Why is catalyst added while preparing
oxygen from decomposition of \( K C l O_{3} ? \)
A. to increase the rate of reaction
B . \( K C l O_{3} \) decomposes at lower temperature
c. catalyst undergoes no change chemically or in mass
D. all of the above


Select in incorrect statement:
a) alimentary canal begins with an anterior cavity called buccal cavity.
b) tooth is embedded in a socket of
mandible bone only
c) human shows strict diphyodont type of dentition.
d) oesophagus and the trachea open into the phatynx
\( A \cdot a, b, c \& d \)
B. a, b \&
\( c \cdot a, c \& d \)
D. \( a, b \& d \)


Evaluate \( \int \frac{\log (x / e)}{(\log x)^{2}} d x \)
A \( \cdot \frac{\log x}{x}+c \)
B. \( \frac{x}{\log x}+c \)
c. \( \frac{x}{\log (x)^{2}}+c \)
D. \( \frac{(\log x)^{2}}{x}+c \)


A circuit containing a \( 20 \Omega \) resistor and
0.1 \( \mu F \) capacitor in series is connected to 230 V AC supply of angular frequency 100 rad \( s^{-1} . \) The impedance of the circuit is
A \( \cdot 10^{5} \Omega \)
B . \( 10^{4} \Omega \)
\( \mathbf{c} \cdot 10^{6} \Omega \)
D. \( 10^{10} \Omega \)


A constant current(0.5 amp) is passed
for 1 hour through (i) aqueous \( A g N O_{3} \)
(ii) aqueous \( C u S O_{4} \) and (iii) molten
\( A l F_{3}, \) separately. The ratio of the mass of the metals deposited on the cathode
is? \( \left[M_{A g}, M_{C u}, M_{A l} \) are molar masses \right. of the respective metals].
A \( \cdot M_{A g}: 2 M_{C u}: 3 M_{A l} \)
B. \( M_{A g}: M_{C u}: M_{A l} \)
\( \mathbf{c} \cdot 6 M_{A g}: 3 M_{C u}: 2 M_{A l} \)
D. \( 3 M_{A g}: 2 M_{C u}: M_{A} \)


Energy efficiency during electroplating is usually in the range:
\( A \cdot 50 \) to \( 70 \% \)
B. 80 to 85 \%
c. 85 to \( 90 \% \)
D. 90 to 99 \%


Leaves may be simple or compound.
Which of the given figures show(s)
compound leaves?
\( A \). a only
B. \( b \), c and donly
C . a and donly
D. All of these


An ideal gas having initial pressure \( \boldsymbol{P} \)
volume \( V \) and temperature \( T \) is allowed to expand adiabatically until its volume becomes \( 5.66 V \) while its temperature fall to \( \frac{T}{2} . \) How many degrees of freedom
do the gas molecules have?


Eight players \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \ldots \ldots \boldsymbol{P}_{8} \) play a
knock-out tournament. It is known that
whenever the players \( P_{i} \) and \( P_{j} \) play,
the player \( \boldsymbol{P}_{i} \) will win if \( i<j \). Assuming
that the players are paired at random in each round, the probability that the
player \( \boldsymbol{P}_{4} \) reaches the final is \( \boldsymbol{k} / \mathbf{7} \) 0. Find
\( \boldsymbol{k} \)


If a radioactive element \( _{79} A u \) emits \( \beta \)
particle, what is the new group? \( _{79} A u \) belongs to group I B (copper family)?
\( A \cdot \mid A \)
B. IB
\( c \cdot \| A \)
D. II B


In the titration of a solution of a weak
\( \operatorname{acid} H A \) and \( N a O H, \) the \( p H \) is 5.0
after \( 10 m L \) of \( N a O H \) solution has
been added and 5.60 after
\( 20 m L N a O H \) has been added.
What is the value of \( p K_{a} \) for \( H A ? \)
A . 5.15
B. 5.3
\( c .5 .6 \)
D. None of these


Very short answer type. Name the exact part of the uriniferous tubule which is directly influenced by
ADH.


Which of the following is true?
A. The ratio of sides of two similar triangles is same as the ratio of their corresponding altitudes.
B. The ratio of sides of two similar triangles is same as the ratio of their corresponding perimeters.
C. The ratio of sides of two similar triangles is same as the ratio of their corresponding area
D. The ratio of sides of two similar triangles is same as the ratio of their corresponding medians.


A coil carrying a heavy current and having large number of turns is mounted in a N-S vertical plane. A current flows in the clockwise direction.
A small magnetic needle at its centre will have its north pole in
A. east-north direction
B. west-north direction
c. east-south direction
D. west-south direction


The waveforms of a light wave traveling
in vacuum are given by \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{c} \)
The angle made by the direction of propagation of light with the \( X \) -axis is
A \( \cdot 0^{\circ} \)
B \( \cdot 45^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( \cos ^{-1} \frac{1}{\sqrt{3}} \)


Mixture of \( K N O_{3} \) and \( K N O_{2} \) can
oxidise \( C r_{2} O_{3} \) to \( C r O_{4}^{2-} \)
If true enter 1 , else 0


Q Type your question
having track,is \( \mathrm{M}=1 \mathrm{kg} \) and rests over a smooth horizontal floor.A cylinder of
radius \( r=10 \mathrm{cm} \) and mass \( \mathrm{m}=0.5 \mathrm{kg} \) is hanging by thread such that axes of cylinder and track are in same level and surface of cylinder is in contact with the track as shown in figure.When the thread is burnt, cylinder starts to move
down the track.Sufficient friction exists
between surface of cylinder and track so that cylinder does not slip. Calculate velocity of axis of cylinder and velocity
of the block when it reaches bottom of
the track.Also find force applied by
block on the floor at that moment. \( (g=10 \)
\( \left.\boldsymbol{m} / \boldsymbol{s}^{2}\right\rangle \)


Solubility is the amount of the present in the saturated solution at a
particular temperature
A. solute
B. solvent
c. dispersed phase
D. dispersed medium


If the value of Avogadro number is \( 6.023 \times 10^{23} \) mol \( ^{-1} \) and the value of
Boltzmann constant is \( 1.380 \times \)
\( 10^{-23} J K^{-1}, \) then the number of
significant digits in the calculated value of the universal gas constant is :
A .4
B. 5
\( c \cdot 3 \)
D. 2


In the following circuit diagram the
value of resistance \( X \) for the potential
difference between \( \mathrm{B} \) and \( \mathrm{D} \) is zero :
\( A .4 \) ohm
B. 6 ohm
\( c .8 \) ohm
D. 9 ohm


In a group of 10 children, there are 6
boys and 4 girls, 3 children are selected at random. Find the probability that the selected group have only one special girl.


Count total number of S.F. in \( 6.020 \times \)
\( 10^{23} \)


\( N \) cells, each of emf \( E \) and internal
resistance \( r, \) are connected in a closed
ring so that the positive terminal of each cell is joined to the negaive terminal of the next cell as shown in the
adjoining diagram. Any two points of this ring are connected through an
external resistance \( R \). Find the current
\( \operatorname{in} R \)


Show the variation of the emf generated
versus time as the armature is rotated
with respect to the direction of the
magnetic field.


In a right angled triangle, the other two
angles are:
A . acute
B. obtuse
c. right
D. none of these


How many significant figures are there in \( 30100 ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 5 \)
D. none of these


If the A.M. of the roots of a quadratic equation is \( \frac{8}{5} \) and \( A . M . \) of their reciprocals is \( \frac{8}{7}, \) then the quadratic equation is
A \( \cdot 5 x^{2}-8 x+7=0 \)
B. \( 5 x^{2}-16 x+7=0 \)
c. \( 7 x^{2}-16 x+5=0 \)
D. \( 7 x^{2}+16 x+5=0 \)


The \( K_{a} \) values of formic acid and acetic
acid are respectively \( 1.77 \times 10^{-4} \) and
\( 1.75 \times 10^{-5} . \) The ratio of the acid
strength of \( 0.1 M \) acid is:
A . 10
в. 3.178
c. 0.3
D. \( 0 . \)
E. 100


The resultant amplitude, when two
waves of same frequency but with
amplitudes \( a_{1} \) and \( a_{2} \) superimpose with a phase difference of \( \pi / 2 \) will be
A \( \cdot a_{1}^{2}+a_{2}^{2} \)
B \( \cdot \sqrt{a_{1}^{2}+a_{2}^{2}} \)
c \( \cdot a_{1}-a_{2} \)
D. \( a_{1}+a_{2} \)


Simplify the multiplication of complex numbers: \( (\mathbf{0}, \mathbf{1}) \times(\mathbf{0}, \mathbf{1}) \)
A \( \cdot(-1,-1) \)
в. (-1,0)
c. (0,1)
()
D. None of these


An inductor \( 20 \mathrm{mH} \), a capacitor \( 100 \mu \mathrm{F} \) and a resistor \( 50 \Omega \) are connected in
series across a source of emf, \( \mathrm{V}=10 \)
\( \sin 314 t . \) The power loss in the circuit is?
A . 2.74 w
в. 0.79 w
c. \( 1.13 \mathrm{w} \)
D. \( 0.43 \mathrm{w} \)


With what velocity should an \( \alpha \) -particle
travel (expressed in \( n \times 10^{6} m s e c^{-1} \)
take the value of \( n \) to the nearest
integer) towards the nucleus of a
copper atom so as to arrive at a
distance \( 10^{-13} \) metre from the nucleus
of the copper atom?


Assertion
To a solution of potassium chromate, if
a strong acid is added, it changes its color from yellow to orange.
Reason
The color change is due to the change in
oxidation state of potassium chromate.
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 are correct.


One mole of sugar is dissolved in two moles of water. The vapour pressure of the solution relative to that of pure
water is:
\( A \cdot 2 / 3 \)
B. \( 1 / 3 \)
c. \( 3 / 2 \)
D. \( 1 / 2 \)


Factorize using identities
\( t^{4}-625 \)


In the adjoining figure, if \( D \) is the
\( \tan x \)
midpoint of \( \mathrm{BC} \), then the value of \( \frac{t}{\tan y^{0}} \)
is:
\( A \)
B. 3
\( c \)
D.


If the radius of the earth were to shrink
by one percent, its mass remaining the same, acceleration due to gravity on the
earth's surface would:
A. decrease
B. reamain unchanged
c. increase
D. be zero


Assertion
On reacting \( M g \) with \( C l_{2}, M g C l_{2} \) is
formed and not \( M g C l \)
Reason
\( M g^{2+} \) ion has stable octet
configuration and not \( M g^{+} \)
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


Which of the following will not given butanoic acid as one of the product?
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} B r \frac{M g}{E t h e r} \quad \underbrace{(i) C O_{2}}_{(i i) H C l / H_{2}} \)
B \( \cdot C H_{3} C H_{2} C H_{2} B r \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
c. \( _{C H_{3} C H_{2} C H O+H C N} \stackrel{H^{+}+H_{2} \mathcal{O}}{\longrightarrow} \)
D. \( C H_{3} C H_{2} C H_{2} C H=C H_{2 H^{+} / H_{2} O}^{K M n O_{4}} \)


Platelets are formed by \( \ldots . . P . . . . . \) of special cells in \( \dots . Q \)
A. P- - Division, Q - Bone Marrow
B. P- Division, Q - Lymph nodes
c. P- Fragmentation, Q - Bone Marrow
D. P- - Fragmentation, Q - Lymph nodes


Instead of walking along two adjacent sides of a rectangular field,a boy book a short - cut along the diagonal of the field and saved a distance equal to \( 1 / 2 \)
the longer side. The ratio of the shorter side of the rectangle to the longer side
was:
\( A \)
B.
\( c \cdot \frac{1}{4} \)
0.3
\( E \)


A real image is formed where two or
more :
This question has multiple correct options
A. reflected rays meet
B. refracted rays meet
C . reflected rays appear to meet
D. refracted rays appear to meet


The centroid of the triangle whose vertices are (4,-8),(-9,7) and (8,13) is
в. (1,3)
c. (1,5)
(年. (1,5)
D. (1,9)


If \( (N, P, A s) \) was Dobereiner's triads
then what would be the absolute error in
atomic mass of phosphorous as compared to the original mass?
Atomic mass: Nitrogen \( =14 \) amu, Arsenic \( =\mathbf{7 4 . 9} \) amu, Phosphorous \( =\mathbf{3 1} \)
amu
A. 13.45
B. 12.45
c. 15.55
D. 16.55


Out of \( \boldsymbol{C u}_{2} \boldsymbol{S}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{S}, \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S} \) and \( \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \)
roasting will convert the minerals into
metals in case of
A. \( C u_{2} S, \) ZnS
в. \( H g S, Z n S \)
c. \( C u_{2} S, A g_{2} S \)
D. \( H g S \)


What is the ratio of CGS to MKS unit of
acceleration?
A \( \cdot \frac{m}{c m} \)
в. \( \frac{m}{s} \)
c. \( \frac{c m}{s} \)
D. \( \frac{c m}{m} \)


Formation of polymeric products required which of the following
material?
A. Ethandiol
B. Acetal
c. EDTA
D. Formaldehyde


The value of \( A . \bar{A} \) in Boolean algebra is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c . A \)
D. \( \bar{A} \)


At \( 100^{\circ} \mathrm{C} \), value of \( \boldsymbol{K}_{\boldsymbol{w}} \) is
\( \begin{array}{ll}\text { A. } 1.0 \times 10^{-14} & m^{2}\end{array} \)
B. less than 1.0 \( \times 10^{-14} \mathrm{m}^{2} \)
C. greater than \( 1.0 \times 10^{-14} \mathrm{m}^{2} \)
D. zero


A LC-circuit contains a \( 20 m H \) inductor
and a \( 50 \mu F \) capacitor with an initial
charge of \( 10 m C . \) The resistance of the
circuit is negligible. Let the instant the
circuit is closed be \( t=0 \)
(a) What is the total energy stored initially. Is it conserved during the LCoscillations?
(b) What is the natural frequency of the circuit?
(c) At what times is the energy stored?
(i) completely electrical (ie., stored in the capacitor)?
(ii) completely magnetic (i.e., stored in the inductor)?
(d) At what time is the total energy shared equally between the inductor and the capacitor


\( \int x \sin ^{-1} x \cdot d x \)


Nuclear Fission is best explained by:
A. Liquid droplet theory
B. Yukawa - meson theory
C. Independent particle model of the nucleus
D. Proton-proton cycle


What is the expected product formed from the reaction between 2 -butene and
\( C l_{2} ? \)
A. 1 -chlorobutane
B. 2-chlorobutane
c. 2,3 -dichlorobutane
D. 2,2-dichlorobutane


Which statement is correct?
A. Fumaric acid is stronger than Maleic acid.
B. Maleic acid is stronger than fumaric acid
C. Both (a) and ( b)
D. None of the above


John Dalton proposed which theory?
A. Theory of molecules
B. Atomic mass theory
c. Theory of atoms
D. Law of conservation of substances


freadings of spring balances \( S_{1}, S_{2}, S_{3} \)
and \( S_{4} \) are a \( \mathrm{kg}, \mathrm{b} \mathrm{kg}, \mathrm{c} \) kg respectively then choose the correct option
\( A \cdot a<b<c<d \)
B. b \( <c<d \)
\( c \cdot c=a<b<d \)
\( D \cdot d=a \)


The magnetic moment of electron is :
A. \( 9.27 \times 10^{-24} \) Joule/Tesla ander
B . \( 9.27 \times 10^{-24} \) Tesla/Joule
c. \( 9.27 \times 10^{-23} \) Joule/Tesla
D. \( 9.27 \times 10^{-23} \) Tesla/Joule


\( \frac{\sqrt{6}}{8} \)
\( \frac{8}{6} \)
\( \frac{8}{0} \)


Which of the following metal is a micronutrient for plants?
A. Molybdenum
B. Copper
c. zinc
D. All of above


Assertion
Protons or hydrogen ions produced by photolysis of water accumulate in the lumen of thylakoids.
Reason
Photolysis of water takes place in inner membrane of thylakoid.
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


Which of the following name formula
combinations is not correct?
\( \mathbf{A} \cdot K\left[\operatorname{Cr}\left(N H_{3}\right)_{2} C l_{4}\right]- \) Potassium
diamminetetrachlorochromate(III)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4}\left(H_{2} O\right) I\right] S O_{4} \)
Tetraammineaquaiodocobalt(III) sulphate
C \( \cdot K_{2}\left[P t(C N)_{4}\right] \) - Potassium tetracyanoplatinate(II)
D. \( \left[M n(C N)_{5}\right]^{2-} \) - Pentacyanomanganate (II) ion


The Sl unit of amplitude of oscillation is
A . cm
в.
\( c \cdot k m \)
D. none of these


The colour of halogens progressively
deepens from fluorine to iodine
because:
A. halogens of higher atomic number absorb light of longer wavelength since the difference in energy between the ground state and excited state decreases as the atomic number increases
B. fluorescence and phosphorescence become more intense as the atomic numbers of halogen increases
C. the standard electrode potential increases from \( I_{2} \) to \( F_{2} \)
D. halogens of higher atomic number absorb light of shorter wavelength since the difference in energy between the ground state and excited state increases as the atomic number increases


The relation between \( u, v \) (u is the object distance and v is the image distance ) and f for mirror is given by:
A \( \cdot f=\frac{u v}{u-v} \)
B. \( f=\frac{2 u \times v}{u+v} \)
c. \( f=\frac{u \times v}{u+v} \)
D. none of these


Magnetic lines of force
A. form closed circuits
B. cannot intersect
C . are crowded together near the poles
D. all the above are correct


Which one of the following anions can undergo both oxidation and reduction?
A. \( C r_{2} O_{7}^{2} \)
в. \( N O_{3} \)
c. \( O C l^{-} \)
\( D \cdot S^{2} \)


Explain the difference between Buna- \( N \)
and Buna- \( S \).


\( 2.2016 \mathrm{g} \) of acetaldehyde produced 13.9
kcal of heat on combustion in \( \boldsymbol{O}_{2} \)
Calculate the heat of combustion of
\( C H_{3} C O O H \) will be:
A. 279 kcal
B. 972 kcal
c. २७.९ kcal
D. 2.79 kcal


Find out the missing particle in the following nuclear reaction?
\( _{1}^{2} \boldsymbol{H}+_{29}^{63} \boldsymbol{C u} \rightarrow_{30}^{64} \boldsymbol{Z} \boldsymbol{n}+(?) \)
A. Proton
B. Neutron
c. Electron
D. Positron
E . Deuteron


Assertion
f \( \vec{a}=\hat{i}, \vec{b}=\hat{j} \) and \( \vec{c}=\hat{i}+\hat{j} \) then \( \vec{a} \) and
\( \vec{b} \) are linearly independent but \( \vec{a}, \vec{b} \) and \( \vec{c} \) are linearly dependent.
Reason
If \( \vec{a} \) and \( \vec{b} \) are linearly dependent and \( \vec{c} \) is any vector then \( \vec{a}, \vec{b} \) and \( \vec{c} \) are linearly dependent.
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


\( \cot ^{-1} \frac{x y+1}{x-y}+\cot ^{1} \frac{y z+1}{y-z}+ \)
\( \cot ^{-1} \frac{x z+1}{z-x} \)
\( A \)
B. -
\( c \cdot 0 \)
D. none of these


Give scientific names of man, domestic
cat, peepal tree, frog, honey bee, china
rose


A steel wire of \( 4.0 \mathrm{m} \) in length is
stretched through \( 2.0 \mathrm{mm} \). The crosssectional area of the wire is \( 2.0 m m^{2} .1 \)
Young's modulus of steel is \( 2.0 \times \) \( \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \mathbf{m}^{\mathbf{2}} \) find
(i) the energy density of
wire
(ii) the elastic potential energy stored in the wire.


Suppose a pure Si crystal has \( 5 \times 10^{28} \)
atoms \( m^{-3} . \) it is doped by 1 ppm
concentration of pentavalent As. Calculate the number of electrons and
holes. Given that \( n_{1}=1.5 \times 10^{16} m^{-3} \)


Metal which is silvery light, malleable and ductile and the boiling point is
around \( 2050^{\circ} C \) is:
A . zinc
B. iron
c. aluminium
D. tin


The average angular velocity of the
spinning motion of the Earth in rads\( ^{-1} \)
will be :
A \( \cdot \frac{\pi}{43,200} \)
в. \( \frac{2 \pi}{43,200} \)
c. \( \frac{\pi}{86,400} \)
D. \( \frac{4 \pi}{86,400} \)


The least value of \( 2 \log _{100} a- \)
\( \log _{a} 0.0001, a>1 \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. none of these


Assertion
A small amount of alchohol is added to
chloroform bottles
Reason
Alcohol acts as inhibitor for oxidation of
choloroform.Also it reacts with \( C O C l_{2} \)
to give harmless diethyl carbonate
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


Let \( x \) be the energy needed to raise the
temperature of 5 moles of \( N_{2} \) held at
constant pressure by one degree. Let \( y \) be the energy needed to raise temperature of 5 moles of \( C 0 \) by one degree with constant pressure. Then ratio \( x: y \) is -
A . 5: 7
B. 1:
\( c \cdot 7: 5 \)
D. 7: 9
E. 7: 2


When a plane mirror is placed
horizontally on a level ground at a distance of 60 meters from the foot of a
tower the top of the tower and its image in the mirror subtends at the eye, an
angle of \( 90^{\circ} . \) Find the height of the
tower


Identify the pair of binary corresponds in which nitrogen exhibits the lowest
and the highest oxidation state.
A. \( N H_{3}, N O_{2} \)
в. \( N_{3} H, N_{2} O_{5} \)
c. \( N_{2}, H N O_{3} \)
D. \( N_{2} O, N_{2} O_{5} \)


Two particles \( X \) and \( Y \) having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field
and describe circular paths of radii \( \boldsymbol{R}_{1} \)
and \( R_{2}, \) respectively. The ratio of
masses of \( X \) and \( Y \) is
\( ^{\mathbf{A}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2} \)
B. \( \left(\frac{R_{2}}{R_{1}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
D. \( \left(\frac{R_{1}}{R_{2}}\right) \)


A drop of liquid having radius \( 2 \mathrm{mm} \) has
a terminal velocity \( 20 \mathrm{cms}^{-1} \), the
terminal velocity of a drop 1mm radius will be:
A. \( 40 \mathrm{cms}^{-1} \)
B. \( 20 \mathrm{cms}^{-1} \)
c. \( 10 \mathrm{cms}^{-1} \)
\( D \cdot 5 \mathrm{cms}^{-1} \)


The cells which pass the
instructions from brain to different
parts of the body are called as
A. Muscle tissue
B. Neurons
c. Red blood cells
D. White blood cell


\( \frac{\sqrt{3}}{5} \)


Find the voltage \( V_{a b} \) in the circuit shown
in figure.
\( A \cdot+3 V \)
\( B .-3 v \)
\( c \cdot+6 v \)
\( 0 .-6 \)


In physical adsorption, the adsorbent and adsorbate are held together by the:
A. Ionic force
B. Covelent force
c. van dar Waal's force
D. H-bonding


\( \mathbf{A} \)
\( 20 k g \) body is pushed with just
enough force to start it moving across a
floor and the same force continues to
act afterwards. The coefficient of static
and kinetic friction are \( 0.6 \& 0.2 \)
respectively. The acceleration of the
body is :
A \( \cdot 6 m / s^{2} \)
B . \( 1 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 2 m / s^{2} \)
D. \( 4 m / s^{2} \)


In aqueous solutions, amino acids
mostly exist as:
A. \( N H_{2}-C H(R)- \) COOH
B . \( N H_{2}-C H(R)-C O O^{-} \)
c. \( N H_{3}^{+}-C H(R)- \) COOH
D. \( H_{3} N^{+}-C H(R)-C O O^{-} \)


State the function of saliva.


\( \mathbf{A} \)
\( 340 A \) long segment of DNA molecule
has 20 thymine nitrogenous bases, what will be the number of guanine nitrogen bases in the same segment?
A . 10
B . 40
c. 80
D. 160


A rainbow has circular shape because:
A. The earth is spherical
B. Rain drops are spherical
c. The sun is spherical
D. None of these


In a fresnel's bi-prism experiment, the
refracting angles of the prism were \( 2.5^{\circ} \) and the refracting index of the glass was \( 1.5 . \) With the single slit \( 10 \mathrm{cm} \) from the bi-prism ,fringes were formed on a screen \( 1 \mathrm{m} \) from the single slit. The fringe width is \( 0.1375 \mathrm{mm} \). The wavelength of light is
A. 600 nm
B. 1200 nm
c. \( 60 A^{\circ} \)
D. 120 A


The exponent of 18 in \( 200 !, \) is
\( \mathbf{A} \cdot 24 \)
B. 46
c. 47
D. 48


Solve: \( -(x-3)+4>-2 x+5 \) when \( x \)
is a integer


The intensity of radiation emitted by the
sun has its maximum value at a
wavelength of \( 510 n m \) and that emitted
by the North Star has the maximum value at 350 nm. If these stars behave
like black bodies, the ratio of the
surface temperature of the sun and the North Star is
A . 1.46
B. 0.69
c. 1.21
D. 0.83


\( f(\vec{a}, \vec{b} \text { are the position vectors of } A, B \) respectively, find the position vector of a point \( C \) in \( A B \) produced such that \( A C= \) \( 3 \mathrm{AB} \) and that a point \( \mathrm{D} \) in BA produced such that \( \mathrm{BD}=2 \mathrm{BA} \)


What we call the conductivity of a magnetic substance for the lines of
force with respect to air?
A. Magnetic induction
B. Magnetic permeability
c. Magnetic flux density
D. Intensity of magnetization


Flowering in short day plants is induced
by
A. Short days and interrupted long nights
B. Short days and uninterrupted long nights
c. short nights
D. Long day with interrupted night


Part not belonging to nephron tubule is:
This question has multiple correct options
A . Glomerules
B. Bowman's capsule
c. collecting duct
D. Loop of Henle


The straight lines \( \imath_{1}, \imath_{2} \) and \( \imath_{3} \) are parallel and lie in the same plane. A
total of \( \mathrm{m} \) points are taken on the line \( \imath_{1} \)
n points on \( \imath_{2}, \) and \( \mathrm{k} \) points on \( \imath_{3} . \) How many triangles are there whose vertices are at these points?


A helicopter is flying south with a speed
of \( 50 \mathrm{kmh}^{-1} \). A train is moving with the
same speed towards east. The relative
velocity of the helicopter as seen by the passengers in the train will be \( 50 \sqrt{2} \mathrm{kmh}^{-1} \) towards
A. northwest
B. southwest
c. northeast
D. southeast


Which one of the following possesses kinetic energy?
A. A moving car
B. A compressed spring
c. water stored in the reservoir of a dam
D. A car parked in the garage


The kind of energy present in fossil fuels
is :
A. chemical energy
B. heat energy
c. potential energy
D. mechanical energy


Which of the following is a type of biogas plant?

This question has multiple correct options
A. Fixed dome type
B. Floating gas holder type
c. Fixed fuel type
D. Moving chamber type


An aluminium rod (Young's modulus \( = \) \( \left.\mathbf{7} \times \mathbf{1 0}^{\mathbf{9}} \mathbf{N} / \mathbf{m}^{\mathbf{2}}\right) \) has a breaking strain of
\( 0.2 \% . \) The minimum cross-sectional
area of the rod in order to support a load
of \( 10^{4} \) Newton's is:
\( \mathbf{A} \cdot 1 \times 10^{-2} m^{2} \)
B. \( 1.4 \times 10^{-3} m^{2} \)
\( \mathrm{c} \cdot 3.5 \times 10^{-3} \mathrm{m}^{2} \)
D. \( 7.1 \times 10^{-4} m^{2} \)


f \( 2 x-3 y=-8 \) and \( 4 x+3 y=2 \) then
find the value of \( x \)


Find the point(s) on the curve \( y^{3}+ \)
\( 3 x^{2}=12 y \) where the tangent is vertical
(parallel to \( y-a x i s) \)


\( a, b, c \) are in A.P. and the points \( \boldsymbol{A}(\boldsymbol{a}, \mathbf{1}), \boldsymbol{B}(\boldsymbol{b}, \mathbf{2}) \) and \( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{3}) \) are such
that \( (O A)^{2},(O B)^{2} \) and \( (O C)^{2} \) are also in A.P; \( O \) being the origin, then This question has multiple correct options
A \( \cdot a^{2}+c^{2}=2 b^{2}-2 \)
B. \( a c=b^{2}+1 \)
c. \( (a+c)^{2}=4 b^{2} \)
D. \( a+b+c=3 b \)


State and explain Coulomb's inverse square law in electricity.


Assertion
A hydrogen-filled balloon stops rising after it has attained a certain height in the sky.
Reason
The atmospheric pressure decreases with height and becomes zero when the maximum height is attained.
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


Which of the following complex ions absorbs the light of minimum wavelength?
\( ^{\mathrm{A}} \cdot\left[C o\left(H_{2} O\right)_{6}\right]^{3+} \)
B \( \cdot\left[\mathrm{CoF}_{6}\right]^{3-} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}(C N)_{6}\right]^{3-} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)


Assertion
Be and Mg do not impart characteristic colour to the flame.
Reason
Both Be and Mg have high ionization energy.
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


Indicate the correct product of the
following reaction.
(1)
\( (\|) \)
(III)
\( A \)
B . II
\( \mathbf{C} \cdot \| \mathbf{I}+\mathbf{I V} \)
D. There is no net reaction


\( 10 \mathrm{mL} \) of water required \( 1.47 \mathrm{mg} \) of \( K_{2} C r_{2} O_{7}\left(M . w t_{.}=294\right) \) for oxidation of
dissolved organic matter in presence of acid. Then the \( C .0 . D \) of water sample is:
A. 2.44 ppm
B. 24 ppm
c. 32 ppm
D. 1.6 ppm


\( 100 m l \) of \( 0.2 M H C l \) are mixed with
\( \mathbf{1 0 0} \boldsymbol{m l} \) of \( \mathbf{0 . 2} \boldsymbol{M} \boldsymbol{C H}_{3} \boldsymbol{C O O N a}, \) the \( \boldsymbol{p} \boldsymbol{H} \)
of the resulting solution would be nearly:
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( 0 . \)
c. 2.875
D. 1.


Explain the meaning of the statement
current rating of a fuse is \( 5 \mathrm{A} \) '.


One end of an ideal spring is fixed to a
wall at origin \( O \) and axis of spring is
parallel to x-axis. A block of mass \( \boldsymbol{m}= \)
1 kg is attached to free end of the
spring and it is performing SHM. Equation of position of the block in coordinate system shown in figure is
\( \boldsymbol{x}=\mathbf{1 0}+\mathbf{3} \sin (\mathbf{1 0} \boldsymbol{t}) . \) Here, \( \boldsymbol{t} \) is in second
and \( x \) in cm. Another block of mass
\( M=3 k g, \) moving towards the origin
with velocity \( 30 \mathrm{cm} / \mathrm{s} \) collides with the block performing SHM at \( t=0 \) and gets
stuck to it. Calculate new amplitude of oscillations


A change of \( 8 m A \) in the emitter current brings a change of \( 7.9 m A \) in the collector current. The value of \( \alpha \) is
A. \( 80 / 79 \)
B. \( 79 / 80 \)
c. 79
D. 80


A microscope in which maximum magnification is achieved, but the object cannot be seen by eye is called
A. simple microscope
B. Dissecting microscope
c. Electron microscope
D. Phase contrast microscope
E. Compound microscope


Oppositely charged clouds, coming closer to each other, cause:
A. induction
B. conduction
c. lightning
D. none of the above


Hard water is passed through an ionic
exchange resin containing \( -\boldsymbol{S O}_{3} \boldsymbol{H} \) group. The outcoming water is free of the following ions
A \( \cdot C l \)
в. \( N O_{3} \)
c. \( H_{3} O^{+} \)
D. \( C a^{+2} \)


Sphagnum is used as packing material for transporting living plants because of its
A. Acidic nature it does not undergo decay
B. Creeping capacity
c. water absorbing capacity
D. Both A and C


Assertion
STATEMENT-1: In a region where uniform electric field exists, the net
charge within volume of any size is zero.
Reason

STATEMENT-2: The electric flux within
any closed surface in a region of uniform electric field is zero.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. statement- - is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


In uniform circular motion
A. both velocity and speed are constant
B. speed is constant but velocity changes
C. both speed and velocity change
D. velocity is constant but speed changes


Contribution of methane to global
warming is
A . \( 6 \% \)
B. 14\%
c. 20\%
D. 30\%


Oblique sketches of solid shapes can be drawn as per measurements on
paper
A. non-isometric
B. isometric
c. blank
D. None of these


The wave length of second line in the Balmer series of hydrogen spectrum is equal to: (R=Rydberg constant)
\( \mathbf{A} \cdot 36 / 5 R \)
в. \( 5 R / 36 \)
c. \( 3 R / 16 \)
D. \( 16 / 3 R \)


Meeta and Reeta are two sisters one is
in class VI another is in Class VII, The numbers of student in class VI is 25 and
in class VII is 30. Find the probability that both of them get first position in their respective classes.


How much electricity in terms of Faraday is required to produce 100 g of
Ca from molten \( C a C l_{2} ? \)
A . 1 F
в. 2 F
\( c .3 \) F
D. 5


Read the above bar graph and answer
the following question

Which state is the largest producer of
wheat?


The percentage of lanthanides and iron, respectively, in Misch metal are:
\( \mathbf{A} \cdot 50,50 \)
B. 75,25
c. 90,10
D. 95,5


Number of atom in one molecule of
sulphur:
A . 8
B. 4
\( c .3 \)
D. None of the above


A sphere of radius \( R \), density \( D \) and
specific heat \( S \) is heated to temperature \( \theta \) and surrounding is at
temperature \( \theta_{0} . \) Its rate of fall of temperature will be proportional to
A. \( D S / R \)
в. \( R / D S \)
\( \mathrm{c} .1 / R D S \)
D. \( R D S \)


When the strength of the current
flowing through a coil is increased,
which of the following statements is
true for it?
A. Strength of the magnetic field decreases
B. Strength of the magnetic field increases
C. Amount of heat generated due to resistance decreases
D. Strength of the magnetic field remains constant


What kind of lens would form an
inverted and magnified image?


The power dispensed across resistance \( R \) which is connected across a battery
of potential \( V \) is \( P . \) If resistance is doubled then the power becomes
A. \( 1 / 2 \)
B. 2
c. \( 1 / 4 \)
\( D \)


Find Sum of Series \( \tan ^{2} x \tan 2 x+ \)
\( \frac{1}{2} \tan ^{2} 2 x \tan 4 x+\frac{1}{2^{2}} 4 x \tan 8 x+\dots \)
\( n \) terms.


As the reaction proceeds, the rate of
reaction:
A. decreases
B. remains constant
c. increases
D. depends on the substance


f an isosceles \( \triangle A B C \) in which \( A B= \)
\( A C=6 \mathrm{cm} \) is inscribed in a circle of
radius \( 9 \mathrm{cm} . \) Find area of the triangle.
\( \mathbf{A} \cdot 8 c m^{2} \)
B. \( 8 \sqrt{2} c m^{2} \)
\( c \cdot 6 c m^{2} \)
D. none


Liver of sulphur is a mixture of :
A. Potassium pentasulphide \( (A) \) and potassium thiosulphate \( (B) \)
B. Potassium carbonate \( (C) \) and potassium thiosulphate
\( (B) \) above
C. Potassium disulphide \( (D) \) and potassium thiosulphate \( (B) \) above
D. \( (B) \) and \( (D) \) above


A stone tied to one end of the string is revolved round a rod in such a way that the string winds over the rod and get shortened. In this process which of the following quantities remain constant?
A. Moment of inertia
B. Momentum
c. Angular momentum
D. Kinetic energy


Write four differences between
interference and diffraction.


The length \( x \) of a rectangle is decreasing at the rate of \( 5 \mathrm{cm} / \mathrm{minute} \) and the width y is increasing at the rate of \( 4 \mathrm{cm} / \mathrm{minute} . \) When \( x=8 \mathrm{cm} \) and
\( y=6 \mathrm{cm} \) find the rates of change of
perimeter, and
(b) the area of the
rectangle.


A few substances are arranged in the increasing order of forces of attraction between their particles. Which one of the following represents a
correct arrangement?
A. Water, air, wind
B. Air, sugar, oil
c. oxygen, water, sugar
D. Salt, juice, air


The osmotic pressure of a solute is 600 \( \mathrm{mm} \) at \( 300 \mathrm{K} \). The solution is diluted
and the temperature is raised to \( 400 \mathrm{K} \)
and the solution shows an osmotic
pressure of \( 200 \mathrm{mm} \). The solution was
diluted to \( x \) times. \( x \) is :


Identify redox reaction among the following:
A. acid-base neutralization
B. precipitation reaction
c. metal displacement reaction
D. all the above


Two wheels are constructed, as shown in Figure, with four spokes. The wheels are mounted one behind the
other so that an observer normally sees a total of eight spokes but only four spokes are seen when they happen to align with one another. If one wheel spins at 6 rev/min, while other spins at
8 rev/min in same sense, how often
does the observer see only four spokes?
A. 4 times a minute
B. 6 times a minute
c. 8 times a minute
D. Once in a minute


A car with a vertical windsheld moves in
a rain storm at a speed of \( 40 \mathrm{km} / \mathrm{hr} \) The rain drops fall vertically with constant speed of \( 20 m / s . \) The angle at
which rain drops strike the windsheild
is
A. \( \tan ^{-1} \frac{5}{9} \)
в. \( \tan ^{-1} \frac{9}{5} \)
c. \( \quad \) tan \( ^{-1} \frac{3}{2} \)
D. \( \tan ^{-1} \frac{2}{3} \)


The above figure represents which of the following fractions?
A \( \cdot \frac{9}{7} \)
B. \( 2 \frac{1}{2} \)
c. \( _{4} \frac{1}{2} \)
D. \( _{2} \frac{1}{4} \)


Name the membrane that covers the
heart.


Assertion
The blood pressure in humans is greater at the feet than at the brain
Reason
Pressure of a liquid is hdg
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


Which of the following is an example of
a random experiment?
This question has multiple correct options
A. Selecting a card from a pack of playing cards.
B. Measuring the weight of a person.
C. Finding the length of your pencil box.
D. Throwing two coins together.


Which of the following can be related to china rose?
A. Anthers are fused
B. Filaments are fused in a single mass
C. Filaments are fused to form many groups
D. All the stamens are free


Suppose that the lines which bisect the
exterior angles at \( B \) and \( C \) of \( \Delta A B C \)
meet at \( D . \) Then find \( \angle B D C \)


Which of the following statements are
true?
(a) Proteins are the heteropolymer of \( \alpha \)
amino acid.
(b) Sugar found in nucleic acid, is in the
form of \( \beta \) -form.
(c) Nucleic acids show acidic nature.
(d) 5-methyl uracil binds with first carbon atom of ribose sugar.
(e) Collagen is most abundant protein in plant world.
\( A \cdot a, b, e \)
B. \( a, b, d \)
\( c \cdot b, c, d, e \)
D. a, b, c


Fill in the blanks:
The two types of aliphatic unsaturated hydrocarbons are and


If two lenses of power +1.5 D and +1.0 D are placed in contact, then the effective power of combination will be:
A .4 .5 D
B. 2.5 D
\( c \cdot 5.40 \)
D. 4.2 D


Why is the \( \boldsymbol{E}^{0} \) value of \( \boldsymbol{M} \boldsymbol{n}^{+3} / \boldsymbol{M} \boldsymbol{n}^{+2} \)
couple much more positive than \( \boldsymbol{C r}^{+\mathbf{3}} / \boldsymbol{C r}^{+\mathbf{2}} \)
A. Due to larger third ionisation enthalpy of Mn.
B. Due larger third ionisation enthalpy of Cr.
c. Due to smaller third ionisation enthalpy of Mn.
D. Due to lesser hydration enthalpy of Cr.


The bond with highest bond energy is:
A. sigma bond between non-polar atoms
B. sigma bond between polar atoms
C. triple bond between polar atoms
D. triple bond between non-polar atoms


Draw a schematic diagram of a reflecting telescope (Cassegrain) Write its two advantages over a refracting telescope.


In the Haber process for the industrial manufacturing of ammonia involving the reaction
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \) at
200atm pressure in the presence of a
catalyst, a temperature of about \( 500^{\circ} \mathrm{C} \)
is used. This is considered as optimum temperature for the process because:
A. yield is maximum at this temperature
B. catalyst is active only at this temperature
c. energy needed for the reaction is easily obtained at this temperature
D. rate of the catalytic reaction is fast enough while the yield is also appreciable for this exothermic reaction at this temperature


The ascending order of \( \boldsymbol{A}= \) \( \sin ^{-1}\left(\log _{3} 2\right), B=\cos ^{-1}\left(\log _{3}\left(\frac{1}{2}\right)\right) \)
and \( C=\tan ^{-1}\left(\log _{1 / 3} 2\right) \) is
A. \( \mathrm{C}, \mathrm{B}, \mathrm{A} \)
в. В, А, С
c. \( \mathrm{c}, \mathrm{A}, \mathrm{B} \)
D. B, C, A


Say true or false:
For polynomials \( p(x) \) and any non-zero
polynomial \( g(x), \) there are polynomials \( \boldsymbol{q}(\boldsymbol{x}) \) and \( \boldsymbol{r}(\boldsymbol{x}) \) such that \( \boldsymbol{p}(\boldsymbol{x})= \)
\( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{q}(\boldsymbol{x})+\boldsymbol{r}(\boldsymbol{x}), \) where \( \boldsymbol{r}(\boldsymbol{x})=\mathbf{0} \) or
\( \operatorname{degree} r(x)<\operatorname{degree} g(x) . \) This
statement is correctly explains the remainder theorem.
A . True
B. False


Solve:
\( \int_{0}^{2} x \sqrt{x+2} d x \)


A correct statement is/are:
This question has multiple correct options
\( \mathbf{A} \cdot\left[M n B r_{4}\right]^{-2} \) is tetrahedral
B. \( \left[N i\left(N H_{3}\right)_{6}\right]^{+2} \) is an inner orbital complex
\( ^{\mathbf{C}} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{+2} \) is paramgnetic
D \( \cdot\left[\operatorname{CoBr}_{2}(e n)_{2}\right]^{-} \) exhibits linkage isomerism


The length \( L \) (in centimetre) of a copper
rod is a linear function of its
Celsius temperature \( C . \) In an experiment, if \( L=124.942 \) when \( C= \) 20 and \( L=125.134 \) when \( C=110 \)
express \( L \) in terms of \( C \)


The sum of the numbers 436.32,227.2 and 0.301 in appropriate significant figures is :
A . 663.821
B. 664
c. 663.8
D. 663.812


State Gauss's Law in Electrostatics.


Six resistors each of \( 10 \Omega \) are
connected as shown. Find the
equivalent resistance in ohms between
points \( X \) and \( Y \)


Two metal spheres of radii a and b are connected by a thin wire. Their separation is very large compared to their dimensions. The capacitance of
this system is?
\( \mathbf{A} \cdot 4 \pi \varepsilon_{0}(a b) \)
В . \( 2 \pi \varepsilon_{0}(a+b) \)
C \( .4 \pi \varepsilon_{0}(a+b) \)
D. \( 4 \pi \varepsilon_{0}\left(\frac{a^{2}+b^{2}}{2}\right)^{2} \)


\( 50 g \) of copper is heated to increase its
temperature by \( 10^{\circ} \mathrm{C} . \) If the same
quantity of heat is given to \( 10 \mathrm{gm} \) of water, the rise in temperature is (specific heat of copper \( =420 \) J
\( k g^{-1} K^{-1}, \) specific heat of water \( =4200 \)
\( \left.k g^{-1} K^{-1}\right) \)
\( A \cdot 5^{\circ} \mathrm{C} \)
B . \( 6^{\circ} \mathrm{C} \)
\( c \cdot 7^{o} \)
D. \( 8^{\circ} \mathrm{C} \)


An ideal dipole of dipole moment \( \vec{p} \) is placed in front of an uncharged conducting sphere of radius \( R \) as shown
A \( \cdot \) The potential at point \( A \) is \( \frac{K P}{(r-R)^{2}} \)
B. The potential at point A is \( \frac{K P}{r^{2}} \)
C the potential due to dipole at point B is \( \frac{K P}{(r+R)^{2}} \)
D. The potential due to dipole at point B is \( \frac{K}{r^{2}} \)


A compound of ammonia which sublimes on heating is:
A. ammonium sulphate
B. ammonium nitrate
c. ammonium chloride
D. ammonium nitrite


Two uniform solid spheres having unequal masses and unequal radii are
released from the same height on a
rough incline. If the sphere roll without
slipping,
A. The heavier sphere reaches the bottom first
B. The bigger sphere reaches the bottom first
C. The two spheres reach the bottom together
D. The information given is not sufficient to tell which sphere will reach the bottom first.


Prior to the work of Avery, MacLeod and McCarty (1933-44), the genetic material through to be
\( A \). a Protein
B. RNAA
c. DNA
D. a Carbohydrate


Find \( m \) if the following equation holds
true: \( 1.2+4.3+9.4+\ldots n^{2}(n+1)= \)
\( \frac{n}{m}(n+1)(n+2)(3 n+1) \)


A coil has an inductance of \( 0.7 ~ H \) and is
joined in series with a resistance of
220\Omega. When an alternating emf of \( 220 V \) at \( 50 ~ c p s \) is applied to it, then the
wattless component of the current in the circuit is (take \( 0.7 \pi=2.2) \)
\( \mathbf{A} \cdot 5 A \)
B. \( 0.5 A \)
\( \mathbf{c} \cdot 0.7 A \)
D. \( 7 A \)


Which of the following not represents redox reactions?
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{2} \stackrel{\theta}{\boldsymbol{O}} \boldsymbol{H} \longrightarrow \boldsymbol{2} \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
II. \( Z n+C u S O_{4} \longrightarrow Z n S O_{4}+C u \)
III. \( 2 M n O_{4}^{\ominus}+3 M n^{2+}+4 \stackrel{\theta}{O} H \longrightarrow \)
\( \mathbf{5} M n O_{2}+2 H_{2} O \)
IV. \( 2 C u^{\oplus} \longrightarrow C u+C u^{2+} \)
\( A \)
в. ।, ॥
c. ॥ा, ।॥
D. ॥, ॥I, IV


If two numbers \( p \) and \( q \) are chosen
randomly from the set \{1,2,3,4\} with replacement, then the probability that \( p^{2} \leq 4 q \) is equal to
A \( \cdot \frac{1}{4} \)
B. \( \frac{3}{16} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{9}{16} \)
E. \( \frac{7}{16} \)


Draw a labelled diagram showing the magnetic field lines of a loop carrying current. Mark the direction of current
and the direction of
magnetic field by arrows in your diagram.


The smallest disease causing agent is
A. Virion
B. Viroid
c. Prion
D. Mycoplasma


In which cases are the law of
conservation of mass followed?
This question has multiple correct options
\( \mathbf{A} \cdot 10 \mathrm{g} \mathrm{CaCO}_{3} \) on heating gives \( 0.1 \mathrm{mole} \mathrm{CaO} \) and \( 2.24 \mathrm{L} \)
\( C O_{2} \) at \( \mathrm{NTP} \)
B. 1 mole \( N_{2} \) and 1 mole \( H_{2} \) combine to form 2 moles of
\( N H_{3} \)
C. 0.2 mole \( S O_{2} \) combines with 3.2 g \( O_{2} \) to form 0.2
moles \( S O_{3} \)
D. 1 g \( H_{2} \) combines with 0.5 g \( O_{2} \) to form 1.5 g \( H_{2} O \)


Find the induced emf about ends of the
rod in each case.
(ii)


What is chemistry?
A. Study of substances.
B. Investigation of reactions and properties.
C. Study of reactions to form new substances.
D. All of the above.


Red and white phosphorus will differ
but not in:
A . smell
B. solubility in \( C H C I_{3} \).
c. exhibiting phosphorescence.
D. reactions with \( H N O_{3} \)


What is the order of rotational
symmetry of the given figure?
\( A \cdot 6 \)
B. 4
\( c \cdot 8 \)
D. None of these


One half of a convex lens is covered with
black paper. Will this lens produce a complete image of the object? Explain your observations.


Hydrocarbons are obtained from Kerogens through
A. catalysis
B. catagenesis
c. cataphoresis
D. bacterial and Fungal decomposition


An \( \alpha \) particle is moving along a circle of radius \( R \) with a constant angular velocity \( \omega . \) Point \( A \) lies in the same
plane at a distance \( 2 R \) from the centre.
Point \( A \) records magnetic
field produced by \( \alpha \) particle. If the minimum time interval between two successive times at which \( A \) records
zero magnetic field is \( ^{\prime} t^{\prime}, \) the angular
speed \( \omega, \) in terms of \( t \) is
A \( \cdot \frac{2 \pi}{t} \)
в. \( \frac{2 \pi}{3 t} \)
c. \( \frac{\pi}{3 t} \)
D. \( \frac{\pi}{t} \)


Five blocks \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \) \& \( \boldsymbol{E} \) of equal
masses but made of different
substances as shown in above figure,
are heated to \( 100^{\circ} \mathrm{C} \) and placed on
separate \( 10 k g \) blocks of ice that are at a
temperature of \( 0^{\circ} \mathrm{C} \). Identify which substance melts the greatest amount
of ice?
A. The substance with the lowest specific heat
B. The substance with the highest specific heat
C. The substance with the greatest surface area
D. The substance with the smallest surface area
E. The substance that started with the highest temperature


Indicate the point of the complex plane
\( z \) which satisfy the following equation.
\( \operatorname{lm} z^{2}=0 \)


lonic solutions are good conductors
of Electricity.
A. True
B. False


Simplify the following algebraic
expression.
\( 14 c-13 c-17+8 \)
A \( . c=-9 \)
B \( . c=9 \)
c. \( c=-25 \)
D. \( c=25 \)


Which one of the following compounds gives methane on treatment with
water?
\( \mathbf{A} \cdot A l_{4} C_{3} \)
в. \( C a C_{2} \)
c. \( v c \)
D. sic


Arrange the following ions according to their flocculation power in the
coagulation of negative sol \( N a^{+}, A l^{+3}, B a^{+2} \)


For two molecules of glucose, glycolysis uses and produces ATP molecules
A. 4 and 8
B. 2 and 4
\( c \cdot 2 \) and 8
D. 2 and 2


There are two bodies of masses in and
m/2 respectively. Find the ratio of the force acting on them if their velocity-
time graphs are as shown below:
A .2: 3
B. can't be determined
\( c \cdot 2: 2 \)
D. 12:3


The largest atom among the following is:
A. sodium
B. silicon
c. potassium
D. calcium


Sketch the cross section of soil and
label the various layers.


A motorboat is racing towards the north at \( 25 k m h^{-1} \) and the water current in
that region is \( 10 \mathrm{kmh}^{-1} \) in the direction
of \( 60^{\circ} \) east of south. The resultant
velocity of the boat is:
\( \mathbf{A} \cdot 11 \mathrm{kmh}^{-1} \)
B . 22 \( k m h^{-1} \)
c. \( 33 \mathrm{kmh}^{-1} \)
D. \( 44 \mathrm{kmh}^{-1} \)


The sigma bonds present in benzene ring are:


The smaller area enclosed by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \)
where \( f(x) \) is polynomial of least degree satisfying \( \left[\lim _{x \rightarrow 0} 1+\frac{f(x)}{x^{3}}\right]^{\frac{1}{x}}=e \)
and the circle \( x^{2}+y^{2}=2 \) above the \( x- \)
axis is
A \( \cdot \frac{\pi}{2}+\frac{3}{5} \)
в. \( \frac{\pi}{2}-\frac{3}{5} \)
c. \( \frac{\pi}{2}-\frac{6}{5} \)
D. None of these


Statement I: The function \( f(x) \) in the
figure is differentiable at \( x=a \)
Statement II: The function \( f(x) \)
continuous at \( x=a \)
A. Both Statement I and Statement II are true and the
Statement II is the correct explanation of the Statement I
B. Both Statement I and Statement II are true and the Statement II is not the correct explanation of the Statement I
c. Statement l is true but Statement II is false
Statement I is false but Statement II is true


The resistivity of alloys is
than its constituent elements.
A. higher
B. lower
c. same
D. none


Solve:
\( \left(3 x^{2}+y^{2}\right) d y+\left(x^{2}+3 y^{2}\right) d x=0 \)


A man can swim with a speed of 4
\( k m h^{-1} \) in still water. He crosses a river 1
\( \mathrm{km} \) wide that flows steadily at \( 3 \mathrm{kmh}^{-1} \) If he makes his strokes normal to the
river current, how far down the river
does he go when he reaches the other bank?
A. \( 500 \mathrm{m} \)
B. 600 \( m \)
c. 750 \( m \)
D. 850 \( \mathrm{m} \)


Write balanced chemical equation for
the following. Action of ozone on hydrogen peroxide.


An object of mass \( 10 \mathrm{kg} \) is to be kept at rest on an inclined plane making an
angle of \( 37^{0} \) to the horizontal by
applying a force \( F \) along the plane upwards as shown in Fig. The
coefficient of static friction between the
object and the plane is 0.2 . Find the magnitude of force \( F \) [Take \( \left.g=10 m s^{-2}\right] \)
\( \sin 37^{\circ}=0.6 \)
\( \cos 37^{\circ}=0.8 \)


The element which resembled cobalt,
nickel and was placed in Newland's table far away from those elements was:
A. sodium
B. calcium
\( c . \) iron
D. chlorine


Which of the following are examples of
endothermic reactions?
This question has multiple correct options
A. Combustion of methane
B. Decomposition of water
C. Dehydrogenation of ethane to the ethylene
D. Conversion of graphite to diamond


Choose the incorrect statement.
A. Alternating current is oscillatory
B. Electric power is transmitted over long distances using alternating current
C. Frequency of alternating current in India is \( 50 \mathrm{Hz} \)
D. Alternating current can be used for electrolysis of copper chloride.


The distance between two consecutive
crests in a wave train produced on a string is \( 5 \mathrm{cm} \). If two complete waves
pass through any point per second, the velocity of the wave is
A. \( 10 \mathrm{cms}^{-1} \)
B. \( 2.5 \mathrm{cm} \mathrm{s}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{cms}^{-1} \)
D. \( 15 \mathrm{cms}^{-1} \)


Differentiate between translation and
translocation.


What is dispersion of white light? What is the cause of such dispersion? Draw a diagram to show the dispersion of white light by a glass prism.


A sum of Rs. 69,300 is to be divided
between two boys \( A \) and \( B, 21 \) and 22 years old respectively, in such a way that, if their portions be invested at
10 per cent per annum compound interest, they will receive equal
amounts on reaching 24 years of
age. What is the share of John in the
original sum of money?


Photochemical among is due to the
presence of :
A. Oxides of sulphur
B. Oxides of nitrogen
c. Oxides of carbon
D. Lead


Evaluate :
\( \int_{0}^{\pi / 2} x \cos 2 x d x \)


\( \int_{0}^{\pi / 2} \frac{1}{1+\sqrt{\tan x}} d x \)
A . 0
в.
\( c \cdot \frac{\pi}{4} \)
D. \( -\frac{\pi}{4} \)


The number of significant figures in
\( \mathbf{0 . 0 0 0 6 0} \mathrm{m} \) is:
A.
B. 2
\( c \cdot 3 \)
\( D \)


The numbers shown in the Venn
diagram represent the number of
elements in each subset. Find \( [(\boldsymbol{F} \cup \)
\( \boldsymbol{G}) \cap \boldsymbol{H}^{\prime} \)
\( A \cdot 3 \)
B. 13
\( c \cdot 15 \)
D. 18


If \( 2 x+y=23 \) and \( 4 x-y=19 ; \) find
the values of \( x-3 y \) and \( 5 y-2 x \)
A. The values of \( x-3 y \) and \( 5 y-2 x \) are -20 and 31 respectively
B. The values of \( x-3 y \) and \( 5 y-2 x \) are 0 and 3 respectively
c. The values of \( x-3 y \) and \( 5 y-2 x \) are 14 and -9
respectively
D. The values of \( x-3 y \) and \( 5 y-2 x \) are 5 and 23 respectively


Sugden introduced singlet linkage in which one electron is donated instead of
one pair of electrons.
A. True
B. False


Xenon has closed shell configuration but is known to give compounds with fluorine because:
A. xe atom has large size and lower ionisation potential as compared to other noble gases
B. Xe has unpaired electrons which can form covalent bonds
c. xe has highest boiling point hence it can form compounds with fluorine
D. fluorine is the smallest element hence it can react with all noble gases


What is the product formed?
A. \( \quad O C H_{2} C H_{3} \)
B.
\( c \)
D. none of the above


IUPAC name of the above compound is:
A. bicyclo[3,2,1]-octan-2-oic acid
B. bicyclo-[3,2,1]-octane-8-carboxylic acid
C. bicyclo-[3,2,1]-octan-8-oic acid
D. none of these


Sucrose is a non reducing sugar due to :
A . \( 1-2 \) linkage
B. 1-4 linkage
c. \( 1-5 \) linkage
D. 1-6 linkage


Q Type your question-
alternatives given:
Chlorobenzene can be converted into
phenol by heating in aqueous sodium hydroxide solution at a temperature of
\( 623 \mathrm{K} \) and a pressure of 300 atm. However, the rate of reaction can be
increased by the presence of certain
groups in the benzene ring.

What will be the order of reactivity of following compounds towards the above
substitution reaction?
A. iii \( > \) ii \( >i \)
B. ii > iii > i
\( \mathbf{C} \cdot \mathbf{i}>\mathbf{i} \mathbf{i}>\mathbf{i} \) ii
D. i > iii > ii


Suppose that you are in a cave deep
within the earth. Are you safe from thunder and lightning? Justify your
answer


How many sides does a regular polygon
has if each of it's interior angle is \( 120^{\circ} ? \)


In a triangle \( A B C, \angle A=90^{\circ}, \) and \( A D \)
is the altitude. Complete the relation \( \frac{B D}{B A}=\frac{A B}{D B}-\left(\frac{\ldots \ldots .}{A B \times B D}\right) \)


State the following statement is True or
False
The variance of first \( n \) even natural
numbers is \( \frac{n^{2}-1}{4} \)
A . True
B. False


Which weed is known as terror of
Bengal? Why it is very difficult to get rid of them form water bodies?


A man of 60 kg gains 1000 cal of heat by eating 5 mangoes. His efficiency is \( 56 \% \) To what height he canjump by using
this energy?
\( \mathbf{A} \cdot 4 m \)
в. \( 20 m \)
\( c .28 m \)
D. \( 0.2 m \)


The values of \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a C O}_{3} \) and \( \mathrm{CaC}_{2} \mathrm{O}_{4} \) are \( 4.7 \times 10^{-9} \) and \( 1.3 \times 10^{-9} \)
respectively at \( 25^{\circ} \mathrm{C} \). If the mixture of these two is washed with water, what is
the concentration of \( C a^{2+} \) ions in
water?
A \( \cdot 7.746 \times 10^{-5} M \)
В. \( 5.831 \times 10^{-5} M \)
c. \( 6.856 \times 10^{-5} M \)
D. \( 3.606 \times 10^{-5} M \)


is widely used as fuel in factories and thermal power stations.
A. Petroleum
B. LPG
c. coal
D. cNG


The most reactive compound for electrophilic nitration will be:
A. toluene
B. benzoic acid
c. nitrobenzene
D. benzene


Two isotopes of an elements \( Q \) are \( Q^{97} \)
(23.4\% abundance) and \( Q^{94} \) (76.6\%
abundance). \( Q^{97} \) is 8.082 times heavier
\( \operatorname{than} C^{12} \) and \( Q^{94} \) is 7.833 times
heavier than is \( C^{12} \). What is the average
atomic weight of the elements \( Q ? \)
A .94 .702
B. 78.913
c. 96.298
D. 94.695


The differential equation of family of circles with fixed radius 5 units \( \& \)
centre lies on the line \( y=2, \) is
A \( \cdot(y-2) y^{\prime 2}=25-(y-2)^{2} \)
B・ \( (y-2)^{2} y^{\prime 2}=25-(y-2)^{2} \)
c. \( (x-2) y^{\prime 2}=25-(y-2)^{2} \)
D・ \( (x-2) 2 y^{\prime 2}=25-(y-2)^{2} \)


Which is the most important group on
earth?
A. Mosses
B. Tracheophyta a
c. Bryophyta
D. Liverworts


Two waves having the intensities in the ratio 9: 1 produce interference. The ratio of maximum to minimum intensity is equal to
\( A \cdot 4: 1 \)
B. 9: 1
\( c \cdot 2: \)
D. 10: 8


Which represents disproportionation?
This question has multiple correct options
\( \mathbf{A} \cdot 2 C u^{+} \rightarrow C u^{2+}+C u \)
B \( \cdot 3 I_{2} \rightarrow 5 I^{-}+I^{5+} \)
\( \mathbf{c} \cdot C u^{2+}+Z n \rightarrow Z n^{2+}+C u \)
\( \mathbf{D} \cdot P C l_{5} \rightarrow P C l_{3}+C l_{2} \)


Electric spark is the electrical discharge when a electric
field creates an ionised channel. Fill in
the blank.
A. sufficiently strong
B. moderate
c. weak
D. very weak


The density of an equilibrium mixture of \( N_{2} O_{4} \) and \( N O_{2} \) at \( 101.32 K P_{a} \) is 3.62
\( g d m^{3} \) at \( 288 \mathrm{K} \) and \( 1.84 \mathrm{g} d m^{3} \) at \( 348 \mathrm{K} \)
What is the heat of the reaction for the
following reaction?
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2}(g) \)
B. \( \Delta_{r} H=75.68 \) kJ \( \mathrm{mol}^{-1} \)
C . \( \Delta_{r} H=95.7 \) kJ \( \mathrm{mol}^{-1} \)
D. \( \Delta_{r} H=151.3 \) kJ \( \mathrm{mol}^{-1} \)


The vapour pressure of a solution
having \( 2.0 g \) of solute \( X \) (gram atomic
\( \left.\operatorname{mass}=32 g \operatorname{mol}^{-1}\right) \operatorname{in} 100 g \) of \( C S_{2} \)
(vapour pressure \( =854 \text { torr }) \) is 848.9 torr. The molecular formula of the solute
is:
\( \mathbf{A} \cdot X \)
в. \( X_{2} \)
\( c \cdot X_{4} \)
D. \( X_{8} \)


Two circular coils made up of identical
wires of length \( 40 \mathrm{cm} \) have respectively 8 and 4 turns and the current flowing through the second coil is 4 times
greater than in the first coil. The ratio of magnetic induction at their centres is :
A . 2: 3
B. 3:
\( c \cdot 1: \)
D. 1: 2


The function \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{5}\left[\frac{\boldsymbol{x}}{\mathbf{5}}\right], \) where \( \mathrm{N} \) is the set of
natural numbers and \( [x] \) denotes the
greatest integer less than or equal to \( x \)
is
A. one-one but not onto
B. neither one-one nor onto
c. onto but not one-one
D. one-one and onto


The moment of the torque of a force
along a turning point is the force multiplied by the distance
to the force from turning point. Fill in
the blank.
A. Perpendicular
B. Horizontal
c. Both A and B
D. None


Identify the correct set representing
properties of Methanol.
A. Colourless, volatile, poisonous, miscible
B. Colourless, volatile, non-poisonous, miscible
C . Colourless, volatile, poisonous, immiscible
D. Colourless, non-volatile, poisonous, miscible


Short / Long Answer Type Questions:
Draw and explain a series of diagrams that illustrate the stages of meiosis I.


If \( x=n \pi-\tan ^{-1} 3 \) is a solution of the
equation \( 12 \tan 2 x+\frac{\sqrt{10}}{\cos x}+1=0 \)
then
A. \( n \) is any integer
B. n is an even integer
c. \( n \) is a positive integer
D. \( n \) is an odd integer


The projection of the join of the two points (1,4,5),(6,7,2) on the line whose d.s's are (4,5,6) is
A \( \cdot \frac{17}{\sqrt{77}} \)
B. \( \frac{7}{6} \)
c. 21
D. \( \frac{7}{9} \)


Find the area of the triangle formed by
tangents from the point (4,3) to the circle \( x^{2}+y^{2}=9 \) and the length of the
line joining their points to contact.?


If \( z=\frac{\sqrt{3}}{2}+\frac{i}{2}(i=\sqrt{-1}), \) then \( (1+ \)
\( \left.i z+z^{5}+i z^{8}\right)^{9} \) is equal to
A . -1
B. 1
c. 0
D \( \cdot(-1+2 i)^{9} \)


Find the net electric flux through the
entire cube


The image of the point (1,6,3) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) has the
coordinates
A. (1,1,7)
в. (0,1,7)
c. (1,0,7)
D. None of these


If \( f(x)=\left\{\begin{array}{cl}a x+3, & x \leq 2 \\ a^{2} x-1, & x>2\end{array}, \) then the \right.
values of \( a \) for which \( f \) is continuous for
all \( x \) are
A. 1 and -2
B. 1 and 2
c. -1 and 2
D. -1 and -2
E. 0 and 3


When a coin and a feather are dropped simultaneously from the same height, the coin strikes the ground first. This is
because of:
A. gravitational force
B. mass of coin
c. friction
D. none of these


State three effects of radioactive
pollution.


In which of the following plant axillary bud is modified into the tendril?
A. Pitcher plant
B. cactus
c. snake gourd
D. Pumpkin


The de-Broglie wavelength \( \lambda_{n} \) of the electron in the nth orbit of hydrogen
atom is
A. Inversely proportional to \( n \)
B. Proportional to \( n^{2} \)
c. Proportional to \( n \)
D. Inversely Proportional to \( n^{2} \)
E. Inversely proportional to radius of the orbit in the nth state


In which case second has lower boiling point than first? This question has multiple correct options
A . Li, K
в. Ве, Мg
\( c \cdot \operatorname{li}, c s \)
D. са, мв


Name the monomer present in the
following polymer
¡) Polyvinyl chloride.
ii) Natural rubber.


The best regents to resolve racemic
mixture of 2-hydroxy butanoic acid
would be:
\( A \)
\( B \)
\( c \)
\( D \)


reduce or abolish pain without causing impairment of consciousness, mental confusion, incoordination, paralysis or some other disturbances of nervous system.
A. Antacids
B. Antiseptics
c. Analgesics
D. Tranquilizerss


A rod of length \( 10 \mathrm{cm} \) lies along the principal axis of concave mirror of focal
length \( 10 c m \) in such a way that its end
closer to the pole is \( 20 \mathrm{cm} \) away from the mirror. The length of the image is-
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 2.5 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


If \( a \) and \( b \) are real, then show that the
principal value of arg \( a \) is 0 or \( \pi \) according to \( a \) is positive or negative and that of arg \( b \) is \( \pi / 2 \) or \( -\pi / 2 \)
according to \( b \) is positive or negative.


A smooth body is released from rest at a
point \( A \) at the top of a smooth curved track of vertical height \( 40 \mathrm{cm} . \) What is
the speed of the body at the bottom of
the curved track? How far along the
adjoining smooth inclined plane will the
body go?


The outermost limiting layer of Mycoplasma is made up of
A. Cell wall.
B. Cell membrane
c. Mucilaginous sheath.
D. Slime layer.


A charged particle (charge q) is moving in a circle of radius \( R \) with uniform
speed v. The associated magnetic
moment \( \mu \) is given by
A \( \cdot q v R \)
в. \( _{q v} \frac{R}{2} \)
\( \mathbf{c} \cdot q v R^{2} \)
D. \( _{q v} \frac{R^{2}}{2} \)


For the next three (03) items that follow
The number of telephone calls received
in 245 successive one minute intervals
at an exchange is given below in the following frequency distribution.
Number of calls
\[
2
\]
Frequency
\( \begin{array}{llll}14 & 21 & 25 & 43\end{array} \)
What is the mean of the distribution?
A . 3.76
B. 3.84
c. 3.96
D. 4.05


Which amongst the following has largest size?
A . \( A l \)
B. \( A l^{3} \)
c. \( C l \)
D. \( C l^{-} \)


The difference between the simple interest and the compound interest (compounded annually) on Rs 2000 for 2 years at \( 8 \% \) per annum will be
A. Rs 10
B. Rs 20
\( c \cdot \operatorname{Rs} 13 \)
D. Rs 25


a) What is denaturation of proteins?
b) What are essential Amino Acids?
Give one example.


The gas that cannot be collected over
water is:
A. \( \mathrm{N}_{2} \)
B. \( \mathrm{O}_{2} \)
\( c \cdot \mathrm{so}_{2} \)
D. PH \( _{3} \)


Four particles \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) and \( \boldsymbol{D} \) with
\( \operatorname{masses} \boldsymbol{m}_{\boldsymbol{A}}=\boldsymbol{m}, \boldsymbol{m}_{B}=2 \boldsymbol{m}, \boldsymbol{m}_{C}=3 \boldsymbol{m} \)
and \( m_{D}=4 m \) are at the corners of a
square. They have accelerations of
equal magnitude with directions as
shown. The acceleration of the centre of
mass of the particles is
A \( \cdot \frac{a}{5}(\hat{i}-\hat{j}) \)
B・ \( \frac{a}{5}(\hat{i}+\hat{j}) \)
\( c, \) zer
D. \( a(\hat{i}+\hat{j}) \)


A light ray is travelling between two media as given below. The angle of incidence on the boundary in all the
cases is \( 30^{\circ} . \) Identify the sequence of increasing order of angles of refraction.
a) Air to water
b) Water to glass
c) Glass to water
\( A \cdot a, b, c \)
B. b, c, a
\( c \cdot c, a, b \)
D. a, c, b


Assertion
A ray incident along normal to the mirror retraces its path.
Reason
In reflection, angle of incidences is always equal to angle of reflection.
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


Which of the following is a \( 3^{\circ} \) amine?
A. Propan -2 - amine
B. N-Methyl ethanarnine
c. Allyl amine
D. \( N, N- \) Diethylbutan \( -1- \) amine


The diagram shows equipotential lines
from an unknown charge configuration.
Determine where in the diagram the
field is closest to uniform:
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


In two concentric circle, prove that all
chords of the outer circle which touch
the inner are of equal length.


Find the co-ordinates of image of point object P formed after two successive
reflection at concave mirror and then at
convex


\( A B C D \) is a trapezium in which \( A B \| \) \( D C, A B=16 \mathrm{cm} \) and \( D C=24 \mathrm{cm} . \) If
\( E \) and \( F \) are respectively the midpoints of \( A D \) and \( B C, \) then \( a r(A B F E)= \) \( \frac{9}{11} a r(E F C D) \)
A . True
B. False


Compare the properties of a typical metal and a non-metal on the basis of
the following.

Conductivity of heat and electricity:
A. Metals are good conductor of heat and electricity
B. Non metals are good conductor of heat and electricity
C. Metals are bad conductor of heat and electricity
D. Both B and C


Tahina spectabilis is a gigantic palm found only in remote parts of north-west Madagascar. It lives for about 50 years, then flower only once, and dies soon after. What is the common name of this
flower?
A. suicide palm
B. Queen palm
c. Raffia palm
D. Areca palm


The product of fermentation is
A. Ethanol and lactic acid
B. Acetic acid and lactic acid
C. Ethanol and acetic acid
D. All of the above


A body has an initial velocity of \( 3 m / s \)
and has an acceleration of \( 1 \mathrm{ms}^{-2} \)
normal to the direction of the initial
velocity. Then its velocity \( 4 s \) after the
start is
A \( \cdot 7 m s^{-1} \) along the direction of initial velocity
B. \( 7 m s^{-1} \) along the normal to the direction of the initial velocity
c. \( 7 m s^{-1} \) mid-way between the two directions
D \( \cdot 5 m s^{-1} \) at an angle of \( \tan ^{-1} \frac{4}{3} \) with the direction of the initial velocity


How many unpaired electrons are present in \( \boldsymbol{N} \boldsymbol{i}^{2+} \) ?
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c \cdot 4 \)
D. None of the above


\( \ln \) an \( A P, \operatorname{given} a=7, a_{13}=35, \) find \( d \)
and \( S_{13} \)


The diagram shows the displacementtime graph for a vibrating body. Name the type of vibration produced by the vibrating body :


The focal length, f of a concave mirror is:
A. Positive
B. Negative
c. zero
D. None


Which term of the \( A P: 3,8,13,18, . . \) is
\( \mathbf{7 8} ? \)
\( \mathbf{A} \cdot t_{1} \)
B . \( t_{18} \)
\( c \cdot t_{14} \)
D. None of these


If the acceleration due to gravity inside
the earth is to be kept constant, then
the relation between the density \( d \) and the distance \( r \) from the centre of earth
will be
\( \mathbf{A} \cdot d \propto r \)
B. \( d \propto r^{1 / 2} \)
c. \( d \propto 1 / r \)
D. \( d \propto \frac{1}{r^{2}} \)


Which of the following elements has least number of electrons in its M shell?
\( A \cdot K \)
в. мп
c. \( \mathrm{Ni} \)
D. sc


Amount in g of simple containing \( 80 \% \) NaOH required to prepare 60 litre of 0.5 M solution is :
A . 1000
B. 1200
\( c \cdot 1500 \)
D. 1600


The equation to the hyperbola of given
transverse axis whose vertex bisects
the distance between the centre and
focus, is given by
A \( \cdot 3 x^{2}-y^{2}=3 a^{2} \)
B . \( x^{2}-3 y^{2}=a^{2} \)
c. \( x^{2}-y^{2}=3 a^{2} \)
D. None of these


\( \underbrace{\frac{c}{x}} \)


Calculate magnetic flux density of the magnetic field at the centre of a
circular coil of 50 tunrs, having radius of \( 0.5 \mathrm{m} \) and carrying a current of \( 5 \mathrm{A} \)


A hole is
A. a positively charged electron.
B. an electron in the valence band.
C. an unfilled covalent bond.
D. an excess electron in covalent bond.


Which of the following statement is
false?
A. Bridgehead halides are inert towards both \( S_{N} 1 \) and
\( S_{N} 2 \) reactions.
B. The first step in both \( S_{N} 1 \) and \( E 1 \) reactions is the
same
C \( . S_{N} 2 \) reaction is favoured by weak nucleophile and protic solvent.
D. \( E 2 \) eliminations are favoured by the use of a solvent of low polarity and high concentration of a strong base.


The path followed by a projectile is called its:
A. trajectory
B. range
c. amplitude
D. none of these


One litre sample of a mixture of
methane gas and \( O_{2} \) measured at \( 25^{\circ} C \)
and 740 torr was allowed to react at
constant pressure in a calorimeter which together with its content has a heat capacity of 1260 cal/degree. The complete combustion of methane to
\( C O_{2} \) and \( H_{2} O \) caused a temperature rise in calorimeter of 0.667 K. The
percentage of \( C H_{4} \) in original mixture
was:
Given: \( \Delta \boldsymbol{H}_{\text {combustion}} \) of \( \boldsymbol{C} \boldsymbol{H}_{4} \) is
\( -210.8 k c a l m o l^{-1} \)
A . \( 10 \% \)
в. 20\%
c. \( 15 \% \)
D. 30\%


"Stratospheric ozone is formed naturally by chemical reactions involving solar ultraviolet radiation (sunlight) and oxygen molecules, which make up \( _{--} \) of the atmosphere."
A . 21\%
в. 22\%
c. 23\%
D. 24\%


Two complex numbers are represented
by ordered pairs \( z_{1}:(3,4) \& z_{2}:(4,5) \)
which of the following is true for \( z_{1}+z_{2} \)
\( ? \)
This question has multiple correct options
\( \mathbf{A} \cdot z_{1}+z_{2}=(7,9) \)
B . \( z_{1}+z_{2}=(7+9 i) \)
\( \mathbf{c} \cdot z_{1}+z_{2}=(1,9) \)
D. None of these


\( \Delta A B C \) is an isosceles triangle with
\( A B=A C . A D \) bisects \( \angle A . \) Prove that
\( \angle B=\angle C \)


Find the degree of the polynomial: 5
\( \boldsymbol{x}^{2} \)


In filling the gasoline tank of an
aeroplane the metal nozzle of the hose
from the gasoline truck is always carefully connected to the metal of the aeroplane by a wire before the nozzle is inserted in the tank. Explain, why?


A sample of \( A g C l \) was treated with
\( 5 m L \) of \( 1.5 M N a_{2} C O_{3} \) solution to
\( \operatorname{give} A g_{2} C O_{3} . \) The remaining solution
contained \( 0.0026 g C l^{-} \) per litre
Calculate the solubility product of \( A g C l \)
\( \left(\boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C O}_{3}\right)=\boldsymbol{8} \cdot \boldsymbol{2} \times \mathbf{1 0}^{-12}\right) \)


Find the area of the shaded region in
given Fig.where arcs drawn with
centres \( A, B, C \) and \( D \) intersect in pairs
at mid-points \( P, Q, R \) and \( S \) of the sides
\( A B, B C, C D \) and \( D A, \) respectively of a
square \( A B C D(\text { Use } \pi=3.14) \)
\( \mathbf{A} \cdot 30.96 \mathrm{cm}^{2} \)
B. \( 90.96 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 120.96 \mathrm{cm}^{2} \)
D. \( 180.96 \mathrm{cm}^{2} \)


The volume of one mole of an ideal gas
with the adiabatic exponent \( \gamma \) is changed according to the relation \( V= \) \( \frac{a}{T} \) where a is a constant. Find the
amount of heat absorbed by the gas in the process, if the temperature is increased by \( \Delta T \)


Construct \( \Delta A B C \) in which \( A B=5 \mathrm{cm} \)
\( \angle B=45^{\circ} \) and \( B C=6 c m \)


\( \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a} \boldsymbol{C O}_{3} \downarrow \)
\( +2 N a O H \)
This reaction made the basis of
manufacturing of NaOH in earlier days and pH of the solution was found to be greater than \( 14 . \) This indicates that
concentration of NaOH is very high. Hence, pH is greater than 14 If true enter 1 , else enter 0 .


For a reaction \( \boldsymbol{X} \rightarrow \boldsymbol{Y} \) ), heat of reaction
is \( +83.68 k J, \) energy of reactant \( X \) is
\( 167.36 k J \) and energy of activation is \( 209.20 k J . \) Calculate
(i) threshold
energy (ii) energy of product \( Y \) and (iii) energy activation of the reverse reaction
\( (\boldsymbol{Y} \rightarrow \boldsymbol{X}) \)


Write the names of Inert gases.


If the radius of a sphere is found to be
\( 3 c m \pm 0.01 c m, \) find the percentage
error in the determination of its volume.


The value of \( \lim _{n \rightarrow \infty} e^{\frac{3 i}{n}} \cdot \frac{3}{n}=? \)
A \( \cdot e^{4}-1 \)
B. \( e^{3}-1 \)
c. \( e^{5}-1 \)
D. \( e^{3}-2 \)


\( C-C l \) bond of chlorobenzene in
comparison to \( C-C l \) bond of methyl
chloride is:
A. longer and weaker
B. shorter and weaker
c. shorter and stronger
D. Ionger and stronger


Consider a sample of a pure beta-active
material. Choose the correct one of the
following.
A. All the beta particles emitted have the same energy
B. The beta particles originally exist inside the nucleus and are ejected at the time of beta decay
C. The antineutrino emitted in a beta decay has zero mass and hence, zero momentum
D. The active nucleus changes to one of its isobars after the decay


How can an element be defined as
consisting of any mixture of atoms with a given atomic number?
A. Determines the mass of of element in the mixture
B. Determines the chemical properties of an element
c. Both A and B
D. None of the above


Choose the correct option of
temperature at which carbon reduces
Fe0 to iron and produces CO.
A. Below temperature at point
B. Approximately at the temperature corresponding to point
c. Above temperature at point A but below temperature at point
D. Above temperature at point


A particle of mass \( m=5 \) unit is
moving with a uniform speed \( \boldsymbol{v}=\mathbf{3} \sqrt{\mathbf{2}} \)
unit in the \( X \) OY plane along the line \( y= \) \( x+4 . \) The magnitude of the angular
momentum of the particle about the origin is :
A. 60 unit
B. \( 40 \sqrt{2} \) unit
c. zero
D. 7.5 unit


Assertion
A planet moves faster, when it is closer
to the sun in its orbit and vice versa
Reason
Orbital velocity for an orbiting planet is
constant
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Helium is found as a monoatomic gas.
Explain this on the basis of M.O.T.


A geostationary satellite
A. moves faster than the near Earth satellite.
B. has a time period less than that of a near Earth satellite.
C . revolves about the polar axis.
D. is stationary in space.


Which one of the following is not a structural part of a transcription unit in
DNA?
A. A promoter
B. The structural gene
c. The inducer
D. A terminator


Which is the highest peak?
\( A \cdot A \)
B. E
\( c \cdot c \)
\( D \cdot B \)


The median of the following discrete series is
\( \begin{array}{lllllll}x_{i} & 3 & 6 & 5 & 8 & 12 & 7\end{array} \)
\( f_{i} \quad 5 \quad 2 \quad 4 \quad 6 \quad 7 \)
A. 7
B. 8
c. 9
D. 6


The total energy of an electron revolving in the second orbit of hydrogen atom is?
A. -13.6 ev
B. -1.51 eV
c. -3.4 ev
D. zero


Drugs can inhibit the catalytic activity of enzymes by binding at
A . active sites
B. allosteric sites
c. both active sites and allosteric sites
D. core of an enzyme


Noble gases are group of elements which exhibit very
A. High chemical activity
B. Low chemical activity
c. Minimum electronegativity
D. Much paramagnetic properties


A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function
of time t. Which of the following statements is true. Assume that the
particle started at \( t=0 \) at its mean position
A. P.E. is maximum when \( t=0 \)
B. T.E. is zero when \( t=0 \)
c. K.E. is maximum when \( t=0 \)
D. K.E. is minimum when t =


Three infinite planes have a uniform
surface charge density \( \sigma \) on is surface.
All charges are fixed.On each of the
three infinite planes parallel to the \( y- \)
\( z \) plane placed at \( x=-a, x=0 \) and
\( \boldsymbol{x}=\boldsymbol{a} . \) The potential difference between
\( A \) and \( C \) is:
\( A \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
c. \( \frac{\sigma a}{2 \varepsilon_{0}} \)
D.


The equivalent resistance of eight equal resistances in series is 48 ohms. What
would be the equivalent resistance if they are connected in parallel?
A \( \cdot \frac{3}{4} \Omega \)
в. \( \frac{4}{3} \Omega \)
c. \( 4 \Omega \)
D. 3\Omega


Sterile flower.


Which one is a better fuel, coal or coke?
A. Coke is a better fuel because coke produces more heat on burning as compared to coal
B. Coal is a better fuel because coal does not produce more heat on burning as compared to coke
C. Both are of equal efficiency
D. None of these


Verify that the following function can be regarded as p.d.f for the random
variable \( \boldsymbol{X} \)
-1 \begin{tabular}{r}
1 \\
\hline
\end{tabular} \( \mathbf{0} \)
1
\( P(x) \)
-0.2 0.2


Statement I: EEG is of immense
diagnostic value in the cardiac disease Statement II: Defects in cardiac
functions can be reflected in changes in the pattern of electrical potentials recorded in the EEG
A. Statement - - lis True, Statement - -II is True, Statement I is correct
B. Statement-lis True, Statement- -II is True; Statement I is NOT a correct explanation for the statement - -
c. Statement- - I is True, Statement- - II is false
D. Both the statements are false


For the values \( x_{1}, x_{2} \dots \dots x_{101} \) of a
distribution \( x_{1}<x_{2}<x_{3}<\dots . .< \)
\( x_{100}<x_{101} . \) The mean deviation of this
distribution with respect to a number will be minimum when k is equal to
A. \( x_{1} \)
в. \( x_{5} \)
c. \( x_{50} \)
D. \( \frac{x_{1}+x_{2}+\ldots . .+x_{101}}{101} \)


Draw the structures of the following
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)


In Fig. Force \( F \) is gradually increased from zero. Draw the graph between applied force \( F \) and tension \( T \) in the
string. The coefficient of static friction
between the block and the ground is \( \mu_{s} \)


A force of \( 12 N \) pulls a block of mass
\( 3.5 k g \) through a rope of of mass \( 0.5 k g \) The block is resting on a horizontal frictionless surface. What is the force of
reaction exerted by the block on the
rope?


The radius of a circular wheel is \( 1 \frac{3}{4} m \) How many revolutions will it make in
traveling \( 11 k m ? \)


Consider a circle \( x^{2}+y^{2}+a x+b y+ \)
\( c=0 \) lying completely in first quadrant.
If \( \mathrm{m}_{1} \) and \( \mathrm{m}_{2} \) are the maximum and
minimum values of y/x for all ordered pairs \( (x, y) \) on the circumference of the
circle, then the value of \( \left(\boldsymbol{m}_{1}+\boldsymbol{m}_{2}\right) \) is
A \( \cdot \frac{a^{2}-4 c}{b^{2}-4 c} \)
в. \( \frac{2 a b}{b^{2}-4 c} \)
c. \( \frac{2 a b}{4 c-b^{2}} \)
D. \( \frac{2 a b}{b^{2}-4 a c} \)


(1) Define the following
(i) Henry's law
(ii) Normality.


In the figure given above, \( A D \) is a
straight line, \( O P \) perpendicular to \( A D \)
and 0 is the centre of both circles. If
\( \boldsymbol{O A}=\mathbf{2 0} \boldsymbol{c m}, \boldsymbol{O B}=\mathbf{1 5} \boldsymbol{c m} \) and \( \boldsymbol{O P}= \)
\( 12 \mathrm{cm} . \) what is \( A B \) equal to?
\( A \cdot 7 \mathrm{cm} \)
\( 3.8 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
\( 0.12 \mathrm{cm} \)


Osteoid means
A. Calcified bone matrix
B. Calcified cartilage matrix
C. Uncalcified bone matrix
D. Fibrocartilage


which of the following statement is/are
true for co-planar vectors?
This question has multiple correct options
A. Any of three non-coplanar vectors are linearly independent
B. Any three co-planar vectors are linearly independent.
C. If \( a \) and \( b \) are two non-zero non-collinear vectors then
there exist any vector \( r \) coplanar with \( a \) and \( b \) such that \( r=x a+y b \)
D. Both \( B \) and \( C \) are correct.


The type of corolla aestivation in pea flower is
A. valvate
B. Twisted
c. Imbricate
D. Vexillary


The densities of air at \( 25^{\circ} \mathrm{C} \) and \( 100^{\circ} \mathrm{C} \)
\( \operatorname{are} 1.2 g L^{-1} \) and \( 0.9 g L^{-1} \) respectively Assuming that the air obey's Charle's law the value of absolute zero of
temperature in degree Celsius is:
B . \( 200^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot-200^{\circ} \mathrm{C} \)
D. \( 0^{\circ} \mathrm{C} \)


If \( \frac{1-x+6 x^{2}}{x-x^{3}}=\frac{A}{x}+\frac{B}{1-x}+\frac{C}{1+x} \)
then \( \mathbf{A}= \)
\( A \)
B . 2
\( c .3 \)
D. 4


Out of boiling point (I), entropy (II), pH
(III) and e.m.f. of a cell (IV).
how many of them are intensive


The percentage degree of hydrolysis of a salt of weak acid \( (\boldsymbol{H} \boldsymbol{A}) \) and weak base \( (B O H) \) in its \( 0.1 ~ M \) solution is found
to be \( 10 \% \). If the molarity of the solution is \( 0.05 M, \) the percentage hydrolysis of
the salt should be:
A . \( 5 \% \)
B. \( 10 \% \)
\( c \cdot 20 \% \)
D. none of the above


Write differential rate equation for the reaction, \( 2 A+B \rightarrow \) product.


Construct an isosceles triangle whose
base is \( 8 \mathrm{cm} \) and altitude \( 4 \mathrm{cm} \) and then
another triangle whose sides are \( 1 \frac{1}{2} \) times the corresponding sides of the isosceles triangle.


\( \lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x} \) equals to
A .
B.
\( c \cdot 0 \)
D. none of these


A line makes angles \( \alpha, \beta, \gamma \) with the
positive directions of the axes of
reference. The value of \( \cos 2 \alpha+ \)
\( \cos 2 \beta+\cos 2 \gamma \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot-1 \)
D. 0


If the pressure acting on an ideal gas that is kept at constant temperature is multiplied by four, its volume
A . triples
B. reduces to \( 1 / 3 \)
c. increased by four
D. reduces to \( 1 / 4 \)
E. there is not enough information to tel


The energy stored in magnetic field
produced by a metal sphere is 4.5 J. If the sphere contains \( 4 \mu C \) charge, its
radius will be :
\( \left[\text { Take }: \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} N-m^{2} / C^{2}\right] \)
A. 32 mm
B. \( 16 \mathrm{mm} \)
c. \( 20 \mathrm{mm} \)
D. 28 mm


When \( \mathrm{N} \) and \( \mathrm{S} \) both are present in an organic compound, the sodium extract
with \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \) gives:
A. green colour
B. blue colour
c. yellow colour
D. red colour


The number of protons, neutrons and
orbital electrons in particles form
letters \( A \) to \( F \) are given in the following
table.
\begin{tabular}{llll}
Particle & Protons & Neutrons & Electrons \\
\( A \) & 3 & 4 & 2 \\
\( B \) & 9 & 10 & 10 \\
\( C \) & 12 & 12 & 12 \\
\( E \) & 17 & 20 & 17 \\
\( F \) & 18 & 22 & 18 \\
\hline
\end{tabular} Choose from the table the letters that
represent an atom of inert gas.
\( \mathbf{A} \cdot B \) and \( F \)
B. \( F \)
\( \mathbf{c} \cdot A \) and \( B \)
D. \( A \)


Which of the following is true regarding greenhouse effect?
A. Increase in the temperature of the earth due to high concentration of \( \mathrm{NO}_{2} \)
B. Increase in the temperature of the earth due to high concentration of \( \mathrm{SO}_{2} \)
C. Increase in the temperature of the earth due to high concentration of \( \mathrm{N}_{2} \)
D. Increase in temperature of the earth due to highh concentration of \( \mathrm{CO}_{2} \)


A boy throws a ball of mass \( 0.5 \mathrm{kg} \) upwards with an initial speed of \( 14 \mathrm{m} / \mathrm{s} \) The ball reaches a maximum height of
8m. The amount of energy dissipated by air drag acting on the ball during the ascent is
A . 4.9
B. 9.8
c. 0 J
D. 13.8 J


Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0. What is the maximum
tension,that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed \( 6.9 \times 10^{7} \) pa ?
Assume that each rivet is to carry onequarter of the load
\( A \cdot 3 \)
в. 2.5
\( c \cdot 4 \)
D. 5


Evaluate :
\( \Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right| \)


If Darwin's theory of pangenesis shows similarity with theory of inheritance of acquired characters, then what shall be correct according to it?
A. Useful organs become strong and developed, while useless organs become extinct. These organs help in the struggle for survival
B. Size of organs increase with ageing
c. Development of organs is due to willpower
D. There should be some physical basis of inheritance


The area of the circle is \( 25 \pi \) sq. cms.
Find the length of its arc subtending an angle of \( 144^{\circ} \) at the centre. Also find the
area of the corresponding sector.


Thigmotropism is best exhibited by
A. Tendrilss
B. Stem apex
c. Root apex
D. Leaf apex


Complete the following:
Mass \( = \) \( \times \) density
A. Volume
B. Area
c. width
D. Density


Extinction of flora and fauna can be
caused by
A. Aforestation
B. Deforestation
c. Reforestation
D. None of the above


Find the middle term of the expansion of \( \left(\sqrt{\boldsymbol{x}}-\frac{\mathbf{1}}{\boldsymbol{x}}\right)^{\mathbf{6}} \)


The crystal fied stabilization energy
\( (C F S E) \) of \( \left[F e\left(H_{2} O\right)_{6}\right] C l_{2} \) and
\( \boldsymbol{K}_{2}\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right], \) respectively, are:
A. \( -0.4 \Delta_{o} \) and \( -0.8 \Delta_{t} \)
B. \( -0.4 \Delta_{o} \) and \( -1.2 \Delta_{t} \)
c. \( -2.4 \Delta_{o} \) and \( -1.2 \Delta_{t} \)
D. \( -0.6 \Delta_{o} \) and \( -0.8 \Delta \)


The magnification of a magnifying lens of focal length \( 5 \mathrm{cm} \) is : (final image is at \( \infty) \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 5


True or False :
Three positive (red) and three negative
(blue) point charges are arranged
symmetrically around a circle centered
on point \( P \) as shown in the diagram. Al
point charges are of the same
magnitude.
Electric Field at \( \mathrm{P} \) will be zero while
electric potential at point \( P \) will be non
zero.
A. True
B. False


Which one of the following combinations is found in DNA ?
A. Guanine and guanidine
B. Guanidine and cytosine
c. Guanine and cytosine
D. Adenine and guanidine


The time elapsed between \( 33 \% \) and \( 67 \% \) completion of a first order reaction
is 30 minutes. What is the time needed
for \( 25 \% \) completion?
A. 15.5 min
в. 12.5 min
c. 18.5 min
D. 16.5 min


\( H C N \) and \( H N C \) are:
A. metamers
B. functional isomers
c. positional isomers
D. chain isomers


The following picture depicts the DNA
What is the structure of DNA ?
A. Spherical
B. Double Helix
C. Dumbell
D. Renal and longitudinal


If \( \boldsymbol{X}=\{1,2,3, \dots, 10\} \) and \( A= \)
\( \{1,2,3,4,5\} . \) Then, the number of
subsets \( B \) of \( X \) such that \( A-B=\{4\} \)
is
\( A \cdot 2^{5} \)
B \( \cdot 2^{4} \)
\( \mathbf{c} \cdot 2^{5}-1 \)
D.
E \( .2^{4}-1 \)


The image of the point (-1,3,4) in the
plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot(15,11,4) \)
в. \( \left(\frac{9}{5},-\frac{13}{5}, 4\right) \)
\( c \cdot(8,4,4) \)
D. None of these


An \( A C \) source is rated \( 220 V, 50 H z \)
The average voltage, is calculated in a time interval of 0.01 s. It
A. must be zero
B. may be zero
\( c . \) is never zero
D. is \( (220 / \sqrt{2}) V \)


The force experienced by the cathode rays when they pass through a uniform electric field of intensity \( \bar{E} \) is:
A. in the direction of the electric field
B. in the direction opposite to that of the electric field
c. at right angles to the electric field
D. zero, because cathode rays do not have any charge


Subtract \( 1-p^{3} \) from \( 2 p^{3}-3 p q^{2}-2 q^{3} \)


If ' \( x^{\prime} \) varies inversely as ' \( y^{\prime} \) and \( x=7 \)
when \( \boldsymbol{y}=\mathbf{9} \)
(a) Find constant of variation \( (k) \)
(b) Write equation of variation.
(c) Find ' \( y^{\prime} \) when \( x=9 \)


The actual formula of sodium chloride
is:
A . \( N a C l \)
B. \( N a^{+} C l^{-} \)
c. \( \left(N a^{+} C l^{-}\right)_{n} \)
D. \( N a_{n} C l_{n} \)


The upper portion of an inclined plane of
inclination \( \alpha \) is smooth and the lower
portion is rough. A particle slides down
from rest from the top and just comes to rest at the foot. If the ratio of smooth
Iength to rough length is \( m: n \), find the
coefficient of friction.
A \( \cdot \mu=\left(\frac{m-n}{n}\right) \tan \alpha \)
B \( \cdot \mu=\left(\frac{m+n}{m}\right) \tan \alpha \)
\( \mathbf{c} \cdot_{\mu}=\left(\frac{m-n}{m}\right) \tan \alpha \)
D. \( \mu=\left(\frac{m+n}{n}\right) \tan \alpha \)


Which one of the following oxide is also called chromic acid?
A. \( C r O_{2} \)
в. \( C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{CrO}_{3} \)
D. \( \mathrm{CrO} \)


How do plants get rid of their excretory products?
A. Shedding leaves
B. Shedding bark
c. Both A and B
D. Shading fruits


Find the sum of odd integers between 1 and 1000 which are divisible by 3
\( \mathbf{A} \cdot 83667 \)
B . 54954
\( \mathbf{c} .99999 \)
D. 79894


A cylindrical container of radius \( 6 \mathrm{cm} \)
and height \( 15 \mathrm{cm} \) is filled with ice
cream. The whole ice cream has to be
distributed to 10 children in equal
cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the
radius of the ice-cream cone.


\( \frac{8}{0} \)


Discuss the transport of gases \( \left(O_{2} \) and \right.
\( \left.C O_{2}\right) \) in the blood.


A train covered a certain distance at a
uniform speed. If the train would have been \( 6 \mathrm{km} / \mathrm{h} \) faster, it would have taken
4 hours less than the scheduled time.
And, if the train were slower by \( 6 \mathrm{km} / \mathrm{h} \)
it would have taken 6 hours more than
the scheduled time. Find the length of
the journey.


Diethyl amine when treated with nitrous acid yields:
A. diethyl ammonium nitrite
B. ethyl alcoho
c. N-nitroso diethyl amine
D. triethyl ammonium nitrite


Consider the letters of the word
'MATHEMATICS'. Possible number of
words in which no two vowels are
together is
A \( \cdot 7 !^{8} C_{2} \frac{4 !}{2 !} \)
в. \( \frac{7 !^{8}}{2 !} C_{4} \frac{4 !}{2 !} \)
c. \( \frac{7 !^{8}}{2 ! 2 !} C_{4} \frac{4 !}{2 !} \)
D. \( \frac{7 !}{2 ! 2 ! 2 !}^{8} C_{4} \frac{4 !}{2 !} \)


A fourth charge with charge \( +3 q \) is
slowly moved in from infinity to point \( \boldsymbol{P} \)
How much work must be done in this
process?
\( A \)
в. \( \frac{3 q^{2}}{2 \pi \epsilon_{0} a} \)
c. \( \frac{3 q^{2}}{\sqrt{3} \pi \epsilon_{0} a} \)
D. \( \frac{3 q^{2}}{4 \pi \epsilon_{n}} \)


Decreasing order of acidic strength of following compounds is:
\( (x) \)
\( \mathbf{A} \cdot x>y>z \)
В. \( y>x>z \)
\( \mathbf{c} . z>y>x \)
D. \( z>x>y \)


Write the cell reaction and calculate the
emf of the cell
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g}, \mathbf{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H}^{+}(\mathbf{0 . 5} \boldsymbol{M}) \| \boldsymbol{K} \boldsymbol{C l}(\mathbf{1} \boldsymbol{M}) \)
\( \operatorname{at} 25^{\circ} C, E=0.28 V \)


gm molar solution is :
A. \( 1 \mathrm{gm} \) mole of solute dissolved in \( 1000 \mathrm{ml} \) of solvent.
B. \( 1 \mathrm{gm} \) mole of solute dissolved in \( 1000 \mathrm{ml} \) of solution.
C. \( 1 \mathrm{gm} \) of solute dissolved in \( 1000 \mathrm{ml} \) of solvent
D. \( 1 \mathrm{gm} \) of solute dissolved in \( 1000 \mathrm{ml} \) of solution.


\( a \) \( e^{-} \)


Bentham and Hooker proposed their system of classification in
A. Genera Plantarum
B. Species Plantarum
c. Historia Plantarum
D. Historia Naturae


Calculate: \( \sqrt{4} \)


5.2 moles of aqueous solution of 1 L of methyl alcohol, \( C H_{3} O H \) is supplied.
What is the mole fraction of methyl alcohol in the solution?
A. 0.100
B. 0.190
c. 0.086
D. 0.050


In the A.C. circuit shown, keeping' \( \boldsymbol{K} \)
pressed, if an iron rod is inserted into
the coil, the bulb in the circuit
A. Gets damaged
B. Glows less brightly
c. Glows with same brightness (as before the rod is inserted
D. Glows more brightly


A radiation \( A \) is focused by a proper
device on the bulb of a thermometer.
Mercury in the thermometer shows a
rapid increase. The radiation \( \boldsymbol{A} \) is:
A . infrared radiation
B. visible light
c. ultraviolet radiation
D. X-rays


A cylindrical vessel of cross-sectional area, \( s \), is left out in the rain in which
water is falling vertically downward
with the velocity, \( v, \) in the still air. When the wind starts blowing in North-East
direction with velocity, \( v, \) the rate of collection of water in the vessel is
A . \( v . s \)
В. \( \sqrt{2} v . s \)
c. \( 2 v . s \)
D. \( 2 \sqrt{2} v . s \)


Which colour code is used for live wire?
A. Red
B. Black
c. Green
D. Yellow


us
and radius \( 0.5 \mathrm{m} \) is initially at rest on a
horizontal frictionless surface. Three
forces of equal magnitude \( 0.5 N \) are
applied simultaneously along the three
sides of an equilateral triangle \( \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \)
with its vertices on the perimeter of the
disc (see figure). One second after applying the forces, the angular speed
of the disc in \( r a d s^{-1} \) is:
\( A \cdot 2 \)
B. 4
\( c .5 \)
\( D \)


The area of a rhombus is \( 84 \mathrm{m}^{2} \) and its
length of one diagonal is 24 m. Find the side of the rhombus


Answer in 3 to 5 sentences:
Define biodiversity. Write any two types of biodiversity.


Rutherford was the first physicist to carry artificial transmutation from one element into another. In his experiment he bombarded nitrogen with alpha particles to produce isotope of
A. Hydrogen
B. Carbon
c. oxygen
D. Helium


\( f(x) \) is cubic polynomial which has local maximum at \( \mathbf{x}=-1 . \) If \( \mathbf{f}(\mathbf{2})= \)
\( \mathbf{1 8}, \mathbf{f}(\mathbf{1})=-\mathbf{1} \) and \( \mathbf{f}(\mathbf{x}) \) has local
minima at \( \mathbf{x}=\mathbf{0}, \) then
This question has multiple correct options
A. the distance between (-1,2) and \( (a, f(a)), \) where \( x=a \) is the point of local minima is \( 2 \sqrt{5} \)
B. f(x) is increasing for \( x \in[1,2 \sqrt{5} \)
\( \mathrm{c} . \mathrm{f}(\mathrm{x}) \) has local minima at \( \mathrm{x}=1 \)
D. the value of \( f(0)=5 \)


For a reaction to be spontaneous in neither direction, which of the following is/are correct regarding the closed
system?
(1) \( (\Delta G)_{T, P}=0 \)
(2) \( (\Delta G)_{T, P}<0 \)
(3) \( (\Delta G)_{U, V}=0 \)
(4) \( (\Delta G)_{U, V}>0 \)
codes:
A. 1,2,3 are correct
B. 1 and 2 are correct
c. 2 and 4 are correct
D. 1 and 3 are correct


Burning of fossil fuels is the main
cause of release of dioxide
gas in air.


A plane mirror makes an angle of \( 30^{\circ} \) with the horizontal. If a vertical ray
strikes the mirror, find the angle between the mirror and the reflected ray
\( ? \)


Which of the following is incorrect for
glycolysis?
A. It produces ATP
B. It uses ATP
c. End products are \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \) 0
D. None of the above


If \( a \) and \( b \) are the non-zero distinct roots
of \( x^{2}+a x+b=0, \) then the least value
of \( x^{2}+a x+b \) is
A \( \cdot \frac{3}{2} \)
B. 9
c. \( -\frac{9}{4} \)
D.


What happens when sulphur dioxide gas is passed through an aqueous solution of a Fe(III) salt?


The radius of a solid sphere is 'r' cm. It is bisected, then the total surface area of the two pieces obtained is
\( \mathbf{A} \cdot 8 \pi r^{2} c m^{2} \)
B . \( 4 \pi r^{2} c m^{2} \)
c. \( 5 \pi r^{2} c m^{2} \)
D. \( 6 \pi r^{2} c m^{2} \)


Find the remainder after dividing
\( \left(6 y^{5}+15 y^{4}+16 y^{3}+4 y^{2}+10 y-35\right) \)
by \( \left(3 y^{2}+5\right) \)


The distance between the pair of parallel lines \( x^{2}+2 x y+y^{2}-8 a x- \)
\( 8 a y-9 a^{2}=0 \) is
A \( .2 \sqrt{5} a \)
an
в. \( \sqrt{10} a \)
\( c \cdot 10 a \)
D. \( 5 \sqrt{2} a \)


A rod of length \( 50 \mathrm{cm} \) moves with a
speed of \( 10 \mathrm{cm} / \mathrm{s} \), in a uniform
magnetic field of strength \( 10 G \) at an
angle of \( 30^{\circ} \) with the field. The emf
induced across the ends of the rod is :
A. 5000 CGS unit
B. \( 2500 \mathrm{CGS} \) unit
c. 7500 CGS unit
D. \( 1000 \mathrm{CGS} \) unit


Leaf fall occurs in a tree when there is
increase in concentration of
A . Gibberellin
B. Cytokinin
c. Auxin
D. ethylene


The species of coral which is used in jewellery.
A. corallium
B. Anthocodium
c. Gorgonium
D. Fungia


A travelling wave pulse defined as \( y= \) \( \frac{10}{5+(x+2 t)^{2}} . \) In which direction and
with what velocity is the pulse propagating?


Solve the following simultaneous equations by substitution method and find the value of \( x 3 x-2 y=4 ; 6 x+ \)
\( 7 y=19 \)


The compound formed when ethene
reacts with hydrogen is
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
c. \( C_{2} H_{2} \)
D. \( C_{3} H_{8} \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}(\mathbf{1}+\boldsymbol{a} \cos \boldsymbol{x})-\boldsymbol{b} \sin \boldsymbol{x}}{\boldsymbol{x}^{3}}, \boldsymbol{x} \neq \)
0 \( \operatorname{and} f(0)=1, \) then values if 'a' and 'b'
so that 'f' is continuous are
A \( \cdot \frac{5}{2}, \frac{3}{2} \)
B. \( \frac{5}{2}, \frac{-3}{2} \)
c. \( -\frac{5}{2}-\frac{3}{2} \)
D. \( \frac{1}{2}-\frac{3}{2} \)


The angle of incidence of a ray for which
the angle of refraction is \( 90^{\circ} \) is called
A. Scattering angle
B. Reflex angle
c. critical angle
D. optical angle


Calculate the power of a source if it
produces an energy of 250 joules in 10
sec.
A. 2500w
B. 2.5w
c. 25w
D. ow


Find \( \boldsymbol{A}, \) if \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{2} \\ \mathbf{0} & \mathbf{9}\end{array}\right] \) and \( \boldsymbol{A}- \)
\( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & -\mathbf{6} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \)


The frequency of radio waves corresponding to a wavelength of \( 10 \mathrm{m} \)
is
\( \mathbf{A} \cdot 3 \times 10^{7} H z \)
B \( .3 .3 \times 10^{8} \mathrm{Hz} \)
\( \mathbf{C} \cdot 3 \times 10^{9} H z \)
D. \( 3 \times 10^{-7} \mathrm{Hz} \)


In an isothermal change of an ideal gas, \( \Delta U=0 . \) The change in the heat energy \( \Delta Q \) is equal to
\( \mathbf{A} \cdot 0.5 W \)
в. \( W \)
c. \( 1.5 W \)
D. 2 \( W \)


Find the cube of 23