Which of the following is substituted purines?
A. Adenine
B. Cytosine
c. Thymine
D. Uracil


Pick correct statement(s):
This question has multiple correct options
A. Newton's \( 3^{r d} \) law is applicable for all frames of reference and all systems
B. Presence of a conductor near another conductor
increases capacitance of system
c. Magnetic moment of a toroid is zero
D. In a perfectly inelastic collision two colliding objects will always stick together after collision


Two spherical balls \( A \) and \( B \) made of the same material, are heated to the same temperature. They are then placed in identical surroundings. If the
diameter of \( A \) is twice that of \( B \), ratio of
the rates of cooling of \( A \) and \( B \) will be
A . 1: 1
B . 2: 1
c. 4: 1
D. 1: 4


Linear elastic deformation is governed
by
A. Hooke's Law
B. Euler Bernoulli's equation
c. both
D. none


A bag contains 6 black and 8 white
balls. One ball is drawn at random. What
is the probability that the ball drawn is
white?
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{7} \)
\( c \cdot \frac{1}{8} \)
D.


\( P \) is any point on the circumcircle of
\( \triangle A B C \) other than the vertices. \( H \) is the
orthocenter of \( \triangle A B C, M \) is the mid-
point of \( \boldsymbol{P H} \) and \( \boldsymbol{D} \) is the mid-point of
\( B C . \) Then
A. \( A P \) is opposite side of \( D M \)
B. \( D M \) is parallel to \( A P \)
c. \( D M \) is perpendicular to \( A P \)
D. None of these


n figure if PQR is tangent to circle at \( \mathrm{Q} \)
whose centre is \( 0 . A B \) is a chord parallel
to PR and \( \angle B Q R=70^{\circ} \) then \( \angle A Q B \) is
equal to
\( \mathbf{A} \cdot 20 \)
B. 40
\( c .35 \)
D. 45


\( ^{200} \boldsymbol{X} \rightarrow^{110} \boldsymbol{A}+^{90} \boldsymbol{B}+\boldsymbol{E} \boldsymbol{n} e \boldsymbol{r} \boldsymbol{g} \boldsymbol{y} \)
If the binding energy per nucleon for \( X, A \) and \( B \) are \( 7.4 \mathrm{MeV}, 8.2 \mathrm{MeV} \) and
8.2 MeV respectively, the minimum
energy required to bring in this reaction will be :
A. 90 Mev
B. 100 MeV
c. 120 Mev
D. 160 Mev


The International Space Station is
currently under construction. Eventually, simulated earth gravity may become a reality on the space station. What would the gravitational field through the central axis be like under
these conditions?
A. zero
B. \( 0.25 g \)
\( \mathrm{c} .0 .5 \mathrm{g} \)
D. \( 0.75 g \)
E . \( 1 g \)


Which one of the following acts as a
Lewis base in complexes?
\( A \cdot C O_{2} \)
B. BF \( _{3} \)
c. \( \mathrm{NH}_{3} \)
D. BCI


The population \( P \) of a town decreases at a rate proportional to the number by which the population exceeds-10 30, proportionality constant being \( \mathrm{k}>0 \) Find Population at any time \( t \) given initial population of the town being \( 2500 ., \) then \( P=1000+1500 e^{-k t} \)
then \( k=? \)
A \( \cdot k=\frac{1}{10} \ln \left(\frac{5}{3}\right) \)
B . \( k=\frac{-1}{10} \ln \left(\frac{5}{3}\right) \)
c. \( k=\ln \left(\frac{5}{3}\right) \)
D \cdot \( k=\frac{1}{10} \ln \left(\frac{3}{5}\right) \)


Which term best describes the nuclear
material present during interphase?
A. Chromosomes
B. Chromatids
c. Chromatin
D. centromeres
E. Centrioles


For the reaction \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons \)
\( 2 N H_{3}(g) \) in a vessel, after the addition
of equal number of moles of \( N_{2} \) and \( H_{2} \)
equilibrium state is achieved. Which of the following is correct?
\( \mathbf{A} \cdot\left[H_{2}\right]=\left[N_{2}\right] \)
B \cdot \( \left[H_{2}\right]<\left[N_{2}\right] \)
\( \mathbf{c} \cdot\left[H_{2}\right]>\left[N_{2}\right] \)
D・ \( \left[H_{2}\right]>\left[N H_{3}\right] \)


Identify the following elements.
a) \( _{25} X^{55} \)
b) \( _{17} X^{35} \)
c) \( _{20} X^{40} \)


A poisonous gas is adsorbed at activated charcoal. The activated
charcoal is:
\( A \). absorber
B. adsorbate
c. adsorbent
D. absorbate


A metal wire of length 1 m and crosssection area \( 2 m m^{2} \) and Young's
modulus of elasticity \( \boldsymbol{Y}=\mathbf{4} \times \)
\( 10^{11} N / m^{2} \) is stretched by \( 2 m m . \) Then
A. the restoring force developed in the wire is 1600 N
B. the energy density in the wire is \( 4 \times 10^{5} \mathrm{J} / \mathrm{m}^{3} \)
c. the restoring force developed in the wire is 400 N
D. the total elastic energy stored in the wire is \( 1.6 ~ J \)


The pressure in a water pipe on the ground floor of a building is 40000 pascal, whereas on the first floor it is
10000 pascal. Find the height of the
first floor. (Take \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \) ).


The building units of various crystalline forms of boron are:
A \( \cdot B_{12} \) icosahedral units
B. \( B_{4} \) tetrahedral units
c. \( B_{6} \) octahedral units
D. \( B_{6} \) cubical units


Which of the following is the emulsion of water in oil?
A. Buttermilk
B. Milk
c. cold cream
D. Vanishing cream


A charge \( Q \) is placed inside the sphere of radius \( a \) then what will be the value of
charge that will be accumulated on the surface of the sphere,
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( Q \)
c. \( -Q \)
D. - 2Q


If additive inverse of \( \frac{4}{18} \) is added to it
then the result will be


The difference between \( C . I \) and \( S . I \) on
the amount of \( R s .15000 \) for 2 years is
Rs.96. What is the rate of interest


State True or False.
Gamma rays are electromagnetic
radiations of wavelengths of \( 10^{-6} \mathrm{cm} \) to
\( 10^{-5} \mathrm{cm} \)
A. True
B. False


A current carrying loop is placed in a uniform magnetic field pointing in negative z direction. Branch PQRS is a tree quarter circle, while branch PS is straight. If force on branch PS is \( \mathrm{F} \), force on branch PQR is:
\( A \cdot \sqrt{2} F \)
в. \( \frac{F}{\sqrt{2}} \)
с. \( \frac{\pi F}{\sqrt{2}} \)
\( \mathbf{D} \cdot \sqrt{2} \pi F \)


Find empirical formula of the compound if \( M=68 \% \) (Atomic mass
\( =34 \) and remaining \( 32 \% \) oxygen
A . \( M O \)
в. \( M_{2} O \)
c. \( M O_{2} \)
D. \( M_{2} O_{3} \)


\( \boldsymbol{x}=\sin \boldsymbol{t} \quad \boldsymbol{y}=\cos \boldsymbol{m} \boldsymbol{t} \)
Prove \( :\left(\boldsymbol{1}-\boldsymbol{x}^{2}\right) \boldsymbol{y}_{n+2}-(\boldsymbol{2} \boldsymbol{n}+\boldsymbol{1}) \boldsymbol{y}_{n+1}- \)
\( \left(\boldsymbol{n}^{2}-\boldsymbol{m}^{2}\right) \boldsymbol{y}_{n}=\boldsymbol{0} \)


The electrical appliances in a house are
connected in :
A. series
B. parallel
c. either in series or parallel
D. both in series and parallel


State whether the given statement is True or False :
The value of \( G \) is high if the radius of the body is more and less if radius is less.
A . True
B. False


For a gaseous phase reaction \( \boldsymbol{A}+ \) \( \mathbf{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{A} \boldsymbol{B}_{2}, \boldsymbol{K}_{C}=\mathbf{0 . 3 4 7 5} \boldsymbol{L}^{2} \boldsymbol{m o l} \boldsymbol{e}^{-\mathbf{2}} \mathbf{a} \)
\( 200^{\circ} \mathrm{C} \). When 2 moles of \( B \) are mixed
with one mole of \( A \), what total pressure
is required to convert \( 60 \% \) of \( A \) in \( A B_{2} \) ?
A \( . P=1.8 a t m \)
B. \( P=63 \) atm
c. \( P=181.5 \) atm
\( D . P=34 a t m \)


Based on cross-multiplication method, solve the following pair of equations by cross multiplication rule \( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{3 5}, \mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{2 8} \)
Then
A. \( x=4, y=5 \)
B. \( x=5, y=4 \)
c. \( x=6, y=3 \)
D. \( x=3, y=6 \)


How is the acceleration due to gravity on earth surface related to the mass \( M \)
and radius \( R \) of earth?
A \( \cdot g=\frac{G}{M R^{2}} \)
в. \( g=\frac{M}{G R^{2}} \)
c. \( _{g}=\frac{G M}{R} \)
D. \( g=\frac{G M}{R^{2}} \)


Two quadrilaterals, a square and a rectangle are not similar as they \( \ldots \). in shape as well as size.
A . Differ
B. Are same
c. Do not siffer
D. Angles also differ


Your lab partner mixed two colorless
solutions in the test tube. He sees no
observable changes in the resulting mixture and is unable to detect any
change in temperature. Based on these observations, what type of reaction has
taken place?
A. A physical reaction
B. A chemical reaction
c. An exothermic reaction
D. No reaction has taken place


An electron (of mass \( \mathrm{m} \) ) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is \( (c= \) speed of light in vacuum)
\( ^{A} \cdot \frac{1}{c}\left(\frac{E}{2 m}\right)^{1 / 2} \)
B \( \cdot c(2 m E)^{1 / 2} \)
\( c \)
\[
\left(\frac{E}{2 m}\right)^{1 / 2}
\]
D \( \frac{1}{c}\left(\frac{2 E}{m}\right)^{1 / 2} \)


Phase difference between a particle at a
compression and a particle at the next
rarefaction is
A. zero
в. \( \frac{\pi}{2} \)
\( c \)
D.


Which sub shell is filled up progressively
in actinoids?
\( A \cdot 4 f \)
B. 5f
\( c \cdot 6 d \)
D. 7s


Evaluate
\( 8 \sqrt{3} \operatorname{cosec}^{2} 30^{\circ} \sin 60^{\circ} \cos 60^{\circ} \cos ^{2} 45^{\circ} \)
A \( \cdot 2 \sqrt{3} \)
B. \( 4 \sqrt{3} \)
\( c \cdot 8 \sqrt{3} \)
D. \( 12 \sqrt{3} \)


\( \ln \) a \( \triangle A B C, \) side \( A B \) has the equation
\( 2 x+3 y=29 \) and the side \( A C \) has the
equation \( x+2 y=16 . \) If the mid point
of \( B C \) is \( (5,6), \) then the equation of \( B C \)
is
A. \( 2 x+y=7 \)
B . \( x+y=1 \)
c. \( 2 x-y=17 \)
D. None of these


Twelve players \( S_{1}, S_{2}, \dots, S_{12} \) play in a chess tournament. They are divided into
six pairs at random. From each pair a winner is decided. It is assumed that all
players are of equal strength. The probability that exactly one of \( S_{1} \) and \( S_{2} \) is among the six winners is
A \( \cdot \frac{6}{11} \)
в. \( \frac{5}{11} \)
c. \( \frac{4}{11} \)
D. None of these


\( \operatorname{Let} f(x)=\left\{\begin{array}{c}\sin x, \quad \text { for } x \geq 0 \\ 1-\cos x, & \text { for } x<0\end{array} \) and \right.
\( g(x)=e^{x} \). Then \( (g o f)^{\prime}(0) \) is


When freshly precipitated \( F e(O H)_{3} \) is
boiled with water in the presence of few drops of dil. \( \boldsymbol{H} \boldsymbol{C l} \), a hydrated ferric
oxide sol is obtained. This method is
termed:
A. dialysiss
B. peptization
c. ultrafiltration
D. electro-dispersion


"Nat (cation) is smaller than \( N a \)
(atom)."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Let \( f(x)=\sin ^{23} x-\cos ^{22} x \) and
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2}} \tan ^{-\mathbf{1}}|\boldsymbol{x}| \)
Then, the number of values of \( x \) in
interval \( [-10 \pi, 20 \pi] \) satisfying the equation \( f(x)=\operatorname{sgn}(g(x)), \) is \( 5 a \) Then
\( a \) is


What is used as a fuel injet planes?
A . Liquid Petrol
B. Diesel oil
c. Kerosene
D. Gasolene


Choose the correct statements among
the following.
This question has multiple correct options
A. Heat capacity is the product of mass of specific heat
B. In SI system, thermal capacity and water equivalent are numerically equal
C. Heat always flows from higher temperature body to lower temperature body.
D. At thermal equilibrium, rate of heat flow from hot body equal to the rate of heat flow from cold body.


State work-energy theorem. Prove it for
a variable force.


Oil found in groundnut accumulates in
A. Embryo
B. cotyledons
c. Endosperm
D. None of the above


If \( N_{2} \) gas bubbled through water at
\( 293 K \) how many millimoles of \( N_{2} \) gas
would dissolve in 1 litre of water?

Assume that exerts a partial pressure
of \( 0.987 b a r \)
Given that Henry's law constant for \( N_{2} \)
at \( 293 K \) is \( 76.48 K b a r \)
A. 0.716
B. 0.62
c. 0.93
D. 0.54


When two capacitors of capacities \( 3 \mu F \)
and \( 6 \mu F \) are connected in series and
connected to \( 120 V, \) the potential
difference across \( 3 \mu F \) is:
A . \( 40 V \)
B. \( 60 V \)
c. \( 80 V \)
D. \( 180 V \)


A particle moves on a straight line in
such way that it covers 1 st half
distance with speed \( 3 m / s \) and next half
distance in 2 equal time intervals with
speeds \( 4.5 m / s \) and \( 7.5 m / s \)
respectively. Find average speed of the particle.


According to above histogram, How
many workers earn less than Rs \( 850 ? \)
A . 30
B. 20
\( c \cdot 10 \)
D. 40


\( \frac{2 x^{2}+2 x+1}{x^{3}+x^{2}}= \)
A \( \cdot \frac{1}{x}-\frac{1}{x^{2}}-\frac{1}{x+1} \)
в. \( \frac{1}{x}-\frac{1}{x^{2}}+\frac{1}{x+1} \)
c. \( \frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x+1} \)
D. \( \frac{1}{x}+\frac{1}{x^{2}}-\frac{1}{x+1} \)


Two plane mirrors are placed such they
make \( 0^{\circ} \) angle with each other .How many images, of an object placed between them, are formed?
\( A \cdot O \)
B. 2
\( c \)
D. Infinite


Which of the following statements
about kinetic energy (K.E.) is true?
A. All objects moving with the same velocity have the same K.E
B. The K.E. of a body will quadruple if its velocity doubles
C. As the velocity of a body increases, its K.E. decreases
D. The K.E. of a body is independent of its mass


Which of the following characteristics is not a function of humus in soil?
A. Provides nutrients
B. Raises pH
c. Retains moisture
D. Humus does all of the above in soil


Prove that in an isosceles triangle, the
median to the base is also
perpendicular.


When electrophorus is charged, the electricity is obtained from :
A. Cat's skin
B. Metallic plate
c. sole
D. Ebonite plate


Which of the following alcohols is dehydrated most easily with conc.
\( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A \( \cdot p-O_{2} N C_{6} H_{4} C H(O H) C H_{3} \)
в. \( p-C l C_{6} H_{4} C H(O H) C H_{3} \)
c. \( p-C H_{3} O C_{6} H_{4} C H(O H) C H_{3} \)
D. \( C_{3} H_{5} C H(O H) C H_{3} \)


The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule at
temperature \( \mathrm{T} \) is \( \mathrm{x} / \mathrm{y} \) then value of \( x+y \) is


The gaseous mixture contains oxygen and nitrogen in the ratio of 1: 8 by
mass. The ratio of their respective
number of molecules \( \left(N_{O_{2}}: N_{H_{2}}\right) \) is
A .1: 8
B. 1: 1
\( c \cdot 7: 64 \)
D. 1: 2


A die is thrown 100 times with
frequency for the outcomes 1,2,3,4,5
and 6 as given this following table Find the probability of getting
Number greater than 5 as an outcome.


Select the correct statements among
the following:
This question has multiple correct options
A. Milk is emulsion of fat in water.
B. An emulsifier stabilizes the emulsion
C. Emulsifier forms a thin film around the droplets of dispersed phase
D. Milk is an emulsion of protein in water


The total work done on a particle is equal to the change in its kinetic energy. This statement is applicable in
A . Always
B. Only if the force acting on the body are conservative
c. only in the inertial frame
D. Only if no external force is acting


Which statement is false in the
following statement?
A. A triangle has three sides.
B. A cylinder has four faces which are circles
c. Faces of the cuboid are in the shape of a rectangle.
D. Faces of the cube are in the shape of square


Solve the following pairs of equations by
reducing them to a pair of linear
equations:
\( \frac{1}{2 x}+\frac{1}{3 y}=2, \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)


The formulae of oxides formed when
barium burns in presence of oxygen are:
A. \( B a_{2} O, B a O \)
в. \( B a O, B a O_{2} \)
с. \( B a O, B a_{2} O_{2} \)
D. \( B a_{2} O, B a O_{2} \)


The minimum energy to ionize an atom is also the energy required to:
A. add one electron to the atom
B. excite the atom from its ground state to its first excited state
C. remove one outermost electron from the atom
D. remove one innermost electron from the atom


Which of the following proteins is found in the thick filaments of skeletal
muscle?
\( A \). Actin
B. Troponin
c. Myosin
D. Tropomyosin


Friction between any two objects is due
to
A. attraction between them
B. repulsion between them
c. some adhesive forces between them
D. irregularities on the surfaces


Two identical coils each of radius \( R \) and
each carrying a current \( I \) in the same
direction are placed along a common axis and separated by distance \( R \). At the midpoint between the two coils the
A. Magnetic field is zero
B . Magnetic field is \( 0.8 \sqrt{0.8} \mu_{0} I / R \)
C. Second derivative of magnetic field \( d^{2} B / d x^{2}=0 \)
D. First derivative of magnetic field \( d B / d x=0 \)


If the charge of \( 10 \mu C \) and \( -2 \mu C \) are
given to two plates of a capacitor which
are connected across a battery of \( 12 V \)
find the capacitance of the capacitor.
в. \( 0.5 \mu F \)
c. \( 0.41 \mu F \)
D. \( 0.66 \mu F \)


With the help of a circuit diagram, explain how a metre bridge can be used to find the unknown resistance of a
given wire.


The sum of the first five terms and the
sum of the first ten terms of an AP are
same. Which one of the following is the correct statement?
A. The first term must be negative
B. The common difference must be negative
c. Either the first term or the common difference is negative but not both
D. Both the first term and the common difference are negative


Which one of these is a herbicide?
A . DDT
в. ВНС
c. Dioxin
D. Dieldrin


Four charges are placed at the
circumference of the dial of a clock as
shown in figure. If the clock has only
hour hand, then the resultant force on a
positive charge \( q_{0} \) placed at the centre,
points in the direction which shows the
time as :-
A . 1: 30
B. 7:30
\( c \cdot 4: 30 \)
D. 10: 30


Which of the following is known as invert soap?
A. Pentaerythritol monostearate
B. Trimethyl stearyl ammonium bromide
c. Ethoxylated nonphenol
D. sodium stearyl sulphate


A body has a positive charge of \( 8 x \)
\( 15^{-19} C . \) It has
A. an excess of \( 5 e^{-} \)
B. a deficiency of \( 5 e^{-} \)
c. an excess of \( 8 e^{-} \)
D. a deficiency of \( 8 e^{-} \)


Evaluate the integral \( \int_{1}^{2} \sqrt{(x-1)(2-x)} d x \)
A. \( \frac{\pi}{8} \)
в.
c. \( \frac{1}{8} \)
D.


Which of the following oxide is most acidic?
A. \( N a_{2} O \)
в. \( M g O \)
\( \mathrm{c} \cdot \operatorname{si0}_{2} \)
D. \( C l_{2} O_{7} \)


A naked sporangium occurs in
A. Cellular slime moulds
B. Acellular slime moulds
c. commonly acellular slime moulds but at times cellular slime moulds
D. All slime moulds


Let \( * \) be a binary operation on the set of all non zero real numbers, given by \( a * \)
\( \boldsymbol{b}=\frac{\boldsymbol{a} \boldsymbol{b}}{\mathbf{5}} \forall \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{R}-\{\mathbf{0}\}, \) find the value of
\( x, \) given that \( 2 *(x * 5)=10 \)


The focal length of the objective of a telescope is \( 60 \mathrm{cm} . \) To obtain a
magnification of 20 for the relaxed eye, the length of telescope should be
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( \mathbf{c} \cdot 63 c m \)
D. \( 57 \mathrm{cm} \)


So that the torque acting on it is zero


Mike needs \( 30 \% \) to pass. If he scored
212 marks and falls short by 13 marks, what was the maximum marks he
could have got?
A .750
в. 850
c. 725
D. 700


How many allotropes do sulphur have?
A .4
B. 20
\( c \cdot>20 \)
D. 10


Water supply in the plant is due to
A. Osmosis
B. Guttation
c. cohesion force
D. Imbibition


The greatest value of the term independent of \( x, \) as \( \alpha \) varies over \( R \) in
the expansion of \( \left(x \cos \alpha+\frac{\sin \alpha}{x}\right) \) is
B. \( ^{20} C_{19} \)
c. \( 20 C_{6} \)
D. \( ^{20} C_{6}\left(\frac{1}{2}\right)^{10} \)


Changes in which one or more new substances are formed are called
changes.
A. chemical
B. physical
c. both \( A \) and \( B \)
D. none of the above


The medium of plasma is
A. Acidic
B. Basic
c. Neutral
D. None of the above


Sulphur dioxide levels in the atmosphere can be reduced by using:
A. catalytic converters in industry
B. Static electricity to attract it in Factory chimneys
c. More efficient car-engines.
D. Low-sulphur fuels


Two parallel wires carrying current in
the same direction attract each other
because of
A. potential difference between them
B. mutual inductance between them
c. electric forces between them
D. magnetic forces between them


All of the following activities affect the
quality and quantity of clean water except
A. Industrial waste disposal into waterways
B. Overgrazing of livestock
c. Oil spills
D. Excessive use of artificial fertilizers in agriculture
E. over fishing and hunting of marine organisms


The thinnest bubble film in air that can
possibly strongly reflect red light
because of constructive interference
makes up a certain bubble. How could we create the thinnest
bubble film that will strongly reflect
purple light?
A. Use a thicker film than the film used for the "red" bubble
B. Use a film with a higher index of refraction than the film used for the "red" bubble
C. Make a bubble larger than the "red" bubble
D. Make a bubble smaller than the "red" bubble
E. Use a thinner film than the film used for the "red" bubble


The number of relations from \( \boldsymbol{A}= \)
\{2,6\} to \( B=\{1,3,5,6,7\} \) that are not
functions from \( A \) to \( B \) is


Hormone oxytocin at the time to birth acts on uterus by
A. Stimulating the smooth muscles to contract
B. Reducing the lumen of uterus
c. Increasing the movement of foetus
D. Producing rhythmic movements in uterus


Which of the following options represents the correct bond order?
A \( \cdot O_{2}^{-}>O_{2}<O_{2}^{+} \)
В \( \cdot O_{2}^{-}<O_{2}>O_{2}^{+} \)
\( \mathrm{c} \cdot O_{2}^{-}>O_{2}>\mathrm{O}_{2}^{+} \)
D. \( O_{2}^{-}<O_{2}<O_{2}^{+} \)


The most important function of inflorescence is to help in
A. Dispersal of seeds
B. Help in fertilization
c. Attracting insects for pollination
D. Forming large number of fruits


Specify the reagents in which addition to alkene is syn or anti.


The displacement (in \( \mathrm{m} \) ) of a particle of mass 100 gram from its equilibrium position is given by \( \boldsymbol{y}=\mathbf{0 . 0 1} \sin 2 \pi(t+ \)
0.4). Select the correct option(s):
This question has multiple correct options
A. The time period of motion is 1 sec.
B. The time period of motion is \( \frac{1}{7.5} \) sec
c. The maximum acceleration of the particle is \( 0.04 \pi^{2} m / s^{2} \)
D. The force acting on the particle is zero when the displacement is 0.05m


It is difficult to burn a heap of green leaves but dry leaves catch fire easily.
A. True
B. False


The graph of the equation \( x y=k, \) where
\( k<0, \) lies in which two of the
quadrants shown above?
A . I and II
B. I and III
c. II and III
D. II and IV
E . III and IV


Round off following number upto four significant figures
\( \mathbf{2 . 0 0 8 2 3} \)
\( \mathbf{A} \cdot 2.008 \)
в. 2.0082
c. 2.0083
D. 2


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\cos ^{-1}\left(4 \boldsymbol{x}^{3}-\mathbf{3} \boldsymbol{x}\right)\right),=\therefore \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{m}}{\sqrt{\mathbf{1}-\boldsymbol{x}^{k}}} . \) Find \( \boldsymbol{k}-\boldsymbol{m} \) ?


micrometer is \( \quad \) kilometer.
A \( \cdot 10^{-9} \)
B. \( 10^{-8} \)
\( \mathbf{c} \cdot 10^{-10} \)
D. \( 10^{8} \)


In voltaic cell, oxidation takes place at:
A . positive electrode
B. negative electrode
c. cathode
D. none of the above


The work done on the system in an adiabatic compression depends on:
This question has multiple correct options
A. the increase in internal energy of the system
B. the decrease in internal energy
c. the change in volume of the system
D. all of the above


Evaluate:
\( \lim _{x \rightarrow \infty} \frac{2+\cos ^{2} x}{x+2007} \)


When the maximum clock rate is
quoted for a logic family, it applies to a
A. Shift register
B. Flip-flop
c. counter
D. single logic gate


The dissociation constants for
HCOOH and \( C H_{3} \) COOH are \( 2.1 \times \)
\( 10^{-4} \) a.nd \( 1.8 \times 10^{-5} \) respectively.
Calculate the relative strengths of the
acids.


A family has two children. What is the
probability that both the children are boys given that at least one of them is a boy?


In a series LCR circuit \( \mathrm{R}=4 \Omega, \mathrm{XL}=5 \Omega \) and
\( X_{C}=8 \Omega, \) the current
A. leads the voltage by \( \tan ^{-1}(3 / 4) \)
B. leads the voltage by tan \( ^{-1}(5 / 8) \)
C . leads the voltage by tan \( ^{-1}(3 / 5) \)
D. leads the voltage by \( \tan ^{-1}(5 / 9) \)


If \( A \) and \( B \) are square matrices of the same order, explain, why in general? \( (A+B)^{2} \neq A^{2}+2 A B+B^{2} \)


A carnivore eats
A. Sprouted seeds
B. Milk
c. Green leaves
D. Flesh of other animals


UV radiation from sun causes a
reaction that produces
A. carbon oxide
B. sulphur dioxide
c. fluorides
D. ozone


Distinguish which one is initial valued
ordinary differential equation and
boundary valued ordinary differentia equation:
\( \mathbf{y}^{\prime \prime}+\mathbf{2} \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}(\boldsymbol{\pi})=\mathbf{1} ; \boldsymbol{y}^{\prime}(\boldsymbol{\pi})=\mathbf{2} \)
¡) \( \boldsymbol{y}^{\prime \prime}+\mathbf{2} \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}(\mathbf{0})=\mathbf{1} ; \boldsymbol{y}^{\prime}(\mathbf{1})=\mathbf{1} \)


Chrome green is
\( \mathbf{A} \cdot P b C r O_{4}+F e^{I I I}\left[F e^{I I}(C N)_{6}\right] \)
\( \mathbf{B} \cdot C r_{2} O_{5} \)
\( \mathbf{c} \cdot P b C r O_{4} \)
D. \( F e C r O_{4} \)


An electric bulb is made of tungsten
filament of resistance \( R \Omega \). It is marked
\( 100 W \) and \( 230 V . \) Then, the value of \( R \) is
A. \( 300 \Omega \)
в. \( 529 \Omega \)
\( \mathbf{c} .739 \Omega \)
D. \( 100 \Omega \)


Ashokbhai goes to an electric shop to buy an electric bulb to obtain light in a small room of his home. Which of the
following statement is scientifically
correct
A. Give bulb of \( 60 \mathrm{V} \)
B. Give bulb of \( 60 \mathrm{J} / \mathrm{s} \)
c. Give bulb of \( 60 A \)
D. Give bulb of \( 60 \mathrm{W} \)


Match the following and pick the correct
combination
\( \begin{array}{lllll} & \text { LIST I } & & \text { LIST II } & \\ \text { A } & \text { Kupffer Cells } & \text { 1 } & \begin{array}{l}\text { Small } \\ \text { intestine }\end{array} \\ \text { B } & \beta \text { cells } & \text { 2 } & \text { PCT } \\ \text { C } & \begin{array}{l}\text { Brush border } \\ \text { cell }\end{array} & \text { 3 } & \begin{array}{l}\text { Liver } \\ \text { sinusoids }\end{array} \\ \text { D } & \text { Paneth cells } & 4 & \text { Pituitary } \\ & \text { 5 } & \begin{array}{l}\text { Islets } \\ \text { Langerhans }\end{array}\end{array} \)
A \( \cdot A-5, B-3, C-2, D- \)
B. A- 3, B- 5, C- 2, D-
C. \( A-2, B-5, C-1, D-3 \)
D. A- \( 1, \) B- \( 2, \) C- \( 3, \) D-


A fair die is rolled. Consider events \( \boldsymbol{E}= \)
\( \{1,3,5\}, F=\{2,3\} \) and \( G= \)
\{2,3,4,5\} Find
(i) \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \) and \( \boldsymbol{P}(\boldsymbol{F} \mid \boldsymbol{E}) \)
(ii) \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{G}) \) and \( \boldsymbol{P}(\boldsymbol{G} \mid \boldsymbol{E}) \)
(iii) \( P((E \cup F) \mid G) \) and \( P((E \cap F) \mid G) \)


In the given circuit diagram, the value
of resistance \( X \) in ohm when the bridge
is balanced will be -
4
B.
c. 10
D. 12


A sinusoidal progressive wave is generated in a string. It's equation is given by \( y=(2 m m) \sin (2 \pi x- \)
\( \mathbf{1 0 0} \pi \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) . \) The time when particle
at \( x=4 m \) first passes through mean
position, will be
A \( \cdot \frac{1}{150} \sec \)
в. \( \frac{1}{12} \) sec
c. \( \frac{1}{300} \) sec
D. \( \frac{1}{100} \) sec


Using identities, evaluate \( 998^{2} \)
A . 995704
B. 996004
c. 992004
D. 990004


\( D_{2} O \) is used more in:
A. chemical industry
B. nuclear moderator
c. pharmaceutical preparation
D. insecticide preparations


Which of the following statement is not
correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In Lanthanoid series ionic radius of \( \mathrm{Ln}^{3+} \) ions
decreases
C. La is actually an element of transition series rather than Lanthanoid series
D. Atomic radii of Zr and Hf are same because of
Lanthanoid contraction


A compound contains 7 carbon atoms, 2
oxygen atoms and \( 9.96 \times 10^{-24} g \) of
other elements. The molecular mass of
compound is \( \left(N_{A}=6 \times 10^{23}\right) \)
A. 122
в. 116
\( c .148 \)
D. 154


A column of \( \mathrm{Hg} \) of \( 10 \mathrm{cm} \) length is contained in the middle of a narrow
horizontal \( 1 \mathrm{m} \) long tube which is closed at both ends. Both the halves of the tube
contain air at a pressure \( 76 \mathrm{cm} \) of Hg. The distance of the column of Hg be
displaced if the tube is held vertically is
A. 3 cms
B. 2 cms
c. \( 4 \mathrm{cms} \)
D. \( 1 \mathrm{cm} \)


Which of the following represents the phase change from gas directly to solid?
A. Deposition
B. Sublimation
c. Liquefaction
D. Fusion
E. Vaporization


The reactant \( X \& Y \) of following
reactions are:
\( \mathbf{A} \)
B.
\( c \)
D.


Which of the following metals are found in native state?
\( A g, P t, C, S i, N, O, M g, N a, P b \)
\( A \cdot A g, P t, C, N, O \)
B. Ag, Pt, Mg
c. Ag, Pt, Pb, Mg
D. Ag, Pt


Calculate the mass defect.
A . 2.014 и
в. 1.0087 и
c. \( 0.01876 u \)
D. 0.0234 и


What will be products formed when
above epoxide reacts with \( \boldsymbol{C H}_{3} \boldsymbol{O H} \) in
acidic and in basic medium?
A . Acidic - \( \left(C H_{3}\right)_{2} C O H-C H_{2}\left(O C H_{3}\right) \); Basic
\( \left(C H_{3}\right)_{2} C\left(O C H_{3}\right)-C H_{2} O H \)
B. Acidic - (CH3)_COH - CH \( _{2}\left(O C H_{3} \) ); Basic - \right. \( \left(C H_{3}\right)_{2} C O H-C H_{2}\left(O C H_{3}\right) \)
c. Acidic - \( \left(C H_{3}\right)_{2} C\left(O C H_{3}\right)-C H_{2} O H ; \) Basic
\( \left(C H_{3}\right)_{2} C O H-C H_{2}\left(O C H_{3}\right) \)
D. Acidic- \( \left(C H_{3}\right)_{2} C\left(O C H_{3}\right)-C H_{2} O H ; \) Basic\( \left(C H_{3}\right)_{2} C\left(O C H_{3}\right)-C H_{2} O H \)


All living things depend on which chemical element?
A. Oxygen
B. Nitrogen
c. Hydrogen
D. Phosphorous


Let \( S_{n}=\sum_{k=1}^{n} k \) denote the sum of the
first \( n \) positive integers. The numbers
\( \boldsymbol{S}_{1}, \boldsymbol{S}_{2}, \boldsymbol{S}_{3}, \ldots, \boldsymbol{S}_{99} \) are written on \( \boldsymbol{9 9} \)
cards. The probability of drawing a card with an even number written on it is
A \( \cdot \frac{1}{2} \)
в. \( \frac{49}{100} \)
c. \( \frac{49}{99} \)
D. \( \frac{48}{99} \)


To determine the Young modulus of a wire, several measurements are taken.
In which row can the measurement not
be taken directly with the stated apparatus?
A. measurement: area of cross-section of wire apparatus : micrometer screw gauge
B. measurement: extension of wire ; apparatus: vernier scale
c. measurement: mass of load applied to wire ; apparatus : electronic balance
D. measurement: original length of wire ; apparatus metre rule


Fibre-free matrix present in
A. Tendons
B. Ligaments
c. Lymph
D. Cartilage


A glass bulb is balanced by a brass weight in a sensitive beam balance. Now the balance is covered by a glassjar which is then evacuated. Then:
A. the beam will remain horizontal
B. the pan containing the bulb will go down
c. the pan containing the bulb will go
D. none of the above


Charge can be a multiple of \( e \), i.e. ne. Which of the following can be a value of
\( \boldsymbol{n} ? \)
A . 27
B. 1.5
c. 30.5
D. 0.99999


Two bodies have their moments of
inertia I and 21 respectively about their axis of rotation.lf their kinetic energies
of rotation are equal, their angular
momenta will be in the ratio-
A \( \cdot \sqrt{\frac{3}{1}} \)
в. \( \sqrt{\frac{6}{1}} \)
c. \( \sqrt{\frac{2}{1}} \)
D. \( \sqrt{\frac{5}{1}} \)


If \( x \) is real, then find the solution of
\( \sqrt{x+1}+\sqrt{x-1}=1 \)
A \( \cdot \frac{5}{4} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{3}{5} \)
D. No such \( x \) exists


A milkman adds a very small amount of baking soda to fresh milk. The pH will :
A. increase
B. decrease
c. same as milk
D. none of these


Solve :
\( \cos ^{-1}\left(\log _{2} x\right)=0 \)


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


Perpendiculars dropped from the midpoints of two sides of a triangle to the third side are equal.


Yield of each step as actually carried out in laboratory is given above each arrow. What is overall yield of the
reaction?
A . 60\%
в. 21\%
c. \( 40 \% \)
D. 68\%


Find the conjugates of the following complex numbers:
\( \frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)} \)
A \( \cdot \frac{63}{25}-\frac{16}{25} i \)
В \( \cdot \frac{62}{25}+\frac{16}{25} i \)
c. \( \frac{63}{25}+\frac{17}{25} i \)
D. \( \frac{63}{25}+\frac{16}{25} i \)


Integrate:
\( \int \cos x \log \cos x d x \)


For natural number \( n, 2^{n}(n-1) !<n^{n} \)
if
\( \mathbf{A} \cdot n<2 \)
\( \mathbf{B} \cdot n>2 \)
c \( . n \geq 2 \)
D. Never


Which one of the following reagents is
used for detection of unsaturation in
alkenes?
A. \( N a O H+C a O \)
B. cold dilute alkaline \( K M n O_{4} \)
c. \( C l_{2} / h v \)
D. \( K O H / C_{2} H_{5} O H \)


10 kg storage battery has an average
specific heat of \( 0.2 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C} \). When fully charged, the energy content of the battery is 1 kcal. If the entire energy were used to raise the temperature,
then the temperature would increase by
A. \( 0.2^{\circ} \mathrm{C} \)
B. \( 0.5^{\circ} \mathrm{C} \)
c. \( 200^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)


Crypts of Lieberkuhn occur in
A. Pancreas and secrete pancreatic juice
B. Small intestine and secrete digestive enzymes
C. Stomach and secrete dilute hydrochloric acid
D. Stomach and secrete pepsin


The distance of the point (1,-2,3) from the plane \( x-y+z=5 \) measured parallel to the line \( \frac{x}{2}=\frac{y}{3}=\frac{z}{-6} \) is
A .
B . 19
c. 155
D. \( \sqrt{271} \)


How many significant digits does the measurement \( 13.284 g \) possess?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. 4
E . 5


Homogeneous equilibrium is one in which there are:
A. no phases
B. two phases
c. one phase
D. all the three phases


What is the physical state of water at
\( 257^{0} C ? \)


\( |\psi(x, y, z, t)|^{2} \) represents:
This question has multiple correct options
A. probability of finding the particle in the space
B. probability distribution function
C . stationary state
D. None of these


A charge \( Q \) is placed at each of the opposite corners of a sequare. A charge \( q \) is placed at each of the other two
corners. If the net electric force on \( Q \) is
zero, then \( Q / q \) equals:
A . -1
B. 1
c. \( -\frac{1}{2} \)
D. \( -2 \sqrt{2} \)


Let two planes \( p_{1}: 2 x-y+z=2, \) and
\( \boldsymbol{p}_{2}: \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}-\boldsymbol{z}=\boldsymbol{3} \) are given. The
image of plane \( P_{1} \) in the plane mirror
\( P_{2} \) is
A. \( x+7 y-4 z+5=0 \)
B. \( 3 x+4 y-5 z+9=0 \)
c. \( 7 x-y+2 z-9=0 \)
0
D. \( 7 x+y+9 z+9=0 \)


Find the total surface area of a solid
hemisphere of radius \( 10 \mathrm{cm} . \) [Use \( \pi= \)
3.14]


\( A B C \) is an isosceles triangle, If the
coordinates of the base are \( B(1,3) \) and
\( C(-2,7), \) the coordinates of vertex \( A, \) is
\( ^{\mathbf{A}} \cdot\left(-\frac{1}{2},-4\right) \)
в. (1,6)
\( ^{c} \cdot\left(\frac{5}{6}, 6\right) \)
D. None of these


Which of the following is chemical formula of Oleum?
\( A \cdot H_{2} S_{2} O_{8} \)
в. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)


Water poured into an inverted conical vessel of which the radius of the base is
\( 2 \mathrm{m} \) and height \( 4 \mathrm{m}, \) and the rate of 77 litres/minute. The rate at which the
water level is rising at the instant when the depth is \( 70 \mathrm{cm} \) is: (use \( \pi=22 / 7 \) )
A. \( 10 \mathrm{cm} / \mathrm{min} \)
в. \( 20 \mathrm{cm} / \mathrm{min} \)
c. \( 40 \mathrm{cm} / \mathrm{min} \)
D. None


'Red tides' are produced by massive blooms of which of the following?
A. Diatoms
B. Red algae
c. Dinoflagellates
D. Brown algae


Assertion
The pressure exerted by solids is a little different from that of fluids
Reason
There is loose interactions of atoms
molecules in solids
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


State whether weight is a scalar or vector quantity?


Loss of a beta particle is equivalent to:
A. increase of one neutron only
B. decrease of one neutron only
\( c . \) both 1 and 2
D. none of these


The focal length of a convex lens of
refractive index 1.5 is \( f \) when it is
places in air. When it is immersed in a
liquid it behaves as a converging lens its focal length becomes \( x f(x>1) \). The refractive index of the liquid
\( A \cdot>3 / 2 \)
B. \( <(3 / 2) \) and \( >1 \)
\( c \cdot<3 / 2 \)
D. all of these


If \( x, y, z \) are three consecutive positive integer, then \( \log (1+z x) \) is
equal to


the terminal velocity \( v_{r} \) ) in downward direction inside a highly viscous liquid
placed inside a large container. The
height of liquid in the container is \( \boldsymbol{H} \)
The ball attains the terminal velocity
just before striking the bottom of the
container. Draw graph between velocity
of the ball and distance moved by the
ball before terminal velocity.


Which of the following is not true about
polymers?
A. Polymers are high molecular mass macro-molecules.
B. Polymers may be of natural or synthetic origin.
C. Condensation polymers are made up of one type of monomers only.
D. They have high viscosity and do not carry any charge.


Which enzyme fixes \( C O_{2} \) in Calvin
cycle?
A. RUBP carboxylase
B. PEP carboxylase
c. Carbonic anhydrase
D. Hexokinase


A process in which a change is brought by a ferment such as yeast, enzymes which convert sugar into ethyl alcohol is
called:
A. polymerisation
B. acetylation
c. hydrogenation
D. fermentation


In a Rutherford scattering experiment
when a projectile of charge \( Z_{1} \) and
mass \( M_{1} \) approaches a target nucleus
of charge \( Z_{2} \) and mass \( M_{2} \), the
distance of closest approach is \( r_{0} . \) The
energy of the projectile is :
A . Directly proportional to mass \( M_{1} \)
B. Directly proportional to \( M_{1} \times M_{2} \)
C. Directly proportional to \( Z_{1} Z_{2} \)
D. Inversely proportional to \( Z_{1} \)


\( \operatorname{Let} f(x)=2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \)
Then
A \( \cdot f^{\prime}(2)=f^{\prime}(3) \)
B . \( f^{\prime}(2)=0 \)
\( \mathbf{c} \cdot f^{\prime}(1 / 2)=16 / 5 \)
D. All of these


Which of the following has greatest \( \boldsymbol{H}- \)
bonding?
A. Acetone
B. Ethanol
c. Methanol
D. All have same


Examine the Rolles theorem is
applicable to the followng function. Find the number of points the following function is not continous?
\( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \boldsymbol{\epsilon}[\boldsymbol{2}, \boldsymbol{2}] \)


A ray refracts through a prism symmetrically such that the net
deviation of the ray is \( 42^{\circ} . \) If the
refracting angle of the prism is \( 56^{\circ} \)
Find the angle of incidence.
A \( \cdot 14^{\circ} \)
B . \( 28^{\circ} \)
\( c \cdot 49^{\circ} \)
D. none of these


A uniform cylinder rests on a cart as shown. The coefficient a static friction
between the cylinder and the cart is 0.5 fthe cylinder is \( 4 \mathrm{cm} \) in diameter and
\( 10 \mathrm{cm} \) in height, then what is the minimum acceleration \( \left(\text { in } m s^{-2}\right) \) of the cart needed to cause the cylinder to tip
over?


Consider the outermost electronic
configuration of silicon as follow:
\( [N e] 3 s^{2} 3 p^{2} \)
The given electronic configuration follows:
A. Aufbau's principle
B. Paul's rule
c. Hund's rule
D. All of the above


A pulse of sound wave travels a distance \( l \) in helium gas in time \( T \) at \( a \)
particular temperature. If at the same temperature a pulse of sound wave is propagated in oxygen gas, it will cover
the same distance \( l \) in time.
A . \( 4.36 T \)
в. \( 0.23 T \)
\( c .3 T \)
D. \( 0.46 T \)


Which of the following halides is capable of exhibiting enantiomerism?
A. Ethyl chloride
B. Isopropyl bromide
c. sec-Butyl iodide
D. tert-Butyl chloride


What is requirement for sodium in milligrams per day?
A . 400
B. 500
\( c \cdot 600 \)
D. 700


and \( C \) have radii \( a, b \) and \( c(a<b<c) \)
and surface charge densities on them
\( \operatorname{are} \sigma,-\sigma, \) and \( \sigma \) respectively. The
values of \( \boldsymbol{V}_{\boldsymbol{A}} \) and \( \boldsymbol{V}_{\boldsymbol{B}} \) will be:
A \( \cdot \frac{\sigma}{\epsilon_{0}}(a-b+c), \frac{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{b}-b+c\right) \)
B \( \cdot \frac{\sigma}{\epsilon_{0}}(a-b+c), \frac{\sigma}{\epsilon_{0}} \frac{a^{2}}{c} \)
c. \( \frac{\sigma}{\epsilon_{0}}(a+b-c), \frac{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{c}-b+c\right) \)
\( \stackrel{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{c}-\frac{b^{2}}{c}+c\right), \frac{\sigma}{\epsilon_{0}}(a-b+c) \)


What are alloys? Name an important alloy which contains some of the
lanthanoid metals. Mention its uses.


First land inhabiting plants are
A. Angiosperms
B. Gymnosperms
c. Bryophytes
D. Pteridophytes


PDI for natural polymers is generally close to:
A . zero
B.
c. 10
D. 100


Which of the following statement is
true?
A. Absolutely pure water does not contain any ions
B. London forces is directly proportional to more number of loosely held elctron
C. Allene is polar due its non planar structure
D. \( C H_{3} O C H_{3} \) is less volatile than \( C_{2} H_{5} O H \) due to higher
molecular weight


The electrolysis of molten NaOH
liberates \( 0_{2} \) at anode.
If true enter 1 , else enter 0 .


Which salt predominates in bone
matrix?
A. Sodium chloride
B. Sodium carbonate
c. Calcium phosphate
D. Magnesium phosphate


Electromagnetic wave of intensity \( 1400 W / m^{2} \) falls on metal surface on
area \( 1.5 m^{2} \) is completely absorbed by
it. Find out force exerted by beam.
A \( \cdot 14 \times 10^{-5} N \)
В. \( 14 \times 10^{-6} N \)
\( \mathbf{c} \cdot 7 \times 10^{-5} N \)
D. \( 7 \times 10^{-6} N \)


The arsenious sulphide solution has negative charge. Which of the following compounds has the maximum coagulating power for precipitating it?
\( \mathbf{A} \cdot 0.1 N Z n\left(N O_{3}\right)_{2} \)
в. \( 0.1 \mathrm{N} \mathrm{Na}_{3} \mathrm{PO}_{4} \)
\( c \cdot 0.1 N Z n S O_{4} \)
D. \( 0.1 \mathrm{N} \) AlCl\( _{3} \),


A circular smooth road of radius \( r= \)
\( 20 m \) is banked for vehicles moving at a
speed of \( v=36 k m p h \). If the friction
coefficient between the road and the
road and the Tyre is \( 0.3, \) find the maximum speed of a vehicle going around this curved road.
A. \( 29.39 k m p h \)
в. \( 39.29 k \) три
c. \( 40.39 k m p h \)
D. None of these


Non-metallic oxides are either \( \ldots \) or \( \ldots \) in
nature.
A. Neutral, acidic
B. acidic,basic
c. Neutral, basic
D. acidic,acidic


A radioactive sample at any instant has
its disintegration rate 5000 disintegrations per minute. After 5
minutes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute)
is
A. \( 0.4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)


Particles having positive charge occasionally come with high velocity from the sky towards the earth on account of magnetic field of earth, they would be deflected towards:
A. North
B. South
\( c . \) East
D. west


If the diagonal of cube is \( \sqrt{300} \mathrm{cms} \) then the surface area (in sq. cm) is
A. 300
в. 600
\( c .1200 \)
D. 2400


Resistance \( R, 2 R, 3 R \ldots N R \) if, \( N R \ldots \) are connected in parallel. Their resultant resistance will be
A.
B. R/2
\( c \cdot 0 \)
D. \( \infty \)


f \( 0 \leq x \leq 1, \) then \( \tan \left\{\frac{1}{2} \sin ^{-1} \frac{2 x}{1+x^{2}}+\frac{1}{2} \cos ^{-1} \frac{2 x}{1+x^{2}}\right\} \)
\( A \)
B.
c. \( \frac{2 x}{1+x^{2}} \)
\( D \)


Which of the following conditions are correct for real solutions showing negative deviation from Raoult's law?
A \( \cdot \Delta H_{M i x}<0 ; \Delta V_{M i x}>0 \)
B. \( \Delta H_{M i x}>0 ; \Delta V_{M i x}>0 \)
c. \( \Delta H_{M i x}>0 ; \Delta V_{M i x}<0 \)
D. \( \Delta H_{M i x}<0 ; \Delta V_{M i x}<0 \)


Oryza sativa is the binomial name of the rice plant, the sativa stands for
A. Specific name
B. Specific epithet
c. Genus name
D. Specific nomenclature


For which of the following species sum
spin quantum number of all electrons
comes out to be zero?
A \( \cdot C r^{+}(Z=24) \)
в. \( \operatorname{Sc}(Z=21) \)
c. \( C r^{+}(Z=29) \)
D. \( N a(Z=11) \)


A mixture of light, consisting of wavelength 590nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The
central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4 th bright fringe of the unknown light. From this data, the wavelength of the unknown light is
A. \( 885.0 \mathrm{nm} \)
B. 442.5 nm
c. \( 776.8 \mathrm{nm} \)
D. 393.4 nm


What happens when silver is leached
with \( N a C N \) in the presence of air?


Molarity is expressed as:
A. Gram/litre
B. Moles/litre
c. Litre/mole
D. Moles/1000 gms


The vector equation of the plane through the point (1,-2,-3) and
parallel to the vectors (2,-1,3) and
(2,3,-6) is \( \bar{r}= \)
A \( \cdot(1+2 t+2 s) \bar{i}-(2+t-3 s) \bar{j}-(3-3 t+6 s) \bar{k} \)
B. \( (1+2 t+2 s) \bar{i}+(2+t+3 s) \bar{j}-(3+3 t+6 s) \bar{k} \)
c. \( (1+2 t+2 s) \bar{i}+(2+t+3 s) \bar{j}+(3+3 t+6 s) \bar{k} \)
D. \( (1+2 t+2 s) \bar{i}+(2+t-3 s) \bar{j}+(3+3 t+6 s) \bar{k} \)


Neutronless neutral atom is
\( A \cdot H \)
в. не
c. Na
D.


If \( f \) and \( g \) are differentiable functions
then \( D *(f g) \) is equal to
A. \( f D * g+g D * f \)
В. \( D * f D * g \)
C \( \cdot f^{2} D * g+g^{2} D * f \)
D \( \cdot f(D * g)^{2}+g(D * f)^{2} \)


toppr
-०६ा॥
Q Type your question
energy in a rooa cnaın. Eacn trophic level in the food chain is
represented by a bar in the pyramid,
with primary producers forming the
foundation of the pyramid. The size of
each block represents the productivity at each trophic level per unit of time.
In the above example, approximately
how much energy available in each
trophic level is converted into new
biomass in the trophic level above it?
\( \mathbf{A} \cdot 1 \% \)
B . \( 5 \% \)
c. \( 10 \% \)
D. \( 50 \% \)
E . \( 100 \% \)


Find the equation to the conic passing through the origin and the points
\( (1,1),(-1,1),(2,0), \) and (3,-2)
Determine its species.


What will hapen to the image formed by a mirror if half of it is covered with a
black paper?


I ne gıven mgure represenis a sıngle nephron from a mammalian kidney.
Identify the labelled parts, match them
with the functions (i-iv) and select the
correct option.
(i) The site of ultrafiltration.
(ii) Particularly sensitive to ADH.
(iii) The main site for the re-absorption
of glucose and amino acids.
(iv) Largely responsible for the
maintenance of blood pH.
A \( \cdot(\text { i) }-A, \) (ii)-E, (iii)-C, (iv)-D
B. (i)-A, (ii)-B, (iii)-C, (iv)-D
C \( \cdot(i)-A,(\text { ii })-B,(i i i)-C,(i v)-E \)
D. (i)-A, (ii)-B, (iii)-D, (iv)-E


Which statements (s) is (are)correct?
This question has multiple correct options
A. \( A \pi- \) bond is weaker then \( \sigma \) -bond
B. \( A \sigma- \) bond is weaker then \( \pi- \) bond
C. A double bond stronger then H-bond
D. A covelent bond stronger then H-bond


Find the sum
\( \sum_{i=1}^{10} 8 *(1 / 4)^{i-1} \)


\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(s) \rightleftharpoons \boldsymbol{C u S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \)
\( +2 H_{2} O(g) ; K_{p}=4 \times 10^{-4} a t m^{2} \) if the
vapour pressure of water is 38 torr then percentage of relative humidity is:
Assume all data at constant
temperature)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 10
c. 40
D. none of these


More than 4 on atleast one of the three successive throws, If the answer is \( \frac{a}{b} \)
where the HCF of \( a \) and \( b \) is 1 , then find
\( \boldsymbol{b}-\boldsymbol{a} \)


Number of \( \sigma \) and \( p i \) bonds in acetanilide is
respectively.
A . 19,4
в. 16,4
c. 20,3
D. 19,3


1 g metal \( \mathrm{M}^{2+} \) was discharged by the passage of \( 1.81 \times 10^{22} \) electrons. What
is atomic mass of metal (write answer
as the nearest after diving atomic mass by 20)?


Which of the following acids does not contain - COOH group?
A. Carbamic acid
B. Barbituric acid
c. Lactic acid
D. succinic acid


Calculate the total entropy change for the transition at \( 368 \mathrm{K} \) of 1 mol of
sulphur from the monoclinic to the
rhombic solid state. Given \( \Delta \boldsymbol{H}= \)
\( -401.7 J m o l^{-1} \) for the transition
Assume the surroundings to be an ice-
water. Both at \( \mathbf{0}^{o} \boldsymbol{C} \) ?
A. \( -1.09 J K^{-1} \)
B . \( 1.47 J K^{-1} \)
c. \( 0.38 J K^{-1} \)
D. \( 0.76 J K^{-1} \)


Methanogens have a unique form of energy metabolism in which \( \ldots \). is
used to reduce


In a potentiometer arrangement, a cell of emf \( 1.25 \mathrm{V} \) gives a balance point at \( 35.0 \mathrm{cm} \) length of the wire. If the cell is replaced by another cell and the balance point shifts to \( 63.0 \mathrm{cm}, \) what is the emf
of the second cell?


Who gave the 'Theory of pangenesis'?
A. Lamarck
B. wallace
c. Haeckel
D. Darwin


Find the intervals of convexity and
concavity of the Gaussian curve \( \boldsymbol{y}= \) \( e^{-x^{2}} \) and also find the point of inflection


Interpret \( \mathrm{K}^{\prime}-\mathrm{K} \)


What is the approximate molecular
mass of dry air containing \( 78 \% \mathrm{N}_{2} \) and
\( 22 \% \mathrm{O}_{2} ? \)
A . 48.88
B. 18.88
c. 28.88
D. 38.88


There is an equiconvex lens of focal length of \( 20 \mathrm{cm} \). If the lens is cut into tow equal parts perpendicular to the optical axis, the focal length of each part will be
A. \( 20 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


The average value of the pressure varying from 2 to 10 atm if the pressure p and the volume \( v \) are related by
\( \boldsymbol{p} \boldsymbol{v}^{3 / 2}=\mathbf{1 6 0} \) is -


A line joining places of equal declination
is called
A . aclinical
B. isoclinical
c. isodynamical
D. isogonal


Evaluate the given integral.
\( \int \frac{\cos 2 x-1}{\cos 2 x+1} d x \)
A. \( \tan x-x+C \)
B. \( x+\tan x+C \)
c. \( x-\tan x+c \)
D. \( -x-\cot x+C \)


The resultant of all the forces acting on the body in static equilibrium should be
equal to
A. one
B. zero
c. Two
D. More than one


The standard enthalpy of formation of carbon - di - sulphide ( \( l \) ) is:
Given the standard enthalpy of combustion of carbon (s), sulphur (s)
\& carbon - di - sulphide ( \( l \) ) are :
-393.3,-293.72 and
\( -1108.76 k J m o l^{-1} \) respectively.
A. \( 128.02 \mathrm{kJ} \)
J.
B. 456.21kJ
c. 232.56 kJ
D. 871.25 kJ


Methylene blue is adsorbed on
activated charcoal at \( 25^{\circ} \mathrm{C} \) from its
aqueous solution. For this process,
select the correct statement.
A. The adsorption requires activation at \( 25^{\circ} \mathrm{C} \)
B. The adsorption is accompanied by a decrease in enthalpy
c. The adsorption increases with increase of temperature
D. The adsorption is irreversible


In what time will Rs. 1000 amount to Rs.
1331 at \( 10 \% \) p.a. in \( C \) l?
A . 4 years
B. 3 years
c. 2 years
D. 1 year


Find: \( \lim _{x \rightarrow 0^{+}} \frac{1}{x} \)
\( A \cdot O \)
B. \( -\infty \)
\( C \cdot \infty \)
D. does not exist


The volumes of two cylinders are as a:
b, and their heights are as \( c: \) d. Find the ratio of their diameters.
A \( \cdot \frac{a d}{b c} \)
B. \( \frac{a d^{2}}{a c^{2}} \)
c. \( \sqrt{\frac{a d}{b c}} \)
D. \( \sqrt{\frac{a}{b}} \times \frac{c}{d} \)


Draw the graph of each of the following equations:
¡) \( \boldsymbol{x}=\mathbf{5} \)


The correct order of increasing number of alpha particles passing undeflected through the foils of \( A u, A g, C u \) and \( A l \)
of 1000 atoms thickness each in a
simulated alpha particle scattering experiment of Rutherford would be:
A. \( A u<A g<C u<A l \)
в. \( A l<C u<A g<A u \)
c. \( A u<C u<A l<A g \)
D. \( A g<C u<A l<A u \)


A beam balance of unequal arm length is used by an unscruplus trader. When an object is weighed on left pan. The
weight \( i \) found to be \( W_{1} . \) When the
object is weighed on the right plan, the weight is found to be \( W_{2} \). If \( W_{1} \neq W_{2} \)
the correct weight of the object is
A. \( \frac{W_{1}+W_{2}}{2} \)
В. \( \sqrt{W_{1} W_{2}} \)
c. \( \sqrt{W_{1}^{2}+W_{2}^{2}} \)
D. \( \sqrt{W_{2}^{2}-W_{1}^{2}} \)


A \( 10 m \) long uniform metallic write
having a resistance of \( 20 \Omega \) is used as a potentiometer wire. This wire is
connected in series with another
resistance of \( 480 \Omega \) and a battery of emf \( 5 V \) having negligible internal resistance. If an unknown emf e is
balanced across \( 6 m \) of the
potentiometer wire, calculate:
(i) The potential gradient across the potentiometer wire.
(ii) The value of the unknown emf e.


Which of the following is dolomite:
A \( \cdot C a C O_{3} \cdot M g C O_{3} \)
в. \( C u_{2} S, \) Fe\( _{2} S_{3} \)
c. \( C d S \)
D. ZnS


Assertion
Resistivity of material may change with
temperature.
Reason
Resistivity is a material property and
independent on temperature.
A. If both Assertion and Reason are correct and Reason is
the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct


Is it necessary to have two waves of
equal intensity to study interference pattern? Will there be an effect on clarity if the waves have unequal intensity?


In Meiosis, the chromosome number in
the daughter cells are reduced to half
that of their parent cells. Guess, what
would happen, if the reduction of chromosome number is not done?


Solve the following pair of linear equation:
\( \frac{1}{3 x+y}+\frac{1}{3 x-y}=\frac{3}{4}, \frac{1}{2(3 x+y)} \)
\( \frac{1}{2(3 x-y)}=\frac{-1}{8}, 3 x+y \neq 0,3 x- \)
\( \boldsymbol{y} \neq 0 \)


The lowest pressure (the best vaccum) that can be created in laboratory at \( 20^{\circ} \mathrm{C} \) is \( 10^{-10} \mathrm{mm} \) of \( \mathrm{Hg} \). At this
pressure, the number of ideal gas
molecules per \( c m^{3} \) will be
A. \( 3.22 \times 10^{12} \)
B . \( 1.61 \times 10^{12} \)
c. \( 3.29 \times 10^{6} \)
D. \( 3.22 \times 10^{5} \)


In which of the following characters, the angiosperms resemble gymnosperms?
A. Presence of ovule
B. Absence of endosperm
c. Presence of vessels
D. Mode of fertilisation


Which of the following species has
maximum tendency to form complexes?
\( A \cdot L a^{3} \)
B. \( L u^{3} \)
\( c \cdot \operatorname{ad}^{3} \)
D. \( \mathrm{ce}^{3} \)


Five Mark Questions:
(a) Explain the mechanism of sex determination in humans.
(b) Differentiate between male heterogamety and female heterogamety with the help of an example of each


A \( 100 \Omega \) resistor is connected to a
\( 220 V, 50 H z A C \) supply. Find net power
consumed over a full cycle:
\( \mathbf{A} \cdot 121 W \)
B . \( 242 W \)
c. \( 368 W \)
D. \( 484 W \)


The maximum height reached by ball, as measured from the ground would be
A. \( 73.65 \mathrm{m} \)
B. 116.25 m
c. \( 82.56 \mathrm{m} \)
D. \( 63.25 \mathrm{m} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) show that
\( A^{2}= \)
\( \left[\begin{array}{cc}\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right] \) and \( A^{\prime} A=I \)


What is average rate of a chemical
reaction?


A basic process in reproduction is the creation of a \( \ldots \ldots . . . . . . . \) copy.
A. RNA
B. DNA
c. Nucleus
D. Mitochondria


Two gases are sent through the opposite ends of an open tube. A white ring has been observed at some point in
the tube. Identify the gases.
A. \( N_{2} \) and \( O_{2} \)
в. \( N O \) and \( O_{2} \)
c. \( N H_{3}, C l_{2} \)
D. \( H C l, N H_{3} \)


If \( -8+n=\frac{5 n}{4}, \) then \( n= \)
A . -40
в. -32
c. -16
D. -4


Solve :
\( \int \frac{d x}{\sqrt{x-x^{2}}} \)
\( \mathbf{A} \cdot 2 \sin ^{-1} \sqrt{x}+c \)
B. \( 2 \sin ^{-1} x+c \)
\( \mathbf{c} \cdot 2 x \sin ^{-1} x+c \)
\( \mathbf{D} \cdot \sin ^{-1} \sqrt{x}+c \)


How many rectangles congruent to this rectangle are there in the following diagram?
\( A \cdot 6 \)
B. 7
\( c \cdot s \)
D. 15


The number of ways in which 6 rings can be worn on the four fingers of one hand is
\( \mathbf{A} \cdot 4^{6} \)
в. \( ^{6} C_{4} \)
\( c \cdot 6^{4} \)
D. None of these


Solve the linear equation:
\( \boldsymbol{m}+\mathbf{1 0}=\mathbf{1 6} \)


A ship \( A \) is moving Westwards with a speed of \( 10 \mathrm{km} h^{-1} \) and a ship \( \mathrm{B} 100 \mathrm{km} \)
South of \( A \) is moving northwards with a speed of \( 10 \mathrm{km} h^{-1} \). The time after
which the distance between them
becomes shortest is
\( \mathbf{A} \cdot 0 h \)
в. \( 5 h \)
c. \( 5 \sqrt{2} h \)
D. \( 10 \sqrt{2} h \)


A ray of light is incident on the surface
of a glass plate at an angle of incidence equal to Brewster's angle \( \phi \). If \( \mu \) represents the refractive index of glass with respect to air, then the angle between the reflected and the refracted
rays is
\( A \cdot 90^{\circ}+\phi \)
B . \( \sin ^{-1}(\mu \cos \phi) \)
c. \( 90^{\circ} \)
D. \( 90-\sin ^{-1}\left(\frac{\sin \phi}{\mu}\right) \)


Which of the following is a disproportionation reaction?
A \( \cdot C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)
B \( \cdot 2 C r O_{4}^{2-}+2 H^{+} \rightarrow C r_{2} O_{7}^{2-}+H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3}+2 \mathrm{H}^{+} \rightarrow \mathrm{Ca}^{2+}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \)
D. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)


What is a concentration of ores? Explain the process with diagram by which metallic ore with sulphide as an
impurity is purified.


What is the total number of elementary events associated to the random
experiment of throwing three dice together


Which of the following will exhibit \( s p^{3} \) hybridization?
A. \( X e O_{3} \)
в. \( B F_{3} \)
c. \( B C l_{3} \)
D. \( B B r_{3} \)


There are 2 gates to enter a school and 3 staircases from first floor to the second
floor. How many possible ways are there for a student to go from outside the school to a classroom on the second
floor and come back?


A plane has a takeoff speed of \( 88.3 m / s \)
and requires \( 1365 m \) to reach that speed. Determine the acceleration of
the plane.
A \( \cdot 3.86 m / s^{2} \)
B. \( 2.86 m / s^{2} \)
c. \( 2.8 m / s^{2} \)
D. \( 2.6 \mathrm{m} / \mathrm{s}^{2} \)


Identify isostructural pairs from \( N F_{3}(I), N O_{3}^{-}(I I), B F_{3}(I I I), H_{3} O^{+}(I L \)
A . । \& ॥, ॥ा \& ।
B. I \& V, II \& III
c. । \& ाए, ॥ \& ॥
D. I \& IV, III \& v


If an electric dipole is placed inside a sphere filled with water, then among the following which statement is correct?
A. Water does not permit electric flux to enter into space
B. Electric flux entering into sphere is equals to electric flux leaving the sphere
c. Electric flux is coming towards the sphere
D. Electric flux is coming out of sphere


What is entropy? Write its units.


Assertion
\( A l C l_{3} \) is called aluminum trichloride.
Reason
Prefixes are used when naming
covalent compounds.
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 pressure outside a jet plane flying at high altitude falls considerably below atmospheric pressure at sea level. The air inside the cabin must therefore be
pressurized to protect the passengers. What is the pressure(in atmosphere) in the cabin if the barometer reading is
\( 688 \mathrm{mm} \) of Hg?
A. 0.905 atm
B. 6.88 atm
c. 9.05 atm
D. Data, insufficient


\( K F \) combines with \( H F \) to form \( K H F_{2} \)
The compound contains the species:
A \( \cdot K^{+}, F^{-} \) and \( H^{*} \)
B. \( K^{+}, F^{-} \) and \( H F \)
c. \( K^{+} \) and \( \left[H F_{2}\right]^{-} \)
D. \( [K H F]^{+} \) and \( F_{2} \)


The longitude on which the Indian Standard Time is based is:
\( \mathbf{A} \cdot 60^{\circ} E \)
B \( \cdot 66 \frac{1^{\circ}}{2}^{E} \)
\( \mathbf{c} \cdot 72 \frac{1^{0}}{2} E \)
D. \( 82 \frac{1^{\circ}}{2}^{E} \)


Consider the following statements and arrange in the order of true/false as
given in the codes.
\( \boldsymbol{S}_{1}: \) Cuprite, limorite and Zincite are
oxide ores.
\( S_{2}: \) Dolomite contains \( C a C O_{3} \) and
\( M g C O_{3} \)
\( S_{3}: \) Chalcocyte and azurite are ores of
copper.
\( \boldsymbol{S}_{4}: \) Feldspar and mica minerals contain
aluminium.
A. TT TT
B. FTFF
c. F F T T
D. TTFT


Absolute zero corresponds to
A . - 273 \( K \)
B . - 273 \( ^{\circ} \mathrm{C} \)
c. \( 273^{\circ} F \)
D. none of these


The shortest distance joining the magnetic poles of a magnet is known as magnetic length.
A. True
B. False


The smallest resistance that can be
obtained by the combination of \( n \)
resistors, each of resistance \( \boldsymbol{R} \) is:
A \( \cdot n^{2} R \)
в. \( n R \)
c. \( \frac{R}{n^{2}} \)
D. \( \frac{R}{n} \)


The fastest mode of transmission of
heat is Radiation.
A . True
B. False


The structural formulae of some
organic compounds are given below:
i. \( C H_{3}-C H_{2}-C O-C H_{3} \)
ii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \)
iii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
¡v. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
a. Which of these is an alkane?
b. Write the structural formula of the
position isomer of the third compound.
c. Which of the given compounds are functional isomers?
d. Write the structural formula of the
chain isomer of the fourth compound.


Determine the domain and range of the
relation R defined by \( \boldsymbol{R}=\left\{\left(\boldsymbol{x}, \boldsymbol{x}^{3}\right): \boldsymbol{x} \) is \right.
a prime number less than \( 10\} \)


A point moves in such a way that the difference of its distance from two point
(8,0) and (-8,0) always remains 4 Then, the locus of the point is:
A . A circle
B. A parabola
c. An ellipse
D. A hyperbola


Find the ratio of speed of sound in
hydrogen to the speed of sound in
oxygen at \( 1270 K \)


The present position of hydrogen in the modern periodic table completely justifiable.
A. True
B. False


Number of lone pairs around
phosphorus in \( \boldsymbol{P} \boldsymbol{C l}_{5}, \boldsymbol{P C l}_{4}^{+} \) and \( \boldsymbol{P C l}_{6}^{-} \)
are respectively
A. 0,1,2
B. 0,0,0
c. 1,2,3
\( \mathbf{D} \cdot 0,2,1 \)


Find the odd one out.
Coal, Petroleum, Natural Gas, Nuclear
power.
A . coal
B. Petroleum
c. Natural gas
D. Nuclear power


If \( y=\sin \theta, \) then for what value of \( \theta, \) the
relative error in y is minimum?
A \( \cdot 90^{\circ} \)
в. \( 30^{\circ} \)
\( c \cdot 0^{0} \)
D. \( 45^{\circ} \)


Match the reactions in column I with
their respective characteristics given in column II.


A doctor has prescribed a corrective lens of power +1.5 D to a patient. Find the focal length of the lens in centimeter. Is the prescribed lens diverging or converging?


The value of Ke for the reaction, \( 2 A \rightleftharpoons \)
\( B+C \) is \( 2 \times 10^{-3} . \) At a given time, if
the composition of reaction mixture is
\( [\boldsymbol{A}]=[\boldsymbol{B}]=[\boldsymbol{C}]=\mathbf{3} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
Which is true?
A. The reaction will proceed in forward direction
B. The reaction will proceed in backward direction
C. The reaction will proceed in any direction
D. None of the above


Which of the following processes will be
at equilibrium?
This question has multiple correct options
A. Water maintained at \( 233 \mathrm{K} \) in a closed container.
B. Sulphur dioxide being released in atmosphere at 298
K.
C. Heating calcium carbonate at \( 773 \mathrm{K} \) in a closed kiln.
D. Formation of ammonia at \( \left(300^{\circ} \mathrm{C}\right) \) temperature.


By the reduction of \( H N O_{3} \) to \( N O_{2} \) the number of electrons involved per mole
of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is
\( A \cdot 8 \)
B. 6
\( c \cdot 3 \)
D. 4


A steady current \( I \) flows through a wire
of radius \( r, \) length \( L \) and resistivity \( \rho \)
The current produces heat in the wire. The rate of heat loss in a wire is
proportional to its surface area. The steady temperature of the wire is independent of
A. \( L \)
B. \( r \)
c. \( I \)
D.


The perpendicular distance of \( \vec{A}(1,4,-2) \) from the segment BC where \( \vec{B} \) (2,1,-2) and \( \vec{C}(0,-5,1) \) is
\( A \cdot \frac{3}{7} \sqrt{26} \)
B \( \cdot \frac{6}{7} \sqrt{26} \)
\( \mathbf{c} \cdot \frac{4}{7} \sqrt{26} \)
\( D \cdot \frac{2}{7} \sqrt{26} \)


If the imaginary part of \( \frac{z-4}{z-2 i} \) is 0
then the locus of \( z \) is
A. Ellipse
B. Circle
c. Straight line
D. Parabola


The maximum possible denticities of a ligand given below towards a common transition and inner-transition metal
ion, respectively, are:
A. 6 and 8
B. 8 and 6
c. 8 and 8
D. 6 and 6


Which of the following Hydrocarbon is
used as a fuel?
A. \( C O_{2} \)
B. \( C_{4} H_{10} \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C H_{3} \) СООН


A sample of HI \( \left(9.30 \times 10^{-3}\right) \) mol was
placed in an empty \( 2.00 L \) container at 1000 \( K \).After equilibrium was reached,
the concentration of \( I_{2} \) was \( 6.29 \times \)
\( \mathbf{1 0}^{-4} \quad \boldsymbol{M} . \) Calculate the value of \( \boldsymbol{K}_{C} \) at
\( 1000 K \) for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)


Which one of the following is the difference between asexual and
sexual types of reproduction?
A. Asexual-gametes are produced, Sexual-gametes are not produced.
B. Asexual-gametes are not produced, Sexual- gametes are produced.
c. Asexual- no fertilization and zygote formation, Sexual fertilization and zygote formation
D. Both B and C


The main plant body of Pteridophytes is
A. Sporophyte
B. Gametophyte
c. Haploid
D. None of the above


If \( W_{1}, W_{2}, W_{3} \) and \( W_{4} \) for an ideal gas are magnitude of work done in isothermal, adiabatic, isobaric and isochoric reversible expansion processes, the correct order will be :
A \( . w_{1}>w_{2}>w_{3}>w_{4} \)
в. \( w_{3}>w_{2}>w_{1}>w_{4} \)
c. \( w_{3}>w_{2}>w_{4}>w_{1} \)
D. \( w_{3}>w_{1}>w_{2}>w_{4} \)


\( \mathbf{1} \)
\( \boldsymbol{m} \) long wire is folded in the form of a
circular coil and 100 m \( A \) electric
current is flowing in it, then magnetic
field at a point \( 1 ~ m \) away from its centre
on its axis :
\( ^{\text {A }} \cdot \frac{10^{-5}}{4 \pi} T \)
в. \( \frac{10^{-8}}{2 \pi} T \)
\( ^{\text {c. }} \cdot \frac{10^{-5}}{2 \pi} T \)
D. \( \frac{10^{-8}}{4 \pi} T \)


When burning potassium is brought in
\( \boldsymbol{S O}_{2} \) then:
This question has multiple correct options
A. it stop burning.
B. it forms potassium thiosulphate.
c. it forms potassium sulphite.
D. sulphur is obtained as product


Which one is not an allylic halide?
A. 3-Chloro cyclohex-1-ene
B. 1-chloro but-1-ene
c. 1 -chloro but-2-ene
D. 3-Chloro prop-1-ene


The correct value of dip angle at a place is
\( 45^{\circ} . \) If the dip circle is rotated by \( 45^{\circ} \) out of the meridian, then the tangent of the
angle of apparent dip at the place is :
A .
в. 0.5
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{2} \)


A particle moves under the effect of a
force \( F=c x \) from \( x=0 \) to \( x=x_{1}, \) the
work done in the process is
A \( \cdot c x_{1}^{2} \)
B. \( \frac{1}{2} c x_{1}^{2} \)
\( c \cdot 2 c x_{1}^{2} \)
D. zero


A stone is dropped from a height of 1.25
\( \mathrm{m} . \) If \( \mathrm{g}=10 \mathrm{m} \mathrm{s}^{-2}, \) what is the ratio of the
distances traveled by it during the first and the last second of its motion?
A. cant say
B. 1: 9
\( c \cdot 1: 8 \)
\( D \cdot 2: 9 \)


In \( \triangle A B C, A B=A C . \) Points \( D \) and \( E \)
are on the sides \( B C \) and \( A C \)
respectively such that \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{A} \boldsymbol{E} \). If
\( \angle B A D=30^{\circ}, \) then the measure of
\( \angle E D C \) is:
A \( .10^{\circ} \)
B . 15
\( c \cdot 20 \)
D. 25


Mark the following rational numbers on number line.
\( \frac{-8}{3} \)


Which of the following has the highest bond order?
A \( . N_{2} \)
в. \( O_{2} \)
c. \( H e_{2} \)
D. \( H_{2} \)


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{C}-\boldsymbol{A} \)


Which of the following thermodynamic
processes can be reversed?
A. Heating of an oven
B. Combustion of petrol.
c. Free expansion of gases
D. Isothermal expansion of an ideal gas in a cylinder with frictionless piston.


The colour of \( C u C r_{2} O_{7} \) solution in
water is green because
A \( \cdot C u^{2+} \) ion is green
в. \( C r_{2} O_{7}^{2} \)
c. both the ions are green
D. \( C u^{2+} \) ion is blue and \( C r_{2} O_{7}^{2-} \) ion is yellow


The correct combination of names for
isomeric alcohols with molecular
formula \( C_{4} H_{10} O \) is/are:

This question has multiple correct options
A. tert-butanol and 2-methylpropan-2-ol
B. tert-butanol and 1, 1-dimethylethan-1-ol
c. n-butanol and butan-1-ol
D. isobutyl alcohol and 2-methylpropan-1-ol


If the average velocity of the molecules
of a gas is doubled, then what will happen to their most mean square velocity?
A. Doubled
B. Halvedd
c. Becomes \( \sqrt{2} \) times
D. Becomes \( \frac{1}{\sqrt{2}} \) times


The diagram shows the sketch of an electrolytic cell used in the extraction of
aluminium. What is the substance of
which the electrodes \( A \) and \( B \) are made?
A. Carbon and graphite
B. Zinc and copper
c. copper and iron
D. None of the above


What is the pH value of a solution whose hydroxyl ion concentration is \( 1 \times 10^{-2} M ? \)


In the figure above, point \( \mathrm{B} \) lies on \( \overline{\boldsymbol{A} C} \).
Find a possible value of \( \boldsymbol{X}, \) if \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
are integers.
A \( .30^{\circ} \)
B. \( 35^{\circ} \)
\( c \cdot 40^{\circ} \)
\( D .50 \)
E. 55


Green plants are called \( _{---} \) since they
synthesise their own food


Birth-rate in India is high because of
A. illiteracy
B. social orthodoxy
c. desire of a male child
D. all of the above


The acceleration due to gravity on the surface of moon is \( 1.7 \mathrm{m} \mathrm{s}^{-2} . \) What is the
time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? \( (\mathrm{g} \) on the surface of earth is \( 9.8 \mathrm{m} \mathrm{s}^{-2} \) )


If an angle \( a \) is divided into two parts \( A \)
\& \( B \) such
that \( A-B=x \) and \( \tan A: \tan B= \)
\( K: 1, \) then the value of \( \sin x \) is
A \( \cdot \frac{k+1}{k-1} \sin \alpha \)
B. \( \frac{k}{k+1} \sin \alpha \)
c. \( \frac{k-1}{k+1} \sin \alpha \)
D. none of the above


If \( 24 \cot A=7, \) find the value of \( \sin A \)


Root cambium is derived from
A. Primary meristem
B. Secondary meristem
c. Intercalary meristem
D. Apical meristem


top
Q Type your question
Ball \( X \) has an initial velocity of
\( 3.0 m s^{-1} \) in a direction along line \( A B \)
Ball \( Y \) has a mass of \( 2.5 k g \) and an
initial velocity of \( 9.6 m s^{-1} \) in a
direction at an angle of \( 60^{\circ} \) to line \( A B \)
The two balls collide at point \( B \). The
balls stick together and then trave along the horizontal surface in a
direction at right-angles to the line \( \boldsymbol{A B} \) as shown in Fig.

Determine the difference between the
initial kinetic energy of ball \( X \) and the initial kinetic energy of ball \( Y \). difference in kinetic energy \( = \)
\( \boldsymbol{J} \)


The tendency of two species to disproportionate can be determined by examining the:
A. Phase diagram
B. Volume vs Temperature graph
c. Frost diagram
D. Heat capacity vsTemperature graph


Which of the following statements are
correct for an electron that has \( n=4 \)
and \( m=-2 ? \)
This question has multiple correct options
A. The electron may be in a \( d \) -orbital
B. The electron is in the \( 3^{r d} \) -orbital
C . The electron may be in a \( p \) -orbital
D. The electron must have the spin quantum number \( = \) \( 1 / 2 \)


Two moles of \( P C l_{5} \) is heated in a closed
vessel of 2 litre capacity. When the equilibrium is attained, \( 40 \% \) of it has been found to be disssociated. What is
\( \boldsymbol{K}_{c} \) in \( \boldsymbol{m o l} / \boldsymbol{d} \boldsymbol{m}^{3} ? \)


The freezing point of equimolal aqueous solution will be highest for :
A. \( C_{6} H_{5} N H_{3} C l \)
в. \( C a\left(N O_{3}\right)_{2} \)
c. \( L a\left(N O_{3}\right)_{3} \)
D. \( C_{6} H_{12} O_{6} \)


An electromagnetic wave of frequency
\( \boldsymbol{v}=\mathbf{3} \) MHz passes from a vacuum into
a dielectric medium with permittivity
\( =4, \) Then
A. Wavelength and frequency both become half.
B. Wavelength is doubled and frequency remains unchanged.
C. Wavelength and frequency both remains unchanged.
D. Wavelength is halfved and frequency remains unchanged.


A bryophyte which harbours a nitrogen fixing blue-green alga in its thallus is
A. Pogonatum
B. Riccia
c. Marchantia
D. Anthoceros


What would be expected to happen if \( (a) \)
\( G A_{3} \) is applied to rice seedlings. (b) Dividing cells stop differentiating.
\( (c) A \)
rotten fruit gets mixed with unripe fruits
(d) You forget to add cytokinin to the culture medium.


Write the formulae of the following compounds. Potassium tetracyanoaurate (III) ion.


Determine by choosing the best option for the similarly of triangles theorem. \( D E \| B C . \) Both \( \triangle A D E \& \triangle A B C \) are
similar by:
A. SAS
B. SSS
\( c \cdot A A A \)
D. AAS


Statement 1: If dot product and cross product of \( \vec{A} \) and \( \vec{B} \) are zero, it implies that one of the vector \( \vec{A} \) and \( \vec{B} \) must be
a null vector.

Statement 2: Null vector is a vector with
zero magnitude.
A \( . \) a) statement- -1 is false, statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false


The sequence of filling electrons in different shells is determined by:
A. Octet rule
B. Hund's rule
c. Aufbau rule
D. All the above


Find \( \boldsymbol{y} \) when \( \boldsymbol{x}=\frac{\mathbf{3}}{\mathbf{2}} \) when \( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{1 2} \)


An electron enters a parallel plate
capacitor with horizontal speed \( \mu \) and is
found to deflect by angle \( \theta \) on leaving the capacitor as shown. It is found that \( \tan \theta=0.4 \) and gravity is negligible. If
the initial horizontal speed is doubled,
then tan will be.
A. 0.1
B. 0.2
c. 0.8
D. 1.6


Every matter can be seen.
A. True
B. False


Maxwell's laws of distribution of
velocities shows that
A. the number of molecules with most probable velocity is very large
B. the number of molecules with most probable velocity is small
C. the number of molecules with most probable velocity is zero
D. the number of molecules with most probable velocity is exactly equal to 1


Blister copper is:
A . pure copper
B. ore of copper
c. alloy of copper
D. impure copper


A freely falling body crosses points \( P, Q \)
and \( R \) with velocities \( v, 2 v \) and \( 3 v \)
respectively. Find the ratio of the distances \( P Q \) to \( Q R \)


Assertion : Pyrethrum is collected from th
e leaves of Chrysanthemum cinerarifolium.
Reason

Pyrethrin is prepared from pyrethrum.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


For an elementary process \( 2 X+Y \rightarrow \)
\( Z+W \). the molecularity is-
\( A \cdot 2 \)
B.
\( c .3 \)
D. unpredictable


Evaluate the following
\( (0.98)^{2} \)
A .0 .9664
B. 0.9604
\( c .0 .9864 \)
D. 0.9964


How many structural isomers can be
represented by alkane, \( C_{5} H_{10} ? \)


The hydration energy of \( M g^{2+} \) is greater than that of :
A \( . A 1^{3} \)
В. \( N a^{+} \)
\( c \cdot B e^{3} \)
D. \( M g^{3+} \)


There are 12 intermediate stations
between two places \( A \) and
B. Find the
number of ways in which a train can be
made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive


If \( A \) and \( B \) are two events such that
\( \mathbf{2} \boldsymbol{P}(\boldsymbol{A})=\mathbf{3} \boldsymbol{P}(\boldsymbol{B}), \) where \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{A})< \)
\( P(B)<1, \) then which one of the
following is correct?
A. \( P(A \mid B)<P(B \mid A)<P(A \cap B) \)
в. \( P(A \cap B)<P(B \mid A)<P(A \mid B) \)
c. \( P(B \mid A)<P(A \mid B)<P(A \cap B) \)
\( D(A \cap B)<P(A \mid B)<P(B \mid A) \)


Encircle whichever of the following:
a) is the stronger nucleophile (aprotic
solvent) : \( \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
b) is the stronger nucleophile (protic
solvent) \( : \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
c) is the stronger base \( : \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
d) is the stronger nucleophile (protic solvent): \( N H_{3} \) or \( N H_{2} N H_{2} \)
e) is the better leaving group:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-} \boldsymbol{o r} \boldsymbol{C H}_{2} \boldsymbol{S O}_{3}^{-} \)


The reaction \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \) is
started with initial number of moles of
1,2 and 3 for \( N_{2}, H_{2}, N H_{3} \) in a 1 L vessel
If \( x \) moles of \( N_{2} \) under go dissociation
then at equilibrium the number of moles of each substance remaining are:
A. \( 1-x, 2-3 x, 2 x \)
B. \( 1-x / 3,2-x, x / 3 \)
c. \( 1-x, 2-x, 3+x \)
D. \( 1-x, 2-3 x, 3+2 x \)


Without expanding prove that the determinant
\( \left|\begin{array}{ccc}\sin A & \operatorname{Cos} A & \sin (A+\theta) \\ \sin B & \cos B & \sin (B+\theta) \\ \sin C & \cos C & \sin (c+\theta)\end{array}\right|=0 \)


The mass of oxygen with which 13.5 g of aluminium will completely react is:
\( A \cdot 48 \)
B. \( 8 g \)
c. \( 12 g \)
D. 16 g


In aluminate ion, the coordination
number of aluminium is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
\( D \)


Solve:
\( \int_{0}^{\pi / 6} \frac{\cos 2 x}{(\cos x-\sin x)^{2}} d x \)
\( \mathbf{A} \cdot_{-\log }\left(\frac{\sqrt{3}-1}{2}\right) \)
\( ^{\mathbf{B}}-\log \left(\frac{\sqrt{3}+1}{2}\right) \)
\( \mathbf{c} \cdot \log \left(\frac{\sqrt{3}+1}{2}\right) \)
D. None of these


If a charged particle projected in a gravity-free room deflects This question has multiple correct options
A. there must be an electric field
B. there must be a magnetic field
c. both fields cannot be zero
D. both fields can be non-zero


A particle is executing SHM along the \( x \)
axis given by \( x=A \) sin\omegat. What is the mangnitude of the average acceleration of the partical between \( t=0 \) and \( (T / 4) s \) where \( T \) is the time period of oscillation


The distance of the centre of mass of
the system from the centre of bigger sphere at the moment of collision is
4
3.27
\( c \cdot 3 r \)
D. 47


If the number of selections of 3
difference letters from the word
\( \boldsymbol{S U M} \boldsymbol{A} \boldsymbol{N} \)


What experiment do you suggest to understand Faradays law?What items are required? What suggestions do you give to get good results of the experiment? Give precautions also.


The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age.
The present ages, in years, of the son and the father are respectively,
A. 4 and 24
B. 5 and 30
c. 6 and 36
D. 3 and 24


What weight of sodium contains the
same number of atoms as those in 8
grams of oxygen?
A. \( 10.5 g \)
в. \( 13.5 g \)
c. \( 11.5 g \)
D. \( 14.2 g \)


A block of mass \( 10 k g \) is released on a
fixed wedge inside a cart which is
moved with constant velocity \( 10 \mathrm{ms}^{-1} \)
towards right. There is no relative
motion between block and cart. Then
work done by normal reaction on block
in two seconds from ground frame will
be \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . \( 1320 J \)
В. \( 960 J \)
c. \( 1200 J \)
D. \( 240 J \)


Calculate the total positive or negative charge on a \( 2.35 g \) copper penny. Given
Avogadro number \( =6.02 \times 10^{23} \)
atomic number of copper \( =29 \) and
atomic mass of copper \( =\mathbf{6 3 . 5} \)


Which one of the following mixture does not act as a buffer solution?
A. Boric acid and borax
B. Sodium phosphate \& disodium hydrogen phosphate
c. Sodium propionate and propionic acid
D. Sodium acetate and sodium propionate


Shew that \( \left(a^{2}+b^{2}+c^{2}-b c-c a-\right. \)
\( \boldsymbol{a b})\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{z}^{2}-\boldsymbol{z}^{2}-\boldsymbol{y} \boldsymbol{z}-\boldsymbol{z} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{y}\right) \)
may be put into the form \( A^{2}+B^{2}+ \)
\( C^{2}-B C-C A-A B \)


A resistance of \( 2 \Omega \) is connected across one gap of a metre bridge (the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown
resistance greater than \( 2 \Omega \) is connected across the other gap. When these resistances are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is:
A . \( 4 \Omega \)
в. 3 \( \Omega \)
\( c \cdot 5 \Omega \)
D. \( 6 \Omega \)


Which of the following are primary standard?
This question has multiple correct options
A . Oxalic acid
B. Potassium permanganate
c. Potassium dichromate
D. Sodium hydroxide


Describe briefly with the help of a circuit diagram, how a potentiometer is used to determine the internal
resistance of cell.


Hydrogen form a 'bridge' in the chemical structure of which of the following compound?
A. Hydrogen peroxide
B. Diborane
\( c \cdot \mid c e \)
D. Lithium hydride


The top soil is darker
and
A. Is drier than subsoil
B. Is richer in \( \mathrm{Na} \) and \( \mathrm{Mg} \)
C. Is wetter than subsoil
D. Contains more organic matter


Heat cannot by itself flow from a body at lower temperature to a body at higher temperature is a statement of
consequence of
A. second law of thermodynamics
B. conservation of momentum
c. conservation of mass
D. first law of thermodynamics.


Dimensions of \( \frac{1}{\mu_{o} \epsilon_{o}}, \) where symbols
have their usual meaning, are
A \( \cdot\left[L^{-1} T\right] \)
B . \( \left[L^{-2} T^{2}\right]^{2} \)
c. \( \left[L^{2} T^{-2}\right] \)
D・ \( \left[L T^{-1}\right] \)


At What distance from a converging
lens of focal length \( 12 \mathrm{cm} \) must an object be placed in order that an image
of magnification 1 will be produced?


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


Catenation i.e. linking of similar atoms depends on size and electronic
configuration of atoms. The tendency of catenation in Group 14 elements follows
the order:
A. \( C>S i>G e>S n \)
в. \( C>>S i>G e \approx S n \)
c. \( S i>C>S n>G e \)
D. \( G e>S n>S i>C \)


A charge of \( 5 \times 10^{-10} C \) is given to a
metal cylinder of length \( 10 \mathrm{m}, \) placed in air. The electric intensity at a distance of \( 0.2 \mathrm{m} \) from its axis is :
A. \( 4.5 \vee / \) m
B. \( 45 \mathrm{V} / \mathrm{m} \)
c. \( 450 \mathrm{V} / \mathrm{m} \)
D. \( 100 \mathrm{v} / \mathrm{m} \)


If the light moving in a straight line bends by small but fixed angle while entering in different medium, it may be a case of :
A. reflection of light
B. refraction of light
c. scattering of light
D. dispersion of light


Find the slope of the line whose
inclination is
\( 5 \pi / 6 \)


Annual rings and growth rings are formed due to the fluctuations in the
activity of
A. Xylem
B. Phloem
c. xylem and phloem
D. Cambium


Plants respond to various stimuli by
A. Shedding leaves
B. Growing
c. Felling of fruits
D. Peeling of bark


The ends \( A \) and \( B \) of a rod of length \( l \) have velocities of magnitudes \( \left|\overrightarrow{\boldsymbol{v}}_{\boldsymbol{A}}\right|= \)
\( \boldsymbol{v} \quad \) and \( \left|\overrightarrow{\boldsymbol{v}}_{\boldsymbol{B}}\right|=2 \boldsymbol{v}, \) respectively. If the
inclination of \( \vec{v}_{A} \) relative to the rid is \( \alpha \)
find the:
(a) inclination \( \beta \) of \( \vec{v}_{B} \) relative to the
rod.
(b) angular velocity of the rod


The vector \( \boldsymbol{T}+\mathbf{2} \overline{\boldsymbol{y}}+\boldsymbol{2} \boldsymbol{k} \) restated
through an angle \( \theta \) and doubled in
magnitude then it becomes \( 2 T+ \)
\( (2 x+2)\}+(6 x-2) k \) values of \( x \) are
A \( \cdot 1, \frac{1}{3} \)
B. \( -1, \frac{1}{3}= \)
c. \( 1, \frac{-1}{3} \)
D. (0,3)
() (0,3)


Polarizability of halide ions increases in
the order:
A \( \cdot F^{-}<I^{-}<B r^{-}<C l \)
B. \( C l^{-}<B r^{-}<I^{-}<F^{-} \)
c. \( I^{-}<B r^{-}<C l^{-}<F^{-} \)
D. \( F^{-}<C l^{-}<B r^{-}<I^{-} \)


Choose the correct answer on basis of
reactivity:
\( (\mathbf{I}) \)
\( A \cdot(1)<(11)<(11) \)
B. (III) < (II) < (I)
\( c \cdot(1)<(111)<(11) \)
D. (III) <(I) <(II)


The position vector of a particle of mass \( \boldsymbol{m}=\mathbf{6 k g} \) is given as \( \overrightarrow{\boldsymbol{r}}=\left[\left(\boldsymbol{3} \boldsymbol{t}^{2}-\boldsymbol{6} \boldsymbol{t}\right) \hat{\boldsymbol{i}}+\right. \)
\( \left.\left(-4 t^{3}\right) \hat{j}\right] \) m. Find
(i) the force \( (\vec{F}=m \vec{a}) \) acting on the
particle.
(ii) the torque \( (\vec{\tau}=\vec{r} \times \vec{F}) \) with respect
to the origin, acting on the particle.
(iii) the momentum \( (\vec{p}=m \vec{v}) \) of the
particle.
(iv) the angular momentum \( (\vec{L}=\vec{r} \times \vec{p}) \) of the particle with respect
to the origin.
A \( \cdot\left(\text { i) }(36 \hat{i}-144 t \hat{j}) N \text { (ii) }\left(-288 t^{3}+864 t^{2}\right) \hat{k} \text { (iii) }(36 t-\right. \)
36)\( \hat{i}-72 t^{2} \hat{j}(\text { iv })\left(-72 t^{4}+288 t^{3}\right) \hat{k} \)
B . (i) (63 \( i-144 t \hat{j}) N \) (ii) \( \left(-288 t^{3}+864 t^{2}\right) \hat{k} \) (iii) \( (36 t- \) 36)\( \hat{i}-72 t^{2} \hat{j}(\text { iv })\left(-72 t^{4}+288 t^{3}\right) \hat{k} \)
C . (i) (36 \( \hat{i}-144 \text { tj }) N \) (ii) \( \left(-28 t^{3}+84 t^{2}\right) \hat{k} \) (iii) \( (36 t- \) 36)\( \hat{i}-72 t^{2} \hat{j}(\text { iv })\left(-72 t^{4}+288 t^{3}\right) \hat{k} \)
D . (i) (36 \( \hat{i}-144 t \hat{j}) N \) (ii) \( \left(-288 t^{3}+864 t^{2}\right) \hat{k} \) (iii) \( (3 t- \) 6)\( \hat{i}-72 t^{2} \hat{j} \) (iv) \( \left(-72 t^{4}+288 t^{3}\right) \hat{k} \)


The haemoglobin from red corpuscles of most mammals contains
approximately \( 0.33 \% \) of iron by weight. The molecular weight of haemoglobin is \( 67,200 . \) The number of iron atoms in
each molecule of haemoglobin is :
A . 1
B. 2
\( c \cdot 3 \)
\( D \)


An experiment involving absorption of oxygen and its quantitative estimation would involve use of :
A . caustic soda
B. pyrogallol
c. conc. sulphuric acid
D. turpentine oil


There is a uniform magnetic field \( B \) in a
circular region of radius \( R \) as shown in
figure, whose magnitude changes at
the rate of \( d B / d t . \) The emf induced
across the ends of a circular concentric
conducting arc of radius \( \boldsymbol{R}_{1} \) having
angle \( \theta \) as shown \( \left(-O A O^{\prime}=\theta\right) \) is
\( ^{\mathrm{A}} \cdot \frac{\theta}{2 \pi} R_{1}^{2} \frac{d B}{d t} \)
\( ^{\text {В }} \cdot \frac{\theta}{2}^{R^{2}} \frac{d B}{d t} \)
\( c . \theta 2 \pi R \)
D. None of these


Select the correct option:
The correct sequence of flow of
electrons n the light reaction is
A. PSII, plastoquinone, cytochromes, PSI, ferredoxin
B. PSI, plastoquinone, cytochromes, PSII ferredoxin
c. PSI, ferredoxin, PSII
D. PSI, plastoquinone, cytochromes, PSII, ferredoxin


Which of the following is the respiratory product in plants?
A. Glucose
B. Carbon dioxide
c. oxygen
D. None of the above


A car is standing \( 200 m \) behind a bus,
which is also at rest. The two start
moving at the same instant but with
different forward accelerations. The bus
has acceleration \( 2 m / s^{2} \) and the car has
acceleration \( 4 m / s^{2} . \) The car will catch up with the bus after a time of:
A. \( \sqrt{110 s} \)
s
В. \( \sqrt{120 s} \)
c. \( 10 \sqrt{2} s \)
D. \( 15 s \)


Two metallic spheres \( S_{1} \) and \( S_{2} \) are
made of the same material and have
identical surface finish. The mass of \( S_{1} \)
is three times to that of \( S_{2} \). Both
the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of
\( S_{1} \) to that \( S_{2} \) is :
A \( \cdot \frac{1}{3} \)
в. \( \left(\frac{1}{3}\right)^{\frac{1}{3}} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{1} \)


The graph of \( \sqrt{C} \) vs \( \Lambda_{m} \) for an aqueous solution of which substance is not
obtained as a straight line?
A. \( H C l \)
в. \( N a O H \)
c. \( N a C l \)
D. \( H C N \)


A balloon is going upwards with velocity \( 12 \mathrm{m} / \mathrm{s} \). It releases a packet when it is a height of \( 65 \mathrm{m} \) from the ground. How much time will the packet take to reach the ground if \( g=10 m / s^{2} \)
A. 5 second
B. 6 second
c. 7 second
D. 8 second


Find the modulus and argumrent of the
following complex numbers and hence express each of them in the polar form:
\( \frac{1+2 i}{1-3 i} \)


A golf ball has a mass of 40 g, and a speed of \( 45 \mathrm{m} / \mathrm{s}, \) if speed can be measured within accuracy of \( 2 \% \) calculate the uncertainty in the position.
A . \( 1.56 \times 10^{-30} \)
В. \( 1.46 \times 10^{-33} \mathrm{m} \)
c. \( 1.47 \times 10^{-23} \mathrm{m} \)
D. \( 1.47 \times 10^{-30} \mathrm{m} \)


In the binomial expansion of \( (a- \)
\( b)^{n}, n \geq 5, \) the sum of
5 th and 6 th terms is zero then a/b equal
to
A \( \cdot \frac{5}{n-4} \)
B. \( \frac{6}{n-5} \)
c. \( \frac{n-5}{6} \)
D. \( \frac{n-4}{5} \)


An object is placed \( 25 \mathrm{cm} \) from a convex lens whose focal length is \( 10 \mathrm{cm} . \) The image distance is
A. \( 50 \mathrm{cm} \)
B. \( 16.66 \mathrm{cm} \)
c. \( 6.66 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Statement 1: Hydrogen peroxide, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is a good oxidizing agent.

Statement 2: The hydrogen in \( H_{2} O_{2} \) has
+1 oxidation number.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


CO is isostructural with
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{Sn} C l_{2} \)
\( \mathbf{B} \cdot H g C l_{2} \)
\( \mathbf{c} \cdot S C l_{2} \)
\( \mathbf{D} \cdot Z n I_{2} \)


Why is photo respiration is considered as a destructive activity?


2-Acetoxybenzoic acid is called:
A . paracetamol
B. aspirin
c. heroine
D. mordant dye


Steam at \( 100^{\circ} \mathrm{C} \) is passed into 20 g of
water acquires a temperature of \( 80^{\circ} \mathrm{C} \) the mass of water presents will be [Take
specific heat of water 1 cal \( g^{-1} c^{-1} \) latent heat of steam \( \left.=\$ \$ 540 \text { lcal } \mid g^{\wedge}\{-1\} \$ \$\right] \)
A. \( 31.5 g \)
в. \( 42.5 g \)
c. \( 22.5 g \)
D. \( 24 g \)


\( \left(x^{3}-y^{3}\right) d x+x y^{2} d y=0 . \) Solving this
we get \( \frac{\boldsymbol{k}}{\boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{y}^{m} / \boldsymbol{n} \boldsymbol{x}^{r}} . \) Find \( \boldsymbol{m}+\boldsymbol{n}+\boldsymbol{r} ? \)


The tallest Pteridophyte is
A. Alsophila
B. cyathia
c. Dryopteris
D. Selaginella


Two events \( A \) and \( B \) are such that
\( P(A)=\frac{1}{4}, P(A \mid B)=\frac{1}{4} \) and \( P(B \mid A)= \)
\( \mathbf{1} \)
\( \overline{2} \)
Consider the following statements:
(I) \( P(\bar{A} \mid \bar{B})=\frac{3}{4} \)
(II) \( A \) and \( B \) are mutually exclusive
\( (\| I) P(A \mid B)+P(A \mid \bar{B})=1 \)
Then
A. Only (I) is correct
B. Only (I) and (II) are correct
C. Only (I) and (III) are correct
D. Only (II) and (III) are correct


Allyl cyanide contains \( \sigma \) and
\( \pi \) -bonds.
\( \mathbf{A} \cdot 5 \sigma, 7 \pi \)
B. \( 9 \sigma, 3 \pi \)
c. \( 3 \sigma, 4 \pi \)
D. \( 9 \sigma, 9 \pi \)


Which one of the following cannot be the probability of an event.
A \( \cdot \frac{1}{3} \)
в. \( \frac{11}{36} \)
c. \( -\frac{2}{3} \)
\( D \)


Choose the correct answers from the
alternatives given :
Which of the following engage in lactate fermentation?
A. Lactobacillus cells
B. Muscle cells
c. Sulphate-reducing bacteria
D. Both (a) and (b)


\( H_{2} O_{2} \) used in rocket has the
concentration:
A . \( 50 \% \)
B. 70\%
c. \( 30 \% \)
D. 90\%


Which of the following environmental conditions are essential for optimum growth of Mucor on a piece of bread?
A. Temperature of about \( 25^{\circ} \mathrm{C} \)
B. Temperature of about \( 5^{\circ} \mathrm{C} \)
C. Relative humidity of about \( 5 \% \)
D. Relative humidity of about \( 95 \% \)
E. A shady place.
F. A brightly illuminated place. Choose the answer from the following options.
\( A \cdot B \) and \( D \) only
B. B, C and Fonly
C. \( A, C \) and \( E \) only
D. \( A, D \) and \( E \) only


Solve the following equation:
\( \cos x \cos 2 x \cos 3 x=\frac{1}{4} \)


Assuming that in an atom, neutron
\( \left(m_{n}\right) \) and electron \( \left(m_{e}\right) \) are bound to
each other by gravitational force only and electron are moving around neutron and assuming Bohr's quantization rule to be valid.The expression for energy of
electron in \( n^{t h} \) level comes out to be
\( \left.\frac{(a-4) G^{2} m_{n}^{2} m_{e}^{2}}{4 n^{2} h^{2}} V \quad \text { (where } h=\frac{h}{2 \pi}\right) \)
Find the value of ' \( a \) '


With the increasing altitude, gauge
pressure:
A. increases
B. decreases
c. remains same
D. becomes zero


A body of mass \( 1.0 \mathrm{kg} \) is rotating on a circular path of diameter \( 2.0 \mathrm{m} \) at the rate of 10 rotations in 31.4 s. Calculate:
i) angular momentum of the body
ii) rotational kinetic energy


Optical axis of a thin equi-convex lens is the X-axis. The coordinate of a point object and its images are \( (-20 c m, 1 c m) \) and \( (25 c m,-2 c m) \)
respectively
A. the lens is located at \( x=5 \mathrm{cm} \)
B. the lens is located at \( x=-5 c m \)
c. the focal length of the lens is 10 cm
D. the focal length of the lens is \( 15 \mathrm{cm} \)


A thin uniform rod has mass \( 1.2 \mathrm{kg} \) and length \( 4 \mathrm{m} \). Find its moment of inertia a
transverse axis through its center of
mass.


Find a relationship between \( x \) and \( y \) so that the distance between the points
\( (x, y) \) and (-2,4) is equal to 5
A \( \cdot x^{2}+y^{2}+4 x-8 y-4=0 \)
B . \( x^{2}+y^{2}+4 x-8 y-5=0 \)
c. \( x^{2}+y^{2}+4 x-8 y-6=0 \)
D. \( x^{2}+y^{2}+4 x-8 y-53=0 \)


Plants reproducing by spores such as mosses and ferns are grouped under the general term
A. Cryptogams
B. Bryophytes
c. sporophytes
D. Thallophytes


The correct statement about the
following disaccharide is:
\( (\mathbf{i}) \)
il
A. ring (i) is pyranose with \( \alpha- \) glycosidic link
B. ring (i) is furanose with \( \alpha- \) glycosidic link
C . ring
(ii) is furanose with \( \alpha- \) glycosidic link
D. ring
(ii) is pyranose with \( \beta- \) glycosidic link


Which of the following quantities related to an electron has a finite upper
limit?
A . Mass
B. Momentum
c. speed
D. Kinetic energy


If \( A \) and \( B \) are two events, such that \( P(A \)
or \( \mathrm{B} \) ) \( =\mathrm{P}(\mathrm{A}), \) then
A. events A and B are mutually exclusive
B. events A and B are statistically independent
c. event B is a subset of event A
D. event A is a subset of event B


The displacement of an oscillating particle varies with time 't' (in seconds) \( \operatorname{according} \operatorname{as} x=2 \cos (0.5 \pi t) \) metre
Then amplitude and time period are :
\( A \cdot 1 m, 4 s \)
B. 2 \( m, 4 \) s
\( c \cdot 2 m, 2 s \)
D. \( 1 \mathrm{m}, 2 \mathrm{s} \)


A car is turning along a horizontal
circular road.The centripetal force in
this case is
A. \( F_{1} \) provided by the friction between the tyres and the road
B. \( F_{g} \) the weight of the car and the persons sitting in the
car
C. \( F_{N} \) the normal reaction force on the car due to the
road
D. \( F_{g}-F_{N} \), the difference of weight and the normal reaction


Measure of one angle of linear pair is given. Find the measure of another
angle:
\( \mathbf{1 0 7}^{\circ} \)


The distance of two planets from the Sun are \( 10^{13} \) and \( 10^{12} \mathrm{m}, \) respectively. The ratio
of time periods of these two planets is
A. \( \frac{1}{\sqrt{10}} \)
B. 100
c. \( \frac{10}{\sqrt{10}} \)
D. \( \sqrt{10} \)


(a) Name any two copper releasing
IUDs.
(b) Explain how do they acts as effective contraceptive in human females.


Most of the natural hydrocarbons are:
A . cis
B. trans
c. both \( A \) and \( B \)
D. none of above


A bag contains 5 white, 7 red and 3
black balls. If a ball is chosen at random
Find the probability that it is not red.


An object of \( 5 \mathrm{cm} \) is placed before a concave mirror at a distance of \( 40 \mathrm{cm} \)
If its focal length is \( 20 \mathrm{cm} \) then what is the magnification of the image.
A . 40
B. 20
c. 5
D. -