Chlorine gas is passed in an aqueous potassium iodide solution to form potassium chloride solution and solid iodine. Identify the type of the reaction:
\( \mathbf{A} \)
Decompostion reaction
\( \mathbf{B} \)
Double Displacement reaction
\( \mathbf{c} \)
Displacement reaction
D. None of these


Solve \( : \int_{0}^{\frac{\pi}{2}} \tan ^{5} x \cos ^{8} x d x \)


Identıty In wnıch or the rollowıng grapns
does the moving object reverse its
direction?
\( A \)
B.
\( c \)
D.
E .


Define optical activity. How many optical isomers are possible for glucose?


Which of the following statements
is/are false?
This question has multiple correct options
A. A fast reaction has a large rate constant and short half-life
B. Half life depends on concentration of reactants for first order reaction.
C. For a first order reaction, the half-life is independent of concentration
D. The half-life of a reaction is half the time required for the reaction to go to completion


A coin is tossed 6 times. Find the
probability of getting atleast 3 heads.


Correct sequence of plants in a
hydrosere is
\( \mathbf{A} \cdot \) Pistia \( \rightarrow \) Volvox \( \rightarrow \) Scirpus \( \rightarrow \) Hydrilla \( \rightarrow \) Oak \( \rightarrow \) Lantana
B. Oak \( \rightarrow \) Lantana \( \rightarrow \) Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus
C. Oak \( \rightarrow \) Lantana \( \rightarrow \) Scirpus \( \rightarrow \) Pistia \( \rightarrow \) Hydrilla \( \rightarrow \) Volvox
D. Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus \( \rightarrow \) Lantana \( \rightarrow \) Oak


Draw the graphs of the following
equations:
\( \mathbf{2} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{6}=\mathbf{0} \)
\( 2 x+3 y-18=0 \)
\( \boldsymbol{y}-\mathbf{2}=\mathbf{0} \)
Find the vertices of the triangle so obtained. Also, find the area of the
triangle.


If \( Q \) (alkali metal) reacts with fluorine and oxygen, the molecular formula of fluoride and oxide respectively are:
A. \( Q F_{3}, Q_{2} O_{3} \)
в. \( Q F, Q_{2} O \)
\( \mathbf{c} \cdot Q F_{2}, Q O \)
D. None of these


Acids and esters having the same number of carbon atoms are:
A. functional isomers
B. tautomers
c. metamers
D. not isomers


If \( P(A)=P(B), \) then
\( A \cdot A \) and \( B \) are the same events
B. \( A \) and \( B \) must be same events
C. \( A \) and \( B \) may be different events
D. A and B are mutually exclusive events.


What steady current can be drawn from
an accumulator of capacity 80 Ah?
A. \( 4 A \) for 20 hrs
B. 40 A for 6 hrs
\( \mathrm{c} .20 \mathrm{A} \) for \( 5 \mathrm{hrs} \)
D. \( 2 A \) for 100 hrs


Assertion
Fluorine always exhibits an oxidation
state of -1 in its compounds.
Reason
Fluorine has maximum
electronegativity and it contain seven electrons in its valence shell.
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


Kidneys, lungs, gills and sweat glands,
are parts the of system in animals.
A. Digestive
B. Excretory
c. Blood circulation
D. Nervous


One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9
black balls. One ball is taken from each
bag. What is the probability that both the balls will be of the same colour?
A \( \cdot 207 / 625 \)
B. \( 191 / 625 \)
c. \( 23 / 625 \)
D. \( 227 / 625 \)


The oxide of a metal (R) can be reduced by the metal (P) and metal (R) can
reduce the oxide of metal (Q). Then the
decreasing order of the reactivity of metal (P), (Q) and (R) with oxygen is :
\( A \cdot P>Q>R \)
B. P>R > Q
c. \( R>P>Q \)
D. \( Q>P>R \)


Basic strength of \( N H_{4} O H \) in presence
of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{I} \)
A. Increase
B. Remains unchanged
c. Decreases
D. Some times increases or sometimes decrease


All of the following are the examples of fossil fuels except:
A. petroleum
B. coal
c. natural gas
D. charcoal


The type of bond between the atoms in a nitrogen molecule is :
A. hydrogen bond
B. ionic bond
c. polar covalent bond
D. pure covalent bond
E. metallic bond


A resistor \( R, \) an inductor \( L \) and \( a \)
capacitor \( C \) are connected in series to a
source of frequency \( n \). If the resonant
frequency is \( n \), then the current lags behind voltage, when
\( \mathbf{A} \cdot n=0 \)
в. \( n<n_{r} \)
\( \mathbf{c} \cdot n=n_{r} \)
D \( \cdot n>n_{r} \)


Which of the following is a source of instant energy?
A. Salt
B. Glucose
c. water
D. starch


The digits of a 3 -digit number are in \( A P \) and their sum is \( 15 . \) The number
obtained by reversing the digits is 594 less than the original number. Find the
number.


In a region with a cold climate, the
aquatic plants and animals can survive even when the atmospheric
temperature goes below \( 0^{\circ} C \) Comment on the above statement


Let \( R \) be a reflexive relation on a finite
set A having n elements, and let there be m ordered pairs in R. Then:
\( \mathbf{A} \cdot m \geq n \)
в. \( m \leq n \)
c. \( m=n \)
\( \mathbf{D} \cdot m=-n \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}^{100} \) is equal to
\( \mathbf{A} \cdot 2^{100} A \)
в. \( 2^{99} \) А
\( c \cdot 100 A \)
D . \( 299 A \)


(a) Define one tesla.
(b) Derive an expression for force experienced by a current carrying straight conductor placed in a magnetic field. How can we find the direction of force?


Electrons with a kinetic energy of
\( 6.023 \times 10^{4} J / \) mol are evolved from the
surface of a metal when it is exposed to
radiation of a wavelength of 600 nm. The minimum amount of energy
required to remove an electron from the metal atom is:
A \( .2 .3125 \times 10^{-19} \mathrm{J} \)
B . \( 3 \times 10^{-19} J \)
\( c \cdot 6.02 \times 10^{-19} J \)
\( J \)
D. \( 6.62 \times 10^{-34} J \)


In old age arteries carrying blood in the human body become narrow resulting in an increase in the blood pressure. This follows from:
A. Pascal'law
B. Stoke's law
c. Bernoulli's principle
D. Archimedes principle


Radiations of two different frequencies
whose photon energies are \( 3.4 e V \) and \( 8.2 e V \) successive illuminate a metal
surface whose work function is \( 1.8 e V \)
The ratio of the maximum speeds of the
emitted electrons will be:
A . 1: 1
B. 1: 2
\( c \cdot 1: 3 \)
D. 1: 4


Bleaching powder \( \left(C a O C l_{2}\right) \) has two types of chlorine atoms with oxidation
number of +1 and \( -1 . \) It can be
represented as:
A \( \cdot C a^{2+}\left(C l O_{2}^{-}\right) C l^{-} \)
в. \( C a^{2+}\left(C l O_{3}^{-}\right) C l^{-} \)
c. \( C a^{2+}\left(C l O^{+}\right) C l^{-} \)
D. \( C a^{2+}\left(C l O^{-}\right) C l^{-} \)


The work done to move a charge on an equipotential surface is?
A . Infinity
B. Less than 1
c. Greater than 1
D. zero


An object is displaced from position
vector \( r_{1}=(2 i+3 j) m \) to \( r_{2}=(4 i+6 j) m \) under
the action of a force \( F=\left(3 x^{2} i+2 y j\right) N . \) Finf the work done by this force.


If differential equation of family of curves \( \boldsymbol{y} \ln |\boldsymbol{c} \boldsymbol{x}|=\boldsymbol{x}, \) where \( c \) is an
arbitrary constant, is \( \boldsymbol{y}^{\prime}=\frac{\boldsymbol{y}}{\boldsymbol{x}}+\boldsymbol{\phi}\left(\frac{\boldsymbol{x}}{\boldsymbol{y}}\right) \)
for some function \( \phi \), then \( \phi(2) \) is equal
to?


A and \( \mathrm{B} \) are two points on the circle
\( \mathbf{x}^{2}+\mathbf{y}^{2}=1 . \) If the \( \mathbf{x} \) co-ordinates of \( \mathbf{A} \)
and \( \mathrm{B} \) are the roots of the equation
\( x^{2}+a x+b=0 \) and the \( y \)
coordinates of \( \mathbf{A} \) and \( \mathbf{B} \) are the roots of
the equation \( \mathbf{y}^{2}+\mathbf{b y}+\mathbf{a}=\mathbf{0} \) then the
equation of the line \( A B \) is
A \( \cdot a x+b y=0 \)
B. \( a x+b y+1=0 \)
c. \( b x+a y+a+b=0 \)
D. \( a x+b y+a+b+1=0 \)


Chlorine reacts with excess of ammonia
to form :
A \( \cdot N H_{4} C l \)
в. \( N_{2}+H C l \)
c. \( N_{2}+N H_{4} C l \)
D. \( N_{2}+N C l_{3} \)


The length and breadth of a metal sheet are \( 3.124 m \) and \( 3.002 m \) respectively.
The area of this sheet upto four correct
significant figure is :
A \( .9 .378 \mathrm{m}^{2} \)
В. \( 9.37 m^{2} \)
c. \( 9.378248 \mathrm{m}^{2} \)
D. \( 9.3782 \mathrm{m}^{2} \)


A book which is positioned on the floor is moved to a table that is one
meter above the floor. The book has:
A. Gained sound energy
B. Lost chemical energy
c. Gained potential energy
D. Gained kinetic energy
E. Lost nuclear energy


Find the value of \( K \), If the roots of the
following quadratic equation are equal \( : x^{2}+K x^{2}+1=0 \)


A spring of force constant \( 800 \mathrm{N} / \mathrm{m} \) has
an extension of \( 5 \mathrm{cm} \). Find work done in
extending it from \( 5 \mathrm{cm} \) to \( 15 \mathrm{cm} \)


Differentiate between. Stroke volume and cardiac output


What are the units of magnetic moments and magnetic induction?


Solve
\( \left(15 y^{4}+10 y^{3}-3 y^{2}\right) \div 5 y^{2} \)


ff \( \boldsymbol{x}=\boldsymbol{a} \sin \boldsymbol{\theta}+\boldsymbol{c} \cos \boldsymbol{\theta} \) and \( \boldsymbol{y}= \)
\( \boldsymbol{a} \cos \boldsymbol{\theta}-\boldsymbol{c} \sin \boldsymbol{\theta}, \operatorname{then} \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{a}^{2}+\boldsymbol{c}^{2} \)
A . True
B. False


An electromagnetic wave is radiated by
a \( 100 \mathrm{W} \) bulb. If efficiency of the bulb is \( 20 \% \) then the amplitude of magnetic field at a distance of \( 1 \mathrm{m} \) is (Consider bulb as a point source)


The reaction \( ; F_{2}+\frac{1}{2} O_{2} \longrightarrow O F_{2} \)
shows \( \Delta H= \) is
A. negative
B. positive
c. zero
D. none of the above


A turn of radius \( 20 m \) is banked for the
vehicles going at a speed of \( 36 k m / h . \) If the coefficient of static friction between
the road and the tyre is \( 0.4, \) what are the possible speeds of a vehicle so that it neither slips down nor skids up?
A \( .14 .7 \mathrm{km} / \mathrm{h} \) and \( 54 \mathrm{km} / \mathrm{h} \)
B. \( 14.2 \mathrm{km} / \mathrm{h} \) and \( 50 \mathrm{km} \)
c. \( 11.7 k m / h \) and \( 44 \mathrm{km} / \mathrm{h} \)
D. \( 17.7 \mathrm{km} / \mathrm{h} \) and \( 34 \mathrm{km} / \mathrm{h} \)


In an electron gun the control grid is given a negative potential relative to cathode in order to
A. Decelerate electrons
B. Repel electrons and thus to control the number of electrons passing through it
c. To select electrons of same velocity and to converge them along the axis
D. To decrease the kinetic energy of electrons


A piece of material moves very slowly towards a pole of magnet. The material
must be
A. Diamagnetic
B. Ferromagnetic
c. Paramagnetic
D. Ferrimagnetic


Mention the important considerations required while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED).What should be
the order of band gap of an LED if it is required to emit light in the visible range?


The relation between the slope of
isothermal curve and slope of adiabatic
Curve:
A. Slope of adiabatic curve \( =\gamma \) times slope of isothermal
curve
B. Slope of isothermal curve \( =\gamma \) times slope of adiabatic
curve
C. Slope of adiabatic curve \( =\gamma^{2} \) times slope of isothermal curve
D. Slope of isothermal curve \( =\gamma^{2} \) times slope of adiabatic curve


In a prokaryotic cell, cell division takes
place by ............................. type of reproduction


In series \( L-C-R \) circuit voltage drop
across resistance is \( 8 V, \) across
inductor is \( 6 V \) and across capacitor is
\( \mathbf{1 2} V \). Then
A. Voltage of the source will be leading in the circuit
B. Voltage drop across each element will be less than the applied voltage.
c. Power factor of the circuit will be \( 3 / 4 \)
D. None of the above


Write the value of \( \int \boldsymbol{X} \boldsymbol{a}^{\boldsymbol{x}^{2}+1} \boldsymbol{d} \boldsymbol{x} \)


Solve \( 6 x^{2}-5 x-25=0 \)


Which of the following true for an
offspring formed as a result of sexual
reproduction?
A. The offspring gets a full set of genes from the mother and from the father.
B. The offspring gets half the genes from the mother and half the genes from the father.
C. The offspring gets all of its genes from the father.
D. The offspring gets a random mixture of genes from the mother and father
E. The offspring gets all of its genes from the mother.


An electron beam projected along positive \( x \) -axis deflects along the positive y-axis.lf this deflection is caused by a magnetic field,what is the direction of the field?


Why does physisorption decrease with the increase of temperature?


A plane progressive wave is
represented by the equation \( \boldsymbol{y}= \) \( 0.25 \cos (2 \pi t-\pi x) . \) The equation of a
wave with double the amplitude and half the frequency but travelling in the opposite direction will be
A. \( y=0.5 \cos (\pi t-\pi x) \)
B. \( y=0.5 \cos (\pi t+\pi x \)
c. \( y=0.25 \cos (\pi t+2 \pi x) \)
D. \( y=0.5 \cos (2 \pi t+2 \pi x) \)


When you walk or run you push your foot \( _{\text {一一一一一一一一 }} \) (forwards, backwards)


If \( A=\left[\begin{array}{ccc}2 & 3 & 1 \\ 0 & -1 & 5\end{array}\right], B=\left[\begin{array}{ccc}1 & 2 & -1 \\ 0 & -1 & 3\end{array}\right] \)


Choose the correct answer among the alternatives given:
In the reaction products are?
\[
\langle\vec{J}\rangle-\mathrm{OCH}_{3} \stackrel{\mathrm{HBr}}{\longrightarrow}
\]
\( A \)
(a) \( \quad B r-\langle\overline{\quad}\rangle-O C H_{3} \) and \( H_{2} \)
\( B \)
(b) \( \langle\vec{J}\rangle-\mathrm{Br} \) and \( \mathrm{CH}_{3} \mathrm{Br} \)
\( c \)
(c) \( \quad\langle\bar{f}\rangle-\mathrm{Br} \) and \( \mathrm{CH}_{3} \mathrm{OH} \)
\( D \)
(d) \( \langle\vec{y}\rangle-\mathrm{OH} \) and \( \mathrm{CH}_{3} \mathrm{B}_{\mathrm{r}} \)


Observe the following figure and answer the questions:
(a) How did the human brain go on changing?
(b) Give examples of human progress?


There are three forces acting on an object : 6 N to the left, 5 N to the right and \( 3 \mathrm{N} \) to the left.What is the net force
acting on the object?
\( A \cdot 4 N \)
B. 4 N left
c. 4 N right
D. 8 N left
E. None of above


Until when does the charged particle
transmits charge to other?
A. Until the overall repulsive forces between electrons is minimised.
B. Until the overall repulsive forces between electrons is maxmised.
C. Until the overall repulsive forces between electrons is become neutral
D. None


In the circuit shown in fig., the potential
difference between the points \( C \) and \( D \) is balanced against \( 40 \mathrm{cm} \) length of
potentiometer wire of total length 100 \( \mathrm{cm} . \) In order to balance the potential
difference between the points D and \( E \) the jockey should be pressed on
potentiometer wire at a distance of
A . \( 16 \mathrm{cm} \)
B. 32 \( \mathrm{cm} \)
\( c .56 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)


The number of solution of the equation
\( 1+x^{2}+2 x \sin \left(\cos ^{-1} y\right)=0 \) is :
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


A group of plants or animals with
similar characters of any rank is
A. species
B. Genus
c. Order
D. taxon


Which among the following is the
longest phase of cell cycle?
A. Prophase
B. Telophase
\( c \cdot G_{1} \)
D. \( G_{2} \)


If \( \boldsymbol{A}^{T} \boldsymbol{B}^{T}=\boldsymbol{C}^{T} \) then \( \mathbf{C}= \)
\( A \cdot A B \)
B. BA
\( c . \) вс
D. ABC


Classification means \( _{--}- \) - of things.
A. dividing
B. grouping
c. removal
D. none of these


\( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{4}) \boldsymbol{Q}(\boldsymbol{7},-\boldsymbol{2}) \) and \( \boldsymbol{R}(-\boldsymbol{2},-1) \) are
vertices of \( \triangle P Q R \) write equation of
median


A steady current passes through a wire
of non-uniform cross-section. The
quantities which depend on the Area of
cross-section are:
A. Free electron density
B. Resistivity
C. Drift velocity
D. Charge crossing in a given time interval


A container filled with liquid up to height \( h \) is place on a smooth horizontal
surface. The container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves
in a backward direction with
acceleration \( a \) and finally, when all the liquid is drained out, it acquires a
velocity \( v . \) Neglect mass of the container. In this case
A. both \( a \) and \( v \) depend on \( h \)
B. only a depends on \( h \)
c. only \( v \) depends on \( h \)
D. neither \( a \) nor \( v \) depends on \( h \)


Which of the following structure of eye can be artificially implanted?
A. Cornea
B. Lens
c. Retina
D. Cornea and lens both


During nuclear explosion, one of the products is \( ^{90} \) Sr with half life of 28.1 yr. If \( 1 \mu g \) of \( ^{90} S r \) was absorbed in the
bones of a newly born baby instead of calcium, how much of it will remain
after 10 year and 60 year if it is not lost metabolically.


Write the slope of the line whose
inclination is \( 45^{\circ} \)


ff \( f, g: R \rightarrow R \) be two functions defined
as \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+\boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}|-\boldsymbol{x} \) for
all \( x \in R \). Then, find \( f \circ g \) and \( g \circ f \) Hence, find \( \boldsymbol{f} \circ \boldsymbol{g}(-\boldsymbol{3}), \boldsymbol{f} \circ \boldsymbol{g}(\boldsymbol{5}) \) and \( \boldsymbol{g} \)
\( \boldsymbol{f}(-2) \)


\( N_{2} \) molecule contains
and \( \quad \boldsymbol{\pi}- \) bonds
A. one, four
B. three, two
c. one, two
D. none


A solid ball is placed on a rough horizontal surface with initial velocity
of its \( C O M \) as \( v_{0} \) and initial angular
velocity \( \omega_{0} \) as shown and given in List 1


Most abundant uncombined element
present in atmosphere is :
A . ca
в. Мв
\( c \cdot A \)
\( D \)


Pollen tube of gymnosperms is
commonly
A. Unbranched and rich in starch
B. Branched and lack starch
C. Branched and rich in starch
D. Unbranched as well as lack starch


A Parallel platecapacitor made of circular plates each of radius \( \boldsymbol{R}= \)
\( 6.0 \mathrm{cm} \) has a capacitance \( 100 \mathrm{pF} \) is
connected to \( 230 \mathrm{V} \) of \( \mathrm{AC} \) supply of 300 rad/sec.frequency. The rms value of
displacement current
A. \( 6.9 \mu A \)
B . \( 2.3 \mu A \)
c. \( 9.2 \mu A \)
D. \( 4.6 \mu A \)


Use the given Venn-diagram to find: B -
4
3. 10
\( c \)
P


Write any three distinctions between \( p \) type and n-type semiconductor


The surface area of three conterminous
faces of a furniture is \( 5,10,20 \mathrm{q} . \mathrm{cm} \) respectively. Find the volume of the
cuboid.
A \( \cdot 2 \sqrt{10} \mathrm{cm}^{3} \)
B . \( 20 \sqrt{10} \mathrm{cm}^{3} \)
c. \( 40 \sqrt{10} \mathrm{cm}^{3} \)
D. \( 10 \sqrt{10} \mathrm{cm}^{3} \)


27 metal balls each of radius r are
melted together to form one big sphere of radius R. Then the ratio of surface
area of the big sphere to that of a ball is
A . 9: 1
B. 3: 2
c. \( \sqrt{27}: \sqrt{5} \)
D. \( \sqrt{3}: 1 \)


A cubical ball is taken to a depth of \( 200 \mathrm{m} \) in a sea. The decrease in volume
observed to be \( 0.1 \% \). The bulk modulus of
the ball is \( \left(10=m s^{-2}\right) \)
\( \begin{array}{ll}\text { A. } 2 \times 10^{7} & \text { Pa } \\ a\end{array} \)
В. \( 2 \times 10^{6} \) Ра
C \( .2 .1 \times 10^{9} \) Pa
D. \( 1.2 \times 10^{9} \) Pa


The converse of the statement "if \( \boldsymbol{p}<\boldsymbol{q} \)
then \( p-x<q-x^{\prime \prime} \) is :
A. If \( p<q \), then \( p-x>q-x \)
B. If \( p>q \), then \( p-x>q-x \)
C. If \( p-x>q-x \), then \( p>q \)
D. If \( p-x<q-x \), then \( p<q \)


Find out the wavelength of the electron
orbiting in the ground state of hydrogen
atom


Which of the following reagents maybe used to distinguish between but-2-yne and but-1-yne.
\( \mathbf{A} \cdot B r_{2} \) in \( C C l_{4} \)
B. Dilute \( K M n O_{4} \)
c. concentrated \( H_{2} S O_{4} \)
D. Ammonical \( C u C l \)


The one aspect, which is not a salient feature of genetic code, is its being
A. Ambiguous
B. Universal
c. specific
D. Degenerate


A saprophytic bryophyte found in the Himalayas is
A. Sphagnum
B. Marchantia
c. Parella
D. Buxbaumia


A toy car released with the same initial
speed will travel farthest on:
A. muddy surface.
B. polished marble surface
c. cemented surface
D. brick surface


An ideal mirror:
A. Absorbs all the amount of light incident on it
B. Refracts all the light
C. Reflects all the light
D. None of the above


Which of the following is the worst conductor of heat
(A) Asbestos
(B) Rubber
(B) Plastic
(C) Graphite


What is the total number of sigma bonds and pi bonds in the following
molecules? \( \boldsymbol{C}_{2} \boldsymbol{H}_{3} \boldsymbol{C l}, \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{H}_{3} \boldsymbol{C}-\dot{\boldsymbol{C}}=\stackrel{\boldsymbol{H}}{\boldsymbol{C}}- \)
\( \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \)


Sweat contains
A. Urea
B. Water
c. Sodium chloride
D. All of the above


Which sublevel is filled just before \( 5 f ? \)
A . \( 4 f \)
B. \( 7 s \)
c. \( 5 d \)
D. \( 6 d \)


If the distance between (8,0) and \( A \) is 7
then coordinates of the point \( A \) can not
be
A. (8,-7)
B. (8,7)
\( c \cdot(1,0) \)
\( D \cdot(0,-8) \)


Natural rubber is not used in making
footwear for polar regions because:
A. natural rubber becomes soft at temperature lower \( \operatorname{than} 10^{\circ} C \)
B. natural rubber becomes brittle at temperature lower \( \operatorname{than} 10^{\circ} C \)
C . natural rubber melts at temperature lower than \( 10^{\circ} \mathrm{C} \)
D. natural rubber becomes stronger at temperature lower \( \operatorname{than} 10^{\circ} C \)


Functional kidney of frog's tadpole is
A. Pronephros
B. Mesonephros
c. Holonephros
D. Metanephros


If in two circles, arcs of the same length
subtend angles \( 60^{\circ} \) and \( 75^{\circ} \) at
the centre, find the ratio of their radii.


Write three numbers whose decimal
expansions are non terminating and non recurring


Find the area of the shaded segment.
A . 11
B. 12
c. 13
D. 14


In Kjeldahl's method of estimation of
nitrogen, \( K_{2} S O_{4} \) acts as a/an:
A. oxidising agent
B. catalytic agent
c. hydrolysing agent
D. boiling point elevator


If the frequency of an A.C is made 4 times of its initial value, the inductive
reactance will
\( A \cdot \) be 4 times
B. be 2 times
c. be half
D. remain the same


The secondary windings of a transformer in which the voltage is stepped down are usually made of thicker wire than the primary. Explain why.


In a series LCR circuit at resonance, the
appiled ac voltage is \( 220 \mathrm{V} \). If bthe potential drop across the inductance is \( 110 V, \) then the potential drop across the resistance is
A \( \cdot 110 \sqrt{2} V \)
B. \( 110 V \)
c. \( 220 V \)
D. \( 220 \sqrt{2} V \)


Find the value of the determinant with
out expanding:
\( \left|\begin{array}{lll}5 & 2 & 3 \\ 7 & 3 & 4 \\ 9 & 4 & 5\end{array}\right| \)


The angle of dip at a certain place where the horizontal and vertical components of the earth's magnetic field are equal
is?
A \( .30^{\circ} \)
B . \( 75^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 45^{\circ} \)


A wire of length \( L \) and mass per unit
length \( 6.0 \times 10^{-3} k g m^{-1} \) is put under
tension of \( 540 \mathrm{N} \). Two consecutive
frequencies that it resonates at are:
\( 420 H z \) and \( 490 H z . \) Then \( L \) in meters
is:
\( \mathbf{A} \cdot 1.1 m \)
B. \( 5.1 \mathrm{m} \)
c. \( 2.1 m \)
D. \( 8.1 \mathrm{m} \)


Which of the following are endothermic
processes?
This question has multiple correct options
A. combustion of glucose
B. decomposition of water
C. dehydrogenation of ethane to ethene
D. conversion of graphite to diamond


The graph of \( 2 x+3 y=6 \) is
represented by
\( A \)
3
c. ॥
D. IV


When a volatile liquid is introduced into an evacuated closed vessel at a
particular temperature, both evaporation and condensation take place simultaneously. The system reaches equilibrium state when:
A. the liquid is completely transformed into the corresponding vapour
B. equal amounts of liquid and vapour are present in the
C. the rate of evaporation becomes equal to the rate of condensation
D. liquid cannot be converted into vapour and vice versa


The electromagnetic waves of frequency
range 100 to \( 300 G H z \) are used in


\( A 2 \times 2 \) matrix whose elements \( a_{i j} \) are
given by \( a_{i j}=i-j \) is
\( \mathbf{A} \cdot\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] \)


The focal length of a thin biconvex lens is \( 20 \mathrm{cm} . \) when an object is moved from a distance of \( 25 \mathrm{cm} \) in front of it to 50
\( \mathrm{cm}, \) the magnification of its image
changes from \( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{50} . \) The ratio of
\( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{50} \) is :
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Find out which of the following sequence are arithmetic progression. For those which are arithmetic
progression, find out the common difference. \( \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \dots \dots \)


The coordinates of a point on the line ye where perpendicular from the line \( 3 x+4 y=12 \) is 4 units, are
A \( \cdot\left(\frac{3}{7}, \frac{5}{7}\right) \)
в. \( \left(\frac{3}{2}, \frac{3}{2}\right) \)
\( c \cdot\left(-\frac{8}{7},-\frac{8}{7}\right) \)
D. \( \left(\frac{32}{7},-\frac{32}{7}\right) \)


In a cuboid, if the sum of the lenghth of
edges is represented by \( S \), the total
surface area is represented by \( \boldsymbol{T} \) and the length of diagonal is represented by
\( D, \) then the value of \( D \) is
A \( \cdot \sqrt{\frac{52}{4}-T} \)
В. \( \sqrt{\frac{S^{2}}{14}-T} \)
c. \( \sqrt{\frac{s^{2}}{16}+T} \)
D. \( \sqrt{\frac{S^{2}}{16}-T} \)


Which of these cell organelles stores starch grains and oil drops?
A. Mitochondria
B. Leucoplast
c. chloroplast
D. Ribosome


Two parallel beams of positrons moving
in the same direction will
A. Repel each other
B. Will not interact with each other
c. Attract each other
D. Be deflected normal to the plane containing the two beams


BNHS is abbreviation of
A. Banaras Natural history Society
B. Bombay Natural History Society
C. Botanical North Himalayan Survey
D. Biological Natural History Society


If natural uranium is used as fuel, the moderator used will be
A. Ordinary water
B. Graphite
c. Boron
D. Heavy water


Consider the linear inequations and
solve them graphically:
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}-\mathbf{2}>\mathbf{0} ; \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4} ; \boldsymbol{x}> \)
\( \mathbf{0} ; \boldsymbol{y} \geq \mathbf{0} \)
The solution region of these inequations
is a convex polygon with sides.
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 7


\( (A): \int e^{x}\left(\log x+x^{-2}\right) d x= \)
\( e^{x}\left(\log x-\frac{1}{x}\right)+c \)
\( (\mathrm{R}): \int e^{x}\left[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}^{\prime}(\boldsymbol{x})\right] \boldsymbol{d} \boldsymbol{x}=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{c} \)
A. Both A and R are true and R is the correct explanation
of
B. Both A and R are true but R is not correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Sum of two integers is \( +62 . \) If one of the integer is \( -48, \) then the other integer is
A \( .+14 \)
в. -14
c. -110
D. +110


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \) is
A. injective but not surjective
B. surjective but not injective
c. injective as well as surjective
D. neither injective nor surjective


Which one of the following could not be liberated from a suitable electrolyte by the passage of 0.25 faraday of electricity through that electrolyte
A. 0.25 mole of \( \mathrm{Ag} \)
B. \( 16 g \) m of \( \mathrm{Cu} \)
\( c \cdot 2 g m \) of \( 0_{2}(g) \)
D. 2.8ltrs of H at stp


Two soap bubbles of different radii \( \boldsymbol{R}_{1} \)
and \( R_{2}(<R) \) coalesee to form an
interface of radius \( R, \) The correct value
of R is
A. \( R=R_{1}-R_{2} \)
в. \( R=\frac{R_{1}+R_{2}}{2} \)
c. \( \frac{1}{R}=\frac{1}{R_{2}}-\frac{1}{R_{1}} \)
D. \( \frac{1}{R}=\frac{1}{R_{2}}+\frac{1}{R_{1}} \)


True fish possess gills and fins. Which one of the following is not a true fish?
A. Carassius
B. Hythalamincthyes
c. Hippocampus
D. Lepisma


When we cool a gas below its condensation point, the K.E. of its
molecules:
A . increases
B. decreases
c. remains the same
D. first decreases then increases


\( \operatorname{Let} A=\{1,2,3,4\} \) and \( B=\{x, y, z\} \)
Consider the subset \( \boldsymbol{R}= \)
\( \{(1, x),(1, y),(2, z),(3, x)\} \) of \( A \times B . \) Is
R, a relation from A to B? If yes, find domain and range of R. Draw arrow
diagram of \( R \) and represent \( R \) in a tabular form.


Rochelle salt is :
A. sodium tartarate
B. sodium potassium tartarate
c. ammonium tartarate
D. potassium ammonium tartarate


Sirius can be located by which constellation?
A. The great Bear
B. Cassiopeia
c. Orion
D. Leo Major


Write the following relation in the Roster
form and hence find its domain and
range \( R=\left\{\left(a, a^{2}\right) / a \) is a prime \right.
number less than \( 15\} \)


Prove that:
\( \int \frac{d x}{x^{5}} \)


Number of roots of the equation \( z^{10}- \) \( z^{5}-992=0 \) where real parts are
negative is
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
c. 5
D. 6


An atom which has a mass number of 14
and has 8 neutrons is an:
A. isotope of oxygen
B. isobar of oxygen
c. isotopes of carbon
D. isobar of carbon


Explain why phenol in water or polarprotic give \( \boldsymbol{O}-\boldsymbol{P} \) tribromo
product but in nonpolar medium like
\( C S_{2} C C l_{2} \) image ortho or \( p \) bromo product?


\( A B C D \) and \( P Q R C \) are rectangle where
\( Q \) is the mid-point of \( A C . \) Prove that
\( \boldsymbol{D} \boldsymbol{P}=\boldsymbol{P C} \)


Why is bat included under mammals?


At a party, 8 bottles of soft drink are
served for every batch of 5 children. How
many bottles would be served if 40
children were present at the party?


A particle is moving in a straight line with constant acceleration 'a' and
initial velocity \( v_{0} . \) Average velocity
during first \( t \) second is
A \( \cdot v_{0}+\frac{1}{2} \mathrm{at} \)
B. \( v_{0}+a t \)
c. \( \frac{v_{0}+a t}{2} \)
D. \( \frac{v_{0}}{2} \)


Consider the following reaction. The product (A) is:
\( A \)
в.
\( c \)
\( D \)


A ring takes time \( t_{1} \) in slipping down an inclined plane of length \( L \), whereas it
takes time \( t_{2} \) in rolling down the same
plane. The ratio of \( t_{1} \) and \( t_{2} \) is :
B . \( 1: 2^{\frac{1}{2}} \)
\( c \cdot 1: 2 \)
D. \( 1: 2^{\frac{1}{7}} \)


The force of attraction between the two
bodies \( (A, B) \) depend upon:
A. mass of \( A \)
B. mass of \( B \)
c. distance between them
D. all of the above


Which of the following is easier to hold
with a greasy palm?
A . a glass tumbler
B. a polished crockery piece
c. a metal container
D. an earthen pot


Which pair is incorrect?
A. Patella - knee cap
B. Malleus - hammer bone
C. Sternum - chest bone
D. Stapes - anvil bone


Find the area of the triangle whose
vertices are:
¡) (2,3),(-1,0),(2,-4)
ii) (-5,-1),(3,-5),(5,2)


A particle moves in a straight path such that its velocity is always 4 times its acceleration. if its velocity at time \( t=0 \) is \( 2 m / s e c, \) its velocity at \( T=2 s e c, \) is
A \( . \sqrt{2 e} m / \) sec
B . \( 2 \sqrt{e} m / \) sec
c. \( \frac{\sqrt{e}}{2} m / \) sec
D. \( \frac{2}{\sqrt{e}} m / \) sec


The refractive index of a prism is measured using three lines of a
mercury vapor lamp. If \( \mu_{1}, \mu_{2} \) and \( \mu_{3} \) are
the measured refractive indices for
these green, blue and yellow lines respectively, then
A \( \cdot \mu_{2}>\mu_{3}>\mu_{1} \)
В . \( \mu_{2}>\mu_{1}>\mu_{3} \)
c. \( \mu_{3}>\mu_{2}>\mu_{1} \)
D. \( \mu_{1}>\mu_{2}>\mu_{3} \)


A metal M of equivalent mass E forms
an oxide of molecular formula \( M_{x} O_{v} \)
The atomic mass of the metal is given by the correct equation.
\( A \cdot 2 E(y / x) \)
B. xyE
\( c \cdot E / y \)
D. y/E
E. E/2 (x/y)


What are the characteristics of heating element used in electric heating
device?


A solid spherical non-conductor of radius \( 5 \mathrm{cm} \) has the potential of \( 50 \mathrm{V} \) at its outer surface. The potential at its center is
A .100
B. 75 v
c. zero
D. 50 v


Earth pulls every object towards it with a force called:
A. Friction
B. Gravity
c. Tension
D. Collision


If all the angles of a triangle measure
less than \( 90^{\circ} \), then such a triangle is
called
A. Right angled triangle
B. Obtuse angled triangle
c. Acute angled triangle
D. None of these


Which of the following is called Berthelot's salt?
\( \mathbf{A} \cdot\left(N a P O_{3}\right)_{6} \)
в. NaOCl
c. \( K C l O_{3} \)
D. \( K H F_{2} \)


Which of the following is called energy currency of the cell?
A . ATP
в. мАDР \( H_{2} \)
\( \mathbf{c} \cdot C_{6} H_{12} O_{6} \)
D. \( C_{2} H_{5} \) ОН


Q Type your question-
where the symbols have their usual
meanings. Which of the following
graphs correctly depicts this variation?
\( A \)
\( (a) \)
в.
(b)
\( c \)
\( (c) \)
D. None of thes


Solve : 2 kL \( _{\text {一一一一一 }} \) hL \( = \)
daL=


What are the materials which contain
at least two pure substances and show
the properties of their constituents called?
A. A compound
B. An element
c. A mixture
D. A solution


The ratio in which the plane \( \vec{r} .(\hat{i}-2 \hat{j}+ \) \( \mathbf{3} \hat{k})=17 \) divides the line joining the points \( (-2 \hat{i}+4 \hat{j}+7 \hat{k}) \) and \( (3 \hat{i}-5 \hat{j}+ \)
\( \mathbf{8} \hat{\boldsymbol{k}}) \) is
A .1: 5
B. 1: 10
\( c .3: 5 \)
D. 3: 10


Organic and Inorganic compounds differ from each other in terms of :
A. melting point
B. catenation.
c. isomerism.
D. All of the above.


The activity of a catalyst is due to the presence of active centres on it.
A. True
B. False


In a Geiger Marsden experiment, calculate the distance of closest
approach to the nucleus of \( Z=\mathbf{7 5} \)
when an \( \alpha \) -particle of \( 5 M e V \) energy impinges on it before it comes momentarily to rest and reverse its direction.
How will the distance of closest
approach be affected when the kinetic energy of the \( \alpha \) -particle is doubled?


Increasing strength of H-bonding \( (\boldsymbol{X}- \)
\( --\boldsymbol{H}-\boldsymbol{X}) \) in \( \boldsymbol{S}, \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{C l}, \boldsymbol{N} \) is:
A. \( C l<S<N<O<F \)
в. \( N<C l<S<O<F \)
c. \( S<C l<N<O<F \)
D. \( S<N<C l<O<F \)


If \( \arg z<0 \) then \( \arg (-z)-\arg z \) is
equal to
A . \( \pi \)
в. \( -\pi \)
\( c \cdot-\frac{\pi}{2} \)
D.


Outer electronic configurations of
\( \boldsymbol{K}, \boldsymbol{C u}, \) and \( \boldsymbol{C r} \) are respectively :
A \( \cdot 4 s^{1}, 3 d^{10}, 3 d^{5} \)
B . \( 4 s^{2}, 3 d^{10}, 3 d^{4} \)
c. \( 4 s^{1}, 3 d^{9}, 3 d^{4} \)
D・ \( 4 s^{2}, 3 d^{9}, 3 d^{4} \)


Currents \( I_{1} \) and \( I_{2} \) flow in the wires
shown in figure. The field is zero at
distance \( x \) to the right of \( O . \) Then
\( x=\left(\frac{I_{1}}{I_{2}}\right) a \)
3. \( x=\left(\frac{I_{2}}{I_{1}}\right) a \)
\( x_{x}=\left(\frac{I_{1}-I_{2}}{I_{1}+I_{2}}\right) a \)
\( x=\left(\frac{I_{1}+I_{2}}{I_{1}-I_{2}}\right) a \)


A line source emits a cylindrical expanding wave. If the medium absorbs no energy then the amplitude will vary with distance \( r \) from the source as
proportional to
A \( \cdot r^{-1} \)
B . \( r^{-2} \)
\( c \cdot r^{-1 / 2} \)
\( \mathbf{D} \cdot r^{1 / 2} \)


mole of amino cobalt chloride on
treating with an excess of \( A g N O_{3} \)
solution gives 2 moles of \( A g C l \)
precipitate. The number of \( C l^{-} \) ions
which satisfies both primary and secondary valency of cobalt in the complex is:
A .2
B. 3
\( c . \)
D.


The field created by the current in the
bop at point \( C \) will be
\( A \cdot-\frac{\mu_{0}}{4 \pi} \hat{k} \)
B. \( -\frac{\mu_{0}}{8 \pi} \)
c. \( -\frac{\mu_{0} \sqrt{2}}{\pi} \)
D. non


Match the following and find the correct
pairs:
List List II
(a) Fleming's
(e) Direction of induced current left hand rule
(b) Right hand
(f) Magnitude and direction of thumb rule \( \quad \) magnetic induction
(c) Biot-Savart
(g) Direction of force due to law \( \quad \) magnetic induction
(d) Fleming's
(h) Direction of magnetic lines right hand rule due to current
\( A \cdot a-g, b-e, c-f, d-h \)
B. \( a-g, b-h, c-f, d-e \)
\( \mathbf{C} \cdot a-f, b-h, c-g, d-e \)
D. a-h, b-g, c-e, d-f


What is the effect on specific charge if the speed of electron increases?
A. Decreases
B. Increases
c. Remains same
D. None


Find \( \int \frac{d x}{x\left(x^{3}+1\right)^{2}} \)


Some gaseous equilibrium are following:
\( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{K}}{\rightleftharpoons} \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \)
\( 2 C O+O_{2} \stackrel{K_{1}}{\rightleftharpoons} 2 C O_{2} \)
\( 2 H_{2}+O_{2} \stackrel{K_{2}}{\rightleftharpoons} 2 H_{2} O \)
then find out the relation between
equilibrium constants :-
A \( \cdot K=K_{1} K_{2} \)
B. \( K=\left(K_{1} K_{2}\right)^{2} \)
C . \( K=\left(K_{1} K_{2}\right)^{-1 / 2} \)
D. \( K=\left(K_{1} / K_{2}\right)^{1 / 2} \)


\( \underbrace{g_{k_{n}}^{n} p_{n}} \)


Find the mean deviation about the
mean for the data
4,7,8,9,10,12,13,17


Ethyl alcohol exhibits acidic character on reacting with:
A . Acetic acid
B. Sodium metal
c. Hydrogen iodide
D. Acidic potassium dichromate


There is a planet name 'ALLEN' which has radius three times that of the earth
and density two times that of the earth. The acceleration due to gravity on 'ALLEN' will be
A \( \cdot \frac{1}{9} \) times that of earth's gravity
B. \( \frac{2}{9} \) times that of earth's gravity
c. 6 times that of earth's gravity.
D. 3 times that of earth's gravity


In metallurgy, the concentration of ore
is followed by the dressing of ore.
A. True
B. False


Adam's apple is easily observed in
A. Boys
B. Girlss
c. Both boys and girls
D. None of the above


\( \frac{\boldsymbol{C}_{\mathbf{0}}}{\mathbf{1}}+\frac{\boldsymbol{C}_{\mathbf{1}}}{\mathbf{2}}+\frac{\boldsymbol{C}_{\mathbf{2}}}{\mathbf{3}}+\ldots \ldots \ldots+\frac{\boldsymbol{C}_{\mathbf{1 0 0}}}{\mathbf{1 0 1}} \) equals
A \( \cdot \underline{\underline{2}^{101}} \)
101
B. \( \frac{2^{101}-1}{101} \)
c. \( \frac{3^{101}}{101} \)
D. \( \frac{3^{101}-1}{101} \)


The enzyme which converts glucose to ethyl alcohol is :
A. zymase
B. invertase
c. maltase
D. diastase


Recognise the figure and find out the
correct matching.
A. A-Primary structure, B-Secondary structure
B. A-Secondary structure, B-Primary structure
C. A-Secondary structure, B-Tertiary structure
D. A-Tertiary structure, B-Quaternary structure


Sound travels the fastest in which of the
following mediums?
A. water
B. steel
c. Air
D. Kerosene oil


The range of the function \( f(x)= \)
\( \sin ^{-1}\left(\log _{2}\left(-x^{2}+2 x+3\right)\right) \) is
A. \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
B. \( \left[-\frac{\pi}{2}, 0\right] \)
c. \( \left[0, \frac{\pi}{2}\right] \)
D. [-1,1]


\( f\left(\mu_{s}, \mu_{k}, \mu_{r} \) are coefficients of static \right.
friction, sliding friction and rolling friction then
A \( \cdot \mu_{s}<\mu_{k}<\mu_{r} \)
B . \( \mu_{k}<\mu_{r}<\mu_{s} \)
c. \( \mu_{r}<\mu_{k}<\mu_{s} \)
D. \( \mu_{r}=\mu_{k}=\mu_{s} \)


Which of the following reactions proceed in forward direction with an
increase in temperature?
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g)+3000 c a l \)
B \( \cdot N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g)-43200 c a l \)
\( \mathbf{c} \cdot N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+22400 c a l \)
\( \mathbf{D} \cdot C(g)+O_{2}(g) \rightleftharpoons C O_{2}(g)+94300 c a l \)


The total flux passing through the cube
is
A \( .-0.135 N m^{2} C^{-1} \)
B . \( -0.054 N m^{2} C^{-1} \)
¿. \( 0.081 N m^{2} C^{-} \)
D. zer


Convert the ration 3: 4 into percentage.


As a group, acoelomates are
characterized by:
\( A \cdot \) a body cavity called a haemocoel
B. deuterostome development
C . a coelom that is not completely lined with mesoderm
D. a solid body without a cavity surrounding internal
organs


The value of \( b \) such that scalar product of the vector \( (\hat{i}+\hat{j}+\hat{k}) \) with the unit vector parallel to the sum of the vectors \( (2 \hat{i}+4 \hat{j}-5 \hat{k}) \) and \( (b \hat{i}+2 \hat{j}+3 \hat{k}) \) is 1
is
A . -2
B. -
\( c .0 \)
D.


If a number of little droplets of water of
surface tension \( \sigma, \) all of the same
radius \( r \) combine to form a single drop
of radius \( R \) and the energy released is
converted into kinetic energy, find the velocity acquired by the bigger drop.


In a radioactive decay, an element \( _{Z} X^{A} \) emits four \( \alpha \) -particles, three \( \beta \) -particles and eight gamma photons. The atomic number and mass number of the
resulting final nucleus are
A. \( Z-11, A-16 \)
в. \( Z-5, A-13 \)
c. \( Z-5, A-16 \)
D. \( Z-8, A-13 \)


The equation \( x-2=0 \) on number line
is represented by
\( A \). a line
B. a point
c. infinitely many lines
D. two lines


Consider two equivalent, triangular hollow prisms \( A \) and \( B \) made of thin glass plates and arranged with negligible spacing as shown in the figure. A beam of white light is incident on prism A from the left. Given that the
refractive index of water is inversely
related to temperature, the beam to the right of prism B would NOT appear white if :
A . both prisms are filled with hot water \( \left(70^{\circ} \mathrm{C}\right) \)
B. both prisms are filled with cold water \( \left(7^{\circ} \mathrm{C}\right) \)
c. both prisms are empty
D. prism A is filled with hot water ( \( 70^{\circ} \mathrm{C} \) ) and prism with cold water \( \left(7^{\circ} \mathrm{C}\right) \)


The focal lengths of the objective and the eyepiece of a compound microscope are \( 2.0 \mathrm{cm} \) and \( 3.0 \mathrm{cm}, \) respectively. The distance between the objective and the eyepiece is \( 15.0 \mathrm{cm} . \) The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance, in \( c m \)
of the object and the image produced by the objective, measure from the objective lens, are respectively
A . 2.4 and 12.0
B. 2.4 and 15.0
c. 2.0 and 12.0
D. 2.0 and 3.0


Green house gas among the following is/are:
A. carbon dioxide
B. nitrogen oxides
c. methane
D. all of the above


Find \( A M \) of 7 and 27


A moving block having mass \( m \), collides with another stationary block having mass \( 4 m . \) The lighter block comes to
rest after collision. When the initial
velocity of the lighter block is \( v \), then the value of coefficient of restitution \( (e) \) will
be:
A . 0.5
B. 0.25
c. 0.4
D. 0.8


Draw labelled diagram of Haber process for the manufacture of ammonia and
write chemical equation?


Write the general valence shell electronic configuration of p-block elements.


A tower of height b and a flagstaff on top of tower subtend equal at a point on the ground, distant a from the base of the
tower. The height of the flagstaff is
A \( \cdot \frac{b^{2}}{a+b} \)
B. \( \frac{b(a+b)}{a-b} \)
c. \( \frac{b^{2}}{a-b} \)
D. \( b\left(\frac{a^{2}+b^{2}}{a^{2}-b^{2}}\right) \)


The formula of cassiterite is :
\( \mathbf{A} \cdot P b S o_{4} \)
B. \( S n O_{2} \)
\( \mathrm{c} \cdot P b O_{2} \)
D. None of these


(i) Write Hell - Volhard - Zelinsky reaction.
(ii) Write cross - aldol condensation.
(iii) Ethanoic acid is weaker acid than
benzoic acid. Why?


Clavicle is a constituent of
A. Pectoral girdle
B. Fore limbs
C. Hind limbs
D. Pelvic girdle


The specific heat of a gas is found to be 0.075 calories at constant volume and
its formula \( \boldsymbol{w} \boldsymbol{t} \) is \( \mathbf{4 0} . \) The atomicity of the gas would be:
A. one
B. two
c. three
D. four


When the coil and the magnet are both stationary
A. there is no deflection in the galvanometer.
B. galvanometer deflects
c. galvanometer bursts.
D. none


If \( A \) is required event and \( S \) is the
sample space, \( \boldsymbol{n}(\boldsymbol{A})=\mathbf{3}, \boldsymbol{n}(\boldsymbol{S})=\mathbf{6} \)
then find \( \boldsymbol{P}(\boldsymbol{A}) \)


If the self inductance of 500 turns coil
is \( 125 \mathrm{mH} \), then the self inductance of
the similar coil of \( 800 \mathrm{mH} \)
A. \( 48.8 \mathrm{mH} \)
B. 200 mH
c. \( 290 \mathrm{mH} \)
D. 320 mH


Solve \( \& \) graph the solution set of \( 3 x+ \)
\( 6 \geq 9 \) and \( -5 x>-15, x \in R \)


What is known as Ocean thermal
energy?
A. The Sun's heat warms the surface water a lot more
than the deep ocean water which creates ocean's naturally available temperature gradient
B. The Moon's heat warms the surface water a lot more
than the deep ocean water which creates ocean's naturally available temperature gradient.
C. The Solar cell's heat warms the surface water a lot more than the deep ocean water which creates ocean's naturally available temperature gradient.
D. None


Three bodies a ring \( (R), \) a solid cylinder
\( (C) \) and a solid sphere \( (S) \) having same
mass and same radius roll down the
inclined plane without slipping. They
start from rest, if \( v_{R}, v_{C} \) and \( v_{S} \) are
velocities of respective bodies on reaching the bottom of the plane, then:
A \( \cdot v_{R}=v_{C}=v_{S} \)
в. \( v_{R}>v_{C}>v_{S} \)
c. \( v_{R}<v_{C}<v_{S} \)
D. \( v_{R}=v_{C}>v_{S} \)


Bond energy of different halogen molecules will lie in the sequence
\( \boldsymbol{C l}_{2}>\boldsymbol{B r}_{2}>\boldsymbol{F}_{2}>\boldsymbol{I}_{2} \)
A. True
B. False


What is order of reaction? Write unit of
rate constant \( K \) for the zero order, first
order and second order reaction.


If \( e^{y}(x+1)=1 \) show that \( \frac{d y}{d x}=-e^{y} \)


Consider two events \( A, B \) of an
zperiment satisfying \( \boldsymbol{P}(\boldsymbol{A} \cup \overline{\boldsymbol{B}})=\frac{\mathbf{3}}{\boldsymbol{4}} \boldsymbol{\&} \)
\( P(B)=\frac{1}{2}, \) then \( P\left(\frac{A}{B}\right) \) is equal to
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.


Let \( A \) be a \( 3 \times 3 \) matrix such that
\[
\boldsymbol{A} \times\left[\begin{array}{lll}
\mathbf{1} & \mathbf{2} & \mathbf{3} \\
\mathbf{0} & \mathbf{2} & \mathbf{3} \\
\mathbf{0} & \mathbf{1} & \mathbf{1}
\end{array}\right]=\left[\begin{array}{lll}
\mathbf{0} & \mathbf{0} & \mathbf{1} \\
\mathbf{1} & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \mathbf{1} & \mathbf{0}
\end{array}\right]
\]
Then \( \boldsymbol{A}^{-1} \) is :
A.
\[
\left[\begin{array}{lll}
3 & 2 & 1 \\
3 & 2 & 0 \\
1 & 1 & 0
\end{array}\right]
\]
B.
\[
\left[\begin{array}{lll}
0 & 1 & 3 \\
0 & 2 & 3 \\
1 & 1 & 1
\end{array}\right]
\]
c.
\[
\left[\begin{array}{lll}
3 & 1 & 2 \\
3 & 0 & 2 \\
1 & 0 & 1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{lll}
1 & 2 & 3 \\
0 & 1 & 1 \\
0 & 2 & 3
\end{array}\right]
\]


A wood \( 1 \mathrm{cm} \) thick required to make a box of dimensions \( 24 c m \times 22 c m \times \)
\( 17 \mathrm{cm}, \) is
A \( \cdot 2276 \mathrm{cm}^{3} \)
B . \( 2500 \mathrm{cm}^{3} \)
c. \( 2600 c m^{3} \)
D. \( 2376 c m^{3} \)


Two components in the ratio of \( x: y \)
form an azeotropic mixture. They are
mixed in the ratio of \( x: 2 y, \) how many
moles one of the pure component \( \boldsymbol{y} \) will be evaporated before getting azeotropic
solution?


State whether given statement is True or False
Glass is a good insulator.
A. True
B. False


Optoelectronic devices work on:
A . light
B. electrical current
c. both \( A \) and \( B \)
D. none of the above


Assertion
Two bodies at different temperatures, if brought in thermal contact do not necessarily settle to the mean temperature.
Reason
The two bodies may have different thermal capacities.
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


What is Emulsion?


Draw a sketch that shows the standing
waves pattern.


In figure, there is a conducting ring having resistance \( R \) placed in the plane
of paper in a uniform magnetic field \( B_{0} \) If the ring is rotating in the plane of paper about an axis passing through
point \( \boldsymbol{O} \) and perpendicular to the plane
of paper with constant angular speed \( \omega \) in clockwise direction, then
A. point \( O \) will be at higher potential than \( A \)
B. the potential of point \( B \) and \( C \) will different
c. the current in the ring will be zero
D. the current in the ring will be \( 2 B_{0} \omega r^{2} / R \)
E. answer required


In hydrogen atomic spectrum, a series limit is found at \( 12186.3 \mathrm{cm}^{-1} \). Then it
belongs to :
A. Lyman series
B. Balmer series
c. Paschen series
D. Brackett series


The best solution to combat greenhouse
effect is
A. To use diesel vehicles
B. To stop infra-red from entering the earth
C. Afforestation and growing abundant plants
D. All of the above


A bulb of unknown volume V contains a
gas at 1 atm pressure. This bulb was
connected to another evacuated bulb of
volume \( 0.5 \mathrm{L} \) through a stop cock. When the stop cock was opened, the pressure
at each bulb becomes \( 7.58 \times 10^{4} \) Pa
mm while the temperature remained constant. Calculate V in litres.


Assertion
In Rutherford's gold foil experiment, very
few \( \alpha \) -particles are deflected back.
Reason

Nucleus present inside the atom is heavy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of rational numbers \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \)
where \( \boldsymbol{p}, \boldsymbol{q} \in \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6} \) is
A . 23
B. 32
\( c \cdot 36 \)
D. 63


If the two angles of a triangle are unequal, then the smaller angle has the
side opposite to it.
A. Smaller
B. Larger
C. May be smaller may be larger
D. The side will be equal to one of the opposite sides


Short / Long Answer Types:
What is the relationship between the
Krebs cycle and electron transport chain?


The fusion of light elements take place at about the temperatures of about
\( \mathbf{A} \cdot 30^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 10,000^{\circ} \mathrm{C} \)
D \( .2 \times 10^{0} \mathrm{C} \)


If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sin ^{2} a x}{x^{2}}, w h e n x \neq 0 \text { is continuous at } \\ k, w h e n x=0\end{array}\right. \)
\( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{k}=? \)
\( A \cdot a \)
в. \( a^{2} \)
\( c .-2 \)
D. -


Q Type your question
equal area \( A \) are used at the four
openings to keep the water in
equilibrium. Now an additional force \( \boldsymbol{F} \) is applied at each piston. The increase
in the pressure at the centre of the
container due to this addition is
\( A \cdot F \)
\( \bar{A} \)
B. 2 \( A \)
c. \( \frac{4 F}{A} \)
\( D \)


If \( f(x) \) is a function satisfying \( f\left(\frac{1}{x}\right)+ \)
\( x^{2} f(x)=0 \) for all non-zero \( x, \) then \( \int_{\sin \theta}^{\operatorname{cosec} \theta} f(x) d x \) equals to:
A \( \cdot \sin \theta+\operatorname{cosec} \theta \)
B. \( \sin ^{2} \theta \)
\( \mathrm{c} \cdot \operatorname{cosce}^{2} \theta \)
D. None of these


A particle of charge \( Q \) and mass \( m \)
travels through a potential difference \( V \) from rest. The final momentum of the
particle is:
A \( \cdot p=\sqrt{\frac{Q m}{V}} \)
в. \( P=\sqrt{Q V} \)
c. \( P=\sqrt{2 m Q V} \)
D. \( P=\sqrt{\frac{2 Q V}{m}} \)


A steel rod of length \( I, \) area of cross
section \( A, \) Young's modulus \( E \) and linear
coefficient of expansion a is heated through \( t^{\circ} C . \) The work that can be
performed by the rod when heated is
A \( \cdot(E A a t) \times(l a t) \)
B \( \cdot \frac{1}{2}(E A a t) \times(l a t) \)
c. \( \frac{1}{2}(E A a t) \times \frac{1}{2}(l a t) \)
D. 2(EAat)(lat)


Moonj is used to make furniture.
A. True
B. False


If \( \vec{A}=\vec{B}+\vec{C}, \) and the magnitudes of \( \vec{A} \) \( \vec{B}, \vec{C} \) are \( 5,4, \) and 3 units, then the angle between \( \vec{A} \) and \( \vec{C} \) is
A \( \cdot \cos ^{-1}\left(\frac{3}{5}\right) \)
B. \( \cos ^{-1}\left(\frac{4}{5}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{3}{4}\right) \)
D. \( \frac{\pi}{2} \)


Construct a triangle \( A B C \) in which
\( B C=8 c m, \angle B=45^{\circ} \) and \( A B- \)
\( A D=3.5 \mathrm{cm} \)


An atom has \( 2 K, 8 L \) and \( 5 M \) electrons.
Choose the correct statement(s)
regarding it.
A. Trivalent anion of this atom will have
12 protons in its nucleus.
B. Trivalent cation of this atom will have
six p-electrons in it.
C. This atom form an amphoteric oxide
of formula \( X_{2} O_{3} \)
D. One of its allotrope is tetra atomic
\( \left(X_{4}\right) \)
A. \( A \) and \( B \)
B. \( B \) only
c. \( B \) and \( C \)
D. \( B \) and \( D \)


The Braille code used by blind people use dot patterns for words. How many dot patterns or characters are
used for this code?
A . 52
B. 63
\( c \cdot 48 \)
D. 26


If \( \frac{a+b}{1-a b}, b \) and \( \frac{(b+c)}{1-b c} \) are in A.P., then
\( c, a b c, a \) are in
A. A.P.
в. G.P.
c. н.P
D. none of these


A steel wire is stretched by 1 kg wt. If the radius of the wire is doubled,
its Young's modulus will:
A. remain unchanged
B. become half
c. become double
D. become four times


Find the number of real numbers in
the solution set of following \( \frac{2 x}{5}+1<-3 \)
A . 10
B. 11
\( c \cdot 9 \)
D. Infinite


Two spheres are placed into free fall
from rest. Sphere B has a mass three
times larger than sphere A.Which statement(s) correctly explains the situation?
I. Sphere B falls faster.
Il. Sphere B has more momentum when the two reach the ground.
III. Both spheres reach the ground with
the same kinetic energy
A. I only
B. II only
c. I and III only
D. II and II only
E . ।, II, and III


For all \( a, b \in R \) the function \( f(x)= \)
\( 3 x^{4}-4 x^{3}+6 x^{2}+a x+b \) has
A. no extremumm
B. exactly one extremum
c. exactly two extremum
D. three extremum


Write the special characteristics/features of the human
excretory system


In the figures given below, write which
lines form a pair of parallel lines and
write them in the form of symbols:
(1)
(2)
(3)
(4)


Eye lens is a:
A. transparent double-convex lens
B. transparent double-concave lens
C . transparent concavo-convex lens
D. None of these


Some of the following are suspensions:
I : Fog ;
Il: Air ;
III : Blood
IV : Paint ;
V: Aerosol sprays ;
VI : Pearl
True suspensions are :
A . ।, ॥।, ॥।
B. ॥I, IV, V
c. ।, ॥ा, v
D. I, II,V


Assertion
\( I O_{3}^{-} \) is reduced to \( I^{+} \) but intermediate
gives violet color in \( C C I_{4} \) (taken as
medium).
Reason
\( I_{2} \) is formed as the intermediate
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


With the increase in the area of contact
of an object, the pressure:
(Note : Thrust remains same)
A. Increases
B. Decreases
c. Is not affected
D. None of these


State whether given statement is True or False.

The motion of a giant wheel is a circular motion
A. True
B. False


State whether the given statement is True or False:
A small isolated conductor has a large
positive charge. The electric field inside this conductor will be zero.
A. True
B. False


A hydrocarbon has molecular formula
\( C_{4} H_{6} . \) Which of the class of
hydrocarbons cannot have this formula?
A. A cycloalkene
B. A bicycloalkane
c. A diene
D. A bicycloalkene


If \( y=a^{\frac{1}{2} \log _{a} \cos x} . \) Find \( \frac{d x}{d} \)


A charge \( Q \) is located at the centre of a
sphere of radius \( R \) Calculate the flux
going out through the surface of the
sphere
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)
в. \( \frac{Q}{4 \pi \epsilon_{0} R} \)
c. \( \frac{Q}{4 \pi R^{2}} \)
D. \( \underline{Q} \)


\( A, B \) and \( C \) start a business each
investing Rs 20000 After 5 months \( A \) withdraw Rs \( 5000, \) B withdraw Rs 4000 and \( C \) invests \( R s 6000 \) more \( A t \) the end
of the year a total profit of Rs 69900 was recorded Find the share of each
A. Rs. 20500, Rs.27200, Rs. 22200
B. Rs. 20500, Rs.25200, Rs. 24200
c. \( R s .20500, \) Rs.21200, Rs. 28200
D. Rs. 20500, Rs.23200, Rs. 26200


Why are noble gases missing from Newland's octaves?


A particle executing simple harmonic motion with time period T. The time period with which its kinetic energy oscillates is
A. \( T \)
B . 2 T
c. 4 न
D.


Assuming the mass of Earth to be ten times the mass of Mars, its radius to be
twice the radius of Mars and the
acceleration due to gravity on the
surface of Earth is \( 10 \mathrm{m} / \mathrm{s}^{2} \). Then the
acceleration due to gravity on the surface of Mars is given by.
A \( \cdot 0.2 m / s^{2} \)
B. \( 0.4 m / s^{2} \)
c. \( 2 m / s^{2} \)
D. \( 4 m / s^{2} \)
E \( .5 \mathrm{m} / \mathrm{s}^{2} \)


Choose the statement that best
describes given compounds.
A. 1,3,4 represent same compounds
B. 1 and 3 are isomer of 2 and 4
C. 1,4 are isomer represent the compound
D. All the structure represent the same compound


The reaction of chlorine with \( \mathrm{CO} \) in the
presence of sun light gives:
A \( \cdot \mathrm{COCl}_{2} \)
в. \( \mathrm{co}_{2} \mathrm{cl}_{2} \)
c. HOCl
D. \( \mathrm{H}_{2} \mathrm{C} 1_{2} \mathrm{O}_{2} \)


If two angles of a triangle are \( \tan ^{-1}(2) \)
and \( \tan ^{-1}(3), \) then the third angle is
\( ^{A} \cdot \frac{\pi}{4} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


Which is true about Trypanosoma
A. Polymorphic
B. Monogenetic
C. Facultative parasite
D. Non-pathogenic


If \( \boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{k}}\right)=\boldsymbol{C} \) for \( \mathbf{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then \( \boldsymbol{P}(\boldsymbol{A}) \)
equals
A \( \cdot 1 / 2 \)
в. \( 2 / 3 \)
\( c \cdot 1 / 6 \)
D. \( 1 /(n+1) \)


The only family showing resupination is
A. Leguminosae
B. Compositae
c. orchidaceae
D. Malvaceae


set the following vectors in the increasing order of their magnitudes.
a) \( 3 i+4 j \)
b) \( 2 i+4 j+6 k \)
c)2i+2j+2k
A. b,a c
B. \( c, a, b \)
\( c \cdot a, c, b \)
\( D \cdot a, b, c \)


The volume of anatomically dead space, air in the lungs of human beings is normally
A. 230 mL
B. 210 mL
\( c . \) 190 \( \mathrm{mL} \)
D. 150 mL


The standard deviation of some
temperature data in \( ^{\circ} \boldsymbol{C} \) is \( 5 . \) If the data
were converted into \( ^{\circ} \boldsymbol{F} \), the variance
would be
\( A \cdot 81 \)
B. 57
\( c . \) 36
D. 25


What is sound and how is it produced?


Which of the following is not relevant to
the structure of double helical DNA?
A. The helix makes one complete spiral turn every \( 34 A^{\circ} \)
B. The diameter of the helix is \( 20 A^{\circ} \)
C. The distance between adjacent nucleotide is \( 3.4 \mathrm{A}^{\circ} \)
D. Each strand of helix has a backbone made up of alternating ribose sugar and phosphate
E. The two adjacent sugar molecules joined with phosphate by phosphodiester bond.


A body of mass \( 6 \mathrm{kg} \) is moving with uniform velocity along a straight line when a force of \( 12 \mathrm{N} \) is acting on it. If \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}, \) find the frictional
force acting on the body.
\( A \cdot 6 N \)
B. 12 N
\( c \cdot 18 N \)
D. 24 N


Short / long answer type questions.
Describe the events involved in the
process of breathing.


what is the physical significance of negative energy of electron in atom?


Examine the continuity of the function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\frac{\log \boldsymbol{x}-\log \mathbf{7}}{\boldsymbol{x}-\mathbf{7}} & \text { for } \boldsymbol{x} \neq \mathbf{7} \\
\mathbf{7}, & \text { for } \boldsymbol{x}=\mathbf{7}
\end{array}\right.
\]
at \( x=7 \)


Histogens capping root apical meristem is
A. Dermatogen
B. Calyptrogen
c. Periblem
D. Plerome


time taken to empty the tank to half its
original value. \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


What is the direction of force on the loop if \( \frac{d i}{d t} \) is positive


Body A is in contact with body B, which is in contact with body C. The
temperature of A is more than B which
is more than C. Which of the following is the correct direction of flow in
accordance with the zeroth law of
thermodynamics.
\( A \cdot A \) to \( B \) to \( c \)
B. A to B and C to B
\( c \cdot c \) to \( B \) to \( A \)
D. B to A and B to C


One surface of a lens is convex and the
other is concave. If the radii of
curvatures are \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}, \) then the lens
Will be convex, if :
A. \( R_{1}<R_{2} \)
в. \( R_{1}>R_{2} \)
c. \( R_{1}=R_{2} \)
D. None of these


Verify the following:
\( \frac{-13}{24} \times\left(\frac{-12}{5} \times \frac{35}{36}\right)= \)
\( \left(\frac{-13}{24} \times \frac{-12}{5}\right) \times \frac{35}{36} \)


The quantities \( \frac{1}{\log _{4} 3}, \log _{3} 8, \frac{1}{\log _{16} 3} \) are
in
A. A.P.
в. G.P.
c. н.P
D. None of these


Charges of \( q \) coulomb but of alternately
opposite signs are placed along the \( x- \) axis at \( x=1, x=2, x=4, \ldots \) and so on. The
electric potential at the point \( x=0 \) due to
all these charges will be
A \( \cdot \frac{q}{2 \pi \epsilon_{0}} \)
в. \( \frac{q}{3 \pi \epsilon_{0}} \)
c. \( \frac{2 q}{3 \pi \epsilon_{0}} \)
D. \( \frac{q}{6 \pi \epsilon_{0}} \)


A train is approaching the platform with a speed of \( 4 m s^{-1} \). Another train is
leaving the platform with the same
speed. The velocity of sound is \( 320 m s^{-1} \)
If both the trains sound their whistles
at frequency \( 230 \mathrm{Hz} \), the number of beats heard per second will be :
\( A \cdot 10 \)
B. 8
c. 7
D. 6


Which of the following reactions are correctly represented? This question has multiple correct options
\( \mathbf{A} \)
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \frac{(\mathrm{i}) \mathrm{D}^{+}}{(\mathrm{iij}) \mathrm{H}_{2} \mathrm{O}} \mathrm{CH}_{3}-\mathrm{CH}_{2}-\underset{\mathrm{OH}}{_{\mathrm{I}}}-\mathrm{CH}-\mathrm{CH}_{2} \mathrm{D}
\]
B.
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \frac{(\mathrm{i}) \mathrm{H}^{+}}{(\mathrm{ii}) \mathrm{D}_{2} \mathrm{O}} \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2} \mathrm{O}
\]
\( c \)
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \frac{(\mathrm{i}) \mathrm{H}^{+}}{(\mathrm{ij}) \mathrm{H}_{2} \mathrm{O}} \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2} \mathrm{O}
\]
D.
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \frac{(\mathrm{i}) \mathrm{D}^{+}}{(\mathrm{ii}) \mathrm{D}_{2} \mathrm{O}} \mathrm{CH}_{3}-\mathrm{CH}_{2}-\underset{\mathrm{OD}}{_{1}}-\mathrm{CH}-\mathrm{CH}_{2} \mathrm{D}
\]


\( 5 \frac{2}{3}= \)
A \( \cdot \frac{13}{3} \)
B. 30
c. \( \frac{17}{3} \)
D. 10


If mean: median of a certain data is 2
3, what is the ratio of its mode and
mean?
A .3: 2
B. 5: 2
\( c .3: 5 \)
D. 2: 3


In the figure, find the value of \( x \)
\( \mathbf{A C}=\mathbf{C D} \)


Assertion
Symptoms of emphysema develops when a person living on plains ascends
and stays on a mountain.
Reason
Air pressure and partial pressure of oxygen falls with the rise in altitude.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In which octant, does (-4,2,3) lie?
A . Ill
в. vıи
\( c \cdot v \)
D. I


If the largest angle of a triangle is twice the sum of the other two and the
smallest one is one-fourth of the
largest, then the angles are:
\( \begin{array}{l}\text { A } \cdot 120^{\circ}, 40^{\circ}, 20^{\circ} \\ ^{\circ}\end{array}, 12^{\circ}, 10^{\circ}, 1^{\circ} \)
в. \( 120^{\circ}, 30^{\circ}, 30^{\circ} \)
c. \( 90^{\circ}, 45^{\circ}, 45^{\circ} \)
D. \( 90^{\circ}, 60^{\circ}, 30^{\circ} \)


For what value of \( \mathrm{m}, \) the points (3,5)
\( (m, 6) \) and \( \left(\frac{1}{2}, \frac{15}{2}\right) \) are collinear?


If \( \left(p^{2}-2 p+1\right) x^{2}-\left(p^{2}-3 p+2\right) x+ \)
\( p^{2}-1=0 \) has more then two roots
then \( p= \)


A magnifying glass has \( f=12 \mathrm{cm} . \) To produce maximum angular magnification the object should be placed at a distance of (Least distance
of clear vision \( =25 \mathrm{cm} \) ):
\( A \cdot 71 \mathrm{cm} \)
B. \( 68 \mathrm{cm} \)
c. \( 8.4 \mathrm{cm} \)
D. 8.1 \( \mathrm{cm} \)


Which of the following does not show oscillatory motion?
A. Swingg
B. Clock
c. See-saw
D. Pendulum


Find the direction cosines of the vector
joining the points \( A(1,2,-3) \) and \( B(-1,-2,1) \) directed from \( A \) to \( B \)


Law of constant composition is same as
the law of:
A. conservation of mass
B. conversation of energy
c. multiple proportion
D. definite proportion


The population of a village increases continuously at the rate proportional to the number of its inhabitants present at
any time. If the population of the village was 20,000 in 1999 and 25000 in the year \( 2004, \) what will be the population of the village in \( 2009 ? \)


When the price of a pressure cooker was increased by \( 15 \% \), the sale of pressure cooker decreased by \( 15 \% \) What was the net effect on the sales?
A. No effect
B. 15 \% increase
c. \( 2.25 \% \) increase
D. 2.25 \% decrease


Which of the following pairs has both members from the same group of periodic table?
A. \( M g, B a \)
в. \( M g, N a \)
c. \( M g, C u \)
D. \( M g, K \)


The colour of Lanthanoids and Actinoids
is due to:
A. s-ftransitions
B. p-f transitions
c. d-f transitions
D. f-f transitions


In the absence of atmosphere, the sky
appears:
A . coloured
B. blue
c. indigo
D. black


What are \( X \) and \( Y \) in the following reaction? \( \boldsymbol{C F}_{2} \boldsymbol{C l}_{2} \stackrel{\boldsymbol{u v}}{\longrightarrow} \boldsymbol{X}+\boldsymbol{Y} \)
\( \mathbf{A} \cdot \dot{C} l C F_{2}, \dot{C l} \)
в. \( C_{2} F_{4}, C l_{2} \)
c. \( C \dot{F} C l_{2}, \dot{F} \)
\( \mathbf{D} \cdot: C C l_{2}, F_{2} \)


A body falls through a distance 'h' in a
certain time on the earth. Then if the
same body is related on another planet having mass and radius twice as that of the earth, the distance through which it falls in the same time is:
\( A \cdot \frac{h}{2} \)
в. \( 2 h \)
\( c \cdot h \)
D. \( 4 h \)


How are isotopes of the same element
different?
A. They will have different locations on the periodic table.
B. They will have different numbers of electrons.
C. They will have undergo different chemical reactions.
D. They have different numbers of protons
E. They have different numbers of neutrons.


Which of the following gives blue flame when burn and is not very soluble in
water?
A. \( O_{2} \)
в. \( C O_{2} \)
c. \( N_{2} \)
D. \( H_{2} S O_{4} \)
ह. \( H e \)


Which of the following are liquid at
room temperature?
A. Alkenes having \( 5-11 \) carbon atoms per molecule
B. Alkenes having \( 5-15 \) carbon atoms per molecules
C. Alkynes having \( 5-13 \) carbon atoms per molecules
D. All of these


White light is passed through a dilute solution of potassium permagnate. The spectrum produced by the emergent light is
A. Band emission spectrum
B. Line emission spectrum
c. Band absorption spectrum
D. Line absorption spectrum


The molar conductance of a solution
with dilution while its
specific conductance with
dilution.
A. increases, decreases
B. decreases, decreases
c. increases, increases
D. decrease, increases


In certain polar solvents \( \boldsymbol{P} \boldsymbol{C l}_{5} \)
undergoes an ionisation reaction in
which \( C l^{-} \) ion leaves one \( P C l_{5} \)
molecule and attaches itself to another
\( 2 P C l_{5} \rightleftharpoons P C l_{4}^{+}+P C l_{6}^{-} \)
What are the changes in the geometrical shapes that occur in this ionisation?
A. Trigonal Bipyramidal to tetrahedral and octahedral
B. Trigonal Bipyramidal to pentagonal planar and square planar
c. Pentagonal planar to tetrahedral and octahedral
D. None of these


An object is placed at a distance of 40
\( \mathrm{cm} \) in front of a concave mirror of focal
length \( 20 \mathrm{cm} . \) The image produced is:
A. real, inverted and smaller in size
B. real, inverted, and of same size
c. real and erect
D. virtual and inverteo


Among the following which is not
isoelectronic with others?
\( \mathbf{A} \cdot H F \)
в. \( H_{2} \),
c. \( N H_{3} \)
D. \( C O \)


Finely powdered clay and limestone mixed with water is introduced in:
A. drum mixer
B. rotary kiln
c. pan-type granulator
D. dryer


The ratio of root mean square velocity to the average velocity of a gas molecule at a particular temperature is:
A .1 .086: 1 \)
B . 1: 1.086
c. 2: 1.086
D. 1.086: 2


When a \( 2 \mu \mathrm{C} \) charge is carried from point \( A \) to point \( B, \) the amount of work done by the electric field is \( 50 \mu \). What
is the potential difference and which point is at a higher potential?
A \( .25 V, B \)
в. \( 25 V, A \)
\( c \cdot 20 V, B \)
D. Both are at same potential


Statement: Acids containing hydrogen
and a non-metallic element other than
oxygen are hydroacids.

State whether the given statement is
true or false.
A. True
B. False


What is the percentage of p-character of hybrid orbitals of carbon in methane,
ethene and ethyne respectively?
A. 75,66,50
В. 50,66,75
\( \mathbf{c} \cdot 25,33,50 \)
D. 50,33,25


\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) values for \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are
\( 10^{-3}, 10^{-8} \) and \( 10^{-12} \) respectively. If
\( \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{1 0}^{-14}, \) then which is
correct?
A. Dissociation constant of \( H P O_{4}^{2-} \) is \( 10^{-12} \)
B. \( K_{b} \) of \( H P O_{4}^{2-} 10^{-6} \)
C. \( K_{b} \) of \( H_{2} P O_{4}^{-} 10^{-1} \)
D. All are correct


Two objects with unlike charges will:
A. attract each other
B. repel each other
C. neither attract nor repel
D. either attract or repel


In a triangle \( A B C, \) the least value of \( \tan ^{2} \frac{A}{2}+\tan ^{2} \frac{B}{2}+\tan ^{2} \frac{C}{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \sqrt{3} \)
D. \( \frac{2}{3} \)


In Amoeba which of the following helps in digestion?
A. Pseudopodia
B. Cytoplasm
c. Nucleus
D. vacuole


Which of the following process is used for concentration of ore?
A. Froth flotation
B. Electrolytic methods
c. smelting
D. Hoop's process


The moment of force of \( 5 N \) about a
point \( \boldsymbol{P} \) is \( 20 \mathrm{Nm} \). Calculate the
distance of point of application of the
from the point \( \boldsymbol{P} \)
\( A .3 m \)
в. \( 0.6 m \)
\( c .4 m \)
D. \( 10 m \)


Which pair belongs to basidiomycetes:
A. Puffball and Claviceps
B. Peziza and Stink Horn
C. Morchella and Mushroom
D. Bird Nest Fungus and Puffball


Numerical value of work done is
maximum in case of:
\( \mathbf{A} \cdot C_{3} H_{8}(g)+50_{2}(g) \longrightarrow 3 C O_{2}(g)+4 H_{2} O(l) \)
B. \( C(s)+C O_{2}(g)+\longrightarrow 2 C O(g) \)
\( \mathbf{c} \cdot F e(s)+4 H_{2} O(g)+\longrightarrow F e_{3} O_{4}(s)+4 H_{2}(g) \)
\( \mathbf{D} \cdot N H_{4} C l(s) \longrightarrow N H_{3}(g)+H C l(g) \)


Starting from a bare rock or a site of
volcanic eruption trace the organisms
that participate in the process of succession.


Cathode rays of velocity \( 10^{6} m s^{-1} \)
describe an approximate circular path of radius \( 1 \mathrm{m} \) in an electric field of
\( 400 V c m^{-1} . \) If the velocity of cathode
rays is doubled, the value of the electric
field needed so that the rays describe the same circular path is
A. \( 1200 V c m^{-1} \)
B. \( 100 \mathrm{Vcm}^{-1} \)
c. \( 800 V c m^{-1} \)
D. \( 1600 V c m^{-1} \)


How many nodal planes are present in
\( 4 d_{z^{2}} ? \)
\( A \cdot 2 \)
B.
c. zero
D. 3


A solution \( (x, y) \) of \( x^{2}+2 x \sin x y+1= \)
\( \mathbf{0} \) is
This question has multiple correct options
A \( .(1,0) \)
В. \( (1,7 \pi / 2) \)
D. (-1,0)


Two nucleons are at a separation of one Fermi. Protons have a charge of \( +1.6 \times \)
\( 10^{-19} \) C. The net nuclear force between
them is \( F_{1}, \) if both are neutrons, \( F_{2} \) if
both are protons and \( F_{3} \) if one is proton and the other is neutron. Then.
A \( . F_{1}=F_{2}>F_{3} \)
в. \( F_{1}=F_{2}=F_{3} \)
c. \( F_{1}<F_{2}<F_{3} \)
D. \( F_{1}>F_{2}>F_{3} \)


Which bonds stabilizes the fibrous and
globular shapes of proteins? This question has multiple correct options
A. Hydrogen bonds
B. Covalent bonds
c. Disulphide linkages
D. Van der Waals forces


is a part of the brain involved in memory, emotion and fear.
A. Amygdala
B. limbic System
c. Thalamus
D. Hippocampus


The figure gives experimentally measured B vs. H variation in a
ferromagnetic material. The retentivity
co-ercivity and saturation, respectively, of the material are :
A. \( 1.5 T, 50 A / m \) and 1.07
B. \( 150 A / m, 1.0 T \) and \( 1.5 T \)
c. \( 1.5 T, 50 A / m \) and 1.07
D. \( 1.0 T, 50 A / m \) and 1.57


Assertion(A): Let \( \boldsymbol{f}(\boldsymbol{x}) \) be twice
differentiable function such that
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=-\boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) . \) If
\( \boldsymbol{h}(\boldsymbol{x})=[\boldsymbol{f}(\boldsymbol{x})]^{2}+[\boldsymbol{g}(\boldsymbol{x})]^{2} \) and \( \boldsymbol{h}(\mathbf{1})=\mathbf{8} \)
\( \operatorname{then} h(2)=8 \)
Reason (R): Derivative of a constant
function is zero.
A. Both A and R are true R is correct reason of A
B. Both A and R are true R is not correct reason of A
c. A is true but R is false
D. A is false but R is true


Write the name of monomers used for
getting the following polymers:
(i) Teflon
(ii) Buna-N


Find the value of unknown \( x \) in the
following diagram.


Optically active substances are those
which
A. produce polarized light
B. rotate the plane of polarization of the polarized light.
c. produce double refraction
D. convert a plane polarized light into circularly polarized light


The increase in pressure required to decrease the 200 litres volume of a
liquid by \( 0.004 \% \) in kPa is : (bulk modulus of the liquid \( =2100 M P a) \)
A . 8.4
B. 84
c. 92.4
D. 168


Balmer gives an equation for wavelength of visible radiation of \( \mathrm{H} \) spectrum as \( \lambda=\frac{k n^{2}}{n^{2}-4} . \) The value of
in terms of Rydberg's constant R is
\( A \cdot R \)
B. 4R
c. \( \frac{R}{4} \)
D. \( \frac{4}{R} \)


For \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} ; \boldsymbol{x} \in[-1,1], \) the
constant of Meanvalue theorem is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D.


The kinetic energy of an electron, which is accelerated in the potential
difference of \( 100 V, \) is
A . \( 1.6 \times 10^{-10} \mathrm{J} \)
в. \( 1.6 \times 10^{8} \mathrm{J} \)
c. \( 1.6 \times 10^{-17} J \)
D. \( 1.6 \times 10^{-18} \mathrm{J} \)


By increasing the number of turns in the coil, the strength of the magnetic field:
A . decreases
B. increases
c. first decreases then increases
D. remains unchanged


The electronegativity order increases in the order:
A. \( \mathrm{C}, \mathrm{N}, \mathrm{Si}, \mathrm{P} \)
B. \( N, \) Si, \( C, P \)
c. \( \mathrm{si}, \mathrm{P}, \mathrm{C}, \mathrm{N} \)
D. \( P, \) Si, \( N, C \)


\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots \ldots \ldots . .+(\mathbf{2 n}- \)
1) \( (2 n+1)=\frac{n\left(4 n^{2}+6 n-1\right)}{3} \) is true
for
A. Only natural number \( n \geq 4 \)
B. Only natural numbers 3 \( \leq n \leq 10 \)
c. All natural numbers n
D. None


Ozone reacts with \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right] \) to
form:
A. \( F e_{2} O_{3} \)
B \( \cdot \operatorname{Fe}(O H)_{3} \)
\( \mathbf{c} \cdot F e(O H)_{2} \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


The wavelength of a certain electron
transition in the hydrogen spectrum is 4864 A. Identify the transition.
A. Third line Balmer
B. First line Lyman
c. First line Paschen
D. second line Balmer


Reducing sugar can reduce:
A. Aldehydes to alcohols
B. Ferric salts to ferrous salts
C. Chlorates to chlorides
D. Fehling solution to cuprous oxide


Q Type your question
(density \( \rho) \) moves with a velocity \( ^{\prime} v^{\prime} \)
inside the tube and comes to rest inside
the bubble. The surface tension of the
soap solution is \( T . \) After some time the
bubble, having grown to a radius' \( r^{\prime} \)
separates from the tube. Find the value
of ' \( r^{\prime} \). Assume that \( r>>b \) so that you
can consider the air to be falling
normally on the bubble's surface.
A \( \cdot \frac{4 T}{P v^{2}} \)
в. \( \frac{4 T}{P v} \)
c. \( \frac{2 T}{P v^{2}} \)
D. \( \frac{4 T}{P_{v}^{3}} \)


One fifth of a number is \( 19 . \) What will be
\( 42 \% \) of that number will be?
A . 38
в. 41.1
c. 39.9
D. 43
E. None of these


Charges \( 1 \mu c \) are placed at each of the four corners of a square of side \( 2 \sqrt{2} m \)
The potential at the point of intersection of the diagonals is
\( \left(K=9 \times 10^{9} S I \quad \text { unit }\right) \)
\( \mathbf{A} \cdot 18 \times 10^{3} V \)
B. \( 1800 V \)
c. \( 18 \sqrt{2} \times 10^{3} V \)
D. None of these


Write the approximate value of specific heat capacity of water in S.I. unit.
A \( \cdot 420 J k g^{-1} K^{-1} \)
B . \( 400 J k g^{-1} K^{-1} \)
c. \( 2100 J k g^{-1} K^{-1} \)
D. \( 4200 J k g^{-1} K^{-1} \)


In the extraction of copper from its sulphide ore, the metal is finally
obtained by the reduction of cuprous oxide with:
A. Copper (I) sulphide \( \left(C u_{2} S\right) \)
B. Sulphur dioxide \( \left(S O_{2}\right) \)
c. Iron sulphide (Fes)
D. Carbon monoxide (CO)


Primary and secondary valency of
\( \boldsymbol{P t} \) in \( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 4,4 \)
B. 4,6
\( c \cdot 6,6 \)
D. 4,2


A road runs parallel to a vertical cliff at a distance of \( 680 \mathrm{m} \) as shown in the
figure. A truck, standing at \( P \) sounded the horn at an instance and the truck
driver hears the echo after \( 4 s \). But the
sound of the horn was heard twice by a
person standing at \( Q \) within an interval
of \( 2 s . \) Give reasons why the person at \( Q \) heard the sound twice. Neglecting the wind velocity. Calculate how far the person was from the truck?


Check whether the following pairs of
triangles are congruent. If they are
congent, state the congruence criterion.


A small child tries to move a large
rubber toy placed on the ground. The toy
does not move but gets deformed under her pushing force \( (\overrightarrow{\boldsymbol{F}}) \) which is obliquely upward as shown. Then
A \( \cdot \) The resultant of the pushing force \( (\vec{F}), \) weight of the toy, normal force by the ground on the toy and the frictional force is zero
B. The normal force by the ground is equal and opposite to the weight of the toy
C . The pushing force \( (\vec{F}) \) of the child is balanced by the equal and opposite frictional force
D. The pushing force \( (\vec{F}) \) of the child is balanced by the total internal force in the toy generated due to deformation


Let the sequence \( a_{1}, a_{2}, \ldots-\ldots--a_{n} \)
form an A.P. and let \( a_{1}=0, \) prove that
\[
\frac{\boldsymbol{a}_{\boldsymbol{3}}}{\boldsymbol{a}_{2}}+\frac{\boldsymbol{a}_{\boldsymbol{4}}}{\boldsymbol{a}_{\boldsymbol{3}}}+\frac{\boldsymbol{a}_{\boldsymbol{5}}}{\boldsymbol{a}_{\boldsymbol{4}}}+_{--------}+\frac{\boldsymbol{a}_{\boldsymbol{n}}}{\boldsymbol{a}_{\boldsymbol{n}-\boldsymbol{1}}}-
\]
\( \boldsymbol{a}_{2}\left(\frac{\mathbf{1}}{\boldsymbol{a}_{2}}+\frac{\mathbf{1}}{\boldsymbol{a}_{3}}+\ldots+\frac{\mathbf{1}}{\boldsymbol{a}_{n-2}}\right)=\frac{\boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}}{\boldsymbol{a}_{2}}+ \)
\( \frac{\boldsymbol{a}_{2}}{\boldsymbol{a}_{n-1}} \)


Name the device used to increase the
voltage at the generating station.
A. Transformer
B. Capacitor
c. Diodes
D. None of the above


Block A has a weight of 300N and block
B has a weight of 50 N. If the coefficient
of kinetic friction between the incline
and block \( A \) is \( \mu_{k}=0.2 . \) Determine the speed of block A after it moves \( 1 \mathrm{m} \) down
the plane, starting from rest. Neglect the mass of the cord and pulleys.


An ideal inductor is in turn put across
\( 220 V, 50 H z \) and \( 220 V, 100 H z \)
supplies. The current flowing through it in the two cases will be then
A. equal
B. different
c. zero
D. infinite


State the condition for the following:
A lens has both its focal lengths equal.
A. Medium is different on either side of lens.
B. Medium is same on either side of lens
c. No condition required
D. Can't say


Is 'Dolly' living now-a-days?


What is mean by dispersive power of a
transparent material?


Calculate the pH of the buffer solution
containing 0.15 mole of \( N H_{4} O H \) and
0.25 mole of \( N H_{4} C l . K_{b} \) for \( N H_{4} O H \)
is \( 1.8 \times 10^{-5} \)


A car travels along a circular path of radius \( \left(\frac{50}{\pi}\right) \mathrm{m} \) with a speed of \( 10 \mathrm{m} / \mathrm{s} \)
Then what is its displacement after 17.5 seconds.
\( A \cdot \frac{50 \sqrt{2}}{\pi} \)
B. \( \frac{50 \sqrt{3}}{\pi} \)
c. \( \frac{100 \sqrt{2}}{\pi} \)
D. 175


State whether true or false:
Linear molecules have \( 3 N-5 \)
vibrational degrees of freedom, whereas
non linear molecules have \( 3 N-6 \)
vibrational degrees of freedom, where \( N \) is no. of atoms present in a molecule.
A. True
B. False


By splitting into prime factors, find the
square root of:
194481


Say true or false. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes
is 1: 2: 3
A. True
B. False


The eccentricity of the ellipse \( \frac{x^{2}}{a^{2}}+ \) \( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) if its latus-rectum is equal to
one half of its minor axis, is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D. None of these


A cylindrical vessel open at the top is \( 20 c m \) high and \( 10 c m \) in diameter. \( A \)
circular hole whose cross-sectional
\( \operatorname{area} 1 c m^{2} \) is cut at the centre of the
bottom of the vessel. Water flows from a
tube above it into the vessel at the rate
\( 100 \mathrm{cm}^{3} s^{-1} . \) The height of water in the
vessel under steady state (in cm) is


Determine enthalpy change for,
\[
\boldsymbol{C}_{3} \boldsymbol{H}_{8}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g})+
\]
\( \boldsymbol{C H}_{4}(\boldsymbol{g}) \) at \( 25^{\circ} \boldsymbol{C} \). using heat of
combustion values under standard
conditions.
\[
\begin{array}{llll}
\text { Compounds } & \boldsymbol{H}_{2}(\boldsymbol{g}) & \boldsymbol{C H}_{4}(\boldsymbol{g}) & \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{6}} \\
\boldsymbol{\Delta H}^{\mathrm{o}} \text { in } & -285.8 & -890.0 & -1560.0
\end{array}
\]
kJ/mol
The standard heat of formation of
\[
C_{3} H_{8}(g) \text { is }-103.8 k J m o l^{-1}
\]
A. \( -55.7 k J \)
B . \( -75.5 k J \)
c. -55.7
D. None of these


What is the focal length of a convex lens of focal length \( 30 \mathrm{cm} \) in contact with a concave lens of focal length 20cm? Is
the system a converging or a diverging lens? Ignore thickness of the lenses.


Across the lanthanide series, the basicity of the lanthanide hydroxides?
A. Increases
B. Decreases
c. First increase and then decrease
D. First decrease and then increase


A ball of mass \( m \) is thrown vertically
upwards. Another ball of mass \( 2 m \) is
thrown simultaneously at an angle \( \theta \) with horizontal. Both of them hit the
ground at the same time when thrown from the same height. The heights attained by the two are in the ratio?
A .2:
B. 1:
\( c \cdot 1: \cos \theta \)
D. \( 1: \sec \theta \)


Ammonia forms the complexion
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) with copper ions in the
alkaline solution because:
A. in acidic solutions, protons coordinate with ammonia molecules
B. in acidic solutions, hydration protects copper ions.
c. in alkaline solutions, insoluble \( C u(O H)_{2} \) is precipitated which is soluble in excess of any alkali
D. copper hydroxide is an atmospheric substance.


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


Differentiate between Anaerobic
Respiration and Fermentation:


A metal was irradiated by light of frequency \( 3.2 \times 10^{15} s^{-1} . \) The
photoelectron produced had its \( \mathrm{KE}, 2 \) times the KE of the photoelectron which was produced when the same metal was irradiated with a light of frequency \( 2.0 \times 10^{15} s^{-1} . \) What is the ionization
energy of metal?


A point charge \( q \) is located at the point \( (0,0,-a) . \) Consider a hemispherical surface of radius 'a' with its centre at
the origin and \( z \geq 0 . \) The modulus of the electric flux through the hemispherical
surface is:
A \( \cdot q / €_{0} \)
B \( \cdot q /\left(2 \sqrt{2} \in_{0}\right) \)
\( ^{\mathbf{c}} \cdot\left(1-\frac{1}{\sqrt{2}}\right) q / \epsilon_{0} \)
D \( \left(1-\frac{1}{\sqrt{2}}\right) q /\left(2 \in_{0}\right) \)


When a uniform wire of radius r is
stretched by a \( 2 k g \) weight, the increase
in its length is 2.00 mm. If the radius of
the wire is \( r / 2 \) and other conditions
remain in the same, increase in
its length is
A. \( 2.00 \mathrm{mm} \)
в. \( 4.00 \mathrm{mm} \)
c. \( 6.00 m m \)
D. \( 8.00 m m \)


A material has Poisson's ratio \( 0.2 . \) If a
uniform rod of its suffers longitudinal
strain \( 4.0 \times 10^{-3}, \) calculate the
percentage change in its volume.
A . \( 0.15 \% \)
B . \( 0.02 \% \)
c. \( 0.24 \% \)
D. 0.48\%


The average kinetic energy of a molecule of a perfect gas is :
A \( \cdot \frac{2}{3} k T \)
B. \( 1.5 k T \)
c. \( 2.5 k T \)
D. none of these


A dog weighting \( 5 k g \) is standing on a flat boat so that it is \( 10 \mathrm{m} \) from the
shore. The walks on the boat towards
the shore and then halts. The boat
weights \( 20 k g \) and one can assume that
then no friction between it and the
water. How far is the dog from the shore
at the end of this time?
\( \mathbf{A} \cdot 3.2 m \)
в. \( m \)
\( c .10 m \)
D. \( 6.8 m \)


How many dimension does a surface
has ?


What is momentum? Write its SI unit.
Interpret force in terms of momentum
Represent the following situation graphically Momentum versus mass when velocity
is constant


The radius of a circular park is 50 m.A
circular concrete footpath of width \( 5 \boldsymbol{m} \)
is construction around the park. Find the cost of construction at the rate of
Rs50 per \( \boldsymbol{m}^{2} \) ?


Which of the followings are correct
regarding ionization?
A. It refers to the formation of a charged atom or molecule, from the gain or loss of a full electron
B. Its neither a gain of electron nor a loss of electron
c. Both \( A \) and \( B \)
D. None of these


In majority of radioactive elements, the ratio of the number of neutrons to that
of protons
A . decreases
B. increases
c. remains constant
D. sometimes decreases sometimes increases


The condition that the equation \( a x+ \)
\( b y+c=0 \) represent a linear equation
in two variables is :
A \( . a \neq 0, b=0 \)
в. \( b \neq 0, a=0 \)
c. \( a=0, b=0 \)
D. \( a \neq 0, b \neq 0 \)


Oxides of the various metals are
converted into metal by heating but not in :
A. \( A g_{2} O \)
B. Cuo
c. Hgo
D. all are correct


The elements posses stable electronic
configuration are called as
A. Transition metals
B. Non-transition metals
c. Noble gases
D. None of these


A man throws balls into the air one after
the other, throwing one when other is at the highest point. How high the balls rise if he throws twice a second?
A . \( 2.45 \mathrm{m} \)
B. 1.25m
c. \( 19.6 \mathrm{m} \)
D. \( 4.9 \mathrm{m} \)


During germination, stem grows upward and root goes downward because
A. It depends upon light
B. Of auxin
c. It does not depend on light
D. of epinasty and hyponasty


What reactant must be present for a reaction to be classified as
combustion?
A \( \cdot C l_{2} \)
в. \( C H_{4} \)
\( c \cdot O_{2} \)
D. \( C O \)


\( 0.3500 g \) of potassium oxalate is titrated with \( 37.40 m L \) of sodium
permaganate to reach a pink end point in the following reaction:
\( \mathbf{5} C_{2} O_{4(a q)}+2 M n O_{4(a q)}^{-}+16 H_{(a q)}^{+} \rightarrow \)
\( \mathbf{2} M \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4(a q)}+\boldsymbol{6} \boldsymbol{S} \boldsymbol{O}_{4(a q)}^{2-}+\mathbf{1 0} \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})}+ \)
\( \mathbf{8} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
What was the concentration of the
sodium permanganate?


Chromosomes were first observed in
A. Nasturtium
B. Hydrilla
c. Tradescantia
D. oenothera


For which of the following reactions \( \boldsymbol{K}_{\boldsymbol{p}} \)
and \( K_{c} \) are not same?
A \( \left.\cdot H_{2}(g)+C l_{(} g\right) \rightleftharpoons 2 H C l(g) \)
B \( \cdot 2 S O_{3}(g) \rightleftharpoons 2 S O_{2}(g)+O_{2}(g) \)
c. \( N_{2}\left(g+O_{2} \rightleftharpoons 2 N O(g)\right. \)
D. None of these


Henry's law constant for oxygen
dissolved in water is \( 4.34 \times 10^{4} \) atm at
\( 25^{C} . \) If the partial pressure of oxygen in air is 0.4 atm. Calculate the
concentration (in moles per litre) of the dissolved oxygen in water in
equilibrium with air at \( 25^{\circ} C \)
\( \mathbf{A} \cdot 5.11 \times 10^{-4} \)
В. \( 5.11 \times 10^{-3} \)
c. \( 9.2 \times 10^{-6} \)
D. \( 0.92 \times 10^{-6} \)


BOD stands for
A. Biological organism death
B. Biochemical organic matter decay
C. Biotic oxidation demand
D. Biochemical oxygen demand


An Insulated vessel contains \( 0.4 \mathrm{kg} \) of
water at \( 0^{\circ} \mathrm{C} . \) A piece of \( 0.1 \mathrm{kg} \) ice at
\( -15^{\circ} C \) is put into it and steam at
\( 100^{\circ} \mathrm{C} \) is bubbled into it until all ice is
melted and finally the contents are
liquid water at \( 40^{\circ} \mathrm{C} \). Assume that
the vessel does not give or take any heat and there is no loss of matter and heat
to the surroundings. Specific heat of ice is \( 2.2 \times 10^{3} J k g^{-1} K^{-1} \) heat of fusion of
water is \( 333 \times 10^{3} J k g^{-1} \) heat of
vaporization of water is \( 2260 \times \)
\( 10^{3} J k g^{-1} . \) The amount of steam that
was bubbled into the water is:
A . \( 34.7 g \)
в. \( 236 g \)
C . 0.023 g
D. \( 48.01 g \)


Let \( f \) be a twice differentiable function
[0,2] show that if \( f(0)=0, f(1)=2 \)
and \( f(2)=4 \) then there is some point
\( \boldsymbol{x}_{0} \in[\mathbf{0}, \mathbf{2}] \) such that \( \boldsymbol{f}^{\prime \prime}\left(\boldsymbol{x}_{0}\right)=\mathbf{0} \)


Is 0.21 the multiplicative inverse of \( 4 \frac{16}{21} \)
\( ? \)
A. Yes
B. No
c. cannot say
D. None


The bond angle in \( A s H_{3} \) is greater than
that in:
A . \( N H_{3} \)
в. \( H_{2} O \)
c. \( B C l_{3} \)
D. None of these


When oil and water are into the same
vessel, two layers are observed with the less dense oil on top. These two liquids
are said to be:
A. hydrophilic
B. hydrophobic
c. insoluble
D. immiscible


How many different products can be obtained by multiplying two or more of the numbers 3,5,7,11 (without repetition)?


The metal that can not displace
hydrogen from dil. \( \boldsymbol{H} \boldsymbol{C l} \) is:
\( A . A l \)
в. \( F e \)
c. \( C u \)
D. \( Z n \)


Two block \( A \) and \( B \) are connected to
each other as shown is fig. and spring
and pulley. The block \( B \) slides at a
horizontal top surface of stationary block \( C, \) and block \( A \) slides along
vertical slides of \( C \), both with same
uniform speed. The coefficient of friction between the block is \( 0.2(l) \)
spring constant of spring is \( 1960 N / m \)
f mass of block is \( 2 k g \). Find energy
stored in spring,


Hydrogen does not combine with:
A. antimony
B. sodium
C. bismuth
D. helium


In a very long solenoid of radius \( \boldsymbol{R} \), if
the magnetic field changes at the rate of \( d B / d t . A B=B C . \) The induced emf
for the triangular circuit \( A B C \) shown in
figure is :
\( ^{A} \cdot_{R^{2}}\left(\frac{d B}{d t}\right) \)
в. \( _{4 R^{2}}\left(\frac{d B}{d t}\right. \)
\( ^{\mathrm{C}} \cdot \frac{1}{2} R^{2}\left(\frac{d B}{d t}\right) \)
D. \( 2 R^{2}\left(\frac{d B}{d t}\right. \)


For how long current of \( 3 \mathrm{A} \) has to passed through \( A g N O_{3} \) solution to coat a
metal surface of \( 80 \mathrm{cm}^{2} \) area and
thickness of \( 5 \times 10^{-4} c m . \) The density of
silver is \( 10.5 \mathrm{gm} / \mathrm{cm}^{3} \)


Which of the following change the activity of radioisotope?
A. Temperature
B. Pressure
c. chemical environment
D. None of the above


In a sequence, if \( S_{n} \) is the sum of the
first \( n \) terms and \( S_{n-1} \) is the sum of the
first \( (n-1) \) terms, then the \( n^{t h} \) term is
A. \( S_{n-2} \)
в. \( S_{n}-S_{n-1} \)
\( \mathbf{c} \cdot S_{n+1}-S_{n} \)
D. \( S_{n+1}-S_{n-1} \)


Which of the following ring compounds obeys Huckel's rule?
A \( \cdot C_{4} H_{4}^{-1} \)
B. \( C_{4} H_{4}^{+1} \)
c. \( C_{4} H_{4}^{-2} \)
D. \( C_{4} H_{4} \)


The probability of an event is greater than or equal to and less than or
equal to 1
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. -2
D. - 3


Ammonia and the ammonium ion can be differenciated by:
A. an neutron
B. a proton
c. a electron
D. hydroxide


Let \( f: N \rightarrow N \) be defined by \( f(n)= \) \( \left\{\begin{array}{l}\frac{n+1}{2}, \text { if } \mathrm{n} \text { is odd } \\ \frac{n}{2}, \text { if } \mathrm{n} \text { is even }\end{array}\right\} \) for all \( n \in N \)
State whether the function \( f \) is bijective.
Justify your answer


A square loop of side \( a \) and a straight
long wire are placed in the same plane as shown in figure. The loop has a
resistance \( \boldsymbol{R} \) and inductance \( \boldsymbol{L} \). The
frame is turned through \( 18^{\circ} \) about the
axis \( O O^{\prime} . \) What is the electric charge
that flows through the loop?
\( ^{\mathbf{A}} \cdot \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{2 a+b}{b}\right) \)
в. \( \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{b}{b^{2}-a^{2}}\right) \)
c. \( \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{a+2 b}{b}\right) \)
D. None of these


A hollow iron ball (A) and a solid iron
ball (B) and cricket ball (C) are dropped from the same height. Which among the three balls reaches the ground first? Assuming there is no resistance
due to air.
\( A \cdot A \)
B. B
\( c \cdot c \)
D. All the three balls reaches ground simultaneously


Acidified solution of chromic acid on
treatment with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) yield:
\( A \cdot C r O_{3}+H_{2} O+O_{2} \)
в. \( C r_{2} O_{3}+H_{2} O+O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5}+\mathrm{H}_{2} \mathrm{O} \)
D. \( H_{2} C r_{2} O_{7}+H_{2} O+O_{2} \)


The compound \( Y \) is:
\( \mathbf{A} \cdot C_{6} H_{4} C l_{2} \)
\( \mathbf{B} \cdot C_{6} H_{3} C l_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5}-C_{6} H_{5} \)
\( \mathrm{D} \cdot C_{6} H_{5}-C_{2} H_{5} \)


\( A B C \) is a right-angled triangle and 0 is
the mid point of the side opposite to the right angle. Explain why 0 is equidistant from \( A, B \) and \( C \) (The dotted lines are drawn additionally to help you)


Tincture of iodine is -
A . aqueous solution of \( I_{2} \)
B. solution of \( I_{2} \) in aqueous \( \mathrm{KI} \)
C . alcoholic solution of \( I_{2} \)
D. aqueous solution of \( K I \) I.


The focal length of a spherical mirror is its radius of curvature.
A . half
B. twice
c. thrice
D. equal to


The energy releasing process in which
the substrate is oxidized without an
external electron acceptor is called as
A. Aerobic respiration
B. Glycolysis
c. Fermentation
D. Photorespiration


Name a chemical which removes \( C O_{2} \)
from the air.


An ideal gas is enclosed in a container of volume \( V \) at a pressure \( P . \) It is being
pumped out of the container by using a pump with stroke volume \( v \). What is
final pressure in container after \( n- \)
strokes of the pump? (assume
temperature remains same).
\( ^{\mathbf{A}} \cdot P\left(\frac{V}{V+v}\right)^{n} \)
B. \( \frac{P V}{(V-v)^{n}} \)
c. \( P \frac{V^{n}}{v^{n}} \)
\( P\left(\frac{V}{V-v}\right)^{n} \)


The molar conductivities of \( K C l, N a C l \)
and \( K N O_{3} \) are 152,128 and
\( 111 S c m^{2} m o l^{-1} \) respectively. What is
the molar conductivity of \( N a N O_{3} ? \)
\( \mathbf{A} \cdot 101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 87 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( -101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( -391 S \mathrm{cm}^{2} \mathrm{mol}^{-} \)


\( P \) is a point on the ellipse having (3,4) and (3,-2) as the ends of minor axis. If the sum of the focal distances of \( \boldsymbol{P} \) be
equal to 10 then its equation is
A \( \cdot \frac{(x-3)^{2}}{36}+\frac{(y-1)^{2}}{12}=1 \)
в. \( \frac{(x-3)^{2}}{36}+\frac{(y-1)^{2}}{25}=1 \)
c. \( \frac{(x-3)^{2}}{25}+\frac{(y-1)^{2}}{9}=1 \)
D. \( \frac{(x-3)^{2}}{16}+\frac{(y-1)^{2}}{7}=1 \)


Prove that \( \tan (x-y)=\frac{\tan x-\tan y}{1+\tan x \tan y} \)


Find the average of first 20 multiples of
7


One side of a parallelogram is \( \frac{3}{4} \) times its adjacent side. If the perimeter of the parallelogram is \( 70 \mathrm{cm}, \) find the sides of the parallelogram.


The above laboratory setup can be used
to prepare:
A. gas lighter than air and soluble in water
B. gas heavier than air and soluble in water
c. gas soluble in water that reacts with water
D. gas insoluble in water
E. gas that reacts with water


What is an example of a single replacement reaction?
A. \( A+X \rightarrow A X \)
в. \( A X \rightarrow A+X \)
c. \( A+B X \rightarrow A X+B \)
D. \( A X+B Y \rightarrow A Y+B X \)
E . \( A+X \rightarrow B+Y \)


The unit of resistivity of the material is
A . \( \Omega \)
в. \( \Omega m \)
\( c . \Omega / m \)
D. \( m / \Omega \)