The coefficient of \( x^{53} \) in the following
expansions. \( \sum_{m=0}^{100} 100 C_{m}(x-3)^{100-m} \cdot 2^{m} \) is
A. \( ^{100} C_{47} \)
B. \( ^{100} C_{53} \)
\( \mathbf{c} .-_{100} 0_{53} \)
D. \( -100 C_{10} \)


An organic compound (E) \( \left(C_{5} H_{8}\right) \) on hydrogenation gives a compound (F)
\( \left(C_{5} H 12\right) . \) Compound (E) on ozonolysis gives formaldehyde and 2-ketopropanal. Deduce the structure of the compound
(E).
A. cyclopentene
B. 1,4 pentadiene
c. 1,3 pentadiene
D. 2 methyl 1,3 butadiene


An infant was having a sound sleep, he suddenly woke up with the noise of the drums outside. Which receptor in the infant is responsible for the detection of
the sound?
A. Gustatory receptor
B. Auditory receptor
c. olfactory receptor
D. None of the above


Among the following which one is the richest source of proteins
A. Wheat (Triticum vulgare)
B. Rice (Oryza sativa)
c. Gram (Cicer arietinum)
D. Ground nut (Arachis hypogea)


The gravitational field intensity at a point \( 10,000 \mathrm{km} \) from the centre of the
earth is \( 4.8 N k g^{-1} . \) The gravitational
potential at the point is
A \( .-4.8 \times 10^{7} J k g^{-1} \)
B . \( -2.4 \times 10^{7} \mathrm{Jkg}^{-1} \)
C \( .4 .8 \times 10^{6} \mathrm{Jkg}^{-1} \)
D. \( 3.6 \times 10^{6} \mathrm{Jkg}^{-1} \)


Which is more hard, sponge or iron?


The distance between the ends of the
wings of an airplane is \( 50 m \). It is flying in a horizontal plane at a speed of \( 360 K m / \)hour. The vertical component
of earth's magnetic field at that place is \( 2.0 \times 10^{-4} W b / m^{2}, \) then the potential
difference induced between the ends of
the wings will be
A . \( 0.1 v o l t \)
B. \( 1.0 v o l t \)
c. \( 0.2 v o l t \)
D. \( 0.01 v \) volt


Meristematic tissue occurs in
A. Stems
B. Roots
c. All growing tips
D. Both of the (A) and (B)


A bar magnet, held horizontally, is set into angular oscillations in the earth's
magnetic field. Its time periods are \( T_{1} \)
and \( T_{2} \) at two places where the angles of
dip are \( \theta_{1} \) and \( \theta_{2} \) respectively. The ratio
of the resultant magnetic fields at these two places will be:
This question has multiple correct options
A. \( T_{1} \sin \theta_{1}: T_{2} \sin \theta_{2} \)
B. \( T_{\mathrm{i}} \cos \theta_{1}: T_{2} \cos \theta_{2} \)
c. \( T_{2}^{2} \sin \theta_{2}: T_{1}^{2} \sin \theta_{1} \)
D. \( T_{2}^{2} \cos \theta_{2}: T_{1}^{2} \cos \theta_{1} \)


A triangle has a base \( 6 \mathrm{cm} \) and has the same area as a circle of radius \( 6 \mathrm{cm} \) the
altitude of the triangle in cm is


The total number of configurational isomers of the given compound are:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}= \)
CHCHOHCHOHCH\( _{3} \)
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Select the proper effect of growth
regulator, which is acidic in nature and
is synthesized more in darkness.
A. Under the condition of water-stress, it stimulates the
process of closing of stomata.
B. Retained chlorophyll in leaves.
C. It induces drooping of leaf and flowers.
D. Mobilization of storage compounds during germination.


By which of the following active uptake
of water is affected?
A. Transpiration power of the root hairs
B. Typical tissue organization
C. Tension due to transpiration
D. Osmotic concentration of the cell sap of the leaves


On warming silver in \( \boldsymbol{O}_{3}: \)
A. oxidation of the metal takes place
B. formation of ozonide takes place
c. alternate oxidation of the metal and reduction of oxide
takes place
D. reduction of metal takes place


For a zero order reaction:
\( \mathbf{A} \cdot t_{1 / 2} \propto R_{o} \)
B \( \cdot t_{1 / 2} \propto \frac{1}{R_{o}} \)
\( \mathbf{c} \cdot t_{1 / 2} \propto R_{o}^{2} \)
D \( t_{1 / 2} \propto \frac{1}{R_{o}^{2}} \)


Which of the following statement(s) is (are) true about heart?
A. Left atrium receives oxygenated blood from different parts of body while right atrium receives deoxygenated blood from lungs.
B. Left ventricle pumps oxygenated blood to different body parts while right ventricle pumps deoxygenated blood to lungs.
C. Left atrium transfers oxygenated blood to right ventricle which sends it to different body parts.
D. Right atrium receives deoxygenated blood from different parts of the body while left ventricle pumps oxygenated blood to different parts of the body.
\( E . \) Both \( B \) and \( D \)


Area of right triangle \( M O B \) is 16
sq.units. If \( \boldsymbol{O} \) is the origin and the
coordinates of \( A \) are \( (8,0), \) what are the
coordinates of B ?
\( A \cdot(0,4) \)
B. (0, 2)
\( c \cdot(-1,1) \)
\( \mathbf{D} \cdot\left(0, \frac{1}{2}\right) \)


If \( 33 \% \) HI decompose at a particular
temperature, \( K_{c} \) for the reaction is
equal to?
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I} \rightleftharpoons \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \)
A . \( 1 / 6 \)
B . \( 1 / 4 \)
c. \( 1 / 16 \)
D. \( 1 / 8 \)


Find the slope and \( y \) -intercept of the
line \( 0.2 x-y=1.2 \)
A. slope \( =0.2, y \) -intercept \( =-1.2 \)
B. slope \( =1.2, y \) -intercept \( =-1.2 \)
c. slope \( =0.2, y \) -intercept \( =-2.2 \)
D. slope \( =0.2, y \) -intercept \( =-1.3 \)


\( \lim _{x \rightarrow 2} \frac{\sum 32 x}{x^{3}-p} \)


In a cell, the following reaction takes
place: \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C u} \boldsymbol{S O}_{4} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{C u} \)
The cell can be represented as:
A \( \cdot C u\left|C u S O_{4} \| F e\right| F e S O_{4} \)
B . \( P t\left|C u S O_{4} \| F e S O_{4}\right| P t \)
c. \( F e\left|F e S O_{4} \| C u S O_{4}\right| C u \)
D. \( C u S O_{4}\left|C u \| F e S O_{4}\right| F e \)


\( M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+ \)
\( 2 H_{2} O \)
If 1 g of \( H C l \) and 1 g of \( M n O_{2} \) is heated together, the maximum weight of \( C l_{2} \) gas evolved will be:
A .2 g
B. 0.975 g
c. \( 0.486 \mathrm{g} \)
D. 0.972 g


In Pheretima, septa are absent in
segments of
A \( .5 / 6,10 / 11 \)
B. 5/6, 7/8
c. \( 6 / 7,7 / 8 \)
D. First four segments


Solve :
\[
\boldsymbol{x}^{2}-\boldsymbol{8} \boldsymbol{x}+\mathbf{1 2}=\mathbf{0}
\]


The first and second dissociation
constants of an acid \( \boldsymbol{H}_{2} \boldsymbol{A} \) are \( \mathbf{1 . 0} \times \)
\( 10^{-5} \) and \( 5.0 \times 10^{-10} \) respectively. The
overall dissociation constant of the acid
will be:
A \( .5 .0 \times 10^{15} \)
В. \( 5.0 \times 10^{-15} \)
c. \( 0.2 \times 10^{5} \)
D. \( 5.0 \times 10^{-5} \)


If \( n(A)=m \) and \( n(B)=n ; \) then
\( \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B})=\boldsymbol{m} \boldsymbol{n} \)
What is the value of \( n(A \times B)=m n \). if
\( \boldsymbol{m}=\boldsymbol{6} \) and \( \boldsymbol{n}=\boldsymbol{8} \)


A bag contains cards which are
numbered from 2 to \( 90 . \) A card is drawn
at random from the bag. Find the probability that it bears
(i) a two digit number
(ii) a number
which is a perfect square


It is a common experience that after a rainfall, the objects at a distance are seen more clearly. Why?


Choose the correct statement from the
following.
A. Right kidney slightly lower than the left one due to stomach
B. Left kidney slightly lower than the right one due to live
c. Right kidney slightly lower than the left kidney due to liver
D. Right kidney slightly upper than the left kidney due to liver


Suppose the loop in Exercise is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initia
value of \( 0.3 \mathrm{T} \) at the rate of \( 0.02 \mathrm{T} s^{-1} . \) If
the cut is joined and the loop has a resistance of 1.6 ohm , how much power is dissipated by the loop as heat? What is the source of this power?
Exercise :
I A rectangular wire loop of sides \( 8 \mathrm{cm} \) and \( 2 \mathrm{cm} \) with a small cut is moving out of a region of uniform magnetic field of magnitude \( 0.3 \mathrm{T} \) directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is \( 1 \mathrm{cm} \)
\( s^{-1} \) in a direction normal to the (a)
longer side,
(b) shorter side of the loop?
For how long does the induced voltage last in each case?


If the angle between incident ray and
normal is \( 30^{\circ}, \) choose the correct option:
A. Angle between incident ray and mirror \( =60^{\circ} \)
angle between reflected ray and mirror \( =60^{\circ} \)
Angle between normal and the mirror \( =90^{\circ} \)
B. Angle between incident ray and mirror \( =30^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =30^{\circ} \)
C. Angle between incident ray and mirror \( =120^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =30^{\circ} \)
D. Angle between incident ray and mirror \( =60^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =120^{\circ} \)


Write the structures of monomers used
to obtain the following polymers:
(a) Neoprene
(b) PHBV
(c) Bakelite


Write any two postulates of Werner's theory of coordination compounds.


You have studied mitosis in onion root
tip cells. It has 14 chromosomes in each cell. Can you tell how many
chromosomes will the cell have at \( G_{1} \)
phase, after \( \mathrm{S} \) phase, and after \( \mathrm{M} \)
phase? Also, what will be the DNA
content of the cells at \( G_{1}, \) after \( S \) and at
\( G_{2}, \) if the content after M phase is \( 2 C ? \)


Producer gas is a mixture of:
A \( \cdot C O+H_{2} \)
в. \( H_{2}+C H_{4} \)
c. \( C O+N_{2}+H_{2} \)
D. \( C O+H_{2} O \)


Let \( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{x}^{2} / 2 . \) If the graph of \( \boldsymbol{f}(\boldsymbol{x}) \)
is translated 2 units up and 3 units left and the resulting graph is that of \( g(x) \) \( \operatorname{then} g(1 / 2)= \)
A .
B . \( -1 / 8 \)
c. \( -2 / 8 \)
D. \( -33 / 8 \)
E . \( 13 / 8 \)


If the charge on a capacitor is increased by 2 colomb, the energy stored in it increases by \( 21 \% \). The original charge on the capacitor is
A . 10
B. 20
c. 30
D. 40


Given a current carrying wire of non-
uniform cross-section. Which one of the
following is constant through out the length of wire?
A. Current only
B. Current and drift speedd
c. Drift speed only
D. Current, electric field and drift speed


Which of the following statement is
incorrect?
A. \( N O \) is heavier than \( O_{2} \)
B. The formula of heavy water is \( D_{2} O \)
C. Nitrogen diffuses faster than oxygen through an orifice.
D. \( N H_{3} \) can be used as a refrigerant.


Molar conductances of \( B a C l_{2}, H_{2} S O_{4} \)
and \( H C l \) are \( x_{1}, x_{2} \) and \( x_{3} S c m^{2} m o l^{-1} \)
at infinite dilution. If specific
conductance of saturated \( B a Z O_{4} \)
solution is of \( y S c m^{-1}, \) then \( k_{s p} \) of
\( B a S O_{4} \) is:
A. \( \frac{10^{3} y}{2\left(x_{1}+x_{2}-2 x_{3}\right)} \)
В. \( \frac{10^{6} y^{2}}{\left(x_{1}+x_{2}-2 x_{3}\right)^{2}} \)
c. \( \frac{10^{6} y^{2}}{4\left(x_{1}+x_{2}-2 x_{3}\right)^{2}} \)
D. \( \frac{x_{1}+x_{2}-2 x_{3}}{10^{6} y^{2}} \)


The kilowatt hour is the unit of


A quantity of aluminium has a mass of
54g. What is the mass of same number
of magnesium atoms?
A. \( 12.1 g \)
в. \( 24.3 g \)
c. \( 48.6 g \)
D. \( 97.2 g \)


Which of the following is not a primary amine?
A. tert - Butylamine
B. sec-Butylamine
c. Isobutylamine
D. Dimethylamine


Solve for \( z:(i-z)(1+i)=2 i \)


Two copper spheres, \( A \) and \( B \), are identical in all respect but A carries a charge of \( -3 \mu C \) whereas \( B \) Is charged
to \( +1 \mu C \). The two spheres are brought together until they touch and then separated by some distance. Which of the following statements is true concerning the electrostatic force \( \boldsymbol{F} \) between the spheres?
A. \( F=0 \) as one of the spheres is uncharged
B. \( F=0 \) as both the spheres are uncharged
c. \( F \) is attractive
D. F is repulsive


Zener diode is a voltage regulation device.
A . True
B. False


The slope of the tangent to the curve \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{1}, \boldsymbol{y}=\boldsymbol{t}^{3}-\mathbf{1} \) at \( \boldsymbol{x}=\mathbf{1} \) is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-2 \)
\( D \cdot \infty \)


A bag contains 10 white and 15 black
balls. Two balls are drawn in succession
without replacement. What is the probability that first is white and second is black?


A solution which is \( 10^{-3} M \) each in
\( M n^{2+}, F e^{2+}, Z n^{2+} \) and \( H g^{2+} \) is treated
with \( 10^{-16} M \) sulphide ion. If \( K_{s p} \) of \( M n S, F e S, Z n S \) and \( H g S \) are
\( 10^{-13}, 10^{-18}, 10^{-24} \) and \( 10^{-53} \)
respectively, which one will precipitate first?
A. FeS
в. \( M g S \)
c. Нg S
D. ZnS


If \( R \) divides the line segment joining \( P(2, \)
3, 4) and \( Q(4,5,6) \) in the ratio -3: 2 then the value of the parameter which
represents R is
в. \( =(10,9,8) \)
\( \mathbf{c} .=(10,8,9) \)
\( \mathbf{D} .=(9,10,8) \)


Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system
A \( \cdot 4 m w^{2} r \)
B. \( 10 m w^{2} \)
c. \( 30 m w^{2} r \)
D. \( 20 m w^{2} r \)


if sum=1 product \( =-6 \) then find the 2 numbers.


The potential energy of a simple
pendulum will be maximum when it is-
A. At the turning points of oscillations
B. At the equilibrium
C. In between the above two cases
D. At any position, it has always a fixed value


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2}^{\boldsymbol{x}} \)
Determine
(i) Range of \( \boldsymbol{f} \)
(ii) \( \{x: f(x)=1\} \)
(iii) whether \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \)
holds.


\( A, B, C \) are pair wise independent.
A. True
B. False


A charged particle (charge q) is moving in a circle of radius \( R \) with uniform
speed
A \( \cdot \frac{q v R}{2} \)
B \( \cdot q v R^{2} \)
c. \( \frac{q v R^{2}}{2} \)
D. \( q v R \)


The construction of \( 3 \times 4 \) matrix \( A \)
whose elements \( a_{i j} \) is given by \( \frac{(i+j)^{2}}{2} \) is
\( \mathbf{A} \cdot\left[\begin{array}{llll}2 & 9 / 2 & 8 & 25 \\ 9 & 4 & 5 & 18 \\ 8 & 25 & 18 & 49\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cccc}2 & 9 / 2 & 25 / 2 & 9 \\ 9 / 2 & 5 / 2 & 5 & 45 / 2 \\ 25 & 18 & 25 & 9 / 2\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{cccc}2 & 9 / 2 & 8 & 25 / 2 \\ 9 / 2 & 8 & 25 / 2 & 18 \\ 8 & 25 / 2 & 18 & 49 / 2\end{array}\right] \)
D. None of these


Essential nutrients are
A. Made by the body
B. Supplied by food
C. Enzymes
D. Alcohol


On hydrolysis of interhalogen compound,oxyhalide ion is formed from:
A. larger halogen
B. smaller hallogen
c. both the halogens
D. more electronegative halogen


Assertion
Ultrasonic waves are longitudinal
waves of frequency greater than 20,000 \( \mathrm{Hz} \)
Reason
The maximum frequency of audible sound waves is \( 20,000 \mathrm{Hz} \)
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


\( \mathrm{X}^{\prime} \) is a group of stars visible during winter season in the late evening. It resembles a hunter in the kneeling position. What is 'X'?
A. Ursa Major
B. Orion
c. cassiopeia
D. Aquarius


Figure shows the field produced by two
point charges \( +q \) and \( -q \) of equal
magnitude but opposite signs \( (a n \) electric dipole). Find the electric flux
through each of the closed surfaces \( A \)
B, C and D.


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


Variable valency in general is shown by :
A. gaseous elements
B. non-metals
c. s-block elements
D. d-block elements


Eggs which have yolk in the centre surrounded by cytoplasm are called as
A . Centrolecithal
B. Homolecithal
c. Microlecithal
D. Alecithal


Match the following columns.


(a) Bleaching of flowers by chlorine is
stable but bleaching of \( S O_{2} \) is unstable
Why?
(b) Water is liquid while hydrogen sulphide is a gas at normal temperature. Why?


TEL is a compound used as
\( A \). antibiotic
B. antiseptic
c. antiknocking
D. None of these


Two thin lenses, when in contact,
produce a combined power +10 dioptre When they are \( 0.25 \mathrm{m} \) apart, the power reduce to +6 dioptre. The power of the lenses in dioptre, are:
A . 1 and 9
B. 2 and 8
\( c \cdot 4 \) and 6
D. 5 each


Define antioxidants. Draw structure of
BHT.


Activated charcoal is used to remove
coloring matter from pure substances.
It works by:
A. oxidation
B. reduction
c. bleaching
D. adsorption


A solenoid \( 30 c m \) long is made by
winding 2000 loops of wire on an iron
rod whose cross-section is \( 1.5 \mathrm{cm}^{2} \). If
the relative permeability of the iron is \( 6000, \) what is the self-inductance of the
solenoid?
\( \mathbf{A} \cdot 15 H \)
в. \( 2.5 H \)
\( c .3 .5 H \)
D. \( 0.5 H \)


Let \( \boldsymbol{A}=\left[\begin{array}{c}\mathbf{3} \boldsymbol{x}^{2} \\ \mathbf{1} \\ \mathbf{6} \boldsymbol{x}\end{array}\right], \boldsymbol{B}=[\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}] \) and \( \boldsymbol{C}= \)
\( \left[\begin{array}{ccc}(x+2)^{2} & 5 x^{2} & 2 x \\ 5 x^{2} & 2 x & (x+2)^{2} \\ 2 x & (x+2)^{2} & 5 x^{2}\end{array}\right] \)
three given matrices, where \( a, b, c \) and
\( \boldsymbol{x} \in \boldsymbol{R}, \) Given that \( \boldsymbol{t r} .(\boldsymbol{A B})=\boldsymbol{t r} .(\boldsymbol{C}) \vee \)
\( \boldsymbol{x} \in \boldsymbol{R}, \) where \( \boldsymbol{t r} .(\boldsymbol{A}) \) denotes trace of \( \boldsymbol{A} \)
Find the value of \( (\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \)
\( A \cdot 6 \)
B.
\( c \cdot 8 \)
D.


Which direction will you face if you start facing east and make \( \frac{1}{2} \) of a revolution clockwise?


What should be added to \( x^{2}+x y+y^{2} \)
to obtain \( 2 x^{2}+3 x y ? \)


A right isosceles triangle of side \( a \) has
charges \( \boldsymbol{q},+\boldsymbol{3} \boldsymbol{q} \) and \( -\boldsymbol{q} \) arranged on its
vertices as shown in the figure. What is
the electric potential at point \( \boldsymbol{P} \) midway
between the line connecting the \( +q \) and
\( -q \) charges?
A \( \cdot \frac{3 q}{r \epsilon_{6} a} \)
В. \( \frac{3 q}{\sqrt{2} \pi \epsilon a a} \)
c. \( \frac{q}{\pi \epsilon_{a} a} \)
D. \( \frac{3 q}{2 \sqrt{2} \pi \epsilon_{0} a} \)


State whether the given statement is
True or False \( \int_{0}^{2} e^{x} d x \) can be represented as
\( 2 \lim _{n \rightarrow \infty} \frac{1}{n}\left[e^{0}+e^{\frac{2}{n}}+e^{\frac{4}{n}}+\ldots \ldots+e^{\frac{2(n-1)}{n}}\right] \)
A. True
B. False


For two position of lens, the images are obtained on a fixed screen. If the size of
the object is \( 2 \mathrm{cm} \) and size of diminished image is \( 0.5 \mathrm{cm}, \) the size of the other image will be
A. \( 1 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


Prove the following:
\[
\left|\begin{array}{ccc}
\boldsymbol{a}^{2} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a} \boldsymbol{c}+\boldsymbol{c}^{2} \\
\boldsymbol{a}^{2}+\boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2} & \boldsymbol{a} \boldsymbol{c} \\
\boldsymbol{a b} & \boldsymbol{b}^{2}+\boldsymbol{b} \boldsymbol{c} & \boldsymbol{c}^{2}
\end{array}\right|=\boldsymbol{4} \boldsymbol{a}^{2} \boldsymbol{b}^{2} \boldsymbol{c}^{2}
\]


The most important distinctive character of chordata is the presence of
A. Vertebral column
B. Hairy skin
c. Notochord
D. All of the above


Assertion
The expression \( n !(10-n) ! \) is
minimum for \( n=5 \)
Reason
The expression \( ^{2 m} C_{r} \) attains maximum
value for \( \boldsymbol{m}=\boldsymbol{r} \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true


The figure depicting neuron is given The correct identification of labels I, II
III and IV respectively is
A . I- Dendrite, , I- Cell body, III-Axon, IV- Synaps
B. I- Dendrites, Il- Nucleus, II- Axon, IV- Axon endings
C. I- Axon, II- Nucleus III- Dendrites, IV- Axon endings
D. I- Dendron, II- Cell body, II- Axon, IV -Dendrites


Let circles \( C_{1} \) and \( C_{2} \) an Argand plane
be given by \( |z+1|=3 \) and \( |z-2|=7 \)
respectively. If a variable circle
\( \left|z-z_{0}\right|=r \quad \) be inside circle \( C_{2} \) such
that it touches \( C_{1} \) externally and \( C_{2} \)
internally then locus of \( z_{0} \) describes a
conic \( \boldsymbol{E} \) whose eccentricity is equal to
A \( \cdot \frac{1}{10} \)
B. \( \frac{3}{10} \)
c. \( \frac{5}{10} \)
D. \( \frac{7}{10} \)


Find the coefficient of \( x^{50} \) in the
expression:
\( (1+x)^{1000}+2 x(1+x)^{999}+ \)
\( \mathbf{3} x^{2}(\mathbf{1}+\boldsymbol{x})^{\mathbf{9} 9 \mathbf{8}}+\ldots .+\mathbf{1 0 0} \mathbf{1} \boldsymbol{x}^{\mathbf{1 0 0 0}} \)
A \( .^{1000} \mathrm{C}_{50} \)
В. \( ^{1001} \mathrm{C}_{50} \)
\( \mathbf{c} \cdot^{1002} C_{50} \)
D. \( ^{1003} \Omega_{50} \)


Show that \( 3+\frac{1}{1+} \frac{1}{6+1+} \frac{1}{6+} \dots= \)
\( 3\left(1+\frac{1}{3+2+3+2+\cdots}\right) \)


In reaching her destination, a backpacker walks with an average velocity of \( 1 m / s, \) due west. This average
velocity results, because she hikes for
\( 6 k m \) with an average velocity of \( 3 m / s \) due west, turns around, and hikes with
an average velocity of \( 0.3 m / s \) due east.How far to east did she walk (in
kilometers)?
A. 1.714
в. 2
\( c .6 \)
D


Which warms up faster when same
amount of heat is applied to iron and
silver?


In the gas equation \( P V=R T \), Vis the
volume of
A. 1 mol of gas
B. \( 1 \mathrm{g} \) of gas
\( c \cdot \operatorname{gas} \)
D. 1 litre of gas


Which of the following is the non-
metric unit of length?
A. millimeters
B. centimeters
c. meters
D. inches


(A) Fenestra
(B) Pedical
(C) Lacinia (D)
Flagellum, E) Gelea (F) Mentum (G) Palpifer (H) Cardo (I) Glossa
Which of the above is found in the first
pair of maxillae in the case of a
cockroach?
A. \( c, \) E G and
B. A, C, E and I
c. \( A, F, \) G and 1
D. B, E, G and I


At equilibrium temperature, the rate of
flow of heat energy from one body to the other and back is the same. Is the
statement True or False
A. True
B. False


A circle that has its center its center at
the origin and passes through (-8,-6) will also pass through the point:
A \( \cdot(1,10) \)
B. (4,7)
\( c \cdot(7,7) \)
D. \( (9, \sqrt{19}) \)


State one activity to prove that air is a bad conductor of electricity


Two long straight parallel wires separated by a distance, carrying equal currents exert a force \( F \) per unit length on each other. If the distance of
separation is doubled, and the current in each is halved, the force per unit length, between them will be :
\( A \cdot F \)
B. F/2
\( c \cdot F / 4 \)
D. F/


In traffic signals colour
light is used to stop vehicles because it
has \( _{\text {一一一一一一 }} \) wave length. (Hint:
scattering of light is inversely proportional to the fourth power of its wavelength)


Which of the following resonating structures of 1 -methoxy-1, 3-butadiene
is least stable?
A \( \cdot \bar{C} H_{2}-C H=C H-C H=\dot{O}-C H_{3} \)
B. \( C H_{2}=C H_{2}-\bar{C} H_{2}-C H=\dot{O}-C H_{3} \)
\( \mathbf{c} \cdot \bar{C} H_{2}-C \dot{H}-C H=C H-O-C H_{3} \)
D. \( C H_{2}=C H-\stackrel{+}{C H}-\bar{C} H-O-C H_{3} \)


The first term of arithmetic progression is 1 and the sum of the first nine terms
equal to \( 369 . \) The first and the ninth
term of a geometric progression conicide with the first and the ninth
term of the arithmetic progression. Find the seventh term of the geometric progression.


If on division of a polynomial \( p(x) \) by a polynomial \( g(x), \) the quotient is zero, what is the relation between the \( \operatorname{degrees} \) of \( p(x) \) and \( g(x) ? \)
\( A \cdot \operatorname{deg} p(x)<\operatorname{deg} g(x) \)
B. \( \operatorname{deg} p(x)>\operatorname{deg} g(x) \)
c. cannot be determined
D. can't say


In 1911 , the physicist Ernest Rutherford discovered that atoms have a tiny, dense nucleus by shooting pisitively charged particular at a very thin gold foil. A key physical property which led Rutherford to use gold that it was
A. Electrically conducting
B. Highly malleable
c. shiny
D. none-rective


A wave travelling along positive x-axis
is given by \( =A \sin (\omega t-k x) . \) If it is
reflected from a rigid boundary such that \( 80 \% \) amplitude is reflected, then equation of reflected wave is
\( \mathbf{A} \cdot y=A \sin (\omega t+0.8 k x) \)
B . \( y=-0.8 A \sin (\omega t+k x) \)
c. \( y=A \sin (\omega t+k x) \)
D \( \cdot y=0.8 A \sin (\omega t+k x) \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{1} & \mathbf{0} & \mathbf{3} \\ -\mathbf{2} & \mathbf{- 3} & \mathbf{0}\end{array}\right], \) then \( \boldsymbol{A}+\mathbf{2} \boldsymbol{A}^{\prime} \)
equals
A. \( A \)
B . \( A^{\prime} \)
\( c \cdot-A \)
D. \( 2 A \)


In Young's double slit experiment, the
two slits act as coherent sources of
equal amplitude 'a' and of wavelength \( \lambda \)
In another experiment with the same
set up, the two slits are sources of equal
amplitude 'a' and wavelength \( \lambda \), but
have \( 90^{\circ} \) phase difference. The ratio of intensity of light at the midpoint of the screen in the first case to that in the
second case is
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 2
c. 3: 4
D. 4: 3


A particle of charge \( q \) and mass \( m \) moves in a circular orbit of radius r with
angular speed \( \omega . \) The ratio of the
magnitude of its magnetic moment to that of its angular momentum depends
on
A. \( \omega \) and \( q \)
B. \( \omega, q \) and \( m \)
c. \( q \) and \( m \)
D. \( \omega \) and \( m \)


\( A B C \) is a frictionless circular track of
radius \( R \). A particle of mass \( m \) kg is
released from point \( \boldsymbol{P}(\boldsymbol{O P}=\boldsymbol{R} / \mathbf{2}) \)
After collision with the track, particle moves along the track, then coefficient
of restitution is
A . 0.5
B. 0.3
\( c .0 .2 \)
D. non


How many nodes are present in \( 3-\mathrm{p} \) orbitals? Represent diagrammatically.


A charged dust particle of radius \( 5 \times \) \( 10^{-7} \mathrm{m} \) is located in a horizontal
electric field having an intensity of \( 6.28 \times 10^{5} v / m . \) The surrounding
medium is air with coefficient of
viscosity \( \boldsymbol{\eta}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{N S} / \mathbf{m}^{2} . \) If the
particle has a charge of \( 7.2 \times 10^{-15} \)
then it moves with a uniform horizontal
speed of
A . 10
в. 20
\( c .30 \)
D. 40


The sum of the number of neutrons and
proton in the isotopes of hydrogen is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
\( D \)


A wave train has the equation \( y= \) \( 4 \sin (30 \pi t+0.1 x) \) where \( x \) is in \( \mathrm{cm} \) and
\( t \) in seconds. What is the frequency of
the source? How much time does a
wave pulse take to reach a point \( 30 \mathrm{cm} \)
from it??


Assertion
Cyclotron does not accelerate electron.
Reason
Mass of the electrons is very small.
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 transfer of \( \boldsymbol{H}_{2} \) gas occurs from north
pole to desert area, which form of
hydrogen is stable?
Desert
A. Ortho
B. Para
\( c . \) Both
D. None


An infinite number of charges each equal to q are placed along the \( X- \) axis at \( x= \) \( 1, x=2, x=4, x=8 \ldots \ldots \) and so on. The
potential and field respectively due to this set of charges at the origin is :
A \( \cdot \frac{q}{3 \pi \epsilon_{0}} \) and \( \frac{q}{2 \pi \epsilon_{0}} \)
в. \( \frac{q}{2 \pi \epsilon_{0}} \) and \( \frac{q}{3 \pi \epsilon_{0}} \)
c. \( \frac{q}{4 \pi \epsilon_{0}} \) and \( \frac{q}{3 \pi \epsilon_{0}} \)
D. \( \frac{q}{2 \pi \epsilon_{0}} \) and \( \frac{q}{4 \pi \epsilon_{0}} \)


Assertion
When current is represented by a straight line, the magnetic field will be circular.
Reason
According to Fleming's left hand rule, direction of force is parallel to the magnetic field
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


Identify tthe compounds which are reduced and oxidised in the following
reaction.
\( \mathbf{3} N_{2} \boldsymbol{H}_{4}+\mathbf{2} \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-} \rightarrow \mathbf{3} \boldsymbol{N}_{2}+\mathbf{2} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot N_{2} H_{4} \) is oxidised and \( B r O_{3}^{-} \) is reduced
B. \( B r O_{3}^{-} \) is oxidised and \( N_{2} H_{4} \) is reduced
C. \( B r O_{3}^{-} \) is both reduced and oxidised
D. This is not a redox reaction


In the fig; we have \( X \) and \( Y \) as the mid-
points of \( A C \) and \( B C \) and \( A X=C Y \)
Then,
This question has multiple correct options
A. \( A C=B C \)
В. \( A C=A B \)
\( \mathbf{c} . A B=B C \)
\( \mathrm{D} \cdot C X=C Y \)


Lay down the positions of the points whose polar coordinates are
\( \left(-1,-180^{\circ}\right) \)


\( x \in\{\text { real numbers }\} \) and \( -1<3-2 x \leq \)
\( 7, \) evaluate \( x \) and represent it on a number line.


Refer to the given figure and select the
incorrect option regarding it.
A. It belongs to Class Basidiomycetes.
B. It is a non-edible, poisonous mushroom.
C. It possesses an umbrella like basidiocarp.
D. The basidiospores in it, are exogenously produced on the basidium


The metal which can displace hydrogen from acid is:
A . silver
B. calcium
c. mercury
D. gold


Four charges \( +\boldsymbol{Q},-\boldsymbol{Q},+\boldsymbol{Q},-\boldsymbol{Q} \) are
placed at the corners of a square taken order. At the centre of the square:
A. \( E=0, V=0 \)
B. \( E=0, V \neq 0 \)
c. \( E \neq 0, V=0 \)
D. \( E \neq 0, V \neq 0 \)


A semi-circular conducting ring acb of radius \( R \) moves with constant speed \( v \)
in a plane perpendicular to uniform
magnetic field \( B \) as shown in figure. Identify the correct statement
A \( \cdot V_{a}-V_{c}=B R v \)
В. \( V_{b}-V_{c}=B R v \)
c. \( V_{a}-V_{b}=0 \)
D. None of these


During a negative beta decay.
A. An atomic electron is ejected
B. An electron which is already present within the nucleus is ejected
C. A neutron in the nucleus decays emitting an electron
D. A part of the binding energy of the nucleus is converted into an electron


Two trains of length \( 500 m \) and \( 1000 m \) moving in opposite direction with same
speed crosses each other in 10 sec, find their speed:
A. \( 75 \mathrm{m} / \mathrm{s} \)
в. \( 150 m / s \)
c. \( 100 \mathrm{m} / \mathrm{s} \)
D. None of these


Find \( (-5 i)\left(\frac{3}{5} i\right) \)


When a solution is diluted at constant
temperature, its vapour pressure:
A. increases
B. decreases
c. remains same
D. may increase or decrease


One curie is equal to
\( \mathbf{A} \cdot 3.7 \times 10^{10} \) disintegration/sec
B. \( 3.2 \times 10^{8} \) disintegration/sec
C \( .2 .8 \times 10^{10} \) disintegration/sec
D. None of these


The output characteristic of an \( n-p-n \) transistor represent:
\( \left[I_{C}=\text { Collector current, } V_{C E}= \) potential \right. difference between collector and
emitter, \( \boldsymbol{I}_{B}= \) Base current, \( \boldsymbol{V}_{\boldsymbol{B} \boldsymbol{B}}= \)
voltage given to base; \( V_{B E}= \) the potential difference between base and emitter \( ] \)
A. changes in \( I_{C} \) as \( I_{B} \) and \( V_{B B} \) are changed
B. changes in \( I_{C} \) with changes in \( V_{C E}\left(I_{B}=\text { constant }\right) \)
c. changes in \( I_{B} \) with changes in \( V_{C E} \)
D. changes in \( I_{C} \) as \( V_{B E} \) is changed


S.TF :Q defined by \( f(x)=2 x+3 / x-3 \)
is one -one but not onto


In which of the following the final image
is erect?
A. Compound microscope
B. Astronomical telescope
c. simple microscope
D. All of the above


State True and False :
During the day, land gets heated faster
than water.
A. True
B. False


If \( \mathbf{5} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ \mathbf{4} & \boldsymbol{x}\end{array}\right] \) and \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}}=\boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\boldsymbol{I} \)
then \( x=? \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. -3
c. 2
D. -2


A hormone that stimulates an endocrine
gland to grow and secrete its hormone is known as
A. Endocrine hormone
B. Tropic hormones
c. Exocrine hormone
D. None of these


Indicate the wrong statement according to valence bond therory:
A. a sigma bond is stronger then \( \pi \) bond
B. p-orbitals always have only sidewise overlapping
c. s-orbitals never form \( \pi \) - bonds
D. there can be only one sigmabond between two atoms


Elements are classified into four major
categories:
A. Metals.
B. non-metals.
c. Metalloids
D. Noble Gases
E. All of the above.


Bleaching action of chlorine is permanent while bleaching action of sulphur dioxide is temporary, why?


Surface of the eye is protected from bacterial infection by enzyme
A. Carbonic enhydrase
B. Urease
c. Lysozyme
D. Zymase


If the system of equations \( 2 x+3 y- \)
\( \mathbf{5}=\mathbf{0}, \mathbf{4} \boldsymbol{x}+\boldsymbol{k} \boldsymbol{y}-\mathbf{1 0}=\mathbf{0} \) has an infinite
number of solutions, then
A \( \cdot k=\frac{3}{2} \)
в. \( _{k \neq \frac{3}{2}} \)
c. \( k \neq 6 \)
D. \( k=6 \)


Fill in the blanks in the following conversions:
¡) \( 1 k m=\dots \dots \dots . . m m=\dots \dots \dots . . p m \)
ii) \( 1 \boldsymbol{m} \boldsymbol{g}=\ldots \ldots \ldots \boldsymbol{k} \boldsymbol{g}=\ldots \ldots \ldots \boldsymbol{n} \boldsymbol{g} \)
iii) \( 1 m L=\dots \dots \dots . . L=\dots \dots \dots . d m^{3} \)


A uniform spherical shell of mass \( M \) and radius \( R \) rotates about a vertical
axis on frictionless bearing. A massless
cord passes around the equator of the
shell, over a pulley of rotational inertia \( \boldsymbol{I} \)
and radius \( R \) and is attached to a small
object of mass \( m \) that is otherwise free to fall under the influence of gravity
There is no friction of pulley's axle; the
cord does not slip on the pulley. What is
the speed of the object after it has fallen
a distance \( h \) from rest? Use work-energy
considerations


\( 23 g m \) of sodium of reaction with methyl alcohol gives:
A. half mole of \( H_{2} \)
B. one mole of \( H_{2} \)
c. one mole of \( O_{2} \)
D. none


What will happen, if the sperm
containing ' \( X^{\prime} \) chromosomes fertilises
the Ovum?
A. Female child born
B. Male child born
c. can not guess
D. None


Sodium lamps are used in foggy
conditions because:
A. yellow light is scattered less by the fog particles
B. yellow light is scattered more by' the fog particles
C . yellow light is unaffected during its passage through the fog
D. Wavelength of yellow light is the mean of the visible part of the spectrum


The reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3}+ \)
Heat, will be favoured by:
A. high temperature and low pressure
B. low temperature and high pressure
c. high temperature and high pressure
D. low temperature and low pressure


A transversal intersects two parallel
lines. if the measure of one of the angle is \( 50^{0} \), then the measure of its
corresponding angle is
A \( \cdot 40^{\circ} \)
B. \( 130^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 50^{\circ} \)


A sample of pure \( \boldsymbol{P} \boldsymbol{C l}_{5} \) was introduced
into an evacuated vessel at 473 K. After
equilibrium was attained,
concentration of \( P C l_{5} \) was found to be
\( \mathbf{0 . 5} \times \mathbf{1 0}^{-1} \mathbf{m o l} \mathbf{L}^{-\mathbf{1}} \)
\( \boldsymbol{P} \boldsymbol{c l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \boldsymbol{K}_{C}= \)
\( 8.3 \times 10^{-3} \) mol \( L^{-1} \)
В. 0.04 М
c. \( 0.2 M \)
D. \( 0.02 \mathrm{M} \)


Green house effect is due to
A. Accumulation of \( O_{3} \) and depletion of \( O_{2} \)
B. Accumulation of \( O_{3} \) and \( C O_{2} \)
C. Depletion of \( C O_{2} \) and \( O_{3} \)
D. Accumulation of green plants


In the case of a plane mirror, from the mirror distance of the image is equal to the distance of the object.
A. True
B. False


Vexillary aestivation is characteristic of
A. Mimosoideae
B. Caesalpinoideae
c. Papilionaceae
D. All of the above


PQR is a triangle right angled at \( P \) and M is a point on QR such that PM \( \perp \) QR. Show that \( \boldsymbol{P} \boldsymbol{M}^{2}=\boldsymbol{Q} \boldsymbol{M} \cdot \boldsymbol{M} \boldsymbol{R} \)


South African cricket captain lost the
toss of a coin 13 times out of \( 14 . \) The
chance of this happening was
A \( \cdot \frac{7}{2^{13}} \)
в. \( \frac{1}{2^{13}} \)
c. \( \frac{13}{2^{14}} \)
D. \( \frac{13}{2^{13}} \)


A man of \( 80 \mathrm{kg} \) attempts to jump from a small boat of mass \( 40 \mathrm{kg} \) on to the shore. He can generate a relative velocity of \( 6 \mathrm{m} / \mathrm{s} \) between himself and
boat. His velocity towards the shore is:
\( A \cdot 4 m / s \)
B. \( 8 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2 m / s \)
D. 3 \( \mathrm{m} / \mathrm{s} \)


The reaction that take place in nuclear reactor is:
A. Nuclear fusion
B. Nuclear fission
c. controlled nuclear fission
D. Double decomposition


If the distance of one of the focus of
hyperbola from the two directrices of hyperbola are 5 and \( 3, \) then its eccentricity is
A \( \cdot \sqrt{2} \)
B. 2
\( c \cdot 4 \)
D.


If \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{4})=\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{2})+\boldsymbol{f}(\boldsymbol{x}+ \)
6) then find the period of \( f(x) \)


\( \int x^{3}(\log x)^{2} d x=\frac{x^{4}}{4}(\log x)^{2} \)
\( \frac{1}{8} x^{4} \log x+\frac{1}{4 k} x^{4} . \) Find the value of \( k \)


If the frequencies of an ultrasonic wave and an electromagnetic wave are same,
then:
A. their wavelength will be same
B. wavelength of electromagnetic wave will be less than that of ultrasonic wave
c. wavelength of electromagnetic wave will be more than that of ultrasonic wave
D. the wavelengths of both will be nearly equal


Liquid benzene burns in oxygen
according to:
\( 2 C_{6} H_{6}+15 O_{2} \rightarrow 12 C O_{2}+6 H_{2} O \)
If density of liquid benzene is \( 0.88 \mathrm{g} / \mathrm{cc} \)
what volume of \( \boldsymbol{O}_{2} \) at \( \mathrm{STP} \) is needed to
complete the combustion of 39 cc of liquid benzene?
A. 11.2 litre
B. 74 litre
c. \( 0.074 \mathrm{m}^{3} \)
D. 37 \( d m^{3} \)


In a purely inductive circuit, the
current:
A. is in phase with the voltage
B. is out of phase with the voltage
C . leads the voltage by \( \pi / 2 \)
D. lags behind the voltage by \( \pi / 2 \)


The value of
\( \lim _{|x| \rightarrow \infty} \cos \left(\tan ^{-1}\left(\sin \left(\tan ^{-1} x\right)\right)\right) \) is equal
to
A . -1
B. \( \sqrt{2} \)
\( c \cdot-\frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}} \)


The pole strength of a bar magnet is 2 Am. If the field at poles are \( 0.2 \mathrm{T} \) and 0.22 T, then the force acting on the bar magnet is
consider field direction to be same
A. \( 0.4 \mathrm{N} \)
B. 0.04N
c. \( 0.44 \mathrm{N} \)
D. 0.8N


The \( n^{t h} \) term of a Geometric Progression
is \( a_{n}=a r^{n-1}, \) where \( r \) represents
A. Common difference
B. Common ratio
c. First term
D. Radius


Preparation of Lyophobic sols by chemical method involves:
A. double decomposition
B. oxidation and reduction
c. hydrolysis
D. all of these


Which one of the following removes temporary hardness of water?
A. Slaked lime
B. Plaster of paris
c. \( C a C O_{3} \)
D. Hydrolith


Define the following term. Volume charge density.


Which of the following can not be used to differentiate meiosis with mitosis?
A. Replication of chromosome before division
B. Exchange of genetic material
c. Formation of tetrad
D. \( 2 \& 3 \) both


Discuss the consequences of
lanthanide contraction.


The length of \( D C= \)
B
\( c .30 \)
D


Frictional force can't be measured in
\( \mathbf{A} \cdot \mathbf{k g} \) wt
B. Newton
c. Dyne
D. \( k g m s^{-} \)


An ideal gas is initially at \( P_{1}, V_{1} \) is
expanded to \( P_{2}, V_{2} \) and then
compressed adiabatically to the same
volume \( V_{1} \) and pressure \( P_{3} \). If \( W \) is the
net work done by the gas in the complete process which of the following
is true.
A. \( W>0 ; P_{3}>P_{1} \)
В. \( W<0 ; P_{3}>P_{1} \)
\( \mathbf{c} \cdot W>0 ; P_{3}<P_{1} \)
D. \( W<0 ; P_{3}<P_{1} \)


In an \( n \) -p-n transistor circuit, the collector current is \( 10 m A \). If \( 90 \% \) of the
electrons emitted reach the collector,
then
This question has multiple correct options
A. the emitter current, the will be \( 9 m A \)
B. the base current will be \( 1 m A \)
c. the emitter current will be \( 11.11 m A \)
D. The base current will be \( 1.11 \mathrm{mA} \)


For the given cell reaction: \( \boldsymbol{F e}^{2+}+ \) \( \boldsymbol{C} \boldsymbol{e}^{4+} \rightleftharpoons \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+} . \) The equilibrium
constant is:
(Given: \( \boldsymbol{E}_{C e^{4+} / C e^{3+}}^{\circ}= \)
\( \left.\mathbf{1 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e^{3+}}^{\circ}=\mathbf{0 . 6 8} \boldsymbol{V}\right) \)


What are Food Additives? Why are they
used?


Assertion
Virtual object can't be seen by human
eye
Reason
Virtual object is formed by converging
rays.
A. Both Assertion and Reason are correct and Reason is
the correct explanation 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


Is \( A^{\prime} \cup B^{\prime}=(A \cap B)^{\prime} \) ? Also, verify if \( A^{\prime} \cap B^{\prime} \)
\( =(A \cup B)^{\prime} \)
A. Yes
B. No
\( c \). Can't Say
D. Cannot be determined


A planet is moving in an elliptical orbit If \( T, U, E \) and \( L \) are its kinetic energy,
potential energy, total energy and magnitude of angular momentum respectively, then which of the following
statement is true.
\( \mathbf{A} \cdot T \) is conserved
B. \( U \) is always positive
c. \( E \) is always negative
D. \( L \) is conserved but the direction of vector \( \vec{L} \) will continuously change


Evaluate: \( \int \frac{\boldsymbol{d x}}{\sin ^{2} x+5 \sin x \cos x+2} \)


A car moves first for 0.1 hour with a
velocity of \( 20 k m / h, \) then for 0.4 hour
with a velocity of \( 60 k m / h \) and in the
last for 0.2 our with a velocity of \( 20 k m / h . \) Draw a time-velocity graph for the car and use it to find
(i) How much distance the car moves in the first time
interval
(ii) How much distance the car
moves in the whole journey. (iii) How much time the car takes in first \( 14 k m \) Indicate that the area in your graph which indicates the journey of first \( \mathbf{1 4 k m} \)


Charges \( Q \) each are placed at each of two opposite corners of a square. Charges \( q \) each are placed at each of
the other two corners. Find the relation
between \( q \) and \( Q, \) when the net force on
Q is zero.
A \( \cdot_{q}=-\frac{3 Q}{2 \sqrt{2}} \)
в. \( _{q}=+\frac{Q}{2 \sqrt{2}} \)
c. \( _{q=-\frac{Q}{\sqrt{2}}} \)
D. \( _{q}=-\frac{Q}{2 \sqrt{2}} \)


Solve \( : \lim _{x \rightarrow 1} \frac{x^{431}+3 . x^{221}-2 . x^{39}-2}{x-1}= \)


An unpolarized light beam is incident
on a surface at an angle of incidence
equal to Brewsters angle. Then,
A. the reflected and the refracted beam are both partially polarized
B. the reflected beam is partially polarized and the refracted beam is completely polarized and are at right angles to each other
C. the reflected beam is completely polarized and the refracted beam is partially polarized and are at right angles to each other
D. both the reflected and the refracted beams are completely polarized and are at right angles to each other.


Which of these components is more in Iymph than in blood?
A. RBC
B. Nutrients
c. Lipids
D. oxygen


If \( \bar{E} \& \bar{F} \) are the complementary events of events E \& F respectively \& if 0 \( < \) \( \boldsymbol{P}(\boldsymbol{F})<1, \) then
This question has multiple correct options
\( \mathbf{A} \cdot P(E \mid F)+P(\bar{E} \mid F)=1 \)
B . \( P(E \mid F)+P(E \mid \bar{F})=1 \)
c. \( P(\bar{E} \mid F)+P(E \mid \bar{F})=1 \)
D. \( P(E \mid \bar{F})+P(\bar{E} \mid \bar{F})=1 \)


Assertion
Brittle materials, which includes cast
iron, glass, and stone, are characterized by the fact that rupture occurs without
any noticeable prior change in the rate
of elongation.
Reason
There is no neck formation in stress
strain curve for brittle material.
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 process is not involved in the extraction of Fe?
A. Gravity separation
B. Leaching
c. Roasting
D. Carbon reduction


Find the difference
between 3.477773 .47777 and 2.85888


Zepto \( =10^{-x}, \) then \( x \) is ?


Number of orbits present in argon is:
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


Choose the incorrect statement about
effective nuclear charge.
A. \( Z_{e f f}=Z-\sigma(\sigma \text { is Slater's screening constant }) \)
B. \( Z_{\text {eff}} \) increases as we move across the period
C. \( Z_{\text {eff}} \) decreases from top to bottom in a group
D. \( Z_{\text {eff}} \) is constant or almost constant for f-block elements


DNA replicates during:
\( \mathbf{A} \cdot G_{2} \) phase
B. M phase
c. s phase
D. \( G_{1} \) phase


Statement-1
Radiation involves transfer of heat by
electromagnetic waves. Statement-2
Electromagnetic waves do not required any material medium for propagation.
A. Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation for Staement-
c. statement-1 is true, statement-2 is false.
D. Statement- 1 is false, Statement-2 is true


The half-life period for a first order reaction is:
A. Independent of concentration
B. Proportional to concentration
c. Inversely proportional to concentration
D. Inversely proportional to the square of the concentration


Integrate \( \int \frac{x^{2} d x}{x^{6}-a^{6}} d x \)


Balance the following equation:
\( \boldsymbol{H} \boldsymbol{g}_{2}(\boldsymbol{C} \boldsymbol{N})_{2}+\boldsymbol{C} \boldsymbol{e}^{4+} \rightarrow \boldsymbol{C} \boldsymbol{O}_{3}^{-}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+ \)
\( \boldsymbol{H} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}+\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+} \)


Name the kingdom to which these organisms belong:
A multicellular heterotrophic organism with a nucleus and capacity for locomotion.
A multicellular, heterotrophic, non-
motile organism with a nucleus. A unicellular organism with a nucleus
A multicellular, autotrophic, a nonmotile organism with a nucleus.


Which of the following ether is not cleaved by HI even at \( 525 \mathrm{K} \) ?
A. \( C_{6} H_{5}-O-C H_{3} \)
в. \( C_{6} H_{5}-O-C_{6} H_{5} \)
c. \( C_{6} H_{5}-O-C_{3} H_{7} \)
D.


The gametes are formed in most of the multicellular organisms by a process of cell division called as
A. Mitosis
B. Replication
c. Meiosiss
D. Prophage


The vapour pressure of water is \( 92 \mathrm{mm} \) at \( 323 \mathrm{K} .18 .1 \mathrm{g} \) of urea are dissolved in 100g of water. The vapour pressure is
reduced by \( 5 \mathrm{mm} \). Calculate the molar
mass of urea.


The M phase of cell cycle consist of
\( A \cdot G_{1}, S, \) and \( G_{2} \) phase
B. Prophase, metaphase, anaphase, telophase
c. Interphase, prophase, metaphase, anaphase, telophase
D. Only prophase


From which embryonic structure, the vertebral column develops?
A. Neural canal
B. Archenteron
c. Notochord
D. Blastocoel


A magnet makes 40 oscillations per minute at a place having magnetic field intensity of \( 0.1 \times 10^{-5} \) T. At another place, it takes 2.5 seconds to complete one vibration. The value of earth's
horizontal field at that place is
A . \( 0.25 \times 10^{-6} \mathrm{T} \)
в. 0.36 \( \times 10^{-6} \) т
c. \( 0.66 \times 10^{-8} \mathrm{T} \)
D . 1.2 \( \times 10^{-6} \) न


Write one use of Zeolite.


The aerosol is a kind of colloid in which:
A. gas is dispersed in solid
B. solid is dispersed in gas
C. liquid is dispersed in water
D. gas is dispersed in liquid


Find \( \lim _{x \rightarrow 1} f(x), \quad \) where \( \quad f(x)= \)
\( \left\{x^{2}-1, \quad x \leq 1-x^{2}-1, \quad x>1\right\} \)


If \( \sum_{i=1}^{9}\left(x_{i}-5\right)=9 \) and \( \sum_{i=1}^{9}\left(x_{i}-5\right)^{2}= \)
\( 45, \) then the standard deviation of the 9
\( \operatorname{times} x_{1}, x_{2}, \dots, x_{9} \) is
A . 9
B. 4
\( c \cdot 3 \)
\( D \cdot 2 \)
\( E \)


The hormone that promotes reabsorption of water from glomerular filtrate is
A. Oxytocin
B. Vasopressin
c. Relaxin
D. Calcitonin


In young's experiment, the fringe width at a distance of \( 50 \mathrm{cm} \) from the slits, of
light of wavelength \( 6000 \AA \) is \( 0.048 \mathrm{cm} \) The fringe width at the same distance for \( \lambda=5000 \AA \) will be :
A . \( 0.04 \mathrm{cm} \)
B. \( 0.4 \mathrm{cm} \)
\( c .0 .14 c m \)
D. \( 0.45 \mathrm{cm} \)


State whether the statements are true
or false-

Frictional force is a non-contact force.
A. True
B. False


Explain the following terms with
suitable examples.
(i) cationic detergents
(ii) anionic detergents and
(iii) non-ionic detergents.


Two spherical soap bubbles of radii \( a \)
and \( b \) in vacuum coaleasce under
isothermal conditions. The resulting bubbles has a radius given by:
A \( \cdot \frac{(a+b)}{2} \)
B. \( \frac{a b}{a+b} \)
c. \( \sqrt{a^{2}+b^{2}} \)
\( \mathbf{D} \cdot a+b \)


Codon is present in:
A . t-RNA
B. m-RNA
c. fats
D. r-RNA


Read the following statements and select the correct option. Statement 1: It is not possible to photograph a virtual image. Statement 2: An image is said to be virtual if the reflected or refracted rays
are diverging in nature
A. Both statement 1 and statement 2 are true and statement 2 is the correct explanation of statement 1
B. Both statement 1 and statement 2 are true but statement 2 is not the correct explanation of statement 1.
c. statement 1 is true but statement 2 is false
D. Statement 1 is false but statement 2 is true


Two electric bulbs whose resistance are
in the ratio of 1: 2 are connected in
parallel to a constant voltage source. The ratio of the power dissipated in them will be:
A .1: 4
B. 1: 2
c. 1: 1
D. 2: 1


Find the oxidation number of Sodium in
NaCl.
\( A \cdot+1 \)
B. - -
\( c \cdot+2 \)
\( D \cdot-2 \)


A wire of fixed length is wound on a solenoid of length I and radius r. Its self inductance is found to be L. Now, if
same wire is wound on a solenoid of
ength \( \frac{l}{2} \) and radius \( \frac{r}{2}, \) then self inductance will be
A . 2L
в. \( \frac{L}{2} \)
c. \( 3 L \)
D. 4L


A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of \( 2.0 \mathrm{m} \) from the
goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is \( 19.6 \mathrm{cm} \) from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationary goli without falling on the ground earlier?


Find the \( 7^{t h} \) term of the GP, whose first
term is 6 and common ration is \( \frac{2}{3} \)


The electric potential at a certain
distance from a point charge \( Q \) is \( 810 V \) and electric field is \( 300 N / C \). The minimum speed with which a particle of charge \( -Q \) and mass \( m=6 x \)
\( 10^{-16} k g \) should be projected from that
point so that it moves into the field free region is:
A \( \cdot 9 \times 10^{6} m / s \)
в. \( 81 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 81 \times 10^{4} m / s \)
D. \( 9 \times 10^{4} m / s \)


The combined effect of mass and
velocity is taken into account by a physical quantity called:
A. Moment of momentum
B. Moment of force
c. Momentum
D. None of these


Taung baby is
A. Dryopithecus
B. Australopithecus
C . Peking Man
D. Piltdown Man


Which of the following pairs is correctly
matched?
A. Fibrous joint- Between phalanges
B. cartilaginous joint- Skull bones
c. Gliding joint- Between zygapophyses of the successive vertebrae
D. Hinge joint- Between vertebrae


The body temperature of a healthy person is \( 98.6 F . \) Calculate the
corresponding temperature on the
Kelvin scale.


Coal can be converted into:
A. synthetic petrol
B. coal gas
c. electricity
D. All of these


\( \frac{\sin (\boldsymbol{A}-\boldsymbol{B})}{\cos \boldsymbol{A} \cos \boldsymbol{B}}+\frac{\sin (\boldsymbol{B}-\boldsymbol{C})}{\cos \boldsymbol{B} \cos \boldsymbol{C}}+ \)
\( \frac{\sin (\boldsymbol{C}-\boldsymbol{A})}{\cos \boldsymbol{C} \cos \boldsymbol{A}}=\boldsymbol{0} \)


Mole fraction of solute present in an aqueous solution having molality equal to 2 is:
A . 0.9653
B. 0.347
c. 0.653
D. 0.0347


Coenzyme A helps in
A. Oxidative phosphorylation
B. Substrate level phosphorylation
C. Breakdown of pyruvate
D. Activation of acetyl group


A source oscillates with a frequency 25
Hz and the wave propagates with 300 \( \mathrm{m} / \mathrm{s} . \) Two points \( \mathrm{A} \) and \( \mathrm{B} \) are located at distances \( 10 \mathrm{m} \) and \( 16 \mathrm{m} \) away from the
source. The phase difference between \( A \) and B is
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
\( c \)
D . 2 \( \pi \)


The rate constant of a reaction
increases by 3 times for every \( 10^{0} C \) rise in temperature uniformly, in the range
of \( 20^{\circ} \mathrm{C} \) to \( 80^{\circ} \mathrm{C} \). If the rate constant at
\( 30^{\circ} \mathrm{C} \) is \( \mathrm{K}, \) then what is its value at
\( 60^{0} C ? \)
\( A \cdot 9 K \)
в. 27К
\( c \cdot 6 k \)
D. 81K


Mark the correct set of ferromagnetic substances.
A. Iron, cobalt and nickel
B. Iron, copper and lead
c. silicon, bismuth and nickel
D. Aluminium, sodium and copper


The atomic and ionic radii \( \left(M^{3+} \text { ions }\right) \)
of Lanthanide elements decrease with
increase in atomic number. This effect
is called as:
A. Lanthanoid contraction
B. Lanthanoid expansion
c. Actinoid contraction
D. none of these


In graphs of the electronic band
structure of solids, the band gap
generally refers to the
between the top of the valence band and
the bottom of the conduction band in
insulators and semiconductors.
A. current difference
B. energy difference (in electron volts)
c. hole difference
D. none of the above


Prove that \( 1+\tan 2 \theta \tan \theta=\sec 2 \theta \)


If the frequency of the source is doubled in Young's double slit experiment, then fringe width \( (\boldsymbol{\beta}) \) will be-
A. unchanged
B. \( \beta / 2 \)
\( c \cdot 2 \beta \)
D. \( 3 \beta \)


In the decay process:
\( \boldsymbol{A} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{C} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{D} \)
This question has multiple correct options
\( \mathbf{A} \cdot A \) and \( B \) are isodiapheres
B. \( A \) and \( D \) are isotopes
C. \( B, C \) and \( D \) are isobars
D. \( A \) and \( C \) are isotones


Very short answer type.
Besides ADH, which other hormones
contribute to the regulation of water reabsorption?


Graph is plotted between maximum
kinetic energy of electron with frequency of incident photon in Photo electric effect. The slope of curve will be
A. Charge of electron
B. Work function of metal
c. Planck's constant
D. Ratio of planck constant and charge of electron


Assertion
A rocket moves forward by pushing the
surrounding air backwards.
Reason
It derives the necessary thrust to move forward according to Newton's third law of motion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A neutral atom has \( 2 K \) electrons, \( 8 L \)
electrons and \( 6 M \) electrons. Predict
from this:
(a) its atomic number,
(b) total number
of \( s \) -electrons
(c) total number of \( p \)
electrons,
(d) total number of \( d \)
electrons.


Which of the following options shows the same property between a rectangle and a square?
A. Both have only 1 pair of parallel lines
B. Both have all the angles of measure \( 90^{\circ} \)
c. Diagonals cut each other perpendicularly
D. Both have all sides of equal length


Assertion
A spaceship while entering the earth's atmosphere is likely to catch fire.
Reason
The temperature of upper atmosphere is very high.
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 phosphate of a metal has the
formula \( M H P O_{4} . \) The formula of its
chloride would be :
A . \( M C l \)
в. \( M C l_{2} \)
c. \( M C l_{3} \)
D. \( M_{2} C l_{3} \)


Two bullets are fired horizontally with different velocities from the same
height.

Which will reach the ground first?
A. Slower one
B. Faster one
c. Both will reach simultaneously
D. It cannot be predicated


Assertion
Benzene (boiling point \( 353 K \) ) and
methanol (boiling point \( 338 K \) ) are
separated by simple distillation.
Reason

Fractional distillation is used to
separate two liquids from their mixture
when their boiling points differ by \( 25^{\circ} C \)
or less.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Calculate the change in potential
energy of a particle of charge \( +\boldsymbol{q} \) that is
brought from a distance of \( 3 r \) to a
distance of \( 2 r \) in the electric field
of charge \( -q ? \)
\( \mathbf{A} \cdot k q^{2} / r \)
B \( .-k q^{2} / 6 r \)
c. \( k q^{2} / 4 r^{2} \)
D. \( -k q^{2} / 4 r^{2} \)
E . \( k q^{2} / r^{2} \)


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}^{5}+\mathbf{1} \mathbf{1} \boldsymbol{x}^{4}+\mathbf{9} \mathbf{0} \boldsymbol{x}^{2}-\mathbf{1} \mathbf{9} \boldsymbol{x}+\mathbf{5} \mathbf{3} \)
is divided by \( x+5, \) then the remainder
is:
A. 100
B . -100
\( c \cdot-102 \)
D. 102


Which of the following halides undergoes nucleophilic substitution most readily?
A \( \cdot p-H_{3} C C_{6} H_{4} C l \)
в. \( O-M e O C_{6} H_{4} C l \)
c \( \cdot p-C l C_{6} H_{4} C l \)
D. \( C_{6} H_{5} C H(C l) C H_{3} \)


Three ions \( H^{+}, H e^{+} \) and \( O^{+2} \) having
same kinetic energy pass through a region in which there is a unit magnetic field perpendicular to their velocity,
then
A \( \cdot H^{+} \) will be least deflected
B. \( H e^{+} \) and \( O^{+2} \) will be deflected equally
c. \( O^{+2} \) will be deflected most
D. All will be deflected equally


The function \( f(x)=\frac{\tan \left\{\pi\left[x-\frac{\pi}{2}\right]\right\}}{2+[x]^{2}} \)
where \( [x] \) denotes the greatest integer
\( \leq x, \) is
A. continuous for all values of \( x \)
B. Discontinuous at \( x=\frac{\pi}{2} \)
c. Not differentiable for some values of \( x \)
D. Discontinuous at \( x=-2 \)


Assertion
Magnification of a convex mirror is always positive, but that of a concave mirror may be both positive or negative.
Reason
It depends on the sign convention
chosen.
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


Write the structrual formula of the
major product in the following case:
Ethene mixed with air is passed under
pressure over a silver catalyst at \( 250^{\circ} \mathrm{C} \)


How many lines of symmetry does the
figure have?
A. 0
B. 1
\( c \cdot 2 \)
\( D \)


Form the differential equation of the family of circles touching the X-axis at the origin.


The process of purification of metals is represented by the following scheme \( \$ \$ \) Ti \( 1,+|, 2|_{-} 2 \mid, \) loverset \( \left\{250^{\wedge}\{\text { lcirc }\} C\right\} \)
\{ᅵrightarrow \( \} \) ।. Til \( _{-} \) 4) , loverset \( \{1400 \text { \wedge }\{\text { lcirc }\} \)
3), Jbegin \{matrix Jill pure lend \( \{\text { matrix }\} \backslash_{,+} \backslash, 1_{-} 2 \$ \$ \)
A. cupellation
B. poling
c. electrolytic refiningg
D. van-Arkel method


Whenever light travels from denser
medium to a rarer medium:
A. it bends away from the normal
B. it bends towards the normal
C . it passes undeviated
D. it always reflects back


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]^{2}+\sqrt{\{\boldsymbol{x}\}} \) where \( \mathbb{D} \boldsymbol{\&} \)
Orespectively denotes the greatest integer and fractional part functions, then which of the following is
correct?
A. \( f(x) \) is continuous at all integral points
B. \( f(x) \) is not differentiable \( \forall x \in I \)
c. \( f(x) \) is discontinuous as \( x \in I-\{1\} \)
\( f(x) \) is continuous \( \& \) differentiable at \( x=0 \) 0


How do gymnosperms and angioperms
differ from each other?
A. Gymnosperms have naked seed but angiosperms have seed coat
B. Gymnosperm have leaves but angiosperms do not have leaves
C. Gymnosperms are seed bearing plant but seed is absent in angiosperm
D. Both A and B


When a horse pulls a wagon, the force that causes the horse to move forward
is the force:
A. the ground exerts on it
B. it exerts on the ground
c. the wagon exerts on it
D. it exerts on the wagon


What are the factors that are essential
for photosynthesis?


A purse has only one rupee and two rupee coins in it. The number of two rupee coins is one third the number of
one rupee coins. If the purse has Rs. 115. Find the number of two rupee
coins.
A . 20
B . 23
c. 18
D. 25


Consider the reaction:
\( \boldsymbol{R} \boldsymbol{C H O}+\boldsymbol{N H}_{2} \boldsymbol{N} \boldsymbol{H}_{2} \rightarrow \boldsymbol{R C H}=\boldsymbol{N} \)
\( N H_{2} \)
What sort of reaction is it?
A. Free radical addition-elimination reaction
B. Electrophilic substitution-elimination reaction
c. Nucleophilic addition-elimination reaction
D. Electrophilic addition-elimination reaction


The probability of getting the rotten egg from a lot of 400 eggs is \( 0.035 . \) Find the
number of rotten eggs in the lot.


A force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{6} \hat{\boldsymbol{k}} \) is acting at a
point \( \vec{r}=2 \hat{i}-6 j-12 \hat{k} . \) The value of \( \alpha \)
for which angular momentum about origin is conserved is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D.


The magnification produced by a concave mirror
A. is always more than one
B. is always less than one
c. is always equal to one
D. may be less than or greater than one


Hydraulic separation method is used for the concentration of which ore?
This question has multiple correct options
A . Cassiterite
B. Haematite
c. Calamine
D. Galena


For a dilute solution, Raoult's law states
that:
A. The relative lowering of vapour pressure is equal to the mole fraction of solute
B. The relative lowering of vapour pressure is equal to the mole fraction of solvent
C. The relative lowering of vapour pressure is proportional to the amount of solute in solution
D. The vapour pressure of the solution is equal to the mole fraction of solvent


\( \int x \sin ^{3} x d x \)


Define the term pollination. Differentiate between self pollination
and cross pollination. What is the
significance of pollination?


If \( y=7 x-x^{3} \) and \( x \) increases at the
rate of 4 units per second, how fast is
the slope of the curve changing when
\( x=2 ? \)


Construct a cyclic quadrilateral EFGH
with \( \mathrm{EF}=5.2 \mathrm{cm}, \angle \mathrm{GEF}=50^{\circ}, \mathrm{FG}=6 \mathrm{cm} \)
and \( \angle \mathrm{EGH}=40^{\circ} \)


If \( y=\frac{(a x+b)(c x+d)}{(a x-b)(c x-d)}, x \neq \frac{b}{a}, \frac{d}{c} \) then
find \( \frac{d y}{d x} \)


The increasing order of \( p K_{b} \) for the
following compounds will be :
Refer above image.
\( (\mathbf{A}) \)
\( (\mathbf{B}) \)
(C) \( \mathbf{C H}_{3} \mathbf{N H C H}_{3} \)
A. \( (A)<(B)<(C) \)
B. \( (C)<(A)<(B) \)
c. \( (B)<(C)<(A) \)
D. \( (B)<(A)<(C) \)


A stone dropped from the top of a tower travels \( 4.9 \mathrm{m} \) in the last second, then the
velocity of the stone on reaching the
ground is
A \( \cdot 19.6 m^{-1} \)
в. \( 9.8 m s^{-1} \)
\( \mathrm{c} \cdot 4.9 \mathrm{ms}^{-1} \)
D. \( 29.4 m s^{-1} \)


Select the incorrect statement(s).
A. Enzyme catalysed reactions are usually hydrolytic in nature
B. Enzyme catalysed reactions takes place with evolutions of gases
C. The rate of reaction does not depend upon enzyme concentration
D. Enzymes are colloidal in nature


The term independent of \( x \) in the expansion of \( \left(x-\frac{1}{x}\right)^{4}\left(x+\frac{1}{x}\right)^{3} \) is
A . -3
B.
\( c .3 \)
D.


A flat plate moves normally towards a discharging jet of water at the rate of \( \mathbf{3} \boldsymbol{m} / \boldsymbol{s} . \) The jet discharges the water at
the rate of \( 0.1 m^{3} / s \) and at the speed of
\( 18 m / s . \) The force exerted on the plate
due to the jet is:
в. 2100 N
c. \( 2450 N \)
D. \( 1560 N \)


What positive value(s) of \( x, \) less than
\( 360^{\circ}, \) will give a minimum value for \( 4-2 \) \( \sin x \cos x ? \)
\( A \cdot \frac{\pi}{4} \) only
B . \( \frac{5 \pi}{4} \) only
\( \mathbf{c} \cdot \frac{\pi}{2} \) and \( \frac{5 \pi}{2} \)
D. \( \frac{3 \pi}{2 \pi} \)
E \( \cdot \frac{\pi}{4} \) and \( \frac{5 \pi}{4} \)


Which of the following is correct?
A. Wavelength of light used can change the angle of deviation of a prism
B. Wavelength of light used can not change the angle of deviation of a prism
C. Blue light, the angle of deviation of a prism, changes the most.
D. None of the above


Find the value of the other five
trigonometric functions for the
following:
\( \tan x=\frac{3}{4}, x \) in quadrant \( I I I \)


The shape of \( C l F_{3} \) molecule is:
A . tetrahedral
в. T shape
c. linear
D. trigonal


State the following statement is True or False
The zeros of the polynomial \( (x- \)
2) \( \left(x^{2}+4 x+3\right) \) are \( 2,-1 a n d-3 \)
A. True
B. False


What is true about this figure?
A. It is a quadrilateral
B. It is a polygon
c. It is an octagon
D. It is a regular polygon


Cell constant of a conductivity cell is
generally obtained by measuring conductance of aqueous solution of
A. \( B a C l_{2} \)
в. LiCl
c. \( K C l \)
D. \( M g C l_{2} \)


Match column 'A' with column'B' as
regard to characteristics of a flame and
its zones.
'A'
1. Hottest part (No
a. Dark inner zone
Blue zone
2. Partial decomposition
b.
3. Unburnt vapours of c. Luminous zone
d. Non-luminous
zone
4. Complete combustion
\( A \cdot a-1, b-2, c-3, d-4 \)
B. \( a-2, b-3, c-4, d-1 \)
\( c \cdot a-3, b-4, c-2, d-1 \)
\( D \cdot a-4, b-1, c-2, d-3 \)


Evaluate \( : \lim _{x \rightarrow 0} \frac{1-\cos x}{x} \)


What does the slope of the graph
represent?


Calculate the de Broglie wavelength of an electron having kinetic energy of
\( 1.6 \times 10^{-6} \) erg \( \left(m_{e}=9.11 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{2 8}} \boldsymbol{g}, \boldsymbol{h}=\mathbf{6 . 6 2} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{e r g}-\boldsymbol{s e c} \)
B . \( 0.00029 A^{\circ} \)
c. \( 0.0122 A^{\circ} \)
D. \( 1.29 A^{\circ} \)


Father's age is 10 more than twice age of his son. What is the number of
variables if the statement is written in
the form of linear equation?
A. one
B. Two
c. Multivariable
D. Non-linear


Find the remainder when we divide
\( \boldsymbol{x}^{7} \boldsymbol{y}-\boldsymbol{x} \boldsymbol{y}^{7} \) by \( (\boldsymbol{x}+\boldsymbol{y})\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \)


The mean
is
A. The statistical or arithmetic average
B. The middlemost score
C. The most frequently occurring score
D. The best representation for every set of data


The dimensional formula for Areal
velocity is :
A \( \cdot M^{0} L^{-2} T^{-1} \)
B . \( M^{0} L^{-2} T^{1} \)
c. \( M^{0} L^{2} T^{-1} \)
D. \( M^{0} L^{2} T^{1} \)


Perimeter of the figure is
\( \mathbf{A} \cdot 68.2 \mathrm{cm} \)
\( \mathbf{B} \cdot 68.1 \mathrm{cm} \)
\( \mathrm{C} \cdot 86.3 \mathrm{cm} \)
D. \( 68.3 \mathrm{cm} \)


Range of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}} \) is
\( A \cdot(-\infty, \infty) \)
В \cdot [-1,1]
\( c \cdot\left[-\frac{1}{2}, \frac{1}{2}\right] \)
D. \( [-\sqrt{2}, \sqrt{2}] \)


A tightly-wound, long solenoid carries a current of \( 2.00 A \). An electron is found to
execute a uniform circular motion
inside the solenoid with a frequency of \( 1.00 \times 10^{8} \) rev \( s^{-1} \).Find the number of
turns per metre in the solenoid.


Three equal masses \( 3 k g \) are connected
by massless string of cross-sectional
area \( 0.005 c m^{2} \) and Young's modulus
\( 2 \times 10^{11} N m^{2} . \) In the absence of friction
the longitudinal strain in the wire:
\( \mathbf{A} \cdot A \) is \( 10^{-4} \)
B. \( B \) is \( 2 \times 10^{-4} \)
\( c . \) Both a and \( b \)
D. None of these


Fill in the blank:
A sudden shaking or trembling of the Earth, caused by a disturbance deep inside the Earth's crust, is known as
A. tsunami
B. flood
c. earthquake
D. landslides


For the function \( f \) graphed in the \( x y- \)
plane above, if \( \boldsymbol{f}(-\mathbf{2 . 5})=\boldsymbol{k}, \) then find
\( \boldsymbol{f}(\mathbf{2 k}) ? \)
A . 0
B.
c. 1.5
D. 2
E . 0.5


If \( \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{cc}\boldsymbol{k} & \boldsymbol{k}-\mathbf{1} \\ \boldsymbol{k}-\mathbf{1} & \boldsymbol{k}\end{array}\right] \) then \( \left|\boldsymbol{A}_{\mathbf{1}}\right|+ \)
\( \left|\boldsymbol{A}_{2}\right|+\ldots+\left|\boldsymbol{A}_{2015}\right|=? \)
\( A \cdot 0 \)
в. 2015
c. \( (2015)^{2} \)
D. \( (2015)^{3} \)


Find the charge enclosed in the cylinder
A \( \cdot 1.1 \times 10^{-6} \)
В. \( 1.1 \times 10^{-9} \)
c. \( 1.1 \times 10^{-11} \)
D. \( 1.1 \times 10^{-12} \)


In a gamma decay process, the internal energy of a nucleus of mass \( M \)
decreases, a gamma photon of energy \( \boldsymbol{E} \)
and linear momentum \( \boldsymbol{E} / \boldsymbol{c} \) is emitted
and the nucleus recoils. Find the
decrease in internal energy.


Salt of which of the elements are mostly
blue in colour?
A. cu
B. zn
c. \( \mathrm{Fe} \)
D. cr


The \( \frac{\boldsymbol{n}}{\boldsymbol{p}} \) ratio of \( _{1} \boldsymbol{H}^{1} \) is :
\( A \)
B. 2
\( c \cdot 3 \)
D.


\( 92 U^{238} \) changes to \( _{85} U^{210} \) by a series of
\( \alpha \) and \( \beta \) decays. Find the number of \( \alpha \) decays undergone (an integer)


If the unit of mass, length and time be each doubled,then how the unit of power will change.


A transition state represents the state
of highest energy in passing from reactant to product. If true enter 1 , if false enter 0 .


The diagram given represents a certain stage of mitosis:
\( (i) \) Identify the stage of cell division.
\( (i i) \) Name the parts labelled \( A \) And \( B \)
\( (i i i) \) What is the unique feature observed in this stage?
\( (i v) \) How many daughter cells formed
from this type of cell division?


In biological terminology, a group of similar organisms which are capable of interbreeding and producing fertile offspring's is called.
A. species
B. Genus
c. Tribe
D. Family


Which materials are excreted by
kidneys and lungs?
\begin{tabular}{|c|c|c|}
\hline & kidneys & lungs \\
\hline A & carbon dioxide & carbon dioxide \\
B & carbon dioxide & urea \\
c & urea & carbon dioxide \\
D & urea & urea \\
\hline
\end{tabular}


Find the area of that part of the circle
\( x^{2}+y^{2}=16 \) which is exterior to the
parabola \( \boldsymbol{y}^{2}=\mathbf{6} \boldsymbol{x} \)


When cell has stalled DNA replication
fork, which checkpoint should be
predominantly activated?
A.
B. Both Ga M and M
\( c \cdot G_{1} / s \)
\( D \cdot G_{2} / M \)


Which pair of compounds is expected to show similar color in aqueous medium?
A. \( F e C l_{3} \) and \( C u C l_{2} \)
в. \( V O C l_{2} \) and \( C u C l_{2} \)
c. \( V O C l_{2} \) and \( F e C l_{2} \)
D. \( F e C l_{2} \) and \( M n C l_{2} \)


A man engaged a servant on the condition that he would pay him Rs. 90 and a turban after a service of one year.
He served only for nine months and received the turban and Rs. \( 65 . \) The
price of the turban is:
A . Rs. 25
B. Rs. 18.75
c. Rs. 10
D. Rs. 2.50


If \( f(A) \) is a proper subset of \( B \), then \( f \) \( A \rightarrow B \) is called a/an \( \ldots \ldots . . \) function
A . into
B. onto
c. one - one
D. indentity


\( \lim _{x \rightarrow 2} \frac{x^{5}-32}{x^{3}-8}= \)
\( A \cdot \frac{3}{20} \)
B. \( \frac{20}{3} \)
c. \( \frac{10}{3} \)
D. \( \frac{3}{10} \)


\( \ln \triangle A B C, A B=B C=K, A C=\sqrt{2} k, \) then
\( \triangle A B C \) is a :
This question has multiple correct options
A. Isosceles triangle
B. Right-angled triangle
c. Equilateral triangle
D. Right isosceles triangle


Atoms with three of their outer most
orbits incompletely filled with electrons
are present in:
A. Lanthanides
B. Representative elements
c. s - block elements
D. transitional elements


Find the area \( \left(\text { in } m^{2}\right) \) of the trapezium
PQRS with height PQ given in the figure.


If resistance of \( 100 \Omega \) and the
inductance of 0.5 henry and capacitance of \( 10 \times 10^{6} \) farad are
connected in series through \( 50 \mathrm{Hz} \) A.C supp;y, then impedence is
A. \( 1.8765 \Omega \)
B. \( 18.76 \Omega \)
c. \( 187.6 \Omega \)
D. 101.3\Omega


Explain self-induction of a coil. Arrive at an expression for the induced emf in a
coil and the rate of change of current in ¡t


Green house effect is increase in
temperature of earth due to
A. High concentration of \( N O_{2} \)
B. High concentration of \( S O_{2} \)
C. High concentration of \( C O_{2} \)
D. High concentration of \( c 0 \)


The price of a table is \( R s .400 \) more than
that of a chair. If 6 tables and 6 chairs
together cost \( R s .4800, \) by what percent is the price of the chair less than that of the table ?
\( \mathbf{A} \cdot 33 \frac{1}{3} \% \)
в. \( 50 \% \)
\( \mathbf{c} \cdot 66 \frac{2}{3} \% \)
D. None of these


In an organic compound, Kjeldahl's method is used for the estimation of:
A. Halogens
B. Sulphur
c. Nitrogen
D. oxygen


A car starts from rest and acceleration
\( \operatorname{at} 4 m / s^{2} \) for \( 5 s . \) After that it moves
with constant velocity for \( 25 s \) and then
retards at \( 2 m / s^{2} \) until it comes to rest. The total distance travelled by the car is
\( \mathbf{A} \cdot 650 m \)
B. \( 527 m \)
c. \( 675 m \)
D. 573 m


Determine the current in each branch of
the network shown in Fig.


The configuration \( 1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1} \) shows:
A. excited state of \( O_{2}^{-} \)
B. excited state of neon atom
c. excited state of fluorine atom
D. ground state of fluorine atom


The \( p K_{a} \) of acetic acid and \( p K_{b} \) of
\( N H_{4} O H \) are 4.76 and \( 4.75 . \) Calculate
the \( p H \) of ammonium acetate ions.


If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{3}}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


If the reaction \( A \rightleftharpoons B \) has \( \Delta G^{o}=0 \)
then its equilibrium constant will be equal to:


A proton is accelerated to \( 225 V \). Its deBroglie wavelength is:
\( \mathbf{A} \cdot 0.0019 n m \)
B. \( 0.02 n m \)
c. \( 0.003 n m \)
D. \( 0.4 n m \)


A particle located at \( x=0 \) at time \( t=0 \)
starts moving along the positive \( x \) direction with a velocity 'v' that varies as \( \boldsymbol{v}=\boldsymbol{\alpha} \sqrt{\boldsymbol{x}} . \) The displacement of the
particle varies with time as?


Calculate value of \( ^{\prime} \ln \left(K_{e q}\right)^{\prime} \) for the
reaction at \( 250 \mathrm{K} \)
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
Given: \( \boldsymbol{H}_{f}^{0}\left(\left(\boldsymbol{N} \boldsymbol{O}_{2}\right) \boldsymbol{g}\right)= \)
\( +40.407 k J / m o l \)
\( \boldsymbol{H}_{f}^{0}\left(\left(\boldsymbol{N}_{2} \boldsymbol{O}_{4}\right) \boldsymbol{g}\right)=+\mathbf{7 0 k} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{S}_{\boldsymbol{r}}^{\boldsymbol{0}}=\mathbf{1 0 J} \boldsymbol{K}^{-\mathbf{1}} \)
A .4
B . - -
\( c \cdot 1.2 \)
D. -1.2


\( 18.72 \mathrm{g} \) of a substance 'X' occupies 1.81 \( c m^{3} . \) What will be its density measured in correct significant figures?
A \( \cdot 10.3 \mathrm{g} \mathrm{cm}^{-3} \)
В. \( 10.34 \mathrm{g} \mathrm{cm}^{-3} \)
C. \( 10.4 \mathrm{g} \mathrm{cm}^{-3} \)
D. \( 10.3425 \mathrm{g} \mathrm{cm}^{-3} \)


Construct a cyclic quadrilateral \( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \boldsymbol{S} \)
in which \( \boldsymbol{P Q}=\mathbf{5} \mathrm{cm}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{6} \mathrm{cm}, \boldsymbol{P} \boldsymbol{R} \)
\( =3.5 \mathrm{cm} \) and \( R S=5 \mathrm{cm} \)


Find six rational number between \( \frac{1}{2} \) and \( \frac{2}{3} \)


If \( 0.1 \mathrm{M} H C I \) is mixed in the solution
containing only \( 0.1 M C d^{2+} \) ions and
saturated with \( \boldsymbol{H}_{2} \boldsymbol{S}, \) then \( \left[\boldsymbol{C} \boldsymbol{d}^{2+}\right] \)
remaining in the solution after \( C d S \)
stops to precipitate is
A \( \cdot 10^{-8} \)
B. \( 8.2 \times 10^{-9} \)
c. \( 5.6 \times 10^{-6} \)
D. \( 5.6 \times 10^{-10} \)


The colourless species is (are):
A . VCl
B. voso \( _{4} \)
\( c \cdot \) Nas vo \( _{4} \)
\( D \cdot\left[V\left(H_{2}\right)_{6}\right] S O_{4} \cdot H_{2} O \)


The water found below the water table is
called
A. rock water
B. groundwater
c. underwater
D. both \( C \) and \( D \)


Find the cosine of the angle between two diagonals of a cube?
A \( \cdot \frac{1}{3} \)
B. \( \frac{2 \sqrt{2}}{3} \)
\( c \cdot \frac{1}{2} \)
D. None of thes


The enzyme required for transcription is
A. Restriction enzyme
B. DNA polymerase
c. RNA polymerase
D. RNase


Which element has the symbol \( W ? \)
A. Silver
B. Vanadium
c. Tin
D. Platinum
E . Tungsten


The equation of the plane through the line of intersection of the planes \( a x+ \)
\( b y+c z+d=0 \) and \( a^{\prime} x+b^{\prime} y+c^{\prime} z+ \)
\( \boldsymbol{d}^{\prime}=\mathbf{0} \) and parallel to the line \( \boldsymbol{y}=\mathbf{0} \) and
\( z=0 \) is-
A \( \cdot\left(a b^{\prime}-a^{\prime} b\right) x+\left(b c^{\prime}-b^{\prime} c\right) y+\left(a d^{\prime}-a^{\prime} d\right)=0 \)
B \cdot \( \left(a b^{\prime}-a^{\prime} b\right) x+\left(b c^{\prime}-b^{\prime} c\right) y+\left(a d^{\prime}-a^{\prime} d\right) z=0 \)
C \( \cdot\left(a b^{\prime}-a^{\prime} b\right) y+\left(a c^{\prime}-a c^{\prime}\right) z=\left(a d^{\prime}-a^{\prime} d\right) \)
D. None of these.


If \( \boldsymbol{f}\left(\boldsymbol{x}+\frac{1}{x}\right)=\boldsymbol{x}^{3}+\frac{1}{x^{3}}- \)
\( 4\left(x^{2}+\frac{1}{x^{2}}\right)+13 \) then \( f(2+\sqrt{3})= \)
В. \( 19-4 \sqrt{3} \)
c. \( 15-4 \sqrt{3} \)
D. \( 7-4 \sqrt{3} \)


Rusting of iron is catalysed by which of the following:
A . \( F e \)
в. \( Z n \)
\( c \cdot 0_{2} \)
\( \mathbf{D} \cdot H^{+} \)


A gas contained in a cylinder is filled with a frictionless piston expands
against a constant pressure 1 atmosphere from a volume of 4 litre to a
volume of 14 litre. In doing \( s o, \) it absorbs \( 800 J \) thermal energy from
surroundings. Determine \( \Delta U \) for the
process.


The Zeroth law of thermodynamics leads to the concept of
A. internal energy
B. heat content
c. pressure
D. temperature
E. work done


\( X \) is a strong \( _{--}-_{--} \) agent and has ionization potential
A. reducing, high
B. oxidizing, high
c. oxidizing, low
D. reducing, low


In thermal equilibrium concepts, heat lost by hot body is equal to
A. Heat gained by hot body
B. Heatgained by cold body
c. Both (a) and (b)
D. None of these


Three points \( (0,0),(3, \sqrt{3}),(3, \lambda) \) form an equilateral triangle, then \( \lambda \) is equal
to
\( A \cdot 2 \)
B. -3
\( c .-4 \)
D. \( \sqrt{3} \)


Assertion
Among isomeric alkanes, branching increases the boiling points.
Reason
branching lowers the intermolecular van der waals force of attraction.
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 wrong but Reason is correct.


Find the vector equation of line joining the points (2,1,3) and (-4,3,-1)
\( \mathbf{A} \cdot \bar{r}=2(1-3 \lambda) \bar{i}-(1+2 \lambda) \bar{j}-(3-4 \lambda) \bar{k} \)
B . \( \bar{r}=2(1-3 \lambda) \bar{i}-(1+2 \lambda) \bar{j}+(3-4 \lambda) \bar{k} \)
C \( . \bar{r}=2(1-3 \lambda) \bar{i}+(1+2 \lambda) \bar{j}+(3-4 \lambda) \bar{k} \)
D. \( \bar{r}=2(1+3 \lambda) \bar{i}+(1+2 \lambda) \bar{j}+(3+4 \lambda) \bar{k} \)


The energy of a neutron in eV whose de-
Broglie wavelength is \( 1 \mathrm{A} \)
A \( \cdot 1.67 \times 10^{-22} z V \)
В. \( 8.13 \times 10^{-2} \mathrm{eV} \)
c. \( 6.62 \times 10^{-22} e V \)
D. \( 3.23 \times 10^{-2} \mathrm{eV} \)


If \( a+b+\ldots+l \) are in \( G . P ., \) then prove
that its sum \( \frac{b l-a^{2}}{b-c} \)


\( n(A)=m \) and \( n(B)=n ; \) then
\( A \cdot n(A)+n(B)=n(A+B) \)
B. \( n(A)-n(B)=n(A+B) \)
C. \( A \times B=m n \)
\( D \cdot n(A) \times n(B=n(A \times B) \)


A flag is to be coloured in four stripes by
using 6 different colours,no two consecutive stripes being of the same color.This can be done
A. 1500 ways
B. 750 ways
\( c \cdot 6^{4} \) ways
D. none of these


Out of 800 families with 4 children
each, the expected number of families
having 2 boys and 2 girls
A. 100
в. 200
c. 300
D. 400


Why is pine oil used in froth floatation
method?


If \( \tan ^{-1} 4=4 \tan ^{-1} x, \) then \( x^{5}-7 x^{3}+ \)
\( 5 x^{2}+2 x \) is equal to


What proportion of good student are male?
A. 0
B. 0.73
\( c \cdot 0.4 \)
D. 1.0


In the extraction of nickel by Mond's process, the metal is obtained by:
A. electrochemical reduction
B. thermal decomposition
c. chemical reduction by aluminium
D. reduction by carbon


The bond order of \( N O \) molecule
is
A . 1.5
B . 2.
c. 2.5
D. 3.0


The two components of an ecosystem
are
A. Biotic and abiotic
B. Plants and animals
c. weeds and micro-organism
D. Plants and light


A \( 15.0 \mu F \) capacitor is connected to a
\( 220 V, 50 H z \) source. Find the
capacitive reactance and the current \( (\mathrm{rms} \text { and peak }) \) in the circuit. If the frequency is doubled, what happens to the capacitive reactance and the
current?


State true or false
\( \boldsymbol{S} \boldsymbol{O}_{2} \) contains sulphur and oxygen in 1:
1 mass ratio.
A . True
B. False


\( \boldsymbol{i}^{n}+\boldsymbol{i}^{\boldsymbol{n}+1}+\boldsymbol{i}^{\boldsymbol{n}+\mathbf{2}}+\boldsymbol{i}^{\boldsymbol{n}+\mathbf{3}}(\boldsymbol{n} \in \boldsymbol{N}) \) is
equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c.
D.


Assertion
STATEMENT 1: Let \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), f^{\prime}(2)=-\frac{2}{5} \)
Reason
STATEMENT
\( 2: \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)=\pi \)
\( 2 \tan ^{-1} x \forall x>1 \)
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE


The correct order of acidic strength of
carboxylic acid is:
A. formic acid< benzoic acid< acetic acid
B. formic acids acetic acid < benzoic acid
C. acetic acid< formic acid< benzoic acid
D. acetic acid< benzoic acid< formic acid


Solve:
\( \frac{d y}{d x}=e^{4 x-3 y} \)


The maximum separation between the floor of elevator and the ball during its flight would be
A . \( 12 \mathrm{m} \)
B. 15 \( m \)
c. \( 9.5 \mathrm{m} \)
D. 7.5 \( m \)


Which of the following statements
regarding catalyst is not true?
A. A catalyst remains uncharged in composition and quantity at the end of the reaction.
B. A catalyst can initiate a reaction.
C. A catalyst does not alter the equilibrium in a reversible reaction.
D. Catalysts are sometimes very specific in respect of reaction


Ozone depletion in stratosphere shall result in.
A. Forest fires
B. Increased incidence of skin cancer
c. Global warming
D. None of the above


If a slab of insulating material \( 4 \times \) \( 10^{-5} m \) thick is introduced between the
plates of a parallel plate capacitor, the distance between the plates has to be increased by \( 3.5 \times 10^{-5} m \) to restore the
capacity to original value. Then the dielectric constant of the material of
slab is :
\( A \cdot 8 \)
B. 6
c. 12
D. 10


Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and
(b) Plancks
constant.
500
\[
\lambda(n m)
\]
450
\( v \times 10^{-5}\left(\mathrm{cms}^{-1}\right) \) 2.55 4.35


For an object projected from the ground with speed \( u \). The horizontal range is two times the maximum height attained by it. The horizontal range of the object is:
\( ^{\mathbf{A}} \cdot \frac{2 \mu^{2}}{3 g} \)
B. \( \frac{3 \mu^{2}}{4 g} \)
c. \( \frac{3 \mu^{2}}{2 g} \)
D. \( \frac{4 \mu^{2}}{5 g} \)


While preparing dilute sulphuric acid from concentrated sulphuric acid in the
laboratory, the concentrated sulphuric acid is added slowly to water with constant stirring. Explain why?


If function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{3}-\boldsymbol{a}^{3}}{\boldsymbol{x}-\boldsymbol{a}}, \) is
continuous at \( x=a \) then the value of
\( f(a) \) is
\( \mathbf{A} \cdot 2 a \)
В \( .2 a^{2} \)
\( c \cdot 3 a \)
D. \( 3 a^{2} \)


Assertion
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow 2 \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g})+185 \boldsymbol{k} \boldsymbol{J} \)
This reaction is exothermic.
Reason
Heat is being evolved.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A charge \( Q \) is placed at the centre of the open end of a cylindrical vessel of radius \( R \) and height \( 2 R \) as shown in
figure. The flux of the electric field through the surface (curved surface \( + \) base) of the vessel is
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{Q}{2 E_{0}}\left(1+\frac{1}{\sqrt{2}}\right) \)
c. \( \frac{Q}{4 \epsilon_{0}} \)
D. \( \frac{Q}{\sqrt{5} \epsilon_{0}} \)


If a \( 360 m L \) sample of helium contains
0.25 moles, how many molecules of chlorine gas would occupy the same volume at the same pressure and temperature?
A. \( 1.2 \times 10^{24} \)
В. \( 6.022 \times 10^{23} \)
с. \( 3.01 \times 10^{23} \)
3
D. \( 1.51 \times 10^{23} \)
E \( .7 .55 \times 10^{22} \)


Which of the following determines the direction of magnetic field due to a current carrying conductor?
A. Faraday's law of electromagnetic induction
B. Fleming's left hand rule
c. Lenz's law
D. Maxwell's cork screw rule


Henry, the Sl unit of inductance can be
written as :
A. weber ampere-
B. volt second ampere \( ^{-1} \)
c. joule ampere \( ^{-1} \)
D. ohm s \( ^{-1} \)


The upper chambers of the heart are called
A. Auricles
B. Ventricles
c. spiracles
D. Tentacles


Which one is represented correctly in terms of Stock notation?
A. \( F e C l_{3} \) : Iron (II) chloride
B. \( N O_{2}: \) Nitrogen peroxide
C. \( N O_{2}: \) Nitrogen (IV) oxide
D. \( N O_{2} \) : Nitrogen dioxide


A capacitor is to be provide smoothing
for a half wave rectifier. In which of the
following diagrams is capacitor correctly connected?
\( A \)
B.
\( c \)
\( D \)


Two dice are thrown. The events
\( A, B, C, D, E \) and \( F \) are described as follows:
\( A= \) Getting an even number on the
first die.
\( B= \) Getting an odd number on the first
die.
\( C= \) Getting at most 5 as sum of the number on the two dice.
\( D= \) Getting the sum of the numbers on
the dice greater than 5 but less than 10 .
\( \boldsymbol{E}=\operatorname{Getting} \) at least 10 as the sum of the numbers on the dice.
\( \boldsymbol{F}= \) Getting an odd number on one of
the dice

Describe the following events: \( A \) and \( B, B \) or \( C, B \) and \( C, A \) and \( E, A \) or \( F, A \) and \( \boldsymbol{F} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\sin |\boldsymbol{x}| \) and \( \boldsymbol{g}(\boldsymbol{x})=\tan |\boldsymbol{x}| \) then
discuss the continuity of \( \boldsymbol{f}(\boldsymbol{x}) \pm \)
\( g(x) ; \frac{f(x)}{g(x)} \) and \( f(x) \cdot g(x) \)
A \( . f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \)
\( (2 n+1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
B. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are continuous at \( x=(2 n+ \) 1) \( \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
C. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \)
\( (2 n+1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is continuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
D. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \) \( (2 n-1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{\pi}{2} ; n \in 1 \)


If the density of a planet is double than
that of the earth and the radius is 1.5
times that of the earth, the acceleration
due to gravity on the surface of the planet is
\( A \)
\( \frac{3}{4} \) times that on the surface of earth
B. 3 times that on the surface of earth
c. \( \frac{4}{3} \) times that on the surface of earth
D. 6 times that on the surface of earth


A mixture of ethane and ethene
occupies 40 litre at 1.00 atm and at 400
K.The mixture reacts completely with
\( 130 \mathrm{g} \) of \( \mathrm{O}_{2} \) to produce \( \mathrm{CO}_{2} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \)
Assuming ideal gas behaviour,
calculate the mole fractions of \( C_{2} H_{6} \)
and \( C_{2} H_{4} \) in the mixture.


An element has atomic number 79
Predict the group and period in which the element is placed.
A. 2nd group, 7th period
B. 11th group, 6th period
C. 13th group, 6th period
D. 12th group, 6th period


The figure shows the graphical
variation of the reactance of a capacitor
with frequency of ac source.

Draw the graph showing the variation of
the reactance of this inductor with
frequency.


Q Type your question
3
second. Frequency of wave emitted by source is \( 300 H z . X X^{\prime} \) is line along
common diameter of wave fonts
passing through \( ^{\prime} A^{\prime} . \) Distance between two consecutive wave fonts along line
\( X X^{\prime} \) is \( 0.9 m \) and \( 1.3 m \) in the right and
left of point \( A \) respectively. At some
instant source is at point \( \boldsymbol{A} \). Detector is
placed at point \( A . \) Detector is placed at
point \( ^{\prime} Q^{\prime} . A Q \) makes an angle \( 60^{\circ} \) with
line \( X X^{\prime} . \) If frequency of wave received by detector is \( \boldsymbol{f} \boldsymbol{H} \boldsymbol{z}, \) then \( \frac{\boldsymbol{f}}{\mathbf{1 1 0}}(\text { in } \boldsymbol{H} \boldsymbol{z}) \)
is equal to


Which of the following observations
were obtained from \( \alpha \) -particle
scattering experiment?
A. Most of the fast moving \( \alpha \) -particles passed straight through the gold foil
B. Some of the \( \alpha \) -particles were deflected by the foil by small angles
c. One out of every 12000 particles appeared to rebound
D. All of the above


On mixing, heptane and octane form an
ideal solution. At \( 373 \mathrm{K} \), the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and
45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0 gm of heptane and 35 gm of octane will be:(molar mass of heptane \( = \)
\( 100 \mathrm{gmo} 1^{-1} \) and of octane \( = \)
\( \left.114 \operatorname{gmol}^{-1}\right) \)
\( \mathbf{A} \cdot 72.0 \mathrm{kPa} \)
B . \( 36.1 \mathrm{kPa} \)
c. \( 96.2 \mathrm{kPa} \)
D. \( 144.5 \mathrm{kPa} \)


When a transverse plane wave traverses a medium, individual particles execute periodic motion given by the equation \( \boldsymbol{y}=\mathbf{0 . 2 5} \cos (2 \pi \boldsymbol{t}-\boldsymbol{\pi} \boldsymbol{x}) . \) The phase
difference for two positions of same particle which are occupied by time intervals 0.4 second apart is
A \( .144^{\circ} \)
B. \( 135^{\circ} \)
\( \mathrm{c} \cdot 72^{\circ} \)
D. \( 108^{\circ} \)


Assertion
The process of fusion of a sperm with an ovum is called fertilisation
Reason
Only one sperm can fertilise an ovum.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is "Spitting of Silver"? How is it
prevented?


Assertion
Hybridisation influences the bond length and bond enthalpy in organic compounds.
Reason
More the s character of hybrid orbital, shorter and stronger will be the bond
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Identify the type of modified root and
select the correct statement regarding
¡t.
A. It is the tuberous root of Dahlia that stores inulin as reserve food.
B. It is modified taproot that occurs in Dahlia.
C. It is a modified adventitious that stores reserve food
material
D. These roots are modified to provide mechanical support to the plant


A person with normal near point \( 25 \mathrm{cm} \) using a compound microscope with objective of focal length \( 8.0 \mathrm{mm} \) and an eye piece of focal length \( 2.5 \mathrm{cm} \) can bring an object placed at \( 9.0 \mathrm{mm} \) from the objective in sharp focus. The separation between two lenses and
magnification respectively are
A \( .9 .47 \mathrm{cm}, 88 \)
B. 3.36 \( \mathrm{cm}, 44 \)
c. \( 6.00 \mathrm{cm}, 22 \)
D. 7.49 cm, 11


Find the equation of the circle circumscribing a square ABCD with side I and \( A B \) and \( A D \) as coordinate axes


Solve:
\( x^{3}-x^{2}-14 x+14 \)


How does the intensity of transmitted
light depend upon the angle between \( * \) the polariser and analyser? Show it graphically


For what values of \( k \) will be \( k+9,2 k- \)
1 and \( 2 k+7 \) are the consecutive terms
of AP.


In the nuclear reaction \( _{1} H^{2}+_{1} H^{2} \rightarrow_{2} \)
\( H e^{3}+_{0} n^{1} \) if the mass of the deuterium
atom \( =2.014741 a m u, \) mass of \( _{2} H e^{3} \)
atom \( =3.016977 a m u, \) and mass of
neutron \( =1.008987 a m u, \) then the \( Q \)
value of the reaction is nearly
A. 0.00352 Mev
B. 3.27 MeV
c. 0.82 Mev
D. 2.45 MeV


Give few examples where displacement of an object is in the direction opposite to the force acting on the object.


Find the sum of \( n \) terms. Also find the
sum of infiite terms
\( 1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots \)


Give the two methods by which rusting of iron can be prevented.


Total internal energy of a system can never be evaluated but the change in internal energy can be determined by Ist law of thermodynamics. If true enter 1 , else enter 0 .


Assertion (A) : Meterbridge wire is made
up of manganin. Reason (R) : The temperature coeffiecient of resistance is very small
for manganin.
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not a correct explanation of
c. A is true but R is false
D. A is false but R is true


Find the slope of the line passing through the points \( C(3,5) \) and
\( \boldsymbol{D}(-\mathbf{2},-\mathbf{3}) \)


Which of the following gives vital information about the plants?
A. Binomial nomenclature
B. Vernacular names
c. synonyms
D. Trinomial nomenclature


Young modulus of elasticity of brass is \( 10^{11} N / m^{2} . \) The increase in its energy
on pressing a rod of length \( 0.1 m \) and
cross-sectional area \( 1 \mathrm{cm}^{2} \) made of
brass with a force of \( 10 \mathrm{kg} \) along its
length,will be \( x \times 10^{-7} \). Find \( x \)


For zero order reactions, the linear plot was obtained for \( [A] \) vs t. The slope of the line is equal to:
\( A \cdot k_{0} \)
B. \( -k_{0} \)
c. \( \frac{0.693}{K_{o}} \)
D. \( -\frac{K_{o}}{2.303} \)


Which of the following is correct for any thermodynamic system?
A. The internal energy changes in all processes
B. Internal energy and entropy are state functions
c. The change in entropy can never be zero
D. Heat gained or lost in an adiabatic process is always zero


Discuss the change in energy and arrangement of molecules on increasing the temperature of ice from
\( -5^{\circ} \mathrm{C} \) to \( 10^{\circ} \mathrm{C} \) at 1 atm pressure.


Which of the following sets of atomic masses do not correspond to Dobereiner's triad?
This question has multiple correct options
A. 7,23,39
B. 20, 38, 56
c. 47,91,178
D. 54, 95, 183