An inelastic ball is dropped from a height of \( 100 \mathrm{cm} . \) Due to collision with the earth \( 20 \% \) of its energy is lost. To what height will the ball rise?
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


If \( \boldsymbol{A}(\mathbf{0}, \mathbf{3}), \boldsymbol{B}(\mathbf{0}, \mathbf{0}), \boldsymbol{C}(\mathbf{4} . \mathbf{0}) \) be the
vertices of a triangle. Then the triangle is
A. isosceles
B. equilateral
c. right angled
D. none of these


The common oxidation state for sulphur
is :
\( A \cdot+4 \)
B. +6
c. both a and \( b \)
D. none of these


State whether given statement is True or False

Sound waves travel faster in air than in
water
A. True
B. False


The sphere of living matter together with water, air and soil on the surface of
earth is called as
A. Lithosphere
B. Biosphere
c. Hydrosphere
D. Atmosphere


An atom of radium combines with two
atoms of chlorine to form RaCl
molecule. The radioactivity of \( \boldsymbol{R} \boldsymbol{a} \boldsymbol{C l}_{2} \)
will be :
A. zero
B. one-half of the same quantity of Ra
C. one-third of the same quantity of Ra
D. as much as that of the same quantity of Ra


When n-butane is heated in the
presence of \( A l C l_{3} / H C l \) it will be converted into :
A. ethane
B. propane
c. butene
D. isobutane


Assertion
Montreal protocol, was signed at Montreal (Canada) in 1987 to control the
emission of ozone depleting substances.
Reason
Kyoto protocol, held in kyoto (Japan) in
\( 1997, \) has specified the commitments of
different countries to mitigate climate
change.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following cannot be considered as a decomposer?
A. Fungi
B. Bacteria
c. Hyenas
D. Earthworms
E. Dung beetles


Match the following
\( \mathbf{A} \)
(i) \( -a,(i i)-b,(i i i)-c,(i v) d \)
B. (i) \( -b,(i i)-c,(i i i)-a,(i v)-d \)
C. (i) - b, (ii) - a, (iii) - d, (iv) c
D. (i) - d, (ii) - c, (iii) - b, (iv) - a


Match list I with list II and select the
correct answer using the codes given
below the lists.
List - I List- 1
1.
Heavy
water
2. Temporary
hard
water
\( A \)
Bicarbonates of
\( M g \) and \( C a \) in
water
B. No foreign ions in
water
3. Softwater
permanent
hard
water
\( A \cdot 1-C, 2-D, 3-B, 4-A \)
B. \( 1- \) B, \( 2-A, 3-C, 4-D \)
\( c \cdot 1-B, 2-D, 3-C, 4-A \)
D. \( 1-C, 2-A, 3-B, 4-C \)


Calculate the amount of heat required
to convert 100 g of ice at \( 0^{\circ} \mathrm{C} \) into the
water at \( 0^{\circ} \mathrm{C}: \) Given:Specific latent heat of fusion of ice \( =336 J / g \)
A. 33600
B. 3360 J
c. 67200
D. 6720 J


What coefficient is needed for fluorine
to balance the following equation? \( \boldsymbol{L} \boldsymbol{i}+\boldsymbol{F}_{2} \rightarrow \boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


The diagram below shows part of the \( \operatorname{graph} \) of \( y=\frac{b-x}{c x+d} \)
The \( x \) intercept is (6,0)
The vertical asymptote is \( \boldsymbol{x}=-3 \)
The horizontal asymptote is \( y=-1 \)
Find the value of \( \boldsymbol{d} \)


In radioactive isotope of hydrogen, 2
neutrons are present.
A. True
B. False


Calculate the \( \mathrm{pH} \) of \( 10^{-8} \mathrm{M} \mathrm{HCl} \)
\( A \cdot 8 \)
B. 6
\( c \cdot 7 \)
D. 6.98


Arjun wants to invest Rs 15,000 in two types of bonds. He earns \( 12 \% \) in the first type and \( 15 \% \) in the second. His
investment in \( 15 \% \) bond, if he has a total earning of Rs \( 1,950, \) is
A. Rs 10,000
B. Rs 5,000
c. \( R s 6,000 \)
D. Rs 7,000


A light rigid rod of length \( \boldsymbol{L}=\frac{8}{5} \mathrm{m} \)
hinged at one end has a bob of mass \( \mathrm{m} \)
attached to its other end. Find speed (in
\( \mathrm{m} / \mathrm{s} \) ) of bob at the lowest point when rod is released from vertical position.


Which of the following is exonephric nephridia?
A. Pharyngeal nephridia
B. Septal nephridia
c. Integumentary nephridia
D. Integumentary and pharyngeal nephiridia


A convex lens of focal length \( 15 \mathrm{cm} \) is placed in front of a plane mirror at a distance \( 25 \mathrm{cm} \) from the mirror. Where
on the optical axis and from the centre of the lens should be small object be placed such that the final image coincides with the object?
A. \( 15 \mathrm{cm} \) and on the opposite side of the mirror
B. \( 15 \mathrm{cm} \) and between the mirror and the lens
c. \( 7.5 \mathrm{cm} \) and on the opposite side of the mirror
D. \( 7.5 \mathrm{cm} \) and between the mirror and the lens


A body of weight \( W_{1} \) is suspended from
the celling of a room through a chain of
weight \( W_{2} \) The earth pulls the chain by a force equal to:
\( A \cdot W_{2} \)
B. \( \left(W_{1}+W_{2}\right) / 2 \)
\( \mathbf{c} \cdot\left(W_{1}+W_{2}\right) \)
D. \( W_{1} \times W_{2} \)


Basophilic prokaryotes
A. Grow and multiply in very deep marine sediments
B. Occur in wawter containing high concentrations of barium hydroxide
C. Readily grow and divide in sea water enriched in any soluble salt of barium
D. Grow slowly in highly alkaline frozen lakes at high altitiudes


Different minerals are being mined from within the earth and multi-
storeyed are being constructed. Due to this activity theoretically
A. Angular speed of earth would increase
B. Angular momentum would increase
c. Time period of earth would decrease
D. Length of day would increase


Fresh milk has a pH of 6. Explain why the pH changes as it turns into curd?


The biotic components of an ecosystem includes
A. Producers, consumers and decomposers
B. Producers and consumers
c. Producers only
D. Consumers only


Among ( A or B ) which follows a \( \boldsymbol{S} \boldsymbol{N}_{\mathbf{1}} \)
mechanism?
A. \( \left(C H_{3}\right)_{3} C C l \) or
B. \( \boldsymbol{C H}_{3} \boldsymbol{C l} \)
[Give your answer in terms of A or B]


\( \sin x \frac{d y}{d x}+3 y=\cos x, \) solving it gives
\( \left(\frac{1}{3}+y\right) \tan ^{k} \frac{x}{2}=c+2 \tan \frac{x}{2}-x \)
find k?
\( A \)
B. 2
\( c \cdot 5 \)
\( D \)


\( \frac{2 x+5}{3}=3 x-10 \)


\( \mathbf{f} \mathbf{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}=-\mathbf{2} \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{b}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{c}^{2} \boldsymbol{x}\end{array}\right| \)
Then, \( f(x) \) is a polynomial of degree
A .2
B. 3
\( c .4 \)
\( D \)


The amount of charge required in Faraday to get \( 40 g A l \) from almuna by electrolysis
A \( \cdot \frac{50}{3} \)
в. \( \frac{40}{3} \)
c. \( \frac{40}{9} \)
D. \( \frac{50}{9} \)


Assertion: Dry cell is a primary cell and
lead storage cell is a secondary cell Reason: A primary cell can only be used once while secondary cells are rechargeable.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


In the chemical reactions, the
compounds \( A \) and \( B \) respectively are:
A. nitrobenzene and fluorobenzene
B. phenol andbenzene
c. benzene diazonium chloride and fluorobenzene
D. nitrobenzene and chlorobenzene


Differentiate with respect to \( x \) :
\( \frac{x^{2}+2}{\sqrt{\cos x}} \)


The fractional increase in volume of a
wire of circular cross section, if its lingitudinal strain is \( 1 \%(\sigma=0.3) \)
A . 0.4
B. 0.04
c. 0.004
D. 4


In a photo electric experiment, when
intensity of incident light increases:
A. photo-current increases
B. photo-current decreases
C. kinetic energy of emitted photoelectrons increases
D. kinetic energy of emitted photoelectrons decreases


Sclereids found in seed coat of pules
are
A. Macrosclereids
B. Brachysclereids
c. osteosclereids
D. Asterosclereids


Select the incorrect statement w.r.t
prokaryotic cells
A. Cytoplasm lacks membrane bound organelles
B. Sap vacuoles are absent
C. Chromosome possesses acidic protein i.e. polyamine
D. Lack streaming movement of cytoplasm
E. None of the above


Q Type your question
along horizontal rails from left to right
At time 't', it retards. Then the reaction
by the floor on the box is given best by?
4
B.
\( c \)
\( D \)


Phenol reacts with acetone in the
presence of conc. Sulphuric acid to form
\( a C_{15} H_{16} O_{2} \) product. The structural
formula of the product is:
\( A \)
B.
c. \( _{X} \begin{array}{l}O-C_{6} H \\ O C_{6} H_{5}\end{array} \)
\( D \)


The potential difference between point B
and \( \mathrm{C} \) of the circuit is
A \( \cdot \frac{\left(C_{2}-C_{1}\right)}{V} \)
B. \( \frac{\left(C_{4}-C_{3}\right)}{V} \)
c. \( \frac{\left(C_{2} C_{3}-C_{1} C_{4}\right)}{\left(C_{1}+C_{2}+C_{3}+C_{4}\right)} \cdot V \)
D. \( \frac{C_{1} C_{4}-C_{2} C_{3}}{\left(C_{1}+C_{2}\right) \times\left(C_{3}+C_{4}\right)} \cdot V \)


The food chain in which microbes
breakdown, energy rich compounds, synthesized by producers is called as
A. Ecosystem
B. Parasitic food chain
c. Detritus food chain
D. Predator food chain


If \( \tan \alpha=K \cot \beta, \) then \( \frac{\cos (\alpha-\beta)}{\cos (\alpha-\beta)} \)
equals
A \( \cdot \frac{1+K}{1-K} \)
в. \( \frac{1-K}{1+K} \)
c. \( \frac{K+1}{K-1} \)
D. \( \frac{K-1}{K+1} \)


In the given figure, if area of \( \triangle A D E \) is
\( 60 \mathrm{cm}^{2} ; \) state, giving reason, the area of
\( \triangle A B E \)
A \( \cdot 60 \mathrm{cm}^{2} \)
В. \( 120 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 160 \mathrm{cm}^{2} \)
D. \( 210 \mathrm{cm}^{2} \)


Primary succession is development of
communities on
A. Newly exposed habitat.
B. Cleared forest area
c. Freshly harvested crop field.
D. Pond filled after a dry season


Select the correct option regarding the
properties of dioxygen?
A. Dioxygen never reacts with metals
B. Dioxygen is diamagnetic in nature.
C. Combination of dioxygen with other elements is highly exothermic process
D. Dioxygen liquefies at \( 55 \mathrm{K} \) and freezes at \( 90 \mathrm{K} \)


The slight separation of charge, or
polarization
A. reduces the electric field within the dielectric.
B. increases the electric field within the dielectric.
C. doesn't effect the electric field within the dielectric.
D. none of the above


How and why do monosubstituted
alicyclic compounds not exhibit positional isomerism?


How many moles of electron weight one kilogram?
в. \( \frac{1}{9.108} \times 10^{3} \)
c. \( \frac{6.023}{9.108} \times 10^{54} \)
D. \( \frac{1}{9.108 \times 6.023} \times 10^{8} \)


Which of the following is a suitable example for illustrating the law of conservation of mass? (Atomic mass of
\( \boldsymbol{O}=\mathbf{1 6} ; \boldsymbol{H}=\mathbf{1}) \)
A. \( 18 g \) of water is formed by the combination of 16 g oxygen with \( 2 g \) of hydrogen
B. \( 18 g \) of water in liquid state is obtained by heating 18 g of ice
c. \( 18 g \) of water is completely converted into vapour state n heating
D. \( 18 \mathrm{g} \) of water freezes at \( 4^{\circ} \mathrm{C} \) to give same mass of ice


The solution of the equation \( 9 \cos ^{12} x+ \)
\( \cos ^{2} 2 x+1=6 \cos ^{6} x \cos 2 x+ \)
\( 6 \cos ^{6} x-2 \cos 2 x \) is/are:
\( \mathbf{A} \cdot \mathbf{x}=\mathbf{n} \pi+\frac{\pi}{2} ; \mathbf{n} \in \mathbf{I} \)
в. \( _{x}=n \pi+\cos ^{-1}(\sqrt[4]{\frac{2}{3}}), n \in I \)
c. \( _{x=n \pi-\cos ^{-1}}(\sqrt[4]{\frac{2}{3}}), n \in I \)
D. none of the above


Which of the following is/are correct statement(s)?
This question has multiple correct options
A. The motional EMF generated by a magnetic force on a moving wire is case of Lorentz force
B. The transformer EMF generated by an electric force due to a changing magnetic field is the result of Faraday law.
C. The motional EMF generated by a magnetic force on a moving wire is case of Faraday's law.
D. Both B and C are correct.


Assertion
When methanol is added to water,
boiling point of water increases.
Reason
When a volatile solute is added to a
volatile solvent, elevation in boiling point is observed.
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


Find the volume and surface area of a sphere of radius \( 2.1 \mathrm{cm} .\left(\pi=\frac{22}{7}\right) \)


A man \( 160 \mathrm{cm} \) high stands in front of a plane mirror. His eyes are at a height of \( 150 \mathrm{cm} \) from the floor. Then the
minimum length of the plane mirror for him to see full length image is :
\( A \cdot 85 \mathrm{cm} \)
B. 170 cm
\( c \cdot 80 \mathrm{cm} \)
D. 340 cm


Match the column I with column II and
mark the appropriate choice.
Column I
(A) \( 3 d \) -transition series
(i) Z=58 to Z=71
(B) Lanthanoid series
(ii) \( \mathrm{Z}=39 \) to \( \mathrm{Z}=48 \)
(C) Actinoid series
(iii) \( z=21 \) to \( z=30 \)
(D) 4d-transition series
(iv) \( z=90 \) to \( z=103 \)
\( A \cdot(A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B. (A) \( \rightarrow \) (ii), (B) \( \rightarrow \) (iii), (C) \( \rightarrow \) (iv), (D) \( \rightarrow \) (i)
C. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(\text { ii }) \)
D. \( (A) \rightarrow(\text { iv) },(B) \rightarrow(\text { iii) },(C) \rightarrow(i),(D) \rightarrow\text { (ii) } \)


Shape of \( \left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{N} \) with respect to \( \boldsymbol{N} \)
is:
A. pyramidal
B. tetrahedral
c. trigonal planar
D. T-shaped


Frequency of vibration of a particle is 10
Hz. If the amplitude of vibration is doubled, what will be the change in frequency of vibration
A. frequency doubles
B. frequency becomes halved
c. frequency remains same
D. frequency quadruples


To make gloves for an electrician, the material that is most suitable is rubber
Which material has most similar
properties?
A. Mol
в. мо२
\( c \cdot \) моз
D. All of the above


Young's modulus of the material of a wire is \( Y \). If it is under a stress \( S \), the
energy stored per unit volume is given
by:
A \( \cdot \frac{1}{2} \frac{S}{Y} \)
в. \( \frac{1}{2} \frac{S^{2}}{Y} \)
c. \( \frac{1}{2} \frac{s}{Y^{2}} \)
D. \( \frac{1}{2} \frac{S^{2}}{Y^{2}} \)


What is the common ratio of the G.P.
\( \boldsymbol{a}_{\boldsymbol{n}}=-\boldsymbol{4} . \boldsymbol{3}^{\boldsymbol{n}-1} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


A nucleus of atomic number \( Z \) and
mass number \( A \) emits a \( \beta \) -particle.The
atomic number and mass number of
resulting nucleus is
A. \( Z, A \)
B. \( Z+1, A \)
c. \( Z, A+1 \)
D. \( Z-1, A-1 \)


What does Green Chemistry in terms of environment mean?
A. Greenhouse effect
B. Reaction related to depletion of ozone layer
c. Photosynthetic reactions in plants
D. Reduction in the use and production of hazardous chemicals


95
80
\( 0 \% \)
99
90


When the disc of gold leaf electroscope is touched with positively charged glass rod the charge on the leaves of gold leaf electroscope is :
A. positive
B. negative
c. neutral
D. none of these


If \( \boldsymbol{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right) ; I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right), \) then
\( 10 A^{-1} \) is equal to
A \( .4 I-A \)
B. \( 6 I-A \)
c. \( A-4 I \)
D. \( A-6 I \)


A carrom board (4ft \( \times 4 \) ft square) has the queen at the centre. The queen, hit by the stricker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen from the centre to the hole.


What do you mean by fundamental \& derived quantities? Give the derived
unit of Force.


If the water molecules in 1.0 g of water were distributes uniformly over the
surface of earth, If there are \( 6.5 \times 10^{-x} \)
such molecules would there be in
\( 1.0 \mathrm{cm}^{2} \) of earth's surface, then what is
the value of \( x ? \)


State True or False.
High pressure and low voltage should be maintained in the discharge tube for the production of cathode rays.
A . True
B. False


If you have a finite geometric sequence, the first number is 2 and the common
ratio is \( 4, \) what is the 3 rd number in the
sequence?
\( A \cdot 8 \)
B. 16
\( c \cdot 32 \)
D. 64


An equation is given here \( \left(\boldsymbol{P}+\frac{\boldsymbol{a}}{\boldsymbol{V}^{2}}\right)= \)
\( b \frac{9}{V} \) where \( P= \) pressure, \( V= \) Volume
and \( \theta= \) Absolute temperature. if \( a \) and \( b \)
are constants, the dimension of a will
be
\( \mathbf{A} \cdot\left[M L^{-5} T^{-1}\right] \)
B \( \cdot\left[M L^{5} T^{1}\right] \)
C \( \cdot\left[M L^{5} T^{-2}\right] \)
D \( \cdot\left[M L^{-1} L^{5} T^{2}\right] \)


Define and give example of Essential amino acids:


Which of the following is only acidic in
nature?
\( \mathbf{A} \cdot B e(O H)_{2} \)
в. \( M g(O H)_{2} \)
\( \mathbf{c} \cdot B(O H)_{3} \)
D. \( A l(O H)_{3} \)


0. (-2,4),(4,8),(10,7) and (11,-5) are the
vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram.


Factorize:
\( 9 a^{2}+\frac{1}{9 a^{2}}-2-12 a+\frac{4}{3 a} \)
A \( \cdot\left(3 a-\frac{1}{3 a}\right)\left(3 a-\frac{1}{3 a}-4\right) \)
B. \( \left(a-\frac{1}{3 a}\right)\left(7 a-\frac{1}{3 a}-1\right) \)
c. \( \left(3 a-\frac{1}{3 a}\right)\left(2 a-\frac{1}{3 a}-4\right) \)
D. \( \left(3 a-\frac{1}{3 a}\right)\left(4 a-\frac{1}{3 a}-1\right) \)


Other than spirogyra, fragmentation also occurs in
A. Amoeba
B. Hydra
c. Planaria
D. None of the above


If \( \boldsymbol{w}=\mathbf{3}-\mathbf{2} \boldsymbol{i} \) and \( \boldsymbol{z}=-\mathbf{2}+\mathbf{4} \boldsymbol{i}, \) then \( \frac{\boldsymbol{w}}{\boldsymbol{z}} \)
can be written as \( a+b i, \) which is
equivalent to
A \( -\frac{3}{2}-\frac{1}{2} i \)
B. \( -\frac{7}{10}-\frac{2}{5} i \)
c. \( \frac{13}{20}-\frac{1}{2} i \)
D. \( \frac{7}{6}+\frac{2}{3} i \)


According to Ohm's law the graph of potential difference and current is
A. Straight line passing through origin
B. Curved
c. Line having an intercept on \( x \) -axis
D. Circular


In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is
made out of:
A. platinum
B. carbon
c. pure aluminium
D. copper


a) Calculate the energy associated with the first orbit of \( H e^{+} . \) What is the
radius of this orbit?
b) What is the lowest value of \( n \) that
allows 'g' orbitals to exist?


Study of relationship between electricity and magnetism is called
A. Current electricity
B. Electric magnetism
c. Magneto electricity
D. Electromagnetism


Hybridisation state of \( X e \) in \( X e F_{2} \)
\( X e F_{4}, \) and \( X e F_{6} \) respectively are:
\( \mathbf{A} \cdot s p^{2}, s p^{3} d, s p^{3} d^{2} \)
B . \( s p^{3} d, s p^{3} d^{2}, s p^{3} d^{3} \)
c. \( s p^{3} d^{2}, s p^{3} d, s p^{3} d^{3} \)
D \( \cdot s p^{2}, s p^{3}, s p^{3} d \)


Does there exist a geometric progression containing 27,8 and 12 as
three of its terms?


Carbohydrates are broadly divided into monosaccharides, oligosaccharides
and polysaccharides.
(a) Write one example each of monosaccharide and oligosaccharide.
(b) (i) Write any one method for the preparation of glucose.
(ii) What is peptide linkage?


The temperature of a wire is doubled. The Young's modulus of elasticity will?
A. also double
B. become four times
c. remain same
D. decrease


Calculate the period of revolution of Jupiter around the Sun. The ratio of the
radius of Jupiter's orbit to that of the Earth's orbit is 5
(Period of revolution of the Earth is 1
year)


The self inductance of a coil having 400 turns is \( 10 \mathrm{mH} \). The magnetic flux through the cross section of the coil corresponding to Current \( 2 \mathrm{mA} \) is
\( \mathbf{A} \cdot 4 \times 10^{-5} \mathbf{W} \mathbf{b} \)
B. \( 2 \times 10^{-3} \mathrm{wb} \)
\( c \cdot 3 \times 10^{-5} w b \)
D. \( 8 \times 10^{-3} \mathrm{wb} \)


Sodium chloride and sodium iodide
react with concentrated sulfuric acid
Which statements are correct?
1. Sodium chloride is not oxidised by concentrated sulfuric acid.
2. No colour change is seen when concentrated sulfuric acid is added to
sodium chloride
3. Sodium iodide is oxidised by concentrated sulfuric acid.
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Which of the following units could be used to describe solubility?
\( A \cdot g / s \)
в. \( g / l \)
\( c \cdot k g / s \)
D. mol/s


SHORT ANSWER TYPE
How would you prove that the air you breathe out is warmer?


Find the \( H C F \) of 65 and 117 and
express it in the form \( 65 m+117 n \)


To determine the Young's modulus of a wire, the formula is \( Y=\frac{F}{A}, \frac{L}{\triangle l} ; \) where
\( \boldsymbol{L}= \)length\( , \boldsymbol{A}=\operatorname{area~of~cross-section~} \)
of the wire, \( \triangle \boldsymbol{L}= \) Change in length of the wire when stretched with a force \( F \)
The conversion factor to change it from CGS to MKS system is
A . 1
B. 10
c. \( 0 . \)
D. 0.01


Two liquids \( A \) and \( B \) form ideal
solutions. At \( 300 K \), the vapour
pressure of solution containing 1 mole
of \( A \) and 3 mole of \( B \) is 550 mm \( H g . A t \)
the same temperature, if one more mole
of \( B \) is added to this solution, the
vapour pressure of the solution increases by 10 mm \( H g . \) Determine the vapour pressure of \( A \) and \( B \) in the pure
\( \operatorname{states}(\operatorname{in} \operatorname{mm} H g) \)
A .400,600
B .500,500
\( \mathbf{c} .600,400 \)
D. None of these


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} \) and \( \phi(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}+\cos ^{2} \boldsymbol{x} \)
Show that both functions are equal?


Equation of a tangent to the curve \( y= \) \( \cos (x+y), 0 \leq x \leq 2 \pi \) that is parallel
to the line \( x+2 y=0 \) is
A \( \cdot x+2 y=\frac{\pi}{2} \)
в・ \( x+2 y=\frac{\pi}{4} \)
c. \( x+2 y=\pi \)
D. \( x+y=\pi \)


Solve:
\( \mathbf{3}(\boldsymbol{t}-\mathbf{5})-\mathbf{1 6} \boldsymbol{t}=\mathbf{1 2}-\mathbf{2}(\boldsymbol{t}-\mathbf{3}) \)


Energy required to break ethane into its
constituent atoms is \( 2860 K J \). If the
\( C-H \) bond energy is \( 420 \mathrm{KJ}, \) the \( C-C \)
bond energy is:


The total number of isotopes of hydrogen and the number of radioactive isotopes among them, respectively, are:
A . 2 and 0
B. 3 and 2
\( c .3 \) and 1
D. 2 and 1


A load of \( 10 \mathrm{kg} \) is suspended by a metal
wire 3 m long and having a cross-
sectional are \( 4 m m^{2} . \) Find (a) the stress
(b) the strain and
(c) the elongation.
Young modulus of the metal is \( 2.0 \times \) \( 10^{11} N m^{-2} \)


During the molecular functioning of genes, which process converts RNA into protein?
A. Trancription
B. Translation
c. Transfection
D. Transfusion


Which of the following is the main cause of late discovery of neutron?
A. Neutron is highly unstable particle
B. Neutron in nucleus moves very fast
c. Neutron is charge-less particle
D. All of the above


A biased coin with probability \( P,(0<p< \)
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is \( \frac{2}{5} \) then \( P= \)
\( A \cdot \frac{2}{5} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \cdot \frac{3}{5} \)


The wavelength associated with a
photon of energy 3.31 eV is nearly
A. \( 4000 A^{\circ} \)
B. 3750 \( A^{\circ} \)
C \( .5000 A^{\circ} \)
D. 400 A \( ^{\text {о }} \)


Which of the following statements
is/are not true?
This question has multiple correct options
A. All ortho-para directing groups activates the ring
B. All ortho-para directing groups except halogens activate the ring
C. All meta-directing groups have \( \pi \) -bond on the atom directly attached to the ring
D. All meta directing groups are deactivating.


Evaluate the given integral. \( \int x \sin 2 x d x \)


When a metal sphere is heated
maximum percentage increase occurs in its :
A. Density
B. Surface area
c. Radius
D. volume


A prism of refractive index \( \sqrt{2} \) has
refracting angle \( 60^{\circ} . \) Answer the
following questions In order that a ray suffers minimum deviation it should be incident at an
angle :
A \( .45^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 30^{\circ} \)
D. none


Assuming the bond direction to the z-
axis, which of the overlapping of atomic orbitals of two atoms \( (A) \) and \( (B) \) will
result in bonding?
(I) \( s \) -orbital of \( A \) and \( p_{x} \) orbital of \( B \)
(II) \( s \) -orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(III) \( p_{y} \) orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(IV) \( s \) -orbital of both \( (A) \) and \( (B) \)
A. I and IV
B. I and II
c. Ill and IV
D. II and IV


The end product of fermentation of
sugars by Lactobacillus bacteria is
A . Lactic acid
в. \( C O_{2} \)
C. Methyl alcohol and \( C O_{2} \)
D. Butyl alcohol.


Draw a parallelogram \( A B C D \) in which \( B C=5 \mathrm{cm}, A B=3 \mathrm{cm} \) and \( \angle A B C= \)
\( 60^{0} . \) divide it into triangles \( B C D \) and
\( A B D \) by the diagonal \( B D . \) Construct
the triangle \( B D^{\prime} C^{\prime} \) similar to \( B D C \) with scale factor \( \frac{4}{3} . \) Draw the line
\( \operatorname{segment} D^{\prime} A^{\prime} \) parallel to \( D A, \) where \( A^{\prime} \)
lies on extended side \( B A \). Is \( A^{\prime} B C^{\prime} D^{\prime} \) a
parallelogram?
A. Yes
B. No
c. Data insufficient
D. Ambiguous


An element has 1 st shell fully filled and in
2nd shell has 6 electrons. Explain.


\( \int e^{2 x-3}+7^{4-3(x / 2)}+\sin \left(3 x-\frac{1}{2}\right)+ \)
\( \cos \left(\frac{2}{5} x-2\right)+a^{3 x+2} d x \)


Maximum oxidation state of uranium
and plutonium are respectively:
A. 4 and 6
B. 5 and 6
\( c .6 \) and 7
D. 6 and 8


The potential energy for a force field \( \overrightarrow{\boldsymbol{F}} \) is given by \( U(x, y)=\sin (x+y) \)
Magnitude of the force acting on the particle of mass \( m \) at \( \left(0, \frac{\pi}{4}\right) \) is
\( A \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.


A particle of mass \( m \) and momentum \( \vec{p} \) moves on a smooth horizontal table and
collides directly and elastically with a similar particle (of mass \( m \) ) having momentum \( -2 \vec{p} \). The \( \operatorname{loss}(-) \) or gain
\( (+) \) in the kinetic energy of the first particle in the collision is-
A \( \cdot \quad \frac{p^{2}}{2 m} \)
В. \( -\frac{p^{2}}{4 m} \)
c. \( +\frac{3 p^{2}}{2 m} \)
D. zero


pH of any neutral solution is:
A. 0
B. 1
c. 14
D. 7


alkylation reaction?
\( \mathbf{A} \)
B.
\( c \)
D.


If the coefficient of variation and
standard deviation of a distribution are
\( 50 \% \) and 20 respectively, then its mean is
A .40
B. 30
c. 20
D. none of these


Evaluate the following:
\( \mathbf{1 0 4}^{\mathbf{3}}+\mathbf{9 6}^{\mathbf{3}} \)


An arrow diagram.


What is the total amount of dividend
paid by the company?


If \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{2}, \mathbf{1 0}, \mathbf{1}), \boldsymbol{Q} \) are
collinear points and \( Q_{x}=-1, \) then
\( \boldsymbol{Q}_{z}= \)
A . -3
B. 7
\( c \cdot-14 \)
D. -


By observing the diagram, answer the
following.
a) How does the pressure at A differ
from the pressure at B.?
b) The pressure at \( B \) is greater than the
pressure at D. Is it true?. Justify your
answer.
c) Compare the pressure at \( A \) and \( C \).
d) If the water is replaced with mercury,
how would this affect the pressure at \( A \)
and D?


Maxwell in his famous equations of electromagnetism, introduced the
concept of
A . ac current
B. displacement current
c. impedance
D. reactance


What is the main principle involved in
voltaic cell?
A. Conversion of chemical energy into heat energy
B. Conversion of heat energy into electrical energy
C. Conversion of chemical energy into electrical energy
D. Conversion of electrical energy into chemical energy


Which statement correctly completes
the statement?
Except for glycerine, which is achiral, all
the amino acids present in proteins.:
\( \mathbf{A} \)
\( H_{3}^{+} N H C O_{2} H \)
are chiral, but racemic
B. \( H_{2} N C H C O_{2} H \)
have the L configuration at their \( \alpha \) carbon
\( c \)
\( H_{3}^{+} \stackrel{R}{N C}_{H C O_{2}^{-}} \)
have the \( R \) configuration at their \( \alpha \) carbon
D. \( R \)
\( H_{2} N C H C O_{2}^{-} \)
have the S configuration at their \( \alpha \) carbon


Stamens attached to petals are
A. Antipetalous
B. Epipetalous
c. Epiphyllous
D. Episepalous


\( \frac{\cos \theta}{\sin \theta} \times \frac{\tan \theta}{\csc \theta} \)


A bulb marked \( 12 V, 24 W \) operates 12
volt battery for 20 minutes. The current flowing through it is :
A \( .2 A \)
в. \( 0.5 A \)
\( c \cdot 1 A \)
D. \( 1.5 A \)


A 2.50 gram sample of which of the following would have the greatest mass of sulfur?
A. \( S r S ; \) molar mass \( =119.69 g / \mathrm{mol} \)
B. \( B e S \); molar mass \( =41.08 g / \mathrm{mol} \)
C . \( K_{2} S \); molar mass \( =110.26 g / \) mol
D. \( N a_{2} S ; \) molar mass \( =78.07 g / m o l \)


The general solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{y}+\boldsymbol{x}}+\boldsymbol{e}^{\boldsymbol{y}-\boldsymbol{x}} \) is
A \( \cdot e^{-y}=e^{x}-e^{-x}+c \)
B . \( e^{-y}=e^{-x}-e^{x}+c \)
\( \mathbf{c} \cdot e^{-y}=e^{x}+e^{-x}+c \)
D. \( e^{y}=e^{x}+e^{-x}+c \)
where \( c \) is an arbitrary constant


Three fluids 1,2 and 3 have Bulk Moduli
of \( k 1, k 2 \) and \( k 3 \) respectively. If \( k 1>k 2> \)
k3, which liquid will have the highest compressibility
A . liquid 1
B. liquid 2
c. liquid 3
D. theyll have equal compressibilities


\( z_{1} \) and \( z_{2} \) are two non-zero complex
numbers such that \( z_{1}=2+4 i \)
\( z_{2}=5-6 i, \) then \( z_{2}-z_{1} \) equals
A. \( 3-10 i \)
B. \( 3+10 i \)
c. \( 7-2 i \)
D. \( 10-24 i \)


What are the indications for mineral
deficiency in plants?


Why is sodium extract made acidic
with acetiuc acid before the addition of
lead acetate in the test of sulphur?


Predict the position of the elements
which form the largest cation and the
smallest anion in the modern periodic
table.


Burning of hydrogen in air is:
A. exothermic reaction
B. endothermic reaction
c. both exothermic and endothermic
D. none of the above


The rate of the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( B r_{2}(g) \rightarrow 2 H B r(g) \) is given by:
\( \boldsymbol{r}=\boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{B} \boldsymbol{r}_{2}\right]^{1 / 2} \)
Which among the following is correct?
A. Order of reaction is 2
B. Molecularity of reaction is 2
c. order of reaction is 1.5
D. Molecularity of reaction is 2.5


The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the
velocity of the particle is \( 0.8 m / s \) at \( x=0, \) the velocity of the particle at \( x= \)
1.4 is \( (\text { in } m / s) \)
A . 1.6
B. 1.2
c. \( 1 . \)
D. None of these


An ideal gas obeying kinetic gas equation:
A. can be liquefied if its temperature is more than critical temperature
B. can be liquefied at any value of any value T and P
C. can not be liquefied under any value of \( T \) and \( P \)
D. can be liquefied if its pressure is more than critical
pressure


A particle of mass \( m \) is moving along
\( x- \) axis with speed \( v \) when it collides
with a particle of mass \( 2 m \) initially at
rest. After the collision, the first particle
has come to rest and the second
particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the
two places? \( (\boldsymbol{\theta}>\mathbf{0}) \)
A. each piece moves with speed \( v \).
B. each piece moves with speed \( v / 2 \)
c. one of the piece moves with speed \( v / 2 \), the other moves with speed greater than \( v / 2 \).
D. each piece moves with speed greater than \( v / 2 \)


short steel rods each of cross-sectional
\( \operatorname{area} 5 c m^{2} . \) The lower ends of \( A \) and \( B \)
are welded to a fixed plate \( C D . \) The
upper end of \( A \) is welded to the \( L- \)
shaped piece \( \boldsymbol{E F G}, \) which can slide
without friction on upper end of \( \boldsymbol{B} . \mathbf{A} \)
horizontal pull of \( 1200 N \) is exerted at
\( G \) as shown. Neglect the weight of \( \boldsymbol{E F G} \)
Longitudinal stress in \( \boldsymbol{A} \) is
A. Tensile in nature and having magnitude \( 180 N / m^{2} \)
B. Tensile in nature and having magnitude \( 240 N / m^{2} \)
c. compressive in nature and having magnitude \( 180 N / c m^{2} \)
D. Compressive in nature and having magnitude \( 240 N / c m^{2} \)


The primary to secondary turns ratio of a transformer is given as \( 2: 3 . \) If the current through the primary coil is \( 3 A \) then the current through load resistance is
\( A \cdot 1 A \)
в. 4.5 А
\( c \cdot 2 A \)
D. 1.5 A


The focal length of a concave mirror is and the distance from the object to the principal focus is p. The ratio of the size of the real image to the size of the object is:
A. \( -\frac{f}{p} \)
в.
\[
\left(\frac{f}{p}\right)^{2}
\]
\( c \)
\[
\left(\frac{f}{p}\right)^{\frac{1}{2}}
\]
D. \( -\frac{p}{f} \)
E . \( -f p \)


Show with the help of a labelled graph how their wavelength \( (\lambda) \) varies with their linear momentum (p).


Arrange the following in order of decreasing acidic strength.pnitrophenol (I), p-cresol (II), m-cresol
(III), phenol (IV):
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
C. \( |>|||>||>\mid V \)
D. \|\|\( >\|>1>1 v \)


How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its
amplitude if the period is \( 24 s \) and
particle starts from rest
A . \( 12 s \)
B . 2 s
\( c \cdot 4 s \)
D. \( 6 s \)


A coil is wound on a transformer of
rectangular cross-section. If all the linear dimensions of the transformer
are increased by a factor 2 and the number of turns per unit length of the coil remains the same, the self
inductance increases by a factor of
A .4
B. 8
c. 12
D. 16


Construct an equilateral triangle of side
\( \mathbf{5 . 5} \mathrm{cm} \)


\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) in baking powder:
A. Behaves as an acid in moist condition and decomposes \( N a H C O_{3} \) to give \( C O_{2} \)
B. Behave as a base in moist condition and gives \( H_{3} P O_{4} \)
c. Behaves as binder
D. Behaves as a filler


For healthy eye least distance of
distinct vision is


Find the derivative of \( \boldsymbol{y}= \) \( \frac{1}{4} \ln \frac{x^{2}-1}{x^{2}+1} \)


Calculate the standard deviation for the
given frequency distribution:
C.I.
\[
\begin{array}{cc}
1-5 & 1 \\
6-10 & 2 \\
11-15 & 3 \\
16-20 & 4 \\
\hline N=10 &
\end{array}
\]


The largest interval lying in \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \) for which the function
\( \left[f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (c o\right. \)
is defined, is-
A . \( [0, \pi] \)
в. \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)
c. \( \left[-\frac{\pi}{4}, \frac{\pi}{2}\right) \)
D. \( \left[0, \frac{\pi}{2}\right) \)


Differentiate the functions with respect
to \( x \)
\( \sec (\tan (\sqrt{x})) \)


In the region of space \( \dot{E} \) and \( \dot{B} \) are parallel. A beam of cathode-rays moving in the same direction as \( \dot{E} \) enters the
space. Which of the following conclusions is correct
A. The cathode rays will travel straight
B. The cathode rays wil lbe deflected towards right
c. The speed of cathode ray particles increases
D. The speed of cathode ray particles decreases


Larger particles scatter light at the end of the spectrum the least.
A. Blue
B. Green
c. violet
D. Red


One molar solution of which substance
will have maximum O.P?
A. Nacı
B. Glucose
c. Fructose
D. starch


Synovial fluid is present in
A. spinal canal
B. Cranial cavity
C. Freely movable joints
D. All of the above


What do you understand by following.
(i) Dissociation constant of an acid
(ii) Solubility product
(iii) Heterogenous equilibrium


\( H_{2} \) does not show litmus test. From
this, we can say, that the oxide of
hydrogen is in nature.
A . acidic
B. neutral
c. basic
D. amphoteric


In Period 3 of the Periodic Table, element
B is placed to the left of element A. On the basis of this information, choose
the correct word from the brackets of
complete the following statement.
(i) The element B would have(lower/higher) metallic character
than \( A \)
(ii) The element A would probably have(lesser/higher) electron affinity than B.
(iii) The element A would have(greater/smaller) atomic size than
B.


Explain two physiological effects of auxia.


Explain the formation of a Rainbow.


length \( L, \) pivoted at its centre and
balanced with a weight \( W \) at a distance
\( x \) from the left end is shown in the
figure. Two positive point charges
q and \( 2 q \) are attached at the left and
right ends of the rod. A distance \( h \)
directly below each of these charges is
a fixed positive charge \( Q \). The distance
\( x^{\prime} \) in terms of \( q, Q, L \) and \( W \) is
(Assume than \( L>>h \) and neglect
masses of the point charges)
A.
\( ^{\mathbf{B}} \cdot \frac{4 q Q L+\varepsilon_{0} h^{2} W L}{8 \pi h^{2} W} \)
\( ^{\mathbf{C}} \cdot \frac{q Q L+4 \pi \varepsilon_{0} h^{2} W L}{8 \pi \varepsilon_{0} h^{2} W} \)
D. \( \frac{q Q L+\varepsilon_{0} h^{2} W L}{h^{2} W} \)


The value of \( a_{1}+a_{2} \) is equal to
A . 30
B. -30
c. 27
D. -27


The valence electrons are involved in
formation of covalent bonds is/are
called:
A. non-bonding electrons
B. Ione pairs
c. unshared pairs
D. None of these


\( f \frac{4 a b^{2}\left(-5 a b^{3}\right)}{10 a^{2} b^{2}}=-K b^{3} \) then value of
\( \boldsymbol{K} \) is


Global warming is caused by
greenhouse effect. Justify.


Assertion
Krebs cycle is amphibolic.
Reason
Krebs cycle produces maximum amount of ATP.
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


Find total number of subsets of \( \{p: p \) is a letter in the word 'poor'?


Angle which the normal ray makes with
the mirror is equal to:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 180^{\circ} \)


Drive an expression for Electric field due to an Electric dipole at a point on the axial line.


Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities
\( K \) and \( 2 K, \) respectively.The equivalent thermal conductivity of the slab is
A \( \cdot 2 / 6 K \)
B. \( \sqrt{2} \) к
\( c .3 K \)
D. \( 4 / 3 K \)


Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
The sum of the digits of a two-dlgit number is \( 9 . \) Also, nine times this
number is twice the number obtained
by reversing the order of the digits. Find
the number
A. Number is 18
B. Number is 36
c. Number is 81
D. None of these


Consider a sinusoidal travelling wave
shown in the given figure. The wave
velocity is \( +40 c m / s . \) Find the frequency
of the wave.
A \( .20 H z \)
B. \( 30 H z \)
c. \( 25 H z \)
D. \( 10 H z \)


Addition of \( N a_{2} C O_{3} \) to the solution of
an oxide in water produces \( C O_{2} . \) This experiment indicates that:
A. the oxide is basic
B. the oxide is amphoteric
c. the oxide is that of the a metal
D. the oxide is that of the a non-metal


Two trains \( A \) and \( B \) each of length 400 m are moving on two parallel tracks with a uniform speed \( 72 \mathrm{km} h^{-1} \) in the same
direction with \( A \) ahead of \( B \). The driver of
B decides to overtake \( A \) and accelerates
by \( 1 \mathrm{m} s^{-2} \). If after 50 s, the guard of \( B \) just brushes past \( A, \) what was the original distance between them?
A. \( 450 \mathrm{m} \)
B. 1000 \( \mathrm{m} \)
\( c . \) 1250 \( m \)
D. 2250 \( \mathrm{m} \)


Name The reciprocal of frequency
A. Time period
B. Amplitude
c. Intensity
D. None


The weight of coffee (in gms) in 70 packets is given below. Determine the modal weight of coffee in packets
202 \( \quad 203 \)
Packe
A . \( 201 \mathrm{gms} \)
в. \( 201.70 \mathrm{gms} \)
\( c \cdot 202 g m s \)
D. 202.70 gms


A barometric liquid having high density produces a shorter column of liquid.
A. True
B. False


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( [\boldsymbol{x}]^{2}+[\boldsymbol{x}+\mathbf{1}]-\mathbf{3}, \) where \( [\boldsymbol{x}] \) denotes the
greatest integer less than or equal to \( x \) Then, \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. many-one and onto
B. many-one and into
c. one-one and into
D. one-one and onto


Chromium plating is done on many articles so that they
A. Have shiny appearance
B. Do not corrode
c. Resist Scratches
D. All of these


State the S.I. units of mass and weight.
A. gand kg
B. kg and g
c. \( \mathrm{kg} \) and \( \mathrm{N} \)
D. \( \mathrm{N} \) and \( \mathrm{kg} \)


Potash alum is represented by the formula:
A \( \cdot K_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \)
B . \( K \cdot A l\left(S O_{4}\right)_{2} \cdot 12 H_{2} O \)
c. Both (a) and (b)
D. None of these


The adiabatic Bulk modulus of a
diatomic gas at atmospheric pressure is
A. \( 0 \mathrm{Nm}^{-2} \)
B. \( 1 \mathrm{Nm}^{-2} \)
c. \( 1.4 \times 10^{4} N m^{-2} \)
D. \( 1.4 \times 10^{5} \mathrm{Nm}^{-2} \)


Atomic number of a few elements are
given below:
10,20,7,14
Identify the period to which these elements belong?
A. 2,4,2,3
B. 3, 2, 3, २.
c. 2,2,3,3
D. 3, 3, 2, 2.


When an electron transitions from \( n= \)
2 to \( n=5, \) will it be visible to the naked
eye?
A. Yes, the emission occurs at 434 nm which is the blue range of light
B. Yes, the emission occurs at 434 nm which is the red range of light
c. No, the absorption occurs at the infrared red region of the electromagnetic spectrum
D. No, the absorption occurs in the blue range of light but our eyes are unable to detect absorption


The value of the integral \( \int_{0}^{\overline{2}} \sin ^{5} x d x \)
is
A \( \cdot \frac{4}{15} \)
B. \( \frac{8}{5} \)
c. \( \frac{8}{15} \)
D. \( \frac{4}{5} \)


Let \( \vec{u} \) be a vector on rectangular system
with sloping angle \( 60^{\circ} . \) Suppose that \( |\vec{u}-\hat{i}| \) is geometric mean of \( |\vec{u}| \) and \( |\vec{u}-2 \hat{i}|, \) where \( \vec{i} \) is the unit vector along
\( x \) -axis, then \( |\vec{u}| \) has the value equal to \( \sqrt{a}-\sqrt{b}, \) where \( a, b \in N . \) Find the value \( \frac{(\boldsymbol{a}+\boldsymbol{b})^{3}+(\boldsymbol{a}-\boldsymbol{b})^{3}}{\mathbf{7}} \)


If \( A \) is non-singular and \( (A+I)(A- \)
\( \mathbf{3} \boldsymbol{I})=\mathbf{0} \) then \( \mathbf{3} \boldsymbol{A}^{-1}-\boldsymbol{A}+\mathbf{2} \boldsymbol{I} \)
A . \( I \)
B.
c. \( 2 I \)
D. \( 6 I \)


Match column A with column B


In Kjeldahl's method, nitrogen present is quantitatively converted to
A. \( N_{2} \)
B . \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( N O_{2} \)
D. \( N H_{3} \)


Explain Fleming's left hand rule with the help of labelled diagram.


If there is an error of \( 0.01 \mathrm{cm} \) in the
diameter of a sphere then percentage error in surface area when the radius \( = \)
\( 5 c m, \) is
A . \( 0.005 \% \)
B. \( 0.05 \% \)
\( c \cdot 0.1 \% \)
D. \( 0.2 \% \)


If the Poisson's ratio of a solid is \( \frac{2}{5}, \) then the ratio of its young's modulus to the rigidity modulus is
A \( \cdot \frac{5}{4} \)
в. \( \frac{7}{15} \)
c. \( \frac{14}{9} \)
D. \( \frac{14}{5} \)


Solve:\( \int \frac{2 x+5}{x^{2}+5 x+6} d x \)


The first I.P. values in electron volts of
nitrogen and oxygen atoms are respectively given by :
A \( .14 .6,13.6 \)
в. 13.6,14.6
c. 13.6,13.6
D. 14.6,14.6


\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x})=& \frac{|\boldsymbol{x}|}{\boldsymbol{x}} \boldsymbol{x} \neq \mathbf{0} \\
\mathbf{0} \boldsymbol{x}=\mathbf{0}
\end{aligned}
\]
Check whether \( f(x) \) is continous or not
at \( x=0 \)


Which of the following statements are
correct?
This question has multiple correct options
A. Water in test tube can be made to boil by placing it in a bath of boiling water
B. Heat can not be stored in a body
C. With increase in pressure, melting point decreases
D. Vapour can be directly converted into solid


The area enclosed between the
parabolas \( \boldsymbol{y}^{2}=\mathbf{1 6} \boldsymbol{x} \) and \( \boldsymbol{x}^{2}=\mathbf{1 6} \boldsymbol{y} \) is
A \( \cdot \frac{64}{3} \) sq.units
в. \( \frac{256}{3} \) sq.units
c. \( \frac{16}{3} \) sq.units
D. None of these


Assertion
The value of equilibrium constant depends on the stoichiometry of the equation. BECAUSE
Reason
The value of equilibrium constant does not change when the equation is multiplied or divided by a number.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( y=x \tan y, \) then \( \frac{d y}{d x} \) is equal to
A. \( \frac{\tan y}{x-x^{2}-y^{2}} \)
в. \( \frac{y}{x-x^{2}-y^{2}} \)
c. \( \frac{\tan y}{y-x} \)
D. \( \frac{\tan x}{x-y^{2}} \)


In the electrolysis of aqueous sodium
chloride solution which of the half cell
reaction will occur at anode?


A parallel plate capacitor is made of two
square plates of side ' \( a \) ', separated by a
distance \( d(d<<a) \). The lower
triangular portion is filled with a
dielectric of dielectric constant \( \boldsymbol{K}, \) as
shown in the figure. The capacitance of this capacitor is :
\( \mathbf{A} \cdot \frac{1}{2} \frac{k \in_{0} a^{2}}{d} \)
B. \( \frac{k \in_{0} a^{2}}{d} \ln K \)
c. \( \frac{k \in_{0} a^{2}}{d(K-1)} \ln K \)
D. \( \frac{k \in_{0} a^{2}}{2 d(K+1)} \)


The most reactive metal is:
A. sodium
B. magnesium
c. potassium
D. calcium


A mass \( M \) at rest is broken into two
pieces having masses \( m \) and \( (M-m) \)
The two masses are then separated by a distance \( r . \) The gravitational force between them will be the maximum
when he ratio of the masses \( [\boldsymbol{m}:(\boldsymbol{M}- \)
\( \boldsymbol{m}) \) of the two parts is
A . 1:
B. 1: 2
\( c \cdot 1: 3 \)
D. 1: 4


Poise is the unit of :
A. pressure
B. friction
c. surface tension
D. viscosity


How many terms of the series \( 2+6+ \)
\( 18+. \) must be taken to make the sum
equal to \( 728 ? \)


In combustion, the substance reacts
with
A. hydrogen
B. oxygen
c. nitrogen
D. carbon dioxide


10 mL of hydrogen combines with 5 mL
of oxygen to yield water. When 200 mL of hydrogen at STP is passed over heated
\( C u O, \) the \( C u O \) loses 0.144 g of its weight. State the law illustrated by these chemical combinations.
A. Law of multiple proportion
B. Law of constant composition
c. Law of reciprocal proportion
D. None of the above


toppr
Q Type your question
temperature of the gas is the same. Which of the following graphs best
represent the cyclic process in T-V
diagram
\( A \)
\( A) \)
B.
\( B \) )
\( c \)
\( (\mathrm{C}) \)
0
\( (D) \)


Waves produced in the sonometer wire
are
A. transverse and progressive
B. transverse and stationary
c. longitudinal and progressive
D. longitudinal and stationary


A body goes to \( 10 \mathrm{km} \) north and \( 20 \mathrm{km} \)
east. The displacement from initia point is
A \( .22 .36 \mathrm{km} \)
B. \( 2 \mathrm{km} \)
\( \mathbf{c} .5 \mathrm{km} \)
D. \( 20 \mathrm{km} \)


If head means one and tail means two
then coefficients of quadratic equation
\( a x^{2}+b x+c=0 \) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A \( \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{7}{8} \)
D.


The elements having the general configuration, \( 4 f^{1-14} 5 s^{2} 5 p^{6} d^{0-1} 6 s^{2} \) are
referred as
A. alkali metals
B. transition elements
c. lanthanoids
D. actinides


Composition of azurite mineral is:
A. \( C u C O_{3} . C u O \)
в. \( C u\left(H C O_{3}\right)_{2} . C u(O H)_{2} \)
\( \mathbf{c} \cdot 2 C u C O_{3} \cdot C u(O H) \)
D. \( C u C O_{3} .2 C u(O H) \)


How many degrees of unsaturation are there the following compound?
\( \mathbf{A} \)
B
\( c \cdot 10 \)
\( D \)


ff \( \frac{\mathbf{3 x}+\mathbf{4}}{(x+1)^{2}(x-1)}=\frac{A}{x-1}+\frac{B}{x+1}+ \)
\( \frac{C}{(x+1)^{2}}, \) then \( C= \)
A. \( -\frac{1}{2} \)
B. \( -\frac{1}{4} \)
\( c \cdot-\frac{7}{4} \)
D. \( -\frac{1}{4} \)


What is the difference between the
pressure on the bottom of a pool and the
pressure on the water surface?
A \( . g h \)
B. \( \frac{g}{h} \)
c. 0
D. none


Integrate \( \int x \cos ^{-1} x d x \)


Two magnetic poles of strengths \( 40 A m \) and \( 10 A m \) are separated by a distance
of \( 20 \mathrm{cm} \) in air. The force between them
if the distance is reduced to \( 10 \mathrm{cm} \) is
A \( \cdot 4 \times 10^{-3} N, 10^{-3} N \)
B . \( 10^{-3} N, 4 \times 10^{-3} N \)
c. \( 2 \times 10^{-3} N, 10^{-3} N \)
D. \( 10^{-3} N, 2 \times 10^{-3} N \)


In Bentham and Hooker's system
classification, ranales are included
under
A. Calyciflorae
B. Inferae
c. Disciflorae
D. Thalamiflorae


Identify the final product of the reaction
\[
\mathrm{CH}_{3} \mathrm{MgBr}+\mathrm{CH}_{2} \mathrm{CH}_{2} \rightarrow \stackrel{\mathrm{H}, \mathrm{O}^{+}}{\longrightarrow} ?
\]
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H_{3} C H_{2} O H \)
\( c \)
\[
\triangle
\]
D. \( C H_{3} C H_{2} C H_{2} O H \)


\( * \)
\( * \)
\( * \)
\( k \)


What is transpiration? Where does it
occur?


City garbage can be used to produce
A. sewage sludge
B. useful articles
c. biogas and maure
D. All the above.


When the vapours of tertiary butyl alcohol are passed through heated copper at \( 573 K \), the product formed is:
\( \mathbf{A} \cdot B u t-2-e n e \)
в. \( 2- \) Виtanone
c. \( 2- \) Methyl - propene
D. Butanal


Triple fusion in Capsella bursa pastoris is
fusion of male gamete with.
A. Eggg
B. synergid
c. Secondary nucleus
D. Antipodal


A ray of light is incident at the glass-
water interface at angle \( i, \) it emerges
finally parallel to the surface of water,
then the value of \( \mu_{g} \) would be
A \( \cdot(4 / 3) \sin (i) \)
B. \( [1 / \sin (i)] \)
\( c \cdot 4 / 3 \)
D.


Check the commutativity and associativity of the following binary operation:
\( *^{\prime} \) on \( Q \) defined by \( a * b=a+a b \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Q} \)


Write the place value of the underlined digit of the following decimal numbers:
(i) 82.61
(ii) 5.24


The correct order of energy difference
between adjacent energy levels in \( H \)
atom:
\( \mathbf{A} \cdot E_{2}-E_{1}>E_{3}-E_{2}>E_{4}-E_{3} \)
B \( \cdot E_{2}-E_{1}>E_{4}-E_{3}>E_{3}-E_{2} \)
\( \mathbf{c} \cdot E_{4}-E_{3}>E_{3}-E_{2}>E_{2}-E_{1} \)
D \( \cdot E_{3}-E_{2}>E_{4}-E_{3}>E_{2}-E_{1} \)


What is the angle between \( \vec{P} \times \vec{Q} \) and \( \overrightarrow{\boldsymbol{Q}} \times \overrightarrow{\boldsymbol{P}} ? \)
A. zero
В. \( \pi / 2 \)
\( c . \pi \)
D. none of the above


Which among the following has the highest calorific value?
A . Petrol
B. Kerosene
c. Ethanol
D. woodd


The wave number for the shortest
wavelength transition in Paschal series of \( L i^{2+} \) lon is: \( \left(R: 109677 c m^{-1}\right) \)
A \( \cdot 27420 \mathrm{cm}^{-1} \)
B. \( 164515 \mathrm{cm}^{-1} \)
\( \mathbf{c} \cdot 219354 \mathrm{cm}^{-1} \)
D. \( 109677 \mathrm{cm}^{-1} \)


Given the geometric progression
\( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots . \) The term 12288 would
occur as the
A \( \cdot 11^{t h} \) term
B. \( 12^{\text {th}} \)term
\( \mathbf{c} \cdot 13^{t h} \)term
D. \( 14^{\text {th}} \)term


When light is incident on a glass block at polarizing angle
a) reflected ray is plane polarized
b) reflected and refracted rays are perpendicular
c) reflected and refracted rays are
partially polarized
d) refracted ray is partially polarised
\( A \cdot a, c \) and \( d \) are correct
B. a, b and d are correct
\( c \cdot b, c \) and \( d \) are correct
D. a, b and c are correct


Materials suitable for permanent
magnet, must have which of the
following properties?
A. High retentivity, low coercivity and high permeability
B. Low retentivity, low coercivity and low permeability
c. Low retentivity, high coercivity and low permeability
D. High retentivity, high coercivity and high permeability


The van't Hoff factor of \( B a C l_{2} \) at \( 0.01 \mathrm{M} \)
concentration is \( 1.98 . \) The percentage of
dissociation of \( B a C l_{2} \) at this
concentration is:
A .49
B. 69
\( c \cdot 89 \)
D. 100


Dalton had suggested that an atom is indivisible.
A . True
B. False


(a) Write the relation between object
distance \( (u), \) image distance \( (v) \) and
focal distance \( (\boldsymbol{f}) \) of a spherical lens.
(b) What is magnification?
(c) The refractive index of glass with respect to air is \( \frac{3}{2} \) and the refractive index of water with respect to air is \( \frac{4}{3} . \) If the speed of light in air is \( 3 \times 10^{8} m / s \)
find the speed of light in (i) glass, (ii) water


In earthworms setae are present in all
segments except
A. First and the last segments
B. First segment
c. Clitellum and last segments
D. First clitellum and last segments


When steam is passed over hot coke, it
produces:
A. producer synthesis gas
B. synthesis gas
c. teargas
D. coal gas


n Fig. \( A B=A C \) and \( D B=D C, \) find
the ratio \( \angle A B D: \angle A C D \)


\( P h-\stackrel{0}{C}-O H \stackrel{S O C l_{2}}{\longrightarrow}(A) \underset{P d-B a S O_{4}}{C}(B) \)
Product (B) is:
A.
\[
P h-C_{-} H
\]
в. \( P h-C H_{2}-O H \)
c. \( P h-C H_{2}-C l \)
D. \( P h-C H=C H_{2} \)


Find the direction cosines of the line
\( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{2}}=\frac{\mathbf{2} \boldsymbol{y}-\mathbf{5}}{\mathbf{3}} ; \boldsymbol{z}=-\mathbf{1} \)


Which of the following molecules has the shortest carbon-carbon single bond length?
A. \( C H_{2}=C H-C-C H_{3} \)
в. \( C H_{2}=C H-C=N \)
c. \( C H_{2}=C H-C=O \)
D. \( C H_{2}=C H-C H=C H_{2} \)


The acidic amino acid is:
A. Aspartic acid
B. Alycine
c. serine
D. Tyrosine


Amongst the following the strongest base is:
A. benzylamine
B. aniline
c. m-nitroaniline
D. p-nitroaniline


Unpolarised light of intensity \( 32 \mathrm{W} \mathrm{m}^{-2} \)
passes through three polarizes is crossed with that of the first. The
intensity of final emerging light is 3 \( \mathrm{W} \mathrm{m}^{-2} . \) The intensity of light transmitted by first polarizer will be
\( A \cdot 32 W m^{-2} \)
B. \( 16 \mathrm{W} \mathrm{m}^{-2} \)
\( c \cdot 8 w m^{-2} \)
D. \( 4 \mathrm{Wm}^{-2} \)


Deserts can be converted into green
land by
A. Tropical trees
B. Oxylophytes
c. Halophytes
D. Psammophytes


Identify the symptoms of indigestion.
A. Fever
B. Bloating
c. Growling stomach
D. Both B and C


The products for the following reactions
are:
(i) \( C H_{3}-C_{H}^{B r}-C H_{2}-C H_{3}+ \)
alc. \( \boldsymbol{K O H} \rightarrow \boldsymbol{X} \)
(ii) \( \boldsymbol{C H}_{3}-\underset{_{\mathrm{I}}^{\mathrm{CH}}}{\boldsymbol{H}}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \stackrel{\boldsymbol{O}_{3}}{\longrightarrow} \)
\( \boldsymbol{Y}+\boldsymbol{Z} \)
A. \( X=\left(C H_{3}\right)_{2} C=C H_{2}, Y=C H_{3} C H_{2} C H O, Z= \)
\( C H_{3} C H_{2} C H O \)
B. \( X=C H_{2}=C H_{2}, Y=C H_{3} C H O, Z=C H_{3} C O O H \)
c. \( X=C H_{3}-C H=C H-C H_{3}, Y=C H_{3}-C H \)
D. \( X=C H_{3}-C H=C\left(C H_{3}\right)_{2}, Y=H C H O, Z= \)
\( C H_{3} C H O \)


A uniform rod of length L and mass M is pulled horizontally on a smooth surface
with a force F. Determine the elongation
of rod if Young's modulus of the
material is \( Y \)


If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors and the angles between \( \vec{a}, \vec{b} \) and \( \vec{b}, \vec{c} \) and \( \vec{c}, \vec{a} \) are \( \frac{\pi}{6}, \frac{\pi}{3} \)
and \( \frac{\pi}{4} \) respectively, then \( |\vec{a}+\vec{b}+\vec{c}| \)
A . 3
B. \( 4+\sqrt{3}+\sqrt{2} \)
c. \( \sqrt{4+3+2} \)
D. None of these


Which metal is usefull for protection of iron by corrosion?
A. Aluminium
B. Sodium
c. zinc
D. copper


Assertion
A positive catalyst increases the rate of a reaction.
Reason
In presence of a catalyst, the activation energy of the reaction increases.
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 spherical uniform planet is rotating about its axis. The velocity of a point on
its equator is \( V \). Due to the rotation of
a planet about its axis the acceleration due to gravity \( g \) at equator is \( \frac{1}{2} \) of \( g \) at
poles. The escape velocity of a particle
on the pole of a planet in terms of \( V \) is
A \( \cdot V_{e}=2 V \)
B. \( V_{e}=V \)
\( \mathrm{c} \cdot_{V_{e}}=\frac{V}{2} \)
D. \( V_{e}=\sqrt{3} V \)


Assertion
In Lewis structures of \( N F_{3} \) and \( C O_{3}^{2-} \)
nitrogen and carbon occupy the central position whereas fluorine and oxygen
occupy the terminal positions.
Reason
In Lewis representation, the least electronegative atom occupies the central position in the molecule/ion.
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


Observe the given situation and answer the following questions. Rahul and Ravi are playing in a ground. They start
running from the same point \( x \) simultaneously in the ground and reach point \( Y \) at the same time by following paths marked 1 and 2 respectively, as shown in the figure.
Which of the following is correct
statement for the given situation?
A. Rahul covers a longer distance with a lower speed
B. Rahul covers a longer distance with a higher speed
C. Rahul and Ravi both cover different distances with same speed.
D. Ravi covers a shorter distance with higher speed


what is the distance of the point (p,q,r) from the \( x \) -axis ?


The light of wavelength \( 6328 A^{\circ} \) is incident on a slit of width 0.2 mm
perpendicularly, the angular fringe width will be:
A \( \cdot 0.36^{\circ} \)
B. \( 0.18^{\circ} \)
\( c \cdot 0.72^{\circ} \)
D. \( 0.09^{\circ} \)


The relation between frequency (n) and wavelength \( (\lambda) \) is given by (v is velocity, n is frequency and \( T \) is time-period)
в. \( n=\frac{\lambda}{v} \)
c. \( v=\frac{n}{\lambda^{2}} \)
D. \( n=\frac{T}{\lambda} \)


toppr
\( Q \)
Its specitication. Name the tnree independent quantities conventionally used to specify the earth's magnetic field.
(b) The angle of dip at a location in
southern India is about \( 18^{\circ} . \) Would you
expect a greater or smaller dip angle in Britain?
(c) If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?
(d) In which direction would a compass free to move in the vertical plane point
to, if located right on the geomagnetic north or south pole?
(e) The earth's field, it is claimed, roughly approximates the field due to a dipole of magnetic moment \( 8 \times \) \( 10^{22} J T^{-1} \) located at its centre. Check
the order of magnitude of this number
in some way.
(f) Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions.
How is such a thing possible at all?


True or False
Natural fibres are obtained from plants and animals where as synthetic fibres are obtained by chemical processing of petrochemicals.


A matrix consisting of a single column of m elements is know as
A. Column matrix
B. Row matrix
c. Square matrix
D. Null matrix


What is pH? What is its range? What
are the negative impacts if the pH of
soil is too low or too high?


The dimensional formula of wave
number is :
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{0} L^{-1} T^{0}\right] \)
C . \( \left[M^{0} L^{0} T^{-1}\right] \)
D. \( \left[M^{-1} L^{-1} T^{0}\right] \)


The father of ATP cycle is
A. White
B. Lipmann
c. Pasteur
D. Buchner


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C}+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \boldsymbol{A} \boldsymbol{g}^{+} \)
This method of extraction of Ag by the complex formation and then its displacement is called:
A. Parke's method
B. Mac Arthur-Forest method
c. Serpek method
D. Hall's method


Which of the following halogen exchange reaction will occur in
acetone?
A. \( R-I+N a C l \rightarrow \)
в. \( R-F+K C l \rightarrow \)
c. \( R-C l+N a l \rightarrow \)
D. \( R-F+A g B r \rightarrow \)


If \( R=\{(x, y) / 3 x+2 y=15 \text { and } x, y \epsilon N\} \)
the range of the relation \( \mathrm{R} \) is
A \( \cdot\{1,2\} \)
B . \( \{1,2, . ., 5\} \)
c. \( \{1,2, ., 7\} \)
D. \{3,6\}


Which alky halide has maximum
density?
\( \mathbf{A} \cdot C_{3} H_{7} F \)
B \( \cdot C_{2} H_{5} C l \)
\( \mathrm{c} \cdot C H_{3} B r \)
D. \( C H_{3} I \)


Mark the following rational numbers on
the number line.
\( \frac{3}{2} \)


A mapping from \( N \) to \( N \) is defined as follows
\( \boldsymbol{f}: \boldsymbol{N} \longrightarrow \boldsymbol{N} \)
\( \boldsymbol{f}(\boldsymbol{n})=(\boldsymbol{n}+\mathbf{5})^{2}, \boldsymbol{n} \in \boldsymbol{N} \)
\( (N \) is the set of natural numbers). Then,
A. \( f \) is not one to one
B. \( f \) is onto
c. \( f \) is both one to one and onto
D. \( f \) is one to one but not onto


What are the dimensions of \( \boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \boldsymbol{\epsilon}_{0}} ? \)
(Given, N is the unit of force, with
dimensions \( M L T^{-2} \) )
A \( \cdot C^{2} N^{-1} M^{-2} \)
в. \( N M^{2} C^{-2} \)
c. \( N M^{2} C^{2} \)
D. Unitless


Let \( A=\{5,6,7,8\} ; B=\{-11,4,7,-10,-7,-9, \)
-13\} and \( \boldsymbol{f}= \)
\( \{(x, y): y=3-2 x, x \epsilon A, y \epsilon B\} \)
(i) Write down the elements of \( f . \) (ii)
What is the co-domain?
(iii) What is the range?
(iv) Identify the type of function.


If the final volume of the gas is given by
\( \boldsymbol{x} \times \mathbf{1 0}^{-1} \boldsymbol{L}, \) then find \( \boldsymbol{x} \) ?


Addition of mineral acid to an aqueous
solution of Borax, the compound formed is:
A. Puroboric acid
B. Boron hydride
c. Meta boric acid
D. orthoboric acid


Evaluate:
\( \int \sin ^{4} x \cos ^{4} x d x \)


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


"Be dissolves in alkali to give
\( N a_{2} B e O_{2} \) and \( H_{2} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


The volume of a cube with diagonal of length d units is \( \frac{d^{3}}{3 \sqrt{3}} \) cu.units
State True or False.
A . True
B. False
c. Data Insufficient
D. None of the above


\( A B \) and \( C D \) are two perpendicular diameters of a circle with centre \( 0,0 D \) is
the diameter of smaller circle.If \( O A=7 \)
\( \mathrm{cm} \),then the area of the shaded region in
figure,is
\( A \cdot 66.5 c m^{2} \)
В. \( 66 c m^{2} \)
\( c \cdot 65 c m^{2} \)
D. \( 67.5 \mathrm{cm}^{2} \)


A long string under tension of \( 100 N \)
has one end at \( x=0 . \) A sinusoidal
wave is generated at \( x=0 \) whose
equation is given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Find the average power transmitted by
the wave.


The rate of \( E_{1} \) reaction depends upon:
A. the concentration of substrate
B. the concentration of nucleophile
C. the concentration of substrate as well as nucleophile
D. neither the concentration of substrate nor of nucleophile


Which is natural satellite of Earth?
A. INSAT
B. Moon
c. sputnik
D. Aryabhatta


A defect of vision caused due to
excessive curvature of the cornea is:
A. myopia
B. hypermetropia
c. astigmatism
D. presbyopia


Positive electric flux indicates that
electric lines of force are directed
from a point charge.
A. Outwards
B. Onwards
c. Outwards or inwards
D. None of these


Name the purest form of commercia
ion.


Which of the following components of blood fights infection?
A. White blood cells
B. Platelets
c. Red blood cells
D. All of these


The epoch of beginning of human life is
A. Palaeocene
B. Pleistocene
C. Pliocene
D. Holocene


How are the functions of the
reproductive organs in human beings controlled?


The equation of a longitudinal wave is
represented as \( \boldsymbol{y}=20 \cos \pi(50 t-x) \)
its wavelength is
A. \( 5 m \)
в. \( 2 m \)
\( c .50 m \)
D. 20m


An object of \( 2 \mathrm{cm} \) height is placed at a distance of \( 16 \mathrm{cm} \) from a concave mirror
which produces a real image \( -3 c m \) height. What is the focal length \( \& \) position of the image?


The index of refraction for diamond is
2.42. For a diamond in the air (index of
refraction \( =1.00 \), what is the smallest
angle that a light ray inside the diamond can make with a normal and
completely reflect back inside the diamond (the critical angle)?
A \( \cdot 90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 68^{\circ} \)
D. \( 66^{\circ} \)
E \( .24^{\circ} \)


A rocket is launched upward from the
Earth's surface whose velocity-time
graph is shown in figure.

The maximum height attained by
the rocket is:
\( \mathbf{A} \cdot 1 k m \)
B. \( 10 \mathrm{km} \)
\( \mathbf{c} \cdot 100 \mathrm{km} \)
D. \( 60 \mathrm{km} \)


Evaluate the following
\( (97)^{2} \)
A. 9409
в. 9049
\( c .9949 \)
D. 4949


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{6} & \mathbf{1 0} & \mathbf{1 0 0} \\ \mathbf{7} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{9} & \mathbf{1 0}\end{array}\right], \) then
\( \operatorname{Tr}\left(\boldsymbol{A}^{T}\right)= \)
(Tr denotes trace of a matrix)
A . -17
B. 17
\( c \cdot-\frac{1}{15} \)
D. \( \frac{1}{17} \)


A wire having a linear density of 0.05 \( \mathrm{gm} / \mathrm{cm} \) is stretched between two rigid supports with a tension of \( 4.5 \times 10^{7} \)
dynes. It is observed that the wire resonates at a frequency of 420 cycles/sec. The next higher frequency at which the same wire resonates is 490
cycles/sec. The length of wire is approximately
A. \( 314 \mathrm{cm} \)
B. 254 cm
c. \( 214 \mathrm{cm} \)
D. 354 cm


State whether the following statements
are true or false.

Ethylene stimulates leaf release, while auxin keeps leaves from falling.
A. True
B. False


Let \( A \) be a set of \( n \) distinct elements.
Then, the total number of distinct
functions from \( A \) to \( A \) is \( \ldots \) and out of
these \( \ldots . \) are onto functions.


An electron initially at rest is accelerated through a potential difference of one volt. The energy gained by the electron is:
A. 15
B . \( 1.6 \times 10^{-19} \mathrm{J} \)
\( \mathbf{c} \cdot 10^{-19} J \)
D. None of these


Are the following name correct according to IUPAC system of nomenclature? If not, give the correct
names.
Pent-3-yne


Oxidation number is \( \mathrm{S} \) in \( \left(C H_{3}\right)_{2} S O \) is :
A. zero
B. +1
\( c \cdot+2 \)
\( D \cdot+3 \)


The value of \( \Delta G_{r}^{\circ} \) of gaseous mercury is \( 31 k J / \) mole. At what external pressure
mercury start boiling \( 25^{\circ} C \)
\( \mathbf{A} \cdot 10^{-5.44} \)
B. \( 10^{-12.5} \)
D. \( 10^{-3.12} \)


A steel wire of length \( 4 m \) is stretched by
a force of \( 100 N . \) The work done to
increase the length of the wire by \( 2 m m \) is
A . 0.4 .5
в. \( 0.2 J \)
\( c .0 .1 J \)
D. \( 1 . \)


The ureters of opisthonephric kidneys represents
A. Wolffian ducts in male
B. Mullerian duct in female
c. Wolffian duct in both sexes
D. Both A and B


The number of electrons required to balance the given equation is
\( N O_{3}^{-}+4 H^{+}+e^{-} \longrightarrow 2 H_{2} O+N O \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 2
\( c \cdot 3 \)
D.


In a moderately asymmetrical distribution the distance between mean
\( \& \) median is 'k' times the distance
between mean \( \& \) mode, then 'k' equals
\( \mathbf{A} \cdot \mathbf{3} \)
B. 2
\( c \cdot \frac{2}{3} \)
D. None of these


Obtain the expression for the intensity of electric field near a uniformly
charged straight wire of infinite length with the help of Gauss theorem.


An edge of a variable cube is increasing at the rate of \( 3 \mathrm{cm} / \mathrm{s} \). How fast is the
volume of the cube increasing when the
edge is \( 10 \mathrm{cm} \) long?
A. \( 900 \mathrm{cm}^{3} / \mathrm{s} \)
B. \( 920 \mathrm{cm}^{3} / \mathrm{s} \)
\( \mathbf{c} .850 \mathrm{cm}^{3} / \mathrm{s} \)
D. \( 950 \mathrm{cm}^{3} / \mathrm{s} \)


State True or False.
The three quantum numbers were clearly explained in terms of Schrodinger wave equation.
A. True
B. False


A man running round a race course note
that the sum of the distances of two
flag posts from him is 8 meters. The
area of the path he encloses in square meters if the distance between the flag
posts is 4 is:
\( \mathbf{A} \cdot 15 \pi \)
в. \( 12 \pi \)
c. \( 18 \pi \)
D. \( 8 \sqrt{3} \pi \)


For an A.P. given below find \( t_{20} \) and \( S_{10} \) \( \frac{1}{6}, \frac{1}{4}, \frac{1}{3}, \dots \)
A \( \cdot \frac{7}{4}, \frac{65}{12} \)
в. \( \frac{5}{4}, \frac{63}{12} \)
c. \( \frac{5}{4}, \frac{65}{12} \)
D. \( \frac{7}{4}, \frac{63}{12} \)


Solve: \( \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots . .+ \)
\( \frac{1}{1892}+\frac{1}{1980}=? \)


Column I represent the size of the soil
particles and Column II represents type of solid components. Which of the following is correct match for the Column I and Column II.

Column I
A.
0.2 to 2.00
mm
B. Less than
\( 0.002 \mathrm{mm} \)
(ii) \( \quad \) Clay
0.02 to 0.2
\( \mathrm{mm} \) coarse sanc
\( \begin{array}{ll}\text { c. } & \text { (iii) } \\ \text { menticle }\end{array} \)
D. 0.002 to 0.02
\( \mathrm{mm} \)
(iv) fine sand
particle
\( A \cdot A-(i i), B-(i i i), C-(i v), D-(i) \)
B. A - (iv), B - (i), C - (iii), D - (ii)
c. \( A- \) (iii), \( B- \) (ii), \( C-(i v), D- \) (i)
D. None of the above


Find the value of \( \lambda \) for which the points
\( (6,-1,2),(8,-7, \lambda) \) and (5,2,4) are
collinear.


What is the geometry of water molecule?
A . Distorted tetrahedral
B. Tetrahedral
c. Trigonal planer
D. Diagonal


State Fleming's left hand rule.


A formula analogous to the Rydberg formula applies to the series of spectral
lines which arise from transitions from
higher energy level to the lower energy
level of hydrogen atom.
A muonic hydrogen atom is like a hydrogen atom in which the electron is
replaced by a heavier particle, the muon'. The mass of the muon is about
207 times the mass of an electron,
while the charge remains same as that
of the electron. Rydberg formula for hydrogen atom is:
\( \frac{1}{\lambda}= \)
\( \boldsymbol{R}_{\boldsymbol{H}}\left[\frac{\mathbf{1}}{\boldsymbol{n}_{\mathbf{1}}^{2}}-\frac{\mathbf{1}}{\boldsymbol{n}_{2}^{2}}\right]\left(\boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 0 9 6 7 8 c m}^{-1}\right) \)
Radius of first Bohr orbit of muonic
hydrogen atom is
A \( \cdot \frac{0.259}{207} \dot{A} \)
B. \( \frac{0.529}{207} \),
c. \( 0.529 \times 207 \hat{A} \)
D. \( 0.259 \times 207 \dot{A} \)


State whether true or false.
As the distance of the planet from the sun increases, the period of revolution decreases.
A. True
B. False


If \( \sec ^{-1} x+\sec ^{-1} y+\sec ^{-1} z=3 \pi \)
then \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c .3 \)
\( D \)


A satellite orbiting the Earth at \( 400 \mathrm{km} \) above the surface of the Earth has a \( 2 m \)
long antenna oriented perpendicular to
the Earth's surface. At the equator the Earth's magnetic field is \( 8 \times 10^{-5} T \) and
is horizontal. Assuming the orbit to the circular, find emf induced across the
ends of the antenna.(Given radius of
\( \left.\operatorname{earth} R_{e}=6400 K m\right) \)
A. \( 1.3 V \)
В. \( 1.2 V \)
c. \( 1.0 V \)
D. \( 0.12 V \)


The substance which is used to
stimulate the increase in apple size is
A . Auxin
B. Ethylene
c. Promalin
D. Morphactins


\( \underset{x \rightarrow 0}{\operatorname{Lt} \frac{(1+x)^{6}-1}{(1+x)^{5}-1}}= \)
\( A \cdot \frac{1}{2} \)
B. 6 5
c. 1
\( D \)


If \( y=\frac{1}{2}\left(\sin ^{-1} x\right)^{2}, \) then find \( (1- \)
\( \left.\boldsymbol{x}^{2}\right) \boldsymbol{y}_{2}-\boldsymbol{x} \boldsymbol{y}_{1} \)
Where \( y_{1} \) and \( y_{2} \) denote first and second
derivatives of \( y \) respectively.
A . -1
B. 0
c. 1
D. 2


speea or cu m/s releases a pomo ac a
height of \( 80 \mathrm{m} \) above ground as shown.
At the same instant a Hunter of
negligible height starts running point at below it, to catch the bomb with
speed \( 10 \mathrm{m} / \mathrm{s} \). After two seconds he
realized that he cannot make it, he
stops running and immediately holds
his gun and fires in such a direction so
that just before bomb hits the ground,
bullet will hit it. what should be a firing
speed of bullet. (take \( g=10 \mathrm{m} / \mathrm{s}^{2} \) )
A. \( 70 \mathrm{m} / \mathrm{s} \)
B. \( 20 \sqrt{1} 0 \mathrm{m} / \mathrm{s} \)
c. \( 10 \sqrt{10} \mathrm{m} / \mathrm{s} \)
D. None of above


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{\cos \boldsymbol{x}}{\mathbf{1}+\sin \boldsymbol{x}}\right) \)
A. \( -\frac{1}{2} \)
B. \( -\frac{1}{4} \)
\( c \cdot-\frac{1}{8} \)
D. 3


Weights of \( 20 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are suspended from the ends of a light rod \( 5 \mathrm{m} \) long, so at which point the rod must be suspended by means of a string to keep it horizontal?
A. At \( 3 \mathrm{m} \) from 20kg weight
B. At \( 3 \mathrm{m} \) from 30kg weight
c. At \( 4 \mathrm{m} \) from 20kg weight
D. At \( 4 \mathrm{m} \) from 30 kg weight


The radius of a circle is increasing
uniformly at the rate of \( 3 \mathrm{cm} / \mathrm{s} \). Find the rate at which the area of the circle is
increasing when the radius is \( 10 \mathrm{cm} \)


Q Type your question
uniform field between the parallel
plates as shown in figure. Assume that
the field between the plates is uniform
and directed vertically downward, and
that the field outside the plates is zero. The electron enters the field at a point
midway between the plates. Mass of electron is \( 9.1 \times 10^{-31} k g . \) If the electron
just misses the upper plate, the time of flight of the electron up to this instant is :
A \( \cdot 1.25 \times 10^{-9} s \)
в. \( 32.5 \times 10^{-6} s \)
C \( \cdot 1.25 \times 10^{-10} s \)
D. \( 32.5 \times 10^{-8} s \)


An air bubble inside water oscillates
due to some explosion with period T. If
\( T \propto P^{a} d^{b} E^{c} \) then determine the values
of \( a, b \) and \( c . \) Here \( P, d \) and \( E \) are the static pressure, density and total energy of explosion of water, respectively.
A \( \cdot a=\frac{5}{6}, b=1, c=\frac{1}{3} \)
B. \( a=-\frac{5}{6}, b=\frac{1}{2}, c=\frac{1}{3} \)
c. \( a=1, b=1, c=1 \)
D. \( a=0, b=0, c=1 \)


In a potentiometer arrangement, a cell of emf \( 1.25 \mathrm{V} \) gives a balance point at 35 cm length of the wire. If the cell is replaced by another cell, the balance point shifts to \( 63 \mathrm{cm} \), then emf of the second cell is
A . \( 4.25 \mathrm{v} \)
B. 2.25
c. 3.25 \( v \)
D. \( 1.25 \mathrm{v} \)


The time required for \( 100 \% \) completion of a zero order reaction is:
\( \mathbf{A} \cdot a k \)
в. \( \frac{a}{2 k} \)
c. \( \frac{a}{k} \)
D. \( \frac{2 k}{a} \)


A vessel of volume \( V \) contains a mixture
of 1 mole of hydrogen and 1 mole of oxygen(both considered as ideal). Let
\( f_{1}(v) d v \) denote the fraction of
molecules with speed between v and
\( (\boldsymbol{v}+\boldsymbol{d} \boldsymbol{v}) \) with \( \boldsymbol{f}_{2}(\boldsymbol{v}) \boldsymbol{d} \boldsymbol{v}, \) similarly for
oxygen. then
\( \mathbf{A} \cdot f_{1}(v)+f_{2}(v)=f(v) \) obeys the Maxwell's distribution law
B. \( f_{1}(v), f_{2}(v) \) will obey the Maxwell's distribution law separately
C. Neither \( f_{1}(v) \) nor \( f_{2}(v) \) will obey the Maxwell's distribution law
D. \( f_{2}(v) \) and \( f_{1}(v) \) will be the same


\( \mathbf{f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{4} \\ \mathbf{- 1} & \mathbf{0} & \mathbf{7} \\ \mathbf{- 4} & \mathbf{- 7} & \mathbf{0}\end{array}\right] \) then \( \mathbf{A}^{\mathbf{T}}= \)
\( A \)
в. - А
\( c \)
D. \( A^{2} \)


\( \frac{x-a}{x-b}+\frac{x-b}{x-a}= \)


If electric field in a region is radially
outward with magnitude \( \boldsymbol{E}=\boldsymbol{A} \boldsymbol{r}, \) the
charge contained in a sphere of radius \( r \) centred at the origin is :
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \varepsilon_{0}} A r^{3} \)
В. \( 4 \pi \varepsilon_{0} A r^{3} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{A}{r^{3}} \)
D. \( \frac{4 \pi \varepsilon_{0} A}{r^{3}} \)


Choose the correct answer from the
alternatives given. In the pulmonary circuit, the \( _{--} \) hearts
half pumps blood to lungs, then blood flows to the heart.
A. right; oxygen-poor
B. right; oxygen-rich
c. left; oxygen-poor
D. Ieft; oxygen-rich


In an election,there were only two
candidates for the post of president. The winning candidate got \( 53 \% \) of the total votes. His oppponent got 31000 votes which represented \( 31 \% \) of the total votes. Find the number of votes


A piece of copper and another of
germanium are cooled from room temperature to \( 77 \mathrm{K} \), the resistance of :
A. each of them increases
B. each of them decreases
c. copper decreases and germanium increases
D. copper increases and germanium decreases


State the use of echo by a bat, dolphin and fisherman.


The ratio \( \frac{A X}{X D} \) is
\( A \cdot 5 \)
2
B. 6
\( c \cdot 7 \)
\( \overline{3} \)
\( D \)


How does the presence of benzoquinone inhibit the free radical polymerisation of a vinyl derivative?


A glass tube of \( 2 \mathrm{m} \) length is filled with
water. The water can be drained out
slowly at the bottom of the tube. If a vibrating tuning fork of frequency 500 \( \mathrm{Hz} \) is brought at the upper end of the tube and the velocity of sound is 300 \( \mathrm{m} / \mathrm{s}, \) then the total number of
resonances obtained will be
\( A \cdot 6 \)
B. 7
\( c \cdot 2 \)
D.


A mass m rotates in a vertical circle of
radius \( \mathrm{R} \) and has a circular speed \( v_{c} \) at
the top. If the radius of the circle is increased by a factor of \( 4, \) circular speed at the top will be
A. decreased by a factor of 2
B. decreased by a factor of 4
c. increased by a factor of 2
D. increased by a factor of 4


\( X \) is a Normally distributed variable
with mean \( =30 \) and standard deviation
\( =4 . \) Find \( P(x>21) \)
A . 0.9878
B. 0.9383
c. 0.9975
D. 0.9126


The approximate value of \( (33)^{1 / 5} \) is
A . 2.0125
B. 2.1
c. 2.0
D. none of these


Reading of the voltmeter is
A. \( 2 v \)
B. 2.04
c. \( 1.96 \mathrm{v} \)
D. 1.0


r.m.s. speed of ideal gas at \( 127^{\circ} \mathrm{C} \) is \( 200 m / s, \) the r.m.s. speed of same ideal
gas at temperature \( 227^{\circ} \mathrm{C} \) is:
A. \( 100 \sqrt{5} \)
5
в. \( 200 \sqrt{5} \)
\begin{tabular}{l}
\( c \cdot 100 \sqrt{15} \) \\
\hline
\end{tabular}
D. \( 100 \sqrt{10} \)


The combination of two layers of opposite charges around the colloidal particle is called Helmholtz electrical double layer. The potential difference between the fixed layer and the diffused layer of opposite charge is called:
A. electrode potential
B. zeta potential
c. adsorption potential
D. diffused potential


A ray of light incident normally on the first face of an equilateral prism undergoes total internal reflection at the second face if refractive index \( \mu \) is
A \( \cdot \) less than \( \frac{\sqrt{3}}{2} \)
B. less than \( \frac{2}{\sqrt{3}} \)
c. more than \( \frac{\sqrt{3}}{2} \)
D. more than \( \frac{2}{\sqrt{3}} \)


Statement 1: There can be
displacement of an object even in the absence of any force acting on it. Statement 2: An object in uniform motion in a straight line shows
displacement even when the net force acting on it is zero.
A. Both statement 1 and statement 2 are true and statement 2 is correct explanation of statement
B. Both statement 1 and statement 2 are true, but statement 2 is not correct explanation of statement
c. statement 1 is true but statement 2 is false
D. Statement 1 is false but statement 2 is true


What will be density \( \left(\operatorname{in} g m L^{-1}\right) \) of 3.60 molar sulphuric acid having \( 29 \% \) by mass? \( \left(\text {Molar mass}=\mathbf{9 8 g m L}^{-1}\right) \)
A . 1.88
B. 1.22
\( c \cdot 1.45 \)
D. 1.64


Explain simple microscope on the basis of the following points:
(a) Ray diagram for the formation of image;
(b) Expression for magnifying power when the final image is formed:
(i) At the least distance of distinct
vision;
(ii) At infinity.


In which of the following species hyperconjugation is possible? Stability of carbocation, alkyl free radical and alkene can be explained on the basis of hyperconjugation. In all
these cases there is the presence of
hydrogen atom at the adjacent \( s p^{2} \)
hybridised carbon atom. Total no of
hyperconjugating structures depends upon the no of hydrogen atoms present
at adjacent carbon atom of \( s p^{2} c- \) atom
more the hyperconjugating structure more is the stability of ions.
\( \mathbf{A} \cdot C H_{3}-\stackrel{+}{C H_{2}} \)
B. \( C_{6} H_{5}-C H_{3} \)
\( \mathbf{c} \cdot C H_{2}=C H_{2} \)
D. \( \quad C H_{3}-C_{I_{3}}^{C H_{3}}-C H=C H_{2} \)


"Xe \( F_{2} \) and \( X e F_{6} \) can be kept in a dry
pyrex vessels while \( X e F_{4} \) attacks
these."
Answer whether the above statement is
true or false.
If true enter 1 , else 0


The equation of state for a certain gas is \( P=\frac{R T}{V_{m}-b}-\frac{a}{V_{m}}, \) where a and b are
constants distinct from zero. Ascertain
whether the gas has a critical point or
not. Answer as 1 if the gas has critical
point and as \( 2, \) if no critical point.


The power loss is less in transmission lines, when :
A. Voltage is less but current is more
B. Both voltage and current are more
c. Voltage is more but current is less
D. Both voltage and current are less


Electric potential is :
A. a scalar quantity
B. a vector quantity
C. neither scalar nor vector
D. sometimes scalar and sometimes vector


Two blocks \( A \) and \( B \) of masses \( 3 m \) and
\( \mathrm{m}, \) respectively, are connected by a massless and inextensible string. The
whole system is suspended by a massless spring as shown. The magnitudes of accelerations of \( A \) and \( B \), immediately after the string is cut, are respectively:
A \( \cdot g, g \)
В. \( g, \frac{g}{3} \)
\( c \cdot \frac{g}{3}, g \)
D. \( \frac{g}{3}, \frac{g}{3} \)


Overall nerves slow down the body and divert energy to digestion and other basic housekeeping tasks; and nerves slow down housekeeping tasks and increase overall activity, in times of heightened awareness or excitement.
A. Autonomic; Somatic
c. Parasympathetic; sympatheticç
D. Peripheral; Central


Uranus has
satellites.
A. 7
B. 17
c. 27
D. 37


How do mendel's experiments show
that
(a)traits may be dominant or recessive?
(b) inheritance of two traits is
independent of each other


The hybridisation of \( \mathrm{Xe} \) is \( \mathrm{sp}^{3} \mathrm{d}^{2} \) in :
A. \( \mathrm{XeF}_{2} \)
в. \( \mathrm{xe} \mathrm{e}_{4} \)
c. \( \mathrm{xeF}_{4} \)
D. \( \mathrm{xeO}_{3} \)


Find the order of the differential
equations of all circles in the plane XOY
which have their centres on x-axis and
have give radius.


ABCD is a square of 1 metre side of a
non-conducting material. Four metallic spheres of 4,5,8 and \( 10 \mathrm{cm} \) diameters are placed at the four corners. All of
them are connected by a fine metallic wire and charge of 540 units is imparted to the system. The potential at the centre of the square is :
(in cgs system)
A \( \cdot \frac{540 \sqrt{2}}{400} \)
B. \( \frac{540 \sqrt{2}}{200} \)
c. \( \frac{540 \sqrt{2}}{100} \)
D. \( \frac{540 \sqrt{2}}{10} \)


Which of the following metals does not produce hydrogen gas when added to
acid?
A. Potassium
B. Gold
c. zinc
D. Leadd


In the fig. \( A P \) and \( B P \) are the tangents draw from an external point P. Prove
that \( \angle A O B \) and \( \angle A P B \) are
supplementary


The crossection of a canal is a
trapezium. The breadths of the top and
bottom of the canal are \( 8 m \) and \( 6 m \)
respectively. If the earth of volume \( 112 \times 10^{4} m^{3} \) is taken out to build the
canal of \( 50 \mathrm{km} \) long, then the depth of the canal will be
\( \mathbf{A} \cdot 3.2 m \)
B. \( 3.8 m \)
c. \( 4.0 m \)
D. 4.2 \( m \)


Veena's car radio will run from a \( 12 \vee \) car
battery that produces a current of 0.20 A even when the car engine is turned off The car battery will not longer operate when it has lost \( 1.2 \times 10^{6} J \) of energy. If
Veena gets out of the car, leaving the radio on by mistake, how long will it
take for the car battery to go completely dead, i.e., lose all energy?


HI cannot be prepared by the action of
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on \( \mathrm{K} \) I because \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is
\( -? \)
A. oxidising agent
B. reducing agent
c. A and B
D. None of these


Cytokinesis refers to
A. Division of chromosomes
B. Division of cytoplasm
C. Division of nucleus
D. None of the above


A horse is placed for grazing inside a
rectangular field \( 70 m \) by \( 52 \mathrm{m} \) and is
tethered to one corner by a rope \( 21 \mathrm{m} \)
long. On how much area can it graze?
A \( .346 .5 \mathrm{cm}^{2} \)
В. \( 360 \mathrm{cm}^{2} \)
c. \( 350.5 \mathrm{cm}^{2} \)
D. \( 380 c m^{2} \)


Two circular coils of radii \( 5 \mathrm{cm} \) and 10
cm carry currents of 2 A.The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres
coincide.Magnitude of magnetic field at the common centre of coil is
This question has multiple correct options
A. \( 8 \pi \times 10^{-4} T \) if currents in the coils are in same ser
B . \( 4 \pi \times 10^{-4} T \) if currents in the coils are in opposite
sense
c. zero if currents in the coils are in opposite sense
D. \( 8 \pi \times 10^{-4} T \) if currents in the coils are in opposite
sense


Define the following terms with a suitable example of each:
(a) Tranquilizers
(b) Antibiotics
(c) Non-ionic detergents


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{3}, \mathbf{0}) \) and foci are
(±2,0)


Which one of the following compounds is an isomer of 1-butanol?
A. 2-Methyl-2-butanol
B. 1-Methy|-2-butanol
c. 3-Methyl-2-butanol
D. 2-Methyl-1-propanol


Modes of controlling pollution in large cities include(s):
A. less use of insecticides
B. proper disposal of organic wastes, sewage and industrial effluents
c. shifting of factories out of the residential area
D. all the above


A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number \( 1,2,3, \dots \dots ., 12 \) as shown in figure. What is the probability that it will point to multiple of \( 4 ? \)
\( A \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
E. None of these


Assertion
A particle has constant acceleration is
x-y plane. But neither of its acceleration
components \( \left(a_{x} \text { and } a_{y}\right) \) is zero. Under
this condition particle can not have
parabolic path.
Reason
In projectile motion, horizontal component of acceleration is zero.
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


What Benjamin Franklin invented?
A. Bifocal spectacles
B. Radio
c. Barometer
D. Hygrometer


A stone thrown upwards with speed \( u \) attains maximum height \( h \). Another stone thrown upwards from the same
point with sapped \( 2 u \) attains maximum
height \( \boldsymbol{H} \). What is the relation between
\( h \) and \( H ? \)
A. \( 2 h=H \)
\( H \)
в. \( 3 h=H \)
\( c \cdot 4 h=H \)
D. \( 5 h=H \)


is a suitable technique of separation of the components from a mixture of calcium sulphate and camphor.
A. Sublimation
B. Distillation
c. Sedimentation
D. None of the above


Solve the inequalities for real \( x \) \( \frac{3(x-2)}{5} \leq \frac{5(2-x)}{3} \)


Select the incorrect statement(s).
This question has multiple correct options
A. All Arrhenius acids are also Bronsted acids but all
Arrhenius bases are not Bronsted bases.
B. All Lewis bases are Bronsted bases.
C. All Bronsted acids are Lewis acids.
D. Conjugate base of a strong acid is weak.


Find \( \left|\begin{array}{lll}\log e & \log e^{2} & \log e^{3} \\ \log e^{2} & \log e^{3} & \log e^{4} \\ \log e^{3} & \log e^{4} & \log e^{5}\end{array}\right| \)
\( A \)
B.
\( c .4 \log e \)
\( \mathbf{D} \cdot 5 \log e \)


of same length but made up of different
materials and kept as shown, an be, if
the meeting point is the origin of \( c 0 \)
ordinates
\( ^{\mathrm{A}} \cdot\left(\frac{L}{2}, \frac{L}{2}\right) \)
B \( \cdot\left(\frac{2 L}{3}, \frac{L}{2}\right) \)
c. \( \left(\frac{L}{3}, \frac{L}{3}\right) \)
D \( \cdot\left(\frac{L}{3}, \frac{L}{6}\right) \)


In a series LCR circuit,the inductive
reactance is twice the resistance and the capacitance reactance is \( \frac{1}{3}^{r d} \) the
inductive reactance. The power factor of
the circuit is:
A . 0.5
B. 0.6
\( c .0 .8 \)
D.


How is an electromagnet different from a permanent magnet?


Energy flow and energy transformations of a living system follow:
A. Law of limiting factors
B. Law of thermodynamics
c. Leibig's law of minimum
D. Biogenetic law


When an electron falls from a higher
energy a lower energy level, the difference in the energies appears in the from of electromagnetic radiation Why cannot it be emitted as other forms
of energy?


The solubility of \( C a F_{2}(K=3.4 \times \)
\( \mathbf{1 0}^{-11} \) ) in \( 0.1 M \) solution of \( N a F \) would
be:
A \( \cdot 3.4 \times 10^{-12} M \)
В. \( 3.4 \times 10^{-10} M \)
c. \( 3.4 \times 10^{-9} M \)
D. \( 3.4 \times 10^{-13} M \)


Longest plant cells are
A. vessels
B. Trachieds
c. cotton fiber
D. Fibres of Ramie


In a potentiometer wire experiment, the
emf of a battery in the primary circuit is \( 20 V \) and its internal resistance is \( 5 \Omega \)
There is a resistance box in series with
the battery and the potentiometer wire, whose resistance can be varied from
\( 120 \Omega \) to \( 170 \Omega \). Resistance of the
potentiometer wire is \( 75 \Omega \). The following potential differences can be measured using this potentiometer This question has multiple correct options
\( \mathbf{A} \cdot 5 V \)
B. \( 6 V \)
c. \( 7 V \)
D. \( 8 V \)


What are the forces imparted by
atmosphere on the walls of a room of
dimension \( 6 m \times 5 m \times 4 m ?(1 \mathrm{Atm} .= \)
\( \mathbf{1 0}^{\mathbf{5}} \boldsymbol{N} / \boldsymbol{m}^{\mathbf{2}} \mathbf{)} \)
\( \mathbf{A} \cdot 7 \times 10^{6} N \)
B \( \cdot 2 \times 10^{7} N \)
C \( .2 \times 10^{8} N \)
D. \( 2 \times 10^{6} N \)


A battery of emf \( 15 \mathrm{V} \) and internal resistance of \( 4 \Omega \) is connected to a
resistor. If the current in the circuit is 2
A and the circuit is closed. Resistance
of the resistor and terminal voltage of the battery will be.
A \( .2 .5 \Omega, 6 \vee \)
B. \( 3.5 \Omega, 6 v \)
c. \( 2.5 \Omega, 7 v \)
D. \( 3.5 \Omega, 7 \vee \)


Of the following, the most recent ancestors of vascular plants were probably
A. Mosses
B. Red algae
c. Horsetails
D. Green algae


Thermal conductivity of standard SWNT along its length is Watt/m.K.
A . 3500
B. 35,000
c. 350
D. 3600


To make an n-type semiconductor, an
intrinsic semiconductor is doped with
A. gallium
B. indium
c. boron
D. arsenic


The four wires from a larger circuit
intersect at junction A a shown. What is
the magnitude and direction of the
current between points \( A \) and \( B ? \)
A. 2 A from \( A \) to \( B \)
B. 2 A from \( B \) to \( A \)
C. 3 A from A to B
D. 3 A from B to A


In an experiment, the refractive index of glass was observed to be
\( \mathbf{1 . 4 5}, \mathbf{1 . 5 6}, \mathbf{1 . 5 4}, \mathbf{1 . 4 4}, \mathbf{1 . 5 4}, \mathbf{1 . 4 4}, \mathbf{1 . 5 4} \)
and \( 1.53 . \) Calculate mean value of refractive index


Which of the following belongs to the actinide series of elements?
A .
B. Ta
c.
D. Lu


Which one moves with greatest speed:
A . \( \alpha \) -rays
B. \( \beta \) -rays
c. \( \gamma \) -rays
D. cathode rays


Q Type your question
1vace, ivabr and 1 vat
(A) The concentration of \( A g^{+} \) required to initiate precipitation of each of \( A g I, A g B r \) and \( A g C l \) are \( 1.5 \times 10^{-13} \)
\( 3.3 \times 10^{-10} \) and \( 1.6 \times 10^{-7} \)
respectively.
(B) The percentage of \( I^{-} \) precipitated before \( A g B r \) precipitates is \( 99.95 \% \)
(C) The percentage of \( I^{-} \) precipitated
before \( C l^{-} \) precipitates is \( 99.999917 \% \)
Given that;
\( \left(\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{I})=\mathbf{1 . 5} \times \mathbf{1 0}^{-\mathbf{1 6}}\right. \)
\( \boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{B r})=\boldsymbol{3} \boldsymbol{3} \times \mathbf{1 0}^{-13} \)
\( \left.\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l})=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{1 0}}\right) \)
Which of the above-given option(s) is/are correct?
A. Only A
B. A and B
c. B and c
D. A, B and C


Among \( \mathrm{K}, \mathrm{Ca}, \mathrm{Fe} \) and \( \mathrm{Zn}, \) the elements which can form more than one binary compound with chlorine is:
\( A \cdot F e \)
B. zn
\( c \cdot k \)
D. ca


Assertion
On satellites we feel weightlessness. Moon is also a satellite of earth. But we
do not feel weightlessness on moon.
Reason
Mass of moon is considerable.
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


\( \int \frac{e^{x}-1}{e^{x}+1} d x \)
A \( \cdot \log \left(e^{x}+1\right)-\log e^{x} \)
B \( \cdot 2 \log \left(e^{x}-1\right)-\log e^{x} \)
C \( \cdot 2 \log \left(e^{x}+1\right)-\log e^{x} \)
D \( \cdot 2 \log \left(e^{x}+1\right)+\log e^{x} \)


A particle \( A \) having a charge of \( 2.0 \times \)
\( 10^{-6} C \) is held fixed on a horizontal
table. A second charged particle of mass \( 80 g \) stays in equilibrium on the table at a distance of \( 10 \mathrm{cm} \) from the
first charge. The coefficient of friction
between the table and this second
particle is \( \mu=0.2 . \) Find the range
within which the charge of this second
particle may lie.


If \( p \) and \( q \) are the perpendicular distances from origin to the straight
\( \operatorname{lines} x \sec \theta-y \operatorname{cosec} \theta=a \) and
\( \boldsymbol{x} \cos \boldsymbol{\theta}+\boldsymbol{y} \sin \boldsymbol{\theta}=\boldsymbol{a} \cos 2 \boldsymbol{\theta} \)
then which of the following is correct?
\( \mathbf{A} \cdot 4 p^{2}+q^{2}=a^{2} \)
B \( \cdot p^{2}+q^{2}=a^{2} \)
C \( \cdot p^{2}+2 q^{2}=a^{2} \)
D. \( 4 p^{2}+q^{2}=2 a^{2} \)


Nitrogen dioxide and sulphur dioxide have some properties in common. Which property is shown by one of these compounds, but not by the other?
A. is soluble in water
B. is used as a food-preservative.
c. forms 'acid-rain'.
D. is a reducing agent


A ball is dropped from a height. If it
takes 0.200 ss to cross the last \( 6.00 m \)
before hitting the ground, find the height from which it is dropped. Take \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2} \)


Natural rubber or raw rubber consists of
basic material latex which is a
dispersion of isoprene. During the treatment, this isoprene forms a high molecular weight polymer of isoprene. Natural rubber can be obtained from
five hundred different species of plants.
Which rubber is not a polydiene?
A. Polyisoprene
B. Polychloroprene
c. Thiokal rubber
D. Nitrile rubber


Solve the different equation:-
\( \left(\tan ^{-1} y-x\right) d y=\left(1+y^{2}\right) d x \)


Which of the following compound will have highest boiling point?
A. water
B. Ethanol
c. Methanol
D. Dimethylethene


The half life of a radioactive nucleus is
50 days.The time interval \( \left(t_{2}-t_{1}\right) \)
between the time \( t_{2} \) when \( \frac{2}{3} \) of it has
decayed and the time \( t_{1} \) when \( \frac{1}{3} \) of it
had delayed is-
A. 50 days
B. 60 days
c. 15 days
D. 30 days


Multiply (-3) and (+5)


The negation of \( \boldsymbol{q} \vee \sim(\boldsymbol{p} \wedge \boldsymbol{r}) \) is?


Maximum -l effect is exerted by the
group:
A . \( -C_{6} H_{5} \)
в. \( -O C H_{3} \)
c. \( -C l \)
D. \( -N O_{2} \)


The intensity at the maximum in a
Young's double slit experiment is \( \boldsymbol{I}_{0} \)
Distance between two slits is \( \boldsymbol{d}=\mathbf{5} \boldsymbol{\lambda} \)
where \( \lambda \) is the wavelength of light used
in the experiment. What will be the intensity in front of one of the slits on
the screen placed at a distance \( D= \)
\( 10 d ? \)
\( \mathbf{A} \cdot I_{0} \)
в. \( \frac{I_{0}}{4} \)
c. \( \frac{3}{4} I_{0} \)
D. \( \frac{I_{0}}{2} \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}\left(\boldsymbol{C}_{6} \boldsymbol{H}_{5}\right)- \)
\( N H_{2} \)
The IUPAC name of the compound is :
A. \( 1- \) Amino -1 - phenyl - 2 - methyl propane
B. 2- Methyl-1- phenyl propan-1 - amine
c. 2- Methyl-1- amino -1 - phenyl propane
D. 1- -Isopropyl -1 - phenyl methyl amine


A die is thrown. \( A \) is the event that
prime number comes up, \( B \) is the event
that the number divisible by three comes up, \( C \) is the event that the
perfect square number comes up. Then, \( A, B \) and \( C \) are :
A. Mutually exclusive
B. Mutually exhaustuve
c. Same
D. None of these


Which of the following compounds has
\( s p^{2} \) -hybridization?
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
\( c \cdot N_{2} O \)
D. \( C O \)