If \( x \) and \( y \) are complex numbers, then system of equations \( (1+i) x+(1- \)
\( \boldsymbol{i}) \boldsymbol{y}=1,2 i \boldsymbol{x}+2 \boldsymbol{y}=1+\boldsymbol{i} \) has
A. unique solution
B. no solution
c. infinite numbers of solution
D. none of these


Is it possible to define the matrix \( A+B \)
when
A has 3 rows and \( \mathrm{B} \) has 2 columns


All the organism uses oxygen to
produce energy except
A. Humans
B. Mango tree
c. clostridium
D. Pseudomonas


What will be \( \angle X O Y \) if arc \( A B= \) arc
\( X Y \) and \( \angle A O B=60^{\circ} ? \)
\( A \cdot 30^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
D. 60


Materials which allow only larger currents to flow through them are
A. Insulators
B. Semi-conductors
c. conductors
D. Alloys


Which type of rain can cause soil pollution?
A. Acid rain
B. Tropical rain
c. Temperate rain
D. All of these


Molar heat capacity of water in equilibrium with ice at constant
pressure is:
A. zero
B. \( \infty \)
c. \( 40.45 k J K^{-1} \) mol\( ^{-1} \)
D. \( 75.48 J K^{-1} \mathrm{mol}^{-1} \)


The area included between the
parabolas \( y^{2}=4 x \) and \( x^{2}=4 y \) is
A \( \cdot \frac{8}{3} \) sq unit
B. 8 sq unit
c. \( \frac{16}{3} \) sq unit
D. 12 sq unit


The temperature at which molecular energy is minimum on Kelvin
temperature scale is called:
A. Absolute Zero Temperature
B. Zero Energy Temperature
c. Absolute Temperature
D. None of These


Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.


Which of the following values corresponds to the value of energy required to remove the second electron
from the ground state of helium atom?
A. 27.2 ev
B. 13.6 ev
c. 6.8 ev
D. 54.4 ev


The rate of a chemical reaction
generally increases rapidly even for
small temperature increase because of a rapid increase in:
A. Collision frequency
B. Fraction of molecules with energies in excess of the activation energy
c. Activation energy
D. Average kinetic energy of molecules


Correct order of excretory organs in cockroach, earthworm and rabbits are
respectively
A. Skin, malpighian tubules, kidney
B. Malpighian tubules, nephridia, kidney
c. Nephridia, malpighian tubules, kidney
D. Nephridia, kidney, green gland


Which of the following letters will be seem without any change in a plane mirror?
A.
B. T
\( c \cdot L \)
D.


Balance the following equation by ion electron method.
\( Z n+B r O_{4}^{-}+O H^{-}+H_{2} O \rightarrow \)
\( \left[\boldsymbol{Z n}(\boldsymbol{O H})_{4}\right]^{2-}+\boldsymbol{B r}^{-} \)


The inner lining of the kidney tubules has
A. Cuboidal epithelium
B. Columnar epithelium
c. Squamous epithelium
D. None of the above


Complete the following reaction:
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \longrightarrow ? \)


Which of the following will give \( \boldsymbol{H}_{2} \) gas
with dilute \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)
A. \( M g \)
в. \( Z n \)
c. \( C u \)
D. \( H g \)


The density of \( 85 \% \) Phosphoric acid is \( 1.70 g c m^{-3} . \) What is the volume of a
solution that contains \( 17 g m \) Phosphoric acid?


Mixture of ice and water is form a
A. closed system
B. open system
C. isolated system
D. heterogeneous system


Solve the differential equation:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{y} \tan \boldsymbol{x}=\mathbf{0} \)


In a \( \triangle A B C, \) let \( P \) and \( Q \) are points on
\( A B \) and \( A C \) respectively sucvh that
\( P Q \mid B C . \) Prove that the median \( A D \)
bisects \( \boldsymbol{P} \boldsymbol{Q} \)


Area bounded by the lines \( y=x, x= \)
\( -1, x=2 \) and \( x \) -axis is
A \( \cdot \frac{5}{2} \) sq. units
B. \( \frac{3}{2} \) squnits
c. \( \frac{1}{2} s q \) units
D. None of these


For the reaction of one-mole zinc dust
with one more sulphuric acid in a bomb
calorimeter, \( \Delta U \) and \( w \) correspond to:
[Hint: In bomb calorimeter, \( \boldsymbol{w}= \)
\( \mathbf{0}, \mathbf{\Delta} \boldsymbol{U}=\boldsymbol{q}(-\boldsymbol{v} e)] \)
A. \( \Delta U, 0, W=0 \)
в. \( \Delta U<0, W<0 \)
c. \( \Delta U>0, W=0 \)
D. \( \Delta U>0, W>0 \)


Which of the following is a chemical
compound?
A. Salt
B. Iron
c. oxygen
D. Diamond


Fill in the blanks:
\( \frac{-\mathbf{7}}{\mathbf{9}}+\ldots \ldots=3 . \) Hence find the sum of
the numerator and denominator so
obtained.


In dicot root showing secondary growth,
cork is found
A. External to primary cortex
B. Inner to epidermis and outer to pericycle
C. Outer to endodermis and inner to primary cortex
D. Inner to endodermis and external to primary phloem


Which contains hydrogen bonds?
\( \mathbf{A} \cdot H F \)
в. \( H C l \)
\( \mathbf{c} \cdot H B r \)
D. \( H I \)


Unit of power is
\( A \cdot H p \)
B. Kilowatt hour
c. watt
D. None


If \( (x-1) \) divides \( m x^{3}-2 x^{2}+25 x- \)
26 with remainder \( 0, \) find the value of \( m \)


The rate of growth of population is proportional to the number present. If the population doubled in the last 25
years and the present population is 1 lac, when will the city have population \( 4,00,000 ? \)


A body of mass \( 5 k g \) is whirled in vertical
circle by a string \( 1 \mathrm{m} \) long. Calculate velocity at top of the circle for just looping the vertical loop.
A. \( 3.1 m / s \)
в. \( 7 m / s \)
\( \mathrm{c} \cdot 9 \mathrm{m} / \mathrm{s} \)
D. \( 7.3 \mathrm{m} / \mathrm{s} \)


During every financial year, the value of a machine depreciates by \( 10 \% \). Find the original value (cost) of a machine which depreciates by Rs. 2,250 during the second year.


A particle starts from rest with
acceleration \( 2 m s^{2}, \) The distance moved
by particle in 5 sec is:
A . \( 22 \mathrm{m} \)
B. 28 m
c. \( 25 \mathrm{m} \)
D. 13 \( m \)


Predict the correct product when \( C l_{2} \) passed through \( \boldsymbol{H}--\boldsymbol{0}^{\mathbf{8}}--\boldsymbol{0}^{18}--\boldsymbol{H} \)
solution.
A \( \left.\cdot H^{+} C l^{-}+O_{2} \text { (both oxygen having } 18\right) \)
B. HOCl and \( H C l O_{2} \) (all oxygen having 18 )
c. \( H C l O_{4} \) and \( H C \) ( all oxygen having 18 )
D. \( C l_{2} O \) and \( H_{2} O \) (all oxygen having 18


If a stock has \( 2 n=48 \) and scion
microspore cell has \( 2 n=24 \) then root cell and the microspores will have how many chromosomes respectively?
\( A \cdot 12,48 \)
B. 48, 12
c. \( 24, \) 12
D. 24, 96


Without actual division, check whether \( \frac{47}{14} \) is terminating or not.


Which of the following is not a redox
reaction?
A. Burning of candle
B. Rusting of iron
c. Dissolving a saltin water
D. Dissolving Zn in dil. \( H_{2} S O_{4} \)


The amplitude of vibrations measured on the Richter's scale increase by steps of about
A . 10
B. 20
\( c . \) 30
D. 40


Give the balanced equation to prepare
Nitric oxide. Which type of oxide is Nitric oxide?


During \( \beta \) -decay, the mass of atomic
nucleus:
A. decreases by 1 unit
B. increases by 1 unitt
c. decreases by 2 units
D. remains unaffected


A substance of mass \( 49.53 g \) occupies
\( 1.5 \mathrm{cm}^{3} \) of volume. The density of the
substance (in \( g c m^{-3} \) ) with correct number of significant figures is :
A. 3.3
B. 3.302
c. 3.30
D. 3.300


A string of length \( 0.4 \mathrm{m} \& \operatorname{mass} 10^{2} \mathrm{kg} \)
is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time, \( \Delta \) t. The minimum value of \( \Delta t \) which allows
constructive interference between
successive pulses is:
A . \( 0.05 \mathrm{s} \)
B. 0.10 s
c. \( 0.20 \mathrm{s} \)
D. 0.40 s


Which pair is not correct for the
instrument used in the laboratory and
their uses from the following?
Instrument uses
To measure the electric
\( \begin{array}{ll}\text { (A) } & \text { Voltmeter }\end{array} \quad \) potential difference
To measure the electric
(B) \( \quad \) Ammeter \( \quad \) current
To detect the presence
(C) Galvanometer of current
To supply the electric
(D) \( \quad \) Resistor \( \quad \) energy to circuit
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)


Earth's magnetic field inside a closed iron box, as compared to that outside is
A. same
B. less
c. more
D. zero


The vapour pressure of two pure liquids \( A \) and \( B \) which from an ideal solution
are 500 and 800 torr respectively at
\( 300 K . \) A liquid solution \( A \) and \( B \) for
which the mole fraction of \( A \) is 0.60 is
contained in a cylinder closed by a piston on which the pressure can be
varied. What will be the pressure when 1 mol of the mixture has been vaporized?


Rust forms on:
A. Tin
B. copper
c. Iron
D. Lead


Classify the following into
monosaccharides and disaccharides.
Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose.


What is the maximum value of binding
energy per nucleon?
\( A \cdot 8 \mathrm{MeV} \)
B. 8.8 MeV
c. 7.6 Mev
D. 1.1 Mev


Write the structural formula of the two
isomers of butane.


When a wave travels through medium
A. particles are transferred from one place to another
B. energy is transferred in a periodic manner
C. energy is transferred at a constant speed
D. none of the above statements is applicable


the diagram shows the propagation of a
wave. Which points are in same phase?
\( A \cdot F \) and \( G \)
B. \( C \) and \( E \)
\( \mathrm{C} \cdot \mathrm{B} \) and \( \mathrm{G} \)
D. \( B \) and \( F \)


Ammonium nitrate \( \left(N H_{4} N O_{3}\right. \)
phosphorus as \( P_{2} O_{5} \) and potassium
as \( K_{2} O \) is called :
A . organic manure
B. mixed fertilizers
c. insecticides
D. pesticides


The sum to \( n \) terms of the services \( \frac{3}{1^{2}}+ \) \( \frac{5}{1^{2}+2^{2}}+\frac{7}{1^{2}+2^{2}+3^{2}}+\dots \dots \) is
A \( \cdot \frac{3 n}{n+1} \)
В. \( \frac{6 n}{n+1} \)
c. \( \frac{g n}{n+1} \)
D. \( \frac{12 n}{n+1} \)


A large tank is filled with water to a height H. A small hole is made at the
base of the tank. It takes 71 time to
decrease the height of water to \( \frac{H}{\eta}(\eta> \)
1) and \( T_{2} \) time to take out the rest of 11
water. If \( T_{1}=T_{2} \) then the value of \( \eta \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Find the differential equation of family of circles of all of radius \( 5, \) with their
centres on the y-axis.


A reversible engine takes heat from a
reservoir at \( 527^{\circ} \mathrm{C} \) and gives out heat to
\( a \sin k \) at \( 127^{\circ} \) C. How many Joules/s must it take from the
reservoir to perform useful mechanical
work at the rate of \( 750 W ? \)
A . 257.14
B. 1500
c. 457.14
D. 557.14


What is the maximum number of \( \boldsymbol{O}_{2} \)
molecules which one haemoglobin molecule can carry?


Which one of the following exceeds
octet rule?
A \( \cdot \mathrm{NCl}_{3} \)
в. PCls
c. \( \mathrm{PCl}_{5} \)
D. NH


Expansion of \( (3 x+2)^{3} \) is \( 27 x^{3}+8+ \)
\( 18 x(3 x+2) \)
A. True
B. False


The electric and magnetic field differ in
that :
A. the electric lines of force are closed curves, while magnetic field lines are not
B. the magnetic field lines are closed, while electric lines are not
C. the electric lines can give direction of electric field, while magnetic lines cannot
D. the magnetic lines can give direction of magnetic field, while electric lines cannot


(A) In tangent galvanometer the circular frame is rotated until the plane of the coil is parallel to magnetic meridian
(B) In tangent galvanometer current through it is related to deflection of needle as
A. A is true, B is false
B. A is false, B is true
c. A \& B are true
D. A \& B are false


\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 0 4} \) at \( \boldsymbol{m} \) at \( \boldsymbol{8} 99 \) K for the
equilibrium shown below. What is the equilibrium concentration of \( C_{2} H_{6} \) when it is placed in a flask at 4.0 atm pressure and allowed to come to
equilibrium?
\( \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)


Which of the following statement is
true?
A. Diethyl ether is almost as soluble in water as n-butyl alcohol
B. Diethyl ether is more soluble in water than n-butyl alcohol.
C. Diethyl ether is less soluble in water than n-butyl alcohol.
D. Diethyl ether is sparingly soluble in water whereas \( n \) butyl alcohol is highly soluble in water.


Write the consequences of lanthanide
contraction?


A body accelerates uniformly from rest to a velocity of \( 1 \mathrm{m} s^{-1} \) in 15 second. In
what time the kinetic energy of the body will be \( \frac{2}{9} J .[\text { Take mass of body as } 1 \mathrm{kg}] \)
A. 4 s
B. 8s
\( c \cdot 10 s \)
D. 12s


Which of the following is not correct for haloalkanes?
A. Density is directly proportional to the mass of compound
B. Haloalkanes are slightly soluble in water
c. Boiling Point depends upon the intermolecular forces of attraction
D. None of these


If heat is supplied to the system it
A. does work only
B. increase the internal energy
C. either does work or increase the internal energy or
both
D. does nothing


Assertion
Borax bead test is applicable only to coloured salts.
Reason
In borax bead test, coloured salts are
decomposed to give coloured metal
metaborates.
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 hot body, obeying Newton's law of cooling is cooled down from its peak
value \( 80^{\circ} C \) to an ambient temperature of \( 30^{\circ} C . \) It takes 5 minutes in cooling
down from \( 80^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \). How much
time will it take to cool down from
\( 62^{\circ} \mathrm{C} \) to \( 32^{\circ} \mathrm{C} ? \)
(Given \( \ln 2=0.693, \ln 5=1.609) \)
A. 9.6 minutes
B. 3.75 minutes
c. 8.6 minutes
D. 6.5 minutes


A group of 100 candidates have their
average height \( 163.8 \mathrm{cm} \) with coefficient of variation \( 3.2 . \) What is the
standard deviation of their heights?
A . 5.24
в. 2.24
\( c .7 .24 \)
D. None of these


In the following, one of the six trigonometric ratios is given. Find the
values of the other trigonometric ratios. \( \sin \theta=\frac{\sqrt{3}}{2} \)


Prove that, if \( a, b, c \) and \( d \) be positive rationals such that, \( a+\sqrt{b}=c+\sqrt{d} \)
then either \( a=c \) and \( b=d \) or \( b \) and \( d \)
are squares of rationals.


Meena draws magnetic field lines of field close to the axis of a current
carrying circular loop. As she moves away from the centre of the circular loop she observes that the lines keep on diverging. How will you explain her observation:


\( " L i_{2} C O_{3} \) and \( N a_{2} C O_{3} \) are
thermally stable." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Which one of the following is not the vector quantity?
A . Torque
B. Displacement
c. velocity
D. None of the above


Assuming the speed of sound in air equal to \( 340 m s^{-1} \) and in water equal to
\( 1360 m s^{-1}, \) find the time taken to trave
a distance \( 1700 \mathrm{m} \) by sound in water
A . \( 0.8 s \)
B. \( 1 s \)
c. \( 1.5 s \)
D. \( 1.25 s \)


Two soap bubbles of radii \( r_{1} \) and
\( r_{2}\left(r_{a}>r_{2}\right) \) are connected by a tube
Then.
A . Air flows from the bubble of radius \( r_{1} \) to the bubble of
radius \( r_{2} \) till their size become equal
B. Air flows from the bubble of radius \( r_{1} \) to the bubble of
radius \( r_{2} \) till their sizes are interchanged
c. Air flows from smaller bubble to the bigger
D. There is no flow of air


The reaction, \( \boldsymbol{X} \longrightarrow \boldsymbol{Y}(\text { Product }) \)
follows first order kinetics. In 40
minutes, the concentration of \( \boldsymbol{X} \)
changes from \( 0.1 ~ M \) to \( 0.025 M \), then
the rate of reaction when concentration
of \( \boldsymbol{X} \) is \( \mathbf{0 . 0 1} \boldsymbol{M} \) is:
A \( \cdot 1.73 \times 10^{-4} \mathrm{M} / \mathrm{min} \)
B . 3.47 \( \times 10^{-5} \mathrm{M} / \mathrm{min} \)
c. \( 3.47 \times 10^{-4} \mathrm{M} / \mathrm{min} \)
D. \( 1.73 \times 10^{-5} \mathrm{M} / \mathrm{min} \)


Equimolal solutions \( A \) and \( B \) show depression in freezing point in the ratio
2:1. A remains in the normal state in
solution B will be :
A. Normal in solution
B. Dissociated in solution
C. Associated in solution
D. Hydrolysed in solution


A Proton and an / alpha particle are
accelerated through a potential difference of \( 100 \mathrm{V} \). The ratio of the
wavelength associated with the proton to that associated with an / alpha
particle is
A .1: 2
B . 2: 1
\( \mathbf{c} \cdot 22: 1 \)
D. \( 2 \sqrt{2}: 1 \)


In order to decompose 9 grams of water
\( 142.5 K J \) heat is required. Hence the enthalpy of formation of water is:
A \( .+142.5 \mathrm{KJ} \)
B . -142.5 KJ
c. +285 KJ
D . -285 KJ


n fig, \( O \) is the centre of a circle \( A B= \)
\( \mathbf{1 6} \mathrm{cm}, \boldsymbol{C D}=\mathbf{1 4} \mathrm{cm}, \operatorname{seg} \boldsymbol{O} \boldsymbol{M} \perp \mathbf{s e g} \)
\( A B, \operatorname{seg} O N \perp \operatorname{seg} C D . \) If \( O M=6 \mathrm{cm} \)
then length of \( \operatorname{seg} O N \) is \( \sqrt{m} \mathrm{cm} . \) So, \( m \)
is
A \( . m=149 c m^{2} \)
В \( \cdot m=51 c m^{2} \)
\( \mathrm{c} \cdot m=51 \mathrm{cm} \)
D. \( m=149 \mathrm{cm} \)


Find the product of the following pair of monomial.
\( 4 p^{3},-3 p \)


The velocity of the liquid coming out of a small hole of a vessel containing two
different liquid of densities \( 2 \rho \) and \( \rho \)
shown in the figure is
A \( \cdot \sqrt{6 g h} \)
B. \( 2 \sqrt{g h} \)
\( c \cdot 2 \sqrt{2 g h} \)
\( D \cdot \sqrt{g h} \)


Two particles are in SHM along same line. Time period of each is \( T \) and
amplitude is \( A . \) After how much time
will they collide if at time \( t=0 . \) First particle is at \( x_{1}=+\frac{A}{2} \) and moving
towards positive \( x- \) axis and second particle is at \( x_{2}=-\frac{A}{\sqrt{2}} \) and moving
towards negative \( x- \) axis.
A \( \cdot \frac{18}{19} T \)
в. \( \frac{19}{48} \mathrm{T} \)
c. \( \frac{48}{19} T \)
D. \( \frac{19}{18} \mathrm{T} \)


Which is a better mode of reproduction sexual or asexual? Why?


Find the edge of a cube whose volume is
216 cubic centimetres.


Tyloses are
A. Tracheal plugs which plugs with the lumen of the vessels and tracheids
B. Compound sieve plates
c. specialized secretory cells
D. Laticiferous channels


For the pivoted slender rod of length \( l \) as
shown in figure., find the angular
velocity as the bar reaches the vertical
position after being released in the
horizontal position


Area common to the curves \( y^{2}=a x \)
and \( x^{2}+y^{2}=4 a x \) is equal to
A \( \cdot(9 \sqrt{3}+4 \pi) \frac{a^{2}}{3} \)
B . \( (9 \sqrt{3}+4 \pi) a^{2} \)
c. \( (9 \sqrt{3}-4 \pi) \frac{a^{2}}{3} \)
D. None of these


Both light and sound waves produce
diffraction. It is more difficult to observe
the diffraction with light waves
because:
A. light wave do not require medium
B. wavelength of light waves is far smaller
c. light waves are transverse
D. speed of light is far greater


Study the following graph and fill in the
blanks.
\( A \)
Liquid Gas Freezing point Melting point
B. Boiling Melting Boiling point Melting point
\( c \)
usion Vaporisation Melting point Boiling poin
D.
vap


A body falls freely under effect of gravity The ratio of distance covered by the
body in 1,2,3 seconds respectively is :
A. 1: 3: 5
5
B. 1: 2: 3
c. 1: 4: 9
D. None of above


Two resistors of resistances \( \boldsymbol{R}_{1}= \)
\( 100 \pm 3 o h m \) and \( R_{1}=200 \pm 4 o h m \) are
connected (a) in series, (b) in parallel. Find the equivalent resistance of the
(a) series combination,
(b) parellel
combination. Use for \( (a) \) the relation
\( \boldsymbol{R}=\boldsymbol{R}_{1}+\boldsymbol{R}_{2} \) and for \( (\boldsymbol{b}) \)
\( \frac{1}{R^{\prime}}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \) and \( \frac{\triangle R^{\prime}}{R^{\prime 2}}=\frac{\triangle R_{1}}{R_{1}^{2}}+ \)
\( \frac{\triangle \boldsymbol{R}_{2}}{\boldsymbol{R}_{2}^{2}} \)


How does pruning help in making the hedge dense?
A. The apical shoots grows faster after pruning.
B. It releases wound hormones.
c. It induces the differentiation of new shoots from the rootstock
D. It frees axillary buds from apical dominance.


Figure shows plane waves refracted
from air to water using Huygen's principle \( a, b, c, d, e \) are lengths on the diagram. Find the ratio of refractive
index of water w.r.t. air.


The process in which metal surface is made inactive is called:
A. passivation
B. galvanising
c. corrosion
D. pickling


Arrange the following in order of property indicated for each set:
a. \( F_{2}, C l_{2}, B r_{2}, I_{2} \) -increasing bond dissociation enthalpy.
b. \( H F, H C l, H B r, H I- \) increasing
acid strength.
c. \( N H_{3}, P H_{3}, A s H_{3}, S b H_{3}, B i H_{3} \)
increasing base strength.


A car is moving with a speed of 40 \( \mathrm{Km} / \mathrm{hr} . \) If the car engine generates 7 kilowatt power, then the resistance in the path of motion of the car will be- -
A. \( 360 N \)
B. \( 630 N \)
c. zero
D. \( 280 N \)


\( \lim _{x \rightarrow 0^{+}} \frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}} \) equals to
A. 1
B. \( \frac{1}{2} \)
\( c \cdot \infty \)
\( D \)


The compound (A) is:
\( A \)
в.
c.
D. Both (a) and (b)


A sphere of mass \( 40 \mathrm{kg} \) is attracted by a
second sphere of mass \( 15 \mathrm{kg} \), when their
centres are \( 20 \mathrm{cm} \) apart, with a force of
0.1 milligram weight. Calculate the value of gravitational constant.
\( \mathbf{A} \cdot=8.53 \times 10^{-11} N m^{2} k g^{-2} \)
B. \( =6.53 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2} \)
\( \mathbf{c} .=7.53 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2} \)
D. \( =9 \times 10^{-11} N m^{2} k g^{-2} \)


When the distance between the object and the plane mirror increases:
A. The image remains same
B. The size of the image will become less than the size of the object
c. The distance between the image and the plane mirror increases
D. The distance between the image and the plane mirror decreases


Consider a real valued function \( \boldsymbol{f} \) \( \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfying \( \boldsymbol{f}\left(\frac{\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}}{\mathbf{5}}\right)= \)
\( \frac{2 f(x)+3 f(y)}{5} \forall x, y \in R \quad \) and \( f(0)= \)
\( \mathbf{2} ; \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1} \)
Minimum distance of a point on graph
of \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) from origin is less than or
equal to
A. \( \sqrt{2} \) units
B. \( \frac{1}{2} \) units
c. \( \frac{1}{\sqrt{5}} \) units
D. \( \frac{1}{\sqrt{7}} \) units


Gibbs- Helmholtz equation is
A \( . \Delta G=\Delta H-T \Delta S \)
в. \( \Delta G=\Delta H+T \Delta S \)
c. \( \Delta G=T \Delta H-\Delta S \)
D. none of these


The numbers \( a, b \) and \( c \) are between 2
and 18 such that
(i) their sum is 25
\( (i i) \) the numbers \( 2, a, b \) are in A.P
\( (i i i) \) the numbers \( b, c, 18 \) are consecutive terms of a G.P.
If \( a, b, c \) are the roots of \( x^{3}+q x^{2}+ \)
\( r x+s=0 \) then the value of \( ^{\prime} r^{\prime} \) is
A. 184
в. 196
c. 220
D. 224


The D.E of the family of circles which
touch the \( y \) -axis at the origin is:
A \( y_{1}=\frac{x^{2}-y^{2}}{x y} \)
B. \( y_{1}=\frac{x^{2}-y^{2}}{2 x y} \)
C \( y_{1}=\frac{y^{2}-x^{2}}{2 x y} \)
D. \( y_{1}-\left(y^{2}-x^{2}\right)+x y=0 \)


The average value of output direct current in a full wave rectifier is
A \( \cdot I_{0} / \pi \)
в. \( I_{0} / 2 \)
c. \( \pi I_{0} / 2 \)
D. \( 2 I_{0} / \pi \)


In an electro chemical process, a salt
bridge is used
a) to maintain electro neutrality in each solution.
b) to complete the circuit so that current
can flow
c) as an oxidising agent
d) as a colour indicator
A. only a is correct
B. a and b are correct
c. a, b and care correct
D. all are incorrect


f the line \( \left(\frac{x}{2}+\frac{y}{3}-1\right)+\lambda(2 x+y- \)
1) \( =0 \) is parallel to \( x \) -axis then \( \lambda= \)
\( A \cdot-\frac{1}{2} \)
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{4} \)
D.


If \( x^{2}-b x+c=0 \) has equal integral
roots, then
This question has multiple correct options
A. \( b \) and \( c \) are integers
B. \( b \) and \( c \) are even integers
\( \mathrm{c} . b \) is an even integer and \( c \) is a perfect square of an integer
D. none of these


What is the name of the above reaction?
A. Williamson's synthesis
B. Gatterman-Koch process
c. Etard reaction
D. Hoffmann elimination reaction


Between 1 and \( 31, m \) arithmetic means
are inserted, so that the ratio of the \( 7^{t h} \)
and \( (m-1)^{t h} \) mean is \( 5: 9 . \) Then the
value of \( m \) is
A . 12
B. 13
c. 14
D. 15


State whether true or false.
A coin moving over a carrom board exhibits rectilinear motion.
A. True
B. False


Armoured cell wall and biflagellated cells are characteristic of
A. Bascillariophyta
B. Pyrrophyta
c. Euglenophyta
D. cyanophyta


Which of the following compounds can exist in enantiomeric forms?
A. 3-methyl butanoic acid
B. Cis-2-butene
c. Isopropyl amine
D. 1-methyl butanamine


A particle \( P \) is a moving in a circle of radius e with a uniform speed \( v . C \) is
the centre of the circle, and \( A B \) is a
diameter, If \( P \) is at \( B \), the angular
velocities of \( \boldsymbol{P} \) about \( \boldsymbol{A} \) and \( \boldsymbol{C} \) are in the
ratio
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1


Which is not true about \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \)
A. It is a network solid
B. It is attacked by molten NaOH
c. It is attacked by HF
D. It is the basic structural unit of silicates


The equation \( 3 x^{2}-2 x y+y^{2}=0 \)
represents:
A . a circle
B. hyperbola
c. a pair of lines
D. none of these


f \( \tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)= \)
find the value of \( x \)
\( \overline{\mathbf{4}} \)


\( \int(3 x-2) \sqrt{x^{2}+x+1} d x= \)


The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is
\( \mathbf{A} \cdot 96 \)
в. 144
\( c \cdot 512 \)
D. 576


Which liquid is found on the feather of birds and animal fur?


The distance travelled by particle from
\( \boldsymbol{t}=\mathbf{0} \) to \( \boldsymbol{t}=\mathbf{2} \) seconds is:
\( \mathbf{A} \cdot 2 m \)
B. \( 3 m \)
c. \( 4 m \)
D. \( 6 m \)


A particle of mass M is moving in a
horizontal circle of radius R with
uniform speed \( V \). when it moves from one point to a diametrically opposite point, its
A. kinetic energy changes by \( M V^{2} / 4 \)
B. momentum does not change
c. momentum changes by 2 MV
D. kinetic energy changes by \( M V^{2} \)


The maximum number of structural
isomers possible for the hydrocarbon
having the molecular formula \( C_{4} H_{6} \) is:
A \( \cdot 12 \)
B. 3
\( c \cdot 9 \)
D. 5


What is the hybridization of the chlorine
\( \operatorname{atom} \operatorname{in} C l F_{3} \) molecule?


If \( \boldsymbol{A}(\overrightarrow{\boldsymbol{a}}), \boldsymbol{B}(\overrightarrow{\boldsymbol{b}}), \boldsymbol{C}(\overrightarrow{\boldsymbol{c}}) \) be the vertices
of a triangle whose circumcentre is the origin, then orthocenter is given by
\( \frac{\vec{a}+\vec{b}+\vec{c}}{3} \)
\( ^{\mathrm{B}} \frac{\vec{a}+\vec{b}+\vec{c}}{2} \)
c. \( \vec{a}+\vec{b}+\vec{c} \)
D. None of these


For a cube and a sphere made of same material, what should be the ratio of the
side of the cube to the radius of the
sphere such that both of them have the
same thermal capacity?
A \( \cdot \sqrt[3]{\frac{4}{3} \pi} \)
B. \( \sqrt[3]{\frac{5}{3} \pi} \)
c. \( \sqrt[3]{\frac{3}{4} \pi} \)
D. \( \sqrt[3]{\frac{2}{3} \pi} \)


Heat of combustion of \( \boldsymbol{C} \boldsymbol{H}_{\boldsymbol{4}(\boldsymbol{g})} \) at
constant volume is measured in bomb
calorie-meter at \( 298.2 \mathrm{K} \) and found to be
885389 find the valve of enthalpy.
\( N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)} \)


A hydrocarbon with molecular formula
would give a single \( C_{9} H_{11}, S O_{3} H \)
product on sulphonation?
\( A \)
B.
\( c \)
\( D \)


When an ideal capacitor is charged by dc battery, no current flows, However, When an ac source is used, the current
flows continuously. How does one explain this, based on the concept of displacement current?


A body projected vertically up with a velocity 'u' attains a maximum height
H. If it is thrown up with velocity \( 2 u, \) it attains a maximum height of
A . २
B. H/2
c. \( 4 \mathrm{H} \)
D. H/4


f the length of the chord \( Y Z \) is equal to
the radius of the circle \( O Y \), find \( \angle Y X Z \)
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 80^{\circ} \)
D. 100


Angle of dip \( \delta \) and latitude \( \lambda \), on earth's
surface are related as
\( \mathbf{A} \cdot \tan \delta=2 \tan \lambda \)
B. \( \tan \delta=\cot \lambda \)
\( \mathbf{C} \cdot \tan \delta=\frac{\tan \lambda}{2} \)
D. \( \tan \delta=\tan \lambda \)


Pyruvic acid is a product of
A . Acety
B. CoA
c. starch
D. Glucose


A proton is projected with a speed of
\( 3 \times 10^{6} m / s \) horizontally from east to
west. A uniform magnetic field B of strength \( 2 \times 10^{-3} T \) exists in the
vertically upward direction the magnitude of magnetic force on proton is \( \boldsymbol{F} \times \mathbf{1 0}^{-16} \boldsymbol{N} \). What is the value of \( \boldsymbol{F} \) ?


The characters related to ascomycetes
are
A. Septate branched mycelium
B. Mitospores produced exogenously in chains
C. \( 4-8 \) ascospores inside a sac like ascus
D. All of the above


\( M e_{3} C-\stackrel{V}{C}-M e \frac{[O]}{\Delta} \)
Find out the major product of the reaction.


Statement-1: In clarks process excess
of lime is not added to water sample to
remove temporary hardness. Statement-2: Addition of excess of milk
of lime causes permanent hardness.
A. Statement-1 is true, Statement-2 is true; Statementis a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true; Statement- is not a correct explanation for Statement-
c. Statement- 1 is true, Statement- 2 is false.
D. Statement-1 is false, Statement-2 is true


18 g glucose \( \left(C_{6} H_{12} O_{6}\right) \) is added to
\( 178.2 \mathrm{g} \) of water. The vapour pressure of this aqueous solution at \( 100^{0} C \) in torr
is:
A . 7.60
B. 76.00
c. 752.40
D. 759.00


Once you toss a coin, you will get the result as head or tail. Doing this action is called an
A . space
B. sample
c. experiment
D. event


If \( a, b \) and \( c \) are three non-zero vectors
such that \( a \cdot|b \times c|=0 \) and \( b \) and \( c \) are
not parallel then \( a, b \) and \( c \) are
A. Collinear
B. Coplanar
c. May be both
D. None


The common raw material used in the
preparation of soap and detergent is:
A. sulphuric acid
B. sodium hydroxide
c. stearic acid
D. long chain hydrocarbons


State which of the following are equation (with a variable) given reason and tell your answer. identify the variable from the equation with a variable.
\( \frac{3 q}{2}<5 \)


\( 1^{2}, 5^{2}, 7^{2}, 73 \dots \dots \dots \) is it an AP? If yes, then
what is it's common difference?
A. No
B. Yes, \( d=15 \)
c. Yes, \( d=24 \)
D. Yes, \( d=25 \)


Construct \( \triangle A B C \) such that \( A B= \)
\( \mathbf{2 . 5} \mathbf{c m}, \boldsymbol{B C}=\mathbf{6} \boldsymbol{c m} \) and \( \boldsymbol{A} \boldsymbol{C}=\mathbf{6 . 5} \boldsymbol{c m} \)
Measure \( \angle B \)


The stress-strain plot for wires made of two materials (I and II) is presented
schematically in the accompanying
figure. The points \( C_{I} \) and \( C_{I I} \) represent
fracture points of the two materials
and II respectively. It can be concluded
from these graphs that
A. material I has Young's modulus larger than that of materia
B. the linear region of material I extends to a larger valu of stress than that of material II
c. both materials I and II are equally brittle
D. material l is more ductile than materia


The correct electronic configuration of
neutral \( C a \) and \( O \) are respectively:
\( \mathbf{A} \cdot C a:[A r] 4 s^{2} \)
\( O:[H e] 2 s^{2} 2 p^{4} \)
B . \( C a:[A r] 3 s^{2} \)
\( O:[H e] 2 s^{2} 2 p^{5} \)
\( \mathbf{c} \cdot \operatorname{Ca}:[A r] 4 s^{2} \)
\( O:[H e] 2 s^{2} 2 p^{6} \)
\( \mathbf{D} \cdot \operatorname{Ca}:[A r] 4 s^{2} \)
\( O:[H e] 2 s^{2} 2 p^{2} \)


\( 4 H_{3} P O_{3} \longrightarrow 3 H_{3} P O_{4}+P H_{3} \)
Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) is \( ( \) as nearest integer)


An inductance of negligible resistance whose reactance is \( 22 \Omega \) at \( 200 H z \) is
connected to 200 volt. If the line
frequency is known to be 50 cycles/second, the equation for the line voltage is :
A. 0.0175 Henry
B. 0.175 Henry
c. 1.75 Henry
D. 17.5 Henry


Which one of the following is a geometric progression?
A. 3,5,9,11,15
в. 4,-4,4,-4,4
c. 12,24,36,48
D. 6,12,24,36


Boiling point of water at normal atmospheric pressure is
\( \mathbf{A} \cdot 0^{\circ} C \)
B . \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 110^{\circ} \mathrm{C} \)
D. \( -5^{\circ} C \)


Two magnetic dipoles are lying as
shown in figure. the separation ' \( d \)
between them is very large. A point
charge \( Q \) is projected with some speed \( v \) as shown. The force experienced by
the charged particle is:
A . 0
B. \( \frac{4 \sqrt{2} \mu_{0} M Q v}{\pi d^{3}} \)
c. \( \frac{\sqrt{2} \mu_{0} M Q v}{\pi d^{3}} \)
D. \( \frac{2 \sqrt{2} \mu_{0} M Q v}{\pi d^{3}} \)


In the figure, seg \( P S \) intersects \( \operatorname{seg} T K \)
in the point \( R . \angle T \) and \( \angle K \) are right
angles. State whether \( \triangle P T R \) and
\( \triangle S K R \) are similar. If yes, by which
test?


Assertion
Density \( = \) specific gravity \( \times 0.99823 \) at
\( \mathbf{2 0}^{\circ} \boldsymbol{C} \)
Reason
Density \( = \) specific gravity at \( 4^{\circ} C \)
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


At constant temperature, the pressure of a fixed amount of gas is inversely proportional with its volume. This law is popularly known as:
A. Charle's law
B. Boyle's law
c. Gay Lussac's law
D. Avogadro's law


Given that, \( y=\sin x\left(x^{2}\right) e^{x} \), find \( y^{\prime} \) at
\( \boldsymbol{x}=\mathbf{0} \)


toppr
Q Type your question
time period is proportional to \( \sqrt{\frac{\boldsymbol{m}}{\boldsymbol{k}}}, \) as can be seen easily using dimensional analysis. However, the motion of a
particle can be periodic even when its
potential energy increases on both
sides of \( x=0 \) in a way different from
\( k x^{2} \) and its total energy is such that the
particle does not escape to infinity.
Consider a particle of mass m moving
on the \( x \) -axis. Its potential energy is
\( V(x)=\alpha x^{4}(\alpha>0) \) for \( |x| \) near the
origin and becomes a constant equal to
\( V_{0} \) for \( |x| \geq X_{0}(\text { see figure }) \)
The acceleration of this particle for
\( |\boldsymbol{x}|>\boldsymbol{X}_{0} \) is?
A. Proportional to \( V_{0} \)
B. Proportional to \( \frac{V_{0}}{m X_{0}} \)
C. Proportional to \( \sqrt{\frac{V_{0}}{m X_{0}}} \)
D. Zero


The value of \( \cos ^{-1}\left(-\frac{1}{2}\right)+ \)
\( \sin ^{-1}\left(-\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\right) \) is
\( A \cdot \frac{\pi}{3} \)
B.
c. \( \frac{2 \pi}{3} \)
D. none of these


Elimination of bromine from \( 2- \)
bromobutane results in the formation
of:
A. Equimolar mixture of 1 and \( 2- \) butane
B. Predominantly - 2 - butene
c. Predominantly \( -1- \) butene
D. Predominantly2 - butyne


Steroid nucleus contains:
A. Two cyclohexane and two cyclopentane rings
B. Three cyclohexane and two cylopentane rings
c. Four cyclohexane rings only
D. Three cyclohexane and one cyclopentane rings


A stone of mass \( m \) tied to one end of a
wire of length \( L \). The diameter of the
wire is \( D \) and it is suspended vertically. The stone is now rotated in a horizontal
plane and makes an angle \( \theta \) with the
vertical. If Young's modulus of the wire
is \( Y, \) then the increase in the length of
the wire is then
\( ^{\mathbf{A}} \cdot \frac{4 m g L}{\pi D^{2} Y} \)
B. \( \frac{4 m g L}{\pi D^{2} Y \sin \theta} \)
c. \( \frac{4 m g L}{\pi D^{2} Y \cos \theta} \)
D. \( \frac{4 m g L}{\pi D^{2} Y \tan \theta} \)


During a cytological study conducted on the chromosomes of insects, it was
observed that only \( 50 \% \) of the sperms had a specific structure after spermatogenesis. Name the structure and write its significance in sex determination of insects.


Which is the first open university in
India?
A. Andhra Pradesh Open University
B. Yashwantrao Chavan Maharashtra Open University
C. Indira Gandhi National Open University
D. Nalanda Open University


(a) Construct a complete transcription unit with promoter and terminator on the basis of the hypothetical template
strand given below:
(b) Write the RNA strand transcribed from the above transcription unit along
with its polarity.


Which of the following compounds is/are gives red or violet solution when treated with neutral ferric chloride
solution.


Which of the following play significant role in depletion of ozone layer?
A. Oxides of nitrogen
B. Oxides of carbon
c. oxides of sulphur
D. None of these


Can a traingle have
A \( \cdot 55^{\circ}, 55^{\circ} \) and \( 80^{\circ} \)
B . \( 33^{\circ}, 74^{\circ} \) and \( 73^{\circ} \)
c. \( 85^{\circ}, 95^{\circ} \) and \( 22^{\circ} \)
D. \( 25^{\circ}, 95^{\circ} \) and \( 32^{\circ} \)


Which term of an A.P \( 7,3,-1, \ldots \) is
\( -89 ? \)


The temperature of equal masses of three different liquids \( A, B \) and \( C \) are
\( 12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C} \) and \( 28^{\circ} \mathrm{C} \) respectively. The
temperature when \( A \) and \( B \) are mixed is
\( 16^{\circ} \mathrm{C} \) and when \( \mathrm{B} \) and \( \mathrm{C} \) are mixed it is
\( 23^{\circ} \mathrm{C} . \) What should be the temperature
when \( A \) and \( C \) are mixed?
A \( \cdot 20.25^{\circ} \mathrm{C} \)
В. \( 15.87^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)


When a big drop of water is formed from
\( n \) small drops of water, the energy loss
is \( 3 E, \) where \( E \) is the energy of the bigger drop. If \( R \) is the radius of the
bigger drop and \( r \) is the radius of the
smaller drop, then number of smaller drops \( (n) \) is:
A \( \cdot \frac{4 R}{r^{2}} \)
в. \( \frac{4 R}{r} \)
c. \( \frac{2 R^{2}}{r} \)
D. \( \frac{4 R^{2}}{r^{2}} \)


An oxide which forms salts when it
reacts with both acids and alkali is :
A . acidic oxide
B. basic oxide
c. amphoteric oxide
D. none of the above


Evaluate the following integral:
\( \int \frac{\sin 2 x}{(a+b \cos 2 x)^{2}} d x \)


How many grams of each of the following elements must be taken to get
mole of the element?
A) Sodium
B) Sulphur
C) Copper


Cell reaction is spontaneous when :
A. G is negative
B. G is positive
c. E is positive
D. E is negative


Which of the following is/are electromagnetic wave(s)?
A. Microwaves
B. Radio wave
c. Infrared radiation
D. All of the above


Assertion
Newton's law of gravitation resembles Coulomb's law of electrical forces.
Reason
Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant
in place of the gravitational constant.
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


How many minimum carbons required for Chain isomerism and Position
isomerism in alkenes?


Among the following mixtures, dipoledipole as the major interaction, is
present in
A. Benzene and ethanol
B. Acetonitrile and acetone
C. KCl and water
D. Benzene and carbon tetrachloride


Show that \( 3 e^{x} \tan y d x+(1- \)
\( \left.e^{x}\right) \sec ^{2} y d y=0 \)


Explain rocket propulsion.


Dalton based his relative atomic weight
scale on:
A. hydrogen
B. oxygen
c. helium
D. lithium
E. carbon


In the system, \( C a F_{2}(s) \rightleftharpoons \)
\( C a^{+2}(a q)+2 F^{-} \) increasing the
concentration of \( C a^{2+} \) ions four times
will cause the equilibrium
concentration of \( \boldsymbol{F}^{-} \) ions to change to
times the initial value.
A . 4
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D.


\( (C-C l) \) bond in \( C H_{2}=C H-C l \)
(vinyl chloride) is stabilised in the same
way as in:
A. benzyl chloride
B. benzoyl chloride
c. chlorobenzene
D. allyl chloride


A square lawn is surrounded by a path
\( 2.5 m \) wide. If the are of path is \( 165 m^{2} \) find the area of the lawn


The force \( F \) which is applied to \( 1 k g \)
block initially at rest varies linearly with
time as shown in the figure. Find velocity of the block at \( t=4 s \)
A \( .100 \mathrm{m} / \mathrm{s} \)
B. \( 200 \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 4 m / s \)


The radii of two of the first four Bohr
orbits of the hydrogen atom are in the
ratio \( 1: 4 . \) The energy difference
between them may be
A. either \( 12.09 e V \) or \( 3.4 e V \)
B. either \( 2.55 e V \) or \( 10.2 e V \)
c. either \( 13.6 e V \) or \( 3.4 e V \)
D. either \( 3.4 e V \) or \( 0.85 e V \)


What is electric field intensity at any point on the axis of a charged rod of length ' \( L \) ' and linear charge density' \( \lambda \) '?
The point is separated from the nearer end by a.


A particle is moving in a circular path of
radius a under the action of an attractive potential \( U=-\frac{K}{2 r^{2}} . \) Its total
energy is


Solve
\( \mathbf{7}(\boldsymbol{x}-\mathbf{2})=\mathbf{4 9} \)


The difference between simple interest and compound interest at yearly intervals, on Rs. 3000 for 2 years at \( 6 \% \)
is
A . Rs. 20.80
B. Rs. 15.80
c. Rs. 10.80
D. Rs. 9.80


Which of the following is a state of
matter?
A. Quark-gluon plasma
B. Quantum spin liquid
c. superfluid
D. All of above


Initially a body is a rest. If its
acceleration is \( 5 m s^{-2} \) then the
distance travelled in the \( 18^{t h} \) second is:
\( \mathbf{A} \cdot 86.6 m \)
B. \( 87.5 m \)
\( c .88 m \)
D. \( 89 m \)


There is a fixed potential difference
between the two ends of a
potentiometer. Two cells are connected
in series in such a way that in one
arrangement they help each other where as in the second arrangement they oppose each other. The balance point for these two combinations is obtained at
\( 120 \mathrm{cm} \) and \( 60 \mathrm{cm} \) length respectively. The ratio of the emf of the cell is:
A \( \cdot 2: \)
B. 3:
\( c \cdot 1: 1 \)
D. 4:


toppr
Q Type your question_
spool has mass \( m \), edge radius \( K \) and
is wound up to a radius \( r, \) its moment of
inertia about its own axis is \( \boldsymbol{I} \). The free
end of the thread is attached as shown
in figure. So that the thread is parallel
to the inclined plane. \( T \) is the tension in
the thread. Which of the following is
correct?
This question has multiple correct options
A. The linear acceleration of the spool axis down the
slope is \( \frac{m g \sin \theta-T}{m} \)
B. Angular accelerations is \( \frac{T r}{2 I} \)
C. The linear acceleration of the spool axis down the
plane is \( \frac{T r^{2}}{I} \)
D. The acceleration of the spool axis down the slope is
\( \frac{\frac{1}{1} \theta}{m r^{2}} \)


Subtract the following algebraic
expressions.
\( -4 g \) from \( -10 g \)
\( A \cdot 6 g \)
B. - -14g
c. \( -6 g \)
D. 148


When two bodies collide, they
each other.
A. Push
B. Pull
c. Moves towards
D. All


Anhydrous magnesium chloride is obtained by heating the hydrated salt with dry
A. HCl.
в. Nacı
\( c \cdot \) both
D. none


2-Methylpropane on monochlorination under photochemical condition gives:
A. 2 -Chloro-2-methylpropane as major product.
B. (1:1) Mixture of 1-chloro-2-methylpropane and 2chloro-2-methylpropane.
C. 1 -Chloro-2-methylpropane as major product
D. (1:9) Mixture of 1-chloro-2-methylpropane and 2chloro-2-methylpropane.


To measure the radius of the drop
Millikan used \( _{-1-}- \) law of freely
falling drops.
A. Poiseuille's
B. Ostwald's
c. Brewester's
D. stoke's


The centroid of Tetraheadron
(3,4,5),(2,5,9),(5,2,8),(2,5,2)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \) find
the \( \boldsymbol{A}+\boldsymbol{B} \)


If \( \sin \theta=\frac{1}{2}, \) show that \( (3 \cos \theta- \)
\( \left.4 \cos ^{3} \theta\right)=0 \)


Observe the experimental sets \( [A] \) and
\( [\boldsymbol{B}] \)
Observe the test tube \( A \) and \( B \). From the
list given below, choose the
combination of response of shoot and
root that are observed in \( B \)
A. Positive phototropism and positive geotropism
B. Negative phototropism and positive geotropism
C. Positive phototropism and negative geotropism
D. Only negative phototropism


The odour of phosphorus pentoxide is:
A. garlic
B. sour
C. pungent
D. none of these


One side of a parallelogram is \( 8 \mathrm{cm} . \) If the corresponding altitude is \( 6 \mathrm{cm}, \) then its area is given by
A \( \cdot 24 \mathrm{cm}^{2} \)
B. \( 36 \mathrm{cm}^{2} \)
c. \( 40 \mathrm{cm}^{2} \)
D. \( 48 \mathrm{cm}^{2} \)


A Pitot tube (Shown in figure above) is mounted along the axis of a gas
pipeline whose cross-sectional area is
equal to \( S \). Assuming the viscosity to be negligible, the volume of gas flowing across the section of the pipe per unit time, if the difference in the liquid columns is equal to \( \Delta h, \) and the densities of the liquid and the gas are
\( \rho_{0} \) and \( \rho \) respectively is \( Q= \) \( \boldsymbol{S} \sqrt{\frac{\boldsymbol{x} \boldsymbol{\Delta} \boldsymbol{h} \boldsymbol{\rho}_{0} \boldsymbol{g}}{\boldsymbol{\rho}}} . \) Find the value of \( \boldsymbol{x} \)


Which of the following reactions shows
reducing nature of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. \( P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
B. \( A g_{2} O+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \)
c. \( 2 H C H O+H_{2} O_{2} \rightarrow 2 H C O O H+H_{2} O \)
D. \( N a_{2} S O_{3}+H_{2} O_{2} \rightarrow N a_{2} S O_{4}+H_{2} O \)


Identify the differentiate between leucoplasts and chromoplasts.
A. Leucoplasts- colourless plastids, chromoplasts coloured plastids
B. Leucoplasts- coloured plastids, chromoplasts colourless plastids
c. Leucoplasts- help in storage of food, chromoplasts help in photosynthesis, pollination
D. Both A and C


If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) then prove the
following \( \sin 2 A+\sin 2 B+\sin 2 C= \)
\( 4 \sin A \cdot \sin B \cdot \sin C \)


The small aerating pores seen on cork layer of woody stem are
A . Guard cells
B. Subsidiary cells
c. Trichomes
D. Lenticels


A solid sphere is rolling purely on a rough horizontal surface with speed of
center \( u=12 \mathrm{m} / \mathrm{s} . \) It collides
inelastically with a smooth vertical wall at a certain moment, the coefficient of restitution being \( \frac{1}{2} . \) How long (in sec) after the collision, the sphere will begin
pure rolling? [coefficient of friction between the
sphere and the ground is \( \frac{3}{35} \)
A . 16
B . 12
\( c .6 \)
D. 13


In gaseous discharge tube,the colour of
light emitted by helium is:
A. yellow
B. red
c. blue
D. green


The number of bijection that can be
defined from \( \boldsymbol{A}=\{1,2,8,9\} \) to \( \boldsymbol{B}= \)
\{3,4,5,10\} is
\( \mathbf{A} \cdot 4^{4} \)
B \( \cdot 4^{2} \)
\( c \cdot 24 \)
D. 18


Which block of the periodic table contains elements with the general electronic configuration? \( (n-2) f^{1-14}(n-1) d^{0-1} n s^{2} \)
A. s-block
B. p-block
c. d-block
D. f-block


For polynomial \( \boldsymbol{P}(\boldsymbol{x})=\mathbf{6} \boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \mathbf{9} \boldsymbol{x}^{\mathbf{2}}+ \)
\( \mathbf{4 4} \boldsymbol{x}+\mathbf{2 1}, \) find \( \mathbf{P}(-\mathbf{2}) \)


Solve the following equations. \( \sqrt{3}-\tan x=\tan \left(\frac{\pi}{4}-x\right) \)


Prove that \( \log _{2} 3 \) is an irrational
number.


Methanol and acetone can be separated
by:
A. Fractional distillation
B. Distillation
c. Steam distillation
D. Vacuum distillation


Find the arithmetic mean of first 10
natural numbers.
A . 55
в. 550
\( c .5 .5 \)
D. None of the above


Which of the following is a polyamide?
A. Teflon
в. Nylon -6,6
c. Terylene
D. Bakelite


A force-time graph for the motion of a body is shown in figure. Change in linear momentum between 0
and 8 s is:
A. zero
B. 4 N-s
\( c \cdot 8 \) Ns
D. None


The common ratio of \( \mathrm{GP} \mathbf{4}, \mathbf{8}, \mathbf{1 6}, \mathbf{3 2}, \dots . \)
is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


Which type of organisms are called as
pathogens?
A. The organisms which cause a disease.
B. The organisms which cause weakness.
C. The organisms which cause an infection.
D. none of these


\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}), \boldsymbol{K}= \)
\( 10^{-9} \) at \( 300 K . \) The value of \( p_{c o_{2}} \) is \( 10^{-x} \)
\( x \) is


Rational numbers are closed under
substraction.
A. True
B. False
c. Cannot be determined
D. None


Let \( f(x) \) be a function in [0,5] such that
\( \boldsymbol{f}^{2}(\boldsymbol{x})=\mathbf{1} \forall \boldsymbol{x} \in[\mathbf{0}, \mathbf{5}] \) and \( \boldsymbol{f}(\boldsymbol{x}) \) is
discontinuous at all integers in \( [\mathbf{0}, \mathbf{5}] \) Find total number of fuctions.


Three square with the same center and corresponding parallel sides are drawn. The distance between the the sides of
successive square is 3 and the side length of the largest square is \( 22, \) as shown. what is the perimeter of the smallest square?
A . 40
B. 100
c. 10
D. 64
E. 20


A body of mass \( 2 k g \) initially at rest moves under the action of an applied
horizontal force of \( 7 N \) on a table with
coefficient of kinetic friction \( =\mathbf{0 . 1} \)
Compute the Work done by the applied force in \( 10 s \)
в. \( 890 J \)
c. \( 1000 J \)
D. \( 5000 J \)


Which of the following is/are true?
This question has multiple correct options
A. Van der Waals forces are responsible for the formation of molecular crystals
B. Branching lowers the boiling points of isomeric organic compounds due to decrease in van der Waals forces of attraction.
C. In graphite, van der Waals forces act between the carbon layers.
D. In diamond, van der Waals forces act between the carbon layers.


Taxonomical aids are helping hands of taxonomy, and two of them functions for ex-situ conservation strategy, these
are?
A. Botanical garden and herbarium
B. Zoological parks and museums
c. zoological parks and botanical gardens
D. Museums and botanical gardens


The minimum speed of wind necessary for the satisfactory working of a wind generator to produce electricity is about:
A. \( 15 \mathrm{km} / \mathrm{h} \)
B. 20 \( \mathrm{m} / \mathrm{h} \)
\( c \cdot 12 m / s \)
D. \( 50 \mathrm{km} / \mathrm{h} \)


What is the special technique used for
separation and identification of the constituents in the mixture?


In a particular experiment, a gas undergoes adiabatic expansion satisfying the equation \( V T^{3} \) =constant.
The ration of specific heats, \( \boldsymbol{Y} \) is:
A . 4
B. 3
\( c \cdot \frac{5}{3} \)
D.


Find out the current in the circuit
shown above. (Assume the diode used
in the circuit is ideal)
A. \( 20 \mathrm{mA} \)
B. 200 mA
c. \( 0.2 \mathrm{A} \)
D. \( 40 \mathrm{A} \)


If \( M(x, y) \) is equidistant from \( A(a+ \) \( b, b-a) \) and \( B(a-b, a+b), \) then
A. \( b x+a y=0 \)
В. \( b x-a y=0 \)
\( \mathbf{c} \cdot a x+b y=0 \)
D. \( a x-b y=0 \)


\( \boldsymbol{T}_{50} \) (Half-life period) of first - order
reaction is 10 minute. Starting with
\( 10 m o l L^{-1}, \) rate after 20 minute is :
A \( \cdot 0.0693 m o l L^{-1} \min ^{-1} \)
В. \( 0.0693 \times 2.5 \) molL\( ^{-1} \) min \( ^{-1} \)
\( \mathbf{c} \cdot 0.0693 \times 5 m o l L^{-1} \min ^{-1} \)
D. \( 0.0693 \times 10 \) molL\( ^{-1} \) min \( ^{-1} \)


The \( p H \) of a solution which is \( 0.1 M \) sodium acetate and \( 0.01 M \) acetic acid
\( \left(p K_{a}=4.74\right) \) would be:
A . 4.2
B. 5.1
\( c .5 .74 \)
D. None of these


In a vacuum diode, the space around
the cathode which is filled with
electrons, is called
A. space charge
B. electric field
c. magnetic field
D. electron cloud


When sulphur dioxide is passed in an acidified \( K_{2} C r_{2} O_{7} \) solution, the
oxidation state of sulphur is changed from:
A . +4 to 0
B. +4 to +2
\( \mathbf{c} \cdot+4 \) to +6
D. +6 to +4


The rate constant of a first order
reaction is 0.0693 min\( ^{-1} \)
Time (in minutes) required for reducing
an initial concentration of 20 mol \( l i t^{-1} \)
to 2.5 mol \( l i t^{-1} \) is :
A . 40
B. 30
c. 20
D. 10


When the light is very bright, then:
A. Iris makes pupil expand
B. Iris makes pupil contract
C. Iris and pupil remain as they are
D. None of these


In which of the following process the system and surrounding comes back to its original state after the process is complete?
A. Quasi-static Process
B. Reversible process
c. Both a and \( b \)
D. Isobaric process


If the ratio of the masses of two plane
what will be the ratio of their accelera


Translocation of organic materials is best explained by
A. Active transport
B. Transpiration pull
c. Imbition theory
D. Mass flow hypothesis


The solution showing positive deviation from ideal behaviour has
azeotrope.
A. negative
B. positive
c. neutral
D. ideal


\( \int\left(\frac{4 e^{x}-25}{2 e^{x}-5}\right) d x=A x+ \)
\( \boldsymbol{B} \log \left|\mathbf{2} e^{x}-\mathbf{5}\right|+\boldsymbol{c}, \) then
A. \( A=5, B=3 \)
В. \( A=5, B=-3 \)
\( \mathbf{c} \cdot A=-5, B=3 \)
D. \( A=-5, B=-3 \)


Why defects in the myelin sheath is
dangerous?
A. Action potentials would be conducted too slowly along the neurons
B. Muscles would not contract when stimulated
C. The thyroid gland would not be able to produce thyroxine
D. The bone tissue would not be properly maintained


A conducting square loop of side \( L \) and
resistance \( R \) moves in it's plane with a
uniform velocity \( v \) perpendicular to one of it's sides. A magnetic induction \( B \) constant in time and space, pointing perpendicular to and into the plane of the loop exists everywhere. The current induced in the loop is
A \( \cdot \frac{B L v}{R}, \) clockwise
B. \( \frac{B L v}{2 R} \) clockwise
c. \( \frac{2 B L v}{2 R} \) anticlockwise
D. zero


An object of mass ' \( m \) ' is kept on a
horizontal platform. The platform is
oscillating vertically with amplitude ' \( a \) '
and period 'T". The weight of object at lowest position is:
A \( . m g+m a \omega^{2} \)
B. \( m a \omega^{2} \)
\( \mathrm{c} \cdot m g \)
D. \( m g-m a \omega^{2} \)


Which end of the inductor, \( a \) or \( b \), is at a
higher potential?


Assertion
Extraction of gold from its native ore
involves leaching the metal ore with dilute solution of NaCN in presence of
air.
Reason
This is an oxidation reaction and leads
to the formation of a soluble complex.
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 wire carrying current \( i \) has the configuration shown in the figure. Two semi-infinite straight sections, each tangent to the same circle, are
connected by a circular arc, of angle \( \boldsymbol{\theta} \)
along the circumference of the circle,
with all sections lying in the same plane. What must \( \theta \) (in rad) be in order
for \( B \) to be zero at the center of
the circle?


Light propagates \( 2 \mathrm{cm} \) distance in
glass of refractive index 1.5 in time \( t_{0} \)
In the same time \( t_{0}, \) light propagates a
distance of \( 2.25 \mathrm{cm} \) in a medium. The
refractive index of the medium is :
A \( .4 / 3 \)
B. \( 3 / 2 \)
\( c \cdot 8 / 3 \)
D. none of these


The correct chemical formula for
ammonium phosphate is:
A. \( N_{2} H_{6} P O_{4} \)
в. \( \left(N H_{3}\right)_{3} P O_{4} \)
\( \mathrm{c} \cdot\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4} \)
D. \( \left(N H_{4}\right)_{2} P O_{4} \)


Solve:
\( \lim _{u \rightarrow 1} \frac{\sqrt{u^{2}+8}}{\sqrt{u^{2}+3}}-\frac{\sqrt{10-u^{2}}}{\sqrt{5-u^{2}}} \)


Assertion
G-phase is also called anaphase, as during this phase the cell stores ATP for
cell division.
Reason
Cell produces structural and functional proteins. Cell's metabolic rate is high and is controlled by the enzymes.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


n figure , one car is at rest and velocity of light from head light is \( C \), then velocity of light from head light for the moving car at velocity v,would be


1 ampere is same as
\( \mathbf{A} \cdot 1 C s^{-1} \)
B. \( 1 C s \)
\( \mathbf{c} \cdot 1 J C^{-1} \)
D. \( 1 V C^{-1} \)


A lens behaves as a converging lens in air and as a diverging lens in water. The refractive index of the material is
A. Equal to unityyy
B. Equal to 1.33
c. Between unity and 1.33
D. Greater than 1.33


Draw Venn diagrams to illustrate \( \boldsymbol{A} \backslash \boldsymbol{B} \)


Consider the following three
statements:
\( P: 5 \) is a prime number
\( Q: 7 \) is a factor of 192
\( \mathrm{R}: \) L.C.M. of 5 and 7 is 35
Then the truth value of which one of
thefollowing statements is true?
A \( \cdot(P \wedge Q) \vee(\sim R) \)
в. \( (\sim P) \wedge(\sim Q \wedge R) \)
c. \( (\sim P) \vee(Q \wedge R) \)
D. \( P \vee(\sim Q \wedge R) \)


The Henry's law constant for the
solubility of \( N_{2} \) gas in water at \( 298 K \) is \( 1 \times 10^{5} \) atm. The mole fraction of \( N_{2} \) in
air is \( 0.8 . \) Calculate the number of
moles of \( N_{2} \) dissolved in 10 moles of
water at \( 298 K \) and 5 atm.
A \( \cdot 5 \times 10^{-4} \)
В. \( 3 \times 10^{-5} \)
c. \( 4 \times 10^{-4} \)
D. \( 4 \times 10^{-5} \)


A sphere of radius \( 10 \mathrm{cm} \) and mass
\( 25 k g \) is attached to the lower end of a
steel wire of length \( 5 m \) and diameter
\( 4 m m \) which is suspended from the ceiling of a room. The point of support is \( 521 \mathrm{cm} \) above the floor. When the
sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the
ball at its lowest position in \( \boldsymbol{m} / \boldsymbol{s} \) \( \left(\boldsymbol{Y}_{\text {steel}}=\mathbf{2} \times \mathbf{1 0}^{11} \boldsymbol{N} / \boldsymbol{m}^{2}\right) \)


Which of the following are the products shown by the reaction of methoxyethane with \( \boldsymbol{H} \boldsymbol{I} \) ?
\( \mathbf{A} \cdot C_{2} H_{5} I+C H_{3} O H \)
в. \( C H_{3} I+H_{2} O \)
c. \( C_{2} H_{5} O H+H_{2} O \)
D. \( C_{2} H_{5} O H+C H_{3} I \)


Q Type your question
observation table are shown in figure.
SI.No. \( \quad \) R(lomegal) \( \quad l(c m) \)
1000
100
1.5
1
Which of the readings is inconsistent?
4
B. 1
\( c \cdot 2 \)
2


A solid metallic sphere is placed in a
uniform electric field. Which of the
curves shown in figure represent the
lines of force correctly?
\( \mathbf{A} \cdot(a) \)
B. \( (b) \)
\( c \cdot(c) \)
\( \mathbf{D} \cdot(d) \)


Match List I (Substances) with List-II
(Processes employed in the
manufacture of the substance) and
select the correct option.
List - (Substances)
A. Sulphuric acid
1. Haber's process
B. Steel
2. Bessemer's
process
c. Sodium hydroxide \( \quad 3 \). Leblanc process
D. Ammonia
A. \( A-1, B-4, C-2, D-3 \)
в. \( A-1, B-2, C-3, D-4 \)
c. \( A-4, B-3, C-2, D-1 \)
D. \( A-4, B-2, C-3, D-1 \)


Which of the following object is/are in equilibrium?
This question has multiple correct options
A . A sleeping cat
B. A flask resting on a table
c. A rocking see-sawwew
D. A man walking


Chromosomes are composed of
A. DNA, RNA, histones, non-histones
B. DNA and histones
C. DNA and RNA
D. DNA, RNA and histones


A person walks \( 100 \mathrm{m}, \) holding a suitcase of weight \( 100 \mathrm{N} \). The work done by the applied force is \( J \)
\( \mathbf{A} \cdot 10000 \)
в. 100
c. \( Z e r o \)
D. 5000


Fill in the blank.
Atmospheric pressure with increase in
altitude.
A. increases
B. decreases
c. remains constant
D. may increase or decrease


Eccentricity of the conic represented by \( \boldsymbol{x}=\frac{\boldsymbol{e}^{\boldsymbol{a}}+\boldsymbol{e}^{-\boldsymbol{a}}}{\mathbf{2} \sqrt{\mathbf{3}}}, \boldsymbol{y}=\frac{\boldsymbol{e}^{\boldsymbol{a}}-\boldsymbol{e}^{-\boldsymbol{a}}}{\mathbf{2}} \) is


A die is thrown. If \( A \) is the event that the
number on upper face is less than 5
then write sample space and event \( A \) in
set notation.


A weak acid \( H X \) has the dissociation
constant \( 1 \times 10^{-5} M . \) It forms a salt
\( N a X \) on reaction with alkali. The
percentage hydrolysis of \( 0.1 \mathrm{M} \) solutions of \( N a X \) is:
A. \( 0.0001 \% \)
B . \( 0.01 \% \)
c. \( 0.1 \% \)
D. \( 0.15 \% \) \%


Isotopes of an element do not have:
A. same number of electrons
B. same physical properties
c. same chemical properties
D. same electrical charge on the nucleus


Fo parabola \( 3 y^{2}=16 x, \) equation of
directrix and length of latus rectum is
A \( \cdot x=\frac{-4}{3}, \frac{3}{4} \)
B. \( x=\frac{4}{3}, \frac{4}{3} \)
c. \( y=\frac{-4}{3}, \frac{4}{3} \)
D. \( x=\frac{-4}{3}, \frac{16}{3} \)


Slope between PV and P at constant
temperature is:
A . zero
B.
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\sqrt{2}} \)


Find \( x \)


A chemical process in which a substance reacts with oxygen to give off
heat is
A. respiration
B. combustion
c. explosion
D. conduction


If the sum of \( 1+\frac{1+2}{2}+\frac{1+2+3}{3}+ \)
\( \ldots \) to \( n \) terms is \( S, \) then \( S \) is equal to
A \( \cdot \frac{n(n+3)}{4} \)
в. \( \frac{n(n+2)}{4} \)
c. \( \frac{n(n+1)(n+2)}{6} \)
D. \( n^{2} \)


Cork is a derivative of
A. Cork cambium (phellogen) or extra fascicular cambium
B. Vascular cambium
C. Fascicular cambium
D. Interfascicular cambium


The thermal conductivity of the plate depends upon
A. the temperature difference between the two sides
B. the thickness of the plate
c. the area of the plate
D. nature of the material


The middle term in the expansion of
\( \left(x+\frac{1}{x}\right)^{10} \)
A \( \cdot \) io \( C_{4} \cdot \frac{1}{x} \)
в. \( ^{10} C_{5} \)
c. \( _{10} \mathrm{C}_{5} . \frac{1}{x} \)
D. \( ^{10} C_{6} . x \)


Which of the following does not happen
when nitric acid reacts with calcium
carbonate?
A. Carbon dioxide is evolved
B. Hydrogen is evolved.
c. Calcium nitrate is formed.
D. water is formed


To prevent a piece of iron from rusting which one of the following metals will provide the best coating?
A. zinc
B. copper
c. Aluminium
D. Leadd


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{2-x}-\sqrt{2+x}}{x} \)
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( -\frac{1}{\sqrt{3}} \)
\( c \cdot-\frac{1}{2} \)
D. \( -\frac{1}{\sqrt{2}} \)


Solve:
\( \frac{1}{5}\left(\frac{1}{3 x}-5\right)=\frac{1}{3}\left(3-\frac{1}{x}\right) \)


Garima purchased a briefcase with an additional \( 10 \% \) discount on the reduced
price after deducting \( 20 \% \) on the labelled price If the labelled price was Rs 1400 at what price did she purchased the briefcase?
A . Rs 980
B. Rs 1008
c. Rs 1056
D. Rs 1120


State whether the given statement is
True or False :
Tremors on the Earth can also be
caused by the eruption of a volcano.
A. True
B. False


Identify whether the following sequence is a geometric sequence or not.
2,6,18,54


Give reasons for the following. Stationary coil and stationary magnet can not produce induced electric
current


Assertion
lodination of alkanes is carried out in
the presence of oxidising agents like
\( H I O_{3} \) or \( H N O_{3} \)
Reason
lodination of alkanes is an irreversible
reaction.
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 numbers 1 to 12 indicate
different positions of the Earth in its
orbit around the sun. Which number
indicates the position of the Earth in the
month of Chingam (Leo)?


Intake of food is called
A. Ingestion
B. Egestion
c. Digestion
D. Nutrition


Heat is measured by the principle of :
A . length
B. calorimetry
c. temperature
D. all of the above


Q Type your question
corresponding to some points in the
figure are:
\( \boldsymbol{P}_{\boldsymbol{A}}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{P a} \)
\( \boldsymbol{V}_{\boldsymbol{A}}=\boldsymbol{2} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{m}^{-3} \)
\( \boldsymbol{P}_{\boldsymbol{B}}=\boldsymbol{8} \times 10^{4} \boldsymbol{P} \boldsymbol{a} \)
\( V_{C}=5 \times 10^{-3} m^{-3} \)
In the process \( A B, 600 J \) of heat is added
to the system and in process BC, 200 J of
heat is added to the system. The change
in internal energy of the system in
process AC would be
A. 560
B. 800J
c. 600 J
D. 640


Define a drug. What are the characters
of an ideal drug?


In a simple slit diffraction pattern intensity and width of fringes are
A. Unequal width
B. Equal width
c. Equal width and equal intensity
D. Unequal width and unequal intensity


If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.


The free-body diagram will be identical
to the one we drew in the example of the
frictionless plane, except we will have a vector for the force of friction in the
negative \( x \) direction. What is the work
done on the box by the force of kinetic
friction?
A \( . \) \mumgh \( \sin 30^{\circ} \)
B. \( \mu \) mgh tan30 \( ^{\text {0 }} \)
c. \( \mu m g h \cot 30^{\circ} \)
D. \( \mu \) mgh \( \cos 30^{\circ} \)


Which one of the following statement is
not correct for \( N_{2} ? \)
A. It has small size
B. It is a typical non metal
C. It does not eadily react with oxygen
D. d-orbitals are available for bonding


For which of the following processes,
\( \Delta S \) is negative?
A \( \cdot N_{2}(g, 273 K) \rightarrow N_{2}(g, 300 K) \)
B. \( N_{2}(g, 1 \text { 1atm }) \rightarrow N_{2}(g, \text { 5atm }) \)
c. \( C(\text {diamond}) \rightarrow C(\text {graphite}) \)
D. \( H_{2}(g) \rightarrow 2 H(g) \)


What is meant by water of crystallization of a substance? Describe an activity to show the water of crystallization.


Standard entropies of \( X_{2}, Y_{2} \) and \( X Y_{3} \) are 60,40 and \( 50 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) respectively.
For the reaction:
\( \frac{1}{2} X_{2}+\frac{3}{2} Y_{2} \rightleftharpoons X Y_{3}, \Delta H=-30 \mathrm{kJ} \) to
be at equilibrium, the temperature should be:
\( A \cdot \) 750 \( \kappa \)
B. 1000
c. \( 1250 \mathrm{k} \)
D. 500 K


How is a prokaryotic cell different from a eukaryotic cell?


The phase difference between two waves from successive half period
zones or strips is :
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. zero


Draw a labelled diagram of an image formed by a compound microscope, with the image at least distance of distinct vision. Write any one
expression for its magnifying power


For the reaction \( 3 A(g)+B(g) \rightleftharpoons 2 C(g) \)
at a given temperature \( \mathrm{K}=9.0 \mathrm{What} \) must be the volume of the flask, if a
mixture of 2.0 mol each of 2.0 mol each of \( A, B \) and \( C \) exist in equilibrium?
A . \( 6 L \)
B. 9L
c. 36L
D. None of these


Which of the following will have same value of van't Hoff factor as that of
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] ? \)
A \( \cdot A l_{2}\left(S O_{4}\right)_{3} \)
в. \( A l C l_{3} \)
c. \( A l\left(N O_{3}\right)_{3} \)
\( \mathbf{D} \cdot A l(O H)_{3} \)


If \( A \) is a scalar matrix with scalar \( k \neq 0 \)
of order \( 3, \) then \( k A^{-1} \) is:
A \( \cdot \frac{1}{k} I \)
в. \( \frac{1}{k^{2}} \)
\( c \cdot k^{2} I \)
D. \( \frac{1}{k^{3}} \)


Inverse of a diagonal matrix is
A. Symmetric
B. A skew-symmetricc
c. A diagonal matrix
D. None of these


Which of the following reaction(s) is/are non-stereospecific but stereoselective?
A. \( S N_{1} \)
в. \( E_{1} \)
c. \( E_{2} \)
D. \( E_{1} c B \)


Which one of the following functions is
not one-one?
\( \mathbf{A} \cdot f:(-1, \infty) \rightarrow R \) given by \( f(x)=x^{2}+2 x \)
B \( \cdot g:(2, \infty) \rightarrow R \) given by \( g(x)=e^{x^{3}-3 x+2} \)
C \( . h: R \rightarrow R \) given by \( h(x)=2^{x(x-1)} \)
D \( \quad \phi:(-\infty, 0) \rightarrow R \) given by \( \phi(x)=\frac{x^{2}}{x^{2}+1} \)


The position vectors \( \vec{a}, \vec{b}, \vec{c} \) of three points satisfy the relation \( 2 \vec{a}+7 \vec{b}+ \)
\( \mathbf{5} \vec{c}=\overrightarrow{0} . \) Are these points collinear?


If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by:
A. the circle
B. the square
c. the equilateral triangle
D. the triangle and square have equal perimeters greater than that of circle


A thin metal rod of length \( 0.6 m \) is in
vertical straight position on horizontal floor. This rod is falling freely to a side without slipping. The angular velocity of rod when its top end touches floor, is :
A .7 rads\( ^{-1} \)
B. 4.2 rads\( ^{-1} \)
c. 3.5 rads\( ^{-1} \)
D. \( 2.1 \mathrm{rads}^{-1} \)


Thickness of stem increase due to
activity of
A. Cambium
B. Xylem
c. Phloem
D. Shoot apex


Which one of the following statements
is not correct?
A. Oxidation number of \( \sin \left(N H_{4}\right)_{2} S_{2} O_{8} \) is +6
B. Oxidation number of 0 s in \( O s O_{4} \) is +8
C. Oxidation number of \( \sin H_{2} S O_{5} \) is +8
Dexidation number of 0 in \( K O_{2} \) is \( -\frac{1}{2} \)


The additive inverse of \( z \) is
\( A \cdot 0 \)
B. \( z \)
\( c .-z \)
D.


A lead-acid battery of a car has an e.m.f. of \( 12 V . \) if the internal resistance of the
battery is 0.5 ohm, the maximum
current that can be drawn from the
battery will be
\( A .30 A \)
в. \( 20 A \)
\( c \cdot 6 A \)
D. \( 24 A \)


Find the sum of the following series up to \( n \) terms: \( 6+.66+.666+\dots \)


following reaction:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{D}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \stackrel{D_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{X} \)
\( A \)
B.
\( c \)
\( D \)


Three forces of magnitude \( 6 N, 6 N \) and
\( \sqrt{72} N \) act at a corner of a cube along
three sides as shown in the figures.The
resultant of these forces is:
A . 12 N along ob
B. 18 N along of
c. \( 18 N \) along \( 0 c \)
D. 12 N along of


The half life of a radioactive substance
is 20 minutes. The time taken between
\( 50 \% \) decay and \( 87.5 \% \) decay of the substance will be
A . 30 minutes
B. 40 minutes
c. 25 minutes
D. 10 minutes


Given reason whether the following is an equation or not:
\( (x-2)^{2}=x^{2}-4 x+4 \)


The intercepts of the plane \( 2 x-3 y+ \)
\( \mathbf{5} z-\mathbf{3 0}=\mathbf{0} \) are
A. 15,-10,6
в. 5,10,6
c. \( 1 / 8,-1 / 6,1 / 4 \)
D. 3,-4,6


The binomial distribution whose mean
is 9 and the variance is 2.25 is
\( ^{\mathbf{A}} \cdot\left(12, \frac{1}{2}, \frac{1}{2}\right) \)
B \( \cdot\left(12, \frac{2}{3}, \frac{1}{3}\right) \)
\( ^{\mathbf{c}} \cdot\left(12, \frac{5}{6}, \frac{1}{6}\right) \)
D. \( \left(12, \frac{3}{4}, \frac{1}{4}\right) \)


A liquid of mass \( \mathrm{m} \) and specific heat \( \mathrm{c} \) is heated to temperature 2T. Another liquid of mass m/2 specific heat \( 2 c \) is
heated to a temperature T. If these two liquids are nixed, the resulting temperature mixture is
\( A \cdot(2 / 3) T \)
B. (8/5) T
\( c \cdot(3 / 5) T \)
D. (3/ 2)T


Vascularisation in plants occurs
through.
A. Differentiation of procambium followed by primary phloem and then primary xylem
B. Differentiation of procambium followed by development of xylem and phloem
C. Simultaneous differentiation of procambium, xylem and phloem
D. Differentiation of procambium is immediately followed by development of secondary xylem and secondary phloem


For the given orbital in Column I, the
only CORRECT combination for any
hydrogen-like species is
\( A \cdot(1 \vee) \)
(iv)
B. (III) (iii) (P)
\( c .(11) \) (ii)
(P)
D. (I) (ii) (S)


If \( \frac{3 \pi}{2} \leq x \leq \frac{5 \pi}{2}, \) then \( \sin ^{-1}(\sin x) \) is
equal to-
\( A \)
B. \( -x \)
c. \( 2 \pi-x \)
D. \( x-2 \pi \)


Class is present between
A. Kingdom and phylum
B. Phylum and order
c. order and family
D. Family and genus


Explain the factors affecting enzyme
activity


pH of human urine is
\( A \cdot 9 \)
B. 6
\( c \cdot 4 \)
D. 3


An electric dipole moment \( \vec{P}=(2.0 \hat{i}+ \) \( 3.0 \hat{j}) \mu \) is placed in a uniform electric field \( \overrightarrow{\boldsymbol{E}}=(\mathbf{3 . 0 \hat { \boldsymbol { i } }}+\mathbf{2 . 0 \hat { \boldsymbol { k } }}) \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{C}^{-\mathbf{1}} \)
This question has multiple correct options
A . The torque that \( \vec{E} \) exerts on \( \mathrm{P} \) is \( (0.6 \hat{i}-0.4 \hat{j}-0.9 \hat{k}) \)
\( \mathrm{Nm} \)
B. The potential energy of the dipole is 0.9 J
c. The potential energy of the dipole is 0.6
D. If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3


A square loop ABCD, carrying a current
\( I_{2}, \) is placed near and coplanar with a
long straight conductor XY carrying a
current \( I_{1}, \) as shown in the figure. The
net force on the loop will be :
A \( \cdot \frac{\mu_{0} I_{1} I_{2}}{2 \pi} \)
В. \( \frac{\mu_{0} I_{1} I_{2} L}{2 \pi} \)
c. \( \frac{2 \mu_{0} I_{1} I_{2} L}{3 \pi} \)
D. \( \frac{2 \mu_{0} I_{1} I_{2}}{3 \pi} \)


Each side of a cube is measured to
7.203 \( \mathrm{m} \). Find the volume of the cube up
to appropriate significant figures.


Ratio of the Bohr radius of protium, deuterium and tritium atoms is:
A .1: 2: 3
B. 1: 1: 1
c. 3: 2: 1
D. 2: 3: 4


When a vapour is excited at low
pressure by passing an electric current through it, a spectrum is obtained.
a) Draw a spectral series of emission lines in hydrogen.
b) Name the different series of hydrogen
atom
c) In which region Lyman series is located.


When a carpet is beaten with a stick,
dust comes out of it. Explain.


How many unpaired \( e^{-} \) are present in \( \left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-} ? \)
A .
B. 2
\( c \)
D. 3


Give reasons:
Blood goes only once in one cycle through the heart in fishes.


A ray of light incident on an equilateral
prism shows minimum deviation of \( 30^{\circ} \)
The speed of light through the glass prism is :
A \( .2 .5 \times 10^{8} \mathrm{m} / \mathrm{s} \)
B. \( 2.121 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 3.2 \times 10^{8} \mathrm{m} / \mathrm{s} \)


A bag contains 5 red, 6 white and 7
black balls. Two balls are drawn at
random. What is the probability that both balls are red or both are black?
A \( \cdot \frac{31}{153} \)
в. \( \frac{30}{153} \)
c. \( \frac{33}{153} \)
D. \( \frac{32}{153} \)


If the constant term in the binomial
expansion of \( \left(x^{2}-\frac{1}{x}\right)^{n}, n \quad \epsilon \quad N \) is 15
then the value of \( n \) is equal to


A ray ol IIght Is Incıdent normally orn orne
face of a prism as shown in figure. The
refractive index of the material of the
5
prism is \( \frac{-a n d}{3} \) the prism is immersed
in water of refractive index \( \frac{x}{2} \) then 3
This question has multiple correct options
A \( \cdot \) The angle of emergence \( \Theta_{2} \) of the ray is \( \sin ^{-1}\left(\frac{5}{8}\right) \)
B. The angle of emergence \( \Theta_{2} \) of the ray is \( \sin ^{-1}\left(\frac{5}{4 \sqrt{3}}\right) \)
C the angle of emergence \( \Theta_{2} \) of the ray is \( \sin ^{-1}\left(\frac{7}{3 \sqrt{4}}\right) \)
D. Total internal reflection will not occur at P if the refractive index of water increases to a value greater
\( \operatorname{than} \frac{5}{2 \sqrt{3}} \) by dissolving some substance


Find the value of \( \sin \left(15^{0}\right) \)
A \( \frac{\sqrt{3}-1}{2 \sqrt{2}} \)
B. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
c. \( \frac{\sqrt{3}-1}{\sqrt{2}} \)
D. None of these


John Ray introduced the term species.
A. True
B. False


Give reasons for the sulphur has greater tendency for catenation then oxygen.


Let \( A \) and \( B \) be two sets such that
\( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{3} \) and \( \boldsymbol{n}(\boldsymbol{B})=\mathbf{2} . \) If
\( (x, 1),(y, 2),(z, 1) \) are in \( A \times B \) find \( A \)
and \( B \) where \( x, y \) and \( z \) are distinct
elements


Gold sol can be prepared by:
A. hydrolysis of gold(III) chloride
B. oxidation of gold by aqua-regia
C . peptization
D. treating gold
(III) chloride with metallic zinc
E. reduction of gold (III) chloride with formalin solution


In which state, terrace farming is
practised?
A. Punjab
B. Haryana
c. Plains of Uttar Pradesh
D. Jammu and Kashmir


For the equilibrium \( S r C l_{2} \)
\( 6 H_{2} O(s) \rightleftharpoons S r C l_{2} \cdot 2 H_{2} O(s)+ \)
\( 4 H_{2} O(g) \) the equilibrium constant
\( K_{P}=16 \times 10^{-12} a t m^{4} \) at \( 1^{\circ} C . \) If one
litre of air saturated with water vapour
at \( 1^{\circ} \mathrm{C} \) is exposed to a large quantity of
\( \boldsymbol{S} \boldsymbol{r} \boldsymbol{C l}_{2} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(s), \) what weight of water
vapour will be absorbed? Saturated
vapour pressure of water at \( 1^{\circ} \boldsymbol{C}= \)
7.6 torr.
A \( .7 .2 \mathrm{mg} \)
B . \( 3.25 \mathrm{mg} \)
c. \( 2.3 \mathrm{mg} \)
D. \( 8.5 \mathrm{mg} \)


\( \frac{\mathbf{d}^{2} \mathbf{x}}{\mathbf{d} \mathbf{y}^{2}} \) equals
A \( \cdot\left(\frac{\mathrm{d}^{2} \mathbf{y}}{\mathrm{d} \mathbf{x}^{2}}\right)^{-1} \)
B \( \cdot \quad-\left(\frac{\mathrm{d}^{2} \mathbf{y}}{\mathrm{d} \mathbf{x}^{2}}\right)^{-1}\left(\frac{\mathrm{d} \mathbf{y}}{\mathrm{d} \mathbf{x}}\right)^{-3} \)
C \( \cdot\left(\frac{\mathrm{d}^{2} \mathbf{y}}{\mathrm{d} \mathbf{x}^{2}}\right)\left(\frac{\mathrm{d} \mathbf{y}}{\mathrm{d} \mathbf{x}}\right)^{-2} \)
D \( \cdot \)
\( -\left(\frac{\mathrm{d}^{2} \mathbf{y}}{\mathrm{d} \mathbf{x}^{2}}\right)\left(\frac{\mathrm{d} \mathbf{y}}{\mathrm{d} \mathbf{x}}\right)^{-3} \)


\( \ln Y D S E, d=2 m m, D=2 m \) and
\( \lambda=500 n m . \) If intensity of two slits are
\( l_{0} \) and \( 9 l_{0}, \) then find the intensity at \( \boldsymbol{y}=\frac{1}{6} \boldsymbol{m m} \)
A \( .7 l_{0} \)
B. \( 10 l_{0} \)
c. \( 16 l_{0} \)
D. \( 4 l_{0} \)


The equation of an alternating voltage is \( V=100 \sqrt{2} \sin 100 \pi t \) volt. The RMS
value of voltage and frequency will be respectively
A. \( 100 V, 50 H z \)
в. \( 50 V, 100 H z \)
c. \( 150 V, 50 H z \)
D. \( 200 V, 50 H z \)


Integrate the function \( \frac{e^{5 \log x}-e^{4 \log x}}{e^{3 \log x}-e^{2 \log x}} \)


If two parallel lines are cut by a transversal, then each pair of
corresponding angle are
A . congruent
B. obtuse
c. acute
D. \( 90^{\circ} \)


In the colloidal state the particle size
ranges:
A. below 1 nm
B. between \( 1 \mathrm{nm} \) to \( 1000 \mathrm{nm} \)
c. less than 100 nm
D. None of the above


A Zener diode
A. is a lightly doped junction diode
B. heavily doped junction diode.
C . is either p-type or n-type.
D. has no p-njunction.


First experiment related to the method of hydroponics was done by
A. Knop
в. ні||
c. Arnon
D. sachs


Integrate the rational function \( \frac{1}{\left(e^{x}-1\right)} \)


A box contains 100 tickets numbered
\( 1,2, \dots, 100 . \) Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not
more than \( 10 . \) The probability that the
minimum number on them is 5 is
A \( \cdot \frac{1}{9} \)
B. \( \frac{2}{9} \)
\( c \cdot \frac{3}{9} \)
D. \( \frac{4}{9} \)


Which of the following statements
regarding hydrogen peroxide is false?
A. It is a strong oxidising agent
B. It is decomposed by \( M n O_{2} \)
C. It behaves as a reducing agent
D. It is more stable in Basic solution


The instrument that is based on the
principle that when an object is placed between first principal focus and the optic centre of convex lens, an upright, virtual and enlarged image on the same side of the object is formed, is
A. Telescope
B. Projector
c. camera
D. simple microscope


The cost of pair of shoes is \( R s .450 . \) The
sales tax charged was \( 6 \% \). Find the bill
amount.


If \( A \) is a \( 3 \times 3 \) skew-symmetric matrix,
then the trace of \( A \) is equal to
A . -1
B.
c. \( |A| \)
D. 0


Which of the following statements are
incorrect ?
This question has multiple correct options
\( \mathbf{A} \cdot \ln B_{2} H_{6}(s) \) there are four \( 2 c-2 e^{-} \) bonds
B. \( \ln \left(\text { Si } H_{3} \text { ) }_{3} \ddot{P} \) there is back bonding \right.
\( \mathrm{C} \cdot\left(C H_{3}\right)_{3} \ddot{N} \) and \( \left(S i H_{3}\right)_{3} \ddot{N} \) are pyramidal
D. \( A l_{2} C l_{6}(s) \) has banana bonding


Find the magnetic field at \( P \) due to the
arrangement shown
A \( \cdot \frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{d}}\left(1-\frac{1}{\sqrt{2}}\right) \otimes \)
B. \( \frac{2 \mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{d}} \otimes \)
C. \( \frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{d}} \otimes \)
D. \( \frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{d}}\left(1+\frac{1}{\sqrt{2}}\right) \otimes \)


The specific heat of a gas in a polytropic process is given by
A. \( \frac{R}{\gamma-1}+\frac{R}{N-1} \)
в. \( \frac{R}{1-\gamma}+\frac{R}{1-N} \)
c. \( \frac{R}{\gamma-1}-\frac{R}{N-1} \)
D. \( \frac{R}{1-\gamma}-\frac{R}{1-N} \)


The displacement-time graph being a straight line parallel to the displacement axis implies
A . infinite velocity
B. zero velocity
c. positive velocity
D. negative velocity


Assertion
van Arkel method is used for refining of
zinc.
Reason
In this method impure metal is evaporated to obtain the pure metal as
distillate.
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 train is travelling at a speed of \( 108 k m / h . \) Brakes are applied so as to
produce a uniform retardation of \( 1 m / s^{2} . \) Find how far the train will go before it is brought to rest:
\( \mathbf{A} .800 m \)
B. \( 450 m \)
c. \( 1000 m \)
D. \( 1050 m \)


\( \lim _{n \rightarrow \infty} \frac{2^{3}-1^{3}}{2^{3}+1^{3}} \cdot \frac{3^{3}-1^{3}}{3^{3}+1^{3}} \cdots \frac{n^{3}-1}{n^{3}+1} \)
equals
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c.
D.


Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in
aircraft navigation
(b) used to treat muscular strain
(c) used as a diagnostic tool in medicine
Write in brief, how these waves can be
produced


Epidemic jaundice can occur in which of the following conditions?
A. Hepatitia A
B. Hepatitia B
c. Hepatitia c
D. Hepatitia D


A demagnetize a small ferromagnet, a current of \( 2 A \) is required to be passed
in a solenoid of length \( 20 \mathrm{cm} \) and
number of turns 100. The coercivity of
the magnet is:
B. \( 1000 A m^{-1} \)
c. \( 1250 A m^{-1} \)
D. \( 3750 A m^{-1} \)


A beam of light consisting of red, green and blue colors is incident on a rightangled prism. The refractive indices of the material of the prism for the above red, green, and blue wavelengths are \( 1.39,1.44, \) and \( 1.47, \) respectively. The prism will
A. separate part of the red color from the green and blue color
B. separate part of the blue color from the red and green color
c. separate all the three colors from one another
D. not separate even partially any color from the other two colors


The value of \( x \) is :
A . 3
B. 4
\( c .5 \)
D. 6


The gametophytic generation in pteridophytes is commonly called
A. Thallus
B. Plant body
c. Prothallus
D. Protonema


Prove that: \( \sec ^{6} \boldsymbol{A}-\tan ^{6} \boldsymbol{A}=\mathbf{1}+ \)
\( \mathbf{3} \tan ^{2} \boldsymbol{A}+\mathbf{3} \tan ^{\mathbf{4}} \boldsymbol{A} \)


Chlorine acts as bleaching agent only in
presence of :
A. Sunlight
B. Moisture
c. Dry air
D. Pure oxygen


Which one of the following is the
structure of polyacrylonitrile?
\( \left(\begin{array}{c}C H_{2}-C H \\ _{C l}\end{array}\right) \)
\( \left(\begin{array}{cc}c & c^{l} \\ C H_{2}-c & l \\ & \mid \\ c l\end{array}\right) \)
\( \left(\begin{array}{cc} & C N \\ C H_{2}- & C \\ & _{C O O C H_{3}}\end{array}\right) \)


If \( 2 x-7-5 x^{2} \) has maximum value at
\( x=a, \) then \( a=\dots \dots \)
A. \( -1 / 5 \)
в. \( 1 / 5 \)
\( c \cdot 34 / 5 \)
D. \( -34 / 5 \)


Find the absolute maximum and
minimum values of function given by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}+\mathbf{8} \) in the interval \( [\mathbf{1}, \mathbf{5}] \)


In the given figure, find
\( \angle C F B \)


In which of the following solvent/(s), aldehydes and ketones are soluble?
A. Alcohol
B. ether
c. benzene
D. All of the above


Which one of the following is not a strong electrolyte?
A. \( H C l \)
в. \( H N O_{3} \)
c. \( H_{2} S O_{4} \)
D. \( H C O O H \)


Which one of the following is an amphoteric oxide?
\( A \cdot S O_{2} \)
в. \( B_{2} O_{3} \)
\( c \cdot Z n O \)
D. \( N a_{2} O \)


A cylindrical tennis ball container can
contain maximum three ball stacked on
one another. The top and bottom balls
also touch the lid and the base of the
base of the container respectively. If the
volume of a tennis ball is \( 240 \mathrm{cm}^{3} \), then
what is the volume of the container?
A \( \cdot 1080 \mathrm{cm}^{3} \)
B. \( 840 \mathrm{cm}^{3} \)
c. \( 1440 \mathrm{cm}^{3} \)
D. \( 720 \mathrm{cm}^{3} \)


If \( X, Y, Z \) are the three sums of money
such that \( Y \) is a simple interest on \( X \)
and \( Z \) is a simple interest on \( Y \) for
same time and rate, then
\( \mathbf{A} \cdot X^{2}=Y Z \)
В. \( Y^{2}=Z X \)
c. \( Z^{2}=X Y \)
D. \( X Y Z=1 \)


Find the quotient the and remainder of the following division:
\( \left(2 x^{2}-3 x-14\right) \div(x+2) \)


Photon of frequency \( \boldsymbol{v} \) has a momentum
associated with it. If \( c \) is the velocity of
light, the momentum is :
\( \mathbf{A} \cdot v / c \)
B. hv \( c \)
c. \( h v / c^{2} \)
D. \( h v / c \)


Which of the following elements shows the property of catenation?
A .
B. Li
c. Ве
\( D \)


The electron density of \( 3 d_{x y} \) orbital in \( Y Z \) plane is:
A . 50\%
B. 95\%
c. 33.33\%
D. 0\%


With reference to a right handed system of mutually perpendicular unit vectors \( i, j, k, \alpha=3 i-j \) and \( \beta=2 i+j-3 k . \)
\( \beta=\beta_{1}+\beta_{2}, \) where \( \beta_{1} \) is parallel to \( \alpha \)
and \( \beta_{2} \) is perpendicular to \( \alpha, \) then This question has multiple correct options
A \( , \beta_{1}=\frac{3}{2} i+\frac{1}{2} j \)
в. \( \beta_{1}=\frac{3}{2} i-\frac{1}{2} j \)
c. \( _{\beta_{2}}=\frac{1}{2} i+\frac{3}{2} j-3 k \)
D. \( _{\beta_{2}}=\frac{1}{2} i-\frac{3}{2} j-3 k \)


Which of the following is correct?
A \( \cdot \vec{a} \cdot(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}+\vec{d} \cdot \vec{c} \)
В . \( \vec{a} .(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}-\vec{d} . \vec{c} \).
c. \( \vec{a} \times(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}+\vec{a} \cdot \vec{c} \)
D. All of the above


Formaldehyde polymerises to give:
A. Paraformaldehyde
B. Paraldehyde
c. Formalin
D. Formic acid


If the cube root of a number, which is 8
more than a number \( n \) equals \( -0.5, \) find
the value of \( n \)
A . -15.625
в. -8.794
c. -8.125
D. -7.875
E . 421.875


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


Peak of the density/pressure distance curve represents:
A. maximum rarefaction
B. maximum compression
c. minimum compression
D. minimum rarefacton


If 400 dollars is deposited in a bank account for 4 years at \( 8 \% \) per annum. Compare interest using simple interest formula and compound interest formula

This question has multiple correct options
A . \( \mathrm{Cl}=144.195 \)
B. \( \mathrm{S} 1=200 \)
c. \( \mathrm{c} 1>\mathrm{s} \)
D. SI <C


\( \lim _{x \rightarrow-1^{+}} \frac{\sqrt{\pi}-\sqrt{\cos ^{-1} x}}{\sqrt{x+1}} \) is equal to
A \( \cdot \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{2 \pi}} \)
c. \( \frac{1}{\sqrt{\pi}} \)
D. none of these


Find the values of \( c \) that satisfy the MVT
for integrals on [-2,3]
\( \boldsymbol{f}(\boldsymbol{t})=\mathbf{8} \boldsymbol{t}+\boldsymbol{e}^{-\boldsymbol{3} \boldsymbol{t}} \)
В. \( c=-0.0973 \)
c. \( c=1.0973 \)
D. \( c=0.0973 \)


For \( \mathrm{NADPH}+\boldsymbol{H}^{+} \) formation
A . only PS lis required
B. only PS II is required
c. both PS I and PS I I are required
D. only stroma is required


The acceleration of free fall for object moving near the surface of Earth is:
A \( \cdot 9.81 m s^{-2} \)
B. \( 9.31 m s^{-2} \)
c. \( 8.81 m s^{-2} \)
D. \( 10.81 m s^{-2} \)


Which oxide of nitrogen exist as hydrated form in solid state.
A. Nitrous oxide
B. Nitrogen trioxide
c. nitrogen dioxide
D. Nitrogen pentaoxide


Probability of getting a prime (or) composite is
A. Mutually exclusive
B. Likely
c. 0
D. None


The magnetic filed (dB) due to smaller element (dl) at a distance \( (\vec{r}) \) from element carrying current i, is
\( ^{\mathbf{A}} \cdot d B=\frac{\mu_{0} i}{4 \pi}\left(\frac{\vec{d} l \times \vec{r}}{r}\right) \)
B. \( d B=\frac{\mu_{0} i}{4 \pi} i^{2}\left(\frac{\vec{d} l \times \vec{r}}{r^{2}}\right) \)
\( ^{\mathbf{c}} d B=\frac{\mu_{0} i^{3}}{4 \pi} i\left(\frac{\vec{d} l \times \vec{r}}{2 r^{2}}\right) \)
\( ^{\mathrm{D}} d B=\frac{\mu_{0}}{4 \pi} i\left(\frac{\vec{d} l \times \vec{r}}{r^{3}}\right) \)


When copper is treated with a certain
concentration of nitric acid, nitric oxide
and nitrogen dioxide are liberated in equal volumes according to the equation:
\( \boldsymbol{x} \boldsymbol{C u}+\boldsymbol{y} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \longrightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( N O+N O_{2}+H_{2} O \)
The coefficients of \( x \) and \( y \) are
respectively:
\( A \cdot 2 \) and 3
B. 2 and 6
c. 1 and 3
D. 3 and 8


Which of the following statement about hydrogen spectrum are correct? This question has multiple correct options
A. All the lines of Lyman series lie in ultraviolet region
B. All the lines of Balmer series lie in visible region
C. All the lines of Paschen series lie in infrared region
D. None of the above


What is the purpose of anode in a
Cathode ray tube?
A. To provide potential energy to electrons
B. To provide kinetic energy to protons
C . To provide potential energy to protons
D. To provide kinetic energy to electrons


If \( \frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x-y}{4} \)
then the values of \( x \) and \( y \) is
A \( . x=1, y=3 \)
B. \( x=5, y=2 \)
c. \( x=3, y=3 \)
D. \( x=2, y=6 \)


Find the remainder when \( p(x)=x^{3}+ \)
\( 3 x^{2}+3 x+1, \) is divided by \( x \)
\( A \)
B.
\( c \cdot-1 \)
D.


A farmer wishes to start a 100 sq.m
rectangular vegetable garden. since he has only \( 30 \mathrm{m} \) barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the
dimension of the garden.
A. \( 20 m, 5 m \) or \( 10 m, 10 m \)
В. \( 2 m, 5 m \) or \( 10 m, 10 m \)
\( \mathrm{c} .20 \mathrm{m}, 5 \mathrm{m} \) or \( 1 \mathrm{m}, 10 \mathrm{m} \)
D. None of these


The oxide of nitrogen which forms dimer
is


Atom is the word derived from the Greek
word atomio, which means:
A. uncutable
B. cutable
c. in between
D. combined


In the given fig. if \( A D=B C \) and \( A D \| B C \)
then:
\( A, A B=A D \)
B. AB = DC
\( c \cdot B C=c D \)
D. None


After karyogamy followed by meiosis, spores are produced exogenously in
A. Agaricus
B. Neurospora
c. saccharomyces
D. Alternaria


Draw the graph of straight line \( y= \)
\( -2 x+3 . \) Use your graph to find the
area between the line and co-ordinate
axes.
A. 4.66 sq.units
B. 3.25 sq.units
c. 2.25 sq.units
D. 5.66 sq.units


Which of the following is/are example(s) of induced radioactivity
reaction?
Select correct statement(s)
A. Photon or particle is ionised and collected by the positive electrode in a Geiger counter
B. A scintillation counter contains a phosphor, a substance that emits a flash of light when struck by a photon or particle.
c. Both of the above
D. None of the aobve


At which temperature do the readings of the celcius and the Fahrenheit scales
coincide?
A . 0
в. 100
\( c .-40 \)
D. -80
E. None of the above


A block of carbon, \( 1.0 \mathrm{cm} \) by \( 2.0 \mathrm{cm} \) by
\( 5.0 \mathrm{cm}, \) has a resistance of 0.015
between its two smaller faces. What is
the resistivity of carbon?
A \( \cdot 1 \times 10^{-8} \Omega m \)
В. \( 2 \times 10^{-8} \Omega m \)
c. \( 4 \times 10^{-5} \Omega m \)
D. \( 6 \times 10^{-8} \Omega m \)


Rajkumar said to you that the magnetic field lines are open and they start at north pole of bar magnet and end at south pole. What questions do you ask Rajkumar to correct him by sayingfield lines are closed?


Which of the following is true in context
of Eddy currents?
A. By Lenz's law, an eddy current creates a magnetic field that opposes the magnetic field that created it.
B. Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faraday's law of induction
C. Eddy currents are a cause of energy loss in alternating current (AC) inductors, transformers, electric motors and generators etc.
D. All of the above


Pollution due to sewage can be reduced by
A. Creating separate chemical toilets.
B. Constructing septic tanks.
c. Letting off drainage in rivers.
D. Both A and B


If \( y \) is a function of \( x, \) then \( \frac{d^{2} y}{d x^{2}}+ \) \( y \frac{d y}{d x}=0 . \) If \( x \) is a function of \( y, \) then the
equation becomes
A \( \cdot \frac{d^{2} x}{d y^{2}}+x \frac{d x}{d y}=0 \)
в. \( \frac{d^{2} x}{d y^{2}}+y\left(\frac{d x}{d y}\right)^{3}=0 \)
c. \( \frac{d^{2} x}{d y^{2}}-y\left(\frac{d x}{d y}\right)^{2}=0 \)
D \( \cdot \frac{d^{2} x}{d y^{2}}-x\left(\frac{d x}{d y}\right)^{2}=0 \)


A moving electron has kinetic energy \( \boldsymbol{K} \) When a certain amount of work is done, it moves with one quarter of its velocity in opposite direction. Find the work in
terms of \( \boldsymbol{K} \)
A \( \cdot \frac{-15}{16} K \)
в. \( \frac{-17}{16} K \)
c. \( \frac{-5}{4} K \)
D. \( \frac{-3}{4} K \)


Both isotopes and isobars differ in their chemical properties. (True/False)


If \( a, b, c \) form a system of linearly independent vectors then show that the
system of vectors \( a-2 b+c, 2 a-b+c \)
and \( 3 a+b+2 c \) is also linearly
independent.


Aluminium is usually found in +3 oxidation state. In contrast, thallium
exists in +1 and +3 oxidation states.
This is due to:
A. lanthanoid contraction
B. lattice effect
c. diagonal relationship
D. inert pair effect


Gloal warming is a serious outcome of:
A. water pollution
B. land pollution
c. industrial pollution
D. none of the above


The diameters of two steel wires are in
the ratio \( 2: 3 . \) Their lengths are equal When same force is applied on them, the ratio of the elongation produced is
A .4: 9
B. 9: 4
c. 3: 2
D. 2: 3


Which of the following act for protection of body (defensive) in some Protozoa?
A. Nematocysts
B. Statocysts
c. Lasso cells
D. Trichocyst


Which is less acidic than phenol?
This question has multiple correct options
A. 2,4,6-Trimethyl phenol
в. \( C H_{3} \) ОН
c. p-Nitropheno
D. \( H_{2} O \)


Chlorobenzene is prepared commercially by
A. Raschig process
B. Wurtz Fitting reaction
c. Friedel-craft's reaction
D. Grignard reaction


An object executing SHM has an acceleration of \( 0.2 m / s^{2} \) at a distance of \( 0.05 m \) from position. Calculate the period of SHM in seconds.
A . 2.1435
B. 3.1428
c. 1.432
D. 4.321


Which graph best illustrates the electric potential along the \( x \) axis, from \( x=-a \operatorname{tox}=a ? \)
\( A \)
B. I
c. ॥॥
D. IV


A path 7 meters wide surrounds a
circular lawn \( 252 \mathrm{m} \) in diameter. Find
the area of path.


BOD of two samples of water A and B were \( 120 \mathrm{mg} / \mathrm{l} \) and \( 400 \mathrm{mg} / \mathrm{l} \)
respectively. Which sample is more polluted.


Tax on imports is an example of
A. Indirect tax
B. Trade barrier
c. Sales tax
D. Direct tax


Find the correct match
\( A \)
\( A-3, B-6, C-2, D-5, E-4 \)
, E -
B. \( A-5, B-2, C-3, D-6 \)
\( C \cdot A-3, B-1, C-2, D-5, E-4 \)
D. \( A-4, B-6, C-5, D-2 \)


Hypermetropia is a synonym for:
A. Short-sight defect
B. Long sight defect
c. Bad vision due to old age
D. None of these


\( \int e^{x} \cos x d x=\frac{e^{x}}{2} f(x)+C \) then range of
\( f(x) \$ \$=\dots \)
A . [0,1]
в. [-1,1]
c. [-1,0]
D. \( [-\sqrt{2}, \sqrt{2}] \)


Evaluate: \( \lim _{x \rightarrow 2} \frac{x-2}{\sqrt{x+2}-2} \)


A sphere of radius \( r \) lies inside a cube
and touches each of the six sides of the
cube. Calculate the volume of the cube
in terms of \( r \)
A \( \cdot r^{3} \)
B \( .2 r^{3} \)
\( c \cdot 4 r^{3} \)
D. \( \frac{4}{3} \pi r^{3} \)
E \( .8 r^{3} \)


Which of the following statement is
incorrect?
A. Non-metals are electro-positive in nature
B. Metals are electro-positive in nature
C. Metals are present on the left hand side of the periodic table
D. Non-metals are present on the right hand side of the periodic table


Evaluate:
\[
\begin{array}{l}
\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\tan ^{-1}(-\sqrt{3})+ \\
\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)
\end{array}
\]


The maximum number of hydrogen
bonds that can be formed by a water
molecule are:


Write one word for each of the following:
(a) A group of similar cells to perform a specific function.
(b) Cells least specialised in the plants.
(c) Cells responsible for increase in diameter of the stem and root of dicot
plants.


The maximum speed of a particle o a
trailing wave is \( v_{0}, \) then find the speed
of a particle wen the displacement is half of the maximum value
A \( \cdot \frac{v_{0}}{2} \)
в. \( \frac{\sqrt{3} v_{0}}{2} \)
c. \( \frac{\sqrt{3} v_{0}}{4} \)
D. \( v_{0} \)