Area of a trapezium shaped field is \( 84 m^{2} \& \) height is \( 7 m \) if one of them the parallel side is \( \frac{3}{5} \) of the other find
their length.


When \( C l_{2} \) is passed through moist slaked lime, the compound formed is :
A. \( C a O_{2} C l_{2} \)
в. \( C a O_{2} C l \)
c. \( C a O C l \)
D. \( \operatorname{CaCl}_{2} \mathrm{O}_{4} \)


Irregular flowers are
A. Asymmetrical
B. Symmetrical
C. Achlarnydcius
D. All of these


If a nucleus such as \( ^{226} R a \), that is
initially at rest, undergoes \( \alpha- \) decay
then which of the following statement is true?
A. The alpha particle has more kinetic energy then the daughter nucleus
B. The alpha particle has less kinetic energy then the daughter nucleus
C. The alpha particle and daughter nucleus both have same kinetic energy
D. We cannot say anything about kinetic energy of alpha particle and daughter nucleus


Two functions \( f(x) \) and \( g(x) \) are defined as \( f(x)=\log _{10}\left|\frac{x-2}{x^{2}-10 x+24}\right| \) and
\( \boldsymbol{g}(\boldsymbol{x})=\sin ^{-1}\left(\frac{\mathbf{2}[\boldsymbol{x}]-\mathbf{3}}{\mathbf{1 5}}\right), \) where
denotes greatest integer function, then the number of even integers for which
\( f(x)+g(x) \) is defined, is


Out of \( \mathrm{H}, \mathrm{C} \) and \( \mathrm{F} \) which has largest
atomic size?


If the expansion \( \left(x^{2}+\frac{1}{x^{3}}\right)^{n} \) is to contain an independent term, then what should be the value of \( n \) ?


During the oxidation of arsenite ion, \( A s O_{3}^{3-}, \) to arsenate ion, \( A s O_{4}^{3-}, \) in alkaline medium, the number of moles of hydroxide ions consumed per mole of arsenite ion is
\( A \cdot 2 \)
B. 3
\( c \cdot 2 / 3 \)
D. 3/2


Which product of petroleum is used to drive heavy vehicles like trucks?
A . Petrol
B. Kerosene
c. Diesel
D. None of these


Mark the incorrect statement.
A. The metallic body is connected to the earth wire.
B. The earth wire, has insulation of red colour.
\( c \cdot \) both
D. none


in figure carrying current \( \boldsymbol{I} . \boldsymbol{A} \boldsymbol{B} \) and \( \boldsymbol{B} \boldsymbol{C} \)
parts are straight, long, and at right
angle. At \( D \) wire forms a circular turn
DM \( N D \) of radius \( R . A B, B C \) parts are
tangential to circular turn at \( N \) and \( D \)
The magnetic field at the centre of
circle is
A \( \cdot \frac{\mu_{0} I}{2 \pi R}\left(\pi-\frac{1}{\sqrt{2}}\right) \)
B. \( \frac{\mu_{0} I}{2 R} \)
c. \( \frac{\mu_{0} I}{2 \pi R}\left(\pi+\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathrm{D}} \cdot \frac{\mu_{0} I}{2 \pi R}(\pi+1) \)


What type of bond is formed, if the atoms involved has electronegativity difference as \( 2 ? \)
A. Metallic
B. Covalent
c. lonic
D. Polar covalent
E. Hydrogen bonding


What is the exchange particle for strong nuclear interaction?
A. neutrino
B. positron
c. \( \pi \) meson
D. \( \alpha \) - particle


Differentiate between
Tidal volume and residual volume


Column \( I \) has some statements about
the system shown in column \( I I, \) Match appropriate column.


An organic substance bind to an enzyme for its activity is called as
A. coenzyme
B. cofactor
c. Apoenzyme
D. None of the above


A current loop consists of two identical
semicircular parts each of radius \( \mathrm{R} \), one
lying in the \( x \) -y plane and the other in \( x-z \)
plane. If the current in the loop is i., the
resultant magnetic field due to the two
semicircular parts at their common
centre is
A \( \cdot \frac{\mu_{0} i}{\sqrt{2} R} \)
В. \( \frac{\mu_{0} i}{2 \sqrt{2} R} \)
c. \( \frac{\mu_{0} i}{2 R} \)
D. \( \frac{\mu_{0} i}{4 R} \)


The length of an elastic string is \( a \) metre when the longitudinal tension is \( 4 \mathrm{N} \) and \( b \) metre when the longitudinal
tension is 5 N. The length of the string in metre when longitudinal tension is \( 9 N \) is :
\( \mathbf{A} \cdot a-b \)
B. \( 5 b-4 a \)
c. \( 2 b-\frac{1}{4} a \)
D. \( 4 a-3 b \)


Two balloons are filled, one with pure He gas and the other by air, respectively. If the pressure and temperature of these
baloons are same then the number of
molecules per unit volume is:
A. More in the He filled balloon
B. Same in both balloons
c. More in air filled balloon
D. In the ratio of 1: 4


The radii and Young's moduli of two
uniform wires \( A \) and \( B \) are in the ratio
2: 1 and 1: 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire \( A \) is one percent, the percentage
increase in length of the wire \( B \) is:
A . 1.0
в. 1.5
\( c .2 .0 \)
D. 3.0


The price of an article diminished twice successively, first by \( 30 \% \) and then by 40 \%. The original price was Rs. 1000 what is it now?
A . Rs. 400
B. Rs. 300
c. Rs. 240
D. Rs. 420


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


On adding \( H_{2} O \) to \( B i C l_{2} \) solution in \( H C l, \) the compound produced is:
\( \mathbf{A} \cdot B i_{2} O_{3} \)
B \( \cdot B i(O H)_{3} \)
c. В гОС
D. BiOCl


Densities of diamond and graphite are
3.5 and \( 2.3 g / m L \) respectively. Increase of pressure on the equilibrium:
\( C(\text {diamond}) \rightleftharpoons C(\text {graphite}) \)
A. favours backward reaction
B. favours forward reaction
c. has no effect
D. increases the reaction rate


If \( 1400 \times x=1050 . \) Then, \( x=? \)
A \( \cdot \frac{1}{4} \)
B. 3
\( c \cdot \frac{2}{3} \)
D.
E. None of these


Match the Following:
\begin{tabular}{lll|l}
& Column - I & & Column \\
& & -II \\
A & Weight & p & Scalar \\
B & Mass & q & Vector \\
C & Force & r & kilogram \\
D & Quantity of matter in a body & s & Kgwt (or) kgf
\end{tabular}
\( A \cdot A-q, s ; B-p, r ; C-q, s ; D-p, r \)
B. A-r,s; B-p,q; C-q,s; D-p,r
C. \( A-q, s ; B-p, r ; C-q, r ; D-p, s \)
D. A-q,s; B-p,s; C-q,r; D-p,


Find the sum of the following series to \( n \)
terms:
\( 1 \times 2+2 \times 3+3 \times 4+4 \times 5+\dots \)
A \( \cdot \frac{n}{4}(n-1)(n+2) \)
B \( \cdot \frac{n}{3}(n-1)(n-2) \)
c. \( \frac{n}{2}(n-1)(n+1) \)
D \( \cdot \frac{n}{3}(n+1)(n+2) \)


An atom of \( _{53}^{131} I \) and an atom of \( _{53}^{127} I \) contain the same number of:
A. Quarks
B. Neutrons
c. Nucleons
D. Protons


In a p-type semiconductor, the acceptor
level lies
A. near the conduction band
B. half way between conduction and valence bands
C. within conduction band
D. near the valence band


The enzyme, which combines with non-
protein part to form a functional enzyme is known as
A. Co-enzyme
B. Holoenzyme
c. Apoenzyme
D. Prosthetic group


Read the following conversation. Teacher: "If you want to collect virtual
image, which mirror do you select?" Bharathi: "convex mirror"
Sowmya: "concave mirror" Firoz : "plane mirror"
What do you think? Who is correct?
Explain


What changes occur when acidified \( C r_{2} O_{7}^{2-} \) ion reacts with \( H_{2} O_{2} \) solution
in presence of ether solvent?
A. orange colour of solution turns blue
B. Oxidation state of \( C r \) atom increases
c. oxidation state of \( C r \) atom remains constant
D. Orange colour turns green


Find the sum of the series \( 1^{2}+\left(1^{2}+\right. \)
\( \left.\mathbf{2}^{2}\right)+\left(\mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}\right)+\dots \)


For the following distribution function \( F(x) \) of a r.v \( X \) is given
\[
\begin{array}{ccccc}
x & 1 & 2 & 3 & 4 \\
F(x) & 0.2 & 0.37 & 0.48 & 0.62
\end{array}
\]
Then \( P(3<x \leq 5)= \)
A . 0.48
в. 0.37
c. 0.27
D. 1.47


The electronic configuration of the element with maximum electron
affinity is :
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{3} \)
B . \( 1 s^{2}, 2 s^{2} 2 p^{5} \)
C. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{3} \)


HOOC \( - \) CHOH \( - \) CHOH \( - \)
CHOH - CHOH - CHOH
COOH

The number of meso isomers of the
given above molecule is:


What is recycling of waste? Explain with one example. State two advantages of recycling?


Describe two important uses of each of the following: (i) caustic soda (ii) sodium carbonate
(iii) quicklime.


The amplitude of \( 1+\cos x-i \sin x \) is
A \( \cdot \frac{x}{2} \)
B.
\( c \cdot-\frac{x}{2} \)
D. \( 2 x \)


The other name(s) for Ursa Major is
are
A. the Big Dipper
B. the Saptarshin
\( \mathbf{c} \). the Great Bear
D. all of the above


Find the number of donor atoms in thionitro ligand \( (N O S) \)


Evaluate:
\( \mathbf{1}^{2} \boldsymbol{c}_{1}+\mathbf{2}^{2} \boldsymbol{c}_{2}+\mathbf{3}^{2} \boldsymbol{c}_{3}+\boldsymbol{4}^{2} \boldsymbol{c}_{4}+\ldots \ldots+\boldsymbol{n}^{2} \boldsymbol{c}_{n} \)


A magnet is placed in earth's magnetic field with south pole of the magnet
pointing north. At the neutral point This question has multiple correct options
A. The earth's magnetic field is zero
B. The fields of the magnet and the earth are equal and in opposite direction
C. The magnet's magnetic field is zero
D. The net magnetic field is zero


Zeroth law of thermodynamics is not
valid for which one of the following?
A \( \cdot 50 \) ml of water at \( 25^{\circ} \mathrm{C} \) is mixed with \( 150 \mathrm{ml} \) of water at
\( 25^{\circ} \mathrm{C} \)
B. \( 500 \mathrm{ml} \) of milk at \( 15^{\circ} \mathrm{C} \) is mixed with \( 100 \mathrm{ml} \) of water at
\( 15^{\circ} \mathrm{C} \)
\( \mathrm{c} .5 \mathrm{kg} \) of wet steam at \( 100^{\circ} \mathrm{C} \) is mixed with \( 50 \mathrm{kg} \) of dry and saturated steam
D. \( 10 \mathrm{ml} \) of water at \( 20^{\circ} \mathrm{C} \) is mixed with \( 10 \mathrm{ml} \) of Sulfuric acid at \( 20^{\circ} \mathrm{C} \)


A germanium specimen is doped with aluminum. The concentration of
acceptor atoms is \( 10^{21} \) atoms \( / m^{3} \). Given that the intrinsic concentration of
electron-hole pairs is \( 10^{19} / m^{3}, \) the concentration of electrons in
the specimen is
A \( \cdot 10^{17} / m^{3} \)
В. \( 10^{15} 5 m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{3} / m^{3} \)


Q Type your question \( \sqrt{07} \)
What is and
\( \mathbf{A} \cdot(A) \)
\( -b-t-3 \)
\( (B) \)
\( -c-s-4 \)
\( (C) \)
\( -a-q-1 \)
\( (D) \)
\( -e-r-5 \)
\( (E) \)
\( -d-p-2 \)
\( \mathbf{B} \cdot(A) \)
\( -c-s-3 \)
\( (B) \)
\( -b-s-4 \)
\( (C) \)
\( -a-t-1 \)
\( (D) \)
\( -e-r-5 \)
\( (E) \)
\( -d-p-2 \)
\( \mathbf{C} \cdot(A) \)
\( -d-p-3 \)
\( (B) \)
\( -e-r-4 \)
\( (C) \)
\( -a-q-1 \)
\( (D)-c-s-5 \)
\( (E)-b-t-2 \)
D. None of these


Which of the following substance(s) dissolves in water?
This question has multiple correct options
A. Vinegar
B. Groundnut Oi
c. Lemon Juice
D. Kerosene


Which catalyst is used for the
industrial production of hydrogen?
A. Iron
B. Nickel
c. vanadium pentaxide
D. Palladium


The equilibrium constant for a reaction
is \( K, \) and the reaction quotient is \( Q \). For a reaction mixture, the ratio \( \frac{K}{Q} \) is 0.33 This means that:
A. the reaction mixture will equilibrium to form more reactant species
B. the reaction mixture will equilibrium to form more product species
c. the equilibrium ratio of reactant to product concentrations will be 3
D. the equilibrium ratio of reactant to product concentrations will be 0.33


Two electric bulbs have ratings respectively of \( 25 W, 220 V \) and \( 100 W, 220 V \). If the bulbs are connected
in series with a supply of \( 440 V, \) which bulb will fuse?
\( \mathbf{A} \cdot 25 W \) bulb
B. \( 100 W \) bulb
c. Both of these
D. None of these


The molecules shown are:
and
A. enentiomer
B. constitutional isomers
C. identical
D. diastereomers.


Write the degree of the differential
equation \( a^{2} \frac{d^{2} y}{d x^{2}}=\left\{1+\left(\frac{d y}{d x}\right)^{2}\right\}^{1 / 4} \)


An object moving with kinetic energy \( K E=100 J \) and momentum \( p= \)
\( 50 k g m / s . \) Find out the mass of the
moving object?
A \( .2 k g \)
в. \( 4 k g \)
c. \( 6.25 k g \)
D. \( 12.5 k g \)
E . \( 25 k g \)


\( C(\text { diamond }) \rightarrow C(\text { graphite }), \Delta S_{300}= \)
\( \mathbf{1 0} \) cal \( \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{C}(\text { diamond })+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{9 1} \)
kcal \( m o l^{-1} \) at \( 300 K \)
\( \boldsymbol{C}(\text { graphite })+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{x} \) at
\( \mathbf{3 0 0 K} \)
\( x \) is:
A. -81 kcal
B. 101 kcal
c. -94 kcal
D. 88 kcal


The most energetic electromagnetic radiations are:
A. microwaves
B. ultraviolet waves
c. \( X \) -rays
D. gamma rays


Expand the following binomials expressions. \( (x-3)^{5} \)


Identify the part "B" from the shown
figure of human eye :
A. Retina
B. Iris
C. Cornea
D. Pupil


The equivalent capacitance of
capacitors \( 6 \mu F \) and \( 3 \mu F \) connected in
series is
\( \mathbf{A} \cdot 3 \mu f \)
B. \( 2 \mu f \)
c. \( 4 \mu f \)
D. \( 6 \mu f \)


Mercury is closer to the Sun than the
Venus. But Venus is hotter than Mercury
This is because
A. Mercury has no atmosphere and Venus has a thick atmosphere which can retain the heat.
B. Mercury is mostly made up of sedimentary rocks while Venus contains igneous rocks.
C. Mercury being closer to the Sun, Sun absorbs the heat of the Mercury.
D. All of the above are true.


A well of diameter \( 3 m \) is dug 14 m
deep. The earth taken out of it has been
spread evenly all around it to a width of \( 4 m \) to form an embankment. Find the
height of the embankment


How is phenol prepared from Benzene Sulphonic acid?


Find area bounded by \( x^{2}+y^{2} \leq \)
\( 2 a x, y^{2} \geq a x, x \geq 0, y \leq 0 \)


\( A C^{2}=B C \times A B \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


What is \( P(Z=10) \) equal to \( ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 5 \)


What are the effects of air pollution?
i. greenhouse effect
ii. smog
iii. respiratory disease
¡v. acid rain
\( \mathbf{A} \cdot \mathbf{i}, \mathbf{i} ; \) ii
B. ii, iii, iv
c. iii, iv,
D. i, ii, iii, iv


A copper wire of length \( l \) is bent into a
semicircle. It is moved with a velocity \( \boldsymbol{v} \) in a region where magnetic field is uniform and perpendicular to the plane of the wire. If the strength of the field is
\( B \) then emf induced is
\( \mathbf{A} \cdot B l v \)
в. \( \quad B \frac{l}{\pi} v \)
c. \( _{B} \frac{2 l}{\pi} v \)
D. none of these


Find the 6 th term from the end of the
A.P. \( 17,14,11, \dots \dots,-40 ? \)


One mole of an ideal gas at standard temperature and pressure occupies 22.4 L(molar volume). What is the ratio
of molar volume to the atomic volume of
a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 ). Why is this ratio so large?


List the hormones secreted by the following:
(a) Hypothalamus
(b) Pituitary
(c) Thyroid
(d) Parathyroid
(e) Adrenal
(f) Pancreas
(g) Testis
(h) Ovary
(i) Thymus
(j) Atrium
(k) Kidney
(i) G-l Tract


slowly neated tIII all the mercury spılls
over
\( P_{a t m}=76 \mathrm{cm} \) of Hg column
Statement 1: The temperature of gas continuously increases.

Statement 2: According to first law of
thermodynamics \( d Q=d U+d W \)
where symbols have their usual
meaning.
A. Statement1 is true, statement 2 is true and statement 2 is correct explanation for statement 1
B. Statement1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement
c. Statement 1 is true statement 2 is false
D. Statement 1 is false, statement 2 is true


State whether true or false:
Relative permeability and absolute permeability have the same units.
A. True
B. False


A solid sphere of mass \( m \) and radius \( R \) is placed on a plank of equal mass,
which lies on a smooth horizontal
surface. The sphere is given a sharp impulse in the horizontal direction so
that it starts sliding with a speed of \( v_{0} \)
Find the time taken by the sphere to
start pure rolling on the plank. The coefficient of friction between plank
and sphere is \( \mu \)


Which term is a class of molecules that
contain only single bonds between
carbon atoms?
A. Alkynes
B. Hydrocarbons
c. Alkenes
D. Alkanes
E. Functional groups


Different type of reflex arc
is
A. Somatic Reflex arc
B. Visceral Reflex arcc
c. Both A and B
D. None of these


In which of the following compounds when hydrolysis occurs oxidation number of central atom will be +6 in at
least one of the products?
\( A \cdot S O_{2} F_{2} \)
в. \( X e F_{4} \)
c. \( X e F_{6} \)
D. \( S O_{2} C l_{2} \)


I: The roots of \( a(b-c) x^{2}+b(c-a) x+ \)
\( c(a-b)=0 \) are real and equal, then
\( a, b, c \) are in G.P.
II: The number of solutions of \( \mid x^{2}- \) \( 2 x+2 \mid=3 x-2 \) is 4
Which of the above statement(s) is/are
true?
A. only।
B. only II
c. both I and II
D. neither I nor II


Assertion
In p-block elements a lot of variation in properties of elements in a group is observed.
Reason
Difference in inner core of electronic
configuration greatly influences the physical and chemical properties of
elements.
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.


Chemically, rust is \( \mathrm{Fe}_{2} \mathrm{O}_{3} \cdot \mathrm{XH}_{2} \mathrm{O} \)
If true enter 1 , else enter 0 .


A block released from rest from the top
of a smooth inclined plane of angle \( \boldsymbol{\theta}_{\mathbf{1}} \)
reaches the bottom in time \( t_{1} \). The same
block released from rest from the top of another smooth inclined plane of angle
\( \theta_{2}, \) reaches the bottom in time \( t_{2} \). If the
two inclined planes have the same height, the relation between \( t_{1} \) and \( t_{2} \) is
\( A \)
\[
\frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right)^{1 / 2}
\]
B. \( \frac{t_{2}}{t_{1}}=1 \)
c. \( \frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right) \)
D.
\[
\frac{t_{2}}{t_{1}}=\left(\frac{\sin ^{2} \theta_{1}}{\sin ^{2} \theta_{2}}\right)
\]


If you have several \( 2.0 \mu F \) capacitors,
each capable of withstanding 200 volts without breakdown how would you
assemble a combination having minimum number of capacitors and of given equivalent capacitance which capable of withstanding 1000 volts
\( (A) 0.40 \mu F \)
(B) \( 1.2 \mu F, \) capable of withstanding
\( \mathbf{1 0 0 0} \) volts.


Substance \( \boldsymbol{X} \)
(1) reacts with \( \boldsymbol{H}_{2} \boldsymbol{S} \) to produce white
turbidity.
(II) changes light green solution of
\( F e S O_{4} \) into yellow colour.
(III) reacts with moisture to give
pungent smelling gas.
Hence \( \boldsymbol{X} \) is:
A. \( K M n O_{4} \)
в. \( K_{2} C r_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \)
D. \( C a O C l \)


In the given figure, when galvanometer
shows no deflection, the current (in
ampere flowing through \( 5 \Omega \)
resistance will be
A . \( 1.7 A \)
В. \( 0.6 A \)
\( c .0 .9 A \)
D. \( 1.2 A \)


A man throws balls into the air one after
another. He always throws a ball when the previous one thrown has just reached the highest point. The height to which each ball rises, if he throws 5
balls per second is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
A . \( 0.31 \mathrm{m} \)
B. 0.20 \( m \)
c. \( 0.42 \mathrm{m} \)
D. \( 0.53 \mathrm{m} \)


Select correct definition of light year:
A. The distance travelled by the light in a year
B. The distance travelled by the atoms in a year
C. The distance travelled by the earth in a year
D. The distance travelled by the sound in a year


Sum to infinite terms the following
series:
\( 1+4 x+7 x^{2}+10 x^{3}+\ldots,|x|<1 \)


The equilibrium constant for the
reaction
\( \boldsymbol{P}+\boldsymbol{Q} \rightleftharpoons \boldsymbol{R}+\boldsymbol{S} ; \boldsymbol{K}_{c}=\mathbf{0 . 2} \)
hence, the equilibrium constant for the following reaction will be:
\( \boldsymbol{R}+\boldsymbol{S} \rightleftharpoons \boldsymbol{P}+\boldsymbol{Q} \)


A body initially at rest is moving with uniform acceleration a. Its velocity after
n seconds is v. The displacement of the body in last 2 s is :
A \( \cdot \frac{2 v(n-1)}{u} \)
B. \( \frac{v(n-1)}{n} \)
c. \( \frac{v(n+1)}{n} \)
D. \( \frac{2 v(n+1)}{n} \)


Find area of \( \boldsymbol{y}=\boldsymbol{x}^{2} \) from \( \boldsymbol{x}=\boldsymbol{2} \) to \( \boldsymbol{x}=\boldsymbol{4} \)


Presence of ethylene gas causes fruits to ripen. As fruit ripens, it produces increasing amounts of ethylene.
This is an example of
A. Positive feedback
B. Negative feedback
c. Homeostasis
D. Endocrine regulation


Post-mitotic phase of the cell in which
active synthesis of RNA and proteins takes place is
A. S-phase
B. Amitotic phase
c. \( G_{2}- \) phase
D. \( G_{1}- \) phase


A bullet of mass \( m \) is fired into a large
block of wood of mass \( \mathrm{M} \) with velocity \( \mathrm{v} \) The final velocity of the system is?
\( ^{\mathbf{A}} \cdot\left(\frac{m}{M-m}\right)^{v} \)
в. \( \left(\frac{m+M}{M}\right) v \)
\( ^{\mathbf{c}} \cdot\left(\frac{M-m}{M}\right) v \)
D. \( \left(\frac{m}{m+M}\right) v \)


Find the slope and \( y \) -intercept of the
line \( 2 x+2 y=-2 \)
A. slope \( =1, \) y-intercept \( =-3 \)
B. slope = -1, y-intercept = -1
c. slope \( =1, y \) -intercept \( =3 \)
D. slope \( =1, y \) -intercept \( =1 \)


The function \( \boldsymbol{y}=\boldsymbol{a} \log |\boldsymbol{x}|+\boldsymbol{b x}^{2}+\boldsymbol{x} \)
has its extremum values at \( x=-1 \) and
\( x=2 \) then
A \( a=2, b=-1 \)
- \( 1, a=2, b=2=2 \)
В. \( a=2, b=-1 / 2 \)
c. \( a=-2, b=1 / 2 \)
D. None of these


Influence of genes in controlling the activity of living organism is through
A. Photosynthesis
B. Protein synthesis
c. Vitamins
D. Hormones


A current of \( 16 A \) is made to pass
through a conductor in which the
number density of free electrons is \( 4 x \) \( 10^{28} m^{-3} \) and its area of cross section
is \( 10^{-5} m^{2} . \) The average drift velocity of free electrons in the conductor is:
A \( .2 .5 \times 10^{-4} \mathrm{ms}^{-1} \)
B . \( 3.2 \times 10^{-4} \mathrm{ms}^{-1} \)
c. \( 6.4 \times 10^{-4} \mathrm{ms}^{-1} \)
D. \( 1.6 \times 10^{-4} \mathrm{ms}^{-1} \)


Which one is the correct diagram for
Resistivity vs Temperature for Metals?


Find the arithmetic mean for the table
given below using direct method:
A. 14.18
B. 12.54
\( c \cdot 13.72 \)
D. 15.61


A bulb is connected to a cell. How is the
resistance of circuit affected if another
identical bulb is connected in parallel?
A. Resistance is tripled.
B. Resistance remains same
c. Resistance is doubled
D. Resistance is one half


Calculate the electric potential at the
center of the square:
\( A \)
в. \( k \frac{29}{x^{2}} \)
\( c \cdot_{k} \frac{4 q}{c^{2}} \)
D. \( k \frac{49}{6} \)
\( E \)
\[
k \frac{(4 \sqrt{2})}{s}
\]


In the given figure, \( A B \| C D \) and
\( \boldsymbol{E F} \perp \boldsymbol{C D} \) and \( \angle \boldsymbol{G} \boldsymbol{E C}=\mathbf{1 3 2}^{\boldsymbol{o}} . \) Find
\( \angle \boldsymbol{E} \boldsymbol{G} \boldsymbol{F} \)
A \( \cdot 43^{\circ} \)
B. \( 42^{\circ} \)
\( c \cdot 48 \)
\( D \cdot 44^{\circ} \)


Height of the image of an principal axis produced by a convex lens is double the object height. If the focal length of the
lens is \( 20 \mathrm{cm} \), then the image distance from lens is :
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} \cdot 40 \mathrm{cm} \)
D. Both (1)\( \&(2) \)


Let \( X \) and \( Y \) be two random variables.
The relationship \( \boldsymbol{E}(\boldsymbol{X} \boldsymbol{Y})=\boldsymbol{E}(\boldsymbol{X}) \)
\( \boldsymbol{E}(\boldsymbol{Y}) \) holds
A . Always
B. If \( E(X+Y)=E(X)+E(Y) \) is true
c. If \( X \) and \( Y \) are independent
D. If \( X \) can be obtained from \( Y \) by a linear transformation


If \( a=\hat{i}+\hat{j}, b=2 \hat{j}-\hat{k} \) and \( r \times a= \)
\( \boldsymbol{b} \times \boldsymbol{a}, \boldsymbol{r} \times \boldsymbol{b}=\boldsymbol{a} \times \boldsymbol{b}, \) then a unit vector
in the direction of \( r \) is?
A \( \cdot \frac{1}{\sqrt{11}}(\hat{i}+3 \hat{j}-\hat{k}) \)
B. \( \frac{1}{\sqrt{11}}(\hat{i}-3 \hat{j}+\hat{k}) \)
c. \( \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \)
D. None of these


Decarboxylation of salts of carboxylic acids is carried out in presence of alcoholic KOH.
A. True
B. False


In which of the following pairs are both the ions coloured in aqueous solution?
[At. No. \( : S c=21, T i=22, N i= \)
\( \mathbf{2 8}, \boldsymbol{C u}=\mathbf{2 9}, \boldsymbol{C o}=\mathbf{2 7}] \)
A \( \cdot N i^{2+}, T i^{3+} \)
B. \( S c^{3+}, T i^{3+} \)
\( \mathbf{c} \cdot S c^{3+}, C o^{2+} \)
D. \( N i^{2+}, C u^{+} \)


A card from pack of 52 cards is lost. From the remaining card of the pack, one card is drawn and is found to be
heart, find the probability of missing card to be
(I) heart (II) club.


All of the following are involved in prokaryote protein synthesis except
A. Introns are removed from the mRNA transcript
B. RNA polymerase copies DNA into RNA nucleotides to produce mRNA
C. Translation occurs simultaneously with transcription.
D. Transcription and translation occur in the cytoplasm.
E. All of the above events occur in prokaryote protein synthesis


When chlorine is passed through hot
conc. sodium hydroxide, products are:
This question has multiple correct options
A. sodium chlorate
B. sodium perchlorate
c. sodium chloride
D. sodium hypochloride


If \( x-\frac{1}{x}=5, \) then \( x^{3}-\frac{1}{x^{3}} \) equals
A . 125
в. 130
c. 135
D. 140


Pick out the wrong statement.
A. Gauss's law of magnetism is given by \( \alpha \phi B . d s=0 \)
B. An EM wave is a wave radiated by a charge at rest and propagates through electric field only
C. A time varying electric field is a source of changing magnetic field
D. Faraday's law of EM induction is \( \phi E . d I=-\frac{d \phi_{B}}{d t} \)


Potential energy of a bar magnet of magnetic moment \( M \) placed in a magnetic field of induction \( B \) Such that
it makes an angle \( \theta \) with the direction
of \( B \) is \( \left(\operatorname{take} \theta=90^{\circ} \) as datum) \right.
\( \mathbf{A} \cdot-M B \sin \theta \)
B. \( -M B \cos \theta \)
c. \( M B(1-\cos \theta) \)
D. \( M B(1+\cos \theta) \)


Assertion
In an electrochemical cell, the electrode
that is the site of reduction is called the
anode.
Reason
Oxidation always occurs at the cathode.
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


1 MeV is equal to
\( \mathbf{A} \cdot 1.6 \times 10^{13} \)Joules
B . \( 1.6 \times 10^{13} \) cal.
C \( .1 .6 \times 10^{13} \) ergs
D. None of these


For a total internal reflection, which of
the following is correct?
A . Light travel from rarer to denser medium
B. Light travel from denser to rarer medium.
c. Light travels in air only.
D. Light travels in water only.


Calculate approximate \( p H \) of the resultant solution formed by titration of
\( 25 m L \) of \( 0.4 M N a_{2} C O_{3} \) with \( 50 m L \)
of \( 0.025 M H C l \)
[Given that: \( p K_{a_{1}}=6.4 \) and \( p K_{a_{2}}= \)
10.3 for \( H_{2} C O_{3} \)
A .5 .92
B. 11.14
\( c .6 .4 \)
D. 5.88


Answer the following briefly:
What is meant by 'Power of
accommodation' of the eye? Name the part of the eye responsible for the same.


The lanthanide element that has the
electronic configuration \( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{7} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2} \)
is:
A. Lutetium
B. Terbium
c. Ytterbium
D. Gadolinium


Out of the given statements which of the
following are true:
A) Work done in moving a charge on equipotential surface is zero.
B) Electric lines of force are always
normal to equipotential surface.
C) When two like charges are brought closer, the electrostatic potential energy of the system is decreased.
D) Electric lines of force converge at
positive charge and diverge at negative charge.
\( A \cdot A, B, C, D \) are true
B. \( A, B, C \) are true
c. \( A, B \) are true
D. A only true


The halogen that is most easily reduced
is:
A. \( F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


(a) Explain the following
(i) Henry's law about a dissolution of a gas in a liquid.
(ii) Boiling paint elevation constant for a solvent.
(b) A solution of glycerol \( \left(C_{3} H_{8} O_{3}\right) \) in
water was prepared by dissolving some glycerol in 500 g of water. This solution
has a boiling point of \( 100.42^{\circ} \mathrm{C} \). What
mass of glycerol was dissolved to make
this solution? \( \left(K_{b} \text { for water }=0.512 \mathrm{K} \mathrm{kg}\right. \)
\( \left.\operatorname{mol}^{-1}\right) \)


For which among the following equimolar aqueous solutions Van't Hoff factor has the lowest value?
A. Aluminium Chloride
B. Potassium Sulphate
c. Ammonium chloride
D. urea


The precipitate formed in Carius method is:
A . \( A g I \)
в. \( A g C l \)
c. \( A g B r \)
D. all of the above


Do you expect different products in solution when aluminium(III) chloride
and potassium chloride treated
separately with
(i) normal water (ii)
acidified the water, and (iii) alkaline
water? Write equations wherever
necessary.


Which of the following bones form a link between axial and appendicular skeleton?
A. First rib
B. Clavicle
c. Scapula
D. Both (a) and (b)


Number of real values of \( \left|\begin{array}{ccc}\mathbf{3}-\boldsymbol{x} & \mathbf{2} & \mathbf{2} \\ \mathbf{2} & \mathbf{4}-\boldsymbol{x} & \mathbf{1} \\ \mathbf{- 2} & \mathbf{- 4} & \mathbf{- 1}-\boldsymbol{x}\end{array}\right| \) is singular
then
\( A \cdot 1 \)
B. 3
\( c \cdot 2 \)
D. infinite


In the given figure, \( A B C \) is a triangle in
which \( \mathrm{D} \) and \( \mathrm{E} \) are the middle points of
\( \mathrm{BC} \) and \( \mathrm{AC} \) respectively. If \( \boldsymbol{A O}=\mathbf{6} \mathrm{cm} \)
find the length of 0 D.
\( A \cdot 3 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
\( D, 2 \mathrm{cm} \)


Angle of reflection is the angle between reflected ray and the ......... (incident ray, normal).


If four points are \( \boldsymbol{A}(\boldsymbol{6}, \boldsymbol{3}), \boldsymbol{B}(-\boldsymbol{3}, \boldsymbol{5}), \boldsymbol{C}(\boldsymbol{4},-\boldsymbol{2}) \) and \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \)
then the ratio of the areas of \( \triangle P B C \)
and \( \triangle A B C \) is
A \( \cdot \frac{x+y-2}{7} \)
в. \( \frac{x-y-2}{7} \)
c. \( \frac{x-y+2}{2} \)
D. \( \frac{x+y+2}{2} \)


The unit calorie belongs to:
A . heat
B. temperature
\( c . \) work
D. coefficient of linear expansion


Two solenoids have identical
geometrical construction but one is made of thick wire and the other of thin
wire. Which of the following quantities are different for the two solenoids?
This question has multiple correct options
A. Self-inductance
B. Rate of Joule heating if the same current goes through them
c. Magnetic field energy if the same current goes through them
D. Time constant if one solenoid it connected to one battery and the other is connected to another battery


Which of the following statement is
incorrect?
A. At high temperature an low pressure gas shows ideal behaviour
B. Gas can be liquefied above critical temperature on applying pressure
C. He gas shows positive deviation at \( 273 K \)
D. All of these


For a reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \longrightarrow \boldsymbol{C}, \) the
amount of \( C \) formed by starting the reaction with 5 moles of \( A \) and 8 moles
\( \boldsymbol{B} \) is:
A. 5 mol
B. 8 mol
c. 16 mol
D. 4 mol


Identify the IUPAC name of the compound.
\( \boldsymbol{H}_{2}-\boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C l} \)


Three gases \( A, B \) and \( C \) are at same temperature if their r.m.s speed are in the ratio \( 1: \frac{1}{\sqrt{2}}: \frac{1}{\sqrt{3}} \) then their molar
masses will be in the ratio:
A .1: 2: 3
B. 3: 2: 1
c. \( 1: \sqrt{2}: \sqrt{3} \)
D. \( \sqrt{3}: \sqrt{2}: 1 \)


When the margins of sepals or petals overlap one another without any particular direction, the condition is
termed as
A. Vexillary
B. Imbricate
c. Twisted
D. valvate


The process of photosynthesis and respiration cause the cycling of through the environment
A. carbon
B. water
c. Nitrogen
D. Hydrogen


Which of the following is not true for the care of teeth?
A. we should not chew the food
B. We should not eat too many sweets.
c. we should brush twice a day.
D. we should eat raw fruits and vegetables


From the stability constant (hypothetical values) given below,
predict which is the strongest ligand?
\( \mathbf{A} \cdot C u^{2+}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right]^{2+}, K=4.5 \times 10^{11} \)
B. \( C u^{2+}+4 C N^{-} \rightarrow\left[C u(C N)_{4}\right]^{2-}, K=2.0 \times 10^{27} \)
\( \mathbf{c} \cdot C u^{2+}+2 e n \rightarrow\left[C u(e n)_{2}\right]^{2+}, K=3.0 \times 10^{15} \)
D \( \cdot C u^{2+}+4 H_{2} O \rightarrow\left[C u\left(H_{2} O\right)_{4}\right]^{2+}, K=9.5 \times 10^{8} \)


An athlete of mass \( 70.0 \mathrm{kg} \) applies a force of \( 500 \mathrm{N} \) to a \( 30.0 \mathrm{kg} \) luge, which is initially at rest, over a period of 5.00 s before jumping onto the luge. Assuming there is no friction between the luge and
the track on which it runs, what is its
velocity after the athlete jumps on?
A. \( 12.5 \mathrm{m} / \mathrm{s} \)
B. 25.0 \( \mathrm{m} / \mathrm{s} \)
c. \( 35.7 \mathrm{m} / \mathrm{s} \)
D. 83.3 \( \mathrm{m} / \mathrm{s} \)
E . \( 100 \mathrm{m} / \mathrm{s} \)


\( K_{a} \) for ascorbic acid, \( H A s c, \) is \( 5 \times \)
\( 10^{-5} . \) Calculate the hydrogen ion
concentration and percentage hydrolysis in an aqueous solution in
which the concentration of \( A s c^{-} \) ions is
\( \mathbf{0 . 0 2} \boldsymbol{M} \)


Cite an experiment to show that sound
needs a material medium for its
propagation:


Which is not correct about
monosaccharides?
This question has multiple correct options
A. Optically active polyhydroxy carbonyl compounds.
B. Fructose \& glucose can not be distinguish by \( B r_{2} / H_{2} O \)
c. Glucose and mannose are anomers.
D. Fructose \& glucose can be distuinguish by Fehling's solution


Positive deviation from Raoult's law is
shown by which of the following mixtures?
A. Benzene and toluene
B. \( C H C l_{3} \) and acetone
c. Ethanol and water
D. \( H C l \) and water


Solve: \( \frac{d y}{d x}+2 y \tan x=\sin x, \) given that
\( y=0, \) when \( x=\frac{\pi}{3} . \) Show that maximum value of \( y \) is \( \frac{1}{8} \)


Assertion
The area of the triangle formed by the
points \( \boldsymbol{A}(\mathbf{2 0 0 7}, \mathbf{2 0 0 9}), \boldsymbol{B}(\mathbf{2 0 0 8}, \mathbf{2 0 1 1}) \)
\( C(2009,2010) \) will be same as the
area formed by the points \( \boldsymbol{P}(\mathbf{0}, \mathbf{0}) \)
\( Q(1,2), R(2,1) \)
Reason
The area of the triangle remains same
w.r.t to transition of co-ordinate axes.
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


Carbon has \( _{\text {一一一一一一一一一一 }} \) unpaired electrons in its outermost shell.
A .2
B. 3
\( c \cdot 5 \)
\( D \)


The number of solutions of the equation
\( \tan ^{-1}(x-1)+\tan ^{-1}(x)+\tan ^{-1}(x+ \)
1) \( =\tan ^{-1}(3 x) \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


Boron has two isotopes, \( _{5} B^{10} \) and \( _{5} B^{11} \)
and the atomic weight of boron is 10.81
The ratio of \( _{5} B^{10}:_{5} B^{11} \) in nature would
be:
A. 19: 81
B. 10: 11
c. 15: 16
D. 81: 19


The distance of \( n^{t h} \) bright band on the
screen from the central bright band on either sides of central bright band is
A \( \cdot x_{n}=\frac{n \lambda D}{d} \)
B・ \( _{x_{n}}=(2 n-1) \frac{\lambda D}{d} \)
c. \( _{x_{n}}=\frac{n \lambda d}{D} \)
D. \( x_{n}=(2 n-1) \frac{\lambda D}{2 d} \)


Student 1 is
grips wrench here
(wrench turns winch clockwise)
A. correct, because the torque that the wrench must exert to lift the block depend on the wrench's length
B. correct, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length
C. incorrect, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length
D. incorrect, because using a longer wrench decreases the torque it must exert on the winch.


In stem, cork cambium originates from
some
A. Outer cells of cortex
B. Fascicular and interfascicular cambium
C. Inner cells of cortex
D. Endodermis


In addition to carbon monoxide \( (C O) \)
and carbon dioxide \( \left(C O_{2}\right), \) there is a third compound of carbon called carbon
sub-oxide. If a \( 2.500 g \) sample of carbon
sub-oxide contains \( 1.32 g \) of \( C \) and \( 1.18 g \) of \( O, \) using the law of multiple proportions, a possible formula of carbon sub-oxide can be deduced. What
is the number of carbon atoms in such
a formula?


\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{C l} \) is an octahedral
coordination compound. Write the IUPAC name of the above coordination
compound.


Given is the diagram of agarose gel
kept under UV light. Mention the positive and negative
terminals.


In a moving-coil instrument, the coil is suspended in a radial magnetic field instead of a uniform magnetic field This is done to :
A. Increase the sensitivity of the instrument
B. increases the accuracy of the instrument
c. make the instrument compact and protable
D. make its deflection proportinal to current through it


If three apples cost Rs. 45 , how much would five apples cost?


State Faraday's laws of electromagnetic
induction.


\( \int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x= \)


Assertion
The lungs are situated in thoracic chamber which is anatomically an airtight chamber.
Reason
Such an arrangement is essential to avoid any change in pulmonary volume.
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


Match the compounds in column I with
their
characteristics/test(s)/reagents(s)/ste reochemistry given in column II Matching can be one or more than one.


which of the following statements are
true:
(ii)
A. In circuit 1 lamp does not glow but in circuit 2 lamp glows
B. In circuit 1 as well as 2 lamp does not glow
c. In circuit 1 lamp glows but in 2 lamp does not glow
D. In both circuit lamp glows


Balance the following equations by
oxidation number method.
\( \boldsymbol{K} \boldsymbol{I}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{I}_{2}+\boldsymbol{S} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Which of the following is/are polyamide molecule?
A. Terylene
B. Rayon
c. Nylon - 6
D. Polystyrene


\( \operatorname{Let} f(x)=\cos ^{-1}\left(\frac{x^{2}}{1+x^{2}}\right) . \) The range
of \( \boldsymbol{f} \) is
\( \mathbf{A} \cdot\left[0, \frac{\pi}{2}\right] \)
B. \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
c. \( \left[-\frac{\pi}{2}, 0\right] \)
D. none of these


\( 5.6 \mathrm{g} \) of an organic compound on burning with excess of oxygen gave 17.6
\( \mathrm{g} \) of \( \mathrm{CO}_{2} \) and \( 7.2 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \). The organic
compound is:
A \( \cdot C_{6} H_{6} \)
в. \( C_{4} H_{8} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C H_{3} C O O H \)
E . \( C H_{3} C H O \)


The value of
\( \lim _{x \rightarrow 0}\left[\tan ^{-1}\left(\frac{2 x+1}{4 x+1}\right)-\frac{x}{4}\right] \) is equal to
\( A \cdot \frac{\pi}{4} \)
B. \( -\frac{\pi}{2} \)
c. \( \frac{-\pi}{4} \)
D. \( -\frac{3 \pi}{4} \)


How does the formation of \( 2^{\circ} \) and \( 3^{\circ} \)
amines can be avoided during the
preparation of \( 1^{\circ} \) amines by alkylation?


The area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{x}^{3} \) and \( \boldsymbol{y}=\sqrt{\boldsymbol{x}} \) is, (in square
units):
A \( \cdot \frac{5}{3} \)
в.
c. \( \frac{5}{12} \)
D. \( \frac{12}{5} \)


Name the class of fish where tail fin is
heterocoel.


\( \lim _{x \rightarrow 1} \frac{x^{4}-3 x^{3}+2}{x^{3}-5 x^{2}+3 x+1} \)


Assertion
Tracheids and the tracheae, the dead tissues are chief conducting tissues and their death is of great advantage to
plants.
Reason
In the dead tissues, the water and
solutes move freely and have not to diffuse through any differentially
permeable membranes, making conduction rapid and efficient.
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


Choose the correct answers from the
alternatives given Which one of the following is the basic unit of classification?
A. species
B. Genus
c. Family
D. Phylum


If the distance of earth from the sun
reduces to one fourth of its present
value then the length of the year will become
A . \( 1 / 6 \) of present year
B. 1/8 of present year
c. \( 1 / 4 \) of present year
D. \( 1 / 2 \) of present year


A block attached to a spring, pulled by a constant horizontal force, is kept on a
smooth surface as shown in the figure.
Initially, the spring is in the natural state. Then the maximum positive work
that the applied force \( F \) can do is:
(Given that spring does not break)
\( ^{\mathbf{A}} \cdot \frac{F^{2}}{K} \)
B. \( \frac{2 F^{2}}{K} \)
\( c \cdot \infty \)
D. \( \frac{F^{2}}{2 K} \)


Write the rational numbers that are
equal to their reciprocals.


In which pair(s) is/are the stronger bond found in the first species? This question has multiple correct options
A \( \cdot O_{2}^{-}, O_{2} \)
в. \( N_{2}, N_{2} \)
c. \( N O^{+}, N O^{-} \)
D. \( C O, O_{2}^{2+} \)


The field view is maximum for
A. concave mirror
B. plane mirror
c. convex mirror
D. None of the above


An electron and a proton are projected with same velocity perpendicular to a
magnetic field.Which particle will describe the smaller circle?


The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994 \\ 4 & 19999 & 193\end{array} \)
Loan(in
crores 33
55
of rupees)
With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding
year.


In which of the following acids, \( \boldsymbol{P}-\boldsymbol{P} \)
bonds is present?
A. Tetrapolyphosphoric acid \( \left(H_{6} P_{4} O_{13}\right) \)
B. Pyrophosphoric acid \( \left(H_{4} P_{2} O_{6}\right) \)
C. Hypophosphoric acid \( \left(H_{4} P_{2} O_{6}\right) \)
D. Polymetaphosphoric acid \( \left(H P O_{3}\right)_{n} \)


The HCF of 196 and 38416 using Euclid algorithm is
A. 191
в. 192
c. 193
D. 196


A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be :
A \( \cdot \frac{5}{3} \)
B. \( \frac{3}{5} \)
c. \( \frac{15}{13} \)
D. \( \frac{13}{15} \)


In triangle \( A B C . D \) and \( E \) are points on side \( A B \) such that \( A D=D E=E B \)
Through \( D \) and \( E \), lines are drawn
parallel to \( B C \) which meet side \( A C \) at
points \( \boldsymbol{F} \) and \( \boldsymbol{G} \) respectively. Through \( \boldsymbol{F} \)
and \( G \) lines are drawn parallel to \( A B \)
which meet side \( B C \) at points \( M \) and
\( N \) respectively
State whether true or false \( \boldsymbol{B} \boldsymbol{M}= \)
\( M N=N C .(\text { Enter } 1 \text { if true or } 0 \)
otherwise)


If the latus rectum of an ellipse is equal to half of minor axis, then find its
eccentricity.


A \( 1 \mathrm{kg} \) mass executes SHM with an amplitude \( 10 \mathrm{cm}, \) it takes \( 2 \pi \) seconds to
go from one end to the other end. The
magnitude of the force acting on it at any end is :
A . \( 0.1 \mathrm{N} \)
B. 0.2 N
c. \( 0.5 \mathrm{N} \)
D. 0.05 N


Find the value of
\( [4+3 \sqrt{-20}]^{1 / 2}+[4-3 \sqrt{-20}]^{1 / 2} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B \( \cdot 2(3+\sqrt{5}) \)
\( \mathbf{c} \cdot 2(3-\sqrt{5}) \)
D. \( 2 \sqrt{5} \)


Fusion reaction takes place at about :
A \( \cdot 9 \times 10^{2} K \)
В. \( 3 \times 10^{3} K \)
\( \mathbf{c} \cdot 3 \times 10^{4} K \)
D. \( 3 \times 10^{6} K \)


Which of the following statements
is/are incorrect regarding bryophytes?
A. Zygote undergoes meiosis to produce sporophyte.
B. Zygote undergoes mitosis to form embryo proper.
C. Fertilization takes place in presence of water.
D. Sporophyte is parasitic over gametophyte.


In a vacuum suspended unit, when the brakes are on, the piston and diaphragm has on both sides of it
A. Atmospheric pressure
B. Vacuum
c. Hydraulic pressure
D. Air pressure


Ammonia gas on passing through copper sulphate solution gives:
A. yellow colour solution
B. blue colour solution
c. brown colour solution
D. red colour solution


Explain the leaching process of silver and gold using chemical reactions?


Name the category and the principle involved in the use of contraceptives.


Compare \( L i \) and \( B e \) according to the
polarisation of cations:
A \( \cdot L i^{+}<B e^{2+} \)
B . \( L i^{+}>B e^{2} \)
c. \( L i^{+}=B e^{2+} \)
D. None of these


If \( \boldsymbol{\alpha} \) and \( \beta \) are two different values of \( \boldsymbol{\theta} \)
lying between 0 and \( 2 \pi \) which satisfy
\( 3 \cos \theta+4 \sin \theta=6 . \) Find the value of
\( \sin (\alpha+\beta) \)


A spring of spring constant \( 5 \times 10^{3} \frac{N}{m} \)
is stretched initially by \( 5 \mathrm{cm} \) from the unstretched position. The work required to further stretch the spring by another \( 5 \mathrm{cm} \) is
\( \mathbf{A} \cdot 6.25 N m \)
B . \( 12.50 \mathrm{Nm} \)
c. \( 18.75 N m \)
D. \( 25.00 \mathrm{Nm} \)


A ball of mass m moving with a constant velocity strikes against a ball
of same mass at rest. If \( e= \)
coefficient of restitution, then what
will be the ratio of velocity of two balls
after collision?
A \( \frac{1-e}{1+e} \)
в. \( \frac{e-1}{e+1} \)
c. \( \frac{1+e}{1-e} \)
D. \( \frac{2+e}{e-1} \)


Find the smallest number by which 9000 shoud be divided so that the
quotient becomes a perfect cube?
\( A \cdot 3 \)
B. 9
c. 27
\( D \)


An electric bulb is rated at \( 220 \mathrm{V}, 100 \mathrm{W} \)
What safe current can be passed through it ?
\( \mathbf{A} \cdot 2 \cdot 20 A \)
B . \( 3.50 A \)
c. \( 0.45 A \)
D. \( 0.50 A \)


Which of the following has the highest value of \( p H ? \)
A. \( H C l \)
в. ма а Н
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( C H_{3} \) СООН


In Millikan's oil drop experiment, an oil drop of density 8 times of air is held
stationary by applying a field E. The field required to hold another drop of same radius and carrying same charge but density is 22 times the density of air is
\( A \cdot E \)
B . 2E
c. зЕ
D. 4E


Due to hectic and busy schedule, Mr. Angad made his life full of tensions and
anxiety. He started taking sleeping pills to overcome the depression without consulting the doctor. Mr. Deepak, a close friend of Mr. Angad, advised him to stop taking sleeping pills and suggested to change his lifestyle by doing Yoga, meditation and some physical exercise. Mr. Angad followed his friend's advice and after few days he
started feeling better. After reading the above passage, answer the following:
(i) What are the values (at least two)
displayed by Mr. Deepak?
(ii) Why is it not advisable to take
sleeping pills without consulting
doctor?
(iii) What are tanquilizers? Give two examples.


What is the gravitational potential
energy?


Formation of \( S O_{3} \) from \( S O_{2} \) and \( O_{2} \) is a
reaction.


A drop \( (0.05 \mathrm{mL}) \) of \( 12.0 \mathrm{M} \) HCl is
spread over a sheet of thin aluminium foil. Assuming that the acid dissolves
through the foil, the area is \( x \times \)
\( 10^{-1} \mathrm{cm}^{2} \) of the hole produced, then \( x \)
is :
(Density of \( A l=2.70 g c m^{-3} \)
thickness of the foil \( =0.10 \mathrm{mm} \)


If \( y=\sec x+\tan x, \) then \( \frac{d y}{d x}= \)
A. xsecx
B. ysecx
c. \( y \sin x \cos x \)
D. xy


Statement \( 1: \Delta H \) for combustion of
ethane and ethyne are -341.1 and -310.0
kcal respectively.

Statement 2: Ethyne is the better gas
welder.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is
not a correct explanation of statement 1
C. Statement 1 is true, Statement 2 is False.
D. Statement 1 is False, Statement 2 is True.


Assertion
A disc-shaped magnet is deviated above a superconducting material that has been cooled by liquid nitrogen.
Reason

Superconductors repel a magnet.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Consider the following reaction
sequence, \( \boldsymbol{C H}_{3} \boldsymbol{C} \equiv \boldsymbol{C H} \frac{2 \operatorname{mole}}{\boldsymbol{H C l}} \boldsymbol{A} \frac{\boldsymbol{H e a t}}{\boldsymbol{a q . K O H}} \boldsymbol{B} \)
The products \( (A) \) and \( (B) \) are, respectively:
\( \mathbf{A} \cdot(A): C H_{3} C H_{2} C H C l_{2} \) and \( (\mathbf{B}): C H_{3} C H_{2} C H O \)
B . (A): \( C H_{3} C(C l)_{2} C H_{3} \) and
(В): \( C H_{3} C O C H_{3} \)
c. \( (\mathrm{A}): C H_{3} C(C l)_{2} C H_{3} \) and
(В): \( C H_{3} C \equiv C H \)
D・(A): \( C H_{3} C H(C l) C H_{2} C l \) and
(В) \( : C H_{3} C H(O H) C H_{2} C l \)


Equations of a stationary wave and a travelling wave are \( \boldsymbol{y}_{1}= \)
\( \mathbf{1} \sin (\boldsymbol{k} \boldsymbol{x}) \cos (\boldsymbol{\omega} \boldsymbol{t}) \) and \( \boldsymbol{y}_{2}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}- \)
\( k x \). The phase difference between two
points \( x_{1}=\frac{\pi}{3 k} \) and \( x_{2}=\frac{3 \pi}{2 k} \) is \( \phi_{1} \) for
the first wave and \( \phi_{2} \) for the second wave.The ratio \( \frac{\phi_{1}}{\phi_{2}} \) is
A.
B. 5/6
\( c \cdot 3 / 4 \)
D. 6/7


The most abundant metal in the earth
crust is:
A. copper
B. Silver
c. Aluminium
D. silicon


\( M \) is the midpoint of side \( Q R \) of
\( \triangle P Q R . P S \perp Q R \) Prove that: \( P Q^{2}+ \)
\( \boldsymbol{P R}^{2}=\mathbf{2 P M}^{2}+\mathbf{2 Q} \boldsymbol{M}^{2} \)


For any two sets \( A \) and \( B \), show that the
following statements are equivalent.
(i) \( \boldsymbol{A} \subset \boldsymbol{B} \)
(ii) \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \)
(iii) \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{B} \)
(iv) \( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{A} \)


Explain the term copolymerisation and give two examples.


Assertion
\( M g \) get oxidized, when heated in \( C O_{2} \)
atmosphere.
Reason
\( M g \) has strong affinity to oxygen.
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


Leaf base is sheathing in
A. Wheat
B. Maize
c. Grass
D. All of the above


Which of the following are the first to have closed circulatory system?
A. Molluscs
B. Annelids
c. Arthropods
D. Echinoderms


The most common fuel for a fission
reaction in a nuclear reactor is:
A. Uranium 230
B. Uranium 238
c. Californium 238
D. Thorium 234


A concave lens of focal length produces an image equal to \( \frac{1}{n} \) of the size of the object, the distance of the object from the lens is:
A \( \cdot(n-1) f \)
в. \( (n+1) f \)
c. \( \left(\frac{n-1}{n}\right) f \)
D. \( \left(\frac{n+1}{n}\right) f \)


The vapour density of oxygen is (Nearest integer)


A curve passes through the point \( (2 a, a) \) and is such that sum of subtangent and abscissa is equal to a. Its equation is
A \( \cdot(x-a) y^{2}=a^{3} \)
в. \( (x-a)^{2} y=a^{3} \)
c. \( (x-a) y=a^{2} \)
D. \( (x+a) y=a^{2} \)


Ammonium hydrogen sulphide dissociates as follows
\( N H_{4} H S(s) \rightleftharpoons N H_{3}(g)+H_{2} S(g) \)
If solid \( N H_{4} H S \) is placed in an evacuated flask at certain temperature it will dissociate until the total pressure
is 600 torr.
a) Calculate the value of equillibrium constant for the dissociation reaction
b) Addional \( N H_{3} \) is introduced into the equillibrium mixture without changing the temperature until partial pressure
of \( N H_{3} \) is 750 torr, what is the partial
pressure of \( \boldsymbol{H}_{2} \boldsymbol{S} \) under these conditions? What is the total pressure in the flask?


Find the middle terms of the equation of
\( \left(x^{4}-\frac{1}{x^{3}}\right)^{11} \)
\( \mathbf{A} \cdot-462 x^{9}, 462 x^{2} \)
B . \( -462 x^{8}, 462 x^{4} \)
c. \( 462 x^{7},-462 x^{3} \)
D. None of these


Oxidation state of Iron in Hemoglobin is:
\( A \cdot+2 \)
\( B \cdot+4 \)
\( c \cdot+6 \)
D.


If \( T \) be the period of revolution of \( a \)
planet revolving around sun in an orbit of mean radius \( R \), then identify the correct graph from the following.
This question has multiple correct options
\( A \)
B.
\( c \)
D. None of these


The bond order depends on the number of electrons in the bonding and antibonding orbitals. Which of the following statements is/are correct about bond order?
A. Bond order cannot have a negative value.
B. It always has an integral value
c. It is a nonzero quantity.
D. It can assume any value-positive, integral or fractional, including zero.


A potentiometer wire \( 10 \mathrm{m} \) long has a resistance of \( 40 \Omega . \) It is connected in
series with a resistance box and a \( 2 \mathrm{V} \)
storage cell. If the potential gradient along the wire is \( 0.1 \mathrm{mV} / \mathrm{cm}, \) the resistance in the box is
\( A \cdot 760 \Omega \)
B. 260\Omega
c. \( 1060 \Omega \)
D. \( 960 \Omega \)


State whether the following statements
are true or false.

Digestive enzymes are secreted in an inactive form in the alimentary canal
A. True
B. False


State whether the following statement is true or false.

If \( P \) divides \( O A \) internally in the ratio
\( \lambda_{1}: \lambda_{2} \) and \( Q \) divides \( O A \) externally in
the ratio \( \lambda_{1}: \lambda_{2} \), then \( O A \) is the
harmonic mean of \( O P \) and \( O Q \)
A. True
B. False


Find the distance between (8,-8) from
the origin.


The family of elements which consists of atoms that have valence electrons in
a \( d \) subshell is:
A. alkali metals
B. alkaline earth metals
c. noble gases
D. halogens
E. transition metals


Diols (I-IV) which react with \( C r O_{3} \) in
aqueous \( H_{2} S O_{4} \) and yield products that readily under go dercarboxylation on heating, are:
\( (\mathrm{I}) \)
A. I and \( J \)
B. II and III
c. \( I I \) and \( I V \)
D. \( I \) and \( I V \)


Which of the following nucleus is fissionable by slow neutrons:
\( \mathbf{A} \cdot-92 U^{238} \)
B . \( -93 N p^{23} \)
\( \mathbf{c} \cdot-92 U^{235} \)
D. \( _{2} I l e^{4} \)


A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved
surface is \( 30 c m \) and the refractive
index of the lens material is \( 1.5, \) then
the focal length of the lens (in cm) is


To construct a \( \triangle A B C \) in which \( B C=10 \)
\( \mathrm{cm} \) and \( \mathrm{B}=60^{\circ} \) and \( \mathrm{AB}+\mathrm{AC}=14 \mathrm{cm}, \) then
the length of BD used for construction
A. \( 7 \mathrm{cm} \)
B. \( 14 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


I wo plane mırrors or lengtn \( \boldsymbol{L} \) are
separated by distance \( L \) and a man \( M_{2} \)
is standing at distance \( L \) from the
connecting line of mirrors as shown in
figure. A man \( M_{1} \) is walking in a
straight line at distance \( 2 L \) parallel to
mirrors at speed \( u, \) then \( \operatorname{man} M_{2} \) at 0
will be able to see image of \( M_{1} \) for time
\( A \cdot \frac{4 L}{u} \)
B. \( \frac{3 L}{u} \)
\( c \cdot \frac{6 L}{u} \)
D. \( \frac{9 L}{_{n}} \)


In the given figure, the acceleration of
block A with respect to ground is (Neglect friction)
\( A \cdot \underline{g} \)
3
в. \( \frac{g}{3} \sqrt{10} \)
c. \( \frac{2 g}{3} \)
\( D \)


Three voltmeters, all having different resistances, are joined as shown.When some potential difference is applied \( \operatorname{across} A \) and \( B, \) their readings are
\( \boldsymbol{V}_{1}, \boldsymbol{V}_{2}, \boldsymbol{V}_{3} \)
A \( \cdot V_{1}=V_{2} \)
B. \( V_{1} \neq V_{2} \)
c. \( V_{1}+V_{2}=V_{3} \)
D. \( V_{1}+V_{2}>V_{3} \)


There were three circular tracks made
in a park having the same middle point but their radii was different. These
tracks will be called
A. Not similar
B. Similar
c. congruent
D. All of the above


The collision in which the relative
velocity is zero after collision is
A . perfectly elastic
B. perfectly inelastic
C . partially elastic
D. sometimes elastic and sometimes inelastic


The creation of voltage or electric current in a material upon exposure to light is termed as
A. photo-ionic effect
B. thermi-ionic effect
c. photo-voltaic effect
D. None of these.


Which statement below is
incorrect regarding balanced
equations?
A. \( C+O_{2} \rightarrow C O_{2} \) is balanced and is a synthesis reaction
B. \( C a C O_{3} \rightarrow C a O+C O_{2} \) is balanced and is a
decomposition reaction
C \( . N a+C l_{2} \rightarrow N a C l \) is not balanced but demonstrates a
synthesis reaction
D. \( K I+P b\left(N O_{3}\right)_{2} \rightarrow P b I_{2}+K N O_{3} \) is balanced and is a
single replacement reaction
E \( \cdot 2 H_{2} O \rightarrow 2 H_{2}+O_{2} \) is balanced and demonstrates a
redox reaction


Show that the given differential equation is homogeneous and solve
them
\( \frac{d y}{d x}=\frac{x^{2}-2 y^{2}+x y}{x^{2}} \)


Select the incorrect option
A. Luminous flux and radiant flux have same dimensions
B. Luminous flux and luminous intensity have same dimensions
C. Radiant flux and power have same dimension
D. Relative luminosity is a dimensionless quantity


Fill in the blanks:
the diameter of a circle passes through


can cause sea levels to rise
dramatically.
A. Global warming
B. Rock slide
c. water pollution
D. None of the above


Ratio of the size of the image to the size
of the object is known as:
A. Focal plane
B. Transformation ratio
c. Efficiency
D. None of these


When 0.1 mole of solid NaOH is added
in \( 1 \mathrm{L} \) of \( 0.1 \mathrm{M} N H_{3} \) (aq) then which
statement is going to be wrong?
\( \left(\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{5}}, \log \mathbf{2}=\mathbf{0 . 3}\right) \)
A. degree of dissociation of \( N H_{3} \) approaches to zero
B. Change in pH would be 1.85
c. concentration of \( \left[N a^{+}\right]=0.1 M,\left[N H_{3}\right],= \) \( 0.1 M,\left[O H^{-}\right]=0.2 M \)
D. on addition of \( O H^{-}, K_{b} \) of \( N H_{3} \) does not changes


Complete the given statement. The
voltage across each light bulb in a
parallel circuit:
A. is equal to the voltage of the battery
B. is determined by the resistance of the bulb
C. is determined by the current flowing through the bulb
D. is equal to the sum of the voltages lost in each bulb
E. is equal to the total current divided by the resistance of the bulb


For a given length of a pendulum, the time period is maximum
A. on the surface of the earth
B. on the surface of the moon
c. on the centre of the earth
D. none of these


If the lines \( \boldsymbol{p}_{1} \boldsymbol{x}+\boldsymbol{q}_{1} \boldsymbol{y}=\mathbf{1}, \boldsymbol{p}_{2} \boldsymbol{x}+\boldsymbol{q}_{2} \boldsymbol{y}= \)
1 and \( p_{3} x+q_{3} y=1 \) be concurrent
show that the points \( \left(p_{1}, q_{1}\right),\left(p_{2}, q_{2}\right) \)
and \( \left(p_{3}, q_{3}\right) \) are collinear
A. vertices of right angle triangle
B. vertices of an equilateral triangle
c. vertices of an isosceles triangle
D. Collinear


Select the correct order of ions with
respect to their ionic radii.
A. \( Y^{3+}<L u^{3+}<E u^{3+}<L a^{3+} \)
B . \( L u^{3+}<Y^{3+}<E u^{3+}<L a^{3+} \)
c. \( L u^{3+}<E u^{3+}<L a^{3+}<Y^{3+} \)
D. \( L a^{3+}<E u^{3+}<L u^{3+}<Y^{3+} \)


From the following data, the activation
energy for the reaction \( (\text { cal } / \text { mol }) \) is:
\[
\boldsymbol{H}_{2}+\boldsymbol{I}_{2} \longrightarrow \mathbf{2} \boldsymbol{H} \boldsymbol{I}
\]
\( T(K) \quad 1 / T\left(K^{-1}\right) \quad \log K \) \( \begin{array}{lll}769 & 1.3 \times 10^{-3} & 2.9 \\ 667 & 1.5 \times 10^{-3} & 1.1\end{array} \)
A \( \cdot 4 \times 10^{4} \)
B. \( 2 \times 10^{4} \)
\( c \cdot 8 \times 10^{4} \)
D. \( 3 \times 10^{4} \)


\( K O_{2}( \) potassium superoxide ) is used in
oxygen cylinders in space and submarines because, it :

This question has multiple correct options
A. decomposes to give oxygen
B. eliminates moisture
\( c . \) absorbs \( C O_{2} \)
D. produces ozone


If the tangent to the curve \( y=x \log x \) at
\( (c, f(x)) \) is parallel to the line-segment
joining \( \boldsymbol{A}(\mathbf{1}, \boldsymbol{0}) \) and \( \boldsymbol{B}(\boldsymbol{e}, \boldsymbol{e}), \) then \( \mathbf{c}=\ldots \)
A \( \cdot \frac{e-1}{e} \)
B. \( \log \frac{e-1}{e} \)
c. \( \frac{1}{e^{1-e}} \)
D. \( \frac{1}{e^{e-1}} \)


Choose the correct answer among the alternatives given:
Consider the following statements each
with one or two blanks.
(A) Lippes loop is a (i). IUD while multiload 375 is a \( (\mathrm{ij}) \) IUD.
(B) Surgical methods of contraception are also called as (iii), methods.
(C) High MMR and IMR play a significant role in \( ( \) iv ) human
population. Which one of the following options,
gives the correct fill ups for the
respective blank numbers from
(i) to
(iv) in the above statements?
A. (i) copper releasing,
(ii) non-medicated (iv) decreasing
B. (iii) barrier, (iv) increasing
c. (i) non-medicated,
(ii) copper releasing, (iv) decreasing
D. (i) copper releasing, (ii) non-medicated, (iii) sterilisation


Molarity and molality of a solution of a liquid (mol wt=50) in aqueous solution
is 9 and 10 respectively. What is the density of solution?
\( \mathbf{A} \cdot 1 g / c c \)
в. \( 0.95 g / c c \)
c. \( 1.05 g / c c \)
D. \( 1.35 g / c c \)


The thermal decomposition of a
molecule shows first order kinetics. The
molecule decomposes \( 50 \% \) in 120 min. How much time it will take to
decompose \( 90 \% ? \)
A. 300 min
B . 360 min
c. 398.8 min
D. 400 min


Which is true about \( N_{2} O_{5} ? \)
This question has multiple correct options
A. It is anhydride of \( H N O_{3} \)
B. In solid state it exists as \( \left[N O_{2}^{+}\right]\left[N O_{3}^{-}\right] \)
C. It is structurally similar at \( P_{2} O_{5} \)
D. It can be prepared by heating \( H N O_{3} \) over \( P_{2} O_{5} \)


Braille writer slate and stylus is a type
of resource for blind people that is called tactual aid
A. True
B. False


Assertion
\( F_{1} \) particles are present in the inner
mitochondrial membrane.
Reason
An electrochemial proton gradient formed on the inner mitochondrial
membrane, forms ATP.
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


From the following data, calculate the standard enthalpy of formation of Propane \( \Delta_{f} H^{\ominus} C H_{4}=-17 K c a l m o l^{-1} \)
\( \Delta_{f} \boldsymbol{H}^{\ominus} \boldsymbol{C}_{2} \boldsymbol{H}_{6}=-\mathbf{2} 4 \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o l}^{-1} \)
\( \boldsymbol{B} \boldsymbol{E}(\boldsymbol{C}-\boldsymbol{H})=\boldsymbol{9} \boldsymbol{9} \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o l}^{-1}(\boldsymbol{C}- \)
\( C)=84 K c a l m o l^{-1} \)
A \( \cdot \Delta_{f} H=-31 \) Kcalmol \( ^{-1} \)
B. \( \Delta_{f} H=+31 K \) calmol \( ^{-1} \)
\( \mathbf{c} \cdot \Delta_{f} H=0 K c a l m o l^{-1} \)
D. None of these


The two monomers used in the
preparation of dextron are:
A. 3 -hydroxy butanoic acid and 3-hydroxy pentanoic acid.
B. \( \epsilon \) amino caproic acid and glycine.
C . isobutylene and isoprene.
D. lactic acid and glycolic acid.


How many atoms are in one mole of
water?
B. \( 3.476 \times 10^{-2} \)
c. \( 1.717 \times 10^{-2} \)
D. \( 1.204 \times 10^{2} \)
E . \( 2.414 \times 10^{-1} \)


If \( A B=0, \) then for the matrices \( A= \) \( \left[\begin{array}{cc}\cos ^{2} \theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & \sin ^{2} \theta\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}\cos ^{2} \phi & \cos \phi \sin \phi \\ \cos \phi \sin \phi & \sin ^{2} \phi\end{array}\right], \theta-\phi \) is
A \( \cdot \) an odd muliple of \( \frac{\pi}{2} \)
B. an odd multiple of \( \pi \)
C . an even multiple of \( \frac{\pi}{2} \)
D.


Evaluate the definite integral \( \int_{0}^{\pi}\left(\sin ^{2} \frac{x}{2}-\cos ^{2} \frac{x}{2}\right) d x \)


A narrow waistline, wide hip and oily
skin are the secondary signs of puberty in
A. Males
B. Females
c. Both A and B
D. Not gender-based


topp
Q Type your question
the same wire as shown in figure.
\( A E F D \) is a square of side \( 1 m \) and
\( \boldsymbol{E B}=\boldsymbol{F C}=\mathbf{0 . 5 m .} \) The entire circuit is
placed in a steadily increasing, uniform magnetic field directed into the plane of paper and normal to it. The rate of
change of the magnetic field is \( 1 T s^{-1} \)
The resistance per unit length of the
wire is \( 1 \Omega m^{-1} \). Find the magnitude ano
direction of the current in the segment \( A E, B E \) and \( E F \)
\( ^{\mathbf{A}} \cdot \frac{6}{22} A, E \) to \( A ; \frac{7}{22} A, B \) to \( E ; \frac{1}{22} A, F \) to \( E \)
B. \( \frac{1}{22} A, \) E to \( A ; \frac{6}{22} A, E \) to \( B ; \frac{7}{22} A, F \) to \( E \)
c. \( \frac{7}{22} A, \) E to \( A ; \frac{6}{22} A, B \) to \( E ; \frac{1}{22} A, F \) to \( E \)


The equations of a line are given by \( \frac{\mathbf{4}-\boldsymbol{x}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{3}}{\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{6}} . \) Write the
direction cosines of a line parallel to this line.


What is polarization of light?


Starch is used to test even the small
amounts of
A. sucrose in aqueous solution
B. glucose in aqueous solution
C . \( I_{2} \) in aqueous solution
D. maltose in aqueous solution


Beilstein test is used for the detection
of which element in organic compound?
A. \( N \)
в. \( C l \)
\( c . N a \)
D. \( P \)


Two slits are separated by a distance of \( 0.5 m m \) and illuminated with light of wavelength \( \lambda=6000 A \). If the screen is
placed at 2.5 m from the slits. The
distance of the third bright fringe from the centre will be
A. \( 1.5 \mathrm{mm} \)
B. \( 3 m m \)
\( c .6 m m \)
D. \( 9 \mathrm{mm} \)


Assertion
\( P C l_{4} \) exists but \( N C l_{5} \) does not exist.
Reason
\( d- \) orbital in \( P \) -atom takes part in
chemical bonding, this lacks in \( N- \)
atom.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The angular momentum of a particle rotating with an angular velocity \( \omega \) distant \( r \) from a given origin is I. If the origin is shifted by \( 2 r, \) then the new angular momentum of the particle with same angular velocity will be
A . 2
в. 9
\( c \cdot 4 \)
\( D \cdot 3 \)


Assertion
In imbricate aestivation, out of five
petals, one is completely internal, one is completely external and in each of the
remaining three petals, one margin is
internal and the other is external.
Reason

Ascending imbricate aestivation is found in Cassia and Gulmohur.
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


Principal quantum number gives the
of an electron and its distance
from the nucleus.
A. angular momentum
B. energy
c. velocity
D. centrifugal force


When a satellite has an elliptical orbit, the plane of the orbit
A. sometimes passes through the centre of earth
B. does not pass through the centre of earth
c. passes through the centre of earth always
D. none of the above


\( \operatorname{Let} f(x)=\left\{\begin{array}{cl}\min \left\{x, x^{2}\right\}, & x \geq 0 \\ \max \left\{2 x, x^{2}-1\right\}, & x<0\end{array}\right. \)
Then which of the following is not true?
A. \( f(x) \) is continuous at \( x=0 \)
B. \( f(x) \) is not differentiable at \( x=1 \)
\( \mathrm{c} . f(x) \) is not differentiable at exactly three points
D. none of these


With boiling water or steam, diethylether results in the formation of:
A \( \cdot\left(C_{2} H_{5}\right)_{2} S O_{4} \)
в. \( C_{2} H_{5} O H \)
c. \( C H_{2}=C H_{2} \)
D. \( C_{2} H_{5} O H+C_{2} H_{5} S O_{4} \)


An elements forms two oxides
containing respectively 53.33 and 36.36 percent of oxygen. These figures illustrate the law of :
A. Conservation of mass
B. constant proportions
c. Reciprocal proportions
D. Multiple proportions


Express in standard form \( (x-a)(x-b) \)


Assertion
When a cell is placed in hypertonic solution, it shrinks.
Reason
Reverse osmosis is used for
desalination of water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


One mole of stachyose on hydrolysis
yields:
A. 1 mole of glucose +1 mole of fructose +2 mole of galactose
B. 2 mole of glucose +1 mole of fructose +1 mole of galactose
C. 1 mole of glucose +2 mole of fructose +1 mole of galactose
D. 2 mole of glucose +2 mole of fructose


According to Rutherford, the electron revolves around the nucleus in definite
orbits but :
A. Rutherford did not specify the number of orbits and the number of electrons in each orbit
B. Rutherford did specify the number of orbits and the number of electrons in each orbit
C. Rutherford did not specify the number of orbits and the number of protons in each orbit
D. Rutherford did not specify the number of orbits and the number of neutrons in each orbit


A metal nitrate gives black ppt. with \( \mathrm{Kl} \) and on adding excess of Kl it gives orange colour. It is:
A \( \cdot \mathrm{Hg}^{+} \)
B. Bit \( ^{3} \)
\( c \cdot \operatorname{sn}^{+} \)
D. \( P b^{+2} \)


Two unknown resistrance \( X \) and \( Y \) are
connected to left and right gaps of a meter bridge and the balancing point is obtained at \( 80 \mathrm{cm} \) from left. When a \( 10 \Omega \) resistance is connected in paralle to \( x \) the balance point is \( 50 \mathrm{cm} \) from left. The values of \( X \) and \( Y \) respectively are
\( A \cdot 40 \Omega, 9 \Omega \)
B. 30\Omega ,7.5\Omega
c. \( 20 \Omega, 6 \Omega \)
D. \( 10 \Omega, 3 \Omega \)


The \( \alpha \) amino acid which contains the
aromatic side chain is:
A. proline
B. tyrosine
c. valine
D. serine


a) Write the equations for the steps in
\( \boldsymbol{S}_{N} 1 \) mechanism of the conversion of teri-Butyl bromide into tert-Butyl alcohol
b) Explain Fitting reaction.
c) Name the reagent used in the dehydrohalogenation of haloalkanes.


Among the give the number of aromatic compound(s) is:


A solid rectangular block of mass \( 200 k g \) has the dimensions \( l=2 m, b= \)
\( 1 m, h=0.5 m . \) It lies on a horizontal
floor on sides \( l \) and \( b \). The minimum
work needed to turn it so that it lies
on the sides \( b \) and \( h \) is:
A . zero
B. \( 1500 J \)
c. \( 3000 J \)
D. \( 2000 J \)


Match items given in A suitably with
items given \( B \) and \( C \)
\begin{tabular}{|c|c|c|}
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{C} \) \\
\hline Microphone & Sonar & Electrical energy gets convented to sund energy \\
\hline Ultra sonic sound & Permanent magnet & Sound energy gets converted to electrical energy Conventiennal source of energy \\
\hline CNG & Butane & Non-conventional source of energy \\
\hline
\end{tabular}


A object starts from rest at \( t=0 \) and
accelerates at a rate given by \( a=6 t \)
What is its velocity?
A \( .6 t \)
B. \( 3 t^{2} \)
\( c \cdot 6 t^{2} \)
D. 0


\( \boldsymbol{K}_{a_{1}}, \boldsymbol{K}_{a_{2}} \) and \( \boldsymbol{K}_{a_{3}} \) values of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are
\( 10^{-3}, 10^{-6} \) and \( 10^{-12} \) respectively. If
\( \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{1} \mathbf{0}^{-14}, \) then:
What is \( K_{b} \) is \( H P O_{4}^{-} ? \)


Calculate the distance from the surface
of the earth at which the acceleration
due to gravity is the same below and
above the surface of the earth.


A capacitor of capacitance \( 15 n F \)
having dielectric slab of \( \varepsilon r=2.5 \)
dielectric strength \( 30 \mathrm{MV} / \mathrm{m} \) and potential difference \( =30 \) volt. Calculate
the area of plate.
В. \( 4.2 \times 10^{-4} \mathrm{m}^{2} \)
c. \( 8.0 \times 10^{-4} \mathrm{m}^{2} \)
D. \( 9.85 \times 10^{-4} m^{2} \)


Evaluate: \( \lim _{x \rightarrow 3}\left[\frac{1}{x-3}+\frac{9 x}{27-x^{3}}\right] \)


Discuss basic characteristics of
Gram +ve and Gram -ve bacteria.


Solve:
\( (x-y)^{2} \frac{d y}{d x}=a^{2} \)


Which of the following is/are optoelectronic devices?
A. photodiodes
B. solar cells
c. light emitting diodes
D. all of the above


Study the figure which shows the effect
of light on the rate of photosynthesis
based on the graph, answer the following question:
What does \( C \) represent on the curve?
A. It represents that at higher light intensity there is no further increase in photosynthesis and other factors become limiting.
B. It represents that at lower light intensity there is no further increase in photosynthesis and other factors become limiting.
c. Maximum light intensity which can affect the rate of photosynthesis
D. None of the above


If \( f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x \) and
\( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) then \( \boldsymbol{f}(\mathbf{1})= \)
A \( \cdot 1-\frac{\pi}{4} \)
B. \( \frac{\pi}{4}-1 \)
c. \( \tan 1-\frac{\pi}{4} \)
D. None of these


If \( z_{1}=a+i b \) and \( z_{2}=c+i d \) are
complex numbers such that \( \left|z_{1}\right|= \)
\( \left|z_{2}\right|=1 \) and \( \operatorname{Re}\left(z_{1} \bar{z}_{2}\right)=0, \) then the pair
of complex numbers \( \omega_{1}=a+i c \) and
\( \omega_{2}=b+i d \) satisfies
This question has multiple correct options
\( \mathbf{A} \cdot\left|\omega_{1}\right|=1 \)
В \( \cdot\left|\omega_{2}\right|=1 \)
c. \( \operatorname{Re}\left(\omega_{1} \overline{\omega_{2}}\right)=0 \)
D. \( \omega_{1} \bar{\omega}^{2}=0 \)


Solubility of \( H g_{2} C l_{2} \) in water is \( S \)
moln4 litre \( ^{-1} \). The \( K_{s p} \) of \( H g_{2} C l_{2} \) is
A \( \cdot 16 S^{4} \)
в. \( 16 S^{3} \)
c. \( 4 S^{3} \)
D. \( 4 S^{2} \)


The differential equation whose solution is \( y^{2}=3 a y-x^{3} \) is
A \( \cdot\left(x^{3}-y^{2}\right) \frac{d y}{d x}=3 x^{2} y \)
B. \( \left(x^{3}-y^{2}\right) \frac{d y}{d x}=3 x y \)
c. \( \left(x^{3}-y\right) \frac{d y}{d x}=3 x y^{2} \)
D. \( \left(y^{2}-x^{3}\right) \frac{d y}{d x}=3 x y \)


Let \( z \) be a complex number such that \( \left|\frac{\boldsymbol{z}-\boldsymbol{i}}{\boldsymbol{z}+\mathbf{2} \boldsymbol{i}}\right|=\mathbf{1} \) and \( |\boldsymbol{z}|=\frac{\mathbf{5}}{\mathbf{2}} . \) Then the
value of \( |z+3 i| \) is?
\( A \cdot \frac{7}{2} \)
в. \( \frac{15}{4} \)
\( c \cdot 2 \sqrt{3} \)
D. \( \sqrt{10} \)


Is it safe for an electrician to carry out
electrical repairs outdoors during heavy downpour ? Explain


Assertion: Chemical messengers are chemicals that enable communication
of message between two neurons or
between neurons and muscles.
Reason : Chemicals enter the cell
through receptor.
A. Both Assertion and Reason are incorrect.
B. Both Assertion and Reason are correct
c. Both Assertion and Reason are correct and Reason is the incorrect explanation for Assertion.
D. Assertion is correct but Reason is incorrect
E. non of these
\( F \). A and \( B \)


Find the value of \( ^{10} \boldsymbol{C}_{5}+\mathbf{2} .\left(^{10} \boldsymbol{C}_{4}\right)+^{10} \boldsymbol{C}_{3} \)


Jelly Fish Aurelia occurs abundantly in
A. Mumbai coast
B. Tamil Nadu Coast
c. Bay of Bengal
D. All of the above


The shortest distance of \( (a, b, c) \) from \( x \) axis is
A \( \cdot \sqrt{a^{2}+b^{2}} \)
B. \( \sqrt{b^{2}+\mathrm{c}^{2}} \)
c. \( \sqrt{c^{2}+a^{2}} \)
D. \( \sqrt{a^{2}+b^{2}+c^{2}} \)


Which of the following is an electrophile?
A \( \cdot H_{2} O \)
в. \( S O_{3} \)
c. \( N H_{3} \)
D. \( R O R \)


Match the following


Which of the following is a type of soap?
A. Hard soap
B. Soft soap
c. Both \( A \) and \( B \)
D. None of above


A bag contains 4 white, 7 black and 5
green balls. What is the probability of picking white?


A plane banks its wings \( 30^{\circ} \) relative to
the horizontal to enter into a circular
turn. The circular path has a radius of
\( 1500 m \)
Which of these values best represents the velocity of the plane if the lift force exerted on the wings is equal to twice the weight of the plane?
A. \( 120 m / s \)
в. \( 140 \mathrm{m} / \mathrm{s} \)
c. \( 160 \mathrm{m} / \mathrm{s} \)
D. 240m/s
E. \( 320 m / s \)


If the pressure of a gas contained in a closed vessel increases by \( \times \% \) when heated by \( 1^{0} C \), its initial temperature is
A \( \cdot \frac{100}{x} \) Kelvin
B. \( \frac{100}{x} \) Celsius
C. \( \frac{x+100}{x} \) Kelvin
D. \( \frac{100-x}{x} \) Celsius


The process responsible for the movement of water from roots to all
other parts of plants is
A. Evaporation of water from the leaves
B. Capillary action
c. Hydrophyllic compounds
D. Active transport.
E. Both A and B.


For the reactions, \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}, \boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \boldsymbol{C} \rightleftharpoons \)
D, equilibrium constants are
\( \boldsymbol{K}_{1}, \boldsymbol{K}_{2}, \boldsymbol{K}_{3} \) respectively
What is the value of the equilibrium constant for \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} ? \)
\( \mathbf{A} \cdot K_{1}, K_{2}, K_{3} \)
в. \( K_{1} \times K_{2} \times K_{3} \)
c. \( K_{1} K_{2} / 3 \)
D. None of these


A particle of mass \( \mathrm{M} \) is moving in a
circle with constant speed \( v, \) between two position at the ends of a diameter, the particle's
A. Momentum changes by mv
B. kinetic energy changes by1/2mv \( ^{2} \)
c. Momentum changes by 2 mv
D. Kinetic energy changes by \( m v^{2} \)


Sulphur is extracted by Frasch process. If true enter 1 else 0


In humans, which structure receives
blood from the lungs?
A. Aorta
B. Pulmonary artery
c. Pulmonary vein
D. Renal vein
E. Femoral artery


Which of the following complexes is not expected to exhibit isomerism?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \)
B. \( \left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{2} C l_{2}\right] \)
D. \( \left[N i(e n)_{3}\right]^{2+} \)


Serum differs from blood in lacking
A . Globulins
B. Albumins
c. clotting factors
D. Antibodies


If the distance between Arun and Ajay becomes 10 times of initial value, then
the gravitational force between them becomes \( _{-1-} \) times of the initial
value.
A. 100
B. 10
c. \( \frac{1}{100} \)
D. \( \frac{1}{10} \)


A gas obeys the relation \( V \propto \frac{1}{T^{2}} . \) The \( \frac{C_{p}}{C_{v}} \) value for the gas is
A . 1.50
B. 1.30
c. 1.70
D. 2


Write any two Algebraic expressions with the same degree.
A. \( x y+y z, 2 x+3 y+5 \)
B. \( x y+y z, 2 x^{2}+3 x+5 \)
c. \( x y+y z, 2 x^{3}+3 x+5 \)
D. none


Which of the following statement(s)
is/are correct?
A. Conduction current obeys Ohm's law whereas displacement current does not.
B. Conduction current is the actual current whereas displacement current is the apparent
current produced by time varying electric field.
C . Conduction current density is represented by \( \overrightarrow{J_{c}}=\sigma \vec{E} \) whereas displacement current
density is given by \( \overrightarrow{J_{d}}=\frac{\overrightarrow{\delta E}}{\delta t} ; \sigma= \) conductivity of the element, \( \vec{E}= \) electric field
D. All of the above


The number of hydrogen bonds formed
by a molecule each of \( \mathrm{H}_{2} \mathrm{O}, \mathrm{HF} \) and \( \mathrm{NH}_{3} \)
respectively are :
\( \mathbf{A} \cdot 2,2,3 \)
B. 4,2,3
c. 2,1,3
D. 4,4,3


Which of the following carbohydrates develop blue colour on treatment with iodine solution?
A. Glucose
B. Sorbose
c. starch
D. Fructose


What is formed when calcium carbide
reacts with heavy water?
A. \( C_{2} D_{2} \)
в. \( C a D_{2} \)
\( \mathbf{c} \cdot C a_{2} D_{2} O \)
D. \( C D_{2} \)


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( a_{i j}=\frac{(2 i+j)^{2}}{2} \)


Polygons are figures.
A. many sided
B. one sided
c. has no sides
D. two sides


The coercivity of a small magnet where the ferromagnet gets demagnetised is
\( 3 \times 10^{3} A m^{-1} . \) The current required to
be passed in a solenoid of length \( 10 \mathrm{cm} \)
and number of turns \( 100, \) so that the magnet gets demagnetised when inside the solenoid, is:
A . \( 6 A \)
в. 30 тА
\( c .60 m A \)
D. \( 3 A \)


A particle starts at the origin and moves along the \( x \) -axis in such a way
that its velocity at the point \( (x, 0) \) is
given by the formula \( \frac{d x}{d t}=\cos ^{2} \pi x \)
Then the particle never reaches the point on:
A \( \cdot x=\frac{1}{4} \)
в. \( _{x}=\frac{3}{4} \)
c. \( _{x}=\frac{1}{2} \)
D. \( x=1 \)


\( 25 g \) hydrocarbon of burning with
excess of air produces \( 88 g C O_{2} \) and \( 9 g \)
water. Mass of \( C \) and \( H \) in the
hydrocarbon is:
A. \( C=24 g, H=1 g \)
в. \( C=20 g, H=5 g \)
c. \( C=18 g, H=7 g \)
D. \( C=19 g, H=6 g \)


Find the cube root of 15625 by prime factorization method.


Determine the maximum number of
common tangents that can be drawn for each pair of circles shown.


Other than yeast, which of the following organism reproduces by budding?
A. Algae
B. Fern
c. Amoeba
D. Hydra


An equation of the tangent to the circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\mathbf{4} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}+\boldsymbol{4}=\mathbf{0} \) which
makes equal intercepts on the coordinate axes, is given by This question has multiple correct options
A \( . x+y=2 \sqrt{2} \)
В. \( x-y=2 \sqrt{2} \)
c. \( x+y+2 \sqrt{2}=0 \)
D. \( x-y+2 \sqrt{2}=0 \)


In Doberenier triads, the atomic weights of the elements in a triad are in
increasing order.
A. True
B. False


If functions \( \boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{g}(\boldsymbol{x}) \) are defined
on \( R \rightarrow R \) such that
\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x}) &=\boldsymbol{x}+\boldsymbol{3}, \boldsymbol{x} \in \text { rational } \\
&=\mathbf{4} \boldsymbol{x}, \boldsymbol{x} \in \text { irrational } \\
\boldsymbol{g}(\boldsymbol{x}) &=\boldsymbol{x}+\sqrt{\mathbf{5}}, \mathbf{x} \in \text { irrational } \\
&=-\boldsymbol{x}, \boldsymbol{x} \in \text { rational }
\end{aligned}
\]
then \( (\boldsymbol{f}-\boldsymbol{g})(\boldsymbol{x}) \) is
A. one-one \& onto
B. neither one-one nor onto
c. one-one but not onto
D. onto but not one-one


We are able to see objects because
A. they absorb light
B. they reflect light
C. total internal reflection takes place in them
D. all the light is refracted through them


Which of the following explains the
reason why atomic radii decrease
across a period?
A. As you move across the period, the number of protons increases, which increases the nuclear charge. The number of electrons remains the same creating a larger Coulombic attraction and decreasing the radii
B. As you move across the period, the number of protons and electrons increases. The increased Coulombic attraction decreases the overall size of the atom.
C. As you move across the period, the number of protons remains constant while the number of electrons
increases. The decreased Coulombic attraction
decreases the overall size of the atom.
D. The atomic radii do not decrease across a period. It actually increases, duh!


When a metal plate is introduced
between the two plates of a charged capacitor and insulated from them,
then
This question has multiple correct options
A. the metal plate divides the capacitor into two capacitors connected in parallel to each other
B. the metal plate divides the capacitor into two capacitors connected in series with each other
C. the metal plate is equivalent to a dielectric of zero dielectric constant
D. the metal plate is equivalent to a dielectric of infinite dielectric constant


Hyperventilation or hyperpnoea causes
A. Increased carbon dioxide concentration of blood
B. Decreased blood carbon dioxide concentration
C. Temporary stoppage of respiration
D. Both B and C


Read the following statements and answer whether the given statement is true or false.

The Lenz's law is consistent with the law
of conservation of energy.
A. True
B. False


Assertion
The first ionization energy of Be is
greater than that B.
Reason
2p orbital is lower in energy than 2 s.
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


Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and \( (0, \)
-1,0)
This question has multiple correct options
A. The potential at the origin is zero.
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero.
D. The field at all points on the z-axis, other than the origin, acts along the z-axis


If \( 0 \leq x \leq \pi \) and \( 81^{\sin ^{2} x}+81^{\cos ^{2} x}=30 \)
then \( x \) is equal to
This question has multiple correct options
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \frac{5 \pi}{6} \)
D. \( \frac{2 \pi}{3} \)


Complete the following diagram in Fig. of a transformer and name the parts
labelled \( A \) and \( B \). Name the part you
have drawn to complete the diagram
What is the material of this part ? Is
this transformer a step-up or step-down
? Give reason.


The resistance of a metallic conductor
increases with temperature due to:
A. change in carrier density
B. change in dimension of the conductor
C. increase in the number of collisions among the carriers
D. increase in the rate of collisions between the carriers and the vibrating atoms of the conductor.


When the frequency of the voltage applied to a series RC circuit is increased, the phase angle
A . increases
B. decreases
c. remains the same
D. becomes erratic


\( y=\frac{1}{\sqrt{(4+3 \cos x)}} \) Is the function one-
one ? Explain


Very short answer type:
What is a bicollateral vascular bundle?


How many atoms of \( B F_{3} \) lie in the same
plane?


Two long straight wires are set parallel
to each other at separation \( r \) and each
carries a current \( i \) in the same
direction. The strength of the magnetic field at any point midway between the two wires is
A \( \cdot \frac{\mu_{0} i}{\pi r} \)
в. \( \frac{2 \mu_{0}}{\pi r} \)
c. \( \frac{\mu_{0} i}{2 \pi r} \)
D. zero


Which labelled structure is responsible
for increasing body temperature as a
result of infection?
\( A \cdot w \)
B. \( x \)
\( c . \mathbf{Y} \)
\( D \)


Why do veins have thin walls as
compared to arteries?
A. Veins collect the blood from different organs and bring it back to the heart
B. The blood in the vein is in low pressure than artery
C. The blood in the vein is in high pressure than artery
D. Both A and B


Any subset of sample space is called
A. event
B. probability
c. outcome
D. exprement


Find the slope and \( y \) -intercept of the
line \( -\mathbf{5 x}+\boldsymbol{y}=\mathbf{5} \)
A. slope \( =5, y \) -intercept \( =-5 \)
B. slope \( =5, y \) -intercept \( =-4 \)
c. slope \( =5, y \) -intercept \( =5 \)
D. slope \( =5, y \) -intercept \( =-1 \)


Construct a right angled triangle whose
perimeter is equal to \( 10 \mathrm{cm} \) and one
acute angle equal to \( 60^{\circ} \)


Last \( e^{-} \) acceptor during ETS is
\( A \cdot O_{2} \)
B. cyt \( a \)
\( \mathbf{c} \cdot \operatorname{cyt} a_{2} \)
D. cyt \( a_{3} \)


At what position the fluid experiences
more pressure
A. At the bottom of container
B. At top of container
c. In the middle of container
D. Outside the container


If \( f(x)=x^{2}-3 x-\frac{3}{x}+\frac{1}{x^{2}}, \) then
\( f\left(\frac{1}{x}\right) \) is
\( A \)
в. \( f(x) \)
c. \( f(-x) \)
D . \( -f(x) \)


A marine dinosaur
is
A. Ichthyosaur
B. Pelycosaur
c. Pterosaur
D. Tyrannosaurus


Displacement current is continuous:
A. when electric field is changing in the circuit
B. when magnetic field is changing in the circuit
C. in both types of fields
D. through wires and resistance only


Which of the following salt undergoes
hydrolysis?
A. \( C H_{3} \) СООК
в. \( \operatorname{NaNO}_{3} \)
c. \( K C l \)
D. \( K_{2} S O_{4} \)


The virial equation for 1 mole of a real gas is written as:
\( P V=R T \)
\( \left[1+\frac{A}{V}+\frac{B}{V^{2}}+\frac{C}{V^{3}}+\ldots . . . . . . . . . . \) to the higher \right.
power of \( n] \)
Where \( A, B \) and \( C \) are known as virial coefficients. If Vander Waal's equation is written in virial form, then what will
be the value of B?
A. \( _{a-\frac{b}{R T}} \)
B . \( b^{3} \)
c. \( _{b-\frac{a}{R T}} \)
D. \( b^{2} \)


\( = \)
\( = \)
\( = \)
\( = \)
\( \equiv \)
\( 1=\underbrace{x^{\text {There }}} \)


Greatest genetic diversity can be brought about by the process of
A. Binary fission
B. Sexual reproduction
c. Asexual reproduction
D. Alternation of generations
E. Binary fission and conjugation


Any organism performed all the activities by single cell is called as
A. Multicellular
B. Unicellular
c. Acellular
D. Plants


Define the term 'drift velocity' of charge
carriers in a conductor and write its
relationship with the current flowing through it.


Explain why during electroplating, the article to be plated is always made the
cathode?


In a circular current-carrying conductor,
the face of the coil towards the observer
behaves like a south pole if the current
flows
A. In clockwise direction
B. In anticlockwise direction
C. In alternating clockwise and anticlockwise direction
D. First in anticlockwise for some time then in clockwise
direction


A particle hanging from a massless
spring stretches it by \( 2 c m \) at the eath's surface. How much will the same
particle stretch the spring at a height of \( 2624 K m \) from the surface of the earth?
(Radius of the earth \( =6400 K m) \)
\( A \cdot 1 c m \)
B. \( 2 c m \)
\( c .3 c m \)
D. \( 4 c m \)


In a Mendelian dihybrid cross, if one trait shows incomplete dominance and
other trait shows homozygous dominant lethality then what will be the phenotypic ratio of progenies obtained
in \( F_{2} \) generation?
\( \mathbf{A} \cdot 9: 3: 3: 1 \)
B. 2: 4: 2: 1: 2: 1
c. 3: 1
D. 1: 2: 1: 2: 4: 2: 1: 2: 1


The weight of a person on a planet \( A \) is about half that on the Earth. He
can jump upto \( 0.4 \mathrm{m} \) height on the surface of the Earth. How high he can jump on the planet \( A \) ?
\( \mathbf{A} \cdot 0.4 \mathrm{m} \)
B. \( 0.2 \mathrm{m} \)
c. \( 0.8 \mathrm{m} \)
D. \( 1.6 \mathrm{m} \)


This question has four choices \( (A),(B) \)
(C) and (D) out of which ONE or MORE
are correct.
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \sqrt{x^{2}+2 x}-x, \) then
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow \infty} g(x)=1 \)
B. \( \lim _{x \rightarrow-\infty} f(x)=1 \)
c. \( \lim _{x \rightarrow-\infty} f(x)=-1 \)
D. \( \lim _{x \rightarrow \infty} g(x)=-1 \)


A solenoid coil is wound on a frame of
rectangular cross section. If all the linear dimension of the frame are
increased by a factor of two and the number of turns per unit length of the coil remains the same, the self-
inductance increases by a factor of
A .4
B. 8
c. 12
D. 16


Assertion
2,4-Dimethyl hex-2-ene has 4
stereoisomer
Reason
It show geometrical isomerism
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


differentiate \( e^{-2 \tan ^{-1} x^{2}} \)


Select most stable complex:
A \( \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{3} \)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{2}(e n)_{2}\right]^{+3} \)
\( \mathbf{c} \cdot\left[C o(e n)_{3}\right]^{+3} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4}(e n)\right]^{+3} \)


List I and List II contains four entries
each. Entries of List I are to be
matched some entries of List II. One or
more than one entries of List I may
have the match with the same entry
of List II


Which type of average is most affected by extreme values in the data?
A. Mean
B. Mode
c. Median
D. All of the above


Which of the following is true for Krebs cycle?
A. Isocitrate \( \rightarrow \) Fumrate \( \rightarrow \alpha \) ketoglutarate
B. \( \alpha \) Ketoglutarate \( \rightarrow \) Oxalosuccinate \( \rightarrow \) Isocitrate
c. oxalosuccinate \( \rightarrow \) Isocitrate \( \rightarrow \alpha \) ketoglutarate
D. Isocitrate \( \rightarrow \alpha \) ketoglutarate \( \rightarrow \) Succinate


A car moves from \( A \) to \( B \) with a speed of \( 30 k m p h \) and from \( B \) to \( A \) with a speed of 20kmph. What is the average speed of
the car?
A. \( 25 k m p h \)
в. \( 24 k \) три
\( c .50 k m p h \)
D. \( 10 k m p h \)


In India, herbarium plant specimens are
arranged according to the system of classification of
A. Bentham and Hooker
B. R. H. Whittaker
c. carl woese
D. None of the above


The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula \( \boldsymbol{E}=\boldsymbol{h v} \) (for
energy of a quantum of radiation photon) and obtain the photon energy in units of \( e V \) for different parts of the
electromagnetic spectrum. In what ways are the different scales of photon
energies that you obtain related to the sources of electromagnetic radiation.?


A particle moves along the curve \( y= \)
\( a x^{2}, \) with constant speed \( v . \) The
acceleration at the origin of coordinates
being (where \( a \text { is a constant }) \)
A \( \cdot \frac{v^{2}}{2 a} \)
B. \( 2 a v^{2} \)
c. \( \frac{v^{2}}{a} \)
D. \( a v^{2} \)


In which compound \( I I^{n d} \) resonating
structure is less stable then \( I^{s t} \) ?
\( A \cdot x \)
B. Y
\( c \cdot z \)
D. All of these


Fill in the blanks with approprite words. is a method of sexual reproduction where two hyphae meet together.


Match the columns and find the correct
combination:
\begin{tabular}{cc|c|c}
& \( \mathrm{I} \) & & \( \mathrm{II} \) \\
\( \mathrm{a} \) & Zeatin & 1 & Flowering hormone \\
\( \mathrm{b} \) & Florigen & 2 & Synthetic auxin \\
\( \mathrm{c} \) & \( \mathrm{IBA} \) & \( 3 . \) & Cytokinin \\
\( \mathrm{d} \) & \( \mathrm{NAA} \) & \( 4 . \) & Natural auxin
\end{tabular}
\( A \)
\( a-3, b-1, c-4, d-2 \)
B. \( a-4, b-1, c-2, d-3 \)
\( c \cdot a-3, b-4, c-1, d-2 \)
D. \( a-2, b-1, c-4, d-3 \)
\( \mathrm{E} \cdot \mathrm{a}-1, \mathrm{b}-2, \mathrm{c}-3, \mathrm{d}-4 \)


Q Type your question
(a) The size of the atom in the
Thomsons model is \( \dots-m \) atomic size
in Rutherford's model.
(much greater than/no different from/much less than.)
(b) In the ground state of ........... electrons are in stable equilibrium, while in electrons always experience a net force. (Thomsons model/ Rutherfords model.)
(c) A classical atom based on \( \ldots \). is
doomed to collapse.
(Thomsons model/ Rutherfords model.)
(d) An atom has a nearly continuous mass distribution in \( a \)........... but has a
highly non-uniform mass distribution
in
(Thomsons model/ Rutherfords model.)
(e) The positively charged part of the atom possesses most of the mass in
(Rutherfords model / both the models.)


\( \int_{0}^{1} \frac{x\left(2 x^{2}+1\right)}{x^{8}+2 x^{6}-x^{2}+1} d x= \)
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{2 \sqrt{3}} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{\pi}{6} \)


\( Y, K, \eta \) represent respectively the young's modulus, bulk modulus and
rigidity modulus of a body. If young's modulus is twice the bulk modulus,
then :
A \( . \eta=6 \mathrm{K} / 7 \)
в. \( \eta=7 \mathrm{K} / 9 \)
c. \( \eta=9 \) К/7
D. \( Y=18 K / 7 \)


Which of the following properties is
different for neutral atoms of the
isotopes of the same element?
A. Atomic number
B. Mass
c. Number of electrons
D. General chemical reactions


Assertion
A stationary charged particle in a magnetic field does not experience a force.
Reason
The force acting on a charged particle does not depend on velocity of the
particle
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 ball is gently dropped from a height of \( 20 m . \) If its velocity increases uniformly
at the rate of \( 10 m s^{-2}, \) with what
velocity will it strike the ground? After what time will it strike the ground?


Sensory crista of ampulla of mammalian ear is connected with
A. Sense of balance
B. Sense of low hearing
c. Sense of loud hearing
D. Secretion of ear wax


The current synthesis of poly-carbonate is an application of:
A. green revolution
B. green chemistry
C. waste management
D. none of above


Nucleon is a common name for
A. Proton and electron
B. electron and neutron
c. neutron only
D. neutron and proton