A \( 2 F \) capacitor is initially charged to \( 20 V \) and then shorted across a \( 5 m H \)
inductor. The angular frequency of oscillation is.
A. \( 1000 \mathrm{rad} / \mathrm{s} \)
B. 100 rad/s
c. \( 10000 \mathrm{rad} / \mathrm{s} \)
D. \( 10 \mathrm{rad} / \mathrm{s} \)


Prove that the function \( f: R \rightarrow R \) be
defined by \( f(x)=\left(x^{2}+1\right)^{35} \) is not one
one.


A conducting rod PQ of length \( L=1.0 \mathrm{m} \) is
moving with a uniform speed \( v=2.0 \mathrm{m} / \mathrm{s} \)
in a uniform field \( B=4.0 \) T directed into
the paper. A capacitor of capacity \( \mathrm{C}=10 \mu \)
Fis connected as shown in the figure.
Then charge on the capacitor is \( 10 \alpha \mu \mathrm{C} \)
Find the value of \( \boldsymbol{\alpha} \)
\( A \cdot 7 \)
B. 8
\( c \cdot s \)
D. 10


The sum of 2 numbers is 7 and their
product is 12 find the numbers.


IUPAC name of DDT is:
A. \( 1,1^{\prime}-(2,2,2-\text { Trichloroethane- } 1,1-\text { diyl }) \) bis \( (4- \) chlorobenzene)
B. p, p-dichloro diphenyl trichloro ethene
C. \( p, p \) -dichloro diphenyl trichloro benzene
D. p, p-tetra chloro ethane


Which of the following venn-diagrams
best represents the sets of females,
mothers and doctors?
\( A \)
B.
\( c \)
D.


If the edges of cube are halved, then its volume become is
A. 4 times
B. 8 times
c. \( \frac{1}{8} \) times
D. \( \frac{1}{2} \) times


If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right| \) then the value of \( \boldsymbol{A}+ \)
\( \boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\ldots+\boldsymbol{A}^{n}=? \)
\( A \cdot A \)
B. nA
c. \( (n+1) A \)
\( D \)


If \( f(x)=\left\{\begin{array}{cc}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}, \) then at \right.
\( \boldsymbol{x}=\mathbf{0} \) the function \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. Continuous
B. Differentiabl
c. continuous but not differentiable
D. None of the above


The acceleration (a) of SHM at mean
position is :
A. zero
B. \( \propto x \)
\( c \cdot \propto x^{2} \)
D. None of these


Compound that is both paramagnetic and coloured is:
A. \( K_{2} C r_{2} O_{7} \)
B. \( \left(N H_{4}\right)_{2}\left[T i C I_{6}\right] \)
\( c \cdot v o s O_{4} \)
D. \( K_{3}\left[C u(C N)_{4}\right] \)


Given that tangent \( \overrightarrow{A B} \) is \( 4 \mathrm{cm} \) and radius \( \overline{C D} \) is \( 3 \mathrm{cm}, \) the length \( \overline{B C}=? \)
\( A \)
B. 2
\( c \)
\( D \cdot 4 \)


For the reaction equilibrium, \( 2 N O B r(g) \leftrightharpoons 2 N O(g)+B r_{2}(g) \)
If \( P_{B_{1}}=\frac{P}{9} \) at equilibrium and \( P \) is total
pressure, the ratio of \( \frac{K_{P}}{P} \) is equal to:
A \( \cdot \frac{1}{9} \)
в. \( \frac{1}{81} \)
c. \( \frac{1}{27} \)
D.


The planet having the largest number of satellites amongst the following is
A. Jupiter
B. Saturn
c. uranus
D. Mars


Desert can be converted into a lush
green land by planting
A. Terrestrial plant.
c. Halophytes.
D. Psammophytes.


The volume occupied by one molecule of
water (density \( 1 g / c m^{3} \) ) is:
\( \mathbf{A} \cdot 18 \mathrm{cm}^{3} \)
В. \( 22400 \mathrm{cm}^{3} \)
c. \( 6.023 \times 10^{-23} \mathrm{cm}^{3} \)
D. \( 3.342 \times 10^{-23} \mathrm{cm}^{3} \)


A particle having mass 10 g oscillates according to the equation \( \boldsymbol{x}= \)
\( (2.0 \mathrm{cm}) \sin \left[\left(100 s^{-1}\right) t+\pi / 6\right] . \) Find
the amplitude, the time period and the force constant (b) the position, the
velocity and the acceleration at \( t=0 \)


If \( B \) is the set of even positive integers
then \( f: N \rightarrow B \) defined by \( f(x)=2 x \) is
A. one - one only
B. onto only
c. neither one-one nor onto
D. bijective


What is the total number of Deaths due
to Autos and Motorcycles together?
A . 6958
B. 5942
\( c .6176 \)
D. 7784


In \( n \) -p-n transistor, the arrow head on emitter represents that the conventional current flows from
A. base to emitter.
B. emitter to base
c. emitter to collector.
D. base to collector.


The estimation of available chlorine in
bleaching powder is done by
A. Acid-base titration
B. Permanganometric titration
c. lodimetric titration
D. lodometric titration


The expression \( 2 x^{3}+b x^{2}-c x+d \)
leaves the same remainder, when
divided by \( x+1 \) or \( x-2 \) or \( 2 x-1 . \) Find
\( \boldsymbol{b} \) and \( \boldsymbol{c} \)


On electrolysis of aqueous \( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3} \) sol, using inert electrode:
A. the coagulation of particles of dispersed phase occur near cathode
B. as will deposit at cathode
c. sulphur will deposit at cathode
D. \( H_{2} \) gas will evolve at cathode


If you are given a specimen, what are
the steps that you would follow to classify it?


The following are some statements about
galvanic cell.
1) The cell reaction will be obtained by
summing up the reactions in the two half
cells.
2) \( E^{0} \) cell \( =E^{0} \) cathode \( -E_{\text {Anode }}^{0} \)
3) \( E_{C e l l}^{0}=E_{\text {reduction electrode }}^{0}-E_{\text {oxidation electrode }}^{0} \)
4) \( E^{0} \) Cell \( =E^{0}_{L . H . E}-E^{0} R . H . E \)
The correct combination is :
A. only I and III are correct
B. only I and II are correct
C. only I,II,III are correct
D. all are correct


Find out which of the following sequences are arithmetic progressions. For those which are arithmetic
progressions, find out the common
difference. \( \mathbf{0},-\mathbf{4},-\mathbf{8},-\mathbf{1 2}, \dots \)


Fill in the blanks.
When equal volumes of nitrogen gas
and oxygen gas at low pressures are
sparked, they react at \( 3000^{\circ} \mathrm{C} \), to form
gas.


Two spherical balls of mass 10 kg each are placed \( 10 \mathrm{cm} \) apart.Find the
gravitational force of attraction
between them.


Show that one and only one out of
\( \boldsymbol{n}, \boldsymbol{n}+2 \) or, \( \boldsymbol{n}+\boldsymbol{4} \) is divisible by \( \boldsymbol{3} \)
where \( n \) is any positive integer.


A parallel plate condenser with plate separation d is charged with the help of
battery so that \( V_{0} \) energy is stored in
the system. The battery is now removed. a plate of dielectric constant k and thickness d is placed between the plates of condenser. The new energy of
the system will be :
A. \( V_{0} k^{-2} \)
B. \( k^{2} V_{0} \)
c. \( V_{0} k^{-1} \)
D. \( k V_{0} \)


Identify the wrong pair of statements.
I) During plant succession, some species colonise an area and
populations become more
numerous, whereas populations of other species decline and even disappear.
II) Both hydrarch and xerarch successions lead to mesic conditions.
III) Secondary succession is a slow
process when compared to primary
succession.
IV) In the successive seral stages, there is no change in the diversity of species
of organisms.
\( \mathbf{A} \cdot\|,\| \)
B. ।, ॥
c. ॥॥, IV
D. I, III


Magnesium on reaction with very dilute \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) gives:
A . \( N O \)
в. \( N_{2} \),
\( \mathrm{c} \cdot H_{2} \)
D. \( N O_{2} \)


An \( 1800 W \) toaster, a \( 1.3 K W \) electric
fan and \( 100 W \) lamp are plugged in the same \( 120 V \) circuit i.e., all the three
devices are in parallel. What is the approximate value of the total current
(i.e. sum of the current drawn by the
three devices) through circuit?
A \( .40 A \)
в. \( 120 A \)
\( c .18 A \)
D. \( 27 A \)


\( H I \) was heated in a sealed tube at
\( 400^{\circ} \mathrm{C} \) till the equilibrium was reached.
\( H I \) was found to be \( 22 \% \) decomposed.
The equilibrium constant for dissociation is:
A . 1.99
B. 0.0199
c. 0.0796
D. 0.282


State Dobereiner's Triads giving one
example.


The permanent magnetic moment of atoms or molecules of a diamagnetic
material is
A. small
B. large
c. negative
D. zero


In a certain region of space,electric field is along the z-direction throughout The magnitude of electric field is however not constant, but increases
uniformly along the positive z-direction at the rate of \( 10^{5} N \quad C^{-1} m^{-1} . \) Torque
experienced by the system is:
\( \mathbf{A} \cdot 10^{2} N \)
В. \( 10^{-2} N \)
c. zero
D. \( 10^{3} N \)


Vertices of a parallelogram \( A B C D \) are
\( \boldsymbol{A}(\mathbf{3}, \mathbf{1}), \boldsymbol{B}(\mathbf{1 3}, \mathbf{6}), \boldsymbol{C}(\mathbf{1 3}, \mathbf{2 1}) \) and
\( D(3,16) . \) If a line passing through the origin divides the parallelogram into two congruent parts then the slope of the line is
A \( \cdot \frac{11}{12} \)
в. \( \frac{11}{8} \)
c. \( \frac{25}{8} \)
D. \( \frac{13}{8} \)


The product of two numbers is 119 and their AM is 12. Find the numbers.


Do you observe anything happening
around the zinc granules?
Is there any change in its temperature?
Why is glass tube not dipped in di
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
How is \( H_{2} \) gas collected by downward
displacement or upward displacement
of water?

Is \( H_{2} \) gas soluble or insoluble in water?
s \( H_{2} \) gas heavier or lighter than air?


Which of the following factors will not favour backward reaction?
\( \boldsymbol{C l}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{F}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{C} \boldsymbol{I} \boldsymbol{F}_{3}(\boldsymbol{g}), \Delta \boldsymbol{H}= \)
\( -\boldsymbol{v} e \)
A. Addition of inert gas at constant pressure
B. Addition of \( C l_{2} \) gas
c. Increase in temperature of reaction
D. Increasing the volume of the container


Goitre can occur as a consequence of al
except
A . Graves' disease
B. lodine defiency
c. Pituitary adenoma
D. Excessive intake of exogenous thyroxine


The quantity \( \frac{2 U}{f k T} \) represents (where \( U= \) internal energy of gas
A. mass of the gas
B. kinetic energy of the gas
c. number of moles of the gas
D. number of molecules in the gas


The internal energy of one gram of
helium at \( 100 \mathrm{K} \) and one atmospheric pressure is?
A . 100
B . 1200 J
c. 300
D. 500


Moment of inertia of thin uniform rod of
length \( l \) is equal to:
\( ^{A} \cdot \frac{m l^{2}}{6} \)
в. \( \frac{m l^{2}}{12} \)
c. \( \frac{m l^{2}}{4} \)
D. \( \frac{m l^{2}}{24} \)


Match the polymer in column-A with
their main use in column-B and choose
the correct answer.
Column B Whe 1
(A) Paints and
lacquers
(B) Column - A
Polystyrene
Glyptal
Polyvinyl
Chloride
Bakelite Rain coats
(C) Manufacture
of toys
(D) Computer
discs
\( A \)
(A) - (ii), (B) - (iv), (C) - (iii), (D) - (i)
B. (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i)
\( c \)
(A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
D. (A) - (ii), (B) - (i), (C) - (iii), (D) - (iv)


Box I contains 2 white and 3 red balls
and box II contains 4 white and 5 red
balls. One ball is drawn at random from
one of the boxes and is found to be red.
Then, the probability that it was from box \( \| \), is?
\( ^{\mathrm{A}} \cdot \frac{54}{44} \)
в. \( \frac{54}{14} \)
c. \( \frac{54}{104} \)
D. None of these


The first term of a G.P. is \( 1 . \) The sum of
the third and fifth term is \( 90 . \) Find the
common ratio of the G.P.


Illustrate a glycosidic, peptide and a phosphodiester bond. What is meant by the tertiary structure of proteins?


The value of \( \mathbf{1 0 0 0}\left[\frac{\mathbf{1}}{\mathbf{1 \times 2}}+\frac{\mathbf{1}}{\mathbf{2} \times \mathbf{3}}+\frac{\mathbf{1}}{\mathbf{3} \times \mathbf{4}}+\dots+\overline{\mathbf{9} c}\right. \)
is equal to
A. 1000
в. 999
\( c .1001 \)
D. \( \frac{1}{990} \)


Plants of which one of the following groups of genera are pollinated by the same agency?
A. Triticum, cocos, Mangifera
B. Ficus, Kigelia, Casuarina
c. Salvia, Morus, Euphorbia
D. Bombax Butea, Bauhinia


The wave length of K-ray line of an anti cathode element of atomic number \( Z \) is
nearly proportional to:
\( A \cdot Z^{2} \)
B . \( (Z-1)^{2} \)
c. \( 1 /(z-1) \)
D. \( 1 /(Z-1)^{2} \)


If a plant has fibrous root, what type of venation are its leaves likely to have?


Two slits in Young's experiment have widths in the ratio \( 1: 25 . \) The ratio of
intensity at the maxima and minima in the interference pattern, \( \frac{\boldsymbol{I}_{\max }}{\boldsymbol{I}_{\min }} \) is
A \( \cdot \frac{4}{9} \)
B. \( \frac{9}{4} \)
c. \( \frac{121}{49} \)
D. \( \frac{49}{121} \)


If radius of sphere is doubled, what is the ratio of volume of original sphere to
that of second?
A . 1: 4
B . 8: 1
\( \mathrm{c} \cdot 1: 8 \)
D. None


If \( 10^{5} g \) of a sample of water contains
16.2 \( g \) of \( C a\left(H C O_{3}\right)_{2} \), then the hardness of water is
A. 200 ppm
В. 300 ppm
c. 60 ppm
D. 100 ppm


Find the integral of \( \int\left(2 x^{2}-3 \sin x+\right. \) \( \mathbf{5} \sqrt{\boldsymbol{x}}) \boldsymbol{d} \boldsymbol{x} \)


A sine wave with an rms value of \( 12 V \) is
riding on a dc level of \( 18 V . \) The maximum value of the resulting waveform is
A . \( 6 V \)
в. 30
\( \mathrm{c} .35 \mathrm{V} \)
D. \( 0 V \)


(i) \( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(l)=\boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s}) \)
\( \Delta H_{180^{\circ} C}=-15.26 k c a l \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})=\boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{180^{\circ} C}=\mathbf{6 8 . 3 7} \boldsymbol{k c a l} \)
(iii) \( C a(s)+\frac{1}{2} O_{2}(g)=C a O(s) \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{180^{\circ} C}=-151.80 k c a l \)
From the following data, the heat of
formation of \( \boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s}) \) at \( \mathbf{1 8}^{\circ} \boldsymbol{C} \) is:
A . -98.69 kcal
B . -235.43 kcal
c. 194.91 kcal
D. 98.69 kcal


The conjugate of \( z+2 \bar{z} \) is:
\( \mathbf{A} \cdot 2 \bar{z}+z \)
B. \( \bar{z}+2 z \)
c. \( \bar{z}-2 z \)
\( \mathbf{D} \cdot \bar{z}-z \)


Draw the molecular orbital formed on
sideways overlap of \( 2 p_{x} \) with \( 2 p_{x} \)


How can you minimize backlash error?


Find the domain of definition of the
following function:
\( y=\sqrt{\sin ^{2} x-\sin x} \)


On cubical expansion
A. Length increases
B. Breadth increases
\( c . \) Both
D. None


What is the final temperature of the
mixture of 300 g of water at \( 25^{\circ} \mathrm{C} \)
added to 100 of ice at \( 0^{\circ} C \)
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 1^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 2^{o} C \)
D. \( 3^{\circ} \mathrm{C} \)


Double fertilization takes place in
A. Angiosperms
B. Gymnosperms
c. Spermatophyta


Evaluate the following definite integral:
\( \int_{1}^{2} e^{2 x}\left(\frac{1}{x}-\frac{1}{2 x^{2}}\right) d x \)


The octet rule is not obeyed in:
This question has multiple correct options
A. \( C O_{2} \)
в. \( B C l_{3} \)
c. \( P C l_{5} \)
D. \( S i F_{4} \)


Which of the following may be discontinuous across a charged
conducting surface?
A. Electric potential
B. Electric intensity
c. Both electric intensity and potential
D. None of these


Show that the internal energy of the air (treated as an ideal gas) contained in a room remains constant as the
temperature changes between day and night. Assume that the atmospheric around remains constant and the air in
the room maintains this pressure by communicating with the surrounding through the windows etc.


If \( \boldsymbol{x}=\mathbf{9}^{\frac{1}{3}} \mathbf{9}^{\frac{1}{9}} \mathbf{9}^{\frac{1}{27}} \dots \dots \infty, \boldsymbol{y}= \)
\( \mathbf{4}^{\frac{1}{3}} \mathbf{4}^{\frac{-1}{9}} \mathbf{4}^{\frac{1}{27}} \ldots . \infty, \) and \( \boldsymbol{z}=\sum_{r=1}^{\infty}(\mathbf{1}+\boldsymbol{i})^{-\boldsymbol{r}} \)
then \( \arg (x+y z) \) is equal to
A.
B・tan" \( ^{-1}\left(\frac{\sqrt{2}}{3}\right) \)
c. \( -\tan ^{-1}\left(\frac{\sqrt{2}}{3}\right) \)
\( D \cdot-\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


The ocean is estimated to supply \( 10- \)
\( 20 \% \) of atmospheric
significant contributions coming from biomass burning, salt marshes and wood-rotting fungi.
A. methyl chloride
B. methyl bromide
c. methyl iodide
D. None of these


Fill in the blank.
Water droplets acts as a
A. small prisms
B. small glasses
c. small lenses
D. small pieces of glass


Let \( S \) be non-empty subset of \( \boldsymbol{R} \) then consider the following statement "Every number \( x \in S \) is an even
number."

Negation of the statement will be
A. There is no number \( x \in S \) which is even
B. There exists a number \( x \in S \) which is not even
C. There exists a number \( x \in S \) which is odd
D. \( (B) \) and \( (C) \) both


What conclusion can be obtained from
the observation that when the prongs of a sound making tuning fork touch
a beaker, the water gets splashed?
A. that the prongs of tuning fork are vibrating
B. the prongs of tuning fork produce ultrasound
c. waves are produced on the surface of water
D. all the above


S.I. unit of electrical capacity.
A. Stat Farad
B. Farad
c. Coulomb
D. stat Coulomb


The following questions are based on the preparation of ammonia gas in the laboratory:
How is ammonia gas collected?


A hydrogen electrode is immersed in a
solution with \( \mathrm{pH}=0 \) (HCl). By how much will the potential (reduction) change if an equivalent amount of NaOH is added
to the solution? (Take \( p_{H_{2}}=1 \) atm, \( T= \) \( 298 \mathrm{K} \)
A. Increase by \( 0.41 \mathrm{v} \)
B. Increase by 59 mv
c. Decrease by \( 0.41 \mathrm{v} \)
D. Decrease by 59 mv


Diethyl ether and n-propyl methyl ether
are:
A. metamers
B. chain isomerism
c. geometrical isomerism
D. position isomerism


Derive the Lens Maker's formula.


In a circle a central angle of \( 60^{\circ} \)
intercepts an arc of 15 inches. How many inches is the radius of the circle?
A \( \cdot \frac{45}{\pi} \)
в.
\( c \cdot 4 \)
D. \( \frac{2 \pi}{3} \)
E. not computable from given data


State whether true or false.
The linear momentum of a body at rest
is zero.
A. True
B. False


In the following equilibrium, \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g), \) when 5 moles of
each is taken and the temperature is
kept at \( 298 K \), the total pressure was
found to be 20 bar.
(Given: \( \Delta G_{f} N_{2} O_{4}= \)
\( \left.\mathbf{1 0 0 k J}, \Delta G_{f_{N O_{2}}}^{o}=\mathbf{5 0} k J\right) \)
(a) Find \( \Delta G \) of the reaction at \( 298 K \)
(b) Find the direction of the reaction.


It is accurate to say that the corona contains heat?
A. Yes
B. No
C. In particular conditions, say during solar eclipse, it contains heat
D. None of these


The vapour pressures of two liquids \( A \)
and B in their pure states are in the ratio of \( 1: 2 . \) A binary solution of \( A \) and \( B \)
contains \( A \) and \( B \) in the mole proportion of \( 1: 2 . \) The mole fraction of \( A \) in the
vapour phase of the solution will be:
A . 0.33
B. 0.2
c. 0.25
D. 0.52


Sum the series:
\( \mathbf{2}^{1 / 4} \cdot \mathbf{4}^{\mathbf{1} / 8} \cdot \mathbf{8}^{\mathbf{1} / \mathbf{1 6}} \cdot \mathbf{1 6}^{\mathbf{1} / 32} \ldots . \) is equal


The details of tricarboxylic acid pathway was worked out by
A. Miescher
B. Hans Krebs
c. Pasteur
D. None of the above


Why water drops (dew) form on flowers and grass during morning hours of
winter season?


The greatest positive argument of complex number satisfying \( |z-4|= \) \( \operatorname{Re}(z) \) is
A.
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{2} \)
D.


Which of the following statements is/are correct about the ionic product of
water?
This question has multiple correct options
A \( . \) K (equilibrium constant of water) \( <\mathrm{K}_{w} \)
\( \mathbf{B} \cdot \mathrm{pK}>\mathrm{pK}_{w} \)
C \( \left.. \text { At } 100^{\circ} \mathrm{C} \mathrm{Kw}=7.5 \times 10^{-14} \text {(moles } / \text {lit}\right)^{2} \)
D. Ionic product of water at \( 25^{0} \mathrm{Cis} 10^{-14} \)


Two Straight metallic strips each of thickness t and length I are rivetted together. Their coefficients of linear
expansions are \( \alpha_{1} \) and \( \alpha_{2} . \) If they are
heated through temperature \( \Delta T \), the
bimetallic strip will bend to form an arc of radius
\( \mathbf{A} \cdot t /\left[\left(a_{1}+a_{2}\right) \Delta T\right] \)
B \( \cdot t /\left[\left(a_{2}-a_{1}\right) \Delta T\right] \)
c. \( t\left(a_{1}+a_{2}\right) \Delta T \)
D. \( t\left(a_{2}+a_{1}\right) \Delta T \)


Which of the following set of elements is written in order of their increasing metallic character?
A. \( B e<M g<C a \)
в. \( N a<L i<K \)
с. \( M g<A l< \) S \( i \)
D. \( C<O<N \)
N


Form the differential equation
corresponding to \( y=e^{m x} \) by
eliminating m.


In a medium in which a transverse
progressive wave is travelling the phase difference between two points with a distance of separation \( 1.25 \mathrm{cm} \) is \( \frac{\pi}{4} . \)
the frequency of the wave is \( 1000 H z \)
its velocity will be
A \( \cdot 10^{4} m / s \)
в. \( 125 \mathrm{m} / \mathrm{s} \)
c. \( 100 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Solve the following quadratic equation
for \( x \)
\( 4 x^{2}+4 b x-\left(a^{2}-b^{2}\right)=0 \)


Draw a graph between \( y=p(x), \) where
polynomial having three zeros.


A nucleus \( _{z}^{A} X \) emits an \( \alpha \) -particle with velocity \( v . \) The recoil speed of the daughter nucleus is:
A. \( \frac{A-4}{4 v} \)
в. \( \frac{4 v}{A-4} \)
\( c \)
D. \( \frac{v}{4} \)


The equation \( 2 x-5 y=9 \) has:
A. no solution
B. one solution
c. two solutions
D. infinitely many solutions


Find the differential of
\( \mathbf{y}=\left(\sin ^{-1} \mathbf{x}\right)^{2}+\mathbf{A} \cos ^{-1} \mathbf{x}+\mathbf{B} \) where
\( A, B \) are arbitrary constants


The process by which DNA of nucleus passes genetic information to mRNA is
called as
A. Translocation
B. Transcription
c. Translation
D. Transportation


Plum Pudding Model of the Atom was given by:
A. Thomson
B. Rutherford
c. Bohr
D. chadwick


A solution turns methyl orange pink. It can turn the universal indicator to:
A . violet
B. blue
c. orange
D. green


A compound contains equal masses of
the elements \( A, B \) and \( C . \) If the atomic
masses of \( A, B \) and \( C \) are 20,40 and 60
respectively, the empirical formula of the compound is
A \( . A_{3} B_{2} C \)
в. \( A B_{2} C_{3} \)
c. \( A B C \)
D. \( A_{6} B_{3} C_{2} \)


An elastic circular wire of length \( \ell \)
carries a current \( I_{0} . \) It is placed in a
uniform magnetic field \( \vec{B} \) (out of paper)
such that its plane is perpendicular to the direction of \( \vec{B} \). The wire will
experience:
A. No force
B. A stretching force
c. A compressive force
D. A touque


When \( C O_{2} \) is passed through lime water, it turns milky. The milkiness is due to:
A. \( C a C O_{3} \)
в. \( C a(O H)_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C O_{2} \)


\( 0.25 g \) of an element \( M \) reacts with
excess fluorine to produce \( 0.547 g \) of the
hexafluoride \( M F_{6} . \) What is the
element?
A \( . C r \)
в. \( M o \)
\( c \cdot s \)
D. \( T e \)


A cylinder of radius \( R \) and length Lis placed in the uniform electric field \( \mathrm{E} \) parallel to the cylinder axis. The total flux from the curved surface of the cylinder is
given by :
A \( \cdot 2 \pi R^{2} E \)
в. \( \frac{\pi R^{2}}{E} \)
c. \( \frac{\pi R^{2}-\pi R}{E} \)
D. zero


If \( C \) and \( D \) are two events such that
\( \mathbf{C} \subset \mathbf{D} \) and \( \mathbf{P}(\mathbf{D}) \neq \mathbf{0}, \) then the correct
statement among the following is
\( ^{\mathbf{A}} \cdot p\left(\frac{C}{D}\right)=\mathrm{P}(\mathrm{C}) \)
\( ^{\mathbf{B}} \cdot p\left(\frac{C}{D}\right) \geq \mathrm{P}(\mathrm{C}) \)
\( ^{c} \cdot p\left(\frac{C}{D}\right)<\mathrm{P}(\mathrm{C}) \)
\( P\left(\frac{C}{D}\right)=\frac{P(D)}{P(C)} \)


An element X has mass number \( 10, \) and
number of neutrons = 7. Then what will
be the number of proton?
A . 10
B. 3
c. 7
D. 17


Find \( x \) in terms of \( a, b \) and \( c \) \( \frac{a}{x-a}+\frac{b}{x-b}=\frac{2 c}{x-c} \) where \( x \neq \)
\( \{a, b, c\} \)


Which of the following oxides is/are not amphoteric in character? This question has multiple correct options
A. \( \mathrm{caO} \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( S n O_{2} \)


(a) Explain the co-ordination isomerism and ionisation isomerism with
example.
(b) Explain Radio-Carbon dating.


Using \( N a_{2} C O_{3}, \) both temporary and permanent hardness can be removed. If this is true enter 1 , if false enter 0 .


The expansion \( ^{n} C_{r}+4 .^{n} C_{r-1}+ \)
\( \mathbf{6} \cdot^{n} \boldsymbol{C}_{\boldsymbol{r}-\mathbf{2}}+\mathbf{4} \cdot^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}-\mathbf{3}}+^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}-\mathbf{4}}= \)
A. \( ^{n+4} C_{r} \)
В \( \cdot 2 \cdot^{n+4} C_{r-1} \)
\( c \cdot 4 \cdot^{n} c \)
D. \( 11 .^{n} c_{r} \)


If \( A \) and \( B \) are two sets, then \( A \cap \)
\( (B \cup A)^{c} \) equals
A. \( A \)
в. \( B \)
\( c \cdot \phi \)
D. none of these


The hydride ion, \( H^{-} \) is a stronger base
than its hydroxide ion \( O H^{-} . \) Which of the following reactions will occur, if sodium hydride \( (N a H) \) is dissolved in
water?
\( \mathbf{A} \cdot H_{(a q)}^{-}+H_{2} O \rightarrow H_{3} O \)
B. \( H_{(a q)}^{-}+H_{2} O_{(l)} \rightarrow O H^{-}+H_{2} \)
\( \mathbf{c} \cdot H^{-}+H_{2} O_{(l)} \rightarrow \) no reaction
D. None of the above


Two charges \( 5 \times 10^{-8} C \) and \( -3 x \)
\( 10^{-8} C \) are located \( 16 \mathrm{cm} \) apart. At what
point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.


Two wires have their lengths in the ratio
1: 3 diameters in the ratio 2: 3 and
their materials have specific
resistances in the ratio \( 2: 1 . \) Then the
ratio of their resistances is :
A . 1: 3
в. 3: 1
c. 2: 3
D. 3: 2


If \( C_{0} . C_{1}, C_{2}, \dots, C_{n} \) are the coefficients
of the expansion of \( (1+x)^{n}, \) then the value of \( \sum_{0}^{n} \frac{C_{k}}{k+1} \) is
A .
в. \( \frac{2^{n}-1}{n} \)
c. \( \frac{2^{n+1}-1}{n+1} \)
D. None of these


Define Reflection.


\( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \) is:
A. monobasic and weak Lewis acid
B. monobasic and weak Bronsted acid
C. monobasic and strong Lewis acid
D. tribasic and weak Bronsted acid


Assertion
In the reaction below, the final product
will be a meso diacid
Reason
The initial step of rection is \( S_{N} 2 \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


why are the electrons held together in
the orbits


The \( 11^{t h} \) term and the \( 21^{s t} \) term of an
A.P. are 16 and 29 respectively, then find the first term and common difference.


Statement(A): For green house effect, presence of green plants is essential.
Statement \( (\mathrm{R}): C O_{2} \) and water vapour
present in the atmosphere absorb the re-emitted IR radiation from the
earths surface and warm the air
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of A
c. \( A \) is true and \( R \) is false
D. A is false and R is true


Salt is used in our food because:
A. it makes the food tasty
B. we sweat and lose salt
C. it helps in production of hydrochloric acid required to digest the food
D. it makes water absorb food particles better


Solve \( \boldsymbol{x}+\mathbf{2}+\boldsymbol{y}+\mathbf{3}+ \)
\( \sqrt{(x+2)(y+3)}=39 \)
\( (x+2)^{2}+(y+3)^{2}+(x+2)(y+ \)
3)\( =741 \)


The pair of compounds which cannot exist together in aqueous solution is:
A. \( N a_{2} C O_{3} \) and \( N a H C O_{3} \)
в. \( N a H C O_{3} \) and \( N a O H \)
c. \( N a O H \) and \( N a H_{2} P O_{4} \)
D. Both (B) and (C)


What is the basis of classification of
vertebrata into sub groups?
A. Notochord
B. Vertebral column
c. organs of respiration
D. organs of reproduction


Value of \( \tan 15^{\circ} \) is
This question has multiple correct options
A \( \cdot \frac{\sqrt{3}-1}{\sqrt{3}+1} \)
B. \( 2-\sqrt{3} \)
\( c \cdot 2+\sqrt{3} \)
D. \( \sqrt{3}-1 \)


The specific conductivity of \( 0.1 \mathrm{N} \) KCl solution is 0.0129 ohm \( ^{-1} \mathrm{cm}^{-1} \). The
resistance of the solution in the cell is
100 \( \Omega \). The cell constant of the cell will
be
A . 1.10
B. 1.29
c. 0.56
D. 2.80


Population generally increases because of
A. high birth rate
B. relatively lower death rate
c. immigration
D. all of the above


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 \( \cdot v_{0}+2 g+3 f \)
B . \( v_{0}+g / 2+f / 3 \)
\( \mathbf{c} \cdot v_{0}+g+f \)
D . \( v_{0}+g / 2+f \)


Suppose that the acceleration of a free fall at the surface of a distant planet
was found to be equal to that at the surface of the earth. If the diameter of
the planet were twice the diameter of
the earth, then the ratio of mean density
of the planet to that of the earth would be:
A . 4: 1
B . 2: 1
c. 1: 1
D. 1: 2


What is the value of \( \left(\frac{1}{\sin 45^{0}}-\sin 45^{0}\right)\left(\frac{1}{\cos 45^{0}}-\cos 45^{0}\right. \)


Which of the following is not a
conclusion of Rutherford experiment?
A. An atom has a very small compact nucleus
B. An atom is mainly empty space
C. An atom's mass is concentrated in the nucleus
D. An atom has a very dense nucleus
E. An atom has a negatively charged nucleus


Identify the correct Structure of
dichromate ion.
\( A \)
в.
c.
\( D \)


The \( \boldsymbol{E}^{o} \) for, \( \boldsymbol{M} \boldsymbol{n}^{4+}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+} \) is
equal to:
A . 1.23 v
B. 2.46 V
c. \( 0.56 v \)
D. -0.56


Suppose a ball of mass \( \mathrm{m} \) is thrown vertically upward with an initial speed \( v \) Its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentums of the ball
are same. Is this an example of conservation of momentum?
A. Yes
B. No
c. Sometimes
D. None of these


A crystal of intrinsic silicon at room
temperature has a carrier
concentration of \( 1.6 \times 10^{16} / m^{3} . \) If the
donor concentration level is \( 0.48 \times \)
\( 10^{20} / m^{3}, \) then the concentration of
holes in the semiconductor is:
A \( \cdot 5.3 \times 10^{12} / m^{3} \)
B . \( 4 \times 10^{11} / m^{3} \)
c. \( 4 \times 10^{12} / m^{3} \)
D. \( 5.3 \times 10^{11} / m^{3} \)


The sides of a rhombus ABCD are
parallel to the lines, \( x-y+2=0 \) and
\( 7 x-y+3=0 . \) If the diagonals of the
rhombus intersect at \( \boldsymbol{P}(1,2) \) and the vertex A(different from the origin) is on the \( y \) -axis, then the ordinate of \( A \) is?


Differentiate between.
Respiration and breathing.


A metal \( M \) of molar mass 96 g \( m o l^{-1} \) reacts with fluorine to form a salt that
can be represented as \( M F_{x} \). In order to determine \( x .9 .18 \mathrm{g} \) of the sample of the salt is dissolved in 100 g of water and its boiling point was determined to be
\( 374.38 \mathrm{K} \). What is the value of \( x \) ?
Given: \( \boldsymbol{K}_{\boldsymbol{b}}(\boldsymbol{w} \boldsymbol{a} \boldsymbol{t e r})=\mathbf{0 . 5 1 2} \boldsymbol{K} \boldsymbol{k g m o l}^{-1} \)
Assume complete dissociation of salt
A . \( x=2 \)
в. \( x=4 \)
c. \( x=5 \)
D. \( x=7 \)


A body initially at rest and sliding along
a frictionless track from a height \( h \) (as
shown in the figure) just completes as
vertical of diameter \( \boldsymbol{A B}=\boldsymbol{D} \). The
height \( h \) is equal to:
A \( \cdot \frac{3}{2} D \)
в. \( D \)
c. \( \frac{5}{4} D \)
D. \( \frac{7}{5} L \)


Out of given paramagnetic substance (Calcium, Chromium, Oxygen and Tungsten) which substance has maximum susceptibility?
A. Calcium
B. Chromium
c. oxygen
D. Tungsten


Proof is defined as
percentage by volume of alcohol in ethanol-water mixture.
\( A \). twice
B. thrice
c. half
D. four times


Find the integrals of the functions in Exercises 1 to 22
1. \( \sin ^{3}(2 x+1) \)
2. \( \sin ^{3} x \cos ^{3} x \)
\( 3 \cdot \frac{\cos x-\sin x}{1+\sin 2 x} \)


\( A \gamma \) ray photon produces an electron positron pair. If the rest mass energy of electron is 0.51 Mev and the total
kinetic energy of electron - positron pair is \( 0.78 M e V \) then the energy of \( \gamma- \) ray
photon is \( M e v \) is
A . 0.78
в. 1.8
c. 1.28
D. 0.28


The value of \( c \) in Lagrange's theorm for
the function \( f(x)=\log \sin x \) in the
interval \( [\boldsymbol{\pi} / \mathbf{6}, \mathbf{5} \boldsymbol{\pi} / \mathbf{6}] \) is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 2 \)
\( \mathrm{c} \cdot 2 \pi / 3 \)
D. none of these


What is the purpose of filament in electron gun inside a cathode ray tube?
A. To support the cathode
B. To protect the cathode
c. To cool the cathode
D. To heat the cathode


Find the sum of the series
\( \frac{3 \cdot 5}{5 \cdot 10}+\frac{3 \cdot 5 \cdot 7}{5 \cdot 10 \cdot 15}+\frac{3 \cdot 5 \cdot 7 \cdot 9}{5 \cdot 10 \cdot 15 \cdot 20}+ \)
\( \dots \infty \)


According of Newton's Third Law of Motion, action and reaction are equal and opposite. The resultant force is not zero because
A. They act at different times
B. They act on different bodies
c. Their lines of action are different
D. They act on the same body


Which of the following can be used to lift giant industrial machines?
A. electromagnets
B. permanent magnets
c. both A and B
D. none of the above


If one-third of \( H I \) decomposes at a
particular temperature, \( \boldsymbol{K}_{c} \) for the equilibrium is:
\( \boldsymbol{H} \boldsymbol{I} \rightleftharpoons \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \)
A . \( 1 / 16 \)
B. \( 1 / 4 \)
\( c \cdot 1 / 6 \)
D. \( 1 / 2 \)


Calculate the mass of a photon of
sodium light having wavelength \( 5894 A \)
and velocity \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
\( \left(h=6.6 \times 10^{-34} K g m^{2} s^{-1}\right) \)


After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A. Inspiratory Reserve Volume(IRV) + Expiratory Reserve Volume (ERV) + Tidal Volume (TV)+ Residual Volume(RV)
B. IRV + RV + ERV
c. \( \mid R V+T V+E R V \)
D. \( T V+R V+E R V \)


Melting temperature for double stranded molecules are converted into
single stranded molecules. Which one
of the following DNA will have the highest melting temperature?
A. DNA with \( 15 \% \) guanine
B. DNA with 30\% cytosine
C. DNA with \( 40 \% \) Thymine
D. DNa with \( 50 \% \) adenine


Dinoflagellates glow during dark,
because
A. Their body contains large amount of phosphorus
B. Their body is covered by luminiscent layer
C. They absorb light and emit some part of it
D. of chemical reaction between luciferin-luciferase


The product formed in the reaction is :
\( A \)
B.
\( c \)
D.


Write the full name of LED.


In transforming 0.01 mole of \( P b S \) to
\( P b S O_{4}, \) the volume of 10 volume \( H_{2} O_{2} \)
required will be:
A. \( 11.2 \mathrm{mL} \)
B. \( 22.4 \mathrm{mL} \)
c. \( 33.6 m L \)
D. \( 44.8 \mathrm{mL} \)


The dimensions of torque are
\( \mathbf{B} \cdot\left[M L^{2} T^{-2}\right] \)
c. \( \left[M^{2} L^{2} T^{-2}\right] \)
D. \( \left[M L T^{-1}\right] \)


What is the focal length of double
concave lens kept in air with two
spherical surface of radii \( \boldsymbol{R}_{1}=\mathbf{3 0} \boldsymbol{c m} \)
and \( R_{2}=60 \mathrm{cm} . \) Take refractive index
of lens as \( \mu=1.5 \)


Integrate the function \( \frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}} \)


Which among the following equations represents the first law of thermodynamics under isobaric conditions?
A \( \cdot \Delta U=q_{p}-P_{e x} \cdot \Delta V \)
В \( \cdot q_{v}=\Delta U \)
\( \mathbf{c} \cdot \Delta U=W \)
D. \( W=-q \)


Which one keeps its stomata open during night and closed during day?
A. cactus
B. Water lily
\( c . \) Ivy
D. Hibiscus


Solve: \( \sin \left(\tan ^{-1} x\right),|x|<1 \) is equal to
A \( \cdot \frac{x}{\sqrt{1-x^{2}}} \)
в. \( \frac{1}{\sqrt{1-x^{2}}} \)
c. \( \frac{1}{\sqrt{1+x^{2}}} \)
D. \( \frac{x}{\sqrt{1+x^{2}}} \)


Solve:
\( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


If \( P=\left(\frac{-3}{4}\right)^{3}, Q=\left(\frac{-2}{5}\right)^{2}, R= \)
\( (0.3)^{2}, S=(-1.2)^{2} \) which of the
following is true?
A. \( P>Q>R>S \)
в. \( S>P>Q>R \)
c. \( S>Q>R>P \)
\( \mathbf{D} \cdot S>R>P>Q \)


Two unknown resistances are
connected in two gaps of a meter-
bridge. The null point is obtained at \( 40 \mathrm{cm} \) from left end. A \( 30 \Omega \) resistance is
connected in series with the smaller of the two resistances, the null point shifts
by \( 20 \mathrm{cm} \) to the right end. The value of
smaller resistance in \( \Omega \) is
A . 12
B . 24
\( c .36 \)
D. 48


A person cannot see distinctly objects
kept beyond 2 m. This defect can be
corrected by using a lens of power:
A . \( +0.5 D \)
в. \( -0.5 D \)
c. \( +0.2 D \)
D. \( -0.2 D \)


Oxidation number of phosphorous is lowest in:
A. hypophosphorous acid
B. ortho phosphorous acid
c. meta phosphorous acid
D. pyro phosphorous acid


The refractive index \( (\mu) \) of glass is found to have the values 1.49,1.50,1.52,1.54 and 1.48
Calculate the mean value of refractive
index.
A . 1.49
в. 1.50
c. 1.51
D. 1.52


Find the value of \( \cos 37^{\circ} 16^{\prime} \)


A body of mass 10 gm moving with a velocity of \( 20 \mathrm{cm} s^{-1} \) collides with a stationary mass of \( 90 \mathrm{gm} \). The collision is perfectly inelastic. Find the percentage loss of kinetic energy of
the system.
A.
B. 50
c. 90
D. 100


In a very ideal imaginary condition, a sample of ice was taken, and its osmotic pressure was found to be 0.274 \( \operatorname{atm} \) at \( 300 \mathrm{K} \) (density \( =1 \mathrm{g} / \mathrm{mL} \) ). Thus, number of water units attached to one
water unit is
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D .5 \)


A body is moved in a direction opposite to the direction of force acting on it. Work is done is:
A. against the force
B. zero
c. along the force
D. none of these


\( A, B, C \) are the points
\( (-2,-1),(0,3),(4,0) . \) Then the co-
ordinates of the point \( D \) such that \( A B C D \) is a parallelogram are
A. (2,-4)
в. (2,4)
c. (-2,-4)
D. None of these


First member of ether series on reaction
with sodium and liquified ammonia
gives
A. methanol+methane
B. ethane+methanol
c. ethanol
D. ethane


Find the H.C.F. of 180,252 and 324 using Euclid division of lemma.


A body travelling with uniform acceleration crosses two points \( A \) and
\( B \) with velocities \( 20 m s^{-1} \) and \( 30 m s^{-1} \)
respectively. The speed of the body at mid-point of \( A \) and \( B \) is:
A \( \cdot 25 m s^{-1} \)
B . \( 25.5 \mathrm{ms}^{-1} \)
c. \( 24 m s^{-1} \)
D. \( 10 \sqrt{6} \mathrm{ms}^{-1} \)


The two masses \( m_{1} \) and \( m_{2} \) are joined
by a spring as shown. The system is dropped to the ground from a height. The spring will be
A. neither compressed nor stretched regardless of the value of \( m_{1} \) and \( m_{2} \)
B. neither compressed nor stretched only when \( m_{1}=m_{2} \)
c. stretched when \( m_{2}>m_{1} \)
D. compressed when \( m_{2}<m_{1} \)


Which of the following has been used in the manufacture of non-inflammable
photographic films?
A. Cellulose nitrate
B. Cellulose xanthate
c. cellulose perchlorate
D. Cellulose acetate


A cord is used to lower vertically a block
of mass \( M, \) through a distance \( d \) at a constant downward acceleration of \( \frac{g}{8} \) Then the work done by the cord on the block is
A. \( \frac{M g d}{8} \)
в. \( \frac{3 M g d}{8} \)
c. \( M g d \)
D. \( \frac{-7 M g d}{8} \)


In a pressure cooker, the pressure inside increases and hence the boiling
point of water decreases thereby food
cooks faster.
A . True
B. False


Assertion
Plants utilizing first RuBP in \( C O_{2} \)
fixations are called \( C_{3} \) plants
Reason
Plants utilizing first PEP in \( C O_{2} \)
fixations are called \( C_{4} \) plants
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the distance between two equal points charges is doubled and their individual charges are also doubled,
what would happen to the force between them?


When drawing Lewis dot structures, what should you do if you run out of electrons before all atoms are satisfied?
A. Leave it as is.
B. Try double or triple bonds
c. Make a resonance structure
D. Add the missing electrons


The molecular formula of Iron (III)
sulphide is:
A \( \cdot \) FeS \( _{3} \)
в. \( F e_{2} S_{3} \)
c. \( F e S_{2} \)
D. \( F e_{3} S_{4} \)


Select the group of plants that possess
stilt roots.
A. Zea mays, Rhizophora mangal
B. Pandanus odoratissimus, Ficus benghalensis
c. Rhizophora mangal, Hedera helix
D. Ficus benghalensis, Pisum sativum


A straight wire with a resistance of \( r \)
per unit length is bent to form an angle
2 \( \alpha \). A rod of the same wire
perpendicular to the angle bisector (of
\( 2 \alpha) \) forms a closed triangular loop. This loop is placed in a uniform magnetic
field of a induction \( B \). Calculate the
current in the wires when the rod moves
at a constant speed \( V \)


Heterotrophic nutrition is present in
A. Vallisneria
B. Pistia
c. Drosera
D. opuntia


Which of the following is correct
sequence in Krebs cycle?
A. Isocitric acid \( \rightarrow \) Oxalosuccinic acid \( \rightarrow \alpha \) -ketoglutaric acid
B. Oxalosuccinic acid \( \rightarrow \) Isocitric acid \( \rightarrow \alpha \) -ketoglutaric acid
C \( . \alpha \) -ketoglutaric acid \( \rightarrow \) Isocitric acid \( \rightarrow \) Oxalosuccinic acid
D. Isocitric acid \( \rightarrow \alpha \) -ketoglutatric acid \( \rightarrow \) Oxalosuccinic acid


State whether true or false.
A boy on a swing exhibits both oscillatory motion and periodic motion
A. True
B. False


In binomial nomenclature, the first
name refers to
A. Order
B. Class
c. Genus
D. Species


Is \( * \) defined on the set \{1,2,3,4,5\} by
\( a * b=L C M \) of \( a \) and \( b, a \) binary
operation ? Justify your answer


What is the path difference of destructive interference:
A \( . n \lambda \)
B. \( n(\lambda+1) \)
c. \( \frac{(n+1) \lambda}{2} \)
D. \( \frac{(2 n+1) \lambda}{2} \)


Find the area of the triangle formed by
the lines \( x=3, y=2 \) and \( 3 x+4 y=29 \)


What is the type of hybridisation of \( N \) atom in amines?
\( \mathbf{A} \cdot s p \)
B. \( s p^{2} \)
c. \( d s p^{2} \)
\( D \cdot s p^{3} \)


Assertion
The density of water remains constant as it is cooled from room temperature
until its temperature reaches \( 4^{\circ} C \)
Reason

Below \( 4^{\circ} C \),the density increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following metal is refined by distillation method?
A. zinc
B. Iron
c. Tin
D. copper


What is combustion?


The sum of 100 observations and the
sum of their squares are 400 and 2475 respectively. Later on, three observations, 3,4 and \( 5, \) were found to
be incorrect. If the incorrect
observations are omitted, then the variance of the remaining observations
is.
A . 8.00
B. 8.50
c. 8.25
D. 9.00


What happens when sulphuric acid is
diluted by adding water to concentrated
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) Explain.


While the arrow moves towards its
target, the force acting on it are due to gravity and due to of air.
A . gravitational force
B. muscular force
c. magnetic force
D. frictional force


Davisson Germer experiment explained the wave nature of electrons through
A. Electron diffraction
B. Electron interference
c. Electron scattering
D. Failed to explain wave nature of electrons


Assertion
Bis(dimethylglyoximato)nickel(II) can show geometrical isomerism.
Reason
Tetrahedral complexes with chiral structures exhibit optical isomerism.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following statement is
wrong?
A. The fibrous nature of Wrought iron is due to the slag present in it.
B. The loss of iron is Bessemer process is due to the formation of \( F e S i O_{3} \) slag.
C. In Bessemer process carbon monoxide formed burns with blue flame at the mouth of the furnace.
D. In blast furnace \( F e_{2} O_{3} \) is reduced to iron mainly by coke.


The pressure of a gas is increased four times and its absolute temperature two times. The ratio of its final volume to its
initial volume is
A . 1: 2
B. 2:
\( c \cdot 1: \)
D. 3:


Among III-A group elements the elements with highest and lowest I.P.
values are:
A . В, T
B. B, In
c. В, Al
D. B, Ga


Equally shared between them Covalent
bond is present in
A. \( N a_{a} S \)
в. \( A l C l_{3} \)
c. \( N a H \)
D. \( K_{2} \),


For a planet revolving around sun, if \( a \) and \( b \) are the respective semi-major and semi-minor axes, then the square of its time period is proportional to
\( ^{\mathbf{A}} \cdot\left(\frac{a+b}{2}\right)^{3} \)
\( ^{\mathbf{B}} \cdot\left(\frac{a-b}{2}\right)^{3} \)
\( c \cdot b^{3} \)
D. \( a^{3} \)


If \( 2 \% \) of the main current is to be
passed through a galvanometer of resistance \( G \), then resistance of the
shunt required is
A \( \cdot \frac{G}{50} \)
в. \( \frac{G}{49} \)
c. \( 49 G \)
D. \( 50 G \)


What is the Brewster angle for water?
The refractive index of water with
respect to air is 1.33


Solve the differential equation \( \left(x^{2}-\right. \)
\( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}+2 \boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=0 ; \) given that \( \boldsymbol{y}=\mathbf{1} \)
when \( \boldsymbol{x}=\mathbf{1} \)


Explain reversible and irreversible process. Describe the working of Carnot
Engine. Obtain an expression for its efficiency.


A flask has a volume of \( 0.25 d m^{3} . \) What
volume of air will be displaced from the
flask if it is heated from \( 300 K \) to
\( \mathbf{3 6 0} \boldsymbol{K} ? \)
\( \mathbf{A} \cdot 0.25 d m^{3} \)
в. \( 0.5 d m^{3} \)
c. \( 0.05 d m^{3} \)
D. None of these


What do you understand by the thermal
effect of electric current?


The \( p H \) of \( H C l \) is \( 1.1 .10 m l \) of this
solution is reacted with \( 40 \mathrm{ml} \) of
NaOH solution whose \( p H=12 . \) The
\( p H \) of resulting solution is:
\( (\log (1.2)=0.108) \)
\( \mathbf{A} \cdot 2.892 \)
B. 1.892
c. 32.892
D. 11.842


When a solution of \( C H C l_{3} \) and acetone is formed, the solution is non-ideal with
deviation from Raoult's
law.The vapour pressure of such a solution will be
corresponding ideal solution.
A. Positive, more
B. Negative, more
c. Negative ,less
D. Positive , less


A person walks at a velocity \( v \) in a
straight line forming an angle \( \alpha \) with
the plane of a plane mirror. the velocity
at which he approaches his image is:
\( A \)
B. \( v \sin \alpha \)
\( \mathbf{c} \cdot 2 v \sin \alpha \)
D. \( 2 v \cos a \)


A solid cone of height \( H \) and base
radius \( H / 2 \) floats in a liquid of density
\( \rho . \) It is hanging from the ceiling with the
help of string. The force by the fluid on
the curved surface of the cone is \( \left(P_{0}=\right. \)
atmospheric pressure)
A \( \cdot \pi H^{2}\left(\frac{p_{0}}{4}+\frac{\rho g H}{3}\right) \)
\( ^{\text {В }} \cdot \frac{\pi H^{4}}{2} \cdot \rho g \)
c. \( \frac{\pi H^{2}}{4}\left(\frac{p_{0}}{4}+\rho g H\right) \)
D. \( \frac{\pi H^{2}}{4}\left(p_{0}+\rho g H\right) \)


When 1 mol of pure \( A g_{2} C O_{3} \) is strongly heated, calculate the weight of residue obtained in \( \mathfrak{g m} \)


Two particles of mass \( M_{A} \) and \( M_{B} \) and
there velocities are \( V_{A} \) and \( V_{B} \)
respectively collides. After collision they inter changes their velocities then ratio of \( \frac{\boldsymbol{M}_{\boldsymbol{A}}}{\boldsymbol{M}_{\boldsymbol{B}}} \) is:
A \( \cdot\left(\text { a) } \frac{V_{A}}{V_{B}}\right. \)
в. (b) \( \frac{V_{B}}{V_{A}} \)
c.
(c) \( \frac{V_{A}+V_{B}}{V_{B}-V_{A}} \)
D. (d)


\[
\begin{array}{c}
4 F e S+7 O_{2} \longrightarrow 2 F e_{2} O_{3}+4 S O_{2} \\
C r_{2} O_{7}^{2-}+2 H^{+}+3 S O_{2} \longrightarrow \\
2 C r^{3+}+3 S O_{4}^{2-}+H_{2} O
\end{array}
\]
1 \( g \) sample of \( F e S \) was roasted with oxygen gas \( S O_{2} \) thus formed required
\( 10 m L \) of \( 0.05 M K_{2} C r_{2} O_{7} \) solution in acidic medium. Calculate percentage of \( F e S \) in the sample. \( (F e=56, S=32) \)
A . \( 1.2 \% \)
B. \( 1.32 \% \)
c. \( 1.5 \% \)
D. None of these


If \( f(x)=\frac{\sin ([x] \pi)}{x^{2}+x+1}, \) when
: \( ] \) denotes
the greatest integer function, then


A ball is thrown vertically upward with
speed \( v_{1}, \) and it returns to ground with
speed \( v_{2} . \) If air resistance is not ignored,
then, choose the correct alternative:
\( \mathbf{A} \cdot v_{1}=v_{2} \)
B. \( v_{2}>v_{1} \)
\( \mathbf{C} \cdot v_{1}>v_{2} \)
D. Nothingcanbesaid


To bring a unit positive charge from infinity to a point in an electric field, some work has to done, which is called:
A. potential energy
B. electric potential
c. electric field
D. electric induction


Two numbers \( X \) and \( Y \) are chosen at
random (without replacement) from the \( \operatorname{set} 1,2, \dots, 5 N . \) The probability that
\( X^{n} \sim Y^{n} \) is divisible by 5 is
A \( \frac{N-1}{5 N-1} \)
в. \( \frac{4(4 N-1)}{5(5 N-1)} \)
c. \( \frac{17 N-5}{5(5 N-1)} \)
D. None of these


If the distance between the centres of
earth and moon is \( \mathrm{D} \) and mass of earth
is 81 times that of moon. At what
distance from the centre of earth
gravitational field will be zero:
A \( \cdot \frac{D}{2} \)
в. \( \frac{3 D}{2} \)
c. \( \frac{4 D}{5} \)
D. \( \frac{D}{10} \)


The Van't Hoff factors \( i \) for an electrolyte which undergoes dissociation and association in solvents are respectively:
A. greater than one and less than one
B. less than one and greater than one
c. less than one and less than one
D. greater than one and greater than one


If sum of the perpendicular distances of a variable point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) from the lines
\( \boldsymbol{x}+\boldsymbol{y}-\mathbf{5}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is
always \( 10 . \) Show that \( P \) must move on a
line.


Explain the process of secondary treatment given to the primary effluent up to the point it shows significant change in the level of biological oxygen demand (BOD) in it.


Find the distance of the point (-1,1) from the line \( 12(x+6)=5(y-2) \)


Balance the following equations:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{I}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}^{3+}+\boldsymbol{I}_{2}+ \)
\( H_{2} O \)
\( \mathbf{A} \cdot C r_{2} O_{7}^{2-}+6 I^{-}+14 H^{+} \rightarrow 2 C r^{3+}+3 I_{2}+7 H_{2} O \)
B. \( C r_{2} O_{7}^{2-}+I^{-}+14 H^{+} \rightarrow 2 C r^{3+}+3 I_{2}+7 H_{2} O \)
\( \mathbf{c} \cdot C r_{2} O_{7}^{2-}+6 I^{-}+7 H^{+} \rightarrow 2 C r^{3+}+I_{2}+7 H_{2} O \)
D. None of these


ff \( y=x-x^{2} \), then the derivative of
\( \boldsymbol{y}^{2} \boldsymbol{w} \cdot \boldsymbol{r} \cdot \boldsymbol{t} \cdot \boldsymbol{x}^{2} \) is
A \( \cdot 2 x^{2}+3 x-1 \)
B . \( 2 x^{2}-3 x+1 \)
c. \( 2 x^{2}+3 x+1 \)
D. None of these


The chemical composition of the slag formed during smelting process is :
A \( \cdot \) Cusio \( _{3} \)
в. Fesi Оз\( _{3} \)
\( \mathrm{c} \cdot \operatorname{casi} O_{3} \)
D. \( C u_{2} O . S i O_{2} \)


If \( \sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0, x> \)
\( 0, \) then
This question has multiple correct options
\( \mathbf{A} \cdot x=1 \)
В. \( x=\sqrt{2}+1 \)
c. \( x=\sqrt{2}-1 \)
D. \( x=3 \)


What is the value of friction force f for
the following value of applied force \( \mathrm{F} \) ?
a. \( 1 \mathrm{N} \) b. \( 2 \mathrm{N} \) c. \( 3 \mathrm{N} \) d. \( 4 \mathrm{N} \) e. \( 20 \mathrm{N} \)
Assume the coefficient of friction to be
\[
\boldsymbol{\mu}_{s}=\mathbf{0 . 3}: \boldsymbol{\mu}_{\boldsymbol{k}}=\mathbf{0 . 2 5}
\]
Mass of the body is \( \mathrm{M}=1 \mathrm{kg} \). (Assume
\[
\begin{array}{l}
\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \\
\qquad \begin{array}{l}
\sqrt{w}+r \\
\end{array}
\end{array}
\]


Muscles attached to the vocal cords can
make them
A. tight only
B. loose only
c. both loose and tight as per requirement
D. neither loose nor tight


\( \Delta U^{\ominus} \) of combustion of methane is
\( -X k J m o l^{-1} \) The value of \( \Delta H^{\ominus} \) is
\( A \cdot=\Delta U^{\ominus} \)
в. \( >\Delta U^{\text { }} \)
\( \mathrm{c} \cdot<\Delta U^{\circ} \)
D.


If \( 270^{\circ}<A<360^{\circ}, 90^{\circ}<B< \)
\( 180^{\circ}, \cos A=\frac{5}{13}, \tan B=-\frac{15}{8}, \) then
\( \sin (\boldsymbol{A}+\boldsymbol{B})= \)
A \( \cdot \frac{140}{221} \)
в. \( \frac{171}{221} \)
c. \( \frac{140}{171} \)
D. \( \frac{221}{171} \)


If kinetic energy of an electron is
reduced by \( (1 / 9) \) then how many times its de Broglie wavelength will increase?
A . 3
B. 4
c. 5
D. 6


If 18 men can do a piece of work in 18
days, how many men would do it in 27 days?


Coleorrhiza is a cap like covering over
A. Plumule in a dicot
B. The radical in a monocot
c. Radicle in dicot
D. Plumule in a monocot


Which of the following statements is correct about the role of collectors
added during forth floatation process?
A. Collectors enhance the non-wettability of ore particles
B. Collectors enhance the wettability of gangue particles
c. collectors help in separating two sulphide ores present in the mixture
D. collectors help ore particles to settle down below the froth


Which of the following is not a mineral acid?
A. Hydrochloric acid
B. Citric acid
c. sulphuric acid
D. Nitric acid


Show that motion of bob of pendulum
with small amplitude is linear \( S . H . M \) Hence obtained an expression for its period. What are the factors on which its period depends?


Assertion \( (A): \) Moist \( C l_{2} \) bleaches the
vegetable colouring matter Reason \( (\mathrm{R}): \mathrm{Cl}_{2} \) is a strong reducing
agent.
A. A and R are true, R is correct explanation of A
B. A and R are true,R is not correct explanation of A
c. A is true, but R is false
D. A is false, but R is true


Hydrogen - Oxygen fuel cells are used in
space craft to supply:
A. power for heat and light
B. electrical power
c. oxygen
D. water


Distinguish between IRV and ERV.


Aqueous solution of \( \mathrm{PBr}_{3} \) conducts
electricity due to the presence of:
\( A . \) HOBr
в. НВг
c. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{O} \)


A car of mass \( 1200 \mathrm{kg} \) is moving with a speed of \( 81 \mathrm{km} / \mathrm{hr} \). Calculate its kinetic
energy.


Vitamin \( B_{1} \) is :
A . Riboflavin
B. Cobalamin
c. Thiamine
D. Pyridoxine


is the mass, in grams, of
one mole of atoms in a monatomic
chemical element.
A. Gram atomic mass
B. Gram molecular mass
c. Equivalent weight
D. Formula weight


State true or false:
Sum of the three angles of a triangle is
\( \mathbf{1 8 0}^{\circ} \)
A. True
B. False


If \( z=i^{9}+i^{19}, \) then \( z \) is equal to
\( \mathbf{A} \cdot 0+0 i \)
B. \( 1+0 i \)
\( c \cdot 0+i \)
D. \( 1+2 i \)


Find the values of the following determinant, where \( \boldsymbol{i}=\sqrt{-1} \) \( \left|\begin{array}{cc}\mathbf{2} \boldsymbol{i} & -\mathbf{3} i \\ \boldsymbol{i}^{\mathbf{3}} & -\mathbf{2} \boldsymbol{i}^{5}\end{array}\right| \)


Form the differential equation by eliminating arbitrary constants from the relation \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{\boldsymbol{5} \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{-\boldsymbol{5} \boldsymbol{x}} \)


At the metaphase plate during metaphase II of meiosis, there are
A. chromosomes consisting of one chromatid
B. unpaired duplicated chromosomes
c. bivalents (tetrads)
D. homologous pairs. of chromosomes


Name various units of classification in
their hierarchical levels and explain these with examples.


The binding energies of the nuclei \( A \) and
B are \( E_{a} \) and \( E_{b} \) respectively. Three nuclei of the element B fuse to give one nucleus of element A and an energy Q is
released. Then, \( E_{a}, E_{b}, Q \) are related as :
A \( \cdot E_{a}-3 E_{b},=Q \)
в. \( 3 E_{b}-E_{a},=Q \)
c. \( E_{a}+3 E_{b},=Q \)
\( \mathbf{D} \cdot E_{b}+3 E_{a},=Q \)


The number of spherical lead shots each \( 4.2 \mathrm{cm} \) in diameter that can be obtained from a rectangular solid with diameter \( 66 \mathrm{cm} \times 42 \mathrm{cm} \times 21 \mathrm{cm} \) is
A. 750
B. 3000
\( c \cdot 1500 \)
D. None of the above


The eccentricity of the conic \( \frac{\mathbf{7}}{r}=\mathbf{2}+ \)
\( 3 \cos \theta \) is
A . -3
в. 3
\( c \cdot \frac{3}{2} \)
D.


The class of phylum Protozoa to which Noctiluca belongs is
A. Rhizopoda
B. Sporozoa
c. Mastigophora
D. Ciliate


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\log \left(\frac{1-\boldsymbol{x}^{2}}{1+\boldsymbol{x}^{2}}\right) \)


Consider the following reaction:
The compound \( D \) is an ortho-isomer
and E is a \( p- \) isomer. The compounds
\( D \) and \( E, \) respectively are :
A. Phthalic acid and isophthalic acids
B. Isophthalic and phthalic acids
c. Terephthalic and phthalic acids
D. Phthalic and terephthalic acids


What do you mean by scattering of light? Write its use in daily life?


\( y=\tan ^{-1} \frac{\sin x}{1+\cos x} \) then prove that \( \frac{d y}{d x}=\frac{1}{2} \)


Assertion
The minimum distance between an
object and its real image formed by a convex lens is \( 2 f \)
Reason
The distance between object and its real image is minimum when its
magnification is one.
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


Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Z} \text { and }(\boldsymbol{a}+\boldsymbol{b}) \) is
even \( \} \) Show that \( R \) is an equivalence relation on Z.


Calculate the wavelength of the spectral
line, when the electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2


When released from ovary, human egg
contain
A. one Y chromosome
B. Two X chromosome
c. one x chromosome
D. xy chromosome


The most important safety method used for protecting home appliances from short circuiting or overloading is
A. earthing.
B. use of fuse
c. use of stabilizers
D. use of electric meter.


Which of the following is a true statement for the acids of phosphorus
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} ? \)
A. The order of their acidic strength is \( H_{3} P O_{4}> \) \( H_{3} P O_{3}>H_{3} P O_{2} \)
B. All of them are reducing in nature.
c. All of them are tribasic acids
D. The geometry phosphorus is tetrahedral in all the three


The sum of all odd proper divisors of
360 is
A . 77
B. 78
\( c \cdot 81 \)
D. none of these


Match List-I (Compounds) with List-I
(Oxidation states of Nitrogen) and
select answer using the codes
given below the lists.
\begin{tabular}{llll}
List - 1 & & List - II \\
\hline\( (a) \) & \( \mathrm{NaN}_{3} \) & (1) & +5 \\
\( (b) \) & \( \mathrm{N}_{2} \mathrm{H}_{2} \) & (2) & +2 \\
\( (c) \) & \( \mathrm{NO} \) & (3) & \( -\frac{1}{3} \) \\
\( (d) \) & \( \mathrm{N}_{2} \mathrm{O}_{5} \) & (4) & -1
\end{tabular}
\( A \)
\( a-3 \quad b-4 \quad c-2 \)
\( \begin{array}{llll}\text { В. } a-4 & b-3 & c-2 & d-1\end{array} \)
\( d-2 \)
2 \( c-1 \) \( b-4 \)
c. \( a-3 \)
\( \begin{array}{llll}\text { D. } a-4 & b-3 & c-1 & d-2\end{array} \)


Find the acceleration of the vehicle.
A. \( 0.1 \mathrm{Ams}^{-2} \)
B. \( 0.3 \mathrm{ms}^{-2} \)
D. \( 1 \mathrm{ms}^{-2} \)


In a DNA molecule cytosine is \( 18 \% \) Percentage of adenine would be
A . 32\%
B. 64\%
c. 36\%
D. 18\%


What is the correct order of covalent
size of the following?
\( \mathrm{Cu} \)
A \( . \mathrm{Cu}=\mathrm{Ni} \)
B. cusNi
\( c \cdot c u>N i \)
D. None of these


The length of a metal is \( l_{1} \) when the
tension in it is \( T_{1} \) and is \( l_{2} \) when the
tension is \( T_{2} . \) The original length of the wire is :
A \( \cdot \frac{l_{1}+l_{2}}{2} \)
в. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{1}+T_{2}} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \sqrt{T_{1} T_{2} l_{1} l_{2}} \)


The properties or physical constants which are lower for hydrogen than that of deuterium are:
This question has multiple correct options
A. Activation energy
B. Melting point
c. Latent heat of fusion
D. Number of neutrons


How much is the total saving of Saroj in the months March and April?


Kruti took a loan at simple interest at \( 6 \% \) in the first year with an increase of \( 0.5 \% \) in each subsequent year. She paid Rs. 3375 as interest after 4 year. How much loan did she take?
A. Rs. 12500
B. Rs. 15800
c. Rs. 33250
D. Rs. 30, 000


First codon of uracil nucleotides, UUU was deciphered by
A. Mathaei
B. Khorana
c. Nirenberg
D. Both A and C


Mention the exact location of the
following structures:
(i) Thylakoids
(ii) Organ of Corti
(iiii) Lenticels
\( (i v) \) Bicuspid valve
(v) Loop of Henle


Which alkene would you expect to be
most reactive towards acid-catalysed
hydration?
\( \mathbf{A} \)
B.
\( c \)
D. \( C H_{2}=C H C H_{2} C H_{3} \)


If the projection of the line segment \( A B \) on the coordinate axes are 2,3,6 then
the square of the sines of the angles made by \( A B \) with \( O Y \) axis is
A \( \cdot \frac{3}{7} \)
B. \( \frac{3}{49} \)
\( c \cdot \frac{4}{7} \)
D. \( \frac{40}{49} \)


Carbon monoxide is a poisonous gas
which when inhaled in too much
quantity causes headache, nausea, vomiting and even death. The toxicity of carbon monoxide is due to
A. Its greater a ffinity for hemoglobin as compared to carbon dioxide
B. Its lower affinity for hemoglobin as compared to carbon dioxide
c. Its greater affinity for hemoglobin as compared to oxygen
D. Its greater affinity for oxygen as compared to hemoglobin


Complete the statement of the first law of motion. "A body at rest stays at and a body in motion stays in unless an \( _{---} \) is applied"
A. Motion; Rest; External Force
B. Rest; Motion; External Force
c. Rest; Motion; Internal Force
D. None of these


What is the best term to describe the
rearrangement that causes the conversion of 3 -bromo- 2,2
dimethylbutane to 2,3 -dimethyl-2butanol?
A. 1,2 -methyl shift
B. 1, 3- hydride shift
c. 1,3 -methyl shift
D. 1,2 - hydride shift


Select correct statement(s):
This question has multiple correct options
A. In graphite, only three electrons (out of four) are involved in \( \sigma \) bonding.
B. \( \pi- \) bonding electrons in graphite are delocalized over the whole structure.
C. Conduction of electricity in graphite is due to mobile electrons.
D. Diamond is insulator due to absence of mobile
electrons.


If \( \lim _{x \rightarrow 2} \frac{x^{n}-2^{n}}{x-2}=80 \) and \( n \in N, \) find
\( \mathbf{n} \)


The range of \( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\boldsymbol{x}+ \)
\( \cos ^{-1} x \) is:
\( \mathbf{A} \cdot[-1,3+\pi] \)
В. \( [0, \pi-1] \)
c. \( [-1,2+\pi] \)
D. \( [-1, \pi] \)


The equation of a simple harmonic motion is given by \( \boldsymbol{x}=\mathbf{6} \sin \mathbf{1 0 t}+ \)
\( 8 \cos 10 t, \) where \( x \) is in \( \mathrm{cm}, \) and \( t \) is in
seconds. Find the resultant amplitude
A . 20
B . 10
c. 30
D. 50


Which of the following is not a compound?
A. Sulphur dioxide
B. Chalk
c. Lead
D. Sulphuric acid


Draw the electron dot structure of
ethyne and also draw its structural formula


An azeotropic solution of two liquids has a boiling point higher than either of the boiling points of the two liquids when it :
A . is saturated
B. shows no deviation from Rault's law
c. shows negative deviation from Rault's law
D. shows positive deviation from Rault's law


How much work is done in dragging a box of mass. \( 100 \mathrm{kg} \) on a level floor through a distance of \( 10 \mathrm{m} \) ? \( \mu \) between
the box and the floor is 0.4 and the force
is applied parallel to the floor. \( g= \)
\( 9.8 m / s^{2}(9320 J) \)


Two students Anil and Ashima
appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima
will qualify the examination is 0.10 . The probability that both will quailfy the examination is 0.02 . Find the
probability that
(a) Both Anil and Ashima will not
qualify the examination. (N)
(b) Atleast one of them will not qualify the examination. (N)
(c) Only one of them will qualify the examination. (N)


If \( \Delta Q \) and \( \Delta W \) represents the heat
supplied to the system and the work done on the system respectively, then the first law of thermodynamics can be written as
A. \( \Delta Q=\Delta U+\Delta W \)
в. \( \Delta Q=\Delta U-\Delta W \)
c. \( \Delta Q=\Delta W-\Delta U \)
D. \( \Delta Q=-\Delta W-\Delta U \)


A current in the windings on a toroid is
2 A. There are 400 turns and the mean
circumferential length is \( 40 \mathrm{cm} . \) If the magnetic field inside is \( 1 T \), the relative permeability is :
A . 200
B. 2500
\( c \cdot 400 \)
D. 150


An electrochemical cell stops working
after some time because:
A. electrode potential of both the electrodes becomes zero
B. electrode potential of both the electrodes become equal
C . one of the electrode is eaten away.
D. the reaction starts proceeding in opposite direction


A compound microscope has an objective lens of \( 1.0 \mathrm{cm} \) focal length and
an eye-piece of \( 2.5 \mathrm{cm} \) of focal length.
When the object is placed at \( 1.1 \mathrm{cm} \) from the objective, the final image is at the least distance of direct vision. Thus,
the magnification produced is
A . 10
B. 11
\( c .100 \)
D. 110


If \( \sqrt{3}(\sqrt{7}-\sqrt{3})=\sqrt{a}+b, \) then find the
values of a and b.


Number of \( C=O \) groups in thymine
and \( \mathrm{X} \) are equal. Now, \( \mathrm{X} \) is
A. cytosine
B. uraci
c. adenine
D. guanine


A sounding body of negligible dimension emitting a frequency of 150 \( \mathrm{Hz} \) is dropped from a height. During its fall under gravity it passes near a balloon moving up with a constant velocity of \( 2 \mathrm{m} / \mathrm{s} \) one second after it stared to fall. The difference in the
frequency observed by the man in balloon just before and just after crossing the body will be :
(Given that - velocity of sound \( = \)
\( \mathbf{3 0 0 m / s ; g}=\mathbf{1 0 m / s ^ { 2 }} \)
A . 12
B. 6
\( c \cdot 8 \)
D. 4


The line through (1,5) parallel to \( x \) -axis
is
A. \( x=1 \)
B. \( y=5 \)
c. \( y=1 \)
D. x = 5


Which of the following metals directly
combine with hydrogen gas to give a hydride?
A . Au
B. Ni
\( c \cdot c a \)
D. cu


\( H_{2} S \) reacts with lead acetate to form a
black compound which reacts with
\( H_{2} O_{2} \) to form another compound. The colour of this another compound is:
\( A \cdot \) pink
B. black
c. yellow
D. white


For decolourisation of 1 mole of
\( K M n O_{4}, \) the moles of \( H_{2} O_{2} \) required
is:
A \( \cdot 1 / 2 \)
B. 3/2
\( c \cdot 5 / 2 \)
D. \( 7 / 2 \)


Which of the following is not the case with image formed by a plane mirror:
A. It is erect
B. It is virtual
c. It is diminished
D. It is at the same distance as the object


The mass of a bucket containing water is \( M_{0} . \) The bucket is pulled steadily up from a well of depth d. Due to a hole in the bucket the water is pouring out at a uniform rate and as a result the mass of
the bucket with water at the top of the
well reduces to M. Then the amount of
work done in pulling up the bucket is?
A \( \cdot\left(M_{0}-M\right) g d \)
в. \( \frac{1}{2}\left(M_{0}-M\right) g d \)
c. \( \left(M_{0}+M\right) g d \)
D. \( \frac{1}{2}\left(M_{0}+M\right) g d \)


Actual distance of object from plane
surface
A . \( 40 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( c \cdot 20 c m \)
D. \( 20 / 3 c m \)


Two boys enter a running escalator on the ground floor in a shopping mall and they do some fun on it. The first boy
repeatedly follows \( p_{1}=1 \) step up and
then \( q_{1}=2 \) steps down whereas the
second boy repeatedly follows \( p_{2}=2 \)
steps up and then \( q_{2}=1 \) step down.
Both of them move relative to escalator
with speed \( v_{r}=50 c m s^{-1} . \) If the first
boy takes \( t_{1}=250 s \) and the second boy
\( \operatorname{takes} t_{2}=50 s \) to reach the first floor
how fast is the escalator running?


A cell constructed by coupling a standard copper electrode and a standard magnesium electrode has emf
of 2.7 volts. If the standard reduction
potential of the copper electrode is +0.34 volt, that of magnesium
electrode is:
A . +3.04 volts
B. -3.04 volts
c. +2.36 volts
D. -2.36 volts


Let \( \{x\} \) denote the fractional part of \( x \) Then \( \lim _{x \rightarrow 0} \frac{\{x\}}{\tan \{x\}} \) is equal to
A . -1
B. 0
\( c . \)
D. Does not exist


f \( \boldsymbol{y}=\log (\log \sin \boldsymbol{x}), \) then evaluate \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


The table below shows the members in
"Stree-Sakti Kudambasree" Sorted
according to their ages.
Number of members Age group in the
20-30 \( 30-40 \) \( 40-50 \quad 10 \) \( 50-60 \) \( 50-60 \)
\( 60-70 \)
\( 70-80 \) 35 Total
a. If the members are arranged in
increasing order of gas, the member at
what position is taken as media?
b. What is assumed to be age of the
member at the 13 th position?
c. Find the median of the ages.


\( f(x)=x^{2} \) in \( 2 \leq x \leq 3 \) Is Rolle's
theorem applicable?


Which one of the following is a wasteful
process?
A. Photorespiration
B. Respiration
c. Photosynthesis
D. ETS


Gravity is defined as:
A. The push of the earth
B. The force of the earth
C. The capacity of the earth
D. The pull of the earth


If \( x \) and \( Y \) are the matrices of order \( 2 x \)
2 each and \( 2 X-3 Y=\left|\begin{array}{cc}-7 & 0 \\ 7 & -13\end{array}\right| \) and
\( \mathbf{3} \boldsymbol{X}+\mathbf{2} \boldsymbol{Y}=\left|\begin{array}{cc}\mathbf{9} & \mathbf{1 3} \\ \mathbf{4} & \mathbf{1 3}\end{array}\right|, \) then what is \( \boldsymbol{Y} \)
equal to?
A. \( \left|\begin{array}{cc}1 & 3 \\ -2 & 1\end{array}\right| \)
B. \( \left|\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right| \)
\begin{tabular}{l|ll|l}
& 3 & 2 \\
-1 & 5
\end{tabular}
D. \( \left|\begin{array}{cc}3 & 2 \\ 1 & -5\end{array}\right| \)


A long rod \( A B C \) of mass \( m \) and length \( L \)
has two particles of masses \( m \) and \( 2 m \) attached to it as shown in the figure. The system is initially in the horizontal position. The work to be done to keep it vertical with \( A \) at the bottom is \( (g= \)
acceleration due to gravity)
\( \mathbf{A} \cdot 2 m g L \)
в. \( \frac{3 m g L}{2} \)
c. \( \frac{5 m g L}{2} \)
D. \( 3 m g L \)


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


Figure shows a wheatstone bridge circuit.
Which of the following correctly shows
the currents \( I_{1}, I_{2} \) and \( I_{3} \) in the correct
decreasing order of magnitude?
\( \mathbf{A} \cdot I_{1}, I_{2}, I_{3} \)
B \( \cdot I_{2}, I_{3}, I_{1} \)
\( \mathbf{c} \cdot I_{2}, I_{1}, I_{3} \)
D. \( I_{3}, I_{2}, I_{1} \)


A car of mass \( M \) is moving on a
horizontal circular path of radius \( r . A t \)
an instant, its speed is \( \boldsymbol{v} \) and is
increasing at the rate \( a \). Then
This question has multiple correct options
A. The acceleration of the car is towards the centre of the path
B. The magnitude of the frictional force on the car is greater than \( \frac{m v^{2}}{r} \)
C. The friction coefficient between the ground and the car is not less than a/g
D. The friction coefficient between the ground and the car is \( \mu=\tan ^{-1} \frac{v^{2}}{r g} \)


Integrate \( \int e^{x}\left(\frac{x^{2}+3 x+3}{(x+2)^{2}}\right) d x \)


Statement 1: Water is a good solvent for
ionic and/or polar covalent substance. Statement 2: Water shows hydrogen
bonding between oxygen atoms.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


\( A \) vertical tower stands on a declivity
which isinclined at \( 15^{0} \) to the horizon.
From the foot of the tower a man
ascends the declivity for80 feet and then finds that the tower subtends an
angle of \( 30^{0} . \) The height of the tower is
A \( \cdot 20(\sqrt{6}-\sqrt{2}) f t \)
B . \( 40(\sqrt{6}-\sqrt{2}) f t \)
c. \( 40(\sqrt{6}+\sqrt{2}) f t \)
D. \( 40 \mathrm{ft} \)


Use the following diagram to complete
the statement about the human
nephron-
A. The composition of the filtrate would be must like plasma in the tubule next to the
B. The urine would be most concentrated in the collecting duct next to letter
C. Most of the glomerular filtrate is reabsorbed into pentubular capillary next to the
D. Conducting of urine to pelvis of the kidney from the structure next to the letter
E. Most water is reabsorbed by the structure next to the letter


A hydrocarbon contains carbon and hydrogen in the molar ratio of \( 1: 1.5 . \) The correct molecular formula of the
compound is
A \( \cdot C_{2} H O_{3} \)
в. \( C_{4} H_{6} \)
c. \( C H_{3} \)
D. impossible to predict from the given data


Define Tyndall effect. Differentiate between electrophoresis and electroosmosis.


The primary valence of the metal ion is satisfied by :
A. neutral molecules
B. positive ions
c. negative ions
D. all


From a \( 200 m \) high tower, one ball is
thrown upwards with speed of \( 10 m / s \) and another is thrown vertically downwards at the same speed simultaneously. The time difference of their reaching the ground will be
nearest to
A . \( 12 s \)
B. \( 6 s \)
c. \( 2 s \)
D. \( 1 s \)


Nylon is an example of:
A. polyester
B. polysaccharide
c. polyamide
D. polythene


All humans on earth today may differ widely in their facial features, colour,
height, etc. Yet, they belong to a single species Homo sapiens. Give one reason why they are not considered belonging
to different species.


In the adjoining figure, the arms of two
angels are parallel, if \( \angle A B C=70^{\circ}, \) find
\( (i) \angle D G C(i i) \angle D E F \)


An aeroplane is in a level flight at \( 144 k m / h r \) at an altitude of \( 1000 m \)
How far from a given target a bomb be released from it to hit the target ?(take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \mathbf{)} \)
\( \mathbf{A} \cdot 566 m \)
B. \( 671.43 m \)
c. \( 471.34 m \)
D. \( 371.34 m \)


Soap and detergents are the source of organic pollutants like
A. Glycerol
B. Polyphosphates
c. Sulphonated hydrocarbons
D. All of these


The potential energy of a particle with displacement \( x \) is \( U(x) . \) The motion is simple harmonic. If k is a positive
constant then
A \( \cdot U=k x \)
B. \( U=k \)
c. \( U=-k x^{2} / 2 \)
\( \mathbf{D} \cdot U=k x^{2} \)


Solve linear equation:
\( \frac{x-5}{3}=\frac{x-3}{5} \)


The maximum value of \( n<101 \) such
that \( 1+\sum_{k=1}^{n} i^{k}=0 \) is
A . 96
B. 97
c. 99
D. 100


Find area curved by three circles
\( \mathbf{A} \cdot(5 \pi-3 \sqrt{3}) \) units \( ^{2} \)
\( \mathbf{B} \cdot(5 \pi+4 \sqrt{3}) \) units \( ^{2} \)
\( \mathbf{c} \cdot(5 \pi+3 \sqrt{3}) \) units \( ^{2} \)
\( \mathbf{D} \cdot(5 \pi+3 \sqrt{2}) \) units \( ^{2} \)


Find the cube of 30


Antihistamines are neurologically active drugs and affect the message transfer mechanism.

If this is true enter 1 , if false enter 0 .


The equilibrium constant for the given
reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I} \) is correctly
given by expression.
\( ^{\mathbf{A}} \cdot_{K_{c}}=\frac{\left[H_{2}\right]\left[I_{2}\right]}{[H I]} \)
в. \( K_{c}=\frac{\left[H_{2}\right]\left[I_{2}\right]}{[2 H I]} \)
\( ^{\mathrm{c}} \cdot_{K_{c}}=\frac{\left[H_{2}\right]\left[I_{2}\right]}{[H I]^{2}} \)
D. \( K_{c}=\frac{[H I]^{2}}{\left[H_{2}\right]\left[I_{2}\right]} \)


n the figure, \( P Q=Q R=R S=S P \)
Then triangles are congruent by the postulate
A. sss
B. sas
\( c \cdot \) ASA
D. All of these


Explain the cleansing action of soaps.


The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}3 x-1, & \text { if } x<1 \\ x^{2}, & \text { if } x>2\end{array} \) continuous on \right.
A \( \cdot(-\infty, 1) \)
B. \( (2, \infty) \)
C \( .(-\infty, 1) \cup(2, \infty) \)
D. (1,2)


A large cylindrical vessel contains water to a height of \( 10 m \). It is found that
the thrust acting on the curved surface is equal to that at the bottom. if
atmospheric pressure can support a water column of \( 10 m, \) the radius of the
vessel is :
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
\( c .5 m \)
D. 25


The electronegativity of the elments \( \mathrm{C}, \mathrm{N}, \mathrm{Si} \) and \( \mathrm{P} \) increases in the order of \( \mathrm{Si} \)
\( P, C, N \)
If true enter 1 , else enter 0 .
A


Which quadrant \( 180<\theta<270 \)
degrees lies?
A . quadrant I
B. quadrant III
c. quadrant!
D. quadrant IV


Let \( x \) be a number which exceeds its
square by the greatest quantity. Then \( x \)
is equal to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{4} \)
D. none of these


If the points \( (h, 3,-4),(0,-7,10) \) and \( (1, k, 3) \) are collinear, then \( h+k \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c. -4
D. 14


Evaluate each of the following using identities:
¡) \( (399)^{2} \)
ii) \( (0.98)^{2} \)
iii) \( 991 \times 1009 \)
A . i ) 159876 ì 0.9
iii) 876590
в. ¡ ¡) 135879
ii) 0.87
iii) 896750
\( c \cdot \) i) 15920
ii) 0.9604
iii) 999919
D. i) 138760
ii) 0.9
iii) 999999


How would you explain the coincidence of the experimental facts with the results obtained by a ray diagram in terms of behavior of images formed by lenses?


If \( 10 \mathrm{ml} \) of \( \mathrm{H}_{2} \mathrm{O}_{2} \) solution requires \( 25 \mathrm{m} \) of \( \frac{\mathbf{N}}{\mathbf{2 0}} \mathbf{K M n O}_{4} \) for complete oxidation in acidic medium, then the mass (in g)
of available \( O_{2} \) per litre present in the solution is:
A . 1
B. 2
\( c .3 \)
D. 4


The average force necessary to stop a hammer with 25 Ns momentum in 0.05
sexpressed in \( \mathrm{N} \) is
A . 25
B. 50
\( c \cdot 125 \)
D. 500


Kreb's cycle produces
A. \( 2 \mathrm{CO}_{2} \)
в. \( 3 \mathrm{CO}_{2} \)
\( \mathrm{c} \cdot 4 \mathrm{cO}_{2} \)
D. \( 6 \mathrm{CO}_{2} \)


Evaluate \( \int_{0}^{1} \frac{1}{\sqrt{1+x}-\sqrt{x}} d x \)


Find the projection of the vector \( \hat{\mathbf{i}}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) on the vector \( \mathbf{7} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{8} \hat{\boldsymbol{k}} \)


The molecular formula of heavy water
is:
A \( \cdot D_{3} O \)
в. \( D_{2} \),
c. \( D O \)
D. \( D O_{2} \)


A particle is oscillating simple harmonically with angular frequency \( \omega \)
and amplitude \( A . \) It is at a point \( (A) \) at certain instant (shown in figure). At this instant it is moving towards mean positive (B). It takes time \( t \) to reach
position (B). If time period of
oscillations is \( T, \) the average speed
between \( A \) and \( B \) is :
A \( \cdot \frac{A \sin \omega t}{t} \)
B. \( \frac{A \cos \omega t}{t} \)
c. \( \frac{A \sin \omega t}{T} \)
D. \( \frac{A \cos \omega t}{T} \)


Find the area bounded by the curve \( y= \) \( \cos , x- \) axis and the ordinates \( x=0 \)
and \( x=2 \pi \)


\( \bigoplus{-}^{\mathrm{cH}=\mathrm{cH}_{2}} \frac{(\mathrm{i}) \mathrm{C}_{2}}{(\mathrm{i}) 2 \mathrm{NaNH}_{2}} \)
\( \left\langle\frac{c}{\mid}_{\mathbf{H}}=\mathrm{cHc}\right. \)
\( \left\langle\frac{c}{\mid}_{\mathbf{H}}=\mathbf{c H N H}_{2}\right. \)
\( \left\langle\frac{c}{\left.\right|_{\mathrm{Cl}}=\mathrm{CH}_{2}}\right. \)
\( \langle c \equiv \mathrm{c} \)


The radius of water cone at \( t=1 \) is
\( \mathbf{A} \cdot R[1-k / H] \)
B . \( R[1-H / k] \)
\( \mathbf{c} \cdot R[1+H / k] \)
D \cdot \( R[1=k / H] \)


The differential coefficient of log (tan
\( x \) )is
A \( .2 \sec 2 x \)
B. \( 2 \cos e c 2 x \)
\( \mathbf{c} \cdot 2 \sec ^{2} x \)
D. \( 2 \cos e c^{2} 2 x \)


Switch is always connected to the
wire.
A . live
B. neutral
c. ground
D. live and ground


The phase of moon between new moon and full moon are referred to as:
A. waxing of the moon
B. waning of the moon
c. crest of the moon
D. synodic month of the moon


What is the name and symbol of the element with atomic number \( 112 ? \)
A. Ununbium, Uub
B. Unnilbium, Unb
c. Ununnillum, uun
D. Ununtrium, Uut


One of the diagonals of a rhombus is equal to a side of the rhombus. The
angles of the rhombus are
\( \mathbf{A} \cdot 60^{\circ} a n d 80^{\circ} \)
B \( \cdot 60^{\circ} \) and \( 120^{\circ} \)
c. \( 120^{\circ} \) and \( 240^{\circ} \)
D. \( 100^{\circ} \) and \( 120^{\circ} \)


Find the sum of series \( 1+(2)(3)+ \)
\( (4)+(5)(6)+7+\ldots . \) upto 50 term


Inside a railway car a plumb bob (a heavy mass suspended by a thread) is suspended from the roof and a helium filled balloon is tied by a string to the
floor of the car. When the railway car accelerates to the right, then
A. Both the plumb bob and balloon move to the left
B. Both the plumb bob and balloon move to the right
c. Plumb bob moves to the left and the balloon moves to the right
D. Plumb bob moves to the right and the balloon moves to the left


Assertion
During an ecological succession, the
number of species increases, the
community biomass increases and the community's ratio of respiration to photosynthesis also increases.
Reason
At climax community of an ecological
succession, the rate of photosynthesis of a community is almost equal to the rate of respiration.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A cell contains two hydrogen electrodes. The negative electrode is in
contact with a solution of \( 10^{-6} \mathrm{M} \)
hydrogen ions. The \( E M F \) of the cell is
\( 0.118 V \) at \( 25^{\circ} C . \) The concentration of
hydrogen ions at the positive electrode is:
A \( \cdot 10^{-4} M \)
В. \( 10^{-3} M \)
\( \mathrm{c} \cdot 10^{-1} M \)
D. None of these


Describe the various modes of fixation
of anther over filament.


Assertion
Light nuclei are most stable if \( \boldsymbol{N}=\boldsymbol{Z} \)
while heavy nuclei are more stable if \( N>Z .(N \rightarrow \) number of neutrons
\( Z \rightarrow \) number of protons
Reason
As the number of protons increases in a nucleus, the Coulomb's repulsive force increases, which tends to break the
nucleus apart. So, to keep the nucleus stable, more number of neutrons are needed which are neutral in nature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which is correct statement?
As the \( s \) -character of a hybrid orbital decreases
(1) The bond angle decreases
(II) The bond strength increases
(III) The bond length increases
(IV) Size of orbitals increases
\( A \cdot(1),(111) \) and \( (1 \vee) \)
B. (II), (III) and (IV)
c. (l) and (II)
D. All are correct


Prokaryotic cell is one, which does not
have
A. Proper nucleus
B. Endoplasmic reticulum and mitochondria
C. Proper nucleus and most of cell organelles
D. Cell wall


Reactions in zeolite catalyst depend on:
A. pores
B. apertures
c. size of cavity
D. all of the above


The mass of an atom of carbon is:
A. \( 1 g \)
В. \( 1.99 \times 10^{-23} g \)
c. \( 1 / 12 g \)
D. \( 1.99 \times 10^{23} g \)


Which of the following statement is not \( c \)
Orrect?
\( \mathbf{A} \cdot L a(O H)_{3}, \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series, ionic radius of \( L n^{3}+ \) ions
decreases
C. \( L a \) is actually an element of transition series rather than lanthanide series
D. Atomic radii of \( Z r \) and \( H f \) are same because of lanthanide contraction


What is an artificial kidney haemodialysis? Write the use of
haemodialysis.


Which of the following statements below should be followed while using the symbol for a unit of a physical quantity? This question has multiple correct options
A. The symbol named after a scientist should begin with a capital letter
B. They can take plural forms.
c. They can be written in full
D. They should be written only in the agreed symbols while using symbols.


Identify the part "C" from the shown
figure of human eye :
A. Retina
B. Cornea
c. Pupil
D. Iris


Evaluate: \( \int \frac{x+3}{(x-1)\left(x^{2}+1\right)} d x \)


State the following statement is true or
false
The probability of an event can be greater than one also.
A. True
B. False


Without finding the cubes, factorise the following:
\( (x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3} \)


receptors are responsible for the detection of taste.
A. Gustatory receptors
B. Olfactory receptors
c. Auditory receptors
D. Both A and B


The sum of any three distinct natural
numbers arranged in ascending order is 200 such that the second number is a
perfect cube. How many possible values are there for this number?
\( A \cdot 4 \)
B. 3
c. 2
\( D \)


A disc is freely rotating with an angular speed co on a smooth horizontal plane. It is hooked at a rigid peg \( P \) and rotates about P without bouncing. Its angular
speed after the impact will be equal to:
\( A \)
\( B \cdot \frac{\omega}{3} \)
\( c \cdot \frac{w}{2} \)
D. None of these


\( \lim _{x \rightarrow \infty}(\sqrt{x^{2}+8 x+3}-\sqrt{x^{2}+4 x+3}) \)
equals
A .
B . \( \infty \)
\( c \cdot 2 \)
D.


A metallic sphere of mass M falls through glycerine with a terminal velocity v. If we drop a ball of mass \( 8 \mathrm{M} \) of same metal into a column of
glycerine, the terminal velocity of the ball will be
A \( .2 v \)
B. \( 4 v \)
\( c \cdot 8 v \)
D. \( 16 v \)


The quantity of heat required to heat 1 mole of a monoatomic gas through one degree \( K \) at constant pressure is:
A . 3.5
B. 2.5 R
\( c \cdot 1.5 R \)
D. none of these


On what principle is Kirchhoff's current
law based?


A m..... of light consists of a bundle of light
rays.


According to Cartesian sign convention, in ray optics:
A. All distances in the direction of incident ray are taken positive
B. All distances are taken negative
C. All distances in the direction of incident ray are taken negative
D. All distances are taken positive


The students in a class are seated
according to their marks in the previous examination.0nce, it so happens that four of the students got equal marks and therefore the same rank To decide
their seating arrangement, the teacher wants to write down all
possible arrangements one in each of
separate bits of paper in order to choose one of these by lots. How many bits of paper are required?


Identify the reagents underlined in the following equations as nucleophiles or electrophiles:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{O H}^{-} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)


The mean distance of Jupiter from the
sun is nearly 5.2 times the corresponding distance between earth and sun. Using Kepler's Law, find the period of revolution of Jupiter in its
orbit.


Which of the following molecular formula does not show chain
isomerism?
A. \( C_{4} H_{10} \)
в. \( C_{4} H_{8} \)
c. \( C_{4} H_{6} \)
D. \( C_{4} H_{8} O \)


An aqueous solution is 1 molal in \( K I \)
Which change will cause the vapour pressure of the solution to increase?
A. Addition of \( N a C l \)
B. Addition of \( N a_{2} S O_{4} \)
c. Addition of 1 molal \( K I \)
D. Addition of water


A solid hemisphere is mounted on a solid cylinder, both having equal radii. If the whole solid is to have a fixed
surface area and the maximum
possible volume, then the ratio of the height of the cylinder to the common radius is
A . 1: 1
B. 1: 2
c. 2: 1
D. \( \sqrt{2}: 1 \)


f a positively charged pendulum is oscillating in a uniform electric field as shown in Figure. Its
time period of SHM as compared to that when it was uncharged.
A. will increase
B. Will decrease
c. will not change
D. Will first increase then decrease


Ethyl alcohol to trichloroacetic acid


In the adjoining figure line \( \mathrm{p} \| \) line \( \mathrm{q} \) Line \( t \) and line \( s \) are transversals. Find
measure of \( \angle \mathbf{x} \) and \( \angle \mathbf{y} \) using the
measures of angles given in the figure


A buffer solution is prepared by mixing \( 10 \mathrm{ml} \) of \( 1.0 \mathrm{M} \) acetic acid \( \& 20 \mathrm{ml} \) of 0.5
M sodium acetate and then diluted to
\( 100 \mathrm{ml} \) with distilled water. If the \( p K_{a} \) of
\( C H_{3} C O O H \) is \( 4.76 . \) What is the pH of the buffer solution prepared? (1998)
A . 3.84
B. 4.76
\( c \cdot 4.34 \)
D. 5.21


Steam at \( 100^{0} C \) causes ......... severe
burns than water at \( 100^{0} C \)
A . less
B. more
c. same
D. cant say


A force \( F \) is applied horizontally on a cylinder in the line of centre as shown in
the figure. The cylinder is on a rough surface of coefficient of friction \( \mu . \) The
direction of the friction force acting on the cylinder will be
A. In the direction of \( F \)
B. zero
c. In the opposite direction of \( F \)
D. Cannot be ascertained


Atomic wt. of \( C l=35.5 \) and of \( I=127 \)
According to Doeberiner triad rule
atomic wt. of \( \boldsymbol{B r} \) will be:
A . 80.0
B. 162.5
c. 81.25
D. 91.5


An impulse is supplied to a moving
object with the force at an angle of \( 120^{\circ} \) with the velocity vector. The angle
between the impulse vector and the change in momentum vector is
A \( \cdot 120^{\circ} \)
в. \( 0^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 240^{\circ} \)


In order that a ray suffers minimum
deviation, it should be incident at an
angle of:
A \( \cdot 45^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 30^{\circ} \)
D. none of the above


If \( \sin A=\frac{3}{5}, \) and \( \cos A=\frac{4}{m}, \) then \( m \) is


In the light of carrier concept, the transport of ion across the membrane
against concentration gradient is
A. Passive process
B. Non-osmotic process
c. osmotic process
D. Active process


Factorize \( 25 m^{2}-70 m n+49 n^{2} \)


Behind a thin converging lens having both the surfaces of the same radius
\( \mathbf{1} \boldsymbol{c m}, \) a plane mirror has been placed. The image of an object at a distance of
\( 40 \mathrm{cm} \) from the lens is formed at the
same position. What is the refractive
index of the lens?
A . 1.5
B. \( 5 / 3 \)
\( c \cdot 9 / 8 \)
D. None of these


Fill in the blank
All squares are (similar,
congruent)
A. similar
B. congruent
c. Undefined
D. None of these


The combustion of methane is written
as
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} O(l) \)
The difference between enthalpy change and energy change is equal to:
\( \mathbf{A} \cdot-2 R T \)
B.
c. \( R T \)
D. \( \frac{R T}{2} \)


Which of the following has a bond formed from the transfer of electrons?
A \( \cdot H_{2} \)
в. \( C O_{2} \)
c. \( H_{2} O \)
D. \( N a C l \)
E \( \cdot C H_{2} C H_{2} \)


"S
indicated is involved in resonance?
This question has multiple correct options
A.
B.
\( c \)
D.
E . \( C H_{2}=C H-C H_{2}^{\Theta} \)
F. \( C H_{2}=C H-C H=\ddot{N} H \)


Root cap regenerated/dead torn cells of root cap are replaced by the activity of
A. Plerome
B. Dermatogen
c. Calyptrogen
D. Periblem


A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the
following statement is correct?
A. Diffraction pattern is not observed on the screen in the case of electrons
B. The angular width of the central maximum of the diffraction pattern will increase
c. The angular width of the central maximum will decreases
D. The angular width of the central maximum will remain unaffected


Name the following:
(a)A chordate animal having flame cells
as excretory structures.
(b) Cortical portions projecting between the medullary pyramids in human kidney.
(c) A loop of capillary running parallel to
the Henles loop.


\( \sum_{i}^{N} \)


A coil of 100 turns and 5 square
centimeter is placed in a magnetic field
\( \mathrm{B}=0.2 \mathrm{T} . \) The normal to the plane of the coil makes an angle of 60 with the direction of the magnetic field. The magnetic flux linked with the coil is :
A \( \cdot 5 \times 10^{-3} \mathrm{wb} \)
B. \( 5 \times 10^{-5} \mathrm{wb} \)
\( c \cdot 10^{-2} w b \)
D. \( 10^{-4} \mathrm{wb} \)


A polarizer and an analyzer are oriented so that the maximum amount of lights
is transmitted. Fraction of its
maximum value is the intensity of the
transmitted light reduced when the
analyzer is rotated through (intensity of
incident light \( =\boldsymbol{I}_{\boldsymbol{o}} \boldsymbol{)} \)
a) \( 30^{\circ} \) b) \( 45^{\circ} \)
c) \( 60^{\circ} \)
A \( .0 .375 I_{0}, 0.25 I_{0}, 0.125 I_{0} \)
B. \( 0.25 I_{0}, 0.375 I_{0}, 0.125 I_{0} \)
C \( \cdot 0.125 I_{0}, 0.25 I_{0}, 0.0375 I_{0} \)
D. \( 0.125 I_{0}, 0.375 I_{0}, 0.25 I_{0} \)


Growth rings (annual rings) are formed by activity of
A. Cambium
B. Xylem
c. Phloem
D. Both xylem and phloem


If all the fractions \( \frac{3}{5}, \frac{1}{8}, \frac{8}{11}, \frac{4}{9}, \frac{2}{7}, \frac{5}{7} \) and
\( \frac{5}{4} \) are arranged in descending order of
\( \overline{\mathbf{1 2}} \)
their values which one will be the third?
A \( \cdot \frac{1}{8} \)
B. \( \frac{3}{5} \)
c. \( \frac{5}{12} \)
D. \( \frac{8}{11} \)


If a lens diverges a parallel beam of light, the lens is -
A. convex
B. Concave
c. cylindrical
D. Parabolic


According to Maxwell electromagnetic theory, through which path an electron should fall into the nucleus in
Rutherford's atomic model:
A. Circular
B. Spiral
c. Zig-zag
D. Straight line


Identify total number of compounds
Which are unstable at room
temperature?
\( A \)
B.
\( c \)
D.


Prove that \( n^{2}-n \) is divisible by 2 for
every positive integer.


Which of the following conclusion can be drawn from the result \( \oint \bar{B} \cdot d \bar{A}=0 \)
A. Magnetic field is zero everywhere
B. Magnetic monopole cannot exist
c. Magnetic lines of force do not intersect each other
D. A current produces magnetic field


The salinity of sea water is
A . \( 2.5 \% \)
в. 3.5\%
c. \( 4.5 \% \)
D. 5.5\%


Solve the following matrix equation for
\( x \)
\( [\boldsymbol{x}-\mathbf{5}-\mathbf{1}]\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{2} \\ \mathbf{0} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{0} & \mathbf{3}\end{array}\right]\left[\begin{array}{l}\boldsymbol{x} \\ \mathbf{4} \\ \mathbf{1}\end{array}\right]=\mathbf{0} \)


One can not see through fog because:
A. fog absorbed light
B. light is scattered by the droplets in fog
C. light surfers total reflection by the droplets in the fog
D. the refractive index of fog is in infinity


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H O H}-\boldsymbol{C H}_{3} \)
Write the IUPAC name of the compound.


The molarity \( (M) \) of \( K M n O_{4} \) solution in basic medium is :
\( \mathbf{A} \cdot 0.8 M \)
в. \( 0.08 M \)
c. \( 0.26 M \)
D. \( 0.026 M \)


During complete metabolism of glucose, the number of ATP formed is
\( A \cdot 2 \)
B. 12
c. 36
\( D \cdot 44 \)


System in which there is no exchange of matter, work or energy from surroundings is:
A . closed
B. adiabatic
c. isolated
D. isothermal


The metabolism of an antibiotic, \( ^{\prime} \boldsymbol{A}^{\prime} \) is
first-order rate process. The rate constant 'K' for this process depends on temperature and body weight but for a
70 kg man at \( 37^{\circ} \mathrm{C} \) its value is \( \boldsymbol{K}= \) \( 3.0 \times 10^{-5} \mathrm{sec}^{-1} . \) How long after taking
the first pill containing \( 400 \mathrm{mg} \) of antibiotic must this man take the
second pill to keep the concentration at
200 mg per 100 kg body weight? (Assume instantaneous uniform distribution of the antibiotic
throughout the body?
A \( \cdot 0.7 \times 10^{4} \sec \)
B. \( 1.5 \times 10^{4} \) sec
c. \( 1.4 \times 10^{4} \) sec
D. \( 3.6 \times 10^{4} \) sec


Parrots are
A. Herbivores
B. Frugivores
c. sanguivores
D. Detritivores


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


Using the identity \( (\boldsymbol{a}-\boldsymbol{b})^{2}=\boldsymbol{a}^{2}- \)
\( 2 a b+b^{2} \) compute \( (x-6)^{2} \)


Is there any number whose perfect cube
ends with \( 8 ? \)
(Yes or No)


Differentiate \( \cos ^{-1}\left(4 x^{2}-3 x\right) ; x \epsilon\left(\frac{1}{2}, 1\right) \)


Why do we see dew drops on leaves in
the early morning?


Write te structural formula and names
of all four possible aldol condensation products from ethanal and propanal


\( f\left|\begin{array}{ccc}\mathbf{6} i & -\mathbf{3} i & \mathbf{1} \\ \mathbf{4} & \mathbf{3} i & -\mathbf{1} \\ \mathbf{2 0} & \mathbf{3} & \boldsymbol{i}\end{array}\right|=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)


Which of the following compounds is obtained on passing ethanol vapours on
heated \( \boldsymbol{A l}_{2} \boldsymbol{O}_{3} \) ?
A. Ethylether
B. Acetone
c. Ethane
D. Ethanol


Components of environment are
A. Biotic
B. Abiotic
C. Resources and regulatory factor
D. All of the above


Consider the velocity vs. time graph as
shown in above figure. Find out the time interval during which the speed of the object increasing?
\( A \cdot A B \)
B. BC
\( c \cdot c D \)
D. DE
\( E . E F \)


The mucosal lining of the oesophagus of mammals is made up of
A. Simple columnar epithelium
B. Squamous epithelium
c. Stratified cuboldal epithelium
D. Stratified columnarepithelium


How does number of valence electrons
vary on moving from left to right In the first period of a periodic table?
A .
в.
\( c \cdot 2 \)
D.


\( \underset{x \rightarrow 1}{L t} \frac{(2 x-1)(\sqrt{x}-1)}{2 x^{2}+x-3} \)


Statement I: \( ^{40} \mathrm{Ca} \) is a neutral atom
Statement II: It has the same number of
protons and neutrons
Are both the above statements true?