The standard reduction potential of normal calomel electrode and reduction
potential of saturated calomel
electrodes are 0.27 and 0.33 volt
respectively. What is the concentration
of \( C l^{-} \) in saturated solution of \( K C l ? \)
A . \( 0.1 M \)
в. \( 0.01 M \)
c. \( 0.001 M \)
D. None


Solve the following systems of linear equations
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{5} \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{3} \)
\( \boldsymbol{x}+\boldsymbol{z}=\boldsymbol{4} \)


Which postulate of Dalton's atomic
theory the result of the law of conservation of mass?


The union of two equivalence relations
¡s:
A. always an equivalence relation
B. reflexive and symmetric but needn't be transitive
C. reflexive and transitive but need not be symmetric
D. None of these


The area (in square units) of a regular hexagon, each side of which is 2 units,
is
\( A \cdot 8 \)
B. 10.392 (approx.)
c. 12.5
D. 18


Kinetic energy of photoelectrons
increases with increase in freqency of the light incident on the metal surface.
A. True
B. False


A tangential force of \( 2100 N \) is applied
on a surface of area \( 3 \times 10^{-6} m^{2} \) which
is \( 0.1 m \) from a fixed face. The force
produces a shift of \( 7 \mathrm{mm} \) of upper surface with respect to bottom. Th4n
the modulus of rigidity of the material.
В. \( 5 \times 10^{10} \mathrm{Nm}^{-2} \)
c. \( 15 \times 10^{10} N m^{-2} \)
D. \( 1 \times 10^{10} \mathrm{Nm}^{-2} \)


Name the phenomenon which shows the
quantum nature of electromagnetic radiation.


A copper wire of cross sectional area
\( 3 m m^{2} \) carrying a current of \( 4 A \) has \( 10^{29} \) free electrons \( / m^{3} . \) If this wire is
now placed in a field of induction \( 0.15 T \) perpendicular to wire. The force on each electron is :
A . \( 20 \times 10^{-25} \mathrm{N} \)
В. \( 37.5 \times 10^{-25} N \)
\( \begin{array}{ll}\text { С } & 10 \times 10^{-25} N\end{array} \)
D. \( 41.7 \times 10^{-25} N \)


What are broad-spectrum antibiotics? How are polythene and neoprene prepared?


A body of mass 5 kg at rest is under the action of a force which gives it a
velocity given by \( v=3 t \mathrm{m} / \mathrm{s}, \) here \( t \) is
time in seconds. The work done by the force in two seconds will be:
\( \mathbf{A} \cdot 90 J \)
B. \( 45 J \)
\( c .180 J \)
D. \( 30 J \)


mole of phenol reacts with bromine to give 2,4,6 -tribromophenol. The amount of bromine required is:
A. 3.0 moles
B. 1.5 moles
c. 4.5 moles
D. 6.0 moles


A radioactive decay can form an isotope of the original nucleus with the emission of particles
A. One \( \alpha \) and four \( \beta \)
B. One \( \alpha \) and two \( \beta \)
c. one \( \alpha \) and one \( \beta \)
D. Four \( \alpha \) and one \( \beta \)


A van is moving with a speed of 72 \( k m p h \) on a level road, where the
coefficient of friction between tyres and
road is \( 0.5 . \) The minimum radius of
curvature, the road must have, for safe
driving of van, is \( \left(g=10 m / s^{2}\right) \)
A. \( 80 m \)
в. \( 40 \mathrm{m} \)
\( c .20 m \)
D. \( 4 m \)


expected to disintegrate by:
A. \( \alpha \) -emission
B. \( \beta \) -emission
C. positron emission
D. proton emission


An organism which has Malpighian tubule as excretory organ can be placed in phylum
\( \mathbf{A} \)
Arthropda
\( \mathbf{B} \)
Annelida
\( \mathbf{c} \)
Platyhelminthes
D. None of the above


The property of the alkaline earth
metals which increases with their
atomic number is:
A. ionisation energy
B. electronegativity
c. solubility of their hydroxides in water
D. solubility of their sulphates in water


Pick out the false statement:
This question has multiple correct options
A. the electropostive character of alkali metals decreases with increases in atomic number
B. lithium is a hard metal and cannot be cut with a knife
C. Alkali metals are strong reducing agents
D. the electro-negativities of all alkali metals remain the
same.


The equation of the line passing
through the point \( P(1,2) \) and cutting
the lines \( x+y-5=0 \) and \( 2 x-y=7 \)
at \( A \) and \( B \) respectively such that the
harmonic mean of \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) is \( \mathbf{1 0} \), is
A \( \cdot y-2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}-\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x-1) \)
в. \( y+2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}+\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x+1) \)
c. \( y-2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}+\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x-1) \)
D. None of the above


Four harmonic waves of equal
frequencies and equal intensities \( I_{0} \)
have phase angles \( 0, \pi / 3,2 \pi / 3, \) and \( \pi \)
When they are superposed, the intensity
of the resulting wave is \( n I_{0} . \) The value of
n is


Butter is an emulsion of type :
A. water in oil
B. oil in water
c. oil and oil
D. none of the above


Derive an expression for angular
momentum


A man sold 10 eggs for 5 rupees and gained \( 20 \% . \) How many eggs did he buy for 5 rupees?
A \( \cdot 12 \)
в. \( \frac{25}{12} \)
c. 25
D. None


The concentration of dissolved oxygen
(DO) in cold water can go upto:
A. 10 ppm
B. 14 ppm
\( c .16 \mathrm{ppm} \)
D. 8 ppm


Explain the following phenomenon by means of balanced equation:
(a) When the solution (b) is heated,
turbidity reappears.
(b) The turbidity of solution (a) eventually disappears when continued exhaling is made through it
(c) When the solution
(b) is heated,
turbidity reappears.


Solve the following pair of equations by cross multiplication rule.
\( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{a}+\boldsymbol{b}, \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}=\boldsymbol{a}^{2}-\boldsymbol{b}^{2} \)
A . \( x=1, y=a b \)
в. \( x=a+b, y=b \)
c. \( x=a, y=b \)
D. \( x=b, y=1 \)


toppr
Q Type your question
\( A \)
3
\( c \)
\( D \)


Applying forward bias in p-njunction, the potential barrier
A. increases
B. decreases
c. remains unchanged
D. becomes zero


Find the value of \( \tan 9^{\circ}-\tan 27^{\circ}- \)
\( \tan 63^{\circ}+\tan 81^{\circ} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. 1
D. 4


Which of the following quantity is different from others?
A. work
B. Kinetic energy
c. Force
D. Potential energy


The type of isomerism present in
pentaammine nitro chromium (III) chloride is :
A . optical
B. linkage
c. hydrate
D. polymerization


A wheel makes 12 revolutions per hour
The radians it turns through in 20
minutes is:
\( A \cdot 8 \pi^{c} \)
В . \( 16 \pi^{c} \)
\( c \cdot 24 \pi^{c} \)
D. \( 32 \pi^{c} \)


What are respiratory substrates? Name
the most common respiratory
substrate.


A charge \( +\mathrm{Q} \) is located in space at the
point \( (\boldsymbol{x}=\mathbf{1} \boldsymbol{m}, \boldsymbol{y}=\mathbf{1 0 m}, \boldsymbol{z}=\mathbf{5} \boldsymbol{m}) \)
What is the total electric flux that
passes through the yz-plane?
A \( \cdot \frac{Q}{\varepsilon_{0}} \)
в. \( \frac{Q}{3 \varepsilon_{0}} \)
c. \( \frac{Q}{6 \varepsilon_{0}} \)
D \( \cdot \frac{Q}{2 \varepsilon_{0}} \)


Which one of the following generates new genetic combinations leading to mutations
A. Nucellar polyembryony
B. Vegetative reproduction
c. Parthenogenesis
D. Sexual reproduction


The attractive forces between polar
molecules are
between non-polar molecules are
forces.
A. dipole-dipole, London
B. London, dipole-dipole
C. induced dipole-induced dipole, London
D. London, induced dipole-induced dipole


A science teacher has arranged the
following sets of test tubes as She asked the students to find out the
incorrect statement about the above
experimental set-up.
\( 15 \mathrm{mL} \)
Potassium
hydroxide
\( + \)
\( 10 \mathrm{mL} \)
Vinegar
A. Turmeric solution turns red in test tubes 1 and
B. China rose indicator turns green in test tubes 2 and
c. Methyl orange turns yellow in test tubes 1 and
D. Phenolphthalen remains colourless in test tubes 2 and


A transformer has 50 turns in the
primary and 1000 turns in the secondary. If the primary is connected
to a \( 220 V \) DC supply, what will be the voltage across the secondary?


State whether these sentences are true
(T) or false (F).
Carbon dioxide is an important
constituents of air.
A. True
B. False


Find the surface area of a sphere of
diameter:
\( \mathbf{3 . 5} \mathrm{cm} \)


Name the reaction


Assertion
Copper obtained after bessemerization
is known as blister copper.
Reason
Blisters are produced on the surface of the metal due to escaping of dissolved
\( \boldsymbol{S O}_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Heat energy is supplied at a constant
rate to \( 100 \mathrm{g} \) of ice at \( 0^{\circ} \mathrm{C} \). The ice is
converted into water at \( 0^{\circ} \mathrm{C} \) in 2
minutes. How much time will be
required to raised the temperature of water from \( 0^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \) ? [Given:
specific heat capacity of water \( = \)
\( 4.2 J g^{-1 \circ} C^{-1}, \) specific latent heat of
ice \( =\mathbf{3 3 6} \boldsymbol{J} \boldsymbol{g}^{-\mathbf{1}} \)


At same pressure,temperature and volume what will be deviation for both
\( \operatorname{gases} N_{2} \operatorname{gas} \) and \( H e \) gas
A. Same deviation
B. Deviation for \( N_{2}>H e \)
c. Deviation for \( H e>N_{2} \)
D. No deviation for both gases


Force developed in cortex of root which pushes water into xylem of root is
A. Root pressure
B. Turgor pressure
c. osmotic pressure
D. Diffusion


The heat of combustion of methane is
\( -880 \mathrm{kJ} \mathrm{mol}^{-1} . \) If \( 3.2 \mathrm{g} \) of methane is
burnt
\( A \cdot 88 k J \)
B. 264 kJ
c. 176 kJ
D. 440 kJ


The cyclotrimetaphosphoric acid is:
\( \mathbf{A} \cdot\left(H P O_{3}\right)_{3} \) and contains total 9 bonds
B. \( H_{3} P_{3} O_{6} \) and contains total 12 bonds
C \( \cdot\left(H P O_{3}\right)_{3} \) and contains total 15 bonds.
D. \( H_{3} P_{3} O_{9} \) and contains \( 18 \sigma- \) bonds


How can you use the gold leaf electroscope to detect the nature of charge on a body?


Carbon tetrachloride has no net dipole moment because of :
A. its planar structure
B. its regular tetrahedral structure.
c. similar sizes of carbon and chlorine atoms.
D. similarelectron affinities of carbon and chlorine


Check, whether the half plane \( 3 x+ \) \( 6 y \geq 0 \) contains \( (1,1), \) if so shade the
plane containing \( (\mathbf{1}, \mathbf{1}) \)


\( D_{2} O \) is used as a promoter in nuclear reactors to speed down the neutrons If this is true enter 1 , if false enter 0 .


Water exists in which of the following
state?
A. solid
B. liquid
c. gas
D. all of above


The intensity of atmospheric electric
field is :
A. same in winter as in summer
B. lesser in winter than in summer
c. greater in winter than in summer
D. none of the above


The concentration of \( \mathrm{CO}_{2} \) in a soft drink
bottled with a partial pressure of \( \mathrm{CO}_{2} \) of
4.0 atm over the liquid at \( 25^{\circ} \mathrm{C} \) is \( 1.2 \times \)
\( 10^{-1} \) M. The Henry's law constant for
\( C O_{2} \) at this temperature is
A \( \cdot 3.0 \times 10^{-2} \mathrm{mol} / \mathrm{L}- \) atm
B . \( 4.5 \times 10^{-3} \) mol \( / L- \) atm
c. \( 5.6 \times 10^{-3} \mathrm{mol} / \mathrm{L}- \) atm
D. \( 2.3 \times 10^{-2} \mathrm{mol} / \mathrm{L}- \) atm
E. More information is needed to solve the problem.


A thin prism of angle \( 15^{\circ} \) made of glass
of refractive index \( \mu_{1}=1.5 \) is combined
with another prism of glass of refractive
index \( \mu_{2}=1.75 . \) The combination of the
prism produced dispersion without deviation. The angle of the second prism
should be :
A \( \cdot 5^{\circ} \)
B . \( 7^{\circ} \)
\( c \cdot 10^{\circ} \)
D. \( 12^{\circ} \)


Thus, lithium shows similarities to
magnesium and beryllium to aluminium in many of their properties. This type of diagonal similarity is commonly referred to as diagonal relationship in the periodic table. The
diagonal relationship is due to the similarity in ionic sizes and / or charge
/ radius ratio of the elements.


Find the equation of line of intersection of planes \( \vec{r} \cdot(3 \vec{i}-\vec{j}+\vec{k})=1 \) and \( \vec{r} \)
\( (3 \vec{i}+4 \vec{j}-2 \vec{k})=2 \)


Which of the following lanthanoid ions is diamagnetic? (Atoms, \( C e= \)
\( \mathbf{5 8}, \boldsymbol{S m}=\mathbf{6 2}, \boldsymbol{E u}=\mathbf{6 3}, \boldsymbol{Y b}=\mathbf{7 0} \mathbf{)} \)
A \( \cdot Y b^{2} \)
в. \( C e^{2} \)
\( \mathrm{c} \cdot \mathrm{Sm}^{2+} \)
D. \( E u^{2} \)


Preparation of benzene from phenol is:
A. reduction
B. oxidation
C. addition
D. dehydrogenation


A body is thrown vertically upwards
from \( A, \) the top of the tower. It reaches
the ground in time \( t_{1} \). If it is thrown
vertically downwards from \( A \) with the
same speed, it reaches the ground in
time \( t_{2} . \) If it is allowed to fall freely from
\( A, \) then the time it takes to reach the
ground is given by
A \( \cdot t=\frac{t_{1}+t_{2}}{2} \)
B. \( t=\frac{t_{1}-t_{2}}{2} \)
C \( . t=\sqrt{t_{1} t_{2}} \)
D \( \cdot t=\sqrt{\frac{t_{1}}{t_{2}}} \)


Le Chatelier's principle is applicable to:
A. Only homogeneous chemical reversible reactions
B. Only heterogeneous chemical reversible reactions
C. Only physical equilibria
D. All systems, chemical or physical, in equilibrium


If particle takes \( t \) seconds less and acquires a velocity of \( \mathrm{v} \mathrm{m} / \mathrm{s} \) more in falling through the same distance on to planets where the acceleration due to gravity are \( 2 g \) and \( 8 g \) respectively, then
A. \( v=4 g t \)
B. \( v=5 g t \)
c. \( v=2 g t \)
D. \( v=16 g t \)


If the velocity of electron in the first
Bhors orbit of H atoms is \( s 2.19 \times \)
\( 10^{6} m / s . \) calculate the velocity of
electron in Bohrs second orbit?


Two balls were thrown vertically upwards with different velocities, what
is the shape of the graph between distance between the balls and time
before either of the two collide with
ground?
A. Straight line passing through origin
B. Parabola
c. circle
D. None of the above


What is the basement membrane?


Why does a gas from a small container when transferred to a large container
occupy all the space available?
A. Gas has no definite mass
B. Gas has no definite shape
c. Gas has no definite volume
D. Gas has no definite density


In PS I, the reaction centre Chl a has absorption maxima at whereas in PS II, the reaction centre Chl
a has absorption maxima at
A. \( 700 \mathrm{nm}, 680 \mathrm{nm} \)
B. \( 680 \mathrm{nm}, \) 700nm
c. \( 400 \mathrm{nm}, 500 \mathrm{nm} \)
D. 700 \( \mathrm{nm}, 800 \mathrm{nm} \)


The equilibrium constant for the
reaction \( \boldsymbol{H}_{2(g)}+\boldsymbol{C l}_{2(g)} \Leftrightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}_{(g)} \) is
\( K p, \) at the given temperature. Find out the equilibrium constant for the reaction \( \boldsymbol{H} \boldsymbol{C l}_{(\boldsymbol{g})} \Leftrightarrow \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C} \boldsymbol{l}_{2} \)
A \( \cdot \frac{1}{K_{p}^{2}} \)
в. \( K_{p}^{2} \)
c. \( \frac{1}{\sqrt{K_{p}}} \)
D. \( \sqrt{K_{p}} \)
E . \( K_{p}^{3} \)


A planet is revolving round the sun in an elliptical orbit. The work done on the planet b the gravitational force of sun is
zero.
This question has multiple correct options
A. In some parts of the orbit
B. In any part of the orbit
c. In no part of the orbit
D. In one complete revolution


When a body is in equilibrium, which of the following must be true?
A. There is no force acting on it.
B. The sum of all the forces acting on it must be zero.
c. The sum of all the forces acting on it is not equal to zero
D. There are exactly two forces acting on the body


\( \int \frac{d x}{4 \sin ^{2} x+4 \sin x \cos x+5 \cos ^{2} x}= \)
\( A \cdot \tan ^{-1}(2 \tan x+1)+c \)
B. \( \tan ^{-1}\left(\tan x+\frac{1}{2}\right)+c \)
c. \( \frac{1}{8} \tan ^{-1}\left(\tan x+\frac{1}{2}\right)+c \)
D. \( \frac{1}{4} \tan (2 \tan x+1)+c \)


The constant \( c \) of Rolle's theorem for the
function \( \boldsymbol{f}(\boldsymbol{x})=\log \frac{\boldsymbol{x}^{2}+\boldsymbol{a} \boldsymbol{b}}{(\boldsymbol{a}-\boldsymbol{b}) \boldsymbol{x}} \) in \( [\boldsymbol{a}, \boldsymbol{b}] \)
where \( \mathbf{0} \notin[\boldsymbol{a}, \boldsymbol{b}] \) is
A. \( \sqrt{a b} \)
в. \( \frac{a+b}{2} \)
c. \( \frac{a-b}{2} \)
D. \( \frac{b-a}{2} \)


For the reaction :-
\[
\begin{array}{c}
2 \operatorname{Ca} \boldsymbol{S O}_{4}(\boldsymbol{s}) \rightleftharpoons \mathbf{2} \boldsymbol{C a O}(\boldsymbol{s})+ \\
\boldsymbol{2 S O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \\
\boldsymbol{K}_{\boldsymbol{p}}=1.45 \times 10^{-5}(\boldsymbol{a t m})^{3} \text { at } \mathbf{1 6 2 5} \boldsymbol{K} . \text { If }
\end{array}
\]
mole fraction of \( S O_{2} \) is 0.4 at
equilibrium, the dissociation pressure
of \( C a S O_{4} \) in \( m m \) of \( H g \) at \( 1625 K \) is \( X \)
atm. \( 100 X \) is


Three-sevenths =
\( A \cdot \frac{3}{17} \)
в. \( \frac{13}{7} \)
\( c \cdot \frac{3}{7} \)
D. one


\( y=\tan ^{-1} \frac{\sin x}{1+\cos x}, \) then find \( 4 \frac{d y}{d x} \)


Explain the statement "relative density
of brass is \( 8.4 " \)


Presence of following gas in the exhaust gases of a vehicle indicates the incomplete combustion of fuel:
A. \( \mathrm{cO} \) and water vapour
B. \( c \) о
\( c \cdot N O_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


The dihalides in which halogen atoms are attached to adjacent carbon atoms
are termed:
A. vicinal dihalides
B. geminal dihalides
c. both \( A \) and \( B \)
D. none of the above


Density remaining constant, if earth
contracts to half of its present radius,
duration of the day would be (in minutes
A . 45
B. 80
c. 100
D. 120


Which of following is a true fish?
A. Dog fish
B. Silver fish
c. star fish
D. whale


Which is the metallic element?
A. \( Y \)
в. \( x \)
c. Both \( A \) and \( B \)
D. None of the above


Which of the following is/are true when milk changes into curd?
(i) Its state is changed from liquid to semi liquid.
(ii) It changes colour.
(iii) It changes taste.
(iv) The change cannot be reversed. Choose the correct statement.
\( \mathbf{A} \cdot i, i i \)
B. \( i i, \) ii i
c. \( i, i i i, \) iv
D. \( i, i v \)


The weather forecast in a week has
been summarised as above.
Based on the above information answer
the questions A school wants to arrange a picnic for its students. What is the best day for
that?
\begin{tabular}{|l|l|l|l|}
\hline Day & Max. & Min. & Forecast \\
\hline Sun & \( 36^{\circ} \mathrm{C} \) & \( 24^{\circ} \mathrm{C} \) & Sunny and hot \\
Mon & \( 34^{\circ} \mathrm{C} \) & \( 22^{\circ} \mathrm{C} \) & Sunny \\
Tue & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Dry and cloudy \\
Wed & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
Thu & \( 27^{\circ} \mathrm{C} \) & \( 16^{\circ} \mathrm{C} \) & Rain \\
Fri & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Light showers \\
Sat & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
\hline
\end{tabular}
A. Monday
B. Tuesday
c. Thursday
D. Friday


In a single slit diffraction pattern,
\( (a) \)
the intensity \( I, \) at a point where the total phase difference between the
wavelets from top to bottom of the slit is
66 rad.
(b) If this point is \( 7^{0} \) away from the central maxima. Find the width of
the slit. Given: \( \lambda=600 n m \)


The value of determinant is
\[
\left|\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\mathbf{2 b} & \boldsymbol{a}+\mathbf{3} \boldsymbol{b} \\
\boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{a}+\mathbf{3} \boldsymbol{b} & \boldsymbol{a}+\mathbf{4} \boldsymbol{b} \\
\boldsymbol{a}+\mathbf{4} \boldsymbol{b} & \boldsymbol{a}+\mathbf{5} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{6 b}
\end{array}\right|
\]


Boric acid on heating at \( 100^{\circ} \mathrm{C} \) gives:
\( \mathbf{A} \cdot B_{2} O_{3} \)
в. \( H_{2} B_{4} O_{7} \)
c. \( H B O_{2} \)
D. \( H_{2} B O_{3} \)


As per bohr model, the minimum energy (in eV) required to remove an electron from the ground state of double ionized
Li atom(Z=3) is:
A . 1.5
B. 13.6
\( c . \) 50.8
D. 122.4


Compare relative stability of the
following resonating structure.
(ii)
(iii)
\( \mathbf{A} \cdot(i)>(i i)>(i i i) \)
\( \mathbf{B} \cdot(i i)>(i)>(i i i) \)
\( \mathbf{c} \cdot(i)>(i i i)>(i i) \)
\( \mathbf{D} \cdot(i i)>(i i i)>(i) \)


At room temperature and pressure, two flasks of equal volumes are filled with
\( H_{2} \) and \( S O_{2} \) separately. Particles which
are equal in number, in the two flasks
are:
A. atoms
B. electrons
c. molecules
D. neutrons


Why do girls grow faster than boys at
the age of \( 12 ? \)
A. Girls reach puberty earlier than boys.
B. Boys reach puberty earlier than girls.
C. Girls normally take in more proteins at the age of 12.
D. Boys normally consume less food.


f \( a, b, c \in R^{+} \) and \( 2 b=a+c, \) then
check the nature of roots of equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)


The magnetic flux through a coil perpendicular to the plane is varying according to the relation \( \varphi= \)
\( \left(5 t^{3}+4 t^{2}+2 t-5\right) \) wb. Calculate the
induced current through the coil at \( t= \)
2 sec, if the resistance of the coil is \( 5 \Omega \)


What is the work done by a force of \( 2 \mathrm{N} \) in displacing a body by \( 2 \mathrm{m} \) in the direction of the force?
A \( \cdot 4 J^{2} \)
в. \( 6 J \)
c. \( 4 J \)
D. \( 48 J \)


\( \lim _{x \rightarrow \infty} \sqrt{\frac{x-\sin x}{x+\cos ^{2} x}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. None of these


The probability of an ordinary year
having 53 Tuesdays is:
A \( \cdot \frac{2}{7} \)
B. \( \frac{1}{7} \)
\( c \cdot \frac{3}{7} \)
D.


Find the values of \( x, \) if \( \left|\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right|=\left|\begin{array}{ll}\boldsymbol{x} & \mathbf{3} \\ \mathbf{2} \boldsymbol{x} & \mathbf{5}\end{array}\right| \)


In the given figure, \( \frac{Q R}{Q S}= \) \( \frac{Q T}{P R} \) and \( \angle 1=\angle 2 . \) Show that \( \Delta P Q S \sim \)
\( \Delta T Q R \)


What will be the effect on phytochrome in a plant subjected to continuous red light
A . Level of phytochrome will decrease
B. Phytochrome will be destroyed
c. Phytochrome synthesis will increase
D. None of these


The atomic no. of carbon is
A. 5
B. 6
\( c \cdot 12 \)
D. 14


The correct name for the compound
given below is:
A. 2-methyl-1-butene
B. 2-ethyl-1-propene
c. 2-ethyl-2-propene
D. 2-methyl-2-butene


Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8)


\( \int x^{x} \log (e x) d x \) is equal to
A \( \cdot x^{x}+c \)
B. \( x \cdot \log x+c \)
\( \mathbf{c} \cdot(\log x)^{x}+c \)
D. \( x^{\log x}+c \)


If \( a+\frac{1}{a}=6 \) and \( a \neq 0 ; \) find \( a^{2}-\frac{1}{a^{2}} \)
\( \mathbf{A} \cdot \pm 24 \sqrt{3} \)
B. \( \pm 4 \sqrt{2} \)
\( c \cdot \pm 24 \sqrt{2} \)
D. \( \pm 4 \sqrt{3} \)


A hollow conducting spherical shell of radius \( R \) is charged with \( Q \) coulomb.
The amount of work done for moving any
charge \( q \) from the centre to the surface of the shell will be
A \( \cdot \frac{q Q}{4 \pi \epsilon_{0} R} \)
B. Zero
c. \( \frac{Q q}{\pi \epsilon_{0} R} \)
D \( \frac{2 Q q}{\pi \epsilon_{0} R} \)


What is the body organisation of complex organisms?


The term law of total probability is sometimes taken to mean the
A. Law of total expectation
B. Law of alternatives
c. Law of variance
D. None of these


Mortar is a mixture of:
A. lime and water
B. lime and sand
C. lime, sand and water
D. lime and cement


Does pure water conduct electricity? If
not, what can we do to make it
conducting?


Simplify the expression for \( f(x) \) and
then find \( \boldsymbol{f}^{\prime}(\boldsymbol{x}), \) if
\( \boldsymbol{f}(\boldsymbol{x})\left(\frac{\boldsymbol{2} \sqrt{\boldsymbol{x}}+\boldsymbol{3} \sqrt[4]{\boldsymbol{x}}}{\sqrt{\mathbf{1 6} \boldsymbol{x}}+\mathbf{1 2} \sqrt[4]{\boldsymbol{x}}+\boldsymbol{9}}-\frac{\sqrt[4]{\boldsymbol{x}}-\boldsymbol{3}}{\boldsymbol{2} \sqrt[4]{\boldsymbol{x}}+\boldsymbol{3}}\right. \)
\( \mathbf{3} \)


If the radius of a planet is doubled keeping density constant, what will be the value of escape velocity
A. Escape velocity remains same
B. Escape velocity doubles
c. Escape velocity becomes halved
D. Escape velocity becomes one fourth


A square loop of side \( 20 \mathrm{cm} \) is initially
kept \( 30 \mathrm{cm} \) away from a region of uniform magnetic filed of \( 0.1 \mathrm{T} \) as shown
in the figure. It is then moved towards
the right with a velocity of \( 10 \mathrm{cm} \mathrm{s}^{-1} \) till
it goes out of the field. plot a graph
showing the variation of
(i) magnetic flux \( (\phi) \) through the loop
with time(t).
(ii) induced emf \( (\varepsilon) \) in the loop with
time t.
(iii) induced current in the loop, if it has
resistance of \( 0.1 \Omega \)


A pure sample of chloroform is usually obtained from:
A \( \cdot C H_{3} C H_{2} O H \)
в. \( C H_{3} C H O \)
c. \( C H_{3} C O C H_{3} \)
D. \( C C l_{3} C H(O H)_{2} \)


Assuming the compounds to be completely dissociated in aqueous solution, identify the pair of the solutions that can be expected to be isotonic at the same temperature.
A . \( 0.1 \mathrm{M} \) Urea and \( 0.01 \mathrm{M} \) Nac
B. 0.02 M NaCl and 0.01 M \( N a_{2} S O_{4} \)
D. 0.01 M Sucrose and 0.02 M glucose


A suspension of \( C a O C l_{2} \) in water is heated with ethanol. The product
formed is:
A. ethylene
B. ethanol
c. trichloromethane
D. chloroethane


Solve the equation
\( 7^{6-x}=x+2 \)


Assertion
The voltage of mercury cell remains
constant for its life time.
Reason
Overall cell reaction does not involve
any ion.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The relative number of atoms of
different elements in a compound are as follows: \( A=1.33, B=1 \) and \( C=1.5 \)
The empirical formula of the compound is:
A. \( A_{2} B_{2} C_{3} \)
3
B. \( A B C \)
\( \mathbf{c} \cdot A_{8} B_{6} C_{9} \)
D. \( A_{3} B_{3} C_{4} \)


One card is drawn at random from a
pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A \( \cdot \frac{1}{13} \)
в. \( \frac{2}{13} \)
c. \( \frac{3}{13} \)
D. \( \frac{4}{13} \)


Heavy water violence is formed on
combining deuterium with:
A. oxygen
B. lithium
c. hydrogen
D. helium


Chromosomes connected with sex
determination are
A. Autosomes
B. Heterosomes
c. oxysomes
D. B-chromosomes


The name of compound \( (A) \) is:
A. Methyl- \( \alpha \) -D-glucofuranoside
B. Methyl- \( \beta \) -D-glucofuranoside
C . Methyl- \( \alpha \) -D-glucopyranoside
D. Methyl- \( \beta \) -D-glucopyranoside


Assertion (A): The maximum area of the
rectangle inscribed in a circle of radius 5 units is 50 square units Reason
(R): The maximum area of the
rectangle inscribed in a circle is a
square
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
c. A is true and \( \mathrm{R} \) is false
D. A is false and R is true


\( \operatorname{Let} g^{\prime}(x)>0 \) and \( f^{\prime}(x)<0 \forall x \epsilon R, \) then
This question has multiple correct options
A. \( f(f(x+1))>f(f(x-1)) \)
в. \( f(g(x-1))>f(g(x+1)) \)
\( \mathbf{c} . g(f(x+1))>g(f(x-1)) \)
D. \( g(g(x+1))>g(g(x-1)) \)


Which one is not disaccharide?
A. Lactose
B. Sucrose
C . Maltose
D. starch


The radius of gyration of a body is \( 18 \mathrm{cm} \) when it is rotating about an axis passing through center of mass of body. If radius of gyration of same body is 30 \( \mathrm{cm} \) about a parallel axis to first axis then, perpendicular distance between
two parallel axes is:
\( A \cdot 12 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. 36 cm


Evaluate:
\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{3}}+\frac{2^{2}}{n^{3}}+\frac{3^{2}}{n^{3}}+\ldots+\frac{n^{2}}{n^{3}}\right] \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


The Tyndall effect is not observed in:
A. suspensions
B. emulsions
c. colloidal solutions
D. true solutions


A string of mass \( 3 \mathrm{kg} \) is under tension of 400N. The length of the stretched string
is \( 25 \mathrm{cm} . \) If the transverse jerk is stuck
at one end of the string find the
velocity?
A \( \cdot 25 \pi^{2} m s^{-2} \)
B. \( -5 \pi^{2} m s^{-2} \)
\( \mathbf{c} \cdot 5 \pi^{2} m s^{-2} \)
D. \( -25 \pi^{2} m s^{-2} \)


The following bar graph (Fig. 23.14) represents the heights (in \( \mathrm{cm} \) ) of 50
students of Class XI of a particular
school. Study the graph and answer the following questions:
State whether true or false:
The number of students in the class
having their heights less than \( 150 \mathrm{cm} \) is
12.
A. True
B. False


In one year, the population of a village increased by \( 10 \% \) and on the next year, it decreased by \( 10 \% \). If the end of the 2 nd year, the population was \( 7920, \) what was it in the beginning?
\( A \cdot 8500 \)
B. 8000
\( c \cdot 8100 \)
D. 840


How does the creation of variations in a
species promote survival?


Which of the following are correctly matched ?
1. Arsenic poisoning - Black-foot disease
2. Secondary effluent treatment Biological process
3. Pyrolysis - Waste disposal
4. Tubifex - Water pollution indicator
5. Biomagnification - Degradable
pollutants
A. 1,2,3 and 5
B. 1,3,4 and 5
c. 2,3,4 and 5
D. 1,2,4 and 5
E. 1,2,3 and 4


The thallus of Volvox is called as
\( \mathbf{A} \). Trichome
B. Coenobium
c. coenocyte
D. Parenchymatous


For a given gas \( T_{c}=40 \mathrm{K} \) hence, \( T_{i} \) is:
A . \( 40 \mathrm{k} \)
в. 270 к
\( c \cdot 135 k \)
D. 540 K


The points (3,2,0),(5,3,2) and \( (-9,6,-3), \) are the vertices of a triangle \( A B C . A D \) is the internal
bisector of \( \angle B A C \) which meets \( B C \) at
D. Then the co-ordinates of \( D \), are
A \( \cdot\left[\frac{17}{16}, \frac{57}{16}, \frac{19}{8}\right] \)
В. \( \left[\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right] \)
\( ^{\mathbf{c}} \cdot\left[0,0, \frac{17}{16}\right] \)
D. \( \left[\frac{17}{16}, 0,0\right] \)


Mahavir lent a certain sum at \( 5 \frac{3}{4} \% \) p. a. After 5 years the interest was Rs. 570
less than the sum, the sum was
A. Rs. 900
B. Rs. 1700
c. Rs. 2500
D. Rs. 800


Which of the following combination does not form molecular orbitals?
\( \mathbf{A} \cdot S+S \)
в. \( P_{x}+P_{y} \)
\( \mathrm{c} \cdot P_{x}+P_{x} \)
D. \( P_{z}+P_{z} \)


Removal of adsorbate from the surface
of adsorbent is called
A. desorption
B. absorbation
c. adsorbation
D. none


Find the sum of \( p \) terms of the series whose \( n^{t h} \) term is \( \frac{n}{a}+b \)


The centre of a circle is at \( (-6,4) . \) If one end of a diameter of the circle is at the
origin, then find the other end


If \( \frac{(1+x)(1+2 x)(1+3 x)}{(1-x)(1-2 x)(1-3 x)}=K+ \)
\( \frac{\mathbf{A}}{\mathbf{1}-\mathbf{x}}+\frac{\mathbf{B}}{\mathbf{1}-\mathbf{2} \mathbf{x}}+\frac{\mathbf{C}}{\mathbf{1}-\mathbf{3} \mathbf{x}}, \) then which
of the following is correct
\( \mathbf{A} \cdot \mathbf{K}=6 \)
B. \( A=12 \)
c. \( \mathrm{B}=30 \)
\( \mathbf{D} \cdot \mathbf{C}=-20 \)


The magnitude of a position vector in a XY plane is \( 4 . \) Its slope is \( \frac{1}{\sqrt{3}}, \) then the position vector is:
A. \( \sqrt{3 i}+3 \)
B . \( 2 \sqrt{3} \hat{i}-2 \hat{j} \)
c. \( 2 \sqrt{3 i}+2 \hat{j} \)
D. \( 2 \hat{i}+2 \sqrt{3} \hat{j} \)


Find the velocity of photo electron
librated by electromagnetic radiation of
wavelength \( 18 n m \) from stationary \( H e^{+} \) ion in the ground state.


Wire of a certain material is stretched
slowly be dep10. Its new resistance and specific resistance becomes
respectively.
A. Both remain same
B. 1.1 times in both
c. 1.2 times, 1.1 times
D. 1.21 times, same


If \( \boldsymbol{A}=\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right], \) satisfies the matrix
equation \( A^{2}=k A, \) write the value of \( k \)


If in \( Q .104, \) we are told that a white ball
has been drawn, find the probability
that it was drawn from the first urn.
\( ^{A} \cdot \frac{5}{9} \)
в. \( \frac{2}{3} \)
c. \( \frac{2}{9} \)
D. \( \frac{7}{9} \)


which of the following is not characteristic of interhalogen compounds?
A. They are more reactive than halogens.
B. They are covalent in nature
c. They have low boiling point and are non-volatile
D. they are diamagnetic.


What is the formula of colorless
inactive gas D?
A. \( N_{2} \)
в. \( H_{2} \)
c. \( N H_{3} \)
D. \( N O \)


Calculate the percent of hydrolysis in a \( \mathbf{0 . 0 6} M \) solution of \( \boldsymbol{K} \boldsymbol{C} \boldsymbol{N} \)
Use \( :\left[\boldsymbol{K}_{a(\boldsymbol{H} C N)}=\boldsymbol{6} \times \mathbf{1 0}^{-\mathbf{1 0}}\right] \)
A . \( 1.667 \% \)
B . \( 7.45 \% \)
c. \( 34.67 \% \)
D. None of these


The \( _{--}-_{-}- \) product of two sets is the set of all possible ordered pairs whose first component is a member of the first
set and whose second component is a member of the second set.
A. cartesian
B. coordinate
c. simple
D. discrete


Insulin is dissolved in suitable solvent
and the osmotic pressure \( (\pi) \) of solutions of various concentrations
\( \left(g / c m^{3}\right) C \) is measured at \( 27^{0} C . \) The slope is plot of \( \pi \) against \( C \) is found to
be \( 4.1 \times 10^{-3} \).the molecular mass of
insulin is?


A person saves \( 9 \% \) of his salary every month. If his salary is \( R s .24000 . \) Find his saving per year?


At a certain location, the strength of the electric field is \( 30.0 N / C . \) A charge of \( 3.00 C \) is placed at this location. How much force does this charge
experience due to the electric field?
A. \( 90.0 N \)
n
B . \( 10.0 N \)
c. \( 0.100 N \)
D. \( 270 N / C \)
E . \( 3.33 N / C \)


Duodenum, jejunum and ileum are the parts associated to
A. Stomach
B. Small intenstine
c. Large intenstine
D. colon


In a basic aqueous solution chloromethane undergoes a
substitution reaction in which \( C l^{-} \) is
replaced by \( \boldsymbol{O H}^{-} \) as.
\( \boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{a q})+\boldsymbol{O H}^{-} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{a q})+\boldsymbol{C l}^{-}(\boldsymbol{a q}) \)
The equilibrium constant of above reaction \( \boldsymbol{K}_{c}=\mathbf{1} \times \mathbf{1 0}^{\mathbf{1 5}} . \) If a solution is
prepared by mixing equal volumes of \( 0.1 M C H_{3} C l \) and \( 0.2 M N a O H(100 \% \)
dissociated) then \( \left[O H^{-}\right] \) concentration
at equilibrium in mixture will be
A. \( 0.1 M \)
в. \( 0.5 M \)
\( c .0 .2 M \)
D. \( 0.05 M \)


Which type of isomerism is shown by alkanes?
A. Chain isomerism
B. Position isomerism
c. Metameirsm
D. Functional group isomerism


\( 1.6 \mathrm{g} \) of an organic compound gave \( 2.6 \mathrm{g} \) of magnesium pyrophosphate. The percentage of phosphorus in the compound is:
A . 45.38\%
в. 54.38\%
c. 37.76\%
D. 19.02\%


The value of the determinant \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \mathbf{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right| \)
is equal to
A \( \cdot a^{3}-b^{3} \)
В . \( a^{3}+b^{3} \)
\( c \cdot 0 \)
D. none of these


The displacement of \( x \) of a particle moving in one dimension is related to time by the equation \( t=(\sqrt{x}+3) \)
where \( x \) is in \( m \) and \( t \) in \( s . \) The
displacement, when velocity is zero, is
\( \mathbf{A} \cdot 1 m \)
B. \( 2 m \)
\( c .4 m \)
D. zero


and
sublimatory substances


An object is kept at a distance of \( 16 \mathrm{cm} \) from a thin lens and the image formed is real. If the object is kept at a distance of \( 6 \mathrm{cm} \) from the same lens, the image formed is virtual. If the sizes, of the
images formed are equal, the focal length of the lens will be
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 17 \mathrm{cm} \)
\( \mathbf{c} \cdot 21 c m \)
D. \( 11 \mathrm{cm} \)


The position of \( B r \) in the compound in
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C}(\boldsymbol{B r})\left(\boldsymbol{C H}_{3}\right)_{2} \) can be
classified as:
A . ally!
B. ary!
c. viny!
D. secondary


A certain negative ion \( X^{-2} \) has in its
nucleus 18 neutrons and 18 electrons in
its extra nuclear structure. What is the
mass number of the most abundant
isotope of 'X'?
A. 35.46
B. 32
\( c \cdot 36 \)
D. 39


The time period of a vibrating body is
0.01 sec. Its frequency will be :
A \( \cdot 1.0 s^{-1} \)
B. \( 10.0 s^{-1} \)
c. \( 100.0 s^{-1} \)
D. \( 1000.0 s^{-1} \)


Neuroglia cells differ from neurons in having
A. No Nissi's granules
B. No radiating processes
c. No cyton
D. No nucleus


What is a chemical reaction?
A. Reaction that is always endergonic.
B. Rearrangement of electrons in a chemical bond.
c. Both \( A \) and \( B \)
D. None of the above.


Colour of the flame is dependent on the
A. supply of oxygen
B. nature of fuel
c. ignition temperature of the fuel
D. All of the above


For the redox reaction
\( M n O_{4}^{\ominus}+C_{2} O_{4}^{2-}+H^{\oplus} \longrightarrow M n^{2+}+ \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
the correct coefficients of the reactions
for the balanced reaction are:
\( \begin{array}{lll}\text { A. } M n O_{4}^{\ominus} & C_{2} O_{4}^{2-} & H^{\oplus}\end{array} \)
\( 2 \quad 5 \quad 16 \)
B. \( M n O_{4}^{\ominus} \quad C_{2} O_{4}^{2-} \quad H^{\oplus} \)
\( 16 \quad 5 \quad 2 \)
\( \begin{array}{lll}\text { c. } M n O_{4}^{\ominus} & C_{2} O_{4}^{2-} & H^{\oplus}\end{array} \)
16
D. \( M n O_{4}^{\ominus} \quad C_{2} O_{4}^{2-} \quad H^{\oplus} \)


Construct \( \Delta A B C, \) such that \( B C= \)
\( 6 c m, \angle A B C=100^{0} \) and \( A C-A B= \)
\( 2.5 c m \)


The shape of \( I F_{7} \) molecule is:
A. pentagonal bipyramidal
B. trigonal bipyramidal
c. octagonal
D. \( T \) - shape


Cellobiose, the hydrolytic breakdown product of cellulose is
A. A monosaccharide
B. A disaccharide
c. A tetrasaccharide
D. A trisaccharide


The friction between two bodies
produces
A. Motion
B. Expansion
c. Heat
D. None


Product of n positive numbers is unity. The sum of these numbers can not be
less than
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( n \)
\( c \cdot n^{2} \)
D. None of these


toppr
Q Type your question_
frictionless surface. The block is
stretched by \( 0.2 m \) and released from
rest at \( t=0 . \) It then executes simple
harmonic motion with angular frequency \( \omega=\frac{\pi}{3} r a d / s \)
Simultaneously at \( t=0, \) a small
pebble is projected with speed \( \boldsymbol{v} \) from
point \( P \) at an angle of \( 45^{\circ} \) as shown in
the figure. Point \( P \) is a a horizontal
distance of \( 10 \mathrm{m} \) from \( \mathrm{O} \). If the pebble
hits the block at \( t=1 \) sec, the value of \( v \)
is \( \left(\operatorname{take} g=10 m / s^{2}\right): \)
\( \mathbf{A} \cdot \sqrt{50} m / s \)
B. \( \sqrt{51} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot \sqrt{52} m / s \)
D. \( \sqrt{53} \mathrm{m} / \mathrm{s} \)


Assertion
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \cdot \sin \boldsymbol{x} \) is differentiable at
\( \boldsymbol{x}=\mathbf{0} \)
Reason
If \( f(x) \) is not differentiable and \( g(x) \) is differentiable at \( x=a \), then \( f(x) \cdot g(x) \)
will be differentiable at \( \boldsymbol{x}=\boldsymbol{a} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Two resistors of resistances \( 10 \Omega \) and
\( 20 \Omega \) are connected in parallel. A battery
supplies \( 6 A \) of current to the
combination. Calculate the current in
each resistor.


The dimensional formula for Young's
modulus is :
\( \mathbf{A} \cdot\left[M L^{-1} T^{-2}\right] \)
B \( \cdot\left[M^{0} L T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-2}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)


Which of the following function has extreme point?
\( \mathbf{A} \cdot 2^{x} \)
B . \( \log _{10} x \)
c. \( x-[x] \)
D. all of these


Write any two difference between soap
and detergent?


Which one is most stable to heat:
A . \( H C l O \)
в. \( H C l O_{2} \)
c. \( H C l O \)
D. \( H C l O_{4} \)


solve :
\( \int(a x+b)^{2} d x \)


If \( \boldsymbol{y}=[\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}-\mathbf{1}}]^{15}+ \)
\( [x-\sqrt{x^{2}-1}]^{15}, \) then \( \left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+ \)
\( x \frac{d y}{d x} \) is equal to
A . \( 125 y \)
B . \( 225 y^{2} \)
c. \( 225 y \)
D. \( 224 y^{2} \)


Which of the following pair represents elements of same group?
A . Q, R
B. P,Q
\( c \cdot P, s \)
D. Q,


Two adjacent sides of parallelogram are \( 24 \mathrm{cm} \) and \( 18 \mathrm{cm} . \) If the distance
between the longer sides is \( 12 \mathrm{cm} \); find the distance between the shorter sides.
A. \( 9 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. Data insufficient


Find the value of \( x \) if the distance
between the points (2,-11) and \( (x,-3) \) is 10 units.
A. 6
B. 8
\( c .9 \)
D. 4


The total number of electrons shared
between two boron atoms in \( B_{2} H_{6} \) is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


A capacitor has been charged by a DC
source. What are the magnitude of conduction and displacement current, when it is fully charged?


Describe anomalous behaviour of
fluorine with the other elements of
group 17 with reference to:
Oxidation state


The Henry's law constant for the
solubility of \( N_{2} \) gas in water at \( 298 K \) is
\( 1.0 \times 105 \) atm. The mole fraction of \( N_{2} \)
in air is \( 0.8 . \) The number of moles of \( N_{2} \)
from air dissolved in 10 moles of water
at \( 298 K \) and 5 atm pressure is
A \( \cdot 4 \times 10^{-4} \)
B . \( 4 \times 10^{-5} \)
\( \mathbf{c} \cdot 5 \times 10^{-4} \)
D. \( 4 \times 10^{-6} \)


Two wires of the same material and
length are stretched by the same force. Their masses are in the ratio \( 3: 2 . \) Their
elongations are in the ratio
A .3: 2
B. 9: 4
c. 2: 3
D. 4: 9


Solve : \( \int_{-2}^{2}|2 x+3| d x \)


The correct explanation for the partt
shown by the arrow is that
A. It is hydrophilic.
B. It forms the outer layer of the plasma membrane
c. It is composed of phosphate atoms
D. It contains nonpolar covalent bonds
E. It is capable of hydrogen bonding


Which one of the following oxides is neutral?
A . \( c o \)
B. \( \operatorname{sn} O_{2} \)
\( c \cdot z n 0 \)
\( D \cdot \sin _{2} \)


In any chemical reaction, equilibrium is supposed to be establish when:
A. Mutual opposite reaction undergo
B. concentration of reactants and resulting products are equal
c. Velocity of mutual reaction becomes equal
D. The temperature of mutual opposite reactions becomes equal


The treatment of benzene with
isobutene in the presence of sulphuric acid gives:
A. isobutyl benzene
B. tert-butyl benzene
c. n-Butyl benzene
D. No reaction


Which of the following half-reactions is correctly balanced?
A \( \cdot M n O_{4}^{-} \rightarrow M n^{2+}+4 H_{2} O \)
B. \( C u+2 A g^{+} \rightarrow 2 A g+C u^{2+} \)
\( \mathbf{c} \cdot H_{2}+O H^{-} \rightarrow 2 H_{2} O \)
\( \mathbf{D} \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
E \( \cdot 2 F^{-}+2 e^{-} \rightarrow F_{2} \)


Myxamoebae' of slime moulds are This question has multiple correct options
A. Active vegetative forms
B. Stages to overcome unfavourable conditions
c. Gametes, which undergo sexual reproduction
D. Resultants of sexual reproduction


An experiment was set up as shown in
the figure below. After some time, the water level in test tube \( A \) fell down but
not in test tube B.

Why was there a fall in the water level of test tube \( A \) and not in that of test
tube B?


Which statements about conductivity
of distilled water are correct?
This question has multiple correct options
A. It possesses almost non-conducting nature
B. It is obtained by distillation of water several times
C. It is contaminated with little acid
D. None of the above


What is isothermal process?


Suppose the elements \( X \) and \( Y \)
combine to form two compounds \( \boldsymbol{X} \boldsymbol{Y}_{2} \)
and \( X_{3} Y_{2} . \) When 0.1 mole of \( X Y_{2} \)
weighs \( 10 g \) and 0.05 mole of \( X_{3} Y_{2} \)
weighs \( 9 g \), the atomic weights of \( X \) and
\( \boldsymbol{Y} \) are:


Which of the following sources of light is different from others
A. Sunlight
B. White light
c. Light from a bulb
D. sodium light


Number of binding sites in allosteric
enzyme is
A. one
B. Two
c. Three
D. Four


Select the correct option:
Increase in girth of the plant as a result of the activities of primary and secondary lateral meristems is called
A. primary growth
B. Iateral growth
c. secondary growth
D. intercalary growth


\( A B C D \) is a rectangle such that \( A C+ \)
\( A B=5 A D \) and \( A C-A D=8, \) then
the area of rectangle \( A B C D \) is
A . 36sq. units
B. 50. sq. units
c. 60 sq. units
D. cannot be found


Discuss about determining mass
percentage of oil from oil seed.


The sum of first 45 natural number is
A. 1035
в. 1280
c. 2070
D. 2140


When a nucleus with atomic number \( Z \)
and mass number \( A \) undergoes a
radioactive decay process
This question has multiple correct options
A. both \( Z \) and \( A \) will decrease, if the process is \( \alpha^{-} \) decay
B. \( Z \) will decrease but \( A \) will not change, if the process is \( \beta+ \) decay
C \( . Z \) will increase but \( A \) will not change, if the process is \( \beta- \) decay
D. \( Z \) and \( A \) will remain unchanged, if the process is \( \gamma \) decay


For the reduction of \( F e O \) with \( C \) at the
temperature corresponding to \( (D) \)
which of the following statements is
correct?
A. Carbon reduces \( F e O \) below the temperature at point
(D)
B. \( \triangle G^{0} \) value for overall reduction with \( C O \) is zer
\( \mathrm{c} . \triangle G^{0} \) value for the reaction at point
(D) is positive
D. Below point
(D), for the metal exists in molten state


How many ATP's are produced by complete oxidation of PEP?


Solve the following inequalities graphically in two-dimensional plane:
\( 2 x+y \geq 6 \)


When the applied force is doubled, then friction becomes:
A. doubled
B. halved
c. can't say
D. zero


A particle \( (\boldsymbol{m}=\mathbf{1} \boldsymbol{k} \boldsymbol{g}) \) slides down a
frictionless rack (AOC) starting from
rest at a point \( A \) (height \( 2 m \) ). After
reaching \( C, \) the particle continuous to
move freely in air as a projectile. When
it reaching its highest point \( \boldsymbol{P} \) (height
1 \( m \) ), the kinetic energy of the particle
(in J) is : (Figure drawn is schematic and not to scale; take \( g=10 m s^{-2} \)


Which zone of a flame does a goldsmith use for melting gold and silver and why?


In a random experiment, a fair die is rolled until two fours are obtained in
succession. The probability that the experiment will end in the fifth throw of the die is equal to:
A \( \cdot \frac{150}{6^{5}} \)
в. \( \frac{175}{6^{5}} \)
c. \( \frac{200}{6^{5}} \)
D. \( \frac{225}{6^{5}} \)


Glycerin can be purified by:
A. vacuum distillation
B. simple distillation
C. steam distillation
D. fractional distillation


Light travels in a straight line with
constant speed of \( 3 \times 10^{8} m s^{-1} \) What is
the acceleration of light?


When the values of inductance and
capacitance in an \( L-C \) circuit are
\( 0.5 H \) and \( 8 \mu F \) respectively then
current in the circuit is maximum. The
angular frequency of alternating e.m.f. applied in the circuit will be
A \( .5 \times 10^{3} \) Radian/sec
B. 50 Radian/sec
c. \( 5 \times 10^{2} \) Radian/sec
D. 5 Radian/sec


Which of the following numbers are not perfect cubes?
\( \mathbf{2 1 6} \)


Reverberation of sound is due to
A. multiple refractions
B. multiple reflections
C . multiple diffractions
D. multiple polarization


mRNA that carries information for
complete polypeptide synthesis is
A. Muton
B. codon
c. operon
D. Reading frame


(a) Draw the molecular structures of the
following compounds:
(i) \( N_{2} O_{5} \)
(ii) \( \boldsymbol{X}_{e} \boldsymbol{O} \boldsymbol{F}_{4} \)
(b) Explain the following observations
(i) Sulphur has a greater tendency for catenation than oxygen.
(ii) \( I-C l \) is more reactive than \( I_{2} \)
(iii) Despite lower value of its electron gain enthalpy with negative sign,
fluorine \( \left(F_{2}\right) \) is a stronger oxidizing
agent than \( C l_{2} \)


An organic substance bound to an enzyme and essential for its activity is called as
A. Apoenzyme
B. Isoenzyme
c. coenzyme
D. Holoenzyme


A person sitting on the top of a tall building is dropping balls at regular intervals of one second. Find the
position of the \( 3 r d, 4 \) th and 5 th ball when the 6 th ball is being dropped
A. \( 24.1 \mathrm{m}, 19.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) above the top
B. 44.1 \( \mathrm{m}, 19.6 \mathrm{m} \) and 4.9 \( \mathrm{m} \) bellow the top
c. \( 44.1 \mathrm{m}, 12.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) bellow the top
D. \( 41.4 \mathrm{m}, 29.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) bellow the top


Law of multiple proportions is not applicable for the oxides (s) of
A. carbon
B. iron
c. nitrogen
D. aluminium


The number of continuous and
derivable function(s) \( f(x) \) such that
\( f(1)=-1, f(4)=7 \) and \( f(x)>3 \) for
all \( \boldsymbol{x} \in \boldsymbol{R} \) is/are
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinite


The mean of the ungrouped data is given by
\( ^{\mathrm{A}} \cdot \operatorname{Mean}=\frac{\sum x_{i}}{\sum f} \)
B. \( \operatorname{Mean}=\frac{\sum x}{n} \)
c. \( \operatorname{Mean}=\frac{\sum f x}{\sum n} \)
D. mean \( =a+\frac{\sum f x}{\sum n} \)


What is the median for the following data?
shoe size \( \quad 2 \quad 3 \quad 4 \quad \) 5
1 frequency \( \quad 10 \quad 20 \quad 12 \quad 14 \)
A .4
B. 5
\( c \cdot 6 \)
\( D \)


\( \int\left(3 x^{2}+2 x\right) d x \)


The electric flux over the surface of a
sphere if it is charged with \( 10 \mu C \) is
A \( \cdot 36 \pi \times 10^{4} \quad N m^{2} / C \)
B . \( 36 \pi \times 10^{-4} \quad N m^{2} / C \)
\( \begin{array}{ll}\text { C. } 36 \pi \times 10^{6} & \text { N } m^{2} / C\end{array} \)
D. \( 36 \pi \times 10^{-6} \quad \mathrm{Nm}^{2} / \mathrm{C} \)


Evaluate and write in standard form
\( (4-2 i)(-3+3 i), \) where \( i^{2}=-1 \)
A \( .6+18 i \)
B. \( -6+18 i \)
c. \( 12+18 i \)
D. \( 6-18 i \)


Solve \( \int \frac{x^{2}+5 x-1}{\sqrt{x}} d x \)


State whether the given statement is True or False.

An eye is said to be long-sighted, if the image of a distant object is formed in front of retina.


Equation for the following reaction.
\( \boldsymbol{C u}+\boldsymbol{x} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( 2 H_{2} O+2 N O_{y} \)
Find the value of \( x \) and \( y \)
A. \( x=4, y=2 \)
В. \( x=1, y=2 \)
c. \( x=2, y=2 \)
D. \( x=4, y=1 \)


Percentage errors in the measurement of mass and speed are \( 2 \% \) and \( 3 \% \) respectively. The error in the estimation
of kinetic energy obtained by measuring mass and speed will be:
A. 8\%
B. २\%
c. 12\%
D. 10\%


How many permutations of 4 letters can
be made out of the letters of the word
examination?


The reaction of calcium carbide with
\( H_{2} O \) gives :
A. \( C_{2} H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. \( C H_{4} \)


Which resistor is difficult to make of
having a value less than about 2 Ohms?
A. Iron Resistor
B. Carbon Resistor
c. Wire wound Resistor
D. Both b and c


Show that the tangent of an angle
between the lines \( \frac{x}{a}+\frac{y}{b}=1 a n d \frac{x}{a}- \)
\( \frac{y}{b}=1 i s \frac{2 a b}{a^{2}-b^{2}} \)


Which among these is not a homeotherm?
A. Aptenodytes
B. Testudo
c. Delphinus
D. Neophron


Suppose \( f \) is differentiable on \( R \) and
\( \boldsymbol{a} \leq \boldsymbol{f}^{\prime}(\boldsymbol{x}) \leq \boldsymbol{b} \) where \( \boldsymbol{x} \in \boldsymbol{R} \) where
\( \boldsymbol{a}, \boldsymbol{b}>\mathbf{0} . \) If \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \) then
A \( \cdot f(x) \leq \min (a x, b x) \)
B . \( f(x) \geq \min (a x, b x) \)
c. \( a \leq f(x) \leq b \)
D. \( a x \leq f(x) \leq b x \)


\( \int \sqrt{1+\sin x} d x= \)
A \( \cdot \frac{1}{2}\left(\sin \frac{x}{2}+\cos \frac{x}{2}\right)+c \)
B \( \cdot \frac{1}{2}\left(\sin \frac{x}{2}-\cos \frac{x}{2}\right)+c \)
c. \( 2 \sqrt{1+\sin x}+c \)
D. \( -2 \sqrt{1-\sin x}+c \)


State where \( (\sqrt{6}+\sqrt{9}) \) is rational or
not


When the current in a wire is \( 1 A \), the
drift velocity is \( 1.2 \times 10^{-4} \mathrm{ms}^{-1} . \) The
drift velocity when current becomes 5 A
is
A \( \cdot 1.2 \times 10^{-4} \mathrm{ms}^{-1} \)
В. \( 3.6 \times 10^{-4} \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 6 \times 10^{-4} m s^{-1} \)
D. \( 4.8 \times 10^{-4} \mathrm{ms}^{-1} \)


On a ship sailing in pacific ocean where
temperature is \( 23.4, \) a balloon is filled with \( 2 \mathrm{L} \) air. What will be the volume of
the balloon when the ship reaches Indian ocean, Where temperature is
\( \mathbf{2 6 . 1} ? \)


Biomagnification of DDT in a aquatic food chain starting from water having a concentration of 0.003 ppb may go, in fish eating birds, upto
A. 2 ppm
B. 25 ppm
c. 50 ppm
D. 100 ppm


\( \lim _{x \rightarrow a} \frac{\sin x-\sin a}{x-a} \)


Two soap bubbles of radii \( a \) and \( b \)
combine to form a single bubble of radius \( c \). If \( P \) is the external pressure,
then Surface Tension of the soap solution is:
A \( \cdot \frac{P\left(c^{3}+a^{3}+b^{3}\right)}{4\left(a^{2}+b^{2}+c^{2}\right)} \)
B \( \frac{P\left(c^{3}-a^{3}-b^{3}\right)}{4\left(a^{2}+b^{2}-c^{2}\right)} \)
c. \( P c^{3}-4 a^{2}-4 b^{2} \)
D. \( P c^{3}-2 a^{2}+3 b^{2} \)


A precipitate of \( A g C l \) is formed when
equal volumes of the following are \( \operatorname{mixed}\left[\boldsymbol{K}_{s p} f o r \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 0}^{-\mathbf{1 0}}\right] \)
A \( \cdot 10^{-4} M A g N O_{3} \) and \( 10^{-7} M H C l \)
B. \( 10^{-5} M A g N O_{3} \) and \( 10^{-6} M H C l \)
c. \( 10^{-5} M A g N O_{3} \) and \( 10^{-4} M H C l \)
D. \( 10^{-6} M A g N O_{3} \) and \( 10^{-6} M H C l \)


Choose the correct statement from the
following:
This question has multiple correct options
A \( . \) He gas diffuses \( \sqrt{2} \) times more than \( O_{2} \)
B. \( O_{2} \) gas diffuses 2 times more than \( S O_{2} \)
\( \mathrm{C} \cdot \mathrm{CH}_{4} \) gas diffuse \( \sqrt{2} \) times more than \( \mathrm{O}_{2} \)
D. \( H_{2} \) difusses \( \sqrt{2} \) times more than \( H e \) gas


The components used in Rutherford's
experiment:
\( \mathbf{A} \cdot \beta \) -particles, which impinged on a metal foil and got absorbed
B. \( \gamma \) -rays, which impinged on a metal foil and ejected electrons
C. helium atoms, which impinged on a metal foil and got scattered
D. helium nuclei, which impinged on a metal foil and got scattered


Which of the following indicates
ascending order of the fractions?
A. \( \frac{4}{13}, \frac{2}{7}, \frac{3}{11}, \frac{1}{5} \)
B. \( \frac{1}{5}, \frac{2}{7}, \frac{3}{11}, \frac{4}{13} \)
C. \( \frac{1}{5}, \frac{3}{11}, \frac{2}{7}, \frac{4}{13} \)
D. \( \frac{2}{7}, \frac{1}{5}, \frac{3}{11}, \frac{4}{13} \)


The real bleaching agent present in bleaching powder is:
A. chlorine
B. oxygen
c. сао
D. None of the above


Two spherical bodies the mass \( M \) and \( \mathbf{5} M \boldsymbol{m} \) and radii \( \boldsymbol{R} \) and \( \mathbf{2} \boldsymbol{R} \) respectively
are released in free space with initial
separation between their centres equal
to \( 12 R \) If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is:
\( \mathbf{A} \cdot 2.5 R \)
B. \( 4.5 R \)
c. \( 7.5 R \)
D. \( 1.5 R \)


\( \int \sqrt{\frac{1-x}{1+x}} d x= \)


The variation of 20 observations is \( 5 . \) If
each observation is multiplied by 2 then what is the new variance of the
resulting observations?
A . 5
B. 10
c. 20
D. 40


\( a \) moles of \( P C l_{5} \) are heated in a closed
container to equilibrate \( \boldsymbol{P} \boldsymbol{C l}_{5(\boldsymbol{g})} \rightleftharpoons \)
\( \boldsymbol{P C l}_{5(g)}+\boldsymbol{C l}_{2(g)} \) at a pressure of \( \boldsymbol{P} \) atm.
If \( x \) moles of \( P C l_{5} \) dissociate at
equilibrium, then:
A \( \cdot \frac{x}{a}=\frac{K_{P}}{K_{P}+P} \)
\( ^{\mathbf{B}} \cdot \frac{x}{a}=\left(\frac{K_{P}+P}{K_{P}}\right)^{1 / 2} \)
\( \stackrel{x}{a}=\left(\frac{K_{P}}{P}\right)^{1 / 2} \)
\( \stackrel{x}{a}=\left(\frac{K_{P}}{K_{P}+P}\right)^{1 / 2} \)


In hydrogen atom the energy difference between the states \( n=2 \) and \( n=3 \) is
Ee \( V \). The ionisation potential of \( H \)
atom is:
A . \( 3.2 E \)
в. \( 5.6 E \)
\( c .7 .2 E \)
D. \( 13.2 E \)


The ratio of the latent heat of steam to
latent heat of ice
A . \( 4 / 9 \)
B. 9/4
c. \( 4 / 27 \)
D. 27/4


Assertion
Chlorine reacts more rapidly with \( \boldsymbol{H}_{2} \) in
comparison to \( D_{2} \)
Reason
\( D-C l \) bond is stronger in comparison
to \( \boldsymbol{H}-\boldsymbol{C l} \) bond.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


ntegrate the function \( \frac{x+2}{\sqrt{x^{2}+2 x+3}} \)


A circular coil connected to a cell of
e.m.f \( \boldsymbol{E} \) produced a magnetic field. The
coil is unwound, stretched to double its length, rewound into a coil of \( \frac{1}{3} \) of the original radius and connected to a cell
of e.m.f \( \boldsymbol{E}_{1} \) to produce the same field at
the centre. Then \( \boldsymbol{E}_{\mathbf{1}} \) is :
\( \mathbf{A} \cdot \frac{E}{2} \)
B. \( \frac{2 E}{3} \)
c. \( \frac{9 E}{4} \)
D. \( \frac{E}{6} \)


Using remainder theorem, find the remainder when \( 4 x^{3}+5 x-10 \) is
divided by \( \boldsymbol{x}-\mathbf{3} \)
A . 197
в. 113
\( c \cdot-1 \)
D. 0


When a gas expand adiabatically -
A. No energy is required for expansion
B. Energy is required and it comes from the wall of the container of the gas
C. Internal energy of the gas is used in doing work
D. Law of conservation of energy does not hold


If the velocity of the body is quadrupled then the momentum of the body
doubles.
A. True
B. False


With the increase in atomic number,
screening effect increases both in group and period.
A. True
B. False


The statement(s) that is/are true for the
halides of oxygen \( \left(X_{2} O\right) \) is/are:
A. the bond angles of \( X_{2} O \) (where \( X \) is halogen) are in the decreasing order \( F_{2} O>C l_{2} O>B r_{2} O \)
B. the halides of oxygen (except \( F_{2} O \) ) are easily hydrolyzedd
C. the halides of oxygen \( \left(X_{2} O\right) \) have square planar geometry
D. the molecules have linear shape


In an Aprotic solvent, which relative ordering best describes the nucleophilicity of the halide ions?
A. lodide> Bromide> Chloride>> Flouride
B. lodide> Bromide> Chloride> Flouride
c. lodide< Bromides Chlorides Flouride
D. lodide< Bromide> Chloride> Flouride


Electric work done on the nitrogen gas
is
\( \mathbf{A} \cdot 72 k J \)
B. \( 36 k J \)
\( \mathbf{c} .18 k J \)
D. \( 9 k J \)


The probabilities of solving a problem
by three students \( A, B \) and \( C \) are \( \frac{1}{2}, \frac{3}{4} \) and \( \frac{1}{4} \) respectively. The probability that the problem will be solved is
\( ^{A} \cdot \frac{3}{32} \)
в. \( \frac{3}{16} \)
c. \( \frac{29}{32} \)
D. None of the above


Common name for methanol is:
A. volemitol
B. rubbing alcohol
c. wood spirit
D. xylitol


If the value of \( \theta \) increases then the
magnetic moment value
A. Increases
B. Decreases
c. Remains same
D. Cannot be said


50 plants were planted each school out of 10 schools. After a month, the number of planets that survived are given below:Find Mean and Variance
school
\[
2
\]
Number of planet 35
survived


The butter of tin is represented by:
A. \( S n C l_{2} .5 H_{2} O \)
в. \( \operatorname{Sn} C l_{2} \)
\( \mathrm{c} \cdot \operatorname{Sn} C l_{4} \)
D. \( S n C l_{4} .5 H_{2} O \)


Show that de Broglie wavelength of electrons accelerated \( V \) volts is very
nearly given by:
\( \lambda(i n \dot{A})=\frac{150^{1 / 2}}{V} \)


Factorise:
\( 6 x y\left(a^{2}+b^{2}\right)+8 y z\left(a^{2}+b^{2}\right)- \)
\( \mathbf{1 0 x z}\left(\mathbf{a}^{2}+\mathbf{b}^{\mathbf{2}}\right) \)


If \( \boldsymbol{R} \) be a relation \( < \) from \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \)
to \( B=\{1,3,5\} \) i.e., \( (a, b) \in \mathrm{R} \) if \( a<b \)
then find \( R O R^{-1} \)


fthe rate of change in \( y=\frac{x^{3}}{3}-2 x^{2}+ \)
\( 5 x+7 \) is two times the rate of change
in \( \boldsymbol{x}, \) then \( \boldsymbol{x}= \)
A .2,3
в. 1,3
c. 1,2
D. 2,5


Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on \( r \) for \( r / a>>1 \) and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).


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


When white phosphorus is heated at \( 473 \mathrm{K} \) under high pressure, what will happen?
A. \( \alpha \) - Black phosphorus is formed
B. \( \beta \) -Black phosphorus is formed
c. Red phosphorus is formed.
D. No change would be observed


Clothes do not protect us from
A. heat
B. cold
c. blood pressure
D. dust and germs


The peroxide effect in anti-Markovnikov
addition involves
A. The heterolytic fission of the double bond
B. The homolytic fission of the double bond
c. A free-radical mechanism
D. An ionic mechanism


Glucose saline is used as:
A. salt drink
B. health drink
c. soft drink
D. re-hydrating solution


A current of 1 amp is flowing in the
sides of an equilateral triangle of side
\( 4.5 \times 10^{-2} \mathrm{m} . \) Find the magnetic field at
the centroid of triangle.


\( \mathbf{f} \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\mathbf{2}^{r-1} & \mathbf{2}\left(\mathbf{3}^{r-1}\right) & \mathbf{4}\left(\mathbf{5}^{r-1}\right) \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \mathbf{2}^{n}-\mathbf{1} & \mathbf{3}^{n}-\mathbf{1} & \mathbf{5}^{n}-\mathbf{1}\end{array}\right| \)
then prove that \( \sum_{r=1}^{n} D_{r}=0 \)


In which of the following condition diabetic coma is due to hyposecretion of insulin?
A. Glucose level increased in blood
B. Keto acidosis formation take place
C. Dehydration process start
D. All of the above


Two satellites \( A \) and \( B \) of the same
mass are revolving around the earth in the concentric circular orbits such that
the distance of satellite \( B \) from the
centre of the earth is thrice as
compared to the distance of the
satellite \( A \) from the centre of the earth.
The ratio of the centripetal force acting on \( B \) as compared to that on \( A \) is
A \( \cdot \frac{1}{3} \)
B. 3
c. \( \frac{1}{9} \)
D. \( \frac{1}{\sqrt{3}} \)


From 3 boys \( \& 2 \) girls,commit a of 2 people is to be made. Then probability of minimum 1 boy in the committee is?


Which one of the following is best
indicator of \( S O_{2} \) pollution?
A . Pinus
B. Fem
c. Lichen
D. Algae


Balance the following equation.
\( Z n C O_{3} \longrightarrow Z n O+C O_{2} \)


ABCD is a parallelogram and \( A C, B D \) are its diagonals Express \( \overrightarrow{A B} \) and \( \overrightarrow{A D} \) in terms of \( \overrightarrow{\boldsymbol{A C}} \) and \( \overrightarrow{\boldsymbol{B D}} \)
A \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \)
B \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \)
c \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \)
D・ \( \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \)


There is an unpaired electron in superoxide ion.
If true enter 1 , else enter 0 .


Find the interest and the amount,
respectively on Rs. 750 in 3 years 4
months at \( 10 \% \) per annum.
A. Rs.225 and Rs.1, 000
B. Rs.250 and Rs.1, 000
c. Rs.250 and Rs.1, 150
D. Rs.250 and Rs.1050


Table 1
Table - 2
(a) Potential difference across battery
\( A \quad(p) A \)
(b) Potential difference across battery
\( B \quad(q) B \)
(c) Power is supplied by battery
\( (r) 14 V \)
(d) Power is consumed by battery
\( (s) 9 V \)
none
\( A \cdot a-p ; b-p ; c-q ; d-r \)
B. \( a-q ; b-q ; c-r ; d-s \)
\( c \cdot a-r, b-t, c-p, d-q \)
\( D \cdot a-r ; b-r ; c-s ; d-t \)


Assertion
Wilting occurs due to loss in turgidity
Reason

Turgor pressure checks the excessive
entry of water into cells
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


State whether True or False:
A relay is an electromagnetically controlled mechanical device in which
electrical contacts are opened or closed by a magnetizing current.
A. True
B. False


If we hang a body of mass \( m \) with the
cord, the tension can be given as:


What is the concentration of a solution
of 2,000 grams of water in which 684
grams of sucrose, \( C_{12} H_{22} O_{11} \) is
dissolved?
A. 25 molar
B. 0.5 molal
c. 1 molal
D. 5 molar
E. 1 molar


Describe the construction of a
compound microscope. Derive an expression for its total magnification. Draw a ray diagram for the formation of image by a compound microscope.


(i) Differentiate between adsorption and absorption
(ii) Out of \( M g C l_{2} \) and \( A l C l_{3}, \) which one
is more effective in causing coagulation of negatively charged sol and why?
(iii) Out of sulphur sol and proteins,
which one forms multimolecular
colloids?


A coil of inductance \( 8.4 m H \) and
resistance \( 4.2 \Omega \) is connected to \( 10 V \)
battery. The time constant of the circuit
is
\( \mathbf{A} \cdot 2 m s \)
в. \( 0.5 m s \)
c. \( 4 m s \)
D. \( 0.25 \mathrm{ms} \)


2 cubes of volumes \( 664 \mathrm{cm}^{3} \) are joined
end to end. Fin the surface area of the
reacting cuboid.


Find the HCF of 92690,7378 and 7161
by Euclid's division algorithm.
A . 29
B. 30
c. 31
D. 32


A force of \( 10 \mathrm{N} \) acts on a body of \( 2 \mathrm{kg} \) mass for a distance of \( 1 \mathrm{m} \). The kinetic
energy received by the body is:
A . 20
B. 10 J
c. 5 J
D. 2.5


An ideal gas is found to obey an
additional law \( V P^{2}= \) constant. The gas
is initially at temperature T and volume
V. When it expands to a volume 2 V, the temperature becomes:
A \( \cdot \frac{T}{\sqrt{2}} \)
в. 27
c. \( \frac{2 T}{\sqrt{2}} \)
D. 47


A 5 V zener diode is used to regulate the
voltage across load resistor \( \boldsymbol{R}_{L} \) and the
input voltage varies in between \( 10 \mathrm{V} \) to \( 15 \mathrm{V} . \) The load current also varies from 5
\( \mathrm{mA} \) to \( 50 \mathrm{mA} \). Find the value of series
resistance R.
Given, \( \boldsymbol{I}_{Z}(\boldsymbol{m} \boldsymbol{i} \boldsymbol{n})=\boldsymbol{2} \boldsymbol{0} \boldsymbol{m} \boldsymbol{A} \)
A . \( 70 \Omega \)
B. \( 90.91 \Omega \)
c. \( 142.86 \Omega \)
D. \( 71.43 \Omega \)


At higher altitudes, the air becomes rarer and amount of oxygen per liter of air decreases.

Increase in all of the following would
compensate this decrease for performing normal biological functions
of our body, except
A. The concentration of haemoglobin
B. The number of red blood cells
c. The temperature of the body
D. The rate of breathing


\( 0-0 \)
\( 0-0 \)
\( 0=0 \)
\( 0-0 \)


Formation of ATP in photosynthesis and respiration is an oxidation process which utilises the energy from
A. cytochromes
B. Ferredoxin
c. Electrons
D. Carbon dioxide.


A cricket ball of \( 0.5 \mathrm{kg} \) is moving with a
velocity of \( 100 \mathrm{ms}^{-1} \). The wavelength
associated with its motion is:
A. \( 1 / 100 \mathrm{cm} \)
B. \( 66 \times 10^{-34} \) m
D. 6.6 \( \times 10^{-28} \mathrm{m} \)


Match the following
\( \begin{array}{ll}\text { Set A } & \text { Set B } \\ \text { 1. Adenine } & \text { a. } C_{5} N_{5} H_{5} O \\ \text { 2. Guanine } & \text { b. } C_{4} N_{2} H_{4} O_{2} \\ \text { 3. Uracil } & \text { c. } C_{5} N_{5} H_{5} \\ \text { 4. Thymine } & \text { d. } C_{5} N_{2} H_{6} O_{2}\end{array} \)
\( \mathbf{A} \)
\( 1-c ; 2-a ; 3-d ; 4-b \)
B. \( 1-c ; 2-b ; 3-d ; 4-e \)
c. \( 1-b ; 2-c ; 3-d ; 4-a \)
D. \( 1-c ; 2-a ; 3-b ; 4-d \)


Mention phase transition based on which the solid room fresheners work.
A. Evaporation
B. Condenzation
c. occlusion
D. Sublimation


A copper wire having a resistance of 0.01 ohm in each metre is used to wind
a 400 turn solenoid of radius \( 1.0 \mathrm{cm} \)
and length \( 20 \mathrm{cm} . \) Find the emf of a battery which when connected across the solenoid will cause a magnetic field
of \( 1.0 \times 10^{-2} \) T near the centre of the
solenoid.


Excess salt is responsible for ulcers
If this is true enter \( 1, \) if false enter 0 .


Gymnosperms maintain their dominance over angiosperms in
A. Colder regions of world
B. Warmer regions of world
c. Antarctica
D. Oceans


Assertion
NaCl is precipitated when \( H C l \) gas is
passed in a saturated solution of \( N a C l \)
Reason
HCl is a strong acid.
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


Assertion: A mixture of \( C H_{3} \) COOH
and \( C H_{3} C O O N H_{4} \) is not a buffer
solution.

Reason: An acidic buffer contains
the mixture of a weak acid and its salt
with a strong base.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct


Consider earth to be a homogeneous
sphere. Scientist \( \boldsymbol{A} \) goes deep down in a
mine and scientist \( B \) goes high up in a
balloon. The gravitational field measured by
A. \( A \) goes on decreasing and that by \( B \) goes on increasing
B. \( B \) goes on decreasing and that by \( A \) goes on increasing
c. Each decreases at the same rate
D. Each decreases at different


A block of weight \( 5 N \) is pushed against
a vertical wall by a force \( 12 N \).The coefficient of friction between the wall
and block is \( 0.6 . \) The magnitude of the force exerted by the wall on block is
A. \( 12 N \)
B. \( 5 N \)
\( c .7 .2 N \)
D. \( 13 N \)


A thin plane membrane separates
hydrogen at \( 27^{\circ} \mathrm{C} \) from hydrogen at \( 127^{\circ} \)
C, both being at the same pressure. A plane sound wave enters from the cooler to the hotter side. If the angle of
incidence on the membrane is \( 30^{\circ} \mathrm{C} \)
then the angle of refraction is
\( ^{A} \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
B. \( \sin ^{-1}\left(\frac{2}{\sqrt{8}}\right) \)
\( c \cdot \sin ^{-1}\left(\frac{3}{\sqrt{8}}\right) \)
D. \( \sin ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


A conducting rod of resistance is
moving with constant velocity \( v_{1} \) then
the force required to keep rod moving is
\( \frac{v B^{2} l^{2}}{R} \)
в. \( \frac{2 v B^{2} l^{2}}{R+r} \)
c. \( \frac{v B^{2} l^{2}}{R+r} \)
D. zer


In animal tissue culture which of the
following radioactive nucleotide is used to measure RNA synthesis?
A. Adenine
B. Cytosine
c. Guanine
D. Thymine
E. Uracil


As many as different
combination of water are possible from \( 1 H^{1},_{1} H^{2},_{1} H^{3} \) and \( _{8} O^{16},_{8} O^{17} \) and \( _{8} O^{18} \)
A \( \cdot 12 \)
B. 32
\( c \cdot 18 \)
D. 15


Find the seventh term of the geometric
sequence \( 1,-3,9,-27, \dots \)
A . - 243
B. -30
\( c \cdot 81 \)
D. 189
E . 729


Tyndall phenomenon is shown by:
A. dilute solution
B. colloidal solution
c. suspension
D. true solution


Write the negation of the following
statements
i) \( \sqrt{7} \) is a rational number.
ii) Length of both diagonals of any rectangle are equal


On the hydrogenation of oils, the catalyst used is:
A. platinum
B. manganese dioxide
c. molybdenum
D. nickel


The largest value in a collection of data
is \( 7.44 . \) If the range is \( 2.26, \) then find the smallest value in the collection.


p-njunction diode acts as
A. ohmic resistance
B. non-ohmic resistance
c. both \( A \) and \( B \)
D. amplifier


The plasticity behaviour of a material
determines the
A. elastic behavior of the material
B. resistance of the material to electric fields
C. viscous behavior of the material and is irrecoverable.
D. resistance of the material to magnetic fields


\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
In above reaction, at equilibrium
condition mole fraction of \( \boldsymbol{P C l}_{5} \) is \( \mathbf{0 . 4} \)
and mole fraction of \( C l_{2} \) is \( 0.3 . \) Then
find out mole fraction of \( \boldsymbol{P} \boldsymbol{C l}_{3} \)
A . 0.3
B. 0.7
\( c .0 .4 \)
D. 0.6


In Spirogyra, asexual reproduction takes
place by
A. Breaking up of filaments into smaller bits.
B. Division of a cell into two cells.
C. Division of a cell into many cells.
D. Formation of young cells from older cells.


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


The IUPAC name of the given compound
¡s:
A. 2-methyl spiro [5.4] dec-1-ene
B. 2-Methyl spiro [4.5] dec-1-ene
c. 2 -methyl spiro [4.5] dec- 2 -ene
D. 2-methyl spiro [5.4] dec-2-ene


Which one can be represented as the
symbol of time?
A .
в. \( F \)
\( c \)
D. None


Detergents are less or non bio-
degradable when compare with soaps. For detergents to be bio-degradable in
nature, the non-polar part of the
molecule should:
A. consist of a hydrocarbon with more branching
B. consist of a hydrocarbon with more number of branches and unsaturation
C. have straight or open chain hydrocarbons
D. be replaced by aromatic rings substituted by alkyl groups


A bar of mass \( M \) and length \( L \) is in pure
translatory motion and its centre of
mass has velocity \( V \). It collides and sticks to a second identical bar which
is initially at rest. (Assume that it becomes one composite bar of length
\( 2 L \) ). The angular velocity of the
composite bar after collision will be :
This question has multiple correct options
A \( \cdot \frac{3}{4} \frac{V}{L} \)
в. \( \frac{4}{3} \frac{V}{L} \)
c. counterclockwise
D. Clockwise


Define the term "tissue""


Persistent calyx forming a cover around the fruit is found in
A. Argemone mexicana
B. Ageratum conyzoides
c. Withania somnifera
D. Brassica campestriss


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & \mathbf{0}\end{array}\right], \) then \( \boldsymbol{A}^{-1} \) is
A . \( -A \)
в.
\( c \cdot 1 \)
D. None of these


A parallel plate capacitor is charged
and then isolated. The effect of
increasing the plate separation on charge, potential and capacitance respectively are:
A. constant, decreases, decreases
B. increases, decreases, decreases
c. constant, decreases, increases
D. constant, increases, decreases


A coil having 200 turns has a surface
area of \( 0.15 m^{2} . \) A magnetic field of
strength \( 0.2 T \) applied perpendicular to this changes to \( 0.6 \mathrm{T} \) in \( 0.4 \mathrm{s} \), then the induced emf in the coil is
A . 45
B. 30
c. 15
D. 60


In the food chain, Man is a
A. Producer
B. Consumer
c. Both producer and consumer
D. Producer and decomposer


Which of the following is least ionic?
\( \mathbf{A} \cdot A g C l \)
в. \( K C l \)
c. \( B a C l_{2} \)
D. \( C a C l_{2} \)


Process of removal of gangue from the
ore are based on:
A. differences between physical and chemical properties of the gangue and the ore
B. difference between densities of gangue and ore
C. difference between melting point between of gangue and ore
D. all of the above


Add the following algebraic expressions:
(i) \( 2 x^{2}+3 x+5,3 x^{2}-4 x-7 \)
(ii) \( x^{2}-2 x-3, x^{2}+3 x+1 \)
(iii) \( 2 t^{2}+t-4,1-3 t-5 t^{2} \)
(iv) \( \boldsymbol{x y}-\boldsymbol{y} \boldsymbol{z}, \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x} \boldsymbol{z}, \boldsymbol{z} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{y} \)
\( (v) a^{2}+b^{2}, b^{2}+c^{2}, c^{2}+a^{2}, 2 a b+ \)
\( 2 b c+2 c a \)


Which of the following pair of matrices are equal?
A. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right],\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right],\left[\begin{array}{ll}4 & 0 \\ 4 & 4\end{array}\right] \)
\( ^{\mathbf{C}} \cdot\left[\begin{array}{ll}4 & 7 \\ 3 & 2\end{array}\right],\left[\begin{array}{cc}3+1 & \sqrt{49} \\ \frac{7-1}{2} & \sqrt{4}\end{array}\right] \)
D. none of the above


How much time does it take for the
Earth to revolve around itself?
A. 365 days
B. 24 hours
c. 30 hours
D. 4 weeks


Let \( *^{\prime} \) be the binary operation on the set
\{1,2,3,4,5\} defined by \( a *^{\prime} b= \)
H.C.F. of \( a \) and \( b \). Is the operation \( *^{\prime} \)
same as the operation \( * \) defined in above? Justify your answer


Find the median for the following frequency distribution table :
\( \begin{array}{lccc}\text { Class- } & 0 & 5 & 10 \\ \text { interval } & 5 & 10 & 15\end{array} \) \( - \)
frequency \( \quad 5 \quad 3 \) 9


Two copper spheres, one of large size and the other small, are heated to the
same temperature. Which will cool
first??
A . bigger
B. smaller
c. both in equal time
D. insufficient data to reply


Which gas is responsible for the depletion of ozone layer?
A. Carbon dl oxide
B. Methane
c. cluroflorocarbon
D. Sulphur di oxide


For the reaction, \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}), \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{p}_{C O_{2}} \)
A. True
B. False


If the probability of \( x \) to fail in the
examination is 0.3 and that for \( Y \) is 0.2
then the probability that either \( \boldsymbol{X} \) or \( \boldsymbol{Y} \) fail in the examination is
A . 0.5
B. 0.44
\( c .0 .6 \)
D. None of these


State whether given statement is True or False

Radiant heat can easily pass through air
A. True
B. False


Urinary excretion of 'Na' is regulated by
A. Anterior pituitary
B. Posterior pituitary
c. Adrenal cortex
D. Adrenal medulla


Differentiate between.
Vital capacity and total lung capacity


In a shooting game, John shoots the balls 20 times out of 40 trials. What is
the empirical probability of the
shooting event?
A \( \cdot \frac{3}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{7}{2} \)


f \( a, b, c \) are in \( G . P, \) then
\( a\left(b^{2}+c^{2}\right)=c\left(a^{2}+b^{2}\right) \)
A. True
B. False


A particle travels first half of the total
distance with speed \( v_{1} . \) In second half distance, constant speed in \( \frac{1}{3} r d \) time is \( v_{2} \) and in remaining \( \frac{2}{3} r d \) time constant
sped is \( v_{3} \). Find average speed during the complete journey.


Write daily life uses of heating effect of electric current


Mendeleev's Periodic Table was
published in a in 1872.
A. German journal
B. US journal
c. Russian journal
D. None of the above


Transition elements are also known as
\( \mathbf{A} \cdot d- \) block elements
B. \( f \) - block elements
c. \( s \) - block elements
D. None of these


The amount of work done in moving a unit positive charge from infinity to a given point is known as:
A. Nuclear potential
B. Potential energy
c. Electric potential
D. Gravitational potential


Two coils 'P' and 'Q' are separated by
some distance. When a current of 3 A
flows through coil 'P', a magnetic flux of
\( 10^{-3} \) Wh passes through 'Q'. No current is passed through 'Q'. When no current
passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is?
A \( \cdot 6.67 \times 10^{-3} \mathrm{Wb} \)
В. \( 6.67 \times 10^{-4} \mathrm{wb} \)
c. \( 3.67 \times 10^{-4} \mathrm{wb} \)
D. \( 3.67 \times 10^{-3} \mathrm{Wb} \)


toppr
Q Type your question
\( \sqrt{\boldsymbol{L}} \boldsymbol{C} \)
with the help of an external agent. A
uniform magnetic field \( B \) exists in
space and is directed into the plane of the figure. (circuit part remains at rest)
(left part is at rest)
This question has multiple correct options
A the rms value of current in the circuit is \( \frac{\pi B a^{2}}{R \sqrt{2 L C}} \)
B. The rms value of current in the circuit is \( \frac{\pi B a^{2}}{2 R \sqrt{2 L C}} \)
C. The maximum energy stored in the capacitor is \( \frac{\pi^{2} B^{2} a^{4}}{8 R^{2} C} \)
D. The maximum power delivered by the external agent is \( \frac{\pi^{2} B^{2} a^{4}}{4 L C R} \)


The olive oil used in froth floatation
process is called:
A. frothing agent
B. collecting agent
c. conditioning agent
D. Iubricating agent


A gas with formula \( C_{n} H_{2 n+2} \) diffuses
through the porous plug at a rate onesixth of the rate of diffusion of hydrogen gas under similar conditions. The
formula of gas is?
A. \( C_{2} H_{6} \)
в. \( C_{10} H_{22} \)
c. \( C_{5} H_{12} \)
D. \( C_{6} H_{14} \)


The freezing point depression constant
for water is \( 1.86^{\circ} \mathrm{C} \boldsymbol{m}^{-1} . \) If \( 5 \mathrm{g} N a_{2} \mathrm{SO}_{4} \)
is dissolved in 45 g \( H_{2} O \), the freezing
point is changed by \( -3.82^{\circ} \mathrm{C} \)
Calculate the van't Hoff factor for
\( N a_{2} S O_{4} \)
A .0 .381
B . 2.05
\( c .2 .63 \)
D. 3.11


Of the total fresh water, ground water constitutes
A . 90\%
B . 10\%
c. 30\%
D. 44.2\%


The mole fraction of benzene in a
solution containing \( 39 \% \) by mass in an organic solvent of molecular mass 122
is :
A . 0.5
B. 0.6
\( c .0 .4 \)
D. 0.35


Which among the following is called
woody grass?
A. Bamboos (Dendrocalamus)
B. Aloe
c. Date palm (Phoenix dactylifera)
D. Rice (Oryza sativa)


London dispersion force is the only intermolecular force that works on
what?
A. Noble gases and nonpolar molecules
B. Polar molecules
c. Noble gases
D. Nonpolar molecules
E. Solids


For a spontaneous reaction the \( \Delta G \) equilibrium constant \( K \) and \( E_{\text {cell }}^{0} \) will be
respectively:
A. \( -v e,>1,-v e \)
В. \( -v e,<1,-v e \)
c. \( +v e,>1,-v e \)
D. \( -v e,>1,+v e \)


Eight droplets of mercury, each of radius 1 mm, coalesce into a single
drop.
(a) Find the radius of the single drop? [Surface tension of mercury \( = \)
\( \left.\mathbf{0 . 4 6 5} \boldsymbol{J} / \boldsymbol{m}^{2}\right] \)


Which type of sexual reproduction is found in volvox?
A. Isogamous
B. Anisogamous
c. oogamous
D. All of these


Prove that the difference of the infinite
continued fractions \( \frac{1}{a+b+c} \frac{1}{c+} \dots, \frac{1}{b+a+c+} \dots ., \) is equal to
\( \frac{a-b}{1+a b} \)


2-Phenylethanol may be prepared by the reaction of phenylmagnesium bromide with:
A. \( H C H O \)
в. \( C H_{3} C H O \)
c. \( C H_{3} \) СОСН \( _{3} \)
D.


Which of the following statements is
incorrect?
\( \mathbf{A} \cdot \) Among \( O_{2}^{+}, O_{2}, \) and \( O_{2} \) the stability decreases as \( O_{2}^{-}>O_{2}^{+}>O_{2} \)
B. \( H e_{2} \) molecule does not exist as the effect of bonding and anti-bonding orbitals cancel each other
\( \mathbf{c} \cdot C_{2}, O_{2}^{2-} \) and \( L i_{2} \) are diamagnetic
D. \( \ln F_{2} \) molecule, the energy of \( \sigma_{2 p_{z}} \) is more than \( \pi_{2 p_{x}} \) and
\( \pi_{2 p_{y}} \)


The barrier potential in a p-njunction is \( 0.3 V . \) The current required is \( 6 m A . \) The
emf of the cell required for use in the circuit if a resistance of \( 200 \Omega \) is
connected in series with junction is (in volt)


\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) on heating liberates gas The same gas will be obtained by :
A. heating \( N H_{4} N O_{2} \)
B. heating \( N H_{4} N O_{3} \)
C. treating \( M g_{3} N_{2} \) with \( H_{2} O \)
D. heating \( H_{2} O_{2} \) on \( N a N 0_{2} \)


Verify the following
(i) (0,7,-10),(1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle
(ii) (0,7,10),(-1,6,6) and (-4,9,6) are the vertices of a right angled triangle
(iii) (-1,2,1),(1,-2,5),(4,-7,8) and (2,-3,4) are the vertices of a parallelogram


Mark the incorrect statement.
A catalyst :

This question has multiple correct options
A. remains chemically unchanged at the end of a chemical reaction
B. is used up in the course of a reaction
C. is a reactant required in small quantity
D. is not specific


Two particles are moving with velocities
\( V_{1} \) and \( V_{2} . \) Their relative velocity is the maximum, when the angle between their velocities is :
A. zero
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D.


Soap bubble looks coloured due to
A. dispersion
B. reflection
c. interference
D. None of these


A floor is \( 5 \mathrm{m} \) long and \( 4 \mathrm{m} \) wide. \( \mathrm{A} \) square carpet of sides \( 3 \mathrm{m} \) is laid on the floor. Find the area of the floor that is
not carpeted.


Hydrolysis of urea is an example of
A. Homogenious reaction
B. heterogenious reaction
C. Biomolecular reaction
D. Both a and b


Mechanism of aerobic respiration was
discovered by
A. Kreb
B. Calvin
c. Hatch and Slack
D. Pasteur


A weight of \( 5 \mathrm{N} \) is moved upon a frictionless inclined plane from \( R \) to \( Q \)
as shown. What is the work done in
joule?
A \( \cdot 15 \)
B. 20
\( c \cdot 25 \)
D. 35


Hydrogen acts as an oxidising agent in the reaction with:
\( \mathbf{A} \cdot B r_{2} \)
в. \( C a \)
c. \( N_{2} \)
D. \( S \)


If \( S_{r} \) denotes the sum of the first \( r \) terms of an \( A P \) then \( \frac{S_{3 r}-S_{r-1}}{S_{2 r}-S_{2 r-1}} \) is
equal to
A \( .2 r-1 \)
в. \( 2 r+1 \)
c. \( 4 r+1 \)
D. \( 2 r+3 \)


Two blocks are connected by a spring. The combination is suspended, at rest,
from a string attached to the ceiling, as
shown in \( F \) ig. 6.208 The string breaks
suddenly. Immediately after the sting breaks, what is the initial downward
acceleration of the upper block of mass \( 2 m ? \)


The maximum number of unpaired electrons available in the higher oxidation state of sulphur is:
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
D.


The velocity-time graph of a car is as shown in the figure above. Find the acceleration and deceleration
of the car if its total displacement is
\( \mathbf{9 0 m} \)


Assertion
\( \mathrm{E}^{0} \) value of single electrode is determined experimentally by combining the electrode with SHE
Reason
SHE is taken as a reference electrode
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Give reasons to show that the following are chemical changes:
Adding of calcium to water:
This question has multiple correct options
A. new substance is formed with different properties
B. new substance is formed and has the same properties
c. The reaction is reversible
D. The reaction is irreversible


Explain how a metal rim slightly
smaller than a wooden wheel can be
fixed on it.


A printed page is seen through a glass slab place on it. The printed words appear raised. This is due to:
A. Refraction at the upper surface of the slab
B. Refraction at the lower surface of the slab
c. Partial reflection at the upper surface of the slab
D. Partial reflection at the lower surface of the slab


The survey of a manufacturing company producing a beverage and snacks was done. It was found that it
sells orange drinks at \( \$ 1.07 \) and choco chip cookies at \( \$ 0.78 \) the maximum.
Now, it was found that it had sold 57
food items in total and earned about
\( \$ 45.87 \) of revenue. Find out the
equations representing these two
A. \( \left\{\begin{array}{l}x+y=45.87 \\ 1.07 x+0.78 y=57\end{array}\right. \)
В \( \cdot\left\{\begin{array}{l}x+y=57 \\ 1.07 x+0.78 y=45.87\end{array}\right. \)
c. \( \left\{\begin{array}{l}x+y=47 \\ 0.78 x+1.07 y=45.94\end{array}\right. \)
D. \( \left\{\begin{array}{l}x+y=47 \\ 107 x+78 y=45.94\end{array}\right. \)


Smoke precipitator works on the
principle of :
A. distribution law
B. neutralization of charge on colloids
C . Le Chaterlier's principle
D. addition of electrolytes


Simplify: \( \left(-10 a^{3} b+12 a^{2} b^{2}-6 a b^{3}\right)- \)
\( \left(8 a^{3} b+6 a^{2} b^{2}-9 a b^{3}\right) \)


In what time will Rs. 8000 amount to Rs.
8820 at \( 5 \% \) p.a.compounded annually?


Assertion
Alkaline earth metals have lower
densities than alkali metals.
Reason
Atomic radii of alkaline earth metals
are larger than that of corresponding alkali metals.
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


\( \cos \left(\tan ^{-1} \frac{3}{4}\right)=? \)
\( A \cdot \frac{3}{5} \)
\( B \cdot \frac{4}{5} \)
\( c \cdot \frac{4}{9} \)
D. none of these


Prove that:
\[
\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2 c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}
\end{array} \mid=
\]
\( \mathbf{2}(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)


Which of the following is a
photochemical reaction product?
A. Flourides
B. \( \operatorname{coand} C O_{2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3} \)
D. \( O_{3} \)


Two small loud speakers \( A \) and \( B \) are
driven by the same amplifier as shown in Fig and emit pure sinusoidal waves
in phase. Speaker \( A \) is \( 1 \mathrm{m} \) away as
shown and speaker \( B \) is 2 m away from the amplifier. The microphone is \( 4 \mathrm{m} \)
away from the amplifier in transverse direction as indicated in the Figure. For what frequencies destructive
interference will occur at \( P: \)
A. 500 HZ, 1500 нZ, 2500 Hz,...
B. 500 Нz, 1000 Нz, 1500 Нz,...
c. 1250 Нz, 1750 Нz, 2250 Нz,..
D. 1000 Hz, 2000 Hz


In the Modern Periodic Table, calcium (atomic number 20 ) is surrounded by elements with atomic numbers
12,19,21 and \( 38 . \) Which of these have physical and chemical properties resembling calcium?


If \( a b=2 a+3 b, a>0, b>0 \) then the
minimum value of \( a b \) is
A . 12
B . 24
\( c \cdot \frac{1}{4} \)
D. none of these


A metal X on heating in nitrogen gas
gives Y. Y on treatment with \( \boldsymbol{H}_{2} \boldsymbol{O} \) gives a colourless gas which when passed
through \( C u S O_{4} \) solution gives a blue colour.Y is :
A \( \cdot \operatorname{Mg}\left(\mathrm{NO}_{3}\right)_{2} \)
B . \( \mathrm{Mg}_{3} \mathrm{N}_{2} \)
c. \( \mathrm{NH}_{3} \)
D. \( \mathrm{MgO} \)


A consumption tax imposed by the government on the sale of goods and services is called
A. vat
B. sales tax
c. income tax
D. business tax


The areas of two similar triangles are
45 sq. \( \mathrm{cm} \) and 80 sq.cm. The sum of their perimeters is \( 35 \mathrm{cm} . \) Find the perimeter of each triangle in cm.
\( \mathbf{A} \cdot 15,20 \)
B. 13,22
c. 17,18
D. None of these


Integrate:
\( \int \frac{x^{2}+1}{(x+1)^{3}(x-2)} d x \)


The resultant moment of all the forces
acting on the body about the point of rotation should be
A. Greater than one
B. Smaller than one
c. zero
D. one


f \( \boldsymbol{y}=\log _{7}(\log \boldsymbol{x}) \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


From the following statements write down which is not applicable to mass of
an object.
(a) It is a fundamental quantity.
(b) It is measured using physical balance.
(c) It is measured using spring balance.


000
0
0
\( \infty \)
00


The energy density in a parallel plate capacitor is given as \( 1.8 \times 10^{-9} J / m^{3} \)
The value of the electric field in the
region between the plates is :
\( \left(\epsilon_{0}=9 \times 10^{-12}\right) \)
\( \mathbf{A} \cdot 6.6 N C^{-1} \)
B. \( 20 N C^{-1} \)
\( \mathbf{c} \cdot 66 N C^{-1} \)
D. \( 2 N C^{-1} \)


The ratio of the radii if gyration of a circular disc and a circular ring of same
masses and radii about a tangential axis parallel to their plane is
A. \( \sqrt{6}: \sqrt{5} \)
B. \( 1: \sqrt{2} \)
c. \( \sqrt{5}: \sqrt{6} \)
D. None of these


Which form of phosphorous is most stable?
\( \mathbf{A} \cdot \operatorname{Red} \mathbf{P} \)
B. White
c. Black
D. Scarlet P


Describe characteristics and uses of
coke.


A hot body is allowed to cool. The surrounding temperature is constant at
\( 30^{\circ} \mathrm{C} . \) The body takes time \( t_{1} \) to cool
from \( 90^{\circ} \mathrm{C} \) to \( 89^{\circ} \mathrm{C} \) and time \( t_{2} \) to cool
from \( 60^{\circ} \mathrm{C} \) to \( 59.5^{\circ} \mathrm{C} \). Then
A \( \cdot t_{2}=2 t_{1} \)
B. \( t_{2}=\frac{t_{1}}{2} \)
c. \( t_{2}=4 t \)
D. \( t_{2}=t_{1} \)


An unbanked curve has a radius of \( 60 m \)
Coefficient of friction between the tyre
of truck and road is \( 0.75 . \) The distance
between two front wheel of truck is \( 2 m \)
If the truck exceeds the speed of safe
limit, then select the correct statement and justify your asnwer.
1) Inner wheels leave the ground first.
2) Outer wheels leave the ground first.


A train starts from rest and moves with
a constant acceleration for the first \( 1 \mathrm{km} \)
For the next \( 3 \mathrm{km}, \) it has a constant
velocity and for last \( 2 \mathrm{km} \), it moves with constant retardation to come to rest
after a total time of motion of 10 min.
Find the maximum velocity and the three time intervals in the three types of
motion.


Alkynes are heavier than water.
A. True
B. False


Functional megaspore in an angiosperm develops into
A. Embry
B. Ovule
c. Endosperm
D. Embryo saç


A square has the perimeter \( 40 \mathrm{cm} \) What is the sum of the diagonals?


Dinesh bought an article for Rs. 374
which included a discount of \( 15 \% \) on
the marked price and a sales-tax of \( 10 \% \) on the reduced price. Find the
marked price of the article.


The threshold frequency for a
photosensitive metal is \( 3.3 \times 10^{14} H z . \) If
light of frequency \( 8.2 \times 10^{14} H z \) is
incident on this metal, the
cutoff voltage for the photoelectric emission is nearly:
A . \( 1 v \)
B. 2V
c. \( 3 v \)
D. \( 5 v \)


Which of the following arrangements represent increasing oxidation number
of the central atom?
A \( \cdot C r O_{2}^{-}, C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4} \)
B . \( C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-} \)
c. \( C r O_{2}^{-}, C l O_{3}^{-}, M n O_{4}^{-}, C r O_{4}^{2} \)
D. \( C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-}, C l O_{3} \)


The magnetic moment of complex ion is
2.83 BM. The complex ion is :
\( \mathbf{A} \cdot\left[V\left(H_{2} O\right)_{6}\right]^{3+} \)
B . \( \left[\operatorname{Cr}\left(\text { Ha }_{2} \text { O }\right)_{6}\right]^{3} \) '
c. \( \left[C u(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[M n C l_{4}\right]^{2} \)


State whether given statement is True or False

The resistor voltage is always out of phase with the current.
A. True
B. False


The Bohr model of the atom was able to
explain the Balmer series because:
A. larger orbits required electrons to have more negative energy in order to match the angular momentum.
B. differences between the energy levels of the orbits matched the difference between energy levels of the line spectra.
c. electrons were allowed to exist only in allowed orbits and nowhere else
D. none of the above


Given two independence events \( A \) and \( B \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \overline{\boldsymbol{B}}) \)


Identify the following pairs of angles are complementary or supplementary:
\( 80^{\circ}, 10^{\circ} \)


Answer the following:
What is the impedance of a capacitor of capacitance \( C \) in an \( A C \) circuit using source of frequency n Hz?


The ratio of maximum to minimum
intensity due to superposition of two waves is \( \frac{49}{9} . \) Then the ratio of the
intensity of component waves is
A \( \cdot \frac{25}{4} \)
в. \( \frac{16}{25} \)
c. \( \frac{4}{49} \)
D. \( \frac{9}{49} \)


An alternative voltage given by \( V= \) \( 140(\sin 314 t) \) is connected across a
pure resistor of \( 50 \Omega \). Find
(i) The frequency of the source.
(ii) The rms current through the
resistor.


Decarboxylation of malonic acid gives:
A \( . C H_{4} \)
в. \( C H_{3} \) СООН
c. both (a) and (b)
D. none of the above


A ball is drawn at random from box \( \boldsymbol{I} \)
and transferred to box \( I I \). If the
probability of drawing a red ball from box \( I, \) after this transfer, is \( \frac{1}{3}, \) then the correct option(s) with the possible
values of \( n_{1} \) and \( n_{2} \) is (are)
This question has multiple correct options
A \( \cdot n_{1}=4 \) and \( n_{2}=6 \)
B . \( n_{1}=2 \) and \( n_{2}=3 \)
c. \( n_{1}=10 \) and \( n_{2}=20 \)
D. \( n_{1}=3 \) and \( n_{2}=6 \)


\( \lim _{\boldsymbol{n} \rightarrow \infty} \frac{1}{n} \sum_{\boldsymbol{r}=1}^{\boldsymbol{2} \boldsymbol{n}} \frac{\boldsymbol{r}}{\sqrt{\boldsymbol{n}^{2}+\boldsymbol{r}^{2}}} \) equals
\( \mathbf{A} \cdot 1+\sqrt{5} \)
B \( .-1+\sqrt{5} \)
\( \mathrm{c} \cdot-1+\sqrt{2} \)
D. \( 1+\sqrt{2} \)


Which cannonball travels farther?
\( A \cdot A \)
B. B
C. Both reaches same height
D. cannot be judged


The element that can be used as
acceptor impurity to dope silion is :
A. Antimony
B. Arsenic
c. Boron
D. Phosphorous