Explain the process of secondary growth in the stelar region of a dicot stem


Five resistances are connected as
shown in figure. The effective resistance
between the points \( A \) and \( B \) is
A \( \cdot \frac{10}{3} \Omega \)
B. \( \frac{20}{3} \Omega \)
c. \( 15 \Omega \)
D. \( 6 \Omega \)


Which of the following pairs of solutions is isotonic?
A. \( 6 \% \) urea and \( 6 \% \) glucose \( (w / v) \)
B. \( 18 \% \) urea and \( 18 \% \) glucose \( (w / v) \)
\( c .6 \% \) urea and \( 18 \% \) fructose \( (w / v) \)
D. \( 34.2 \% \) sucrose and \( 60 \% \) glucose \( (w / v) \)


Consider the situation shown in the
figure. The capacitor A has a charge \( q \) on
it, whereas \( \mathrm{B} \) is uncharged. The charge
appearing on the capacitor \( \mathrm{B} \), after a long time of closing the switch is:
A. zero
B. \( \frac{q}{2} \)
\( c \cdot q \)
D. \( 2 q \)


Two dice are thrown. What is the
probability that the sum of the two dice
is greater than \( 3 ? \)
A. \( 1 / 4 \)
B . \( 3 / 4 \)
c. \( 5 / 6 \)
D. \( 11 / 12 \)
\( E \)


Amongst the following, identify the species with an atom in +6 oxidation
state.
\( \mathbf{A} \cdot\left[M n O_{4}\right]^{-} \)
B . \( \left[\operatorname{Cr}(C N)_{6}\right]^{3-} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)


Glyptal is the polymer of \( ? \)
A. Ethylene glycol
B. Ethylene glycol and phthalic acid
C. Ethylene glycol and adipic acid
D. Caprolactum


\( \int_{-2}^{0}\left(x^{3}+3 x^{2}+3 x+(x+1) \cos (x+\right. \)
1) \( d x \)


is basic necessity for all terrestrial forms of life.
A. water
в. oxygen
c. Iron
D. None of the above


(1)Name the material prepared by using wood pulp.
(2)Name the natural polymer.


Reactions take place in
presence of light.
A. Electrolytic reaction
B. Hydrolytic reaction
c. condensation reaction
D. Photochemical reaction


In insulator
A. valence band is partially filled with electrons
B. conduction band is partially filled with electrons
c. conduction band is filled with electrons and valence
band is empty
D. conduction band is empty and valence band is filled with electrons


Assertion
When two coils are wound on each
other, the mutual induction between
the coils is maximum.
Reason
Mutual induction does not depend on
the orientation of the coils.
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 in a p-njunction diode, a square input signal of \( 10 V \) is applied as shownThen
the output signal across \( R_{L} \) will be
\( A \)
в.
\( c \)
D.


\( \int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\tan x}} \) is equal to
A \( \cdot \frac{\pi}{12} \)
в. \( \frac{\pi}{2} \)
c.
D.


Balance the following equation by
oxidation number method.
\( Z n+H N O_{3} \rightarrow Z n\left(N O_{3}\right)_{2}+ \)
\( N H_{4} N O_{3}+H_{2} O \)


The following pie chat gives the marks second in an examination by a student in Hindi, English, Mathematics, Social
Science and Science. If the total marks
obtained by the student were 540
answer the following questions. All values are shown in degrees.
How many more marks were obtained
by the student in Mathematics than in
Hindi?


Reduction in vascular tissue, mechanical tissue and cuticle is
characteristic of
A. Xerophytes
B. Mesophytes
c. Epiphyttes
D. Hydrophytes


The work done in carrying a charge a circle of radius with a charge 'Q' at the
center is:
A. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q Q}{r} \)
в. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q Q}{\pi r} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q Q}{2 \pi r} \)
D. zero


Soil pollution is the outcome of
A. deforestation
B. pesticides and herbicides
c. industrial waste
D. all of above


What is centripetal acceleration? Drive an impression for centripetal acceleration.


The IUPAC name of isobutylamine is:
A. isopropyl methyl amine
B. isopropyl methanamine
c. 2 -methyl-1-propanamine
D. 2-methyl-3-propanamine


If two parallel chords of length \( 8 \mathrm{cm} \) and
\( 6 \mathrm{cm} \) in a circle of radius \( 5 \mathrm{cm} \) are on
the opposite sides of the center then the
distance between the parallel chords is
A . \( 5 \mathrm{cm} \)
в. 6 ст
\( c .7 \mathrm{cm} \)
D. None of these


Integrate \( \int\left(\sin ^{-1} x\right)^{2} d x \)


The waves are represented by the following equations
\( \boldsymbol{y}_{1}=\mathbf{5} \sin 2 \boldsymbol{\pi}(\mathbf{1 0} \boldsymbol{t}-\mathbf{0 . 1} \boldsymbol{x}) \)
\( \boldsymbol{y}_{2}=\mathbf{1 0} \sin 2 \pi(\mathbf{2 0} \boldsymbol{t}-\mathbf{0 . 2} \boldsymbol{x}) \)
Ratio of intensities \( \frac{\boldsymbol{I}_{2}}{\boldsymbol{I}_{1}} \) will be :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 4 \)
D. 16


Find the inverse of the following matrix by using elementary row transformation
\( \left[\begin{array}{cc}\mathbf{3} & \mathbf{1 0} \\ \mathbf{2} & \mathbf{7}\end{array}\right] \)


Two forces act on either side of rigid
body of negligible mass suspended by string as shown in the figure. If \( \mathrm{R} \) is the resultant force the tension of the string
\( T=----- \) gwt
\( A \cdot 26 \)
B. 41
c. 82
D. 16


An object is thrown horizontally from a
point ' \( \boldsymbol{A}^{\prime} \) from a tower and hits the
ground \( 3 s \) later at \( B \). The line from ' \( A \) ' to
\( B^{\prime} \) makes an angle of \( 30^{\circ} \) with the
horizontal. The intial velocity of the
object is :
(take \( \left.\mathfrak{g}=10 m / s^{2}\right) \)
A. \( 15 \sqrt{3} \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
c. \( 10 \sqrt{3} \mathrm{m} / \mathrm{s} \)
D. \( \frac{25}{\sqrt{3}} m / s \)


Assertion: In optical fibre, the diameter of the core is kept small.

Reason: This smaller diameter of the
core ensures that the fibre should have incident angle more than the critical angle required for total internal reflection.
A. Both assertion and reason are true but the reason is the correct explanation of assertion
B. Both assertion and reason are true but the reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Reason is true but assertion is false


Assertion
Half-filled and fully-filled degenerate orbitals are more stable.
Reason
Extra stability is due to the symmetrical distribution of electrons
and exchange energy.
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


When a light ray reflects from the boundary surface the following will change
A. frequency
B. velocity
c. intensity
D. phase


If Atom 1 has 19 protons and 22 neutrons and Atom 2 has 20 protons
and 22 neutrons, are these isotopes of the same element?
A. There is not enough information to determine this.
B. No, because they have different numbers of protons.
c. No, because they have the same number of neutrons.
D. Yes, because they have different numbers of protons
E. Yes, because they have the same number of neutrons


The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are \( v \) and respectively.The density of air is \( \mathrm{p} \) and surface area of wings is A.The dynamic lift on the wing is-


Which of the following has the highest boiling point ?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{4} C \)
в. \( \left(C H_{3}\right)_{2} C H C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} C H_{2} C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H_{3} \)


A solid sphere of radius \( R \) made of a
material of bulk modulus B surrounded
by a liquid in a cylindrical container.A massless piston of area A floats on the surface of the liquid. Find the fractional decreases in the radius of the sphere
\( \left(\frac{d R}{R}\right) \) when a mass \( M \) is placed on the
piston to compress the liquid:
A \( \cdot\left(\frac{3 M g}{A B}\right) \)
B \( \cdot\left(\frac{2 M g}{A B}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{M g}{3 A B}\right) \)
D. \( \left(\frac{M g}{2 A B}\right) \)


Arrange \( \boldsymbol{x}^{8}+\boldsymbol{x}+\boldsymbol{x}^{12}-\boldsymbol{3} \boldsymbol{x}^{7}+\boldsymbol{x}^{9}+1 \) in
descending powers of \( x \)


Which part of the cell stores nutrients?
A. Mitochondria
B. Vacuole
c. Ribosome
D. Oxysome


A car moving with constant acceleration covered the distance
between two points \( 60.0 m \) apart in
\( 6.00 s . \) Its speed as it passes the second point was \( 15.0 m / s . \) At what prior
distance from the first was the car at
rest?
A. \( 7.5 \mathrm{m} \)
B. \( 15 \mathrm{m} \)
\( c .60 m \)
D. \( 30 m \)


Define kinetic energy.


In cyathium inflorescence
A. single male flower is surrounded by female flowers.
B. male and female flowers are borne in different plants
C. there is only one male and one female flower
D. single female flower is surrounded by many peripheral male flowers.


Number of electrons in \( M \) shell of an
element with atomic number 28 is
A . 18
B. 16
\( c \cdot 8 \)
D. 2


Which of the following properties of soil decreases due to deforestation?
A. Nutrient content
B. Fertility
c. Texture
D. All of the above


Hydroboration of isobutylene followed by oxidative alkaline hydrolysis gives:
A. \( 1- \) Butanol
B. \( 2- \) Butanol
c. Isobutyl alcohol
D. Tertiary butyl alcohol


When the load on a wire is increased
from \( 3 k g w t \) to \( 5 k g w t \) the elongation increases from 0.61 \( m m \) to \( 1.02 m m \)
The required work done during the extension of the wire is:
A \( \cdot 16 \times 10^{-3} J \)
В. \( 8 \times 10^{-2} J \)
c. \( 20 \times 10^{-2} J \)
D. \( 11 \times 10^{-3} J \)


Find out the arrow or arrows which give
the direction of a force vector.
A. Arrow A only
B. Arrow B only
c. Arrow c only
D. Arrows A and D
E. Arrows B and E


What is peptization?


A particle is moving in a circular path of radius r. Its displacement after moving through half the circle would be:
A. zero
B.
\( c \cdot 2 r \)
D. \( \frac{2}{r} \)


Waste product produced during respiration in plant are
A. \( C O_{2} \)
B. Water
c. oxygen
D. Both A and B


Arsenic containing medicine used for
the treatment of syphilis, is :
A. erythromycin
B. ofloxacin
c. tetracycline
D. salvarsan


The integral part of \( (\sqrt{2}+1)^{2} \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


If \( \cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha- \)
\( \beta)=-\frac{3}{2}, \) then
This question has multiple correct options
A. \( \sum \cos \alpha=0 \)
B. \( \sum \sin \alpha=0 \)
c. \( \sum \cos \alpha \sin \alpha=0 \)
D. \( \sum(\cos \alpha+\sin \alpha)=0 \)


The metallic luster exhibited by sodium is explained by :
A. diffusion of sodium ions
B. oscillations of loose electrons
c. excitation of free protons
D. existence of body centered cubic lattice


What sum lent out at Cl will amount to
Rs. 968 in 2 years at \( 10 \% \) p.a. interest?
A . Rs. 800
B. Rs. 1000
c. Rs. 1200
D. None of these


A denser medium of refractive index 1.5
has a concave surface of radius of
curvature \( 12 \mathrm{cm} . \) An object is situated in the denser medium at a distance of 9
\( \mathrm{cm} \) from the pole. Locate the image due
to refraction in air
A. A real image at \( 8 \mathrm{cm} \)
B. A virtual image at \( 8 \mathrm{cm} \)
c. A real image at \( 4.8 \mathrm{cm} \)
D. A virtual image at \( 4.8 \mathrm{cm} \)


Two different adiabatic parts for the
same gas intersect two isothermals at
\( T_{1} \) and \( T_{2} \) as shown in P-V diagram
Then the ratio of \( \frac{V_{a}}{V_{b}} \) will be:
A \( \cdot \frac{V_{c}}{\longrightarrow} \)
\( \overline{V_{d}} \)
B. \( \underline{V}_{d} \)
\( V_{c} \)
\( c \cdot \gamma \frac{V_{d}}{V} \)
D. \( \frac{1}{\sim} \frac{V_{d}}{V} \)


A microelement is the one which is
A. more important than the macroelement
B. less important than the macroelement
C. present in very small quantities in the soil
D. needed in very small amounts but is as important as a macroelement


Assertion
Dielectric materials can be solids,
liquids, or gases.
Reason
Usage of dielectric depends on the application i.e.Industrial coatings such as parylene provide a dielectric barrier between the substrate and its
environment.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the total number of stereoisomer
for each compound:


A boy blowing a whistle, is running away from a wall towards an observer with a
speed of 1 ms \( ^{-1} \). The frequency of
whistle is \( 680 \mathrm{Hz} \). The number of beats
heard per second by the observer will be
\( \left(\operatorname{given} v=340 m s^{-1}\right) \)
A. zero
B. 2
\( c \cdot 4 \)
D. 8


Two different plants associated with the
discovery of two different phytohormones having common biosynthetic precursor exhibit one of the following character each.
I- Versatile anthers
II- Compound spadix
III- Pentalocular ovary
IV- Trifoliate compound leaves
The correct answer is:
A . Il and III
B. I and III
c. ॥ and IV
D. I and IV


Give reason:
Is Beilstein test a satisfactory test for detection of halogens?


If two angle of a triangle are \( \sin ^{-1}\left(\frac{1}{\sqrt{5}}\right) \) and \( \sin ^{-1}\left(\frac{1}{\sqrt{10}}\right), \) then third angle is
\( A \cdot \frac{\pi}{4} \)
B.
\( c \cdot \frac{3 \pi}{4} \)
D. \( \frac{2 \pi}{3} \)


Atrial natriuretic factor-
A. increases blood pressure
B. decreases blood pressure
C. increases absorption of \( N a^{+} \)
D. is a vasconstrictor


Manohar is the owner of a jewellery
shop. Which property of gold he uses the most in his business?
A. conductivity
B. Ductility
c. Malleability
D. Sonorosity


The articulation of atlas, the first
vertebrae facilitates
A. Rotatory motion
B. Sliding motion
c. sideways motion
D. One way motion


Which is the magnitude of force on a
current I carrying conductor of length \( l \) placed in a magnetic field B ?
A \( . B I l^{2} \)
в. Вl/
c. \( B l I \)
D. \( B I^{2} \)


\( \triangle P Q R \) is right angled at \( Q, Q X \perp \)
\( \boldsymbol{P R}, \boldsymbol{X} \boldsymbol{Y} \perp \boldsymbol{R} \boldsymbol{Q} \) and \( \boldsymbol{X} \boldsymbol{Z} \perp \boldsymbol{P Q} \) are
drawn. Prove that \( \boldsymbol{X} \boldsymbol{Z}^{2}=\boldsymbol{P} \boldsymbol{Z} \times \boldsymbol{Z} \boldsymbol{Q} \)


The phenomenon of Tyndall's effect is not observed in:
A. Emulsion
B. Colloidal solution
c. True solution
D. Gel


\( m_{2}=2 k g \) are connected by an ideal
spring, rest on a rough
horizontal surface. The spring is unstressed. The spring constant of
spring is \( \boldsymbol{K}=\mathbf{2} \boldsymbol{N} / \boldsymbol{m} . \) The coefficient
of friction between blocks and
horizontal surface is \( \mu=\frac{1}{2} . \) Now the
left block is imparted a velocity \( u \)
towards right as shown. The largest
value of \( u(\text { in } m / s) \) such that the block
of mass \( m_{2} \) never moves is (Take \( g= \)
\( \left.10 m / s^{2}\right) \)
A . 10
B. 20
\( c .5 \)
D.


The value of \( a \) for which the equation \( a^{2}+2 a+\csc ^{2} \pi(a+x)=0 \) has a
solution, is/are
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D.


Which of the following is a chemical property of hydrogen?
A. It is monoatomic.
B. It is less dense than air.
c. It is odorless.
D. It is colorless
E. It combusts in the presence of oxygen


Which gas is known to shield the earth
from harmful ultraviolet radiation?
A \( . \) CO
в. \( C O_{2} \)
c. \( C F C s \)
D. \( S O_{2} \)
E. \( O_{3} \)


Which of the following does not has fundamental unit?
A. Mass
B. Time
c. Force
D. length


Assertion
If the value of mode and mean are 60
and 66 respectively, then the value of median is 64
Reason
Median \( =\frac{1}{2}(\bmod e+2 \text { mean }) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the diagram, \( P Q R \), is an isosceles
triangle and \( Q R=5 \) units.
The coordinates of \( Q \) are:
A \( .(4,5) \)
B. (3,4)
\( c \cdot(2,4) \)
D. (1,4)


If \( A \) is an idempotent matrix satisfying, \( (I-0.4 A)^{-1}=I-\alpha A, \) where \( I \) is the
unit matrix of the same order as that of
\( A, \) then the value of \( |9 \alpha| \) is equal to


ff \( f(x)=1+x+x^{2}+\ldots \ldots+x^{1000}, \) then
\( \boldsymbol{f}^{\prime}(-1)=\ldots . . \)
A . -50
B . -500
c. -100
D. 500500


The paramagnetic moment \( \boldsymbol{O}_{2}^{-} \) is:
A. 1.732
B. 3
c. 1.5
D. 2.5


How many grams of methane need to react with 32 g of oxygen to make 22 g of \( C O_{2} \) and 18 g of water?
A. 32 g
B. 22 \( g \)
\( c \cdot 18 g \)
\( D \cdot 8 g \)


Assertion
\( N a C l \) is not a conductor of electricity
in solid state whereas it does conduct
electricity in aqueous solution as well as in molten state.
Reason
In solid \( N a C l, \) the ions have fixed positions in the lattice structure and there are no free ions but in aqueous
solution or molten state, the ions can move freely and thus conduct electricity.
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 number of terms in the expansion
\( (2 x+y)^{n}-(2 x-y)^{n} \) is \( 8, \) then the
value of \( n \text { is } \ldots \ldots . . . . \text { (where } n \text { is odd }) \)
A . 17
B. 19
c. 15
D. 13


Colloidal sols are more effective for
medical purposes because:
A. they have smaller surface area
B. they have larger surface area
c. their assimilation is difficult
D. they can be easily prepared


Write balanced equations for the following:
(i) \( N a C l \) is heated with sulphuric acid
in the presence of \( M n O_{2} \)
(ii) Chlorine gas is passed into a solution of \( N a I \) in water


Write the complement (in degree) of
each of the following angles: \( 30^{\circ} \)


For any acute angle \( \theta, \) find \( \sin ^{2} \theta+ \)
\( \cos ^{2} \theta \)
A .
B. 2
\( c \cdot 3 \)
D.


This smallest fox lives in the deserts of
North Africa. It has large ears that radiate body heat and help keep the fox
cool. Name this animal.
A. Fennec fox
B. Red fox
c. Grey fox
D. Kit fox


Given \( P=0.0030 \mathrm{m}, Q=2.40 \mathrm{m}, \mathrm{R}=3000 \)
\( \mathrm{m}, \) Significant figures in \( \mathrm{P}, \mathrm{Q}, \mathrm{R} \) are respectively.


Let \( \vec{a}, \vec{b}, \vec{c} \) be position vectors of three vertices of triangle \( A B C, \) find the area of triangle \( A B C \)


Find the oxidation number of Ni in
\( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \)


(i) What type of isomerism is shown by
the complex \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} ? \)
(ii) On the basis of crystal field theory, write the electronic configuration for \( 4 d \)
ion if \( \Delta_{0}>P \)
(iii) Write the hybridization and shape of \( \left[\boldsymbol{C o F}_{6}\right]^{3-} \) (Atomic number of \( \mathrm{Co}=27 \) ).


What will be the ratio between the
radius of \( 3^{r} d \) shell of \( L i^{+2} \& \) radius of
\( 3^{r d} \) shell of the hydrogen atom?


If \( A \) is \( 3 \times 4 \) matrix and \( B \) is matrix such
that \( A^{\prime} B \) and \( B A^{\prime} \) are both defined, then \( B \)
is of the type.
\( A \cdot 3 \times 4 \)
B. \( 3 \times 3 \)
\( \mathbf{c} \cdot 4 \times 4 \)
D. \( 4 \times 3 \)


Modern taxonomic studies do not deal
with
(a) External structure
(b) Structure of cell
(c) Internal structure
(d) Phylogeny
(e) Ontogeny
(f) Nutrition
\( A \cdot(d) \) and \( (f) \)
B. (b) and (c)
\( c \cdot(a) \) and \( (c) \)
D. (c) and (e)


The hydration of ionic compounds
involve:

This question has multiple correct options
A. evolution of heat
B. weakening of attractive forces
c. dissociation into ions
D. none of these


Which of the following statements is
the inverse of

"Our pond floods whenever there is a
thunderstorm."?
A. If there is a thunderstorm, then our pond floods
B. If we do not get a thunderstorm, then our pond does not flood.
c. If our pond does not flood, then we did not get a thunderstorm
D. None of the above


Find the actual lower and upper class
limits and also the class marks of the
classes : \( 1.1-2.0,2.1-3.0, \) and
\( \mathbf{3 . 1}-\mathbf{4 . 0 .} \)


Which of the following is not an intrauterine device?
B. Multiload-375
c. Norplant
D. Lippes loop


Find the value of \( \mathrm{K} \) so that \( (\boldsymbol{K}+ \)
2) \( ,(4 K-6) \) and \( (3 K-6) \) are three
continuous terms of AP.


We can see books even though it does not emit light because
A . It is always visible
B. It absorbs light
c. It reflects light
D. Neither absorbs nor reflects light


State whether true or false:
Comets and meteoroids are also the
minor members of the solar system.
A. True
B. False


The most abundant element in the
universe is thought to be:
A. Hydrogen
B. Carbon
c. oxygen
D. Nitrogen


State True or False.
One atmospheric pressure at sea level is equal to \( 760 \mathrm{cm} \) of \( \mathrm{Hg} \).
A. True
B. False


What is celestial object?
A. Naturally occurring physical entity which exists in observable universe
B. Artificially occurring physical entity which exists in observable universe
C. Naturally occurring physical entity which exists in observable solar system
D. None


Construct a tangent to a circle of radius
\( 4 \mathrm{cm} \) from a point on the concentric
circle of radius \( 6 \mathrm{cm} \) and measure its
length. Also verify the measurement by actual calculation.


The diagram shows a box in the shape of a cube of lengths 2 m.The box is packed with cubes of lengths 1 cm.How
many cubes does it hold?
A. 8000
B. 8000000
c. 4000000
D. 40000


Passive absorption of water from the soil is mainly affected by
A. Tissue organisation of root
B. Sucking power of root hairs
c. Tension of cell sap due to transpiration
D. osmotic concentration of cell sap


The correct order of increasing bond length of \( C-H, C-O, C-C \) and
\( \boldsymbol{C}=\boldsymbol{C} \) is :
A. \( C-H<C-O<C-C<C=C \)
в. \( C-H<C=C<C-O<C-C \)
c. \( C-C<C=C<C-O<C-H \)
D. \( C-O<C-H<C-C<C=C \)


In the quadrilateral (1) given below,
\( A B|| D C, E \) and \( F \) are mid point of \( A D \)
and \( B D \) respectively. Prove that
\( G \) is mid point of \( B C \)


A neutron is moving with velocity \( u \). It
collides head-on and elastically with an
atom of mass number A. If the initial
kinetic energy of the neutron is \( \mathrm{E} \), how much kinetic energy is retained by the
neutron after the collision?
[Assume fission doesn't take place]
\( ^{\mathbf{A}} \cdot\left[\frac{A}{(A+1)}\right]^{2} E \)
В. \( \left[\frac{A}{(A+1)^{2}}\right] E \)
\( ^{\mathbf{C}} \cdot\left[\frac{(A-1)}{(A+1)}\right]^{2} E \)
D. \( \left[\frac{(A-1)}{(A+1)^{2}}\right] E \)


One of the following is impermeable to
\( \boldsymbol{H}_{2} \boldsymbol{O} \) normally
A. PCT
B. DCT
C. Descending limb of loop of Henle
D. Ascending limb of loop of Henle


Determine the separation between 1st and 2 nd dark fringes from the left end air cavity.
A \( \cdot \frac{3 L}{7}+\frac{2 \lambda_{0}}{\mu} \)
B. \( \frac{5 L}{7} \)
c. \( \frac{4 L}{7} \)
D. \( \frac{6 L}{7} \)


is the Moment of inertia of \( \triangle A B C \)
(equilateral) about and an axis passing through 0 (D,E,F are midpoints). And
point 0 is the center of \( \triangle A B C . I_{o} \) is a
moment of inertia of a remaining
triangle when \( \triangle \) DEF is cut from \( \triangle A B C \).
A \( \cdot \frac{15}{16} I \)
в. \( \frac{3}{1} I \)
c. \( \frac{I_{o}}{4} \)
D. \( \frac{16}{15} I \)


In the adjoining figure, \( O A B C \) is a square of side \( 7 \mathrm{cm} . O A C \) is a quadrant
of a circle with \( O \) as centre. The area of
the shaded region is
A . \( 10.5 \mathrm{cm}^{2} \)
В. \( 38.5 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 49 c m^{2} \)
D. \( 11.5 \mathrm{cm}^{2} \)


In an isobaric process, the work done by a di-atomic gas is \( 10 \mathrm{J} \), the heat given to the gas will be?
A . \( 35 J \)
в. \( 30 J \)
c. \( 45 J \)
D. \( 60 J \)


During which of the following intervals did life originate on the Earth?
A. Mesozoic era
B. Proterozoic eon
c. cambrian period
D. Archean eon


Which among the following has lowest
vapour pressure?
A \( .0 .5 M A l_{2}\left(S O_{4}\right)_{3} \)
B. \( 12 \% \) Urea solution
c. \( 1 M \) NaCl \( (a q) \)
D. \( 18 \% \) Glucose solution


Which one belongs to monera?
A. Amoeba
B. Escherichia
c. Gelidium
D. Spirogyra


Find the slope of the line, which makes
an angle of \( 30^{\circ} \) with the positive
direction of \( y \) -axis measured anticlockwise


If \( a=0.1039 \), then the value of
\( \sqrt{4 a^{2}-4 a+1}+3 a \) is:
A . 0.1039
B. 0.2078
c. 1.1039
D . 2.1039


Photographic paper is developed with
alkaline hydroquinone.
Select the correct answer.
A. Hydroquinone is the oxidant
B. \( A g^{+} \) is the oxidant
C \( . B r^{-} \) is the oxidant
D. \( A g^{+} \) is the reductant


Which of the following has highest heat capacity?
A. \( 10 g \) of water
B. 4g of water
c. \( 100 g \) of copper
D. \( 10 g \) of Mercury


For the combustion reaction at \( 298 K \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\mathbf{1} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}(\boldsymbol{s}) \)
Which of the following alternative is
correct?
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. \( \Delta \)Hand\( \Delta U \) bear no relation with each other


The structure of \( X e F_{2} \) involves
hybridization of the type:
\( A \cdot s p^{3} \)
B . \( d s p^{2} \)
\( c \cdot s p^{3} d \)
D. none of these


Solution of the differential equation
\( x d y-y d x=0 \) represents.
A. A parabola whose vertex is at origin.
B. A circle whose centre is at origin
c. A rectangular hyperbola.
D. A straight line passing thorugh origin.


\( \lim _{x \rightarrow 2}\left(\left(\frac{x^{3}-4 x}{x^{3}-8}\right)^{-1}-\left(\frac{x+\sqrt{2 x}}{x-2}-\frac{ }{\sqrt{x} x}\right.\right. \)
is equal to
\( A \cdot \frac{1}{2} \)
B . 2
\( c \cdot 1 \)
D. None of these


Which element has:
(a) two shells, both of which are completely filled with electrons?
(b) the electronic configuration \( 2,8,2 ? \)
(c) a total of three shells, with four
electrons in its valence shell?
(d) a total of two shells, with three
electrons in its valence shell?
(e) twice as many electrons in its second shell as in its first shell?


Which of the following is a non-redox
process?
This question has multiple correct options
A \( \cdot S O_{4}^{2-} \rightarrow S O_{3} \)
B. \( C r_{2} O_{7}^{2-} \rightarrow C r O_{4}^{2} \)
\( \mathbf{c} \cdot P O_{4}^{3-} \rightarrow P_{2} O_{7}^{4} \)
\( \mathrm{D} \cdot C_{2} O_{4}^{-2} \rightarrow C O_{2} \)


Which of the following statements contains a reference to displacement?
I. The town is a five mile drive along the
winding country road.
II. The town sits at an altitude of \( 940 \mathrm{m} \)
III. The town is ten miles north, as the
crow flies.
A. I only
B. III only
c. I and III only
D. II and III only
E . I, II, and III


The thermistors are usually made of:
A. metals with low temperature coefficient of resistivity
B. metals with high temperature coefficient of resistivity
C. metal oxides with high temperature coefficient of resistivity
D. semiconducting materials having low temperature coefficient of resistivity


Two bulbs of \( 100 \mathrm{W} \) and \( 40 \mathrm{W} \) are
connected in series. The current
through the 100 W bulb is 1A. The
current through the 40 W bulb will be
A \( .0 .4 A \)
в. \( 0.6 A \)
\( c .0 .8 A \)
D. \( 1 A \)


The number of electrons present in \( 1 C \) of charge is
A \( \cdot 4.25 \times 10^{18} \)
B. \( 6.25 \times 10^{18} \)
c. \( 3.25 \times 10^{18} \)
D. \( 2.25 \times 10^{18} \)


The circle of least confusion is the
position where
A. marginal rays converge.
B. paraxial rays convergee
c. best image with least area can be seen.
D. blurred image with maximum area can be seen


If \( a, b \) and \( c \) arc in arithmetic progression then \( \frac{b-a}{c-b} \) is equal to
\( A \cdot \frac{b}{a} \)
B.
\( c \cdot 1 \)
D. \( 2 a \)


Construct the logic symbol, Boolean expression and truth table for an AND
gate.


\( \frac{1}{(x+1)\left(x^{2}+2 x+2\right)}=\frac{A}{x+1}+ \)
\( \frac{B x+C}{(x+1)^{2}+1} \Rightarrow A+B= \)
\( A \cdot 2 \)
B. -
\( c \)
\( D \)


In succulent plants R.Q. is less than one because of
A. Complete oxidation
B. Complete reduction
c. Incomplete reduction
D. Incomplete oxidation


\( \int_{0}^{\pi / 2} \frac{d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} \) equals-
A . \( \pi / a b \)
B. \( 2 \pi / a b \)
c. \( a b / \pi \)
D. \( \pi / 2 a b \)


Which of the following is unicellular?
A. Euglena
B. Pinus
c. Moss
D. Rhizopus


A tiny bar magnet is kept close to a long current carrying straight wire placed along the z axis. When the center of the magnet is at \( (a, 0.0) \) and it is oriented along the z axis, it experiences
A. no net force but a net torque.
B. neither net force nor net torque
c. both a net force and a net torque.
D. a net force but no net torque


Which of the following are basic oxides?
\( M n_{2} O_{7}, V_{2} O_{3}, V_{2} O_{5}, C r_{2} O_{3}, C r O \)
A. \( M n_{2} O_{7} \) and \( V_{2} O_{3} \)
B. \( V_{2} O_{3} \) and \( C r O \)
c. \( C r O \) and \( C r_{2} O_{3} \)
D. \( V_{2} O_{5} \) and \( V_{2} O_{3} \)


In a mixture of acetic acid and sodium
acetate, the ratio of concentrations of
the salt to the acid is increased ten
times. Then the \( p H \) of the solution:
A. Increases by one
B. Decreases by one
c. Decreases ten fold
D. Increases ten fold


Two identical 5 kg blocks are moving with same speed of \( 2 m / s \) towards each other along a friction-less horizontal
surface. The two blocks collide, stick
together and come to rest. Consider two
blocks as a system, the work done on
the system by the external forces will
be:
A . 20 Joule
B . -20 Joule
c. 0 Joule
D. None of these


Find out no. of reflection after which
light ray will exit from (Given \( \sin 40^{0}= \)
0.64)
A. 130000
B . 57735
c. 140000
D. 150000


Differentiate w.r.t. \( \boldsymbol{x} \)
\( \boldsymbol{y}=\boldsymbol{e}^{\cos (\boldsymbol{6} \boldsymbol{x}-\mathbf{1})} \)


A velocity-time graph is shown below in figure (i) and (ii) find the acceleration
and displacement
A. \( 3.2 \mathrm{m} \mathrm{s}^{-2}, 40 \mathrm{m} ; 5 \mathrm{s} \mathrm{m} s^{-2}, 60 \mathrm{m} \)
B. \( 4.2 \mathrm{m} \mathrm{s}^{-2}, 40 \mathrm{m} ; 5 \mathrm{s} \mathrm{m} s^{-2}, 60 \mathrm{m} \)
c. \( 3.2 \mathrm{m} s^{-2}, 50 \mathrm{m} ; 5 \mathrm{m} s^{-2}, 60 \mathrm{m} \)
D. \( 3.2 \mathrm{m} \mathrm{s}^{-2}, 40 \mathrm{m} ; 6 \mathrm{m} s^{-2}, 60 \mathrm{m} \)


According to Robert Constanza, \( 50 \% \) of
the total cost for ecosystem services
goes to
A. Recreation
B. Soil formation
c. Nutrient cycling
D. climate regulation
E. Habitat for wildlife


The IUPAC name of the given
compounds is:
A. 1,1 -dimethyl-3-hydroxy cyclohexane
B. 3,3-dimethyl-1-hydroxy cyclohexane
c. 3,3 -dimethyl cyclohexanol
D. 1,1-dimethyl-3-cyclohexanol


Device which works on Joule's law of
heating
A. Electric bulb
B. Electric heater
c. Electric iron
D. All


Given \( a_{12}=37, d=3, \) find a and \( S_{12} \)
\( \mathbf{A} \cdot 4,246 \)
B. 6,268
\( \mathbf{c} \cdot 9,296 \)
D. 3,264


A hair dresser stand with her nose 20
\( \mathrm{cm} \) in front of a plane mirror for what distance must she focus her eyes in
order to see her nose in the mirror?
A. \( 50 \mathrm{cm} \)
B. 30 cm
\( c .60 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


A massless platform is kept on a light elastic spring, as shown in the figure.
When particle of mass \( 0.1 \mathrm{kg} \) is dropped on the pan from a height of \( 0.24 \mathrm{m} \), the
particle strikes the pan, and the spring
is compressed by \( 0.01 \mathrm{m} . \) From what
height should the particle be dropped to
cause a compression of \( 0.04 \mathrm{m} ? \)
A. \( 0.96 \mathrm{m} \)
B . \( 2.96 \mathrm{m} \)
c. 3.96 \( m \)
D. \( 0.48 \mathrm{m} \)


If a function \( f \) satisfy \( f\left(\frac{x+y}{3}\right)= \) \( \frac{\mathbf{2}+\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{\mathbf{3}} \) for real \( \mathbf{x} \) and \( \mathbf{y} \)
\( \boldsymbol{f}^{\prime}(2)=3 \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is equal to
A \( \cdot-\frac{1}{12} x^{3}+x^{2} \)
B . \( 24 \log (3 x+2) \)
\( \mathbf{c} \cdot(3 x+2) \)
D. \( \frac{3}{4} x^{2}+2 \)


A particle in a certain conservative force field has a potential energy given by \( U=\frac{20 x y}{z} . \) The force exerted on it is?
A \( \cdot\left(\frac{20 y}{z}\right) \hat{i}+\left(\frac{20 x}{z}\right) \hat{j}+\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
B. \( -\left(\frac{20 y}{z}\right) \hat{i}-\left(\frac{20 x}{z}\right) \hat{j}+\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
\( ^{\mathrm{c}} \cdot\left(\frac{20 y}{z}\right) \hat{i}-\left(\frac{20 x}{z}\right) \hat{j}-\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
D \( \cdot\left(\frac{20 y}{z}\right) \hat{i}+\left(\frac{20 x}{z}\right) \hat{j}-\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)


If the variance of a random variable \( X \) is
\( \sigma^{2}, \) then the variance of the random
variable X-5 is??
\( \mathbf{A} \cdot 5 \sigma^{2} \)
B . \( 25 \sigma^{2} \)
\( \mathbf{c} \cdot \sigma^{2} \)
D. \( 2 \sigma^{2} \)


\( \mathbf{A} \)
\( 40 \mathrm{kg} \) box rests on the horizontal floor
of truck which is initially at rest on a horizontal road. The coefficient of
kinetic friction between the floor and
the box is 0.2 . The truck at time \( t=0 \)
accelerates constantly at \( 5 m s^{-2} \) and the box is \( 6 m \) away from the rear
opening of the truck. Find
(i) the time \( ^{\prime} \boldsymbol{t}^{\prime} \)
when the boxjust falls off the floor of the truck (ii) the distance travelled by
the truck during the interval (iii) distance covered by the box with
respect to road.


A village has a population of 4640 persons, out of which \( 25 \% \) are voters. In an election, if \( 15 \% \) voters did not vote,
how many voters cast their votes?
\( \mathbf{A} \cdot 2958 \)
в. 2784
c. 696
D. 986


Imagine that spherical mirrors were not known to human beings. Guess the
consequences.


ff \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) such that \( \boldsymbol{A} \) satisfies the
relation \( \boldsymbol{A}^{2}-(\boldsymbol{a}+\boldsymbol{d}) \boldsymbol{A}=\mathbf{0}, \) then
inverse of \( \boldsymbol{A} \) is
A . \( I \)
в.
c. \( (a+d) A \)
D. none of these


In the depression in freezing point
experiment, it is found that:
This question has multiple correct options
A. the vapour pressure of the solution is less than that of pure solvent.
B. the vapour pressure of the solution is more than that of pure solvent.
C . only solute molecules solidfy at freezing point.
D. only solvent molecules solidfy at freezing point.


The Tyndall effect associated with
colloidal particles is due to:
A. presenece of electrical charges
B. scattering of light
c. absorption of light
D. reflection of light


If \( \boldsymbol{A}=\{1,2\}, \) form the \( \operatorname{set} \boldsymbol{A} \times \boldsymbol{A} \times \boldsymbol{A} \)


Which one is most reactive towards \( S_{N} \)
reaction?
\( \mathbf{A} \cdot \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right) \mathrm{Br} \)
B. \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \) Br
\( \mathrm{c} \cdot \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C}\left(\mathrm{CH}_{3}\right)\left(\mathrm{C}_{6} \mathrm{H}_{5}\right) \mathrm{Br} \)
D. \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{Br} \)


Movement of Sunflower towards the
direction of Sun is
A. Photonasty
B. Phototropism
c. Nyctinasty
D. seismonasty


Give the graphical representation of the following equation
(a) On the number line and
(b) On the
Cartesian plane \( 2 x-9=0 \)


If dichloromethane \( (D C M) \) and water
\( \left(H_{2} O\right) \) are used for differential extraction, which one of the following statements is correct?
A. \( D C M \) and \( H_{2} O \) would stay as lower and upper layer respectively in the S.F.
B. \( D C M \) and \( H_{2} O \) will be miscible clearly
c. \( D C M \) and \( H_{2} O \) would stay as upper and lower layer respectively in the separating funnel (S.F.)
D. \( D C M \) and \( H_{2} O \) will make trubid/colloidal mixtur


Statement: \( M g C l_{2} .6 H_{2} O \) on heating
forms \( M g C l_{2} \)
State whether the given statement is true or false.
A. True
B. False


A person having eye problems should eat:
A. spinach, carrot
B. egg, milk
c. rice, banana
D. meat, apple


Which of the following is a gaseous hormone?
A. Kinetin
B. Zeatin
c. Auxin
D. Ethylene


A current I flows in a infinitely long wire with cross section in the form of a
semicircular ring of radius R. The magnitude of the magnetic induction at its axis is
A \( \cdot \frac{\mu_{0} I}{\pi^{2} R} \)
в. \( \frac{\mu_{0} \mathrm{I}}{2 \pi^{2} \mathrm{R}} \)
c. \( \frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{R}} \)
D. \( \frac{\mu_{0} I}{4 \pi \mathrm{R}} \)


A monoatomic ideal gas undergoes a process ABC. The heat given to the gas
is
A . 7.5 PV
B. 12.5 PV
\( c .16 .5 \mathrm{Pv} \)
D. 20.5 PV


Balbiani rings are sites of which of the following?
A. DNA replication
B. RNA and protein synthesis
c. synthesis of lipids
D. Synthesis of polysaccharides


The material used for brake drum is
A. Alluminum alloy
B. Cast steel
c. Pressed steel
D. cast Iron


Differentiate between.
Parasite and saprophyte


If \( [\mathbf{x}] \) stands greatest integer \( \leq \mathbf{x} \) then
the value of \( \left|\begin{array}{ccc}{[\boldsymbol{e}]} & {[\boldsymbol{\pi}]} & {\left[\boldsymbol{\pi}^{2}-\boldsymbol{6}\right]} \\ {[\boldsymbol{\pi}]} & \boldsymbol{\pi}^{2}-\boldsymbol{6} & {[\boldsymbol{e}]} \\ {\left[\boldsymbol{\pi}^{2}-\boldsymbol{6}\right]} & {[\boldsymbol{e}]} & {[\boldsymbol{\pi}]}\end{array}\right| \) equals
\( A \cdot-8 \)
B. 8
\( c \cdot-1 \)
\( D \)


A circular coil of 16 turns and radius 10
\( \mathrm{cm} \) carrying a current of \( 0.75 \mathrm{A} \) rests
with its plane normal to an external
field of magnitude \( 5.0 \times 10^{-2} \) T. The coil
is free to turn about an axis in its plane perpendicular to the filed direction. When the coil is turned slightly and released, it oscillates about its stable
equilibrium with a frequency of \( 2.0 / s \) What is the moment of inertia of the
coil about its axis of rotation?
A \( .1 .2 \times 10^{4} g-c m^{2} \)
B. \( 3 \times 10^{4} k g-m^{2} \)
c. \( 0.3 \times 10^{4} k g-m^{2} \)
D. \( 1.2 \times 10^{4} k g-m^{2} \)


We got promising results by using radioactive isotopes for the treatment of:
A. diabetes
B. heart disease
c. cancer
D. pneumonia


Speed of a body describing its motion
is
A. Direction
B. State
c. Type
D. Rapidity


Sulphur dioxide acts as an oxidizing
agent as well as a reducing agent. Give one reaction each to show its oxidizing
nature and its reducing nature.


Give one example in which 10 V may be
fatal
This question has multiple correct options
A. when touched to tongue
B. when touched with wet hand
C. when touched with unaided hand
D. when it is a storage battery


The possible structural isomers of an alkane are nine. The alkane is:
A. \( C_{4} H_{10} \)
B. \( C_{3} H_{8} \)
\( \mathbf{c} \cdot C_{6} H_{14} \)
D. \( C_{7} H_{16} \)


Consider the conic \( e x^{2}+\pi y^{2}-2 e^{2} x- \)
\( 2 \pi^{2} y+e^{3}+\pi^{3}=\pi e . \) Suppose \( P \) is any
point on the conic and \( S_{1}, S_{2} \) are the
foci of the conic, then the maximum
value of \( \left(\boldsymbol{P S}_{1}+\boldsymbol{P S}_{2}\right) \) is
A \( . \pi e \)
в. \( \sqrt{\pi e} \)
\( c \cdot 2 \sqrt{\pi} \)
D. \( 2 \sqrt{e} \)


If ball of metal is compressed by doubling the pressure then Bulk modulus of material of ball
A. will be doubled
B. will be halvedd
c. will become four times
D. will be same


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


The denitrifying bacteria are
A. Micrococcus denitrificans
B. Pseudomonas
c. Thiobacillus
D. All of the above


If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vector and \( \lambda \) is
a real number, then the vectors \( \vec{a}+ \) \( 2 \vec{b}+3 \vec{c}, \lambda \vec{b}+\mu \vec{c} a n d(2 \lambda-1) \vec{c} \) are
coplanar when
\( \mathbf{A} \cdot \mu \epsilon R \)
B \( \cdot \lambda=\frac{1}{2} \)
c. \( \lambda=0 \)
D. All value are correct


A water drop of radius 1 m \( m \) is sprayed
into \( 10^{6} \) droplets of same size at
constant temperature. If surface
tension of water is \( 72 \times 10^{-3} N / m \)
then the work done is
A \( .8 .95 \times 10^{-5} \) ergs
B. \( 8.95 \times 10^{-5} \mathrm{J} \)
c. \( 17.9 \times 10^{-5} \mathrm{J} \)
D. \( 17.9 \times 10^{-5} \) ergs


What is rainwater harvesting? Describe the method of rainwater harvesting.


With due regard to significant figures, the value of \( 46.7-10.04 \) is :
A. 36.7
B. 36.00
c. 36.66
D. 30.6


Find the number of sides of a regular
polygon if each exterior angle
measures: \( 60^{\circ} \)


Fill in the blank.
Two line segments are congruent if


The temperature of a gas is due to
A. P.E. of its molecules
B. K.E. of its molecules
C. Attractive forces between molecules
D. Repulsive forces between molecules


Why according to you flora and fauna should be conserved?


Why is a photodiode is used in reverse
bias?
A. Photocurrent flows only in reverse bias
B. Thermally generated current is large in reverse bias as compared to the photocurrent
C. Photocurrent is large in forward bias as compared to the forward bias current.
D. Photocurrent is significant in reverse bias as compared to the reverse bias current.


Arrange benzene, n-hexane and ethyne in decreasing order of acidic behaviour. Also give reason for this behaviour.
\[
\begin{array}{c}
\text { Ethyne }>\text { Benzene }>\quad n \text { -Hexane } \\
\mathrm{H}-\mathrm{C}=\mathrm{C}-\mathrm{H} \\
s p
\end{array}
\]


Assertion
Sky appears blue.
Reason
Colloidal particles of dust scatter blue
light.
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


The trinomial \( a x^{2}+b x+c \) has no real
roots, \( a+b+c<0 . \) Find the sign of
the number \( c \)


The atomic number of a few elements
are given below:
(i) 10
(ii) 20
(iii) 7
(iv) 14
Identify the elements.


If \( M \) is mass of the Sun, then the mass
of a white dwarf star may be
\( \mathbf{A} \cdot M \)
в. \( 2 M \)
\( c .3 M \)
D. \( 4 M \)


Fill the blank.
Voltmeter is always connected in \( \ldots \) with the device.
A. series
B. parallel
c. series and parallel both
D. the cell


A rectangular piece is \( 20 \mathrm{m} \) long and 15 \( \mathrm{m} \) wide. Form its four corners,
quadrants of radii \( 3.5 \mathrm{m} \) have been cut Find the area of the remaining part.


In uniform circular motion, direction of velocity goes on changing continuously, however the magnitude of velocity is constant.
A. True
B. False


Which is not a true dioxide?
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
c. \( M n O_{2} \)
D. \( \operatorname{sio}_{2} \)


A certain region of a soap bubble
reflects red light of vacuum wavelength
\( \boldsymbol{\lambda}=\mathbf{6 5 0 n m} . \) The minimum thickness
that this region of soap bubble could
have is \( 13 \times 10^{-x} \) m. Find \( x \)
(The index of refraction of the soap film
is \( 1.25) \)


Assertion
The concentration of pollutants in water or atmosphere is often expressed in terms of ppm.
Reason
Concentration in parts per million can be expressed as mass to mass, volume
to volume and mass to volume
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


When \( \mathrm{CO}_{2} \) is passed into aqueous
This question has multiple correct options
\( \mathbf{A} \cdot \mathrm{Na}_{2} \mathrm{CrO}_{4} \) solution, its yellow colour changes to orange
B. \( \mathrm{K}_{2} \mathrm{MnO}_{4} \) solution, it disproportionates to \( \mathrm{KMnO}_{4} \) and
\( \mathrm{MnO}_{2} \)
\( \mathrm{C} \cdot \mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) solution, its orange colour changes to green
D. \( \mathrm{KMnO}_{4} \) solution, its pink colour changes to green


Potential difference across depletion
regions
A. creates due to build up of space charge
B. limits further diffusion of electrons and holes across the depletion plane
c. should not be zero
D. both \( A \) and \( B \)


The magnetic moment \( (\mu) \) of a revolvng
electron around the nucleus varies with
principle quantum number n as
\( \mathbf{A} \cdot \mu \propto n \)
в. \( \mu \propto 1 / n \)
c. \( \mu \propto n^{2} \)
D. \( \mu \propto 1 / n^{2} \)


\( \frac{\sin (n+1) A+2 \sin n A+\sin (n-1) A}{\cos (n-1) A-\cos (n+1) A} \)
is equal to
A \( \cdot \tan \frac{A}{2} \)
B. \( \cot \frac{A}{2} \)
\( c \cdot \tan A \)
D. \( \cot A \)


An astronaut whose mass is \( 84 k g \) on earth will have a mass of approximately
14 \( k g \) on the moon
A. True
B. False


Which wall is at higher potential?
A. Inner
B. Outer
c. Both at same potential
D. None


Drive an expression for drift velocity of free electrons in a conductor.


Law of conservation of mass was put
forward by :
A. Lavoisier
B. Dalton
c. Priestly
D. Thomson


Can two obtuse angles be
supplementary?


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}, \) if
\( \boldsymbol{x} \in \boldsymbol{Q} \) and \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{6} \) if \( \boldsymbol{x} \in \boldsymbol{R}-\boldsymbol{Q} \)
then
A. f is continuous at \( x=1 \) and \( x=2 \)
B. fis not continuous at \( x=1 \) and \( x=2 \)
c. \( f \) is continuous at \( x=1 \) but not at \( x=2 \)
D. fis continuous at \( x=2 \) but not at \( x=1 \)


Polynomials of degrees 1,2 and 3 are called
polynomials respectively.
A. cubic, linear, quadratic
B. linear, quadratic, cubic
c. quadratic, linear, cubic
D. none of the above


A point charge q is placed at origin. Let \( \vec{E}_{A}, \vec{E}_{B} \) and \( \vec{E}_{C} \) be the electric fields at three points \( A(1,2,3), B(1,1,-1) \) and \( C(2,2,2) \) due to charge q. Then :
\( \mathbf{A} \cdot \vec{E}_{A} \perp \vec{E}_{B} \)
В . \( \vec{E}_{A}=\vec{E}_{B} \)
\( \mathbf{c} \cdot|\overrightarrow{E_{B}}|=|\overrightarrow{E_{C}}| \)
D \( \cdot\left|\vec{E}_{B}\right|=8\left|\vec{E}_{C}\right| \)


The fringe width of interference fringes for red colour is \( \beta . \) The fringe width for violet colour will be nearly:
\( \left(\lambda_{R e d}=620-740 n m, \lambda_{V i o l e t}=380-\right. \)
\( 450 n m) \)
\( A \cdot \beta \)
в. \( 2 \beta \)
\( c \cdot \frac{\beta}{4} \)
D. \( \frac{\beta}{2} \)


Which of the following arrangement is correct in ascending order?
A. species < genus < order < family
B. Genus < species < family < order
c. order \( < \) family < genus \( < \) species
D. species < genus < family < order


A gas is heated through \( 1^{\circ} \mathrm{C} \) in a closed vessel and so the pressure increases by \( 0.4 \% . \) The initial temperature of the gas
was:
A . \( -23^{0} C \)
В. \( +23^{0} C \)
c. \( +250^{\circ} \mathrm{C} \)
D. \( +523^{0} C \)


A ballon filled with air at \( 47^{\circ} \mathrm{C} \) has volume
of 3 litre. If ballon is kept in a room its
volume becomes 2.7 litre, the
temperature of the room is :
\( \mathbf{A} \cdot 5^{\circ} \mathbf{C} \)
B. \( 10^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)


What is follicular atresia?


What is the frequency of light emitted
when an electron in a hydrogen atom jumps from \( 2^{n d} \) orbit to \( 1^{s t} \) orbit?
A \( .24 .63 \times 10^{-34} \mathrm{Hz} \)
В. \( 13.6 \times 10^{-34} \mathrm{Hz} \)
c. \( 3.4 \times 10^{-34} \mathrm{Hz} \)
D. \( 1.6 \times 10^{-24} \mathrm{Hz} \)


Find the kinetic energy of this electron
as it comes out of the metal
A. 0.46 ev
B. 0.31 ev
\( c \cdot 0.23 \mathrm{ev} \)
D. None of these


Prove the mathmatical induction that
\( \frac{1}{\log _{x} 2, \log _{x} 4}+\frac{1}{\log _{x} 4, \log _{x} 8}+ \)
\( \ldots .+\frac{1}{\log _{x} 2^{n-1}, \log _{x} 4^{n}} \)
\( =\left(1-\frac{1}{n}\right) \frac{1}{\left(\log _{x} 2\right)^{2}}, x>0, \neq-1 n \epsilon N \)


If \( A^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right] \), then
\( (A B)^{-1}=? \)


With the help of a diagram, describe how food gets digested and assimilated in the human digestive system.


The radius \( R \) of the soap bubble is doubled under iso-thermal condition. If
\( \boldsymbol{T} \) be the surface tension of soap bubble The work done in doing so is given by:
\( \mathbf{A} \cdot 32 \pi R^{2} T \)
В . \( 24 \pi R^{2} T \)
c. \( 8 \pi R^{2} T \)
D. \( 4 \pi R^{2} T \)


The average translational kinetic energy of air molecules is \( 0.040 e V \)
\( \mathbf{1} e V=\mathbf{1 . 6} \times \mathbf{1 0}^{-19} \mathbf{J} \) ). Calculate the
temperature of the air. Boltzman's
constant \( k=1.38 \times 10^{-23} J K^{-1} \)


Among the following essential amino acid is:
A. alanine
B. valine
c. proline
D. serine


Let \( R \) be the set of all real numbers. If
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that
\( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|^{2} \leq|\boldsymbol{x}-\boldsymbol{y}|^{3}, \forall \boldsymbol{x}, \boldsymbol{y} \varepsilon \boldsymbol{R}, \) then
\( f^{\prime}(x) \) is equal to
A. \( f(x) \)
B. 1
\( c \cdot 0 \)
D. \( x^{2} \)
\( E \)


A charged particle moving at right angles to a uniform magnetic field:
A. Gains energy
B. Loses energy
c. Neither gains nor loses energy
D. Either gains or loses energy


The number of hydrogen atoms bridging
the boron
atoms in a diborance molecule is (1991)
A . 1
B. 2
\( c \cdot 3 \)
D.


The reaction, \( R C l+N a I \stackrel{\text { Dry acetone }}{\longrightarrow} \)
\( R-I+N a C l \) is known as:
A. Wurtz reaction
B. Fittig reaction
c. wurtz - Fitting reaction
D. Finkelstein's reaction


A police jeep is chasing a culprit going on a motorbike. The motorbike crosses
a turning at a speed of \( 72 \mathrm{km} / \mathrm{h} \). The jeep follows it at a speed of \( 90 \mathrm{km} / \mathrm{h} \)
crossing the turning ten seconds later than the bike.

Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
A. \( 3 k m \)
в. 5 kт
\( \mathrm{c} \cdot 1 \mathrm{km} \)
D. \( 7 \mathrm{km} \)


A plane electromagnetic wave propagating in \( x(-) \) direction as a wave function (in Sl units) is given as
\( \mathbf{\Phi}(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 x\right. \)
\( \mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{t} \)
The speed of the wave is
A. \( 3 \times 10^{6} \) m / \( s \)
В. \( 3 \times 10^{7} \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 9 \times 10^{14} \mathrm{m} / \mathrm{s} \)


The main difference between bathing
and washing soap is:
A. bathing soaps are potassium salts of fatty acids while washing soaps are sodium salts of fatty acids.
B. bathing soaps are sodium salts of fatty acids while washing soaps are potassium salts of fatty acids.
C. bathing soaps are cationic in nature while washing soaps are anionic.
D. bathing soaps are calcium salts of fatty acids while washing soaps are magnesium salts of fatty acids.


The surface area of the cuboid is
\( \mathbf{1 6 9} m^{2} . \) Its length is \( 3 \mathrm{m} \) and height is 9
m. Find its width.
A \( .4 .79 \mathrm{m} \)
B. \( 4.5 \mathrm{m} \)
c. \( 4 \mathrm{m} \)
D. \( 5 \mathrm{m} \)


Egg laid after fertilization is diploid.
A. True
B. False


Which of the reactions defines \( \Delta \boldsymbol{H}_{\boldsymbol{f}}^{o} \) ?
A. \( C_{\text {diamond}}+O_{2}(g) \longrightarrow C O_{2}(g) \)
B \( \cdot \frac{1}{2} H_{2}(g)+\frac{1}{2} F_{2}(g) \rightarrow H F(g) \)
C. \( N_{2}(l)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
\( ^{\mathrm{D}} \cdot \operatorname{CO}(g)+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) \)


Give both chemical equation of 'Mond process' used in nickel refining:


What is the least amount of
energy required by a man to lift an object weighing \( 1000 \mathrm{N} \) to a height of \( 2 m ? \)
A. 500 J
B. 2000 N
c. \( 500 \mathrm{N} \)
D. 2000 J


Molisch reagent is used to identify following compound?
A. Glucose
B. Raffinose
c. D-oxribose
D. All of these


Two spherical bobs, one metallic and
the other of glass, of the same size are allowed to fall freely from the same height above the ground. Which of the two would reach earlier and why?


Woolen clothes are prepared from
A. Wool warms
B. Carbon compounds
c. Fleece of sheep
D. cotton plants


toppr OG
Q Type your question_
is \( 50^{\circ} \mathrm{C} \) and \( 15 \Omega \) respectively The rate of
change of resistance \( R \) with temperature \( \frac{1}{2} \Omega /^{\circ} C \) and rate of decrease of temperature of \( R \) is \( \frac{(e n 3)}{100} \)
times the temperature difference from
surrounding Assume the resistance \( R \)
loses heat only in accordance with
newton's law of cooling If key k is closed
at \( t=0 \) then choose the incorrect option
A. The value of R for which power dissipation in it is maximum is \( 5 \Omega \)
B. Temperature of R when power dissipation in it is maximum is \( 30^{\circ} \mathrm{C} \)
C. Time after which power dissipation in it is maximum is 100 sec
D. Current throughout 10 v battery when power dissipation in \( R \) is maximum is 2.5 A


Acid rain is due to pollution of
A. Dust
B. Pesticides
c. \( S O_{2} \) and \( N O_{2} \)
D. Carbon particle


In
T.S. Pheretima, the correct sequence of body wall layers from outer to inner side
(a) Circular muscles
(b) Parietal peritoneum
(c) Epidermis
(d) Cuticle
(e) Longitudinal muscles
A. \( c \) be a d
B. \( d c \) e a b
\( c \cdot d c a e b \)
D. d b a ec


Which of the following is isoprene?
A \( \cdot C H_{2}=C H-C H=C H_{2} \)
в. \( C H_{2}=C\left(C H_{3}\right)-C H=C H_{2} \)
c. \( C H_{2}=C(C l)-C H=C H_{2} \)
D. \( C H_{2}=C\left(C H_{3}\right)-C\left(C H_{3}\right)=C H_{2} \)


Solve the equation \( 3 \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)- \)
\( 4 \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)+2 \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)=\frac{\pi}{3} \)


Find the area of the region bounded by
the curve \( y=4-x^{2}, x \) -axis and the line
\( x=0 \) and \( x=2 \)
A \( \cdot \frac{11}{3} \)
в. \( \frac{16}{3} \)
\( c \cdot \frac{16}{5} \)
D.


\( \gamma \) - globulins are synthesized inside
A . Liver
B. Bone marrow
c. Lymph and lymphoid tissue
D. Kidney


There are four men and six women on
the city councils. If one council number
is selected for committee at random,
how likely that it is a women?


How will you convert:
(i) Propene to propan-1-ol?
(ii) Ethanal to propan-2-ol?


Use the relationship \( \Delta G^{\circ}=-n F E_{\text {cell }}^{\circ} \) to
estimate the minimum voltage required
to electrolyse \( A l_{2} O_{3} \) in the Hall-Heroult
process. \( \Delta G_{f}^{\circ}\left(A l_{2} O_{3}\right)=-1520 k J m o l^{-1} \)
\( \Delta G_{f}^{\circ}\left(C O_{2}\right)=-394 k J m o l^{-1} \)
The oxidation of the graphite anode to
\( C O_{2} \) permits the electrolysis to occur at a
lower voltage than if the electrolysis
reactions were:
\( A l_{2} O_{3} \rightarrow 2 A l+3 O_{2} \)
What is the approximate value of low
voltage?
\( A \cdot 2 V \)
B. 3 V
\( c \cdot 4 v \)
D. \( 5 v \)


Solve
\( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}=\mathbf{6}, \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)


A hydrogen-like an atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to
the third Bohr orbit is \( 47.2 e V \). The
atomic number of this nucleus is
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 5


Formula mass unit of \( N a_{2} C O_{3} .10 H_{2} O \)
is :
A . 290
B. 286
\( c \cdot 180.02 \)
D. 105.97


Integrative system in the body are
A. Endocrine system
B. Nervous system
C. Blood vascular system
D. Both endocrine and nervous system


Branched leaf spines occur in
A. Acacia
B. opuntia
c. Berberis vulgaris
D. Asparagus


Solve \( \int x^{2} \cos x d x \)


Set the angles made by following vectors with \( x \) -axis in increasing order:
a) \( 3 \hat{i}+4 \hat{j} \)
b) \( 4 \hat{i}+3 \hat{j} \)
c) \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
\( A \cdot a, b, c \)
B. \( c, b, a \)
\( c \cdot b, c, a \)
D. a, c, b


\begin{tabular}{ll|l|l}
& Column I & & Column II \\
a. & Enthalpy & p. & Intrinsic property \\
b. & Temperature & q. & Path function \\
c. & Free energy & r. & Function \( U, P, V \) \\
d. & Work & s. & State function
\end{tabular}
\( \mathbf{A} \cdot(a-r, s),(b-p, s),(c-r, s),(d-q) \)
\( \mathbf{B} \cdot(a-r),(b-s),(c-r, s),(d-q, r) \)
\( \mathbf{C} \cdot(a-r, s),(b-r),(c-p, s),(d-q) \)
D \( .(a-q),(b-p, s),(c-s),(d-q, s) \)


If a body is in rotational equilibrium
under the action of three force, the lines
of action of the three forces must be
either concurrent of parallel.


The value of
\( \lim _{n \rightarrow \infty} \frac{1}{(n+1)}+\frac{1}{(n+2)}+\frac{1}{(n+3)}+\dots \)
\( ? \)
A \( \cdot \log 4 \)
в. \( \log 2 \)
\( c \cdot \log 3 \)
D. \( \log 5 \)


If \( |\bar{a}+\bar{b}|=|\bar{a}-\bar{b}| \) then
A \( . \bar{a} \| \bar{b} \)
B. \( \bar{a} \perp \bar{b} \)
\( \mathbf{c} \cdot \bar{a}=\bar{b} \)
D. None of these


Energy cannot be measured in
A . \( J s \)
в. \( W \) s
\( c . k W h \)
D. erg


Write the resonance structures of \( C O_{3}^{-2} \)
and \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}^{-} \)


Find the value of \( \boldsymbol{x}: \frac{\mathbf{4}}{\mathbf{5}} \boldsymbol{x}+\mathbf{1 1}=\frac{\mathbf{1}}{\mathbf{1 5}} \)


"Carnallite is \( K C l \cdot M g C l_{2} \cdot 6 H_{2} O \)
If true enter 1 , if false enter 0


The specific heat of copper is \( 0.385 \mathrm{J} / \mathrm{g} \)
\( ^{o} C \) ). If 34.2 g of copper, initially at \( 25^{\circ} \mathrm{C} \)
absorbs \( 4.689 \mathrm{kJ} \), what will be the final
temperature of the copper?
A . \( 25.4^{\circ} \mathrm{C} \)
B . \( 27.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 356^{\circ} \mathrm{C} \)
D. \( 381^{\circ} \mathrm{C} \)


In how much time will a sum of money
double itself if invested at \( 8 \% \) simple
interest per annum?


Palmarosa is
A. Cymbopogon martinii
B. Cymbopogon nardus
C. Vetiveria zizanioides
D. Setaria italica


The molarity of 600 g \( H_{2} \) O is ?
A. 50
B. 55.5 M
c. 33.10
D. Cannot be calculated


reaction:
\( A \)
\( B \)
\( c \)
D. Cannot sa


In the equation, \( N a_{2} C O_{3}+x H C l \rightarrow \)
\( 2 N a C l+C O_{2}+H_{2} O, \) the value of \( x \)
is:
A . 1
B . 2
\( c .3 \)
D. 4


Why does the sky appear blue?
A. The color of water is reflected on the sky
B. Fine particles in the atmosphere scatter light of shorter wavelength
C. The water molecules in the atmosphere makes the sky appear blue
D. None of these


Evaluate \( \lim _{x \rightarrow o} \frac{a x+\sin x}{b \sin x} \)


What is the major organic product of
the following reaction?
\( A \)
B.
\( c \)
\( D \)


What is the \( \sin (\boldsymbol{\alpha}+\boldsymbol{\beta})- \)
\( 2 \sin \alpha \cos \beta+\sin (\alpha-\beta) \) equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 \sin \alpha \)
\( c \cdot 2 \sin \beta \)
\( D \cdot \sin \alpha+\sin \beta \)


This question relates to the electron energy level diagram below. The
questions are about a hydrogen
electron located at \( \boldsymbol{E}_{3} \)
\( -.38 e v \)
\( \boldsymbol{n}=\mathbf{6} \)
\( -54 e v \)
\( \boldsymbol{n}=\mathbf{5} \)
\( -85 e v \)
\( \boldsymbol{n}=\mathbf{4} \)
\( \mathbf{- 1 . 5 2 e v}_{-}-\mathbf{3} \)
\( -3.39 e v_{-1-t-1} n=2 \)
\( \mathbf{- 1 3 . 6 e v}_{-\mathbf{n}=\mathbf{1}} \)
what is the emission energy when it
moves to \( \boldsymbol{E}_{2} \) ?
\( \mathbf{A} \cdot+66 e V \)
B. \( +.98 e V \)
c. \( +1.87 e V \)
D. \( -10.2 e V \)
E . \( +12.08 e V \)


Two coherent points sources \( S_{1} \) and \( S_{2} \)
vibrating in phase emit light of wavelength \( \lambda \). The separation between
them is \( 2 \lambda \). The light is collected on a
screen \( \sum \) placed at a distance \( D>>\lambda \)
from the slit \( S_{1} \) as shown, in the fig.
Find the minimum distance so that
intensity at \( P \) is equal to intensity at \( O \)
A . \( D \)
B . \( D_{/ 3} \)
c. \( \sqrt{3} D \)
D. \( D_{/ 2} \)


A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plae as shown in figure. The observed interference fringes from this combination shall be
A. straight
B. circular
c. equally spaced
D. having fringe spacing which increases as we go outward


Which of the following is used as \( \mathrm{S} \) I prefixes:
A. Femto
B. Atto
c. zepto
D. All of the above


\( \ln \) an oscillating \( \boldsymbol{L}-\boldsymbol{C} \) circuit, the
maximum charge on the capacitor is \( Q \) The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is:
A \( \cdot \frac{Q}{2} \)
B. \( \frac{Q}{\sqrt{2}} \)
c. \( \frac{Q}{\sqrt{3}} \)
D. \( \frac{Q}{3} \)


The direction cosines of the lines
bisecting the internal angle \( \theta \) between the lines whose direction cosines are
\( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \) are
\( \mathbf{A} \cdot<l_{1}+l_{2}, m_{1}+m_{2}, n_{1}+n_{2}> \)
B. \( <\frac{l_{1}+l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \sin \frac{\theta}{2}}> \)
c. \( <\frac{l_{1}+l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \cos \frac{\theta}{2}}> \)
D. none of these


The standard Gibbs free energy change
\( \left(\Delta G^{o}\right) \) at \( 25^{\circ} C \) for the dissociation of
\( N_{2} O_{4}(g) \) to \( N O_{2}(g) \) is (given,
equilibrium constant \( =\mathbf{0 . 1 5}, \boldsymbol{R}= \)
\( 8.314 J K / m o l) \)
\( \begin{array}{ll}\text { A. } 1.1 & k J\end{array} \)
B. \( 4.7 k J \)
c. \( 8.1 k J \)
D. 38.2 k \( J \)


Water containing heavier isotope of oxygen is known as water


\( 16.0 \mathrm{g} \) of NaOH is present in \( 100 \mathrm{ml} \) of an aqueous solution. Its density is 1.06 g/ml. Mole fraction of the solute is approximately:
\( \mathbf{A} \cdot 25 / 27 \)
B. 2 /27
c. \( 1 / 27 \)
D. \( 26 / 27 \)


Which device is used to measure the
potential difference between two points of a conductor in the laboratory?
A. Voltameter
B. Ammeter
c. Potentiometer
D. Galvanometer


A cell of negligible resistance and emf 2 volt is connected to a series
combination of 2,3 and 5 ohm. The
potential difference in volts between the terminals of 3 -ohm resistance will be:
A. \( 0.6 v o l t \)
B. \( \frac{2}{3} \) volt
c. \( 3 v o l t s \)
D. \( 6 v o l t s \)


A mixture of \( C u S O_{4} \) and \( C u S O_{4} .5 H_{2} O \)
has a mass of 1.245 g. After heating, it drives off all the water, the mass is only
0.832 g. What is the mass (in \( m g \) ) of
\( C u S O_{4} .5 H_{2} O \) in the mixture?


How many types of cells are present in vascular cambium?
A. Two types, fusiform and ray initial
B. Only fusiform initial
c. only ray initial
D. Three types fusiform, ray and medullary rays


If the lens is thick what will be its focal
length in air?
A \( \cdot \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}+\frac{t(n-1)}{n R_{1} R_{2}}\right. \)
B. \( \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}-\frac{t(n-1)}{n R_{1} R_{2}}\right) \)
c. \( \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}+\frac{t(n+1)}{n R_{1} R_{2}}\right] \)
D. none of these


\( \operatorname{Let} A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right] . \) If \( u_{1} \) and \( u_{2} \) are
column matrices such that \( \boldsymbol{A} \boldsymbol{u}_{1}=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \)
and \( A u_{2}=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right] \) then \( u_{1}+u_{2} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{c}-1 \\ 1 \\ 0\end{array}\right. \)
B. \( \left[\begin{array}{c}1 \\ -1 \\ -1\end{array}\right. \)
\( \mathbf{c} \cdot\left[\begin{array}{c}-1 \\ -1 \\ 0\end{array}\right. \)
D. \( \left[\begin{array}{c}-1 \\ 1 \\ -1\end{array}\right. \)


A square loop \( A B C D \) carrying a
current \( i, \) is placed near and coplanar
with a long straight conductor \( \boldsymbol{X} \boldsymbol{Y} \)
carrying a current \( I, \) the net force on the
loop will be:
A \( \cdot \frac{2 \mu_{0} I i}{3 \pi} \)
B. \( \frac{\mu_{0} I i}{2 \pi} \)
c. \( \frac{2 \mu_{0} \text { Ii } L}{3 \pi} \)
D. \( \frac{\mu_{0} I i L}{2 \pi} \)


Si of high purity to be used in
semiconductor can be prepared by following methods:
\( . S i O_{2}+2 C \rightarrow S i+2 C O \)
॥. \( S i+2 C l_{2} \rightarrow S i C l_{4} \)
\( S i C l_{4}+2 M g \rightarrow S i+2 M g C l_{2} \)
Better method is :
\( A \)
B. ॥
c. both (A) and (B)
D. None of these


A system is pushed by a force \( \boldsymbol{F} \) as
shown in figure. All surfaces are smooth except between \( B \) and \( C . \) Friction
coefficient between \( B \) and \( C \) is \( \mu \)
Minimum value of \( \boldsymbol{F} \) to prevent block \( \boldsymbol{B} \)
from down ward slipping is


The process by which a solid changes directly into gas is called:
A. decantation
B. sublimation
c. condensation
D. sedementation


000
voe


A sum becomes 8000 in 3 years and
10000 in 6 years at C.I. Find the sum.


Find area of parallelogram \( \boldsymbol{A B C D} \) if \( A B=8 \mathrm{cm}, B C=4 \mathrm{cm} \) and distance
between the two parallel lines \( A B \) and
\( C D \) is \( 3 \mathrm{cm} . \) Find the distance between
\( A D \) and \( B C \)


The number of distinct real roots of \( \left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0 \) in the
nterval \( -\frac{\pi}{4}<x \leq \frac{\pi}{4} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 1
\( D \cdot>2 \)


In the given figure, \( A B \| D C, \angle B A D= \)
\( 90^{0}, \angle C B D=28^{0} \) and \( \angle B C E=65^{0} \)
Then \( \angle A B D=? \)
\( A \cdot 32 \)
B .37
\( c \cdot 43 \)
\( D \cdot 53^{\circ} \)


If \( \tan \theta+\tan 2 \theta+\tan \theta \tan 2 \theta=1 \) then
general value of \( \boldsymbol{\theta} \) is
\( \mathbf{A} \cdot n \pi ; n \in I \)
в. \( n \pi \pm \frac{\pi}{3} ; n \in I \)
c. \( \frac{n \pi}{3}+\frac{\pi}{12}, n \in I \)
D. None of these


A conducting wire of length \( \ell \) and mass
\( m \) can slide without friction on two
parallel rails and is connected to
capacitance \( C . \) Whole system lies in a
magnetic field \( B \) and a constant force
\( F \) is applied to the rod. Then
This question has multiple correct options
A. the rod moves with constant velocity
B. the rod moves with an acceleration of \( \frac{F}{m+B^{2} \ell^{2} c} \)
c. there is constant charge on the capacitor
D. charge on the capacitor increases with time
E. answer required


An unbanked curve has a radius of
\( 60 m . \) The maximum speed at which a
car can make a turn if the coefficient of
static friction is \( 0.75, \) is:
A . \( 2.1 \mathrm{m} / \mathrm{s} \)
в. \( 145 \mathrm{m} / \mathrm{s} \)
c. \( 21 \mathrm{m} / \mathrm{s} \)
D. \( 7 \mathrm{m} / \mathrm{s} \)


How many metamers are possible for molecular formula \( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{1 1}} \boldsymbol{N} \) ?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


In the electrolysis of alumina using cryolite, the reaction that takes place at cathode is:
\( \mathbf{A} \cdot 4 H_{2} O+4 e^{-} \rightarrow 2 H_{2}+4 O H^{-} \)
B \( \cdot 4 A l^{3+}+12 e^{-} \rightarrow 4 A l \)
c. \( 6 F_{2}+2 A l_{2} O_{3} \rightarrow 4 A l F_{3}+3 O_{2} \)
D. \( 12 F^{-} \rightarrow 6 F_{2}+12 e^{-} \)


Express each of the following without using decimals:
\( 3.05 k m \)


In a triangle \( A B C, \) the co-ordinates of
vertices \( A, B \) and \( C \) are (4,7),(-2,3)
and (0,1) respectively. find the
equation of median through vertex \( \boldsymbol{A} \) Also, find the equation of the line
through vertex \( B \) and parallel to \( A C \)


A man hangs from a rope attached to a hot-air balloon. The mass of the man is
greater than the mass of the balloon
and its contents. The system is stationary in air. If the man now climbs up to the balloon using the rope, the
centre of mass of the 'man plus balloon
system wiii
A. remain stationary
B. move up
c. move down
D. first move up and then return to its initial position


The area of the region bounded by \( x= \)
\( \mathbf{0}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}=\mathbf{2}, \boldsymbol{y} \leq \boldsymbol{e}^{\boldsymbol{x}} \) and
\( \boldsymbol{y} \geq \ln \boldsymbol{x}, \) is
\( \mathbf{A} \cdot 6-4 \ln 2 \)
B. 4 \ellп \( 2-2 \)
\( c \cdot 2 \ln 2 \)
D. \( 6-2 \) \ellп 2


Find four different solution of \( 4 x+y=9 \)


lonization of phosphoric acid gives:
A \( \cdot H_{2} P O_{4}^{-} \)
в. \( H P O_{4}^{-2} \)
\( \mathrm{c} \cdot P O_{4}^{-3} \)
D. all of these


A compound microscope consists of two convex lenses of focal length \( 2 \mathrm{cm} \)
and \( 5 \mathrm{cm} . \) When an object is kept at a
distance of \( 2.1 \mathrm{cm} \) from the objective, a virtual and magnified image is formed \( 25 \mathrm{cm} \) from the eye piece. Calculate the magnifying power of the microscope.


Billy jogs \( 2.5 k m \) east in 45 minutes,
takes a water break for 12 minutes, and
then walks west at a rate of \( 0.65 k m / h \) for 30 min. What is Billy's average
velocity? (Answer units: km/hr)
A . 1.52
B. 1.96
\( c \cdot 2 \)
D. 1.45


ff \( f(x+y)=f(x) \cdot f(y) \) for all \( x \) and \( y \)
and \( f(15)=2, f^{\prime}(0)=3, \) then \( f^{\prime}(5) \) will
be
A .2
B. 4
\( c \cdot 6 \)
D. 8


The electronic configuration of an element is \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{5}, 4 s^{1} \)
This represents its:
A. excited state
B. ground state
c. cationic form
D. anionic form


A student has rectangular sheet of dimensions \( 14 \mathrm{cm} \times 22 \mathrm{cm} . \) He wants to
make a cylinder in such a way so that volume is minimum. Find the height of cylinder.


Match the following
\( \begin{array}{lllll}\text { List I } & & \text { List II } & \\ \text { Adjustment } & & & \\ \text { of focal } & \text { a } & \text { Accommodation } \\ \text { length } & & & \\ \text { 2 } & \begin{array}{l}\text { distance of } \\ \text { distinct vision }\end{array} & \text { b } & \text { Infinity } \\ \text { 3 } & \begin{array}{l}\text { Farthest point } \\ \text { of visibility }\end{array} & \text { c } & \text { 25 cm } \\ \text { 4 } & \begin{array}{l}\text { Vision } \\ \text { impairment }\end{array} & \text { d } & \text { Cataract }\end{array} \)
A . \( 1-b, 2-c, 3-a, 4-d \)
B. 1-d, 2-c, 3-b, 4-a
c. \( 1- \) a, \( 2-c, 3-b, 4-d \)
D. 1-c, 2-a, 3-d, 4-b


With increase in frequency of an A.C.
supply, the inductive reactance
A. decreases
B. increases directly with frequency
C. increases as square of frequency
D. decreases inversely with frequency


Aquatic animal with prehensile tail is
A. Chamaeleon
B. Macaca
c. Exocoetus
D. Hippocampus


Sporophyte with indefinite growth occurs in
A . Liver worts
B. Horn worts
c. Mosses
D. Fern


Write the uses of Lanthanides and
Actinides.


Convex spherical mirror is also known
as
A. Diverging mirror
B. Converging mirror
c. cylindrical mirror
D. Real mirror


In a chemical reaction \( \boldsymbol{X} \rightarrow \boldsymbol{Y} \), it is
found that the rate reaction doubles
when the concentration of \( \boldsymbol{X} \) is
increased four times. The order of the
reaction with respect to \( \boldsymbol{X} \) is:
A . 1
B. 2
\( c \cdot 2 \)
D. \( \frac{1}{2} \)


\( \boldsymbol{x}^{2}-(\boldsymbol{m}-\mathbf{3}) \boldsymbol{x}+\boldsymbol{m}=\mathbf{0}(\boldsymbol{m} \in \boldsymbol{R}) \) be a
quadratic equation. Find the value of \( \boldsymbol{m} \)
for which both the roots are equal:
A \( \cdot\{1,9\} \)
B.
\( c .3 \)
D. \{4,11\}


toppr
Q Type your question
quantities in relation to the energy of the comet-star system-kinetic energy
(KE) gravitational potential energy
\( (G P E), \) speed of comet (Speed), and mechanical energy of system (ME) Choose the table that is correctly filled
in with \( x \) 's.

Notice that in some boxes for certain
quantities neither box is checked, indicating that the particular quantities is the same at both
positions. Assume any loss of mass of the comet or the star is insignificant.
0 \( G \) \( \because . . . . \)
4
\begin{tabular}{|l|l|l|}
\hline & Position 1 & Position 2 \\
\hline KE greater & \( \mathrm{x} \) & \\
GPE greater & \( \mathrm{x} \) & \\
Speedgreater & \( \mathrm{x} \) & \\
MEgreater & \( \mathrm{x} \) & \\
\hline
\end{tabular}
B.
\begin{tabular}{|l|l|l|}
\hline & Position 1 & Position 2 \\
\hline KE greater & & \( \mathrm{x} \) \\
GPE greater & & \( \mathrm{x} \) \\
Speed greater & & \( \mathrm{x} \) \\
MEgreater & & \( \mathrm{x} \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|l|}
\hline & Position 1 & Position 2 \\
\hline KE greater & \( \mathrm{x} \) & \\
GPE greater & \( \mathrm{x} \) & \\
Speedgreater & \( \mathrm{x} \) & \\
ME greater & & \\
\hline
\end{tabular}
\( D \)
\begin{tabular}{|l|l|l|}
\hline & Position 1 & Position 2 \\
\hline KE greater & \( \times \) & \\
GPE greater & & \( \times \) \\
Speedgreater & \( \times \) & \\
MEgreater & & \\
\hline
\end{tabular}
E \begin{tabular}{|l|l|l|}
\hline & Position 1 & Position 2 \\
\hline KEgreater & & \( \times \) \\
GPEgreater & \( \times \) & \\
Speedgreater & & \( \times \) \\
ME greater & & \\
\hline
\end{tabular}


\( f(x)=\left(a-x^{n}\right)^{\frac{1}{n}} \) then \( f o f(x) \) is?


Select the number of incorrect
statements for the process of fermentation.
A. It involves only partial breakdown of
glucose.
\( \mathrm{B} N A D H_{2} \) is oxidized to NAD by reduction of organic compound.
C. No ATP are produced during fermentation as it is extracellular
process in some microbes.
D. There is no ETS and Kreb's cycle.
E. Maximum concentration of alcohol in
alcohol in alcoholic brevarage is \( 100 \% \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Average density of the earth
A. does not depend on \( g \)
B. is a complex function of \( g \)
C. is directly proportional to \( g \)
D. is inversely proportional to \( g \)


A compound contains 1 carbon atoms
and 2 oxygen atoms. The molecular
mass of compound (in \( g \) ) is


If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{1+\boldsymbol{x}^{2}+\boldsymbol{x}^{4}}{1+\boldsymbol{x}+\boldsymbol{x}^{2}}\right)=\boldsymbol{a} \boldsymbol{x}+ \)
\( b, \) then \( (a, b)= \)
A. (-1,2)
B. (-2,1)
c. (2,-1)
D. (1,2)


In the clathrates of xenon with water the
nature of bonding in \( \mathrm{Xe} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \)
molecule is:
A . covalent
B. hydrogen bonding
c. coordinate
D. dipole-induced dipole


Prove that \( \left|\begin{array}{lll}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x}^{3} \\ \mathbf{1} & \boldsymbol{y} & \boldsymbol{y}^{3} \\ \mathbf{1} & \boldsymbol{z} & \boldsymbol{z}^{3}\end{array}\right|=(\boldsymbol{x}+\boldsymbol{y}+ \)
\( z(x-y)(y-z)(z-x) \)


The energy required to melt 1 g ice is
33J. The number of quanta of radiation of frequency \( 4.67 \times 10^{13} \mathrm{sec}^{-1} \) that
must be absorbed to melt 10 g ice is:
B. \( 3.205 \times 10^{23} \)
c. \( 9.076 \times 10^{2} \)
D. None of the above


If the displacement equation of a particle from its mean position is given as \( \boldsymbol{y}=\mathbf{0 . 2} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+ \)
\( 1.5 \pi) \cos (10 \pi t+1.5 \pi) \) then, the
motion of particle is
A. Non-periodic
B. Periodic but not SHM
c. SHM with period 0.2
D. SHM with period 0.1 s


\( 2 A \rightarrow \) Product, follows the first order
kinetics. If the half life period of the reaction at \( [\boldsymbol{A}]_{\text {initial}}=\mathbf{0 . 2} \) mole lit\( ^{-1} \) is
20 min. then the value of rate constant
would be:-
\( A \cdot 4 \sec \)
B. 20 sec
c. 4 litmol\( ^{-1} \min ^{-1} \)
D. None of these


In which of the following pair, both the metals are obtained by electrolysis of their salts in molten state?
\( A \). Na and \( A l \)
B. Al and Cu
c. Al and Fc
D. Fc and Cu


Raschig's process is employed for the commercial preparation of
A. ethyl chloride
B. grignard's reagent
c. hydroxylamine
D. ethanol


A new temperature scale uses \( X \) as a
unit of temperature, where the
numerical value of the temperature \( t_{x} \)
in this scale is related to the absolute
temperature \( T \) by \( t_{x}=3 T+300 . \) If the
specific heat of a material using this
unit is \( 1400 \mathrm{Jkg}^{-1} \mathrm{X}^{-1} \) its specificne in
the S.I. system of units is
A. \( 4200 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
B. \( 1400 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)
\( \mathbf{C} \cdot 466.7 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)
D. impossible to determine from the information provided


The ultrasonic waves produced in SONAR is of frequency
A. \( 60,000 \mathrm{Hz} \)
B. 50,000Hz
c. \( 20,000 \mathrm{Hz} \)
D. All


Which of the following oxides of nitrogen exist as a crystalline ionic compound in solid state?
A. Nitrous oxide
B. Nitrogen trioxide
c. Nitrogen dioxide
D. Nitrogen pentaoxide


Derive the following equation for a uniformly accelerated motion, where
the symbols have their usual meanings:
\( s=u t+\frac{1}{2} a t^{2} \)


When polynuclear hydrocarbons enter
human body, they cause cancer but
they do not affect DNA.
A. True
B. False


A rocket of initial mass 6000 kg ejects
mass at a constant rate of \( 16 k g / s \) with
constant relative speed of \( 11 k m / s \) What is the acceleration of the rocket a
minute after the blast? (Neglect gravity)
\( \mathbf{A} \cdot 28.7 \mathrm{m} / \mathrm{s}^{2} \)
B . \( 34.9 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 39.4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 27.8 \mathrm{m} / \mathrm{s}^{2} \)


Which of the following compounds will not undergo azo coupling reaction with benzene diazonium chloride?
A. Aniline
B. Phenol
c. Anisole
D. Nitrobenzene


Orthophosphoric acid \( \frac{\text {gentleheat}}{220^{\circ}} \boldsymbol{X} \)
What is/are correct about \( X ? \)
A. it is a tetra basic acid
B. It contains one P- - -0- - -P bond
c. It is a dibasic acid
D. on hydrolysis it produces metaphosphoric acid.


The urethra is surrounded by sphincter muscles.
A . True
B. False


Displacement vs time curve for a
particle SHM is as shown in the figure:
Which of the following statements is
correct?
A. Phase of the oscillator is same at \( t=0 \) s and \( t=2 \) s
B. Phase of the oscillator is same at \( t=2 \) s and \( t=5 \) s
c. Phase of the oscillator is same at \( t=1 \) s and \( t=7 \) s
D. Phase of the oscillator is same at \( t=1 \) s and \( t=5 \) s.


Assertion
A conducting equilateral loop abc is
moved translationally with constant
speed \( \boldsymbol{v} \) in uniform inward magnetic
field \( B \) as shown. Then: \( V_{a}-V_{b}= \)
\( \boldsymbol{V}_{\boldsymbol{b}}-\boldsymbol{V}_{\boldsymbol{c}} \)
Reason
Point \( a \) is at higher potential than point
\( \boldsymbol{b} \)
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


Assertion
Molecular nitrogen is less reactive than
molecular oxygen.
Reason
The bond length of \( N_{2} \) is shorter than
that of oxygen.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false


Common impurities present in bauxite
are:
A. \( C u O \)
в. \( Z n O \)
\( c \cdot C a O \)
D. \( \operatorname{si} 0_{2} \)


A diminished image of an object is to be obtained on a screen \( 1.0 \mathrm{m} \) from it. This
can be achieved by appropriately placing
A. a concave mirror of suitable focal length
B. a convex mirror of suitable focal length
c. a convex lens of focal length less than \( 0.25 \mathrm{m} \)
D. a concave lens of suitable focal length


What is the smallest number by which
18522 must be divided so that the
quotient is a perfect cube?


Among the second period which group element form most acidic oxide.
A \( \cdot 17^{t h} \) group
B. \( 14^{\text {th}} \) group
C. \( 15^{\text {th}} \) group
D. \( 16^{\text {th }} \) group


The probability distribution of a
discrete random variable \( X \) is:
\[
\boldsymbol{X}=\boldsymbol{x} \quad \mathbf{1} \quad \boldsymbol{2} \quad \boldsymbol{3}
\]
\( P(X= \)
\( x) \)
\[
3 k
\]
\( 4 k \) \( k \quad 2 k \)
\[
\text { Find } P(X \leq 4)
\]
\( \mathbf{A} \cdot \frac{2}{3} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{5}{6} \)


The standard e.m.f. of a cell involving one electron change is found to \( 0.591 \mathrm{V} \)
at \( 25^{\circ} \mathrm{C} \). The equilibrium constant of the
reaction is:
A \( \cdot 10^{30} \)
B . \( 10^{5} \)
\( c \cdot 10^{10} \)
D. \( 10^{\text { }} \)


\( H_{2} S \) a toxic gas with rotten egg like smell, is used for the qualitative
analysis. If the solubility of \( H_{2} S \) in water at \( S T P \) is 0.195 m, calculate
Henry's law constant.


The de-Broglie wavelength of a \( H e- \)
atom in a container at \( 300 K \) is:
\( \left(\operatorname{luse} v_{a v g}\right) \)
\( \mathbf{A} \cdot 0.79 \stackrel{\circ}{A} \)
B \( \cdot 0.45 \stackrel{\circ}{h} \)
\( c \cdot 0.68 \stackrel{\circ}{8 A} \)
D. \( 0.89 \stackrel{\circ}{A} \)


A metal that exists as a liquid at room temperature is obtained by heating its sulphide in the prescence of air. Identify the metal and its ore and the give the reaction involved?


Which is unique to meiosis and does
not occur in mitosis?
A. Homologous chromosomes cross over
B. Homologous chromosomes pair and form bivalents
C. Homologous chromosomes behave independently
D. Chromatids are separated during anaphase


Which of these is a characteristic test
for ozone?
A. It does not give a brown solution with alcoholic benzidine
B . It tails mercury to form \( H g_{g} O \)
c. It gives blue colour to trimethyl base paper
D. All of these are confirming tests for ozone


Basic unit or smallest taxon of
taxonomy/classification is
A. species
B. Kingdom
c. Family
D. Variety


Based on the sides, classify the
following triangles


State True or False.
It is not necessary that both oxidation and reduction should takes place in the
same redox reaction.
A. True
B. False


A rocket is moving at a constant speed in space by burning its fuel and ejecting out the burnt gases through a nozzle.
There is a change in:
A. momentum of the rocket
\( c \cdot \operatorname{both} A \& B \)
D. None of the above


Calculate the molality of 1 L solution of
\( 93 \% H_{2} S O_{4} \) (weight/volume). The
density of the solution is 1.84 g. (If the answer is \( x, \text { then find }[x]) \)


This Indian scientist and his group
contributed immensely to \( C_{4} \) photosynthesis research
A. J.C. Bose
B. v.s.Rama Das
c. P.K.K. Nair
D. c.G.K Ramanujan


If \( \boldsymbol{p}=\cos \boldsymbol{x}-\sin \boldsymbol{x}, \boldsymbol{q}=\frac{1-\sin ^{3} \boldsymbol{x}}{1-\sin \boldsymbol{x}}, \boldsymbol{r}= \)
\( \frac{1+\cos ^{3} x}{1+\cos x} \)
What is the value of \( p+q+r ? \)
\( A \cdot O \)
B.
\( c \cdot 2 \)
D. 3


At room temperature, \( 27^{\circ} \mathrm{C} \), the resistance of a heating element is
100 \( \Omega \). What is the temperature(in \( ^{\circ} C \) )
of the element if the resistance is found
to be \( 117 \Omega \) ? Given that the temperature coefficient of the material of the
resistor is \( 1.70 \times 10^{-4} C^{-1} \)


What is the empirical formula of vanadium oxide if 2.74 g of metal oxide contains 1.53 g of metal?
\( A \cdot V_{2} O_{3} \)
в. \( V O \)
\( c \cdot V_{2} O_{5} \)
D. \( V_{2} O_{7} \)


serve as the intracellular highway
for transport.
A. Endoplasmic reticulum
B. Golgi apparatus
c. Cell membrane
D. Mitochondria


What will be the sign of the product if
we together multiply 199 negative integers and 10 positive integers?
A. Negative
B. Positive
c. can't say
D. Data is insufficient


Two organisms with different corerelated morphological characters belongs to
A. One biological species
B. One taxonomic species
c. Two biological species
D. Two taxonomic species


Which of the following bones helps to
hold the muscles of flight in birds?
A. Shoulder bone
B. Breast bone
c. Tail bone
D. None of the above


Which of the following group of
characters is present in all chordates in
some or other stage in their life
A. Mammary glands, hair and gill slits
B. Notochord, gill slits and dorsal tubular nervous system
C. Notochord, scales and dorsal tubular nervous system
D. Gill slits vertebral column and notochord


If \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{1+\cos ^{2}\left(\boldsymbol{x}^{2}\right)}, \) then
\( f^{\prime}\left(\frac{\sqrt{\pi}}{2}\right) \) equal to
A \( \cdot \frac{\sqrt{\pi}}{6} \)
в. \( -\sqrt{\frac{\pi}{6}} \)
c. \( \frac{1}{\sqrt{6}} \)
D. \( \frac{\pi}{\sqrt{6}} \)


The catalyst used in the oxidation of
\( \boldsymbol{S O}_{2} \) to \( \boldsymbol{S O}_{3} \) is
A. Glycerine
B. Nickel
c. Manganese dioxide
D. Platinised asbestos


A satellite S is moving in an elliptical orbit around the earth. The mass of the
satellite is very small compared to the
mass of the earth
A. the acceleration of S is always directed towards the centre of the earth
B. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
C. the total mechanical energy of S varies periodically with time
D. the linear momentum of S remains constant in magnitude


Evaluating the following:
\( (\sqrt{3}+1)^{5}-(\sqrt{3}-1)^{5} \)


An electron is not deflected on passing
through a certain region because:
This question has multiple correct options
A. there is no magnetic field in that region
B. there is a magnetic field but velocity of the electron is parallel to the direction of magnetic field
C. the electron is a charge less particle
D. none of the above


A rod of mass \( ^{\prime} M^{\prime} \) is subjected to force
\( t^{\prime} \) and \( ^{\prime} 2 f^{\prime} \) at both the ends as shown in
the figure. If young modulus of
its material is ' \( y^{\prime} \) and its length is \( L \)
find total elongation of rod.
A \( \cdot \frac{f l}{2 A y} \)
в. \( \frac{f l}{A y} \)
c. \( \frac{3 f l}{2 A v} \)
D. \( \frac{4 f l}{2 A y} \)


Let \( \boldsymbol{f}_{\boldsymbol{p}}(\boldsymbol{a})=\boldsymbol{e}^{\frac{i a}{p^{2}}} \cdot \boldsymbol{e}^{\frac{2 i a}{p^{2}}} \cdot \boldsymbol{e}^{\frac{3 i a}{p^{2}}} \ldots \cdot \boldsymbol{e}^{\frac{i a}{p}} \)
(Where \( i=\sqrt{-1} \) and \( p \in \)
\( N) \) then \( \lim _{n \rightarrow \infty} f_{n}(\pi) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. -1
D. \( -i \)


A sphere of mass \( m \) moving with velocity \( v \) hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in
terms of \( e \) )
A \( \cdot \frac{v_{1}}{v_{2}}=\frac{1+e}{1-e} \)
B. \( \frac{v_{1}}{v_{2}}=\frac{1-e}{1+e} \)
c. \( \frac{v_{1}}{v_{2}}=\frac{1+e}{2} \)
D. \( \frac{v_{1}}{v_{2}}=\frac{1-e}{2} \)


In succession, complexities in
structure are
A. Drastically increasing
B. Slowly increasing
c. Not increasing
D. constant


Which of the following cells are involved in the defensive mechanism?
A. Neutrophils
B. Lymphocytes
c. Macrophages
D. All of the above


The coefficient of performance of a carnot refrigerator working between \( 30^{\circ} \mathrm{C} \) and \( 0^{C} \) is
A . 10
B.
\( c \cdot 9 \)
D.


Find the equation of the ellipse whose
foci are \( (\mathbf{0}, \pm \mathbf{6}) \) and length of the minor
axis is 16


The ionisation energy for excited hydrogen atom in \( e V \) will be
A . 13.6
B. less than 13.6
c. greater than 13.6
D. 3.4 or less


Assertion
Deforestation is one main factor
contributing to global warming.
Reason
Besides \( C O_{2}, \) two other gases, methane and CFCs, are also included under green
house gases.
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


Calculate the standard enthalpy of
formation of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{I}) \) from the
following data:
\( C H_{3} O H(I)+\frac{3}{2} O_{2}(g) \rightarrow C O_{2}(g)+ \)
\( 2 H_{2} O(l) ; \triangle_{r} H^{\theta}=-726 k J m p l^{-1} \)
\( \boldsymbol{C}_{ \text {graphite } )}+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \triangle_{c} \boldsymbol{H}^{\boldsymbol{\theta}}= \)
\( -393 k J m o l^{-1} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \triangle_{f} \boldsymbol{H}^{\boldsymbol{\theta}}= \)
\( -286 k J m o l^{-1} \)


100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Number \( \begin{array}{ccc}\mathbf{1 -} & \mathbf{4}- & \mathbf{7 -} \\ \mathbf{4} & \mathbf{7} & \mathbf{1 0}\end{array} \) of letters
Number
of
30
surnames
Determine the median number of
letters in the surnames. Find the mean
number of letters in the surnames?
Also, find the modal size of the
surnames.


Sonali pounded a stake into the ground, when she attached a rope to both the stake and her dog's collar, the dog could reach 9 feet from the stake in any direction. Find the approximate area of the lawn, in square feet, the dog could
reach from the stake. \( (\pi=3.14) \)
A . 28
B. 57
\( c .113 \)
D. 254


For a GPS navigation to track a mobile
device, we use :-
A. 3 -satellites one for latitude, another for longitude and third for altitude
B. 4 -satellites one for altitude and 3 for position on ground
C. 2 -satellites one for position on ground one for altitude
D. 1 satellite only


The correct structure of \( \boldsymbol{P C l}_{3} \boldsymbol{B r}_{2} \) is:
\( A \)
в.
\( c \)
\( D . \) Both (2)\( \&(3) \)


A piece of blue glass when heated to a high temperature and a piece of red glass at room temperature are taken inside a dimly-lighted room. Then:
A. The blue piece will look blue and the red piece will look red as usual
B. The red piece will look brighter red and the blue piece will look ordinary blue
c. The blue piece will look brighter red compared to the red piece
D. Both the piece will look equally red


\( \ln \frac{a}{8}+\frac{a}{4}=6 \) the value of a is
A. 122
B. -16
c. 16
D.


Draw hysteresis curve (B-H curve) for a ferromagnetic substance


\( \left(A_{V}\right) \) and load resistance \( \left(R_{L}\right) \) is :
\( A \)
\( B \)
\( c \)
D.


Which of the following is a characteristic of wind energy?
A. Renewable source
B. Non renewable source
c. Not echo friendly.
D. costly.


State whether the following statement
is True or False.

The sum of three odd numbers is even.
A. True
B. False


Which of the following aldehyde is mostly used as plasticizer?
A. Formaldehyde
B. Acetaldehyde
c. Butyraldehyde
D. Benzaldehyde


The number of solutions of the equation \( \frac{\sec x}{1-\cos x}=\frac{1}{1-\cos x} \) in \( [0,2 \pi] \) is
equal to
\( A \cdot 3 \)
B. 2
\( c \)
\( D \)


\( \boldsymbol{A} \rightarrow \boldsymbol{B} \)
The reaction rate for the above reaction
is:
\( ^{\mathbf{A}} \cdot \frac{d[A]}{d t} \)
в. \( -\frac{d[B]}{d t} \)
c. \( -\frac{d t}{d[A]} \)
D. \( -\frac{d[A B]}{d t} \)


ì iuur 0
\( 10^{-2} m^{2} \) which has inductance \( L= \)
10m \( H \) and negligible resistance is
placed in a time-varying magnetic field.
Figure shows the variation of B with
time for the interval of 4 s. The field is
perpendicular to the plane of the loop (given at \( t=0, B=0, I=0) . \) The value
of the maximum current induced in the
loop is :
\( \mathbf{A} \cdot 0.1 \mathrm{mA} \)
B. \( 10 \mathrm{mA} \)
C. \( 100 \mathrm{mA} \)
D. Data insufficient


The correct order of hybridization of the central atom in the following species is:
\( N H_{3},\left[P t C l_{4}\right]^{2-}, P C l_{5} \) and \( B C l_{3} \)
B . \( s p^{3}, d s p^{2}, d s p^{3}, s p^{2} \)
C \( \cdot d s p^{2}, s p^{2}, s p^{3}, d s p^{3} \)
D. \( d s p^{2}, s p^{3}, s p^{2}, d s p^{3} \)


Which is not found in mushroom?
A. Eukaryotic structure
B. Dikaryotic mycelium
c. Basidiospores
D. Ascospores


Which one of the following is true for any two square matrices \( A \) and \( B \) of
same order?
\( \mathbf{A} \cdot(A B)^{T}=A^{T} B^{T} \)
B . \( \left(A^{T} B\right)^{T}=A^{T} B^{T} \)
c. \( (A B)^{T}=B A \)
D. \( (A B)^{T}=B^{T} A^{T} \)


A sphere of diameter \( r \) is cut from a solid sphere of radius r such that the centre of mass of remaining part be at maximum distance from original centre, then this distance is :
A \( \cdot \frac{r}{2} \)
B. \( \frac{r}{3} \)
c. \( \frac{r}{14} \)
D. None of these


The velocity of the object over the
interval (2,4) is :
A. \( 10 \mathrm{m} / \mathrm{s} \)
\( B .5 \mathrm{m} / \mathrm{s} \)
c. \( 20 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)


(i) Give an account of the structure of
different kinds of neurons.
(ii) Describe neurosecretory neurons.


In thermodynamic equilibrium there
are no net flows of
matter or of energy, either within a
system or between systems.
A. microscopic
B. macroscopic
c. electron
D. both \( A \) and \( B \)


Two skaters P and Q are skating towards each other. Skater P throws a
ball towards Q every 5s such that it always leaves her hand with speed 2
\( m s^{-1} \) with respect to the ground.
Consider two cases:
(i) P runs with speed \( 1 \mathrm{ms}^{-1} \) towards \( \mathrm{Q} \)
while \( Q \) remains stationary
(ii) \( Q \) runs with speed \( 1 m s^{-1} \) towards \( P \) while P remains stationary

Note that irrespective of speed of \( P, \) ball always leaves P's hand with speed 2
\( m s^{-1} \) with respect to the ground. lgnore gravity. Balls will be received by \( Q \)
A. one every 2.5 s in case ( (1) and one every 3.3 s in case (II)
B. One every 2 s in case (I) and one every 4 s in case(ll)
c. one every 3.3 s in case (I) and one every 2.5 s in case (II)
D. one every 2.5 s in case ( (1) and one every 2.5 s in case (I)


A number of discs, each of momentum
Mkgm/s are striking a wall at the rate
of \( n \) discs per minute. The force associated with these discs, in
newtons, would be
A. \( \frac{M n}{60} \)
в. \( 60 M n \)
c. \( \frac{M}{60 n} \)
D. \( \frac{n}{60 M} \)


Which of the following is not true about
structure of diamond and graphite?
A. In diamond, each carbon is \( s p^{3} \) hybridised while in
graphite each carbon is \( s p^{2} \) hybridised
B. In diamond, carbon atoms are closely packed in crystal lattice while graphite has layer structure.
C. Diamond is a hard substance while graphite is a soft substance.
D. Graphite is thermodynamically very less stable as compared to diamond and is amorphous form of carbon.


Regarding the uses of hydrogen
I) It is used in the synthesis of
ammonia.
Il) It is used as reducing agent in the
extraction of tungsten.
III) It is the source of solar energy.
IV) It is the major fuel in nuclear
reactors.
The correct statements are:
\( \mathbf{A} \cdot \) ।, ॥ and \( \| 1 \)
B. II and III
c. ॥, ॥ा and IV
D. All are correct


The wavelength photon obtained by electron transition between two level in
H-atom and singly ionised \( \boldsymbol{H} e \) are \( \boldsymbol{\lambda}_{\mathbf{1}} \)
and \( \lambda_{2} \) respectively, then:
A \( \cdot \lambda_{2}=\lambda_{1} \)
B \( \cdot \lambda_{2}=2 \lambda_{1} \)
c. \( \lambda_{2}=\lambda_{1} / 2 \)
D. \( \lambda_{2}=\lambda_{1} / 4 \)


A nucleus at rest undergoes \( \boldsymbol{\alpha}- \) decay
emitting an \( \alpha- \) particle of de Broglie
wavelength \( \lambda=5.76 \times 10^{-15} \mathrm{m} . \) If the
mass of the daughter nucleus is
223.610 amu and that of the \( \alpha- \)
particle is 4.002 amu, determine the
total kinetic energy in the final state, Hence, obtain the mass of parent nucleus in amu. \( (1 a m u= \) \( \left.\mathbf{9 3 1 . 4 7 0} M e V c^{-\mathbf{2}}\right) \)


Which of the following statements are
true about acceleration due to gravity?
This question has multiple correct options
A. \( g \) decreases in moving away from the centre if \( r>R \)
B. \( g \) decreases in moving away from the centre if \( r<R \)
C. \( g \) is zero at the centre of the earth
D. \( g \) decreases if earth stops rotating on its axis


Differentiate: \( y=\sin (2 x+3) \) w.r.t \( x \)


Pressure of a gas at constant volume is proportional to
A. Total internal energy of the gas
B. Average kinetic energy of the molecules
C. Average potential energy of the molecules
D. Total energy of the gas


One atomic mass unit is equal to:
A \( \cdot 1.66 \times 10^{-27} g \)
B . \( 1.66 \times 10^{-24} g \)
c. \( 1.66 \times 10^{-23} g \)
D. \( 1.66 \times 10^{-25} g \)


ASSERTION: In the extraction of
Ag, complex \( \mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right] \) is reacted
with Zn.

REASON: Zn is a d-block transition
metal.
A. If both assertion and reason are CORRECT, and reason
is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion
C. If assertion is CORRECT but reason is INCORRECT
D. If assertion is INCORRECT but reason is CORRECT


Enterocoelous coelom is found in
A. Deuterostomia
B. Astomia
c. Protostomia
D. Blastostomia


A satellite is moving in a circular orbit
around earth with a speed \( V \), If its mass
is \( \mathrm{m} \), then its total energy will be.
A \( \cdot \frac{3}{4} m v^{2} \)
B. \( m v^{2} \)
c. \( \frac{1}{2} m v^{2} \)
D. \( -\frac{1}{2} m v^{2} \)