The high boiling point of water is due to:
A . its high specific heat
B. hydrogen bonding
c. high dielectric constant
D. low dissociation constant


At equilibrium \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1}, \) then:
A \( \cdot \Delta G^{\circ}=0 \)
B . \( \Delta G^{\circ}=+v e \)
c. \( \Delta G^{\circ}=-v e \)
D. \( \Delta G^{\circ}=+v e, o r-v e \)


Calculate the period of a wave, which is having the wavelenght \( 17 ~ m \) and wave velocity \( 340 m / s \)


Identify correct statements.
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S O_{4} \) can be used for drying \( H_{2} S \) gas.
B. \( H_{2} S \) is a better reducing agent than water.
C . Reaction of \( H_{2} S O_{4} \) with \( B a C l_{2} \) shows its oxidising
nature.
D. \( H_{2} S \) can form coloured precipitate's with metal ions.


Use the Venn diagram to answer the
following questions
(i) List the elements of \( \boldsymbol{U}, \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{E} \cup \boldsymbol{F} \)
and \( \boldsymbol{E} \cap \boldsymbol{F} \)
(ii) Find \( n(U), n(E \cup F) \) and \( n(E \cap F) \)


Three identical bulbs are connected in
parallel with a battery. The current drawn from the battery is \( 6 A \). If one of
the bulbs gets fused, what will be the total current drawn from the battery?
\( \mathbf{A} \cdot 6 A \)
в. \( 2 A \)
\( c .4 A \)
D. \( 8 A \)


wherever the air pressure is higher,
there will be a stronger force or push against an object. Is the statement True or False
A. True
B. False


A new temperature scale uses \( X \) as a
unit of temperature, where the
numerical value of the temperature \( t_{x} \)
in this scale is related to the
absolute temperature \( \mathrm{T} \) by \( t_{x}=3 \mathrm{T}+300 \)
If the specific heat of a material using
this unit is \( 1400 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \) its
specific heat in the S.1. system of units
is :
\( \mathbf{A} \cdot 4200 J k g^{-1} K^{-1} \)
B . \( 1400 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
c. \( 466.7 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. Impossible to determine from the information provided


Which one of the following is a stop codon?
A . UAGGGGGG
B. UAC
c. AUG
D. UcA


Assertion
The smaller the orbit of a planet around
the Sun, the shorter is the time it takes
to complete.
Reason
According to Kepler's third law of planetary motion, square of time period is proportional to cube of mean distance from Sun.
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


The magnitude of the earth's magnetic
field at the north pole is \( B_{0} . \) A horizontal
conductor of length \( l \) moves with a
velocity \( v . \) The direction of \( v \) is
perpendicular to the conductor. The induced emf is
This question has multiple correct options
A. zero, if \( v \) is vertical
B. \( B_{0} l v, \) if \( v \) is vertical
c. zero, if \( v \) f is horizontal
D. \( B_{0} l v, \) if \( v \) is horizontal
E. answer required


Ultraviolet light causes
A. Destruction of hydrogen bonds between complementary DNA strands
B. Photodynamic action
c. sticky metaphases
D. Formation of pyrimidines


What is the work done in moving a test charge \( q \) through a distance \( 4 \mathrm{cm} \) along the equatorial axis of an electric dipole?
A . 4
B. 40
\( c \)
D.


Liquid in solid type colloids in which dispersion phase is solid and dispersion medium is liquid are called gels.
Enter 1 if true else enter 0


Decrease 300 by \( 24 \% \)
A . 238
в. 220
c. 235
D . 228


At \( t=2 s, \) the position of central
maxima is
A. \( 2 m m \) above \( C \)
B. \( 2 m m \) below \( C \)
\( \mathrm{c} .4 \mathrm{mm} \) above \( C \)
D. \( 4 m m \) below \( C \)


The displacement of a particle executing simple harmonic motion is given by equation \( y=0.3 \sin 20 \pi(t+0.05) \)
where time \( t \) is in second and
displacement y is in metre. calculate the values of amplitude, time period initial phase and initial displacement of the particle


Circle with centre 0 and radius 25 cms
has a chord \( A B \) of length of 14 cms in it.
Find the area of triangle AOB?


Which of the following observations are true for Hans Oersteds experiment?
a. When current passes through the
wire the compass needle comes to restt
in a direction along the Earths magnetic field.
b. When placed just above the wire, North Pole of the compass needle deflects towards the east when current
is passes from A to B.
c. When placed just below the wire, North Pole of the compass needle deflects towards the east when current is passes from B to A i.e. on reversing the direction of current
\( A \cdot \) a and \( c \)
B. a and b
\( c . \) b and \( c \)
D. All of the above


In a longitudinal wave, the density of particles is more at a compression.
A. True
B. False


The white solid compound \( A \)
decomposes quite rapidly on heating in
the presence of a black substance \( X \) to
form a solid compound B and a gas C. When an aqueous solution of compound B is reacted with silver nitrate solution, then a white precipitate of silver
chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.
What is the general name of substances like X?


Two charges \( Q \) and \( -2 Q \) are placed at some distance. the locus of points in
the plane of the charges where the potential is zero will be
A. Straight line
B. Circle
c. Parabola
D. ellipse


A magnetic dipole in a constant
magnetic field has
A. Minimum potential energy when the torque is maximum.
B. Zero potential energy when the torque is minimum.
C. Zero potential energy when the torque is maximum.
D. Maximum potential energy when the torque is maximum.


The visible region of hydrogen spectrum was first studied by
A. Lyman
B. Balmer
c. Pfund


If \( n=6, \) the correct sequence for filling of electrons will be:
A \( \cdot n s \rightarrow n p \rightarrow(n-1) d \rightarrow(n-2) f \)
B . \( n s \rightarrow(n-2) f \rightarrow(n-1) d \rightarrow n p \)
C \( \cdot n s \rightarrow(n-1) d \rightarrow(n-2) f \rightarrow n p \)
D. \( n s \rightarrow(n-2) f \rightarrow n p \rightarrow(n-1) d \)


Component of reaction at the hinge in
the horizontal direction is
\( ^{A} \cdot \frac{F}{4} \)
B. \( F \)
c. \( \frac{F}{3} \)
D. \( \frac{F}{2} \)


Write down the significant figures in the following
\( 1.5238 \mathrm{N} \)
2. 4200kg
A .4,4
в. 4,2
c. 4,3
D. 5,3


When a force of 1 N causes a
displacement of \( 1 \mathrm{m}, \) in its own direction, then work done is:
A. one joule
B. One ampere
c. One kilo Newton
D. One farad


A man on a wharf \( 12 \mathrm{mt} \) above the water
level pulls in a rope to which a boat is
attached at the rate of 1 mt per second.
At what rate is the boat approaching the shore, when there is still 13 mt rope out
?
\( \mathbf{A} \cdot 2.6 \mathrm{m} / \mathrm{sec} \)
B . \( 2 \mathrm{m} / \mathrm{sec} \)
c. \( 5 \mathrm{m} / \mathrm{sec} \)
D. \( 6.5 \mathrm{m} / \mathrm{sec} \)


If \( E_{1}, E_{2} \) and \( E_{3} \) represent respectively the kinetic energies of an electron, an alpha particle and a proton each having same de Broglie wavelength then:
A. \( E_{1}>E_{3}>E_{2} \)
в. \( E_{2}>E_{3}>E_{1} \)
c. \( E_{1}>E_{2}>E_{3} \)
D. \( E_{1}=E_{2}=E_{3} \)


Choose the incorrect statement:
A. the speedometer of a car measures its instantaneous speed
B. the velocity of a body is always greater than the speed of that body.
C. the position-time graph of a body moving with variable velocity is a curve.
D. velocity-time graph of a uniform motion is a straight line parallel to time-axis.


The vermiform appendix is situated at the junction of
A. Large intestine and small intestine
B. Small intestine and duodenum
c. Anus and rectum
D. Stomach and duodenum


The acceleration due to gravity on the surfcae of a planet is one-fourth of the value on Earth. When a brass ball is
brought to this planet, its:
A. mass is halved
B. weight is halved
c. mass becomes one-fourth
D. weight becomes one-fourth
E. mass and weight remain the same


Coils in the resistance boxes are made
from doubled up insulated wires
A. to cancel the effect of self induction
B. to nullify the heating effect
c. to nullify the Peltier effect
D. to reduce effective length of the wire


Which element has the symbol Ti?
A. Tin
B. Leadd
c. Titanium
D. Thallium
E. Technetium


Pick out the pair in which the energy change of one is reverse of the energy change in the other :
(1) radio
(2) fluorescent lamp
(3) toaster
(4) photoelectric cell
A . 1 and 2
B. 2 and 3
\( c \cdot 2 \) and 4
D. 3 and 4


Mycorhhiza is an example of :-
A. Key-stone species
B. Endemic species
c. Critical link species
D. Rare species


Which of the following is the most acidic?
A. \( P_{2} O_{5} \)
B. \( N_{2} O_{5} \)
\( \mathrm{c} \cdot \mathrm{Sb}_{2} \mathrm{O}_{5} \)
D. \( A s_{2} O_{5} \)


Find the amount and the compound
interest on \( R s .160000 \) for 2 year at \( 10 \% \) per annum compound interest half-
yearly.


A sound wave of frequency 500 Hz covers a distance of \( 1000 \mathrm{m} \) in \( 5 \mathrm{s} \)
between points \( x \) and \( y . \) Then the number of waves between \( x \) and \( y \) are
A. 5000
B. 2500
\( c \cdot 100 \)
D. 500


If the voltage across the filament is increased, the cutoff wavelength.
A. Will increase
B. Will decrease
c. will remain unchanged
D. will change


The first organic substance ever prepared in the laboratory from the inorganic compound is:
A . urea
B. ethyl alcohol
c. methane
D. ethane


Name the radiations absorbed by ozone layer. What would happen to living ones
on earth of ozone layer around us disappears?


Solve \( \int_{0}^{h} x(h-x) d x \)
\( ^{A} \cdot_{I}=\frac{h^{3}}{3} \)
в. \( _{I=} \frac{h^{3}}{6} \)
\( ^{\mathrm{C}} \cdot_{I}=-\frac{h^{3}}{6} \)
D. None of these


Among the following, which one can not be further broken down by chemical
means?
A. Cation
B. Inert Gas
c. crystal
D. Anion
E. Element


A man raises a box of mass \( 50 k g \) to a
height of \( 2 m \) in 2 minutes, while
another man raises the same box to the
same height in 5 minutes. Compare the work done by them.
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1


Assertion
\( N \) -atom in \( N H_{3} \) is \( s p^{3} \) hybridised and
bond angle is \( 107^{\circ} \)
Reason
\( l p-b p \) repulsion (VSEPR) decreases
bond angle to \( 107^{\circ} \)
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


Rust is a lan
This question has multiple correct options
A. hydrated
B. anhydrous
c. acidic
D. basic


A circular racetrack of radius \( 300 m \) is
banked at an angle of \( 15^{\circ} . \) If the
coefficient of friction between the
wheels of a race car and the road is 0.2
(a) What is the optimum speed of the race car to avoid wear and tear on its
tires?
(b) What is the maximum permissible speed to avoid slipping?


Four wires made of same material have
different lengths and radii. The wire having more resistance in the following is
A \( .1=100 \mathrm{cm} \mathrm{r}=1 \mathrm{mm} \)
B. \( 1=50 \mathrm{cm} \mathrm{r}=2 \mathrm{mm} \)
c. \( 1=100 \mathrm{cm} \mathrm{r}=1 / 2 \mathrm{mm} \)
D. \( 1=50 \mathrm{cm} \mathrm{r}=1 / 2 \mathrm{mm} \)


The equation \( x+e^{x}=0 \) has
A. only one real root
B. only two real roots
c. no real root
D. none of these


The point on the curve \( y=x^{2} \) which is
nearest to (3,0) is
A . (1,-1)
B. (-1,1)
c. (-1,-1)
D. (1,1)


If \( y=\ln (\operatorname{cosec} x-\cot x) \) then \( \frac{d y}{d x} \)
equals to
A. \( \operatorname{cosec} x+\cot x \)
B. \( \cot x \)
\( \mathbf{c} \cdot \sec x+\tan x \)
D. \( \operatorname{cosec} x \)


Velocity of a particle varies as
\( \boldsymbol{v}=\mathbf{2} \boldsymbol{t}^{3}-\mathbf{3} \boldsymbol{t}^{2} \) in \( \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r} \)
If \( ; t=0 \) is taken at 12: 00 noon, tis in
hr
Find the time between 12: 00 noon
and 1: 00 pm at which speed is
maximum.
B. \( 1: 00 \mathrm{pm} \)
c. 11: 00 am
D. \( 2: 00 \mathrm{pm} \)


A sample of \( C a C O_{3} \) has \( \mathrm{Ca} 40 \%, \mathrm{C} 12 \% \)
\( 048 \% \) by mass. If the law of constant proportions is true then find the mass
of \( \mathrm{Ca} \) in \( 5 \mathrm{g} \) of \( \mathrm{CaCO}_{3} \) obtained from
another source.


If \( a=107, b=13 \) using Euclid's
division algorithm find the values of \( q \)
and \( r \) such that \( a=b q+r \)
A \( \cdot q=8, r=8 \)
В . \( q=8, r=3 \)
c. \( q=0, r=3 \)
D. None of these


Assertion
The mass of a nucleus can be either
less than or more than the sum of the
masses of nucleons present in it.
Reason
The whole mass of the atom is
concentrated in the nucleus.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A tall, cylindrical chimney falls over when its base is ruptured. Treat the
chimney as a thin rod of length \( 55.0 \mathrm{m} \)
At the instant it makes an angle of
\( 35.0^{\circ} \) with the vertical as it falls, what
are
(a) the radial acceleration of the top,
and
(b) the tangential acceleration of the top. (Hint : Use energy considerations, not a torque.)
(c) At
what angle \( \theta \) is the tangential acceleration equal to g?


When you heat the water in a pot, it
boils. What do you infer from above
observation?
A. Heat is a form of energy
B. Water can boil itself
c. water develops heat on its own
D. None of the above


The amount of work done in increasing
the length of a wire through \( 1 \mathrm{cm} \) will be
A. \( \frac{Y A}{2 L} \)
в. \( \frac{Y L}{2 A} \)
c. \( \frac{Y L^{2}}{2 A} \)
D. None of these


Evaluate the following limits. \( \lim _{x \rightarrow a} \frac{\sin x-\sin a}{x-a} \)


Which of the following statements is
incorrect?
A. When a material is under tensile stress, the restoring forces are caused by interatomic attraction while under compressional stress, the restoring force is due to interatomic repulsion
B. The stretching of a coil is determined by its shear modulus
C. Rubber is more elastic than steel
D. Shearing stress plays an important role in the buckling of shafts


Use distributive property of multiplication of rational numbers and
simplify:
(i) \( \frac{-5}{4} \times\left(\frac{8}{9}+\frac{5}{7}\right) \)
(ii) \( \frac{2}{7} \times\left(\frac{1}{4}-\frac{1}{2}\right) \)


Thermal plants have installed
A. Cyclone collector
B. Porous filters
C. Electrostatic precipitators
D. Adsorbents


Write down difference between terylene
fibre and Buna -S- rubber (elastomers).


The locus of a point which moves such that the difference of its distances from
two fixed points is always a constant is
A . A straight line
B. A circle
c. An ellipse
D. A hyperbola


Differentiate \( \sqrt{\frac{1-\tan x}{1+\tan x}} \)


Which of the following is true?
A. In an endothermic equilibrium reaction, activation energy required for a forward reaction is higher than that for a backward reaction
B. To an endothermic equilibrium reaction, activation energy required for a forward reaction is higher than that for a backward reaction
C. Activation energy required for both forward and backward reaction is same in equilibrium
D. No activation energy is required for an exothermic backward equilibrium reaction


Add \( \left(6 a b^{3}-5 a b\right)\left(2 a^{2}+b-\right. \)
5) \( , a b\left(a^{2}+1\right) \) and \( a b^{3}\left(3 a^{3}+2 b+1\right) \)


Which of the following metals on
treatment with alkali will liberate \( \boldsymbol{H}_{2} \)
gas? This question has multiple correct options
A. Be
B. sn
c. Ga
D. In


Which property of lens deviates rays
more?
A. Short focal length
B. Long focal length
c. Small aperture
D. Large aperture


Non-directional orbital is:
\( \mathbf{A} \cdot 3 s \)
B . \( 4 f \)
c. \( 4 d \)
D. \( 4 p \)


Binding energy per nucleon of \( _{1} H^{2} \) and
\( _{2} H e^{4} \) are \( 1.1 M e V \) and \( 7.0 M e V \)
respectively. Energy released in the process \( _{1} H^{2}+_{1} H^{2} \longrightarrow_{2} H e^{4} \) is
A. \( 20.8 \mathrm{MeV} \)
в. \( 16.6 \mathrm{MeV} \)
c. \( 25.2 \mathrm{MeV} \)
D. \( 23.6 \mathrm{MeV} \)


Which of the following is a unit of atmospheric pressure.
A. torr
B. bar
c. \( a t m \)
D. all of the above


Phycobiont and mycobiont together
constitute :
A. Phycomycetes
B. Lichens
c. Phycobilins
D. Mycorrhiza


A simple microscope has a focal length of 5cm. The magnification at the least distance of distinct vision is
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
D.


State True or False.
\( B e H_{2} \) is an ionic hydride.
A. True
B. False


Which is true for a wave? (here \( n= \)
frequency, \( T= \) time period
\( \mathbf{A} \cdot \mathbf{n T}=1 \)
B. \( \frac{n}{T}=2 \)
c. \( n=T \)
D. None of these


The correct order regarding the
solubility of alkaline earth metal halides in water is :
A \( \cdot B e C l_{2}<M g C l_{2}<C a C l_{2}<S r C l_{2}<B a C l_{2} \)
в. \( M g C l_{2}<C a C l_{2}>B e C l_{2}>B a C l_{2}>S r C l_{2} \)
C. \( B a C l_{2}>M g C l_{2}>C a C l_{2}>B e C l_{2}>S r C l_{2} \)
D. \( B e C l_{2}>M g C l_{2}>C a C l_{2}>S r C l_{2}>B a C l_{2} \)


Orbital acceleration of an electron is:
A \( \cdot \frac{n^{2} h^{2}}{4 \pi^{2} m^{2} r^{3}} \)
B. \( \frac{n^{2} h^{2}}{2 n^{2} r^{3}} \)
c. \( \frac{4 n^{2} h^{2}}{\pi^{2} m^{2} r^{3}} \)
D. \( \frac{4 n^{2} h^{2}}{4 \pi^{2} m^{2} r^{3}} \)


After a thunder-shower, a man walks
out into his porch. Looking to the east, he finds a rainbow that has formed
above his neighbour's house. What time of day is it?
A. Morning
B. Noon
c. Night
D. Evening


A quantity of \( 0.62 g \) of \( N a_{2} C O_{3} . H_{2} O \) is
added to \( 100 \mathrm{ml} \) of \( 0.1 N-H_{2} S O_{4} \)
solution. The resulting solution would be
A . acidic
B. alkaline
c. neutral
D. buffer


If we create vacuum in container \( A \) at
\( 25^{\circ} C \) then:
Container
\( (\mathbf{A}) \)
A. water will be completely vaporised in the container
B. there will be no vaporisation in the container
C. the equilibrium will establish in between water vapour and liquid \( H_{2} O \) and vapour pressure of water will
remain same as it would be in presence of atmospheric pressure
D. the equilibrium in between \( H_{2} O(v) \) and \( H_{2} O(l) \) will
establish but vapour pressure of \( H_{2} O(v) \) will be more
than as it would be in presence of atmospheric
pressure


A cubical water tank measures 3 feet
sides. Find its surface area.
A \( .9 f t^{2} \)
B. \( 50 f t^{2} \)
c. \( 52 f t^{2} \)
D. \( 54 f t^{2} \)


If the electric flux entering and leaving
a closed surface are \( 6 \times 10^{6} \) and \( 9 \times \)
\( 10^{6} S I \) units respectively, then the
charge inside the surface of
permittivity of free space \( \omega_{0} \) is
A. \( \omega_{0} \times 10^{6} \)
В . \( -\omega_{0} \times 10^{6} \)
c. \( -2 \omega_{0} \times 10^{6} \)
D. \( 3 \omega_{0} \times 10^{6} \)
E \( .2 \omega_{0} \times 10^{6} \)


Find \( \frac{d y}{d x}=\sin ^{-1} x \)


Which does not pertain to facilitated transport
A. High selectivity
B. Transport saturation
c. Uphill transport
D. Requirement of special membrane


The Slunit for force is:
A. Torr
B. Newton
c. Joule
D. Dyne


The temperature of 5 mol of a gas which was held at constant volume was
changed from \( 100^{\circ} \mathrm{C} \) to \( 120^{\circ} \mathrm{C} \). The
change in internal energy was found to be 80 . \( J \). The total heat capacity of the gas at constant volume will be equal to
\( \mathbf{A} \cdot 8 J / K \)
в. \( 0.8 \mathrm{J} / \mathrm{K} \)
c. \( 4 J / K \)
D. \( 0.4 J / K \)


How many rounds of Calvin cycle are required to form one hexose molecule?
A .2
B. 6
\( c \cdot 4 \)
\( D \)


A vehicle is moving on a track with
constant speed as shown in figure. The apparent weight of the vehicle is
A. Maximum at \( A \)
B. Maximum at \( B \)
c. Maximum at \( C \)
D. Maximum at \( A, B \) and \( C \)


Which of the following has the highest density?
A. Kerosene
B. water
c. Iron
D. woodd


Nitrogenase enzyme is present in?
A. Prokaryotes
B. Eukaryotes
\( c . \) Both
D. None


Freon acts as:
A. dehydrating agent
B. explosive
C . refrigerant
D. oxidising agent


In an Isosceles triangle \( A B C, \tan ^{2} B- \)
\( \sec ^{2} B+2 \)


The correct combination is:
\( \mathbf{A} \cdot\left[N i(C N)_{4}\right]^{2-} \) -tetrahedral; \( \left[N i(C O)_{4}\right] \) -paramagnetic
B. \( \left[N i C l_{4}\right]^{2-} \) -paramagnetic; \( \left[N i(C O)_{4}\right] \) -tetrahedral
\( \mathbf{c} \cdot\left[N i C l_{4}\right]^{2-} \) -diamagnetic; \( \left[N i(C O)_{4}\right] \) -square-planar
D. \( \left[N i C l_{4}\right]^{2-} \) -square-planar; \( \left[N i(C N)_{4}\right]^{2-} \) -paramagnetic


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\log \left(\frac{1+\boldsymbol{x}}{1-\boldsymbol{x}}\right) \)


\( 20 g m \) of a binary electrolyte (mol.wt. \( = \)
100) are dissolved in 500 g of water. The freezing point of the solution is \( -0.74^{\circ} \)
C. \( \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6} \) K \( \boldsymbol{m o l}^{-1} \). The degree of
ionization of the electrolyte is:
A. \( 50 \% \)
(年 5500
B. \( 75 \% \)
\( c \cdot 100 \% \)
D. \( 0 \% \)


Animal fibers generally comprise of:
A. collagen.
B. keratin
c. both \( A \) and \( B \).
D. triglycerides.


If \( x \) is the ratio of currents it takes to
produce 4.5 g of platinum from molten
\( P t C l_{3} \) and \( P t C l_{5}, \) then \( 10 x \)
is
Electrolysis in each case is carried out for \( 1 \mathrm{min} 40 \) s. (Atomic Mass of \( \mathrm{Pt}= \)
195.0)


The value of \( p \) if \( 3, p, 12 \) are in GP
A. 6
B. 4
\( c .9 \)
D. None


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 2} & \mathbf{0} \\ \mathbf{2} & \mathbf{1} & \mathbf{3} \\ \mathbf{0} & \mathbf{- 2} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}^{-1}= \)


Which among the following statements is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot p H=-\log _{10} H_{3} O^{+} \)
B. pH decreases with increase of temperature
C. \( \mathrm{pH} \) cannot be zero, negative or more than 14
D. If a solution is diluted ten times, its pH increases by 1


The arrangement shown in the figure
performs the logic function of
A. AND gate
B. NAND gate
c. or gate
D. XOR gate


Which of the following is not a mixture of hydrocarbons?
A. candle wax
B. kerosene
c. vegetable oil
D. paraffin oil


Henry has Rs. 1200 in a savings account
that earns \( 12 \% \) annually. How much will he have in 4 years?
\( \mathbf{A} \cdot 488 \)
в. 576
c. 676
D. 528


Find the median of the following data.
\( \begin{array}{lllll}\text { class } & 0- & 20- & 40- & 60 \\ \text { interval } & 20 & 40 & 60 & 800\end{array} \)
12 Frequency \( \quad 8 \quad 10 \)
A . 45
B. 40
c. 55
D. 50


Fill in the blanks with appropriate
words.

Urine is carried from the kidneys by \( _{\text {. ............ to the urinary bladder. }} \)


Assertion
Heat of hydrogenation of \( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \)
is greater than \( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
Reason
\( C H_{3} \) give additional effect to double
bond
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In a concentracttion cell:
A. two electrodes are of difference elements
B. two electrolytic solutions of the same electrolyte but having different concentrations are used
C. electrolyte of one strength but electrodes of two different concentrations are used
D. both
(b) and \( (c) \)


In Thomson's plum-pudding model,
electrons are not:
A. negatively charged
B. present in every type of atom
C . collected together in the center of the atom
D. scattered throughout a blob of positively charged material


What are the two types of nerves? Write their functions.


Cube of any odd number is even
A. True
B. False
c. Depends on the number
D. Data Insufficient


If two events \( A \) and \( B \) such that \( P\left(A^{c}\right) \)
\( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}\left(\boldsymbol{A B}^{c}\right)=\mathbf{0 . 5}, \) then
\( \boldsymbol{P}\left[\boldsymbol{B} /\left(\boldsymbol{A} \cup \boldsymbol{B}^{c}\right)\right]= \)
A . 0.25
B. 0.50
c. 0.75
D. None of these


The ages (in years) of a family of 6 members are 1,5,12,15,38 and 40 The standard deviation is found to be 15.9
After 10 years the standard deviation is
A . increased
B. decreased
c. remains same
D. none of these


The versatile chemistry of elemental sulfur is largely due
to
A. highly reactive nature
B. catenation
c. low weight
D. all of the above


Which one of the following sets of ions represents a collection of isoelectronics
species?
A. \( K^{+}, C l^{-}, C a^{2+} \)
B. \( B a^{2+}, S r^{2+}, K^{+}, C a^{2+} \)
c. \( N^{3}-, O^{2-}, C a^{2+}, S^{2} \)
D. \( L i^{+}, N a^{+}, M g^{2+}, C a^{2+} \)


Which of the following has more inertia
\( ? \)
A bicycle or a train


A quartz lamp with iodine vapour releases ultraviolet light which falls on
a photoelectric cell. If a thick glass plate is now introduced between the
lamp and photoelectric cell then:
A. the photoelectric current increases
B. the maximum kinetic energy of photoelectrons decreases
c. the photoelectric current decreases
D. the maximum kinetic energy of photoelectrons increases


Classical smog is also called:
A. oxidising smog
B. reducing smog
c. photochemical smog
D. summer smog


Chlorofluorocarbons are not
recommended to be used in
refrigerators, because they
A. Increase temperature
B. Depletes ozone
c. Affects environment
D. Affects human body


Put in the form \( A+i B \)
\( \frac{(\cos x+i \sin x)(\cos y+i \sin y)}{[\cot u+i](1+i \tan v)} \)
\( \mathbf{A} \cdot \sin u \cos v[\cos (x+y-u-v)-i \sin (x+y-u-v)] \)
B \( \cdot \sin u \cos v[\cos (x+y-u-v)+i \sin (x+y-u-v)] \)
\( \mathbf{C} \cdot \sin v \cos u[\cos (x+y-u-v)+i \sin (x+y-u-v)] \)
\( \mathbf{D} \cdot \sin v \cos u[\cos (x+y-u-v)-i \sin (x+y-u-v)] \)


Fill in the blanks:
\( (-3) \times \dots \dots \dots=3 \)


The order, degree of the differential
equation of all circles of radius \( r, \) having centre only axis passing through the origin is (where \( r \) is arbitrary constant)
A . 1,1
в. 2,1
c. \( 3, \)
D. 4,2


The reduction potential of hydrogen
half-cell will be negative if:
\( \mathbf{A} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=1 \) atom and \( \left[\mathrm{H}^{+}\right]=2.0 \mathrm{M} \)
\( \mathbf{B} \cdot \mathbf{p}\left(\mathbf{H}_{2}\right)=1 \) atm and \( \left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} \)
\( \mathbf{C} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{atm} \) and \( \left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} \)
\( \mathbf{D} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{atm} \) and \( \left[\mathrm{H}^{+}\right]=2.0 \mathrm{M} \)


Above an infinitely large plane carrying
charge density \( \sigma, \) the electric field points up and is equal to \( \frac{\sigma}{2 \epsilon_{0}} . \) What is the magnitude and direction of the
electric field below the plane?
\( A \cdot \sigma / 2 \epsilon_{0}, \) down
В \( \cdot \sigma / 2 \epsilon_{0}, \) up
\( \mathrm{c} \cdot \sigma / \epsilon_{0}, \) down
D. \( \sigma / \epsilon_{0}, \) up


One mole of a mixture of \( C O \) and \( C O_{2} \) requires exactly 20 g of \( N a O H \) in solution for complete conversion of all
the \( C O_{2} \) into \( N a_{2} C O_{3} \). If the mixture (one mole) is completely
oxidised to \( C O_{2} \), then weight of \( N a O H \)
to be used is:
A \( .60 \mathrm{g} \)
в. \( 80 \mathrm{g} \)
c. \( 40 \mathrm{g} \)
D. 20 g


(i) Why do transition elements show variable oxidation states?
(ii) Name the element showing
maximum number of oxidation states
among the first series of transition metals from \( \boldsymbol{S} \boldsymbol{c}(\boldsymbol{Z}=\boldsymbol{2} \mathbf{1}) \) to \( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{Z}=\boldsymbol{3} \boldsymbol{0}) \)
(iii) Name the element which shows
only +3 oxidation state
(iv) What is lanthanoid contraction?
Name an important alloy which contains some of the lanthanoid metals


In an interference experiment, monochromatic light is replaced by white light we will see:


The molecules of medium vibrate about
their mean positions during heat transfer in the process of
A. Conduction
B. Radiation
c. convection
D. None


The area of a sector of a circle of radius
\( \mathbf{7} \mathrm{cm} \) and central angle \( 120^{\circ} \) is
A \( \cdot 152 \mathrm{cm}^{2} \)
B. \( \frac{154}{3} \mathrm{cm}^{2} \)
c. \( \frac{128}{3} \mathrm{cm}^{2} \)
D. \( 128 \mathrm{cm}^{2} \)


Which type of isomerism is shown by but-1-yne and but-1,2-diene?
A. Functional isomerism
B. Chain isomerism
c. Ring chain isomerism
D. Position isomerism


A hydrogen like species (atomic number \( Z \) ) is present in a higher excited
state of quantum number \( n \). This excited atom can make a transition to
the first excited state by successive emission of two photons of energies \( 10.20 e V \) and \( 17.0 e V \) respectively. Alternatively, the atom from the same excited state can make a transition to
the second excited state by successive emission of two photons of energy \( 4.25 e V \) and \( 5.95 e V \) respectively.
Determine the value of \( Z \).
A . 1
B. 2
\( c \cdot 3 \)
D. 4


In which of the following, the body is an aggregation of amoeboid cells?
A. Acellular slime moulds
B. Cellular slime moulds
c. Diatoms
D. Dinoflagellate


In the aqueous solution of sulphuric acid, the mole fraction of water is 0.849
The molality of the solution is:
A \( .8 .9 m \)
B. \( 0.19 m \)
\( \mathrm{c} .9 .8 \mathrm{m} \)
D. \( 15 \mathrm{m} \)


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |\vec{c}|=\sqrt{3}, \) then
A. \( \alpha=1, \beta=-1 \)
1
в. \( \alpha=1, \beta=\pm 1 \)
c. \( \alpha=-1, \beta=\pm 1 \)
D. \( \alpha=\pm 1, \beta=1 \)


According to laws of reflection, angle of incident is equal to the angle of reflection. On what condition this
statement is true?
A. It is always true
B. It is true sometimes
c. This is true only under special conditions
D. It can never happen


A tradesman marks his goods \( 25 \% \) above the cost price and allows his
customers 12 \% reduction on their bills.
What percent profit does he make?


Intersection point of lines \( \boldsymbol{x}=\mathbf{2}, \boldsymbol{x}= \)
-2 is
A. (0,0)
(年) \( 0,0,0,0,0,1, \)
в. (1,1)
c. It does not exist
D. None


In a transformer the number of turns of
primary coil and secondary coil are 2.5 and 2 respectively and \( 140 \mathrm{V} \) is applied on primary coil, then find the ratio of current in primary and secondary coils.


A road is \( 8 m \) wide. Its average radius of
curvature is \( 40 m . \) The outer edge is
above the lower edge by a distance of
1.28m. Find the velocity for which the
road is most suited? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


A uniform disc of mass \( m \), radius \( r \) and
a point mass \( m \) are arranged as shown
in the figure. The acceleration of point
mass is : (Assume there is no slipping
between pulley and thread and the disc
can rotate smoothly about a fixed
horizontal axis passing through its
centre and perpendicular to its plane).
A \( \cdot \frac{g}{2} \)
B. \( \frac{g}{3} \)
\( c \cdot \frac{2 g}{3} \)
D. None of these


The scores obtained by 50 students in
an examination is tabulated as shown
below.
\( \begin{array}{ll}\text { Score } & \text { Number of students } \\ \text { below 10 } & 3 \\ \text { below 20 } & \text { 7 } \\ \text { below 30 } & \text { 13 } \\ \text { below 40 } & \text { 22 } \\ \text { below 50 } & \text { 32 } \\ \text { below 60 } & \text { 40 } \\ \text { below 70 } & \text { 46 } \\ \text { below 80 } & \text { 50 }\end{array} \) Find the median score


If the quotient of \( x^{4}-11 x^{3}+44 x^{2}- \)
\( 76 x+48 . \) When divided by \( \left(x^{2}-7 x+\right. \)
12) is \( A x^{2}+B x+C \), then the
descending order of \( A, B, C \) is
A. \( A, B, C \)
в. \( B, C, A \)
c. \( A, C, B \)
D. \( C, A, B \)


Let \( S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots \) find the
sum of first 20 terms of the series
A \( \cdot \frac{2^{20}-1}{2^{20}} \)
в. \( \frac{2^{19}-1}{2^{19}} \)
\( ^{\mathrm{c}} \cdot \frac{2^{20}-1}{2^{19}} \)
D. \( \frac{2^{19}-1}{2^{20}} \)


heat energy is being produced in a resistance in a circuit at the rate of
100 \( W \). The current of \( 2 A \) is flowing in
the circuit. what must be the value of
the resistance (in \( \Omega) ? \)


Which of the following statements
is/are correct?
This question has multiple correct options
A. Liebig's method is used for the quantitative estimation of both \( C \) and \( H \)
B. Dumas method is used for the quantitative estimation of \( \mathrm{N} \) in all nitrogen-containing organic compounds.
C. In Liebig's combustion method, dry CuO is used.
D. Silver salt method is a chemical method for the determination of equivalent mass of organic acids.


Assertion
Decrease in free energy causes
Spontaneous reaction.
Reason
Spontaneous reactions are invariably
exothermic.
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


Diphenyl amine gives a deep blue colour with a solution of :

This question has multiple correct options
A \( \cdot F e^{3} \)
B. \( N O_{3}^{-} \)
c. \( N O_{2} \)
D. \( C l \)


A current of dry air was passed through a series of bulbs containing 1.25 g of a solute \( A_{2} B \) in 50 g of water and then through pure water. The loss in mass of the former series of bulbs was 0.98 g and in the later series 0.01 g. If the molar
mass of \( A_{2} B \) is \( 80, \) the degree of
dissociation of \( A_{2} B \) is (divide answer by \( 10): \)


Which of the following contains alcoholic functional group?
\( ^{\mathbf{A}}+_{H}-O-H_{\perp}^{H}-H \)
в. \( C H_{2}=C H-C H_{2} O H \)
\( ^{\mathrm{c}} \mathrm{CH}_{3}-\underset{_{c t_{3}}^{\mathrm{C}}}{C}-O-_{H} \)
D. All of the above


Centigrade or Celsius scale can be
converted into Kelvin scale by which of
the following formula?
\( \mathbf{A} \cdot^{o} C= \) Temperature in \( \mathrm{Kelvin}+273.15 \)
B \( \cdot^{\circ} C= \) Temperature in Kelvin -273.15
C \( \cdot^{\circ} C= \) Temperature in Fahrenheit +273
D. \( ^{o} C= \) Temperature in Fahrenheit -273


A drug which is effective in curing malaria is:
A. aspirin
B. quinine
c. morphine.
D. analgin.


Consider a positronium atom consisting of a positron and an electron each having mass \( m \) (equal to mass of electron) in the orbit around its centre
of mass. This structure lasts for \( 10^{-6} s \)
only. Find the energy levels for this model.


The crystalline salt, \( N a_{2} S O_{4} x H_{2} O \) on
heating losses \( 55.9 \% \) of its weight. The formula of the crystalline salt is :
A. \( N a_{2} S O_{4} .5 H_{2} O \)
B. \( N a_{2} S O_{4} .7 H_{2} O \)
c. \( N a_{2} S O_{4} \cdot 10 H_{2} O \)
D. \( N a_{2} S O_{4} .2 H_{2} O \)


Which of the following carboxylic acid is most acidic in character -
A. o-methyl benzoic acid
B. m-methyl benzoic acid
c. p-methyl benzoic acid
D. Benzoic acid


Two table tennis ball are suspended by threads at same height and separated by a distance of \( 15 \mathrm{cm} . \) A steam of air
injected in between them continuously, then the ball will be
A. Repel each other
B. Come closer
c. Not move at all
D. oscillate to and fro


The standard half cell reduction
potential for \( A g^{+} \mid A g \) is \( 0.7991 V \) at
\( 25^{\circ} \mathrm{C} . \) Given that the experimental value
of \( \boldsymbol{K}_{s p}=\mathbf{1 . 5 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \) for \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
calculate the standard half cell
reduction potential for the \( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
electrode.
A \( .0 .2192 V \)
В. \( -0.2192 \mathrm{V} \)
c. \( -1.2192 \mathrm{V} \)
D. \( 1.219 V \)


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \frac{(5 \sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5 \sqrt{2}} \)


Assertion
Positive charge always moves from a higher potential point to lower potential point
Reason
Electric potential is a vector quantity
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


A common biocontrol agent for the control of plant diseases caused by fungi is
A. Agrobacteriumm
B. Glomus
c. Trichoderma
D. Baculovirus


The RMS velocity of hydrogen is \( \sqrt{7} \) times the RMS velocity of nitrogen. If \( \boldsymbol{T} \)
is the temperature of gas, then:
A \( \cdot T_{\left(H_{2}\right)}=T_{\left(N_{2}\right)} \)
B . \( T_{\left(H_{2}\right)}>T_{\left(N_{2}\right)} \)
c. \( T_{\left(H_{2}\right)}<T_{\left(N_{2}\right)} \)
D. \( T_{\left(H_{2}\right)}=\sqrt{7} T_{\left(N_{2}\right)} \)


Which of the above compounds will not
show enolisation?
\( (\mathbf{A}) \)
(B)
\( (\mathrm{C}) \)
\( (\mathbf{D}) \)
his question has multiple correct options
\( A \cdot(A) \)
в. \( (B) \)
\( c \cdot(C) \)
D. \( (D) \)


The colloidal dispersion of a liquid in a liquid is called:
A. mixture
B. emulsion
c. precipite
D. none of these


Let \( S_{1} \) and \( S_{2} \) be the two slits in Young's double-slit experiment. If central maxima is observed at \( \boldsymbol{P} \) and angle
\( \angle S_{1} P S_{2}=\theta, \) then the fringe width for
the light of wavelength \( \lambda \) will be
(assume \( \theta \) to be a small angle)
\( A \cdot \lambda / \theta \)
в. \( \lambda \theta \)
c. \( 2 \lambda / \theta \)
D. \( \lambda / 2 \theta \)


The escape velocity of an object on a planet whose radius is 4 times that of
the earth and \( g \) value 9 times that on
the earth, in \( \mathrm{kms}^{-1} \) is
A. 33.6
B. 67.2
c. 16.8
D. 25.2


An electric motor driven pump fills an overhead tank placed at a height of 20
\( \mathrm{m} \) from the ground-level sump at a rate
of 20,000 litre water per hour.The motor has an operating resistance of \( 22 \Omega \) and is connected across a \( 220 \mathrm{V} \) source.The
efficiency of this motor is (Useg \( = \)
\( \left.9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 12.5 \% \)
B. \( 73.5 \% \)
c. \( 49.5 \% \)
D. \( 22.5 \% \)


A particle is projected from the ground
with an initial velocity of \( 20 \mathrm{m} / \mathrm{s} \) at an
angle of \( 30^{\circ} \) with horizontal. The
magnitude of change in velocity in a time interval from \( t=0 \) to \( t=0.5 \mathrm{s} \) is
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot 5 \mathrm{m} / \mathrm{s} \)
в. \( 2.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)


If \( x^{2}+\frac{1}{x^{2}}=1022, \), then find \( x+\frac{1}{x} \)


X reacts with calcium carbonate giving
\( C O_{2} \) and \( H_{2} O \) and turns methyl orange
to:
A . yellow
B. red
c. no color change
D. pink


a) i) Explain the preparation of Buna-N.
ii) Give an example for thermosetting polymer.
b) Name the monomers used in the
preparation of polythene and natural rubber.


\( \ln \operatorname{an} A C \) circuit \( V \) and \( I \) is given by
\( \boldsymbol{V}=\mathbf{1 0 0 0} \sin (\mathbf{1 0 0 0} \boldsymbol{t}) \) volt
\( \boldsymbol{I}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 0} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \boldsymbol{m} \boldsymbol{A} \)
The power dissipation in the circuit in one complete cycle is.
\( \mathbf{A} \cdot 25 W \)
B. \( 25 \sqrt{3} \)
c. \( 100 \mathrm{W} \)
D. 10 W


Let \( R \) a relation on the set \( N \) be defined
by \( \{(x, y) \mid x, y \in N, 2 x+y=41\} . \) Then
\( \boldsymbol{R} \) is
A. Reflexive
B. Symmetric
c. Transitive
D. None of these


The values of a \( \& \mathrm{b} \) so that the
polynomial \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{a} \boldsymbol{x}^{2}-\mathbf{1 3} \boldsymbol{x}+\boldsymbol{b} \) is
divisible by \( (x-1) \&(x+3) \) are
A. \( a=15, b=3 \)
3
в. \( a=3, b=15 \)
\( \mathbf{c} \cdot a=-3, b=15 \)
D. \( a=3, b=-15 \)


If the focal length of a magnifying glass is \( 2.5 \mathrm{cm}, \) it can magnify an object:
A. 15 times
B. 11 times
c. 2.5 times
D. None of these


\( \boldsymbol{S O}_{2} \) oxidises?
\( \mathbf{A} \cdot M g \)
в. \( H_{2} S O_{4} \)
\( \mathbf{c} \cdot K_{2} C r_{2} O_{7} \)
D. All of these


The number of quantum numbers required for the designation of an orbital in an atom is:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


What is the name of the alkane shown?
A. 2,3 -diethyl-3-methylheptane
B. 2,3-diethyl-3-methyloctane
C. 3-methyl-2,3-diethyloctane
D. 4-ethyl-3,4-dimethylnonane


Evaluate (i) \( \boldsymbol{i}^{998} \)


Steel is heated to below red heat and
then, cooled slowly. The process refers
to:
A. hardening
B. annealing
c. tempering
D. nitriding


Bleaching action of \( S O_{2} \) is due to
A. its reducing nature
B. its oxidising nature
c. its acidic nature
D. its both oxidising as well as reducing nature


Given an example of an ion or molecule
containing Al that has an incomplete
octet


Give plausible explanation for each of the following:
(i) Cyclohexanone forms cyanohydrin in good yield but 2,2,6 trimethylcyclohexanone does not.
(ii) There are two \( N H_{2} \) groups in semicarbazide. However, only one is
involved in the formation of
semicarbazones.
(iii) During the preparation of esters from a carboxylic acid and an alcohol in the presence of an acid catalyst, the water or the ester should be removed as
soon as it is formed.


The negation of the statement:"If
become a teacher, then I will open a
school" is
A. I will become a teacher and I will not open a school.
B. Either I will not become a teacher or I will not open a school
c. Neither I will become a teacher nor I will open a school
D. I will not become a teacher or I will open a school.


The value of
\( \sin 10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ} \) is:
\( ^{A} \cdot \frac{1}{36} \)
в. \( \frac{1}{32} \)
c. \( \frac{1}{18} \)
D. \( \frac{1}{16} \)


Which of the following polymer is stored in the liver of animals?
A. Amylose
B. Cellulose
c. Amylopectin
D. Glycogen


In \( \Delta A B C, A B=5, B C=6, A C=7 \)
\( \Delta P Q R-\Delta A B C . \) Perimeter of \( \Delta P Q R \)
is \( 360 . \) Find \( \mathrm{PQ}, \) QR and PR.


If the coil of the generator starts rotating faster then:
A. voltage produced by the generator increases.
B. current produced by the generator increases.
c. Both A and B
D. No effect on the value of current and voltage


The partial pressure of oxygen in the alveoli of the lungs is
A. Equal to that in the blood.
B. More than that in the blood
c. Less than that in the blood.
D. Less than that of carbon dioxide


A flim projector magnifies a flim of area 100 square centimeter on screen. If
linear magnification is 4 then area of magnified image on screen will be-
A. \( 1600 s q . c m \)
в. 800 sq.cm
c. \( 400 s q . c m \)
D. 200 sq.cm


Assertion (A): Nuclear fusion reactions
are considered as thermo-nuclear
reactions
Reason (R): The source of stellar energy
is nuclear fusion
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Write one structural difference between
low-density polythene and high-density polythene


Heisenberg's uncertainty principle rules out the exact simultaneous
measurement of :
A. probability and intensity
B. energy and velocity
c. charge density and radius
D. position and velocity


The correct sequence of organelles in which glycolate and glyoxylate are produced sequentially in photorespiration is
A. Chloroplast and mitochondria
B. Chloroplast and peroxisome
c. Peroxisome and mitochondria
D. Peroxisome and chloroplast


Adsorption of a gas on solid metal surface is spontaneous and exothermic then :
A. \( \Delta H \) increases
B. \( \Delta S \) increases
c. \( \Delta G \) increases
D. \( \Delta S \) decreases


Fill in the blanks.
During reverse bias of the diode there is a small current of the order of micro
ampere due to


The exam scores of all 500 students
were recorded and it was determined
that these scores were normally distributed. If Jane's score is 0.8
standard deviation above the mean,
then how many, to the nearest unit,
students scored above Jane?


\( \int_{-1}^{1} \frac{d x}{x^{2}+2 x+5} \)


Blue light of wavelength 480 nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incidence. Assuming that the
index of refraction of the oil is 1.2 and
that of the glass is \( 1.6, \) what is the minimum thickness of the oil film
(other than zero)?
This question has multiple correct options
A . \( 100 n m \)
B. 200nm
c. 300 nm
D. None


Consider the following statements:
A. Condom, diaphragm and cervical caps ate the common barriers used to
prevent pregnancy.
B. Oral pills and vaginal pills are the chemical method practiced for the
prevention of pregnancy.
C. Intra-Uterine Contraceptive Devices (IUCDs) prevent implantation in the
uterus.
D. Vasectomy and tubectomy are the surgical methods practiced for birth
control.
The correct ones are given in
\( A \cdot A, B, C \) and \( D \)
B. \( B, c \) and \( D \)
c. A and D
D. \( c \) and \( D \)


Value of \( \tan ^{-1}\left\{\frac{\sin 2-1}{\cos 2}\right\} \) is
A \( \cdot \frac{\pi}{2}-1 \)
B \cdot \( 1-\frac{\pi}{4} \)
c. \( 2-\frac{\pi}{2} \)
D. \( \frac{\pi}{4}-1 \)


Area of a sector having radius \( 12 \mathrm{cm} \) and arc length \( 21 \mathrm{cm} \) is
A \( \cdot 126 ~ c m^{2} \)
B. \( 252 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 33 \mathrm{cm}^{2} \)
D. \( 45 \mathrm{cm}^{2} \)


Which of the following concentration has the largest degree of dissociation for a weak acid?
\( \mathbf{A} \cdot 1.0 M \)
B. \( 0.5 M \)
c. \( 0.10 M \)
D. \( 0.01 M \)


Very Short Answer Types:
Give a specific scientific term for each
of the following. The period between two successive mitotic divisions.


Find the value of other five
trigonometric ratios:
\( \tan x=-\frac{5}{12}, x \) lies in second quadrant.


A person pushing a stroller starts from rest, uniformly accelerating at a rate of
\( 0.5 m / s^{2} 1 . \) What is the velocity of the stroller after it has travelled \( 4.75 \mathrm{m} \) ?
A . \( 2.18 \mathrm{m} / \mathrm{s} \)
в. \( 5.18 m / s \)
c. \( 9.18 m / s \)
D. \( 1.28 \mathrm{m} / \mathrm{s} \)


Which statement is correct?
A. All bacteria are autotrophic
B. All bacteria are heterotrophic
C. All bacteria are photosynthetic
D. Mostly bacteria are heterotrophic but some are autotrophic


Figure shows the position-time graph of
a particle of mass \( 4 k g . \) What is the \( (a) \)
force on the particle for \( t<0, t> \)
\( 4 s, 0<t<4 s \)
(b) impulse at \( t=0 \) and \( t \)
\( =4 \) s? (Consider one-dimensional
motion only).


Find the odd one out:
A. Solar day
B. Moon day
c. second
D. Light year


Solve :
\( \cot ^{-1}\left(\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right) \)
A \( \cdot_{\pi}-\frac{x}{2} \)
в. \( _{\pi+\frac{x}{2}} \)
c. \( \frac{x}{2} \)
D . \( 2 \pi \)


If \( a^{2}+b^{2}=1, \) then \( \frac{(1+b+i a)}{(1+b-i a)} \) is
A .
B. 2
c. \( b+i a \)
\( \mathbf{D} \cdot a+i b \)


toppr
Q Type your question
inspection should convince you that they are indeed different. Now, how their
physical and chemical properties differ? Generally,
i) Cis-isomer has more dipole moment
than trans-isomer.
ii) Cis is less stable than trans.
iii) The boiling points of cis isomers are
more than those of trans isomers
(remember boiling points are directly
related to polarity which is determined by dipole moment).
iv) Chemical reactivities of cis and
trans also differ from each other.
The number of diastereomeric pairs
and enantiomeric pairs respectively, in the set of stereoisomers of the
compound \( \boldsymbol{C H} \boldsymbol{C l}=\boldsymbol{C H}- \)
\( \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C}_{2} \boldsymbol{H}_{5} \) are
Comprehension-1 You are given two compounds
A .2,2
\( c \)
D. 2,


A solld sphere of radıus \( r \) Is tloating at
the interfare of two immiscible liquids
of densities \( p_{1} \) and \( p_{2}\left(p_{2}>p_{1}\right), \) half of
its volume lying in each. The height of
the upper liquid column from the
interfare of the two liquids is \( h . \) The
force exerted on the upper liquid is
(atmosphere pressure \( =p_{o} \) and
acceleration due to gravity is \( g \) ):
\( ^{\mathbf{A}} \cdot p_{0} \pi r^{2}+\left(h-\frac{2}{3 r}\right) \pi r^{2} p_{1} g \)
B. \( \left(h-\frac{2}{3 r}\right) \pi r^{2} p_{1} g \)
c. \( \frac{2}{3} \pi r^{3} p_{1} g \)
\( \mathbf{D} \cdot P_{0} \times \pi r^{2} \)


Which of the following compound is
amphoteric in nature?
\( A \)
\( \mathrm{C}_{2} \mathrm{H}_{5}-\mathrm{NH}-\sqrt{0} \)
в. \( C H_{3} \) СООН
c.
D. \( C H_{3} C O N H_{2} \)


The \( p H \) of \( 10^{-6} \mathrm{M} H C l, 10^{-7} \mathrm{M} H C l \) and
\( 10^{-8} \) M \( H C l \) respectively is:
\( \mathbf{A} \cdot 6,7,8 \)
в. 6,6.79,6.98
c. 6,6.79,7.02
D. 6,6.98,8


Which of the following is used as washing soda and for softening hard
water?
A. Sodium carbonate
B. Calcium hydroxide
c. Sodium hydrogen carbonate
D. Magnesium hydroxide


Two plane mirrors are parallel to each other and spaced \( 20 \mathrm{cm} \) apart. \( \mathrm{A} \) luminous point is placed between them at a distance \( 5 \mathrm{cm} \) from one mirror
Determine the distances of the first
nearest images from each other.
A . 10
B. 70
\( c .35 \)
D. 40


Which of the following pair of gases cannot be separated by diffusion
method?
\( \mathbf{A} \cdot S O_{2} \) and \( H_{2} \)
B. \( C O_{2} \) and \( N_{2} O \)
c. \( N H_{3} \) and \( N_{2} \)
D. \( C O_{2} \) and \( H_{2} \)


\( \ln H_{2}-O_{2} \) fuel cell a reaction occuring
at cathode is:
A. \( 2 H_{2} O+O_{2}+4 e^{-} \rightarrow 4 O H^{-} \)
В. \( 2 H_{2}+O_{2} \rightarrow 2 H_{2} O(l) \)
\( \mathrm{c} \cdot H^{+}+O H^{-} \rightarrow H_{2} \mathrm{O} \)
D. \( H^{+}+e^{-} \rightarrow \frac{1}{2} H_{2} \)


Calculate Mean deviation about median
for the given data
\( \begin{array}{llll}\text { Marks } & \begin{array}{l}100- \\ 110\end{array} & \begin{array}{l}110- \\ 120\end{array} & \begin{array}{l}120- \\ 130\end{array}\end{array} \)
Frequency 4
A . 10.5
в. 31.5
c. 12.5
D. 66.16


Assertion
A charge \( q \) is placed on a height \( h / 4 \)
above the centre of a square of side \( b \)
The flux associated with the square is independent of side length.
Reason
Gauss's law is independent of size of the Gaussian surface.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


When a weight of \( 10 \mathrm{kg} \) is suspended
from a copper wire of length \( 3 m \) and diameter 0.4 mm. Its length increases
by \( 2.4 \mathrm{cm} . \) If the diameter of the wire is doubled, then the extension is its length
will be :
A \( .7 .6 \mathrm{cm} \)
в. \( 4.8 \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. \( 0.6 \mathrm{cm} \)


The oxidation number of iron in \( \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4} \)
is:
\( A \cdot+2 \)
B. +3
\( c \cdot \frac{8}{3} \)
D. \( \frac{2}{3} \)


If the difference between the
circumference and radius of a circle is
\( 37 \mathrm{cm}, \) then the area of the circle is
\( A \cdot 111 \mathrm{cm}^{2} \)
B. \( 148 \mathrm{cm}^{2} \)
\( c \cdot 259 \mathrm{cm}^{2} \)
D. \( 154 \mathrm{cm}^{2} \)


Figures (a) and (b) show the refraction
of a ray in air incident at \( 60^{\circ} \) with the
normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in a glass when the angle
of incidence in water is \( 45^{\circ} \) with the
normal to a water-glass interface [Fig.
\( (c)] \)


\( A \) speaks the truth '3 times out of \( 4^{\prime} \) and
\( B \) speaks the truth '2 times out of 3 ', \( A \)
die is thrown. Both assert that the
number turned up is 2. Find the probability of the truth of their assertion.


A particle is initially at rest, it is subjected to a linear acceleration \( a, \) as
shown in the figure. The maximum
speed attained by the particle is
A. \( 605 \mathrm{m} / \mathrm{s} \)
B. \( 110 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} .55 \mathrm{m} / \mathrm{s} \)
D. \( 550 \mathrm{m} / \mathrm{s} \)


The maximum strain energy that can be stored in a body is known as:
A. impact energy
B. toughness
c. proof resilience
D. none of the above


Which of the following reactions is most exothermic?


A ball of mass \( m \) is released from \( A \)
inside a smooth wedge of mass \( m \) as
shown in the figure. What is the speed
of the wedge when the ball reaches
point \( B ? \)
\( A \)
B \( \cdot \sqrt{2 g R} \)
\( c \)
D. \( \sqrt{\frac{3}{2} g R} \)


Write negation of:
All natural numbers are integers and
all integers are not natural numbers.
A. All natural numbers are not integers and all integers are not natural numbers
B. All natural numbers are integers and all integers are natural numbers.
C. Some natural numbers are integers and all integers are not natural numbers.
D. All natural numbers are not integers and some integers are natural numbers.


Find the concentration of the
conduction electrons.
A \( \cdot 2.5 \times 10^{20} \mathrm{m}^{-3} \)
В. \( 2.5 \times 10^{26} \mathrm{m}^{-3} \)
c. \( 2.5 \times 10^{28} \mathrm{m}^{-3} \)
D. \( 2.5 \times 10^{30} m^{-3} \)


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \operatorname{given} \) by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{1} \)


reduces toxicity,
minimizes waste, saves energy, and cuts down on the depletion of natura resources. It allows for advances in
chemistry to occur in a much more
environmentally benign way
A. Green chemistry
B. Green revolution
c. waste management
D. None of the above


In humans, bile juice is secreted by
A. Pancreas
B. Small intestine
c. Esophagus
D. Liver


\( 0.1 m^{3} \) of water at \( 80^{0} C \) is mixed with
\( 0.3 m^{3} \) of water at \( 60^{0} \) C.The final
temperature of the mixture is
A \( \cdot 65^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} C \)
D . \( 75^{\circ} \mathrm{C} \)


State true or false.
Animals like camels walk easily in the desert as broad feet exert great
pressure on the sandy ground.


The value of \( K_{c} \) for the reaction: \( 2 A \rightleftharpoons \)
\( B+C \) is \( 2 \times 10^{-3} \). At a given time the
composition of reaction mixture is
\( [\boldsymbol{A}]=[\boldsymbol{B}]=[\boldsymbol{C}]=\mathbf{3} \times \mathbf{1 0}^{-4} \boldsymbol{M} . \) In which
direction the reaction will proceed?
A. Forward
B. Backward
c. At equilibrium
D. Forward or Backward


Write the IUPAC name of the compound.
\[
\begin{array}{c}
\boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C O O H} \\
\boldsymbol{O H}
\end{array}
\]


Eutrophication is related to
A. Water pollution
B. Air pollution
c. Land pollution
D. Cultural pollution


Seed habit first established in
A. Pteridophytes
B. Gymnosperms
c. Angiosperms
D. None of the above


The differential equation, whose solution is \( \boldsymbol{y}=\boldsymbol{a} \cos (\log \boldsymbol{x})+ \)
\( \boldsymbol{b} \sin (\log \boldsymbol{x}), \) is:
A \( \cdot x^{2} y_{2}-x y_{1}+y=0 \)
В. \( x^{2} y_{2}+x y_{1}-y=0 \)
c. \( x^{2} y_{2}+x y_{1}+y=0 \)
D. \( x^{2} y_{2}-x y_{1}-y=0 \)


Two concentric coils of radius \( r \) are
kept mutually perpendicular to each other. If current flowing through both
the coils is \( I, \) then the resultant
magnetic moment due to the two coils will be
A . \( \sqrt{2} I \pi r^{2} \)
В. \( \sqrt{2} I r^{2} \)
c. \( \sqrt{2} I r \)
D. \( 2 \pi r^{2} \)


The bleaching action of \( H_{2} O_{2} \) is due to
which one of the following reactions?
A. \( P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
в. \( H_{2} O_{2} \rightarrow H_{2} O+[O] \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2}+[\mathrm{O}] \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} \)
D. \( H_{2} O_{2}+O_{3} \rightarrow H_{2} O+2 O \)


Match the following (column I with column II).
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { (a) Chlamydomonas } & \text { (i) Moss } \\ \text { (b) cycas } & \text { (ii) Pteridophyta } \\ \text { (c) Selaginella } & \text { (iii) Algae } \\ \text { (d) Sphagnum } & \text { (iv) Gymnosperm }\end{array} \)


If \( A(3, y) \) is equidistant from points \( P(8,-3) \) and \( Q(7,6), \) find the value of \( y \) and find the distance \( \boldsymbol{A} \boldsymbol{Q} \)


From the following exact of the sine
table, the value of \( \sin 37^{0} 27^{\prime} \) is equal to
\( 12^{\prime} 18^{\prime} 24^{\prime} 30^{\prime} 36^{\prime} 42^{\prime} 48^{\prime} 54^{\prime} 1^{\prime} 2 \)
A . 0.6075
B. 0.6081
c. 0.6088
D. 0.6115


Let \( * \) a binary operation on \( \boldsymbol{Q}-\{1\} \)
defined by \( a * b=a+b-a b \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Q}-\{1\} \)
Then, find the identity element in \( Q- \)
\{1\}


Which polymer is matched with
incorrect use?
A. High density polythene - Buckets, pipes
B. Nylon 6,6 - Ropes, bristles for brushes
C. Orlon - Synthetic wool, carpets
D. Glyptal - Electrical switches, combs


The area of a trapezium is \( 138 m^{2} \). The distance and the difference between the
lengths of the parallel sides are \( 12 m \)
and 7 m respectively. Find the lengths of the parallel sides.


Angle in a semicircle is
A. Acute angle
B. Straight angle
C. Right angle
D. Obtuse angle


A \( 50 W, 100 V \) lamp is to be connected to an AC mains of \( 200 \mathrm{V}, 50 \mathrm{Hz} \). What capacitor is essential to be put in series with the lamp?
A \( \cdot \frac{25}{\sqrt{2}} \mu F \)
в. \( \frac{50}{\pi \sqrt{3}} \mu F \)
c. \( \frac{50}{\sqrt{2}} \mu F \)
D. \( \frac{100}{\pi \sqrt{3}} \mu F \)


The sum of 10 terms of GP \( \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+ \)
. is-
A \( \cdot \frac{2^{10}-1}{2^{10}} \)
B. \( \frac{2^{9}-1}{2^{9}} \)
c. \( \frac{2^{10}-1}{2^{9}} \)
D. \( \frac{2^{9}-1}{2^{10}} \)


There are 45 boys and girls in a class. Given the probability that a boy is chosen is \( \frac{4}{15} . \) Find the number of girls
\( A \cdot 8 \)
B. 12
c. 25
D. 33


The force of repulsion between two similar magnetic poles each of strength
\( 2 A m \) at a distance \( 2 m \) from each other
in vacuum is :
A \( \cdot 10^{-5} N \)
В. \( 10^{-7} N \)
c. \( 10^{-3} N \)
D. \( 2 \times 10^{-7} N \)


The equation of a plane progressive wave is given by \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
The dimension of \( (\omega / k) \) is that of
A. frequency
B. velocity
c. wavelength
D. inverse of velocity


A metal rod moves at a constant
velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following:
A. The entire rod is at the same electric potentia
B. There is an electric field in the rod
c. The electric potential is highest at the center of the rod and decrease toward its ends
D. The electric potential is lowest at the center of the rod and increases toward its ends


Solve \( \frac{2 x+3}{2 x-3}+\frac{2 x-3}{2 x+3}=\frac{17}{4} \)


How much heat would be required to
convert \( 14 \mathrm{kg} \) of ice at \( 0^{\circ} \mathrm{C} \) into water of
\( 0^{\circ} \mathrm{C} ? \)
A . 4704 J
в. 4704 k
c. 336 J
D. 336 kJ


Write any six chemical properties of
Non-metals.


Statement A: Photorespiration decreases photosynthesis output.
Statement B: In photorespiratory pathway, neither ATP nor NADPH is
produced.
A. Both the statements \( A \) and \( B \) are correct.
B. Both the statements A and B are wrong.
C. Statement A is correct and Statement B is wrong.
D. Statement B is correct and statement A is wrong.


The strongest acid is:
A. acetic acid
B. trichloroacetic acid
C . dichloroacetic acid
D. monochloroacetic acid


The commercial name for
peroxydisulphuric acid :
A. Caros acid.
B. Marshalls acid
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \) Crystals
D. Sulphurous acid


State Maxwell's theory of
electromagnetic wave related to light Write down four characteristics of
electromagnetic waves.


Which one of the following traits of garden pea studied by Mendel was a recessive feature?
A. Green seed colour
B. Green pod colour
c. Round seed shape
D. Axial flower position


The line joining (-1,0) and \( (-2,-\sqrt{3}) \) makes with the \( x \) -axis an angle equal to
\( A \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. 75


Two concentric conducting shells A and
B are of radii Rand 2 R. A charge \( + \) q is placed at the centre of the shells Shell B is earthed and a charge q is given to shell A. The charge on outer surface of A is \( n q \), find \( n \)


Two waves of amplitudes \( A \) and \( 3 A \) are superposed and they have a phase difference of \( \pi . \) What kind of
interference is possible
A. constructive interference
B. Destructive interference
c. Interference depends on wavelength difference
D. Interference depends on frequency difference


Among the following the most reactive towards alcoholic \( K O H \) is:
A. \( C H_{2}=C H B r \)
в. \( C H_{3} C O C H_{2} C H_{2} B r \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br} \)
D. \( C H_{3} C H_{2} C H_{2} B r \)


Which is incorrect about coenzyme?
A. Every coenzyme is a cofactor and every cofactor is a coenzyme
B. Every coenzyme is a cofactor and every cofactor is not a coenzyme
C. Most of the coenzymes are nucleotides and are composed of vitamins
D. Coenzymes are the active constituents of enzymes


Law of definite proportion does not apply to nitrogen oxide because:
A. Atomic weight of nitrogen is not conserved
B. Molecular weight of nitrogen is variable
c. Equivalent weight of nitrogen is variable
D. Atomic weight of oxygen is variable


Using electron-transfer concept, identify the oxidant and reductant in
the following redox reactions.
(a) \( Z n(s)+2 H^{+}(a q) \longrightarrow \)
\( Z n^{2+}(a q)+H_{2}(g) \)
(b) \( 2\left[F e(C N)_{6}\right]^{3-}(a q)+2 O H^{-}(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
(c) \( 2\left[F e(C N)_{6}\right]^{3-}(a q)+2 O H^{-}(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)


Resolve into partial fractions \( \frac{x^{2}+2}{(x+1)^{3}(x-2)} \)
A \( \cdot \frac{6}{(x+2)}+\frac{6}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
B. \( -\frac{6}{(x+2)}+\frac{6}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
C \( \cdot-\frac{6}{(x+2)}+\frac{3}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
D \( \cdot-\frac{3}{(x+2)}-\frac{3}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)


Under what conditions can hydrogen be made to combine with sulphur?


If the change in the value of \( g \) at height
\( h \) above earth surface is the same as
that at depth \( x\left(x \quad \text { or } \quad h<R_{e}\right), \) then
A \( \cdot x=h^{2} \)
в. \( x=h \)
c. \( _{x}=\frac{h}{2} \)
D. \( x=2 h \)


If \( \boldsymbol{A}=\left(\begin{array}{rr}\mathbf{4} & -\mathbf{2} \\ \mathbf{5} & -\mathbf{9}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{8} & \mathbf{2} \\ \mathbf{- 1} & -\mathbf{3}\end{array}\right) \)
find \( \mathbf{6} \boldsymbol{A}-\mathbf{3} \boldsymbol{B} \)


Displacement - time graphs of a body in motion along a line is represented by four curves \( (a),(b),(c) \) and \( (d) . \) Which of
the curves indicated retardation
motion?


Write the procedure involved in the acid and leaf experiment to understand the concept "how the stomach gets
protected from its own acid secretions" Compare the observations with the
changes that takes place in human digestive system.


Use mathematical induction to prove:
\( \frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\dots+ \)
\( \frac{1}{(2 n-1)(2 n+1)}=\frac{n}{2 n+1} \)


The plant of ONGC got collapsed in the recent years which was a chastic
damage to them. How can we prevent
this?


If the expression \( \left(125-x^{3}\right)=(5- \)
\( x)\left(x^{2}+a x+b\right), \) then the value of a is
A . 4
B. 2
\( c .-7 \)
D.


A right circular cylinder has Height as
\( 30 c m \) and Radius as \( 35 c m \) find its
\( \boldsymbol{C S A} \)


A transition element \( X \) has a
configuration \( [A r] 3 d^{4}, \) in its +3 oxidation state. Its atomic number is:
A . 25
B. 26
c. 22
D. 19


Evaluate \( \sum_{k=1}^{n}\left(2^{k}+3^{k-1}\right) \)


A solid having six equal square faces is called a
A. Cube
B. Cuboid
c. Square
D. Rectangle


Which of the following phenomena cannot be explained by scattering of light ?
A. Blue colour of sky
B. Colour of clouds
c. Tyndall effect
D. Formation of rainbow


Explain hybridization of central atom in
\( : C C l_{4} \)


Find derivative of \( (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b})^{n}(\boldsymbol{c} \boldsymbol{x}+\boldsymbol{d})^{\boldsymbol{n}} \)


The correct order of increasing \( s- \)
character (in percentage) in the hybrid orbitals of following molecules/ions is:
(।) \( C O_{3}^{2-} \)
\( (\|) \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{4}} \)
\( (\|\|) \boldsymbol{I}_{3}^{-} \)
\( (\mid V) N C l_{3} \)
\( (\vee) B e C l_{2} \)
\( A \cdot\|<\| I<I V<I<V \)
B. \( \|<I V<\| I<V<1 \)
\( c \cdot \||<||<|<V<\mid V \)
D. \( \|<I V<\| I<1<V \)


To a person going east in a car with a velocity of \( 25 k m p h, \) a train appears to move towards north with a velocity of \( 25 \sqrt{3} k m p h . \) The actual velocity
\( A .5 \mathrm{kmph} \)
B. 25 kmph
c. \( 50 \mathrm{kmph} \)
D. 53 kmph


A firm has the cost function \( C=\frac{x^{3}}{3}- \)
\( 7 x^{2}+111 x+50 \) and demand function
\( \boldsymbol{x}=\mathbf{1 0 0}-\boldsymbol{p} \)
Write the total revenue function in
terms of \( \boldsymbol{x} \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a continuous function such that \( \boldsymbol{f}(\boldsymbol{x})-\mathbf{2} \boldsymbol{f}\left(\frac{\boldsymbol{x}}{\mathbf{2}}\right)+\boldsymbol{f}\left(\frac{\boldsymbol{x}}{\mathbf{4}}\right)=\boldsymbol{x}^{\mathbf{2}} \)
The equation \( f(x)-x-f(0)=0 \) have
exactly:
A. no solution
B. one solution
c. two solutions
D. Infinite solutions


If two waves of same frequency and
amplitude superpose to produce resultant of the amplitude of either wave, then their phase difference is-
\( A \)
в. \( 2 \pi / 3 \)
c. \( \pi / 3 \)
D. Zero


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


Neutral litmus solution have
A. no effect of acidic solution
B. no effect of alkaline solution
C. both \( A \) and \( B \)
D. none of these


A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of
10. If we can approximate the distribution of these grades by a normal distribution, what percent of the
students should fail the test (grades \( < \)
60)\( ? \)
A . 15.21
в. 23.2
c. \( 15.87 \% \)
D. 16.23


Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{m} \boldsymbol{i} \boldsymbol{n} \cdot(\boldsymbol{x}+1, \sqrt{1-\boldsymbol{x}}), \) then
area bounded by \( y=f(X) \& x \) -axis is
\( \mathbf{7} \)
\( \overline{6} \) square units.
Reason
\( \min \) of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}x+1 & \text { for }-1 \leq x<0 \\ \sqrt{1-x} & , 0<x \leq 1\end{array}\right. \)
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


Balance the following redox equations by oxidation number method occur in
acidic medium:
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{C r}_{2} \boldsymbol{O}_{7(a q)}^{2-} \rightarrow \boldsymbol{O}_{2(g)}+\boldsymbol{C r}_{(a q)}^{3+} \)


In which structure peripheral vascular bundles are generally smaller than centrally located ones? This question has multiple correct options
A. Dicot stem
B. Monocot stem
c. Dicot root
D. Monocot root


Which of the following ions is diamagnetic? This question has multiple correct options
A. \( B e E t_{2} \)
в. АlМе\( _{3} \)
c. \( B_{2} H_{6} \)
D. \( \operatorname{Si}\left(C H_{3}\right)_{4} \)


Why do noble gases have comparatively
large atomic sizes?


State whether the following statements
are true or false.

Organ formation in the callus of tobacco
pith is controlled by the balance of concentrations between auxin and
cytokinins.
A. True
B. False


Heat is absorbed by a body but its
temperature does not rise. Which of the following statements explains the phenomena?
A. No increase in internal energy takes place
B. Only kinetic energy of vibration increases
c. Increase in kinetic energy in balanced by decrease in potential energy
D. Only potential energy of intermolecular force field increases


The areas of cross section of two wires
of the same material are in the ratio 1:
2 and their lengths are in the ratio 2: 1
If their ends have the same potential differences then currents through
them will be in the ratio of
A .1: 2
B . 2: 1
c. 1: 4
D. 4: 1


The placentation in a multilocular ovary
where the ovules are borne over the
entire inner surface is called as
A. Pendulous
B. Marginal
c. superficial
D. Parietal


For anionic hydrolysis, \( p H \) is given by:
A \( \cdot p H=\frac{1}{2} p K_{w}=\frac{1}{2} p K_{b}-\frac{1}{2} \log c \)
B. \( _{p H=} \frac{1}{2} p K_{x}+\frac{1}{2} p K_{a}-\frac{1}{2} p K_{b} \)
c. \( _{p H=} \frac{1}{2} p K_{w}+\frac{1}{2} p K_{a}+\frac{1}{2} \log c \)
D. none of the above


Suppose an electron is attracted towards the origin by a force \( \frac{\mathbf{k}}{\mathbf{r}} \) where \( \mathbf{k}^{\prime} \) is a constant and \( \mathbf{r}^{\prime} \) is the distance of
the electron from the origin. By applying Bohr model to this system, the radius of the \( n^{\text {th }} \) orbital of the electron is found to
be \( \mathbf{r}_{\mathbf{n}}^{\text {' and the kinetic energy of the }} \)
electron to be' \( \mathbf{T}_{\mathbf{n}} . \) Then which of the
following is true?
A \( \cdot \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n} \)
B. \( \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^{2} \)
\( c \cdot \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^{2}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^{2} \)
D. \( T_{n} \) independent of \( n, r_{n} \propto n \)


Evaluate the following integral:
\( \int_{0}^{\pi} 1+\sin x d x \)


Why do atomic masses of most of the
elements in atomic mass units involve
fraction?


On what factors does the capacitance of
a parallel plate capacitors depends?


Differentiate \( \boldsymbol{y}=\mathbf{1 0}^{\boldsymbol{x}}+\mathbf{1 0}^{\tan \boldsymbol{x}} \)


A \( 5.8 \% \) solution of \( N a C l \) has vapour
pressure closest to
A . \( 5.8 \% \) solution of urea
B. 2 \( M \) solution of glucose
c. \( 1 M \) solution of urea
D. 5.8 \% solution of glucose


\( \Delta G^{o} \) versus \( T \) plot in the Ellingham's diagram slopes downward for which of the reaction?
\( ^{\mathbf{A}} \cdot c+\frac{1}{2} O_{2} \rightarrow C O \)
в. \( c O+\frac{1}{2} O_{2} \rightarrow C O_{2} \)
\( \mathrm{c} \cdot_{2 A g+\frac{1}{2}} O_{2} \rightarrow A g_{2} O \)
D. \( _{M g+\frac{1}{2} O_{2} \rightarrow M g O} \)


Consider the following statements.
\( S_{1}: \) The percentage of s-character in the
orbital forming \( S-S \) bonds and \( P-P \)
bonds in \( S_{8} \) and \( P_{4} \) molecules respectively are same.
\( S_{2}: \ln S F_{4} \) the bond angles, instead of
being \( 90^{\circ} \) and \( 180^{\circ} \) are \( 89^{\circ} \) and \( 177^{\circ} \) respectively due to the repulsions between lone pair and bond pairs of electrons.
\( S_{3}: \) Aqueous \( H_{3} P O_{4} \) is syrupy (i.e more viscous than water)
\( S_{4}: S i O_{2} \) crystal maybe considered as giant molecule in which eightmembered rings are formed with alternate silicon and oxygen atoms of these:
A. \( S_{1} \& S_{4} \) are correct only
B . \( S_{2}, S_{3} \& S_{4} \) are correct only.
c. \( S_{1}, S_{2}, S_{3} \& S_{4} \) are correct
D. \( S_{1}, S_{2} \& S_{3} \) are correct only.


In the figure above, \( A D=A C=C B \)
If the value of \( y \) is \( 28^{\circ}, \) what is the value
of \( x ? \)


Which of the following is not a good practice to conserve fuel?
A. Using public transport system
B. Using motor bike to travel short distances
c. using bicycle to travel short distances
D. Walking the short distances


Bell laboratory has developed superconductor at a temperature of
A. 30 K
в. 40 к
\( c . \) 50 \( k \)
D. 60


A bucket tied to a string is lowered at a constant acceleration of \( g / 4 \). If the mass of the bucket is \( m \) and is lowered
by a distance \( d \), the work done by the string on bucket will be:(assume the string to be massless, acceleration due
to gravity \( =g) \)
A \( \cdot \frac{1}{4} m g d \)
в. \( -\frac{3}{4} m g d \)
c. \( -\frac{4}{3} m g d \)
D. \( \frac{4}{3} m g d \)


Why are Haloarenes less reactive than
haloalkane.


The oxidation number of Na in NaCl:
A. 0
B. - -
\( c \cdot+1 \)
D. 2
\( E \cdot+2 \)


Explain the process of digestion in human beings.


Suppose a population \( A \) has 100
observations \( 101,102, \ldots, 200 \) and
another population \( B \) has 100
observations \( 151,152,153, \dots, 250 . \) If
\( V_{A} \) and \( V_{B} \) represent the variances of
the two populations respectively, then \( \frac{\boldsymbol{V}_{\boldsymbol{A}}}{\boldsymbol{V}_{\boldsymbol{B}}} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{9}{4} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{3} \)


Which of the following Energy stabilise
the \( \triangle \boldsymbol{H}_{f} \) of \( \boldsymbol{N a C l} \) the most?
A. Lattice Enthalpy
B. Bond dissociation Enthalpy
c. Electron Affinity Enthalpy
D. Ionisation Enthalpy


'Thermal pollution' means dumping heat in an ecological system, like a lake or a pond. Thermal power plants have to
throw some heat into a 'sink' because of
they:
A. get overheated
B. have special anti-pollution laws
c. follow the local sanitation laws
D. follow the second natural law of thermodynamics


Statement 1: A supersaturated solution of glucose in boiling water crystallizes as it cools.

Statement 2 : The solubility increases as the temperature increases.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1
c. statement 1 is correct but statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Match the wall components with the
type of tissues/ tissue system listed. Choose the answer which gives the correct combination of alphabets.
\begin{tabular}{llll}
& List I & & List II \\
\cline { 8 - 5 } A & Suberin & 1 & Sclerenchyma \\
B & Lignin & 2 & Collenchyma \\
c & Pectin & 3 & Epidermis \\
D & Cutin & 4 & Phellem
\end{tabular}
A \( \cdot A-4, B-1, C-2, \)
B. A-1,B-4, C-2, D-3
c. \( A-4, \) В- \( 2, C-1, D-3 \)
D. A- 4, B-1, C-3


A ray of light passes from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) \& bends towards the normal, comment on
the refractive index of \( A \& B \)


Evaluate:
\( \lim _{x \rightarrow \frac{\pi}{3}} \frac{\sin \left(\frac{\pi}{3}-x\right)}{2 \cos x-1} \)


\( 38 k g \) of rice costs \( R s .275 .50 . \) What is
the cost of \( 20 k g \) of such rice?


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


"If \( p, \) then \( q^{\prime \prime} \) is logically equivalent to which of the following?
I. If \( q, \) then \( p \)
II. If not \( p, \) then not \( q \)
III. If not \( q, \) then not \( p \)
A. None of the above
B. III Only
c. I and II only
D. I and III only
E. I, II and III


For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \) the correct
choice is
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing agent
B. \( H_{3} P O_{3} \) is dibasic and non-reducing agent
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic and reducing agent
D. \( H_{3} P O_{3} \) is tribasic and non-reducing agent


Which among the following factors changes the value of ionic product of
water?
A. Change in temperature
B. Addition of acid
c. Addition of base
D. Addition of either acid and base


The maximum number of \( 90^{0} \) angles
between bond pair-bond pair of electrons is observed in:
A. \( d s p^{3} \) hybridisation
B . sp \( ^{3} \) d hybridisation
c. \( d s p^{2} \) hybridisation
D. \( s p^{3} d^{2} \) hybridisation


The dimension of coefficient of viscosity
\( \eta \) is :
\( \mathbf{A} \cdot\left[M L^{-1} T^{-1}\right] \)
\( \mathbf{B} \cdot\left[M L T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-1}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)


How is propanone converted into-
(i) Propan - 2 - ol
(ii) 2 - Methylpropan \( -2- \) ol?


A hydrogen like atom with atomic number \( Z \) is in higher excited state of quantum number 'n'. This excited state
atom can make a transition to the first
excited state by successively emitting two photons of energies \( 10 \mathrm{eV} \) and \( 68.2 \mathrm{eV} \) respectively. Alternatively the atom from the same the same excited
state can make a transition to the 2 nd
excited state by emitting two photons of energies \( 4.25 \mathrm{eV} \) and \( 5.95 \mathrm{eV} \) respectively Calculate the value of \( z \)


\( \lim _{x \rightarrow \infty} \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} \) is equal to
A . 0
B.
\( c \cdot \log 2 \)
D. \( e^{4} \)


Solve: \( \sin x \frac{d y}{d x}-y=\sin x \cdot \tan \frac{x}{2} \)


Which of the following has only one orbital?
A. \( d \)
B.
\( c \cdot f \)
\( D \)


Evaluate \( \lim _{n \rightarrow \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{6 n}\right) \)
\( A \cdot \log 6 \)
B. \( 3 \log 2 \)
c. \( 2 \log 3 \)
D. \( \log 3 \)


What are the meanings of following symbols? Write your role accordingly?


The gases which absorb most of IR (infrared) rays are
\( A \cdot \mathrm{s} \mathrm{O}_{2}, \mathrm{CO}_{2}, \) and \( \mathrm{NO}_{2} \)
B. \( \mathrm{SO}_{2}, \mathrm{CH}_{4}, \) and \( \mathrm{O}_{3} \)
\( \mathrm{c} \cdot \mathrm{co}_{2}, \mathrm{CH}_{4}, \) and \( \mathrm{cFCs} \)
D. \( \mathrm{NO}_{2}, \mathrm{CO}_{2}, \) and \( \mathrm{O}_{3} \)


An organic compound which produces a bluish-green coloured flame on heating in presence of copper is:
\( A \). chlorobenzene
B. benzaldehyde
c. anlline
D. benzoic acid


The design, development and implementation of chemical products and process to reduce or eliminate the
use and generation of substances hazardous to human health and
environment is called
A. Green Revolution
B. Green Chemistry
c. Environmental Chemistry
D. waste Management


In the reaction, \( 2 N_{2} O_{5} \rightarrow 4 N O_{2}+O_{2} \)
initial pressure is 500 atm and rate
constant \( k \) is \( 3.38 \times 10^{-5} s e c^{-1} . \) After 10
minutes the final pressure of \( N_{2} O_{5} \) is:
A. 490 atm
B. 250 atm
c. 480 atm
D. 420 atm


The terminal velocity of a rain drop is \( 30 c m / s, \) If the viscosity of air is \( 1.8 \times \) \( 10^{-5} N s m^{-2}, \) The radius of rain drop is:
A. \( 0.01 m m \)
B. \( 0.5 m m \)
c. \( 0.05 \mathrm{mm} \)
D. \( 1 \mathrm{mm} \)


Study the following statements regarding food chains and select the
correct ones.
(i) Removal of \( 80 \% \) tigers from an area resulted in greatly increased growth of vegetation.
(ii) Removal of most of the carnivores
resulted in an increased population of deers.
(iii) The length of food chains is generally limited to \( 3-4 \) trophic levels
due to energy loss.
(iv) The length of food chains may vary from 2 to 8 trophic levels.
\( A \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (i) and (iii)
D. (iii) and (iv)


Differentiate between striated,
unstriated and cardiac muscles on the
basis of their structure and
site/location in the body.


The colour are characterised by which of following character of light.
A. Frequency
B. Amplitude
c. wavelength
D. Velocity


Which of the following is \( 3^{0} \) amine?
A. 1-methylcyclohexylamine
B. Triethylamine
c. Tert-butylamine
D. N-methyl aniline


Calculate \( L \)
\( \mathbf{A} \cdot 0.5300 H \)
B. \( 0.0013 H \)
c. \( 0.0004 H \)
D. \( 0.0253 H \)


The principal value of \( \sin ^{-1} x \) lies in the
interval
A \( \cdot\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
B. \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
c. \( \left[0, \frac{\pi}{2}\right] \)
D. \( [0, \pi] \)


Is the following sequence an \( A P ? \) If
true, find the common difference \( d \) and
write three more terms.
\( 0.2,0.22,0.222, .0 .2222, . . \)


Evaluate \( \left|\begin{array}{ll}\cos 65^{\circ} & \sin 65^{\circ} \\ \sin 25^{\circ} & \cos 25^{\circ}\end{array}\right| \)


Construct a triangle of sides \( 4 \mathrm{cm}, 5 \mathrm{cm} \) and \( 6 \mathrm{cm} \) and then a triangle similar to it whose sides are \( \frac{3}{5} \) time of the
corresponding sides of the given triangle.


n fig, if \( \boldsymbol{A B}\|\boldsymbol{C D}, \boldsymbol{C D}\| \boldsymbol{E F} \) and \( \boldsymbol{y} \)
\( z=3: 7 \) find \( x \)


Which of the following State has highest literary rate?
A. Maharashtra
B. Gujarat
c. Kerala
D. None of the above


A bat flies at a constant speed of \( 0.04 V \)
toward a large tree trunk (where \( \boldsymbol{V} \)
denotes the speed of sound), the bat emits an ultrasonic pulse. The pulse is reflected off the tree and returns to the
bat, which can detect and analyse the returning signal. If the returning signal has a frequency of \( 61 k H z \), Find out the
frequency of the original ultrasonic
pulse?
\( \mathbf{A} .56 k H z \)
в. \( 62 k H z \)
\( c .68 k H z \)
D. \( 74 k H z \)
E \( .78 k H z \)


The relative abundance of two rubidium
isotopes of atomic weights 85 and 87 are \( 75 \% \) and \( 25 \% \) respectively. The
average atomic weight of rubidium is:
A. 75.5
B. 85.5
\( c .86 .5 \)
D. 87.5


What is the meaning of "ectothermal animal"?
A. The animals whose body temperature varies with environmental temperature
B. The animals whose body temperature do not vary with environmental temperature
c. The animals who can maintain their body temperature.
D. All of the above


If the \( p^{t h} \) term of the series of positive numbers \( 25,22 \frac{3}{5}, 20 \frac{1}{2}, 18 \frac{1}{4}, \dots \) is
numerically the smallest, then the \( p^{t h} \)
is.
A \( \cdot \frac{1}{4} \)
B.
c. \( \frac{1}{3} \)
D.


Which curve corresponds to the
temperature dependence of the rate \( \boldsymbol{R} \)
of a simple one step reaction?
\( A \)
в.
c.
D. None of the above


Consider the following reaction,
\( \mathbf{5} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{x} \boldsymbol{C l} \boldsymbol{O}_{\mathbf{2}}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{x} \boldsymbol{C l}^{-}+ \)
\( \boldsymbol{y} \boldsymbol{O}_{2}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} . \) The reaction is balanced
if
A \( . x=5, y=2 \)
в. \( x=2, y=5 \)
c. \( x=4, y=10 \)
D. \( x=5, y=5 \)


What forms when an acid loses a
proton?
A \( \cdot p H \)
в. \( p O H \)
c. ка
D. Conjugate base


Which of the following set of apparatus
will be useful to prove the laws of
reflection?
A. A spherical mirror, a sheet of white paper
B. A plane mirror, a laser light, a pencil, a protractor, a sheet of white paper
c. A mirror, a sheet of black paper
D. A laser light


Calyptra is derived from
A. Archegonia
B. capsule
c. Antheridia
D. Columella


Which of the following is correct about the earth's magnetic field?
A. Earth's magnetic field is nearly dipolar
B. It is approximately aligned with earth's rotation axis
c. It spontaneously reverses every 200,000 years
D. All of these


What are the different methods of
contraception?


You have three resistors of values
\( 2 \Omega, 3 \Omega, \) and \( 5 \Omega . \) If they are in parallel then the total resistance is :
\( \mathbf{A} \cdot 0.97 \Omega \)
в. \( 2 \Omega \)
\( c .10 \Omega \)
D. 3.


The oscillating electric and magnetic
vectors of an electromagnetic wave are
oriented along
A. the same direction but differ in phase by \( 90^{\circ} \)
B. the same direction and are in phase.
C. mutually perpendicular directions and are in phase.
D. mutually perpendicular directions and differ in phase by \( 90^{\circ} \)


Assertion
In a constant pressure process if we neglect the friction between piston then
we can definetly say that the process
has to be reversible.
Reason
Since there is always an equilibrium on
piston due to constant pressure we can say that it is reversible process.
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


In the figure \( A O C \) is a diameter of the circle and are \( \overline{\boldsymbol{A} \times \boldsymbol{B}}=\frac{1}{2} \overline{\boldsymbol{B} \boldsymbol{Y} \boldsymbol{C}} \). Find
\( \angle B O C \)


The annual growth of capital of a
business is \( 7 \% . \) At present, the capital
is Rs. 12000. What will be the capital
after 3 years?


Sublimation cannot be used for
purification of:
A . urea
B. camphor
c. benzoic acid
D. napthalene


What were the three major observations
Rutherford made in the gold foil
experiment?


Let \( f \) be a continuous function on \( \mathrm{R} \)
satisfying \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}(1)=\boldsymbol{4} \) then \( \boldsymbol{f}(\boldsymbol{3}) \) is
equal to


The radius of a coil decreases steadily
at the rate of \( 10^{2} \mathrm{m} / \mathrm{s} \). A constant and
uniform magnetic field of induction \( 10^{3} W b / m^{2} \) acts perpendicular to the plane of the coil. The radius of the coil when the induced e.m.f. in the coil is \( 1 \mu \)
\( v, \) is
\( ^{A} \cdot \frac{2}{\pi} \mathrm{cm} \)
в. \( \frac{3}{\pi} \mathrm{cm} \)
c. \( \frac{4}{\pi} \mathrm{cm} \)
D. \( \frac{5}{\pi} \mathrm{cm} \)


Degree of the polynomials \( \frac{x^{23}+x^{14}-x^{16}}{x^{2}} \) is
\( A \cdot 2 \)
B . 23
c. 14
D. 21


The product of oxygenation of RUBP is
A. Phosphoglycerate
B. Phosphoglycolate
c. oxaloacetate
D. Both A and B


Scattering of light is defined as:
A. Splitting of light into its component colours
B. Deflection of light in different directions when light is incident on extremely small particles
c. Bending of light on change of medium
D. reversal of light direction from a shiny surface


Find the value of \( \cos \theta-\cos 3 \theta+\cos 4 \theta \)
when \( \boldsymbol{\theta}=\mathbf{4 5}^{\circ} \)
A. \( \frac{\sqrt{3}}{2} \)
B. \( \sqrt{3}-1 \)
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{2}-1 \)


If the points (0,4),(4,0) and \( (5, p) \) are collinear, then value of \( p \) is
A . -1
B. 7
\( c \cdot 6 \)
D.


Factorise:
\( \boldsymbol{p}^{3}(\boldsymbol{q}-\boldsymbol{r})^{3}+\boldsymbol{q}^{3}(\boldsymbol{r}-\boldsymbol{p})^{3}+\boldsymbol{r}^{3}(\boldsymbol{p}-\boldsymbol{q})^{3} \)


Three identical bodies, each of mass \( m \)
are pushed by a force \( \boldsymbol{F} \) on a frictionless
table a shown in the figure. Then:
A. Net force on \( X \) is \( F \)
B
C. Force applied by \( Y \) on \( Z \) is equal net force on \( X \)
D. Net force on \( Y \) is equal to zero


toppr
Q Type your question.
following graph best represents the relation between the force exerted by
the table on the chain with time?
(Assume that the fallen part
immediately comes to rest after
collision with table and does not form a
heap)
\( A \)
3
\( c \)
D


\( H_{3} P O_{4} \) is a tri basic acid and one of its
salt is \( N a H_{2} P O_{4} . \) What volume in ml of
1M NaOH solution should be added to
\( 12 g \) of \( N a H_{2} P O_{4} \) to convert it into
\( N a_{3} P O_{4} ? \)


For an elementary reaction \( \boldsymbol{X}(\boldsymbol{g}) \rightarrow \) \( \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Z}(\boldsymbol{g}), \) the half-life period is \( \mathbf{1 0} \)
min. In what period would the concentration of \( X \) be reduced to \( 10 \% \)
of original concentration?
A . 20 Min
B. 33Min
c. 15Min
D. 25Min


Find ten rational numbers between \( \frac{-2}{5} \) and \( \frac{1}{2} \)
A \( \frac{-7}{20}, \frac{-11}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0, \frac{1}{20} \) and \( \frac{2}{20} \)
B. \( \frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0, \frac{1}{20} \) and \( \frac{2}{20} \)
C. \( \frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0, \frac{1}{20} \) and \( \frac{13}{20} \)
D. \( \frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0, \frac{15}{20} \) and \( \frac{2}{20} \)


Three convex lenses are available
having focal lengths of \( 4 \mathrm{cm}, 40 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively. Which one would you choose as a magnifying glass and why?


The IUPAC name of Chloropicrin is:
A. Trichloronitromethane
B. 1, 1, 1-trichloro-2-methyl-2-propanol
c. 3-hydroxybutanal
D. 2, 2, 2-trichloroethanal


Atoms combine with each other to
each other.
A. stabilize
B. attain alkali metal configuration
C. reduce their mass
D. none of the above


Which of the following species has same number of unpaired electrons?
This question has multiple correct options
A \( \cdot C r^{3} \)
B. \( M n^{2+} \)
\( \mathrm{c} \cdot F e^{3} \)
D. \( C u^{2} \)


Guess and write why does pole vault jumper land on thick mats of foam?


Match the columns and find the correct
combination:
\begin{tabular}{llll}
& \multicolumn{2}{l} { I } \\
a & Auxin & II & \\
b & Cytokinin & 2. & Inhibitor of growth \\
c & Gibberellin & 3. & Apical dominance \\
d & Ethylene & 4. & Epinasty \\
& Abscisic & 5. & Induces amylase synthesis
\end{tabular}
\( A \)
\( a-3, b-1, c-5, d-4, e-2 \)
B. \( a-4, b-5, c-1, d-3, e-2 \)
c. \( a-2, b-1, c-5, d-3, e-4 \)
D. \( a-3, b-1, c-5, d-2, e-4 \)
E. \( a-4, b-1, c-5, d-3, e-2 \)


In the Bohr Model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton
and the electron. If \( a_{o} \) is the radius of
the ground state orbit, \( m \) is the mass,
and \( e \) is the charge on the electron, and
\( \epsilon_{o} \) is the permittivity of vacuum, then the speed of the electron is:
A . 0
в. \( \frac{e}{\sqrt{\epsilon_{o} a_{o}}} \)
c. \( \frac{e}{\sqrt{4 \pi \epsilon_{c} a_{o} m}} \)
D. \( \sqrt{\frac{4 \pi \epsilon_{o} a_{o} m}{e}} \)


Which of these non-metals would be
most reactive?
A. \( P \)
в. \( S \)
c. \( C l \)
D. \( H e \)
E . \( N e \)


Taking the earth to be a uniform sphere of radius \( 6400 \mathrm{km} \) and the value of \( g \) at
the surface to be \( 10 \mathrm{m} s^{-2} \), calculate the
energy needed to raise a satellite of
mass \( 2000 \mathrm{kg} \) to a height of \( 800 \mathrm{km} \) above the earth's surface and to set it
into circular orbit at that altitude.
B. \( 8 \times 10^{10} \) J.
\( \mathbf{c} \cdot 9 \times 10^{10} J \)
D. \( 1.8 \times 10^{10} \) J.


Evaluate the following integral as limit of sum:
\( \int_{0}^{2} e^{x} d x \)


Which is true of glycolysis
A. In aerobic organisms, it is the only process in respiration
B. In this process glucose undergoes complete oxidation to form pyruvic acid
C. Enzyme hexokinase catalyses phosphorylation of glucose to glucose 6 -phosphate
D. ATP is utilised in conversion of PEP to pyruvic acid
E. \( \mathrm{NADH}+H^{+} \) is formed when
1, 3-biphosphoglyceric acid is converted to 3-phosphoglyceric acid


A hot and a cold body are kept in
vacuum separated from each other. Which of the following causes decrease in temperature of the hot body?
A. conduction
B. radiations
c. convection
D. the temperature of the bodies remain unchanged


If the distance between two masses is
doubled, the gravitational attraction between them Is doubled
A . Is doubled
B. Becomes 4 times
c. Is reduced to half
D. Is reduced to a quarter


State whether the following statements are true or false.

After fire a primary succession starts at a very rapid rate
A. True
B. False


\( \int_{0}^{\infty} f\left(x+\frac{1}{x}\right) \frac{\ln x}{x} d x \)
A. is equal to zero
B. is equal to one
\( \mathrm{c} \cdot_{\text {is equal to }} \frac{1}{2} \)
D. can not be evaluated


Out of the seven characters of pea
studied by Mendel,gens for three were situated on chromosome number four
(flower position,pod shape and plant height.) Suppose if they were closely situated and were linked then which of
the following rule would not have been discovered or explained Mendel?
A. Law of dominance
B. Law of seggregation
c. Law of independent assortment
D. Law of purity of gametes


Fill in the blank.
When body is performing uniform circular motion, its \( _{-}-_{-}-_{-}- \) changes at every points.


Calculate molarity of \( K O H \) in the solution prepared by dissolving its \( 5 g \) in enough water to from 500ml of solution
A . 0.20
B. 0.16
c. 0.005
D. 0.10


Evaluate \( \int(7 x-2) \sqrt{3 x+2} d x \)


The function \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \) where \( \boldsymbol{N} \) is
the set of natural numbers, defined by \( f(x)=7 x+11 \) is
A. injective
B. surjective
c. bijective
D. none of these


Three bodies \( A, B \) and \( C \) are moving in
a straight line in the same direction
such that relative velocity of \( A \) w.r.t \( B \) is
\( 2 m / s, \) relative velocity of \( B \) w.r.t \( C \) is
\( \mathbf{5} \boldsymbol{m} / \boldsymbol{s} \)
Find the relative velocity of \( C \) w.r.t \( A \)
A \( .-3 m / s \)
в. \( 2 m / s \)
c. \( -2 m / s \)
D. \( 3 m / s \)


Some redox reactions are given in Column I. Match them with correct mole
ratio of oxidizing to reducing agents given in Column II.


The figure shows sex determination in
humans.

What are the right substitutes for the
numbers 1 to 6?


The adjoining figure shows a negatively charged electroscope. If a negatively charged rod is brought close to, but not
touching, the knob, the two leaves will :
A. move closer together
B. move farther aparttt
c. not move at all
D. None of these


Umbel inflorescence is found in
A . Musa
B. Colocasia
c. Coriandrum
D. Helianthus


Why CFL is better in comparison to bulb
\( ? \)
A. Because bulb produce heat which results in wastage of electricity and CFL saves electricity.
B. Because bulb produce heat which results in production of more electricity than CFL
C. Because CFLs size is bigger than bulb
D. Because CFL produce heat which results in saving of electricity.


toppr IN
Q Type your question
the correct answer in the blanks.
Answer
\( (i)_{6}^{12} C+_{1}^{1} H \longrightarrow_{7}^{13} N \)
\( (i i)_{13}^{27} A l+_{1}^{1} H \longrightarrow_{12}^{24} M g+_{2}^{4} H e \)
\( (i i i)_{92}^{235} U+_{0}^{1} n \longrightarrow_{56}^{140} B a+_{36}^{93} K r+ \)
\( \mathbf{3}_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n} \)
\( (i v)_{33}^{75} A s+_{1}^{2} H \longrightarrow_{25}^{56} M n+9_{1}^{1} H+ \)
\( 12_{0}^{1} n \)
\( (\boldsymbol{v})_{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \longrightarrow_{2}^{4} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
Answers:
A: Projectile capture
B: Spallation
C: Fusion
D: Projectile capture and particle emission
E: Fission
Select the correct answers according to
the given codes.
\( \mathbf{A} \cdot(i)-A,(i i)-D,(i i i)-E,(i v)-B,(v)-C \)
B . \( (i)-D,(i i)-C,(i i i)-A,(i v)-E,(v)-B \)
C \( .(i)-A,(i i)-B,(i i i)-C,(i v)-D,(v)-E \)
D. \( (i)-E,(i i)-D,(i i i)-C,(i v)-B,(v)-A \)


Soaps do not work with hard water
containing calcium and magnesium
ions because:
A \( \cdot C a^{2+} \) and \( M g^{2+} \) ions form insoluble calcium and magnesium salts in the form of scum
B. \( N a^{+} \) and \( K^{+} \) present in soap react with \( C a^{2+} \) and hinder the cleansing process
C . a large amount of soap is to be used in presence of \( C a^{2+} \) and \( M g^{2+} \)
D. scum formed by the combination of \( N a^{+}, C a^{2+} \) and \( M g^{2+} \) stick to the cloth and are not removed on agitation


In conduction, heat flows from:
A. Hotter to hotter region
B. Colder to hotter region
C. Hotter to colder region
D. Colder to colder region


If \( g(x)=x^{2}+x-2 \) and \( \frac{1}{2} g o f(x)= \)
\( 2 x^{2}-5 x+2, \) then which is \( f(x) \)
A \( .2 x-3 \)
B. \( -2 x-3 \)
c. \( x-3 \)
D. \( x+3 \)


8
\( d \)
8
\( d \)


The total pressure after 200 seconds, if
the initial pressure is 0.1 atm is
A. 0.154 atm
B. 0.248 atm
c. 0.174 atm
D. 0.114 atm


\( f\left(a_{1}, a_{2}, a_{3}, \dots . . \) are in G.P. then the value \right.
of determinant \( \left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right| \) equal
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 2 \)
D. 4