You are given 'mn' wires of equal
resistance, If \( m \) wires are in series and
n such combinations are in parallel the
resultant resistance is \( R_{1} \). If \( n \) wires are
in series and m such combinations are
in parallel, the resultant resistance is
\( R_{2} . \) Then \( \frac{R_{1}}{R_{2}} \) is:
A . 1: 1
B. \( m: n \)
\( \mathbf{c} \cdot m^{2}: n^{2} \)
D. \( n^{2}: m^{2} \)


A capillary tube, made of glass is
dipped into mercury. Then:
A. mercury rises in the capillary tube.
B. mercury descends in capillary tube.
C. mercury rises and flows out of capillary tube.
D. mercury neither rises nor descends in the capillary tube


In Vallisneria, stomata are
A. Present on upper epidermis of leaf.
B. Present on lower epidermis of leaf.
C. Present on both the epidermis of leaf.
D. Absent.


The moment of inertia of a uniform rod
of length \( 2 l \) and mass ' \( m \) ' about an axis through centre and inclined at an angle
\( \theta \) to rod is:
A \( \cdot \frac{m l^{2}}{3} \sin ^{2} \theta \)
B. \( \frac{m l^{2}}{6} \cos ^{2} \theta \)
c. \( \frac{m l^{2}}{2} \cos ^{2} \theta \)
D. \( \frac{m l^{2}}{12} \cos ^{2} \theta \)


Calculate the degree of ionization of
\( 0.05 \mathrm{M} \) acetic acid of its \( _{p} \boldsymbol{K}_{a} \) value is 4.74. How is the degree of dissociation affected when its solution is also (a)
\( 0.01 \mathrm{M} \) and
(b) \( 0.1 \mathrm{M} \) in hydrochloric acid?


\( \ln \) a \( \triangle A B C, \) if \( \angle A=72^{\circ} \) and \( \angle B=63^{\circ} \)
find the \( \angle C \)


The distance of planet Jupiter from the
Sun is 5.2 times that of the earth. Find
the period of revolution of Jupiter
around the Sun.


At \( 298 \mathrm{K} \) the entropy of rhombic sulphur \( 32.04 \mathrm{J} / \mathrm{mol} \mathrm{K} \) and that of monoclinic
sulphur is \( 32.68 \mathrm{J} / \mathrm{mol} \) K. The heat of
their combustion are respectively
-298246 and \( -297948 J m o l^{-1} . \Delta G \)
for the reaction; \( S_{r h o r m b i c} \rightarrow S_{m o n o c l i n i c} \)
will be :
A . 107.28
B. 10.728 J
c. 107.28 k
D. 10728 J


Assertion
Azeotropic mixtures are formed only by non-ideal solutions and they may have boiling points either greater than both the components or lesser than both the
components.
Reason
The composition of the vapour phase is same as that of the liquid phase of an azeotropic mixture.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following pairs has both elements from the same group?
A. \( M g, R a \)
в. \( M n, C l \)
c. \( M g, C u \)
D. \( M g, C l \)


State true or false:
Every integer is a rational number.
A. True
B. False


\( \int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)


If \( \boldsymbol{\alpha}, \boldsymbol{\beta}(\boldsymbol{\alpha}<\boldsymbol{\beta}) \) are the roots of the
equation \( 6 x^{2}+11 x+3=0 \) then which
of the following are real? This question has multiple correct options
\( A \cdot \cos ^{-1} \alpha \)
B. \( \sin ^{-1} \beta \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} \alpha \)
D. Both \( \cot ^{-1} \alpha \) and \( \cot ^{-1} \beta \)


The equation for Freundlich adsorption
isotherm is:
A \( \cdot \frac{x}{m}=K p^{1 / n} \)
B . \( x=m K p^{1 / n} \)
c. \( x / m=K p^{-n} \)
D. all of these


Among the following compounds most basic amino acid is:
A. Iysine
B. asparagine
c. serine
D. histidine


The amplitude of a particle executing
SHM about 0 is \( 10 \mathrm{cm} . \) Then:
A. when the KE is 0.64 times of its maximum KE, its displacement is 6 cm from 0
B. its speed is half the maximum speed when its displacement is half the maximum displacement
\( c . \) Both
(a) and
(b) are correct
D. Both (a) and
(b) are wrong


Which of the following effects of current
does not depend on the direction of
current?
A. Lighting and chemical effects
B. Heating and lighting effects
c. Heating and magnetic effects
D. Magnetic and chemical effects


Out of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{4} \boldsymbol{O}_{6}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5} \) and
\( H_{2} S_{2} O_{8} \) peroxy acids are :
A. \( H_{2} S_{2} O_{3}, H_{2} S_{4} O_{6} \)
в. \( H_{2} S_{4} O_{6}, H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{5}, \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)
D. \( H_{2} S_{2} O_{3}, H_{2} S_{2} O_{8} \)


Find the sum to infinity of the geometric series \( 2+\frac{2}{3}+\frac{2}{9}+\dots \)


The reduction of an oxide by aluminium
is called:
A. Kroll's process
B. Van Arkel process
c. Ellingham process
D. Goldschmidt's aluminothermite process


Two loud speakers \( L_{1} \) and \( L_{2}, \) driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from
zero and the detector at D records a
series of maxima and minima. If the
speed of sound is \( 330 \mathrm{m} / \mathrm{s} \) then the
frequency at which the first maximum is observed is :
A . \( 165 \mathrm{Hz} \)
в. ззо нz
c. 495 нz
D. 660 нz


If we throw a stone in a pond of standing
water, the waves produced are:
A. transverse in nature
B. longitudinal in nature.
c. a combination of transverse and longitudinal in nature
D. of some other type


Find the number of solutions of the
equation \( \cos \left(\cos ^{-1} x\right)= \)
\( \operatorname{cosec}\left(\operatorname{cosec}^{-1} x\right) \)
A.
B.
\( c \cdot 2 \)
D.


What is an example for a double salt?
A. Cuprammonium sulphate
B. Mohr's salt
c. Potassium ferricyanide
D. Hexamminecobalt(III) chloride


A passenger sitting in a train with his face in the direction of the moving train, tosses a coin which falls behind him. It
means that motion of the train is
A . accelerated
B. uniform
c. retarded
D. along circular tracks


A body of mass \( 4 \mathrm{kg} \) moving with a velocity of \( 9 \mathrm{m} / \mathrm{s} \). Collides with a body of \( 8 \mathrm{kg} \) at rest. The coefficient of restitution is \( 0.33 . \) After collision the
velocity of body having mass \( 4 \mathrm{kg} \) is:
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3 m / s \)
D. \( 9 \mathrm{m} / \mathrm{s} \)


Prove that
\( \operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right)\right) \)
\( \sqrt{\mathbf{3}-\boldsymbol{a}^{2}}, \) where \( \boldsymbol{a} \in[\mathbf{0}, \mathbf{1}] \)


Which of the following gas is present in large quantity in atmosphere?
A. oxygen
B. Hydrogen
c. Nitrogen
D. Methane


A slice of banana weighing 2.502 g was burnt in a bomb calorimeter producing
a temperature rise of \( 3.05^{\circ} \mathrm{C} \). The combustion of \( 0.316 \mathrm{g} \) of benzoic acid in the same calorimeter produced a
temperature rise of \( 3.24^{\circ} \mathrm{C} \). The heat of combustion of benzoic acid at constant
volume is \( -3227 k J \) mol\( ^{-1} . \) If the
average banana mass is 125 g, the kilojoules of energy can be obtained from 1 average banana is: (nearest integer value)


Manufacture of sulphuric acid by contact process involves dissolution of
\( S O_{3} \) in \( H_{2} S O_{4} \) and not in water. Justify


If \( x^{p} \) occurs in the equation \( \left(x^{2}+\frac{1}{x}\right)^{2 n} \) prove that its coefficient is
\( \frac{\mid 2 n}{\mid \frac{1}{3}(4 n-p)} \mid \frac{1}{3}(2 n+p) \)


First order reaction completes \( 20 \% \) in 5 min. How much time it will take for \( 60 \% \)
completion?
A . 26.5 min
B . 20.5 min
c. \( 19.5 \mathrm{min} \)
D. 18 min


From the Ellingham graphs on carbon, which of the following statements is false?
A \( \cdot C O_{2} \) is more stable than \( C O \) at less than 983 k
B. \( C O \) reduces \( F e_{2} O_{3} \) to \( F e \) at less than 983 k
c. \( C O \) is less stable than \( C O_{2} \) at more than 983 k
D. \( C O \) reduces \( F e_{2} O_{3} \) to \( F e \) in the reduction zone of Blast furnace


The efficiency of machine is reduced due to friction.
A. True
B. False
c. Ambiguous
D. Data insufficient


Select the correct options:
A. Due to lanthanide contraction \( Z r \) and \( H f \) have almost equal size.
B. \( d \) - and \( f \) -orbitals do not shield the nuclear charge very effectively
c. Both
(A) \( \&(\mathrm{B}) \) are correct statements.
D. Both
(A) \&
(B) are incorrect statements.


The magnitude of the average electric field normally present in the atmosphere just above the surface of
the Earth is about \( 150 N / C \), directed
inward towards the center of the Earth.
This gives the total net surface charge
carried by the Earth to be : [Given \( \epsilon_{0}= \) \( \mathbf{8 . 8 5} \times \mathbf{1 0}^{-12} \mathbf{C}^{2} / \mathbf{N}-\boldsymbol{m}^{2}, \boldsymbol{R}_{E}=\mathbf{6 . 4} \times \)
\( \mathbf{1 0}^{\mathbf{6}} \boldsymbol{m} \)
A \( .+660 k C \)
в. \( -660 k C \)
\( c .-680 k C \)
D. \( +680 k C \)


In convection, heat is transferred
A. upwards
B. downwards
c. sideways
D. in all directions


Use Euclid's algorithm to find the HCF of
4052 and 12576


The stability of ferric ion is due to
A. half filled f-orbitals
B. half filled d-orbitals
C. completely filled f-orbitals
D. completely filled d-orbitals


If the energy, \( E=G^{p} h^{q} c^{r}, \) where \( G \) is the
universal gravitational constant, h is the Planck's constant and c is the
velocity of light, then the values of \( p, q \) and \( r \) are, respectively
A \( \cdot-1 / 2,1 / 2 \) and \( 5 / 2 \)
B. \( 1 / 2,-1 / 2 \) and \( -5 / 2 \)
c. \( -1 / 2,1 / 2 \) and \( 3 / 2 \)
D. \( 1 / 2,-1 / 2 \) and \( -3 / 2 \)


Silver nitrate solution is kept in a
laboratory in colored reagent bottles.


Evaluate \( : \lim _{x \rightarrow a} \frac{x^{m}-a^{m}}{x^{n}-a^{n}}= \)


The impulse of a body is equal to:
A. Rate of change of its momentum.
B. Change in its momentum.
C. The product of force applied on it and the time of application of the force.
D. Both (B) and (C)


Can you locate the electron within
\( \mathbf{0 . 0 0 5 n m ?} \)


The domestic sewage in large cities
A. Is processed by aerobic and then anaerobic bacteria in the secondary treatment in sewage treatment plant \( (\mathrm{STPs}) \)
B. When treated in STPs does not really require the aeration step as the sewage contains adequate oxygen.
C. Has very high amounts of suspended solids and dissolved salts.
D. Has a high BOD as it contains both aerobic and anaerobic bacteria.
E. Is processed by anaerobic bacteria in the primary treatment and by aerobic bacteria in the secondary treatment in sewage treatment plant (STPs)


If the magnetic moment of magnet is \( 0.8 \times 10^{-3} A m^{2} \) and the force acting on
each pole in a uniform magnetic field strength of 0.48 gauss, is \( 0.512 \times 10^{-6} N \)
The distance between the poles of the magnet is : (in \( c m) \)
A . 25
в. 12.5
c. 15
D. 7.5


Match each item in Column I with
appropriate one/s in Column I
Select the correct alternative:
\( A \cdot A-V I I, B-I, C-I \)
B. A-IV, B-I, C-II
c. A-VII, B-V, C-VI
D. A-IV, B-II, C-V


Which of the following statement(s) is/are incorrect?
I. Cellulose is a polysaccharide
composed of a large number of \( \beta-D \) glucose units.
II. \( \beta \) -D-glucose units in cellulose are joined by \( \beta \) -glycosidic linkages.
III. Starch is a mixture of amylose and amylopectin.
IV. Amylose is a branched chain
polysaccharide.
V. Amylopectin is a linear polysaccharide.
A . only
B. only III
c. ॥ and III
D. IV and v


A steel ball of mass \( m \) falls in a viscous
liquid with terminal velocity \( v, \) then the
steel ball of mass \( 8 m \) will fall in the
same liquid with terminal velocity:
\( A \)
B. \( 4 v \)
\( c \cdot 8 v \)
D. \( 16 \sqrt{2} v \)


Find the solution of the following:
If \( 5 x+4>8 x-11, \) then \( x<? \)


\( H_{2} \) is present in the free state in sun
and stars.
A. True
B. False


Two concentric circular coil of radius
\( 20 c m \) and \( 30 c m \) carries current \( 2 A \) and
\( 3 A \) respectively in opposite direction
then magnetic field at centre will be :-
A. \( 4 \pi \times 10^{-7} \)
В. \( 2 \pi \times 10^{-7} \)
c. \( 2 \times 10^{-7} \)
D. 0


Q Type your question
order
(a) \( 2 p_{y} \) orbitals of each oxygen atom overlap laterally/sidewise to form a pi
bond.
(b) Thus, a double bond between two
oxygen atoms in which one \( p_{z}-p_{z} \)
sigma bond and \( \mathrm{p}_{y}-\mathrm{p}_{y} \pi \) bond is
formed.
(c) All the three \( 2 p \) orbitals are
perpendicular to each other. Hence \( 2 p_{z} \)
orbitals of each oxygen atom overlap end to end to form a sigma bond.
(d) The electronic configuration of oxygen is \( O: 1 s^{2} 2 s^{2} 2 p_{x}^{1} 2 p_{y}^{2} 2 p_{z}^{1} \)
A \( \cdot c a d b \)
B. \( d c a b \)
\( c \cdot c d b a \)
\( D \)


The value of \( \sin \left(\tan ^{-1} x+\cot ^{-1} x\right) \) is


Which of the following group cannot participate in resonance with any
group?
\( \mathbf{A} \cdot_{-C H_{2}} \)
В. \( -N H_{3} \)
c. il \( -N^{\oplus} \)
D. \( -N O \)


Assertion
Both 138 g of \( K_{2} C O_{3} \) and 12 g of carbon have same number of carbon atoms.
Reason

Both contain 1 g atom of carbon which contains \( 6.022 \times 10^{23} \) carbon atoms.
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


A cycle tube has volume \( 2000 \mathrm{cm}^{3} \)
Initially the tube is filled to \( 3 / 4 \) th of its
volume by air at pressure of \( 105 N / m^{2} \)
It is to be inflated to a pressure of \( 6 x \) \( 10^{5} N / m^{2} \) under isothermal conditions.
The number of strokes of pump, which
\( \operatorname{gives} 500 c m^{3} \) air in each stroke,
to inflate the tube is
A . 2
B. 12
\( c \cdot 42 \)
D. 1


Invert sugar is
A. leavorotatory
B. dextrorotatory
C . optically inactive
D. racemic mixture


Determine the degree of association (polymerisation) for the reaction in
aqueous solution \( 6 H C H O \rightleftharpoons \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{1 2}} \boldsymbol{O}_{\boldsymbol{6}} \)
If observed(mean) molar mass of
\( H C H O \) and \( C_{6} H_{12} O_{6} \) is 150
A . 0.50
B. 0.833
c. 0.90
D. 0.96


Which of the following statements is incorrect?
A. It is not possible to compress a gas at a temperature below \( T_{c} \)
B. At a temperature below \( T_{c} \), the molecules are close enough for the attractive forces to act, and condensation occur
C. No condensation takes place above \( T_{c} \)
D. The kinetic energy of the gas molecules is higher above \( T_{c} \), and the attraction between them decreases


One complete set of negative and positive values of alternating quantities is called
A. Time period
B. Amplitude
c. Frequency
D. cycle


The correct match is:
List - I \( \quad \) List - II
A. \( A-2, B-3, C-1, D-5 \)
B. \( A-3, B-4, C-5, D-2 \)
C \( \cdot A-1, B-3, C-4, D-2 \)
D. \( A-4, B-2, C-1, D-3 \)


Which of the following is correct?
A. Catalyst undergoes permanent chemical change.
B. Particle size of solute in true solution is \( 10^{-3} \mathrm{m} \)
C. Starch solution is a hydrosol.
D. Hydrolysis of liquid ester in the presence of mineral acid is an example of heterogeneous catalysis reactions.


Construct a \( \triangle A B C, \) when \( A B= \)
\( \mathbf{5} . \mathbf{2} \mathbf{c m}, \angle \mathbf{A}=\mathbf{3 0}^{\circ} \) and \( \angle \mathbf{B}=\mathbf{7 5}^{\circ} \)


Sap wood is otherwise called as
A. Duramen
B. Alburnum
c. Pith
D. Medullary rays


Which one of the following material will reflect sound better?
A. Thermocole
B. Curtain made from cloth
c. steel
D. Paper


Let \( A \) be a finite set, lf \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \) is
onto. Show that \( f \) is one-one


\( \boldsymbol{\epsilon}_{0} \) is known as the
A. electrical permeability of free space
B. electrical permittivity of free space
C. magnetic permeability of free space
D. None of these


The difference of two numbers is 5 and the difference of their reciprocals is \( \frac{1}{10} \) Find the numbers.
A. 10,50
в. 10,5
c. 10,-510,-5
D. 0,5


What do you mean by corrosion? How
can you prevent it?


The hybridization of carbon in diamond, graphite and acetylene is respectively:
В \( . s p, s p^{2}, s p^{3} \)
\( \mathbf{c} \cdot s p^{3}, s p^{2}, s p \)
\( \mathbf{D} \cdot s p^{2}, s p^{3}, s p \)


The number of disulphide linkages present in insulin are:
A . 4
B. 3
\( c \cdot 2 \)
\( D \)


What is the direction of movement of
sugar in phloem?
A. Non-multidirectional
c. Downward
D. Bi-directional


The conduction of impulse takes from
SA node to
A. AV node
B. Bundle of Hiss
c. Purkinjee fibres
D. Cardiac muscles


A ball thrown up vertically returns to the thrower after 6 s Find it's initial velocity.
A. 20 \( \mathrm{m} / \mathrm{s} \)
B. 40 \( \mathrm{m} / \mathrm{s} \)
\( c .35 \mathrm{m} / \mathrm{s} \)
D. 30 \( \mathrm{m} / \mathrm{s} \)


State True or False.
Ductility is not same as malleability.
A. True
B. False


If \( x^{4}+\frac{1}{x^{4}}=119, \) then the value of \( x- \)
\( \frac{1}{-} \) is
\( x \)
\( A \cdot 6 \)
B. 12
c. 11
D.


The mass of carbon anode consumed
(giving the only carbon dioxide) in the production of \( 270 \mathrm{kg} \) of aluminium
metal from bauxite by the Hall process is:
[Atomic mass : \( A l=27] \)
A. \( 90 \mathrm{kg} \)
в. \( 540 \mathrm{kg} \)
c. \( 180 \mathrm{kg} \)
D. 270 \( k g \)


Erythroblastosis foetalis is caused when fertilisation takes place between gametes of
A \( \cdot R h^{-} \) female and \( R h^{+} \) male
B. \( R h^{+} \) female and \( R h^{-} \) male.
c. \( R h^{+} \) female and \( R h^{+} \) male
D. \( R h^{-} \) female and \( R h^{-} \) male


Electrolysis involves conversion of
chemical energy to electrical energy.
A. True
B. False


Find the value of \( p \) for which the points \( (-5,1),(1, p) \) and (4,-2) are collinear
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c .-1 \)
D. 2


In the reaction of p-chlorotoluene with
\( \boldsymbol{K} \boldsymbol{N} \boldsymbol{H}_{2} \) in liquid \( \boldsymbol{N} \boldsymbol{H}_{3}, \) the major
product is:
A . o-toluidine
B. m-toluidine
c. p-toluidine
D. p-chloroaniline


Which of the following trees/plants have seeds enclosed in the fruit?
A. Angiosperms
B. Gymnosperms
c. cryptogams
D. All of the above


Which of the following function is not performed by underground stem?
A. Reproduction
B. Assimilation
c. Perennation
D. storage


Four \( C l_{2} \) molecules undergo a loss and
gain of 6 mole of electrons to form two
oxidation states of \( C l \) in auto redox
change. What are the \( +v e \) and \( -v e \)
oxidation states of \( C l \) in the change:
A \( \cdot C l^{5+}, C l^{\circ} \)
в. \( C l^{7+}, C l^{-} \)
\( \mathbf{c} \cdot C l^{3+}, C l^{\circ} \)
D. \( C l^{3+}, C l^{-} \)


Obtain the product of: \( r n,-m n, m n p \)
A \( .-m^{3} n^{3} p \)
В. \( -m^{2} n^{2} p \)
c. \( m^{2} n^{2} p \)
D. \( -m^{3} n^{2} p \)


Respiratory quotient may be represented as
A. \( O_{2} \) taken in/C \( O_{2} \) evolved
B. \( C O_{2} \) evolved/O \( _{2} \) taken in
\( c \cdot O_{2} \) taken in
D. \( C O_{2} \) taken in


A remote sensing satellite is revolving in an orbit of radius x over the equator
of earth. If the area on each surface in
which satellite can not send message is \( \operatorname{given} \operatorname{as}\left(1-\frac{\sqrt{x^{2}-R^{2}}}{x}\right) s \pi R^{2} . \) Find \( s \)


When hydrogen and oxygen combine to form water, they form:
A. an unstable compound
B. a stable mixture
c. an unstable mixture
D. an extremely stable compound


For what values of \( x, \) the numbers
\( -\frac{2}{7}, x,-\frac{2}{7} \) are in \( G . P ? \)


Hydrolysis of starch involves the use of
the enzyme:
A. maltase
B. zymase
c. invertase
D. diastase


The function of Anti-transpirants is:
A. Reduce the rate of transpiration without affecting carbon assimilation
B. Reduce the rate of transpiration affecting carbon assimilation
C. Reduce the rate of transpiration affecting growth of plant
D. Reduce the rate of transpiration affecting protein synthesis of plant


Nylon is:
A. polyester
B. polyamide
C . orlon
D. terylene


Integrate:
\( \int_{0}^{\pi} \frac{d x}{5+3 \cos x} \)


\( A, B \) and \( C \) are three large, paralle
conducting plates, placed horizontally
\( A \) and \( C \) are rigidly fixed and earthed. \( B \)
is given some charge. Under
electrostatic and gravitational forces, \( \boldsymbol{B} \)
may be :
This question has multiple correct options
A. in equilibrium midway between \( A \) and \( C \)
B. in equilibrium if it is closer to \( A \) than to \( C \)
c. in equilibrium if it is closer to \( C \) than to \( A \)
D. \( B \) can never be in stable equilibrium


Which element has least atomic
diameter?
A. \( F \)
в. \( F e \)
\( c \cdot C l_{2} \)
D. \( N a \)


(ii) 196 and 38220


Four point charges are fixed in position
at the corners of a square, as shown in above figure
Find out the direction of the total
electrostatic force on the charge in the lower right-hand corner of the square?
A.
B. 4
\( c \)
\( D \)
E. The electric force on this charge is


The structure of isoprene is:
\( \mathbf{A} \cdot C H_{2}=C\left(C_{2} H_{5}\right)-C H=C H_{2} \)
B. \( C H_{2}=C\left(O C O H_{3}\right)-C H=C H_{2} \)
\( \mathbf{c} \cdot C H_{2}=C\left(C H_{3}\right)-C H=C H_{3} \)
\( \mathbf{D} \cdot C H_{2}=C H-C=C H \)


A potentiometer wire of length \( 100 \mathrm{cm} \) has a resistance of 10 ohm. it is connected in series with a resistance
and an accumulator of e.m.f \( 2 \mathrm{V} \) and of
negligible internal resistance. A source of e.m.f. \( 10 \mathrm{m} \) V is balanced against a length of \( 40 \mathrm{cm} \) of the potentiometer wire. What is the value of external
resistance?
A. 480 ohm
B. 1120 ohm
c. 790 ohm
D. 640 ohm


As shown in the figure three \( p-v \)
diagrams .In which case the work done
is minimum.
\( A \)
B. I
c. III
D. cannot say


BOD of lake becomes high by :-
A. Vehicles
B. Wind mill
c. Smoke and ammonia
D. Detergents


A thin uniform bar of length L and mass \( 8 \mathrm{m} \) lies on a smooth horizontal table.
Two point masses \( m \) and 2 m are moving in the same horizontal plane from opposite sides of the bar with
speeds \( 2 v \) and \( v \) respectively. The masses stick to the:
A \( \cdot \frac{6 v}{5 l} \)
в. \( \frac{3 v}{5 l} \)
c. \( \frac{6 v}{11 l} \)
D. \( \frac{6 v}{l} \)


The starting material used in Sandmeyer's reaction is
A. phenol
B. haloarene
c. haloalkene
D. benzenediazonium chloride


Azotobacter and Bacillus polymyxa are
A. Decomposers
B. Non-symbiotic nitrogen fixers
C. Symbiotic nitrogen fixers
D. Pathogenic bacteria


A frog sits on the end of a long board of length \( L=10 c m . \) The board rests on
frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is minimum take of speed
\( v \) in \( m s^{-1} \) relative to the ground that the frog follows to do the tricks?
[Assume that the board and frog have equal masses?]
A \( \cdot 2 \sqrt{5} m s^{-1} \)
B. \( 5 m s^{-1} \)
D. \( 10 \sqrt{2} \mathrm{ms}^{-1} \)


Which of the following metals on reacting with sodium hydroxide solution produce hydrogen gas?
a. \( \boldsymbol{C u} \)
b. \( \boldsymbol{A l} \)
c. \( \boldsymbol{F} \boldsymbol{e} \)
d. \( Z n \)
A. b and c
B. b and d
\( c . \) a and \( d \)
D. bonly


Let \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{n \times n} \) be a square matirx and
let \( c_{i j} \) be cofactor of \( a_{i j} \) in A. If \( C=\left[c_{i j}\right] \)
then
B . \( |C|=|A|^{n-1} \)
c. \( |C|=|A|^{n-2} \)
D. none of these


The production of silk from the
silkworm by artificial rearing on commercial scale is called apiculture
A. True
B. False


There is a large difference in the boiling points of butanal and butan-1-ol due to:
A. intermolecular hydrogen bonding in butan-1ol
B. intramolecular hydrogen bonding in butanal
c. higher molecular mass of butan-1-ol
D. resonance shown by butanal.


Which of the following statements is
incorrect?
A. Term 'Nothospecies' refers to the naturally occurring interspecific hybrids
B. As the species do not change with time, therefore they are considered as static groups
C. Metabolism and response to external stimuli are considered as the defining properties of living organisms
D. Hibiscus rosa-sinensis belongs to the same family to which Althaea rosea and Gossypium hirsutum belong to


\( S b F_{5} \) reacts with \( X e F_{4} \) and \( X e F_{6} \) to
form ionic compounds \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}\right]\left[\boldsymbol{S} \boldsymbol{b} \boldsymbol{F}_{6}^{-}\right] \)
and \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}^{-}\right] . \) The geometry of
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+},\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right] \) ion respectively is:
A. square pyramidal, T-shaped
B. bent T-shaped, square pyramidal
c. see-saw, square pyramidal
D. square pyramidal, see saw


A proton and an \( \alpha \) -particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is \( 10 c m, \) the radius of \( \alpha \) -orbit is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 10 \sqrt{2} \mathrm{cm} \)
\( c \cdot 20 c m \)
\( D .5 \sqrt{2} c m \)


Show that reflected and refracted
beams are mutually perpendicular
when the angle of incidence is equal to polarizing angle.


If \( \overline{\boldsymbol{a}}=\mathbf{2} \overline{\mathbf{i}}-\mathbf{3} \overline{\mathbf{j}}+\overline{\mathbf{k}}, \overline{\boldsymbol{b}}=_{-} \overline{\mathbf{i}}+\overline{\mathbf{k}}, \overline{\boldsymbol{c}}= \)
\( 2 \bar{j}-\bar{k}, \) then the area of the parallelogram is having diagonals \( \bar{a}+\bar{b} \) and \( \bar{b}+\bar{c}(\text { in square units }) \) is
A \( \cdot \sqrt{21} \)
B. \( \frac{\sqrt{21}}{2} \)
c. \( \sqrt{19} \)
D. \( \frac{\sqrt{19}}{2} \)


0.001 mol of \( C o\left(N H_{3}\right)_{5}\left(N O_{3}\right)\left(S O_{4}\right) \)
was passed through a cation exchanger and the acid coming out of it required
\( 20 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) NaOH for neutralisation.
Hence, the complex is:
\( \mathbf{A} \cdot\left[C o\left(N H_{3}\right)_{5} S 0_{4}\right] N O_{3} \)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} N O_{3}\right] S O_{4} \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\right]\left(S O_{3}\right)\left(N O_{3}\right) \)
D. none of these


As pressure is increased, what will happen to the following reactions? Match the colum:
Column - Column - II
(P) \( P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+ \)
(1) Shift to forward
\[
C l_{2}(g)
\]
(2) Shift to
(Q) \( 2 N O_{2}(g) \rightleftharpoons N_{2} O_{4}(g) \quad \) backward
(R) \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
(3) No effect
(S) \( a A(g)+b B(g) \rightleftharpoons c C(g) \)
(4) Cannot predict
\( A \cdot 1234 \)
B. 213 4
\( c \cdot 2143 \)
D. 4312


Pressure on the walls by any fluid is due
to
A. inelastic collisions of the molecules on the walls.
B. elastic collisions of the molecules on the walls.
c. electrostatic attraction of molecules with the
molecules of the wall.
D. electrostatic repulsion of molecules with the molecules of the wall.


gas turns colourless nitrogen monoxide into brown fumes of nitrogen dioxide.
\( A \). Ammonia
B. Nitrogen
c. Bromine
D. oxygen


Two children are at opposite ends of an iron pipe. One strikes his end of the iron pipe with a stone. Find the ratio of times taken by the sound wave in air and in iron to reach the other child. Given,
velocity of sound in air is \( 344 \mathrm{m} s^{-1} \) and that in iron is \( 5130 m s^{-1} \)
A \( \frac{t_{1}}{t_{2}}=14.3 \)
в. \( \frac{t_{1}}{t_{2}}=11.9 \)
c. \( \frac{t_{1}}{t_{2}}=14.9 \)
D. \( \frac{t_{1}}{t_{2}}=10.4 \)


The coordinates of a point \( \boldsymbol{P} \) on the line
\( 2 x-y+5=0 \) such that \( |P A-P B| \) is
maximum where \( A \) is (4,-2) and \( B \) is
(2,-4) will be
A \( .(11,27) \)
B. (-11,-17)
c. (-11,17)
D. (0.5)


The distance between the lines \( 5 x- \)
\( 12 y+65=0 \) and \( 5 x-12 y-39=0 \)
is
\( A \cdot 4 \)
B. 16
\( c \cdot 2 \)
D.


A high molecular weight molecule built from a large number of small molecules
is called a
A. monomer
B. isomer
C. polymer
D. tautomer


The ionization potential of the hydrogen atom is \( 13.6 \mathrm{V} \). The energy needed to ionize a hydrogen atom which is in its second excited state is about
A. 3.4 ev
B. 2.5 ev
c. \( 10.2 \mathrm{ev} \)
D. 13.6 ev


Monomers of Natural Rubber and
Neoprene are Respectively:
\( \begin{array}{c}\mathbf{A} \cdot C H_{3}-C=C H-C H_{3}, C H_{3}-C=C H-C H_{3} \\ _{C H_{3}}\end{array}=\begin{array}{c}C_{3}=C H H \\ C l\end{array} \)
\( \mathbf{B} \cdot C H_{2}=C-C H=C H_{2} C H_{2}=C-C H=C H_{2} \)
\( _{C H_{3}} \)
\( \mathbf{c} \cdot C H_{2}=C H-C H=C H_{2}, C H_{2}=C H-C l \)
\( \mathbf{D} \cdot C H_{2}=C-C H=C H_{2} C H_{2}=C-C H=C H_{2} \)
\( C l \)


Main function of glomerulus is
A. Reabsorption of water
B. Filtration of urine
c. Reabsorption of \( N a^{\text {t }} \)
D. concentration of urine


Chondrichthyes is characterised by
A. Placoid scale
B. Placoid scale and ventral mouth
c. ventral mouth
D. Ctenoid scale and ventral mouth


If \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2}, \boldsymbol{P}(\boldsymbol{B})=0, \) then \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}) \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. Not defined
D.


Which of the following are nucleophiles?
This question has multiple correct options
A \( . P H_{3} \)
в. \( F^{\circ} \)
c. \( P h_{3} S^{\text { }} \)
D. \( H_{2} O \)


Population explosion in India is due to
A. climate
B. Increased death rate
c. Lack of education
D. All of the above


The image formed behind a mirror and that formed behind a magnifying glass
A. are of same nature
B. are of different nature
c. are of same nature only in space
D. are of different nature only in space


If \( \boldsymbol{f}:\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \rightarrow(-\infty, \infty) \) is defined
by \( f(x)=\tan x, \) then \( f^{-1}(\sqrt{3})= \)


In figure, \( \boldsymbol{K} \boldsymbol{X} \boldsymbol{M} \) is a tangent to the
circumcircle \( C \) of \( \triangle X Y Z \) such that
\( \boldsymbol{L} \boldsymbol{M} \| \boldsymbol{Y} \boldsymbol{Z} . \) Show that \( \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{X} \boldsymbol{Z} \)


In the function \( f(x)=a x^{3}+b x^{2}+ \)
\( 11 x-6 \) satisfies condition of rolle's
therorem in [1,3] and \( f^{\prime}\left(2+\frac{1}{3}\right)=0 \) then value of \( a \) and \( b \) are respectively
A. 1,-6
B. -1,6
c. -2,1
D. \( -1, \frac{1}{2} \)


Find the multiplicative inverse of the
complex numbers given the following:
\( 4-3 i \)


The distance between \( P\left(x_{1}, y_{1}\right) \) and
\( Q\left(x_{2}, y_{2}\right) \) is \( P Q=\left|x_{2}-x_{1}\right|, \) when PQ is
parallel to the \( x \) -axis. If True enter 1 else 0


(a)The pointer in the galvanometer deflects, when a bar magnet pushed or away from the coil connected to a galvanometer. Identify the phenomenon causing this deflection and write the factors on
which the amount and direction of the
deflection depends. State the laws describing this phenomenon.
(b) Sketch the change in flux, emf and force when a conducting rod PQ of resistance \( \mathrm{R} \) and length I moves freely to and fro between \( A \) and \( C \) with speed \( v \)
on a rectangular conductor placed in uniform magnetic field as shown in the figure.


A \( 5.0 A \) current is setup in an external
circuit by a \( 6.0 \mathrm{V} \) storage battery for 6.0
min. The chemical energy of the battery is reduced by
A \( \cdot 1.08 \times 10^{4} J \)
B . \( 1.08 \times 10^{-4} J \)
c. \( 1.8 \times 10^{4} J \)
D. \( 1.8 \times 10^{-4} J \)


A vessel contains 1 mole \( \boldsymbol{P} C l_{5}(g) \) at 4
\( \operatorname{atm} \) and 0.5 mole \( P C l_{3} \) formed at
equilibrium. Now, equilibrium pressure of mixture is (assume ideal behavior)
\( A \cdot 16 \) atm
B. 6 atm
\( c \cdot 2 \) atm
D. 4.5 atm


If the unit place of a number is \( 7, \) then find the unit digit of its cube.
A . 1
B. 3
c. 5
\( D \)


The separation of colloidal particles (or purification of sol) from particles of molecular dimensions is known as:
A. photolysis
B. dialysiss
c. pyrolysis
D. peptization


Which of the following has a non zero dipole moment?
A. \( P C l_{5} \)
в. \( C l F_{3} \)
c. \( X e F_{4} \)
D. \( C_{2} H_{5} C \equiv C C_{2} H_{5} \)


Evaluate:
\( \int \frac{x-x^{2}}{x^{2}-2 x-3} d x \)


Assertion
Plant taxonomy is known as systematic botany
Reason
Taxonomy involves only plant classification.
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 and Reason is incorrect
D. Assertion is incorrect and Reason is correct.


Which of the following statements
is/are false for sulphurdioxide?
A. It reacts with dry chlorine in presence of charcoal to form sulphuryl chloride
B. It reduces \( K I O_{3} \) to iodine in acidic medium
C. It when passed through a solution of sodium sulphide, produces \( N a_{2} S O_{3} \)
D. It oxidises \( S n C l_{2} \) to \( S n C l_{4} \) in presence of \( H C l \)


Calcium carbide is hydrolyzed using heavy water. What are the products formed?
\( \mathbf{A} \cdot C a(O H)_{2}, C_{2} D_{2} \)
B. \( C a(O D)_{2}, C_{2} D_{2} \)
c. \( C a(O D)_{2}, C D_{4} \)
D. \( C a(O H)_{2}, C D_{1} \)


Consider the following redox reaction:
\( 2 S_{2} O_{3}^{2-}+I_{2} \longrightarrow S_{4} O_{6}^{2-}+2 I^{\ominus} \)
This question has multiple correct options
A \( \cdot S_{2} O_{3}^{2-} \) gets reduced to \( S_{4} O_{6}^{2} \)
B. \( S_{2} O_{3}^{2-} \) gets oxidised to \( S_{4} O_{6}^{2} \)
c. \( I_{2} \) gets reduced to \( I^{\ominus} \)
\( \mathbf{D} \cdot I_{2} \) gets oxidised to \( I^{\ominus} \)


Which of the following is a basic dye?
A. Alizarin
B. Malachite green
c. Indigo
D. Orange-I


Identify \( X \) in the equation given below.
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3}+\boldsymbol{S O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{2}+ \)
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{X} \)
A \( . H_{2} S \)
в. \( S O_{3} \)
c. \( H_{2} S O_{4} \)
D. \( H_{2} S O_{3} \)


Ammonia cannot be dried over regular dehydrating agent like:
A \( \cdot H_{2} S O_{4} \)
в. \( P_{2} O_{5} \)
C. Anhydrous \( C a C l_{2} \)
D. None of these


A piece of cloth costs rupees \( 75 . \) If the piece is four meters longer and each
meter costs rupees 5 less, the cost remains unchanged. What is the length of the piece?
A. 12 meters
B. 8 meters
c. 10 meters
D. 6 meters


The true statement among following is:
A. Energy released per nucleon is same in both fission and fusion reaction
B. Energy released per nucleon is more in fission than in fusion reaction
C. Energy released per nucleon is less in fission than in fusion reaction
D. No energy is released in fusion reaction


What will be the magnitude of torque on an electric dipole having dipole moment of \( 4 \times 10^{-9} \mathrm{cm} \) placed in a uniform
electric field of intensity of \( 5 \times \)
\( 10^{4} N C^{-1} \) making an angle \( 180^{\circ} \) with
the field.
A \( \cdot 10^{-4} N-m \)
В. \( 2 \times 10^{-4} N-m \)
\( c .0 \) (zero)
D. \( 10^{-6} N-m \)


Which among the following is most reactive metal?
A. Aluminium
B. Copper
c. Tin
D. Calcium


A pair of unbiased dice is rolled
together till a sum is either 5 or 7 is
obtained, The probability that 5 comes
before 7 is
A . \( 2 / 5 \)
в. \( 3 / 5 \)
c. \( 4 / 5 \)
D. none of these


State whether true or false:
The image formed by a compound microscope is real, inverted and magnified.
A. True
B. False


Which of the following analgesics is not habit forming?
A. Morphine
B. Aspirin
c. codeine
D. Heroin


How can electrical conductivity of metals, insulator and semiconductors
be explained qualitatively?


Distance of origin from line \( (1+ \) \( \sqrt{3}) y+(1-\sqrt{3}) x=10 \) along the line
\( \boldsymbol{y}=\sqrt{\mathbf{3}} \boldsymbol{x}+\boldsymbol{k} \) is
A \( \cdot \frac{5}{\sqrt{2}} \)
B. \( 5 \sqrt{2}+k \)
c. 10
D. 5


Solid sphere, hollow sphere, solid cylinder and hollow cylinder of same mass and same radii simultaneously start rolling down from the top of an inclined plane. The body that takes
longest time to reach the bottom is:
A. Solid sphere
B. Hollow sphere
c. solid cylinder
D. Hollow cylinder


State the converse and contrapositive of each of the following statements:
(i) \( p: A \) positive integer is prime only if it has no divisors other than 1 and itself
(ii) \( q: \) I go to a beach whenever it is a
sunny day
(iii) \( r: \) If it is hot outside then you feel
thirsty


Find the pressure exerted by a man weighing \( 90 k g \) on the ground.
(a) when he is standing on one of his
feet having an area of \( 90 \mathrm{cm}^{2} \)
(b) when he is lying flat. The area of his body in contact with the ground is \( 0.9 m^{2} . \) Given \( g=10 m s^{-2} \)


If the function \( f \) is defined by \( f(x)= \) \( 3 x+4, \) then \( 2 f(x)+4= \)
\( \mathbf{A} \cdot 5 x+4 \)
B. \( 5 x+8 \)
c. \( 6 x+4 \)
D. \( 6 x+8 \)
E \( .6 x+12 \)


Diagonals \( A C \) and \( B D \) of a parallelogram ABCD intersect each other at \( 0 . \) If
\( O A=3 \mathrm{cm} \) and \( O D=2 \mathrm{cm} \) determine
the lengths of \( A C \) and \( B D \)


\( p H \) of \( 0.1 \mathrm{M} N a_{2} H P O_{4} \) and \( 0.2 \mathrm{M} \)
\( N a H_{2} p O_{4} \) are respectively:
\( \left(p K_{a} \text { for } H P O_{4} \text { are } 2.2,7.2 \text { and } 12.0\right) \)
A . 4.7,9.6
B. 9.6, 4.7
c. 4.7,5.6
D. 5.6, 4.7


Combustion reaction of coke is a/an
reaction.
A. exothermic
B. auto-catalytic
c. endothermic
D. none of these


\( N_{2} H_{4} \) is thermodynamically
endothermic compound but is kinetically stable.
A. True
B. False


How much amount of heat is required to raise the temperature of 100 g of water from \( 30^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} ? \) The specific heat
of water \( =4.2 J g^{-1 o} C^{-1} \)
A . 25.5 k
B. 29.4 k
c. \( 30 k J \)
D. 40 kJ


The stress versus strain graphs for wi
shown in the figure. If \( Y_{A} \) and \( Y_{B} \) are
then
A. \( Y_{B}=2 Y_{A} \)
B. \( Y_{A}=Y_{B} \)
c. \( Y_{B}=3 Y_{A} \)
D. \( Y_{A}=3 Y_{B} \)


Let \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{4} \boldsymbol{\pi}] \rightarrow[\mathbf{0}, \boldsymbol{\pi}] \) be defined by
\( f(x)=\cos ^{-1}(\cos x) . \) The number of
points \( \boldsymbol{x} \in[\mathbf{0}, \mathbf{4} \boldsymbol{\pi}] \) satisfying the
equation \( f(x)=\frac{10-x}{10} \) is


Which of the following option w.r.t. increasing bond order is correct?
A \( \cdot N O<C_{2}<O_{2}^{-}<H e^{+} \)
в. \( C_{2}<N O<H e^{+}<O_{2}^{-} \)
c. \( H e^{+}<O_{2}^{-}<N O<C_{2} \)
D. \( H e^{+}<O_{2}^{-}<C_{2}<N O \)


Watch column A mame or the
Scientists) with column B (their
contributions towards the
understanding of the atomic structure).
Column A Column \( \mathbf{B} \)
A. Ernest Rutherford
1. Indivisibility of atoms
B. J.J Thompson
2. Stationary orbits
C. Dalton
3. Concept of nucleus
D. Neils Bohr
4. Discovery of electrons
E. James Chadwick
5. Atomic number
F. E Goldstein
6. Neutron
G. Moseley \( \quad \) 7. Canal rays
\( \mathbf{A} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 6, F \rightarrow 7, G \rightarrow 5 \)
\( \mathbf{B} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 6, D \rightarrow 2, E \rightarrow 1, F \rightarrow 5, G \rightarrow 5 \)
\( \mathbf{C} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 6, F \rightarrow 5, G \rightarrow 5 \)
\( \mathbf{D} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 5, F \rightarrow 7, G \rightarrow 6 \)


It becomes easier to open or close a door turning about its hinges if the force is applied at the:
A. Two third of the door
B. Free edge of the door
c. Middle of the door
D. Point near the hinges


The distance between the lines \( 4 x+ \)
\( 3 y=11 \) and \( 8 x+6 y=15 \) is :
\( A \cdot \frac{7}{2} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{7}{5} \)
D. \( \frac{7}{10} \)


A moving charge will produce
A. no field
B. a magnetic field.
c. a small electric field.
D. None of these


The probability distribution of a random
variable \( X \) is given below
\( \boldsymbol{X}=\boldsymbol{x} \) \( \begin{array}{ll}-1.5 & -0.5\end{array} \) \( \mathbf{0 . 5} \)
\( P[X= \)
\( X] \)\( \quad 0.05 \) 0.25 0.15
The variance of \( \boldsymbol{X} \) is
A . 1.6
B. 0.24
c. 0.84
D. 0.75


Statement 1: If the amplitude of a
simple harmonic oscillator is doubled,
its total energy becomes four times.
Statement 2: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic
oscillator.
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 the correct explanation for Statement
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false


Find the point on the X-axis, which are at a distance of \( 2 \sqrt{5} \) from the point
\( (7,-4) . \) How many such point are there?


Consider the two vectors \( \vec{A}=3 \hat{i}-2 \hat{j} \) and \( \vec{B}=-\hat{i}-4 \hat{j} . \) Calculate \( (a) \vec{A}+ \)
\( \overrightarrow{\boldsymbol{B}} \cdot(\boldsymbol{b}) \overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}} \)
\( (c)|\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}| \cdot(\boldsymbol{d})|\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}}| \)
and \( (e) \) the directions of \( \vec{A}+\vec{B} \) and \( \overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}} \)


Volkman's canals occur in
A. Bone
B. Cartilage
c. Liver
D. Internal ear


Describe the structure of synovial joint with the help of a neat labelled diagram.


Temperature above which gas cannot be liquefied is called critical temperature,
\( T_{c} \)
If true enter 1 , else enter 0
\( A \)


Mid way between the two equal and similar charges, we placed the third equal and similar charge. Which of the following statements are correct, concerned to the equilibrium along the line joining the charges?
A. The third charge will experience a net force inclined to the line joining the charges.
B. The third charge is in a stable equilibrium.
c. The third charge is in an unstable equilibrium.
D. The third charge will experience a net force perpendicular to the line joining the charges.


Why is the purification of water and
nutrient salts so important in studies involving mineral nutrition using hydroponics?


The 9 horizontal and 9 vertical lines on
an \( 8 \times 8 \) chess-board form \( r \) rectangles
and \( s \) squares. Then, the ratio \( s: r \) in its
lowest terms is
A \( \cdot \frac{1}{6} \)
в. \( \frac{17}{108} \)
c. \( \frac{4}{27} \)
D. None of the above


Write the simplest form of \( \tan ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right), 0<x<\frac{\pi}{2} \)


Calcium and \( \ldots . . . . . . . . \) gives rigidity to
bones and teeth
A. Oxalate
B. Pectate
c. carbonate
D. Phosphate
E. Sulphate


Suppose you walk from home to the bus
stand at \( 4 k m / h \) and immediately return at \( x \) km/h. If the average speed is \( 6 \mathrm{km} / \mathrm{h} \) then \( \mathrm{x} \) is.
\( \mathbf{A} \cdot 8 k m / h \)
в. \( 10 k m / h \)
\( \mathrm{c} .12 \mathrm{km} / \mathrm{h} \)
D. Cannot be determined unless the distance from home to bus stand is known


In Young's double slit experiment with
sodium vapour lamp of wavelength 589 tun and the slits 0.689 min apart, the
half angular width of the central maximum is
A \( \cdot \sin ^{-1}(0.01) \)
B. \( \sin ^{-1}(0.0001) \)
c. \( \sin ^{-1}(0.001) \)
D. \( \sin ^{-1}(0.1) \)


The vapour pressure of water at room temperature is \( 23.8 \mathrm{mm} \) Hg. The vapour
pressure of an aqueous solution of sucrose with mole fraction 0.1 is equal
to:
\( \mathbf{A} \cdot 23.9 \mathrm{mm} \mathrm{Hg} \)
B. \( 24.2 \mathrm{mm} \) Hg
c. \( 21.42 \mathrm{mm} \) Hg
D. \( 31.44 \mathrm{mm} \) нв


\( \int \frac{d x}{3 x^{2}+13 x-10} \)


A ball in thrown from a roof top at an
angle \( 45^{\circ} \) above the horizontal. It hits
the ground a few second later. At what
point during its motion, does the ball have greatest acceleration?


The orbital angular momentum of an electron revolving in a p-orbital is :
A . zero
в. \( \frac{h}{\sqrt{2} \pi} \)
\( c \cdot \frac{h}{2 \pi} \)
D. \( \frac{1}{2} \frac{h}{2 \pi} \)


The reabsorption of the sodium from glomerular filtrate is regulated by the hormone
A. Glucagon
B. Secretin
c. Aldosterone
D. Adrenaline


In voluntary muscle movement, which of the following condition occurs if ATP is
present?
A. Myosin to bind to actin
B. Myosin to become separated from actin
c. Tropomyosin to bind to troponin
D. Tropomyosin to become separated from troponin
E. Tropomyosin to become separated from actin


The number of faradays of electricity required to decompose \( 100 \mathrm{ml} \) water (density \( =0.99 \mathrm{gm} / \mathrm{ml} \) ) is:
A .2
B. 11
\( c .100 \)
D. 5.5


Which one of the following planets has largest number of natural satellites or
moons?
A. Jupiter
B. Mars
c. saturn
D. Venus


Which of the following is the correct match with respect to the given
question? ABCD' is a rhombus such that
\( \angle A C B=40^{\circ} \) then \( \angle A D B= \)
\[
\begin{array}{ll}
\mathbf{7 0}^{o} & \text { As } \angle A D B=\mathbf{1} / \mathbf{2}\left(\mathbf{1 8 0}^{\circ}-\mathbf{4 0}^{\circ}\right) \\
45^{\circ} & \angle C+\angle D=90^{\circ}
\end{array}
\]
50
\[
\angle B C D=80^{\circ} \Rightarrow \angle A D C=100^{\circ} \therefore
\]
\[
\angle A D B=(1 / 2) x 100^{\circ}
\]
\( 60^{0} \quad \) All sides are equal
\( \mathbf{A} \cdot(a) \rightarrow(i) \)
B. \( (c) \rightarrow(i i i) \)
c. \( (d) \rightarrow(i i i) \)
D. \( (b) \rightarrow(i v) \)


Which among the following is a chain growth polymer?
A. Nylon
B. Bakelite
c. Terylene
D. Teflon


When the liquid between two ends allow
electric current, then :
A. bulb of tester glows
B. only heating of the tester takes place
c. bulb of the tester does notglow
D. none of the above


Which of the following statements are correct statement(s) about
pyrophosphoric acid \( \left(\boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}\right) \) ?
This question has multiple correct options
A. It contains P in +5 oxidation state
B. It is dibasic acid
c. It is a reducing agent
D. It contains one P-O-P bond


Q Type your question
\( A \)
\( (A) \rightarrow(\text { iii }),(B) \rightarrow(i),(C) \rightarrow(i i),(D) \rightarrow(i v) \)
\( \mathbf{B} \cdot(A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(i i) \)
C \( \cdot(A) \rightarrow(\text { ii }),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow( \) iii)
D. \( (A) \rightarrow(\text { iv }),(B) \rightarrow(i i),(C) \rightarrow(i),(D) \rightarrow(\text { iii }) \)


A car bulb connected to a 12 volt battery
draw 2 A current when glowing. What is the resistance of the filament of the
bulb?
A . \( 3 \Omega \)
в. \( 6 \Omega \)
\( c .9 \Omega \)
D. 24


What happens to the size of the image of the flame formed on the screen?


If \( a-b=4 \) and \( a+b=6, \) find \( a b \)
A .
B. 5
\( c \cdot 2 \)
D. 6


Factorise \( \boldsymbol{X}^{2}-\mathbf{7} \boldsymbol{X}+\mathbf{1 0}=\mathbf{0} \)


What will be the magnetic field at a
distance r when an electric current
flows through these things?
Wire single turn of wire Several turn of wire


A uniform wire of length \( l=5 \pm 0.05 \mathrm{cm} \)
and radius \( r=0.5 \pm 0.005 \mathrm{cm} \) has
mass \( \boldsymbol{m}=\mathbf{0 . 4}+\mathbf{0 . 0 0 4 g} . \) The maximum
percentage error in its density is
\( A \)
B. 2
\( c \cdot 4 \)
D. 5.8


One mole of \( N_{2} H_{4} \) loses 10 moles of
electrons to form a new compound \( \boldsymbol{A} \)
Assuming that all the nitrogen appears in the new compound, what is the oxidation state of nitrogen in \( A \) ? [There is no change in the oxidation state of hydrogen \( ] \)
A \( .+1 \)
B. -3
\( c \cdot+3 \)
D. +5


\( \left(\sqrt[3]{3}+\left(\begin{array}{c}5 \\ 36 \\ i\end{array}\right)^{3} \) is an integer where \right.
\( \boldsymbol{i}=\sqrt{-1} . \) The value of the integer is
equal to.
A .24
B . -24
c. -22
D. -21


Pteridophytes differ from Bryophytes in having
A. Vascular tissues
B. Archegonia
c. Motile antherozoids
D. Alternation of generation


What do you mean by a potential
difference of 1 volt?


Two satellites \( A \) and \( B \) of equal mass
move in the equatorial plane of the earth, close to earth's surface. Satellite A moves in the same direction as that of
the rotation of the earth while satellite \( \mathrm{B} \)
moves in the opposite direction. Calculate the ratio of the kinetic energy of \( \mathrm{B} \) to that of \( \mathrm{A} \) in the reference frame
fixed to the earth. \( \left(g=9.8 m s^{-2} \) and \right.
radius of the earth \( =\mathbf{6 . 3 7} \times \mathbf{1 0}^{6} \mathbf{k m} \) ).


Assertion
The presence of large magnetic flux through a coil maintains a current in
the coil if the circuit is continuous.
Reason
Magnetic flux is essential to maintain
an Induced current in the coil.
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


Seed habit, originated firstly in some
A. Pteridophytes
B. Pines
c. Monocots
D. Dicots


What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.


A century has
A. 100 years
B. 100 months
c. 100 seconds
D. 100 weeks


An experiment needs to heat a small
sample to temperature \( 900 K, \) but the
only available large object has
maximum temperature of 600 \( K . \) Could
the experimenter heat the sample to
\( 900 K \) by using a large lens to concentrate the radiation from the large
object onto the sample as shown below?
A. Yes, if the front area of the large object is at least 1.5 times the area of the front of the sample
B. Yes, if the sample is placed at the focal point of the lens
c. It is not possible
D. Yes, if the volume of the large object is atleast 1.5 times the volume of the sample


A load of \( 4.0 \mathrm{kg} \) is suspended from a ceiling through a steel wire of length \( 20 m \) and radius \( 2.0 m m . \) It is found
that the length of the wire increases by
\( 0.031 m m \) as equilibrium is achieved. If
\( \boldsymbol{g}=\mathbf{3 . 1} \boldsymbol{x} \boldsymbol{\pi} \boldsymbol{m} \boldsymbol{s}^{-2}, \) the value of young's
modulus in \( N m^{-2} \) is
\( \mathbf{A} \cdot 2.0 \times 10^{12} \)
B . \( 4.0 \times 10^{11} \)
\( \mathbf{c} \cdot 2.0 \times 10^{11} \)
D. \( 0.02 \times 10^{9} \)


A eighth part of a full circle i.e. a octant subtends an angle of \( \ldots \) at the centre.
A \( \cdot 60^{\circ} \)
B . \( 45^{\circ} \)
\( c .90^{\circ} \)
D. None of these


Which of the following phenols has lowest solubility in water?
A. Phenol
B. o-Nitrophenol
C. m-Nitrophenol
D. p-Nitrophenol


A double ionized lithium atom is
hydrogen-like with atomic number 3
(a) Find the wavelength of the radiation required to excite the electron in \( \boldsymbol{L} \boldsymbol{i}+ \)
+ from the first to the third Bohr orbit.
(lonization energy of the hydrogen atom
equals \( 13.6 e V \lambda \)
(b) How many spectral lines are
observed in the emission spectrum of the above excited system?
A . \( 114.7 A^{\circ} \), Three lines.
B. \( 113.7 A^{\circ} \), four lines.
c. \( 115.7 A^{\circ} \), two lines.
D. \( 116.7 A^{\circ} \), one lines.


Which one is the most soluble in water?
A. Uric acid
B. Urea
c. Fatty acids
D. casein


Which of the following is the formula of prussian blue?
\( A \)
\( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
в. \( F e_{2}\left[F e(C N)_{6}\right]_{3} \)
c. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)
D. \( F e_{3}\left[F e(C N)_{6}\right]_{4} \)


The main sequence on the H-R diagram includes
A. about 90 percent of all stars
B. white dwarfs
c. red giants
D. pulsars


Find the compound interest on
Rs. 10000 for 12 month at \( 10 \% \) per
annum. If the interest is compounded.
Quarterly


Figure shows the position-time graph of
a particle of mass 4 kg. Let the force on
the particle for \( t<0,0 F_{1}, F_{2} \) and \( F_{3} \)
respectively. Then
A \( \cdot F_{1}=F_{2}=F_{3}=0 \)
B. \( F_{1}>F_{2}=F_{3} \)
\( \mathrm{c} \cdot F_{1}>F_{2}>F_{3} \)
\( F_{1}<F_{2}<F_{3} \)


For a reversible chemical reaction
where the forward process is
exothermic, which of the following
statements is correct?
A. The backward reaction has higher activation energy than the forward reaction
B. The backward and the forward processes have the same activation energy
C. The backward reaction has lower activation energy
D. No activation energy is required at all since energy is liberated in the process


A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}4 \boldsymbol{x}^{2}-\mathbf{1} ; & -\mathbf{3} \leq \boldsymbol{x}<\mathbf{2} \\ \mathbf{3} \boldsymbol{x}-\mathbf{2} ; & \mathbf{2} \leq \boldsymbol{x} \leq \mathbf{4} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} ; & \mathbf{4}<\boldsymbol{x} \leq \mathbf{6}\end{array}\right. \)
Find:
\( \frac{\boldsymbol{f}(\boldsymbol{3})+\boldsymbol{f}(-1)}{2 \boldsymbol{f}(\boldsymbol{6})-\boldsymbol{f}(1)} \)


A particle of mass \( 1 g m \) and charge \( 1 \mu C \)
is held at rest on a frictional horizontal
surface at distance \( 1 \mathrm{m} \) from a fixed
charge \( 2 m C . \) If the particle is released, it will be repelled. The speed of the particle when it is at a distance of \( 10 m \)
from the fixed charge will be:
A \( \cdot 60 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
\( \mathrm{c} .90 \mathrm{ms}^{-1} \)
D. \( 180 m s^{-1} \)


Sterile portions of sporophylls of Cycas and Pinus are
A. Paraphyses
B. Apophysis
c. Hypophysis
D. Epiphyses


Different communities appearing and replacing one another are called as
A. Climax community
B. Seral communites
c. Pioneer community
D. successive communites


The methods used in protecting the
metals are:
A. galvanizing
B. alloying
c. electroplating
D. all of these


Solve the following minimal
assignment problem and hence find
minimum time where \( ^{\prime}-^{\prime} \) indicates
that job cannot be assigned to the
machine:
\( - \)


Which of the following does not reduce Benedict's solution?
A. sucrose
B. Aldehyde
c. Glucose
D. Fructose


The mean of given data is
\( \begin{array}{cccccc}\mathbf{x} & 2 & 4 & 6 & 8 & 10 \\ f & 7 & 4 & 5 & 5 & 4\end{array} \)
\( \mathbf{A} \cdot 5.6 \)
B . 6.4
\( c \cdot 6 \)
D. None of these


The stress-strain graphs are shown in
the figure for two materials \( A \) and \( B \) are
shown in figure. Young's modulus of \( \boldsymbol{A} \)
is greater than that of \( B \).
Reason
The Young's modules for small strain is, \( Y=\frac{\text {stress}}{\text {strain}}= \) slope of linear portion of
graph; and slope of \( A \) is more than that
of \( B \)
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Pseudo first-order rate for the reaction,
\( A+B \longrightarrow P, \) when studied in \( 0.1 M \) of
\( B \) is given by \( -\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}] \) where
\( k=1.85 \times 10^{4} \mathrm{sec}^{-1} \). Calculate the
value of second order rate constant.


The circumference of the front wheel of
a cart is \( 30 \mathrm{ft} \) long and that of the back wheel is 36 ft long. What is the distance travelled by the cart when the front wheel has done five more revolutions
than the rear wheel?
A \( .20 f t \)
B. 25 ft
c. \( 750 f t \)
D. \( 900 f t \)


To show that a simple pendulum executing a simple harmonic motion it
is necessary to assume that
A. length of the pendulum is small.
B. mass of the pendulum is small
c. acceleration due to gravity is small.
D. amplitude of the oscillation is small.


A battery has six cells in series and each cell has an electromagnetic force \( 1.5 V \) and internal resistance \( 1 \Omega . \) If
an external load of resistance \( 24 \Omega \) is
connected to it. The potential drop across the load is
A. \( 7.2 V \)
B. \( 0.3 V \)
c. \( 6.8 V \)
D. \( 0.4 V \)


Choose the correct statement:
A. Only fruits and vegetables are good for our eyes
B. Only food derived from animals are good for our eyes
C. Food derived from both animals and plants are important for healthy eyes
D. Only proper light conditions are important for eye health


Which molecule has trigonal pyramidal
molecular geometry?
A. \( H_{2} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( C O_{2} \)
E. \( N H_{3} \)


At the critical micelle concentration
(CMC), the surfactant molecules:
A. decompose
B. dissociate
c. associate
D. become completely soluble


Which of the following methods is not
used to
estimate nitrogen in the laboratory?
A. Kjeldahls method
B. Dumas method
c. Carius method
D. Both 1 and 3


n-type semiconductor is :
A. negatively charged
B. positively charged
c. neutral
D. may be positive or negative


If the resistance of a circuit is halved
and the potential difference is kept constant, then the current will become
A. 4 times
B. 8 times
c. double
D. half


The dimensional formula for pressure
gradient is :
A \( \cdot M L^{-1} T^{-2} \)
B . \( M^{1} L^{-2} T^{-2} \)
c. \( M^{1} L^{2} T^{-2} \)
D. \( M^{1} L^{-1} T^{-3} \)


A person standing symmetrically between two cliffs claps his hands and starts hearing series of echoes at intervals of 1 sec. If speed of sound in air is \( 340 \mathrm{m} / \mathrm{s} \), the distance between the parallel cliff must be
A. 340 \( m \)
B. 680 \( m \)
c. \( 1020 \mathrm{m} \)
D. \( 170 \mathrm{m} \)


Last traces of water is removed from
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) by
A. electrolysis
B. crystallisation
c. condensation
D. evaporation


In electrolyte concentration cell:
This question has multiple correct options
A. the electrode material and the solution in both halfcells are composed of the same substances
B. only the concentrations of solutions of the same substances is different
\( \mathbf{c} \cdot E_{c e l l}^{\circ}=0 \)
D. the Nernst equation reduces to \( E_{\text {cell}}= \) \( -\left(\frac{0.0591}{n}\right) \log Q \) at \( 25^{\circ} \mathrm{C} \)


What are the products \( (x) \) and \( (y) \) formed in the above reaction?


A radioactive substance X decays into another radioactive substance Y.

Initially, only \( X \) was present. \( \lambda_{x} \) and \( \lambda_{y} \) are the disintegration constants of \( \mathbf{X} \)
and Y. \( N_{y} \) will be maximum when \( \left(N_{y} \) is \right.
atoms of \( Y \) )
A \( \cdot \frac{N_{y}}{N_{x}-N_{y}}=\frac{\lambda_{y}}{\lambda_{x}-\lambda_{y}} \)
В. \( \frac{N_{x}}{N_{x}-N_{y}}=\frac{\lambda_{x}}{\lambda_{x}-\lambda_{y}} \)
c. \( \lambda_{y} N_{y}=\lambda_{x} N_{x} \)
D. \( \lambda_{y} N_{x}=\lambda_{x} N_{y} \)


Plants take in \( \ldots \) and give
out
A. Oxygen, Carbon dioxide
B. Carbon dioxide, Oxygen
c. Oxygen, Nitrogen
D. None of the above


A Wheatstone bridge consisting of four \( \operatorname{arms} \) of resistances \( P, Q, R, S \) is most
sensitive when :
A. All the resistance are equal
B. All the resistance are unequal
c. The resistances \( P \) and \( Q \) are equal but \( R>>P \) and \( S>>Q \)
D. The resistance \( P \) and \( Q \) are equal but \( R<<P \) and \( S< \) \( <Q \)


If the function \( f(x)=x^{3}-6 x^{2}+a x+ \)
\( b \) satisfies Rolle's theorem in the
interval [1,3] and \( f^{\prime}\left(\frac{2 \sqrt{3}+1}{\sqrt{3}}\right)=0, \) then
A \( . a=-11 \)
B. \( b=-6 \)
\( \mathbf{c} \cdot a=6 \)
D. \( a=11 \)


How the transport of \( O_{2} \) and \( C O_{2} \) by blood happens?
A. With the help of WBCs and blood serum
B. With the help of platelets and corpuscles
c. with the help of RBCs and blood plasma
D. With the help of RBCs and wBCs


State whether true or false.
As a planet moves around the sun it
sweeps equal areas in equal intervals of time.
A. True
B. False


Evaluate \( : \lim _{x \rightarrow 2} \frac{3 x^{2}-x-10}{x^{2}-4} \)


The condition for the vectors \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) to be the sides of a parallelogram taken in order is
A . \( \vec{a}+\vec{b}=\vec{c}+\vec{d} \)
В . \( \vec{a}+\vec{b}=\vec{c}+\vec{d}=0 \)
c. \( \vec{a}+\vec{c}=\vec{b}+\vec{d} \)
D . \( \vec{a}+\vec{c}=\vec{b}+\vec{d}=0 \)


In a given region a charge particle is moving under the effect of electric and magnetic field with uniform velocity \( \vec{v}=(\hat{i}+\hat{j}-\hat{k}) \mathrm{m} / \mathrm{s} \) and magnetic field
is given as \( \vec{B}=(2 \hat{i}+\hat{j}-2 k) \) T. The
electric field is given as?
\( \mathbf{A} \cdot(i+j-k) \mathrm{V} / \mathrm{m} \)
B. \( (i-j+k) \vee / m \)
c. \( (i+k) \vee / m \)
D. \( (-i-k) \vee / \) m


Ammonia formed during digestion is processed in
A. Liver
B. Small intestine
c. Large intestine
D. Stomach


The earth has Volume 'V' and surface
area 'A' then its capacitance would be


Find the derivative of \( \sin x \) with respect
to \( x \) from first principles.


The primary valency and secondary valency of central metal ion and the no. of total ions produced in aqueous
solution for \( \boldsymbol{K}\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{X})_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \)
complex respectively is
A. 3,4,2
в. 4,4,2
\( \mathrm{c} .3,6,2 \)
D. 3,6,1


A particle is projected vertically upwards from the surface of the
earth(radius R) with a kinetic energy equal to half of the minimum value
needed for it to escape. Find the height to which it rises above the surface of
earth.


There are four numbers in A.P. Their
sum is 20 and sum of their squares is
120. Find largest of those numbers?


A certain sum amounts to \( R s .5107 .60 \)
in 2 years at the rate of \( 13 \% \) per annum
the sum is
A. \( R s .4107 \)
B. Rs. 3107.60
c. \( R s .4000 \)
D. \( R s .4110 \)


The torque equation for a physical
pendulum making an angle \( \theta \) with the vertical is given by
A \( \cdot d^{2} \theta / d t^{2}=-(m g L / I) \cos \theta \)
B . \( d^{2} \theta / d t^{2}=-(m g L / I) \sin \theta \)
C \( \cdot d^{2} \theta / d t^{2}=-(m g L / 2 I) \sin \theta \)
D \( \cdot d^{2} \theta / d t^{2}=-(m g L / 2 I) \cos \theta \)


An ideal gas is expanded irreversible against 10 bar pressure from 20 litre to 30 litre. Calculate ' \( q^{\prime} \) if process is
isoenthalpic.
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( +100 J \)
\( c \cdot-100 J \)
D. \( +10 k J \)


What is biomagnification?


A material capable of absorbing large amount of energy before fracture is
known as
A. Ductility
B. Toughness
c. Resilience
D. Plasticity


An organic dye, cosin used to detect end point of precipitation titration by adsorption, is called:
A. absorption indicator
B. adsorption indicator
c. chemical indicator
D. none of the above


\( 2 S O_{3} \rightleftharpoons 2 S O_{2}+O_{2} . \) If \( K_{c}=100, \alpha=1 \)
half of the reaction is completed, the
concentration of \( S O_{3} \) and \( S O_{2} \) are
equal, the concentration of \( O_{2} \) is ?
A. \( 0.001 M \)
M
в. \( \frac{1}{2} S O_{2} \)
\( \mathrm{c} \cdot 2 \) times of \( \mathrm{SO}_{2} \)
D. Data incomplete


The performance of students in 1 st term
and 2 nd term is as given below. Draw a double bar graph choosing appropriate scale and answer the following:
Hindi Maths Subject: English
\( 1^{s t} t e r m: \) 1 67 72
\( 2^{n d} \) term:
70 65
In which subject, has the children improved their performance the most?


An object is moving along a straight line with a uniform speed of \( 10 m / s \) Plot a graph showing distance versus
time from \( t=0 \) to \( t=10 s \)


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


Choose the correct reason(s) for the
stability of the Iyophobic colloidal
particles.
This question has multiple correct options
A. Preferential adsorption of ions on their surface from the solution
B. Preferential adsorption of solvent on their surface from the solution
C. The attraction between different particles having opposite charges on their surface
D. The potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles


Three cubes each of side \( 5 \mathrm{cm} \) are
joined end to end. Find the surface area of the resulting Cuboid
A \( \cdot 350 \mathrm{cm}^{2} \)
В. \( 300 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 250 \mathrm{cm}^{2} \)
D. \( 200 \mathrm{cm}^{2} \)


What is the lowest value of \( n \) that allows
g orbitals to exist?


\( \tan \left(2 \cos ^{-1} \frac{3}{5}\right)= \)
\( A \cdot \frac{8}{3} \)
B . \( \frac{24}{25} \)
\( c \cdot \frac{7}{25} \)
\( D \cdot \frac{-24}{7} \)


A uniform metre scale balances
horizontally on a knife edge placed at \( 55 \mathrm{cm} \) mark. When a mass of \( 25 g \) is supported from one end, then the mass of the scale is:
A. \( 200 g \)
в. \( 225 g \)
c. \( 350 g \)
D. \( 275 g \)


Two names referring to same thing
A. Krebs cycle and Calvin cycle.
B. Tricarboxylic acid cycle and citric acid cycle.
C. Citric acid cycle and Calvin cycle.
D. Tricarboxylic acid cycle and urea cycle.


A nail is driven into a wooden board by using a hammer. The impact of the hammer on the head of nail produces a
thrust of \( 25 N . \) If the area of the head is
\( 0.5 m m^{2} \) and of the tip is \( 0.1 m m^{2}, \) find
the pressures on the head and on the tip of the nail.
A \( \cdot 5 \times 10^{7} P a ; 2.5 \times 10^{8} P a \)
B . \( 2.5 \times 10^{7} P a ; 5.5 \times 10^{8} P a \)
c. \( 3.5 \times 10^{7} P a ; 2.5 \times 10^{8} P a \)
D. \( 5 \times 10^{7} P a ; 3.5 \times 10^{8} P a \)


The potential difference b/w \( A \& B \) in the figures is.
A . 24V
B. 14V
c. 32v
\( D \cdot 48 V \)


A small body \( A \) is fixed to the inside of \( a \)
thin rigid hoop of radius \( R \) and mass
equal to that of the body \( A \). The hoop rolls without slipping over a horizontal plane; at the moments when the body \( A \)
gets into the lower position, the centre
of the hoop moves with velocity \( v_{0} \) figure shown above). If the hoop moves without bouncing for \( v_{0}=\sqrt{x g R} \), then
find the value of \( x \)


Aryl halide is less reactive than alkyl halide towards nucleophilic substitution because:
A. of less stable carbonium ion
B. due to large \( C-C l \) bond energy
c. of inductive effect
D. of resonance stabilization and \( s p^{2} \) hybridization of \( C \) attached to halide


find the ratio in which YZ-plane divides the line joining \( \boldsymbol{A}(\mathbf{2}, \mathbf{4}, \mathbf{5}) \) and
\( \boldsymbol{B}(\boldsymbol{3}, \boldsymbol{5},-\boldsymbol{4}) \)


Find the sum of 20 terms of a series of
which every even term is 2 times the
term the term before it and every odd terms is 3 times the before it and the
first term is unity?


Modulus of rigidity is defined as the ratio of
A . Longitudinal stress to longitudinal strain
B. Volumetric stress to volumetric strain
c. shear stress to shear strain
D. Linear stress to linear strain


Study the bar graph representing the
number of persons in various age
groups in a town shown in Fig. 23.9
Observe the bar graph and answer the
following questions:

What is the percentage of the youngest
age-group persons over those in the oldest age group? If the answer is \( 466 \frac{a}{3} \)
What is the value of 'a'?


An acid-base indicator has \( \boldsymbol{K}_{\boldsymbol{H} \text { In }}= \)
\( 3.0 \times 10^{-5} . \) The acid form of the
indicator is red and the basic form is
blue. The change in \( \left[\boldsymbol{H}^{+}\right] \) required to
change the indicator from \( 75 \% \) red to
\( 75 \% \) blue is:
A \( \cdot 8 \times 10^{-5} \) М
В. \( 9 \times 10^{-5} \) М
c. \( 1 \times 10^{-5} \) М
D. \( 3 \times 10^{-4} \mathrm{M} \)


Two thin infinite parallel sheets have uniform surface densities of charge \( +\boldsymbol{\sigma} \)
and \( -\sigma . \) Electric field in the space
between the two sheets is:
A \( \cdot \sigma / \epsilon_{0} \)
в. \( \sigma / 2 \epsilon_{0} \)
\( \mathbf{c} \cdot 2 \sigma / \epsilon_{0} \)
D. zero


Flux \( \phi( \) in webers) in a closed circuit of resistance 10 ohm varies with time \( t \) (in
seconds according to the equation \( \phi=6 t^{2}-5 t+1 . \) What is the
magnitude of the induced current in 0.25 second :
A. \( 0.8 \mathrm{A} \)
B. 1.2 A
c. 0.6 A
D. \( 0.2 \mathrm{A} \)


\( \boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \frac{N i / 300^{0} C}{\longrightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{6} \)
to get back the ethene, ethane must be:
A. dehydrogenated in the presence of \( C u \) at \( 300^{\circ} \mathrm{C} \)
B. heated to \( 450^{\circ} \mathrm{C} \) in the presence of \( \mathrm{H} \mathrm{NO}_{3} \) vapoar
c. heated \( 170^{\circ} \mathrm{C} \) in the presence of conc. \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. heated to \( 750^{0} C \)


The final product in the given reaction
is:
\( A \)
B
\( c \)
D. A and B both


A plane wave of monochromatic light falls normally on a uniformly thin film of oil which covers a glass plate. The wavelength of source constructive interference is observed for \( \lambda_{1}=5000 \stackrel{\circ}{A} \) and \( \lambda_{2}=10000 A \) and for no other
wavelength in between. If \( \mu \) of oil is 1.25
and that of glass is \( 1.5, \) the thickness of film will be
A . 0.2
B. 0.1
\( c .0 .8 \)
D. 0.4


Assertion
Displacement-time equation of two particles moving in a straight line are, \( s_{1}=2 t-4 t^{2} \) and \( s_{2}=2 t+4 t^{2} \)
Relative velocity between the two will go on increasing.
Reason
If velocity and acceleration are of same sign then speed will increase.
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 is incorrect but Reason is correct


What is the amount of chlorine evolved
when 2 ampere of current is passed for
30 minutes in an aqueous solution of
NaCl?
A \( .66 g \)
в. \( 1.32 g \)
\( \mathrm{c} \cdot 33 \mathrm{g} \)
D. \( 99 g \)


Elements with high melting point are
present in:
A . p-block elements
B. s-block elements
c. d-block elements
D. None of these


Actiniod contraction is more than
lanthanold contraction because:
A. energy of 4 f and 5f orbitals are same
B. 5 forbitals are more diffused as compared to 4 f orbitals
c. actinoids show greater range of oxidation states than lanthanoids
D. actinoids are highly reactive


Find the equation of normal to the parabola \( y^{2}=4 a x \) which passes
through the point \( (-6 a, 0) \). and
suspended at \( 60^{\circ} \)


From the following metals whose nitrate
produces \( N O_{2} \) gas on heating?
A . Na a
в.
\( c \cdot P b \)
D. None of the above


The diode cannot be
A. the simplest of semiconductor devices.
B. having characteristics that closely match those of a simple switch
C. is a multi terminal device
D. none of the above


Optical fibre work on the principle of
A. Refraction of light
B. Total internal reflection
c. Reflection of light
D. All


How many molecules of \( C O_{2} \) are
released in citric acid cycle :-
A. one
B. Two
c. Three
D. Four


According to Bohr, 'Angular momentum of an orbiting electron is quantised' What is meant by this statement?


Ethyl chloride \( \left(C_{2} H_{5} C l\right), \) is prepared by
reaction of ethylene with hydrogen chloride:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}(\boldsymbol{g}) ; \triangle \boldsymbol{H}=-\mathbf{7} \mathbf{2} . \mathbf{3} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
What is the value of \( \triangle \boldsymbol{U} \) (in \( \mathbf{k J} \) ), if \( \mathbf{7 0} \boldsymbol{g} \) of ethylene and \( 73 g \) of \( H C L \) are
allowed to react at \( 300 K ? \)
\( \mathbf{A} \cdot-69.8 \)
в. -180.75
c. -174.5
D. -139.6


Why does a sharp knife enable us to cut through things more easily?
A. The pressure exerted is lesser when the same force is used
B. The pressure exerted is greater when the same force is used
c. The sharp edge can pass through the material slowly
D. The sharp edge is not felt when cutting through the materia


Which of the following is/are correct about 1 mole electrons?
This question has multiple correct options
A . \( 6.023 \times 10^{23} \) electrons
В . \( 5.48 \times 10^{-7} \mathrm{kg} \)
c. 96500 coulomb charge
D. None of these


Reaction of iron filings with powered sulfur is known as:
A. precipitation
B. oxidation-reduction
c. distillation
D. hydration
E. condensation


In the aqueous solution of soaps above
CMC (Critical Micelle Concentration):
This question has multiple correct options
A. The cations associates to form the aggregates
B. The anions to form the clusters of colloidal dimension
C. The polar ends forming the clusters are directed towards water
D. The non polar (Hydrocarbon) ends are directed towards water


Which one of the following processes
involve chemical reactions?
A. Storing of oxygen gas under pressure in a gas cylinder
B. Liquefaction of air
C. Keeping petrol in a china dish openly
D. Heating copper wire in presence of air at high temperature


In hexose monophosphate shunt, the
number of \( C O_{2} \) molecules evolved is
A. Same as in glycolysis
B. Less than glycolysis
c. More than glycolysis
D. Much lesser than the glycolysiss


The following circuit acts as a
A. half wave rectifier
B. amplifier
C. full wave rectifier
D. oscillator


A cylindrical vessel of height 500 mm
has an orifice (small hole) at its bottom.
The orifice is initially closed and water
is filled in it up to height \( \boldsymbol{H} \). Now the top
is completely sealed with a cap and orifice at the bottom is opened. Some
water comes out from the orifice and
the water level in the vessel becomes
steady with height of water column being 200 mm. Find the fall in height (in \( m m) \) of water level due to opening of the orifice. (Take atmospheric pressure \( =1.0 \times 10^{5} N / m^{2}, \) density of water
\( =1000 \mathrm{kg} / \mathrm{m}^{3} \) and \( g=10 \mathrm{m} / \mathrm{s}^{2} \)
(Neglect any effect of surface tension.)


How many litres of ethene would be produced when \( 2.62 g \) of vinyl magnesium bromide is treated with 224ml of ethyne at STP.
A. 0.224 litre
B. 0.08 litre
c. 0.448 litre
D. 1.12 litre


The value of \( c, \) for which the line \( y= \)
\( 2 x+c \) is a tangent to the circle \( x^{2}+ \)
\( \boldsymbol{y}^{2}=\mathbf{1 6}, \) is
A . \( -16 \sqrt{5} \)
B. 20
c. \( 4 \sqrt{5} \)
D. \( 16 \sqrt{5} \)


The third ventricle of the brain is
situated in the
A. Base of telencephalon
B. Roof of metencephalon
c. Roof of diencephalon
D. Base of myelencephalon


The Poissons ratio for inert gases is:
A . 1.40
B . 1.66
\( c \cdot 1.34 \)
D. None of these


f \( x, y, z \) are positive then minimum
value of
\( \boldsymbol{x}^{\log y-\log z}+\boldsymbol{y}^{\log z-\log x}+\boldsymbol{z}^{\log \boldsymbol{x}-\log \boldsymbol{y}} \) is
\( A \cdot 3 \)
B.
c. 9
D. 16


If each edge of a cuboid is increased by
\( 50 \%, \) then the percentage increase in the surface area is
\( \mathbf{A} .50 \)
в. 125
c. 150
D. 300


The split-ring type commutator is used in generators to:
A. Convert AC to DC
B. Convert DC to ACC
c. Induce emf
D. Induce magnetism


Semicircular canals in vertebrate
are responsible for
A. Detection of change of atmospheric pressure
B. Orientation of animal with regard to sunn
c. Maintenance of balance when the organism is in motion
D. Regulation of speed of animal


What is the molarity of \( 2.00 g \) of \( N a O H \) dissolved in a total solution volume of
\( 250 m L ? \)
\( \mathbf{A} \cdot 0.2 M \)
в. \( 0.5 \mathrm{M} \)
c. \( 0.008 M \)
D. 252 М


Draw a labelled diagram of the malpighian tubules transfer section.


Preshrink cotton is called:
A. natural cotton
B. terycotton
c. sanforized cotton
D. none of the above


In the below example, identify the
motion of the objects.
A. A and B exhibit pure rotation, while C represents pure translation
B. A exhibits pure rotation, while C represents pure translation
c. B exhibits pure rotation, while C represents pure
translation
D. A and B exhibit pure rotation, while C represents pure translation plus rotation


Two coherent sources have intensities
in the ratio \( 25: 16 . \) Find the ratio of
intensities of maxima to minima?


In a solution of 7.8 gm benzene \( C_{6} H_{6} \)
and 46.0 gm toluene \( \left(C_{6} H_{5} C H_{3}\right), \) the
mole fraction of benzene in this solution
is:
A . \( 1 / 6 \)
B. \( 1 / 5 \)
\( c \cdot 1 / 2 \)
\( D \cdot 1 / 3 \)


Read the following statements and answer as true or false.

The presence of carbon in pig iron
makes it brittle.
A. True
B. False


The area (in square units) bounded by
\( \boldsymbol{y}=\boldsymbol{x} e^{|x|} \) and lines \( |\boldsymbol{x}|=\mathbf{1}, \boldsymbol{y}=\mathbf{0}, \) is
A .4
B. 6
\( c .1 \)
D. 2


The reflex arcs in which one or more
interneurons connect the afferent and
efferent signals are
A. Autonomic reflex
B. Somatic reflex
c. Monosynaptic reflex
D. Polysynaptic reflex


Find the mode for the following data: (4 and \( 5) \)
\( \begin{array}{lllll}\text { class } & 0- & 7- & 14- & 21- \\ 7 & 14 & 21 & 28\end{array} \)
Area 26 31 35


The xylem which has metaxylem towards the centre and protoxylem is present towards the periphery is known
as
A. Endarch
B. Mesarch
c. Exarch
D. None of the above


\( K_{1} \) and \( K_{2} \) for oxalic acid are \( 6.5 \times \)
\( 10^{-2} \) and \( 6.1 \times 10^{-5} \) respectively. What
will be \( \left[\boldsymbol{H} \boldsymbol{O}^{-}\right] \) in a \( \mathbf{0 . 0 1} \boldsymbol{M} \) solution of
sodium oxalate?
A \( .9 .6 \times 10^{-6} \)
B. \( 1.4 \times 10^{-1} \)
c. \( 1.3 \times 10^{-6} \)
D. \( 1.3 \times 10^{-8} \)


Identical charges q each are placed at
the eight corners of a cube of side \( b \)
Find the electrostatic potential energy of a charge \( +q \) placed at the center of the cube


Select the correct statements:
A. The electric lines of force are always closed curves.
B. Electric line of forced is parallel to equipotential surface
C. Electric line of force is perpendicular to equipotential surface.
D. Electric line of force is always the path of a positively charged particle.


Two bodies are projected vertically upwards from one point with the same initial velocity \( v_{0} . \) The second body is
projected \( t_{0} s \) after the first. How long after will the bodies meet?
A \( \cdot \frac{v_{0}}{2 g}+\frac{t_{0}}{2} \)
в. \( \frac{v_{0}}{g}+\frac{t_{0}}{2} \)
c. \( \frac{v_{0}}{g}+\frac{t_{0}}{4} \)
D. \( \frac{2 v_{0}}{g}+\frac{t_{0}}{2} \)


Solve the following. \( 3 a^{2} x^{2}+8 a b x+4 b^{2}=0,(a \neq 0) \)


Three of the following pairs of the human skeletal parts are correctly matched with their respective inclusive skeletal category and one pair is not matched. Identify the non-matching pair.
A. Malleus and stapes \( \rightarrow \) Ear ossicles
B. Sternum and ribs \( \rightarrow \) Axial Skeleton
C. Clavicle and glenoid cavity \( \rightarrow \) Pelvic girdle
D. Humerus and ulna \( \rightarrow \) Appendicuar skeleton


The reaction used to join railway tracks involves reducing agent:
\( A \cdot A \)
в. Мв
\( c \cdot c \)
D. co


A solid sphere of radius \( R \) has moment
of inertia \( I \) about its geometrical axis. If
it is melted into a disc of radius \( r \) and
thickness \( t \). If its moment of inertia
about the tangential axis (which is perpendicular to plane of the disc), is also equal to \( I, \) then the value of \( r \) is
equal to:
A.
B.
c. \( \frac{3}{\sqrt{15}} R \)
\( D \)


Say true or false:
A positive integer is of the form \( 3 q+1 \)
\( \boldsymbol{q} \) being a natural number, then you write its square in any form other than \( 3 m+1, \) i.e.,3m or \( 3 m+2 \) for some
integer \( \boldsymbol{m} \)
A. True
B. False


The lac operon model is
A. Inducible
B. Repressible
c. Both A and B
D. Degenerate


Fourteen elements following
Lanthanum are called Lanthanoids:
(a) What is Lanthanoid contraction?
Give reason for it.
(b) \( K M n O_{4} \) is a purple coloured
crystal and it acts as an oxidant. How
will you prepare \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) from \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} ? \)


If \( \vec{A} \) and \( \vec{B} \) are two vectors, the value of \( (\vec{A}+\vec{B}) \times(\vec{A}-\vec{B}) \) is then
B . \( -2(\vec{B} \times \vec{A}) \)
C . \( (\vec{B} \times \vec{A}) \)
D. \( (\vec{A} \times \vec{B}) \)


Identify the correct statement regarding
a spontaneous process
1) For a spontaneous process in an isolated system, the change in entropy is positive
2) Endothermic process are never
spontaneous
3) Exothermic processes are always spontaneous
(4) Lowering of energy in
the reaction process is the only criterion for spontaneity


Aldehydes and ketones both undergo condensation with:
A. \( N H_{2} O H \)
в. \( \operatorname{NaHSO}_{3} \)
c. \( H C N \)
D. \( R M g X \)


\( \frac{d}{d} \)


A box is being lifted by a fork-lift truck.
The weight o fthe box is \( 3000 N \). The
force exerted by the fork-lift truck on the
box is \( 3500 N \) vertically upwards. What
is the resultant vertical force on the
box?
fork
A. \( 500 N \) downwards
B. \( 500 N \) upwards
c. \( 6500 N \) downwards
D. \( 6500 N \) upwards


In ground state, all the elements of group 13 of the periodic table are having same number of :
A . nuclear particles
B. occupied principal energy levels
c. electrons
D. valence electrons
E . neutrons


The working transistor with its three legs marked \( \mathrm{P}, \mathrm{Q}, \) and \( \mathrm{R} \) is tested using a
multimeter. No conduction is found
between \( P \& Q . \) By connecting the common (negative) terminal of the
multimeter to \( \mathrm{R} \) and the other
(positive) terminal to \( \mathrm{P} \) or \( \mathrm{Q}, \) some
resistance is seen on the multimeter.
The correct statement for the transistor
is
A. It is an n-p-n transistor with \( \mathrm{R} \) as base
B. It is a p-n-p transistor with \( \mathrm{R} \) as collector
C. It is a p-n-p transistor with \( R \) as emitter
D. It is an n-p-n transistor with \( \mathrm{R} \) as collector


The solution of \( \frac{d y}{d x}+1=e^{x+y} \) is:
A \( \cdot e^{-(x+y)}+x+c=0 \)
B \( \cdot e^{-(x+y)}-x+c=0 \)
c. \( e^{x+y}+x+c=0 \)
D. \( e^{x+y}-x+c=0 \)


Vasopressin stimulates reabsorption of water and reduction of urine secretion.
Vasopressin is also called
A. Synovial fluid
B. Neurotransmitter
c. Antidiuretic hormone
D. Growth regulating substance


Compound \( (X) C_{4} H_{8} O \) decolourises Baeyer's reagent. It undergoes
hydrolysis on reaction with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and produces (Y) and (Z). Both (Y) and
(z) give positive iodoform test. But, only
(Y) gives positive Tollen's test.Choose
the correct statements.
This question has multiple correct options
\( A \)
\( (Y) \stackrel{a q_{1} N a O H(10 \%) \Delta}_{\longrightarrow} C H_{3}-C H=C H-C H O \)
B. Pyridinium chlorochromate (PCC)
(z)
\( c \)
\( (\mathrm{X}) \frac{\mathrm{B} \mathrm{r}_{2} / \mathrm{CCl}_{4}}{\longrightarrow} \mathrm{CH}_{2}-\mathrm{CH}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \)
\( \mathrm{Br} \quad \mathrm{Br} \)
\( D \)
\[
(X) \frac{(i) O_{3}}{(i j) Z n / H_{2} O}(Y)+\text { other product }
\]


Reaction of dilute \( H C l \) with Maltose
gives:
A. D-glucose
B. D-fructose
c. D-glucose and D-fructose
D. D-galactose


Which of the following metals, absorb hydrogen? This question has multiple correct options
\( A \cdot Z n \)
B. Pd
\( c \cdot P t \)
D.


Assertion
STATEMENT-1: If output of a AND gate is fed to OR gate, it is called NOR gate.
Reason
STATEMENT-2: If output of a AND gate is fed to NOT gate, it is called NAND gate.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


The velocity of a particle is \( \boldsymbol{v}=\boldsymbol{v}_{0}+ \)
\( g t+f t^{2} . \) If its position is \( x=0 \) at \( t=0 \)
then its displacement after unit time \( (t=1) \) is
A \( \cdot v_{0}+2 g+3 f \)
в. \( v_{0}+\frac{g}{2}+\frac{f}{3} \)
\( \mathbf{c} \cdot v_{0}+g+f \)
D. \( v_{0}+\frac{g}{2}+f \)


If the unit of length is doubled and that of mass and time is halved, the unit of
energy will be :
A. doubled
B. 4 times
\( c .8 \) times
D. same


The resistors in parallel in the following
circuit are
\( \mathbf{A} \cdot R_{2} \quad \) and \( \quad R_{3} \)
\( \mathbf{B} \cdot R_{1} \quad \) and \( \quad R_{2} \)
\( \mathbf{C} \cdot R_{1} \quad \) and \( \quad R_{3} \)
\( \mathbf{D} \cdot\left(R_{1}+R_{2}\right) \quad \) with \( \quad R_{3} \)


O is any point in the interior of \( \Delta A B C \). Prove that
\( A B+B C+C A>O A+O B+O C \)


Which of the following is an example of
heterogeneous catalysis?
\( \mathbf{A} \cdot 4 N H_{3(g)}+5 O_{2(g)} \stackrel{\left.P t_{s}\right)}{\leftrightarrow} 4 N O_{(g)}+6 H_{2} O_{(g)} \)
B \( \cdot 2 S O_{2}+O_{2} \stackrel{N O_{(g)}}{\rightarrow} 2 S O_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COOCH}_{3(l)}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{HClaa}}{\rightarrow} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{OH} \)
D. \( C_{12} H_{22} O_{11}+H_{2} O^{H_{2} S O_{4}} C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)


Strongest hydrogen bond is present in:
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H C l_{3} \)
\( \mathbf{c} \cdot\left[C H_{3}\right]_{2} C H O H \)
D. \( \left[C H_{3}\right]_{3} C O H \)


A hydrogen-like atom (atomic number
\( Z \) ) is in a higher excited state of
quantum number ' \( n \) '. This excited atom can make a transition to the first
excited state by successively emitting two photons of energies \( 10.2 e V \) and
17.0 \( e V \), respectively. Alternatively, the
atom from the same excited state can
make a transition to the second excited
state by successively emitting two photons of energies \( 4.25 e V \) and \( 5.95 e V \)
respectively. The values of \( n \) and \( Z \) are,
respectively
A. 6 and 6
B. 3 and 3
c. 6 and 3
D. 3 and 6


During burning of a candle, different zones of combustion in the flame are
listed below:
A. outermost zone
B. innermost zone
C. middle zone
The correct order of temperature of
zones is :
A. \( A>B>C \)
в. \( C>B>A \)
c. \( B>C>A \)
D. \( A>C>B \)


In figure, what is the approximate area
of triangle NJL?
A. 3.5
B. 53.72
c. 57.72
D. 80.53
E . 115.44


Give Reason:
A histogram is a two dimensional
\( \operatorname{graph} \)


We have all heard the phrase "opposites attract but like repels." This is especially true for ionic compounds. Which one of the following has the largest lattice energy as a result of this attraction?
A . Licl
в. \( N a C l \)
\( \mathrm{c} \cdot K_{2} \mathrm{O} \)
D. \( M g C l_{2} \)


\( \frac{1}{m} \)

\( m \)


Fill in the blank.
The following truth table with \( A \) and \( B \)
as inputs is for \( _{-}- \) gate.
\( \begin{array}{lll}\text { A } & \text { B } & \text { Output } \\ & & \\ 1 & \text { 0 } & 1 \\ \text { 1 } & 1 & \text { 0 } \\ \text { 0 } & 1 & 1 \\ \text { 0 } & \text { 0 } & \text { 0 }\end{array} \)
A. AND
B. OR
c. хок
D. NOR


\( \tan i\left[\log _{e}\left(\frac{a-i b}{a+i b}\right)\right] \) is equal to
A \( \cdot \frac{a^{2}-b^{2}}{2 a b} \)
в. \( \frac{2 a b}{a^{2}+b^{2}} \)
\( c \cdot a b \)
D. \( \frac{2 a b}{a^{2}-b^{2}} \)


Doctor has prescribed a lens having power \( +1.5 D . \) What would be the focal
length of the lens? What is the type of
lens and what must be the defeat of
vision?


Find H.C.F of 81 and 237
Also express it as a linear combination
of 81 and 237 i.e, H.C.F of \( 81,237= \)
\( 81 x+237 y \) for some \( x, y \)
[Note: Values of \( x \) and \( y \) are not unique]


Among
\( \boldsymbol{B}_{2} \boldsymbol{H}_{6}, \boldsymbol{B}_{3} \boldsymbol{N}_{3} \boldsymbol{H}_{6}, \boldsymbol{N}_{2} \boldsymbol{O}, \boldsymbol{N}_{2} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3} \)
and \( H_{2} S_{2} O_{8}, \) the total number of
molecules containing covalent bond between two atoms of the same kind is


Two identical metal sphere carrying
charges of \( 9 \times 10^{-9} C \) and \( -3 \times 10^{-9} \mathrm{C} \)
are brought in contact and then they are separated by a distance of \( 3 \mathrm{m} \) and kept in a medium of dielectric constant 5
what is the electrostatic force between
them ?
A \( .1 .25 \times 10^{-9} N \)
В. \( 1.8 \times 10^{-9} N \)
c. \( 3 \times 10^{-9} N \)
D . \( 2.5 \times 10^{-9} N \)


Action and reaction
A. always act on two different bodies
B. are equal in magnitude
C . act in opposite directions
D. All the above


Use Euclids division algorithm to find
the HCF of: 867 and 225


Why do musical instruments create
sound on being played?
A. Because they vibrate.
B. Because they have a secret music player in them
c. Both A and B
D. Can't say


Which of the following states of matter are called fluids?
A. Solid, Gas
B. Solid, Liquid
c. Liquid, Gas
D. Solid, Liquid, Gas


Which of the following is a unit of Volume?
A. Meters per second
B. Cubic millimeters
c. Litres
D. Both B and C


Two rails are algebraically represented by the equations \( 3 x-5 y-20=0 \) and \( 6 x- \) \( 10 y+40=0 \)


The probability of finding out an electron at a point within an atom is
proportional to the :
A. Square of the orbital wave function i, e \( \psi^{2} \)
B. Orbital wave function i.e.
c. Hamiltonian operator i.e.H
D. Principal quantum number i.e.


A prism of refractive index \( \sqrt{2} \) has
refracting angle \( 60^{0} \). Angle of minimum
deviation is:
A \( \cdot 45^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 30^{0} \)
D. none


It is difficult to cut cloth using a pair of scissors with blunt blades. Explain.


If a is an even integer and b is an odd integer, which of the following must be
even?
\( \mathbf{A} \cdot a b+1 \)
B. \( a^{2}+3 \)
c. \( a^{2}+b^{2} \)
D. \( b^{2}+3 \)


A convex lens of focal length \( 40 \mathrm{cm} \) is in contact with a concave lens of focal
length \( 25 \mathrm{cm} . \) The power of the
combination is
A . 1.50
B . -1.5
\( c \cdot 6.5 D \)
D . -2.5D


The rate of simple reaction \( 2 N O+ \)
\( O_{2} \longrightarrow 2 N O_{2}, \) when the volume of the
reaction vessel is doubled.


Marshall's acid or perdisulphuric acid
\( \left(H_{2} S_{2} O_{8}\right) \) can be prepared by
electrolytic oxidation of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) as :
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \)
\( O_{2} \) and \( H_{2} \) are byproducts. In such an
electrolysis \( 9.72 \mathrm{L} \) of \( H_{2} \) and \( 2.35 \mathrm{L} \) of \( O_{2} \)
were produced at S.T.P. What is the
weight of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \) formed?


The compound B formed in the sequence of reaction, \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{P C l}_{5}}{\longrightarrow} \boldsymbol{A} \frac{\text {alcoholic}}{\boldsymbol{K O H}} \boldsymbol{B} \)
is:
A. Propene
B. Propyne
C. Propane
D. Propanol


A force of \( 16 N \) is distributed uniformly
on one surface of a cube of edge \( ^{\prime} 8^{\prime} c m \)
The pressure on this surface is:
A \( .3500 P a \)
в. \( 2500 P a \)
c. \( 4500 P a \)
D. 2000Pa


In the figure shown, a ring A is initially
rolling without sliding with a velocity \( \mathbf{v} \) on the horizontal surface of the body B
(of same mass as \( A \) ). All surfaces are
smooth. B has no initial velocity. The
maximum height reached by A on B is \( \frac{v^{2}}{x g} . \) Find \( x \)


Rakesh lifts a heavy book from the floor
of the room and puts it in the book shelf
of height \( 2 m . \) In this process, he takes 5 seconds. On which of the following does the work done by him depend?
A. Mass of the book and the time taken to do work
B. Weight of the book and the height of the book shelf
c. Height of the book shelf and the time taken to do work
D. Mass of the book, height of the book shelf and the time taken to do work


The weight of body can be zero. True or false.
A . True
B. False


The resistance of the series
combination of two resistance is \( \mathrm{S} \)
When they are joined in parallel through total resistance is P. If \( S=n P \), then the
minimum possible value of \( n \) is?
A . 4
B. 3
\( c \cdot 2 \)
\( D \)


In water molecule, the two \( \boldsymbol{O}-\boldsymbol{H} \)
bonds are oriented at an angle of \( 104.5^{\circ} \)
\( \ln B F_{3}, \) the three \( B-F \) bonds are
oriented at an angle of \( 120^{\circ} . \ln B e F_{2} \)
the two \( B e-F \) bonds are oriented at
an angle of \( 180^{\circ} . \) Which of the following will have highest dipole moment?
A. \( B e F_{2} \)
в. \( B F_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. All have zero dipole moment


Let \( A B C \) be a acute angled triangle such that \( A=\frac{\pi}{3} \) and \( \cos B \cos C=P \)
The possible range of values of \( \boldsymbol{P} \) will be
A \( \cdot\left(-\frac{1}{4}, \frac{1}{4}\right] \)
в. (0,1]
\( c \cdot\left[\frac{1}{3}, \infty\right) \)
\( \mathbf{D} \cdot[1, \infty) \)


The electronic configuration of the
element which is just above the
element with atomic number 43 in the
same periodic group is:
\( \mathbf{A} \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{5}, 4 s^{2} \)
B \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{5} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{6}, 4 s^{1} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{1} 4 p^{6} \)


The radius \( (r), \) length \( (l) \) and resistance
\( (R) \) of a thin wire are \( (0.20 \pm 0.01) \mathrm{cm} \)
\( (800 \pm 0.1) \mathrm{cm}, \) and \( (301 \pm 1) \Omega \)
respectively. The error in the specific resistance is :
A . 10.34\%
B . 45.4\%
c. 26\%
D. 27.5\%


In the given figure, a bar magnet is quickly moved towards a conducting loop having a capacitor. Predict the
polarity of the plates \( A \) and \( b \) of the capacitor.


Is the function \( f \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \leq 1 \\ \boldsymbol{5}, \boldsymbol{i f} \boldsymbol{x}>1\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} ? \) At \( \boldsymbol{x}=\mathbf{1} \) ? At \( \boldsymbol{x}= \)
\( \mathbf{2} ? \)


Formation of \( N i(C O)_{4} \) and subsequent
its decomposition into Ni and CO (recycled) makes the basis of Monds process \( N i+4 C O \stackrel{T_{1}}{\rightarrow} N i(C O)_{4} \stackrel{T_{2}}{\longrightarrow} \)
\( N i+4 C O \)
\( T_{1} \) and \( T_{2} \) are:
A \( \cdot 100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
B . \( 50^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \)
c. \( 50^{\circ} \mathrm{C}, 230^{\circ} \mathrm{C} \)
D. \( 230^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)


A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder
with a man and the other end to the
counterweight of mass \( M . \) The man of
mass \( m \) climbs up a distance \( h \) with
respect to the ladder and then stops. If the mass of the rope and the friction in
the pulley axle are negligible, find the displacement of the centre of mass of
this system.


How many megacoulombs of positive
charge are in 1.00 mol of neutral
molecular hydrogen \( \operatorname{gas}\left(\boldsymbol{H}_{2}\right) \)


Lower members of aliphatic carboxylic acid are soluble in water. This is due to:
A. water is non electrolyte
B. due to London forces
c. formation of hydrogen bonds with water
D. van der-waals interaction with water molecules


3 g of activated charcoal was added to \( 50 \mathrm{mL} \) of the acetic acid solution
\( (0.06 N) \) in a flask. After an hour, it was filtered and the strength of the filtrate was found to be \( 0.042 N . \) The amount of
acetic acid adsorbed (per gram of charcoal) is :
A. \( 18 \mathrm{mg} \)
B. \( 36 \mathrm{mg} \)
c. \( 42 \mathrm{mg} \)
D. \( 54 \mathrm{mg} \)


In \( \Delta A B C, A B=A C . D, E \) and \( F \) are
mid-points of the sides \( B C, C A \) and
\( A B \) respectively. then, \( : A D \) is
perpendicular to \( \boldsymbol{F C} \) If the above statement is true then
mention answer as 1 , else mention 0 if false


In an experiment of verification of
Ohm's law, following observations are obtained:
Potential difference 0.5
\( \begin{array}{lll}\text { 1.0 } & \text { 1.5 } & \text { 2.0 }\end{array} \) \( v \) (in volt')
Current
in 0.2
\( 0.4 \quad 0.6 \)
ampere
From observation table the resistance
in circuit is
A. \( 2.5 \Omega \)
в. \( 2 \Omega \)
\( c .5 \Omega \)
D. \( 3 \Omega \)


To find out the concentration of \( S O_{2} \) in
the air (in parts per million, i.e., ppm),
the data was collected for 30 localities
in a certain city and is presented below:
Concentration of \( S O_{2}(\text { in ppm }) \) Frequency
\( 0.00-0.04 \)
\( 0.04-0.08 \)
\( 0.08-0.12 \)
\( 0.12-0.16 \)
\( 0.16-0.20 \)
\( 0.20-0.24 \)
Find the mean concentration of \( S O_{2} \) in
the air.


A force \( \boldsymbol{F} \) is applied on free end of a
string such mass of \( 18 k g \) remain
stationary. Then value of \( \boldsymbol{F} \) will be:
\( \mathbf{A} \cdot 180 N \)
B. \( 90 N \)
c. \( 60 N \)
D. \( 30 N \)


Find the range of values of \( t \) which \( 2 \sin t=\frac{1-2 x+5 x^{2}}{3 x^{2}-2 x-1} \) where \( t \epsilon\left[-\frac{\pi}{2}, \frac{\pi}{2}\right. \)


A good moderator should
A. be a gas
B. have an appetite for neutrons
c. be lighter in mass number
D. be heavier in mass number


A machine raises a load of \( \mathbf{7 5 0} \boldsymbol{N} \)
through a height of \( 16 m \) in \( 5 s . \) Calculate
energy spent by machine:
A. \( 12000 k J \)
в. \( 12 k J \)
c. \( 1200 J \)
D. \( 120 k J \)


Write the following rational number in decimal form \( \frac{23}{2^{3} \cdot 5^{2}} \)


If \( \boldsymbol{v}=\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{4}, \) Find the
acceleration of the particle when velocity of the particle is zero.
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot 3 \)
D. none of these