Evaluate the following integral
\( \int \frac{\operatorname{cosec} x}{\log \tan \frac{x}{2}} d x \)


Which of the following is/ are property of non-metals?
(a) Non-metals are malleable.
(b) Non-metals are non ductile.
(c) Non-metals are brittle.
A \( \cdot \) a,
в. b,
\( c \cdot \) a,
\( D \cdot a, b, c \)


The resultant of two given vectors is minimum when angle between them is equal to
A \( .90^{\circ} \)
в. \( 0^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 60^{\circ} \)


If \( \boldsymbol{A}=(\mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}), \boldsymbol{B}=(\mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( \boldsymbol{B}-\boldsymbol{B} \)
\( A \cdot \phi \)
B . \{0\}
c. \{6,7\}
D. \{4\}


A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular hexagon. Magnitude of impulse applied at each
corner is:
A . \( m v \)
B. \( m v \sqrt{3} \)
c. \( \frac{m v}{2} \)
D. \( \frac{m v}{\sqrt{3}} \)


A nucleus \( _{11}^{24} N a \) is \( \beta \) -radioactive. What general name is given to the product nucleus with respect of \( _{11}^{24} \) Na?
A . isotope
B. isonucleus
c. isobar
D. isoelectron


Triiodomethane has antiseptic property
because of:
A. liberation of iodoform
B. liberation of free iodine
c. formation of phosgene gas
D. none of these


The precipitate of \( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}}=\mathbf{1 . 7} \times\right. \)
\( \left.10^{-10}\right) \) is obtained when equal volumes
of which of the following are mixed?
A \( \cdot 10^{-4} M C a^{+2}+10^{-4} M F^{-} \)
B . \( 10^{-2} M C a^{+2}+10^{-3} M F^{-} \)
c. \( 10^{-5} C a^{+2}+10^{-5} M F^{-} \)
D. \( 10^{-3} M C a^{+2}+10^{-5} M F^{-} \)


The number of ways to rearrange the
letters of the word CHEESE is
A . 119
в. 240
\( c .720 \)
D. 6


Consider the following statements regarding chemical equilibrium:
(1) For the gaseous reaction, the equilibrium can be established in open vessel.
(2) The state of equilibrium is dynamic
in nature.
(3) If the temperature is kept constant,
the colour of the reacting system changes with time. Which of the statements given above is /are correct?
\( A \)
B. 2
c. 3 only
D. 2 and 3 only


If \( \frac{x+3}{3}-\frac{x-2}{2}=1, \) then find \( p, x+ \)
\( 3-(p+2)=5 \)


The \( D . E \) of the family of concentric
circles with centre at origin is
A. \( x d x+y d x=0 \)
B. \( x=y \frac{d y}{d x} \)
c. \( \frac{d y}{d x}=\frac{y}{x} \)
D. \( \frac{d y}{d x}=\frac{x^{2}}{y^{2}} \)


If all the permutations of the letters in the word 'OBJECT' are arranged (and numbered serially) in alphabetical
order as in a dictionary, then the \( 717^{t h} \)
word is
A. толесв
в. тоЕлвс
c. тосле
D. толсве


The lattice energy of \( \mathrm{NaCl}(\mathrm{s}) \) using the following data will be:
heat of sublimation of \( N a(s)=S \)
\( (I E)_{1} \) of \( N a(g)=I \)
bond dissociation energy of \( C l_{2}(g)=D \)
electron affinity of \( C l(g)=-E \)
heat of formation of \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l}(\boldsymbol{s})=-\boldsymbol{Q} \)
A \( \cdot \) Lattice energy \( -U=S+I+\frac{D}{2}-E-Q \)
B. Lattice energy \( -U=S-I+\frac{D}{2}-E-Q \)
c. Lattice energy \( -U=S+I+\frac{D}{2}+E-Q \)
D. Lattice energy \( -U=S-I-\frac{D}{2}+E+Q \)


The largest algae is
A. Laminaria
B. Macrocystis
c. Nereocystis
D. Sargassum


The letters of the word \( C \) OC \( H I N \) are
permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of
words that appear before the word
COCHIN is


Compare \( C-O \) bond strength
amongst:
A \( \cdot C O>C O_{2}>C O_{3}^{2} \)
в. \( C O>C O_{3}^{2-}>C O_{2} \)
\( c \cdot C O_{3}^{2-}>C O_{2}>C O \)
D. \( C O<C O_{3}^{2-}<C O_{2} \)


On the pole of the Earth a body is
imparted velocity \( v_{0} \) directed vertically
up. Knowing the radius of the Earth and
the free-fall acceleration on its surface,
the height to which the body will ascend is given as \( h=\frac{R v_{0}^{2}}{x g R-v_{0}^{2}} . \) The air drag
is to be neglected. Find \( x \)


Let \( A \) be a square matrix of order 3 write the value of \( |2 A|, \) where \( |A|=4 \)


If \( f(x)=\log _{e}\left\{\frac{u(x)}{v(x)}\right\}, u(1)=v(1) \)
and \( u^{\prime}(x)=v^{\prime}(x)=2, \) then \( f^{\prime}(1) \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. none of these


In the calculation of \( R M S \) velocity in
\( c m / \)sec\( , \) the units of \( R \) should be in:
A . erg/mole \( -K \)
B. joules/mole - K
c. cals\( / \)mole \( -K \)
D. ergs


If \( \triangle A B C \) has differnence side length
\( a, b, c \) and \( a^{2}, b^{2}, c^{2} \) as side will again
form another \( \triangle P Q R, \) then \( \triangle A B C \) will
always be
A. Acute angle triangle only
B. Obtuse angle triangle only
c. Something Acute or something obtuse depending on value of \( a, b \) and \( c \)
D. None of these


Calculate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{6+x}-\sqrt{6-x}}{x} \)


In reverse osmosis the flow of solvent
molecules is from:
A. solution side to solvent side
B. solvent side to solution side
c. solvent molecules stay unmoving
D. none of these


The element symbol for hydrogen is:
\( A \cdot K \)
B.
c. не
D. Hn


A bag \( A \) contains 2 white and 3 red balls
and a bag \( B \) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bags and is found to be red. The probability that it was drawn from \( \operatorname{bag} B \) is \( \frac{25}{X}, \) then find the value of \( X \)


How does the total surface area of a box
change if Each dimension is doubled?
Express in words. Can you find the area if each dimension is multiplied \( n \) times?


\( \operatorname{Both}\left[N i(\mathbf{C O})_{4}\right] \) and \( \left[N i(C N)_{4}\right]^{2-} \) are
diamagnetic. The hybridization of nickel in these complexes, respectively, are:
\( \mathbf{A} \cdot \mathbf{s p}^{3}, \mathbf{s p}^{3} \)
\( \mathbf{B} \cdot \mathbf{s p}^{3}, \mathrm{dsp}^{2} \)
\( \mathbf{c} \cdot \mathrm{d} \mathbf{s} \mathrm{p}^{2}, \mathrm{sp}^{3} \)
D. \( \operatorname{dsp}^{2}, \operatorname{dsp}^{2} \)


Find the remainder when \( p(x)=x^{2}+ \)
\( 3 x+4 \) is divided by \( x+1 \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Aeroplanes are streamlined to reduce
friction
A . True
B. False


A proton, a deutron and an \( \alpha \) -particle with same kinetic energy enter perpendicularly in a uniform magnetic
field, then the ratio of radii of their
circular paths is
B . \( \sqrt{2}: 1: 1 \)
c. \( 1: \sqrt{2}: 1 \)
D. \( 1: 2: \sqrt{2} \)


The foot of the perpendicular from the
point \( \boldsymbol{A}(\mathbf{7}, \mathbf{1 4}, \mathbf{5}) \) to the plane \( \mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}- \)
\( z=2 \) is?
A. (3,1,8)
в. (1,2,8)
c. (3,-3,5)
D. (5,-3,-4)


Find the derivative of \( \boldsymbol{y}=\frac{1}{\boldsymbol{x}}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}}+ \)
\( \frac{\mathbf{3}}{\boldsymbol{x}^{\mathbf{3}}} \)


Which process is used for extraction of
Ag from silver coin?
A. Prake process
B. Cyanide process
c. Froth flotation
D. Monds process


The direction of acceleration due to
gravity depends:
A. on the direction of motion of a body
B. on the direction of motion of body's acceleration
c. on the direction of motion of body's velocity
D. none of these


Which of the following reasons states
that parathyroid is hormone is a
hypercalcemic hormone?
A. PTH also stimulates reabsorption of Ca2+ by the renal tubules
B. PTH increases Ca2+ absorption from the digested food
C. PTH control the metabolism of carbohydrates, proteins and fats
D. Both A and B


Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in \( \mathrm{km} / \mathrm{hr} \) )
is
A . 10
B. 18
\( c . \) 36
D. 72


How many among the following organisms hve linear ds DNA as their
genetic material? Homo sapiens, Escherichia coil Drosophila, \( \phi \times 174 \) bacteriophage
A . 1
B. 4
\( c .3 \)
D.


The graph drawn between presure and
volume in boyles law experiment is
shown in figure, then:
A \( \cdot T_{1}>T_{2} \)
в. \( T_{2}>T_{1} \)
\( c \cdot T_{1}=T_{2} \)
D. \( \frac{T_{1}}{T_{2}}=C \)


A body has a total charge of \( 6.4 \times 10^{-19} \)
coulomb. It is :
A. possible
B. not possible
c. may or may not be possible
D. Data insufficient


Which of the following group bear maximum number of elements?
\( \mathbf{A} \cdot 3^{r d} \) group
B. \( 2^{n d} \) group
c. \( 18^{\text {th }} \) group
D. \( 13^{\text {th }} \) group


Solve the equation for \( x \) \( \sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x, x \neq 0 \)


A simple harmonic motion has an amplitude \( A \) and time period \( T . \) Find the time required by it to travel directly from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\boldsymbol{A} / \mathbf{2} \)


Hypophysectomy leads to
\( \mathbf{A} \). Heart attack
B. Increased digestion
C. Death
D. Regression of reproductive function


The upper end of wire of radius \( 4 m m \)
and length \( 100 \mathrm{cm} \) is clamped and its
lower end is twisted through an angle of
\( 30^{0} . \) The angle of shear is:
A \( \cdot 18^{\circ} \)
B. 36
\( c \cdot 0.12 \)
D. 0.36


Equal masses of \( H_{2^{\prime}} O_{2} \) and methane
have been take in a contaier of volume
at temperature \( 27^{\circ} \mathrm{C} \) in identical
conditions. the ratio of the volume of
\( \operatorname{gases} H_{2}: O_{2}: \) methane would be:
A. 8: 16: 1
B . 16: 8: 1
c. 16: 1: 2
D. 8: 1: 2


Simplify: \( \sqrt[3]{\frac{216}{2197}} \)
\( A \cdot \frac{36}{27} \)
в. \( \frac{66}{23} \)
\( c \cdot \frac{6}{13} \)
D. None of the above


Anna went to the market to buy some
boxes to store things. She
was surprised to find boxes one inside
the other. They were \( \ldots \ldots \) boxes.
A. Not similar
B. Ambiguous
c. same size
D. similar


f \( \frac{129}{2000}=\frac{129}{2 m} \times 5 n \) find the values of
\( m \) and \( n \)


If \( \cos \alpha+\cos \beta=0=\sin \alpha+\sin \beta \)
then \( \cos 2 \alpha+\cos 2 \beta \) is equal to
A \( .-2 \sin (\alpha+\beta) \)
B. \( -2 \cos (\alpha+\beta) \)
\( \mathbf{c} \cdot 2 \sin (\alpha+\beta) \)
D. \( 2 \cos (\alpha+\beta) \)


If \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{1 0}}, \) then find
the concentration of the \( A g^{+} \) ion in a
saturated solution of \( A g C l ? \)
A \( \cdot 1.7 \times 10^{-10} M \)
В. \( 3.4 \times 10^{-10} M \)
c. \( 1.3 \times 10^{-5} M \)
D. 2.6 \( \times 10^{-5} M \)


\( \ln \mathbf{A P} a_{3}=\mathbf{2 1}, \boldsymbol{a}, \mathbf{3}=\mathbf{2 1}, \boldsymbol{a}_{\mathbf{1}} \mathbf{0}=\mathbf{6 3} \) find
\( \boldsymbol{a}_{\mathbf{5 0}} \)


There is \( 50 \% \) dimer formation of benzoic
\( \operatorname{acid}\left(C_{6} H_{5} C O O H\right) \) in benzene
solution.
\( 2 C_{6} H_{5} C O O H \rightleftharpoons\left(C_{6} H_{5} C O O H\right)_{2} \)
Hence the abnormal molecular weight of benzoic acid ( theoretical value \( =122 \)
\( \left.g m o l^{-1}\right) \) is:
A. \( 61 \mathrm{g} \) mol \( ^{-1} \)
B. 244 g mol-
c. \( 163 \mathrm{g} \) mol \( ^{-1} \)
D. 81 g \( m o l^{-1} \)


A coin is tossed repeatedly until it shows head. Let \( X \) be the number of
tosses required to get head. Write the probability distribution of \( \boldsymbol{X} \)


Consider the binary operation o defined
by the following tables on set \( \boldsymbol{S}= \)
\[
\{a, b, c, d\}
\]
\( \begin{array}{llll}\circ & \text { a } & \text { b } & \text { c } & \text { d }\end{array} \) \( \begin{array}{lllll}\mathrm{a} & \mathrm{a} & \mathrm{a} & \mathrm{a} & \mathrm{a} \\ \mathrm{b} & \mathrm{a} & \mathrm{b} & \mathrm{c} & \mathrm{d} \\ \mathrm{c} & \mathrm{a} & \mathrm{c} & \mathrm{d} & \mathrm{b} \\ \mathrm{d} & \mathrm{a} & \mathrm{d} & \mathrm{b} & \mathrm{c}\end{array} \)
Show that the binary operation is commutative. Write down the identitie
and list the inverse of elements.


Assertion
Nitric acid stains the skin
Reason
Nitric acid reacts with proteins to form yellow nitrated products is formed when the acid contacts epithelial cells of skin
giving it a stain.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is true about a solution that has \( [\boldsymbol{O H}]=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{8}} \)
M?
A. The pHis 8 and the solution is acidic
B. The \( \left[H^{+}\right]=1.0 \times 10^{-8} \mathrm{M} \) and the solution is basic
c. The pHis 6 and the solution is acidic
D. The \( \left[H^{+}\right]=1.0 \times 10^{-6} \mathrm{M} \) and the solution is basic
E . The \( \left[H^{+}\right]=1.0 \times 10^{-14} \mathrm{M} \) and the solution is neutral


Humidity is
A. The amount of air present in any region.
B. The amount of any liquid present in air.
C. The amount of water vapour present in air
D. The amount of elements and compound present in air.


As you have learnt in the text, a
geostationary satellite orbits the earth at a height of nearly \( 36,000 \mathrm{km} \) from the
surface of the earth. What is the
potential due to earth's gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth \( =6.0 \times 10^{24} k g, \) radius \( =6400 \)
\( \mathbf{k m} \)


The width of each of five continuous
classes in a frequency distribution is 5 and the lower class limit of the lowest
class is 10 The upper class limit of the highest class is
A . 25
B. 30
\( c .35 \)
D. 50


An insurance company issued 3000 scooters, 4000 cars and 5000 trucks.
The probabilities of the accident involving a scooter, a car and a truck are 0.02,0.03 and 0.04 respectively. One of the insured vehicles meet with an
accident. Find the probability that it is a
(i) scooter
(ii) car (iii) truck.


Use graphical method
Maximize: \( \boldsymbol{z}=\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \)
Subject to:
\( x+2 y \leq 40 \)
\( 6 x+5 y \leq 150 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


Calculate the degree of ionisation and \( p H \) of \( 0.05 \mathrm{M} \) solution of a weak base
having the ionization constant \( \left(\boldsymbol{K}_{c}\right) \) is \( 1.77 \times 10^{-5} . \) Also calculate the
ionisation constant of the conjugate acid of this base.


Assertion: Blue colour of sky appears
due to scattering of blue colour. Reason: Blue colour has shortest wave
length in visible spectrum.
A. both assertion and reason are true and reason is the correct explanation of assertion
B. both assertion and reason are true but the reason is not the correct explanation of assertion
c. assertion is true but reason is false
D. both the assertion and reason are false
E. reason is true but assertion is false


\( \operatorname{Let} A=\left|\begin{array}{ll}\mathbf{5} & \mathbf{0} \\ \mathbf{1} & \mathbf{0}\end{array}\right| \) and \( \boldsymbol{B}=\left|\begin{array}{ll}\mathbf{2 0} & \mathbf{5} \mid \\ -\mathbf{1} & \mathbf{0}\end{array}\right| \)
\( \mathbf{4} \boldsymbol{A}+\mathbf{5} \boldsymbol{B}-\boldsymbol{C}=\mathbf{0}, \) then \( \boldsymbol{C} \) is
\( \mathbf{A} \cdot\left|\begin{array}{cc}5 & 25 \\ -1 & 0\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{cc}120 & 25 \\ -1 & 0\end{array}\right| \)
\( \mathbf{c} \cdot\left|\begin{array}{cc}5 & -1 \\ 0 & 25\end{array}\right| \)
\( \mathbf{D} \cdot\left|\begin{array}{cc}5 & 25 \\ -1 & 5\end{array}\right| \)


Multipolar neuron means.
A. With one dendron and one axon
B. With many dendrons and one axon
c. With one dendron and no axons
D. With many dendrons and no axons


If \( \cos A=\frac{4}{5}, \cos B=\frac{12}{13}, \frac{3 \pi}{2}<A, B< \)
\( 2 \pi, \) find the values of the following.
\( (i) \cos (A+B) \)
(ii) \( \sin (A-B) \)


When a ray of light strikes a plane mirror along the normal, the angle of incidence is -
A . \( 90^{\circ} \)
B. zero
\( c \cdot 45 \)
D. none of these


The value of the dielectric constant at
room temperature \( (25 \mathrm{C}, \text { or } 77 \mathrm{F}) \) for air is
A. 1.00059
в. 2.00059
c. 0.0009
D. 0.00059


manometer M as shown. The stop cock
S controls the flow of air. AB is dipped
into a liquid whose surface tension is \( \sigma \)
On opening the stop cock for a while, a
bubble is formed at \( \mathrm{B} \) and the
manometer level is recorded, showing a
difference \( h \) in the levels in the two
arms. If \( \rho \) be the density of manometer
liquid and \( r \) the radius of curvature of
the bubble, then the surface tension \( \sigma \)
of the liquid is given by
\( \mathbf{A} \cdot \rho h r g \)
B. 2 phrg
c. 4 phrg
D. \( \frac{r h \rho g}{4} \)


A magnetic field directed along \( Z \) axis varies as \( \mathrm{B}=\mathrm{BO} \times \mathrm{aB}=\mathrm{BOxa} \) directed along
\( X \) axis, the induced emf (in volts) in the
loop is
A . 3
B . 2
\( c .5 \)
D. 6


Column I
( organic compounds ( products of
oxidised by \( H I O_{4} \) ) \( \left.H I O_{4} \text { oxidation }\right) \)


If the \( \operatorname{lines} 3 x-4 y-7=0 \) and \( 2 x- \)
\( 3 y-5=0 \) are two diameters of a circle
of area 154 square units, the equation of the circle is :
A. \( x^{2}+y^{2}+2 x-2 y-62=0 \)
B . \( x^{2}+y^{2}-2 x+2 y-62=0 \)
c. \( x^{2}+y^{2}-2 x+2 y-47=0 \)
D. \( x^{2}+y^{2}+2 x-2 y-47=0 \)


The \( 3^{r d} \) crest of a transverse wave from
its centre of disturbance is \( 32.4 \mathrm{cm} \)
away. The \( 6^{t h} \) crest of this wave is
\( 75.6 c m \) from its centre of disturbance.
a) Find the wave length of the wave.
b) If time period of a wave is \( 0.2 s, \) what
will be the velocity of the wave?


Using the information in the preceding problem, calculate the solubility
product of \( A g I \) in water at \( 25^{0} C \)
\( \left[\boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+}, \boldsymbol{A} \boldsymbol{g}}^{\boldsymbol{o}}=+\mathbf{0 . 7 9 9} \quad \boldsymbol{v o l t}\right] \)
A \( \cdot 1.97 \times 10^{-17} \)
В. \( 7.91 \times 10^{-17} \)
c. \( 1.79 \times 10^{-17} \)
D. \( 9.17 \times 10^{-17} \)


A ball is thrown from ground at an angle
\( \theta \) with horizontal and with an initial
speed \( u_{0} . \) For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when
it hits the ground for the first time is \( V_{1} \)
After hitting the ground, the ball rebounds at the same angle \( \theta \) but with
a reduced speed of \( u_{0} / \alpha . \) Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of
motion is \( 0.8 V_{1}, \) the value of \( \alpha \) is


The incorrect IUPAC convention is -
(May have one or more correct answers)
This question has multiple correct options
A. Heat gained by system +ve sign
B. Work done by system - ve sign
C. Work done on the system +ve sign
D. Heat gained by system -ve sign


Find the unknown value \( \boldsymbol{x}: \frac{\mathbf{5}}{\mathbf{1 3}}+\boldsymbol{x}= \)
\( \frac{5}{13} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{5}{13} \)
D. \( \frac{2}{13} \)


Which of the following is/are true about deformation of a material?
A. Deformation capacity of the plastic hinge and resilience of the connections are essential for goodd plastic behavior
B. Deformation capacity equations considering yield stress and gradient of moment
c. Different materials have different deformation capacity
D. All of the above


What is \( \boldsymbol{P H}_{3} \) ?


The focal length of an equiconvex lens is greater than the radius of curvature of any of the surfaces.Then the refractive index of the material of the lens is
A. greater than o but less than 1.5
B. greater than 1.5 but less than 2.0
c. greater than 2.0 but less than 2.5
D. greater than 2.5 but less than 3.0


Fill in the blanks with suitable words
A ray of light passes undeviated after
refraction from a thin lens when it is
incident at


The line drawn in the given figure
represents
A \( \cdot y=-3 x+4 \)
3. \( y=-\frac{1}{3} x+4 \)
c. \( y=\frac{1}{3} x-4 \)


When the temperature of body is equal to that of atmosphere, then
A. Heat transfer will take place between body and atmosphere
B. There is no exchange of heat
C. The body is in unstable equilibrium
D. None of the above


A rubber cord of length \( 40 \mathrm{cm} \) and area
of cross section \( 4 \times 10^{-6} \mathrm{m}^{2} \) is extended
by 10cm. If the energy gained is 20 joule young's modulus of rubber is
\( \mathbf{A} \cdot 10^{8} N m^{-2} \)
B . \( 2 \times 10^{8} \mathrm{Nm}^{-2} \)
\( \mathbf{c} \cdot 4 \times 10^{8} \mathrm{Nm}^{-2} \)
D. \( 1.5 \times 10^{6} N m^{-2} \)


The diagonals of a parallelogram are \( 2 \hat{i} \) and \( 2 \hat{j} \). What is the area of the parallelogram?
A. 0.5 unit
B. 1 unit
c. 2 unit
D. 4 unit


A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then
A. the weight of body will become zero
B. the weight of body will become infinite
c. the mass of the body will become zero
D. the body will vanish in air


A particle moving along a circular path
of radius \( 6 m \) uniform speed of \( 8 m s^{-1} \)
The average acceleration when the particle completes one half of the revolution is -
A \( \cdot \frac{16}{3 \pi} m / s^{2} \)
B. \( \frac{32}{3 \pi} m / s^{2} \)
c. \( \frac{64}{3 \pi} m / s^{2} \)
D. None of these


Assertion
Esterification is a process in which a sweet smelling substance is produced
Reason
When ester react with sodium
hydroxide an alcohol and sodium salt of
carboxylic acid are obtained.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statements is
not correct?
\( \mathbf{A} \cdot T i\left(N 0_{3}\right)_{4} \) is a colourless compound
B. \( \left.\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right)\right] \mathrm{Cl}_{3} \) is a coloured compound
\( \mathbf{C} \cdot K_{3}\left[V F_{6}\right] \) is a colourless compound
D \( \cdot\left[C u\left(N C C H_{3}\right)_{4}\right] B F_{4} \) is a colourless compound


If area bounded by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\frac{1}{3}}(\boldsymbol{x}-\mathbf{1}) \)
\( x- \) axis is \( A \) then find the value of \( 28 A \)
A . 5
B. 6
\( c \cdot 7 \)
D. 9


The percentage error in a measurement
of \( 6 m m \text { is } 0.1 \% \text { , the error is (in } m m) \)
A . 0.6
B. 0.06
c. 0.006
D. 0.001


The IUPAC name of the following
compound is:
A. 1-Phenylpropan-2-ol
B. 3-Phenylpropan-2-ol
c. 2-Hydroxypropylbenzene
D. None of these


Which of the following is not a gel?
A. cheese
B. Jellies
c. curd
D. Milk


Solve the following systems of equations graphically:
\( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6} \)
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)


Select the compound(s) having basicity
equal to 2
This question has multiple correct options
A. \( H_{2} S O_{4} \)
в. \( H_{3} P O_{4} \)
\( \mathrm{c} . H_{3} P O_{3} \)
D. \( H_{2} S_{2} O_{7} \)


Assume that a drop of water is spherical and its diameter is one tenth of a cm. A conical glass has equal height to its diameter of rim. If 2048000 drops of water fill the glass
completely then find the height of the glass


Probability \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 7}, \boldsymbol{P}(\boldsymbol{B})= \)
\( \mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3}, \) then \( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right) \) is
equal to
A . \( 0 . \)
в. 0.3
\( c .0 .2 \)
D. 0.4


Prove that \( \sqrt{3} \) is a irrational number.


If a measured quantity has \( n \) significant figures, the reliable digits in
it are :
\( A \cdot n \)
B. n-
\( c \cdot 2 n \)
D. n/2


The \( P^{H} \) of \( 10^{-3} M \) mono acidic base, if
it is \( 1 \% \) ionised is:
A . 5
B. 8
\( c \cdot 3 \)
D.


Match the following and choose the
correct option:
(A) Adipose tissue
(i) Nose
(B) Stratified epithelium
(ii) Blood
(C) Hyaline cartilage
(iii) Skin
(D) Fluid connective tissue
(iv) Fat storage
\( A \cdot A-(i) ; B-(i i), C-(i i i) ; D-(i v) \)
B. A- (iv); B- (iii), C- (i); D- (ii)
C \( . \) A- (iii); B- (i), C- (iv); D- (ii)
D. A- (ii); B- (i), C- (iv); D- (iii)


Assertion
Concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) reacts with \( \boldsymbol{K} \boldsymbol{C l} \)
to give \( C l_{2} \) gas.
Reason
\( H C l \) cannot be oxidised by
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. Both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion,
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion
c. Assertion is CORRECT, but reason is INCORRECT
D. Assertion is INCORRECT, but reason is CORRECT


A satisfactory photographic print is obtained at a distance of \( 2 \mathrm{m} \) from a 60
Cd lamp when the exposure time is 10 s. The time of exposure required for the same quality print at a distance \( 4 \mathrm{m} \) from a 120 Cd lamp is:
A. 5 s
B. 10 s
\( c \cdot 20 s \)
D. 25 s


Discuss the continuity of the following function at the indicated point(s):
\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{array}{l}|\boldsymbol{x}| \cos \left(\frac{1}{\boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0} \\ \mathbf{0}, \quad \boldsymbol{x}=\mathbf{0}\end{array} \quad, \text { at } \boldsymbol{x}=\mathbf{0}\right. \)


A force of \( 500 N \) acts on a square piece of plywood, each of whose sides is \( 5 m \)
long. Calculate the pressure acting on the piece of plywood.
A \( .500 \mathrm{Nm}^{-2} \)
B. \( 100 N m^{-2} \)
c. \( 2500 N m^{-2} \)
D. \( 20 N m^{-2} \)


The destruction of the biological nature and activity of proteins by heat or chemical agent is called as:
A. dehydration
B. denaturation
c. denitrogenation
D. deammination


Template theory suggests
A. Amino acids have to be activated
B. Acylation
C. Combination of amino acid with tRNA first
D. All of the above


The value of the intgral \( \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{a-\sin \theta}{a+\sin \theta}\right) d \theta, a>0 \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 5


The layers of cells lying between endodermis and vascular bundle is
A. cortex
B. Pith
c. Pericycle
D. Exodermis


An electron in \( 2^{n d} \) orbit gains energy
and goes to \( 4^{t h} \) orbit. What are the
difference in angular momentums experienced by the electron due to the transition?


f' \( \lambda^{\prime} \) for the vectors \( 2 i+3 j-4 k \& \)
\( 4 i-2 j+\lambda k \) are orthogonal is \( \frac{1}{m} \)


Product \( (A) \) and \( (B) \) in above reaction is
\( \begin{array}{c}o \\ o^{-}-S\end{array}-O-H, O^{-}-S-O-C H_{3} \)
в. \( \begin{array}{c}o \\ o^{-}-S_{-}^{\prime}\end{array}-\begin{array}{c}^{o} \\ _{o^{-}}\end{array} \)
\( c \)


You have to design a compound microscope with objective lens of focal length \( 1 \mathrm{cm} . \) The object should be placed at \( \ldots . . . \) distance from the lens.
\( A \cdot 8 m m \)
B. \( 11 \mathrm{mm} \)
c. \( 22 \mathrm{mm} \)
D. \( 2 \mathrm{cm} \)


Let \( \boldsymbol{y}=\boldsymbol{a} \cos (\log \boldsymbol{x})+\boldsymbol{b} \sin (\log \boldsymbol{x}) \) is a
solution of the differential equation \( \boldsymbol{x}^{2} \frac{d^{2} y}{d x^{2}}+\boldsymbol{x} \frac{d y}{d x}+\boldsymbol{y}=0 . \) Prove


Solve: \( 8 x+\frac{21}{4}=3 x+7 \)
A \( \cdot \frac{2}{9} \)
B. \( \frac{7}{20} \)
c. \( \frac{6}{17} \)
D. \( \frac{4}{21} \)


A motorboat, whose speed in \( 15 \mathrm{km} / \mathrm{hr} \)
in still water goes \( 30 \mathrm{km} \) downstream
and comes back in a total of 4 hours 30
minutes. The speed of the stream (in \( \mathrm{km} / \mathrm{hr}) \) is:


What is 'Green house effect'?


Write first four terms of the \( A P, \) when
the first term a and the common
difference d are given as follows:
\( (i) a=10 d=10 \)
(ii) \( a=-2, d=0-3 \)
(iii) \( a=4, d=-3 \)
(iv) \( a=-1, d=\frac{1}{2} \)
\( (v) a=-1, d=\frac{1}{2} \)


The circuit shown below acts as:
A. Tuned filter
B. Low pass filter
c. High pass filter
D. Rectifier


Solve the differential equation:
\( \cos x \frac{d y}{d x}+y=\sin x \)


The critical angle of a certain medium is \( \sin -1(35) \sin -1(35) \) The polarizing
angle of the medium is:
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{4}{5}\right) \)
B. \( \tan ^{-1}\left(\frac{5}{3}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{3}{4}\right) \)
D. \( \tan ^{-1}\left(\frac{4}{3}\right) \)


What are the main postulates of kinetic molecular theory of gases?


A prism of refractive index \( \sqrt{2} \) has
refracting angle \( 60^{\circ} \) answer the
question Angle of minimum deviation is:
A \( .45^{\circ} \)
B. 90
\( c \cdot 30 \)
D. none


The ozone layer in earth's atmosphere is crucial for human survival because it
A. Has ions
B. Reflects radio signals
C. Reflects ultraviolet rays
D. Reflects infrared rays


A point particle of mass \( 0.1 k g \) executing SHM with amplitude of \( 0.1 m \) When the particle passes through the mean position is \( \mathrm{KE} \) is \( 8 \times 10^{-3} \mathrm{J} \)
Obtain the equation of motion of this particle if the initial phase of oscillation
is \( 45^{\circ} \)


Pressure over ideal binary liquid
mixture containing 10 moles each of liquid \( A \) and \( B \) is gradually decreased
isothermally. If \( P_{A}^{\circ}=200 m m H g \) and
\( P_{B}^{\circ}=100 m m H g, \) the pressure at
which half of the liquid is converted into
vapour is:
A. \( 150 \mathrm{mm} \) Hg
в. \( 166.5 \mathrm{mm} \) ну
c. \( 133 \mathrm{mm} \) нg
D. 141.4 mm нg


Using long division method, divide the polynomial \( 20 x^{2}-32 x-16 ; 5 x+2 \)
A \( .4 x+8 \)
B. \( 4 x-6 \)
c. \( 4 x-3 \)
D. \( 4 x-8 \)


Find the value of unknown \( x \) in the
following diagram


f \( \triangle A B C \sim \triangle A D E \) and ar \( (\triangle A D E)= \)
\( 9 \operatorname{ar}(\triangle A B C) \) then \( \frac{B C}{D E} \) is equal to
\( A \)
B. 1
\( c \cdot \frac{3}{4} \)
D. None of these


Many factors are responsible for the reactivity and chemical behavior of an
atom. Which one is the most important
factor?
A. The number of protons in the atom's nucleus
B. The number of neutrons in the atom's nucleus
c. The number of protons and neutrons in the atom's nucleus
D. The ratio of protons to neutrons in the atom's nucleus
E. The number of electrons in the atom's valence shell


A ball (solid sphere) of mass \( m \) is
rolling on a smooth horizontal surface
as shown in figure. At an instant the
magnitude of the velocity of the centre
of mass is \( v_{0} \) and its angular velocity is \( \omega \frac{v_{0}}{2 R}, \) where \( R \) is the radius of the ball.
The total kinetic energy of the rolling
ball at this instant is:-
\( \mathbf{A} \cdot \frac{7}{5} m R^{2} \omega_{0}^{2} \)
B. \( \frac{11}{5} m R^{2} \omega_{0}^{2} \)
\( c \)
D.


Choose the correct statement.
A. Polar molecules have permanent electric dipole moment
B. \( C O_{2} \) molecule is a polar molecule
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{O} \) is a non-polar molecule
" The dipole field at large distances falls of as \( \frac{1}{r^{2}} \)
E. The dipole moment is a scalar quantity


Identify the principal quantum number for the last electron that is added to
sodium?
A.
B. 2
\( c \cdot 3 \)
D. 5
E. 4


n \( \triangle A B C, \angle A B C=90^{\circ}, A D= \)
\( D C, A B=12 \mathrm{cm} \) and \( B C=6.5 \mathrm{cm} \)
Find the area of \( \triangle A D B \)


Streamline flow are more likely for liquids with
A. High density and low viscosity
B. Low density and high viscosity
c. High density and high viscosity
D. Low density and low viscosity


If the function \( f \) is continuous at \( x=0 \)
find \( \boldsymbol{f}(\mathbf{0}) \)
where \( \boldsymbol{f}(\boldsymbol{x})=\frac{\cos 3 \boldsymbol{x}-\cos \boldsymbol{x}}{\boldsymbol{x}^{2}}, \boldsymbol{x} \neq \mathbf{0} \)


Define collision frequency. Give an example for Pseudo-first order reaction.


Assign oxidation number to the
underlined element in \( \boldsymbol{H}_{4} \underline{\boldsymbol{P}}_{2} \boldsymbol{O}_{7} \)


A ball of mass \( 5 k g \) experience a force
\( F=2 x^{2}+x . \) Work done in displacing
the ball by \( 2 \mathrm{m} \) is then
A \( \cdot \frac{22}{3} J \)
в. \( \frac{44}{3} J \)
c. \( \frac{32}{3} J \)
D. \( \frac{16}{3} J \)


If \( P(x, y, z) \) is a point on the line segment joining \( A(2,2,4) \) and \( B(3,5,6) \) such that projection of \( \overline{O P} \) on axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \) respectively, then \( P \) divide \( A B \) in the ratio
A .3: 2
B. 2: 3
c. 1: 2
D. 1: 3


Find the area of the following parallelogram


Which among the following is/ are
correct for a first order reaction?
This question has multiple correct options
A. The degree of dissociation is equal to \( \left(1-e^{-k t}\right) \)
B. A plot of reciprocal concentration of the reactant vs time gives a straight line.
C. The time taken for the completion of 75\% reaction is thrice the \( t_{1 / 2} \) of reaction.
D. The pre-exponential factor in the Arrhenius equation has the dimension of time, \( T^{-1} \)


The equilibrium constants for the
reactions are
\[
\begin{array}{l}
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \stackrel{\boldsymbol{K}_{1}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} ; \boldsymbol{K}_{1} \\
\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} \stackrel{\boldsymbol{K}_{2}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{2} \\
\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \stackrel{\boldsymbol{K}_{3}}{\rightleftharpoons} \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{3}
\end{array}
\]
The equilibrium constant for,
\[
\boldsymbol{H}_{3} \boldsymbol{P O}_{4} \rightleftharpoons \mathbf{3} \boldsymbol{H}^{+}+\boldsymbol{P O}_{4}^{3-} \text { will }
\]
be:
\( \mathbf{A} \cdot K_{1} / K_{2} K_{3} \)
B. \( K_{1} \times K_{2} \times K_{3} \)
\( \mathbf{c} \cdot K_{2} / K_{1} K_{3} \)
\( \mathbf{D} \cdot K_{1}+K_{2}+K_{3} \)


The decrease in the freezing point of an aqueous solution of a substance is
\( 1.395 k \) and that in the
freezing point of benzene solution of
the same substance is \( 1.280 k . \) Explain
the difference in \( \Delta T \).
The substance:
A. dissociates in the aqueous solutio as well as in the benzene solution
B. forms complex in solution
c. associates in the benzene solution
D. dissociates in the aqueous solution and not in the benzene solution


Lanthanoids are
A. 14 elements in the sixth period(atomic number \( =90 \) to
103) that are filling 4f-sublevel
B. 14 elements in the seventh period(atomic number \( =90 \) to 103 ) that are filling \( 5 f \) -sublevel
C. 14 elements in the sixth period(atomic number \( =58 \) to
71) that are filling \( 4 f \) -sublevel
D. 14 elements in the seventh period(atomic number \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel


Scientific name of plants are mostly derived from which of the following language?
A. Greek
B. French
c. sanskrit
D. Latin


Which one is an example of wood fibres?
A. Hemp
B. Flax
c. cotton
D. zingiber.


In birds, excretion of nitrogenous wastes, mainly as uric acid, is helpful
for
A . eliminating excess body water
B. conserving body water
c. eliminating excess body heat
D. eliminating excess sugar


Which of the following is not a locomotory organelle of protozoans
A. Pseudopodia
B. cilia
c. Flagella
D. Parapodia


If two sets \( A \) and \( B \) are having 39
elements in common, then the number
of elements common to each of the sets
\( A \times B \) and \( B \times A \) are
\( \mathbf{A} \cdot 2^{3} \)
в. \( 39^{2} \)
c. 78
D. 35


Explain fuel-cell in detail.


The equation of the image of the circle \( x^{2}+y^{2}-6 x-4 y+12=0 \) by the
line mirror \( \boldsymbol{x}+\boldsymbol{y}-\mathbf{1}=\mathbf{0} \) is
A \( \cdot x^{2}+y^{2}+2 x+4 y+4=0 \)
B . \( x^{2}+y^{2}-2 x+4 y+4=0 \)
c. \( x^{2}+y^{2}+2 x+4 y-4=0 \)
D. \( x^{2}+y^{2}+2 x-4 y+4=0 \)


A metal wire of length I, area of crosssection A and Young's modulus Y behaves as a spring of spring constant k given by.
A \( \cdot k=\frac{Y A}{l} \)
B. \( k=\frac{2 Y A}{l} \)
c. \( _{k}=\frac{Y A}{2 l} \)
D. \( k=\frac{Y l}{A} \)


The molar heat of combustion of \( C_{2} H_{2} \)
carbon and hydrogen are -1300 kJ, -393.5 kJ and -282.6 kJ respectively. The enthalpy of \( C_{2} H_{2} \) in kJ mol \( ^{-1} \) is:
A. 620.3
B. -226.8
c. +226.8
D. 1980


Pericarp and petals contain
A. Chloroplast
B. Chromoplast
c. Leucoplast
D. Etioplast


Explain the following reactions of
chloroform:
(i) Effect of air and sunlight,
(ii) Reimer
Tiemann reaction.


\( \operatorname{Let} A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right] \) and \( B=A^{10} \)
Then the sum of elements of the first
column of \( \boldsymbol{B} \) is


Stem and leaves of bryophyta plants are
A. Analogous to stem and leaves of higher plants
B. Homologous to stem and leaves of higher plants
C. Both analogous and homologus
D. None of the above


The equilibrium \( 2 C u^{+} \rightleftharpoons C u^{0}+C u^{2+} \)
in aqueous medium at \( 25^{0} \mathrm{C} \) shifts towards the left in the presence of This question has multiple correct options
A \( . N O_{3}^{-} \)
в. \( C l \)
c. \( S C N^{-} \)
D. \( C N^{-} \)


is the unit for the rate
of a chemical reaction.
A. Mole \( I^{-1} \) s
B. Mole \( \left.\right|^{-1} \mathrm{s}^{-1} \)
c. Mole I s
D. Mole \( 1^{-1} \)


Find the number of photons of radiation of frequency \( 5 \times 10^{13} s^{-1} \) that must be
absorbed in order to melt one gm ice when the latent heat of fusion of ice is
\( 331.5 j / g \)
A \( \cdot 10^{2} \)
2
B. \( 10^{25} \)
\( c \cdot 10^{28} \)
D. \( 10^{35} \)


Of the following metals, the most reactive metal is:
A . \( F e \)
в. \( N i \)
\( c \cdot P t \)
D. \( A u \)


Prove that \( \left|\begin{array}{lll}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}^{\prime}+\boldsymbol{b}^{\prime} \boldsymbol{c} & \boldsymbol{b}^{\prime} \boldsymbol{c}^{\prime} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a}^{\prime}+\boldsymbol{c}^{\prime} \boldsymbol{a} & \boldsymbol{c}^{\prime} \boldsymbol{a}^{\prime} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{b}^{\prime}+\boldsymbol{a}^{\prime} \boldsymbol{b} & \boldsymbol{a}^{\prime} \boldsymbol{b}^{\prime}\end{array}\right|= \)
\( \left(\boldsymbol{a} \boldsymbol{b}^{\prime}-\boldsymbol{a}^{\prime} \boldsymbol{b}\right)\left(\boldsymbol{b} \boldsymbol{c}-\boldsymbol{b}^{\prime} \boldsymbol{c}\right)\left(\boldsymbol{c} \boldsymbol{a}^{\prime}-\boldsymbol{c}^{\prime} \boldsymbol{a}\right) \)


Which of the following quantities is scalar?
A. Dipole moment
B. Electric force
c. Electric field
D. Electric potential


A conductor \( A \) is given a charge of
amount \( +\mathrm{Q} \) and then placed inside a deep metal cab \( \mathrm{B} \), without touching it:
This question has multiple correct options
A. the potential of A does not change when it is placed inside
B. if B is earthed, \( +Q \) amount of charge will flow from it into the earth
\( \mathrm{C} \). if \( \mathrm{B} \) is earthed, the potential of \( \mathrm{A} \) will be reduced
D. either(b) or (c) are true, or both are true only if the outer surface of B is connected to the earth and not its
inner surface


\( N H_{3} \) releases during which of the following process?
A. Photorespiration
B. Dark respiration
c. сАм
D. All of the above


Determine the values of \( \mathrm{m} \) and \( n \) so that
the following system of linear equations have infinite number of solutions:
\( (2 m-1) x+3 y-5=0 \)
\( 3 x+(n-1) y-2=0 \)


In a Youngs interference experimental
arrangement the incident yellow light is composed of two wavelength \( 5890 A \) and 5895 A. The distance between the
slits is \( 10^{-3} m \) and the screen is-placed
1 \( m \) away. Upto what order can fringes be seen on the screen? And how far from
the centre of the screen does this
occur?


How is it possible to detect the filling of a bottle under a water tap by hearing the sound at a distance?


If you want to hear a train approaching
from far away, it is more convenient to
put the ear to track because
A. it is more convenient to put the ear to the track
B. it is more convenient to put the ear away from the track
c. both can be true
D. none is true


The bond present in \( C H_{4} \) is :
A . covalent
B. ionic
c. hydrogen
D. Van der Waals


The lines \( 2 x-3 y=5 \) and \( 3 x-4 y=7 \)
intersect at the center of the circle
whose area is 154 sq. units, then equation of circle is
A \( \cdot x^{2}+y^{2}-2 x+2 y=47 \)
B. \( x^{2}+y^{2}+2 x-2 y=31 \)
c. \( x^{2}+y^{2}-2 x-2 y=47 \)
D. \( x^{2}+y^{2}-2 x-2 y=31 \)


\( \mathbf{f} \boldsymbol{z}=\left|\begin{array}{ccc}\mathbf{3}+\mathbf{3} \boldsymbol{i} & \mathbf{5}-\boldsymbol{i} & \mathbf{7}-\mathbf{3} i \\ \boldsymbol{i} & \mathbf{2} \boldsymbol{i} & -\mathbf{3} i \\ \boldsymbol{3}-\mathbf{2} \boldsymbol{i} & \mathbf{5}+\boldsymbol{i} & \mathbf{7}+\mathbf{3} \boldsymbol{i}\end{array}\right| \), then
A. z is purely real
B. z is purely imaginary
\( c \cdot 0 \)
D. none of these


If \( 27=a^{3}, \) find the value of \( a \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


\( \int \frac{t^{2}}{t^{3}+1} d t= \)


The transpose of a column matrix is
A. zero matrix
B. diagonal matrix
c. column matrix
D. row matrix


Find coefficient of \( x^{4} \) in \( \left(1+x+x^{3}+\right. \)
\( \left.\boldsymbol{x}^{4}\right)^{10} \)


The sequence \( -10,-6,-2,2, \dots \dots \)
\( \mathbf{A} \cdot \) is an \( A \cdot P ., \) Reasons \( d=-16 \)
B. is an \( A . P ., \) Reasons \( d=4 \)
C. is an \( A \).P., Reasons \( d=-4 \)
D. is not an \( A . P \)


Scattering of light occurs when a beam of light is passed through?
A. Bloodd
B. water
c. copper sulphate solution
D. Brine


Which of the following reagent is used for the separation of acetaldehyde from acetophenone?
A. \( N H_{2} O H \)
B. \( N a O l \)
c. Tollen's reagent
D. \( C_{6} H_{5} N H N H_{2} \)


If displacement \( s \) at time \( t \) is \( s=t^{3}- \) \( 3 t^{2}-15 t+12, \) then acceleration at
time \( t=1 \) sec is
A \( \cdot \) 6units \( / \) sec \( ^{2} \)
B. - 6units/sec \( ^{2} \)
\( c \cdot 0 \)
D. 4units \( / \)sec\( ^{2} \)


Mitosis usually results in the production of diploid daughter cells with identical genetic complement.


Which of the following contains olefinic bond.
A . Citric acid
B. Malic acid
c. Fumaric acid
D. Ethylene chloride


\( \int \frac{\cos x}{\sqrt[3]{\sin ^{2} x}} d x= \)
A \( \cdot 3 \sqrt[3]{\sin x}+c \)
B. \( 3 \sqrt[3]{\sin ^{2} x}+c \)
c. \( \sqrt[3]{\sin x}+c \)
D. \( \sqrt[3]{\sin ^{2} x}+c \)


A particle has an initial velocity of \( 3 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s} \) and a constant
acceleration of \( (4 \hat{i}-3 \hat{j}) m / s^{2} . \) Its
speed after one second will be equal to:
A. 0
B. \( 7 \sqrt{2} \frac{m}{s} \)
c. \( \sqrt{50} \frac{m}{s} \)
D. 25 m/sec


Percentage of land covered by forests in India is
A . 9-18\%
B . 18-27\%
c. 27-36\%
D. More than 50\%


Assertion
Gaussian surface is considered
carefully.
Reason
The point where electric field to be
calculated should be within the surface.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


If \( P(E)=0.05, \) what is the probability of
"not E" ?


Assertion
Reptiles and amphibians show
metachrosis.
Reason
They have neurohormones in their skin.
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 value of ' \( a \) ' so that the curves \( y= \) \( 3 e^{x} \) and \( y=\frac{a}{3} e^{-x} \) are perpendicular to
each other:
A \( \cdot \frac{1}{3} \)
B. - 1
\( c .3 \)
D.


A player caught a cricket ball of mass
\( 150 g \) moving with \( 20 \mathrm{ms}^{-1} . \) If the
catching process is complete in 0.1 sec This question has multiple correct options
A. Force exerted by the ball on the hand of player is \( 30 N \)
B. Force exerted by the ball on the hand of players is 40 N
c. Impulse of the ball is \( 3 N-S \)
D. Force exerted by the ball on the hand of players is 50 N


Assertion
Ammonia is a compound.
Reason
Ammonia \( \left(N H_{3}\right) \) consists of molecules
of two different elements, nitrogen and hydrogen, bonded together.
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


List I
A. Van Arkel's \( \quad \) 1. Refining of silver method
B. Solvay process
2. Purification of titanium
3. Manufacture of
C. Cupellation
\[
N a_{2} C O_{3}
\]
4. Purification of copper
D. Poling
Match List I with List II select the
correct answer using the codes gives
below the lists:
A . A-2, B-1, C-3, D-4
B. \( A-4, B-3, C-2, D-5 \)
c. \( A-2, B-3, C-1, D-4 \)
D. A-5, B-1, C-3, D-4


Find the position vector of the midpoint of the vector joining the points \( P(2,2,4) \) and \( Q(4,1,-2) \)


The persistence of sound in a closed enclosure, due to continuous reflections
at the walls, even after the source has
stopped producing sound is known as:
A. The persistence of hearing
B. An echo
c. Reverberation
D. The ultrasounds


What is the area of the region bounded by \( \mathrm{X} \) -axis, the curve \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and the two ordinates \( x=\frac{1}{2} \) and \( x=1 ? \)
A \( \cdot \frac{5}{12} \) sq unit
B. \( \frac{5}{6} \) sq unit
c. \( \frac{7}{6} \) sq unit
D. 2 sq unit


Give possible expressions for the length and breadth of the rectangle whose area is \( 3 x^{2}-8 x+5 \)


In \( \Delta A B C, \) if \( \angle A=35^{\circ} \) and \( \angle B=65^{\circ} \)
then the longest side of the triangle is :
A . AC
B. AB
c. вс
D. None of these


The radius of a circular plot is \( 56 \mathrm{m} \). How much will it cost to fence the plot with 4 rounds of wire at the rate of Rs. 40 per meter ?


Simplify the following \( : i^{457} \)


Position vector that defines position of
vector in three dimensions having
formula of
A \( \cdot \sqrt{\left(a^{2}+b^{2}+c^{2}\right)} \)
B. \( \sqrt{(a+b+c)} \)
C \( \cdot \sqrt{\left(a^{2}-b^{2}+c^{2}\right)} \)
D. \( \left(a^{2}+b^{2}+c^{2}\right) \)


One millimole \( O_{2} \) gas is dissolved in
\( \mathbf{5 4 0 0} \mathrm{ml} \) water at \( 25^{\circ} \mathrm{C} \). Calculate the
Henry's law constant \( \boldsymbol{K}_{\boldsymbol{H}} \) for this
solution. \( p_{O_{2}}=2 \times 10^{-8} \) bar.


For the reaction \( 4 N H_{3}+5 O_{2} \rightarrow \)
\( 4 N O+6 H_{2} O, \) the rate of reaction with
respect to \( N H_{3} \) is \( 2 x 10^{-3} M s^{-1} . . \) Find
the rate of the reaction with respect to
oxygen in \( M s^{-1} \)


The synaptonemal complex first
appears at
A. Leptotene
B. Pachytene
c. zygotene
D. Diplotene


Hydroponics is growing plants in
A. water
B. Soil culture
c. Solution of mineral nutrients
D. Tissue culture medium


The unit of an electrical parameter
whose formula is \( \left[M^{1} L^{2} T^{-3} A^{-2}\right] \) is:
A. ohm
B. ampere
c. volt
D. newton


Evaluate: \( \int \tan ^{-1} \sqrt{x} d x \)


The electric field of an electromagnetic
wave in free space is given by \( \vec{E} 10 \cos \left(10^{7} t ! k x\right) \hat{j} V / m \) where \( t \) and \( x \)
are in seconds and metres respectively. It can be iferred that
(i) the wavelength \( \% \) is \( 188.4 \mathrm{m} \)
(ii) the wave number \( k \) is 0.33 rad/m
(iii) the wave amplitude is \( 10 \mathrm{V} / \mathrm{m} \)
(iv) the wave is propagating along \( +x \) direction
Which one of the following pairs of
statements is correct?
A . (iii) and (iv)
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iii)


Define corrosion. What is meant by
rust? Write the chemical formula of
rust.


What is the blending theory of
inheritance?
A. Mendels theory of how the traits of parents are passed to offspring through the gametes
B. Darwins theory of how traits are passed from all parts of the parents body into the gamete to be transmitted to the offspring
C. The modern theory of how genetic information is passed from parents to offspring
D. An old theory that said that offspring show traits intermediate between those of the parents


Find the mean from the following frequency distribution of marks at a test in class.
Maks
10
;
No. of students
76
\[
(f)
\]


Fresnel diffraction is produced due to light rays falling on a small obstacle.
The intensity of light at a point on a screen beyond an obstacle depends on:
A. the focal length of lens used for observation
B. the number of half-period zones that superpose at the point
c. the square of the sum of the number of half period zones
D. the thickness of the obstacle


It is not possible to construct a triangle
with which of the following sides?
A. \( 8.3 \mathrm{cm}, 3.4 \mathrm{cm}, 6.1 \mathrm{cm} \)
B. \( 5.4 \mathrm{cm}, 2.3 \mathrm{cm}, 3.1 \mathrm{cm} \)
c. \( 6 \mathrm{cm}, 7 \mathrm{cm}, 10 \mathrm{cm} \)
D. \( 3 \mathrm{cm}, 5 \mathrm{cm}, 5 \mathrm{cm} \)


There are two parallel lines,one of which
has the equation \( 3 x+4 y=2 . \) If the
lines cut an intercept of length 5 on the
line \( x+y=1 \) then the equation of the
other line is
A \( \cdot_{3 x+y}=\frac{\sqrt{6}-2}{2} \)
в. \( 3 x+4 y=\frac{\sqrt{6}-2}{2} \)
c. \( 3 x+4 y=7 \)
D. none of these


An electronic transition from \( M \) shell
\( =3 \) to \( K \) shell \( (n=1) \) takes place in a hydrogenatom. Find the wavelength of radiation emited. \( \left(R=109,677 \mathrm{cm}^{-1}\right) \)
A \( \cdot 1026 A^{\circ} \)
\( ^{\circ} \)
B . \( 1.026 \times 10^{-5} \mathrm{m} \)
c. \( 1.026 \times 10^{-3} \mathrm{cm} \)
D. none of these


Using toothpaste in daily life is the example of
A. acidic reaction
B. basic reaction
c. neutralization reaction
D. none of these


(i) In Searle's experiment, after every step of loading, one waits for sometime
\( (2 \text { or } 3 \text { min }) \) before taking reading.
(ii) In this duration, the wire becomes free from kinks.
A. Both (i) and (ii) are true and
(ii) is reason for (i)
B. Both (i) and (ii) are true but (ii) is not reason for (i)
c. only (i) is true
D. Only (ii) is true


Systematics or Taxonomy
means
A. Identification
B. Nomenclature
c. classification
D. All of the above


Prove that:
\( \cot ^{2} \frac{\pi}{6}+\operatorname{cosec} \frac{5 \pi}{6}+3 \tan ^{2} \frac{\pi}{6}=6 \)


Give appropriate terms for the onset of
reproduction phase in a female.


The co-ordinates of the point of intersection of the diagonals of the square ABCD is (1,7)

If true then enter 1 and if false then
enter 0


The constant of proportionality which relates energy to the frequency of electromagnetic radiation is Planck's constant and its value is :
A \( \cdot 06.62 \times 10^{-34} J s \)
B. \( 3.1 \times 10^{-31} J s \)
\( \mathbf{c} \cdot 6.67 \times 10^{23} J s \)
D. none of these


Which glycosidic linkage is present in Maltose?
A \( \cdot \alpha-D-(+)-g l u \operatorname{cose}\left(C_{1}\right)-O-\left(C_{2}\right)-\beta-D- \)
\( (-)-g l u c o s e \)
B. \( \beta-D-(+)-g l u \operatorname{cose}\left(C_{1}\right)-O-\left(C_{4}\right)-D-(+)- \)
glucose
c. \( \alpha-D-(+)-g l u c o s e\left(C_{1}\right)-O-\left(C_{4}\right)-D-(+) \)
glucose
D. \( \beta-D-(+)-g l u \operatorname{cose}\left(C_{1}\right)-O-\left(C_{4}\right)-D-(-)- \)
glucose


Out of \( C \) and \( C O, \) which is a better
reducing agent at \( 673 K ? \)


The mean sand standard deviation of
marks obtained by 50 students of a class in three subjects Mathematics, Physics and chemistry are given below:
Subject Mathematics Fhysics
Mean \( \quad 42 \)
Standard 12 deviation
Which of the three subjects shows the highest variability in marks and which shows the
lowest?


Crystalline form of Sulphur is:
A . plastic sulphur
B. colloidal sulphur
c. monoclinic sulphur
D. All of these


calorie \( ^{\circ} \boldsymbol{C}^{-1}= \)
\( \mathbf{A} \cdot^{\circ} C^{-1} \)
\( 4.8 J K^{-1} \)
B . \( ^{\circ} C^{-1} \)
\( 4.2 J K^{-1} \)
c. \( 1000 C a l \)
D. All


If \( a, b, c \) are in \( A . P . \) and \( P \) is the \( A . M . \)
between \( a \) and \( b, \) and \( q \) is the \( A . M \)
between \( b \) and \( c, \) show that \( b \) is the
A. \( M . \) between \( p \) and \( q \)


A progressive wave is represented by \( y= \) \( 12 \sin (5 t-4 x) \mathrm{cm} . \) On this wave, how far
away are the two points having phase
difference of \( 90^{\circ} ? \)
A \( \cdot \frac{\pi}{2} c m \)
в. \( \frac{\pi}{4} c m \)
с. \( \frac{\pi}{8} \mathrm{cm} \)
D. \( \frac{\pi}{16} \mathrm{cm} \)


A non ideal solution was prepared by
mixing \( 30 \mathrm{ml} \) chloroform and \( 50 \mathrm{ml} \) acetone. The volume of mixture will be :
\( A \cdot>80 m l \)
в. \( <80 m l \)
\( \mathrm{c} .=80 \mathrm{ml} \)
\( D>80 m l \)


Solve: \( \int \frac{5 x-2}{1+2 x+3 x^{2}} \cdot d x \)


Two solutions of \( K N O_{3} \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) are prepared
seperately.The molarity of both is \( 0.1 M \)
and osmotic pressure is \( \boldsymbol{P}_{1} \) and \( \boldsymbol{P}_{2} \) respectively. The correct relationship between the
osmotic pressure is :
A \( \cdot P_{2}>P_{1} \)
В. \( P_{1}=P_{2} \)
\( \mathbf{c} \cdot P_{1}>P_{2} \)
D. \( \frac{P_{1}}{P_{1}+P_{2}}=\frac{P_{2}}{P_{1}+P_{2}} \)


During the rocket propulsion, gases ejecting with velocity \( 1 k m / s \) relative to
rocket. The rate of fuel consumption is \( \frac{\boldsymbol{m}}{\mathbf{1 0}} \boldsymbol{k g} / \boldsymbol{s}, \) where \( \boldsymbol{m} \) is the instantaneous
mass of the rocket. If air resistance
varies according to equation \( \boldsymbol{f}= \) \( 0.15 m v, \) then terminal velocity of the
rocket is:-
A. \( 300 \mathrm{m} / \mathrm{s} \)
в. \( 600 \mathrm{m} / \mathrm{s} \)
c. \( 7.92 \mathrm{m} / \mathrm{s} \)
D. \( 11.2 \mathrm{m} / \mathrm{s} \)


The amount of a chemical substance is
reported as
A. mole
B. mass
c. volume
D. density


Which of the following applications
illustrates that evaporation leads to
cooling?
A. Perspiration in human body
B. Transpiration in leaves
c. water in earthern post
D. All of the above


Velocity of light is same in all media. (State True or False)
A. True
B. False
c. Nither
D. Either


Which of the following soil is transported by wind?
A. Alluvial
B. Aerial
c. Eolian
D. Glacial


\( -\frac{2}{5} \)
\( \frac{10}{10} \)
0.4


Breathing movement can be estimated by This question has multiple correct options
A. Spirometer
B. Sphygmomanometer
c. Respirometer
D. None of the above


Differentiate between the 'Budding of Hydra' and 'Binary fission of Amoeba'.


The total number of lone pair of electrons in the given molecule is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Which of the event listed below is not
observed during mitosis?
A. Chromatin condensation
B. Movement of centrioles to opposite poles
c. Appearance of chromosomes with two chromatids joined together at the centromere
D. crossing over


The number of nonzero diagonal
matrices of order 3 satisfying \( A^{2}=A \) is


From the adjoining figure, calculate the
values of \( \boldsymbol{a} \)
A \( \cdot 46^{\circ} \)
B. 38
\( c \cdot 56^{\circ} \)
D. none of the above


The addition of electrons in an atom is
called
A. reduction
B. fusion
c. magnetization
D. None of these


Ammonia burns with oxygen to give


Calculate the total number of electrons
present in \( 18 m L \) of water


The correct order of \( K_{b} \) value of
following is:
\( \left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \ddot{\boldsymbol{N}} \boldsymbol{H}, \boldsymbol{N} \boldsymbol{H}_{3}, \ddot{\boldsymbol{N}}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{3} \)
\( \mathbf{A} \cdot 1>2>3 \)
В. \( 1>3>2 \)
c. \( 3>2>1 \)
D. \( 3>1>2 \)


The current in LCR circuit is maximum
when :
A \( . X_{L}=0 \)
В . \( X_{L}=X_{C} \)
c. \( X_{C}=0 \)
D. \( X_{L}^{2}+X_{C}^{2}=1 \)


If the velocity of a body moving in a straight line is proportional to the square root of the distance traversed,
then it moves with
A. variable force
B. constant force
c. zero force
D. zero acceleration


Find 'x' and 'y' if \( x^{2}-y^{2}-i(2 x+y)= \)
\( \mathbf{2} i \)


In the Young's double slit experiment, intensities of black and bright fringes
are 1 and 4 respectively, the ratio of amplitudes of sources will be :
A . 1: 1
B. 1: 2
c. 3: 1
D. 1: 4


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x}{\sqrt{1+x^{2}}}, \) then \( (\text { fofof }(x)) \) is
A \( \cdot \frac{x}{\sqrt{1+x^{2}}} \)
В. \( \frac{x}{\sqrt{1+3 x^{2}}} \)
c. \( x \)
D.


A student performs a titration with different burettes and finds titre values
of \( 25.2 \mathrm{mL}, 25.25 \mathrm{mL} \) and \( 25.0 \mathrm{mL} . \) The
number of significant figures in the average titre value is:
A . 3
B. 4
\( c \cdot 2 \)
D. none of the above


The formation of cyanohydrin from a ketone is an example of :
A. Nucleophilic substitution
B. Nucleophilic addition
c. Electrophilic addition
D. Electrophilic substitution


Determine the contrapositve of each of the following statements:
If he has courage he will win.


A ball is thrown vertically upwards. It goes to height \( 19.6 \mathrm{m} \) and then returns
back to the ground, findThe initial velocity of the ball The total time taken of journey.
The final velocity of the ball when it strikes the ground \( \left(g=9.8 m s^{-2}\right) \)


The correct relationship is
A \( \cdot A+C . I=P \)
B. C.I.-P=A
c. \( \mathrm{c} . \mathrm{L}=\mathrm{A}-\mathrm{p} \)
D. None of these


\( k g \cdot m / s^{2} \) is the unit of
A. Momentum
B. Velocity
c. Force
D. Acceleration


If an electron in hydrogen atom jumps from an orbit of level \( n=3 \) to an orbit of
level \( n=2 \), emitted radiation has a
frequency (R=Rydberg's constant, C=velocity of light)
\( ^{A} \cdot \frac{3 R C}{27} \)
в. \( \frac{R C}{25} \)
c. \( \frac{8 R C}{9} \)
D. \( \frac{5 R C}{36} \)


Paramagnetic behaviour is observed in
out of \( \boldsymbol{O}_{3}, \boldsymbol{O}_{2}, \boldsymbol{N} \boldsymbol{O} \) and
\( N O_{2} \)
This question has multiple correct options
\( A \cdot O_{3} \)
в. \( O_{2} \)
c. \( N O \)
D. \( N O_{2} \)


A conducting wire in the shape of \( Y \)
with each side of length \( l \) is moving in a uniform magnetic field B, with a uniform speed v as shown in the figure.
The induced emf at the two ends \( X \) and
Y of the wire will be
A. zero
в. 2Blv
\( c . \) 2Blv \( \sin (\theta / 2) \)
D. 2Blv \( \cos (\theta / 2) \)


What is the primary valency of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} ? \)


A circle is inscribed in a square and
then a smaller square is inscribed in the circle. The ratio of the area of the
smaller square to that of the larger square is
A . 1: 4
B. \( \sqrt{2}: 2 \)
\( c \cdot 1: 2 \)
D. \( 1: \sqrt{2} \)
E . 2: 3


Resonance is possible in?
A. \( C H_{3}-C O-C H_{3} \)
В. \( C H_{3}=C H-C H O \)
\( \mathbf{c} \cdot C H_{2}=C H-C H_{2}-C H O \)
D. \( C H_{2}=C H-C H_{2}-C H=C H_{2} \)


A person reaches a point directly opposite on the other bank of a river. The velocity of the water in the river is \( 4 m s^{-1} \) and the velocity of the person in
still water is \( 5 m s^{-1} \). If the width of the
river is \( 84.6 ~ m, \) time taken to cross the
river in seconds is:
A . 9.4
B. 2
c. 84.6
D. 28.2


Suppose Mr. Ramesh have rupee 2,3
and 5 notes. In howmany ways he can
get a sum of rupees 83 such that atleast one note of each type is present and the number of 2 rupee note(s) is less than number of 3 rupee note(s) which is again less than the number of
5 rupees note \( (s) \)
A . 8
B. 9
c. 10
D. 12


(a) Draw the structures of the following:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{2}} \)
(ii) \( B r F_{3} \)
(b) Write the structural difference
between white phosphorus and red phosphorus?


Some equations are solved on the basis
of a certain system. Find the correct
answer for the unsolved equation on that basis. If \( 324 \times 289=35,441 \times \)
\( \mathbf{4 8 4}=\mathbf{4 3}, \mathbf{6 2 5} \times \mathbf{4 0 0}=\mathbf{4 5}, \) find the
value of \( 256 \times 729 \)
A . 33
B . 35
c. 43
D. 34


\( N_{2} \) can be obtained by passing \( N H_{3} \)
into suspension of bleaching powder. If true enter 1 , else 0


Phenol is acidic because of the
resonance stabilization of its conjugate base, namely:
A. phenoxide ion
B. epoxide ion
c. benzoate ion
D. none of these


Calgon is an artificial zeolite for removing permanent hardness.
A. True
B. False


State Le Chatelier's principle.


The radioactive decay rate of a
radioactive element is found to be \( 10^{3} \) disintegrations / second at a certain time. If the half life of the element is one
second, the decay rate after one second is x disintegrations per sec and after three seconds is y disintegrations per sec. Then \( y / x= \)


The order of size of an IC is:
\( \mathbf{A} \cdot 10^{-3}-10^{-1} m \)
B \( \cdot 10^{1}-10^{3} m \)
C \( \cdot 10^{-1}-10^{1} m \)
D. \( 10^{-9}-10^{-6} m \)


Which of the following order(s) is/are
incorrect?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} P O_{4}>H_{3} P O_{3}>H_{3} P O_{2} \) (reducing character)
B. \( N_{2} O<N O<N_{2} O_{5} \) (oxidation state on nitrogen
atom)
\( \mathbf{C} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3}(\text { basicity }) \)
D \( \cdot S b H_{3}>N H_{3}>A s H_{3}>P H_{3} \) (reducing character)


Find the shortest wavelength in Paschen series if, the longest
wavelength in Balmer series is \( 6563 A^{0} \)


Healthy ecosystems are the base of a wide range of ecosystem services,
Justify.


\( \int_{0}^{2 x} \sqrt{1+\sin x} d x \)
A \( \cdot \sin \frac{x}{2}-\cos \frac{x}{2}-\frac{\pi}{2}+C \)
B. \( \sin \frac{x}{2}-\cos \frac{x}{2}+\frac{\pi}{2}+C \)
c. \( 2 \sin x-2 \cos x+2 \)
D. None of these


Find \( : \int \log x \cdot d x \)


The value of \( \frac{7 \pi^{\circ}}{9} \) in sexagesimal measure is
A \( .120^{\circ} \)
B. \( 130^{\circ} \)
c. \( 140^{\circ} \)
D. \( 150^{\circ} \)


If the surface tension of a liquid increases proportional to the \( n \) th power of its density then what is the value of \( n \)
A . 1
B . 2
\( c .3 \)
\( D \)


If \( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{C} \) are the distinct roots, of the
equation \( x^{2}-x+1=0, \) then \( \alpha^{101}+ \)
\( \beta^{107} \) is equal to
A .
B. 2
\( c \cdot-1 \)
D.


If the \( p K_{a} \) of a weak acid \( H A \) is 4.80
and the \( p K_{b} \) of a weak base \( B O H \) is
4.78. Then, the \( p H \) of an aqueous
solution of the corresponding salt, \( \boldsymbol{B A} \)
will be:
A. 8.23
B. 9.41
c. 7.01
D. 5.91


If the origin is the centroid of the
triangle \( P Q R \) with vertices \( \boldsymbol{P}(\mathbf{2} \boldsymbol{a}, \mathbf{2}, \mathbf{6}), \boldsymbol{Q}(-\mathbf{4}, \mathbf{3} \boldsymbol{b},-\mathbf{1 0}) \) and
\( \boldsymbol{R}(\mathbf{8}, \mathbf{1 4}, \mathbf{2 c}), \) then find the values of \( \boldsymbol{a}, \boldsymbol{b} \)
and \( c \)


A force \( F=-4 x-8 \) is acting on a block where \( x \) is position of block in meter The energy of oscillation is 32 J, the block oscillate between two points Position of extreme position is:
\( A \cdot 6 \)
B. 0
\( c \cdot 4 \)
D. 3


A black body has a wavelength of \( \lambda \) at
temperature \( 2000 K . \) Its corresponding
wavelength at temperature \( 3000 K \) will
be:
A \( \cdot \frac{2 \lambda}{3} \)
в. \( \frac{3 \lambda}{2} \)
c. \( \frac{4 \lambda}{9} \)
D. \( \frac{9 \lambda}{4} \)


What amount will sum up to Rs. 12100 at \( 10 \% \) p.a. in Cl in 2 years?
A . 10,000
B. 11,000
c. 9,000
D. 8,000


Intramolecular H-bonding is absent in:
A . o-methylbenzaldehyde
B. p-methoxybenzaldehyde
c. o-nitropheno
D. all of these


A. Silanes are good reducing agents.
B. \( S i O_{2} \) is a giant tetrahedral polymer.
C. \( S n C l_{4} \) acts as bronsted base. The correct option is :
A. A and B are true
B. B and C are true
c. only c is true
D. all are true


A particle of mass \( M \) is moving in a
horizontal circle of radius \( \boldsymbol{R} \) with
uniform speed \( V . \) When it moves from one point to a diametrically opposite point, its
A
B. momentum does not change
c. momentum changes by \( 2 M V \)
D. kinetic energy changes by \( M V^{2} \)


If \( \vec{a}, \vec{b}, \vec{c} \) are three coplanar vectors then find the magnitude of their vector sum. It is given \( \vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}, \vec{c}=-3 \hat{j} \)
A \( \cdot \sqrt{5}, 297^{\circ} \)
B . \( \sqrt{5}, 63^{\circ} \)
c. \( \sqrt{3}, 297^{\circ} \)
D. \( \sqrt{3}, 63^{\circ} \)


paramagnetic substance will look like
\( A \)
B.
\( c \)
D.


Bone is a
A. Epithelium tissue
B. Muscular tissue
C. Connective tissue
D. Nervous tissue


Two capacitators having capacitances
\( C_{1} \) and \( C_{2} \) are charged with \( 120 V \) and
\( 200 V \) batteries respectively. When they
are connected in parallel now, it is found that the potential on each one of them is zero. Then:
A \( \cdot 8 C_{1}=5 C_{2} \)
В. \( 9 C_{1}=5 C_{2} \)
\( \mathbf{c} \cdot 3 C_{1}=5 C_{2} \)
D. \( 5 C_{1}=3 C_{2} \)


Which radiation is used for satellite
communication?
A. Micro waves
B. X rays
c. Gamma rays
D. Infra red rays


Which metal is used in thermometer?
A. copper
B. Mercury
\( c . \) sodium
D. Silver


If the vectors \( 3 \vec{p}+\vec{q} ; 5 \vec{p}-3 \vec{q} \) and \( 2 \vec{p}+ \)
\( \vec{q} ; 4 \vec{p}-2 \vec{q} \) are pairs of mutually perpendicular vectors.


If \( \vec{a} \cdot \hat{i}=\vec{a} \cdot(\hat{i}+\hat{j})=\vec{a}(\hat{i}+\hat{j}+\hat{k}), \) thus
\( \vec{a}= \)
\( A \)
B . \( \hat{i}+j \)
c. \( \hat{k}-\hat{j} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)


Paul Ehrlich promoted which activity in chemists?
A. Studying the relationship between structure and metabolism.
B. Studying the relationship between structure and reaction.
c. studying the relationship between structure and mechanism
D. studying the relationship between structure and activity


Which of the following compounds are called unsaturated compounds - that
is, it/they add/ \( s \boldsymbol{H}_{2} \) catalytically at ordinary condition of temperature?
\( A \)
в.
\( c \)
D.


\( A B C D \) is a quadrilateral in which all four sides are equal. Show that both
pairs of opposite sides are parallel.


Arrange the following in decreasing
order of their reactivity with ar electrophile


In which of the following processes is acetyl CoA not involved?
A. Fatty acid breakdown
B. Embden-Meyerhof pathway
c. Fatty acid synthesis
D. Transamination


Two parallel wires \( 2 \mathrm{m} \) apart carry currents of 2 A and 5 A respectively in the same direction, the force per unit
length acting between these two wires is:
A \( \cdot 2 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
В. 3 \( \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
c. \( 1 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
D. \( 4 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)


A stone is dropped from a height of 20
m. How long will it take to reach the ground? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 2 s \)
B. 0.5
\( c \cdot 4 s \)
\( D \cdot 1 \mathrm{s} \)


Kinetic energy of gas depends on:
A. temperature
B. pressure
c. surface area
D. both \( A \) and \( B \)


One haemoglobin carries how many
molecules of \( \boldsymbol{O}_{2} ? \)
\( A \cdot 4 \)
B. 2
\( c \cdot 6 \)
D.


A sample of hard water contains 111
ppm of \( C a C l_{2} . \) The degree of hardness of this sample of water is:
A. 11
в. 150
c. 100
D. 180


Q Type your question.
resistance of \( 12 \Omega \) are connected thick
conducting strips, as shown in the figure. A battery and a galvanometer (With a sliding jockey connected to it) are also available connections are to be made to
measure the unknown resistance \( \boldsymbol{X} \)
using the principle of Wheatstone bridge. Answer the following questions.
(a) Are there positive and negative terminals on the galvanometer
(b) copy the figure is your answer book and show the battery and the galvanometer (With jockey) connected at appropriate points.
(c) After appropriate connections are made, it is found that no deflection
takes place in the galvanometer when the sliding jockey touches the wire at a
distance of \( 60 \mathrm{cm} \) from \( A . \) Obtain the
value of the resistance of \( \boldsymbol{X} \)


Potassium combines with two isotopes of chlorine \( \left(^{35} C l \text { and }^{37} C l\right) \) respectively to form two samples of \( K C l \) Their formation follows the law of:
A. constant proportions
B. multiple proportions
c. reciprocal proportions
D. none of these


Can two acute angles form a linear
pair?


Which process can be used for production of sulfuric acid from sulfur burning or for regeneration of the spent acid from alkylation plants?
A. Moisture sulphuric acid
B. Wet sulphuric acid
c. Dry sulphuric acid
D. Alkylating sulphuric acid


The Schrodinger wave equation is based on which nature of electron?
A. wave
B. Particle
c. atomic
D. Both A and E


In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other
subjects. The class contains how many students?
A . 35
B. 42
\( c .52 \)
D. 60


A conical flask is full of water. The flask
has base radius \( a \) and height \( 2 a \). The water is poured into a cylindrical flask of base-radius \( \frac{2 a}{3} . \) Find the height of water in the cylindrical flask.
A \( \cdot \frac{5}{2} a \)
B. \( 2 a \)
c. \( \frac{3}{2} a \)
D. 1a


Many Lanthanoid elements are used to
prepare
A . ceramic materials
B. water softener
c. superconducting materials
D. enzyme catalysts


Evaluate the given integral.
\( \int \sin ^{-1}\left(3 x-4 x^{3}\right) d x \)


Prove that
\[
\frac{\sin (\theta+\phi)-2 \sin \theta+\sin (\theta-\phi)}{\cos (\theta+\phi)-2 \cos \theta+\cos (\theta-\phi)}=
\]
\( \tan \theta \)


By using the properties of definite integrals, evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x \)


An electron is moving near to a
conducting loop then the induced
current in the loop is-
A . clockwise
B. anticlockwise
c. first anticlockwise and then clockwise
D. no current


\( \cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}= \)
A \( \cdot \frac{23 \pi}{20 \pi} \)
B. \( \frac{7 \pi}{10} \)
\( c \cdot \frac{7 \pi}{20} \)
D. \( \frac{17 \pi}{20 \pi} \)


Conjugate acid of a weak base is always stronger. What will be the decreasing order of basic strength of the following conjugate bases?
\( \boldsymbol{O H}^{-}, \boldsymbol{R O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}, \boldsymbol{C l}^{-} \)


The equation of the circumcircle of the triangle formed by the lines \( y+\sqrt{3} x= \) \( \mathbf{6}, \boldsymbol{y}-\sqrt{\mathbf{3}} \boldsymbol{x}=\mathbf{6} \) and \( \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot x^{2}+y^{2}+4 x=0 \)
В. \( x^{2}+y^{2}-4 y=0 \)
c. \( x^{2}+y^{2}-4 y=12 \)
D. \( x^{2}+y^{2}+4 x=12 \)


Specific heat at constant volume of a monoatomic gas is 0.75 cal/g. 1 mole of this gas requires 3 cal of heat to raise the temperature of 1 mole of this gas.
The heat required to raise the
temperature through \( 1^{\circ} \mathrm{C} \) of 1 -mole gas
at constant pressure is:
A. 5
B. 6
\( c \cdot 3 \)
D.


Write the IUPAC names for the
following compounds:
(i) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{ONO}\right] \mathrm{Cl}_{2} \)
(ii) \( \mathrm{K}_{3}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right] \)
A. (i) Pentammonianitritocobalt (III) chloride
(ii) Potassiumhexacyanochromate (II)
B. (i) Pentammonianitratocobalt (II) chloride
(ii) Potassiumhexacyanidechromate (III)
C. (i) Pentamminenitritocobalt (III) chloride
(ii) Potassiumhexacyanochromate (III)
D. (i) Pentamminenitrocobalt (II) chloride
(ii) Potassiumhexacyanchromate (III)


If the earth does not rotate on its axis,
the change in the weight of a body at the equator would be about (Take radius of earth-6400 \( \mathrm{km} \) )
A. 0.003\%v larger
B. 0.3\% longer
c. \( 0.3 \% \) smaller
D. 0.003\% smaller


Find the volume of a cuboid whose
breadth is half of its length and height is doubled the length.
A \( \cdot \ell^{3} \) cubic units
B. \( 2 \ell^{3} \) cubic units
c. \( 5 \ell^{3} \) cubic units
D. None of these


SI Unit for mass is :
A. Newton
B. Ounces
c. stones
D. Kilogram


Hemichordates are the connecting link between
A. Urochordates and cephalochordates
B. Cephalochordates and vertebrates
c. Urochordates and vertebrates
D. Non-chordates and chordates


A copper wire carries a current of
density Assuming that one free electrone corresponding to each copper atom,evalute the distance which will be covered by an electrone during its displacement along the wire


Which one of the following shows the best percentage?
A \( \cdot \frac{384}{540} \)
в. \( \frac{425}{500} \)
c. \( \frac{570}{700} \)
D. \( \frac{480}{660} \)


Write uses of Bakelite.


What term is used in reference to an
aqueous solution's osmotic pressure?
A. Chemical pH indicator
B. Acid/base buffer
c. Anhydrous solution
D. Hypotonic solution
E. Supersaturated solution


If an element has 22 electrons then
what will be its atomic number?
A . 10
B. 25
c. 15
D. 22


Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system is conserved.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement is NOT a correct explanation for Statement-1
c. statement- - 1 is True, Statement- 2 is False
D. Statement- -1 is False, Statement-2 is True


In the long form of periodic table, the total number of period is:
A. 5
B. 7
\( c \cdot 8 \)
D.


One of the oxoacid salts on heating with
conc. \( H N O_{3} \) and ammonium
molybdate, gives yellow ppt. What is this ion?
\( \mathbf{A} \cdot P O_{3}^{3} \)
B \( \cdot P O_{4}^{3} \)
\( \mathbf{c} \cdot S O_{4}^{2-} \)
D. \( C l \)


In a coil of resistance \( 10 \Omega \), the induced
current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is-


An air bubble rises from the bottom to
the surface of lake and it is found that
its diameter is doubled. If the height of water barometer is \( 11 \mathrm{m} \), the depth of the lake in meters is
A. \( 70 \mathrm{m} \)
B. 77m
\( c .7 .7 \mathrm{m} \)
D. 78m


One atom of an element X weighs \( 6.644 \times 10^{-23} . \) Calculate the number of
gram atoms in \( 40 \mathrm{kg} \) of it.
A \( \cdot 10^{2} \)
B . \( 10^{3} \)
\( c \cdot 10^{-2} \)
D. \( 10^{4} \)


The peak voltage of an AC supply is
\( 300 V . \) What is the rms voltage?
A \( .121 .2 V \)
\( V \)
B. 212.1V
c. \( 343.4 V \)
D. \( 434.3 V \)


(a) What are isotopes?
(b) State modern periodic law.
(c) Name two noble gas.


If all the atoms of \( 1 k g \) of deuterium undergo fusion approximately how much energy could be released?
A \( .7 .87 \times 10^{13} \mathrm{J} \)
B . \( 9 \times 10^{11} \) calories
c. \( 9 \times 10^{12} k W h \)
D. \( 79 \times 10^{7} k W h \)


The term feedback refers to the effect of
A. Substrate on the rate of enzymatic reaction
B. End product on the rate of enzymatic reaction
C. Enzyme concentration on its rate of reaction
D. An external compound on the rate of enzymatic reaction


Formation of both peptide and glycosidic bonds involves
A. Hydration
B. Dehydration
c. Esterification
D. Acidification


Which group of elements in a periodic table can be used as strong reducing agents?
A. VIIA
B. IVA
c. vı
\( D \cdot \) IA


What is IUPAC name of \( \left[\boldsymbol{C o}(\boldsymbol{e n})_{3}\right]^{+3} \) ?


Ramesh is doing experiment with a mirror. If an erect image with height 0.75 times to that of object's size is formed. Can you guess the mirror?


Which one is correct for \( \boldsymbol{k}=\boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{E}_{a} / \boldsymbol{R} \boldsymbol{T}} \) ?
A \( \cdot E_{a} \) is energy of activation
B. R is Rydberg's constant
c. \( \mathrm{k} \) is equilibrium constant
D. A is adsorption


Read the following statements and answer as true or false.
By hydrogenation, vegetable oils convert into vanaspati ghee
If true enter 1 , else enter 0


What is the speed of each during overtaking?


If \( 0.5 L \) of \( 0.6 M S n S O_{4} \) solution is
electrolysed for a period somin using a
current of


The oxidation state of \( \mathrm{P} \) in \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is :
\( A \cdot+3 \)
\( B .+5 \)
\( c \cdot+7 \)
D. None of these


The number of unpaired electrons in chromium atom are:
A .2
B. 3
\( c \cdot 4 \)
\( D \)


The D.E of the family of prabolas of which has a latus retum and whose
axes are parallel to \( x- \) axis
A \( \cdot y_{1}^{3}+2 a y_{2}=0 \)
B . \( y_{1}^{3}+a y_{2}=0 \)
c. \( y_{1}^{3}+4 a y_{2}=0 \)
D. \( y_{1}^{3}+3 a y_{2}=0 \)


n Fig.1, 0 is the centre of circle, \( A B \) is a
chord and \( A T \) is the tangent at \( A \). If
\( \angle A O B=100^{\circ}, \) then \( \angle B A T \) is equal to
A \( \cdot 100^{\circ} \)
B. \( 40^{\circ} \)
\( c \cdot 50 \)
D. 9 ?


Consider the function.
\( f(x)=3 x^{4}-20 x^{3}-12 x^{2}+288 x+1 \)
In which one of the following intervals is the function decreasing?
\( \mathbf{A} \cdot(-1,0) \)
в. (0,2)
c. \( (2, \infty) \)
D. none of these


The fundamental frequency of vibration of \( 1 \mathrm{cm} \) long string is \( 256 \mathrm{Hz} \). If the length of the string is reduced to \( \frac{1}{4} c m \) keeping the tension unaltered, the new fundamental frequency will be
A \( .256 \mathrm{Hz} \)
в. 512 Нг
c. \( 1024 \mathrm{Hz} \)
D. \( 2048 \mathrm{Hz} \)


Prove that \( [\overrightarrow{\boldsymbol{a}} . \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}+\overrightarrow{\boldsymbol{d}}]=[\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}]+ \)
\( [\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{d}}] \)


Give reason as to why woolen clothes are more preferable in winter.


The median of 19 observations of a
group is \( 30 . \) If two observations with
values 8 and 32 are further included,
then the median of the new group of 21 observations will be:
A . 28
B . 30
\( c .32 \)
D. 34


A circle has two equal chords \( A B \) and
\( A C, \) chord \( A D \) bisects \( B C \) in \( E . \) If \( A C=12 \)
and \( A E=8 c m, \) then the measure of \( A D \)
is ?
A \( .24 \mathrm{cm} \)
B. \( 18.5 \mathrm{cm} \)
c. \( 18 \mathrm{cm} \)
D. \( 19 \mathrm{cm} \)


The outermost layer of earth is known
as:
A . crust
B. Plate
c. core
D. zone


Obtain an expression for the mutual inductance of two long solenoids.


Which of the following best describes
biodegradation?
A. A minor change in an organic molecule
B. Fragmentation of a complex organic molecule
C. Complete transformation of the organic molecule to mineral forms
D. All of the above
E. None of the above


The alkali metals form salt-like
hydrides by the direct synthesis at elevated temperature. The thermal
stability of these hydrides decreases in which of the following orders?
A. \( N a H>L i H>K H>R b H>C s H \)
в. \( L i H>N a H>K H>R b H>C s H \)
c. \( C s H>R b H>K H>N a H>L i H \)
D. \( K H>N a H>L i H>C s H>R b H \)


A compound on analysis gave the following percentage composition by weight: Hydrogen \( =9.09 \%, \) Oxygen \( = \)
\( 36.36 \%, \) Carbon \( =54.55 \% . \) It's vapour
density is \( 44 . \) If the molecular formula of
the compound is \( C_{x} H_{y} O_{z}, \) then find the
value of \( \boldsymbol{x}, \boldsymbol{y} \) and \( \boldsymbol{z} \)
A. \( x=4, y=8, z=2 \)
в. \( x=3, y=6, z=3 \)
c. \( x=5, y=10, z=4 \)
D. None of the above


Silver crystallises in fcc lattice. If edge length of the cell is \( 4.07 \times 10^{-8} \mathrm{cm} \) and
density is \( 10.5 g \mathrm{cm}^{3} \), calculate the
atomic mass of silver.


The Base-Emitter voltage for a CE
transistor used as an amplifier is \( 0.02 \mathrm{V} \) An input signal given to this transistor results in a change of base current by, \( 20 \mu A \) and a changes of \( 2 \mathrm{mA} \) takes
place in the collector current. Calculate the following quantities:
1. Input resistance.
2. A.C. current gain
3. Transconductance.
4. If the load resistance is \( 5 k \Omega \) what will
be the voltage gain.


A smooth ball 'A' moving with velocity 'V' collides with another smooth initial ball
at rest. After collision both the balls
move the same speed with angle
between their velocities \( 60^{0} . \) No external
force acts on the systems of balls.
Choose the correct option(s).
A \( \cdot \) The speed of each ball after the collision is \( \frac{V}{\sqrt{3}} \)
B. The speed of each ball after the collision is \( \frac{2 V}{\sqrt{3}} \)
C. The magnitude of change in momentum of ball B is \( \left(\frac{m V}{\sqrt{3}}\right) \)
D. The magnitude of change in momentum of ball B is \( \left(\frac{2 m V}{\sqrt{3}}\right) \)


An electric cell of emf \( E \) is connected
across a copper wire of diameter \( \boldsymbol{d} \) and
length \( l . \) The drift velocity of electrons in
the wire is \( v_{d} . \) If the length of the wire is
changed to \( 2 l \), the new drift velocity of electrons in the copper wire will be:
\( \mathbf{A} \cdot v_{d} \)
в. \( 2 v_{d} \)
c. \( v_{d} / 2 \)
D. \( v_{d} / 4 \)


of length \( L \) and resistance \( 9 r \) is joined
to the cell \( D \) of emf \( \varepsilon \) and internal
resistance \( r . \) The cell \( C^{\prime} s \) emf is \( \varepsilon / 2 \) and
its internal resistance is \( 2 r \). The
galvanomater \( G \) will show no deflection
when the length \( A J \) is
' \( \frac{4 L}{9} \)
\( 3 \cdot \frac{5 L}{9} \)
c. \( \frac{7 L}{18} \)
D. \( \frac{11}{18} \)


Fill in the blanks:
The power circuit in the house uses ampere fuse.
A. 5
B . 15
\( c .50 \)
D. 220


Schleiden (1838) proposed cell to be structural and functional unit of life.
His idea was a/an
A. observation
B. Assumption.
c. Generalisation.
D. Hypothesis.


The average binding energies of
deuterium and \( \alpha \) -particle are \( 1.12 \mathrm{MeV} \)
and \( 7.1 \mathrm{MeV} \) respectively. The energy
that liberates in the reaction \( _{1} H^{2}+_{1} H^{2} \)
\( \rightarrow_{2} H e^{4} \) is
MeV.
\( \mathbf{A} \cdot 23.92 \)
B . 25
c. 25.6
D. 15.8


A square plate lies in the xy plane with its centre at the origin and its edges parallel to the \( x \) and \( y \) axes. Its moments of inertia about the \( x, y \) and \( z \) axes are
\( I_{x}, I_{y}, \) and \( I_{z} \) respectively, and about a
diagonal it is \( \boldsymbol{I}_{D} \)
A \( \cdot I_{x}=I_{y}=\frac{1}{2} I_{z} \)
В . \( I_{x}=I_{y}=2 I_{z} \)
c. \( I_{D}=I_{x} \)
D \( \cdot I_{D}=I_{z} \)


A man pay 5 paisa tax on Re.1. If the total tax paid by him is Rs.1550 \( \cdot 0, \) then
on how much amount did he pay the \( \operatorname{tax} ? \)
A . Rs.31000
B. Rs.30000
c. Rs.15500
D. Rs.15505


A certain nucleus \( X \) has a mass
number 14 and atomic number \( 6 . \) The
nucleus \( X \) changes to \( _{7}^{14} Y \) after the loss of a particle. Represent this change in the form of an equation.


Which of the following is not an oxidation reaction?
A. 1,3 Bis PGAL to 1,3 Bis PGAA
B. 1,3 Bis PGA to 3 - PGA
c. Pyruvic acid to acetyl CoA
D. Malic acid to oxaloacetic acid


In the diagram \( M N \) is a straight line on a Cartesian plane. The coordinates of \( N \) \( \operatorname{are}(12,13) \) and \( M N^{2}=9 \) units. The
coordinates of \( M \) are:
A \( .(21,13) \)
B. (12,22)
c. (12,4)
D. (3,13)


Eye colour in fruitfly is a sex linked trait and the cross of white eyed female with red eyed male gives red eyed females and white eyed males. Rarely this cross may give all white eyed females and red eyed males. This was found to be due to non-disjunction of
A. Two Y chromosomes in female fly
B. Two X chromosomes in female fly
c. Four Y chromosomes in male fly
D. Four \( x \) chromosomes in male fly


Mixture of \( K B r \) and \( K B r O_{3} \) in acidic
medium can be used as brominating
agent
The chemical reaction is, \( 5 B r^{-}+ \)
\( \boldsymbol{x} \boldsymbol{B r} \boldsymbol{O}_{3}^{-}+\boldsymbol{6} \boldsymbol{H}^{+} \rightarrow \boldsymbol{3} \boldsymbol{B r}_{\boldsymbol{y}}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
Then \( \boldsymbol{x}+\boldsymbol{y} \) is :
\( A \cdot 6 \)
B. 3
\( c .5 \)
D. 1


Which of the following statements is
true?
\( \mathbf{A} \cdot H_{3} P O_{3} \) is stronger acid than \( H_{2} S O_{3} \)
B. In aqueous medium, HF is a stronger acid than HCI
C \( . H C l O_{4} \) is a weaker acid than \( H C l O_{3} \)
D. \( H N O_{3} \) is a stronger acid than \( H N O_{2} \)


Why is it difficult to read from image of
a book in plane mirror?
A. Due to lateral inversion
B. Due to scattering
c. Due to vertical inversion
D. Due to loss on reflection


An RLC circuit has \( f_{1} \) and \( f_{2} \) as the half
power frequency and \( f_{0} \) as the resonant frequency. The Q factor of the circuit is given by:
A \( \cdot \frac{f_{1}+f_{2}}{2 f_{0}} \)
в. \( \frac{f_{1}-f_{0}}{f_{2}-f_{0}} \)
c. \( \frac{f_{0}}{f_{1}-f_{2}} \)
D. \( \frac{f_{1}-f_{2}}{f_{0}} \)


\( \boldsymbol{S}_{\boldsymbol{n}}=\boldsymbol{2} \boldsymbol{n}^{2}+\boldsymbol{3} \boldsymbol{n} ; \) then \( \boldsymbol{d}=\ldots \)
A . 13
B. 4
\( c .9 \)
D. -2


What is the shape of the covalent
molecule \( M X_{3} ? \)


Which of the following atoms and ions are iso electronic(i.e have the same
number of electrons) with a neon atom:
\( \mathbf{C}, \mathbf{O}^{2-}, \mathbf{N}^{-}, \mathbf{F}^{+}, \mathbf{N a}^{+}, \mathbf{A} \mathbf{l}^{\mathbf{3}+} \)
A \( \cdot \mathrm{N}^{-}, \mathrm{Na}^{+}, \mathrm{Al}^{3+} \)
B. \( c, O^{2}-, N a^{+}, F^{+} \)
\( \mathbf{c} \cdot \mathbf{0}^{2-}, \mathbf{N a}^{+},\left.\mathbf{A}\right|^{3} \)
D. \( c, 0^{2}-, F^{+},\left.A\right|^{3+} \)


A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is \( 8 c m \) and the
total height of the cup is \( 11.5 \mathrm{cm} \). Find
the total surface area of the cup. (Take
\( \left.\pi=\frac{22}{7}\right) \)


medium that contains excess glucose.
The graph below shows glucose
utilisation under different growth
conditions. \( (A),(B), \) and \( (C) \) in the graph
indicates.
A. A- Anaerobic respiration
B- Introduction of \( O_{2} \) to culture medium
C- Aerobic respiration
B. A- Aerobic respiration
B-Introduction of \( C O_{2} \) to culture medium
C- Anaerobic respiration
C. A- Aerobic respiration
B- Supply of organic triphosphate
C- Aerobic respiration
D. A- Aerobic respiration
B- - Introduction of CO to culture medium
C- Anaerobic respiration


Two tiny spheres carrying charges 1.8 \( \mu C \) and \( 2.8 \mu C \) are located at \( 40 \mathrm{cm} \)
apart. The potential at the mid-point of the line joining the two charges is
A \( \cdot 3.8 \times 10^{4} v \)
B . \( 2.1 \times 10^{5} \mathrm{v} \)
c. \( 4.3 \times 10^{4} v \)
D. 3.6 \( \times 10^{5} \mathrm{v} \)


If a salt of weak acid or base is added to
a solution of its acid or base
respectively, the:
This question has multiple correct options
A. dissociation of acid or base is diminished
B. the \( p H \) of the solution in case of acid increases and in case of base decreases
c. mixing of two leads for precipitation
D. none of the above


A mass \( M \) is lowered with the help of a
string by a distance \( x \) at a constant
acceleration \( g / 2 . \) The work done by the string will be
A. \( M g x \)
в. \( -\frac{M g x}{2} \)
c. \( \frac{1}{2}^{M g x^{2}} \)
D. \( M g x^{2} \)


Which substance can be used as male
contraceptive in future?
A. FSH
B. Testosterone
c. Progesterone
D. LH


An unbiased cubical die whose faces
are numbered 1 to 6 is rolled once. Find
the probability of getting a square
number on the top face.


From Brewster's law, except for polished metallic surface, the polarising angle
A. depends on wavelength and is different for different colours
B. independent of wavelength and is different for different colours
C. independent of wavelength and is same for different colours
D. depends on wavelength and is same for different colours


Let \( A=\{1,2,3,4\} \) and \( R=\{(2,2),(3,3),(4, \)
4), \( (1,2)\} \) be a relation on A. Then R is
A. Reflexive
B. Symmetric
c. Transitive
D. None of these


Two circles touch internally. The sum of their areas is \( 116 \pi \) sq. \( \mathrm{cm} \) and the
distance between their centers is \( 6 \mathrm{cm} \)
The radii of the given circles are
A. \( 8 \mathrm{cm} \& 20 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \& 10 \mathrm{cm} \)
c. \( 6 \mathrm{cm} \) \& \( 8 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \) \& \( 9 \mathrm{cm} \)


Explain with examples what is meant
by a 'mole' of a substance.


The capacity of a parallel plate air capacitor is \( 2 \mu F \) and voltage between the plates is changing at the rate of
\( 3 V / S . \) The displacement current in the capacitor is:
\( \mathbf{A} \cdot 2 \mu F \)
в. \( 3 \mu F \)
c. \( 5 \mu F \)
D. \( 6 \mu F \)


If \( y=\sqrt{\frac{1+\sin x}{1-\sin x}} \) then \( \frac{d y}{d x}=? \)
A \( \cdot \frac{1}{2} \sec ^{2}\left(\frac{\pi}{4}-\frac{x}{2}\right) \)
B \( \cdot \frac{1}{2} \csc ^{2}\left(\frac{\pi}{4}-\frac{x}{2}\right) \)
\( ^{\mathrm{c}} \cdot \frac{1}{2} \csc \left(\frac{\pi}{4}-\frac{x}{2}\right) \cot \left(\frac{\pi}{4}-\frac{x}{2}\right) \)
D. none of these


Which of the following is a source of direct current.
A . Cell
B. Electromagnet
c. Bulb
D. Switch


Solve the linear inequations:
\( -2 \leq \frac{1}{2}-\frac{2 x}{3} \leq 1 \frac{5}{6}, x \in N \)
Then \( \frac{15}{4} \geq x \geq-2 \)
A. True
B. False


Correct energy profile for amine inversion and hybridization of nitrogen in transition state is:
\( (\mathbf{A}) \)


an isochoric reversible process
\( \mathbf{A} \cdot \Delta U=19.90 k J, \Delta H=24.058 k J ; w=0 \)
B . \( \Delta U=-19.90 k J, \Delta H=24.058 k J ; w=0 \)
C \( . \Delta U=19.90 k J, \Delta H=-24.058 k J ; w=0 \)
D. None of these


Which of the following properties of
hydrogen is incorrect?
A. Like halogens, hydrogen exists as a diatomic gas
B. Like halogens, hydrogen exhibits - 1 oxidation state in its compounds with metals
C. Like halogens, hydrogen is liberated at cathode
D. The ionization energy of hydrogen is quite close to halogens


Which will produce the least heat on
complete hydrogenation?
\( A \)
\( H_{2} C=C H-C=C H_{2} \)
в. \( \begin{array}{ll}c H_{3} & c h\end{array} \)
\( H_{2} C=C-C=C H_{2} \)
\( c \)
\( D \)


In the circuit shown in the figure, there are two parallel plate capacitors each of
the capacitance \( C \) The switch \( S_{1} \) is
pressed first to fully charge the
capacitor \( C_{1} \) and then released. The
switch \( S_{2} \) is then pressed to charge the
capacitor \( C_{1} \) 2. After some time, \( S_{2} \) is
released and then \( S_{3} \) is pressed. After
some time,
A. the charge on the upper plate of \( C_{1} \) is \( 2 C V_{o} \)
B. The charges on the upper plate of \( C_{1} \) is \( C V_{o} \)
c. The charge on the upper plate of \( C_{2} \) is 0
D. The charge on the upper plate of \( C_{2} \) is \( -C V_{o} \)


\( \frac{\sqrt{6}}{\frac{1}{4}} \)


For which of the following compounds, the Lassaigne's test for the detection of
nitrogen will fail?
A. \( H_{2} N-C O-N H_{2} \)
в. \( C_{6} H_{5}-N H-N H_{2} .2 H C l \)
c. \( N H_{2}-N H_{2} .2 H C l \)
D. \( H_{2} N-C O-N H-N H_{2} . H C l \)


Prove \( \frac{\cos 9 x-\cos 5 x}{\sin 17 x-\sin 3 x}=-\frac{\sin 2 x}{\cos 10 x} \)


The acceleration due to gravity at the
poles and the equator is \( g_{p} \) and \( g_{e} \) respectively. If the earth is a sphere of
radius \( R_{E} \) and rotating about its axis
with angular speed \( \omega, \) then \( g_{p}-g_{e} \) is
then given by
\( ^{\mathrm{A}} \cdot \frac{\omega^{2}}{R_{E}} \)
B. \( \frac{\omega^{2}}{R_{E}^{2}} \)
c. \( \omega^{2} R_{E}^{2} \)
D. \( \omega^{2} R_{E} \)


For a heater rated at \( 4 k W ; 220 V \)
Calculate the resistance of the heater
element.
A . \( 20 \Omega \)
B . \( 21.6 \Omega \)
c. \( 200 \Omega \)
D. \( 12.2 \Omega \)


Evalute \( \int \frac{\cot x}{\sqrt{\sin x}} d x \)


A wire has a nonuniform cross sectional
area as shown in the figure. A steady
current i flows through it. Which one of
the following statements is correct?
A. Drift speed of the electrons is constant
B. Drift speed of decreases on moving from A to B
C. Drift speed of increases on moving from A to B
D. Drift speed varies randomly


Give a scheme of reactions that do not
involve disproportionation of the oxides of nitrogen.


The correct increasing order of basic nature among Be, Mg, Ca and Sr is :
A. \( B e<C a<M g<S r \)
в. \( B e<M g<S r<C a \)
c. \( B e<M g<C a<S r \)
\( \mathrm{D} \cdot \mathrm{Ca}<\mathrm{Sr}<\mathrm{Be}<\mathrm{Mg} \)


A tennis ball has a mass of \( 56.7 g m \) and
is served by a player with a speed of 180kmph. The work done in serving the ball is nearly:
\begin{tabular}{l}
A. 7105 \\
\hline
\end{tabular}
в. \( 71 J \)
\( \mathrm{c} .918 \mathrm{J} \)
D. \( 91.8 J \)


Two identical balls of equal masses \( A \)
and \( \mathrm{B} \), are lying on a smooth surface as shown in the figure. Ball A hits the ball B (which is at rest) with a velocity \( v= \) \( 16 m s^{-1} . \) What should be the minimum
value of coefficient of restitution
between \( A \) and \( B \) so that \( B \) just reaches the highest point of inclined plane?
\( \left(g=10 m s^{-2}\right) \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{3} \)


Nature of \( A l_{2} O_{3} \) (Aluminium oxide) is
A . Acidic
B. Basic
c. Amphoteric
D. Neutral


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{Q} \rightarrow \boldsymbol{Q}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{1} \)


What is the final product? \( \boldsymbol{C H} \)
The compound \( \boldsymbol{C H}_{3}-\boldsymbol{C}=\boldsymbol{C H}- \)
\( C H_{3} \) on reaction with \( N a l O_{4} \) in the
presence of \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}} \)
A. \( C H_{3} C O C H_{3} \)
в. \( C H_{3} C O C H_{3}+C H_{3} C O O H \)
c. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
D. \( C H_{3} C H O+C O_{2} \)


The oxidation potential of a hydrogen
electrode at \( p H=10 \) and \( P_{H_{2}}=1 \) is:
A . \( +0.51 V \)
B. \( 0.00 V \)
c. \( +0.590 V \)
D. \( +0.059 V \)


Which part of cockroach has both endoskeleton and exoskeleton
A. In head region
B. Thoracic region
c. Abdominal region
D. In all regions


A straight line \( L \) on the \( x y \) -plane
bisects the angle between \( O X \) and \( O Y \)
What are the direction cosines of \( L ? \)
A \( \cdot(1 / \sqrt{2}, 1 / \sqrt{2}, 0) \)
в. \( (1 / 2, \sqrt{3} / 2,0) \)
c. (0,0,1)
D. \( (2 / 3,2 / 3,1 / 3) \)


Nucleic acid occurs in
A . Golgi body
B. Lysosomes
c. Cytoplasm
D. Mitochondria and chloroplast


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


For an element, \( \boldsymbol{A}=\mathbf{3 4} \) and \( \boldsymbol{N}=\mathbf{1 9} \)
What is the atomic number of the
element?
\( A \cdot 34 \)
B . 19
\( c .53 \)
D. 15


Let the function \( f(x)=\sin x+\cos x \)
be defined in \( [0,2 \pi], \) then \( f(x) \)
A \( \cdot \) increases in \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)
B. decreases in \( \left[\frac{\pi}{4}, \frac{5 \pi}{4}\right] \)
C . increases in \( \left[0, \frac{\pi}{4}\right] \cup[\pi, 2 \pi] \)
D. decreases in \( \left[0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, 2 \pi\right] \)


Kidney of which of the following can filter coelomic fluid, as well as blood
and is also archinephric?
A. Myxine
B. Petromyzon
c. Amphioxus
D. All of the above


For the Paschen series the value of \( n_{1} \)
and \( n_{2} \) in the expression \( \Delta E=R_{H} \times \) \( c\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right] \) is:
A \( \cdot n_{1}=1, n_{2}=2,3,4 \)
в. \( n_{1}=2, n_{2}=3,4,5 \dots \)
c. \( n_{1}=3, n_{2}=4,5,6 \)
D. \( n_{1}=4, n_{2}=5,6,7 \)


If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi \), then
prove that \( x^{2}+y^{2}+z^{2}+2 x y z=1 \)


Select the incorrect statement with
respect to vegetative propagation.
A. Banana is multiplied by means of rhizome
B. Bulbils are the vegetative propagules seen in Agave
C. Aquatic plants are multiplied by offsets
D. Aquatic plants are multiplied by runner


State the reason why the relation \( \boldsymbol{S}= \)
\( (a, b) \in R \times R: a \leq b^{3} \) on the set \( R \) of
real numbers is not transitive.


In a large metropolitan area, the probabilities are 0.87,0.36,0.36,0.30
that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or
both kinds of sets. What is the
probability that a family owns either any one or both kinds of sets?


Assertion
Dipole moment of bromobenzene is same as chloro benzene.
Reason
Dipole moment of \( C l-C \) bond is
greater than \( B r-C \) bond.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A wire has non-uniform cross-section
as shown in figure. A steady current
flows through it. The drift speed of
electrons at points \( \boldsymbol{P} \) and \( \boldsymbol{q} \) is \( \boldsymbol{v}_{\boldsymbol{p}} \) and \( \boldsymbol{v}_{\boldsymbol{Q}} \)
A \( \cdot v_{p}=v_{Q} \)
В \( \cdot v_{p}<v_{Q} \)
с. \( v_{p}>v_{Q} \)
Data insufficient


If the line \( \sqrt{5} x=y \) meets the lines \( x= \)
\( \mathbf{1}, \boldsymbol{x}=\mathbf{2}, \ldots, \boldsymbol{x}=\boldsymbol{n}, \) at points \( \boldsymbol{A}_{\mathbf{1}}, \boldsymbol{A}_{\mathbf{2}}, \dots \)
\( A_{n} \) respectively then \( \left(O A_{1}\right)^{2}+ \)
\( \left(O A_{2}\right)^{2}+\ldots+\left(O A_{n}\right)^{2} \) is equal to \( (0 \) is
the origin)
A \( \cdot 3 n^{2}+3 n \)
B. \( 2 n^{3}+3 n^{2}+n \)
\( \mathbf{c} \cdot 3 n^{3}+3 n^{2}+2 \)
D.
\( \left(\frac{3}{2}\right)\left(n^{4}+2 n^{3}+n^{2}\right) \)


Given, pH of a solution A is 3 and is mixed with another solution B having pH 2. If both are mixed, then the
resultant pH of the solution will be:
A . 3.2
в. 1.9
\( c .3 .4 \)
D. 3.5