Assertion \( (A): \sin ^{2} \theta+\sin ^{2}\left(\theta+60^{0}\right)+ \)
\( \sin ^{2}\left(\theta-60^{0}\right)=\frac{3}{2} \)
Reason \( (\mathrm{R}): \cos \alpha+\cos \left(120^{0}+\alpha\right)+ \)
\( \cos \left(120^{0}-\alpha\right)=0 \)
A. Both A and R are true and R is the correct explanation to A
B. Both A \& R are true but R is not the correct explanation to \( A \)
c. A is true, R is false
D. A is false, R is true


How long will it take to reach mars from
the Earth?
A. 8 days
B. 6 days
c. 60 days
D. 80 days


Atomic Radius is of the order \( 10^{-8} \mathrm{cm} \& \)
nucleus order of \( 10^{-13} \mathrm{cm} . \) Calculate
what fraction of atom is occupied by nucleus?
A \( \cdot 10^{-14} \times V_{\text {atom}} \)
B . \( 10^{-13} \times V_{\text {atom}} \)
c. \( 10^{-15} \times V_{\text {atom}} \)
D. \( 10^{-11} \times V_{\text {atom }} \)


The greater the critical temperature of a gas, the easier is the liquefaction of the
gas.
A. True
B. False
c. Nither
D. None of the above


Let \( \vec{a}, \vec{b} \) be the position vectors of points \( A \) and \( B \) with respect to \( O \) and \( |\vec{a}|=a,|\vec{b}|=b \) the points \( C \) and \( D \)
divides \( A \) internally and externally in the ratio 2: 3 If \( \overrightarrow{O C} \) and \( \overrightarrow{O D} \) are
perpendicular then
A \( \cdot 9 a^{2}=4 b^{2} \)
В. \( 4 a^{2}=9 b^{2} \)
c. \( 9 a=4 b \)
D. \( 4 a=9 b \)


The force of gravity cannot act at a
distance. State true or false.
A. True
B. False


What kind of system is shown in the
graph?
A. consistent
B. inconsistent
c. non-linear
D. dependent


How may sub-atomic particles are present in an a-particles used in Rutherford's scattering experiment?
A. No. of Protons - 4
No. of Neutrons - 0,
No. of Electrons - 0
B. No. of Protons - 2.
No. of Neutrons - 0,
No. of Electrons - 2
c. No. of Protons - 2 ,
No. of Neutrons - 2,
No. of Electrons - 0
D. No. of Protons - 2
No. of Neutrons - 2,
No. of Electrons -


The intensity of the central maximum in Youngs double-slit experiment is \( 4 I \) The intensity at the first minimum is zero and the distance between two
consecutive maxima is \( \boldsymbol{w} \). The distance
from the central maximum to the
position where the intensity falls to \( I \) is
A \( \frac{2}{3} \omega \)
в. \( \frac{1}{4} \omega \)
c. \( \frac{1}{2} \omega \)
D. \( \frac{1}{3} \)


An \( n-p-n \) transistor has three leads
\( A, B \) and \( C . \) Connecting \( B \) and \( C \) by
moist fingers, \( A \) to the positive lead of
an ammeter, and \( C \) to the negative lead
of the ammeter, one finds large
deflection. Then, \( A, B \) and \( C \) refer
respectively to :
A. Emitter, base and collector
B. Base, emitter and collector
c. Base, collector and emitter
D. collector, emitter and base


While separating a mixture of ortho and para nitrophenols by steam distillation, name the isomer which will be steam
volatile? Give reason.


The function of an axon is
A. Transformation of nerve impulse
B. Reception of stimuli from neurons
C. Reception of external stimuli
D. Conduction of nerve impulse


The figure given above shows three
velocity-substrate concentration curves
for an enzyme reaction. What do the
curves 1,2 and 3 depict respectively?
A. 1 - Normal enzyme reaction, 2 - competitive inhibition
3- Non-competitive inhibition
B. 1 - Enzyme with an allosteric modulator added, 2 Normal enzyme activity, 3 - Competitive inhibition
C. 1 - competitive inhibition added,
2 - Enzyme with allosteric substance
3 - Normal enzyme reaction
D. 1 - Normal enzyme reaction
2 - Non-competitive inhibitor added, 3 - Allosteric inhibitor added


Write down two special features of climax community.


The solubility product of \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) at
\( 298 K \) is \( 6.0 \times 10^{-31} . \) The concentration
of hydroxide ions in a saturated
solution of \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) will be :
A \( \cdot\left(2.22 \times 10^{-31}\right)^{1 / 4} \)
B. \( \left(4.86 \times 10^{-29}\right)^{1 / 4} \)
c. \( \left(18 \times 10^{-31}\right)^{1 / 2} \)
D. \( \left(18 \times 10^{-31}\right)^{1 / 4} \)


\( \mathrm{CP} \) is \( , 500, \) Loss \( =30 \% . \) Find loss


What are the main uses of chlorine,
sodium and caustic soda? Why has
demand for chlorine increased
dramatically?


Which energy is produced by nuclear fission or nuclear fusion?
A. Thermal Energy
B. Geothermal energy
C. Nuclear energy
D. Tidal Energy


Which of the following is used as fluorinating agent?
A. \( S F_{6} \)
в. \( S F_{4} \)
\( \mathrm{c} \cdot S_{2} \mathrm{Cl}_{2} \)
D. \( S F_{2} \)


State true or false:
A set of rational number is a subset of a
set of real numbers
A. True
B. False


\( \boldsymbol{p}: \) He is hard working.
\( \boldsymbol{q}: \) He will win
The symbolic form of "If he will not win then he is not hard working", is
\( \mathbf{A} \cdot p \Rightarrow q \)
в. \( (\sim p) \Rightarrow(\sim q) \)
c. \( (\sim q) \Rightarrow(\sim p) \)
D. \( (\sim q) \Rightarrow p \)


The value of \( \cos 90^{\circ} \) is
A.
B. 0
\( c \cdot \sqrt{3} \)
D. \( \frac{1}{\sqrt{3}} \)


Juhi sells a washing machine for Rs. \( 13,500 . \) She loses \( 20 \% \) in the bargain. What was the price at which she bought it


Predict product of the above given reaction:
A . cyclohexene
B. cyclohexanol
c. cyclohexanone
D. cyclohexane


select a suitable identity and find the following products \( \left(a x^{2}+b y^{2}\right)\left(a x^{2}+b y^{2}\right) \)


Two constant parallel forces act on a
wheel provided in a transistor for
tunning as shown in the figure. If the
wheel rotates then the work done per
rotation will be
A. 0.05 joule
B. 0.0015 joule
c. 0.031 joule
D. 0.062 joule


What do you understand by the term non-stoichiometric hydrides? Do you expect this type of the hydrides to be formed by alkali metals? Justify your
answer


Assertion
A spherical equipotential surface is not
possible for a point charge.
Reason
A spherical equipotential surface is possible inside a spherical capacitor.
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


Precious Red Coral is / Coral used in
ornaments is
A. Asterias
B. Fungia
c. corallium
D. Tubipora


On a long horizontally moving belt, a child runs to and fro with a speed \( 9 \mathrm{km} \)
\( \boldsymbol{h}^{-1}( \) with respect to the belt) between
his father and mother located \( 50 \mathrm{m} \)
apart on the moving belt. The belt moves
with a speed of \( 4 \mathrm{km} h^{-1} \). For an
observer on a stationary platform, the speed of the child running in the direction of motion of the belt is
\( A \cdot 4 \mathrm{km} h-1 \)
B. 5 km \( h-1 \)
c. \( 9 \mathrm{km} h-1 \)
D. 13 km \( h-1 \)


The current in a coil changes from \( 1 m A \) to \( 5 m A \) in 4 milli second. If the
coefficient of self-induction of the coil is
\( 10 m H \) the magnitude of the "self-
induced" emf is:
A . \( 10 \mathrm{mV} \)
B. \( 5 \mathrm{mV} \)
c. \( 2.5 \mathrm{mV} \)
D. \( 1 \mathrm{mV} \)


Suppose that two cards are drawn at random from a deck of cards. Let \( X \) be
the number of aces obtained. Then the
value of \( \boldsymbol{E}(\boldsymbol{X}) \) is
A \( \cdot \frac{37}{221} \)
в. \( \frac{5}{13} \)
c. \( \frac{1}{13} \)
D. \( \frac{2}{13} \)


If the gravitational force of earth suddenly disappears, then which of the following is correct?
A. weight of the body is zero
B. Mass of the body is zero
c. Both mass and weight becomes zero
D. Neither the weight nor the mass is zero.


Rutherford's experiment on scattering
of alpha particles showed for the time
that the atom has:
A . Electrons
B. Protons
c. Neutrons
D. Nucleus


The set of letters needed to spel
"CATARACT" and the set of letter needed
to spell "TRACT" are equal
A. True
B. False


Figure shows three concentric thin
spherical shells \( A, B, \) and \( C \) of radii \( R \)
\( 2 R, \) and \( 3 R \) respectively. The shell B is
earthed and \( A \) and \( C \) are given charges
and \( 2 q \) respectively. If the charge on
surfaces \( 1,2,3, \) and 4 are \( q_{1}, q_{2}, q_{3}, \) and
\( q_{4} \) respectively, then match the
following columns :


What is the molecular formula of the
product formed when benzene is treated with ethyl chloride in the presence of
anhydrous aluminium chloride?
A. \( C_{8} H_{10} \)
в. \( C_{6} H_{6} \)
c. \( C_{8} H_{12} \)
D. \( C_{6} H_{14} \)


Erosion can be caused by which of the following?
A. Rain falling on steeply sloping land
B. A very hard rainfall
c. Rain falling on bare soil
D. All of the above


Who wrote the book "Origin of Species"?
A. G.J. Mende
B. Lamarck
c. Hugo de Vries
D. Charles Darwin


A current passes through an ohmic
conductor of nonuniform cross section.
Which is the following quantities are independent of the cross-section? This question has multiple correct options
A. The charge crossing in a given time interval
B. Drift speed
c. Current density
D. Free-electron density


The value of \( \left(\int x \cdot e^{-x} d x\right) \) is,


The electric potential at a point in free space due to a charge \( Q \) coulomb is \( Q \times 10^{11} \mathrm{V} . \) The electric field at that
point is:
A . 12 \( \pi \varepsilon_{0} Q \times 10^{22} \mathrm{Vm}^{-1} \)
В . \( 4 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
C . \( 12 \pi \varepsilon_{0} Q \times 10^{20} \mathrm{Vm}^{-1} \)
D. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V m^{-1} \)


Which of the following is the functional group for carboxylic acids?
\( A \)
\[
>C=0
\]
B.
\( c \)
\( -\mathrm{OH} \)
\( D \)


Let \( z \) be a complex number such that the imaginary part of z is nonzero and a \( =z^{2}+z+1 \) is real. Then a cannot take
the value
A . -1
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{4} \)


Given the terms \( a_{10}=\frac{3}{512} \) and \( a_{15}= \) \( \frac{3}{16384} \) of a geometric sequence, find the exact value of the term \( a_{30} \) of the
sequence.


Which of the following bond has highest bond energy?
A. F-F
в. cl-cı
c. Br-Br
D. \( 1- \)


For synthesis of a glucose molecule (with 686 kcal) the energy utilized during photosynthesis is
A. 288 kCal
B. 436 kCal
c. 7914 kCal
D. 686 kCal


The correct relationship between free
energy change in a reaction and the
corresponding equilibrium constant \( K_{c} \)
is:
\( \mathbf{A} \cdot-\Delta G=R T \ln K_{c} \)
\( \mathbf{B} \cdot \Delta G^{o}=R T \ln K_{c} \)
\( \mathbf{c} \cdot-\Delta G^{o}=R T \ln K_{c} \)
\( \mathbf{D} \cdot \Delta G=R T \ln K_{c} \)


The enthalpy of vaporization of water at \( 100^{\circ} \mathrm{C} \) is \( 40.63 \mathrm{KJ} \) mol\( ^{-1} \). The value \( \Delta \boldsymbol{E} \)
for this process would be:
A . 37.53 К J \( m o l^{-1} \)
B. 39.08 К J mol \( ^{-1} \)
c. 42.19 К и \( m o l^{-1} \)
D. 43.73 К」 \( m o l^{-1} \)


Which of the following agents does not cause contraction of the mesangial cells in the glomerulus?
A. Noradrenaline
B. Histamine
c. Dopamine
D. vasopressin


A man applying a force \( \boldsymbol{F} \) upon a stretched spring is stationary in a compartment moving with constant
speed \( v . \) If the compartment covers a
distance \( L \) in some time \( t, \) then
This question has multiple correct options
A. The man acting with force F on spring does the work \( (w)=F L \)
B. The total work performed by man on the compartment with respect to ground is zero
c. The work done by friction acting on man with respect to ground is, (w) \( =F L \)
D. The total work done by man with respect to ground is \( (w)=F L \)


A number consists of 7 digits whose
sum is \( 59 ; \) prove that the chance of its being divisible by 11 is \( \frac{4}{21} \)


The solubility in water is more for:
A. \( B a C O_{3} \)
в. \( B e C O_{3} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( M g C O_{3} \)


The electric field due to the electric
potential \( V=\left(2 x^{2}-4 x\right) \) is
\( \mathbf{A} \cdot(4 x+4) \hat{i} \)
B. \( (4 x-4) \hat{i} \)
c. \( (-4 x+4) \hat{i} \)
D. \( (-4 x-4) \hat{i} \)


If \( ^{8} C_{r}-^{7} C_{3}=^{7} C_{2}, \) find \( r \)


The correct statement is :
A. Most reactive and most poisonous V group element is white phosphorus molecule
B. High reactivity of white phosphorus is due to large internal strain in \( \mathrm{P} \) 4 molecule
c. Bismuth is mono atomic
D. All the above


A long solenoid of radius \( 2 \mathrm{cm} \) has 100
turns/cm and carries a current of \( 5 A \). A
coil of radius \( 1 \mathrm{cm} \) having 100 turns and a total resistance of \( 20 \Omega \) placed inside the solenoid co-axially. The coil is connected to galvanometer. If current in the solenoid is reversed in direction.
Fine the charge flow through the galvanometer.
A \( \cdot 2 \times 10^{-4} \mathrm{C} \)
B. \( 1 \times 10^{-4} \mathrm{C} \)
c. \( 4 \times 10^{-4} \mathrm{c} \)
D. \( 8 \times 10^{-4} \mathrm{C} \)


The standard reduction potential of
\( A g^{+} \mid A g \) electrode is 0.80 volt.
Calculate the standard electrode
potential of \( \boldsymbol{C l}^{-}|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}| \boldsymbol{A} \boldsymbol{g} \) at \( \boldsymbol{2} \boldsymbol{5}^{\circ} \boldsymbol{C} \)
Given solubility product, \( \boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l})= \)
\( 1.8 \times 10^{-10} \)


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{x}_{4} \)
Given
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{H}}=\boldsymbol{x}_{\boldsymbol{1}} \)
\( \boldsymbol{E}_{\boldsymbol{O}-\boldsymbol{O}}=\boldsymbol{x}_{\boldsymbol{2}} \)
\( \boldsymbol{E}_{\boldsymbol{O}-\boldsymbol{H}}=\boldsymbol{x}_{\boldsymbol{3}} \)
\( \Delta H_{F} \) of \( H_{2} O \) vapour is:
A \( \cdot x_{1}+\frac{x_{2}}{2}-x_{3}+x_{4} \)
B \( \cdot 2 x_{3}-x_{1}-\frac{x_{2}}{2}-x_{4} \)
c. \( _{x_{1}+\frac{x_{2}}{2}-2 x_{3}-x_{4}} \)
D. \( x_{1}+\frac{x_{2}}{2}-2 x_{3}+x_{4} \)


\( \left[M^{1} L^{2} T^{-3}\right] \) are the dimensions of \( \ldots \)
A. pressure
B. power
c. force
D. work


Find the ratios in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on
either side of the straight line. \( 2 x+3 y=5 ;(0,0) \) and (-2,1)


The relation between voltage sensitivity
\( \left(\sigma_{v}\right) \) and current sensitivity \( \left(\sigma_{i}\right) \) of \( a \) moving coil galvanometer is (resistance of galvanometer is \( G \) ).
A \( \cdot \frac{\sigma_{i}}{G}=\sigma_{v} \)
в. \( \frac{\sigma_{v}}{G}=\sigma \)
c. \( \frac{G}{\sigma_{v}}=\sigma \)
D. None of the above


A cylindrical water tank of diameter
1.4 \( m \) and height 2.1 \( m \) is being fed by a pipe of diameter \( 3.5 \mathrm{cm} \) through which
water flows at the rate of \( 2 m / s \) Calculate the time, it takes to fill the
\( \operatorname{tank} \)


All the elements in a group in the periodic table have similar:
A. atomic weights
B. number of valence electrons
c. mass number
D. atomic number


Allyl phenyl ether can be prepared by
heating:
A \( \cdot C H_{2}=C H-C H_{2}-B r+C_{6} H_{5} O N a \)
В. \( C_{6} H_{5}-C H=C H-B r+C H_{3}-O N a \)
c. \( C_{6} H_{5} B r+C H_{2}=C H-C H_{2}-O N a \)
D. \( C H_{2}=C H-B r+C_{6} H_{5}-C H_{2}-O N a \)


Prove \( \boldsymbol{G}=\frac{\boldsymbol{E}}{\mathbf{2}(\mathbf{1}+\boldsymbol{v})} \)


A body of mass \( \mathrm{m} \) is placed on earth surface which is taken from earth
surface to a height of \( \boldsymbol{h}=\mathbf{3} \boldsymbol{R} \) then
change in gravitational potential energy is:
\( ^{A} \cdot \frac{m g R}{4} \)
в. \( \frac{2}{3} m g R \)
c. \( \frac{3}{4} m g R \)
D. \( \frac{m g R}{2} \)


A short linear object of length \( b \) lies along the axis of a concave mirror of
focal length \( f \) at a distance u from the pole of the mirror. The size of the image is approximately equal to
\( A \)
\[
^{b}\left(\frac{u-f}{f}\right)^{\frac{1}{2}}
\]
в.
\[
b\left(\frac{b}{u-f}\right)^{\frac{1}{2}}
\]
\( c \)
\[
b\left(\frac{u-f}{f}\right)
\]
\( D \)
\[
b\left(\frac{f}{u-f}\right)^{2}
\]


Prove that:
\( \frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=2 \sec \theta \)


If \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}=\alpha, \) then
\( x^{2}= \)
\( \mathbf{A} \cdot \cos 2 \alpha \)
B. \( \sin 2 \alpha \)
\( c \cdot \tan 2 \alpha \)
D. \( \cot 2 \alpha \)


Arrange the following in order of increasing conductivity of heat:
copper, air, water, mercury


In
\( 1831, \) the British vinegar merchant Peregrine Phillips patented a more economical process for producing sulfur trioxide and concentrated
sulfuric acid, now known as
the
A. vitrol process
B. leblanc process
c. vinegar process
D. contact process


A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun
and the Earth in terms of the new unit if
light takes 8 min and 20 s to cover this distance?
A. 100 unit
B. 500 unit
c. 2 unit
D. 20 unit


Polarity of a bond depends on the difference in the electronegativity of the bonded atoms. The higher the difference in the electronegativity, the higher will be the polarity of the bond.

The boiling point of \( I C l \) is about \( 40^{\circ} C \)
higher than \( B r_{2} \). This might be because
A. \( I-C l \) bond is stronger than \( B r-B r \) bond
B. I.E. of \( I<I . E \) of \( B r \)
c. \( I-C l \) is polar whereas \( B r_{2} \) is non-polar
D. the size of \( I>B r \)


According to the first law of reflection,
which angles will be equal?
\( A \cdot A=C \)
\( B . B=D \)
\( C \cdot A=B \)
\( D \cdot B=C \)


Which of the following is practical
applications of the law of conservation
of linear momentum?
This question has multiple correct options
A. When a manjumps out of a boat on the shore, the boat is pushed slightly away from the shore
B. A person left on a frictionless surface can get away from it by blowing air out of his mouth or by throwing some object in a direction opposite to the direction in which he wants to move.
C. Recoiling of a gun
D. None of these


What is the atomic number (Z) of the
noble gas that reacts with fluorine?
A . 54
B. 10
c. 18
D. 2


If \( (a+i b)(c+i d)=A+i B \), then show
\( \operatorname{that}\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)=A^{2}+B^{2} \)


\( \boldsymbol{S}+\frac{\mathbf{3}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}+\mathbf{2} \boldsymbol{x} \) kcal
\( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{y} \) kcal
The heat of formation of \( S O_{2} \) is:
A . \( y-2 x \)
B. \( 2 x+y \)
c. \( x+y \)
D. \( 2 x / y \)


A current of 1 A flows in a length \( 0.1 \mathrm{m} \) placed in a magnetic field of \( 0.5 \mathrm{T} \) Calculate the force acting on the wire when the wire makes an angle of
(i) \( 90^{\circ} \) and
(ii) \( 0^{\circ}, \) with respect to the magnetic field.


Calculate the standard internal energy
change for the reaction \( \boldsymbol{C}_{(\text {graphite})}+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{C O}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\( \Delta_{f}^{o} \) at \( 25^{\circ} ; H_{2} O(g)=-241.8 k J m o l^{-1} \)
\( \boldsymbol{C O}(\boldsymbol{g})=-110.5 \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)


Show that \( \int_{0}^{\frac{\pi}{2}}[2 \log \sin x- \)
\( \log (\sin 2 x)] d x=\frac{\pi}{2} \log _{e}\left(\frac{1}{2}\right) \)


What is the difference between the
images formed by a large and a small
mirror?


Radioactivity is the caused by the disintegration of
A. Atom
B. Ion
c. Molecule
D. Nucleus


Reaction, \( 3 C l O^{-} \rightarrow C l O_{3}^{-}+2 C l \)
occurs in following two steps. I. \( C l O^{-}+C l O^{-} \stackrel{K_{1}}{\longrightarrow} C l O_{2}^{-}+C l^{-} \) (Slow
step)
\( \mathrm{Il.} \mathrm{ClO}_{2}^{+} \mathrm{ClO}^{-} \stackrel{k_{2}}{\longrightarrow} \mathrm{ClO}_{3}^{-}+\mathrm{Cl}^{-} \) (Fast
step) Then, the rate of given reaction is:
\( \mathbf{A} \cdot k_{1}\left[C l O^{-}\right] \)
B. \( k_{1}\left[C l O^{-}\right]^{2} \)
c. \( k_{2}\left[C l O_{2}^{-}\right]\left[C l O^{-}\right] \)
D. \( k_{2}\left[C l O^{-}\right]^{3} \)


A body of mass \( 1 k g \) is made to trave with a uniform acceleration of
\( 30 \mathrm{cm} / \mathrm{s}^{2} \) over a distance of \( 2 \mathrm{m} \), the work done is:
\( \mathbf{A} \cdot 6 J \)
в. \( 60 J \)
\( c .0 .6 . J \)
D. 0.3 .5


\[
\begin{array}{l}
\boldsymbol{A}_{\mathbf{1}}=\left[\boldsymbol{a}_{1}\right] \\
\boldsymbol{A}_{2}=\left[\begin{array}{lll}
\boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\
\boldsymbol{a}_{\boldsymbol{4}} & \boldsymbol{a}_{5}
\end{array}\right] \\
\boldsymbol{A}_{\boldsymbol{3}}=\left[\begin{array}{lll}
\boldsymbol{a}_{\boldsymbol{6}} & \boldsymbol{a}_{\boldsymbol{7}} & \boldsymbol{a}_{\boldsymbol{8}} \\
\boldsymbol{a}_{\boldsymbol{9}} & \boldsymbol{a}_{\boldsymbol{1 0}} & \boldsymbol{a}_{11} \\
\boldsymbol{a}_{\boldsymbol{1 2}} & \boldsymbol{a}_{\boldsymbol{1 3}} & \boldsymbol{a}_{14}
\end{array}\right] \ldots \ldots \boldsymbol{A}_{\boldsymbol{n}}=[\ldots .]
\end{array}
\]
where \( \quad a_{r}=\left[\log _{2} r\right]([.] \) denotes
greatest integer. Then trance of \( \boldsymbol{A}_{\mathbf{1 0}} \)


Equal volumes of two immiscible
liquids of densities \( \rho \) and \( 2 \rho \) are filled in
a vessel as shown figure. Two small
holes are punches at depth \( h / 2 \) and
\( 3 h / 2 \) from the surface of lighter liquid.
If \( v_{1} \) and \( v_{2} \) are the velocities of a flux at
these two holes then \( v_{1} / v_{2} \) is :
A \( \cdot \frac{1}{2 \sqrt{2}} \)
в. \( \overline{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)


Beryllium and aluminium exhibit many properties which are similar. But, the two elements differ in:
A. Forming covalent halides
B. Forming polymeric hybrids
c. Exhibiting maximum covalency in compounds
D. Exhibiting amphoteric nature in their oxides


The solubility product of \( A g B r \) is \( 4.9 \times \)
\( 10^{-9} . \) The solubility of AgBr will be:
A. \( 7 \times 10^{-4} \) mole /litre
B. \( 7 \times 10^{-5} g / \)litre
c. \( 1.316 \times 10^{-2} g / \)litre
D. \( 1 \times 10^{-3} \) mole \( / \)litre


According to Laplace, during the propagation of sound in a gas, an adiabatic change takes place in the medium.
A. True
B. False


Assertion
Distance and displacement are different physical quantities.
Reason
Distance and displacement have same dimension.
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 is incorrect and Reason is correct


Pneumatophore is present in
A. Rhizophora
B. Cholobranchia
c. Pistea
D. None of the above


Which of the following pairs is correctly
matched ?
(a) X-ray spectra
A. Experimental observation -
Phenomenon - Charge on the nucleus
B. Experimental observation -
(b) a- particle scattering
Phenomenon - Quantized electron orbit
C. Experimental observation -
(c) Emission spectra
Phenomenon - Quantization of energy
D. Experimental observation -
(d) The photoelectric effect
Phenomenon - The nuclear atom


The difference between primary
succession and secondary succession
is that
A. Primary succession occurs on soil
B. Primary succession begins with lichens
C. Primary succession begins with plant species
D. secondary succession involves animal species
E. Secondary succession involves the weathering of rock


Heavy hydrogen has neutron
and \( --- \) proton in the nucleus.
A . 2 and 1
B. 1 and 2
c. 1 and 1
D. 2 and 2


Select the correct statement(s) for
double salt:
This question has multiple correct options
A. Double salts are stable in solid state but loose their
identity in aqueous solution.
B. In double salt the properties of constituent ions are not changed in their aqueous solution.
C. Double salts are stable in solid-state and do not lose their identity in aqueous solution.
D. In double salt the properties of constituent ions are changed in their aqueous solution.


Which of the following is a type of motion?
A. Circular
B. Rectilinear
c. Periodic
D. All of the above


If \( f(x)=\ln \left(x^{2}-x+2\right) ; R^{+} \rightarrow R \) and
\( \boldsymbol{g}(\boldsymbol{x})=\{\boldsymbol{x}\}+\mathbf{1} ;[\mathbf{1}, \mathbf{2}] \rightarrow[\mathbf{1}, \mathbf{2}], \) where
\( \{x\} \) denotes fractional part of \( x \). Find
the domain and range of \( f(g(x)) \) when defined.


Explain with the help of two examples how the participation of local people has led to conservation of forest in the
past.


toppr LOGIN JolN Now
Q Type your question
Which table gives the correct directions
for the magnetic field at the two
positions around the wire?
wire field on right side of
(6)
wire head on with conventional
current flow out of page
\( A \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward right side of page \\
Below the Wire & toward bottom of page \\
\hline
\end{tabular}
B. \begin{tabular}{|l|c|}
\hline & Direction of Field \\
\hline Right of the Wire & toward left of page \\
Below the Wire & toward top of page \\
\hline
\end{tabular}
\( \mathbf{c} \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward top of page \\
Below the Wire & toward right side of page \\
\hline
\end{tabular}
D.
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward bottom of page \\
Below the Wire & toward left side of page \\
\hline
\end{tabular}
\( E \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward lower left portion of page \\
Below the Wire & toward upper right portion of page \\
\hline
\end{tabular}


Why does obtaining the image of the sun on a paper with the help of a concave mirror burn the paper?


A glass marble, whose mass is \( 100 g m \)
falls from a height of \( 20 m \) and
rebounds to a height of 5 m. Find the impulse and average force between the marble and the floor, if the time during which they are in contact is 0.01 sec.


A wheel has a constant angular acceleration of \( 3.0 \mathrm{rad} / \mathrm{s}^{2}, \) During a
certain \( 4.0 s \) interval, it turns through an angle of 120 rad. Assuming that. \( a t=0 \)
angular speed \( \omega_{0}=3 r a d / s \) how long is
motion at the start of this 4.0 second
interval?
\( \mathbf{A} \cdot 7 s \)
B. \( 9 s \)
c. \( 4 s \)
D. \( 10 s \)


State Biot - Savart law. Deduce the
expression for the magnetic field at a point on the axis of a current carrying circular loop of radius 'R' distant 'x' from
the center. Hence, write the magnetic field at the center of a loop.


Universal gravitational constant \( G \)
proportional to distance \( r \) between two
masses as-
A \( \cdot r^{2} \)
B.
\( c \cdot 1 / r \)
D. does not depend upon \( r \)


Work done by air when it expands from
\( \mathbf{5 0} \) litres to 150 litres at a constant
pressure of 2 atmosphere is
A \( \cdot 2 \times 10^{4} \) joules
B. 2 \( \times 100 \) joules
C \( .2 \times 10^{5} \times 100 \) joules
D. \( 2 \times 10^{6} \times 100 \) joules


In the figure, \( A D \) is the internal
bisector of \( \angle A \) and \( C E \| D A \). if \( C E \)
meets \( B A \) produced at \( E, \) prove that \( \Delta C A E \) is isosceles.


Which one respiratory complex is coupled with ETS for ATP synthesis?
A. Complex
B. Complex III
c. complex IV
D. Complex


Which of the following relations is
correct?
A. \( E=m c \)
B . \( E=m c^{2} \)
c. \( E=2 m c^{2} \)
D. \( E=m c^{2} / 4 \)


If the cathode and the anode are kept at
the same potential, the emitted electrons have
A. the maximum KE equal to 1.36 ev
B. the average KE equal to (1.36/2) ev
c. the maximum KE depends upon the material
D. none of the above


Lymph
A. Transports \( O_{2} \) to brain
B. Transports \( C O_{2} \) to lungs
C. Returns interstitial fluid to blood
D. Returns RBCs and WBCs to lymph nodes


The kinetic energy of a moving body is given by \( K=2 v^{2}, K \) being injoules
and \( v \) in \( \mathrm{m} / \mathrm{s} \). Its momentum when
traveling with a velocity of \( 2 m s^{-1} \) will
be :
A \( .16 \mathrm{kgms}^{-1} \)
в. \( 4 \mathrm{kgms}^{-1} \)
c. 8 kgms\( ^{-1} \)
D. 2 kgms \( ^{-1} \)


(i) Find the area bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) \) between the points where
it crosses the x-axis.
(ii) Find the area between the curves
\( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}^{3} \)


If \( f(x)=x^{3} \) and \( g(x)=\sin 2 x, \) then
A \( \cdot g[f(1)]=1 \)
B. \( f(g(\pi / 12)=1 / 8 \)
c. \( g f(2)=\sin 2 \)
D. none of these


Inflorescence consisting of sessile bisexual flowers arranged acropetally on an elongated axis is?
A. Spandix
B. Catkin
c. Raceme
D. Spike


The number of teeth that grow twice in
human life is
A . 4
B. 12
\( c \cdot 20 \)
D. 28


Which of the following is a plant hormone?
A . Insulin
B. Thyroxin
c. Oestrogen
D. cytokinin


Which among the group-15 elements does not exists as tetra atomic
molecule?
A. Nitrogen
B. Phosphorus
c. Arsenic
D. Antimony


A solution containing \( 10.2 g \) per glycerin per liter of a solution is found to be
isotonic with \( 2 \% \) solution of glucose molar mass \( 180 . \) Calculate the molar
mass glycerin.
A. 97.89 g/mol
в. 183.24 g/mol
c. \( 91.8 \mathrm{g} / \mathrm{mol} \)
D. None of these


Which of the following is produced during the following reaction? \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \frac{575 \boldsymbol{K}}{Z n O, C r_{2} O_{3}} \)
A. Ethanol
B. Ethanal
c. Methanol
D. Methanal


How many strings of letters can possibly by formed using the above rules such that the third letter of the
string is e?
\( A \cdot 8 \)
B. 9
\( c \cdot 10 \)
D. 1


In the reaction,
\( \boldsymbol{2} \boldsymbol{A l}(\boldsymbol{s})+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{l}^{3+}(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( \mathbf{6} C l^{-}\left(a q_{\cdot}\right)+3 H_{2}(g) \)
\( \mathbf{A} \cdot 11.2 H_{2}(g) \) at \( \mathrm{STP} \) is produced for every mole of \( H C l(a g .) \) consumed
B. 6 LHCl \( (\text { ag. }) \) is consumed for every 3 L \( H_{2}(E \) ) produced
C \( .33 .6 L H_{2}(g) \) is produced regardless of temperature and pressure for every mole of \( \mathrm{Al} \) that reacts
D. \( 67.2 L H_{2}(g) \) at SIT is produced for every mac of Al that reacts


In p-type semiconductor, conduction is
due to
A. greater number of holes and less number of electrons.
B. only electrons.
C . only holes.
D. greater number of electrons and less number of holes.


Three allotropes \( (A),(B) \) and \( (C) \) of
phosphorous in the following change are respectively:
\( A \frac{513 K}{1200 a t m} \)
\( \boldsymbol{B} \frac{1200 a t m}{\text {In an inert atm. and then rapid cooling to room}} \)
\( C \)
A. white, red, white
B. black, white, red
c. red, black, white
D. red, violet, black


The brown haze of photochemical smog is largely attributable to:
A . \( N O \)
в. \( N O_{2} \)
c. \( C H_{3} \underset{d}{_{0}} C O O N O_{2} \)
D. \( C H_{2}=C H C H O \)


If \( f(x)= \) \( \left\{\begin{array}{c}\frac{1-\sin x}{(\pi-2 x)^{2}} \cdot \frac{\log \sin x}{\log \left(1+\pi^{2}-4 \pi x+x^{2}\right)} \\ k\end{array}\right. \)
is continuous at \( x=\frac{\pi}{2}, \) then \( k \) is equal
to.
A \( \cdot-\frac{1}{16} \)
B. \( -\frac{1}{32} \)
\( c \cdot-\frac{1}{64} \)
D. \( -\frac{1}{28} \)


The product \( (A) \) and \( (B) \) are
respectively:
A. \( K I, I_{2} \)
в. \( I_{2}, K I O_{3} \)
c. \( K I O_{3}, K I O_{4} \)
D \( \cdot I_{2}, I_{2} \)


Two rigid boxes containing different ideal gases are placed on a table. Box \( \boldsymbol{A} \) contains one mole of nitrogen at
temperature \( T_{o}, \) while box \( B \) contains one mole of helium at temperature
\( (7 / 3) T_{0} . \) The boxes are then put into thermal contact with each other, and
heat flows between them until the
gases reach a common final
temperature (Ignore the heat capacity of boxes).Then, the final temperature of
\( \operatorname{gases}, \boldsymbol{T}_{f}, \) in the terms of \( \boldsymbol{T}_{\boldsymbol{o}} \) is:
\( ^{\mathbf{A}} \cdot T_{f}=\frac{3}{7} T_{0} \)
\( ^{\mathrm{B}} \cdot_{T_{f}}=\frac{7}{3} T_{0} \)
\( ^{\mathbf{C}} \cdot_{T_{f}}=\frac{3}{2} T_{0} \)
\( ^{\mathrm{D}} \cdot_{T_{f}}=\frac{5}{2} T_{0} \)


Write the value of the determinant \( \left|\begin{array}{cc}\mathbf{3} & \mathbf{- 1} \\ \mathbf{2} & \mathbf{1}\end{array}\right| \)


Graph the solution set
\( |\boldsymbol{x}|=\mathbf{1} \)
\( A \)
B.
c.
D.


\( n \stackrel{L t}{\rightarrow} \infty \)
\( \left\{\frac{\sqrt{\mathbf{1}}+\sqrt{\mathbf{2}}+\sqrt{\mathbf{3}}+\ldots+\sqrt{\boldsymbol{n}}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}\right\}= \)
\( A \cdot O \)
B.
\( c \cdot 2 / 3 \)
D. 3/2


In a transcription, unit promoter is said to be located towards
A. \( 3^{\prime} \) end of structural gene
B. 5' end of structural gene
c. 5 ' end of template strand
D. 3' end of non-template strand


Which of the following fluorides does
not exist?
A. \( N F_{5} \)
в. \( P F_{5} \)
c. \( A s F_{5} \)
D. \( S b F_{5} \)


The dissociation energy of \( \boldsymbol{H}_{2} \) is
\( 482.5 K J / \) mol. If \( H_{2} \) is exposed to radiant energy of wavelength \( 124 \mathrm{nm} \) what \( \% \) of radiant energy will be converted into K.E?
\( \left(1 \frac{e v}{a t o m} 5=96 k J / m o l .\right) \)


If two parallel lines are intersected by a transversal, then prove that bisectors of the interior angles from a rectangle.


If the number \( 93215 x 2 \) is completely divisible by \( 11, \) then \( x \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
D. 4


The compound \( Y \) is:
\( A \)
\( B \)
\( c \)
D.


Give reason for the following:
The mass number of an atom is slightly less than the actual atomic mass.


A bottle of liquor ammonia should be cooled before opening. Give reason.


If the inductance of a coil in 1 henry then its effective resistance in a \( D . C \) circuit
will be
\( A \cdot \infty \)
B. zero
\( c \cdot 1 \Omega \)
D. 2 \( \Omega \)


The area bounded by curves


Which one of the following statements
İs incorrect?
A. All halogens have weaker \( X \) -X bond than \( X \) - X' bond, in interhalogens (except F-F bond in fluorine)
B. Radius ratio between iodine and fluorine (among halogens) is maximum
C. Interhalogen compounds are more reactive than halogen compounds
D. Among interhalogen compounds, maximum number of atoms are present in iodine fluoride


Carrier proteins are involved in the
A. Active transport of ions
B. Passive transport of ions
c. water transport
D. Both A and B


\( \alpha- \) particles of 6 MeV energy is
scattered back from a silver foil.
Calculate the maximum volume where
the entire charge of the atom is
supposed to be accumulated.
\( [Z \text { for silver }=47] \)
A . \( 3.6 \times 10^{-28} \mathrm{m}^{3} \)
В. \( 5.97 \times 10^{-42} \mathrm{m}^{3} \)
c. \( 6.55 \times 10^{-71} m^{3} \)
D. \( 48 \times 10^{-42} m^{3} \)


Write \( I U P A C \) name of \( \left[P t C l_{2}\left(N H_{3}\right)_{2}\right] \)


What force should be applied on the
wedge so that block over it does not
move? (All surfaces are smooth).
\( \mathbf{A} \cdot F=(M+m) g \cot \theta \)
B . \( F=(M+m) g \tan \theta \)
\( \mathbf{C} \cdot F=(M+m) g \sin \theta \)
\( \mathbf{D} \cdot F=(M+m) g \cos \theta \)


Refer to the given figure which shows
sectional view of two types of coelom, \( A \)
and B. Select the correct option which
represents groups of animals that
possess A or B.
A. A-Aschelminthes and Annelids; B-Echinoderms and Chordates
B. A-Annelids, Echinoderms and Chordates; BAschelminthes
C. A-Echinoderms and Chordates; B-Aschelminthes and Annelids
D. A-Aschelminthes; B-Annelids, Echinoderms and Chordates


The height of mercury which exerts the
same pressure as \( 20 \mathrm{cm} \) of water column is : ( Given relative density of
mercury=13.56)
A \( .1 .47 \mathrm{cm} \)
B. \( 14.8 \mathrm{cm} \)
\( c \cdot 148 \mathrm{cm} \)
D. None of these


A charged particle travels along the
inside of a straight hollow tube 2.0 metre long. The particle is uniformly accelerated. What is the time spent by the particle in the tube if it enters at a
speed of \( 1000 \mathrm{m} \) s and leaves at 9000 \( \mathrm{m} / \mathrm{s} \)
A \( \cdot 2 \times 10^{-4} \) seconds
B. \( 5 \times 10^{-4} \) seconds
c. \( 4 \times 10^{-4} \) seconds
D. 2.5 \( \times 10^{-4} \) seconds


A mass of stainless steel spoon is 0.04
kg and specific heat is \( 0.50 k J / k g \times^{o} C \)
Then calculate the heat which is
required to raise the temperature \( 20^{\circ} C \)
to \( 50^{\circ} \mathrm{C} \) of the spoon.
A. 200 J
B. 400
c. \( 600 \mathrm{J} \)
D. 800
E . 1,000


Spore formation is the most common
asexual method of reproduction in:
A. Protozoa
B. Tubers
c. Fungi
D. Algae


Which tool allows liquids to be swirled with a low risk of spilling?
A . Crucible
B. Evaporating dish
c. Tonds
D. Erlenmeyer flask
E. Mortar and pestle


Each edge of a cube is increased by \( 50 \% \) The percentage increase in the surface area of the cube is
A . 50
в. 125
\( c .150 \)
D. 225


In a right angled triangle, prove that the line segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.


Draw the line joining the following
points. \( P(-4,5) \) and \( Q(3,-4) \)


Find the \( 8 t h \) term in series
4,8,16,32


If \( \boldsymbol{A}=\left[\begin{array}{ccc}0 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 4\end{array}\right] \) and \( B=\left[\begin{array}{cc}1 & -2 \\ -1 & 0 \\ 2 & -1\end{array}\right] \)
Check \( A B=B A ? \)


The minimum time for which the
stimulus must be applied in order to
obtain a response is
A. Conversion time
B. Conduction time
c. Presentation time
D. Reaction time


Alum purifies water due to:
A. adsorption
B. peptisation
c. coagulation
D. dialysis


Homo erectus erectus is the zoological
name of
A. Java ape man
B. Peking man
c. Neanderthal man
D. Nut cracker man


True or False
Elements are classified for their
systematic study.


\( \lim _{x \rightarrow \infty} \sin ^{-1} \sin \left(\frac{x^{2}+2}{x^{2}+1}\right) \) is equal to
(where [.] and \( \{.\} \) denote greatest integer and fractional part function respectively) This question has multiple correct options
A \( \cdot \lim _{x \rightarrow \infty}\left[\frac{x^{2}+2}{x^{2}+1}\right] \)
B. \( \lim _{x \rightarrow \infty} \frac{x^{2}+2}{x^{2}+1} \)
\( ^{\mathbf{C}} \lim _{x \rightarrow \infty}\left\{\frac{x^{2}+2}{x^{2}+1}\right\} \)
D. \( \lim _{x \rightarrow \infty}\left\{\frac{x^{2}}{x^{2}+1}\right\} \)


In an equilibrium \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{A} \)
and \( B \) are mixed in a vessel at
temperature \( \boldsymbol{T} \). The initial
concentration of \( A \) was twice the initial
concentration of \( B \). After the
equilibrium has reached, concentration
of \( C \) was thrice the equilibrium
concentration of \( B . \) Calculate \( \boldsymbol{K}_{\boldsymbol{C}} \)
A . 0.14
B. 65
\( c .3 .6 \)
D. 1.8


The focal lengths of the objective and
eyepiece of a telescope are \( 60 \mathrm{cm} \) and 5cm respectively.The telescope is focused on an object \( 360 \mathrm{cm} \) from the objective and the final image is formed at a distance of \( 30 \mathrm{cm} \) from the eye of
the observer. The length of the telescope is
A. \( 66.3 \mathrm{cm} \)
B. 86.3 cm
\( c .76 .3 \mathrm{cm} \)
D. \( 96.3 \mathrm{cm} \)


The species \( M n O_{4}^{-} \) in acidic medium is decolourized by:
A \( \cdot F e^{2} \)
B. \( C_{2} O_{4}^{2} \)
\( \mathbf{c} \cdot N O_{2}^{-} \)
D. all of the above


is the common variety of coal used in household.
A. Anthracite
B. Bituminous
c. Peat
D. Lignite


The ion or group detected by \( \boldsymbol{K}_{2}\left[\boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}\right] \)
is:
A. NO
в. \( C l \)
c. \( N H^{-2} \)
D. \( N H_{3} \)


According to JJ Thomson's atomic model, negative charges are embedded
in:
A. a lump of positive charge
B. a lump of neutral particles
c. alump of small atoms
D. the nucleus


The deep red colouration is due to the
formation of:
\( \mathbf{A} \cdot \operatorname{Fe}\left(C H_{3} C O O\right) \)
в. \( F e(O H)_{2} C H_{3} C O O \)
c. \( \left[F e_{3}(O H)_{2}\left(C H_{3} C O O\right)_{6}\right]^{+} \)
D. \( \left[F e_{3}\left(C H_{3} C O O\right)_{6}\right. \)


Which one is the general formula of
monohydric alcohols?
A. \( C_{n} H_{2 n} O H \)
в. \( C_{n+1} H_{2 n} O H \)
c. \( C_{2 n} H_{2 n+2} \) OH
D. \( C_{n} H_{2 n+1} O H \)


The rate of change of current needed to induce an emf of \( 8 V \) in \( 0.1 H \) coil is
A . \( 0.8 A / s \)
В. \( 0.125 A / s \)
c. \( 80 A / s \)
D. \( 8 A / s \)


A narrow beam of light that is moving in a defined direction is:
A. wave
B. compression
\( c \cdot \) ray
D. rarefaction


The differential equation of a particle executing SHM along y-axis is
A \( \cdot \frac{d^{2} y}{d t^{2}}+\omega^{2} y=0 \)
B. \( \frac{d^{2} y}{d t^{2}}-\omega^{2} y=0 \)
\( ^{\text {C } \cdot \frac{d^{2} x}{d t^{2}}+\omega^{2} x=0} \)
D. \( \frac{d^{2} x}{d t^{2}}-\omega^{2} x=0 \)


Short / long answer type questions. Oxygen enters the blood from the
alveolar air but carbon dioxide leaves
the blood to enter the alveolar air.
Explain.


Carborundum is:
A . \( S i C \)
в. \( A l_{2} O_{3} . H_{2} O \)
c. \( A l_{2}\left(S O_{4}\right)_{3} \)
D. \( A l C l_{3} \)


If the orthocentre, circumcentre of a
triangle are (-3,5,2),(6,2,5)
respectively then the centroid of the triangle is
\( \mathbf{A} \cdot(3,3,4) \)
В. \( \left(\frac{3}{2}, \frac{7}{2}, \frac{9}{2}\right) \)
c. (9,9,12)
D. \( \left(\frac{9}{2} \frac{-3}{2}, \frac{3}{2}\right) \)


Fuel efficiency depends on:
A. properties of fuel
B. properties of engine
C. Both A and B
D. None of the above


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{10} \log _{10}\left(1+x^{3}\right) \) is
A. \( (-1,+\infty) \)
(i) \( (-1,-\infty) \)
B. \( (0,+\infty) \)
\( c \cdot[0,+\infty) \)
D. (-1,0)


In the adjoining figure, if line \( l \| m \) and
line \( n \) is the transversal, what is the
value of \( x \)
\( A \cdot 65 \)
в. \( 50^{\circ} \)
\( c \cdot 41^{0} \)
D. \( 130^{\circ} \)


What is photoautotrophs?


The total surface area of a solid right
circular cylinder is \( 231 \mathrm{cm}^{2} \). Its curved surface area is two thirds of the total
surface area. Find height of the
cylinder.


Name the substance dissolved in pure
water to make it a conductor of
electricity.


Which compound does not give positive test in Lassaigne's test for nitrogen?
A. Urea
B. Hydrazine
c. Azobenzene
D. Phenyl hydrazine


Real gases behave ideally at:
A. Low pressure, high temperature
B. Low pressure, low temperature
C. High pressure, low temperature
D. None of these


An unbiased coin is tossed 8 times.
Find by using binomial distribution the probability of getting atleast 3 heads


Among the following molecules, \( p-p \) overlap takes place in:
A \( . H_{2} \)
в. \( B e C l_{2} \)
\( c \cdot F_{2} \)
D. \( H F \)


Monds process is used for:
A . \( N i \)
в. \( A l \)
c. \( F e \)
D. \( C u \)


The muscle fatigue occurs due to accumulation of
A. \( C O_{2} \)
B. Lactic acid
c. creatine phosphate
D. Myosin ATPase


A graph is plotted between \( E_{\text {cell}} \) and \( \log _{10}\left[\frac{Z n^{2+}}{C u^{2+}}\right] \) The curve was linear with
intercept
on \( E_{\text {cell}} \) axis equal to 1.10 V. Calculate \( E_{\text {cell}} \)
for
\( \left.Z n\right|_{0.1 M} ^{Z n^{2+}}||_{0.01 M}^{C u^{2+}} \mid C u \)
A . 1.07
B. 1.129 v
c. \( 0.059 v \)
D. 0.0295 V


The correct order of
pseudohalide,polyhalide and interhalogen are
\( \mathbf{A} \cdot B r I_{2}^{-}, O C N^{-}, I F_{5} \)
B \( \cdot I F_{5} \cdot B r I_{2}^{-}, O C N^{-} \)
\( \mathbf{c} \cdot O C N^{-}, I F_{5}, B r I_{2}^{-} \)
D. \( O C N^{-}, B r I_{2}^{-}, I F_{5} \)


Which of the following statement is incorrect?
A. Enzymes exist in colloidal state
B. Enzymes are catalysts
c. Enzymes can catalyze any reaction
D. Urease is an enzyme


Find the vector equation of the line joining points \( 2 \hat{i}+\hat{j}+3 \hat{k} \) and \( -4 \hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)


The value of rate constant of a pseudo
first order reaction
A. depends on the concentration of reactants present in small amount
B. depends on the concentration of reactants present in excess
C. is independent of the concentration of reactants
D. depends only on temperature


A ray incident at \( 15^{\circ} \) on one refracting
surface of a prism of angle \( 60^{\circ} \) suffers a
deviation of \( 55^{\circ} . \) What is the angle of
emergence?
A . \( 90^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. None of these


In photoelectric effect, the slope of the straight line graph between stopping potential and frequency of the incident light gives the ratio of Planck's constant
to
A. Charge of electron
B. Work function
c. Photoelectric current
D. K.E. of electron


Consider a sinusoidal travelling wave shown in figure. The wave velocity is \( +40 c m / s . \) The velocity of a particle at
point \( P \) at the instant shown is \( -126 \times \)
\( 10^{-x} m / s . \) Find \( x \)
4
B. 2
\( c \cdot 4 \)
\( D \)


The least count of a stop watch is 0.2 s.
The time of 20 oscillations of a
pendulum is measured to be 25 s. The percentage error in the measurement of
time will be:
A . \( 16 \% \)
в. 1.8 \%
c. \( 0.8 \% \)
D. 0. \%


Application of adsorption in pharmacy and allied field is/are:
This question has multiple correct options
A. Decolourising agents
B. Adsorption chromatography
c. Purified talc
D. None of the above


About above reaction the incorrect
statement is
Product
A. The name of reaction is Riemer teimann's reaction
B. The intermediate in the reaction is dichloro carbene
c. The final product is o-hydroxy benzaldehyde
D. The final product is benzyl chloride


The period of small oscillations is
A \( \cdot \pi a \sqrt{\frac{m}{C}} \)
В. \( \pi a \sqrt{\frac{2 m a}{c}} \)
C \( \cdot 2 \pi \sqrt{\frac{2 m a^{3}}{C}} \)
D. \( 2 \pi a \sqrt{\frac{m a}{C}} \)


\( \boldsymbol{y}=\sin ^{-1}\left[\log _{3}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right)\right] \Rightarrow-1 \leq \)
\( \log _{3}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right) \leq \mathbf{1} \)


Which one of the following is an example of a thermosetting polymer?
\( c \)
\( D \)


Cap cells occur in
A. Oedogonium
B. Diatoms
c. Dinoflagellates
D. Euglena


Let \( S=\{2,4,6,8, \dots . .20\} . \) What is the maximum number of subsets does \( \boldsymbol{S} \)
have ?
A . 10
B . 20
c. 512
D. 1024


Arrange the following sulphates of alkaline earth metals in order of decreasing thermal stability:
\( B e S O_{4}, M g S O_{4}, C a S O_{4}, S r S O_{4} \)
A \( \cdot B e S O_{4}>M g S O_{4}>C a S O_{4}>S r S O_{4} \)
в. \( \operatorname{SrSO}_{4}>\operatorname{Mg} S O_{4}>\operatorname{CaSO}_{4}> \)Ве\( S O_{4} \)
c. \( \operatorname{SrSO}_{4}>\operatorname{CaSO}_{4}>\operatorname{MgSO}_{4}>\operatorname{BeSO}_{4} \)
\( \mathrm{D} \cdot \operatorname{SrSO}_{4}>\operatorname{CaSO}_{4}>\operatorname{Be} \mathrm{SO}_{4}>\mathrm{MgSO}_{4} \)


In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the
centre. Identical charges of magnitude \( q \) are placed at \( (n-1) \) corners. The field
at the centre is
A. \( _{k^{2}} \frac{q}{r^{2}} \)
в. \( _{(n-1) k \frac{q}{r^{2}}} \)
c. \( \frac{n}{n-1} k^{\frac{q}{r^{2}}} \)
D. \( \frac{n-1}{n} k \frac{q}{r^{2}} \)


State whether the following statements are True or False.
If \( \mathrm{E}=0, \) at all points of a closed surface, The electric flux through the surface is zero.
A. True
B. False


A closed iron ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling
magnet is:
A. equal to g
B. less thang
c. more than g
D. depends on the diameter of the ring and length of magnet


Find the roots of the equation \( 2 x^{2}- \) \( \boldsymbol{x}+\frac{\mathbf{1}}{\mathbf{8}}=\mathbf{0} \)


Five identical resistor are initially arranged a shown in the figure be clear
lines. If two similar resistances
are added as shown by the dashed lines
then change in resistance in final and
initial arrangement is
\( \mathbf{A} \cdot 2 \Omega \)
B. \( 1 \Omega \)
\( c \cdot 3 \Omega \)
D. \( 4 \Omega \)


If uncertainty in the measurement of position and momentum of an electron are equal, then uncertainty in the measurement of its velocity ??
A \( \cdot 8 \times 10^{12} \mathrm{m} \mathrm{s}^{-1} \)
B. \( 6 \times 10^{12} \mathrm{m} \mathrm{s}^{-1} \)
c. \( 4 \times 10^{12} \mathrm{m} \mathrm{s}^{-1} \)
D. \( 2 \times 10^{12} \mathrm{m} \mathrm{s}^{-1} \)


A particle falls from a height ' \( h^{\prime} \) upon a
fixed horizontal plane and rebounds. If
\( e^{\prime} \) is the coefficient of restitution, the
total distance travelled before it comes
to rest is
\( ^{\text {A }} \). \( h\left(\frac{1+e^{2}}{1-e^{2}}\right) \)
B \( \quad h\left(\frac{1-e^{2}}{1+e^{2}}\right) \)
c. \( \frac{H}{2}\left(\frac{1-e^{2}}{1+e^{2}}\right) \)
D. \( \frac{H}{2}\left(\frac{1+e^{2}}{1-e^{2}}\right) \)


A light ray of a single wavelength is incident on the prism. The emergent light is best described by a:
A. spectrum of component colours
B. laterally shifted ray of same wavelength.
c. light ray of same wavelength deviated by an angle.
D. light ray of different wavelength deviated by an angle


Wavelength associated with an electron
having kinetic energy \( 3 \times 10^{-25} J \) is
\( x \times 10^{-7} \) m. What is the value of \( x ? \)
\( A \cdot 9 \)
B. 4
\( c .5 \)
D. 6


The work function of a substance is 4.0
eV. The longest wavelength of light that can cause photo electron emission from this substance is approximately:
A. \( 540 \mathrm{nm} \)
B. 440 nm
\( c .310 \mathrm{nm} \)
D. 220 nm


The rate of change of linear momentum of a body falling freely under gravity is equal to it's


The IUPAC name of the following compound is 2,4,6 - tribromophenol.
A. True
B. False


What is the value of 1 nano-second in
second?
A \( \cdot 10^{-9} \)
\( 9^{-9} \)
B. \( 10^{-6} \)
\( c \cdot 10^{-8} \)
D. \( 10^{-10} \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{4} \)
then
A. \( f \) may be one-one and onto
B. \( f \) is one-one and onto
c. fis one-one but not onto
D. fis neither one-one nor onto


Find the integrals of the function:
\( \sin ^{4} x \)


In the following functional human lung studies, identify the total lung capacity.
A) Inspiratory capacity (IC)
B) Functional residual capacity (FRC)
C) Vital capacity (VC)
D) Inspiratory reserve volume (IRV)
E) Residual volume (RV)
F) Expiratory reserve volume (ERV)
G) Tidal volume (TV)
The correct answer is
\( A \cdot(D)+(F) \)
B. \( (A)+(D) \)
\( c \cdot(B)+(C) \)
\( D \cdot(c)+(E) \)


Assertion
Lenz's law violates the principle of conservation of energy.
Reason
Induced emf always opposes the change in magnetic flux responsible for
its production.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the unit digit of \( 2 \times 3 \times 4 \times \ldots \times \)
\( \mathbf{9 9} \)


A bucket placed in the open where the rain is falling vertically. If a wind begins to blow horizontally at double the velocity of the rain, how will the rate of filling of the bucket change?
A. Remain unchanged
B. Doubled
c. Halved
D. Become fourtimes


A derivable function \( \boldsymbol{f}: \boldsymbol{R}^{+} \rightarrow \boldsymbol{R} \)
satisfies the condition \( f(x)-f(y) \geq \)
\( \ln \frac{x}{y}+x-y ; \forall x, y \in R^{+} . \) If \( g \) denotes
the derivative of \( f \) then the value of the \( \operatorname{sum} \sum_{n=1}^{100} g\left(\frac{1}{n}\right) \) is \( 1030 k . \) Find the
value of \( k \)


How many sides does a regular polygon have if each of its interior angles is
\( \mathbf{1 6} \mathbf{5}^{\mathbf{0}} \) ?
A. Number of sides \( =24 \)
B. Number of sides= 30
c. Number of sides \( =36 \)
D. Number of sides \( =42 \)


Which of the following is vinyl group?
A \( \cdot\left(C H_{3}\right)_{2} C H- \)
B. \( H C \equiv C- \)
c. \( H_{2} C=C H-C H_{2}- \)
D. \( C H_{2}=C H- \)


Consider a young's doluble slit experiment as shown in figure. What
should be the slit seperation din term
of wavelength \( \lambda \) such that the first
minima occurs directly in front of the
slit \( \left(\boldsymbol{S}_{1}\right) ? \)
\( A \)
B.
c. \( \frac{\lambda}{(\sqrt{5}-2)} \)
D. \( \frac{\lambda}{2(\sqrt{5}-2)} \)


A biconvex lens, \( f_{1}=20 c m, \) is placed 5
\( \mathrm{cm} \) in front of a convex mirror, \( \boldsymbol{f}_{2}= \)
15 \( c m . \) An object of length 2 cm is
placed at a distance \( 10 \mathrm{cm} \) from the lens. If overall magnification is \( X / 3 \) Then find out the value of \( X ? \)


Number of mitochondria is maximum
in part of uriniferous tubule
A . PCT
B. Loop of Henle
c. DcT
D. Bowmans capsule


A fruit vendor sells fruits from his shop. Selling prices of Apple, Mango and Orange are Rs. \( 20, \) Rs. 10 and Rs. 5 each
respectively. The sales in three days are given below
\( \begin{array}{llll}\text { Day } & \text { Apples } & \text { Mangoes } & \text { Oranges } \\ 1 & 50 & 60 & 30 \\ 2 & 40 & 70 & 20 \\ 3 & 60 & 40 & 10\end{array} \)
Write the matrix indicating the total amount collected on each day and
hence find the total amount collected
from selling of all three fruits combined.


On increasing the reverse bias to a large value in a p-njunction, diode
current
A. Increases slowely
B. Remains fixed
c. suddenly increases
D. Decreases slowly


A man buys a plot of land at
\( R s 3,00,000 . \) He sells one third of the plot at a loss of \( 20 \% \). Again, he sells two
-fifth of the plot left at a profit of \( 25 \% \) At what price should he sell the remaining plot in order to get a profit of \( 10 \% \) on the whole?


The length \( \ell, \) breadth b and thickness of a block of wood were measured with
the help of a measuring scale. The results with permissible errors are \( \ell= \) \( 15.12 \pm 0.01 \mathrm{cm}, \mathrm{t}=5.28 \pm 0.01 \mathrm{cm} . b= \)
\( 10.15 \pm 0.01 \mathrm{cm} . \) The percentage error in volume upto proper significant figures is :
A . 0.28\%
B . 0.36\%
c. \( 0.48 \% \)
D . 0.64\%


In triangle \( A B C, X Y \| A C \) and divide the triangle into two parts of equal areas. Find the ratio \( \frac{\boldsymbol{A} \boldsymbol{X}}{\boldsymbol{A B}} \)


A bird of mass \( 1.23 \mathrm{kg} \) is able to hover by imparting a downward velocity of 10
\( \mathrm{m} / \mathrm{s} \) uniformly to air of density 'p' \( \mathrm{kg} / \mathrm{m}^{3} \)
over an effective area \( 0.1 m^{2} . \) The
acceleration due to gravity is \( 10 \mathrm{m} / \mathrm{s}^{2} \)
Then the magnitude of 'p' in \( \mathrm{kg} / m^{3} \)
A . 0.34
B. 0.89
c. 1.23
D. 4.8


Which of the following statements
is/are true?
This question has multiple correct options
A. Tritium is the isotope of hydrogen with 1 neutron
B. Deuterium is more reactive than hydrogen
C \( \cdot D_{2} O \) concentration in water is higher than \( T_{2} O \)
D. Boiling point of hydrogen is lower than that of deuterium


A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its
negative terminal. Let \( Q_{+} \) and \( Q_{-} \) be
the charges appearing on the positive and negative plates respectively. Calculate the potential difference between the two plates.


Two equal charges are separated by a
distance \( d . A \) third charge placed on a
perpendicular bisector at \( x \) distance will experience maximum coulomb force when :
A \( \cdot x=\frac{d}{\sqrt{2}} \)
B. \( x=\frac{d}{2} \)
c. \( _{x}=\frac{d}{2 \sqrt{2}} \)
D. \( _{x}=\frac{d}{2 \sqrt{3}} \)


Which of the following complexes will have a tetrahedral shape?
B . \( \left[P d(C N)_{4}\right]^{2} \)
c. \( \left[N i(C N)_{4}\right]^{2} \)
D. \( \left[N i C l_{4}\right]^{2} \)


The line \( L_{1} \) given by \( \frac{x}{5}+\frac{y}{b}=1 \) passes
through the point \( M(13,32) . \) The line
\( L_{2} \) is parallel to \( L_{1} \) and has the equation \( \frac{x}{c}+\frac{y}{3}=1 . \) Then the distance
between \( L_{1} \) and \( L_{2} \) is
A. \( \sqrt{17} \)
в. \( \frac{17}{\sqrt{15}} \)
c. \( \frac{23}{\sqrt{17}} \)
D. \( \frac{23}{\sqrt{15}} \)


The intermediate product between \( \alpha \) ketoglutaric acid and succinic acid in TCA cycle is
A . Acetyl CoA
B. succinyl CoA
c. Fumarate
D. Oxalosuccinic acid


How many of the following compounds
do not react with \( \boldsymbol{H}_{2} / \boldsymbol{N} \boldsymbol{i} ? \)
Propanenitrile Methylethanoate
Pentan-2-one Ethanoic acid

Benzenecarbonylchloride But-1-yne Propanamide Nitroethane
A .4
B. 5
\( c \cdot 3 \)
D. None of these


The scientist awarded Nobel prize in
1959 for in vitro synthesis of polyribonucleotide was
A. Mendel
B. Calvin
c. Khorana
D. Ochoa


Prove that every identity relation on a set is reflexive, but the converse is not
necessarily true.


Classical smog is also called
as
A. London smog
B. sulphurous acid smog
c. Both \( A \) and \( B \)
D. Los angles smog


In the figure, there are four arcs
carrying positive and negative charges.
All of them have same charge density \( \lambda \)
Pick incorrect statement(s).
This question has multiple correct options
A. The net dipole moment for the given charge distribution is \( (4 \sqrt{5}) \lambda R^{2} \)
B. The resultant electric field at the center is zero
C. If a uniform \( \vec{E} \) is switched on perpendicular to the plane, charge distribution starts rotating about \( X \) -axis
D. Potential at the centre of the given charge distribution
is non-zero


Find the minimum value of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{e^{x}}{[x+1]}, x \geq 0 \)


Which of the following solutions is more concentrated than the others?
A. \( 5.3 \mathrm{gm} \) of \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) in \( 500 \mathrm{ml} \) solution
B. 5 gm of \( N a O H \) in 100 ml solution
c. 3.65 gm of \( H C l \) in 750 ml solution
D. 4.9 gm of \( H_{2} S O_{4} \) in \( 1000 \mathrm{ml} \) solution


Mark the correct statement(s) from the
following for image formation of a real
object.
This question has multiple correct options
A. Image formed by a single convex mirror can be real
B. Image formed by a single convex mirror can be virtual
C. Image formed by a single convex mirror can be magnified
D. Image formed by a single convex mirror can be inverted


Angular momentum of an electron is quantized according to:
A. Planck
B. Rutherford
c. Bohr
D. Thomson


In the circuit shown (fig), the coil has inductance and resistance. When X is
joined to \( Y \), the time constant is \( \tau \) during the growth of current. When the
steady state is reached, heat is
produced in the coil at a rate P. \( X \) is now joined to Z. After joining \( X \) and \( Z \)
A. the total heat produced in the coil is \( P \tau \)
B. the total heat produced in the coil is \( \frac{1}{2} P \tau \)
\( c . \) the total heat produced in the coil is \( 2 P \tau \)
D. the data given are not sufficient to reach a conclusion


The ratio of the radii of the planets \( P_{1} \)
and \( P_{2} \) is \( k_{1} . \) The corresponding ratio of the acceleration due to the gravity on
them is \( k_{2} \). The ratio of the escape velocities from them will be
A \( \cdot k_{1} k_{2} \)
в. \( \sqrt{k_{1} k_{2}} \)
\( \mathbf{c} \cdot \sqrt{\left(k_{1} / k_{2}\right)} \)
D. \( \sqrt{\left(k_{2} / k_{1}\right)} \)


Which of the following numbers lies between \( \frac{-5}{2} \) and \( \frac{3}{4} ? \)
A .
B. 0
c. -3
D. 3


Assertion: Magnetic force between two short magnets, when they are co-axial follows inverse square law of distance. Reason : The magnetic forces between two poles do not follow inverse square
law of distance
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


It is possible to take pictures of those objects which are not fully visible to the eye using camera films sensitive to
A. ultraviolet rays
B. infrared rays
c. microwaves
D. radiowaves


Fourier predicted the green house effect and it was coined by
A. Fourier
B. Tanseley
c. Arrhenius
D. Odum


Which of the following statements is
false for isopentane?
A \( . \) It has three \( C H_{3} \) groups.
B. It has one \( C H_{2} \) group.
C . It has one \( C H \) group.
D. It has a carbon which is not bonded to hydrogen.


Number of possible spectral lines which may be emitted in Brackett series in \( H \)
atom, if electrons in 9 th excited state returns to ground state are:
A . 5
B . 45
\( c .6 \)
D. 21


Find the shortest distance between the
skew lines:
\( l_{1}: \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-2}{4} \)
\( l_{2}: \frac{x+2}{4}=\frac{y-0}{-3}=\frac{z+1}{1} \)


Which of the following forms vortex
ring?
A \( \cdot P_{2} O_{5} \)
в. \( P H_{3} \)
c. \( N H_{3} \)
D. None of the above


In which of the following reactions chlorine acts an oxidising agent.
¡) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H}+\boldsymbol{C l}_{2} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{H C l} \)
ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{C C l}_{3} \boldsymbol{C H O}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
iii) \( C H_{4}+C l \stackrel{h v}{\longrightarrow} C H_{3} C l+H C l \)
The correct answer is :
A. (i) only
B. (ii) only
c. (i) and (iii)
D. (i), (ii) and (iii)


Newton's law of cooling is a special case of
A. Kirchoffs law
B. Weins law
c. Stefan-Boltzmanns law
D. Plancks law


State whether true or false.
A periscope works on the principle of reflection
A. True
B. False


According to JJ Thomson's atomic model, negative charges are embedded
in:
A. A lump of positive charge
B. A lump of neutral particles
c. A lump of small atoms
D. The nucleus


The coordinates of points on the line joining the points \( \boldsymbol{P}(\boldsymbol{3},-\boldsymbol{4}) \) and \( Q(-2,5) \) that is twice as far from \( P \) as from \( Q \) is
A \( \cdot\left(\frac{-1}{3}, 2\right) \)
в. \( \left(\frac{2}{3}, 2\right) \)
c. \( \left(\frac{1}{3}, 4\right) \)
D. \( \left(\frac{4}{3}, 2\right) \)


An alkene \( A\left(C_{10} H_{20}\right) \) on oxidative
ozonolysis yields two molecules of
\( \left(C_{5} H_{10} O\right) B . B \) on treatment with
\( \boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{I} \boldsymbol{H}_{4} \) yields \( \mathbf{C}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{12} \boldsymbol{O}\right) \) which can't
be resolved into enantiomers. Which of
following is correct?
A. A: 3,4-diethyl-3-hexene
B. B: 3-pentanone
c. \( c: 3 \) -pentanol
D. All of them are correct


The most abundant element in the
atmosphere is :
A. Phosphorus.
в. Oxygen
c. Nitrogen.
D. Carbon.


The area of a circle is 314 sq. \( \mathrm{cm} \) and area of its minor sector is 31.4 sq. cm.
Find the area of its major sector.
A \( .282 .6 \mathrm{cm}^{2} \)
в. \( 200.6 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 180.04 \mathrm{cm}^{2} \)
D. 1220.09cm \( ^{2} \)


Lateral overlap of \( \boldsymbol{P} \) orbitals leads to the
formation of
A. \( \pi \) bond
B. metallic bond
c. sigma bond
D. ionic bond


Three capacitors connected in series
have an effective capacitance of \( 4 \mu F \). If one of the capacitance is removed, the net capacitance of the capacitor increases to \( 6 \mu F . \) The removed
capacitor has a capacitance of
\( \mathbf{A} \cdot 2 \mu F \)
в. \( 4 \mu F \)
\( \mathbf{c} \cdot 10 \mu F \)
D. \( 12 \mu F \)
E \( .24 \mu F \)


The variance of first \( n \) natural numbers,
is
\( ^{\text {A } \cdot \frac{n+1}{2}} \)
B. \( \frac{n^{2}+1}{12} \)
c. \( \frac{n^{2}-1}{6} \)
D. \( \frac{n^{2}-1}{12} \)


In the nuclear reaction pictured below, what is the missing nuclide? \( _{1}^{2} \boldsymbol{H}+\mathbf{7}^{14} \boldsymbol{N} \rightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+? \)
B . \( _{6}^{13} \mathrm{C} \)
\( \mathbf{c} \cdot \frac{14}{7} N \)
D. \( _{6}^{1} C \)
E \( \cdot \frac{12}{6} C \)


Assertion
Phytoplankton, algae \( \& \) higher plants are chief producers in pond ecosystem.
Reason
Many algae are responsible for
production of ethanol.
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 consequences of deforestation is
A. Global warming
B. Flood
C. Extinction of flora and fauna
D. All of the above


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}\} \)
be two sets \( R \) be a relation from \( A \) to \( B \)
defined by the phrase \( "(x, y) \in R \Rightarrow \)
\( \boldsymbol{x}>\boldsymbol{y}^{\prime \prime} . \) Find relation \( \boldsymbol{R} \) and its domain
and range


Explain \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{c}^{2} \)


A truck is moving along frictionless rail track at a speed of \( 18 m / s \).The mass of
the truck is \( 8000 k g \).If it starts raining,what will be the speed of the
compartment when it has collected water equal to \( 1000 k g \)
A. \( 3 m / s \)
в. \( 6 m / s \)
\( \mathrm{c} \cdot 8 \mathrm{m} / \mathrm{s} \)
D. \( 16 m / s \)


Which of the following remained unchanged for last many million years?
A . Pinus
B. Rice
c. Acacia
D. Ginkgo


Angle (in rad) made by the vector \( \sqrt{3} \hat{i}+\hat{j} \) with the \( x \) -axis:
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.


The hydrolysis constant for the reaction \( A l^{3+}+H_{2} O \rightleftharpoons A l(O H)^{2+}+H^{+} \) is
\( 1.7 \times 10^{-10}, \) what is \( \left[H^{+}\right] \) in \( 0.1 M \)
\( A l C l_{3} \) solution?
A \( \cdot 4.00 \times 10^{-6} M \)
В. \( 4.28 \times 10^{-6} \) М
c. \( 4.12 \times 10^{-6} \) М
D. None of these


A \( 10 \mathrm{V} \) battery with internal resistance 1
\( \Omega \) and a \( 15 V \) battery with internal
resistance \( 0.6 \Omega \) are connected in
parallel to a voltmeter. The reading in
the voltmeter will be close to
\( A, 11.9 \mathrm{V} \)
в. 13.1
c. \( 24.5 \mathrm{v} \)
D. \( 12.5 \mathrm{v} \)


Evaluate: \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a}(\boldsymbol{b}+\boldsymbol{c}) \\ \mathbf{1} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{a}) \\ \boldsymbol{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{c}(\boldsymbol{a}+\boldsymbol{b})\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c . a b c \)
D. \( a^{2}+b^{2}+c^{2} \)


In the expansion of \( \left(x^{3}-\frac{1}{x^{2}}\right)^{n}, n \in N \)
if the sum of the coefficient of \( x^{5} \) and
\( x^{10} \) is \( 0, \) then \( n \) is
A . 25
B. 20
c. 15
D. None of these


\( \begin{array}{ll}\sqrt{(\mathrm{i}) \mathrm{Hg}(\mathrm{OAc})_{2}} & \mathrm{Dil} \mathrm{H}_{2} \mathrm{SO}_{4} \\ +\mathrm{THF}+\mathrm{H}_{2} \mathrm{O} & (\mathrm{i}) \mathrm{B}_{2} \mathrm{H}_{6} \\ (\mathrm{ii}) \mathrm{NaBH}_{4} / \mathrm{O}_{\mathrm{H}} & +\mathrm{THF} \\ (\mathrm{B}) & (\mathrm{ii}) \mathrm{H}_{2} \mathrm{O}_{2}\end{array} \)
\( A \)
\( (\mathbf{A}) \)
\( (\mathbf{B}) \)
\( (\mathrm{C}) \)
\( B \)
\( c \)
\( D \)


Compound \( C_{4} H_{8} O_{2} \) exists in various structures as shown:

Which statement(s) is/are correct?
(1)
(II)
\( (\mathrm{III}) \)
\( (\mathrm{IV}) \)
A. compounds land II give iodoform test: Compound gives white turbidity on heating with Lucas reagent while compound II reduces Tollens reagent
B. compound III gives silver mirror with \( \left[A g\left(N H_{3}\right)_{2}\right] \) and does not react with NaoBr
C. compound IV on acid hydrolysis gives \( C_{2} H_{5} \) COOH and MeOH
D. compound v on heating is decarboxylated to propane


Show that the line \( \frac{x}{a}+\frac{y}{b}=1, \) tocuhes the curve \( y=b . e^{\frac{-x}{a}} \) at the point where
the curve intersects the axis of \( y \)


For the expression \( a x^{2}+7 x+2 \) to be
quadratic, the necessary condition is
\( \mathbf{A} \cdot a=0 \)
B. \( a \neq 0 \)
\( ^{c} \cdot_{a}>\frac{7}{2} \)
D. \( a<-1 \)


Secondary growth occurs due to activity
of.
A. Cork cambium
B. vascular cambium
c. Intercalary meristem
D. Both A and B


According to widely accepted, "Fluid
mosaic model" cell membranes are
semi-fluid, where lipids and integral proteins can diffuse randomly. In recent years, this model has been modified in
several respects. In this regard, which of
the following statements is incorrect?
A. Proteins in cell membranes can travel within the lipid bilayer.
B. Proteins can remain confined within certain domains of the memberane.
C. Proteins can also undergo flip-flop movements in the lipid bilayer.
D. Many proteins remain completely embedded within the lipid bilayer.


A metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The magnet falls with an acceleration:
A. Equal to \( g \)
B. Less than \( g \)
c. Greater than \( g \)
\( D . \) none


A spherical mirror whose inner hollow surface is the reflecting surface is a -
A. convex mirror
B. concave mirror
c. convex lens
D. concave lens


How many lines of symmetry are there for an equilateral triangle.


\( O_{3} \) is diamagnetic molecule. If it has all
\( 0-O \) bond lengths equal then enter 1
else enter 0


Write three significance of Henderson Hasselbalch equation?


When domestic sewage mixes with
river water
A. Small animals like rats will die after drinking river water.
B. The increased microbial activity release micro nutrients, such as iron.
C. The increased microbial activity uses up dissolved oxygen.
D. The river water is still suitable for drinking as impurities are only about \( 0.1 \% \)


The area of the quadrilateral formed by the points (0,0),(1,0),(1,4) and (0,2) is
A. 3
B. 2
\( c \cdot 4 \)
D. 5


The e/m ratio for cathode rays:
A. is constant
B. varies as the atomic number of the element forming the cathode in the discharge tube changes
C. varies as the atomic number of the gas in the discharge tube varies
D. has the smallest value when the discharge tube is filled with hydrogen


Find the area cut off from the parabola
\( 4 y=3 x^{2} \) by the straight line \( 2 y= \)
\( 3 x+12 \)
A. 25 sq.units
B. 27sq.units
c. \( 36 s q \).units
D. 16 sq.units


State whether these sentences are true
(T) or false (F).
The atmosphere is composed mainly of nitrogen and oxygen.
A. True
B. False


Which nerve is called as dentist's
nerve?
A . Facial
B. Trigeminal
c. vagus
D. Hypoglossal


The factor which influences unicellular
organisms to keep spherical shape is
A. Surface tension
B. Osmosis
c. viscosity
D. Protoplasm


The solubility of water decreases rapidly with the increase in the size of groups attached to carbonyl
group.
A. alkyl
B. aryl
c. phenyl
D. benzyl


In an a.c. circuit, containing an inductance and a capacitor in series, the current is found to be maximum
when the value of inductance is
0.5henry and of capacitance is 8F. The
angular frequency of the input A.C. Voltage must be equal to
A. 0.5
B. 0.10
\( c \)
D. 0.3


The function of heavy water in a nuclear
reactor to:
A. slow down the neutrons
B. increase the neutrons
c. stop the electrons
D. none of these


Consider a conductor of variable cross
section in which current is flowing from
cross section 1 to 2 . Then
This question has multiple correct options
A. current passing through both the cross sections is the same
B. current through 1 is less than that through 2
c. drift velocity of electrons at 1 is less than that at 2 .
D. drift velocity is same at both the cross sections


Simplify combining like terms:
\( \left(3 y^{2}+5 y-4\right)-\left(8 y-y^{2}-4\right) \)


In a class \( 5 \% \) of boys and \( 10 \% \) of girls have an I.Q of more than \( 150 . \) In this class
\( 60 \% \) of students are boys. If a student is
selected at random and found to have
an I.Q. of more than \( 150 . \) Find the probability that the student is a boy.
A \( \cdot \frac{3}{7} \)
B. \( \frac{23}{7} \)
\( c \cdot \frac{3}{5} \)
D. None of these


A pair of adjacent coil has a mutual
inductance of \( 1.5 \mathrm{H} \). If the current in
one coil changes from 0 to \( 20 A \) in 0.5
sec, what is the change of flux linkage with the other coil?


If \( \overrightarrow{\boldsymbol{A}}=2 \hat{\boldsymbol{i}}+\boldsymbol{7} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+ \)
\( 5 \hat{k} \) Find the component of \( \vec{A} \) and \( \vec{B} \)


Field inside a solenoid is
A. directly proportional to its length
B. directly proportional to current
C. inversely proportional to number of turns
D. inversely proportional to current


Line segment joining the centre to any point on the circle is a radius of the circle.
A. True
B. False


If \( A \) and \( B \) are two events such that \( P(A \cup B) \geq \frac{3}{4} \) and \( \frac{1}{8} \leq P(A \cap B) \leq \)
\( \mathbf{3} \)
\( \overline{\mathbf{8}}^{\prime} \)
then
This question has multiple correct options
A \( \cdot P(A)+P(B) \geq \frac{7}{8} \)
B . \( P(A)+P(B) \leq 11 / 8 \)
\( c \cdot P(A) P(B) \leq \frac{3}{8} \)
D. None of these


For a gas having molar mass \( \mathrm{M} \), specific heat at constant pressure can be given
as:
A \( \cdot \frac{\gamma R}{M(\gamma-1)} \)
в. \( \frac{\gamma}{R M} \)
c. \( \frac{M}{R(\gamma-1)} \)
D. \( \frac{\gamma R M}{\gamma+1} \)


\( \left|\begin{array}{lll}a^{2}+\lambda^{2} & a b+c \lambda & c a-b \lambda \\ a b-c \lambda & b^{2}+\lambda^{2} & b c+a \lambda \\ c a+b \lambda & b c-a \lambda & c^{2}+\lambda^{2}\end{array}\right| \mid \begin{array}{cc}\lambda & c \\ -c & \lambda \\ b & -a\end{array} \)
\( \left(1+a^{2}+b^{2}+c^{2}\right)^{3}, \) then the value of \( \lambda \)
is
\( A \cdot 8 \)
в. 2
\( c \)
\( D \)


A solution is to be kept between \( 68^{\circ} F \)
and \( 77^{\circ} F . \) What is the range in
temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by \( \boldsymbol{F}=\frac{\mathbf{9}}{\mathbf{5}} \boldsymbol{C}+\mathbf{3 2} ? \)


A particle of mass \( m_{1} \) moving with
velocity \( v \) strikes with a mass \( m_{2} \) at rest, then the condition for maximum
transfer of kinetic energy is :
\( \mathbf{A} \cdot m_{1}>>m_{2} \)
в. \( m_{2}>>m_{2} \)
\( \mathbf{c} \cdot m_{1}=m_{2} \)
D . \( m_{1}=2 m_{2} \)


At what point \( p(x, y) \) of the curve \( y= \) \( e^{-|x|} \) should a tangent be drawn so that
area of the triangle bounded by the
tangent and the co-ordinate axes be
greatest?
\( \mathbf{A} \cdot(\pm e, 1) \)
B \( \cdot\left(\pm 1, \frac{1}{e}\right) \)
\( ^{c} \cdot\left(1, \pm \frac{1}{e}\right) \)
D \( \cdot(\pm 1, e) \)


An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{8} \boldsymbol{H}_{6}\right) \) gives brick red precipitate with ammoniacal
solution of \( C u_{2} C l_{2} . \) A on treatment with
ammoniacal solution of \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) yields
\( B\left(C_{8} H_{8} O\right), \) B gives positive iodoform test \( \mathrm{B} \) can also be prepared by the reaction of benzene with acetic
anhydride in presence of \( A l C l_{3} \) identify \( A \) and \( B \)


FAC is congruent to GEC. Which
statement can NOT be proven??
\( A \cdot A F \cong G E \)
B. \( \angle F C A \cong \angle G C E \)
\( c . \angle C A F \cong \angle C D G \)
\( . A C \cong E C \)
\( C \)


Which of the following statements is not true about canal rays?
A. They travel in straight line.
B. They are made up of positively charged particles.
C. Their e/m ratio is same for all gases.
D. These rays produce fluorescence on \( Z n S \) screen.


Salivary glands of cockroach open on
A . Maxilla
B. Hypopharynx
c. Labium
D. Labrum


A parallel beam of monochromatic light
of wavelength \( 663 \mathrm{nm} \) is incident on a
totally reflecting plane mirror. The angle
of incident is \( 60^{\circ} \) and the number of
photons striking the mirror per second
is \( 1.0 \times 10^{19} . \) If the force exerted by light
beam on the mirror is \( Y \times 10^{-8} N . \) Find
\( Y \)


An atom has an electronic
configuration 2,8,7
(a)Name the group to which it belongs
to:
(b)To which of the following elements would it be chemically similar?
\( [N(7), F(9), P(15), A r(18)] \)


Which of the following involves the loss of two protons and two electrons?
A. Deamination
B. Dehydrogenation
c. carboxylation
D. None of the above


Name the following compound according to the IUPAC system or
nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C O C H}_{3} \)


Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:
A. spheres
B. planes
c. paraboloids
D. ellipsoids.


Using the properties of determinant and
without expanding, prove that:
\( \left|\begin{array}{lll}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{array}\right|=0 \)


In the magnetic meridian of a certain
place the horizontal component of earth's magnetic field is \( 0.25 \mathrm{G} \) and dip
angle is \( 60^{\circ} . \) The magnetic field of the earth at this location is
\( \mathbf{A} \cdot 0.50 \mathrm{G} \)
B. 0.52 G
c. 0.54 G
D. 0.56 G


Graphite is a good conductor of electricity due to ?
A. Its giant tetrahedral polymer structure
B. Its high refractive index
c. Presence of free and mobile electrons
D. High IP value of carbon


When a man stands m a moving escalted the goes up in 50 sec and
when he walks up the moving escalator he goes in 30 sec,then find the five in which man walks up the stationar escalator.


Milk is an example of :
A. Suspension
B. True solution
c. Emulsion
D. None of the above


A body moving along a circular path will
have :
A. a constant speed
B. a constant velocity
c. no tangential velocity
D. a radial acceleration


Identify the species which can give both conjugate acid and conjugate base:
A \( \cdot N H_{4}^{+} \)
в. \( H_{2} P O_{4}^{-} \)
\( \mathbf{c} \cdot P O_{4}^{3} \)
D. \( H_{3} O^{+} \)


The average of 7 consecutive numbers
is n. If the next two numbers are
included, the average will be....


At equilibrium, if \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1}, \) then
A. \( \Delta G^{\circ}=0 \)
В. \( \Delta G^{\circ}>1 \)
c. \( \Delta G^{\circ}<1 \)
D. none of the above


Find the number of relations from
\( \{\boldsymbol{m}, \boldsymbol{o}, \boldsymbol{t}, \boldsymbol{h}, \boldsymbol{e}, \boldsymbol{r}\} \) to \( \{\boldsymbol{c}, \boldsymbol{h}, \boldsymbol{i}, \boldsymbol{l}, \boldsymbol{d}\} \)
A . 30
B . \( 30^{2} \)
\( c \cdot 2^{30} \)
D. 60


An object kept on the principal axis and infront of a spherical mirror, is moved along the axis itself. Its lateral magnification \( \mathrm{m} \) is measured, and plotted versus object distance |ul for a
range of \( u \), as shown in fig. The magnification of the object when it is placed at a distance \( 20 \mathrm{cm} \) in front of
the mirror is:
\( A \cdot- \)
B.
\( c \)
D. 2


A ball collides elastically with another ball of the same mass. The collision is
oblique and initially one of the ball was at rest. After the collision, the two balls
move with same speeds. What will be the angle between the velocity of the
balls after the collision?
A \( .30^{\circ} \)
B . 45
\( c \cdot 60 \)
D. 90


Mustard gas can be prepared by the reaction of ethylene with:
\( A \cdot S F_{6} \)
в. \( \mathrm{SF}_{4} \)
\( c \cdot \operatorname{sCl}_{2} \)
D. None of the above


Figures \( (a) \) and \( (b) \) refer to the steady
flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?


Which of the following do not exist?
This question has multiple correct options
A. \( S H_{6} \)
в. \( H F O_{4} \)
\( \mathrm{c} . F e I_{3} \)
D. \( H C l O_{3} \)


Q Type your question
\( A \)
B.
\( c \)
\( D \)


\( 1 D= \)


A frame thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film.When the portion \( A \) is punctured with a pin, the thread:
A. becomes concave towards A
B. becomes convex towards A
c. either (a) or (b) depending on the size of A with respect to
D. remains in the initial position


Which is /are true statements/
reactions?

This question has multiple correct options
\( \mathbf{A} \cdot A l_{4} C_{3}+H_{2} O \rightarrow C H_{4} \)
B \( \cdot C a C_{2}+H_{2} O \rightarrow C_{2} H_{2} \)
\( \mathbf{c} \cdot M g_{2} C_{3}+H_{2} O \rightarrow C H_{3} C \equiv C H \)
D \( \cdot M e_{3} C-H+K M n O_{4} \stackrel{H^{+}}{\longrightarrow} M e_{3} C-O H \)


Some green beetles appear among the red beetle because
A. Beetles become green by accumulating chlorophyll from the green leaves that they eatt
B. Natural variations occur during sexual reproduction
c. Red beetles mimic green colour of leaves whenever they see crows.
D. Beetles change colour from red to green with change of season


Vascular bundles are closed when they
A. Have cambium
B. Lack cambium
c. Lack pericycle
D. Lack endodermis


Two photons having
A. Equal wavelengths have equal linear momenta
B. Equal energies have equal linear momenta
C. Equal frequencies have equal linear momenta
D. Equal linear momenta have equal wavelengths


Barium hydroxide is an alkali. It reacts with hydrochloric acid. How does the pH of the hydrochloric acid change as an excess of aqueous barium hydroxide is added?
A. The pH decrease from \( p H \) 14 and becomes constant at \( p H \)
B. The pH decreases from \( p H \) 14 to about \( p H \)
c. The pHincreases from \( p H \) 1 and becomes constant at \( p H \)
D. The pH increases from \( p H \) 1 to about \( p H \) 14


The direction cosines of the line joining the points (2,3,-1) and (3,-2,1) are
в. \( \frac{1}{\sqrt{30}},-\sqrt{\frac{5}{6}} \cdot \sqrt{\frac{2}{15}} \)
c. \( \frac{-1}{30}, \frac{1}{6},-\frac{1}{15} \)
D. none of these


Consider the earth as a short magnet
with the centre coinciding with the centre of the earth and dipole moment \( M \). The angle of dip \( \theta \) at the place where the magnetic latitude is \( \lambda \) is :
A \( \cdot \tan ^{-1}(2 \tan \lambda) \)
B. \( \tan ^{-1}(\tan \lambda) \)
\( c \cdot \tan ^{-1}(\tan \lambda / 2) \)
D. \( \tan ^{-1}(4 \tan \lambda) \)


Cartilage present in trachea, larynx and bronchi is
A. Fibrous
B. Elastic
c. Hyaline
D. Calcified


\( \ln \) an \( L C \) oscillation circuit, \( L= \)
\( \mathbf{1} \boldsymbol{H}, \boldsymbol{C}=\frac{\mathbf{1}}{\mathbf{4}} \boldsymbol{F} \) and maximum charge in
capacitor is \( 4 C . \) Match the following two
columns. Note that in column II all
values are in their respective Sl units


Assertion
Tracheae, primary, secondary and tertiary bronchi are supported by incomplete cartilaginous rings.
Reason
These rings of cartilage make the wall
non-collapsible.
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


Electronegativity across the period:
A. increases
B. decreases
c. remains constant
D. can't be predicted


The simplified form of the expression given below is :\( y^{4}-x^{4}-y^{3} \)
\( \frac{x(x+y) x}{y^{2}-x y+x^{2}} \)
A . 1
B.
\( c \cdot-1 \)
D. 2


What is Zone refining method?


A student is standing at a distance of
\( \mathbf{5 0} \) metre from the bus. As soon as the
bus begins its motion with an
acceleration of \( 1 \mathrm{ms}^{-2} \), the students
starts running towards the bus with a
uniform velocity \( u \). Assuming the motion to be along a straight road, the
minimum value of \( u, \) so that the
student is able to catch the bus is:
\( \mathbf{A} \cdot 8 m s^{-1} \)
B. \( 5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 12 \mathrm{ms}^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


Cavity formed by separation of cells in a
tissue is
A. Schizogenous cavity
B. Lysigenous cavity
c. schizolysigenous cavity
D. Stomatal complex


The reaction \( : Z n^{2+}(a q)+ \)
\( \mathbf{2} e^{-} \rightarrow \boldsymbol{Z} \boldsymbol{n} \)
\( (s) \) has a electrode
potential of \( 0.76 V \) This means:


Which one of the following has a negative sign, on the basis of new
Cartesian sign Convention?
A. Image distance for a convex mirror
B. Height of a virtual and erect image
C. Focal length of a convex mirror
D. object distance for a concave mirror


Which of the following algae secrete "saxitoxin"?
A. Gonyaulax
B. Oscillatoria
c. Noctiluca
D. Pyrocystis


A nucleus of sodium- \( 21, \frac{21}{11} N a, \) decays to form a new nucleus containing 10 protons and 11 neutrons.

Which leptons are emitted from the
sodium-21 nucleus during the decay?
A. A positron and an antineutrino
B. A positron and a neutrino
c. An electron and an antineutrino
D. An electron and a neutrino


Assertion
In the electrolytic reduction of \( A l_{2} O_{3} \)
cryolite is used.
Reason
Cryolite is an ore of aluminium.
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 and Reason is correct.


Factorize:
\( 4 x y-x^{2}-4 y^{2}+z^{2} \)
\( \mathbf{A} \cdot(z+x-2 y)(z-x+2 y) \)
B . \( (z-x-2 y)(z-x+2 y) \)
\( \mathbf{c} \cdot(z+x-2 y)(z-x-2 y) \)
D. \( (z+x-2 y)(z-x+y) \)


Decline in hearing power begins after the age of
A. 50 years
B. 35 years
c. 45 years
D. 10 years


If the sum of first \( n \) terms of an A.P is
\( \frac{1}{2}\left(3 n^{2}+7 n\right), \) then find its \( n \) th term Hence write its 20 th term.
A \( \cdot a_{n}=5 n+2, a_{20}=12 \)
B \( \cdot a_{n}=7 n+2, a_{20}=62 \)
c \( \cdot a_{n}=3 n+2, a_{20}=62 \)
D. None of these


Particles of masses \( \boldsymbol{m}, \boldsymbol{2 m}, \boldsymbol{3} \boldsymbol{m}, \ldots(\boldsymbol{n}) \boldsymbol{m} \)
grams are placed on the same line at distances \( l, 2 l, 3 l, \dots(n) l \) cm from a fixed point. The distance of the centre of mass of the particles from the fixed
point in centimetres is:
A \( \cdot \frac{(2 n+1) l}{3} \)
в. \( \frac{l}{n+1} \)
c. \( \frac{n\left(n^{2}+1\right) l}{2} \)
D. \( \frac{2 l}{n\left(n^{2}+1\right)} \)


Identify the condition necessary for the conversion of \( B \) and \( C \)
A. \( B \) - hot and conc. \( N a O H, C- \) cold and dil. \( N a O H \)
в. \( B \) - conc. \( N a O H, C- \) per chloric acid
c. \( B \) - per chloric acid, \( C- \) sodium chloride
D. \( B \) - sodium chloride, \( C- \) conc. NaOH


Six identical uniform rods
\( P Q, Q R, R S, S T, T U \) and \( U P \) each
weighing \( \mathrm{W} \) are freely joined at their
ends to form a hexagon. The rod \( P Q \) is
fixed in a horizontal position and
middle points of \( \boldsymbol{P Q} \) and \( \boldsymbol{S T} \) are
connected by a vertical string. The tension in string is
\( A \cdot W \)
В. \( 3 W \)
\( c .2 W \)
0.44


At \( 25^{\circ} C, \) the equivalent conductance at
infinite dilution of \( H C l, C H_{3} C O O N a \)
and \( N a C l \) are 426.1,91.0 and
\( 126.45 c m^{2} \Omega^{-1} e q^{-1} \) respectively, the
\( \wedge_{\infty} \) for \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}\left(\boldsymbol{i n} \boldsymbol{c m}^{-1} \boldsymbol{\Omega}^{-1} \boldsymbol{e q}^{-1}\right) \)
is:
\( \mathbf{A} \cdot 391.6 \)
B. 390.6
\( c .389 .6 \)
D. 388.6


Prove the following:
\( \left|\begin{array}{lll}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c}\end{array}\right|=\mathbf{2}\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right| \)


The compound that causes general
antidepressant action on the central
nervous system belongs to the class of:
A. analgesics
B. tranquilizers
c. narcotic analgesics
D. antihistamines


An open vessel containing air is heated from \( 300 \mathrm{K} \) to \( 400 \mathrm{K} \). The fraction of air
originally present which goes out of it is:
A. \( 3 / 4 \)
B. \( 1 / 4 \)
\( c \cdot 2 / 3 \)
D. 1/8


State whether the following conversions are oxidation or reduction?
\( \boldsymbol{P b O}_{2}+\boldsymbol{S O}_{2} \rightarrow \boldsymbol{P b S O}_{4} \)


A particle of mass \( m \) is dropped from a height \( h \) above the ground. At the same
time another particle of the same mass is thrown vertically upwards from the ground with a speed of \( \sqrt{2 g h} \). If they collide head on completely inelastically, the time taken for the combined mass to reach the ground, in units of \( \sqrt{\frac{\boldsymbol{h}}{\boldsymbol{g}}} \) is:
A \( \cdot \sqrt{\frac{3}{4}} \)
B. \( \frac{1}{2} \)
c. \( \sqrt{\frac{1}{2}} \)
D. \( \sqrt{\frac{3}{2}} \)


\( \ln \beta^{+} \) decay process, the following changes take place inside the nucleus
A \( \cdot \frac{A}{Z} X \longrightarrow_{Z-1}^{A} Y+e^{+}+\gamma \)
B . \( _{Z} X \longrightarrow_{Z+1}^{A} Y+e^{-}+\gamma \)
\( \mathbf{c} \cdot_{Z}^{A} X \longrightarrow_{Z}^{A} Y+e^{-}+\gamma \)
D \( \cdot \frac{A}{Z} X \longrightarrow_{Z}^{A} Y+e^{-}+\bar{\gamma} \)


State Ampere's circuital law.


Organelles having enzymes involved in photorespiration are
A. Mitochondria, chloroplasts and ribosomes
B. Mitochondria, peroxisomes and chloroplasts
c. Mitochondria, nucleus and ribosomes
D. Mitochondria, peroxisomes and glyoxysomes


A volume of 100 ml of water gas
containing some \( C O_{2} \) was mixed with
\( 100 m l \) of oxygen and mixture exploded. The volume after an explosion was 100 ml. On introducing \( N a O H \) the volume was reduced to 52.5 ml. If
the volume ratio of \( C O, H_{2} \) and \( C O_{2} \) in
the original sample is \( a b: c d: 2 \)
calculate the value of \( ^{\prime} a b c d^{\prime} \)


cosmic rays, solar radiation, naturally occurring radioactive elements are all
sources of
A. External background radiation
B. Internal background radiation
c. Radioactive radiation
D. All of the above


Identify the stage of mitosis with its characteristics
A. Metaphase - chromosomes moved to spindle equator, chromosomes made up of two chromatids
B. Anaphase - Centromeres split, chromatids separate and start moving away
c. Late Prophase - chromosomes move to spindle equator
D. Metaphase - spindle fibers attached to kinetochores, centromeres split and chromatids separate


A particle is projected vertically upwards with velocity \( 40 \mathrm{m} / \mathrm{s} \). Take \( g=10 m / s^{2} . \) Find the displacement
and distance traveled by the particle during its time of flight.


The vapour pressure of pure benzene at
\( 88 C \) is \( 960 \mathrm{mm} \) and that of toluene at
the same temperature is \( 380 \mathrm{mm} \) of
benzene. At what mole fraction of
benzene. the mixture will boil at \( 88^{\circ} \mathrm{C} \) ?
A . 0.655
B. 0.345
\( c \cdot 0.05 \)
D. 0.25


Write the names and structures of the
monomers of the following polymers.
(i) Polystyrene
(ii) Dacron
(iii) Teflon


Write a note on how forests influence
the quality of our air, soil and water resources?


\( A, B, \) and \( C \) are three elements with
atomic number \( 6,11, \) and 17
respectively. Which of these cannot
form ionic bond and why?


Assume that water issuing from the end of a horizontal pipe, 7.5 m above the ground, describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position \( 2.5 \mathrm{m} \) below the line of the pipe, the flow of water has curved outward from \( 3 \mathrm{m} \), beyond the
vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground?


The wavelength of light emitted by
electron in \( C^{5+} \) ion during transition from \( n=3 \) to \( n=1 \) is approximately:
A. 2.85 nm
B. 3.6 пт
\( c .8 .7 n m \)
D. \( 9.8 n m \)


\( \int_{-\pi / 2}^{\pi / 2} \cos t \cdot \sin \left(2 t-\frac{\pi}{4}\right) d t= \)
A \( \frac{\sqrt{2}}{3} \)
B. \( -\frac{\sqrt{2}}{3} \)
\( c \cdot \frac{\sqrt{3}}{1} \)
D. \( \frac{1}{\sqrt{3}} \)


A cubical vessel of height \( 2 \mathrm{m} \) is full of water. The work done in pumping the water out of the vessel is?
A . \( 72.3 \mathrm{kJ} \)
B. \( 78.4 \mathrm{kJ} \)
c. \( 64.5 \mathrm{kJ} \)
D. \( 57.9 \mathrm{kJ} \)


Draw a triangle ABC. Draw it's median AD


If the terminal speed of a sphere of gold
(density \( \left.=19.5 k g / m^{3}\right) \) is \( 0.2 m / s \) in a viscous liquid(density \( \left.=1.5 k g / m^{3}\right) \) find the terminal speed of a sphere of silver (density \( =10.5 k g / m^{3} \) ) of the same size in the same liquid
A. \( 0.4 m / s \)
В. \( 0.133 m / s \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)


On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles,
and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been
between
A \( \cdot \frac{290}{12.5} \) and \( \frac{290}{11.5} \)
В \( \cdot \frac{295}{12} \) and \( \frac{285}{11.5} \)
c. \( \frac{285}{12} \) and \( \frac{295}{12} \)
D. \( \frac{285}{12.5} \) and \( \frac{295}{11.5} \)
E \( \cdot \frac{295}{12.5} \) and \( \frac{285}{11.5} \)


Which of the following molecules are expected to exhibit intermolecular \( \mathrm{H} \)
bonding?
I. Acetic acid
Il. o-nitrophenol
III. m-nitrophenol
IV. o-boric acid
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ।
B. ।, ॥।, IV
c. ।, ॥ा, ।V
D. II, III, IV


Explain how is the height of mercury column in tube of a simple barometer is
a measure of the atmospheric pressure.


The distance between two thin long
straight parallel conducting wires is \( b \) On passing the same current \( i \) in them, the force per unit length between them will be
A \( \cdot \frac{\mu_{0} i}{2 \pi b} \)
В. \( \frac{\mu_{0} i^{2}}{2 \pi} \)
c. \( \frac{\mu_{0} i^{2}}{2 \pi b} \)
D. zero


A particle of mass \( 10 g \) is executing simple harmonic motion with an
amplitude of \( 0.5 m \) and periodic time of \( \left(\frac{\pi}{5}\right) s . \) The maximum value of the force acting on the particle is:
A . \( 25 ~ N \)
B. \( 5 N \)
c. \( 2.5 N \)
D. \( 0.5 N \)


The law used by Newland to arrange elements is known as


The focal length of a convex mirror is
its radius of curvature.
A. equal to
B. half of
c. two times
D. negative of


Cetryltrimethyl ammonium bromide is a popular:
A. anionic detergent
B. cationoic detergent
c. non-ionic detergent
D. sweetener


Medusa of Obelia is
A. Carnivorous
B. Herbivorous
C. Detritus feeder
D. Omnivorous


\( \sqrt{1+3+5+7+\dots} \)


Among the following complexes (K-P):
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C} \boldsymbol{N}_{6}\right]-\boldsymbol{K} \) and \right.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3}-\boldsymbol{L} \)
\( N a_{3}\left[C o(\text {oxalate})_{3}\right]-M \) and
\( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{2}-\boldsymbol{N} \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{P t}(\boldsymbol{C N})_{4}\right]-\boldsymbol{O} \) and
\( \left[\boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}-\boldsymbol{P} \)
the diamagnetic complexes are:
A. K.L,M,N
в. к,м,о,
c. L,M,O,
D. all


A body dropped from a height \( h \) with an initial speed zero, strikes the ground with a velocity \( 3 k m / h \). Another body of
same mass dropped from the same
height \( h \) with an initial speed \( u= \)
\( 4 k m / h . \) Find the final velocity of
second mass, with which it strikes the
ground.
\( \mathbf{A} \cdot 3 k m / h \)
в. \( 4 \mathrm{km} / \mathrm{h} \)
\( \mathrm{c} .5 \mathrm{km} / \mathrm{h} \)
D. \( 6 \mathrm{km} / \mathrm{h} \)


The following histogram shows the
frequency distribution of the ages of 22
teachers in a school:

What are the class marks of the classes
7


If following data belongs to an adult male
Cardiac index \( = \)
cardiac output
Total body sur face
Total body surface area in adult \( =1.7 m^{2} \) Cardiac index
4litre / mt./ \( m^{2} \)
Heart rate
\( 68 / \) minute
End systolic volume
Total body surface area \( -1.7 m^{2} \)
Then choose the correct set of option.
A. cardiac output = 5 litre/minute. ; stroke volume = 70 \( \mathrm{ml} . ; \mathrm{EDV}=120 \mathrm{ml} \)
B. c.0. = 5 litre/minute. ; SV = 100 m!.; EDV = 50 m!


What do you mean by significant figures?


What is the hybridisation of carbon and oxygen in electronic structure of ether?
A \( \cdot s p^{3} \) and \( s p^{2} \)
B. \( s p^{3} \) and \( s p^{3} \)
c. \( s p \) and \( s p \)
D. \( s p^{2} \) and \( s p^{2} \)


If \( x=\sqrt{6}+\sqrt{5}, \) then \( x^{2}+\frac{1}{x^{2}}-2=? \)
A \( \cdot 2 \sqrt{6} \)
B. \( 2 \sqrt{5} \)
\( c \cdot 24 \)
D. 20


If \( y \) is expressed in terms of a variable \( x \) as \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \) then \( \boldsymbol{y} \) is called
A. Explicit function
B. Implicit function
c. Linear function
D. Identity function


Which of the following statements is true of a measure of dispersion?
A. Mean deviation does not follow algebraic value
B. Range is crudest measure
c. coefficient of variation is a relative measure
D. All the above statements


If \( \boldsymbol{A}=\left[\begin{array}{c}-1 \\ 2 \\ \mathbf{3}\end{array}\right], \boldsymbol{B}=[-\mathbf{2},-\mathbf{1},-\mathbf{4}] \) verify
that \( (\boldsymbol{A B})^{T}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)


A particle executes simple harmonic motion between \( x=-A \) and \( x=+A \).The
time taken by it to go from 0 to A /2 is \( T \)
1 and to go from \( A / 2 \) to \( A \) is \( T_{2} . \) Then
\( A \cdot T_{1}<T_{2} \)
B . \( T_{1}>T_{2} \)
\( \mathrm{c} \cdot \mathrm{T}_{1}=\mathrm{T}_{2} \)
D. \( \mathrm{T}_{1}=2 \mathrm{T}_{2} \)


The radius of the first Bohr orbit of hydrogen atom is 0.59 , the radius of
the third orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) will be:
\( \mathbf{A} \cdot 8.46 \stackrel{\circ}{A} \)
в. 0.705 А
\( \mathbf{c} \cdot_{1.59 A}_{A}^{\circ} \)
D \( \cdot 2.38 \stackrel{\circ}{A} \)