During lactic acid fermentation
A \( \cdot O_{2} \) is used, \( C O_{2} \) is liberated
B. Neither \( O_{2} \) is used nor \( C O_{2} \) liberated
\( \mathrm{c} \cdot O_{2} \) is not used, \( C O_{2} \) is liberated
D. \( O_{2} \) is used, \( C O_{2} \) is not liberated


Explain the following reactions:
(a) Carbylamine reaction
(b) Sandmeyer reaction


Why are the world's major ocean fisheries located in cold regions?


The value of \( \int_{-\pi / 2}^{\pi / 2} \sqrt{\frac{1}{2}(1-\cos 2 x)} d x \) is
\( A \cdot 0 \)
B. 2
\( c \cdot \frac{1}{2} \)
D. None of these.


The number of points on the line \( x+ \)
\( \boldsymbol{y}=\mathbf{4} \) which are unit distance apart
from the line \( 2 x+2 y=5 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. \( \infty \)


A plane mirror is made up of
A. Few metre thick glass plate
B. Few mm thick glass plate
C. Few cm thick glass plate
D. None


Of the two solvent \( H_{2} O \) and \( D_{2} O \)
NaCl dissolves:
A. equally in both solvents
B. only in \( H_{2} O \) but remains insoluble in \( D_{2} O \)
c. more in \( D_{2} \) O
D. more in \( H_{2} \) O


The amount of heat required to change from liquid state to gaseous state
without rise in its temperature is
called


Let \( M \) be the set of all \( 2 \times 2 \) matrices
with entries from the set \( \boldsymbol{R} \) of real
numbers. Then the function \( \boldsymbol{f}: \boldsymbol{M} \rightarrow \boldsymbol{R} \)
defined by \( \boldsymbol{f}(\boldsymbol{A})=|\boldsymbol{A}| \) for every \( \boldsymbol{A} \in \boldsymbol{M} \)
is
A. one-one and onto
B. neither one-one nor onto
c. one-one but not onto
D. onto but not one-one


is a mode of asexual reproduction.
A. cloning
B. Budding
c. Pollination
D. Germination


Space between the plates of a parallel plate capacitor is filled with a dielectric slab. The capacitor is charged and then
the supply is disconnected to it. If the slab is now taken out, then:
A. work is not done to take out the slab
B. energy stored in the capacitor reduces
c. potential difference across the capacitor is decreased
D. potential difference across the capacitor is increased


A police van moving on a highway with a speed of \( 30 \mathrm{km} h^{-1} \) fires a bullet at a
thief's car speeding away in the same
direction with a speed of \( 192 \mathrm{km} h^{-1} . \) If
the muzzle speed of the bullet is 150
\( \mathrm{m} s^{-1}, \) with what speed does the bullet
hit the thief's car?
\( \mathbf{A} \cdot 95 \mathrm{m} \mathrm{s}^{-1} \)
B . \( 105 \mathrm{m} s^{-1} \)
C. \( 115 \mathrm{m} s^{-1} \)
D. \( 125 \mathrm{m} s^{-1} \)


Which one is a product of aerobic respiration?
A . Malic acid
B. Ethyl alcohol
c. Lactic acid
D. Acetic acid


The ionization potential of elements in any group decreases from top to bottom. This is due to:
A. increase in the size of an atom
B. increase in the atomic number
c. increase in the screening effect
D. both increase in the size of an atom and increase in the screening effect


A voltmeter is connected in parallel with a variable resistance are which is in
series and an ammeter and call. For one
value of \( R, \) metres read \( 0.3 \mathrm{A} \) and 0.9
volt. For another value of \( R \) the readings are 0.25 ampere and 1.0 volt. What is the internal resistance of the cell?
A . \( 0.5 \Omega \)
B. 2\Omega
c. \( 1.2 \Omega \)
D. 12


Match the item in column I with column
I and choose the correct answer.
\( \begin{array}{ll}\text { Column } 1 & \text { Column } 2 \\ \text { A. Microspermae } & \text { 1. Alismaceae } \\ \text { B. Epigynae } & \text { 2. Liliaceae } \\ \text { C. Calycinae } & \text { 3. Iridaceae } \\ \text { D. Apocarpae } & \text { 4. Orchidaceae } \\ \text { E. Coronarieae } & \text { 5. Palmae }\end{array} \)
\( \mathbf{A} \)
\( A-3, B-2, C-1, D-5, E-4 \)
B. \( A-2, B-4, C-3, D-5, E-1 \)
\( C \cdot A-4, B-3, C-5, D-1, E-2 \)
D. \( A-4, B-1, C-3, D-5, E-2 \)


The amount of work done is pumping water out of a cubical vessel of height
\( \mathrm{m} \) is nearly (Given \( \rho_{w a t e r}=1000 \mathrm{kg} / \mathrm{m}^{3} \)
A . 5,000
в. 10,000
c. 5 J
D. 10 J


For the reactions,
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}, \boldsymbol{K}_{c}=\mathbf{1} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \boldsymbol{K}_{c}=\mathbf{3} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D}, \boldsymbol{K}_{c}=\mathbf{5} . \boldsymbol{K}_{c} \) for reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A . 15
B. 5
\( c .3 \)
D.


Assertion
Hn \( m R N A \) is larger than \( m R N A \)
Reason
Hn \( R N A \) has no translating introns and has more exons than required for translation.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


State True or False.
The average speed of a gas varies linearly with increase of temperature.
A. True
B. False


If a man from sea
coast goes to Everest peak then
A. His breathing and heart beat will increase
B. His breathing and heart beat will decrease
C. His respiratory rate will decrease
D. His heart beat will decrease


Sl unit of electric power is


Enzyme alternate oxidase is inhibited by
\( A \). NADP
B. SHAM (Salicyl hydroxamic acid)
c. Both A and B
D. None of these


The length of similar components
produced by a company is approximated by a normal distribution model with a mean of \( 5 \mathrm{cm} \) and a
standard deviation of \( 0.02 \mathrm{cm} . \) If a
component is chosen at random, what is the probability that the length of this component is between 4.96 and 5.04
\( \mathrm{cm} ? \)
\( \mathbf{A} \cdot 0.9544 \)
B. 0.1236
c. 0.7265
D. 0.9546


Which of the following set of three items are true, as each set belongs to the category mentioned against them?
A. Lysine, glycine, thiamine - Amino acids
B. Myosin, oxytocin and gastrin - Hormones
c. Rennin, helicase and hyaluronidase - Enzyme
D. optic nerve, oculomotor, vagus - sensory nerves


The length of the normal from origin to
the plane \( x+2 y-2 z=9 \) is equal to
A . 2 units
B. 3 units
c. 4 units
D. 5 units


There is a very specific rule by which one can predict the carcinogenic activity of hydrocarbons or their derivatives.
A. True
B. False


The \( 4^{t h} \) term of a geometric sequence is \( \frac{2}{3} \) and the seventh term is \( \frac{16}{81} . \) Find the geometric sequence


The increasing order of electron gain enthalpy of the following substances is:
\[
\boldsymbol{O}<\boldsymbol{S}<\boldsymbol{S} \boldsymbol{e}<\boldsymbol{T} \boldsymbol{e}
\]
If the order of bond dissociation
enthalpy is correct, enter 1 else 0.


The mean free path of a gas varies with
absolute temperature as:
A. \( T \)
B. \( T^{-1} \)
\( c \cdot T^{2} \)
\( \mathbf{D} \cdot \mathbf{T}^{4} \)


Caustic alkalis are corrosive.
A. True
B. False


Solve for \( x \) and \( y, \) if \( \left(\begin{array}{l}x^{2} \\ y^{2}\end{array}\right)+3\left(\begin{array}{c}2 x \\ -y\end{array}\right)= \)
\( \left(\begin{array}{c}-\mathbf{9} \\ \mathbf{4}\end{array}\right) \)


In a Geiger-Marsden experiment, calculate the distance of closest
approach to the nucleus of \( Z=80 \)
when \( \alpha \) -particle of \( 8 M e V \) energy
impinges on it before it comes momentarily to rest and reverses its direction. How will the distance of
closest approach be affected when the
kinetic energy of the \( \alpha \) -particle is doubled?


A mixture of \( C S_{2} \) vapour and nitrogen monoxide, \( N O \), gives a vivid blue flame
when ignited. A yellow solid is left afterwards. Write the equation.
A \( \cdot 2 N O(g)+C S_{2} \rightarrow \underset{\text {yellowssild}}{2 S(s)}+N_{2}(g)+C O_{2}(g) \)
B. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoild }}{2 S(s)}+N_{2} O(g)+C O(g) \)
c. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoid }}{2 S O(s)}+N_{2}(g)+C O(g) \)
D. \( 2 N O(g)+C S_{2} \rightarrow \underset{\text { yellowsoild }}{2 S(s)}+N_{2} O_{2}(g)+C(g) \)


Nascent hydrogen is obtained from
reaction between :
A. \( N a \) and \( C_{2} H_{5} O H \)
B. \( A l \) and \( N a O H \)
c. \( Z n \) and \( d i l . H_{2} S O_{4} \)
D. All of these


If the coefficient of second, third and
fourth terms in the expansion if \( (1+ \)
\( x)^{2 n} \) are in A.P, the \( 2 n^{2}-3 n \) is equal to
A. -7
B. 14
\( c .6 \)
D. -6


\( 6.022 \times 10^{22} \) molecules of \( N_{2} \) at NTP
will occupy a volume of:
A .22 .4 litres
B. 2.24 litres
c. 6.02 litres
D. \( 6.02 \mathrm{mL} \)


When light passes from air to glass, it experiences a change of:
A. speed only
B. wavelength and speed
c. frequency only
D. frequency and speedd


If the circumference of the inner edge of a hemispherical bowl is \( \frac{132}{7} \mathrm{cm} \) then what is the capacity?
A \( \cdot 12 \pi c m^{3} \)
в. \( 18 \pi c m^{3} \)
\( \mathbf{c} \cdot 24 \pi c m^{3} \)
D. \( 36 \pi c m^{3} \)


Assertion
On cooling, the brown colour of \( N O_{2} \) disappears.
Reason
On cooling \( N O_{2} \) forms dimer \( \left(N_{2} O_{4}\right) \) resulting in the pairing of the odd
electrons in \( N O_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the area of the following triangles.


The light coming from the sun is stored as energy in plants by the process of photosynthesis. This happens by converting carbon dioxide and water into:
A. green leaves
B. carbohydrates
c. fats
D. plants hormones


If \( X \) and \( Y \) are two elements which
belong to same group of Newland's periodic table, how many elements exists between \( X \) and \( Y ? \)
A . 4
B. 5
\( c \cdot 6 \)
D.


Lyophobic colloids are:
A . reversible
B. irreversible
c. water loving
D. solvent loving


Which one of the following is ethyl - 4
(dimethyl amino) butanoate?
\( A \)
B.
\( c \)
D.


Which of the following graphs should be used to represent the percentage of boys and girls in a class?
A. Bar graph
B. Pie chart
c. Line graph
D. Venn diagram


Class \( \begin{array}{cccc}2- & 4- & 6- & 8- \\ 4 & 6 & 8 & 10\end{array} \) \( 10- \)
12 interval
frequency \( 2 \quad 4 \quad 6 \) 10 5
What is the mode for the grouped data?
A .10 .5
B. 12.5
c. 13.7
D. 9.1


In a G.P. the \( 3^{r d} \) term is \( 24 \& 6^{t h} \) term is
192. Find the \( 10^{t h} \) term.


The complex, \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
has octahedral shape.
A. True
B. False


A particle starts from point \( A \) moves along a straight line path with an acceleration given by \( a=p-q x, \) where
\( p, q \) are constants and \( x \) is distance
from point \( A . \) The particle stops at point
B. The maximum velocity of the particle is
A. \( \underline{p} \) \( q \)
B. \( \frac{p}{\sqrt{q}} \)
c. \( \frac{q}{p} \)
D. \( \frac{\sqrt{q}}{p} \)


In the given reaction:
\( [X] \) will be :
A. Only syn oxime
B. Only anti oxime
\( c . \) mixture of syn and anti oxime
D. secondary amide


According to Rutherford atom model, the spectrum emitted by an atom is :
A. Line spectrum
B. Continuous spectrum
c. continuous absorption spectrum
D. Band spectrum


\( -32 \times x=160,-23 \times y=-115 \)
What is the value of \( x \div y ? \)
A . -1
B.
\( c .-5 \)
D. 5


The rods of length \( L_{1} \) and \( L_{2} \) are made of materials whose coefficient of linear
expansion are \( \alpha_{1} \) and \( \alpha_{2} \) respectively.If the difference between the two length of independent of temperature, then
A \( \cdot \frac{L_{1}}{L_{2}}=\frac{\alpha_{1}}{\alpha_{2}} \)
B. \( \frac{L_{1}}{L_{2}}=\frac{\alpha_{2}}{\alpha_{1}} \)
c. \( L_{1}^{2} \alpha_{1}=L_{2}^{2} \alpha_{2} \)
D. \( \alpha_{1}^{2} L_{1}=\alpha_{2}^{2} L_{2} \)


A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When excess of this gas
reacts with \( N H_{3} \) an unstable trihalide
is formed. In this process, the oxidation state of nitrogen changes from
A. 0 to -3
B. -3 to 0
\( \mathbf{c} \cdot-3 \) to +5
D. -3 to +3


Find the term \( t_{10} \) of an A.P.
\( 4,9,14, \dots \)


State True or False.
Deforestation increases the chances of
natural calamities
A. True
B. False


The probability that a student is not a swimmer is \( \frac{1}{5} . \) Then the probability that out of five students, four are swimmers
is
\( ^{\mathbf{A}} \cdot_{^{5}} C_{4}\left(\frac{4}{5}\right)^{4} \frac{1}{5} \)
\( ^{\mathrm{B}}\left(\frac{4}{5}\right)^{4} \frac{1}{5} \)
\( ^{\mathbf{c}} \cdot_{^{5}} C_{1} \frac{1}{5}\left(\frac{4}{5}\right)^{4} \)
D. none of these.


Find the increase in pressure required to decrease the volume of water sample
by \( 0.01 \% \). Bulk modulus of water \( = \) \( 2.1 \times 10^{9} N m^{-2} \)
A \( \cdot 4.3 \times 10^{4} N / m^{2} \)
B. \( 1.8 \times 10^{7} N / m^{2} \)
c. \( 2.1 \times 10^{5} N / m^{2} \)
D. \( 3.7 \times 10^{4} N / m^{2} \)


If \( S \) is any point in the interior of \( \Delta P Q R \) prove that \( (\boldsymbol{S} \boldsymbol{Q}+\boldsymbol{S} \boldsymbol{R})<(\boldsymbol{P} \boldsymbol{Q}+\boldsymbol{P} \boldsymbol{R}) \)


Solve the following equations and verify
your answers:
\( \frac{1-9 y}{19-3 y}=\frac{5}{8} \)


Given \( \xi=\{x: x \text { is a natural number }\} \) \( A=\{x: x \text { is an even number } x \in N\} \) \( \mathrm{B}=\{\mathrm{x}: \mathrm{x} \text { is an odd number, } \mathrm{x} \in \mathrm{N}\} \)
Then \( (\boldsymbol{B} \cap \boldsymbol{A})-(\boldsymbol{x}-\boldsymbol{A})=\dots \)
\( A \cdot \phi \)
в.
\( c . B \)
D. \( A-B \)


Why fluorine is a stronger oxidizing agent than chlorine?


Identify the common property for a chemical reaction at dynamic equilibrium.
A. The measurable properties like concentration, density colour, pressure etc remain constant at constant temperature
B. The forward and backward reactions take place with the same rate
c. It can be achieved from both directions
D. All of the above


Which of the following is obtained in carbylamine reaction?
A. \( C_{6} H_{5} N H_{2} \)
в. \( C O C l_{2} \)
\( \mathbf{c} \cdot C_{6} H_{5} C N \)
D. \( C_{6} H_{5} N C \)


Write balanced chemical equations for
the conversion of \( C r O_{4}^{2-} \) to \( C r_{2} O_{7}^{2-} \) in acidic medium and \( C r_{2} O_{7}^{2-} \) to \( C r O_{4}^{2-} \)
in basic medium.


In Young's double slit experiment, one of
the slit is wider than other, so that
amplitude of the light from one slit
double of that from other slit. If \( \mathbf{I}_{\mathbf{m}} \) be
the maximum intensity, the resultant
intensity I. When they interfere at phase difference \( \phi \) is given by
A \( \cdot \frac{I_{m}}{9}(4+5 \cos \phi) \)
B. \( \frac{I_{m}}{3}\left(1+2 \cos ^{2} \frac{\phi}{2}\right) \)
C \( \cdot \frac{I_{m}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right) \)
D. \( \frac{I_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right) \)


Two copper wires whose masses are 8
and 12 gm have lengths in the ratio 3: 4 Their resistances are in the ratio.
A . 4: 9
B. 16: 9
c. 27: 32
D. 27: 128


The life of all multicellular organisms through sexual reproduction starts as a
A. Zygote
B. Sperm cell
c. Haploid cell
D. Eggg


The compound which produces propane on heating with HI in presence of red phosphorus is
A. \( C H_{3} C H_{2} C H_{2} I \)
в. \( C H_{3} C H_{2} C H O \)
c. \( C H_{3} C H_{2} C H_{2} O H \)
D. All of three


Graphite is used for making electrodes and articles like writing pencils. It is made by heating coke with some silica for many hours in:
A. a blast furnace
B. a high electric furnace
c. the presence of air
D. a blast of steam under pressure


The book Power of movement in plants
was written by
A. Priestly
B. Mendel
c. Darwin
D. Aristotle


Two identical glass \( \left(\mu_{g}=3 / 2\right) \)
equiconvex lenses of focal length \( f \) are
kept in contact. The space between the two lenses is filled with water \( \left(\mu_{w}=\right. \)
4/3). The focal length of the combination is
\( A \cdot f \)
в. \( \frac{f}{2} \)
c. \( \frac{4 f}{3} \)
D. \( \frac{3 f}{4} \)


A magnetic moment of an electron orbiting in a circular orbit of radius \( r \)
with a speed \( v \) is equal to:
A \( \cdot \frac{e v r}{2} \)
в. \( e v r \)
c. \( \frac{e r}{2 v} \)
D. none of these


A step-up transformer of turns ratio 2: 1 has \( 50 \mathrm{Hz} \) AC voltage applied to primary The frequency of AC output voltage across secondary is :
A. zero
B. 25 Hz
c. 50 нz
D. 100 нz


Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train is 120 metres, in how much time (in seconds) will they cross each
other if travelling in opposite direction?
A . 10
B. 12
c. 15
D. 20


A ball of superconducting material is dipped in liquid nitrogen and placed near a bar magnet. In which direction will it move?
A. Away from bar magnet
c. Around the bar magnet
D. Remain constant


\( A B C D \) is a quadrilateral, \( E \) is the point of intersection of the line joining the midpoints of the opposite sides. If \( O \) is any point and \( \overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+ \) \( \overrightarrow{O D}=x \vec{O} E, \) then \( x \) is equal to
\( A \cdot 3 \)
B. 9
\( c \cdot 7 \)
D.


The ammonia evolved from the
treatment of \( 0.30 g \) of an organic compound for the estimation of nitrogen was passed in 100 m \( L \) of 0.1 \( M \) sulphuric acid. The excess of acid required \( 20 m L \) of 0.5 sodium hydroxide solution hydroxide solution for complete neutralization. The organic compound is:
A. acetamide
B. thiourea
c. urea
D. benzamide


What are the characteristic features of
Euglenoids?


A stone is thrown upwards from a tower with a velocity \( 50 m s^{-1} \). Another stone
is simultaneously thrown downwards from the same location with a velocity \( 50 m s^{-1} . \) When the first stone is at the
highest point, the relative velocity of the second stone with respect to the first stone is (assume that second stone has
not yet, reached the ground
A. zero
B. \( 50 m s^{-1} \)
\( c \cdot_{100 m s^{-}} \)
D. \( 150 \mathrm{ms}^{-1} \)


A uniform capillary tube of length \( l \) and
inner radius \( r \) with its upper end sealed
is submerged vertically into water. The
outside pressure is \( p_{0} \) and surface
tension of water is \( \gamma \). When a length \( x \) of
the capillary is submerged into water, it is found that water levels inside and
outside the capillary coincide, the value
of \( x \) is
A.
\[
\frac{l}{\left(l+\frac{p_{0} r}{4 \gamma}\right)}
\]
B. \( l\left(l-\frac{p_{0} r}{4 \gamma}\right) \)
\( ^{\mathbf{c}} \cdot_{l}\left(l-\frac{p_{0} r}{2 \gamma}\right) \)
D.
\[
\left(l+\frac{p_{0} r}{2 \gamma}\right)
\]


Which of the following scientist gave the name hydrochloric acid to \( H C l ? \)
A. Joseph Louis Gay-Lussac
B. Lavoiser
c. cavendish
D. Glauber


A uniform scale is kept in equilibrium
when supported at the \( 60 \mathrm{cm} \) mark and
a mass \( M \) is suspended from the
\( 90 \mathrm{cm} \) mark as shown in the figure.
State with reasons whether the weight
of the scale is greater than, less than or
equal to mass \( M \)
\( \mathbf{A} \cdot 3 M \)
в. \( 4 M \)
\( c .5 M \)
D. \( M \)


When dry chlorine gas is bubbled through molten Sulphur, a red liquid is formed. What is its composition?


An excised leaf does not turn yellow if it is induced to root. This is attributed to
synthesis in root of
or
Leaf ageing is retarded by
A. Ethylene
B. Cytokinins
c. Gibberellins
D. Auxins


ff \( f(x)=2 x-3, a=2, l=1 \) and \( \epsilon= \)
0.001 then \( \delta>0 \) satisfying \( 0<\mid x- \)
\( \boldsymbol{a}|<\boldsymbol{\delta},| \boldsymbol{f}(\boldsymbol{x})-\boldsymbol{l} \mid<\boldsymbol{\epsilon}, \) is:
A. 0.005
B. 0.0005
c. 0.001
D. 0.0001


State whether true or false:
During destructive interference, the crest of one wave meets the trough of the other wave.
A. True
B. False


The number of 4 letter word that can be
made with the letter of the word
COMBINATION is
A . 2354
в. 2454
\( c .1454 \)
D. None of these


For the following circuits, the potential
difference between \( X \) and \( Y \) in volt is:
4
B. 4 3
\( c \)
D. 5


When 3 -methylbutan-2-ol is treated with HBr, the following reaction takes place:
Give a mechanism for this reaction.
(Hint : The secondary carbocation formed in step II rearranges to a more stable tertiary carbocation by a
hydride ion shift from 3rd carbon atom.


If the particle moves from \( A \) to \( B \) as
shown in figure, then the ratio of displacement to distance covered by particle is (if \( \mathrm{R} \) is the radius of track)
\( A \cdot \frac{2 \sqrt{2}}{3 \pi} \)
в. \( \frac{3 \pi}{2 \sqrt{2}} \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. \( \frac{\pi}{2 \sqrt{2}} \)


Name the blood cells, whose reduction
in number can cause clotting disorder, leading to excessive loss of blood from the body
A. Erythrocytes
B. Leucocytes
c. Neutrophills
D. Thrombocytes


Unit of electric power may also be expressed as:
A. volt ampere
B. kilowatt hour
c. watt second
D. joule secono


\( f\left(a_{1}, a_{2}, \dots a_{n} \) be an A.P.of tive terms, \right. then \( \sum_{k=1}^{n} a_{k} \geq n \sqrt{a_{1}^{2}+(n-1) d a_{1}} \)
where dis common difference of A.P. If
you think this is true write 1 otherwise
write 0 ?


Which of the following compounds will undergo Cannizzaro reaction?
A. \( C H_{3} C H O \)
в. \( C H_{3} \) СОСН\( _{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C H O \)
D. \( C_{6} H_{5} C H_{2} C H O \)


\( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma \) -rays emitted from a radioactive source are passed through
a \( 0.5 c m \) thick aluminium sheet. The out
going radiations will consist of
A. \( \alpha, \beta \) and \( \gamma \) -rays
B. \( \gamma \) and \( \beta \) -rays only
c. \( \gamma \) rays only
D. \( \alpha \) rays only


A body of mass M collides with a wall
with velocity \( V \) and rebounds with the same speed. Its change in momentum is equal to :
A. zero
в. му
c. гму
D. 3MV


When a hydrogen sample in the ground state is bombarded then what potential is required to accelerate electron so
that first Paschen line is emitted, then
calculate the energy difference?
A . 2.55
B. 0.65
c. 12.09
D. 12.75


\( H_{3} A O_{4} \) has \( 31.6 \% \) of "A" by mass. The atomic mass of the atom "A" is:
A . 17
B. 3
c. 35.5
D. 40


If \( f: R^{+} \rightarrow R^{+}, f(x)=x^{2}+2 \) and \( g: \)
\( \boldsymbol{R}^{+} \rightarrow \boldsymbol{R}^{+}, \boldsymbol{g}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\mathbf{1}} \)
then \( (\boldsymbol{f}+\boldsymbol{g})(\boldsymbol{x}) \) equals
A. \( \sqrt{x^{2}+3} \)
B. \( x+3 \)
c. \( \sqrt{x^{2}+2}+(x+1) \)
D. \( x^{2}+2+\sqrt{(x+1)} \)


Explain allosteric inhibition with an example.


The electrical conductivity of a semiconductor increases when
electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The forbidden band
energy for the semiconductor in \( e V \) is
A . 0.5
B. 0.9
\( c .0 .7 \)
D. 1.


f \( \boldsymbol{x}+\boldsymbol{y}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{2} \\ \mathbf{0} & \mathbf{9}\end{array}\right] \) and \( \boldsymbol{x}-\boldsymbol{y}= \)
\( \left[\begin{array}{cc}\mathbf{3} & \mathbf{6} \\ \mathbf{0} & -\mathbf{1}\end{array}\right] \) Find the value of \( \boldsymbol{x} \) and \( \boldsymbol{y} \)


The weight of an object:
A. is the quantity of the matter it contains
B. refers to its inertia
C. is the same as its mass but is expressed in different unit
D. is the force with which it is attracted towards the earth


With the help of necessary circuit diagram, explain the working of a photodiode used for detecting optical signals.


Which of the following chemical names correctly corresponds to the chemical
structure shown?
A. Ethanol
B. Ethane
c. Ethene
D. Ether


Find the point on the curve \( 9 y^{2}=x^{3} \)
where normal to the curve has non zero
x-intercept and both x-intercept and \( y \) intercept are equal


Prove the following
\( \sec \theta(1-\sin \theta)(\sec \theta+\tan \theta)=1 \)


Transformer works on \( 220 V . \) Its
efficiency is \( 80 \% \). Output power is \( 8 K W . \) Primary current is
approximately.
\( \mathbf{A} \cdot 35 A \)
в. \( 18 A \)
\( c .22 A \)
D. \( 45 A \)


If an object is placed \( 25 \mathrm{cm} \) in front of
the converging lens forms an image
\( 20 c m \) behind the lens, then what is the
focal length of the lens?


Hydrolysis of an ester gives a carboxylic acid which on Kolbe's electrolysis yields
ethane. The ester is
A. ethyl methanoate
B. methyl ethanoate
c. propylamine
D. ethylamine


Starting from aniline how will you prepare benzene diazonium chloride
and chlorobenzene from the later?
Explain giving chemical reactions involved.


If \( P \) is a point, then how many tangents to a circle can be drawn from the point \( P, \) if it lies On the circle.
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


Isotopes could find a position in Mendeleev's periodic table. State whether the given statement is
true or false.
A. True
B. False


Which of the following is an example of catenation?
A \( \cdot C H_{4} \)
B. \( C H O \)
c. \( C C l_{2} \)
D. \( C_{2} H_{6} \)


The size of an object as perceived by an eye depends primarily on
A. Actual size of the object
B. Distance of the object from the eye
c. Aperture of the pupil
D. Size of the image formed on the retina


In the circuit shown here, at which point
is the current least?
\( A \)
B.
\( c . R \)
\( D \)


The argument of the complex number \( \sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right) \) is
A \( \cdot \frac{6 \pi}{5} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{9 \pi}{10} \)
D. \( \frac{2 \pi}{5} \)


If a charged particle goes unaccelerated in a region containing electric and magnetic fields This question has multiple correct options
A. \( \vec{E} \) must be perpendicular to \( \vec{B} \)
B . \( \vec{v} \) must be perpendicular to \( \vec{E} \)
c. \( \vec{v} \) must be perpendicular to \( \vec{B} \)
D. \( E \) must be equal to \( v B \)


The magnification produced by a mirror is \( \frac{1}{3} \) then the type of mirror is
A. Concave
B. convex
c. Plane
D. Planar


The self inductance of a choke coil is
mH. when it is connected with a 10 VDC
source then the loss of power is 20 watt.
When it connected with 10 volt \( A C \)
source loss of power is 10 watt. The frequency of AC source will bw-
\( A \cdot 50 \mathrm{Hz} \)
B. 60 Н
c. 80 н
D. 100 нz


In Young's experiment, the wavelength
of monochromatic light used is 6000 A. the optical path difference between the rays from the two coherent sources at
point \( P \) on the screen is \( 0.0075 \mathrm{mm} \) and at a point \( Q \) on the screen is \( 0.0015 \mathrm{mm} \) How many bright and dark bands are observed between the two points \( P \) and
Q?


Molecular mass of water
\( \mathbf{A} \cdot 18 u \)
в. \( 16 u \)
c. \( 15 u \)
D. \( 10 u \)


Chloroprene is the monomer of:
A. PVC
B. Neoprene
c. Polystyrene
D. Polythene


For the two compounds, the vapour
pressure of (2) at a particular temperature is expected to be:-
\( (i) \)
(ii)
A. Higher than (i)
B. Lower than that of (i)
c. Same as that of (i)
D. Can be 'higher or lower depending upon the size of the vessel


Roll a fair die twice. Let \( A \) be the even
that the sum of the two rolls equals six,
and let \( B \) be the even that the same
number comes up twice. What is \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) ? \)
A \( \cdot \frac{1}{6} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{1}{5} \)
D. none of these


Assertion
All the materials always have the same colour, whether viewed by reflected light or through transmitted light.
Reason
The colour of material does not depend
on nature of material.
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


Assertion
The last element in a group is radioactive
Reason
In case of elements with high atomic
masses, nucleus is unstable.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( (\cos x)^{y}=(\cos y)^{x} \) then find \( \frac{d y}{d x} \)


Sodium, potassium and lithium are stored under oil, give reason.


A \( 4.0 \mathrm{cm} \) high object is placed at a
distance of \( 60 \mathrm{cm} \) from a concave lens
of focal length \( 20 \mathrm{cm} . \) Find the size of the image.


If \( \vec{a}, \vec{b}, \vec{c} \) are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then the centroid of the triangle satisfies which of the following relation?
A \( \cdot \vec{a}+\vec{b}+\vec{c}=0 \)
B \cdot \( \overrightarrow{a^{2}}=\overrightarrow{b^{2}}+\overrightarrow{c^{2}} \)
c. \( \vec{a}+\vec{b}-\vec{c}=0 \)
D. None of these


Assertion
In chemisorption, adsorption keeps on increasing with temperature.
Reason
Heat keeps on providing more and more
activation energy.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of (A).
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect


Two non ideal batteries are connected
in series. Consider the following
statements
(A) The equivalent emf is larger than either of the two emfs.
(B) The equivalent internal resistance is
smaller than either of the two internal
resistances.
A. Both A and B are correct
B. A is correct but B is wrong
C. B is correct but A is wrong
D. Both A and B wrong


Define elasticity.


Consider the following process \( \Delta \boldsymbol{H}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l}) \)
\( \frac{1}{2} \boldsymbol{A} \rightarrow \boldsymbol{B}+\mathbf{5 0} \)
\( \mathbf{3} \boldsymbol{B} \rightarrow \mathbf{3} \boldsymbol{C}+\boldsymbol{D}-\mathbf{1 2 5} \)
\( \boldsymbol{E}+\boldsymbol{A} \rightarrow \mathbf{2} \boldsymbol{D}+\mathbf{3 5 0} \)
For \( \boldsymbol{B}+\boldsymbol{D} \rightarrow \boldsymbol{E}+\mathbf{2} \boldsymbol{C}, \boldsymbol{\Delta} \boldsymbol{H} \) will be:
A . 325 kJ/mol
B. 525 kJ/mol
c. - 375 kJ/mol
D. -325 kJ/mol


Mobile electrons carriers in ETS in
mitochondrial membrane are
A. \( P Q, P C \)
в. \( C o Q, C y t c \)
c. \( P Q, \) Cyt \( c \)
D. \( P C, C o Q \)


Sound is produced by vibration. Define
vibration.
A. Vibration is a rapid to and fro motion of the object.
B. Vibration is a circular motion of the object.
C. Vibration is a translational motion of the object.
D. None of the above


If the radius of a circle is increased by 3 times then the diameter increases by
times
\( A \cdot 4 \)
B. 6
\( c \cdot 3 \)
D. 8


Find the volume of sphere whose radius
is \( 3 \mathrm{cm} \)


A particle performs SHM on a straight line with time period \( T \) and amplitude
A. The average speed of the particle between two successive instants, when
potential energy and kinetic energy become same is
A \( \cdot \frac{A}{T} \)
в. \( \frac{4 \sqrt{2} A}{T} \)
c. \( \frac{2 A}{T} \)
D. \( \frac{2 \sqrt{2} A}{T} \)


Diatom frustule is made of
A. Silica
B. Calcium carbonate
C . Calcium hydroxide
D. Both B and C.


The 17 th term of an AP exceeds its 10 th
term by 7. Find the common difference.


Find the equation of a straight line cutting off an intercept -1 from \( y- \) axis and being equally inclined to the axes.


Association of m-RNA with several
ribosomes is called
A. Polysome
B. Tranposons
c. Both A and B
D. None of the above


The quantity of \( C O_{2} \) in atmosphere can be decreased by :
A. Rain
B. Forests
c. vegetation
D. All of the above


At what distance should an object be placed from a convex lens of focal length \( 18 \mathrm{cm} \) to obtain an image at
\( 24 c m \) if on the other side. What will be
the magnification produced in this
case?


Assertion
A body is moved from \( x=2 \) to \( x=1 \)
under a force \( \boldsymbol{F}=\mathbf{4} \boldsymbol{x} \), the work done by
this force is negative.
Reason
Force and displacement are in opposite directions.
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


Assertion
Positive catalysts lower the activation energy of the reaction whereas heat of reaction remains same.
Reason
Heat of reaction is equal to the difference between activation energies for forward and the backward reactions.
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


If the sum of the roots of the equation \( x^{2}-x=k(2 x-1) \) is zero, find \( k \)


Draw a neat labelled diagram of reflection of light from a plane reflecting surface on the basis of wave theory.


Find the standard deviation of the
numbers 62,58,53,50,63,52,55


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


How many tangents can be drawn on the circle of radius \( 5 \mathrm{cm} \) form a point lying outside the circle at distance \( 9 \mathrm{cm} \)
from the center


Solve \( \frac{x}{3}+\frac{y}{5}=1,7 x-15 y=21 \)


Which of the following properties are similar for isotopes?
A. Physical properties
B. Chemical properties
c. Both physical and chemical properties
D. Neither physical nor chemical properties


The bulb does not glow in the set up
shown in the figure. List the possible
reasons. Explain your answer.


Give the chemical formula of calcium
sulphate hemihydrate.
A \( \cdot \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \)
в. \( \operatorname{caSO}_{4}: \frac{1}{2} H_{2} \mathrm{O} \)
c. \( \operatorname{cas} O_{4} \cdot 10 H_{2} O \)
D. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)


Draw a neat diagram of \( A C \) dynamo
and label the parts.


\( A \) and \( B \) are the points (2,0) and (0,2) respectively. The coordinates of the point \( P \) on the line \( 2+3 y+1=0 \) are
A. (7,-5) if |PA - PBl is maximum
B. \( \left(\frac{1}{5}, \frac{1}{5}\right) \) if \( |P A-P B| \) is maximun
c. (7,-5) if \( \mid P A-P B / \) is minimum
D. \( \left(\frac{1}{5}, \frac{1}{5}\right) \) if \( \mid \) PA - PB l is minimun


The number of books issued from a
library in five days is given below. Represent the information in the form of
a bar graph


Two bodies \( A \) and \( B \) of same mass are
moving with velocities \( \boldsymbol{v} \) and \( 2 \boldsymbol{v} \) respectively. What is the ratio of their momentum?
A . 3: 2
B. 2:
c. 1: 2
D. 1:


Which of the following deformations is/are irreversible?
This question has multiple correct options
A. Elastic deformation
B. Plastic deformation
c. Fracture
D. All of the above


In triangle \( A B C ; \) angle \( A=90^{\circ}, \) side
\( A B=x c m, A C=(x+5) c m \) and
area \( =150 \mathrm{cm}^{2} \). Find the sides of the
triangle.


\( \ln \Delta A B C, \) ray BD bisects \( \angle A B C \) and ray
\( \mathrm{CE} \)
bisects \( \angle A C B \) If \( \operatorname{seg} A B \cong \operatorname{seg} A C \)
then prove that \( E D \| B C \)


The refractive index of glass in
maximum for :
A . red color
B. yellow color
c. violet color
D. green color


Work done in a reversible process is always maximum hence, the total entropy of system and surrounding is always:
A. negative
B. positive
c. zero
D. infinity


Assertion
Ohm's law is not valid if current
depends on voltage non-linearly.
Reason
Ohm's law is a fundamental law of
nature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{T}= \)
\( \{x: x \text { is a letter in the word 'TEETH' }\} \)
find all its subsets.


The total number of cyclic isomers
possible for a hydrocarbon with the
molecular formula \( C_{4} H_{6} \) is:
\( A \cdot O \)
B.
\( c \cdot 2 \)
D. 3
\( E \cdot 4 \)
\( F .5 \)
\( G \cdot 6 \)
\( \mathrm{H} \cdot 7 \)
1. 8
J. 9


The cycle in which pyruvic acid is
broken down in the presence of oxygen is known as
A. Glycolysis
B. Kreb's cycle
c. Anaerobic respiration
D. None of the above


The oil drop experiment by R.A. Millikan was performed to find
A. charge on the neutron
B. charge on the electron
c. charge on the Proton
D. None of these


Which of the following would not form upon electolysis of aqueous solution of potassium propanoate?
A. Butane
B. Ethyl ethanoate
c. Ethyl propanoate
D. Ethene


The succession that starts on
abandoned crop land is
A. Primary succession
B. xerarch succession
c. secondary succession
D. Hydrarch succession


Sulphur on reaction with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives
\( A \cdot S O_{2} \)
в. \( H_{2} \)
\( c \cdot S O_{3} \)
D. \( H_{2} \)


'Accelerators', in rubber technology, are organic sulphur compounds used as:
A. catalysts for vulcanization
B. carbon black binders for tyres
c. fillers
D. speed increasers for nylon tyres


What is the fifth term of the arithmetic
sequence \( 2,_{-}, 8, \ldots, \ldots ? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 11
c. 13
D. 14
E . 15


Choose the correct statement among
the following options:
A. When displacement is zero, distance travelled is not necessarily zero
B. When displacement is zero, distance travelled is also zero
C. When distance is zero, displacement is not zero
D. Distance travelled and displacement are always equal


Describe the extraction of two metals
and two non-metals by electrolysis.


In reflection, light travels through:
A. only one medium
B. two media
c. three media
D. more than three media


Fill in the blanks with \( >,< \) or \( = \)
(i) \( 22 \times(-36)+(-42) \div(-3) \square 9 \times \)
\( 56 \times(-8) \)
(ii) \( 26-22+21 \div(-7) \square 43-11-13 \)
(iii) \( (-16) \div[(-13)+(-3)] \square 12 \div \)
\( [(-3)-0] \)
\( A \cdot(i)->,(\text { ii) }-<, \text { (iii) }-= \)
B. (i)-<, (ii)-<, (iii)->
\( c \cdot(i)->,(\text { ii) }-<, \text { (iii) }-> \)
D. (i)-=, (ii)->, (iii)-


Coronary sulcus is?
A. Transverse groove
B. Longitudinal sulcus
C. Also known as Inter-ventricular sulcus
D. Inter-articular septum


Three machines \( A, B \) and \( C \) produce respectively \( 50 \%, 30 \% \) and \( 20 \% \) of the total number of items of a factory. The
percentage of defective output of these machines are \( 3 \%, 4 \% \) and \( 5 \% \) respectively. if an item selected at random, find the probability that the item is non-defective.


Enzyme pepsin acts upon food at a pH
of approximately
A. 2 to change proteins into peptones
B. 7 to change proteins to peptones
C. 2 to change proteins into amino acids
D. 4 to change protein into proteoses


Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area \( 1.0 \times 10^{-7} m^{2} \)
carrying a current of 1.5 A. Assume that
each copper atom contributes roughly one conduction electron. The density of copper is \( 9.0 \times 10^{3} k g m^{-3} \) and its
atomic mass is 63.5 amu.
В. \( 1.1 \times 10^{-3} \mathrm{ms}^{-1} \)
D. \( 2.1 \times 10^{3} \mathrm{ms}^{-1} \)


The tension in the string is:
A. 600 N
B. 80 N
c. 1200 N
D. \( 800 \mathrm{N} \)


Prove that \( \sin ^{-1}\left(\frac{8}{17}\right)+\sin ^{-1}\left(\frac{3}{5}\right)= \)
\( \cos ^{-1}\left(\frac{36}{85}\right) \)


What is value of \( (-i)^{12} \)


\( x \) and \( y \) are two \( +v e \) numbers suchs that \( x y=1 . \) Then the minimum value of \( x+y \) is
A . 4
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. 2


\( S-S \) bond is present in :
A \( \cdot \alpha-\left(S O_{3}\right)_{n} \)
B \( \cdot \gamma-\left(S_{3} O_{9}\right) \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{8} \)


An echo is heard, if between the source and the reflector is
atleast \( 17 \mathrm{m} \)
A. time
B. distance
c. arc length
D. none of these


The freezing point of water in Kelvin scale is:
A . \( 73.15 K \)
В. \( 173.15 K \)
c. \( 273.15 K \)
D. \( 373.15 K \)


Products \( A \) and \( B \) respectively are
4
\( B \)
c. Reaction is not possibl
D. None of thes


Two parallel plate air capacitors of
same capacity' \( C^{\prime} \) are connected in
series to a battery of emf ' \( E^{\prime} . \) Then one
of the capacitors is completely filled
with dielectric material of constant \( ^{\prime} \boldsymbol{K}^{\prime} \)
The change in the effective capacity of
the series combination is
A \( \cdot \frac{C}{2}\left[\frac{K-1}{K+1}\right] \)
B \( \cdot \frac{2}{C}\left[\frac{K-1}{K+1}\right] \)
c. \( \frac{C}{2}\left[\frac{K+1}{K-1}\right] \)
\( ^{\mathrm{D}} \cdot \frac{C}{2}\left[\frac{K-1}{K+1}\right]^{2} \)


The difference in the mass of 100 each
mole of sodium atoms and sodium ions
is 5.48002 g. Calculate the mass of an electron from the above data.
A \( \cdot 9.1 \times 10^{-28} \mathrm{kg} \)
В. \( 9.1 \times 10^{-31} k g \)
c. \( 5.4002 \times 6.022 \times 10^{-31} k g \)
D. \( 5.4002 \times 6.022 \times 10^{-28} \mathrm{kg} \)


A scientific way of doing things involve
A. Identifying the problem.
B. collecting data.
c. Hypothesizing a possible theory
D. All of the above


Which of the following easily catalyse
the decomposition of \( H_{2} O_{2} \) when stored?
(i) Rough surface
(ii) sunlight
(iii) Dust particles
(iv) Metals
A. (ii)and (ii)
B. (i),(ii) and (iii)
c. (ii) and (iii)
D. All of these


At what temperature \( \left(^{0} C\right), \) in the case
of mercury (Hg) drops abruptly to zero?
A. 3.2
B. 4.2 K
\( c .5 .2 k \)
D. 6.2 K


The velocity of projection of a projectile is given by : \( \vec{u}=5 \hat{i}+10 \hat{j} . \) Range is:
A \( .2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 10 m \)


\( \left|\begin{array}{ccc}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right|=2016 K \)
then value of \( \boldsymbol{K} \) is
A . 24
B. 84
c. \( \frac{1}{24} \)
D. \( \frac{1}{84} \)


\( \operatorname{Let} A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right] \) and \( 10 B= \)
\( \left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] . \) If \( B \) is the inverse of
matrix \( A \), then \( \alpha \) is
\( A \)
в.
\( c \cdot 2 \)
\( D \)


Concave lens is used to correct
A. Myopia
B. Presbiopia
C. Hypermetropia
D. cataract


Identify the principle behind the
concentration of bauxite ore:
A. magnetic property of impurities in white bauxite
B. low specific gravity of \( A l_{2} O_{3} \)
C . amphoteric nature of \( A l_{2} O_{3} \)
D. high melting point of \( A l_{2} O_{3} \)


From the understanding of cartesian sign convention for reflection by spherical mirror, students took part in group discussion for FA - 1 in classroom.
Who is wrong in the group discussion? Alpesh : All the distances are measured
from the pole of a mirror parallel to the
principal axis. Beena: The distances measured in the
direction of incident ray are taken
positive. Chamak: The height measured upward
and perpendicular to principal axis is taken negative.
Daksha : The height measured downward and perpendicular to principal axis is taken as positive.
A. Champak and Daksha
B. Only Champak
c. Alpesh and Beena
D. only Daksha


Which vitamins are present in much smaller amounts in cells?
A. \( A \)
в. \( D \)
c. \( B \) and \( C \)
D. \( K \)


Write the correct letter from column I
against the entry number in column lin
your answer book, \( z \neq 0 \) is a complex number


Which of the following condition favours the reduction of a metal oxide to metal?
A. \( \Delta H=+v e, T \Delta S=+v e \) at low temperature
B. \( \Delta H=+v e, T \Delta S=-v e \) at any temperature
C. \( \Delta H=-v e, T \Delta S=-v e \) at high temperature
D. \( \Delta H=-v e, T \Delta S=+v e \) at any temperature


In the preparation of \( \boldsymbol{C H} \boldsymbol{C l}_{3} \) from
ethanol and moist bleaching powder, the latter provides:
A \( \cdot C H_{3} C H O \)
в. \( H C l \)
\( \mathbf{c} \cdot \) Both \( C H_{3} C H O \) and \( H C l \)
D. Calcium formate


Assertion: Thallium
(III) hydroxide is highly soluble in water.
Reason: Thallium
(III) hydroxide is the
most basic among 13th group
hydroxides.
A. Assertion is True, Reason is True, Reason is a correct explanation of Assertion
B. Assertion is True, Reason is True, Reason is not a correct explanation of Assertion
c. Assertion is True, Reason is False
D. Assertion is False, Reason is True


A wire of resistance \( 100 \Omega \) is doubled
on itself. The new resistance is
A. 100 ohms
B. 200 ohms
c. 300 ohms
D. 400 ohms


If \( \boldsymbol{y}=\sec \sqrt{\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) equals-
A \( \cdot \frac{b}{b \sqrt{a+b x}} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
в. \( \frac{b}{2 \sqrt{a+b x}} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
c. \( 2 b \sqrt{a+b x} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
D. None of these


Sunken stomata occur in
A. Mango
B. Guava
c. Hydrilla
D. Nerium


An effective air-pollution control equipment is an attachment that electrically attracts pollutant particles in hot, escaping gases. It is known as:
A. an electric condenser
B. a gas condenser
c. an air purifier
D. an electrostatic precipitator


Solve the equation \( \sqrt{3} \cos x-\sin x=1 \)
A \( \cdot x=2 n \pi-\frac{\pi}{3} \pm \frac{\pi}{3}, n \in Z \)
В . \( x=2 n \pi-\frac{\pi}{6} \pm \frac{\pi}{3}, n \in Z \)
c. \( x=2 n \pi-\frac{\pi}{6} \pm \frac{\pi}{6}, n \in Z \)
D. None of these


Write cubes of 5 natural numbers which
are of the form \( 3 n+1(e . g .4,7,10,, . . .) \) and
verify the following:
'The cube of a natural number of the
form \( 3 n+1 \) is a natural number of the
same form'.


The length of a room is \( 5 m, \) breadth is
\( 3.5 m \) and height is \( 4 m . \) Find the total
expenditure of whitewashing on the four walls and roof at the rate of 15 per
square meter. (Answer correctly up to 1 decimal place)


When unpolarized light beams are incidents in the air into glass \( (n=1.5 \) at polarising angle)
A. reflected beams is 100 polarised
B. reflect and refracted beams are partially polarised
c. the reason for
(a) is that almost all the light is reflected
D. all the above


Very short answer type.
Why does blood not clot in blood
vessels?


A bacteria population increases sixfold
in 10 hours. Assuming normal growth, how long did it take for their population
to double?
A. 3.93 hrs
B. 3.87 hrs
\( c .3 .72 \) hrs
D. 3.54 hrs


Swetha is wearing a sharp edged high heeled footwear. Madhu is wearing a flat footwear. If both the girls are having same weight and both are stepping over your foot, whose footwear will cause
more pain to your foot? Why?


\( N_{2} \) can be obtained by passing \( N H_{3} \)
over red-hot copper
(II) oxide.


A solution of calcium in liquid ammonia when evaporated to dryness gives a complex:
A. Pure \( C a \)
в. \( \left[\mathrm{Ca}\left(\mathrm{NH}_{3}\right)_{x}\right]^{2+} \)
\( c \)
\( \left[\mathrm{Ca}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2} \)
D. \( C a\left(N H_{3}\right)_{6} \)


Write a short note on dispersion of light.


If \( \Delta t \rightarrow 0 \) the average rate changes to
A . infinitesimal rate
B. small rate
c. instantaneous rate
D. fast rate


Name a mammal where RBC are
nucleated.


The minimum energy required for the photo-emission of from the surface of
metal is \( 4.95 \times 10^{-19} \) J. Calculate the
critical frequency and the
corresponding wavelength of the photon required to eject the electron.


In the set of triangles in a plane the relation 'is similar to' is an equivalence relation. Prove


At what depth in an ocean will a bubble
of air have one fifth the volume is will
have on reaching the surface?
(Atmospheric pressure \( =76 \mathrm{cm} \) of \( \mathrm{Hg} \) and density of \( \mathrm{Hg}=13.6 \mathrm{gcm}^{-3} \)


The rotation of the Earth having radius
\( R \) about its axis speeds upto a value
such that a man at latitude angle \( 60^{\circ} \)
feels weightless. The duration of the day in such case will be.
A \( \cdot 8 \pi \sqrt{\frac{R}{g}} \)
в. \( 8 \pi \sqrt{\frac{g}{R}} \)
\( ^{c} \cdot \pi \sqrt{\frac{R}{g}} \)
D. \( 4 \pi \sqrt{\frac{g}{R}} \)


The common difference of an A.P. in
which \( a_{25}-a_{12}=-52 \) is:
A .4
B. -4
\( c \cdot-3 \)
D. 3


Evaluate
\( \int \frac{x+2}{\sqrt{x^{2}+4 x+1}} \cdot d x \)


Which sublevel can occupy a maximum of 10 electrons?
A . s
B. f
\( c \cdot p \)
D.


Einstein was awarded a Noble Prize for:
A. Photo electric effect
B. Compton effect
c. Theory of relativity
D. None of the above


Which of the following experiments does NOT have equally likely outcomes?
A. Choose a number at random from 1 to 7
B. Toss a coin
c. choose a letter at random from the word school
D. None of the above


A cricket ball is thrown up with a speed
of \( 19.6 m s^{-1} . \) The maximum height it
can reach is
\( \mathbf{A} \cdot 9.8 m \)
в. \( 19.6 \mathrm{m} \)
c. \( 29.4 m \)
D. 39.2 \( m \)


One angle of a seven sided polygon is
\( 108^{\circ} \) and each of the other six angles is
\( x^{\circ} . \) The value of \( x \) is
\( \mathbf{A} \cdot 114^{\circ} \)
B. \( 121^{\circ} \)
\( \mathrm{c} \cdot 131^{\circ} \)
D. \( 132^{\circ} \)


Suppose the distance between earth
and sun becomes half of its present
distance. What is likely to happen to
life?


Which process is important for production gametes in living organism performing sexual production in context with chromosomes?
A. Inequal fission
B. Meosis
c. Mitosis
D. Multiple fission


Complete the following table if \( \boldsymbol{x} \propto \boldsymbol{y} \)
\[
x
\]
\( \begin{array}{lllll}1 & 2 & 3 & - & 5\end{array} \)
\( 4 \quad 8 \) 16 \( - \) \( y \) 1


The units of solubility product of silver
chromate \( \left(A g_{2} C r O_{4}\right) \) will be
A \( \cdot m o l^{2} L^{-2} \)
B \( \cdot m o l^{3} L^{-3} \)
\( \mathrm{c} \cdot \operatorname{mol} L^{-1} \)
D. molL"


Two long wires are hanging freely. They are joined first in parallel and then in
series and then are connected with a
battery. In both cases which type of force acts between the two wires?
A. Attraction force when in parallel and repulsion force when in series
B. Repulsion force when in parallel and attraction force when in series
c. Repulsion force in both cases
D. Attraction force in both cases


toppr
Q Type your question
close to each other. Is the magnitude of
electrostatic force between them
exactly given by \( Q_{1} Q_{2} / 4 \pi \epsilon_{0} r^{2}, \) where \( r \)
is the distance between their centres?
(b) If Coulomb's law involved \( 1 / r^{3} \)
dependence (instead of \( 1 / r^{2} \) ),would Gauss' law be still true?
(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
(d) What is the work done by the field of
a nucleus in a complete circular orbit of the electron? What if the orbit is
elliptical?
(e) We know that electric field is
discontinuous across the surface of a
charged conductor. Is electric potential also discontinuous there?
(f) What meaning would you give to the capacitance of a single conductor?
(g) Guess a possible reason why water has a much greater dielectric constant \( (=80) \) than say, mica \( (=6) \)


To protect iron against corrosion, the most durable metal plating on it, is :
A. nickel plating
B. tin plating
C. copper plating
D. zinc plating


Which scientist discovered that the
same amount of space was occupied by equal numbers of molecules of gases, irrespective of whether it was hydrogen or chlorine or fluorine?
A. Gay-Lussac
B. Avogadro
c. Marconi
D. wohler


In steady horizontal flow:
A. The pressure is greatest where the speed is least
B. The pressure is independent of speed
C. The pressure is least where the speed is least
D. (a) and
(c) are correct


To how much angel does the earth revolve around sun in 2 days?


The maximum velocity of a body
undergoing S.H.M. is \( 0.2 m / s \) and its
acceleration at \( 0.1 \mathrm{m} \) from the mean
position is \( 0.4 m / s^{-2} \) The amplitude of
the S.H.M. is:
A . \( 0.25 m \)
в. \( 0.3 m \)
\( \mathrm{c} .0 .1 \mathrm{m} \)
D. \( 1.05 m \)


During anaerobic respiration the conversion of pyruvate into acetaldehyde, along with co-enzyme TPP, the cofactor required is
A. \( M g^{++} \)
B. \( M n^{++} \)
\( \mathbf{c} \cdot F e^{++} \)
D. \( Z n^{++} \)


State Le-chatlier's principle.


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{a^{1 / 2}+2}{a+2 a^{1 / 2}+1}-\frac{a^{1 / 2}-2}{a-1}\right) \cdot \frac{a^{1 / 2}+1}{a^{1 / 2}} \)


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{C} \)


If there were no atmosphere, the average temperature on earth surface would be
A. lower
B. higher
c. same
D. \( 0^{\circ} \mathrm{C} \)


\( X, Y \) and \( Z \) are three elements in the
third period.
X reacts with chlorine to give a liquid
product.
Y reacts with chlorine to give a solid
product that dissolves in water to give a
solution of \( \mathrm{pH} 7 \)
z reacts with chlorine to give a solid product that dissolves in water to give a
solution of \( \mathrm{pH} 6 \) Which elements are good conductors of electricity?
A. \( x \) and \( Y \)
B. Y and Z
c. Y only
D. Zonly


Which of the following plant structures evolved for the first terrestrial forests?
A. Flowers
B. Naked seeds
c. covered seeds
D. vascular tissue
E. Deciduous leaves


For the following reaction, identify the
gaseous product formed. \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \rightarrow \)
A \( . C O \)
в. \( C O_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} O \)


Determine the major product of the
given reaction:


8
8
8
8


Find GM of 4,9
\( A \cdot 4 \)
B. 6
\( c .9 \)
D. 7


Vinegar is a:
A. \( 5-8 \% \) solution of acetic acid in water
B. 25-30\% solution of acetic acid in water
C. \( 40-45 \% \) solution of acetic acid in water
D. \( 45-50 \% \) solution of acetic acid in water


Find the largest number that divides
2053 and 967 and leaves a remainder of
5 and 7 respectively.


To cool a liquid just below its f.pt. is
called super cooling.
If true enter 1 , if false enter 0 .


Prove that
\[
\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\
\boldsymbol{a}^{\mathbf{3}} & \boldsymbol{b}^{\mathbf{3}} & \boldsymbol{c}^{\mathbf{3}}
\end{array}\right] \mid=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-
\]
\( \boldsymbol{a})(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \)


Ethyne is isoelectronic with:
A. chlorine
B. oxygen
c. nitrogen gas
D. \( C O_{2} \)


Write down correct order of covalent
character of the following.
\( \mathbf{a} \cdot \mathbf{L i C I}, \mathbf{N a C l}, \mathbf{R b C l}, \mathbf{K C} \)
b. \( \mathrm{NaCl}, \mathrm{Mg} C l_{2}, \mathrm{Si} C l_{4} \)
c. \( \operatorname{sn} C l_{2}, \operatorname{sn} C l 4 \)


STATEMENT - 1: Gas ejected from rocket will never exert thrust on the rocket if
the ejected gas and the rocket move in the same direction.
STATEMENT - 2 : To exert thrust on
rocket in its direction of motion, the ejected gas (w.r.t. rocket) must move opposite to the velocity of rocket (w.r.t. ground)
A. statement-1 is True, Statement-2 is True ; statementis a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True ;statement-2 is NOT a correct explanation for Statement-
c. statement-1 is True, statement-2 is False
D. statement-1 is False, statement-2 is True


Which one of the following is not a Chordata character?
A. Dorsal heart
B. Dorsal and hollow nerve cord
C. Pharyngeal gill slits
D. Post anal tail


The electronic configuration of actinides cannot be assigned with degree of certainty because of :
A. overlapping of inner orbitals.
B. free movement of electrons over all the orbitals
c. small energy difference between 5 f and \( 6 d \) levels.
D. none of the above


Out of every Rs. 10,000 spent during the
decade \( 2001-2010 \) approximately how much was the GDP of Russia during the
half decade \( 2001-2005 ? \)
GDP of Various Countries
A. Rs. 700
B. Rs. 1,400
c. Rs. 2,800
D. None of these


Find square root of \( x=\sqrt{20.25} \)


A biconvex lens of focal length \( 15 \mathrm{cm} \) is in front of a plane mirror. The distance between the lens and the mirror is 10
\( \mathrm{cm} . \mathrm{A} \) small object is kept at a distance of \( 30 \mathrm{cm} \) from the lens. The final image is :
A. virtual and at a distance of 16 cm from the mirror
B. real and at a distance of \( 16 \mathrm{cm} \) from the mirror
c. virtual and at a distance of \( 20 \mathrm{cm} \) from the mirror
D. real and at a distance of \( 20 \mathrm{cm} \) from the mirro


Differentiate between tap root and
fibrous root


The minimum number of vectors having different planes which can be added to give zero resultant is
A .2
B. 3
\( c \cdot 4 \)
D. 5


A toy is in the shape of cone mounted on
hemisphere of same base radius. If the
volume of the toy is \( 231 \mathrm{cm}^{3} \) and its
diameter is \( 7 \mathrm{cm}, \) find the height of the
toy.


A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by
\( 62^{\circ} \mathrm{C}, \) the efficiency of the and sink are
A \( \cdot 80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
в. \( 95^{\circ} \mathrm{C}, 28^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 90^{\circ} C, 37^{\circ} C \)
D . \( 99^{\circ} C, 37^{\circ} C \)


A ball is thrown from a height of \( 12.5 m \) from the ground level in the horizontal direction. It falls at a horizontal
distance of \( 200 m . \) The initial velocity of the ball (approximately) is
A. \( 140 \mathrm{m} / \mathrm{s} \)
в. \( 80 \mathrm{m} / \mathrm{s} \)
c. \( 126 m / s \)
D. \( 120 \mathrm{m} / \mathrm{s} \)


Let \( \boldsymbol{f} \) be a function satisfying
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
and \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1} \) then
This question has multiple correct options
A. \( f \) is differentiable for all \( x \)
B . \( f^{\prime}(x)=f(x) \)
\( \mathbf{c} \cdot f(x)=e^{x} \)
D. \( f \) is continuous for all \( x \)


Identify the tissue not formed during secondary growth in plants.
A. Phellogen
B. Woodd
c. Phellem
D. Pericycle


Ohms Law is not obeyed by :
A . electrolytes
B. discharge tube
c. vacuum tube
D. all of the above


The negative sign in the equation for \( f_{r} \)
says that
A. the direction of force is sometimes opposite to the direction of body's motion
B. the force is in the same direction to the body's motion
c. the force is in the opposite direction to the body's motion
D. None of these


The aqueous solution of \( A I C l_{3} \) is acidic
due to
A. Cation hydrolysis
B. Anion hydrolysis
c. Hydrolysis ofboth anion and cation
D. Dissociation


The specific conductance of a solution
containing 5 g of anhydrous \( B a C l_{2} \) (mol.wt. \( =208 \) ) in \( 1000 \mathrm{cm}^{3} \) of a
solution is found to be 0.0058
ohm \( ^{-1} \mathrm{cm}^{-1} \). Calculate the molar and
equivalent conductivity of the solution.


Tooth decay can be cured by a toothpaste by a reaction called as:
A. redox reaction
B. condensation
c. neutralization
D. none of above


Find the sum of 100 terms of the series
\( \mathbf{1}(\mathbf{3})+\mathbf{3}(\mathbf{5})+\mathbf{5}(\mathbf{7})+\cdots \cdots \)
A. 1353300
B. 1353400
c. 1353200
D. 1353100


Strongest proteolytic enzyme is released by .............. part of alimentary canal
A . lleum
B. Pancreas
c. stomach
D. Liver


(a) Draw the circuit diagram of a ful
wave rectifier using \( \boldsymbol{p}-\boldsymbol{n} \) junction
diode

Explain its working and show the
output, input waveforms.
(b) Show the output waveforms (Y) for
the following inputs \( A \) and \( B \) of
(i) OR gate (ii) NAND gate


Which of the following scientific
phenomenon is involved in
the generation of Hydroelectric power?
A. Motion of charged particles in electromagnetic fields
B. Conversion of gravitational potential energy into electrical energy
C. Bernoullis principle in fluid dynamics
D. Trapping and cooling of atoms by laser beams and magnetic fields


Botanical names of plants are treated in
Latin because
A. Rules of nomenclature were framed by Italian botanists they were speaking Latin.
B. It is very difficult to pronounce Latin names and they convey multiple meanings.
C. Latin was the natural language of many European countries.
D. Latin was a dead language, its word would convey precise meaning. It was the mother of all European languages and all the early botanical literature was in Latin.


Express as kilogram (kg) using decimals:
\( 8 g \)


Two-point charge \( +3 \mu C a n d+8 \mu C \)
each other with a force of \( 40 N \). If a
charge of \( -5 \mu C \) is added to each of them,then the force between them will
become:
A . \( -10 N \)
в. \( +10 N \)
\( \mathrm{c} \cdot+20 N \)
D . \( -20 N \)


In which of the following complexes the nickel metal is in highest oxidation
state?
\( \mathbf{A} \cdot N i(C O)_{4} \)
в. \( K_{2} N i F_{6} \)
C \( \cdot\left[N i\left(N H_{3}\right)_{6}\right]\left(B F_{4}\right) \)
D. \( K_{4}\left[N i(C N)_{6}\right] \)


In which of the following, Il is more
stable than I?
This question has multiple correct options
\( A \)
В \( \cdot_{C H_{2}-O H}^{\oplus} C H_{2}=\stackrel{\oplus}{O H} \)
\( c \)
\( D \)


A stretched rubber has:
A. increased kinetic energy
B. increased potential energy
C . decreased kinetic energy
D. decreased potential energy


When the angle between incident ray and mirror is increased, the angle of reflection:
A. will decrease
B. will increase
c. will remain constant
D. will either increase or decrease


Find the value of \( \frac{1}{1+} \frac{2}{2+} \frac{3}{3+} \cdots \)


Animals breathe, oxygen and give out carbon dioxide
A . True
B. False


\( \begin{array}{rc} & \boldsymbol{C H}_{\mathbf{3}} \\ \text { The IUPAC name of } \boldsymbol{C} \boldsymbol{H}_{3}- & \boldsymbol{C} \\ & \boldsymbol{C H}_{3}\end{array} \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C l} \) is:
A. 1-chloro-2,2-dimethylpropane
B. 3-Chloro-2,2-dimethylpropane
c. 1 -chloro-1,2-dimethylpropane
D. 2-chloro-2,2-dimethylpropane


If the slop of one of the lines represented by \( a x^{2}-6 x y+y^{2}=0 \) is the square of
the other,then the value of a is
A. -27 or 8
B. -3 or 2
c. -64 or 27
D. -4 or 3


It is advised to tie any luggage kept on the roof of a bus with a rope because of :
A. Newtons first law
B. Newtons second law
c. Newtons third law
D. None of these


What is the direction of the electric field
directly south of a positive point charge due to the point charge?
A. North
B. South
\( c . \) East
D. west
E. Down


List 1
A) Autotrophic nutrition
1) Leech
B) Heterotrophic nutrition
2) Paramaecium
C) Parasitic nutrition
3) Deer
D) Digestion in food vaculoes
4) Green plant
Correct match of \( A, B, C \) and \( D \) is
\( A \cdot A-4, B-3, C-2, D-1 \)
B. A- 4, B- 3, C-1, D-2
C. \( A-3, B-4, C-1, D-2 \)
D. \( A-1, B-4, C-3, D-2 \)


For ohmic conductor the drift velocity \( \boldsymbol{v}_{\boldsymbol{d}} \)
and the electric field applied across it are related as :
\( \mathbf{A} \cdot v_{d} \propto \sqrt{E} \)
B \( \cdot v_{d} \propto E^{2} \)
c. \( v_{d} \propto E \)
D. \( v_{d} \propto \frac{1}{E} \)


State true or false
The length of tangent from an external point on a circle is always greater than the radius of the circle.
A. True
B. False


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

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


The equation \( x=a \sin 2 t+b \cos 2 t \) will
represent an SHM
A. True
B. False


State the following statement is True or
False
The digit at ten's place of a two digit number exceeds the square of digit at units place \( (x) \) by 5 and the number formed is \( 61, \) then the equation is
\( \mathbf{1 0}\left(\boldsymbol{x}^{2}+\mathbf{5}\right)+\boldsymbol{x}=\mathbf{6 1} \)
A. True
B. False


Ozone hole is maximum spread over:
A. Europe
B. Antartica
c. India
D. Africa


The number \( N_{Y} \) of nuclei of \( Y \) at \( t= \)
\( T_{1 / 2} \) is
A. \( K \frac{l n 2}{\lambda}+\frac{3}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
в. \( K \frac{l n 2}{\lambda}+\frac{1}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
c. \( \quad K \frac{l n 2}{\lambda}-\frac{1}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
D. \( K \frac{\ln 2}{\lambda}-2\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)


Two parallel wires carrying currents \( \boldsymbol{I}_{1} \)
and \( I_{2} \) in opposite directions and
separated by a distance \( d \) experience a
A . Replusive force \( \mu_{0} I_{1} I_{2} / 2 \pi d \)
B. Attractive force \( \mu_{0} I_{1} I_{2} / 2 \pi d \)
C. Repulsive force \( \mu_{0} I_{1} I_{2} / 2 \pi d^{2} \)
D. Attractive force \( \mu_{0} I_{1} I_{2} / 2 \pi d^{2} \)


The spin of photon is
A.
B. \( \frac{1}{2} \)
c. \( \frac{1}{3} \)
D. None


In elephants, testes are
\( A \cdot \) In abdobmen
B. In scrotal sacs
c. Absent
D. In iguinal canal


The slope of the line joining the points (-21,11) and (15,-7) is
A . -2
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. \( \frac{-1}{2} \)


Find the sum of the digits of the value
of \( \boldsymbol{y}(\log \mathbf{4}) \) if \( \boldsymbol{y}_{2}-\mathbf{7} \boldsymbol{y}_{1}+\mathbf{1} \boldsymbol{2} \boldsymbol{y}= \)
\( \mathbf{0}, \boldsymbol{y}(\mathbf{0})=\mathbf{2}, \boldsymbol{y}_{1}(\mathbf{0})=\mathbf{7} \)


A liquid of density \( \rho \) is filled in a U-tube.
The tube is accelerated with an
acceleration a so that the height of
liquid in its two vertical arms are \( \boldsymbol{h}_{\mathbf{1}} \)
and \( h_{2} \) as shown in the fig, If I is the
length of horizontal arm of the tube, the
acceleration a is:
A \( \cdot \frac{g\left(h_{1}-h_{2}\right)}{2 \quad l} \) towards right
B. \( \frac{g\left(h_{1}-h_{2}\right)}{2 \quad l} \) towards \( \quad \) left
c. \( \frac{g\left(h_{1}-h_{2}\right)}{l} \) towards right
D. \( \frac{g\left(h_{1}-h_{2}\right)}{l} \) towards left


\( A B \) and \( C D \) are two parallel conductors
kept \( 1 \mathrm{m} \) apart and connected by a resistance \( R \) of \( 6 \Omega \) as shown in figure.
They are placed in a magnetic field \( B= \)
\( 3 \times 10^{-2} \mathrm{T} \) which is perpendicular to the
plane of the conductors and directed
into the paper. A wire MN is placed over
\( A B \) and \( C D \) and then made to slide with
velocity \( 2 m s^{-1} . \) (Neglect the resistance of \( A B, C D, \) and \( M N \) ). Calculate the induced current flowing through the resistor R.


A store reported total sales of \( \$ 385 \)
million for February of this year. If the total sales for the same month last year
was \( \$ 320 \) million, approximately what was the percent increase in
sales?
A . \( 2 \% \)
B. \( 17 \% \)
c. \( 20 \% \)
D. \( 65 \% \)
E. \( 83 \% \)


Mushrooms reproduce through
A. spores
B. Mycelial fragmentation
c. Buds on the leaf margin
D. Both A and B


Consider a thin square sheet of side \( \boldsymbol{L} \)
and thickness \( t, \) made of a material of
resistivity \( \rho . \) The resistance between
two opposite faces, shown by the shaded areas in the figure is
A. directly proportional to L
B. directly proportional to t
c. independent of
D. independent of t


Determine the order and degree(if defined) of the following differentia
equation. \( \left(\frac{\boldsymbol{d} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}}\right)^{\boldsymbol{4}}+\boldsymbol{3} \boldsymbol{s} \frac{\boldsymbol{d}^{2} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}^{2}}=\mathbf{0} \)


Hess's Law is used
A. When a directly measured enthalpy change of reaction is not available
B. To calculate an enthalpy change value through multiple steps
C. Because enthalpy is a State Function
D. As an easy way to calculate the enthalpy change of a reaction
E. All of these options(A,B,C,D) are correct


Two bodies of masses \( m_{1} \) and \( m_{2} \) are
placed at distance X from each other.
IfX is kept constant and the masses of
the two bodies are increased to \( 2 m_{1} \)
and \( 2 m_{2}, \) then the value of gravitational force between them will become
A. 4 times
B. 2 times
c. 8 times
D. \( 1 / 4 \) times


Figures \( (a),(b),(c) \) and \( (d) \) respectively
correspond to
A. The short-sighted eye, the correction of long-sight, the long-sighted eye and the correction of short-sight
B. The short-sighted eye, the correction of short-sight, the long-sighted eye and the correction of long-sight
c. The long-sighted eye, correction of short-sight, the short-sighted eye and the correction of long-sight
D. The long-sighted eye, the correction of long-sight, the long-sighted eye and the correction of short-sight


The converse of "if \( \boldsymbol{x} \in \boldsymbol{A} \cap \boldsymbol{B} \) then \( \boldsymbol{x} \in \)
\( A \) and \( x \in B " \), is
A. If \( x \in A \) and \( x \in B \), then \( x \in A \cap B \)
B. If \( x \notin A \cap B \), then \( x \notin A \) or \( x \notin B \).
c. If \( x \notin A \) or \( x \notin B, \) then \( x \notin A \cap B \)
D. If \( x \notin A \) or \( x \notin B \), then \( x \in A \cap B \).


Assertion
When the current in a coil changes, it
induces a back emf in the same coil
Reason

Emf is a measure of the inertia of the
coil against the change of current through it.
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


A red sol of \( F e(O H)_{3} \) is mixed with an
equivalent amount of yellow sol of
\( A s_{2} S_{3} . \) Which of the following statement is wrong with respect to the resulting solution?
A. A colourless solution
B. Mutual coagulation
C. Precipitation of \( A s_{2} S_{3} \) and \( F e(O H)_{3} \) both
D. Orange solution


Which of the following is not a first order reaction?
A. Decomposition of \( H_{2} O_{2} \)
B. Decomposition of \( N_{2} O_{5} \)
C. Decomposition of \( N_{2} O \)
D. Decomposition of \( S O_{2} C l_{2} \)


\( \frac{1}{\sin ^{2} \theta}-\cot ^{2} \theta \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
D. -2


Assume that the number of hole-
electron pair in an intrinsic
semiconductor is proportional to
\( e^{\Delta E / 2 k T} . \) Here \( \Delta E= \) energy gap and
\( \boldsymbol{k}=\mathbf{8 . 6 2} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{e V} / \boldsymbol{K} . \) The energy gap
for silicon is \( 1.1 e V . \) The ratio of electron
hole pairs at \( 300 K \) and \( 400 K \) is
\( \mathbf{A} \cdot e^{5.104 \times 10^{-8}} \)
B \( \cdot e^{-5} \)
\( c \cdot c \)
D. \( e^{2} \)


If \( \frac{\sin A}{\sin B}=p \) and \( \frac{\cos A}{\cos B}=q, \) find \( \tan A \)
and \( \tan B \)


Which of the following isomers of phosphorus is thermodynamically most stable?
A. Red
B. White
c. Black
D. Yellow


For a particle in a uniformly accelerated
circular motion
A. Velocity is radial and acceleration has both radial and transverse components
B. Velocity is transverse and acceleration has both radial and transverse components
C. Velocity is. radial and acceleration is transverse only
D. Velocity is transverse and acceleration is radial only


Evaluate the following deteminants:
i) \( \left|\begin{array}{cc}\boldsymbol{x} & -\mathbf{7} \\ \boldsymbol{x} & \mathbf{5} \boldsymbol{x}+\mathbf{1}\end{array}\right| \)
ii) \( \mid \begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array} \)


Z-average molar mass \( \left(\bar{M}_{z}\right) \) is defined
as:
\( ^{\mathbf{A}} \cdot \frac{\sum N i M i^{2}}{\sum N i M i} \)
B. \( \frac{\sum N i M i}{\sum N i} \)
c. \( \frac{\sum N i M i^{3}}{\sum N i M i^{2}} \)
D. \( \frac{\sum N i M i^{3}}{\sum N i M i} \)


Which of the following is the correct statement about the circulatory system
of cockroach?
A. It is closed type of circulatory system.
B. It is a complicated type of circulatory system.
c. It takes place without the participation of tissue
D. It has 13 chambered heart and in each segment one pair of ostia are present.


The given figure shows the colour
changes in test tubes I, II and III, when
China rose indicator is added to them.
The respective solutions in test tubes I,
II and III are
A. Sugar solution, Lime water, Baking powder
B. Sugar solution, Lemonjuice, Vinegar
C. lime water, Sugar solution, Lemon juice
D. Lemon juice, Sugar solution, lime water


A bob of mass \( 10 m \) is suspended
through an inextensible string of length
When the bob is at rest in equilibrium
position two particles, rach of mass \( m \)
strike it as shown in Fig. The particles
stick after collision. Choose the correct
statement from the following.
A. Impulse in the string due to tension is 2 mu.
B. velocity of the system just after collision is \( \nu=\frac{u \sqrt{3}}{14} \)
c. Loss of energy is \( \frac{137}{28} m u^{2} \)
nergy is \( \frac{137}{56} m u^{2} \)


Which of the following quantities is
non-zero at the mean position for a
particle executing SHM?
\( A \cdot \) force
B. acceleration
c. velocity
D. displacement


The correct molecular formula of the
following complexes are:
(a) Pentamminechlorocobalt (III) ion
(b) Lithium tetrahydroaluminate (III)
A \( \cdot(a)\left[C o\left(N H_{3}\right)_{5} C l\right]^{2+} ;(b) L i\left[A l H_{4}\right] \)
B . \( (a)\left[C o\left(N H_{3}\right)_{5} C l\right]^{3+} ;(b) L i_{2}\left[A l H_{4}\right] \)
C \( \cdot(a)\left[C o\left(N H_{3}\right)_{5} C l\right]^{2-} ;(b) L i_{4}\left[A l H_{4}\right. \)
D. None of these


Frictional force always opposes:
A. The state of rest
B. The state of motion
c. None of the above
D. Both the states


The angle between the two vectors \( \vec{A}= \) \( \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=-\hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}} \) is:
A \( \cdot 90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


The arithmetic mean the data
\( 0,1,2,, \dots, n \) with frequencies
\( 1,^{n} C_{1},^{n} C_{2}, \dots^{n} C_{n} \) is
\( A \)
в. \( \frac{2^{n}}{n} \)
c. \( n+1 \)
D.


Using \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{c}^{2}, \) find out the energy
released, when \( 2 u \) of mass is destroyed
completely Take \( 1 \boldsymbol{u}=\mathbf{1 . 6 6} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g} \)
A. \( 4.65 \mathrm{MeV} \)
B. \( 3627 \mathrm{MeV} \)
c. \( 91.5 \mathrm{MeV} \)
D. \( 1865 M e V \)


A capacitor has a resistance of
\( 1200 M \Omega \) and capacitance of \( 22 \mu F \)
When connected to an AC supply of frequency \( 80 \mathrm{Hz} \), the alternating voltage supply required to drive a current of 10
virtual amperes is
A. \( 904 \sqrt{2} V \)
B. 904
D. \( 452 \mathrm{v} \)


In the shown figure half of the part is
disc and other half is a ring both of
mass \( m \) and radius r. Then moment of
inertia of this system about the shown
axis is:
A \( \cdot \frac{3}{4} m r^{2} \)
в. \( \frac{3}{8} m R^{2} \)
\( \mathrm{c} \cdot m r^{2} \)
\( D \cdot \frac{m r^{2}}{1} \)


If A.M. between \( p \) and \( q(p \geq q) \) is two
times the G.M. then \( p: q \) is.
A . 1: 1
B . 2: 1
c. \( (2+\sqrt{3}):(2-\sqrt{3}) \)
D. 3: 1


If \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\boldsymbol{a}|+|\boldsymbol{x}+\boldsymbol{b}|, \boldsymbol{x} \epsilon \boldsymbol{R}, \boldsymbol{b}> \)
\( \boldsymbol{a}>\mathbf{0} . \) Then
\( \mathbf{A} \cdot f^{\prime}\left(a^{+}\right)=1 \)
B . \( f^{\prime}\left(a^{+}\right)=0 \)
c. \( f^{\prime}\left(-b^{+}\right)=0 \)
D. \( f^{\prime}\left(-b^{+}\right)=1 \)


Find the area of the region bounded by
the curves
\( x^{2}+y^{2}=16 \) and \( x^{2}=6 y \)


Is the claim of Mr.Kirkpatrick right?
A . yes
B. No
c. cannot say
D. may be correct or may be not


Two coils \( A \) and \( B \) have mutual
inductance \( 2 \times 10^{-2} \) henry. If the
current in the primary is \( i= \) \( 5 \sin (10 \pi t) \) then the maximum value of
e.m.f. induced in coil B is:
A . \pivolt
в. \( \frac{\pi}{2} \) volt
c. \( \frac{\pi}{3} \) volt
D. \( \frac{\pi}{4} \) volt


n Kaiga Atomic Power reactor plant, the
fuel that can be used is
A. coal
B. Uranium
c. Petrol
D. Natural gas


Assertion: Angular momentum of an
electron in any orbit is given by angular momentum \( =\frac{n . h}{2 \pi}, \) where \( n \) is the
principal quantum number. Reason: The principal quantum number, \( n, \) can have any integral value.
A. If both assertion and reason are true and the reason is
a correct explanation of the assertion.
B. If both assertion and reason are true but reason is not
a correct explanation of the assertion
C. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


One quantum is absorbed per gaseous
molecule of \( \mathrm{Br}_{2} \) for converting into Br
atoms. If light absorbed has wavelength 5000 A, calculate energy required in KJ/mol.


A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the \( n^{t h} \) second to
distance covered in \( n \) seconds is
A \( \cdot \frac{2}{n}-\frac{1}{n^{2}} \)
B. \( \frac{1}{n^{2}}-\frac{1}{n} \)
c. \( \frac{2}{n^{2}}-\frac{1}{n} \)
D. \( \frac{2}{n}+\frac{1}{n^{2}} \)


A translation is applied to an object by
A. Repositioning it along with straight line path
B. Repositioning it along with circular path
C. All of the mentioned
D. none of the mentioned


The distance through which a body falls
in the \( n^{t h} \) second is \( h . \) The distance
through which it falls in the next second
is
\( A \cdot h \)
B. \( h+\frac{g}{2} \)
c. \( h-g \)
D. \( h+g \)


Measurement of the rate of oxygen utilization by a unit volume of water over a period of time is to measure
A. Biochemical oxygen demand
B. Biosynthetic pathway
c. Biogas generation
D. Fermentation


What is a Functional Group?


In YDSE, a white light is formed fringe pattern on the screen. Calculate the path difference of the light waves from the two slits at the center of the first
bright fringe above the central maximum.
A. 0
в. \( \frac{1}{4} \lambda \)
\( c \cdot \frac{1}{2} \lambda \)
D. \( \lambda \)
E \( \cdot \frac{3}{2} \lambda \)


When \( K M n O_{4} \) acts as an oxidising agent and ultimately forms \( \left[M n O_{4}\right]^{2-} \) \( M n O_{2}, M n_{2} O_{3}, M n^{2+}, \) then the
number of electrons transferred in each
case respectively is:
A .4,3,1,5
B. 1, 5, 3, 7
\( c \cdot 1,3,4,5 \)
D. 3, 5, 7,


Roots first originated in
A . Algae
B. Fungi
c. Bryophyta
D. Pteridophyta


During inspiration, the diaphragm
A. Expands
B. Shows no change
c. contracts and flattens
D. Relaxed to become dome shaped


helps in maintaining the supply of nutrients to the growing plants.
A . Herbivores
B. Carnivores
c. Decomposers
D. Omnivores


ff \( A=\left[\begin{array}{ccc}1 & 3 & 1 \\ 2 & 1 & -1 \\ 3 & 0 & 1\end{array}\right], \) then \( \operatorname{rank}(A) \) is
equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B.
\( c \cdot 2 \)
D. 3


When a current of \( 0.5 A \) is passed
through two resistors in series, the potential difference between the ends
of the series arrangement is \( 12.5 \% . \) On connecting them in parallel and passing a current of \( 1.5 A \), the potential difference across them is \( 6 V \). The two
resistances, in ohms, are
\( A \cdot 5,20 \)
B. 5, 15
c. 5,10
D. 15,20


A mercury thermometer is transferred from melting ice to a hot liquid. The
mercury rises to \( 9 / 10 \) of the distance between the two fixed points. Find the temperature of the liquid in Fahrenheit scale.
\( \mathbf{A} \cdot 197^{\circ} F \)
B . \( 162^{\circ} \mathrm{F} \)
\( \mathbf{c} \cdot 112^{\circ} F \)
D. \( 113^{\circ} F \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{6} \boldsymbol{x}=\mathbf{5} \)


Which statement is false?
A. Element of VB group are transition elements.
B. Elements of VA group are all metalloids.
C. Elements of IA and IIA groups are metals.
D. Elements of IVA group are neither strongly electronegative nor strongly electropositive


Two sound waves travel out from a
common point have frequencies \( 30 \mathrm{Hz} \) and \( 40 \mathrm{Hz} \) respectively. Calculate the
phase difference between them after
0.8 second?
A. zero
B.
\( c \cdot \frac{5 \Pi}{2} \)
D. 5\Pi


An external device supplies constant power to a rotating system by applying a torque \( \tau . \) The angular velocity of system varies with torque \( \tau \) as \( (\omega \propto) \)
\( A \)
B. \( \frac{1}{\tau} \)
\( c \cdot \sqrt{\tau} \)
D. \( \frac{1}{\sqrt{\tau}} \)


Show that the function \( y=A x+\frac{B}{x} \) is a solution of the differential equation
\( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}-y=0 \)


What is corrosion?
A. When metal is gradually destroyed through chemical reactions
B. When metal is created through chemical reactions
C. When a redox reaction takes place
D. When a metal is destroyed after exposure to a gas
E. When a solid is destroyed through chemical reactions


The element having electronic configuration.
\( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{s}^{2} \boldsymbol{5} \boldsymbol{p}^{6} \boldsymbol{5} \boldsymbol{f}^{2} \boldsymbol{6} \boldsymbol{s}^{2} \) belongs
to
A. s-block
B. p-block
c. d-block
D. f-block


Which reagent can convert acetic acid into ethanol?
\( \mathbf{A} \cdot S n+H C l \)
B. \( \quad H_{2}+P t \)
c. \( \quad \) Li \( A l H_{4} \)
D. \( N a+ \)alcohol\( l \)


Which of the following oxides are not
neutral?
This question has multiple correct options
A. \( C O \)
B. \( S n O_{2} \)
\( c \cdot Z n O \)
D. \( \operatorname{si} O_{2} \)


Match the column I with column II and
mark the appropriate choice.

Column I
(A)
Metals used as \( \quad \) (i) \( \quad \) Aluminium semiconductors
Electrolytic Zone
(B) reduction \( \quad \) refining
(ii)
Dressing
(C) \( \quad \) Cyanide process \( \quad \) (iii) \( \quad \) of \( Z n S \)
Froth floatation \( \quad, \ldots \) Extraction
(D) \( \quad \) process \( \quad \) (iv) \( \quad \) of \( A g \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i v) \)
B. \( (A) \rightarrow(\text { iii), }(B) \rightarrow(i v),(C) \rightarrow(i \text { i) },(D) \rightarrow(i) \)
C \( .(A) \rightarrow(\text { iv ) },(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii }),(D) \rightarrow(i) \)
\( \mathbf{D} \cdot(A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)


Find the discriminant for the given quadratic equation:
\( \boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}=\mathbf{0} \)
A . -3
B. - 5
\( c .-7 \)
D. - -


Match the correct set of scientists in
relation to cell division.
A. Robert Remak
1. Meiosis
\( B \)
I S.R. Pelc
2. Mitosis A.Howard and
\( \mathrm{C} \)
W. Fleming
3. Amitosis
D. Farmer and Moore
4. Cyclins
sand 5. \( \mathrm{G}_{1}, \mathrm{S} \) \( \mathrm{IG}_{2} \) phase
\( A \cdot A-3, B-2, C-1, D-4 \)
B. \( A-3, B-5, C-2, D-1 \)
C. \( A-4, B-2, C-3, D-5 \)
D. \( A-1, B-2, C-3, D-4 \)


bought my coat in the January sales with \( \frac{1}{3} \) off the original price. What percentage was taken off the price of
the coat?
A . \( 11 \% \)
в. \( 22 \% \)
c. \( 33 \% \)
D. \( 44 \% \)


If \( f(x)=a x+b \) and \( f(f(f(x)))= \)
\( 27 x+13 \) where a and b are real
numbers, then-

This question has multiple correct options
\( A \cdot a+b=3 \)
B. \( a+b=4 \)
\( c \cdot f^{\prime}(x)=3 \)
D. f'(x)=-3


Heat is not transferred by the process of convection in:
A. solid
B. liquid
c. gas
D. none of the above


Find the number of triplets of integers in arithmetic progression, the sum of whose squares is 1994
A . 36
B. 45
c. 12
D. Does not exist


First true land plants are
A. Mosses
B. Ferns
c. Amphibians of plant kingdom
D. Produce flowers


Intramolecular hydrogen bonding is
found in:
A. salicylaldehyde
B. water
c. acetaldehyde
D. phenol


Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is?
A . \( 1 / 6 \)
B . \( 1 / 36 \)
c. \( 12 / 151 \)
D. None of these


LPG releases \( -\ldots_{2} \)
per KWh produced by oil.
A . \( 89 \% \)
B. 81\%
c. 79\%
D. 0\%


Describe an experiment to compare the
thermal conductivities of different
metals.


In common base circuit of a transistor,
current amplification factor is 0.95 Calculate the emitter current if base
current is \( 0.2 \mathrm{mA} \)
A . \( 2 \mathrm{mA} \)
B. \( 4 \mathrm{m} \)
\( c .6 m A \)
D. \( 8 \mathrm{m} \)


The equation of the diagonal through origin of the quadrilateral formed by the \( \operatorname{lines} \boldsymbol{X}=\mathbf{0}, \boldsymbol{Y}=\mathbf{0}, \boldsymbol{X}+\boldsymbol{Y}-\mathbf{1}=\mathbf{0} \)
and \( 6 x+Y-3=0 \) is :
A \( .4 x-3 y=0 \)
В. \( 3 x-2 y=0 \)
c. \( x=y \)
D. \( x+y=0 \)


The two ways of combining atoms are:
A. transfer of valence electrons
B. sharing of valence electrons
C. both \( A \) and \( B \)
D. none of the above


Find the coeffcient of:
\( x^{-7} \) in the expansion of \( \left(a x-\frac{1}{b x^{2}}\right)^{8} \)
ii) \( x^{6} \) in the expansion \( \left(a-b x^{2}\right)^{10} \)


Which of the following sets of quantum numbers is correct for an electron in \( 4 f \)
orbital?
\( A \cdot n=4,1=3, m=+4, s=+\frac{1}{2} \)
B. \( n=4,1=4, m=-4, s=+\frac{1}{2} \)
\( c \cdot n=4,1=3, m=+1, s=+\frac{1}{2} \)
D. \( n=4,1=2, m=2, s=+\frac{1}{2} \)


Let \( R \) be the equivalence relation on the
\( \operatorname{set} Z \) of integers given by \( \boldsymbol{R}= \)
\( \{(a, b): 2 \text { divides } a-b\} . \) Write the
equivalence class \{0\}


Shivam went for buying a CFL from Dmart, what safety mark he should look
for?
A. Agmark
B. ISI mark
c. Trade mark
D. Brand logo


The role of individual mineral element
in plant body has been determined by growing plants with their roots immersed in nutrient solution without
soil. This technique is called as
A. Hydroponics
B. Photolysis
c. Bulk method
D. Bagging
E. Hypostatic


Fluorine is the most reactive among all the halogens, because of it's:
A. small size
B. low dissociation energy of F-F bond
c. large size
D. high dissociation energy of F - F bond


Assuming that the two diodes \( D_{1} \) and
\( D_{2} \) used in the electric circuit shown in
the figure are ideal, find out the value of
the current flowing through \( 1 \Omega \) resistor


The hardness, melting point and boiling point of elements increase from Ce to Lu
because:
A. the attraction between the atoms increases as the size increases
B. the attraction between the atoms decreases as the size increases
c. the attraction between the atoms increases as the size decreases
D. the attraction between the atoms remains the same as the size increases


Bessemer converter is used for the
preparation of
A. steel
B. Wrought iron
c. Pig iron
D. cast iron


Match list-I with list -II.
List I
(A) Lanthanide contraction
\( (p) d \)
block
(B) Diagonal relationship Elements of 3rd period
(C) Typical elements
\( (r) \)
block
(D) Inner transition elements
\( \mathrm{Be}-\mathrm{A} \)
\( A \cdot A-r, B-s, C-q, D-r \)
B. A-p,B -r,C - s, D-q
\( c \cdot A-s, B-q, c-p, D-r \)
D. A - q, B - p, C - r, D- -


What is the reason for the identical
chemical properties of all the isotopes of an element?


Dumas' method involves the
determination of nitrogen content in the organic compound in the form of:
A. \( N H_{3} \)
в. \( N_{2} \)
c. \( N a C N \)
D. \( \left(N H_{4}\right)_{2} S O_{4} \)


Find the value of \( k \) so that the function \( f \)
is continuous at the indicated point. \( f(x)=\begin{array}{cc}k x^{2} & , x \leq 2 \\ 3 & , x>2\end{array} \) at \( x=2 \)
A \( \cdot k=\frac{1}{4} \)
B. \( _{k=\frac{1}{2}} \)
c. \( _{k=\frac{3}{4}} \)
D. \( k=1 \)


Peptisation is a method of preparation of sols. Write a general procedure for peptization


\( \mathbf{A} \)
\( 2.24 L \) cylinder of oxygen at \( 1 a t m \) and
\( 273 K \) is found to develop a leakage.
When the leakage was plugged the pressure dropped to \( 570 m m \) of Hg. The number of moles of gas that escaped will be:
A. 0.025
B. 0.050
c. 0.075
D. 0.09


Discuss the continuity and differentiability of the function, \( \boldsymbol{f}(\boldsymbol{x})=\left[\begin{array}{cc}\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} & |\boldsymbol{x}|>\mathbf{1} \\ \frac{\boldsymbol{x}}{\mathbf{1}-|\boldsymbol{x}|} & |\boldsymbol{x}| \leq \mathbf{1}\end{array}\right] \)


The length of a potentiometer wire is \( l . \) A
cell of emf \( \boldsymbol{E} \) is balanced at a length \( \boldsymbol{l} / \mathbf{3} \)
from the positive end of the wire. If the length of the wire is increased by \( l / 2 . \) At
what distance will the same cell give a balance point?
A \( \frac{2 l}{3} \)
B. \( \frac{l}{2} \)
\( c \cdot \frac{l}{6} \)
D. \( \frac{4 l}{3} \)


\( \ln C H_{3} C O O H \) molecule, the \( C-C \)
bond is formed by:
A \( \cdot s p^{3}-s p^{3} \) overlap
B. \( s p^{2}-s p^{2} \) overlap
c. \( s p^{3}-s p^{2} \) overlap
D. \( s p^{3}- \) sp overlap


Which of the following species are correctly matched with their geometries according to the VSEPR theory? This question has multiple correct options
A. \( B r F_{6}^{+} \rightarrow \) octahedral
B . \( S n C l_{5}^{-} \rightarrow \) trigonal bipyramidal
c. \( C l F_{2}^{-} \rightarrow \) linear
D. \( I F_{4}^{+} \rightarrow \) see-saw


The charge on a sphere of radius \( r \) is \( +Q \) At a point \( P \) which is outside this sphere and at a sufficient distance from it, the
electric field is E. Now, another sphere of radius \( 2 \mathrm{r} \) and charge \( -2 \mathrm{Q} \) is placed with
\( P \) as the centre of this second sphere Then, the electric field at the midpoint
of the line joining the centres of the two spheres is :
A. \( E \)
в. \( 4 E \)
\( c .6 E \)
D. \( 12 E \)


What are the demerits of Mendeleev's
periodic table with respect to the
arrangement of elements in ascending order? (Any three)


The value of \( \sin ^{2} \alpha+\operatorname{cosec}^{2} \alpha \) is always
A. greater than 1
B. less than 1
c. greater than or equal to 2
D. equal to 2


Assertion
(A): Hydrogen has one electron in its orbit but it produces several spectral lines. Reason (R): There are many excited energy levels available.
A. Both A and R are rue and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of
C. A is correct and R is incorrect
D. A is incorrect and R is correct


Which is the biggest physical quantity?
A. A coulomb
B. Charge on an electron
c. charge on a proton
D. Charge on a neutron


A body is tied at the end of a string of length " and rotated in a vertical
circle, The suring is just taut when the body is at highest point. Velocity of the body when the string is in horizontal position is
A. \( 3 \sqrt{g r} \)
B . \( \sqrt{g r} \)
c. \( \sqrt{5 g r} \)
D. \( \sqrt{3 g r} \)


The electric field in a region of space is given by \( \vec{E}=(\hat{5} i+\hat{2} j) N c^{-1} . \) The electric
flux due to this field through an area \( 2 m^{2} \)
lying in the \( Y \) -Z plane in S.I. units is
A . 10
B. 20
c. \( 10 \sqrt{2} \)
2
D. \( 2 \sqrt{29} \)


To make a p-type semiconductor, an intrinsic semiconductor is doped with
A. Gallium or indium
B. Arsenic or phosphorus
c. Aluminium or boron
D. Both (1) and (3)


According to the diagram shown,
identify the normal force :
lined plan
\( A \cdot f \)
\( \mathbf{B} \cdot F \)
c. It may be \( f \) or \( F \)
D. None of the above


\( \mathbf{1 0 0}^{2}-\mathbf{9 9}^{\mathbf{2}}+\mathbf{9 8}^{\mathbf{2}}-\mathbf{9 7}^{\mathbf{2}}+\mathbf{9 6}^{\mathbf{2}}+\mathbf{9 5}^{\mathbf{2}}+ \)
\( \ldots .=\mathbf{S} \) find \( \boldsymbol{S}=? \)


Assertion
The binding energy per nucleon, for
nuclei with the atomic mass number
\( A>100, \) decreases with \( A \)
Reason
The nuclear forces are weak for heavier
nuclei.
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


Two coherent light sources whose intensity ratio is 81: 1 produce interference fringes. If the ratio of intensities of maxima and minima in
the fringe system is x:y. Find \( x-y ? \)


The values of \( a \) for which \( f(x)= \) \( \frac{a^{2} x^{3}}{3}+\frac{3 a x^{2}}{2}+2 x+1 \) is strictly
decreasing at \( \boldsymbol{x}=\mathbf{1} \)
A. \( a \in(-2,-1) \)
в. \( a \in(-1,0) \)
c. \( a \in(1,2) \)
D. \( a \in(-2,1) \)


If the projections ofthe line segment \( A B \)
on the \( y z \) -plane, \( z x \) -plane, \( x y \) -plane are \( \sqrt{160}, \sqrt{153}, 5 \) respectively, then the projection of \( A B \) on the \( z \) -axis is
A \( \cdot \sqrt{12} \)
B. \( \sqrt{13} \)
c. 12
D. 144


The following synthesis can not be
carried out by:
This question has multiple correct options
\( \mathbf{A} \cdot \frac{C l_{2}}{(1)} \frac{I C l / C H_{3} C O O H}{(2)} \frac{I C l / C H_{3} C O O H}{(3)} \frac{Z n d u s t}{(4)} \)
\( \mathbf{B} \cdot \frac{H O B r / H^{+}}{(1)} \frac{C l_{2} / F e}{(2)} \frac{I C l / Z n C l_{2}(e x c e s s)}{(3)}, \frac{N a O H, \Delta}{(4)} \)
\( \mathbf{C} \cdot \frac{H O B r / H^{+}}{(1)} \frac{C l_{2} / F e}{(2)} \frac{I C l / Z n C l_{2}(e x c e s s)}{(3)} \frac{Z n d u s t, C H_{2} C O O H}{(4)} \)
\( \mathbf{D} \cdot \frac{B r_{2} / C H_{3} C O O H}{(1)} \underbrace{\frac{C l_{2} / F e}{(2)}} \frac{I C l / C H_{3} C O O H(\text {excess})}{(3)} \frac{N a N H_{2}}{(4)} \)


In a parallel C-R network with a voltage
source, the current flowing through
resistor is
flowing through the capacitor is
current.
A. conduction, displacement
B. displacement, conduction
C. displacement, displacement
D. conduction, conduction


Prove that the function given by \( f(x)= \)
\( x^{3}-3 x^{2}+3 x-100 \) is inreasing in \( R \)


A point traversed half a circle of radius \( \boldsymbol{R}=\mathbf{1 6 0} \mathbf{c m} \) during time interval \( \boldsymbol{\tau}= \)
10.0 \( s \). Calculate the average velocity.
A. \( 32 c m / s \)
в. \( 25 \mathrm{cm} / \mathrm{s} \)
c. \( 100 \mathrm{cm} / \mathrm{s} \)
D. \( 42.5 \mathrm{cm} / \mathrm{s} \)


Which equation represents the line that
passes through the point (-5,-4) and is parallel to the \( y \) -axis?
A . \( x=-5 \)
B . \( x=-4 \)
c. \( y=-5 \)
D. \( y=-4 \)


The atomic number of potassium is 19 Hence the number of electrons in \( \mathrm{N} \)
shell will be
A . 9
B.
c. 8
D. 2


The velocity of a body is given by the equation \( v=6-0.02 t, \) where \( t \) is the time taken.What does the body
undergo?
A. Uniform retardation of 0.02 \( \mathrm{m} s^{-2} \)
B. Uniform acceleration of 0.02 \( \mathrm{m} \) s \( ^{-2} \)
c. Uniform retardation of \( -0.04 \mathrm{m} s^{-2} \)
D. Uniform acceleration of - 0.04 \( \mathrm{m} \) s \( ^{-2} \)


Which of the following is regarded as the main cause of groundwater
contamination?
A . agricultural products
B. Iandfills
c. septic tanks
D. All of the above main sources of ground water contamination


A particle starts with some initial velocity with an acceleration along the direction of motion. Draw a graph
depicting the variation of velocity
\( (v) \)
along y-axis with the variation of displacement
\( (s) \) along \( x \) -axis.


Which one of the following conditions correctly describes the manner of determining the sex in the given example?
A. Homozygous sex chromosomes (ZZ) determine female sex in birds
B. X0 type of sex chromosomes determine male sex in grasshopper.
c. xo condition in human as found in Turner syndrome determines female sex
D. Homozygous sex chromosomes (XX) produce male in Drosophila


When \( X \) amperes of current is passed through molten \( A l C l_{3} \) for 96.5 seconds.
0.09 grams of aluminium is deposited. What is the value of \( X ? \)
A . 10
B. 20
\( c . \) 30
\( D \cdot 40 \)


Which of the following statement about
Avogadro's hypothesis is correct?
A. Under similar conditions of temperature and pressure, gases react with each other in simple ratio.
B. Under similar conditions of temperature and pressure, equal volumes of all gases contain same number of molecules
C. At NTP all gases contain same number of molecules
D. Gases always react with gases only at the given temperature and pressure


If the resistances of values \( R_{1} \) and \( R_{2} \)
are connected on both ends as shown in
figure, current \( I, \) flowing through
resistance \( R_{1} \) is given by
\( A \)
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
B.
\[
\frac{B l R_{2}\left(v_{1} r_{2}+v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
\( c \)
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}-r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
D.
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)-r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
E . nont


Assertion
Newton's third law of motion is
applicable only when bodies are in
motion.
Reason
Newton's third law applies to all types of forces.e.g. gravitational, electric or magnetic forces etc.
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


\( \boldsymbol{R} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \stackrel{\boldsymbol{P d}-\boldsymbol{B a S O}_{4}}{\boldsymbol{R} \boldsymbol{C H} \boldsymbol{O}}+ \)
HCl. The reaction is known as:
A. Rosenmund reduction
B. Stephen's reaction
c. Wolff-Kishner reduction
D. Clemmensen's reduction


Calculate the time taken by a sound
wave of frequency \( 1000 \mathrm{Hz} \) and wavelength \( 50 \mathrm{cm} \) to travel a distance of \( 500 \mathrm{m} \)
A . 1 s
B. 6 s
\( c \cdot 3 s \)
D. 12