Two long thin conductors \( 10 \mathrm{cm} \) apart
carry currents in the ratio 1: 2 in the
same direction. The magnetic field
midway between them is \( 2 \times 10^{-3} \)
Tesla. The force on 1 metre length of any conductor will be :
\( \mathbf{A} \cdot 2 \pi \times 10^{-3} \) Newton
B. \( 2 \times 10^{-3} \) Newton
c. \( \pi \) Newton
D. 1 Newton


kg of \( _{\text {一一一一一一一一 }} \) can light up 1 bulb
for \( 3 \times 10^{4} \) years.
A. Uranium
B. Halonium
c. Neutronium
D. Hydronium


Which of the following system exchanges only energy but not matter?
B. close system
c. Isolated system
D. None of the above


Write a note on Haemoglobin.


The product \( ^{\prime} X^{\prime} \) on oxidation with
HIO gives:

This question has multiple correct options
A. \( H C H O \)
в. \( C H_{3}-C H O \)
\( c \cdot c o_{2} \)
D. \( H C O O H \)


The ratio of the maximum velocity and maximum displacement of a particle executing SHM is equal to
\( A \cdot n \)
B. \( g \)
c.
\( D . \)


Units of average rate of reaction is:
\( A \cdot \sec ^{-1} \)
B. mole sec \( ^{-1} \)
c. mole \( \mathrm{dm}^{-3} \mathrm{sec}^{-1} \)
D. unitless


If \( 3 y=y+2, \) calculate the value of \( 2 y \)
A .
B . 2
\( c \cdot 3 \)
D. 4


Figure shows a piece of semiconductor pure one) \( \mathrm{S} \) in series with a variable
resistors \( \mathrm{R} \) and a source of constant
voltage \( V . S \) is heated and the current is
kept constant by adjustment of R. Which of the following factors will decrease during the precess?
1. The drift velocity of the conduction electrons in S.
2. The DC resistors of \( S \)
3. The number of conduction electrons
in S.
A. Only 1
B. 1 and 2
c. \( 1,2, \) and 3
D. only


Voice is high pitched in
A. Ages persons
B. Adult males
c. Boys
D. Females


When less amounts of oxygen is present, carbon combines with it to give
gas.
A. carbon dioxide
B. carbon monoxide
c. carbonate
D. none of these


In an A.P., if the first term is 22 , the
common difference is -4 and the sum
to \( n \) terms is \( 64, \) find \( n \)


Find limits of the error when \( \frac{\mathbf{9 1 6}}{\mathbf{1 9 1}} \) is taken for \( \sqrt{\mathbf{2 3}} \)


Which of the following can be made into crystal?
A. Bacterium
B. Amoeba
c. virus
D. None of these


State the cause of dispersion of white light by a glass prism. How did Newton, using two identical glass prisms, show that white light is made of seven colors? Draw a ray diagram to show the path of a narrow beam of white light, through a combination of two identical primes arranged together in inverted position with respect to each other, when it is allowed to fall obliquely on one of the
faces of the first prism of the combination.


Calculate the given expression in the Kelvin scale
\( \frac{\left(24^{3}-21^{3}-3 \times(24)^{2}(21)+3 \times 24 \times\right.}{27} \)
where all numbers are in Celsius scale.
A. 300 к
B. 274 к
c. 282 к
D. 273 к


Select the correct statements with
reference to pheretima (excretory system)
A) Nephridia help in excretion and osmoregulation
B) Septal nephridia collects the wastes from coelomic fluid with the help of
nephrostomes
C) Integumentary nephridia discharge waste materials to the outer body surface through the nephridiopores
D) Septal nephridia and pharyngeal nephridia discharge wastes into luman of gut.
A. \( A, B, C \)
в. \( B, C, D \)
c. \( A, C, D \)
D. \( A, B, C, D \)


To which of the following category does ice-cream belong?
A. Solution
B. Emulsion
c. Element
D. Suspension


A uniform thin circular ring of mass 'M' and radius 'R' is rotating about its fixed axis, passing through its centre and perpendicular to its plane of rotation, with a constant angular velocity \( \omega . \) Two objects each of mass \( \mathrm{m}, \) are attached
gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity of :
A \( \cdot \frac{\omega M}{(M+m)} \)
в. \( \frac{\omega M}{(M+2 m)} \)
c. \( \frac{\omega M}{M-2 m} \)
D. \( \frac{\omega(M+3 m)}{M} \)


The bodies of different masses \( m_{a} \) and
\( m_{b} \) are dropped from two different
heights i.e., a and b. The ratio of time taken by both bodies to drop through these distance is :
A \( \cdot \sqrt{a}: \sqrt{b} \)
В \( \cdot \frac{m_{a}}{m_{b}}: \frac{b}{a} \frac{b}{a} \)
\( c \cdot a: b \)
\( \mathbf{D} \cdot a^{2}: b^{2} \)


Cells are the basic structural units of
living organisms'. Explain.


Which of the following is correct?
A. The value of \( g \) is constant throughout
B. \( g \propto \frac{1}{r^{2}} \)
C \( . g \) is slightly less (by about \( 1 \% \) ) when distance \( <200 m \)
D. \( g \) is slightly greater when distance \( <200 m \)


Check whether 7,49,343 are in
continued proportion or not


An equilateral triangle has area \( A \mathrm{cm}^{2} \) A regular hexagon of maximum area is cut off from the triangle. If the area of
the hexagon is \( 320 \mathrm{cm}^{2} \), then the area \( A \)
is
A \( \cdot 640 \mathrm{cm}^{2} \)
в. \( 480 \mathrm{cm}^{2} \)
\( c \cdot 600 c m^{2} \)
D. \( 400 \mathrm{cm}^{2} \)


Which of the following set of reaction
\( R-C-O H \) as the can not prepare
final product?
A \( \cdot R-M g X+O=C=O \frac{d r y \cdot e t h e r}{\longrightarrow} A \frac{H_{3} O^{+}}{\longrightarrow} \)
в. \( R-C N \frac{S n\left(l_{2}+H C l\right.}{(i i) H_{2} O / H^{+}} \)
\( c \)
D. \( C H_{3}\left(C H_{2}\right)_{8} C H_{2} O H \frac{C r O_{3}}{H_{2} S O_{4}} \)


A car increases its speed from 20 km /
to \( 50 k m / h \) in 10 seconds. Its
acceleration is
A \( \cdot 30 m s^{-2} \)
B . \( 3 m s^{-2} \)
\( \mathrm{c} \cdot 18 \mathrm{ms}^{-2} \)
D. None of these


A machine gun is mounted on the top of
a tower 100 m high. At what angle
should the gun be inclined to cover a maximum range of firing on the ground below? The muzzle speed of bullet is \( 150 m s^{-1} . \) Take \( g=10 m s^{-2} \)


Foramen of Panizza is associated with
A. Brain of reptiles
B. Brain of rabbit
c. Lung of lizardd
D. Heart of crocodile


Abhay made a straight cut through a circular rubber band and then laid the
rubber band flat, as shown in the figure.
Which measure corresponds to the
length of the cut rubber band?
A. Chord
B. Circumference
c. Diameter
D. Radius


\( 4 L \) of \( 0.02 M \) aqueous solution of \( N a C l \)
was diluted by adding \( 1 L \) of water. The
molarity of the resultant solution is:
\( \mathbf{A} \cdot 0.004 \)
B. 0.008
c. 0.012
D. 0.016


If \( \lim _{x \rightarrow-2} \frac{x^{p}+2^{p}}{x+2}=80 \) (where \( p \) is an odd
number), then \( p \) can be
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
D. 9


The given compound is:
A. E form
B. Z form
C. Both of these
D. None of these


Most widely accepted theory of carbohydrate translocation is
A. Mass flow theory
B. Root pressure theory
c. Imbibition theory
D. Transpiration theory


Large crystals of pure substances can be formed from their solutions during
A. crystallization
B. evaporation
c. expansion
D. contraction


Calculate the induced emf in the loop if
the current in both the wires is
changing at the rate \( \boldsymbol{d} \boldsymbol{i} / \boldsymbol{d} \boldsymbol{t} \)


\( p^{3}-(p+1)^{3}=? \)
\( \mathbf{A} \cdot-3 p^{2}-3 p+1 \)
B \( .-3 p^{2}-3 p-1 \)
\( \mathbf{c} \cdot-3 p^{2}+3 p+1 \)
D. \( -3 p^{2}+3 p-1 \)


Lauryl alcohol on treatment with
\( H_{2} S O_{4} \) followed by neutralisation forms a product which is:
A. cationic detergent
B. anionic detergent
c. neutral detergent
D. antidepressant


A letter is known to have come eithe
from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from
London?
A \( \cdot \frac{12}{17} \)
в. \( \frac{5}{17} \)
c. \( \frac{5}{12} \)
D. \( \frac{7}{12} \)


The fruity smell is of a/an:
A. aldehyde
B. ketone
c. alcoho
D. ester


A bar magnet is \( 10 \mathrm{cm} \) long is kept with its north (N)-pole pointing north. A neutral point is formed at a distance of \( 15 \mathrm{cm} \) from each pole:Given the horizontal component of earth's field is 0.4 Gauss, the pole strength of the magnet is
\( A \cdot 9 A-m \)
B. 6.75 A-m
c. 27 A-m
D. 1.35 A-m


Biogas plant is more useful than burning of dung cakes because
A. It is non-pollutant
B. It yields manure as well as fuel gas.
c. It yields important biochemicals.
D. Both A and B


The steam roller is a cylinder \( 56 \mathrm{cm} \) in
diameter and \( 120 \mathrm{m} \) in length,what are
of the road will it cover in 100
revolutions?


An open tank with a square base and
vertical side is to be constructed a
metal sheet so as to hold a given quantity of water. Show that the cost of the material will be least when depth of
the tank is half of its width.


Sound travels faster in gases when compared to solids and liquids.


For the reaction \( 2 N H_{3} \rightarrow N_{2}+3 H_{2} \)
\( \mathbf{f}-\frac{\boldsymbol{d}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right]}{\boldsymbol{d} t}=\boldsymbol{k}_{1}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right], \frac{\boldsymbol{d}\left[\boldsymbol{N}_{2}\right]}{\boldsymbol{d} t}= \)
\( \boldsymbol{k}_{2}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right], \frac{\boldsymbol{d}\left[\boldsymbol{H}_{2}\right]}{\boldsymbol{d} t}=\boldsymbol{k}_{3}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right] \)
then the relation between \( k_{1}, k_{2} \) and \( k_{3} \)
is?
\( \mathbf{A} \cdot k_{1}=k_{2}=k_{3} \)
B. \( k_{1}=3 k_{2}=2 k_{3} \)
c. \( 1.5 k_{1}=3 k_{2}=k_{3} \)
D \( \cdot 2 k_{1}=k_{2}=3 k_{3} \)


Find the \( 20^{t h} \) term and \( n^{t h} \) term of the
following G.P.5, 25, 125,....


The sum of the series
\( \sum_{r=1}^{n}(-1)^{r-1} \cdot^{n} C_{r}(a-r) \) is
\( A \)
B.
c. \( n .2^{n-1}+a \)
D. None of these


\( 1^{s t} \) law of thermodynamics is not adequate in presenting the direction of
process.
A. True
B. False


Two coherent waves are described by
the expressions \( E_{1}=E_{0} \sin \left(\frac{2 \pi x_{1}}{\lambda}-2 \pi f t+\frac{\pi}{6}\right) \)
\( E_{2}=E_{0} \sin \left(\frac{2 \pi x_{2}}{\lambda}-2 \pi f t+\frac{\pi}{8}\right) \)
Determine the relationship between \( \boldsymbol{x}_{1} \)
and \( x_{2} \) that produces constructive
interference when the two waves are
superposed


Find the horizontal velocity of the
particle when it reach the point \( Q \) Assume the block to the frictionless.
take \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
A \( \cdot v=3.13 \frac{m}{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{g} \mathrm{m} / \mathrm{s} \)
D. \( 3.6 \mathrm{m} / \mathrm{s} \)


The difference between a rectangle and
a cube is
A. Rectangle is B-dimensional and cube is 2 dimensional.
B. Rectangle and cube are both 2-dimensional
C. Rectangle is 2-dimensional and cube is 3dimensional.
D. None of these


A coil of area \( 500 \mathrm{cm}^{2} \) having 1000 turns
is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude \( 410^{-5} \)weber \( / m^{2} \). If it is
rotated by 180 degree about an axis passing through one of its diameter in
\( 0.1 \mathrm{sec}, \) find the average induced emf.
A. zero
в. \( 30 m V \)
\( \mathrm{c} .40 \mathrm{mV} \)
\( \mathbf{D} .50 \mathrm{mV} \)


The delay in transmission from the
dorsal to the ventral root across the
spinal cord for the reflex pathways' \( A \) ', B', 'D' and 'C' respectively is 0.5 ms,1.0 \( \mathrm{ms}, 1.5 \mathrm{ms}, \) and \( 2.0 \mathrm{ms} \). Identify the correct option: (Average synaptic delay \( =0.5 \mathrm{ms} \)
A. A=monosynaptic, B=bisynaptic, C=trisynaptic
B. A=monosynaptic, B= trisynaptic, D=bisynaptic
c. A=monosynaptic, C=trisynap tic, D=quadrisynaptic
D. A=monosynaptic, D=trisynaptic, C=quadrisynaptic


The surface of water in contact with
glass wall is
A . Plane
B. concave
c. convex
D. Both b and c


What is the minimum pH of a solution
\( 0.10 M \) in \( M g^{2+} \) from which \( M g(O H)_{2} \)
will not precipitate? \( \boldsymbol{K}_{s p} \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}= \)
\( \mathbf{1} . \mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 1}} \mathbf{M}^{\mathbf{3}} \)


Let \( f(x) \) be differentiable on the interval
\( (0, \infty) \) such that \( f(1)=1, \) and \( \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1 \) for \( \operatorname{each} x>0 \)
Then \( f(x) \) is
A \( \frac{1}{3 x}+\frac{2 x^{2}}{3} \)
в. \( -\frac{1}{3 x}+\frac{4 x^{2}}{3} \)
c. \( -\frac{1}{x}+\frac{2}{x^{2}} \)
D.


If \( \operatorname{Re}(a), \operatorname{Re}(b)>0, \) and \( x=|a-b| \)
\( |\bar{a}+b|, \) then
\( \mathbf{A} \cdot x<0 \)
B . \( x>0 \)
c. \( x \geq 1 \)
D.


If the polynomial \( \left(x^{3}-3 x^{2}+a x+18\right) \)
is divided by \( (x-4), \) the reminder is 58
Find the value of a.


When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increase the internal energy of gas is?
\( A \cdot \frac{2}{5} \)
B.
\( c \cdot \frac{3}{7} \)
\( D \cdot \frac{5}{7} \)


The propagation constant of wave is also called its
A. wavelength
B. frequency
c. wave number
D. angular wave number


Given that \( \bar{X} \) is the mean and \( \sigma^{2} \) is the
variance of \( n \) observations \( X_{1}, X_{2} \dots X_{n} \)
Prove that the mean and variance of the
observations \( a X_{1}, a X_{2}, a X_{3} \ldots a X_{n} \) are
\( a^{-} x \) and \( a^{2} \sigma^{2} \) respectively \( (a \neq 0) \)


The sum of the acute angles of an
obtuse triangle is \( 70^{\circ} \) and their
difference is \( 10^{\circ} . \) The largest angle is:
A \( \cdot 110^{\circ} \)
B. 105
\( c \cdot 100^{\circ} \)
D. \( 95^{\circ} \)


Indicate to what extent the following will conduct electricity and given the mechanism of conduction in each case:
NaCl (aqueous solution)


Electric charge is measured in
A . coulombs
B. amperes
c. volts
D. watts


If \( i_{1}=3 \sin \omega t \) and \( i_{2}=4 \cos \omega t, \) then \( i_{3} \)
is
\( \mathbf{A} \cdot 5 \sin \left(\omega t+53^{\circ}\right) \)
\( \mathbf{B} \cdot 5 \sin \left(\omega t+37^{\circ}\right) \)
\( \mathbf{c} \cdot 5 \sin \left(\omega t+45^{\circ}\right) \)
\( \mathbf{D} \cdot 5 \cos \left(\omega t+53^{\circ}\right. \)


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


Which of the following metals is not extracted by leaching?
A. Aluminium
B. Mercury
c. silver
D. Gold


Transition elements does not show:
A. paramagnetism
B. colour
c. fixed valency
D. all of these


\( \mathbf{A} \)
\( 3 \Omega \) resistor as shown in fig is dipped
in to a calorimeter containing \( \boldsymbol{H}_{2} \boldsymbol{O} \). the
thermal capacity of \( H_{2} O+ \) calorimeter is 2000 J/K. If the circuit is active for 15
minutes find the rise in temperature of
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot 2.4^{\circ} \mathrm{C} \)
В. \( 2.9^{\circ} \mathrm{C} \)
\( c \cdot 3.4^{\circ} C \)
D. \( 1.9^{\circ} \mathrm{C} \)


Find the minimum value of a, such that
function \( f(x)=x^{2}+a x+5, \) is
increasing in interval [1,2]


\( 50 \mathrm{ml} \) of \( 0.2 \mathrm{M} \) solution of a compound
with empirical formula \( \boldsymbol{C o C l}_{3} \cdot \boldsymbol{4} \boldsymbol{N} \boldsymbol{H}_{3} \)
on treatment with excess of
\( A g N O_{3}(a q) \) yields 1.435 g of \( A g C l \)
(white ppt).
Ammonia is not removed by treatment
with concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \mathbf{0}_{\mathbf{4}} \)
The formula of the compound is:
\( \mathbf{A} \cdot \operatorname{Co}\left(N H_{3}\right)_{4} C l_{3} \)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{3}\right. \)
D. \( \left[\operatorname{CoCl}_{3}\left(N H_{3}\right)\right] N H_{3} \)


How many sides does a regular polygon have if the measure of an exterior angle
is \( 24^{0} ? \)
A . 14
B. 13
c. 15
D. 18


Which of the statements given below is
incorrect?
A. \( O N F \) is isoelectronic with \( O_{2} N^{-} \)
B. \( O F_{2} \) is an oxide of fluorine
c. \( C l_{2} O_{7} \) is an anhydride of perchloric acid
\( \mathrm{D} \cdot O_{3} \) molecule is bent


When Halogens are treated with hot and conc. alkalis,major products formed
are:
This question has multiple correct options
A. Hypohalite
B. Halite
c. Halate
D. Halide


Psilophytes, lycophytes, horsetails, and
ferns are plants
A. Multicellular aquatic
B. Seedless vascular
c. Diploid dominant
D. Seed bearing vascular


Which one of the following is mismatched?
A . Fossil fuel burning- Release of \( C O_{2} \)
B. Nuclear power- Radioactive wastes
c. Solar energy- Green house effect
D. Biomass burning- Release of \( C O_{2} \)


If \( A=\{1,2,3\} B=\{4,5\}, \) then find \( A-B \)
\( A \cdot\{1,4,5\} \)
B. \{1,4,3\}
\( c \cdot\{1,2,3\} \)
\( D \cdot\{4,5\} \)


Itd - matic
major product is
\( A \)
\( B \)
\( c \)
D.


Two samples \( A \) and \( B \) of a gas initially at the same pressure and temperature are compressed from volume \( V \) to \( \frac{V}{2}(A \) isothermally and \( B \) adiabatically). The
final pressure of \( \boldsymbol{A} \) is
A. greater than the final pressure of \( B \)
B. equal to the final pressure of \( B \)
c. less than the final pressure of \( B \)
D. twice the final pressure of \( B \)


Two isolated, charged conducting spheres of radii a and b produce the same electric field near their surfaces.
The ratio of electric potentials on their
surfaces is :
A \( \cdot \frac{a}{b} \)
B. \( \frac{b}{a} \)
c. \( \frac{a^{2}}{b^{2}} \)
D. \( \frac{b^{2}}{a^{2}} \)


How many meninges are there to protect the brain?
A. one
B. Two
c. Three
D. Four


Electromotive Force (EMF) may be
defined as:
A. work done per coulomb on the charge.
B. drift velocity of electrons
c. flow of electron.
D. the number of coulombs of charge per second


\( \forall n \in N ; x^{2 n-1}+y^{2 n-1} \) is divisible by?
A. \( x-y \)
B. \( x+y \)
c. \( x y \)
D. \( x^{2}+y^{2} \)


Which number is represented by \( A \), in the following number line?
A . 13
в. \( \frac{6}{13} \)
c. 6
D. \( \frac{0}{13} \)


In positive logic, the logic state 1
corresponds to
A. positive voltage
B. zero voltage
c. lower voltage level
D. higher voltage leve


Contrapositive of the statement "if two number are not equal then their square are not equal is ;
A. If the squares of two number are equal, then the number are not equal
B. If the squares of two number are equal, then the number are equal
C. If the square of two number are not equal then number are equal
D. If the square of two number are not, equal, then the number are not equal


The cell constant of a given cell is \( 0.47 \mathrm{cm}^{-1} . \) The resistance of a solution
placed in this cell is measured to be
31.6 ohm. The conductivity of the
solution \( \left(\text { in } S c m^{-1} \text {where } S \) has usual \right.
meaning) is :
A . 0.15
в. 1.5
c. 0.015
D. 150


(a) Draw the circuit diagram for
studying the characteristics of a
transistor in common emitter
configuration. Explain briefly and show how input and output characteristics are drawn.
(b) The figure shows input waveform \( A \)
and \( \mathrm{B} \) to a logic. Draw the output
waveform for an OR gate. Write the truth
table for this logic gate and draw its logic symbol.


It is commonly believed that only roots develop below the ground. How would you prove that potato tuber is a stem
and not a root?


Give the IUPAC names for the given
compound


\( 100 m l 0.1 M H_{2} O_{2} \) is mixed with
\( 400 m l 0.5 M H_{2} O_{2} . \) The volume of
\( 0.1 M K M n O_{4}(\text { acidic }) \) required to
react with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) mixture is :
A. \( 840 \mathrm{ml} \)
B. 420 m1
\( c .630 \mathrm{ml} \)
D. None of these


In a tug-of-war contest, two men pull on a horizontal rope from opposite sides. The winner will be the man who:
A. exerts greater force on the rope
B. exerts greater force on the ground
c. exerts a force on the rope which is greater than the tension of the rope
D. makes a smaller angle with the vertical


A ray of light travels from air into a perspex block of refractive index 1.5 at
an angle of incidence of \( 45^{0} \). Calculate
the angle of the refraction of the ray at air-to perspex boundary and at perpexto-air boundary
A \( \cdot 28^{0} 7^{\prime} \)
B . \( 25^{0} 87^{\prime} \)
\( \mathbf{c} \cdot 25^{0} \eta^{\prime} \)
D. \( 28^{0} 27^{\prime} \)


Radioactive thymidine is fed to cells about to enter S-phase. It will make
radioactive
A. Euchromatin
B. Heterochromatin
c. Both A and B
D. Neither euchromatin nor heterochromatin


The \( V-t \) graph is shown in the figure for
particle the \( (V m / s) \) acceleration of
particle is
A \( \cdot 22.5 m / s^{2} \)
B. \( 5 m / s^{2} \)
\( \mathbf{C} \cdot-5 m / s^{2} \)
\( \mathbf{D} \cdot-3 m / s^{2} \)


What is cell division? Write two types of cell division?


What can you as an individual do to reduce your consumption of the various
natural resources?


Which of the following is not a factor in determining rate of photosynthesis?
A. \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \)
B. \( \mathrm{cO}_{2} \)
c. ATP
D. Light


Point out incorrect stability order.
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+}<\left[C u(e n)_{2}\right]^{2+}<[C u(\text {trien})]^{2+} \)
\( ^{\mathbf{B}} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3+}<\left[F e\left(N O_{2}\right)_{6}\right]^{3-}<\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
\( ^{\mathbf{C}} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{3+}<\left[R h\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Ir}\left(H_{2} O\right)_{6}\right]^{3+} \)
\( ^{\mathrm{D}} \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{+}<\left[C r\left(N H_{3}\right)_{6}\right]^{2+}<\left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)


What is the role of father in child
development?


What do global problems mean? Which are the global problems that organisms are facing today?


The current voltage graph for a given
metallic wire at two
different temperatures \( T_{1} \) and \( T_{2} \) are
shown in given figure, which of the relation is correct from the following?
A \( \cdot T_{2}>T_{1} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}=T_{2} \)
D. none of these


Catalytic converters, which are fitted into automobiles for reducing the emission of poisonous gases possess which of the following metals as catalyst?
A. Platinum-Palladium
B. Rhodium
c. Lead
D. Both (a) and (b)


An ecosystem contains
This question has multiple correct options
A. Producers
B. Decomposers
c. Lentic
D. Xeric


Assertion (A): Corpuscular theory fails in explaining the velocity of light in air
to water.

Reason (R) : According to corpuscular theory, light should travel faster in denser media than in rarer media.
A. A and R are true R is correct explanation for A
B. A and R are true R is not correct explanation for A
c. A is true but R is false
D. A is false but R is true


What is an expression for the force due to gravity on a body of mass \( m \) ?
\( \mathbf{A} \cdot F=0 \)
В. \( F=m / g \)
c. \( F=g \)
D. \( F=m g \)


If the road of the previous problem is horizontal (no banking), what should be the minimum friction coefficient so
that a scooter going at \( 18 \mathrm{km} / \mathrm{h} \) does not
skid?
A . 0.15
B. 0.2
\( c .0 .25 \)
D. 0.5


Which of the statements are true about
the law of chemical combination?
This question has multiple correct options
A. Potassium combines with two isotopes of chlorine \( \left.^{35} C l \text { and }^{37} C l\right) \) to form two samples of \( K C l . \) Their
formation follows the law of definite composition.
B. Different proportions of oxygen in the various oxides of sulphur proves the law of multiple proportions.
\( \mathrm{C} \cdot H_{2} \mathrm{O} \) and \( \mathrm{H}_{2} S \) contain \( 11.11 \% \) hydrogen and \( 5.88 \% \) hydrogen respectively whereas \( S O_{2} \) contains \( 50 \% \) sulphur. The above data prove the law of reciprocal proportions.
D. In the decomposition of \( N H_{3}\left(2 N H_{3} \stackrel{\Delta}{\longrightarrow} N_{2}+3 H_{2}\right) \)
the ratio of volumes of \( N H_{3}, N_{2} \) and \( H_{2} \) is \( 2: 1: 3 . \) The above data proves the Gay Lussac's law.


\( \int \frac{\boldsymbol{a}^{\boldsymbol{x}}}{\sqrt{\mathbf{1}-\boldsymbol{a}^{2 \boldsymbol{x}}}} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{1}{\log a} \sin ^{-1}\left(a^{x}\right)+c \)
B. \( \frac{1}{\log a} \sinh \left(a^{x}\right)+c \)
c. \( \sin ^{-1}\left(a^{x}\right)+c \)
D. \( \log a \sin ^{-1}\left(a^{x}\right)+c \)


If \( \boldsymbol{A}=\left(\begin{array}{c}\cos \boldsymbol{\alpha} \sin \boldsymbol{\alpha} \\ -\sin \alpha \cos \boldsymbol{\alpha}\end{array}\right), \) find \( \boldsymbol{\alpha} \)
satisfying \( 0<\alpha<\frac{\pi}{2} \) when \( A+A^{T}= \)
\( \sqrt{2} I_{2} ; \) where \( A^{T} \) is transpose of \( A \)


In the event of global warming, which one of the following is most likely to
occur?
A. Existing plant and animal communities will move North in response to warming.
B. Agriculture in the prairie provinces will be redeveloped on soils of the Canadian Shield
c. The anticipated rise in sea level will be caused primarily by the melting of polar ice caps
D. The decomposition of organic matter in the unfrozen surface layer of polar soils will increase


What is the slope of the line parallel to the equation \( 2 y-3 x=4 ? \)
\( A \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{4}{2} \)
D. \( \frac{-3}{2} \)


What is the base of all matter?
A. Compound
B. Mixture
C . Element
D. None of above


Identify the order of matrix \( \left[\begin{array}{ccc}1 & 0 & -4 \\ 2 & -1 & 3\end{array}\right] \)


Proton's relative charge is :
A . -1
B. +1
c. 0
D. -


Silver articles become black on
prolonged exposure to air. This is due to the formation of:
A. \( A g_{3} N \)
в. \( A g_{2} O \)
c. \( A g_{2} S \)
D. \( A g_{2} S \) and \( A g_{3} N \)


The compounds \( (C) \) and \( (D) \)
respectively are:
\( \mathbf{A} \cdot E t N H_{2} \) and \( \operatorname{Pr} C H=O \)
B. \( E t-N H- \)Pr and \( H C O O H \)
\( \mathbf{C} \cdot \operatorname{Pr} N H_{2} \) and \( E t C H=O \)
D. \( E t N H_{2} \) and \( \operatorname{Pr} C H_{2} O H \)


A light particle moving horizontally with a speed of \( 12 \mathrm{m} / \mathrm{s} \) strikes a very heavy block moving in the same direction at \( 10 \mathrm{m} / \mathrm{s} . \) The collision, the particle will


The dissociation constants of two acids
\( \boldsymbol{H} \boldsymbol{A}_{1} \) and \( \boldsymbol{H} \boldsymbol{A}_{2} \) are \( \boldsymbol{3} . \boldsymbol{0} \times 10^{-4} \) and
\( 1.8 \times 10^{-5} \) respectively. The relative
strengths of the acids will be:
A .1: 4
в. 4: 1
c. 1: 16
D. 16: 1


Assertion: A raindrop after falling through some height attains a constant
velocity
Reason: At constant velocity, the
viscous drag is equal to its weight.
A. Both assertion and reason are true and reason is correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
c. Assertion is true but reason is false.
D. Both assertion and reason are false


Large increase in absorption of UV-
radiation of \( 260 \mathrm{nm} \) by melted DNA duplex is called
A. Gaidukov phenomenon
B. Position effect
c. DNA compaction
D. Hyperchromic effect


Iron
(III) oxide is a chemical compound found in haemtitie, an iron ore. Give the formulae of all the irons in iron
(III) oxide.


\( \begin{array}{ll}\text { Column } A & \text { Column B } \\ \text { a) Force } & \text { i) } f \times t \\ \text { b) Momentum } & \text { ii) } m \times a \\ \text { c) Impulse } & \text { iii) } m \times v\end{array} \)
\( \mathbf{A} \cdot a-i i i, b-i i, c-i \)
B . \( a-i i, b-i i i, c-i \)
c. \( a-i, b-i i, c-i i i \)
D. \( a-i i i, b-i, c-i i \)


A compound with molecular formula
\( C_{8} H_{18} O_{4} \) does not give litmus test and
does not give colour with \( 2,4- \) DNP. It
reacts with excess \( M e C \) OCl to give a compound whose vapour density is 152 Compound \( A \) contains how many
hydroxy groups?
A . 1
B. 2
\( c .3 \)
D. 4


Deficiency of which vitamin causes the disease "Rickets".


The cost of a pair of roller skates at a shop was Rs. \( 450 . \) The sales tax charged was \( 5 \% . \) Find the bill amount.


Pieces of copper, silver and gold are dropped into a solution of iron sulphate. The piece that will get a coating of
copper is:
\( A \). iron
B. silver
c. gold
D. None of them


Here is an incomplete net for making a cube. Complete it in at least two
different ways. Remember that a cube
has six faces. How many faces are there in the net here?(Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)


For a first order radio-active decay, the
half-life period is:
A. dependent on the square of the initial concentration
B. dependent on first power of initial concentration
C. dependent on the square root of initial concentration
D. independent on initial concentration


A particle experience a constant acceleration for 20 sec. after starting
from rest, it travels adistance \( s_{1} \) in first
\( 10 \sec \) and a distance \( s_{2} \) in next 10 sec
then
A \( \cdot s_{2}=s_{1} \)
В. \( s_{2}=2 s_{1} \)
\( \mathbf{c} \cdot s_{2}=3 s_{1} \)
D. \( s_{2}=0.5 s_{1} \)


State true or false:
\( x^{2}-5 x+6 \) cannot be written as a
product of two linear factors.
A . True
B. False


Molten \( A l C l_{3} \) is electrolysed with a
current of 0.5 ampere to produce 27 g
Al. How many g-atom of \( A l \) are formed?


The function \( f(x)=\sqrt{3} \cos x+\sin x \)
has an amplitude of
A . 1.37
в. 1.73
\( c \cdot 2 \)
D. 2.73
E . 3.46


Find the area of the greatest of
isosceles triangle that can be inscribed
in a given ellipse having its vertex coincide with one end of major axes?


The product of \( 4 \sqrt{6} \) and \( 3 \sqrt{24} \) is?
A .124
B. 134
\( c \cdot 144 \)
D. 154


Which of the following is the correct increasing order of boiling point of the following compounds?
I) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
II) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
\( \boldsymbol{O} \boldsymbol{H} \)
III) \( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
\( \mathbf{A} \cdot l l<l<l l l \)
в. \( \| l<l l<l \)
c. \( l<l l<l l l \)
D. \( l l<l l l<l \)


A hollow charged conductor has a tiny hole cut into its surface. Show that the
electric field in the hole is \( \left(\sigma / 2 \epsilon_{0}\right) \hat{n} \)
where \( \hat{\boldsymbol{n}} \) is the unit vector in the
outward normal direction, and \( \sigma \) is the
surface charge density near the hole.


In a triangle \( A B C, \angle A-\angle B=30^{\circ} \) and \( \angle A \)
\( \angle C=42^{\circ} ; \) find angle \( A \)
A \( \cdot A=84^{\circ} \)
B \( \cdot A=64 \)
C \( \cdot A=95 \)
D. \( A=92^{\circ} \)


Which GA was first gibberellin to be
discovered?
A \( . G A_{1} \)
в. \( G A_{2} \)
\( \mathrm{c} \cdot G A_{3} \)
D. \( G A_{4} \)


\( \mathbf{A} \)
\( 4.5 \mathrm{cm} \) needle is placed \( 12 \mathrm{cm} \) away from a convex mirror of focal length
15 \( c m . \) Give the location of the image
and the magnification. Describe what happens as the needle is moved farther
from the mirror.


A man of 60 kg gets 1000 cal of heat by eating 5 mangoes. His efficiency is \( 28 \% \) To what height he canjump by using this energy
A. 2 m
B. 20m
\( c .28 m \)
D. \( 0.2 \mathrm{m} \)


The amount of oxygen required to oxidise organic substances present in water is called:
A. Dissolved oxygen (DO)
B. Chemical oxygen demand (COD)
c. Biochemical oxygen demand (BOD)
D. The threshold limit value (TLV)


Which of the following is a reducing sugar?
A. Galactose
B. Gluconic acid
c. \( \beta \) -methyl galactoside
D. sucrose


The osmotic pressure of urea solution
at \( 10^{\circ} \mathrm{C} \) is \( 200 \mathrm{mm} \) becomes \( 105.3 \mathrm{mm} \)
when it is diluted and the temperature
raised to \( 25^{\circ} \mathrm{C} \). The extent of dilution is:
A. 8 times
B. 5 times
c. 4 times
D. 2 times


A body of mass \( 0.1 k g \) is moving with a velocity of \( 15 m / s . \) The momentum associated with the ball will be
A. \( 0.5 k g m / s \)
в. \( 1.5 k g m / s \)
c. \( 2.5 k g m / s \)
D. 3.2Ns


The cube as shown in Fig. has sides of length \( L=10.0 \mathrm{cm} . \) The electric field is
uniform, has a magnitude \( \boldsymbol{E}=\mathbf{4 . 0 0} \times \)
\( 10^{3} N C^{-1}, \) and is parallel to the \( x y- \)
plane at an angle of \( 37^{\circ} \) measured from
the \( +x-a x i s \) towards the \( +y-a x i s \)
Electric flux passing through surface \( \boldsymbol{S}_{6} \)
is
A \( \cdot 24 N m^{2} C^{-1} \)
B. \( -24 N m^{2} C^{-1} \)
\( \mathbf{c} \cdot 32 N m^{2} C^{-1} \)
D. \( -32 N m^{2} C^{-1} \)


Calculate the mode of the frequency distribution
Mark \( \quad \begin{array}{ll}\text { Above } & \text { Above } \\ \mathbf{2 5} & \mathbf{3 5}\end{array} \quad \begin{array}{l}\text { Above } \\ \mathbf{4 5}\end{array} \)
No. of
students
49
42


The value of \( 3 \int_{0}^{\pi / 2} \sqrt{\cos x-\cos ^{3} x} d x \)
is


An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest rotational momentum is (if rotated with same angular momentum)
A. solid sphere
B. spherical shell
c. solid disc
D. thin hollow cylinder


If the magnetic dipole moment of an atom of diamagnetic material,
paramagnetic material and ferromagnetic material are denoted by
\( \mu_{d}, \mu_{p} \) and \( \mu_{f} \) respectively, then
\( \mathbf{A} \cdot \mu_{p}=0 \) and \( \mu_{f} \neq 0 \)
B . \( \mu_{d} \neq 0 \) and \( \mu_{p}=0 \)
C \( \cdot \mu_{d} \neq 0 \) and \( \mu_{f} \neq 0 \)
D. \( \mu_{d}=0 \) and \( \mu_{p} \neq 0 \)


Find the accurate expressions.
\( \mathbf{A} \cdot E=m c^{2} \)
B . \( E=m / c^{2} \)
\( \mathbf{C} \cdot M=E c^{2} \)
D. All of the expressions are accurate.
E \( \cdot c=E m^{2} \)


ABCD is a parallelogram and \( A C, B D \) are its diagonals Express \( \overrightarrow{\boldsymbol{A C}} \) and \( \overrightarrow{\boldsymbol{B D}} \) in terms of \( \overrightarrow{\boldsymbol{A B}} \) and \( \overrightarrow{\boldsymbol{A D}} \) only
A \( \cdot \overrightarrow{A C}=\overrightarrow{A B}+\overrightarrow{A D} \quad ; \overrightarrow{B D}=-\overrightarrow{A B}+\overrightarrow{A D} \)
в. \( \overrightarrow{A C}=\overrightarrow{A B}-\overrightarrow{C B} \quad ; \overrightarrow{B D}=-\overrightarrow{A B}+\overrightarrow{A D} \)
c. \( \overrightarrow{A C}=\overrightarrow{A B}+\overrightarrow{A D} \quad ; \overrightarrow{B D}=\overrightarrow{B C}+\overrightarrow{C D} \)
D. all of the above


The value of \( (127)^{1 / 3} \) to four decimal places is
A .5 .0267
B. 5.4267
c. 5.5267
D. 5.001


In the figure shown, a cubical block is
held stationary against a rough wall by applying force \( F \) then, incorrect
statement among the following is:
A. frictional force, \( f=M g \)
B. \( F=N, N \) is normal reaction
C. F does not apply any torque
D. N does not apply any torque


A transformer has 500 turns of the
primary winding and 10 turns of the secondary winding. Determine the secondary voltage if the secondary circuit is open and the primary voltage is \( 120 \mathrm{V} \)


approaching the first? (answer in Hz)


A point \( P \) on the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \) has the eccentric angle \( \frac{\pi}{8} . \) The sum of the distance of \( P \) from the two foci is
A . 5
B. 6
c. 10
D. 3


The equilibrium constant for a reaction
is \( 20 . \) What will be the value of \( \Delta G ? \)
\( \boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1-1}, \boldsymbol{T}=\boldsymbol{3 0 0} \boldsymbol{K} \)


Find the next two terms of the following
sequence \( : 2,4,6,8, \dots \)


The basicity of phosphoric acid is:
\( A \cdot 1 \)
B . 2
\( c .3 \)
D.


In a school, \( 8 a^{2}+4 a+9 \) students
were enrolled. \( 2 a^{2}-9 a+2 \) students
were boys. How many girls were
enrolled?
A \( \cdot 6 a^{2}-13 a+7 \)
7
B . \( 4 a^{2}+13 a+7 \)
\( \mathbf{c} \cdot 6 a^{2}+13 a+7 \)
D. \( 4 a^{2}-13 a+7 \)


Euclidian geometry cannot be applied to which of the following?
A. Triangle
B. Rectangle
c. sphere
D. Square


To obtain n-type extrinsic semiconductor, the impurity element to be added to germanium should be of valency
A .2
B. 5
\( c \cdot 4 \)
\( D \)


When a steel core is placed in a
solenoid, it acts like an electromagnet.
A. True
B. False


A batsman hits a cricket ball which
then rolls on a level ground. After
covering a short distance, the ball
comes to rest. The ball slows to a stop
because:
A. the batsman did not hit the ball hard enough
B. velocity is proportional to the force exerted on the ball
C. there is a force on the ball opposing the motion
D. there is no unbalanced force on the ball, so the ball
would want to come to rest


State whether the following statements are true or false.

ATP is a protein that supplies energy to
the cell.
A. True
B. False


An ideal gas is subjected to a cyclic process involving four thermodynamic states; the amounts of heat (Q) and work (W) involved in each of these
states are \( Q_{1}=6000 J, Q_{2}= \)
\( \mathbf{5 5 0 0} \boldsymbol{J}, \boldsymbol{Q}_{3}=-\mathbf{3 0 0 0} \boldsymbol{J}, \boldsymbol{Q}_{4}= \)
\( \mathbf{3 5 0 0} \boldsymbol{J} \boldsymbol{W}_{\mathbf{1}}=\mathbf{2 5 0 0} \boldsymbol{J}, \boldsymbol{W}_{\mathbf{2}}= \)
\( -\mathbf{1 0 0 0} \boldsymbol{J}, \boldsymbol{W}_{3}=-\mathbf{1 2 0 0} \boldsymbol{J}, \boldsymbol{W}_{4}=\boldsymbol{x} \boldsymbol{J} . \) The
ratio of the net work done by the gas to
the total heat absorbed by the gas in ' \( \eta \) '.
The values of \( x \) and \( \eta \) respectively are:
\( \mathbf{A} \cdot 500,7.5 \% \)
в. \( 1000,10.5 \% \)
c. \( 1000,21 \% \)
D. \( 1500,15 \% \)


The IUPAC name of the red coloured
\( \operatorname{complex}\left[\boldsymbol{F e}\left(\boldsymbol{C}_{4} \boldsymbol{H}_{7} \boldsymbol{O}_{2} \boldsymbol{N}_{2}\right)_{2}\right] \) obtained
from the reaction of \( F e^{2+} \) and dimethyl
glyoxine
A. bis(dimethyl flyoxime) ferrate(II)
B. bis (dimethyl glyoximato) iron(II)
c. bis (2, 3-butanediol dioximato) iron(II)
D. bis (2, 3-butanedione dioximato) iron(II)


Identify the reason why an observer cannot detect the wave nature of a fast moving truck.
A. The momentum of the truck is too large
B. The velocity of the wave is too large
c. There are no waves to be detected
D. The frequency is too low
E. The wavelengths are too small


Two equal drops of water are falling
through air with. steady velocity v. If the
drops coalesced, what will be the new velocity?


When water was electrolyzed, hydrogen and oxygen were obtained which were collected and found to be \( 16.8 \mathrm{L} \) at \( S T P \)
Then, weight of water electrolyzed is:
\( \mathbf{A} \cdot 18 \mathrm{gm} \)
B. 36 gm
\( \mathrm{c} \cdot 9 \mathrm{gm} \)
D. \( 45 \mathrm{gm} \)


Which polynomial should be added to
\( 2 x^{4}-3 x^{2}+5 x+8 \) to get \( 2 x^{2}-5 x+4 \)
\( ? \)
A \( \cdot x^{3}+5 x^{2}-x \)
B . \( 2 x^{5}+x^{2}-10 x-9 \)
c. \( -2 x^{4}+5 x^{2}-1 \)
D. \( -2 x^{4}+5 x^{2}-10 x-4 \)


are elements which can
accept one or more electrons and form negative ions.
A. Metals
B. Non-metals
c. Metalloids
D. None of these


Assertion
The handle and bristles of a tooth brush
should be made of different material
Reason

The handle of a toothbrush should be
hard and strong while the bristles
should be soft and flexible.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


State what is meant by refraction of light. State Snell's law for refraction of
light and also express it mathematically. The refractive index of air with respect to glass is \( 2 / 3 \) and the refractive index
of water with respect to air is \( 4 / 3 . \) If the
speed of light in glass is \( 2 \times 10^{8} \mathrm{m} / \mathrm{s} \)
find the speed of light in (a) air, (b)
water


What do you understand by ozone layer? Write an essay to participate in the elocution competition on the
importance of ozone layer.


is a process of transfer of
heat by the actual movement of the medium particles.
A. Conduction
B. Convection
c. Radiation
D. All


Which among the following equations represents the reduction reaction taking place in lead accumulator at positive electrode, while it is being used as a source of electrical energy?
\( \mathbf{A} \cdot P b \rightarrow P b^{2} \)
B. \( P b^{4+} \rightarrow P b \)
\( \mathbf{c} \cdot P b^{2+} \rightarrow P b \)
D. \( P b^{4+} \rightarrow P b^{2} \)


Find the derivative of the following functions from the first principals w.r.t
to \( \boldsymbol{x} \)
\( \tan 2 x \)


If \( \vec{e}=l \hat{i}+m \hat{j}+n \hat{k} \) is a unit vector,
then the maximum value of \( l m+ \)
\( m n+n l \) is
A. \( -\frac{1}{2} \)
B.
c. 1
D. \( \frac{3}{2} \)


heated on the flame directly. It crumbled to give white powder of calcium oxide. After cooling, when water is added to it a hissing sound is heard and water started boiling. If it is allowed to stay over night, a clear solution (top layer) is taken and for this experiment
below as lime water.

When carbon dioxide is bubbled into
testtube a clear solution of lime water,
turbidity appears first and later a white precipitate of calcium carbonate is formed. Carbon dioxide is continued to
passed into the same solution and the solution again became clear because of formation of calcium bicarbonate. On
heating the contents of the tube, white precipitate of calcium carbonate
reappears.
Passing of carbon dioxide to lime water gave the following initially
A. Calcium bicarbonate and carbon dioxide
B. Calcium carbonate and water
c. calcium carbonate and carbon dioxide
D. Calcium oxide and water


\( A B C D E \) is a pentagon. the resultant of the forces \( \overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{D C}+\overrightarrow{E D}+ \)
\( \overrightarrow{A E}=k \overrightarrow{A C}, \) then find the value of \( k \)


According to Charles' law.
This question has multiple correct options
A \( \cdot V \propto \frac{1}{T} \)
\( ^{\mathbf{B}} \cdot\left(\frac{d V}{d T}\right)_{P}=K \)
\( ^{\mathbf{C}} \cdot\left(\frac{d T}{d V}\right)_{P}=K \)
\( ^{\mathrm{D}}\left(\frac{1}{T}-\frac{V}{T^{2}}\right)_{P}=0 \)


Find the distance between (12,3,4) and (4,5,2)
A \( \cdot \sqrt{72} \)
B. \( \sqrt{62} \)
\( c \cdot \sqrt{64} \)
D. None of these


Sometimes the behaviour of a chemical
compound can be better to understand
by regarding it as if it exists in a world between two or three different possible structures. This phenomenon is called:
A. a double standard
B. allotropism
c. isomerism
D. resonance


The formula of calamine ore is :
A \( . Z n S \)
в. \( F e C O_{3} \)
\( \mathrm{c} \cdot Z n C O_{3} \)
D. \( C u_{2} S \)


A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities
on the plate are \( +\sigma \) and \( -\sigma \)
respectively. In the region between the plates the magnitude of electric field is:
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
\( c \cdot 0 \)
D. none of these


Which of the following orders is true regarding the acetic nature of monosubstituted acetic acid?
A. Fluoroacetic acid > Chloroacetic acid > Bromoacetic acid
B. Chloroacetic acid <Bromoacetic acid < Fluoroacetic acid
c. Bromoacetic acid < Fluoroacetic acid > Chloroacetic acid
D. Fluoroacetic acid < Bromoacetic acid <Chloroacetic acid


Coke is used in the preparation of :
This question has multiple correct options
\( \mathbf{A} \cdot C O+H_{2} \)
B \( \cdot C O+N_{2} \)
C . Graphite artificially
D. Diamond artificially


The upper limit temperature of a super conductor is
\( \mathbf{A} \cdot 115 \mathrm{K} \)
B. 120 K
c. \( 125 \mathrm{k} \)
D. \( 130 \mathrm{K} \)


A flowerpot falls from a windowsill \( 25.0 m \) above the sidewalk. How much
time does a passerby on the sidewalk below have to move out of the way before the flowerpot hits the ground? (in seconds)
A .2
B . 2.3
\( c \cdot 6 \)
\( D \)


Which of the following is not true about
photosynthesis?
A. In non-cyclic photophosphorylation, water is split and oxygen is released
B. Photosystem-II makes noncyclic photophosphorylation more efficient than does cyclic photophosphorylation
C. Cyclic system is used when there is insufficient \( N A D P^{+} \) present to absorb electrons in plant cells
D. More carbohydrate is produced during cyclic photophosphorylation than during non-cyclic photophosphorylation


An aluminium wire carrying a current has diameter \( 0.84 \mathrm{mm} \). The electric
field in the wire is \( 0.49 V / m . \) What is,
(a) the current carried by the wire?
(b) the potential difference between two points in the wire 12.0 m apart?
(c) the resistance of a \( 12.0 \mathrm{m} \) length of this wire?
Specific resistance of aluminum is \( 2.75 \times 10^{8} \Omega-m \)


Match the column (I) and (II) and select
the correct answer using the codes given below.
ColumnColumn-II
(a)
(1) Halide ore of magnesium Argentite
(b) Cuprite
(2) Carbonate ore of iron
(c) Siderite
(3) Oxide ore of copper
(d) Carnallite
(4) Sulphide ore of silver
A. a-4, b-3, c-2
B. a-1, b-2, c-3, d-4
c. \( a-2, b-3, c-3, d-1 \)
D. a-3, b-4, c-1 \( d-2 \)


Find :
\( 2 \times 2 \)


The most acidic compound among the following is:
A. phenol
B. ethanol
c. 3,5-dinitrophenol
D. 4-methoxy phenol


What transition in \( H e^{+} \) ion shall have
the same wave number as the first line
in Balmar series of H atom?
\( \mathbf{A} \cdot 7 \rightarrow 5 \)
B . \( 5 \rightarrow 3 \)
\( c \cdot 6 \rightarrow 4 \)
\( \mathbf{D} \cdot 4 \rightarrow 2 \)


Milk of sulphur finds its applications in
A. medicines
B. photography
c. head of match stick
D. vulcanization


The \( \% \) of hydrogen in water and hydrogen peroxide is \( 11.2 \% \) and \( 5.94 \% \) respectively. This illustrates the law of:
A. constant proportions
B. conservation of mass
c. multiple proportions
D. law of gaseous volume


A divergent lens has a focal length of 30 \( \mathrm{cm} . \) At what distance should an object
of height \( 5 \mathrm{cm} \) from the optical centre of the lens be placed so that its image is
formed \( 15 \mathrm{cm} \) away from the lens? Find the size of the image also.


Let \( a, \beta, \gamma \) be distinct real numbers. The
points with position vectors ai \( +\beta j+ \) \( \gamma k, \beta i+\gamma j+a k, \gamma i+a j+\beta k \)
A. are collinear
B. form an equilateral triangle
c. form an scalene triangle
D. form a right angled triangle


Answer the following:What is lanthanoid contraction?
Mention one of its consequences.


\( 5.5 m g \) of nitrogen gas dissolves in \( 180 g \) of water at \( 273 K \) and one atm
pressure due to nitrogen gas. The mole fraction of nitrogen in \( 180 g \) of water at
5 atm nitrogen pressure is approximately:
A \( \cdot 1 \times 10^{-5} \)
B. \( 1 \times 10^{-4} \)
c. \( 1 \times 10^{-6} \)
D. \( 1 \times 10^{-3} \)


Write a note on vulcanization of rubber.


One mole of oxygen is expanded from a volume \( 1 \ell \) to \( 2 \ell \) at a constant
temperature \( \boldsymbol{T}=\mathbf{2 8 0} \boldsymbol{K} . \) Find the
change in internal energy of the gas.
\( \mathbf{A} \cdot 9.8 k J \)
B . \( 2.8 k J \)
\( c .0 k J \)
D. 12.8 k


Solve:
\( (i+3 i)^{2}(3+1) \)


The volume of a liquid (v) flowing per second through a cylindrical tube depends upon the pressure gradient
(p/I) radius of the tube (r) coefficient of viscosity ( \( \eta \) ) of the liquid by dimensional method the correct
formula is
A \( \cdot v \alpha \frac{P r^{4}}{\eta l} \)
в. \( v \alpha \frac{P r}{\eta l^{4}} \)
\( ^{\mathrm{c}} \cdot_{V \alpha} \frac{P l^{4}}{\eta r} \)
D. None


Cathode rays gain K.E. when accelerated by an electric field. If they are subjected to a uniform magnetic field, then their
A. Energy increases
B. Momentum increases
C. Energy and momentum decrease
D. Energy and magnitude of momentum remain
unaffected


Three equal resistors connected in series across a source of e.m.f dissipate
10 watts of power. What will be the power dissipated in watts if the same resistors are connected in parallel
across the same source of e.m.f?
A. \( 10 \mathrm{w} \)
B. 30 W
c. \( 90 \mathrm{w} \)
D. \( \frac{10}{3} W \)


Which is a set of acid salts and can
react with base?
A. \( N a H_{2} P O_{2}, N a_{2} H P O_{3}, N a H_{2} P O_{4} \)
B. \( N a_{2} H P O_{3}, N a H_{2} P O_{3}, N a H P O_{4} \)
c. \( \operatorname{NaHCO}_{3}, \operatorname{NaH}_{2} \mathrm{PO}_{3}, \mathrm{Na}_{2} \mathrm{HPO}_{4} \)
D. All of the above


How many 6-letter words with distinct
letters in each can be formed using the
letters of the word EDUCATION? How
many of these begin with I
A. \( ^{9} P_{6^{\prime}}^{8} P_{5} \)
в. \( ^{9} P_{6^{\prime}}^{9} P_{5} \)
\( \mathrm{c} \cdot^{8} P_{6^{\prime}}^{8} P_{5} \)
D. \( ^{8} P_{6^{\prime}}^{8} P_{4} \)


Is \( s p^{3} d^{2} \) hybridization the same as
\( d^{2} s p^{3} \) hybridization?


The solution of the differential equation \( x \frac{d y}{d x}=\frac{y}{1+\log x} \) is :
A. \( y=\log x+C \)
в. \( y=\frac{C}{1+\log x} \)
c. \( y=C(x+\log x) \)
D. \( y=x+\log (C x) \)
E . \( y=C(1+\log x) \)


To measure the specific heat of copper, an experiment is performed in the lab. \( A \) piece of copper is heated in an oven then dropped into a beaker of water. To
calculate the specific heat of copper, the experimenter must know or
measure the value of all of the
quantities below EXCEPT the
A. Original temperatures of the copper and the water
B. Mass of the water
C. Final (equilibrium) temperature of the copper and the water
D. Time taken to achieve equilibrium after the copper is dropped into the water
E. Specific heat of the water


If a rectangle has more than two lines of symmetry,then it must be a square.
A. True
B. False


\( \mathbf{A} \)
\( 2.0 V \) potentiometer used for the
determination of internal resistance of
a \( 1.5 V \) cell. The balance point of the cell
in open circuit is \( 76 \mathrm{cm} \). When a resistor
of \( 9.5 \Omega \) is used in the external circuit of
the cell, the balance point shifts to \( 57 \mathrm{cm} \) length of the potentiometer wire. Determine the internal resistance of the
cell
A \( .1 .7 \Omega \)
В. \( 2.5 \Omega \)
c. \( 1.5 \Omega \)
D. \( 0.5 \Omega \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{a}+\mathbf{1} & \boldsymbol{b}-\mathbf{2} \\ \mathbf{2} \boldsymbol{a}-\mathbf{1} & \mathbf{0} & \boldsymbol{c}-\mathbf{2} \\ \mathbf{2} \boldsymbol{b}+\mathbf{1} & \mathbf{2}+\boldsymbol{c} & \mathbf{0}\end{array}\right] \) is skew
symmetric then \( a+b+c= \)
\( A \cdot 3 \)
B. -3
\( c \cdot \frac{1}{3} \)
\( D \)


The above reaction is a type of intramolecular disproportionation reaction.
If true enter 1 , else enter 0 .
\[
\underbrace{\mathrm{CHO}}_{\mathrm{CHO}} \stackrel{\mathrm{OH}^{-}}{\longrightarrow} \underbrace{\mathrm{COO}^{-}}_{\mathrm{CH}_{2} \mathrm{OH}}
\]
\( A \)


Which of the following is not the harmful product which is produced in the biochemical reactions of the cell of
living organisms?
A. Urea
B. Uric acid
c. Ammonia
D. Lymph


If a.b.c are noncoplanar find the point of intersection of the line passing through the points \( 2 a+3 b-c, 3 a+4 b-2 c \)
with the line joining the points \( a \)
\( 2 b+3 c, d-6 b+b c \)


The \( E_{M^{3+} / M^{2+}}^{0} \) values of \( \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe} \) and
Co are \( -\mathbf{0 . 4 1},+\mathbf{1 . 5 7},+\mathbf{0 . 7 7} \) and
\( +1.97 \mathrm{V} \) respectively. For which one of these metals the change in oxidation
state from +2 to +3 is easiest?
A \( . C r \)
в. \( M n \)
c. \( F e \)
D. \( C o \)


Which of the following statements is
correct about \( \lambda_{a}^{\infty} \) or \( \lambda_{c}^{\infty} \) (i.e., ionic conductivities)?
A. Increases with temperature due to increase in viscosity of medium.
B. Increases with pressure due to decrease in viscosity of medium.
c. Decreases with pressure due to increase in viscosity of medium.
D. Decreases with pressure due to decrease in viscosity of medium


toppr
Q Type your question
current which is then converted into a
digital readout on the display. The electric circuit gives a current of
2.0 mA when a weight of 30N is applied,
and a current of \( 0.5 \mathrm{mA} \) when a weight of \( 5 \mathrm{N} \) is applied

Which calibration curve could represent
this circuit?
\( A \)
B.
\( c \)
\( D \)


In an electric circuit, a fuse is connected :
A. in the live wire
B. in the neutral wire
c. in the earth wire
D. Any of these


If \( t_{0}, \) represents \( n^{t h} \) term of an A.P. \( t_{2}+ \)
\( t_{5}-t_{3}=10 \) and \( t_{2}+t_{9}=17, \) find its
first term and its common difference.


Assertion
Inductance coils are made of copper.
Reason

Induced current is more in wire having
less resistance.
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


Apart from metals,which of these can show ductility?
A. Synnthetic polymers
B. Alloys
c. chewing gums
D. All of these


Solve
\( \frac{33}{u+2}+\frac{12}{v-3}=123 \)
and \( \frac{12}{u+2}+\frac{33}{v-3}=102 \)


(a) A conductor \( A \) with a cavity as
shown in Fig. \( (a) \) is given a charge \( Q \) Show that the entire charge must
appear on the outer surface of the
conductor.
(b) Another conductor \( B \) with charge \( q \)
is inserted into the cavity keeping \( \boldsymbol{B} \)
insulated from \( A . \) Show that the total
charge on the outside surface of \( \boldsymbol{A} \) is
\( \boldsymbol{Q}+\boldsymbol{q} \)
(c) A sensitive instrument is to be
shielded from the strong electrostatic fields in its environment.
Suggest a possible way.
\( (\mathbf{a}) \)
\( \mathbf{b} \)


Clinostat is used in study for
A. Photosynthesis
B. Respiration
c. Geotropism
D. Osmosis


A bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet, an anti-clockwise current is
found to be induced in the ring. Which
of the following may be true? This question has multiple correct options
A. The south pole faces the ring and the magnet moves towards it
B. The north pole faces the ring and the magnet moves towards it.
c. The south pole faces the ring and the magnet moves away from it.
D. The north pole faces the ring and the magnet moves away from it.


The most common oxidation state of
Lanthanoids is:
\( A \cdot+4 \)
\( B \cdot+3 \)
\( c \cdot+6 \)
\( D \cdot+2 \)


A mass \( m \) is thrown vertically upward
into air with initial speed \( u . \) A constant
force \( F \) due to air resistance acts on the
mass during it's travel. Taking into
account the work done against air drag, the maximum distance covered by the mass to reach the top is (Given acceleration due to gravity \( =g \) )
A \( \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u^{2}}{2 g+2 F / m} \)
с. \( \frac{u^{2}}{2 g+F / m} \)
D. \( \frac{u^{2}}{g+F / m} \)


At \( 27 C \) latent heat of fusion of a
compound is 2930 J/mol. Entropy change is :
A. 9.77 J/molk
B. 10.77 J/molk
c. 9.07 J/molk
D. 0.977 J/molk


Spore producing body of a cellular slime mold is
A. Pseudoplasmodium
B. Plasmodium
c. sporangium
D. Sporophore


In a hydraulic lift, used at a service station the radius of the large and small
piston are in the ratio of \( 20: 1 . \) What
weight placed on the small piston will be sufficient to lift a car of mass
\( 1500 k g ? \)
A. \( 3.75 k g \)
в. \( 37.5 k g \)
c. \( 7.5 k g \)
D. \( 75 k g \)


An ideal fluid is:
A. similar to a perfect gas.
B. non-viscous and incompressible.
C . one which satisfies the continuity equation.
D. one which obeys Newton's formula for viscous drag.


Which of the following is a Sandmeyer
reaction?
\( \mathbf{A} \cdot 2 C_{6} H_{5} C l \frac{C u_{2} C l_{2} / H C l}{\longrightarrow} C_{6} H_{6}+C l_{2} \)
\( \mathbf{B} \cdot C_{6} H_{5} N_{2} C l \frac{C u_{2} C l_{2} / H C l}{\longrightarrow} C_{6} H_{5} C l+N_{2} \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \frac{Z n d u s t}{\longrightarrow} C_{6} H_{6}+Z n O \)
\( \mathbf{D} \cdot C_{6} H_{5} N O_{2}+6[H] \stackrel{S n / H C l}{\longrightarrow} C_{6} H_{5} N H_{2}+2 H_{2} O \)


Which of the following book was written by Theophrastus?
A . 'Enquiry into Plants's
B. 'On the Causes of Plants
c. 'Historia Plantarum'
D. All of the above


If light can travel 31 times around the world in 4 seconds, how many times can it circle the world in 10 seconds.
A. 124 times
в. \( 66 \frac{1}{2} \) times
c. \( \quad 82 \frac{1}{2} \) times
D. 77.5 times


Pick the only wrong statement in the
following:
A. Light travels with a speed greater than that of sound
B. Light cannot travel through vacuum
C. Light travels in a straight line
D. Light is a wave motion


A pure inductor \( L, \) a capacitor \( C \) and \( a \)
resistance \( R \) are connected across a
battery of emf \( \mathrm{E} \) and internal resistance
as shown in Fig. Switch \( S_{w} \) is closed at
\( t=0, \) select the correct alternative(s)
A. current through resistance R is zero all the time
B. current through resistance R is zero at \( t=0 \) and \( t- \)
c. maximum charge stored in the capacitor is \( c E \)
D. maximum energy stored in the inductor is equal to the maximum energy stored in the capacito


Pelvic girdle consists of
A. Ilium
B. Ilium and ischium
C. Ilium, ischium and pubis
D. Ischium and pubis


Lead pencil contains:
A. graphite
B. softened leadd
c. galena
D. anglesite


Which of the following is oxone?
A \( . \) К \( O_{2} \)
в. \( N a_{2} O_{2} \)
c. \( L i_{2} O \)
D. None


State whether the following statement
is True or False.
The prefix used for \( 10^{3} \) is kilo.
A. True
B. False


The physical constants which are less
for \( D_{2} O \) than \( H_{2} O \) are:
A. freezing point and boiling point
B. density and viscosity
c. solvating ability and dielectric constant
D. temperature of maximum density


Identify the wrong statement about
meiosis.
A. Pairing of homologous chromosomes
B. Four haploid cells are formed
c. At the end of meiosis number of chromosomes are reduced to half
D. Two cycle of DNA replication occur


Assertion
lonic compounds are generally hard
solids but brittle in nature.
Reason
Brittleness is because to shift in
alignment of its ions.
Hardness is due to the strong forces of
attraction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


The product of the d.cs of the line which makes equal angles with \( o x, o y, o z \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{3} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}} \)


The total energy of the electron in any orbit of one electron containing species is given by the expression:
A \( \cdot-e^{2} / r^{2} \)
B . \( -n^{2} h^{2} / 2 \pi^{2} Z^{2} e^{4} m \)
c. \( -2 \pi^{2} m Z^{2} e^{4} / n^{2} h^{2} \)
D. \( n h / 2 \pi \)


Time alloted for the preparation of an examination by some students is shown in the table. Draw a histogram to show the information.
\( \begin{array}{llll}\operatorname{Time} & \mathbf{6 0}- & \mathbf{8 0 -} & \mathbf{1 0 0}- \\ (\text { minutes }) & \mathbf{8 0} & \mathbf{1 0 0} & \mathbf{1 2 0}\end{array} \)
No. of 14 20 24


Consider following scheme involving oxides and oxy-acids of nitrogen. Out of the following which reactions are
disproportionations?

This question has multiple correct options
A . 2, 10
в. 2,
\( c \cdot 1,1 \)
D. 13,14


The IUPAC name of the compound:
A. 5-chloro-4-methyl hept-5-en-1-yne
B. 5-chloro-4-methyl hept-1-en-5-yne
c. 3-chloro-4-methyl hept-2-en-6-yne
D. 3-chloro-4-methyl hept-6-en-2-yne


The ratio of magnetic fields due to a bar
magnet at the two axial points \( P_{1} \) and
\( P_{2} \) which are separated from each other
by \( 10 \mathrm{cm} \) is \( 25: 2 . \) Point \( P_{1} \) is situated at
10cm from the centre of the
magnet.Points \( P_{1} \) and \( P_{2} \) are on the
same side of magnet and distance of \( \boldsymbol{P}_{2} \)
from the centre is greater than distance
of \( P_{1} \) from the centre of magnet,then magnetic length is
A. \( 5 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


In a school, there are 1000 students, out
of which 430 are girls. It is known that out of \( 430,10 \% \) of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that chosen student is a girl?


A ray of light is incident on the left vertical face of glass cube of refractive
index \( n_{2}, \) as shown in figure. The plane
of incidence is the plane of the page, and the cube is surrounded by liquid (refractive index \( =\{n\}_{-}\{1\} \) ). What is the
largest angle of incidence \( \theta_{1} \) for which
total internal reflection occurs at the
top surface?


The vapour of a substance behaves as a
gas:
A. below critical temperature
B. above critical temperature
\( \mathbf{c} \cdot \operatorname{at} 100^{\circ} C \)
\( \mathbf{D} \cdot \operatorname{at} 1000^{\circ} C \)


Fill in the blanks:A yellow coloured dress would appear to be when viewed through a green filter.
A . black
B. green
c. yellow
D. orange


Find the oxidation number of Oxygen in \( \boldsymbol{C a O} \)
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot-1 \)
\( D \cdot-2 \)


What is the bond angle between \( C l- \)
\( \boldsymbol{O}-\boldsymbol{C l} \) in \( \boldsymbol{C l}_{2} \boldsymbol{O}_{7} ? \)
A \( \cdot 109^{\circ} \)
B. \( 119^{\circ} \)
\( \mathbf{c} \cdot 108^{\circ} 25^{\prime} \)
D. \( 120^{\circ} \)


The probability that a man hits a target is \( \frac{3}{4} . \) If tried 5 time, the probability that he will hit the target at least three
times,is
A \( \cdot \frac{918}{10184} \)
B. \( \frac{884}{10244} \)
c. \( \frac{924}{1024} \)
\( D \cdot \frac{848}{1024} \)


For the given experiment, the independent variable is
A. Amount of light
B. Number of water fleas
C. pH of the water
D. Temperature of the water
E. Average heart rate


\( M g_{2} C_{3} \) reacts with water forming
propyne, \( C_{3}^{4-} \) has:
A. two sigma and two pi bonds
B. three sigma and one pi bonds
c. two sigma and one pi bonds
D. two sigma and three pi bonds


Compared to the one used on Hiroshima, the Nagasaki bomb was rounder and fatter, so it was called "Fat
Man." The fissile material was
A. plutonium 239
B. plutonium 237
c. uranium 235
D. uranium 239


\( \frac{k}{k} \)


A balloon contains \( 14.0 L \) of air at
760 torr. What will be the volume of the
balloon when it is taken to a depth of
10 \( f t \). in a swimming pool? Assume that the temperature of the air and
water are equal (Density: \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} .) \)
A . 11.0
в. 11.3
c. 10
D. 10.8


A projectile of mass \( m \) is thrown with
velocity \( v \) making an angle \( 60^{\circ} \) with the
horizontal. Neglecting air resistance, the change in momentum from the
departure A to its arrival at B, along the
vertical direction is :
A \( .2 m v \)
B. \( \sqrt{3} m v \)
\( c \)
D. \( \frac{m v}{\sqrt{3} v} \)


3 Moles of \( \boldsymbol{P} \boldsymbol{C l}_{5} \) kept in 1 L closed vesse
was allowed to attain equilibrium at \( 380 \mathrm{K} \). Calculate the composition of the
mixture at equilibrium, \( \boldsymbol{K}_{c} \)
A \( \cdot\left[P C l_{5}\right]=1.41 M,\left[P C l_{3}\right]=\left[C l_{2}\right]=2.59 M \)
в. \( \left[P C l_{5}\right]=1.41 M,,\left[P C l_{3}\right]=\left[C l_{2}\right]=1.59 M \)
\( \mathbf{c} \cdot\left[P C l_{5}\right]=1.41 M,,\left[P C l_{3}\right]=\left[C l_{2}\right]=5.59 M \)
D \( \cdot\left[P C l_{5}\right]=1.41 M,,\left[P C l_{3}\right]=\left[C l_{2}\right]=9.59 M \)


Why are seat belts designed in cars to stretch somewhat in a collision?


Application of a forward bias to a \( \mathrm{p}-\mathrm{n} \)
junction
A. widens the depletion zone
B. increases the potential difference across the depletion
zone
C. increases the number of donors on the n side
D. increases the electric field in the depletion zone.


Construct a quadrilateral \( P Q R S \) with
\( \boldsymbol{P Q}=\mathbf{8} \mathrm{cm}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{6} \mathrm{cm}, \angle \boldsymbol{P}= \)
\( \mathbf{6 0}^{\circ}, \angle \boldsymbol{Q}=\mathbf{4 5}^{\circ}, \angle \boldsymbol{R}=\mathbf{6 0}^{\circ} \)


Express dielectric constant in terms of
permittivity of free space?


Which of the following is tetrahedral paramagnetic complex?
A \( \cdot K_{2}\left[P t C l_{4}\right] \)
в. \( K_{2}\left[M n C l_{4}\right] \)
c. \( _{K_{2}}\left[Z n C l_{4}\right] \)
D \( \cdot K_{2}\left[H g l_{4}\right] \)


Ethylenediamine displaces \( H_{2} O \) in the
complex \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \) in three steps.
\[
\left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+}+\boldsymbol{3} \boldsymbol{e} \boldsymbol{n} \rightarrow\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{e} \boldsymbol{n})_{3}\right]^{3+}+
\]
\( 6 H_{2} O \)
Stepwise formation constants are
\[
\begin{array}{l}
\log K_{1}=4.34 \\
\log K_{2}=3.31 \\
\log K_{3}=2.05
\end{array}
\]
Overall formation constant is \( \boldsymbol{A} \times \mathbf{1 0}^{\boldsymbol{B}} \)
\( A+B \) is


The uniparental reproduction is called reproduction while biparental reproduction is termed reproduction. Higher organisms mostly show reproduction
A. Sexual, asexual, sexual
B. Asexual, sexual, asexual
c. Asexual, sexual, sexual
D. Sexual, asexual, asexual


The value of \( \int e^{\tan ^{-1} x}\left(\frac{1+x+x^{2}}{1+x^{2}}\right) d x \)
is equal to
A. \( x e^{\tan ^{-1} x}+C \)
B. \( x^{2} e^{\tan ^{-1} x}+C \)
c. \( \frac{1}{x} e^{\tan ^{-1} x}+C \)
D. \( x e^{\cot ^{-1} x}+C \)


A particle moves on a given line with a constant speed v. At a certain time it is
at a point \( P \) on its straight line path. 0 is fixed point. Show that \( (\overrightarrow{O P} \times \vec{v}) \) is independent of the position P.


Two parallel chords are drawn on the
same side of the centre of a circle of
radius 20. It is found that they subtend
\( 60^{0} \) and \( 120^{0} \) angles at the centre of the circle. Then the perpendicular distance between the chords is:
\( \mathbf{A} \cdot 5(\sqrt{3}-1) \)
B . \( 10(\sqrt{3}-1) \)
c. \( 10(\sqrt{2}-1) \)
() \( 5(\sqrt{2}-1-1) \)
D. \( 5(\sqrt{3}+1) \)


f \( \boldsymbol{x}=\sin t, \boldsymbol{y}=\sin \boldsymbol{k} \boldsymbol{t} \) satisfies
\( \left(1-x^{2}\right) y_{2}-x y_{1}+A y=0 \) then \( A \) is
Equal to
\( A \cdot k \)
B.
\( \mathbf{c} \cdot k^{2} \)
D. \( 1+k \)


State True or False.
Forest Fires and droughts are man made causes of deforestation
A. True
B. False


Three bodies are projected in three different ways: a) vertically up b) vertically down c) horizontally, with same speed from top of a tower. The time taken by the bodies to reach the ground in increasing order would be:
\( \mathbf{A} \cdot t_{b}<t_{a}<t_{c} \)
в. \( t_{c}<t_{a}<t_{b} \)
c. \( t_{b}<t_{c}<t_{a} \)
D \( \cdot t_{a}<t_{b}<t_{c} \)


Two identical balls \( A \) and \( B \) having velocities of \( 0.5 \mathrm{m} / \mathrm{s} \) and \( -0.3 \mathrm{m} / \mathrm{s} \)
respectively collide elastically in one
dimension. The velocities of B and \( A \)
after the collision respectively will be
A. \( 0.3 \mathrm{m} / \mathrm{s} \) and \( 0.5 \mathrm{m} / \mathrm{s} \)
B. -0.5 m/s and 0.3 m/s
c. \( 0.5 \mathrm{m} / \mathrm{s} \) and \( -0.3 \mathrm{m} / \mathrm{s} \)
D. \( -0.3 \mathrm{m} / \mathrm{s} \) and \( 0.5 \mathrm{m} / \mathrm{s} \)


Which of the following is a solution of
\( 2 p+3 q=5 ? \)
A. \( p=-1, q=1 \)
в. \( p=1, q=-1 \)
c. \( p=1, q=1 \)
D. \( p=-1, q=-1 \)


The nucleus \( _{n}^{m} X \) emits \( \alpha \) particle and 2
\( \boldsymbol{\beta} \) particles. The resulting nucleus is:
A \( m-4 \)
\( n-2 \)
В \( \cdot m-6 \)
\( n-4 \)
\( \mathbf{c} \cdot_{n}^{m-6} Z \)
D. \( _{n}^{m-4} X \)


The number of electrons to be removed
from a glass rod in order that it acquires a charge of \( 1 \mu C \) is:
A. \( 6.25 \times 10^{12} \)
B. \( 10^{12} \)
c. \( 6.25 \times 10^{13} \)
D. \( 10^{13} \)


The momentum of a \( 10 \mathrm{kg} \) body moving at \( 36 \mathrm{km} / \mathrm{h} \) is:
A. \( 100 \mathrm{kg} . \mathrm{m} / \mathrm{s} \)
B. 360 kg. m/s
c. \( 3.6 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
D. 36000 kg.m /s


In the above question, the tension in the
two wires, if the direction of the current
is reversed, keeping the magnetic field the same is
A . 1.0
в. 2.0N
c. 3.0
D. 4.0N


A 60 watt bulb carries a current of \( 5 A \)
Find the total charge passing through it in 1 hour.
A . 2000C
B. \( 1800 \mathrm{c} \)
\( c \cdot 12 c \)
D. 360C


\( X_{2} \) represents halogen molecule. Bond
energy of different halogen molecules will lie in following sequences:
A \( \cdot F_{2}>C l_{2}>B r_{2}>I_{2} \)
В. \( C l_{2}>B r_{2}>F_{2}>I_{2} \)
c. \( I_{2}>C l_{2}>B r_{2}>F_{2} \)
D. \( B r_{2}>F_{2}>I_{2}>C l_{2} \)


A satellite is revolving around a planet
in a circuit orbit of radius. ' \( r^{\prime} \) and has
angular momentum \( L \). If it is taken into
a higher orbit of radius \( ^{\prime} \mathbf{4} r^{\prime}, \) the charge
in its angulatr momentum is
A. \( L / 4 \)
B. \( L / 2 \)
c. \( 3 L / 4 \)
D. \( L \)


\( 1 \mathrm{kg} \) of \( \mathrm{NaOH} \) solution contains \( 4 \mathrm{g} \) of NaOH. The approximate concentration
of the solution is:
A. 0.1 molar
B. 0.1 molal
c. decinormal
D. about 0.1 N


In a survey it was found that \( 55 \% \) go for jogging \( , 50 \% \) do yoga \( , 42 \% \) do aerobics, \( 28 \% \) do jogging and yoga, \( 20 \% \) do yoga and aerobics, \( 12 \% \) g for jogging and aerobics and \( 10 \% \) do all three. If each
one of them go for at least one of these, then what percentage do exactly one exercise?
A . 40
B . 45
c. 57
D. 50


Assertion
A change in nitrogen base at the third
position of a codon causes change in
the expression of the codon.
Reason
A codon is mostly read by all the three nitrogen bases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


When \( Z n \) is treated with excess of
NaOH, the product obtained is :
A. \( Z n(O H)_{2} \)
в. \( Z n O H \)
c. \( N a_{2} Z n O_{2} \)
D. none of these


A quadratic equation in \( x \) is \( a x^{2}+ \)
\( \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0}, \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \) are real
numbers and the other condition is
\( \mathbf{A} \cdot a \neq 0 \)
в. \( b \neq 0 \)
c. \( c \neq 0 \)
\( \mathbf{D} \cdot b=0 \)


Which of the following electronic configuration corresponds to an inert gas?
A \( \cdot 1 s^{1} 2 s^{2} 2 p^{5} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)


To get maximum current in a resistance
of \( 3, \) one can use n rows of m cells (connected in series) connected in parallel. If the total no. of cells is 24 and the internal resistance is 0.5 ohm then:
\( A \cdot m=12, n=2 \)
B. \( m=8, n=3 \)
\( c \cdot m=2, n=12 \)
\( D \cdot m=6, n=4 \)


Zone refining method is used for
refining:
A . \( A l \)
в. \( G e \)
c. \( C u \)
D. \( F e \)


IUPAC name of the Wiilkinson's catalyst
\( \left[\boldsymbol{R h C l}\left(\boldsymbol{P} \quad \boldsymbol{P h}_{3}\right)_{3}\right] \)
A. Chlorotris (triphenylphosphine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlorotris (triphenylphosphine) rhodium (VI)


The set of values of \( p \) for which the
points of extremum of the function,
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{3}\left(\boldsymbol{p}^{2}-\mathbf{1}\right) \boldsymbol{x}+\mathbf{1} \) lie
in the interval (-2,4) is
A. (-3,5)
в. (-3,3)
c. (-1,3)
D. (-1,5)


Which of the following can be easily oxidized by air?
A \( \cdot C H_{3} C H_{2} O H \)
B \( \cdot C_{2} H_{5} C l \)
с. \( C H_{3} C H O \)
D. \( C H C l_{3} \)


\( \int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x \)


Number of \( \pi \) bonds in \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Glycosuria is the term used for
A. Loss of glucose in urine
B. Loss of blood in the urine
C. Loss of salts in the urine
D. None of these


The magnetic induction at a distance d
from the magnetic pole of the unknown strength \( m \) is \( B \). If an identical pole is now placed at a distance of \( 2 \mathrm{d} \) from the first pole, the force between the two poles is
A. ms
B. \( \frac{m B}{2} \)
\( \mathbf{c} \cdot \frac{m B}{4} \)
D. 2mB


If the lines given by \( 3 x+2 k y=2 \) and
\( \mathbf{2} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) are parallel, then the
value of \( k \) is
A \( \cdot \frac{-5}{4} \)
B. \( \frac{2}{5} \)
c. \( \frac{15}{4} \)
D. \( \frac{3}{2} \)


Small spherical balls, each of diameter \( \mathbf{0 . 6} \mathrm{cm}, \) are formed by melting a solid sphere of radius \( 3 \mathrm{cm} \). Find the number of balls thus obtained.


Predict which of the following reactions would proceed spontaneously at \( 298 \mathrm{K} ? \)
Take \( \boldsymbol{E}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}^{\boldsymbol{0}}=-\mathbf{0 . 4 4} \boldsymbol{V} \)
This question has multiple correct options
A \( \cdot \operatorname{Co}(s)+F e^{2+}(a q) \rightarrow\left(C o^{2+}(a q)+F e(s)\right. \)
\[
E_{C o^{+2} / C o}^{\ominus}=-0.28 V
\]
B. \( C d^{2+}(a q)+F e(s) \rightarrow C d(s)+F e^{2+}(a q) \)
\[
E_{C d^{2+} / C d}^{\ominus}=0.4 V
\]
c. \( C d(s)+C o^{2+}(a q) \rightarrow C d^{2+}(a q)+C o(s) \)
\[
E_{F e^{2+} / F e}^{\ominus}=-0.44 V
\]
D. \( Z n^{2+}(a q)+H_{2} \rightarrow Z n(s)+2 H^{\oplus} \)
\[
E_{Z n^{2+} / Z n}^{\ominus}=-0.76 V
\]


Which of the following has fractional
bond order?
A \( \cdot O_{2}^{2+} \)
B. \( O_{2}^{2} \)
\( \mathrm{c} \cdot F_{2}^{2} \)
D. \( H_{2}^{-} \)


When two resistances \( R_{1} \) and \( R_{2} \) are
connected in series, they consume 12W
power. When they are connected in parallel, they consume 50W power
What is the ratio of the powers of \( \boldsymbol{R}_{1} \)
and \( \boldsymbol{R}_{2} \)
A . \( 1 / 4 \)
B. 4
c. \( 3 / 2 \)
D. 3


It is likely that Ar will form the anion Ar
\( - \). If true enter 1 , else enter 0


Among the following which has the highest boiling point?
A \( \cdot C H_{3} C H_{2} \) OH
в. \( C H_{3} C H_{2} C H_{3} \)
\( \mathbf{c} \cdot C H_{2}=C H C H_{3} \)
D. \( C H_{3} O C H_{3} \)


Find the zeros of the quadratic
polynomial \( 6 x^{2}-3-7 x \) and verify the
relationship between the zeros and the coefficient of the polynomial.


Process of depositing a thin layer of zinc metal on iron objects is called:
A. rusting
B. corrosion
c. sublimation
D. galvanisation


Name the element which serves as the
cathode in the extraction of aluminium.
A. carbon
B. Graphite rods
c. Iron
D. Aluminium


A particle is dropped from a height ' \( \boldsymbol{H} \) '.
The de Broglie wavelength of the particle depends on height as
A. \( H \)
B. \( H^{-1 / 2} \)
\( \mathrm{c} \cdot H^{0} \)
D. \( H^{1 / 2} \)


\( \mathbf{F}_{2} \) is better oxidising agent than \( \mathbf{B r}_{2} \). It
is due to:
This question has multiple correct options
A. small size of flourine atom
B. more electron repulsions in flourine
c. higher electronegativity of flourine
D. non-metallic nature of fluorine


A man buys eggs at 2 for Rs 1 and an equal number at 3 for \( \operatorname{Rs} 2 \) and sells the whole at 5 for Rs \( 3 . \) His gain or loss
percent is-
A \( \cdot 2 \frac{2}{7} \% \) loss
B \( \cdot 3 \frac{6}{7} \) \% gain
c. \( 3 \frac{2}{7} \) \% loss
D. \( _{2} \frac{6}{7} \) \%


The solution of \( \frac{d y}{d x}+2 y \tan x=\sin x \)
given that \( \boldsymbol{y}=\mathbf{0}, \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\mathbf{3}} \) is
A \( \cdot y=\cos x-2 \cos ^{2} x \)
B . \( y=-\cos x+2 \cos ^{2} x \)
c. \( y=\cos x-\cos ^{2} x \)
D. \( y=2 \cos x-2 \cos ^{2} x \)


Approximate change in the volume V of a cube of side x metres caused by increasing the side by \( 3 \% \) is?


The frequency distribution of the marks
obtained by 100 students in a test carrying 50 marks then the mean is
20- 30 Marks \( \quad \begin{array}{cc}0- & 10- \\ 9 & 19\end{array} \) 29 39
No. of
students 15
20 45
A . 28.3
B . 28
c. 27.3
D. 26.4


Efforts to repeat the cloning of Dolly (the sheep) have been unsuccessful. The scientists who claim to have cloned
Dolly have been challenged to produce additional evidence that Dolly is really derived from an adult cell (an originally claimed), rather than a foetal cell which
might have contaminated the experiment (as the sceplor suggest). Which of the following could provide evidence that Dolly was created from an
adult cell, rather than a foetal cell?
A. Dolly's DNA fingerprints
B. The heterozygosity of random pieces of Dolly's DNA
c. The melting point of Dolly's DNA
D. The length of Dolly's telomeres


Rain drops fall with terminal velocity
due to:
A. Buoyancy
B. Viscosity
c. Low weight
D. surface tension


Verify Rolle's Theorem for the function \( f(x)=e^{x}(\sin x-\cos x) \) on \( \left[\frac{\pi}{4}, \frac{5 \pi}{4}\right] \)


Motion of centre of mass


A closely wound solenoid of 800 turns and area of cross-section \( 2.5 \times 10^{-4} m^{2} \)
carries a current of \( 3.0 A \). Explain the
sense in which the solenoid acts line a
bar magnet. What is its associated
magnetic moment?
\( \mathbf{A} \cdot 6 J / T \)
в. \( 0.9 J / T \)
c. \( 9 J / T \)
D. \( 0.6 J / T \)


In the figure, the radius of the smaller
circle is 3 centimetres, that of the
bigger circle is 6 centimetres and the distance between the centres of the
circles is 15 centimetres. PQ is a
tangent to both the circles. Find its
length.


When a positive integer \( y \) is divided by
\( 47, \) the remainder is \( 11 . \) Therefore, when
\( y^{2} \) is divided by \( 47, \) the remainder will
be
\( A \cdot 7 \)
B. 17
c. 27
D. 37


Which of the following is/are true
statement(s)?
A. Aldehdyes and ketones are polar compounds
B. Many naturally occuring aldehydes and ketones have been used in blending of perfumes and flavouring agents.
C. The ketones are good solvents.
D. All of the above.


(a) If a sperm with 'X' chromosome
fertilizes with an ovum with 'X'
chromosome, what will be the gender of
the baby?
(b) Who determines the sex/gender of
the baby, mother or father?
(c) Is it correct to blame the mother for
giving birth to a baby girl?
(d) Are all our characters resembles our
parents?
Mother's Sex Father's Chromosomes Chromosomes


A function \( f \) from the set of natural
numbers to integers defined by \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{l}\frac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\frac{n}{2}, \quad \text { when } n \text { is even }\end{array}\right. \)
A. neither one-one nor onto
B. one-one but not onto
c. onto but not one-one
D. one-one and onto both


Calorific value of producer gas is low because of:
A . high percent of \( N_{2} \)
B. low percent of \( C O_{2} \)
C. high percent of \( C O_{2} \)
D. low percent of \( N_{2} \)


's
for the nucleophilic addition:
\( \mathbf{A} \)
B.
\( c \)
D.


A mother cell disintegrates into 60
identical cells and each daughter cell further disintegrates into 24 smaller cells. The smallest cells are uniform
cylindrical in shape with the diameter
of \( 120 A \) and each cell is \( 6000 A \) long. The density of the smallest cell is 1.12
\( \mathrm{g} / \mathrm{cm}^{3} . \) If the molar mass of the mother cell is \( x \times 10^{10} g, \) find \( x \) (nearest integer).


The symbol of fluorine is :
\( A \cdot F \)
B. Fe
\( c \cdot F \)
D. Fu


If \( \boldsymbol{A}=\left[\begin{array}{ccc}2 & 52 & 152 \\ 4 & 106 & 358 \\ 6 & 162 & 620\end{array}\right], \) then the
determinant of the matrix \( a d j(2 A) \) is equal to:


The sensitivity of a potentiometer can be increased by
a) increasing the series resistance in the primary circuit
b) decreasing the length of the potentiometer wire
c) using a thin and high resistivity wire as a potentiometer wire
d) increasing the length of the wire
A. a and c are correct
B. b and d are correct
\( c . \) b and c are correct
D. a and d are correct


name two water soluble vitamins, their
sources and the diseases caused due to
their deficiency in diet.


If at each point of the curve \( y=x^{3}- \)
\( a x^{2}+x+1, \) the tangent is inclined at
an acute angle with the positive direction of the \( x \) -axis, then
\( \mathbf{A} \cdot a>0 \)
в. \( a \leq \sqrt{3} \)
c. \( -\sqrt{3} \leq a \leq \sqrt{3} \)
D. none of these


Suppose that \( \boldsymbol{f} \) is a differentiable
function with the property that
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{x} \boldsymbol{y} \) and
\( \lim _{h \rightarrow 0} \frac{1}{h} f(h)=3 \) then
A. \( f \) is a linear function
B \( \cdot f(x)=3 x+x^{2} \)
c. \( f(x)=3 x+\frac{x^{2}}{2} \)
D. None of these


Cyanobacteria are photosynthetic prokaryotes.Which of the following cell structures are absent in cyanobacteria?
I. Cell membrane
II. Nucleus
III. Ribosomes
A. I only
B. II only
c. ॥ only
D. I and II only
E. I and III only


The value of \( \sin ^{-1}\left(x^{2}-4 x+6\right)+ \)
\( \cos ^{-1}\left(x^{2}-4 x+6\right) \) for all \( x \epsilon R \) is
A \( \cdot \frac{\pi}{2} \)
в. \( \pi \)
\( c \cdot 0 \)
D. none of these


Let \( f(x) \) be a real-valued differentiable
function not identically zero such that \( \boldsymbol{f}\left(\boldsymbol{x}+\boldsymbol{y}^{2 n+1}\right)=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \{f(y)\}^{2 n+1}, n \epsilon N \) and \( x, y \) are any real
numbers and \( f^{\prime}(0) \geq 0 . \) Find the value
of \( f(5) \)
A . 0
B. 1
c. 2
D. 5


The sum of the nth term of the
series \( 1.2 .5+2.3 .6+3.4 .7+\ldots . . \) n terms is


Now consider two identical infinite
cylinders, parallel to each other, posed at a distance \( d>2 a \). Find the potential
energy of the system (per unit length)
\( ^{\mathrm{A}} \cdot \frac{-\pi \rho^{2} a^{4}}{2 \epsilon_{0}}\left(\log \frac{d}{a}+0.25\right) \)
\( ^{\mathbf{B}} \cdot \frac{-\pi \rho^{2} a^{4}}{2 \epsilon_{0}}\left(\log \frac{d}{a}+0.5\right) \)
\( ^{\mathbf{C}} \cdot \frac{-\pi \rho^{2} a^{4}}{2 \epsilon_{0}}\left(\log \frac{d}{a}+0.75\right) \)
\( ^{\mathrm{D} \cdot} \frac{-\pi \rho^{2} a^{4}}{2 \epsilon_{0}}\left(\log \frac{d}{a}+1\right) \)


Four particles each of mass \( \mathrm{m} \) are lying symmetrically on rim of disc of mass \( \mathrm{M} \) and radius R. Moment of inertia of this
system about an axis passing through
one of the particles and \( \perp \) to plane of disc is:


Heat is a form of energy.
A. True
B. False


A particle of mass \( 10 \mathrm{gm} \) is placed in a potential field given by \( V=\left(50 x^{2}+\right. \)
100) \( J / k g . \) The frequency of oscillation
in cycles/sec is:
A \( \cdot \frac{10}{\pi} \)
в. \( \frac{5}{\pi} \)
c. \( \frac{100}{\pi} \)
D. \( \frac{50}{\pi} \)


Assertion
The relative among \( u, v \) and \( f \) for the
spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason
The laws of reflection are strictly valid
for plane surfaces but not for large
spherical surfaces.
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


Two masses are balanced on the scale
pictured above. If the bar connecting the two masses is horizontal and massless,
what is the weight of mass \( m \) in terms of M?


If arranged order in ascending which number is in second place?
1234.456,5623.564,2563.965,9856.36
A. 1234.456
B . 5623.564
c. 2563.965
D. 9856.365


The incorrect statement(s) is/are:
A. \( M g \) cannot form complexes
B. \( B e \) can form complexes due to a very small atomic
\( \operatorname{size} \)
C. The first ionisation potential of \( B e \) is higher than that of \( M g \)
D. \( M g \) forms an alkaline hydroxide while \( B e \) forms amphoteric oxides


Oxidation state of Mg in chlorophyll is:
\( A \cdot+2 \)
B. +6
\( c \cdot+3 \)
\( D \cdot+4 \)


The area bounded by the parabola \( y^{2}= \)
\( 4 x \) and the line \( y=2 x-4 \)
A. 9 sq. units
B. 5 sq. units
c. 4 sq. units
D. 2 sq. units


Prove that parallelograms are on the
same base and between the same
parallel lines are equal in area.


Very fine particles mainly scatter coloured light.
A . Red
B. Blue
c. Green
D. Yellow


Which of the following methods is used for obtaining metals of very high purity?
A. Distillation
B. zone refiningg
c. Liquation
D. Electrolytic refining


At a depth of \( 1000 \mathrm{m} \) in an ocean, what is the absolute pressure? Given density of sea water is \( 1.03 \times 10^{3} k g m^{-3}, g= \)
\( 10 m s^{-2} \)
A. 104 atm
B. 100 atm
c. 108 atm
D. 110 atm


Simplify:
\( \boldsymbol{x}^{\boldsymbol{6}}+\boldsymbol{6} \boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{8} \)


A person standing on a train platform listening to the whistle frequency of \( 450 H z \) of the train as it approaches her at a constant speed. As the train approaches the person on the platform, she will hear the frequency (pitch) of the whistle as:
A. Greater than \( 450 H z \) but constant
B. Less than \( 450 H z \) but constant
c. Greater than \( 450 H z \) and steadily increasing
D. Less than \( 450 H z \) and steadily increasing
E. Greater than \( 450 \mathrm{Hz} \) and steadily decreasing


If sides of a triangle are \( 5,6, \) and \( 10, \) and the length of the median of biggest side id \( m, \) then find \( 100 m \)


What is the proper name of the
compound above?
A. 1 -phenoxyethane
B. m-butylhydroxybenzene
C. o-butylhydroxybenzene
D. m-butylphenol


Which of the following gases is adsorbed to maximum extent on the
given surface?
A \( . N H_{3} \)
в. \( H_{2} \)
\( c \cdot N_{2} \)
D. \( O_{2} \)


Reduction process of \( C O_{2} \) and ATP formation in plants has relationship. In this rection, ATP is
A. Formed
B. Utilised
c. Not utilised
D. None of the above


Find the value of \( \left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}} \)


Determine the \( p H \) of a \( 0.2 M \) solution of
pyridine \( C_{5} H_{5} N \)
[For pyridine \( : \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 5} \times \mathbf{1 0}^{-\mathbf{9}} \mathbf{]} \)
\( \mathbf{A} \cdot p H=4.76 \)
в. \( p H=8.43 \)
c. \( p H=9.24 \)
D. \( p H=11.73 \)


If \( f^{\prime}(3)=2 \) then
\( \lim _{h \rightarrow 0} \frac{f\left(3+h^{2}\right)-f\left(3-h^{2}\right)}{2 h^{2}} \) is
\( A \)
B. 2
c. 37
\( D \cdot \frac{1}{1} \)


(i) Name the transformer used in the
power transmitting station of a power plant.
(ii) What type of current is transmitted
from the power station?
(iii) At what voltage is this current available to our household?


In cation exchange resin, the cations of
hard water get replaced by \( \boldsymbol{K}^{+} \) ions. If this is true enter 1 , if false enter 0 .


Let \( \boldsymbol{E}_{a} \) be the electric field due to a
dipole in its axial plane distant \( \ell \) and \( \boldsymbol{E}_{\boldsymbol{q}} \) be the field in the equatorial plane distant \( l^{1}, \) then the relation between \( E_{a} \)
and \( \boldsymbol{E}_{\boldsymbol{q}} \) will be :
\( \mathbf{A} \cdot E_{a}=4 E_{q} \)
В . \( E_{q}=2 E_{a} \)
\( \mathbf{c} \cdot E_{a}=2 E_{q} \)
D. \( E_{q}=3 E_{a} \)


Find number of negative integral
solution of equation \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=-\mathbf{1 2} \)


The number of positive integers
satisfying the inequality
\[
n+1 C_{n-2}-^{n+1} C_{n-1} \leq 100 \text { is }
\]
A. One
B. Eight
c. Five
D. None of these


When two surfaces are polished, the friction coefficient between them
decreases. But the friction coefficient
increases and becomes very large if the
surfaces are made highly smooth.
Explain.


In a multistep reaction, the overall rate of reaction is equal to the :
A. Rate of slowest step
B. Rate of fastest step
c. Average rate of various step
D. The rate of last step


The equation of the plane passing through the intersection of the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6} \) and \( \boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}= \)
\( 0, \) and the point (1,1,1) is
A. \( 20 x+23 y+26 z-69=0 \)
B. \( 20 x+23 y+26 z+69=0 \)
c. \( 23 x+20 y+26 z-69=0 \)
D. None of these


Pea plants were more suitable than cattle for Mendel's experiment because
A. There were no breeding records of cattles
B. Pea plants can be self-fertilised
c. cattle are not easy to mantain
D. All pea plants have 2n chromosomes and fewer genetic traits.


An equilibrium mixture in a vessel of
capacity 100 litre contain 1 mol \( N_{2}, 2 \) mol
\( O_{2} \) and 3 mol \( N O . \) Number of moles of
\( O_{2} \) to be added so that at new
equilibrium the conc. of \( N O \) is found to be 0.04 mol/lit is:
A . \( 101 / 18 \)
в. \( 101 / 9 \)
c. \( 202 / 9 \)
D. none of these


\( \ln \) an \( A . C . \) circuit a capacitor of \( 1 \mu F \)
value is connected to a source of
frequency 1000 rad/sec. The value of capacitive reactance will be
A . \( 10 \Omega \)
в. 100\Omega
c. \( 1000 \Omega \)
D. \( 10,000 \Omega \)


Correct mirror formula is:
A \( \cdot \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \)
в. \( \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \)
c. \( \frac{1}{v}-\frac{1}{u}=\frac{1}{-f} \)
D. \( \frac{1}{v}+\frac{1}{u}=\frac{1}{-f} \)


\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm} \) and \( \mathrm{CD}=24 \)
\( \mathrm{cm}, \) If the chords are on the opposite sides of the centre and the distance
between them is \( 17 \mathrm{cm} \), the radius of the circle is:
A . \( 14 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( c \cdot 13 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Which one of the transition metal ions
have no unpaired electrons?
\( \mathbf{A} \cdot \mathbf{T}_{\mathbf{i}^{+}} \)
B. \( v^{+4} \)
\( c \cdot v^{+3} \)
\( D \cdot c r^{3} \)


A hollow metal sphere of radius \( 10 \mathrm{cm} \) is
charged such that the potential on its surface becomes \( 80 \mathrm{V} \). The potential at the centre of the sphere is?
A . \( 80 v \)
в. 800 V
c. \( 8 v \)
D. zero


An object \( 15 \mathrm{cm} \) high is placed \( 10 \mathrm{cm} \) from the optical center of a thin lens. Its
image is formed \( 25 \mathrm{cm} \) from the optical
center on the same side of the lens as
the object. The height of the image is:
\( \mathbf{A} \cdot 2.5 \mathrm{cm} \)
B. \( 0.2 \mathrm{cm} \)
\( c .16 .7 \mathrm{cm} \)
D. \( 37.5 \mathrm{cm} \)


ATP stands for
A. Adenosine triphosphate
B. Adenine diphosphate
C. Adenosine tetraphosphate
D. Adenine triphosphate


A ray of light incident normally on the
first face of a prism of refracting angle \( A \) and critical angle \( C . \) The ray emerges from the second face of the prism when the following condition satisfies:
A \( . C>A \)
в. \( C \)
c. \( C \geq A \)
D. \( C \leq A \)


Draw two tangents from a point \( 5 \mathrm{cm} \) away from the centre of a circle of
radius \( 3 \mathrm{cm} \)


A current of \( 1 /(4 \pi) \) ampere is flowing in
a long straight conductor. The line integral of magnetic induction around a closed path enclosing the current carrying conductor is
\( \mathbf{A} \cdot 10^{-7} W b m^{-1} \)
В . \( 4 \pi \times 10^{-7} \mathrm{Wb} \mathrm{m}^{-1} \)
c. \( 16 \pi^{2} 10^{-7} W b m^{-1} \)
D. zero


A straight wire of mass \( 200 g \) and length
\( 1.5 m \) carries a current of \( 2 A . \) It is
suspended in mid air by a uniform
horizontal magnetic field \( B \). The
magnitude of \( B \) (in tesla) is :
A . 0.65
в. 0.55
c. 0.75
D. 0.45


5
0
8
8


If the frequency and amplitude of a transverse wave on a string are both doubled, then the amount of energy
transmitted through the string is
A. doubled
B. become 4 time
c. becomes 16 times
D. becomes 32 times


The light which refracts most while
passing through a prism is
A . Red
B. Violet
c. Indigo
D. Yellow


What is the reagent used in Etard
reaction?
A. Chromyl chloride
B. Ethanoyl chloride
c. \( S n C l_{2} \) and \( H C l \)
D. Cadmium chloride


\( A / c \) to ohm's law, \( \frac{V}{I}= \) constant, This constant is known as
A. voltage
B. Current
c. Power
D. Resistance


The line \( 4 y-3 x+\lambda=0 \) touches the
circle \( x^{2}+y^{2}-4 x-8 y-5=0 . \) The
value of \( \lambda \) is
\( \mathbf{A} \cdot 29 \)
B . 10
c. -35
D. None of these


Which amoung the following has maximum boiling point?
A \( . C H_{3}-C H_{2}-\left(C H_{2}\right)-C H_{2} O H \)
B. \( C H_{3}-C H_{2}-C H_{2}-C_{\}^{C H}-C H_{3} \)
\( \mathbf{c} . C H_{3}-C H_{3}-C H-C H_{2}-C H_{3} \)
\( _{O H} \)
D.
\[
\begin{array}{l}C H_{3}-C_{3} \\ _{O H}^{-} C-C H_{2}-C H_{3}\end{array}
\]
OH


If surface tension (S), Moment of inertia
(I) and Planck's constant (h), were to be taken as the fundamental units, the
dimensional formula for linear
momentum would be :-
A \( \cdot S^{3 / 2} I^{1 / 2} h^{0} \)
B. \( S^{1 / 2} I^{1 / 2} h^{0} \)
c. \( S^{1 / 2} I^{1 / 2} h^{-1} \)
\( \mathbf{D} \cdot S^{1 / 2} I^{3 / 2} h^{-1} \)


Which is true for the far sightedness or hypermetropia from the following?
A. Eyelense does not became thin as per requirement
B. Distant object cannot be seen clearly
c. Nearby object cannot be seen clearly.
D. Defect can be corrected by using concave lens


Which of the following is not a part of
the ear?
A. humerus
B. cochlea
c. labyrinth
D. stapes


If one of the two slits of Young's doubleslit experiment is painted so that it transmits half the light intensity as the second slit, then
A. fringe system will altogether disappear
B. bright fringes will become brighter and the dark fringes will become darker
c. both dark and bright fringes will become darker
D. dark fringes will become less dark and bright fringes will become less bright


Echo is due to
A. reflection of sound
B. refraction of sound
c. both reflection and refraction of sound
D. diffraction of sound


'The charge on a body cannot be
\( \mathbf{A} \cdot e \)
B.
c. \( 1.5 e \)
D. all the above


Which hormone is produced by
placenta?
A . GH
B. Gastrin
c. АСТН
D. Progesterone


If the \( p H \) of a solution is \( 8, \) its \( \left[H^{+}\right] \) is:
A \( \cdot \log 10^{-8} \)
B . \( 10^{6} \)
\( c \cdot 10^{-8} \)
D. 8


The potential of neutral wire is:
A. ov
B. 300V
c. \( 220 v \)
D. 1000v


The elements in Group 17 of the Periodic Table are called the halogens. They form stable compounds with both metals and non-metals.
The table gives some data about
\[
F_{2}, H C l \text { and } C a F_{2}
\]
\( \boldsymbol{H C l} \) \( \boldsymbol{F}_{2} \)
Boiling point/ \( K \)
\( 85 \quad 188 \)
relative form 38.0 36.5 mass
Explain why \( C a F_{2} \) has a very high boiling point.


In an organic compound, phosphorus is estimated
as
A. \( M g_{2} P_{2} O_{7} \)
в. \( H_{3} P O_{4} \)
c. \( M g_{3}\left(P O_{4}\right)_{2} \)
D. \( P_{2} O_{5} \)


A charged glass rod will get discharged
on
A. connecting it to the earth
B. connecting it to another glass rod
c. breaking the ends of the rod
D. Any of the above


In in nature there may not be an element for which the principal
quantum number \( n>4 \), then the total
possible number of elements will be
A . 60
B. 32
\( c \cdot 4 \)
\( D \cdot 64 \)


If \( A \) and \( B \) are symmetric matrices of the same order, write whether \( A B- \)
\( B A \) is symmetric or skew-symmetric or
neither of the two.


Which of the following medicines is used for abortion?
A. Mifepristone
B. Misoprostal
c. chloramphenicol
D. Both A and B


Draw a neat and labelled diagram of zone refining process.


Select the correct order of decreasing reactivity of the following compounds towards the attack of Grignard reagent.
(I)Methyl benzoate (II) Benzaldehyde
(III)Benzoyl chloride (IV)Acetophenone
\( \mathbf{A} \cdot\|>\| \backslash>|>| V \)
B. III >IV >|| > |
c. \( \||>||>| \vee>\mid \)
D. II >IV > > >III


Convection currents are possible in solids
A . True
B. False


Which of the following class of forces is different from others?
A. Magnetic force
B. Electrical force
c. Gravitational force
D. Stretching of a spring


Find the slope of the line with
inclination \( 60^{\circ} \)


Toluene \( \frac{K M n O_{4} / K O H / H_{3} O \oplus}{A .} \) What is
A?
A. Acetice acid
B. Benzene
C. Benzoic acid
D. Benzaldehyde


If \( x \) is real, \( x+\frac{1}{x} \neq 0 \) and \( x^{3}+\frac{1}{x^{3}}=0 \)
then the value of \( \left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}\right)^{\mathbf{4}} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 9
c. 16
D. 25


Carnassial teeth, which are pointed molars, would most likely be part of the
dentition of a
A. human
B. cow
c. lion
D. hawk


Find the latus rectum of the parabola \( \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{y}-\mathbf{3} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D.


A plastic ball falls from a height of 4.9 metre and rebounds several times from
the floor. What is the coefficient of
restitution during the impact with the floor if 1.3 seconds pass from the first impact to the second one?
A . 0.9
B. \( 0 . \)
\( c .0 .7 \)
D. 0.8


Let \( A \) and \( B \) be the remainders when the
polynomials \( y^{3}+2 y^{2}-5 a y-7 \) and
\( y^{3}+a y^{2}-12 y+6 \) are divided by \( y+ \)
1 and \( y-2 \) respectively. If \( 2 A+B=6 \)
find the value of \( a \)


Find vector of magnitude 9 equality
inclined to the coordinate axes?


\( \Delta G(H I: g) \equiv+1.7 \quad k J . \) What is the
equilibrium constant at \( 25^{\circ} C \) for
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) ? \)
A. 24.0
B. 3.9
c. 2.0
D. 0.5


Choose the correct answers from the
alternatives given If the sequence of bases in DNA is TAGC,
then the sequence of bases in RNA would be
A . AUCG
B. TAGC
c. АТСС
D. GCTA


In given figure \( A B \) is a line segment
and line \( l \) is its perpendicular bisector.
f a point \( P \) lies on \( l \), show that \( P \) is
equidistant from \( A \) and \( B \)


In beta decay, the typical Q value is approximately:
A \( .2 \mathrm{MeV} \)
B. 1 MeV
\( \mathrm{c} \cdot 1 \mathrm{eV} \)
D. \( 10 \mathrm{MeV} \)


Which of the following metal oxides is white in colour but becomes yellow on heating?
A. \( A g_{2} O \)
в. \( Z n O \)
c. \( F e O \)
D. \( M g O \)


Find the remainder when \( x^{3}+p x^{2}+ \)
\( \boldsymbol{q} \boldsymbol{x}+\boldsymbol{r} \) is divided by \( \boldsymbol{x}^{2}+\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q} \)