A body of mass \( 0.5 k g \) requires \( 3000 J \) of heat in order to raise its temperature
from \( 308 K \) to \( 318 K . \) Calculate its
specific heat.


Two bars of masses \( m_{1} \) and \( m_{2} \)
connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between the bars
and the surface is equal to \( k \). The minimum constant force that has to be
applied in the horizontal direction to the
bar of mass \( m_{1} \) in order to shift the other bar is \( F_{\min }=k g\left(m_{1}+\frac{m_{2}}{x}\right) \)
Find \( x \)


Iron filings and sulphur were mixed together and divided into two parts, \( A \)
and
B. Part A was heated strongly while Part B was not heated. Dilute
hydrochloric acid was added to both the
Parts and evolution of gas was seen in both the cases. How will you identify the gases evolved?


\( \boldsymbol{E}_{\text {cell}} \) is:
A . 1.27v
B. 3.37V
c. \( 4.72 v \)
D. None of these


Two blocks \( P \) and \( Q \) of masses \( 0.3 k g \) and 0.4 kg respectively are stuck to each other by some weak glue as shown in the figure. They hang together at the end of a spring with a spring constant \( \boldsymbol{K}=\mathbf{2 0 0} \boldsymbol{N} \boldsymbol{m}^{-1} . \) If the block \( \boldsymbol{Q} \)
suddenly falls free due to the failure of glue, find
(i) period of SHM of block \( \boldsymbol{P} \)
(ii) The amplitude of its SHM
(iii) The total energy of oscillation of the
system.


Eight identical spherical mercury drops charged to a potential of 20 v each are coalesced into a single spherical drop:
A. The internal Energy of the system remains the same
B. The new potential of the drop is 80 v
c. Internal Energy of he system decreases
D. The potential remains the same i.e. \( 20 \mathrm{v} \)


Prevent the rusting of Iron by:
A . oiling
B. greasing
c. painting
D. all of these


Starting at the origin, a beam of light hits a mirror(in the form of a line) at the
point \( A(4,8) \) and reflected line passes
through the point \( B(8,12) . \) Compute the slope of the mirror.


Explain with suitable examples importance of anatomical evolution


What is the hydrogen ion concentration
of \( 0.1 N C H_{3} C O O H \) solution. The
ionisation constant of \( C H_{3} C O O H \) is
\( 1.8 \times 10^{-5} . \) What is the pH of the
solution?


\( \mathbf{5 0} \) mL of \( \mathbf{0 . 1} \boldsymbol{M} \) solution of a salt
reacted with 25 mL of \( 0.1 ~ M \) solution of
sodium sulphite. The half reaction for the oxidation of sulphite ion is,
\( \boldsymbol{S O}_{3}^{2-}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(\ell) \longrightarrow \boldsymbol{S O}_{4}^{2-}(\boldsymbol{a q})+ \)
\( \mathbf{2} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{2} \boldsymbol{e}^{-} \)
If the oxidation number of metal in the
salt was \( 3, \) what would be the new
oxidation number of metal?
A. 0
B. 1
c. 2
D. 4


A material medium is not necessary for the propagation of sound. State true or false.
A. True
B. False


Peyer's patches produce
A. Enterokinase
B. Lymphocyte
c. мucous
D. Trypsin


While preparing oxygen from
potassium permanganate a plug of cotton must be put in a hard glass test
tube
A . True
B. False


A particle is projected upward from the surface of earth (radius \( =\boldsymbol{R} \) ) with a
speed equal to the orbital speed of a satellite near the earth's surface. The height to which it would rise is
A \( \cdot \sqrt{2} R \)
в. \( \frac{R}{\sqrt{2}} \)
\( c . R \)
D. 2 \( R \)


n-Butane and isobutane are:
A. same compound
B. allotropes
\( \mathrm{C} \). isomers
D. structural isomers


What happens to the image distance in the eye when we increase the distance
of an object from the eye?


In the esterification of alcohol:
A. \( \mathrm{H} \) from alcohol and \( \mathrm{OH} \) from acid is removed as water.
B. OH from alcohol and \( \mathrm{H} \) from acid is removed as water.
C. His replaced by chlorine.
D. His replaced by sodium metal.


What is the valency of carbon in \( \boldsymbol{C H}_{4} \) ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D. 6


Earthquake is also known as:
A. nektons
B. blusters
c. temblors
D. flickers


Mark the correct alternative of the
following. The maximum value of \( x^{1 / x}, x>0 \) is?
A \( \cdot e^{1 /} \)
\( ^{\mathrm{B}}\left(\frac{1}{e}\right) \)
c. 1
D. None of these


Match the terms to these definitions
Abductor, adductor, false rib, joint, supinator, rigor mortis, motor, endplate, spasm, pronator, muscle twitch is an involuntary and abnormal
muscular contraction.


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


If the amount of nitrogen in air is low,
then the burning capacity of air decreases.
A. True
B. False


The principal value of \( \tan ^{-1}\left(\cot \frac{3 \pi}{4}\right) \)
is :
A. \( -\frac{3 \pi}{4} \)
в. \( \frac{3 \pi}{4} \)
\( c \cdot-\frac{\pi}{4} \)
D.


Concentrated nitric acid is used in a
test to detect adulteration of :
A. cooking oil
B. Milk
c. salt
D. Tea powder


In a mixture of milk and water the
proportion of water by weight was \( 75 \% \). If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)


Fill in the blanks.
The equation \( E=m c^{2} \) is derived by the
scientist


Assertion
When a crystal is added to a supersaturated solution of itself, the
crystal does not appear to change.
Reason
The supersaturated solution is holding more solute than its normal solubility
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


What is the unit for EMF?
A. Ampere
B. Potential
c. watt
D. volt


The frequency of light emitted for the
transition \( n=4 \) to \( n=2 \) of \( H e^{+} \) is
equal to the transition in \( \mathrm{H} \) atom
corresponding to which of the following?
A \( . n=3 \) to \( n=1 \)
в. \( n=2 \) to \( n=1 \)
c. \( n=3 \) to \( n=2 \)
D. \( n=4 \) to \( n=3 \)


An object is placed \( 0.40 \mathrm{m} \) from one of
the two lenses \( L_{1} \) and \( L_{2} \) of focal
lengths \( 0.20 \mathrm{m} \) and \( 0.10 \mathrm{m} \) respectively as depicted in the figure. The separation between the lenses is 0.30
"

The final image formed by this two lens
system is at
A. \( 0.13 \mathrm{m} \) to the rignt of the second lens
B . . 05 rn to the right of the second lens
c. \( 0.13 \mathrm{m} \) to the left of the second lens
D. Infinity


Three identical solid spheres each of
mass \( M \) and radius \( R \) are fixed at three
corners of light equilateral triangular
frame of side length \( 3 R \) such that centre of spheres coincide with corners
of the frame. Find the moment of inertia
of these 3 spheres about an axis passing through any side of frame.
\( ^{\mathbf{A}} \cdot \frac{121 M R^{2}}{5} \)
B. \( \frac{159 M R^{2}}{5} \)
c. \( \frac{121 M R^{2}}{20} \)
D. \( \frac{159 M R^{2}}{20} \)


In the circuit shown, the switch \( S_{1} \) is
closed for long time and at \( t=0 \) s, the
switch \( S_{2} \) is closed and \( S_{1} \) is opened
simultaneously. What is the maximum charge (in the unit of \( \mu C \) ) on the \( 4 \mu F \)
capacitor?
A \( \cdot q_{0}=3 \mu C \)
В \( \cdot q_{0}=6 \mu C \)
c. \( q_{0}=3.4 \mu C \)
D \( \cdot q_{0}=6.8 \mu C \)


Ozone hole is caused by
A. Acetylene
B. Ethylene
C. Chlorofluorocarbons
D. Methane


If the roots of the equation \( x^{2}-2 m x+ \)
\( \boldsymbol{m}^{2}+\mathbf{1}=\mathbf{0} \) are imaginary, then \( \boldsymbol{m} \) lies
in
A. \( (1, \infty) \)
)
B. \( (-\infty, \infty) \)
\( c \cdot(-\infty, 1) \)
D. All of these


Two particles are projected under
gravity with speed \( 4 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \) simultaneously from same point and at
angles \( 53^{\circ} \) and \( 37^{\circ} \) with the horizontal
surface respectively as shown in figure.
Then:
This question has multiple correct options
A. Their relative velocity is along vertical direction.
B. Their relative acceleration is non-zero and it is along vertical direction.
C. They will hit the surface simultaneously
D. Their relative velocity is constant and has magnitude \( 1.4 \mathrm{m} / \mathrm{s} \)


Construct a quadrilateral \( A B C D \) with \( A B=9 c m, B C=6 c m, C D=7 c m \)
\( A C=9 c m \) and \( B D=11 \mathrm{cm} \)


Which gas is an antidote of Lewisite poisonous gas used in World War II):
A. Sarin gas
B. МᅵС
c. BAL
D. Mustard gas


Give the circuit symbol of a diode.


Describe the major events in sexual reproduction


A spherical balloon is being inflated so that its volume increases uniformly at
the rate of \( 40 \mathrm{cm}^{3} / \mathrm{min.} \) At \( r=8 \mathrm{cm}, \) its
surface area increases at the rate
\( \mathbf{A} \cdot 8 \mathrm{cm}^{2} / \mathrm{min} \)
B . \( 10 \mathrm{cm}^{2} / \mathrm{min} \)
c. \( 20 \mathrm{cm}^{2} / \mathrm{min} \)
D. none of these


The flux linked with a circuit is given by
\( \phi=(t-2)^{2} . \) The graph between
induced emf (y-axis) and time axis \( (x- \) axis) is
A. Straight line through origin
B. Straight line with negative intercept
c. straight line with positive intercept
D. Parabola


\( f(x=) \frac{|x|}{x}, 0 \neq f(0)=1 f(x) \) at \( x=0 \)
is
A . Left continuous
B. Right continuous
c. Not determined
D. continuous


Formation of \( N a C l \) is accelerated by
which of the following?
A. Individual octet attainment
B. High lattice enthalpy
c. stabilised solid crystal \( (F C C) \)
D. All of the above


Bond energies of H - H and Cl - Cl are \( 430 k J m o l^{-1} \) and \( 242 k J m o l^{-1} \)
respectively. \( \Delta \boldsymbol{H}_{f} \) for HCl is
\( 91 k J m o l^{-1} . \) What will be the bond
energy of H - Cl bond (per mole value)?
A . 672 kJ
B. 182 kJ
c. 245 kJ
D. 88 kJ


Find \( g \circ f \) and \( f \circ g \) when \( f: R \rightarrow R \)
and \( g: R \rightarrow R \) are defined by \( f(x)=x \)
and \( g(x)=|x| \)


If \( x^{2}+\frac{1}{x^{2}}=A \) and \( x-\frac{1}{x}=B \) then least value of \( \frac{\boldsymbol{A}}{\boldsymbol{B}} \) is
A .2
B. \( \sqrt{2} \)
\( c \cdot-\sqrt{2} \)
D. \( 2 \sqrt{2} \)


is properly named:
\( A \cdot(2 S, 3 R, 4 S)-2,4- \) Dichloro-3-methylhexane
B. (3R,4S,5R)- 3,5-Dichloro-4-methylhexane
C. \( (2 S, 3 S, 4 S)-2,4 \) -Dichloro-3-methylhexane
D. \( (2 S, 3 S, 4 R)-2,4 \) -Dichloro-3-methylhexane


If \( \boldsymbol{A}=\left(\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right) \)
If \( A^{2}-4 A=p I \) where \( I \) and \( O \) are the
unit matrix and the null matrix of order
3 respectively. Find the value of \( p \)
A. \( p=2 \)
в. \( p=3 \)
\( \mathbf{c} \cdot p=4 \)
D. \( p=5 \)


Which class of drugs is used in sleeping pills?
A. Antipyretics
B. Tranquilizers
c. Anaesthetic
D. Antimicrobial


Figure shows a vertical force \( \boldsymbol{F} \) that is
applied tangentially to a uniform
cylinder of weight \( W \). The coefficient of
static friction between the cylinder and
all surfaces is \( 0.5 . \) Find the maximum
force in terms of \( W \) that can be applied
without causing the cylinder to rotate.


If a compound statement is made up of
three simple statements, then the
number of rows in the truth table is


On dissolving moderate amount of
sodium metal in liquid \( N H_{3} \) at low temperature, which one of the following
does not occur?
A. Blue coloured solution is obtained
B. \( N a^{+} \) ions are formed in the solution
C . Liquid \( N H_{3} \) becomes good conductor of electricity
D. Liquid ammonia remains diamagnetic


The pair with minimum difference in electronegativity is :-
A . F,C
в. \( \mathrm{c}, \mathrm{H} \)
\( c . \) Р,
D. Na,Cs


\( \lambda_{a} \) and \( \lambda_{m} \) are the wavelengths of a
beam of light in air and medium respectively. If \( \theta \) is the polarising angle, the correct relation between \( \lambda_{a}, \lambda_{m} \) and
\( \boldsymbol{\theta} \) is:
A \( \cdot \lambda_{a}=\lambda_{m} \tan ^{2} \theta \)
B \( \cdot \lambda_{m}=\lambda_{a} \tan ^{2} \theta \)
\( \mathbf{c} \cdot \lambda_{a}=\lambda_{m} \cot \theta \)
D. \( \lambda_{m}=\lambda_{a} \cot \theta \)


The area of the quadrilateral formed by the tangents at the endpoints of the latus recta to the ellipse, \( \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 \)
is
A \( \cdot \frac{27}{4} \)
B. 18
c. \( \frac{27}{2} \)
D. 27


Two small spheres each carrying a charge \( q \) are placed \( r \) metre apart. If one of the spheres is taken around the other
one in a circular path, the work done will
be equal to :
A. force between them \( x \) r
B. force between them \( \times 2 \pi r \)
c. force between them / r \( \pi \) r
D. zero


A \( 15 \mathrm{m} \) long ladder reached a window 12
\( \mathrm{m} \) high from the ground. On placing it against a wall at a distance \( x \) m. Find \( x \)


Which of the following is the right match with the components of transport system of human beings with their functions?
\( \begin{array}{lll} & \text { Components } & \text { Functions } \\ 1 & \text { Heart } & O_{2} \text { transport } \\ 2 & \text { Fibrinogen } & \text { Blood clotting } \\ 3 & \text { RBC } & \text { Forms fibrin } \\ 4 & \text { Platelets } & \text { Pumps blood }\end{array} \)
\( A \)
B. 2
\( c \)
D.


Darwin was influenced by Malthus who in \( 1798, \) wrote that human population increases
Whereas their resources
increases
A. at O percent rate, at O percent rate
B. exponentially, arithmetically
c. exponentially, geometrically
D. arithmetically, geometrically


There are three stations \( A, B \) and \( C \)
five routes for going from station \( \boldsymbol{A} \) to station \( B \) and four routes for going from \( \operatorname{station} B \) to station \( C \)
Find the number of different ways through which a person can go from station \( A \) to \( C \) via \( B \)
A . 10
B. 15
c. 20
D. 25


An aqueous solution of a weak monobasic acid containing 0.1 g in 21.7 g of water freezes at \( 272.813 \mathrm{K} \). If the value
of \( K_{f} \) for water is \( 1.86 \mathrm{K} / \mathrm{m}, \) what is the molecular mass of the monobasic acid.


In series \( L R \) circuit \( X_{L}=R \) and power
factor of the circuit is \( P_{1} \) When
capacitor with capacitance \( C \) such that
\( X_{L}=X_{C} \) is put in series, the power
factor becomes \( P_{2} \) Calculate \( P_{1} / P_{2} \)


A particle of mass 'm' is projected with
a velocity 'u' at an angle ' \( \boldsymbol{\theta}^{\prime} \) with the
horizontal. Work done by gravity during its descent from its highest point to a point which is at half the maximum height is?
A. none of these
B. \( \frac{m u^{2} \sin ^{2} \theta}{4} \)
c. \( \frac{1}{2} m u^{2} \sin ^{2} \theta \)
D \( \cdot \frac{1}{2} m u^{2} \cos ^{2} \theta \)


In which case first has higher solubility than second?
(I) Phenol, Benzene
(II) Nitrobenzene, Phenol
(III) o-Hydroxybenzaldehyde, p-Hydroxy benzaldehyde
\( (\mathrm{IV}) \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}, \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{3} \)
(V) o-Nitrophenol, p-Nitrophenol
A. Only I
B. ॥I,
\( c \cdot 1,1 v \)
D. II, IV


if \( \tan 25^{\circ}=x, \) then
\( \frac{\tan 155^{\circ}-\tan 115^{\circ}}{1+\tan 155^{\circ} \tan 115^{\circ}} \) is equal to
A \( \cdot \frac{1-x^{2}}{2 x} \)
в. \( \frac{1+x^{2}}{2 x} \)
c. \( \frac{1+x^{2}}{1-x^{2}} \)
D. \( \frac{1-x^{2}}{1+x^{2}} \)


A compound \( X \) on heating gives a colourless gas. The residue is dissolved
in water to obtain \( Y . \) Excess \( C O_{2} \) is
passed through aqueous solution of \( \boldsymbol{Y} \)
when \( Z \) is formed. \( Z \) on gentle heating
gives back \( X . \) The compound \( X \) is:
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( C a C O_{3} \)
с. \( _{\text {NaH } \mathrm{CO}_{3}} \)
D. \( N a_{2} C O_{3} \)


\( \ln \) an A.P., if \( a=3.5, d=0, n=101 \)
then \( a_{n} \) will be
\( \mathbf{A} \cdot \mathbf{0} \)
в. 3.
c. 103.5
D. 104.5


The number of points where the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\mathbf{1}+\left[\cos \frac{\pi x}{2}\right], & \mathbf{1}<\boldsymbol{x} \leq \mathbf{2} \\ \mathbf{1}-\{\boldsymbol{x}\}, & \mathbf{0} \leq \boldsymbol{x}<\mathbf{1} \\ |\boldsymbol{s i n} \boldsymbol{\pi} \boldsymbol{x}|, & -\mathbf{1} \leq \boldsymbol{x}<\mathbf{0}\end{array} \) and \right.
\( f(1)=0 \) is continuous but nondifferentiable is/are (where [.] and \{
represent greatest integer and fractional part functions, respectively)
\( A \cdot O \)
в.
\( c \cdot 2 \)
D. none of these


Describe an experimental setup to show
that sunlight can be split up into
constituent colours and then convert it
back to white light


The yellow in egg yolk is a coloring caused by:
A. An FD \& C dye added to the egg.
B. A carotenoid
c. An anthocyanin
D. Natural means.the fat is just yellow


Solve the following differential equation \( \frac{d y}{d x}=3 x \)


If the points \( \boldsymbol{A}(1,2,-1), B(2,6,2) \) and
\( C(\lambda,-2,-4) \) are collinear, then \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .-2 \)
\( D \)


If (7,3),(6,1),(8,2) and \( (P, 4) \) are the vertices of a parallelogram taken in order then the value of \( P \) is :
\( A \cdot 4 \)
B. 6
c. 7
D.


Convert \( 25^{0} C \) to Kelvin scale:
A. \( 98.15 K \)
B . \( 198.15 K \)
c. \( 298.15 K \)
D. \( 398.15 K \)


Find the number of terms in the series \( 20+19 \frac{1}{3}+18 \frac{2}{3}+\ldots . \) of which the sum
is 300 , explain the double answer.


At equilibrium,in solution a certain
\( \operatorname{acid}, \boldsymbol{H} \boldsymbol{A}, \) yields \( [\boldsymbol{H} \boldsymbol{A}]=\mathbf{0 . 9 4} \boldsymbol{M} \) and
\( \left[A^{-}\right]=0.060 M . \) On the basis of the
above data given
(A) Calculate \( K_{a} \)
(B) Is this acid stronger or weaker than
sulfurous acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{2}}\right) ? \)
(C) Calculate \( K_{b} \)
(D) Calculate pH


n the matrix \( \boldsymbol{A}=\left|\begin{array}{cccc}\mathbf{2} & \mathbf{5} & \mathbf{1 9} & -\mathbf{7} \\ \mathbf{3 5} & -\mathbf{2} & \frac{\mathbf{5}}{\mathbf{2}} & \mathbf{1 2} \\ \sqrt{\mathbf{3}} & -\mathbf{1} & \mathbf{- 5} & \mathbf{1 7}\end{array}\right| \)
write.
Order of matrix.


Oxime is the product of the following:
A. \( >C=O+ \) hydrazine
B. \( >C=O+ \) Phenylhydrazine
\( c \)
\[
-\mathrm{C}-\mathrm{O} \mathrm{H}+\mathrm{SOCl}_{2}
\]
D. >CO + Hydroxylamine


A particle moves along a straight line and its velocity at a distance 'x' from the origin is \( k \sqrt{a^{2}-x^{2}} . \) Then acceleration of the particle is
\( A \cdot k \)
B. \( -k^{2} \)
c. \( k x \)
\( \mathbf{D} \cdot-k^{2} x \)


\( N H_{3} \) is formed in the following steps I. \( C a+2 C \rightarrow C a C_{2} \quad 50 \% \) yield
II. \( \boldsymbol{C a} \boldsymbol{C}_{2}+\boldsymbol{N}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C N}_{2}+\boldsymbol{C} \quad 100 \% \)
yield
III. \( \boldsymbol{C a} \boldsymbol{C N}_{2}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3}+ \)
\( \begin{array}{ll}\boldsymbol{C a C O}_{3} & \text { 50\% yield }\end{array} \)
To obtain 2 moles \( N H_{3} \), calcium
required is:
A. 1 mol
B. 2 mol
c. 3 mol
D. 4 mol


State whether true or false:
Specific heat of a substance during its change of state is zero.
A. True
B. False


Which substance below is resonance
stabilized by delocalized pi electrons?
A. Benzene
B. Hydrochloric acid
c. Hydrogen gas
D. Methane e
E. Potassium bromide


Which is non benzenoid aromatic
compound?
A. benzene
B. pyridine
c. toluene
D. phenol


The stamens are united in two bundles
in flowers of
A . Pea
B. China rose
c. Sesbania
D. Both (1) \& (3)


What is the main difference in human
and frog RBCs?
A. Human RBCs are non-nucleated
B. Hemoglobin is found only in human RBCs
c. Human RBCs have nucleus
D. Human RBCs are muti-nucleated


During inelastic collision between two bodies, which of the following quantities always remain conserved?
A. Total kinetic energy
B. Total mechanical energy
c. Total linear momentum.
D. speed of each body


The value of
\( \left(10^{11}-10^{9}-2 \times 11 \times 10^{8}-3 \times 11^{2} \times\right. \)
is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 11^{10} \)
\( c \cdot 11^{11} \)
D. \( 10^{11} \)


\( L i^{2+} \) ion is in the excited state with
wave function of its electron being
denoted by the symbol \( \Psi_{3,1,0} \). How many radiations of different wavelength will
this \( L i^{2+} \) ion will emit upon de-
excitation?
A. zer
B. 6
\( c \)
\( D \)


The hybridisation of carbon atoms in \( C \)
C single bond of above compound is:
\[
\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}
\]
В \( \cdot s p^{3}-s p^{2} \)
\( \mathbf{c} \cdot s p^{2}-s p^{2} \)
D. \( s p-s p^{2} \)


Find the cube root of 3375 by the method of prime factorization.
A . 15
B . 25
c. 35
D. 55


A uniform rod \( A B \) of mass \( m \) and length
is in equilibrium with the help of two
identical inextensible strings as shown
in figure. Choose the correct option \( (s) \)
This question has multiple correct options
A. After cutting the string (2) motion of centre of mass of the rod is circular
B. After cutting the string (2) motion of centre of mass of the rod is not circular
c. Just after cutting the string (2) the acceleration of point A along the string (1) is zero.
D. Just after cutting the string (2) the acceleration of point A perpendicular to the string (1) is not zero.


\( \int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} \cdot d x \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
B. \( \frac{3}{2} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
C \( \cdot \frac{2}{3} \cos ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
D. none of these


To increase the length of brass rod by \( 2 \% \) its temperature should increase by:
\( \left(\propto=0.00002 K^{-1}\right) \)
A . 800
в. 900
\( c .1000 \)
D. 1100


A body is projected with an initial
velocity \( 20 \mathrm{m} / \mathrm{s} \) at \( 60^{\circ} \) to the horizontal. Its initial velocity vector is
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
B. \( 10 \sqrt{3 i}+10 j \)
c. \( 10 i+10 \sqrt{3} j \)
D. \( 5 i+5 \sqrt{3} j \)


The decrease in percentage error:
A. increases the accuracy
B. does not effect the accuracy
C. decreases the accuracy
D. both \( A \) and \( C \)


Find out the angle \( \theta \) made by string
from vertical in equilibrium position
A \( \cdot \tan ^{-1}\left(\frac{m g}{q E}\right) \)
B. \( \sin ^{-1}\left(\frac{m g}{q E}\right) \)
c. \( \cos ^{-1}\left(\frac{m g}{q E}\right) \)
\( \tan ^{-1}\left(\frac{q E}{m g}\right) \)


Which of the following are examples of
scattering of light?
A. Blue color of the sky
B. Reddening of the sun at sunrise and sunset
C. Color of water in deep seas and oceans
D. All of the above


\( N_{2} O_{5} \) is said to be ionic in solid state.
Write the cation and anion in it and the
hybridised state of N atom in cation.
A.
B. sp
\( c \cdot s p^{2} \)
\( D \cdot s p^{3} \)


A mass of \( 200 g m \) has initial velocity \( V_{i}=2 \hat{i}+3 \hat{j} \) and final velocity \( -2 \hat{i}-3 \hat{j} \)
Find magnitude of change in
momentum.
A \( \cdot|\Delta \vec{p}|=3.84 \)
В . \( |\Delta \vec{p}|=3.04 \)
c. \( |\Delta \vec{p}|=1.44 \)
D . \( |\Delta \vec{p}|=2.04 \)


Which of the following is not a draw back
of Werner's theory?
A. does not explain the valency of metal ions in the complex
B. does not give any explanation for the colour of complex compounds
C. does not explain the magnetic behaviour of complex compounds
D. does not correlate electronic configuration of the metal with the formation of complex


Find the area of the region bounded by the curve \( y^{2}=4 x \) and the line \( x=3 \)
\begin{tabular}{l}
A. \( 4 \sqrt{3} \) \\
\hline
\end{tabular}
B. \( 8 \sqrt{3} \)
\( c \cdot 6 \)
D. \( 2 \sqrt{3} \)


The truth value of the statement, "We
celebrate our Independence day on 15 August", is
A . T
B. F
C. neither T nor F
D. Cannot be determined


A salt is made by adding an excess of an insoluble metal oxide to an acid. How
is the excess metal oxide removed from
the mixture?
A. chromatography
B. crystallisation
c. distillation
D. filtration


If \( 25 W \) of power are applied to the primary of an ideal transformer with a
turns ratio of \( 10, \) the power delivered to the secondary load is
A \( .25 W \)
B. \( 0 W \)
c. \( 250 W \)
D. \( 2.5 W \)


A point charge \( q \) is located at the centre of a thin ring of radius \( R \) with uniformly
distributed charge -q. Find the magnitude of the electric field strength vector at the point lying on the axis of the ring at a distance \( x \) from its centre
if \( x>>R \)


A radioactive sample contains two nucleoids \( A \) and \( B \) having decay constant \( \lambda h r^{-1} \) and \( 2 \lambda h r^{-1} . \) Initially
\( 25 \% \) of the decay comes from \( A \). The number of hours it will take before \( 75 \% \)
of the total decay comes from \( A \) is \( n \)
\( (\operatorname{take} \lambda=\ln 3) . \) Find \( n \)


A trader purchases \( 70 \mathrm{kg} \) of tea at Rs.15.00 per kg and 30kg of tea at
Rs.18.00 per kg and mixes the two. If
the packing charges are 5 percent and he would like to make a profit of 20 percent, he should sell the tea at (approximately):
A . \( R s .17 .50 \) per kg
B. Rs.18.20 per kg
c. \( R s .20 \) per kg
D. Rs.19.50 per kg


A body of mass \( 3 k g \) falls from the multi-
storeyed building \( 100 m \) high and
buries itself \( 2 m \) deep in the sand. The
time of penetration is
A. \( 9 s e c \)
B. 0.9 sec
\( c .0 .09 s e c \)
D. 10 sec


Rewrite and complete the following sentences by inserting the correct word
in the space indicated.
is the scientific name of garden pea, which mendel used for his
experiments.


The bond angle and hybridization in
ether \( \left(\boldsymbol{C H}_{3} \boldsymbol{O C H}_{3}\right) \) is:
A . \( 106^{\circ} 51, s p^{3} \)
B . \( 104^{\circ} 31, s p^{3} \)
\( \mathbf{C} \cdot 110^{\circ}, s p^{3} \)
D. None of these


Arrange the following in increasing
order of solubility in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\[
M g F_{2}, C a F_{2}, A g F
\]
A. \( C a F_{2}<M g F_{2}<A g F \)
в. \( M g F_{2}<C a F_{2}<A g F \)
c. \( C a F_{2}<A g F_{2}<M g F \)
D. None of these


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \boldsymbol{2} \\ \boldsymbol{2} & \boldsymbol{\alpha}\end{array}\right] \) and \( |\boldsymbol{A}|^{3}=125 \) then the
value of \( \boldsymbol{\alpha} \) is
A. ±1
B. ±2
\( c .\pm 3 \)
D. ±5


Pyrimidines of RNA are
A. Adenine and thymine
B. Uracil and thymine
C . Cytosine and uracil
D. Cytosine and thymine


In YDSE The intensity of central bright fringe is \( 8 m W / m^{2} . \) What will be the intensity at \( \lambda / 6 \) path difference?
\( \mathbf{A} \cdot 8 m W / m^{2} \)
в. \( 6 m W / m^{2} \)
\( \mathbf{c} \cdot 4 m W / m^{2} \)
\( \mathbf{D} \cdot 2 m W / m^{2} \)


\( \int_{0}^{1}\left(3 x^{2}+5 x+k\right) d x=0 \) find \( k \)


The equation \( 2 x^{2}+3 y^{2}-8 x-18 y+ \)
\( \mathbf{3 5}=\boldsymbol{\lambda} \) represents?
A . A circle for all \( \lambda \)
B. An ellipse if \( \lambda<0 \)
c. The empty set if \( \lambda>0 \)
D. A-point if \( \lambda=0 \)


A \( \alpha \) - particle is accelerated through a potential difference of \( V \) volts from rest. The de-Broglie wavelength associated with it is (in angstrom):
A \( \cdot \sqrt{\frac{150}{V}} \)
в. \( \frac{0.286}{\sqrt{V}} \)
c. \( \frac{0.101}{\sqrt{V}} \)
D. \( \frac{0.983}{\sqrt{V}} \)


A body is kept in cooler surroundings. When the temperature of the body is \( 70^{0} C, \) it cools at the rate of \( 3^{0} C \) per
minute and at \( 50^{0} C \), it cools at the rate
of \( 1.5^{0} C \) per minute. Find the
temperature of the body when it cools at
the rate of \( 1^{0} C \) per minute.


Five persons \( A, B, C, D \) and E occupy seats in a row such that \( A \) and \( B \) sit next
to each other. In how many possible ways can these five people sit?
A .24
B. 48
c. 72
D. 56


The contrapositive statement of
statement "If \( x \) is prime number, then \( x \)
is odd" is
A. If \( x \) is not is prime number, then \( x \) is not odd
B. If \( x \) is not odd, then \( x \) is not a prime number
c. If \( x \) is a prime number, then \( x \) is not odd
D. If \( x \) is not a prime number, then \( x \) is odd


Which is most soluble in water at \( 293 K \)
\( ? \)
A. Helium
B. Neon
c. xenon
D. Krypton


The effective capacity of the network
between terminals A and B is-
\( A \cdot 6 \mu F \)
B. \( 20 \mu F \)
\( \mathbf{c} \cdot 3 \mu F \)
D. \( 10 \mu F \)


The actinoids exhibit more number of
oxidation states in general than
lanthanoids because:
A. the \( 5 f \) orbitals are more buried than the 4 f orbitals
B. there is a similarity between \( 4 f \) and \( 5 f \) orbitals in their angular part of the wave function
C. the actinoids are more reactive than the lanthanoids
D. the \( 5 f \) orbitals extend further from the nucleus than
the \( 4 f \) orbitals


Wilkins X-ray diffraction showed the
diameter of the DNA helix is
B. 20 \( \dot{A} \)
\( c .30 \dot{A} \)
D. 40 a


The process which is responsible for the formation of Delta at a place where
rivers meet the sea is?
A. Colloid formation
B. Peptization
c. Emulsification
D. coagulation


When reaction is at standard state at
equilibrium, then:
A \( \cdot \Delta H^{\circ}=0 \)
B . \( \Delta S^{\circ}=0 \)
c. equilibrium constant \( K=0 \)
D. equilibrium constant \( K=1 \)


If your friend is struck by lightning, how
will you help him?


In the first order reaction \( 75 \% \) of the
reactant disappeared in 1.388 hrs Calculate the rate constant of the
reaction:
A \( \cdot 1 s^{-1} \)
- \( ^{-1} \)
B. \( 2.8 \times 10^{-4} s^{-1} \)
c. \( 17.2 \times 10^{-3} s^{-1} \)
D. \( 1.8 \times 10^{-3} s^{-1} \)


Let \( n>2 \) be an integer and \( f: P \rightarrow R \) a
function defined on the set of points in the plane, with the property that for any
regular n-gon \( \boldsymbol{A}_{\mathbf{1}} \boldsymbol{A}_{\mathbf{2}} \ldots \boldsymbol{A}_{\boldsymbol{n}}, \boldsymbol{f}\left(\boldsymbol{A}_{\mathbf{1}}\right)+ \)
\( \boldsymbol{f}\left(\boldsymbol{A}_{2}\right)+\ldots+\boldsymbol{F}\left(\boldsymbol{A}_{n}\right)=\mathbf{0} . \) Prove that
is the zero function.
A. fis zero function.
B. fis not a zero function
c. f is indefinite function.
D. fis not a function


Which of the following statements is
true for velocity \( (v)- \) time
(t) graph?
A. The curve can be a circle.
B. The area under the curve and above the time axis
between any two instants gives the average acceleration.
C. The slope at any instant gives the rate of change of acceleration at that instant.
D. The area under the curve along the time axis gives the displacement.


The equation of a sound wave is \( y= \) \( 0.0015 \sin (62.8 x+316 t), \) the wave
length of this wave is
A. \( 0.2 u n i t \)
B. 0.1 unit
c. 0.3 unit
D. \( 0.5 u n i t \)


Spherical wavefronts, emanating from a
point source, Strike a plane reflecting surface. What will happen to these wave fronts, immediately after reflection?
A. They will remain spherical with the same curvature, both in magnitude and sign
B. They will become plane wave fronts
c. They will remain spherical, with the same curvature, but sign of curvature reversed
D. They will remain spherical, but with different curvature, both in magnitude and sign


resistance \( r \) is connected across a
resistance \( R \) Resistance \( R \) can be
adjusted to any value greater than or equal to zero. A graph is plotted
between the current
\( (i) \) passing
through the resistance and potential
difference \( (V) \) across it. Select the
correct alternative(s).
A. internal resistance of battery is \( 5 \Omega \)
B. emf of the battery is \( 20 V \)
c. maximum current which can be taken from the battery is \( 4 A \)
D. \( V-i \) graph can never be straight line as shown in the
figur


In each of the following find the value of
\( k, \) for which the points are collinear.
(ii) \( (8,1),(k,-4),(2,-5) \)


Choose the correct order of nucleophilic substitution reaction:
\( A \cdot(111)<(11)<(1) \)
B. (II) < (III) < (I)
\( c \cdot(1)<(111)<(11) \)
D. (I) <(II) <(III)


Which statement below is not
acceptable with the concept
of isotopes?
A. Each elements is composed of atoms
B. All atoms of an element are identical
C. The atoms of different elements have different
chemical and physical properties
D. The combining of elements leads to the formation of compounds
E. In a compound, the kinds and numbers of atoms are constant


What is a vitreous state?


The binding energy per nucleon of \( _{8} O^{16} \)
is \( 7.97 M e V \) and that of \( _{8} O^{17} \) is
\( 7.75 M e V . \) The energy required to
remove one neutron from \( _{8} O^{17} \) is
\( M e V \)
A . 3.62
в. 3.52
c. 4.23
D. 7.86


Sum of coefficients in the expeansion of
\( (a+b+c)^{8} \) is
A. 2154
в. 6561
c. 729
D. 1944


Trichogen cells of epidermis of Cockroach produce
A . Exocuticle
B. Endocuticle
c. Bristles
D. Membrane around bristles


Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories:
A. A coezyme
B. A hormone
c. An enzyme
D. An antibiotic


Why are the coils of electric toasters
made of an alloy rather than a pure
metal?


Two charges \( +Q \) and \( -2 Q \) are placed at \( (- \)
a,0) \( \&(+a, 0) \). The locus of points in the plane of the charges where the potential is zero will be :
A. straight line
B. circle
c. parabola
D. ellipse


Tetrahedral complexes are formed:
I : where the central metal has a low
oxidation state
II : where ligands are weak field
III : where the electronic configuration of the central metal is \( , d^{0}, d^{5} \) or \( d^{10} \)
A . I, II, III only correct
B. I, I I only correct
c. ॥, Ill only correct
D. III only correct


Assertion
The acidic strength of oxyacids of
chlorine are \( \boldsymbol{H} \boldsymbol{C l O}<\boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{2}< \)
\( \boldsymbol{H} \boldsymbol{C l O}_{3}<\boldsymbol{H} \boldsymbol{C l O}_{4} \)
Reason
The order of increasing number of resonating structure of their conjugate
base are \( H C l O<H C l O_{2}< \)
\( \boldsymbol{H} \boldsymbol{C l O}_{3}<\boldsymbol{H} \boldsymbol{C l O}_{4} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is NOT the correct explanation for Assertion
C. The Assertion is true, Reason is false
D. The Assertion is false, Reason is true


Two equal masses are attached to the
two ends of a spring of spring constant
k. The masses are pulled out.
Symmetrically to stretch the spring by a
length \( x \) over its natural length. The
work done by the spring on each mass
during the above stretching is
A \( \cdot \frac{1}{2} k x^{2} \)
B. \( -\frac{1}{2} k x^{2} \)
c. \( \frac{1}{4} k x^{2} \)
D \( \cdot-\frac{1}{4} k x^{2} \)


Assertion
Chlorobenzene on treatment with
\( C l_{2} / A l C l_{3} \) gives mainly \( p \)
dichlorobenzene.
Reason
Chlorine activate the ring towards an electrophile at ortho and para positions.
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


Cardiac output is determined by
A . Heart rate
B. Stroke volume
c. Blood flow
D. Both A and B


When is the direction of scattered light independent of the wavelength?
A. Medium of travel is not air.
B. Particles involved in scattering have size smaller than the wavelength of the incident light wave
c. Particles involved in scattering have size larger than the wavelength of the incident light wave
D. Particles scattering the light wave are not neutral in charge


Where is the intensity of the gravitational field of the earth maximum?
A. Centre of earth
B. Equator
c. Poles
D. Same everywhere


During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to 1.139 g \( m l^{-1} \) and sulphuric acid of the density of \( 1.294 \mathrm{g} \)
\( m l^{-1} \) is \( 39 \% \) by mass and that of the
density of 1.139 g \( m l^{-1} \) is \( 20 \% \) by mass. The battery holds 3.5 litre of acid and the volume practically remained constant during the discharge. Calculate the no. of ampere hour for which the battery must have been used. The charging and discharging reactions
are:
\( \boldsymbol{P b}+\boldsymbol{S O}_{4}^{2-} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2 e} \Longrightarrow \)
charging
\( \boldsymbol{P b O}_{2}+\boldsymbol{4} \boldsymbol{H}^{+}+\boldsymbol{S O}_{4}^{2-}+\boldsymbol{2} e \rightarrow \)
\( P b S O_{4}+2 H_{2} O \Longrightarrow \) discharging
A . \( 2.5 A \)
в. \( 1.7 A \)
\( c .3 .2 A \)
D. None of these


How much AgBr could dissolve in 1.0L of
\( 0.40 \mathrm{M} N H_{3} ? \) Assume that \( A g\left(N H_{3}\right)_{2}^{-} \)
is the only complex formed.
\( \left[\boldsymbol{K}_{f}\left(\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}\right)=\mathbf{1} \times \mathbf{1 0}^{8}\right. \)
\( \left.\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{B r})=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{1 3}}\right] \)
\( [\sqrt{\mathbf{5 0}}=\mathbf{7}] \)


Vestigial pelvic girdle and bones of hind limbs are the characteristic of
A. Whales
B. Otters
c. Rodents
D. sharks


How many Balmer spectral lines will be obtained when the excited electrons
return from 8th shell to 2nd shell?
A . 21
B. 4
c. 10
D. 15


When \( 6 \times 10^{22} \) electrons are used in the
electrolysis of a metalic salt, \( 1.9 \mathrm{gm} \) of the metal is deposited at the cathode The atomic weight of that metal Is 57 So oxidation state of the metal in the
salt is:
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+1 \)
\( D \cdot+4 \)


Which salt can be used to identify coloured cation?
A. Borax
B. Microcosmic salt
c. Both (a) and (b)
D. None of these


State whether given statement is True or False.

Cashless transaction can be carried out
with ATM ?
A. True
B. False


The binding energy per nucleon of \( _{20}^{40} C a \)
is
\( \left(_{20}^{40} C a=39.962589 \mathrm{amu}, m_{p}=1.007825\right. \)
amu; \( m_{n}=1.008665 a m u \) and \( 1 a m u \) is equivalent to \( 931.5 M e V) \)
\( \mathbf{A} .6 .55 M e V \)
в. \( 7.55 \mathrm{MeV} \)
c. \( 8.55 \mathrm{MeV} \)
D. \( 9.55 \mathrm{MeV} \)


\( A . \) another positively charged particle of
mass \( m \) and charge \( +q \) is projected
from a point \( B \) with velocity \( u \) as shown
in figure. The point \( B \) is at the lage distance from \( A \) and at distance \( d \) from
the line \( A C . \) The initial velocity is
parallel to the line \( A C . \) The point \( C \) is at
very large distance from \( A \). The minimum distance (in meter) of \( +\boldsymbol{q} \)
from \( +Q \) during the motion is \( d(1+ \) \( \sqrt{A}) . \) Find the value of \( A \)
(Take \( \boldsymbol{Q} \boldsymbol{q}=\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{m} \boldsymbol{u}^{2} \boldsymbol{d} \) and \( \boldsymbol{d}=(\sqrt{\mathbf{2}}- \)
1) meter)
A . 3
B. 2
\( c \cdot 4 \)
\( D \)


The temperature of 20 litre of nitrogen was increased from \( 100 \mathrm{K} \) to \( 300 \mathrm{K} \) at a
constant pressure. The change in volume will be:
A. 80 litres
B. 60 litres
c. 40 litres
D. 20 litres


Atomicity of phosphorus is:
A. one
B. two
c. three
D. four


Write the number of decimal place in
\( \mathbf{7 . 0 0 3 4 9} \)


Avogadro's law finds an application in the determination of:
A. Atomicity of gas
B. Molecular weights of gases
c. Molecular formula of certain gaseous compounds
D. All the above


If shape of anion is tetrahedral, then the shape of cation formed is :
A. Linear
B. Bent
c. Pentagonal bipyramidal
D. Trigonal planar


A substance contains \( 35.0 g \) nitrogen,
\( 5.05 g \) hydrogen, and \( 60.0 g \) oxygen. How
many grams of oxygen are there in a
\( 200 g \) sample of the substance?
A. \( 10.1 g \)
B. \( 60.0 g \)
c. \( 70.0 g \)
D. 1209
E . \( 140 g \)


Then 'Q' in the reaction is?


An object of mass, \( m \) is moving with a constant velocity v. How much work
should be done on the object in order to bring the object to rest?
A \( \cdot-\frac{1}{2} m v^{2} \)
B. \( \frac{1}{2} m v^{2} \)
c. \( -m v^{2} \)
D. \( -\frac{1}{2} m v \)


Assertion
The number of roots of the equation \( \sin \left(2^{x}\right) \cos \left(2^{x}\right)=\frac{1}{4}\left(2^{x}+2^{-x}\right) \) is 2
Reason
\( A M \geq G M \) for any two positive
numbers.
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


Four identical mirrors are made to
stand vertically to form a square arrangement as shown in a top view. A ray starts from the midpoint M of mirror Ad and after two reflections reaches
cornor D. Then, angle \( \theta \) must be
A \( \cdot \tan ^{-1}(0.75) \)
B \( \cdot \cot ^{-1}(0.75) \)
c. \( \sin ^{-1}(0.75) \)
D \cdot \( \cos ^{-1}(0.75) \)


A ball is thrown vertically upwards. It
has a speed of \( 10 \mathrm{m} s^{-1} \) when it has
reached one half of its maximum
height. How high does the ball rise?
(Take \( \left.g=10 \mathrm{m} s^{-2}\right) \)
A. \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. 20 \( m \)


The zeros of the polynomial \( n^{3}+9 n^{2}+ \)
\( 23 n+15 \) are \( a-d, a \) and \( a+d . \) What
is the value of 'a'?
A . 4
B. -3
\( c .6 \)
D. 3


The soil layer is made up of :
A. R Horizon
B. A Horizon
c. B Horizon
D. C Horizon


If the flux of the electric field through a closed surface is zero, then :
A. The electric field must be zero everywhere on the surface
B. The total charge inside the surface must be zero
c. The electric field must be uniform throughout the closed surface
D. The charge outside the surface must be zero


What is artificial method of vegetative propagation? Describe :
(i) Cutting,
(ii) Budding.


Barium chloride reacts with sodium
sulphate to form Barium sulphate and
sodium chloride. Then, according to the
law of conservation of mass
A. The total mass of reactants, barium chloride and sodium sulphate taken is greater than the total mass of products, barium sulphate, sodium chloride formed
B. The total mass of reactants, barium chloride and sodium sulphate taken is less than the total mass of products, barium sulphate, sodium chloride formed
C. The total mass of the reactants is equal to the total mass of products
D. None of the above


\( N a^{+}-K^{+} \) pump is found in membranes of many cells, like nerve
cells. It works against electrochemical gradient and involve an integral protein ATPase. For each molecule of ATP used
A. 3 ions of \( N a^{+} \) are pumped out and two \( K^{+} \) are taken in
B. 3 ions of \( N a^{+} \) are taken in and \( 2 K^{+} \) are pumped out
\( \mathrm{c} \cdot 2 \) ions of \( N a^{+} \) are thrown out and \( 3 K^{+} \) are absorbec
D. 3 ions of \( K^{+} \) are absorbed and \( 3 N a^{+} \) are pumped out


An ecosystem is not a self-sufficient
unit
A . True
B. False


If the \( p^{t h} \) term of an \( A P \) is \( q \) and its \( q^{t h} \)
term is \( p, \) then its \( (p+q)^{t h} \) term is
\( A \cdot p \)
B. \( q \)
c. \( (p+q) \)
D.


Insert 4 arithmetic means between 3
and 23


In modern days incoming frequency of
radio receiver is superposed with a locally produced frequency produce intermediate frequency which is always constant. This makes tuning of the receiver very simple. This is used in
superheterodyne oscillators.


Acids have much higher boiling points than isomeric esters because:
A. Acids form dimers by H-Bonding
B. Acids are volatile in steam
c. Ester are non-volatile
D. Acids can ionise to give protons in aqueous solution


A: Fresnel diffraction occurs when the
source of light or the screen or both are at a finite distance from the diffracting
device
B: Diffracted light can be used to estimate the helical structure of nuclic
acids
A. A is true, B is false
B. Both A and B are true
c. A is false, B is true
D. Both A and B are false


State True or False. If false, give reasons
for that
If two triangles are congruent, their corresponding angle are equal
A. True
B. False


Which of the following combination show ductility?
A. Aluminium, lead
B. Copper, platinum
c. Tin, brass
D. All of these


A spring-block system is resting on a frictionless floor as shown in the figure.
The spring constant is \( 2.0 \mathrm{Nm}^{-1} \) and the mass of the block is 2.0 kg. lgnore the mass of the spring. Initially, the spring is in an unstretched condition.
Another block of mass \( 1.0 \mathrm{kg} \) moving with a speed of \( 2.0 ~ m s^{-1} \) collides elastically with the first block. The collision is such that the \( 2.0 \mathrm{kg} \) block
does not hit the wall. The distance, in
metres. between the two blocks when
the spring returns to its unstretched position for the first time after the collision is

Round off your answer to nearest integer.


The mean of 10 observations is \( 16.3 . \) If
one observation is registered as 32 instead of 23 , then new mean is
A . 14.8
B. 15.4
\( c \cdot 16 . \)
D. 16.6


What is the basis for the formation of
winds due to heating of different areas
on Earth?
A. The air in cold temperature regions gets cooled, expands and becomes more dense and rises up. It's place is taken by heavier air from adjacent regions.
B. The air in cold temperature regions gets cooled up, expands and becomes less dense and rises up. It's place is taken by heavier air from adjacent regions.
C. The air in high temperature regions gets heated up, expands and becomes less dense and rises up. It's place is taken by heavier air from adjacent regions.
D. The air in high temperature regions gets heated up, contracts and becomes more dense and rises up. It's place is taken by heavier air from adjacent regions.


Prove that one and only one out of
\( \boldsymbol{n}, \boldsymbol{n}+2 \) or \( \boldsymbol{n}+\boldsymbol{4} \) is divisible by \( \boldsymbol{3} ; \) where
\( n \) is any positive integer.


Identify the stage when homologous chromosomes separate but sister chromatids remain associated
A. Metaphase!
B. Anaphase
c. Metaphase II
D. Anaphase II


Find the angle between the pair of lines
given by \( \vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k}) \)
and \( \vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k}) \)


Among statements (a)-(d), the correct
ones are:
(a) Decomposition of hydrogen peroxide gives dioxygen.
(b) Like hydrogen peroxide, compounds,
\( \operatorname{such} \) as \( K C l O_{3}, P b\left(N O_{3}\right)_{2} \) and
\( N a N O_{3} \) when heated liberate dioxygen.
(c) 2-Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide.
(d) Hydrogen peroxide is used for the manufacture of sodium perborate.
\( A \cdot(a),(b) \) and \( (c) \) only
B. (a) and (c) only
\( c \cdot(a),(b),(c) \) and \( (d) \)
D. (a), (c) and (d) only


Following are the weights (in \( \mathrm{kg} \) ) of 10 new born babies in a hospital on a particular day: 3.4,3.6,4.2,4.5,3.9,4.1
\( 3.8,4.5,4.4,3.6 . \) Find the mean \( \bar{X} . \) (in
kg)


The correct labels from A to E are
A. \( A \) - Spathe bract, \( B \) - Female flowers, \( C \) - Male flowers, Neuter flowers, E - Appendage
B. A- Appendage, B - Female flowers, C - Male flowers, D Neuter flowers, E -Spathe bract
C. A - Appendage, B - Male flowers, C - Female flowers, D Neuter flowers, E -Spathe bract
D. A - Appendage, B - Male flowers, C - Neuter flowers, D Female flowers, E - Spathe bract


Which of the following orbit is impossible for an electron according to Bohr's theory?
A \( \cdot m v r=\frac{n h}{2 \pi} \)
в. \( _{m v r}=\frac{h}{\pi} \)
c. \( _{m v r}=\frac{2 h}{\pi} \)
D. \( m v r=\frac{4 h}{2 \pi} \)


What will be the unit digit of \( 137959^{3} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .6 \)
D.


Differentiate \( \log \sqrt{\frac{1+\cos ^{2} x}{\left(1-e^{2 x}\right)}} \) w.r.t. \( x \)


Two flat circular coils are made of two
identical wires each of length \( 20 \mathrm{cm} \) one coil has 4 turns while the second
has \( 2 . \) If the same current flows through the two, then find ratio of the field at
their centre


In the nucleus of helium, if \( F_{1} \) is the net
force between two protons, \( F_{2} \) is the net
force between two neutrons and \( F_{3} \) is the
net force between a proton and a neutron.
Then
A \( \cdot F_{1}=F_{2}=F_{3} \)
в. \( F_{1}>F_{2}>F_{3} \)
c. \( F_{2}>F_{3}>F_{1} \)
D. \( F_{2}=F_{3}>F_{1} \)


After deducting \( 60 \% \) from a certain number and then deducting \( 15 \% \) from the remainder. 1428 is left. What was
the initial number?
A . 4200
в. 3962
c. 4150
D. 4300


Boyle's law is applicable for an:
A. Adiabatic process
B. Isothermal process
c. Isobaric process
D. Isochoric process


Enthalpy of polymerisation of ethylene, as represented by the reaction, \( \boldsymbol{n} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \rightarrow\left(-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\right)_{n} \)
is -100kJ per mole of ethylene.Given bond enthalpy of \( C=C \) bond is \( 600 \mathrm{kJ} \)
\( m o l^{-1}, \) enthalpy of \( C-C \) bond (in
kJ mol) will be :
This question has multiple correct options
A . 2940 kcal mol-1
в. 350 kJ mol \( ^{-1} \)
c. 700 k \( \operatorname{mol}^{-1} \)
D. 1470 kcal mol-


Calculate the ratio of collision
frequencies \( \left(Z_{11}\right) \) for the \( \operatorname{gases} A, B, C \)
respectively
A . 1: 2: 4
B . 4: 2: 1
\( c \cdot 1: 4: 16 \)
D. 16: 4: 1


A uniform stick of mass \( \mathrm{M} \) is placed in a frictionless well as shown in the figure.
The stick makes an angle \( \theta \) with the
horizontal. Then the force which the
vertical wall exerts on right end of stick
is :
A \( \cdot \frac{M g}{2 \cot \theta} \)
в. \( \frac{M g}{2 \tan \theta} \)
c. \( \frac{M g}{2 \cos \theta} \)
D.


When a sound is going away from a stationary observer with the velocity equal to that of sound in air, then the
frequency heard by observer is n times the original frequency. The value of n is
A. 0.5
B. 0.25
c. 1.0
D. no sound is heard


The equation of the latus rectum of the hyperbola \( \frac{(x-4)^{2}}{16}-\frac{(y-3)^{2}}{20}=1 \)
are?
\( \mathbf{A} \cdot x=1 \pm 5 \)
B . \( x=4 \pm 6 \)
c. \( y=2 \pm 6 \)
D. \( y=3 \pm 5 \)


In the figure \( \angle A=\angle C E D, C D= \)
\( \mathbf{8} \boldsymbol{c m}, \boldsymbol{C} \boldsymbol{E}=\mathbf{1 0} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{E}= \)
\( 2 c m, A B=9 c m, A D= \)
\( b \) and \( D E=a \). The value of \( a+b \) is
A. \( 13 \mathrm{cm} \)
В. \( 15 \mathrm{cm} \)
\( c \cdot 12 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


Strongest hydrogen bond is present in:
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H O H \)
D. \( \left(C H_{3}\right)_{3} C O H \)


Fill in the blanks with suitable words:
Electromagnetic waves are
waves


From the differential equation to the family of curves \( y=a e^{-2 x}+b e^{3 x} \) by
eliminating arbitrary constants \( a \) and \( b \)


is nature's most powerful display of static electricity.
A. Current electricity
B. Lightning
c. conduction
D. Induction


Figure below shows a portion of an
electric circuit with the currents in
ampreres and their directions. The
magnitude and direction of the current
in the portion PQ is :
\( A \cdot O A \)
B. 3A from P to Q
\( c . \) 4A from Q to
D. 6 A from \( Q \) to


The lewis acidity of \( B F_{3} \) is less than
\( B C l_{3} \) even though fluorine is more electronegative than chlorine. It is due
to:
A. stronger \( 1 p(B)-3 p(C l) \sigma- \) bonding
B. stronger \( 2 p(B)-3 p(C l) \pi- \) bonding
c. stronger \( 2 p(B)-2 p(F) \sigma- \) bonding
D. stronger \( 2 p(B)-2 p(F) \pi- \) bonding


The oxidant which is used as an
antiseptic is.
A \( \cdot P b B r O_{3} \)
в. \( K B r O_{3} \)
\( \mathrm{c} \cdot \mathrm{CrO}_{3} \)
D. \( K N O_{3} \)


The diagonals of a parallelogram
\( P Q R S \) are along the lines \( x+3 y=4 \)
and \( 6 x-2 y=7, \) then \( P Q R S \) must be
\( a \)
A. rectangle
B. square
c. cyclic quadrialtaral
D. rhombus


The general formula of carboxylic acids
is:
A \( . C_{n} H_{n} \) СООН
B. \( C_{n} H_{2 n-1} \)
c. \( C_{n} H_{2 n-2} \) COOH
D. \( C_{n} H_{2 n+1} C O O H \)


Find the number of reflexive relations
from set \( A \) to \( A \), defined as \( A=a, b, c \)


For a first order reaction, show that time
required for \( 99 \% \) completion is twice the
time required for the completion of \( 90 \% \)
of reaction.


The earth is an approximate sphere. If
the interior contained matter which is
not of the same density everywhere, then on the surface of the earth, the
acceleration due to gravity :
A. will be directed towards the centre but not the same everywhere
B. will have the same value everywhere but not directed towards the centre
c. will be same everywhere in magnitude directed towards the centre
D. cannot be zero at at point


The value of \( (625)^{0.16} \times(625)^{0.09} \) is
\( A \cdot 4 \)
B. 5
c. 25
D. 625


Two uniformly charged plates are pictured above, with four evenly spaced points shown along a horizontal lines between the plates.What is the correct
rank of strength of the electric field at the points, greatest first?
A. 1,2,3,4
B. 4, 3, 2,1
C. The electric field strength is the same at all points
D. 1 and 4 tie, 2 and 3 tie
\( \mathrm{E} \cdot 2 \) and 3 tie, 1 and 4 tie


How is chlorine prepared by electrolytic method? Explain its reaction with
(i) Cold and dil. NaOH
(ii) Slaked lime


Assertion
STATEMENT-1: Two particles undergo rectilinear motion along different straight lines. Then the centre of mass
of system of given two particles also always moves along a straight line.
Reason
STATEMENT-2: If direction of net
momentum of a system of particles having nonzero net momentum) is fixed, the centre of mass of given system moves along a straight line.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True


\( \frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}= \)
A. \( -\frac{63}{25}+\frac{16}{25} i \)
в. \( -\frac{63}{25}-\frac{16}{25} i \)
c. \( \frac{63}{25}+\frac{16}{25} i . \)
D. \( \frac{63}{25}-\frac{16}{25} i \)


Mark correct option(s).
A. Two stream lines may cross each other
B. Two stream lines must cross each other
C. Two stream lines never cross each other
D. None of above


\( F e^{3+} \) compounds are more stable than
\( F e^{2+} \) compounds because:
A. \( F e^{3+} \) has smaller size than \( F e^{2+} \)
B. \( F e^{3+} \) has \( 3 d^{5} \) configuration (half-filled)
C. \( F e^{3+} \) has higher oxidation state
D. \( F e^{3+} \) is paramagnetic in nature


A fisherman lifts a fish of mass \( 250 g \)
from rest through a vertical height of 1.8 \( m \). The fish gains a speed of
\( 1.1 m s^{-1} \)
What is the energy gained by the fish?
A. \( 0.15 J \)
в. 4.3 .5
c. \( 4,4 J \)
D. 4.6 .5


The value of \( -5 \times-12 \times 2 \times-3 \) is
A . -360
B. -380
\( c .-400 \)
D. 360


Assertion
One is every six person in the world in
an Indian.
Reason
In India, there are more females than
males.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The maximum value of the function \( f(x)=\sin \left(x+\frac{\pi}{6}\right)+\cos \left(x+\frac{\pi}{6}\right) \) in
the interval \( \left(0, \frac{\pi}{2}\right) \) occurs at
A \( \cdot \frac{\pi}{12} \)
в.
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{3} \)


A garage mechanic keeps a box of good springs to use as replacements on
customers cars. The box contains 5
springs. A colleague, thinking that the springs are for scrap, tosses three faulty springs into the box. The mechanic picks two springs out of the box while servicing a car. Find the probability that the second spring drawn is faulty.
A \( \cdot \frac{1}{8} \)
B. \( \frac{2}{8} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{4}{8} \)


If a line makes angles \( 90^{\circ}, 60^{\circ} \) and \( 30^{\circ} \)
with the positive direction of \( x, y \) and \( z \) axis respectively find its direction cosines.


What will be the unit in which the
solubility product of \( C a_{3}\left(P O_{4}\right)_{2} \) is
expressed?
A \( \cdot \operatorname{mol} d m^{-3} \)
B. \( m o l^{2} d m^{-6} \)
\( \mathbf{c} \cdot m o l^{3} d m^{-9} \)
D. \( m o l^{5} d m^{-15} \)


The colour of gasoline is an indication of it's:
A. lead susceptibility.
B. octane number
c. gum forming tendency \& thoroughness of refining.
D. both A and B


Three coins are tossed. Describe
two events \( A \) and \( B \) which are mutually
exclusive.


If \( \tan ^{-1}(\cot \theta)=2 \theta \) then \( \theta= \)
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{4} \)
c.
D. None of the above


Find the difference between simple interest and compound interest on
Rs6000 for 2 years at 10\% per
annum


Assertion
If \( f(x)=(x-2)^{3} \) then \( f(x) \) has neither
maximum nor minimum at \( \boldsymbol{x}=\mathbf{2} \)
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\mathbf{0}=\boldsymbol{f}^{\prime \prime}(\boldsymbol{x}) \) when \( \boldsymbol{x}=\mathbf{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The fractional distillation of coal tar
yields:
A. carbon disulphide
B. carbon tetrachloride
c. kerosene oil
D. benzene


Fill in the blanks:
Paraffins are \( _{--}-_{-}- \) aliphatic hydrocarbons


Find the principal value of the following:
\( \operatorname{cosec}^{-1}(-\sqrt{2}) \)


A particle has an initial velocity of \( 3 \hat{i}+ \) \( 4 \hat{i} \) and an acceleration of \( 0.4 \hat{i} \$+0.3 \hat{i} \) Find speed after \( 10 s . \) [Hint: \( \vec{\nu}=\vec{u}+\vec{a} t \)
when \( \vec{a} \) is constant
\( A \cdot 8 \sqrt{2} \)
B. \( 7 \sqrt{2} \)
c. \( 17 \sqrt{2} \)
2
D. \( 18 \sqrt{2} \)


How many moles of acetic acid and
sodium acetate each should be
dissolved to prepare one litre of 0.063 molar buffer solution of pH \( 4.5 ? \)
\( \left(K_{a} \text { for } C H_{3} C O O H=1.8 \times 10^{-5}\right) \)


The disachharide \( \alpha \) - maltose can be
hydrolysed to glucose according to the equation (only magnitude in nearest integer in \( \mathrm{kj} / \mathrm{mol} \) )
\( \boldsymbol{C}_{12} \boldsymbol{H}_{22} \boldsymbol{O}_{11}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \longrightarrow \)
\( \mathbf{2} C_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{a} \boldsymbol{q}) \)
Using the following values, calculate the standard enthalpy change in this
reaction:
\( \Delta_{f} H^{o}\left(H_{2} O, l\right)=-285.85 k J m o l^{-1} \)
\( \Delta_{f} H^{o}\left(C_{6} H_{12} O_{6}, a q\right)=-1263.1 k J \)
\( m o l^{-1} \)
\( \Delta_{f} H^{o}\left(C_{12} H_{22} O_{11}, a q\right)=-2238.3 .1 k J \)
\( m o l^{-1} \)


A conducting ring of radius \( r \) and
resistance \( \boldsymbol{R} \) rolls on a horizontal
surface with constant velocity \( v \). The
magnetic field \( B \) is uniform and is
normal to the plane of the loop. Choose
the correct option.
A. The induced emf between \( O \) and \( Q \) is \( B r v \)
B. \( _{\text {An induced current } I}=\frac{2 B v r}{R} \) flows in the clockwise
direction
Conduced current \( I=\frac{2 B v r}{R} \) flows in the
anticlockwise direction
D. No current flows
E. answer required


The value of
\( \frac{(\mathbf{1 1 9})^{2}+(\mathbf{1 1 9})(\mathbf{1 1 1})+(\mathbf{1 1 1})^{\mathbf{2}}}{(\mathbf{1 1 9})^{\mathbf{3}}-(\mathbf{1 1 1})^{\mathbf{3}}} \) is
\( A \)
B. \( \frac{1}{8} \)
\( c \cdot 230 \)
D. \( \frac{1}{23} \)


The following salt undergoes
hydrolysis:
\( \mathbf{A} \cdot K C I \)
в. \( N H_{4} C l \)
c. \( N a C l \)
D. \( K_{2} S O_{4} \)


If \( x=a, y=b \) is the solution of the equations \( x-y=2 \) and \( x+y=4 \) then the value of a and b are respectively
A . 1 and 3
B. 3 and 2
\( c .3 \) and 1
D. -1 and -3


The figure shown depicts the distance
travelled by a body as a function of time.

The average speed and maximum
speed between 0 and \( 20 s \) are
A. \( 1 m / s, 2.0 m / s \) respectively
B. \( 1 m / s, 1.6 m / s \) respectively
c. \( 2.0 m / s, 2.6 m / s \) respectively.
D. \( 1.3 m / s, 2.0 m / s \) respectively


Which of the following is true
statement?
A. A is staggered conformation and B is eclipsed conformation
B. B is staggered conformation and A is eclipsed conformation
C. Both are eclipsed conformations.
D. Both are staggered conformations


Find the median for the grouped data
given below:
\( \begin{array}{lllll}\text { Marks } & 50- & 60- & 70- & 80 \\ & 60 & 70 & 80 & 9000\end{array} \)
Students 3. 3 4
A. 53.75
в. 63.75
c. 73.75
D. 83.75


The equation of the progressive wave, where \( t \) is the time in second, \( x \) is the distance in metre is \( y=A \cos 240(t- \) \( \left.\frac{x}{12}\right) . \) The phase difference (in Sl units) between two positions0.5m apart is
A . 40
B. 20
c. 10
D. 5


In Hall Heroult's process, the main
reagent is mixed with:
A. \( B_{2} H_{6} \)
B. \( C_{2} H_{6} \)
c. \( N a_{3} A l F_{6} \)
D. \( \operatorname{si} H_{4} \)


Acetic acid is present in vinegar. Curd contains
A . lactic acid
B. tartaric acid
c. picric acid
D. None of the above


In fractional distillation of petroleum, the vapours with highest boiling point:
A. condense in uppermost portion
B. condense in lowermost portion
c. condense in middle portion
D. do not condense


If \( \alpha \) is the degree of dissociation of
\( N a_{2} S O_{4}, \) the vant Hoff's factor \( (i) \) used
for calculating the molecular mass is:
\( \mathbf{A} \cdot 1+\alpha \)
B. \( 1-\alpha \)
\( c \cdot 1+2 \alpha \)
D. \( 1-2 \alpha \)


Consider the. following compound
statementt
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) \( \sqrt{3} \) is a rational number or an
irrational number,
(iii) 125 is a multiple of 7 or 8
(iv) A rectangle is a quadrilateral or a regular hexagon. Which of the above statements is not
true?
A. (i)
B. (ii)
c. (iii)
\( D \cdot(\mid v) \)


Each of 3 committees has 1 vacancy
which is to be filled from a group of 6
people. Find the number of ways the 3 vacancies can be filled if Each person
can serve on atmost 1 committee.


\( 1^{\circ} \mathrm{C} \) rise in temperature is equal to rise
of:
\( \mathbf{A} \cdot 1^{0} F \)
B . \( 9 / 5^{\circ} \mathrm{F} \)
c. \( 5 / 9^{0} F \)
D. \( 33^{0} F \)


Stomata open and close due to
A. Turgor pressure change
B. Hormonal change.
c. Temperature change
D. All of the above.


Assertion
If objective and eye lenses of a microscope are interchanged then it
can work as telescope.
Reason
The objective lens of telescope has small focal length.
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


If \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{\omega}+\boldsymbol{c} \boldsymbol{\omega}^{2}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{\omega}+\boldsymbol{b} \boldsymbol{\omega}^{2}+\boldsymbol{c} \)
and \( z=a \omega^{2}+b+c \omega \) then find the
value of \( \frac{x^{2}}{y z}+\frac{y^{2}}{z x}+\frac{z^{2}}{x y} \)


A source of sound produces waves of wavelength \( 20 \mathrm{cm} \) in air. It is moving with a velocity one-fourth the velocity of sound towards east. The apparent wavelength noted by a man moving in the same direction with velocity equal to \( 2 / 3 \mathrm{rd} \) of velocity of sound wave and at the back of source is :
A . \( 15 \mathrm{cm} \)
B. 50 cm
c. \( 75 \mathrm{cm} \)
D. 80 cm


Where are proteins synthesised inside
the cell?


A clamped string is oscillating in nth
harmonic, then
This question has multiple correct options
A . total energy of oscillations will be \( n^{2} \) times that of
fundamental frequency
B. total energy of oscillations will be \( (n-1)^{2} \) times that
of fundamental frequency
C . average kinetic energy of the string over a complete oscillations is half of the total energy of the string
D. none of these


Substance \( A, C_{5} H_{8} \) is chiral When \( A \) is
treated with \( \boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{t} \boldsymbol{B}, \boldsymbol{C}_{5} \boldsymbol{H}_{10}, \) is
produced \( B \) is achiral \( A \) can be:
A. 1- methylcyclobutene
B. 3-methylcyclobutene
c. trans-1,2-dimethylcyclopropane
D. cyclopentane


The standard reduction potential data
at \( 25^{\circ} \mathrm{C} \) is given below:
\( \mathbf{E}^{\mathrm{o}}\left(\mathbf{F e}^{\mathbf{3}+}, \mathbf{F e}^{\mathbf{2}+}\right)=+\mathbf{0 . 7 7} \mathbf{V} \)
\( \mathbf{E}^{\mathbf{o}}\left(\mathbf{F e}^{\mathbf{2}+}, \mathbf{F e}\right)=-\mathbf{0 . 4 4} \mathbf{V} \)
\( \mathbf{E}^{\mathrm{o}}\left(\mathbf{C u}^{2+}, \mathbf{C u}\right)=+\mathbf{0 . 3 4} \mathbf{V} \)
\( \mathbf{E}^{\circ}\left(\mathbf{C u}^{+}, \mathbf{C u}\right)=+\mathbf{0 . 5 2 V} \)
\( \mathbf{E}^{\mathrm{o}}\left[\mathbf{O}_{2}(\mathbf{g})+\mathbf{4 H}^{+}+\mathbf{4 e}^{-} \rightarrow \mathbf{2} \mathbf{H}_{\mathbf{2}} \mathbf{0}\right]= \)
\( +1.23 V \)
\( \mathbf{E}^{\circ}\left[\mathbf{O}_{2}(\mathbf{g})+\mathbf{2} \mathbf{H}_{2} \mathbf{O}+\mathbf{4} \mathbf{e}^{-} \rightarrow \mathbf{4 0} \mathbf{H}^{-}\right]= \)
\( +0.40 \mathrm{V} \)
\( \mathbf{E}^{\circ}\left(\mathbf{C r}^{3+}, \mathbf{C r}\right)=-\mathbf{0 . 7 4 V} \)
\( \mathbf{E}^{\mathbf{o}}\left(\mathbf{C r}^{2+}, \mathbf{C r}\right)=-\mathbf{0 . 9 1} \mathbf{V} \)
Match \( \mathrm{E}^{0} \) of the redox pair in List 1 with
the values given in List 2 and select the correct answer using the code given below the lists.


Calculate the electric flux through ring shown in figure is:
\( ^{A} \cdot \frac{q}{2 \varepsilon_{0}}\left[1+\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
в. \( \frac{q}{2 \varepsilon_{0}}\left[1-\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
c. \( \frac{q}{\varepsilon_{0}}\left[1-\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
D. zero


Calculate the pH of \( 1.0 L \) of \( 0.10 M \)
pyridine solution to which 0.3 mol of
pyridinium chloride \( C_{5} H_{5} N H^{+} C l, \) has
been added, assuming no change in volume


Plot the points \( A(1,-1), B(-1,4) \) and \( C(-3, \)
-1) on a graph paper to obtain the triangle ABC. Give a special name to the triangle \( A B C \) and, if possible, find its
area.


Short / Long answer type questions. Mushrooms are biodegraders and
proteins-rich food for us. Comment


If \( A+B=225^{\circ}, \) then
\( \frac{\cot \boldsymbol{A}}{\mathbf{1}+\cot \boldsymbol{A}} \cdot \frac{\cot \boldsymbol{B}}{\mathbf{1}+\cot \boldsymbol{B}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. \( \frac{1}{2} \)


Which of the following is a function of nucleosome?
A. It acts as a region of DNA transcription
B. It holds RNA in position
c. It helps in reducing the length of chromatin fibre
D. All of the above


The enthalpy of combustion of diamond
and enthalpy of formation of carbon dioxide has the same value.ffrue enter
else o
A.


Why is photorespiration also called \( C_{2} \)
cycle?


Which is the correct graph?
\( A \)
B.
\( c \)
\( D \)


An open pan \( P \) filled with water (density
\( \boldsymbol{\rho}_{\boldsymbol{w}} \boldsymbol{)} \)
is placed on a vertical rod, maintaining
equilibrium. A block of density \( \rho \) is
placed on one side of the pan as shown
in the figure. Water depth is more than
height of the block.
A. Equilibrium will be maintained only if \( \rho<\rho_{w} \)
B. Equilibrium will be maintained only if \( \rho \leq \rho_{w} \)
C. Equilibrium will be maintained for all relations between \( \rho \) and \( \rho_{w} \)
D. Equilibrium will not be maintained in all cases


Mg burns in air to form two compound
(A) and (B). (A) is sparingly soluble in water and the resulting solution is weakly basic. (B) dissolve in water to
form (C) and gas (D) with dilute \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) gives (E). E on heating gives gas (F)
which behaves as an oxidising agent too. Gas \( F \) on reaction with phosphorus produce an important dehydrating agent (G). The compound G is:
\( \mathbf{A} \cdot P_{4} O_{10} \)
\( \mathbf{B} \cdot H P O_{3} \)
\( \mathbf{c} \cdot P C l_{5} \)
D. \( P_{4} O_{6} \)


The value of \( 108^{\circ} \) in circular measure
is
A \( \cdot 5 \pi^{c} / 3 \)
в. \( 3 \pi^{c} / 5 \)
c. \( \pi^{c} / 5 \)
D. \( 6 \pi^{c} / 7 \)


Though air is bad conductor yet a body kept in air losses heat quickly this is due to
A. Conduction
B. Convection
c. Radiation
D. None of these


The necessary condition for nuclear
fusion is
A. high temperature and high pressure
B. low temperature and low pressure
c. high temperature and low pressure
D. low temperature and high pressure


Science museum foresee
A. Technological changes
B. Environmental changes
c. Climatic changes
D. Behavioural changes


What is carbonisation of coal in
production of coal tar?
A. Heating of coal in absence of air
B. Heating of coal in excess of air
c. Heating of coal while adding carbon
D. Both b and c


If a relation \( ^{\prime} \boldsymbol{R}^{\prime} \) is defined by \( \boldsymbol{R}= \)
\( \left\{(x, y) / 2 x^{2}+3 y^{2} \leq 6\right\}, \) then the
domain of \( \boldsymbol{R}(\boldsymbol{x}, \boldsymbol{y}) \) is
This question has multiple correct options
A \( \cdot x \in[-3,3] \)
B . \( x \in[-\sqrt{3}, \sqrt{3}] \)
c. \( y \in[-\sqrt{2}, \sqrt{2}] \)
D \( \cdot y \in[-2,2] \)


A black body at \( 200 \mathrm{K} \) is bound to exit maximum energy at a wavelength \( 14 \mu \)
m. When its temperature is raised to \( 1000 \mathrm{K}, \) then wavelength at which maximum energy emitted is:
\( A \cdot 14 \mathrm{mm} \)
в. \( 7 \mu m \)
c. \( 2.8 \mu m \)
D. 28 mm


Diffusion of the gases is affected at alveolar level in all the following conditions except
A. Emphysema
B. Tuberculosis
c. Lung fibrosis
D. Asthma


Show that \( A B C D \) is a square where
\( A, B, C, D \) are the points (0,4,1),(2,3,-1),(4,5,0) and (2,6,2)
respectively.


Fluorescent tubes give more light than a filament bulb of same power because
A. the tube contains gas at low temperature
B. ultraviolet light is converted into visible light by fluorescence
c. light is diffused through the walls of the tube
D. it produces more heat than bulb


An astronaut standing on the surface of the moon throws a ball upwards. The ball would:
A. directly fall down from the point it is released
B. hang in space
c. go up and then come back to the surface of the moon
D. keep going up never to come back


Presence of which of the following ion
can be detected using ring test?
A . \( N O \)
B. \( N O_{3}^{-} \)
c. \( C l^{-} \)
D. \( P O_{4}^{3} \)


Differentiate from first principle: \( y=x^{2} \)
\( \mathbf{A} \cdot 2 x \)
B . \( (x-1)^{2} \)
\( \mathbf{c} \cdot x^{3} \)
D. \( \frac{1}{\sqrt{x}} \)


A ray of light passing through an equilateral glass prism from air undergoes minimum duration when angle of incidence is \( \frac{3^{t h}}{4} \) the angle of prism, calculate the speed of light in
prism.


Consider the following three halides:
(i) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)
(ii) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C l} \)
(iii) \( C_{6} H_{5}-C l \)
Arrange C-Cl bond length of these compounds in decreasing order.
A. i > ii > ii i
c. iii > ii > i
D. ii > iii >


A hemispherical tank of radius \( \boldsymbol{R} \) is
completely filled with water. Now an orifice of small area 'a' is made at the
bottom of tank. The time required to
empty the tank is
\( ^{\mathrm{A}} \cdot \frac{14 \pi R^{\frac{5}{2}}}{15 \sqrt{2} a \sqrt{g}} \)
\( ^{\mathrm{B}} \cdot \frac{14 \pi R^{\frac{3}{2}}}{\sqrt{2} a \sqrt{g}} \)
c. \( \frac{14 \pi R^{\frac{5}{2}}}{5 \sqrt{2} a \sqrt{g}} \)
\( \frac{4 \pi R^{\frac{5}{2}}}{15 \sqrt{2} a \sqrt{g}} \)


From the concentrations of \( \mathrm{R} \) at
different times given below. Determine
the average rate of the reaction range: \( R \)
\( \rightarrow P \) in given intervals of time.
\( t(s) \)
\[
\begin{array}{ll}
\text { 0 } & \text { 5 }
\end{array}
\]
\( \mathbf{1} \)
\[
\begin{array}{ll}
10^{-3} \times & 160 \\
\end{array}
\]
40
\( [R]\left(\operatorname{mol} L^{-1}\right) \)
\( \mathbf{A} \cdot 3.5 \times 10^{2} \) to \( 0.42 \times 10^{2} \) mol. \( L^{-1} s^{1} \)
B . \( 7 \times 10^{2} \) to \( 0.84 \times 10^{2} \) mol. \( L^{-1} s^{1} \)
C . \( 8 \times 10^{3} \) to \( 0.37 \times 10^{3} \) mol. \( L^{-1} s^{1} \)
D. \( 16 \times 10^{3} \) to \( 0.75 \times 10^{3} \) mol. \( L^{-1} s^{1} \)


Two chords \( A B \) and \( C D \) of lengths \( 5 \mathrm{cm} \)
and \( 11 \mathrm{cm} \) respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between \( A B \) and \( C D \) is \( 6 \mathrm{cm} \)
find the radius of the circle.


The hormone that helps in the conversion of glucose into glycogen is:
A. cortisone
B. bile acids
c. adrenaline
D. insulin


To prevent soil erosion, farmer plants a hedge across a field. This method works
because
A. The hedge prevents the soil from direct impact of rainwater
B. The roots of plants prevent the soil erosion
c. The hedge absorbs minerals from the soil, which makes it most compact
D. None of the above


The work function of a certain metal is
4.2 eV. Which among the wavelengths \( 390 \mathrm{nm}, 440 \mathrm{nm}, 550 \mathrm{nm} \) and \( 70 \mathrm{nm} \) will
this metal give photoelectric emission?
A. 390 nm only
B. 390 nm, 440 nm only
\( \mathrm{c} .390 \mathrm{nm}, 440 \mathrm{nm} \) and \( 550 \mathrm{nm} \)
D. None of them


The formula for the resistance of a fluid
is:
\( ^{\mathrm{A}} \cdot_{R}=\frac{\pi r^{4}}{8 \eta l} \)
в. \( _{R}=\frac{8 \eta l}{\pi r^{2}} \)
c. \( _{R}=\frac{8 \eta l}{\pi r^{3}} \)
D. \( _{R}=\frac{8 \eta l}{\pi r^{4}} \)


Fruits detached from a tree fall down
due to force of gravity. We know that a force arises due to interaction between
two objects. Name the objects interacting in this case.
A. Earth and tree
B. Earth and fruit
c. Earth and branch
D. None of the above


Monatomic, diatomic and polyatomic
ideal gases each undergo slow adiabatic expansions from the same initial volume and same initial
pressure to the same final volume. The
magnitude of the work done by the
environment on the gas is
A. the greatest for polyatomic gas
B. the greatest for monatomic gas
c. the greatest for diatomic gas
D. the question is irrelevant, there is no meaning of slow adiabatic expansion


The concentration of acetic acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\right. \) \( 1.8 \times 10^{-5} \) ) required to give \( 3.5 \times \)
\( 10^{-4} m o l / L H^{+}, \) is
A. 6.8 mol/L
B. \( 6.8 \times 10^{-3} \) mol \( / \) L
C. \( 1.94 \times 10^{-1} \) mol \( / L \)
D. \( 194 \mathrm{mol} / \mathrm{L} \)


\( \boldsymbol{\alpha}=\sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right) \) and \( \beta= \)
\( \cos ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right) \) then:
\( A \cdot \tan \alpha=\cot \beta \)
B. \( \tan \alpha=-\cot \beta \)
\( \mathbf{c} \cdot \tan \alpha=\tan \beta \)
D. \( \tan \alpha=-\tan \beta \)


What are food preservatives? Give example


You enter a chess tournament where
your probability of winning a game is 0.3 against half the players (call them
type 1 ), 0.4 against a quarter of the players (call them type 2 ), and 0.5 against the remaining quarter of the
players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning?
A. 0.375
в. 0.986
\( c \cdot 0.236 \)
D. 0.135


Prove that for any three vectors \( a, b, c[b \) \( +c c+a a+b]=2[a b c] \)


Which of the following reactions is an example of use of water gas in the synthesis of other compounds?
A \( \cdot C H_{4}(g)+H_{2} O_{(g)} \frac{\frac{1272 k}{N i}}{N} C O(g)+H_{2}(g) \)
B. \( C O_{4}(g)+H_{2} O_{(g)} \frac{673 k}{\text { Cactlyst }} C O_{2}(g)+H_{2}(g) \)
c. \( \left.C_{n} H_{2 n+2}+n H_{2} O_{(} g\right) \frac{1270 k}{N i} n C O+(2 n+1) H_{2} \)
D. \( C O(g)+2 H_{2}(g) \frac{\text { cobalt }}{\text { catalyst }} C H_{3} O H(l) \)


If the magnitude of its angular speed at
\( \boldsymbol{t}=\mathbf{3 . 0 s} \) is \( \boldsymbol{x} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} / \boldsymbol{s}, \) find \( \boldsymbol{2} \boldsymbol{x} \)


Find slope if \( \theta=150^{\circ} \)


If \( 1<x<\sqrt{2}, \) the number of solutions of
the equation \( \tan ^{-1}(x-1)+\tan ^{-1} x+ \)
\( \tan ^{-1}(x+1)=\tan ^{-1} 3 x \) is
A.
B.
\( c \cdot 2 \)
D.


Independent alternation of generation is
found in
B. Spermatophyta
c. Thallophyta
D. Bryophyta


Which one of the following pairs of structures distinguishes a nerve cell
from other types of cell ?
A. Nucleus and mitochondria
B. Perikaryon and dendrites
C. Vacuoles and fibres
D. Flagellum and medullary sheath


If \( \boldsymbol{y}=\tan (\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}) \cdot \) Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


From the table given below, furnish your points of inference.
\begin{tabular}{ll}
Substance & Solubility at \( 25^{\circ} \mathrm{C} \) \\
\( \mathrm{NaCl} \) & \( 36 \mathrm{g} \) \\
\( \mathrm{NaBr} \) & \( 95 \mathrm{g} \) \\
\( \mathrm{Nal} \) & \( 184 \mathrm{g} \) \\
\hline
\end{tabular}


The denominator of a rational number
is greater then its numerator by \( 4 . \) If the numerator is increased by 11 and the
denominator is decreased by \( 1, \) the new number becomes \( 7 / 3 . \) Find the original


In balancing the reaction \( \boldsymbol{x} \boldsymbol{Z} \boldsymbol{n}+ \) \( N O_{3}^{-}+y H^{+} \rightarrow x Z n^{2+}+N H_{4}^{+}+ \)
\( z H_{2} O, x, y \) and \( z \) are respectively:
A .4,10,3
в. 3,8,3
\( \mathrm{c} \cdot 3,10,3 \)
D. 4,3,10


(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the \( n=1,2, \) and 3 levels.
(b) Calculate the orbital period in each of these levels.


Which of the following is a narrow spectrum antibiotics?
A. Penicillin G
B. Dettol
c. Aspirin
D. Analgin


n given figures the two triangles are
\( \operatorname{similar} \Delta A B C \sim \Delta D E F \) if \( E D=7 \) find
the length of \( \boldsymbol{A C} \)
\( A \)
B. 14
\( c \)
\( D \cdot 2 \)


Sum of \( X \) and \( Y \) is \( -2 . \) If \( X=43 \), the \( Y \)
is:
A . 45
в. -45
c. 41
D. -41


Find the derivative of \( \sin ^{2} x \) with respect to \( x \) using product rule


Which of the following has flexidentate character?
A. EDTA
B. en
\( c \cdot P y \)
D. ox


Length of the latusrectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c}, \) is equal to
A \( .2 c \)
B. \( \sqrt{2} c \)
c. \( 2 \sqrt{2} c \)
D. \( 4 c \)


Arrange \( N H_{3}, P H_{3}, A s H_{3}, S b H_{3} \) in
increasing covalent nature :
A. \( N H_{3}>S b H_{3}>A s H_{3}>P H_{3} \)
В. \( P H_{3}>N H_{3}>A s H_{3}>S b H_{3} \)
c. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \)
D. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)


Which of the following is not correct
about xenon hexafluoride?
A. It has oxidation state of +6
B. The hybridisation involved in \( X e F_{6} \) is \( s p^{3} d^{3} \)
c. on hydrolysis it gives Xe, HF and \( O_{2} \)
D. None of these


Choose the correct answer form the
alternatives given. Match the column I with column II and
mark the appropriate choice.
Column I Column I
(A) Quick
lime
(i) Setting fractured bones
(B) Plaster of
Paris
(ii) A constituent of gum chewing
Manufacture Slaked
lime O
\( (c) \)
(iii) bleaching powder
(D) limestone
(iv) Manufacture of dyestuffs
A \( \cdot(A) \rightarrow(i),(B) \rightarrow(i v),(C) \rightarrow(i i),(D) \rightarrow(i i i) \)
B. \( (A) \rightarrow(i v),(B) \rightarrow(i),(C) \rightarrow(i i i),(D) \rightarrow(i i) \)
c. \( (A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i v) \)
\( D \)
\( (i i i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i) \)


Which of the following polymers does not soften on heating?
A. Bakelite
B. Polythene
c. Polystyrene
D. PVC


The decreasing order of power of boron
halides to act as Lewis acids is :
A. \( B F_{3}>B C l_{3}>B B r_{3} \)
B. \( B B r_{3}>B C l_{3}>B F_{3} \)
c. \( B C l_{3}>B F_{3}>B B r_{3} \)
D. \( B C I_{3}>B B r_{3}>B F_{3} \)


Which of the following statements are true about the modern form of the
periodic table?
A. Properties of the elements are the periodic functions of their atomic number
B. There are 7 periods
c. There are 18 numbered groups
D. All of the above


Why do we apply paint on iron articles?


What is the value of the sum
\( \sum_{n=2}^{11}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1} ? \)
\( \mathbf{A} \cdot i \)
в. \( 2 i \)
c. \( -2 i \)
D. \( 1+i \)


Dark bands are
A. A-band
B. B-band
c. I-band
D. Z-line


The interior of a closed figure has a
A. space
B. boundary
c. diagonal
D. None of the above


The total number of groups in Modern Periodic table is
A. 7
B. 17
c. 18
\( D \)


How does the diethyl ether react with the following reagents?
a) \( \boldsymbol{O}_{2} / \) long contact
b) \( H I \) is excess
c) \( P C l_{5} \)
d) \( H O H \)


Water used by most of the industries is drawn from
A. the ground
B. the ocean
c. ice caps
D. All of the above


A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true?
A. Its speed is zero.
B. Its acceleration is zero
c. Its acceleration is opposite to the velocity
D. Its speed may be variable


The sum of the radius and the height of a solid cylinder is \( 37 \mathrm{cm} \) If the total
surface area of the solid is \( 1628 \mathrm{cm}^{2} \)
find the circumference of the base
\( A .30 \mathrm{cm} \)
B. 34 \( \mathrm{cm} \)
c. \( 44 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


Show that \( n(n+1)(2 n+1) \) is multiple
of 6 for every natural number \( n \)


If \( |\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}|=\overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}, \) then \( |\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}| \) is:
\( \mathbf{A} \cdot|\vec{A}|+|\vec{B}| \)
B. \( \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}} \)
\( ^{\mathrm{c}} \cdot \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}+\frac{|\vec{A}||\vec{B}|}{\sqrt{2}}} \)
D \cdot \( \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}+\sqrt{2}|\vec{A}||\vec{B}|} \)


Let \( A \) and \( B \) be two sets such that
\( \boldsymbol{n}(\boldsymbol{A})=\mathbf{5} \) and \( \boldsymbol{n}(\boldsymbol{B})=2 . \) If \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e} \)
are distinct and
\( (a, 2),(b, 3),(c, 2),(d, 3),(e, 2) \) are in
\( A \times B, \) find \( A \) and \( B \)


Find \( Q 1 \) and \( Q 2 \)


The value of \( \sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right) \)
\( A \cdot 0 \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


Consider two vectors \( \vec{A} \) and \( \vec{B} \). Let
these two vectors represent two
adjacent sides of a parallelogram. We construct a parallelogram OACB as shown in the diagram. Which of the following represent the resultant
vector?
\( A \cdot O A \)
в. \( O C \)
\( c . O B \)
D. None


According to Indian and Greek philosophers at 400 B.C., the continuous sub-division of matter would ultimately yield
\( A \). atom
B. electron
c. proton
D. neutron


Which of the following is largest in size among all?
A. Saturn
B. Jupiter
c. Neptune
D. Mercury


Which of the following has lowest ionization potential?
A. \( X e \)
в. \( N e \)
\( \mathrm{c} . \) Не
D. \( A r \)


Which of the following does not help in clotting of blood?
A. Heparin
B. Prothrombin
\( c \cdot c a^{2} \)
D. Exposure to \( 0_{2} \)


A motor car is travelling at speed of \( 30 m / s \) on a circular road of radius
\( 500 m . \) If the speed of the car is
increasing at the rate of \( 2.0 m / s^{2} \), then
the total acceleration will be
A \( \cdot 1.8 m / s^{2} \)
B \( \cdot 2 m / s^{2} \)
c. \( 2.7 m / s^{2} \)
D. \( 3.8 m / s^{2} \)


If
\( \frac{n}{^{n} C_{r}+4^{n} C_{r+1}+6^{n} C_{r+2}+4^{n} C_{r+3}+^{n} C} \)
\( \frac{\boldsymbol{r}+\boldsymbol{k}}{\boldsymbol{n}+\boldsymbol{k}}, \) then the value of \( \boldsymbol{k} \) equals
A . 1
B. 2
\( c \cdot 4 \)
D. None of these


Mohit baked 2000 cookies. He sold 600
of them and gave the rest equally to 20 of his friends. How many cookies did
each of his friends receive?
A . 18
B. 70
c. 80
D. 1400


If \( z \) is a complex number \( z=9-12 i \)
find \( |z| \)
A . 15
B. 16
c. 17
D. 8


Assertion
When two unlike charges are brought nearer, their electrostatic potential
energy decreases.
Reason
All conservative forces act in the
direction of decreasing potential
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


The angles in a right angled isosceles
triangle are:
A \( \cdot 60^{\circ}, 60^{\circ}, 60^{\circ} \)
B . \( 90^{\circ}, 60^{\circ}, 30^{\circ} \)
c. \( 90^{\circ}, 45^{\circ}, 45^{\circ} \)
D . \( 70^{\circ}, 50^{\circ}, 60^{\circ} \)


The room temperature is \( +20^{\circ} \mathrm{C} \) when
outside temperature is \( -20^{\circ} \mathrm{C} . \) Room
temperature is \( +10^{\circ} \mathrm{C} \) when outside
temperature is \( -40^{\circ} \mathrm{C} \). The
temperature of the radiator heating the
room is:
A \( \cdot 70^{\circ} \mathrm{C} \)
В. \( 60^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} \mathrm{C} \)
D. \( 40^{\circ} \mathrm{C} \)


Two samples of HCl of \( 1.0 \mathrm{M} \) and \( 0.25 \mathrm{M} \)
are mixed. Find volumes of these
samples taken in order to prepare 0.75
M HCI solution. Assume no water is
added.
(1) \( 20 \mathrm{mL}, 10 \mathrm{mL} \)
(III) \( 100 \mathrm{mL}, 50 \mathrm{mL}(\mathrm{III}) \)
\( 40 \mathrm{mL}, 20 \mathrm{mL}(\mathrm{IV}) 50 \mathrm{mL}, 25 \mathrm{mL} \)
A . ।, ॥।, IV
B. ।, ॥
c. ॥, ॥ा, । v
D. I, II, III, IV


Solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}= \)
\( \tan x(1+y \sin x) \) is given by
A \( \cdot \operatorname{cosec} x=-y+1+C e^{-y} \)
B. \( y=\tan x+C e^{X} \)
c. \( \sin x e^{y}=1+y+C \)
D. \( \operatorname{cosec} x=y+C e^{y} \)


It is sometimes necessary to remove colouring matter contained as an impurity in glass. Glass is decolourised by:
A. wood charcoal
B. manganese dioxide
c. bleaching powder
D. hydrogen


p-njunction diode can be used as
A. amplifer
B. detector
c. oscillator
D. capacitor


The additive inverse of 17 is:
A. -17
B. 17
c. \( \frac{1}{17} \)
D. \( -\frac{1}{17} \)


Solve the following inequality \( \frac{-2 x+5}{x+6}>-2 \)


For the following distribution:
Mark less than 102030405060
No. of students 312 27 577580
The modal class is
A . \( 10-20 \)
B. 20 - 30
\( c \cdot 30-40 \)
D. 50 - 60


\( O_{3} \) does not give ozonide with :
A. 2-Butene
B. Benzene
c. 2-Pentyne
D. Neopentane


What are the dispersed phase and dispersion medium in milk?


When the right ventricle in the human heart contracts, the blood moves to
A. Aorta
B. Brain
c. Lungs
D. Pulmonary arteries


If the potential energy of a spring is \( V \) on stretching it by \( 2 \mathrm{cm} \) then its potential energy when it is stretched by \( 10 \mathrm{cm} \) will be
A. v/25
B. 5 v
c. v/ 5
D. 25 V


Read the following statements and pick
the correct choice
Statement A: With increase in
temperature, viscosity of a gas increases and that of a liquid
decreases.
Statement B: If the density of a small sphere is equal to the density of the liquid in which it is dropped, then the terminal velocity of the sphere will be
zero.
A. Both A and B are true
B. Both A and B are false
c. A is true and B is false
D. B is true but A is false.


Find the equation of a straight line:
with slope 2 and \( y- \) intercept 3


Collect 5 examples of palindromic sequence by consulting your teacher. Better try to create a palindromic sequence by following base-pair rules.


The initial concentration of \( N_{2} O_{5} \) in
the first order reaction \( N_{2} O_{5}(g) \longrightarrow \)
\( 2 N O_{2(g)}+\frac{1}{2} O_{2(g)} \) was \( 11.24 \times \)
\( \mathbf{1 0}^{-\mathbf{2}} \) mol \( \quad \boldsymbol{L}^{-1} \) at 318 K. The
concentration of \( N_{2} O_{5} \) after 60
minutes was \( 0.20 \times 10^{-2} \) mol \( L^{-1} \)
Calculate the rate constant of the
reaction at \( 318 \mathrm{K} \)


Who found Calcutta Medical College?
A. Lord William Bentinck
B. Warren Hastings
C. Ram Mohan Roy
D. Lord George Bentinck


Find out the total sum B.A of \( <72^{\circ} \) and
\( 90^{\circ} \) in pentagonal pyramidal shape.


Suppose we throw a dice once?
(i)What is the probability of getting a
number greater than \( 4 ? \)


DNA and RNA are the information
molecules of the cell. Explain clearly the differences in the basic structure of
these two molecules.


When an iron cylinder of diameter \( 0.20 \mathrm{cm} \) and length \( 30 \mathrm{cm} \) is kept parallel to a magnetic field of intensity
\( 4800 A / m \) the cylinder acquires a pole
strength of \( 9 A m . \) Find the permeability
of the material of the rod?
A \( .0 .075222 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
B . \( 9.522 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
c. \( 75.22 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
D. \( 7.522 \times 10^{-4} \mathrm{H} / \mathrm{m} \)


Which of the following is known as dead burnt?
A. Gypsum
B. Plaster of Paris
c. Anhydrite
D. None of these


A dog of mass \( m \) is walking on a pivoted
disc of radius \( R \) and mass \( M \) in a circle
of radius \( R / 2 \) with an angular
frequency \( n . \) The disc will revolve in
opposite direction with frequency:
\( A \cdot \frac{m n}{M} \)
B. \( \frac{m n}{2 M} \)
c. \( \frac{2 m n}{M} \)
D. \( \frac{2 M n}{M} \)


Write down advantages and disadvantages of fossil fuel.


Assertion
In an atom, the velocity of electrons in
the higher orbits keeps on decreasing.
Reason
Velocity of electron in an orbit is inversely proportional to the radius of
the orbit.
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


Differentiate w.r.t \( \boldsymbol{x}: \boldsymbol{x}^{\boldsymbol{y}}+\boldsymbol{y}^{\boldsymbol{x}}=\mathbf{1} \)


State whether given statement is True or False

During refraction through prism a ray bends away from its base.
A. True
B. False


Pure water can be obtained from sea
water by:
A . centrifugation
B. plasmolysis
c. reverse osmosis
D. sedimentation


In a class of 100 students, 55 students
have passed in Mathematics and 67 students have passed in physics. Then the number of students who have
passed in physics only is
A . 22
B. 33
c. 10
D. 45


A flywheel of radius \( R \) and of moment of
inertia \( I \) can be rotated in vertical plane without friction about its natural axis. \( A \)
light string is wound over the wheel and a body of weight \( W \) is suspended at the other end of string. The angular acceleration of wheel when suspended body is released is:
\( \mathbf{A} \cdot \frac{W R}{I} \)
B. less than \( \frac{W R}{I} \)
c. greater than \( \frac{W R}{I} \)
D. \( \geq \frac{W R}{I} \)


Find the distance between the points (-1,-3) and the midpoint of the line segment joining (2,4) and (4,6)
A . \( \sqrt{5} \)
B. \( 2 \sqrt{5} \)
c. \( 4 \sqrt{5} \)
D. \( \sqrt{3} \)


If \( p \) and \( q \) are two statement then \( (p \leftrightarrow \)
\( \sim q) \) is true when
A. \( p \) and \( q \) both are true
B. \( p \) and \( q \) both are false
C. \( p \) is false and \( q \) is true
D. None of these


What is the effect of temperature on the
resistance of a metal? The resistance of
a platinum resistances thermometer at
\( 0^{\circ} \mathrm{C} \) temperature is \( 3.0 \Omega \) and at \( 100^{\circ} \mathrm{C} \) it
is \( 3.75 \Omega . \) Its resistance at an unknown
temperature is \( 3.15 \Omega \). Find the value of
the unknown temperature


Differentiate between reduction
division and equational division


Biological Oxygen Demand (BOD) is a
measure of
A. Industrial wastes poured into water bodies
B. Extent to which water is polluted with organic compound
C. Amount of carbon monoxide inseparably combined with haemoglobin
D. Amount of oxygen needed by green plants during night


A coil of radius \( \pi \) meters, 100 turns
carries a current of \( 3 A \). The magnetic induction at a point on its axis at a distance equal to \( \sqrt{3} \) times its radius from its centre is :
A. \( 7.2 \times 10^{-6} \mathrm{Wbm}^{-2} \)
в. \( 7.4 \times 10^{-6} \mathrm{Wbm}^{-2} \)
c. \( 7.5 \times 10^{-6} \mathrm{Wbm}^{-2} \)
D. \( 7.83 \times 10^{-6} \mathrm{Wbm}^{-2} \)


A powerful magnet attracts
A. all materials.
B. only ferromagnetic materials and their ores.
C. some materials and repels some other materials.
D. only iron and its ores but does not repel any material.


Find the angle between the vectors:
\( \boldsymbol{a}=\{-1,2,-2\} \) and \( \boldsymbol{b}=\{\mathbf{6}, \mathbf{3},-\mathbf{6}\} \)


Represent the following families of curves by forming the corresponding differential equation(a, b being parameters). \( x^{2}+y^{2}=a^{2} \)


Why reflecting telescope is superior in comparison to refracting telescope? Write two reasons.

Magnifying power of a telescope is 8 When it is adjusted for parallel rays the distance between eyepiece and objective lens is \( 18 \mathrm{cm} . \) Determine the focal length of both the lenses.


The organic compouds \( A \) and \( B \) react
with sodium metal and release \( \boldsymbol{H}_{2} \) gas.
A and B react with each other to given ethyl acetate. Then \( A \) and \( B \) are
A. \( C H_{3} \) COOHand \( C_{2} H_{5} \) OH
в. \( H C O O H a n d C_{2} H_{5} O H \)
c. \( C H_{3} \) COOHand \( C H_{3} \) OH
D. \( C H_{3} \) СООНапдНСООН


It was the largest known carnivorous marsupial of modern times. It was native to Tasmania and believed to have
become extinct in \( 20^{t h} \) century. Which
animal are we talking about?
A. Thylacine
B. Macropod
c. Dasyurid
D. wombat


Find the complementary angle of \( 45 \frac{1}{2}^{\circ} \)


If \( f(x)=\frac{x}{1+x \tan x}, x \in\left(0, \frac{\pi}{2}\right) \) then
This question has multiple correct options
A. \( f(x) \) has exactly one point of minima
B. \( f(x) \) has exactly one point of maxima
C \( f(x) \) is many one in \( \left(0, \frac{\pi}{2}\right) \)
D. \( f(x) \) has maximum at \( x_{0} \) where \( x_{0}=\cos x_{0} \)


At the polarising angle \( \left(\boldsymbol{\theta}_{B}\right), \) angle of refraction is given by :
A \( .90^{\circ} \)
В. \( 90^{\circ}+\theta_{B} \)
c. \( 90^{\circ}-\theta_{B} \)
D. \( \frac{90^{\circ}}{\theta_{B}} \)


The group of small pieces of rock revolving around the sun between the orbits of mass and Jupiter are called
A. Meteorites
B. Asteroids
c. Meteors
D. comets


Hybridisation of central atom in \( \boldsymbol{N} \boldsymbol{F}_{3} \)
is:
\( A \cdot s p^{3} \)
B . \( s p \)
\( c \cdot s p^{2} \)
D. \( d s p^{2} \)


If \( \sec A=\operatorname{cosec} B=\frac{5}{3}, \) then the value
of \( (\boldsymbol{A}+\boldsymbol{B}) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 90^{\circ} \)
\( \mathbf{c} \cdot<90^{\circ} \)
\( \mathbf{D} \cdot>90^{\circ} \)


How much percentage of oxygen is expired?
A . \( 7 \% \)
B. 25\%
c. \( 15 \% \)
D. \( 20 \% \)


Explain the Indian concept in context of the origin of the universe?


In a car a rear view mirror having a
radius of curvature \( 1.50 \mathrm{m} \) forms a
virtual image of a bus located \( 10.0 \mathrm{m} \)
from the mirror. The factor by which the mirror magnifies the size of the bus is
close to
A . 0.06
B. 0.07
\( c \cdot 0.08 \)
D. 0.09


Ozone is an oxidizing and reducing agent. Explain with one example of
each.


In the following equilibrium reaction \( \mathbf{2} \boldsymbol{A} \rightleftharpoons \boldsymbol{B}+\boldsymbol{C}, \) the equilibrium
concentration of \( A, B \) and \( C \) are \( 1 \times \)
\( \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M}, \mathbf{2} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \) and \( \mathbf{3} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
respectively at \( 300 K \)
Then what is the value of \( K_{c} \) for this
equilibrium reaction at the same temperature?
A \( \cdot \frac{1}{6} \)
B. 6
c. \( \frac{1}{36} \)
D. 36
E \( \cdot \frac{1}{24} \)


The perimeter of a rectangle is \( 50 m \) and its breadth is \( 12 m \). Find its :
(i) length
(ii) area


The differential equation of a wave is :
A \( \cdot \frac{d^{2} y}{d t^{2}}=v^{2} \frac{d^{2} y}{d x^{2}} \)
B. \( \frac{d^{2} y}{d x^{2}}=v^{2} \frac{d^{2} y}{d t^{2}} \)
c. \( \frac{d^{2} y}{d x^{2}}=\frac{1}{v} \frac{d^{2} y}{d t^{2} y} \)
D. \( \frac{d^{2} y}{d x^{2}}=-v \frac{d^{2} y}{d t^{2}} \)


The solution of \( \frac{d y}{d x}=\left(\frac{y}{x}\right)^{1 / 3} \) is:
\( \mathbf{A} \cdot x^{2 / 3}+y^{2 / 3}=c \)
B \( \cdot y^{2 / 3}-x^{2 / 3}=c \)
\( \mathbf{C} \cdot x^{1 / 3}+y^{1 / 3}=c \)
D \( \cdot y^{1 / 3}-x^{1 / 3}=c \)


The potential difference between the
ends of a resistance \( \mathrm{R} \) is \( V_{R}, \) between
the ends of capacitor is \( V_{C}=2 V_{R} \) and
between the ends of inductance is \( V_{L}= \)
\( 3 V_{R} \) then the alternating potential of
the source in terms of \( V_{R} \) will be:
A \( \cdot \sqrt{2} V_{R} \)
в. \( V_{R} \)
c. \( \frac{V_{R}}{\sqrt{2}} \)
D. \( 5 V_{R} \)


Two vectors \( A \) and \( \sqrt{3} A \) are acting
perpendicular to each other. What is the angle of resultant vector with \( \boldsymbol{A} \)


An accumulator of emf 2 Volt and
negligible internal resistance is
connected across a uniform wire of
length \( 10 \mathrm{m} \) and resistance \( 30 \Omega \). The
appropriate terminals of a cell of emf
\( \mathbf{1 . 5} V \) olt and internal resistance \( 1 \Omega \) is
connected to one end of the wire, and
the other terminal of the cell is
connected through a sensitive galvanometer to a slider on the wire. If the length of the wire which is required to produce zero deflection of the galvanometer is \( \frac{x}{2} m . \) Find \( x \)


Critical angle is the angle of in denser medium for which the angle of in rarer
medium is
A . incidence, incidence, \( 90^{\circ} \)
B. refraction, refraction, \( 90^{\circ} \)
c. incidence, refraction, \( 90^{\circ} \)
D. refraction, incidence, \( 90^{\circ} \)