Infinite charges of magnitude \( q \) each
are lying at \( \boldsymbol{x}=\mathbf{1}, \mathbf{2}, \mathbf{4}, \mathbf{8}, \dots \dots \dots \) metre on
X-axis. The value of intensity of electric
field at point \( x=0 \) due to these
charges will be
A \( \cdot 12 \times 10^{9} q N / C \)
в. zero
c. \( 6 \times 10^{9} q N / C \)
D. \( 4 \times 10^{9} q N / C \)


To a piece of charcoal sulfuric acid is
added. Then
A. there is no reaction
B. water gas is formed
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{CO}_{2} \) are evolved
D. \( C O \) and \( S O_{2} \) are evolved


Assertion
STATEMENT-1: The minimum value of
the intercepts cut on tangent by a tangent to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)
between the coordinate axes is \( a+b \)
Reason

STATEMENT-2: For each pair of two negative real numbers a and b, nequality \( \frac{\boldsymbol{a}+\boldsymbol{b}}{\mathbf{2}} \geq-\sqrt{\boldsymbol{a} \boldsymbol{b}} \) holds.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement- - is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


The discovery of proved that
atom is divisible.


Which of the following is/ are correct statement(s)?
A. Portland cement is the most commonly used cement for construction work.
B. Portland cement is made from raw material which consist of \( 60 \% \) lime (calcium oxide), \( 25 \% \) silica (silicon dioxide), \( 5 \% \) alumina. The rest is iron oxide and gypsum (calcium sulphate)
C . Portland cement gets its name from the stone quarried from the Isle of Portland in England which has a similar texture.
D. All of the above


0 toppr 5
Q Trpesourr
a.
в.
\( c_{0} \cdot d- \)
o.


A flat coil, \( C \) of \( n \) turn, area \( A \) and
resistance \( R \), is placed in a uniform
magnetic field of magnitude \( \boldsymbol{B} \). The plane of the coil is initially perpendicular to \( B \). The coil is rotated
by an angle \( \theta \) about a diameter and
charge of amount \( Q \) flows through it. The plane of the coil is initially kept
parallel to \( B \). The coil is rotated by an
angle \( \theta \) about the diameter
perpendicular to \( B \) and charge of
amount \( Q \) flows through it.Choose the correct alternatives
This question has multiple correct options
A \( \cdot \theta=90^{\circ}, Q=(\operatorname{Ban} / R) \)
B . \( \theta=180^{\circ}, Q=(2 B a n / R) \)
C \( \cdot \theta=180^{\circ}, Q=0 \)
D . \( \theta=360^{\circ}, Q=0 \)
E. answer required


Error due to eye vision is termed as:
A. climax error
B. sight error
c. parallax error
D. visional error


A vector \( \vec{A} \) points vertically upward and \( \vec{B} \) points towards south. Then the vector product \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}} \) is:
A. along west
B. along east
c. along north
D. vertically downward


The Van't Hoff factor of \( N a C l \) assuming \( 100 \% \) dissociation is :
A . \( 1 / 2 \)
B . 2
c. 1
D. 3


How can the following compounds be obtained from phenol?
(i) \( 2,4,6- \) Tribromophenol
\( (i i) 2,4,6 \)
Trinitropheno
(iii) Benzene
(iv) Ortho
and para-cresol.


A body weighs \( 60 \mathrm{kg} \) on the earth's surface. What would be its weight at the centre of the earth?
A. 60 kg-wt
B. 6 kg-wt
c. \( 60 \times 9.8 \mathrm{kg} \) -wt
D. zero


Differentiate the following functions
with respect to \( x: \) \( \tan ^{-1}\left(\frac{a+b x}{b-a x}\right) \)


Which of the following unicellular organism has a macronucleus for trophic function and one or more micronuclei for reproduction?
A. Euglena
B. Amoeba
c. Paramecium
D. Trypanosoma


How should a man wearing spectacles
work with a microscope?
A. He should keep on wearing spectacles
B. He should take off spectacles
C. He cannot use the microscope at all
D. Wearing or taking off makes little difference
E. None of these


If the electronic configuration of metal \( A \) is (2,8,7) and that of metal \( B \) is (2,8
2) then :
a. Which metal is less reactive?
b. Write the names of the two metals.
c. Write the balanced chemical
equation of reaction of any one metal with hydrochloric acid.


Calculate the wavelength of radiation emitted producing a line in Lyman series, when an electron falls from fourth stationary state in hydrogen \( \operatorname{atom}\left(\boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}}\right) . \) If the
answer is \( x \times 10^{-8} \mathrm{m} \), then find the
value of \( x \)


A box of weight \( 150 k g f \) has \( 1.47 k J \)
of gravitational potential energy stored in it. Find the height of the box above the ground. Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{N} \boldsymbol{k} \boldsymbol{g}^{-1} \)
A . \( 10 m \)
в. 4.9 т
c. \( 2.45 m \)
D. \( 1 m \)


What is the degree of the polynomial \( \boldsymbol{p}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}^{3}-\boldsymbol{8} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x} ? \)
\( A \cdot 3 \)
B . 2
\( c \cdot 1 \)
D.


Which of the following is the flavouring agent for food, beverages etc?
A. Acetone
B. Formaldehyde
c. Benzaldehyde
D. Phenol


An aluminium rod (length \( l_{1} \) and
coefficient of linear expansion \( \alpha_{A} \) ) and
a steel rod (length \( l_{2} \) and coefficient of
linear expansion \( \alpha_{B} \) ) are joined together. If the length of each rod increased by the same amount when
their temperature are raised by \( t^{\circ} C \)
then \( l_{1} / l_{2}+1 \) is:
\( \mathbf{A} \cdot \alpha_{A} / \alpha_{B} \)
в. \( \alpha_{B} / \alpha_{A} \)
c. \( \alpha_{B} / \alpha_{A}+1 \)
D. \( \alpha_{A} / \alpha_{B}+1 \)


A committee of 10 is to be formed from
8 teachers and 12 students of whom 4
are girls. In how many ways this can be
done, so that the committee contains
atleast four of either groups (teachers and students) and atleast 2 girls and
atleast 2 boys are in the committee.


What is giant molecules?


Which part of the -COOH group gets cleaved in the esterification with
alcohol?
A. only H atom
B. only OH partttt
c. either 1 or 2
D. c- oн bond


The pentose sugar in DNA and RNA has
the:
A. open chain structure
B. pyranose structure
c. furanose structure
D. All of the above


For a Binomial distribution mean and
variance is given by
A \( . n p, n p q \)
B . \( n^{2} p, N^{2} p^{2} q^{2} \)
c. \( n^{2} p^{2}, N^{2} p^{2} q^{2} \)
D. None of these


Two flask \( A \) and \( B \) of equal volumes
maintained at temperature \( 300 K \) and
\( 700 K \) contain equal mass of \( H e(g) \) and
\( N_{3}(g) \) respectively. What is the ratio of
total translational kinetic energy of gas in flask \( A \) to the flask \( B ? \)


What is the state of hybridisation of
carbon in
(a) \( C O_{3}^{-2}(b) \) diamond (c)
graphite?


Find the weight of a substance if its molecular weight is 70 and in the
gaseous form it occupies \( 10 \mathrm{L} \) at \( 27^{\circ} \mathrm{C} \)
and \( 760 \mathrm{mm} \) Hg pressure.
A. 32.5 \( g \)
B. 35.5 g
c. \( 28.38 \mathrm{g} \)
D. None of the above


Find \( \lim _{x \rightarrow 1} f(x), \) where \( f(x)= \)
\( \left\{\begin{array}{ll}x^{2}-1, & x \leq 1 \\ -x^{2}-1, & x>1\end{array}\right. \)


A chord of a circle of radius \( 12 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the centre.
Find the area of the corresponding segment of the circle. (Use \( \pi=3.14 \)
and \( \sqrt{\mathbf{3}}=\mathbf{1 . 7 3} \)
A \( \cdot 17.43 \mathrm{cm}^{2} \)
B. \( 13.08 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 11.66 \mathrm{cm}^{2} \)
D. \( 9.64 c m^{2} \)


If -1 is a zero of the polynomial \( p(x)= \) \( a x^{3}-x^{2}+x+4, \) find the value of \( a \)


The number of unpaired electrons in valence shell of silicon is:
A . 2
B. 3
c. 1
\( D \)


Two slits separated by a distance of
1 \( m m \) are illuminated by light of wavelength \( 6.5 \times 10^{-7} \) m. Interference
fringes are oberved on a screen placed
at a distance of 1 from the slits.
Calculate the distance between the
third dark fringe and fifth bright fringe.


For a spontaneous process, which of the following is true?
A \( \cdot \Delta S_{s y s} \) is positive
B. \( \Delta S_{\text {surr}} \) is positive
\( \mathbf{c} \cdot \Delta S_{t o t a l} \) is positive
D. \( \Delta S_{\text {total }} \) is negative


Physical independence of force is a
consequence of
A. First law of motion
B. Second law of motion
c. Third law of motion
D. All of these laws


A square loop is placed in \( x-y \) plane
as shown in figure. Magnetic field in the region is \( \vec{B}=-B_{0} x \hat{k} . \) The induced
current in the loop is anticlockwise.
Reason
f inward magnetic field from such a loop increases, then current should be
anticlockwise
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The height at which the value of acceleration due to gravity becomes \( 50 \% \) of that at the surface of the earth.
(Radius of the earth \( =6400 \mathrm{km} \) ) is:
A. 2630
B. 2640
\( c \cdot 2650 \)
D. 2660


How all life processes contribute to growth and development of body?


\( \mathrm{H}_{2} \mathrm{O} \) is a liquid where as \( \mathrm{H}_{2} \mathrm{S} \) is a gas.
This is due to
A. the molecular mass of \( \mathrm{H}_{2} \mathrm{S} \) is more than that of \( \mathrm{H}_{2} \mathrm{O} \)
B. the molecular mass of \( \mathrm{H}_{2} \mathrm{S} \) is less than that of \( \mathrm{H}_{2} \mathrm{O} \)
C . Presence of hydrogen bond in \( \mathrm{H}_{2} \mathrm{S} \)
D. absence of hydrogen bond in \( \mathrm{H}_{2} \mathrm{S} \)


If the length of second's hand of a clock
is \( 10 \mathrm{cm}, \) the speed of its tip \( \left(\text { in } \mathrm{cm} \mathrm{s}^{-1}\right) \)
is nearly
\( A \cdot 2 \)
в. 0.5
c. 1.5
D.


Rubber is heated with sulphur and the process is known as:
A. Galvanization
B. Vulcanization
c. Bessemerization
D. Sulphonation


Q Type your question
climbıng up. Identıty the type of tendrıl
that is seen in Clematis
\( A \)
в.
\( c \)
D.


Which of the following may be dissolved
in water?
A. Alcohol
B. Ether
c. Amine
D. all of these


Assertion
The acceleration of an object at a
particular time is the slope of the velocity-time graph at that instant of time.
Reason
For uniform motion acceleration is zero.
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


Calculate the percentage ionization of
\( 0.01 \mathrm{M} \) acetic acid in \( 0.1 \mathrm{M} \) HCl. \( K_{a} \) of
acetic acid is \( 1.8 \times 10^{-5} \)
A . \( 0.18 \% \)
B. 0.018\%
c. \( 1.8 \% \)
D. 18\%


A carbon filament has resistance of 120
\( \Omega \) at \( 0^{0} C . \) The resistance of a copper
filament connected in series with
carbon so that the combination has
same resistance at all temperatures
must be
\( \alpha \) of carbon \( =-7 \times 10^{-4} /^{0} C ; \alpha \) of
\( \operatorname{copper}=4 \times 10^{-3} /^{0} C \)
A . \( 120 \Omega \)
B. 21\Omega
\( c \cdot 60 \Omega \)
D. 210\Omega


The transition from the state \( n=4 \) to
\( \boldsymbol{n}=\mathbf{3} \) in hydrogen-like atom results in
ultraviolet radiation. Infrared radiation
will be obtained in the transition from?


What is the monomer unit of natural
rubber?
A. Isoprene
B. Ethene
c. Neoprene
D. Tetrafluro ethene


Find composite of \( f \) and \( g \) and express
it by formula:
\( \boldsymbol{f}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{4}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{6})\} \)
\( \boldsymbol{g}=\{(\mathbf{3}, \mathbf{6}),(\mathbf{4}, \mathbf{8}),(\mathbf{5}, \mathbf{1 0}),(\mathbf{6}, \mathbf{1 2})\} \)


If the wavelength is equal to the distance travelled by the electron in one second, then:
\( A \cdot \lambda=\frac{h}{p} \)
B. \( \lambda=\frac{h}{m} \)
\( c \cdot \lambda=\sqrt{\frac{h}{p}} \)
D. \( \lambda=\sqrt{\frac{h}{m}} \)


Convert \( \frac{7 \pi}{36} \) into degrees.


The first stable product of Calvin cycle
is
A. 3- phosphoglycerate.
B. 1,3- biphosphoglycerate.
c. Glyceraldehyde-3- phosphate.
D. Ribulose-5- phosphate.


The product obtained in this reaction is:
A \( \cdot C H_{3} C H_{2} O H \)
в. \( \left(C H_{3}\right)_{2} \) СНОН
c. \( C H_{3} C H_{2} C H_{2} O H \)
D. \( H O-C H_{2}-C H_{2}-C H_{2}-C H_{2}-O H \)


\( f(x)=\left\{\begin{array}{cc}e^{\cos x} \cdot \sin x & \text { for }|x| \leq 2 \\ 2 & \text { otherwise }\end{array}\right. \)
then \( \int_{-2}^{3} f(x) d x \) is equal to
A .
B.
\( c \cdot 2 \)
\( D \)


A semiconductor having electron and
hole mobilities \( \mu_{n} \) and \( \mu_{p} \) respectively.
if its intrinsic carrier density is \( n_{i}, \) then
what will be the value of hole
concentration \( P \) for which the
conductivity will be minimum at a
given temperature?
A \( \cdot n_{i} \sqrt{\frac{\mu_{n}}{\mu_{p}}} \)
В \( \cdot n_{h} \sqrt{\frac{\mu_{n}}{\mu_{p}}} \)
\( \mathbf{c} \cdot n_{i} \sqrt{\frac{\mu_{p}}{\mu_{n}}} \)
D. \( n_{h} \sqrt{\frac{\mu_{p}}{\mu_{n}}} \)


After having spent \( 35 \% \) of the money on machinery, \( 40 \% \) on raw materiall and
\( 10 \% \) on staff, a person is left with Rs. \( 60,000 . \) Find the total amount of money spent on machinery and the raw
material.


Which of the following is/ are application (s) of flip-flop?
A. Bounce elimination switch
B. Latch
c. counters
D. All of the above


Find the value of \( x \) if
i) \( 30 \% \) of \( x \) is 285
ii) \( 57 \% \) of \( x \) is 228


Direction angle of a vector is \( 30^{\circ}, \) then
find the vector.
B. \( \sqrt{3} b \hat{i}+b \hat{j} \)
c. \( a \hat{i}+b \hat{j} \)
D. \( \sqrt{3} a \hat{i}+\sqrt{3} 3 \hat{j} \)


An astronomical telescope and a Galilean telescope use identical objective lenses. They have the same magnification, when both are in normal adjustment. The eyepiece of the astronomical telescope has a focal length \( \mathrm{f} \). This question has multiple correct options
A. The tube length of the two telescope differ by f.
B. The tube length of the two telescopes differ by 2 f
c. The Galileans telescope has shorter tube length
D. The Galileans telescope has longer tube length.


How will you distinguish :Temporary
hard water and permanent hard water?


\( (-35)+(-32) \) is equal to
A . 67
B. -67
\( c .-3 \)
D. 3


The standard enthalpy of formation of \( F e O \) and \( F E_{2} O_{3} \) is \( -65 k c a l m o l^{-1} \)
and \( -197 k c a l m o l^{-1} \) respectively
mixture of two oxides contains \( F e O \)
and \( F e_{2} O_{3} \) in the mole ratio \( 2: 1 . \) If by
oxidation, it is changed into a 1: 2 mole ratio mixture, how much of thermal
energy will be released per mole of the initial mixture?
A. 13.4 kcal/mole
в. 14.6 kcal/mole
c. \( 15.7 \mathrm{kcal} / \mathrm{mole} \)
D. 16.8 kcal/mole


An electric dipole of moment P is placed along the lines of force of electric field \( E \)
and is in equilibrium. the work done in
deflecting it through an angle of \( 180^{0} \) is equal to-
\( \mathbf{A} \cdot P E \)
в. \( +2 P E \)
c \( .-2 P E \)
D. \( Z E R O \)


The length \( x \) of rectangle is decreasing at the rate of \( 5 \mathrm{cm} / \mathrm{minute} \) and the
width \( y \) is increasing at the rate of 4 \( \mathrm{cm} / \mathrm{minute} . \) When \( \boldsymbol{x}=\mathbf{8} \mathrm{cm} \) and \( \boldsymbol{y}=\mathbf{6} \)
\( \mathrm{cm}, \) find the rates of change of the area of the rectangle.


Chordae tendineae are found in
A. ventricles of heart
B. joints of legs
c. ventricles of brain
D. atria of heart


Which one of the following will not conduct electricity?
A. solid NaCl
B. \( C u S O_{4} \) solution
c. graphite
D. acidified water


Choose the correct answers from the
alternatives given :
The osmotic pressure of pure water is
\( A \cdot O \)
B. 0.1
\( c \)
D. 10


The coefficients of self induction of two
coils are \( L_{1}=8 \mathrm{mH} \) and \( L_{2}=2 \mathrm{mH} \)
respectively. The current rises in the two coils at the same rate. The power given to the two coils at any instant is same. The ratio of induced emf's in the coils
will be :
A. \( \frac{V_{1}}{V_{2}}=4 \)
B. \( \frac{V_{1}}{V_{2}}=\frac{1}{4} \)
c. \( \frac{V_{1}}{V_{2}}=\frac{1}{2} \)
D. \( \frac{V_{1}}{V_{2}}=\frac{1}{3} \)


An element \( X \) (atomic number 17 ) reacts
with an element Y (atomic number 12)
to form a divalent halide. Where do \( x \)
and Y are placed in the modern periodic table? (mention the group and period of each


Sliding friction is \( \ldots \ldots . . . . . . . . \) than rolling friction.fill in the blank.
A. greater
B. less
c. same as
D. cant say


Solution of differential equation
\( \sin y \cdot \frac{d y}{d x}+\frac{1}{x} \cos y=x^{4} \cos ^{2} y \) is
A \( \cdot x \) sec \( y=x^{6}+C \)
B. \( 6 x \) sec \( y=x+C \)
c. \( 6 x \) secy \( =x^{6}+C \)
D. \( 6 x \) sec \( y=6 x^{6}+C \)


Which incorrect statement?
A. All halogens form oxyacids
B. All halogens show -1, +1,+3,+5,+7 oxidation states.
C. Hydrofluoric acid forms \( K H F_{2} \) and \( K_{2} F_{2} \) and attacks
glass.
D. Oxidising power is in order \( F_{2}>C l_{2}>B r_{2}>I_{2} \)


Assertion
If \( \boldsymbol{x}_{\boldsymbol{i}}=(2 \boldsymbol{i}-\mathbf{1}) ; \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3} \ldots . \) Then, the
sum of the deviations of \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \dots \dots \boldsymbol{x}_{\boldsymbol{n}} \)
from \( \boldsymbol{x}=\boldsymbol{n} \) is zero
Reason
The algebraic sum of the deviations of a
set of observations about their mean is
zero.
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


Add \( a+b-3, b-a+3, a-b+3 \)


\( 18 A r^{40} \) and \( _{19} K^{40} \) are a pair of
A. isomers
B. isobars
c. isotopes
D. isotones


Which of the following can act as both Bronsted acid as well as Bronsted base?
(i) \( H C O O^{-} \quad(\text { ii }) N H_{3} \quad(\text { iii }) O^{2-} \)
\( \boldsymbol{H} \boldsymbol{S O}_{4}^{-} \)
B. ii and iii
c. ii and iv
D. i and iv


Which of the following instruments is
used to measure magnetic field?
A. Thermometer
B. Pyrometer
c. Hygrometer
D. Flux meter


What does term \( S B R \) stand for \( ? \) write
its application.


There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper.
Then
A. current is induced in the loop in the anti-clockwise direction
B. current is induced in the loop in the clockwise direction
c. ac is induced in the loop
D. no current is induced in the loop


Evaluate the following:
\( (7 x-2 y)^{2} \)
\( (3 x+7 y)^{2} \)


Find the total number of stereoisomer
for each compound.
\( \mathbf{A} \cdot \mathbf{5} \)
B. 2
\( c \cdot 6 \)
D. None of these


What was the idea of Paul Ehrlich?
A. Chemicals which would adversely affect the invading bacteria but not the host, can be used for the
treatment of diseases caused by the bacteria
B. Chemicals which would adversely affect the invading bacteria but not the host, cannot be used for the treatment of diseases caused by the bacteria.
C. Chemicals which would adversely affect the invading bacteria but not the guest, can be used for the treatment of diseases caused by the bacteria.
D. Chemicals which would adversely affect the invading bacteria also the guest, can be used for the treatment of diseases caused by the bacteria.


A metal that forms a stable binary
halide of formula \( A X_{2}(X= \) Halogen) is :
\( A \)
B. 2
\( c \cdot 3 \)
D.


During the change of \( O_{2} \) to \( O_{2}^{-} \) ion, the electron adds on which one of the
following orbitals?
\( A \cdot \pi \) orbital
B \( \cdot \sigma^{*} \) orbital
c. \( \sigma \) orbital
D・ \( \pi^{*} \) orbital


If the altitude of an equilateral triangle is \( \sqrt{6}, \) then the area is:
\begin{tabular}{l}
A \( 2 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 2 \sqrt{3} \)
\( c \cdot 3 \sqrt{3} \)
D. \( 6 \sqrt{2} \)
E. 12


A spherometer has 10 threads per \( \mathrm{cm} \) and its circular scale has 50 divisions.
The least count of the instrument is
A . \( 0.01 \mathrm{cm} \)
B. \( 0.02 \mathrm{cm} \)
c. \( 0.002 \mathrm{cm} \)
D. \( 0.2 \mathrm{cm} \)


Identify the sets of electronic transitions associated with release of
energy and absorption of energy.
\( A \cdot n=4 \) to \( n=1 ; n=2 \) to \( n=1 \)
B. \( n=4 \) to \( n=3 ; n=4 \) to \( n=2 \)
\( c \cdot n=3 \) to \( n=5 ; n=2 \) to \( n=3 \)
D. \( n=3 \) to \( n=2 ; n=1 \) to \( n=2 \)


Algae differ from Riccia and Marchantia
in having
A. Multicellular body
B. Pyrenoids in the cells
c. Multicellular sex organs
D. Thalloid body


Name one property of waves that do not
change when the wave passes from one medium to another


Which of the following groups of forces could be in equilibrium?
A. \( 3 N, 4 N, 5 N \)
в. \( 4 N, 5 N, 10 N \)
c. \( 30 N, 40 N, 80 N \)
D. \( 1 N, 3 N, 5 N \)


State whether true or false.
The focal length of a spherical mirror is double its radius of curvature.
A. True
B. False


Which choice below would affect best,
the rate of reaction?
A. Cool the reaction down
B. Add a catalyst
c. Decrease the pressure
D. Use larger pieces of solid reactants
E. Decrease the concentration of the reactants


Differentiation of \( (2 x+3)^{6} \) with respect
to \( x \) is
A \( \cdot 12(2 x+3)^{5} \)
B. \( 6(2 x+3)^{5} \)
c. \( 3(2 x+3)^{5} \)
D. \( 6(2 x+3)^{6} \)


If the linear momentum of a particle is \( 2.2 \times 10^{4} k g m s^{-1}, \) then what will be its
de-Broglie wavelength ? (Take hr. 6.6 \( x \) \( \left.10^{-34} J s\right) \)
A \( \cdot 3 \times 10^{-29} \mathrm{m} \)
B. \( 3 \times 10^{-29} \) о \( m \)
c. \( 6 \times 10^{-29} \mathrm{m} \)
D. \( 6 \times 10^{-29} \) и \( m \)


\( 1.525 g \) of an organic compound was kjeblahlised and the ammonia so produced was passed through \( 30 m l \) of 1 \( N \) HCl.The remaining \( H C l \) was
further neutralised by 120 ml of \( \frac{N}{10} N a O H \) solution. Calculate the \( \% \) nitrogen in the compound.


In an ideal transformer turn ratio is 2: 3
If input voltage is \( 100 \mathrm{V} / 60 \mathrm{Hz} \), then
output voltage is
A . 150 V/90 нz \( z \) z
B. 150 V/40 нZ
c. \( 150 \vee / 60 \) Н \( z \)
D. 66.6 V/60 нz


Formula of Freon-112 is:
A \( \cdot C_{2} F_{2} C l_{4} \)
в. \( C F_{2} C l_{2} \)
c. \( C F C l_{3} \)
D. \( C C l_{3} F \)


Argentite is an ore of :
A . iron
B. gold
c. platinum
D. silver


Q Type your question_
substance?
\( \mathbf{A} \)
B.
\( \mathbf{C} \)
D.
Temperature
E .


If the average of the following data is
100. Find the value of \( p \)
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline\( x: \) & 10 & 20 & 30 & 40 & 50 & 60 \\
\hline\( f: \) & 2 & 4 & \( p \) & 8 & 10 & 12 \\
\hline
\end{tabular}
A . -26
B. -28
c. -25
D. -24


When iodoform is heated with silver
powder, the gaseous product formed is:
A. ethene
B. ethyne
c. ethane
D. silver iodate


Find the mean deviation about the
mean for the following data.


For a chemical reaction to occur, all of
the following must happen except.
A. A large enough number of collisions must occur
B. Chemical bonds in the reactants must break
C. Reactant particles must collide which enough energy for change to occur
D. Reactant particles must collide with correct orientation


In a class of 50 boys, 35 like horror movies, 30 like war movies and 5 like neither. Find the number of those that
like both.
A . 20
B . 25
c. 15
D. 28


If \( f: R \rightarrow R \) be a differentiable function and \( f(0)=0 \) and \( f^{\prime}(0)=1 \) then
\( \lim _{x \rightarrow 0} \frac{1}{x}\left[f(x)+f\left(\frac{x}{2}\right)+\ldots+f\left(\frac{x}{100}\right)\right] \)
equals
A . 1
B \cdot \( 1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{100} \)
D. Does not exist


In a bolt factory, three machines \( A, B \) and \( C \) manufacture 25,35 and 40
percent of the total bolts respectively. Out of the total bolts manufactured by
the machines 5,4 and 2 percent are
defective from machine \( A, B \& C \)
respectively. A bolt is drawn at random and is found to be defective. Find the
probability that it was manufactured by
(i) Machine A or \( C \)
(ii) Machine B.


If the mass of a body is \( M \) on the
surface of the earth, the mass of the
same body on the surface of the moon is
A. \( M / 6 \)
в. \( M \)
\( c \cdot 6 M \)
D. zero


The number of valence electrons that
can be present in the second element of any period is:
A . 1
B . 2
\( c .5 \)
D. 7


The plane which bisects the line
segment joining the points (-3,-3,4) and (3,7,6) at right angles, passes through which one of the following points?
A \( .(4,1,7) \)
В. (4,1,-2)
c. (2,3,5)
D. (2,1,3)


If the density of a solution is
\( 3.12 g m / m l^{-1}, \) the mass of \( 1.5 m l \) solution in significant figures is:
A. \( 4.7 g \)
В. \( 4680 \times 10^{-3} g \)
c. \( 4.680 g \)
D. \( 46.80 g \)


The specific heat of \( I_{2} \) in vapour and solid state are 0.031 and 0.055 cal/g respectively. The heat of sublimation of iodine at 200 is 6.096 kcal \( ^{-1} \). The heat
of sublimation of iodine at 250 will be:
\( \begin{array}{lll}\text { A } \cdot 3.8 & \text { kal }-1\end{array} \)
\( \begin{array}{ll}\text { B. } 4.8 & \text { kal }-1 \\ -1\end{array} \)
\( \begin{array}{lll}\text { C. } 2.28 & \text { kcal } & -1\end{array} \)


A p-n photodiode is made of a material with a band gap of \( 2.0 e V . \) The minimum
frequency of the radiation that can be
absorbed by the material is nearly:
\( \mathbf{A} \cdot 10 \times 10^{14} \mathrm{Hz} \)
B . \( 5 \times 10^{14} \mathrm{Hz} \)
c. \( 1 \times 10^{14} H z \)
D. \( 20 \times 10^{14} \mathrm{Hz} \)


Find the \( 4^{t h} \) term of \( \left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18} \)
A . 16500
B . 18564
c. 16540
D. 32600


air expands from 5 liters to 10 liters at 2 atm pressure. External workdone is
A . \( 10 J \)
в. \( 1000 J \)
c. \( 3000 J \)
D. 300J


The horizontal and vertical distances
travelled by a particle in time \( t \) are
given by \( \boldsymbol{x}=\mathbf{6} t \) and \( \boldsymbol{y}=\mathbf{8} \boldsymbol{t}-\mathbf{5} \boldsymbol{t}^{2} . \) If
\( g=10 m / s e c^{2}, \) then the initial velocity
of the particle is -
A. \( 8 \mathrm{m} / \mathrm{sec} \)
B. \( 10 \mathrm{m} / \mathrm{sec} \)
\( \mathrm{c} .5 \mathrm{m} / \mathrm{sec} \)
D. zero


Construct a triangle similar to a given \( \triangle A B C \) such that each of its sides is
\( (3 / 4)^{t h} \) of the corresponding sides of \( \triangle A B C . \) It is given that \( B C= \)
\( 6 c m, \angle B=50^{\circ} \) and \( \angle C=60^{\circ} \)


The equation of motion of a body in
S.H.M is \( \boldsymbol{x}=\mathbf{4} \sin \left(\boldsymbol{\pi} \boldsymbol{t}+\frac{\pi}{3}\right) . \) The
frequency, per minute, of the motion is


In the given in each the current in
each resistance is:
A. \( 0 A \)
B. \( 1 A \)
c. \( 0.25 A \)
D. \( 0.5 A \)


Assertion
Aluminium a good reducing agent.
Reason

Aluminium has strong affinity for oxygen and is thus readily oxidized.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Consider the reaction between \( \mathrm{Zn} \) and
dilute hydrochloric acid forming zinc chloride and liberating hydrogen.


A charged oil drop is suspended in
uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be: (take the mass of the
charge \( =\mathbf{9 . 9} \times \mathbf{1 0}^{-15} \mathbf{k g} \) and \( \mathbf{g}= \)
\( \left.10 m / s^{2}\right) \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
в. \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)


There is a pentagonal shaped park as
shown in the figure. For finding its area
Jyoti and Kavita divided it in two
different ways. Find the ratio of this
park using both ways in \( \mathrm{m}^{2} \)


Name the prism required for obtaining the spectrum of infra red radiation
A. water
B. glass
c. quartz prism
D. rock salt prism


The sides of a hexagon are produced in order. If the measures of exterior angles
so obtained are \( (6 x-1)^{\circ},(10 x+ \)
2) \( ^{\circ},(8 x+2)^{\circ},(9 x-3)^{\circ},(5 x+4)^{\circ} \) and
\( (12 x+6)^{\circ} ; \) Find each exterior angle
B . \( 41^{\circ}, 86^{\circ}, 56^{\circ}, 60^{\circ}, 39^{\circ}, 80^{\circ} \)
C \( \cdot 41^{\circ}, 72^{\circ}, 58^{\circ}, 60^{\circ}, 39^{\circ}, 90^{\circ} \)
D. \( 41^{\circ}, 82^{\circ}, 60^{\circ}, 60^{\circ}, 36^{\circ}, 100 \)


The IUPAC name is:
\[
\begin{array}{l}
C H=C H \\
C H O N H_{2}
\end{array}
\]
A. 1- Amino prop - 2 - enal
B. 3-Amino prop - 2 - enal
c. \( 1- \) Amino -2 - formyl ethane
D. 3 - Amino -1 -oxo prop - 2 - ene


A light container having a diatomic gas enclosed with in is moving with velocity
v. Mass of the gas is \( M \) and number of
moles is \( n \)
What is the kinetic energy of gas with respect to centre of mass of the system? What is the kinetic energy of gas with respect to ground?


The maximum value of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\log x}{x}(x \neq 0, x \neq 1) \) is
\( A \)
B.
\( c \cdot e^{2} \)
D. \( \frac{1}{e^{2}} \)


(i) Draw the geometrical isomer of
\( \operatorname{complex}\left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{2}\right] \)
(ii) On the basis of crystal field theory,
write the electronic configuration for \( \boldsymbol{d}^{4} \)
ion if \( \Delta_{0}<P \)
(iii) Write the hybridization and magnetic behaviour of the complex
\( \left[N i(C O)_{4}\right] \)
(At. no. of Ni=28).


True or False
Rutherford's atomic model was
successful in explaining stability of the
atom


\( \mathbf{s} \frac{\sin ^{-1}}{\cos ^{-1}}=\tan ^{-1} \) a valid relation?


Prove that \( \int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x \)
and hence evaluate
\( \int_{0}^{a} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}} d x \)


Copper sulphate solution \( (250 \mathrm{ml}) \) was electrolysed using a platinum anode and a copper cathode. A constant current of \( 2 \mathrm{mA} \) was passed for 16 minutes. It was found that after
electrolysis, the absorbance of the solution was reduced to \( 50 \% \) of its
original value. Calculate the concentration of copper sulphate in the solution to begin with.
A \( .0 .22 M \)
в. 2 М
c. \( 0.04 M \)
D. \( 0.13 M \)


Main root of tap root system represents
A. Plumule axis of the seed
B. Embryo axis of the seed
C. Radicle axis of the seed
D. Hypocotyl part of the seed


Let \( A, B \) are two sets such that \( n(A)= \) \( \mathbf{6}, \boldsymbol{n}(\boldsymbol{B})=\mathbf{8} \) then the maximum number
of elements in \( n(A \cup B) \) is
A. 7
B. 9
c. 14
D. None


What sorts of informations can you
draw from the following reaction?
\( (\boldsymbol{C N})_{2}(\boldsymbol{g})+\mathbf{2 O H}^{-}(\boldsymbol{a q}) \rightarrow \)
\( \boldsymbol{C N}^{-}(\boldsymbol{a q})+\boldsymbol{C N O ^ { - }}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \)


An object \( 5 \mathrm{cm} \) is placed at a distance of
\( 20 \mathrm{cm} \) in front of a convex mirror of
radius of curvature \( 30 c m \). Find the
position of the image, its nature and size.


In the Lassaignes test the Sulphur
present in the organic compound first changes into:
A. \( N a_{2} S O_{3} \)
в. \( C S_{2} \)
c. \( N a_{2} S O_{4} \)
D. \( N a_{2} S \)


Assertion: Penicillin
\( (G) \) is an
antihistamine.
Reason: Penicillin (G) is effective
against gram-positive bacteria.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct


A uniform wire of resistance \( 1 \Omega m^{-1} \) is
bent into a circle of radius 1 m. The
same wire is connected across a
diameter \( A B \) as shown in the figure.
The effective resistance between \( A \) and
\( \boldsymbol{B} \) is:
\( A \)
B. \( \frac{2 \pi}{\pi+2} \Omega \)
c. \( \frac{\pi+4}{2 \pi} \Omega \)
D. \( \frac{2 \pi}{\pi+4} \Omega \)


A metal ball does not rebound when
struck on a wall, whereas a rubber ball
of same mass when thrown with the
same velocity on the wall rebounds. From this it is inferred that:
A. change in momentum is same in both.
B. change in momentum in rubber ball is more.
c. change in momentum in metal ball is more
D. initial momentum of metal ball is more than that of rubber ball


In an experiment, the percentage of
error occurred in the measurement of
physical quantities \( A, B, C \) and \( D \) are \( 1 \% \) \( 2 \%, 3 \% \) and \( 4 \% \) respectively. Then the
maximum percentage of error in the measurement \( \mathbf{X}, \) where \( \boldsymbol{X}=\frac{\boldsymbol{A}^{\mathbf{2}} \boldsymbol{B}^{\mathbf{1} / \mathbf{2}}}{\boldsymbol{C}^{\mathbf{1} / \mathbf{3}} \boldsymbol{D}^{\mathbf{3}}} \)
will be
A \( \cdot\left(\frac{3}{13}\right) \% \)
B. \( 16 \% \)
c. \( -10 \% \)
D. \( 10 \% \)


Let \( y=\frac{6 x^{3}-45 x^{2}+108 x+2}{2 x^{3}-15 x^{2}+36 x+1} \)
\( \boldsymbol{x} \in(\mathbf{0}, \mathbf{1 0}) \)
Maximum value of \( y \)
A . 3
B . 2
c. \( \frac{86}{29} \)
D. \( \frac{82}{29} \)


Decreased rate of photosynthesis at
high concentration of \( \boldsymbol{O}_{2} \) is referred to a
A. Pasteur effect
B. Emerson effect
c. warburg effect
D. Richmond Lang effect


Complete the correspondence
statement:
\( \Delta A B C \cong \ldots \)
\( \mathbf{A} \cdot \Delta D E C \)
B. \( \Delta C E D \)
\( \mathbf{c} \cdot \Delta E D C \)
D. \( \Delta E C D \)


The method of concentration of the ore
that makes use of difference in density between ore and impurities is called
A. levigation
B. leaching
c. magnetic separation
D. liquation


Which one of the following statements
is not correct about zeolites?
A. These are water softners
B. These do not act as molecular sieves
C. They are complex oxide catalysts commonly used in petrochemical industries
D. The activity of zeolites is increased by heating them in
vacuum


A businessman earns an income of Rs 1
on the first day of his business On every subsequent day he earns an income which is double of that made on the
previous day On the 10 th day of his business his income is (in Rs)
A. 2048
B. 1024
\( c \cdot 512 \)
D. 256


For the titration between hydrochloric acid and sodium carbonate, the indicator used is:
A. potassium permanganate
B. phenolphthalein
c. phenol red
D. methyl orange


Write a balanced chemical equation for
the following.
Action of dilute hydrochloric acid on magnesium sulphate.


Which of the following has the similar composition as lymph?
A. Red blood cells
B. Blood plasma
c. White blood cells
D. Nutrients


Conisder a block of conducting material
of resistivity \( \rho \) shown in fig., Current
enters at \( A \) and leaves at \( D \)

For current entering at \( A, \) the electric
field at a distance 'r' from A is??
A \( \cdot \frac{\rho l}{8 \pi r^{2}} \)
B. \( \frac{\rho l}{r^{2}} \)
c. \( \frac{\rho l}{2 \pi r^{2}} \)
D. \( \frac{\rho l}{4 \pi r^{2}} \)


Calculate the pH of \( 10^{-8} \) molar HCl
solution.


The two adjacent sides \( \boldsymbol{O A}, \boldsymbol{O B} \) of parallelogram are \( 2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( \hat{i}+ \) \( 2 \hat{j}+3 \hat{k} . \) The unit vectors along the
diagonals of the parallelogram are given by
A \( \cdot \frac{(3 \hat{i}+6 \hat{j}-2 \hat{k})}{7} \)
B. \( \frac{(-\hat{i}-2 \hat{j}+8 \hat{k})}{\sqrt{69}} \)
\( \frac{(-3 \hat{i}-6 \hat{j}+2 \hat{k})}{7} \)
D. \( \frac{(\hat{i}+2 \hat{j}-8 \hat{k})}{\sqrt{69}} \)


Mycobiont and phycobiont association
is
A. Symbiotic
B. Commensel
c. Parasitic
D. Helotism


For most materials, the Young's
modulus is \( n \) times the modulus of
rigidity, where \( n \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Solve the following differential equation \( \frac{d y}{d x}=e^{x} \)


Which of the following is a redox
reaction?
\( \mathbf{A} \cdot H_{2} S O_{4} \) with \( N a O H \)
B. In atmosphere, \( O_{3} \) from \( O_{2} \) by lightning
C. Nitrogen oxides form nitrogen and oxygen by lightning
D. Evaporation of \( H_{2} O \)


Which of the following is a correct
statement about current carrying
conductor?
A. On increasing temperature drifts speed of free electron decreases
B. On increasing temperature drift speed of free electron increases
C. On increasing temperature, drift speed of free electron remains same.
D. On increasing P.D. average kinetic energy of electron decreases ( Neglected heating effect of electric current)


Calculate \( (192-214) \)
\( \sin ^{-1}+2 \tan ^{-1}(-\sqrt{3}) \)


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}\} \)
Then find \( A \Delta B \)


How many lines of symmetry are there for an isosceles triangle?
A . 1
B.
\( c \cdot 3 \)
\( D \)


The rate constant for an isomerisation
reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) is \( \mathbf{4 . 5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{m} \boldsymbol{i n}^{-1} . \)
the initial concentration of \( A \) is \( 1 \mathrm{M} \), the
rate of the reaction after 1 hr will be:
A \( \cdot 3.4354 \times 10^{-3} \)
B . \( 4.4554 \times 10^{-3} \)
c. \( 5.4364 \times 10^{-3} \)
D. None of these


A compound consists of \( 47.8 \% \) zinc and
52\% chlorine by mass. The empirical
formula of the compound is \( Z n_{x} C l_{y} \)
where \( x \) and \( y \) can have the values:
A . 1 and 1
B. 1 and 2
c. 2 and 1
D. 2 and 3


If AM of two numbers is twice of their
GM, then the ratio of greatest number to smallest number is
A. \( 7-4 \sqrt{3} \)
B. \( 7+4 \sqrt{3} \)
\( c \cdot 2 \)
D. 5


From the given diagram find the number of elements in \( \left(A^{\prime} \cup B^{\prime}\right) \)


A particle is moving in a straight line such that its distance at any time \( t \) is given by \( s=\frac{t^{4}}{4}-2 t^{3}+4 t^{2}-7 . \) The
acceleration of the particle is minimum
when \( t= \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
\( D \)


The heat released in the neutralisation
of HCl and NaOH is 13.7 kcal/mol, the
heat
released on neutralisation of NaOH with
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is 3.7 kcal/mol.
The \( \Delta H \) of ionisation of \( C H_{3} C O O H \)
is:
A. 10.2 kcal
B. 10 kcal
c. 3.7 kcal
D. 9.5 kcal


When a p-njunction diode is reverse
biased
A. electrons and holes are attracted towards each other and move towards the depletion region
B. electrons and hole move away from the junction depletion region.
C. height of the potential barrier decreases.
D. no change in the current takes place.


Which of the following symbol represents acid dissociation constant?
\( \mathbf{A} \cdot p H \)
B . \( p O H \)
\( \mathbf{C} \cdot K_{a} \)
\( \mathbf{D} \cdot K_{b} \)
\( \mathbf{E} \cdot K_{w} \)


The heat liberated on complete
combustion of \( 7.8 g \) benzene is \( 327 k J \)
This heat has been measured at
constant volume and at \( 27^{\circ} \mathrm{C} \). Calculate
the heat combustion of benzene at
constant pressure.
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A. \( -323.7 k J \) mol \( ^{-1} \)
В. \( -3273.7 k J \) mol\( ^{-1} \)
c. \( 273.7 k J \) mol \( ^{-1} \)
D. \( 3273.7 k J \) mol \( ^{-1} \)


Which of the following is NOT paramagnetic?
A . \( N O \)
B. \( S^{2-} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


The change in unit volume of a material
under tension with increase in its
poisson's ratio will be
A. Increase
B. Decrease
c. Remains same
D. Initially increases and then decreases


Short answer type questions How can you distinguish even-toed ungulates from odd-toed ungulates?


Define uniform circular motion.


A bag contains cards numbered from 1
to \( 49 . \) A card is drawn from the bag at
random, after mixing the card thoroughly. Find the probability that the number on the drawn card is
(i) an odd number
(ii) a multiple of 5
(iii) a perfect square
(iv) an even prime
number


In extraction of metal how many of the following ores involves calcination
process.
(i) Dolomite
(ii) Malachite
(iii) Calcite
(iv) Copperpyrites (vi) Cryolite (vii) Siderite (viii) Iron pyrite (ix) Argentite.


State true or false.
Sulphur is an insulator while selenium
and tellurium are semiconductors.
A. True
B. False


The prothallus represents
A. Gametophyte of fern
B. Sporophyte of angiosperm
C. Sporophyte of gymnosperm
D. Sporophyte of fern


A rectangular room of the dimension
\( 8 m \times 6 m \times 3 m \) is to be painted. If it
\( \operatorname{costs} \) Rs.60 per square metre, find the \( \operatorname{cost} \) of painting the walls of the room.


Write the value of \( 25^{3}-75^{3}+50^{3} \)


Find the square root of 4489 by Division
method.


One end of a steel (density \( p \) ) rectangular girder is embedded into a wall (fig). Due to gravity it sags slightly. Find the radius of curvature of the
neutral layer in the vicinity of the point O if the length of the protruding section of the girder is equal to \( l=6.0 \mathrm{cm} \) and
the thickness of the girder equals \( h= \)
\( \mathbf{1 0} \mathrm{cm} \)
\( ^{\mathrm{A}} \cdot_{R}=\frac{h^{2} E}{p l^{2} g} \)
B. \( \quad R=\frac{h^{2} E}{6 p l^{2} g} \)
c. \( _{R}=\frac{h^{2} E}{3 p l^{2} g} \)
D. \( R=\frac{h^{2} E}{7 p l^{2} g} \)


In humans, the concentration of carbon
dioxide in the plasma
A. Causes increased production of hydrochloric acid
B. Regulates gastric acid production by forming carbonic acid
C. Regulates breathing rate by its effect on the medulla
D. Causes inflammation of the tissues of the bronchial tubes


How chromosomes determine sex of a
baby?


Nucleolus contains
A. Genetic instructions
B. Ribosome assembly line
C. Protein synthesis machinery
D. Enzymes for polysaccharide formation


In the circuit shown, the current in the
1 \( \Omega \) resistor is
\( \mathbf{A} \cdot 1.3 A, \) from \( P \) to \( Q \)
B. \( 0 A \)
c. \( 0.13 A \), from \( Q \) to \( P \)
\( 0.13 A, \) from \( P \) to \( Q \)


Find the angle of intersection of the
following curve:
\( x^{2}+4 y^{2}=8 \) and \( x^{2}-2 y^{2}=2 \)


Write the postulates of Dalton's Atomic theory


Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( C \)
\( \mathbf{A} \cdot(4,0,0) \)
\( \mathbf{B} \cdot(0,3,4) \)
C. (0,3,0)
D. (0,4,0)


Find the value of \( \left|\begin{array}{ccc}53 & 106 & 159 \\ 52 & 65 & 91 \\ 102 & 153 & 221\end{array}\right| \)


Magnification of lens is
A. size of the image
B. \( \frac{\text { image distance }}{\text { object distance }} \)
C. Both A and B
D. None


If you invest 1000 dollars for 3 years and get \( 10 \% \) compounded each year, then the compound interest is
A . 331
в. 341
c. 351
D. 36


In the following figure, if the dimensions
of the trapezoid are as shown and the
area of the trapezoid is \( 144, \) what is the
value of \( x ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6
E. 8


A person has protruding eyes, tachycardia and higher body temperature. He is suffering from
A. Cretinism
B. Hyperthyroidism
c. Diabetes
D. Acromegaly y


A solid cuboid of iron with dimensions
\( 53 c m \times 40 c m \times 15 c m \) is melted and
recast into a cylindrical pipe. The outer and inner diameters of pipe are \( 8 \mathrm{cm} \)
and \( 7 \mathrm{cm} \) respectively. Find the length of
pipe.


The principle section of a glass prism is isosceles triangle \( A B C \) with \( A B=A C, \) the face \( A C \) is silvered. A ray of light is incident normally on the face \( A B \) and after two reflections, it emerges from the base BC perpendicular to the base.
Angle of BAC of the prism is
\( A \cdot 30 \)
B. 36
\( c \cdot 18 \)
\( D \cdot 72 \)


Alcohols of low molecular weight are:
A. soluble in water
B. soluble in water on heating
C . insoluble in water
D. insoluble in all solvents.


An alternating e.m.f. of \( 200 \mathrm{V} \) and 50 cycles is connected to a circuit of
resistance \( 3.142 \Omega \) and inductance
0.01H. The lag in time between the e.m.f. and the current is :
A . \( 1.5 \mathrm{ms} \)
B. 2.5 ms
c. 3.5ms
D. 0.5 ms


\( P \) is produced by the action of chlorine on dry slaked lime. Q is a non-corrosive base and used for
faster cooking. On heating \( R \) at \( 373 K \), it becomes calcium sulphate hemihydrate. Identify \( P, Q \) and \( R \) respectively:
A \( \cdot C a O C l_{2}, N a H C O_{3}, \) gypsum
в. \( C a O, N a_{2} C O_{3}, C a O C l_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2}, \operatorname{NaH} C O_{3}, \operatorname{CaSO}_{4} \)
D. \( \operatorname{CaOCl}_{2}, N a_{2} \mathrm{CO}_{3}, \mathrm{NH}_{4} \mathrm{Cl} \)


A parallel beam of electrons travelling
in x-direction falls on a slit of width d. If
after passing the slit, an electron
acquires momentum \( p_{y} \) in the \( y \)
direction, then for a majority of electrons passing through the slit (h is Planck's constant).
\( \mathbf{A} \cdot\left|P_{y}\right| d<h \)
B . \( \left|P_{y}\right| d \simeq h \)
\( \mathbf{c} \cdot\left|P_{y}\right| d>>h \)
\( \mathbf{D} \cdot\left|P_{y}\right| d>h \)


Prove that the lines joining the middle points of opposite sides of a quadrilateral and the line joining the middle points of its diagonals meet in a point and bisect one another.


If the wavelength of light emitted when an electron fall from the first excited
state to the ground state are \( \lambda \), the wavelength of emitted radiation when an electron fall from meta-stable state
to the ground state will be
A. greater than \( \lambda \)
B. less than \( \lambda \)
\( c \cdot \lambda \)
D. cannot be determined


In a study of equilibrium
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
Starting with 2 mole \( S O_{2} \) and 1.5 mole
\( O_{2} \) in 5 litre flask.Equilibrium mixture
required 0.4 mole \( K M n O_{4} \) in acidic
medium.Hence \( \boldsymbol{K}_{\boldsymbol{C}} \) is:
A. 0.2
B. 5.0
c. 675.0
D. None of these


The eccentricity of an ellipse is \( \frac{\sqrt{3}}{2}, \) its
length of latus rectum is equal to:
A \( \cdot \frac{1}{2}(\text { Length of major axis }) \)
B. \( \frac{1}{3} \) (Length of major axis)
c. \( \frac{1}{4} \) (Length of major axis)
D. \( \frac{2}{3} \) (Length of major axis)


At what phase are the earth, moon and
sun are in approximate alignment? This question has multiple correct options
A. Full Moon
B. New Moon
c. waning crescent
D. waxing crescent


\( \mathbf{2}^{i}=e^{i(l n x)} \)


ype your questio
reactıon?
\( A \)
B.
\( c \)
D.


Two current carrying loops having \( N_{1} \)
turns and \( N_{2} \) turns respectively both
carrying a current equal to \( I \) in the same direction, are placed inside a magnetic field \( B \). If the radii of both
loops are in the ratio 1: 3 then what will
be the ratio of the potential energy of loops in that magnetic field?
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{2 N_{1}}{N_{2}} \)
c. \( \frac{N_{1}}{3 N_{2}} \)
D. \( \frac{N_{1}}{9 N_{2}} \)


If in an A.C.L - \( C \) series circuit, \( X_{L}>X_{C} \)
Hence current
A \( \cdot \) lags behind the voltage by \( \frac{\pi}{2} \) in phase
B. leads the voltage by \( \frac{\pi}{2} \) in phase
c. leads the voltage by \( \pi \) in phase
D. lags behind the voltage by \( \pi \) in phase


Evaluate:
\( \left(\frac{\cos \frac{\pi}{8}-i \sin \frac{\pi}{8}}{\cos \frac{\pi}{8}+i \sin \frac{\pi}{8}}\right)^{4} \)
\( A \)
B. -
\( c \cdot 2 \)
D.


Find the \( x \) -coordinates on the \( x \) -axis.
(excluding \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\infty \)
This question has multiple correct options
A. \( x=4 \lambda \)
B . \( x=7 \lambda / 4 \)
c. \( x=5 \lambda / 4 \)
D. \( x=3 \lambda \)


\( s p^{3} d \) hybridisation results in:
A. a square planar molecule
B. an octahedron molecul
C. a trigonal bipyramid molecule
D. a tetrahedron molecul


If \( \sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}, \) then
\( \cos ^{-1} x+\cos ^{-1} y= \)
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


A uniform cube is subjected to volume compression. Each side gets decreased by \( 1 \%, \) then the bulk strain is
A . 0.01
B. 0.03
c. 0.06
D. 0.09


Solubility product constants \( \left(\boldsymbol{K}_{s p}\right) \) of
salts of types \( M X, M X_{2}, M_{3} X \) at
temperature \( \boldsymbol{T} \) are \( \boldsymbol{4} \cdot \boldsymbol{0} \times \boldsymbol{1 0}^{-8}, \boldsymbol{3} \cdot \boldsymbol{2} \times \)
\( 10^{-4} \) and \( 2.7 \times 10^{-13} \) respectively.
Solubility \( \left(\operatorname{mol} d m^{-3}\right) \) of the salts at
temperature \( \boldsymbol{T} \) are in the order:
A \( . M X>M X_{2}>M_{3} X \)
B. \( M_{3} X>M X_{2}>M X \)
c. \( M X_{2}>M_{3} X>M X \)
D. \( M X>M_{3} X>M X_{2} \)


Select the correct statement \( (s) \)
A. \( \mathrm{HCl} \) and \( \mathrm{HF} \) do not from free radical easily due to larger bond-energy
B. HI with a minimum bond energy is every reactive and
instead from \( \mathrm{I}_{2} \)
C. Both (a) and (b)
D. None of the above


A gas at low temperature does not react with the most of compounds. It is almost inert and is used to create inert
atmosphere in bulbs. The combustion of this gas is exceptionally an endothermic reaction. Based on the
given information, we can conclude that
the gas is :
A. oxygen
B. nitrogen
c. carbon mono-oxide
D. hydrogen


Complete combustion of hydrocarbon produces:
\( A \cdot C O+H_{2} O \)
в. \( C O+H_{2} \)
c. \( C O_{2}+H \)
D. \( C O_{2}+H_{2} O \)


The compound \( \left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{3} \ddot{\boldsymbol{N}} \) is expected
to be:
A . Pyramidal and more basic than \( \ddot{N}\left(C H_{3}\right)_{3} \)
B. Planar and less basic thanN \( \left(C H_{3}\right)_{3} \)
C. Pyramidal and less basic than \( \ddot{N}\left(C H_{3}\right)_{3} \)
D. planar and more basic than \( \ddot{N}\left(C H_{3}\right)_{3} \)


At a constant voltage the heat developed in a uniform wire varies
inversely as the length of the wire used.


Bleaching powder is effective with cold water, but ineffective with hot water.
This is because of:
A. oxidation of chloride radical
B. reduction of chloride radical
c. reduction of hypochlorite radical
D. hydrolysis of hypochlorite radical


Which one of the following is reduced by
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in alkaline medium?
A \( \cdot F e^{2} \)
в. НОС\( l \)
\( \mathbf{c} \cdot K M n O_{4} \)
D. \( P b S \)
E \( . M n^{2+} \)


Find the inverse of the following
matrices:
(a) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}]-\mathbf{1}} & \mathbf{2} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \mathbf{2}\end{array}\right] \)
(b) \( \left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ {[0.3 e m] \sin \theta} & \cos \theta & 0 \\ {[0.3 e m] 0} & 0 & 1\end{array}\right] \)
(c) \( \left[\begin{array}{ccc}2 & 2 & 2 \\ {[0.3 e m] 2} & 5 & 5 \\ {[0.3 e m] 2} & 5 & 11\end{array}\right] \)
(d) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ {[\mathbf{0 . 3 e m}] \mathbf{2}} & \mathbf{4} & \mathbf{5} \\ {[\mathbf{0 . 3 e m}] \mathbf{3}} & \mathbf{5} & \mathbf{6}\end{array}\right] \)
(e) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}]-\mathbf{1}} & \mathbf{2} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \mathbf{2}\end{array}\right] \)


The weight of 30 boxes is 6 kg. What is the weight of 1080 such boxes?


Which breed of Indian goats is known to produced Pashmina?
A. Osmanabadi
B. Kodi aadu
c. changthangi
D. sirohi


A sphere of coefficient of linear
expansion \( \alpha, \) mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is spinning about an axis through its diameter with an angular velocity \( \omega \)
when it is heated such that its
temperature increases by \( \Delta t, \) the
angular velocity becomes.
\( A \)
\[
\omega(1+\alpha \Delta t)^{2}
\]
B.
\[
\frac{\omega}{(1+\alpha \Delta t)^{2}}
\]
c.
\[
\omega(1+\alpha \Delta t)
\]
D. \( \omega \alpha \Delta t \)


Let \( A \) and \( B \) be two sets such that \( A \times B \)
consists of 6 elements. If three
elements of \( A \times B \) are (1,4),(2,6),(3,6)
find \( A \times B \) and \( B \times A \)


Selenium has the unusual property of being a good conductor in light but a poor conductor in the dark. It was,
therefore, used in making.
A. Shaded glass
B. Photo-electric cells
c. Photo chemical celles
D. Chromatic lenses


Reaction
Appearance \( \boldsymbol{H} \boldsymbol{C} \)
Dull gray solid \( \quad \) Dissolved Unknown metal #1 with white lid of clear ğ oxide coating
Solid; Iustrous, Unknown metal #2 smooth silver- \( \quad \) No Reacti
gray surface
Unknown metal #2 could be:
A. silver
B. copper
\( c \cdot \) zinc
D. sodium


The absorption of water due to expenditure of energy is called as
A. Active absorption
B. Non-smotic absorption
c. Passive absorption
D. All of the above


\( 20 \mathrm{ml} \) of a gaseous hydrocarbon required \( 400 \mathrm{ml} \) of air for complete combustion. The air contains \( 20 \% \) by volume of oxygen. The volume of the gaseous mixture after explosion and cooling was found to be \( 380 \mathrm{ml} \)
Volume of residual nitrogen is
A. 300 \( \mathrm{ml} \)
B. 310 m1
c. \( 320 \mathrm{ml} \)
D. 330 m1


Answer the following question based on a hot cathode ray tube. Name the charged particles.


At all points inside a uniform spherical shell -
A. gravitational intensity and gravitational potential both are zero
B. gravitational intensity and gravitational potential both are non- zero
C . gravitational intensity is non- zero and gravitational potential both are zero
D. gravitational intensity is zero and gravitational potential both are non-zero


Answer the following:
What would be the molecular formula for a straight-chain hydrocarbon having 8 carbon atoms with (a) all \( C-C \)
single bonds
(b) One \( C-C \) double
bonds,
(c) One \( C-C \) triple bond?


Deforestation leads to the increased
percentage of which of the following components of the environment?
A. Carbon dioxide
B. Nitrogen
c. oxygen
D. None of the above


A factory produces bulbs. The probability that one bulb is defective is \( \frac{1}{50} \) and they are packed in boxes of \( 10 . \) If the probability that none of the bulbs is defective from a single box is \( \left(\frac{49}{50}\right)^{k} \) then value of \( k \) is


What is the boiling point of water on Kelvin scale? Convert it into centigrade
scale.


Which of the following statements about sound waves is correct?
A. Sound waves are not affected by the medium through which it travels.
B. Sound waves travel faster in air than in liquid.
C. Sound waves travel faster in a solid than in liquids and
gases
D. Sound waves cannot travel through a solid.


If \( S_{r} \) denotes the sum of \( r \) terms of an
\( A P \) and \( \frac{S_{a}}{a^{2}}=\frac{S_{b}}{b^{2}}=c \) then \( S_{c} \) is
A \( . c^{3} \)
в. \( c / a b \)
\( c \cdot a b c \)
D. \( a+b+c \)


The colour of \( _{62} S m^{3+} \) is yellow. The
colour of \( _{66} D y^{3+} \) is:
A. colourless
B. yellow
c. red
D. blue


The area bounded by the curves \( y= \) \( \frac{1}{4}\left|4-x^{2}\right| \) and \( y=7-|x| \) is
A . 18
B. 32
c. 36
D. 64


During an electrolysis of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
perdisulphuric acid \( \left(\boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}\right) \) and \( \boldsymbol{O}_{2} \)
form in equimolar amount. The amount
of \( \boldsymbol{H}_{2} \) that will form simultaneously will
be: \( \left(2 H_{2} S O_{4} \rightarrow H_{2} S_{2} O_{8}+2 H^{+}+\right. \)
\( 2 e^{-} \)
A. Thrice that of \( \mathrm{O}_{2} \) in moles
B. Twice that of \( 0_{2} \) in moles
c. Equal to that of \( \mathrm{O}_{2} \) in moles
D. Half of that of \( \mathrm{O}_{2} \) in moles


Which term of an A.P : 21, 42, 63,.... is 210
\( ? \)
A . gth
B. 10th
c. 12th
D. 11th


The calculated bond order in \( \boldsymbol{H}_{2}^{-} \) ion is:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 1 / 2 \)
c. \( -1 / 2 \)
D.


What are the limitations of JJ.
Thomsons model of the atom?


There are 100 tickets in a raffle
(Lottery). There is 1 prize each of Rs. \( \mathbf{1 0 0 0} /-, \) Rs. \( \mathbf{5 0 0} /- \) and Rs. \( \mathbf{2 0 0} /- \)
Remaining tickets are blank. Find the
expected price of one such ticket.


Let \( f \) be the function \( f(x)=\cos x- \)
\( \left(1-\frac{x^{2}}{2}\right), \) then find the interval in which \( f(x) \) is strictly increasing.
\( A \cdot(-\infty, \infty) \)
в. \( (-2, \infty) \)
c. \( [0, \infty) \)
()
D. \( (0, \infty) \)


Fermentation is
A. Anaerobic respiration
B. Incomplete oxidation of carbohydrates
C . Complete oxidation of carbohydrates
D. None of the above


A parallelepiped is formed by planes
drawn through the points \( \boldsymbol{P}(\boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}) \)
and \( Q(3,4,8) \) parallel to the coordinate
planes. Find the length of edges and diagonals of the parallelepiped.


Family of curves \( \boldsymbol{y}=e^{x}(\boldsymbol{A} \cos \boldsymbol{x}+ \)
\( B \sin x), \) represents the differential
equation?
A \( \cdot \frac{d^{2} y}{d x^{2}}=2 \frac{d y}{d x}-y \)
B. \( \frac{d^{2} y}{d x^{2}}=2 \frac{d y}{d x}-2 y \)
\( ^{\mathbf{C}} \cdot \frac{d^{2} y}{d x^{2}}=\frac{d y}{d x}-2 y \)
D. None of the above


From \( 200 m g \) of \( C O_{2}, 10^{21} \) molecules
are removed the number of \( C O_{2} \)
molecules left are:
A \( \cdot 2.98 \times 10^{-3} \)
В. \( 1.66 \times 10^{-3} \)
c. \( 4.54 \times 10^{-2} \)
D. \( 1.66 \times 10^{-2} \)


The order and degree of the differential equation of the family of circles of fixed
radius \( r \) with centres on the \( y \) -axis, are
respectively.
A .2,2
в. 2,3
\( \mathrm{c} \cdot 1, \)
D. 3,1
E. 1,2


The appetite and satiety centres in the brain of man are located in the region of
the
A. Cerebral hemisphere
B. Cerebellum
D. Hypothalamus


Explain the working of a diode as half wave rectifier.


Evaluate: \( \lim _{x \rightarrow 0}\left(\frac{a^{x}+b^{x}+c^{x}}{3}\right)^{2 / x} \)
A \( . a+b+c \)
В \( \cdot(a b c)^{1 / 3} \)
c. \( (a b c)^{2} \)
D. \( (a b c)^{2 / 3} \)


Solve the differential equation:
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-\boldsymbol{y}=\mathbf{0} \)


Select the correct statements from the
following.
I. Endosperm is generally triploid in angiosperms.
Il. All angiosperms have monosporic and endosporic embryo sac.
III. Angiosperms are characterised by double-fertilization.
IV. All angiosperms show-indirect pollination and siphonogamy.
A . I, II and III
B. ॥, ॥ा and IV
c. ।, III and IV
D. I, II, III and IV


Find the radius of the incircle of a
triangle whose sides are 18,24 and 30


Given a balanced chemical equation for each of the following:
Action of conc. Nitric acid on Sulphur.


Find the general solution of the differential equation \( e^{x} \tan y d x+\left(1-e^{x}\right) \sec ^{2} y d y=0 \)


The process in which metal surface is made inactive is called:
A. passivation
B. galvanizing
c. corrosion
D. pickling


On hydrolysis of starch, we finally get:
A. glucose and fructose
B. glucose
c. fructose
D. sucrose


Find the slope of the line passing through the following pairs:
\( (-1,2 \sqrt{3}) \) and \( (-2, \sqrt{3}) \)
A. \( \sqrt{3} \)
B. \( 3 \sqrt{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{3} \)


Replacement of \( C l \) of chlorobenzene to give phenol requires drastic conditions, but \( C l \) of 2,4 -dinitrochlorobenzene is readily replaced. This is because:
A. \( -N O_{2} \) group makes the ring electron rich at ortho and para positions.
B. - NO group withdraws electrons from meta position
C. \( -N O_{2} \) donate electrons at meta position.
D. \( -N O_{2} \) withdraws electrons from ortho and para positions.


Which of the following statements is
not true about Dobereiner's law of
triads?
A. The law was applicable to all known elements
B. Nitrogen family does not obey the law of triads
C. Dobereiner's classification was not very useful
D. The atomic mass of the central element of each triadd was merely the arithmetic mean of of the atomic masses of other two elements


The correct decreasing order of the acidic strength of the given compound is :
\( A \cdot(|>>(\mid I)>(\| I)>(I V) \)
B. (II)> (III)> (I)> (IV)
\( c \cdot(\|\|)>(\|)>(|D>(\mid V) \)
\( D \cdot(\mid)>(|| \mid)>(||)>(\mid V) \)


The ready source of energy in living cells
is
A. Glucose
B. ATP
c. Glycogen
D. ADP


Coal is free carbon.
A. True
B. False


Select a correct statement from the
following.
A. Presence of chiral carbon is the necessary and sufficient condition for chirality.
B. Presence of chiral carbon is the only condition for optical activity.
C. Molecular symmetry is necessary for optical activity.
D. Presence of chiral carbon is the necessary but not sufficient condition for chirality.


Match list I with list II and select the
correct option.
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ \text { A. } & \text { Gemmules } & \text { 1. } & \text { Agave } \\ \text { B. } & \text { Leaf-buds } & \text { 2. } & \text { Penicillum } \\ \text { C. } & \text { Bulbil } & \text { 3. } & \text { Water hyacinth } \\ \text { D. } & \text { Offset } & \text { 4. } & \text { Sponges } \\ \text { E. } & \text { Conidia } & \text { 5. } & \text { Bryophyllum }\end{array} \)
\( \mathbf{A} \)
\( A-4, B-5, C-1, D-3, E-2 \)
2
B. A- \( 4, B-3, C-2, D-1, E-5 \)
C. \( A-3, B-5, C-4, D-2, E-1 \)
D. \( A-4, B-1, C-5, D-3, E-2 \)
E. \( A-3, B-5, C-4, D-1, E-2 \)


There are three isotopes of oxygen, each
containing 8,9,10 neutrons respectively. The abundance of one isotope
(containing 8 neutrons) is 90\%. The percentage of other isotope, if the
atomic mass of oxygen is \( 16.12, \) are :
A \( .^{17} O=8 \%, 18 O=2 \% \)
B. \( 17 O=2 \%, 18 O=8 \% \)
c. \( 17 O=10 \% \), \( ^{8} O=0 \% \)
D. \( 17 O=4 \%, 18 O=6 \% \)


Write two names of polymer which are
biodegradable.


In which mirror a diminished virtual
image can be obtained?
A. A plane mirror
B. Convex mirror
c. Concave mirror
D. None of these


A line joining places of same declination
is called
A . agonic
B. isoclinic
c. isodynamic
D. isogonal


In the reaction, \( A l C l_{3}+C l^{-} \longrightarrow \)
\( \left[A l C l_{4}\right]^{-}, A l C l_{3} \) acts as a
A . salt
B. Lewis base
c. Lewis acid
D. Bronsted acid


To cube a number, how many times you need to multiply the number with itself?
A. 1 time
B. 2 times
c. 3 times
D. 4 times


Determine at 298 for cell :
\( \boldsymbol{P t}\left|\boldsymbol{Q}, \boldsymbol{Q} \boldsymbol{H}_{2}, \boldsymbol{H}^{+}\right||\mathbf{1} \boldsymbol{M} \boldsymbol{K} \boldsymbol{C l}| \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \mid \boldsymbol{H} \)
the pH when \( \boldsymbol{E}_{\text {cell}}=\mathbf{0} \)
\( \operatorname{given} E_{R P(R H S)}^{\circ}=0.28, E_{R P(L H S)}^{\circ}= \)
0.699 (write the value to the nearest
integer)


The radial part of wave function
depends on the quantum numbers:
This question has multiple correct options
\( A \)
B.
\( c \cdot \mid, m_{1} \)
D. nonly


Solve the equation \( x^{2}-2 b x+\left(b^{2}-\right. \)
\( \left.\boldsymbol{a}^{2}\right)=\mathbf{0} \)


Evaluate the following determinant:
\( \begin{array}{|ccc|}15 & 11 & 7 \\ 11 & 17 & 14 \\ 10 & 16 & 13\end{array} \)


A stream of electrons and protons are
directed towards a narrow slit in a
screen (see figure). The intervening region has a uniform electric field \( \boldsymbol{E} \)
(vertically downwards) and a uniform
magnetic field \( B \) (out of the plane of the
figure) as shown. Then:
This question has multiple correct options
A \( \cdot \) electron and protons with speed \( \frac{|E|}{|B|} \) will pass through
the slitt
B. protons with speed \( \frac{|E|}{|B|} \) will pass through the slit.
electrons of the same speed will not
c. neither electrons nor protons will go through the slitt irrespective of their speed
D. electrons will always be deflected upwards irrespective of their speed


If \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{3}\} \) and \( \boldsymbol{B}=\{1,2\}, \) then \( \boldsymbol{A} \times \)
\( B \) is equal to
A \( \cdot\{(2,1),(2,2),(3,1),(3,2)\} \)
B - \{(1,2),(1,3),(2,2),(2,3)\}
c. \{(2,1),(3,2)\}
D \( \cdot\{(1,2),(2,3)\} \)


The \( (x, y, z) \) co-ordinate of two points \( A \)
and B are given respectively as (0,3,-1) and \( (-2,6,4) . \) The
displacement vector from \( A \) to \( B \) may be given by :
A. \( -2 i+6 j+4 k \)
\( k \)
в. \( -2 i+3 j+3 k \)
c. \( -2 i+3 j+5 k \)
D. \( 2 i-3 j-5 k \)


In equilibrium \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}+\boldsymbol{H}^{+} \)
The equilibrium constant may not
change when:
\( \mathbf{A} \cdot C H_{3} C O O^{-} \) are added
B. \( C H_{3} C O O H \) is added
c. catalyst is added
D. mixture is heated


(a) State Snell's law for refraction of
light.
(b) A concave mirror forms two times
magnified and real image of an object
placed at \( 15 \mathrm{cm} \) from its pole. Determine the distance of image from mirror and focal length of the mirror.


What is the fate of notochord in higher
chordates?
A. Notochord is replaced by vertebral column partly or fully
B. Notochord is converted to vertebral column partly or fully
c. Notochord is converted to nerves
D. None of the above


A child drank 250 lit. on Sunday. On Monday he drank 650 lit. On Tuesday he drank 100 lit. How much in all did the
child drink?
A. 950 lit
B. 1000 litt
c. 850 lit
D. None of these


Q Type your question.
other end of rod is at temperature \( T_{2} \)
and is exposed to atmosphere. The
temperature of atmospheric is \( T_{s} . \) The
lateral part of rod is insulated. If \( \boldsymbol{T}_{2}- \)
\( \boldsymbol{T}_{s}<<\boldsymbol{T}_{s}, \boldsymbol{T}_{2}=\boldsymbol{T}_{s}+\boldsymbol{\Delta} \) Т \( \boldsymbol{\&} \boldsymbol{\Delta} \boldsymbol{T} \propto \)
\( \left(T_{1}-T_{s}\right), \) find proportionality constant
of given equation. The heat loss to
atmosphere is through radiation only and the emissivity of the rod is \( \varepsilon \).
\( A \)
в.
\( c \)
D.


In frog heart, there are cardiac muscles which consist of fibres called
A. Purkinje fibres
B. Myonemes
c. Telodendria
D. Columnae carneae


Which of the following represents the composition of Carnallite mineral?
A. \( K_{2} O \cdot A l_{2} O_{3} \cdot 6 S i O_{2} \)
в. \( K N O_{3} \)
c. \( K_{2} S O_{4} \cdot M g S O_{4} \cdot M g C l_{2} \cdot 6 H_{2} O \)
D. \( K C l \cdot M g C l_{2} \cdot 6 H_{2} O \)


A force of 500 dyne acts on an object
where the object moves through \( 8 m \) in
the direction of force. Calcualate the
work done in this case


Which part of Juxta medullary nephron is found in cortical region
A. Malpigian body
B. Proximal convulated tubule
c. Distal convulated tubule
D. Loop of henle


The energy required to break \( 76 \mathrm{gm} \) gaseous fluorine into free gaseous
atom is 180 Kcal at \( 25^{0} C . \) The bond
energy of F-F bond will be:
A. 180 Kcal
B. 90 Kcal
c. 45 Kcal
D. 104 kcal


Prove that the line joining the mid-
points of two parallel chords of a circle
passes through the centre.


Find work done in each process.


Which of the following compounds has
incorrect IUPAC nomenclature?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C H_{2} C O O C_{2} H_{5} \leftarrow \) ethyl butanoate
B \( \cdot C H_{3} C H\left(C H_{3}\right) C H_{2} C H O \leftarrow \) ethyl butanoate
\( \mathbf{c} \cdot C H_{3} C H\left(C H_{3}\right) C O C H_{2} C H_{3} \leftarrow 2- \) methyl-3-pantanone
D. \( C H_{3} C H\left(C H_{3}\right) C H(O H) C H_{3} \leftarrow \) 2-methyl-3-butanol


Find the equivalent fraction of \( \frac{36}{48} \) with
numerator 9
A \( \cdot \frac{36}{9} \)
B. \( \frac{9}{12} \)
\( c \cdot \frac{9}{48} \)
D. 9


Sometimes you get a mild spark when you touch the metal surface of a car.
What might be the reason?
A. Due to magnetic attraction, a spark is created
B. Due to electrostatic charge residing on the metal as well as on skin, mild spark is observed
C. Car tries to become neutral by donating electrons
D. Its the only path to ground


Explain the type hybridisation, magnetic property and geometry for
\( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-} \) and \( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) using
VB theory.


The planet farthest from the Earth is
A. Pluto
B. Mercury
c. Neptune
D. Saturn


The isoelectronic pair is:
[Note : same valence shell]
A. \( C O, N_{2} \)
в. \( O_{2}, \) NO
c. \( C_{2}, H F \)
D. \( F_{2}, H C l \)


\( \Delta_{f} G^{o} \) at \( 500 K \) for substance \( S \) in liquid state and gaseous state are \( +100.7 k c a l m o l^{-1} \) and
\( +103 k c a l \) mol\( ^{-1} \) respectively. Vapour pressure of liquid \( S \) at \( 500 K \) is approximately equal to: \( (R= \)
\( \left.2 \operatorname{cal} K^{-1} m o l^{-1}\right) \)
A. 0.1 atm
B. 1 atm
c. 10 atm
D. 100 atm


The refractive index of prism is 2. The prism can have a maximum refracting angles of
A \( .90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


A coil of 30 turns of wire each of \( 10 c m^{2} \)
area is placed with its plane perpendicular to a magnetic field of 0.1 \( T . \) When the coil is suddenly withdrawn from the field, a
galvanometer connected in series with
the coil indicated that a \( 10 \mu C \)
charge passes around the circuit. The combined resistance of the coil and
galvanometer is:
A . \( 3 \Omega \)
в. \( 30 \Omega \)
\( c .300 \Omega \)
D. 3000\Omega


Assertion
Hydrogen is a diatomic molecule.
Reason
Hydrogen atom has a single electron in
its outermost shell
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The tangential forces per unit area of the liquid layer required to maintain unit velocity gradient is known as:
A. coefficient of gravitation of liquid layer
B. coefficient of friction between layers
c. coefficient of viscosity of the liquid
D. temperature coefficient of viscosity


Integrate the function \( \frac{1}{\sqrt{9-25 x^{2}}} \)


If \( A=(a, b, c, d), B=(p, q, r, s) . \) then which
of the following are relations from \( A \) to
B? Give reasons for your answer:
This question has multiple correct options
A. \( R_{1}=\{(a, p),(b, r),(c, s)\} \)
B. \( R_{2}=\{(q, b),(c, s),(d, r)\} \)
C. \( R_{3}=\{(a, p),(a, q),(d, p),(c, r),(b, r)\} \)
D. \( R_{4}=\{(a, p),(a, q),(b, s),(s, b)\} \)


\( H_{2} O_{2} \) solutions are stored in dark
colored plastic or wax-coated glass vessels often with negative catalysts such as urea or sodium
stannate added as stabilizers.
State whether the given reaction is True
or False?


Find the coordinates of the point on \( y \)
axis which is nearest to the point (-2,5)


The volume of a ball increases at
\( 4 \pi c . c / \)sec. The rate of increases of radius when the volume is \( 288 \pi c . c . s \) is
A \( \cdot \frac{1}{6} \mathrm{cm} / \mathrm{sec} \)
B \( \cdot \frac{1}{36} \mathrm{cm} / \mathrm{sec} \)
c. \( \frac{1}{9} \mathrm{cm} / \mathrm{sec} \)
D. \( \frac{1}{49} \mathrm{cm} / \mathrm{sec} \)


The azimuthal quantum number indicates the shape of the subshell.
A. True
B. False


An application of electrostatic
induction is

This question has multiple correct options
A. electric generator
B. Van de Graff generator
c. Wimhurst machine
D. transformer


Show that the following points form an equilateral triangle. \( (\sqrt{3}, 2),(0,1) \) and (0,3)


Horn silver is:
A. carbonate mineral
B. chloride mineral
C . sulphate mineral
D. phosphate mineral


Find the principal value of:
\( \sec ^{-1}\left(2 \sin \frac{3 \pi}{4}\right) \)


The following is probabilty distribution
of r.v X.
\[
\begin{array}{lllllll}
\mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \\
p(x) & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6}
\end{array}
\]
then value of k is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


A \( 1.0 \mathrm{m} \) long metallic rod is rotated with
an angular frequency of 400 rad \( s^{-1} \)
about an axis normal to the rod passing through its one end. The other end of the
rod is in contact with a circular metallic
ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the
ring.


Passing \( \boldsymbol{H}_{2} \boldsymbol{S} \) gas into a mixture of \( M n^{2+}, N i^{2+}, C u^{2+} \) and \( H g^{2+} \) ions in
an acidified aqueous solution precipitates.
A. CuS and Hgs
B. MnS and cus
c. Mns and Nis
D. Nis and Hgs


Assertion
In case of aryl halides, halogens are
moderately deactivating
Reason
Halogens are ortho, para directing
groups.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A rectangular hyperbola whose cente is C is cut by any circle of radius \( r \) in four
point \( P, Q, R, \) S. The value of \( C P^{2}+ \)
\( C Q^{2}+C R^{2}+C S^{2} \) is equal to:
A \( \cdot r^{2} \)
B . \( 2 r^{2} \)
\( c \cdot 3 r^{2} \)
D. \( 4 r^{2} \)


Why are earthworms important in soils?
A. Earthworms are segmented which means that they cause more caverns for other bacteria
and microbes to be present underground
B. Earthworms produce fluids which enrich the soil aiding for nitrogen to be present for plant
growth
C. Earthworms inhibit gaseous exchange killing other bacteria which can be harmful to plants
D. Earthworms ingest soil and excrete soil which allows for some chemicals to be


An amount of 0.2 mole of \( A O_{3}^{-} \) gains 1.2
mole of electron in a process. Assuming that there is no change in oxidation state of oxygen, determine the oxidation state of 'A' in product:
\( A \cdot+1 \)
B. -
\( c \cdot 0 \)
\( D \cdot+6 \)


A wire is lying horizontally in the north south direction and there is a horizontal
magnetic field pointing towards the east. Some positive charges in the wire move north and an equal number of
negative charges move south. The direction of force on the wire will be :
A. East
B. Down, into the page.
c. Up, out of the page
D. west


Prove that \( |\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}| \leq|\overrightarrow{\boldsymbol{a}}||\overrightarrow{\boldsymbol{b}}| \)


The most stable complex among the following is:
A \( \cdot_{K_{3}}\left[A l\left(C_{2} O_{4}\right)\right] \)
в. \( \left[P t(e n)_{2}\right] C l \)
c. \( \left[A g\left(N H_{3}\right)_{2}\right] C l \)
D \( \cdot K_{2}[N i(E D T A) \)


Evaluate \( \int \frac{2 x}{x^{2}+3 x+2} d x \)


Write the decay equations and
expressions for the disintegration
energy \( Q \) of the following decay: \( \beta^{-} \) decay, \( \beta^{+} \) decay, electron capture


Let \( m_{P} \) be the mass of a proton, \( m_{n} \) the
mass of a neutron, \( M_{1} \) the mass of a
\( 20 \mathrm{Ne} \) nucleus and \( M_{2} \) the mass of a
10
\( _{20}^{40} C a \) nucleus. Then This question has multiple correct options
A. \( M_{2}=2 M_{1} \)
В . \( M_{2}>2 M_{1} \)
c. \( M_{2}<2 M_{1} \)
D. \( M_{1}<10\left(m_{n}+m_{p}\right) \)


The drug 'Belladonna' is obtained from
A. Atropa
B. Rauwolfia
c. Solanum
D. capsicum


A narrow monochromatic beam of light intensity I is incident on a glass plate. another identical glass plate is kept close to the first one and parallel to it
Each glass plate reflects \( 25 \% \) of the light incident on it and transmit the
remaining. find the ratio of the
minimum and maximum intensity in the interference pattern formed by the two beams obtained after 1 reflection at
each plate.
\( \mathbf{A} \cdot 1: 49 \)
B. 49: 1
c. 1: 23
D. 23: 1


A simple electric motor has an
armature resistance of \( 1 \Omega \) and runs
from a d.c. source of \( 12 V . \) It draws a
current of \( 2 \mathrm{A} \) when unloaded. When a
certain load is connected to it, its speed reduces by \( 10 \% \) of its initial value. The current drawn by the loaded motor is?
\( A \cdot 3 A \)
B. 6 A
c. 2 A
D. 1A


A block of weight \( 100 \mathrm{N} \) is suspended by copper and steel wires of same cross
sectional area \( 0.5 \mathrm{cm}^{2} \) and, length \( \sqrt{3} m \)
and \( 1 m, \) respectively. Their other ends
are fixed on a ceiling as shown in figure. The angles subtended by copper and
steel wires with ceiling are \( 30^{\circ} \) and \( 60^{\circ} \) respectively. If elongation in copper wire
is \( \left(\Delta l_{C}\right) \) and elongation in steel wire is
\( \left(\Delta l_{S}\right), \) then the ratio \( \frac{\Delta l_{C}}{\Delta l_{S}} \) is
(Young's modulus for copper and steel
\( \operatorname{are} 1 \times 10^{11} N / m^{2} \) and \( 2 \times 10^{11} N / m^{2} \)
respectively)


Write one balanced reaction
representing nuclear fusion.


Define ecosystem.


If the position vectors ofthe vertices \( A \) B, C of a triangle ABC are \( 7 \widehat{j}+ \) \( \mathbf{1 0} \widehat{\boldsymbol{k}},-\hat{\mathbf{i}}+\mathbf{6} \widehat{\mathbf{j}}+\mathbf{6} \widehat{\boldsymbol{k}} \) and \( -\mathbf{4} \hat{\mathbf{i}}+\mathbf{9} \hat{\mathbf{j}}+\mathbf{6} \widehat{\boldsymbol{k}} \)
respectively, the triangle is
A . equilateral
B. isosceles
c. scalene
D. right angled and isoscele


At the first minimum adjacent to the central maximum of a single - slit diffraction pattern, the phase difference
between the Huygen's wavelet form the edge of the slit and the wavelet from the midpoint of the slit is:
A \( \cdot \frac{\pi}{8} \) radian
B . \( \frac{\pi}{4} \) radian
c. \( \frac{\pi}{2} \) radian
D. \( \pi \) radian


Assertion: A current flows in a
conductor only when there is an electric field within the conductor.

Reason : The drift velocity of electron in presence of electric field decreases.
A. Both (A) and (R) are true and
(R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


Construct a triangle \( A B C \) in which
\( B C=4.8 \mathrm{cm}, \angle B=30^{\circ} \) and \( A B- \)
\( \boldsymbol{A C}=12 \boldsymbol{c m} \)


When a molecule of pyruvic acid is subjected to anaerobic oxidation and forms lactic acid, it lead to formation of
\( A \cdot N A D+ \)
B. NADH
c. oxygen
D. None of the above


Concentrated \( H_{2} S O_{4} \) cannot be used
for drying up \( \boldsymbol{H}_{2} \boldsymbol{S} \) and \( \boldsymbol{N} \boldsymbol{H}_{3} \)
If true enter 1 , else enter 0 .


X\% of y is y\% of :
\( A \cdot x \)
B. \( 100 x \)
c. \( 10 x \)
\( D \cdot 5 x \)


The areas under velocity-time graph for a particle in a given interval of time represents.
A. velocity
B. acceleration
c. work done
D. displacement


The trend of basicity of lanthanoid
hydroxides:
A. increases across the lanthanoid series
B. decreases across the lanthanoid series
C. first increases and then decreases
D. first decreases and then increases


What is the IUPAC name of
\( \boldsymbol{K}\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{4}\right] ? \)
A. Potassium diamminetetrachlorochromate(III)
B. Potassium diamminetetrachlorochromium(III)
c. Potassium diamminetetrachlorochromate(II)
D. None of these


If two thin lenses of focal length \( f_{1} \) and
\( f_{2} \) are kept in contact to each other then the equivalent focal length of the combination
A. \( \frac{f_{1} f_{2}}{f_{1}+f_{2}} \)
в. \( \frac{f_{1} f_{2}}{f_{1}-f_{2}} \)
c. \( \frac{f_{1}+f_{2}}{f_{1} f_{2}} \)
D. \( \frac{f_{1}-f_{2}}{f_{1} f_{2}} \)


In case of physical adsorption, there is desorption when:
A. temperature increases
B. temperature decreases
c. pressure increases
D. concentration increases


fin \( \Delta \mathrm{ABC}, \angle B=90^{\circ}, \angle C=45^{\circ}, \) then
find the angle \( A \)


Lactose operon is considered to be glucose sensitive due to
A. Catabolite induction
B. Allosteric inhibition
c. Anabolic inhibition
D. None of the above


Correct the following statements.
a) Water boils at \( 100^{0} C \) under
atmospheric pressure.
b) The liquid evaporates above its boiling point.
c) Solids have the largest interparticle
space.
d) Gases have the strongest interparticle forces.


The internal energy of an isolated
system
A. keeps on changing
B. remains constant
c. zero
D. none of these


The inverse of a symmetric matrix is
A. Symmetric
B. Skew-symmetric
c. Diagonal
D. None of these


In a class of 55 students, the number of
students studying in different subject are, 23 in Mathematics, 24 in physics,
19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry
and 4 in all the three subjects. Find the number of students who have taken
exactly one subject.


When a particle moves along a straight
path, then the particle has
A. tangential acceleration only
B. centripetal acceleration only
c. both tangential and centripetal acceleration
D. none of the mentioned


Which one is not dangerous for life and atmosphere?
A. Biopollutants
B. Ozone layer
c. Nuclear blast
D. Deforestation


The differential rate law for the reaction
\( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightarrow 2 \boldsymbol{H} \boldsymbol{I} \) is:
A \( \cdot-\frac{d\left[H_{2}\right]}{d t}=-\frac{d\left[I_{2}\right]}{d t}=-\frac{d[H I]}{d t} \)
B. \( \frac{d\left[H_{2}\right]}{d t}=\frac{d\left[I_{2}\right]}{d t}=\frac{1}{2} \frac{d[H I]}{d t} \)
c. \( \frac{1}{2} \frac{d\left[H_{2}\right]}{d t}=\frac{1}{2} \frac{d\left[I_{2}\right]}{d t}=-\frac{d[H I]}{d t} \)
D. \( -2 \frac{d\left[H_{2}\right]}{d t}=-2 \frac{d\left[I_{2}\right]}{d t}=\frac{d[H I]}{d t} \)


The number of hydroxy groups present in pyrosulphuric acid is:
A .2
B. 3
\( c \cdot 4 \)
\( D \)


The median of given observations arranged in ascending order in \( 25 . \) Find
the value of \( p \) \( \mathbf{1 1}, \mathbf{1 3}, \mathbf{1 5}, \mathbf{1 9}, \boldsymbol{p}+\mathbf{2}, \boldsymbol{p}+\mathbf{4}, \mathbf{3 0}, \mathbf{3 5}, \mathbf{3 9}, \mathbf{4 6} \)
A . 22
B . 24
\( c \cdot 21 \)
D. 26


On exposure to sunlight, chloroform oxidises to:
A. phosgene
B. chloropicrin
c. salicylaldehyde
D. chloral


With reference to polarization angle,
\( \boldsymbol{i}_{\boldsymbol{p}}+\boldsymbol{r}= \)


Statement \( I:^{12} C \)
is an isotope of \( ^{14} \boldsymbol{C} \)
Statement II :The nuclei of both atoms
have the same number of neutrons.
\( \mathbf{A} \cdot \) true, false
B. false, true
c. false, false
D. true, true, correct explanation


Given above is the bar graph indicating
the marks obtained out of 50 in
mathematics paper by 100 students.
Read the bar and answer the following
questions:
What is the number of students
belonging to the highest mark group?


Find equivalent capacitance between \( A \)
and B.


If \( x+\frac{1}{x}=5, \) then find the value of \( x^{3}+\frac{1}{x^{3}} \)
A . 110
B. 115
\( c \cdot 105 \)
D. 100


When the sun rays are incident at an
angle of \( 60^{0} \) then intensity is \( I . \) What will be the intensity if the sun rays are
incident at \( 30^{\circ} ? \)
A \( \cdot \frac{I}{\sqrt{3}} \)
B. \( \sqrt{3} I \)
c. \( 3 I \)
D. \( \frac{1}{3} \)


Homologous chromosomes separates
in which of the following phase of
meiosis?
A. Metaphase!
B. Metaphase II
c. Anaphase!
D. Anaphase II


A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?
A \( \cdot \frac{2}{9} \)
в. \( \frac{1}{14} \)
c. \( \frac{2}{63} \)
D. \( \frac{2}{14} \)


Passengers standing in a bus are thrown outwards when the bus takes a
sudden turn. This is due to:
A. outward pull on them
B. inertia
c. change in momentum
D. change in acceleration


A lyophobic colloid cannot be formed by:
A. mixing dispersed phase and dispersion medium
B. chemical reactions like hydrolysis
c. exchange of solvent
D. peptisation


What are emulsions? How they are
classified? Give one example of each.


The mean of a distribution is 14 and
standard deviation is 5. What is the
value of the coefficient of variation?
\( \mathbf{A} \cdot 57.7 \% \)
B. \( 45.7 \% \)
c. \( 35.7 \% \)
D. None of these


What is meant by a reproductively healthy society? List two measures to
develop such a society.


Find out the temperature of absolute
zero kelvin.
\( \mathbf{A} \cdot 0^{\circ} C \)
в. \( 100^{\circ} \mathrm{C} \)
c. \( 273^{\circ} \mathrm{C} \)
D. \( -273^{\circ} C \)
E \( .-100^{\circ} \mathrm{C} \)


The number of atoms of \( C r \) and \( O \) in a
compound is \( 4.8 \times 10^{10} \) and \( 9.6 \times 10^{10} \)
respectively. Its empirical formula is :
A. \( C r_{2} O_{3} \)
в. \( C r O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{4} \)
D. \( C r O_{5} \)


In India,jute is cultivated during which
season?
A. Rainy
B. Summer
c. winter
D. Throughout the year.


If \( e^{d y / d x}=x+1 \) given that when \( x= \)
\( \mathbf{0}, \boldsymbol{y}=\mathbf{3} \) then minimum (local) value of
\( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) is


A body of mass \( \mathrm{m} \) is dropped from a
height h equal to the radius of the earth
(R) above the tunnel dug through the
earth as shown in the figure. Ignore the
effect of earths rotation and air
resistance, M is mass of earth. Choose
the correct alternative(s):
A. body will oscillate through the earth to a height hon both sides
B. body will execute simple harmonic motion.
c. Motion of the body is periodic.
D. body passes the center of earth with a speed \( \sqrt{\frac{2 G M}{R}} \)


Alkali storage cell is commonly called:
A. lead accumulator
B. edison battery
C. fuel cell
D. all


Which value of \( n \) and \( k \) suggests about the shape of 3s orbital?
\( A \cdot 3,2 \)
в. 1,1
\( c \cdot 3,0 \)
D. 3,3


Divide
\( \left(y^{3}-3 y^{2}+5 y-1\right) \div(y-1) \)


Write a short note on sky wave
propagation.


The hormone that promotes anabolism and inhibits catabolism is the
A. tri iodo Thyroxine
B. auxins
c. insulin
D. morphactin


Lateral style is found in
A. Petunia
B. Mango
c. Sunflower
D. calotropis


When \( 1 F \) of electricity is passed
through acidulated water, \( O_{2} \) evolved is:
A \( \cdot 11.2 d m^{3} \)
B. \( 5.6 d m^{3} \)
c. \( 1.0 d m^{3} \)
D. \( 22.4 d m^{3} \)


In a thermodynamic system, \( Q \)
represents the energy transferred to or from a system by heat and \( W \)
represents the energy transferred to or from a system by work
\( Q>0 \) and \( W=0 \)
\( Q<0 \) and \( W=0 \)
\( W>0 \) and \( Q=0 \)
\( W>0 \) and \( Q=0 \)
Which of the above will lead to an
increase in the internal energy of the system?
A. I only
в. II only
c. Iand IV only
D. II and III only
E. II and IV only


If a and x represent real numbers for
which \( x^{2}=-a, \) which of the following
statements could be true?
I. \( a>0 \)
II. \( \boldsymbol{a}=\mathbf{0} \)
III. \( \boldsymbol{a}<\mathbf{0} \)
A. None
B. II only
c. ॥ा only
D. I and II only
E. II and III only


What is the role of these as food
additives?
i) Sodium benzoate
ii) Aspartame


Derive partial fraction for \( \frac{5 x^{2}+1}{x^{3}-1}= \)
A \( \cdot \frac{3}{x-1}+\frac{2 x+1}{x^{2}+x+1} \)
в. \( \frac{4}{x-1}+\frac{5 x+1}{x^{2}+x+1} \)
c. \( \frac{2}{x-1}+\frac{3 x+1}{x^{2}+x+1} \)
D. \( \frac{1}{x-1}+\frac{4 x+1}{x^{2}+x+1} \)


Fill in the blanks with suitable word:
Heterotrophs depend on and
other for food


The total surface area of a cube is
\( 486 \mathrm{cm}^{2} . \) Calculate its edge


Find the value of the determinant:
\[
\left|\begin{array}{ccc}
\cos (\theta+\phi) & -\sin (\theta+\phi) & \cos 2 \phi \\
\sin \theta & \cos \theta & \sin \phi \\
-\cos \theta & \sin \theta & \cos \phi
\end{array}\right|
\]


The side view of the given cube is
A. square
B. triangle
c. circle
D. parallelogram


Suggest reaction mechanisms for the
formation of given product.


Differentiate the following functions
w.r.t \( \boldsymbol{x} \)
\( (i) \cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \)
\( (i i) \sin ^{-1}(2 x \sqrt{1-x^{2}}) \)


\( Z n(s) / Z n^{2+}(a q) \| C u^{2+}(a q) / C u(s) \)
\( \boldsymbol{E}^{0} z n^{2+} / Z n=-0.76 \mathrm{V} \)
\( \boldsymbol{E}^{0}_{C u^{2+} / C u}=+0.34 \mathrm{V} \)
Calculate \( \boldsymbol{E}_{c e l l}^{0} \) and equilibrium
constant \( \boldsymbol{K} \)


In styrene foam, the dispersed phase and dispersion medium respectively
are:
A. gas, gas
B. gas, solid
c. solid, solid
D. liquid, solid


Fill in the blanks:
Magnification of convex mirror is in
range and of concave
mirror is in range
A \( (0,1),(-\infty, 0) \cup(1, \infty) \)
(1)
B . \( (-1,0),(-\infty, \infty) \)
c. \( (-\infty, \infty),(1, \infty) \)
D \( \cdot(-\infty, \infty),(-1,-\infty) \)


A room is \( 12.5 \mathrm{m} \) long and \( 8 \mathrm{m} \) wide.
square carpet of side \( 8 \mathrm{m} \) is laid on its floor. Find the area of the floor which is
not covered by carpet
\( A \cdot 6 m \)
в. 36 sq.m
\( \mathbf{c} .63 \mathrm{m} \)
D. 63 sq.m


The two anomers of fructofuranose are
A . acetal
B. hemiacetal
c. both A and B
D. none of these


Vectors \( \overrightarrow{\boldsymbol{a}}=-\mathbf{4} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{k}} ; \overrightarrow{\boldsymbol{b}}=\mathbf{1 4} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}- \)
\( \mathbf{5} \hat{k} \) are laid from one point. Vector \( \overrightarrow{\boldsymbol{d}} \)
which is being laid off from the same point dividing the angle between vectors \( \vec{a} \) and \( \vec{b} \) in equal halves and having the magnitude \( \sqrt{\mathbf{6}} \) is
\( \mathbf{A} \cdot \hat{i}+\hat{j}+2 \hat{k} \)
B \( \cdot \hat{i}-\hat{j}+2 \hat{k} \)
c. \( \hat{i}+\hat{j}-2 \hat{k} \)
D . \( 2 \hat{i}-\hat{j}-2 \hat{k} \)


A wire is bent in the form of a rectangle having length twice the breadth. The same wire is bent in the form of a
circle. It was found that the area of the
circle is greater than that of the
rectangle by \( 104.5 \mathrm{cm}^{2} . \) Find the length of the wire.


In an A.P the first term is 2 and the sum
of the first five terms is one fourth of the
next five terms. Show that 20 th term is
-112


Two small objects each with a net charge of \( +Q \) exert a force of magnitude Fon each other. We replace one of the objects with another whose net charge is \( +4 Q . \) We move the \( +Q \) and \( +4 Q \) charges to be 3 times as far apart as they were. What is the magnitude of the force on the \( +4 Q \) charge?
\( A \cdot F \)
B. 4F
\( c \cdot 4 F / 3 \)
D. 4F/9
E. F/3


A ball of mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is
released in the viscous liquid. The value of its terminal velocity is proportional to
\( ^{A} \cdot\left(\frac{1}{r}\right) \) only
в. \( \frac{m}{r} \)
c. \( \left(\frac{m}{r}\right)^{1 / 2} \)
D. m only


Which colour of the light has the Iongest wavelength?
A . Red
B. Blue
c. Green
D. Violet


Length of glass tube in simple barometer is
A. \( 100 \mathrm{mm} \)
в. 1 ст
\( c .100 \mathrm{cm} \)
D. \( 1 \mathrm{mm} \)


The enthalpy of dissociation of \( \boldsymbol{H}_{3} \) is
\( 954 k J / m o l \) and that of \( P_{2} H_{4} \) is \( 1.485 M J \) mol \( ^{-1} . \) What is the bond
enthalpy of the \( P-P \) bond?
A. \( 213 k J / \) mol
в. \( -213 k J / \) тод
c. \( 2757 k J / \) mol
D. None of these


Two particles having position vectors \( \vec{r}_{1}=3 \hat{i}+5 \hat{j} \mathrm{m} \) and \( \vec{r}_{2}=-5 \hat{i}+3 \hat{j} \mathrm{m} \)
are moving with velocities \( \vec{V}_{1}=4 \hat{i}+ \) \( 3 \hat{j} \mathrm{m} / \mathrm{s} \) and \( \vec{V}_{2}=-a \hat{i}+4 \hat{j} \mathrm{m} / \mathrm{s} . \) If they
collide after 2 seconds, the value of \( a \) is:
A . -2
B. -4
\( c .-6 \)
D. -8


In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If \( \mathrm{V} \) and \( \mathrm{B} \) are kept constant, the ratio ( \( \left.\frac{\text { Charge on the ion }}{\text { Mass of the ion }}\right) \) wil be proportional to
A \( -\frac{1}{R} \)
в. \( \frac{1}{R^{2}} \)
\( c \cdot R^{2} \)
D.


If the mean of the data : 7,8,9,7,8,7
\( \lambda, 8 \) is \( 8, \) then the variance of this data
is
A .
B. 1
\( c \cdot \frac{9}{8} \)
D. 2


The distance between (3,5) and (5,3)
A \( \cdot 2 \sqrt{2} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. None


Which of the following will produce maximum wastage of electricity?
A. CFL
B. Electric bulb
c. LED lights
D. All are power savers


Solutions \( A, B, C \) and \( D \) are
respectively \( 0.1 M \) glucose,
\( \mathbf{0 . 0 5} M N a C l, 0.05 M B a C l_{2} \) and
\( 0.1 M A l C l_{3} . \) Which one of the following
pairs is isotonic?
A. \( A \) and \( B \)
B. \( B \) and \( C \)
c. \( A \) and \( D \)
D. \( A \) and \( C \)


The first term of an AP is 5, last term is
45 and the sum is \( 400 . \) Find the number of terms and the common difference.
A. \( n=16 \) and \( d=8 / 3 \)
B. \( n=16 \) and \( d=16 / 3 \)
c. \( n=8 \) and \( d=16 / 3 \)
D. \( n=8 \) and \( d=8 / 3 \)


Find the HCF of 1656 and 4025 by
Euclids division theorem


Afridi purchased an old scooter for Rs.16000. If the cost of scooter after 2
years depreciates to \( R s .14440, \) find the
rate of depreciation.


A vessel contains \( X \) number of molecules of hydrogen gas at a certain temperature and pressure. Under the
same conditions of temperature and
pressure, how many molecules of nitrogen gas would be present in the
same vessel?
\( A \cdot 2 x \)
B. \( x \)
c. \( 0.5 x \)
D. 3x


Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the
voltage difference are \( 3 \% \) each, then
error in the value of resistance of the
wire is
A . \( 6 \% \)
B. Zero
c. \( 1 \% \)
D. 3\%


The electronic configuration of chloride ion is
A . 2,8,7
B. 2, 8,6
c. 2,8,8
D. 2, 8


Which of the following will not function as a buffer solution?
(i) \( N a C l \) and \( N a O H \)
\( (i i) N a O H \) and \( N H_{4} O H \)
\( (\text {iiii}) \boldsymbol{C H}_{3} \)COONH\( _{4} \) and \( \boldsymbol{H C l} \)
\( (i v) \) Borax and boric acid
A \( \cdot(i),(i i),(i i i) \)
B. \( (i i),(i i i),(i v) \)
C. \( (i),(i i i),(i v) \)
D. \( (i),(i i),(i i i),(i v) \)


When light splits after passing through a glass prism into seven colours, the phenomenon is called:
A. reflection of light
B. refraction of light
c. dispersion of light
D. specturm


Number of non-bonding electron pairs
on \( X e \) in \( X e F_{6}, X e F_{4} \) and \( X e F_{2} \)
respectively will be:
\( \mathbf{A} \cdot 6,4,2 \)
B. 1,2,3
c. 3,2,1
D. 0,3,2


Anhydrous \( A l C l_{3} \) is considered as Lewis acid because
A. It accepts a pair of electrons
B. It donates a pair of electrons
c. It releases electrons.
D. It gains electrons


A solution of glucose \( \left(\mathbf{C}_{6} \mathbf{H}_{\mathbf{1 2}} \mathbf{O}_{\mathbf{6}}\right) \) in
water is labelled as \( 10 \% \) by weight. What would be the molality of the solution?
(Molar mass of glucose \( =180 \mathrm{g} \mathrm{mol}^{-1} \) )
A. 0.4
B. 0.6
\( c .0 . \)
D. 0.5


Boron has two isotopes \( \mathrm{B}-10 \) and \( \mathrm{B}-11 . \) I the average atomic mass of boron is 10.80 u. What is the percentage of a heavier isotope?
A. 80
B. 20
\( c . \) 30
D. 70


How does the angular separation between fringes in single slit diffraction experiment change when the distance of separation between the slit and screen is doubled?


Masses \( 8,2,4,2 \mathrm{kg} \) are placed at the corners \( A, B, C, D \) respectively of a square ABCD of diagonal 80 cm. The distance of center of mass from A is:
A. 20 cm
B. 30cm
c. \( 40 \mathrm{cm} \)
D. 60cm


If \( \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{A}}, \) then the angle
between \( A \) and \( B \) is
A . \( \pi \)
в. \( \pi / 3 \)
c. \( \pi / 2 \)
D . \( \pi / 4 \)


Two coils have mutual inductance
\( 0.005 H . \) The current changes in the form coil according to equation, \( \boldsymbol{I}= \)
\( I_{0} \sin \omega t . \) Where \( I_{0}=10 A . \) and \( \omega= \)
\( 100 \pi \) rads/s. The maximum value of
emf in the second coil is :
A . \( 12 \pi \)
B. \( 8 \pi \)
\( c .5 \pi \)
D. \( 2 \pi \)


State True or False.
\( \mathbf{2} a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a= \)
\( \left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\right] \)
A. True
B. False


A completely air tight container contains 100 grams of radioactive material.After 24days, only 12.5 grams
of radioactive material left in the
bottle.Calculate the half-life of this
radioactive material?
A. 24 days
B. 16 days
c. 12 days
D. 8 days
E. 3 days


Q Type your question.
the following species are involved in the
above-mentioned reaction as
intermediates?
This question has multiple correct options
\( A \)
B.
\( c \)
\( D \)


A stone thrown down with a speed \( u \)
takes a time \( t_{1} \) to reach the ground, while another stone, thrown upwards from the same point with the same
speed, takes time \( t_{2} \). The maximum
height of the second stone reaches from
the ground is :
A \( \cdot 1 / 2160 ; g t_{1} t_{2} \)
B . \( g \) 8 \( \left(t_{1}+t_{2}\right)^{2} \)
c. \( g \) 8 \( \left(t_{1}-t_{2}\right)^{2} \)
D. \( 1 / 2 g t_{2}^{2} \)


A hemispherical tank full of water is emptied by a pipe at the rate of \( 3 \frac{4}{7} \) litres per second. How much time will it take
to make the tank half-empty, if the tank
is \( 4 m \) in diameter


Shape selective catalysts are so called
because of :
A. the shape of the catalysts
B. the specificity of the catalysts
C. the size of the pores of the catalysts which can trap only selective molecules
D. their use for only some selected reactions


Can you draw a triangle having: three
lines of symmetry.


Fill in the blanks with appropriate
words.
Strictly speaking interphase is a phase of \( \ldots \ldots . . . . \) metabolism.


Which of the following is not one of the
ways to prevent water pollution?
A. Toxic products like household chemicals and cleaning agents should be stored and disposed property.
B. Pills, liquid or powder medications or drugs should not be thrown into the drain.
C. Farmers should try using natural fertilisers and pesticides.
D. Cooking oil, ghee, mayonnaise and fats should be poured down the drains.


Calculate the ratio of \( \sigma \) bonding
electrons and \( \pi \) bonding electrons in \( B_{2} \) molecule.