Calculate the mean deviation about
mean for the data given here:
\( \begin{array}{lccc}\text { Class } & \mathbf{5} & \mathbf{1 5} & \mathbf{2 5} & \mathbf{3 5} \\ \text { interval } & & & \end{array} \)
Frequency \( \quad 5 \quad 3 \quad 9 \quad 12 \)
\( \mathbf{A} \cdot 10.2 \)
B. 10.4
c. 10.5
D. 11.4


If incident ray is normal to one of the
surfaces of equilateral prism and suffers total internal reflection on
second, then deviation caused by prism
is
A \( \cdot 0^{\circ} \)
В. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 180^{\circ} \)


A truck is carry a box of mass \( \boldsymbol{m}= \)
\( 50 k g \) on its flat horizontal rough
surface with coefficient of friction \( \boldsymbol{p}= \)
0.3. It is crossing a circular track of
radius 27 m. What is the maximum
speed of the truck to that the box does not slide from the muck while moving on the circular path?
\( \mathbf{A} \cdot 18 \mathrm{km} / \mathrm{hr} \)
B. \( 36 \mathrm{km} / \mathrm{hr} \)
c. \( 32.4 \mathrm{km} / \mathrm{hr} \)
D. \( 2.5 \mathrm{km} / \mathrm{hr} \)


In the given figure, a square \( \boldsymbol{O A B C} \) has
been inscribed in the quadrant OPB \( Q \)
If \( \boldsymbol{O} \boldsymbol{A}=\mathbf{2 0} \boldsymbol{c m} \) then the area of the
shaded region is \( [\text {take } \pi=\mathbf{3 . 1 4}] \)
A \( \cdot 214 c m^{2} \)
B. \( 228 c m^{2} \)
\( c \cdot 222 c m^{2} \)
\( \mathrm{D} \cdot 242 \mathrm{cm}^{2} \)


An alternating voltage \( \boldsymbol{E}= \) \( \mathbf{5 0} \sqrt{\mathbf{2}} \sin (\mathbf{1 0 0} t) \boldsymbol{V} \) is connected to a
1 \( \mu F \) capacitor through an ac ammeter. What will be the reading of the ammeter?
A . \( 10 \mathrm{mA} \)
B. \( 5 m A \)
c. \( 5 \sqrt{2} \) mA
D. \( 10 \sqrt{2} \mathrm{mA} \)


Light is an electromagnetic wave. Its speed in vacuum is given by the expression
в. \( \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \)
c. \( \sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \)
D. \( \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)


There are two books of five volumes
each and two books of two volumes
each. In how many ways can these books be arranged in a shelf such that volumes of same books remain
together?
A . 38
B. 34
c. 56
D. 88


Which is mismatched?
A. Bowman's capsule - Glomerular filteration
B. PCT - Absorption of \( N a^{+} \) and \( K^{+} \)
C. DCT - Absorption of glucose
D. None of the above


The internal energy of a perfect gas is:
A. completely kinetic
B. completely potential
C. sum of potential and kinetic energy of the molecules
D. difference of kinetic and potential energy of the molecules


Express the following in terms of trigonometric ratios of angles lying
between 0 and 45:
\( \tan 65^{0}+\cot 49^{0} \)


If the absolute errors in two physical
quantities \( A \) and \( B \) are \( a \) and \( b \) respectively, then the absolute error in
the value of \( A B \) is:
[Disclaimer: The options in the original question have been changed to match with the actual solution / answer.
\( \mathbf{A} \cdot b B-a A \)
B. \( a A+b B \)
\( \mathbf{c} \cdot a B+b A \)
\( \mathbf{D} \cdot a B-b A \)


Enzymes:
A. accelerate bio-chemical reactions
B. consists of amino acids
C. have optimum activity at body temperature
D. have all these properties


Three faradays of electricity are passed
through molten \( A l_{2} O_{3}, \) aqueous
solution of \( C u S O_{4} \) and molten \( N a C l \)
taken in three different electrolytic cells. The amount of \( A l, C u \) and \( N a \) deposited at the cathodes will be in the
ratio of
A. 1 mole : 1 mole : 1 mole
B. 1 mole : 1.5 mole: 3 mole
c. 3 mole : 2 mole : 1 mole
D. 1 mole : 1.5 mole: 2 mole


Tyloses are found in
A. Sclereids
B. Sclerenchyma fibres
c. secondary phloem
D. Secondary xylem


If molecular weight of a polypeptide is \( 15.3 k D a, \) what would be the minimum
number of nucleotides in the \( m R N A \)
that codes for this polypeptide? Assume that molecule weight of each amino acid is 90 Da.
A .510
в. 663
c. 123
D. 17


Can it be possible that an interior angle
of a regular polygon is \( 22^{\circ} ? \)
A. True
B. False
c. Ambiguous
D. Data Insufficient


You are given a resistance wire of length \( 100 \mathrm{cm} \) and a battery of negligible internal resistance. In which of the
following cases is the largest amount of heat generated?
A. When the wire is divided in two parts and both the parts are connected to the battery in parallel
B. When the wire is connected to the battery directly
c. when the wire is divided in to four parts and all the fou parts are connected in parallel to the battery
D. When only half of the wire is connected to the battery


The two types of arrangements of plastics are :
A . linear
B. cross linked
c. both A and B
D. None of above


The displacement of a particle varies according to the relation \( \boldsymbol{x}= \) \( 4(\cos \pi t+\sin \pi t) . \) The amplitude of the
particle is
A . -4
B. 4
c. \( 4 \sqrt{2} \)
D.


Velamen of orchids are formed from
A. Phelloderm
B. Phellogen
c. Dermatogen
D. cortex


A rough ball is thrown such that it
rotates clockwise about a horizontal
axis and simultaneously moves right in viscous air as shown. The force on the
ball due to magnus effect acts
A. Upwards
B. Downwards
c. Towards left
D. Towards right


Which of the following is appropriate for
mass-flow hypothesis?
A. Transpiration pull is responsible for absorption of ions
B. Large amount of ions are also absorbed along with the absorption of water
C. As suction pressure increases, absorption of water increases and along with water, absorption of ion also increases
D. All the given options


A matrix having \( m \) rows and \( n \) columns with \( m=n \) is said to be a
A. rectangular matrix
B. square matrix
c. identity matrix
D. scalar matrix


Monthly income of Suresh is \( R s 20240 \)
He spends \( 12.5 \% \) of his monthly
income on education. Find what amount
he spends on education


The distance (in metre) travelled by a
vehicle in time \( t \) (in seconds) is given by the equation \( s=t^{3}+2 t^{2}+t+1 . \) The
difference in the acceleration between
\( \boldsymbol{t}=\boldsymbol{2} \) and \( \boldsymbol{t}=\boldsymbol{4} \) is
A \( \cdot 12 m / s^{2} \)
B . \( 18 m / s^{2} \)
c. \( 16 m / s^{2} \)
D. \( 14 m / s^{2} \)


Consider the following two statements A and B and identify the correct answer.
A) We cannot define Young's modulus and rigidity modulus for liquids and
gases.
B) The theoretical limits of Poisson's
ratio are 1 to 0.5
A. Both A \& B are true
B. A is false but B is true
c. Both A \& B are false
D. A is true but B is false


Find the following limit:
\( \lim _{x \rightarrow 5} \frac{\sqrt{x-1}-2}{x-5} \)


The \( \boldsymbol{P}-\boldsymbol{P}-\boldsymbol{P} \) angle in \( \boldsymbol{P}_{4} \) molecule
and \( S-S-S \) angle in \( S_{8} \) molecule is (in degree) respectively:
A \( \cdot 60^{\circ}, 107^{\circ} \)
В . \( 107^{\circ}, 60^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ}, 108^{\circ} \)
D. \( 60^{\circ}, 40^{\circ} \)


You have three equal resistances r. The maximum possible number of different resistance values that you can offer is
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
\( D .7 \)


If \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{A} \boldsymbol{B} \) is
produced upto \( C \) such that \( 2 A B=B C \)
then \( C= \)
A. (5,4,6)
в. (6,2,4)
c. (4,5,6)
D. (6,4,5)


The decomposition of \( K C I O_{3} \) to \( K C l \)
and \( O_{2} \) on heating is an example of :
A. intermolecular redox change
B. intramolecular redox change
c. disproportionation or auto redox change
D. none of the above


Membrane separating air in pulmonary alveoli from blood capillaries
A. Alveolar epithelium
B. Cardiac epithelium
c. Endothelium blood capillaries
D. Both A and C


Hydrogen is:
A. electropositive
B. electronegative
C. both electropositive as well as electronegative
D. neither electropositive nor electronegative


Let \( A=\{1,2\} \) and \( B=\{2,3,4\} \)
If \( \boldsymbol{B} \times \boldsymbol{B}= \)
\{(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)
Please enter 1 or else 0


\( A_{3 \times 3} \) is a matrix such that \( |A|= \) \( \boldsymbol{a}, \boldsymbol{B}=(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \) such that \( |\boldsymbol{B}|=\boldsymbol{b} . \) Find
the value of \( \frac{\left(a b^{2}+a^{2} b+1\right) S}{25} \) where \( \frac{1}{2} S=\frac{a}{b}+\frac{a^{2}}{b^{3}}+\frac{a^{3}}{b^{5}}+\dots \dots \dots u p t o \infty \)
and \( \boldsymbol{a}=\mathbf{3} \)


On what factor does refractive index of a
prism depend?


Which of the following chemicals can be added for sweetening of food items at cooking temperature and does not provide calories?
A. sucrose
B. Glucose
c. Aspartame
D. sucralose


501
\( (G e) \) and other of silicon \( (S i) \) are
connected as shown in figure to a
battery of emf 12 v and a load
resistance \( 10 k \) \Omega. The germanium
diode conducts at \( 0.3 \mathrm{V} \) and silicon
diode at \( 0.7 \mathrm{V} \). When a current flows in
the circuit, then the potential of
terminal \( Y \) will be:
\( \mathbf{A} \cdot 12 V \)
B. \( 11 V \)
c. \( 11.3 V \)
D. \( 11.7 V \)


Chipko movement is connected with
A. Conservation of natural resources
B. Plant/forest conservation
C . Plant breeding
D. Project tiger


How much did the maintenance cost
increased in \( 1996-1997 \) when
compared to \( 1997-1998 ? \)
A . 1200
B. 1500
\( c .2500 \)
D. 4500


A box, when hung from a spring balance shows a reading of \( 50 \mathrm{kg} \). If the same box is hung from the same spring balance inside an evacuated chamber,
the reading on the scale will be.
A. \( 50 \mathrm{kg} \) because the mass of the box remains unchanged
B. \( 50 \mathrm{kg} \) because the effect of the absence of the atmosphere will be identical on the box and the spring balance
c. Less than \( 50 \mathrm{kg} \) because the weight of the column of air on the box will be absent
D. More than 50kg because the atmospheric buoyancy force will be absent


\( N^{\prime} \) atoms of a radioactive element
emit \( ^{\prime} \boldsymbol{n}^{\prime} \) alpha particles per second at an instant. Then the half-life of the element is :
A \( \cdot \frac{n}{N} \) sec.
в. \( 1.44 \frac{n}{N} \) sec
c. \( 0.69 \frac{n}{N} \) sec.
D. \( 0.69 \frac{N}{n} \) sec.


Solve:
\( 8 a^{2} b-3 a b+5 b^{2} b y 6 a b \)


Which of the following pairs of carbon
skeletons is an example of isomers?
\( A \)
\[
\mathbf{C}-\mathbf{C}-\mathbf{C} \text { and } \mathbf{C}-\frac{\mathbf{C}}{\mathbf{C}}-\mathbf{C}
\]
B.
\[
\mathbf{C}-\mathbf{C}-\frac{\mathbf{I}}{\mathbf{C}} \text { and } \mathbf{C}-\mathbf{C}-\frac{\mathbf{C}}{\mathbf{C}}-\mathbf{C}
\]
\( c \)
\[
\begin{array}{l}
\mathbf{C} \\
\mathbf{C}-\mathbf{C}-\mathbf{C} \text { and } \mathbf{C}-\mathbf{C}-\mathbf{C} \\
\mathbf{I} \\
\mathbf{C}
\end{array}
\]
D.
\[
\mathbf{C}-\mathbf{C}-\mathbf{C}-\mathbf{C} \text { and } \underset{\mathbf{C}}{\mathbf{C}} \mathbf{C}-\mathbf{C}-\mathbf{C}
\]


If the wavelength of light is \( 4000 A \), then the number of waves in 1 mm length
will be
A . 2500
B . 25
\( c .250 \)
D. 25000


When \( P b S \) is treated with warm dilute
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) the products most likely will be
\( \mathbf{A} \cdot P b^{2+}, S, N O_{2} \)
B . \( P b^{2+}, S, \) NO
c. \( P b O, S, N O \)
D. \( P b O_{2}, S O_{4}^{2-}, N_{2} \)


Offspring are individuals developed as a result of
A. Vegetative multiplication
B. Asexual reproduction
c. Sexual reproduction
D. All the above


Assertion
In India, IUDs like placement of copper-T is one of most widely accepted method of contraception.
Reason
Sterilisation, procedure in the male is called vasectomy.
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


Why is it necessary to use acetic acid and not sulphuric acid for acidification
of sodium extract for testing sulphur by lead acetate test?


A balloon is rising vertically upwards at a velocity of \( 10 \mathrm{m} / \mathrm{s} \). When it is at a
height of \( 45 m \) from the ground,a parachutist bails out from it. After \( 3 \operatorname{second} s \) he openshis parachute and
decelerates at a constant rate of
\( 5 m / s^{-2} . \) What was the height of the parachutist above the ground when he
opened his parachute?(take \( \boldsymbol{g}= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{-\mathbf{2}}\right) \)
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. 30 \( m \)
\( c \cdot 45 m \)
D. \( 60 \mathrm{m} \)


100ml of a solution of HCl with pH value 3 is diluted with \( 400 \mathrm{ml} \) of water. The
new pH of the solution is?
A. 3.7
B. 5.3
c. 4.2
D. 5.6


Charge on electron of mass \( 9.109 \times \)
\( 10^{-31} \mathrm{Kg} \) is:
A \( \cdot 1.603 \times 10^{-19} \mathrm{C} \)
В. \( -1.603 \times 10^{-19} \mathrm{C} \)
c. \( 9.109 \times 10^{-31} \mathrm{C} \)
D. \( -9.109 \times 10^{-31} \mathrm{C} \)


Adding salt to water makes it
salty. Which of the following is true regarding this change?
A. It is a chemical change because a new substance is formed
B. It is a physical change because the original substances can be recovered
C. It is a chemical change because there is exchange of heat
D. It is a physical change because there is a slight change in colour


Let \( z \) and \( \omega \) be the complex numbers.If
\( \boldsymbol{R} \boldsymbol{s}(\boldsymbol{z})=|\boldsymbol{z}-\boldsymbol{2}|, \boldsymbol{R} e(\boldsymbol{\omega})=|\boldsymbol{\omega}-\boldsymbol{2}| \) and
\( \arg (z-\omega)=\frac{\pi}{3}, \) find the value of
\( \operatorname{Im}(z+\omega) \)


\( \operatorname{Let} A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right], a, b, c, d \neq 0, \) then
\( \boldsymbol{B}=\boldsymbol{A} \boldsymbol{A}^{\prime}-\boldsymbol{A}^{\prime} \boldsymbol{A} \) equals
A. \( (a d-b c) I \)
в. \( (a c-b d) I \)
c.
D. none of these


A cylindrical rod magnet has a length of \( 5.0 \mathrm{cm} \) and a diameter of \( 1.0 \mathrm{cm} . \) It has a
uniform magnetization of \( 5.3^{*} 10^{3} \mathrm{A} / \mathrm{m} \) What is its magnetic dipole moment?
A . 20.8 \( m J T^{-1} \)
B . \( 10.8 m J T^{-1} \)
\( \mathbf{c} \cdot 5.8 m J T^{-1} \)
D. 30.8mJT"


If \( \vec{a}=\hat{i}+\widehat{j}+\widehat{k}, \vec{b}=4 \hat{i}+3 \widehat{j}+4 \widehat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \widehat{k} \) are linearly dependent
vectors and \( |\overrightarrow{\boldsymbol{c}}|=\sqrt{\mathbf{3}}, \) then
B. \( a=1, b=\pm 1 \)
c. \( \alpha=-1, \beta=\pm 1 \)
D. \( \alpha=\pm 1, \beta=1 \)


Evaluate the given integral. \( \int x \sin x \cos x d x \)


The pair(s) of coordination
complexes/ions exhibiting the same kind of isomerism is(are):
This question has multiple correct options
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{5} C l\right] C l_{2} \) and \( \left[C r\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
\( \mathbf{B} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \) and \( \left[P t\left(N H_{3}\right)_{2}\left(H_{2} O\right) C l\right]^{+} \)
\( \mathbf{c} \cdot\left[\operatorname{CoBr}_{2} C l_{2}\right]^{2-} \) and \( \left[P t B r_{2} C l_{2}\right]^{2-} \)
\( \mathbf{D} \cdot\left[P t\left(N H_{3}\right)_{3}\left(N O_{3}\right)\right] C l \) and \( \left[P t\left(N H_{3}\right)_{3} C l\right] B r \)


In fibrous proteins, polypeptide chains are held together by?
A. van der waals forces
B. electrostatic forces of attraction
c. hydrogen bonds
D. covalent bonds


Ortho, meta \& para forms of dihalo benzenes are taken in a single container at \( -25^{0} \mathrm{C} \). The container is
slowly heated up to room temperature and after some time it was found that the container was left with a
liquid having some solid residues in it. Solid residue can be:
A. ortho form
B. meta form
c. para form
D. mixture of ortho,meta and para form


In the following circuit the resultant
e.m.f between AB is
\( \mathbf{A} \cdot E_{1}+E_{2}+E_{3}+E_{4} \)
B \( \cdot E_{1}+E_{2}+2 E_{3}+E_{4} \)
\( \mathrm{c} \cdot_{E_{1}}+E_{2}+\frac{E_{3}}{2}+E_{4} \)
D \( \quad E_{1}+E_{2}+\frac{E_{3}}{4}+E_{4} \)


The units of rate of reaction and the rate
constant are identical for a
A. fraction-order reaction
B. zero-order reaction
c. first-order reaction
D. second-order reaction


The value of numerical aperature of the objective lens of a microscope is \( 1.25 . \) If light of wavelength \( 5000 \dot{A} \) is used, the minimum separation between two points, to be seen as distinct, will be :
A \( .0 .24 \mu m \)
в. \( 0.48 \mu m \)
c. \( 0.12 \mu \) m
D. \( 0.38 \mu m \)


Five moles of Hydrogen initially at STP compressed acrobatically so that its temperature becomes \( 73 \mathrm{K} \). The increase in internal of the gas in Kilo joules is:
\( (\boldsymbol{R}-\mathbf{8 . 3} \boldsymbol{j} / \boldsymbol{m o l} \boldsymbol{e}-\boldsymbol{K}: \boldsymbol{\gamma}=\mathbf{1 . 4} \) for
A . 80.5
B. 21.55
c. 41.50
D. 65.55


If the acceleration of a body is zero, does
it mean that its velocity is also zero? (Yes/No)


The difference in height of the mercury column in two arms of U tube
manometer in the arrangement - lis \( \boldsymbol{h}_{1}=\mathbf{6 6 0} \mathrm{mm} . \) In another arrangement -
Il at same temperature, 222 gm of
\( \mathrm{CaCl}_{2} \) is dissolved in \( 324 \mathrm{gm} \) of water and difference in height of mercury
column in two arms is found to be \( h_{2}= \)
\( 680 \mathrm{mm} . \) If the value of degree of
dissociation for \( C a C l_{2} \) in arrangement
-11 is \( \alpha, \) then the value of \( 64 \alpha \) is:
[Atmospheric pressure \( =1 \) atm]
A . 40
B. 38
c. 45
D. 50


Assertion
carbon tetraiodide \( \left(C I_{4}\right) \) is a solid
whereas carbon tetrafluoride \( \left(C F_{4}\right) \) is a
gas.
Reason
This is due to the London dispersion to
dipole-dipole interaction because of the increased polarity.
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


An atomic nucleus \( A \) is composed of 84
protons and 128 neutrons.
(i) The nucleus \( A \) emits an alpha particle and is transformed into nucleus \( B \). What is the composition of
nucleus \( B ? \)
(iii) The nucleus \( B \) emits a beta particle and is transformed into a
nucleus \( C . \) What is the composition of
nucleus \( C ? \)
\( (i i i) \) Does the composition of nucleus \( C \)
change if it emits gamma radiations?


A ray of light travelling in air enters
obliquely into water. Does the light ray
bend towards the normal or away from the normal?


The non-existant metal carbonyl among
tthe following is:
\( \mathbf{A} \cdot C r(C O)_{6} \)
в. \( M n(C O)_{5} \)
c. \( N i(C O)_{4} \)
D. \( F e(C O)_{5} \)


The integral \( \int \frac{d x}{a \cos x+b \sin x} \) is of the
form \( \frac{1}{r} \ln \left[\tan \left(\frac{x+\alpha}{2}\right)\right] \)
What is \( \alpha \) equal to?
A \( \cdot \tan ^{-1}\left(\frac{a}{b}\right) \)
B. \( \tan ^{-1}\left(\frac{b}{a}\right) \)
c. \( \tan ^{-1}\left(\frac{a+b}{a-b}\right) \)
D. \( \tan ^{-1}\left(\frac{a-b}{a+b}\right) \)


The earth's gravitational force at some place in space causes an acceleration
of \( 7 m / s^{2} \) in a \( 1 k g \) mass.What will be
the acceleration of a \( 5 k g \) mass.What
will be the acceleration of a \( 5 k g \) mass
at the same place?
A \( \cdot 7 m / s^{2} \)
B. \( 35 m / s^{2} \)
c. \( 1.4 m / s^{2} \)
D. \( 3.5 m / s^{2} \)


One end of a cylindrical rod is grounded to a hemispherical surface of radius
\( R=20 m m . \) It is immersed in water of
refractive index \( 1.33 . \) If the refractive
index of the hemisphere is \( 1.5 . \) Find the position of an image of an object placed on the axis of the rod inside water at
\( 10 \mathrm{cm} \) from the pole.


Expand \( \frac{1}{x^{4}-5 x^{3}+7 x^{2}+x-8} \) in
descending powers of \( x \) to four terms, and find remainder.


The two branches of the external iliac
artery are
A. Femoral and renal
B. Femoral and sciatic
c. vesciculo-epigastric and femoral
D. Renal and sciatic


A mixture of \( H C O O H \) and \( H_{2} C_{2} O_{4} \) is
heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) The gas
produced is collected and on treating with \( K O H \) solution, the volume of the gas decreases by \( \frac{1}{6} \) th. The molar ratio of two acids in the original mixture is \( x: y \)
The value of \( \boldsymbol{x}+\boldsymbol{y} \) is :


Short / Long Answer Type Questions:
What are biofertilizers? What are their
main sources? What is biological nitrogen fixation? Name two organisms each which fix nitrogen asymbiotically and symbiotically.


No physicist has ever "seen" an electron Yet, all physicists believe in the existence of electrons. An intelligent but superstitious man advances this analogy to argue that 'ghosts' exist even though no one has 'seen' one. How will you refute his argument?


For the following differential equation,
find the general solution.
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}=\boldsymbol{d} \boldsymbol{x} \)


Find the standard deviation of the first
10 natural numbers


The mean of five numbers is 0 and their
variance is \( 2 . \) If three of those numbers
\( \operatorname{are}-1,1 \) and \( 2, \) then the other two numbers are :
\( \mathbf{A} \cdot-5 \) and 3
B. - 4 and 2
c. -3 and 1
D. -2 and 0
E . -1 and -1


Equation \( 6 \sin ^{2} \theta-5 \sin \theta+1=0 \) is
satisfied by
A \( \cdot \theta=\frac{\pi}{2} \)
B. \( \theta=\frac{\pi}{3} \)
\( \mathbf{c} \cdot \theta=\frac{\pi}{4} \)
D・ \( \theta=\frac{\pi}{6} \)


Steel is electroplated with zinc
because zinc has:
A. more lustrous
B. less corrosion resistance
c. more corrosion resistance
D. more heavy


The image of an object which cannot be obtained on a screen is called
A. Enlarged image
B. Real image
c. virtual image
D. Inverted image


How many \( d \) -electrons in \( C u^{+} \) (Atomic
number \( =29 \) ) can have the spin quantum number \( \left(-\frac{1}{2}\right) ? \)
\( A \cdot 3 \)
B. 7
\( c .5 \)
D.


Consider the following statements:
1. The mean and median are equal in
symmetric distribution.
2. The range is the difference between
the maximum value and the minimum
value in the data.
3. The sum of the areas of the rectangle
in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis.
Which of the above statements are
correct?
A. 1 and 2 only
B. 2 and 3 only
c. 1 and 3 only
D. 1,2 and 3


Assertion
SnCl \( _{2} \) is a reducing agent.
Reason
SnCl \( _{2} \) reduces \( F e C l_{3} \) to \( F e C l_{2} \) and
HgCl\( _{2} \) to \( H g \)
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


Column II give the group to which element in column I belong, match
them correctly.


The different words beginning and
ending with a vowel that can be made with all the letters of the word
EQUATION is:
A . 14400
в. 4320
c. 864
D. 1440


Which one of the following is a laboratory weed?
A. Penicillium
B. Aspergillus
c. Neurospora
D. Saccharomyces


Differentiate between Iub and dup
sound.


The waves which propagate in metals
are
A . Longitudinal
B. Transverse
C. Both (a) and (b)
D. None of these


The cube has volume 64 cubic units. If a
largest sphere possible that can be placed inside this cube has radius \( r \)
then the value of \( r \) is
A . 2
B. \( 2 \sqrt{2} \)
\( c \cdot 4 \)
D. 8


The required kinetic energy of an object of mass \( \mathrm{m}, \) so that it may escape, will
be
\( \mathbf{A} \cdot \frac{1}{4} m g R \)
B . \( \frac{1}{2} m g R \)
c. \( \mathrm{mg} \) R
D. 2 mgR


Give the functional group of the following.
\( -\mathrm{OH} \)
A. Aldehydic group
B. Alcoholic group
c. Ketonic group
D. Carboxylic group


The binomial system of nomenclature was initially proposed by
A. Magnus
B. Bauhin
c. caesalpino
D. Dioscorides


Find the order and degree of the
differential equations:
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left[\boldsymbol{y}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{6}\right]^{1 / 4} \)


Bonds involving deuterium are:
A. stronger than the corresponding bonds in hydrogen
B. weaker than the corresponding bonds in hydrogen
C . same as the corresponding bonds in hydrogen
D. stronger than the corresponding bonds in tritum


A proton, a deutron and an \( \alpha \) particle
accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles
to \( B \). What is the ratio of their radii.?
A .2: 1: 1
B. \( 1: \sqrt{2}: \sqrt{2} \)
c. 1: 2: 1
D. 1: 1: 2


The zone of exclusion is associated with
A. Golgi complex
B. Endoplasmic reticulum
c. Mitochondria
D. chloroplast


Two forces are such that the sum of
their magnitude is \( 18 N \) and their
resultant is \( 12 N \) and it is
also perpendicular to the smaller force.Then the magnitude of the forces
are
A \( .12 N, 6 N \)
B . \( 13 N, 5 N \)
c. \( 10 N, 8 N \)
D. \( 16 N, 2 N \)


It is found in such as which cause
dysentery?
A. Other microbes
B. Bacteria
c. Nutrients
D. Inorganic impurities


Derive an expression for the energy stored per unit volume (energy density) in an electric field. OR Obtain an
expression for energy density of a medium.


Copper contains \( 8.4 \times 10^{28} \) free
electrons/ \( m^{3} \). A copper wire of crosssectional area \( 7.4 \times 10^{-7} m^{2} \) carries a
current of 1 A. The electron drifts speed
is approximately:
\( \mathbf{A} \cdot 10^{-8} m / s \)
B. \( 10^{-3} \mathrm{m} / \mathrm{s} \)
c. \( 1 m / s \)
D. \( 10^{-4} \mathrm{m} / \mathrm{s} \)


Hydrogen gas is passed through oil in order to:
A. convert lower oil to higher oil
B. convert liquid oil into solidified oil
c. convert unsaturated hydrocarbon to saturated hydrocarbon
D. all the above statements are wrong


Ozone in the stratosphere is depleted by
A \( \cdot C_{6} F_{6} C l_{6} \)
в. \( C_{7} F_{16} \)
c. \( C F_{2} C l_{2} \)
D. \( C_{6} F_{6} \)


the second layer of the atmosphere reaches \( 48 \mathrm{km} \) above the earth's surface.


\( C H_{3} C H_{2} O H \) can be converted into
\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) by:
A . catalytic hydrogenation
B. treatment with \( L i A l H_{4} \)
c. treatment with pyridinium chlorochromate
D. treatment with \( K M n O_{4} \)


Tha angles of a quadrilateral are in A.P.,
whose common difference is \( 10^{\circ} \). Find
the angles.


\( 1.5 \mathrm{g} C d C l_{2} \) was found to contain \( 0.9 \mathrm{g} \)
Cd. Calculate the atomic weight of Cd.
A . 118
B. 112
c. 106.5
D. 53.25


Probability of four son to a couple is
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{8} \)
c. \( \frac{1}{16} \)
D. \( \frac{1}{32} \)


An element has an atomic number 20 .
How many electrons will be present in \( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N} \) shells of its atom?
A .2,8,6,4
в. 2,8,7,3
c. 3,7,7,3
D. 2,8,8,


Resistance of a conductivity cell filled
with 0.15 mol \( L^{-1} \) NaCl solution is \( 50 \Omega \)
If resistance of the same cell when filled
with 0.02 mol \( L^{-1} \) NaCl solution is 500
\( \Omega, \) calculate the conductivity of 0.02
mol \( L^{-1} \) NaCl solution. (The
conductivity of 0.15 mol \( L^{-1} \) NaCl solution is \( 1.5 \mathrm{s} / \mathrm{m} \) ).


If \( \vec{a}=\hat{i}+2 \hat{j} \) and \( \vec{b}=3 \hat{j}, \) then \( \vec{a} \cdot \vec{b}= \)
A. 3
B . - -
\( c \cdot 6 \)
D. - -


Perxenate ion is:
A \( \cdot X e O_{6}^{4-} \)
B. \( H X e O_{4}^{-} \)
c. \( X e O_{4}^{2} \)
D. \( X e O_{4}^{-} \)


If the electric flux entering and leaving
an enclosed surface respectively are \( \phi_{1} \)
and \( \phi_{2}, \) the electric charge inside the surface will be :
A \( \cdot \frac{\phi_{2}-\phi_{1}}{\varepsilon_{0}} \)
в. \( \frac{\phi_{2}+\phi_{1}}{\varepsilon_{0}} \)
c. \( \frac{\phi_{1}-\phi_{2}}{\varepsilon_{0}} \)
D. \( \varepsilon_{0}\left(\phi_{2}-\phi_{1}\right) \)


Which of the following reactions led to the discovery of neutrons?
A \( \cdot_{6} C^{14}+_{1} p^{1} \rightarrow_{7} N^{14}+_{0} n^{1} \)
B. \( _{4} B e^{9}+_{2} H e^{4} \rightarrow_{6} C^{12}+_{0} n^{1} \)
\( \mathbf{c} \cdot_{5} B^{11}+_{1} D^{2} \rightarrow_{6} C^{11}+_{0} n^{1} \)
D. \( _{4} B e^{8}+_{2} H e^{4} \rightarrow_{6} C^{11}+_{0} n^{1} \)


\( \ln \) a \( \Delta A B C \) median AD is produced to \( x \)
such that \( A D=D X \). Prove that \( A B X C \) is a
parallelogram.


Mendel is famous for his work on
A. Pisum
B. Drosophila
c. Neurospora
D. oenothera


see how much time he would save
taking a shortcut to home from football
practice. He usually walked 6 blocks
south and 9 blocks east. Which picture
shows his shortcut?
\( A \)
B.
\( c \)
D.


The particle A is converted to C via
following reactions then:
\( \boldsymbol{A} \rightarrow \boldsymbol{B}+_{2} \boldsymbol{H} \boldsymbol{e}^{\boldsymbol{4}} \)
\( \boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{2}_{-1} \boldsymbol{e}^{\boldsymbol{0}} \)
A. A and C are isobars
B. \( A \) and \( C \) are isotopes
C. \( A \) and \( B \) are isobars
D. \( A \) and \( B \) are isotopes


In an AC generator, maximum number of lines of force pass through the coil when the angle between the plane of coil and lines of force is


if \( z_{1}=3+4 i \) and \( \operatorname{Im}\left(z_{1} z_{2}\right)=0 \) Find \( z_{2} \)
A \( \cdot z_{2}=3-4 i \)
в. \( z_{2}=3+4 i \)
c. \( z_{2}=3 \pm 4 i \)
D. None of these


An element X occurs in short period
having configuration \( n s^{2} n p^{1} \). the
formula and nature of its oxide is :
A. \( X O_{3, \text { basic }} \)
в. \( X O_{3} \),bcidic
c. \( X_{2} O_{3, \text { amphoteric }} \)
D. \( X_{2} O_{3, \text { basic }} \)


Find the equation to the plane through the point (-1,3,2) and perpendicular to the planes \( x+2 y+2 z=11 \) and
\( 3 x+3 y+2 z=15 \)


Solve:
\( \lim _{x \rightarrow 0} 9 \)


When a die is thrown, list the outcomes
of an event of getting a prime number.
A \( \cdot\{1,4,6\} \)
в. \{2,3,5\}
D. None of these


Choose the correct statements from the
options below with regard to sexual
reproduction
(i) Sexual reproduction does not always require two individuals.
(ii) Sexual reproduction generally involves gametic fusion.
(iii) Meiosis never occurs during sexual reproduction.
(iv) External fertilization is a rule
during sexual reproduction.
\( A \cdot \) (i) and (iv)
B. (i) and (ii)
c. (ii) and (iii)
D. (ii) and (iv)


In Nelson's cell, Cathode is:
A. graphite
B. copper tube
c. porus steel vessel
D. iron tank


The magnetic momentum of
\( \boldsymbol{K}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5}(\boldsymbol{N} \boldsymbol{O})\right] \) is:
A. \( 1.73 B M \)
В. \( 5.47 B M \)
\( \mathrm{c} .6 .9 \mathrm{BM} \)
D. zero


Which one of the following pair of soil and its specific characteristic is incorrectly matched?
A. Terrarossa- most suitable for rose cultivation
B. Chernozems- richest soil on the planet
c. Black soil- rich in calcium carbonate
D. Laterite- contain aluminium compounds


\( Q \) тур
When the fan runs at full speed, its speed becomes constant. This is because the torque due to magnetic field inside the fan is balanced by the torque due to air resistance on the
blades of the fan and the torque due to friction between the fixed part and the shaft of the fan. The electric power going into the fan is spent (i) in the internal resistance as heat, call it \( P_{1}, \) (ii) in doing work against internal friction and air resistance producing heat, sound,
etc., call it \( P_{2} \). When the coil of fan
rotates, an emf is also induced in the coil. This opposes the external emf is also induced in the coil. This opposes
the external emf applied to send the current to the fan. This emf is called
back emf, call it \( e . \) Answer the following questions when the fan is running at full speed.The current flowing into the
fan and the value of back emf \( e \) is
A. \( 200 A, 5 V \)
B . \( 5 A, 200 V \)
c. \( 5 A, 195 V \)
D. \( 1 A, 0 V \)


A leapord leaps a distance of 1 metre in a straight line, 20 times in 1 minute, while catching a prey, then
A. Time period and frequency cannot be determined since the leopard is not returning to its original position
B. The product of its time period and frequency will be unity
c. The time period is infinity
D. The frequency is zero


There are five times the number of two
wheelers as there are three wheelers.
The no of four wheelers are equal to the number of two wheelers. Find the
average number of wheel per vehicle


The height of mercury barometer is \( h \)
when the atmospheric pressure is
\( 10^{5} P a, \) The pressure at \( x \) in the shown
diagram is
\( \mathbf{A} \cdot 10^{5} P a \)
В \( .0 .8 \times 10^{5} \mathrm{Pa} \)
c. \( 0.2 \times 10^{5} P a \)
D. \( 120 \times 10^{5} \mathrm{Pa} \)


The D.E whose solution is \( x y=a x^{2}+\frac{b}{x} \)
is
A \( \cdot x^{2} y_{2}+2 x y_{1}=2 y \)
в. \( x^{2} y_{2}-x y_{1}+2 y=0 \)
c. \( x^{2} y_{2}+x y_{1}+y=0 \)
D . \( x^{2} y_{2}+x y_{1}+2 y=0 \)


One centimetre is equal to
\( A \cdot 5 \mathrm{mm} \)
B. 10 \( \mathrm{mm} \)
\( c .15 \mathrm{mm} \)
D. None of these


Which of the following assertions are
correct?
This question has multiple correct options
A. \( A \) neutron can decay to a proton only inside a nucleus.
B. \( A \) proton can change to a neutron only inside a nucleus.
C. An isolated neutron can change into a proton.
D. An isolated proton can change into a neutron.


A boat goes \( 60 k m \) upstream and downs
stream in \( 6 h r \) and \( 2 h r \) respectively. Determine the product of speed of the
stream and that of the boat in still
water


Calculate the coefficient of range for the
following data.
\begin{tabular}{lll}
No. of wards & 1 & 2 \\
\hline
\end{tabular} 3 \begin{tabular}{r}
4 \\
\hline
\end{tabular}
No. of
\[
32 \quad 57
\]
\( 28 \quad 96 \)
nouses


Which of the following quantities is zero, when a uniform object is being supported at its centre of gravity?
A . Mass
B. Weight
c. Force
D. Moment


Derive the expression to find the unknown resistance in the balanced
condition of wheastone bridge.


When a wave traverses a medium the
displacement of a particle located at \( x \) at a time is given by \( y=a \sin (b t-c x) \) where a, band are constants of the wave,
which of the following is a quantity with dimensions?
A. \( \frac{y}{a} \)
в. \( b t \)
c. \( c x \)
D. \( \frac{b}{c} \)


The end product \( ^{\prime} C^{\prime} \) in the following sequence of chemical reactions is:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{C a C O}_{3}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H e a t}}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{N H_{2} O H}{\longrightarrow} \boldsymbol{C} \)
A. Acetaldehyde oxime
B. Formaldehyde oxime
c. Methyl nitrate
D. Acetoxime


Show that \( \sqrt[3]{125 \times 64}=\sqrt[3]{125} \times \sqrt[3]{64} \)


Which of the following measurement is most precise?
A. \( 5.00 \mathrm{mm} \)
B. \( 5.00 \mathrm{cm} \)
c. \( 5.00 m \)
D. \( 5.00 \mathrm{km} \)


An inorganic substance liberates oxygen on heating and turns an acidic solution of
\( K I \) brown and reduces acidified \( K M n O_{4} \)
solution. The substance is:
A. \( H g O \)
в. \( H_{2} O_{2} \)
c. \( K n O_{3} \)
D \( \cdot \operatorname{Pb}\left(N O_{3}\right)_{2} \)


Find the mass of \( 1.5055 \times 10^{25} \) number
of molecule of aluminium oxide.


Select the incorrect statements:
This question has multiple correct options
A. A few combustion process are endothermic
B. Heat of combustion may be positive
C. Exothermic compounds arc more stable than endothermic compounds
D. Hess's law can he verified experimentally


Formalin is \( \% \) solution of
formaldehyde in water
A . 10
B. 20
\( c \cdot 40 \)
D. 60


Which of the following choice is correct regarding to increase the rate of a
reaction?
A. Decreasing the temperature
B. Increasing the volume of the reaction vessel
c. Reducing the activation energy
D. Decreasing the concentration of the reactant in the reaction vessel


Match List-I with List-II:
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { a) } \overrightarrow{\mathrm{i}} \cdot(\overrightarrow{\mathrm{j}} \times \overrightarrow{\mathrm{k}})+\overrightarrow{\mathrm{j}} \cdot(\overrightarrow{\mathrm{k}} \times \overrightarrow{\mathrm{i}})+\overrightarrow{\mathrm{k}} \cdot(\overrightarrow{\mathrm{i}} \times \overrightarrow{\mathrm{j}}) & \text { e) } 0 \\ \text { b) }(\overrightarrow{\mathrm{i} . \overrightarrow{\mathrm{i}}})+(\overrightarrow{\mathrm{i}} \times \overrightarrow{\mathrm{i}}) & \text { f) } 1 \\ \text { c) }(\overrightarrow{\mathrm{A} \cdot \vec{B}})(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})+(\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{A}})(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}) & \text { g) } 3 \\ \text { d) }(\overrightarrow{\mathrm{i}}+\overrightarrow{\mathrm{j}}) \cdot(2 \overrightarrow{\mathrm{i}}+2 \overrightarrow{\mathrm{k}}) & \text { h) } 2\end{array} \)
\( \mathbf{A} \cdot \mathbf{a} \rightarrow \mathbf{e} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{h} \)
\( \mathbf{B} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{h} ; \mathbf{c} \rightarrow \mathbf{f} ; \mathrm{d} \rightarrow \mathbf{e} \)
\( \mathbf{c} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathrm{d} \rightarrow \mathbf{h} \)
\( \mathrm{D} \cdot \mathrm{a} \rightarrow \mathrm{f} ; \mathrm{b} \rightarrow \mathrm{g} ; \mathrm{c} \rightarrow \mathrm{h} ; \mathrm{d} \rightarrow \mathrm{e} \)


The mammals which possesses both
the reptiles and mammalian characters
are
A. Marsupials
B. Monotremes
c. Equus
D. oryctolagus


Which of the following monomer will
make PHBV more flexible?
A. \( \beta \) - hydroxy butyric acid
B. \( \beta \) - hydroxy velaric acid
c. Glycine
D. Lactic acid


The process which takes place in
absorption tower is
\( \mathbf{A} \cdot \) catalytic oxidation of \( S O_{2} \) to \( S O_{3} \)
B. production of sulphur dioxide by burning sulphur
C. absorption of sulphur trioxide in \( 98 \% \) sulphuric acid
D. none of the above


Consider the following reaction \( \boldsymbol{C C l}_{3} \boldsymbol{C H}=\boldsymbol{C H}_{2} \frac{N a \boldsymbol{B O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{O}_{2} / \boldsymbol{H O C l}} \)
Product\( (P) \)
\( \boldsymbol{P} \) is:
A \( \cdot C C l_{3} C H-C H_{2} C l \)
of
c. \( C C l_{3} C H C H_{2} O H \)
\( d_{l} \)
D. \( C C l_{3} C H C H_{2} \)
1


Find the apparent weight of a man weight \( 49 \mathrm{Kg} \) on earth where he is standing in a life which is irising with
an acceleration of \( 1.2 m / s^{2} i i \) ) going with the same acceleration iii)
falling freely the action gravity iv) going up down with uniform velocity. Given
\( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)


The first Indian built rocket was
launched from:
A. Bangalore
B. Sriharikota
c. Thumba
D. Trivandrum


Exposure of UV radiations causes
A. Damage to eye sight
B. Sunburn
c. skin cancer
D. All of the above


Ozone depletion is occuring widely in the stratosphere, it leads to ozone hole
caused mainly due to
A. Ethylene
B. Methane
c. сесь
D. \( C O_{2} \)


A. Current flow inside the capacitor due to accumulation of charges on the capacitor walls is called displacement
current.
B. Current due to the flow of electrons
due to some potential difference is called as conduction current.
C. Displacement current came into existence when Maxwell observed that
if a magnetic compass is placed between the capacitors the needle gets deflected which signifies presence of magnetic fields which would possibly caused due to some changing current.
D. Displacement current change the actual motion of electric charges. Which of the above statement(s) is/are
correct?
A. A and B only
B. A, B and C only
c. \( c \) only
D. \( A, B, C \) and \( D \)


Two magnetic poles of equal pole strengths each of \( 1.732 A m \) should be
placed at \( _{---} c m s \) apart so that the
force of attraction between them is
0.5 dynes (nearly):
\( \mathbf{A} \cdot \mathbf{6} \)
в. 2.45
c. 24.5
D. \( \sqrt{3} \)


The force required to just move a body
up the inclined plane is double the force
required to just prevent the body from sliding down the plane. The coefficient
of friction is \( \mu . \) If \( \theta \) is the angle of
inclination of the plane, then \( \tan \theta \) is
equal to
\( \mathbf{A} \cdot \mathbf{\mu} \)
в. \( 3 \mu \)
\( c \cdot 2 \mu \)
D. \( 0.5 \mu \)


Using the differential equation of linear
S.H.M, derive an expression for the velocity of a particle performing linearly:


Study of the relationship of energy and transformation of energy in living organisms is known as:
A. catabolise energetic
B. bioenergetics
c. broken energetic
D. anabolic energetiç


A tension of \( 22 \mathrm{N} \) is applied to a copper
wire of cross-sectional area \( 0.02 \mathrm{cm}^{2} \)
Young's modulus of copper is \( 1.1 \times \) \( 10^{11} N / m^{2} \) and Poisson's ratio \( 0.32 . \) The
decrease in cross sectional area will be:
A \( \cdot 1.28 \times 10^{-6} \mathrm{cm}^{2} \)
в. \( 1.6 \times 10^{-6} \mathrm{cm}^{2} \)
c. \( 2.56 \times 10^{-6} \mathrm{cm}^{2} \)
D. \( 0.64 \times 10^{-6} \mathrm{cm}^{2} \)


Thermometer that can measure rapidly changing temperature is:
A. Mercury-in-glass thermometer
B. Alcohol-in-glass thermometer
c. Platinum resistance thermometer
D. Thermocouple thermometer


The width of one of the two slits in
Young's double slit experiment is double of the other slit. Assuming that the amplitude of the light coming from a slit is proportional to the slit width. Find the ratio of the maximum to the
minimum intensity in the interference
pattern


The precursor of coal is:
A . peat
B. lignite
c. anthracite
D. graphite


\( \left(\cos ^{-1} l+\cos ^{-1} m+\cos ^{-1} n\right) \) is equal
to
A . \( 90^{\circ} \)
B. \( 50^{\circ} \)
\( c \cdot 180^{\circ} \)
D. None of these


The midbrain is the part of
A. Metencephelon
B. Telencephelon
c. Mesencephelon
D. Diencephelon


If you chew on a piece of bread long enough, it will begin to taste sweet because
A. maltase is breaking down maltose
B. lipases are forming fatty acids
c. amylase is breaking down starches to disaccharides
D. disaccharides are forming glucose


The osmotic pressure of a solution in atm obtained on mixing each 50 mL of \( 1.2 \% \) mass/volume urea solution and
\( 2.4 \% \) mass/volume glucose solution at \( \mathbf{3 0 0} \mathrm{K} \) is: \( (\boldsymbol{R}=\mathbf{0 . 0 8} \) litre atm
\( \left.\boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)


A hollow cylinder has solid hemisphere
inward at one end and on the other end
it is closed with a flat circular plate. The
height of water is \( 10 \mathrm{cm} \) when flat
circular surface is downward. Find the
level of the water, when it is inverted
upside down, common diameter is \( 7 \mathrm{cm} \)
and height of the cylinder is \( 20 \mathrm{cm} \)


Which of the following has been arranged in order of increasing oxidation number of nitrogen?
A. \( N H_{3}<N_{2} O_{5}<N O<N_{2} \)
B . \( N O_{2}^{+}<N O_{3}^{-}<N O_{2}^{-}<N_{3}^{-} \)
C . \( N H_{4}^{+}<N_{2} H_{4}<N H_{2} O H<N_{2} O \)
D. \( N O_{2}<N a N_{3}<N H_{4}^{+}<N_{2} O \)


For the reaction \( 3 A(g)+B(g) \rightleftharpoons 2 C(g) \)
at a given temperaature, \( \boldsymbol{K}_{c}=\mathbf{9 . 0} \)
What must be the volume of the flask, if
a mixture of 2.0 mol each of \( A, B \) and \( C \)
exist in equilibrium?


Two charged spheres of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
have equal surface charge density. The ratio of their potential at an equidistant external point is
A \( \cdot \frac{R_{2}}{R_{1}} \)
в. \( \left(\frac{R_{2}}{R_{1}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
D. \( \frac{R_{1}}{R_{2}} \)


Which of the following is an organic molecule?
\( A \cdot \operatorname{si0}_{2} \)
B. NH
\( c \cdot H_{2} 0 \)
\( \mathrm{D} \cdot \mathrm{cH}_{4} \)
E. BeF \( _{2} \)


Name one device in which the cathode
ray tube is used.


Two fair die are thrown. The probability the sum of the numbers appearing is 6
is
A \( \cdot \frac{1}{6} \)
в. \( \frac{5}{6} \)
c. \( \frac{1}{36} \)
D. \( \frac{5}{36} \)


The structure of glycine (amino acid) is
\( H_{2} N-C H_{2} C O O^{-}(z \text { witter ion }) \)
Select the correct statement:-
A. Glycine as well as other amino acids are amphoteric
B. The acidic functional group in amino acids is \( N H_{3} \)
C. The basic functional group in amino acids is \( -C O O \)
D. All are correct


A metal is in the form of dispersed phase and water is the dispersion medium. The colloid is termed as:
This question has multiple correct options
A. hydrophobic
B. hydrophilic
c. water-loving
D. water-hating


What is the derivative of \( x^{3} \) with respect
to \( x^{2} ? \)
A \( \cdot 3 x^{2} \)
в. \( \frac{3 x}{2} \)
c. \( x \)
D. \( \frac{3}{2} \)


There are 6 items in column-A and 6
items in column-B. A student is asked
to match each item in column-A with an
item in column-B. The number of
possible (correct or incorrect) answers are there to this question is
A . 720
B. 620
c. 520
D. 820


A hydride is a compound containing
hydride ion, \( \boldsymbol{H}^{-} \). Predict two elements
whose hydrides would contain incomplete octets


When two triangles have corresponding sides equal in length, then the
two triangles are congruent.
A. SAS congruency Theorem
B. AA congruency Theorem
C. AAA congruency Theorem
D. sss congruency Theorem


In the Geiger-Marsden experiment, the
force that scatters particles is
A. nuclear force
B. coulomb force
c. both A and B
D. gravitational force


\( \int \frac{1}{x+x \log x} d x \)


Which of the following nuclides belong
to actinium \( \left(U^{235}\right) \) series? This question has multiple correct options
\( \mathbf{A} \cdot P b^{207} \)
B . \( P o^{215} \)
c. \( P_{o^{213}} \)
D. \( _{1} H^{3} \)


Alkynes can show:
A. geometrical isomerism
B. position isomerism
C. functional isomerism
D. both B and C


Two cars \( A \) and \( B \) approach stationary observer from opposite sides as shown in fig. Observer hears no beats. If the frequency of the horn of the \( \operatorname{car} B \) is \( 504 H z, \) the frequency
of horn of car \( A \) will be :
A \( .529 .2 \mathrm{Hz} \)
в. \( 295.2 \mathrm{Hz} \)
с. \( 440.5 \mathrm{H} \)
D. none of these


An object is placed on the principal axis of a concave mirror at a distance of 60
\( \mathrm{cm} . \) If the focal length of the concave mirror is \( 40 \mathrm{cm} \) then the magnification obtained is equal to:
\( A \cdot 2 \)
B. 1.5
\( c \cdot 3 \)
\( D \)


Describe law of conservation of matter.


Why must the electrostatic potential
inside a hollow charged conductor be
the same at every point?


The specific heat capacity of water is
\( A .8 R \)
в. \( \frac{7}{8} R \)
c. \( 9 R \)
D. \( \frac{9}{7} R \)


\( \lim _{x \rightarrow \infty} 2 x(\sqrt{x^{2}+1}-x)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1 / 2 \)
\( c \cdot 0 \)
D. -


A racemic mixture has a net rotation:
A. to right of original plane
B. to left of original plane
C . to right or left of original plane
D. zero


Draw \( \angle P O Q \) of measure \( 75^{\circ} \) and find
its line of symmetry.


Which of the following statement is
correct?
A. All metals are ductile
B. All non-metals are ductile
c. Generally, metals are ductile.
D. Some non-metals are ductile


What is most general value of \( \theta \) which
satisfies both the equations. \( \sin \theta=-1 / 2 \) and \( \tan \theta=1 / \sqrt{3} \)


Solve: \( \cot \left(\cos e c^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right) \)
A \( \cdot \frac{6}{17} \)
в. \( \frac{3}{17} \)
c. \( \frac{4}{17} \)
D. \( \frac{5}{17} \)


Dimension of \( \frac{\text { magnetic flux }}{\text { electric flux }} \) are
\( \mathbf{A} \cdot\left[L T^{-1}\right] \)
B \cdot \( \left[T L^{-1}\right] \)
\( \mathbf{c} \cdot\left[L^{3} T^{2} A^{-2}\right] \)
D \cdot \( \left[L^{0} T^{0} A^{0}\right] \)


In a \( \Delta A B C \) the sides b and \( c \) are given.
If there is an error \( \Delta A \) in measuring
angle \( A, \) then the error \( \Delta a \) in side a is
given by
\( ^{\text {A }} \cdot \frac{S}{2 a} \Delta A \)
в. \( \frac{2 S}{a} \Delta A \)
\( c \cdot b c \sin A \Delta A \)
D. none of these


State : True or False
Heat required to raise the temperature
of 18 of substance through \( 1^{0} C \) is called
thermal capacity of a substance.


List -I
A. Reactive form of Carbon
HF
B. Acid employed for
Diamond
etching of glass
C. Synthesis gas
Charcoal
D. Unreactive form of Carbon
\( \boldsymbol{C O H}_{2} \)
The correct match with \( A B C D \) is \( ? \)
A. 1234
B. 2 4 31
\( c \cdot 2134 \)
D. 31 4 2


Assertion
Paramagnetic substances get weakly
attracted to a magnet.
Reason
They have tendency to move from a
region of strong magnetic field to weak
magnetic field.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Statement 1: Geostationary satellites may be setup in equatorial plane in orbits of any radius more than earth's
radius.

Statement 2: Geostationary satellites have period of revolution of 24 hrs.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True


Define RQ. Write a short note on RQ.


A long straight wire of radius R carries current \( i . \) The magnetic field inside the wire at distance \( r \) from its centre is
expresses as:
\( \mathbf{A} \cdot\left(\frac{\mu_{0} i}{\pi R^{2}}\right) \cdot r \)
в. \( \left(\frac{2 \mu_{0} i}{\pi R^{2}}\right) \cdot \pi \)
\( ^{\text {c. }}\left(\frac{\mu_{0} i}{2 \pi R^{2}}\right) \cdot r \)
D. \( \left(\frac{\mu_{0} i}{2 \pi R}\right) \cdot \)


Let \( \bar{\alpha}, \bar{\beta}, \bar{\gamma} \) be three vectors such that
\( \overline{\boldsymbol{\alpha}} \cdot(\overline{\boldsymbol{\beta}}+\bar{\gamma})+\overline{\boldsymbol{\beta}} \cdot(\bar{\gamma}+\overline{\boldsymbol{\alpha}})+\bar{\gamma} \)
\( (\bar{\alpha}+\bar{\beta})=\mathbf{0} \) and \( |\overline{\boldsymbol{\alpha}}|=\sqrt{\mathbf{3}},|\bar{\beta}|=\mathbf{2} \) and
\( |\bar{\gamma}|=\mathbf{3} \) then \( |\overline{\boldsymbol{\alpha}}+\overline{\boldsymbol{\beta}}+\bar{\gamma}| \) is
A \( . \sqrt{17} \)
B. 4
\( c .5 \)
D. \( \sqrt{15} \)


\( \boldsymbol{A}_{\text {organic }} \)Compound\( +\boldsymbol{O}_{2} \rightarrow \boldsymbol{X}+\boldsymbol{Y}+\boldsymbol{Z} \)
Compound \( (A) \) in pure form does not
give ppt. with \( A g N O_{3} \) solution. mixture containing \( 70 \% \) of \( (A) \) and \( 30 \% \) of ether is used as an anaesthetic.
Compound \( (X) \) and \( (Y) \) are oxides while \( (\mathrm{Z}) \) is a pungent smelling gas. \( (\mathrm{X} \) is a neutral oxide which turns cobalt
chloride paper pink. Compound (Y) turns lime water milky and produces an acidic solution with water. Compounds
\( (A),(X),(Y) \) and \( (Z) \) respectively will be :
A \( \cdot C H_{4}, H_{2} O, C O_{2}, C l \)
в. \( C H C l_{3}, H_{2} O, C O_{2}, C l_{2} \)
c. \( C H_{3} \) ОН \( , H_{2} \) О \( , \mathrm{CO}_{2}, \mathrm{N}_{2} \)
D. \( N H_{2} C O N H_{2}, H_{2} O, N_{2} O, C O_{2} \)


The diagonals of a rectangle are unequal in length.
A. True
B. False


As opposed to primary sexual characteristics, changes in secondary sexual characteristics are mostly evident in changes in
A. Reproductive capacity
B. The skeleton system
c. The circulatory system
D. External appearance


Second ionization enthalpy of Na is greater than that of Mg.
A. True
B. False


The diurnal rhythms are regulated by
A. Adrenalin
B. Melatonin
c. Serotonin
D. vasopressin


Nitrogen \( (z=7) \) is the element of group V of the periodic table. Which of the following is the atomic number of the next element in the group?
\( A \cdot 9 \)
B. 14
c. 15
D. 17


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{y}=\log \left(\boldsymbol{e}^{\boldsymbol{x}} \sin ^{\boldsymbol{5}} \boldsymbol{x}\right) \)


If \( y=\cos ^{-1}(\sqrt{x}), \) then find \( \frac{d y}{d x} \) using
first principle.
A \( \cdot-\frac{1}{\sqrt{1-x}} \)
в. \( \frac{1}{\sqrt{1-x}} \)
c. \( -\frac{1}{2 \sqrt{x} \sqrt{1-x}} \)
D. \( \frac{1}{2 \sqrt{x} \sqrt{1-x}} \)


Example for an improper fraction from the given options is
A \( \cdot \frac{25}{26} \)
в. \( \frac{12}{13} \)
c. \( \frac{15}{14} \)
D. \( \frac{19}{20} \)


If \( \vec{a} \) and \( \vec{b} \) are unit vectors then what is
the angle between \( \vec{a} \) and \( \vec{b} \) for \( \vec{a}-\sqrt{2 \vec{b}} \)
to be a unit vector?


The IUPAC name of the given structure
is :
A. 5-bromo-6-chloro-1-cyclohexen-3-yne
B. 6-bromo-5-chlorocyclohexen-3-yne
c. 6 -bromo-5-chloro-3-cyclohexen-1-yne
D. 4-bromo-3-chloro-1-cyclohexen-5-yne


Which polymer is used in non-stick cooking vessels?
A. Polythene
B. Isoprene
c. Teflon
D. Neoprene


Four lenses of focal length
\( +15 c m,+20 c m,+150 c m \) and
\( +250 c m \) are available for making an astronomical telescope. To produce the largest magnification, the focal length of the eyepiece should be
A \( .+15 \mathrm{cm} \)
B. +20 cm
\( \mathbf{c} .+150 \mathrm{cm} \)
D. \( +250 c m \)


Q Type your question-
\( x \)
ethanoate.
Melting \( \quad \) Boiling Compound Formula point / \( \quad \) point
0
\[
\text { methyl } \quad C_{3} H_{6} O_{2} \quad-98
\]
ethanoate
\[
\text { ethyl } \quad C_{4} H_{8} O_{2} \quad-84
\]
ethanoate
A student wished to separate a mixture
of methyl ethanoate and ethy
ethanoate which are miscible with one
another. The easiest method of
separating the two would be by:
A. placing the mixture in a separating funnel, allowing the denser liquid to settle to the bottom, and collecting this liquid from the funnel in the normal way
B. performing a fractional distillation, and collecting two liquids in different vessels
C. freezing the mixture, then allowing this solid to sublime the more volatile substance would be
collected first
D. adding the mixture to water and allowing the more soluble compound to dissolve, The other compound could then the removed by filtration


If a body is projected with a velocity of
\( 9.8 m / s \) making an angle of \( 45^{\circ} \) with the horizontal, then the range of the
projectile is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) )
\( \mathbf{A} \cdot 39.2 m \)
в. \( 9.8 m \)
\( \mathrm{c} .4 .9 \mathrm{m} \)
D. \( 19.6 m \)


A body is vibrating 7200 times in one minute. If the velocity of sound is 360 \( \mathrm{m} / \mathrm{s}, \) find (i) frequency of the vibration
in \( \mathrm{Hz}, \) (ii) the wavelength of the sound
produced.
A. \( 120 \mathrm{Hz}, 3 \mathrm{m} \)
в. \( 140 H z, 3 \) т
c. \( 120 H z, 4 m \)
D. \( 140 H z, 4 m \)


Evaluate \( : \quad I=\int \frac{x+9}{x^{2}+5} d x \)


Which of the following situations
correctly describes the similarity between an angiosperm egg and a human egg?
(i) Eggs of both are formed only once in
a lifetime.
(ii) Both the angiosperm egg and human egg are stationary.
(iii) Both the angiosperm egg and human egg are motile transported.
(iv) Syngamy in both results in the formation of zygote.

Choose the correct answer from the
options given below.
\( A \cdot \) (ii) and (iv)
B. (iv) only
c. (iii) and (iv)
D. (i) and (iv)


Aromatic hydrocarbons are :
A. saturated
B. unsaturated
C. both \( A \) and \( B \)
D. none of above


For a spontaneous process, entropy
A. Increases
B. Decreases
c. Unchanged
D. Not clear


The centre of the circle given by \( \mathbf{r} \cdot(\mathbf{i}+ \)
\( 2 \mathbf{j}+2 \mathbf{k})=15 \) and \( |\mathbf{r}-(\mathbf{j}+2 \mathbf{k})|=\mathbf{4} \)
A \( .(0,1,2) \)
в. (1,3,4)
c. (-1,3,4)
D. None of these


If it is known that a dimensionless
number significant in heat energy diffusion in case of convective heat transfer is given by \( \frac{A^{a} B}{C} \) then the value
of a is, (dimension of \( \boldsymbol{A}=\boldsymbol{M} \boldsymbol{L}^{2} \boldsymbol{T}^{-2} \boldsymbol{K}^{-1} \)
\( \left.B=L^{-1} T^{-1}, C=M L^{1} T^{-3} K^{-1}\right) \)
A . -
B. 2
\( c \)
\( D \cdot-2 \)


The specmc conductances in oh \( m^{-1} c m^{-1} \) of four electrolytes
\( P, Q, R \) and \( S \) are given in brackets:
\( P\left(5.0 \times 10^{-5}\right) \)
\( Q\left(7.0 \times 10^{-8}\right) \)
\( \boldsymbol{R}\left(\mathbf{1} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{1 0}}\right) \)
\( \boldsymbol{S}\left(\boldsymbol{9} \cdot \boldsymbol{2} \times \mathbf{1} \boldsymbol{0}^{\boldsymbol{3}}\right) \)
The one that offers highest resistance to the passage of electric current is:
A . \( P \)
в. \( Q \)
\( c . s \)
D. \( R \)


Using determinants show that points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}) \) and \( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \)
are col-linear.


A ball is thrown upward and reaches a height of 64 feet, its initial velocity
should be \( (\boldsymbol{g})=\mathbf{3} 2 \boldsymbol{f} \boldsymbol{t} / \boldsymbol{s e c}^{2} \)
A. \( (1) 64 f t / \) sec
в. \( (2) 72 f t / \) sec
c. \( (2) 32 f t / \) sec
D. \( (4) 4096 f t / \) sec


Portland cement is manufactured by using:
A. Limestone, clay and sand
B. Limestone, gypsum and sand
c. limestone, gypsum and alumina
D. limestone, clay and gypsum


What is the percentage change in the value of \( g \) on shifting from equator to poles on the Earth's surface? Difference in radius of Earth at poles
and equator is \( 21 \mathrm{km} \)
A . 4.5\%
B . 0.65\%
c. 0.05\%
D. 0.43\%


Find the solution of \( \frac{d y}{d x}=2^{y-x} \)


Explain with reason, sign convention of \( \Delta S \) in the following reaction.
\[
N_{2(g)}+3 H_{2(g)} \longrightarrow 2 N H_{3(g)}
\]


A small, magnetized sphere A of pole strength \( m \) is counter-poised by a pan in a balance. Another magnetised sphere B of the same mass as \( A \) is placed below \( A \) so that their centres are at a distance
\( 1 \mathrm{cm} . \) If \( \mathrm{A} \) and \( \mathrm{B} \) are unlike poles of same strength and to restore counter the weight in the pan is increased by \( 500 g m \) the pole strength of each sphere is:
A \( .1 .4 A m \)
B. \( 9.8 A m \)
c. \( 0.7 A m \)
D. \( 70 A m \)


Solve and verify your answer \( \frac{2}{21} x+8=x+6 \)


2 moles of \( P C l_{5} \) when heated in a
closed vessels of 2 litre capacity at
equilibrium \( 40 \% \) of \( P C l_{5} \) dissociated
in \( P C l_{3} \) and \( C l_{2} . \) What is the value of the equilibrium constant?
A. 0.267
B. 0.786
c. 0.345
D. 1.879


Heads of Lettuce are
A. Undeveloped inflorescence
B. Unopened flowers
c. Buds
D. Modified stems


What is meant by division algorithm
give example?


Calculate the formula unit mass (u) of
\( N a_{2} O \)
\( [\boldsymbol{N} \boldsymbol{a}=\mathbf{2 3}, \boldsymbol{O}=\mathbf{1 6}] \)
\( \mathbf{A} \cdot 60 \)
B. 62
c. 61
D. 59


Find the current in each branch


The magnetic flux linked with a coil, in webers, is given by the equation \( \phi= \)
\( 8 t^{2}-3 t+5 . \) Then the magnitude of
induced emf at 4 sec will be
A . 15 v
B . \( -61 \mathrm{v} \)
c. 13 v
D. 21 v


Write down the domain of the function
\( \csc ^{-1} x \)


Obtain an expression for equivalent capacitance when three capacitors \( C_{1}, C_{2} \) and \( C_{3} \) are connected in series.


\( Y \) in the given reaction is:
\( -\mathrm{Br} \frac{\text { ether }}{\mathrm{Mg}}>\mathrm{X} \frac{(\mathrm{i}) \mathrm{H}_{2} \mathrm{O}}{(\mathrm{ii}) \mathrm{HCl}}>\mathrm{Y}(\text { main product }) \)
A. hexane
B. cyclohexane
c. cyclohexylcyclohexane
D. cyclohexylether


What is the mean blood pressure in the
aorta?


is the ecosystem's response to the addition of artificial or natural
nutrients in water bodies.
A. Condensation
B. Eutrophication
c. Dispersion
D. Diffusion


Extraction of gold \( (A u) \) involves the
formation of complex ions ' \( X^{\prime} \) and ' \( Y \) '.
\[
\begin{array}{r}
\text { Gold ore } \frac{\text { Roasting }}{\mathbf{C N}^{-}, \mathbf{H}_{2} \mathbf{O}, \mathbf{O}_{2}} \text { , } \mathbf{H} \boldsymbol{O}^{-}+^{\prime} \\
\boldsymbol{Z} \boldsymbol{n} \quad \boldsymbol{Y}^{\prime}+\boldsymbol{A} \boldsymbol{u}
\end{array}
\]
\( X^{\prime} \) and ' \( Y^{\prime} \) are respectively
A \( \cdot A u(C N)_{2}^{-} \) and \( Z n(C N)_{4}^{2} \)
B . \( A u(C N)_{4}^{3-} \) and \( Z n(C N)_{4}^{2} \)
C \( \cdot \operatorname{Au}(C N)_{3}^{-} \) and \( Z n(C N)_{6}^{4} \)
D. \( A u(C N)_{4}^{-} \) and \( Z n(C N)_{3} \)


Which one will give nucleophilic
addition reaction?
A \( \cdot C H_{3} C H O \)
в. \( C H_{3} \) СОСН\( _{3} \)
c. \( C H_{2}=C H_{2} \)
D. \( C H_{3}-C H_{3} \)


Write the IUPAC name of the given
compound \( \boldsymbol{H}-\begin{array}{ccccc}\boldsymbol{H} & \boldsymbol{H} & \boldsymbol{H} & \boldsymbol{H} & \boldsymbol{H} \\ \boldsymbol{C} & - & \boldsymbol{C} & -\boldsymbol{C} & - & \boldsymbol{C} & -\boldsymbol{C} \\ \boldsymbol{H} & \boldsymbol{O} \boldsymbol{H} & \boldsymbol{H} & \boldsymbol{C H}_{3} & \boldsymbol{H}\end{array}-\boldsymbol{H} \)


Consider the following statements \( A \) and \( \mathrm{B} \) and identify the correct choice
A) For a given value of angle of incidence, the angle of deviation produced by a prism increases with increasing of refractive index of the prism
B) Angle of deviation produced by a thin prism is independent of angle of incidence
A. A is true and B is false
B. A is false and B is true
c. A and B are true
D. A and B are false


If \( x y=\tan ^{-1}(x y)+\cot ^{-1}(x y), \) then \( \frac{d y}{d x} \)
is equal to
A \( \cdot \frac{y}{x} \)
B. \( -\frac{y}{x} \)
c. \( \frac{x}{y} \)
D. \( -\frac{x}{y} \)


The valve present between the left auricle and left ventricle is
A. Tricuspid valve
B. Bicuspid valve
c. Mitral valve
D. Aortic valve


Flowering of Chrysanthemum is inhibited by
\( A \cdot \) IAA
в. \( G A_{3} \)
c. cytokinin
D. Ethylene


\( \mathrm{f} A=\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right] \) then find \( A^{-1} \)


If \( \boldsymbol{u}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 b} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{y}^{2}, \boldsymbol{u}^{\prime}=\boldsymbol{a}^{\prime} \boldsymbol{x}^{2}+ \)
\( 2 b^{\prime} x y+c^{\prime} y^{2}, \) then prove that
\( \left|\begin{array}{ccc}\boldsymbol{y}^{2} & -\boldsymbol{x} \boldsymbol{y} & \boldsymbol{x}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{\prime} & \boldsymbol{b}^{\prime} & \boldsymbol{c}^{\prime}\end{array}\right|= \)
\( \left|\begin{array}{cc}\boldsymbol{a x}+\boldsymbol{b y} & \boldsymbol{b x}+\boldsymbol{c y} \\ \boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y} & \boldsymbol{b}^{\prime} \boldsymbol{x}+\boldsymbol{c}^{\prime} \boldsymbol{y}\end{array}\right|= \)
\( -\frac{1}{y}\left|\begin{array}{cc}u & u^{\prime} \\ a x+b y & a^{\prime} x+b^{\prime} y\end{array}\right| \)


Initially, equation of ellipse was \( 3 x^{2}+ \)
\( 4 y^{2}=12 . \) Keeping major axis constant
ellipse is bulge to form circle (with major axis as diameter). Its eccentricity
changes at a rate \( 0.1 / \) sec. Time taken to form this circle is
A . 2 sec
B. 3 sec
c. 5 sec
D. 7 sec


A \( 3.0 k g \) lump of clay is moving to the
left at \( 4.0 m / s . \) It collides in a perfectly inelastic collision with a \( 6.0 k g \) lump of
clay moving to the right at \( 2.0 m / s \) What is the total kinetic energy after
the collision?
\( A \cdot 62 J \)
в. \( 36 J \)
c. \( 25 J \)
D. \( 12 . J \)
E . \( 0 . J \)


What is the correct order of size of \( \mathrm{Pd} \)
\( \mathrm{Pt}, \) Ni?


If \( \Delta S=\frac{q_{r e v}}{T}, \) then choose the incorrect
statement(s).
This question has multiple correct options
A. \( \Delta S \) is defined only for reversible process.
B. For irreversible process and same process taking place reversibly, \( \Delta S \) is same
C. \( \Delta S_{s y s} \) is always negative for irreversible process
D. None of the above


If \( y=\sin (\sin x), \) then prove that \( \frac{d^{2} y}{d x^{2}}+ \)
\( \tan x \frac{d y}{d x}+y \cos ^{2} x=0 \)


Draw a neat, labelled energy level diagram for H atom showing the transitions. Explain the series of spectral lines for H atom, whose fixed
inner orbit numbers are 3 and 4
respectively. The work functions for potassium and caesium are \( 2.25 \mathrm{eV} \) and
2.14eV respectively. Is the photoelectric effect possible for either of them if the
incident wavelength is \( 5180 A ? \) [Given: Planck's constant= 6.63 \( x \)
\( 10^{-34} \mathrm{J}_{. \mathrm{S}} \)
Velocity of light \( =3 \times 10^{8} m / s ; 1 e V= \)
\( \left.\mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{J}\right] \)


Two platinum electrodes were
immersed in a solution of \( C u S O_{4} \) and
electric current was passed through the solution. After some time, it was found
that colour of \( C u S O_{4} \) disappeared with evolution of gas at the electrode. The colorless solution contains:
A. Platinum sulphate
B. Copper hydroxide
c. copper sulphate
D. Sulphuric acid


Three vectors \( \vec{P}, \vec{Q}, \vec{R} \) are such that the \( |\overrightarrow{\boldsymbol{P}}|=|\overrightarrow{\boldsymbol{Q}}|,|\overrightarrow{\boldsymbol{R}}|=\sqrt{\mathbf{2}}|\overrightarrow{\boldsymbol{P}}| \) and \( \overrightarrow{\boldsymbol{P}}+\overrightarrow{\boldsymbol{Q}} \)
\( +\vec{R}=0 . \) The angle between \( \vec{P} \) and \( \vec{Q}, \vec{Q} \) and \( \vec{R} \) and \( \vec{P} \) and \( \vec{R} \) will be respectively.
B . \( 90^{\circ}, 45^{\circ} \), \( 45^{\circ} \)
c. \( 45^{\circ}, 90^{\circ}, 90^{\circ} \)
D . \( 45^{\circ}, 135^{\circ}, 135^{\circ} \)


A uniform disc of radius \( \boldsymbol{R}=\mathbf{0 . 2 m} \) kept
over a rough horizontal surface is given
velocity \( \omega_{0} . \) After some time its kinetic
energy becomes zero. If \( v_{0}=10 m / s \)
find \( \omega_{0} \)


In the process of plasmolysis
A. Endosmosis occurs
B. Exosmosis occurs
c. Imbibition occurs
D. Diffusion occurs


Write \( \frac{120 m^{2} n^{-3}}{60 m^{5} n^{-2}} \) in simplest form
using only positive exponents. Assume that \( m \neq 0 \) and \( n \neq 0 \)
A \( \cdot \frac{2 n}{m^{3}} \)
в. \( \frac{2}{m^{3} n} \)
c. \( \frac{2 m^{3}}{n} \)
D. \( \frac{1}{2 m^{3} n} \)


\( \int(\log x)^{2} d x= \)
A \( \cdot x\left[(\log x)^{2}-2 \log x+2\right]+c \)
B . \( x\left[(\log x)^{2}+2 \log x+2\right]+c \)
C \( \cdot\left[(\log x)^{2}-2 \log x+2\right]+c \)
D. \( \left[(\log x)^{2}+2 \log x+2\right]+c \)


In an SHM, restoring force is \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \)
where \( k \) is force constant, \( x \) is
displacement and \( A \) is the amplitude of motion, then the total energy depends
upon
A. \( k, A \) and \( M \)
в. \( k, x, M \)
\( c \cdot k, A \)
D. \( k, x \)


\( 68 \% H N O_{3} \) and \( 32 \% H_{2} O \) by mass forms:
A. Maximum boiling azeotrope
B. Minimum boiling azeotrope
C. mixture which shows positive deviation
D. Ideal solution


Which of the following statements
about the autotrophs is incorrect?
A. They synthesise carbohydrates from carbon dioxide and water in the presence of sunlight and chlorophyll.
B. They store carbohydrates in the form of starch.
C. They convert carbon dioxide and water into carbohydrates in the absence of sunlight.
D. They constitute the first trophic level in food chains.


The number of lines of atomic hydrogen
spectrum fall within the wavelength
range from 94.5 to 130.0 nm is:


A wave is associated with matter when
it is:
A. stationary
B. in motion with a velocity
C. in motion with velocity of light
D. in motion with velocity greater than that of light


The self-inductance of an air core
solenoid of 100 turns is 1 m \( H \). The self-
inductance of another Solenoid of 50
turns (with the same length and crosssectional area) with a core having relative permeability 500 is
A . \( 125 \mathrm{mH} \)
B. 24 mH
c. \( 60 \mathrm{mH} \)
D. 30 mH
E. \( 45 \mathrm{mH} \)


A green plant turns pale, when transferred to prolonged darkness. It represents a phenomenon called as
A. Etiolation
B. Chlorosis
c. cytorrhisis
D. Paleolation


Which one of the following is most probably not a case of uniform circular
motion?
A. Motion of a racing car on a circular track
B. Motion of the moon around the earth
c. Motion of a toy train on a circular track
D. Motion of seconds hand on the circular dial of a watch


The last structure to be reached by a tracer substance injected into a
patient's superior vena cava before leaving heart is
A. Right ventricle
B. Left ventricle
c. Pulmonary veins
D. Left atrium
E. Right atrium


The highest number of species among the following belong to :
A. Fungi
B. Mosses
c. Algae
D. Lichens


The bond, that exists in a
semiconductor is
A. covalent bond
B. ionic bond
c. metalic bond
D. hydrogen bond


When a bucket is half full, the weight of
the bucket and the water is 10 kg. When the bucket is two-thirds full, the total
weight is 11 kg. What is the total weight, in kg, when the bucket is completely full?
A . 12
в. \( 12 \frac{1}{2} \)
\( c \cdot_{12} \frac{2}{3} \)
D. 13


A man travelling east at \( 8 \mathrm{km} \) per hour
find that the wind seems to blow
directly from the north. On doubling the speed, he finds that it appears to come from N-E. Find the velocity of the wind and it's direction.
A. \( 8 \sqrt{2} \), its direction is from \( N-S \). . Its direction is
B. \( 8 \sqrt{2} \), its direction is from \( N-w \)
c. \( 8 \sqrt{2} \), its direction is from s-w.
D. None of these


Diarrheal disease control program was
started in
A. 1995
B. 2005.
c. 1978
D. 1969.


A charged particle of mass \( 5 \times 10^{-6} \mathrm{kg} \) is
held stationary in space by placing it in an electric field of strength \( 10^{6} N / C \)
directed vertically downwards. The charge on the particle is: \( \left(g=10 m / s^{2}\right) \)
A. \( -20 \times 10^{-5} \mu C \)
B. \( -5 \times 10^{-5} \mu C \)
c. \( 5 \times 10^{-5} \mu C \)
D. \( 20 \times 10^{-5} \mu C \)


Give an example each for (a) Artificial sweetening agents
(b) Narcotic
analgesics.


Which of the following kind of energy depends upon the mass and the square of speed of a body?
A. Kinetic
B. Potential
c. Electrostatic
D. Nuclear


The formula \( V=I R \) is applicable to
A. Ohmic conductors only
B. Non ohmic conductors only
c. Both Ohmic \& Non ohmic conductors
D. Neither ohmic nor non ohmic conductors


Consider the following statements:
i) Atomic hydrogen is obtained by passing hydrogen through an electric
arc.
ii) Hydrogen gas will not reduce heated aluminium oxide.
iii) Finely divided palladium absorbs large volume of hydrogen gas.
iv) Pure nascent hydrogen is best
obtained by reacting \( N a \) with \( C_{2} H_{5} O H \)
Which of the above statement(s) is/are
correct?
A. i only
B. ii only
c. i, ii and iii
D. ii, iii and iv


Where SONARs are fitted?
A. Over ships and submarines
B. Below ships and submarines
C. Beside ships and submarines
D. none


Which of the following element is
responsible for oxidation of water to \( O_{2} \)
is biological processes?
\( A \cdot F e \)
B. cu
c. мn
D. Mo


A body starts from rest and is uniformly
accelerated. for 30 s. The distance
travelled in the first 10 s is \( x_{1}, \) next 10 s
is \( x_{2} \) and the last 10 s is \( x_{3} . \) Then \( x_{1} \)
\( x_{2}: x_{3} \) is the same as
A .1: 2: 4
B. 1: 2: 5
\( c \cdot 1: 3: 5 \)
\( D \cdot 1: 3: 9 \)


Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe
circular paths of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} . \) Then
the ratio of their respective masses
\( \left(M_{1} / M_{2}\right) \) is
\( \mathbf{A} \cdot R_{1} / R_{2} \)
B. \( \left(R_{1} / R_{2}\right)^{2} \)
c. \( \left(R_{2} / R_{1}\right) \)
as
D. \( \left(R_{2} / R_{1}\right)^{2} \)


In which of the following reactions, the oxidation state of nitrogen is not changed?
A . Action of very dilute \( H N O_{3} \) on magnesium.
B. Action of dilute \( H N O_{3} \) on zinc.
c. Action of conc. \( H N O_{3} \) on copper.
D. Action of very dilute \( H N O_{3} \) on zinc.


Given the matrices
\[
\begin{array}{l}
\boldsymbol{A}=\left[\begin{array}{lll}
2 & 1 & 1 \\
3 & -1 & 0 \\
0 & 2 & 4
\end{array}\right], B=\left[\begin{array}{lll}
9 & 7 & -1 \\
3 & 5 & 4 \\
2 & 1 & 6
\end{array}\right] \\
\text { and } \boldsymbol{C}=\left[\begin{array}{lll}
2 & -4 & 3 \\
1 & -1 & 0 \\
9 & 4 & 5
\end{array}\right]
\end{array}
\]
Verify that \( (\boldsymbol{A}+\boldsymbol{B})+\boldsymbol{C}=\boldsymbol{A}+(\boldsymbol{B}+ \)
\( C) \)


Which statements are correct?
This question has multiple correct options
A. Bond energy of \( C \equiv O \) and \( N \equiv N \) are respectively
1070 and \( 946 k J \) mol\( ^{-1} \)
B. \( C O \) has resonating structure but \( N_{2} \) not
C. Bond order of both \( C O \) and \( N_{2} \) is three
D. Bond order of both \( C O^{+} \) and \( N_{2}^{+} \) are same


Assertion
Ethanol boils at lower temperature than
ethane.
Reason
The molecular weight of ethanol is
higher than that of ethane.
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


Frequency of variation of kinetic energy of a simple harmonic motion of
frequency n is
A . \( 2 n \)
в. \( n \)
\( c \cdot \frac{n}{2} \)
D. 3 n


Natural fibres can be defined as:
A. substances produced by plants and animals
B. man-made fibres produced industrially
C . synthetic fibres
D. none of the above


Draw the circuit diagram of a voltage regulator using zener diode.


Evaluate :
\( \mathbf{4} \mathbf{9} \times(-\mathbf{9 7}) \)


Assertion
The \( Q_{c} \) for the reaction:
\( 2 S O_{2}(g)+O_{2}(g) \leftrightharpoons 2 S O_{3}(g) \) is \( Q_{c}= \)
\( \frac{\left[\boldsymbol{S O}_{3}\right]^{2}}{\left[\boldsymbol{S O}_{2}\right]^{2}\left[\boldsymbol{O}_{2}\right]} \)
Reason
When \( Q_{c}<K_{c}, \) the reaction is not at
equilibrium and it will fast in backward direction.
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


Find \( \left|\begin{array}{lll}\mathbf{4} & \mathbf{6} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} & \mathbf{9} \\ \mathbf{7} & \mathbf{1} & \mathbf{5}\end{array}\right| \)


Which out of the following is used for making disposable cups?
A. LDFE
B. PS
\( c \cdot P P \)
D. PVC


Calculate the osmotic pressure at \( 25^{\circ} \mathrm{C} \) of a solution containing 1 g of glucose and 1 g of sucrose in 1 litre of solution. If it were not known that the solute was
a mixture of glucose and sucrose, what would be the molecular weight of solute corresponding to the calculated osmotic pressure?


If \( A, B \) and \( C \) are three events such that
\( \boldsymbol{P}(\boldsymbol{B})=\frac{1}{2} ; \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C}^{\prime}\right)=\frac{1}{3} \) and
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B} \cap \boldsymbol{C}^{\prime}\right)=\frac{1}{336} \operatorname{then} \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C}) \) is
equal to \( \dots \)
A \( \cdot \frac{328}{2016} \)
в. \( \frac{330}{2016} \)
c. \( \frac{324}{2016} \)
D. \( \frac{320}{2016} \)


An iron sphere of mass \( 10 \mathrm{kg} \) has the
same diameter as an
aluminium sphere of mass is \( 3.5 \mathrm{kg} \) Both spheres are dropped simultaneously from a tower. When they are \( 10 \mathrm{m} \) above the ground, they have
the same
A. acceleration
B. momenta
c. potential energy
D. kinetic energy


Absolute scale of temperature is known
as (Celsius scale, Kelvin scale)


Find the \( A M, G M \) and \( H M \) between 12
and 30


\( C a\left(H C O_{3}\right)_{2} \) and \( C a(O H)_{2} \) cannot be stored in the same vessel.
If true enter 1 , else enter 0 .


If a ray of light incident on a plane mirror is such that it makes an angle of
\( 30^{\circ} \) with the mirror, then the angle of
reflection is
\( A \cdot 30 \)
B . 45
\( c .55 \)
D. \( 60^{\circ} \)


The angle of elevation of the top of a building from the foot of the tower is 30
and the angle of elevation of the top of
the tower from the foot of the building is
\( 60^{\circ} . \) If the tower is 48 meters high, find
the height of the building (in \( \mathrm{m} \).)


The maximum amount of electrical
energy that can be obtained from one
mole of \( N_{2} O_{3} \) is :
\( \mathbf{A} \cdot-245.11 k J \)
B. -125.10kJ
c . \( -255.43 k J \)
D. None of these


If for a binomial distribution \( \bar{x}=\frac{6}{5} \) and the difference between mean and variance is \( \frac{6}{25} . \) The number of trials is
A . 8
B. 7
\( c .6 \)
D.


The term infinite dilution refers when:
A. \( \alpha \rightarrow 1 \), for weak electrolytes
B. an electrolyte is 100\% dissociated
c. all interionic effects disappears
D. all of the above


\( \mathrm{cm} \) and having a resistance of 0.2 ohm
is allowed to slide over two paralle
thick metallic rails with uniform
velocity of \( 0.2 \mathrm{m} / \mathrm{s} \) as shown in the
figure. The rails are situated in a
horizontal plane. If the horizontal
component of earth's magnetic field is
\( 0.3 \times 10^{-4} \mathrm{T} \) and a steady state current
of \( 3 \mu A \) is induced through the rod. The
angle of dip will be :
A \( \cdot \tan ^{-1}\left(\frac{3}{4}\right) \)
B. \( \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{3}) \)
D \( \tan ^{-1}\left(\frac{1}{3}\right) \)


Long refractory period is found in
A. White fibres of skeletal muscle
B. Red fibres of skeletal muscle
c. Smooth muscle
D. cardiac muscle


Two opposite forces \( F_{1}=120 N \) and
\( F_{2}=80 N \) act on an elastic plank of
modulus of elasticity \( \boldsymbol{Y}=\boldsymbol{2} \times \)
\( 10^{11} N m^{2} \) and length \( l=1 m \) placed
over a smooth horizontal surface. The
cross-sectional area of the planck is \( S=0.5 m^{2}, \) the change in length of the
plank is \( \boldsymbol{x} \times \mathbf{1 0}^{-9} \boldsymbol{m} \)
A . 1.0
B. 1.5
c. \( 1 . \)
D. 1.


Which of the following defines the effect of deforestation on environment?
A . Level of \( \mathrm{CO}_{2} \) in the atmosphere will rise
B. Global warming
c. Both A and B
D. None of the above


Determine graphically the minimum value of the objective function \( Z=50 x+20 y \ldots(1) \)
subject to the constraints:
\( 2 x y \geq 5 \dots(2) \)
\( \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{3} \dots(\mathbf{3}) \)
\( 2 x-3 y \leq 12 \dots(4) \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \ldots(\mathbf{5}) \)


Show that if \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \)
are \( 1-1, \) then \( g o f: A \rightarrow C \) is also 1
\( \mathbf{1} \)


The species undergoin disproportionation is:
\( \mathbf{A} \cdot B r O_{4}^{-} \)
B. \( B r O_{3}^{-} \)
\( \mathbf{c} \cdot H B r O \)
\( \mathbf{D} \cdot B r \)


The study of teeth is called as
A. Dentistry
B. Dermatology
c. Neurology
D. Cardiology


Write balanced chemical equations for
the reaction of a burning of aluminum
in the air.


Amongst the elements \( \mathrm{B} \), Al, \( \mathrm{C} \) and \( \mathrm{Si} \),
the element having most metallic character is:
\( A \cdot A \)
B.
\( c . \) в
D. si


The body cells in Cockroach discharge their nitrogenous waste in haemolymph mainly in the form of
\( A \). Ammonia
B. Potassium urate
c. urea
D. Calcium carbonate


What is the percentage of calcium in
calcium carbonate \( \left(\boldsymbol{C a} \boldsymbol{C O}_{3}\right) \) ?
A . 30\%
B. 40\%
c. 50\%
D. 60\%


The repository of plant taxonomy and systematics is
A. Red data book
B. Herbarium
c. Botanical garden
D. Genomic library


Milk is an example of:
A. emulsion
B. suspension
c. foam
D. sol


The unit of magnification is:
\( \mathbf{A} \cdot \mathbf{m} \)
В \( \cdot m^{2} \)
\( \mathrm{c} \cdot m^{-1} \)
D. None of these


The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double slit experiment is :
A . infinite
B. five
c. three
D. zero


Most of the radio active elements are
present in
A. Lanthanoids
B. Actinoids
c. Representative elements
D. Second transition series


Fraunh offer line of the solar system is an example of:
A. line absorption specturm
B. emission of line system
c. line emission spectrum
D. emission of band spectrum


Hydrogen chloride was first prepared
from:
A. ammonia and potassium chloride
B. rock salt and concentrated sulphuric acid
C . potassium ferrate and ammonium chloride
D. zinc chloride and sulphuric acid


A piston of cross-sectional area
\( 100 \mathrm{cm}^{2} \) is used in a hydraulic press to
exert a force of \( 10^{7} \) dyne on the water. The cross sectional area of the other
piston which supports an object having a mass of \( 2000 \mathrm{kg} \) is
A \( \cdot 100 \mathrm{cm}^{2} \)
B. \( 10^{9} \mathrm{cm}^{2} \)
c. \( 2 \times 10^{4} \mathrm{cm}^{2} \)
D. \( 2 \times 10^{10} \mathrm{cm}^{2} \)


In hydrogen atom, energy of first excited state is \( -3.4 e V . \) Then find out the \( K E \)
of the same orbit of hydrogen atom.
A. +3.4 eV
B. \( +6.8 e V \)
c. \( -13.6 e V \)
D. \( +13.6 e V \)


If \( x \) is the temperature \( \left(\text { in }^{\circ} C\right) \) at which
liquid \( H_{2} O \) will be in equilibrium with its vapours \( (\Delta H \quad \text { and } \quad \Delta S \) for vaporization are \( 40.7 k J m o l^{-1} \) and \( \left.0.11 k J m o l^{-1} K^{-1} \text {respectively }\right), \) then \( x \) is:


A given resistor cannot carry currents exceeding 20 A, without exceeding its maximum power dissipation ratings. By forced air cooling suppose that we increase the rate at which heat can be
carried by a factor of \( 2 . \) Now the maximum current that the resistor can
carry is
A. \( 10 A \)
В. \( 20 \sqrt{2} A \)
\( c \cdot 30 \sqrt{2} A \)
D. \( 40 A \)


A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface
is:
A \( \cdot \frac{E}{c} \)
в. \( \frac{2 E}{c} \)
c. \( E c \)
D. \( \frac{E}{c^{2}} \)


Nitrogen gas is absorbed by :
A. Aluminium carbide
B. Calcium carbide
C. Ferrous sulphate
D. Calcium hydroxide


If a simple pendulum of length L has maximum angular displacement \( \boldsymbol{\theta} \) then the maximum kinetic energy of the
bob of mass \( \mathrm{m} \) is
A \( \cdot \frac{1}{2} m(L / g) \)
В. \( m g L(1-\cos \theta) \)
c. \( (m g L \sin \theta) / 2 \)
D. \( m g / 2 L \)


The energy possessed by wind is:
A. kinetic energy
B. potential energy
c. thermal energy
D. sound energy


Which of the following compounds may give blood red colouration while performing Lassaigne's test for nitrogen? This question has multiple correct options
A. \( \left(N H_{2}\right)_{2} C O \)
в. \( \left(N H_{2}\right)_{2} C=S \)
c. \( p-N H_{2} C_{6} H_{4} S O_{3} H \)
D. \( C_{6} H_{5} S O_{3} H \)


State whether the following sequence is
an A.P. or not:
\( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots \)


Knots in stems are formed due to
A. Tumors formed due to bacterial infection of wounds.
B. Outgrowth of secondary tissue over wounds.
C. Injury caused by insects.
D. None of the above.


(iii) If \( f^{\prime \prime}(x)<0 \forall x \epsilon(a, b) \) and \( (c, f(c)) \)
is a point lying on the curve \( y=f(x) \)
where \( a<c<b \) and for that value of
\( c, F(c) \) has a maximum, then \( f^{\prime}(c) \)
equals
A \( \cdot \frac{f(b)-f(a)}{b-a} \)
в. \( \frac{2}{b-a}\{f(b)-f(a)\} \)
c. \( \frac{2 f(b)-f(a)}{2 b-a} \)
D.


If \( f(x)=\log \left(\frac{x^{2}+a b}{x(a+b)}\right), \) then the
value of \( ^{\prime} C^{\prime} \) for which \( f^{\prime}(c)=0 \) in \( [a, b] \)
\( \mathbf{A} \cdot C=\pm \sqrt{\frac{a}{b}} \)
B. \( C=\pm \sqrt{a b} \)
\( ^{c} \cdot c=\pm \sqrt{\frac{b}{a}} \)
D. none of these


Find the moment \( t_{0} \) at which the velocity vector forms an angle \( \frac{\pi}{4} \) with the acceleration vector.
A \( t_{0}=\frac{1}{3 \alpha} \)
в. \( t_{0}=\frac{2}{\alpha} \)
c. \( _{t_{0}}=\frac{3}{\alpha} \)
D \( t_{0}=\frac{1}{\alpha} \)


(a) Ethanoic acid reacts with ethanol in
the presence of concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(i) Name the organic product formed.
(ii) Give the name of the reaction.
(iii) What is the role of \( H_{2} S O_{4} \) in the
above reaction?
(b) The molecular formula of an organic
compound is \( C H_{3} C O O H \)
(i) Write the IUPAC name of this
compound.
(ii) Give one use of this compound.


Which statement is correct about the
following reaction?
\( \mathrm{ZnO}+\mathrm{CO} \rightarrow \mathrm{Zn}+\mathrm{CO}_{2} \)
A. zno is being oxidized
B. co is being reduced
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is being oxidized
D. zno is being reduced


A member of Class Chlorophyceae is
A. Chlamydomonas
B. Volvox
c. Ulothrix
D. all of these


Solve the differential equation:
\( \frac{d y}{d x}=\frac{x^{2}-y^{2}}{2 x y} \)


The \( T S A \) of cube \( =726 \mathrm{cm}^{2} \) find the
edge.


Which of the following metals (s) is/are commercially extracted by self reduction method from their
corresponding ore? This question has multiple correct options
A. \( C u \)
в. \( F e \)
c. \( P b \)
D. \( H g \)


Complement angle of
A . \( 77.4^{\circ} \)
B .67 .3
\( c \cdot 76.3^{\circ} \)
D. \( 77.3^{\circ} \)


A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass number 80 and 120
If binding energy per nucleon for parent atom is 6.5 MeV and for daughter nucle
is \( 7 \mathrm{MeV} \) and \( 8 \mathrm{MeV} \) respectively, then the energy released in the decay is \( X \times \)
\( 110 M e V \).Find the value of \( X \)
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
\( D \)


Strong electrolyte of the following is?
\( \mathbf{A} \cdot 01 M H A c \)
в. \( 0.1 \mathrm{M} \) НС\( l \)
c. \( 0.1 M \) KCl
D. \( 0.1 M \) NaCl


The smallest ketone and its next
homologue are reacted with \( \mathrm{NH}_{2} \mathrm{OH} \) to form oximes. Which of the following statement is true?
A. Two different oximes are formed
B. Three different oximes are formed
c. Two oximes are optically active
D. All oximes are optically active


The following equation is a qudratic equation.
\( 16 x^{2}-3=(2 x+5)(5 x-3) \)
A. True
B. False


Which of the following sequence is correct for decreasing order of ionic
radius?
A \( \cdot S e^{-2}, I^{-}, B r^{-}, O^{-2}, F^{-} \)
B . \( I^{-}, S e^{-2}, O^{-2}, B r^{-}, F^{-} \)
c. \( S e^{-2}, I^{-}, B r^{-}, F^{-}, O^{-2} \)
D. \( I^{-}, S e^{-2}, B r^{-}, O^{-2}, F^{-} \)


Three shots are fired at a target in
succession. The probabilities of a hit in the first shot is \( \frac{1}{2}, \) in the second \( \frac{2}{3} \) and in the third shot is \( \frac{3}{4}, \) In case of exactly one hit, the probability of destroying the target is \( \frac{1}{3} \) and in the case of exactly two hits \( \frac{7}{11} \) an in the case of three hits is \( 1.0 . \) Find the probability of destroying the target in three shots
\( A \cdot 3 \)
\( \overline{4} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{5}{8} \)
D. 4


The \( \operatorname{set} A=x:|2 x+3|<7 \) is equal to
A. \( -10<2 x<4 \)
в. \( -11<2 x<4 \)
c. \( -12<2 x<4 \)
D. \( -13<2 x<4 \)


Very short answer type. From the following description of teeth pattern, give the likely feeding habit of the animal to which it belongs: incisors, well developed canines, sharply cusped
premolars, and reduced numbers of molars.


Total number of inner transition
elements in the periodic table is:
A . 10
B. 14
\( c \cdot 28 \)
D. 30


un tne basıs or Ivlenaeleevs rerıoaıc
Table given below, answer the question
that follow the table:
Ref. image
Besides gallium, which two other
elements have since been discovered
for which Mendeleev had left gaps in his
Periodic Table? Using atomic masses of
Li,NaLi,Na, find the average atomic
mass of and compare it with the atomic
mass of. State the conclusion drawn
from this activity.


The total number of electrons present in \( 18 m L \text { water (density } 1 g / m L) \) is:
A. \( 6.023 \times 10^{23} \)
В. \( 6.023 \times 10^{24} \)
c. \( 6.023 \times 10^{25} \)
D. \( 6.023 \times 10^{21} \)


If \( \boldsymbol{P}=(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{Q}=(\mathbf{3}, \mathbf{6}, \mathbf{9}) \) and \( \boldsymbol{R} \) is a
point of trisection of \( \boldsymbol{P Q}, \) then \( \boldsymbol{R}_{\boldsymbol{y}}= \)
\( A \cdot \frac{4}{3} \)
B . 2
\( c .3 \)
D.


A small compass needle of magnetic moment ' \( m^{\prime} \) is free to turn about an axis
perpendicular to the direction of
uniform magnetic field 'B'. The moment of inertia of the needle about the axis is
I'. The needle is slightly disturbed from its stable position and then released. Prove that it executes simple harmonic motion. Hence deduce the expression for its time period.


Define scattering of light.


In a zero-order reaction, if the initial
concentration of the reactant is
doubled, the time required for half the reactant to be consumed:
A. increases two-fold
B. increases four-fold
c. decreases by half
D. does not change


Two \( \pi \) and half \( \sigma \) bonds are present in:
A \( \cdot N_{2}^{+} \)
в. \( N_{2} \)
\( c \cdot O_{2}^{+} \)
D. \( O_{2} \)


A person can see only the objects placed between \( 1.2 m \) and \( 5 m . \) Explain this defect and what is the nature and power of lens used to correct this defect?


Prove that \( \frac{\boldsymbol{n}_{2}}{\boldsymbol{v}}-\frac{\boldsymbol{n}_{1}}{\boldsymbol{u}}=\frac{\boldsymbol{n}_{2}-\boldsymbol{n}_{1}}{\boldsymbol{R}} \)
When refraction occurs of a convex
spherical refracting surface and the ray travels from rearer to denser medium


Find the square root of the following number by division method: 28224


A. Antimony trisulphide
B. Glass powder
C. Potassium chlorate
D. Red phosphorus The head of a modern safety match
stick contains
A. A and
B. B and C
\( c \cdot c \) and \( D \)
D. c and A


Fill in the blanks
Myopia can be corrected by using lens.


Aluminium is more reactive than iron.
But aluminium is less easily corroded than iron because:
A. aluminium is a noble metal
B. oxygen forms a protective oxide layer on aluminium surface
C. iron unergoes reaction easily with water
D. iron forms both mono and divalent ions


If \( f \) is even function and \( g \) is an odd
function, then \( f_{o} g \) is \( \ldots \). What fun.
A. Even
B. Odd
C. Neither even nor odd
D. Either even


Reaction of \( \boldsymbol{R}-\mathbf{2}- \) butanol with \( \boldsymbol{p}- \)
toluenesulphonyl chloride in pyridine followed by reaction with \( L i B r \) gives:
A. \( R-1 \) -butyl bromide
B. \( R-2 \) -butyl tosylare
c. \( R-1 \) -butyl tosylate
D. \( R-2 \) -butyl bromide


The length of a wire increases by \( 1 \% \) on loading a \( 2 k g \) weight on it. Calculate the linear strain in the wire.


The path of a charged particle moving in
a magnetic field can be a :
This question has multiple correct options
A. Straight line
B. Circle
c. Parabola
D. Helix


A certain compound on burning in air forms three oxides. One of the oxides
turned lime water milky, the other
turned anhydrous \( C u S O_{4} \) blue and
third formed a solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{9} \)
Compound is formed of :
A. \( S, N \) and \( H \)
B. \( S, N \) and \( C \)
c. \( s, c \) and \( H \)
D. \( S, H \) and \( N a \)


A circular plane sheet of radius \( 10 \mathrm{cm} \) is
placed in a uniform electric field of \( \mathbf{5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \quad \mathbf{C}^{-1}, \) making an angle of \( \mathbf{6 0}^{\mathbf{0}} \)
with field. The electric flux through the sheet is
\( \begin{array}{lll}\text { A } \cdot 1.36 \times 10^{2} N & \text { m }^{2} & C^{-1}\end{array} \)
B . \( 1.36 \times 10^{4} N \quad m^{2} \quad C^{-1} \)
\( \begin{array}{lll}\text { С } \cdot 0.515 \times 10^{2} N & \text { m }^{2} & C^{-1}\end{array} \)
\( \begin{array}{lll}\text { D. } 0.515 \times 10^{4} N & \text { m }^{2} & C^{-1}\end{array} \)


Aspirin has the formula \( C_{9} H_{8} O_{4} \)
Number of moles of aspirin in a tablet weighing \( 500 \mathrm{mg} \) is \( x \times 10^{-5} . \) Then, the
value of \( x \) is


\( f(x)=x^{4}-3 x^{2}+4 \) in the interval [-4
4]. Is Rolle's theorem applicable?


Find the coordinates of the focus axis of
the parabola the equation of directrix and the length of the latus rectum for \( y \) \( 2=10 x \)


The catalytic activity of transition metals and their compounds is ascribed mainly to:
A. their unfilled d-orbitals
B. their ability of adopt variable oxidation states
c. their chemical reactivity
D. their magnetic behaviour


The total number of matrices formed
with the help of 6 different numbers are
\( \mathbf{A} \cdot \mathbf{6} \)
в. \( 6 ! \)
c. \( 2(6 !) \)
D. \( 4(6 !) \)


The optical path of a monochromatic light is the same if it goes through 2.00 \( \mathrm{cm} \) of glass or \( \mathrm{x} \mathrm{cm} \) of ruby. If the refractive index of glass is 1.510 and that of ruby is 1.760 find the value of \( x \)
is
\( \mathbf{A} \cdot 1.716 \)
B. 1.525
c. 2.716
D. 2.525


Calculate the electrode potential of the
electode
\( Z n / Z n^{2+}(\text {conc.}=0.1 M) \) at \( 25^{\circ} C \)
Given that \( \boldsymbol{E}_{Z n, Z n^{2+}}^{\circ}=\mathbf{0 . 7 6 1 8} \) volt.


Biological importance of ozone layer is:
A. ozone layer stops ultraviolet rays
B. ozone layer reduces green house effect
C. ozone layer reflects radio waves
D. ozone layer controls \( O_{2} / H_{2} \) radio in atmosphere


When the resistivity of all pure metals increases, then the temperature will :
A. decrease
B. increase
c. remain constant
D. first decrease and then increase


The phenomenon of uptake of water at
the expense of energy by the cell and usually against the osmotic gradient is
known as
A. Active absorption
B. Passive absorption
c. osmosis
D. Diffusion


Two bodies \( A \) and \( B \) are said to be in
thermal equilibrium with each other, if :
A. heat flows from A to B
B. heat flows from B to A
c. both the bodies lose equal amounts of heat to the atmosphere
D. heat does not flow from either A or B


An electric dipole has the magnitude of its charge as \( q \) and its dipole moment is
p. It is placed in a uniform electric field
E. If its dipole moment is along the direction of the field, the force on it and
its potential energy are respectively:
A. q. E and p. E
B. zero and minimum
c. q. E and maximum
D. 2q. E and minimum


If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{m} \sin ^{-1} \boldsymbol{x}} \)
Then \( \left(1-x^{2}\right)\left(\frac{d y}{d x}\right)^{2}=A y^{2}, \) then \( A= \)
?
A . \( m \)
B. \( -m \)
\( \mathrm{c} \cdot m^{2} \)
D. \( -m^{2} \)


The Poissons ratio of a material is \( 0.4 . \) If
a force is applied to a wire of this material, there is a decrease of the
cross-sectional area by \( 2 \% \). The percentage increase in its length is
A . \( 3 \% \)
в. 2.5\%
c. \( 1 \% \)
D. 0.5\%


A ball is projected from the ground at an
angled of \( 45^{\circ} \) with the horizontal surface. It reaches a maximum height of \( 120 \mathrm{m} \) and returns to the ground.
Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of
\( 30^{\circ} \) with the horizontal surface. The
maximum height it reaches after the bounce, in metres, is


Newton's Third law is equivalent to the:
A. law of conservation of linear momentum
B. law of conservation of angular momentum
C. law of conservation of energy
D. law of conservation of energy and mass


Evaluate
\( 12(2 x-3 y)^{2}-16(3 y-2 x) \)


The value of \( \sum_{r=0}^{n-1}^{n} C_{r} /\left(^{n} C_{r}+^{n} C_{r+1}\right) \)
equals
\( \mathbf{A} \cdot n+1 \)
в. \( n / 2 \)
\( \mathbf{c} \cdot n+2 \)
D. none of these


Two digits are formed from the digits
0,1,2,3,4 where digits are not repeated. Find the probability of the events that the number so formed is an
even number.


The act of breathing air into the body with the help of lungs is called
A. Ingestion
B. Inhalation
c. Exhalation
D. Absorption


Find the rate of change of the area of a
circle with respect to its radius \( r, \) when
\( \boldsymbol{r}=\mathbf{5} \mathrm{cm} \)


Which of the following gives off a purple vapour when sublimes?
A. Sodium hydroxide, NaOH(s)
B. Graphite, c(s)
c. Iron(III) chloride, \( F e C l_{3}(s) \)
D. sucrose, \( C_{12} H_{22} O_{11} \) (s)
E . lodine, \( I_{2} \) (s)


Interhalogen compounds are more reactive than the individual halogens because:
A. they are prepared by direct combination of halogens
B. X-X' bond is weaker than X-X or X '-X' bonds
c. they are thermally more stable than halogens
D. there is a large difference in their electronegativity


What should be the density of an aqueous solution of urea
\( (\text {molarmass}=\mathbf{6 0} \boldsymbol{g} / \text { mol}) \) such that
the molarity and molarity of the solution become equal?
A. \( 16.0 g / m l \)
в. \( 1.6 g / m l \)
c. \( 1.06 g / m l \)
D. \( 1.16 g / m l \)


How many X chromosomes are present in a male?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


The vertical component of the earth's
magnetic field is zero at a place where the angle of the dip is :
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A man of mass \( 60 \mathrm{kg} \), standing on a platform, is executing SHM in a vertical plane. The displacement from mean position is \( y=0.5 \sin (2 \pi t) . \) The
minimum value of frequency ( \( f \) ) for
which the man will feel weightlessness at the highest point is :
A \( \cdot \sqrt{g} / 2 \pi \)
в. \( \sqrt{2 g} / 2 \pi \)
c. \( \sqrt{g / 2 \pi} \)
D. \( \sqrt{3 g} / 2 \pi \)


State whether the given statement is true or false:

Atomic mass of an element is same as
the mass of a single atom of that
element.
A. True
B. False


The number of real solution of the
equations \( \sin \left(e^{x}\right)=5^{x}+5^{-x} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinitely many


The energy of a photon of light with wavelength \( 5000 A \) is approximately \( 2.5 e V . \) This way the energy of an X-ray
photon with wavelength \( 1 A \) would be:
A. \( \frac{2.5}{(5000)^{2}} e V \)
в. \( 2.5 \times 5000 \) eV
c. \( \frac{25}{(5000)^{2}} \cdot e V \)
D. \( \frac{2.5}{5000} e V \)