\( \int \sec ^{2} x \cdot \operatorname{cosec}^{2} x d x= \)
\( \mathbf{A} \cdot \tan x-\cot x+c \)
B. \( \tan x+\cot x+c \)
c. \( -\tan x+\cot x+c \)
\( D \cdot \sec x \tan x+c \)


An equipotential surface is a surface with constant value of potential at all points on the surface. What is the amount of work done in
moving a \( 2 \mu c \) charge between two
points at \( 3 c m \) apart on an equipotential
surface?


In the given, lewis structure of \( S_{2} O_{3}^{2-} \)
formal charge present on sulphur
atoms 1 and 2 respectively are:
A. \( z e r o,+1 \)
\( \mathbf{B} \cdot+1,+1 \)
\( \mathbf{c} .+2,+2 \)
D. zero, zero


In mitosis, splitting of chromatids up to the centromere takes place in
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


Prachi makes a saturated solution of
potassium chloride in water at \( 353 \mathrm{K} \) and leaves the solution to cool at room
temperature. What would she observe as the solution cools? Explain.


Acid rain is caused by
A. industries
B. power plants
c. automobiles
D. all of above


Before entering the TCA cycle, pyruvic acid converted into acetyl CoA. This process is known as
A. Oxidative carboxylation
B. Oxidative dehydration
c. oxidative decarboxylation
D. Reductive phosphorylation


Describe the two merits of long form periodic table over the Mendeleev's
periodic?


The force experience by charged 'q' moving with velocity with 'v' in magnetic filled be is given by \( \mathrm{F}=\mathrm{qvB} \) Find the dimension of mag field.


Find the fringe width for the pattern
obtained under given arrangement on
the screen.
\( ^{A} \cdot \frac{\lambda f}{2 t} \)
в. \( \frac{\lambda f}{t} \)
c. \( \frac{t f}{\lambda} \)
D. \( \frac{t f}{2 \lambda} \)


The best conductor of heat is
A. Silver
B. Bronze
c. Aluminium
D. copper


If \( \bar{a}, \bar{b}, \bar{c} \) are the position vectors of the points \( A, B, C \) respectively and \( 3 \bar{a}+ \) \( 4 \bar{b}-7 \bar{c}=\overline{0}, \) find the ratio in which
point \( B \) divides the segment \( A C \)


Each capacitors has capacitance \( C \) in
Fig.
Find \( \boldsymbol{C}_{\boldsymbol{A} \boldsymbol{B}} \)
\( A \)
B. 2
\( c \cdot c / 2 \)
D. 3C/2


What is the best (most
accurate)possible representation of the
stereochemical outcome of the addition
of HBr to (R)-4-bromopent-1-ene?
\( A \)
B.
\( c \)
\( D \)


Eccentricity of ellipse \( \frac{x^{2}}{a^{2}+1}+\frac{y^{2}}{a^{2}+2}=1 \)
is \( \frac{1}{\sqrt{3}} \) then length of Latusrectum is
\( A \cdot \frac{8}{\sqrt{3}} \)
B. \( \frac{4}{\sqrt{3}} \)
\( c \cdot 2 \sqrt{3} \)
D. \( \frac{\sqrt{3}}{2} \)


Which type intermolecular force is most likely the most significant intermolecular force for a compound with a low boiling point and a medium molecular weight?
A. Dipole-dipole attraction
B. Hydrogen bonding
c. van der waals forces
D. None of the above


If the rms value of sinusoidal input to a full wave rectifier is \( \frac{v_{o}}{\sqrt{2}}, \) then the rms value of the rectifier's output is?
A \( \cdot \frac{v_{o}}{\sqrt{2}} \)
B. \( \frac{v_{o}^{2}}{\sqrt{2}} \)
c. \( \frac{v_{o}^{2}}{2} \)
D. \( \sqrt{2} V_{o}^{2} \)
E \( .2 V_{o}^{2} \)


If \( X \) represents an element of atomic
number 9 and \( Y \) an element of atomic
number \( 20, \) the compound formed by these elements would be :
A . ionic with formula \( Y X_{2} \)
B. covalent with formula \( Y X_{2} \)
c. ionic with formula \( Y X \)
D. covalent with formula \( Y X \)


A man grows into a giant such that his linear dimensions increases by a factor of \( 9 . \) Assuming that his density remains same, the stress in the leg will change
by a factor of the
A \( \cdot \frac{1}{81} \)
B. 9
\( c \cdot \frac{1}{9} \)
D. 81


Multiply:
\( (-5) \times 8 \) and \( 3 \times(-2) \)
A . 240
B. 420
\( c \cdot-240 \)
D. -420


The functional group present in carboxylic acids is?
A . -coon
B. -co-
c. - -०
D. -CHO


A plane mirror produces a magnification of:
A. zero
B. - -
\( c \cdot+1 \)
D. Between 0 and +1


Very short answer type:
Why is propagation through grafting not successful in monocots?


Find \( p \) if the following have real factors
is
\( 4 x^{2}+3 p x+8=0 \)


\( \frac{x^{2}+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+ \)
\( \frac{B}{x-2}+\frac{C}{x-3} \)
\( \Rightarrow \boldsymbol{A}+\boldsymbol{C}= \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


Fill in the blank.
is most commonly caused by charge separation in cumulonimbus clouds, or thunderheads.
A. Strom
B. Lightning
c. cyclone
D. Hurrican


\( x \)
\( x \)
\( x \)


Four equal circles are described about
four corners of a square so that each
touches two of the others as shown in
the fig. Find the area of the shaded
portion, each side of the square
measuring \( 28 \mathrm{cm} \)


When two identical wires on a
sonometer are kept under same tension, their fundamental frequency is \( 500 H z . \) In order to produce five beats per second, the percentage change in the tension of one of the wires will be:
A . \( 2 \% \)
B. \( 4 \% \)
\( c .6 \% \)
D. \( 8 \% \)


The resistance of solution decreases
with increase in temperature.
A. True
B. False


are
obtained from cotton plant and sheep
respectively.
A. Wool and cotton
B. cotton and wool
c. silk and wool
D. Wool and silk


The viruses contain
A. Proteins only
B. DNA only
C. Nucleic acids only
D. Proteins, DNA or RNA (nucleic acids)


Solids expand more than gases
A. True
B. False


If \( a \) is directly proportional to \( b \) and \( b \) is inversely proportional to \( c . \) Then
what is the proportionality between \( a \)
and \( c ? \)
A . Direct
B. Inverse
c. sometimes direct sometimes inverse
D. Can't be determined


The observation done in preparation of
oxygen by potassium chlorate was:
A. Potassium chlorate melts and decomposes
B. No reaction
c. Potassium chlorate changes its colour
D. Chlorine is evolved as a by-product


When one body rolls over the surface of another body, which kind of friction
does it produce?
A. Static
B. Rolling
c. Fluid
D. sliding


The average depth of Indian ocean
is about 3000 m. The value of fractional
compression \( \frac{\Delta V}{V} \) of water at the
bottom of the ocean is:
[Given that the bulk modulus of water
is \( 2.2 \times 10^{9} N m^{-2}, g=9.8 m s^{-2} \) and
\( \left.\rho_{H_{2}} O=1000 k g . m^{-3}\right] \)
A. \( 3.4 \times 10^{-2} \)
B . \( 1.34 \times 10^{-2} \)
c. \( 4.13 \times 10^{-2} \)
D. \( 13.4 \times 10^{-2} \)


8
8
8


A magnetic field is produced by the two
magnets as shown, the magnetic field
is
A. uniform
B. non-uniform and \( N \) is a strong end
C. non-uniform and \( S \) is a strong end
D. uniform and both \( N \) and \( S \) ends are equally strong


Prism angle of a glass prism is \( 10^{\circ} . \) It's refractive index of red and violet color is
1.51 and 1.52 respectively. Then its dispersive power will be
A. 0.015
B. 0.020
c. 0.011
D. 0.019


Identify the part 'A' from the shown
figure of human eye :
A. Retina
B. Cornea
c. Pupil
D. Iris


The maximum number of sublevels,
orbitals and electrons in n-shell of an
atom are respectively
A .4,12,32
B. 4,16,30
c. 4,16,32
D. 4,32,64


Name the property of matter due to which a body continues in its state of rest or uniform motion unless an
external force acts on it is:
A. Inertia
B. Elasticity
c. viscosity
D. Density


State whether given statement is True or False

The quality factor (Q) is the ratio of true
power to apparent power.
A. True
B. False


Write the short note on the following. Esterification Reaction
Saponification Reaction
Soap and detergents


Solve the following equations:
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\frac{\mathbf{1}}{\boldsymbol{x}}+\frac{\mathbf{1}}{\boldsymbol{y}}+\frac{\mathbf{1}}{\boldsymbol{z}}=\frac{\mathbf{7}}{\mathbf{2}}, \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\mathbf{1} \)


Prove that intersection of equivalence
relations on a set is also an equivalence relation.


The volume of a gas is 5 litres at \( \mathrm{N} \). T.P. what will be its volume at \( 273^{0} \mathrm{C} \) and at
a pressure of four atmospheres
A. 5 litres
B. 2 litres
c. 4 litres
D. 2.5 litres


A bullet is fired from a rifle. If rifle
recoils freely, then K.E. of the rifle is:
A. less than that of the bullet
B. more than that of the bullet
c. same as that of the bullettet
D. equal or less than that of the bullet


Plastic deformation in a material
begins at
A. Qpoint
B. Yield point
c. Proportionality limit
D. Elastic limit


\( N a_{2} C O_{3} \) is used in one of the steps
during the extraction process of silver
from silver coin
State true or false
A . true
B. false
c. cannot be determined
D. none of the above


The charge on a particle is 100 times that of electron. It is revolving in a circular path of radius \( 0.8 \mathrm{m} \) at a frequency of \( 10^{t h} \) revolutions per second. The magnetic field at the centre of path will be -
A \( \cdot 10^{-16} b_{0} \)
0
B. \( \frac{10^{-7}}{\mu} \)
\( \mathbf{c} \cdot 10^{-17} \mu \)
D. \( 10^{-6} \mu \)


A particle has initial velocity \( (3 \hat{i}+ \) \( 4 \widehat{j}) m / s \) and has acceleration \( (0.4 \hat{i}+ \)
\( 0.3 \hat{j}) m / s^{2} . \) Calculate its speed after
\( \mathbf{1 0 s} \)


A single conservative force \( F(x) \) acts on a \( 1.0-k g \) particle that moves along the
x-axis. The potential energy \( U(x) \) is
\( \operatorname{given} \operatorname{by} U(x)=20+(x-2)^{2} \) where \( x \)
is in meters. At \( \boldsymbol{x}=\mathbf{5 . 0} \mathrm{m}, \) the particle
has a kinetic energy of 20 J.What is the
mechanical energy of the system?
A . \( 35 J \)
B. \( 64 J \)
c. \( 86 J \)
D. \( 49 J \)


Solve \( \int(2 t-4)^{-4} d t \)


A plane progressive wave travelling in \( -Y \) direction is represented by the equation \( 2 \cos (2 \pi t+\pi y) . \) If this wave was
travelling in \( X \) direction, the frequency of the wave would have been
A. doubled
B. remains same
c. tripled
D. halved


Complete the following chemical reaction and classify the into (a) hydrolysis, (b) redox and
(c) hydration reactions.
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \)


\( 4 \int \frac{a^{6}+x^{8}}{x} d x \) is equal to
B. \( a^{6} \ln \frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}+c \)
\( I=\sqrt{a^{6}+x^{8}}+\frac{a^{3}}{2} \ln \left|\frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}\right|+c \)
\( ^{\mathrm{D}} a^{6} \ln \frac{\sqrt{a^{6}+x^{8}}+a^{3}}{\sqrt{a^{6}+x^{8}}-a^{3}}+c \)


Identify the correct pair of statements.
(i) Pericycle parenchymatous in dicot root but sclerenchymatous in mature
monocot root
(ii) Pericycle of both dicot and monocot root produces lateral roots during secondary growth
(iii) All cells of dicot root endodermis
are passage cells
(iv) Xylem is produced in centripetal manner in roots of fruit bearing plants.
A. (ii) and (iii)
B. (iii) and (iv)
c. (i) and (ii)
D. (i) and (iv)


toppr \( = \)
Q Type your question
\( A \)
B.
\( c \)
\( D \)


Select the correct option given below:
n \( \triangle A B C, D, E \) and \( F \) are midpoint of \( A B, B C \) and \( A C \) respectively. If
perimeter of \( \triangle A B C=40 \) then find the
perimeter of \( \triangle D E F \)
4.10
в. \( \frac{40}{3} \)
\( c \cdot 20 \)
D.


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{3}(\boldsymbol{a}-\boldsymbol{7}) \boldsymbol{x}^{2}+ \)
\( 3\left(a^{2}-9\right) x-2 \) where \( a>0, \) has \( + \) ive
point of maximum then a varies over an interval of length
\( A \cdot \frac{8}{7} \)
B. \( \frac{6}{7} \)
\( c \cdot \frac{4}{7} \)
D.


Four vertices of a tetrahedron are
(0,0,0),(4,0,0),(0,-8,0) and
\( (0,0,12) . \) Its centroid has the
coordinates
A \( \cdot\left(\frac{4}{3},-\frac{8}{3}, 4\right) \)
В. (2,-4,6)
c. (1,-2,3)
a 5
D. none of these


Naturally occurring amino acids have configuration:
\( A \cdot D \)
B.
c. either D or \( L \)
D. neither D nor L


Match the refining methods (Column I) with metals (Column II)
\( \begin{array}{ll}\text { Column I } & \text { Column } \\ \text { (Refining } & \text { II } \\ \text { methods) } & \text { (Metals) }\end{array} \)
(I) Liquation
(a) \( z \)
(II) zone Refining (b) \( N \)
(III) Mond Process (c) sn
(IV) Van Arkel Method (年) (d) Ga
\( A \)
\( (1)-(b) ;(11)-(c) ;(111)-(d) ;(11)-(a) \)
B. (1) - (b); (II) - (d); (III) - (a); (IV) - (c)
\( c \cdot(1)-(c) ;(11)-(a) ;(111)-(b) ;(11)-(d) \)


Two wires are aligned side by side and both are hooked into different circuits
in which the current is switched on to
allow current to flow in each circuit.
Identify the correct statement.
A. The two currents destructively with each other
B. The two currents constructively interfere with each other
c. The two wires attract and move closer
D. The two wires repel and move away
E. The two wires remain still


n figure, chords \( \overline{P Q} \) and \( \overline{R S} \) intersect
at \( \mathrm{T} . \) If \( \boldsymbol{m} \angle \boldsymbol{R}=\mathbf{5 0}^{\boldsymbol{o}} \) and \( \boldsymbol{m} \angle \boldsymbol{P}=\mathbf{4 6}^{\boldsymbol{o}} \)
the number of degrees in minor arc PR
is
\( A \cdot 84 \)
B. 168
\( c \cdot 42 \)
D. 130
E. cannot be determine


A nuclear transformation is denoted by
\( X(n, \alpha)_{3}^{7} L i . \) Which of the following is
the nucleus of element \( \boldsymbol{X} \) ?
A \( \cdot^{12} C_{6} \)
В \( \cdot \frac{10}{5} B \)
\( c \cdot_{5}^{9} B \)
\( \mathrm{D} \cdot_{4}^{11} \mathrm{Be} \)


Define displacement current.


Assertion
The only way to get \( F_{2} \) from \( F^{-} \) is to oxidise electrolytically
Reason
The recovery of halogens from their halides requires an oxidation process.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of electrons per second flowing through any cross-section of the wire carrying current of \( 1 A \) is
A \( \cdot 3.12 \times 10^{16} \)
В. \( 1.6 \times 10^{18} \)
c. \( 6.25 \times 10^{16} \)
D . 3.12 \( \times 10^{18} \)
E . \( 6.25 \times 10^{18} \)


The order the matrix is \( \left[\begin{array}{lll}2 & 3 & 4 \\ 9 & 8 & 7\end{array}\right] \) is
\( \mathbf{A} \cdot 4 \times 3 \)
B. \( 3 \times 2 \)
\( c \cdot 2 \times 3 \)
D. \( 3 \times 1 \)


Apical dominance is not affected by
A. Indole acetic acid
B. Gibberellic acid
c. Indole acetaldehyde
D. Indole butyric acid


The oxidation number of \( C r \) is +6 in :
This question has multiple correct options
A \( \cdot \operatorname{Fe} C r_{2} O_{4} \)
в. \( K C r O_{3} C l \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5} \)
\( \mathrm{D} \cdot\left[\mathrm{Cr}(\mathrm{OH})_{4}\right]^{8} \)


Fill in the blank:
Mercury and have no
natural satellites
A. Mars
B. Saturn
c. venus
D. Jupiter


The products of the following reactions is(are):
\( \mathbf{C}_{2} \mathbf{H}_{5} \mathbf{B} \mathbf{r}+\mathbf{2} \mathbf{N} \mathbf{a}+\mathbf{C} \mathbf{H}_{3} \mathbf{B} \mathbf{r} \stackrel{d r y e t h e r}{\rightarrow} ? \)
A. ethane
B. propane
c. butane
D. ethane, propane and butane


Fill up the table from the given choice.
Element Oxidation number
-2 in most compounds
(i) in Oxygen \( \quad H_{2} O_{2} \) and
(ii) in \( O F_{2} \)
Halogen
- 1 for
(iii) in all its compounds
(iv) in most of its compounds Hydrogen
(v)in binary metallic hydrides
Sulphur
(vi) in all sulphides
\( \mathbf{A} \cdot(i)+1(i i)+1(i i i) C l(i v)+1(v)-1(v i)+2 \)
B. \( (i)-1(i i)+2(i i i) F(i v)+1(v)-1(v i)-2 \)
\( \mathbf{c} \cdot(i)-1(i i)+1(i i i) F(i v)+1(v)+2(v i)+2 \)
D. \( (i)+1(i i)+2(i i i) C l(i v)+1(v)+1(v i)+6 \)


An auditorium of dimensions \( (100 \times \) \( 40 \times 10) m^{3} \) contains \( 1000 m^{2} \)
curtains of absorption coefficient \( 0.2 m^{-2}, 2000 m^{2} \) of carpets of
absorption coefficient \( 0.7 m^{-2} . \) If 1000
men of absorption coefficients 0.9 per
person are sitting in the hall, then reverberation time is
A . \( 2.7 s \)
B. \( 7.2 s \)
\( c .3 .5 s \)
D. 3.7


\( 15 \mathrm{cc} \) of gaseous hydrocarbon required \( 45 \mathrm{cc} \) of oxygen for complete
combustion and \( 30 \mathrm{cc} \) of \( C O_{2} \) was
formed. The formula of the gaseous compound is:
A. \( C_{3} H_{16} \)
B. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{4} H_{10} \)
D. \( C_{2} H_{4} \)


In which of the following properties, the two enantiomers of lactic acid differ
from each other?
A. Sign of specific rotation
B. Density
c. Melting point
D. Refractive index


Verify Rolle's theoremlquad for the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{-\boldsymbol{x}} \sin \boldsymbol{x}, \boldsymbol{x} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{\pi}] \)


The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of a fraction is
\( 0.25, \) the angle of inclination of the plane is
A \( \cdot 36.8 \)
B . 45
\( c .30 \)
D. \( 42.6^{\circ} \)


Nature's prime balancing and life supporting mechanism operates between
A. Photosynthesis and respiration
B. Evaporation and photosynthesis
c. Evaporation and respiration
D. Transpiration and photosynthesis


Find the inverse of the following \( \operatorname{matrices} \boldsymbol{A}=\left(\begin{array}{ccc}2 & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{1} & \mathbf{1}\end{array}\right) \)


Two equal negative charges are fixed at the points \( (0, \pm a) \) on the \( y \) -axis. \( A \) positive charge \( Q \) is released from rest at the points \( (2 a, 0) \) on the \( x \) -axis. The
charge \( Q \) will :
A. execute simple harmonic motion about the origin
B. move to the origin ad remain at rest
c. move to infinity
D. execute oscillatory but not simple harmonic motion


The red colour to the red blood cells is
due to the presence of
A. Immunoglobin
B. Leghemoglobin
c. Haemoglobin
D. Hemolymph


In the relation \( F=\frac{G M m}{r^{2}}, \) the quantity \( G \)
A. depends on the value of \( g \) at the place of observation.
B. is used only when the earth is one of the two masses.
C. is greatest at the surface of the earth
D. is universal constant in nature.


A student performs an experiment for determination of \( g\left(=\frac{4 \pi^{2} l}{T^{2}}\right), l \approx 1 m \)
and he commits an error of \( \Delta l \). For T he
takes the time of n oscillations with the
stop watch of least count \( \Delta T \) and the
commits a human error of 0.1 sec. For
which of the following data, the measurement of \( g \) will be most
accurate?
A. \( \Delta l-5 m m, \Delta T-0.2 \sec , n-10 \), Amplitude of oscillation \( 5 \mathrm{mm} \)
B. \( \Delta l=5 m m, \Delta T-0.2 \) sec \( , n-20, \) Amplitude of oscillation-
\( 5 \mathrm{mm} \)
c. \( \Delta l-5 m m, \Delta T-0.1 \sec , n- \)
\( 20, \) Amplitude of oscillation \( 1 \mathrm{mm} \)
D. \( \Delta l \) -1mm, \( \Delta T \) -0.1sec, \( n-50 \), Amplitude of oscillation-
\( \mathrm{mm} \)


Which of the following is the weakest base?
A . \( N a O H \)
в. \( \operatorname{Ca}(O H)_{2} \)
с. \( N H_{4} O H \)
D. KOH


Which of the following reaction occurs at
the cathode during the charging of lead
storage battery?
\( \mathbf{A} \cdot P b \rightarrow P b^{2+}+2 e^{-} \)
B \( \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
\( \mathbf{c} \cdot P b O_{2}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
D \( \cdot P b S O_{4}(s)+2 H_{2} O \rightarrow P b O_{2}(s)+4 H^{+}+S O_{4}^{2-}+2 e^{-} \)


For a first order reaction, \( (A) \rightarrow \) product
the concentration of A changes from 0.1 M to \( 0.025 \mathrm{M} \) in 40 minutes. The rate of
reaction when the concentration of A is
\( 0.01 \mathrm{M}, \) is:
A \( \cdot 1.73 \times 10^{-5} \mathrm{Mmin}^{-1} \)
В. \( 3.47 \times 10^{-4} \) М \( \min ^{-1} \)
\( \mathbf{c} \cdot 3.47 \times 10^{-5} \mathrm{Mmin}^{-1} \)
D. \( 1.73 \times 10^{-4} \mathrm{M} \min ^{-1} \)


The capacity of parallel plate capacitor depends on:
A. metal used to make plates
B. thickness of plate
c. potential applied across the plate
D. area of plate


The figure is a graph of the coordinate
of a spider crawling along the \( x \) -axis. \( (a) \)
Graph its velocity and acceleration as
functions of time,
(b) In a motion
diagram, show the position, velocity,
and acceleration of the spider at the five
times: \( t=2.5 s, t=10 s, t=20 s, l=30 s \)
and \( t=37.5 \) s.


Find the area of a square, if the
measure of its each diagonal is \( 12 \mathrm{cm} \)


Write the minors and cofactors of each
element of the first column of the
following matrices \( \boldsymbol{A}=\left[\begin{array}{lll}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right] \)


A very long magnet of pole strength \( 4 A m \) is placed vertically with its one pole on the table. The distance from the pole, the
neutral point will be formed is :
\( \left(B_{H}=4 \times 10^{-5} T\right) \)
A. \( 0.5 m \)
в. \( 0.1 m \)
c. \( 0.15 m \)
D. \( 0.2 m \)


In the extraction of aluminium ;
(i) name the process of concentration of bauxite.
(ii) write the cathode reaction in
electrolytic reduction of alumina.
(iii) write the function and chemical
formula of cryolite.
(iv) write a chemical equation for the action of heat on aluminium hydroxide.
(v) why is it necessary to replace anodes time to time?


Solve the determinant \( \left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ -\boldsymbol{y} & \boldsymbol{x}\end{array}\right| \)


In the following table, given that \( a \) is the
first term, \( d \) the common difference and
\( a_{n} \) the \( n t h \) term of the \( A P \)
(i)
(ii) \( \begin{array}{ccccc}a & d & n & a_{n} \\ 7 & 3 & 8 & \dots \\ -18 & \dots & 10 & 0 \\ \dots & -3 & 18 & -5 \\ -18.9 & 2.5 & \dots & 3.6 \\ 3.5 & 0 & 105 & \dots\end{array} \)
(iii)
(iv)
\( (v) \)
A. \( (i) a_{n}=13(i i) d=1(i i i) a=46(i v) n=9(v) a_{n}=3.5 \)
B. \( (i) a_{n}=36(i i) d=7(i i i) a=46(i v) n=13(v) a_{n}=3.5 \)
C \( \cdot(i) a_{n}=18(i i) d=3(i i i) a=46(i v) n=4(v) a_{n}=3.5 \)
D \( \cdot(i) a_{n}=28(i i) d=2(i i i) a=46(i v) n=10(v) a_{n}=3.5 \)


The velocity \( V \) of a body moving along a
straight line varies with time \( t \) as \( v= \)
\( 2 t^{2} e^{-t}, \) where \( v \) is in \( m / s \) and \( t \) in second
The acceleration of body is zero at \( t= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 2 s \)
\( c .3 \)
D. Both (A) and (B)


An organic compound contains carbon, hydrogen and oxygen. Its elemental analysis gave \( C=38.71 \% \) and
\( \boldsymbol{H}, \boldsymbol{9 . 6 7 \%} \) and \( \boldsymbol{O}=\mathbf{5 1 . 6 2 \%} . \) The
empirical formula of the compound would be:
A \( . C H O \)
в. \( C H_{4} \) О
c. \( C H_{3} O \)
D. \( C H_{2} O \)


Fuels burn to produce heat, light and:
A. \( C O_{2}+ \) water vapour
B. \( C O+O_{2} \)
c. \( C O_{2}+H_{2} \)
D. \( C O+H_{2} \)


If \( y=f(x) \) is continuous on [0,6] differentiable on \( (0,6), f(0)=-2 \) and
\( f(6)=16, \) then at some point between
\( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\mathbf{6}, \mathbf{f}^{\prime}(\mathbf{x}) \) must be equal to?
A . -18
B. -3
\( c .3 \)
D. 14


If \( 30 x^{3}+45 x^{2}-10 x \) is divided by \( 5 x \)
find the resulting coefficient of \( x \)
\( A \cdot 6 \)
B. 9
c. 25
D. 40


Give the balanced equation for the
conversion of argentite into metallic silver.


A planet of mass \( m \) moves around the
sun in an elliptical orbit. Find the total mechanical energy using conservation laws.


By what percentage was the maintenance cost in \( 1997-1998 \) was
lower compared to \( 1999-2000 ? \)
A . \( 33.55 \% \)
B. \( 69.07 \% \)
\( c .54 .23 \% \)
D. \( 67.12 \% \)


A pilot takes off from an airport at \( 15^{\circ} \mathrm{S} \)
latitude and flies \( 55^{\circ} \) due North. What
latitude the pilot has reached?
\( A \cdot 55^{\circ} \mathrm{N} \)
B . \( 40^{\circ} \) N
\( c \cdot 70^{\circ} \)
D. \( 15^{\circ} \mathrm{N} \)


(a) Define the following terms related to proteins:
(i) Peptide linkage
(ii) Primary structure
(iii) Denaturation


The volume of a sphere is \( 1.76 \mathrm{cm}^{3} . \) The
volume of 25 such spheres taking into account the significant figure is:
A \( \cdot 0.44 \times 10^{2} c m^{3} \)
В. \( 44.00 \mathrm{cm}^{3} \)
\( c \cdot 44.0 c m^{3} \)
D. \( 44 \mathrm{cm}^{3} \)


A phosphate mineral has formula
\( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{x}} \boldsymbol{P}_{3} \boldsymbol{O}_{12} \boldsymbol{F} . \) Thus \( \boldsymbol{x} \) is


The area bounded by parabola \( \boldsymbol{y}^{2}=\boldsymbol{x} \)
straight line \( y=4 \) and \( y-a x i s \) is-
A \( \cdot \frac{16}{3} \)
B. \( 7 \sqrt{2} \)
c. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)


In which one of the following, expenditure of energy is required?
A. Osmosis
B. Diffusion
c. Active transport
D. Passive transport


\( \sqrt{i}+\sqrt{-i}=? \)
A \( \cdot \sqrt{2} \)
B. \( -\sqrt{2} \)
\( c \cdot \pm \frac{1}{\sqrt{2}} \)
D. \( \pm \sqrt{2} \)


Two particles move in space with
nonzero initial relative velocity and
nonzero constant relative acceleration.
Then:
This question has multiple correct options
A. It is possible that motion of one particle with respect to another is straight line
B. Path of one as observed by another will always be curved
C. It is possible that one particle will be at rest with respect to another at a certain moment during the motion
D. The particles will always be moving away from each other


Four particles each of mass \( m \) are lying symmetrically on the rim of a disc of mass \( M \) and radius \( R \). The moment of
inertia of this system about an axis passing through one of the particles and perpendicular to the plane of the disc is :
A \( \cdot 16 m R^{2} \)
в. \( \quad(3 M+16 m) \frac{R^{2}}{2} \)
\( \mathrm{c} \cdot_{(3 m+16 M)} \frac{R^{2}}{2} \)
D. Zero


The equi-potential surface in the region
are
A. planes parallel to \( X Y \) plane
B. planes parallel to \( Z Y \) plane
C. planes parallel to \( X Z \) plane
D. None of the above


It is known as squirting cucumber
A. cucurbita
B. Ecballium
c. Nicotianna
D. Calotropis


The condition for destructive
interference is path difference should
be equal to :
A. odd integral multiple of wavelength
B. Integral multiple of wavelength
c. odd integral multiple of half wavelength
D. Integral multiple of half wavelength


Assertion
Sound waves do not travel through
vacuum
Reason
Sound waves are mechanical waves
which require a medium for their
propogation
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


\( \alpha- \) particles can be detected using :
A. thin aluminium sheet
B. barium sulphate
c. zinc sulphide screen
D. gold foil


As one considers orbits with higher values of \( n \) in a hydrogen atom, the
electric potential energy of the atom
A. decreases
B. increases
c. remains the same
D. does not increase


\( \log \frac{K_{p}}{K_{c}}+\log R T=0 \) is true relationship
for the following reaction:
A \( . P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
в. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
c. \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
D. \( (b) \) and \( (c) \) both


\( \boldsymbol{B} \boldsymbol{X}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{B} \boldsymbol{X}_{3} \cdot \boldsymbol{N} \boldsymbol{H}_{3}+ \) Heat of
adduct formation \( (\Delta H) \)
The numerical value of \( \Delta H \) is found to
be maximum for:
\( A \cdot B F_{3} \)
в. \( B C l_{3} \)
\( \mathrm{c} . B B r_{3} \)
D. \( B I_{3} \)


\( N i(C O)_{4} \) and \( \left[N i(C N)_{4}\right]^{-2} \) both are
tetrahedral in shape.
A. True
B. False


Five conducting plates are placed parallel to each other Separation
between them is \( d \) and area of each
plate is \( A \). Plate number 1,2 and 3 are
connected with each other and at the
same time through a cell of emf \( \boldsymbol{E} \). The
charge on plate number 1 is
\( \mathbf{A} \cdot E \varepsilon_{0} A / d \)
B . \( E \varepsilon_{0} A / 2 d \)
\( \mathbf{c} \cdot 2 E \varepsilon_{0} A / d \)
D. zero


Incorrect about geometrical growth
A. After mitosis both daughter cells retain the capacity of division
B. Growth pattern follows sigmoid curve
C. Less common than arithmetic growth in the plants
D. Growth rapidly increases


Imagine a cannon being fired on the surface of the moon. Then
A. the sound will be heard at the surface of the earth during all seasons
B. the sound will not be heard at the surface of the earth
c. the sound will be heard at the surface of the earth during the rainy season
D. no sound will be heard on the earth but it can be heard on the moon


Cell constant of a conductivity cell is:
A. specific conductance / resistance
B. specific conductance \( \times \frac{1000}{\text { Normality }} \)
c. specific conductance / conductance
D. conductance / specific conductance


The nth term of the A.P. is \( 2 n-5 \), then
the series is :
A. \( -3,-1,1, \ldots \)
.
в. \( 3,1,-1, \ldots \)
c. \( 2,5,8, \dots \dots \)
D. \( 1,7,13, \ldots \ldots \)


The electric field at a point \( 2 \mathrm{cm} \) from an infinite line charge of linear charge density \( 10^{-7} \mathrm{cm}^{-1} \) is?
A \( \cdot 4.5 \times 10^{4} N C^{-1} \)
B. \( 9 \times 10^{4} N C^{-1} \)
c. \( 9 \times 10^{2} N C^{-1} \)
D. \( 18 \times 10^{4} N C^{-1} \)


A teacher one day pointed out to his students the peculiar fact that water is a unique liquid that freezes exactly at
\( 0^{\circ} \mathrm{C} \) and boils exactly at \( 100^{\circ} \mathrm{C} . \) He
asked the students to find the correct
statement based on this fact.
Which of the statements is true
regarding the above fact?
A. Water dissolves anything however sparingly the dissolution may be
B. Water is a polar molecule.
C. Boiling and freezing temperatures of water were used to define a temperature scale.
D. Liquid water is denser than ice


The number of times by which an electron is lighter than a hydrogen
atom:
A . 1840
в. 1837
\( c .1836 \)
D. none of the above


Ammonia is a weak base that reacts
with water according to the equation:
\( N H_{3}(a q)+2 H_{2} O(l) \quad \rightleftharpoons \)
\( N H_{4}^{+}(a q)+O H^{-}(a q) \)
Which of the following conditions will decrease the moles of ammonium in
water?
This question has multiple correct options
A. Addition of \( H C l \)
B. Addition of \( N a O H \)
c. Addtion of \( N H_{4} C l \)
D. Addition of \( H_{2} O \)


In the given figure, \( D E \| B C \) and
\( A D: D B=5: 4, \) find \( \frac{\operatorname{area}(\Delta D F E)}{\operatorname{area}(\Delta C F B)} \)
4. 5: 9
B . 25: 16
c. 25: 81
D. 81: 25


Which is the monomer of Neoprene in
the following?
A \( \cdot C H_{2}=C H-C=C H \)
B. \( C H_{2}=C\left(C H_{3}\right)-C H=C H_{2} \)
c. \( C H_{2}=C(C l)-C H=C H_{2} \)
D. \( C H_{2}=C H-C H=C H_{2} \)


Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
(i) 243
(ii) 256
(iii) 72
(iv) 675
\( \mathbf{1 0 0} \)


Which of the following statement is correct about an aqueous solution of an acid and a base?
(i) Higher the pH, stronger the acid.
(ii) Higher the pH, weaker the acid.
(iii) Lower the pH, stronger the base.
(iv) lower the pH, weaker the base.
\( A \cdot \) (i) and (iii)
B. (ii) and (iii)
c. (i) and (iv)
D. (ii) and (iv)


In a certain population, only 0.03 percent of the people have physical trait
X. On the average, it will be necessary to screen how many people to find six percent of them with trait X?
A. 180
в. 200
\( c .1800 \)
D. 20000


What will be the order of reaction and
rate constant for a chemical change
having \( \log t_{50} \% \) vs log concentration of
\( (A) \) curves as:
A \( .0,1 / 2 \)
B. 1,1
c. 2,2
D. 3


Which of the following is found exclusively in the sea water?
A. Prawns
B. Trygon
c. crabs
D. oysters


The peak voltage of 220 Volt \( A C \) mains (in Volt) is :
A. 155.6
B. 220.0
\( c .31 \)
D. 440.0


Magnetic flux \( \phi \) linked with a stationary loop of resistance \( R \) vaires with time \( t \)
as \( \phi=a t(T-t) . \) Amount of heat
generated in loop during time interval \( \boldsymbol{T} \)
is
\( ^{\mathbf{A}} \cdot \frac{a T}{3 R} \)
\( ^{\mathbf{B}} \cdot \frac{a^{2} T^{2}}{3 R} \)
c. \( \frac{a^{2} T^{2}}{R} \)
D. \( \frac{a^{2} T^{3}}{3 R} \)


toppr
Q Type your question
end, the shape of wave at time \( t=3 s \) is
\( A \)
B.
\( c \)
\( D \)


The value of \( \int \frac{\log x}{(x+1)^{2}} d x \) is
A \( \cdot \frac{-\log x}{x+1}+\log x-\log (x+1)+C \)
B. \( \frac{\log x}{x+1}+\log x-\log (x+1)+C \)
c. \( \frac{\log x}{x+1}-\log x-\log (x+1)+C \)
D. \( \frac{-\log x}{x+1}-\log x-\log (x+1)+C \)


A curve passing through the point (1,1) is such that the intercept made by a tangent to it on \( x \) -axis is three times the
x co-ordinate of the point of tangency, then the equation of the curve is:
A \( \cdot y=\frac{1}{x^{2}} \)
в. \( y=\sqrt{x} \)
c. \( y=\frac{1}{\sqrt{x}} \)
D. none


Which of the following statement is
true?
A. Mother determines the sex of the child.
B. Father inherits the character to the son only.
C. Father inherits the character to daughter only.
D. None of the above.


Rutherford's experiment established
that:
This question has multiple correct options
A. inside the atom there is a heavy positive centre
B. nucleus contains protons and neutrons
C. most of the space in an atom is empty
D. size of nucleus is very small


A cell of emf \( e_{1} \) in the secondary circuit gives null deflection for \( 1.5 \mathrm{m} \) length of potentiometer of wire length \( 10 \mathrm{m} \). If
another cell of emf \( e_{2} \) is connected in
series with \( e_{1} \) then null deflection was
obtained for \( 2.5 \mathrm{m} \) length. Then \( \mathrm{e}_{1}: \mathrm{e}_{2} \) is:
A . 3: 5
B. 5: 3
\( c \cdot 3: 2 \)
D. 2: 3


For a particle performing uniform circular motion, choose the incorrect
statement from the following.
A. Magnitude of particle velocity (speed) remains constant
B. Particle velocity remains directed perpendicular to radius vector
c. Direction of acceleration keeps changing as particle moves
D. Magnitude of acceleration does not remain constant


The construction of \( \Delta L M N \) when
\( M N=7 \mathrm{cm} \) and \( m \angle M=45^{\circ} \) is not
possible when difference of \( L M \) and
\( \boldsymbol{L} \boldsymbol{N} \) is equal to:
A . 4.5
B. 5.5
\( c .6 .5 \)
D. 7.5


Find the unknown number: \( \dots \dots \dots-. . \) \( \frac{3}{7}=\frac{3}{7} \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. 1
\( c \cdot \frac{3}{7} \)
D.


A piece of paper appears to be attracted
to a charged ebonite rod, even before
they touch (see fig.). The charge at B is:
A. positive
B. may be positive or negative
c. no charge
D. negative


Dichorism means
A. selective absorption of unpolarised light.
B. selective absorption of dispersed light.
C . selective absorption of scattered light.
D. selective absorption of one of the polarised component.


In a coaxial, straight cable, the central conductor and the outer conductor
carry equal currents in opposite directions. The magnetic field is zero:
A. outside the cable
B. inside the inner conductor
c. inside the outer conductor
D. in between the two conductors


Light from the sun strikes the concave
mirror pictured below. The image of the
sun is formed at the point indicated.
When we place an object closer to the
mirror than this point, what are the
characteristic of the image formed
(Size is compared to object)?
A. Larger, real, inverted
B. Smaller, real, inverted
c. Smaller, virtual, upright
D. Larger, virtual, upright
E. No image is formed


Two solutions of glucose have osmotic
pressures 1.5 and \( 2.5 a t m .1 L \) of first is
mixed with \( 2 L \) of second solution, the
osmotic pressure of the resultant solution is:
A . \( 2.5+1.5 a t m \)
B. 2.5 - 1.5atm
c. \( \frac{2.5+1.5}{2} \) at
D. \( 2.16 a t m \)


Bhopal gas tragedy in 1984 was caused by :
A. carbon monoxide
B. phosgene
c. methyl isocyanide
D. methyl isocyanate


Assertion
Soaps and detergent are macro-
molecular colloids.
Reason
Soaps and detergent are molecules of
large size.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In which of the following pairs, indicated bond is of greater strength?
and
\( A \)
B. I
c. Both are equal
D. None of the above


Choose the correct answer from the
alternatives given Which of the following is most closely associated with the Calvin cycle?
A. ATP production
B. Oxygen production
c. Carbon dioxide fixation
D. Carbon dioxide production


A satellite is launched into a circular
orbit of radius \( R \) around the earth.
Another second satellite is launched
into an orbit of radius \( 1.01 R \). The
period of the second satellite is longer than that first by approximately
A . \( 0.5 \% \)
в. \( 1.0 \% \)
c. \( 1.5 \% \)
D. 3.0\%


Amit carried a box up the flight of stairs
shown in the diagram

He did \( 150 \mathrm{J} \) of work in the process. The
mass of the box is
A \( .7 .5 \mathrm{kg} \)
B. \( 75 \mathrm{kg} \)
\( \mathbf{c} \cdot 15 k g \)
D. \( 150 \mathrm{kg} \)


lonic compounds does not exits as molecules.
A. True
B. False


When we see an object, the image formed on the retina is
(i) real (ii) virtual(iii) erect (iv) inverted
A. (i) and (iv) only
B. (i), (ii), (iii)
c. (iv) only
D. (ii) and (iv)


Observation Time (in \( \quad \boldsymbol{P}_{\boldsymbol{x}} \) (in \( \mathrm{mm} \)
minute) \( \quad \) of \( \mathrm{Hg} \)
800
00 to
At constant temperature and volume \( \boldsymbol{X} \)
\[
\text { decomposes as } 2 \mathrm{X}(\mathrm{g}) \rightarrow 3 \mathrm{Y}(\mathrm{g})+
\]
\( 2 \mathrm{Z}(\mathrm{g}), \) where \( \mathrm{P}_{x} \) is the partial pressure
of \( X . \) What is the order of reaction with
respect to \( X ? \)
(i) Find the rate constant.
(ii) Find the time for \( 75 \% \) completion of the reaction.
(iii) Find total pressure when pressure
of \( X \) is \( 700 \mathrm{mm} \) of Hg.


Statement-I: Alkali metals dissolve in
liquid ammonia to give blue solutions Statement-II: Alkali metals in liquid ammonia give solvated species of the
type \( \left[M\left(N H_{3}\right)_{n}\right]^{+}(M=\text { alkali metals }) \)
A. Statement-l is true; Statement-ll is true; Statement-I is the correct explanation for Statement-
B. Statement-l is true; Statement-ll is true; Statement-1 is not the correct explanation for statement-
c. Statement-l is true; Statement-ll is false
D. Statement-I is false; Statement-II is true


The length of a wire under stress changes by \( 0.01 \% . \) The strain produced is
A \( \cdot 10^{-4} \)
B. 0.01
c. 1
D. \( 10^{4} \)


The rate of photosynthesis decreases if the wavelength of visible light exceeds \( 680 \mathrm{nm} . \) This was shown by which scientist and what is it's reason?
A. Black man - Law of limiting factor
B. Calvin and Benson - Photooxidation
c. Emerson and Arnold - Red drop
D. Ruben and Kamen - Photolysis


The value of \( (a+b)^{2}-2(a-b)^{2}+ \)
\( (a-b)(a+b) \) is
A \( \cdot 4 a b-b^{2} \)
B . \( 2 a b-b^{2} \)
\( c \cdot 3 a b-b^{2} \)
D. \( 6 a b-2 b^{2} \)


A motor car is travelling at \( 30 m / s \) on a
circular road of radius \( 500 m \). It is
increaseing in speed at the rate of
\( 2 m / s^{2} . \) Then the acceleration of the car
will be
A \( \cdot 4 m / s^{2} \)
B . \( 3 m / s^{2} \)
c. \( 2.7 m / s^{2} \)
D. \( 8 m / s^{2} \)


Coke is a smokeless fuel.
A. True
B. False


Find the magnitude of charge appearing on each piece


If \( \boldsymbol{A}=(\mathbf{0}, \mathbf{0}, \mathbf{2}), \boldsymbol{B}=(\sqrt{\mathbf{2}}, \sqrt{\mathbf{2}}, \mathbf{2}), \boldsymbol{C}= \)
\( (\sqrt{2}, \sqrt{2}, 0) \) and \( D= \)
\( \left(\frac{8 \sqrt{2}-20}{17}, \frac{12 \sqrt{2}+4}{17}, \frac{20-8 \sqrt{2}}{17}\right) \)
then \( A B C D \) is a
A. rhombus
B. square
c. parallelogram
D. none of these


Astronomical unit (AU) is the distance
between earth and the sun, 1 AU is equal
to the
A \( \cdot 1.496 \times 10^{8} k m \)
В. \( 9.46 \times 10^{12} k m \)
c. \( 3.084 \times 10^{13} k m \)
D. \( 4.596 \times 10^{15} \mathrm{km} \)


Precious stones, such as gem stones,
are products of
A. Volcanic rocks
B. Sedimentary rocks
c. Metamorphic racks
D. Igneous rocks


(i) Write the balanced chemical
equation to prepare ammonia gas in the laboratory by using an alkali
(ii) State why concentrated sulphuric acid is not used for drying ammonia
gas.
(iii) Why is ammonia gas not collected
over water?


The element evolving two different
gases on reaction with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is :
A. \( P \)
в. \( C \)
\( \mathrm{c} . \) Н \( g \)
D.


Find
\( \sqrt{\boldsymbol{i}}+\sqrt{-\boldsymbol{i}} \)


Adrenal gland is associated with
A. Pharynx
B. Pancreas
c. Kidney
D. Brain


A body is moving in a circle with a speed of \( 1 m s^{-1} . \) This speed increases
at a constant rate of \( 2 m s^{-1} \) every second. Assume that the radius of the
circle described is 25 m. The total
acceleration of the body after \( 2 s \) is:
\( \mathbf{A} \cdot 2 m s^{-2} \)
B. \( 25 m s^{-2} \)
c. \( \sqrt{5} m s^{-2} \)
D. \( \sqrt{7} m s^{-2} \)


If \( y=\frac{1}{\sqrt{a^{2}-x^{2}}}, \) find \( \frac{d y}{d x} \)


A body thrown vertically up reaches a maximum height of 50m. Another body
with double the mass thrown up with
double the intial velocity will reach a maximum height of
\( \mathbf{A} \cdot 100 m \)
B. \( 200 m \)
\( c .400 m \)
D. \( 50 m \)


At constant temperature, the osmotic
pressure of a solution is:
This question has multiple correct options
A. directly proportional to the concentration
B. inversely proportional to the molar mass of solute
C. directly proportional to the square of the concentration
D. directly proportional to the square root of the concentration


The highest ionization energy is exhibited by:
A. halogens
B. alkaline earth metals
c. transition metals
D. noble gas


In the circuit shown below, \( V_{A} \) and \( V_{B} \)
are the potentials at \( A \) and \( B, R \) is the
equivalent resistance between A and B,
\( S_{1} \) and \( S_{2} \) are switches, and the diodes
are idea
This question has multiple correct options
\( \mathbf{A} \cdot \) if \( V_{A}>V_{B}, S_{1} \) is open and \( S_{2} \) is closed then \( R=8 \Omega \)
B. if \( V_{A}>V_{B}, S_{1} \) is closed and \( S_{2} \) is open then \( R=12.5 \Omega \)
C. if \( V_{A}>V_{B}, S_{1} \) is open and \( S_{2} \) is closed then \( R=12.5 \Omega \)
D. if \( V_{A}>V_{B}, S_{1} \) is closed and \( S_{2} \) is open then \( R=8 \Omega \)


\( A l F_{3} \) is soluble in \( H F \) only in presence
of \( K F \). It is due to the formation of :
A. \( A l H_{3} \)
B . \( K\left[A l F_{3} H\right] \)
c. \( K_{3}\left[A l F_{3} H_{3}\right] \)
D. \( K_{3}\left[A l F_{6}\right] \)


Identify the compound A among the
following compounds.
A. o-terephthalic acid
B. o-terephthalaldehyde
C. Salicylic acid
D. None of these


Everything in the universe is made up of material called as
A . life
B. water
c. matter
D. None of the above


Express \( 0 . \overline{38} \) as a rational number in
simplest form.


Equation of the curve through the origin satisfying \( \boldsymbol{d} \boldsymbol{y}=(\sec \boldsymbol{x}+\boldsymbol{y} \tan \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \) is:
A. \( y \sin x=x \)
B. \( y \cos x=x \)
\( \mathbf{c} \cdot y \tan x=x \)
D. none of these


A majority of farmers in India depend
upon for irrigating their
crops.
A . rains
B. tube wells
c. hand pumps
D. canals


Find the median of the following values:
37,31,42,43,46,25,39,45,32


\( \boldsymbol{C O}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O H} \)
Which catalyst is used in the above
reaction?
\( \mathbf{A} \cdot M n O_{2} \)
в. \( F e C l_{3} \)
c. \( P d C l_{2} \)
D. \( Z n O / C u O \)


Find the tenth term of the A.P:
\( \mathbf{7}, \mathbf{1 3}, \mathbf{1 9}, \mathbf{2 5}, \dots \)


The angle between incident ray and
reflected ray is \( 90^{\circ} . \) Find the angle of
reflection.
A \( .90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. Can't be predicted


A compound \( A \) dissociate by two parallel first order paths at certain temperature \( \boldsymbol{A}(\boldsymbol{g}) \stackrel{\boldsymbol{k}_{1}\left(\min ^{-1}\right)}{\longrightarrow} \boldsymbol{2} \boldsymbol{B}(\boldsymbol{g}) \boldsymbol{k}_{1}=\boldsymbol{6} . \boldsymbol{9} \boldsymbol{3} \times \)
\( 10^{-3} \min ^{-1} \)
\( \boldsymbol{A}(\boldsymbol{g}) \stackrel{\boldsymbol{k}_{2}\left(\min ^{-1}\right)}{\longrightarrow} \boldsymbol{C}(\boldsymbol{g}) \boldsymbol{k}_{2}=\boldsymbol{6} . \boldsymbol{9} \boldsymbol{3} \times \)
\( 10^{-3} \min ^{-1} \)
The reaction started with 1 mole of pure
\( A^{\prime} \) in 1 litre closed container with initial
pressure 2 atm. What is the pressure (in atm) developed in container after 50 minutes from start of experiment?
A . 1.25
в. 0.75
c. 1.50
D. 2.50


\( \int \frac{\sec ^{2} x d x}{\sqrt{\tan ^{2} x+4}}= \)
A \( \cdot \ln (\tan x+\sqrt{\tan ^{2} x+4})+C \)
B. \( \frac{1}{2} \ln (\tan x+\sqrt{\tan ^{2} x+4})+C \)
c. \( \ln \left(\frac{1}{2} \tan x+\frac{1}{2} \sqrt{\tan ^{2} x+4}\right)+C \)
D. None of these


Action and reaction act on:
A. same body in opposite directions
B. different bodies in opposite directions
C. different bodies, but in same direction
D. same body in same direction


The human offspring can be of two types with \( \mathrm{XX} \) and \( \ldots \ldots . . . \) chromosomes.
A. \( x y \)
B. xxx
\( c \cdot x x x \)
D. YY


Match the second column with the first
column:


If the points \( (1,1, p) \) and (-3,0,1) be equidistant from the plane \( \vec{r} .(3 \hat{i}+ \) \( 4 \hat{j}-12 \hat{k})+13=0, \) then find the value
of \( p \)


The precipitate of \( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{s p}=\mathbf{1 . 7} \times\right. \)
\( \left.10^{-10}\right) \) is obtained when equal volumes
of the following are mixed
\( \mathbf{A} \cdot 10^{-4} M C a^{2+}+10^{-4} M F^{-} \)
B. \( 10^{-2} M C a^{2+}+10^{-3} M F^{-} \)
c. Both A and B
D. None of these


Rutherfords alpha particle scattering experiment, which established the nuclear model of the
atom, used a beam of:
A. alpha particles, which impinged on a metal foil and got scattered
B. beta particles, which impinged on a metal foil and got absorbed
c. helium atoms, which impinged on a metal foil and got scattered
D. helium nucleus, which impinged on a metal foil and ejected electrons


Elements of which of the following \( \operatorname{group}(s) \) of periodic table do not form hydrides?
A. Groups 7, 8, 9
B. Group 13
c. Groups 15,16,17
D. Group 14


are those with
structure similar to that of earth.


The IUPAC name of acetyl acetone is :
A. pentane-2,5-dione
B. pentane-2,4-dione
c. hexane- 2,4 -dione
D. butane-2,4-dione


If, \( A=\{5,7\}, B=\{7,5\}, \) then \( A \) and \( B \)
are
A. Equal sets
B. Unequal sets
c. Null sets
D. None of these


Which among the following alloys is
used in making instruments for
electrical measurement?
A. Stainless steel
B. Manganin
c. spiegeleisen
D. Duralumin


Four fifth of a number is 4 more than
three fourth of the number. Find the
number.


Consider two satellites \( A \) and \( B \) of equal
mass \( \mathrm{m}, \) moving in the same circular
orbit about the earth, but in the
opposite sense as shown in Figure. The orbital radius is \( r \). The satellites
undergo a collision which is perfectly
inelastic. For this situation, mark out
the correct statement(s). [Take mass of
earth as \( \mathrm{M}] \)
(6)
A. The satellites starts falling towards center of the earth.
B. The total energy of the two satellites plus earth system just after collision is \( -2(G M m) / r \)
C. The total energy of two satellites plus earth system just after collision is \( -(G M m) / 2 r \)
D. The combined mass(two satellites) will fall towards the earth just after collision.


These two quadrilaterals are similar
What is the value of \( x \) (the length of B'C')
A \( \cdot 2 \frac{2}{3} \)
B. 5
\( c \cdot 6 \)
D. \( 6 \frac{2}{3} \)


Assertion
Inspiration occurs due to muscular
relaxation.
Reason
During inspiration, the diaphragm and
external intercostal muscle contract
simultaneously.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The image of the needle placed \( 45 \mathrm{cm} \) from a lens is formed on a screen placed \( 90 \mathrm{cm} \) on the other side of the lens. The
displacement of the image, if the needle is moved by \( 5.0 \mathrm{cm} \) away from the lens is
A. \( 10 \mathrm{cm} \), toward the lens
B. \( 15 \mathrm{cm} \), away from the lens
c. \( 15 \mathrm{cm} \), towards the lens
D. \( 10 \mathrm{cm}, \) away from the lens


Which one of the following is correct about \( H \) -bonding in nucleotide?
A. \( A-T, G-C \)
в. \( A-G, T-C \)
\( c \cdot G-T, A-C \)
D. \( A-A, T-T \)


Is 1188 a perfect cube? If not, by which smallest natural number should it be
divided so that the quotient is a perfect cube?
A . 44
B. 33
\( c \cdot 22 \)
D. 1


A person trying to lose weight by burning fat lifts a mass of \( 10 k g \) upto a
height of \( 1 m 1000 \) times. Assume that
the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work dine only when the weight is lifted up? Fat supplies \( 3.8 \times 10^{7} J \) of energy
per kg which is converted to
mechanical energy with a \( 20 \% \) efficiency rate. Take \( g=9.8 m s^{-2} \)
A \( \cdot 6.45 \times 10^{-3} k g \)
в. \( 9.89 \times 10^{-3} k g \)
c. \( 12.89 \times 10^{-3} k g \)
D. 2.45 \( \times 10^{-3} k g \)


Thiamine is a:
A. pyrimidine
B. purine
C. carbohydrate
D. vitamin \( \left(B_{1}\right) \)


The coordinates of the points in which the line joining the points (2,5,-7) and (-3,-1,8) are intersected by the \( y-z \)
plane are
A \( \cdot\left(0, \frac{13}{5},-1\right) \)
B \( \cdot\left(0, \frac{-13}{5},-2\right) \)
D. \( \left(0, \frac{13}{5}, \frac{2}{5}\right) \)


Prove that:
\( \left|\begin{array}{ccc}a^{2}+2 a & 2 a+1 & 1 \\ 2 a+1 & a+2 & 1 \\ 3 & 3 & 1\end{array}\right|=(a-1)^{2} \)


Which of the following reagents will
best convert nitrobenzene into \( 2,4,6- \)
trichlorobromobenzene?
A. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{Cl}_{2}(a q), \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C} ; \mathrm{CuBr} \)
B . \( C l_{2} / A l C l_{3}, S n C l_{2} / H C l, N a N O_{2} / H C l-0^{o} C ; C u B r \)
c. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{Br}_{2}-\mathrm{H}_{2} \mathrm{O}, \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C} ; \mathrm{CuCl} \)
D. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C}, \mathrm{H}_{2} \mathrm{O}, \mathrm{Cl}_{2}(\mathrm{aq}) ; \mathrm{HB} \)


Alkanes are saturated hydrocarbons
because :
A. they have double bonds
B. they have triple bonds
c. they have single bonds
D. they do not have bonds


A transistor is a two junction and two terminal device
A. True
B. False


National tree of India is
A. Mangifera indica
B. Azadirachta indica
C. Ficus bengalensis
D. Ficus religiosa


If a and b are two unequal positive numbers, the:
A \( \cdot \frac{2 a b}{a+b}>\sqrt{a b}>\frac{a+b}{2} \)
B . \( \sqrt{a b}>\frac{2 a b}{a+b}>\frac{a+b}{2} \)
C \( \cdot \frac{2 a b}{a+b}>\frac{a+b}{2}>\sqrt{a b} \)
D \( \cdot \frac{a+b}{2}>\frac{2 a b}{a+b}>\sqrt{a b} \)
E \( \cdot \frac{a+b}{2}>\sqrt{a b}>\frac{2 a b}{a+b} \)


In gymnosperms, the ovule is naked because
A. Ovary wall is absent
B. Integuments are absent
c. Perianth is absent
D. Nucellus is absent


A particle of mas \( m \) carrying charge \( q \) is released from restm in a uniform
electric field of intensity \( \boldsymbol{E} \). The kinetic energy acquired by the particle after moving a distance of \( x \) is (neglect gravitational force):
A \( . q E x \)
В \( \cdot q E x^{2} \)
\( \mathbf{c} \cdot q E^{2} x \)
D. \( q^{2} E x \)


Density of carbon monoxide is
maximum at:
\( \mathbf{A} \cdot 0.5 a t m \) and \( 273 K \)
B. 4 atm and \( 500 K \)
c. 2 atm and \( 600 K \)
D. 6 atm and \( 1092 K \)


What characteristic property of light is responsible for the blue colour of the
sky?
A. Interference
B. Diffraction
c. scattering
D. Dispersion


When a light ray is directed parallel to
principal axis of a concave mirror
A. real image is formed
B. a diminished image is formed
c. inverted image is formed
D. All the above


The order of reaction for which half-life
period is independent of initia
concentration is:
A. zero
B. first
c. second
D. third


In the circuit shown in figure, if the
diode forward voltage is \( 0.3 V, \) the
voltage difference between \( A \) and \( B \) is
A. \( 1.3 V \)
B . \( 2.3 V \)
c.
D. \( 0.5 V \)


Decompose the vector \( \vec{b}=6 \hat{i}-3 \hat{j}-6 \hat{k} \) into two vectors, \( \vec{c} \) and \( \vec{d} \), one of which is parallel and the other perpendicular to the vector \( \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)


A sine wave is travelling in a medium. particular particle has zero displacement at a certain instant. the particle closest to it having zero displacement is at a distance
\( A \cdot \lambda / 4 \)
B. \( \lambda / 3 \)
c. \( \lambda / 2 \)
\( D . \lambda \)


If a graph is plotted between \( T^{2} \) and \( r^{3} \)
for a planet, then its slope will be
A \( \cdot \frac{4 \pi^{2}}{G M} \)
в. \( \frac{G M}{4 \pi^{2}} \)
\( \mathrm{c} .4 \pi G M \)
D. zero


The compound \( C_{4} H_{10} O \) can show
A. chain isomerism
B. position isomerism
c. functional isomerism
D. all of the above


What is the distance between the
\( \operatorname{lines} 3 x+4 y=9 \) and \( 6 x+8 y=18 ? \)
A.
B. 3 units
c. 9 units
D. 18 units


the number of real solutions of the
equation \( \tan ^{-1} \sqrt{x^{2}-3 x+2}+ \)
\( \cos ^{-1} \sqrt{4 x-x^{2}-3}=\pi \) is
A. one
B. two
c. zero
D. infinite


\( \int_{\pi / 4}^{3 \pi / 4} \frac{d x}{1+\cos x} \) is equal to
\( A \cdot 2 \)
B. -2
\( c \cdot 1 / 2 \)
D. \( -1 / 2 \)


Q Type your question-
\( T_{A}=300 \mathrm{K} . \) At time \( t=0 \) the
temperature of \( X \) is \( T_{0}=400 K . \) It cools
according to Newton's law of cooling. At
time \( t_{1}, \) its temperature is found to be
\( 350 \mathrm{K} \)
At this time \( \left(t_{1}\right), \) the body \( X \) is connected to a large body Y at atmospheric temperature \( \boldsymbol{T}_{\boldsymbol{A}}, \) through a conducting rod of length L, cross-
sectional area \( A \) and thermal
conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area \( A \) of the connecting rod is small compared to the surface area of \( X . \) Find the temperature of \( X \) at
time \( t=3 t_{1} \)
A. \( \quad \frac{2 K A}{I} \) ti
\[
T=\left[12.5 e^{\frac{C L}{1}}+900\right] K
\]
B. \( \left.\quad \frac{2 K A}{C^{t_{1}}}+300\right] K \)
\( T=\left[12.5 e^{C L}\right. \)
c. \( \left.\quad \frac{2 K A}{l^{t_{1}}}+600\right] K \)
\( T=\left[12.5 e^{C L}\right. \)
D. \( \quad T=\left[12.5 e^{\frac{2 K A}{C L} t_{1}}+700\right] K \)


The following table gives the current \( i \)
through two devices for several values
of potential difference \( V \) of Device 1 Device \( 2(\text { SI Units }) \)
\( \begin{array}{llll}\text { Device } & \text { Device } & \text { Device } & \text { Device } \\ 1 & 1 & 2 & 2 \\ V & I & V & I \\ 2 & 4.5 & 2 & 1.5 \\ 3 & 6.75 & 3 & 2.2 \\ 4 & 9 & 4 & 2.8\end{array} \)
A. Device 1 is ohmic, device 2 is non ohmic
B. Device 1 is non ohmic, device 2 is ohmic
c. Both are non ohmic.
D. Both are ohmic


Explain why a real image can be
projected on a screen but a virtual image cannot.


Three major ways for metabolism of
pyruvic acid produced in glycolysis are
A. Lactic acid fermentation, alcoholic fermentation and aerobic respiration.
B. Oxaloacetic acid fermentation, lactic acid fermentation, aerobic fermentation.
C. Alcoholic fermentation, oxaloacetic acid fermentation, citric acid fermentation.
D. Citric acid fermentation, lactic acid fermentation, alcoholic fermentation.


Which of following act as middleman?
A. wвс
B. Lymph
c. Plasma
D. Blood


The rear wheels of a car are turning at an angular speed of 60 rad/s. The brakes are applied for 5 s, causing a uniform angular retardation of
\( 8 r a d / s^{-2} . \) The number of revolutions turned by the rear wheels during the braking period is about:
A . 48
B. 96
\( c .32 \)
D. 12


Identify 'A' and 'B' in the following reaction and rewrite the complete
reaction.
\[
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r}+\boldsymbol{A g C N} \stackrel{\boldsymbol{\Delta}}{\rightarrow}
\]
\( \frac{\boldsymbol{N} \boldsymbol{a}}{\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}} \)
Explain Hoffmann bromamide degradation reaction.


State True or False
From the following figure, we can say:
\( \angle A C D=\angle C B E \)
\( 4 . \) True
3. Falss


Which of the following is the most abundant isotope of chlorine?
A. Chlorine -35
B. Chlorine - 35.45
c. Chlorine-36
D. Chlorine -37


How many EDTA
(ethylenediaminetetraacetic acid) molecules are required to make an
octahedral complex with \( C a^{2+} ? \)
A . six
B. three
c. one
D. two


When the base of a triangle is increased by \( 10 \% \) and the altitude to this base is
decreased by \( 10 \% \), the change in area is
A . \( 1 \% \) increase
B. \( \frac{1}{2} \% \) increase
\( c .0 \% \)
D. \( 1 \% \) decrease


is the replacement of diazonium group by \( -O H \) group using cuprous salts. The product is Haloarene.
A. Sandmeyer's reaction
B. Michel reaction
c. ozonolysis
D. None of these


When an apple falls from a tree what happens to its gravitational potential energyjust as it reaches the ground?


Which will contain undissociated
aqueous particles?
A. A 0.01-molar solution of HNO
B. A 0.01-molar solution of \( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
c. A 0.01-molar solution of \( \operatorname{Cu}\left(\mathrm{NO}_{3}\right)_{2} \)
D. A 0.01-molar solution of NaNO
E. A 0.01-molar solution of NaOH


The melting points of four solids \( A, B, C \)
and D are \( 78^{\circ} \mathrm{C}, 213^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \) and
\( 154^{\circ} \mathrm{C} . \) Arrange them in increasing order of their interparticle forces of attraction.


Reactivity of elements ........ down the
group.
A. increases
B. decreases
c. increases and then decreases
D. decreases and then increases


A tank of height \( 5 m \) is full of water. There is a hole of cross sectional area
\( 1 \mathrm{cm}^{2} \) in its bottom. The initial volume
of water that will come out from this
hole per second is
A \( \cdot 10^{-3} m^{3} / s \)
B . \( 10^{-4} \mathrm{m}^{3} / \mathrm{s} \)
c. \( 10 m^{3} / s \)
D. \( 10^{-2} \mathrm{m}^{3} / \mathrm{s} \)


Ciliated funnels found on the ventral
side of kidney in Frog are
A. Ostia
B. Nephrostomes
c. Bidders organs
D. Corpora adiposa


Aerobic respiration occurs in
A. Thylakoid.
B. Golgi body.
c. Grana
D. Mitochondria.


Addition of ethylene glycol (non-volatile) to water lowers the freezing point of water and hence it is used as antifreeze.
Addition of any substance to water
lowers its freezings point of water.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true


Which will be the third element among
the given elements to complete given Doberiener triad?
(Atomic mass of Be \( 9 ; \) Na \( 23 ; \) Mg \( 24 ; \) si 28; Cl 35; Ca 40)
\( \mathrm{Be},_{-}-_{-}, \mathrm{Ca} \)


Light of wave length \( \lambda \) air enters into
two medium of refractive indices \( \mu \) and
\( \mu / 2 . \) Two points \( P_{1} \) and \( P_{2} \) lying along the path of this light as shown in the figure. The phase difference between these two point is \( k \frac{\left(\pi \mu X_{0}\right)}{\lambda} . \) Then find
the value of \( \mathrm{k} \)
\( A \)
B.
\( c .5 \)
D.
E. None of thes


State Brewster's law of polarization of
light.


Find the atomic number and mass
number of the last member in the
following series:
(a) \( _{88}^{226} R a \stackrel{-\alpha}{\longrightarrow} R n \quad-\alpha \)
\( \boldsymbol{R} \boldsymbol{a} \boldsymbol{A} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{R} \boldsymbol{a} \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{R} \boldsymbol{a} \boldsymbol{C} \)
(b) \( _{Z}^{M} A \stackrel{-\alpha}{A} B^{-\beta} C^{-\beta} \)
\( \boldsymbol{D} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{E} \)


Find the value of following if \( x=-1 \) \( x(x)^{2}-(3 x)^{2} \)


In the system of equations \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{4} \boldsymbol{x} \boldsymbol{y} \)
and \( \frac{1}{x}+\frac{2}{y}=10, \) the value of \( x \) and \( y \)
will be
A \( \cdot-\frac{1}{3} \) and \( \frac{1}{6} \)
B \( \cdot \frac{1}{5} \) and \( \frac{1}{6} \)
c. \( -\frac{1}{2} \) and \( \frac{1}{6} \)
D. \( +\frac{1}{3} \) and \( -\frac{1}{2} \)


A sphere of radius \( 1.00 \mathrm{cm} \) is placed in
the path of a parallel beam of light of large aperture. The intensity of the light is \( 0.50 W \quad c m^{-2} . \) If the sphere
completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere


The magnitude of the lattice energy of a soild increases if:
A. the ions are large
B. the ions are small
c. the ions are of equal size
D. charges on the ions are smal


The biotic and abiotic components interacting with each other in a pond form
A. a community
B. a population
c. an ecosystem
D. a biome


Calculate the median of the farm size
for the following data:
\( \begin{array}{lllll}\text { Farm } & 2- & 5- & 8- & 11- \\ \text { size } & 5 & 8 & 11 & 14\end{array} \)
12 Rooms \( \quad 4 \quad 8 \)
A. 9.125
B. 8.125
c. 7.125
D. 6.125


Among the elements of the second period pick out the element which has a smallest atomic radius.
A. \( F \)
в. \( L \) i
\( c . c \)
D. Ne


The length of a given cylindrical wire is increased by \( 100 \% . \) Due to the consequent decrease in diameter the
change in the resistance of the wire will be :-
A . 300\%
B . 200\%
\( c \cdot 100 \% \)
D. 50\%


What is aminoacylation? State its significance.


Identify the experiment for the
statement "Toss a coin to get head or
tail".
A. Tossing a coin
B. Rolling of a dice
c. Throw a die
D. Pick a card


A sphere of mass \( m_{1}=2 k g \) collides
with a sphere of mass \( m_{2}=3 k g \) which
is at rest. Mass \( m_{1} \) will move at right angle to the line joining centres at the
time of collision, if the coefficient of
restitution is
A \( \cdot \frac{4}{9} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
D. \( \sqrt{\frac{2}{3}} \)


When one faraday of electricity is passed through three electrolytic cells containing \( \boldsymbol{A} \boldsymbol{g}^{+}, \boldsymbol{N} \boldsymbol{i}^{2+} \) and \( \boldsymbol{C} \boldsymbol{r}^{3+} \) ions
respectively, the deposited \( A g \) (At. mass \( =108), N i(\text { At. mass }=59) \) and
\( \boldsymbol{C r}(\boldsymbol{A} \boldsymbol{t} . \boldsymbol{m} \boldsymbol{a} \boldsymbol{s} \boldsymbol{s}=\mathbf{5} \boldsymbol{2}) \)
are
A. \( A g=108 g, N i=29.5 g, C r=17.3 \mathrm{g} \)
в. \( A g=108 g, N i=59 g, C r=52 g \)
c. \( A g=108 g, N i=108 g, C r=17.3 g \)
D. \( A g=108 g, N i=29.5 g, C r=166 g \)


Consider the following statements [1] \( \mathrm{CM} \) of a uniform semicircular disc of
radius \( R=2 R / \pi \) from the centre
[2] CM of a uniform semicircular ring of radius \( R=4 R / 3 \pi \) from the centre
[3] CM of a solid hemisphere of radius \( \boldsymbol{R}=\boldsymbol{4} \boldsymbol{R} / \mathbf{3} \boldsymbol{\pi} \) from the centre
[4] CM of a hemisphere shell of radius \( \boldsymbol{R}=\boldsymbol{R} / 2 \) from the centre
Which statement are correct:
A \( \cdot 1,2,4 \)
в. 1,3,4
\( c \cdot 4 \) only
D. 1,2 only


When two isomeric aromatic liquid compounds \( A \) and \( B \) having hydrogen bond, are heated. Compound A boils at a lower temperature than B.
Which statement is correct?
This question has multiple correct options
A. Intermolecular H bonding present in A
B. Intramolecular H bonding present in A and B both
c. Intramolecular H bonding present in B
D. Intramolecular H bonding present in A


Out of \( C_{6} H_{5} C H_{2} C l \) and
\( C_{6} H_{5} C H C l C_{6} H_{5}, \) which is more easily
hydrolysed by aqueous \( K O H ? \)


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( \frac{(i+j)^{2}}{2} \)


By hormone application, it is possible to
obtain seedless fruits. In which of the following, it is undesirable to obtain
seedless fruits?
A. Tomato
B. orange
c. watermelon
D. Pomegranate


Consider the graph given in figure.
When of the following options does not
show instantaneous rate of reaction at
\( 40 s: \)
\( A \)
B. \( \frac{V_{4}-V_{2}}{50-300} \)
\( c \cdot \frac{V_{3}-V_{2}}{40-30_{2}} \)
D. \( \frac{V_{3}-V_{1}}{40-200} \)


f \( \pi / 2 \) and \( \pi / 4 \) are respectively the
arguments nof \( Z_{1} \) and \( \overline{Z_{2}} \), what is the
value of \( \arg \left(z_{1} / z_{2}\right) \)


A disc is rotating with an angular speed of \( \omega . \) If a child sits on it which of the
following is conserved?
A. Kinetic energy
B. Potential energy
c. Linear momentum
D. Angular momentum


Which gives violet color with borax?
A . \( F e \)
в. \( P b \)
c. \( C o \)
D. \( M n \)


A square and an equilateral triangle have same perimeters. If diagonal of square is \( 12 \sqrt{2} c m, \) then side of traingle
is


If \( A B C D \) is a parallelogram whose diagonals intersect at \( O \) and \( \triangle B C D \) is
an equilateral triangle having each side of length \( 6 \mathrm{cm} \), then the length of diagonal \( \boldsymbol{A C} \) is
A \( \cdot 2 \sqrt{3} \mathrm{cm} \)
B. \( 6 \sqrt{3} \mathrm{cm} \)
c. \( 3 \sqrt{6} \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


Block \( A \) has a weight of \( 300 N \) and
block \( B \) has a weight of \( 50 N . \) The coefficient of kinetic friction between
the incline and block \( \boldsymbol{A} \) is \( \boldsymbol{\mu}_{\boldsymbol{k}}=\mathbf{0 . 2} \)
Determine the speed of block \( \boldsymbol{A} \) after it
moves \( 1 \mathrm{m} \) down the plane, starting
from rest. Neglect the mass of the cord
and pulleys. (Take \( g=10 m / s^{2} \) )
A. \( 1.12 m / s \)
в. \( 1.2 m / s \)
c. \( 1.32 m / s \)
D. \( 1.4 m / s \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{5} \\ \mathbf{6} & \mathbf{7}\end{array}\right], \) then find \( \boldsymbol{A}+\boldsymbol{A}^{\prime} \)


Find the area of the partitions cut off by the hyperbola \( x^{2}-3 y^{2}=1 \) from the
ellipse \( x^{2}+4 y^{2}=8 \)


A steel wire of length 4.7 m and cross-
sectional area \( 3 \times 10^{-6} m^{2} \) stretches by
the same amount as a copper wire of length \( 3.5 m \) ad cross-sectional area of
\( 4 \times 10^{-6} m^{2} \) under a given load. The
ratio of Young's modulus of steel to that of copper is
A . 1.8
в. 3.6
c. 0.6
D. 8.7


\( \Delta G=\Delta G^{\ominus}+R T l o g K \)
A. True
B. False


A glass wind screen whose inclination with the vertical can be changed is
mounted on a car. The car moves
horizontally with a speed of \( 2 m / s . A t \)
what angle \( \alpha \) with the vertical should
the wind screen be placed so that the rain drops falling vertically downwards
with velocity \( 6 m / s \) strike the wind
screen perpendicularly?
\( \mathbf{A} \cdot \tan ^{-1}(3) \)
B \( \cdot \tan ^{-1}(4) \)
c. \( \tan ^{-1}\left(\frac{1}{3}\right) \)
D. \( \tan ^{-1}\left(\frac{1}{4}\right) \)


A ring of radius \( R \) rolls without sliding
with a constant velocity. If the radius of curvature of the path followed by any particle of the ring at the highest point
of its path is \( x R \). Find \( x \)


If true enter 1 , else enter 0 .
The hybridized orbitals always form \( \sigma \)
bonds.
\( A \)


The diagram below shows two
transparent materials-material G and
material P. The black path is the path of
a light ray through the materials.
Which of the following statement is
true?
A. The sine of the angle that the light ray makes with the normal in substance G is greater than the sine of the angle that the light ray makes with the normal in substance P
B. Light travels more slowly in material P than it does in material G
C. Material G must be air of vacuum
D. Material P must be air or a vacuum
E. The index of refraction of substance \( P \) is less than the
index of refraction of substance


If \( a \) and \( b \) are real numbers between 0
and 1 such that the points \( z_{1}=a+ \)
\( i, z_{2}=1+b i \) and \( z_{3}=0 \) from an
equilateral triangle, then find the values
of \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C N}+\mathbf{2 H}_{2} \stackrel{\boldsymbol{P d}}{\longrightarrow} \)
Which of the following compound is formed in the above reaction?
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C H_{2} N H_{2} \)
в. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} N H_{2} \)
D. None of the above


Chronic bronchitis and emphysema are
more vulnerable to:
A. acid rains
B. water pollutants
c. smog
D. nitrogen oxides


Define the atomic mass unit.


A current i, indicated by the crosses in
figure, is established in a strip of
copper of height h and width w. A
uniform field of magnetic induction B is applied at right angle to the strip.
f the drift velocity \( v_{d} \) of the electrons is
\( \boldsymbol{v}_{\boldsymbol{d}}=\mathbf{1 . 4} \times \mathbf{1 0}^{-\boldsymbol{x}} \boldsymbol{m} \boldsymbol{s}^{-1} . \) Find \( \mathbf{x} \)


Three capacitance of capacity \( 10 \mu F, 5 \mu F \) are connected in parallel.
The total capacity will be :
\( \mathbf{A} \cdot 10 \mu F \)
в. \( 5 \mu F \)
\( \mathbf{c} \cdot 20 \mu F \)
D. None of the above


Assertion
Consider the polynomial function \( f(x)=\frac{x^{7}}{7}-\frac{x^{6}}{6}+\frac{x^{5}}{5}-\frac{x^{4}}{4}+\frac{x^{3}}{3}- \)
\( \frac{x^{2}}{2}+x . \) The equation \( f(x)=0 \) cannot
have two or more roots.
Reason
Rolle's theorem is not applicable for \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) on any interval \( [\boldsymbol{a}, \boldsymbol{b}], \) where
\( \boldsymbol{a}, \boldsymbol{b} \boldsymbol{\epsilon} \boldsymbol{R} \)
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 best reagent for converting, 2 phenylpropanamide into 1 phenylethanamine is:
A \( \cdot \operatorname{excess} H_{2} / P t \)
в. \( N a O H / B r_{2} \)
c. \( N a B H_{4} / \) methanol
D. \( L i A l H_{4} / \) ether


The form in which carbon leaves the
citric acid cycle is
A. Acetalehyde
B. Carbon dioxide
c. Ethanol
D. None of these


Assertion
Angular speed of a planet around the sun increases, when it is closer to the
sun.
Reason
Total angular momentum of the system
remains constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The moment of inertia of a uniform
circular disc about its diameter is 200 gm \( c m^{2} \). Then its moment of inertia
about an axis passing through its center and perpendicular to its circular face is
A \( \cdot 100 \mathrm{gm} \mathrm{cm}^{2} \)
в. 200 gm \( c m^{2} \)
\( \mathrm{c} \cdot 400 \mathrm{gm} \mathrm{cm}^{2} \)
D. 1000 gm \( c m^{2} \)


Let \( 3 x-5 \leq x-2 \) then find the
maximum value of \( 10 x \)


Object Convex Convex Image Pin \( \quad \) Lens \( \quad \) Mirror \( \quad \mathrm{P} \)
22.2 \( 32.2 \mathrm{cm} \)
\( 45.8 \mathrm{cm} \)
To find the focal length of a convex mirror, a student records the following
data:

The focal length of the convex lens is \( \boldsymbol{f}_{1} \)
and that of mirror is \( f_{2} \). Then taking
index correction to be negligibly small,
\( \boldsymbol{f}_{1} \) and \( \boldsymbol{f}_{2} \) are close to :
\( \mathbf{A} \cdot f_{1}=7.8 \mathrm{cm} \quad f_{2}=12.7 \mathrm{cm} \)
B \( \cdot f_{1}=12.7 \mathrm{cm} \quad f_{2}=7.8 \mathrm{cm} \)
\( \mathbf{c} \cdot f_{1}=7.8 \mathrm{cm} \quad f_{2}=25.4 \mathrm{cm} \)
D. \( f_{1}=15.6 \mathrm{cm} \quad f_{2}=25.4 \mathrm{cm} \)


A ballon starts rising from the ground with an acceleration of \( 1.25 \mathrm{m} / \mathrm{s}^{2} \). After
\( 8 s \) a stone is released from the balloon.
The stone will (take \( \left.g=10 m / s^{2}\right) \)
A. have a displacement of \( 50 \mathrm{m} \)
B. cover a distance of 40 \( \mathrm{m} \) in reaching the ground
c. reach the ground in 4 s
D. reach the ground in 16 s


Which of the following has highest boiling point?
A \( . N H_{3} \)
в. \( P H_{3} \)
c. \( A s H_{3} \)
D. \( S b H_{3} \)


Light year is the
A. light emitted by the sun in one year.
B. the time taken by light to travel from sun to earth.
C. the distance travelled by light in free space in one year.
D. the time taken by earth to go once around the sun.


The ratio of two sides of parallelogram
is 3: 5 and its perimeter is \( 48 \mathrm{cm} . \) Find the sides of the parallelogram


The oxide which is neither acidic nor
basic is:
A. \( A s_{2} O_{3} \)
в. \( S b_{4} O_{10} \)
\( c \cdot N_{2} O \)
D. \( N a_{2} O \)


The largest angle of a triangle is twice
the sum of the other two and the
smallest one is one fourth of the largest,
the angles are
A \( \cdot 120^{0}, 40^{0}, 20^{0} \)
В . \( 120^{0}, 30^{0}, 30^{0} \)
c. \( 90^{\circ}, 45^{\circ}, 45^{\circ} \)
D. \( 90^{0}, 60^{0}, 30^{0} \)


The solubility product of a saturated
solution of \( A g_{2} C r O_{4} \) in water at \( 298 \mathrm{K} \) will
be................, if the EMF of the cell:
\( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g}^{\oplus}\left(\boldsymbol{s} \boldsymbol{a} \boldsymbol{t} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4} \boldsymbol{s o l}\right) \| \boldsymbol{A} \boldsymbol{g}(\boldsymbol{0} . \boldsymbol{1} \boldsymbol{M} \)
is \( 0.164 V \) at \( 298 \mathrm{K} \)
A. \( 2.287 \times 10^{-12} M^{3} \)
B . \( 2.659 \times 10^{-12} M^{3} \)
c. \( 1.965 \times 10^{-12} M^{3} \)
D. None of these


A man running round a race course notes that the sum of the distance of
two flag posts from him is always \( 10 m \) and the distance between the flag posts
is 8 m. The area of the path he encloses
in square metres is:
A . \( 15 \pi \)
в. \( 20 \pi \)
c. \( 27 \pi \)
D. \( 30 \pi \)


The dimensions of \( \epsilon_{0} \mu_{0} \)
\( \mathbf{A} \cdot\left[L T^{-1}\right] \)
B . \( \left[L T^{-2}\right] \)
c. \( \left[L^{2} T^{-2}\right] \)
\( \mathbf{D} \cdot\left[L^{-2} T^{-2}\right] \)


Assertion
The stress-strain behaviour varies from
material to material.
Reason
A rubber can be pulled to several times its original length and still returns to its
original shape.
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


Choose the correct answer from the
alternatives given

Capillaries are structurally suited for
the exchange of substances because:
A. their walls are composed of only one layer of squamous cells
B. velocity of blood flow is slow
c. they form networks that increase the surface area for diffusion
D. all of the above


Linear velocity of first sphere after it again starts rolling without slipping is-
A \( \cdot \frac{2}{5} R \omega \)
в. \( \frac{2}{7} R \omega \)
c. \( \frac{7}{10} R \omega \)
D. \( \frac{7}{5} R \omega \)


For a certain frequency distribution, the values of Median and Mode are 95.75
and 95.5 respectively. Find the Mean
A . 95.175
B. 95.475
c. 95.875
D. 96.975


Find the equation of the plane passing through the points (2,3,-4) and (1,-1,3) and parallel to the \( x- \) axis.


\( \boldsymbol{K}_{s p} \) of \( M \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2} \) is \( 1 \times \)
\( \mathbf{1 0}^{-\mathbf{1 2}}, \mathbf{0 . 0 1} \boldsymbol{M} \mathbf{M g} \mathbf{C l}_{\mathbf{2}} \) will
be precipitating at the limiting pH:
\( A \cdot 8 \)
B. 9
\( c \cdot 10 \)
D. 12


\( \int_{0}^{1} \frac{4 x^{3}}{\sqrt{1-x^{8}}} d x=? \)
\( A \cdot \pi \)
в. \( -\pi \)
c. \( \pi / 2 \)
D . \( -\pi / 2 \)


In Bredig's Arc method,the stabilizer
used is:
\( \mathbf{A} \cdot C a(O H)_{2} \)
в. \( C a O \)
c. КОН
D. \( K_{2} \) O


A force of 100 dynes acts on mass of 5
\( \mathrm{gm} \) for 10 sec. The velocity produced is:
A. \( 2 \mathrm{cm} / \mathrm{sec} \)
B. 20 cm/sec
c. \( 200 \mathrm{cm} / \mathrm{sec} \)
D. 2000 cm/sec


\( f(x)=-(x-1)^{2}+10 . \) Find \( f(1) \)


With respect to an ore, Ellingham diagram helps to predict the feasibility if its:
A. vapour phase refining
B. zone refiningg
c. electrolysis
D. thermal reduction


Points \( \mathrm{M} \) and \( \mathrm{N} \) are taken on the
diagonal AC of a parallelogram ABCD such that \( A M=C N \)
BMDN is a


Viscosity is very low for?
\( A \cdot A r \)
в. \( x_{e} \)
c. не
D. Kr


If \( 33 ! \) is divisible by \( 2^{n}, \) then find the
maximum value of \( n \)


The inter nuclear distance in \( H_{2} \) and
\( C l_{2} \) molecules are 74 and 198 pm.
respectively. The bond length of \( H C l \)
may be:
\( \mathbf{A} \cdot 136 p m \)
в. \( 272 \mathrm{pm} \)
c. \( 135.919 \mathrm{pm} \)
D. \( 271.919 \mathrm{pm} \)


Electronic configuration of Mg is:
\( \mathbf{A} \cdot 1 s^{2} 2 s^{1} p^{5} 3 s^{2} 3 d^{2} \)
B. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} p^{7} 3 s^{1} \)
D. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{2} \)


Complete the following chemical reactions:
\( \mathbf{i} \boldsymbol{S}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
ii \( \boldsymbol{S O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightarrow \)
iii \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}(\boldsymbol{l})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)


Find the nth term of the sequence
\( 0.7,0.77,0.777 \ldots \)


On heating iodine and sand which will sublime?
A. Sand
B. lodine
c. Both a and \( b \)
D. None of them


Methyl cyanide on reaction with sodium
and \( C_{2} H_{5} O H \) forms:
A. ethyl amine
B. ethanoic acid
c. ethanimine
D. none of these


Two platinum electrodes were
immersed in a solution of \( C u S O_{4} \) and electric current was passed through the solution. After some time, it was found
that colour of \( C u S O_{4} \) disappeared with
evolution of gas at the electrode. The colorless solution contains:
A \( . C u S O_{4} \)
в. \( H_{2} S O_{4} \)
\( c \cdot \operatorname{both} A \& B \)
D. None of the above


\( \sum_{x, y, z} x^{2}\left(y^{2}-z^{2}\right)=? \)
A. \( x^{2}+y^{2}+z^{2} \)
B . \( x^{2} y^{2}+y^{2} z^{2}+z^{2} x^{2} \)
c. 0
D. \( y^{2}+z^{2} \)


What is the concentration above which
sulphate causes laxative effect?
\( A \cdot 500 \) ppm
B. 500 ppb
c. 100 ppm
D. 100 ppb


Petroleum is formed under the earth's
crust by chemical changes in:
A. Vegetable matter
B. Inorganic matter
c. Animal matter
D. Both vegetable and animal matter


\( \tan (\pi \cos \theta)=\cot (\pi \sin \theta) \) then the
value(s) of \( \cos \left(\theta-\frac{\pi}{4}\right) \) is (are)
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
c. \( \pm \frac{1}{2 \sqrt{2}} \)
D. \( \frac{1}{3 \sqrt{2}} \)


Show that \( _{92}^{230} U \) does not decay be emitting a neutron or proton. Given:
\( M\left(_{92}^{230} U\right)=230.033927 a m u \)
\( M\left(_{92}^{230} U\right)=229.033496 a m u \)
\( M\left(_{92}^{229} P a\right)=229.032089 a m u \)
\( \boldsymbol{m}(\boldsymbol{n})=\mathbf{1 . 0 0 8 6 6 5 a m u} \)
\( \boldsymbol{m}(\boldsymbol{p})=\mathbf{1 . 0 0 7 8 2 5 a m u} \)


A particle \( A \) is moving towards North with an acceleration of \( 5 m s^{-2} \) and
particle \( B \) is moving North-East direction with an acceleration of
\( 5 \sqrt{2} m s^{-2} . \) Find relative acceleration of
particle \( A \) with respect to particle \( B \)


In the general electronic configuration, \( (n-2) f^{1-14}(n-1) d^{01} n s^{2}(\text { where } n=7) \)
the configuration will be of:
A. lanthenides
B. actinides
c. transition elements
D. none


The range of the function \( \boldsymbol{f}(\boldsymbol{x})=-\mid \boldsymbol{x} \)
\( 2 \mid-3 \) is
A. \( y \geq 2 \)
в. \( y \leq-3 \)
c. \( y \geq-3 \)
D. \( y \leq-2 \)
E \( . y \geq-2 \)


If the body is moving in a circle of
radius \( r \) with a constant speed \( v \). Its angular velocity is:
A \( \cdot \frac{v^{2}}{r} \)
B. \( v r \)
c. \( \frac{v}{r} \)
D. \( \frac{r}{v} \)


In a series of 3 one-day cricket matches between teams \( A \) and \( B \) of a college, the probability of team A winning or drawing are \( 1 / 3 \) and \( 1 / 6 \) respectively. If a
win, loss or draw gives 2,0 and 1 point
respectively, then what is the
probability that team A will score 5
points in the series?
A \( \cdot \frac{17}{18} \)
B. \( \frac{11}{12} \)
\( c \cdot \frac{1}{12} \)
D. \( \frac{1}{18} \)


Structure which maintains the shape of the eye ball and the area of no vision.


(a) Draw structure of the following
compounds:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)
(ii) \( N_{2} O_{5} \)
(b) Write the structural difference
between white phosphorus and red phosphorus.


A cricketer hits 120 runs in 150 balls
during a test match. \( 20 \% \) of the runs came in \( 6 s, 30 \% \) in \( 4 s, 25 \% \) in \( 2 s \) and
the rest in singles. How many runs did he score in singles?
A . 16
B. 4
c. 20
D. 30


State Biot-Savart's law. Define unit of
current


Assertion
Glycolysis takes place in the cytoplasm.
Reason

Enzymes for glycolysis are found in the
cytoplasm.
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


On the set \( Z \) of integers, if the binary
operation \( * \) is defined by \( a * b=a+ \)
\( b+2, \) then find the identity element.


A particle starts from rest at \( t=0 \) and
undergoes an acceleration \( a \) in \( m s^{-2} \)
with time \( t \) in second which is as shown
Calculate the particle's velocity at 2 s, 3
\( \mathbf{s}, \mathbf{4} \)


Find the maximum extension in the
spring
A \( \cdot \frac{1}{4} v_{0} \sqrt{\frac{m}{5 k}} \)
В \( \cdot \frac{3}{4} v_{0} \sqrt{\frac{m}{5 k}} \)
\( ^{\mathbf{c}} \cdot \frac{1}{3} v_{0} \sqrt{\frac{m}{5 k}} \)
D. \( \quad \frac{1}{8} v_{0} \sqrt{\frac{m}{5 k}} \)


Physical adsorption of a gaseous species may change to chemical adsorption with:
A. decrease in temperature
B. increase in temperature
c. increase in surface area of adsorbent
D. decrease in surface area of adsorbent


Assertion
Oxidation of glucose by \( B r_{2} \) water gives
saccharic acid.
Reason
Bra water oxidized -CHO and alcohol.
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


Time taken by the ball to reach the ground after crossing the elevator.


When \( 1 g \) of water at \( 100^{\circ} \mathrm{C} \) gets converted into steam at the same
temperature, the change in volume is approximately:
A \( .1 c c \)
в. \( 1000 \mathrm{cc} \)
\( c .1500 c c \)
D. \( 1670 c c \)


Let \( A \) be a matrix of order \( 3 \times 4 . \) If \( R_{1} \)
denotes the first row of \( A \) and \( C_{2} \)
denotes its second column, then
determine the orders of matrices \( \boldsymbol{R}_{1} \)
and \( C_{2} \)


Find the value of \( x \) such that
\( -\frac{2}{7}, x,-\frac{7}{2} \) are three consecutive terms of a G.P.


Write in simplest form \( \sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right] \)


A ladder \( 24 \mathrm{ft} \) long leans against a vertical wall. The lower end is moving away at the rate of \( 3 \mathrm{ft} \) lsec. Find the rate
at which the top of the ladder is moving downwards, if its foot is \( 8 \mathrm{ft} \) from the
wall.


The chemical compounds which are produced by host plants due to infection as a defense reaction to pathogen are
called as
A. Phytotoxin
B. Phytol
c. Phytotron
D. Phytoalexins


If \( A \) and \( B \) are square matrices of same
order, then which of the following is
correct -
A. \( A+B=B+A \)
в. \( A+B=A B \)
c. \( A B=B A \)
D. \( A B=B+A \)


Newton postulated his corpuscular theory of light on the basis of
A. Newton's rings
B. Rectilinear propagation of light
c. colour through thin flims
D. Dispersion of white light into columns


Take, bulk modulus of water \( \boldsymbol{B}= \)
\( \mathbf{2 1 0 0} \boldsymbol{M P a} \)
What increase in pressure is required to decrease the volume of 200 litres of
water by 0.004 percent?
A \( .210 k P a \)
в. \( 840 \mathrm{kPa} \)
c. \( 8400 k P a \)
D. \( 84 k P a \)


A locomotive is propelled by a turbine whose axle is parallel to the axes of
wheels. The turbine's rotation direction
coincides with that of wheels. The
moment of inertia of the turbine rotor
relative to its own axis is equal to \( \boldsymbol{I}= \)
\( 240 k g \cdot m^{2} . \) If the additional force
exerted by the gyroscopic forces on the rails when the locomotive moves along
a circle of radius \( R=250 m \) with
velocity \( \boldsymbol{v}=\mathbf{5 0} \boldsymbol{k m} / \boldsymbol{h} \) is \( \boldsymbol{F}_{\boldsymbol{a d d}}= \)
\( \frac{x}{10} k N . m, \) find the value of \( x . \) The gauge
is equal to \( l=1.5 m . \) The angular
velocity of the turbine equals \( n= \)
1500 rpm


Fill in the blanks with appropriate words.
If the sequences of bases in a segment of a DNA strand were adenine, thymine, cytosine, guanine, then the sequence in a complementary strand of newly made mRNA would be


What is the net charge on an neutral
atom?
A. positive
B. negative
c. zero
D. none of these


\begin{tabular}{l}
\( E \) \\
\( L \) \\
\( L \) \\
\hline
\end{tabular}


If \( 3^{4 x}=(81)^{-1} \) and \( 10^{1 / y}=0.0001, \) find
the value of \( 2^{-x+4 y} \)


How many words can be formed with the
letters of FAILURE when all the vowels
should come together?


Gammexane is:
A. chlorobenzene
B. hexachlorobenzene
C. hexachlorocyclohexane
D. dichlorodiphenyltrichloroethane.


Which of the following is not a
spontaneous reaction \( i e, \) has
equilibrium constant \( (K) \) less than
one?
This question has multiple correct options
\( A \)
\[
\mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}+\mathrm{CH}_{3} \mathrm{Li} \rightleftharpoons \mathrm{CH}_{3}-\mathrm{C}=\mathrm{CLi}+\mathrm{CH}_{4}
\]
в.
\[
\begin{array}{l}
\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}+\mathrm{CH}_{3} \mathrm{CH}_{3} \mathrm{ONa}= \\
\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CNa}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}
\end{array}
\]
\( c \)
\[
\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CNa} \rightleftharpoons
\]
\[
\mathrm{CH}_{3} \mathrm{COONa}+\mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}
\]
\( D \)
\[
\begin{array}{l}
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2}+\mathrm{CH}_{3}-\mathrm{C}=\mathrm{CNa} \rightleftharpoons \\
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHNa}+\mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}
\end{array}
\]


A resistance of \( 4 \Omega \) and a wire of length
\( 5 m \) and resistance \( 5 \Omega \) are joined in
series and connected to a cell of e.m,f,
\( \mathbf{1 0} V \) and internal resistance \( 1 \Omega . A \)
Parallel combination of two identical
cells is balanced across \( 300 \mathrm{cm} \) of the
wire. the e.m.f. \( \boldsymbol{E} \) each cell is then:
A \( .1 .5 ~ V \)
в. \( 3.0 V \)
\( c .0 .67 V \)
0.1 .33


Represent set \( A, B, C \) such that \( A \subset \) \( \boldsymbol{B}, \boldsymbol{A} \cap \boldsymbol{C}=\boldsymbol{\phi} \) and \( \boldsymbol{B} \cap \boldsymbol{C} \neq \boldsymbol{\phi} \) by Venn
diagram. The number of separate
regions representing \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C}) \)
is/are:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. None of these


The phase diagram for solvent and solutions is shown in the figure. What
represents the normal boiling point of
the solution?
\( A \)
B.
\( c \cdot c \)
\( D \)


Two roads intersect at right angle; one
goes along the \( x \) -axis, another along the
y-axis. At any. two cars \( A \) and \( B \) moving
along \( \boldsymbol{y} \) and \( \boldsymbol{x} \) directions; respectively, meet at intersection. Draw the direction
of the motion of car \( A \) as seen from car
\( \boldsymbol{B} \)


Assertion: It is safe to stir \( 1 \mathrm{M} A g N O_{3} \)
solution with a copper spoon.
\[
\begin{aligned}
\text { Reason: } \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g} \oplus \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus} &=\mathbf{0 . 8 0} \boldsymbol{V} \\
\boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{\ominus} &=\mathbf{0 . 3 4} \boldsymbol{V}
\end{aligned}
\]
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Let \( S \) be the set of all values of \( x \) such
\( \operatorname{that} \log _{2 x}\left(x^{2}+5 x+6\right)<1 \) then the
sum of all integral value of \( x \) in the set
S, is
\( A \cdot O \)
B. 8
\( c \cdot s \)
D. 10


A dielectric slab fills the lower half of a
parallel plate capacitor as shown in
figure :
(Take plate are as \( \boldsymbol{A} \) )
This question has multiple correct options
A . equivalent capacity of the system is \( \left(\left(\varepsilon_{0} A / 2 d\right)(1+\right. \)
\( K) \)
B. the net charge of the lower half of the left hand plate is \( 1 / K \) times the charge on the upper half of the plate
C. net charges on the lower and upper halves of the left hand plate are different
D. net charge on the lower hand of the left hand plate is \( \frac{K \varepsilon_{0} A}{2 d} \times V \)


To prevent food from spoilage by microorganism, which substance is
used?
A. Aspartame
B. Arneto
c. Salt of sorbic acid
D. Tetrazine


Neoprene is a polymer made by using
acetylene as a raw material. It is used
as:
A. rubber in diving suits
B. plastic for car panels
c. plastic for dining tables
D. material for electrical switches


What happens when carbon dioxide gas is bubbled through lime water?


The function of boiling the sodium
extract with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) before testing the halogen is:
A. to convert \( F e^{++} \) into \( F e^{++}+ \)
B. to make solution clear
c. to make solution acidic
D. to destroy cyanide and sulphide ions


How is population density calculated?


The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-
section. If the length of the wire is \( 36 \mathrm{m} \) find the radius of its cross-section.
A \( .0 .8 \mathrm{cm} \)
B. \( 0.5 \mathrm{cm} \)
\( c .0 .3 \mathrm{cm} \)
D. \( 0.1 \mathrm{cm} \)


Prove that \( \frac{^{n} C_{r}}{n-1}=\frac{n}{r} \) where \( 1 \leq \)
\( \boldsymbol{r} \leq \boldsymbol{n} \)


Find the coordinates of the foot of
perpendicular drawn from the point \( A(-1,8,4) \) to the line joining the points \( B(0,-1,3) \) and \( C(2,-3,-1) . \) Hence,
find the image of the point \( A \) in the line
\( \boldsymbol{B C} \)


Wavelength of the first line of Balmer
series is 600 n m. The wavelength of second line of the Balmer series will be:
A. \( 444 n m \)
B. \( 800 n m \)
\( \mathbf{c} .388 n m \)
D. \( 632 n m \)


Which of the following reveals the muscle disorders?
A. ECG
B. EEGG
c. Емя
D. All of the above


Assertion
Statement \( -1: P C l_{3} \) on hydrolysis
\( \operatorname{gives} H_{3} P O_{3} \)
Reason
Statement \( -2: H_{3} P O_{3} \) exists in two
tautomeric forms:
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement -1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. statement -1 is true, statement -2 is false
D. Statement - 1 is false, Statement - 2 is true


Two point charges \( +q \) and \( +q \) are fixed \( \operatorname{at}(a, 0,0) \) and \( (-a, 0,0) . \) A third point
charge \( -q \) is at origin. State whether its equilibrium is stable, unstable or neutral if it is slightly displaced along
\( y- \) axis.
A . Stable
B. Unstable
c. Neutral
D. Data insufficient


(i) What is meant by the terms
amplitude and frequency of a wave?
(ii) Explain why stringed musical instruments, like the guitar, are provided with a hollow box.


Evaluate the following limits. If \( \lim _{x \rightarrow a} \frac{x^{9}-a^{9}}{x-a}=9, \) find all possible
values of a.
\( \mathbf{A} \cdot 2,-2 \)
B. 1,-1
c. 1,0
D. None of these


A car travels on a straight road from point \( A \) to point \( B \) in four hours, and then from point \( B \) back to point \( A \) in six
hours. The distance between the two
points is \( 240 k m \)

Find out the car's average velocity?
\( \mathbf{A} \cdot 0 k m / h \)
в. \( 48 k m / h \)
c. \( 50 k m / h \)
D. \( 60 k m / h \)
E . \( 100 k m / h \)


The sum of digits of a two-digit number is \( 13 . \) If the number is subtracted from
the one obtained by interchanging the digits, the result is \( 45 . \) What is the
number.


An astronaut accidentally gets separated out of his small spaceship accelerating in
inter stellar space at a constant rate \( 50 m s^{-2}, \) what is the acceleration of the
astronaut the instant after he is outside
the spaceship? (Assume that there are no
nearby starts to extract gravitational
force on him).


1.0 g magnesium atoms in vapour phase absorbs \( 50.0 \mathrm{kJ} \) of energy to
convert all Mg into Mg ions. The energy absorbed is needed for the following changes:
\[
\boldsymbol{M} \boldsymbol{g}(\boldsymbol{g}) \longrightarrow \boldsymbol{M} \boldsymbol{g}^{+}(\boldsymbol{g})+\boldsymbol{e} ; \boldsymbol{\Delta} \boldsymbol{H}=
\]
\( 740 k J m o l^{-1} \)
\[
\begin{array}{c}
\boldsymbol{M} \boldsymbol{g}^{+}(\boldsymbol{g}) \longrightarrow \boldsymbol{M} \boldsymbol{g}^{2+}(\boldsymbol{g})+\boldsymbol{e} ; \boldsymbol{\Delta} \boldsymbol{H}= \\
\mathbf{1 4 5 0} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1}
\end{array}
\]
Find out the \( \% \) of \( M g^{+} \) and \( M g^{2+} \) in the final mixture
A . \% \( M g^{+}=68.28 \% \), \% of \( M g^{2+}=31.72 \% \)
B . \% \( M g^{+}=58.28 \% \), \% of \( M g^{2+}=41.72 \% \)
c. \% \( M g^{+}=78.28 \% \), \% \( o f M g^{2+}=21.72 \% \)
D. None of these


Two identical blocks \( A \) and \( B \), each of
mass 'm' resting on a smooth horizontal surface, are inter connected by spring of stiffness 'K'. If the block B is acted on by
a horizontal force ' \( \mathrm{F}^{\prime} \) and the elongation
of the spring is 'e', the relative acceleration between the
blocks is equal to
A \( \cdot \frac{F}{2 m} \)
B. \( \frac{F-K e}{m} \)
\( \mathbf{c} \cdot \frac{F-2 K e}{m} \)
D. \( \frac{K e}{m} \)


The displacement of a particle is given by \( \boldsymbol{y}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \boldsymbol{t}^{2}-\boldsymbol{d} \boldsymbol{t}^{4} . \) The initial
velocity and acceleration, respectively,
are
A \( . b,-4 d \)
В. \( -b, 2 c \)
c. \( b, 2 c \)
D. \( 2 c,-4 d \)


What is true for reversible process?
A. It increases the overall work done.
B. It decreases the overall work done.
C. Overall work done remains constant
D. Both b and c


A circular hoop of mass \( M \) and radius
\( R \) is suspended from a nail in the wall.
Its moment of inertia about an axis
along the nail will be:
A. Zero
В. \( M R^{2} \)
\( \mathrm{c} \cdot 2 \mathrm{M} R^{2} \)
D. \( \frac{M R^{2}}{2} \)


Gymnosperm plants do not produce fruits because they do not have
A. Ovary
B. Gametes
c. Fertilization
D. None of the above


For the conversion of liquid into a solid:
A. orderliness decreases and entropy decreases
B. orderliness increases and entropy increases
c. both are not related
D. orderliness increases and entropy decreases


What is the product of the reaction?
\( A \)
B.
\( c \)
\( D \)


Major products formed in the reaction of t-butyl methyl ether with \( H I \) are
\( A \)
and
and \( \quad \mathbf{H}_{3} \mathbf{C}-\mathbf{O H} \)
\( c \)
\( \mathbf{H}_{3} \mathbf{C}-\mathbf{O H} \quad \) and
D
and \( \mathbf{H}_{3} \mathbf{C}-\mathbf{O} \mathbf{H} \)


After an interval of one day, \( \frac{1}{16} t h \) initia amount of a radioactive material
remains in a sample. Then, its half-life
is
\( \mathbf{A} \cdot 6 h \)
в. \( 12 h \)
\( c .1 .5 h \)
D. \( 3 h \)


Let \( a, b, c \) be such that
\[
\frac{1}{(1-x)(1-2 x)(1-3 x)}=\frac{a}{1-x}+
\]
\( \frac{b}{1-2 x}+\frac{c}{1-3 x} \) then \( \frac{a}{1}+\frac{b}{3}+\frac{c}{5}= \)
A \( \cdot \frac{1}{15} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{1}{5} \)
D. 1 \( \overline{3} \)


At \( p H=2, E_{Q u i n h y d r o n e} \) will be:
\( \left(E_{Q u i h y d r o n e}^{o}=1.30 V\right) \)
A . \( 1.36 V \)
B . \( 1.30 V \)
c. \( 1.42 v \)
D. \( 1.20 V \)


Two planets are revolving around the
Earth with velocities \( v_{1}, v_{2} \) and in radii
\( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \) respectively. Then
A \( \cdot v_{1}=v_{2} \)
в. \( v_{1}>v_{2} \)
c. \( v_{1}<v_{2} \)
D. \( \frac{v_{1}}{r_{1}}=\frac{v_{2}}{r_{2}} \)


Solve \( \int \frac{x e^{x}}{(x+1)^{2}} d x \)
A \( \cdot \frac{e^{x}}{x+1}+C \)
в. \( \frac{x}{(x+1)^{2}}+C \)
c. \( e^{x}(x+1)+C \)
D. \( x(x+1)^{2}+C \)


A coil with an area of \( 0.50 m^{2} \) and a
resistance of 7 ohms is completely in a changing magnetic field. If the current in the coil is 2.0 Amps,
what is the rate of change of the magnetic field?
A. \( 3.5 T / s \)
в. \( 7 T / s \)
c. \( 14 T / s \)
D. \( 28 T / s \)


What is the electronic arrangement of G
\( ? \)
A. 2,2,5
B. 2, 4, 3
c. 2,7
D. 2, 5, 2


A block of mass \( 50 \mathrm{kg} \) is projected
horizontally on a rough horizontal floor.
The coefficient of friction between the
block and the floor is \( 0.1 . \) The block
strikes a light spring of stiffness \( \boldsymbol{k}= \)
\( 100 N / m \) with a velocity \( 2 m / s . \) The
maximum compression of the spring is
\( A \cdot 1 m \)
3. \( 2 m \)


Number of \( \boldsymbol{P}-\boldsymbol{P} \) bonds in \( \boldsymbol{P}_{4} \boldsymbol{S}_{3} \) is:
\( A \cdot 3 \)
B. 1
\( c \cdot 0 \)
D. 2


Prove the following by using the first
principle \( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+\ldots \ldots+\mathbf{3}^{n-1}=\frac{\left(\mathbf{3}^{n}-\mathbf{1}\right)}{\mathbf{2}} \)