \times b \)
\( b \)
В. \( b=a \times a \times a \)
\( c, a=a \times b \times a \)
\( a \)
D. \( a=a \times b \times b \)


Represent the following pair of equations graphically and write the coordinates of points where the line intersects \( \boldsymbol{y} \) -axis
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{6} \)
\( 2 x-3 y=12 \)


A Nall Ul mass U.c ng resus un diverica
post of height \( 5 \mathrm{m} \). A bullet of mass 0.01
kg, traveling with a velocity \( V m / s \) in a
horizontal direction, hits the centre of
the ball. After the collision, the ball and
bullet travel independently. The ball hits
the ground at a distance of \( 20 m \) and
the bullet at a distance of \( 100 \mathrm{m} \) from
the foot of the post. The initial velocity
\( V \) of the bullet is
\( A \cdot 250 m / s \)
B . \( 250 \sqrt{2} \mathrm{m} / \mathrm{s} \)
c. \( 400 \mathrm{m} / \mathrm{s} \)
D. \( 500 \mathrm{m} / \mathrm{s} \)


When \( C l_{2} \) water is added to an aqueous
solution of potassium halide in presence of chloro form a violet colour is
obtained on adding more of \( C l_{2} \) water; the violet colour disappears and a colourless solution is obtained. This
test confirms the presence of the following in aqueous solution:
A . lodide
B. Bromide
c. chloride
D. Bromide and chloride


When light waves suffers reflection at the interface from air to glass, the change in phase of reflected waves is
equal to
A . 0
в. \( \frac{\pi}{2} \)
c. \( \pi \)
D. \( 2 \pi \)


We sit in the room with windows open,
then:
A. Air pressure on the floor of the room equals the atmospheric pressure but the air pressure on the ceiling is negligible
B. Air pressure is nearly the same on the floor, the walls and ceiling
C. Air pressure on the floor equals the weights of the air column inside the room (from floor to ceiling ) per unit area
D. Air pressure on the walls is zero since the weight of air acts downwards


Classify the following number as rational or irrational -
(i) \( 2-\sqrt{5} \)
(ii) \( (3+\sqrt{23})-\sqrt{23} \)
(iii) \( \frac{2 \sqrt{7}}{7 \sqrt{7}} \)
(iv) \( \frac{1}{\sqrt{2}} \)
(v) \( 2 \pi \)


In which quadrant is \( \theta \), if \( \sin \theta \) is
positive and \( \cos \theta \) is negative?
\( A \)
B. I
\( c \)
D. IV


The unit of stress is:
A . \( k g m^{-2} \)
B. \( N k g^{-1} \)
c. \( N m^{-2} \)
D. \( N \)


The solution of the equation \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{2} \)
will be
A .2,-1
в. \( _{0,-1,-\frac{1}{5}} \)
\( \mathrm{c} \cdot_{-1,-\frac{1}{5}} \)
D. None of these


Light is incident normally on face \( A B \) of
a prism as shown in figure. A liquid of
refractive index \( \mu \) is placed on the face
AC of the prism. The prism is made of glass of refractive index \( 3 / 2 \). The limit of
\( \mu \) for which total internal reflection
takes place on face AC is :
A \( \cdot_{\mu}<\frac{3 \sqrt{3}}{4} \)
В \( \cdot \mu>\sqrt{\frac{5}{2}} \)
c. \( \mu>\sqrt{2} \)
D. \( \mu<\sqrt{3} \)


Degree measure of \( \left(\frac{7 \pi}{6}\right)^{c} \) is
A \( .210^{\circ} \)
B . \( 240^{\circ} \)
\( c \cdot 270 \)
D. None of these


Find the derivative of \( y=\sqrt{x^{2}+1} \)


A bullet of mass 2.5 g moving with a velocity of \( 500 m s^{-1}, \) enters a wooden
block and comes out of it with a velocity of \( 100 m s^{-1} . \) Find the work done by the
bullet while passing through the wooden block.
A. 100 J
B. 300 J
c. \( 500 \mathrm{J} \)
D. 800 J


A capacitor connected to a \( 10 V \) battery
collects a charge \( 40 \mu C \) with air as dielectric and \( 100 \mu \mathrm{C} \) with oil as
dielectric. The dielectric constant of oil
is
\( A \cdot 2 \)
в. 2.5
\( c \cdot 4 \)
D. 10


White phosphorus is stored in:
A. ether
B. water
c. alcohol
D. kerosene oi


The ratio of energies of photons with
wavelengths \( 2000 A^{0} \) and \( 4000 A^{0} \) is:
A \( \cdot 1 / 4 \)
B. 4
\( c \cdot 1 / 2 \)
D. 2


If \( \vec{A}=a \hat{i}+2 \hat{j}-5 \hat{k}, \vec{B}=2 \hat{i}-\hat{j}-4 \hat{k} \)
are perpendicular to each other, the
value of \( \boldsymbol{a} \) is:
\( A \cdot 9 \)
B. -9
\( c \cdot 4 \)
\( D \cdot-4 \)


If \( (\cos x)^{y}=(\sin y)^{x} \) then \( \frac{d y}{d x}= \)
A \( \cdot \frac{\log (\sin y)+y \tan x}{\log (\cos x)-x \cot y} \)
B. \( \frac{\log (\sin y)-y \tan x}{\log (\cos x)+\cot y} \)
c. \( \log (\sin y) \)
D. \( \frac{\log (\cos x)}{\log (\sin y)} \)


The change in the sequence of amino acids of a protein results in:
A. same protein
B. different protein
c. same protein with weaker peptide linkage
D. none of these


The decreasing order of energy for the electrons represented by the following sets of quantum numbers is :
1. \( n=4, l=0, m=0, s=\pm 1 / 2 \)
\( 2 . n=3,1=1, m=1, s=-1 / 2 \)
3. \( n=3,1=2, m=0, s=+1 / 2 \)
4. \( n=3, l=0, m=0, s=-1 / 2 \)
\( A \cdot 1>2>3>4 \)
B \( .2>1>3>4 \)
\( (-3>1>2>4 \)
D. \( 4>3>2>1 \)


If
\( \lim _{n \rightarrow \infty} \frac{1^{a}+2^{a}+\ldots . .+n^{a}}{(n+1)^{a-1}[(n a+1)+(n a+2)+} \)
for some positive real number
\( \overline{\mathbf{6 0}} \)
a, then a is equal to
A \( \cdot \frac{15}{2} \)
B. 8
c. \( \frac{17}{2} \)
D.


If the length of the major axis of the ellipse \( \left(\frac{x^{2}}{a^{2}}\right)+\left(\frac{y^{2}}{b^{2}}\right)=1 \) is three
times the length of minor axis, its eccentricity is:
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{\frac{2}{3}} \)
D. \( \frac{2 \sqrt{2}}{3} \)


A group consists of 4 girls and 7 boys. In
how many ways can a team of 5 members be selected is the team
has no girl?


Which of the following are Primary colors ?
A. Red, blue, yellow
B. Red, orange, yellow
c. Red, blue, green
D. Red, green, cyan


Calculate the work done to move a
charge 5 C between two points \( A \) and \( B \), if both the points are maintained at same potential of \( 6 \mathrm{V} \)
A. zero
B . 6 J
c. 3 J
D. 12 J


In a 20 litre vessel initially \( 1-1 \) mole
\( C O, H_{2} O, C O_{2} \) is present, then for the
equilibrium of \( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \) following is true?
A. \( H_{2}, \) more than 1 mole
B. \( C O, H_{2} O, H_{2} \) less then 1 mole
c. \( C O_{2} \& H_{2} O \) both more than 1 mole
D. All of these


\( \frac{8-i}{8} \)


Find the sum of the coefficients of the
terms of the expansion \( \left(1+x+2 x^{2}\right)^{6} \)


What is organisation?


A student was given four unknown colourless samples labelled \( A, B, C \) and D and asked to test their pH using pH paper. He observed that the colour of pH paper turned to light green, dark red, light orange and dark blue with samples \( A, B, C \) and \( D \) respectively. the correct sequence of increasing order of
the pH value for samples is -
\( A \cdot A<B<C<D \)
B. \( A<D<C<B \)
\( c \cdot c<B<A<D \)
\( D \cdot B<C<A<D \)


Neglect friction. Find accelerations of
\( m, 2 m \) and \( 3 m \) as shown in the figure.
The wedge (inclination \( =30^{\circ} \) ) is fixed


A \( 0.50 k g \) object moves in a horizontal circular track with a radius of \( 2.5 m . \) An
external force of \( 3.0 N, \) always tangent
to the track, causes the object to speed
up as it goes around. The work done by the external force as the mass makes
one revolution is:
A \( .24 J \)
B. \( 47 J \)
c. \( 58 J \)
D. \( 67 J \)


If the vectors \( \overline{\boldsymbol{a}}=\mathbf{3} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}-\mathbf{2} \overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}= \)
\( -\overline{\boldsymbol{i}}+\mathbf{3} \overline{\boldsymbol{j}}+4 \overline{\boldsymbol{k}}, \overline{\boldsymbol{c}}=\mathbf{4} \overline{\boldsymbol{i}}-\mathbf{2} \overline{\boldsymbol{j}}-\mathbf{6} \overline{\boldsymbol{k}} \) form
the sides of the triangle then length of the median bisecting the vector \( c \) is
A. \( \sqrt{12} \) units
B. \( \sqrt{6} \) units
c. \( 2 \sqrt{6} \) units
D. \( 2 \sqrt{3} \) units


A uniform circular disc placed on a
rough horizontal surface has initially
velocity \( v_{0} \) and an angular velocity \( \omega_{0} \) as
shown in the figure. The disc comes to
rest after moving some distance in the direction of motion. Then \( \frac{v_{0}}{r \omega_{0}} \) is
A . \( 1 / 2 \)
B.
\( c \cdot 3 / 2 \)
D. 2


Assertion
(A): When a solid Copper sphere and solid Wooden sphere, both having the same mass, are pinning about their own axis with same
angular velocity, then the wooden sphere has greater angular momentum.
Reason (R): Wood is less denser than
Copper. So radius of Wooden sphere is
more than that of Copper and so greater
moment of inertia.
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
c. \( A \) is true and \( R \) is false
D. A is false and R is true


Which of the following is true for \( C O_{2} \) concentration?
A. More, in alveolar air than in expired air
B. More in expired air than in alveolar air
C. More in inspired air than in alveolar air
D. More in inspired air than in expired air.


A sample of \( 0.16 g C H_{4} \) was subjected
to the combustion at \( 27^{\circ} C \) in a bomb
calorimeter. The temperature of the
calorimeter. The temperature of the
calorimeter system (including water)
was found to rise by \( 0.5^{\circ} \mathrm{C} \). Calculate
the heat of combustion of methane at
(i) constant volume and
(ii) constant pressure. the thermal capacity of calorimeter system is
\( 17.0 k J K^{-1} \) and \( R= \)
\( 8.314 J K^{-1} m o l^{-1} \)


Neutron decay in free space is given as follows
\( \mathbf{o} \boldsymbol{n}^{\mathbf{1}} \longrightarrow \mathbf{1} \boldsymbol{H}^{\mathbf{1}}+\mathbf{i} \boldsymbol{e}^{\mathbf{0}}+[\mathbf{]} \)
Then the parenthesis [] represents a
A. neutrino
B. photon
c. antineutrino
D. graviton


Define the term: Corrosion


The electronic configuration of \( \boldsymbol{R} \boldsymbol{b}^{+} \) in absence of Aufbau Principle, is:
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{6} \)
B \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{3} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{4} \)
c. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{3} \)
D. None of these


Which scientist firstly knew about planet?


Initially, the spheres \( A \) and \( B \) are the
potential \( V_{A} \) and \( V_{B} \) respectively. Now
sphere \( \mathrm{B} \) is earthed by closing the switch. The potential of A will now
become \( _{--} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( V_{A} \)
\( \mathbf{c} \cdot V_{A}-V_{B} \)
D. \( V_{B} \)


toppr ०६
Q Type your question
In tigure. I nen the Key \( \mathbf{K} \) Is pressed to
complete the circuit. Finally the net
charge on upper plate and net charge the circuit. Finally the net charge on
upper plate and net charge on lower
plate of capacitor \( C \) is positive.

Reason : In a parallel plate capacitor
both plates always carry equal and
opposite charge.
A. If both Assertion arid Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.


The basic character of oxides
\( M g O, S r O, K_{2} O, N i O, C s_{2} O \) increase
in the
order:
A \( . M g O>S r O>K_{2} O>N i O>C s_{2} O \)
в. \( C s_{2} O<K_{2} O<M g O<S r O<N i O \)
c. \( N i O<M g O<S r O<K_{2} O<C s_{2} O \)
D. \( K_{2} O<N i O<M g O<S r O<C s_{2} O \)


The amount of the solute present in the saturated solution at a particular
temperature is called its:
A. solubility
B. saturation
c. solvent concentration
D. none of the above


'The action and reaction are equal in
magnitude'. Is this statement true and which law is related with it?
A. Yes, Newton's second law
B. Yes, Newton's third law
c. No, Newton's third law.
D. Yes, Newton's first law.


Given inside a circle, whose radius is
equal to \( 13 \mathrm{cm}, \) is a point \( \mathrm{M} \) at a distance \( 5 \mathrm{cm} \) from the centre of the
circle. A chord \( A B=25 \mathrm{cm} \) is drawn
through M. The lengths of the segments into which the chord \( A B \) is divided by
the point \( M \) in \( C M \) are
A. 12,13
в. 14,11
c. 15,10
D. 16, 9


Which of the following species has the ground state electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} ? \)
A . Sulfide ion, \( S^{2-} \)
в. \( H S O_{4}^{-} \)
c. \( K O H \)
D. \( H N O_{3} \)
E \( \cdot C_{2} O_{4}^{2} \)


A horse is tied to a post by a rope If the horse moves along a circular path always keep the rope tight and describes 88 metres when it has traced
out \( 72^{\circ} \) at the center, then the length of
rope is
\( A \cdot 60 m \)
B. \( 65 m \)
\( c .70 m \)
D. \( 72 m \)


A nurse applies a force of \( 3.8 N \) to the
syringe's piston of radius \( 0.9 \mathrm{cm} \). Find the increase in pressure of the fluid in the syringe?
A . \( 14.927 k P a \)
в. 469.13 Ра
\( \mathbf{c} .46 .9 \mathrm{mPa} \)
D. 422 Pa


is the additive inverse of \( \frac{-3}{11} \)
A \( \cdot \frac{-3}{11} \)
в. \( \frac{11}{3} \)
c. -1
D. \( \frac{3}{11} \)


A solid sphere of radius \( R \) and density \( \rho \) is attached to one end of a mass-less
spring of force constant \( k . \) The other end of the spring is connected to another solid sphere of radius \( \boldsymbol{R} \) and density \( \mathbf{3} \boldsymbol{\rho} \) The complete arrangement is placed in
a liquid of density \( 2 \rho \) and is allowed to
reach equilibrium. The correct
statement(s) is (are)

This question has multiple correct options
A \( \cdot \) the net elongation of the spring is \( \frac{4 \pi R^{3} \rho g}{3 k} \)
B. the net elongation of the spring is \( \frac{8 \pi R^{3} \rho g}{3 k} \)
c. the light sphere is partially submerged
D. the light sphere is completely submerged


Given that \( x, y, z \) are positive real
numbers such that \( x y z=32 . \) The
minimum value of \( x^{2}+4 x y+4 y^{2}+ \)
\( 2 z^{2} \) is equal to
\( \mathbf{A} \cdot 64 \)
в. 256
c. 96
D. 216


The half reaction which correctly represents the change that takes place
in the reaction between \( H_{2} O_{2} \) and
alkaline potassium ferricyanide is?
A \( \cdot H_{2} O_{2}+2 H^{+}+2 e^{-} \rightarrow 2 H_{2} O \)
в. \( H_{2} O_{2} \rightarrow 2 H^{-}+O_{2}+2 e^{-} \)
c. \( H_{2} O_{2} \rightarrow 2 H^{-}+O_{2}+2 H_{2} O+2 e^{-} \)
D. \( H_{2} O_{2}+2 e^{-} \rightarrow 2 O H \)


In anaerobic respiration, the number of
ATP molecules produced is equal to
A . 1
в. 2.
\( c \cdot 3 \)
\( D \cdot 8 \)


topp
solul
rroev
\( m \)
ime
\( m \)


Find the derivative of \( y=\log ^{3}\left(x^{2}\right) \)


Number of bond pair and lone pair of
electrons in \( \boldsymbol{O} \boldsymbol{F}_{2} \) are:
A .2,6
в. 2,8
c. 2,10
D. 1,9


If the value of \( C \) in a series RLC circuit is
decreased, the resonant frequency
A. is not affected
B. increases
c. is reduced to zero
D. decreases


The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell
balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.


\( \int \frac{1}{1+x^{3}} d x= \)
A \( \cdot \frac{1}{3} \log |x+1|-\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
B \( \cdot \frac{1}{3} \log |x+1|+\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
c. \( \frac{1}{3} \log |x+1|-\frac{1}{6} \log \left|x^{2}-x+1\right|- \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
D. \( -\frac{1}{3} \log |x+1|+\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)


The industrial revolution in England and
Western Europe more than two centuries ago was triggered by some key scientific and technological advances.What were these advances?


\( \boldsymbol{C O C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{1}= \)
\( \mathbf{0 . 3 2 9} \)
\( \mathbf{2} \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2}= \)
\( 2.24 \times 10^{22} \)
Calculate the equilibrium constant for the reaction given below from the data
given above at \( 1000 K \)
\( \mathbf{2} \boldsymbol{C O C l}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)


Compare thermal stability of \( Z n O \)
\( C d O \) and \( H g O \)
A. \( Z n O>C d O>H g O \)
в. \( C d O>Z n O>H g O \)
c. \( Z n O>H g O>C d O \)
D. \( H g O>Z n O>C d O \)


There are 5 tube-lights each of \( 40 W \) in a house. These are used on an average
for 5 hrs / day. In addition, there is an immersion heater of \( 1500 W \) used on
an average for 1 h \( / \) day. The number of
units of electricity that are
consumed in a month of 30 days is:
A. 25 units
B. 50 units
c. 75 units
D. 100 units


In the transmission of power the voltage of power generated at the generating stations is stepped up from \( 11 \mathrm{kV} \) to 132 kV before it is transmitted. Why?


The diagram given represents a stage during cell division. Study the same and answer the question that follows. Draw a neat labeled diagram of the stage that comes before the stage shown in the diagram, keeping the chromosome number constant.


The vast amount of seaweeds present in ocean may provide an endless source of:
A. Carbon monoxide
B. Hydrogen sulphide
c. Methane
D. None of these


How will you bring about the following conversion?
4-nitroaniline to 1,2,3 -tribromobenzene


Short / Long Answer Types:
What are the three pathways involved in the complete breakdown of glucose to
carbon dioxide \( \left(C O_{2}\right) \) and water \( \left(H_{2} O\right) \)
? What reaction is needed to join two of
these pathways?


The potential energy of a proton is \( 3.2 \times 10^{-18} J \) at a particular point. The
electric potential at this point is:
(Given charge on a proton is \( 1.6 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) \)
A . \( 5 V \)
B. \( 10 V \)
\( c .20 V \)
D. \( 15 V \)


\( G \) is a set of all rational numbers except
-1 and \( * \) is defined by \( a * b=a+b+ \)
\( a b \) for all \( a, b \in G, \) in the group \( (G, *) \)
the solution of \( 2^{-1} * x * 3^{-1}=5 \) is
\( \mathbf{A} \cdot 71 \)
B. 68
c. \( 63 / 5 \)
D. \( 72 / 5 \)


In an experiment, \( 4.90 \mathrm{g} \) of copper oxide
was obtained from \( 3.92 g \) of copper. In another experiment, \( 4.55 g \) of copper oxide gave,on reduction, \( 3.64 g \) of copper. show that these figures verify the law of constant proportions.


Let \( \boldsymbol{A}= \)
\( \{x \in W, \) the set of whole numb
\( \boldsymbol{B}= \)
\( \{\boldsymbol{x} \in \boldsymbol{N}, \) the set of natural num
and \( C=\{3,4\}, \) then how many
elements will \( (A \cup B) \times C \) conatin?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 8
c. 10
D. 12


Assertion
STATEMENT -1: If \( x, y, z \) are the sides of
a triangle such that \( x+y+z=1 \), then \( \left[\frac{2 x-1+2 y-1+2 z-1}{3}\right] \geq((2 x- \)
1) \( (2 y-1)(2 z-1))^{1 / 3} \)
Reason
STATEMENT-2: For positive numbers their A.M., G.M. and H.M. satisfy the relation \( \boldsymbol{A} . \boldsymbol{M} .>\boldsymbol{G} . \boldsymbol{M} .>\boldsymbol{H} . \boldsymbol{M} \)
A. Statement-1 is True, Statement-2 is True; Statement
-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-
c. Statement- - is True, Statement- -2 is False
D. Statement-1 is False, Statement-2 is True


An urn contains 2 white and 2 black
balls. A ball is drawn at random. If it is
white it is not replaced into the urn. Otherwise it is along with another ball
of same colour. The process is repeated. the probability that the third ball drawn is black is a/b (no common divisor),
then \( b-a= \)


The order of the differential equation of
all parabolas whose axis of symmetry
along \( x \) -axis is:
A .2
B. 3
\( c . \)
D. None of these


Which of the following series of transitions in the spectrum of hydrogen atom fall in visible region?
A. Lyman series
B. Balmer series
c. Paschen series
D. Brackett series.


A glass prism has how many rectangular surfaces?
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
\( D \)


If both the objects have the same PE
curve as shown in the figure, then
A . For objects having total energy \( E_{2} \), all values of r are possible
B. For the object having total energy \( E_{2} \), values of \( r<r_{0} \)
are only possible
C. For the object having total energy \( E_{1} \), all values of rare possible
D. None of the above


Assertion
Benzaldehyde does not undergoes aldol condensation
Reason
Benzaldehyde does not contain acidic \( \alpha \)
-Hydrogen
A. Statement- -I is True, Statement-II is True ; Statement-I is a correct explanation for Statement-
is NOT a correct explanation for Statement-
c. statement-l is True, Statement-II is False
D. Statement-lis False, Statement-II is True


Assertion : Agricultural output increased several times after introduction of DDT.
Reason: DDT was the first insecticide use
d on a wide scale.
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
E. If the assertion is false but reason is true


Match the following colums.
\begin{tabular}{ll|ll}
& Column I & & Columns II \\
A. & Polyuria & 1. & WBCs pus in urine \\
B. & Pyuria & 2. & High level of uric acid in blood \\
C. & Gout & 3. & Excess of urine output \\
D. & Haematuria & 4. & Presence of blood (RBCs) in urine
\end{tabular}
\( \mathbf{A} \)
B. \( A-2, B-3, C-1, D-4 \)
C. \( A-1, B-2, C-3, D-4 \)
D. \( A-4, B-3, C-2, D-1 \)


In which of the followings intra
hydrogen bonding is present?
A. Ortho-nitrophenol
B. Meta-nitrophenol
c. Para-nitrophenol
D. All of these


Which of the following statement is
correct?
A. AC generator generates a higher voltage
B. DC generator generates a higher voltage
C. AC generator has a permanent magnet whereas a DC generator has an electromagnet
D. There is a split-ring commutator in a DC generator but not in an AC generator


The atrio-ventricular valves of the heart
is prevented from turning inside out by tough strands of connective tissue
is called as
A. Tendinous cords
B. Tricuspid
c. Pocket valve
D. Mitral valve


Why do mountaineers usually suffer from nose-bleeding at high altitudes?


The perimeter of a triangle is \( 9 m^{2}- \)
\( 2 n+8 \) and its two sides are \( 4 m^{2}+3 n \)
and \( 7 m^{2}+5 n-12 . \) Find the third side
of the triangle.
A \( \cdot m^{2}-10 n-10 \)
B. \( -2 m^{2}-10 n+20 \)
c. \( -2 m^{2}-14 n+20 \)
D. \( m^{2}-10 n+10 \)


The following truth table is for which
gate?
\( \begin{array}{lll}A & B & Y=A+B \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
A. AND
B. OR
c. Nor
D. NAND


In the figure given, lines \( X Y \) and \( M N \)
intersect at \( 0 . \) If \( \angle P O Y=90^{\circ} \) and \( a: b= \)
\( 2: 3, \) then \( \angle X O N \) is equal to
A . \( 126^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 180^{\circ} \)


If \( \boldsymbol{y}=\boldsymbol{a} \cos (\log \boldsymbol{x})+\boldsymbol{b} \sin (\log \boldsymbol{x}) \) then
prove that \( \boldsymbol{x}^{2} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}=\boldsymbol{0} \)


Which of the following statement
relates to the body plan of an animal?
A. Its general structure
B. Its general form and the functional interrelationship of its parts
c. Its general form and its evolutionary history
D. All of the above


What is the maximum number of
emission lines when the excited
electron of \( \mathrm{H} \) atom in \( \mathrm{n}=6 \) drops to the ground state?


Standard Deviation of n observations
\( a_{1}, a_{2}, a_{3} \dots \dots a_{n} \) is \( \sigma \) Then the standard
deviation of the observations
\( \lambda a_{1}, \lambda a_{2}, \dots, \lambda a_{n} \) is
\( A \cdot \lambda \sigma \)
B. - \( \lambda \sigma \)
c. \( |\lambda| \sigma \)
D. \( \lambda^{n} \sigma \)


The equation corresponding to the wave number of spectral line in the Brackett series:
A \( \cdot R\left[\left(1 / 2^{2}\right)-\left(1 / 4^{2}\right)\right] \)
B . \( R\left[\left(1 / 4^{2}\right)-\left(1 / 5^{2}\right)\right] \)
c. \( R\left[\left(1 / 3^{2}\right)-\left(1 / 5^{2}\right)\right] \)
D. \( R\left[\left(1 / 5^{2}\right)-\left(1 / 6^{2}\right)\right. \)


\( \ln C O_{3}^{2-}, \) all the three \( C-O \) bonds are
of identical length. State whether the above statement is
true or false
A. The statement is true
B. The statement is false
c. Neither
D. \( \ln C O_{2}^{2-} \), all the three \( C-O \) bonds are of identical length


Write the molecular formula and
structural formula of the following
substances?
a) Phosphinic acid
b) Oleum
c) Perbromic acid.


Consider the following equilibrium:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{N} \boldsymbol{H}_{2}^{-} \)
Why \( N H_{3} \) undergo self ionization?


The value of the integral \( \int_{-\pi}^{\pi}(\cos a x- \) \( \sin b x)^{2} d x, \) where \( a \) and \( b \) are integers,
is
A \( .2 \pi(1+a+b) \)
B. 0
c. \( \pi \)
D. \( 2 \pi \)


If optical rotation produced by the
compound \( [A] \) is \( +65^{0}, \) then produced
by the compound [B] is?
\( [\mathrm{A}] \)
\( [\mathrm{B}] \)
\( a \cdot k b^{-} \)
\( \mathbf{A} \cdot+65^{0} \)
B . \( -65^{\circ} \)
c. zero
D. Unpredictable


Bowman's glands are located in the
A. Proximal end of coniferous tubules
B. Anterior pituitary
C. Female reproductive system of cockroach
D. Olfactory epithelium of nose


Assertion
The number 1.202 has four significant
figures and the number 0.0024 has two significant figures.
Reason
All the non zero digits are significant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the term independent of \( x \) in \( (x+ \) \( \left.\frac{1}{x}\right)^{4} \)


Write the S.I. unit of activity.
A. Becquerel
в. Henry
\( \mathrm{c} \cdot O h m \)
D. Mendel


Give reasons:
(i) Name the method of refining of nickel.
(ii) What is the role of cryolite in the extraction of aluminium?
(iii) What is the role of limestone in the extraction of iron from its oxides?


Figure shows a wedge of mass \( 2 k g \)
resting on a frictionless floor. A block of
mass \( 1 \mathrm{kg} \) is kept on the wedge and the
wedge is given an acceleration of 5
\( m / \sec ^{2} \) towards right. Then:
A. Block will remain stationary w.r.t. wedge
B. The block will have an acceleration of \( 1 \mathrm{m} / \mathrm{sec}^{2} \) w.r.t. the wedge
C. Normal reaction on the block is \( 11 N \)
D. Net force acting on the wedge is \( 2 N \)


Divide as directed \( 5(2 x+1)(3 x+5) \div \)
\( (2 x+1) \)


2K coins (K is an integer) each with probability P(O
\( ^{A} \cdot \frac{K}{2 K+1} \)
в. \( \frac{K+1}{2 K} \)
c. \( \frac{K+1}{2 K+1} \)
D. \( \frac{2 K}{K+1} \)


Which of the following is not a permissible arrangement of electrons
in an atom?
A \( \cdot n=3,1=2, m=+1, s=-\frac{1}{2} \)
B \( \cdot n=4,1=0, m=0, s=-\frac{1}{2} \)
\( c \cdot n=5,1=3, m=0, s=+\frac{1}{2} \)
D. \( n=3,1=2, m=-3, s=-\frac{1}{2} \)


Which of the following energies is used for generating electricity?
A. Solar energy
B. Nuclear energy
c. wind energy
D. All of these


We have taken a saturated solution of
\( A g B r . K_{s p} \) of \( A g B r \) is \( 12 \times 10^{-14} .1 f \)
\( 10^{-7} \) mole of \( A g N O_{3} \) are added to 1 litre of this solution find conductivity (specific conductance) of this solution in terms of \( 10^{-7} \mathrm{Sm}^{-1} \)
Given: \( \lambda_{A g^{+}}^{0}=6 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)
\( \lambda_{B r^{-}}^{0}=8 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \) and
\( \lambda_{N O_{3}^{-}}^{0}=7 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1}[ \) If answe
is \( X \) then give answer in form of \( \frac{X}{11} \)


3 volumes of hydrogen are required to combine with one volume of nitrogen to form 2 volumes of ammonia. When 1
mole of hydrogen is allowed to react with the mole of nitrogen, the two gases?
A. Do not combine
B. Combine and both the gases are used up completely
c. \( 2 / 3 \) mole of nitrogen remains unreacted
D. Some hydrogen remains uncombined


The solubility product \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{B} \boldsymbol{i}_{2} \boldsymbol{S}_{3} \) is
\( 1.2 \times 10^{-98} . \) The solubility of \( B i_{2} S_{3} \) is
approximately:
A \( \cdot 1 \times 10^{-33} \)
В. \( 1 \times 10^{-20} \)
c. \( 1 \times 10^{-27} \)
D. \( 1 \times 10^{-24} \)


To which of the following species, the octet rule is not applicable? This question has multiple correct options
A. \( B r F_{5} \)
B. \( S F_{6} \)
c. \( I F_{7} \)
D. \( C O_{2} \)


If the collector current changes from \( 2 m A \) to \( 3 m A \) in a transistor when
collector - emitter voltage is increased from \( 2 V \) to \( 10 V \), the output
resistance is
\( \mathbf{A} \cdot 1 K \Omega \)
B. \( 8 K \Omega \)
\( \mathbf{c} \cdot 8 m \Omega \)
D. \( 1 \mathrm{m} \Omega \)


Assertion
During storms, communication may be disrupted, and electrical discharges may be seen between sharp points on signalling equipment that is
inadequately earthed.
Reason
Atmospheric electricity often has an effect on electrical communications.
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


Hibernating animals have tissues containing mitochondria with a
membrane protein that accelerates
electron transport while blocking the synthesis of ATP.What is the
consequence of this?
A. Energy is saved because glycolysis and the citric acid cycle shuts down
B. The energy of respiration is converted into heat
c. Hibernating animals can synthesize fat instead of wasting energy of respiration
D. Pyruvate is converted to lactic acid by anaerobic fermentation


Evaluate \( \lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}},(a \neq 0) \)
A \( \cdot \frac{2}{3 \sqrt{3}} \)
B \( \cdot \frac{4}{3 \sqrt{3}} \)
c. \( \frac{5}{3 \sqrt{3}} \)
D. \( \frac{7}{3 \sqrt{3}} \)


Motile, asexual and endogenous spores produced in algal members are called
A. Zoosphores
B. Aplanospores
c. conidia
D. cyst


Acid catalysed hydrolysis of the cyclic
acetal gives:
A. ethanal and 2 -chlorocyclohexanol
B. ethanol and 2 -chlorocyclohexanol
C. 1,2 -ethanediol and 2 -chlorocychlohexanone
D. 1,2 -ethanediol and 2 -chlorocyclohexanol


The following lines are \( \hat{\boldsymbol{r}}=(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}})+ \)
\( \lambda(\hat{i}+2 \hat{j}-\hat{k})+\mu(-\hat{i}+\hat{j}-2 \hat{k}) \)
A. collinear
B. skew-lines
c. co-planar lines
D. parallel lines


A smooth dielectric slab \( A \) of mass \( m \)
and dielectric constant \( k \) is placed
between the plates of a parallel plate capacitor and connected to another
block \( B \) of equal mass \( m \) through a
string and pulley arrangement as shown in the figure.
The capacitor plates with separation \( \delta \)
and width \( b \) are connected to a battery
of emf \( \boldsymbol{E} \) as shown in the figure. The
pulley and string are massless and \( \boldsymbol{E}=\sqrt{\frac{\boldsymbol{m} \boldsymbol{g} \boldsymbol{\delta}}{\boldsymbol{b}(\boldsymbol{k}-\mathbf{1}) \in_{0}}} \)


Find the value of \( \cos 75^{\circ} \)


Assertion
Let \( A, B \) and \( C \) be three events such
that \( \boldsymbol{P}(\boldsymbol{C})=\mathbf{0} \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0} \)
Reason
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C})=\boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Differentiate between.
Venous heart and pulmonary heart


The mass of an object is a measure of inertia:
A. quantitative
B. qualitative
c. absolute
D. average


The value of \( \int_{0}^{\sqrt{2}}\left[x^{2}\right] d x, \) where [.] is the greatest integer function, is
A \( .2-\sqrt{2} \)
B. \( 2+\sqrt{2} \)
c. \( \sqrt{2}-1 \)
D. \( \sqrt{2}-2 \)


Consider \( \Delta A B C \) with \( A \equiv(\vec{a}), B \equiv(\vec{b}) \)
and \( C=(\vec{c}), \) ff \( \vec{b} .(\vec{a}+\vec{c})=\vec{b} \cdot \vec{b}+ \)
\( \vec{a} \cdot \vec{c} ;|\vec{b}-\vec{a}|=3 ;|\vec{c}-\vec{b}|=4 \) then the
angle between the medians \( \overline{A M} \) and
\( B D \) is
A. \( \pi-\cos ^{-1}\left(\frac{1}{5 \sqrt{13}}\right) \)
в. \( \pi-\cos ^{-1}\left(\frac{1}{13 \sqrt{5}}\right) \)
c. \( \cos ^{-1}\left(\frac{1}{5 \sqrt{13}}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{13 \sqrt{5}}\right) \)


Uric acid forms in body by
A. Phospholipid
B. Glucose
c. DNA
D. RNA


A particle hanging from a massless spring stretches it by \( 2 \mathrm{cm} \) at earths surface. How much will the same
particle stretch the spring at a height of \( 2624 \mathrm{km} \) from the surface of the earth? (Radius of earth \( =6400 \mathrm{km} \) ).
A \( .1 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
\( \mathrm{c} .3 .3 \mathrm{cm} \)
D. 4 cm


A diatomic molecule is formed by two
atoms which may be treated as mass
points \( m_{1}, \) and \( m_{2} \) joined by a massless rod of length r. Then, the moment of inertia of the molecule about an axis
passing through the centre of mass and perpendicular to rod is :
A. zero
B. \( \left(m_{1}+m_{2}\right) r^{2} \)
c. \( \frac{\left(m_{1}+m_{2}\right)}{m_{1} m_{2}} r^{2} \)
D. \( \left(\frac{m_{1} m_{2}}{m_{1}+m_{2}}\right) r^{2} \)


Which one of the following statements is incorrect about rock salt type?
A . It has fcc arrangement of \( \mathrm{Na}^{-} \)
B. Nat and Cl-ions have a co-ordination number of 6: 6
c. A unit cell of \( N a C l \) consists of four \( N a C l \) units
D. All halides of alkali metals have rock-salt type structure


Let \( \boldsymbol{A}=\{\mathbf{1},-\mathbf{1}\} . \) Then find \( \boldsymbol{A} \times \boldsymbol{A} \)


Identify in which type of wave, particles moves parallel to the wave direction?
A. longitudinal
B. transverse
c. s waves
D. seismic
E. electromagnetic


Two identical p-njunctions may be
connected in series with a battery in three different ways as shown in the
circuit diagrams. In which circuit
diagram will the potential drop across
the p-njunctions be equal?
A. Circuit (1)
B. Circuit (2)
c. circuit (3)
D. Circuit (2) and (3)


Friction is a/an
A . self-adjusting force
B. necessary evil
C. important force in daily life
D. all the above


Assertion
It is not possible for a system unaided
by an external agency to transfer heat
from a body at lower temperature to
another at a higher temperature.
Reason
It is not possible to violate the 2 nd law
of thermodynamics.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following molecule is having least ionic character?
A \( \cdot F e C l_{2} \)
в. \( Z n C l_{2} \)
c. \( M g C l_{2} \)
D. \( N a C l \)


The electronegativities of nitrogen and chlorine are almost same. However,
\( N H_{3} \) exists as liquid whereas \( H C l \) as
gas due to between the
molecules of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
A. van der Walls force of attraction
B. ionic bonding
c. H-bonding
D. dipole-dipole interaction


Match the cations from List I with their
properties in List II.


In Sl unit gravitational unit of force is called
A. \( G f \)
в. \( K g f \)
\( c . N \)
D. All


Which of the following alkali metal ions has lowest ionic mobility in aqueous solutions?
\( \mathbf{A} \cdot R b^{+} \)
B. \( C s^{ } \)
c. \( N a^{+} \)
\( \mathbf{D} \cdot L i^{+} \)


Which of the following is used as a method of purification for silicon?
A. Electrolytic refining
B. Liquation
c. zone refining
D. Distillation


Soaps do not create water pollution
because:
A. soaps are insoluble in water
B. soaps are soluble in water
c. soaps are fairly bio-degradable
D. soaps are non-biodegradable


Using the expressions for charge and current for L-C oscillator, explain L-C oscillations.


statement 1: In Young's experiment, the fringe width for dark fingers is different from that for white fringes. statement 2: In Young's double slit experiment the fringes are performed with a source of white light, then only black and bright fringes are observed.
A. If both statement 1 and statement 2 are true but statement 2 is the correct explanation of statement
B. If both statement 1 and statement 2 are true but statement 2 is not the correct explanation statemen
c. If statement 1 is true but statement 2 is false
D. If both the statement 1 and statement 2 are false
E. If statement 2 is true but statement 1 is false


For the following reaction: \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 7} \times \)
\( 10^{7} \) at \( 25^{\circ} C \)
\( A g^{+}(a q .)+2 N H_{3}(g) \rightleftharpoons \)
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]^{+} \)
what value of \( \Delta G^{o} \) in \( k J ? \)
A. -41.2
B. -17.9
\( \mathrm{c} \cdot+17.9 \)
\( \mathbf{D} .+41.2 \)


Is linear momentum of a system always
conserved?


When plaster of paris comes in contact
with water it sets into a hard mass. The
composition of the hard mass is:
A \( \cdot \operatorname{CaSO}_{4} \cdot H_{2} O \)
в. \( \operatorname{CaSO}_{4} \cdot \operatorname{Ca}(O H)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} .2 \mathrm{Ca}(\mathrm{OH})_{2} \)


If the extremities of a diagonal of a square are (1,-2,3) and (4,2,3) then the area of the square is
A . 25
B. 50
c. \( \frac{25}{2} \)
D. \( \sqrt{50} \)


The \( C l^{-} \) ion is formed, when \( ^{\prime} C l^{\prime} \) atom
loses an electron.
A. True
B. False


The water equivalent of a calorimeter is
10g and it contains 50g of water at \( 15^{\circ} \)
C. Some amount of ice, initially at \( -10^{\circ} \) \( \mathrm{C} \) is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was
dropped (when specific heat of ice \( = \) 0.5cal \( g m^{-1} o^{-1} \), specific heat of
water \( =1.0 \) cal \( g m^{-1 o} C^{-1} \) and latest
heat of melting of ice \( =\mathbf{8 0} \) cal \( \boldsymbol{g m}^{-1} \) )?
A . 108
B. \( 18 g \)
\( \mathbf{c} \cdot 20 g \)
D. 30g


The azeotropic solution of two miscible
liquids:
This question has multiple correct options
A. Can be seperated by simple distillation
B. May show positive or negative deviation from Raoult's law
C . Are supersaturated
D. Behave like single pure component and boil at a fixed temperature


Assertion: Virtual object can't be seen
by human eye. Reason: Virtual object is formed by
converging rays.
A. Both assertion and reason are correct and reason is
the correct explanation of the assertion
B. Both assertion and reason are correct, but reason is not the correct explanation of the assertion
C. Assertion is correct but reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both assertion and reason are incorrect


Let \( f(x)=\frac{x^{2}-x}{x^{2}+2 x}, \) then \( \frac{d}{d x}\left[f^{-1}(x)\right] \) is
equal to
\( \mathbf{A} \cdot-\frac{3}{(1-x)^{2}} \)
B. \( \frac{3}{(1-x)^{2}} \)
c. \( \frac{1}{(1-x)^{2}} \)
D. \( -\frac{1}{(1-x)^{2}} \)


The mechanism of phosphorylation is
depicted in the diagram below. Study it
carefully and mark the correct option.
A. The diagram depicts photosynthetic phosphorylation taking place in the chloroplast. The incident light should be shown in the diagram
B. The diagram depicts oxidative phosphorylation taking place in mitochondria. However, the flow of electrons should be shown in the reverse direction
c. Diagram depicts the basic process of both oxidative as well as photosynthetic phosphorylation. However, the proton concentration should be high inside and low outside
D. The diagram correctly depicts the oxidative phosphorylation occuring in all heterotrophic isms


An isotone of \( \mathrm{Ge}_{32}^{77} \) is:
i. \( \mathbf{G e}_{32}^{76} \)
ii. \( A \mathbf{s}_{33}^{78} \)
iii. \( \mathrm{Se}_{34}^{79} \)
¡v. \( \operatorname{Se}_{34}^{78} \)
A. only (i) and (ii)
B. only (ii) and (iii)
c. only (ii) and (iv)
D. (ii), (iii) and (iv)


\( ;(b)-(v) \) (d) \( - \) (iii) \( ;(e)- \) (i)
\( A \cdot(a)-(i i) \)
; (c) - (iv)
\( (n) \)
\( (\mathrm{i}) \) (b) \( -(v) ;(c)-(\text { iii) } ;(d)-(i v) ;(e)-(i) \)
(b) \( -(i v) ;(c)-(v) ;(d)-(i i i) ;(e)-(i i) \) :
-1
i)
(iii) \( (b)-(v) \) \( (c)- \) in (d) \( :(e)-(i) \)
\( D \cdot(a) \)
- (ii) :


If the vectors \( 2 x \hat{i}-y \hat{j}-4 \hat{k} \) and \( 10 \hat{i}+ \) \( \hat{\boldsymbol{y}}+5 \hat{k} \) are perpendicular, then the locus of \( (x, y) \) is
A. A Parabola with vertex at (1,0) and latus rectum 10
B. A Parabola with vertex at (0,1) and latus rectum 20
c. A Parabola with vertex at (1,0) and latus rectum 20
D. A Parabola with vertex at (0,1) and latus rectum 10


What is momentum? Write its SI unit.
Interpret force in terms of momentum
Represent the following graphically.


Linnaeus described 5900 species of
plants in his book
(1753) and 4326 species of animals in
his book
A. Philosophia Botanica, Genera Plantarum
c. systema Naturae, Species Plantarum
D. species Plantarum, systema Naturae


f a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{j}-4 \hat{i}+\alpha \hat{k}, \) then the
value of \( \alpha \)
A . -
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)


Which among the following can be shaped into thin sheets?
A. Oxygen
B. Chlorine
c. Nitrogen
D. Tungsten


A closed curve encircles several conductors.The line integral \( \int \overrightarrow{\boldsymbol{B}} \cdot \boldsymbol{d} \overrightarrow{\boldsymbol{l}} \)
around this curve is \( 3.83 \times 10^{-7} T-m \)
What is the net current in the
conductors?
A . \( 0.1 A \)
в. \( 0.2 A \)
\( c .0 .3 A \)
D. \( 0.4 A \)


\( \boldsymbol{E}_{1}=\frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}-\mathbf{1}=\mathbf{0},(\boldsymbol{a}>\boldsymbol{b}) \) and
\( \boldsymbol{E}_{2}=\frac{\boldsymbol{x}^{2}}{\boldsymbol{k}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}-\mathbf{1}=\mathbf{0},(\boldsymbol{k}<\boldsymbol{b}) \boldsymbol{E}_{2} \) is
inscribed in \( E_{1} . \) If \( E_{1} \) and \( E_{2} \) have same
eccentricities then length of minor axis
of \( \boldsymbol{E}_{2}=\boldsymbol{p}\left(\mathrm{LLR} \text { of } \boldsymbol{E}_{1}\right) \) then \( \boldsymbol{p}=? \)
A \( \cdot \frac{1}{2} \)
B. 1
\( c \cdot \frac{2}{3} \)
D.


The acceleration-time graph of a
particle moving in a straight line is
shown in fig. The velocity of the
particle at time \( t=0 \) is \( 2 \mathrm{m} / \mathrm{s} \). The
velocity after 2 s will be:
\( A \cdot 6 \mathrm{m} / \mathrm{s} \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2 m / s \)
D. \( 8 \mathrm{m} / \mathrm{s} \)


Statement: Cathode rays deflect in the
presence of a magnetic field.
A. True
B. False


If area bounded by to curves \( \boldsymbol{y}^{2}=4 a x \)
and \( y=m x \) is \( \frac{a^{2}}{3}, \) then the value of \( m \) is
A .2
B. - 1
\( c \cdot \frac{1}{2} \)
D. none of these


Statement 1: The ideal gas law does not hold under low temperatures and high
pressure. Statement 2: Interactions between
particles cannot be neglected under these conditions.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Catalyst the rate of reaction.
A. increases
B. decreases
C. both (a) and (b) above
D. none of these


If \( 1.8 \times 10^{19} \) molecules of \( N O_{2} \) are
removed from 10 mg of \( N O_{2} \), how many
moles of \( N O_{2} \) are left?
\( \mathbf{A} \cdot 3.87 \times 10^{4} \)
B . \( 1.87 \times 10^{-4} \)
c. \( 1.87 \times 10^{4} \)
D. \( 2.87 \times 10^{-4} \)


Burning of coal and diseal releases:
This question has multiple correct options
A \( \cdot N O_{2} \)
в. \( S O_{2} \)
\( c \cdot C O_{2} \)
D. None of these


\( \int_{1}^{2}\left(\frac{x-1}{x^{2}}\right) e^{x} d x \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{5} & \mathbf{2} \\ \mathbf{1} & -\mathbf{3}\end{array}\right], \) then adj \( \mathbf{A} \) is equal to
A. \( \left[\begin{array}{ll}-3 & -2 \\ -1 & -5\end{array}\right] \)
(年) 0
В. \( \left[\begin{array}{cc}3 & -2 \\ -1 & 5\end{array}\right] \)
c. \( \left[\begin{array}{ll}5 & 1 \\ 2 & 3\end{array}\right] \)
D. \( \left[\begin{array}{ll}3 & 2 \\ 1 & 5\end{array}\right] \)


Correct order at \( C \) -H bond dissociation
energy of following compound:
(।) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{H} \)
(II) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{H} \)
\( (\| I) C H_{3}=C H-C H_{2}-H \)
\( (I V) C_{6} H_{5}-H \)
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. IV>1> || > |||
D. II>I>VI>III


decomposes white light
into its constituent colors.
A. Flat glass slab
B. Convex mirror
c. Concave mirror
D. Prism


Q Type your question
infinitely long wire carrying a constant
current \( I . \) The sides \( P Q \) and \( R S \) are
parallel to the wire. The wire and the
loop are in the same plane. The loop is
rotated by \( 180^{\circ} \) about an axis parallel to
the long wire and passing through the
mid-points of the sides \( Q R \) and \( P S . \) The
total amount of charge which passes through any point of the loop during
rotation is
A \( \cdot \frac{\mu_{0} I a}{2 \pi r} \ln 2 \)
B. \( \frac{\mu_{0} I a}{\pi r} \ln 2 \)
c. \( \frac{\mu_{0} I a^{2}}{2 \pi r} \ln 2 \)
D. cannot be found because time of rotation is not given
E. answer required


Find the value of \( p \) for which the given
simultaneous equation has unique solution:
\( \mathbf{8} \boldsymbol{x}-\boldsymbol{p} \boldsymbol{y}+\mathbf{7}=\mathbf{0} ; \quad \mathbf{4} \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{3}= \)
\( \mathbf{0} \)
A. All values of \( p \) except 4
в. \( p=7 \)
\( \mathbf{c} \cdot p=6 \)
D. All values of \( p \) except 5


Two concave lenses \( L_{1} \) and \( L_{2} \) are kept
in contact with each other. If the shape between the two lenses are filled with a
material of smaller refractive index the
magnitude of the focal length of the combination
A. becomes undefined
B. remains unchanged
c. Increase
D. Decrease


Leave grow due to presence of
A. Apical meristan
B. Diffused meristem
C . Intercalary meristem
D. Mass meristem


Explain how does the melting point change on moving from group- 1 to group- 2 in the periodic table?


The resistance of a wire is 50 ohm. Then
the graph between \( \log V \) and \( \log I \) is :-
A. straight line
B. parabola
c. hyperbola
D. circle


Which of the following statement is
incorrect?
A. Type \( X Y_{3} \) interhalogen compounds possess T-shape structure.
B. Type \( X Y_{5} \) interhalogen compounds possess square pyramidal structure.
C. Type \( X Y_{3} \) interhalogen compounds are formed by \( s p^{3} d \) hybridisation.
D. Type \( X Y_{5} \) interhalogen compounds are formed by \( s p^{3} d^{3} \) hybridisation.


Plumed seeds occur in
A. Naravelia
B. Taraxacum
c. Calotropis
D. colutea


If the surface shown in fig is
frictionless, the ratio of \( T_{1} \) and \( T_{2} \) is:
A . 10: 1
B . 4: 1
\( c .5: 4 \)
D. 5: 1


A material that does not allow
electricity to flow through it is called \( a / a n \)
A. Electrical appliance
B. Electrical conductor
c. Electrical Insulator
D. None of these


Who coined the term meiosis?
A. Hertwig and Van Bevedin
B. Sutton and Boveri
C. Hofmeister and Waldeyer
D. Farmer and Moore


Shape of chromosome can be best observed during
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


If \( x \) co-ordinate of a point is 2 and \( y \) co-
ordinate is \( 0, \) then ordered pair for its
coordinate on \( X Y \) plane is
A \( .(0,0) \)
в. (2,2)
D. (2,0)


An ideal gas expands from a volume of
\( 6 d m^{3} \) to \( 16 d m^{3} \) against the constant
external pressure of \( 2.026 \times 10^{5} N m^{-} 2 \)
Find enthalpy change if \( \Delta u \) is \( 418 J \)


A cannon ball of mass \( 500 g \) is fired
with a speed of \( 15 m s^{-1} \). Find its
momentum.
A . \( 7500 k g \) m \( s^{-1} \)
B. \( 3750 k g \) m \( s^{-1} \)
c. \( 7.5 k g m s^{-1} \)
D. 3.75kg m s \( ^{-1} \)


Let \( A=\left(\begin{array}{l}3^{2} \\ 5\end{array}\right) \) and \( B=\left(\begin{array}{c}8-1 \\ 3\end{array}\right) . \) Find the
matrix \( \mathrm{C} \) if \( \boldsymbol{C}=\mathbf{2} \boldsymbol{A}+\boldsymbol{B} \)


Beryllium atom in beryllium fluoride is:
A \( \cdot s p^{3} \) hybridised
B. \( s p^{2} \) hybridised
c. sp hybridised
D. Unhybridised


If the solubility of the salt
\( \boldsymbol{L} \boldsymbol{i}_{3} \boldsymbol{N} \boldsymbol{a}_{3}\left(\boldsymbol{A l} \boldsymbol{F}_{6}\right)_{2} \) is \( \boldsymbol{x}, \) then its solubility
product would be:
\( \mathbf{A} \cdot 972 x^{8} \)
В . \( 1458 x^{8} \)
\( \mathbf{c} \cdot 2916 x^{8} \)
D. None of the above


Differences in climates in various areas
of the Earth result largely from
A. ocean currents
B. complexity of the food chain in a particular region
c. movements of plates of the Earths crust
D. differences in the amount of sunlight striking at different latitudes


\( \int \frac{1}{\left(1+x^{2}\right) \sqrt{p^{2}+q^{2}\left(\tan ^{-1} x\right)^{2}}} d x \) is
equal to
A \( \cdot \frac{1}{p} \log \left|p\left(\tan ^{-1} x\right)+\sqrt{p^{2}+\left(q \tan ^{-1} x\right)^{2}}\right|+C \)
B. \( \frac{1}{p} \log \left|\left(p \cot ^{-1} x\right)+\sqrt{p^{2}+\left(p \cot ^{-1} x\right)^{2}}\right|+C \)
c. \( \frac{1}{q} \log \left|q\left(\cot ^{-1} x\right)+\sqrt{p^{2}+\left(q \cot ^{-1} x\right)^{2}}\right|+C \)
D \( \cdot \frac{1}{q} \log \left|q\left(\tan ^{-1} x\right)+\sqrt{p^{2}+\left(q \tan ^{-1} x\right)^{2}}\right|+C \)


Root pressure is caused by
A. Osmosis
B. Diffusion
c. Passive transport
D. Uphill transportt


Generally, organic compounds are:
A. amorphous
B. complexes
c. covalent
D. electrovalent


An example of short day plant is
A. Maize
B. Radish
c. chrysanthemum
D. wheat


If the electron is at an infinite distance
from the nucleus, then its energy will be
A . infinite
B. finite
c. zero
D. one


From a solid sphere of mass \( M \) and
radius \( R \) a spherical portion of radius \( \boldsymbol{R} \)
\( \frac{1}{2} \) is removed, as shown in the figure. Taking gravitational potential \( V=0 \) at
\( r=\infty, \) the potential at the centre of the
cavity thus formed is : \( (G= \) gravitational constant)
\( ^{A} \cdot \frac{-2 G M}{3 R} \)
в. \( \frac{-2 G M}{R} \)
\( c \cdot \frac{-G M}{2 R} \)
D. \( \frac{-G M}{R} \)


The potential difference between the
plates of a capacitor separated by \( 3 \mathrm{mm} \) is \( 12.0 \mathrm{V} \). Calculate the magnitude of \( \mathrm{E} \) between the plates?


Out of the following metals, that can be obtained by electrolysis of the aqueous solution of their salts is/are:
This question has multiple correct options
\( A \cdot A g \)
B. Au
c. \( c u \)
D. Mg


The pollutants released by jet aeroplanes inthe atomsphere as fluorocarbons are called:
A. photochemical oxidants
B. photochemical reductants
c. aerosols
D. physical pollutants


Which of the following does not uses formaldehyde in its preparation?
A. Melamine polymer
B. Bakelite
c. РнВу
D. preservation of biological specimens


Sulfide ores are common for the metals:
\( A \cdot A g, \) Cu and \( P b \)
B. Ag, Cu and sn
c. \( A g, \) Mg and Pb
D. Al, Cu and Pb


As atomic radii increases, ionisation
potential:
A. increases
B. decreases
c. remains same
D. none of the above


B and Si resemble each other in their
properties. If true enter 1 , else enter 0


Bleaching powder is insoluble in cold
water.
A . True
B. False


The circuit below shows three identical
resistors labeled \( 1,2, \) and \( 3 . \) The reading on the ammeter is 12.0 A. How much
current flows in each resistors?
A. 4.0 A
в. 12.0 А
c. 36.0 А
D. we cannot determine the current values without knowing the resistor va
E. we cannot determine the current values without knowing the batter


Solve the following sets of simultaneous equations. \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{4} ; \mathbf{2} \boldsymbol{x}-\mathbf{5} \boldsymbol{y}=\mathbf{1} \)


Which of the following is a cyaclic oxoacid?
A. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)
в. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{6} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{P}_{3} \mathrm{O}_{9} \)
D. \( \mathrm{H}_{5} \mathrm{P}_{5} \mathrm{O}_{15} \)


In borax bead test,which colour is given
by \( \boldsymbol{C r}_{2} \boldsymbol{O}_{3} ? \)
A . Red
B. Yellow
c. Green
D. Black


Malpighian body is constituted by
A. Glomerulus only
B. Glomerulus and Bowman's capsule
c. Glomerulus and efferent vessel
D. Glomerulus, Bowmans capsule and efferent vessel


A. square matrix \( \boldsymbol{A} \) of order \( \mathbf{3}, \) has \( |\boldsymbol{A}|= \)
\( 5, \) find \( \mid A \) adjal


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


Assertion
A capacitor blocks the direct current in
the steady state.
Reason
The capacitive reactance of the capacitor is inversely proportional to
frequency \( f \) of the source of emf.
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


Consider an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?
A \( . a b(\pi-1) \)
B. \( 2 a b(\pi-1) \)
c. \( a b(\pi-2) \)
D. None of the above


Which of the following is a Lanthanide element?
A . Ac
B. Al
c. Nd
D. Pd


Which of the following induces flowering in short day plant?
A . Gibberellin
B. Cytokinin
c. Auxin
D. Ethylene


Biomass based energy can be obtained
from:
This question has multiple correct options
A. direct burning of wood, agricultural residue etc.
B. biomass may be converted in to some other form of fuel which can release energy.
C. bacterial decomposition of organic matters like cow dung, agricultural wastes, human excreta etc. in presence of water in absence of air, a mixture of
\( C H_{4}, C O_{2}, H_{2}, H_{2} S \) etc.
D. burning of industrial waste.


Which of the following statements is
not correct?
A. Forests protects the soil from erosion.
B. Plants and animals in a forest are dependent on one another.
C. Forest do not influence the climate and water cycle.
D. Soil helps the forests to grow and regenerate.


A long wire carries a current \( 5 A \). The
energy stored in the magnetic field
inside a volume \( 1 \mathrm{mm}^{3} \) at a distance
10cm from the wire is
A \( \cdot \frac{\pi}{4} \times 10^{-13} J \)
В \( \cdot \frac{\pi}{2} \times 10^{-13} J \)
C . \( \pi \times 10^{-13} \mathrm{J} \)
D. \( \frac{\pi}{8} \times 10^{-13} \mathrm{J} \)


For any two events \( A \) and \( B \) in a sample
space
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A / B) \geq \frac{P(A)+P(B)-1}{P(B)}, P(B) \neq 0, \) is always true
B . \( P(A \cap B)=P(A)-P(\bar{A} \cap \bar{B}) \) does not hold
C \( . P(A \cup B)=1-P(\bar{A}) P(\bar{B}), \) if \( \mathrm{A} \) and \( \mathrm{B} \) are independent
D. \( P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( \mathrm{A} \) and \( \mathrm{B} \) are disjoint


\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} . \) In this reaction \( \boldsymbol{k}_{f} \) is \( \boldsymbol{2} \times \mathbf{1 0}^{-3} \)
and \( k_{b} \) is \( 5 \times 10^{-4} . \) Determine the value
of \( \boldsymbol{K}_{c} \)
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
D. 7


Find all possible value of \( a \), if \( \lim _{x \rightarrow a}\left(\frac{x^{9}-a^{9}}{x-9}\right)^{x}=\lim _{x \rightarrow 3}(6+x) \)
A . 6
B.
c. 9
D. 16


Differentiate between zoological parks
and botanical gardens.


Find the area of the following
trapeziums


Adrenaline and ephedrine contain:
A \( \cdot 1^{\circ} \) amino group
B. \( 2^{\circ} \) amino group
c. \( 3^{\circ} \) amino group
D. quaternary amino group


The salt \( A l(O H)_{3} \) is involved in the following two equilibria.
\( \boldsymbol{A l}(\boldsymbol{O H})_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A l}^{3+}(\boldsymbol{a q})+ \)
\( \mathbf{3} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{K}_{s p} \)
\( A l(O H)_{3}(s)+O H(a q) \rightleftharpoons \)
\( \boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{K}_{c} \)
Which of the following relationship is correct when the solubility is minimum?
\( ^{\mathbf{A}}\left[O H^{-}\right]=\left(\frac{K_{s p}}{K_{C}}\right)^{1 / 3} \)
\( ^{\mathrm{B}}\left[O H^{-}\right]=\left(\frac{K_{C}}{K_{s p}}\right)^{1 / 4} \)
\( ^{\mathrm{c}}\left[O H^{-}\right]=\sqrt{\left(\frac{K_{s p}}{K_{C}}\right)^{1 / 4}} \)
D. None of these


In young's double-slit experiment using mono chromatic light of wavelength \( \mathbf{A} \) the intensity of light at a point on the
screen where path difference is \( \lambda \) is \( K \) units. What is the intensity if light at a point where path difference is \( \lambda / 3 ? \)


Which of the following pairs may give equal numerical values of the temperature of a body?
A. Fahrenheit and celsius
B. Celsius and kelvin
c. Kelvin and Reaumur
D. None of these


The activity of a radioactive element decreases to one-third of the origina
activity \( I_{0} \) in a period of nine years. After a further lapse of nine years, its activity will be
A \( \cdot I_{0} \)
B . \( (2 / 3) I_{0} \)
C \( \cdot\left(I_{0} / 9\right) \)
D・ \( \left(I_{0} / 6\right) \)


Simplify combining like terms. \( 21 b-32+7 b-20 b \)


The specific rate constant of the
decomposition of \( N_{2} O_{5} \) is \( 0.008 m i n^{-1} \)
The volume of \( O_{2} \) collected after 20
minute is \( 16 \mathrm{mL} \). The volume in \( \mathrm{ml} \) that
would be collected at the end of
reaction. \( N O_{2} \) formed is dissolved in
\( \boldsymbol{C C l}_{4} \) is


The rate of uric acid excretion per day
through urine is
A. Nil
B. 0.2 gm to 0.7 gm
c. \( 0.7 \mathrm{gm} \)
D. \( 2 \mathrm{gm} \)


Given \( l=28, S=144 \) and there are
total 9 terms. Find \( a \)


Integrate the function \( \tan ^{-1} \sqrt{\frac{1-x}{1+x}} \)


What is the angle between the straight
\( \operatorname{lines}\left(m^{2}-m n\right) y=\left(m n+n^{2}\right) x+n^{3} \)
and \( \left(\boldsymbol{m} \boldsymbol{n}+\boldsymbol{m}^{2}\right) \boldsymbol{y}=\left(\boldsymbol{m} \boldsymbol{n}-\boldsymbol{n}^{2}\right) \boldsymbol{x}+\boldsymbol{m}^{3} \)
where \( \boldsymbol{m}>\boldsymbol{n} ? \)
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left(\frac{2 m n}{m^{2}+n^{2}}\right) \)
B. \( \tan ^{-1}\left(\frac{4 m^{2} n^{2}}{m^{4}-n^{4}}\right) \)
\( ^{\mathbf{C}} \cdot \tan ^{-1}\left(\frac{4 m^{2} n^{2}}{m^{4}+n^{4}}\right) \)
D. \( 45^{\circ} \)


If \( f(g(a))=0 \) where \( g(x)=\frac{x}{4}+2 \) and
\( \boldsymbol{f}(\boldsymbol{x})=\left|\boldsymbol{x}^{2}-\boldsymbol{3}\right|, \) find the possible value
of \( \boldsymbol{a} \)
This question has multiple correct options
A. \( -8+4 \sqrt{3} \)
(
B . \( -(8+4 \sqrt{3}) \)
\( c \cdot 6 \)
D. 18


\( f\left(\frac{2}{3} 1 \frac{5}{3}\right) \quad\left[\frac{2}{3} \frac{2}{3} \frac{4}{3}\right] \) and \( B=\left[\frac{2}{5} \frac{3}{5} \frac{4}{5} \frac{4}{5}\right], \) then
compute \( 3 A-5 B \)


Assertion
At depth \( h \) below the water surface
pressure is \( P . \) Then at depth \( 2 h \)
pressure will be \( 2 P . \) (Ignore density variation)
Reason
With depth pressure increases linearly.
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


What is wavefront? Explain laws of refraction of light on the bases of
Huygens wave theory.


Two short bar magnets with magnetic moments 400 ab \( A c m^{2} \) and \( 800 a b A \)
\( c m^{2} \) are placed with their axis in the same straight line with similar poles facing each other and with their centres
at \( 20 \mathrm{cm} \) apart from each other. Then
the force of repulsion is:
Disclaimer: No option as 0.08 dyne was
given in the original paper.
A. 12 dyne
B. 6 dyne
c. 0.08 dyne
D. 150 dyne


If \( m=2, \) find the value of \( \frac{5 m}{2}-4 \)


The shape of wave front at a very large distance from source is
A. Circular
B. Spherical
c. cylindrical
D. Plane


An unknown circuit draws a current of
2A from a 12 V battery equivalent resistance is


\( \lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h}, x \neq 0 \)


What is the name of the following reaction?


A gene encoding for polypeptide of 50 amino acids get mutated at 25 codon; UAU becoming UAA. The result would be
A. Polypeptide of 24 amino acid
B. Two polypeptides one with 24 amino acids and second with 25 amino acids
c. A polypeptide with 49 amino acid
D. A polypeptide of 25 amino acids


Evaluate: \( \int_{0}^{1} \frac{1}{\sqrt{1+x}-\sqrt{x}} d x \)


A \( 2.0 \mathrm{cm} \) tall object is placed \( 15 \mathrm{cm} \) in front of a concave mirror of focal length
10 \( c m . \) What is the size and nature of
the image?
\( \mathbf{A} \cdot 4 \mathrm{cm}, \) real
B. \( 4 \mathrm{cm} \), virtual
c. \( 1.0 \mathrm{cm}, \) real
D. None of these


\( \frac{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{3}}{\boldsymbol{x}^{3}}=\frac{\boldsymbol{A}}{\boldsymbol{x}}+\frac{\boldsymbol{B}}{\boldsymbol{x}^{2}}+\frac{\boldsymbol{C}}{\boldsymbol{x}^{3}} \Rightarrow \boldsymbol{A}+ \)
\( \boldsymbol{B}-\boldsymbol{C}= \)
\( A \cdot 6 \)
B. 3
\( c \)
\( D \)


Assertion
For the reaction, \( N a_{2} C O_{3}+H C l \rightarrow \)
\( N a C l+N a H C O_{3}, \) the suitable
indicator is phenolphthalein.
Reason
Phenolphthalein provides its colour in
acidic medium.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is molal elevation constant? Drive
its equation and give its unit.


Lymph is
A. Blood minus R.B.C
B. Blood minus W.B.C
C. Blood minus cells
D. Plasma minus protein


The inner ear also contains a complex
system called ....A... located above the
\( \dots .8 \dots \)
Fill the blank \( A \) and \( B \) with the correct
option.
A. A - Vestibular apparatus, B - Cochlea
B. A - Cochlea, B - Vestibular apperatus
c. A - otolith organ, B - Semicircular canal
D. A - Crista ampullaris, B - Semicircular canal


\( K \) is the radius of gyration of a thin rod
when it is rotating about an axis perpendicular to the length of the rod and is passing through it's centre. The length of that rod is :
A . \( 12 K \)
в. \( 3 K \)
c. \( 2 \sqrt{3} K \)
D. \( \sqrt{3} K \)


Heart wall is made of
A. Myocardium
B. Epicardium
c. Endocardium
D. All of the above


The pH value of gastric juice in human stomach is about 1.8 and in the small
intestine it is about \( 7.8 . \) The \( p K_{a}, \) value
of aspirin is \( 3.5 . \) Aspirin will be :
A. Completely ionised in the small intestine and in the stomach
B. Unionised in the small intestine and in the stomach
c. lonised in the small intestine and almost unionised in the stomach
D. lonised in the stomach and almost unionised in the small intestine


According to Rutherford's \( \alpha \) -scattering
experiment, which of the following
statement is true?
A. The electrons in the gold foil absorbed the alpha particles and changed energy levels.
B. Most of the alpha particles passed through the foil undeflected.
C. A few of the alpha particles knocked the nucleus completely out of the atom.
D. A large percentage of alpha pantries were turned back when striking the foil
E. The gold foil began to emit a bright-line spectrum.


Two identical thin rings, each of radius
10cm carrying charges \( 10 C \) and \( 5 C \) are
coaxially placed at a distance \( 10 \mathrm{cm} \) a part. The work done in moving a charge
\( q \) from the centre of the first ring to that
of the second is
A \( \cdot \frac{q}{8 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) \)
В. \( \frac{q}{8 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right) \)
c. \( \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) \)
D. \( \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right) \)
E \( \cdot \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{3}+1}{\sqrt{2}}\right) \)


Sthavara of Susrata were
A. Animals
B. Fishes
c. Quadrupeds
D. Plants


Find the Modulas and argument of \( \frac{1+i}{1-i} \)


At \( 25^{\circ} C, \Delta H_{f}\left(H_{2} O, I\right)= \)
\( -56700 J / \) mol and energy of
ionization of \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{I})=\mathbf{1 9 0 5 0} \boldsymbol{J} / \)moll
the reversible EMF at \( 25^{\circ} \mathrm{C} \) of the cell is
\( 414 \times 10^{-x}, \) then the value of \( x \) is \( ? \)
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g})(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H}^{+} \| \boldsymbol{O} \boldsymbol{H}^{-} \mid \boldsymbol{O}_{2}(\boldsymbol{g})(\boldsymbol{1} \)
if at \( 26^{\circ} \mathrm{C} \) the emf increase by 0.001158
\( \mathbf{V} \)
Ans in \( \mathrm{V} \)


Which color band in the color coding of a resistor has the multiplier \( 10^{-1} \) ?
A. Silver
B. Gold
c. Yellow
D. orange


If \( A B>A C \) and length of median from
\( C \) is 4 units, then the length of median
from \( B \) can be-


A potentiometer circuit shown in the
figure is set up to measure emf of cell \( \mathrm{E} \)
As the point P moves from X to Y, the
galvanometer G shows deflection
always in one direction, but the
deflection decreases continuously until Y is reached. The balance point between
\( X \) and \( Y \) maybe obtained by
A. Decreasing the resistance \( R \) and decreasing \( v \)
B. Decreasing the resistance R and increasing
C. Increasing the resistance \( R \) and increasing \( v \)
D. Increasing the resistance \( R \) and decreasing


Arrange Li, Na, K, Rb, Cs in order of
increasing electron-affinity:
A. \( C s<R b<K<N a<L i \)
в. \( K<N a<C s<R b<L i \)
c. \( C s<K<R b<L i<N a \)
D. None of these


The V A group clement that doesnt
directly react with chlorine:
A \( . N_{2} \)
B. As
\( c \cdot s b \)
D. Bi


Construct a right-angled \( \angle A B C \) such
that \( \angle B=90^{\circ}, A B=8 \mathrm{cm} \) and \( A C= \)
10 \( c m . \) Find length \( B C \)


Which one is de novo mutation?
A. \( \pi \times \pi \rightarrow \pi \)
B. \( t t \times t t \rightarrow T t \)
\( \mathbf{c} \cdot \mathbf{T} \mathbf{t} \times \mathbf{t t} \rightarrow \mathbf{T} \)
D. \( \mathrm{Tt} \times \mathrm{Tt} \rightarrow \pi \), Tt, t \( \mathrm{t} \)


Which of the following is not an ionic compound?
A. Sodium hydride
B. Carborundum
c. Potassium oxide
D. Calcium carbide


State whether the following statement
is True or False.

If two lines intersect each other,then the
vertically opposite angles are equal.
A. True
B. False


Construct a triangle \( A B C \) in which
\( \boldsymbol{B C}=\mathbf{8 c m}, \angle \boldsymbol{B}=\mathbf{4 5}^{\circ} \boldsymbol{a n d} \boldsymbol{A B}-\boldsymbol{A C}= \)
\( \mathbf{3 . 5 c m} \)


A small ball of volume \( V \) made of
paramagnetic with susceptibility \( \chi \) was slowly displaced along the axis of a current-carrying coil from the point where the magnetic induction equals \( B \)
out to the region where the magnetic field is practically absent. What amount of work was performed during this process?


Assertion
From the relation \( C=\frac{q}{V} . \) We can say
that, if more charge q is given q is given to a conductor, its capacity should
increase.
Reason
Ratio \( \frac{q}{V} \) will remain constant for a given
conductor.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A cube has a side of length \( 1.2 \times \)
\( 10^{-2} m . \) Calculate its volume.
A \( .1 .7 \times 10^{-6} m^{3} \)
В. \( 1.73 \times 10^{-6} m^{3} \)
D. \( 1.732 \times 10^{-6} m^{3} \)


\( \lim _{x \rightarrow \pi / 4} \frac{1-\cot ^{3} x}{2-\cot x-\cot ^{3} x} \) is
A \( \cdot \frac{11}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Irregular reflection obeys laws of reflection
A . True
B. False


Solve:
\( \lim _{x \rightarrow 27} \frac{\left(x^{1 / 3}+3\right)\left(x^{1 / 3}-3\right)}{x-27} \)


A uniform metre rule balances
horizontally on a knife edge placed at the \( 58 c m \) mark when a weight of \( 20 g f \) is suspended from one end. What is the weight of the rule?
A. \( 10500 g f \)
в. \( 105 g f \)
c. \( 1.05 g f \)
D. \( 11.6 g f \)


Which of the following can be used as the halide component for Friedel-Crafts
reaction?
A. chloroethene
B. Isopropyl chloride
c. Chlorobenzene
D. Bromobenzene


What is the maximum number of
emission lines when the excited
electron of a hydrogen atom in \( n=6 \) drops to ground state?
\( A \cdot 6 \)
B. 15
\( c . \) 30
D. 10


If the median of the distribution given
below is \( 28.5, \) find the values of \( x \) and \( y \)
\( \begin{array}{ll}\text { Class interval } & \text { Frequency } \\ 0-10 & 5 \\ 10-20 & x \\ 20-30 & 20 \\ 30-40 & 15 \\ 40-50 & y \\ 50-60 & 5 \\ \text { Total } & 60\end{array} \)


Ionization energy of \( \boldsymbol{H} \boldsymbol{e}^{+} \) is \( \mathbf{1 9 . 6} \times \) \( 10^{-18} \) Jatom\( ^{-1} . \) The energy of the first
stationary state \( (n=1) \) of \( L i^{2+} \) is
A \( .4 .41 \times 10^{-16} \) Jatom \( ^{-1} \)
B. \( -4.41 \times 10^{-17} \) Jatom\( ^{-1} \)
C . \( -2.2 \times 10^{-15} \) Jatom \( ^{-1} \)
D. \( -8.82 \times 10^{-17} \) Jatom\( ^{-1} \)


Which statement explains why the element carbon forms so many
compounds with different shape?
A. Carbon atoms combine readily with oxygen
B. Carbon atoms have very high electronegativity.
c. Carbon readily forms ionic bonds with other carbon atoms.
D. Carbon readily forms covalent bonds with other carbon atoms


The equation of the circle with center (1,2) and tangent \( x+y-5=0 \) is
A \( \cdot x^{2}+y^{2}+2 x-4 y+6=0 \)
B . \( x^{2}+y^{2}-2 x-4 y+3=0 \)
c. \( x^{2}+y^{2}-2 x-4 y-8=0 \)
D. \( x^{2}+y^{2}-2 x-4 y+8=0 \)


Which of the following acts both as endocrine (ductless) and exocrine (with
duct) gland?
A. Pancreas
B. Liver
c. Adrenal
D. Kidney


The equilibrium constant for the given
reaction is 100 .
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O_{2}(g) \)
What is the equilibrium constant for the reaction given below?
\( N O_{2}(g) \rightleftharpoons \frac{1}{2} N_{2}(g)+O_{2}(g) \)
A . 10
B.
c. \( 0 . \)
D. 0.01


toppr
Q Type your question
tound in
(b) Worms causing disease
elephantiasis is
(c) The open circulatory system is found where the coelomic cavity is
filled with blood.
\( (d) \)
are known to have
pseudocoelom.
A. (a) Liver fluke (Fasciola hepatica)
(b) Filarial worm (Wuchereria bancrofti)
(c) Arthropods
(d) Nematodes
B. (a) Liver fluke (Fasciola hepatica)
(b) Arthropods
(c) Nematodes
(d) Filarial worm (Wuchereria bancrofti)
C . (a) Filarial worm(Fasciola hepatica)
(b) Liver fluke (Wuchereria bancrofti)
(c) Arthropods
(d) Nematodes
D. (a) Filarial worm (Wuchereria bancrofti)
(b) Liver fluke (Fasciola hepatica)
(c) Nematodes
(d) Arthropods


Boiling water can be measured by
A. Clinical thermometer
B. Laboratory thermometer
C. Both may be used conveniently
D. Both of them can not be used


In Paramecium undigested food is eliminated from the body through
A. cytoproct
B. Contractile vacuoles
c. General body surface
D. cytostome


Assertion
Pulling a lawn roller is easier than
pushing it.
Reason
pulling decreases the apparent weight
as the vertical component of the pulling
force acts upward.
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.


Prove that
\[
\left|\begin{array}{ccc}
\boldsymbol{x}+\boldsymbol{y}+\mathbf{2} \boldsymbol{z} & \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{y}+\boldsymbol{z}+\mathbf{2} \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{x} & \boldsymbol{z}+\boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}
\end{array}\right|
\]
\( 2(x+y+z)^{3} \)


Acoelomate animals with flame cells
are
A. Platyhelminthes
B. Annelida
c. Ascheminthes
D. Arthropoda