Acceleration of a body thrown up from
the surface of the earth is equal to
A \( \cdot 9.8 m s^{-2} \)
B \( .-9.8 m s^{-2} \)
c. \( 19.6 m s^{-2} \)
D. zero


A full wave p-n diode rectifier uses a
load resistance of \( 1300 \Omega \). No filter is
used. If the internal resistance of each
diode is \( 9 \Omega \), then the efficiency of this full wave rectifier is
A. \( 80.64 \% \)
B . \( 40.6 \% \)
c. \( 13.9 \% \)
D. \( 100 \% \)


If \( a, b, c \) are sides of the \( \triangle A B C \) such
that
\( \left(1+\frac{b-c}{a}\right)^{a} \cdot\left(1+\frac{c-a}{b}\right)^{b} \)
\( \left(1+\frac{a-b}{c}\right)^{c} \geq 1, \) then triangle \( \triangle A B C \)
must be
A. right angled
B. isosceles
c. obtuse
D. equilateral


Assertion
Each N-atom is \( s p^{3}- \) hybridised in
\( N_{2} H_{4} \)
Reason
It has gauche conformation
Read the above assertion and reason and
choose the correct statement regarding
it.
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


Assertion
Domain of \( f(x) \) is singleton.
Reason

Range of \( \boldsymbol{f}(\boldsymbol{x}) \) is singleton.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The square of a proper fraction is
than the given fraction.
A. smaller
B. greater
c. equal
D. none


The atomic number of \( \boldsymbol{S} \boldsymbol{n} \) is \( \mathbf{5 0 .} \) The
shape of gaseous \( S n C l_{2} \) molecule is:
A. \( C l-S n-C l \) (linear)
B.
\( c \)
D.


\( \mathbf{A} \)
\( 2 k g \) mass starts from rest on an
inclined smooth surface with
inclination \( 30^{\circ} \) and length 2 m. How much will it travel before coming into rest on a horizontal frictional surface
with frictional coefficient of 0.25
\( A \cdot 4 M \)
B. 6 M
\( c \cdot 8 M \)
\( D \cdot 2 M \)


11.2 litres of a gas at STP weighs 14 g. The gas could not be:
A \( . N_{2} \)
в. \( C O \)
\( \mathbf{c} \cdot B_{2} H_{6} \)
D. \( N_{2} \) O


In the figure, \( P Q R S \) is a parallelogram with \( P Q=15 c m \) and \( R Q=10 c m . L \) is
a point on \( R P \) such that \( R L: L P=2: \)
3. \( Q L \) produced meets \( R S \) at \( M \) and \( P S \)
produced at \( N . \) Find the lengths of \( P N \)
and \( \boldsymbol{R} \boldsymbol{M} \)
A. \( P N=15 \mathrm{cm} ; R M=10 \mathrm{cm} \)
B. \( P N=10 \mathrm{cm} ; R M=10 \mathrm{cm} \)
c. \( P N=25 \mathrm{cm} ; R M=15 \mathrm{cm} \)
D. \( P N=25 \mathrm{cm} ; R M=10 \mathrm{cm} \)


In Dracaena, vascular bundles are
A. Amphivasal
B. Amphicribal
C. Radial
D. Bicollateral


An object is moving along the \( x \) -axis
whose position time is given.Which
portion of \( \boldsymbol{x}-\boldsymbol{t} \) graph is not practically
possible?
\( A \cdot A B \)
В. \( B C \)
\( c \cdot C D \)
D. \( D E \)


Which of the following statements are
true?
This question has multiple correct options
A. Impulse is the product of force and time for which the force acts.
B. Sl unit of impulse is N s.
C. When two bodies have the same velocity; the lighter body has more momentum.
D. Conservation of linear momentum has no connection
with "Newton's third law of motion""


A double concave thin lens made out of
glass \( (\mu=1.5) \) have radii of curvature
\( 500 \mathrm{cm} . \) This lens is used to rectify the defect in vision of a person. The far point of the person will be at
\( A \cdot 5 m \)
B. 2.5 \( m \)
c. \( 1.25 \mathrm{m} \)
D. \( 1 \mathrm{m} \)


The reflection taking place from the walls of a building is called:
A. regular reflection
B. diffused reflection
c. multiple reflection
D. internal reflection


Find the area of the circle \( 4 x^{2}+4 y^{2}= \)
9 which is interior to the parabola \( x^{2}= \)
\( 4 y \)


the thermal capacity of 40 g of aluminium \( \left(\text {specific } \quad \text {heat}=\frac{0.2 c a l}{g m \times C}\right) \)
is
A. \( 40 \mathrm{cal} / C \)
B. 160cal/C
c. 200 cal \( / C \)
D. 8cal/C


A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting a 4 digit code with the proper combination of each of the 4 rings.Maximum how many codes can be formed to open the lock?


Which is not a macromolecule?
A . Palmitate
B. Starch
c. DNA
D. Insulin


The radius of wavefront as the waves
propogate:-
A. decreases
B. increases
c. becomes zero
D. some times decreases sometimes increases


A parallel plate capacitor is connected
to a cell. It's positive plate \( A \) and the
negative plate B have charges \( +\boldsymbol{Q} \) and
\( -Q \) respectively. A third plate \( C \)
identical to \( A \) and \( B \) with charge \( +Q \) is
now introduced midway between the plates \( A \) and \( B \) parallel to them What is the charge on the inner surface of \( A \) ?
A \( \cdot Q \)
в. \( \frac{\mathrm{Q}}{2} \)
c. \( \frac{3 Q}{2} \)
D. \( \frac{\mathrm{Q}}{4} \)


On nitration, the major product that chlorobenzene gives is:
A. 1-chloro-4-nitrobenzene
B. 1-chloro-3-nitrobenzzne
c. 1,4 -dinitrobenzene
D. 2,4,6 -trinitrobenzene


Which of the following statements about Radioactive pollution are correct?
1. It causes genetic changes in the animals.
2. It causes disbalance among different minerals in the soil.
3. It hinders blood circulation.
4. It causes cancers.
Select the correct answer from the
codes given below:
A . 1 and 2
B. 1 and 4
c. 1,3 and 4
D. 2, 3 and 4


Let \( R \) and \( S \) be two equivalence relations
on set A. Prove that \( \boldsymbol{R} \cap \boldsymbol{S} \) is an
equivalence relation.


Two waves in a string (all in Sl units)
\( \operatorname{are} y_{1}=0.6 \sin (10 t-20 x) \) and \( y_{2}= \)
\( 0.4 \sin (10 t+20 x) \)
Statement-1: Stationary wave can be formed by their superposition but net energy transfer through any section will
be non-zero
Statement-2: Their amplitudes are
unequal.
\( A \). If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement- 2 is not the correct explanation of statement- 1
c. If statement-1 is true and statement-2 is false
D. If statement- 1 is false and statement- 2 is true


Explain the spectral series of hydrogen atom (diagram not necessary)


What is the sum of all even numbers
between \( 500 \& 600 ? \)
\( \mathbf{A} \cdot 26950 \)
B. 27500
c. 27950
D. 26500


A proton is kept at rest. A positively charged particle is released from rest at
a distance \( d \) in its field. Consider two
experiments; one in which the charged particle is a proton and in another a positron. In the same time \( t, \) the work
done on the two moving charged
particles is
A. Same as the same force law is involved in the two experiments
B. Less for the case of a positron, as the positron moves away more rapidly and the force on it weakens
C. More for the case of a positron, as the positron moves away a larger distance
D. Same as the work done by charged particle on the stationary proton


The contrapositive of the statement "If you believe in yourself and are honest
then you will get sucess" is
A. If you do not believe yourself and are dishonest then you will not get success.
B. If you do not believe yourself and are dishonest then you will get success
c. If you get success then you are honest and you also believe in yourself.
D. If you will not get success then you don't not believe in yourself or are not honest


Which one of the following includes all the other lower taxa?
A . Class
B. Order
c. Genus
D. Species


A sample of gas has a volume of 0.2 litres measured at 1 atm pressure and
\( 0^{\circ} \mathrm{C} . \) At the same pressure, at \( 273^{\circ} \mathrm{C} \)
its volume will become:
A. 0.1 litre
B. 0.4 litre
c. 0.8 litre
D. 0.6 litre


Statement 1: Transition metal
compounds are often colored.
Statement 2: They frequently possess partially filled d-orbitals.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Select correct statement:
A. In the decomposition of an oxide, into oxygen and gaseous metal, entropy increases.
B. Decomposition of an oxide is an endothermic change.
C. To make \( \Delta G^{\circ} \) negative, temperature should be high
enough so that \( \mathrm{T} \Delta S^{\circ}>\Delta H^{\circ} \)
D. All of the above are correct statements.


Find the orbital magnetic dipole moment of the electron in a hydrogen
atom


Hydrocarbon containing minimum
mass \( \% \) of carbon will have which of the
following characteristics?
A. Has mass ratio \( \mathrm{C}: \mathrm{H}=1: 4 \)
B. Produces double moles of \( H_{2} O \) than \( C O_{2} \) upon complete combustion
c. Contains carbon in its maximum possible oxidation state
D. can be used as a reducing agent


When \( C O_{2} \) dissolves in water, the
following equilibrium is establishes, \( \boldsymbol{C O}_{2}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-}, \) for
which the equilibrium constant is
\( 3.8 \times 10^{-7} \) and \( p H=6.0 . \) The ratio of
\( \left[\boldsymbol{H} \boldsymbol{C O}_{3}^{-}\right] /\left[\boldsymbol{C O}_{2}\right] \) is
A . \( 3.8 \times 10^{-18} \)
в. 3.8
c. 0.38
D. 13.8


Which of the following statements is
incorrect?
A. The frequency of radiation is inversely proportional to its wavelength
B. Energy of radiation increases with increase in frequency
C. Energy of radiation decreases with increase in wavelength
D. The frequency of radiation is directly proportional to its wavelength


At \( 25^{\circ} \mathrm{C}, 1 \) mol of \( A \) having a vapour
pressure of 100 torr and 1 mol of \( B \) having a
vapour pressure of 300 torr were
mixed.
The vapour at equilibrium is removed, condensed and the condensate is
heated back to \( 25^{\circ} C \)

The vapour now formed are again removed, recondensed and analyzed.If the mole fraction of \( A \) in this
condensate is \( 1 \times 10^{-x} \), then what is the
value of \( \mathbf{x} ? \)


A car standing at the top of a hill would be an example of what type of energy?
A. Kinetic
B. Topical
c. Potential
D. Beneficial
E. Residual


The angle of incidence is increased for an incident ray on a reflecting surface, the angle between the incident and reflected rays ultimately approaches at what value?
A. zero
B . 45
\( c \cdot 90 \)
D. \( 180^{\circ} \)


The dissociation of ammonium
cabbamate may be represented by the equation:
\( N H_{4} C O_{2} N H_{2}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( C O_{2}(g) \Delta H^{\circ} \) for the forward reaction is
negative. The equilibrium will shift from right to left if there is :
This question has multiple correct options
A. a decrease in pressure
B. an increase in temperature
c. an increase in concentration of ammonia
D. an increase in the concentration of carbon dioxide


If \( ^{12} C_{r+1}=^{12} C_{3 r-5}, \) find \( r \)


What is the valency of \( C_{2} O_{4} \) ion?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Guttation occurs through the
A. Roots
B. Hydathode.
c. Trichome
D. Stomata.


Which reaction does not represent autoredox or disproportionation?
A \( \cdot C l_{2}+2 O H^{-} \rightarrow C l^{-}+C l O^{-}+H_{2} O \)
B. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot 2 C u^{+} \rightarrow C u^{+2}+C u \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \longrightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)


Compounds are shown with the no. of \( R M g X \) required for the complete reaction. Select the incorrect option.
A. \( C H_{3} C O O C_{2} H_{5} \)
в. \( C H_{3} \) СООС \( l_{2} \)
с. НОСН\( _{2} \)СООС\( _{2} \)Н\( _{5} \)
D.


A group of 100 candidates attending a physical test for recruitment have their average height as \( 163.8 \mathrm{cm} \) with
coefficient of variation \( 3.2 . \) What is the
standard deviation of their heights?


An experiment showed that in a lead chloride solution, 6.21 g of lead combined with 4.26 g of chlorine. The empirical formula of this chloride is:
\( \mathbf{A} \cdot P b C l_{2} \)
в. \( P b_{2} C l_{2} \)
c \( . P b C l \)
D. \( P b C l_{4} \)


In a circle whose radius is \( 8 \mathrm{cm}, \) a chord
is drawn at a point \( 3 \mathrm{cm} \). from the centre of the circle. The chord is divided
into two segments by a point on it. If one segment of the chord is \( 9 \mathrm{cm}, \) What is the length of the other segment?


A cart is running at an average speed of \( 3.6 k m / h r . \) How much time will it take
to go 380 metres?


A circular loop of radius R carrying a current lis placed in a uniform magnetic field B perpendicular to the
loop. The force on the loop is:
A \( .2 \pi R I B \)
В. \( 2 \pi R I^{2} B^{3} \)
\( \mathbf{c} \cdot \pi R^{2} I B \)
D. zero


Prove that the lines represented by \( 3 x^{2}-8 x y-3 y^{2}=0 \) and \( x+2 y=3 \)
From the sides of an isosceles right angled triangle.


The number of nucleons in the isotope
of an atom \( z X^{m} \) are
\( A \cdot m \)
B. z
\( c \cdot m+z \)
\( D \cdot m-z \)


Show that \( \sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{\sin A}{1+\cos A} \)


During electrolysis of \( 1 \mathrm{L}, 1 \mathrm{M} \) AgNO \( _{3} \) using silver electrodes, 9.65 A current is used for one hour. Assuming the volume to remain unchanged, the molarity of
\( A g N O_{3} \) at the end of the electrolytic
process is :
A. 1 м
B. 0.36 м
c. 0.64 М
D. None of these


Three particles, each having a charge of
\( 10 C \) are placed at the corners of an
equilateral triangle of side \( 10 \mathrm{cm} \). The
electrostatic potential energy of the system is :
A . \( 100 J \)
В. \( 27 \times 10^{12} J \)
c. 0
\( D \cdot \infty \)


Which of the following time measuring devices is most precise?
A. A wall clock
B. An atomic clock
c. A digital watch
D. stop watch


Producer gas is not a good fuel because:
A. it contains \( C O \) which is poisonous
B. it contains \( C O_{2} \)
c. it contains \( C O_{2} \) which does not burn
D. it contains \( N_{2} \) which does not burn


Using properties of determinants prove the following:
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x}^{2} \\ \boldsymbol{x}^{2} & \mathbf{1} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{1}\end{array}\right|=\left(1-\boldsymbol{x}^{3}\right)^{2} \)


Nephridia of Pheretima are
A . Meganephridia
B. Micronephridia
c. Metanephridia
D. Both B and C


A metal from period IV is added to water and a vigorous reaction takes place with the evolution of a gas.Which
statements are correct?
1. Oxygen is evolved
2. Hydrogen is evolved
3. The resulting solution is acidic
4. The resulting solution is basic
A. 1 and 3 only
c. 2 and 4 only
D. 1 and 4 only


Potentiometer wire length is \( 10 m \)
having a total resistance of \( 10 \Omega \). If a
battery of emf 2 volts (of negligible internal resistance) and a rheostat are
connected to it them the potential
gradient is \( 20 m V / m ; \) find the resistance imparted through the rheostat


Which one of these is completely
cartilaginous fish?
A. cat fish
B. Flying fish
c. Dog fish
D. Gold fish


Simplify :
\( 3 a-2 b-a b-(a-b+a b)+3 a b+ \)
\( \boldsymbol{b}-\boldsymbol{a} \)


The sequence of various components of
a growth curve are
A. Lag, log, stationary
B. Log, lag, stationary
c. Log, stationary, lagg
D. Stationary, log, lag


Which of the following statements are incorrect?

If \( f(x) \) and \( g(x) \) are one to one then
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{x}) \)
II If \( f(x) \) and \( g(x) \) are one to one then
\( \boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{g}(\boldsymbol{x}) \)
III If \( f(x) \) is odd then it is necessarily
one to one
A. I and II only
B. I land III only
\( \mathrm{c} \). ।, ॥ and ॥|
D. None of the above


If we imagine ideally smooth surfaces kept in contact, the frictional force
acting between them is :
A. zero
B. a finite value but not zero
c. very large
D. we can't predict


A straight conductor \( 0.1 \mathrm{m} \) long moves in a uniform magnetic field 0.1 T. The velocity of the conductor is \( 15 \mathrm{m} / \mathrm{s} \) and is directed perpendicular to the field. The emf induced between the two ends
of the conductor is:
A . \( 0.10 \mathrm{v} \)
B. 0.15 \( v \)
c. \( 1.50 v \)
D. 15.00


The intensity of an electric field between the plates of a charged condenser of plate area \( A \) will be :
A \( . A /\left(q \varepsilon_{0}\right) \)
в. \( q A / \varepsilon_{0} \)
c \( \cdot q /\left(\varepsilon_{0} A\right) \)
D. none of these


Westrosol is:
A \( \cdot C l_{2} C=C H C l \)
в. \( C H C l_{2}-C H C l_{2} \)
c. \( C H_{2} C l-C H_{2} C l \)
D. \( C H_{3}-C C l_{3} \)


Chlorine is displaced from potassium chloride solution by iodine.
A. True
B. False


At what temperature will the rms speed
of hydrogen be the same as that of
oxygen at \( 25^{\circ} \mathrm{C} ? \)


An ideal gas having initial pressure \( P \) volume \( V \) and temperature \( T \) is allowed to expand adiabatically until its volume becomes \( 5.66 \mathrm{V} \) while its temperature
falls to \( T / 2 . \) How many degrees of freedom do the gas molecules have?
A. 7
B. 5
\( c \cdot 6 \)
D.


Excess of \( K l \) was added to
\( 100 m l H_{2} O_{2} \) solution of unknown
strength along with sufficient \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) lodine liberated was titrated against
\( 40 m l \) of \( 0.1 M \) hypo solution. The
concentration of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution is:
A \( .0 .04 \mathrm{N} \)
в. 0.04 М
c. \( 0.68 g m / L \)
D. \( 0.02 \mathrm{M} \)


The sum of ' \( n^{\prime} \) terms of series
\[
\left(1-\frac{1}{n}\right)+\left(1-\frac{2}{n}\right)+\left(1-\frac{3}{n}\right)+
\]
will be:


Use the formula \( v=\sqrt{\frac{\gamma P}{\rho}} \) to explain
why the speed of sound in air
(a) is independent of pressure,
(b) increases with temperature,
(c) Increases with humidity.


\( \mathbf{f}\left[\begin{array}{rr}\boldsymbol{a}+\mathbf{4} & \mathbf{3} \boldsymbol{b} \\ \mathbf{8} & -\mathbf{6}\end{array}\right]=\left[\begin{array}{cc}\mathbf{2} \boldsymbol{a}+\mathbf{2} & \boldsymbol{b}+\mathbf{2} \\ \boldsymbol{8} & \boldsymbol{a}-\mathbf{8} \boldsymbol{b}\end{array}\right] \)
then write the value of \( a-2 b \)


A cnarge + \( \ell \) Is locatea somewnere
inside a vertical cone such that the
dept of the charge from the free surface
of the cone is \( H . \) It is formed that the
flux associated with the cone with thw
curved surface is \( \frac{3 Q}{5 \epsilon_{0}} \)

If the charge is raised vertically through a height \( 2 H \) then the flux through the curved surface is
\( \mathbf{A} \cdot \frac{3 Q}{5 \epsilon_{n}} \)
B. \( \frac{2 Q}{5 \epsilon_{n}} \)
\( c \cdot \frac{4 Q}{5 \epsilon_{n}} \)
D. Zero


In a plot of \( \log k \) vs \( 1 / T, \) the slope is
A \( \cdot \frac{-E_{a}}{2.303} \)
в. \( \frac{E_{a}}{2.303 R} \)
c. \( \frac{E_{a}}{2.303} \)
D. \( \frac{-E_{a}}{2.303 R} \)


Specific gravity of the body is numerically equal to of the
body.
A. apparent weight in water
B. density
c. relative density
D. thermal capacity


\begin{tabular}{l}
2 \\
\( c \) \\
\( c \) \\
\hline
\end{tabular}


Mushroom gland in cockroach is located in
A. 2nd -5th segments
B. 3rd-5th segments
c. 6 th-7th segments
D. 7th-8th segments


In the reaction,
\( \boldsymbol{M} \boldsymbol{g}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{X}+\boldsymbol{H}_{2} \)
What is \( X ? \)
\( \mathbf{A} \cdot M g O \)
В. \( M g(O H)_{2} \)
c. \( M g H_{2} \)
D. None of these


If the wavelength of a sound of frequency \( 350 \mathrm{Hz} \) is \( 0.5 \mathrm{m}, \) find the velocity of sound.
A. 700 \( \mathrm{m} s^{-1} \)
B. 175 \( \mathrm{m} \mathrm{s}^{-1} \)
c. \( 17.5 \mathrm{m} s^{-1} \)
D. 70 \( \mathrm{m} s^{-1} \)


A sample of water is vaporized and tested in a mass spectrometer. There are 3 isotopes of hydrogen, \( 1 H,^{2} H \) and
3. H. There are 2 isotopes of oxygen, \( ^{15} \boldsymbol{O} \) and \( ^{16} \) O.

How many peaks would be expected to be found on the mass spectrum?
A . 3
B. 4
\( c .5 \)
D. 6


Huygens's concept of secondary wave
A. allows us to find the focal length of a thick lens
B. is a geometrical method to a find a wavefront
\( \mathrm{C} \). is used to determine the velocity of light
D. is used to explain polarisation


Which of the gases listed below would not be collected via water
displacement?
A \( . C O_{2} \)
в. \( C H_{4} \)
\( c \cdot O_{2} \)
D. \( N H_{3} \)
E \( . H_{2} \)


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


It is said that the Taj Mahal may be
destroyed due to
A. Flood in Yamuna river
B. Decomposition of marble as a result of high temperature
c. Air pollutants released from oil refinery of Mathura
D. All of the above


Number of unpaired electron in sulphur
is:
A .2
B. 6
c. 8
\( D \)


The angle of contact in case of liquid depends upon which of the following?
A. nature of liquid and solid
B. material which exists above free surface of liquid
c. both of them above
D. None


If \( \frac{x^{a^{2}}}{x^{b^{2}}}=x^{16}, x>1, \) and \( a+b=2, \) what
is the value of \( a-b ? \)
\( A \cdot 8 \)
B. 14
\( c \cdot 16 \)
D. 18


Two stationary objects are in
an equilibrium position on a seesaw.
The first object has a mass of \( 3 k g \) and
rests \( 10 m \) from the pivot. The other
rests \( 1 m \) from the pivot. Find out the
mass of the second object.
A. \( 0.3 k g \)
B. \( 3 k g \)
c. \( 10 k g \)
D. \( 30 k g \)
E . \( 50 k g \)


Which of the following vitamins is water soluble?
A. Vitamin E
B. Vitamin D
c. Riboflavin
D. Retinol


A solid conducting sphere of radius a
having a charge \( q \) is surrounded by
a concentric conducting spherical shell
of inner radius \( 2 a \) and outer radius \( 3 a \)
as shown in figure. Find the amount of heat produced when switch is closed \( \left(\boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0}}\right) \)
\( ^{\mathrm{A}} \cdot_{K}=\frac{k q^{2}}{2 a} \)
в. \( _{K}=\frac{k q^{2}}{3 a} \)
\( ^{\mathrm{c}} \cdot_{K}=\frac{k q^{2}}{4 a} \)
D. \( _{K}=\frac{k q^{2}}{6 a} \)


Which of the following solutions is the product of the neutralization reaction between \( 10 \mathrm{ml} 0.2 M K O H \) and \( 10 m l \)
\( \mathbf{0 . 2} M \mathbf{H I} \)
A. \( 0.1 M \) KI\( _{3} \).
B. \( 0.1 M K I \)
c. \( 0.2 M K I \)
D. \( 0.4 M K I \)
ह. \( 0.4 M \) НОН


The ratio of energy to frequency of electromagnetic radiation is called:
A. Bohr's constant
B. Rydberg's constant
c. Plancks constant
D. Ritz constant


The focal length is the distance from the optical center of the lens and its principal
A. focus
B. axis
c. center of curvature
D. Iens


A wire of length \( L \) has a linear mass
density \( \mu \) and area of cross-section \( \boldsymbol{A} \) and Young's modulus \( Y \) is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is:
\( ^{\text {A } \cdot \frac{\mu g L^{2}}{Y A}} \)
в. \( \frac{\mu g L^{2}}{2 Y A} \)
c. \( \frac{2 \mu g L^{2}}{Y A} \)
D \( \cdot \frac{2 \mu g L^{2}}{3 Y A} \)


\( 0.1 g m \) of \( C O_{2} \) occupies a volume of
\( 320 c c \) at certain condition. Under
similar condition \( 0.2 g \) of dioxide of
element \( x \) occupies \( 440 c c \). Calculate
atomic weight of \( x \)


In prokaryotes, mitochondria are absent. Krebs cycle occurs over
A. Cytoplasm
B. Nucleoid
c. Ribosome
D. Plasma membrane


Find the area lying above \( x \) -axis and included between the circle \( x^{2}+y^{2}= \)
\( 8 x \) and inside of the parabola \( y^{2}=4 x \)
is \( m \pi+\frac{32}{3} . \) Find the value of \( m \)


A heater coil is cut into two equal parts
and only one part is used in the heater. Then the heat generated becomes:
A. One fourth
B. Half
c. Double
D. Four times


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 5\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}1 & 3 \\ -1 & 0 \\ 2 & 4\end{array}\right] . \) Show that \( (A B)^{\prime}=? \)
A \( \cdot B^{\prime} A^{\prime} \)
в. \( A^{\prime} B^{\prime} \)
c. \( A B^{\prime} \)
D. \( A^{\prime} B \)


When the switch \( S \), in the circuit shown
is closed, then the value of current \( i \) will
be
\( 4.3 A \)
В. \( 5 A \)
\( c .4 A \)
D. \( 2 A \)


Find the equation whose roots are the
reciprocals of the roots of \( 3 x^{2}-5 x+ \)
\( \mathbf{7}=\mathbf{0} \)
A \( \cdot 7 x^{2}-5 x+3=0 \)
B . \( 7 x^{2}+5 x+3=0 \)
c. \( 4 x^{2}-5 x+3=0 \)
D. \( 7 x^{2}-5 x+7=0 \)


if \( \sin \theta=\frac{1}{2} \) and \( \cos \theta=-\frac{\sqrt{3}}{2}, \) then
the general value of \( \theta i s(n \epsilon z) \)
A \( \cdot 2 n \pi+\frac{5 \pi}{6} \)
В \( \cdot 2 n \pi+\frac{\pi}{6} \)
c. \( _{2 n \pi+\frac{7 \pi}{6}} \)
D. \( 2 n \pi+\frac{\pi}{4} \)


Heat flow can occur due to which of the
following situation
A. Pressure difference
B. Temperature difference
c. Density difference
D. None of these


A dancer is rotating on smooth horizontal floor with an angular
momentum \( L \). The dancer folds her
hands so that her momentof inertia
decreases by \( 25 \% \). The new angular momentum is.
A \( \cdot \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{L}{2} \)
D. \( L \)


If \( \sqrt{5-12 i}+\sqrt{-5-12 i}=z, \) then
principal value of arg z can be This question has multiple correct options
A \( \cdot-\frac{\pi}{4} \)
в. \( \frac{\pi}{4} \)
c. \( \frac{3 \pi}{4} \)
D. \( -\frac{3 \pi}{4} \)


Let \( z_{k}(k=0,1,2, \dots, 6) \) be the roots of
the equation \( (z+1)^{7}+z^{7}=0, \) then \( \sum_{k=0}^{6} R e\left(z_{k}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{3}{2} \)
c. \( -\frac{7}{2} \)
D. \( \frac{7}{2} \)


A block of mass m shown in figure is in equilibrium. If it is displaced further by
\( x \) and released find its acceleration just after it is released. Take pulleys to be light and smooth and strings light.


Angular momentum in an orbit is \( 3 n \)
The value of \( n \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Two identical capacitors are joined in
parallel and charged to a potential \( V \)
Capacitors are separated and then connected in series, i.e., the positive plate of one is connected to the negative plate of other. Identify the correct
option:
A. The charges on the free plates are enhanced.
B. The charges on the free plates decrease.
c. The energy stored in the system increase
D. The potential difference between the free plates is \( 2 V \)


Observe the given multiplies of 37
\( 37 \times 3=111 \)
\( 37 \times 6=222 \)
\( 37 \times 9=333 \)
\( 37 \times 12=444 \)
Find the product of \( 37 \times 27 ? \)
A . 999
B. Greatest 3 digit number
c. Either A or B
D. Smallest 3-digit number


The correct labeling of different terms
used in coordination compounds is:
A. (i) Central atom, (ii) lonisation sphere, (iii) coordination number,
(iv) Ligands
B. (i) Ligands,
(ii) Coordination number, (iii) Valency, (iv) Ionisation sphere
C . (i) lonisation sphere
(ii) Ligands, (iii) Coordination number, (iv) Central atom
D. (i) Ligands,
(ii) lonisation sphere, (iii) Coordination number, (iv) Central atom


Express as metres (m) using decimals:
\( \mathbf{3} \boldsymbol{m} \mathbf{6 5} \boldsymbol{c m} \)


Draw the graphs of the equations \( x= \) \( \mathbf{3}, \boldsymbol{x}=\mathbf{5} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{0} . \) Also, find the
area of the quadrilateral formed by the lines and the \( x \) -axis.


In coconut, black covering (thin layer) adherent to the kernel around the
endosperm is
A. Mesocarp
B. Pericarp
c. Seed coat
D. None of the above


If the element \( A \) has three electrons in
an outer shell and \( B \) has six electrons
in an outer shell, then the formula of the compound formed by these element will be:
A. \( A_{3} B_{2} \)
в. \( A_{2} B_{3} \)
\( \mathrm{c} \cdot A B_{3} \)
D. \( A_{6} B_{3} \)


An object of mass \( m \) slides down a hil
of height \( h \) and of arbitrary shape and stop at the bottom because of friction.
The coefficient of friction may be different for different segments of the path. Find the work required to return the object to its initial position along the same path by by a tangential force
A \( . m g h \)
в. 2 тун
c. \( -m g h \)
D. It cant be calculated


Solve :
\( \frac{1}{1.2}+\frac{1}{2.3}+\ldots . .+\frac{1}{n(n+1)}=? \)


Very Short Answer Types:
Give a specific scientific term for each
of the following. Phase in the cell cycle when protein and RNA are synthesized.


A shopkeeper buys a tin for \( R s .50 \) and
sells it for \( R s .46 . \) Find his loss or gain
percentage?
A. \( 4 \% \) loss
B. 8\% loss
c. \( 4 \% \) gain
D. 8\% gain


Evaluate: \( \int \frac{x e^{x}}{(x+1)^{2}} d x \)


What is the total number of children
entered in to the library between \( 0-30 \)
hours?
istogran
\( A \cdot 45 \)
в. 55
\( c .100 \)
\( D, 11 \)


Expand \( (5-6 \sqrt{3})^{2} \)
A. \( 133+30 \sqrt{3} \)
В. \( 133-60 \sqrt{3} \)
D. \( 83+30 \sqrt{3} \)


The surface area of a cube whose
volume is \( 343 m^{3} \) is \( \mathrm{K} \mathrm{cm}^{2} \) the value of
\( \mathrm{K} \) is
A . 180
B. 364
\( c \cdot 294 \)
D. 394


The stability of an ionic compound is mostly due to:
A. ionization energy
B. electron affinity
c. lattice energy
D. electronegativity


The following reactions take place in the blast furnace in the preparation of impure iron. Identify the reaction pertaining to the formation of the slag.
A \( \cdot F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(l)+3 C O_{2}(g) \)
B . \( \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+\operatorname{CO}_{2}(g) \)
\( \mathbf{c} \cdot \operatorname{CaO}(s)+\operatorname{Si} O_{2}(s) \rightarrow \operatorname{CaSiO}_{3}(s) \)
D \( \cdot 2 C(s)+O_{2}(g) \longrightarrow 2 C O(g) \)


The distance (in \( \mathrm{km} \) ) of 40 engineers from their residence to their place of
work were found as follows:
\[
\begin{array}{ccccccccc}
5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 \\
19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 \\
7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18
\end{array}
\]
\( \begin{array}{llllll}\mathbf{1 2} & \mathbf{1 4} & \mathbf{2} & \mathbf{9} & \mathbf{6} & \mathbf{1 5}\end{array} \) 15
\[
7
\]
What is the empirical probability that an engineer lives:
(i) less than \( 7 k m \) from her place of
work?
(ii) more than or equal to \( 7 k m \) from her
place of work?
(iii) within \( \frac{1}{2} k m \) from her place of work?


The amplitude and frequency of a wave represented by the equation :
\( \boldsymbol{Y}=\mathbf{2} \boldsymbol{A} \cos ^{2}(\boldsymbol{k} \boldsymbol{\gamma}-\boldsymbol{\omega} \boldsymbol{t}) \) are :
A \( \cdot 2 A, \frac{\omega}{2 \pi} \)
в. \( A, \frac{\omega}{\pi} \)
\( c \cdot \sqrt{A}, \frac{\omega}{\pi} \)
D. \( \sqrt{A}, \frac{\omega}{2 \pi} \)


A dog weighing \( 5 \mathrm{kg} \) is standing on a flat boat so that it is 10 metres from the shore. It walks \( 4 \mathrm{m} \) on the boat towards
the shore and then halts. The boat
weighs \( 20 \mathrm{kg} \) and one can assume that there is no friction between it and water
The dog from the shore at the end of this
time is:
A. \( 3.4 \mathrm{m} \)
B. \( 6.8 m \)
c. \( 12.6 \mathrm{m} \)
D. \( 10 \mathrm{m} \)


The main constituent of petroleum gas is ethane:
A . True
B. False


What is the difference between
molecular mass and formula unit mass
\( ? \)
A. Molecular mass is for molecules, and formula mass is for ionic compounds.
B. Molecular mass is for ionic compounds, and formula mass is for molecules
c. Both are exactly same
D. None of above.


Bordered pits are formed in :
A. Sieve cells
B. Vessel wall
c. Campanion cells
D. Sieve tube wall


Of 28 people in a park, 12 are children and the rest are adults. 8 people have to leave at \( 3 \mathrm{pm} ; \) the rest do not. If, after 3
\( \mathrm{pm}, \) there are 6 children still in the park, how many adults are still in the park?
A . 14
B . 18
c. 15
D. 16


An ideal monoatomic gas is taken
around the cycle \( A B C D A \) as shown in
\( \boldsymbol{P}-\boldsymbol{V} \) diagram.The Work done during
the cycle is
\( A \cdot P V \)
в. \( 0.5 P V \)
\( c .2 P V \)
D. \( 3 P V \)


Consider a gas with density \( \rho \) and \( C \) as
the root mean square velocity of its molecules contained in a volume. If the
system moves as a whole with velocity
then the pressure exerted by the gas
is :
\( \mathbf{A} \cdot \frac{1}{3} \rho C^{2} \)
B \( \cdot \frac{1}{3} \rho(C+v)^{2} \)
c. \( \frac{1}{3} \rho(C-v)^{2} \)
D \( \cdot \frac{1}{3} \rho\left(C^{2}-v^{2}\right) \)


A fan produces a feeling of comfort because:
A. A fan supplies cool air
B. Of the evaporation of sweat
c. Fan increase the humidity in air
D. Fan decrease the humidity in air


Application of adsorption is/are:
A. For desiccation or dehumidification
B. Heterogeneous catalysts
C. For both heterogenous catalysts and for desiccation o dehumidification
D. None of the above


The lines represented by \( 3 x+4 y=8 \) and \( p x+2 y=7 \) are parallel. Find the value of
\( p \)


Depression in f.pt. is more pronounced if camphor is used as a solvent in place of water for same mass of solute and
solvent.
If true enter \( 1, \) if false enter 0


For the circuit shown in the Figure, the current through the inductor is \( 0.9 A \)
while the current through the condenser
is \( 0.4 A \)
A. current drawn from generator \( 1=1.13 \mathrm{A} \)
B. \( \omega=\frac{1}{(1.5 L C)} \)
\( \mathbf{C} \cdot I=0.5 \mathrm{A} \)
\( D \cdot I=0.6 A \)


The myelin sheath provides \( \ldots \ldots . . \) to the
axon.
A. Mechanical support
B. Electrical insulation
c. Both A and B
D. None of the above


toppr
Q Type your question-
\( F_{2} . \) The object weighs \( 10 \mathrm{N} \). There is
negligible friction between the rods and
cords. Angle \( \boldsymbol{\theta} \) is \( \mathbf{9 0}^{\circ} \)

Which row of the table gives an angle \( \theta \)
of \( 90^{\circ} ? \)
\( F_{1} / N \)
\( 6 . \)
4.0
8.0
8.0
\( A \)
B. B
\( c \)
D


The magnetic flux through a loop is varying according to a relation \( \phi= \) \( 6 t^{2}+7 t+1 \) where \( \phi \) is in milliweber
and \( t \) is in second. What is the e.m.f.
induced in the loop at \( t=2 \) second?


Which is enolisable?
A. Benzophenone
B. 2, 4 - pentanedione
c. phenyl- t- butyl ketone
D. All the above


The value of \( \sin 50^{\circ}-\sin 70^{\circ}+\sin 10^{\circ} \)
is
A . 0
B.
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\sqrt{2}} \)


A cricket ball of mass 120 g is moving with a velocity of \( 12 \mathrm{m} s^{-1} . \) It turns back
and moves with a velocity of \( 20 \mathrm{m} s^{-1} \)
when hit by a bat. Find the impulse if the force acts on the ball for 0.02 s.
A \( \cdot 4 \) N
B. 8 N s
c. 32 N \( s \)
D. 192 N s


The area of the curve \( y^{2}=(7-x)(5+ \)
\( x \) ) above \( x \) -axis and between the
ordinates \( x=-5 \) and \( x=1 \) is \( n \pi \). Find
\( \boldsymbol{n} \)


In the given circuit, the steady state
voltage drop
across the capacitor \( C \) is
\( A \cdot \frac{V r_{r}}{r_{2}+r_{3}} \)
B. \( \frac{V r_{r}}{r_{1}+r_{3}} \)
\( c \cdot \frac{V r_{r}}{r_{1}+r_{2}} \)
D. \( \frac{V r_{r}}{r_{1}+r_{2}} \)


If the constant term of the binomial expansion \( \left(2 x-\frac{1}{x}\right)^{n} \) is \( -160, \) then \( n \) is equal to -
A .4
B. 6
c. 8
D. 10


State whether the given statement is
true or false :

Friction is necessary to perform many tasks
A. True
B. False


'Raman Effect' is named after which of
the following Indian scientists?
A. Dr. A. P. J. Abdul Kalam
B. C. V. Raman
c. Homi Jehangir Bhabha
D. Jagadish Chandra Bose


When 0.5 g of sulfur is burnt to \( S O_{2} 4.6 \) kJ heat is liberated. What is the
enthalpy of formation of sulfur dioxide? \( (S=32 \text { and } O=16) \)
\( A \cdot+294.4 \mathrm{kJ} \)
B . \( +147.2 \mathrm{kJ} \)
c. - -147.2 kJ
D . -294.4 kJ


A piece of resistance wire has
resistance of \( 4 \Omega . \) Its diameter is
doubled. Now its resistance will be :
\( \mathbf{A} \cdot 8 \Omega \)
B. 2\Omega
c. \( 4 \Omega \)
D. 12


Three roots of the equation, \( x^{4}-p x^{3}+ \)
\( \boldsymbol{q} \boldsymbol{x}^{2}-\boldsymbol{r} \boldsymbol{x}+\boldsymbol{s}=\boldsymbol{0} \) are \( \tan \boldsymbol{A}, \tan \boldsymbol{B} \boldsymbol{\&} \)
\( \tan C \) where \( A, B, C \) are the angles of \( a \) triangle. The fourth root of the bi
quadratic is
A \( \frac{s^{2}-s q+s}{r+(s-q) p} \)
B. \( \frac{s^{2}+s q+s}{r+(s+p) q} \)
c. \( \frac{s^{2}-s q+s}{r-(s-p) q} \)
D. \( \frac{s^{2}-s q-s}{r-(s-q) p} \)


Write the equation for the laboratory preparation of Lead sulphate from lead nitrate using sulfuric acid.


A charged particle \( X \) moves directly towards another charged particle Y. For the 'X plus Y' system, the total
momentum is p and the total energy is
\( E \)
This question has multiple correct options
A. p and \( E \) are conserved if both \( x \) and \( Y \) are free to move
B. (A) is true only if \( x \) and \( Y \) has similar charges.
c. If \( Y \) is fixed, \( E \) is conserved but not \( p \)
D. If \( Y \) is fixed, neither E nor \( p \) is conserved


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{2} & \mathbf{1} & \mathbf{0} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{U}_{1}, \boldsymbol{U}_{2}, \boldsymbol{U}_{3} \) be
column
matrices satisfying \( \boldsymbol{A} \boldsymbol{U}_{1}= \) \( \left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], A U_{2}=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], A U_{3}=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right] . \) If \( U \) is
\( 3 \times 3 \) matrix whose columns are
\( \boldsymbol{U}_{1}, \boldsymbol{U}_{2}, \boldsymbol{U}_{3}, \) then \( |\boldsymbol{U}|= \)
A . 3
B. -3
\( c \cdot \frac{3}{2} \)
\( D \)


If the energy and momentum of a photon are \( \mathrm{E} \) and \( \mathrm{p} \) respectively, then the velocity of photon will be This question has multiple correct options
A. \( \frac{E}{p} \)
\( ^{\text {В }}\left(\frac{E}{p}\right)^{2} \)
\( c \cdot E p \)
D. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)


Find the sum the infinite G.P.:
\( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots \dots \)
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{2} \)
c. \( \frac{49}{27} \)
D. 8


In cardiac cycle, maximum time is
taken by
A. Atria systole
B. Atria diastole
c. Ventricle systole
D. Ventricle Diastole


A planar structure of length L and width Wis made of two different optical
media of refractive indices \( n_{1}=1.5 \)
and \( n_{2}=1.44 \) as shown in figure. If \( L> \)
\( >W, \) a ray entering from end \( A B \) will
emerge from end \( \mathrm{CD} \) only if the total internal reflection condition is met
inside the structure. For \( \boldsymbol{L}=\mathbf{9 . 6 m}, \) if
the incident angle \( \theta \) is varied, the
maximum time taken by a ray to exit
the plane \( \mathrm{CD} \) is \( t \times 10^{-9} \mathrm{s} \), where \( \mathrm{t} \) is
[Speed of light \( c=3 x \)
\( \left.10^{8} \mathrm{m} / \mathrm{s}\right] \)


Find the common difference \( d \) for an \( A P \)
where \( a_{1}=10 \) and \( a_{20}=466 \)


Natural rubber is obtained as 'latex'
which is a milky, white fluid from
rubber trees. Latex is a:
A. mixture of rubber and gum
B. colloidal dispersion of rubber in water
c. solution of rubber in water
D. paste of rubber, clay and water


Obtain the differential equation of the
family of circles \( x^{2}+y^{2}+2 g x+ \)
\( 2 f y+c=0 ; \) where \( g, f \) and \( c \) are
arbitrary constants.
\( ^{A} \cdot\left[1+\left(y^{\prime}\right)^{2}\right] y^{\prime \prime}-3 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
\( ^{\mathrm{B}}\left[1+\left(y^{\prime \prime}\right)^{3}\right] y-2 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
\( ^{\mathbf{C}}\left[1+\left(y^{\prime \prime}\right)^{2}\right] y^{\prime \prime}-3 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
D. None of these


Water plays an important role in :
A. hydrological cycle
B. water cycle
c. both A and B
D. none of above


The gas which causes yellowing of Tajmahal:
A \( . H_{2} S \)
в. \( S O_{2} \)
\( c \cdot C O_{2} \)
D. \( N O_{2} \)


A radioactive element A decays by the sequence and with half-lives given below:
\( \boldsymbol{A} \frac{\boldsymbol{\alpha}}{\mathbf{3 0} \text { min }} \boldsymbol{B} \frac{\boldsymbol{2} \boldsymbol{\beta}}{\boldsymbol{2} \text { days }} \boldsymbol{C} \)
Which of the following statements about this system are correct?
This question has multiple correct options
A. The mass number of B is greater than A
B. After two hours, less than \( 10 \% \) of the intial A is left
c. Maximum amount of B present at any time is less than \( 50 \% \) of the initial amount of \( A Q \)
D. The atomic numbers of A and C are the same


Match List - I (Mixture to be separated) with the List - II (Method used) and
select the correct option using the
codes given below.

List -I (mixture to be \( \quad \) List - II (Method separated) used)
\( (I) \)
(A) Petroleum products \( \quad \) Chromatography
\( (B) \) Camphor and rock salt
\( (I I) \) Centrifugation
\( (C) \) Cream from milk
\( (I I I) \) Sublimation
\( (D) \) Coloured components
\( (I V) \) Fractional in a dye distillation
\( \mathbf{A} \cdot A-I, B-I I, C-I I I, D-I V \)
B . \( A-I I, B-I V, C-I I I, D-I \)
c. \( A-I V, B-I I I, C-I, D-I I \)
D. \( A-I V, B-I I I, C-I I, D-I \)


If the standard electrode potential
constant for a cell is \( 2 V \) at \( 300 K \) the
equilibrium constant (K) for the
reaction
\( Z n(s)+C u^{2+}(a q) \rightleftharpoons Z n^{2+}(a q)+ \)
\( C u(s) \) at \( 300 K \) is approximately.
\( \left(\boldsymbol{R}=\mathbf{8} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}, \boldsymbol{F}=\right. \)
\( 96000 C m o l^{-1} \)
A \( \cdot e^{16} \)
B. \( e^{32} \)
\( c \cdot e^{-160} \)
D. \( e^{-8} \)


A bag A contains 4 green and 6 red balls. Another bag B contains 3 green and 4 red balls. If one ball is drawn from
each bag, find the probability that both are green.
\( A \cdot 13 / 70 \)
B. \( 1 / 4 \)
\( c \cdot 6 / 35 \)
D. 8/35


Classify which of the following pair is a compound and a mixture?
A . Air, ocean water
B. Water, glucose
c. Glucose, Salt
D. Water, air


Milk of magnesia used as a medicine
for treating indigestion is a substance
that -
A. Helps in disintegration of food products leading to their facile metabolism.
B. Combines with gastric hydrochloric acid thereby enhancing the latter's efficiency
C. Improves the enzymatic activities inside the stomach.
D. Neutralises excess acidity, providing a buffered medium inside the stomach.


Three men \( A, B \) and \( C \) of masses
\( 40 k g, 50 k g \) and \( 60 k g \) are standing on
a plank of mass \( 90 \mathrm{kg} \), which is kept on
a smooth horizontal plane. If \( A \) and \( C \)
exchange their positions then mass \( B \)
will shift
A. \( 1 / 3 m \) towards left
B. \( 1 / 3 m \) towards right
c. will not move w.r.tground
D. \( 5 / 3 m \) towards left


If \( A \) and \( B \) are independent events of \( a \) random experiment such that \( P(A \cap B)=\frac{1}{6} \) and \( P(\bar{A} \cap \bar{B})=\frac{1}{3} \)
then \( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{4}, \frac{1}{3} \)
B. \( \frac{1}{2}, \frac{1}{3} \)
c. \( \frac{1}{2}, \frac{1}{5} \)
D. \( \frac{2}{3}, \frac{1}{5} \)


What is the charge of 96 amu of \( S^{2-} ? \)
A \( .2 C \)
B . \( 3.2 \times 10^{-19} C \)
c. \( 9.6 \times 10^{-19} C \)
D. \( 6 C \)


Complete the following equation:-
\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{N H}_{2} \boldsymbol{O H} \rightarrow \)


An electron is at ground state of the \( \mathrm{H} \)
atom. Minimum energy required to
excite the \( H \) atom into second excited
state is:
A. 13.6 eV
B. 12.1 eV
c. 10.2 eV
D. 3.4 eV


The cambium is
A. Apical meristem
B. Lateral meristem
C . Intercalary meristem
D. Secondary meristem


\( \underset{\boldsymbol{n} \rightarrow \infty}{\boldsymbol{L} \boldsymbol{t}} \sum_{\boldsymbol{r}=0}^{\boldsymbol{n}-\mathbf{1}} \frac{\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{r}^{2}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{\pi}{4} \)


Which of the following is not formed in
the reaction of \( X e \) with \( F_{2} ? \)
A. \( \mathrm{xeOF}_{4} \)
в. \( \mathrm{XeF}_{2} \)
c. \( \mathrm{xeF}_{4} \)
D. XeF \( _{6} \)


A vessel is in the form of a hollow
hemisphere mounted by a hollow cylinder. The diameter of the
hemisphere is \( 14 \mathrm{cm} \) and the total
height of the vessel is \( 13 \mathrm{cm} \). Find the
inner surface area of the vessel.


The sum of four numbers in AP is 176
The product of 1st and last is 1855. The mean of middle two is
\( \mathbf{A} \cdot 42 \)
B. 41
c. 44
D. 53


\( X e F_{6} \) on hydrolysis produces:
A \( \cdot X e O F_{4} \)
в. \( X e O_{2} F_{2} \)
\( \mathbf{c} \cdot X e O_{3} \)
D. \( X e O_{2} \)


\( \frac{1}{\text { The vaue of } 13} \frac{1}{5} .17^{\frac{1}{5}}-(221)^{\frac{1}{5}} \) is


Pick up the true fish from the following:
A. Devil fish
B. Flying fish
c. cray fish
D. Cuttle fish


Suresh and Ramesh together invested
144000 rupees in the ratio 4: 5 and
bought a plot of land After some year
they sold it at a profit of \( 20 \% . \) What is the profit each of them got?


Multimolecular colloids are present in:
This question has multiple correct options
A. sol of sulphur
B. sol of protein
c. sol of gold
D. soap solution


The structure of \( X e F_{2} \) involves
hybridization of the type:
\( A \cdot s p^{3} \)
B. \( d s p^{2} \)
\( \mathrm{c} \cdot s p^{3} d \)
D. \( s p^{3} d^{2} \)


Figure shows a negatively charged ebonite rod A which is brought near an uncharged metal sphere P touching the other uncharged metal sphere \( Q \). Both
the spheres \( P \) and \( Q \) stand on separate insulating stands. Keeping rod \( A \) in position, sphere \( Q \) is removed by holding the insulating stand of it. State the kind of charge on
spheres \( P \) and \( Q \). Give reason to your
answer.
A. Spheres \( Q \) and \( P \) has positive charge
B. Spheres Q and P has negative charge
c. sphere \( Q \) has negative charge and sphere \( P \) has positive charge
D. spheres \( Q \) and \( P \) has no charge


Write \( \tan ^{-1}\left[\frac{\sqrt{1+x^{2}}-1}{x}\right], x \neq 0 \)
the simplest form.


toppr
Q Type your question
with decrease in the depth?
\( A \)
\( B \)
\( c \)
\( D \)


There are two paths to prepare a compound \( (\boldsymbol{A})(2-\text { methyl }-\text {hex }- \)
1en \( -3-\text { yne }) . \) Which of the following
statements is correct?
A. Path \( I \) is feasible
B. Path \( I I \) is feasible
c. Both paths are feasible
D. Both paths are not feasible


Draw the right triangle whose sides are \( 3 \mathrm{cm}, 4 \mathrm{cm} \) and \( 5 \mathrm{cm} \) and construct its
centroid


There are 3 bags each containing 5
white balls and 2 black balls and 2 bags each containing 1 white balls and 4 black balls, a black ball having been drawn, find the chance that it came from the first group.
A \( \cdot \frac{28}{43} \)
в. \( \frac{15}{43} \)
c. \( \frac{15}{28} \)
D. \( \frac{13}{28} \)


Below are the heating-cooling curves for
five different substance. Heat is added
uniformly to the same mass of each
substance at exactly the same rate.
Which substance has the greatest
latent heat of fusion?
\( A \)
\( B .2 \)
\( c \cdot 3 \)
D. 4
\( E \)


A system is provided 50 joule of heat and work done no the system is 10 J. The change in in iternal energy during the process is
A . \( 40 \mathrm{J} \)
B. 60 J
c. 80
D. 50 J


A simple harmonic motion has an amplitude \( A \) and time period \( T . \) Find the time required by it to travel directly from \( \boldsymbol{x}=-\frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}}, \) to \( \boldsymbol{x}=\frac{\boldsymbol{A}}{\sqrt{\mathbf{2}}} \)


Many insects, such as ants, inject
formic acid, a weak acid, when they bite
or sting. Describe the type of compound that should be used to treat the bite.


What would be the reactant and reagent
used to obtain 2,4 dimethylpentan-3-ol?
A. Propanal and propyl magnesium bromide.
B. 3 - Methylbutanal and 2 - methyl magnesium iodide.
C. \( 2, \) 2-Dimethylpropanone and methyl magnesium iodide
D. 2 - Methylpropanal and isopropyl magnesium iodide


\( C r O_{5} \) has oxidation number of \( C r \) as
+6. This implies it has two peroxy linkages. If true enter 1 , else enter 0
A.


The mean of two samples of sizes 200 and 300 were found to be 25 and 10
respectively. Their standard deviations
were 3 and 4 respectively. The varience of combined sample size of 500 is
\( \mathbf{A} \cdot 64 \)
B. 65.2
c. 67.2
D. 64.2


The impression of the image formed on the retina of the human eye remains for
about:
A \( \cdot \frac{1}{10} s \)
в. \( \frac{1}{24} s \)
c. \( \frac{1}{16} s \)
D. \( \frac{1}{20} s \)


If the distance of the point on \( y=x^{4}+ \)
\( 3 x^{2}+2 x \) which is nearest to the line
\( \boldsymbol{y}=2 \boldsymbol{x}-\mathbf{1} \) is \( \mathbf{p}, \) Find \( \mathbf{5} \boldsymbol{p}^{2} \)


Common characteristic between
Bryophytes and pteridophytes is
A. Vascularization
B. Terrestrial habitat
c. water for fertilization
D. Independent sporophyte


Two coils \( A \) and \( B \) having turns 300 and 600 respectively are placed near each other, on passing a current of 3.0 ampere in \( A \), the flux linked with \( A \) is 1.2
\( x 10^{-4} \) weber and with \( B \) it is \( 9.0 \times 10^{-5} \)
weber. The mutual induction of the
system is:


Find the values of constant \( a, b \) and \( c \) so
that
(i) \( \lim _{x \rightarrow 0} \frac{a x e^{x}-b \log (1+x)+c x e^{-x}}{x^{2} \sin x}= \)
2


Lanthanides and actinides are
recognised as:
A. \( s \) - block elements
B. \( d \) -block elements
c. \( f \) -block elements
D. \( p \) -block elements


Drops of liquid of density \( d \) are floating
half immersed in a liquid of density \( \rho . \) If
the surface tension of liquid is \( \boldsymbol{T} \) then the radius of the drop will be \( (\boldsymbol{d}= \) density of liquid drop).
A \( \cdot \sqrt{\frac{3 T}{g(2 d-\rho)}} \)
в. \( \sqrt{\frac{6 T}{g(2 d-\rho)}} \)
c. \( \sqrt{\frac{2 T}{g(2 d-\rho)}} \)
D. \( \sqrt{\frac{3 T}{g(4 d-3 \rho)}} \)


Define autotrophs.


When a glass rod is rubbed with silk, it
is said to be positively charged. Which of the following statement is true?
A. Electrons move from silk to glass
B. Electrons move from glass to silk
c. Protons move from silk to glass
D. Protons move from glass to silk


A solenoid is \( 1.5 m \) long and its inner
diameter is \( 4.0 \mathrm{cm} \). It has 3 layers of
winding's of 1000 turns each and carries a current of 2.0 amperes.The magnetic flux for a cross-section of the solenoid is nearly.
A . \( 4.1 \times 10^{-5} \) weber
B. \( 5.2 \times 10^{-5} \) weber
c. \( 6.31 \times 10^{-3} \) weber
D . \( 2.5 \times 10^{-7} \) weber


\( \alpha-D- \) fructofuranose is a aldopentose
A. True
B. False


Two fixed frictionless inclined plane
making an angle \( 30^{\circ} \) and \( 60^{\circ} \) with the
vertical are shown in the figure. Two blocks \( A \) and \( B \) are placed on the two planes. What is the relative vertical
acceleration of A with respect to B?


Find the value of \( x \) in the following:
\( \cos 2 x=\cos 60^{\circ} \cos 30^{\circ}+ \)
\( \sin 60^{\circ} \sin 30^{\circ} \)


Cell constant \( = \)
A. Resistance \( \times \) conductance
B. Resistance \( \times \) specific conductance
C . Conductance \( \times \) specific resistance
D. Resistance \( \times \) specific resistance


In Young's double slit experiment the two slits are illuminated by light of
wavelength \( 5890^{\circ} \mathrm{A} \) and the distance between the fringes obtained on
the screen is \( 0.2^{\circ} . \) If the whole
apparatus is immersed in water then
the angular fringe width will be (refractive index of water is \( 4 / 3 \) ):
A .0 .30
then 0.0 .030
в. \( 0.15^{\circ} \)
\( c \cdot 15 \)
D. \( 30^{\circ} \)


The half life for \( \alpha \) -decay of uranium \( 92 U^{228} \) is \( 4.47 \times 10^{8} y r . \) If a rock
contains \( 60 \% \) of original \( _{92} U^{228} \) atoms, then its age is \( [\operatorname{take} \log 6=0.778, \log 2=0.3] \)
A \( \cdot 1.2 \times 10^{7} y r \)
B. \( 3.3 \times 10^{8} y r \)
c. \( 4.2 \times 10^{9} y r \)
D. \( 6.5 \times 10^{9} y r \)


The Sl unit of charge is.....
A. ohm
B. volt
\( c . \) farad
D. coulomb


If the pressure of a gas is doubled then its thermal conductivity will :
A. remain constant
B. decrease
c. decrease exponentially
D. increase


The common characteristics between
tomato and potato will be maximum at the level of their
A. Family
B. Order
c. Division
D. Genus


The correct structure of monomers of
buna \( -\boldsymbol{N} \) is:
A \( \cdot C H_{2}=C H-C H=C H_{2}+C H_{2}=C H-C N \)
\( B \)
\( c \)
\( D \)


If the mean and variance of a binomial
distribution are 4 and 2 respectively,
then the probability of 2 successes of that binomial variate \( \boldsymbol{X}, \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{219}{256} \)
c. \( \frac{37}{256} \)
D. \( \frac{7}{64} \)


If the earth stops rotating about its axis, then the magnitude of gravity
A. increases everywhere on the surface of earth
B. will increase only at the poles
c. will not change at the poles
D. All of the above


Reaction of iron filings with powdered
sulfur is a \( _{--}- \) - process.
A. precipitation
B. oxidation-reduction
C. distillation
D. hydration
E. condensation


Latha dropped some crystals of
\( K M n O_{4} \) in a beaker of water and
observing to know what happens.What
is the phenomenon that occurs in the experiment?


Calculate the concentration of solution
which contains 5 g of salt dissolved in 100 g water
A . 5.26
B. 9.52
\( c \cdot 4.54 \)
D. 4.76


Which of the following chemical bonds
has most ionic character?
A . \( L i H \)
в. \( H F \)
\( \mathrm{c} . \mathrm{CsH} \)
D. \( H I \)


Define Rectangular components of
vector


State whether true or false.
During upward motion of a body
projected vertically upward, the angle
between velocity and 'g' is \( 90^{\circ} \)
A. True
B. False


(a) Volume of one molecule of
\( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{d}=\mathbf{1} \boldsymbol{g}^{-\mathbf{3}}\right) \)
(b) Radius of \( \boldsymbol{H}_{2} \boldsymbol{O} \) molecule (assuming if spherical)


Duct of Wirsung is a duct of
A . Liver
B. Pancreas
c. Gall bladder
D. Duodenum


Water barometer is possible provided barometer tube is \( _{--}---m \) long.
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D. 11


Assertion : "The Biological Species" concept helps us to ask how species are formed.
Reason : The concept of biological species focuses our attention on the
question of how reproductive isolation
comes about.
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


The particle of a medium vibrates about their mean position whenever a wave travels through that medium. The phase
difference between the vibrations of two
such particles
A. varies with time only
B. varies with distance separating them only
c. varies with time as well as distance
D. is always zero


What fraction of the candles on the cake
is lit?
\( A \cdot \frac{4}{7} \)
B. \( \frac{4}{3} \)
\( c \cdot 3 \)
7
\( D \cdot \frac{1}{1} \)
4


The product of two consecutive natural
numbers is \( 12 . \) The equation form of this statement is
A. \( x^{2}+2 x-12=0 \)
B . \( x^{2}+1 x-12=0 \)
c. \( x^{2}+1 x+12=0 \)
D. \( x^{2}+2 x+12 \)


All the atoms of same element have
same
A. mass number
B. atomic number
c. atomic mass
D. All of the above


The standard emf of a galvanic cell involving cell reaction with \( n=2 \) is found to be \( 0.295 \mathrm{V} \) at \( 25 \mathrm{C}^{\circ} \). The
equilibrium constant of the reaction would be
(Given, \( \boldsymbol{F}=\mathbf{9 6 5 0 0} \boldsymbol{C m o l}^{-1}, \boldsymbol{R}= \)
\( \left.8.314 J K^{-1} m o l^{-1}\right) \)
A \( .2 .0 \times 10^{11} \)
B . \( 4 \times 10^{12} \)
\( c \cdot 1 \times 10^{2} \)
D. \( 1 \times 10^{10} \)


Spring scale reads \( 20 N \) as it pulls a
\( 4.0 \mathrm{kg} \) object across a table. What is the
magnitude of the force exerted by object on the spring scale?
A. \( 40 N \)
в. \( 20 N \)
c. \( 4 N \)
D. \( 5 N \)


A car takes 1 hour less to cover a
distance of \( 200 \mathrm{km} \) if its speed is
increased by \( 10 \mathrm{km} / \mathrm{hr} \), than its usual
speed. What is the usual speed of the
car.


Find the product of \( x^{2} y z \times x y^{2} z^{3} \)
A \( \cdot x^{3} y^{3} z^{4} \)
В. \( x^{3} y^{3} z^{3} \)
c. \( x^{3} y^{4} z^{3} \)
D. \( x^{3} y^{3} z \)


Evaluate :
\( (-\sqrt{-1})^{4 n+3}, n \in N \)
A . \( -i \)
B.
\( c \cdot 1 \)
D. -


Solubility of \( A g B r \) will be minimum in:
A. pure water
в. \( 0.1 \mathrm{M} \) СаВг\( _{2} \)
c. \( 0.1 \mathrm{M} \) NaBr
D. \( 0.1 \mathrm{M} \) AgNO \( _{3} \)


H-atom is exposed to electromagnetic radiation of \( \lambda=1025.6 A \) and excited
atom gives out induced radiations. What is the minimum wavelength of these induced radiations?
A. \( 102.6 \mathrm{nm} \)
B. \( 12.09 \mathrm{nm} \)
c. \( 121.6 \mathrm{nm} \)
D. \( 810.8 \mathrm{nm} \)


A concentrated solution of lead nitrate
in water can be stored in
A. an iron vessel
B. a copper vessel
c. a zinc vessel
D. a magnesium vessel


Cathode ray particles have a mass of times that of hydrogen
nucleus.
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{1}{10} \)
\( c .1840 \)
D. \( \frac{1}{1840} \)


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


Choose the correct options.
Having two eyes facilitates in:
A. Increasing the field of view
B. Giving 3 dimensional view
C. Developing the concept of distance / size.
A. A only
B. A and B only
c. B only
D. \( A, B \) and \( C \)


A thermometer reads \( 0^{\circ} \mathrm{C} \) as \( 10^{\circ} \mathrm{C} \) and
\( 100^{\circ} \mathrm{C} \) as \( 90^{\circ} \mathrm{C} \) then
Find the correct temperature if the
thermometer reads \( 20^{\circ} \mathrm{C} \)
A \( \cdot 20^{\circ} \mathrm{C} \)
B . \( 12.5^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 25^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)


Find the cube root of 614125 using
prime factorization:
A . 65
B. 75
c. 85
D. 95


A car is moving on a frictionless (in the radial direction) circular banked road,
with a banking angle of \( 15^{\circ}, \) find the
velocity of the car. Mass of car is \( 600 k g \), the radius of the
circular road \( =10 m \)
Assume \( \boldsymbol{g}=\mathbf{9 . 8 1} \boldsymbol{m} / \boldsymbol{s}^{2} \)
A. \( 4.26 \mathrm{m} / \mathrm{s} \)
B. \( 5.12 \mathrm{m} / \mathrm{s} \)
c. \( 51.2 \mathrm{m} / \mathrm{s} \)
D. 42.6 m/s


\( Q \) туре уочт question
rod. The rod can revolve in a vertical
plane around the point A. What horizontal velocity must be imparted to the end of the rod \( C \) to deflect it to the
horizontal position? (Given acceleration
due to gravity \( =g \)
4. \( \sqrt{2 g} \)
\( 3 \cdot \sqrt{2 \cdot 4 g} \)
\( c \cdot \sqrt{3 g} \)
\( -\sqrt{3.60} \)
0


Assertion
\( S O_{2} \) and \( S O_{3} \) obey 'law of multiple
proportions'.
Reason
Every sample of \( S O_{2} \) contains 1 part
sulphur and 1 part oxygen by mass. Read the above assertion and reason and choose the correct option regarding
it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
c. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following benefication processes is used for the mineral,
\( A l_{2} O_{3} \cdot 2 H_{2} O ? \)
A. Froth-flotation
B. Liquation
c. Leaching
D. Magnetic separation


The sum of \( 15, x, 51,2 x+3 \) is 114 find
\( x \)


As compared to whole body, the head of new born human baby is
A. One-third
B. One-half
c. one-fifth
D. One-fourth


Ideal solution is formed when its
components:
A. have zero heat of mixing only
B. have zero volume change on mixing only
C. have zero heat of mixing and zero volume change
D. can be converted into gases


Match the following
Dominant
gametophytic
generation
a. Bog
moss
2
True moss
Riccia fluitans .
b. Moss
3. Aquatic
3. Riccia fluitans
4. Show heterospory
d. Aryophyte
A. \( 1-a, 2-c, 3-d, 4-b \)
B. \( 1-d, 2-a, 3-c, 4-b \)
C. \( 1-b, 2-c, 3-a, 4-d \)
D. \( 1-a, 2-d, 3-c, 4-b \)


1 calorie is equal to
A. 2.18 joules
B. 3.18 joules
C. 4.18 joules
D. 5.18 joules


Cedarwood oil is obtained from the
heartwood of
A. Cedrus
B. Thuja occidentalis
c. Tagetes
D. Juniperus


If the mean deviation of the numbers 1
\( \mathbf{1}+\mathbf{d}, \mathbf{1}+\mathbf{2} \mathbf{d}, \ldots, \mathbf{1}+\mathbf{1 0 0} \mathbf{d} \) from their
mean is \( 255, \) then the dis equal to
A . 10.0
в. 20.0
c. \( 10 . \)
D. 20.2


A wire in the shape of an equilateral
triangle with sides of length \( 1.00 m \) is
kept in a magnetic field of \( 2.00 T \)
pointing to the right. Find out the magnitude of the magnetic flux passing through the triangle?
A. \( 0 W b \)
в. \( 1.00 \mathrm{Wb} \)
c. \( 1.73 W b \)
D. 2.00Wb
E. \( 3.46 W b \)


Which pathway involves cell wall and
intercellular spaces both?
A. Vascular pathway
B. Protoplast pathway
c. symplast pathway
D. Apoplast pathway


What kind of compound is Sodium Chloride or \( N a C l \)
A. Covalent Compound
B. Electrovalent Compound
c. Co-ordinate Covalent
D. None of these


How does mass change with increase in temperature?
A. Unchanged
B. Increases
c. Decreases
D. Can't say


Among the given nutrients, milk is a
poor source of


Assertion
Newland's law of octaves of elements is
a function of their state that the
property of every eighth element is the repetition of the first.
Reason
In order to fit new elements into his
table Newland adjusted two elements in the same colum.
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.


In a triangle \( A B C \) \( \operatorname{acos}^{2}\left(\frac{C}{2}\right)+c \cos ^{2}\left(\frac{A}{2}\right)=\frac{3 b}{2}, \) then the
\( \operatorname{sides} a, b, c \)
A. Satisfy \( a+b=c \)
B. are in \( A . P \).
c. are in \( G . P \)
D. are in \( H . P \)


Explain the mechanism of 'sex
determination' in birds. How does it
differ from that of human beings?


Write the structure of
orthophosphorous acid and give its basicity.


In human body, toxic substances are detoxified in
A. Kidney
B. Lungs
c. Liver
D. Stomach


The type of food which starts digesting in stomach is
A. Fats
B. Carbohydrate
c. Protein
D. All of the above


Physical properties of isotopes are different.
A. True
B. False


From a square of uniform density, a
portion removed as shown in fig. Find
the center of mass of the remaining
portion if the side of the square is a.


Match the column


A metal sphere of mass m having cavity inside has an instantaneous upward acceleration 'a' when released from rest
fully submerged in a liquid of density \( d_{1} \)
Taking the density of the metal as \( d_{2} \)
find the volume of the cavity in the
sphere


Given \( A=\{2,3,4\}, B=\{2,5,6,7\} \)
Construct an example of each of the following
(i) an injective mapping from \( A \) to \( B \)
(ii) a mapping from \( A \) to \( B \) which is not injective.
(iii) a mapping from \( \mathrm{B} \) to \( \mathrm{A} \)


Environmental degradation means
A. Overall lowering of environmental qualities.
B. The adverse change brought in by human activities.
C . Ecological imbalance
D. All the above


Find the equation to, and the length of the perpendicular drawn from the point
(1,1) upon the straight line \( 3 x+4 y+ \)
\( 5=0, \) the angle between the axes being
\( 120^{\circ} \)


The cube root of negative integer is This question has multiple correct options
A. negative
B. complex
c. real
D. positive


A circular loop of rope angular velocity
\( \omega \) about an axis through its center on a horizontal smooth platform. Velocity of pulse (with re: ill 4 w rope) produced due to slight radial displacement given by:
\( A \cdot \omega L \)
в. \( \frac{\omega L}{2 \pi} \)
c. \( \frac{\omega L}{\pi} \)
D. \( \frac{\omega L}{4 \pi^{2}} \)


Which one of the following has highest boiling point?
A. \( H_{3} C C H_{2} C H_{2} C H_{2} C l \)
в. \( \left(H_{3} C\right)_{2} C H C H_{2} C l \)
c. \( \left(H_{3} C\right)_{3} C C l \)
D. \( H_{3} C C H_{2} C H(C l) C H_{3} \)


The number of base substitution
possible in amino acid codons is
A. 26
B. 264
\( c .535 \)
D. 549


The velocity of a body depends on time
according to the equation \( \boldsymbol{v}=\mathbf{2 0}+ \)
\( 0.1 t^{2} . \) The body is undergoing:
A. Uniform acceleration
B. Uniform retardation
c. Non-uniform acceleration
D. Zero acceleration


Find the angle of intersection of the
following curve:
\( x^{2}=27 y \) and \( y^{2}=8 x \)


If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of
these would be the most suitable?
A \( \cdot \quad m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=0 \)
в. \( \quad_{m} \frac{d^{2} x}{d t^{2}}-b \frac{d x}{d t}+k x=0 \)
c. \( _{m} \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}-k x=0 \)
D. \( _{m} \frac{d^{2} x}{d t^{2}}-b \frac{d x}{d t}-k x=0 \)


Ribozyme is
A. An enzyme, which helps in protein synthesis
B. An enzyme, which joins thymine to adenine
C. An enzyme, which helps in degeneracy
D. Exceptional to eukaryotes


The maximum number of electrons
that L shell can accommodate are :
A . 4
B. 8
c. 16
D. 32


On mixing, heptane and octane form an ideal solution. At \( 373 \mathrm{K} \), the vapour pressure of the two liquid components (heptane and octane) are \( 105 \mathrm{kPa} \) and
45 kPa respectively. Vapour pressure of the solution obtained by mixing 25 g of heptane and 35 g of octane will be :
(molar mass of heptane \( =100 \) g \( m o l^{-2} \) and of octane \( =114 \) g \( m o l^{-1} \)
A \( .96 .2 k P a \)
в. \( 144.5 k P a \)
c. \( 72 k P a \)
D. \( 36.1 k P a \)


\( 10 k g \) of hot water in a bucket at \( 70^{\circ} \mathrm{C} \)
is cooled for taking a bath adding to it
\( 20 k g \) water at \( 20^{\circ} C . \) What is the
temperature of the mixture? (Neglect the thermal capacity of the bucket)
A \( \cdot 30.67^{\circ} \mathrm{C} \)
в. \( 36.67^{\circ} \mathrm{C} \)
\( c \cdot 60.67^{\circ} C \)
D. \( 46.67^{\circ} \mathrm{C} \)


Select the correct option.
\( \mathbf{A} \cdot \Delta H_{f}[H(g)] \) is equal to \( \Delta H_{\text {atomisation}} \) of \( H_{2}(g) \)
B. \( \Delta H_{B E}[(H-H)] \) is equal to \( \Delta H_{f} \) of \( H(g) \)
\( \mathbf{C} \cdot \Delta H_{B E}[(H-H)] \) is equal to \( \Delta H_{\text {atomisation}} \) of \( H_{2}(g) \)
D. \( \Delta H_{\text {combustion}}\left[H_{2}(g)\right] \) is equal to \( \Delta H_{f} \) of \( \left[H_{2}(g)\right] \)


A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the length of a window, the top of the window being at a distance of \( 3 \mathrm{m} \) from the top of the building. If the speed of the ball at the top and the bottom of the
window are \( V_{T} \) and \( V_{B} \) respectively,
then \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s e c}^{2}\right) \)
A \( \cdot V_{T}+V_{B}=12 m s^{-1} \)
в. \( V_{T}-V_{B}=4.9 \mathrm{ms}^{-1} \)
c. \( V_{B} V_{T}=1 \mathrm{ms}^{-1} \)
D. \( \frac{V_{B}}{V_{T}}=1 \mathrm{ms}^{-1} \)


Find the equation of the circle which
passes through (2,3) and (4,5) and the centre lies on the straight line \( y- \)
\( 4 x+3=0 \)


In a class test (+3) marks are given for
every correct answer and (-2) marks are given for every incorrect answer and
no marks for not attempting any
question.
(i) Radhika scored 20 marks.
If she has got 12 correct answers, how
many questions has she attempted incorrectly?
(ii) Mohini scores (-5) marks in this test, though she has got 7
correct answers How many questions has she attempted incorrectly.


The credit for the discovery of rings of the Saturn goes to
A. Kepler
B. Galileo
c. Newton
D. copernicus


Which is the predominant phase in the life-cycle of the Bryophyte?
A. Gametophyte
B. Capsule
c. seta
D. Sporophyte


Which of the following property is not always true for metrics but in numbers?
A. \( A+B=0 \)
B. AB = BA
\( \mathrm{c} \cdot \mathrm{AB}=0 \)
D. None of the


In the circuit shown in figure. Current
through \( R_{1} \) is independent of
A \( . R_{2} \)
в. \( R_{3} \)
\( c \cdot R_{4} \)
D. All of these


Downward flow of organic and even some inorganic solutes takes place
from the leaves through the stem by way of
A. Phloem by protoplasmic streaming
B. All parenchymatous cells of the stem by diffusion of
C. Phloem by mass flow of solutes from higher turgor pressure of leaf mesophyll cells along a turgor pressure gradient in phloem cells
D. Phloem by diffusion


Conjugate base of \( \boldsymbol{H} \boldsymbol{S O}_{\boldsymbol{4}}^{-} \) is:
A \( \cdot H_{2} S O_{4} \)
B. \( S O_{4}^{2-} \)
\( c \cdot s o_{4} \)
D. \( H_{2} S O_{4}^{-} \)


Draw the molecular orbital diagram of
\( N_{2}, N_{2}+N_{2}-. \) Write their electronic
configuration, find the bond order and predict their magnetic behaviour

Arrange the above in increasing order of bond length.


State whether given statement is True
or False:

Sound travels faster in vacuum than in
air.
A. True
B. False


Two balls of same mass are dropped
from the same height \( h, \) on to the floor
The first ball bounces to a height \( \boldsymbol{h} / \mathbf{4} \) after the collision and the second ball
into a height \( h / 16 . \) The impulse applied by the first and second ball on the floor
are \( I_{1} \) and \( I_{2} \) respectively. Then
A \( \cdot 5 I_{1}=6 I_{2} \)
B \( .6 I_{1}=5 I_{2} \)
\( \mathbf{c} \cdot I_{1}=2 I_{2} \)
D. \( 2 I_{1}=I_{2} \)


Which of the following is not an attribute of enzymes?
A. They are proteinaceous in nature.
B. They speed up the rate of biochemical reactions
c. They are specific in nature.
D. They are used up in reactions


Consider the following statements for
micelles, which is/are correct?
This question has multiple correct options
A. At critical micelle concentration, several properties of solution of surfactants such as molar conductivity, surface tension and osmotic pressure change
B. Micelles from ionic surfactants can be formed only above a certain temperature called the Kraft temperature
C. Micelle formation is exothermic
D. Micelles are associated colloids


The Speed of light in vacuum is:
A \( \cdot 2 \times 10^{10} \mathrm{m} / \mathrm{s} \)
B . \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 4 \times 10^{5} \mathrm{m} / \mathrm{s} \)
D. \( 2 \times 10^{12} \mathrm{m} / \mathrm{s} \)


After working in a factory for a month, a man complains about a ringing in his ears. What might be wrong with him? What do you think may have caused his
problem? What can you suggest to him to prevent further hearing loss?


In the given figure, \( P Q \mathrm{cm}, M \) is the
mid-point of \( \boldsymbol{Q} \boldsymbol{R} \) ?
Also, \( M N \perp P R, Q S=7 \mathrm{cm} \) and \( T R= \)
\( 21 c m, \) then \( M N=? \)
\( \mathbf{A} \cdot 14 \mathrm{cm} \)
\( \mathbf{B} \cdot 12.5 \mathrm{cm} \)
c. \( 31 \mathrm{cm} \)
D. 25 cm


105 mL of pure water at \( 4^{\circ} \mathrm{C} \) is
saturated with \( N H_{3} \) gas yielding a
solution of density \( 0.9 g m L^{-1} \) and
containing \( 30 \% N H_{3} \) by mass. The
volume (in litres) of \( N H_{3} \) gas at \( 4^{\circ} C \)
and \( 775 \mathrm{mm} \) of Hg, which was used to saturate the water is (as the nearest
integer):


Steady state is represented by:
A. Getting raw materials
B. Intake of food and energy.
C. Intake of materials and energy, elimination of wastes and dissipation of energy.
D. Removal of waste products and intake of raw materials.


toppr
-०६॥
Q Type your question_
placed the ends \( (X \text { and } Y) \) of each
object, near the north pole of the bar magnet and recorded his observations
in the table below.
End Y brought End X
Object brought near near
to N pole to N pole
N pole repelled \( \quad \) N pole attracted "
N pole
attracted \( \quad \) N pole repelled
\( \begin{array}{ll}\text { N pole } & \text { N pole remains } \\ \text { remains } & \text { stationary } \\ \text { stationary } & \end{array} \)
Which of the object(s) is/are the magnet?
Bar magnet Object
A. P only
\( c \)
D. P and R only


Consider the following statements:
(a) No net force acts on a rain drop
falling vertically with a constant speed.
(b) If net force acting on the body is
zero, momentum of the body remains
constant.
(c) Particle of different masses falls
with different acceleration on earth.
(d) It is easier to start motion in a
heavier body than a lighter body. Which of the above statements are
correct?
\( A \cdot(b) \) and \( (c) \)
B. (a) and (b)
c. \( (a),(b) \) and \( (d) \)
D. All of the above


Which letter represents the wavelength
of the light in the Young's double slit
experiment?
\( A \cdot A \)
B. B
\( c . c \)
D.
\( E \)


A hollow cylinder has a charge \( q \)
coulomb within it. If \( \phi \) is the electric flux in units of volt-meter associated
with the curved surface \( \mathrm{B} \), the flux
linked with the plane surface A in units of volt-meter will be?


A glass prism of refractive index 1.5 is immersed in water of refractive index
4/3. A light ray incident normally on
face \( A B \) is totally reflected at face \( A C \) if
\( \mathbf{A} \cdot \sin \theta>8 / 9 \)
B. \( \sin \theta<2 / 3 \)
\( c \cdot \sin \theta=\sqrt{3} / 2 \)
D. \( 2 / 3<\sin \theta \leq 8 / 9 \)


A thin lens of focal length f has a diameter d of its aperture and forms an image of intensity I. Now the central part of the aperture up to a diameter \( \frac{\boldsymbol{d}}{\mathbf{2}} \) is blocked by white paper. Then This question has multiple correct options
A the focal length changes to \( \frac{f}{2} \)
B. the focal length remains the same as \( f \)
c. the intensity of the image changes to \( \frac{3 I}{4} \)
D. the intensity of the image changes to \( \frac{I}{4} \)


In household m long wire \( 2.05 \mathrm{mm} \) in
diameters often used. Find the
resistance of a \( 35.0 \mathrm{m} \) long wire. Specific resistance wire copper is \( 1.72 \times 10^{-8} \Omega-m \)


f \( e^{y}(x+1)=1, \) show that \( y_{2}=y_{1}^{2} \)


Explain how offspring of parents in sexual reproduction have the same
number of chromosomes.


If \( \boldsymbol{f}(\boldsymbol{x}) \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\left|x^{2}-x\right|}{x^{2}-x}, x \neq 0,1 \\ 1, \quad x=0 \quad \text { then } f(x) \text { is } \\ -1, \quad x=1\end{array}\right. \)
continuous for all
\( A \)
B. \( x \) except at \( x=0 \)
c. \( x \) except at \( x=1 \)
D. \( x \) except at \( x=0 \) and \( x=1 \)


Numerically, calorie is bigger than joule.
A . True
B. False


Let \( \boldsymbol{u}=(\mathbf{1},-\mathbf{2}, \mathbf{3}) \) and \( \boldsymbol{v}=(\mathbf{4}, \mathbf{5},-\mathbf{1}) \)
find \( \boldsymbol{u} \cdot \boldsymbol{v} \)


The largest and the shortest distance of
the earth from the sun is \( r_{1} \) and \( r_{2} \). Its
distance from the sun when it is at
perpendicular to the major axis of the orbit drawn from the sun:
\( \mathbf{A} \cdot\left(r_{1}+r_{2}\right) / 4 \)
B . \( \left(r_{1}+r_{2}\right) /\left(r_{1}-r_{2}\right) \)
\( \mathbf{c} \cdot 2 r_{1} r_{2} /\left(r_{1}+r_{2}\right) \)
D. \( \left(r_{1}+r_{2}\right) / 3 \)


If two sources have a randomly varying phase difference \( \varphi(t) \) the resultant
intensity will be given by
A. \( I_{0} \)
в. \( \frac{I_{0}}{2} \)
c. \( 2 I_{0} \)
D. \( \frac{I_{0}}{\sqrt{2}} \)


A complex compound of cobalt has
molecular formula containing five \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, one \( N O_{2} \) group and two \( C l \)
atoms for one \( C \) otom. One mole of this
compound produces three moles of ions in aqueous solution. On reacting with
an excess of \( A g N O_{3} \) solution,
two moles of \( A g C l \) get precipitated. The
ionic formula of the compound is:
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} N O_{2} C l\right]\left[\left(N H_{3}\right) C l\right] \)
B \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right]\left[C l\left(N O_{2}\right)\right. \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right] C l_{2} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\right]\left[\left(N O_{2}\right) C l_{3}\right] \)


Draw the structure of xenon
tetrafluoride molecule and state the
hybridization of the central atom and the geometry of the molecule.


Find the amount of sodium nitrate
dissolved in \( 200 g \) of solvent if the mass by mass percent of solute in solution is
\( \mathbf{2 0 \%} \)
A . \( 20 g \)
в. \( 50 g \)
c. \( 30 g \)
D. \( 40 g \)


The white anhydrous copper sulphate is heated to high temperature, it gives:
A \( \cdot C u S O_{4} \cdot 5 H_{2} O \)
в. \( C u S O_{4} . H_{2} O \)
c. \( C u S O_{4}+S O_{3} \)
D. \( C u O \)


Gradual addition of electronic shell in
the noble gases causes a decrease in their?
A. Ionization energy
B. Atomic radius
c. Boiling point
D. Density


Pick the wrong statement from the
following.
A. Consumption of citrus fruits and green leafy vegetables in food prevents scurvy.
B. Deficiency of Vitamin \( B_{6} \) (pyridoxime) results in convulsions.
C. Deficiency of vitamin D causes xerophthalmia.
D. Sources of Vitamin \( B_{1} \) are yeast, milk, green vegetables and cereals.


Five beats per second are produced on vibrating two closed organ pipes simultaneously. If the ratio of their lengths is \( 21 / 20 \), then their frequencies will be
A. 105 Hz and 100 нz
B. 105 Hz and 110 нz
c. 100 Hz and 105 н \( z \)
D. 110 Hz and 105 нz


Which of the following is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta H=\Delta U+\Delta(P V) \) when \( P \) and \( V \) both changes
B. \( \Delta H=\Delta U+P \Delta V \) when pressure is constant
C \( . \Delta H=\Delta U+V \Delta P \) when volume is constant
D. \( \Delta H=\Delta U+P \Delta V+V \Delta P \) when \( P \) and \( V \) both
changes


Name the gas in each of the following:
The gas produced when copper reacts with concentrated nitric acid


What happens when some charge is placed on a soap bubble?
A. Its radius decreases
B. Its radius increases
c. The bubble collapses
D. None of these


A farmer moves along the boundary of a square field of slide \( 10 \mathrm{m} \) in 40 s. What
will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?


The thickness of the depletion region is
of the order of of a
micrometre.
A. one-hundredth
B. one-tenth
c. one-thousandth
D. None of these


Tin cans used for storing food, are made by electroplating tin onto:
A . iron
B. gold
c. silver
D. copper


If a particle of \( 1 K g \) at mars is pushed through a distance of \( 5 m \). Calculate the
total work done. \( \left(\operatorname{given} \mu_{m}=0.3 \) and \right.
\( \left.\boldsymbol{g}_{m}=\mathbf{5} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A . \( 10 J \)
в. 7.5 .5
\( c .0 J \)
D. None


\( 100 \mathrm{mL} \) solution of \( 0.1 \mathrm{M} H C l \) was
titrated with 0.2 \( N a O H \) solution. The
titration was discontinued after the
addition of \( 30 \mathrm{mL} \) of \( \mathrm{NaOH.} \) The
remaining titration was completed with the addition of 0.5 M \( K O H . \) The volume
of \( K O H \) required for completing the titration is:
\( A \cdot 8 m L \)
в. \( 16 m L \)
c. \( 32 m L \)
D. \( 64 m L \)


Find the Arithmetic mean of the
following data using direct method.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Marks obtained & 50 & 60 & 70 & 80 & 90 & 100 \\
\hline No of students & 3 & 7 & 5 & 2 & 10 & 2 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 75.17 \)
B . 67.17
\( \mathbf{c} .76 .1 \)
D. 57.177


EFGH is a rhombus such the angle
EFG is \( 60^{\circ} . \) The magnitude of vectors \( \overrightarrow{F H} \) and \( \{m \overrightarrow{E G}\} \) are equal where \( m \) is a scalar. What is the value of \( m ? \)
\( A \cdot 3 \)
в. 1.5
\( c \cdot \sqrt{2} \)
D. \( \sqrt{3} \)


If \( a=\hat{i}+\hat{j}+\hat{k}, b=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( c=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |c|=\sqrt{3}, \) then the value of
\( \alpha \) and \( \beta \) are respectively
A. ±1,1
в. ±2,1
c. 0,±1
D. None of these


If \( \boldsymbol{A}=\left(\begin{array}{l}23 \\ 4 \\ 5\end{array}\right), \) then find the transpose of \( \boldsymbol{A} \)


Mark the correct order of decreasing
acid strength of the following
compounds
\( A \cdot(v)>(i v)>(i i)>(i)>( \) iii)
B. (ii)> (iv) > (i) > (iii) > (v)
\( c \cdot(i v)>(v)>(\text { iii) }>(\text { ii })>( \text { i) } \)
D. (v) > (iv) > (iii) > (ii) > (i)


The vapour pressure is least for?
A. pure water
B. \( 0.1 \mathrm{m} \) aqueous urea
c. \( 0.2 \mathrm{m} \) aqueous urea
D. 0.3m aqueous urea


Arrange the following radiations in the order of their increasing wavelength:
\( X \) -rays, infra red rays, radio waves,
gamma rays and micro waves.
A. Gamma rays, X -rays, infra red rays, radio waves micro waves
B. Gamma rays, micro waves, X-rays, infra red rays radio waves.
c. Gamma rays, infra red rays, \( X \) -rays, micro waves radio waves.
D. Gamma rays, \( X \) -rays, infra red rays, micro waves radio waves


An instrument box placed on a table is given a push. It is observed that it stops its motion after some time. What is the
force that stopped its motion?
A . Gravitational force
B. Tension force
c. Friction force
D. Mechanical force


f \( x, y \) are rational numbers such that
\( (x+y)+(x-2 y) \sqrt{2}=2 x-y+ \)
\( (x-y-1) \sqrt{5} \) then
A. \( x=1, y=1 \)
B. \( x=2, y=1 \)
c. \( x=5, y=1 \)
D. \( x \) and \( y \) can take infinitely many values


The emulsifying agent in milk is:
A . lactic acid
B . fat
c. lactose
D. casein


Which of the following options is correct regarding spontaneity of a process occurring on a system in which only pressure-volume? work is involved and S, \( G, C I, H, V, \) and \( P \) have usual meaning as in thermodynamics?
A \( \cdot(d G)_{U, V}<0,(d S)_{T, V}>0 \)
B . \( (d H) s, v<0,(d G)_{T, P}<0 \)
c. \( (d U)_{s, V}<0,(d G)_{T, V}<0 \)
D \( \cdot(d S)_{H, P}>0,(d G)_{T, P}<0 \)


If \( \cos y=x \cos (a+y), \) find \( \frac{d y}{d x} \)


n given figure, If \( \boldsymbol{E} \boldsymbol{F}\|\boldsymbol{D} \boldsymbol{C}\| \boldsymbol{A} \boldsymbol{B} \). prove
that \( \frac{\boldsymbol{A} \boldsymbol{E}}{\boldsymbol{E} \boldsymbol{D}}=\frac{\boldsymbol{B} \boldsymbol{F}}{\boldsymbol{F} \boldsymbol{C}} \)


The number of chromatids, in a chromosome at anaphase is
A. 2 in mitosis and 1 in meiosis
B. 1 in mitosis and 2 in meiosis
c. 2 each in mitosis and meiosis
D. 2 in mitosis and 4 in meiosis


There is a mixture of three solid
compounds \( A, B \) and \( C . \) Out of these
compounds \( A \) and \( C \) are soluble in water
and compound \( C \) is sublimable also. In what sequence the following techniques can be used for their effective
separation?
I. Filtration
II. Sublimation
III. Crystallisation from water extract
IV. Dissolution in water
\( A \cdot(\|),(1),(1 \vee),(1 \mid) \)
B. (IV), (I), (II), (III)
c. \( (1),(11),(11),(1 \vee) \)
\( D \cdot(11),(1 V),(1),(11) \)


The reagent which does not give acid chloride on treating with a carboxylic acid is:
A \( . P C l_{5} \)
в. \( C l_{2} \)
c. \( \operatorname{socl}_{2} \)
D. \( P C l_{3} \)


If sec \( \alpha \) and \( \csc \alpha \) are the roots of \( x^{2}- \)
\( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\boldsymbol{0} \) then
A \( \cdot p^{2}=q(q-2) \)
B . \( p^{2}=q(q+2) \)
c. \( p^{2}+q^{2}=2 q \)
D・ \( p^{2}+q^{2}=1 \)


The spore bearing structure seen in bread mold is
A. Sporangiumm
B. Sporophyll
c. sporophyte
D. sori


Which one of the following is true for an
exothermic reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} . \) If \( \boldsymbol{E}_{f} \) and
\( E_{b} \) are the activation energies of
forward and backward reactions
respectively?
\( \mathbf{A} \cdot E_{f}>E_{b} \)
B . \( E_{f}=E_{b} \)
\( \mathbf{c} \cdot E_{f}=-E_{b} \)
D \( \cdot E_{f}<E_{b} \)


Potassium metabisulphite is a:
A. Preservative
B. Antioxidant
c. Artificial sweetner
D. Both (a) and (b)


Fill in the blanks with appropriate
words.
Tyloses are found in


A body of mass \( 10 g m \) moving with a
velocity of \( u_{1} c m / s \) collides with a
stationary mass of \( 90 g \) m. The collision is perfectly elastic. Find the percentage loss of kinetic energy of the first body.
A . 36
B . 48
c. 64
D.


A point \( P \) divides the line segment joining the points \( \boldsymbol{A}(\mathbf{3},-\mathbf{5}) \) and \( B(-4,8) \) such that \( \frac{A P}{P B}=\frac{K}{1} . \) If \( P \) lies
on the line \( x+y=0, \) then find the
value of \( k \)


If \( \sin ^{-1}\left(\frac{2 p}{1+p^{2}}\right)-\cos ^{-1}\left(\frac{1-q^{2}}{1+q^{2}}\right)= \)
\( \tan ^{-1}\left(\frac{2 x}{1+x^{2}}\right), \) then the value of \( x \) is equal to
A \( \cdot \frac{p+q}{1+p q} \)
в. \( \frac{p-q}{1-p q} \)
c. \( \frac{p-q}{p q-1} \)
D. \( \frac{p-q}{p q+1} \)


The taste receptors of cockroach are
A. Compounds eyes
B. Companiform sensillae
C. Palps of maxillary and labium
D. tactile hairs


Find the distance between the following
pair of points. (5,7) and the origin
A \( \cdot \sqrt{74} \)
B. \( \sqrt{64} \)
c. \( \sqrt{34} \)
D. None of these


Distinguish between
(a) IRV and ERV
(b) Inspiratory capacity and Expiratory
capacity
(c) Vital capacity and total lung capacity


If in the fermentation of sugar in an
enzymatic solution that is \( 0.12 M \), the
concentration of the sugar is reduced to \( 0.06 M \) in \( 10 h \) and \( 0.03 M \) in \( 20 h, \) what
is the order of the reaction:
\( A \)
B. 2
\( c \cdot 3 \)
D.


If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & -1 & 3 & 2 \\ 5 & -4 & 7 & 4 \\ 6 & 0 & 9 & 8\end{array}\right), \) Write down the
elements \( a_{24} \) and \( a_{32} \)


A ray of light strikes a transparent rectangular slab of refractive index \( \sqrt{2} \) at an angle of incidence of \( 45^{\circ} . \) The angle between the reflected and refracted rays is:
\( A \cdot 75^{\circ} \)
B. \( 90^{\circ} \)
\( \mathrm{c} \cdot 105^{\circ} \)
D. \( 120^{\circ} \)


Find the total white colour compounds from following
\( \mathbf{A g C l}, \mathbf{A g F} \)
\( F e S O_{4} .7 H_{2} O, Z n S O_{4} .7 H_{2} O \)
Anhydrous \( C u S O_{4}, F e C l_{3}, F e C l_{2} \)


A spherical mirror and a thin spherical lens have focal length of \( -20 \mathrm{cm} . \) The mirror and lens will be:
A. Both concave
B. Both convex
c. Mirror is concave and the lens is convex
D. Mirror is convex but lens is concave


A force of \( 100 N \) acting on a body for 5
second gives it a velocity of \( 20 m s^{-1} \) Calculate the mass of the body.
A. \( 50 \mathrm{kg} \)
B. 25 kg
c. \( 75 \mathrm{kg} \)
D. \( 100 \mathrm{kg} \)


In the following circuit, find the diode current when the diode potential is
\( 0.5 V . \) Also find the forward resistance of
the diode.
A. \( 0.5 A, 1 \Omega \)
B \( .1 A, 0.5 \Omega \)
c. \( 2 A, 1 \Omega \)
D. \( 5 A, 6 \Omega \)


Differentiate \( \tan ^{-1}\left(\frac{\sin x}{1+\cos x}\right) \) w.r.t.


A straight wire carrying a current \( i_{1} \)
amp runs along the axis of a circular
current \( i_{2} \) amp. Then the force of
interaction between the two current
carrying conductors is?
\( A \cdot \infty \)
B. zero
c. \( \frac{\mu_{0}}{4 \pi} \frac{2 i_{1} i_{2}}{r} \mathrm{N} / \mathrm{m} \)
D. \( \frac{2 i_{1} i_{2}}{r} \mathrm{N} / \mathrm{m} \)


A satellite is moving in a circular orbit round the earth. If gravitational pull suddenly disappears,then it
A. Continuous to move with the same speed along the same path
B. Moves with the same velocity tangential to original orbit
c. Falls down with increasing velocity.
D. comes to rest after moving certain distance along original path.


Suppose the complex ion
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2} \boldsymbol{C l}_{2}\right]^{-} \) is
synthesized with two ammine ligands cis to each other, the two aqua ligands
cis to each other and two chloro ligands
cis to each other. Is this complex
optically active?


Charges of \( 5 \times 10^{-6} \) and \( -3 \times 10^{-6} C \)
are kept \( 16 \mathrm{cm} \) apart. Find the position of points on the line joining the charges where the electric potential is zero.


The concentration of \( \left[\boldsymbol{H}^{+}\right] \) and \( [\boldsymbol{O H}]^{-} \) in
a 0.1 M aqueous solution of \( 2 \% \) ionised
weak monobasic acid is
\( \left[\text { ionicproducto fwater }=1 \times 10^{-14}\right] \)
A \( \cdot 0.02 \times 10^{-3} \) M and \( 5 \times 10^{-11} \) M
B. \( 1 \times 10^{-3} \) M and \( 3 \times 10^{-11} \) M
C . \( 2 \times 10^{-3} \) M and \( 5 \times 10^{-12} \) M
D. \( 3 \times 10^{-2} \) M and \( 4 \times 10^{-13} \) M


An ovum of an animal has 2.5 pg of DNA in its nucleus. The amount of DNA at the
end of \( \mathrm{G}_{2} \) phase will be
A. \( 2.5 \mathrm{pg} \)
B. 5 pg
c. \( 250 \mathrm{pg} \)
D. \( 10 \mathrm{pg} \)


Two spheres of masses \( 1 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities of \( 10 \mathrm{m} / \mathrm{s} \) and 5 \( \mathrm{m} / \mathrm{s} \) respectively in the same direction. After the collision the velocity of the lighter sphere decreases by \( 4 \mathrm{m} / \mathrm{s} \). Find the velocity of the heavier sphere after collision and calculate the coefficient of
restitution.


The most common type of molecular weights used in the case of polymer is :
A. number average molecular weight method
B. z - average molecular weight method
c. viscosity average molecular weight method
D. all of the above


Assertion
Sigma bond is stronger than pi bond.
Reason

The strength of a bond depends on the
extent of overlapping.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The \( p H \) of \( 0.001 M H C N \) is:
\( A \cdot 3 \)
в. 11
c. between 3 and 7
D. 7


toppr loGın
Q Type your question
Here, \( \mu \) and \( \Delta \mu \) denote the \( R I \) of 0 th
layer and the difference in \( R I \) between
any two consecutive layers,
respectively. The integer \( m= \)
\( 0,1,2,3, \dots \) denotes the numbers of the
successive layers.

A ray of light from the Oth layer enters
the 1 st layer at an angle of incidence of
\( 30^{0} . \) After undergoing the \( m \) th
refraction, the ray emerges parallel to
the interface. If \( \mu=1.5 \) and \( \Delta \mu= \)
\( 0.015, \) the value of \( m \) is:
\( A \cdot 20 \)
B. 30
\( c \cdot 40 \)
D. 50


Name the two purines of DNA molecule
\( ? \)


A bacterial cell divides in every one
minute. If it takes one hour to fill the
whole cup, then to fill half cup, it will require
A. 30 minutes
B. 59 minutes
c. Three hours
D. 2 hours


\( \left(y^{2}+7 y+10\right) \div(y+5) \)


Simplify these expression and find their values if \( \boldsymbol{x}=\mathbf{3}, \boldsymbol{a}=-\mathbf{1}, \boldsymbol{b}=-\mathbf{2} \)
\( 2-8 x+4 x+4 \)


Prove that the distance between the
origin and the point (-6,-8) is twice the distance between the points (4,0)
and \( (\mathbf{0}, \mathbf{3}) \)


\( 92 U^{238} \) by successive radioactive decays changes to \( _{82} P b^{206} \). A sample of uranium ore was analysed and found to contain \( 1.0 g U^{238} \) and \( 0.1 g P b^{206} \) has accumulated due to decay of uranium, find out the age of ore. \( t_{1 / 2} \) for \( U^{238}= \) \( 4.5 \times 10^{9} y e a r \)


Differentiate
\( \frac{x^{4}}{4}-\frac{x^{-3}}{3}-\frac{2}{x}+C \)


The two particles are at minimum distance from each other after time, \( t= \)
\( \mathcal{S} \)
A .
в. 2.
\( c .3 \)
D. all of these


Once the applied electric current is removed, the electromagnet:
A. retains its magnetism
B. loses its magnetism
c. gets magnetized in opposite direction
D. none of the above


The product (B) is:
A. Benzaldehyde
B. Benzoic acid
C. Phenylacetic acid
D. None of the above


Copper is extracted from the ore copper pyrite by smelting in a blast furnace. The flux used and the slag formed are :
\( \mathbf{A} \cdot f \mid \mathbf{u} \times C a O, \operatorname{slag} C a S i O_{3} \)
B. flux \( S i O_{2}, \) slag \( C a S i O_{3} \)
c. flux \( F e O \), slag \( F e S i O_{3} \)
D. flux \( \operatorname{Si} O_{2} \),slag \( F e S i O_{3} \)


The Sl units of current is


Dikaryon formation is characteristic of
A. Ascomycetes and basidiomycetes
B. Phycomycetes and basidiomycetes
C. Ascomycetes and phycomycetes
D. Phycomycetes and zygomycetes


Evaluate \( : \lim _{x \rightarrow a} \frac{x-a}{|x-a|} \)
\( A \)
B.
\( c .-c \)
D. Does not exist


The method of zone refining of metals is
based on the principal of:
A. Greater mobility of the pure metal than that of the impurity
B. Higher melting point of the impurity than that of the pure metal
C. Greater noble character of the solid metal than that of the impurity
D. Greater solubility of the impurity in the molten state than in the solid


Explain why the atomic radius of oxygen is slightly more than that of nitrogen.


A bag contains 4 white, 5 red and 6 black balls. Three are drawn at random.
Find the probability that (i) no ball drawn is black, (ii) exactly 2 are black
(iii) all are of the same colour.
A \( \cdot \frac{12}{65}, \frac{27}{91}, \frac{6}{91} \)
В. \( \frac{12}{65}, \frac{27}{91}, \frac{24}{455} \)
c. \( \frac{12}{65}, \frac{27}{91}, \frac{14}{455} \)
D. \( \frac{12}{65}, \frac{27}{91}, \frac{34}{455} \)


Explain the following behaviours.
(i) Alcohols are more soluble in water
than the hydrocarbons of comparable molecular masses.
(ii) Ortho-nitrophenol is more acidic
than ortho-methoxyphenol


\( a_{n}=\frac{2 n-3}{6} \)


The specific heat of is negative.
\( A \cdot C O_{2} \)
B. Ne
c. saturated vapoures
D. none


Choose the correct answer from the
alternatives given :
Directions for questions 71 to 75: Study the following graph carefully to answer these questions.

Production (in lakh tonnes) of six units
of a company in 2006 and 2007 What is the difference in the production (in lakh tonnes) of all companies in
\( \mathbf{2 0 0 6} \) and \( \mathbf{2 0 0 7} \) ?
ロ2006 므200
A . 45
В. 75
\( c \cdot 100 \)
0.125


Which of the following conclusions regarding the structure of atom is based on Rutherford's \( \alpha \) -particle scattering experiment?
A. Th positive charge is concentrated in a very smal volume of the atom
B. The positive charge is scattered with the electrons throughout the atom.
c. The volume occupied by the nucleus is half of the volume of atom.
D. Most of the space in the atom is occupied by the neutrons


Nucleotides are made up of
A. Glycerols, fatty acids, and phosphates
B. Sugars, phosphates, and nitrogenous bases
C. Amino groups, hydrogens, and carboxyl groups
D. Protons, neutrons, and electrons
E. Protons and neutrons only


Carbon forms covalent bonds with itself
and other elements such as hydrogen, oxygen, sulphur, nitrogen and chlorine.
A. True
B. False


Cestum is commonly called as
A. Venus's flower basket
B. Brain coral
C . Venus's girdle or belt
D. Dead man's fingers


Keystone species are
A. Species belonging to same period.
B. Species that determine structure of biotic community.
C . Species reproducing sexually.
D. Species recorded only in the fossil state.


In the pinwheel galaxy, atomic number of all elements are the same as that on
earth and paulis principle is obeyed
However the shell closest to the nucleus
is saturated with electrons before the
next shell starts to fill and the process
continues this way, also each orbital can accommodate only one electron having \( +\frac{1}{2} \) spin. If noble gases are defined as the elements with
completely filled outermost shell, which elements would be the nobel gas in
their periodic table?
A \( . A r \)
в. \( S i \)
\( c . F \)
D. Ne


Assertion
\( H_{3} P O_{3} \) is a dibasic acid.
Reason
There are two hydrogen atoms directly
attached to phosphorus.
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


When burned, sulfur forms a gaseous
product \( X \) which can be oxidised to produce a gas \( Y . \) Gas Y reacts with water to produce a product Z. Which row correctly shows the oxidation states of sulfur in \( X, Y \) and \( Z ? \)
\begin{tabular}{ccccc}
& \( \mathbf{x} \) & \( \mathbf{Y} \) & \( \mathbf{z} \) \\
\( \mathbf{A} \) & -2 & +4 & +4 \\
& & & \\
\( \mathrm{B} \) & -2 & +4 & +6 \\
\( \mathrm{C} \) & +4 & +6 & +4 \\
& & & \\
\( \mathrm{D} \) & +4 & +6 & +6 \\
\hline
\end{tabular}
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


An exterior angle of a triangle is equal to the sum of two \( _{\text {一一一一一一 }} \) opposite angles.
A. interior
B. exterior
c. vertical
D. none of these


If \( \Delta G \) is greater than about +20 k \( J \) this
means:
A. the equilibrium constant is so large that virtually all the reactant has become product and the reaction goes to completion
B. the reaction is at equilibrium
C. the equilibrium constant is so small that virtually no product is formed and the reaction does not occur
D. there is no link between delta \( G \) and the equilibrium constant
E. it is impossible to tell from the information given


RCOOH decomposes \( N a H C O_{3} \) to
liberate \( C O_{2} \) which comes
from
A \( . \) NaOH \( \mathrm{CO}_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
с. \( \operatorname{NaH} \mathrm{CO}_{2} \)
D. \( N a H C O \)


In which of the following conditions is the potential for the following half-cell
reaction maximum?
\( 2 H^{+}+2 e^{-} \longrightarrow H_{2} \)
\( \mathbf{A} \cdot 1.0 M H C l \)
B. A solution having \( p H=4 \)
c. Pure water
D. \( 1.0 M \) NaOH


A block of mass of \( 1 k g \) is moving on the
x-axis. A force \( \boldsymbol{F} \) acting on the block
is shown. Velocity of the block at time
\( t=2 s \) is \( -3 m / s . \) What is the speed of
the block at time \( t=4 s ? \)
\( \mathbf{A} \cdot 8 m / s \)
B. \( 2 m / s \)
c. \( 3 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


In which year was the percentage increase in production as compared to the previous year the maximum?
enlizer
A . 2002
B. 2001
\( c \cdot 1997 \)
D. 1996