Two circular coils each of 100 turns are
held such that one lies in the vertical
plane and the other in the horizontal plane with their centres coinciding. The radius of vertical and horizontal coils
are \( 20 \mathrm{cm} \) and \( 30 \mathrm{cm} \) respectively. If the magnetic field at their common centre is zero, find current in each coil
Horizontal component of earth's magnetic field is 27.8 Aim and angle of
dip at this place is \( 30^{\circ} \)


The CGS unit of pressure is
A . dyne \( c m^{-2} \)
B. \( N m^{-2} \)
c. \( J m^{-2} \)
D. dyne \( c m^{-3} \)


The value of the determinant
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega}^{\mathbf{3}} & \boldsymbol{\omega}^{5} \\ \boldsymbol{\omega}^{\mathbf{3}} & \mathbf{1} & \boldsymbol{\omega}^{4} \\ \boldsymbol{\omega}^{\boldsymbol{5}} & \boldsymbol{\omega}^{\boldsymbol{4}} & \mathbf{1}\end{array}\right|, \) where \( \boldsymbol{\omega} \) is an imaginary
cube root of unity,is
A \( \cdot(1-\omega)^{2} \)
B. 3
\( c \cdot-3 \)
D. none of these


\( A \beta \) -pleated sheet organisation in a
polypeptide chain is an example of
A . \( 1^{\circ} \) structure
B. \( 2^{\circ} \) structure
c. \( ^{\circ} \) 3 structure
D. \( 4^{\circ} \) structure


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ -\mathbf{3} & -\mathbf{6}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{7} & \mathbf{2} \\ -\mathbf{3} & -\mathbf{8}\end{array}\right] \)
\( \mathbf{2} \boldsymbol{X}+\boldsymbol{A}=\boldsymbol{B} . \) Find \( \boldsymbol{X} \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}8 & 4 \\ -6 & -8\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}1 & 2 \\ -3 & -6\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}6 & 0 \\ 0 & -2\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{cc}3 & 0 \\ 0 & -1\end{array}\right] \)


A thermally insulated vessel contains
some water at \( 0^{\circ} \mathrm{C} \). The vessel is
connected to a vacuum pump to pump
out water vapour. This results in some
water getting frozen. It is given Latent heat of vaporization of water at \( 0^{\circ} C= \)
\( 21 \times 10^{5} J / k g \) and latent heat of
freezing water \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{J} / \mathbf{k g} . \) The
maximum percentage amount of water that will be solidified in this manner
will be
A. \( 86.2 \% \)
B . \( 33.6 \% \)
c. \( 21 \% \)
D. \( 24.36 \% \)


The soil pore depicted in the image
helps in
A. Storage of air
B. Storage of water
c. Storage of carbon dioxide
D. Both A and B


If \( \left(A+B^{T}\right)^{T} \) is a matrix of order \( 4 \times 3 \)
then the order of matrix B is
\( A \cdot 3 \times 4 \)
B. \( 4 \times 3 \)
\( c \cdot 3 \times 3 \)
D. \( 4 \times 4 \)


The micro-organisms, which can live
without oxygen are:
A. bacteria
B. amoeba
c. paramoecium
D. blue-green algae


Two uniformly large parallel thin plates
having charge densities \( +\sigma \) and \( -\sigma \) are
kept in the \( X Z \) -plane at distance \( d \) apart. Sketch an equipotential surface due to electric field between the plates.
If a particle of mass \( m \) and charge \( -q \) remains stationary between the plates. What is the magnitude and direction of this field?


Explain the reason of different length of equatorial and axial bond in the
structure of \( \boldsymbol{P C l}_{5} \)


Black-foot disease is caused due to
ground water contaminated with
excess of
A. Nitrate
B. Fluoride
c. Arsenic
D. sulphur
E. Mercury


The part of the alimentary canal that
starts from the middle segment of clitellum and extends up to the last
segment is
A. Stomach
B. Gizzardd
c. Intestine
D. Rectum


The angle of deviation by a prism is
\( \left(180^{\circ}-2 A\right) . \) Its critical angle will be
A \( \cdot \sin ^{-1}\left(\tan \frac{A}{2}\right) \)
B. \( \left(\cot \frac{A}{2}\right) \)
c. \( \cos ^{-1}\left(\cot \frac{A}{2}\right) \)
D. \( \cos ^{-1}\left(\tan \frac{A}{2}\right) \)


The slope of the normal to the curve
\( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}-\sin \theta), \boldsymbol{y}=\boldsymbol{a}(1-\cos \boldsymbol{\theta}) \) at
point \( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. \( \frac{1}{\sqrt{2}} \)


In the figure above, \( \overline{A C} \) is a diameter of
the large circle and \( \mathrm{B} \) lies on \( \overline{\boldsymbol{A C}} \) so that
\( A B \) is a diameter of the small circle. If
\( A B=1 \) and \( B C=2, \) Calculate the
area of the shaded region.
\( A \cdot \frac{\pi}{4} \)
в.
\( c \cdot 2 \pi \)
D. \( \frac{9 \pi}{4} \)
E . \( 9 \pi \)


In how many years will the compound
interest on Rs. \( 32,000, \) at the rate of 5
per cent per annum, be Rs. \( 5,044 ? \)


When the distance between the object
and the plane mirror increases.
A. The image remains same
B. The size of the image will become less than the size of the object
c. The distance between the image and the plane mirror increases
D. The distance between the image and the plane mirror decreases


Identify the correct statement.
A. Soaps are better than detergents in hard water
B. Soaps are salts of alkyl benzene sulphonic acids
C. Detergents clean well even in acidic medium
D. The non ionic hydrocarbon end of soap has property to attract water


toppr
Q Type your question-
of the electric field and the electric
potential \( V(r) \) with the distance \( r \) from
the centre, is best represented by which
graph ?
\( A \)
\( B \)
\( c \)
\( D \)


Let \( f \) be a differentiable function
satisfying \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{z})+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{z})=\mathbf{1 4} \) for all \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \in \boldsymbol{R} \)
Then
\( \mathbf{A} \cdot f^{\prime}(x)<0 \) for all \( x \in R \)
B . \( f^{\prime}(x)=0 \) for all \( x \in R \)
C \( \cdot f^{\prime}(x)>0 \) for all \( x \in R \)
D. none of these


The coefficients of self induction of two
inductance coils arc \( 0.01 \mathrm{H} \) and \( 0.03 \mathrm{H} \)
respectively. When they are connected in series so as to support each other then the resultant self inductance
becomes 0.06 Henry. The value of coefficient of mutual induction will be-
A . \( 0.02 \mathrm{H} \)
B. 0.05
c. \( 0.01 \mathrm{H} \)
D. ZERO


Suppose there are three urns
containing 2 white and 3 black balls: 3 white and 2 black balls, and 4 white and
one black ball respectively. There is equal probability of each urn being chosen. One ball is drawn from an urn
chosen at random. The probability that a white ball is drawn is \( \frac{k}{15} . \) Find the
value of \( k \)


The natural frequency of the circuit shown in fig. is
A \( \frac{1}{\sqrt{L C}} \)
B. \( \frac{1}{2 \sqrt{L C}} \)
c. \( \frac{2}{\sqrt{L C}} \)
D. none of these


The ratio of the angular speed of hours hand and second hand of a clock is
A . 1: 1
B. 1: 60
c. 1: 720
D. 3600 : 1


Four metals \( Z n, F e, C u \) and \( A l \) are
taken and added to the following solutions one by one. The results obtained are tabulated below
Metal \( \quad Z n S O_{4}(a q) \quad F e S O_{4}(a q) \) Displaced \( Z n \) \( \mathrm{Fe} \quad \) No reaction \( \begin{array}{ll}C u & \text { No reaction }\end{array} \quad \) No reaction \( A l \) Displaced \( \quad \) Displaced
From the above data, the decreasing
order of reactivity of metals is
A. \( A l>C u>F e>Z n \)
в. \( A l>Z n>F e>C u \)
c. \( A l>Z n>C u>F e \)
D. \( A l>F e>C u>Z n \)


An element has three electrons in the
4th shell, the atomic number of the
element is:
A . 13
B . 21
c. 27
D. 31


A cubic polynomial is a polynomial of degree
A .
B.
\( c \cdot 3 \)
\( D \)


Find the area enclosed by the curves \( y=4 x^{2} \) and \( y^{2}=2 x \)


The threshold energy of a metal is 10 sV Identify the incorrect option. (E = energy of one photon)
A. If \( E=12 e V \), photoelectric effect occurs
B. If \( E=15 e V \), kinetic energy of electron is more than option (A)
C. If intensity of photon increase but energy remain same, the kinetic energy of photoelectron remain same
D. If intensity of photon increase but energy remain same, the kinetic energy of photoelectron increase


In the following redox reaction, number
of moles of \( C u(O H)_{2} \) reduced by one
mole of \( N_{2} H_{4} \) is :
\( \boldsymbol{C u}(\boldsymbol{O H})_{2}(\boldsymbol{s})+\boldsymbol{N}_{2} \boldsymbol{H}_{4}(\boldsymbol{a q}) \longrightarrow \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{N}_{2}(\boldsymbol{g}) \)


In the reaction \( M g+C l_{2} \rightarrow M g C l_{2} \)
Chlorine may be regarded as:
A. an oxidising agent
B. a reducing agent
c. a catalyst
D. providing an inert medium


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & -\mathbf{2} & \mathbf{3}\end{array}\right] \quad \boldsymbol{B}=\left[\begin{array}{c}-\mathbf{1} \\ \mathbf{2} \\ -\mathbf{3}\end{array}\right], \) then
\( \boldsymbol{A}+\boldsymbol{B} \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}0 & 0 & 0\end{array}\right] \)
B. 0
0
\( \mathbf{c} \cdot\left[\begin{array}{ll}-1 & 4\end{array}\right] \)
D. not defined


What will be the major product of the
given reaction?


One mole of \( N_{2} O_{4}(g) \) at \( 300 K \) is kept in a closed container under one
atmosphere. It is heated to \( 600 K \) when
\( 20 \% \) by mass of \( N_{2} O_{4}(g) \) decomposes
to \( N O_{2}(g) . \) The resultant pressure is:
A. 1.2 atm
B. 2.4 atm
\( c .2 .0 \) atm
D. 1.0 atm


Identify a polymorphic coelenterate.
A. Physalia
B. Fungia
c. Hydra
D. All of the above


toppr oGın
Q Type your question
position \( x=12 \mathrm{m} \) on the line.
A proton placed at any point on the line
between the two charges will
experience a net force due to the two
charges. The net force acting on the
proton is shown as a function of
position in the graph, where positive
values of force represent rightward
force.

What is the sign of each charge, and
which charge is stronger?
A. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 1.
B. Charge 1 is positive, Charge 2 is positive, and the stronger charge is Charge 1
c. charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 2
D. Charge 1 is negative, Charge 2 is negative, and the stronger charge is Charge 2 .
E. Charge 1 is negative, Charge 2 is negative, and the stronger charge is Charge 1.


The most important layer of atmosphere is
A. Troposphere
B. Thermosphere
c. Mesosphere
D. None of these


Which is the line segment for the
median \( O \) from the triangle \( P Q R ? \)
A. \( \overline{Q T} \)
в. \( \overline{P O} \)
\( c \cdot \overline{O R} \)
D. \( \bar{Q} O \)


What do you mean by ozone hole? What
are its consequences?


\( N a N O_{2} \) and \( N a N O_{3} \) are used as food
additives and generally added to meat.
A. True
B. False


The velocity of sound in a gas is
\( 30 m s^{-1} \) at \( 27^{\circ} C . \) What is the velocity of
the sound in the same gas at \( 127^{\circ} \mathrm{C} \) ?
A \( \cdot 20 m s^{-1} \)
B. \( 30 m s^{-1} \)
D. \( 60 m s^{-1} \)


The pressure that has to be applied to
the ends of a steel wire of length \( 10 c m \)
to keep its length constant when its
temperature is raised by \( 100^{\circ} \mathrm{C} \) is:
(For steel Young's modulus is \( 2 \times \)
\( 10^{11} N m^{-2} \) and coefficient of thermal
expansion is \( 1.1 \times 10^{-5} K^{-1} \) )
A \( \cdot 2.2 \times 10^{7} \) Ра
B . \( 2.2 \times 10^{6} \) ра
c. \( 2.2 \times 10^{8} \) Pa
D. \( 2.2 \times 10^{9} \) pa


The value of
\( \left|\begin{array}{ccc}a_{1} x+b_{1} y & a_{2} x+b_{2} y & a_{3} x+b_{3} y \\ b_{1} x+a_{1} y & b_{2} x+a_{2} y & b_{3} x+a_{3} y \\ b_{1} x+a_{1} & b_{2} x+a_{2} & b_{3} x+a_{3}\end{array}\right| \) is
equal to
A \( \cdot x^{2}+y^{2} \)
B.
\( \mathbf{c} \cdot a_{1} a_{2} a_{3} x^{2}+b_{1} b_{2} b_{3} y^{2} \)
D. none of these


When air is replaced by a dielectric medium of force constant \( \mathrm{K} \), the
maximum force of attraction between
two charges, separated by a distance :
A. decreases K times
B. increases K times
C. remains unchanged
D. becomes \( \frac{1}{K^{2}} \) times


The process of zinc plating on iron sheet is known as
A. annealing
B. roasting
c. galvanization
D. smelting


Solve:
\( \mathbf{5}+\mathbf{5}^{2}+\mathbf{5}^{3}+\ldots \ldots+\mathbf{5}^{n} \)


The kinetic energy of an electron in the first Bhor orbit of hydrogen is :
A. 13.6 eV
B. 6.8 eV
c. \( -13.6 e V \)
D. 27 eV


What is the specific heat capacity of balsa wood?
A . \( 0.7 \mathrm{kcal} / \mathrm{kg}^{\circ} \)
B. 0.48 kcal/kg'c
c. 0.8 kcal/kg'c
D. 0.5 kcal/kg'c


Q Type your question
in a room which is at temperature \( \boldsymbol{\theta}_{0} \)
the graph between the temperature \( \boldsymbol{T} \) of
the metal and time \( t \) will be closet to:
\( A \)
B.
\( c \)
\( D \)


Contains carbon that are \( s p^{2} \)
hybridized:
\( \mathbf{A} \cdot C_{2} H_{5} \)
B. \( C_{2} H_{4} \)
c. \( C_{2} H_{2} \)
D. \( C_{2} H_{5} O H \)
E \( \cdot C_{3} H_{8} \)


In how many ways can the letters of the
word PERMUTATIONS be arranged
if there are always 4 letters between \( P \)
and \( S ? \)


A metallic rod of length \( l \) and cross
sectional area \( A \) is made of a material
of Young modules \( Y \). If the rod is
elongated by an amount \( y, \) then the work done is proportional to
A \( . y \)
B. \( \frac{1}{y} \)
c. \( y^{2} \)
D. \( \frac{1}{y^{2}} \)


Conjoint, collateral, open and endarch
vascular bundles are found in
A. Monocot stem
B. Monocot root
c. Dicot root
D. Dicot stem


Name the process of converting vegetable oil to vegetable ghee.


Fill in the blank:
The smallest part of the moon that
appears in the sky is called
A. full moon
B. half moon
c. crescent moon
D. quarter moon


H.O.M.O (Highest Occupied Molecular Orbital) of CO molecular is:
A. Non-bonding M.O. with slight antibonding character
B. Non-bonding M.O. with slight bonding character
c. Pure non-bonding M.O
D. None of the above


Using clay, a student made a right
circular cone of height \( 48 \mathrm{cm} \) and base
radius \( 12 \mathrm{cm} . \) Another student reshapes
it in the form of a sphere. Find the
radius of the sphere


If \( \boldsymbol{a}_{\boldsymbol{i}}>\mathbf{1} \) for all \( \boldsymbol{i} \boldsymbol{\epsilon} \boldsymbol{N}, \) then \( \log _{\boldsymbol{a}_{2}} \boldsymbol{a}_{\boldsymbol{1}}+ \)
\( \log _{a_{3}} a_{2}+\ldots+\log _{a_{n}} a_{n-1}+\log _{a_{1}} a_{n} \)
has the minimum value
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 0 \)
D. none of these


The majority carriers in a p-type semiconductor are
A. Electrons
B. Holes
c. Both A and B
D. Impurities


What is the length of human DNA
containing \( 6.6 \times 10^{9} \) bp nitrogen
bases?
\( \mathbf{A} \cdot 22 n m \)
B. \( 0.22 \mathrm{mm} \)
\( \mathbf{c} .2 .2 \mathrm{m} \)
D. 22m


A certain sound has a frequency of 256
hertz and a wavelength of \( 1.3 \mathrm{m} \). What difference would be felt by a listener between the above sound and another
sound travelling at the same speed, but of wavelength \( 2.6 \mathrm{m} ? \)


Methyl cyanide on hydrolysis gives:
A . acetic acid.
B. acetaldehyde
c. acetone.
D. methyl amine.


Figure shows some equipotential lines distributed in space. A charged object
is moved from point \( A \) to point \( B \)
A. The work done in figure (i) is the greatest.
B. The work done in figure (ii) is the least.
C. The work done is the same in figure (i), (ii) and (iii)
D. The work done is the same in figure (iii) is greater than figure
(ii) but equal to that in figure (i).


The ionization energy of \( L i^{++} \) is equal
to
\( \mathbf{A} \cdot 9 h c R \)
в. \( 6 h c R \)
\( \mathbf{c} \cdot 2 h c R \)
D. \( h c R \)


Explain with the neat labelled diagram
of the structure of Stomata.


A person of mass M kg is standing on a lift. If the lift moves vertically upwards according to given v-t graph then find out the weight of the man at the
following instants : \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
1) \( t=1 \) second
2) \( t=8 \) seconds
3) \( t=12 \) seconds


Four resistances of each 20 ohm are
connected to form a square \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \)
The resultant resistance between the
corners \( A C \) and the resistance between
\( A B \) are:
A \( .40 \Omega, 15 \Omega \)
B. \( 15 \Omega, 40 \Omega \)
c. \( 15 \Omega, 20 \Omega \)
D. \( 20 \Omega, 15 \Omega \)


The formula and molecular mass of
common salt is :
A. \( N a C l, 58.5 \)
в. \( M g C l_{2}, 46 \)
c. \( C a C l_{2}, 62 \)
D . \( \mathrm{FeCl}_{3}, 54 \)


Write the equation of reaction of chlorobenzene:
Sulphonation


Glucose and amino acids are
reabsorbed in the
A. Proximal tubule
B. Distal tubule
c. collecting duct
D. Loop of Henle


A sphere contracts in volume by \( 0.01 \% \) when taken to the bottom of sea \( 1 \mathrm{km} \) deep. Find bulk modulus of the material
of sphere
A. \( 9.8 \times 10^{6} M / M^{2} \)
В. \( 1.2 \times 10^{10} N / M^{2} \)
c. \( 9.8 \times 10^{10} N / M^{2} \)
D. \( 9.8 \times 10^{11} N / M^{2} \)


0.75 mole of solid \( ^{\circ} A_{4}^{\prime} \) and 2 moles of
gaseous \( \boldsymbol{O}_{2} \) are heated in a sealed
vessel, completely using up the reactants and producing only one compound. It is found that when the temperature is reduced to the initial temperature, the contents of the vessel
exhibit a pressure equal to half the original pressure. What conclusions can be drawn from these data the
product of the reaction?
A. \( A_{2} O_{5} \)
в. \( A_{3} O_{4} \)
\( c \cdot A_{2} O_{2} \)
D. none of these


\( \frac{\partial}{\phi} \)
\( \delta \)
\( \delta \)


Measurement of the rate of
oxygen consumption in unit volume of water over a period of time is done to find out
A. Biogas generation
B. Biological oxygen demand
c. Biosynthetic pathways
D. Fermentation


An electromagnetic field exists only when there is
A. an increasing current
B. decreasing current
c. voltage
D. current


The maximum Coulomb force that can
act on the electron due to the nucleus in
a hydrogen atom will be:-
A. \( 0.82 \times 10^{-8} N \)
N \( . . ~ \)
В. \( 0.082 \times 10^{-8} N \)
c. \( 8.2 \times 10^{-8} N \)
D. \( 820 \times 10^{-8} N \)


Oxygen forms hydride which is to litmus.
A . red
B. blue
c. neutral
D. depends on temperature


Obtain an expression for acceleration due to gravity at a height \( h \) above the
earth's surface.


An organic compound containing sulphur is estimated by Carius method
in which fuming \( H N O_{3} \) is used to convert S into:
A. \( S O_{3}^{2-} \)
B. \( S O_{4}^{2-} \)
\( c \cdot S O_{3} \)
D. \( S O_{2} \)


A radioactive nucleus with decay
constant \( 0.5 / s \) is being produced at a constant rate of 100 nuclei/s. If at \( t= \)
0 there were no nuclei, the time when
there are 50 nuclei is
A . \( 1 s \)
B. \( 2 \ln \left(\frac{4}{3}\right) \) s
\( c \cdot \ln 2 \)
D. \( \ln \left(\frac{4}{3}\right) \) s


The number of Faradays required to
produce 0.5 mol of free metal from \( \mathbf{A} \mathbf{l}^{\mathbf{3}+} \)
is
\( A \cdot 3 \)
B. 2
\( c \cdot 6 \)
D. 1.5


Solve: \( (-12) \times(-3) \times 4 \times(-6)=? \)
\( \mathbf{A} \cdot-144 \)
B . -908
c. +864
\( \mathbf{D} \cdot-864 \)


Draw a right triangle which the sides (other than hypotenuse) are of lengths
\( 4 \mathrm{cm} \) and \( 3 \mathrm{cm} . \) Then construct another
\( \mathbf{5} \)
triangle whose sides are \( \frac{-\operatorname{times}}{3} \) the corresponding sides of the given triangle.


A long wire carries a current of 90 A from east to west direction. Magnetic
field due to current at a point which is \( 1.5 \mathrm{m} \) just below the wire.


The possible value(s) of ' \( \boldsymbol{\theta} \) ' satisfying
the equation \( \sin ^{2} \theta \tan \theta+ \)
\( \cos ^{2} \theta \cot \theta-\sin 2 \theta=1+\tan \theta+ \)
\( \cot \theta, \) where \( \theta \in[0, \pi] \) is/are
A.
в. \( \pi \)
c. \( \frac{7 \pi}{12} \)
D. None of these


Let's write the measurement of the
angles of triangle \( A B C \) if \( A B=B C \)
and \( \angle B A C+\angle A C B=50^{\circ} \)


The number of integral values of \( k \) for
which the equation \( \sin ^{-1} x+ \)
\( \tan ^{-1} x=2 k+1 \) has a solution is
A . 1
B. 2
\( c .3 \)
D. 4


Fill in the blank:
A student while solving a problem on convex mirror makes mistake and uses
sign for focal length, and proceeds. The solution for location of image will be
concave mirror.
\( A \cdot \) same as
B. different from
c. either same or different from
D. having no relation with


Manufacture of which of the following does not require limestone as a raw
material?
A . Quick lime
B. Baking soda
c. Glass
D. Plaster of Paris


The relation 'is a sister of in the set of
human beings is
A. only transitive
B. only symmetric
c. equivalent
D. None of these


Assertion
Statement -I: NaCl when exposed in air
it becomes wet.
Reason
Statement -II: NaCl contains
hygroscopic impurities like \( C a C l_{2} \)
\( M g C l_{2} \) etc.
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


Sum of a number and its reciprocal is \( \mathbf{5} \frac{1}{\mathbf{5}} . \) Then the required equation is
A \( \cdot y^{2}+\frac{1}{y}=\frac{26}{5} \)
B. \( 5 y^{2}-26 y+5=0 \)
c. \( y^{2}+\frac{1}{y}+\frac{26}{5}=0 \)
D. \( 5 y^{2}+26 y+5=0 \)


If a straight line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)
with the \( x, y, z \) axes respectively, then show that \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=2 \)


How many pairs of cranial nerves originate from the brain of rat?
A . 12
B. 8
\( c \cdot 9 \)
D. 1
E. 10


IUPAC name of the compound?
A. hexanoic acid \( 5-a l-1 \)
B. 6 -oxohexanoic acid
C. hexanal-1-carboxylic acid
D. none of these


A \( 15 \Omega \) resistor, a \( 220 \mu \mathrm{H} \) coil, and a \( 60 p F \) capacitor are in series across an
ac source. What is the bandwidth of the
circuit?
\( \mathbf{A} \cdot 138 M H z \)
в. \( 10,866 \mathrm{Hz} \)
\( \mathbf{c} .1,907 H z \)
D. \( 138 k H z \)


Assertion (A): Paracetamol is widely used as analgesic even though it is an
antipyretic.
Reason (R): It is administrated to
aspirin-sensitive patients.
Choose the correct option.
A. A is true, R is true and R is the correct explanation of A
B. A is true, R is true and \( R \) is not the correct explanation of A
c. A is true, R is false
D. A is false, R is true


A pair of dice is thrown 4 times. If
getting a total of 9 in a single throw is considered as a success then find the
mean and variance of successes.


In the following figure, ABCD is a
parallelogram.If \( \angle A B P=x \angle C B P \),then
find the value of \( \boldsymbol{x} \)


Find integers 'a' and 'b' such that \( \left(x^{2}-\right. \) \( x-1) \) divides \( a x^{17}+b x^{16}+1 \)


The plane of a dip circle is set in the geographic meridian. Then the apparent
dip is \( \left(\delta_{1} \text { is the actual dip and } \delta_{2} \) is the \right. declination):
A \( \cdot \theta=\tan ^{-1}\left(\frac{\tan \delta_{1}}{\tan \delta_{2}}\right) \)
B . \( \theta=\tan ^{-1}\left(\tan \delta_{1} \cos \delta_{2}\right) \)
c. \( \theta=\tan ^{-1}\left(\frac{\tan \delta_{2}}{\cos \delta_{1}}\right) \)
D. \( \theta=\tan ^{-1}\left[\tan \delta_{1} \cos \delta_{2}\right] \)


\( 90 \% \) of the first-order reaction is
completed in 70 minutes. The velocity
constant of the reaction is:
A .0 .0329
B. 0.329
c. 3.29
D. 0.0293


Action of \( \boldsymbol{P C l}_{5} \) on \( \boldsymbol{S O}_{2} \) chiefly yields:
A \( . P O C l_{3} \)
в. \( P_{4} S_{3} \)
c. \( s O_{2} C l_{2} \)
D. \( S O_{3} \)


A vertical tower stands on a horizontal
plane and is surmounted by a vertical flagstaff of height 5 meters. At a point
on the plane, the angles of elevation of the bottom and the top of the flagstaff
are respectively \( 30^{\circ} \) and \( 60^{\circ} . \) Find the
height of the tower.


For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) the correct
choice is:
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing
B. \( H_{3} P O_{3} \) is dibasic and non-reducing
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic and reducing
D. \( H_{3} P O_{3} \) is tribasic and non-reducing


Find the value of \( \sum_{n=1}^{13} i^{n}+i^{n+1} \)


The steel balls \( A \) and \( B \) have a mass of
\( 500 g \) each and are rotating about the
vertical axis with an angular velocity of
4 rad/s at a distance of \( 15 C M \) from
the axis. Collar \( C \) is now forced down
until the balls are at a distance of
\( 5 C M \) from the axis. How much work
must be done to move the collar down?


What is \( 25 \% \) of 480


In the electrochemical cell
\( H_{2}(g), 1 a t m\left|H^{+}(1 M)\right|\left|C u^{2+}(1 M)\right| C u(s) \)
which one of the following is the correct value of reduction potential?
A . \( 1.10 \mathrm{V} \)
B. 0.110
c. \( 1.50 \mathrm{v} \)
D. 0.220


A particle of mass \( \mathrm{M} \) is situated at the
center of a spherical shell of same mass and radius a. The gravitational potential
at a point situated at \( \frac{a}{2} \) distance from
the centre, will be
\( \mathbf{A} \cdot-\frac{3 G M}{a} \)
B. \( -\frac{2 G M}{a} \)
\( \mathbf{c} \cdot-\frac{G M}{a} \)
\( \mathrm{D} \cdot-\frac{4 G M}{a} \)


An element L consists of molecules:
What type of bonding is present in the particles that make up L?


Find the Coefficient of Variation for
Factory \( \boldsymbol{B} \)
A \( .0 .15555 \% \)
B. \( 0.25714 \% \)
c. \( 0.36934 \% \)
D. \( 0.42548 \% \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\log \left(\log _{\frac{1}{3}}\left(\log _{7}(\sin \boldsymbol{x}+\boldsymbol{a})\right)\right) \)
be defined for every real value of \( x, \) then
the possible value of \( a \) is This question has multiple correct options
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 6


Succession in a water body leads to formation of
A. Mesophytic vegetation
B. Xerophytic vegetation
c. Halophytic vegetation
D. Epiphytic vegetation


Point out the false statements.
A. Colloidal sols are homogenous
B. Colloids carry +ve or -ve charges
C . Colloids show Tyndall effect
D. The size range of colloidal particles is \( 10 \AA-1000 A \)


A particle doing S.H.M. having
amplitude \( 5 \mathrm{cm}, \) mass \( 5 \mathrm{kg} \) and angular
frequency 5 is 1 cm from mean position.
Find potential energy and kinetic
energy.
\( \mathbf{A} \cdot K \cdot E .=150 \times 10^{-4} J . P . E .=6.25 \times 10^{-4} J \)
B . \( K . E .=6.25 \times 10^{-4} J . P . E .=150 \times 10^{-3} J \)
C \( . K . E .=6.25 \times 10^{-4} J . P . E .=6.25 \times 10^{-4} J \)
D . \( K . E .=150 \times 10^{-3} \mathrm{J.P.E.}=150 \times 10^{-4} \mathrm{J} \)


Which of the following order is true about the force of attraction between
particles of states of matter?
A. Gas > Solid > Liquid
B. Solid > Liquid>Gas
c. Gas 'Liquid > Solid
D. Liquid > Gas> Solid


A long straight wire of radius R carries a
steady current \( I_{o}, \) uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance r from the centre of the wire, in
the region \( r>R \), is?
A \( \cdot \frac{\mu_{o} I_{o}}{2 \pi r} \)
В \( \cdot \frac{\mu_{o} I_{o}}{2 \pi R} \)
\( ^{\mathbf{C}} \cdot \frac{\mu_{o} I_{o} R^{2}}{2 \pi r} \)
D. \( \frac{\mu_{o} I_{o} r^{2}}{2 \pi R} \)
E \( \cdot \frac{\mu_{o} I_{o} r^{2}}{2 \pi R^{2}} \)


Pyrolusite is \( M n O_{2} \stackrel{I}{\rightarrow} M n O_{4}^{2-} \stackrel{I I}{\rightarrow} \)
\( M n O_{4} \)
Steps I and II are respectively:
This question has multiple correct options
A. fuse with KOH / air and electrolytic oxidation.
B. fuse with \( K O H / K N O_{3} \) and electrolytic oxidation.
c. fuse with conc. \( H N O_{3} / a i r \) and electrolytic reduction.
D. dissolve in \( H_{2} O \) and oxidation


a. Write any two differences between
lyophilic and lyophobic colloids.
b. What is heterogeneous catalysis?
Give an example.
c. Give an expression for Freundlich adsorption isotherm.


A ray of light is incident on a glass slab
making an angle of \( 60^{0} \) with the surface. Calculate the angle of
refraction in glass and the velocity of light in glass if the refractive index of glass and the velocity of light in air are 1.5 and \( 3.0 \times 10^{8} \mathrm{m} / \mathrm{s} \) respectively.
A \( \cdot 28^{\circ} 30^{\prime}, 3 \times 10^{8} \mathrm{ms}^{-1} \)
B . \( 40^{\circ} 20^{\prime}, 2.5 \times 10^{8} \mathrm{ms}^{-1} \)
C. \( 35^{\circ} 15^{\prime}, 2 \times 10^{8} \mathrm{ms}^{-1} \)
D. \( 28^{\circ} 30^{\prime}, 2.5 \times 10^{8} \mathrm{ms}^{-1} \)


In one second, a current of 10 A changes through a coil. The induced emf is \( 10 v \) then, self-inductance of the coil is
A . २
B. 5H
c. \( 1 \mathrm{H} \)
D. 0.5H


Which one of the following oxides in
neutral?
A. \( \operatorname{si} O_{7} \)
в. \( \operatorname{Sn} \mathrm{O}_{2} \)
\( c \cdot Z n O \)
D. \( C O \)


Which of these reactions are redox
reactions?
\( 16 N O(g)+4 N H_{3}(g) \rightarrow 5 N_{2}(g)+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\( 22 S O_{2}(g)+O_{2}(g) \rightarrow 2 S O_{3}(g) \)
3. \( \boldsymbol{S O}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


The reason for greater range of oxidation states in actinoids is
attributed to:
A. \( 4 f \) and \( 5 d \) levels being close in energies.
B. the radioactive nature of actinoids
c. actinoid contraction.
D. \( 5 f, 6 d \) and \( 7 s \) levels having comparable energies


Covalent compounds can be dissolved
in:
A. Benzene
B. Ether
c. Alcohol
D. All of these


Define non-metallic character.
\( A . \) An atom is said to be a non-metal if it loses one or
more electrons when supplied with energy
B. An atom is said to be a non-metal if it loses only one electron when supplied with energy
C. An atom is said to be a non-metal if it gains one or more electrons when supplied with energy
D. An atom is said to be a non-metal if it gains only one electron when supplied with energy


What is the maximum number of
covalent bonds than an atom of carbon
can form?
A . 1
B. 2
\( c .3 \)
D. 4


Identify which number cannot be a probability? This question has multiple correct options
A . \( 0 . \)
B . -0.45
c. 1
D. 1.


Ampere's circuital law is given by:
A \( \cdot \oint \bar{H} \cdot \overline{d l}=\mu_{0} I_{e n c} \)
B . \( \oint \bar{B} . \overline{d l}=\mu_{0} I_{e n c} \)
\( \mathbf{c} \cdot \oint \bar{B} \cdot \bar{d} l=\mu_{0} I \)
D . \( \oint \bar{H} . \overline{d l}=\mu_{0} I \)


A sound wave of wavelength \( 32 \mathrm{cm} \) enters the tube as shown in the figure.
Then the smallest radius \( r \) so that a
maximum of sound is heard at
detector is :
\( A \cdot 7 \mathrm{cm} \)
в. 14 ст
\( c \cdot 21 c m \)
D. 28 ст


What is the reaction occuring at the
anode in Down's process for the extraction of sodium?
A \( \cdot 4 O H^{-} \rightarrow 2 H_{2} O+O_{2}+4 e^{-} \)
B. \( N a^{+}+l e^{-} \rightarrow N a \)
\( \mathbf{c} \cdot 2 C l^{-} \rightarrow C l_{2}+2 e^{-} \)
D. \( N a O H \rightarrow N a^{+}+O H^{-} \)


\( \int_{0}^{\pi / 2} \cos x d x \)


Before using the tangent galvanometer its coil is set in:
A. Magnetic meridian
B. Perpendicular to magnetic meridian
c. It does not require any setting
D. It does not required any setting


State True or False.
\( f(a, b, c, d \) are four positive real
numbers such that \( a b c d=1 \), then \( (1+a)(1+b)(1+c)(1+d) \geq 16 \)
A. True
B. False


What is the main principle of sulphuric
acid production by lead chamber
process?
A. Moist \( S \) in presence of nitrogenous oxides (active catalyst) is oxidized to sulphur trioxide which is oxidised to sulphuric acid
B. Moist \( S O_{2} \) in presence of nitrogenous oxides is oxidized to sulphur monoxide which reacts water to produce sulphuric acid
C. Moist \( S \) in presence of nitrogenous oxides is oxidized to sulphur trioxide which reacts water to produce sulphuric acid
D. Moist \( S O_{2} \) in presence of nitrogenous oxides is oxidized to sulphur trioxide which reacts water to produce sulphuric acid


In Krebs cycle, second decarboxylation
occurs during
A. Pyruvate Acetyl CoA
B. - -Ketoglutarate Succinyl CoA
c. oxalosuccinic acid-Ketoglutarate
D. Malic acid Fumaric acid


\( y \)
\( y \)
\( y \)
\( y \)
\( y \)


The equation of the circle and its chord are respectively \( x^{2}+y^{2}=a^{2} \) are
\( x \cos \alpha+y \sin \alpha=p . \) The equation of
the circle of which this chord
is diameter is
A \( \cdot x^{2}+y^{2}-2 p x \cos \alpha-2 p y \sin \alpha+2 p^{2}-a^{2}=0 \)
B . \( x^{2}+y^{2}-2 p x \cos \alpha-2 p y \sin \alpha+p^{2}-a^{2}=0 \)
C \( \cdot x^{2}+y^{2}-2 p x \cos \alpha+2 p y \sin \alpha+2 p^{2}-a^{2}=0 \)
D. None of these


In which direction does current flow in
an electric circuit ? Also, write the SI unit of electric current.


Which of the following are true about the brain?
(a) The main thinking part of brain is hindbrain.
(b) Centres of hearing, smell, memory, sight etc., are located in forebrain.
(c) Involuntary actions like salivation, vomiting, blood pressure are controlled
by the medulla in the hindbrain.
(d) Cerebellum does not control posture
and balance of the body.
A. (a) and (b)
B. (a), (b) and (c)
\( c \cdot(b) \) and \( (c) \)
D. (c) and (d)


A needle of length \( 5 \mathrm{cm}, \) placed \( 45 \mathrm{cm} \) from a lens form an image on a screen placed \( 90 \mathrm{cm} \) on the other side of the
lens. The type of lens and its focal length
are :
A. convex, 30 cm
B. concave, 30 cm
c. convex, \( 60 \mathrm{cm} \)
D. concave, 60 cm


On mixing \( 10 \mathrm{mL} \) of acetone with \( 40 \mathrm{mL} \) of chloroform, the total volume of the solution is:
\( A \cdot<50 m L \)
B. > 50 \( m \) L
\( c_{c}=50 \mathrm{mL} \)
D. Can not be predicted


The hypothalamus regulates:
A. heart rate
B. glandular secretions
c. body temperature
D. all of the above


STRUCTURED/APPLICATION/SKILL TYPE
The volume of air in the lungs and the rate at which it is exchanged
during inspiration and expiration was measured.

The following diagram shows a group of lung volumes and capacities. Study the diagram carefully and explain briefly the following:
nspiratory reserve volume


The decreasing order of diffusion is
A. Gas > Solid > liquid
B. Liquid > Gas > Solid
c. solid > Liquid > Gas
D. Gas > Liquid > Solid


Find the middle term(s) of \( \left(\frac{x^{3 / 2} y}{2}+\right. \)
\( \left.\frac{2}{x y^{3 / 2}}\right)^{13} \)


A conductor A is given a charge of amount \( +Q \) and then placed inside a
deep metal can B, without touching it.
Then:
This question has multiple correct options
A. The potential of A does not change when it is place inside B.
B. If \( B \) is earthed, \( +Q \) amount charge flows from it into the earth.
C. If \( B \) is earthed, the potential of \( A \) is reduced
D. Either (B) or (C) is true or both the true only if the outer surface of B is connected to earth and not its inner surface


A non-zero current passes through the galvanometer F shown in the circuit
when the key 'K' is closed and its value
does not change when the key is opened. Then which of the following statement(s) is/are true?
This question has multiple correct options
A. The galvanometer resistance is infinite
B. The current through the galvanometer is \( 40 \mathrm{mA} \)
c. After the key is closed, the current through \( 200 \Omega \) resistor is same as the current through the \( 300 \Omega \) resistor
D. The galvanometer resistance is \( 150 \Omega \)


One of the rectangular components of a force of \( 50 \mathrm{N} \) is \( 30 \mathrm{N} \). The other
rectangular component will be :
A. \( 40 \mathrm{N} \)
B. 30 N
\( c . \) 35 \( \mathrm{N} \)
D. 45 N


Acid strength of oxoacids of halogen is
in order:
\( \mathbf{A} \cdot H O F>H O C l>H O B r>H O I \)
B . \( H O I<H O B r<H O C l<H O F \)
\( \mathbf{c} \cdot H O I>H O C l>H O B r>H O F \)
D. \( H O C l>H O B r>H O I>H O F \)


The important water pollutants are:
A) Inorganic compounds
B) Organic compounds C) Fluorides
\( A \cdot A \& B \)
B. B \& \( c \)
\( c \cdot A \& C \)
D. \( A, B \& C \)


Elements which occupied the position in the Lother Meyer curve, on the peaks,
were:
A. alkali metals
B. highly electropositive elements
c. elements having large atomic volume
D. all of the above


A compound of general formula
\( C_{n} H_{2 n} O_{2} \) could be :
A . an acid
B. a diketone
C. an ether
D. an aldehyde


\( \mathbf{3 . 6}+\mathbf{6 . 9}+\mathbf{9 . 1 2}+\ldots+\mathbf{3 n}(\mathbf{3 n}+\mathbf{3})= \)
A \( \frac{n(n+1)(n+2)}{3} \)
B. \( 3 n(n+1)(n+2) \)
c. \( \frac{(n+1)(n+2)(n+3)}{3} \)
\( \frac{(n+1)(n+2)(n+4)}{4} \)


How many numbers of five digits can be
formed from the numbers 2,0,4,3,8
when repetition of digits is not allowed?


If the d.rs of two lines are 1,-2,3 and \( 2,0,1, \) then the d.rs of the line
perpendicular to both the given lines is
A. -2,5,4
в. 2,-5,4
c. 2,5,-4
D. 1,5,-4


Mass of one atom of an element is
\( 2.66 \times 10^{-23} g . \) This mass is equal to :
A. 16 amu
В . \( 2.39 \times 10^{-9} \mathrm{J} \)
c. Both are correct
D. None of these


24 cells, each having the same e.m.f. and 2 ohm internal resistance, are used to draw maximum current through an
external resistance of 3 ohm. The cells
should be connected:
\( \mathbf{A} \cdot \) In series
B. in parallel
c. \( \ln 4 \) rows, each row having 6 cells
D. In 6 rows, each row having 4 cells


As you move from top to bottom on the periodic table, what generally happens to the atomic radius?
A. It decreases
B. It decreases, then increases
c. It remains constant
D. It increases, then decreases
E. It increases


Heavy water \( \left(D_{2} O\right) \) is used in Atomic
Reactors as -
A. Coolant
B. Controller
c. shield
D. Moderator


L shell has how many subshell?
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


Solve the equation:-
\( (3 x+2 y)^{2}+(3 x-2 y)^{2} \)


Three numbers are chosen at random
without replacement from \( 1,2, \ldots .10 . \) The probability that the minimum of the
chosen numbers is 3 , or their maximum
is \( 7, \) is
A \( \cdot \frac{7}{40} \)
B. \( \frac{5}{40} \)
c. \( \frac{11}{40} \)
D. None of these


Number of moles of \( K_{2} C r_{2} O_{7} \) require
to reduce one mole of \( S n^{2+} \) ions is
\( A \cdot 1 / 3 \)
B. 3
\( c \cdot 1 / 6 \)
D. 6


Read the following statements and answer as true or false. Unsaturated hydrocarbons give
addition reactions.
If true enter 1 , else enter 0


Which of the following acids doesnot
exist in the free form?
A. \( H_{2} S O_{2} \)
в. \( H_{2} S_{2} O_{3} \)
c. \( \mathrm{H}_{2} \mathrm{SO}_{3} \)
D. \( H_{2} S O_{4} \)


If these numbers form positive odd integer \( 6 q+1, \) or \( 6 q+3 \) or \( 6 q+5 \) for some \( q \) then \( q \) belongs to:
This question has multiple correct options
A. integers
B. rational
c. real
D. none of these


Find \( |\vec{x}|, \) if for a unit vector \( \vec{a},(\vec{x}-\vec{a}) \)
\( (\vec{x}+\vec{a})=12 \)
Answer required


A man and a child are holding a uniform rod of length \( L \) in the horizontal direction in such a way that one fourth weight is supported by the child. If the child is at one end of the rod then the
distance of man from another end will
be:
A \( \cdot \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{L}{3} \)
D. \( \frac{2 L}{3} \)


Why is electronegativity directly
proportional to \( s \) character?


Floral formula of Solanaceae is
A. \( \mathrm{Br} \oplus \bigoplus_{\mathrm{C}(5)} \mathrm{A}_{5} \mathrm{G}_{(2)} \)
B.
\( \oplus \bigoplus_{(5)} \mathrm{C}_{(5)} \mathrm{A}_{5} \mathrm{G}_{(2)} \)
\( \mathrm{Br} \)
c.
\( \oplus \bigoplus_{(5)} \widehat{C}_{(5)} \mathrm{A}_{5} \mathrm{G}_{(2)} \)
\( \mathrm{Br} \)
\( \mathrm{Br} \oplus \bigoplus_{\mathrm{K}_{5} \mathrm{C}_{(5)}} \mathrm{A}_{5} \mathrm{G}_{(2)} \)


When chlorine water is exposed to
sunlight \( O_{2} \) is liberated. Hence:
A. hydrogen has little affinity to \( O_{2} \)
B. hydrogen has more affinity to \( O_{2} \)
C. hydrogen has more affinity to \( C l_{2} \)
D. it is a reducing agent


Which of these devices uses a magnet or electromagnet to make it work?
A. An electric bell
B. A compact disc
c. A microchip
D. All of these


Molarity of \( 4 \% \) (w/v) solution of \( N a O H \)
is:
A . \( 0 . \)
B. 0.5
c. 0.001
D. 1.0


35 workers can build a house in 16
days. How many days will 28 workers working at the same rate take to build
the same house?
A. 16 days
в. 28 days
c. 20 days
D. 10 days


Soaps and detergent industries uses:
A . lower fatty acids
B. higher fatty acids
c. esters
D. alcohols


Choose the correct answer from the
alternatives given In the systemic circuit, the \( _{--} \) hearts half pumps \( _{--} \) blood to all body regions:
A. right; oxygen-poor
B. right; oxygen-rich
c. left; oxygen-poor
D. Ieft; oxygen-rich


If \( I_{n}=\int_{0}^{\infty} e^{-x} x^{n-1} d x, \) then
\( \int_{0}^{\infty} e^{-\lambda x} x^{n-1} d x \) is equal to?
A \( . \lambda I_{n} \)
B. \( \frac{1}{\lambda} I \)
c. \( \frac{I_{\mathrm{n}}}{\lambda^{\mathrm{n}}} \)
D. \( \lambda^{n} I_{n} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{5} \\ \mathbf{7} & \mathbf{- 9}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{6} & \mathbf{- 4} \\ \mathbf{2} & \mathbf{3}\end{array}\right], \) find
\( (4 A-3 B) \)


An iron ball and a wooden ball of the
same radius are released from a height \( \mathrm{H} \) in vacuum. The times taken by both of them to reach the ground are
A . roughly equal
B. unequal
c. exactly equal
D. in the inverse ratio of their diameters


The sets \( A=\{\text { letters of the world 'FLOW' }\} \) and \( \mathrm{B}=\{\text { letters of the word 'FOLLOW' }\} \)
are :
A. Equivalent sets
B. Equal sets
c. singleton sets
D. Null sets


The length of a plant axis increases by
A. Apical meristem
B. Lateral meristem
c. Dermatogen
D. Pleurome


The amplitude and modulus of the complex number \( -2+2 \sqrt{3} i . \) is 4 and \( \underline{\boldsymbol{\pi}} \)
\( \overline{\mathbf{3}} \)
A. True
B. False


Divide 4500 into two parts such that \( 5 \% \) of the first part is equal to \( 10 \% \) of the second part.
A . 300
B. 250
c. 3000
D. 2500


Which of the following reaction
equation is wrongly labeled?
\( \mathbf{A} \cdot F e+C r^{3+} \rightarrow F e^{3+}+C r(r e d o x) \)
B \( \cdot K B r+H_{2} O \rightarrow H B r+K O H \) (hydrolysis)
\( \mathbf{c} \cdot C H_{4}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \) (combustion)
D. \( C H_{4}+C l_{2} \rightarrow C H_{3} C l+H C l \) (addition)
E \( \cdot C O_{2}+H_{2} O \rightarrow H_{2} C O_{3} \) (synthesis)


Compounds such as alcohols and glucose contain hydrogen but are not categorized as acids. Why?


Whenever there is a change in the
magnetic flux linked with a closed
circuit, an emf and a current are
induced in the circuit. This statement is
referred to as:
A. Lenz's law
B. Faraday's second law of electromagnetic induction
C. Faraday's first law of electromagnetic induction
D. Laplace's law


A bus is moving with a speed of \( 10 \mathrm{ms}^{-1} \)
on a straight road. A scooterist wishes
to overtake the bus in 100 s. If the bus is
at a distance of \( 1 \mathrm{km} \) from the scooterist, with what speed should the scooterist chase the bus?
A. \( 40 \mathrm{ms}^{-1} \)
B. 25 \( m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 20 \mathrm{ms}^{-1} \)


Draw a neat diagram of an A.C.
generator.


One gas bleaches the colour of the
flowers by reduction, while the other by oxidation
A. \( N H_{3} \) and \( S O_{3} \)
B. CO and Cu
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{Cl}_{2} \)
D. \( H_{2} S \) and \( M n C l_{2} \)


Assertion
Cytokinin treatment results in the
increase in the RNA content.
Reason
Cytokinin inhibits protein degradation.
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


In figure, potential at A is :-
4.22
\( B,-3 V \)
\( c-1.5 v \)
\( 0 .-2.51 \)


In SHM, select the wrong statement, where \( F \) is the force, \( a \) is the
acceleration and \( v \) is the velocity of the
particle in SHM.
A \( \cdot \vec{F} \times \vec{v} \) is a null vector
В . \( |\vec{F} \times \vec{a}|=0 \) (always)
c. \( \vec{F} \times \vec{a}<0 \)
D. \( \vec{a} \cdot \vec{x}<0 \)


\( \operatorname{lf} \Delta=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \) and \( A_{2}, B_{2}, C_{2} \) are
respectively cofactors of \( a_{2}, b_{2}, c_{2} \) then
\( a_{1} A_{2}+b_{1} B_{2}+c_{1} C_{2} \) is equal to
\( A \cdot-\Delta \)
B.
\( c \cdot \Delta \)
D. none of these


If three points \( (h, 0),(a, b) \) and \( (0, k) \) lie on a line, show that \( \frac{a}{h}+\frac{b}{k}=1 \)


The pressure at point \( C \) is given by
A \( \cdot \frac{3 P_{0}}{2^{0.4}} \)
в. \( \frac{3 P_{0}}{2^{1.4}} \)
c. \( 3 P_{0} \times 2^{0.4} \)
D. \( 3 P_{0} \times 2^{1.4} \)


\( \ln \) a \( L C \) circuit. Angular frequency at resonance is \( \boldsymbol{w} \). What will be the new
angular frequency when inductor's
introduces is made 2 times and
capacitance is made 4 times?
A \( \cdot \frac{w}{\sqrt{2}} \)
в. \( \frac{w}{2 \sqrt{2}} \)
c. \( 2 w \)
D. \( \frac{2 w}{\sqrt{2}} \)


The space between the plates of a parallel plate capacitor is filled with a dielectric' whose 'dielectric constant'
varies with distance as per the relation,
\( \boldsymbol{K}(\boldsymbol{x})=\boldsymbol{K}_{o}+\boldsymbol{\lambda} \boldsymbol{x}(\boldsymbol{\lambda}=\boldsymbol{a} \text { constant }) \) The
capacitance \( C, \) of this capacitor, would be related to its 'vacuum' capacitance
\( C_{o} \) as per the relation:
\( ^{\mathbf{A}} \cdot c=\frac{\lambda d}{\ln \left(1+k_{o} \lambda d\right)} C_{o} \)
B. \( c=\frac{\lambda}{d \cdot \ln \left(1+k_{o} \lambda d\right)} C_{o} \)
\( ^{\mathrm{c}} \cdot_{C}=\frac{\lambda d}{\ln \left(1+\lambda d / K_{o}\right)} C_{o} \)
D. \( c=\frac{\lambda}{d \cdot \ln \left(1+k_{o} / \lambda d\right)} C_{o} \)


Assertion
A sphere, a cube and thin circular plate
of the same mass are made of the same
material. If all of them are heated to the
same high temperature the rate of
cooling is maximum for the plate and minimum for the sphere.
Reason
The rate of loss of heat by radiation is proportional to the surface area.
A. Assertion is False and Reason is True
B. Reason is False and assertion is True
c. Both Assertion and Reason are True and reason correctly explains assertion
D. Both Assertion and Reason are True but assertion does not correctly explain reason


Q Type your question-
less than \( \mathbf{U}^{\mathbf{v}} \) ( . If the tnickness or the lce
layer formed on the surface grows from
\( 2 c m \) to \( 4 c m \) in 1 hour, the atmosphere temperature will be (Thermal
conductivity of ice, \( \boldsymbol{K}=\mathbf{4} \times \)
\( 10^{-3} \) cal \( c m^{-1} s^{-1 o} C^{-1}, \) density of ice
\( =0.9 g c c^{-1} . \) Latent heat of fusion of ice
\( =80 \mathrm{cal} g^{-1} \) Neglect the change of
density during the state change. Assume that the water below the ice
has \( 0^{\circ} \mathrm{C} \) temperature every where.)
Formed ice
\( --- \)
A. \( -20^{\circ} \mathrm{C} \)
B. \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-30^{\circ} C \)
D. \( -15^{\circ} \mathrm{C} \)


A circular loop of wire is in the same
place as an infinitely long wire carrying a constant current i. Four possible motion of the loop are marked by \( \mathrm{N}, \mathrm{E}, \mathrm{W} \)
and \( \mathrm{S} \) as shown.
A clockwise current is induced in the
loop when loop is pulled towards
\( A \)
B.
\( c \cdot w \)
\( D \)


The value of self inductance of a coil is
\( 5 H . \) The value of current changes from
\( 1 A \) to \( 2 A \) in 5 sec., then value of
magnitude of induced emf in it :-
A . \( 10 V \)
в. \( 0.1 V \)
\( c .1 .0 V \)
D. \( 100 V \)


The hot water pipes used to heat up the room are painted
A. white
B. yellow
\( c \cdot \) red
D. black


(Lambda, Hertz) is
the unit of frequency, and just means how many cycles per second. It is abbreviated as \( \mathrm{Hz} \)


Which of the following is not a valid reason for using cotton clothes in
Summer?
A. cotton clothes attract cool air
B. cotton clothes absorb sweat from the body
c. cotton exposes the sweat to atmosphere for evaporation
D. cotton is light in weight


Four positive charges \( (2 \sqrt{2}-1) Q \) are
arranged at the four corner of a square. Another charge q is placed at the centre of the square. Resulting force acting on each corner charge is zero if q is :
A \( \cdot \frac{-7 Q}{4} \)
в. \( \frac{-4 Q}{7} \)
\( c \cdot-Q \)
D. \( -(\sqrt{2}+1) Q \)


Which of the following molecules is common to respiration mediated breakdown of major biomolecules?
A. AcetylCOA
B. Glucose 6-phosphate
c. Fructose 1, 6 - biphosphate
D. Pyruvic acid


Which of the following pairs of compounds is isoelectronic and isostructural?
A. \( I F_{3}, X e F_{2} \)
в. \( B e C l_{2}, X e F_{2} \)
\( \mathbf{c} \cdot \operatorname{TeI}_{2}, X e F_{2} \)
D. \( I B r_{2}^{-}, X e F_{2} \)


If the radius of a nucleus \( ^{256} X \) is 8
fermi, then the radius of \( ^{4} \) He nucleus
will be:
A. 16 fermi
B. 2 fermi
c. 32 fermi
D. 4 fermi


Sodium extract gives blood red colour
when treated with \( F e C l_{3} \). Formation of
blood red colour confirms the presence
of:
A. only nitrogen
B. only sulphur
c. only halogens
D. both nitrogen and sulphur


Which of the following division of kingdom plantae and sub-kingdom cryptogamae can reproduce sexually by formation of gametes.
A. Thallophyta
B. Bryophyta
c. Pteridophyta
D. All of above


Place value of 9 in 7,92,83,456
\( \mathbf{A} \cdot 9,000 \)
B. 9
c. 90,00,000
D. 90,000


Introduction of inert gas at constant
volume to a gaseous reaction at equilibrium, results in formation of :
A. same amount of product
B. more quantity of product
c. less quantity of product
D. no product


At high altitudes, the boiling of water
takes place below \( 100^{\circ} \mathrm{C} \) because :
A. the atmospheric pressure is low
B. the temperature is low
c. the atmospheric pressure is high
D. none of the above


Find the value of \( \boldsymbol{m}, \) if \( \boldsymbol{x}=\boldsymbol{2}, \boldsymbol{y}=\mathbf{1} \) is a
solution of the equation \( 2 x+3 y=m \)


Match the following.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \begin{array}{l}\text { I. Sandy } \\ \text { soil }\end{array} & \text { A. } 85 \% \text { sand }+15 \% \text { clay or silt } \\ \begin{array}{l}\text { II. Loam } \\ \text { soil }\end{array} & \text { B. } 70 \% \text { sand }+30 \% \text { clay or silt } \\ \text { III. Silt } & \begin{array}{l}\text { C. } 50 \% \text { sand }+50 \% \text { clay or silt or } \\ \text { both }\end{array}\end{array} \)
\( \mathbf{A} \)
I-A, II-D, |II-C
B. ।- \( A,\|-B,\| I-D \)
C . \( \mid-A, \) II- \( D, \| I-B \)
D. I- A, II-B, III- C
\( E \cdot|-A,| I-C,|I|-D \)


Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at a
center.


ff \( p(x) \) be a polynomial satisfying the
identity \( p\left(x^{2}\right)+2 x^{2}+10 x=2 x p(x+ \)
1) \( +3, \) then function \( p(x) \) is
A. One-one
B. Many-one
c. Periodic
D. Even


If the radius of moon is \( 1.7 \times 10^{6} m \) and
its mass is \( 7.34 \times 10^{22} \) kg. Then its
escape velocity is
A \( \cdot 2.4 \times 10^{3} \mathrm{ms}^{-1} \)
В. \( 2.4 \times 10^{2} \mathrm{ms}^{-1} \)
c. \( 3.4 \times 10^{3} \mathrm{ms}^{-1} \)
D. \( 3.4 \times 10^{2} \mathrm{ms}^{-1} \)


If \( \frac{(x+1)^{2}}{x\left(x^{2}+1\right)}=\frac{A}{x}+\frac{B x+C}{x^{2}+1}, \) then
\( \cos ^{-1}\left(\frac{A}{C}\right)= \)
A. \( \frac{\pi}{6} \)
в.
c.
D.


Show that kinetic energy is always lost
in inelastic collision.


Diarrhoea is the \( _{--}-_{-}-_{-} \) leading cause of death in children under five
years old.
A. 2nd
B. 3rd
c. 4 th
D. sth


Nuclear attraction is often the deciding control factor for the association of
natural molecules to
a given metal ion. Which one of the
following represents the correct order of stability of the ions? \( \left[\boldsymbol{B e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right]^{2+},\left[\boldsymbol{M} \boldsymbol{g}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right]^{2+}, \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{C}\right. \)
\( \left.\left.\mathbf{A} \cdot\left[B e\left(H_{2} O\right)_{4}\right]^{2+}>S r\left(H_{2} O\right)_{4}\right]^{2+}\right]>\left[M g\left(H_{2} O\right)_{4}\right]^{2+}> \)
\( \left[C a\left(H_{2} O\right)^{4}\right]^{2+} \)
B . \( \left[C a\left(H_{2} O\right)_{4}\right]^{2+}>\left[M g\left(H_{2} O\right)_{4}\right]^{2+}>\left[B e\left(H_{2} O\right)_{4}\right]^{2+}> \)
\( \left.\operatorname{Sr}\left(H_{2} O\right)_{4}\right]^{2+} \)
C \( \cdot\left[\operatorname{Sr}\left(H_{2} O\right)_{4}\right]^{2+}>\left[C a\left(H_{2} O\right)_{4}\right]^{2+}>\left[M g\left(H_{2} O\right)_{4}\right]^{2+}> \)
\( \left[\operatorname{Be}\left(H_{2} O\right)_{4}\right]^{2+} \)
D. \( \left[B e\left(H_{2} O\right)_{4}\right]^{2+}>\left[M g\left(H_{2} O\right)_{4}\right]^{2}>\left[C a\left(H_{2} O\right)_{4}\right]^{2+}> \)
\( \left.\operatorname{Sr}\left(H_{2} O\right)_{4}\right]^{2+} \)


Give the IUPAC names of the following compounds:
Glycerol


If \( A+B+C=\pi \) then the expression \( \frac{\sin 2 A+\sin 2 B-\sin 2 C}{\sin 2 A+\sin 2 B+\sin 2 C} \) reduces to


The role of the axon is to
A. Integrate signals from the dendrites
B. Release neurotransmitter
C. Conduct the impulse to the synaptic terminal
D. Synthesize cellular components


Curved surface area and circumference
at the base of a solid right circular cylinder are 4400 sq. \( \mathrm{cm} \) and \( 110 \mathrm{cm} \) respectively. Find its height and diameter.


How will you convert:
(i) Propene to Propan-2-ol?
(ii) Phenol to 2,4,6-trinitrophenol?


Fill in the blank:
of charges on surfaces of clouds leads to lightning.
A. Accumulation
B. Leakage
c. conduction
D. Induction


\( \delta \) \( \delta \delta \)
\( \delta_{d} \)
\( 8 . d \)


On the basis of organization, animals are grouped into
A. Metazoa and Eumetazoa
B. Protozoa and Metazoa
c. Protozoa and Parazoa
D. Parazoa and Metazoa


Write two examples of plants with tendrils.


Let \( y=\sin ^{-1}(\cos x) \) then find \( \frac{d y}{d x} \)


Let \( A, B, C, D \) be (not necessarily
square) real matrices such that \( \boldsymbol{A}^{\boldsymbol{T}}= \)
\( \boldsymbol{B C D} ; \boldsymbol{B}^{\boldsymbol{T}}=\boldsymbol{C D A} ; \boldsymbol{C}^{\boldsymbol{T}}=\boldsymbol{D A B} \) and
\( D^{T}=A B C \) for the matrix \( S=A B C D \)
then which of the following is/are true This question has multiple correct options
A \( \cdot S^{3}=S \)
B. \( S^{2}=S^{4} \)
c. \( S=S^{2} \)
D. none of these


A lift starts from the top of a mine shaft
and descends with a constant speed of
\( 10 m / s .4 \) sec later a boy throws a stone
vertically upwards from the top of the shaft with a speed of \( 30 m / s . \) If stone
hits the lift at a distance \( x \) below the
shaft write the value of \( \frac{x}{3}(\text { in } m) \) \( \left[\text { Take }: \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right]( \) given value of
\( \mathbf{2 0} \sqrt{\mathbf{6}}=\mathbf{4 9}) \)


Define Permitivity of vacuum \( \left(\boldsymbol{E}_{\mathbf{0}}\right) \)


Divide the following and write your answer in lowest terms: \( \frac{3 x^{2}-x-4}{9 x^{2}-16} \div \) \( \frac{4 x^{2}-4}{3 x^{2}-2 x-1} \)
A \( \frac{3 x+1}{4(3 x+4)} \)
В. \( \frac{3 x-1}{4(3 x+4)} \)
c. \( \frac{3 x+1}{4(3 x-4)} \)
D. None of these


A ballet dancer spins with angular velocity of 2.8 rev/s with her arms stretched out and moment of inertia
about the vertical axis. She then
retracts her arms and moment of
inertial becomes 0.71 about the same
axis. Find the new angular velocity
A. 3.2 rev / s
B. 4 rev/s
c. 4.8 rev/s
D. 5.6 rev / s


Photosynthetic Active Radiation (PAR) has which of the following range of wavelengths?
A. \( 400-700 \mathrm{nm} \)
B. 450-920 nm
c. \( 340-450 \mathrm{nm} \)
D. 500-600 nm


For the function \( f(x) \) which value of \( a \) is
not possible
A \( \cdot \frac{1}{4} \)
B. \( -\frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


If the midpoints of the sides of an equilateral triangle are connected, then they divide it into four triangles all
of which are
A. congruent
B. Similar in shape
C. Different
D. None of these


For the infinite series \( 1-\frac{1}{2}-\frac{1}{4}+\frac{1}{8}- \)
\( \frac{1}{16}-\frac{1}{32}+\frac{1}{54}-\frac{1}{128}-\ldots . \quad \) let \( S \) be
the (limiting) sum. Then \( S \) equals
A. 0
в. \( \frac{2}{7} \)
\( c \cdot \frac{6}{7} \)
D. \( \frac{9}{32} \)
E \( \frac{27}{32} \)


The function \( \boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] \)
defined by \( f(x)=e^{x^{3}-3 x+2} \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into


The mean temperature can be obtained
by
A. Average of the temperature recorded during the month
B. Calculate the average of such average temperatures
over many years
C. Average of the temperature recorded during one year
D. Both option A and B


Calculate the area of a parallelogram
with a base of \( 12 \mathrm{m} \) and height of \( 5 \mathrm{m} \)
\( \mathbf{A} \cdot 59 m^{2} \)
в. \( 60 m^{2} \)
\( \mathbf{c} \cdot 61 m^{2} \)
D. 62 \( m^{2} \)


India museum was established in
A . 1759
B. 1814
\( c . \) 1955
D. 1957


Louis de -Broglie is credited for his work
on
A. Theory of relativity
B. Electromagnetic theory
c. Matter waves
D. Law of distribution of velocities


Identify D:
\( \mathbf{A} \cdot C H_{3} O H \)
B \( \cdot C_{2} H_{6} O \)
\( \mathbf{c} \cdot C_{2} H_{5} O \)
\( \mathrm{D} \cdot C_{4} H_{10} \mathrm{O} \)


Show that the vectors \( 2 \hat{i}-\hat{j}+\hat{k}, \hat{i}- \) \( \mathbf{3} \hat{\boldsymbol{j}}-\mathbf{5} \hat{\boldsymbol{k}} \quad \) and \( \quad \mathbf{3} \hat{\mathbf{i}}-\mathbf{4} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}} \) form the
vertices of a right angled triangle.


A certain radioactive material can
undergo three different types of decay, each with a different decay constant \( \lambda, 2 \lambda, \) and \( 3 \lambda . \) Then, the effective decay
constant \( \lambda_{e f f} \) is equal to \( n \lambda \). What is
the value of n?


Assertion
Higher plants have meristematic regions for indefinite growth.
Reason
Higher plants have root and shoot spices
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


Write a short note on heterocyclic base present in nucleic acids. (structure is
not required)


Organic chemistry is the chemistry of specific \( - \) compounds.
A. oxygen
B. chlorine
c. nitrogen
D. carbon


Which amongst the following reactions cannot be used for the preparation of the halogen acid?
A \( \cdot 2 K B r+H_{2} S O_{4}(\text { Conc. }) \rightarrow K_{2} S O_{4}+2 H B r \)
В. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4}(\text { Conc. }) \rightarrow \mathrm{NaHSO}_{4}+\mathrm{HCl} \)
c. \( N a H S O_{4}+N a C l \rightarrow N a_{2} S O_{4}+H C l \)
D. \( C a F_{2}+H_{2} S O_{4}(\text {conc.}) \rightarrow C a S O_{4}+2 H F \)


The sum of two positive integers multiplied by the bigger number is 204 and their difference multiplied by the
smaller number is \( 35 . \) The numbers are :
A . 12,5
B. 13,4
\( c \cdot 14,3 \)
D. 24, 10


In any electric circuit, when the switch is on and the current is flowing through it why do the wire, switches, bulb or devices in the circuit become hot?
A. Because of the heating effect of electric current
B. Because of the magnetic effect of electric current
c. Because of the luminous effect of electric current
D. None of these


Find the general solution of the differential equation:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{y}}{\boldsymbol{x}}+\sin \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right) \)


The radius of a circular garden is \( 90 \mathrm{m} \) There is a road \( 9 \mathrm{m} \) wide around it. Find
total area of the road and the cost of
levelling the road at Rs.5 per sq.m.


How many electrons should be removed
from a coin of mas \( 1.6 \mathrm{g} \), so that it may
float in an electric field of intensity \( 10^{9} \) N/C directed upward?
A \( .9 .8 \times 10^{7} \)
B . \( 9.8 \times 10^{5} \)
\( \mathbf{c} \cdot 9.8 \times 10^{3} \)
D. \( 9.8 \times 10^{1} \)


A vessel with a symmetrical hole in its
bottom is fastened on a cart. The mass
of the vessel and the cart is 1.5 kg. With
what force \( F\left(\text { in } \times 10^{2} N\right) \) should the
cart be pilled so that the maximum amount of water remains in the vessel.
The dimensions of the vessel are as
shown in the figure. Given that \( b= \)
\( \mathbf{5 0} c \boldsymbol{m}, \boldsymbol{c}=\mathbf{1 0} \boldsymbol{c m} \) area of base \( \boldsymbol{A}= \)
\( 40 c m^{2}, L=20 c m, g=10 m / s^{2} \)


Q Type your question
them are correct
(i) In Primary treatment First, floating debris of waste is removed by sequence filters
(ii) The Soil and small pebbles are
removed by sedimentation in settling
tanks
(iii)The sediment is called primary sludge and supernatant is effluent.
(iv) The Sludge is taken for Secondary
treatment.
(v) Lower the B.O.D., higher Is water
pollution. (vi)When DDT enters the food chain
then they reach water and are easily degradable. (vii)Discharge of sewage water into river water will decrease its B.O.D.
(viii) Chlorine is added to disinfect
drinking water
A \( . \) (i), (ii), (iii), (iv)
B. (i), (ii), (iii), (vii)
\( \mathbf{c} \cdot(\mathbf{i}),(\mathbf{i} i)(\mathbf{i v}),(\mathbf{v}) \)
D. (i), (iv),(v), (viii)


The system shown in figure is in
equilibrium. The string between \( A \) and
\( B \) is cut. The acceleration of block \( B \)
will be?
\( A \)
B. \( g / 3 \)
\( c \)
D. None of these


A couple has two children. Find the probability that both the children are males, if it is known that at least one of the children is male.
(ii) females, if it is known that the elder child is a female.


Fill in the blanks with \( >,< \) or \( =\operatorname{sign} \) \( (-3)+(-6) \dots \dots \dots(-3)-(-6) \)


The image formed by a plane mirror is
the object.
\( \mathbf{A} \)
A. smaller than
B. bigger than
C. of the same size as
D. cannot be determined


In the arrangement of resistances shown below. The effective resistance
between points \( A \) and \( B \) is
A . \( 20 \Omega \)
в. \( 30 \Omega \)
\( c .90 \Omega \)
D. \( 110 \Omega \)


Power gain for \( N-P-N \) transistor is
\( 10^{6}, \) input resistance \( 100 \Omega \) and output
resistance \( 1000 \Omega \). find out current
gain.
A. 100
в. 150
\( c \cdot 200 \)
D. 50


Henry's law constant for the molality of methane in benzene at \( 298 \mathrm{K} \) is \( 4.27 \times \)
105 mm \( H g \). Calculate the solubility of
methane in benzene at \( 298 K \) under
\( 760 m m H g \)


Show that the Balmer series occurs between \( 3647 \dot{A} \) and \( 6563 \hat{A} \)
\( \left(\boldsymbol{R}=\mathbf{1} . \mathbf{0} \mathbf{9} \mathbf{6} \mathbf{8} \times \mathbf{1} \mathbf{0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}}\right) \)


From 4 officers and 8 jawans, in how
many ways can 6 be chosen such that to include exactly one officer.


Suppose a voltmeter of resistance \( 660 \Omega \) reads the voltage of a very old cell to be
1.32 volt while a potentiometer reads its voltage to be 1.44 volt. The internal resistance of the cell is:
A . \( 30 \Omega \)
B. \( 60 \Omega \)
\( c \cdot 6 \Omega \)
D. \( 0.6 \Omega \)


Give the main drawback of Rutherford's
model.


The random error which exists
invariably in screw gauge is:
A. least count error
B. zero error
c. gross error
D. backlash error


Which of the following is a condition for burning?
A. Ignition temperature
B. Combustible substance
c. Gaseous environment
D. All of above


An aqueous blue coloured solution of a
transition metal nitrate reacts with
\( H_{2} S \) in acidic medium to give a black precipitate (X), which dissolves in \( \boldsymbol{K} \boldsymbol{N} \) solution forming a clear solution of (Y). The blue solution on reaction with
\( K I \) in weakly acidic medium becomes intensely brown and produces a white precipitate (Z).
The electron configuration of the transition metal ion is

This question has multiple correct options
\( \mathbf{A} \cdot[A r] 3 d^{9} \)
B . \( [A r] 3 d^{10} \)
c. \( [K r] 4 d^{9} \)
D. \( [K r] 4 d^{1} \)


hierarchy of various taxonomic
categories. Identify the missing categories(A, B and
C) and select the correct statements
regarding these.
(i) \( A \) is the taxonomic category which
contains a number of related genera.
(ii) Examples of category B are Monocotyledoneae, Dicotyledoneae, Mammalia, etc.
(iii) \( \mathrm{C} \) represents the basic unit of taxonomic hierarchy.
(iv) Examples of category \( C \) are Fungi
Monera, Protista, etc.
\( A \cdot \) (i) and (ii)
B. (iii) and (iv)
C . (i), (ii) and (iv)
D. (i), (ii), (iii) and (iv)


If \( k+\left|k+z^{2}\right|=|z|^{2}\left(k \epsilon R^{-}\right), \) then
possible argument of \( z \) is
A .
в. \( \pi \)
c. \( \frac{\pi}{2} \)
D. None of these


Fluorine reacts with ice and results in
the change:
\[
\begin{array}{r}
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{F}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g})+ \\
\boldsymbol{H O F}(\boldsymbol{g})
\end{array}
\]
i) Justify that this reaction is a redox
reaction.
ii) Write the substances oxidized and
reduced.
iii) Write the name of the substances
which acts as reducing agent and oxidizing agent.


Silver is found in nature both in native
and combined state.
A. True
B. False


How is chlorine produced by electolytic
method?


Percussion instruments are musical
instruments that are played by
A. banging
B. shaking
c. both A and B
D. hitting


You are provided with a negatively charged gold leaf electroscope. State and explain what happens when an uncharged metal rod is brought near the disc of electroscope.
A. Divergence increases
B. Divergence decreases
c. Divergence remains same
D. can't say


One mole of a gas expands by \( 3 L \)
against a constant pressure of 3 atmosphere. Calculate the work done in L atmosphere.


Maximum height. (in m)
A . 20
B. 40
\( c .60 \)
D. 80


Which of the following is natural element?
A. Pm
B . La
c. Pu
D. Np


At what angle the rectangular mirrors are set to each other in Kaleidoscope?
A. 90 degree
B. 30 degree
c. 60 degree
D. 120 degree


For a particle performing SHM:
A. The kinetic energy is never equal to the potential
energy
B. The kinetic energy is always equal to the potential energy
C. The average kinetic energy in one time period is equal to the average potential energy in this period.
D. The average kinetic energy in any time interval is never equal to average potential energy in that interval.


If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2}, \) then \( x= \)
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot-\frac{1}{2} \)
D. \( \frac{\sqrt{3}}{2} \)


A simple leaf can be differentiated from the pinnae of a compound leaf on the basis of presence or absence of
A. number of pinnae
B. shape of lamina
c. axillary bud
D. lateral buds


Name the method which can give
following product


Two equal poles repel each other with a
force of \( 10^{-3} \) N. When placed 2 cm apart in
air, the pole strength of each is (in amp-
\( \mathrm{m}) \)
A . \( 4 \pi \)
B. 2
\( c \cdot 4 \)
D. 2\pi


A particle is moved from (0,0) to \( (a, a) \) under a force \( F=3 i+4 j \) ) from two paths.
Path 1 is \( 0 P \) and path 2 is \( Q O P \). Let \( W_{1} \)
and \( \mathrm{W}_{2} \) be the work done by this force in two paths. Then:
A. \( w_{1}=w_{2} \)
B. \( w_{1}=2 w_{2} \)
\( c \cdot w_{2}=2 w_{1} \)
\( D \cdot W_{1}=4 W_{2} \)


Electrons are represented as:
\( \mathbf{A} \cdot e \)
B \( \cdot e^{-} \)
\( \mathbf{c} \cdot e^{+} \)
\( \mathrm{D} \cdot e^{+} \)


A cyclic heat engine does \( 50 \mathrm{kJ} \) of work per cycle. If efficiency of engine is \( 75 \% \) the heat rejected per cycle will be:
A . 60.6
B. 16.6
c. 200
D. 600


The first major industrial demand for
sulfuric acid for making sodium
carbonate was the
A . vitrol process
B. oiling vitrol process
c. leblanc process
D. nordhausen process


A straight line is drawn through the point \( p(2,3) \) and is inclined at an angle
of \( 30^{\circ} \) with the \( x- \) axis, the co-ordinates
of two points on it at a distance of 4 from \( p \) is/are
A \( \cdot(2+2 \sqrt{3}, 5),(2-2 \sqrt{3}, 1) \)
B . \( (2+2 \sqrt{3}, 5),(2+2 \sqrt{3}, 1) \)
c. \( (2-2 \sqrt{3}, 5),(2-2 \sqrt{3}, 1) \)
D. none of these


Which one of the following vitamins is water soluble?
A. Vitamin \( B \)
B. Vitamin \( E \)
c. Vitamin \( K \)
D. Vitamin \( A \)


How many \( N a^{+} \) ions are present in
\( 100 m L \) of \( 0.25 M \) of \( N a C l \) solution?
A. \( 0.25 \times 10^{23} \)
В. \( 1.505 \times 10^{22} \)
C. \( 15 \times 10^{22} \)
D. \( 2.5 \times 10^{23} \)


Consider the following statements \( (A- \)
C) each with one or two blanks.
(A)(1) are the most abundant cells (60-
\( 65 \text { per cent }) \) of the total WBCs and (2) are the least (0.5-1 per cent) among
them.
(B)Platelets are cell fragments produced from (3)
(C)During clot formation, fibrins are formed by the conversion of inactive in the plasma by the enzyme (5). Which one of the following options,
gives the correct fill ups for the respective blank numbers from
(1) to
(5)
in the statements?
A. (I)-Neutrophils, (2)-basophils, (4)-fibrinogens, (5) thrombin
B. (3)-mast cells, (4)-throm bo kinase, (5)prothrombin
c. (3)-megakaryocytes,
(4) prothrombin, (5)thrombin
D. (1)-Basophils, (2)-neutrophils, (3)-reticulocytes


The power supplied by the battery will be:
A. \( 15 \mathrm{w} \)
B. 24 W
c. \( 3.6 \mathrm{w} \)
D. 20 W


Assertion
No. of spherical balls that can be made out of a solid cube of lead whose edge is \( 44 \mathrm{cm}, \) each ball being \( 4 \mathrm{cm} \). in diameter, is 2541
Reason
Number of balls = (Volume of one
ball)/(Volume of lead)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( \lim _{x \rightarrow 0}\left[\frac{(1+x)^{\frac{1}{8}}-(1-x)^{\frac{1}{8}}}{x}\right] \)


Let \( A=\{0,1,2,3\} \) and define a relation \( R \)
as follows
\( R=\{(0,0),(0,1),(0,3),(1,0),(1,1),(2,2) \)
(3,0),(3,3)\}
Is \( \mathrm{R} \) reflexive, symmetric and transitive
\( ? \)


Tincture of iodine has antiseptic
properties. This solution is made by dissolving:
A. iodine in potassium iodide
B. iodine in vaseline
c. iodine in water
D. iodine in alcohol


Lungs ventilation movement are due to
the movements of
A. coastal muscles and diaphragm
B. coastal muscles only
c. Diaphragm only
D. wall of the lungs


How did Hershey and Chase prove that DNA is the genetic material?


A scrubber in the exhaust of a chemical industry removes
A. Hydrogen sulphide
B. Sulpher dioxide
c. Nitrous oxide
D. Carbon monoxide


Using triangle inequality theorem check whether the given side lengths
\( \boldsymbol{a}=\mathbf{3}, \boldsymbol{b}=\mathbf{5} \) and \( \boldsymbol{c}=\mathbf{1} \) will form a
triangle or not


Assertion
Two point coherent sources of light \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are placed on a line as shown in
figure. \( P \) and \( Q \) are two points on that
line. If at point \( \boldsymbol{P} \) maximum intensity is observed, then maximum intensity should also be observed at \( Q \)
Reason
In the figure, the distance \( \left|\boldsymbol{S}_{1} \boldsymbol{P}-\boldsymbol{S}_{2} \boldsymbol{P}\right| \)
is equal to distance \( \left|\boldsymbol{S}_{1} \boldsymbol{Q}-\boldsymbol{S}_{2} \boldsymbol{Q}\right| \)
\[
\vec{Q} \quad \overrightarrow{s_{1}} \quad \dot{S_{2}} \quad \dot{P}
\]
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


n different toys are to be distributed among n children. Find the number of
ways in which these toys can be distributed so that exactly one child
gets no toy


A wire carrying a current of \( 5 A \) is placed perpendicular to a magnetic induction of \( 2 T . \) The force on each centimeter of
the wire is
A. \( 0.1 N \)
в. \( 10 N \)
c. \( 100 N \)
D. \( 1 N \)


If the difference between the
circumference and radius of a circle is
\( 37 \mathrm{cm}, \) then the area of the circle is
A \( \cdot 111 c m^{2} \)
В. \( 148 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 259 \mathrm{cm}^{2} \)
D. \( 154 \mathrm{cm}^{2} \)


An equation of a line through the point
(1,2) whose distance from the point
(3,1) has the greatest value is
A \( y=2 x \)
\( x \)
B. \( y=x+1 \)
c. \( x+2 y=5 \)
D. \( y=3 x-1 \)


Assertion
The pollen tube is believed to release some stimulus for the increased growth
in the ovary wall.
Reason
The auxins can increase the activity of ovary even in the absence of pollen grain or pollen tube.
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


Energy in a current carrying coil is stored in the form of
A . electric field
B. magnetic field
c. dielectric strength
D. heat


The number of quanta of radiation of frequency \( 4.98 \times 10^{14} s^{-1} \) required to
melt 100 g of ice are (latent heat of melting of ice is 33 joule per \( g \) ):
A \( \cdot 10^{20} \)
B. \( 10^{2} \)
\( c \cdot 10^{24} \)
D. \( 6.023 \times 10^{21} \)


State the law of limiting factor


How many structural and
stereoisomers could be obtained by monochlorination of propene with
chlorine?
\( A \cdot 2 \)
B. 5
\( c \cdot 3 \)
D. 4


Energy levels I, II, Ill of a certain atom correspond to increasing values of
energy i.e., \( \boldsymbol{E}_{\boldsymbol{I}}<\boldsymbol{E}_{\boldsymbol{I I}}<\boldsymbol{E}_{\boldsymbol{I I I}} . \) If \( \boldsymbol{\lambda}_{1}, \boldsymbol{\lambda}_{2}, \boldsymbol{\lambda}_{3} \)
be the wavelengths of radiations corresponding to the transitions III to II
II to I and III to I respectively, which of the following relations is correct?
A. \( \lambda_{1}=\lambda_{2}+\lambda_{3} \)
B. \( \lambda_{3}=\frac{\lambda \lambda_{2}}{\lambda_{1}+2_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D \( \cdot \lambda \frac{2}{3}=\lambda_{1}^{2}+\lambda \frac{2}{2} \)


In the above question, find out the magnitude of net force exerted by the
pulley on the road \( \boldsymbol{R}_{\mathbf{1}} \)
A \( .2 F \)
в. \( F \)
c. \( 2 \sqrt{2} F \)
D. \( \frac{F}{\sqrt{2}} \)


Two clocks are being tested against a
standard clock located in a nationa
laboratory. At 12: 00: 00 noon bv the standard clock, the readings of the two
clocks are:
\( \begin{array}{lll} & \text { Clock 1 } & \text { Clock 2 } \\ \text { Monday } & 12: 00: 05 & 10: 15: 06 \\ \text { Tuesday } & 12: 01: 15 & 10: 14: 59 \\ \text { Wednesday } & 11: 59: 08 & 10: 15: 18 \\ \text { Thursday } & 12: 01: 50 & 10: 15: 07 \\ \text { Friday } & 11: 59: 15 & 10: 14: 53 \\ \text { Saturday } & 12: 01: 30 & 10: 15: 24 \\ \text { Sunday } & 12: 01: 19 & 10: 15: 11\end{array} \) If you are doing an experiment that requires precision time interval
measurements, which of the two clocks
will you prefer?


Among the alkali metals \( C s \) is the most
reactive because:
A. its incomplete shell is nearest to the nucleus
B. it has a single electron in the valence shell
C. it is the heaviest alkali metal
D. its outermost electron is more loosely bound than the outermost electron ofthe other alkali metals


The ratio in which (2,3) divides the line
segment joining (4,8),(-2,-7) is
A. 2: 1 externally
B. 2: 3
c. 4: 3 externally
D. 1: 2


Which of the following ions is a good oxidising agent?
\( A \cdot E u^{2} \)
B. \( \mathrm{ce}^{4} \)
\( c \cdot y b^{2} \)
D. \( \mathrm{Sm}^{2+} \)


A dynamo makes 100 cycles per second. The frequency of the AC is
A. \( 100 \mathrm{Hz} \)
в. 200 нz
c. 50 нz
D. 400 нz


Calculate the forces \( F(y) \) associated with the following one-dimensional
potential energies:
(a) \( U=-\omega y \)
(b) \( U=a y^{3}-b y^{2} \)
\( (c) U=U_{0} \sin \beta \gamma \)


Find the distance between the parallel
lines
\( 3 x+2 y=7 \) and \( 9 x+6 y=5 \)


What is so important about the troposphere?
A. Layer of water at or near Earths surface
B. Contains ozone
c. It contains weather and the oxygen that we breath
D. All of the above


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{1}{a-\sqrt{2}}-\frac{a^{2}+4}{a^{3}-\sqrt{8}}\right) \)
\( \left(\frac{a}{\sqrt{2}}+1+\frac{\sqrt{2}}{a}\right)^{-1} \)


When 100 g of a saturated solution is evaporated at \( 50^{\circ} \mathrm{C}, 50 \mathrm{g} \) of solid is left over. Find the solubility of the
substance at \( 50^{\circ} \mathrm{C} \)
A . 100
B. 50
c. 75
D. 28


Find the direction ratio of the line
\( \frac{x-1}{2}=3 y=\frac{2 z+3}{4} \)


\( \ln \) an \( A C \) circuit, voltage \( V=V_{0} \sin \omega t \)
and inductor L is connected across the
circuit.Then the instantaneous power
will be
\( ^{\mathrm{A}} \cdot \frac{V_{0}^{2}}{2 \omega L} \sin \omega t \)
B. \( \frac{-V_{-}^{2}}{2 \omega L} \) sinwt
c. \( \frac{-V_{0}^{2}}{2 \omega L} \sin 2 \omega t \)
D. \( \frac{V_{0}^{2}}{\omega L} \sin 2 \omega t \)


Find the number of nitrates which gives
\( N O_{2} \) gas on heating from the following:
Nitrogen dioxide is released on heating:
\( N H_{4} N O_{3}, K N O_{3}, N a N O_{2}, P b\left(N O_{3}\right)_{2} \)


Evaluate the integral \( \int_{-1}^{1}(\sqrt{1-x+x^{2}}-\sqrt{1+x+x^{2}}) d x \)
\( A \cdot \frac{1}{2} \)
в.
c. 0
\( D \)


connected across a \( 4 m \) long uniform
wire having resistance \( 4 \Omega / m . \) The cells
of small emfs \( \epsilon_{1}=2 V \) and \( \epsilon_{2}=4 V \)
having internal resistance \( 2 \Omega \) and \( 6 \Omega \)
respectively, are connected as shown in
the figure. If galvanometer shows no
deflection at the point \( N, \) the distance
of point \( N \) from the point \( A \) is equal to
\( A \cdot \underline{1}_{-} \)
\( B \cdot 1 \)
\( -n \)
c. \( 25 \mathrm{cm} \)
D. 50


The \( p H \) of a \( 0.02 M \) ammonia solution
which is \( 5 \% \) ionized will be:
\( A \cdot 2 \)
B. 5
\( c \cdot 7 \)
D. 11


Differentiate the following functions
w.r.t. \( \boldsymbol{x} \)
\( e^{\operatorname{cosec}^{2} x} \)


Assertion
If refractive index of one medium is
equal to refractive index of second
medium, then beam does not bend at
all.
Reason
The bending of light does not depend on refractive indices of media.
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


Identify the correct order of reactivity in electrophilic substitution reactions of the following compounds:
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. ॥>।>॥|> >V
D. II>III>1>IV


Construct a quadrilateral \( R E A D, \) when
\( \boldsymbol{R} \boldsymbol{E}=\mathbf{3 . 5 1} \mathrm{cm}, \boldsymbol{E} \boldsymbol{A}=\mathbf{4 . 3} \mathrm{cm}, \boldsymbol{A D}= \)
\( 4.8 \mathrm{cm}, \angle E=105^{\circ} \& \angle R=55^{\circ} \)


If the current in a primary coil of transformer decreases from \( 0.8 \mathrm{A} \) to 0.2
\( A \) in 4 millisecond, then calculate induced emf in the secondary coil
[Coefficient of mutual induction is 1.76
\( \mathrm{H}] \)


The figure obtained by joining the midpoints of the sides of a rhombus taken
in order is
A . a square
B. a rhombus
c. a rectangle
D. parallelogram


What is the density (in \( g m / \)lit ) of wet air with \( 75 \% \) relative humidity at 1 at
and \( 300 K ? \) Given : vapour pressure of
\( H_{2} O \) is 30 torr and average molar
mass of air is \( 29 g / \) mol.
Write as the nearest integer:


The angular momentum of an electron revolving in a circular orbit is
What is its magnetic moment?
A \( \cdot \frac{m}{2 e} \)
B. \( \frac{e J}{2 m} \)
\( c \cdot \frac{2 m}{e J} \)
\( D \cdot \frac{e m J}{2} \)


A particle of mass \( m \) is moving in
horizontal circle of radius \( r \) with
uniform speed \( v \). When it moves from one point to a diametrically opposite point its
A. KE changes by \( m v^{2} \).
B. KE changes by \( \frac{1}{4} m v^{2} \).
c. momentum does not change.
D. momentum changes by \( 2 m v \)


In a uniform circular motion, the angle
between the velocity and acceleration is
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 75^{\circ} \)
E \( .90^{\circ} \)


Diphenyl hydrazine is same as:
A. azoxybenzene
B. azobenzene
c. hydrazobenzene
D. aniline


What are the various energy
transformations that occur when you
are riding a bicycle?


Calculate the solubility of \( A g C N \) in a
buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{3 . 0} \)
\( \boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N})=\mathbf{1 . 2} \times \)
\( \mathbf{1 0}^{-16}, \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{C N})=\mathbf{4 . 8} \times \mathbf{1 0}^{-\mathbf{1 0}} . \) There
is no \( C N^{-} \) or \( A g^{+} \) ion in the buffer
previously.


Fibres are obtained from
A. \( \mathrm{Xylem}, \) phloem and sclerenchyma
B. Xylem, phloem, sclerenchyma and epidermis
C . Xylem, parenchyma and epidermis
D. Xylem, parenchyma and endodermis


In the electric field due to a point
charge \( \boldsymbol{q}, \) a test charge is carried from
\( A \) to the points \( B, C, D \) and \( E \) lying on
the same circle around \( q \). The work done
is
A. the least along \( A B \)
B. the least along \( A D \)
C. zero along any one of the paths \( A B, A D, A C \) and \( A E \)
D. the least along \( A E \).


Point charge \( q_{0} \) is placed inside a cone of base radius 'R', x distance below
centre of the top surface as shown in figure.Find electric flux related to
curved surface of the cone:-
A \( \cdot \frac{q}{2 \varepsilon_{0}} \)
в. \( \frac{q}{\varepsilon_{0}}-\frac{q}{2 \varepsilon_{0}}\left(1-\frac{x}{\sqrt{R^{2}+x^{2}}}\right) \)
c. \( \frac{q}{\varepsilon_{0}}\left(1-\frac{x}{\sqrt{R^{2}+x^{2}}}\right) \)
D. \( \frac{q}{\varepsilon_{0}} \times\left(\frac{x}{\sqrt{R^{2}+x^{2}}}\right) \)


Find out displacement of B till velocity becomes equal
A. \( 7.5 \mathrm{m} \)
B. 10
\( c \cdot 13.25 \mathrm{m} \)
D. \( 12.5 \mathrm{m} \)


At low pressure, the fraction of the surface covered follows:
A. zero-order kinetics
B. first order kinetics
c. second order kinetics
D. fractional order kinetics


Assertion (A): Propagation of light through an optical fibre is due to total internal reflection taking place at the core-cladding interface. Reason (R) : Refractive index of the material of the core of the optical fibre is greater than that of air.
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false and (R) is true


The triad of nuclei that is isotonic is:
\( \mathbf{A} \cdot_{6}^{14} C, \frac{15}{7} N,_{9}^{17} F \)
В . \( _{6}^{12} C, \frac{14}{7} N, \) ' \( _{19}^{9} F \)
\( \mathbf{C} \cdot_{6}^{14} C, \frac{14}{7} N,_{9}^{17} F \)
\( \mathbf{D} \cdot_{6}^{14} C, \frac{14}{7} N, \frac{19}{9} F \)


I: If \( \mathrm{f}^{\prime}(\mathrm{a})<0 \) then the function \( \mathrm{f} \) is
decreasing at \( \mathbf{x}=\mathbf{a} \)
Il: If \( f \) is decreasing at \( x=a \) then
\( \mathbf{f}^{\prime}(\mathbf{a})<\mathbf{0} \)
Which of the above statements are true
\( ? \)
A. only
B. only II
c. both land II


The reagent that has action on glass is:
A . aqua regia
B. hydrofluoric acid
c. oleum
D. fuming nitric acid


Figure \( (3-E 6) \) shows \( x-t \) graph of a
particle. Find the time \( t \) such that the average velocity of the particle during the period 0 to \( t \) is zero


"Of the alkali metal carbonates, only
\( L i_{2} C O_{3} \) decomposes to give \( C O_{2} \) and
metal oxide."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


A solution contains \( 3.22 g \) of \( H C l O_{2} \) in
\( 47.0 g \) of water. The freezing point of the
solution is \( 271.10 K \)

Calculate the fraction of \( H C l O_{2} \) that
undergoes dissociation to \( \boldsymbol{H}^{+} \) and
\( C l O_{2}^{-} \)
Given: \( \boldsymbol{K}_{f}(\boldsymbol{w} \boldsymbol{a} \boldsymbol{t e r})=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1} \)
B. \( \alpha=0.204 \)
C . \( \alpha=0.30 \)
D. \( \alpha=0.60 \)


Circular single stranded DNA occurs in bacteriophage
\( \mathbf{A} \cdot T_{2}, T_{4} \)
в. \( \phi \times 174, \) М 13
c. \( T_{3}, \phi 6 \)
D. \( \delta, T_{5} \)


Term tertiary, secondary and primary amine represents the:
A. number of amino groups
B. nature of C atom
c. degree of substitution on nitrogen
D. degree of uunsaturation


The meiosis takes place in
A. Apical meristem
B. Inter calary meristem
C. Reproductive cells
D. Vegetative cells


What does this \( \lambda \) symbol indicates?


A chemist is preparing to analyse samples that will contain no more than \( 0.5 \mathrm{g} \) of uranium. His procedure calls for
preparing the uranium as \( U^{4+} \) ion and
oxidizing it by \( M n O_{4}^{-} \) in acid solution:
\( \boldsymbol{U}^{4+}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{U} \boldsymbol{O}_{2}^{2+}+ \)
\( \boldsymbol{M} \boldsymbol{n}^{2+}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
If he wants to react the total \( U^{4+} \)
sample with a maximum of \( 50 \mathrm{ml} \) of \( K M n O_{4} \) solution, what concentration does he choose? \( (\mathrm{U}=238) \)
A. 0.0336 M
B. 0.0168 М
c. 0.168 м
D. 0.0672 M


Who among the following was a paleobotanist?
A. P. Maheshwari
B. S.R. Kashyap
c. Birbal Sahni
D. v. Purir


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}\sqrt{1+k x}-\sqrt{1-k x} & \text { for } & -1 \leq x<0 \\ x & \text { for } 0 \leq x<1\end{array}\right. \)
is continuous at \( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{k}= \)


Which one of the following is a possibility for most of us in regard to breathing, by making a conscious effort?
A. One can breathe out air totally without oxygen
B. One can breathe out air through Eustachian tube by closing both nose and mouth
c. one can consciously breathe in and breathe out by moving the diaphragm alone, without moving the ribs at all
D. The lungs can be made fully empty by forcefully breathing out all air from them.


The amount of biodegradable organic matter in sewage water can be estimated by measuring
A. Biochemical Oxygen Demand (BOD)
B. The growth of anaerobic bacteria in water
c. Biogeological oxygen demand
D. The growth of aerobic bacteria in water


A rod of mass \( m \) spins with an angular speed \( \omega=\sqrt{g / l}, \) Find its
a. Kinetic energy of rotation.
b. kinetic energy of translation
c. Total kinetic energy.


A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy
is stored in the capacitor?


\( 32 \% \) of the teachers in a school females
and the number of male teachers is 85
Find the total number of teachers in the
school.


The resultant magnetic moment due to two currents carrying concentric coils of radius \( r, \) mutually perpendicular to
each other will be
A. \( \sqrt{2} i \)
B. \( \sqrt{2} i \pi r^{2} \)
\( \mathbf{c} \cdot 2 \pi r^{2} \)
D. \( \sqrt{2} i r^{2} \)


The electronic configuration, \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6}, 3 d^{9} \) represents a
A. Metal atoms
B. non metals atom
c. non-metallic anionic
D. metallic cation


The cost of \( 2 \mathrm{kg} \) of apples and \( 1 \mathrm{kg} \) of grapes on the day was found to be Rs.
160. After a month the cost of \( 4 \mathrm{kg} \) of
apples \( 2 \mathrm{kg} \) of grapes is \( \mathrm{Rs} .300 \) Represent the situation algebraically.


The rate of change of the area of a circle with respect to its radius \( r \) at \( r=6 c m \)
is.
\( \mathbf{A} \cdot 10 \pi \)
в. \( 12 \pi \)
\( c \cdot 8 \pi \)
D. \( 11 \pi \)


Calomel electrode is reversible with
respect to:
\( A \cdot H^{+} \) ions
B. \( \mathrm{Hg}_{2}^{2+} \) ions
c. \( \mathrm{cl}^{-} \) ions
D. None of these


Fix up one end of a slinky to a hook and hold it horizontally. Vibrate the other end to and fro along the length of the spring. If you look the spring carefully, you will see some parts of the spring are pushed closer, while some other
parts are pulled apart.
A. the portions which are pushed closer are called compressions
B. the portions which are pulled apart are called rarefactions
c. both a and \( b \)
D. none


In
1911, the physicist Emest Rutherford discovered that atoms have a tiny, dense nucleus by shooting positively charged particles at a very thin gold foil A key physical property which led Rutherford to use gold that it was.
A. Electrically conducting
B. Highly malleable
c. shiny
D. None-reactive


Area bounded by the parabola \( y^{2}=x- \)
3 and \( x=5, \) is \( \dots . s q \) units
\( A \cdot \frac{8 \sqrt{2}}{3} \)
B. \( 4 \sqrt{2} \)
\( \mathrm{c} \cdot 3 \sqrt{2} \)
D. \( 5 \sqrt{2} \)


The deflection of the magnetic needle in
the galvanoscope connected to the
stationary circular coil AB(see figure) increases if
A. The strength of the magnet is decreased
B. The velocity of the magnet is increased
c. The number of turns in the coil is increased
D. Both B and C


Why are in the household electric
circuits the electric appliances
(instruments) connected in parallel combination?


Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the
poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others
worked?
A. Existence of point attractive
B. Magnetic power in lodestone
c. Magnetic power in needle
D. swinging of magnetic needle


Blood circulation that starts in
capillaries and ends in capillaries is called
A. Portal circulation
B. Hepatic circulation
c. cardiac arrest
D. None of the above


Which of the following elements does not belong to p-block?
A . sr
B. Po
c. As
D. Ga


Which among the following substances is not a component of the mixture used
for glazing pottery?
A. Feldspar
B. Silica
c. Borax
D. Alumina


In dicot roots, cells of which of the
following region show Casparian strips?
A. Cambium
B. Endodermis
c. Pericycle
D. Hypodermis


Find number of \( p \pi-d \pi \) bonds in
(a) Disulphate
(b) triphosphate
trimetaphosphate
(d) trimer of \( S O_{3} \)
\( (e) P_{4} O_{10} \)
\( (f) P_{4} O_{6} \)


Chlorine reacts with excess of ammonia
to form:
A \( \cdot N H_{4} C l \)
в. \( N_{2}+H C l \)
c. \( N_{2}+N H_{4} C l \)
D. \( N_{2}+H C l_{3} \)


\( \operatorname{Let} \mathbf{L}=\lim _{\mathbf{x} \rightarrow 0}= \)
\( \frac{\boldsymbol{a}-\sqrt{\boldsymbol{a}^{2}-\boldsymbol{x}^{2}}-\frac{\boldsymbol{x}^{2}}{\boldsymbol{4}}}{\boldsymbol{x}^{4}}, \boldsymbol{a}>0 \) If \( \boldsymbol{L} \) is finite
then
This question has multiple correct options
\( \mathbf{A} \cdot a=2 \)
B. \( a=1 \)
\( c \cdot_{L}=\frac{1}{64} \)
D. \( L=\frac{1}{32} \)


The atrio-ventricular node is situated
A. Near the bicuspid valve
B. In between the atrium
c. At the base of inter-auricular septumm
D. In the interventricular septum


In the given circuit, the value of resistance effect of the coil Lis exactly
equal to the resistance R. Bulbs B1 and B2 are exactly identical. Answer the following question.
a) Which one of the two bulbs lights up earlier, when key k is closed and why?
b) What will be the comparative brightness of the two bulbs after sometime if the key \( \mathrm{K} \) is kept closed
and why?


The magnetic field due to a current carrying circular loop of radius \( 3 \mathrm{m} \) at a point on the axis at a distance of \( 4 \mathrm{m} \)
from the centre is \( 54 \mu T . \) What will be its
value at the centre of the loop?
A. \( 250 \mu T \)
в. \( 150 \mu T \)
c. \( 125 \mu T \)
D. \( 75 \mu T \)


Q Type your question.
\( H C l \) at \( 0-5^{\circ} C, \) and this mixture is
added to p-toludine (p-methyl aniline)?
\( A \)
3
\( c \)
\( D \)


Which of the following atoms should
have the highest 1st electron affinity?
A. \( F \)
B. \( O \)
\( c . N \)
D. \( C l \)


Consider the time interval \( t=2.0 s \) to
\( \boldsymbol{t}=\mathbf{4} . \mathbf{0} \boldsymbol{s} \)
The magnetic field is perpendicular to
the plane of the loop.


For two given events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
is :
This question has multiple correct options
A. not less than \( P(A)+P(B)-1 \)
B. not greater than \( P(A)+P(B) \)
c. equal to \( P(A)+P(B)-P(A \cup B) \)
D. equal to \( P(A)+P(B)+P(A \cap B) \)


The concentration of a solution is
\( \mathbf{1 0}^{-4} \boldsymbol{M} \) for \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) for \( \boldsymbol{B r}^{-} \) and
\( 10^{-3} \mathrm{M} \) for \( I^{-} . A g N O_{3}(s) \) is added slowly to the solution. If the minimum
concentration of \( \boldsymbol{A} \boldsymbol{g}^{+} \) required to start
precipitation of all three ions is \( 10^{-x} \)
then the value of \( x \) is
\( \left[\text { Given, } \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-\mathbf{1 0}}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{1 3}}, \boldsymbol{K}_{\boldsymbol{s p}(\boldsymbol{A g I})}=\mathbf{1 0}^{-\mathbf{1 7}}\right] \)


Assertion \( (A): H_{2} S \) is more volatile than
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason (R): Oxygen atom is smaller in size as compared to sulphur.
A. Both \( A \) and \( R \) are true and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are true and \( R \) is not the correct explanation of
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true


Sodium metal should be stored under
kerosene.


Faraday's laws of electrolysis are related to the:
A. the atomic number of the cation
B. the atomic number of anion
c. the equivalent weight of the electrolyte
D. the speed of the cation


If four moles of electrons are transferred
from anode to cathode in a experiment
on electrolysis of water, then total volume of the two gases produced at
STP will be:
\( \mathbf{A} \cdot 224 L \)
B. \( 72.6 L \)
c. \( 67.2 L \)
D. \( 89.4 L \)


A car is moving with speed \( 10 m / s \) on a
circle path of radius \( 2 m \). If speed is
increasing at the rate of \( 10 m / s^{2} . \) The acceleration of car is
\( \mathbf{A} \cdot \sqrt{26} m / s^{2} \)
B . \( 10 \sqrt{26} \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 5 \sqrt{26} m / s^{2} \)
D. \( 10 \sqrt{13} \mathrm{m} / \mathrm{s}^{2} \)


Write the symbols of the first ten elements in the periodic table with the atomic numbers.


Consider the reaction of chloromethane
with \( O H^{-} \) in aqueous solution
\( \boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{a q})+ \)
\( O H(a q) \stackrel{K_{f}}{\underbrace{K_{r}}} C H_{3} O H(a q)+C l(a q) \)
At \( 25^{\circ} C, \) the rate constant for the
forward reaction is \( 6 \times 10^{6} M^{1} s^{-1}, \) and
the equilibrium constant \( K_{c} \) is \( 1 \times 10^{16} \)
Calculate the rate constant for the
reverse reaction at \( 25^{\circ} C \)
A \( .3 \times 10^{22} \)
B . \( 6 \times 10^{22} \)
C \( \cdot 12 \times 10^{22} \)
D. \( 12 \times 10^{23} \)


Which one of the following is used as a test for aliphatic primary amines?
A. Tollen's test
B. Fehling's lest
c. Isocyanide test
D. Azo dye test
E. Phthalein fusion test


Assertion
Chlorine gas disproportionate in hot \( \& \) conc. NaOH solution
Reason
NaCl and NaOCl are formed in the above
reaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the area of the triangle below
A . 20
в. 30
\( c .35 \)
D. 40


The \( C-H \) bond in propane is:
A \( \cdot \sigma s p-s \)
B \( \cdot \operatorname{csp}^{2}-s \)
c. \( \sigma p-s \)
D. \( \sigma s p^{3}-s \)


What happens to the following after
fertilization?
Calyx


If \( \boldsymbol{n}=\mathbf{1} \mathbf{2} \boldsymbol{m}(\boldsymbol{m} \in \boldsymbol{N}),^{n} \boldsymbol{C}_{0}- \)
\( \frac{\boldsymbol{n} \boldsymbol{C}_{2}}{(\mathbf{2}+\sqrt{\mathbf{3}})^{2}}+\frac{\boldsymbol{n}_{\mathbf{4}}}{(\mathbf{2}+\sqrt{\mathbf{3}})^{4}}- \)
\( \frac{n \boldsymbol{C}_{\mathbf{6}}}{(\mathbf{2}+\sqrt{\mathbf{3}})^{6}}+\dots=(-\mathbf{1})^{\boldsymbol{m}}\left(\frac{\sqrt{\boldsymbol{p}}}{\mathbf{1}+\sqrt{\boldsymbol{Q}}}\right)^{n} \)
then \( \boldsymbol{P}-\boldsymbol{Q} \) is:


The 0 - 0 bond length in ozone is
A . \( 1.54 \mathrm{A}^{\circ} \)
B . \( 1.27 \mathrm{A}^{\circ} \)
c. \( 1.34 \mathrm{A}^{\circ} \)
D. \( 1.10 \mathrm{A}^{\circ} \)


The chief source of aromatic
compounds is :
A . Fruits
B. Oil of winter green
c. Petroleum
D. Ants


A square plate \( A B C D \) of mass \( m \) and
side \( l \) is suspended with the help of two
ideal strings \( P \) and \( Q \) as shown
determine the acceleration \( \left(\text { in } m / s^{2}\right) \) of
corner \( A \) of the square just at the
moment the string \( Q \) is cut \( (g= \)
\( \left.10 m / s^{2}\right) \)


Find the freezing point of a solution containing 0.5 mole of glucose dissolved in 200 g of \( H_{2} \) O? (Given that \( \boldsymbol{K}_{f} \) for water is \( 1.86 \quad \boldsymbol{K} \boldsymbol{m}^{-1} \)
A . -4.65
B . -2.65
c. -14.65
D. -8.65


A ball is dropped from a cliff. Find
(a) its speed \( 2 s \) after it is dropped
(b) its speed when it has fallen through \( 78.4 m, \) and
(c) the time taken in falling through
\( \mathbf{7 8 . 4 m} \)


As compared to concrete, steel has compressive strength:
A. 25 times less
B. equal
c. 25 times more
D. 5 times more


\( H_{2} O_{2} \) is formed by which of the following compound?
A \( \cdot N a_{2} O_{2} \)
в. \( N a O H \)
c. \( N a_{2} \) Q
D. \( K O_{2} \)