\( \boldsymbol{i}^{2}=-\mathbf{1}, \) then \( \boldsymbol{i}^{2}+\boldsymbol{i}^{4}+\boldsymbol{i}^{\boldsymbol{6}}+\boldsymbol{i}^{\boldsymbol{8}}+\ldots+ \)
\( (2 n) \) terms is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot i \)
D. \( -i \)


Find the compound interest of 500 for 1 year, compounded semi-annually at the rate of \( 3 \% \) per six months.
A . 20.50
B. 10.45
c. 30.45
D. 42.89


Which of the following is correct for hydbridization of C-atom?
A. \( C H_{4}-S P^{3} \)
B. \( C_{2} H_{4}-s p^{2} \)
c. \( C_{2} H_{2}-s p \)
D. All of these


In a practical unit if the unit of mass
becomes double and that of u it of time
becomes half, then 8 joules will equal to unit of work
\( A \cdot 8 \)
B. 4
\( c \)
D. 10


A mixture of polarised and unpolarised
light is incident on a polariser. As the
polariser is rotated through \( 360^{\circ}, \) it is
found that the minimum and the
maximum of the transmitted intensity
is in the ratio \( 1: q . \) The ratio of
intensities of polarised to unpolarised light in the incident beam is
A \( \cdot \frac{1}{2}(q-1): 1 \)
в. \( _{1: \frac{1}{2}(q-1)} \)
c. \( \frac{1}{2} q: 1 \)
D. \( _{1}: \frac{1}{2} q \)


Assertion
Statement \( -1: d_{o-o} \) in \( O_{2} F_{2} \) and \( O_{2} \)
molecules are almost same.
Reason
Statement \( -2: O_{2} F_{2} \) exists as ion pair
structure of \( \left[\boldsymbol{O}_{2} \boldsymbol{F}\right]^{+}[\boldsymbol{F}]^{-} \) form and
achieves the bond length closer to \( \boldsymbol{O}_{2} \)
molecule.
A. Statement -1 is true, Statement -2 is true and Statement - 2 is correct explanation for Statement
1
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1.
c. Statement -1 is true, Statement -2 is false.
D. Statement -1 is false, Statement -2 is true


PQRS is a parallelogram. QM is the
height from \( Q \) to \( S R \) and \( Q N \) is the height
from \( Q \) to PS. If \( S R=12 c m \) and \( Q M=7.6 \)
\( \mathrm{cm} . \) Find the area of the parallelogram
PQRS.


Haloarenes react with halogens in the presence of as the
catalyst to give ortho-para isomers.
A . ferric chloride
B. sodium chloride
C. potassium chloride
D. magnesium chloride


\( \mu_{1}, \mu_{2} \) are the refractive indices of two
media A and B. If \( \mu_{1}>\mu_{2}, \) when two
light rays travel from air to medium \( \mathbf{A} \) and air to medium B with the same
angle. of incidence then the angle of
refractions are \( r_{1} \) and \( r_{1} \) respectively.
What is the relation between \( r_{1} \) and \( r_{2} ? \)
A. \( r_{1}=r_{2} \)
B . \( r_{1}<r_{2} \)
c. \( r_{1}>r_{2} \)
D. \( r_{1} \geq r_{2} \)


The ratio of \( \sigma \) and \( \pi \) bonds in benzene
is:
A . 4: 1
B. 6: 1
c. 4: 3
D. 8: 1


At \( 80^{\circ} \mathrm{C}, \) the vapour pressure of pure
liquid \( A \) is 520 mmHg and that of pure liquid \( B \) is 1000 mmHg. If a mixture
solution of \( A \) and \( B \) boils at \( 80^{\circ} \) and 1
atm pressure, the amount of \( A \) (mole
percent) in the mixture is:
A . \( 50 \% \)
B. 54\%
c. \( 32 \% \)
D. 44\%


\( 4 x+1 \geq 17, \) where \( x \in N \)
A \( \cdot\{5,6,7, \ldots\} \)
в. \( \{4,5,6, \ldots\} \)
c. \( \{1,2,3, \ldots\} \)
D. None of these


\( a, e \) is a subset of
\( \{x: x \) is a vowel in the English alphabet
\( . \text { Enter } 1 \text { if true or } 0 \text { otherwise }) \)


Which of the following is a chain-growth polymer?
A. Nucleic acid
B. Starch
c. Polystyrene
D. Proteins


What would be magnetic moment of
\( \boldsymbol{G} \boldsymbol{d}^{+3}(\boldsymbol{Z}=\mathbf{6 4}) ? \)
A. 7.9 BM
B. 3.62 ВМ
c. \( 10.60 \mathrm{BM} \)
D. 9.72 ВМ


Evaluate using expansion of \( (a+b)^{2} \) or
\( (a-b)^{2}: \)
\( (9.4)^{2} \)
A . 88.36
B. 88.46
c. 89.16
D. 89.56


In the given triangle, \( A B \) is parallel to
\( \boldsymbol{P Q} \cdot \boldsymbol{A P}=\boldsymbol{c}, \boldsymbol{P C}=\boldsymbol{b}, \boldsymbol{P Q}=\boldsymbol{a}, \boldsymbol{A B}=\boldsymbol{x} \)
What is the value of \( x ? \)
A・ \( x=a-\frac{a c}{b} \)
B. \( x=b+\frac{a c}{b} \)
c. \( x=b-\frac{a c}{b} \)
D. \( x=a+\frac{a c}{b} \)


Water boils when:
A. saturated vapour pressure of water becomes equal to the atmospheric pressure
B. boiling point of water becomes more than atmospheric pressure
C . saturated vapour pressure of water is less than atmospheric pressure
D. vapour pressure of water becomes more than atmospheric pressure


: A sphere
Il: A cube
III: A thin circular plate;
All made of the same material having the same mass are initially heated to
\( 200^{0} \mathrm{C} . \) Identify the order in which the objects cool faster when left in air
at room temperature:
A. III,II and I
B. II, I and III
c. ।, ॥ and III
D. II, III and I


The relation between energy E and momentum p of a photon is
A \( . E=p c \)
B. \( E=\frac{p}{c} \)
c. \( p=E c \)
D. \( \quad E=\frac{p^{2}}{c} \)


The device, which can be used to detect whether an object is charged, is:
A. telescope
B. microscope
c. electroscope
D. none of the above


Calculate mean deviation about
median for the given data
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 4 \\ & 10 & 20 & 30 & 5\end{array} \)
5 Frequency 4
A . 2.3
в. 11.3
c. 12
D. 15


Why is use of aspartame limited to cold foods and drinks?


Draw the variation of magnetic field (B) with magnetic intensity (H) when a ferromagnetic material is subjected to a cycle of magnetisation.


Illustrate the taxonomical hierarchy with suitable examples of a plant and an animal.


The electronic configuration of chlorine
atom is :
A \( \cdot 1 s^{2} 2 s^{2} p^{6} 3 s^{3} p^{5} \)
B \( \cdot 1 s^{2} 2 s^{3} p^{6} 3 s^{3} p^{4} \)
C. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{5} \)
D. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{6} \)


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


Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?
A \( \cdot(n-1) d^{8} n s^{2} \)
B . \( (n-1) d^{5} n s^{2} \)
c. \( (n-1) d^{3} n s^{2} \)
D・ \( (n-1) d^{5} n s^{1} \)


Calculate the total positive or negative
charge on a \( 3.11 g \) copper penny. Given
Avogadro number \( =6.02 \times 10^{23} \)
atomic number of copper \( =29 \) and
atomic mass of copper \( =\mathbf{6 3 . 5} \)
A \( \cdot 3.37 \times 10^{5} \mathrm{C} \)
B . \( 2.37 \times 10^{5} \mathrm{C} \)
c. \( 1.37 \times 10^{5} C \)
D. \( 0.37 \times 10^{5} C \)


Light selects the least time path to
travel between two points. This principle
was stated by


Cell membrane in Eukaryotes is?
A. Exclusively selective permeable
B. Mainly selective permeable with semi permeability
C. Mainly semi permeable with selective permeability
D. Selective \& semi-permeability equally


Integrate:
\( \int \frac{1+109 x}{x \cdot 109 x} \cdot d x \)


A transformer core is laminated to
A. reduce hysteresis loss
B. reduce eddy current loss
c. reduce copper loss
D. reduce all of the above loss


Identify the element if it has mass
number 14 and 8 neutrons.
A. Isotope of oxygen
B. Isobar of oxygen
c. Isotope of carbon
D. Isobar of carbon


Points \( (\mathbf{6}, \mathbf{8}),(\mathbf{3}, \mathbf{7}),(-\mathbf{2},-\mathbf{2}) \) and
(1,-1) are joined to form a quadrilateral. What will be the structure of the quadrilateral?
A. Rhombus
B. Parallelogram
c. square
D. Rectangle


A block of steel heated to \( 100^{\circ} \mathrm{C} \) is left
in a room to cool. Which of the curves
shown in figure depicts the correct behaviour?
4
B.
\( c \)
D. None of thes


Mention against each of the following whether regular or diffused reflection will take place when a beam of light strikes. Justify your answer in each
case.
(a) Polished wooden table
(b) Chalk powder
(c) Cardboard surface
(d) Marble floor with water
(e)Mirror
(f) Piece of paper


Define the term polymerisation


The mass of \( \mathrm{O}_{2} \) molecule is 16 times that
\( \mathrm{H}_{2} \) molecule. The rms velocity of \( \mathrm{O}_{2} \)
molecule at room temperature \( \mathrm{C}_{r m s} \). The
rms velocity of \( \mathrm{H}_{2} \) molecule at the same
temperature will be:
A \( \cdot \frac{C_{r m s}}{16} \)
в. \( \frac{C_{r m s}}{4} \)
\( \mathbf{c} \cdot 4 C_{r m s} \)
D. \( 16 C_{r m} \)


If \( \sin ^{-1}(x)+\sin ^{-1}(2 x)=\frac{\pi}{3}, \) then \( x= \)
A \( \cdot \frac{3}{28} \)
B. \( \frac{\sqrt{3}}{28} \)
c. \( \sqrt{\frac{3}{28}} \)
D. \( \frac{3}{\sqrt{28}} \)


Hamburger
phenomenon is also known as
A. Hydrogen shift mechanism
B. Chloride shift mechanism
C. Carbonic acid shift mechanism
D. Sodiumpotassium pump


Phosphine \( \left[\boldsymbol{P} \boldsymbol{H}_{3}\right] \) decomposes to
produce \( P_{4}(g) \) and \( H_{2}(g) . \) What would be the change in volume when 100 ml
of \( \boldsymbol{P} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is completely decomposed \( ? \)
\( \mathbf{A} \cdot 50 m l \)
в. \( 500 \mathrm{ml} \)
c. \( 75 \mathrm{ml} \)
D. \( 250 \mathrm{ml} \)


Select the detergent that is used to prepare cosmetics.
A . DDBS
B. Polyethylene glycol
c. Cetyltrimethylammonium chloride
D. LAS


The cementation process is:
A. gel formation
B. emulsion formation
c. both of \( A \) and \( B \)
D. none of the above


Three numbers are chosen at random
without replacement from \( \{1,2,3, \ldots, 8\} \) The probability that their minimum is
3, given that their maximum is \( 6, \) is:
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{2}{5} \)


Equation of straight line \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}= \)
\( 0, \) where \( 3 a+4 b+c=0, \) which is at
maximum distance from \( (1,-2), \) is
A. \( 3 x+y-17=0 \)
B. \( 4 x+3 y-24=0 \)
c. \( 3 x+4 y-25=0 \)
D. \( x+3 y-15=0 \)


Which of the following statements is
true?
A. Boys will reach puberty at an earlier age than girls.
B. At about the age of \( 12, \) girls will grow more rapidly than boys.
C. At the end of rapid growth, girls are normally heavier than boys.
D. Between the age of 4 to \( 12, \) girls will grow faster than boys


Which kind of catalysis can be explained on the basis of adsorption
theory?
A. Homogeneous catalysis
B. Heterogeneous catalysis
c. Negative catalysis
D. Auto catalysis


In a meter-bridge experiment with
resistance \( R_{1} \) in left gap and resistance
\( X \) in right gap, null point is obtained at
\( 40 \mathrm{cm} \) from left end. With a resistance
\( R_{2} \) in left gap and same resistance \( X \) in
right gap, null point is obtained at
\( 50 \mathrm{cm} \) from left end. Where will be null
point if \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) are put first in series
and then in parallel, in the left gap and
right gap still containing \( X ? \)


Find the current through the conductor
during its motion


Find the general solution of the
congruence \( 98 x-1 \equiv 0(\bmod .139) \)


The cryoscopic constant for acid is \( 3.6 \mathrm{K} \) kg/mol. A solution of 1 g of a hydrocarbon in 100 g of acetic acid
freezes at \( 16.60^{\circ} \mathrm{C} \). The hydrocarbon contains \( 92.3 \% \) carbon.lf the molecular
formula is \( C_{x} H_{y} \). Find the value of \( x \) and
\( y: \)
A. \( x=2, y=4 \)
В. \( x=3, y=8 \)
c. \( x=4, y=10 \)
D. \( x=6, y=6 \)


For reflection of light from a plane
surface:
A. the incident ray, reflected ray and the normal all lie in the same plane
B. the angle of incidence is equal to the angle of reflection
c. both \( A \) and \( B \) are true
D. none of A and B is true


No vessels are found in the wood of
A. Pine
B. Eucalyptus
c. Teak
D. Sheesham


Two diamonds begin a free fall from rest
from the same height, 1.0 s apart. How long after the first diamond begins to fall will the two diamonds be \( 10 \mathrm{m} \)
apart? Take \( g=10 m / s^{2} \)


Speed of efflux is
A \( \cdot \sqrt{3 g h} \)
в. \( \sqrt{2 g h} \)
\( c \cdot \sqrt{g h} \)
D. \( \frac{1}{2} \sqrt{2 g h} \)


subtract \( 2 x^{2} y^{2}-5 x y+y^{2} \) from \( 2 y^{2}+ \)
\( 6 x^{2} y^{2}-x y \)


What is isomerism? Write the isomers
of butane.


A person who is moving parallel to the
charge and at the same velocity as the
charge will measure.
A. A magnetic field and an electric field due to the moving charge.
B. A magnetic field, but not an electric field due to the moving charge.
C. An electric field, but not a magnetic field due to the moving charge.
D. Neither an electric field nor a magnetic field due to the moving charge.
E. A decrease in the amount of charge.


How many primary amines are possible
with the molecular formula \( C_{4} H_{11} N ? \)
A .2
B. 3
\( c \cdot 4 \)
D.


Simplify the polynomial and write it in standard form:
\( \left(x^{4}-3\right)(3 x-4)+2 x^{3}\left(2 x^{2}-2\right) \)


A group of interbreeding organisms is referred to be belonging to the same
A. species
B. Order
c. Genus
D. Family


The position in the periodic table to which \( F e \) and \( Z n \) elements belong to
A . Alkali metal
B. Alkaline earth metal
c. d-block
D. None of these


What is the magnitude of the gravitational force between the Earth
and \( 1 k g \) object on its surface?
(Mass of the Earth is \( 6 \times 10^{24} k g \) and
radius of the Earth is \( 6.4 \times 10^{6} m \)
A. 9.770
B. 10 N
\( c \cdot 9 N \)
D. 9.5 N


Find the equation for the graph above.
\( \mathbf{A} \cdot x=3 \)
\( \mathbf{B} \cdot y=3 \)
C. \( y=-5 \)
D. \( x=-5 \)


Find the value of \( \sin ^{-1}\left(\cos \frac{33 \pi}{5}\right) \)


Assertion
Kelvin Temperature Scale has the
Absolute Zero.
Reason
At Absolute Zero, the molecular energy
is minimum
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


For flow of a fluid to be turbulent:
A. fluid should have high density
B. velocity should be large
C. reynold number should be less than 2000
D. both (a) and (b)


In which element rule(c) (i) is followed?
A \( \cdot 29^{c} \)
B. 24 \( ^{c} \)
\( c \cdot 26^{F e} \)
D. \( 25^{M n} \)


The angle between the diagonals of a cube with edges of length 1 is:
\( A \cdot \sin ^{-1}(1 / \sqrt{3}) \)
B . \( \cos ^{-1}(1 / \sqrt{3}) \)
c. \( \tan ^{-1}(1 / \sqrt{3}) \)
D. \( \cot ^{-1}(1 / \sqrt{3}) \)


Find the area of the closed figure bounded by the following curve \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{x}^{2}, \boldsymbol{y}=\mathbf{2} \)


Two mole of ideal diatomic gas
\( \left(C_{V, m}=5 / 2 R\right) \) at \( 300 \mathrm{K} \) and 5 atm
expanded irreversibly and adiabatically to a final pressure of 2 atm against a
constant pressure of 1 atm.Calculate \( q \) \( \mathrm{w}, \Delta \boldsymbol{H} \) and \( \Delta \boldsymbol{U} \)


How do seeds and fruits develop in angiosperms? Explain with examples.


If 50.0 milliters of \( 3.50 \mathrm{M} H_{2} S O_{4} \mathrm{be} \)
diluted in order to make \( 2.00 \mathrm{M} H_{2} S O_{4} \)
what should be the final volume in
mililiters?
A . 25.0
B. \( 60 . \)
c. 87.5
D. 93.2
E . 101


Find the solution set to the inequality
\( 2 x+1 \geq 9 ? \)
\( \mathbf{A} \)
B.
c.
D.


Select redox reaction from the following
A \( . Z n+C u S O_{4} \rightarrow Z n S O_{4}+C u \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( N a O H+2 H C l \rightarrow N a C l_{2}+H_{2} O \)
D. \( C a C O_{3} \rightarrow C a O+C O_{2} \)


With the help of a circuit diagram
describe the method to find the internal
resistance of a cell using potentiometer.


In the reaction sequence, \( \boldsymbol{X} \) is:
A. cyclohexanone
B. caprolactamm
c. \( H O\left(C H_{2}\right)_{6} N H_{2} \)
D. hexamethyline disocyanat


State true or false.
Given universal set= \( = \) \( \left\{-6,-5 \frac{3}{4},-\sqrt{4},-\frac{3}{5},-\frac{3}{8}, 0, \frac{4}{5}, 1,1 \frac{2}{3}, v\right. \)
From the given set, the set of integers is \( \{-6,-\sqrt{4}, 0,1\} \)
A. True
B. False


The partially decomposed organic matter is formed by a process called
A. Fragmentation
B. Humification
c. Mineralization
D. Leaching


Calculate the mass of urea
\( N H_{2} C O N H_{2} \) required in making 2.5 kg of 0.25 molal aqueous solution.


Which one of the lanthanoids is
radioactive in nature?
A . cs
B. Np
\( c \cdot c e \)
D. Pm


Which of the following is secondary amine?
A. \( C H_{3}-N H_{2} \)
в.
\[
C-N_{L}^{C}^{\ominus}-C
\]
c. \( C H_{3}-N H C H_{3} \)
D. \( C H_{3}-N\left(C H_{3}\right)_{2} \)


Which of the following has the smallest bond length?
A . \( N O^{+} \)
в. \( N O \)
\( c \cdot N O \)
D. Equal


Torque acting on an electric dipole in a uniform electric field is maximum if the angle between \( \vec{P} ; \) and \( \vec{E} \) is:
A \( .180^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


The hydrolysis of \( N C l_{3} \) results in the
formation of
A. hydrogen chloride, hypochlorous acid
B. ammonia, hypochlorous acid
c. ammonia, chlorous acid
D. chloric acid, ammonia


Assertion (A): Poles of a magnet can
never be separated Reason (R): Since, each atom of a
magnetic material is a magnet in itself
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of A
C. A is true, but R is false
D. A is false, but R is true


A \( 30 V, 90 W \) lamp is to be operated on
a \( 120 V D C \) line. For proper glow, a
resistor of ..... should be connected in
series with the lamp
A . 10
B. 20
c. 30
D. 40


matchings?
This question has multiple correct options
A. Metamers
B. Functional isomers
glucose fructose
C. Tautomers
\( D \)
Ethanol (Alcohol)
Metamers


If \( l(\bar{b} \times \bar{c})+m(\bar{c} \times \bar{a})+n(\bar{a} \times \bar{b})=0 \)
And at least one of \( l, \boldsymbol{m}, \boldsymbol{n} \) is not zero then the vectors \( \bar{a}, \bar{b}, \bar{c} \) are
A. Parallel
B. Coplanar
c. Mutually perpendicular
D. None of these


f \( y=\sin \left(2 \sin ^{-1} x\right), \) then prove that
\( \frac{d y}{d x}=2 \sqrt{\frac{1-y^{2}}{1-x^{2}}} \)


Which one is wrong with respect to
photorespiration?
A. It occurs in chloroplasts
B. It occurs in day time only
C. It is characteristic of \( C_{4} \) plants
D. It is characteristic of \( C_{3} \) plants


Suppose \( J=\int \frac{\sin ^{2} x+\sin x}{1+\sin x+\cos x} d x \) and
\( K=\int \frac{\cos ^{2} x+\cos x}{1+\sin x+\cos x} d x . \) If \( C \) is an
arbitrary constant of integration then which of the following is correct?
A \( \cdot J=\frac{1}{2}(x-\sin x+\cos x)+C \)
B. \( J=K-(\sin x+\cos x)+C \)
\( \mathbf{c} . J=x+K+C \)
D. \( K=\frac{1}{2}(x-\sin x+\cos x)+C \)


What is the correct letter code for
tryptophan?
\( A \cdot w \)
B. Y
\( c \cdot L \)
\( D \)


Match the following procedures.


The number of beta particles emitted when \( \frac{239}{92} U \rightarrow_{94}^{239} P u \) is


A \( 5.25 \% \) solution of a substance is isotonic with a \( 1.5 \% \) solution of urea
(molar mass \( =60 g \) mol \( ^{-1} \) ) in the same
solvent. If the densities of both the
solutions are assumed to be equal to
\( 1.0 g c m^{-3}, \) molar mass of the substance will be:
в. \( 90.0 g \) mol\( ^{-1} \)
c. \( 115.0 g \) mol \( ^{-1} \)
D. \( 105.0 g \) mol \( ^{-1} \)


Show that cube of any position integer
will be in the form of \( 8 m \) or \( 8 m+1 \) or
\( 8 m+3 \) or \( 8 m+5 \) or \( 8 m+7, \) where \( m \)
is a whole number.


The enthalpies of formation of \( \boldsymbol{C O}_{2(\boldsymbol{g})}, \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \) and \( \boldsymbol{C}_{2} \boldsymbol{H}_{4(\boldsymbol{g})} \) are
respectively -393.5,-286 and \( +52.3 k J m o l^{-1} . \) The enthalpy change
for the combustion of \( C_{2} H_{4(g)} \) is :
A . \( 1306 k J m o l^{-1} \)
В. \( 1411.3 \mathrm{kJmol}^{-1} \)
c. \( -509.7 k J m o l^{-1} \)
D. \( -731.5 k J m o l^{-1} \)


A rectangular loop of sides \( a \) and \( b \) is
placed in \( \boldsymbol{x}-\boldsymbol{y} \) plane. A uniform but
time varying magnetic field of strength \( \vec{B}=20 t \hat{i}+10 t^{2} \hat{j}+50 \hat{k} \) is present in
the region. The magnitude of induced
emf in the loop at time \( t \) is :
A. \( 20+20 t \)
B . 20
\( c .20 t \)
D. zero


\( \lim _{x \rightarrow 3^{-}} \frac{|x-3|}{x-3}= \)


When the muscles of the heart
contract?
A. Blood is pumped from the right ventricle into the lungs.
B. Blood flows from the lungs into the left auricle.
C. Blood is pumped into the right auricle from all over the body
D. None of the above.


How many reduction divisions are
necessary for the formation of 200 grains of wheat?
A . 250
B. 150
\( c \cdot 200 \)
D. 360


The application of synthetic plant
hormone like IAA, IBA and NAA are best
described as?
A. Prevent early fruit fall before harvesting and its used to produce parthenocarpic fruit
B. Prevent early fruit tall only
c. To produce both seed less fruits with seeds
D. To produce larger fruit


The removal of salt bridge from Daniell cell brings in the following changes:
A \( \cdot E_{Z n / Z n^{2+}}^{o} \) changes
B . \( E_{C u / C u^{2+}}^{o} \) changes
C. \( E_{\text {clu }}^{o} \) drops to zero
D. none of the above


The number of tripeptides possible from three different amino acids is:
A \( \cdot 8 \)
B. 27
\( c \cdot 9 \)
D. 6


A regular hexagon \& a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is \( (\sqrt{3}-1), \) then the side of the hexagon
is
A \( \cdot \sqrt{2}+1 \)
B. \( \frac{\sqrt{3}+1}{2} \)
c. 2
D. \( \sqrt{2} \)


Valence shell electronic configuration of
Barium is:
\( A \cdot 5 s^{2} \)
B. \( 6 s^{2} \)
\( c \cdot 5 s \)
D. \( 6 s^{\text {। }} \)


The first three of four given numbers are
in G.P. and last three are in A.P. whose
common difference is \( 6 . \) If the first and
last numbers are same, then first will
be?
A . 2
B. 4
\( c \cdot 6 \)
D. 8


If \( \left[\begin{array}{lll}1 & x & 1\end{array}\right]\left[\begin{array}{lll}1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2\end{array}\right]\left[\begin{array}{l}1 \\ 1 \\ x\end{array}\right]=0, \) then
\( \boldsymbol{x}= \)
A. \( \frac{-9 \pm \sqrt{35}}{2} \)
B. \( \frac{-7 \pm \sqrt{53}}{2} \)
c. \( \frac{-9 \pm \sqrt{53}}{2} \)
D. \( \frac{-7 \pm \sqrt{35}}{2} \)


For the following reaction at a particular
temperature, according to the
equations
\( \mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \)
\( 2 N O_{2}+\frac{1}{2} O_{2} \rightarrow N_{2} O_{5} \)
\( A \cdot E_{1}>E_{2} \)
в. \( E_{1}<E_{2} \)
C. \( E_{1}=2 E_{2} \)
D. \( \sqrt{E_{1} E_{2}^{2}}=1 \)


An object falls from a bridge that is
\( 45 m \) above water. It falls directly into a small boat moving with constant velocity that is \( 12 ~ m \) from the point of impact when the object was released.
The speed of the boat is
A. \( 3 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
c. \( 5 m / s \)
D. \( 6 \mathrm{m} / \mathrm{s} \)


The band of colours obtained on a
screen on passing white light through a prism is called:
A . a spectrum
B. a dispersion band
c. scattering
D. none of these


it is a process in which a solid substance is directly converted into its
vapours by application of heat and vapour is reconverted into solid by
subsequent cooling. The method is used when one of the components undergoes sublimation and other components are not decomposed by heating. F or example, naphtha -


Frequency used in navigating SONAR is
\( \mathbf{A} \cdot 60,000 H z \)
в. \( 50,000 H z \)
c. \( 20,000 H z \)
D. none of these


Double convex lenses are to be
manufactured from a glass of refractive index \( 1.55, \) with both faces of same
radius of curvature. What is the radius
of curvature required if the focal length is to be \( 20 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 11 \mathrm{cm} \)
B. 22 cm
\( c \cdot 7 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Assertion
\( H_{2} O_{2} \) and \( N_{2} H_{4} \) have oxidising as well
as reducing nature
Reason
Both have equivalent mass of 8
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In general if two points are on \( x- \) axis,
which formula do you apply for distance between them and if two points are on \( \boldsymbol{y}-\operatorname{axis}, \) which formula do you apply for distance between them and why?


n given figure, If \( \triangle P O S \sim \triangle R O Q \)
prove thar PSI|QR.


\( \operatorname{Let} \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\mathbf{2}^{\boldsymbol{r}-\mathbf{1}} & \mathbf{2} \mathbf{.} \boldsymbol{3}^{\boldsymbol{r}-\mathbf{1}} & \boldsymbol{4} \mathbf{.} \mathbf{5}^{\boldsymbol{r}-\mathbf{1}} \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{\gamma} \\ \mathbf{2}^{\boldsymbol{n}}-\mathbf{1} & \boldsymbol{3}^{\boldsymbol{n}}-\mathbf{1} & \mathbf{5}^{\boldsymbol{n}}-\mathbf{1}\end{array}\right| \)
Then, the value of \( \sum_{r=1}^{n} D_{r} \) is
\( \mathbf{A} \cdot \alpha \beta \mathbf{\gamma} \)
B . \( 2^{n} \alpha+3^{n} \beta+4^{n} \gamma \)
\( c \cdot 2 \alpha+3 \beta+4 \gamma \)
D. None of these


Among the elements \( C a, M g, P \) and \( C l \)
the order of increasing atomic radii is:
A. \( M g<C a<C l<P \)
в. \( C l<P<M g<C a \)
c. \( P<C l<C a<M g \)
D. \( C a<M g<P<C l \)
\( l \)


In the dichromate anion \( C r_{2} O_{7} \)
A. all Cr- O bonds are equivalent
B. \( 6 \mathrm{cr} \) - 0 bonds are equivalent
c. \( 3 \mathrm{cr} \) -o bonds are equivalent
D. no bonds in \( C r_{2} O_{7} \) are equivalent


The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{6}\right] \) is :
A. Hexafluoroplatinate(VI)xenon.
B. Xenonhexafluoroplatinate(V).
c. xenonhexafluoroplatinate(VI).
D. Xenoniumhexafluoroplatinum(V)


If the fourth term in the expansion of
\( (p x+1 / x)^{n} \) is \( 5 / 2 \) then the value of \( p \)
is
\( A \)
B. 1/2
\( c \cdot 6 \)
D.


A sphere of diameter \( r \) is cut from a solid sphere of radius r such that the centre of mass of remaining part be at maximum distance from original centre, then this distance is :


Why is the work done on an object
moving with uniform circular motion
zero?


The most significant contribution towards the development of periodic table was made by:
A. Mendeleev
B. Avogadro
c. Dalton
D. Cavendish


Express the following as the product of exponent through prism factorization
\( \mathbf{1 1 5 6} \)


Angle between p orbitals is:
A \( \cdot 90^{\circ} \)
B . \( 180^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 109^{\circ} 28 \)


In human body, chlorinated hydrocarbons accumulate in
A. Bones
B. Brain
c. Fatty tissue
D. skin


Solve the equation \( z^{2}+z|z|+\left|z^{2}\right|=0 \)


If \( z_{1} \) and \( z_{2} \) are two complex numbers
such that \( \left|z_{1}+z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}, \) then
This question has multiple correct options
A \( \cdot z_{1} \overline{z_{2}} \) is purely imaginary
B . \( z_{1} / z_{2} \) is purely imaginary
c. \( z_{1} \overline{z_{2}}+\overline{z_{1}} z_{2}=0 \)
D. \( O, z_{1}, z_{2} \) are vertices of a right triangle


A constant torque of \( 31.4 \mathrm{Nm} \) is exerted on a pivoted wheel. If the angular acceleration of the wheel is \( 4 \pi r a d / s e c^{2}, \) then the moment of
inertia will be
A \( \cdot 5.8 \mathrm{kg}-\mathrm{m}^{2} \)
в. \( 4.5 \mathrm{kg}-\mathrm{m}^{2} \)
c. \( 5.6 \mathrm{kg}-\mathrm{m}^{2} \)
D. \( 2.5 \mathrm{kg}-\mathrm{m}^{2} \)


Match the items in List 1 with the items
in List 2


Write the component statement of the following compounds statements and check whether the compound statement is true or false:
The sand heats up quickly in the sun and does not cool down fast at night


Which of the following represents effect \( /(s) \) of a chemical change?
A. Heat, light or any other radiation (ultraviolet, for example) may be given off or absorbed.
B. Sound may be produced
C. A change in smell may take place or a new smell may be given off.
D. All of the above


\( A B C \) is a right angled triangle is which
\( \angle A=90^{\circ} \) and \( A B=A C . \) Find \( \angle B \) and
\( \angle C \)


A 0.2 molal solution of KCl freezes at
\( -0.68^{\circ} \mathrm{C} . \) If \( K_{f} \) for \( H_{2} O \) is \( 1.86, \) the
degree of dissociation of \( \boldsymbol{K} \boldsymbol{C l} \) is:
A . \( 75 \% \)
B. \( 83 \% \)
\( c .65 \% \)
D. \( 92 \% \)


A spring is kept compressed by a toy car of mass \( 150 g . \) On releasing the car it moves with a speed of \( 0.2 m s^{-1} . \) So, the elastic potential energy of the spring is
\( A .3 m J \)
B. \( 3 J \)
c. \( 1.5 m J \)
D. \( 4 m J \)


Identify which of the following
statements is FALSE.
A. The vapor pressure of a liquid decreases with increasing atmospheric pressure.
B. The value of an equilibrium constant is dependent on temperature
C. The rate of a spontaneous reaction cannot be determined solely by its Gibbs free energy.
D. During a phase transition, the temperature of a substance must be constant.


Represent the following rational numbers on the number line:
\( \frac{-8}{5} ; \frac{3}{8} ; \frac{2}{7} ; \frac{12}{5} ; \frac{45}{13} \)


Two identical photocathodes receive
light of frequencies \( f_{1} \) and \( f_{2} \). If the
velocities of the photoelectrons (of
mass \( m \) ) coming out are \( v_{1} \) and \( v_{2} \)
respectively, then
A.
\[
v_{1}-v_{2}=\left[\frac{2 h}{m}\left(f_{1}-f_{2}\right)\right]^{\frac{1}{2}}
\]
B. \( v_{1}^{2}-v_{2}^{2}=\frac{2 h}{m}\left(f_{1}-f_{2}\right) \)
c. \( \quad v_{1}+v_{2}=\left[\frac{2 h}{m}\left(f_{1}-f_{2}\right)\right]^{\frac{1}{2}} \)
D. \( v_{1}^{2}+v_{2}^{2}=\frac{2 h}{m}\left(f_{1}-f_{2}\right) \)


If the relation \( \boldsymbol{R}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) where \( \boldsymbol{A}= \)
\( \{1,2,3,4\}, B=\{1,3,5\} \) is defined by
\( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}<\boldsymbol{y}, \boldsymbol{x} \in \boldsymbol{A}, \boldsymbol{y} \in \boldsymbol{B}\} \) then
find \( R \) and \( R^{-1} \)


If \( \boldsymbol{x}^{p} \cdot \boldsymbol{y}^{\boldsymbol{q}}=(\boldsymbol{x}+\boldsymbol{y})^{\boldsymbol{p}+\boldsymbol{q}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{y}{x} \)
B. \( -\frac{y}{x} \frac{y}{x} \)
c. \( \frac{x}{y} \)
D. \( -\frac{x}{y} \)


A wheel starts rotating from rest at time \( t=0 \) with a angular acceleration
of 50 radians/s\( ^{2} . \) The angular
acceleration \( (\alpha) \) decreases to zero
value after 5 seconds. During this
interval, \( \alpha \) varies according to the
question \( \boldsymbol{\alpha}=\boldsymbol{\alpha}_{0}\left(1-\frac{\boldsymbol{t}}{\mathbf{5}}\right) \)
The angular velocity at \( \boldsymbol{T}=\mathbf{5} \boldsymbol{s} \) will be
\( \mathbf{A} \cdot 10 \mathrm{rad} / \mathrm{s} \)
B. \( 250 \mathrm{rad} / \mathrm{s} \)
C \( .125 \mathrm{rad} / \mathrm{s} \)
D. \( 100 \mathrm{rad} / \mathrm{s} \)


The nature of the graph of pressure 'P' against reciprocal of volume 'V' of an ideal gas at constant temperature is
A. a straight line not passing through origin
B. a parabola
c. a straight line passing through origin
D. a rectangular hyperbola


The \( x \) -y plane divides the line joining the points (-1,3,4) and (2,-5,6)
A. internally in the ratio 2: 3
B. externally in the ratio 2: 3
c. internally in the ratio 3: 2
D. externally in the ratio 3: 2


\( \ln \) an A.P., if \( m^{t h} \) term is \( n \) and the \( n^{t h} \)
term is \( \mathrm{m}, \) where \( \boldsymbol{m} \neq \boldsymbol{n} \) find the \( \boldsymbol{p}^{t h} \)
term.
A \( . m+n+p \)
в. \( m-n+p \)
c. \( m+n-p \)
\( \mathbf{D} \cdot m-n-p \)


Maltose is made up of:
A. two \( \alpha-D \) - glucose
B. normal \( \beta-D- \) glucose
c. \( \alpha- \) and \( \beta-D- \) glucose
D. fructose


If \( \vec{A}=4 \hat{i}+6 \widehat{j} \) and \( \vec{B}=2 \hat{i}+3 \hat{j} \).Then :
\( \mathbf{A} \cdot \vec{A} \cdot \vec{B}=29 \)
в . \( \vec{A} \times \vec{B}=0 \)
\( ^{\mathbf{c}} \cdot \frac{|\vec{A}|}{|\vec{B}|}=\frac{2}{1} \)
D. angles between \( \vec{A} \) and \( \vec{B} \) is 30


Assertion
If refractive index of one medium is
equal to refractive index of second
medium, then beam does not bend at
all.
Reason
The bending of light does not depend on refractive indices of media.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The cause of irreversibility of a natura
process is:
state
B. A process often involves dissipative effects
c. Both A and B
D. None of the above


If \( \boldsymbol{A}=\boldsymbol{B}=\mathbf{1}, \) then in terms of Boolean
algebra the value of \( \boldsymbol{A} . \boldsymbol{B}+\boldsymbol{A} \) is not
equal to
\( \mathbf{A} \cdot B \cdot A+B \)
в. \( B+A \)
\( c . B \)
D. \( \bar{A} . B \)


\( 100 g \) of liquid \( A \) (molar mass \( \left.140 g m o l^{-1}\right) \) was dissolved in \( 1000 g \) of liquid B (molar mass \( 180 g \) mol\( ^{-1} \) ). The
vapour pressure of pure liquid B was
found to be 500 torr. Calculate the
vapour pressure of pure liquid \( A \) and its vapour pressure in the solution if the
total vapour pressure of the solution is
475 torr.


Compounds having the same composition but different structural formulas:
A. are used for substitution products
B. are called isomers
c. are called polymers
D. have the same properties
E . are usually alkanes


The wavelength of radiation is \( \lambda_{0} \) When
an electron jumps from third to second orbit of hydrogen atom. For the electron to jump from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be
A \( \cdot \frac{16}{25} \lambda_{0} \)
в. \( \frac{20}{27} \lambda_{0} \)
c. \( \frac{27}{20} \lambda_{0} \)
D. \( \frac{25}{16} \lambda_{0} \)


Soil erosion is due to
A. Fast running rivers
B. Heavy rains
c. Occasional rains
D. wind


The nature of linkage in organic compounds is generally:
A. Ionic bond
B. Covalent bond
c. co-ordinate covalent
D. Metallic bond


The highest boiling point among the hydrides of group 14,15,16 and 17 stands for:
A. \( H_{2} O \)
в. \( H I \)
c. \( P H_{3} \)
D. \( \operatorname{si} H_{4} \)


An object of mass \( m \) sliding along a frictionless surface collides with the
stationary object of mass \( m \). The two
bodies stick together. If the kinetic
energy of the two-body system is \( \boldsymbol{E} \) Calculate the initial velocity of the first object before impact?
A \( \cdot \sqrt{E / 2 m} \)
B. \( \sqrt{2 E / 2 m} \)
c. \( \sqrt{2 E / m} \)
D. \( \sqrt{E / m} \)
E \( .2 \sqrt{E / m} \)


arranged at the equatorial plate (see Fig. 1 ). When these cells are treated with colchicine, cell division is arrested and
the cells never enter anaphase. If we were to compare a colchicine treated
cell at metaphase and an untreated cell
in the same phase, we notice that
chromosomes are more dispersed and do not arrange themselves on the
equatorial plate in the treated cells (see Fig \( 2 .) \) Using this information, which of the
following will be affected by colchicine?
A . Centromere
B. Spindle fiber
c. Centriole
D. Arms of chromosomes


When a die is thrown, list the outcomes
of an event of getting
a) A prime number
b) A number greater than 6


The differential equation for all the straight lines which are at a unit distance from the origin is
\( ^{A} \cdot\left(y-x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{B}}\left(y+x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{c}}\left(y-x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{D} \cdot}\left(y+x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)


The emf of cell
\( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{I}(\boldsymbol{s})(\mathbf{0 . 0 5 M}) \boldsymbol{K I} \| \mathbf{0 . 0 5 M} \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \)
is \( 0.788 V . \) The solubility product of
\( A g I \) is:
A \( \cdot 1.1 \times 10^{-15} \)
В. \( 1.4 \times 10^{-15} \)
c. \( 1.1 \times 10^{-17} \)
D. none of these


The diameter of neck and bottom of a
bottle are \( 2 \mathrm{cm} \) and \( 10 \mathrm{cm} \) respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of \( 1.2 k g f, \) the amount of force
applied on the bottom is
B. \( F=15 ~ k g f \)
c. \( F=1.2 k g f \)
D. \( F=60 \mathrm{kg} f \)


A uniform thin rod of length Lis hinged
about one of its end and is free to rotate
about the hinge without friction. Neglect the effect of gravity. A force F is
applied at a distance \( x \) from the hinge on the rod such that force is always
perpendicular to the rod. Find the normal reaction at the hinge as
function of 'x', at the initial instant
when the angular velocity of rod is zero.


Which hormone control activity of zona glomerulosa of adrenal gland?
A. Renin
B. Thyroxine
c. АDH
D. FSH


\( \mathbf{n}\left[\boldsymbol{F} e\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3}, \operatorname{six} \boldsymbol{H}_{2} \boldsymbol{O} \) are joined
by primary valency (PV) and three \( C l \) are joined by secondary valency (SV). If true enter 1 , else enter 0 .


The median of a set of 9 distinct
observations is \( 20.5 . \) If each of the
largest 4 observations of the set is
increased by \( 2, \) then the median of the
new set
A. remains the same as that of the original set
B. is increased by 2
c. is decreased by 2
D. is two times the original median


Name one fish like reptile that evolved from land reptile about 200 million
years ago?


At a certain temperature, a ferromagnetic material becomes
paramagnetic. What is this temperature called?


A relation \( R \) is defined from a \( \operatorname{set} A= \)
[2,3,4,5] to a \( \operatorname{set} B=[3,6,7,10] \) as
follows:
\( (x, y) \in R \Leftrightarrow x \) is relatively prime to \( y \)
Express \( R \) as a set of ordered pairs and determine its domain and range.


How many faces a cube has?
A .4
B. 6
c. 8
D. 12


For reading small letters with a lens
A. one has to keep a convex lens at a distance between \( F \) and \( 2 \mathrm{F} \) from the book.
B. one has to keep a concave lens at a distance less than the focal length from the book
C. one has to keep concave lens at a distance between and \( 2 \mathrm{F} \) from the book
D. One has to keep a convex lens at a distance less than the an focal length from the book
E. None of these


Major role of minor elements inside
living organisms is to act as
A. Binder of cell structure
B. Constituent of hormones
c. Building blocks of important amino acids
D. cofactor of enzymes


The force of attraction between two unit
point masses separated by a unit distance is called
A. Gravitational potential
B. Acceleration due to gravity.
c. Gravitational field
D. Universal gravitational constant.


\( \mathbf{f} \boldsymbol{A}=\{\mathbf{6}, \mathbf{9}, \mathbf{1 1}\} \) and \( \boldsymbol{B}=\boldsymbol{\phi} \),find \( \boldsymbol{A} \cup \boldsymbol{B} \)


Evaluate the given integral. \( \int \sqrt{\frac{x}{1-x}} d x \)
\( A \cdot \sin ^{-1} \sqrt{x}+C \)
\( \mathbf{B} \cdot \sin ^{-1}[\sqrt{x}-\sqrt{x(1-x)}]+C \)
\( \mathbf{c} \cdot \sin ^{-1}[\sqrt{x(1-x)}]+C \)
D. \( \sin ^{-1} \sqrt{x}-\sqrt{x(1-x)}+C \)


In the given reaction,
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \leftrightharpoons \boldsymbol{A}+\boldsymbol{B}( \) equilibrium reaction
in room temperature)
\( A \) and \( B \) cannot be:
This question has multiple correct options
A. \( N_{2} O_{3} \)
в. \( N_{2} O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. hydronium ions


A ray of light propagates from glass (refractive index \( =3 / 2 \) ) to water
(refractive index \( =4 / 3 \) ).The value of the
critical angle:
\( A \cdot \sin ^{-1}(1 / 2) \)
B \( \cdot \sin ^{-1}\left(\frac{\sqrt{8}}{9}\right) \)
\( c \cdot \sin ^{-1}(8 / 9) \)
\( D \cdot \sin ^{-1}(5 / 7) \)


Velocity of de Broglie wave is given by:
\( ^{A} \cdot \frac{c^{2}}{v} \)
в. \( \frac{h v}{m c} \)
\( c \cdot \frac{m c^{2}}{h} \)
D. \( v \lambda \)


Which of the following is a narcotic analgesic?
A. Aspirin
B. Pencillin
c. Heroin
D. Tylenol


If \( A \) is any square matrix of order 2
then \( a d j(a d j A)= \)
A. \( A \)
B. \( \operatorname{det} A \)
\( c \cdot A^{-1} \)
D. None of these


\( \frac{9}{\frac{1}{2}} \)


If the forward bias on p-njunction is
increased from zero to \( 0.045 V \), then no
current flows in the circuit. The
contact potential of junction i.e. \( V_{B} \) is
A. zero
B. \( 0.045 V \)
C. more than \( 0.045 V \)
D. less than \( 0.045 V \)


In the figure \( , \boldsymbol{A B}= \)
\( A C \quad \) and \( \quad \angle B A C=20^{\circ} . \) The points \( D \)
on \( A B \) and \( E \) on \( A C \) are such that
\( A D=D E=E C . \) Then \( \angle B D C \) equals.
\( 4 \cdot 10^{\circ} \)
B . \( 20^{\circ} \)
\( c \cdot 30 \)
D. \( 80^{\circ} \)


The percentage hydrolysis in \( 0.003 M \)
aqueous solution of \( N a O C N\left(K_{a} \) for \right.
\( \left.\boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{N} \text { is } \boldsymbol{3} \boldsymbol{3} \boldsymbol{3} \times \mathbf{1 0}^{-4} \boldsymbol{M}\right) \) is:
A . \( 0.1 \% \)
B. \( 0.01 \% \)
\( c .0 .5 \% \)
D. \( 0.8 \% \)


During translation, activated amino
acids get linked to (RNA). This process is commonly called as
A. charging of tRNA
B. discharging of tRNA
c. aminoacylation of tRNA
D. both (a) and (c).


What is oxidation number of \( C r \) in
\( \left[\boldsymbol{C r}\left(\boldsymbol{O}_{2}\right)_{4}\right]^{3-} ? \)


The maximum velocity of a particle, executing simple harmonic motion with an amplitude \( 7 m m, \) is \( 4.4 m / s . \) The period of oscillation is
A. \( 100 s \)
B. \( 0.01 s \)
\( c \cdot 10 s \)
D. \( 0.1 s \)


The general solution of the equation \( \sin ^{100} x-\cos ^{100} x=1 \) is
A \( \cdot 2 n \pi+\frac{\pi}{3}, n \epsilon I \)
В \( \cdot n \pi+\frac{\pi}{2}, n \epsilon I \)
c. \( n \pi+\frac{\pi}{4}, n \epsilon I \)
D. \( 2 n \pi-\frac{\pi}{3}, n \epsilon I \)


Consider an atom with the electron
configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \)
Which successive ionization energy will be significantly higher than the previous value?
A. First ionization energy.
B. Second ionization energy
c. Third ionization energy.
D. Fourth ionization energy


An air bubble of diameter 2 mm rises
steadily through a solution of density \( 1750 k g / m^{3} \) at the rate of \( 0.35 c m / s \) Coefficient of viscosity of the solution is (Assume mass of the bubble to be
negligible) :
A . 9 poise
B. 6poise
c. 11 poise
D. 4 poise


The persistence of audible sound due to
the successive reflections from the
surrounding objects even after the source has stopped to produce that sound is
called
A . reflection
B. echo
c. reverberation
D. rarefaction


Write the following decimals in the place value table.
\( \mathbf{0 . 2 9} \)


Deuterium occurs in trace amounts
naturally as deuterium gas represented
as:
\( A \cdot D_{2} \)
в. \( ^{2} H_{2} \)
c. both A and B
D. \( ^{2} D \)


The following three objects (1) a metal
tray,
(2) a block of wood, and (3) a
wooden cap are left in a closed room
overnight. Next day the temperature of
each is recorded as \( T_{1}, T_{2}, \) and \( T_{3} \)
respectively. The likely situation is :
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{3}>T_{2}>T_{1} \)
c. \( T_{3}=T_{2}>T_{1} \)
D. \( T_{3}>T_{2}=T_{1} \)


Which gas has the highest partial pressure atmosphere?
A. \( C O_{2} \)
в. \( H_{2} \) о
\( c \cdot O_{2} \)
D. \( N_{2} \)


Dalton viewed chemical change as:
A. a transfer of electrons
B. a transfer of protons
C . a rearrangement of atoms
D. a change of atoms from one type into another


India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points
1,2,3 are 0.45,0.05 and 0.50
respectively. Assuming that outcomes are independent, the probability of India getting at least 7 points is
A .0 .0624
B. 0.0875
c. 0.8750
D. 0.0250


Prove that:
\( \boldsymbol{a}_{n^{2}+1}=\left(\boldsymbol{n}^{2}+\mathbf{1}^{2}\right)-\left(\boldsymbol{n}^{2}+\mathbf{1}\right)+\mathbf{1}= \)
\( \left(n^{2}+n+1\right)\left(n^{2}-n+1\right)= \)
\( \mathbf{A} \cdot a_{n-1} a_{n} \)
В \( \cdot a_{n+1} a_{n} \)
\( \mathbf{c} \cdot a_{n+1} a_{n-1} \)
D. \( a_{n+2} a_{n} \)


Suppose you are riding a bike with a speed of \( 10 m s^{-1} \) due east relative to a
person A who is walking on the ground towards east. If your friend B walking on the ground due west measures your
speed as \( 15 m s^{-1}, \) find the relative
velocity between two reference frames
and B.


sin the sind
uniform cross section is filled with
water and is mounted on a rotatable
shaft as shown in figure. If the tube is
rotated with a constant angular velocity
\( \omega, \) then
A. Water levels in both sections A and B go up
B. Water level in section A goes up and that in B comes down
c. water level in section A comes down and that in B it
goes up
D. Water levels remain same in both sections


Actinides have higher tendency to form complexes than Lanthanides, due to
A. Higher charge and smaller size
B. Smaller charge and larger size
c. They are radioactive
D. They are electropositive


The field potential inside a charged ball of radius \( \mathrm{R} \) and centre at o depends only
on distance from its center as \( V(r)= \)
\( \boldsymbol{\alpha} \boldsymbol{r}^{2}+\boldsymbol{\beta} \) when \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are \( + \) ve constant
now choose correct options
A . electric field inside the ball \( E_{r}=-2 \alpha r \)
B. electric flux passing through an imaginary sphere of radius r centre at 0 will be \( -2 \pi \alpha r^{4} \)
C. volume charge density p(r) inside ball is \( -6 \varepsilon_{0} \alpha \)
D. electric energy of charged ball will be \( \frac{48}{5} \pi \varepsilon_{0} \alpha^{2} R^{5} \)


\( \ln \) a \( \Delta A B C, \angle A>\angle B . \) If \( \sin A \) and
\( \sin B \) satisfy the equation \( 3 \sin x- \)
\( 4 \sin ^{3} x-k=0,0<k<1, \) then \( \angle C \) is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{5 \pi}{6} \)


Find the shortest distance between the \( \operatorname{lines} \vec{r}=\hat{i}+2 \hat{j}+3 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+ \)
\( \mathbf{4} \hat{\boldsymbol{k}}) \) and \( \overrightarrow{\boldsymbol{r}}=\mathbf{2} \hat{\boldsymbol{i}}+\mathbf{4} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}+\boldsymbol{\mu}(\mathbf{4} \hat{\boldsymbol{i}}+ \)
\( \mathbf{6} \hat{\boldsymbol{j}}+\mathbf{8} \hat{\boldsymbol{k}}) \)


Why is helium used in weather
observation balloons?


If \( \boldsymbol{a}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{4} & \mathbf{2}\end{array}\right], \) than show that \( |\mathbf{2} \boldsymbol{A}|= \)
\( \mathbf{4}|\boldsymbol{A}| \)


toppr
Q Type your question
Assurite muldy unly A 2 anu \( \cup \cup 2 \) art
present
\( A \)
B.
\( c \)
\( D \)


A cell of e.m.f. \( \boldsymbol{E} \) having an interna
resistance \( r \) is connected to an external
resistance \( R \). The potential difference \( V \)
across the resistance \( r \) varies with \( R \) as
shown in the figure by the curves
\( A \cdot A \)
8. \( B \)
\( c \)
D. \( D \)


The ratio of \( p H \) of a solution containing
1 mole of \( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}+\mathbf{1} \) mole of
\( H C l \) per litre and of other solution
containing 1 mole of \( C H_{3} C O O N a+1 \)
mole of acetic acid per litre is:
A \( \cdot p H_{1}: p H_{2}:: 2: 5 \)
B . \( p H_{1}: p H_{2}:: 1: 2 \)
c. \( p H_{1}: p H_{2}:: 2: 3 \)
D. none of these


If the variance of the random variable \( \boldsymbol{X} \)
is \( 4, \) then the variance of the random
variable \( 5 X+10 \) is
A. 100
B. 10
c. 50
D. 25


Find the mode for the following data:
\( \begin{array}{lllll}\text { class } & 0- & 2- & 4- & 6- \\ \text { interval } & 2 & 4 & 6 & 8\end{array} \)
6 Frequency
A . 5.2
в. 5.3
\( c .5 . \)
D. 5.5


The sound waves starts vibrating when
it reaches:
A. pinna
B. stirrup
c. tympanic membrane
D. all


The element \( X \) with electronic
configuration 2,8,8,2 belongs to
A \( \cdot 2^{n d} \) Period
B. \( 3^{r d} \) Period
\( \mathbf{c} \cdot 4^{t h} \) Period
D. \( 5^{\text {th}} \)period


A charge \( Q \) is placed at each of two
opposite corners of a square. A charge \( q \)
is laced at each of the two opposite corners of the square. If the resultant electric field on \( Q \) is zero, then
\( ^{\mathbf{A}} \cdot Q=-\frac{q}{2 \sqrt{2}} \)
в. \( Q=-2 \sqrt{2} q \)
c. \( Q=-2 q \)


The angle between the incident ray and
the emergent ray in a glass prism is called as
A. angle of emergence
B. angle of reflection
c. angle of refraction
D. angle of deviation


Supposing the earth suddenly contracts to half of its radius, what will be the
length of the day?
A. 12 hours
B. 8 hours
c. 6 hours
D. No change


What proportion of the \( f \), generation will be short will wrinkled seeds when
pure tall round plant is crossed with pure dwarf wrinkled seeded plant?
A. None
B. 25\%
c. \( 50 \% \)
D. \( 75 \% \)


A conducting rod is moved with a
constant velocity \( v \) in a magnetic field. A potential difference appears across
the two ends
\( \mathbf{A} \cdot \) if \( \vec{v} \| \vec{l} \)
B. if \( \vec{v} \| \vec{B} \)
c. if \( \vec{l} \mid \vec{B} \)
D. none of these


Which of the following does not possess alpha hydrogen?
A. Acetaldehyde
B. Formaldehyde
c. Acetone
D. Phenyl acetaldehyde


Generally stomata found on the lower surface of leaf. Thus, approximate percentage of transpiration through abaxial surface is
A . 47 \%
в. 57\%
c. 67 \%
D. 97\%


is used as laundry soap.
A. Hard soap
B. Soft soap
\( \mathbf{c} . \) Both \( A \) and \( B \)
D. None of above


Match the list I with list II and choose
the correct option.
\( \begin{array}{ccccc} & \text { List I } & & \text { List II } & \\ \mathrm{A} & \text { Oxytocin } & 1 & \begin{array}{l}\text { Milk ejection } \\ \text { hormone }\end{array} \\ \mathrm{B} & \text { Glucagon } & 2 & \begin{array}{l}\text { Increase in heart } \\ \text { rate }\end{array} \\ \mathrm{C} & \text { Adrenaline } & 3 & \begin{array}{l}\text { Increases blood } \\ \text { glucose }\end{array} \\ \mathrm{D} & \text { Thyroxine } & 4 & \text { Controls BMR }\end{array} \)
\( \mathbf{A} \)
B. A- 2, B-3, C-4,D-1
C. A-3, B- 4, C- 2, D-1
D. A- 4, B- 2, C-1, D-3


If a particle is kept at rest at origin,
another particle starts from (5,0) with a velocity of \( -4 \hat{i}+3 \hat{j} \). Find their
closest distance of approach.
\( A .3 m \)
в. \( 4 m \)
\( c .5 m \)
D. \( 2 m \)


millimeter \( _{--} \) - picometer.
A . \( 10^{9} \)
B. \( 10^{-9} \)
\( c \cdot 10^{8} \)
D. \( 10^{10} \)


Assertion: V-t graph for gas at constant pressure is a straight line passing through origin (t-temperature in Celsius) Reason: volume is directly proportional to temperature (kelvin) at constant
pressure.
\( A \). Both assertion
(A) and reason
(R) are correct and gives the correct explanation
B. Both assertion (A) and reason
(R) are correct but \( R \) doesnt give the correct explanation
c. A is true but R is false
D. A is false but R is true


The emulsifying agent forms an
interfacial film between suspended particles and the medium. The principal
emulsifying agents for \( \boldsymbol{O} / \boldsymbol{W} \) emulsions
are?


When the concentration of \( \boldsymbol{K}^{+} \) across a
cell membrane drops from \( 0.01 M \) to
\( 0.001 M, \) the potential difference across the membrane is:
A . \( 0.0 V \)
B. \( 0.0059 V \)
c. \( 0.059 V \)
D. \( 0.59 V \)


The out put of a dynamo using a split ring commutator is
A . dc
B. ac
c. fluctuating dc
D. half wave rectified da


Imagine a planet having the same density as that of the earth but radius
is three times the radius of the earth. If
acceleration due to gravity on the surface of the earth is \( g \) and that on the said planet is \( g^{\prime} \), then
A \( \cdot g^{\prime}=\frac{g}{9} \)
B . \( g^{\prime}=9 g \)
c. \( g^{\prime}=\frac{g}{27} \)
D. \( g^{\prime}=3 g \)


Which among the following has molecular mass of 36.5 u?
A. Carbon molecules
B. Hydrogen molecules
c. sulphur molecules
D. Hydrochloric acid


Find the rate of interest when the
following are given. Principal \( =\boldsymbol{R} \boldsymbol{s} \boldsymbol{3} \mathbf{5 0} \) Time \( =\frac{\boldsymbol{2} \mathbf{1}}{\mathbf{2}} \) years
\( \boldsymbol{I}=\boldsymbol{R} \boldsymbol{s} \mathbf{1} \mathbf{4 0} \)


If the refractive index of medium \( b \) with
respect to medium \( a \) and that of
medium \( c \) with respect to medium b are given, then the refractive index of a
medium \( c \) with respect to a medium \( a \) can be found by using the relation
\( \boldsymbol{n}_{c a}=\boldsymbol{n}_{b a} \times \ldots \ldots \)
\( \mathbf{A} \cdot n_{d} \)
B. \( n_{a} \)
\( c \cdot n_{a} \)
D. \( n_{b a} \)


Radiations with successful adaptations in case of insects is a result of
A. Genetic divergence
B. Micro-evolution
c. Macro-evolution
D. Mega-evolution


The plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0} \) and the
line \( \frac{x}{1}=\frac{y}{2}=\frac{z}{3} \) are related as
A. Parallel to the plane
B. At right angle to the plane
c. Lies in the plane
D. Meets the plane obliquely


Sketch larynx and explain its function
in your own words:


If a mixture of \( O_{2} \) and \( O_{3} \) is having
\( V_{r m s}=12.92 m / s \) at \( 300 K . \) Calculate
mole percentage of \( O_{2} \) in the mixture.
A. 35 \%
B. 20\%
c. \( 66.67 \% \) \%
D. none of these


A ball falls from a height of \( 10 \mathrm{m} \) on to a horizontal plane. if the coefficient 0
restitution is 0.6. the height to which it
rebounds after 2 collision is
approximate.
\( \mathbf{A} \cdot 2.24 m \)
B. \( 0.47 m \)
\( \mathrm{c} .0 .3 \mathrm{m} \)
D. \( 1.296 \mathrm{m} \)


The equation of the curve whose slope at any point is equal to \( y+2 x \) and
which passes through the origin is


Out of 12000 voters in a constituency, \( 60 \% \) voted. Find the number of people voted in the constituency?


Volume of air breathed in or out during normal breathing is called as
A. Vital capacity
B. Inspiratory reserve volume
c. Expiratory reserve volume
D. Tidal volume


Carry out the following divisions \( -54 l^{4} m^{3} n^{2} \) by \( 9 l^{2} m^{2} n^{2} \)


Assertion
If both functions \( f(t) \) and \( g(t) \) are
continuous on the closed interval \( [\boldsymbol{a}, \boldsymbol{b}] \)
differentiable on the open interval \( (a, b) \)
and \( g^{\prime}(t) \) is not zero on that open
interval, then there exists some \( c \) in
\( (a, b) \) such that \( \frac{f^{\prime}(c)}{g^{\prime}(c)}=\frac{f(b)-f(a)}{g(b)-g(a)} \)
Reason
If \( f(t) \) and \( g(t) \) are continuous and
differntiable in \( [a, b], \) then there exists
some \( c \) in \( (a, b) \) such that \( f^{\prime}(c)= \) \( \frac{\boldsymbol{f}(\boldsymbol{b})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \) and \( \boldsymbol{g}^{\prime}(\boldsymbol{c})=\frac{\boldsymbol{g}(\boldsymbol{b})-\boldsymbol{g}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \)
from Lagrange's mean value theorm.
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


Test the continuity of the function \( f \) at \( \mathbf{x}=\mathbf{0}, \) where
\[
\begin{array}{l}
\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \sin \left(\frac{1}{x}\right) \text { for } \boldsymbol{x} \neq \mathbf{0} \\
\quad=\mathbf{1} \text { for } \boldsymbol{x}=\mathbf{0}
\end{array}
\]


Draw the diagram of a DC dynamo and label the following parts:
a) Split rings
b) Armature coil


A battery of \( 9 V \) is connected in series
with resistors of \( 0.5,0.3,0.4,0.2, \) and 12
How much current would now through the 0.4 resistors?
\( \mathbf{A} \cdot 22.5 A \)
B . \( 2.25 A \)
c. \( 0.67 A \)
D. \( 6.7 A \)


Suppose \( 10^{-17} \) J of light energy is needed by the interior of the human eye to see an object. How many photons of green light \( (\lambda=550 n m) \) are needed to
generate this minimum amount of
energy?


Assertion
Pressure, volume and temperature are
all extensive properties.
Reason
Extensive properties depend upon the
amount and nature of the substance.
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


In the following (unbalanced) reaction:
\( \boldsymbol{I}^{-}+\boldsymbol{O}_{3} \longrightarrow \boldsymbol{O}_{2}+\boldsymbol{I}_{2} \)
What is oxidising agent?
\( A \cdot O_{3} \)
B . \( I^{-} \)
c. None
D. Both


Differentiate w.r.t. \( \boldsymbol{x} \)
\( \boldsymbol{y}=e^{3 x-2} \sin 3 x \)


A beam of incident light rays falls
onto the glass plate. Possible angles for
the reflected and refracted rays are
shown as \( \mathrm{E}, \mathrm{D}, \mathrm{C}, \mathrm{B} \& \mathrm{A} \) in the figure above dentify which of the following best
represents the reflected ray?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
\( E . \)


\( S O_{2} \) reacts with \( C l_{2} \) and water to form
A \( \cdot H_{2} S O_{4} \)
в. \( H C l \)
c. \( H_{2} S O_{4} \) and \( H C l \)
D. None of the above


If the roots of \( a x^{2}-b x-c=0 \) change
by the same quantity, then the expression in \( a, b, c \) that does not
change is
A \( \cdot \frac{b^{2}-4 a c}{a^{2}} \)
в. \( \frac{b-4 c}{a} \)
c. \( \frac{b^{2}+4 a c}{a^{2}} \)
D. none of these


An element has atomic number 17 and
mass number \( 37 . \) There are 17 electrons
outside the nucleus. Find the number of
neutrons in it.
A . 20
B . 21
c. 17
D. 37


The inert form of carbon is:
This question has multiple correct options
A. diamond
B. graphite
c. coal
D. charcoal


The amplitude and time period of a particle of mass \( 0.1 \mathrm{kg} \) executing simple harmonic motion are \( 1 \mathrm{m} \) and \( 6.28 \mathrm{s} \) respectively. Then its (i)angular frequency,
(ii) acceleration at
a displacement of \( 0.5 \mathrm{m} \) are respectively
A \( \cdot 1 \mathrm{rad} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B. 2 rad/s, 1 m/s'
c. \( 0.5 \mathrm{rad} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s}^{2} \)
D. 1 rad/s, \( 1 \mathrm{m} / \mathrm{s}^{2} \)


The surface area of a sphere is \( 616 \mathrm{cm}^{2} \) What is its volume? \( \left[\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
A. \( 1277.33 \mathrm{cm}^{3} \)
В. \( 1437.33 \mathrm{cm}^{3} \)
c. \( 1627.33 \mathrm{cm}^{3} \)
D. \( 1337.33 \mathrm{cm}^{3} \)


For a first order reaction \( \mathbf{A} \rightarrow \mathbf{P}, \) the
temperature (T) dependent rate constant \( (k) \) was found to follow the equation \( \log k=-(2000) \frac{1}{T}+6.0 \) The
pre-exponential factor \( \mathbf{A} \) and the
activation energy \( \mathbf{E}_{\mathbf{a}}, \) respectively, are:
A . \( 1.0 \times 10^{6} \mathrm{s}^{-1} \) and \( 9.2 \mathrm{kJmol}^{-1} \)
В. \( 1.0 \times 10^{6} \mathrm{s}^{-1} \) and \( 16.6 \mathrm{kJmol}^{-1} \)
C. \( 6.0 s^{-1} \) and 16.6 kJmol \( ^{-1} \)
D. \( 1.0 \times 10^{6} \mathrm{s}^{-1} \) and \( 38.3 \mathrm{kJmol}^{-1} \)


A uniformly tapering vessel shown in figure, is filled with liquid of density
\( 900 k g / m^{3} . \) The force that acts on the base of the vessel due to liquid is :
\( A \cdot 3.6 \mathrm{N} \)
в. 7.2
\( c \cdot 9.0 \mathrm{N} \)
D. 12.6


Animals die due to excess of carbon
dioxide gas because it is poisonous.
A. True
B. False


are used in making electric generators and electric motors.
A. electric current
B. magnetes
c. cables
D. all


Blood clotting requires
\( A \cdot N a^{+} \) and \( K^{+} \)
B. \( \mathrm{Na}^{+} \) and prothrombin
C \( \cdot \mathrm{Ca}^{2+} \) and thromboplastin
D. None of the above


Solve: \( \cos ^{7}\left(\sin \frac{4 \pi}{3}\right) \)


Molecular formula of cyclopentane is :
A. \( C_{6} H_{12} \)
в. \( C_{6} H_{14} \)
c. \( C_{5} H_{10} \)
D. \( C_{5} H_{12} \)


limit of BOD prescribed by Central Pollution Control Board for the
discharge of industrial and municipal
waste waters into natural
surface waters, is -
\( A .<3.0 \mathrm{ppm} \)
B. <10 ppm
\( c .<100 \mathrm{ppm} \)
D. < 30 ppm


Check if (2,3) will lie on the graph of \( (y-2 x)=-3, \) without drawing the
graph.


The equation of the line farthest from (-5,-4) belonging to the family of \( \operatorname{lines}(2+\lambda) x+(3 \lambda+1) y+2(2+ \)
\( \lambda)=0, \) where \( \lambda \) is a variable parameter
is
A. \( 3 x+4 y+6=0 \)
в. \( 3 x+4 y+3=0 \)
c. \( 4 x+3 y+3=0 \)
D. \( 4 x+3 y-3=0 \)


A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage strength is nearly:
A . 1\%
B. 3\%
c. \( 10 \% \)
D. 90\%


64 identical spheres of charge \( q \) and capacitance \( C \) each are combined to form a large sphere. The charge and capacitance of the large sphere is:
\( A \cdot 64 q, c \)
B. 169, 4C
\( c \cdot 649,4 c \)
D. \( 169,64 \mathrm{c} \)


A transverse wave is travelling along a string from left to right. The fig. represents the shape of the string (snap-shot) at a given instant. At this instant Which points have maximum
magnitude of velocity

Write sum of those points in the answer


The magnetic flux through a coil is \( 4 x \) \( 10^{-4} W / b / m^{2} \) at time \( t=0 . \) It reduces
to \( 10 \% \) of its original value in 't' seconds.If the induced e.m.f is \( 0.72 m V \) then the time \( t \) is:
\( \mathbf{A} \cdot 0.25 s \)
B. \( 0.05 s \)
c. \( 0.75 s \)
D. \( 1 s \)


Given the relation \( R=\{(1,2),(2,3)\} \) on the set \( \{1,2,3\}, \) the minimum number of ordered pairs which when added to R make it an equivalence relation is
A. 5
B. 6
\( c \cdot 7 \)
\( D \)


toppr
Q Type your quess
of potential difference across it is
3
\( c \)
D


A sealed tank contains water to a height
of \( 11 \mathrm{m} \) and air at 3 atm. Water flower
out from the bottom of a tank through a small hole. The velocity of efflux is \( (g= \)
\( \left.10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 18.1 \mathrm{ms}^{-1} \)
B. 24.2 \( m s^{-1} \)
c. \( 20.4 m s^{-1} \)
D. 28.6 \( m s^{-1} \)


The masses of \( 10 k g \) and \( 20 k g \) respectively are connected by a
massless spring. A force of \( 200 N \) acts
on the \( 20 k g \) mass. At the instant shown
the \( 10 k g \) mass has an acceleration of
\( 12 m s^{-2}, \) what is the acceleration of
\( 20 k g \) mass \( ? \)
A \( \cdot 12 m s^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( 20 m s^{-2} \)


Prove that \( ^{n} \boldsymbol{P}_{r}=^{n-1} \boldsymbol{P}_{r}+\boldsymbol{r} \cdot^{n-1} \boldsymbol{P}_{r-1} \)


The compass needle of the airplane shows that it is heading due North and
speedometer indicates a velocity
\( 240 k m h^{-1} . \) Wind is blowing \( 100 k m h^{-1} \)
due east. Find the velocity of airplane
with respect to earth.
A \( \cdot 260 m s^{-1}, 23^{\circ} \) East of North
B. \( 260 \mathrm{ms}^{-1}, 23^{\circ} \) West of North
\( \mathbf{c} \cdot 260 m s^{-1}, 32^{\circ} \) East of North
D. none of these


Which of the following force balance the electrostatic force of attraction between
the positively and negatively charged particles in Rutherford model?
A. The negatively charge particles repulsion.
B. The high velocity of the electrons moving in circular path
c. The linear movement of the nucleus
D. None of these


List 2 shows five systems in which two objects are labelled as \( X \) and \( Y \). Also in
each case a point \( P \) is shown. List 1 gives some statements about \( X \) and/or \( Y \).
Match these statements to the
a ppropriate system(s) from List 2.


A ray of light denser medium strikes a
rarer medium at an angle of incidence \( i \)
shown in the figure. The reflected and
refracted rays make angle \( 90^{\circ} \) with
each other. The angles of reflection and
refraction are \( r \) and \( r^{\prime} . \) The critical angle
is :
A \( \cdot \sin ^{-1}(\cot r) \)
B \( \cdot \sin ^{-1}(\tan i) \)
c. \( \sin ^{-1}\left(\tan r^{\prime}\right) \)
D \( \cdot \tan ^{-1}(\sin i) \)


If \( a, b, c \) are the sides of a triangle \( A B C \) show that \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq 3 \)


What is the reason for using Tungsten as a filament in electric bulb?


Soaps are sodium salts of fatty acids,
RCOONa; e.g. \( C_{17} H_{35} C O O^{-} N a^{+} . \) It
gives an insoluble precipitate / layer with
A \( \cdot C a^{2+}( \) aq)
B. \( M g^{2+}(\text { aq }) \)
c. HCI (aq)
D. All of these


Assertion
Turbulence is always dissipative.
Reason
High reynold number promotes
turbulence.
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


Carbonic acid \( \left(\boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}\right), \) a diprotic acid
has \( \boldsymbol{K}_{a_{1}}=\mathbf{4 . 0} \times \mathbf{1 0}^{-\mathbf{7}} \) and \( \boldsymbol{K}_{a_{2}}= \)
\( \mathbf{7} . \mathbf{0} \times \mathbf{1 0}^{-11} . \) What is the \( \left[\boldsymbol{H} \boldsymbol{C O}_{\mathbf{3}}^{-}\right] \) of \( \mathbf{a} \)
\( 0.025 \mathrm{M} \) solution of carbonic acid?
A \( .7 .8 \times 10^{-3} \)
B. \( 6.6 \times 10^{-4} \)
c. \( 10^{-10} \)
D. \( 1.0 \times 10^{-4} \)


Rickettsia constitute a group under
A. Bacteria
B. Viruses
C. Independent group between bacteria and viruses
D. Fungi


The value of \( f(2) \) is
\( A \cdot 2 \)
B. 4
\( c .6 \)
D. 8


Calculate the electrical energy
consumed when a current of 4.5
ampere flows through a resistance of 4 ohms for 30 minutes.


5
3
3
8
8


How many unpaired electrons are
present in the Brown Ring complex
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N} \boldsymbol{O})\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)


Short / Long answer type questions. Describe the structure of a lichen, and
name the three different types.What is the nature of this fungal association?


Give the structure of the compound
Phenyl acetaldehyde


In a coil of resistance \( 10 \Omega \), the induced
current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is-


The current I and voltage V graphs for a given metallic wire at two different
temperatures \( T_{1} \) and \( T_{2} \) are shown in
figure.lt is concluded that
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
\( \mathrm{c} \cdot T_{1}=T_{2} \)
D. Nothing can be decided


Under some conditions, a material can be heated above or cooled below the
normal phase change temperature without a phase change occurring. The resulting state :
A. may be stable
B. may be unstable
c. must be stable
D. must be unstable


Which of the following will change the value of the equilibrium constant for the reaction?
\( N_{2}(g)+O_{2}(g) \leftrightharpoons 2 N O(g) \)
A . Add more \( N_{2} \)
B. Increase of pressure
c. Use a smaller reaction vessel
D. Increase the temperature


Q Type your question_ \( \sqrt{0} \)
a uructure
\begin{tabular}{c|cc}
& Characters & Monocot root & Dicot root \\
(i) & Vascular bundle & Polyarch i.e., more than 6 vascular bundles & Diarch to hexarch i.e., \( 2-6 \) vascular bundles \\
(ii) & Cambium & Absent & Present, so secondary growth occurs \\
(iii) & Pith & Poorly developed & Well developed large pith \\
& & Gives rise & \\
(iv) & Activity of pericycle & to secondary roots and cork cambium & Gives rise to lateral roots only \\
\hline
\end{tabular} dentify the incorrect differences and
select the correct option.
A. (i) and (iii)
B. (i) and (iv)
C . (iii) and (iv)
D. (ii) and (iii)


Two points \( A \) and \( B \) are situated at
distance \( x \) and \( 2 x \) respectively from the
nearer pole of a magnet 2cm long. The
ratio of magnetic field at \( A \) and \( B \) is?
A. 4: 1 exactly
B. 4 : 1 approximately
c. 8: 1 exactly
D. 8: 1 approximately


Which term of the G.P. \( 2,2 \sqrt{2}, 4, \dots \)
is 32?


Which compound is solid?
A. \( C O_{2} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot P H_{3} \)
D. \( \operatorname{si} 0_{2} \)


Complete the following sentence A current carrying solenoid behaves like
\( a \)
A. bar magnet
B. resistance
c. inductance
D. none of these


Select the wrong statement
A. Presence of chromogenic substrate gives blue colour colonies if the plasmid in the bacteria does not have an insert
B. Retroviruses in animals have the ability to transform normal cells into cancerous cellsın microinjection, cells are bombarded with high velocity microparticles of gold or tungsten coated with DNA
C. since DNA is a hydrophilic molecule it cannot pass through cell membranes
D. DNA is a negatively charged molecule


In the following figure, \( S \) is any point on
side \( \mathrm{BC} \) of \( \Delta \mathrm{ABC} \Delta \mathrm{ABC} \). Then \( \mathrm{AB}+\mathrm{BC}+\mathrm{CA} \)
२२४S
A. True
B. False


Heart beat becomes faster on
stimulation from
A. Sympathetic nerves and adrenaline
B. Sympathetic and parasymapathetic nerves
C. Parasympathetic nerves and epinephrine
D. Parasympathetic nerves and acetylcholine


70 number of student's height are
measured in cm as shown in the
histogram. How many students have
heights more than \( 180 \mathrm{cm} \)
A. 40
B. 63
\( c \cdot 38 \)
D. 32


Lewis Acids are electron acceptors.
A. True
B. False


To manufacture computer chips, many chemicals, large amounts of water, and energy are required which is harmful to environment. a process is discovered which significantly reduces the quantities of chemicals, energy, and water needed to produce chips. This is an application of:
A. Green chemistry
B. waste management
c. revolution resource recovery
D. Green revolution


The Bohr's radius for the fifth orbit of
the hydrogen atom will be:
A . 0.529 A
B. 2.645 A
C. \( 13.225 \mathrm{A} \)
D. none of above


Acetic acid reacts with \( P C l_{5} \) to form:
A. \( C H_{2} \) ClCOOH
в. \( C H C l_{2} C O O H \)
c. \( C H_{3} C O C l \)
D. \( C H_{3} \) COOCl


Solve \( : \mathbf{5}-\frac{\mathbf{2} \mathbf{d}+\mathbf{7}}{\mathbf{9}}=\mathbf{0} \)
A . 19
B. 14
\( c .9 \)
D.


Which of the following happens with the increase in body temperature due to enhanced metabolic activities in the
human body?
A. Oxyhaemoglobin dissociation curve will shift to right side at tissue level
B. Affinity of haemoglobin for oxygen will increase at tissue leve
C. Sensitivity of chemoreceptors to \( p O_{2} \) increases dramatically white it falls for \( p C O_{2} \& H^{+} \)
D. Bohr's effect will not occur


Find the smallest number by which 64
must be divided so that the result is a
perfect cube.


The ratio of the energy of photon of \( 2000 A^{0} \) wavelength to that of \( 4000 A^{0} \)
wavelength is:
\( A \cdot 1: 4 \)
B. 4: 1
\( c \cdot 1: 2 \)
D. 2:1


Eccentricity of hyperbola \( \frac{\boldsymbol{x}^{2}}{\boldsymbol{k}}-\frac{\boldsymbol{y}^{2}}{\boldsymbol{k}}=\mathbf{1} \)
A \( \cdot \sqrt{1+k} \)
B. \( \sqrt{1-k} \)
\( c \cdot \sqrt{2} \)
\( D \cdot 2 \sqrt{2} \)


Continuous circulation of water from
the earth to the sky and back to the earth is called
A. Precipitation
B. Circulation
c. Water cycle
D. None of these


Explain the double helix structure of DNA with a labelled diagram.


The angle between the dipole moment and electric field at any point on the equatorial plane is :
A \( \cdot 0^{\circ} \)
B. 90
c. \( 180^{\circ} \)
D. \( 45^{\circ} \)


If \( f(x)=x e^{x(1-x)}, \) then \( f(x) \) is
A \( \cdot \) increasing on \( \left[-\frac{1}{2}, 1\right] \)
B. decreasing on R
C. increasing on R
D. decreasing on \( \left[-\frac{1}{2}, 1\right] \)


The tangent at any point \( P(a \cos \theta, b \sin \theta) \) on the ellipse \( \frac{x^{2}}{a^{2}}+ \)
\( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) meets the auxiliary circle at two
point which subtend a right angle at the centre, then eccentricity is
A \( \cdot \frac{1}{\sqrt{1+\sin ^{2} \theta}} \)
в. \( \frac{1}{\sqrt{2-\cos ^{2} \theta}} \)
c. \( \frac{1}{\sqrt{1+\tan 2 \theta}} \)
D. noneofthese


Assertion
\( V_{r m s} \) and \( V_{\text {mean }} \) of gaseous molecules is nearly of the order of velocity of sound.
Reason
The sound travels in air because of
vibrational molecular 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


Light oil fraction can be obtained by following fractional distillation:
A. coal
B. Coke
c. coal tar
D. coal gas


Derive an expression for moment of inertia about its tangent perpendicular to the plane.


Cambium is lateral meristem that
takes part in
A. Internodal growth
B. Axial growth
c. Growth of branches
D. Increasing girth of stem and root


\( \operatorname{Let} \theta \in\left(0, \frac{\pi}{4}\right) \) and \( t_{1}=(\tan \theta)^{\tan \theta}, t_{2}= \)
\( (\tan \theta)^{\cot \theta}, t_{3}=(\cot \theta)^{\tan \theta} \operatorname{then} t_{4}= \)
\( (\cot \theta)^{\cot \theta}, \) then
A \( \cdot t_{1}<t_{2}<t_{1}<t_{4} \)
В \( \cdot t_{2}>t_{1}>t_{3}>t_{4} \)
c. \( t_{3}>t_{1}>t_{2}>t_{4} \)
D. \( t_{2}>t_{3}>t_{1}>t_{4} \)


Two large vertical and parallel metal plates having a separation of \( 1 \mathrm{cm} \) are
connected to a DC voltage source of potential difference \( X . \) A proton is released at rest midway between the two plates. It remains at rest in the air then \( X \) is:
A \( \cdot 1 \times 10^{-5} V \)
В. \( 1 \times 10^{-7} V \)
c. \( 1 \times 10^{-9} V \)
D. \( 1 \times 10^{-10} V \)


\( 40 m l \) of ammonia gas, taken in an
audiometer tube, was subjected to
sparks till the volume did not further
change. The volume was found to
increase by 40 ml. 40 ml of oxygen gas
then mixed and the mixture was further
exploded. The gases remained were 30 ml. Deduce the formula of ammonia.
(Ammonia contain \( N \) and \( H \) only).


Inflorescence in Solanaceae is
A. Racemose
B. Cymose
c. Hypanthodium
D. verticillaster


Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{3} \cot ^{3} \boldsymbol{x}-\cot \boldsymbol{x}+ \)
\( \int \cot ^{4} x d x \) and \( f\left(\frac{\pi}{2}\right)=\frac{\pi}{2}, \) then
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \mathbf{A} \cdot \pi-x \)
B. \( x-\pi \)
c. \( \frac{\pi}{2}-x \)
D. \( x \)


Distinguish between the saturated and unsaturated solution using the data given below:
a) 16 g \( N a C l \) in 100 g water.
b) 36 g \( N a C l \) in 100 g water (Note - Solubility of \( N a C l \) is \( 36 g \) )


A solution is a homogeneous mixture of two or more substances. Which of the
following is a solution?
A . Milk
B. Smoke
c. Brass
D. Face Cream


Primary roots and its branches constitutes to
B. Tap root system
c. Fibrous roots
D. Seminal roots


A player throws a ball vertically upwards. The ball attains a height of
\( 25 m \) and returns back. Find the initial
speed of the ball.


Factorize the following expressions:
\( \mathbf{5} a^{2}+35 a \)


Dispersion of light is caused due to
A. intensity of light
B. density of medium
c. wavelength
D. none of the above


In the given reaction, \( [\boldsymbol{X}] \) and \( [\boldsymbol{Y}] \) are:
4
and
в.
and
\( c \)
\( D \)


There photo dlodes \( D_{1}, D_{2} \) and \( D_{3} \) are made of semiconductor having band
\( \operatorname{gap} 2.5 e V, 2 e V \) and \( 3 e V \) respectively. Which one will be able to detect light of
wavelength \( 6000 A^{\circ} ? \)
A. \( D_{1} \)
в. \( D_{2} \)
\( c \cdot D_{3} \)
D. \( D_{1} \) and \( D_{2} \) both


Ionic reactions are
A . fast
B. slow
c. very slow
D. medium


Which of the following is an insecticide?
A. Bakelite
B. Aspirin
c. DDT
D. TNT


Simplify the expression \( \left(2 x^{4}-5 x^{4}\right)^{2} \)
and choose the correct option.
A . \( -21 x^{8} \)
В. \( -6 x^{8} \)
\( \mathrm{c} \cdot 9 x^{8} \)
D. \( 9 x^{16} \)


Which of the following shows configurational isomerism?
A. Diethyldimethylammonium iodide
B. Dimethylpropylamine
c. Methylethylpropyl ammonium bromide
D. None of these


If the distance between two unlike poles is doubled then the force of attraction
between them becomes
times its original value.
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot 2 \)
D. 4


A point \( A \) is \( 26 c m \) away from the centre
of a circle and the length of tangent
drawn from \( A \) to the circle is 24 cm. Find
the radius of the circle.
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 15 \mathrm{cm} \)


The chemical formula for copper pyrites is :
A. \( C u F e S_{2} \)
в. \( C u_{2} S \)
\( \mathbf{c} \cdot C u_{2} O \)
D. \( C u C O_{3} \cdot C u(O H)_{2} \)


Hormone that maintains the blood
glucose level within the limit is:
A. thyroxine
B. insulin
c. testosterone
D. epinephrine


A disaccharide, on hydrolysis, gives:
A. two molecules of the same monosaccharide
B. one molecule each of the same monosaccharide
C. three molecules of the same monosaccharide
D. two molecules of the same or one molecule each of
two different monosaccharides


prove that:
\( \frac{\sin 5 x-2 \sin 3 x+\sin x}{\cos 5 x-\cos x}=\tan x \)


The graph between \( |\Psi|^{2} \) and \( r( \) radial
distance) is shown below. This
represents:
A . 3s orbital
B. 1s orbital
c. 2p orbital
D. 2s orbital


If a star can convert all the He nuclei
completely into oxygen nuclei, the energy released per oxygen nuclei is:
[Mass of \( H e \) nucleus is \( 4.0026 a m u \) and
mass of oxygen nucleus is \( 15.9994 a m u \)
A. \( 7.6 \mathrm{MeV} \)
B. 56.12 MeV
c. \( 10.24 \mathrm{MeV} \)
D. \( 23.9 \mathrm{MeV} \)


Given \( M=(0,1,2) \) and \( N=(1,2,3) \)
Find \( (\boldsymbol{N}-\boldsymbol{M}) \times(\boldsymbol{N} \cap \boldsymbol{M}) \)
\( A \cdot\{(3,1),(3,2)) \)
B. \{(3,-1),(3,-2)
c. \{(-3,-1),(-3,2)\}
\( \mathbf{D} \cdot\{(3,-1),(-3,-2)\} \)


In animals, mitotic cell division is only
seen in?
A. Haploid somatic cells
B. Diploid somatic cells
c. Diploid meiocytes
D. 1 and 3


An organic compound whose empirical and molecular formula are same.
Contains \( 20 \% \) carbon, \( 6.7 \% \) hydrogen,
\( 46.7 \% \) nitrogen, and the rest oxygen on
heating it yields ammonia, leaving a solid residue. The solid residue gives a violet colour with dilute solution of
alkaline copper sulphate the organic compound is
\( \mathbf{A} \cdot N H_{2} C O O N H_{4} \)
B . \( C H_{3} C O O N H_{4} \)
\( \mathbf{c} \cdot N H_{2} N H C H O \)
D. \( H C O O N H_{4} \)
E \( . N H_{2} C O N H_{2} \)


Essential constituents of plants and
animal tissues are :
A. N and P
B. \( N \) and As
c. cu and \( \mathrm{Mg} \)
D. Ca and Mg


Which of the following is/are incorrectly
named?
This question has multiple correct options
\( \mathbf{A} \)
\( B \)
\( c \)
2-Methyl cycloheptene
\( D \)
cyclohexen


The force of friction is
normal reaction between the surfaces.
A. Inversely propotional to
B. directly propotional to
c. propotional to the square of
D. independent of


What is the distance travelled by sound in air when a tuning fork of frequency \( 256 H z \) completes 25 vibrations? The
speed of sound in air is \( 343 m s^{-1} \)


Aqueous solution of borax is :
A. neutral
B. amphoteric
c. basic
D. acidic


\( \frac{\mathbf{3} \boldsymbol{x}^{2}+\mathbf{5}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)^{2}}=\frac{\boldsymbol{A}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)}+\frac{\boldsymbol{B}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)^{2}} \Rightarrow \)
\( (A, B)= \)
A \( .(2,3) \)
в. (3,2)
c. (2,-3)
D. (-2,3)


In terms of polar character which one of
the following orders is correct?
\( \mathbf{A} \cdot H_{2} S<N H_{3}<H_{2} O<H F \)
B. \( H_{2} S<N H_{3}<H_{2} S<H F \)
\( \mathbf{c} \cdot H F>H_{2} O<N H_{3}<H_{2} S \)
\( \mathbf{D} \cdot N H_{3}<H_{2} O<H F<H_{2} S \)


The figure shows a capacitor having three layers of equal thickness and same area as that of plate. the layer
first is vaccum, second is conductor
and third is dielectric of dielectric
constant \( K . \) The ratio of energy stored
in region three to total energy stored in capacitor three is :
A \( \cdot \frac{1}{K+1} \)
в. \( \frac{3}{K+1} \)
\( c \cdot \frac{4}{K+3} \)
D. \( \frac{4}{K+1} \)


A person in a vehicle is moving away from a vertical mountain with uniform
velocity. When the vehicle is at a distance \( 975 \mathrm{m} \) from mountain, the person blows a horn and hears its echo after 6 s. If velocity of sound in air is 340
\( \mathrm{ms}^{-1}, \) the velocity of the vehicle is :
A. 36 kmph
B. 54 kmph
c. 72 kmph
D. 90 kmph


Which among the following is not the
property of ideal gas?
A. It consists of a large number of identical molecules.
B. They do not obeys Newtons law of motion.
C. The volume occupied by the molecules themselves is negligible compared to the volume occupied by the gases
D. They obeys Newtons law of motion.


Number of water molecules in one litre
of pure water is :
A. \( 6.023 \times 10^{23} \)
3 \( 3.02 \times 10^{3} \times 10^{-63} \)
B. \( 3.45 \times 10^{25} \)
c. \( 55.4 \times 10^{23} \)
D. \( 18 \times 10^{23} \)


One of the resonating structure of \( \boldsymbol{S O}_{4}^{-2} \)
is as shown.

Which set formal charge on oxygen and
bond order is correct?
A. -0.5 and 1.5
B. 1.5 and 3
C. 2 and 3
D. 1.5 and 1.5


A storage battery has e.m.f. 15 volt and internal resistance 0.05 ohm. Its terminal
voltage when it is delivering 10 ampere is:
A. 30 volt
B. 1.00 volt
c. 14.5 volt
D. 15.5 volt


If \( \tan ^{-1} y=4 \tan ^{-1} x, \) then \( \frac{1}{y} \) is zero for
A \( . x=1 \pm \sqrt{2} \)
B. \( x=\sqrt{2} \pm \sqrt{3} \)
c. \( x=3 \pm 2 \sqrt{2} \)
D. all value of \( x \)


Most abundant element in the earth's
crust is:
A. Hydrogen
B. Oxygen
c. Aluminium
D. silicon


The charge is negative, then the electric lines of forces are
A. straight lines converging towards the charge
B. concentric circle with charge at the centre
c. straight lines radiating away from the charge
D. Non of these


Which line shows the path of gamma
radiation in a magnetic field?
\( A \)
B.
\( c \)
0.0
\( E \)


The electronegativity of fluorine
obtained from the following data is \( x \) \( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{H}}=\mathbf{1 0 4} . \boldsymbol{2} \boldsymbol{k} \boldsymbol{c} \boldsymbol{n} \boldsymbol{m} \boldsymbol{l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{F}-\boldsymbol{F}}=\mathbf{3 6 . 6} \) kcal \( \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{F}}=\mathbf{1 3 4 . 6} \boldsymbol{k c a l} \boldsymbol{m o l}^{-1} \)
Electronegativity of hydrogen \( =2.1 \)
Find the value of \( x \) to the nearest
integer.


Three charger \( q . Q \) and \( 4 q \) are placed in
a straight, line of length \( L \) at points
distant \( 0, L / 2 \) and \( L \) respectively from one end in other to make the net force
on \( q \) zero the charge \( Q \) must be eqyal to:
A. \( -q \)
в. \( 2 q \)
c. \( -\frac{q}{2} \)
D. \( q \)


A quadrilateral whose all sides are equal and has four right angles is called
\( a \)
A. rectangle
B. rhombus
c. kite
D. square


An electron with K.E. \( 6 e V \) is incident on
a hydrogen atom in its ground state.The collision:
A. must be elastic
B. may be partially elastic
c. must be completly inelastic
D. may be partially inelastic


A small metal ball of mass ' \( m \) ' is
dropped in a liquid contained in a
vessel, attains a terminal velocity ' \( V \) '. If a metal ball of same material but of
mass \( ^{\prime} 8 m^{\prime} \) is dropped in same liquid then the terminal velocity will be.
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. 8V


A particle moves in a straight line in such a way that its velocity at any point is given by \( v^{2}=2-3 x, \) where \( x \) is
measured from a fixed point. The acceleration is
A. uniform
B. zero
c. non-uniform
D. indeterminate


Acetic acid is a weak acid.
A. True
B. False


A voltmeter reads \( 4 V \) when connected
to a parallel plate capacitor with air as a dielectric. When a dielectric slab is
introduced between plates for the same configuration, voltmeter reads \( 2 V \) What is the dielectric constant of the
material?
A . 0.5
B. 2
c. 8
D. 10


There are \( n \) AM's between \( 1 \& 31 \) such
that \( 7 t h \) mean: \( (n-1)^{t h} \) mean \( =5: 9 \)
then find the value of \( n \)


In mammals, Haversian canals are
connected with each other by transverse canals, which are called as
A. Semicircular canals
B. Volkmann canals
c. Inguinal canals
D. Bidder's canals


Solve
\( \lim _{x \rightarrow 0}\left(\frac{1^{x}+2^{x}+3^{x}+\ldots+n^{x}}{n}\right)^{1 / 2}= \)


-I contains 3 red and 4 black balls Bag
while another Bag -ll contains 5 red and 6 black b alls. One ball is drawn at
random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag -II.


If repeated measurements give values close to one another, the number is:
A. surely precise
B. surely accurate
c. surly precise and accurate
D. all of these are correct


The most suitable electrolyte for the coagulation of arsenic sulphide will be :
A. \( A l C l_{3} \)
в. \( B a C l_{2} \)
c. \( N a C l \)
D. KCl


Interspecific resource competition is shown by one of the pair of organisms
A. Hare and rat
B. Rat and beetle
c. Hawk and tree
D. Deer and hare
E. Hawk and hare


Assertion
Cotton is a polymer.
Reason
A polymer is a very big molecule made
of many small repeating units of
compounds called monomers.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A man wears socks of two colours -
Black and brown. He has altogether 20
black socks and 20 brown socks in a
drawer. Supposing he has to take out of the socks in the dark, how many must
he take out to be sure that he has a
matching pair?
A . 3
B . 20
\( c .39 \)
D. None of these


Two cars \( A \) and \( B \) are at rest at same
point initially. If \( A \) starts with a uniform velocity of \( 40 \mathrm{m} / \mathrm{sec} \) and \( \mathrm{B} \) starts in the same direction with a constant
acceleration of \( 4 m / s^{2}, \) then \( B \) will
catch \( A \) after how much time?
A . 10 sec
B. 20 sec
c. 30 sec
D. 35 sec


2.0 mole of \( P C l_{5} \) were introduced in a
vessel of 5.0 L capacity of a particular
temperature. At equilibrium, \( P C l_{5} \) was
found to be \( 35 \% \) dissociated into \( P C l_{3} \)
and \( C l_{2} . \) The value of \( K_{c} \) for the
reaction:-
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \)
A. 0.075
B. 0.377
\( c \cdot 1.33 \)
D. 13.3


Assertion
Thigh muscles can get tired but not the muscles of ventricle of heart.
Reason
Muscles of thigh are voluntary whereas that of heart are involuntary muscles.
A. If both the assertion and the reason are true and the reason is correct explanation of the assertion.
B. If both the assertion and the reason are true but the reason is not correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


When the margins of sepals or petals overlap one another without any particular direction the condition is
termed as
A. Imbricate
B. Twisted
c. valvate
D. Vexillary


For the reaction:
\( \mathbf{2} N \boldsymbol{O}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{(g)}+\boldsymbol{O}_{2(g)},\left(\boldsymbol{K}_{c}=\right. \)
\( \left.1.8 \times 10^{-6} \text {at } 184^{\circ} C\right)(R= \)
\( \mathbf{0 . 0 8 2} \)Latm\( /(\text {mol. } \boldsymbol{K}) \)
When \( K_{p} \) and \( K_{c} \) are compared at
\( 184^{\circ} \mathrm{C}, \) it is found that
A. Whether \( K_{p} \) is greater than, less than or equal to \( K_{c} \) depends upon the total gas pressure
в. \( K_{p}=K_{c} \)
c. \( K_{p} \) is less than \( K_{c} \)
D. \( K_{p} \) is greater than \( K_{c} \)


A direct-vision prism is made out of
three prisms, each with a refracting
angle of \( \phi=60^{\circ}, \) attached to each other
as shown in Fig. Light of a certain
wavelength is incident on the first
prism. The angle of incidence is \( 30^{\circ} \) and
the ray leaves the third prism parallel to
the direction of incidence. The refractive
index of the glass of the first and third
prisms is \( 1.5 . \) Find the refractive index of the material of the middle prism.
\( (\sqrt{6}=2.45) \)


If the cost of \( 93 \mathrm{m} \) of a certain kind of
plastic sheet is Rs \( 1395, \) then what would it cost to buy \( 105 \mathrm{m} \) of such plastic sheet?


Slaked lime is obtained when water is
added to:
A \( \cdot \operatorname{CaSO}_{4} \cdot \frac{1}{2} \mathrm{H}_{2} \mathrm{O} \)
в. \( C a C l_{2} \)
\( c \cdot C a O \)
D. \( C a C O_{3} \)


If the first order reaction involves
gaseous reactant and gaseous products the units of its rate are:
A . atm
B. \( a t m-s e c \)
c. \( a t m-s e c^{-1} \)
D. \( a t m^{2}-s e c^{2} \)


The electrostatic force between two
point charges \( q_{1} \) and \( q_{2} \) at separation ' \( r^{\prime} \) is given by \( F=\frac{K q_{1} q_{2}}{r^{2}} . \) The constant \( K \)
A. depends on the system of units only
B. depends on the medium between the charges only.
c. depends on both the system of units and the medium between the charges.
D. is independent of both the system of units and the medium between the charges


Solve the following system of equations by the method of substitution:
\( 3 x-7 y=7,11 x+5 y=87 \)


A ball is thrown vertically up with a velocity of \( 14.7 m / s \) from the top of a
tower of height \( 49 \mathrm{m} . \) On its return, it misses the tower and finally strikes the ground. The time that elapsed from the instant the ball was thrown until it
passes the edge of the tower is
A . \( 1.5 s \)
B . \( 3 s \)
\( c \cdot 6 s \)
D. \( 0.5 s \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{1-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}\right)= \)
A \( \cdot \frac{2}{1+x^{2}} \)
B \( \cdot \frac{-1}{1+x^{2}} \)
c. \( \frac{1}{1+x^{2}} \)
D. \( \frac{-2}{1+x^{2}} \)


A ball of mass \( \mathrm{m} \) is dropped on to a floor from certain height, collision is perfectly elastic and the ball rebounds
to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.
A. mg
B. > mg
\( \mathrm{c} \cdot<\mathrm{mg} \)
D. none of these


In a class, there are 18 girls and 16 boys. The class teacher wants to choose
one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What
is the probability that the name written on the card is:
(i) the name of a girl
(ii) the name of a
boy


The nitrogen containing compound
produced in the reaction of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) with
\( P_{4} O_{10} \) is :
This question has multiple correct options
A . can also be prepared by reaction of \( P_{4} \) and \( H N O_{3} \)
B. is diamagnetic
c. contains one \( N-N \) bond
D. reacts with \( N a \) metal producing a brown gas


Which of the following is the regulatory protein of a muscle?
A. Tubulin
B. Myosin
c. Tropomyosin
D. All of the above


Na Cl is an ionic compound. How is an ionic bond is formed in \( N a C l ? \)


Describe the events taking place during
interphase. What is the Go (quiescent phase) cell cycle?


Write an expression of magnetic flux density 'B' at a point in end-on position or an axial position of a magnetic dipole. (Derivation not required.)


A square plate is of mass \( M \) and length
of the edge is 2a. Its Moment of inertia
about its centre of mass axis,
perpendicular to its plane is equal to \( l_{0} \)
Four identical disks are cut from the
plane. Find the Moment of inertia of
leftover square about the same axis.


Pollution can be controlled by:
A. Sewage treatment
B. Manufacturing electrically operated vehicles
C. By checking atomic blasts
D. All of the above


Explain why fossil fuels are exhaustible
natural resources.


When a thin convex lens is put in
contact with a thin concave lens of the
same focal length, the resultant combination has focal length equal to:
A \( \cdot \frac{f}{2} \)
в. \( 2 f \)
c. zero
D. \( \infty \)


\( 10.0 g m s \) of \( C a C O_{3} \) on heating gave
\( 4.4 g m s \) of \( C O_{2} \) and \( 5.6 g m s \) of \( C a O \) This observation is in agreement with
the:
A. law of constant composition
B. law of multiple proportion
c. law of reciprocal proportion
D. law of conservation of mass


The correctly reported answer of the addition of 4.523,2.3 and 6.24 will have significant figures:
A. Two
B. Three
c. Four
D. Five


A cuboid is \( 3 \mathrm{cm} \) high, \( 4 \mathrm{cm} \) wide and 5 cm long. What is its volume?
\( \mathbf{A} \cdot 60 \mathrm{cm}^{3} \)
B. \( 50 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 150 \mathrm{cm}^{3} \)
D. \( 100 \mathrm{cm}^{3} \)


The sum of two numbers is 6 times
their geometric mean show that numbers are in the ratio \( (3+2 \sqrt{2}): \) \( (3-2 \sqrt{2}) \)


A body cell of an organism has 8 chromosomes. Which describes the
chromosome composition of one of the body cells after interphase?
A. Sixteen chromosomes made up of 16 chromatids
B. Sixteen chromosomes made up of 8 chromatids
c. Eight chromosomes made up of 8 chromatids
D. Eight chromosomes made up of 16 chromatids
E. Four chromosomes made up of 8 chromatids


What type of isomerism is exhibited the
\( \operatorname{complex}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)


A satellite of mass \( 1000 k g \) is supposed
to orbit the earth at a height of \( 2000 k m \)
above the earth's surface. Find the
potential energy of the earth-satellite
system.


If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to
corresponding segments of the other chord.


Find inverse of the matrix
\( \left[\begin{array}{ccc}1 & -1 & 1 \\ 0 & 1 & 1 \\ 3 & 2 & -4\end{array}\right] \) by elementary
transformation.


Consider a hemispherical surface of
radius \( r, \) a positive point charge \( q \) is kept at the centre of hemisphere. The electric flux through this hemisphere is
A . zero
в. \( \frac{q}{\varepsilon_{0}} \)
c. \( \frac{q}{2 \varepsilon_{0}} \)
D. \( \frac{2 q}{\varepsilon_{0}} \)


Hydraulic press works on the principle of Pascal's principle
A . True
B. False


For a positive integer \( n \) \( (1-i)^{n}\left(1-\frac{1}{i}\right)^{n}=k^{n}, \) find the value
of \( k \)


On the heating curve diagram the
section representing liquid only is
\( A \cdot P Q \)
B. QR
c. RS
D. st


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} \) and
\( \boldsymbol{g}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\max \{f(t)\}, \quad 0 \leq t \leq x \quad 0 \leq x \leq 1 \\ 3-x, \quad 1<x \leq 2\end{array}\right. \)
Then in the interval \( [0,2], g(x) \) is
This question has multiple correct options
A. Continuous for all \( x \)
B. Differentiable for all \( x \)
c. Discontinuous at \( x=1 \)
D. Not differentiable at \( x=1 \)


Which of the following sets belongs to the same class of algae?
A. Chara, Fucus, Polysiphonia
B. Volvox, Spirogyra, Chlamydomonas
c. Porphyra, Ectocarpus, Ulothrix
D. Sargassum, Laminaria, Gracilaria


The drift velocity of electrons in silver
wire with cross-sectional area \( 3.14 \times \)
\( 10^{-6} m^{2} \) carrying a current of \( 20 A \) is.
Given atomic weight of \( \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8} \)
density of silver \( =10.5 \times 10^{3} k g / m^{3} \)
A . \( 2.798 \times 10^{-4} \mathrm{m} / \mathrm{sec} \)
в. \( 67.98 \times 10^{-4} \mathrm{m} / \mathrm{sec} \)
c. \( 0.67 \times 10^{-4} \mathrm{m} / \mathrm{sec} \)
D. \( 6.798 \times 10^{-4} \mathrm{m} / \mathrm{sec} \)


The IUPAC name of the following compound is dodec\( -10-e n-4- \)
\( \boldsymbol{y} \boldsymbol{n}-\boldsymbol{3}, \boldsymbol{8}-\boldsymbol{d} \boldsymbol{i} \boldsymbol{o l} \)
A . True
B. False


A thin spherical conduction shell of radius R has a charge q. another charge \( \mathrm{Q} \) is placed atthe centre of the shell. The electrostatic potential at a point \( \mathrm{P} \) at a distance \( \mathrm{R} / 2 \) from thecentre of the shell is
A \( \cdot \frac{2 Q}{4 \pi \varepsilon_{0} \mathrm{R}} \)
в. \( \frac{2 Q}{4 \pi \epsilon_{0} \mathrm{R}}-\frac{2 \mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{R}} \)
c. \( \frac{2 \mathrm{Q}}{4 \pi \epsilon_{6} \mathrm{R}}+\frac{\mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{R}} \)
D. \( \frac{(\mathrm{q}+\mathrm{Q})}{4 \pi \varepsilon_{0}} \frac{2}{\mathrm{R}} \)


Part of alimentary canal meant for reabsorption of water from chyle is
A. Small intestine
B. Colon
c. Large intestine
D. Rectum


Which of the following compound is expected to be coloured?
A. \( A g_{2} S O_{4} \)
в. \( C u F_{2} \)
c. \( M g F_{2} \)
D. cucl


State True or False.
The five rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \) are \( \frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30} \)
A. True
B. False


For any two events \( A \) and \( B \) in a sample
space:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A / B) \geq \frac{P(A) P(B)-1}{P(B)} P(B) \neq 0 \) is always true
B \( \cdot P(A \cap \bar{B})=P(A)-P(A \cap B) \), does not hold
\( \mathbf{c} \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}), \) if \( A \) and \( B \) are independent
D \( \cdot P(A \cup B)=1=P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint.


What is Kohlrausch's law?


How is chlorine prepared in Deacon's
process?


Which of the following compounds undergo nucleophilic substitution
reactions?
A. Isopropyl chloride
B. Ethyl bromide
c. Benzyl chloride
D. vinyl chloride


The solution of \( y^{\prime}-y=1, y(0)=1, \) is given by \( y(x)= \)
\( A \cdot-\exp (x) \)
B. \( -\exp (-x) \)
\( c \cdot 1 \)
D. \( 2 \exp (x)-1 \)


The IUPAC name for methyl acetate is :
A. ethoxymethane
B. Methyl ethanoate
c. ethylmethanoate
D. methoxy ethane


The azeotropic solutions of two
miscible liquids:
A. can be separated by simple distillation
B. are supersaturated solutions
C. behave like a single component and boil at a constant temperature
D. none of the above


A heater coil operates at \( 1200 v \) when
connected to a \( 240 W \) supply.The
resistivity and area of across section of the coil are :
A \( \cdot A=\frac{\rho l}{7000} \)
в. \( A=\frac{\rho l}{8000} \)
c. \( _{A}=\frac{\rho l}{6000} \)
D. \( _{A}=\frac{\rho l}{600} \)