The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \) is 1 at
\( 27^{\circ} \mathrm{C} \) and 4 at \( 47^{\circ} \mathrm{C} . \) Calculate enthalpy
change for: \( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g}) \)
(Given \( \boldsymbol{R}=\mathbf{2} \) cal / mol. \( \boldsymbol{K} \) ).
A \( .-13.31 \mathrm{kcal} / \mathrm{mol} \)
B. \( 13.31 \mathrm{kcal} / \mathrm{mol} \)
c. \( -19.2 \mathrm{kcal} / \mathrm{mol} \)
D. \( 55.63 \mathrm{kcal} / \mathrm{mol} \)


A barometer reads \( 75 \mathrm{cm} \) of Hg. When
\( 2 \mathrm{cc} \) of air at atmpospheric pressure is introduced into the space above the mercury level, the volume of this space becomes 50 cc. The length by which the mercury column descends is
A. \( 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. 25 cm


A bag contains 3 white, 3 black, and 2 red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red.
A \( \cdot \frac{1}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{3} \)
D. None of these


The part of atmosphere which is consists of variable gasses with unknown composition is called
A. Stratosphere
B. Hetrosphere
c. Homosphere
D. None of these


If 10 g of liquid at \( 300 \mathrm{K} \) is heated to 350 K, the liquid absorbs 6 kcals. Determine the specific heat of the liquid in cal/
\( \boldsymbol{g}^{\circ} \boldsymbol{C} \)
A. 6
B. 12
\( c \cdot 60 \)
D. 120
E. 600


An urn A contains 4 white and 6 redd
balls. Three balls are drawn at random the expected number of red balls drawn
is
A. 3.0
B. 1.8
\( c \cdot 1.2 \)
D. 1.6


Calculate the volume occupied by 0.01 moles of helium gas at STP.
A . 2.24
B. 0.224 L
c. \( 22.4 \mathrm{L} \)
D. None of the above


The following data were obtained during the first order thermal decomposition of
\( S O_{2} C l_{2} \) at a constant volume.
\[
\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})
\]
Total pressure/
atm Experiment A Time \( / s^{-1} \)
100
Calculate the rate of the reaction when
total pressure is 0.65 at \( m \)


Assertion
In the Daniel cell, if concentration of
\( C u^{2+} \) and \( Z n^{2+} \) ions are doubled, the
emf of the cell will not change.
Reason
f the concentration of ions in contact
with the metals is doubled, the
electrode potential is doubled.
A. assertion is true, reason is true; reason is correct explanation for assertion.
B. assertion is true, reason is true; reason is NOT a correct explanation for assertion
c. assertion is true, reason is false
D. assertion is false, reason is true


Fuming nitric acid is
A. nitric acid dissolved in nitrogen dioxide
B. nitric acid dissolved in nitrous oxide
C. nitric acid dissolved in nitrogen oxide
D. nitric acid dissolved in sulphur dioxide


For what value of \( \boldsymbol{x} \) will \( l_{1} \) and \( l_{2} \) be
parallel lines
\( \mathbf{A} \cdot 32^{\circ} \)
B \( \cdot 12^{\circ} \)
\( c \cdot 42^{\circ} \)
D. None of these


IUPAC name of the given compound is:
A. 3-bromo-2-methylpentanal
B. 2-bromo-3-methylpentanone
c. 2 -bromo- -s-methylhexanone
D. 3-bromo-2-methylhexanone


\( 46.2 \times 10^{-2}= \)
A . 0.0462
B. 0.462
c. 4.62
D. 462


Drum A undergoes
A. rotational motion
B. translational motion
c. rotational as well as translational motion
D. None of these


A bullet travelling at \( 100 \mathrm{ms}^{-1} \) suddenly hits a concrete wall. If its K.E. is
converted completely into heat, the
raise in temperature is
\( \left(s=100 J k g^{-1} K^{-1}\right) \)
A. 20k
в. 40k
\( c . \) 50k
D. 60k


f \( \boldsymbol{y}=\log [\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}], \) show that
\( \left(x^{2}+a^{2}\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=0 \)


Find the compound interest at the rate
of \( 14 \% \) per annum for 1 year on the sum of \( R s 12,000 \) compounded half-yearly.


Which of the following is the application of cryogenic techniques?
A. Many infra-red cameras require their detectors to be cryogenically cooled.
B. Certain rare blood groups are stored at low temperatures, such as 165 C
c. Experimental research on certain physics phenomena such as spintronics and magnetotransport properties
D. All of the above


Match the triplet codons mentioned in
list I with their amino acids mentioned
in listcolumn II and select the correct
option from the given codes.


Which of the following are Bronsted acids as well as Bronsted bases?
\( N H_{3}, H S O_{4}^{-}, H_{2} S O_{4}, H C O_{3}^{-}, H_{3} O \)


A non-biodegradable toxic chemical has entered into the food chain. Which type
of food habit will you suggest to a man, vegetarian or non-vegetarian? Explain with the help of a food chain. The food
chain which you would suggest, is
advantageous in an another aspect. How?


The wave theory of Light was proposed by
A. Newton
B. Huygens
c. Frenel
D. Yung


\( \int \frac{10 x^{9}+10^{x} \log _{e} 10 d x}{x^{10}+10^{x}} \) equals
A \( \cdot 10^{x}-x^{10}+C \)
B. \( 10^{x}+x^{10}+C \)
c. \( \left(10^{x}-x^{10}\right)^{-1}+C \)
D. \( \log \left(10^{x}+x^{10}\right)+C \)


If the galvanometer \( \mathrm{G}_{0}, \) reads zero, the
value of \( \mathrm{R} \) is
\( A \cdot 25 \Omega \)
B. 75\Omega
c. \( 100 \Omega \)
D. \( 125 \Omega \)


The compound which does not react
with \( K M n O_{4} \) is :
A. perdisulphuric acid
B. sulphurous acid.
c. hydrogen sulphide.
D. hydrogen peroxide.


The number of solutions of \( \sin 3 x= \)
\( \cos 2 x, \) in the interval \( \left(\frac{\pi}{2}, \pi\right) \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
D.


The arithmetic mean between \( 2+\sqrt{(2)} \) and \( 2-\sqrt{(2)} \) is
A .2
B. \( \sqrt{(2)} \)
c. 0
D.


The radii of two planets are respectively
\( R_{1} \) and \( R_{2} \) and their densities are
respectively \( \rho_{1} \) and \( \rho_{2} . \) The ratio of the
accelerations due to gravity at their
surfaces is
A \( \cdot g_{1}: g_{2}=\frac{\rho_{1}}{R_{1}^{2}}: \frac{\rho_{2}}{R_{2}^{2}} \)
\( \mathbf{B} \cdot g_{1}: g_{2}=R_{1} R_{2}: \rho_{1} \rho_{2} \)
\( \mathbf{c} \cdot g_{1}: g_{2}=R_{1} \rho_{1}: R_{2} \rho_{1} \)
\( \mathbf{D} \cdot g_{1}: g_{2}=R_{1} \rho_{1}: R_{2} \rho_{2} \)


AC generator is also h/a
A. convertor
B. invertor
c. alternator
D. none


The curvature of the eye lens can be
modified by
A. ciliary muscles
B. iriss
c. pupil
D. cornea


If elements of quantum number greater
than ' \( n^{\prime} \) were not allowed, the number of possible elements in nature would have
been
A \( \cdot \frac{1}{2} n(n+1) \)
\( ^{\mathbf{B}}\left\{\frac{n(n+1)}{2}\right\}^{2} \)
c. \( \frac{1}{6} n(n+1)(2 n+1) \)
D. \( \frac{1}{3} n(n+1)(2 n+1) \)


What is true about the given
carbohydrate?
A. It anomerizes in solution phase
B. It is a reducing sugar
C. It shows the phenomenon of inversion of sugar in acidic medium
D. It shows mutarotation


When an electron falls from \( 2^{n d} \) energy
level to ground state then which of the following will produce shortest
wavelength?
A \( \cdot B e^{3+} \) ion
B. \( D \) -atom
c. \( H- \) atom
D. \( H e^{+} \) ion


1 gram graphite on combustion in oxygen liberates \( 7.82 \mathrm{kcal} \) of heat. The amount of
heat evolved when 1 mole of oxygen is used in this oxidation process is:
\( \mathbf{A} \cdot 7.82 k c a l \)
B. 78.2 kcal
c. 9.384 kcal
D. \( 93.84 \mathrm{kcal} \)


Which of the following are not true
about hexagonal close packing?
A. It has a coordination number of 6
B. It has \( 26 \% \) empty space
C . It is \( A B C A B C \ldots \ldots \) type of arrangement
D. It is as closely packed as body centred cubic packing


Increasing order ofatomic/ionic size:
\( \boldsymbol{I}^{+}<\boldsymbol{I}<\boldsymbol{I}^{-} \)
If true enter 1 , else enter 0 .
\( A \cdot 1 \)


What is the natural source of \( N a_{2} C O_{3} ? \)
A. Nitre
B. Chile salt peter
c. Dolomite
D. Trona


State whether the given statement is
True or False.
The front portion of the eye is filled with vitreous humour.


Sets of travelling waves are given as shown in above figure Identify which set of waves has already been through interference?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E.


An element has number of electrons \( =2 \)
Then what will be its atomic number?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 3 \)
\( D \)


Production of alcohol by yeast
fermentation is
A. Anaerobic
B. Aerobic
c. Light dependent
D. Both A and C


The elastic relaxation time is minimum
for
A. glass
B. quartz
c. rubber
D. clay


Which of the following elements is
needed as a component in cell membranes, nucleic acids and energy
transfer?
A. Sulphur
B. Phosphorus
c. Calcium
D. Potassium


Assertion
Oxygen is more electronegative than
sulphur, yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic, while \( \boldsymbol{H}_{2} \boldsymbol{O} \)
is neutral.
Reason
H-S bond is weaker than O-H bond.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The sum and difference of two
perpendicular vectors of equal length
are
A. Perpendicular to each other and of equal length
B. Perpendicular to each other and of different lengths
c. of equal length and have an obtuse angle between them
D. of equal length and have an acute angle between them


A series resonant circuit contains \( \boldsymbol{L}= \) \( \frac{5}{\pi} m H, C=\frac{200}{\pi} \mu F \) and \( R=100 \mu \). If a
source of emf \( e=200 \sin 1000 \pi t \) is
applied, then the rms current is:
A \( .2 A \)
в. \( 200 \sqrt{2} A \)
D. \( 1.41 A \)


The rate constant for a zero order
reaction is \( 2 \times 10^{-2} \) mol \( L^{-1} s e c^{-1}, \) if
the concentration of the ractant after
\( 25 \sec \) is \( 0.25 M, \) calculate the initial concentration
A \( .0 .75 M \)
B. \( 1.5 M \)
c. 0.375
D. None of these


A force of 5 N acts on a body of weight \( 9.8 \mathrm{N} . \) What is the acceleration
produced in \( \boldsymbol{m} / \boldsymbol{s e c}^{2} \)
A. \( 49.00 \mathrm{m} / \mathrm{s}^{\wedge 2} \)
B. \( 5.00 \mathrm{m} / \mathrm{s}^{2} 2 \)
c. \( 1.46 \mathrm{m} / \mathrm{s}^{2} \) ?
D. \( 0.5 \mathrm{m} / \mathrm{s}^{\wedge} 2 \)


The animal that mostly depends on Metabolic water' to survive for long periods without drinking water
A. Didelphis
B. Ornythorhynehus
c. Macropus
D. Dipodomys


The lightest gas is :
A. nitrogen
B. helium
c. oxygen
D. hydrogen


A water wave in a shallow tank passes
through a gap in a barrier. What
happens to the speed and what happens
to the wavelength of the wave as it
passes through the gap?
A. speed - decreases ; wavelength - decreases
B. speed - decreases ; wavelength - remains constant
C. speed - remains constant; wavelength - decreases
D. speed - remains constant; wavelength - remains constant


Tunica corpus theory was given by
A. Schmidt
B. Hanstein
c. Nageli
D. Schuessler


State whether the given statement is
True or False :

Conductors when charged transfer all
charges to the entire surface of the
conductor.
A. True
B. False


A rectangle plot of land measures \( 45 \mathrm{m} \) \( \times 30 \mathrm{m} . \) A boundary wall of height \( 2.4 \mathrm{m} \) is built all round the plot at a distance
of \( 1 \mathrm{m} \) from the plot. Find the area of the inner surface of the boundary wall.
A \( \cdot 226.2 m^{2} \)
В. \( 457.2 m^{2} \)
D. \( 291.2 m^{2} \)


The escape velocity on the earth is \( 11.2 k m / s . \) A planet has twice the radius of earth and same mean density as earth Then the escape velocity on planet in \( k m / s \) will be :
A . 5.6
B. 11.2
c. 22.4
D. 16.5


Trace the succession of plants on. a dry
bare rock.


In succulents, respiratory quotient is less than one due to
A. Incomplete oxidation
B. Incomplete reduction
c. complete reduction
D. Complete oxidation


\( \boldsymbol{C C l}_{3} \boldsymbol{C H O}+\boldsymbol{N O} \longrightarrow \boldsymbol{C H C l}_{3}+ \)
\( N O+C O \)
The rate of the reaction above is equal
to rate \( =\boldsymbol{k}\left[\boldsymbol{C C l}_{3} \boldsymbol{C H O}\right][\boldsymbol{N O}] \)
If the concentration is expressed in mol \( \mathrm{L}^{-1}, \) find the unit of \( k ? \)
A \( \cdot \mathrm{Lmol}^{-1} \mathrm{s}^{-1} \)
B. molL \( ^{-1} \mathrm{s}^{-1} \)
c. \( L^{2} \) mol \( ^{-2} s^{-1} \)
D. s \( ^{-1} \)


Silicon is the main constituent of
A. alloys
B. rocks
c. animals
D. vegetables


To what temperature should water be
heated so that its vapor pressure
equals the vapor pressure chloroform at
\( 40^{\circ} \mathrm{C} ? \)
\( \mathbf{A} \cdot 40^{\circ} C \)
\( \mathbf{B} \cdot 50^{\circ} C \)
\( \mathbf{c} \cdot 60^{\circ} C \)
D. \( 70^{\circ} \mathrm{C} \)
\( E \cdot 80^{\circ} C \)


A proton (mass \( m \) ) accelerated by a
potential difference \( V \) files through a
uniform transverse magnetic filed \( \boldsymbol{B} \)
The field occupies a region of space by
width ' \( d^{\prime} . \) If \( ^{\prime} \alpha^{\prime} \) be the angle of deviation
of proton from initial direction of motion
(see figure), the value of \( \sin \alpha \) will be
A \( \cdot \frac{B}{2} \sqrt{\frac{e d}{m V}} \)
B. \( e V \sqrt{\frac{B d}{2 m}} \)
\( ^{c} \cdot \frac{B}{2} \sqrt{\frac{e}{2 m V}} \)
D \( \cdot B d \sqrt{\frac{e}{2 m V}} \)


If the velocity of light \( C, \) the universal
gravitational constant \( G, \) and Planck's
constant \( h \) are chosen as fundamental
units, the dimension of mass in this
system are
A \( \cdot h^{1 / 2} C^{1 / 2} G^{-1 / 2} \)
\( \mathbf{B} \cdot h^{-1} C^{-1} G \)
\( c \cdot h C G^{-1} \)
D. \( h C G \)


Identify the wrong statement
A. In male grasshoppers, \( 50 \% \) of the sperms have no sex chromosome.
B. Usually female birds produce two types of gametes based on sex chromosomes.
c. The human males have one of their sex chromosomes much shorter than the other.
D. The male fruit fly is heterogametic.
E. In domesticated fowls, the sex of the progeny depends on the type of sperm that fertilizes the egg.


The area bounded by the tangent and
normal to the curve \( y(6-x)=x^{2} \) at
(3,3) and the \( x \) -axis is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
c. 15
D. 3


The mean life time of a radionuclide, if
its activity decreases by \( 4 \% \) for every \( 1 h \) would be (product is non-radioactive,
i.e., stable)
A . \( 25 h \)
в. \( 1.042 h \)
\( c \cdot 2 h \)
D. \( 30 h \)


Let \( x_{1}, x_{2}, x_{3}, x_{4} \) be four non zero
numbers satisfying the equation \( \tan ^{-1} \frac{a}{x}+\tan ^{-1} \frac{b}{x}+\tan ^{-1} \frac{c}{x}+ \)
\( \tan ^{-1} \frac{d}{x}=\frac{\pi}{2} \)
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \sum_{i=1}^{4} x_{i}=a+b+c=d \)
\( ^{\mathrm{B}} \cdot \sum_{i=1}^{4} \frac{1}{x_{1}}=0 \)
\( \mathbf{c} \cdot \Pi_{i=1}^{4} x_{i}=a b c d \)
D. \( \left(x_{1}+x_{2}+x_{3}\right)\left(x_{2}+x_{3}+x_{4}\right)\left(x_{3}+x_{4}+x_{1}\right)\left(x_{4}+x_{1}+\right. \)
\( \left.x_{2}\right)=a b c d \)


The function \( f(x)=x^{2} \) is decreasing in
\( A \cdot(-\infty, \infty) \)
в. \( (-\infty, 0) \)
\( c \cdot(0, \infty) \)
D. \( (-2, \infty) \)


A coil and a magnet moves with their constant speeds \( 5 m / \)sec and \( 3 m / \)sec
respectively, towards each other, then induced emf in coil is \( 16 m V . \) If both
moves in the same direction, then
induced emf in the coil:
\( \mathbf{A} \cdot 15 m V \)
в. \( 4 m V \)
c. \( 64 m V \)
D. zero


millimeter is
\( \mathbf{A} \cdot 10^{-15} \)
B \( \cdot 10^{-14} \)
c. \( 10^{-13} \)
D. \( 10^{-16} \)


When \( 10 \mathrm{ml} \) of \( H_{2} \) and \( 12.5 \mathrm{ml} \) of \( C l_{2} \) are
allowed to react,the final mixture
contains under the same conditions.
A. 22.5 ml of \( H C l \)
B. 12.5 ml of \( H C l \)
c. \( 20 \mathrm{ml} \) of \( \mathrm{HCl} \)
D. 2.5 \( \mathrm{ml} \) of \( \mathrm{Cl}_{2} \) and \( 20 \mathrm{ml} \) HCl


When a steady current \( I \) flows through
a resistor of resistance \( \boldsymbol{R} \) under
a constant potential difference \( V \) for
time \( t, \) the electrical work done
by charge carrier is \( W= \)
A . \( V I t \)
в. \( I^{2} R t \)
\( c \cdot \frac{V^{2} t}{R} \)
D. Any of these


The number of chambers in the heart of
a frog is
A. one
B. Two
c. Three
D. Four


Insulin is made of
A. \( \alpha \) chain of 21 amino acids and second \( \beta \) chain of 30
amino acids
B. \( \alpha \) chain of 31 amino acids and second \( \beta \) chain of 20
amino acids
C. Disulphide linkages
D. Both A and C


Which of the following oxides is anhydride of nitrous acid?
A. \( N_{2} O_{3} \)
a
в. \( N O_{2} \)
c. \( N O \)
D. \( N_{2} O_{4} \)


According to classical theory, the proposed path of an electron in Rutherford atomic model was
A. circular
B. straight line
c. parabolic
D. spiral


In a closed container rates of
evaporation and condensation are
same. What this statement indicate?
A. A general rule for predicting solubility
B. Conversion of solid phase to the liquid phase
C. It represents relationship between absolute temperature and the kinetic energy of particles
D. It represents relationship between volume and temperature at constant pressure
E. A state in which the liquid and gas phases are in equilibrium


What is hysteresis? Define the terms 'coercivity' and 'retentivity' of a ferromagnetic material.


In silkworm, if juvenile hormone is absent at the time of larval moulting, the worm will
A . Die
B. Moult into larval stage
c. Moult into pupa
D. Moult into adult


A dorsiventral leaf has
A. Palisade tissue on both sides
B. Spongy tissue on both sides
C. Palisade tissue on upper side and spongy tissue on lower side
D. Spongy tissue on upper side and palisade tissue on lower side


Assertion
Fluorine has only-1 oxidation state in
compounds.
Reason
Fluorine has maximum
electronegativity and electron-affinity.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The equilibrium constant for the
reaction, \( \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
\( \operatorname{at} 715 K \) is \( 6.0 \times 10^{-2} M^{-2} . \) If in a
particular reaction, there are 0.25 mol \( L^{-1} \) of \( H_{2} \) and 0.06 mol \( L^{-1} \)
of \( N H_{3} \) present, calculate the
concentration of \( N_{2} \) at equilibrium.


Q Type your question
\( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2}(g) \Delta H= \)
\( -99 k j / \) mole \( , \Delta s=+69 J K^{-1} \) mole \( ^{-1} \)
Addition of solution of KI causes \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
to decompose very rapidly as well
Step -1 (slow) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{l} \rightarrow \boldsymbol{l} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Step -2 (fast)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{l} \boldsymbol{O} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{r}+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
Overall reaction:
\( 2 H_{2} O_{2} \rightarrow H_{2} O+O_{2}(g) \)
The above experiment causes a big fluff of foam to spiral out of the beaker Elephant toothpaste reaction) Identify the wrong statement.
rhis question has multiple correct options
A \( \cdot H_{2} O_{2} \) is thermodynamically and kinetically unstable
B. LO (aq) is the reaction intemediate
c. the elephant tooth paste is hot to toch
D. a glowing splint if plunged into the elephant toothpaste will catch fire


Find the \( 20^{t h} \) and \( n^{t h} \) terms of the G.P.
\( \frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \dots \)


\( \vec{A} \) and \( \vec{B} \) are two vectors in a plane at an
angle of \( 60^{0} \) with each other. \( \vec{C} \) is
another vector perpendicular to the plane containing vectors \( \overrightarrow{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{B}} \) Which of the following relations is possible?
A \( \cdot \vec{A}+\vec{B}=\vec{C} \)
в. \( \vec{A}+\vec{C}=\vec{B} \)
c. \( \vec{A} \times \vec{B}=\vec{C} \)
D. \( \vec{A} \times \vec{C}=\vec{B} \)


\( \frac{E}{L} \)


If prothallus cell directly forms a fern plant it will be
A. Apospory
B. Apogamy
C. Parthenocarpy
D. Parthenogeneis


Consider the function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}x\{x\}+1,0 \leq x<1 \\ 2-\{x\}, 1 \leq x \leq 2\end{array} \text { where }\{x\}\right. \)
denotes the fractional part of \( x \). Find
incorrect statements.
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exist
в. \( f(0) \neq f(B) \)
c. \( f(x) \) is continuous in [0,2]


A ball is drawn at random from a box
containing 10 red, 30 white, 20 blue and
15 orange marbles. The probability of a ball drawn is red, white or blue \( \ldots \)
A \( \cdot \frac{1}{3} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{5} \)


\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{2}-\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b}^{2}-\boldsymbol{c} \boldsymbol{a} & \boldsymbol{c}^{2}-\boldsymbol{a} \boldsymbol{b}\end{array}\right|= \)
\( A . \)
\( B \)
\( c . a b c \)
D. \( (a-b),(b-c),(c-a) \)


The KE of the electron in an orbit of
radius 'r' in hydrogen atom is proportional to (e=electronic charge)
\( ^{A} \cdot \frac{e^{2}}{r^{2}} \)
B. \( \frac{e^{2}}{2 r^{3}} \)
c. \( \frac{e^{2}}{r} \)
D. \( \frac{e^{2}}{2 r^{2}} \)


Powder is used in carrom board for:
A. Increasing friction
B. Decreasing friction
c. Decoration
D. None of the above


A diver looking up through the water sees the outside world contained in a
circular horizon. The refractive index of water is \( \frac{4}{3}, \) and the diver's eyes are 15 cm below the surface of water. Then the
radius of the circle is :
A. \( 15 \times 3 \times \sqrt{5} \) ст
В. \( 15 \times 3 \sqrt{7} \) ст
c. \( \frac{15 \times \sqrt{7}}{3} \mathrm{cm} \)
D. \( \frac{15 \times 3}{\sqrt{7}} \mathrm{cm} \)


Choose the answer below that
accurately describes the correct molecular shape for the molecule
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4} \)
A. Tetrahedrral
B. Trigonal pyramidal
c. Trigonal bipyramidal
D. Square pyramidal
E. Flat


You would recollect from previous unit that the mesophyll cells in the leaves, have a large number of chloroplasts. Usually the chloroplasts align themselves along the walls of the mesophyll cells, such that they get the optimum quantity of the incident light. When do you think the chloroplasts will
be aligned with their flat surfaces parallel to the walls? when would they be perpendicular to the incident light?


Assertion
When a wire is stretched to two times
its length keeping the diameter same, its resistance becomes 4 times
Reason
Resistance is directly proportional to length of wire
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


Statement- \( \mathrm{I}:\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C} \boldsymbol{C O C}\left(\boldsymbol{C H}_{3}\right)_{3} \)
and acetone can be distinguished by
the reaction with \( N a H S O_{3} \)

Statement- \( \|: S O_{3}^{-2} \) is the nucleophile in bisulphate addition.
A. Both the statements are true and statement-ll is the correct explanation of statement-
B. Both statements are true but statement-ll is not the correct explanation of statement-
c. statement-l is true but statement-ll is false
D. Statement-I is false but statement-II is true


Echo is a type of
A. Reflected sound
B. Refracted sound
C. Neither reflected sound nor refracted sound
D. None of these


The compressibility of water is \( 4 \times 10^{-5} \)
per unit atmosphere pressure. The
decrease in volume of \( 100 \mathrm{cm}^{3} \) water
under a pressure of 100atm will be
A \( \cdot 0.4 \mathrm{cm}^{3} \)
B. \( 4 \times 10^{-5} \mathrm{cm}^{3} \)
c. \( 0.025 \mathrm{cm}^{3} \)
D. \( 0.04 \mathrm{cm}^{3} \)


If the length of side of an equilateral triangle inscribed in a circle of radius 4
\( \operatorname{cmis} 4 \sqrt{m} \cdot \) Find \( m \)


What is the energy associated with \( 3^{r d} \)
energy shell of hydrogen atom?
В. \( -0.342 \times 10^{-19} \mathrm{J} \)
c. \( -0.126 \times 10^{-19} \mathrm{J} \)
D. \( -2.41 \times 10^{-19} \mathrm{J} \)


The ratio of the molar amounts of \( \boldsymbol{H}_{2} \boldsymbol{S} \)
needed to precipitate the metal ions
from \( 20 \mathrm{ml} \) each of \( 1 \mathrm{M} C d\left(N O_{3}\right)_{2} \) and
\( \mathbf{0 . 5} \boldsymbol{M} \boldsymbol{C u} \boldsymbol{S O}_{4} \) is:
A . 1:
B. 2:1
\( c \cdot 1: 2 \)
D. indefinite


A \( 220 \mathrm{V} \) main supply is connected to a resistance of \( 100 \mathrm{k} \Omega \). The effective
current is?
A. \( 2.2 \mathrm{mA} \)
B. \( 2.2 \sqrt{2} \mathrm{mA} \)
c. \( \frac{2.2}{\sqrt{2}} \mathrm{m} \)
D. None of these


Distinguish between ethane [saturated]
\& ethene [unsaturated] by drawing their structural formulae.


Let \( x \in N \) Let \( x \) be a perfect square. Let
\( f(x)= \) the quotient when \( x \) is divided
by 5 and \( g(x) \) the remainder when \( x \) is divided by 5. Then \( \sqrt{\boldsymbol{x}}=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{x}) \)
holds for \( x \) equal to
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{0} \)
B . 16
c. 25
D. none of these


Which one of the following is a coelenterate?
A. Sea fan
B. Sea dollar
c. Sea cucumber
D. Sea horse


All particles are situated at a distance
\( R \) from the origin. The distance of centre
of mass of the body from the origin will
be
A. More than \( R \)
B. Less than \( R \)
c. Equal to \( R \)
D. At the origin


An animal phylum is defined on the basis of
A. The uniqueness of its DNA content
B. The uniqueness of its body plan
c. Type of body plan symmetry
D. Fundamental habitat (aquatic terrestrial, etc.


HCOOH reacts with conc. \( H_{2} S O_{4} \) to
produce
A. \( c o \)
в. \( C O_{2} \)
c. No
D. \( N O_{2} \)


If \( p \) is a prime number, then \( n^{p}-n \) is
divisible by \( p \) for all \( n, \) where
A \( . n \in N \)
B. \( n \) is odd natural number
c. \( n \) is even natural number
D. \( n \) is not a composite number


Which table correctly matches the numbered equations below with the correct nuclear process?
1) \( \frac{1}{1} \boldsymbol{H}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+\boldsymbol{\gamma} \)
2) \( 241 A m \rightarrow_{93}^{237} N p+_{2}^{4} H e \)
\( 95^{1} A m^{2} e^{23} \)
3) \( _{92}^{235} \boldsymbol{U}+_{0}^{1} \boldsymbol{n} \rightarrow_{56}^{139} \boldsymbol{B} \boldsymbol{a}+_{36}^{94} \boldsymbol{K} \boldsymbol{r}+\boldsymbol{3}_{0}^{1} \boldsymbol{n} \)
4) \( \begin{array}{l}138 \\ 53\end{array} \boldsymbol{I} \rightarrow_{54}^{138} \boldsymbol{X} \boldsymbol{e}+_{-1}^{0} \boldsymbol{e}+\overline{\boldsymbol{v}} \)
A. 1 alpha decay 2 nuclear fission 3 beta decay 4 nuclear fusion
B. 1 nuclear fission 2 alpha decay 3 nuclear fusion 4 beta decay
c. 1 nuclear fusion 2 alpha decay 3 nuclear fission
4 beta decay
D. 1 Nuclear fusion 2 beta decay 3nuclear fission 4 alpha decay
E. 1 beta decay 2alpha decay ear fusion
ear fission


If incident ray CA and reflected ray BD
are parallel to each other. Find the angle
of inclination between the mirrors.
A \( \cdot i_{1}+i_{2}=\theta \)
B. \( i_{1}+i_{2}=\frac{1}{2} \theta \)
\( \mathbf{c} \cdot i_{1}+i_{2}=2 \theta \)
\( D \cdot \) none


\( N a^{+} \) is coloured.
If the given statement is correct enter 1
else enter 0


Two resistors equal resisitances are joined in series and a current is passed through the combination. Neglect any
variation in resistance as the
temperature changes. In a given time interval
This question has multiple correct options
A. equal amounts of thermal energy must be produced in the resistors
B. unequal amount of thermal energy may be produced
c. the temperature must rise equally in the resistors
D. the temperature may rise equally in the resistors


A quadrilateral in which both pairs of opposite sides are parallel is a
A . square
B. rhombus
c. rectangle
D. parallelogram


For a metallic wire, the ratio \( \frac{V}{i} \) (where,
\( \mathbf{V}= \) applied potential difference and \( \mathbf{i}= \)
current flowing
A. is independent of temperature
B. increases as the temperature rises
C. decreases as the temperature rises
D. increases or decreases as temperature rises depending upon the metal.


A simple pendulum is suspended from
the ceiling of a car accelerating
uniformly on a horizontal road. If the
acceleration is \( a_{0} \) and the length of the
pendulum is \( l \), find the time period of
small oscillations about the mean
position
\( \mathbf{A} \)
B.
\( ^{\mathrm{C}} 2 \pi \frac{\sqrt{l}}{\left(a_{0}^{2}+g^{2}\right)^{1 / 4}} \)
D. \( \pi \frac{\sqrt{l}}{\left(a_{0}^{2}+g^{2}\right)^{1 / 4}} \)


Sprinkling of powder on the carrom
board


Ligulate corolla is found in
A. Sunflower
B. Delphinium
\( c . \) Pea
D. cucurbita


If bromine atom is available in the form
of say, two isotopes 79
35 \( \mathrm{Br}(49.7 \%) \) and
\( 81 B r(50.3 \%) . \) Calculate the average
35
atomic mass of bromine atom.


Glycogen is a branched chain polymer
of \( \alpha-D- \) glucose units in which chain
is formed by C-1 - C-4 glycosidic linkage whereas branching occurs by the formation of C-1 - C-6 glycosidic linkage. Structure of glycogen is similar to
A. amylose
B. amylopectin
c. cellulose
D. glucose


Breaking of big Organic molecules in the presence of enzymes is called:
A. cracking
B. pyrolysis
c. fermentation
D. oxidation


In the fourth quadrant, and
trigonometric ratios are positive
A . \( \cos \), sec
B. sin, cos
\( c \cdot \sin , \operatorname{cosec} \)
D. tan, cot


Non-cyclic photophosphorylation results in production of
A. ADP
B. ATP
c. NADPH
D. ATP and NADPH


The shaded part of the figure is
\( \mathbf{A} \cdot A \cap B \)
В. \( A \cup B \)
\( c \cdot A+B \)
\( \mathbf{D} \cdot \cup-A \)


A saturated solution of \( A g_{2} S O_{4} \) is
\( \mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{M} . \) The value of its solubility
product is
\( \mathbf{A} \cdot 6.25 \times 10^{-6} \)
В. \( 6.25 \times 10^{-4} \)
c. \( 15.625 \times 10^{-6} \)
D. 3.125 \( \times 10^{-6} \)


Which of the following pairs of compounds will not form H-bonds with
each other?
A. Ethanol-methanol
B. Ethanol-water
c. chloroform-acetone
D. carbon tetrachloride-acetone


The compounds given below are:
and
A. enantiomers
B. ifrntical
C. regiomers
D. diastereomers


Which pair of ions is colourless.
A \( \cdot M n^{+3}, C O^{+3} \)
B. \( F e^{3+}, C r^{+3} \)
c. \( Z n^{2+}, S c^{3+} \)
D. \( T i^{2+}, C u^{2+} \)


Which of the following is not a characteristic of humus?
A. It is rich in organic matter such as lignin and cellulose
B. It is colloidal in nature and serves as a reservoir of
nutrients
C. It is highly resistant to microbial action and undergoes slow decomposition
D. It is further degraded by the process of humification


If the intensities of two interfering
waves be \( I_{1} \) and \( I_{2} \), the contrast between maximum and minimum
intensity is maximum, when
A \( \cdot I_{1}>>I_{2} \)
В . \( I_{1}<<I_{2} \)
c. \( I_{1}=I_{2} \)
D. either \( I_{1} \) or \( I_{2} \) is zero


Which is best for plant growth?
A. Loamy soil
B. silt
c. sandy soil
D. Clay soil


The angle made by the line joining the points (2,0) and \( (-4,2 \sqrt{3}) \) with \( x \) axis is -
A \( .120^{\circ} \)
В . \( 60^{\circ} \)
\( \mathbf{c} \cdot 150^{\circ} \)
D. \( 135^{\circ} \)


A particle executing SHM of amplitude \( 4 c m \) and \( T=4 s . \) The time taken by it to
move from positive extreme position to half the amplitude is
A . \( 1 s \)
B. \( \frac{1}{3} s \)
c. \( \frac{2}{3} \)
D. \( \sqrt{\frac{3}{2}} s \)


What is the inductance of the inductor?
A \( .9 .31 \mu H \)
в. о.931цн.931ин
D. \( 93.1 \mu H \)


The supplement angle of the
complement of \( 30^{\circ} \) is
A \( .150^{\circ} \)
B . \( 120^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 210^{\circ} \)


A \( 20 k g \) load is suspended by a wire of
\( \operatorname{cross} \operatorname{section} 0.4 m m^{2} . \) The stress
produced in \( \mathrm{N} / \mathrm{m}^{2} \) is :
\( A \cdot 4.9 \times 10^{-6} \)
B. \( 4.9 \times 10^{8} \)
\( c \cdot 49 \times 10^{8} \)
D. 2.45 \times 10 \( ^{-6} \)


If \( f(x) \) is continuous and \( f\left(\frac{9}{2}\right)=\frac{2}{9} \) \( \operatorname{then} \lim _{x \rightarrow 0} f\left(\frac{1-\cos 3 x}{x^{2}}\right) \) is equal to


Explain froth flotation process of copper pyrites.


State the difference between the first
trophic levels of detritus food chain and grazing food chain


Which property among the following is same for both hydrogen and deuterium molecules?
A. Bond energy
B. Melting point
c. Boiling point
D. Bond length


Force is
A . a push
B. a pull
c. both \( A \) and \( B \)
D. none of these


In the third excited state the number of
unpaired electrons in chlorine atom is:
A. 5
B. 7
\( c \cdot 3 \)
\( D \)


Among the following, the correct
statement is:
\( \mathbf{A} \cdot \) Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is better electron donor
because the lone pair of electrons occupies spherical s orbital and is less directional
B. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is better electron donor
because the lone pair of electrons occupies \( s p^{3} \) orbital and is more directional
C. Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is a better electron donor
because the lone pair of electrons occupies \( s p^{3} \) orbital and is more directional
D. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is better electron donor because the lone pair of electrons occupies spherical s orbital and is less directional


\( 60 \% \) of the first-order reaction was
completed in 60 min. The time taken for
reactants to decompose to half of their original amount will be:
\( \mathbf{A} \cdot \approx 30 \min \)
в. \( \approx 60 \) min
\( \mathbf{c} . \approx 90 \min \)
\( \mathbf{D} \cdot \approx 45 \min \)


Round off 2.0082 to four significant figures.
A . 2.008
B. 2.0082
c. 2.009
\( D \)


A common form of polyester is :
A . Nylon
B. Rayon
c. PET
D. Acrylic


An acidic solution of \( C u^{2+} \) salts
containing \( 0.4 \mathrm{g} \) of \( C u^{2+} \) is electrolyzed until all the copper is deposited. The electrolysis is continued for seven more
minutes with the volume of solution
kept at \( 100 \mathrm{mL} \) and the current at \( 1.2 \mathrm{A} \) The volume (in \( \mathrm{mL} \) ) of gases evolved at STP during the entire electrolysis is :
(write your answer to nearest integer)


There are following extraction process
of silver but not:
A. as a side product in electrolytic refining of copper
B. Parkes process in which \( Z n \) is used to extract silver by solvent extraction from molten lead
C. by reaction of silver sulphide with \( K C N \) and then the reaction of a soluble complex with \( Z n \)
D. by heating \( N a\left[A g(C N)_{2}\right] \)


The image shows an outline for which
experiment?
A. Cavendish Experiment
B. Newton's Experiment
C. Kepler's Experiment
D. None of these


Amit was given an increment of \( 20 \% \) on his salary. If his new salary is Rs.30600, what was his salary before the increment?


The following data gives the number (in thousands) of applicants registered with an Employment Exchange during.
\[
1995-2000
\]
Year 1995 \( \quad 1996 \quad \) 1997
Number of applicants registered
20
24
in thousands
Construct a bar graph to represent the above data.


The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) is equal
to (where \( e \) is the eccentricity of the hyperbola)
A \( . \) be
в.
\( c \cdot a b \)
D. \( a \)


In a solar cell current is generated due to bond breakage in which region?
A. Depletion region
B. n-region
c. p-region
D. None of these


The area bounded by the parabola \( y^{2}= \)
\( 5 x+6 \) and \( x^{2}=y \)


(a) Write using Biot - Savart Law, the expression for magnetic field \( \vec{B} \) due to an element \( \overrightarrow{d l} \) carrying current \( I \) at a distance \( \vec{r} \) from it in a vector form.
Hence derive the expression for the magnetic field due to a current carrying loop of radius \( R \) at a point \( P \) distant \( x \) from its centre along the axis of the
loop.
(b) Explain how Biot - Savart law enables one to express the Ampere's circuital law in the integral form, viz.,
\[
\overrightarrow{\boldsymbol{B}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{l}=\boldsymbol{\mu}_{\boldsymbol{o}} \boldsymbol{I}
\]
where \( I \) is the total current passing through the surface.


In the circuit shown in Fig, the current
has a value equal to
\( A \cdot 1 A \)
B. 2A
\( c \cdot 4 A \)
D. 3.5A


Two waves are travelling in the same direction along a stretched string. The
waves are \( 90^{0} \) out of phase. Each wave
has an amplitude of \( 4.0 \mathrm{cm} . \) The amplitude of the resultant wave is
\( 5.66 \times 10^{-x} \) m. Find \( x \)
\( A \)
B. 2
\( c \cdot 8 \)
D. 4


Assertion
Physical adsorption of molecules on the surface requires activation energy.
Reason
Because the bonds of adsorbed
molecules are broken.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of (A).
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect


\( A 60 J \) of heat is added to the system, resulting in 15 J of work being done by the system. The remaining 45 J of heat is released. Find out the efficiency of the system?
A. \( 100 \% \)
B. 75 \%
c. \( 45 \% \)
D. 25\%
E . \( 15 \% \)


A planar object made up of a uniform square plate and four semicircular
discs of the same thickness and
material is being acted upon by four forces of equal magnitude as shown. The coordinates of point of application of forces is given by
A . \( (0, a) \)
в. \( (0,-a) \)
\( c .(a, 0) \)
D. \( (-a, 0) \)


Give the IUPAC names of the given
compounds:
\[
\begin{array}{c}
\text { } \\
\text { н-с-С - он }
\end{array}
\]


The value of universal gravitational constant on earth for a particle of mass
5 kgs is
В. \( 6.67 \times 10^{-7} \)
c. \( 5 \times 6.67 \times 10^{-11} \)
D. \( 6.67 \times 10^{-23} \)


On moving from left to right across a period in the table, the metallic
character:
A . increases
B. decreases
c. remains constant
D. first increases and then decreases


In a stationary wave that from as a result of reflection of waves from an
obstacle, the ratio of the amplitude at an antinode to the amplitude at node is
6. What percentage of energy is transmitted?


\[
\begin{array}{lllll}
X=x & -2 & -1 & 0 & 1 \\
P(X= & 0.1 & K & 0.2 & 2 K
\end{array}
\]
\( x) \)
is the probability distribution of random variable \( X \). Find the value of \( K \)
and variance of \( \boldsymbol{X} \)


The equation of the standing wave in a string clamped at both ends, vibrating in its third harmonic is given by \( \boldsymbol{y}=\mathbf{0 . 4} \sin (\mathbf{0 . 3 1 4} \boldsymbol{x}) \cos (\mathbf{6 0 0} \boldsymbol{\pi} \boldsymbol{t}) \) where
\( x \) and \( y \) are in \( \mathrm{cm} \) and \( t \) in sec.
a) the frequency of vibration is \( 300 H z \)
b) the length of the string is \( 30 \mathrm{cm} \)
c) the nodes are located at \( x= \)
\( \mathbf{0}, \mathbf{1 0 c m}, \mathbf{3 0 c m} \)
A. Only a is true
B. a, b are true
\( c . b, c \) are true
D. a, b, care true


Select the option that correctly
identifies the different genera \( (A, B, C \) and D) of Kingdom Fungi shown in figure
A. A - Mucor, B - Saccharomyces, C - Morchedia, D Amanita
B. A - Mucor, B - Saccharomyces, C - Penicillium, D Agaricus
c. A - Rhizopus, B - Sacchaormyces, C - Asperillius, D Morchella
D. A - Aspergillus, B - Rhizopus, C - Penicillium, D Agaricus


Eye lens contains a watery liquid called:
A. Aqueous humour
B. Peroxide
c. Vitreous humour
D. None of these


Short / Long type answer type
questions. What is Iymph? Explain its two functions and write about its
circulation.


State whether the set is finite or
infinite:
The set of points on a line


The P wave in the ECG indicates
A. Atrial depolarization
B. Rapid ventricular depolarization
C. Absolute refractory period
D. Repolarization of the ventricles


The ratio of the absorption of an
auditorium to that of a person is \( 1000 . \) If 500 persons are accommodated in that
auditorium then the ratio of the
reverberation times with and without
audience is:
A \( \cdot 1 / 3 \)
B. 2/3
\( c \cdot 3 / 2 \)
D. \( 3 / 4 \)


The number of ways in which n books can be arranged can be arranged on a shelf so that two particular books shall not be together is
A \( \cdot(n-2)(n-1) \)
в. \( (n-1) n ! \)
c. \( (n-2) n ! \)
D. None of these


Which among the following is a climber?
A. Cabbage
B. Pea
c. Potato
D. Yam


Which is/are a female Sex Hormone(s)?
A. Estrogen
B. Estradiol
c. Progesterone
D. All of the above


Outline the reaction sequence for the
conversion of ethene to ethyne (the number of steps should not be more
than two
A. \( A: H O C l \) в: кон
B. A: Bromine water B: Diethyl amine
c. \( A: \mathrm{Cl}_{2}, h \nu \mathrm{B}: \mathrm{Ca}(\mathrm{OH})_{2} \)
D. A: Bromine water \( B: K O H \)


Which one of the following hormones is responsible for uterine contraction
during parturition?
A. Relaxin
B. Vasopressin
c. oxytocin
D. Prolactin


If \( P \) is the pressure of gas, then the
kinetic energy per unit volume of the gas is:
A \( . P / 2 \)
в. \( P \)
c. \( 3 P / 2 \)
D. 2


J.B. Sumner isolated first enzyme from jack beans as
A. Amylase
B. Trypsin
c. Urease
D. Renin


Which of the following reactions does
not show the acidic nature of ethyne?
A. Acetylene reacts with sodamide to form sodium acetylides.
B. When passed through ammoniacal cuprous chloride solution, a red precipitate is formed.
C. Acetylene reacts with chlorine in the dark to form di or tetrachlorides.
D. Acetylene when passed through ammoniacal silver nitrate gives a white precipitate.


A particle is moving in the \( x \) -y plane. At certain instant of time,the components of its velocity and acceleration are as
follows: \( \boldsymbol{v}_{\boldsymbol{x}}=\mathbf{3} \quad \boldsymbol{m} \boldsymbol{s}^{-1}, \boldsymbol{v}_{\boldsymbol{y}}=\boldsymbol{4} \quad \boldsymbol{m} \boldsymbol{s}^{-1} \)
\( \boldsymbol{a}_{\boldsymbol{x}}=\mathbf{2} \quad \boldsymbol{m} \boldsymbol{s}^{-2} \) and \( \boldsymbol{a}_{\boldsymbol{y}}=\mathbf{1} \quad \boldsymbol{m} \boldsymbol{s}^{-1} . \) The
rate of change of speed at this moment is:
\( \mathbf{A} \cdot \sqrt{10} m s^{-2} \)
B. \( 4 m s^{-2} \)
c. \( \sqrt{5} m s^{-2} \)
D. \( 2 m s^{-2} \)


A bag contains 4 red and 5 black balls, a second bag contain 3 red and 7 black
balls. One ball is drawn at random from
each bag, find the probability that the
ball are of the same colour.


The area (in sq. units) of the region described by
\( \left\{(x, y) ; y^{2} \leq 2 x \text { and } y \geq 4 x-1\right\} \) is
\( A \cdot \frac{7}{32} \)
в. \( \frac{5}{64} \)
c. \( \frac{15}{64} \)
D. \( \frac{9}{32} \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
is \( 3.81 \times 10^{2} \) at \( 600 \mathrm{K} \) and \( 2.69 \times 10^{3} \)
at 700 K. Calculate \( \Delta_{r} H \)
\( A \cdot 68.248 \mathrm{kJ} \)
B. 69.04 kJ
c. 71.89 k
D. 80.09 kJ


The sum of the first \( n \) terms of an A.P is
\( 4 n^{2}+2 n . \) Find the \( n \) th term of this A.P.
A. \( 5 n-2 \)
B. \( 8 n-2 \)
c. \( 3 n-2 \)
D. None of these


\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{6} 4 s^{2} \)
The given electronic configuration is
for:
A . Na
B. Fe
c. \( C l^{-} \)
D. Rb
E \( . C a^{+} \)


The photon energy in units of eV for electromagnetic waves of wavelength
\( 2 c m \) is:
A \( .2 .510^{-19} \)
B. \( 5.210^{-16} \)
c. \( 3.210^{-16} \)
D. \( 6.210^{-5} \)


Q Type your question
aissipatea is nignest? (Neglect the
internal resistance of the power supply)
\( A \)
B.
\( c \)
\( D \)


The maximum value of \( \frac{17}{3}-\left(x-\frac{4}{5}\right)^{2} \) is
A \( \cdot 4 / 5 \)
B. \( -4 / 5 \)
c. \( 17 / 3 \)
D. \( -17 / 3 \)


What is impact on benzene in magnetic
field :
A. Strong attract
B. Weakly attract
c. strongly repel
D. weak repel


The Haber process is used for producing ammonia from nitrogen and hydrogen. This reaction could be forced to produce
more ammonia by:
A. Increasing the reaction pressure
B. Decreasing the reaction pressure
c. Adding a catalyst
D. Both b and c
E. None of the above


Write the uses of actinides.


A flask contains argon and chlorine in
the ratio of 2: 1 by mass. The
temperature of the mixture is \( 27^{0} C . \) The ratio of average kinetic energies of two gases per molecule is
A . 1: 1
в. 2: 1
\( c .3: 1 \)
D. 6: 1


Bacterial pili are involved in
A. Asexual reproduction
B. Sexual reproduction
c. Saprophytic nutrition
D. Antibiotic resistance


\( \mathrm{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \) is formed while testing:
A \( \cdot N O_{3}^{-} \)
B. \( C l^{-} \)
\( \mathrm{c} \cdot \mathrm{Cr}^{3} \)
D. \( F e^{3} \)


To find the convergence factor between the units of same physical quantities in two different system


Transformation of light energy into nerve impulse is a
A. Mechanical process
B. Physical process
c. chemical process
D. Biochemical process


The arithmetic mean (average) of the first \( n \) positive integers is
A \( \cdot \frac{n}{2} \)
в. \( \frac{n^{2}}{2} \)
c. \( n \)
D. \( \frac{n-1}{2} \)
E \( \cdot \frac{n+1}{2} \)


How are proteins denatured?


Mention the differences between the
mechanisms of the regulation of gene
activity in lac operon and trp operon in
E. coli


Which of the following does not exist?
This question has multiple correct options
\( A \cdot H S_{6} \)
B. \( \mathrm{HPO}_{4} \)
\( \mathbf{c} \cdot \) Fel \( _{3} \)
D. \( \mathrm{HClO}_{4} \)


\( \operatorname{Let} \boldsymbol{F}(\boldsymbol{x})=\left|\begin{array}{ccc}\sin \boldsymbol{x} & \cos \boldsymbol{x} & \sin \boldsymbol{x} \\ \cos \boldsymbol{x} & -\sin \boldsymbol{x} & \cos \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{1} & \boldsymbol{1}\end{array}\right| \)
Which of the following statement hold true?
This question has multiple correct options
A \( \cdot \) Range of \( F(x) \) is \( (-\infty, \infty) \)
B \( \cdot F^{\prime}\left(\frac{\pi}{2}\right)= \)
c. \( F(x) \) is bounded
D. \( F(x) \) is continuous and differentiable every where in its domain


The angle formed between the incident
ray and the normal is called
A. angle of incidence
B. angle of reflection
c. angle of refraction
D. none of the above


How will you convert Benzene to Benzoic
acid?


The conversion of aluminium hydroxide to pure alumina is carried out by:
A. addition of \( A l(O H)_{3} \) crystals
B. thermal decomposition
c. precipitation
D. none of these


An optical fibre is made of quartz filaments of refractive index 1.70 and it
has a coating of material whose refractive index is \( 1.45 . \) The range of
angle of incidence for one laser beam to suffer total internal reflection is
\( \mathbf{A} \cdot 0^{\circ} \) to \( 56.8^{\circ} \)
B . \( 0^{\circ} \) to \( 62.6^{\circ} \)
\( \mathbf{c} \cdot 0^{\circ} \) to \( 90^{\circ} \)
D. \( 0^{\circ} \) to \( 180^{\circ} \)


\( p^{t h} \) term of the series \( \left(3-\frac{1}{n}\right)+\left(3-\frac{2}{n}\right)+\left(3-\frac{3}{n}\right) \dots \dots \)
will be
\( A \cdot 3+\frac{p}{n} \)
B \( \cdot 3-\frac{p}{n} \)
c. \( 3+\frac{n}{p} \)
D. \( 3-\frac{n}{p} \)


A particle is moving with velocity \( \vec{v}= \) \( K(y \hat{i}+x \hat{j}), \) where \( K \) is a constant. The
general equation for its path is
A \( \cdot y^{2}=x^{2}+ \) contant
B . \( y=x^{2}+ \) contant
C \( \cdot y^{2}=x+ \) contant
D. \( x y= \) contant


The number of lines of symmetry for a
\( 50^{\circ}-50^{\circ}-80^{\circ} \) triangle is:


If the position vector of the vertices of a triangle are \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} ; \boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \boldsymbol{\&} \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}, \) then find the area of the
triangle.
A. \( \sqrt{5} m^{2} \)
B. \( 5 m^{2} \)
\( c \cdot 25 m^{2} \)
D. \( 2 m^{2} \)


Main component of fungal cell wall is :
A. Cellulose
B. Chitin
c. Pectin
D. Dextrin


Which plant hormone help in active absorption of water?
A . Auxin
B. GAA
c. cytokinin
D. ABAA


Temperature at which Fahrenheit and kelvin pair of scales give the same reading will be
A \( . \theta=-40 \)
B . \( \theta=40 \)
c. \( \theta=574.25 \)
\( \mathbf{D} \cdot \theta=512.45 \)


The number of real solutions of the
equation \( e^{x}=x \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. 0
D. none of these


Which one of the following is not a unit of Young's modulus?
\( \mathbf{A} \cdot N m^{-1} \)
B. \( N m^{-2} \)
c. mega pascal
D. dyne \( c m^{-2} \)


Find the sum of \( 1+4+7+10+\dots \dots \)
to 22 terms


The average kinetic energy of the
molecules of an ideal gas at \( 10^{\circ} \mathrm{C} \) has the value E. The temperature at which the kinetic energy of the same gas becomes \( 2 \mathrm{E} \) is
\( \mathbf{A} \cdot 5^{\circ} C \)
В \( \cdot 10^{\circ} \mathrm{C} \)
\( c \cdot 40^{\circ} C \)
D. None of these


Using formal charge, which of the
following would be the least likely structure for dinitrogen monoxide based on the knowledge that oxygen is NOT the central atom?
\( A \)
\[
\mathrm{N} \longrightarrow \mathrm{N}=0
\]
в.
\[
\mathrm{N}=\mathrm{N}=0
\]
c.
\[
\mathrm{N} \equiv \mathrm{N}-\mathrm{O}
\]
D. All three structures are equally likely as drawn


Find the frequency of light which ejects electrons from a metal surface, fully
stopped by a retarding potential of \( 3.3 V \) If photo electric emission begins in
this metal at a frequency of \( 8 \times 10^{14} \mathrm{Hz} \)
calculate the work function (in eV) for this metal.


The line joining the points \( \boldsymbol{A}(\mathbf{0}, \mathbf{5}) \) and
\( B(4,2) \) is perpendicular to the line joining the points \( C(-1,-2) \) and \( D(5, b) . \) Find the value of \( b \)


Is it possible to photograph a virtual image?
A. Yes
B. No
c. sometimes
D. Yes, provided that object is virtual


Hormone involved in the discharge of
pancreatic juice in mammals is
A. Secretin
B. Gastrin
c. cholecystokinin
D. Enterogastrone


The effective resistance between the
points \( X \) and \( Y \) in the given circuit is
\( A \cdot 8 / 3 \Omega \)
B. \( 8 \Omega \)
\( c .4 \Omega \)
D. \( 2 \Omega \)


Calgon (sodium metaphosphate) finds application as:
A. artificial jewel
B. paints
c. a resin
D. washing powder


Which of the following is true for friction?
A. It is necessary to perform many tasks.
B. It produces heat.
c. It wears out the surfaces in contact
D. All of the above


An \( 8 k g \) cat is dragged along a hardwood
floor such that her final velocity is
\( 80 \mathrm{cm} / \mathrm{s} \) after being dragged through
\( 2 m \)
She is initially at rest. In this time interval, the work done on the cat by the normal force exerted by the floor is closest to:
A. zero
в. \( 1.88 J \)
c. \( 2.56 J \)
D . 78.48J
E . 156.965


The metabolic activities of root cells are
the main cause of water absorption in
A. Passive absorption
B. Active absorption
c. Both passive and active absorption
D. None of the above


In the figure magnetic field points into the plane of paper and the conducting
rod of length \( l \) is moving in this field
such that the lowest point has a velocity
\( \boldsymbol{v}_{1} \) and the topmost point has the
velocity \( v_{2}\left(v_{2}>v_{1}\right) . \) The emf induced is
given by:
\[
\begin{array}{cccc}
x & x & x & x \\
x & x & x_{2} & x \\
x & x & x & x \\
x & \vec{x} & v_{1} & x & x
\end{array}
\]
\( \mathbf{A} \cdot B v_{1} l \)
B. \( B v_{2} l \)
\( c \)
\[
\frac{1}{2} B\left(v_{2}+v_{1}\right) l
\]
D.
\[
\frac{1}{2} B\left(v_{2}-v_{1}\right) l
\]


The presence of auxins in a solution could be tested by
A. Avena sativa stem tip test
B. Carbon tetrachloride test
c. lodine test
D. Defoliation test


Which of the following ions forms a hydroxide that is highly soluble in water?
A \( . K^{\text {t }} \)
в. \( Z n^{2} \)
c. \( N i^{2} \)
D. \( A l^{3} \)


Reaction \( 2 B a O_{2}(s) \rightleftharpoons 2 B a O(s)+ \)
\( O_{2}(g) ; \Delta H=+v e . \) At equilibrium
condition, Pressure of \( O_{2} \) is depends on
A. Increase mass of \( B a O_{2} \)
B. Increase mass of Bao
C. Increase temp. at \( E q^{m} \)
D. Increase mass of \( B a O_{2} \) and Bao both


If \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) are in A.P. and A.M. of \( \boldsymbol{x} \) and \( \boldsymbol{y} \) is
a and that to \( y \) and \( z \) is \( b \), then \( A . M \). of \( a \)
and \( b \) is.
\( A \cdot x \)
B. \( y \)
\( c \cdot z \)
D. \( \frac{1}{2(x+y)} \)


Ordinary CuO is used in Liebig's combustion method for estimation of
carbon and hydrogen in organic compounds.
A. True
B. False


A cylindrical vessel with internal diameter \( 10 \mathrm{cm} \) and height \( 10.5 \mathrm{cm} \) is full of water. A solid cone of base diameter \( 7 \mathrm{cm} \) and height \( 6 \mathrm{cm} \) is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take \( \left.\pi=\frac{22}{7}\right) \)
\( \mathbf{A} \cdot(\mathbf{i}) 77 \mathrm{cm}^{3} \) and (ii) \( 748 \mathrm{cm}^{3} \)
B. (i) 70 \( c m^{3} \) and (ii) \( 740 \mathrm{cm}^{3} \)
c. \( \left(\text { i) } 85 ~ c m^{3} \text { and (ii) } 786 ~ c m^{3}\right. \)
D. (i) 88 \( c m^{3} \) and (ii) \( 797 \mathrm{cm}^{3} \)


Which compound is missing in the reaction given below?
\( 2 N a O H+\left(N H_{4}\right)_{2} S O_{4} \rightarrow ?+N a_{2} S O \)
A. \( O_{2} \)
в. \( H_{2} \)
c. \( N_{2} \)
D. \( 2 N H_{3} \)


Congression is a phenomenon of
A. Movement of sister chromatids towards the poles
B. Pairing of homologous chromosomes
C. Separation of paired chromosomes
D. Bringing the chromosomes on equator of spindle apparatus


If
\( A \rightarrow \) products is a first order reaction then, write the integrated law equation.


During electrolysis, electrons are being added directly to the metal ions at the
A. anode
B. cathode
c. both \( A \) and \( B \)
D. none of the above


A ball of mass m moving with a velocity u collides head on with a second ball of
mass \( m \) at rest. Coefficient of
restitution is e.

The ratio of the final and initial
velocities of the first ball is
A \( \cdot \frac{1-e}{1+e} \)
B. \( \frac{1+e}{1-e} \)
c. \( \frac{1+e}{2} \)
D. \( \frac{1-e}{2} \)


Doubling the thickness of the wire
A. doubles the young's modulus of the wire
B. halves the young's modulus of the wire
C. keeps the young's modulus constant
D. decreases the young's modulus of the wire by \( 1 / 8 \) th


The most nearest prehistoric ancestor
of present man may be
A. Java ape man
B. Cro-Magnon man
c. Neanderthal man
D. Peking man


Add: \( a+b+a b ; b-c+b c \) and \( c+ \)
\( a+a c \)


Expand the following terms.
BOD, STP, MTP, UTR, MALT


Solve the following pair of simultaneous equations:
\( \frac{a}{4}-\frac{b}{3}=0 ; \frac{3 a+8}{5}=\frac{2 b-1}{2} \)
A \( . a=-4.5, b=12 \)
в. \( a=4, b=-5 \)
c. \( a=14, b=10.5 \)
D. \( a=12, b=11.5 \)


If \( \tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}, \) Then \( x \) is
equal to
A. -1
в. \( \frac{1}{6} \)
c. \( _{-1, \frac{1}{6}} \)
D.


Which of the following phenomenon is involved in Tyndall effect?
A. Reflection of light.
B. Refraction of light
c. scattering of light.
D. Magnification of light.


(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?


In \( \Delta \) ABC \( \angle A=65^{0} \) and \( \angle B=25^{\circ} C \)
Name the hypotenuse.


Solve
\( \tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha} \)


A uniform rope of length \( 12 \mathrm{m} \) and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. \( A \)
transverse pulse of wavelength \( 0.06 \mathrm{m} \) is produced at the lower end of the rope.
What is the wavelength of the pulse
when it reaches the top of the rope?
A. \( 0.06 \mathrm{m} \)
B. 0.03
c. \( 0.12 \mathrm{m} \)
D. 0.09 \( m \)


Write the formulae of any two oxoacids
of sulphur.


A symmetrical form of the line of intersection of the planes \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b} \)
and \( \boldsymbol{z}=\boldsymbol{c} \boldsymbol{y}+\boldsymbol{d} \) is :
A. \( \frac{x-b}{a}=\frac{y-1}{1}=\frac{z-d}{c} \)
\( ^{\text {В }} \cdot \frac{x-b-a}{a}=\frac{y-1}{1}=\frac{z-d-c}{c} \)
c. \( \frac{x-a}{b}=\frac{y-0}{1}=\frac{z-c}{d} \)
D. \( \frac{x-b-a}{b}=\frac{y-1}{0}=\frac{z-d-c}{d} \)


The coefficient of \( x^{11} \) in the expansion of
\( \left(1-2 x+3 x^{2}\right)(1+x)^{11} \) is
A . 164
в. 144
c. 116
D. none of these


The number of permutation of the letters of the word \( H I N D U S T A N \)
such that neither the pattern \( ^{\prime} \boldsymbol{H} \boldsymbol{I} \boldsymbol{N}^{\prime} \)
nor \( ^{\prime} D U S^{\prime} \) nor \( ^{\prime} T A N^{\prime} \) appears, are :
A . 166674
B. 169194
c. 166680
D. 181434


Which of the following statements are
correct?
A. PAHs can occur in air attached to dust particles.
B. Some PAH particles can readily evaporate into the air from soil or surface waters
C. both \( A \) and \( B \)
D. none of these


Nif gene is found in
A. Pseudomonas
B. Salmonella
C. Rhizobium
D. Mycobacterium


Identify A to in the following sequence of reaction. \( \boldsymbol{N} \boldsymbol{a}+\boldsymbol{O}_{2} \rightarrow(\boldsymbol{A}) \stackrel{\boldsymbol{H} C l}{\rightarrow} \)
\( (B) \frac{e t h e r}{H^{+} / K_{2} C r_{2} O_{7}} C \)
\( C \) is forms blue colour in ethereal
solution.
A \( \cdot \) A: \( N a_{2} O_{2}, \) B \( : H_{2} O, c: C r O_{3} \)
B. A: \( N a O_{2}, \) В \( : H_{2} O_{2}, \mathrm{C}: C r_{2} O_{7} \)
c. \( A: N a_{2} O_{2}, B: H_{2} O_{2}, c: C r O_{3} \)
D. A: \( N a O, \) В \( : H_{2} O, c: C r O_{3} \)


Which one of the following statements is/are correct?
A. Homo erectus is the ancestor of Homo Sapiens.
B. Fossils of Cro-Magnon has been found in Ethopia
c. Australopithecus is the real ancestor of modern man
D. Neanderthal man is the direct ancestor of Homo sapiens


Value of \( \sqrt[3]{343} \) is:
A. 7
B. - 5
\( c \cdot \frac{7}{5} \)
D.


Find the value of \( x: 8 x 16=6 x+6 \)


When \( \mathrm{PO}_{4} \) and \( \mathrm{NO}_{3} \) is more in the water
of a lake it causes
A. Growth of bacteria
B. Growth of fishes
c. Death of algae
D. Algal bloom


Which of the following is not a green
house gas?
A. \( C O_{2} \)
в. \( C H_{4} \)
\( c \cdot O_{3} \)
D. \( N_{2} X \)


Plant hormones can be used by farmers
to manage plant growth. Give two examples of the commercial value of plant hormones.


The maximum and minimum distance
of earth from sun are \( r_{1} \) and \( r_{2} \)
respectively What will be the distance of earth from sun when its position vector is perpendicular to the major axis of its orbit
A \( \cdot \frac{r_{1}+r_{2}}{4} \)
в. \( \left(\frac{r_{1}+r_{2}}{r_{1}-r_{2}}\right) \)
c. \( \frac{2 r_{1} r_{2}}{r_{1}+r_{2}} \)
D. \( \frac{r_{1}+r_{2}}{3} \)


Froth floatation process used for the
concentration of sulphide ore:
This question has multiple correct options
\( \mathbf{A} \cdot \) is based on the difference in wettability of different minerals
B. uses sodium ethyl xanthate \( \left(C_{2} H_{5} O C S_{2} N a\right) \) as a collector
C. uses \( N a C N \) as depressant in the mixture of \( Z n S \) and \( P b S \) when \( Z n S \) forms soluble complex and \( P b S \) forms froth
D. uses pine oil as frothing agent


How many grams of magnesium oxide is formed when 4.8 gm of magnesium is combined with \( 3.2 \mathrm{gm} \) of oxygen?
A . \( 4.2 \mathrm{gm} \)
B. 3.2 gm
c. 8 gm
D. \( 16 \mathrm{gm} \)


Write the IUPAC name of the given
compound


A right angle triangle ABC having right angle at \( C, C A=a, C B=b \) moves such that the angular points \( A \) and \( B \) slide along x-axis and y-axis respectively. The locus of \( C \) is
A. \( a x+b y+1=0 \)
В. \( a x \pm b y=0 \)
\( \mathbf{c} \cdot a x^{2} \pm 2 b y+y^{2}=0 \)
D. none of these


Two identical pith balls are charged by rubbing against each other. They are suspended from a horizontal rod
through two strings of length \( 20 \mathrm{cm} \) each, the separation between the suspension points being \( 5 \mathrm{cm} . \) In
equilibrium, the separation between
the balls is \( 3 \mathrm{cm} \). Find the mass of each
ball and the tension in the strings. (The
charge on each ball has a magnitude
\( \left.2.0 \times 10^{-8} C\right) \)


Two unequal masses \( \left(M_{1} \text { and } M_{2}\right. \)
)are connected by a string which passes
over a frictionless pulley (Fig. 3.1). If \( \boldsymbol{M}_{\mathbf{1}} \)
\( M_{2} \) and the table are frictionless, the
acceleration of the masses would be
\( A \)
B. \( \frac{M_{1}+M_{2}}{M_{1} g} \)
c. \( \frac{M_{2} g}{M_{1}+M_{2}} \)
D. None of these


The balls, having linear momenta \( \overrightarrow{\mathbf{p}}_{1}= \) \( \mathbf{p} \hat{\mathbf{i}} \) and \( \overrightarrow{\mathbf{p}}_{2}=-\mathbf{p} \hat{\mathbf{i}}, \) undergo a collision in
free space. There is no extemal force
acting on the balls. Let \( \overrightarrow{\mathbf{p}}_{1} \) and \( \overrightarrow{\mathbf{p}}_{2} \) be
their final momenta. The following option(s) is (are) NOT ALLOWED for any
non-zero value of \( \mathbf{p}, \mathbf{a}_{1}, \mathbf{a}_{2}, \mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{c}_{1} \)
and \( \mathbf{c}_{2} \)
This question has multiple correct options
\( \mathbf{A} \cdot \overrightarrow{\mathbf{p}}_{1}=\mathbf{a}_{1} \hat{i}+\mathbf{b}_{1} \hat{\mathbf{j}}+\mathbf{c}_{1} \hat{\mathbf{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \mathrm{i}+\mathrm{b}_{2}
\]
B \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{c}_{1} \hat{\mathrm{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{c}_{2} \hat{\mathrm{k}}
\]
C \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{a}_{1} \mathrm{i}+\mathrm{b}_{1} \hat{\mathrm{j}}+\mathrm{c}_{1} \hat{\mathrm{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \hat{\mathrm{i}}+\mathrm{b}_{2} \hat{\mathrm{j}}-\mathrm{c}_{1} \hat{\mathrm{k}}
\]
D \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{a}_{1} \hat{\mathrm{i}}+\mathrm{b}_{1} \hat{\mathrm{j}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \mathrm{i}+\mathrm{b}_{1} \hat{\mathrm{j}}
\]


The Bohr radius of the fifth electron of
phosphorus (atomic number = 15) acting as dopant in silicon (relative dielectric constant \( =12 \) ) is
A \( \cdot 10.6 ~ A^{\circ} \)
B. 0.53 \( A^{0} \)
c. \( 21.2 A^{\circ} \)
D. None of these


In which of following cases, both the compounds are examples of reducing sugars?
A. Glucose and Sucrose
B. Fructose and Maltose
c. Fructose and sucrose
D. sucrose and Lactose


Assertion
Escherichia coli lives in a symbiotic relationship in the colon of the human body
Reason
The bacterium produces vitamins which are absorbed by the wall of colon into the blood stream
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 type(s) of intermolecular forces exist between the following pair?
\( H B r \) and \( H_{2} S \)
A. Dipole-dipole intermolecular forces
B. Induced dipole interactions
c. Hydrogen bonding
D. None of the above


Two parallel wires \( 1 m \) apart carry
currents of \( 1 A \) and \( 3 A \) respectively in
opposite directions. The force per unit length acting between these two wires is
A \( .6 \times 10^{-7} \mathrm{Nm}^{-1} \) repulsive
B. \( 6 \times 10^{-7} \mathrm{Nm}^{-1} \) attractive
c. \( 6 \times 10^{-5} \mathrm{Nm}^{-1} \)repulsive
D. \( 6 \times 10^{-5} \mathrm{Nm}^{-1} \) attractive


How many EDTA (ethylenediamine tetraacetate) molecule(s) islare
required to make an
octahedral complex with \( \mathrm{Ca}^{2+} \) ?
\( A \)


How many cyclopentane structures (excluding stereoisomers) are possible
for \( \boldsymbol{C}_{\mathbf{7}} \boldsymbol{H}_{\mathbf{1 4}} \)


\( \boldsymbol{F e}_{3} \boldsymbol{O}_{4} \) is called :
A. haematite
B. magnetite
c. cassiterite
D. dolomite


Fill in the bank with \( \langle,>,=\operatorname{sign} \)
a) \( (-3)+(-6)--(-3)-(-6) \)
b)(-21)-(-10)
c)45-(-11)
d)(-25)-(-42)


Which of the following is disposable
battery?
A. Lead acid battery
B. Mercury cell
c. \( N i-C d \) battery
D. None of these


When induced emf in inductor coil is
\( 50 \% \) of its maximum value then stored
energy in inductor coil in the given
circuit will be-
A \( .2 .5 m J \)
\( \mathbf{B} \cdot 5 m J \)
c. \( 15 m J \)
D. 20.5


Which of the following instruments can be used to measure the illuminating power of two sources?
A . Lactometer
B. Manometer
c. salinometer
D. Photometer


Consider a ring rolling down a smooth inclined plane of vertical height 'h' and inclination \( \theta . \) Then the true statement
in the following is?
A. Acceleration along the plane is \( g \sin \theta \) and the potential energy at the topmost point is mgh
B. Acceleration along the plane is g and the potential energy at the top most point is mgh
c. Acceleration along the plane is \( g \sin \theta \) and the potential energy at the top most point as mgh sin \( \theta \)
D. None of these


The increase order for the value of \( e / m \) (charge to mass ratio) for electron \( (e) \) proton \( (p) ; \) neutron \( (n) \) and alpha particle \( (\alpha) \) is:
A \( \cdot e<p<n<\alpha \)
в. \( n<p<e<\alpha \)
c. \( n<p<\alpha<e \)
D. \( n<\alpha<p<e \)


Let \( \boldsymbol{f}: \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \rightarrow(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) be a one-one
function. It is known that only one of the following statements is true:
(i) \( \boldsymbol{f}(\boldsymbol{x}) \neq \boldsymbol{b} \)
(ii) \( f(y)=b \)
(iii) \( f(z) \neq a \)
A \( . f=\{(x, a),(y, b),(z, c)\} \)
B. \( f=\{(x, b),(y, a),(z, c)\} \)
c. \( f=\{(x, b),(y, c),(z, c)\} \)
D. \( f=\{(x, b),(y, c),(z, a)\} \)


If the range for \( \boldsymbol{y}= \)
\( \left(\cot ^{-1} x\right)\left(\cot ^{-1}(-x)\right) \) is
\( \mathbf{0}<\boldsymbol{y} \leq \frac{\boldsymbol{\pi}^{\boldsymbol{a}}}{\boldsymbol{b}} \)
Find the value of \( a+b \)
A . 2
в. 4
c. 5
D. 6


A light bulb is rated at \( 100 \mathrm{W} \) for a \( 220 \mathrm{V} \)
supply. Find the peak voltage of the
source.


Which one of the following is an impossible event?

This question has multiple correct options
A. Rolling a die to get 4
B. Tossing a coin to get tail
c. choosing 4 face cards of spades.
D. Rolling a die for 7


From a uniform disk of radius \( \mathrm{R} \), a
circular hole of radius R/2 is cut out.
The centre of the hole is at R/2 from the
centre of the original disc. Locate the
centre of gravity of the resulting flat body.


Assertion
The value of acceleration due to gravity does not depend upon the mass of the body.
Reason
Acceleration due to gravity is a constant quantity.
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


Simplify:
\( 21-27+3+12 \times(-1) \)


On large scale, tritium is produced by which of the following nuclear
reactions?
A \( \cdot_{3}^{6} L i+_{0}^{1} n \rightarrow_{2}^{4} H e+_{1}^{3} T \)
B \( \cdot_{1}^{2} D+_{1}^{2} D \rightarrow_{1}^{3} T+_{1}^{1} H \)
C \( \cdot \frac{14}{7} N+_{0}^{1} n \rightarrow_{6}^{12} C+_{1}^{3} T \)
D \( \cdot \frac{14}{7} N+_{1}^{1} H \rightarrow_{1}^{3} T+ \) Other fragments


Plastic sulphur is of \( \boldsymbol{S}_{8} \)
molecule.
A. an open chain
B. close chain
c. branch chain
D. none of these


Show that the function \( \boldsymbol{y}=\boldsymbol{A} \cos \boldsymbol{x}+ \)
\( B \sin x \) is a solution of the differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y}=\mathbf{0} \)


Bidirectional translocation of materials
takes place in
A. Xylem
B. Phloem
c. Parenchyma
D. Cambium


Find the derivative of the following functions from first principle:
\( \cos \left(x-\frac{\pi}{8}\right) \)


Which base is employed as the electrolyte in alkaline batteries?
\( \mathbf{A} \cdot C a(O H)_{2} \)
в. \( A l(O H)_{3} \)
c. \( F e O H \)
D. KOH


Two motorcycles \( M_{1} \) and \( M_{2} \) are heading towards each other with a speed of \( 30 k m h^{-1} \) each. A bird flies off
\( M_{1} \) at \( 60 k m h^{-1} \) when distance
between the motorcycles is \( 60 k m \). It
heads towards \( M_{2} \) and then back to \( M_{1} \)
and so on. The total distance the bird
moves till the motorcycles meet is
\( A \cdot 60 k m \)
в. \( 40 \mathrm{km} \)
\( c .50 k m \)
D. 30 km
E. non


The correct statement in respect of
protein haemoglobin is that it:
A. functions as a catalyst for biological reactions
B. maintains blood sugar level
C . acts as an oxygen carrier in the blood
D. forms antibodies and offers resistance to diseases


The smallest value of a collection of
data is 12 and the range is \( 59 . \) Find the largest value of the collection of data.


To which of the following series the transition element from \( Z=39 \) to \( Z=48 \)
belong.
\( A \cdot 3 d \) series
B. \( 4 d \) series
c. \( 5 d \) series
D. \( 6 d \) series


Which the following represents
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O N a+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5}-O H \stackrel{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
c. \( 2 C H_{3} C O O H+2 N a \rightarrow 2 C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)


Fermi energy level for \( \boldsymbol{p}- \)type extrinsic semiconductors lies
A . At middle of the band gap
B. close to conduction band
c. close to valence band
D. None of the above


Which of the following is unique to
mitosis and not a part of meiosis?
A. Homologous chromosomes behave independently
B. Chromatids are separated during anaphase II
C. Homologous chromosomes pair and form bivalents
D. Homologous chromosomes crossover


Find the area of the segment of circle, given that the angle of the sector is
\( 120^{\circ} \) and the radius of the circle is
\( 21 \mathrm{cm} .(\text { Take } \pi=22 / 7) \)


The incorrect statement pertaining to
the adsorption of a gas on a solid
surface is (are):
A. Adsorption is always exothermic
B. Physisorption may transform into chemisorption at high temperature
C. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature
D. Chemisorption is more exothermic than physisorption, however, it is very slow due to higher energy of activation


The Young's modulus of the material of a wire of length L and radius r is \( Y \)
newton per \( m^{2} \). If the length of the wire
is reduced to \( L / 2 \) and the radius to \( r / 2 \) then its Young's modulus will be.
A. \( Y / 2 \)
B.
\( c .2 Y \)
D. \( 4 Y \)


Which of the following is not a molecular formula?
A. \( C_{6} H_{12} O_{6} \)
В \( \cdot C a\left(N O_{3}\right)_{2} \)
c. \( C_{2} H_{4} O_{2} \)
D. \( N_{2} O \)


To detect light of wavelength 500nm, the photodiode must be fabricated
from, a semiconductor of minimum
bandwidth of:
A . \( 1.24 e V \)
B. \( 0.62 e V \)
c. \( 2.48 e V \)
D. \( 3.2 e V \)
E . \( 4.48 e V \)


Change in the direction of light when it passes from one medium to another is called
A. reflection
B. refraction
c. diffraction
D. scattering


The long hydrocarbon chain in a soap is water repelling (hydrophobic), which is called:
A. polar tail
B. ring chain
c. non-polar tail
D. none of the above


Solve the following system of
inequalities graphically \( 2 x-y> \)
\( 1, x-2 y<-1 \)


A race of \( 16 k m \) is completed in taking
4 rounds of a square field. Then find the length and area of the field.


Serous glands located on the tongue are
A. Paratoid gland
B. Sublingual gland
c. von Ebner's gland
D. All of the above


Which graph represents the total heat
developed from time \( t=0 \) by a resistor
carrying a steady current?
\( (\mathbf{A}) \)
\( (\mathbf{D}) \)


When the temperature of water rises, the rate of evaporation
A. increases
B. decreases
c. remain the same
D. first decrease then increases


If metal section of shape H is inserted in
between two parallel plates as shown in figure and \( A \) is the area of each plate then the equivalent capacitance is :
A \( \cdot \frac{A \epsilon_{0}}{a}-\frac{A \epsilon_{0}}{b} \)
В. \( \frac{A \epsilon_{0}}{a+b} \)
c. \( \frac{A \epsilon_{0}}{a}+\frac{A \epsilon_{0}}{b} \)
D. \( \frac{A \epsilon_{0}}{a-b} \)


Electric field at \( Y \) is \( E_{y} \) and electric field
\( \operatorname{at} \mathrm{Z} \) is \( E_{z} . \) Find the value of \( \frac{\boldsymbol{E}_{z}}{\longrightarrow} \)
\( \overline{\boldsymbol{E}_{\boldsymbol{y}}} \)
A \( \frac{\sqrt{3}}{4} \)
B. \( \frac{\sqrt{4}}{3} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{9}{16} \)
E \( \cdot \frac{16}{9} \)


Which of the following is required as inducer(s) for the expression of Lac operon?
A. Glucose
B. Galactose
c. Lactose
D. Lactose and galactose


What is pH of \( 50 \mathrm{ml} \) 0.05 \( (\mathrm{M}) \) NaOH
and \( 50 \mathrm{ml} \) 0.1 \( (\mathrm{N}) \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} \)


Plant seed oil is obtained from
A. Saccharum munja
B. Arachis hypogea
c. Cicer areitinum
D. saccharum officinarum


State whether given statement is True or False.

The displacement of a moving object in a given interval of time is zero. Then, the distance travelled by the object will
also be zero.
A. True
B. False


The correct statement(s) among the following is/are:
This question has multiple correct options
A. beryllium oxide is amphoteric in nature.
B. solubility of sulphates of II A group elements decreases down the group.
C. reducing power of hydride of alkali metal decreases down the group.
D. beryllium has diagonal relationship with aluminum.


The angular momentum of an electron
in the \( 2^{n d} \) excited state ofa Helium ion
\( \left(\boldsymbol{H} \boldsymbol{e}^{+}\right) \) is:
A \( \cdot \frac{h}{2 \pi} \)
в. \( \frac{2 h}{2 \pi} \)
\( c \cdot \frac{3 h}{2 \pi} \)
D. \( \frac{4 h}{2 \pi} \)


Which of the following is used as a catalyst in Friedal kraft's alkylation reaction?
A. Anhydrous \( A l C l_{3} \)
в. \( N a C l \)
c. \( B e C l_{2} \)
D. \( M g C l_{2} \)


Speeds of two identical cars are u and 4u at a specific instant. The ratio of the respective distances at which the two
cars are stopped at the same instant is
A . 1:
B. 1:
\( c \cdot 1: 8 \)
D. 1:16


Among the following, the wrong statement in the case of semiconductor
is:
A. Resistivity is in between that of a conductor and insulator
B. Temperature coefficient of resistance is negative
c. Doping increases conductivity.
D. At absolute zero temperature, it behaves like a conductor


Find \( x \) from the figure


Chloroacetic acid is a stronger acid than acetic acid. Give one reason.


Write one use of diamond.


Iron can be purified by the method of liquation.
A . True
B. False


If \( |\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B} \) then the value of
\( |\vec{A}+\vec{B}| \) is:
\( ^{A} \cdot\left(A^{2}+B^{2}+\frac{A B}{\sqrt{3}}\right)^{1 / 2} \)
в. \( A+B \)
c. \( \left(A^{2}+B^{2}+\sqrt{3} A B\right)^{1 / 2} \)
D. \( \left(A^{2}+B^{2}+A B\right)^{1 / 2} \)


Who among the following gave an incorrect statement?

Rohan : There are more than 1000
varieties of mangoes in India. Priti : Every year, the International Mango Festival is held in Nagpur. Raj : Mango fruit is an excellent source of vitamin \( A, B, C, E \) and
flavonoids.
Simaran : Best 50 varieties of mangoes
are only exhibited in international
Mango Festival
A. Priti and Raj
B. Rohan and Simran
c. Priti and Simran
D. Rohan and Raj


Induced electromotive force in a coil
does not depend on
A. Number of turns in the coil
B. Intensity of the magnetic field
c. Relative speed between coil and the magnet
D. Resistance of the coil


Which of the following reaction(s)
is/are wrong?
\( A \)
B.
\( c \)
D. None of the above


\( 0.53 \mathrm{g} \) of substance gave \( 1.158 \mathrm{g} \) of \( B a S O_{4} \) by Carius method. Calculate the
percentage of sulphur.
A . \( 42.10 \% \)
B . \( 23.3 \% \)
c. \( 32.03 \% \)
D. 30\%


The number of optically active products
obtained from the complete ozonolysis
of the given compound are:
\[
\begin{array}{cc}
\mathrm{CH}_{3} & \mathbf{H} \\
\mathbf{I} & \mathbf{I} \\
\mathbf{G H}_{3}-\mathbf{C H}=\mathbf{C H}-\mathbf{C}-\mathbf{C H}= & \mathbf{C H}-\mathbf{C}-\mathbf{C H}=\mathbf{C H}-\mathbf{C H}_{3} \\
& \mathbf{E}
\end{array}
\]
A.
B.
\( c \cdot 2 \)
\( D \)


Two long conductors, separated by a
distance \( d \) carry current \( I_{1} \) and \( I_{2} \) in the
same direction. They exert a force \( \boldsymbol{F} \) on
each other. Now the current in one of
them increased to two times and its
direction reversed. The distance is also
increased to \( 3 d \). The new value of the
force between them is
A . \( -2 F \)
в. \( F / 3 \)
\( \mathrm{c} \cdot-2 F / 3 \)
D. \( -F / 3 \)


The human hindbrain comprises of
three parts one of which is
A. Spinal cord
B. Corpus callosum
c. Cerebellum
D. Hypothalamus


The vacancy created due to the absence
of an electron in the valence band of a
semiconductor is called a
A . electron
B. hole
c. proton
D. position


or using plants (such as willow) to extract heavy metals can prevent soil pollution.
A. Phytoremediation
B. Biofertilizer
c. Bioremediation
D. None of above


A car is travelling with an acceleration
of \( 2 m / s^{2} . \) If the diameter of the car
wheel is \( 50 \mathrm{cm}, \) the angular acceleration of the wheel is:
A \( .2 .5 \mathrm{rad} / \mathrm{s}^{2} \)
B. 8 rad/s\( ^{2} \)
C \( .5 \mathrm{rad} / \mathrm{s}^{2} \)
D. 4 rad/s\( ^{2} \)


The volume of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) acid \( (\boldsymbol{9} \boldsymbol{8} \% \) by
mass, \( d=1.80 \mathrm{g} / \mathrm{mL} \) ) required to prepare
1 litre of \( 0.1 M H_{2} S O_{4} \) solution is:
A \( .16 .65 \mathrm{mL} \)
B . \( 22.20 \mathrm{mL} \)
\( c .5 .55 \mathrm{mL} \)
D. \( 11.10 \mathrm{mL} \)


Determine the value of the constant \( k \)
so that the function
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{aligned} \frac{\sin 2 x}{\mathbf{5} \boldsymbol{x}}, & \text { if } \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{k}, \text { if } \boldsymbol{x} &=\mathbf{0} \end{aligned}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} \)


The truth table for expression is the given Boolean expression is
\[
(A+B) \cdot \overline{(A \cdot B)}=1
\]
A. \begin{tabular}{|c|c|c|}
\hline\( A \) & \( B \) & \( Y \) \\
\hline 1 & 0 & 0 \\
1 & 1 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0 \\
\hline
\end{tabular}
в. \begin{tabular}{|c|c|c|}
\hline\( A \) & \( B \) & \( Y \) \\
\hline 1 & 1 & 1 \\
0 & 0 & 1 \\
1 & 0 & 0 \\
1 & 0 & 1 \\
\hline
\end{tabular}
c. \begin{tabular}{|c|c|c|}
\hline\( A \) & \( B \) & \( Y \) \\
\hline 0 & 0 & 1 \\
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 1 & 0 \\
\hline
\end{tabular}
D. \begin{tabular}{|c|c|c|}
\hline\( A \) & \( B \) & \( Y \) \\
\hline 1 & 1 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
0 & 0 & 0 \\
\hline
\end{tabular}


Assertion
Suppression of growth of axillary buds is called apical dominance.
Reason

It is due to effect of downward
movement of Auxin from apical region
towards the lower side.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


ff \( [x] \) is the integral part of a real number x. Then, solve \( [\mathbf{2 x}]-[\boldsymbol{x}+\mathbf{1}]= \)
\( 2 x \)


Why are alloys commonly used in electrical heating devices?
A. Due to high resistivity
B. Due to low resistivity
c. Due to high elasticity
D. Due to medium resistivity


Explain mirror formula \( \frac{\mathbf{1}}{\boldsymbol{u}}+\frac{\mathbf{1}}{\boldsymbol{v}}=\frac{\mathbf{1}}{\boldsymbol{f}} \)


A lake on the map has an area of
\( 0.15 \mathrm{cm}^{2} . \) work out the actual area of the
lake.


\( \int \cos ^{-1}\left(\frac{1}{x}\right) d x \) equal to
A \( \cdot x \sec ^{-1} x+\cosh ^{-1} x+c \)
B \( \cdot x \sec ^{-1} x-\cosh ^{-1} x+c \)
c. \( x \sec ^{-1} x-\sin ^{-1} x+c \)
D. \( x \sec ^{-1} x+\sin ^{-1} x+c \)


The circuit below shows six resistors in
a circuit with a voltage source
supplying a voltage, \( V \)
Which table gives the correct voltage
drops across resistor 6 and resistor \( 3 ? \)
A. Voltage Drop across Resistor 6 - Voltage Drop across Resistor \( 3, V / 6-V / 6 \)
B. Voltage Drop across Resistor 6 - Voltage Drop across Resistor \( 3, V-V \)
c. voltage Drop across Resistor 6 - voltage Drop across Resistor \( 3.3 V-V \)
D. voltage Drop across Resistor 6 - Voltage Drop across Resistor \( 3, V / 3-V \)
E : " ge Drop across Resistor 6- Voltage Drop across \( \operatorname{tor} 3, V-V / 3 \)


A bullet moving with a velocity \( u \) passes through a block at rest and free to move.
The two are of equal mass. After passing through the block, the velocity of the emerging bullet is \( f u \). Its velocity relative to the block is :
A. \( f \)
в. \( (1-f) u \)
c. \( (2 f-1) u \)
D. \( (2-f) u \)


f \( \boldsymbol{y}=\boldsymbol{f}\left(\boldsymbol{a}^{\boldsymbol{x}}\right) \) and \( \boldsymbol{f}^{\prime}(\sin \boldsymbol{x})=\log _{e} \boldsymbol{x}, \) then
find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if it exists, where \( \frac{\boldsymbol{\pi}}{\boldsymbol{2}}<\boldsymbol{x}<\boldsymbol{\pi} \)


The taxonomic aid that provides information for the identification of
names of species found in an area is
A. Monograph
B. Manual
c. catalogue
D. Periodical


is rotated about an axis passing
through the point \( P \) as shown in figure.
The magnitude of angular momentum
of the rod, about the rotational axis \( y y^{\prime} \)
passing through the point \( \boldsymbol{P} \) is
A \( \cdot \frac{M L^{2}}{18} \)
B. \( \frac{M(x+y)^{2}}{9} \)
c. \( \frac{M\left(L^{2}+x^{2}\right)}{9} \)
D. \( \frac{M\left(L^{2}+2 y^{2}\right)}{18} \)


When galvanic cell is started, with
passage of time:
This question has multiple correct options
A. spontaneity of the cell reaction decreases; \( E_{c e l l} \) decreases
B. reaction quotient Q decreases; \( E_{\text {cell}} \) increases
C . reaction quotient \( \mathrm{Q} \) increases; \( E_{c e l l} \) decreases
D. at equilibrium \( Q=K_{c} ; E_{c e l l}=0 \)


A coil of inductance \( 300 \mathrm{mH} \) and
resistance \( 2 \Omega \) is connected to a source
of voltage 2 V. The current reaches half of its steady state value in
A . \( 0.05 \mathrm{s} \)
B. 0.1 s
c. \( 0.105 \mathrm{s} \)
\( D \cdot 0.3 \mathrm{s} \)


(1) : For natural polymers, PDI value is always equal to unity
(2) : The ratio of \( \bar{M}_{w} \) and \( \bar{M}_{n} \) of
a polymer is called PDI.
A. Both 1 and 2 are correct and 2 is the correct explanation of the 1
B. Both 1 and 2 are correct but 2 is not the correct explanation of the 1
c. 1 is correct but 2 is in correct
D. 1 is incorrect but 2 is correct


Which of the following statements is correct about inductive effect?
A. Implies the transfer of lone pair of electrons from more electronegative atom to lesser electronegative atom in a molecule
B. Implies the transfer of lone pair of electrons from lesser electronegative atom to the more electronegative atom in a molecul
c. Increases with increase in distance
D. Implies the atoms ability to cause bond polarization


A body is projected horizontally from a height of \( 78.4 m \) with a velocity \( 10 m s^{-1} \) Its velocity after 3 seconds is (
\( \boldsymbol{g}=\mathbf{1 0 m s}^{-1} \) ). (Take direction of
projection on \( \hat{i} \) and vertically upward direction on \( \hat{j} \) ):
\( \mathbf{A} \cdot 10 \hat{i}-30 \hat{j} \)
B. \( 10 \hat{i}+30 \hat{j} \)
c. \( 20 \hat{i}-30 \hat{j} \)
D. \( 10 \hat{i}+10 \sqrt{30} \hat{j} \)


The current in the coil decreases from
10 Amp to 5 Amp in 0.1 second.. Calculate the co-efficient of self-
inductance if induced e.m.f. is \( 5 \mathrm{V} \)


Glycolysis is a:
This question has multiple correct options
A. Redox process
B. Aerobic process
c. oxidative process
D. Reductive process


The values of \( x \) in \( \left(0, \frac{\pi}{2}\right) \) satisfying the equation \( \sin x \cos x=\frac{1}{4} \) are
A \( \cdot \frac{\pi}{6}, \frac{\pi}{12} \)
в. \( \frac{\pi}{12}, \frac{5 \pi}{12} \)
c. \( \frac{\pi}{8}, \frac{3 \pi}{8} \)
D. \( \frac{\pi}{8}, \frac{\pi}{4} \)


An ideal battery of \( 4 V \) and resistance \( R \) are connected in series in the primary
circuit of a potentiometer of length \( 1 \boldsymbol{m} \) and resistance \( 5 \Omega . \) The value of \( R, \) to
given a potential difference of \( 5 m V \)
\( \operatorname{across} 10 c m \) of potentiometer wire is:
\( \mathbf{A} \cdot 490 \Omega \)
в. \( 480 \Omega \)
c. \( 395 \Omega \)
D. \( 495 \Omega \)


Evaluate :
\( \lim _{x \rightarrow 2} \frac{x^{2}-4}{x+3} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. None of these


The time period of an earth satellite in
circular orbit is independent of:
A. the mass of the satellite
B. radius of its orbit
c. both the mass and radius of the orbit
D. neither the mass of the satellite nor the radius of its orbit


Which one of the following numbers is not a complete cube? 64,216,343,256
A . 64
в. 216
c. 343
D. 256


A student uses a converging lens to produce an enlarged virtual image of a scale she wishes to read accurately. The
focal length of the lens is \( 10 \mathrm{cm} \). What
is a suitable distance between the scale
and the lens?
\( A \cdot 8 c m \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Write the truth table of logic OR gate.


Select correct statement(s) about
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)
This question has multiple correct options
A. They are thermodynamically stable
B. Xe-F bond energy is very highh
c. They are endothermic compounds
D. They are exothermic compounds


\( N_{2} O \) resembles formation of molecular
\( O_{2} \) since, it supports combustion.
A. True
B. False


The dissociation of \( N H_{4} O H \) decreases
on addition of \( N H_{4} C l . \) If true write 1
else write 0


\( O \) is centre of the circle. Find the length
of radius, if the chord of length \( 24 \mathrm{cm} \) is
at a distance of \( 9 \mathrm{cm} \) from the centre of
the circle.


If \( f(x)=\frac{1}{x}, g(x)=\sqrt{x} \) and
\( (g o \sqrt{f})(16)= \)
\( A \cdot 2 \)
B.
\( c \cdot \frac{1}{2} \)
D.


Find the maximum value of \( \boldsymbol{I} \)


What is autotrophic nutrition? Give one example of autotrophs.


Find centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particle are \( 100 \mathrm{g} \) \( 150 \mathrm{g}, \) and \( 200 \mathrm{g} \) respectively. Each side of the equilateral triangle is \( 0.5 \mathrm{m} \) long.


The perimeter of a trapezium is \( 52 c m \) and its non-parallel sides are each equal to \( 10 \mathrm{cm} \) and its altitude is \( 8 \mathrm{cm} \)
its Area \( =? \)


Let \( \overrightarrow{\boldsymbol{\alpha}}=\mathbf{3} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{\beta}}=\mathbf{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} . \) If
\( \overrightarrow{\boldsymbol{\beta}}=\overrightarrow{\boldsymbol{\beta}}_{1}-\boldsymbol{\beta}_{2}, \) where \( \overrightarrow{\boldsymbol{\beta}}_{1} \) is parallel to \( \overrightarrow{\boldsymbol{\alpha}} \)
and \( \vec{\beta}_{2} \) is perpendicular to \( \vec{\alpha}, \) then \( \vec{\beta}_{1} \times \)
\( \vec{\beta}_{2} \) is equal to?
\( \mathbf{A} \cdot-3 \hat{i}+9 \hat{j}+5 \hat{k} \)
B . \( 3 \hat{i}-9 \hat{j}-5 \hat{k} \)
c. \( \frac{1}{2}(-3 \hat{i}+9 \hat{j}+5 \hat{k}) \)
D・ \( \frac{1}{2}(3 \hat{i}-9 \hat{j}+5 \hat{k}) \)


A rectangular loop of wire is oriented with the left corner at the origin, one edge along X-axis and the other edge along Y-axis as shown in the figure. A magnetic field is into the page and has
a magnitude that is given by \( \beta=\alpha y \)
where \( \alpha \) is constant. Find the total
magnetic force on the loop if it carries
current \( i \)


Evaluate:
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x+\cos x} d x \)


Assertion
The average and instantaneous velocities have same value in a uniform
motion
Reason
In uniform motion, the velocity of an
object increases uniformly.
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 following gates produces
output of \( 1 ? \)
\( A \)
B
\( c \)
\( D \)


Assertion
Tapeworm, roundworm and pinworm are
endoparasites of human intestine.
Reason
Improperly cooked food is the source of
intestinal infections.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A leaf has labeled as \( A \) has 20 stomata.
A leaf labeled as B has 10 stomata.
Which of the following statement defines the percentage of water vapour released by both the leaves?
A. Leaf A releases more water vapour than leaf \( B \)
B. Leaf A releases less water vapour than leaf B.
c. Leaf A equals leaf
D. None of the above


State whether the given statement is True or False :

Earthquakes occur all the time all over
the world.
A. True
B. False


Why should electrons move in an orbit
round the nucleus?


If \( y=\sin ^{2} x, \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot \cos ^{2} x \)
B. \( 2 \sin x \)
\( \mathbf{c} \cdot \sin x \cos x \)
D. \( \sin 2 x \)


The information from RNA to DNA are
transferred by the process, which is called as
A. Replication
B. Transcription
c. Translation
D. Reverse transcription


Which of the following is not diamagnetic?
A. \( C_{2} \)
B. \( O_{2}^{2} \)
c. \( L i_{2} \)
D. \( N_{2}^{\text {th }} \)


A straight line L through the point (3,-2) is inclined at an angle 60 to the line \( \sqrt{\mathbf{3}} x+y=1 . \) If \( L \) also intersects
the \( x \) -axis, the equation of \( L \) is
A \( \cdot y+\sqrt{3} x+2-3 \sqrt{3}=0 \)
B . \( y-\sqrt{3} x+2+3 \sqrt{3}=0 \)
c. \( \sqrt{3} y-x+3+2 \sqrt{3}=0 \)
D. \( \sqrt{3} y+x-3+2 \sqrt{3}=0 \)


High performance liquid chromatography (HPLC) cannot be used
to :
A. Determine the caffeine content in coffee samples.
B. Identify the various pigments from a leaf extract
c. Determine the mercury content in a fish sample.
D. Separate organic pesticides.


Hot water in an ideal thermos flask is an
example for
(This question may have one or more
correct answers)
This question has multiple correct options
A. Isolated system
c. closed system
D. Adiabatic system


The number of ATP molecules utilised
for the breakdown of one molecule of
glucose during glycolysis is
\( A \cdot 62 \)
B. 2
\( c \cdot 8 \)
\( D \cdot 4 \)


Define the term hyperconjugation.


The order of reactivity of the following
alcohols towards conc. H \( C l \) is:
\( \mathbf{A} \cdot I>I I>I I I>I V \)
В . \( I>I I I>I I>I V \)
\( \mathbf{C} \cdot I V>I I I>I I>I \)
D. \( I V>I I I>I>I I \)


\( X e F_{6}+H_{2} O \rightleftharpoons X e O F_{4}+2 H F \)
constant \( =\boldsymbol{K}_{1}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}+\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \rightleftharpoons \)
\( X e O F_{4}+X e O_{3} F_{2} . \) constant \( =K_{2} \)
Then equilibrium constant for the
following reaction will be: \( -\boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{\boldsymbol{4}}+ \)
\( 2 H F \rightleftharpoons X e O_{4} F_{2}+H_{2} O \)
\( ^{A} \cdot \frac{K_{2}}{K_{1}} \)
в. \( K_{1}+K_{2} \)
c. \( \frac{K_{1}}{K_{2}} \)
D. \( \frac{K_{1}}{\left(K_{2}\right)^{2}} \)


Describe reproduction by spores in Rhizopus.


Which of the following will form an octahedral complex?
A \( \cdot d^{4} \) (low spin)
B. \( d^{8} \) (high spin)
c. \( d^{5} \) (low spin)
D. All of these


State whether true or false:
In good-quality microscopes, lens combinations are used for the objective and eyepiece instead of single lenses.
A. True
B. False


A magnet of dipole moment \( 2 A m^{2} \) is
deflected through \( 30^{\circ} \) from magnetic meridian. The required deflecting
torque is \( \left(B_{H}=0.4 \times 10^{-4} T\right) \)
A \( \cdot 0.4 \times 10^{-4} \mathrm{Nm} \)
B. \( 0.4 \mathrm{Nm} \)
c. \( 0.2 \times 10^{-4} N m \)
D. None of these


The bond between two identical non
metal atoms has a pair of electrons. The
correct statement about this pair is:
A. Unequally shared between the two.
B. Transferred fully from one atom to another
c. Has identical spins
D. Equally shared between the atoms


A.C power is transmitted from a power
house at a high voltage as
A. the rate of transmission is faster at high voltages
B. it is more economical due to less power loss
C. power cannot be transmitted at low voltages
D. a precaution against theft of transmission lines


How is ammonia collected?
A. Ammonia is less dense than air so it is collected by upward delivery.
B. Ammonia is more dense than air so it is collected by upward delivery.
C. Ammonia is more dense than air so it is collected by downward delivery.
D. None of the above


Propanone on reaction with alkyl magnesium bromide followed by hydrolysis will produce?
A. Primary alcohol
B. Secondary alcohol
c. Tertiary alcohol
D. Carboxylic acid


Which of the following is known as chloroform?
A \( \cdot C H_{2} C l_{2} \)
в. \( C H_{3} C l \)
c. \( C H C l_{3} \)
D. \( C C l_{4} \)


Mention any two ecological services for the benefit of mankind.


Match the columns of size with soil
particles
\begin{tabular}{lll|l}
& Column 1 (size) & \multicolumn{2}{c} { Column 2 (soil particle) } \\
a. & 0.2- 2.00 \( \mathrm{mm} \) & (i) & Silt \\
b. & Less than 0.002 \( \mathrm{mm} \) & (ii) & Clay \\
c. & 0.02 - 0.2 \( \mathrm{mm} \) & (iii) & Coarse sand particles \\
d. & \( 0.02-0.02 \) \( \mathrm{mm} \) & (iv) & Fine sand particles
\end{tabular}
B. a- iii, b- ii, c- iv, d-i
c. a- ii, b- iii, c- iv, d-i
D. None of the above


Explain how you can locate the Pole Star
with the help of Ursa Major.


Evaluate \( (10 x-25) \div(2 x-5) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 3 \)
D.


The image of the point with position vector \( \hat{i}+3 \hat{k} \) in the plane \( r \cdot(\hat{i}+\hat{j}+ \)
\( \hat{\boldsymbol{k}})=\mathbf{1} \) is
\( \mathbf{A} \cdot \hat{i}+2 \hat{j}+\hat{k} \)
B \( \cdot \hat{i}-2 \hat{j}+\hat{k} \)
c. \( -\hat{i}-2 \hat{j}+\hat{k} \)
D. \( \hat{i}+2 \hat{j}-\hat{k} \)


Choose the type of enzyme involved in
the following reaction.
\( \boldsymbol{S}-\boldsymbol{G}+\boldsymbol{S}^{\prime} \longrightarrow \boldsymbol{S}+\boldsymbol{S}^{\prime}-\boldsymbol{G} \)
A. Dehydrogenase
B. Transferase
c. Hydrolase
D. Lyase
E. Isomerase


Why is charcoal considered to be a
better fuel than wood?


Find the rate of change of the area of a
circle with respect to its radius \( r \) when
(i) \( r=3 \mathrm{cm} \)
(ii) \( r=4 \mathrm{cm} \)
\( \mathbf{A} \cdot 6 \pi, 8 \pi \)
B . \( 5 \pi, 8 \pi \)
\( \mathbf{c} .4 \pi, 10 \pi \)
D . \( 2 \pi, 8 \pi \)


\( (1-\sqrt{2})^{6}= \)
A \( .98-70 \sqrt{2} \)
В. \( 99-70 \sqrt{2} \)
D. \( 98+70 \sqrt{2} \)


The width of forbidden gap in silicon crystal is \( 1.1 e V . \) When the crystal is
converted into an n-type
semiconductor, the distance of fermi level from conduction band is
A. greater than 0.55 eV
B. equal to 0.55 eV
c. lesser than 0.55 eV
D. equal to \( 1.1 \mathrm{eV} \)


The value of \( \lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{x-2} d t \) is
A . 10
B. 12
\( c \cdot 8 \)
D. 16


Units of parts per million (ppm) or parts per billion (ppb) are often used to describe the concentrations of solutes
in very dilute solutions. The units are
defined as the number of grams of solute per million or per billion grams of solvent. Bay of Bengal has 1.89 ppm of
lithium ions. The molality of \( L i^{+} \) in this water is (atomic number of \( L \) i \( =7 \) ):
A \( \cdot 1.5 \times 10^{-4} m \)
В. \( 1.7 \times 10^{-4} \mathrm{m} \)
c. \( 2.5 \times 10^{-4} m \)
D. \( 2.7 \times 10^{-4} m \)


The air pressure inside out body is equal to the \( _{--}-_{-} ? \)
A. in internal pressure
B. atmospheric pressure
c. both a and \( b \)
D. none of the above


State whether the statement is True or
False:

Two molecules can react only if they have a correct relative orientation.


Evaluate \( \int \frac{\boldsymbol{d x}}{\sqrt{\mathbf{2 a x}-\boldsymbol{x}^{2}}} \)


Water is filled upto height H units in a tank placed on the ground and whose side walls are vertical. A hole is made in
one of the vertical wall such that the emerging stream of water strikes the
ground at the maximum range. If the level in the tank is changing at the rate of R units per second, at that instant the
rate at which range will be changing will be:
A. R/2 units per second
B. R units per second
c. 2R units per second
D. zero


The remote sensing satellite is not used
for:
A. ground water surveys
B. crop yield surveys
c. television broadcasting
D. spying for military purposes


Le-chatlier principle is not applicable
for:
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
В. \( F e(s)+S(s) \rightleftharpoons F e S(s) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)


Find the inverse of the matrix \( \boldsymbol{A}= \) \( \left[\begin{array}{ll}1 & 2 \\ 1 & 3\end{array}\right] \) using elementry
transformations.


Which of the following option is the correct combination?
A. \( I, i v, S \)
в. \( I I I, i i, R \)
c. \( I V, I, P \)
D. \( I I I, \) iii, \( Q \)


Find the following product: \( \left(x^{3}-5 x^{2}+\right. \)
\( 3 x+1) \times\left(x^{2}-3\right) \)
A \( \cdot x^{5}-5 x^{4}+16 x^{2}-9 x+3 \)
B. \( x^{5}-5 x^{4}+16 x^{2}+9 x-3 \)
c. \( x^{5}+5 x^{4}+16 x^{2}-9 x-3 \)
D. \( x^{5}-5 x^{4}+16 x^{2}-9 x-3 \)


Amphoteric hydroxides react with both alkalies and acids.Which of the
following group 2 metal hydroxides is soluble in sodium hydroxide?
\( \mathbf{A} \cdot B e(O H)_{2} \)
в. \( R a(O H)_{2} \)
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( B a(O H)_{2} \)