A small object of mass \( m \) falls freely
from rest under gravity from height \( h \) from the point where it strikes the
inclined plane. Inclined plane is smooth and fixed as shown in figure. The time
of impact is \( t \) and the impact is elastic.
Find the force that the inclined plane applies on the object after the collision.


A long solenoid with length \( l \) and a
radius \( R \) consists of \( N \) turns of
wire,Neglecting the end effects, find the self-inductance.
B . \( \mu_{0} N \pi R^{2} / l \)
c. \( \mu_{0} N^{2} \pi R^{3} l \)
D. \( \mu_{0} N^{3} \pi R^{2} l \)


The difference between \( \Delta H \) and \( \Delta U \) for
the combustion reaction of benzene at
\( 127^{\circ} \mathrm{C} \) is:
A. \( -200 R \)
в. \( -600 R \)
c. \( 200 R \)
D. \( 600 R \)


The halogens (group 17 elements):
A. have an electronic configuration of a noble gas
B. are highly electropositive character
C. show variable oxidation state of -1,+1,+3,+5 and +7 in
their various compounds
D. forms a volatile, covalent hydrides HX in which the halogen (X) shows an oxidation state of +1


Lindlar's catalyst is
A \( \cdot V_{2} O_{5} \)
в. \( T i+A l\left(C_{2} H_{5}\right)_{3} \)
c. \( P d \)
D. \( P d-B a S O_{4}+ \)Quinoline


If true then enter 1 and if false then
enter 0

Can an acute angle be adjacent to an obtuse angle?


How many words can be formed with the
letters of the word 'PARALLEL' so that all
L's do not come together?


Assertion
\( \begin{array}{ccc}\mathbf{\Delta}= & & \\ & \sin \pi & \cos (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) & \tan (\boldsymbol{x}- \\ \sin (\boldsymbol{x}-\boldsymbol{\pi} / \mathbf{4}) & -\cos (\boldsymbol{\pi} / \mathbf{2}) & \log (\boldsymbol{x} \\ \cot (\boldsymbol{\pi} / \mathbf{4}+\boldsymbol{x}) & \log (\boldsymbol{y} / \boldsymbol{x}) & \tan \end{array} \)
0
Reason
A skew symmetric determinant of odd
order equals 0
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 enthalpies of the elements in their standard states are assumed to be:
A. zero at 298 k
B. unit at 298 к
c. zero at all temperatures
D. zero at 273 K


What is convex mirror?
A. curved or bowed outward like outside of a bowl or
sphere
B. curved like inner surface of a bowl or sphere
c. curved inward
D. None


True or False
Potassium is the most reactive alkali
metals.


If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \) and \( \boldsymbol{B}-\boldsymbol{A}=\boldsymbol{\phi} \) then \( \mathbf{A} \)
and B are
A. Overlapping
B. Equivalent
c. Dissiont
D. Equal


Hydrogen exhibits negative oxidation state with:
A.
B.
c. \( c \) ।
D. Na


Alida runs her toy car on dry marble
floor, wet marble floor, newspaper and towel spread on the floor. The force of
friction acting on the car on different surfaces in increasing order will be
A. Wet marble floor, dry marble floor, newspaper and towel
B. Newspaper, towel, dry marble floor, wet marble floor
c. Towel, newspaper, dry marble floor, wet marble floor.
D. Wet marble floor, dry marble floor, towel, newspaper


The incorrect statement about physical adsorption is that:
A. it lacks specificity
B. it is generally reversible
c. porous surfaces are good adsorbent
D. heat of adsorption is quite highh


If a copper wire is stretched to make its
radius decrease by \( 0.1 \% \), the percentage changes in its resistance is approximately
A . \( -0.4 \% \)
B. \( +0.8 \% \)
c. \( +0.4 \% \)
D. \( +0.2 \% \)


What is the meaning of turnover with
reference to enzyme?
A. The number of substrate molecules that molecule of
an enzyme converts into products per minute.
B. The number of substrate molecules that molecule of
an enzyme converts into products per day.
C. The number of substrate molecules that molecule of
an enzyme converts into products per hour.
D. The number of substrate molecules that molecule of
an enzyme converts into products per second.


A plane polarized light is incident on a polariser with its pass axis making
angle \( \theta \) with \( x \) -axis, as shown in the
figure. At four different values of \( \boldsymbol{\theta}, \boldsymbol{\theta}= \)
\( 8^{\circ}, 38^{\circ}, 188^{\circ} \) and \( 218^{\circ}, \) the observed
intensities are same. What is the angle
between the direction of polarization
and \( x \) -axis
\( \mathbf{A} \cdot 203^{\circ} \)
В. \( 45^{\circ} \)
\( c \cdot 98^{\circ} \)
\( D \cdot 128^{\circ} \)


"Heterosporous archegoniatae" is a
name for
A. Fern
B. Gymnosperms
c. Angiosperms
D. Both A and B


Indian style of cooling drinking water is
to keep it in a pitcher having porous walls. Water comes to the outer surface
very slowly and evaporates. Most of the energy needed for is taken from the
water itself and the water is cooled
down. Assume that a pitcher contains \( 10 k g \) of water and \( 0.2 g \) of water comes
out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which
the temperature decreases by \( 5^{\circ} C \)
Specific heat capacity of water \( =4200 J k g^{-1} C^{-1} \) and latent heat of
vaporization of water \( =2 \cdot 27 \times \) \( 10^{6} J k g^{-1} \)


On reaction with \( C l_{2} \), phosphorus forms
two types of halides 'A' and 'B'. Halide 'A' is yellowish-white powder but halide 'B' is colourless oily liquid. What would be the hydrolysis products of 'A' and 'B' respectively?
A. \( H_{3} P O_{4}, H_{3} P O_{3} \)
в. \( H O P O_{3}, H_{2} P O_{2} \)
\( \mathbf{c} \cdot H_{3} P O_{3}, H_{3} P O_{4} \)
D. \( H P O_{3}, H_{3} P O_{3} \)


The value of \( \frac{\sin ^{2} 53+\cos ^{2} 53}{\sec ^{2} 37-\tan ^{2} 37} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot \frac{1}{4} \)
D.


The osmotic pressure of equimolar
solutions of urea, \( B a C l_{2} \) and \( A l C l_{3} \) will
be in the order of:
A \( \cdot A l C l_{3}>U r e a>B a C l_{2} \)
в. Urea\( >B a C l_{2}> \)АlСl\( _{3} \)
c. \( A l C l_{3}>B a C l_{2}>U r e a \)
D. \( B a C l_{2}>A l C l_{3}>U r e a \)


Fill in the blank:
Image formed by a convex is
always virtual and smaller is size.
A. mirror
B. Iens
c. plano mirrors
D. none


Ethanoic acid
This question has multiple correct options
A. is odourless
B. has a pungent smell
C. has smell of rotten egg
D. has a vinegar like odour


Find the ratio of the volume of sphere \( \boldsymbol{A} \)
to sphere \( B \), if the ratio of the surface
area of sphere \( A \) to the surface area of
sphere \( \boldsymbol{B} \) is \( \mathbf{7 2 9}: \mathbf{1} \)
A .27: 1
в. 81: 1
C. 19,683: 1
D. 26,224: 1
E . 531,441: 1


In the quantitative determination of
carbon the \( C O_{2} \)
produced is absorbed in the solution of:
A. Pyrogallol
в. кон
\( \mathbf{c} \cdot \operatorname{ca}(O H)_{2} \)
D. All the above


Discuss the applicability of Rolle's theorem to \( f(x)=\log \left[\frac{x^{2}+a b}{(a+b) x}\right], \) in
the interval \( [a, b] \)
A. Yes Rolle's theorem is applicable and the stationary point is \( x=\sqrt{a b} \)
B. No Rolle's theorem is not applicable due to the discontinuity in the given interval
C. Yes Rolle's theorem is applicable and the stationary point is \( x=a b \)
D. none of these


The correct order of ligands for writing the formula of complex compounds is
A. neutral, anionic, cationic
B. anionic, neutral, cationic
c. anionic, cationic, neutral
D. cationic, neutral, anionic


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


The animals that feed by straining suspended matter and food particles from water is known as
A. Filter feeders
B. Detritivores
c. Fungivores
D. None of the above


Which of the following statements describes monocotyledons?
A. They have fibrous roots
B. Their leaves have parallel venation
c. Their seeds have only one cotyledon
D. All of the above


Which of the following options are incorrect?
A. Decreasing \( I . E_{2}: F>N>0 \)
B. Increasing atomic size : Be < B < Li < Na a
c. Metallic bond strength: Na < Zn < Ca
D. Increasing electron affinity : \( O^{2-}<O^{-}<O^{+}<O \)


Given that \( \sqrt{2} \) is irrational, prove that \( (5+3 \sqrt{2}) \) is an irrational number.


Give scientific reasons:
Elements belonging to the same group have the same valency.


Find the vertex, axis, focus,
directrix,lastusrectum of the parabola. \( x^{2}-2 x+4 y+9=0 \)


Three identical particles each of mass
1 kg are placed touching one another with their centres on a straight line. Their centres are marked \( A, B \) and \( C \)
respectively. The distance of centre of
mass of the system from \( \boldsymbol{A} \) is
\( ^{\text {A } \cdot \frac{A B+A C+B C}{3}} \)
в. \( \frac{A B+A C}{3} \)
c. \( \frac{A B+B C}{3} \)
D. \( \frac{A C+B C}{3} \)


What is an energy gap?
A. the space between two orbital shells
B. the energy equal to the energy acquired by an electron passing a \( 1 V \) electric field
C. the energy band in which electrons can move freely
D. an energy level at which an electron can exist


The compounds \( (A) \) and \( (B) \) in the
equation given above are:
\( \mathbf{A} \cdot C H_{3} C O O H \quad C H_{3} C H_{3} \)
B. \( D C H_{2}-C O O D \quad C H_{4} \)
\( \mathbf{c} \cdot D C H_{2}-C O O H \quad C H_{2} D_{2} \)
\( \mathbf{D} \cdot C h_{3}-C O O D \quad C H_{3} D \)


An atom with the same number of
protons but a different number of
neutrons is :
A . a molecule
B. a mixture of compound
c. an isotope
D. an isomer
E. an acid salt


Three charged particles are initially in position-1. They are free to move and they come to position - 2 , after some
time.Let \( U_{1} \) and \( U_{2} \) be the electrostatic
potential energies in position-1 and
2.Then
A \( \cdot U_{1}=U_{2} \)
в. \( U_{2} \geq U_{1} \)
c. \( U_{2}>U_{1} \)
D. \( U_{1}>U_{2} \)


Urinary bladder is absent in
A. Aves
B. Reptiles
c. Amphibians
D. Mammal


In a Wheatstone bridge (see fig.), Resistances \( P \) and \( Q \) are approximately
equal. When \( R=400 \Omega \), the bridge is
equal. When \( R=400 \Omega \),the bridge is
balanced. On inter-changing \( P \) and \( Q \)
the value of \( \boldsymbol{R}, \) for balance, is \( 405 \Omega \)
The value of \( X \) is close to:
A. 403 ohm
B. 404.5 ohm
c. 401.5 ohm
D. 402.5 ohm


A vessel in the form of a hemispherical
bowl is full of water. The contents are
emptied into a cylinder. The internal radii of the bowl and cylinder are \( 6 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively. Find the height of water in the cylinder(in cm).


The instantaneous values of alternating current and voltages in a circuit are given as
\( \mathrm{i}=\frac{1}{\sqrt{2}} \sin (100 \pi t) \) ampere
\( \mathrm{e}=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \mathrm{volt} \)
The average power in Watts consumed in the circuit is:
A \( \frac{\sqrt{3}}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{8} \)
D. 4


The cube of a two digit number may be a three digit number.
A. True
B. False
c. Insufficient Data
D. None of these


Cigarette gas lighter is made up of:
A. Noble metal
B. Alkali metal
c. Misch metal
D. None of these


A conductance cell was filled with a
0.02 M KCl solution which has a specific conductance of \( 2.768 \times \)
\( 10^{-3} \) oh \( m^{-1} c m^{-1} . \) If its resistance is
82.4 ohm at \( 25^{\circ} \mathrm{C}, \) then the cell constant
is:
A. \( 0.2182 \mathrm{cm}^{-1} \)
В. \( 0.2281 \mathrm{cm}^{-1} \)
c. \( 0.2821 \mathrm{cm}^{-1} \)
D. 0.2381 \( c m^{-1} \)


The objective lens of an optical instrument is an achromat
combination with a focal length of
\( 90 \mathrm{cm} . \) The two lenses possess
dispersive powers 0.024 and 0.036 respectively and are in contact with each other. Then their focal lengths are:
A. \( -30 \mathrm{cm}, 45 \mathrm{cm} \)
в. \( 45 \mathrm{cm}, 30 \mathrm{cm} \)
c. \( 30 \mathrm{cm},-45 \mathrm{cm} \)
D. 30 \( c m,-30 \mathrm{cm} \)


If the unit vectors \( \vec{e}_{1} \) and \( \vec{e}_{2} \) are inclined
at an angle \( 2 \theta \) and \( \left|\vec{e}_{1}-\vec{e}_{2}\right|<1 \), then
for \( \boldsymbol{\theta} \in[\mathbf{0}, \boldsymbol{\pi}], \boldsymbol{\theta} \) may lie in the interval
\( \mathbf{A} \cdot\left[0, \frac{\pi}{6}\right] \)
В \( \cdot\left[\frac{\pi}{6}, \frac{\pi}{2}\right] \)
c. \( \left[\frac{5 \pi}{6}, \pi\right] \)
D. \( \left[\frac{\pi}{2}, \frac{5 \pi}{6}\right] \)


\( \operatorname{Show}\left|\begin{array}{ccc}\boldsymbol{a x} & \boldsymbol{b y} & \boldsymbol{c z} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2} & \boldsymbol{z}^{2} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{y} \boldsymbol{z} & \boldsymbol{z} \boldsymbol{x} & \boldsymbol{x} \boldsymbol{y}\end{array}\right| \)


If \( f(x)=x^{2} \quad \) and \( g(x)=2 x+1 \) be two
real valued function. Find \( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) \) and
\( \frac{f(x)}{g(x)} \)


The mean of the numbers \( a, b, 8,5,10 \) is
6 and the variance is \( 6.80 . \) Then which
one of the following gives possible values of \( a \) and \( b \)
A \( . a=1, b=6 \)
В. \( a=3, b=4 \)
c. \( a=0, b=7 \)
D. \( a=5, b=2 \)


f \( A=\{a, b\} \) and \( B=\{1,2,3\} \) find
\( A \times B \) and \( B \times A \)


At room temperature, copper has free
electron density of \( 8.4 \times 10^{28} m^{-3} . \) The
electron drift velocity in a copper conductor of cross-sectional area of
\( 10^{-6} m^{2} \) and carrying a current of 5.4
\( \mathbf{A}, \mathbf{w} \) ill be
A \( \cdot 4 m s^{-1} \)
B. \( 0.4 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 4 \mathrm{cms}^{-1} \)
D. \( 0.4 \mathrm{mms}^{-1} \)


The waste from toilets can be used for
making
A. Vermicompost
B. Chemical fertilizers
c. Biogas
D. All of these


Which is the first and biggest asteroid discovered?
A. Vesta
B. Titan
c. Ceres
D. charon


Setae are found in all body segments of
earthworm except
A. Last segment
B. First segment
c. Clitellar segment
D. First, last and clitellar segments


The hydrated salt \( N a_{2} C O_{3} \cdot x H_{2} O \)
undergoes \( 63 \% \) loss in mass on heating
and becomes anhydrous. The value of \( x \) is:
A . 10
B. 12
\( c \cdot 8 \)
D. 18


Which is smaller?2497 or 2597


A converging equiconvex lens forms
real image of a particle as shown in
case \( I . \) If now lens is cut as shown in
case \( I I \) then select the correct
alternative/alternatives:
A. Image in case \( I I \) will be at \( 240 \mathrm{cm} \) from lens
B. Image is react
C. Image in case \( I I \) will be at the same location of case \( I \)
D. There will be two distinguished images


Complete the following.


The temperature of a body is 3000 K. The wavelength corresponding to maximum emission of radiation will be
\( A \cdot 1 M \)
в. \( 1 \dot{A} \)
\( \mathrm{c} \cdot 9.76 \times 10^{-7} \mathrm{m} \)
D . \( 48.8 \times 10^{-7} \mathrm{m} \)


The food we take in our body travels through a long and complex path. Which starts from mouth and ends at anus?
Which is the correct sequence of
process on food in digestive system?
A. Digestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion \( \rightarrow \) Ingestion
B. Ingestion \( \rightarrow \) Egestion \( \rightarrow \) Digestion \( \rightarrow \) Absorption
c. Digestion \( \rightarrow \) Ingestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion
D. Ingestion \( \rightarrow \) Digestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion


Velamen tissue is found in
A. Mesophytes
B. Epiphytes
c. Hydrophytes
D. xerophytes


The collecting ducts in the kidney
converge to form
A. Pyramid
B. Calyx
c. Pelvis
D. Columns of Bertin


Explain Malus law for polaroids.


Suppose gravity of earth suddenly becomes zero, then in which direction
will the moon begin to move if no other
celestial body affects it?
A . Radial
B. Tangential
c. cant say
D. None


The compound used to fix a dye to the
fabric is called:
A. mordant
B. lake
c. bleaching agent
D. oxidizing agent


What are non-metallic elements?
A. Elements that have one electron in their valence shell
B. Elements that have one, two or three electrons in their
valence shell
C. Elements that have four, five, six or seven electrons in
their valence shel
D. Elements that have three or four electrons in their
valence shel


Which of the following is true?
A. Diethyl ether has lower density than dibutyl ether.
B. Diethyl ether has higher density than dibutyl ether.
C. Diethyl ether is as dense as dibutyl ether.
D. The relative density of diethyl ether and dibutyl ether depends on the method of their preparation.


A reaction system in equilibrium
according to reaction \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow 2 S O_{3}(g)(k=5) \) in one litre
vessel at a given temperature was
found to be 0.12 mole each of \( S O_{2} \) and
\( \boldsymbol{S} \boldsymbol{O}_{3} \) and 5 mole of of \( \boldsymbol{O}_{2} \) must be added
to this vessel to order that at
equilibrium \( 20 \% \) of \( S O_{2} \) is oxidized to
\( S O_{3} . \) Find out the mass of oxygen formed?
A. \( 0.41245 \mathrm{g} \)
B. \( 11.6 g \)
c. \( 1.6 g \)
D. None of these.


Some of the following properties are important in determining whether an element has metallic properties
I atomic number
II : atomic weight
III : number of valence electrons
IV : number of vacant atomic orbitals
V: total number of electronic shells in
the atom
Select correct properties from the codes given below
A. ।, I, I, III, IV
B. ।, ॥I, IV, v
c. ॥॥, IV
D. \( \| \) II \( , \) IV, \( v \)


The earth receives at its surface
radiation from the sun at the rate of
\( 1400 w / m^{2} . \) The distance of the centre
of the sun from the surface of the earth
is \( 1.5 \times 10^{11} m \) and the radius of the
\( \operatorname{sun} \) is \( 7 \times 10^{8} \) m. Treating sun as a
black body, it follows from the above data that its surface temperature is
\( \mathbf{A} .5801 \mathrm{k} \)
В. \( 10^{6} \) к
c. \( 50.1 \mathrm{k} \)
D. \( 5801^{0} \mathrm{C} \)


An object of mass \( 0.2 k g \) executes SHM along the \( x \) -axis with frequency of \( (25 / \pi) \) Hz. At the point \( x=0.04 m \) the
object has \( \mathrm{KE} \mathbf{0 . 5} \boldsymbol{J} \) and PE \( \mathbf{4} \boldsymbol{J} \). The
amplitude of oscillation is


If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\{3,5,7\} and \( C=\{2,4\} \)
find \( : \boldsymbol{A} \times(\boldsymbol{B}-\boldsymbol{C}) \)
Find the number of elements in such a
set.


Reserve food material of algae is
A. Starch
B. Glycogen
\( c . \) Fat
D. sugar


If \( \boldsymbol{A}=\left[\begin{array}{rrr}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \) then find
\( \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \)
A. \( \left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \)
В. \( \left[\begin{array}{ccc}3 & 3 & 4 \\ 2 & -3 & -4 \\ 0 & -1 & 1\end{array}\right] \)
\( \begin{array}{llll}\text { C. } & {\left[\begin{array}{ccc}3 & 3 & 4 \\ 2 & -3 & 4 \\ 0 & 1 & 1\end{array}\right]}\end{array} \)
D. \( \left[\begin{array}{ccc}3 & -3 & 4 \\ 2 & -3 & -4 \\ 0 & 1 & 1\end{array}\right] \)


Which ray/radiation can be detected by
GM counter?
This question has multiple correct options
A. Alpha
B. Beta
\( c \cdot \gamma \operatorname{ray} \)
D. al


A Mixture of nitrogen and oxygen has a density of \( 1.00 g / 1 \) and the average
molecular weight \( \left(M_{a y}\right) \) of \( 31.2 g \) at
\( 27^{\circ} C \) and \( 600 \mathrm{mm} \) Hg per mole pressure
What is the mole fraction of nitrogen? (Assume ideal gas behavior)
A . 0.8
B. 0.6
\( c .0 .4 \)
D. 0.2


Starch is composed of amylose and
A. amylopectin
B. maltose
c. glycogen
D. none of the above


If a salt bridge is not used between two half cells, what happens to the voltage?
A. Drops to zero
B. Does not change
c. Increases gradually
D. Increases rapidly


A lot contains 20 articles. The
probability that the lot contains exactly
2 defective articles is \( 0 \cdot 4 \) and that lot
contains exactly 3 defective articles is
\( 0 \cdot 6 . \) Articles are drawn from the lot at
random one by one without replacement and are tested till all defective articles
are found. The probability that testing procedure ends at the twelfth testing is
\( \frac{11 k}{1900} . \) Find the value of \( k ? \)


Assertion
The cell potential of mercury cell is \( 1.35 V, \) which remains constant.
Reason

In mercury cell, the electrolyte is a paste of \( K O H \) and \( Z n O \)
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


Active absorption is affected by:
A. Osmotic concentration
B. Associate tissue structures
c. Transpiration
D. sucking capacity of root hair


In the resting state of the neural
membrane, diffusion due to
concentration gradients, if allowed
would drive
A. \( N a^{+} \) into the cell
B. \( N a^{+} \) out of the cell
c. \( K^{+} \) into the cell
D. \( K^{+} \) and \( N a^{+} \) out of the cell


A car is accelerating on a levelled plane and acquires a velocity 3 times of its initial velocity. During this process, the potential energy of the car
A. does not change
B. becomes 1.5 times that of initial potential energy
c. becomes 3 times that of initial potential energy
D. becomes 9 times that of initial potential energy


The value of \( \boldsymbol{I}=\int_{-2}^{0}\left[\boldsymbol{x}^{3}+\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\right. \)
\( (x+1) \cos (x+1)] d x, \) is
A . -4
B. -3
\( c .-2 \)
D. -


Which of the following order is correct for the decreasing reactivity of ring
monobromination of the following
compounds?
A \( I>I I>I I I>I V \)
\( V \)
B. \( I I>I I I>I V>I \)
c. \( I>I I I>I I>I V \)
D. \( I I I>I>I I>I V \)


If \( \int \frac{\boldsymbol{d x}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{2}+\mathbf{4}\right)}= \)
\( \boldsymbol{A} \tan ^{-1}+\boldsymbol{B} \tan ^{-1}\left(\frac{\boldsymbol{x}}{2}\right)+\boldsymbol{C}, \operatorname{then} \boldsymbol{B}= \)
A . \( 1 / 6 \)
B. \( -1 / 6 \)
\( c \cdot 6 \)
D.


The Sl unit of electric flux density is
A. \( N / C \)
в. \( N m^{2} / C \)
c. \( N m / C \)
D. \( N m^{2} \)


Which of the following is not a type of transpiration?
A. Stomatal transpiration
B. Cuticular transpiration
c. Lenticular transpiration
D. Endodermal transpiration


The anion of acetylacetone(acac) forms
\( \mathrm{Co}(a c a c)_{3} \) chelate with \( C o^{3+} . \) The rings
of the chelate are.
A. Five membered
B. Four membered
c. six membered
D. Three membered


\( \mathbf{f} \mathbf{3}^{x+1}=\mathbf{9}^{x-2}, \) find the value of \( \mathbf{2}^{1+x} \)


Write four more rational numbers in
each of the following patterns:
\( \frac{-1}{6}, \frac{2}{-12}, \frac{3}{-18}, \frac{4}{-24}, \dots \)


Write the function in the simplest form:
\( \tan ^{-1} \frac{1}{\sqrt{x^{2}-1}},|x|>1 \)


What constitutes brain stem?


suggested that the ships should be marked with load lines.
A. Samuel plimsoll
B. Einstein
c. Newton
D. Archimedes


i. Trace of the matrix is called sum of
the elements in a principle diagonal of the square matrix.
ii. The trace of the matrix \( \left[\begin{array}{ccc}8 & 7 & 5 \\ 5 & 8 & 2 \\ 7 & 2 & 8\end{array}\right] \)
is 24 Which of the following statement is correct.
A. Only i
B. Only ii
c. Both i and ii
D. Neither i nor i


Solve the following simultaneous
equations:
\( 217 x+131 y=913 \)
\( 131 x+217 y=827 \)
A. \( x=7, y=3 \)
В. \( x=2, y=1 \)
c. \( x=3, y=2 \)
D. \( x=1, y=5 \)


Find all pairs of consecutive odd positive integers both of which are
smaller than 10 such that their sum is
more than 11


Heart of Cockroach is
A. Myogenic
B. Neuromyogenic
c. Neurogenic
D. None of the above.


An electron and a photon each have a
wavelength of \( 1.00 \mathrm{nm} . \) Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.


A letter \( A \) is constructed of a uniform
wire of resistance \( 1 \Omega / c m . \) The sides of
the letter are \( 20 \mathrm{cm} \) and the cross piece
in the middle is \( 10 \mathrm{cm} \) long.The resistance between the ends of the legs will be:
A . \( 32.4 \Omega \)
B. \( 28.7 \Omega \)
c. \( 26.7 \Omega \)
D. \( 24.7 \Omega \)


Maximize \( \boldsymbol{f}=\mathbf{4} \boldsymbol{x}-\boldsymbol{y}, \) subject to the
constraints
\( \mathbf{7} \boldsymbol{x}+\mathbf{4} \boldsymbol{y} \leq \mathbf{2 8}, \mathbf{2 y} \leq \mathbf{7}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


Draw the structure of a nephron and label glomerulus, Bowman's capsule, renal artery, collecting duct.
b) What happen to glucose that enters the nephron along with the filtrate?


A particle is executing simple harmonic simple motion of amplitude \( 5 \mathrm{cm} \) and period 6 s. How long will it take to move from one end of its path on one side of mean position to a position \( 2.5 \mathrm{cm} \) on the same side of the mean position?
A . \( 1 \mathrm{s} \)
B. 1.5 s
\( c \cdot 3 s \)
D. 3.5


Prove \( \left(1+\frac{1}{1}\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right) \dots\left(1+\frac{1}{n}\right) \)
\( (n+1) \)


For a reaction scheme \( \boldsymbol{A} \stackrel{\boldsymbol{k}_{1}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{k}_{2}}{\longrightarrow} \boldsymbol{C}, \) if
the rate of formation of \( B \) is set to be
zero then the concetration of \( B \) is given
by:
\( ^{A} \cdot\left(\frac{k_{1}}{k_{2}}\right)[A] \)
B . \( \left(k_{1}+k_{2}\right)[A] \)
c. \( k_{1} k_{2}[A] \)
D. \( \left(k_{1}-k_{2}\right)[A] \)


A cold Object \( A \) is placed on top of a hot object \( \mathrm{B} \) in a closed system. Identify which of the following is the best description of what occurs in the
system?
I. Both \( A \) and \( B \) eventually reach the
same temperature.
Il. Gravity stops heat from moving up into A.
III. Heat flows from A to B
A. I only
B. II only
C. I and III only
D. II and III only
E . ।, II, and III


From a \( 20 m \) high tower one ball is
thrown upward with speed of \( 10 m / s \) and another is thrown vertically downward at the same speed
simultaneously. The time difference of their reaching the ground will be (in seconds):
A . 3
B. 2
\( c \cdot 4 \)
D.


Use Euclid's division lemma to find the
HCF of 13281 and 15844


Blue colour of sky is due to:
A. dispersion of light
B. scattering of light
C. reflection of light
D. refraction of light


Which of the following statement is
correct?
A. Allotropy of sulphur arises partly because of the great variety of molecular forms that can be achieved by -SS- catenation and partly because of the numerous ways in which the molecules so formed can be arranged within the crystal
B. Both rhombic and monoclinic sulphur have \( S_{8} \)
molecules and therefore, possess same value of specific gravities
C. Ozone on reaction with KI solution buffered with a borate buffer (pH 9.2) yields potassium iodate
D. The ozone layer protects the earth's surface from an excessive concentration of mainly infrared (IR) radiations


The area bounded by the curve \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \)
and the lines \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{1}|, \boldsymbol{x}=\mathbf{2} \) is
given by
\( \mathbf{A} \cdot e^{2}+1 \)
B \( \cdot e^{2}-1 \)
c. \( e^{2}-2 \)
D. \( e-2 \)


Find the total area of 14 squares whose
sides are \( 11 \mathrm{cm}, 12 \mathrm{cm}, \ldots, 24 \mathrm{cm} \)
respectively


Benzyl chloride \( \left(C_{6} H_{5} C H_{2} C l\right) \) can be
prepared from toluene by chlorination
with?
This question has multiple correct options
\( A \cdot S O_{2} C I_{2} \)
в. \( \operatorname{SOCI}_{2} \)
c. \( C I_{2} \)
D. \( N a O C I \)


Which of the following would increase the average speed the ideal gas molecules?
A. Lowering the temperature of gas
B. Compressing the gas with piston
c. Expanding the gas into vacuum
D. Heating the system at constant volume and pressure


At what temperature will the resistance of a copper wire become three times its value at \( 0^{0} \) C? [Temperature coefficient
of resistance for copper \( =4 \times \) \( \left.10^{-3} p e r^{0} C\right]: \)
\( \mathbf{A} \cdot 500^{0} C \)
B . \( 450^{\circ} \mathrm{C} \)
c. \( 600^{0} C \)
D. None of these


A aevice \( x \) is connectea to an ac
sources \( \boldsymbol{V}=\boldsymbol{V}_{0} \) sin \( \boldsymbol{\omega} \boldsymbol{t} . \) The variation of
voltage, current and power in one cycle is in the following graph:
(a) Identify the device 'X'.
(b) Which of the curves \( A, B \) and \( C \)
represent the voltage, current and the
power consumed in the circuit? Justify
your answer.
(c) How does its impedance vary with
frequency of the ac source? Show
graphically.
(d) Obtain an expression for the current
in the circuit and its phase relation with
ac voltage.


The equation of the circle, passing through the point \( (2,8), \) touching the \( \operatorname{lines} 4 x-3 y-24=0 \) and \( 4 x-3 y- \)
\( 42=0 \) and having \( x \) coordinate of the
center of the circle numerically less
then or equal to 8 , is
A \( \cdot x^{2}+y^{2}+4 x-6 y-12=0 \)
B. \( x^{2}+y^{2}-4 x+6 y-12=0 \)
C \( \cdot x^{2}+y^{2}-4 x-6 y-12=0 \)
D. None of these


(a) Deduce the expression, \( N= \)
\( N 0 e^{-\lambda} t, \) for the law of radioactive
decay.
(b)(i) Write symbolically the process expressing the \( \beta+ \) decay of \( _{11}^{22} \) Na. Also write the basic nuclear process underlying this decay.
(ii) Is the nucleus formed in the decay of the nucleus \( _{11}^{22} N a, \) an isotope or isobar?


What is the cumulative frequency of
the interval \( 40-50 ? \)
A . 70
B. 60
\( c .50 \)
D. 80


Let \( \boldsymbol{P}= \) Set of all integral multiples of 3
\( ; Q=\operatorname{set} \) of integral multiples of \( 4 ; R= \) Set of all integral multiples of 6 Consider the following relations:
\( \mathbf{1} \boldsymbol{P} \cup \boldsymbol{Q}=\boldsymbol{R} \)
\( \mathbf{2} . \boldsymbol{P} \subset \boldsymbol{R} \)
3. \( \boldsymbol{R} \subset(\boldsymbol{P} \cup \boldsymbol{Q}) \)
Which of the relations given above is/are correct ?
A. only 1
B . only 2
c. only 3
D. both 2 and 3


Prove that \( \boldsymbol{I}= \)
\( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sec x}}{\sqrt{\operatorname{cosec} x}+\sqrt{\sec x}} d x=\frac{\pi}{4} \)


In the reduction of nitriles to prepare
primary amine:
A. \( L i A l H_{4} \) is used.
B. \( N a B H_{4} \) is used.
c. \( S n / H C l \) is used.
D. none of these


Find the value of \( x \) and \( y \)
A \( \cdot 60^{\circ}, 45^{\circ} \)
B \( .45^{\circ}, 60^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ}, 45 \)
D. \( 60^{\circ}, 60^{\circ} \)


Of the following complex ions, which is diamagnetic in nature?
A \( \cdot\left[N i C l_{4}\right]^{2} \)
B . \( \left[N i(C N)_{4}\right]^{2} \)
\( \mathbf{c} \cdot\left[C u C l_{4}\right]^{2} \)
D. \( \left[\mathrm{CoF}_{6}\right]^{3-} \)


The internal energy of a diatomic gas us
given as \( U=U_{0} V, \) where \( U_{0} \) is a
constant. Molar heat capacity of gas is
A \( \cdot \frac{5}{2} R \)
в. \( \frac{7}{2} R \)
c. \( \frac{9}{2} R \)
D. \( \frac{3}{2} R \)


How is work done by a force measured
when the force:
(i) is in the direction of displacement.
\( (i i) \) is at an angle to the direction of displacement.


Which is used in cancer chemotherapy?
A. cis-platin
B. Zeisse's salt
c. Both (a) and (b)
D. None of these


When the temperature of a gas is \( 20^{0} C \)
and pressure is changed from \( \boldsymbol{P}_{1}= \) \( \mathbf{1 . 0 1} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \) to \( \boldsymbol{P}_{\mathbf{2}}=\mathbf{1 . 1 6 5} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \)
then the volume changes by \( 10 \% . \) The bulk modulus is
A \( .1 .55 \times 10^{5} \mathrm{Pa} \)
в. \( 1.05 \times 10^{5} P a \)
c. \( 1.4 \times 10^{5} P a \)
D. \( 0.115 \times 10^{5} P a \)


For \( \boldsymbol{O} \) being the origin and 3 points \( \boldsymbol{P}, \boldsymbol{Q} \) and \( R \) lie on a plane. If \( \overrightarrow{P O}+\overrightarrow{O Q}= \) \( \overrightarrow{Q O}+\overrightarrow{O R}, \) then \( P, Q, R \) are
A. the vertices of an equilateral triangle
B. the vertices of an isoceles triangle
c. collinear
D. none of these


Let \( x_{1}, x_{2}, \ldots . . x_{n} \) be \( n \) observations and
\( \bar{X} \) be their arithmetic mean. The
formula for the standard deviation is
given by
A \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
B \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
c. \( \sqrt{\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2}} \)
D. \( \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_{i}^{2}+\bar{X}^{2}} \)


In an oscillating \( L C \) circuit, the total
stores energy is \( U \) and the maximum
charge on the capacitor is \( Q . \) When the charge on the capacitor is \( Q / 2, \) the energy stored in the inductor is :
A. \( U / 2 \)
в. \( U / 4 \)
c. \( (4 / 3) U \)
D. \( 3 U / 4 \)


In the circuit shown below
This question has multiple correct options
A. Current flowing in the circuit is \( 200 \mathrm{mA} \)
B. Power supplied by the battery is 2 watt
c. Current from \( X \) to \( Y \) is zero
D. Potential difference across \( 10 \Omega \) is equal to zer


An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. The middle part of the train passes past the same pole with a velocity of
A \( \cdot \frac{u+v}{2} \)
в. \( \frac{u^{2}+v^{2}}{2} \)
c. \( \sqrt{\frac{u^{2}+v^{2}}{2}} \)
D. \( \sqrt{\frac{u^{2}-v^{2}}{2}} \)


Assertion \( (\mathrm{A}): C_{2} H_{5} C l \) gives ethyl benzene with benzene in presence of
anhydrous aluminium chloride.
Reason (R) : Anhydrous aluminium
chloride acts as Lewis acid and
generates ethyl carbonium ion
electrophile.
A. Both A and R are true and R is the correct explanation to A
B. Both A and R are true and R is not the correct explanation to A
c. A is true but R is false
D. A is false but R is true


Moment of inertia of a body about an
axis is \( 4 k g m^{2} . \) The body is initially at rest and a torque of 8 N \( m \) starts acting on it along the same axis. Work done by
the torque in \( 20 s, \) in joules, is :
A . 40
в. 640
c. 2560
D. 3200


If \( \boldsymbol{\theta} \equiv \sin ^{-1} \boldsymbol{x}+\cos ^{-1} \boldsymbol{x}-\boldsymbol{t a n}^{-1} \boldsymbol{x}, \boldsymbol{0} \leq \)
\( x \leq 1, \) then the smallest interval in
which \( \theta \) lies is given by?
A \( \cdot \frac{\pi}{4} \leq \theta \leq \frac{\pi}{2} \)
B. \( -\frac{\pi}{4} \leq \theta \leq 0 \)
c. \( 0 \leq \theta \leq \frac{\pi}{4} \)
D・ \( \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{4} \)


Write the degree of the following polynomial :
\( a b^{2} c d-3 a^{2} b c d^{3}+2 a c^{4} \)
\( A \cdot 7 \)
B. 3
\( c \cdot 2 \)
D. 5


If \( 50 \% \) of \( C O_{2} \) converts to \( C O \) at the
following equilibrium:
\[
\frac{1}{2} C(s)+\frac{1}{2} C O_{2}(g) \rightleftharpoons C O(g)
\]
And the equilibrium pressure is 12 atm.
Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \)


If \( p \) is the length of the perpendicular from the origin on the line \( \frac{x}{a}+\frac{y}{b}=1 \)
and \( a^{2}, p^{2}, b^{2} \) are in A.P. then \( a b \) is equal
to
This question has multiple correct options
A \( \cdot p^{2} \)
B \( \cdot \sqrt{2} p^{2} \)
c. \( -\sqrt{2} p^{2} \)
D. \( 2 p^{2} \)


A charged particle entering a magnetic
field from outside in a direction
perpendicular to the field
A. can never complete one rotation inside the field
B. may or may not complete one rotation in the field depending on its angle of entry into the field
c. will always complete exactly half of a rotation before leaving the field
D. may follow a helical path depending on its angle of entry into the field


If \( \left|z_{1}-1\right| \leq 1,\left|z_{2}-2\right| \leq 2,\left|z_{3}-3\right| \leq 3 \)
then find the greatest value of
\( \left|z_{1}+z_{2}+z_{3}\right| \)
A. the greatest value is 6
B. the greatest value is 7 .
c. the greatest value is \( 9 . \)
D. the greatest value is 12


Arrange the following equations in decreasing order of their number of solutions in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \)
I) \( 3 \sin ^{2} \theta+4 \cos ^{2} \theta=5 \)
II) \( 4 \sin ^{2} \theta+3 \cos ^{2} \theta=\frac{7}{2} \)
|||| \( 3 \mid \sin ^{2} \theta+4 \cos ^{2} \theta=4 \)
A . ॥,|॥,
B. ।, ॥।, III
c. ॥ा,।, ॥
\( \mathbf{D} \cdot\|\|, \) И,


Fill in the blanks with suitable word:
The \( x \) -coordinate is called as


At \( 25^{0} \mathrm{C}, K_{s p} \) for \( P b B r_{2} \) is equal to \( 8 x \)
\( 10^{-5} . \) If the salt is \( 80 \% \) dissociated,
what is the solubility of \( P b B r_{2} \) in mol/litre?
\( ^{A} \cdot\left[\frac{10^{-5}}{1.6 \times 1.6}\right]^{1 / 3} \)
в. \( \left.\frac{10^{-4}}{1.6 \times 1.6}\right]^{1 / 3} \)
\( ^{\mathrm{c}}\left[\frac{10^{-4}}{0.8 \times 0.8}\right]^{1 / 3} \)
D. \( \left.\quad \frac{10^{-5}}{1.6 \times 1.6}\right]^{1 / 2} \)


Given two functions \( f(x) \) and \( g(x) \) such that \( f(x)=\sin (a r c t a n x), g(x)= \)
\( \tan (\arcsin x), \) and \( 0 \leq x<\frac{\pi}{2} . \) The
value of the composite function \( f\left(g\left(\frac{\pi}{10}\right)\right) \) is:
\( \mathbf{A} \cdot 0.314 \)
в. 0.354
c. 0.577
D. 0.707
E . 0.866


Number of hydrogen bonds between guanine and thymine is:
A. 0
B. 3
\( c \)
\( D \)


Frequency (v) and time period (T) are related as
A \( . v \times T=1 \)
B. \( \frac{v}{T}=1 \)
c. \( v=T^{2} \)
D \( \cdot v=T^{-2} \)


A particle moves in the xy-plane with constant acceleration a directed along the negative y-axis. The equation of path of the particle has the form \( y= \) \( b x-c x^{2}, \) where \( b \) and \( c \) are positive
constants. The velocity \( v \) of the particle at the origin of coordinates will be
A \( \cdot \sqrt{\frac{a}{2 c}\left(1+b^{2}\right)} \)
в. \( \sqrt{\frac{a}{4 c}\left(1+b^{2}\right)} \)
c. \( \sqrt{\frac{3 a}{2 c}\left(1-b^{2}\right)} \)
D. none of these


A container is filled with water,
accelerating with acceleration \( 10 m / s^{2} \)
long \( +v e X \) -axis on a smooth horizontal
surface. The velocity of efflux of water at
a point \( \boldsymbol{P} \) at the bottom of the tank and
near its left most corner is
\( \mathbf{A} \cdot 4.43 m / s \)
B. \( 5.48 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 4 m / s \)
D. \( 3 m / s \)


Which of the following is not a state function?
A .
B.
\( c \cdot v \)
\( D \)


Give graph is of which orbital?
A \( .2 p \)
в. 1 .
\( c .2 s \)
\( 0.3 s \)


If the length of the cylinder is measured as \( 25 \mathrm{mm} \), the diameter is \( 3.09 \mathrm{cm} \) and mass of the cylinder is measured as \( 50.0 \mathrm{gm} \) find the density of the cylinder in proper significant figures.(in \( \boldsymbol{g} \boldsymbol{m} / \boldsymbol{c m}^{3} \boldsymbol{)} \)
A . 2.700 \( g m / c m^{3} \)
в. 2.7 \( g m / c m^{3} \)
c. \( 0.27 g m / c m^{3} \)
D. \( 2.70 g m / c m^{3} \)


Find the value of \( k \) for which \( f(x)= \) \( \left\{\begin{array}{l}\frac{1-\cos 4 x}{8 x^{2}}, \text { when } x \neq 0 \\ k, \quad \text { when } x=0\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0} \)


Alary muscle is associated with
A. Heart and circulation
B. Malpighian tubules and excretion
C. Trachea and respiration
D. None of the above


The colored complexes of the transition
elements have color because they:
A. have very high formation constants
B. absorb light of some visible wavelengths
C. absorb light of some ultraviolet wavelengths
D. have unpaired electrons
E. are soluble in water


If \( g \) is acceleration due to gravity on the
earth's surface, the gain in the potential energy of an object of mass \( m \) raised from the surface of the earth to a height equal to the radius \( R \) of the earth is:
A. \( 2 m g R \)
в. \( m g R \)
c. \( \frac{m g R}{4} \)
D. \( \frac{m g R}{2} \)


State the following statement is True or False
\( A \) line passing through (3,4) meets the axes \( O X \) and \( O Y \) at \( A \) and \( B \)
respectively. The minimum area of the triangle \( O A B \) in square units is 34
A . True
B. False


Where does replication of centriole
occur?
A. Interplase
B. Prophase
c. Late prophase
D. Late telophase


To determine the amount of halogen in an organic compound, the compound is
heated with fuming \( H N O_{3} \) in presence
of


Find the velocity \( v \) of the rocket at the
moment when its mass is equal to \( m \), if at the initial moment it possessed the
mass \( m_{0} \) and its velocity was equal to
zero.
A \( \cdot \vec{v}=-\vec{u} \ln \frac{m}{m_{0}} \)
B・ \( \vec{v}=\vec{u} \ln \frac{m}{m_{0}} \)
c. \( \vec{v}=\vec{u} \ln \frac{m_{0}}{m} \)
D・ \( \vec{v}=-\vec{u} \ln \frac{m_{0}}{m} \)


A parallel plate capacitor (fig.) made of circular plates each of radius \( \boldsymbol{R}= \) \( 6.0 \mathrm{cm} \) has a capacitance \( C=100 \mu \mathrm{F} \)
The capacitor is connected to a \( 230 V \) ac supply with a (angular) frequency of 300 rad \( s^{-1} . \) What is the \( r m s \) value of
the conduction current?


Which of the following is not a chemical change?
A. Whipping eggs
B. Burning woodd
c. Digestion
D. All of above


If one of the two electrons of a \( \boldsymbol{H}_{2} \)
molecule is removed, we get a hydrogen
molecular ion \( \boldsymbol{H}_{2}^{+} . \) In the ground state
of an \( H_{2}^{+}, \) the two protons are separated by roughly \( 1.5 A \), and the electron is roughly \( 1 A \) from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.


The minimum value of \( 64 \sec \theta+ \)
\( 27 \cos e c \theta \) when \( \theta \operatorname{lies} \operatorname{in}\left(0, \frac{\pi}{2}\right) \) is
A . 125
в. 625
c. 25
D. 1025


For the same statement as above, the
ratio of the two image sizes for these two positions of the lens is
A. True
B. False


An object travels 10 s with uniform acceleration along a straight line path. During this period if the velocity of the object is increased from
\( 5 m s^{-1} \) to \( 25 s^{-1}, \) then find the distance
travelled by the body?
A . \( 150 \mathrm{m} \)
B. 100 m
c. \( 125 \mathrm{m} \)
D. \( 175 \mathrm{m} \)


Amino acids are building blocks of:
A. carbohydrates
B. proteins
c. vitamins
D. fats


An inductor, a resistor and a capacitor are joined in series with an AC source. As the frequency of the source is
slightly increased from a very low value, the reactance of the
A. inductor increases
B. resistor increases
c. capacitor increases
D. circuit increases


Boiling point is least for:
\( \mathbf{A} \cdot H F \)
в. \( H C l \)
\( \mathbf{c} \cdot H B r \)
D. \( H I \)


p-subshell can accommodate a maximum of how many electrons?
A. 6
B. 8
\( c \cdot 4 \)
\( D \)


In the following reaction \( H_{2} O_{2} \) acts as:
\( A g_{2} O+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \)
A. oxidising agent
B. reducing agent
c. bleaching agent
D. none


A thin rod of length \( 3 \mathrm{L} \) is bent at right
angles at a distance \( L \) from one end.
Locate the centre of mass of the
arrangement w.r.t the corner (see figure). (Given, \( L=1 \mathrm{m} \) )
\( \mathbf{A} \cdot r_{C O M}=(0.2 \hat{i}+0.8 \hat{j}) \mathrm{m} \)
B \( \cdot r_{C O M}=(0.4 \hat{i}+0.6 \hat{j}) \mathrm{m} \)
\( \mathbf{c} \cdot r_{C O M}=(0.5 \hat{i}+\hat{j}) m \)
\( \mathbf{D} \cdot r_{C O M}=(0.2 \hat{i}+0.6 \hat{j}) m \)


2
6
3


At \( 473 \mathrm{K} \), equilibrium constant, \( K_{c} \) for
decomposition of phosphorus pentachloride, \( \boldsymbol{P} \boldsymbol{C l}_{5} \) is \( \boldsymbol{8} . \boldsymbol{3} \times \boldsymbol{1 0}^{-3} . \) If
decomposition is depicted as:
\( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P C l}_{3(g)}+\boldsymbol{C l}_{2(g)} ; \triangle_{r} \boldsymbol{H}^{0}= \)
\( 124.0 k m o l^{-1} \) what would be the effect
on reaction if the temperature is increased?
A. Reaction will shift in the backward direction
B. Reaction will shift in the forward direction
c. Reaction is equilibrium
D. Reaction first moves forward and then remains at equilibrium


Hysteresis is shown by which of the following materials
A. paramagnetic only
B. ferromagnetic only
c. diamagnetic only
D. both B and C


The number of dissimilar terms in the
expansion of \( \left(1-3 x+3 x^{2}-x^{3}\right)^{20} \) is
A . 21
B. 32
c. 41
D. 61


An electric motor rotates a wheel at a
constant angular velocity \( \omega \) while
opposing torque is \( \tau \). The power of that
electric motor is :
A \( \cdot \frac{\pi}{2} \)
B. \( \pi \)
\( c \cdot 2 \tau \omega \)
D. \( \frac{\tau}{\omega} \)


The angle between reflected and
refracted beams is \( 90^{0} \) in the water air
interface. The angle of incidence in
water is
A \( \cdot 60^{\circ} \)
В. \( 53^{\circ} \)
\( c \cdot 30^{0} \)
D. 37


Amina thinks of a number and
subtracts \( \frac{5}{2} \) from it. She multiplies the
result by 8. The result now obtained is 3 times the same number she thought of What is the number?
A . 1
B. 4
\( c .9 \)
D. 5


Detergents do not give scum with hard water because they have:
A. ammonium salts of long chain carboxylic acids
B. sulphonate salts of long chain carboxylic acids
c. both A and B
D. none of these


Which of the following statements is/are true?
1) \( P H_{5} \) and \( B i C l_{5} \) do not exist.
2) \( p \pi-d \pi \) bond is present in \( S O_{2} \)
3) \( I_{3}^{+} \) has bent geometry.
4) \( \operatorname{Se} F_{4} \) and \( C H_{4} \) have same shape
\( A \cdot 1,2,3 \)
в. 1, 3
\( c \cdot 1 \) and 2
D. 1,2,4


For the reaction
\( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
A. \( \Delta H=\Delta E+R T \)
в. \( \Delta H=\Delta E-R T \)
c. \( \Delta H=\Delta E+2 R T \)
D. \( \Delta H=\Delta E-2 R T \)


The correct sequence of taxonomic
hierarchy is
A. Genus \( \rightarrow \) Family \( \rightarrow \) Class \( \rightarrow \) Order \( \rightarrow \) Phylum \( \rightarrow \) Kingdom \( \rightarrow \) Species
B. Species \( \rightarrow \) Genus \( \rightarrow \) Family \( \rightarrow \) Order \( \rightarrow \) Class \( \rightarrow \)
Phylum\( \rightarrow \)Kingdom
c. Species \( \rightarrow \) Family \( \rightarrow \) Genus \( \rightarrow \) Kingdom \( \rightarrow \) Order\( \rightarrow \)Class\( \rightarrow \)Phylum
D. Species \( \rightarrow \) Genus \( \rightarrow \) Family \( \rightarrow \) Class \( \rightarrow \) Order \( \rightarrow \)
Phylum\( \rightarrow \)Kingdom


Write one solution of the equation \( 2 x+ \)
\( \boldsymbol{y}=\mathbf{1 0} \)


Surfactants, having both cationic and anionic centres attached to the same
molecule, are called:
A . cationic surfactant
B. anionic surfactant
c. zwitter-ionic surfactants
D. neutral surfactants


It is a copper moss
A. Bryum
B. Tortella
c. Merceya
D. All of these


(a) Differentiate between soap and
detergents.
(b) Why pure acetic acid is called glacial acetic acid?
(c) What is covalent bond? Write two
properties of covalent compounds.


There are no intercellular spaces in
epithelial tissue
A. True
B. False


Decomposition also has a role to play during photosynthesis. Support the statement.


Growth hormone is secreted by adrenal
gland.
A. True
B. False


A hemispherical bowl is made of steel
\( 0.25 c m \) thick. The inside radius of the
bowl is \( 5 \mathrm{cm} \). Find the volume of steel
used in making the bowl in \( c m^{3} \)


Which compound gives reaction with 2,4-dinitro phenyl hydrazine?
A.
в.
\( c \)
D. All of these


Two angles of a hexagon are \( 90^{\circ} \) and
\( 10^{\circ} \) remaining four angles are equal find each equal angle.


A metal ball \( B_{1} \) (density \( 3.2 g / c c \) ) is dropped in water, while another metal
ball \( B_{2} \) (density \( 6.0 g / c c \) ) is dropped in
a liquid of density \( 1.6 g / c c \). If both the
balls have the same diameter and
attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is
A . 2.0
B. 0.5
c. 4.0
D. Indeterminate due to insufficient dat


The volume of the greatest sphere cut off from a cylindrical wood of base radius \( 1 \mathrm{cm} \) and height \( 5 \mathrm{cm} \) is
A \( \cdot \frac{4}{3} \times(5 \pi) c m^{3} \)
в. \( \frac{4}{3} \pi c m^{3} \)
c. \( 5 \pi c m^{3} \)
D. \( \frac{10 \pi}{3} \mathrm{cm}^{3} \)


Following is the distribution of the size of certain farms from a taluka (tehasil)
Find median size of farms.
\( \operatorname{size} \)
\( \begin{array}{ll}\text { of } & 5 \\ \text { farm } & -\end{array} \)
15
25
35
(in
25
\( 35 \quad 45 \)
\[
15
\]
acres
No. of
2
25
farms
A . 33.60 Acres
B. 37.60 Acres
c. 38.60 Acres
D. 40.60 Acres


Given \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=-\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
and \( \vec{c}=-\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{i}}-\hat{\boldsymbol{k}} \cdot \boldsymbol{A} \) unit vector
perpendicular to both \( \vec{a}+\vec{b} \& \vec{b}+\vec{c} \) is
A \( \cdot \frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}} \)
B. \( j \)
\( c \cdot \hat{k} \)
D. \( \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \)


The equation of ellipse whose major axis is along the direction of \( x \) -axis, eccentricity is \( e=2 / 3 \)
A \( \cdot 36 x^{2}+20 y^{2}=405 \)
B . \( 20 x^{2}+36 y^{2}=405 \)
c. \( 30 x^{2}+22 y^{2}=411 \)
D. \( 22 x^{2}+32 y^{2}=409 \)


Bryophyta are not tall plants due to
A. Absence of meristem
B. Absence of vascular tissues
C. Presence of root system
D. All of the above


If is a binary operation such that \( a * \)
\( b=a^{2}+b^{2} \) then \( 3 * 5 \) is
A . 34
B. 9
\( c \cdot 8 \)
D. 25


When \( N a H C O_{3} \) is added in small
quantity in an experiment showing photosynthesis, what will be the effect
on it?
A. Rate will be lowered
B. Rate will be increased
c. Rate will be normal
D. Process will stop


The lines tangent to the curves \( y^{3}- \) \( x^{2} y+5 y-2 x=0 \) and \( x^{4}-x^{3} y^{2}+ \)
\( 5 x+2 y=0 \) at the origin intersect at
an angle \( \theta \) equal to
A \( \cdot \frac{\pi}{6} \)
B.
c.
D.


Solve \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{f(x)-f\left(\frac{\pi}{4}\right)}{x-\frac{\pi}{4}}, \) where
\( f(x)=\sin 2 x \)


The angular velocity \( \omega(\text { in } \mathrm{rad} / \mathrm{s}) \) is:
A .25
B. 100
\( c .50 \)
D. 75


State whether True or False
It is possible that a battery has some constant value of emf but the potential difference between the plates is zero.
A. True
B. False


Name the three kinds of blood vessels
found in human beings. With the help of suitable diagrams, differentiate between them.


When an object moves with a constant acceleration, under the influence of force of gravitation of the earth only, the object is said to have:
A . free fall
B. accelerated fall
c. projectile motion
D. constant velocity


Consider the following Lewis
Dot structure:
\( [: \ddot{\boldsymbol{N}}=\boldsymbol{N}=\ddot{\boldsymbol{N}}:]^{-} \)
The formal charge on the central \( N \) atom is:


If \( 1 c a l=4.2 J, \) then \( 0.2 c a l g^{-1} o C^{-1}= \)
\( \ldots J k g^{-1} K^{-1} \)
A . 800
B. 820
\( c \cdot 840 \)
D. 860


The given quadratic equations have real roots and roots are Real and equal, \( \sqrt{\frac{3}{2}} \)
\( \mathbf{2} \boldsymbol{x}^{2}-\mathbf{2} \sqrt{\mathbf{6} \boldsymbol{x}}+\mathbf{3}=\mathbf{0} \)
A. True
B. False


The length of the arm of a nutcracker is 15cm. A force of 22.5kgwt is required to cut a nut without cracker. Where should
the nut be placed on the cracker in order to cut it by a force of \( 2.25 k g / w t ? \)
A. \( 1 \mathrm{cm} \) from fulcrum
B. 1.5cm from fulcrum
\( \mathrm{c} .0 .5 \mathrm{cm} \) from fulcrum
D. \( 2.0 \mathrm{cm} \) from fulcrum


Genetic code is a translation of the
language of
A. RNA into that of proteins
B. Proteins into that of RNA
c. Amino acids into that of RNA
D. RNA into that of DNA


Theory of root pressure, is not
acceptable because
A. It is not a potent scientific factor informing the water upward
B. Water continues to rise without root pressure and the later has seldom been observed in gymnosperms
C. Root pressure can take water up to height 100 ft. only
D. None of the above


\( a \)
\( a \)
\( a \)
0


A particle executes simple harmonic
motion between \( \boldsymbol{x}=-\boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{x}=+\boldsymbol{A} \)
The time taken for it to go from 0 to \( A / 2 \)
to \( A \) is \( T_{2} \). Then
A \( \cdot T_{1}<T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}=T_{2} \)
D. \( T_{1}=2 T_{2} \)


An ecosystem is an interacting system
of
A. Communities
B. Communities and their physical environment
c. Populations
D. Individuals


If you chew a piece of bread for a long time it tastes sweet. Why?


The rate of reaction, \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \)
Products, is given by the equation, \( r= \)
\( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] . \) If \( \boldsymbol{B} \) is taken in large excess,
the order of reaction would be:
A .2
B.
c. 0
D. Unpredictable


An air bubble of radius \( 0.1 \mathrm{cm} \) is in a
liquid having surface tension \( 0.06 N / m \) and density \( 10^{3} k g / m^{3} . \) The pressure inside the bubble is
\( 1100 N / m^{2} \) greater than the
atmospheric pressure. At what depth is the bubble below the surface of the
liquid? \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( .0 .20 m \)
B. \( 0.15 \mathrm{m} \)
c. \( 0.1 m \)
D. \( 0.25 \mathrm{m} \)


Find the area of the region common to
be circle \( x^{2}+y^{2}=9 \) and the parabola
\( \boldsymbol{y}^{2}=\mathbf{8} \boldsymbol{x} \)


The moment of inertia of a ring of mass
\( 10 g \) and radius \( 1 c m \) about a tangent to
the ring and normal to its plane is :
A \( \cdot 2 \times 10^{-6} k g m^{2} \)
в. \( 5 \times 10^{-7} \mathrm{kgm}^{2} \)
c. \( 5 \times 10^{-8} k g m^{2} \)
D. \( 4 \times 10^{-6} k g m^{2} \)


The cathode ray experiment is conducted in a discharge tube containing four different gases \( A, B, C \) and \( D, \) the molecular weight of \( A=B>D \) \( >\mathrm{C}, \) then \( \mathrm{e} / \mathrm{m} \) as observed will be:
\( A \cdot A>B>D>C \)
B. \( A<D<B<C \)
\( \mathrm{c} \cdot \mathrm{A}=\mathrm{B}>\mathrm{D}>\mathrm{C} \)
D. \( A=B=C=D \)


Simplify: \( \sin ^{-1}(\cos x) \)


A small mass \( m \) is moved slowly from the surface of the earth to a height \( h \) above the surface. The work done (by an external agent) in doing this is
This question has multiple correct options
A. \( m g h, \) for all values of \( h \)
B. \( m g h, \) for \( h<<R \)
c. \( \frac{1}{2} \) mgR, for \( h=R \)
D. \( -\frac{1}{2} \) mgR, for \( h= \)


A couple produces
A. Linear motion
B. Rotational motion
c. Both \( A \) and \( B \)
D. Nether \( A \) nor \( B \)


The sum and sum of squares
corresponding to length \( X \) (in \( \mathrm{cm} \) ) and
weight \( \boldsymbol{y} \)
(in \( g m) \) of 50 plant products are given below:
\[
\begin{array}{l}
\sum_{i=l}^{50} \boldsymbol{X}_{i}=\mathbf{2 1 2}, \sum_{i=l}^{50} \boldsymbol{X}_{i}^{2}= \\
\mathbf{9 0 2 . 8}, \sum_{i=l}^{50} \boldsymbol{y}_{i}=\mathbf{2 6 1}, \sum_{i=l}^{50} \boldsymbol{y}_{i}^{2}=\mathbf{1 4 5 7 . 6}
\end{array}
\]
Which is more varying the length or weight?


A cube has a side \( l=1.2 \times 10^{-2} \mathrm{m} \)
Calculate its volume \( \left(\operatorname{in} m^{3}\right) \)
A \( \cdot 1.7 \times 10^{-6} \)
В. \( 1.728 \times 10^{-6} \)
c. \( 1.8 \times 10^{-6} \)
D. \( 2 \times 10^{-6} \)


Photovoltaic cells are used in
(i) static charge generator
(ii) printers
(iii) solar panels
(iv) xerox
A . (i), (ii)
B. (i), (iii)
c. (i), (ii), (iii)
D. all of these


Heating of oxalic acid with conc \( . \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
evolves:
This question has multiple correct options
A. \( C O \)
в. \( C O_{2} \)
\( c \cdot S O_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


An electron and a proton are projected with same velocity perpendicular to a
magnetic field. Which particle have greater frequency?


\( x \)
4
ser \( x^{2} \)
and


Polymers are often gigantic molecules consisting of long chains of repeating chemical-units. Which of the following is not a polymer?
A. Rubber
B. Cellulose
c. Protein
D. Glucose


On electrolysing \( K_{2} S O_{4} \) solution using inert electrodes, \( 1.68 L(\mathrm{STP}) \) of gases was
obtained. How many moles of \( M n O_{4}^{-} \) could be reduced to \( M n^{2+} \) by the same
quantity of electricity?
A . 0.10
B. 0.20
c. 0.15
D. 0.02


A foil of aluminium of negligible thickness is inserted in between the
space of a parallel plate condenser. If the foil is electrically insulated, the capacity of the condenser will :
\( A \). increase
B. decrease
c. remain unchanged
D. become zero


Find the direction cosines \( l, m, n \) of a line which are connected by the relation \( l+m-n=0 \) and \( 2 m l-2 m n+n l= \)
0
This question has multiple correct options
A \( \cdot \frac{-2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}} \)
в. \( \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{1}{\sqrt{6}} \)
c. \( \frac{-2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{6}} \)
D. \( \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}} \)


A person weighs 60 kg. The area under the foot of the person is \( 180 \mathrm{cm}^{2} \). Find
the pressure exerted on the ground by
the person. (Take \( \boldsymbol{g}=\mathbf{9 . 8 m s}^{-\mathbf{2}} \) ).
A . \( 32.6 \times 10^{2} P a \)
в. \( 32.6 \times 10^{3} P a \)
c. \( 32.6 \times 10^{4} P a \)
D. \( 32.6 \times 10^{5} P a \)


The displacement \( x \) of a particle varies
with time according to the relation \( \boldsymbol{x}= \)
\( \frac{a}{b}\left(1-e^{-b t}\right) . \) Which of the following is
not correct? \( (a \text { and } b \) are the positive constants.
A \( \cdot \operatorname{At} t=\frac{1}{b}, \) acceleration of the particle is \( -\frac{a b}{e} \)
B. The velocity and acceleration of the particle at \( t=0 \) are \( a \) and \( -a b, \) respectively.
C. The particle cannot reach a point at a distance \( x^{\prime} \) from its starting position if \( x^{\prime}>a / b \)
D. The particle will come back to its starting point as \( t \rightarrow \infty \)


Identify the correct ground state
electrons configuration for \( \boldsymbol{C r} \) :
\( \mathbf{A} \cdot[A r] 3 s^{2} 3 d^{4} \)
B . \( [A r] 3 s^{2} 3 d^{5} \)
c. \( [A r] 4 s^{2} 3 d^{5} \)
D \( \cdot[A r] 4 s^{2} 3 d^{4} \)
E \( \cdot[A r] 4 s^{1} 3 d^{5} \)


Calculate the ratio of average K.E of one molecule of diatomic (rigid) and
diatomic (elastic)at temperature
\( 150^{\circ} \mathrm{C} \)


Some animals living in water have streamlined body shapes. This helps to
A. Store food and fats
B. Reduce resistance in water
c. Reduce loss of water
D. Keep the body warm


\( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C H}_{2} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\longrightarrow} ? \)
Select the correct statement(s)
regarding the (major) product formed in the above reaction:
A. it reduces Fehling's solution
B. it is oxidised by Tollen's reagent
c. it decolourises \( B r_{2}-C C l_{4} \)
D. it gives iodoform test


The state of hybridization of carbon
atom in cyclopropane is:
\( A \cdot s p^{3} \)
B \( \cdot s p^{2} \)
c. \( s p \)
D. \( s p^{3} d \)


Choose the correct answer form the
alternatives given.

All alkali halides are soluble in water
except LiF. The low solubility of LiF in
water is due to its
(i) the low
solubility of Csl is due to
(ii).
LiF is soluble in
A. (i)-low lattice enthalpy (ii)-large hydration enthalpy
(iii)-polar solvents
B. (i)-high lattice enthalpy
(ii)-smaller hydration enthalpy (iii)-non-polar solvents
C . (i)-high hydration enthalpy (ii)-high lattice enthalpy
(iii)-non-polar solvents
D. (i)-smaller high hydration enthalpy (ii)-lattice enthalpy (iii)-polar solvents


The process of forming large crystals of pure substances from their solutions is
known as
A. evaporation
B. purification
c. condensation
D. crystallisation


A change of \( 8 m A \) in the emitter current brings a change of \( 7.9 m A \) in the collector current. The value of \( \beta \) is
A. \( 79 / 80 \)
в. \( 80 / 79 \)
c. 79
D. 80


The acceleration of a particle as
observed from two different frames \( S_{1} \)
and \( S_{2} \) have equal magnitudes of 2
\( m s^{-2} \)
This question has multiple correct options
A. The relative acceleration of the frame may either be zero or \( 4 \mathrm{ms}^{-2} \)
B. Their relative acceleration may have any value between zero to \( 4 \mathrm{ms}^{-2} \)
C. Both the frames may be stationary with respect to the earth
D. The frames may be moving with same acceleration in same direction


Suppose that on the interval [-2,4] the function \( f \) is differentiable, \( f(2)=1 \)
and \( |\boldsymbol{f}(\boldsymbol{x})| \leq \mathbf{5} . \) Find the bounding
function of \( \boldsymbol{f} \) on \( [-\mathbf{2}, \mathbf{4}], \) using LMVT.
A. \( y=-5 x-9 \) and \( y=5 x+11 \)
B. \( y=-5 x+9 \) and \( y=5 x+11 \)
c. \( y=5 x-9 \) and \( y=5 x-11 \)
D. \( y=5 x+9 \) and \( y=5 x-11 \)


A card from a pack 52 cards is lost. From the remaining card of the pack, one card is drawn and is found be
heart, Find the probability that the lost cards were both hearts.


Which of the following statements is
wrong?
A. All the detergents are surfactants.
B. All the soaps are anionic class of detergents.
C. Surfactants possess surface activity whereas detergents possess surface activity as well as cleansing action.
D. All the surfactants are colloidal electrolytes.


The arrangement of the following sets in the proper order is
A. Domain of \( \frac{|\boldsymbol{x}|}{\boldsymbol{x}} \)
B. Range of \( \operatorname{cosec} x \)
C. Range of cot \( x \)
D. Domain of \( \sqrt{x^{2}-4} \)
A. \( C \subset A \subset B \subset D \)
в. \( D \subset B \subset C \subset A \)
c. \( C \subset A \subset D \subset B \)
D. \( D \subset B \subset A \subset C \)


The half-cell reaction is the one that:
A. takes place at one electrode
B. consumes half a unit of electricity
C. involves half a mole of electrolyte
D. goes half way to completion


The \( e / m \) value for cathode rays:
A. varies with the nature of the gas
B. does not vary with the nature of gas
C. could not be determined by J.J Thomson
D. both (b) and (c) are correct


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x & \text { if } & x \text { is rational } \\ 2-x & \text { if } & x \text { is irrational }\end{array} \) Then \right.
fof \( (x) \) is continuous
A. everywhere
B. no where
c. at all irrational \( x \)
D. at all rational \( x \)


Elements are characterized by the
of their atoms.
A. electrons
B. mass
c. protons
D. shape


A body of mass \( 2 \mathrm{kg} \) is thrown vertically upwards with an initial velocity of 20 \( \mathrm{m} / \mathrm{s} . \) What \( \mathrm{m}: \) potential energy at the end of \( 2 s ? g=10 m / s^{2} \)


Oersted and Faraday unified which of the following achievements?
A. Electric and magnetic phenomena
B. Electromagnetism and optics
c. Electro-weak forces
D. Terrestrial and celestial


Which statement is correct for blood
pressure
A. The instrument by which we can measure B.P. is called stethoscope
B. Normal B.P. of the healthy person is \( 140 / 80 \mathrm{mm} \) Hg.
C. Diastolic pressure that shows the state of heart relaxation.
D. Systolic pressure limit is 140 \( \mathrm{mm} \mathrm{Hg} \)


Holoenzymes are complete and active
enzymes.
A. True
B. False


State whether True or False.
Factorization of \( a^{2}-16 b^{2}-2 a-8 b \) is
\( (a+4 b)(a-4 b-2) \)
A. True
B. False


Three capacitors \( 2 \mu F, 3 \mu F \) and \( 6 \mu F \) are connected in series. The effective
capacitance of the combination is:
\( \mathbf{A} \cdot 11 \mu F \)
в. \( 1 \mu F \)
c. \( 1.2 \mu F \)
D. \( 2 \mu F \)


D.E whose solution is \( \boldsymbol{y}= \)
\( e^{x}\left(c_{1} \cos 2 x+c_{2} \sin 2 x\right): \)
\( \mathbf{A} \cdot y_{2}-2 y_{1}+5 y=0 \)
B . \( y_{2}-6 y_{1}+4 y=0 \)
c. \( y_{2}-5 y_{1}+2 y=0 \)
D. \( y_{2}-y_{1}+4 y=0 \)


The inspiratory reserve volume \( + \) tidal
volume + expiratory reserve volume is
the same as
A. Inspiratory capacity + expiratory reserve volume
B. Total lung capacity - functional residual capacity
C. Inspiratory capacity + functional residual capacity
D. Inspiratory capacity + residual volume


Which specific process has negative value of specific heat?
A. Saturated vapours
B. Ice
c. water
D. Vapours


If \( \bar{a}=\bar{i}+2 \bar{j}, \bar{b}=-2 \bar{i}+\bar{j}, \bar{c}=4 \bar{i}+3 \bar{j} \)
find \( x \) and \( y \) such that \( \bar{c}=x \bar{a}+y \bar{b} \)


The gravitational force is a force
A. non-contact force
B. contact
c. frictional
D. destructive


Which of the following statements is
NOT true?
A. When the mass of a body is doubled, the momentum of a body is halved, provided the velocity remains the same.
B. The pain we feel in the hand on hitting the wall is a consequence of Newton's third law of motion.
C. A table-cloth which is pulled from a table without dislodging the dishes is due to inertia of rest.
D. Momentum is a vector quantity


\( \mathbf{f} \boldsymbol{x}=\frac{1}{\mathbf{5}+\frac{\mathbf{1}}{\mathbf{5}+\frac{\mathbf{1}}{\mathbf{5}+} \cdots \cdots}}^{\text {then }} \)
A \( \cdot x^{2}+5 x-1=0 \)
B . \( x^{2}-5 x-1=0 \)
C \( \cdot x^{2}-5 x+1=0 \)
D. \( x^{2}+5 x+1=0 \)


Two identical metallic spheres \( A \) and \( B \) of exactly equal masses are given equal positive and negative charge respectively. Then:
A. mass of \( A> \) Mass of B
B. mass of A <Mass of B
c. mass of \( A= \) Mass of B
D. mass of \( A \geq \) Mass of B


A 280 -day-old radioactive substance
shows an activity of 6000 dps. 140 days
later its activity becomes 3000 dps. What was its initial activity?
A. 20000 dps
в. 24000 dps
c. 120000 dps
D. \( 6000 d \) p


The wind appears to blow from north to
a man moving in the north-east
direction. When he doubles his velocity,
the wind appears to move in the
direction cot \( ^{-1} \)
(2) east of north. If the
actual magnitude of velocity of the wind
is \( V=\frac{1}{\sqrt{x}} \times \) magnitude of velocity of
man and direction along east. Find \( x \)


On a two-lane road, car A is travelling
with a speed of \( 36 \mathrm{km} h^{-1} . \) Two cars \( \mathrm{B} \) and \( C \) approach car \( A \) in opposite
directions with a speed of \( 54 \mathrm{km} h^{-1} \) each. At a certain instant, when the
distance \( A B \) is equal to \( A C, \) both being 1
\( \mathrm{km}, \mathrm{B} \) decides to overtake \( \mathrm{A} \) before \( \mathrm{C} \) does. The minimum required
acceleration of car \( \mathrm{B} \) to avoid an
accident is
A \( \cdot 1 \mathrm{m} \mathrm{s}^{-2} \)
B. \( 1.5 \mathrm{m} s^{-2} \)
\( \mathbf{C} \cdot 2 \mathrm{m} s^{-2} \)
D. 3 \( \mathrm{m} \mathrm{s}^{-2} \)


Which of the following eletrolyte will have maximum flocculation value for
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol?
A . \( N a C l \)
в. \( N a_{a} S \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{3} P O_{4} \)
D. \( K_{2} S O_{4} \)


Degree of the polynomial
\( \left(a^{2}+1\right)(a+2)\left(a^{3}+3\right) \) is
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
\( D \)


Which of the following contains same number of elements?
A. 1st period and Ogroup
B. 6th period and III B group
c. 5th period and III B group
D. 3rd period and VII A group


In \( 1- \) butene number of \( \sigma \) - bonds is:
A . 8
B. 10
c. 11
D. 12


In shown fig. the circular loop of wire is
moved with velocity towards the infinite
current carrying wire. Then
A. No current is induced in loop
B. Current is induced in loop clockwise
c. Current is induced in loop anticlockwise
D. Extra charges are induced on the wire loop


In Fraunhofer diffraction pattern, slit
width is \( 0.2 m m \) and screen is at \( 2 m \)
away from the lens. If wavelength of light used in \( 5000 A \) then the distance
between the first minimum on either
side of the central maximum is \( (\boldsymbol{\theta} \) is
small and measure in radian):
A \( \cdot 10^{-1} m \)
B. \( 10^{-2} \) m
c. \( 2 \times 10^{-2} m \)
D. \( 2 \times 10^{-1} m \)


Describe balance of oxygen in the air.


Negation of "A is in Class \( X^{t h} \) or \( B \) is in
\( \boldsymbol{X} \boldsymbol{I} \boldsymbol{I}^{t h^{\prime \prime}} \) is
A. A is not in class \( X^{t h} \) but \( B \) is in \( X I I^{t h}^{h} \)
c. Either A is not in class \( X^{t h} \) or \( \mathrm{B} \) is not in \( X I I^{t h} \)
D. none of these


Write Newland's Law of Octaves.
Write the name of element having similar properties of the following.
(a) Nitrogen
(b) Lithium


Match List I and List II.
List I
A. Americium
1. Lanthanide
B. Lanthanum
2. Transition metal
C. Promethium
3. Actinide
D. Technician
4. Synthetic element
5. Radioactive element
B. \( A-3,5 ; B-4 ; C-5 ; D-2 \)
c. \( A-5 ; B-1,3 ; C-2,3 ; D-4 \)
D. A - 2,5; B - 2; C - 1,5; D - -


Suppose \( A \) and \( B \) are two \( 3 \times 3 \) non
singular matrices such that \( (A B)^{k}= \)
\( \boldsymbol{A}^{k} \boldsymbol{B}^{k} \)
for \( k=2008,2009,2010, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A B^{-1} A^{-1}=B^{-1} \)
B. \( A^{-1} B^{-2} A=B^{2} \)
\( \mathbf{c} . A B=B A \)
D. \( A^{-2} B^{2} A^{2}=\left(A^{-1} B A\right)^{2} \)


How many play hockey only?


Calculate pH at which \( M g(O H)_{2} \) begin to precipitate form a solution
containing \( 0.1 \mathrm{M} M g^{2+} \) ions.
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}=\mathbf{1} \times \mathbf{1 0}^{-11} \)


\( \boldsymbol{f}(\boldsymbol{\theta})=\sin \theta(\sin \theta+\sin 3 \boldsymbol{\theta}) \operatorname{then} \boldsymbol{f}(\boldsymbol{\theta}) ? \)
\( A \cdot \geq 0 \) only when \( \theta \geq 0 \)
B. \( \leq 0 \) for all real \( \theta \)
\( \mathbf{c} . \geq 0 \) for all real \( \theta \)
D. \( \leq 0 \) only when \( \theta \leq 0 \)


The resistance of a carbon filament at
\( 0^{\circ} \mathrm{C} \) is \( 104 \Omega \). It is connected in series
with an iron wire. The temperature coefficients of resistivity of carbon and
iron are -0.0003 and 0.0052 per \( ^{o} C \) respectively. What must be the resistance of iron wire so that the
combined resistance does not change with temperature?
A \( .1 .8 \Omega \)
B. 3.7 \( \Omega \)
c. \( 6.0 \Omega \)
D. 15 \Omega


Calorific value of \( \boldsymbol{H}_{2} \) gas is \( \mathbf{x} \) kJ \( / \mathrm{g} \) m.
What is heat of formation of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
\( A . x k J \)
B. \( 2 x k J \)
c. \( x / 2 k J \)
D. \( 18 x k J \)


Aestivation of petals in the flower of
cotton is correctly shown in
\( A \)
\( (a) \)
в.
(b)
\( c \)
\( (c) \)
\( D \)
\( (d) \)


A body of mass \( m=3.513 \mathrm{kg} \) is moving
along the \( x \) -axis with a speed of
\( \mathbf{5 . 0 0 m s}^{-1} . \) The magnitude of its momentum is recorded as:
A . 17.56 kgms \( ^{-1} \)
в. 17.57 kgms\( ^{-1} \)
c. \( 17.6 \mathrm{kgms}^{-1} \)
D. 17.565 kgms\( ^{-1} \)


Represent \( (-1-\sqrt{3} i) \) in the polar form.


Total energy of an electron orbiting around the nucleus of an atom is
always negative. What is the significance of this?


Number of points having positive integral co-ordinate lying on the plane \( x+2 y+3 z=15 \) is \( n, \) then \( \frac{n}{2} \) is equal
to
\( \mathbf{A} \cdot \mathbf{6} \)
B. 8
c. 9
D.


Neutralization of an acid with a base,
invariably results in the production of :
\( \mathbf{A} \cdot H_{3} O^{+} \)
в. \( H_{2} \) о
c. \( H^{+} \) and \( O H^{-} \)
D. \( O H^{-} \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) reduces \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \) to \( \boldsymbol{C r}^{2+} \). The
change in oxidation number of \( \boldsymbol{C r} \) is:


The compound \( B \) formed in the
following sequences of reactions is:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{P C l_{3}}{\rightarrow} \boldsymbol{A}^{A l c . \boldsymbol{K O H}} \boldsymbol{B} \)
A. propyne
B. propene
c. propanol
D. propane


What is the full form of PCRA?
A. Petroleum conservation research association
B. petroleum consumption research association
C. petroleum conservation recorces association
D. petrochemical consumption research association


What is hydrogen azide?


Write the relation, represented by the arrow diagram given below, in roster form. Also, write the domain and range
of the relation.


A body of mass \( 1 k g \) falls from a height
of \( 5 m . \) How much energy does it
possess at any instant? (Consider \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A . \( 25 J \)
в. \( 50 J \)
c. 0
D. can not be determined with the help of given data


In the following figure, ABCD is a parallelogram and EFCD is a rectangle. Also, \( A L \perp D C . \) Prove that
(i) \( \operatorname{ar}(\mathrm{ABCD})=\operatorname{ar}(\mathrm{EFCD}) \)
(ii) \( \operatorname{ar}(\mathrm{ABCD})=\mathrm{DC} \times \mathrm{AL} \)


If \( A \) and \( B \) are two square matrices such
that \( B=-A^{-1} B A, \) then \( (A+B)^{2} \) is
equal to
\( \mathbf{A} \cdot A^{2}+B^{2} \)
в. \( O \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)


A body moving with uniform retardation
covers \( 3 k m \) before its speed is reduced to half of its initial value. It comes to
rest in another distance of :
A. \( 1 \mathrm{km} \)
B. \( 2 \mathrm{km} \)
\( \mathbf{c} .3 \mathrm{km} \)
D. \( \frac{1}{2} k m \)


A long straight wire is carrying current
\( l_{1}=\frac{2}{5} A \) along \( +z \) direction. The \( x-y \)
plane contains a closed circular loop carrying and not encircling the straight wire, then the force (in newton) on the
loop will be ?
(radius of the circular loop \( \left.\boldsymbol{R}=\frac{3}{4} \boldsymbol{m}\right) \)
A . 0
B. 2
\( c \cdot-1 \)
D.


Which of the following is the correct order of acidity of a carboxylic acid?
(i) \( C l_{3} C C O O H>C l_{2} C H C O O H> \)
\( \boldsymbol{C l C H}_{2} \boldsymbol{C O O H} \)
(ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C O O H} \)
(iii) \( F_{2} C H_{2} C O O H> \)
\( \boldsymbol{F C H}_{2} \boldsymbol{C O O H}>\boldsymbol{C l C H}_{2} \boldsymbol{C O O H} \)
A. (i) and (ii)
B. (ii) and (iii)
c. (i) and (iii)
D. (i), (ii) and (iii)


Structure of a disaccharide formed by
glucose and fructose is given above
Identify anomeric carbon atoms in monosaccharides units
A. 'a' carbon of glucose and 'a' carbon of fructose
B. 'a' carbon of glucose and 'e' carbon of fructose
c. 'a' carbon of glucose and 'b' carbon of fructose
D. 'f' carbon of glucose and 'f' carbon of fructose


Electron gain enthalpy is positive when:
A \( \cdot O^{-} \) is formed from \( O \)
B. \( O^{2-} \) is formed from \( O^{-} \)
\( \mathrm{c} \cdot O^{+} \) is formed from \( O \)
D. electron affinity is always a negative value


Which will form lactone on treatment
with NaOH?
A. \( \alpha \) -Bromo acid
B. \( \beta \) -Bromo acid
c. \( \beta \) - Hydroxy acid
D. \( \delta \) -Bromo acid


A strain of bacteria doubles in numbers
each day, if today there are 16 million
bacteria, how many days ago were there
500,000 bacteria?


A wire of uniform cross-section is
suspended vertically from fixed point with a load attached to the other end.
What will be the ratio of change in
frequency to the altered new frequency
due to arise of temperature \( t^{\circ} \) C? The
coefficient of linear expansion of wire
is \( \alpha \) and the rise of temperature t is
small.
A \( \cdot \frac{\alpha t}{4} \)
в. \( \frac{\alpha t}{2} \)
\( c \cdot \frac{3 a t}{4} \)
D. \( \alpha \)


Water rises in the stem due to
A. Cohesion and transpiration pull
B. Turgor pressure
c. osmotic pressure
D. None of the above


Which one of these is the ore of
manganese?
A. Pyrolusite
B. Cinnabar
c. Galena
D. Malachite


Find the slope of the line passing the two given points \( (a, 0) \) and \( (0, b) \)


Calculate the mass in mole of \( C O_{2} \) that
will dissolve in enough water to form
\( 900 m L \) of solution at \( 20^{\circ} \mathrm{C} \) if the
partial pressure of \( \boldsymbol{C O}_{2} \) is 1 atm. \( \boldsymbol{K}_{\boldsymbol{H}} \) for \( C O_{2} \) is \( 2.3 \times 10^{-2} \) mol \( / \) litre
\( a t m \)
A . 0.0401 mole
B. 0.0301 mole
c. 0.0217 mole
D. 0.0207 mole


If \( y=\frac{\sin ^{2} x}{1+\cot x}+\frac{\cos ^{2} x}{1+\tan x} \) then \( y^{\prime} \) is
equal to?


In the figure, \( A B C D \) is a quadrilateral.
Name a pair of opposite angles.


Which of the following is not correct regarding terylene?
A. Condensation polymer
B. Synthetic fibre
c. step-growth polymer
D. Known as dacron
E. Thermosetting plastic


If \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{t}+\frac{\mathbf{1}}{\boldsymbol{t}} \) and \( \boldsymbol{x}^{4}+\boldsymbol{y}^{4}=\boldsymbol{t}^{2}+ \)
\( \frac{1}{t^{2}} \) then \( \frac{d y}{d x}= \)
A \( \cdot-\frac{x}{y} \)
в. \( \frac{-y}{x} \)
c. \( \frac{x^{2}}{y^{2}} \)
D. \( \frac{y^{2}}{x^{2}} \)


Why do we not hear the screams of a bat
A. screams are below \( 30,000 \mathrm{Hz} \)
B. the screams are infra sonic
C. the screams are ultra sonic
D. all


If \( \boldsymbol{A}=\int_{1}^{\sin \theta} \frac{\boldsymbol{t}}{1+\boldsymbol{t}^{2}} \boldsymbol{d} \boldsymbol{t} \) and
\( B=\int_{1}^{\operatorname{cosec} \theta} \frac{1}{t\left(1+t^{2}\right)} d t, \) then the value
of determinant \( \left|\begin{array}{ccc}\boldsymbol{A} & \boldsymbol{A}^{2} & \boldsymbol{B} \\ \boldsymbol{e}^{\boldsymbol{A}+\boldsymbol{B}} & \boldsymbol{B}^{2} & -\mathbf{1} \\ \mathbf{1} & \boldsymbol{A}^{2}+\boldsymbol{B}^{2} & -\mathbf{1}\end{array}\right| \)
is
\( A \cdot \sin \theta \)
B. \( \operatorname{cosec} \theta \)
\( c \)
D.


Find direction cosine line \( \boldsymbol{x}=\mathbf{3} \boldsymbol{z}+ \)
\( \mathbf{2}, \boldsymbol{y}=\mathbf{2}-\mathbf{5} \boldsymbol{z} \)


Bakelite is a polymer of
A. benzaldehyde and phenol
B. acetaldehyde and phenol
C. formaldehyde and phenol
D. formaldehyde and benzyl alcohol


Fill in the blanks.
The nuclear reaction that can not be
controlled at present is


Assertion: Rusting of Fe is quicker in saline water than in ordinary water.
Reason: Presence of \( N a^{+} \) and \( C l^{-} \) ions
increase the conductance of the saline
water
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Find the value of following determinant. \( \left|\begin{array}{cc}-1 & 7 \\ 2 & 4\end{array}\right| \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}- \)
\( 3 x+5, \) then find the value of
\( \frac{\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{h}} \) at \( \boldsymbol{h} \neq \mathbf{0} \)
A. \( 4 x+2 h \)
B. \( 4 x+2 h-3 \)
c. \( 4 x-2 h+3 \)
D. \( 4 x-2 h-3 \)


High biological oxygen demand
indicates:
A. the absence of microbial pollution
B. moderate microbial pollution
c. the intense level of microbial pollution
D. all of these


If an object of \( 10 \mathrm{cm} \) height is placed at
a distance of \( 36 \mathrm{cm} \) from a concave
mirror of focal length \( 12 \mathrm{cm} \), find the
position, nature and height of image.


Which of the following reasons can be attributed to prevention of rusting by zinc coating?
A. zinc acts as cathode
B. Zinc acts as anode
c. Iron acts as anode
D. Both (a) and (c)


Two coherent waves are represented by
\( \boldsymbol{y}_{1}=\boldsymbol{a}_{1} \cos \omega t \) and \( \boldsymbol{y}_{2}=\boldsymbol{a}_{2} \sin \omega t . \) The
resultant intensity due to interference will be
B. \( \left(a_{1}^{2}+a_{2}^{2}\right) \)
c. \( \left(a_{1}-a_{2}\right) \)
and
D \( \cdot\left(a_{1}+a_{2}\right) \)


Find the square of common ratio in given G.P. \( \sqrt{\mathbf{2}}, \sqrt{\mathbf{6}}, \mathbf{3} \sqrt{\mathbf{2}}, \mathbf{3} \sqrt{\mathbf{6}} \)


How can the current rating of a cell be increased?
A. by increasing friction
B. by increasing voltage
c. by increasing electrostatic
D. cant be increased


Which of the following constitutes a wind energy
A . Sea breeze
B. Land Breeze
c. Both A and B
D. none of these


A circular coil of wire of \( n \) turns has a
radius \( r \) and carries a current \( i \). Its
magnetic dipole moment is \( M . \) Now the coil is unwound and again rewound into a circular coil of half the initial radius
and the same current is passed through it, then the dipole moment of this new coil is :
A \( \cdot \frac{M}{2} \)
в. \( \frac{M}{4} \)
c. \( M \)
D. 2 \( M \)


Consider the following statements.
I Pig iron is malleable and ductile.
Il : Pig iron can be melted to produce cast iron of desired shapes.
III : Wrought iron is obtained by heating pig iron with iron oxide in a furnace.
Which of the statement(s) given above is/are correct?
A. I only
B. I and II
c. ॥ and III
D. III only


Assertion
Ratio of isothermal bulk modulus and
adiabatic bulk modulus for a
monoatomic gas at a glven pressure is \( \frac{3}{5} \)
Reason This ratio is equal to \( \gamma=\frac{C_{p}}{C_{v}} \)
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


Tissues losing their ability to divide define
A. Histological differentiation
B. Cellular differentiation
c. Molecular differentiation
D. None of the above


If \( a+b+c=0, \) then the equation
\( 3 a x^{2}+2 b x+c=0 \) has, in the interval
(0,1)
A. Atleast one root
B. Atmost one root
c. No root
D. None of these


Spot the mistakes in the given
statements and correct them.
(a) Lanthanides and actinides are
included in the main body of periodic
table.
(b) Titanium, chromium and
manganese are coinage elements.


The temperature bellow which a
material becomes a superconductor is called
A . critical temperature
B. absolute temperature
c. tripple point
D. none of the above


Complex number \( z \) satisfy the equation
\( |z-(4 / z)|=2 . \) Then the value of
\( \arg \left(z_{1} / z_{2}\right), \) where \( z_{1} \) and \( z_{2} \) are complex numbers with the greatest and the least moduli, can be
A . \( 2 \pi \)
в. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
D. none of these


On the axis of a transparent sphere of
refractive index \( (\boldsymbol{n}=\mathbf{2}) \& \) radius \( \mathbf{8 c m} \)
an object is kept at the distance \( 8 \mathrm{cm} \) from the surface of the sphere. Find the
minimum distance of the image after all possible refraction from the surface
of the sphere in cm.


Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( \boldsymbol{A} \)
\( \mathbf{A} \cdot(4,0,0) \)
B. (3,4,0)
C. (3,0,0)
D. (4,3,0)


Find the \( 9 t h \) term in the expansion of
\( \left(3 x-\frac{1}{2 x}\right)^{8}, x \neq 0 \)
A \( \cdot \frac{256}{x^{8}} \)
в. \( \frac{\left(x^{8}\right)^{8}}{256} \)
c. \( \frac{1}{256 x^{8}} \)
D. \( 256 x^{8} \)


The mass defect in a particular nuclear reaction in 0.3 grams.The amount of energy liberated in kilowatt hour is
\( \left(V \text { elocity of } \operatorname{light}=3 \times 10^{8} m / s\right) \)
A \( \cdot 1.5 \times 10^{6} \)
B . \( 2.5 \times 10^{6} \)
\( c \cdot 3 \times 10^{6} \)
D. \( 7.5 \times 10^{6} \)


A worker uses a forklift to move boxes hat weigh either 40 pounds or 65 pound
s each. Let \( x \) be the number of 40
pound boxes and \( y \) be the number of 65
pound. The forklift can carry upto either
45 boxes or a weight of 2400 pound Which of the following systems of inequalities represents this relationship?
\( \left\{\begin{array}{l}40 x+65 y \leq 2,400 \\ x+y \leq 45\end{array}\right. \)
в. \( \left\{\frac{y}{40}+\frac{y}{65} \leq 2,400\right. \)
c. \( \left\{\begin{array}{l}40 x+65 y \leq 45 \\ x+y \leq 2,400\end{array}\right. \)
D. \( \left\{\begin{array}{l}x+y \leq 2,400 \\ 40 x+65 y \leq 2,400\end{array}\right. \)


In the radioactive transformation \( z^{\boldsymbol{X}}^{\boldsymbol{A}} \frac{\boldsymbol{\beta}^{-}}{\boldsymbol{X}} \boldsymbol{z}+\mathbf{1} \boldsymbol{X}_{\mathbf{1}}^{\boldsymbol{A}} \)
\( z-1 X_{2}^{A-4} \longrightarrow Z_{-3} X_{3}^{A-3} \)
which are successively emitted radioactive radiations?
A \( \cdot \beta^{-}, \alpha, \beta^{-} \)
в. \( \alpha, \beta^{-}, \beta^{-} \)
\( \mathrm{c} \cdot \beta^{-}, \alpha, \alpha \)
D \( \cdot \alpha, \beta^{-}, \alpha \)


A solenoid of \( n \) turns carries current
while another solenoid of same length
and of 3 n turns carries current \( 4 I \).
What is the ratio of the magnetic strengths of the two solenoid?
A. 12 times
B. 10times
c. 7 times
D. none of the above


Assertion
Formal charges help in selection of the lowest energy structure from a number of possible lewis structure.
Reason
show +1 formal charge on central 0 marked 1.
A. Both Assertion and Reason are true and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation for Assertion
c. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statement.


In a sequence, \( a_{n}=n^{2}-1 \) then \( a_{n+1} \) is
equal to
A \( \cdot a^{2}-5 n \)
B . \( n^{2}-2 n \)
c. \( a^{2}+10 n \)
D. \( n^{2}+2 n \)


Assertion
Water drops take spherical shape when
falling freely.
Reason
Water has minimum surface tension
among all liquids.
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 radii of two concentric circles are 4
\( \mathrm{cm} \) and \( 5 \mathrm{cm}, \) then the length of each chord of one circle which is tangent to
the other circle is
A. \( 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
\( c \cdot 9 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)


If \( y=\tan ^{-1} x, \) find \( \frac{d^{2} y}{d x^{2}} \) in terms of \( y \)
alone.


Find Kinetic energy of an \( \alpha \) -particle?
\( \left.\boldsymbol{v}=\mathbf{3} \times \mathbf{1 0}^{7}\right) \)
\( \mathbf{A} \cdot 1.3 \times 10^{-5} \) erg
В \( \cdot 2.9 \times 10^{-5} \) erg
c. \( 8.0 \times 10^{18} \) erg
D. \( 8 \times 10^{-18} \) erg


Complete the following reaction:
\( N a N O_{3}+N H_{4} C l \longrightarrow ? \)
\( \mathbf{A} \cdot N a N O_{3}+N H_{4} C l \longrightarrow N H_{4} N O_{3}+N a C l \stackrel{\Delta}{\rightarrow} N_{2} O+ \)
\( 2 H_{2} O \)
B \( \cdot N a N O_{3}+3 N H_{4} C l \longrightarrow 2 N H_{4} N O_{3}+N a C l \triangleq N_{2} O+ \)
\( 2 H_{2} O \)
\( \mathbf{c} \cdot 2 N a N O_{3}+3 N H_{4} C l \longrightarrow 2 N H_{4} N O_{3}+2 N a C l \triangleq \)
\( N_{2} O+2 H_{2} O \)
D. None of these


In an experiment, 18.04 g of mannitol were dissolved in 100 g of water. The vapour pressure of water was lowered by \( 0.309 \mathrm{mm} \) Hg from \( 17.535 \mathrm{mm} \) Hg.
Calculate the molar mass of manitol.
A. \( 150.0 \mathrm{g} / \mathrm{mol} \)
в. \( 184.3 \mathrm{g} / \mathrm{mol} \)
c. \( 140.4 \mathrm{g} / \mathrm{mol} \)
D. 123.21 g/mol


Line through origin and parallel to \( Y \) -
axis is \( \dots \dots \)
A \( \cdot \frac{x}{1}=\frac{y}{0}=\frac{2}{0} \)
B. \( \frac{x}{0}=\frac{y}{1}=\frac{z}{0} \)
\( \mathbf{c} \cdot \frac{x}{1}=\frac{y}{0}=\frac{z}{1} \)
D \( \cdot \frac{x}{1}=\frac{y}{1}=\frac{z}{0} \frac{z}{0} \)


Number of obligatory categories in taxonomy are
A. 7
B. 8
\( c \cdot 9 \)
D.


A straight line parallel to the \( x \) -axis has equation
A. \( x=a \)
B . \( y=a \)
\( \mathbf{c} \cdot y=x \)
D. \( y=-x \)


In photosynthesis solar energy is captured by the pigment called


Which term in the expansion of \( (1+x)^{p} \cdot\left(1+\frac{1}{x}\right)^{q} \) is independent of \( x \)
where \( p, q \) are positive integers? What is the value of that term?


If the two handles of an hydraulic jack are balanced by two masses in the ratio \( 1: 2, \) then the respective areas are in
the ratio of:
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


In context of scattering Fine particles: \( _{---}- \) wavelength :
large particles:
wavelength
A. Long, short
B. Short, long
c. Visible, infrared
D. None of these


Among \( \mathbf{A} l_{2} \mathbf{O}_{3}, \mathbf{S i O}_{2}, \mathbf{P}_{2} \mathbf{O}_{3} \) and \( \mathbf{S O}_{2} \) the
correct order of acid strength is:
\( A \cdot S O_{2}<P_{2} O_{3}<S_{i} O_{2}<A l_{2} O_{3} \)
B. \( \operatorname{si} 0_{2}<\operatorname{SO}_{2}<\operatorname{Al}_{2} \mathrm{O}_{3}<\mathrm{P}_{2} \mathrm{O} \)
c. \( \mathrm{Al}_{2} \mathrm{O}_{3}<\mathrm{Si} \mathrm{O}_{2}<\mathrm{SO}_{2}<\mathrm{P}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{Al}_{2} \mathrm{O}_{3}<\mathrm{SiO}_{2}<\mathrm{P}_{2} \mathrm{O}_{3}<\mathrm{SO}_{2} \)


What would be the major product in the
following reaction?
A . cis-alkene
B. trans-alkene
c. alkane
D. none of these


If the angle of a prism is \( 60^{\circ} \) and angle
of minimum deviation is \( 40^{\circ}, \) then the
angle of refraction will be
A \( .30^{\circ} \)
B . \( 4^{\circ} \)
\( c \cdot 3^{\circ} \)
D. \( 1.5^{\circ} \)


The gas produced by the passage of air over hot coke is:
A. Carbon monoxide
B. Carbon dioxide
c. Producer gas
D. water gas


The strength of the magnetic field of an electromagnet :
A. is always greater than that of a permanent magnet
c. can be adjusted
D. none of the above


Name two metals that do not react with
water at all.


The number of arbitrary constant in the general solution of differential equation of order 3 is
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .3 \)
D.


A body starts to fall freely under gravity. The distances covered by it in first, second and third seconds are in ratio:
A. 1: 3: 5
5
B. 1: 2: 3
c. 1: 4: 9
D. 1: 5: 6


Which percentage is the most likely dissociation constant of a strong acid?
A . \( 0 \% \)
B . \( 0.01 \% \)
c. \( 50 \% \)
D. 99.99\%


Stepping up of voltage by a factor of 100, reduce the current by a factor of
A . 10
B. 100
c. leaves the current unchanged
D. increase the current by a factor of 100


Which of the following species can act as the strongest base?
A. \( -O H \)
B. \( -O R \)
\( \mathbf{c} \cdot-O C_{6} H_{5} \)
\( D \)


A hydrogen electrode placed in a buffer
solution of \( \mathrm{CH}_{3} \mathrm{COONa} \) and acetic acid
in the ratio's \( x: y \) and \( y: x \) has reduction electrode potential values \( \mathrm{E}_{1} \) volt and \( \mathrm{E}_{2} \)
volt respectively at \( 25^{\circ} \mathrm{C} \). The \( \mathrm{pK}_{a} \) values
of acetic acid is \( \left(\mathrm{E}_{1} \text { and } \mathrm{E}_{2} \) are oxidation \right.
potential):
A. \( \frac{E_{1}+E_{2}}{0.118} \)
в. \( \frac{E_{2}-E_{1}}{0.118} \)
c. \( -\frac{E_{1}+E_{2}}{0.118} \)
D. \( -\frac{E_{2}-E_{1}}{0.118} \)


In Young's double slit experiment the distance d between the slits \( S_{1} \) and \( S_{2} \)
is \( 1 \mathrm{mm} \). What should the width of each
slit be \( \operatorname{so~as~to~obtain~} 10^{t h} \) maxima of
the double slit pattern within the central maximum of the single slit
pattern?
A. \( 0.9 \mathrm{mm} \)
B. 0.8 mm
\( c .0 .2 \mathrm{mm} \)
D. 0.6 mm


The number of beats produces per second by two tuning forks when sounded together is \( 4 . \) One of them has frequency of \( 250 H z . \) The frequency of
the other cannot be less than
A \( .254 \mathrm{Hz} \)
B. 252 H
\( \mathrm{c} .248 \mathrm{Hz} \)
D. 246 \( H z \)


The radius of the Earth is approximately
\( 6.4 \times 10^{6} m . \) The instantaneous velocity
of a point on the surface of the Earth at
the equator is \( 4.672 \times 10^{x} \). Find the
value of \( \mathbf{x}: \)


Water scarcity is usually found in
A. Desert conditions
B. Polar regions in winter
C . Only A
D. Both A and B


Solve: \( 2-\frac{3}{5} \)


The sum of the abscissa of all the
points on the line \( x+y=4 \) that lie at a
unit distance from the line \( 4 x+3 y- \)
\( \mathbf{1 0}=\mathbf{0} \) is
A .4
B. -4
\( c .3 \)
D. - 3


Which is the gas used for making vegetables and vanaspathi from vegetable oils?


The sum of the three numbers which
are in arithmetic progression is \( 12 . \) If the third number is three times the first
number, than the product of the numbers is
A . 32
B. 40
c. 24
D. 48


If the points \( A \) and \( B \) are (1,2,-1) and
(2,1,-1) respectively, then \( \overrightarrow{A B} \) is
A. \( \hat{i}+\hat{j} \)
в. \( \hat{i}-\hat{j} \)
c. \( 2 \hat{i}+\hat{j}-\hat{k} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)


\( y=6 x^{3}+3 x^{2}+4 x+5 \)
Find the value of \( \frac{d y}{d x} ? \)


A ball dropped from a \( 20 m \) height loses
\( 40 \% \) of its energy on hitting the ground. Upto what height does the ball rebound?
\( A \cdot 28 m \)
в. \( 8 m \)
\( c .12 m \)
D. 20m


A diatomic gas is heated at certain pressure. What fraction of the heat energy is used to increase the internal
energy?
A \( .3 / 5 \)
B. \( 3 / 7 \)
c. \( 5 / 7 \)
D. \( 5 / 9 \)


Write in ascending order of the surds given in each of the following sets \( \sqrt[4]{625}, \sqrt[3]{343}, \sqrt{100} \)


During one Krebs cycle, the number of
\( C O_{2} \) molecules released is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Out of the following gases under similar condition of temperature and pressure, the velocity of sound will be maximum
in
A. hydrogen
B. nitrogen
c. oxygen
D. chlorine


Fungi lack chlorophyll and hence cannot prepare their own food. To which kingdom do fungi belong and in what form is their food reserved?
A. Mycota, starch
B. Mycota, glycogen
c. Thallophyta, starch
D. Thallophyta, glycogen


A block of mass \( \mathrm{m} \) is kept over another
block of mass \( 2 \mathrm{m} \) and the system rests
on a smooth horizontal surface. The
coefficient of friction between the
blocks is \( 0.50 . \) Find the work done by the
force of friction on the smaller block by the bigger block during a displacement
d the system, when a force mg is applied to the lower block.
\( \mathbf{A} \cdot \frac{m g d}{3} \)
B. mgd
c. \( \frac{m F d}{2(M+m)} \)
D. Zero


Assertion (A): The solubility of aldehydes and ketones in water
decreases with increase of size of the
alkyl group Reason
(R) Alkyl groups are electron releasing groups
A. Both A and R ae true and R is the correct
explanation of A
B. Both A and R are true and R is not the
correct explanation of A
c. A is true but R is false
D. A is false but R is true.


The hybridization of carbon atoms in
\( C-C \) single bond of \( H C \equiv C- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \) is:
A \( \cdot s p^{3}-s p^{3} \)
В \( \cdot s p^{2}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p 2 \)
D. \( s p^{3}-s p \)


Multiple Correct Answers Type
Suppose two particles 1 and 2 are projected in vertical plane
simultaneously.
Their angles of projection are \( 30^{\circ} \) and \( \theta \)
respectively, with the horizontal. Let
they collide after a time \( t \) in air. Then
This question has multiple correct options
A \( \cdot \theta=\sin ^{-1}(4 / 5) \) and they will have same speed just
before the collision
B . \( \theta=\sin ^{-1}(4 / 5) \) and they will have different speed just
before the collision
C . \( x<1280 \sqrt{3}-960 m \)
D. It is possible that the particles collide when both of them are at their highest point.


integrate:
\[
\int \tan ^{-1} x d x
\]


Paired spermathecae occur in Pheretima in which of the following segments?
A. 4,5,6,7
в. 5,6,7,8
\( c \cdot 6,7,8,9 \)
D. 3,4,5,6


When the nucleus of pollen grain fused with the nucleus of ovum ........... is formed.
A. Embryo
B. Fruit
c. Ovule
D. zygote


The motion of train and car belongs to:
A. Translatory motion
B. Rotary motion
c. To \& Fro motion
D. spin motion


\( (C-C l) \) bond in \( C H_{2}=C H-C l \)
(vinyl chloride) is stabilized in the same
way as in:
A. benzyl chloride
B. ethyl chloride
c. chlorobenzene
D. allyl chloride


Let \( \boldsymbol{A}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \boldsymbol{B}= \)
\( 1,3,5,7,9,10,17,26,30 . \) Which of the
following sets of ordered pairs are (i) relations
(ii) functions (iii) neither,
from \( A \) to \( B \)
(a) \( R_{1}=\{(1,3),(3,3),(5,17),(1,2)\} \)
(b) \( R_{2}=\{(3,7),(4,5),(5,30)\} \)
(c) \( R_{3}= \) \( (x, y): x \in A, y \in B, x+y=8 \)
(d) \( R_{4}= \)
\( (x, y): x \in A, y \in B, y=x^{2}+1 \)
(e) \( R_{5}= \)
\( (x, y): x \in A, y \in B, y=2 x-1 \)


Which of the following particles cannot be deflected by magnetic field?
A. Electrons
B. Neutrons
c. \( \alpha \) - particles
D. Protons


Copper matte is a molten mixture of :
A \( \cdot C u_{2} S+F e S(\text { little }) \)
в. \( C u_{2} S+ \) Fe \( O \) (little)
\( \mathrm{c} \cdot \mathrm{Cu}_{2} \mathrm{O}+\mathrm{FeO} \) (little)
D. \( C u_{2} O+F e S(\text { little }) \)


Name two intrauterine contraceptive
devices that affect the motility of
sperms


The unit of \( \frac{G}{g} \) can be written as
\( \mathbf{A} \cdot \frac{K g}{m} \)
B. \( \frac{K g}{m^{2}} \)
\( ^{\mathbf{C}} \cdot \frac{m^{2}}{K g} \)
D. \( \frac{m}{K g} \)


The degree of dissociation of \( 0.1 M \)
\( H C N \) solution is:
A \( \cdot 6.4 \times 10^{-5} \)
B . \( 6.4 \times 10^{-3} \)
c. \( 6.4 \times 10^{-2} \)
D. \( 6.4 \times 10^{-6} \)


Consider the above figure as Periodic
Table. Then the element with a possible
oxidation number of -2 is
\begin{tabular}{|c|c|c|c|c|c|}
\hline \( \mathbf{z}_{\mathbf{L i}} \) & & & & & \( \mathbf{( D )} \) & \( \mathbf{1 0} \) \\
\hline & \( \mathbf{( A )} \) & & & & \( \mathbf{( C )} \) & & \\
\hline \( \mathbf{( B )} \) & \( \mathbf{2 0} \) & & & & & \\
\hline
\end{tabular}
\( \mathbf{A} \)
\( B \)
a
\( D \)


For which range, during unloading the
above curve will be retraced?
A. up to \( O A \) only
B. up to \( O B \)
c. up to \( C \)
D. never retraced its path


Stellate chloroplast is found in
A. Spirogyra
B. Coleochaete
c. oedogonium
D. Zygnema


4 mole of \( S_{2} C l_{4}(g) \) is introduced into a
10 L vessel. The following equilibrium was establised \( S_{2} C l_{4}(g) \rightleftharpoons 2 S C l_{2}(g) \)
At equilibrium 0.2 mol of \( S_{2} C l_{4}(g) \) was present in the vessel. The value of
equilibrium constant is:


The capacity of a parallel plate condenser is \( 10 \mu F \) without the dielectric. Material with a dielectric
constant of 2 is used to fill half-
thickness between the plates. The new
capacitance is \( \mu F \)
A . 10
B . 20
c. 15
D. 13.33


There is no change in volume of a wire due to change in its length of stretching. The Poisson's ratio of the material of the wire is:
A . 0.50
B . - 0.50
\( c \cdot 0.25 \)
D . - 0.25


Calculate the area of a trapezium
whose length of the parallel sides are 30
\( \mathrm{cm} \) and \( 20 \mathrm{cm} \) and distance between the
parallel lines is \( 15 \mathrm{cm} \)


Assertion
A torch bulb give light if operated on \( A C \)
of same voltage and current as DC.
Reason

Heating effect is common to both AC
and DC.
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


Polyester consists of :
A. repeating unit of ether
B. monomer of ester
C. repeating units of ester
D. monomer of ether