The figure shows a conducting ring of radius \( R \). A uniform steady magnetic
field \( B \) lies perpendicular to the plane of
the ring in a circular region of radius \( r(<R) . \) If the resistance per unit length
of the ring is \( \lambda \), then the current induced
in the ring when its radius gets doubled
is
\( ^{A} \cdot \frac{B R}{\lambda} \)
B. \( \frac{2 B R}{\lambda} \)
\( \mathbf{c} . \) zero
D. \( \frac{B r^{2}}{4 R \lambda} \)


In the manufacture of ammonia, what
is the ratio of the reactants taken, i.e.
\( N_{2}: H_{2} ? \)
A . 1: 1
B. 1: 3
c. 3: 1
D. 2: 3


The property satisfied by the division of whole numbers is
A. closure property
B. Commutative property
c. Associative property
D. None of these


A sample of helium gas is at a temperature of \( 300 \mathrm{K} \) and a pressure of 0.5 atm. What is the average kinetic
energy of a molecule of a gas?


Give IUPAC name of :
A .2 -cyano-5-methyl hept- 3 -enal
B. 2 -formy- 5 -methyl hept-3-enenitrile
C. 2 -oxo-5-methyl hept- - 3 -ene-1-nitrile
D. 1 -cyano-1-formyl-4-methyl hex-2-ene


A single electron has change \( |e|= \)
\( \mathbf{1 . 6} \times \mathbf{1 0}^{-19} \mathbf{C} . \) If the current passing
through a conducting wire is \( 0.32 A \) how many electrons would pass through
the wire In one hour?
A. \( 7.2 \times 10^{20} \)
В. \( 7.2 \times 10^{21} \)
c. \( 7.2 \times 10^{19} \)
D. \( 2 \times 10^{18} \)


In a stream line (laminar flow) the
velocity of flow at any point in the liquid:
A. does not vary with time
B. may vary in direction but not in magnitude
C. may vary in magnitude but not in direction
D. may vary both in magnitude and direction


Which one of the following acids would you expect to be the strongest?
A \( \cdot I-C H_{2} C O O H \)
в. \( C l-C H_{2} \) СООН
c. \( B r-C H_{2} \) COOH
D. \( F-C H_{2} C O O H \)


\( \boldsymbol{y}-\boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}=\mathbf{5}\left(\boldsymbol{y}^{2}+\frac{d \boldsymbol{y}}{d x}\right) \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\csc ^{-1}\left(\frac{\sqrt{\boldsymbol{2}}}{\boldsymbol{x}-\sqrt{\mathbf{1}-\boldsymbol{x}^{2}}}\right)\right] \)


The aqueous solution containing which one of the following ions will be colourless:
A \( \cdot F e^{2} \)
B. \( M n^{2+} \)
\( c \cdot T i^{3} \)
\( \mathrm{D} \cdot \mathrm{Sc}^{3} \)


Consider the following statements.
I. Atomic hydrogen is obtained by passing hydrogen through an electric
arc.
Il. Hydrogen gas will not reduce heated aluminium oxide.
III. Finely divided palladium absorbs large volume of hydrogen gas.
Which of the above statement(s) is(are)
correct:
A. I alone
B. ॥ alone
c. I, Il and III
D. II, III
E. None of these


If a person can see an object clearly when it is placed at about \( 25 \mathrm{cm} \) away
from him, he is suffering from:
A. myopia
B. hypermetropia
c. astigmatism
D. none of these


Among the following, the essential amino acid is:
A. Aspartic acid
B. Valine
c. Alanine
D. Serine


Find the value of \( \left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+ \)
\( \left(\frac{1}{4}\right)^{-2} \)


A blog of mass \( \mathrm{m} \) is placed on a cart of mass \( \mathrm{M} \) as shown in the figure, The coefficient of friction between the block
and the cart is \( \mu . \) What is the minimum
acceleration of the cart so that block \( m \)
does not slip on the cart?


Which reducing agent is used for the following conversion?
\( \boldsymbol{R} \boldsymbol{C O O H} \rightarrow \boldsymbol{R} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
A \( . \) Li \( A l H_{4} \)
в. \( N a B H_{4} \)
\( \mathbf{c} \cdot K_{2} C r_{2} O_{7} \)
D. \( K M n O_{4} \)


Column II gives \( n^{t h} \) term for AP given in column I. Match them correctly.
A. \( 119,136,153,170 \dots \)
1. 13 -
\( \mathbf{3} n \)
B. \( 7,11,15,19, \dots . \)
2. \( 9-5 n \)
C. \( 4,-1,-6,-11, \dots \)
\( 3.3+4 n \)
D. \( 10,7,4,3 \dots . \)
\( 4.17 n+ \)
\( \mathbf{1 0 2} \)
A \( \cdot A \rightarrow 3, B \rightarrow 2, C \rightarrow 1, D \rightarrow 4 \)
B. A \( \rightarrow 4, \) В \( \rightarrow 3, C \rightarrow 2, D \rightarrow 1 \)
\( \mathrm{c} \cdot \mathrm{A} \rightarrow 3, \mathrm{B} \rightarrow 4, \mathrm{C} \rightarrow 2, \mathrm{D} \rightarrow 1 \)
D. A \( \rightarrow 1, \) В \( \rightarrow 3, \) С \( \rightarrow 4, \) D \( \rightarrow 2 \)


Write the formula for an oxoacid of
nitrogen with \( N \) in the oxidation state
+3
A \( . H N O_{2} \)
в. \( H_{2} N O_{2} \)
c. \( H N O_{3} \)
D. \( H N O \)


When light rays travelling from one
medium fall at the surface of another
medium \( \ldots . . . . . . . \) the light rays returns
back to the same medium.
\( A \). All of
B. Part of
c. None of
D. can't be determined


Use the identity \( (a+b)(a-b)=a^{2}- \)
\( b^{2} \) to find the product of \( \left(\frac{2 x}{3}+1\right)\left(\frac{2 x}{3}-\right. \)
\( \mathbf{1} \)


Ram is a successful bitcoin investor. He
recently sold one bitcoin for \( \$ 18,000 \) He made a profit of \( 400 \% . \) At what cost did he bought the bitcoin?


Assertion
There is no dispersion of light refracted through a rectangular glass slab.
Reason
Dispersion of light is the phenomenon of splitting of a beam of white light into
its constituent colours.
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


At \( 20^{\circ} C \) the vapour pressure of
\( C H_{3} O H \) and \( C_{2} H_{5} O H \) is \( 94 \mathrm{mm} \) and
\( 44 \mathrm{mm}, \) respectively.

If 20 g of \( C H_{3} O H \) is mixed with 100 g
of \( C_{2} H_{5} O H, \) determine the total
pressure of the solution (in \( \mathrm{mm} \) )


Find the area of the shaded region in
fig:- if \( A B C D \) is a square of side \( 14 \mathrm{cm} \) and \( A P D \times B P C \) are semi circles.


The function of root cap is
A. Protection of root tip and control of geotropic movement
B. Storage of food products
C. Absorption of nutrients
D. None of the above


Which of the following is a common example of fibers?
A. Bakelite
B. Buna-s
c. Nylon - 6,6
D. Nylon - 6


The rate at which ice-ball melts is
proportional to the amount of ice in it. If half of it melts in 20 minutes, the
amount of ice left after 40 minutes compared to it original amount is
\( ^{A} \cdot\left(\frac{1}{8}\right) t h \)
B. \( \left(\frac{1}{16}\right) \) th
\( ^{c} \cdot\left(\frac{1}{4}\right) t h \)
D. \( \left(\frac{1}{32}\right) t h \)


\( \int_{0}^{1} x(1-x)^{4} d x=\frac{1}{C}, \) then \( C=? \)


Which of the following quantities has equivalent units as Impulse?
A. Displacement
B. Velocity
c. Acceleration
D. Linear momentum
E. Kinetic energy


Mesonephric kidney is found in
A. Aves
B. Reptilia
c. Amphibia
D. Mammalia


For any SHM, amplitude is \( 6 \mathrm{cm} \). If instantaneous potential energy is half the total energy then distance of particle from its mean position is
A. 3 cm
B. \( 4.2 \mathrm{cm} \)
c. \( 5.8 \mathrm{cm} \)
D. 6 cm


The EMF of a cell corresponding to the reaction:
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}^{\oplus}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( Z n^{2+}(0.1 M)+H_{2}(g, 1 a t m) \) is \( 0.82 V \)
\( \operatorname{at} 25^{\circ} C \)
The pH of the solution at the hydrogen electrode is:
\( \boldsymbol{E}_{Z n^{2+} \mid \boldsymbol{Z n}}^{\ominus}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{\boldsymbol{H}^{\ominus} \mid \boldsymbol{H}_{2}}^{\Theta}=\mathbf{0} \)
If the value is \( 63 \times 10-x \), then what is
the value of \( x ? \)


What would be the value of \( \triangle \boldsymbol{n}_{g} \) for the
reaction?
\( N H_{4} C l_{s} \rightleftharpoons N H_{3(g)}+H C l_{(g)} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0.5
c. 1.5
D.


Give four rational numbers equivalent
to:
\( \frac{\mathbf{5}}{-3} \)


Match the following list of animals with
their level of organization and choose
the correct sequence:
1 Column - I "
(A)
Organ level \( \quad \) (P) \( \quad \) Pheritima bethere
(B)
Cellular aggregate \( \quad \) (Q) \( \quad \) Fasciola Celular a
level
(C)
Tissue level \( \quad \) (R) \( \quad \) Spongilla
(D) Organ system
level
(s) Obelia
\( A \cdot A-(S), B-(R), C-(P), D-(Q) \)
B. A- (S), B- (Q), C- (R), D- (P)
c. \( A-(Q), B-(S), C-(R), D-(P) \)
D. A- (Q), B- (R), C- (S), D- (P)


If a language of natural numbers has a binary regularly of 0 and \( 1, \) then which one of the following strings represents
the natural number \( 7 ? \)
A . 1
в. 101
c. 110
D. 111


Two point charges \( q_{1} \) and \( q_{2} \) are located
at \( \overrightarrow{r_{1}} \) and \( \overrightarrow{r_{2}} \) respectively in an external
electric field \( E \).Total work done
in assembling this configuration \( \frac{\boldsymbol{E}\left(\boldsymbol{q}_{1}+\boldsymbol{q}_{2}\right)}{\boldsymbol{\delta l}} . \) Type 1 for true and 0 for false


Write the method to determine the
value of an unknown resistance by
meter bridge and derive necessary formula. Draw a circuit diagram.


If the same element is forming oxides in different oxidation states then:
A. that oxide will be neutral in nature in which element will be in its highest oxidation state
B. the oxide will be highest acidic in nature in which element will be in its highest oxidation state
c. that oxide will be amphoteric in nature in which element will be in its highest oxidation state
D. that oxide will be highly basic in nature in which element will be in its highest oxidation state


Edible part of cabbage is
A. Flower
B. Inflorescence
c. Stem
D. Budd


Write the order of the differential
equation associated with the primitive \( \boldsymbol{y}=\boldsymbol{C}_{1}+\boldsymbol{C}_{2} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{C}_{3} \boldsymbol{e}^{-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{C}_{4}}, \) where
\( C_{1}, C_{2}, C_{3}, C_{4} \) are arbitrary constants.


Find the value of \( k \) for which the
equation \( \boldsymbol{x}^{2}+\boldsymbol{k}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{k}-\mathbf{1})+\boldsymbol{2}=\mathbf{0} \)
has real and equal roots.


Two persons of equal height are
carrying a long uniform wooden plank of length \( l . \) They are at distance \( \frac{l}{4} \) and \( \frac{l}{6} \)
from nearest end of the rod. The ratio of
normal reaction at their heads is-
\( \mathbf{A} \cdot 2: 3 \)
B. 1: 3
\( c \cdot 4: 3 \)
D. 1: 2


Match the column I with column II.


The point which is equidistant from the points (-1,1,3),(2,1,2),(0,5,6) and
(3,2,2) is
A \( \cdot(-1,3,4) \)
в. (3,1,4)
c. (1,3,4)
D. (4,1,3)


(II) \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \)
Arrange the following compounds in increasing order of their boiling points:
\( (\mathbf{I}) \)
(III)
\( A \cdot(\mid I)<(1)<(\| 1) \)
B. (I) <(II) <(III)
\( c \cdot(\| I)<(1)<(11) \)
D. (III) <(II) < (I)


The shape of \( s p^{3} d^{2} \) hybridized molecule with 2 lone pairs will be:
A . octahedral
B. square pyramidal
c. square planar
D. tetrahedral


Choose the correct answer from the
alternatives given. The exchange of materials between blood and interstitial fluid occurs only
in:
A. Capillaries
B. Arteries
c. veins
D. Arterioles


If kidneys fail to reabsorb water, the effect on tissue would
A. Remain unaffected
B. Shrink and shrivel
C. Absorb water from blood plasma
D. Take more \( O_{2} \) from blood


Write the medicianl properties of the following plants.
Sarpagandha
Kachnar
Jamun
Arjun
Babool
Neem


In which of the following molecules the central atom does not retain any lone pair of electrons?
A \( \cdot N O_{2} \)
в. \( N H_{3} \)
c. \( B F_{3} \)
D. \( H_{2} O \)


For the process Dry ice \( \rightarrow C O_{2}(g) \)
A. \( \Delta H \) is positive and \( \Delta S \) is negative
B. Both \( \Delta H \) and \( \Delta S \) are negative
c. Both \( \Delta H \) and \( \Delta S \) are positive
D. \( \Delta H \) is negative and \( \Delta S \) is positive


Pick out the correct statement.
A. Compared to a strong acid, a weak acid titration with base starts at a higher pH
B. Compared to a strong acid, a weak acid titration with base starts at a lower pH
\( \mathbf{C} \cdot H C N(a q)+N O_{2}^{-}(a q) \longrightarrow H N O_{2}(a q)+C N^{-}(a q) \)
D. None of these


The magnetic field produced by a current carrying solenoid is similar to the magnetic field produced by a bar
magnet.


A bag contain 6 Red and 4 White balls. 4 balls are drawn one by one without
replacement and were found to be atleast 2 white. Then the probability that next draw of a ball from this bag will give a white ball.


In given figure, \( P Q \) is chord of length
\( 8 c m \) of a circle of radius \( 5 c m, \) the
tangents at \( P \) and \( Q \) intersect at a point
T. Find the length \( \boldsymbol{T} \boldsymbol{P} \)


What is seen on the screen when the
flame is very close (at about 5cm) to
the lens?


World climate is threatened by increase in the concentration of
A. Oxygen
B. Nitrogen
C. Water vapours
D. Carbon dioxide


\( \frac{\delta}{g} \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\{\log (\boldsymbol{x}+\sqrt{\boldsymbol{a}^{2}+\boldsymbol{x}^{2}})\}= \)
A. \( \frac{1}{(x+\sqrt{a^{2}+x^{2}})} \)
в. \( \frac{x}{\sqrt{a^{2}+x^{2}}} \)
c. \( \frac{1}{x(x+\sqrt{a^{2}+x^{2}})} \)
D. \( \frac{1}{\sqrt{a^{2}+x^{2}}} \)


Total number \( \sigma \) and \( \pi \) bonds in carbon
sub-oxide \( \left(C_{3} O_{2}\right) \) is


Explain the purification of sulphide ores by froth floatation method?


Molecular shape of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}, \boldsymbol{S} \boldsymbol{F}_{3}^{+} \) and
\( \boldsymbol{C} \boldsymbol{F}_{3}^{+} \) are
A. the same with 2,1 and 0 lone pairs of electrons respectively
B. different with 2, 1 and 0 lone pairs of electrons respectively
c. different with 0,1 and 2 lone pairs of electrons respectively
D. the same with 2,0 and 1 lone pairs of electrons respectively


Which of the following statement is
false
A. Nephrons perform excretion through filtration, reabsorption and secretion.
B. Nephridia are accessory excretory organs in Prawn
c. Tapeworm have excretory flame cells
D. Nephrons begin with Bowmen's capsule having glomerulus


According to J.J. Thomson's atomic model, negative charges are embedded
in :
A. a lump of positive charge
B. lump of neutral charge
c. a lump of small atoms
D. nucleus


Which of these is not a contact force?
A. Friction
B. Muscular force
c. Magnetic force
D. None of these


The sulphur molecule \( S_{8} \) can be
represented as a:
A . cubical structure
B. spherical structure
c. tetrahedral structure
D. W shaped ring structure


In a parallelogram \( A B C D, A B=10 \mathrm{cm} \) and
\( A D=6 \mathrm{cm} . \) The bisector of \( A \) meets DC in
E. AE and BC produced meet at F. Find the length of CF.
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
\( D \cdot 6 \mathrm{cm} \)


The vapour density of oxygen is than air.
A. slightly heavier
B. slightly lighter
c. extremely heavier
D. extremely lighter


The specific conductance of a \( 0.1 \mathrm{N} \mathrm{KC} \) solution is 0.012 ohm \( ^{-1} c m^{-1} \). The
resistance of the cell containing the
same solution is 55 ohms. Then the
cell constant is :
\( \begin{array}{lll}\text { A } \cdot 0.918 & c m^{-1}\end{array} \)
B. \( 0.66 \mathrm{cm}^{-1} \)
\( \begin{array}{lll}\text { C } \cdot & 1.142 & c m^{-1}\end{array} \)
D. 1.12 cm \( ^{-1} \)


What is wavefront of light waves?


In a neutral object, there are
A . equal number of atoms
B. more protons than electrons
C . equal number of protons and electrons
D. more electrons than protons


Consider the piecewise defined
\[
\text { function }\left\{\begin{array}{ll}
\sqrt{-x}, & \text { if } x<0 \\
0, & \text { if } 0 \leq x \leq 4 . \text { Choose } \\
x-4, & \text { if } x>4
\end{array}\right.
\]
the answer which best describes the
continuity of this function-
A. the function is unbounded and therefore cannot be continuous
B. the function is right continuous at \( x=0 \)
c. the function has a removable discontinuity at 0 and 4 but is continuous on the rest of the real line
D. the function is continuous on the entire real line


Consider the function \( f(x)=\frac{x^{2}-1}{x^{2}+1} \)
where \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \)
At what value of \( x \operatorname{does} f(x) \) attain minimum value?
A . -1
B.
c. 1
D.


Q Type your question
i. If electrical resistivity of metal \( \boldsymbol{X} \) is
lower than that of metal \( Y \), it means
metal \( X \) is better conductor
of electricity than metal \( Y \)
ii. If a wire of resistance \( 8 \Omega \) is doubled
on itself, the resistance of the new wire
will be \( 2 \Omega \)
iii. The coils of electric toasters and
irons are made of an alloy rather than a pure metal because resistivity of the alloy is higher than that of its constituent metals.
iv. If a conductor of length \( 65 \mathrm{cm} \) has a
resistance of \( 4 \Omega, \) the same conductor of
length \( 260 \mathrm{cm} \) will have the resistance
of \( 16 \Omega \)
v. The maximum amount of current that
can pass through a conductor is \( 440 A \)
A. i, iii and v
B. i, ii, iii and iv
c. iii, iv and \( v \)
D. iii and iv only


Assertion
\( \mathbf{3} \boldsymbol{H} \) isotopes does not undergo fusion of
the type \( _{1}^{3} H+_{1}^{2} H \rightarrow \) as it is rarely
found in nature.
Reason
\( \mathbf{3} \boldsymbol{H} \) has half life of \( \approx \mathbf{1 2} \boldsymbol{y} \boldsymbol{e} \boldsymbol{a} \boldsymbol{r} \boldsymbol{s} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the number of distinct triangles with integral valued sides and perimeter as \( 14 ? \)


State newton's second law of motion
and give related expression why does a cricket player lower his hands while catching the ball?


For a transistor, \( \beta=100 . \) The value of \( \alpha \)
is
A . 1.01
B. 0.99
\( c \cdot 100 \)
D. 0.01


The latent heat of fusion of ice is 80
calories per gram at \( 0^{\circ} \) C. What is the
freezing point of a solution of KCl in water containing 7.45 grams of solute 500 grams of water, assuming that the salt is dissociated to the extent of \( 95 \% ? \)
\( \mathbf{A} \cdot T_{f}=-0.73^{\circ} \mathrm{C} \)
B. \( T_{f}=-0.92^{\circ} \mathrm{C} \)
c. \( T_{f}=-1.46^{\circ} \mathrm{C} \)
\( \mathbf{D} \cdot T_{f}=-1.84^{\circ} \mathrm{C} \)


Viruses are classified in which of the
following kingdom?
A. Plantae
B. Animalia
c. Monera
D. None of these


If \( x \) is so small that \( x^{3} \) and higher
powers of \( x \) may be neglected, then \( \frac{(1+x)^{3 / 2}-\left(1+\frac{1}{2} x\right)^{3}}{(1-x)^{1 / 2}} \) may be approximated
as
A \( \cdot \frac{x}{2}-\frac{3}{8} x^{2} \)
B. \( -\frac{3}{8} x^{2} \)
c. \( _{3 x+\frac{3}{8} x^{2}} \)
D. \( 1-\frac{3}{8} x^{2} \)


Simplify:
\( 25 a b c^{2}-15 a^{2} b^{2} c \)


Clamp connections are found in
A. Ascomycetes
B. Zygomycetes
c. saccharomycetes
D. Basidiomycetes.


Though a woman can see the distant objects clearly, she cannot see the objects nearby object clearly. She is suffering from the defect called :
A. long-sight
B. short-sight
c. hind-sight
D. mid-sight


Considering all possible isomeric ketones, including stereoisomers of a compound having a molecular weight of
100. All these isomers are
independently reacted with \( \mathrm{NaBH}_{4} \). The total number of ketones that give a racemic product(s) is/are:
[Note: stereoisomers are also reacted
separately]


Mass of an electron is
A. \( 1 / 1850 g m \)
в. \( .1 g m \)
c. \( 9.1 \times 10^{-28} g m \)
D. None of the above


What is the partition chromatography?


Nuclear energy may become an important source of energy in the future.
Which one of the following statements about nuclear energy is NOT true?
A. Large amounts of energy are produced by a smal mass of fuel
B. Nuclear energy has no harmful effects
c. Nuclear energy produces heat on the sunn
D. Uranium is an important fuel for nuclear energy


The equation of a plane passing through the point \( A(2,-3,7) \) and making equal intercepts on the axes,
is?
A. \( x+y+z=3 \)
в. \( x+y+z=6 \)
c. \( x+y+z=9 \)
D. \( x+y+z=4 \)


If concentration of two weak bases are
same and degree of dissociation \( (\boldsymbol{\alpha}) \) are very less, then their relative strength can be compared by This question has multiple correct options
A \( \cdot \frac{\left[O H^{-}\right]_{1}}{\left[O H^{-}\right]_{2}} \)
в. \( \frac{K_{b_{1}}}{K_{b_{2}}} \)
c. \( \frac{\alpha_{1}}{\alpha_{2}} \)
D. \( \frac{\sqrt{K_{b_{1}}}}{\sqrt{K_{b_{2}}}} \)


Which of the following compounds has the smallest bond angle?
\( A \cdot S O_{2} \)
в. \( H_{2} \) о
\( \mathrm{c} \cdot H_{2} \)
D. \( N H_{3} \)


\( \frac{n}{p} \) ratio of \( _{1} H^{1} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.


For the following half cell reactions, \( \boldsymbol{E}^{\boldsymbol{o}} \) values are also given:
\( M n^{2+}+2 H_{2} O \rightarrow M n O_{2}+4 H^{+}+ \)
\( \mathbf{2} e^{-} ; \quad \boldsymbol{E}^{o}=-\mathbf{1 . 2 3} \mathbf{V} \)
\( M n O_{4}^{-}+4 H^{+}+3 e^{-} \rightarrow M n O_{2}+ \)
\( 2 H_{2} O ; \quad E^{o}=+1.70 V \)
Select the correct statements.
A. \( M n^{2+} \) reacts with \( M n O_{4}^{-} \) in acid solution to form \( M n O_{2} \)
в. \( M n\left(M n O_{4}\right)_{2} \) is stable in acid solution
c. \( M n O_{2} \) disproportionates to \( M n^{2+} \) and \( M n O_{4}^{-} \) in acid solution
D. None of the above


Among the following which are the examples of periodic motion?
(a) A hydrogen molecule rotating about its centre of mass.
(b) A freely suspended bar magnet displaced form its N-S direction and released.
(c) A swimmer completing one (return) trip from one bank of a river to the other
and back.
(d) An arrow release from a bow.


With the help of neat ray diagram. Discuss the construction and working of optical fibre.


What is the nature of the graph : \( y= \)
\( 4\left(1-e^{-2 x}\right) \)
A. exponentially increasing graph
B. exponentially decreasing graph
c. decreasing graph
D. none of these


A 1.00 molal aqueous solution of
trichloroacetic acid \( \left(C C l_{3} C O O H\right) \) is
heated to its boiling point. The solution
has the boiling point of \( 100.8^{\circ} \mathrm{C} \).
Determine the van 't Hoff factor for
trichloroacetic acid. \( \left(K_{b} \text { for water } 0.512 \mathrm{K}\right. \)
\( \left.\operatorname{kg} M o l^{-1}\right) \)
Define the following terms:
(i) Mole fraction
(ii) Isotonic solutions
(iii) Van 't Hoff factor
(iv) Ideal solution


The free electron density is more in
A. Conductors
B. Insulators
c. Semi conductors
D. Electrolytes


What is the atomic number of the
following elements
Potassium iodide, lodine is


\( \triangle X Y Z \) in which \( Y Z=5.8 c m, \angle= \)
\( 100^{\circ}, \angle=40^{\circ} \) Draw the perpendicular
from \( \boldsymbol{Y} \) to \( \boldsymbol{X} \boldsymbol{Z} \)


ArOR ethers are cleaved to give \( \boldsymbol{R I} \)
and \( A r O H \) rather than \( A r I \) and \( R O H \)
A. True
B. False


Given figure of Hydra shows its
reproductive structures and manner of
fertilisation.

Observe and answer that why is it not
showing self fertilisation?
A. Distance between testis and ovary is more
B. Sperms do not swim downwards
c. Ovary matures earlier than testis
D. Testis matures earlier than ovary


The decreasing order of basicity of the
following amines is :
A. \( (I I)>(I I I)>(I V)>(I) \)
в. \( (I)>(I I I)>(I V)>(I I) \)
c. \( (I I I)>(I I)>(I)>(I V) \)
D. \( (I I I)>(I)>(I I)>(I V) \)


Perimeter of a circle is called as
A . area
B. circumference
c. volume
D. none of these


In how many ways is it possible to choose a white square and a black square on a chess board so that the
squares must not lie in the same row or
column -
A . 56
в. 896
c. 60
D. 768


Assertion
According to Mendeleev, the properties of elements are a periodic function of their atomic weights.
Reason
Mendeleev left the gap under aluminium and a gap under silicon, and called these elements Eka-Aluminium
and Eka-Silicon.
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


Usually chordates have red blood containing red blood corpuscles. The blood is red due to the presence of the following pigment.
A. Myoglobin
B. Anthocyanin
C. \( \beta \) -anthocyanin
D. Haemoglobin


Joint between femur and acetabulum is
Known as
A. Hinge joint
B. Saddle joint
c. Gliding joint
D. Ball and socket joint


The synaptonemal complex appears Between homologous chromosomes
In the zygotene stage Composed of DNA + protein Before the pachytene stage
A . 1 and 2
B. 1,3 and 4
c. 2,3 and 4
D. 1,2,3 and 4


Fill in the blanks:
is the purest form of natural
water


What is the geometrical shape of equipotential surface due to a single isolated charge?


A body is projected vertically upwards.
Its momentum is gradually decreasing.
In this
A. it is a violation of law of conservation of linear
momentum
B. momentum of the body alone gets conserved
C. momentum of the body, earth and air molecules together remains constant
D. violates law of conservation of energy.


A graph between the square of the
velocity of a particle and the distance
moved by the particle is shown in the figure. The acceleration of the particle
in kilometre per hour square is:
A . 2250
В. 225
c. -2250
D. -225


Show that \( : \sec ^{2} \theta \times \csc ^{2} \theta=\sec ^{2} \theta+ \)
\( \csc ^{2} \theta \)


Solve in positive integers:
\( 5 x+2 y=53 \)
A. \( x=1,3,5,7,9 ; y=24,19,14,9,4 \)
В. \( x=2,4,6,8,10 ; y=23,20,13,8,3 \)
c. \( x=11,13,15,17,19 ; y=1,3,4,6,9 \)
D. None of these


Medicinal plant harvested from wild for anticancer compound is
A. Taxus baccata
B. Datura stramonium
c. Rauwolfia serpentina
D. Ocimum sanctum


Three positive real numbers \( l, \boldsymbol{m}, \boldsymbol{n} \) are in A.P. with product taken all at a time
is \( 4, \) then the minimum value of \( m \) is
\( \mathbf{A} \cdot 4^{1 / 3} \)
B. 3
\( c \cdot 2 \)
D. \( 1 / 2 \)


\( A(1,2,3), B(0,4,1), C(-1,-1,-3) \) are the
vertices of \( \Delta A B C \) and the bisector of
angle A meets BC in D then D point is
В. \( \left(10, \frac{2}{5}, \frac{1}{2}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{-7}{10}, \frac{5}{10},-\frac{18}{10}\right) \)
D. (3,-5,1)


Boojho made the following sketch (see
fig.) of the solar system. Is the sketch
correct? If not, correct it.


An isobar of \( _{20} C a^{40} \) is :
\( \mathbf{A} \cdot_{18} A r^{40} \)
В. \( 200 a^{38} \)
\( \mathrm{c} \cdot_{20} \mathrm{Ca}^{42} \)
D. \( 18 A r^{38} \)


A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the downward vertical.
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


If \( f(x)=x^{2}+x \) for all \( x \) and if \( f(a- \)
1) \( =-\frac{1}{4}, \) find the value of \( a \)
A. \( -\frac{1}{2} \)
B. \( -\frac{1}{4} \)
\( c \cdot \frac{1}{4} \)
D.
E.


The emulsifying agent used in o/w emulsion is:
A. protein
B. long chain alcohol
c. lampblack
D. heavy metal salts of fatty acids


The quantum yield for decompostion of \( H I \) is 0.2 In a experiment 0.01 moles of
\( H I \) are decomposed. Find the number
of photons absorbed. \( \left(N_{A}=6 \times 10^{23}\right) \)


GH promotes:
A. bone growth
B. cell division
C . protein synthesis
D. all of the above


Assertion
A cation of less size is more favorable
for ionic bond formation.
Reason
If the size of the atoms is small, the
nuclear pull on the electrons is more.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following animals show adaptive radiation based on locomotion?
A. Scorpion, elephant, human
B. Cheetah, kangaroo, mole
c. Praying mantis, seal, python
D. cockroach, squirrel, toadd


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{y}=\log \left(\boldsymbol{4} \boldsymbol{x}-\boldsymbol{x}^{5}\right) \)


Vitamin \( \boldsymbol{B}_{1} \) is:
\( A \). riboflavin
B. ascorbic acid
c. cobalamin
D. thiamine


75 persons can sleep in a room \( 25 \mathrm{m} \) by
\( 9.6 . \) If each person requires \( 16 m^{3} \) of air; find the height of the room.
\( A \cdot 5 m \)
B. 3 m
\( c \cdot 6 m \)
D. \( 7 \mathrm{m} \)


In materials like aluminium and
copper, the correct order of magnitude of various elastic moduli is
A. Young's modulii < shear modulii < bulk modulii.
B. Bulk modulii < shear modulii <Young's modulii
c. shear modulii < Young's modulii < bulk modulii
D. Bulk modulii <Young's modulii < shear modulii


ff \( x+y=5 \) and \( x=3 \), then the value of
\( \boldsymbol{y} \)


Graph \( x^{2}+y^{2}=4 \) in \( 3 D \) looks like
A . Circle
B. Cylinder
c. Hemisphere
D. sphere


The escape velocity for a body projected vertically upwards from the surface of earth is \( 11 \mathrm{km} / \mathrm{s} \). If the body is projected
at an angle of \( 45^{0} \) with the vertical, the escape velocity will be
A. \( 11 \sqrt{2 \mathrm{km} / \mathrm{s}} \)
.
B. 22 km/s
c. \( 11 \mathrm{km} / \mathrm{s} \)
D. \( 11 / \sqrt{2 \mathrm{m}} / \mathrm{s} \)


\( (a . i) i+(a . j) j+(a . k) k= \)
\( A \cdot 0 \)
B. \( a \)
\( c .3 a \)
D. None of these


In the shown arrangement of the
experiment of the meter bridge if \( \boldsymbol{A C} \)
corresponding to null deflection of
galvanometer is \( x, \) what would be its
value if the radius of the wire \( A B \) is
doubled?
\( A \)
B. \( x / 4 \)
\( c \cdot 4 x \)
D. \( 2 x \)


A thin wire of length \( 2 m \) is
perpendicular to the \( x-y \) plane. It is
moved with velocity \( \overrightarrow{\boldsymbol{v}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \hat{k}) m / s \) through a region of magnetic induction \( \vec{B}=(\hat{i}+2 \hat{j}) W b / m^{2} . \) Then
potential difference induced between the ends of the wire is
A . \( 2 V \)
B. \( 4 V \)
\( c .0 V \)
D. none of these


If \( x g \) of an element \( A \) contains \( \frac{y}{80} \) atoms and \( 2 x g \) of an element \( B \)
contains \( \frac{\boldsymbol{y}}{\mathbf{4} \mathbf{0}} \) atoms then the ratio of atomic weights of two elements \( A \) and
\( B \) is:
A . 1: 1
B. 1: 4
c. 4: 1
D. 2: 1


The first and second order derivatives of
a function \( f(x) \) exist at all points in \( (a, b) \) with
\( \mathbf{f}^{\prime}(\mathbf{c})=\mathbf{0}, \) where \( \mathbf{a}<\mathbf{c}<\mathbf{b} . \) Further
more, if \( \mathrm{f}^{\prime}(\mathrm{x})<0 \) at all points on the
immediate left of \( \mathbf{c} \) and \( \mathbf{f}^{\prime}(\mathbf{x})>\mathbf{0} \) for all
points on the immediate right of \( c \), then at \( \mathbf{x}=\mathbf{c}, \mathbf{f}(\mathbf{x}) \) has a
A. local maximum
B. local minimum
c. point of inflexion
D. none of these


What type of curve do we get, if \( x^{2} \) and
\( v^{2} \) are plotted for a particle executing \( \mathrm{SHM}, \mathrm{x} \) and \( \mathrm{v} \) are the position and velocity of the particle:
A . Circle
B. Straight line
c. Ellipse
D. Rectangle


A biprism is placed at a distance of 50 \( \mathrm{mm} \) in front of a narrow slit illuminated by light of wavelength \( 600 \mathrm{nm} \). The virtual images formed by the biprism are \( 0.5 \mathrm{mm} \) apart. Find the width of the
fringes formed on a screen placed 0.75 \( \mathrm{m} \) apart in front of the biprism.
A. \( 0.96 \mathrm{cm} \)
B. \( 0.096 \mathrm{cm} \)
c. \( 0.0096 \mathrm{cm} \)
D. 9.6 \( \mathrm{cm} \)


A rectangle with its dimensions is as shown. A Magnetic mono pole of pole strength ' \( \mathrm{m}^{\prime} \) is placed at the point \( ^{\prime} \mathrm{A}^{\prime} \) and another pole of pole strength '5m' is
placed at the point 'B'. The magnetic force acting between them is 'F'.' If magnetic pole at the point 'B' is moved to the point 'C', Find final magnetic force acting between them.
A \( \cdot \frac{F}{10} \)
в. \( \frac{F}{17} \)
\( c \cdot \frac{F}{20} \)
\( \mathbf{D} \cdot F \)


An alternating current in circuit is
\( \operatorname{given} \) by \( I=20 \sin (100 \pi t+0.005 \pi) A \)
The r.m.s value and the frequency of current respectively are:
A . \( 10 A \) and \( 100 H z \)
B. \( 10 A \) and \( 50 \mathrm{Hz} \)
c. \( 10 \sqrt{2} \) A and \( 50 \mathrm{Hz} \)
D. \( 10 \sqrt{2} \) A and \( 100 \mathrm{Hz} \)


\( A \) and \( B \) invested in a business in ration
7: 6. After 7 months, C joined them with
double the investment made by B. If \( \mathbf{A} \) and \( C \) together got \( \operatorname{Rs} 2380 \) from the total profit after a year, what was the annual profit


the incoming ray suffers total internal reflection (TIR) times as shown. The
prism mhas reflective index \( \mu \) and top
angle \( \theta . \) The emerging ray propagates
horizontally. The refrative index \( \mu= \)
\( \frac{\cos \theta}{\cos n \theta} . \) Find \( n \)


An electron is at rest. Its wavelength is
\( A \cdot 1 \)
B. Infinity
c. \( \frac{h}{m_{e}} \)
D. It has not wave character


What will be the energy of one photon of radiation whose frequency is \( 5 \times \) \( 10^{14} H z ? \)
A. \( 199.51 J \)
в. \( 3.3 \times 10^{-19} \mathrm{J} \)
c. \( 6.626 \times 10^{-34} J \)
D. \( 2.31 \times 10^{5} J \)


Assertion
When \( A g N O_{3} \) is treated with excess of
potassium iodide, colloidal particles
gets attracted towards anode.
Reason
Precipitate adsorb common ions (excess) and thus, become charged.
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


Draw structure of TNT, an explosive.


The relaxation time
(t) is the:
A. Time taken by an electron to drift from one end of a conductor to the other.
B. Time taken by an electron to travel unit distance through the conductor.
c. The time between two successive collisions of a free
electron with the atoms of the metal.
D. Time for which a free electron is subjected to the electric field


The correct relation between \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \) for the given reaction is:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{l}_{1}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H} \boldsymbol{l}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot K_{p}=K_{c}(R T)^{2} \)
В . \( K_{p}=K_{c} \)
c. \( \frac{K_{p}}{R T}=K_{c} \)
D. \( K_{p}=K_{c}(R T)^{-2} \)


A company bought a car that had a
value of Rs. 10000 . each year the value of the car depreciates by \( 15 \% . \) What is the value of the car at the end of 2 years.
A . 7225
B. 6225
c. 5225
D. 4225


Obtain the relation \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{2}) \)
and \( X_{C}=1 / \omega C \) for a pure capacitor
across which an altering \( e m f=V= \)
\( V_{0} \sin \omega t \) is applied. Draw a phasor
diagram showing emf \( V \), current \( I \) and
their phase difference \( \phi \)


There will be no force between two
current carrying wires if currents are
A. Parallel to each other
B. Antiparallel to each other
C. Perpendicular to each other
D. Nothing can be said


State whether given statement is True or False
Air conducts heat
A. True
B. False


In the presence of cobalt chloride
\( \left(\mathrm{CoCl}_{2}\right), \) bleaching powder decomposes
to form:
\( A \cdot C a C O_{3} \)
в. \( C a O C l \)
\( \mathrm{c} \cdot \mathrm{Cl}_{2} \mathrm{O}_{8} \)
D. \( \mathrm{CaCl}_{2} \)


A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are now moved apart by means of insulting handles:
A. the charge on capacitors increases
B. the voltage across the capacitors decreases
c. the capacitance increases
D. the electrostatic energy stored in the capacitor increases


Derive an expression for effective
capacitance of three capacitors
connected in parallel


Solve graphically, the following pairs of equations:
\( 3 x+7 y=27 \)
\( 3-y=\frac{5}{2} x \)
A . \( x=2, y=3 \)
в. \( x=7, y=2 \)
c. \( x=4, y=1 \)
D. \( x=4, y=6 \)


Amongst the following, the total number of compounds soluble in concentrated
\( N H_{3} \) solution is:
\( A g_{2} C r O_{4}, C u(O H)_{2}, P b S O_{3}, A l(O H)_{3} \)
A . 4
B. 7
\( c .5 \)
D. 6


Which of the following is enucleated cell
\( A \). RBC of frog
B. Sieve tube element
c. RBC of Crocodile
D. 1 and 2 both


Factorise the polynomial \( x^{2}-\frac{1}{x^{2}} \)


\( \ln 2015 \) and \( 2017, \) there was very heavy rain in our state. In 2016 , there was no adequate rain. These extreme conditions are due to
A. Uneven distribution of human population
B. Global warming
c. Depletion of ground water
D. Ozone depletion


What is the nature of the displacement time graph of a body moving with constant acceleration?


Find the eleventh term of the A.P.
\( 2,7,12, \dots \)


Arrange these figures in ascending order of cell divisions.
\( A \cdot C, D, A, B \)
B. B, A, D, C
c. \( A, B, C, D \)
D. \( B, D, A, C \)


Solid phosphorous pentachloride behaves as an ionic compound. Explain. Why?


Vairagi bought a table for Rs \( 450 . \) There is Rs 50 additional expenses on this
table. For earning \( 12 \% \) profit, what should be the sale price?


Evaluate the following integral:
\( \int x^{2}+3 x+5 d x \)


The Poisson's ratio of a material is \( 0.5 . \) If
a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4\%. The percentage increase in the length is :
A . 1\%
B. २\%
c. 2.5\%
D. 4\%


Which reducing agent is employed to get copper from the leached low grade
copper ore?


The greater the differences in the areas
of the cylinders, the greater the force output of the big cylinder for hydraulic jack. Fill in the gap
A. Potential
B. Kinetic
c. Rotational
D. Dynamic


If \( I=\int_{8}^{15} \frac{d x}{(x-3) \sqrt{x+1}} \) then \( I \) equals
A \( \cdot \frac{1}{2} \log \frac{5}{3} \)
B. \( 2 \log \frac{1}{3} \)
c. \( \frac{1}{2}-\log \frac{1}{5} \)
D. \( 2 \log \frac{5}{3} \)


Which of the complexes will exhibit the minimum peramagnetic behavior?
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{+2} \)
B. \( \left[M n\left(H_{2} O\right)_{6}\right]^{+2} \)
\( \mathbf{c} \cdot\left[C r\left(H_{2} O\right)_{6}\right]^{+2} \)
D \( \cdot\left[N i\left(H_{2} O\right)_{6}\right]^{+2} \)


A disk has rotational inertia \( 1.22 \times 10^{-3} \)
\( \mathrm{kg}-\mathrm{m}^{2} \) and is attached to an electric drill whose motor delivers a torque of
\( 15.8 \mathrm{N}-\mathrm{m} \)
The angular momentum of the disk 33 ms after the motor is turned on is:
A. \( 0.256 \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
B . 1.012 \( \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
c. \( 0.158 \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
D. 0.521 \( \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)


What is lightning conductor? How does it save high rise buildings from
lightning damage?


The chemical name of vitamin \( C \) is:
A . citric acid
B. acetic acid
c. ascorbic acid
D. oxalic acid


Area of circle in which a chord of length
\( 2 \sqrt{3} \) units, subtends angle \( 120^{\circ} \) at its
center is-
A . \( \pi \) sq units
B. 2 \( \pi \) sq units
c. \( 4 \pi \) sq units
D. None of these


In the given circuit (fig), all the symbols
have their usual meanings. At \( t=0, \) key
Kis closed. Now answer the following
questions. At \( t \rightarrow \infty, \) the equivalent
resistance between \( A \) and \( B \) is :
\( \mathbf{A} \cdot R_{1}+R_{2}+R_{3} \)
B. \( R_{1}+R_{2} \)
\( \mathbf{c} \cdot R_{1}+R_{3} \)
D. None of the above


If \( 2 x-3 y=7 \) and \( (a+b) x-(a+b-3) y=4 a \)
\( +b \) represent coincident lines then a
and b satisfy the equation
\( A \cdot a+5 b=0 \)
B. \( 5 a+b=0 \)
\( c \cdot a-5 b=0 \)
D. \( 5 a-b=0 \)


Two small metallic spheres each of
mass \( \mathrm{m} \) are suspended together with
strings of length \( l \) and placed together
When a quantum of charge \( \boldsymbol{q} \) is
transferred to each the strings make an
angle of \( 90^{\circ} \) with each other. The value
of \( q \) is
A \( \cdot l /\left(_{0} m g\right) \)
в. \( l /\left(16_{o} m g\right) \)
\( \mathbf{c} \cdot l /\left(2_{o} m g\right) \)
D. none of these


How many moles of glucose \( \left(C_{6} H_{12} O_{6}\right) \) should be dissolved into a solution with
a total volume of \( 0.500 L \) to produce a
1 \( M \) glucose solution?
\( \mathbf{A} \cdot 1 \mathrm{mol} \)
B. 24mol
\( c .0 .5 \mathrm{mol} \)
D. 0.25 mol


causes the smut of crop plants.
A. Puccinia
B. cystopus
c. ustilago
D. Agaricus


A cylindrical conductor is placed near other positively charged conductor. The net charge acquired by the cylindrical conductor will be :
A. Positive only
B. Negative only
c. zero
D. Either positive or negative


According to the adsorption theory of catalysis, the rate of reaction increases because:
A. adsorption lowers the activation energy of the reaction
B. concentration of reactant molecules at the active centers of the catalyst becomes high due to adsorption
c. adsorption increases the activation energy of the reaction
D. adsorption decreases the activation energy of the reaction


Prove that \( \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{2}{11}= \)
\( \tan ^{-1} \frac{3}{4} \)


Extraction of Zinc from zinc blende is
achieved by
A. electrolytic reduction
B. roasting followed by reduction with carbon
c. roasting followed by reduction with another metal
D. roasting followed by self-reduction


Turpentine oil is flowing through a tube of length I and radius r. The pressure difference between the two ends of the
tube is p. The viscosity of oil is given \( \boldsymbol{\eta}=\frac{\boldsymbol{p}\left(\boldsymbol{r}^{2}-\boldsymbol{x}^{2}\right)}{\boldsymbol{4} \boldsymbol{v} \boldsymbol{l}}, \) where \( \mathbf{v} \) is velocity of oil
at a distance \( x \) from the axis of the tube.
The dimensional formula of viscosity is
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{1} L^{-1} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1}\right] \)
D \cdot \( \left[M^{-1} L^{-1} T^{1}\right] \)


Calculate \( \sqrt[3]{-1} \)


The relation \( R \) and \( R^{\prime} \) are symmetric in
the set \( A \), then show that \( R \cup R^{\prime} \) and
\( \boldsymbol{R} \cap \boldsymbol{R}^{\prime} \) are symmetric.


The position in the periodic table to which the \( A l \) metal belongs:
A. Alkali metals
B. Alkaline earth metals
c. \( d \) - block elements
D. \( p \) -block elements


If the bond dissociation energies of
\( X Y, X_{2} \) and \( Y_{2} \) (all diatomic
molecules) are in the ratio of 1: 1: 0.5
and \( \Delta H_{f} \) for the formation of \( X Y \) is
\( -200 k J m o l^{-1}, \) the bond dissociation
energy of \( \boldsymbol{X}_{2} \) will be:
A . \( 100 k J m o l^{-1} \)
в. \( 300 k J m o l^{-1} \)
c. \( 200 k J m o l^{-1} \)
D. \( 800 k J m o l^{-1} \)


Antacids are used:
A. to produce acid in the stomach
B. to produce water in the stomach
C. to neutralise the excess base in the stomach
D. to neutralise the excess acid in the stomach


The following equilibrium constants are given:
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} ; K_{1} \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O ; K_{2} \)
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{K}_{3} \)
The equilibrium constant for the
oxidation of 2 mol of \( N H_{3} \) to give NO is?
A \( \cdot_{K_{1}} \cdot \frac{K_{2}}{K_{3}} \)
В. \( \quad K_{2} \cdot \frac{K_{3}^{3}}{K_{1}} \)
\( ^{\mathbf{c}} \cdot_{K_{2}} \cdot \frac{K_{3}^{2}}{K_{1}} \)
D. \( _{K_{2}^{2}} \cdot \frac{K_{3}}{K_{1}} \)


The correct IUPAC name of the alkyl
group, \( \begin{array}{cc}c_{2} H_{5} & c_{2} H_{5} \\ C H_{3}-C H-C H_{2}-C H^{\prime}-C H_{3} & \end{array} \)
A. 2-ethyl-3-sec-butyl propyl
B. 2,4-diethyl pentane
c. 2-ethyl-4-methylhexyl
D. 2-methyl-4-ethylexyl


A temperature difference of \( 15^{\circ} \) on the
Fahrenheit scale
A . 27
B. 59
\( c \cdot-27 \)
\( D .-59 \)


Alcoholic fermentation occurs in the
presence of
A. Zymase.
B. Amylase.
c. Invertase.
D. Maltase.


The drift speed of the conduction
electrons is:
A. \( 2.5 \mathrm{cm} / \mathrm{s} \)
B. \( 5 \mathrm{cm} / \mathrm{s} \)
c. \( 7.5 \mathrm{cm} / \mathrm{s} \)
D. \( 15 \mathrm{cm} / \mathrm{s} \)


Write the component statement of the following compounds statements and check whether the compound statement is true or false:
All rational number are real and all real
number are not complex.


Which of the following is/are grouped under phanerogams?
A. Angiosperms
B. Gymnosperms
c. Pteridophytes
D. Both A and B


Find the velocities of the point \( \boldsymbol{B} \)
A. \( 7.1 \mathrm{cm} / \mathrm{s} \)
B. \( 10 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 5 c m / s \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)


The information in a genetic nucleic
acid resides in
A. The number of nucleotides
B. The kind of nucleotides
c. The sequence nucleotides
D. All of the above


f \( a+b+c=8 \), then the value of
\( (a-4)^{3}+(b-3)^{3}+(c-1)^{3}-3(a- \)
4) \( (b-3)(c-1) \) is:
\( A \cdot 2 \)
B. 4
\( c \cdot 1 \)
\( D \)


The velocity-time graphs of a car and a
scooter are shown in the figure. (i) the difference between the distance
travelled by the car and the scooter in
\( 15 s \) and (ii) the time at which the car
will catch up with the scooter are,
respectively
A \( .337 .5 m \) and \( 25 s \)
B. \( 225.5 m \) and \( 10 s \)
c. \( 112.5 m \) and \( 22.5 s \)
D. \( 11.2 .5 m \) and \( 15 s \)


In convection, the molecules:
A. can move from one place to another place by them self
B. can not move from one place to another place from them self
c. both a and b
D. none of the above


For which of the following orbital wave function does not change its sign at any distance from the nucleus?
A. 3d
B. 2p
\( c \cdot 2 s \)
\( D \cdot 1 \) s


Solve with due regard to significant figures: \( \frac{5.42 \times 0.6753}{0.085} \)


The relationship between the potential difference and the current in a
conductor is stated in the form of a law.
(i) Name the law.
(ii) What does the slope of V-l graph for a conductor represent?
(iiii) Name the material used for making the connecting wire.


The distance between the points
\( (0,0),\left(x_{1}, y_{1}\right) \) is
units
A \( \cdot \sqrt{x_{1}^{2}+y_{1}^{2}} \)
в. \( \sqrt{x_{1}+y_{1}} \)
\( \mathbf{c} \cdot \sqrt{x_{1}^{2}+y_{1}} \)
\( \mathbf{D} \cdot \sqrt{x_{1}+y_{1}^{2}} \)


Distinguish between chemical and physical adsorption.


Which of the following pair is an odd pair?
A. Chitin - Carbohydrates
B. Pectin - Protein
c. steroid - Lipid
D. wax - Lipid


When a compact disc is illuminated by small source of white light, coloured bands are observed. This is due to
A. dispersion
B. diffraction
c. interference
D. reflection


\( \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{Y} \)
\( Y \) is used to remove grease stains from
woollen clothes. Identify \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
А. \( X=H C l, Y=N a O H \)
B. \( X=N H_{4} O H, Y=N H_{3} \)
c. \( X=N H_{3}, Y=N H_{4} O H \)
D. None of these


An aqueous solution of aniline of concentration \( 0.24 M \) is prepared. What
concentration of sodium hydroxide is needed in this solution so that
anilinium ion concentration remains at
\( 1 \times 10^{-8} M ? \)
\( \left(\boldsymbol{K}_{\boldsymbol{a}} \text { for } \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}}^{+}=\boldsymbol{2} . \boldsymbol{4} \times \boldsymbol{1} \boldsymbol{0}^{-\boldsymbol{5}} \boldsymbol{M}\right) \)


Covert \( \frac{2}{3}, \frac{5}{7} \) pair of fraction into like fractions?


If \( a \neq 6, b, c \) satisfy \( \left|\begin{array}{ccc}a & 2 b & 2 c \\ 3 & b & c \\ 4 & a & b\end{array}\right|=0 \)
then \( a b c= \)
\( \mathbf{A} \cdot a+b+c \)
B.
\( c \cdot b^{3} \)
\( \mathbf{D} \cdot a b+b-c \)


A charge \( +q \) is fixed at each of the
points \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{5} \boldsymbol{x}_{0}, \dots \) upto
\( \infty \) on \( \mathrm{X} \) -axis and charge -q is fixed on
each of the points \( \boldsymbol{x}=\mathbf{2} \boldsymbol{x}_{0}, \boldsymbol{x}= \)
\( \mathbf{4} \boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{6} \boldsymbol{x}_{0}, \ldots \boldsymbol{u} \boldsymbol{p} \boldsymbol{a} \)
positive constant. Take the potential at a point due to a charge \( Q \) at a distance \( r \) from it to be \( \frac{Q}{4 \pi \epsilon_{0} r} . \) Then the potentia at the origin due to above system of
charges will be :
A . zero
в. \( \frac{q}{8 \pi \epsilon_{0} x_{0} \log _{e} 2} \)
c. inifinty
D. \( \frac{q \log _{e} 2}{4 \pi \epsilon_{6} x_{0}} \)


Read the following two statements below carefully and state, with reasons,
if it is true or false.
(a) The Young's modulus of rubber is
greater than that of steel.
(b) The stretching of a coil is
determined by its shear modulus.


Which of the following statements is
NOT TRUE in respect of hydrophilic sols?
A. They are quite stable and are not easily coagulated
B. There is considerable interaction between dispersed phase and dispersion medium (water)
C. The sol particles are hydrated
D. They are very sensitive to coagulation by a small concentration of electrolytes


State whether the following statements
are true or false.
The equation \( x^{2}+y^{2}+2 x-10 y+ \)
\( \mathbf{3 0}=\mathbf{0} \) represents the equation of a
circle.
A . True
B. False


An \( L-C-R \) series circuit with \( L= \)
\( \mathbf{0 . 1 2 0 H}, \boldsymbol{R}=\mathbf{2 4 0 \Omega}, \) and \( \boldsymbol{C}=\mathbf{7 . 3 0 \mu} \boldsymbol{F} \)
carries an rms current of \( 0.450 A \) with a
frequency of \( 400 H z . \) What is the impedance of the circuit?


At times ligaments and tendons are overstretched or torn. The phenomenon is
A. Sprain
B. Dislocation
c. Fracture
D. Tension


The value of \( \int_{0}^{2 \pi}|\cos x-\sin x| d x \) is
equal to
A \( \cdot 2 \sqrt{2} \)
B. 2
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)


The mode of the following data is 50 Calculate the value of \( X \)
Marks \( \quad \begin{array}{ccc}50- & 60- & 70- \\ 60 & 70 & 80\end{array} \)
Students 1 2
A . 3
в. 2.8
\( c .5 \)
D.


The stored waste product in plants can be in the form of
A . Latex
B. Resins
c. Gums
D. All of the above


Transpiration cohesion tension theory
operates in
A. Active absorption
B. Passive absorption
c. Active and passive absorption
D. None of the above


The value of \( \int_{0}^{\frac{\pi}{2}} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x \)
is
\( A \cdot 2 \)
B. \( \frac{3}{4} \)
\( c \cdot 0 \)
D. -2


Evaluate \( \boldsymbol{S}=\mathbf{1}+\frac{\mathbf{4}}{\mathbf{5}}+\frac{\mathbf{7}}{\mathbf{5}^{2}}+\frac{\mathbf{1 0}}{\mathbf{5}^{3}}+\dots \dots \)
to infinite terms. Find \( 16 S \)


Srivani walks \( 12 m \) due East and turns
left and walks another 5 m, how far is
she from the place she started?


Which acid can combine with its own
salt?
A. \( H I \)
в. \( H B r \)
c. \( H C l \)
D. \( H F \)


Briefly explain how transpiration helps in upward conduction of water in plants?
\( (a) \)
\( (b) \)


Which of the following is a property of
lactic acid?
lactic acid
A. It decolourises aqueous bromine rapidly
B. It is insoluble in water.
c. It reduces Fehling's reagent.
D. Two molecules react with each other in the presence of a strong acid


Find frequency. \( \left(\operatorname{in} s^{-1}\right) \)
A . 31.85
B. 32
c. 32.58
D. 35.025


The number of chambers in the heart of
fish are
A. one
B. Two
c. Three
D. Four


The magnetic field at the center of the
circular loop as shown in figure, when a
single wire is bent to form a circular
loop and also extends to form straight sections, is :
\( ^{\text {A }} \cdot \frac{\mu_{0} I}{2 R} \odot \)
\( ^{\text {В }} \cdot \frac{\mu_{0} I}{2 R}\left(1+\frac{1}{\pi \sqrt{2}}\right) \odot \)
c. \( \frac{\mu_{0} I}{2 R}\left(1-\frac{1}{\pi \sqrt{2}}\right) \otimes \)
\( \stackrel{\mathrm{D}}{\frac{\mu_{0}}{R}}\left(1-\frac{1}{\pi \sqrt{2}}\right) \otimes \)


Take the potential of the point \( B \) in the
figure, to be zero.
(a) Find the potentials
at the points \( \mathrm{C} \) and \( \mathrm{D} \). (b) If a capacitor is
connected between \( \mathrm{C} \) and \( \mathrm{D} \), What charge
will appear on the capacitor?


Which of the following compounds will have the highest melting point?
A. Chlorobenzene
B. o-Dichlorobenzene
c. m-Dichlorobenzene
D. p-Dichlorobenzene


The capacitance of a capacitor whose reactance is \( 2.00 \Omega \) at \( 50.0 H z \) is \( \frac{x}{10} m F \) Find \( \boldsymbol{x} \)


Majority of lichens are made of


Number of points having distance \( \sqrt{\mathbf{5}} \)
from the straight line \( x-2 y+1=0 \)
and a distance \( \sqrt{13} \) from the line \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}-\mathbf{1}=\mathbf{0}, \) is /are?
A . 1
B . 2
\( c \cdot 4 \)
D. 5


For the reaction, \( \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \)
\( O_{3}(g) ; \Delta H^{o}=-107.2 k J . \) Hence, the
average bond energy in \( \boldsymbol{O}_{3} \) is:
(Assume \( \boldsymbol{O}=\boldsymbol{O} \) bond energy
\( \left.498.8 k J m o l^{-1}\right) \)
A \( \cdot 606.0 k J \) mol\( ^{-1} \)
B. \( 107.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. \( 391.6 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 303.0 kJ mol-1


Describe haplodiploid sex determination system in honey bees.


The figure below compares a part of our eye with a part of a photographic
camera.
(a) Name the corresponding parts of the eye and the camera shown here that are
comparable in function.
(b) Explain the mode of working and the functions of the parts of the eye mentioned above


Differentiate with respect to \( x \) :
\( (\log \sin x)^{2} \)


If cohesion-tension transpiration pul theory is correct, a break in water column should
A. Increase water content of leaves
B. Increase rate of photosynthesis
c. cause wilting of leaves
D. Have no effect at all


When UV light hits oxygen gas
A. it breaks it down to two oxygen atoms
B. it breaks it down to one oxygen atom
c. it breaks it down to three oxygen atoms
D. none of these


A series LCR circuit containing a resistance of \( 120 \Omega \) has angular frequency \( 4 \times 10^{5} \) rad \( / \mathrm{s} \). At resonance
the voltages across resistance and inductance are \( 60 \mathrm{V} \) and \( 40 \mathrm{V} \)
respectively. The angular frequency at which the current in the circuit lags the voltage by \( \frac{\pi}{4} \) is:
A \( \cdot 2 \times 10^{5} r a d / s \)
B . \( 6 \times 10^{5} \mathrm{rad} / \mathrm{s} \)
c. \( 8 \times 10^{5} r a d / s \)
D. \( 10 \times 10^{5} \mathrm{rad} / \mathrm{s} \)


Mass equivalent to the energy \( 931 \mathrm{MeV} \) is:
\( \mathbf{A} \cdot 6.02 \times 10^{-27} k g \)
В. \( 1.662 \times 10^{-27} k g \)
c. \( 16.66 \times 10^{-27} k g \)
D. \( 16.02 \times 10^{-27} \mathrm{kg} \)


Mark the correct statements about the
friction between two bodies.
This question has multiple correct options
A. Static friction is always greater than the kinetic friction.
B. Coefficient of static friction is always greater than the coefficient of kinetic friction.
C. limiting friction is always greater than the kinetic friction.
D. limiting friction is never less than static friction.


The ratio of the acceleration for a solid
sphere (mass ' \( \left.m^{\prime} \text { and radius }^{\prime} R^{\prime}\right) \)
rolling down an incline of angle ' \( \boldsymbol{\theta} \)
without slipping and slipping down the incline without rolling is.
A . 5: 7
B. 2: 3
\( c \cdot 2: 5 \)
D. 7: 5


Extrusion of second polar body from egg nucleus occurs
A. After entry of sperm but before fertilization
B. After fertilization
c. Before entry of sperm into ovum
D. simultaneously with first cleavage


If \( f(x)= \)
\( \left|\begin{array}{ccc}\cos ^{2} x & \cos x \cdot \sin x & -\sin x \\ \cos x \cdot \sin x & \sin ^{2} x & \cos x \\ \sin x & -\cos x & 0\end{array}\right|, \) then
for all \( x \epsilon R, \) the value of \( f(x)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \)
D. None of the above


Calculate normality and molarity of \( 25 \% \)
\( (\mathrm{w} / \mathrm{v}) N H_{3} \) solution:


Sound travels at the fastest speed in
A. steel
B. water
\( c . \) air
D. vacuum


Physical independence of force is a
consequence of
A. Newton's third law of motion
B. Newton's second law of motion
c. Newton's first law of motion
D. All of these


In elementary reaction steps, which of the following is most likely to have the
highest rate?
A. A reaction where three reactants combine
B. A reaction with only one reactant
C. A reaction where two reactants combine
D. A reaction where two reactants undergo double displacement.


A hydrocarbon has \( 3 g \) carbon per gram of hydrogen, hence the simplest formula is :
A \( \cdot C H_{4} \)
в. \( C_{6} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C H_{2} \)


The speed of an object of mass \( 2 k g \) increases from \( 2 m / s \) to \( 4 m / s \) in \( 3 s \)
Find out the total work done on the
object during this time interval?
A . \( 4 J \)
B. 6.5
c. \( 12 J \)
D. 24J
ह. \( 36 J \)


In a horizontal pipe line of uniform cross-section,pressure falls by 5 Pa between two points separated by \( 1 k m \) The change in the kinetic energy per kg of the oil flowing at these points is :
(Density of oil \( =\mathbf{8 0 0} \) kgm \( ^{-3} \) )
A . \( 6.25 x 10^{-3} \mathrm{Jkg}^{-1} \)
B. \( 5.25 x 10^{-4} \mathrm{Jkg}^{-1} \)
c. \( 3.25 x 10^{-5} \mathrm{Jkg}^{-1} \)
D. \( 4.25 x 10^{-2} \mathrm{Jkg}^{-1} \)


Are the following pairs of statements negations of each other?
(i) The number \( x \) is not a rational
number

The number \( x \) is not an irrational
number
(ii) The number \( x \) is a rational number
The number \( x \) is an irrational number


Equal volumes of M/20 urea solution
and M/20 glucose solution are mixed. The mixture will have osmotic pressure:
A. equal to either of the solution
B. less than either of the solution
c. higher than either of the solution
D. zero


Which of the following is aromatic in
nature?
\( A \)
B.
\( c \)
D.
E. None of these


The synthesis of alkyl fluorides is best accomplish by ?
A. free radical fluorination
B. sandmeyer"s reaction
c. Finkelstein reaction
D. swarts reaction


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


A car moves on a circular road
describing equal angles about the centre in equal intervals of time. Which of following statements about the velocity of car are not true? This question has multiple correct options
A. Velocity is constant
B. Magnitude of velocity is constant but the direction changes
c. Both magnitude and direction of velocity change
D. Velocity is directed towards the center of circle


The denominator of fraction is 6 more
than its numerator. If 2 is added to both
the numerator and denominator, the
fraction becomes \( 1 / 2 . \) Find the fraction.
A . \( 2 / 5 \)
в. \( 4 / 6 \)
c. \( 6 / 10 \)
D. \( 1 / 5 \)


In fishes, the exoskeleton is made of
A. Cartilage
B. Bones
c. Hairs
D. Scales


Find the area of a rhombus whose side
is \( 5 \mathrm{cm} \) and whose altitude is \( 4.8 \mathrm{cm} \)


All the elements tend to attain eight electrons in their outermost shell either
by sharing or by transfer of electron. The electronic distribution of \( X=2,7 \) and \( Y= \)
2, 8, 1. What type of bond is formed between \( X \) and \( Y ? \) How is it formed?


Figure shows three resistor configurations \( R 1, R 2 \) and \( R 3 \)
connected to \( 3 V \) battery. If the power
dissipated by the configuration \( \boldsymbol{R} \mathbf{1}, \boldsymbol{R} \mathbf{2} \) and \( R 3 \) is \( P 1, P 2 \) and \( P 3, \) respectively
then
A. \( P 1>P 2>P 3 \)
в. \( P 1>P 3>P 2 \)
c. \( P 2>P 1>P 3 \)
D. \( P 3>P 2>P 1 \)


Identify the term/substance in each of
the following:
(i) The tendency of an atom to attract
electrons to itself when combined in a
compound.
(ii) The method used to separate ore
from gangue by preferential wetting.
(iii) The catalyst used in the conversion of ethyne to ethane
(iv) The type of reactions alkenes
undergo.
(v) The electrons present in the
outermost shell of an atom.


The lowering of activation energy by
catalyst is due to
A. formation of adsorbed activated complex and to provide new pathway to reaction
B. adsorption is always exothermic
C. the adsorbed activated complex possesses lower energy level than simple activated complex
D. all the above


toppr
Q Type your question
time period is proportional to \( \sqrt{\frac{\boldsymbol{m}}{\boldsymbol{k}}}, \) as can be seen easily using dimensional
analysis. However, the motion of a
particle can be periodic even when its
potential energy increases on both
sides of \( x=0 \) in a way different from
\( k x^{2} \) and its total energy is such that the
particle does not escape to infinitely.
Consider a particle of mass m moving
on the x-axis. Its potential energy is
\( \boldsymbol{V}(\boldsymbol{x})=\boldsymbol{\alpha} \boldsymbol{x}^{4}(\boldsymbol{\alpha}>\boldsymbol{0}) \) for \( |\boldsymbol{x}| \) near the
origin and becomes a constant equal to
\( \boldsymbol{V}_{0} \) for \( |\boldsymbol{x}| \geq \boldsymbol{X}_{0}(\text { see figure }) \)
If the total energy of the particle is \( \mathrm{E} \), it
will perform periodic motion only if.
A \( . E<0 \)
в. \( E>0 \)
c. \( V_{0}>E>0 \)
D. \( E>V_{0} \)


Reduce the equation \( x+y-1=0 \) to
slope-intercept form and find its slope
and \( \boldsymbol{y}- \) intercept.


Suggest four measures for control of
human population.


A bag of wheat weighs 100 kg. To what height should it be raised, so that its potential energy may be \( 9800 \mathrm{J}(\mathrm{g}=9.8 \)
\( \left.m s^{-2}\right\rangle \)
A .2
B. 100
\( c .50 \)
\( D \cdot 0 \)


(unisexual, fertilisation, fruit, stamen,
anther, bisexual, pollination, seed,
ovary The ovary of the flower develops into
\( \mathbf{a} \)


Wheel reduce friction due to.
A. more area of contact
B. less area of contact
\( c \cdot \operatorname{size} \)
D. all of the above


The white precipitate (P) is:
\( \mathbf{A} \cdot C u_{2} I_{2} \)
в. \( C u I_{2} \)
\( \mathbf{c} \cdot K_{2}\left[C u I_{4}\right] \)
D. None of the above


Draw an angle of measure \( 45^{\circ} \) and
bisect it.


Assertion
UV radiation cause photo dissociation
of ozone into \( O_{2} \) and 0 thus causing
damage to stratospheric ozone layer.
Reason
Ozone hole is resulting in global warming and climatic change.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following event takes place during diplotene stage of prophase I of meiosis?
A. compaction of chromosomes
B. Formation of synaptonemal complexes
c. Formation of recombinational nodules
D. Dissolution of synaptonemal complex


For an ideal transformer:
A. Output power = Input power
B. Efficiency is \( 100 \% \)
C \( \cdot \frac{V_{s}}{V_{p}}=\frac{I_{p}}{I_{s}} \)
D. All of these


The greatest index of a variable in the
polynomial \( 5 x^{2}+3 x+1 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


van't Hoff equation is
This question has multiple correct options
\( \mathbf{A} \cdot(d / d T) \ln K=-\Delta H / R T^{2} \)
B \( \cdot(d / d T) \ln K=+\Delta H / R T^{2} \)
\( \mathbf{c} \cdot(d / d T) \ln K=-\Delta H / R T \)
D \( \cdot K=A e^{\Delta H / R T} \)


In which of the following reactions, the oxidation state of non-metal increases
by maximum number of units when
they react-with hot conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) ?
A. Carbon
B. Phosphorus
c. sulphur
D. lodine


STATEMENT-1: PMMA (Polymethyl methacrylate) is used for making lenses and light covers. STATEMENT-2:It has excellent light transmission properties.
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Two zinc rods are placed in contact with
dil. \( H N O_{3} \) and conc. \( H N O_{3} \) in two
separate containers A and B. The characteristics of gases evolved in the containers are respectively:
A. The gas in container A turns \( K_{2} C r_{2} O_{7} \) green and the gas in container B turns lead acetate black.
B. A \( \rightarrow \) Pungent smelling gas, B \( \rightarrow \) colourless, odourless gass
\( \mathrm{c} \cdot \mathrm{A} \rightarrow \operatorname{Inflammable} \operatorname{gas}, \mathrm{B} \rightarrow \operatorname{Turns} K_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) green
D. \( A \rightarrow \) Can react with \( O_{2} \) explosively, \( B \rightarrow \) No reaction with \( O_{2} \) at all.


f \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) then
\( \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos \boldsymbol{C} \\ -\sin \boldsymbol{B} & \boldsymbol{0} & \tan \boldsymbol{A} \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\tan \boldsymbol{A} & 0\end{array}\right| \)
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 \sin B \tan A \cos C \)
\( c .1 \)
D. None of these


if \( x_{1}, x_{2}, x_{3} \dots x_{n} \) denote the values of \( x \)
where \( f(x) \) vanishes such that \( x_{1}> \)
\( x_{2}>x_{3} \ldots x_{n}, \) then \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} \frac{r}{x_{r}} \) is equal to
A . -8
B. -4
\( c .-2 \)
D. -


If \( \operatorname{in} \) a \( \Delta A B C ; \frac{\cos A}{7}=\frac{\cos B}{19}= \)
\( \frac{\cos C}{25}=k, \) then
\( \left|\begin{array}{ccc}-1 / k & 25 & 19 \\ 25 & -1 / k & 7 \\ 19 & 7 & -1 / k\end{array}\right|= \)
\( A \)
B.
\( c \cdot 2 \)
\( D \)


A faulty thermometer has \( 90.5^{\circ} \mathrm{C} \) and
\( 0.5^{\circ} \mathrm{C} \) as upper and lower fixed points
respectively. What is the correct temperature if this faulty
thermometer reads \( 15.5^{\circ} \mathrm{C} \)
A \( \cdot 16.67^{\circ} \mathrm{C} \)
B . \( 16^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 15.5^{\circ} \mathrm{C} \)


Oxygen is transported through blood mainly by
A. Leucocytes.
B. Erythrocytes.
c. Thromobocytes.
D. Blood plasma.


How is the volume of water affected
when it boils at \( 100^{\circ} \mathrm{C} ? \)


In the given figure, ABCD is a
parallelogram in which \( \angle B D C=45^{\circ} \)
and \( \angle B A D=75^{\circ} . \) Then, \( \angle C B D=? \)
\( A \cdot 150 \)
3. 105
\( c \cdot 60^{\circ} \)
\( D .75 \)


Distinguish between Inertia of motion and inertia of direction


Consider p-aminophenol
Which positions are activated for electrophilic aromatic substitution
reaction in acidic and basic media
respectively?
A. \( \alpha^{\prime} \) in A and \( \beta \) in B
B. \( \alpha^{\prime} \) in \( A \) and \( \alpha \) in \( B \)
c. \( \beta^{\prime} \) in \( A \) and \( \alpha \) in \( B \)
\( D \cdot \beta^{\prime} \) in \( A \) and \( \beta \) in \( B \)


Give names of two plants which have
tap root.


The latus rectum of a parabola whose focal chord is \( P S Q \) such that \( S P=3 \)
and \( S Q=2, \) is given by
A \( \cdot \frac{24}{5} \)
в. \( \frac{12}{5} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{48}{5} \)


The man-made element which was
made in the nuclear reactor is
A. polonium
B. plutonium
c. thorium
D. uranium


Two projectiles \( A \) and \( B \) thrown with
same speed but angles are \( 40^{\circ} \) and \( 50^{\circ} \) with the horizontal.Then
A . A will fall earlier
B. B will fall earlier
c. both will fall at the same time
D. None of these


The complete solution set of \( |2 x-3|+ \)
\( |\boldsymbol{x}+\mathbf{5}| \leq|\boldsymbol{x}-\mathbf{8}| \) is
\( A \cdot\left[-5, \frac{3}{2}\right] \)
B \( \cdot(-\infty,-5] \)
\( \mathbf{c} \cdot\left[\frac{3}{2}, \infty\right] \)
\( \mathbf{D} \cdot(-\infty,-5] \cup\left[\frac{3}{2}, \infty\right] \)


The resistance of a conductivity cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) is \( 1500 \Omega . \) What is the cell
constant (in \( \mathrm{mm}^{-1} \) ) if the conductivity
of \( 0.001 M K C l \) solution is \( 2 \times 10^{-3} \mathrm{s} \)
\( \mathrm{mm}^{-1} ? \)


Which of the following solutions shows negative deviations from Raoult's law?
A. Ethanol-acetone
B. carbon disulphide-acetone
c. Phenol-aniline
D. n-Hexane-n-Heptane


Who proposed atom as an indestructible entity?
A. Rotherford
B. Dalton
c. Thomson
D. Pauli


Assertion
The voltage of mercury cell remains constant for long period of time.
Reason
It is because net cell reaction does not
involve active species.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following reaction is correct for gaseous and reversible
reaction?
A \( \cdot \frac{K_{p}}{K_{c}}=(R T)^{\Delta n_{g}} \)
в. \( \frac{K_{p}}{K_{x}}=(p)^{\Delta n_{9}} \)
c. \( \frac{K_{C}}{K_{x}}=(p)^{-\Delta n_{g}} \)
D. None of the above


Why is land breeze experienced at night?


If \( \int f(x) d x=f(x), \) then \( \int[j(x)]^{2} d x \) is
A \( \cdot \frac{1}{2}[f(x)]^{2} \)
B . \( [f(x)]^{3} \)
c. \( \frac{[f(x)]^{3}}{3} \)
D \cdot \( [f(x)]^{2} \)


Which of the following species is desirable substance in extraction of
copper but not in extraction of iron?
A \( \cdot \) Casio
в. Fesi Оз\( _{3} \)
\( \mathrm{c} \cdot \operatorname{sio}_{2} \)
D. coke


The adjacent sides of a parallelogram are \( 10 m \) and \( 8 m . \) If the distance
between the longer sides is \( 4 m \), find
the distance between the shorter sides.


How will the reading in the ammeter \( \mathbf{A} \)
of figure be affected if another identical
bulb \( Q \) is connected in parallel to \( P \) as
shown. The voltage in the mains is
maintained at a constant value
A. the reading will be reduced to one-half.
B. the reading will not be affected.
C. the reading will be double of the previous one
D. the reading will be increased fourfold.


Electrons lost by PS II are regained from
\( A \cdot O_{2} \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. None of the above


In the game of cricket, the stumps falls when the ball strikes them. This is an
example of
A. contact force
B. Non contact force
c. Displacement force
D. None


Select the correct sequence of
succession in a pond
A. Submerged plants \( \rightarrow \) Floating plants \( \rightarrow \) Reed swamp stage \( \rightarrow \) Sedges
B. Floating plants \( \rightarrow \) Submerged plants \( \rightarrow \) Reed swamp stage \( \rightarrow \) Sedges
C. Reed swamp stage \( \rightarrow \) Sedges \( \rightarrow \) Floating plants \( \rightarrow \) Submerged plants
D. Sedges \( \rightarrow \) Reed swamp stage \( \rightarrow \) Floating plants \( \rightarrow \) Submerged plants


The peptide linkage formed between
glycine \( \left(N H_{2} C H_{2} C O O H\right) \) and
alanine \( \left(N H_{2}\right)\left(C H_{3}\right) C H C O O H \) to
give glycylalanine can be shown as:
A. \( N H_{2}-C H_{2}-N H-C_{1} H-C O O H \)
\[
C H_{3}
\]
в. \( N H_{2}-C H_{2}-C O N H-_{\left\{_{H_{3}}\right.}^{C} H- \) СООН
c. \( H_{2} N C O C H_{2}-C_{C H_{3}} H-C O N H_{2} \)
D. \( H O O C-C H_{2}-N H-N H-C_{I}^{C} H-C O O H \)


The time period of a particle executing SHM is 2 s. After what time interval from \( t=0, \) will its displacement be half the amplitude:
\( A \cdot(1 / 4) \sec s \)
B. (1/3) secs
c. (1/2) secs
D. 1 sec


The value of charge on th oil droplets experimentally observed were \( -1.6 \times 10^{-19} \) and \( -4 \times 10^{-19} \) coulomb.
the value of the electron charge, indicates by these result is:
A. \( 1.6 \times 10^{-19} \)
В. \( -2.4 \times 10^{-19} \)
c. \( -4 \times 10^{-19} \)
D. \( -0.8 \times 10^{-19} \)


A spring of spring constant \( 5 \times 10^{3} \mathrm{Nm}^{-1} \)
is stretched initially by \( 5 c m \) from the unstretched position. Then the work required to stretch it further by another
\( 5 c m \) is
A. \( 6.25 N m \)
B . \( 12.50 \mathrm{Nm} \)
c. \( 18.75 N m \)
D. \( 25.00 N m \)


State one method by which carbon dioxide is removed from the air?
A. Absorption method
B. Distillation method
c. Adsorption method
D. None of these


Which of the following is true
statement?
A. The boiling point of aldehydes and ketones is higher than less polar ethers and non polar hydrocarbons of comparable molecular masses.
B. The boiling point of aldehydes and ketones is higher than less polar ethers but lower boiling points than non polar hydrocarbons of comparable molecular masses.
C. The boiling point of aldehydes and ketones is lower than less polar ethers but higher boiling points than non polar hydrocarbons of comparable molecular
masses.
D. The boiling point of aldehydes and ketones is lower than less polar ethers and non polar hydrocarbons of comparable molecular masses.


The work function of a certain metal is
\( 3.31 \times 10^{-19} J . \) Then, the maximum
kinetic energy of photoelectrons emitted by incident radiation of wavelength 5000 A is \( \left(G i v e n h=6.62 \times 10^{-34} J-s, c=\right. \)
\( \left.\mathbf{3} \times \mathbf{1 0}^{-\mathbf{8}} \mathbf{m} s^{-1}, \boldsymbol{e}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) \)
A \( .248 e V \)
B. \( 0.41 e V \)
c. \( 2.07 e V \)
D. \( 0.82 e V \)


0.8 can be represented as
\( A \cdot \frac{8}{10} \)
в. \( \frac{8}{100} \)
c. \( \frac{8}{1000} \)
D. None of the above


Gold leaf electroscope is used:
A. to measure the electric charge
B. to detect and test small electric charges
C . to produce electric current
D. to produce electric charges


Convert 4 radians into degree measure
and also convert \( -47^{\circ} 30^{\prime} \) into radian
measure.


Evaluate:
\( \int \frac{1}{a^{x} b^{x}} d x \)


Some drugs do not bind the enzyme's active site, instead, bind to a different site of an enzyme. This site is called:
A. allosteric site
B. substrate site
c. ionic site
D. competitive site


An electric dipole is placed making at an angle 60 deg with an electric field of
strength \( 1 \times 10^{5} N / C . \) It experiences a torque equal to \( 8 \sqrt{3} N-m . \) Calculate
the charge on the dipole, if it is of length
\( 2 \mathrm{cm} \)


Differentiate the following w.r.t. \( x \) \( \cos ^{-1}\left(\frac{3 \cos x-4 \sin x}{5}\right) \)


Assertion
Air is a bad conductor of heat.
Reason
It's molecules are in Brownian motion.
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
pH of a neutral solution is always 7
Reason
pH of a solution does not depend upon
temperature
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


Alkynes show geometrical isomerism.
A. True
B. False


When ethanol mixes in cyclohexane, the intermolecular forces
reduces between ethanol molecule. In
this, liquid pair shows:
A. positive deviation from Raoult's law
B. negative deviation from Raoult's law
c. no deviation from Raoult's law
D. decrease in volume


What is the percentage change in the
overall sales turnover of the five
companies together between 2001
2002 and 2002 - 2003?
A . 17.21\%
B. 14.68\%
c. 12.67\%
D. 21.24\%


The yellow colour of \( H N O_{3} \) is due to the
dissolution of nitrogen dioxide \( \left(N O_{2}\right) \)
A. True
B. False


Which of the following fibres is made of polyamides?
A. Dacron
B. Orion
c. Nylon
D. Rayon


The mean and variance of 7 observation
are 8,16 respectively. If 5 of the
observation are \( 2,4,10,12,14, \) then the \( L C M \) of remaining two observation is
\( \mathbf{A} \cdot 16 \)
B . 24
c. 20
D. 14


What is the characteristic of
metanephric kidney?
A. Hypotonic urine production
B. Excess secretion of uric acid
c. Loop of Henle
D. Hormone production


Solve the following puzzles using the
equations:

The present age of Beena is 2 years
more than Reeta.The present age of Teena is 3 years more than Beena.If the
sum of the ages of Reeta, Beena, and Teena is 79 years, find the present age of all the three of them.
A. Reeta 24 years, Beena 26 years, Teena 29 years
B. Reeta 24 years, Beena 21 years, Teena 29 years
c. Reeta 24 years, Beena 29 years, Teena 29 years.
D. Reeta 24 years, Beena 26 years, Teena 30 years


Find the following limit:
\( \lim _{x \rightarrow 9}\left(\frac{3-\sqrt{x}}{9-x}+\frac{1}{3-\sqrt{x}}-6 \cdot \frac{x^{2}+}{729}\right. \)


A stone dropped into a pond of still water sends out concentric circular
waves from the point of disturbance of water at the rate of \( 4 \mathrm{cm} / \) sec. Find the rate of change of disturbed area at the instant when the radius of wave ring is
\( \mathbf{1 5} c m \)


Best aquarium is located at
A. Madras
B. Trivandrum
C. Calcutta
D. Mumbai


Which of the following is used to
prepare \( C l_{2} \) gas at room temperature
from concentrated \( \boldsymbol{H} \boldsymbol{C l} \) ?
This question has multiple correct options
A. \( M n O_{2} \)
в. \( H_{2} \).
c. \( K M n O_{4} \)
\( \mathrm{D} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)


(a) Name any two phenomena of light which cause the formation of a rainbow.
(b) A particular colour in the rainbow
makes an angle of \( 42.7^{\circ} \) with the line of
vision. What is the colour?
(c) What will be the shape of a rainbow
when viewed from:
¡. Terrace of a house?
ii. Aircraft flying very high.


A man who is standing at a point \( x \) between two parallel walls as shown in the diagram, fires a starting pistol. He hears the first echo after 0.6 s and
another one after \( 0 . \) s.

How long after firing the pistol will he hear the next echo?
A \( .1 .2 \mathrm{s} \)
B . 1.4
\( c \cdot 1.6 s \)
D. 2.4 s


The energy released in the core the sun
is governed by:
A. gamma decay
B. nuclear fusion
c. alpha decay
D. positron emission
E. nuclear fission


Let us suppose that you have discovered a new element of the atomic
number \( 162, \) which you choose to name
khalidium (Kh). Assume that the
normal order of filling of orbitals still prevails in the eighth period.

The new type of orbital used in Kh that
is not used in any known atom is:
\( A \cdot h \)
B.
\( c \cdot f \)
D.


Heavy hydrogen has
neutron and proton in the nucleus.


lonic compounds are soluble in polar solvents.
A. True
B. False


\( \int_{0}^{\infty} \frac{d x}{[x+\sqrt{x^{2}+1}]^{3}} \) is equal to
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{8} \)
\( c \cdot-\frac{3}{8} \)
D. none of these


"No square of a real number is less than
zero" is equivalent to
A. for every real number a, \( a^{2} \) is non negative.
\( \mathbf{B} \cdot \forall a \in R, a^{2} \geq 0 \)
C . either (1) or (2).
D. None of these


In meiosis, synapsis occurs during
A. S-phase
B. Interphase
c. Metaphase
D. Prophase 1


The diagram below shows four orange
spheres moving in circular paths at
constant speeds. The speeds are indicated by the red arrows.
The radius of the circular path for each
indicated by the green arrows. The mass of each sphere is labeled inside the
boundary of the sphere

How do the sphere rank, according to the magnitudes of their accelerations,
greatest first?
A \( \cdot 4,3,1 \) and 2 tie
B. 3,1 and 4 tie, 2
\( c .3,2 \) and 4 tie,
D. 1,2 and 3 tie,
E. 1,3,2,4


According to given figure which of the
following options can be true?
\( \mathbf{A} \cdot Q_{1}>Q_{2}>W \)
B. In real aspects \( Q_{2}=0 \) always
C efficiency of engine is \( =\frac{W}{Q_{1}} \)
D efficiency of engine is \( =1-\frac{Q_{1}}{Q_{2}} \)


An old man while dialing a 7 digit telephone number remembers that the
first four digits consists of one \( 1^{\prime} s, \) one
\( 2^{\prime} s \) and two \( 3^{\prime} s . \) He also remembers that
the fifth digit is either a 4 or 5 while has no memorizing of the sixth digit, he remembers that the seventh digit is 9
minus the sixth digit. Maximum
number if distinct trails he has to try
make sure that he dials the correct
telephone number, is
A . 360
B . 240
c. 216
D. none


The density of water is equal to:
A \( \cdot 10^{-3} \operatorname{kg} m^{-3} \)
B . \( 10^{-2} \mathrm{kgm}^{-3} \)
c. \( 10^{2} \mathrm{kgm}^{-3} \)
D. \( 10^{3} k g m^{-3} \)


If \( \boldsymbol{y}=\boldsymbol{a}+\frac{\boldsymbol{b}}{\boldsymbol{x}}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants and if \( \boldsymbol{y}=\mathbf{1} \) when \( \boldsymbol{x}=-\mathbf{1} \)
and \( y=5 \) when \( x=-5, \) what is the
value of \( a+b ? \)
A. -1
B. 0
\( c \cdot 1 \)
D. 11


Which of the following arrangements is correct on the basis of the increasing \( \mathrm{p} \) character of the hybrid orbitals of the central atoms in the following:
\( C l O_{2}^{-} \)
\( \boldsymbol{C S}_{2} \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{2} \)
A. \( I<I I I<I I \)
В. \( I I>I>I I I \)
c. \( I>I I>I I I \)
D. \( I I I>I>I I \)


The common chord of \( x^{2}+y^{2}-4 x- \)
\( 4 y=0 \) and \( x^{2}+y^{2}=16 \) subtends at
the origin an angle to
A. \( \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( \pi / 5 \)


A globe of steel has a mass of 12 g and a volume of \( 15.2 \mathrm{cm}^{3} \). Find its relative
density wrt water.
A . 0.25
в. 0.79
\( c \cdot 1.25 \)
D. 1.56


Catalytic dehydrogenation of a primary alcohol gives a:
A. secondary alcohol
B. aldehyde
c. ketone
D. ester


A certain volume of dry air at NTP is expanded reversibly to four times its volume
(a) isothermally (b) adiabatically. Calculate the final pressure and temperature in each case, assuming ideal behaviour. \( \left(\frac{C_{P}}{C_{V}} \text { for } a i r=1.4\right) \)


The uneven heating of land takes place
due to
A. Direction of sunlight
B. Direction of wind
c. Temperature of the earth
D. None of the above


When \( 1.88 g \) of \( \operatorname{AgBr}(s) \) is added to a
\( 10^{-3} M \) aqueous solution of \( K B r, \) the concentration of \( \mathrm{Ag} \) is \( 5 \times 10^{-10} \mathrm{M} \). If the
same amount of \( A g B r(s) \) is added to a
\( 10^{-2} \) M aqueous solution of \( A g N O_{F} \)
the concentration of \( B r^{-} \) is:
A . \( 9.4 \times 10^{-9} M \)
В. \( 5 \times 10^{-10} M \)
c. \( 1 \times 10^{-11} M \)
D. \( 5 \times 10^{-11} M \)


\( f(x)=\left|\begin{array}{ccc}x & \cos x & e^{x^{2}} \\ \sin x & x^{2} & \sec x \\ \tan x & 1 & 2\end{array}\right| . \) Find
\( \boldsymbol{f}(\mathbf{0}) ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
\( B \)
\( c .-r \)
D. \( 2 \pi \)


The correct order of decreasing \( \boldsymbol{X}- \) \( O-X \) bond angle is: \( (X=H, F \text { or } C l) \)
A. \( H_{2} O>C l_{2} O>F_{2} O \)
в. \( C l_{2} O>H_{2} O>F_{2} O \)
c. \( F_{2} O>C l_{2} O>H_{2} O \)
D. \( F_{2} O>H_{2} O>C l_{2} O \)


The periods of the periodic table are numbered according to ...................ofthe valence shell.
A. azimuthal quantum number
B. principal quantum number
C. magnetic quantum number
D. spin quantum number


Very short answer type.
How many types of muscles occur in the body of a vertebrate?


Given, \( \boldsymbol{A}=\{\text { Triangles }\}, \boldsymbol{B}=\{ \)
Isosceles triangles \( \} \) \( C=\{\text { Equilateral triangles }\} . \) State
whether the following statement are correct or incorrect. Give reasons.
\( \boldsymbol{C} \subset \boldsymbol{A} \)


The coefficient of range of the data set \{3,1,4,2,5,9,8\} can be represented as \( \frac{p}{q} \) where \( p \) and \( q \) are co-primes. Then the
value of \( (\boldsymbol{q}-\boldsymbol{p})^{2} \) is:


a product \( \boldsymbol{E} \). The product \( \boldsymbol{E} \) would be:
\( A \)
\( B \)
\( c \)
D. none of these


Eccentricity of a hyperbola is always less than 1.
A. True
B. False


Solve :
\( \frac{1+\cos x}{\sin x \cos x} \)


Which law is connected to the working of the Hydraulic brake?


Read the given statements and select
the correct option.

Statement 1: Rahul placed a coloured plastic bottle in front of the beam of a
torch light. Then he placed a transparent sheet of same size on the
other side of bottle. No shadow will form
on the screen.

Statement 2: Translucent objects allow
light to pass through them partially.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1 .
c. Statement 1 is true but statement 2 is false.
D. Statement 1 is false but statement 2 is true


Acceleration-time graph of a particle moving in a straight line is shown in Fig. \( 3.19 . \) Velocity of particle at time \( t=0 \) is \( 2 \mathrm{m} / \mathrm{s} \). Find velocity at the end of fourth second.


In a class of 50 students 35 opted for
Mathematics and 37 opted for Biology How may have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects)
A . 15
B. 17
c. 13
D. 19


A harmonic oscillator vibrates with
amplitude of \( 4 \mathrm{cm} \) and performs 150 oscillations in one minute. If the initial
phase is 450 and it starts moving away from the equation of motion is
A \( \cdot 0.04 \sin \left(5 \pi t+\frac{\pi}{4}\right) \)
B. \( 0.04 \sin \left(5 \pi t-\frac{\pi}{4}\right) \)
c. \( 0.04 \sin \left(4 \pi t+\frac{\pi}{4}\right) \)
D. \( 0.04 \sin \left(4 \pi t-\frac{\pi}{4}\right) \)


Jim has a triangular shelf system that
attaches to his showerhead. The total
height of the system is 18 inches, and
there are three parallel shelves
as shown above. What is the maximum
height, in inches, of a shampoo bottle
that can stand upright on the middle shelf?


The normal boiling point of a liquid is that temperature at which vapour pressure of the liquid is equal to:
A. zero
B. 380 mm of Hg
c. \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 100 \mathrm{mm} \) of \( \mathrm{Hg} \)


The coefficient of limiting friction between the surfaces of contact is the
ratio of the \( \ldots \). friction to the
normal reaction
A. Limting
B. sliding
c. rolling
D. any of these


Atoms present in a molecule of heavy
water are:
A. \( _{1} H^{1},_{8} O^{16} \)
B . \( _{1} H^{2},_{8} O^{18} \)
c. \( _{1} H^{2},_{8} O^{16} \)
D. \( _{1} H^{1},_{8} O^{18} \)


If \( A=\{0,1\} \) and \( B=\{1,2,3\}, \) show that \( \boldsymbol{A} \times \boldsymbol{B} \neq \boldsymbol{B} \times \boldsymbol{A} \)


The inductive reactance of a coil is
\( 2500 \Omega . \) On increasing it's selfinductance to three times, the new inductive reactance will be:
A. \( 7500 \Omega \)
B. 2500\Omega
c. \( 1225 \Omega \)
D. zero


When a sound wave of frequency \( 300 \mathrm{Hz} \) passes through medium, the maximum displacement of a particle of the
medium is \( 0.1 \mathrm{cm} . \) The maximum
velocity of the particle is equal to.
\( \mathbf{A} \cdot 60 \pi \mathrm{cm} / \mathrm{s} \)
B. \( 30 \pi \mathrm{cm} / \mathrm{s} \)
\( \mathrm{c} \cdot 60 \mathrm{cm} / \mathrm{s} \)
D. \( 30 \mathrm{cm} / \mathrm{s} \)


Write the formulae of
PyrosulphuricAcid:
в. \( H_{2} S O_{5} \)
c. \( H_{2} S_{2} O_{8} \)
D. None of these


If \( \sqrt[3]{\mathbf{7 2} \times \boldsymbol{A}}=\mathbf{1 2}, \) then find the value of
\( \boldsymbol{A} \)
A . 12
B . 24
\( c .36 \)
D. 6


Describe an experiment to demonstrate
that air exerts pressure.


In the circuit shown in the figure, the
A.C. source gives a voltage \( V=20 \cos \)
\( (2000 \mathrm{t}) \) volt. Neglecting source resistance, select correct alternative(s).
This question has multiple correct options
A. The reading of voltmeter is 0 V
B. The reading of voltmeter is 5.6
C. The reading of ammeter is 1.4 A
D. The reading of ammeter is 0.47 A


For the reaction
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \boldsymbol{\operatorname { S n }}(l) \)

Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \mathbf{9 0 0} \boldsymbol{K}, \) where the equilibrium steam - hydrogen mixture
was \( 45 \% H_{2} \) by volume.
A . 1.49
B. 1.22
c. 0.67
D. none of these


A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen \( 1 \mathrm{m} \) away. It is observed that the first minimum is at a distance of 2.5
\( \mathrm{mm} \) from the centre of the screen.
Calculate the width of the slit.


The first and the last terms of an A.P are
5 and 45 respectively. If the sum of all its terms is \( 400, \) find its common
difference.
A. \( _{d=\frac{5}{3}} \)
B. \( d=\frac{8}{5} \)
c. \( _{d=\frac{8}{3}} \)
D. None of these


If \( \boldsymbol{f}(\boldsymbol{\theta})=2\left(\sec ^{2} \boldsymbol{\theta}+\cos ^{2} \boldsymbol{\theta}\right), \) then its
value always
A \( \cdot 4>f(\theta)>2 \)
B \( \cdot f(\theta) \geq 4 \)
\( \mathbf{c} \cdot f(\theta)<2 \)
D. \( f(\theta)=2 \)


The first eukaryotic cells emerged during the
A. Palaeozoic
B. Cenozoic
c. Mesozoic
D. Proterozoic


A resistor connected to a battery is heated due to current through it. Which of the following quantity does not vary?
A . resistance
B. drift velocity
c. resistivity
D. number of free electrons


What is the area of the shaded
segment?
\( A \cdot 1 m^{2} \)
3. \( 2 m^{2} \)
\( c \cdot 3 m^{2} \)
D. \( 4 \mathrm{m}^{2} \)


Zone refining process is used for the:
A. Concentration of an ore
B. Reduction of a metal oxide
C. Purification of metal
D. Purification of an ore


The two of the lens above and below axis
is made up of two difference materials. A point object is placed on the principle
axis of the lens.
A . two
B. one
c. no image is formed
D. half


The shape of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{5}}^{-} \) will be:
A. square pyramidal
B. trigonal bipyramidal
c. planar
D. pentagonal bipyramidal


The value of \( \boldsymbol{I}= \)
\( \int_{\pi / 2}^{5 \pi / 2} \frac{e^{\tan ^{-1}(\sin x)}}{e^{\tan ^{-1}(\sin x)}+e^{\tan ^{-1}(\cos x)}} d x \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \)
D. \( \pi / 2 \)


How would you react on this statement?
Electronegativity of nitrogen (N) on Pauling scale is 3.0 in all the nitrogen compounds.


State whether true or false:
A concave mirror can produce both real and virtual images.
A. True
B. False


Which of the following is not an
objective of Green chemistry?
A. It is better to prevent waste than to treat or clean up waste after it has been created
B. The use of auxiliary substances (e.g., solvents, separation agents, etc.) should be made unnecessary wherever possible and innocuous when used.
C. Energy requirements of chemical processes should be recognized for their environmental and economic impacts and should be minimized. If possible, synthetic methods should be conducted at ambient temperature and pressure.
D. None of the above


Find the rank of the matrix \( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}1 & 5 & 9 \\ 4 & 8 & 12 \\ 7 & 11 & 15\end{array}\right] \)


Assertion
The change in kinetic energy of a particle is equal to the work done on it by the net force.
Reason
Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
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


Solve: \( \int \cos ^{3} x d x \)


Which of the following statements
is/are true?
This question has multiple correct options
A. It is impossible to satisfy the octet rule for all atoms in \( X e F_{2} \)
B. For ozone molecule, both the oxygen-oxygen bonds are of equal length.
C. The bond in \( N O^{+} \) should be stronger than the bond in
\( N O \)
D. For ozone molecule, one oxygen-oxygen bond is stronger than the other oxygen-oxygen bond.


Zener diode works on
A. zero bias
B. reverse bias
C. forward bias
D. infinite bias


Which among the following are physical or chemical changes?
(a) Evaporation of petrol
(b) Burning of liquefied Petroleum Gas
\( (\mathrm{LPG}) \)
(c) Heating of an iron rod to red hot.
(d) Curdling of milk
(e) Sublimation of solid ammonium
chloride
\( A \cdot(a),(b) \) and \( (c) \) are physical changes; \( (d) \) and (e)are chemical changes
B. (d), (b) and (e) are physical changes; (a) and (c) are chemical changes
c. (a), (b) and (e) are physical changes; (c) and (d) are chemical changes
D. \( (a),(c) \) and (e) are physical changes; (b) and (d) are chemical changes


A semiconductor is a material with a
small but non-zero band gap that
behaves as an insulator at absolute
zero but allows thermal excitation of
electrons into its
temperatures that are below its melting point.
A. номо
B. valence band
c. conduction band
D. LUMO


How much energy in kilowatt hour is consumed in operating ten 50 watt bulbs for 10 hours per day in a month \( (30 \) days)
A . 1500
B. 5000
c. 15
D. 150


Write two precautions you take, while observing Rhizopus in the laboratory.


Prove that the function given by \( \boldsymbol{f}(\boldsymbol{x})= \) \( \cos x \) is strictly increasing in \( (\pi, 2 \pi) \)


Find the middle term(s) in the
expansion of \( \left(1+3 x+3 x^{2}+x^{3}\right)^{2 n} \)


Chloroplasts are found in the root cells
of
A. Vanda
B. Rhizophora
c. Tinospora
D. Clematis


Which of the following expression is
correct?
\( \mathbf{A} \cdot \frac{d[H I]}{d t}=\frac{k_{3} k_{1}}{k_{2}}\left[H_{2}\right]\left[I_{2}\right] \)
B. \( \frac{d[H]}{d t}=\frac{k_{1} k_{3}}{k_{2}} 2\left[H_{2}\right]\left[I_{2}\right] \)
\( \frac{d[H I]}{d t}=k_{2}\left[H_{2}\right]\left[I_{2}\right]^{2} \)
D. None of the above


Draw a triangle \( A B C \) with side \( B C=6 \)
\( \mathrm{cm}, \angle C=30^{\circ} \) and \( \angle A=105^{\circ} \).Then
construct another triangle whose sides \( \operatorname{are} \frac{2}{3} \) times the corresponding sides of
\( \Delta A B C \)


What will be the volume of \( O_{2} \) at N.T.P
liberated by 5 A current flowing for 193 s through acidulated water?
\( \mathbf{A} \cdot 56 \mathrm{m} \)
B. \( 112 \mathrm{ml} \)
c. \( 158 \mathrm{ml} \)
D. 965 ml


The energy required to break one mole
of \( C l-C l \) bonds in \( C l_{2} \) is \( 242 k J \)
mol \( ^{-1} \). The longest wavelength of light capable of breaking single \( C l-C l \)
bond is:
\( \left(c=3 \times 10^{8} m s e c^{-1}, N_{A}=6.023 \times 10^{2}\right. \)
A. 700 nm
в. 494 пт
c. 594 ит
D. 640 nm


Equation of position (x) with time (t) is given by equation \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{7} \boldsymbol{t}^{2}+\mathbf{5} \boldsymbol{t}+ \)
8 \( m \). The acceleration at time \( t=1 \) sec is :
A \( \cdot 20 m / s e c^{2} \)
B. \( 32 m / \) sec \( ^{2} \)
c. zero
D. \( 14 m / s e c^{2} \)


How industrial effluents effects soil
pollution?
A. By decreasing its fertility
B. By decreasing its water absorbing capacity
c. By increasing its fertility
D. Both A and B


an object \( A B E D \) is placed in front of a
concave mirror beyond the center of
curvature \( C \) as shown in figure. State the shape of the image
\( A \cdot\left|m_{A B}\right|<1 \) and \( \left|m_{E D}\right|<1 \)
B \cdot \( \left|m_{A B}\right|>1 \) and \( \left|m_{E D}\right|<1 \)
c. \( \left|m_{A B}\right|<1 \) and \( \left|m_{E D}\right|>1 \)
D. \( \left|m_{A B}\right|>1 \) and \( \left|m_{E D}\right|>1 \)


The lightning conductor used in building, protects the building by :
A. dissipating the electric charge away from the building
B. conducting the lightning safely to the ground
c. absorbing the electric charge
D. None of these


How should people wearing spectacles
work with a microscope?
A. They should keep on wearing their spectacles.
B. They should never use the microscope.
C. They should take off their spectacles.
D. They may either put on their spectacles or they may take off their spectacles.


An electron moves on a straight line
path \( Y Y^{\prime} \) as shown in figure. A coil is
kept in the right such that \( Y Y^{\prime} \) is in the
plane of the coil. At the instant when the
electron gets closest to the coil (neglect self-induction of the coil),
A. the current in the coil flows clockwise
B. the current in the coil flows anticlockwise
c. the current in the coil is zero
D. the current in the coil does not change the direction as the electron crosses point \( O \)
E. answer required


Which of the following are true for cathode rays? This question has multiple correct options
A. It travels along a straight line
B. It emits \( X \) -rays when strikes a metal
c. It is an electromagnetic wave
D. It is not deflected by magnetic field


\( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}: \Delta H= \)
\( -92 k J \) is Haber \( s \) process for
manufacture of \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}} \)
What is the numerical value of heat of
formation of \( \boldsymbol{N} \boldsymbol{H}_{3} \) ?


The \( p H \) of resulting solution after addition of \( N a C N \) is:
A . 9.86
B. 8.86
c. 6.86
D. 5.86


Photorespiration is favoured by
A. Low temperatures
B. Low light intensity
\( \mathrm{c} \cdot \mathrm{High} \mathrm{O}_{2} \) and \( \operatorname{low} \mathrm{CO}_{2} \)
D. Low \( O_{2} \) and high \( C O_{2} \)


A long-jumper runs before jumping in
order to :
A. cover a greater distance
B. maintain momentum conservation
c. gain energy by running
D. gain momentum


Determine the equation of the curve passing through the origin in the form \( y \) \( =f(x), \) which satisfies the differential equation \( \frac{d y}{d x}=\sin (10 x+6 y) \)


The centigrade \( \left(^{0} C\right) \) scale can be converted into Kelvin scale by the
formula:
A. Temperature in Kelvin + 273
B. Temperature in Kelvin - 273
c. Temperature in Fahrenheit +273
D. Temperature in Fahrenheit - 273


Which of the following product is obtained during reaction of ethanoic acid with diazomethane in presence of dil. H Cl?
A. Methyl acetate
B. Ethyl acetate
c. Methyl formate
D. Ethyl formate