State True or False:
Addition of \( a^{6}-4 a^{4}+6 a, 5 a^{6}+ \)
\( \mathbf{5} a^{4}+\mathbf{6 a}, \mathbf{1 2 a}^{\mathbf{6}}-\mathbf{1 0 a} \) is \( \mathbf{1 8 a}^{\mathbf{6}}+\boldsymbol{a}^{\mathbf{4}}+ \)
\( \mathbf{2} \boldsymbol{a} \)
A. True
B. False


The graph describes an airplane's
acceleration
(a) -time ( \( t \) ) during its
take-off run. The airplane's velocity
when it lifts off at \( t=20 s \) is
A \( \cdot 40 \mathrm{ms}^{-} \)
B. \( 50 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 90 \mathrm{ms}^{-} \)
D. \( 180 \mathrm{ms}^{-1} \)


Find the inverse of the following matrix by using elementary row transformation
\( \left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right] \)


If the given four electronic configurations
(i) \( n=4, l=1 \)
(ii) \( n=4,1=0 \)
(iii) \( n=3,1=2 \)
\( (i v) n=3,1=1 \)
are arranged in order of increasing energy, then the order will be:
A. (iv) < (ii) < (iii) < (i)
B. (ii) < (iv) < (i) < (iii)
c. (i) < (iii) < (ii) < (iv)
D. (iii) < (i) < (iv) < (ii)


Which one of the following is the strongest base in aqueous solution?
A. Trimethylamine
B. Aniline
c. Dimethylamine
D. Methylamine


The total number of orbitals in a
principal shell are :
\( A \cdot n \)
B . \( n^{2} \)
\( c \cdot 2 n^{2} \)
\( D \cdot 3 n^{2} \)


Evaporation of the solution of copper sulfate solution helps in:
A. making the solution concentrated
B. crystallization of copper sulfate
c. both A and B
D. none of these


Polarisation of light proves the.
A. Corpuscular nature of light
B. Longitudinal nature of light
c. Quantum nature of light
D. Transverse nature of light


Find \( k, \) if the given function is
continuous at \( x=2 \) \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\mathbf{3} \boldsymbol{x}-\mathbf{4} \text { for } \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} \\ \mathbf{2} \boldsymbol{x}+\boldsymbol{k} \text { for } \mathbf{2} \leq \boldsymbol{x} \leq \mathbf{4}\end{array}\right. \)


The correct order of the atomic radii of
\( \mathrm{C}, \mathrm{Cs}, \mathrm{Al} \) and \( \mathrm{S} \) is :
\( A \cdot S<C<A \mid<C S \)
B. \( s<c<c s<A l \)
\( c \cdot c<s<c s<A \)
D. \( c<S<A \mid<C \) s


The sum of \( 5^{t h} \) and \( 9^{t h} \) terms of an A.P. is
30. If its \( 25^{t h} \) term is three times its \( 8^{t h} \)
term, find the AP.


Assertion
A mixture of o-nitrophenol and \( p \) nitrophenol can be separated by steam distillation.
Reason
p-nitrophenol is steam volatile whereas o-nitrophenol is not steam volatile.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The direction cosines of a line which is
equally inclined to axes, is given by
A \( \cdot \pm \frac{1}{3} \)
в. \( \pm \frac{1}{\sqrt{3}} \)
\( c . \)
D. 0


Melting of wax is a change.
A. physical
B. chemical
c. both \( A \) and \( B \)
D. none of the above


Assertion
A charge \( q \) is placed inside the square of side b. The flux associated with the
square is independent of side length.
Reason

Gauss's law is independent of size of
the Gaussian surface.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Among the following, the one which is not a "greenhouse gas", is:
A \( \cdot N_{2} O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( O_{2} \)


If for the equilibrium:
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
the value of \( \mathrm{Kp} \) at \( 800 \mathrm{K} \) is \( 27 \times 2^{\lambda / 2} \) and
the equilibrium pressure is 22 atm. Value of \( \lambda \) is :
A . 12
в. 2
c. 10
D. 1
\( E \)


On immersing a glass lens in water, its focal length:
A. will become zero
B. will decrease
c. will increase
D. will become infinite


Oxygen exhibits its +ve oxidation
states in its:
A. Fluorides
B. Chlorides
C. Nitrides
D. Sulphides


\( \underbrace{[L \atop L} \)


Which of the following is a type of mixture in which constituent elements
are not uniformly distributed?
A. Blood
B. Salt and water
c. Bronze
D. None of the above


If \( 9.2 \mathrm{cm} \) is the diameter of the circle,
then its radius is
A \( .4 .1 \mathrm{cm} \)
B. \( 4.6 \mathrm{cm} \)
c. \( 4.8 \mathrm{cm} \)
D. \( 4.3 \mathrm{cm} \)


Evaluate :
i) \( \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
ii) \( \sin ^{-1}\left(-\frac{1}{2}\right) \)


What is the concentration of a cobalt (II)
nitrate solution whose absorbance was
measured at 0.55 in a \( 1.1 \mathrm{cm} \) cuvette
with a molar extinction coefficient of
\( \mathbf{1 . 5} / \boldsymbol{M} \mathbf{c m} ? \)
в. \( 0.60 M \)
c. \( 0.90 M \)
D. \( 1.2 M \)


Solve: \( \int \frac{\sin x-\cos x}{\sqrt{\sin 2 x}} d x \)


A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is
\( A \cdot h e^{2 n} \)
В. \( h e^{n} \)
c. \( \frac{2^{e n}}{h} \)
D. \( \frac{h}{2^{e n}} \)


A monomeric complex of cobalt gave the following results on analysis :
\( C o^{3+}=21.24 \%, N H_{3}=24.77 \%, C l^{-}= \)
\( 12.81 \% \) and \( S O_{4}^{2-}=34.65 \% \)
The compound is diamagnetic and contains no other groups or elements, except water which might be present. What is probable formula of the
compound \( ?\left(M_{C o}=\mathbf{5 9}\right) \)
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l S O_{4}\right] \cdot H_{2} O \)
в. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l S O_{4}\right] .2 H_{2} O \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l H_{2} O\right] S O_{4} \)
D. \( \left[C o\left(N H_{3}\right)_{4} S O_{4}\right] C l .2 H_{2} O \)


Yesterday's closing prices of 2420 different stocks listed on a certain
stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price than yesterday?
A .484
в. 726
\( c .1100 \)
D. 1320
E . 1694


Which of the following statements, about the advantage of roasting of sulphide ore before reduction is not
true?
A. The \( \Delta G_{f}^{0} \) of the sulphide is greater than those for \( C S_{2} \) and \( H_{2} S \)
B. The \( \triangle G_{f}^{0} \) is negative for roasting of sulphide ore to oxide
c. Roasting of the sulphide to the oxide is thermodynamically feasible
D. Carbon and hydrogen are suitable reducing agents for metal sulphides.


In the known interhalogen compounds the maximum oxidation state of
halogen atom is:
\( A \)
B. 5
\( c \cdot 7 \)
D. 8


A convex lens of focal length \( 0.2 \mathrm{m} \) and
made of glass \( \left(^{a} \mu_{g}=1.5\right) \) is immersed
in water \( \left(^{a} \mu_{w}=1.33\right) . \) Find the change in the focal length of the lens.
\( A \cdot 5.8 \mathrm{m} \)
B. 158 m
c. \( 0.58 \mathrm{m} \)
D. \( 5.8 \mathrm{cm} \)


The method of detecting the presence, position and direction of motion of distant objects by reflecting a beam of sound waves is known as
A. RADAR
B. SONAR
c. мIR
D. ско


In which molecule sulphur atom is not
\( \boldsymbol{s} \boldsymbol{p}^{3} \) -hybridized?
\( \mathbf{A} \cdot S O_{4}^{2} \)
в. \( S F_{4} \)
c. \( S F_{2} \)
D. None of these


The potential energy of a particle of mass \( 5 k g \) moving in the \( x \) -y plane is given by the equation, \( U=-7 x+24 y \)
Joule. Here \( x \) and \( y \) are in the meter at
\( \boldsymbol{t}=\mathbf{0}, \) the particle is at the origin and moving with velocity \( (2 i+3 j) m / s . \) The
magnitude of the acceleration of the particle is:
A \( .3 m / s^{2} \)
в. \( 5 m / s^{2} \)
c. \( 31 m / s^{2} \)
D. \( 15 m / s^{2} \)


If two vectors are \( \vec{A}=2 \hat{i}+\hat{j}-\hat{k} \) and \( \vec{B}=\hat{j}-4 \hat{k} \cdot \vec{A} \times \vec{B} \) is perpendicular to
This question has multiple correct options
A . \( \vec{A} \)
в. \( \vec{B} \)
c. \( \vec{A}+\vec{B} \)
D . \( \vec{A}-\vec{B} \)


Hooke's law states that under normal
conditions
A. Stress is inversely proportional to strain till elastic limit
B. Stress is directly proportional to strain till elastic limit
C. Stress is independent of strain
D. Stress is proportional to elastic modulus


Q Type your question
y \( D-D_{0}\lfloor\bar{a} / \) \kappa.
bo 14
\( d \) is placed with it's edges on the \( x \) and \( y \)
axis. The loop is moved with a constant velocity \( \vec{v}=v_{0} \hat{i} . \) The emf induced in
the loop is :
A \( \cdot B_{0} v_{0} d \)
B. \( \frac{B_{0} v_{0} d^{2}}{2 a} \)
c. \( \frac{B_{0} v_{0} d^{3}}{a^{2}} \)
D. \( \frac{B_{0} v_{0} d^{2}}{a} \)


Calculate the total reactance if two
inductor of \( 10 \mathrm{mH} \) and \( 50 \mathrm{mH} \) are
connected in series with \( 10 \mathrm{kHz} \) AC.


The mean of a dist. is \( 4 . \) if its coefficient
of variation is \( 58 \% \). Then the S.D. of the
dist. is
A .2 .23
в. 3.23
c. 2.32
D. None of these


When a spring is extended by \( 2 \mathrm{cm} \) energy stored is 100 J. When extended
by further \( 2 \mathrm{cm}, \) the energy increases by
A . \( 400 J \)
B. \( 300 J \)
c. \( 200 J \)
D. \( 100 J \)


The graph of an equation is given
above. What is the degree of the
polynomial?
\( A \)
B.
\( c \)
\( D \)


If \( \tan y=\sin x \) Find \( \frac{d y}{d x} \)
\( \mathbf{A} \cdot \cos ^{2} y \cos x \)
B. \( \sin x+\cos y \)
\( c \cdot \tan x+\sec x \)
D. None


State the IUPAC names of the following compounds:
(i) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(ii) \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{O} \boldsymbol{O} \boldsymbol{H} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)


Calculate the surface area(in \( c m^{2} \) ) of a
solid cylinder with diameter \( 14 \mathrm{cm} \) and Peight \( 10 \mathrm{cm} .\left(\pi=\frac{22}{7}\right) \)


In clathrate atoms or molecules the
bond formed is :
A . Metallic
B. Covalent
c. lonic
D. They do not form bond


A thermometer is used to measure
A . heat
B. thermal capacity
c. water equivalent
D. temperature


Find the over voltage if electrolysis of brine solution requires \( 2.19 \mathrm{V} \) to produce
\( \mathrm{H}_{2} \) and \( \mathrm{Cl}_{2} . \) (Write your answer upto two
decimal places)
Given: \( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}}^{\boldsymbol{o}}=\mathbf{0} \) and \( \boldsymbol{E}_{C l^{-} / C l_{2}}^{o}= \)
\( -1.36 V \)


The correct order of ionic radii of \( \mathrm{Ce}, \mathrm{La} \)
Pm, and Yb in +3 oxidation state is:
\( \mathbf{A} \cdot L a^{3+}<P m^{3+}<C e^{3+}<Y b^{3+} \)
B \( \cdot Y b^{3+}<P m^{3+}<C e^{3+}<L a^{3+} \)
\( \mathbf{c} \cdot L a^{3+}<C e^{3+}<P m^{3+}<Y b^{3+} \)
D. \( Y b^{3+}<C e^{3+}<P m^{3+}<L a^{3+} \)


If in a series L-C-R ac circuit, the
voltages across \( L, C \) and \( R \) are \( V_{1}, V_{2} \)
and \( V_{3} \) respectively, then the voltage
of the source is always
A. equal to \( V_{1}+V_{2}+V_{3} \)
B. equal to \( V_{1}-V_{2}+V_{3} \)
c. more than \( V_{1}+V_{2}+V_{3} \)
D. none of the above is true


The areas of three adjacent faces of a cuboid are \( a, b \) and \( c . \) If the volume of the cuboid is \( V \), then what is \( V^{2} \) equal
to
A \( \cdot a b c \)
B. \( a b+c \)
c. \( a+b+c \)
D. None of these


There are seven orbitals in a subshell
then the value of \( l \) for it will be
A \( . l=4 \)
в. \( l=3 \)
c. \( l=2 \)
D. \( l=1 \)


Difference between \( n t h \) and \( (n+1) t h \)
Bohr's radius of hydrogen atom is equal to \( (n-1) \) th Bohr's radius. The value of
\( \boldsymbol{n} \) is
A . 1
B . 2
\( c .3 \)
D. 4


If we increase the distance between two
plates of the capacitor, the capacitance will
A. decrease
B. remain same
c. increase
D. first decrease then increase


A voltaic cell is represented as
\( \boldsymbol{A}_{(s)}\left|\boldsymbol{A}_{(a q)}^{+2}\right|\left|\boldsymbol{B}_{(a q)}^{+2}\right| \boldsymbol{B}_{(s)} . \) Which of the
following statements of false regarding
the above cell?
A. The double vertical line indicates salt bridge
B. \( A \) is called the anode and \( B \) is called the cathode
C. The cell reactions are represented as \( A^{2+}+2 e^{-} \rightarrow A \) and \( B \rightarrow B^{2+}+2 e^{-} \)
D. None of the above


Find the emfs \( \varepsilon_{1} \) and \( \varepsilon_{2} \) in the circuit in
Figure. Also find the potential difference
of point \( b \) relative to point \( a \)


Brain Nurtures
A solution of \( C u S O_{4} \) was kept in an iron
pot. After a few days, the iron pot was
found to have a number of holes in it.
How were these holes formed?


What are electromagnetic waves?
Describe Maxwell's electromagnetic theory in brief.


Which of the following is/are incorrect for Humphrey lines of hydrogen spectrum? This question has multiple correct options
A \( \cdot n_{2}=7 \rightarrow n_{1}=2 \)
В \( \cdot n_{2}=10 \rightarrow n_{1}=6 \)
c. \( n_{2}=5 \rightarrow n_{1}=1 \)
D \( \cdot n_{2}=11 \rightarrow n_{1}=3 \)


Movement caused by injury is
A. Traumotropism
B. Rheotropism
c. Traumonasty
D. Rheonasty


Silver can be obtained from silver
glance by:
A. from floatation followed by polling
B. leaching by \( N a C N \) followed by thermal reduction
C . leaching by \( \left(N a C N+O_{2}\right) \) followed cupellation
D. None of these


A fibonacci series is:
A. series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.
B. the simplest is the series \( 1,1,2,3,5,8, \) etc.
C. Both are correct
D. None is correct


Air creates as much pressure as
created by \( \ldots \ldots . c m \) of vertical height of mercury column in a simple barometer.
A .22
B. 36 6
c. 76
D. 260


The difference in electronegativity of carbon-halogen bond is minimum in:
A \( . C-F \)
в. \( C-C l \)
c. \( C-I \)
D. \( C-B r \)


A light wave is incident normally over a slit of width \( 24 \times 10^{-5} \mathrm{cm} . \) The angular
position of second dark fringe from the
central maxima is \( 30^{\circ} . \) What is
wavelength of light?
в. 5000 月
c. \( 3000 \hat{h} \)
D. 1500 月


In Lassaigne's test, the organic compound is fused with a piece of sodium metal in order to:
A. increase the ionisation of the compound
B. decrease the melting point of the compound
c. increase the reactivity of the compound
D. convert the covalent compound into a mixture of ionic compounds


Conver the given fractional numbers to
percent:
\( \frac{\mathbf{3}}{\mathbf{4 0}} \)


What is the purpose of deforestation?
A. Procuring land for cultivation
B. Building houses and factories
c. Making furniture or using wood as fuel
D. All of the above


Chemical formula of Calcium nitride is
\( \boldsymbol{C} \boldsymbol{a}_{3} \boldsymbol{N}_{2} \)
A. True
B. False


A long straight charged wire has the electric field measured as \( 5 N / C \) and
pointing down at a distance of \( 10 \mathrm{cm} \)
above it.

What would the electric field measure
at \( 10 \mathrm{cm} \) below it?
A. \( 10 N / C \) toward the bottom of the screen
B. \( 5 N / C \) toward the bottom of the screenn
c. \( 10 N / C \) toward the top of the screen.
D. \( 5 N / C \) toward the top of the screen


\( V, J \) and \( L \) shaped chromosome occur in which of the following?
A. Prophase
B. Anaphase
c. Metaphase
D. Telophase


Average power consumed by the circuit


What is the area of a regular hexagon with sides of 2.5 in and apothem is 12 in?
\( \mathbf{A} \cdot 89 \) in \( ^{2} \)
B. 14.5 in \( ^{2} \)
c. 80 in \( ^{2} \)
D. 90 in \( ^{2} \)


The molar enthalpy change for
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) at \( \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} K \) and \( \boldsymbol{1} \) at \( \boldsymbol{m} \)
is \( 41 k J / \) mol. Assuming ideal behavior the internal energy change for vaporization of 1 mol of water at \( 373 K \)
and 1 atm in \( \mathrm{kJ} \mathrm{mol}^{-1} \) is:
A . 30.2
в. 41.0
c. 48.1
D. 37.9


The distance moved by the object is
maximum at which point on the graph?
\( A \)
\( B \)
\( c \)
\( D \)
\( E \)


Fill in the blanks
i) For a motor: a permanent magnet, then commercial motor:
ii) Focal length of a lens; metre, then for
power of a lens


The area cut off by the parabola \( y^{2}= \) \( 4 a x \) and its latus rectum is........., if \( a=3 \)


The diameter of the moon is
approximately one-fourth of the diameter of the earth. What fraction of
the volume of the earth is the volume of
the moon?


The diagram shows how some land near
a lake is used. Which of the following is most likely to cause the lake to flood?
A. Cutting down the forest
B. Removing the cattle
c. Taking the silt out of the lake
D. Using pesticides on the crops


The equation of the curve in which sub-
normal varies as the square of the ordinate is ( \( k \) is constant of
proportionality)
A \( \cdot y=A e^{2 k x} \)
B . \( y=e^{k x} \)
C \( \cdot y^{2} / 2+k x=A \)
D. \( y^{2}+k x^{2}=A \)


Calculate the frequency of the radiation emitted when an electronjumps from \( n=3 \) to \( n=2 \) in a hydrogen atom is:
A \( \cdot 4.57 \times 10^{14} s^{-1} \)
В. \( 4.57 \times 10^{16} s^{-1} \)
\( c \cdot 5.01 \times 10^{14} s^{-1} \)
-1
D. \( 5.01 \times 10^{16} s^{-1} \)


Which endocrine gland is not an ectodermal origin?
A. Pineal body
B. Anterior pituitary
c. Adrenal medulla
D. Thymus


Social Forestry Programme was adopted in India during
A . 196
B. 1971
\( c \cdot 1976 \)
D. 1986


Moment of inertia of a thin semi
circular disc \( (\operatorname{mass}=M \& \text { radius }=R) \)
about an axis through point 0 and perpendicular to plane of disc, is given
by :
\( ^{\mathrm{A}} \cdot \frac{1}{4} M R^{2} \)
B. \( \frac{1}{2} M R^{2} \)
c. \( \frac{1}{8} M R^{2} \)
D. \( M R^{2} \)


A body at rest starts sliding from top of a smooth inclined plane and requires 4 seconds to reach bottom. How much
time does it take, starting from rest at top, to cover one-fourth of a distance?
A. 1 second
B. 2 seconds
c. 3 seconds
D. 4 seconds


The following table shows the ages of the patients admitted in a hospital during a year:
25- \( \quad 35 \)
\[
\begin{array}{lll}
\text { Agetin } & \text { 5- } & \text { 15- } \\
\text { years ) } & \text { 15 } & \text { 25 } & \text { 35 }
\end{array}
\]
Number
of patients
Find the mode and the mean of the data
given above. Compare and interpret the two measure of central tendency.


The weakest \( C l-O \) bond is found in :
A. \( C l O_{4}^{-} \)
B. \( C l O_{2}^{-} \)
c. \( C l O^{-} \)
D. \( C l O_{3}^{-} \)


The MRI (magentic resonance imaging) body scanners used in hospitals operate with \( 400 \mathrm{MHz} \) radio frequency energy. The wavelength corresponding to this radio frequency is:
A. \( 0.75 \mathrm{m} \)
B. 0.75 cm
c. \( 1.5 \mathrm{m} \)
D. \( 2 \mathrm{cm} \)


Binding energy per nucleon for helium nucleus \( \left(_{2}^{4} H e\right) \) is \( 7.0 \mathrm{MeV} . \) Find vallue of mass defect for helium nucleus.


The Sun delivers \( 10^{3} W / m^{2} \) of electromagnetic flux to the Earth's
surface. The radiation force on the
roof of dimensions \( 8 m \times 20 m \) will be:
A \( \cdot 3.33 \times 10^{-5} N \)
В. \( 5.33 \times 10^{-4} N \)
\( \mathbf{c} \cdot 7.33 \times 10^{-3} N \)
D. \( 9.33 \times 10^{-2} N \)


An ideal gas in a closed inflexible container has a pressure of 6 atm and a
temperature of \( 27^{\circ} \mathrm{C} \). What will be the
new pressure at \( -73^{\circ} \mathrm{C} \) ?
\( A \cdot 2 a t m \)
B. 3 atm
c. 4 atm
D. 8 atm
E . 9 atm


Let \( \boldsymbol{R}=\left\{\left(\boldsymbol{a}, \frac{\mathbf{1}}{\boldsymbol{a}}\right): \boldsymbol{a} \in \boldsymbol{N} \text { and } \mathbf{1}<\boldsymbol{a}<\right. \)
5 \( \} . \) Find the doman and range of \( R \)


Characteristics of cardiac muscles are
that they
A. Contract quickly and get fatigued
B. Contract quickly and do not get fatigued
c. contract slowly and get fatigued
D. contract slowly and do not get fatigued


A tank has a small hole at its bottom of
area of cross-section a. Liquid is being
poured in the tank at the rate \( V m^{3} / s \) the maximum level of liquid in the container will be(Area of \( \operatorname{tank} A) \)
A. \( \frac{V}{g a A} \)
в. \( \frac{V^{2}}{2 g a^{2}} \)
c. \( \frac{V^{2}}{g A a} \)
D. \( \frac{V^{2}}{2 g a A} \)


A sum of money at compound interest amount to three times of its self in
three years. in how many years will it be nine times of its self?
A. 6 years
B. 5 years
c. 9 years
D. 7 years


A uniform metal disc of radius R is
taken and out of it, a disc of diameter \( \mathrm{R} \)
is cut-off from the end. The center of
mass of the remaining part will be:
A \( \cdot \frac{R}{4} \) from the cente
в. \( \frac{R}{3} \) from the centre
c. \( \frac{R}{5} \) from the cente
D. \( \frac{R}{6} \) from the center


Sodium thiosulphate is used in:
A. photography
B. medicines
c. explosive industry
D. match industry


The function of a fuse wire is
independent of :
A. its specific resistance
B. its radius
c. its length
D. current flowing through it


What is the IUPAC name of the
compound?


Two liquids \( X \) and \( Y \) are perfectly
immiscible. If \( X \) and \( Y \) have molecular
masses in ration \( 1: 2, \) the total vapour pressure of a mixture of \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
prepared in weight ratio 2: 3 should be:
\( \left(\boldsymbol{P}_{X}^{0}=\mathbf{4 0 0} \text { torr }, \boldsymbol{P}_{\boldsymbol{Y}}^{0}=\mathbf{2 0 0} \text { torr }\right) \)
A. 314 torr
B. 466.7 torr
c. 600 torr
D. 700 torr


Wires \( A \) and \( B \) are made from the same
material. Wire A has length 12m and weight 50 g, while wire \( B \) is 18 m long and weighs 40 g. Then the ratio \( \left(R_{A} / R_{B}\right) \) of their resistances will be :
\( A \cdot 16 / 45 \)
B. 415
\( c \cdot 8 / 15 \)
D. 419


Write all the acyclic and cyclic isomers of a compound having molecular
formula \( C_{3} H_{6} O \)


Which of the following is not a purpose to build dams?
A. Prevent flooding of the rivers in the area
B. To prevent flooding of the rivers in the area.
c. To generate hydroelectricity.
D. None of the above


Find the altitude of an equilateral triangle of side \( 5 \sqrt{3} c m \)
A \( .7 .5 \mathrm{cm} \)
в. \( 12.5 \mathrm{cm} \)
\( \mathrm{c} .9 .5 \mathrm{cm} \)
D. \( 8.5 \mathrm{cm} \)


Solve \( (\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)


When fluoride is heated with conc.
\( H_{2} S O_{4} \) and \( M n O_{2} \) the gas evolved is
A. \( H F \)
в. \( F_{2} \)
\( \mathrm{c} \cdot S F_{4} \)
D. None


A current of i ampere is flowing through each ofthe bent wires as shown the
magnitude and direction of magnetic field at 0 is
A \( \cdot \frac{\mu_{0} \mathrm{i}}{4}\left(\frac{1}{\mathrm{R}}+\frac{2}{\mathrm{R}^{\prime}}\right) \)
В. \( \frac{\mu_{0} \mathrm{i}}{4}\left(\frac{1}{\mathrm{R}}+\frac{3}{\mathrm{R}^{\prime}}\right) \)
c. \( \frac{\mu_{0} \text { i }}{8}\left(\frac{1}{R}+\frac{3}{2 R} \prime\right) \)
D. \( \frac{\mu_{0} \mathrm{i}}{8}\left(\frac{1}{\mathrm{R}}+\frac{3}{\mathrm{R}^{\prime}}\right) \)


Write down the number of significant figures in the following.
6428
A. four
B. three
c. \( t w o \)
D. one


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


On passing \( \boldsymbol{H}_{2} \boldsymbol{S} \) into a solution
containing both \( Z n^{2-} \) and \( C u^{2-} \) in
acidic medium, only CuS gets precipitated. This is because:
\( \mathbf{A} \cdot K_{s p} \) of \( C u S<K_{s p} \) of ZnS
B. \( K_{s p} \) of \( C u S=K_{s p} \) of Zns
C. \( K_{s p} \) of \( C u S>K_{s p} \) of ZnS
D. cus is more stable then zns


Expand \( (4 x-3 y)^{3} \)
\( \mathbf{A} \cdot 64 x^{3}-144 x^{2} y+108 x y^{2}-27 y^{3} \)
B. \( 64 x^{3}+144 x^{2} y+108 x y^{2}-27 y^{3} \)
\( \mathbf{c} \cdot 64 x^{3}-144 x^{2} y-108 x y^{2}-27 y^{3} \)
D. None of these


Which of the following is/are true regarding the following linear equation:
\( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{3}}-\frac{\boldsymbol{y}+\mathbf{2}}{\mathbf{2}}=\mathbf{0} \)
A \( \cdot \) It passes through \( \left(0,-\frac{2}{3}\right) \) and \( m=\frac{8}{3} \)
B. It passes through \( \left(0, \frac{8}{3}\right) \) and \( m=-\frac{2}{3} \)
c. \( _{\text {It passes through }}\left(0,-\frac{8}{3}\right) \) and \( m=\frac{2}{3} \)
D . It passes through \( \left(0,-\frac{2}{3}\right) \) and \( m=-\frac{8}{3} \)


For a spontaneous reaction the \( \Delta G \) equilibrium constant \( \left(K_{e q}\right) \) and \( E_{c l l}^{0} \) will be respectively
A . -ve, >1, -ve
B. -ve, <1, -ve
c. \( + \) ve \( ,>1, \), -ve
D. -ve, >1, +ve


\( \mathbf{A} \)
(homogeneous/heterogeneous) mixture of solute and solvent is known as
solution.


An object is dropped from a height \( h \) from the ground. Every time it his the ground it looses \( 50 \% \) of its kinetic energy. The total distance covered as
\( \rightarrow \infty \) is:
\( \mathbf{A} \cdot 2 h \)
B . \( \infty \)
c. \( \frac{5}{3} h \)
D. \( \frac{8}{3} h \)


A car starts from rest to cover distance
\( s . \) The coefficient of kinetic friction
between the road and tire is \( \mu \). The
minimum time in which the car cover
the distance \( s \) is proportional to
\( A \cdot \mu \)
B. \( \sqrt{\mu} \)
\( c \cdot \frac{1}{\mu} \)
D. \( \frac{1}{\sqrt{\mu}} \)


When an inflated tyre bursts, the air escaping out will:
A. get heated up
B. be cooled
c. not undergo any change in its temperature
D. be liquified


Which of the following is not correct
about cyclotron.?
A. It is a machine to accelerate charged particles or ions to high energies.
B. Cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.
C. The operation of the cyclotron is based on the fact that the time for one revolution of an ion is independent of its speed or radius of its orbit
D. The charged particles and ions in cyclotron can move on any arbitary path


Using the principle of mathematical induction, show that;
\( \mathbf{2}+\mathbf{4}+\mathbf{6}+\ldots .+\mathbf{2} \boldsymbol{n}=\boldsymbol{n}^{2}+\boldsymbol{n} \)


The amount of heat produced in a wire depends on its material-
A. Length
B. Thickness
c. Length and thickness
D. None of these


The mass number \( A \) of an atom is equal
to the
A. Number of electrons
B. Number of neutrons + electrons
C. Number of protons + neutrons
D. Number of protons + electrons


Find the inverse of the following matrix by using elementary row transformation:
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & -\mathbf{1}\end{array}\right] \)


According to Huygens, the ether medium pervading entire universe is
A . Less elastic and more dense
B. Highly elastic and less dense
c. Not elastic
D. Much heavier


36 identical cell each having emf 1.5 volt
and internal resistance \( 0.5 \Omega \) are
connected in series with an external
resistance of \( 12 \Omega \). If 6 cells are wrongly connected then current through the circuit will be
A \( \cdot 1.2 \mathrm{A} \)
B. 1 A
\( c \cdot 2 A \)
D. 4 A


Using differentials, find the sum of digits approximate value of the
following up to 3 places of decimal. \( (0.0037)^{\frac{1}{2}} \)


The molar specific heat of oxygen at
constant pressure \( \boldsymbol{C}_{\boldsymbol{P}}= \)
\( \mathbf{7 . 0 3} \mathbf{c a l} / \mathbf{m o l}^{\circ} \mathbf{C} \) and \( \boldsymbol{R}= \)
\( 8.32 J / \) mol \( ^{\circ} \mathrm{C} \). The amount of heat
taken by 5 moles of oxygen when heated
at constant volume from \( 10^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \)
will be approximately.
\( \mathbf{A} \cdot 25 \) cal
в. 50 cal
c. 253 call \( l \)
D. 500 call


If \( e_{1} \) and \( e_{2} \) are the eccentricities of \( a \)
hyperbola \( 3 x^{2}-3 y^{2}=25 \) and its
conjugate respectively, then
A \( \cdot e_{1}^{2}+e_{2}^{2}=2 \)
B . \( e_{1}^{2}+e_{2}^{2}=4 \)
\( \mathbf{c} \cdot e_{1}+e_{2}=4 \)
D. \( e_{1}+e_{2}=\sqrt{2} \)


The equation of line perpendicular to \( x-2 y+1=0 \) and passing through
(1,2) is.
A. \( 3 x-8 y+6=0 \)
B. \( 2 x+y=4 \)
c. \( 3 x-5 y+1=0 \)
D. \( 5 x+3 y=0 \)


If the body is moving in a circle of
radius \( r \) with a constant speed \( v \). Its angular velocity is :
A \( \cdot v^{2} / r \)
B. \( v r \)
c. \( v / r \)
D. \( r / v \)


Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the
potential energy (a) at mean position and (b) at extreme position. A horizontal
disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions per
minute. A 20 gram blob of wax falls on
the disc and sticks to the disc at a
distance of \( 5 \mathrm{cm} \) from its axis. Moment
of inertia of the disc about its axis
passing through its centre of mass is \( 2 \times 10^{-4} k g m^{2} . \) Calculate the new
frequency of rotation of the disc.


Let \( a=2 \hat{i}+\hat{j}+\hat{k}, b=\hat{i}+2 \hat{j}-\hat{j} \) an a
unit vector \( \hat{c} \) be coplanar. If \( \hat{c} \) is perpendicular to \( a \), then \( c \) is equal to
\( \mathbf{A} \cdot(-\hat{j}+\hat{k}) \)
B. \( \pm \frac{1}{\sqrt{2}}(-\hat{j}+\hat{k}) \)
\( ^{\mathrm{C}} \pm \frac{1}{\sqrt{2}}(\hat{j}+\hat{k}) \)
D. None of these


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \frac{1 . \boldsymbol{K H}}{2 . \boldsymbol{P h C H}_{2} \boldsymbol{B r}} \)
\( \boldsymbol{A} \frac{1 . B_{2} H_{6}}{2 . H_{2} O_{2} / O H^{-}} \boldsymbol{B} \)
The end product (B) is:
\( A \)
в.
\( c \)
D.


If \( M_{E} \) is the mass of the earth and \( R_{E} \)
its radius, the ratio of the acceleration
due to gravity and the gravitational constant is:
\( ^{\text {A }} \cdot \frac{R_{E}^{2}}{M_{E}} \)
в. \( \frac{M_{E}}{R_{E}^{2}} \)
c. \( M_{E} R_{E}^{2} \)
D. \( \frac{M_{E}}{R_{E}} \)


In a transistor output characteristics
commonly used in common emitter con
ig ration, the base current \( \boldsymbol{I}_{B}, \) the
collector current \( I_{C} \) and the collector-
emitter voltage \( V_{C E} \) have values of the
following orders of magnitude in the
active region
\( \mathbf{A} \cdot I_{B} \) and \( I_{C} \) both are in \( \mu A \) and \( V_{C E} \) in Volts
B. \( I_{B} \) is in \( \mu A \), and \( I_{C} \) is in \( m A \) and \( V_{C E} \) in Volts
\( \mathbf{C} \cdot I_{B} \) is in \( m A, \) and \( I_{C} \) is in \( \mu A \) and \( V_{C E} \) in \( m V \)
D. \( I_{B} \) is in \( m A \), and \( I_{C} \) is in \( m A \) and \( V_{C E} \) in \( m V \)


Two symmetrical dice are thrown 200 times. Getting a sum of 9 points is considered to be a success. The
probability distribution of successes is
\( ^{\mathbf{A}} \cdot\left(200, \frac{1}{9}, \frac{8}{9}\right) \)
в. \( \left(200, \frac{2}{9}, \frac{7}{9}\right) \)
\( ^{\mathrm{c}} \cdot\left(200, \frac{4}{9}, \frac{5}{9}\right) \)
D \( \cdot\left(200, \frac{1}{4}, \frac{3}{4}\right) \)


A body is constrained to move in the \( y \) direction. It is subjected to a force \( (-2 \hat{i}+15 \hat{j}+6 \hat{k}) \) Newton. The work done by this force in moving the body through a distance of \( 10 \mathrm{m} \) in positive \( y \) direction is:
A. 150
B. 60 J
\( c \ldots-20 J \)
D . - 150 J


The type of hybridization of boron in diborane is ?
A. \( s p \) - hybridization
B. \( s p^{3} \) -hybridization
c. \( s p^{2} \) - hybridization
D. \( s p^{3} d^{2} \) - hybridization


Curie temperature is the temperature
above which
A. a ferromagnetic material becomes paramagnetic
B. a paramagnetic material becomes diamagnetic
C . a ferromagnetic material becomes diamagnetic
D. a paramagnetic material becomes ferromagnetic


The magnitude of non-contact force depends upon:
A. Distance between two bodies
B. Mass of the two bodies
c. chemical properties of the two bodies
D. All of the above


The unit torr is related to the barometric
height as
A. 1 torr \( =1 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 1 torr\( =0.76 \mathrm{m} \) of \( \mathrm{Hg} \)
c. 1 torr\( =1 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 1 torr \( =1 \mathrm{m} \) of \( \mathrm{Hg} \)


A simple microscope consists of a concave lens of power \( 10 \mathrm{D} \) and a convex lens of power 15 D. Its magnification at
near point is (least distance of distinct vision, \( \mathrm{D}= \)
\( 25 \mathrm{cm} \)
A . 2.25
B. 5
\( c \cdot 10 \)
D. 20


A student very cautiously traces the
path of a ray through a glass slab for
different values of the angle of
incidence \( (\angle i) . \) He then measures the
corresponding values of the angle of
refraction \( (\angle r) \) and the angle of
emergence \( (\angle e) \) for every value of the
angle of incidence. On analysing these
measurements of angles, his conclusion would be
A. \( \angle i>\angle r>\angle e \)
B. \( \angle i=\angle e>\angle r \)
\( \mathbf{c} \cdot \angle i, \angle r, \angle e \)
D. \( \angle i=\angle e, \angle r \)


The unit of \( \frac{G}{g} \) is:
A. kg/m
в. \( k g / m^{2} \)
\( \mathbf{c} \cdot m^{2} / k g \)
D. m/kg


On prolonged exposure to air, sodium finally changes to:
A. \( N a_{2} O \)
в. \( N a_{2} O_{2} \)
c. \( N a_{2} C O_{3} \)
D. \( N a O H \)


Which has the largest \( \boldsymbol{O}-\boldsymbol{N}-\boldsymbol{O} \) bond
angle?
A \( \cdot N O_{2} \)
в. \( N O_{2}^{+} \)
\( \mathrm{c} \cdot \mathrm{N} \mathrm{O}_{2}^{-} \)
D. \( N O_{3}^{-} \)


Heat of combustion of \( C_{2} H_{4} \) is
\( -337 K \) Cal. If 5.6 lit \( O_{2} \) is used at STP,
in the combustion heat liberated is
K.Cal.
\( \mathbf{A} \cdot 28.08 \)
B. 14.04
c. 42.06
D. 56.16


Which of the following ligand possess only one coordination site?
\( \mathbf{A} \cdot C O_{3}^{2} \)
B. \( O^{2-} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}^{2-} \)
D. \( [O X]^{2} \)


The coefficient of \( \boldsymbol{I}^{-}, \boldsymbol{I} \boldsymbol{O}_{3}^{-} \) and \( \boldsymbol{H}^{+} \) in
the redox reaction, \( \boldsymbol{I}^{-}+\boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}^{+} \rightarrow \)
\( I_{2}+H_{2} O, \) in the balanced form
respectively are:
\( \mathbf{A} \cdot 5,1,6 \)
в. 1,5,6
c. 6,1,5
D. 5,6,1


A helicopter lifts a 72 kg astronaut, 15
\( m \) vertically from the ocean by means of
a cable. The acceleration of the
astronaut is \( g / 10 . \) What is the velocity of astronaut? \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right) \)
\( \mathbf{A} \cdot 54.2 m s^{-1} \)
B. \( 5.42 \mathrm{ms}^{-1} \)
c. \( 6.42 m s^{-1} \)
D. \( 542 m s^{-1} \)


For perfect gas, the ratio of volume
coefficient of expansion to pressure coefficient is :
A. equal to one
B. less than one
c. more than one
D. an imaginary quantity


\( \sigma \)
\( \sigma \)
\( \varphi \)


A gas has a density of 10 particles \( / m^{3} \) and a molecular diameter of \( 0.1 \mathrm{m} \). What
is its mean free path?
\( \mathbf{A} \cdot 2.25 m \)
в. \( 1 m \)
\( c .3 m \)
D. \( 0.25 m \)


\( 1.4 d m^{3} \) of a gas at a STP weight \( 1.26 \times \) \( 10^{3} \) kg Calculate Molecular mass, Mass of 1 mole


A small ball is projected along the surface of a smooth inclined plane with
speed \( 10 m s^{-1} \) along the direction
shown at \( t=0 . \) The point of projection
is origin, \( z- \) axis is along vertical. The
acceleration due to gravity is \( 10 m s^{-2} \)
Column I lists the values of certain
parameters related to motion of ball
and Column II lists different time
instants Match appropriately.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|} { Column I } & \multicolumn{2}{|c|} { Column II } \\
\hline i. & Distance from \( x \) -axis is \( 2.25 \mathrm{m} \) & a. & \( 0.5 \mathrm{s} \) \\
\hline ii. & Speed is minimum & b. & \( 1.0 \mathrm{s} \) \\
\hline iii. & Velocity makes angle \( 37^{\circ} \) with \( x \) -axis & c. & \( 1.5 \mathrm{s} \) \\
\hline & & d. & \( 2.0 \mathrm{s} \) \\
\hline
\end{tabular}


Why should not medicines be taken
without consulting doctors?


The weakest base among the following
is
A \( . H^{-} \)
B. \( C H_{3}^{-} \)
c. \( C H_{3} O \)
D. \( C l^{-} \)


\( \frac{\frac{\sqrt{2}}{4}}{\frac{1}{4}} \)


What is a Chemical bond?


Fill up the blanks.
The particle of the nucleus that
undergoes change during beta decay is


Prove that \( (\vec{A} \times \vec{B})^{2}=A^{2} B^{2}-(\vec{A} \times \vec{B})^{2} \)


Name the plant hormone responsible for the growth of stem.
A . Gibberellin
B. Axin
c. cytokinins
D. Ethylene


Draw Werner's structure of the
following:
(a) \( C o C l_{3} .6 N H_{3} \)
(b) \( C o C l_{3} .5 N H_{3} \)
(c) \( C o C l_{3} .4 N H_{3} \)
(d) \( C o C l_{3} .3 N H_{3} \)


In a photoemissive cell with executing wavelength \( \lambda \), the fastest electron has to speed v. If the exciting wavelength is changed to \( \frac{3 \lambda}{4}, \) the speed of the fastest emitted electron will be:
\( ^{\mathrm{A}} v\left(\frac{3}{4}\right)^{1 / 2} \)
в. \( _{v}\left(\frac{4}{3}\right)^{1 / 2} \)
\( ^{\mathrm{c}} \cdot \operatorname{lessthan} v\left(\frac{4}{3}\right)^{1 / 2} \)
D. greater than \( v\left(\frac{4}{3}\right)^{1 / 2} \)


Everyone has the right to live. Yet, is everybody getting enough water to live or even water to drink? Why is it that some people have to buy drinking water? Should it be like this? Water on
this earth is for one and all. Some
people draw out water from the ground by deep bore wells. How far is it correct? Have you ever seen this? Why do some people is pump directly in the Jal Board pipe line? What problems would other people face due to this? Do you have any such experience?


Which of following hormone is produced by testis?
A. Progesterone
B. Estradiol
c. Testosterone
D. estrone


Why is the conversion of ethanol to
ethanoic acid an oxidation reaction?
A. Carbon is oxidized.
B. Hydrogen oxidation number is changed.
c. carbon is reduced
D. carbon undergoes disproportination


If \( \boldsymbol{A}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}-\mathbf{5}|\boldsymbol{x}|+\boldsymbol{6}=\mathbf{0}\right\} \)
\( \operatorname{then} n(A)= \)
\( A \cdot 2 \)
B.
\( c \cdot 1 \)
D.


The tip of a needle does not give a sharp image on a screen. This is due to
A. Polarisation
B. Interference
c. Diffraction
D. None of these


Evaluate potential energy per ion for NaCl crystal. Use inter atomic spacing \( 2.82 \times 10^{10} m \)
В. \( 2.67 \times 10^{-19} \mathrm{J} \)
\( \mathbf{c} \cdot 5.67 \times 10^{-19} J \)
D. none


The airthmatic mean of \( 1+\sqrt{2} \) and \( \mathbf{7}+\mathbf{5} \sqrt{\mathbf{2}} \) is \( \sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}} . \) Then \( \mathbf{a}-\boldsymbol{b}= \)
\( A \cdot-1 \)
в.
\( c \cdot 2 \)
\( D \cdot-2 \)


A car is travelling along a circular curve that has a radius of \( 50 \mathrm{m} \). If its speed is \( 16 \mathrm{m} / \mathrm{s} \) and is increasing uniformly at \( 8 m / s^{2}, \) determine the magnitude of its acceleration at this instant.
A \( \cdot 9.5 \mathrm{m} / \mathrm{s}^{2} \)
В. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 8.5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 7.5 \mathrm{m} / \mathrm{s}^{2} \)


The incisor tooth is meant for
A. Biting and cutting
B. Chewing
c. Munching and chewing
D. Munching


In the following circuit, the \( 1 \Omega \) resistor dissipates power P. If the resistor is
replaced by \( 9 \Omega \). the power dissipated in
it is
\( A \)
B. 3P
\( c \cdot 9 P \)
D. P/3


Sum of the product of 1,234 and 78 with 5,678 and 89 is
A. 60,594
B. 60,194
\( \mathbf{c} \cdot 6,05,194 \)
D. 6,01,594


In H-atom, if 'x' is the radius of the first
Bohr orbit, de Broglie wavelength of an electron in 3rd orbit is :
\( \mathbf{A} \cdot 3 \pi x \)
в. \( 6 \pi x \)
c. \( \frac{9 x}{2} \)
D. \( \frac{x}{2} \)


Match the column I with column II and
mark the appropriate choice.
Column II
(A) \( s p^{3} d^{2} \)
\( C_{2} H_{2} \quad \) (i) \( \quad \) hybridisation
(B) \( s p^{3} d^{3} \)
\( S F_{6} \quad \) (ii) \( \quad \) hybridisation
\( \begin{array}{llll}\text { (C) } & S O_{2} & \text { (iii) } & s p \text { hybridisation }\end{array} \)
\( \begin{array}{llll}\text { (D) } & I F_{7} & \text { (iv) } & s p^{2} \text { hybridisation }\end{array} \)
A \( \cdot(A) \rightarrow(i),(B) \rightarrow(\text { iii }),(C) \rightarrow(\text { ii }),(D) \rightarrow(i v) \)
B. \( (A) \rightarrow(\text { iii), }(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i) \)
C. \( (A) \rightarrow(\text { ii) },(B) \rightarrow(\text { iii) },(C) \rightarrow(i),(D) \rightarrow(i v) \)
D. \( (A) \rightarrow(\text { iv ) },(B) \rightarrow(i),(C) \rightarrow(\text { iii }),(D) \rightarrow(\text { ii }) \)


The total number of S-S bonds in a
molecule of Insulin is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Cavity present in the tooth is called as
A. Pulp cavity
B. Nasal cavity
c. Abdominal cavity
D. chest cavity


An ether is more volatile than alcohol
having the same molecular formula. This is due to:
A. intermolecular hydrogen bonding in ethers
B. dipolar character of ethers
c. alcohols having resonance structures
D. intermolecular hydrogen bonding in alcohols


Assertion (A): A disulphonic derivative
of \( H_{2} O_{2} \) is Caro's acid.

Reason (R): Caro's acid has one peroxy
bond.
The correct answer is:
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Classify the following as physical or chemical properties. Zinc dissolves in hydrochloric acid with the evolution of hydrogen gas.
A. Chemical
B. Physical
c. Both \( A \) and \( B \)
D. None of these


Individual components of corolla are called
A. Sepals
B. Petals
c. Tepals
D. Bracts


The reaction \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{B r} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}^{+}+\boldsymbol{B r}^{-} \) is an example of:
A. homolytic fission
B. heterolytic fission
c. cracking
D. all of the above


The adsorption of gases on solid can be described by Freundlich's equation \( \frac{\boldsymbol{x}}{\boldsymbol{m}}=\boldsymbol{k} \boldsymbol{P}^{1 / \boldsymbol{n}} \)
(a)How are the value of K and \( n \)
determined experimentally?
(b) Explain, why should the value of \( n \) be equal to or greater than one.


The largest salivary gland present in human is
A. Submandibulargland
B. Sublingual gland
c. Parotid gland
D. Gastric gland


The solution of \( y d x+x d y=d x+d y \) is:
A. \( x y=x+y+c \)
В \( \cdot x-y \frac{x}{y}+c=0 \)
c. \( x y-x+y=c \)
D. \( x+y \frac{x}{y}+c=0 \)


When is the Wheatstone's bridge said to be most sensitive?


The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately 81 times the mass of the Moon and the
distance between the Earth and the
Moon is \( 3,85,000 k m . \)
A. \( 36,000 \mathrm{km} \) from the Moon
B. 38,500 km from the Moon.
c. \( 34500 \mathrm{km} \) from the moon
D. 30,000 km from the Moon


Which one of the following ionic species has the greatest proton affinity to form the stable compound?
\( \mathbf{A} \cdot I^{-} \)
в. \( H S^{-} \)
\( \mathbf{c} \cdot N H_{2}^{-} \)
D. \( F^{-} \)


The half life of a first order reaction is
1.7 hours. How long will it take for \( 20 \% \) of the reactant to disappear?


If \( 2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) is
independent of \( x \) then
A \( \cdot x \epsilon(1,+\infty) \)
В . \( x \epsilon(-1,1) \)
c. \( x \epsilon(-\infty,-1) \)
D. none of these


If ' \( \alpha \) ' is degree of dimerisation of
\( C H_{3} C O O H \) in benzene, then van't Hoff factor 'i' for circulation of colligative
properties is:
\( \mathbf{A} \cdot 1+\alpha \)
B \( \cdot 1-\frac{\alpha}{2} \)
\( c \cdot 1+\frac{\alpha}{2} \)
D. \( 1+2 \alpha \)


Which of the following phenomena is represented by the diagram?
A. Linkage
B. Independent assortment
c. crossing over
D. Non disjunction
E. Mutation


A bag contains 5 red and 8 white balls. If a ball is drawn at random from the bag,
what is the probability that it will be:
(i) White ball,
(ii) Not a white ball?


Fill in the blanks.
Fissionable isotope of uranium is


Sixteen players \( \boldsymbol{S}_{1}, \boldsymbol{S}_{2}, \ldots . \boldsymbol{S}_{16} \) play in a
tournament. They are divided into eight pairs at random. From each pair a
winner is decided on the basis of a
game played between the two players of the pair. Assume that all the players are of equal strength.
The probability that the player \( S_{1} \) is among the eight winners is \( \frac{1}{k} . \) Find the
value of \( \boldsymbol{k} \)


Three equal resistors are connected as
shown in figure. the maximum power
consumed by each resistor is 18 W. Then the maximum power consumed by the combination is :
A. \( 18 W \)
в. \( 27 W \)
\( c .36 W \)
D. \( 54 W \)


Anaemia is caused by the deficiency of :
A. Iron
B. zinc
c. lodine
D. Calcium


Distinguish between glycolysis and
citric acid cycle.


Derive the formula for the force acting between two parallel current carrying
conductors.


For a particle executing SHM the displacement \( x \) is \( \operatorname{given} \) by \( x=A \operatorname{cost} \) Identify the graph which represents the variation of potential energy (PE) as a function of time \( t \) and displacement \( x \)
A . ।, ॥ I
в. ॥, Iv
c. ॥, ॥
D. I, IV


What is the reason behind the shinning of diamonds and how do you appreciate
it?


Wilkinson's catalyst \( \left[R h\left(P h_{3} P\right)_{3} C l\right] \) is
used for:
A. hydrogenation of oils
B. hydrogenation of alkynes
c. hydrogenation of alkenes
D. polymerisation of alkenes


An object is kept on the principal axis of a concave mirror of focal length \( 10 \mathrm{cm} \) at a distance of \( 15 \mathrm{cm} \) from its pole. The image formed by the mirror is?
A. Virtual and magnified
B. Virtual and diminished
c. Real and magnified
D. Real and diminished


A shopkeeper buys an article at a rebate of \( 20 \% \) on the printed price. He spends
Rs. 40 on transportation of the article. After charging a sales tax of \( 7 \% \) on the printed price, he sells the article for Rs.
1, 070. Find his gain as per cent.
A \( \cdot 4 \frac{1}{16} \% \)
в. \( 11 \frac{1}{13} \% \)
c. \( 14 \frac{1}{20} \% \)
D. \( 19 \frac{1}{21} \% \)


The number of real roots of
\( \sin \left(2^{x}\right) \cos \left(2^{x}\right)=\frac{1}{4}\left(2^{x}+2^{-x}\right) \) is
\( A \)
B. 2
\( c \cdot 3 \)
D. No solution


The radii and Young's modulus of two uniform wires \( A \& B \) are in the ratio
2: 1 and 1: 2 respectively. Both the
wires are subjected to the same longitudinal force. If increase in the length of wire \( A \) is \( 1 \% \). Then the
percentage increase in length of wire \( B \) is :
A . 1
в. 1.5
\( c \cdot 2 \)
\( D \)


What is \( \left|\begin{array}{ccc}-a^{2} & a b & a c \\ a b & -b^{2} & b c \\ a c & b c & -c^{2}\end{array}\right| \) equal to?
A \( .4 a b c \)
B . \( 4 a^{2} b c \)
\( \mathbf{c} \cdot 4 a^{2} b^{2} c^{2} \)
D. \( -4 a^{2} b^{2} c^{2} \)


Purkinje fibres are present in
A. Ventricles
B. Auricles
c. Striated muscle fibre
D. Throughout the heart


The first phase in the breakdown of glucose in animals cells is
A. Krebs cycle
B. Glycolysis
c. Electrons transport system
D. Lipid biosynthesis


Which rule determines the direction of
force experienced by a current Carrying straight conductor placed in a magnetic field which is perpendicular to it.
A. Maxwell right hand grip rule
B. Fleming's left hand rule
C. Fleming's right hand rulel
D. None


The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is.
A. Four times the initial energy
B. Equal to the initial energy
c. Twice the initial energy
D. Thrice the initial energy


\( \ln \) a \( A C \) circuit the current is given by \( \boldsymbol{i}=\mathbf{5} \sin \left(\mathbf{1 0 0 t}-\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) and \( \boldsymbol{V}= \)
\( 200 \sin (100 t) V \) then power
consumption is
\( \mathbf{A} \cdot 20 W \)
в. \( 1000 \mathrm{W} \)
c. \( 500 W \)
D. \( 0 W \)


Represent the following complex
number in trigonometric form:
5


Velocity of light is
A \( \cdot 3 \times 10^{4} k m / s \)
в. \( 3 \times 10^{6} k m / s \)
c. \( 3 \times 10^{5} k m / s \)
D. \( 3 \times 10^{3} k m / s \)


Find the total surface area of cubes
having the following sides.
\( \mathbf{3} c \boldsymbol{m} \)


Find the equation of the circle passing through the points (5,5),(3,7) and has its center on the line \( \boldsymbol{x}-\mathbf{4} \boldsymbol{y}+\mathbf{1 1}=\mathbf{0} \)


Which of the following is sec-butyl alcohol?
A. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{2} C H_{3} \)
c. \( \left(C H_{3}\right)_{2} C H C H_{2} O H \)
D. \( \left(C H_{3}\right)_{3} C C H_{2} O H \)


For the reaction between \( M n O_{4}^{-} \) and
\( C_{2} O_{4}^{-} \) in basic solution, the unbalanced
equation is \( M n O_{4}^{-}+C_{2} O_{4}^{2-} \longrightarrow M n O_{2}(s)+ \)
\( \boldsymbol{C O}_{3}^{2-} \)
In a balanced equation, the number of
\( O H^{-} \) ions is :
\( A \cdot 0 \)
B. 4 on the right
c. 4 on the left
D. 2 on the left


Subtract 1732765 from 3673124 in the
scale of eight.


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}(\mathbf{1}+|\sin \boldsymbol{x}|)^{\frac{a}{|\sin |}}, & -\boldsymbol{\pi} / \boldsymbol{6}<\boldsymbol{x}<\mathbf{0} \\ \boldsymbol{b}, & \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{e}^{\frac{\tan 2 x}{\tan x}}, & \boldsymbol{0}<\boldsymbol{x}<\boldsymbol{\pi} / \boldsymbol{6}\end{array}\right. \)
continuous at \( x=0, \) find the values of
\( a \) and \( b \)
A \( \cdot \frac{3}{2}, e^{3 / 2} \)
B. \( \frac{-2}{3}, e^{-3 / 2} \)
c. \( \frac{2}{3}, e^{2 / 3} \)
D. None of these


What are the harmful effects of
photochemical smog and how can they be controlled?


The solution of iodine in \( K I \) is used to
detect a solution of starch and
glycogen, as it gives:
A. blue colour with starch and red colour with glycogen
B. green colour
c. green colour with starch blue colour with glycogen
D. red colour with starch yellow with glycogen


Statement: One mole of propyne reacts
with \( B_{2} H_{6} / H_{2} O_{2} / O H \) to produce
acetone.
If the given statement is true the enter 1
else enter 0


Predict the structure of the following and indicate whether the bond angles are likely to be dissorted from the
theoretical values:
\( B e C l_{2} \)


f \( t_{n}=4 n-3, \) then find the first two
terms of an A.P.


The IUPAC name of \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right] \) is:
A. potassium tetracyanonickelate (II)
B. potassium tetracyanato nickelate (III)
c. potassium tetracyanatonickel (II)
D. potassium tetracyanonickel (III)


\( (a) \)
\( (b) \)
\( (c) \)
\( (d) \)


Two trains each of length \( 100 m \) moving parallel towards each other at speed \( \mathbf{7} 2 k \boldsymbol{m} / \boldsymbol{h} \) and \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \) respectively. In
how much time will they cross each
other?
\( \mathbf{A} \cdot 4.5 S \)
B. \( 6.67 s \)
\( c .3 .5 s \)
D. \( 7.25 s \)


Assertion
Maximum air flow due to convection
does not occur at the north pole but it
occurs at \( \mathbf{3 0}^{\circ} \) N.
Reason
There is maximum temperature
difference between equator and \( 30^{\circ} \mathrm{N} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which condition of congruence will
satisfy the diagram?
A. SSA
B. AAS
c. ASA
D. sss


A person wants to drive on the vertical surface of a large cylindrical wooden 'well' commonly known as'death well' in a circus. The radius of the well is
2 meter, and the coefficient of friction
between the tyres of the motorcycle and
the wall of the well is \( 0.2, \) the minimum
speed the motorcyclist must have in order to prevent slipping should be
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 15 \mathrm{m} / \mathrm{s} \)
\( c .1 .98 m / s \)
D. \( 25 \mathrm{m} / \mathrm{s} \)


On heating potassium permanganate, one of the following compound is not obtained. Identify the compound.
\( A \cdot O_{2} \)
в. \( M n O \)
c. \( M n O_{2} \)
D. \( K_{2} M n O_{4} \)


State true or false:
If \( u(x) \) and \( v(x) \) are differentiable functions such that \( \frac{u}{v}(x)=7 \) \( \frac{\boldsymbol{u}^{\prime}(\boldsymbol{x})}{\boldsymbol{v}^{\prime}(\boldsymbol{x})}=\boldsymbol{p} \) and \( \left(\frac{\boldsymbol{u}(\boldsymbol{x})}{\boldsymbol{v}(\boldsymbol{x})}\right)^{\prime}=\boldsymbol{q}, \) then
\( \frac{\boldsymbol{p}+\boldsymbol{q}}{\boldsymbol{p}-\boldsymbol{q}}=\mathbf{1} \)
A. True
B. False


If \( \sin (x y)+\frac{y}{x}=x^{2}-y^{2}, \) find \( \frac{d y}{d x} \)


For the redox reaction:
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{y} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}+\boldsymbol{z} \boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{m} \boldsymbol{M} \boldsymbol{n}^{2+}+\boldsymbol{n} \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{p} \boldsymbol{H}_{2} \boldsymbol{O} \)
The values of \( x, y, m \) and \( n \) are:
A. 10,2,5,2
В. 2,5,2,10
c. 6,4,2,5
D. 3,5,2,10


In humans, the sound is produced by:
A . larynx
B. wind pipe
c. vocal cords
D. lungs


Diborane \( \left(B_{2} H_{6}\right) \) reacts independently
with \( O_{2} \) and \( H_{2} O \) to produce :
A. \( H B O_{2} \) and \( H_{3} B O_{3} \)
B. \( H_{3} B O_{3} \) and \( B_{2} O_{3} \)
c. \( B_{2} O_{3} \) and \( H_{3} B O_{3} \)
D. \( B_{2} O_{3} \) and \( \left[B H_{4}\right]^{-} \)


The length and breadth of a room are \( 3 x^{2} y^{3} \) and \( 6 x^{3} y^{2} \) respectively. Find its
perimeter and area.


\( L \lim _{n \rightarrow \infty} t \frac{1}{n}\left[\frac{1}{n+1}+\frac{2}{n+2}+\ldots+\frac{3 n}{4 n}\right] \)
A. \( 3-\ln 4 \)
B. \( 3+\ln 4 \)
c. \( 3 \ln 4 \)
D. None of these


if for the heterogeneous equilibrium
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) ; \mathbf{K}=1 \) at
atm, the temperature is given by:
A \( \cdot T=\frac{\Delta S^{0}}{\Delta H^{0}} \)
В \( \cdot T=\frac{\Delta H^{0}}{\Delta S^{0}} \)
\( \mathbf{c} \cdot T=\frac{\Delta G^{0}}{R^{0}} \)
D \( \cdot T=\frac{\Delta G^{0}}{\Delta H^{0}} \)


ff \( \boldsymbol{I}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] . \boldsymbol{J}= \)
\( \left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \) and \( \quad \boldsymbol{B}= \)
\( \left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right], \quad \) then \( \quad B= \)
A \( . I \cos \theta+J \sin \theta \)
B . \( \operatorname{Isin} \theta+J \cos \theta \)
c. \( \operatorname{Icos} \theta-J \sin \theta \)
D. \( -I \cos \theta-J \sin \theta \)


Which among the following statements
is incorrect for magnesium metal?
A. It burns in oxygen with a dazzling white flame
B. It reacts with cold water to form magnesium oxide and evolves hydrogen gas
C. It reacts with hot water to form magnesium hydroxide and evolves hydrogen gas
D. It reacts with steam to form magnesium hydroxide and evolves hydrogen gas


State whether true or false.
A jute string can be used to make a circuit instead of metal wires,
A. True
B. False


If the points \( (a, 1),(1,2) \) and \( (0, b+1) \)
are collinear, then show that \( \frac{1}{a}+\frac{1}{b}=1 \)


Which of the following phases correspond to the interval between mitosis and initiation of DNA
replication
A. S-Phase
B. \( G_{1} \) -phase
\( \mathrm{c} \cdot G_{2}- \) phase
D. M-phase


In the given figure, \( \boldsymbol{O} \) is a point in the
interior of \( 1 M \) a square \( A B C D \) such
that \( O A B \) is an equilateral triangle.
Show that \( O C D \) is an isosceles
triangle.


Define equipotential surface.


The electron density in the xy-plane in
\( 3 d_{x^{2}-y^{2}} \) orbital is zero. If true enter 1 else enter 0


Which of the following statement(s)
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) If the electric field due to a point charge varies as \( r^{-25} \) instead of \( r^{-2} \), then the Gauss law will still be valid.
B. The Gauss law can be used to calculate the field distribution around an electric dipole.
C. If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
D. The work done by the external force in moving a unit positive charge from point \( A \) at potential \( V_{A} \) to point \( B \) at potential \( V_{B} \) is \( \left(V_{B}-V_{A}\right) \)


The total number of lines of force
passing through a surface is called
A . electric field
B. electric flux
c. electric potetial
D. electrical energy


The law which defines force is:
A. Newton's third law of motion
B. Newton's first law of motion
C. Newton's second law of motion
D. Newton's law of gravitation


Two electrons lying \( 10 c m \) apart are released. What will be their speed when
they are \( 20 c m \) apart?


Find the sum of all natural numbers
lying between 100 and \( 1000, \) which are multiples of 5


A force of \( 10 N \) acts on a \( 5 k g \) body initially at rest. The work done by the force during the first two seconds of motion of the body is
A . \( 30 J \)
в. \( 40 J \)
c. \( 20 J \)
D. \( 80 J \)


\( \frac{w}{h} \)


Fill in the blanks
In minimum deviation position of prism, the angle of incidence is equal to angle of


\( \ln a \Delta A B C, \) it is given that \( A B=A C \)
and the bisectors of \( \angle B \) and \( \angle C \)
intersect at \( 0 . \) If \( \mathrm{M} \) is a point on \( \mathrm{BO} \)
produced, prove that \( \angle M O C=\angle A B C \)


If two zeroes of the polynomial \( x^{4}- \) \( 6 x^{3}-26 x^{2}+138 x-35 \) are \( 2 \pm \sqrt{3} \)
find the other zeroes.


A piece of iron of mass \( 2.0 \mathrm{kg} \) has a
thermal capacity of \( 966 J K^{-1} \). Find its
specific heat capacity in S.I. unit.
A \( \cdot 1932 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
B . \( 241.5 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
c. \( 966 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. 483 Jkg\( ^{-1} K^{-1} \)


Consider the reaction \( \boldsymbol{A}_{2}+\boldsymbol{B} \rightarrow \)
products. If the concentration of \( A_{2} \) and
B are halved, the rate of the reaction decreases by a factor of 8. If the concentration of \( A \) is increased by a factor of \( 2.5, \) the rate increases by the
factor of \( 2.5 . \) What is the order of the
reaction? Write the rate law.


An odd electron molecule among the following is :
A. \( C O \)
в. \( S O_{2} \)
\( c \cdot C O_{2} \)
D. \( N O \)
E. \( O F_{2} \)


Outside a house, \( 1 k m \) from ground zero of a 100 kiloton nuclear bomb explosion, the pressure will rapidly rise to as high as 2.8 atm while the pressure inside the house is 1 atm. If the area
outside the house is \( 50 m^{2} \). The
resulting net force exerted by the air in front of the house is :
A \( \cdot 9.1 \times 10^{6} N \)
B . \( 2.1 \times 10^{7} N \)
c. \( 1.41 \times 10^{7} N \)
D. \( 1.63 \times 10^{7} N \)


Solve:
\( \frac{1}{2} \int \frac{u^{2}}{1+u} d u \)


Electrical charge can be transferred from a charged object to another through
A. vacuum
B. air
c. insulator
D. conductor


The horizontal and vertical components
of earth's magnetic field at a place are \( 0.3 G \) and \( 0.52 G . \) The earth's magnetic
field and the angle of dip are
A \( \cdot 0.3 \mathrm{G} \) and \( \rho=30^{\circ} \)
B. 0.4G and \( \rho=40^{\circ} \)
c. \( 0.5 \mathrm{G} \) and \( \rho=50^{\circ} \)
D. \( 0.6 \mathrm{G} \) and \( \rho=60^{\circ} \)


The process to heat the ore in the presence of excess supply of air below its melting point is called as
A. roasting
B. calcination
c. smelting
D. liquation


The concentration of glucose in plasma is \( 100 \mathrm{mg} / 100 \mathrm{mL} \), and the GFR is 125 \( \mathrm{mL} / \mathrm{min.} \) How much glucose is filtered
per minute?


State Faraday's laws of electromagnetic induction and Lenz's law.


In the reversible reaction \( 2 N H_{3}(g) \Leftrightarrow \)
\( N_{2}(g)+3 H_{2}(g) \) when 1 mol of \( N H_{3} \) is
taken initially in a litre flask and 0.2
moles of \( N_{2} \) are formed at equilibrium.
Its equilibrium constant \( \boldsymbol{K}_{c} \) is:
A . 72
B. \( 12 \times 10^{-2} \)
\( c \cdot 0.3 \)
D. 0.27


A solution of the equation \( 5 \sin ^{2} x+ \)
\( 3 \sin x \cos x-3 \cos ^{2} x=2 \) is
This question has multiple correct options
A \( \cdot_{2 \pi+\tan ^{-1} \frac{-3+\sqrt{69}}{6}} \)
B. \( \quad 7 \pi+\tan ^{-1} \frac{-3-\sqrt{69}}{6} \)
c. \( \tan ^{-1} \frac{-3+\sqrt{69}}{6}-\pi \)
D. \( \tan ^{-1} \frac{-3-\sqrt{69}}{6}-5 \pi \)


A road roller takes 750 complete
revolutions to move once over to level a
road. Find the area of the road if the
diameter of a road roller is \( 84 \mathrm{cm} \) and
length is \( 1 \mathrm{m} \)


If one root of the equation \( x^{2}+p x+ \)
\( 12=0 \) is 4 while the equation \( x^{2}+ \)
\( p x+q=0 \) has equal roots, then one
value of \( q \) is
\( \mathbf{A} \cdot \mathbf{3} \)
в. 12
c. \( \frac{49}{4} \)
D. 4


A ball of radius a is made to oscillate in
a bowl of radius b then time period of vibration of ball is \( (\boldsymbol{b}>\boldsymbol{a}) \)
A \( \cdot 2 \pi \sqrt{\frac{a}{g}} \)
В \( \cdot 2 \pi \sqrt{\frac{b-a}{g}} \)
\( ^{\mathrm{c}} \cdot 2 \pi \sqrt{\frac{b}{g}} \)
D. \( 2 \pi \sqrt{\frac{b+a}{q}} \)


What is \( \int_{0}^{1} \frac{\tan ^{-1} x}{1+x^{2}} d x \) equal to \( ? \)
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{32} \)


Find the sum of the first 50 even
positive integers.


Find the general solution of \( x \cos ^{2} 2 x+ \)
\( \cos ^{2} 3 x=1 \)
A \( \cdot(2 k+1) \frac{\pi}{10}, k \in I \)
В \( \cdot(\pi+1) \frac{\pi}{10} ; k \in I \)
\( c \cdot(2 k-1) \frac{\pi}{10}, k \in I \)
D. Both (A) and (C)


19.7 kg of gold was recovered from a smuggler. The atoms of gold recovered
are:
A. 100
B. \( 6.02 \times 10^{23} \)
c. \( 6.02 \times 10^{24} \)
D. \( 6.02 \times 10^{25} \)


The compound \( 2- \) methy -2
butene on reaction with \( N a I O_{4} \) in the
presence of \( K M n O_{4} \) gives:
\( \mathbf{A} \cdot C H_{3} C O O H \)
B . \( C H_{3} C O C H_{3}+C H_{3} C O O H \)
\( \mathbf{c} \cdot C H_{3} C O C H_{3}+C H_{3} C H O \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CHO}+\mathrm{CO}_{2} \)


The peak emission from a black body at a certain temperature occurs at a wavelength of 9000 A. On increasing its temperature, the total radiation
emitted is increased 81 times. At the
initial temperature when the peak radiation from the black body is
incident on a metal surface, it does not
cause any photoemission from the surface. After the increase of
temperature, the peak radiation from the black body caused photoemission. To bring these photoelectrons to rest, a potential equivalent to the excitation energy between \( n=2 \) and \( n=3 \) Bohr
levels of hydrogen atoms is required. Find the work function of the metal.


A sum of money lent at simple interest amounts to \( R s 3224 \) in 2 years and
Rs 4160 in 5 years. Find the sum and
the rate of interest.
A. \( R s .2500 \)
B. \( R s .2000 \)
c. \( R s .2600 \)
D. \( R s .1600 \)


In which of the following organisms fragmentation occurs?
A. Ferns
B. Bread mould
c. Hydra
D. Spirogyra


At a given temperature and pressure 64
\( \mathrm{gm} \) of Oxygen and \( \mathrm{X} \mathrm{gm} \) of \( \mathrm{H}_{2} \) occupy the same volume. Then \( x=\ldots . . \) gm
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


Which of the following is a favorable factor for cation formation?
A. Low ionisation potential
B. High electron affinity
c. High electronegativity
D. Small atomic size


What is incorrect for ideal solutions?
\( \mathbf{A} \cdot \Delta_{\operatorname{mix}} H=0 \)
B. \( \Delta \) mix \( V=0 \)
C. solutions which obey Raoult's law over the entire range of concentration
D. Solution in which observed vapour pressure is smaller than the ideal vapour pressure


Why can an offspring produced by asexual reproduction be called as a clone? Give reasons.


The reaction of nitrogen and oxygen to form nitric oxide is favored by high temperature.
A. True
B. False


The variance of the series \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+ \)
\( 2 d, \ldots \ldots a+(2 n-1) d, a+2 n d, \) is
\( ^{\text {A } \cdot} \frac{n(n+1)}{2} d^{2} \)
\( ^{\text {В }} \cdot \frac{n(n-1)}{6} d^{2} \)
c. \( \frac{n(n+1)}{6} d^{2} \)
D. \( \frac{n(n+1)}{3} d^{2} \)


Which of the following colour of light undergoes the least deviation while passing through a glass prism?
A . red
B. blue
c. yellow
D. green


Why do goldsmiths use outermost flame to burn gold and silver?


If \( t \) is a parameter, then \( x= \) \( \left(t+\frac{1}{t}\right) y=b\left(t-\frac{1}{t}\right) \) represents
A. an ellipse
B. a circle
c. a pair of straight lines
D. a hyperbola


A solid cylinder of mass \( M \) and radius
\( R \) rolls down an inclined plane without
slipping. The speed of its centre of mass when it reaches the bottom is
A \( \cdot \sqrt{(2 g h)} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{\frac{3}{4} g h} \)
D. \( \sqrt{(4 g / h)} \)


In a bolt factory, machines \( A, B \) and \( C \)
manufacture \( 25 \%, 35 \%, 40 \% \)
respectively. Of the total of their output \( 5 \%, 4 \% \) and \( 2 \% \) are defective. A bolt is
drawn and is found to be defective.
What are the probabilities that it was
manufactured by the machines \( A, B, C \)
\( \mathbf{A} \cdot \frac{25}{69}, \frac{28}{69}, \frac{16}{69} \)
B. \( \frac{28}{69}, \frac{25}{69}, \frac{16}{69} \)
C \( \cdot \frac{25}{69}, \frac{16}{69}, \frac{28}{69} \)
D. \( \frac{16}{69}, \frac{28}{69}, \frac{25}{69} \)


It was the British scientist
who discovered in 1666 that
light consists of seven colours. Fill in
the blank.
A. Henry
B. John Dalton
c. sir issac Newton
D. Einstein


\( \cos ^{-1}(x)=\cot ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right) \) where
is in the common domain of the
functions.
A. True
B. False


Evaluate the following limits. \( \lim _{x \rightarrow 3}\left(\frac{1}{x-3}-\frac{2}{x^{2}-4 x+3}\right) \)


When two isomeric liquid compounds
\( A^{\prime} \) and \( ^{\prime} B^{\prime} \) form \( H- \) bonding are
heated, compound ' \( A^{\prime} \) boils at lower
temperature than' \( B^{\prime} \). Which of the
following is correct for \( ^{\prime} \boldsymbol{A}^{\prime} \) and \( ^{\prime} \boldsymbol{B}^{\prime} \) ?
A. Intermolecular \( H \) -bonding present in' \( A^{\prime} \)
B . Intramolecular \( H \) -bonding present in' \( ^{\prime} A^{\prime} \)
C. Intramolecular \( H \) -bonding present in \( ^{\prime} B^{\prime} \)
D. None of the above


The value of the determinant
\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ m_{\mathbf{C}} & m+\mathbf{C}_{1} & m+\mathbf{2} \\ m & \mathbf{C}_{1} \\ m & \boldsymbol{m}+\mathbf{1} & \boldsymbol{C}_{2}\end{array}\right| \mathbf{~ i s ~ e q u a l ~ t o ~} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. None of these


Which of the following given element has one electron, one proton and no
neutron?
\( \mathbf{A} \cdot H \)
в. \( L \) i
c. \( C l \)
D. \( H \)


Braille system has dot
patterns.
A . 62
B. 63
c. 72
D. 73


\( 2 x y \frac{d y}{d x}=x^{2}+y^{2} \)


Find the smallest number by which 8788 must be multiplied to obtain a perfect cube.


Construct a differential equation by eliminating the arbitrary constants
\( A, B, C \) for the equation \( y^{2}=A x^{2}+ \)
\( \boldsymbol{B} \boldsymbol{x}+\boldsymbol{C} \)


8
asic
placed at a point \( O . \) The arrows show
the direction of the magnetic moment.
The other arrows show different
positions (and orientations of the
magnetic moment) of another identical
magnetised needle \( Q \). The dotted line
represent a circle centre at the
midpoint of \( \boldsymbol{P} \)
Which configuration in this system
corresponds to stable equilibrium?
\( \mathbf{A} \cdot P Q_{1}, P Q_{3} \)
B. \( P Q_{3}, P Q_{5} \)
\( \mathbf{c} \cdot P Q_{2}, P Q_{4} \)
D. \( P Q_{2}, P Q_{3} \)


In scapigerous umbel, the flowers are arranged in manner
A. Corymb
B. Umbel
c. Panicle
D. Monochasial cyme


When a piece of polythene is rubbed with wool, a charge of \( -2 \times 10^{-7} C \) is
developed on polythene. What mass is transferred to polythene?
\( \mathbf{A} \cdot 5.69 \times 10^{-19} k g \)
B . \( 2.25 \times 10^{-19} k g \)
\( \mathbf{c} \cdot 9.63 \times 10^{-19} k g \)
D. \( 11.38 \times 10^{-19} \mathrm{kg} \)


Solve the following system of equation for \( x \) and \( y \) \( \frac{5}{x-1}+\frac{1}{y-2}=2, \frac{6}{x-1}-\frac{3}{y-2}=1 \)


A mineral is called ore if:
A. metal present in the mineral is costly
B. ametal can be extracted from it
C . a metal can be extracted profitably from it
D. a metal can not be extracted from it


Study the structure of maltose and
mark the incorrect statement.
A. Maltose is composed of two \( \alpha-D- \) glucose units
B. \( C-1 \) of one glucose is linked to \( C-4 \) of other unit
C. It is a non-reducing sugar
D. It is a disaccharide


State True or False.
In one mole of a metal, there are
Avogadro's number of molecular
orbitals.
A. True
B. False


If \( m \& M \) denotes the minimum and
maximum value of \( |2 z+1| \) where \( \mid z- \)
\( \mathbf{2} i \mid \leq \mathbf{1} \) then \( (\boldsymbol{m}+\boldsymbol{M})^{2} \) is equal to
A . 17
B. 34
c. 51
D. 68


At grid sub-stations the voltage is stepped up to reduce loss of
A. current
B. electrical energy
c. power
D. resistance


Write two factors affecting on the rate of chemical reaction.


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) if \( \boldsymbol{y}=[\boldsymbol{x}+\sqrt{\boldsymbol{x}+} \sqrt{\boldsymbol{x}}]^{1 / 2}, \) at \( \boldsymbol{x}= \)
\( \mathbf{1} \)
A. \( \frac{3+4 \sqrt{2}}{8 \sqrt{2}(\sqrt{1+\sqrt{2}})} \)
B. Not defined
\( c \cdot 0 \)
D.


In the nuclear reaction \( _{90} T h^{232} \rightarrow_{82} \)
\( P b^{208} . \) The number of \( \alpha \) and \( \beta \) particles
emitted are:
\( \mathbf{A} \cdot 1 \alpha, 4 \beta \)
B. \( 2 \alpha, 2 \beta \)
\( \mathbf{c} \cdot 6 \alpha, 4 \beta \)
D. \( 8 \alpha, 4 \beta \)


Industrially, \( H_{2} O_{2} \) is prepared by the auto-oxidation of 2-alkylanthraquinols.
A. True
B. False


A lead block used to keep the source in
\( \alpha- \) ray scattering experiment. What is
its purpose?


The figure shows a cross-section of a
double glass unit of a window on a
vertical wall. A graph of the temperatures at different points within
the unit is shown next to it. The
temperature difference across the unit
is 13 K. It has a cross-sectional are of 1.3
and the rate of heat flow through it is 65
W. Then the correct statement is (Glass
has a thermal conductivity of
\( \mathbf{1} W \boldsymbol{m}^{-1} \boldsymbol{K}^{-1} \boldsymbol{)} \)
A. The unit is in steady state and in thermal equilibrium.
B. The unit is in steady state but not in thermal equilibrium
C. The unit is not in steady state but is in thermal equilibrium.
D. The unit neither in steady state not in thermal equilibrium.


The five different colored graphs below represent different possible
relationships between voltage across
resistor and current through the
resistor.
Which of the graphs shows the correct
relationship for a resistor that obeys
Ohm's law?
A . red
B. orange
\( c . \) blue
D. purple
E. green


Assertion
STATEMENT1: Work done by a force on a body whose centre of mass does not move may be non-zero.
Reason
STATEMENT2: Work done by a force depends on the displacement of the
centre of mass
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- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True


A compound of aluminium and chlorine is composed of 9.0 g Al for every 35.5 g of chlorine. The empirical formula of the compound is:
A. \( A l C l \)
в. \( A l C l_{2} \)
c. \( A l C l_{4} \)
D. \( A l C l_{3} \)


Which statements are correct for CO
and \( N_{2} \) according to molecular orbital theory?
(I) Bond order of \( \mathrm{CO} \) and \( N_{2} \) are 3 and 3
(II) Bond order of \( \mathrm{CO} \) and \( N_{2} \) are same
(III) During the formation of \( N_{2}^{+} \) from
\( N_{2} \) bond length increases
(IV) During the formation of \( C O^{+} \) from
CO, the bond length decreases.
\( \mathbf{A} \cdot \|, 1 \vee, \)
в. ।, и, II, Iv
\( c \cdot \) ।, ॥
D. ।, и, II


In the adjacent figure, \( A B \) is a chord of
circle with centre \( 0 . \) CD is the diameter
perpendicular to AB. Show that \( A D=B D \)


Construct a quadrilateral ABCD with \( A B=2.5 \mathrm{cm}, B C=3.5 \mathrm{cm}, A D=4.5 \mathrm{cm} \)
\( \angle A=90^{0} \) and \( \angle B=120^{0} \)


A pure semiconductor at absolute zero
has
A. Absence of electrons in the conduction band.
B. All the electrons occupying the valence band.
C . Large \( E_{g} \) value.
D. All of the above.


(a) State the postulates of Daltons atomic theory.
(b) Calculate the concentration in terms of mol/kg when 6.35 g of KCl is dissolved in \( 300 g \) of water. \( [\text { At mass of } \mathrm{K}=39 \mathrm{u}, \mathrm{At} \) mass of \( \mathrm{Cl}=35.5 \mathrm{u}] \)


\( f(x) \) and \( g(x) \) are linear function such that for all \( x, f(g(x)) \) and \( g(f(x)) \) are Identity functions. If \( f(0)=4 \) and \( g(5)= \)
17, compute \( f(2006) \)


The degree of the differential equation
\( \boldsymbol{x}=\mathbf{1}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\mathbf{1}}{\mathbf{2 !}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+ \)
\( \frac{1}{3 !}\left(\frac{d y}{d x}\right)^{3}+\dots \dots \) is?
\( A \cdot 3 \)
B.
c. Not defined
D. None of these


Define bulk modulus of elasticity. Give its units and dimensions.


Light of wavelength \( \lambda \) falls on a metal
having work function \( h c / \lambda_{0} \)

Photoelectric effect will take place only if
\( A \cdot \lambda \geq \lambda_{0} \)
в. \( \lambda \geq 2 \lambda_{0} \)
c. \( \lambda \leq \lambda_{0} \)
D. \( \lambda<\lambda_{0} / 2 \)


Aqua-regia dissolves gold.
which is correct?
A. Aqua regia, or nitro-hydrochloric acid is a highly corrosive mixture of acids, a fuming yellow or red solution.
B. The mixtures is formed by freshly mixing concentrated nitric acid and hydrochloric acid hoptimally in a volume ratio of 1: 3
C. it can dissolve the noble metalsgold and platinum
D. all of these


The electron configuration of \( _{11} N a^{23} \) is
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{5}, 3 s^{2} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{4}, 3 s^{1}, 3 p^{2} \)
D. \( 1 s^{1}, 2 s^{1}, 2 P^{6}, 3 s^{2}, 3 p^{1} \)


When a polyatomic gas undergoes an adiabatic process its temperature and volume are related by the given equation \( T V^{n} \) =constant the
value of \( n \) is?


Percentage of \( K_{2} S O_{4} \) in the sample is:
A . \( 65.75 \% \)
в. 72 \%
\( c .60 .35 \% \)
D. 78.74 \%


\( I f \cos 10^{\circ} \cos 30^{\circ} \cos 50^{\circ} \cos 70^{\circ}=x \)
Find \( 16 x \)


Differentiate the following:\( i=i_{0} e^{\frac{-t}{R C}} \)


A solid cube is subjected to a pressure
of \( \left(5 \times 10^{5} \quad N / m^{2}\right) . \) Each side of the
cube is shortened by then volumetric strain and Bulk modulus of the cube are
\( \begin{array}{ll}\text { A. } 0.03,5 \times 10^{5} & \text { N } / m^{2}\end{array} \)
B. \( 0.03,1.67 \times 10^{7} \quad N / m^{2} \)
C. \( 3,1.67 \times 10^{-7} \quad N / m^{2} \)
D. \( 0.01,1.67 \times 10^{7} \quad N / m^{2} \)


What is the average value of the AC voltage over one complete cycle?
A. zero
в. \( V_{\max } \)
c. \( \frac{2 V_{\max }}{\pi} \)
D. \( \frac{V_{\text {max }}}{2} \)


Which reaction below demonstrates the
lewis definition of acids and bases?
\( \mathbf{A} \cdot H C l+N a O H \rightarrow H O H+N a C l \)
B. \( H_{2} O+N H_{3} \rightarrow O H^{-}+N H_{4}^{+} \)
\( \mathbf{C} \cdot N H_{3}+B F_{3} \rightarrow N H_{3} B F_{3} \)
D. \( H I+K O H \rightarrow H_{2} O+K I \)
E \( \cdot H^{+} O H^{-} \rightarrow H_{2} O \)


Calculate the equivalent resistance between the points \( A \) and \( B \) in the given circuit in ohms.
A. 6
в.
\( c \cdot 2 \)
\( D \)


Compressed oxygen is used for:
A. Welding purpose
B. Airship
C . Refrigerant
D. Soda fountains


Let \( \cos ^{-1}\left(4 x^{3}-3 x\right)=a+b \cos ^{-1} x \)
\( x \epsilon\left[-\frac{1}{2},-1\right) \) then the value of \( a+b \pi \) is
A \( .2 \pi \)
в. \( 3 \pi \)
\( c \)
D. \( -2 \pi \)


An element having atomic number 50 Find its group number and period numbers.


\( \ln \operatorname{arclation} F=a \sin k_{1} x+b \sin k_{2} T \)
where \( F, x \) and \( T \) denote the force
distance and time respectively. Units of
\( k_{1} \) and \( k_{2} \) are respectively a
A. meter, \( s \)
B . meter \( ^{-1}, s^{-1} \)
c. meter \( ^{-1}, s \)
D. meter, \( s^{-1} \)


Few common pins are placed on a table with a glass top. A powerful bar magnet is moved under the glass top. Describe the movement of common pins.
A. move opposite to the direction of magnet
B. move in the direction of magnet
c. not move
D. be thrown up in air.


What happens when a cold and concentrated solution of sodium
chloride reacts with ammonia and
carbon dioxide? Write the equation of
the reaction takes place.


The following mechanism has been
proposed for the reaction of \( N O \) with
\( B r, \) to form \( N O B r \) \( N O_{(g)}+B r_{2(g)} \stackrel{\text {fast}}{\rightleftharpoons} N O B r_{2(g)}, N O+ \)
\( \boldsymbol{B} \boldsymbol{r}_{2(g)}+\boldsymbol{N} \boldsymbol{O}_{(g)} \stackrel{\text {slow}}{\rightleftharpoons} \quad \boldsymbol{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{B} \boldsymbol{r}_{(g)} \)
If the second step is the rate determining step, the order of the
reaction with respect to \( N O_{(g)} \) is:
A.
в.
\( c .3 \)
D.


Our inner ear is shaped like
A. a snail
B. a bird
\( c . \) a bear
D. none of these


Which one of the following is the correct matching of the site of action on the given substrate, the enzyme acting upon it and the end product?
A. Small intestine: \( \rightarrow \) Proteins Pepsin Amino acids
B. Stomach : \rightarrow Fats Lipase Micelles
c. Duodemum: \( \rightarrow \) Triglycerides Trypsin Monoglycerides
D. small intestine : \( \rightarrow \) Starch Amylase Disaccharide (Maltose)


is the example of dicot plant.
A. Mango
B. Banana
c. onion
D. wheat


\( \boldsymbol{X}+\boldsymbol{C}+\boldsymbol{C l}_{2} \stackrel{\text { High Temp. }}{\boldsymbol{Y}} \boldsymbol{H}+\boldsymbol{C O} \)
\( \boldsymbol{Y}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{Z}+\mathbf{2} \boldsymbol{H} \boldsymbol{C l} \)
Compound Y is found in polymeric
structure and is an electron deficient
molecule. The compound Y is:
A. \( B e O \)
в. \( B e C l_{2} \)
\( \mathbf{c} \cdot B e(O H)_{2} \)
D. \( B e O . B e(O H)_{2} \)


If sum of \( 3 r d \) and \( 8 t h \) terms of an \( A . P \)
is 7 and sum of 7 th and 14 th terms is
-3 then find the \( 10 t h \) term.


Which of the following is not a drawback of Ruther-ford atomic model?
A. It failed to explain why electrons just simply fall into the nucleus.
B. It failed to explain why an atom emits discratt spectrum.
C. It failed to explain why only a very small amount of \( \alpha \) paticles get scattered
D. none of these


Consider a uniform electric field \( \boldsymbol{E}= \) \( 3 \times 10^{3} \hat{i} \mathrm{N} / \mathrm{C} \)
(a) What is the flux of
this field through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( y z \) plane?
(b) What is the flux through the same square if the normal to its plane
makes a \( 60^{\circ} \) angle with the \( x \) -axis?


In an AP the sum of first n terms is
\( \frac{3 n^{2}}{2}+\frac{5 n}{2} \) Find \( 25^{t h} \) term


Write the following in simplest form:
\( \tan ^{-1}\left(\frac{\sqrt{\left(1+x^{2}\right)}-1}{x}\right) \)


Which of the following phenomena can be demonstrated by light. But not with sound waves in an air column?
A . Reflection
B. Diffraction
c. Refraction
D. Polarization


If the area of the closed figure bounded by the following curves \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\mathbf{2}- \)
\( \boldsymbol{x}, \boldsymbol{y}=\mathbf{0} \) is k. Find \( 6 \mathbf{k} \)


If \( \alpha \) and \( \beta \) are two zeroes of the
polynomial \( \boldsymbol{x}^{2}-\mathbf{7} \boldsymbol{x}+\boldsymbol{k} \) where \( \boldsymbol{\alpha}-\boldsymbol{\beta}= \)
\( 5, \) find value of \( k \)


The Gibbs free energy change for the reaction for which \( \Delta \boldsymbol{H}=-\mathbf{3 9 3 . 4 k J} \)
and \( \Delta S=-2.9 J K^{-1} \) mol \( ^{-1} \) at \( 298 \mathrm{K} \) is:
\( \mathbf{A} \cdot-352.5 k J \)
В. \( -392.5 k J \)
\( \mathbf{c} .+352.5 k J \)
D. \( +392.5 k J \)


Figure shows three point charges
\( +2 q,-q a n d+3 q . \) Two charges
\( +2 q \) and \( q \) are enclosed within a
surface \( \boldsymbol{S} \)
What is the electric flux due to this
configuration through the surface \( S ? \)


In the primary circuit of potentiometer
the rheostat can be varied from 0 to
10\Omega. Initially it is at minimum
resistance (zero). Find the length \( \boldsymbol{A P} \)
(in \( \mathrm{m} \) ) of the wire such that the
galvanometer shows zero deflection.


The temperature coefficient of a
reaction is:
A. ratio of rate constants at two temperature differing by \( 1^{o} C \)
B. ratio of rate constants at temperature \( 35^{\circ} \mathrm{C} \) and \( 25^{\circ} \mathrm{C} \)
C. ratio of rate constants at temperature \( 30^{\circ} \mathrm{C} \) and \( 25^{\circ} \mathrm{C} \)
D. specific reaction rate by \( 25^{\circ} \)


Assertion(A): Purine bases present in DNA are adenine and guanine. Reason(R): The base uracil is present in
DNA whereas the base thymine is
present in RNA.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of A
c. A is true but R is false
D. .A is false but R is true


The coordinates of the point where the line segment joining \( \boldsymbol{A}(\mathbf{5}, \mathbf{1}, \boldsymbol{6}) \) and \( B(3,4,1) \) crosses the yz plane are
A \( \cdot\left(0, \frac{17}{2}, \frac{13}{2}\right) \)
в. \( \left(0,-\frac{17}{2}, \frac{13}{2}\right) \)
c. \( \left(0, \frac{17}{2},-\frac{13}{2}\right) \)
D. \( \left(0,-\frac{17}{2},-\frac{13}{2}\right) \)


\( C l 2+H_{2} O \rightarrow_{-}----+_{-}---- \)
A. \( H C l, O_{2} \)
в. \( H C l, H O C l_{2} \)
c. \( H C l, \) НОС\( l \)
D. None of above


The vertices of a triangle are \( \boldsymbol{A}(\mathbf{1}, \mathbf{1}), \boldsymbol{B}(\mathbf{4}, \mathbf{5}) \) and \( \boldsymbol{C}(\mathbf{6}, \mathbf{1 3}) . \) Find \( \cos \boldsymbol{A} \)


The nucleus of an element contains
nine protons. Calculate its valency.


Sodium carbonate can be used to
precipitate calcium carbonate by reacting it with:
A. calcium sulphate
B. calcium chloride
c. magnesium oxide
D. both \( B \) and \( C \)


The electric generator is based on which scientific principle?
A. Reflection of ultrasonic waves
B. Superconductivity
c. Faradays laws of electromagnetic induction
D. Magnetic confinement of plasma


Find \( a \) if the \( 17^{t h} \) and \( 18^{t h} \) term of the
expanse on \( (2+a)^{50} \) are equal.


A proton and electron are accelerated by same potential difference starting from
the rest have de-Broglie wavelength \( \lambda_{p} \)
and \( \lambda_{e} \)
A \( \cdot \lambda_{e}=\lambda_{p} \)
в. \( \lambda_{e}<\lambda_{p} \)
\( \mathbf{c} \cdot \lambda_{e}>\lambda_{p} \)
D. none of these


In the figure, if the \( \angle A O B=60^{\circ} \) and
radius is \( 12 \mathrm{cm} \), then find the area of the
segment \( A X B .(\pi=3.14, \sqrt{3}=1.73) \)
A . 14
B . 13.08
c. 12
D. 3.14


If \( \boldsymbol{a}=(\mathbf{0}, \mathbf{1},-\mathbf{1}) \) and \( \boldsymbol{c}=(\mathbf{1}, \mathbf{1}, \mathbf{1}) \) are
given vectors, then find \( |b|^{2}, \) where \( b \)
satisfies \( a \times b+c=0 \) and \( a \cdot b=3 \)
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D. 3


Given that the rate of disappearance of
bromine is \( -3.5 \times 10^{-4} M / s \) for the
following reaction:
\( \boldsymbol{H}_{2(g)}+\boldsymbol{B} \boldsymbol{r}_{2(g)} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(a q)} \)
What is the rate of formation for \( \boldsymbol{H} \boldsymbol{B r} \) ?
A. \( -7.0 \times 10^{-4} \mathrm{M} / \mathrm{s} \)
В. \( -3.5 \times 10^{-4} \mathrm{M} / \mathrm{s} \)
c. \( 3.5 \times 10^{-4} M / s \)
D. \( 7.0 \times 10^{-4} \mathrm{M} / \mathrm{s} \)


Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \circ \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{1} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \)


Let \( P(n): n^{2}+n \) is an odd integer
\( \boldsymbol{P}(\boldsymbol{k}) \Rightarrow \boldsymbol{P}(\boldsymbol{k}+1) \) is true
Then \( P(n) \) is true for all
\( \mathbf{A} \cdot n>2 \)
B \( . n>1 \)
\( c \cdot n \)
D. none of these


A p-n photodiode is made of a material
with a band gap of \( 2.0 \mathrm{eV} \). The minimum frequency of radiation that can be absorbed by the material is nearly:


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{7} & \mathbf{9} \\ -\mathbf{2} & \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right], \) then verify that
\( (i)(A+B)^{T}=A^{T}+B^{T} \)
\( (i i)(A-B)^{T}=A^{T}-B^{T} \)


An electric dipole is kept in a nonuniform electric field. It experiences
A. a force and a torque
B. a force but not a torque
c. a torque but no force
D. neither a force nor a torque


Gas obtained by heating a mixture of ammonium chloride and slaked lime is:
A . \( \mathrm{NH}_{3} \)
B. \( \mathrm{N}_{2} \)
\( c \cdot \mathrm{N}_{2} \mathrm{O} \)
D. NO


\( N O_{2} \) is not obtained when following is
heated.
\( \mathbf{A} \cdot \operatorname{Pb}\left(N O_{3}\right)_{2} \)
в. \( A g N O_{3} \)
c. \( C a\left(N O_{3}\right)_{2} \)
D. \( K N O_{3} \)


Two balls of equal mass are projected from a tower simultaneously with equal speeds. One at angle \( \theta \) above the
horizontal and the other at the same
angle \( \theta \) below the horizontal. The path of
the centre of mass of the two balls is
A. a vertical straight line
B. a horizontal straight line
c. a straight line at angle \( \alpha(<\theta) \) with horizontal
D. a parabola


Decide whether following sequence is
an \( A . P ., \) if so find the \( 20^{t h} \) term of the
progression \( -12,-5,2,9,16,236,30, \dots . \)


A beam of light consisting of two wavelengths \( 65000 \mathrm{A} \) and \( 5200 \mathrm{A} \), is used to obtain interference fringes in Youngs double slit experiment. Suppose the mth bright fringe due to \( 6500 \mathrm{A} \) coincides with nth bright fringe due to \( 5200 \mathrm{A} \) at a minimum distance from
the central maximum. Then
A \( . m=4 ; n=5 \)
B. \( m=5 ; n=4 \)
c. \( m=8 ; n=10 \)
D. \( m=10 ; n=8 \)


If the density of the earth is doubled to that of its original value, the radius
remaining the same, what will be the change in acceleration due to gravity?


Which of the following equations have no real roots ?
A \( \cdot x^{2}-2 \sqrt{3}+5=0 \)
B \( \cdot 2 x^{2}+6 \sqrt{2} x+9=0 \)
c. \( x^{2}-2 \sqrt{3}-5=0 \)
D \( \cdot 2 x^{2}-6 \sqrt{2} x-9=0 \)


Match column I with column II and
select the correct option from the given codes.
Column I Column
A. Royal Botanical Garden, Kew
B. Indian Botanical Garden
(ii) England
C. National Botanical Research Institute
(iii) Howrah
(iv)
D. Llyod Botanical Garden
A. A-(ii), B-(iii), C-(i), D-(iv)
B. A-(i), B-(iii), C-(ii), D-(iv)
C . A-(iv), B-(ii), C-(i), D-(iii)
D. A-(iv), B-(iii), C-(ii), D-(i)


Ethylamine \( \left(C_{2} H_{5} N H_{2}\right) \) can be obtained from N-ethylphthalimide on treatment with:
A . \( N a B H_{4} \)
в. \( C a H_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( N H_{2} N H_{2} \)


The energy needed to excite a hydrogen atom from its ground state to its third excited state is:
A . \( 12.1 e V \)
B. \( 10.2 e V \)
c. \( 0.85 e V \)
D. \( 12.75 e V \)


Fire was first used for protection and cooking by
A. Java man
B. Neanderthal man
c. Peking man
D. Cro-magnon man


At low pressure, the graph of \( \boldsymbol{P} \boldsymbol{V} \boldsymbol{v} \boldsymbol{s} \frac{\mathbf{1}}{\boldsymbol{V}} \)
for a given amount at a constant temperature for a real gas is
A. straight line parallel to x-axis
B. straight line having positive intercept and negative slope
c. straight line passing through origin having positive slope
D. none of the above


Let \( _{y}-y(x) \) be the solution of the
differential equation \( \sin x \frac{d y}{d x}-y \cos x- \)
\( 4 x,_{x} \epsilon(0, \pi) . i f y\left(\frac{\pi}{2}\right)=0 \)
then \( y\left(\frac{\pi}{6}\right) \) is equal to
A \( \cdot-\frac{4}{9} \pi^{2} \)
B. \( -\frac{4}{9 \sqrt{3}} \pi^{2} \)
c. \( -\frac{-8}{9 \sqrt{3}} \pi^{2} \)
D. None of these


A convex mirror of focal length \( 10 \mathrm{cm} \)
cut into two halves and placed before an
object at a distance of \( 10 \mathrm{cm} \) as shown in figure.The separation between
images formed by two halves is:
\( A .1 m m \)
\( \mathbf{B} \cdot 2 m m \)
\( \mathrm{c} .3 \mathrm{mm} \)
\( \mathbf{D} \cdot 9 m m \)


Arrange the following hydrides of group 16 elements in order of increasing
stability:
A. \( H_{2} S<H_{2} O<H_{2} T e>H_{2} S e \)
в. \( H_{2} O<H_{2} T e<H_{2} S e<H_{2} S \)
c. \( H_{2} O<H_{2} S<H_{2} S e<H_{2} T e \)
D. \( H_{2} T e<H_{2} S e<H_{2} S<H_{2} O \)


Nitrogen in soil is an example
for


Exoskeleton of rabbit consists of
A. Hair
B. Hair and hoof
c. Hair and claws
D. Hair, claws and hoof


A : tetracyanomrthane
B : carbon
dioxide
C: benzene \( \quad \) D : 1, 3-bute-di-
ene
Ratio of \( \sigma \) and \( \pi \) bonds is in order:
A. \( A=B<C<D \)
в. \( A=B<D<C \)
c. \( A=B=C=D \)


Prove \( \int_{0}^{a} \boldsymbol{F} \boldsymbol{d} \boldsymbol{x}=\int_{0}^{\boldsymbol{a} / \mathbf{2}} \boldsymbol{F}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}+ \)
\( \int_{0}^{\boldsymbol{a} / 2} \boldsymbol{F}(\boldsymbol{a}-\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \)


Consider the determinant \( \Delta= \)
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right| \)
\( M_{i j}= \) Minor of the element of \( i^{t h} \) row \&
\( j^{t h} \) column
\( C_{i j}= \) Cofactor of element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column.

If all the elements of the determinant
are multiplied by 2, then the value of new determinant is
A . 0
B. \( 8 \Delta \)
\( c \cdot 2 \Delta \)
D. \( 2^{9} \Delta \)


The intensity of two waves is 2 and 3 unit, then average intensity of light in the overlapping region will have the value:
A . 2.5
B. 6
\( c .5 \)
D. 13


Organic compound having covalent bond is :
A. carbon tetrachloride
B. sodium chloride
c. magnesium chloride
D. sodium sulfate


Q Type your question
pill
the Compound (H) is:
4
B.
\( c \)
\( D \)


Simplify \( \frac{5 \cos ^{2} 60^{0}+4 \sec ^{2} 30^{0}-\tan ^{2} 45^{0}}{\sin ^{2} 30^{0}+\cos ^{2} 30^{0}} \)
\( A \cdot-\frac{55}{2} \)
в. \( \frac{67}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{55}{4} \)


Solve \( \boldsymbol{I}=\int \frac{1}{\cos ^{2} x(1-\tan x)^{2}} d x \)
A \( \cdot_{I}=\frac{-1}{1-\cot x}+C \)
B. \( I=\frac{1}{1-\tan x}+C \)
\( ^{c} I=\frac{-1}{1-\tan x}+C \)
D. None of these


Write equations involved in the
preparation of phenol from cumene.


A permanent magnet
A. attracts all substances
B. attracts only ferromagnetic substances
C . attracts magnetic substances and repels all others
D. attracts some substances and repels others


The converse of "If in a triangle \( A B C, A B=A C, \) then \( \angle B=\angle C^{\prime \prime}, \) is
A. If in a triangle \( A B C, \angle B=\angle C \), then \( A B=A C \).
B. If in a triangle \( A B C, A B \neq A C \), then \( \angle B \neq \angle C \).
c. If in a triangle \( A B C, \angle B \neq \angle C \), then \( A B \neq A C \).
D. If in a triangle \( A B C, \angle B \neq \angle C \), then \( A B=A C \).


\( \ln \triangle P Q R, \) point \( S \) is the midpoint of side
\( Q R \). If \( P Q=17, P R=11, P S=13 . \) Find
\( Q R \)


If \( 10^{4 x}=625 \) then find the value of \( 10^{-x} \)


Total number of stereoisomers for the
following compounds are:


Evaluate: \( \lim _{x \rightarrow 2} \frac{(2 x-3)(x-2)}{x^{2}+x-6} \)


A short length linear double-stranded DNA molecule has 110 thymine and 110 guanine bases. The total number of
nucleotide in the DNA fragment will be
A . 110
B. 880
\( c \cdot 440 \)
D. 220


The resistance of a wire of cross-section
'a' and length 'l' is R ohm. The resistance of another wire of the same material
and of the same length but crosssection '4a' will be
\( A \cdot 4 R \)
в. \( \frac{R}{4} \)
\( c \cdot \frac{R}{16} \)
D. 16 R


Characteristic smell of urine is due to
A. Urea
B. Uric acid
c. Urinod substancce
D. Pus


Under action of which force does water
flow from an open tap towards ground?
A. Electrostatic force
B. Magnetic force
c. Gravitational force
D. None of the above


Which of the following compounds can be purified by vacuum distillaiton? This question has multiple correct options
A. Glycerine
B. Glycerol
c. Propane-1,2, 3-triol
D. Ethanol


Two Nicole prisms are kept perpendicular. One of them is illuminated with a light intensity
(natural) \( I_{o} \). Two more nicol prisms are introduced in between symmetrically. Find the light intensity emitted from the last nicol prism.
A \( \cdot \frac{27 I_{0}}{64} \)
в. \( \frac{27 I_{o}}{128_{o}} \)
c. \( _{9} \frac{I_{o}}{32} \)
D. \( \frac{9 I_{0}}{64} \)


The foot of a ladder is \( 6 \mathrm{m} \) away from a
wall and its top reaches a window \( 8 \mathrm{m} \) above the ground. If the ladder is shifted
in such a way that its foot is \( 8 \mathrm{m} \) away from the wall, to what height does its top reaches?
A. \( 6 m \)
B. \( 4 \mathrm{m} \)
\( c .5 \mathrm{m} \)
D. 3 m


Bleaching powder and bleach solution
are produced on a large scale and is used in several house-hold products. The effectiveness of bleach solution is
often measured by iodometry. Bleaching powder contains a salt of an oxoacid as
one of its components. The anhydride of that oxoacid is:
A. \( C l_{2} O \)
в. \( C l_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2} \)
D. \( C l_{2} O_{6} \)
E \( . C l_{2} O_{3} \)
F. \( C l_{2} O_{5} \)
G. \( C l_{3} O_{9} \)
н. \( C l_{3} O_{5} \)


Let \( P(n): a^{n}+b^{n} \) such that \( a, b \) are
even, then \( p(n) \) will be divisible by \( a+b \)
if
\( \mathbf{A} \cdot n>1 \)
B. \( n \) is odd
\( \mathbf{c} \cdot n \) is even
D. none of these


The optical length of an astronomical telescope with magnifying power of 10 for normal vision is \( 44 \mathrm{cm} . \) What is focal
length of the objective?
A. \( 40 \mathrm{cm} \)
B. 22cm
\( c \cdot 10 c m \)
D. \( 4 \mathrm{cm} \)


At some point \( \mathbf{P} \) on the ellipse, the segment \( \mathbf{S S}^{1} \) subtends a right angle,
then its eccentricity is
\( ^{A} \cdot_{e}=\frac{\sqrt{2}}{2} \)
в. \( e<\frac{1}{\sqrt{2}} \)
c. \( e>\frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)


Let \( A \) be a real matrix such that \( A^{67}= \)
\( A^{-1}, \) then
\( \mathbf{A} \cdot|A|=\pm 1 \)
B . \( |A|=1 \)
C. \( A=I, I \) being unit matrix
D. \( A \) is diagonal matrix


Which of the following statements is
correct?
This question has multiple correct options
A. \( S O_{2} \) is anhydride of sulphurous acid.
B. \( S O_{2} \) acts as only oxidising agent.
c. The coloured matter lost colour on exposure to \( S O_{2} \) can regain colour on exposure to atmosphere
D. \( S O_{2} \) can get reduced to sulphur.


The curves \( y=x^{2}-1, y=8 x-x^{2}-9 \)
at
A. Intersect at right angles at (2,3)
B. Touch each other at (2,3)
c. Do not intersect at (2,3)
D. Intersect at an angle \( \frac{\pi}{3} \)


The value of G depends on
A. the nature of the interacting bodies
B. the size of the interacting bodies
C. the mass of the interacting bodies
D. none of these


A force \( \mathbf{F}(-\hat{\mathbf{k}}) \) acts on the origin of the
co-ordinate system. The torque about the point (1,-1) is
A. \( \mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
B . \( -\mathrm{F}(\hat{\mathrm{i}}+\hat{\mathrm{j}}) \)
\( \mathbf{c} \cdot \mathbf{F}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \)
D. \( -\mathrm{F}(\hat{\mathrm{i}}-\mathrm{j}) \)


How sound is produced in flute or clarinet?
A. Air in the tube vibrates
B. Skin of flute vibrates
c. The holes of the flute vibrate
D. No vibration is produced


The order of increasing oxidation number ofs in \( S_{8}, S_{2} O_{8}^{-2}, S_{2} O_{3}^{-2}, S_{4} O_{6}^{-2} \)
is given below:
A. \( S_{8}<S_{2} O_{8}^{2}<S_{2} O_{3}^{2}<S_{4} O_{6}^{2} \)
B . \( S_{2} O_{8}^{2}<S_{2} O_{3}^{2}<S_{4} O_{6}^{2}<S_{8} \)
\( \mathrm{c} \cdot S_{2} \mathrm{O}_{8}^{2}<S_{8}<S_{4} \mathrm{O}_{6}^{2}<S_{2} \mathrm{O}_{3}^{2} \)
D. \( S_{8}<S_{2} O_{3}^{2}<S_{4} O_{6}^{2}<S_{2} O_{8}^{2} \)


Time dependent permanent deformation is called
A. Plastic deformation
B. Elastic deformation
c. Creep
D. Anelastic deformation


Ground state electronic configuration of valence shell electrons in nitrogen
molecule \( \left(N_{2}\right) \) is written as \( \left(S_{2 s}\right)^{2}\left(S *_{2 s}\right)^{2}\left(P_{2 p}\right)^{4}\left(S_{2 p}\right)^{2} \) Hence, the
bond order of nitrogen molecule is:
A .2
B. 3
\( c \cdot 0 \)
D.


An electric charge in uniform motion produces:
A. an electric field only
B. a magnetic field only
c. both electric and magnetic fields
D. no such field at all


What will be the answer in appropriate significant figures as a result of addition of 3.0223 and \( 5.041 ? \)
A . 80.633
в. 8.0633
c. 8.063
D. 806.33


If \( \cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)= \)
\( -\sqrt{m} \sin x . \) Find \( m \)


Show that \( \int \frac{\sin x+\cos x}{\sqrt{(1+\sin 2 x)}} d x=x \)


Find the angle of inclination (in degrees) of the line passing through the points (1,2) and (2,3)
A \( \cdot 60^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{0} \)
D. \( 90^{\circ} \)


For Adsorption phenomenon:
\( \mathbf{A} \cdot \Delta H=+v e, \Delta S=-v e \)
B . \( \Delta H=-v e, \Delta S=+v e \)
\( \mathbf{c} \cdot \Delta H=-v e, \Delta S=-v e \)
D. \( \Delta H=+v e, \Delta S=+v e \)


Define the following term:
Protective colloid


Calculate the mean deviation from the
mean for the scores given below:
\( \mathbf{1 5}, \mathbf{1 1}, \mathbf{1 3}, \mathbf{2 0}, \mathbf{2 6}, \mathbf{1 8}, \mathbf{2 1} \)