Factorise each of the following:
(i) \( 8 a^{3}+b^{3}+12 a^{b}+6 a b^{2} \)
(ii) \( 8 a^{3}-b^{3}-12 a^{2} b+6 a b^{2} \)
(iii) \( 27-125 a^{3}-135 a+225 a^{2} \)
(iv) \( 64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2} \)
\( (v) 27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p \)


A person travelled a distance of \( 3 \mathrm{km} \)
along a straight line in the North direction. Then he travelled \( 2 \mathrm{km} \) in
west direction and then \( 5 \mathrm{km} \) in south
direction.The magnitude of the displace-ment of this person would be
A. \( 2 \sqrt{2} \mathrm{km} \)
B. \( 3 \sqrt{2} \) Кт
c. \( 4 \sqrt{2} \) кт
D. 10 Km


An example in which light emitting diodes are used is :
A. calculator
B. hard drive
c. optical drive
D. analog watch


Find the image of the point (2,-1,5) in the line \( \vec{r}=(11 \hat{i}-2 \hat{j}-8 \hat{k})+ \)
\( \lambda(10 \hat{i}-4 \hat{j}-1 \hat{1} k) \)


Why electrical equipment on burning do not extinguished fire by water?
A. Water shows exothermic reaction with electrical equipment
B. Water conduct electricity with electrical equipment's.
C. Water shows endothermic reaction.
D. Water is a combustible substance.


The electric current \( i \) in the circuit
shown is:
\( \mathbf{A} \cdot 6 A \)
B. \( 2 A \)
\( c \cdot 3 A \)
D. \( 4 A \)


In which property listed below hydrogen does not resemble alkali metals?
A. Tendency to form cation
B. Nature of oxide
c. Combination with halogens
D. Reducing character


Resistance of a conductor of length 'x' is
r'. If its area of cross-section is 'a', What
is its resistivity? What is its unit?


Biological weathering of rock is caused by
A. Lichens
B. Mosses
c. Roots of plants
D. All of the above


A hollow cylinder has a charge \( \boldsymbol{q} \boldsymbol{C} \)
within it. If \( \phi \) is the electric flux in units
of \( V m \) associated with the curved
surface \( \mathrm{B} \), the flux linked with the plane
surface A in units of \( V m \) will be
A \( \cdot \frac{1}{2}\left(\frac{q}{\epsilon_{0}}-\phi\right) \)
B. \( \frac{q}{2 \epsilon_{0}} \)
\( c \cdot \frac{\phi}{3} \)
D. \( \frac{q}{\epsilon_{0}}-\phi \)


If the variance of \( 1,2,3,4,5, \dots, x \) is 10
then the value of \( x \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B . 13
c. 12
D. 10
E. 11


What is an equipotential surface?


If we say that the focal length of a spherical mirror is \( n \) times its radius of
curvature, then \( n \) must be
A . 2.0
в. 1.5
\( c .0 .2 \)
D. 0.5


Choose the correct answer from the
alternatives given.
The pituitary detects a rising hormone concentration in blood and inhibits
the gland secreting the hormone. This is a feedback loop.
A. positive
B. Iong-term
c. negative
D. both (b) and (c)


An electron is shot in a steady electric and magnetic field such that its velocity is \( V \). Electric field \( E \) and
magnetic field \( \boldsymbol{B} \) are
mutually perpendicular. The magnitude
of \( \boldsymbol{E} \) is 1 volt \( / \mathrm{cm} \) and that of \( \boldsymbol{B} \) is
2 tesla. Now it happens that the Lorentz (Magnetic) force cancels with the
electrostatic force on the electron, then
the velocity of the electron is:
A. \( 50 \mathrm{ms}^{-1} \)
B. \( 2 \mathrm{cms}^{-1} \)
c. \( 0.5 \mathrm{cms}^{-1} \)
D. \( 200 m s^{-1} \)


A salt is formed due to the reaction
between an oxy acid containing chlorine and a base containing a monovalent metal of atomic mass \( x \). The number of
oxygen atoms in one molecule of the acid is more than the corresponding 'ic' acid. Calculate the molecular mass of
the salt
A \( \cdot 83.5+\frac{x}{4} \)
B. 99.5 + \( x \)
\( c \cdot 83.5+x \)
D. \( 99.5+\frac{x}{2} \)


\( \ln \operatorname{an} L-C-R \) circuit the
capacitance is changed from \( C \) to \( 4 C \)
For the same resonant frequency, the inductance should be changed from \( \boldsymbol{L} \)
to
A . L/4
B. L/2
c. 2L
D. 4L


LCD stands for:
A. Light Carrying Diode
B. Liquid Crystal Display
C . Long Crystal Display
D. Light Crystal Display


large metal sheet carries an electric current along its surface. Current per unit length is \( \lambda . \) Magnetic field near the metal sheet is
(0)(0)(0)(0)(0)(0)(0)(0)
\( A \cdot \frac{\lambda \mu}{2} \)
B. \( \frac{\lambda \mu}{2 \pi} \)
c. \( \lambda \mu_{0} \)
\( D \cdot \frac{\mu}{2 \pi \pi} \)


Simplify: \( \sin . \cot ^{-1} \tan \cdot \cos ^{-1} x \)


In the esterification \( C_{2} H_{5} O H(l)+ \)
\( \boldsymbol{C H}_{3 k e} \boldsymbol{C O O H}(l) \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{t a 5}(l)+\boldsymbol{H}_{2} \boldsymbol{O}(l) \) an
equimolar mixture of alcohol and acid taken initially yields under equilibrium,the water with mole fraction=0.333.calculate the
equilibrium constant.


Plants which are unable to prepare their food wholly or partially are
A. Autophytes
B. Heterotrophs
c. Halophytes
D. Holophytes


If in the expansion of \( (1+x)^{43}, \) the
coefficient of \( (2 r+1) t h \) term is equal
to coefficient of \( (r+2)^{t h} \) term. Find \( r \) ??


The differential equation of all circles passing through the origin and having their centres on the X-axis, is
A \( x^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( _{y^{2}}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( _{y^{2}=x^{2}+x y \frac{d y}{d x}} \)
D. \( y^{2}=x^{2}+3 x y \frac{d y}{d x} \)


A standing wave is produced on a string
fixed at one end and free at other. The
length of the string must be an
A \( \cdot \) odd integral multiple of \( \frac{\lambda}{4} \)
B. integral multiple of \( \frac{\lambda}{2} \)
c. integral multiple of \( \lambda \)
D. integral multiple of \( \frac{\lambda}{4} \)


Which factor is not limiting in normal conditions for photosynthesis?
A. Light intensity
B. \( \mathrm{cO}_{2} \)
c. water
D. chlorophyll


An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The dipole is rotated through a very smal angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency \( f=\frac{1}{2 \pi} \sqrt{\frac{p E}{1}} \)
Where, \( I= \) moment of inertia of the
dipole.


If \( -1<x<0, \) then \( \cos ^{-1} x \) is equal to
This question has multiple correct options
A \( \cdot \sec ^{-1} \frac{1}{x} \)
B . \( \pi-\sin ^{-1} \sqrt{1-x^{2}} \)
\( \pi+\tan ^{-1} \frac{\sqrt{1-x^{2}}}{x} \)
D. \( \cot ^{-1} \frac{x}{\sqrt{1-x^{2}}} \)


Three charges \( +1 \mu C,+3 \mu C \) and \( -5 \mu C \)
are kept at the vertices of an equilateral triangle of sides \( 60 \mathrm{cm} \). Find the
electrostatic potential energy of the system of charges.


The process of water seepage into the ground is called


If \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\boldsymbol{x}^{2}+\boldsymbol{a}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{c}^{2}\right)} \)
then \( I \) equals
A \( \cdot \frac{1}{b c} \tan ^{-1}(a)+\frac{1}{c a} \tan ^{-1}(b)+\frac{1}{c b} \tan ^{-1}(c)+k \)
B. \( \frac{1}{b^{2}-c^{2}} \tan ^{-1}(a)+\frac{1}{c^{2}-a^{2}} \tan ^{-1}(b)+ \)
\( \frac{1}{a^{2}-b^{2}} \tan ^{-1}(c)+k \)
\( \frac{\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c}{a^{2}+b^{2}+c^{2}}+k \)
D. none of these


A rod of mass \( m \) and length \( 2 R \) is fixed
along the diameter of a ring of same
mass \( m \) and radius \( R \) as shown in
figure.The combined body is rolling without slipping along \( x \) -axis. Find the
angular momentum about z-axis.


By selling an article for Rs.24, a trader
loses as much percent as the cost price of the article. Write an equation to express this information and check if it is convertible to a Quadratic Equation.


Which of the following metals will react
with \( N a O H \) and \( K O H \) to liberate
hydrogen gas?
A. \( Z n, A l, F e \) and \( M g \)
в. \( A l, F e, M g \) and \( S n \)
c. \( Z n, \) Sn and \( A l \)
D. \( F e, M g \) and \( A l \)


ff \( y=y^{\sqrt{x}}+x^{\sqrt{e}}, \) find \( \frac{d y}{d x} \)


Equation of first law of thermodynamics
for an isochoric process is
A \( . \Delta U=W \)
в. \( \Delta Q=W \)
c. \( \Delta U+W=0 \)
D. \( \Delta Q=\Delta U \)


In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible block of
\( \operatorname{mass} \boldsymbol{m}_{2} \) will remain at rest if.
\( ^{\mathrm{A}} \cdot \frac{1}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}} \)
в. \( \frac{4}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}} \)
\( \mathbf{c} \cdot m_{1}=m_{2}+m_{3} \)
D. \( \frac{1}{m_{3}}=\frac{2}{m_{2}}+\frac{3}{m_{1}} \)


Which of the following is useful as a food preservative?
A. Sucralose
B. Salts of sorbic acid
c. Ascorbic acid
D. Citric acid


The unit for the coefficient of apparent
expansion is
A . cm
в. \( c m /^{0} C \)
\( \mathbf{c} \cdot c m^{0} C \)
D. \( /^{\circ} \mathrm{C} \)


Retina in a human eye acts like a:
A. Lens in a camera
B. Shutter in a camera
c. Film on a camera
D. None of these


We sometimes see rainbow in monsoon
season.Which of the fact is not correct
about the rainbow?
A. Dispersion of incident light first, then reflection internally and finally refraction causes rainbow.
B. Water droplets act like small prisms
c. Sometimes there is formation of two rainbows in the
sky
D. Rainbow is formed in the direction of the sun


Assertion
Electric conduction in gases is possible
at normal pressure.
Reason
The electric conduction in gases
depends only upon the potential difference between the electrodes.
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 orientation of electron orbit is
determined by:
\( A \cdot n \)
B. \( l \)
\( c \cdot m \)
D.


Lithium halide that is least soluble in
water has a molecular mass (rounded
to nearest integer)


A proton when accelerated through a potential difference of \( V \) volt has a wavelength \( \lambda \) associated with it. An \( \alpha \)
particle in order to have the same
wavelength \( \lambda \) must be accelerated
through a p.d. of
A. \( \vee / 8 \) volt
B. V/4 volt
c. v volt
D. 2v volt


The hybridisation state of the central atom and shape of the molecules is
given below. Mark the incorrect combination.
A . \( S O_{3}-s p^{2} \) hybridisation, planar triangular
B. \( S O_{2}-s p^{2} \) hybridisation, \( V \) -shaped
c. \( H_{2} S O_{4}-s p^{2} \) hybridisation, \( v \) -shaped
D. \( O_{3}-s p^{2} \) hybridisation, angular


The sum to infinite of the series
\( \mathbf{1}+\frac{2}{3}+\frac{6}{3^{2}}+\frac{10}{3^{3}}+\frac{14}{3^{4}}+\dots \dots \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


The Oxygen dissociation curve is
A. Parabola
B. Slope
c. Sigmoid
D. Straight line


Synthesis gas is:
A. water gas
B. producer gas
C . coal gas
D. semi water gas


The object distance of a lens is \( 30 \mathrm{cm} \)
and the image distance is \( 10 \mathrm{cm} . \) Find
the magnificence of the lens with the help of this decide whether the size of the image is small or big than the size of the object?


The number of molecules present in 8 grams of oxygen gas are
В. \( 3.011 \times 10^{23} \)
c. \( 12.044 \times 10^{23} \)
D. \( 1.55 \times 10^{23} \)


Which of the following compounds does
not give \( N_{2} \) when heated?
A \( . N H_{4} N O_{2} \)
B. \( N H_{4} N O_{3} \)
c. \( \operatorname{NaN}_{3} \)
D. Both A and B


\( \int \sqrt{\frac{x}{x-1}} d x, x \in(0, \pi / 2) \) equals
A \( \cdot \sqrt{x(x-1)}+\log (\sqrt{x}+\sqrt{x-1})+c \)
B . \( \sqrt{x(x-1)}-\log (\sqrt{x}+\sqrt{x-1})+c \)
c. \( \sqrt{x(x-1)}+\log (\sqrt{x}-\sqrt{x-1})+c \)
D. \( \sqrt{x(x+1)}-\log (\sqrt{x}-\sqrt{x+1})+c \)


\( \boldsymbol{f}(\boldsymbol{x})=\left(1-\boldsymbol{x}^{3}\right)^{\frac{1}{3}}, \) then find \( \boldsymbol{f o f}(\boldsymbol{2}) \)


Mark the correct set of ferromagnetic substances
A. iron, cobalt and nickel
B. iron, copper and lead
c. silicon, bismuth and nickel
D. aluminium, sodium and copper.


Find the difference between simple
interest and compound interest on Rs. 2,400 at 2 years at \( 5 \% \) per annum compounded annually.


Generation of Alternating Current in India is done at
\( A \cdot 45 \) Н
в. 50 нz
c. 60 Н
D. 55 Hz


Anything that influences the valence electrons will affect the chemistry of the element. Nuclear mass effects
chemistry of valence electrons.
A. True
B. False


\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \) is equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 2 \)
D.


Two particles move on a circular path (one just inside and the other just
outside) with the angular velocity \( \boldsymbol{w} \)
and \( 5 w \) starting from the same point.
Then
This question has multiple correct options
A. They cross each other at regular intervals of time \( 2 \pi / 4 w \) when their angular velocity are oppositely directed
B. They cross each other at point on the path subtending an angle of \( 60^{\circ} \) at the center if their angular velocity are oppositely directed
C. They cross at intervals of time \( \pi / 3 w \) if their angular velocities are oppositely directed
D. They cross each other at point on the path subtending \( 90^{\circ} \) at the centre if their angular velocity are in the
same sense


\( D 5 W \) refers to one of the solution used
as an intravenous fluid. It is a \( 5 \% \) by
mass solution of dextrose, \( C_{6} H_{12} O_{6} \) in
water. The density of \( D 5 W \) is \( 1.08 g / m l \) The molarity of the solution is
\( \mathbf{A} \cdot 0.3 M \)
в. \( 0.6 M \)
c. \( 0.28 M \)
D. \( 0.26 ~ M \)


It necessary for electrode b to be
continuously replaced.
Reason
At the positive anode, oxygen gas is
formed and at high temperature of the
electrolysis cell it burns and oxidises away the carbon electrodes to form
toxic carbon monoxide or carbon
dioxide.
[Note : Sketch shown is of an electrolytic
cell used in the extraction of
aluminium]
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is not correctly matched?
A. Neoprene
\[
\left[-C H_{2}-C_{C l}=C H-C H_{2}-\right]_{n}
\]
в. \( \left[-N H-\left(C H_{2}\right)_{6}-N H-C O-\left(C H_{2}\right)_{4}-C-O-\right] \)
Nylon-6,6
c. Terylene
\( \mathrm{D} \cdot+\mathrm{CF}_{2}-\mathrm{CF}_{2}+ \)
Teflon


Assertion
Agriculture output increased several
times after introduction of DDT.
Reason
DDT was the first insecticide used on a
wide scale.
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.


Rank the following reactions \( A, B \) and \( C \) in order to increasing rate.
A. \( B>A>c \)
В. \( B>c>A \)
\( c \cdot A>B>c \)
D. \( A>C>B \)


Which one of the following is an insulator?
A. nichrome
B. graphite
c. human body
D. bakelite


Explain the role of pancreas in digestion of various food materials.


The value of \( \sin 0^{\circ} \) is
A. 0
B. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D.


Helium is suitable for low-temperature
gas thermometry because of its:
A. High transition temperature
B. Real behaviour
c. Low boiling point and near-ideal behaviour
D. High boiling point and high polarizability


In a typical bacterial operon, where is an
operator located to prevent
transcription?
A. Upstream of (before) the gene and the region of the promoter where RNA polymerase attaches.
B. Downstream of (after) the gene and the region of the promoter where RNA polymerase attaches.
C. At the location where the RNA polymerase attaches.
D. Between the gene and the region of the promoter where RNA polymerase attaches.


Titanium tetrachloride, \( \boldsymbol{T} \boldsymbol{i} \boldsymbol{C} \boldsymbol{l}_{4}, \) is a
liquid at room temperature and has a very high vapor pressure. Which statement best explains these
observations?
A. Titanium tetrachloride is an ionic compound, with \( T i^{4+} \) and \( C l^{-} \) ions arranged in a lattice
B. Titanium tetrachloride is a molecular substance, with
\( T i C l_{4} \) molecules held together by covalent bonds
c. The bonding in titanium tetrachloride is metallic, with a sea of electrons being shared equally between all the atoms in a sample.
D. Titanium tetrachloride is a network covalent substance, with an essentially infinite lattice of covalently-bonded \( T i \) and \( C l \) atoms
E. Titanium tetrachloride is simply a mixture of titanium atoms and chlorine atoms, which are not bonded to each other in any particular way


When in thermal contact, the quantity
of heat lost by the hotter body is ...... the amount of heat gained by the colder body. (neglect loss of heat due to convection \& radiation)
A. Equal to
B. Greater than
c. Less than
D. cannot say


Say true or false.
A.M. of any \( n \) positive numbers
\( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) is \( A \) then \( A= \)
\( \frac{\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots .+\boldsymbol{a}_{\boldsymbol{n}}}{\boldsymbol{n}} \)
A . True
B. False


Which of the above represents the formula for the most common
compound of \( \boldsymbol{X} \) and \( \boldsymbol{Y} \) ? Where \( \boldsymbol{X} \) is
\( M g \) and \( Y \) is \( S \)
A. \( X_{2} Y \)
\( Y \)
в. \( X Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)
E. \( X Y_{4} \)


A carbonyl compound on reaction with
ilute \( N a O H \) gives 2 -ethyl-3 hydroxyhexanal. The carbonyl compound is :
A. propanal
B. propanone
c. butanal
D. butanone


Consider the function \( g(x)= \) \( \left\{\begin{array}{ll}\frac{1+a^{x}+x a^{x} \ln a}{a^{x} x^{2}} & x<0 \\ \frac{2^{x} a^{x}-x \ln 2-x \ln a-1}{x^{2}} & x>0\end{array}\right. \)
where \( a>0 \)
Find the value of \( a \& g(0) \) so that the function \( g(x) \) is continuous at \( x=0 \)
\( ^{A} \cdot a=\frac{1}{\sqrt{2}}, g(0)=\frac{(\ln 2)^{2}}{8} \)
B. \( a=-\frac{1}{\sqrt{2}}, g(0)=\frac{(l n 2)^{2}}{8} \)
c. \( a=-\frac{1}{\sqrt{2}}, g(0)=\frac{-}{(l n 2)^{2}} 8 \)
D. \( a=\frac{1}{\sqrt{2}}, g(0)=-\frac{(l n 2)^{2}}{8} \)


Which of the following fruit developed from bicarpellary syncarpous ovary with false septum?
A. siliqua
B. Achene
c. capsule
D. All of the above


Which law was given by Antonie \( L \)
Lavoisier?
A. Laws of multiple proportion
B. Law of conservation of mass
C. Both A and B
D. None of the above


Assertion
If \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})>\boldsymbol{P}(\boldsymbol{A}) \) then. \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})> \)
\( \boldsymbol{P}(\boldsymbol{B}) \)
Reason
fevents \( A \& B \) are dependent, then \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=\frac{\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{\boldsymbol{P}(\boldsymbol{B})} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


One radian is equal to angle of
A \( .53 .3^{\circ} \)
B. \( 54.3^{\circ} \)
\( \mathrm{c} \cdot 57.3^{\circ} \)
D. \( 58.3^{\circ} \)


The expression for mean free path is :
A \( \cdot \lambda=\frac{K T}{\sqrt{2} \pi d^{2} P} \)
B. \( \lambda=\frac{\pi d P}{k T} \)
c. \( _{\lambda}=\frac{\pi d^{2} P}{k T} \)
D. \( \lambda=\frac{k T}{\pi d P} \)


Vectors \( \bar{A} \) and \( \bar{B} \) are equal in
magnitude. The magnitude of \( \bar{A}+\bar{B} \) is larger than the magnitude of \( \overline{\boldsymbol{A}}-\overline{\boldsymbol{B}} \) by
a factor of \( n, \) then the angle between them is
A \( \cdot 2 \tan ^{-1}(1 / n) \)
B. \( \tan ^{-1}(1 / n) \)
c. \( \tan ^{-1}(1 / 2 n) \)
D. \( 2 \tan ^{-1}(1 / 2 n) \)


Very short answer type. Suppose a calculus (stone) is blocking a major calyx, what effect might this have on capsular hydrostatic pressure (CIIP) and thus on net filtration pressure (NFP)?


State True or False.
IUPAC representation of atomic number
108 is \( \boldsymbol{U} \boldsymbol{n} \boldsymbol{o} \)
A. True
B. False


A yellow crystalline allotropic form of
sulphur (A) on heating at \( X^{\circ} C \) converts
to another allotropic sulphur (B) that has needle shape. Identify \( A, B, X \)


Which of the following gases can be used for storage of a fresh sample of an oil for a long time?
A. Carbon dioxide or oxygen
B. Nitrogen or oxygen
c. carbon dioxide or helium
D. Helium or nitrogen


Penicillin and vancomycin do not inhibit Mycoplasma as it lacks
A. Cell wall
B. Nucleus
c. Mitochondria
D. Golgi body


In a circle, let \( A B \) be diameter. Let \( P \) is
point on circle. Then measure of angle APB is
A \( .30^{\circ} \)
B . \( 40^{\circ} \)
\( c .90^{\circ} \)
D. \( 60^{\circ} \)


Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that one of them is black and another is red.


A charged particle oscillates about its equilibrium position with an frequency of \( 100 M H z . \) What is the frequency of
electromagnetic waves produced by the oscillator?


The antidiabetic drug which is considered as a postprandial hyperglycaemic regulator is:
A . rosiglitazone
B. piaglitazone
c. repaglinide
D. tolbutamide


Aryl halides are extremely less reactive towards nucleophilic substitution reactions. Give any two reasons.


The value of \( 52-27+67-48 \) is
A .44
B. 45
c. 46
D. -44


A typical river-borne silt particle has a
radius of \( 20 \mu m \) and a density of \( 2 \times \) \( 10^{3} k g / m^{3} . \) The viscosity of water is
1.0 milli-poise. Find the terminal speed with which such a particle will settle to the bottom of a motionless volume of
water


Keeping the number of moles, volume and temperature the same, which of the following are the same for all ideal
gases?
A. rms speed of molecules
B. Density
c. Pressure
D. Average magnitude of momentum


The sounds having frequency less than \( 20 \mathrm{Hz} \) are called ultrasonics.
A. True
B. False


For the non-equilibrium process, \( \boldsymbol{A}+ \) \( B \rightarrow \) Products, the rate is first order
with respect to \( A \) and second-order with
respect to \( B \). If 1.0 mole each of \( A \) and
\( B \) are introduced into a 1 -litre vessel
and the initial rate was \( 1.0 \times 10^{-2} \)
mol/litre-sec. The rate (in mol
litre \( ^{-1} \) sec \( ^{-1} \) ) when half of the reactants
have been used:
A \( \cdot 1.2 \times 10^{-3} \)
В. \( 1.2 \times 10^{-2} \)
c. \( 2.5 \times 10^{-4} \)
D. none of these


Acetic acid reacts with ethanol in the
presence of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) to form \( \boldsymbol{X} \) and
water. Which of the following is \( X ? \)
A. \( C H_{3} C H_{2} C O O C_{2} H_{5} \)
в. \( C H_{3} \) СОСН\( _{3} \)
c. \( C H_{3} C O C_{2} H_{5} \)
D. \( C H_{3} C O O C_{2} H_{5} \)


Run off components of fertilizers rich fields causes
A. Turbidity of water bodies
B. Eutrophication of water bodies
c. Precipertation of toxic chemical
D. Temperature variation in water


Which statement about alkanes is
correct?
A. Ethane has one more carbon atom and one more hydrogen atom than methane
B. They are converted to alcohols by reaction with steam
C. They contain carbon-carbon double bonds
D. They form carbon dioxide and water on combustion


Which of the following compounds has the highest boiling point?
A. \( C_{2} H_{5} O H \)
в. \( C H_{3} \)СООН
c. \( C H_{3} C O C H_{3} \)
D. НСООСН\( _{3} \)


If \( \bar{a}, \bar{b}, \bar{c} \) be three unit vectors, such that \( \bar{a}+\bar{b}+\bar{c} \) is also a unit vector and \( \alpha_{1} \)
\( \alpha_{2}, \alpha_{3} \) be the angles between \( \bar{a} \) and \( \bar{b}, \bar{b} \)
and \( \bar{c}, \bar{c} \) and \( \bar{a} \) respectively, then \( \alpha_{1}, \alpha_{2} \)
\( \boldsymbol{\alpha}_{3} \)
A. All are acute angles
B. All are right angles
C. Has at least one among them obtuse
D. None of these


In which of the following would you expect to find the most highly
conserved sequences of nucleic acids?
A. Structurally critical regions of a polypeptide such as an active site region
B. The intron regions of pre-mRNA sequences
C. Ribosomal RNA sequences
D. Bacterial genes conferring antibiotic resistance


There are 25 radios, 16 of them are out
of order. What percent of radios are out
of order?


\( \operatorname{Let} A=\left[\begin{array}{ccc}1 & -1 & -1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right] \) and \( 10 B= \)
\( \left[\begin{array}{ccc}\mathbf{4} & \mathbf{2} & \mathbf{2} \\ -\mathbf{5} & \mathbf{0} & \boldsymbol{\alpha} \\ \mathbf{1} & \mathbf{- 2} & \mathbf{3}\end{array}\right], \) if \( \boldsymbol{B} \) is the inverse of
matrix \( A \), then \( \alpha \) is
\( A \)
B.
\( c \cdot 2 \)
\( D \)


Assertion
An electrochemical cell can be set-up
only if the redox reaction is
spontaneous.
Reason
A reaction is spontaneous if free energy change is negative.
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


The value of \( \int \frac{\ln n\left(1-\left(\frac{1}{x}\right)\right) d x}{x(x-1)} \) is
A \( \cdot \frac{1}{2}\left[m\left(1-\frac{1}{x}\right)^{2}\right]+C \)
B \( \cdot \frac{1}{2}\left[m\left(1+\frac{1}{x}\right)\right]^{2}+C \)
c. \( \frac{1}{2} \ln (x(x-1))+C \)
D \( \cdot \frac{1}{2}[\ln (x(x-1))]^{2}+C \)


An inductive circuit contains
resistance of 10 ohms and an
inductance of \( 20 \mathrm{H} \). If an A.c voltage of 120 volt and frequency \( 60 \mathrm{Hz} \) is applied to this circuit, the current would be
nearly
A. \( 0.16 a m p \)
B. \( 0.3 a m p \)
c. \( 0.48 a m p \)
D. \( 0.80 a m p \)


A car starts from rest and accelerates
uniformly over a time of 5.21 seconds
for a distance of \( 110 \mathrm{m} . \) Determine the acceleration of the car.
\( \mathbf{A} \cdot 8.10 m / s / s \)
В. \( 8.1 m / s / s \)
c. \( 8.0 m / s / s \)
D. \( 7.10 m / s / s \)


\( a_{n}=(-1)^{n-1} n^{3} ; a_{9} \)


A line makes the same angle \( \theta \) with
each of the \( X \) and \( Z \) -axes. If the angle \( \beta \)
which it makes with \( Y \) -axis, is such
that \( \sin ^{2} \beta=3 \sin ^{2} \theta, \) then \( \cos ^{2} \theta \) equals
A \( \cdot \frac{2}{5} \)
в. \( \frac{1}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{2}{3} \)


Identify the meiotic stage in which the homologous chromosomes separate while the sister chromatids remain
associated at their centromeres
A. Metaphase-II
B. Anaphase- -
c. Anaphase-II
D. Metaphase-


EMF developed by generator depends
upon:
A. size of magnet
B. length of rotating wire
c. radius of wire
D. none of these


Frosted glass is widely used for translucent windows. The region where a transparent adhesive tape is stuck
over the frosted glass becomes transparent. The most reasonable explanation for this is :
A. diffusion of adhesive glue into glass
B. chemical reaction at adhesive tape - glass interface
c. refractive index of adhesive glue is close to that of glass
D. adhesive tape is more transparent than glass


A car is moving at a speed of 72 Km/hour. The diameter of its wheels is
\( 50 \mathrm{cm} . \) If its wheels come to rest after
20 rotations as a result of the
application of brakes, then the angular retardation produced in the car will be
A . -25.5 radians / \( s^{2} \)
B. 0.25 radians / \( s^{2} \)
C. 2.55 radians / \( s^{2} \)
D.


If \( A \) is a square matrix of order \( m \times n \)
then \( a d j(a d j A) \) is equal to
B \( \cdot|A|^{n-1} A \)
\( \mathbf{c} \cdot|A|^{n-2} A \)
D \( \cdot|A|^{n-3} A \)


Find the equivalent resistance in between \( A \) and \( B \) for the circuit shown in
the figure.
A . \( 30 \Omega \)
B. \( 5 \Omega \)
c. \( 10 \Omega \)
D. 20\Omega


Main component of middle lamella is?
A . Mg pectate
B. Calcium pectate
c. calcium carbonate
D. Calcium oxalate


Assertion
\( \boldsymbol{S O}_{3} \) has a planar structure
Reason
\( \boldsymbol{S} \operatorname{atom} \operatorname{in} \boldsymbol{S} \boldsymbol{O}_{3} \) is \( \boldsymbol{s} \boldsymbol{p}^{2} \) hybridized
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A: The corpuscular theory fails in explaining the velocities of light in air and water.
B: According to corpuscular theory, the light should travel faster in a 'denser medium than in a rarer medium.
A. If both A and B are true but the B is the correct explanation of A
B. If both A and B are true but the B is not the correct explanation of A
c. If A is true but B is false
D. If both the A and B are false
E. If B is true but A is false


The distance between the points (5,-9) and \( (11, y) \) is 10 units. Find the values
of \( y \)
A. -2,-17
в. -1,-17
c. -1,-27
D. -1,17


In isotones the atomic number and
mass numbers are:
A. same
B. different
c. equal
D. zero


Which of the following carbocations has
maximum number of resonating
structure?
\( A \)
B.
\( c \)
\( D \)


A small ball is pushed from a height h along a smooth hemispherical bowl of radius R. With what speed should the
ball be pushed so that it just reaches the top of the opposite end of the bowl?
A. \( \sqrt{2 g h} \)
B . \( \sqrt{2} g h(R+h) \)
c. \( \sqrt{2} g(R-h) \)
D. None of these


In Wheat stones bridge shown in the
figure, galvanometer gives no deflection
on pressing the key. The balance
condition for the bridge is :
A \( \cdot \frac{R_{1}}{R_{2}}=\frac{C_{1}}{C_{2}} \)
B. \( \frac{R_{1}}{R_{2}}=\frac{C_{2}}{C_{1}} \)
c. \( \frac{R_{1}}{R_{1}+R_{2}}=\frac{C_{1}}{C_{1}-C_{2}} \)
D. \( \frac{R_{1}}{R_{1}-R_{2}}=\frac{C_{1}}{C_{1}+C_{2}} \)


Choose the correct answer from the
alternatives given.

Which of the following statements about plant hormones is not true?
A. Each naturally occurring hormone has a specific chemical structure
B. Hormones are among the principal internal regulators of plant growth
c. Responses to plant hormones may be observed in nearly any part of a plant
D. All known growth regulators of plant activities are chemicals produced naturally in plants


The reduction potential of a hydrogen electrode containing a solution of \( \boldsymbol{p} \boldsymbol{H}=\boldsymbol{4} \) is:
A . 0.336
B. 4.059 \( v \)
c. - \( 0.236 v \)
D. 3.941


A transformer has 100 turns in the
primary coil and carries 8 A current. If input power is \( 1 \mathrm{kW} \), the number of turns
in secondary coil to have \( 500 \vee \) output will be:
A \( \cdot 100 \)
B. 200
\( c \cdot 400 \)
D. 300


What type of glassware would be used to deliver a solution of base to titrate an
acid to determine the concentration of
the acid?
A. Pipette
B. Burette
c. Volumetric flask
D. Eudiometer
E. Dropper


The splash of sound was heard \( 5.35 s \)
after dropping a stone into a well
122.5m deep. The velocity of sound in
air is:
A. \( 350 \mathrm{cm} / \mathrm{s} \)
в. \( 350 m / s \)
c. 392 cm \( / \) s
D. \( 0 \mathrm{cm} / \mathrm{s} \)


Find the number of sides of regular polygon whose measure of each of its interior angle is \( \frac{360^{\circ}}{7} \)
\( A \cdot 7 \)
B. 8
c. 9
D. 6


\( \lim _{x \rightarrow 0} \frac{\sqrt{4+\sin 3 x}-2}{\log (1+\tan 2 x)}=\frac{3}{a} \cdot \) Find


Why does anode material have good
hydrogen storage capacity for a Nickelmetal hydride battery?


Write expressions for \( \boldsymbol{K}_{\boldsymbol{P}} \) for the
following equilibria:
\( \mathbf{4} N \boldsymbol{H}_{3(g)}+\mathbf{5} \boldsymbol{O}_{2(g)} \rightleftharpoons \boldsymbol{4} \boldsymbol{N} \boldsymbol{O}_{(g)}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \)
\( \boldsymbol{N} \boldsymbol{H}_{3(g)}+\boldsymbol{H} \boldsymbol{C} \boldsymbol{I}_{(g)} \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}_{(s)} \)
\( \mathbf{2} \boldsymbol{C} \boldsymbol{L}_{\mathbf{2}(\boldsymbol{g})}+\mathbf{2} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}} \boldsymbol{C l}_{\mathbf{2}(\boldsymbol{g})} \)


State the main difference between
asexual and sexual reproduction


\( \mathrm{M} \) and \( \mathrm{N} \) are the mid-points of two equal
chords \( A B \) and \( C D \) respectively of \( a \) circle with centre \( 0 . \) Prove that
\( \angle A M N=\angle C N M \)


A student initially at rest on a frictionless frozen pond throws a \( 2 \mathrm{kg} \) hammer in one direction. After the
throw, the hammer moves off in one
direction while the student moves in the
other direction.Then:
A. the hammer will have the momentum with greater magnitude
B. the student will have the momentum with greater magnitude
c. the hammer will have the greater kinetic energy
D. the student will have the greater kinetic energy


If \( \frac{a}{b}-\frac{c}{d}=0 \) and \( b c=7, \) then determine
the true statement among the following.
A. a and b are directly proportional.
B. a and c are inversely proportional.
c. a and d are inversely proportional.
D. b and c are directly proportional.
E. c and d are inversely proportional.


A coil of radius \( \mathrm{R} \) carries a current I.
Another concentric coil of radius \( \boldsymbol{r}(\boldsymbol{r}<<\boldsymbol{R}) \) caries current \( \frac{\boldsymbol{I}}{2} . \) Initially
planes of the two coils are mutually perpendicular and both the coils are
free to rotate about common diameter.
They are released from rest from this
position. The masses of the coils are \( \mathbf{M} \)
and m respectively \( (\boldsymbol{m}<\boldsymbol{M}) . \) During
the subsequent motion let \( K_{1} \) and \( K_{2} \)
be the maximum kinetic energies of the
two coils respectively and let U be the
magnitude of maximum potential
energy of magnetic interaction of the system of the coils. Choose the correct
options.
A \( \cdot \frac{K_{1}}{K_{2}}=\frac{M}{m}\left(\frac{R}{r}\right)^{2} \)
B. \( \quad K_{1}=\frac{U m r^{2}}{m r^{2}+M R^{2}} K_{2}=\frac{U M R^{2}}{m r^{2}+M R^{2}} \)
\( ^{\mathbf{C}} U=\frac{\mu_{0} \pi I^{2} r^{2}}{4 R} \)
D. \( K_{2}>>K_{1} \)


The conducting rod \( a b \), as shown in figure makes contact with metal rails
\( c a \) and \( d b . \) The apparatus is in a uniform magnetic field of \( 0.800 T \), perpendicular to the plane of the figure. If the
resistance of the circuit \( a b d c \) is \( 1.50 \Omega \)
(assumed to be constant), find the force (magnitude and direction) required to keep the rod moving to the right with a constant speed of \( 7.50 m / s . \) You can
ignore friction.


Magnification \( (m)= \)
A \( \cdot \frac{v}{u} \)
в. \( \frac{u}{v} \)
\( c \cdot \frac{h_{o}}{h_{i}} \)
D. \( \frac{h_{i}}{h_{o}} \)


State whether true or False
\( 10 \mathrm{mN} \) is equal to \( 10^{-3} \) dynes.
A. True
B. False


The bulb does not glow in the setup
shown in the given figure. List the
possible reasons. Explain your answer.


Explain hybridization in acetylene?


A concave mirror is made from a hollow
sphere of radius of curvature \( 30 \mathrm{cm} . \) If an object of height \( 2 \mathrm{cm} \) is placed at 10 \( \mathrm{cm} \) from the pole of the mirror, determine the size of the image:
\( A \cdot 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 5} & \mathbf{7} \\ \mathbf{0} & \mathbf{7} & \mathbf{9} \\ \mathbf{1 1} & \mathbf{8} & \mathbf{9}\end{array}\right], \) then trace of
matrix A is.
A . 17
B. 25
\( c .3 \)
D. 12


Two radioactive sources \( A \) and \( B \)
initially contain equal number of radioactive atoms. Source A has a half-
life of 1 hour and source \( \mathrm{B} \) has a half-life
of 2 hours. At the end of 2 hours, the
ratio of the rate of disintegration of \( A \) to that of B is :
A . 1: 2
B. 2:
\( c \cdot 1: 1 \)
D. 1:


Which of the following sets of quantum numbers is correct for an electron in \( 3 d \)
orbital?
A \( \cdot n=3, l=2, m=-3, s=+\frac{1}{2} \)
в. \( n=3, l=3, m=+3, s=-\frac{1}{2} \)
c. \( n=3, l=2, m=-2, s=+\frac{1}{2} \)
D. \( n=3, l=2, m=-3, s=-\frac{1}{2} \)


State the following statement is True or False \( \frac{7}{9} \) has a value of non terminating decimal number
A. True
B. False


The difference between heat of reaction at
constant pressure and constant volume
for the reaction given below at \( 25^{0} \mathrm{C} \) in \( \mathrm{kJ} \)
is: \( 2 C_{6} H_{6(l)}+15 O_{2(g)} \rightarrow 12 C O_{2(g)}+6 H_{2} O_{(l)} \)
A \( .-7.43 \)
B. +3.72
c. - 3.72
D. +7.43


Given below is a DNA segment showing components of lac operon:
In this lac operon:
P
A. Only z,y,a genes are transcribed
B. RNA polymerase binds to operator site
C. Glucose inhibits the expression of structural genes
D. Binding of RNA polymerase to promotes is inhibited by allolactose.


What would be the stoichiometric
coefficient of hydrochloric acid in the following equation? \( -C l_{2}+_{-} H_{2} O \rightarrow_{-} H C l+_{-} H C l O_{3} \)
A . 1
B. 3
c. 5
D. 10


If \( g \) is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass \( \mathrm{m} \) raised from the surface of the earth to a
height equal to the radius \( \mathrm{R} \) of the earth, is:
\( \mathbf{A} \cdot 2 \mathrm{mgR} \)
в. \( \frac{1}{2} \mathrm{mgR} \)
c. \( \frac{1}{4} \mathrm{mgR} \)
D. mgn


Annual rings are found in
A. Monocot stems
B. Dicot stems
C. Monocot roots
D. Dicot roots


Find the sum of first 8 multiples of 3


Let \( z, \omega \) be complex numbers such that
\( \vec{z}+i \vec{\omega}=0 \) and \( A r g(z \omega)=\pi \) then
\( A r g(z)= \)
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{5 \pi}{4} \)
c. \( \frac{3 \pi}{4} \)
D.


Match column-I (chemical composition of precipitates) with column-II (colour of the precipitate) and select the correct answer using the codes given below in the columns:
\( (a) C o\left[H g(S C N)_{4}\right] \)
(p) black
(b) \( \boldsymbol{F e}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]_{2} \)
(q) rosy red
\( (c) N i(d m g)_{2} \)
(r) prussian
blue
(d) PbS
(s) deep blue
\( A \cdot a-s, b-p, c-q, d-r \)
B. a-s, b-r, c-q, d-p
c. \( a-s, b-p, c-r, d-q \)
D. a-p , b-r, c-q, d-s
E. a-p, b-q,c-r, d-s


For which one of the following gaseous equilibrium will an increase in pressure increase the yield of the product:
A \( \cdot 2 H I \rightleftharpoons H_{2}+I_{2} \)
в. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
c. \( H_{2} O+C O \rightleftharpoons H_{2}+C O_{2} \)
D. \( H_{2}+B r_{2} \rightleftharpoons 2 H B r \)


Give reasons.
Intercellular spaces are absent in sclerenchymatous tissue.


The number of replaceable H atoms in the peroxo disulphuric acid is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


A thermometer has wrong calibration. It
reads the melting point of ice as \( -10^{\circ} \)
If it reads \( 60^{\circ} \) in place of \( 50^{\circ} \mathrm{C}, \) what is the temperature of the boiling point of water on this scale.
\( \mathbf{A} \cdot 130^{\circ} \)
B. 90
\( c \cdot 110^{\circ} \)
D. 120


Least number of times must a fair die
be tossed in order to have a probability of at least \( 91 / 216 \), of getting atleast
one six.


In parabola \( y^{2}=18 x \) find the point
where the ordinate is equal to three times the abscissa.


Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{l}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\quad \pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\end{array}
\]
(a) Find whether \( x=2 \) satisfies the
equation
\[
\begin{array}{c}
\tan ^{-1} \frac{x+1}{x-1}+\tan ^{-1} \frac{x-1}{x}= \\
\tan ^{-1}(-7)
\end{array}
\]
If not, then how should the equation be re-written?
(b) \( \tan ^{-1} \frac{4}{3}+\tan ^{-1} \frac{5}{6}+\tan ^{-1} \frac{39}{2}- \)
\( \pi=\dots \)
(c) If \( x_{1}, x_{2}, x_{3}, x_{4} \) are roots of equation
\[
x^{4}-x^{3} \sin 2 \beta+x^{2} \cos 2 \beta-x \cos \beta-
\]
\( \sin \beta=0, \) then prove that
\[
\sum_{i=1}^{4} \tan ^{-1} x_{1}=\frac{\pi}{2}-\beta
\]


If \( e_{1} \) and \( e_{2} \) are the eccentricities of two
conics with \( e_{1}^{2}+e_{2}^{2}=3, \) then the conics
are
A. Ellipses
B. Parabolas
c. circles
D. Hyperbolas


The most common type of electroscope
is
A. Gold leaf electroscope
B. Elongated electroscope
c. swipe electroscope
D. None


To protect iron from corrosion and rust,
it is coated by:
A. Tin
B. Copper
c. zinc
D. Mercury


Given that:
\( 2 F e(s)+\frac{3}{2} O_{2}(g) \longrightarrow \)
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}(\boldsymbol{s}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 9 3} .4 \boldsymbol{k} \boldsymbol{J} \ldots(\boldsymbol{i}) \)
\( M g(s)+\frac{1}{2} O_{2}(g) \longrightarrow M g O(s) ; \Delta H= \)
\( -140.2 k J \ldots .(i i) \)
What is \( \Delta H \) of the reaction?
\( \mathbf{3} M \boldsymbol{g}+\boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \longrightarrow \mathbf{3} M \boldsymbol{g} \boldsymbol{O}+\mathbf{2} \boldsymbol{F} \boldsymbol{e} \)
в. \( -237.3 k J \)
c. \( 2227.2 k \)
D. \( -257.3 k J \)


Which of the following is available in liquid, solid or gas phases as waxes or as rubbers?
A . Artificical silk
B. Bakelite
c. silicone polymers
D. All


Assertion
Chloride ions, \( C l^{-}, \) can be oxidized to
produce chlorine gas.
Reason
Two chloride ions gives up an electron
to form \( C l_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \sigma \)
\( \sigma \)
\( \sigma \)


Let the direction - cosines of the line
which is equally inclined to the axis be \( \pm \frac{1}{\sqrt{k}} . \) Find \( k ? \)
A .2
B. 3
c. 5
D. 6


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{2} \boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\boldsymbol{4}, \) then the
quation \( \frac{1}{x-f(1)}+\frac{2}{x-f(2)}+ \)
\( \frac{3}{x-f(3)}=0, \) has
A. 1 real root
B. 2 real roots
c. all three roots are real
D. no real root exist


If \( 7 x+13 y=27 \) and \( 13 x+7 y=33 \)
find \( x+y \)


In complex hydrides, hydride ions act as ligand and are coordinated to metal
ions. These hydrides are good reducing agents. Which of the following hydrides is not a complex hydride?
A \( . \) Li \( A I H_{4} \)
в. \( N a B H_{4} \)
\( \mathrm{c} \cdot\left(A l H_{3}\right)_{n} \)
D. \( L i B H_{4} \)


If electric field between plates of a
parallel plate capacitor is \( 2 N C^{-1} \) and
charge on two plates are \( 10 \mathrm{C} \) and \( 3 \mathrm{C} \)
then force on one of the plates is
A. 20 N
B. 30 N
c. \( \frac{60}{7} N \)
D. \( \frac{7}{2} N \)


If \( x^{2}+\frac{1}{x^{2}}=7 \) find the value of \( x^{3}+\frac{1}{x^{3}} \)


If the equation \( a x^{2}-6 x y+y^{2} 2 g x+ \)
\( 2 f y+c=0 \) represents a pair of line
whose slopes are \( m \) and \( m^{2}, \) then sum
of all possible values of \( a \) is-
A . 17
в. -19
c. 19
D. -17


For a perfectly rigid body
A. Young's modulus is infinite and bulk modulus is zero
B. Young's modulus is zero and bulk modulus is infinite
C. Young's modulus is infinite and bulk modulus is also infinite
D. Young's modulus is zero and bulk modulus is also
zero


Which of the following is not an example of a motion with a constant
speed but variable velocity?
A. A car moving at \( 80 k m p h \) on a straight road
B. A car moving at \( 80 k \) mph on a square track
c. A car moving at \( 80 k m p h \) on a circular track
D. A car moving at \( 80 k m p h \) on a zig-zag path


Assertion
Reaction quotient is defined in the same way as equilibrium constant at any stage of the reaction.
Reason
If \( Q_{c} \) (reaction quotient) \( <K_{c} \)
(equilibrium constant reaction moves in direction of reactants).
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


Formalin is used in the preparation of:
A. bakelite
B. nylon
c. styrene
D. teflon


What would have happened if the green house gases were totally missing in the earth's atmosphere? Discuss.


A particle executes SHM in a straight line. The maximum speed of the particle
during its motion is \( V_{\text {max}} \). Then the average speed of the particle during the SHM is :
A \( \cdot \frac{V_{m}}{\pi} \)
в. \( \frac{V_{m}}{2 \pi} \)
c. \( \frac{2 V_{m}}{\pi} \)
D. \( \frac{3 V_{m}}{\pi} \)


The entire volume of the blood is filtered
by kidneys - - \( - \) - times a day.
A. Once
B. 5
\( c \cdot 100 \)
D. 60


If the sums of \( p, q \) and \( r \) terms of an A.P. be \( a, b \) and \( c \) respectively, then prove \( \operatorname{that} \frac{\boldsymbol{a}}{\boldsymbol{p}}(\boldsymbol{q}-\boldsymbol{r})+\frac{\boldsymbol{b}}{\boldsymbol{q}}(\boldsymbol{r}-\boldsymbol{p})+\frac{\boldsymbol{c}}{\boldsymbol{r}}(\boldsymbol{p}- \)
\( \boldsymbol{q})=\mathbf{0} \)


If \( \cos A= \)
\( \boldsymbol{m} \cos \boldsymbol{B}, \boldsymbol{t h e n} \cot \frac{\boldsymbol{A}+\boldsymbol{B}}{\boldsymbol{2}} \cot \frac{\boldsymbol{B}-\boldsymbol{A}}{\boldsymbol{2}}= \)
A \( \cdot \frac{m-1}{m+1} \)
в. \( \frac{m+2}{m-2} \)
c. \( \frac{m+1}{m-1} \)
D. none of these


Find out the correct statement
regarding a saturated solution of salt in
water?
A. All dissolving has stopped
B. Crystals begin to grow
C. An equilibrium has been established
D. Crystals of the solute will visibly continue to dissolve
E. The solute is exceeding its solubility


Calculate the work done when a
2N force moves a body through a distance of \( 10 \mathrm{m} \)
A . 10
B. 2 J
c. 5 J
D. 20


Mention any three differences between
lyophilic and lyophobic colloids.


A fist with a mass of 3 kg causes a
fishing pole to bend \( 9 \mathrm{cm} . \) If the amount
of bending varies directly as the mass, how much will the pole bend for a \( 2 k g \) fish ?


The Sl unit of pressure is:
A. atmosphere
B. \( d y n e / c m^{2} \)
c. Pascal
D. mm of Hg


Which of the following compound has only secondary carbon atoms?
A. Cyclohexane
B. Methylcyclopentane
c. 2-Methylpentane
D. Pentane


The group Beroe and Neis is commonly called as
A. Beroids
B. Brain coral
c. Dead men's fingers
D. venus's girdle


Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter's school and then reaches the office What is the extra
distance travelled by Ayush in reaching the office. If the house is situated at
\( (2,4), \) bank at \( (5,8), \) school at (13,14)
and office at (13,26) and the coordinates are in kilometers?(Assume
that all distances covered are in
straight lines).


A rigid triangular frame ABC of mass \( \mathrm{m} \) is hanging from a rigid horizontal rod
PQ. The frame is constrained to move
along horizontal without friction. A bead of mass \( m \) is released from \( B \) that
moves along BC. Magnitude of displacement o frame when bead reaches C is
A \( \cdot \frac{l}{2} \)
B. \( \frac{l}{4} \)
c. \( \frac{3 l}{\sqrt{2}} \)
D. \( \frac{\sqrt{3} l}{4} \)


On the set \( S \) of all real numbers, define a
relation \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a} \leq \boldsymbol{b}\} . \) Show that
\( \mathrm{R} \) is reflexive.


In right triangle \( A B C, B C=7 c m \)
\( \boldsymbol{A C}-\boldsymbol{A B}=\mathbf{1 c m} \) and \( \angle \boldsymbol{B}=\mathbf{9 0}^{\circ} . \) The
value of \( \cos A+\cos B+\cos C \) is
A \( \cdot \frac{1}{7} \)
в. \( \frac{32}{24} \)
c. \( \frac{31}{25} \)
D. \( \frac{25}{31} \)


Statement-I: The equation \( \frac{x^{3}}{4}- \) \( \sin \pi x+3=2 \frac{1}{2} \) has at least one
solution in [2,2]
Because
Statement-II : If \( \boldsymbol{f}:[\boldsymbol{a}, \boldsymbol{b}] \rightarrow \boldsymbol{R} \) be a
function \& let \( c \) be a number such that
\( f(a)<c<f(b), \) then there is at least
one number \( n \in(a, b) \) such that
\( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{c} \)
A. Statement-l is true, Statement-ll is true ; Statement-I is correct explanation for Statement-
is NOT a correct explanation for statement-
c. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true


The simple harmonic motion of a particle is given by \( \boldsymbol{x}=\boldsymbol{a} \sin 2 \boldsymbol{\pi} \boldsymbol{t} . \) Then
the location of the particle from its
mean position at a time \( 1 / 8 \) th of a second is:
\( \mathbf{A} \cdot \boldsymbol{a} \)
B. \( \frac{a}{2} \)
c. \( \frac{a}{\sqrt{2}} \)
D. \( \frac{a}{4} \)
E \( \cdot \frac{a}{8} \)


The correct size for quanta for different contributions of energy for gaseous molecules is :
A. electronic > vibrational > rotational > tranlational
B. electronic < vibrational < rotational < tranlational
c. vibrational > electronic >rotational > tranlational
D. rotational > vibrational > translational > electronic


00
00
00
00


The reactor which produces power due
to fission by fast neutrons and regenerates more fissionable material
than it consumes is
A. Thermal reactor
B. Breeder reactor
c. Both the above
D. None


If \( A \) is a square matrix, then the value of
\( a d j A^{T}-(a d j A)^{T} \) is equal to
A. \( A \)
B. 2|A|I, where I is the identity matrix
c. null matrix whose order is same as that of \( A \)
D. unit matrix whose order is same as that of \( A \)


Calculate the approximate value of
mode for the following data:
\( \begin{array}{lllll}\mathbf{x} & \mathbf{3}- & \mathbf{6}- & \mathbf{9}- & \mathbf{1 2}- \\ \mathbf{6} & \mathbf{9} & \mathbf{1 2} & \mathbf{1 5}\end{array} \)
2 3
A . 14
B. 15
c. 16
D. 17


Let \( \boldsymbol{P}(\boldsymbol{n}) \) be the statement \( \boldsymbol{2}^{\boldsymbol{n}}<\boldsymbol{n} ! \)
where \( n \) is a natural number, then \( P(n) \)
is true for:
A . all \( n \)
B. all \( n>2 \)
c. all \( n>3 \)
D. all \( n<3 \)


Leaf photosynthates are transported to other parts of higher plants through
A. Cambium
B. Pith
c. xylem
D. Phloem


Find the range of \( 3 \cos \theta-4 \sin \theta \)


Consider the set of eight vectors \( V= \) \( \{a \hat{i}+b \hat{j}+c \hat{k} ; a, b, c \in\{-1,1\}\} . \) Three
non-coplanar vectors can be chosen
from \( V \) in \( 2^{p} \) ways. Then \( p \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


The undifferentiated cell of an animal
has 64 chromatids in a metaphase. How many chromosomes will be present
in the gametes if that animal
A . 16
B. 8
\( c .64 \)
D. 32


\( \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}+\sqrt[3]{x^{2}+1}}{\sqrt[4]{x^{4}+1}+\sqrt[5]{x^{4}-1}} \) is equal to
A.
B. -
c. 0
D. - 2


Using Rutherford model of the atom, derive the expression for the tota energy of the electron in hydrogen atom What is the significance of total negative energy possessed by the
electron?


(a) What is detergent?
(b) Explain the causes of Ozone depletion.
(c) Draw a labelled diagram of 'Khadin water harvesting system' and write any two measures of water conservation.


Which of the following are members of Solar system? This question has multiple correct options
A. Asteroids
B. Shooting star
c. sun
D. Artificial satellite


If \( \boldsymbol{x}>\mathbf{0} \) and \( \boldsymbol{x} \boldsymbol{y}=\mathbf{1}, \) the minimum
value of \( (x+y) \) is
A . -2
B.
\( c \cdot 2 \)
D. none of these


Assertion
Specific gravity is dimensionless.
Reason
Specific gravity is density of a
substance measured w.r.t. density of
water at \( 4^{\circ} C \)
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.


Three concentric conducting spherical shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively. Compute the potential at \( r=\frac{5}{2} R: \)
\( A \)
В. \( \frac{-3 Q}{25 \pi \varepsilon_{0} R} \)
\( c \)
D.


Choose the correct statement about
ecological succession.
A. It is a natural progression of plant types that cannot be reversed.
B. It always occurs over a short period of time.
C. The rate can be changed by factors such as fire, clear cutting, and lava flows.
D. It only takes place on freshly cleared or new land such as islands.
E. The rate is very slow and constant.


Find a vector \( \vec{r} \) of magnitude \( 3 \sqrt{2} \) units
which makes and angle \( \frac{\pi}{4} \) and \( \frac{\pi}{2} \) with \( y \) and z-axis respectively


Statement-1: Lithium chloride is
predominately covalent compound. Statement-2: Electronegativity difference between Li and Cl is small.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1
c. statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true


Which of the following option is the
correct order for the basic strength of
metallic hydroxides?
\( \mathbf{A} \cdot C a(O H)_{2}<A l(O H)_{3}<L u(O H)_{3}<C e(O H)_{3} \)
B. \( A l(O H)_{3}<L u(O H)_{3}<C e(O H)_{3}<C a(O H)_{2} \)
\( \mathbf{c} \cdot L u(O H)_{3}<\operatorname{Ce}(O H)_{3}<A l(O H)_{3}<C a(O H)_{2} \)
D \( \cdot L u(O H)_{3}<C e(O H)_{3}<C a(O H)_{2}<A l(O H)_{3} \)


Draw the tangents to the circle from the point \( L \) with radius \( 2.7 \mathrm{cm} . \) Point \( L \) is at
a distance of \( 6.9 \mathrm{cm} \) from the centre \( M \)


A very large area that contains a variety of natural and traditionally managed ecosystem is called?


Find the direction in which a straight line must be drawn through the point \( (1,2), \) so that its point of intersection with the line \( x+y=4 \) may be at a
distance of 3 units from this point.


A bicycle wheel spins 25 times in 5 seconds. Calculate frequency of the wheel
A . \( 15 \mathrm{Hz} \)
B. \( 10 \mathrm{Hz} \)
c. \( 40 \mathrm{Hz} \)
D. 5 нz


Which of the following arrangement of bond dissociation enthalpy of halogens is correct?
A. \( F-F>C l-C l>B r-B r \)
В. \( F-F<C l-C l<B r-B r \)
c. \( F-F>C l-C l<B r-B r \)
D. \( F-F<C l-C l>B r-B r \)


werner ploneerea the rıeld or coordination chemistry in the late
nineteenth century. At that time, a number of compounds of cobalt (III) chloride with ammonia were known,
with general formula \( C o C l_{3} . x N H_{3} \)
\( \boldsymbol{x}=\mathbf{3} \) to \( \mathbf{6} \)
Treatment of these compounds with aqueous HCl acid did not remove the ammonia. However, treatment of the
compounds with excess of \( A g N O_{3} \) at
\( 273 \mathrm{K} \) gave white precipitate of AgCl in varying ratio depending on the structure. Also each complex had electrical conductivity of varying
nature.
There is no reaction of the compound with aqueous HCl indicating that there
is no free \( N H_{3} \). Thus, \( N H_{3} \) ligand is bonded to cobalt(III) by
A. Primary valency
B. Secondary valency
c. Both of these.
D. None of these


Which of the following functions of time represent \( (A) \) simple harmonic, \( (B) \) periodic but not simple harmonic, and
\( (C) \) non-periodic motion? Give period for each case of periodic motion \( (\omega \) is any positive constant):
(a) \( \sin \omega t-\cos \omega t \)
\( (b) \sin ^{3} \omega t \)
(c) \( 3 \cos (\pi / 4-2 \omega t) \)
\( (d) \cos \omega t+\cos 3 \omega t+\cos 5 \omega t \)
\( (e) \exp \left(-\omega^{2} t^{2}\right) \)
(f) \( 1+\omega t+\omega^{2} t^{2} \)


The average thermal energy of a oxygen atom at room temperature \( \left(27^{\circ} C\right) \)
A \( \cdot 4.5 \times 10^{-21} J \)
В. \( 6.2 \times 10^{-21} J \)
c. \( 3.4 \times 10^{-21} J \)
D. \( 1.8 \times 10^{-21} \mathrm{J} \)


The number of significant figures in
10500 is:
A. three
B. four
c. five
D. two


The decimal expansion of the number \( \sqrt{2} \) is?
A . a finite decimal
B. 1.41421
c. non-terminating recurring
D. non-terminating non-recurring


A certain substance decays to \( \frac{1}{32} \) of its
initial activity in 25 days. The half life is:
A. 1 day
B. 3 days
c. 5 days
D. 7 days


The value of
\( \int_{-1}^{1} \max \{2-x, 2,1+x\} d x \) is?
\( \mathbf{A} \cdot \mathbf{4} \)
B. \( \frac{9}{2} \)
\( c \cdot 2 \)
D. none of these


The source of energy of the hot water
spring is geothermal energy.
A. True
B. False
c. Ambiguous
D. Data insufficient


Ethanol is:
A. ionic compound
B. noble gas
C . polar covalent compound
D. non-polar covalent compound


The correct order(s) is/are:
This question has multiple correct options
\( \mathbf{A} \cdot P h-C H_{2}-B r>P h-C l>P h-B r \)
\( \left(S_{N} \text { reaction with } N a O H\right) \)
\( \mathbf{B} \cdot C H_{3}-\underset{\|}{C}-B r>C H_{3}-\underset{\| \atop O}{C}-F>C H_{3}-C-O E t \)
\( _{O} \|_{O} \)
(Hydrolysis with \( N a O H) \)
\( \mathbf{c} \)
\( C H_{3} \)
\( C H_{3}-C H-C O O H>C H_{3}-C H_{2}-C O O H> \)
\( C H_{3}-C O O H \quad \) (rate of esterification)
D \( \left.\cdot \frac{a}{N H_{2}-N H-C_{O}^{b}-C N_{2}}(a>b>c) \quad \text { (Bascicity of } N\right) \)


\( \int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \) is equal to
A \( \cdot 2\left(x \tan ^{-1} x+\ln \left|\cos \left(\tan ^{-1} x\right)\right|\right)+C \)
B・ \( 2\left[\left(x \tan ^{-1} x\right)^{2}+\ln \left|\sec \left(\tan ^{-1} x\right)\right|\right]+c \)
c. \( 2\left[\left(x \tan ^{-1} x\right)^{2}-\ln \left|\cos \left(\tan ^{-1} x\right)\right|\right]+c \)
D. None of these


Which of the following elements will
have maximum metallic
characteristic?
A . Ga
B. Ge
c. As
D. se


Assertion
Mean free path of a gas molecules varies inversely as density of the gas
Reason
Mean free path varies inversely as
pressure of the gas
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 and Reason is correct


Kirchoffs 1st and 2nd laws are based on
conservation of
A. Energy and charge respectively
B. Charge and energy respectively
c. Mass and charge respectively
D. None of these above


Testify the mean value theorem in the interval \( [\boldsymbol{a}, \boldsymbol{b}], \boldsymbol{f}(\boldsymbol{x})=\frac{1}{4 \boldsymbol{x}-1} \) where
\( a=1 \) and \( b=4 \)


Assertion
According to de Broglie, the wavelengths associtated with electrons and other subatomic particles can be
detected experimentally.
Reason
The wavelength associated with any material particle is directly proportional
to its mass.
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 mass defect of a certain nucleus is
found to be 0.03 amu. Its binding energy is:
A. 27.93 ev
B. 27.93 kev
c. 27.93 Mev
D. 27.93 Gev


A window is in the shape of a rectangle surmounted by a semi circle. If the perimeter of the window is of fixed
length I then the maximum area of the window is
A \( \cdot \frac{I^{2}}{2 \pi+4} \)
B. \( \frac{I^{2}}{\pi+8} \)
c. \( \frac{I^{2}}{2 \pi+8} \)
D. \( \frac{I^{2}}{8 \pi+4} \)


For a reversible spontaneous change \( \triangle s \) is:
\( A \cdot \frac{\Delta E}{T} \)
в. \( \frac{P \Delta V}{T} \)
c. \( \frac{q}{T} \)
D. \( R T l o g K \)


Which class of carbon compounds are
responsible for the depletion of ozone
layer at the higher level of the atmosphere?


Which one of the following has no unpaired electrons?
\( A \cdot O_{2} \)
в. \( O_{2}^{-} \)
\( c \cdot O_{2}^{+} \)
D. \( O_{2}^{-} \)


In which of the following, respiration takes place in absence of oxygen?
A. Man
B. Potato
c. Yeast
D. Spirogyra


A ray of white light of incident on a
spherical water drop whose center is \( C \)
as shown in figure. When observed from
the opposite side, the emergent light.
A. Will be white and will emerge without deviating
B. Will be internally reflectedd
C. Will split into different colors such that the angles of deviation will be different for different colors
D. Will split into different colors such that the angles of deviation will be the same for all colors


State whether following statements are True or False:
(a) An electric motor converts mechanical
energy into electrical energy
(b) An electric generator works on principle of electromagnetic induction
(c) The field at the center of a long circular
coil carrying current will be parallel straight lines
(d) A wire with a green insulation is usually the live wire of an electric supply


Which of the following is a poor conductor of electricity?
A \( . C H_{3} C O O N a \)
в. \( C_{2} H_{5} O H \)
c. \( N a C l(a q) \)
D. \( K O H(a q) \)


Which of the following statement is not
correct regarding hydrogen atom?
A. It resembles with halogens in some properties
B. It resembles with alkali metals in some properties
C. It cannot be placed in first group of periodic table
D. It is the lightest element


\( \operatorname{Let} g(x)=x^{6}+a x^{5}+b x^{4}+c^{3}+d x^{2} \)
\( \boldsymbol{g}(\mathbf{1})=\mathbf{1}, \boldsymbol{g}(\mathbf{2})=\mathbf{2}, \boldsymbol{g}(\mathbf{3})=\mathbf{3}, \boldsymbol{g}(\mathbf{4})=\mathbf{4} \)
A . zero
B.
c. 10
D. 727


Which phase of mitosis is essentially the reverse of prophase in terms of nuclear changes?
A. \( s \) - phase
B. Anaphase
c. Telophase
D. Interphase


The carnot cycle has maximum
efficiency?
A. True
B. False


Two identical masses of 5 kg each fall on a wheel from a height of \( 10 \mathrm{m} \). The wheel disturbs a mass of \( 2 \mathrm{kg} \) water, the rise in temperature of water will be:
A \( \cdot 2.6^{\circ} \mathrm{C} \)
в. \( 1.2^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.32^{\circ} \mathrm{C} \)
D. \( 0.12^{\circ} \mathrm{C} \)


Which of the following statements
concerning fluorine and chlorine is
incorrect?
A. Fluorine is more electronegative than chlorine
B. The atomic radius of the fluorine atom is less than
that of the chlorine atom.
C. Fluorine is stronger oxidizing agent than chlorine
D. Both fluorine and chlorine commonly exist in positive and negative oxidation states
E. Both fluorine and chlorine are diatomic gases at room conditions.


Name the monomers present in the
following polymers:
(a) Bakelite
(b) Buna- N


Calculate the area of the quadrilateral \( A B C D \) in which \( A B=32 c m, A D= \)
\( 24 c m, \angle A=90^{\circ} \) and \( B C=C D= \)
\( \mathbf{5} 2 c m \)


In the reaction sequence:
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \frac{\boldsymbol{C H}_{3} M \boldsymbol{g} \boldsymbol{B r}}{\longrightarrow} \boldsymbol{C H}_{4}+ \)
\( (\boldsymbol{A}) \frac{(i) C O_{2}}{(i i) H_{2} O / H^{\oplus}}(B) \)
(B) will be :
A \( \cdot C H_{3}-C \equiv C-C H_{3} \)
B . \( C H_{3}-C \equiv C-M g B r \)
c. \( C H_{3}-C \equiv C- \) COOH
D. \( C H_{3}-C H \equiv C H-C O O H \)


If atomic number of inert gas is \( Z \), then
ionic bond is formed between:
A \( \cdot(Z-1) \) and \( (Z+1) \)
в. \( (Z-2) \) and \( (Z+2) \)
c. both (a) and (b)
D. none of these


The number of positive integral solutions of \( a b c d=210 \) is
A . 16
B. 64
\( c \cdot 256 \)
D. 1028


A container filled with viscous liquid is moving vertically downwards with
constant speed \( 3 v_{0} . \) At the instant shown, a sphere of radius \( r \) is moving vertically downwards (in liquid) has
speed \( v_{0} . \) The coefficient of viscosity is
\( \eta . \) There is no relative motion between
the liquid and the container. Then at the
shown instant, the magnitude of viscous force acting on sphere is:
\( \mathbf{A} \cdot 6 \pi \eta r v_{0} \)
В. \( 12 \pi \eta r v_{0} \)
\( \mathbf{c} \cdot 18 \pi \eta r v_{0} \)
D. 24\pi\etarv


For two particular vectors \( \vec{A} \) and \( \vec{B} \) it is known that \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{B}} \times \overrightarrow{\boldsymbol{A}} . \) What
must be true about the two vectors?
A. At least one of the two vectors must be the zero vector
в. \( \vec{A} \times \vec{B}=\vec{B} \times \vec{A} \) is true for any two vectors
c. one of the two vectors is a scalar multiple of the other vector.
D. The two vectors must be perpendicular to each other


Sum of all integral values of \( \boldsymbol{a} \in[\mathbf{1}, \mathbf{5 0 0}] \)
for which the equation \( [x]^{3}+x-a=0 \)
has a solution ( \( [.] \) denotes the greatest integer function) is
A .1342
в. 512
c. 784
D. 812


When electronjumps from \( n=4 \) level to \( n=1 \) level, the angular momentum
of electron changes by
\( ^{A} \cdot \frac{h}{2 \pi} \)
в. \( \frac{2 h}{2 \pi} \)
c. \( \frac{3 h}{2 \pi} \)
D. \( \frac{4 h}{2 \pi} \)


Both chlorophyll a and b are present in
A. Rhodophyceae
B. Phaeophyceae
c. chlorophyceae
D. None of the above


The number of turns in the coil of an AC
generator is 5000 and the area of the
coil is0.25 \( m^{2} . \) The coil is rotated at the
rate of 100 cycles /sec in the magnetic field of \( 0.2 W / m^{2} . \) then the peak value will be :
A. \( 786 \mathrm{kv} \)
B. 178 kV
c. \( 157 \mathrm{kv} \)
D. 123 kv


Under what condition the force acting
on charge particle moving in the
magnetic field minimum?
A. If it is either moving parallel to the magnetic field intensity.
B. If it is either moving antiparallel to the magnetic field intensity.
C. Charge particle moves perpendicular to the velocity vector.
D. Both A and B


The point (3,4) is the focus and \( 2 x- \)
\( 3 y+5=0 \) is the directrix of a
parabola. Lenghth of latus rectum is
A \( \cdot \frac{2}{\sqrt{13}} \)
в. \( \frac{4}{\sqrt{13}} \)
c. \( \frac{1}{\sqrt{13}} \)
D. \( \frac{3}{\sqrt{13}} \)


toppr
Q Type your question
\( \operatorname{than} \boldsymbol{X} \boldsymbol{e} \boldsymbol{C l}_{2} \)
Reason
\( \boldsymbol{\Delta} \boldsymbol{H} \)
\( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{g}) \longrightarrow \boldsymbol{X} \boldsymbol{e}^{+}(\boldsymbol{g})+\boldsymbol{e}^{-} ; \boldsymbol{I} \) (ionisation
energy
\( \boldsymbol{X}_{2}(\boldsymbol{g}) \longrightarrow 2 \boldsymbol{X}(\boldsymbol{g}) ; \boldsymbol{D}(\text { Bond energy }) \)
\( \mathbf{2} \boldsymbol{X}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \mathbf{2} \boldsymbol{X}^{-}(\boldsymbol{g}) ; \mathbf{2} \boldsymbol{E} \)
(electron affinity)
\( \boldsymbol{X} \boldsymbol{e}^{+}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{X}^{-}(\boldsymbol{g}) \longrightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{X}_{2}(\boldsymbol{g}) ;-\boldsymbol{U} \)
(lattice energy)
\( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{g})+\boldsymbol{X}_{2}(\boldsymbol{g})+\boldsymbol{X} \boldsymbol{e} \boldsymbol{X}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}_{f}= \)
\( \boldsymbol{I}+\boldsymbol{D}+\boldsymbol{2} \boldsymbol{F}-\boldsymbol{U} \)
By taking values of \( I, D, E \) and \( U, \) we
find that \( \Delta H_{f}^{\circ}\left(X e F_{2}\right) \) is more negative than that of \( X e C l_{2} . \) Thus \( X e F_{2} \) is much
more stable.
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


\( \boldsymbol{S O}_{2} \) bleaches by


A bag contains 9 marbles, 3 of which
are red, 3 of which are blue, and 3 of
which are yellow. If three marbles are
selected from the bag at random, what is probability that they are all of different colors?
A \( \cdot \frac{1}{15} \)
в. \( \frac{9}{28} \)
c. \( \frac{1}{19} \)
D. \( \frac{1}{20} \)


Two short bar magnets with magnetic moments \( 8 A m^{2} \) and \( 27 A m^{2} \) are placed
\( 35 \mathrm{cm} \) apart along their common axial
line with their like poles facing each
other. The neutral point is :
A. in midway between them
B. \( 21 \mathrm{cm} \) from weaker magnet
c. \( 14 \mathrm{cm} \) from weaker magnet
D. \( 27 \mathrm{cm} \) from weaker magnet


Brine is:
A. aqueous solution of chloride
B. saturated solution of \( N a C l \)
C . aqueous solution of \( H C l \)
D. common name of bleaching powder


The angular momentum (L)(L) of an electron in a Bohr orbit is given as:
\( ^{A} \cdot L=\frac{n h}{2 \pi} \)
B. \( L=\sqrt{l(l+1) \frac{h}{2 \pi}} \)
\( \mathbf{c} \cdot L=\frac{m g}{2 \pi} \)
D. \( L=\frac{h}{4 \pi} \)


Find the value of \( k \) if
\( \boldsymbol{A}(\mathbf{4}, \mathbf{1 1}), \boldsymbol{B}(\mathbf{2}, \mathbf{5}), \boldsymbol{C}(\boldsymbol{6}, \boldsymbol{k}) \) are collinear
points.


Answer in one word or one sentence:
What is chirality?


A moving charge produces.
A. Only electric field
B. Only magnetic field
C. Both electric and magnetic fields
D. Neither the electric field nor the magnetic field


Which of the following complex numbers is equivalent to \( \frac{3-5 i}{8+2 i} ? \) (Note: \( i=\sqrt{-1}) \)
A \( \cdot \frac{3}{8}-\frac{5 i}{2} \)
в. \( \frac{3}{8}+\frac{5 i}{2} \)
c. \( \frac{7}{34}-\frac{23 i}{34} \)
D. \( \frac{7}{34}+\frac{23 i}{34} \)


Fruits are not found in gymnosperms
because
A. They are seedless plants.
B. They are not pollinatedd
c. They have no ovary.
D. Process of fertilization does not take place in them


State the law of multiple proportions.


A block of mass \( 10 k g \) is placed on rough
inclined plane of variable angle \( \theta \) and
friction coefficient \( \boldsymbol{\mu}_{s}=\boldsymbol{\mu}_{\boldsymbol{k}}=\mathbf{3} / \mathbf{4} \)
When \( \theta \) is \( 37^{\circ} \) net reaction force applied by inclined is \( \vec{N}_{1} \) and when \( \theta=53^{\circ} \) net
reaction force applied by inclined is \( \vec{N}_{2} \) find \( \left|\overrightarrow{\boldsymbol{N}}_{1}\right|-\left|\overrightarrow{\boldsymbol{N}}_{2}\right| \)


A plane passes through (1,-2,1) and is
perpendicular to two planes \( 2 x-2 y+ \)
\( z=0 \) and \( x-y+2 z=4 . \) The distance
of the plane from the point is (1,2,2)
\( A \cdot 0 \)
B.
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)


How many of the given compounds will
react with \( N a H C O_{3} ? \)


The element 119 has not been
discovered. What would be the symbol for this element?
A. \( U u e \)
в. UUe
c. \( U U E \)
D. None of these


Assertion
In liquid retaining structures with fixed or floating covers the gas pressurevdeveloped above liquid surface shall be added to the liquid
pressure
Reason
In plane walls, the liquid pressure is resisted by both vertical and horizontal bending moments.
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


Let \( \vec{r}=\vec{a}+\lambda \vec{l} \) and \( \vec{r}=\vec{b}+\mu \vec{m} \) be two
lines in space where \( \overrightarrow{\boldsymbol{a}}=\mathbf{5} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}} \)
\( \overrightarrow{\boldsymbol{b}}=-\hat{\boldsymbol{i}}+\boldsymbol{7} \hat{\boldsymbol{j}}+\boldsymbol{8} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{l}}=-\boldsymbol{4} \hat{\boldsymbol{i}}+\boldsymbol{7} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
and \( \overrightarrow{\boldsymbol{m}}=-2 \hat{\boldsymbol{i}}-\boldsymbol{5} \hat{\boldsymbol{j}}-\boldsymbol{7} \hat{\boldsymbol{k}} \) then the
position vector of a point which lies on both of these lines, is
\( \mathbf{A} \cdot \hat{i}+2 \hat{j}+\hat{k} \)
B. \( 2 \hat{i}+\hat{j}+\hat{k} \)
c. \( \hat{i}+2 \hat{j}+2 \hat{k} \)
D. Non existent as the lines are skew


Who proposed the concept of Inertia?
A. Gallileo
B. Newton
c. Pascal
D. Einstein


Which of the following is found in Ulva but not in lower plants?
A. Alternation of generation
B. Generations look alike
c. sperms and eggs are produced
D. Both B and C


A quadratic equation whose roots are
\( \operatorname{cosec}^{2} \theta \) and \( \sec ^{2} \theta \operatorname{can} b e \)
A. \( x^{2}-5 x+2=0 \)
B . \( x^{2}-2 \sin 2 \theta x+6 \sin \theta=0 \)
c. \( x^{2}-4 \operatorname{cosec} 2 \theta x+4 \operatorname{cosec} 2 \theta=0 \)
D. none of these


Which of the following chemicals has caused disasters by exploding in the holds of ships in harbours and in
warehouses?
A. Vinegar in bottles under pressure
B. Ammonium nitrate
c. Gold chloride
D. caustic soda


The element having the least number of electron shells is :
A. \( L \)
B.
c. Na
D. cs


Which is the vital link that ensures
continuity of species between organisms of one generation and the next?
A. Sexual reproduction
B. Embryo
c. zygote
D. Fertilisation


The function \( f(x)=x^{2}+b x+c, \) where
\( b \) and \( c \) real constants, describes
A. One-to-one mapping
B. Onto mapping
c. Not one-to-one but onto mapping
D. Neither one-to-one nor onto mapping


Amplitude of a wave is represented by \( A=\frac{c}{a+b-c} . \) Then resonance will
occur when
A. \( b=-c / 2 \)
B. \( b=0 \) and \( a=c \)
c. \( b=-a / 2 \)
D. None of the above


Insulin molecule contains \( S-S \)
linkages. One \( S-S \) linkage is within a
chain, which is numbered as:
A . \( 19-20 \)
B. 7-7
\( c \cdot 6-11 \)
D. all of the above


\[
\text { If } \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{2} \boldsymbol{x} \boldsymbol{y},(\boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R})
\]
and
\( \boldsymbol{A}= \)
\[
\left[\begin{array}{lll}
f\left(x_{1}, y_{1}\right) & f\left(x_{1}, y_{2}\right) & f\left(x_{1}, y_{3}\right) \\
f\left(x_{2}, y_{1}\right) & f\left(x_{2}, y_{2}\right) & f\left(x_{2}, y_{3}\right) \\
f\left(x_{3}, y_{1}\right) & f\left(x_{3}, y_{2}\right) & f\left(x_{3}, y_{3}\right)
\end{array}\right]
\]
such that trace \( (\boldsymbol{A})=\mathbf{0}, \) then which of the following is true (only one option)
A. \( \operatorname{det}(A) \geq 0 \)
в. \( \operatorname{det}(A)=0 \)
\( \mathbf{c} \cdot \operatorname{det}(A) \leq 0 \)
D. \( \operatorname{det}(A)>0 \)


If \( y=\frac{a x+b}{(x-1)(x-4)} \) has a turning
value at (2,-1) find \( a \& b \)
A \( . a=0, b=0 \)
В. \( a=1, b=0 \)
c. \( a=0, b=1 \)
D. \( a=1, b=1 \)


The velocity of a body of mass \( 20 \mathrm{kg} \) increases to \( 400 \mathrm{kgm} / \mathrm{s} \) in \( 5 \mathrm{s} \). If initia velocity was \( 10 \mathrm{m} / \mathrm{s} \), what is the
momentum before the force acts?
A. \( 200 k g . m / s^{2} \)
в. 300 kg.m / \( s \)
c. 200 kg.m \( / s \)
D. 100 kg.m \( / s \)


Green,blue, brown,gold are the color bands on resistors.Find its resistance?
A. \( 580 \Omega \)
в. \( 560 \Omega \)
\( \mathbf{c} \cdot 480 \Omega \)
D. \( 58 \Omega \)


How does uniform circular motion differ
from uniform linear motion?


Calculate \( \frac{1}{x_{1}^{3}}+\frac{1}{x_{2}^{3}}, \) where \( x_{1} \) and \( x_{2} \)
are roots of the equation \( 2 x^{2}-3 a x- \)
\( \mathbf{2}=\mathbf{0} \)


A hemispherical bowl has a radius 3.5
cm. Its volume \( \mathrm{cm}^{3} \)


\( E_{C l O_{4}^{-} / C l O_{3}^{-}}^{o} \) and \( E_{C l O_{3}^{-} / C l O_{2}^{-}}^{o} \operatorname{are}+0.36 V \)
and \( +0.33 V \) respectively. The
equilibrium concentration of per chlorate ion for the given reaction would be:
\[
\begin{array}{rcc}
& \mathbf{2 C l O}_{\mathbf{3}}^{-} \rightleftharpoons \mathbf{C l O}_{\mathbf{2}}^{-}+\mathbf{C l O}_{\mathbf{4}}^{-} \\
\boldsymbol{t}=\mathbf{0} & \mathbf{0 . 1} \mathbf{M} & \mathbf{0}
\end{array}
\]
A \( .0 .19 M \)
B. 0.024
c. 0.24
D. 0.019


\( \int_{0}^{\pi / 2} \sin ^{5} x \cos ^{6} x d x= \)
A \( \cdot \frac{8}{693} \)
в. \( \frac{32}{693} \)
c. \( \frac{8}{99} \)
D. \( \frac{16}{63} \)


The diagram shows the displacement
time graph for a particle moving in a
straight line. The average velocity for
the internalt \( =\mathbf{0}, \boldsymbol{t}=\mathbf{5} \)
\( A \)
3. \( 6 m / s 6 m / s \)
\( \mathrm{c} .-2 m / s \)
D. \( 2 m / s \)


The \( P . V .^{\prime} s \) of the vertices of a \( \triangle A B C \)
\( \operatorname{are} \bar{i}+\bar{j}+\bar{k}, 4 \bar{i}+\bar{j}+\bar{k}, 4 \bar{i}+5 \bar{j}+\bar{k} \)
The \( P . V . \) of the circumcentre of \( \triangle A B C \)
is
A \( \cdot \frac{5}{2} \bar{i}+3 \bar{j}+\bar{k} \)
В \( \cdot 5 \bar{i}+\frac{3}{2} \bar{j}+\bar{k} \)
c. \( 5 \bar{i}+3 \bar{j}+\frac{1}{2} \bar{k} \)
D. \( \bar{i}+\bar{j}+\bar{k} \)


In the figure drawn below, its
dimensions are given in meters. If \( \boldsymbol{C}= \)
\( 3, \) find the total cost to fence the garden
if the cost of fencing is \( 7 / m^{2} \)


The Henr's law constant for \( \mathrm{N}_{2}, \mathrm{O}_{2} \) and
\( \mathrm{CO}_{2} \) in water are 1600,780 and 29 atm
M-1, respectively. Which of these gases has the highest concentration in a
sample of water at 25 degrees \( C \) when
the gas pressure over the water is 1.0 atm?
\( A \cdot N_{2} \)
B. 0,2
\( c \cdot c O_{2} \)
D. can't tell without more information about the samples


Acid rain is caused by or recent reports
of acid rain in some industrial cities are
due to the effect of atmospheric
pollution by
A. Excessive release of \( C O_{2} \) by burning of fuels like wood and charcoal, cutting of forests and increased animal population
B. Excessive release of \( N O_{2} \) and \( S O_{2} \) in the atmosphere by burning of fossil fuel
C. Excessive release of \( N H_{3} \) by industrial plants and coal
gas
D. Excessive release of \( \mathrm{CO} \) in the atmosphere by incomplete combustion of coke, charcoal and other carbonaceous fuel in the of oxygen


Which of the following is / are disadvantage of building large dams for generating hydro electric power?
A. Due to construction of dams, lot of areas of rivers having continuous fresh flowing water, have to be cleared
B. Number of trees have to be cut
c. Destroys not only the plants life but also the animals and birds life dependent on them.
D. All of the above


A fair die is thrown. What is the
probability that the score is not a factor
of 5?
A \( \cdot \frac{1}{5} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D. \( \frac{2}{3} \)


From epithem hydathodes, the water
comes out due to
A. Imibibition pressure
B. Osmotic pressure
c. Root pressure
D. All of the above


Explain Analgesics.


Chlorine has two stable isotopes \( \mathrm{Cl}-35 \)
and Cl-37 with atomic masses 34.96
and 36.95 respectively. If the avg mass of chlorine is 35.43 . Calculate the
percentage abundance.


Last stage of gametophytic generation
is
A . Gametes
B. Zygote
c. spore mother cells
D. spores


For two independent events \( A \) and \( B \) what is \( P(A+B), \operatorname{given} P(A)=\frac{3}{5} \) and
\( P(B)=\frac{2}{3} ? \)
A \( \cdot \frac{11}{15} \)
в. \( \frac{13}{15} \)
\( c \cdot \frac{7}{15} \)
D. 0.65


Evaluate \( \int_{0}^{\infty} \sin x d x \)


Define symport and antiport.


Does the sex of the child depend on the father or it is just a matter of chance?
Discuss.


According to the principle of complementarity, phenomena can have contradictory properties. These properties cannot be explained simultaneously. Identify phenomenon that are examples of complementarity.
A. Mass and weight
B. Heat and temperature
c. Light waves and particles
D. Magnetic and electric fields
E. Frequency and intensity of sound


Choose the odd one w.r.t. fungal group
A. Truffles
B. Morels
C. Drosophila of plant kingdom
D. Toadstools


Choose the correct answers from the
alternatives given. Generally the breathing system in birds:
A. is identical to the human breathing system
B. is merely accelerated by the flight muscles
c. resembles the positive pressure system of a frog
D. requires a flow-through bronchi-lung so constant oxygen absorption can meet the high oxygen demand


A thin bi-convex lens \( (n=1.5) \) has a focal length of \( 50 \mathrm{cm} \) in air.When immersed in a transparent liquid, the focal length is measured to be \( 250 \mathrm{cm} \).The refractive
index of the liquid medium is
A . 1.33
B. 1.46
\( c \cdot 1.30 \)
D. 1.36


Evaluate the following:
\( 0.8 \times \frac{\frac{7}{12}}{\frac{5}{24}} \)
A \( \cdot_{2} \frac{6}{25} \)
в. \( _{3} \frac{6}{25} \)
c. \( \frac{6}{25} \)
D. \( \frac{26}{25} \)


Charge passing through a conductor of \( \operatorname{cross} \operatorname{section} \operatorname{area} A=0.3 m^{2} \) is given
by \( \boldsymbol{q}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{5} \boldsymbol{t}+\mathbf{2} \) in coulomb, when \( \boldsymbol{t} \)
is in second. What is the value of drift
velocity at \( t=2 s ?(\text { Given, } n=2 x \)
\( \mathbf{1 0}^{\mathbf{2 5}} / \boldsymbol{m}^{\mathbf{3}} \mathbf{)} \)
A \( \cdot 0.77 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
B . \( 1.77 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
C \( .2 .08 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
D. \( 0.57 \times 10^{-5} \mathrm{m} / \mathrm{s} \)


The \( 3 r d, 4 t h, \) and 5 th terms in the
expansion \( (x+a)^{n} \) are respectively
\( 84,280, \) and \( 560, \) find the values of \( x, a \)
and \( n \)
A. \( x=1, a=2, n=6 \)
B. \( x=1, a=6, n=7 \)
c. \( x=3, a=2, n=7 \)
D. \( x=1, a=2, n=7 \)


Differentiate with respect to \( x \) :
\( \log _{7}(2 x-3) \)


Hydrogen bonding is absent in ether
A. True
B. False


Consider the following solubility data
for various chromates at \( 25^{\circ} \mathrm{C} \)
\[
\begin{array}{cc}
\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}} \\
\boldsymbol{A} \boldsymbol{g}_{\boldsymbol{2}} \boldsymbol{C r} \boldsymbol{O}_{\boldsymbol{4}} & \boldsymbol{9 . 0} \times \mathbf{1 0}^{-\mathbf{1 2}} \\
\boldsymbol{B a C r} \boldsymbol{O}_{\boldsymbol{4}} & \boldsymbol{2 . 0} \times \mathbf{1 0}^{-\mathbf{1 0}} \\
\boldsymbol{P b C r O}_{\boldsymbol{4}} & \boldsymbol{1 . 8} \times \mathbf{1 0}^{-\mathbf{1 4}}
\end{array}
\]
The chromate that is the most soluble
in water at \( 25^{\circ} \mathrm{C} \) on a molar basis is
\( \mathbf{A} \cdot A g_{2} C r O_{4} \)
B \( . \) BaCr \( \mathrm{O}_{4} \)
\( \mathbf{c} \cdot P b C r O_{4} \)
D. impossible to determine
E. none of these


Early true man was
A. Peking Man
B. Java Man
C. Neanderthal Man
D. Homo habitue


A tangent drawn on the curve obtained by plotting concentration of product mole \( L^{-1} \) ) of the first-order reaction vs
time (min) at the point corresponding
to time minute takes an angle to \( 30^{\circ} \)
with concentration axis Hence the rate
of formations of product after 20 minutes will be:
A. 0.580 mole \( L^{-1} \) min \( ^{-1} \)
B. 1.723 mole \( L^{-1} \) min \( ^{-1} \)
c. 0.290 mole \( L^{-1} \) min \( ^{-1} \)
D. 0.866 mole \( L^{-1} \) min \( ^{-1} \)


Fungal bodies in which entire cell gets
transformed into reproductive structure
are know as:
A. Holocarpic
B. Eucarpic
c. Monocentric
D. Polycentric


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \frac{x}{2}\right)(1-\sin x)}{\left[1+\tan \frac{x}{2}\right][\pi-2 x]^{3}} \)


A particle that carries a charge \( -q \) is placed at rest in uniform electric field
\( 10 N / C . \) It experiences a force and moves in a certain time \( t, \) it is observed to acquire a velocity \( 10 \vec{i}-10 \vec{j} \mathrm{m} / \mathrm{s} \). The
given electric field intersects a surface of area \( A m^{2} \) in the \( X \) -Z plane. Electric flux
through surface is:
в. \( 5 A N m^{2} / C \)
c. \( \sqrt{2} A N m^{2} / C \)
\( \mathbf{D} \cdot 2 \sqrt{5} A N m^{2} / C \)


If \( \cos y=x \cos (a+y) \) then prove that:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\cos ^{2}(\boldsymbol{a}+\boldsymbol{y})}{\sin \boldsymbol{a}} \)


If \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=4 \) then find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{1} \)


Answer the following questions:
1. Explain interhalogen compounds.
2. How is oxygen prepared from the following compound?
\( \boldsymbol{K} \boldsymbol{C l O}_{4} \)


Account for the following.
(i) The \( C-C l \) bond length in
chlorobenzene is shorter than that in
\( \boldsymbol{C H}_{3}-\boldsymbol{C l} \)
(ii) Chloroform is stored in closed dark
brown bottles.


Free body diagrams doesn't play any role in making the calculations on the conditions of the equilibrium of the body.
A . True
B. False


Find the value of:
\( \csc ^{2} 60^{\circ}-\tan ^{2} 30^{\circ} \)


Express \( 25 \sin h x-24 \sin h x \) in the
form \( R \cos h 2(x-\alpha) \) giving the values
of \( \boldsymbol{R} \) and \( \tan \boldsymbol{h} \boldsymbol{\alpha} \)
Hence write down the minimum value
of \( 25 \cos h x-24 \sin h x \) and find the
value of \( x \) at which this occurs, and give
your answer in terms of a natural
logarithms.


In mitosis, chromosome duplication
occurs during
A. Interphase
B. Prophase
c. Late prophase
D. Late telophase


\( f(x)=\left\{\begin{array}{cc}-1, & x<-1 \\ x^{3}, & -1 \leq x \leq 1 \\ 1-x, & 1<x<2 \\ 3-x^{2} & x>2\end{array}, \) then \right.
A. \( \lim _{x \rightarrow-1} f(x)=1 \)
B \( \cdot \lim _{x \rightarrow 1} f(x)=1 \)
c. \( \lim _{x \rightarrow 2} f(x)=-1 \)
D. \( \lim _{x \rightarrow 2^{-}} f(x)=0 \)


Which of the following is a nonbiodegradable pollutant?
A . DDT
B. Sewage
c. Plant leaves
D. Domestic wastes


Uredospores is formed by Puccinia on
A. Wheat
B. Barberry
c. Both A and B
D. Dalbergia and wheat


Consider the following cell reaction:
\[
\begin{array}{c}
2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow \\
2 F e^{2+}(a q)+2 H_{2} O(l) ; E^{o}=1.67 V
\end{array}
\]
\( \mathbf{A t}\left[\boldsymbol{F} \boldsymbol{e}^{2+}\right]=\mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M}, \boldsymbol{P}_{O_{2}}=\mathbf{0 . 1} \) atm
and \( p H=3, \) the cell potential at \( 25^{\circ} C \)
is:
A . 1.47
B. 1.77 V
c. \( 1.87 \mathrm{v} \)
D. 1.57 V


Add: -18,14


From the bar graph What is total no. of
students in class VIII?
A . 45
B. 185
c. 215
D. 245


Which of the following metals would evolve hydrogen from dilute nitric acid?
A. Magnesium
B. Iron
c. copper
D. zinç


\( 65 \% \) by volume is hydrogen gas in the biogas
A . True
B. False
c. Ambiguous
D. Data insufficient


\( \mathbf{0}<\mathbf{x}<\mathbf{2} \boldsymbol{\pi} ; \mathbf{0}<\mathbf{y}<\mathbf{2} \boldsymbol{\pi} \) and
\( 3^{\sin x+\cos y}=1 \) and \( 25^{\sin x^{2}+\cos ^{2} y}=5 \) then
\( (x, y) \) is This question has multiple correct options
\( ^{\mathrm{A}} \cdot\left(\frac{7 \pi}{6}, \frac{\pi}{3}\right. \)
В. \( \left(\frac{7 \pi}{6}, \frac{5 \pi}{3}\right) \)
c. \( \left(\frac{11 \pi}{6}, \frac{\pi}{3}\right) \)
D. \( \left(\frac{11 \pi}{6}, \frac{5 \pi}{3}\right) \)


Solve \( \frac{d y}{d x}=\cos (x+y) \)
Solve \( \frac{d y}{d x}=\cos (x+y) \)


Which of the following are
biodegradable polymers?
This question has multiple correct options
A. PHBV
B. Nylon - 2,6
C . Polyglycolic and polylactic acids
D. Perlon-U


The area of a field in the shape of a
trapezium measure \( 1440 m^{2} . \) The perpendicular distance between its
parallel sides is \( 24 \mathrm{cm} . \) If the ratio of the parallel sides is \( 53, \) then the length of the longer parallel sides is
A. \( 75 \mathrm{m} \)
B. \( 45 \mathrm{m} \)
c. \( 120 \mathrm{m} \)
D. 60 m


Which of the following are not thermosetting polymers? This question has multiple correct options
A. Bakelite
B. polystyrene
c. PVC
D. Melmac


Which of the following genera is characterised by the production of geocarpic fruits?
A. cucurbita
B. Pisum
c. Glycine
D. Arachis


The distance between which two points
is 2 units ?
A \( \cdot(-2,-3) \) and (-2,-4)
B. (0,4) and (6,0)
c. (7,2) and (6,2)
D. (4,-3) and (2,-3)


Sound wave in air are
waves.
A. longitudinal
B. radio
c. transverse
D. electromagnetic


Which of the following compound has the smallest bond angle?
A \( . S H_{2} \)
в. \( N H_{3} \)
\( c \cdot S O_{2} \)
D. \( O H_{2} \)


Give method of preparation, properties
and uses of Freon


Which of the following changes would cause the pointer to deflect through a larger angle?
A. Move the magnet faster
B. Move the magnet away from the solenoid
c. Unwind some of the turns of the solenoid
D. Keep the magnet stationary


If \( q \) is a real number, then which of the
following is incorrect?
\( ^{A} \cdot \sin q=-\frac{1}{5} \)
B. \( \cos q=1 \)
\( \mathbf{c} \cdot \sec q=\frac{1}{7} \)
D. \( \tan q=-20 \)


A truck is moving with a constant velocity of \( 54 k m h^{-1} . \) In which direction
(angle with the direction of motion of
truck) should a stone be projected up
with a velocity of \( 20 \mathrm{ms}^{-1} \), from the
floor of the truck, so as to appear at
right angles to the truck, for a person standing on earth?
A \( \cdot \cos ^{-1}\left(-\frac{3}{4}\right) \)
B. \( \cos ^{-1}\left(-\frac{1}{4}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(-\frac{2}{3}\right) \)
D \( \cdot \cos ^{-1}\left(\frac{3}{4}\right) \)


When compound \( C \) is reacted with water,which reaction takes place?
A. Addition
B. Displacement
c. Disproportionation
D. Substitution


DNA strands are joined by
A. Oxygen bonds
B. Hydrogen bonds
c. Carbon bonds
D. Nitrogen bonds


A couple produces motion in a straight line.
A. True
B. False


One mole is equal to number of atoms as contained in:
A. 18 of carbon
B. \( 6 g \) of carbon
C. 12 g of carbon
D. \( 12 \mathrm{kg} \) of carbon


The compound (F) is:
\( \mathbf{A} \)
B.
c. \( E t-\equiv-E t \)
D. Both (A) and (B)


A conducting loop of radius \( R \) is has a
\( B \) -field directed through it at a
downward angle as shown. Determine
the amount of flux in the loop.
\( \mathbf{A} \)
\( B \)
\( \mathbf{c} \cdot B \pi R^{2} \sin \theta \)
\( \mathbf{D} \cdot B \pi R^{2} \cos \theta \)


Let \( A_{n} \) be the constant number such
that \( c>1 . \) If the least area of the figure
given by the line passing through the point (1,c) with gradient 'm' and the parabola \( \boldsymbol{y}=\boldsymbol{x}^{2} \) is 36 sq.units find the
value of \( \left(c^{2}+m^{2}\right) \)
A \( \cdot 104 \)
B. 105
\( c \cdot 10 \)
D. 100


In a series \( L C R \) circuit \( K=200 \Omega \) and
the voltage and frequency of the main supply are \( 220 V \) and \( 50 H z \)
respectively. On taking out the capacitor from the circuit, the current
leads the voltage by \( 30^{\circ} . \) On taking out the indicator from the circuit the
current leads the voltage by \( 30^{\circ} . \) The power dissipated in the \( L C R \) circuit is :
\( \mathbf{A} \cdot 342 W \)
B. 305 \( W \)
c. \( 209 ~ W \)
D. \( 242 \mathrm{W} \)


The value of \( \Delta E \) for combustion of 16 g
of \( C H_{4} \) is \( -885389 \mathrm{J} \) at \( 298 \mathrm{K} \). The \( \Delta H \)
combustion for \( \boldsymbol{C H}_{4} \) in J \( \boldsymbol{m o l}^{-1} \) at this
temperature will be: (Giventhat, \( \boldsymbol{R}= \)
\( \left.8.314 J K^{-1} m o l^{-1}\right) \)
A. -55337
В. -880430
c. -885389
D. -890348


Select the INCORRECT statement:
\( \mathbf{A} \cdot N_{2} O \) with sodium metal in liquid ammonia forms sodium azide and nitrogen gas is liberated.
B. Ammonia is oxidized to nitrogen by dilute solution of sodium hypochlorite in presence of glue.
C. Ammonium dichromate on heating decomposes to give nitrogen and a green coloured compound.
D. CaNCN on hydrolysis produces a white precipitate and a gas which turns filter paper moistened with copper sulphate solution deep blue.


To get an output of 1. from the circuit
shown in figure the input must be
\( \mathbf{A} \cdot a=0, b=0, c=1 \)
B \( . a=1, b=0, c=0 \)
\( \mathbf{c} \cdot a=1, b=0, c=1 \)
D . \( a=0, b=1, c=0 \)


The value of \( I \) in the figure shown below
is
A . \( 19 A \)
в. \( 21 A \)
\( c .8 A \)
\( D \cdot 4 A \)


Assertion
\( \boldsymbol{L i I}+\boldsymbol{K} \boldsymbol{F} \rightarrow \boldsymbol{L} \boldsymbol{i} \boldsymbol{F}+\boldsymbol{K} \boldsymbol{I}: \) This
reaction is spontaneous in forward side.
Reason

The larger anion stabilizes larger cation
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


Element having atomic number 33 belongs to period:
A . \( I I I \)
в. \( I V \)
\( c \cdot V \)
D. \( V I \)


How would you demonstrate that
momentary current can be obtained by
the suitable use of a magnet, a coil of
wire and a galvanometer?
A. By moving the magnet towards the coil connected to the galvanometer
B. By moving the magnet away from the coil connected to the galvanometer
\( c \cdot \operatorname{both} A \& B \)
D. Insufficient information


A sample of hard water contains
0.005 moles of \( C a C l_{2} \) per litre. What is
the minimum concentration Of
\( N a_{2} S O_{4} \) which must be added for
removing \( C a^{2+} \) ions from the water
sample?
\( \left[K_{s p} \text { for } C a S O_{4} \text { is } 2.4 \times 10^{-5} \text {at } 25^{\circ} C\right] \)
A \( .2 .8 \times 0^{-5} M \)
В. \( 4.8 \times 10^{-3} M \)
c. \( 6.1 \times 10^{-3} M \)
D. \( 4.1 \times 10^{-5} M \)


If the points \( (p .0),(0, q) \) and (1,1) are collinear then \( \frac{1}{p}+\frac{1}{q} \) is equal to
\( A \cdot-1 \)
B.
\( c \cdot 2 \)
D.


A closed vessel contains helium and
ozone at a pressure of \( \mathrm{P} \) atm. The ratio of He and oxygen atoms is 1: 1 . If helium is
removed from the vessel, the pressure of the sytem will reduced to:
\( A \cdot 0.5 P \) atm
B. 0.75 P atm
c. \( 0.25 \mathrm{P} \) atm
D. 0.33 P atm


Electric current is a
A. Scalar quantity
B. Vector quantity
C. Vector quantity when it is due to the flow of positive charges
D. Vector quantity when it is due to electrons


\( \int \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x} d x \) is equal to
A \( \cdot \cot ^{-1}\left(\tan ^{2} x\right)+C \)
B. \( \tan ^{-1}\left(\tan ^{2} x\right)+C \)
C. \( \cot ^{-1}\left(\cot ^{2} x\right)+C \)
D. \( \tan ^{-1}\left(\cot ^{2} x\right)+C \)


Vibrio are
shaped bacteria.


Factorise by using formula:
\( \left(7 \frac{3}{10}\right)^{2}-\left(2 \frac{1}{10}\right)^{2} \) is \( 48 \frac{22}{25} \)
If true then enter 1 and if false then
enter 0


On the ellipse, \( 9 x^{2}+25 y^{2}=225, \) find
the point whose distance to the focus
\( F_{1} \) is four times the distance to the
other focus \( \boldsymbol{F}_{2} \)
\( \mathbf{A} \cdot[-15, \sqrt{63}] \)
\( ^{\text {В }} \cdot\left(\frac{-15}{4}, \frac{\sqrt{63}}{2}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{-15}{4}, \frac{\sqrt{63}}{4}\right) \)
D. \( \left(\frac{-15}{2}, \frac{\sqrt{63}}{2}\right) \)


Which of the following pose threat to historical monument Taj Mahal?
A. Floods in Yanuna river
B. Temperature mediated spoilage of marble
c. Air pollutants from Mathura refinery
D. Weathering of marble


Fill in the blank:
When the measured quantity is not dimensionless, is a
dimensionless error.
A. gross error
B. absolute error
c. instrumental error
D. relative error


How can we test whether a given
compound is ethanoic acid or ethanol?


Among the following particles, belongs to baryons.
A. neutron
B. \( \mu \) -meson
c. positron
D. \Pi-meson


Find the direction cosines of the unit
vector perpendicular to the plane \( \vec{r} \cdot(6 \hat{i}-3 \hat{j}-2 k)+1=0 \) passing
through the origin.


\( \lim _{n \rightarrow \infty} \frac{\left(n^{2}+5 n+6\right)}{(n+4)(n+5)} \) is equal to


The process of concentrating Au and Ag ores is based upon their solubility in :
A . \( N H_{3} \)
в. \( H N O_{3} \)
c. \( H C l \)
D. \( K C N \)


Which part of our body helps us in maintaining the body balance? Answer briefly.


Best material to study meiosis is
A. Root tip
B. Ovary
c. Young anther
D. Pollen grain


Solubility of calcium phosphate (molecular mass, \( M \) ) in water is \( W \) g
per \( 100 m L \) at \( 25^{\circ} C . \) Its solubility
product at \( 25^{\circ} C \) will be approximately:
\( ^{\mathbf{A}} \cdot_{10^{9}}\left(\frac{W}{M}\right)^{5} \)
в. \( _{10^{7}}\left(\frac{W}{M}\right)^{5} \)
\( ^{\mathrm{c}} \cdot_{10^{5}}\left(\frac{W}{M}\right)^{5} \)
\( ^{\mathrm{D}} 10^{3}\left(\frac{W}{M}\right)^{5} \)


Choose the correct statement.
A. \( 100 \% \) efficiency is possible only in reversible process.
B. \( 100 \% \) efficiency is possible in some irreversible
processes.
C. Efficiency and reversibility are not related to each other.
D. \( 100 \% \) efficiency is not possible.


Find the focal length of a lens of power
(-2.0)D. What type of lens is this?


A method of protecting steel and iron from rusting is:
A. rusting
B. corrosion.
c. galvanisation.
D. sublimation


If \( x e^{x y}+y e^{-x y}=\sin ^{2} x, \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is
A \( \cdot 2 y^{2}-1 \)
в. \( 2 y \)
c. \( y^{2}-y \)
D. \( y^{2}+1 \)
E \( \cdot y^{2}-1 \)


How is reproduction carried out in
Hydra?


In the above figure, \( \boldsymbol{O} \) is the centre of
the circle and \( \angle B A C=n^{\circ}, \angle O C B= \)
\( m^{\circ} \) then
A \( \cdot m^{\circ}+n^{\circ}=90^{\circ} \)
B . \( m^{\circ}+n^{\circ}=180^{\circ} \)
\( \mathbf{c} \cdot m^{\circ}+n^{\circ}=120 \)
D . \( m^{\circ}+n^{\circ}=150^{\circ} \)


The determinant
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right| \) is equal to
zero, if-
\( \mathbf{A} \cdot a, b, c \) are in \( A P \)
B. \( a, b, c \) are in GP
\( \mathrm{C} \cdot \alpha \) is a root of the equation \( a x^{2}+b x+c=0 \)
D. \( (x-\alpha) \) is a factor of \( a x^{2}+2 b x+c \)


If the lines through the points (4,1,2) and \( (5, k, 0) \) is parallel to the line through the points (2,1,1) and (3,3,1)
find \( k \)


if a certain car, going with speed \( v_{1} \)
, rounds a level curve with a radius \( \boldsymbol{R}_{1} \) it
is just on the verge of skidding.if its speed is now doubled, the radius of the tightest curve on the same road tht it can round without skidding is:
\( \mathbf{A} \cdot 2 R_{1} \)
в. \( 4 R_{1} \)
c. \( \frac{R_{1}}{2} \)
D. \( \frac{r_{1}}{4} \)


Collodion is a:
A. colloidal sol of cellulose nitrate in water
B. colloidal sol of cellulose acetate in ethyl alcohol
C. colloidal sol of cellulose nitrate in ethyl alcohol
D. colloidal sol of cellulose acetate in water


If 20 litres of mixture containing \( 85 \% \)
milk is mixed with 25 litres of another
mixture, Then the resultant mixture has
\( 60 \% \) milk. Find the percentage of milk in the second mixture.


Find the total resistance across \( A B \)


For the reaction2 \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{A}_{2} \boldsymbol{B} \) rate \( = \)
\( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}]^{2} \) with \( \boldsymbol{k}=\boldsymbol{2} . \boldsymbol{0} \times \)
\( 10^{-6} m o l^{-2} L^{2} s^{-1}, \) what is the rate of the
reaction when \( [\mathrm{A}] \) is reduced to 0.060 molL'-13. the initial rate of reaction
when \( [A]=0.1 m o l L^{-1} a n d[B]= \)
\( 0.2 m o l L^{-1} i s 8 \times 10^{-9} m o l L^{-1} s^{-1} \)