Prove that line segment joining the mid-
points of the diagonals of a trapezium
is parallel to the parallel sides and equal to half their difference.


Which branch study about remains of plant life?
A. Paleontology
B. Palaeobotany
c. Eugenics
D. Palynology


Petroleum is refined by:
A. fractional distillation
B. destructive distillation
C. distillation
D. all of these


Evaluate the given integral.
\( \int \frac{1}{x\left(x^{3}+8\right)} d x \)


The rational number lies between \( \frac{3}{7} \) and \( \frac{2}{3} \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{4}{7} \)
\( c \cdot \frac{3}{7} \)
D.


The changing of focal length of an eyelens to focus the image of an object at varying distances is done by the action
of the :
A. pupil
B. ciliary muscles
c. retina
D. blind spot


In a binomial distribution \( B\left(n, p=\frac{1}{4}\right) \) if the probability of at least one success is greater than or equal to \( \frac{9}{10}, \) then \( n \) is greater than
A \( \cdot \frac{1}{\log _{10} 4+\log _{10} 3} \)
В. \( \frac{9}{\log _{10} 4-\log _{10} 3} \)
c. \( \frac{4}{\log _{10} 4-\log _{10} 3} \)
D. \( \frac{1}{\log _{10} 4-\log _{10} 3} \)


The contrapositive of the statement 'I go to school if it does not rain' is:
A. If it rains, I do not go to school.
B. If I do not go to school, it rains.
c. If it rains, I go to school.
D. If i go to school, it rains


If \( \boldsymbol{A}=\left[\begin{array}{ll}1 & -2 \\ 5 & -3\end{array}\right], \) then \( A+A^{T} \) equals
A. \( \left[\begin{array}{cc}2 & 3 \\ 3 & -6\end{array}\right] \)
В. \( \left[\begin{array}{cc}2 & -4 \\ 10 & -6\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}2 & 4 \\ -10 & 6\end{array}\right] \)
D. None of these


The sky looks blue due to:
A. dispersion effect
B. reflection
C. transmission
D. scattering


A particle has initial velocity \( (2 \vec{i}+3 \vec{j}) \) and acceleration \( (\mathbf{0 . 3} \overrightarrow{\mathbf{i}}+\mathbf{0 . 2 j}) \). The magnitude of velocity after 10 seconds will be
A. 5 units
B. 9 units
c. \( 9 \sqrt{2} \) units
D. \( 5 \sqrt{2} \) units


A particle performs S.H.M. with amplitude \( 25 c m \) and period \( 3 s . \) The minimum time required for it to move
between two points \( 12.5 \mathrm{cm} \) on either
side of the mean position is
A . \( 0.6 s \)
B. \( 0.5 s \)
c. \( 0.4 s \)
D. \( 0.2 s \)


The numbers system which uses alphabets as well as numbers is-
A. Binary numbers system
B. Octal numbers system
c. Decimal numbers system
D. Hexadecimal numbers system


Substances \( X \) and \( Y \) are colorless
gases obtained by combination of sulphur and oxygen. Substance \( \boldsymbol{X} \) results from combination of \( 6.00 g \) of
sulphur with \( 6.00 g \) of oxygen and substance \( Y \) results from combination
of \( 8.60 g \) of sulphur with \( 12.9 g \) of oxygen If the number of moles of oxygen in \( x \)
were \( 10, \) what would be the number of
moles of oxygen in Y?


Write any three differences between photo respiration and dark respiration.


Let \( \boldsymbol{f}, \boldsymbol{g} \) and \( \boldsymbol{h} \) be functions from \( \boldsymbol{R} \) to \( \boldsymbol{R} \)
Show that
(i) \( (\boldsymbol{f}+\boldsymbol{g}) \boldsymbol{o} \boldsymbol{h}=\boldsymbol{f} \boldsymbol{o} \boldsymbol{h}+\boldsymbol{g} \boldsymbol{o} \boldsymbol{h} \)
(ii) \( (\boldsymbol{f} \cdot \boldsymbol{g}) \boldsymbol{o} \boldsymbol{h}=(\boldsymbol{f} \boldsymbol{o} \boldsymbol{h}) \cdot(\boldsymbol{g} \boldsymbol{o} \boldsymbol{h}) \)


An inorganic compound \( (A) \) of \( S, C l \)
and oxygen has vapour density \( 67.5 . \) It reacts with water to form two acids \( (B) \) and \( (C) .(A) \) also reacts with \( K O H_{(a q)} \) to form two salts \( (D) \) and \( (E) .(D) \) and
\( (\boldsymbol{E}) \) gives white precipitate with
\( A g N O_{3} \) and \( B a C l_{2} \) solutions respectively. What are \( (A) \) to \( (E) ? \)


ff \( y=\frac{\sin 4 x}{x^{2}+16}, \) then find \( \frac{d y}{d x} \)


The amount of heat supplied to \( 4 x \) \( 10^{-2} \) kg of nitrogen at room
temperature to rise its temperature by \( 50 C \) at constant pressure is (Molecular
mass of nitrogen is 28 and \( R=8.3 J \)
\( \left.\boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A \( .2 .08 k J \)
в. \( 3.08 k J \)
c. \( 4.08 k J \)
D. \( 5.08 k J \)


Which city has more people reading newspaper than watching T.V?
When reading newspaper people watching TV
A. Patna
B. Kolkata
C. Mumbai
D. Delhi


The number of moles of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) needed to
reduce 1 mole of \( K M n O_{4} \) in acidic
medium are:
A. 2 moles
B. 2.5 moles
c. 5 moles
D. 3 moles


The formation of a dipole is due to two equal and dissimilar point charges placed at a
A. short distance
B. Iong distance
c. above each other
D. None of these


Results of calculations for four different
designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?
A. Deuteron density \( =2.0 \times 10^{12} \mathrm{cm}^{-3} \), confinement time
\( =5.0 \times 10^{-3} s \)
B. Deuteron density \( =8.0 \times 10^{14} \mathrm{cm}^{-3} \), confinement time \( =9.0 \times 10^{-1} s \)
C. Deuteron density \( =4.0 \times 10^{23} \mathrm{cm}^{-3} \), confinement time \( =1.0 \times 10^{-11} s \)
D. Deuteron density \( =1.0 \times 10^{24} \mathrm{cm}^{-3} \), confinement time
\[
=4.0 \times 10^{-12} s
\]


A solution of sodium sulphate in water is electrolysed using inert electrodes.
The products at the cathode and anode are respectively:
A. \( H_{2}, O_{2} \)
в. \( O_{2}, H_{2} \)
c. \( O_{2}, N a \)
D. none of the above


Find the slope of the tangent at (1,2) on the curve \( y=x^{2}-4 x+5 \)


A stone thrown upwards with speed attains maximum height h. Another
stone thrown upwards from the same point with speed \( 2 u \) attains maximum height H. What is the relation between h and H?
\( A \cdot 2 h=H \)
B. \( 3 h=H \)
\( c \cdot 4 h=H \)
\( D \cdot 5 h=H \)


Factorise: \( \boldsymbol{x}^{4}-(\boldsymbol{x}-\mathbf{2})^{4} \)


\( \frac{d(\tan x .)}{d x} \)
\( \mathbf{A} \cdot \sec ^{2} x \)
B. \( \cot ^{2} x \)
\( \mathbf{c} \cdot \cos ^{2} x \)
\( D \cdot \sin ^{2} x \)


If \( f \) is a differentiable function at a point
'a' and \( f^{\prime}(a) \neq 0 \) then which of the
following is true.
A \( \cdot f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a)-f(a-h)}{h} \)
B. \( \frac{1}{2} f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+2 h)-f(a-h)}{2 h} \)
c. \( f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+2 h)-f(a)}{h} \)
D. none of these


Evaluate \( : 24 x-6=0 \)
\( A \cdot \frac{1}{4} \)
B.
\( c \cdot-\frac{1}{4} \)
D. \( -\frac{1}{6} \)


Two particles move parallel to \( x \) -axis about the origin with same amplitude and frequency. At a certain instant they are found at a distance \( \frac{a}{3} \) from the origin on opposite sides but their
velocities are found to be in same
direction.Then the phase difference between two particles will be
A \( \cdot \cos ^{-1}\left(\frac{7}{9}\right) \)
В. \( 180^{\circ} \)
c. \( 45^{\circ} \)
D. None of the above


The total number of magnetic lines of
force originating or terminating on a pole of strength \( \mathrm{m} \) is :
A. \( \frac{\mu_{o} m}{4 \pi} \)
в. \( \frac{m}{\mu_{o}} \)
\( c \cdot m^{2} \)
D. \( \mu_{o} m \)


Rainwater harvesting can be done by:
This question has multiple correct options
A. collecting water by keeping a small container on the top of the building
B. collecting rainwater from the rooftop to a storage tank, through pipes
C. allowing water to go into the ground directly from the roadside drains that collect rainwater
D. none of the above


Explain the mechanism of cleaning action of soap.


Representative elements
are
A. Elements of s and p block
B. Elements of s, p and f block
C. Elements of \( s, p \) and d block
D. Elements of s and d block


If the radius of earth shrinks by \( 1.5 \% \) mass remaining same ), then the value of gravitational acceleration changes by
A. 2 \%
B . - 2 \%
c. 3 \%
D. -3 \%


In silicon dioxide:
A. each \( S i \) atom is surrounded by 4 oxygen atom and each oxygen atom is bonded to 2 silicon atom
B. each silicon atom is surrounded by four \( O_{2} \) atoms and
each \( O_{2} \) is surrounded by 2 silicon atoms
C. each silicon atom is bonded to two oxygen atom
D. none of above


Show that the function \( \boldsymbol{f}: \boldsymbol{R}_{*} \rightarrow \boldsymbol{R}_{*} \)
defined by \( f(x)=\frac{1}{x} \) is one-one, where
\( R_{*} \) is the set of all non-zero real
numbers. Is the result true, if the
domain \( R_{*} \) is replaced by \( N \) with \( c 0 \)
domain being same as \( R_{*} ? \)


Two blocks \( A \) and \( B \) each of mass \( m \) are
placed on a smooth horizontal surface.
Two horizontal forces \( F \) and \( 2 F \) are
applied on blocks \( A \) and \( B \), respectively,
as shown in \( F i g . . \) Block a does not slide
on block B. Then the normal reaction
acting between the two blocks in
(assume no friction between the
blocks)
\( A \cdot F \)
B. \( f / 2 \)
\( c \cdot \frac{F}{\sqrt{3}} \)
D. \( 3 F \)


Cod liver oil is:
A. an emulsion
B. solution
c. colloidal solution
D. suspension


The average force necessary to stop a hammer with 25 N-s momentum in
\( 0.05 s \) expressed in \( N \) is :
A . 500
B. 125
\( c .50 \)
D. 250


Which is example of inverse proportion?
A. Length of edge of square \& its area
B. Speed and time taken
C. Length of edge of square \( \& \) its perimeter
D. Quantity of pencils \& total cost


If the terminal speed of a sphere of gold (density \( \left.=19.5 \quad k g / m^{3}\right) \) is \( 0.2 m / s \) in
a viscous liquid (density \( =1.5 \quad k g / m^{3} \)
), find the terminal speed of a sphere of silver (density \( \left.=10.5 \quad k g / m^{3}\right) \) of the
same size in the same liquid.
A. \( 0.4 m / s \)
в. \( 0.133 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)


A tank 5 m high is half filled with water and then is filled to the top with oil of
density \( 0.85 g c m^{-3} . \) The pressure at
the bottom of the tank, due to these
liquids is
A \( \cdot 1.85 \) g dyne \( c m^{-2} \)
B. 89.25 g dyne \( \mathrm{cm}^{-2} \)
c. 462.5 g dyne \( c m^{-2} \)
D. 500 g dyne \( c m^{-2} \)


Inverse square law of distance is followed by the
A. Gravitational forces
B. Electromagnetic forces
c. Both (a) and (b)
D. Neither (a) and nor (b)


If the output \( Y \) of the following circuit is
1, the inputs \( A B C \) must be :
A .010
В. 100
\( c .101 \)
D. 110


Red light is used as danger signal
because it is:
A. Accepted as symbol
B. Pleasing to the eye
c. sensitive to the eye
D. Having high wavelength


Figure shows five dc sources(cells)
Their emfs are shown in the figure. Emf
of the battery \( A B \) is.
\( 4.8 v \)
B. \( 16 v \)
c. \( 4 v \)
D


When \( \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) is converted into
\( \mathrm{K}_{2} \mathrm{Cr} \mathrm{O}_{4}, \) the change in oxidation number of Cr is
A .
B. 6
\( c \cdot 4 \)
D. 3


In zwitter ionic form, amino acids show behaviour:
A . acidic
B. basic
c. neutral
D. amphoteric


In the adjacent figure, it is given that
\( A B=A C, \angle B A C=36^{\circ}, \angle A D B=45^{\circ} \)
and \( \angle A E C=40^{\circ} . \) Find \( \angle A C B \)


Deflection in the galvanometer is
A. Towards right
B. Left
c. No defection
D. None of these


The period of oscillation of a simple
pendulum of constant length is independent of
\( A \). size of the bob
B. shape of the bob
c. mass of bob
D. all of these


Hydrogen is not more reactive at ordinary temperature, because at ordinary temperature it is in its:
A . gaseous state
B. liquid state
c. molecular state
D. atomic state


Explain the reducing action of carbon mono oxide.


"Systema Naturae" book was written by
A. Engler and Prant
B. Darwin
c. Linnaeus
D. oswald Tippo


Cards of an ordinary deck of playing cards are placed into two heaps. Heapconsists of all the red cards and heap-II
consists of all the black cards. A heap is chosen at random and a card is drawn,
find the probability that the card drawn is a king.


What kind of a molecule is \( \boldsymbol{P C l}_{3} \) ?
A. lonic
B. Polar covalent
c. Non-polar covalent
D. coordinate


Find the slope of the line passing through the following points \( A(-2,1) \) and \( B(0,3) \)
A .
B. - 1
\( c .5 \)
D. - 8


Measuring'Biochemical Oxygen
Demand' is used for
A. Estimating the amount of organic matter in sewage water.
B. Working out the efficiency of oil driven automobile engines.
C. Measuring the activity of Saccharomyces cerevisiae in producing curd on a commercial scale.
D. Working out the efficiency of R.B.Cs. about their capacity to carry oxygen.


In \( \Delta A B C, \angle A=43^{\circ} \) and \( \angle C=70^{\circ} \)
What is the measure of \( \angle B ? \)
\( \mathbf{A} \cdot 63^{\circ} \)
B. \( 65^{\circ} \)
\( c \cdot 66^{\circ} \)
D. \( 67^{\circ} \)


Find the eccentricity of an ellipse in which distance between the foci is 10
and that of focus and
corresponding directrix is 15
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
c. 1
D. \( \frac{3}{4} \)


The proposal to ban supersonic jet planes in Russia is because
A) They travel with very high speed.
B) It is dangerous to travel in them.
C) Their exhaust gases react with ozone
\( A \cdot A \& B \)
B. B
\( c \cdot c \)
D. \( A, B \& C \)


A block is kept on the floor of an elevator at rest. The elevator starts descending
with an acceleration of \( 12 m / s^{2} \). Find
the displacement of the block during the first \( 0.2 s \) after the start. Take \( g= \)
\( 10 m / s^{2} \)


Find the distance between the two
parallel straight lines
\( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \) and \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{d} \)


Find the value of \( x \) and \( y \) using elimination method:
\( \frac{x}{2}+\frac{y}{3}=1 \) and \( \frac{x}{4}+\frac{y}{7}=2 \)
A. (44,-63)
В . (-41,63)
c. (44,63)
D. (-44,-63


Prove that \( y=\frac{4 \sin \theta}{(2+\cos \theta)}-\theta \) is an
ncreasing function of \( \boldsymbol{\theta} \) in \( \left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)


Corolla with four diagonally arranged petals is
A. Vexillary
B. Cruciform
c. Gamopetalous
D. Caryophyllaceous


\( 99 \% \) of a first order reaction, was
completed in 32 minute. When will
\( 99.9 \% \) of the reaction complete?
A. 50 minute
B. 46 minute
c. 49 minute
D. 48 minute


Complete the following statement. The
work done on a system:
A. always changes the potential energy of the system
B. always changes the kinetic energy of the system
C. always changes the momentum of a system
D. can change either the potential energy or kinetic energy of the system
E. is not related to the energy of the system.


Assertion
The endothermic reactions are favoured
at lower temperature and the exothermic reactions are favoured at
higher temperature
Reason
When a system in equilibrium is disturbed by changing the temperature, it will tend to adjust itself so as to
overcome the effect of the change.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the reaction of \( \boldsymbol{H} \boldsymbol{I} \) with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) the
oxidation state of sulphur is changed to
\( -2 . \) Identify the correct balanced
equation:
A \( \cdot H_{2} S O_{4}+2 H I \rightarrow S O_{2}+2 H_{2} O+I_{2} \)
B . \( H_{2} S O_{4}+6 H I \rightarrow S+4 H_{2} O+3 I_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}+8 \mathrm{HI} \rightarrow \mathrm{H}_{2} \mathrm{S}+4 \mathrm{H}_{2} \mathrm{O}+4 \mathrm{I}_{2} \)
D. All of these


Red phosphorous is less soluble and less volatile than white phosphorous because of the formation its structure
described as :
A. polymerised chains
B. hexagonal rings
c. tetrahedral
D. planar sheets


Oxygen combines with nascent oxygen
to form ozone.
A . True
B. False


While cooking, if the bottom of the vessel is getting blackened on the outside, it means that
A. the food is not cooked completely
B. the fuel is not burning completely
c. the fuel is wet
D. all of the above


In a skew-symmetric matrix, the diagonal elements are all
A. one
B. zero
c. different from each other
D. non-zero


The terms 'chance' and 'probability' are
synonymous.
A . True
B. False
c. Both
D. None of above


The length of latus rectum of the hyperbola \( 4 x^{2}-9 y^{2}-16 x-54 y- \)
\( \mathbf{1 0 1}=\mathbf{0} \) is
\( A \cdot \frac{8}{5} \)
B. \( \frac{8}{7} \)
\( c \cdot \frac{8}{9} \)
D. \( \frac{8}{3} \)


If the time taken by the planet to move
from position \( \mathrm{P} \) to \( \mathrm{X} \) and \( \mathrm{Q} \) to \( \mathrm{Y} \) is equal
then the ratio of \( A_{1} \) to \( A_{2} \) is:
A. Greater than one
B. Less than one
c. Equal to one
D. Data insufficient


Very short answer type.
How the process of fission is different
from normal mitotic division?


Zn gives \( \mathrm{H}_{2} \) gas with \( \mathrm{H}_{2} \mathrm{SO}_{4} \) \& HCl but
not with HNO \( _{3} \) because:
A. \( Z n \) act as oxidising agent when react with \( H N O_{3} \)
B. \( H N O_{3} \) is weaker acid then \( H_{2} \) SO \( _{4} \) \& \( H C l \)
C. in electrochemical series \( Z n \) is above hydrogen
D. \( N O_{3}^{\Theta} \) is reduced in prefference to hydronium ion


A horizontal wire \( 0.1 \mathrm{m} \) long carries a current of 5 A. Find the magnitude of the magnetic field, which can support the weight of the wire. Assume wire to be of \( \operatorname{mass} 3 \times 10^{-3} k g m^{-1}: \)
A \( .5 .88 \times 10^{-2} T \)
B . \( 4.88 \times 10^{-3} T \)
\( \mathbf{c} .5 .88 \times 10^{-3} T \)
D. \( 5.88 \times 10^{-4} T \)


A ray of light is reflected by two parallel
plane mirrors \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
Which statement is correct?
A. The angle of incidence at mirror \( X \) is \( 30^{\circ} \)
B. The angle of incidence at mirror \( Y \) is 60
C. The angle of reflection at mirror \( X \) is \( 120^{\circ} \)
D. The angle of reflection at mirror \( Y \) is \( 0^{\circ} \)


\( \int_{0}^{1} \frac{x d x}{\left(x^{2}+1\right)^{2}}= \)
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / 4 \)
D.


The diameter of a sphere is measured with an instrument having least count \( 0.001 \mathrm{cm} . \) The diameter is \( 1.933 \mathrm{cm} . \) The
radius to correct significant figures will
be:
A . \( 0.9665 \mathrm{cm} \)
B. \( 0.966 \mathrm{cm} \)
c. \( 0.967 \mathrm{cm} \)
D. none of these


Animal of which phylum have hooks and
suckers and are endoparasite on other animals?
A. Platyhelminthes
B. Annelida
c. Ascheminthes
D. Arthropoda


Which of the following elements can be
prepared by heating the oxide above
\( 400^{\circ} \mathrm{C} ? \)
\( A \cdot H g \)
\( c . F e \)
3


Solve: \( |2 x-5|<1 \)


What is the mole fraction of the solution
in a \( 1.00 m \) aqueous solution?
A. 1.770
B. 0.0354
c. 0.0177
D. 0.177


In series \( L-R \) circuit, \( X_{L}=R \). Now a
capacitor with \( X_{C}=R \) added in series.
New power factor:
A. Same as initial
B. \( \frac{1}{\sqrt{2}} \) times the initial
c. \( \frac{1}{2} \) times the initial
D. \( \sqrt{2} \) times the initial


Write the name and structures of the
monomers of the following polymers.
(i) Terylene
(ii) Buna-S
(iii) Neoprene


Vinegar is an acid with its key ingredient, acetic acid. It is widely used for food preservation and cooking. The acetic concentration for table vinegar is typically \( 5 \% \) whereas higher concentration upto \( 18 \% \) is used as preservative. The word "vinegar" is derived from vin aigre, meaning "sour wine"

A table vinegar sample contains \( 5 \% \) (mass/mass) of acetic acid.

To what volume \( 10 \mathrm{m} L \) of the above
sample should be diluted to prepare \( 0.10 M \) acetic acid solution. (density
\( 1.05 g m L^{-1}, \) Molar mass of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}-\boldsymbol{6 0 . 0} \boldsymbol{g} \boldsymbol{m o l}^{-1} \mathbf{)} \)


State whether given statement is True or False

A wooden chair feels colder than an iron
chair in winter
A. True
B. False


Fill in the blanks:
\( \sqrt[3]{\ldots \ldots . .}=\sqrt[3]{\boldsymbol{4}} \times \sqrt[3]{\mathbf{5}} \times \sqrt[3]{\boldsymbol{6}} \)


State the postulates of Bohr atom model. Obtain the expression for the radius of the \( n^{t h} \) orbit of an electron
based on Bohr's theory.


The number of numbers greater than
\( 10^{6} \) that can be formed using the digits
of the number \( 2334203, \) if all the digits of the given number must be used, is


Which of the following statements are
true?
This question has multiple correct options
A. Impulse is the product of force and time for which the force acts.
B. Sl unit of impulse is \( N \) s
C. When two bodies have the same velocity; the lighter body has more momentum.
D. Conservation of linear momentum has no connection
with "Newton's third law of motion""


"羊


Inorganic fertilizers are applied each year to fields bordering a lake. The fertilizers run off into the lake and
cause the following six changes which together cause high mortality of fishes.
(i) Aerobic bacteria feed on dead
plants.
(ii) Algae reproduce faster
(iii) Light cannot penetrate the water.
(iv) Oxygen level falls.
(v) Water becomes green.
(vi) Plants under water die.
Which of the following shows the correct order of the changes taking place?
A \( \cdot(\text { iv }) \rightarrow(v \text { i) } \rightarrow(i) \rightarrow(\text { ii }) \rightarrow(v) \rightarrow \) (iii)
B. (ii) \( \rightarrow(v) \rightarrow(\text { iii) } \rightarrow(v i) \rightarrow(i) \rightarrow \) (iv)
\( c \cdot(v) \rightarrow(i i) \rightarrow(\text { iii) } \rightarrow(v i) \rightarrow(i) \rightarrow(\text { iv }) \)
D. (ii) \( \rightarrow(\text { iii) } \rightarrow(v) \rightarrow(\text { iv }) \rightarrow(v \text { i) } \rightarrow(i) \)


One vertex of the equilateral triangle with centroid at the origin and one side
as \( \boldsymbol{x}+\boldsymbol{y}-\mathbf{2}=\mathbf{0} \) is:
A \( \cdot(-1,-1) \)
в. (2,2)
c. (-2,-2)
D. (2,-2)


1atm \( = \)
A. \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 76 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 20 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 25 \mathrm{cm} \) of \( \mathrm{Hg} \)


According to Faraday's first law, the amount of substance deposited at
electrode when an electric current is
passed through electrolyte depends
upon:
This question has multiple correct options
A. amount of current passed
B. dissociation of electrolyte
c. time till which current is passed
D. nature of electrode materia


The quantity in electricity which is equivalent to mass is
A .
B.
\( c \cdot R \)
\( D \)


The activity of radioactive sample is
measured as 9750 counts per minute at \( t=0 \) and as 975 counts per minute
at \( t=5 \) minutes, the decay constant is
approximately
A . 0.922 per minute
B. 0.270 per minute
c. 0.461 per minute
D. 0.39 per minute


If \( T_{n}=3 n+8, \) then \( T_{n-1}= \)
A. \( 3 n+7 \)
B. \( 3 n+6 \)
c. \( 3 n-5 \)
D. \( 3 n+5 \)


(i) Calculate the number of electrons
which will together weighs one gram.
(ii) Calculate the mass and charge of
one mole of electrons.


The correct order of stability of \( \boldsymbol{A l}^{+}, \boldsymbol{A l}^{+\mathbf{2}}, \boldsymbol{A l}^{+\mathbf{3}} \mathbf{i s} \)
A \( \cdot A l^{+3}>A l^{+2}>A l^{+} \)
B. \( A l^{+2}>A l^{+3}>A l^{+} \)
c. \( A l^{+2}<A l^{+}>A l^{+} \)
D. \( A l^{+3}>A l^{+}>A l^{+} \)


Which part of the body contains teeth?
A. Buccal cavity
B. Body cavity
c. Both A and B
D. Tooth cavity


Which of the following is the most
acidic compound?
A. \( C H_{2}=C H_{2} \)
в. \( C H \equiv C H \)
c.
D.


The sideways reversal of the image by plane mirror is called:
A. lateral inversion
B. parallax
c. optical illusion
D. magic


Find \( \frac{d y}{d x} \) of \( x y+y^{2}=\tan x+y \)


A convex lens of focal length \( ^{\prime} f^{\prime} \) cut into
parts first horizontally and then
vertically. Find the focal length of part \( \mathbf{A} \)
of the lens, as shown
A \( . f / 2 \)
B. \( f \)
c. \( 4 f \)
D. \( 2 f \)


Name the chief constituent of cell wall.
A . Cellulose
B. Pectin
c. Lignin
D. Suberin


What is hypermetropia? What are the possible reasons of hypermetropia? How is hypermetropia corrected? Explain with figures.


The semi-vertical angle of a cone is \( 45^{\circ} \)
If the height of the cone is 20.025 , then its approximate lateral surface area is
A . \( 401 \sqrt{2} \pi \)
В. \( 400 \sqrt{2} \pi \)
\( \mathrm{c} \cdot 399 \sqrt{2} \pi \)
D. none of these


The Russian chemist Dmitri Mendeleev
is generally credited with organizing the chemical elements into a
comprehensive periodic table in large part due to the fact that he was able to
use his table to predict the existence of elements, like gallium, that were not known at the time \( (1872), \) but were discovered later.

Which is the best explanation for why Mendeleev was unable to predict the existence of the noble gases (group 18
)?
A. Noble gases are not found on Earth
B. Noble gases are stable and very unreactive, and therefore, have few observable properties
c. Noble gases are synthetic elements and do not occu
D. Noble gases are very reactive and do not exist as stable elements


The change in potential energy, when a body of mass \( m \) is raised to a height \( n R \) from the earth's surface is \( (R= \) radius of earth)
A \( \cdot \operatorname{mg} R\left(\frac{n}{n-1}\right) \)
в. \( n m g R \)
\( ^{\mathbf{c}} \cdot \operatorname{mg} R\left(\frac{n^{2}}{n^{2}+1}\right) \)
D. \( \operatorname{mg} R\left(\frac{n}{n+1}\right) \)


At which stage of life the level of dopamine is more in limbic system?
A. Puberty
B. Adulthood
c. Adolescence
D. None of the above


Why are metals hard?
A. They have free electrons
B. They gain electrons easily
C. They are held by weak forces
D. All of the above


A helium nucleus (charge \( +2 e \) ) completes one round of a circle of
radius \( 0.8 m \) in 2 sec. Find the magnetic field at the centre of the circle.


The first organic compound synthesized in the laboratory from an inorganic compound is:
A. \( N H_{4} N C O \)
в. \( N H_{2}-C O-N H_{2} \)
с. \( C H_{3} \) СООН
D. \( C H_{4} \)


n fig. \( 1, \) AOB is a straight line, the value
of \( x \) is :
\( A \cdot 60 \)
B. 30
\( c \cdot 20 \)
\( D \)


If \( f(x)=\sin ^{2} x+\sin ^{2}\left(x+\frac{\pi}{3}\right)+ \)
\( \cos x \cos \left(x+\frac{\pi}{3}\right) \) and \( g\left(\frac{5}{4}\right)=1 \)
\( \boldsymbol{g}(1)=0 \) then \( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( A \)
в.
\( c \cdot \sin x \)
D. Data is insufficient


An open system can exchange:
A. matter with surroundings
B. energy with surroundings
C. both \( A \) and \( B \)
D. none of the above


A potential difference of 300 volts is applied to a combination of \( 2.0 \mu \mathrm{F} \) and \( 8.0 \mu \mathrm{F} \) capacitors connected in series. The charge on the \( 2.0 \mu \mathrm{F} \) capacitor is :
A . \( 2.4 \times 10^{-4} \) coulomb
B. \( 4.8 \times 10^{-4} \) coulomb
c. \( 7.2 \times 10^{-4} \) coulomb
D. \( 9.6 \times 10^{-4} \) coulomb


Applying Lagranges's MeanValue Theorem for a suitable function \( f(x) \) in
\( [0, h], \) we have \( f(h)+h f^{\prime}(\theta h), 0<\theta< \)
1. Then for \( f(x)=\cos x, \) the value of
\( \lim _{h \rightarrow 0^{+}} \theta \) is
A .
B. 0
\( c \cdot \frac{1}{2} \)
D.


The interaction energy of London force is inversely proportional to sixth power of the distance between two interacting particles but their magnitude depends
upon:
A. charge of interacting particles
B. mass of interacting particles
c. polarisability of interacting particles
D. strength of permanent dipoles in the particles


Which of the following statement(s) about the Modern periodic table is/are incorrect?
(i) The elements in the Modern periodic table are arranged on the basis of their decreasing atomic number.
(ii) The elements in the Modern periodic table are arranged on the basis of their increasing atomic number
(iii) Isotopes are placed in an adjoining group(s) in the periodic table.
A. (i) only
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iii)


If A vessel of thermal capacity 30
calories contains \( 170 g \) of water at
\( 30^{\circ} \mathrm{C} . \) If on dropping a solid at \( 93^{\circ} \mathrm{C} \)
into the calorimeter, then temperature
of mixture becomes \( 33^{\circ} \mathrm{C} \), find the
thermal capacity of solid.


If wave length changes by \( \Delta \lambda \) then change in magnitude of propagation vector is
\( A \cdot \Delta k \)
B . \( 2 \pi \Delta \lambda \)
c. \( \frac{2 \pi}{\lambda} \Delta \lambda \)
D. \( \frac{2 \pi}{\lambda^{2}} \Delta \lambda \)


A cyclist comes to skidding stop in \( 10 \mathrm{m} \) During this process, the force on the cycle due to the road is \( 200 \mathrm{N} \) and is directly opposed to the motion.(a) how much work does the road do on the
cycle?
(b) How much work does the
cycle do on the road?
A. -2000,,20000
B. - 2000 J,1000 J by each tyre
c. 0.2000
D . -2000 J,0 J


If two gases \( A B_{2} \) and \( B_{2} C \) are mixed
the following equilibria are readily
established
\( \boldsymbol{A B}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2} \boldsymbol{C}(\boldsymbol{g}) \rightarrow \boldsymbol{A} \boldsymbol{B}_{3}(\boldsymbol{g})+\boldsymbol{B C}(\boldsymbol{g}) \)
\( \boldsymbol{B C}(\boldsymbol{g})+\boldsymbol{B}_{2} \boldsymbol{C}(\boldsymbol{g}) \rightarrow \boldsymbol{B}_{3} \boldsymbol{C}_{2}(\boldsymbol{g}) \)
If the reaction is started only with \( A B_{2} \)
with \( B_{2} C, \) then which of the following is
necessarily true at equilibrium:
This question has multiple correct options
\( \mathbf{A} \cdot\left[A B_{3}\right]_{e q}=[B C]_{e q} \)
\( \mathbf{B} \cdot\left[A B_{2}\right]_{e q}=\left[B_{2} C\right]_{e q} \)
\( \mathbf{c} \cdot\left[A B_{3}\right]_{e q}>\left[B_{3} C_{2}\right]_{e q} \)
\( \mathbf{D} \cdot\left[A B_{3}\right]_{e q}>[B C]_{e q} \)


Is the color of emergent beam \( X \) white
ight:
A. True
B. False


If true enter 1 , else enter \( 0 . \) The strongest
hydrogen bond is formed between fluorine and hydrogen.


Name a simple living mechanical tissue.


\( \ln \operatorname{areaction} \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{4}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}<0 . \) The formation of
\( A B_{4} \) is not favoured by :
This question has multiple correct options
A. low temperature and high pressure
B. high temperature and low pressure
c. low temperature and low pressure
D. high temperature and high pressure


Charges are placed on the vertices of a square as shown. Let \( \overrightarrow{\boldsymbol{E}} \) be the electric
field and \( V \) be the potential at the
centre. If the charges on \( A \) and \( B \) are interchanged with those on D and \( \mathbf{C} \)
respectively, then:
A \( . \vec{E} \) remains unchanged, \( V \) changes
B. Both \( \vec{E} \) and \( V \) change
C \( . \vec{E} \) and \( V \) remain unchanged
D. \( \vec{E} \) changes, \( V \) remains unchanged


Oxygen molecule is formed by:
A. one axial \( s \) -s overlap and one \( p \) - \( p \) axial overlap
B. two \( p \) - \( p \) axial overlap
C . two \( p-p \) sidewise overlap
D. one \( p-p \) axial and one \( p-p \) sidewise overlap.


The electric field intensity at \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
in the shown arrangement:


(a) Draw the ray diagram showing the formation of image by a compound microscope.
(b) Show that in order to achieve large magnification in a compound microscope the magnitude of focal length of objective and eye piece should be small.


Find \( A M \) of first 250 natural numbers
A. 115
в. 225
\( c \cdot 125 \)
D. 125.5


If 100 times the 100 th term of an A.P.
with non-zero common difference
equals the 50 times its 50 th term. Then
150th term of thus A.P. is
A . -150
B. 150 times the soth term
\( c \cdot \) 150
D.


Bacteria and fungi belong to
A. Autotrophs
B. Primary consumers
c. Decomposers
D. Secondary consumers


The element which easily forms a trinegative ion among the following:
A. Phosphorus
B. Bismuth
c. Arsenic
D. Nitrogen


Identify the given figures of algae and
select the correct option.
A. (A) - Fucus, (B) - Polysiphonia
B. (A) - Dictyota, (B) - Polysiphonia
C. (A) - Dictyota,(B) - Porphyra
D. (A) - Porphyra, (B) - Polysiphonia


The matrix \( \boldsymbol{B} \) is
A. Symmetric
B. Scalar
c. Skew hermitian
D. Skew- symmetric


If \( n \) is an even number, then the digit in
the units place of \( 2^{2 n}+1 \) will be
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7
\( c \cdot 6 \)
D.


The dissociation constants for acetic
acid and \( H C N \) at \( 25^{\circ} C \) are \( 1.5 \times 10^{-5} \)
and \( 4.5 \times 10^{-10} \) respectively. The
equilibrium constant for the following equilibrium would be:
\[
\begin{array}{r}
C N^{-}+C H_{3} C O O H \rightleftharpoons \\
H C N+C H_{3} C O O^{-}
\end{array}
\]
A \( \cdot 3 \times 10^{4} \)
B. \( 3 \times 10^{5} \)
\( \mathrm{c} \cdot 3 \times 10^{-5} \)
D. \( 3 \times 10^{-4} \)


Prove that \( \left|\frac{1-z_{1} \bar{z}_{2}}{z_{1}-z_{2}}\right|<1\left|z_{1}\right|<1< \)
\( \left|z_{2}\right| \)


The products (A) and (B) are:
his question has multiple correct options
\( A \)
в.
\( c \)
Dal


Give an example of a parasitic plant with yellow, slender and tubular stem


Assertion
A ball of mass \( m \) is released from the
top of a smooth inclined plane. At the
same time another ball of same mass
allowed to fall freely from same height. When both balls reaches the bottom of
the plane, momentum will not be equal.
Reason

Momentum depends on the direction of
velocity as well as its magnitude.
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


Define isobars and isotopes.


If \( 4 x+3 y=120, \) find how many non-
negative integer solutions are possible?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 11
c. Infinite
D. None of these


UV light radiation cause
A. Formation of pyrimidines
B. Photodynamic action
c. Breakage of hydrogen bonds in DNA
D. Protein denaturation


Assertion
\( \ln \operatorname{an} A C \) circuit potential difference
across the inductor may be greater than the applied voltage.
Reason
\( \boldsymbol{V}_{C}=\boldsymbol{I} \boldsymbol{X}_{C}, \) whereas \( \boldsymbol{V}=\boldsymbol{I} \boldsymbol{Z} \) and \( \boldsymbol{X}_{\boldsymbol{C}} \)
can be greater than \( Z \) also.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The perimeter of two similar triangles
\( \triangle A B C \) and \( \triangle D E F \) are \( 36 \mathrm{cm} \) and 24
\( \mathrm{cm} \) respectively. If \( D E=10 \mathrm{cm}, \) then
\( A B \) is :
A . \( 12 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)


While opening a tap with two fingers, the forces applied by the fingers are:
A . equal in magnitude
B. parallel to each other
c. opposite in direction
D. all the above


Polymer used to make gasket of pressure cooker is:
A. polythene
B. nylon
c. teflon
D. thiokol


If the molar conductance values of
\( C a^{2+} \) and \( C l^{-} \) at infinite dilution are
respectively \( 118.88 \times \) \( 10^{-4} m^{2} \) mho mol \( ^{-1} \) and \( 77.33 \times \)
\( 10^{-4} m^{2} \) mho mho \( ^{-1} \) then that of \( C a C l_{2} \)
is:
A . \( 118.88 \times 10^{-4} \)
B . \( 154.66 \times 10^{-4} \)
c. \( 273.54 \times 10^{-4} \)
D. \( 196.21 \times 10^{-4} \)


Who was the first to introduce the
concept of antiparticle theoretically.?
A. Niels Bohr
B. Ernest Rutherford
c. Albert Einstein
D. Paul Diraç


Write the maximum number of atoms
having same hybridisation in 2,5 -di-Nchloridothioimino-3, \( 4^{-} \) diazonothiophene
A .4
B. 5
\( c \cdot 6 \)
\( D \)


Which of the following observations cannot be explained by Tyndall Effect?
A. Sunlight entering a smoke filled dark room from a tiny hole
B. Sunlight entering from a canopy of dense forest
c. speed of light in vacuum is \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. Light passed through a milk solution


Write balanced chemical equations for
the reaction between calcium
bicarbonate and dilute hydrochloric
acid.


If the difference between the mode and
median is \( 2, \) then the difference between the median and mean (in the
given order) is?
A .2
B. 4
c. 1
\( D \)


A wheel takes \( \mathrm{m} \) rotations to travel a
certain distance while another whee
whose diameter is four times bigger than it takes n rotations to travel the
same distance. The relation between
A \( \cdot m=4 n \)
B. \( m=2 n \)
\( c \cdot 2 m=n \)
D. \( 4 \mathrm{m}=\mathrm{n} \)


Which among the following elements has smallest atomic size?
\( A \cdot s i \)
B.
\( c \cdot s \)
D. c


Write any two factors that influence the
speed of sound through air.


Solve \( \lim _{x \rightarrow-4} \frac{x+4}{x^{2}-x-20} \)


Water is poured from a height of \( 10 \mathrm{m} \) into an empty barrel at the rate of 1 litre per second. If the weight of the barrel is
\( 10 \mathrm{kg}, \) the weight indicated at time \( t= \)
60 s will be
A . \( 71.4 \mathrm{kg} \)
в. \( 68.6 \mathrm{kg} \)
c. \( 70.0 \mathrm{kg} \)
D. \( 84.0 \mathrm{kg} \)


In what ratio, the point of intersection of the common tangents to hyperbola \( \frac{x^{2}}{1}-\frac{y^{2}}{8}=1 \) and parabola \( y^{2}=12 x \)
divides the foci of the given hyperbola?
A . 3: 4
B. 3: 2
\( c .5: 4 \)
D. 5: 3


Which of the following are APs? If they form an AP, find the common difference
\( d \) and write three more terms.
-1.2,-3.2,-5.2,-7.2


Write the additive inverse of each of \( \frac{2}{8} \) and \( \frac{-5}{9} \)


The surface area of a cube is \( 441 m^{2} \)
Find its side.
\( \mathbf{A} \cdot 8.5 \mathrm{m} \)
B. \( 8.2 \mathrm{m} \)
c. \( 8.1 \mathrm{m} \)
D. \( 8.4 \mathrm{m} \)


Which of the following complex will give
white precipitate with \( \mathrm{BaCl}_{2}(\mathrm{aq}) \) ?
\( A \cdot\left[\cos \left(N H_{2}\right)_{4} S O_{4}\right] N O_{2} \)
B. \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} S O_{4}\right] \mathrm{C} \)
\( \mathbf{c} \cdot\left[\operatorname{cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{SO}_{4} \)
D. Both \( B \) and \( C \)


Identify a local maxima for:
\( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
\( \mathbf{A} \cdot x=2 \)
B. \( x=1 \)
c. \( x=-2 \)
D. \( x=-1 \)


In which of the following reactions have the underlined substance been
reduced?
A. Carbonmonoxide + copperoxide \( \rightarrow \) carbondioxide \( + \) Carbon
copper
в. \( \frac{\text { Copperoxide }}{\text { water }}+ \) hydrochloricacid \( \rightarrow \) copperchloride \( + \)
c. Hydrogen\( + \)ironoxide\( \rightarrow \)iron \( + \)water
D. \( \underline{S t e a m}+ \)iron \( \rightarrow \) ironoxide \( + \)hydrogen


Convert the above compound and note
that \( K M n O_{4} \) can cause cleavage of the
ring in the presence of the activating
OH) group.


Which of the following is not correct for noble gas?
A. Argon is used in electric bulb.
B. Krypton is obtained during radioactive disintegration
c. Half life of radon is 3.8 days
D. Helium is used to produce low temperature


A particle is in S.H.M of amplitude \( 2 \mathrm{cm} \)
At extreme position the force is \( 4 \mathrm{N} \). At the point mid-way between mean and extreme position, the force is :
A. 1 N
B. 2N
c. 3 N
D. 4 N


Draw a pair of tangents to a circle of
radius \( 3 \mathrm{cm} \) which are inclined to each
other at an angle of \( 45^{\circ} \)


\( 200 \mathrm{ml} \) of \( 1 \mathrm{M} \) HCl is mixed with \( 400 \mathrm{m} \)
of \( 0.5 \mathrm{M} \) NaOH. The temperature rise in
the calorimeter was found to
be \( 4.00 \mathrm{C} \). Water equivalent of calorimeter is \( 25 g \) and the specific heat of the solution is 1 cal/mL/degree. If the
theoritical heat of neutralization of a
strong acid and strong base is -13.5 kcal, then the percentage error in this experiment while calculating the heat of neutralization is
A. 7.4
B. 3
\( c \cdot 5.6 \)
D. 4.5


With reference to a semi-conductor
diode, what is meant by
(i) Forward bias
(ii) Reverse bias
(iii) Depletion region.


When a lyophobic colloidal solution is observed under microscope, we can see
A. light scattered by colloidal particle
B. size of the colloidal particle
c. shape of the colloidal particle
D. relative size of the colloidal particle


In the Freundlich's adsorption isotherm equation, \( \log \frac{x}{m}=\log K+\left(\frac{1}{n}\right) \log p \)
the value of \( n \) is:
A. any value from 0 to 1
B. a negative integer
c. a positive integer
D. a positive or a negative fractional number


The radius of a circle with centre 0 is 13
\( \mathrm{cm} . \) The distance of a chord from the
centre is \( 5 \mathrm{cm} . \) Find the length of the chord.
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
\( \mathrm{c} \cdot 13 \mathrm{cm} \)
D. \( 26 \mathrm{cm} \)


A particle of mass \( \mathrm{m} \) and charge \( -\mathrm{q} \) moves diametrically through a uniformly charged sphere of radius R with total charge \( Q \). The angular frequency of the particle's simple harmonic motion, if its amplitude \( <\mathrm{R} \), is given by :
A. \( \sqrt{\frac{1}{4 \pi \varepsilon_{0}} \frac{q Q}{m R}} \)
в. \( \sqrt{\frac{1}{4 \pi \varepsilon_{0}} \frac{q Q}{m R^{2}}} \)
c. \( \sqrt{\frac{1}{4 \pi \varepsilon_{0}} \frac{q Q}{m R^{3}}} \)
D. \( \sqrt{\frac{1}{4 \pi \varepsilon_{0}} \frac{m}{m Q}} \)


A electron experiences a force \( (4.0 \hat{i}+ \) \( \mathbf{3} . \mathbf{0} \hat{\boldsymbol{j}}) \times \mathbf{1 0}^{-\mathbf{1 3}} \boldsymbol{N} \) in a uniform magnetic
field when its velocity is \( 2.5 \hat{k} \times \) \( 10^{7} m s^{-1} . \) The magnetic field vector \( \vec{B} \)
is
\( \mathbf{A} \cdot-0.075 \hat{i}+0.1 \hat{j} \)
B. \( 0.1 \hat{i}+0.075 \hat{j} \)
c. \( -0.075 \hat{i}-0.1 \hat{j}+\hat{k} \)
D. \( -0.075 \hat{i}-0.1 \)


Evaluate: \( \int_{\frac{\pi}{2}}^{\pi} \frac{1-\sin x}{1-\cos x} d x \)


Find the coordinates of the point of
intersection of the axis and the directrix
of the parabola whose focus is (3,3) and directrix is \( 3 x-4 y=2 . \) Find also
the length of the latus-rectum.


Internal energy change in a cyclic
process is zero.
A. True
B. False


What is B?


Assume that a neutron breaks into a
proton and an electron. The energy released during this process is (Mass of neutron \( =1.6725 \times 10^{-27} k g \)
Mass of proton \( =1.6725 \times 10^{-27} k g \)
Mass of electron \( \left.=\mathbf{9} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
B. \( 7.10 \mathrm{MeV} \)
c. \( 6.30 \mathrm{MeV} \)
D. \( 5.40 \mathrm{MeV} \)


The image of the point (2,-1,1) by the
plane \( 3 x+4 y-5 z=0 \) is
A \( \cdot(-2,1,-1) \)
в. \( \left(\frac{2}{3}, \frac{-1}{4}, \frac{-1}{5}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{59}{25}, \frac{-13}{25}, \frac{2}{5}\right) \)
D. none of these


Vascular tissue in higher plants develop from which of the following?
A. Procambium
B. Protoderm
c. Periblem
D. cortex


(a) Complete the following chemical
equations:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{S} \boldsymbol{b} \boldsymbol{F}_{5} \rightarrow \)
(ii) \( C l_{2}+F_{2}(\text {excess}) \rightarrow \)
(b) Explain each of the following:
(i) Nitrogen is much less reactive than
phosphorus.
(ii) The stability of +5 oxidation state
decreases down group 15.
(iii) The bond angles \( (O-N-O) \) are
not of the same value in \( N O_{2}^{-} \) and \( N O_{2}^{+} \)


There is a stream of neutrons with a
kinetic energy of \( 0.0327 \mathrm{eV} \). If the half-
life of neutrons is 700 second, the
percentage fraction of neutron will
decay before they travel a distance of 10 \( \mathrm{km} \) is (multiply answer by 20). (mass of neutron \( =1.675 \times \)
\( \left.10^{-27} k g\right) \)


Find the zero of the polynomial in each of the following: \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{2} \)
A . -2
B. -
c. 0
D. 2


Resolve \( \frac{1}{\boldsymbol{x}^{4}+1} \) into partial fractions.
A \( \frac{(x+\sqrt{2})}{4 \sqrt{2}\left(x^{2}+x \sqrt{2}+1\right)}-\frac{(x-\sqrt{2})}{4 \sqrt{2}\left(x^{2}-x \sqrt{2}+1\right)} \)
B. \( \frac{(x+\sqrt{2})}{\sqrt{2}\left(x^{2}+x \sqrt{2}+1\right)}-\frac{(x-\sqrt{2})}{\sqrt{2}\left(x^{2}-x \sqrt{2}+1\right)} \)
\( ^{\mathbf{C}}-\frac{(x+\sqrt{2})}{2 \sqrt{2}\left(x^{2}+x \sqrt{2}+1\right)}+\frac{(x-\sqrt{2})}{2 \sqrt{2}\left(x^{2}-x \sqrt{2}+1\right)} \)
D. \( \frac{(x+\sqrt{2})}{2 \sqrt{2}\left(x^{2}+x \sqrt{2}+1\right)}-\frac{(x-\sqrt{2})}{2 \sqrt{2}\left(x^{2}-x \sqrt{2}+1\right)} \)


A tin nucleus has charge \( 50 e V \). If the
proton is \( 10^{-12} m \) from the nucleus.
Then, the potential at this position will
be:
A \( .7 .2 \times 10^{8} V \)
B. \( 3.6 \times 10^{4} V \)
c. \( 1.44 \times 10^{4} V \)
D. \( 7.2 \times 10^{4} V \)


For the circuit shown in the figure the
current through the inductor is \( 1.6 A \)
while the current through the condenser is \( 0.4 A \), then the current \( l \) drawn from
the source is :
A \( \cdot 2 \sqrt{2} A \)
B. \( 1.65 A \)
\( c .1 .2 A \)
D. 2.0


A gas is formed by the reaction between
marble pieces and dilute \( \boldsymbol{H} \boldsymbol{C l} \)
(a) Which gas is formed as a result of
this reaction?
(b) Write the balanced chemical
equation for this reaction.
(c) Suggest two ways of increasing the speed of the chemical reaction.


n the arrangement shown in figure above the mass of body 1 is \( \eta=0.4 \) times as great as that of body 2 . The height \( h=20 \mathrm{cm} . \) The masses of the
pulleys and the threads, as well as the
friction are negligible. At a certain moment body 2 is released and the arrangement set in motion. Find the
maximum height that body 2 will go up
to in \( \mathrm{cm} \)


Choose the correct answers from the
alternatives given The dark coloured dead wood present in
the central region of the old tree is
A. Spring wood
B. Heartwood
c. sapwood
D. Cambium


Which is not true about metal
carbonyls?
A. Here CO acts as a Lewis base as well as Lewis acid
B. Here metal acts as Lewis base as well as Lewis acid
C . Here \( d \pi-p \pi \) back bonding takes place
D. Here \( p \pi-p \pi \) back bonding takes place


The main constituent element of
chlorophyll is


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \)
and \( g(x)=\frac{3-2 x}{4} . \) We can say:
This question has multiple correct options
A. \( f \) is neither one-one nor onto
B. \( g \) is one-one but \( f \) is not one-one
c. \( f \) is one-one and \( g \) is onto
D. neither \( f \) nor \( g \) is onto


The vector \( \hat{i}+x \hat{j}+3 \hat{k} \) is rotated
through an angle \( \theta \) and doubled in magnitude,then it becomes \( 4 \hat{i}+(4 x- \)
2)\( \hat{j}+2 \hat{k} . \) The value of \( x \) are
A \( \cdot-\frac{2}{3}, 2 \)
в. \( \frac{1}{3}, 2 \)
c. \( \frac{2}{3}, 2 \)
D. zero, 2


An elongation of \( 0.1 \% \) in a wire of cross-
section \( 10^{-6} m^{2} \) causes a tension of
\( 100 N . Y \) for the wire is
\( \mathbf{A} \cdot 10^{12} N / m^{2} \)
B. \( 10^{11} N / m^{2} \)
\( \mathbf{c} \cdot 10^{10} N / m^{2} \)
D. \( 100 \mathrm{N} / \mathrm{m}^{2} \)


Evaluate \( \left[\begin{array}{cc}\sqrt{\mathbf{3}} & \sqrt{\mathbf{5}} \\ -\sqrt{\mathbf{5}} & \mathbf{3} \sqrt{\mathbf{3}}\end{array}\right] \)


Transform \( x-3 y+5=0 \) to the
parallel axes through the point (1,2)


In a sequence of 21 terms, the first 11
term are in \( A . P \) with common
difference 2 and the last 11 terms are in
\( G . P . \) with common ratio \( 2 . \) If the middle
term of the \( A . P . \) is equal to the middle
term of \( G . P . \) The find the middle term
of the entire sequence.


From the list below, select the shape
that describes the \( H_{2} O \)
A. Linear
B. Bent (v-shaped)
C. Trigonal planar
D. Pyramidal
E. Regular tetrahedral


A person moves \( 30 \mathrm{m} \) north, then \( 20 \mathrm{m} \) east, then \( 30 \sqrt{2} \) m south-west. His
displacement from the original position is:
A. 6 m south-west
B. 28 m south
c. \( 10 \mathrm{m} \) west
D. \( 15 \mathrm{m} \) east


Which one of the following expanded forms of the following acronyms is
correct?
A. IUCN - International Union for Conservation of Nature and Natural Resources
B. IPCC - International Panel for Climate Change
c. UNEP - United Nations Environment Policy
D. EPA - Environmental Pollution Agency


When a sound is reflected from a
distinct object, an echo is produced. Let the distance between the reflecting surface and the source of sound
production remains the same. Do you hear echo sound on a hotter day?


Statement I: \( H C l \) is considered to be an
acid.
Statement II: \( \boldsymbol{H} \boldsymbol{C l} \) is a proton donor.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


For Bragg's diffraction by a crystal to occur, then which of the following is
correct for the X-ray of wavelength \( \lambda \)
and interatomic distance d:
A . \lambda is greater than \( 2 d \)
B. \lambdaequals \( 2 d \)
c. \( \lambda \) is smaller than or equal to \( 2 d \)
D. \lambda is smaller than \( 2 d \)


Vibrations in a body produce sounds. How do you prove it?


When the specific heat of a solid is measured by the method of mixture, the heat is lost to surroundings from the calorimeter by the process of
A. radiation
B. conduction
c. convection
D. both conduction and convection


Which of the following match is correct?
A. Mendeleev periodic table is based on number of protons
B. One of the Doberenier's triad is \( N a, K, R b \)
C. Newland's octave rule is obeyed by \( H, F, C l \)
D. Lother meyer curve plotted between atomic number and atomic weight


A fly-wheel is rotating about its own axis at an angular velocity 11 rad/s. Its angular velocity in revolution per minute \( (r p m) \) is:
A. 105
в. 210
\( c .315 \)
D. 420


Janet thought that plants needed light
and oxygen to grow. She set up four jars as shown to test this idea.

Which jars would be necessary to test
her idea?
A. \( w \) and \( x \) only
B. Wand Y only y
c. \( W, X \) and \( Z \) only
D. W, Y and Z only


Assertion
Carbon is nonmetal.
Reason
Carbon atoms can bond with each other.
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


Describe the various types of Asexual reproduction so as explain in detai spore - formation


A compound has the molecular formula
\( X_{4} O_{6} . \) If 10 g of \( X_{4} O_{6} \) has 5.72 g \( X, \) then
the atomic mass of \( X \) is :
A . 32 amu
B. 64 amu
c. 67 amu
D. 98 amu


Write the value of \( \int \frac{d x}{x^{2}+16} \)


Simplify \( (-90) \times 52+(-52) \times(-25) \)
using a suitable frequency.


Two wires are pictured below, both
carrying current toward the east.
What is the direction of the force
exerted by wire 2 on wire \( 1 ? \)
West
A. North
B. South
c. Up
D. Down
E. East


Which of the following frequencies is associated with the visible region of a
spectrum?
A. \( 3 \times 10^{9} \) cycle / seconds
B. \( 6 \times 10^{14} \) cm cycle / seconds
C. \( 5.0 \times 10^{10-3} \) cycle / seconds
D. None of these


A gas cylinder contains 5 moles of
oxygen gas.The weight of the gas in the cylinder is:
A. \( 80 \mathrm{g} \)
в. \( 120 \mathrm{g} \)
c. \( 160 \mathrm{g} \)
D. \( 40 \mathrm{g} \)


A bus is moving with a velocity \( 10 \mathrm{ms}^{-1} \)
on a straight road. A scooterist wishes
to over take the bus in 100 s. If the bus is
at a distance of \( 1 k m \) from the
scooterist, with what velocity should be scooterist chase the bus?
A \( .50 m s^{-1} \)
В. \( 40 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 30 \mathrm{ms}^{-1} \)
D. \( 20 m s^{-1} \)


Classify simple epithelium tissue on the basis of the structural modification
of the cells. Where do we find ciliated
epithelium in human body Differentiate between Endocrine gland and Excine gland?


Fertilization occurs in human, rabbit
and other placental mammals in
A. Ovary
B. Uterus
c. Fallopian tubes
D. vagina


Find \( C_{A B} \) in the given circuit of given
figure. Assume each capacitor is \( \mathrm{C} \)
A \( \cdot \frac{15 C}{8} \)
B. \( \frac{15 C}{7} \)
c. \( \frac{3 C}{2} \)
D. \( 2 C \)


What is the relation between resistance
\( \mathrm{R} \) and resistivity \( \rho \) of a wire \( ? \)
A \( \cdot R=\frac{\rho A}{l} \)
в. \( R=\frac{\rho l}{A} \)
c. \( R=\frac{A}{\rho l} \)
D. \( _{R}=\frac{l}{\rho A} \)


Suppose Earth has a volume 'V' and surface area 'A'; then its becomes a
large capacitor having the value of capacitance as
A \( \cdot 12 \pi \in_{0} \frac{V}{A} \)
в. \( _{4 \pi \in_{0}} \frac{V}{A} \)
c. \( _{4 \pi \in_{0}} \frac{A}{V} \)
D. \( _{12 \pi \in_{0}} \frac{A}{V} \)


\( \boldsymbol{K}_{a} \) for \( \boldsymbol{H}_{2} \boldsymbol{O} ;\left(\boldsymbol{K}_{\boldsymbol{w}}=\mathbf{1 0}^{-14}\right) \) is \( \mathbf{1 . 8} \times \)
\( 10^{-x} \)
Then find the value of \( x \). (Moar conc. of
pure water is 55.55 )


The melting point of phenol is relatively high for an aryl compound because of the:
A. hydrogen bonding
B. ionic bonding
c. covalent bonding
D. all of them


\( \boldsymbol{p} \boldsymbol{K}_{a} \) of acetic acid is \( \mathbf{4 . 7}, \) which implies
that?
A. pH of 1N acetic acid is 4.74
B. At pH 4.74 , the dissociation of acetic acid is maximum
c. At pH 4.74 half of acetic acid molecules are dissociated in the solution
D. At pH 4.74 , the dissociation of acetic acid is minimumm


State True or False.
Gamma rays produce maximum ionization in gases.
A. True
B. False


The name of the sheath that covers root
apex is
A. Root hairs
B. Parent roots
c. calyptra
D. Root cap


The angles of a triangle are in the ratio
\( 2: 3: 4 . \) Find the angles.


Find the value of \( x, \) in the figure, for which I II \( m \)


The following table gives production yield per hectare of wheat of 100 farms
of a village.
Production yield (in
50- 55- 60 so-
55 kg/ha) 60
\( \begin{array}{ll}65 & 70\end{array} \)
No. of farms
Change the distribution to a more than type distribution and draw its ogive


An alpha nucleus of energy \( \overline{2} \) mv
bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be
proportional to
\( ^{\mathrm{A}} \cdot \frac{1}{\mathrm{Z}} \)
B \( \cdot \mathrm{v}^{2} \)
c. \( \frac{1}{\mathrm{m}} \)
D. \( \frac{1}{v^{4}} \)


Explain the formation of nitrogen
molecule.
A.


Evaluate \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}), \) if \( \boldsymbol{2} \boldsymbol{P}(\boldsymbol{A})= \)
\( \boldsymbol{P}(B)=\frac{\boldsymbol{5}}{13} \) and \( \boldsymbol{P}(\boldsymbol{A} / B)=\frac{2}{5} \)


The periodic time of a body executing SHM is \( 4 s \). After how much interval from
time \( t=0, \) its displacement will be half
of its amplitude?
A . \( 1 / 2 s \)
B. \( 1 / 3 s \)
c. \( 1 / 4 s \)
D. \( 1 / 6 s \)


Which element among those listed below, has the greatest electronegativity?
A . In
B. \( I \)
c. \( S b \)
D. \( T e \)
E . \( S n \)


Two points with coordinates (2,3) and
(2,1) lie on a line. Then
(i) the line is
parallel to which axis?
\( (i i) \) Justify your
answer.
A \( .(i) \) Parallel to \( X \) -axis.
(ii) since \( x \) -coordinate of both the points is \( 2, \) both points lie on the line \( y=2 \) which is parallel to \( Y \) -axis
B. ( \( i \) ) Parallel to \( Y \) -axis.
(ii) since \( y \) -coordinate of both the points is \( 2, \) both points lie on the line \( y=2 \) which is parallel to \( Y \) -axis
c. (i) Parallel to Y-axis.
(ii) since \( x \) -coordinate of both the points is \( 2, \) both points lie on the line \( x=2 \) which is parallel to \( Y \) -axis
D. ( \( i \) ) Parallel to \( X \) -axis.
(ii) since \( y \) -coordinate of both the points is 2 , both points lie on the line \( x=2 \) which is parallel to \( Y \) -axis


The electronic configuration of gadolinium (Atomic No.64) is:
\( \mathbf{A} \cdot[X e] 4 f^{3} 5 d^{5} 6 s^{2} \)
\( \mathbf{B} \cdot[X e] 4 f^{6} 5 d^{2} 6 d^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{8} 5 d^{9} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)


Gravitational unit of force produce an acceleration in a body equal to
\( A \cdot g \)
B. 0
c. \( 2 g \)
D. unit value


Show that the points (1,2,3),(7,0,1)
and (-2,3,4) are collinear.


If the distance 's' metres transversed by
a particle in \( t \) seconds is given by \( s= \)
\( t^{3}-3 t^{2}, \) then the velocity of the particle
when the acceleration is zero, in metre/sec is
\( A \cdot 3 \)
B. - -
\( c \cdot-3 \)
D.


An experimental set up is shown in the figure. Identify the metal \( X \) and \( \operatorname{gas} Y \) respectively in the figure.
A \( \cdot \) zinc, \( H_{2} \) gas
B. Copper, \( C O_{2} \) gas
C. Aluminium, \( C O_{2} \) gas
D. Platinum, \( H_{2} \) gas


One of the following is true moss.
A. Irish moss
B. Bog moss
c. Club moss
D. Reindeer moss


In figure, if triangle \( A B C \) is an
isosceles triangle of perimeter 20
calculate the approximate area of the
circle with center 0
A .26 .83
В. 33.65
\( c .44 .17 \)
D. 57.33
E. 229.34


The work done by an external agent to shift a point mass from infinity to the centre of the earth is W. Then choose the
correct relation.
A. \( w=0 \)
B. \( w>0 \)
\( c \cdot w<0 \)
D. \( w \leq 0 \)


Phototropism of stem and root are due
to
A. Differential hormonal effect
B. Epinasty and hyponasty
C. Effect of light
D. Graviperception


Name any two units of length which are bigger than the metre. Write the
relation
between each of those units and the
metre.


Milk is an example of :
A . Aquasol
B. True solution
c. Aerosol
D. Emulsion


The molecular mass of \( C u S O_{4} .5 H_{2} O \)
is:
(Atomic mass of \( C u=63.5, H=1, O= \)
\( 16, S=32) \)
A. 233.5 gm/mole
B. 249.5 gm/mole
c. \( 251.5 \mathrm{gm} / \mathrm{mole} \)
D. 247.5 gm/mole


Assertion
Sulphur dioxide is a more powerful
reducing agent in alkaline medium
than in acidic medium.
Reason
Sulphur dioxide reacts with hydrogen
sulphide in presence of moisture and
sulphur is precipitated.
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


ff \( (x)=\log (x-2)+\log (x-3) \) and
\( \phi(x)=\log (x-2)(x-3) \)
Are both functions equal?


Let \( k=\lim _{x \rightarrow 0} \frac{x \sin x}{x^{2}}, \) then the value of
\( \frac{5 k+1}{k} \) is


Which of the following is NOT a member of the solar system?
A. An asteroid
B. A satellite
c. A constellation
D. A comet


A spring balance is graduated on sea level. If a body is weighted at consecutively increasing heights from earth's surface, the weight indicated by the balance:
A. Will go on increasing continuously
B. Will go on decreasing continuously
c. will remain same
D. Will first increases and then decreases


\( \int \frac{\tan 2 \theta d \theta}{\sqrt{\cos ^{6} \theta+\sin ^{6} \theta}} \) is equal to
\( \mathbf{A} \cdot \ln \left|\frac{1+\sqrt{1+3 \cos ^{2} 2 \theta}}{\cos 2 \theta}\right|+c \)
B \( \cdot \ln \left|\frac{\sqrt{1+3 \cos ^{2} 2 \theta}}{\cos 2 \theta}\right|+c \)
\( \mathrm{c} \cdot \ln \left|\frac{1+\sqrt{2+3 \cos ^{2} 2 \theta}}{\sin 2 \theta}\right|+c \)
D. None of these


Which of the following statements is
not correct?
A. The velocity of an electron in the first orbit of hydrogen atom is the same as that of an electron in the second
orbit of helium positive ion.
B. The radius of the first orbit in hydrogen atom is the same as that of the second orbit in beryllium tripositive ion.
C. The energy of an electron in the first orbit of hydrogen atom is the same as that of an electron in the second orbit of helium positive ion.
D. The potential energy of an electron in the first orbit of hydrogen atom is the same as that of an electron in the fourth orbit of helium positive ion.


Find the real solution of the equation \( \tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}= \)


The mass of the electron is given \( 9.1 \times \) \( 10^{-31} k g . \) Find the order of magnitude of
the number of electrons of \( 1 k g \)
\( \mathbf{A} \cdot 10^{31} \)
B. \( 10^{-30} \)
\( c \cdot 10^{3} \)
D. \( 10^{-31} \)


The correct IUPAC name for given
compound is:


Which of the following oxides, at the same concentration when dissolved in
water, results in the most acidic
solutions ?
A \( \cdot C O_{2} \)
в. \( B_{2} O_{5} \)
c. \( N_{2} O_{5} \)
D. \( L i_{2} O_{5} \)


Name the sounds of the frequencies
given below \( 10 H z \)
A. ultrasonic
B. infrasonic
c. supersonic
D. None of the above


Which of the following pairs form the
same osazone?
A . Glucose and Fructose
B. Glucose and Galactose
c. Glucose and Arabinose
D. Lactose and Maltose


Mention any two characteristics of SHM (Simple Harmonic Motion).


If radius of a resistor is decreased by
\( 0.5 \% \) by stretching then percentage change in resistance
A . \( 0.5 \% \)
B. 1\%
c. \( 1.5 \% \)
D. 2\%


Two point charges \( q_{1} \) and \( q_{2} \) are fixed at position vectors \( 4 \hat{i} \) and \( 3 \hat{j} \) respectively.
If a third charge \( q_{3} \) is in electrostatic equilibrium, then the position vector of
\( q_{3} \) may be :
This question has multiple correct options
A . \( 2 \hat{i}+1.5 \hat{j} \)
B . \( -2 \hat{i}+4.5 \hat{j} \)
c. \( 4 \hat{i}+3 \hat{j} \)
D. \( 3 \hat{i}+4 \hat{j} \)


If \( f(x)=\sin ^{2} x \) and the composite
function \( g(f(x))=|\sin x|, \) then \( g(x) \) is
equal to
A \( \cdot \sqrt{x-1} \)
B. \( \sqrt{x} \)
c. \( \sqrt{x+1} \)
D. \( -\sqrt{x} \)


What is the name for the number of
protons in an atom?
A. Atomic identity
B. Atomic mass
c. Atomic weight
D. Atomic number


Significant figures in 0.00051 are
\( A \cdot 5 \)
B. 3
\( c \cdot 2 \)
D. 4


Which Euclid's postulate led to the discovery of several other geometries while attempting to prove it using other postulates and axioms
A . Fifth Postulate
B. First Postulate
c. second postulate
D. Third Postulate


List five rational numbers between:
\( \frac{-4}{5} \) and \( \frac{-2}{3} \)


\( \int_{-5}^{5} \log \left(\frac{130-x^{3}}{130+x^{3}}\right) d x \) is equal to
\( \mathbf{A} \cdot \log \frac{57}{5} \)
B. \( 2 \int_{-5}^{5} \log \left(\frac{130-x^{3}}{130+x^{3}}\right) d x \)
c. 0
D. -


A ray of light passes from water to air. How does the speed of light change?


When a fire man directs a powerful
stream of water on a fire from a hose
pipe, the hose pipe tends to go backward. This is an example of Newton's:
A. Law of gravitation
B. First law of motion
c. Second law of motion
D. Third law of motion


The solubility product of \( P b B r_{2} \) is
\( K_{s p}=6.3 \times 10^{-6} \) at room temperature.
If \( 50 \mathrm{ml} \) of \( 0.02 M P b\left(N O_{3}\right)_{2} \) are mixed
with \( 50 \mathrm{ml} \) of \( 0.01 M C a B r_{2}, \) then
A. \( P b B r_{2} \) will precipitate and excess \( B r^{-} \) will remain in
B. \( C a\left(N O_{3}\right)_{2} \) will precipitate
c. \( P b B r_{2} \) will precipitate and excess \( P b^{2+} \) will remain in
D. no precipitate will form


Answer the following question in one
word or one sentence or as per exact requirement of the question.

Write the point where \( f(x)=x \log _{e} x \)
attains minimum value.


When body changes its state from liquid to solid, the change is
A. endothermic
B. exothermic
c. neutral
D. isobaric


Solve the following differential equation \( \frac{d y}{d x}=1-\cos x \)


The inflorescence in Gramineae is
\( \mathbf{A} \cdot \) Raceme
B. Spike
c. spikelet
D. Thyrsus


The correct reagents used in the
conversion are:
\( \mathbf{A} \cdot p=B r_{2} \quad q=a l c . K O H \quad r=N a O H \quad s=A l_{2} O_{3} \)
B \( \cdot p=H B r q=a l c . K O H r=C a C_{2} s=K M n O_{4} \)
C \( \cdot p=H B r \quad q= \) alc. \( K O H \quad r=N a N H_{2} s= \)
red hot irontube
D \( \cdot p=B r_{2} \quad q= \) alc. \( K O H \quad r=N a N H_{2} \quad s= \)
red hot irontube


topp \( E \)
\( Q \) туре уоиг question
3


If \( x^{2}+\frac{1}{x^{2}}=18, \) then the value of
\( \left(x+\frac{1}{x}\right) \) is \( ? \)
A .
B. 3
c. \( \sqrt{20} \)
D. 6


In mammals, the bicuspid (mitral valve), guards the opening between
A. Left atrium and left ventricle
B. Pulmonary vein and left auricle
c. Stomach and intestine
D. Right atrium and right ventricle


You apply a \( 75-N \) force to pull a
child's wagon across the floor at a constant speed \( 0.5 m / s . \) If you increase
your pull to \( 90 N, \) the wagon will then
A. continue to move at \( 0.5 \mathrm{m} / \mathrm{s} \)
B. Speed up immediately and then move at the faster constant speed of \( 0.6 \mathrm{m} / \mathrm{s} \)
c. speed up gradually until it reaches the speed of \( 0.6 m / s \) and then move at that constant speed
D. continue to speed up as long as you keep pulling
E. Do none of the above


The degree of a polynomial \( 4 x^{2}+3 x- \)
7 is
A . 1
B. 3
\( c \cdot 7 \)
D. 2


If \( ^{n} C_{r} \) denots the number of
combinations of \( n \) things taken \( r \) at a
time, then the expression \( ^{n} C_{r+1}+^{n} \)
\( C_{r-1}+2 \times^{n} C_{r} \) equals
A. \( ^{n+2} C_{r} \)
B. \( ^{n+2} C_{r+1} \)
c. \( ^{n+1} C_{r} \)
D. \( n+1 C_{r+1} \)


Which among the following group 15 elements does not exhibit allotropy?
\( A \cdot N \)
B. As
\( c \cdot s b \)
\( D \cdot B \)


Let \( a=2 \hat{i}+\widehat{j}-2 \widehat{k} \) and \( b=\hat{i}+\widehat{j} . \) If \( c \) is
a vector such that \( \boldsymbol{a} . \boldsymbol{c}=|\boldsymbol{c}|,|\boldsymbol{c}-\boldsymbol{a}|= \)
\( 2 \sqrt{2} \) and the angle between \( a \times b \) and \( c \)
is \( 30^{\circ} . \) Then, \( [(a \times b) \times c] \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
D. 3


Identify the type of gas filled in
container \( A \) and \( B \) respectively
A. Mono, mono
B. Dia, dia
C. Mono, dia
D. Dia, Mono


Electromagnetic waves of wavelength ranging from \( 100 A \) to \( 400 A \) comes
under:
A. \( x \) -rahs
B. UV region
c. visible region
D. Infrared region


The length of chord of radius \( 25 \mathrm{cm} \) and
Distance at \( 7 \mathrm{cm} \) is


There is also formation of insoluble
\( C u S \) (black) when copper reacts with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) What is the change in
oxidation number of sulphur?


Prove that \( \frac{\sin 60^{\circ}+\sin 30^{\circ}}{\sin 60^{\circ}-\sin 30^{\circ}}= \)
\( \frac{\tan 60^{\circ}+\tan 45^{\circ}}{\tan 60^{\circ}-\tan 45^{\circ}} \)


Assertion \( : \beta- \) particles have greater
penetrating power than \( \boldsymbol{\alpha}-\boldsymbol{r} \boldsymbol{a} \boldsymbol{y} \boldsymbol{s} \) but
less than \( \gamma- \) rays.
Reason \( : \beta- \) particles are lighter than
\( \boldsymbol{\alpha}-\boldsymbol{r} \boldsymbol{a} \boldsymbol{y} \boldsymbol{s} \) but heavier than \( \boldsymbol{\gamma} \)
A. If both (A) and (R) are correct, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A)
c. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct
E. If both (A) and (R) are incorrect


A particle performs 20 vibrations in 5 secs. The time period of vibration is
A . 2.5
B. \( 0.1 \mathrm{s} \)
c. \( 0.25 \mathrm{s} \)
\( D \cdot 4 s \)


Light waves travel in a vacuum, along the \( X \) -axis. Which of the following may
represent the wave fronts?
\( \mathbf{A} \cdot x=c \)
В. \( y=c \)
\( \mathbf{c} \cdot z=c \)
D. \( x+y+z=c \)


If \( m_{2} \) again comes down and collides
with \( m_{1}, \) then after the collision:
\( \mathbf{A} \cdot m_{1} \) will rise the same height as risen by \( m_{2} \)
B. \( m_{1} \) will rise the less height as risen by \( m_{2} \)
\( \mathrm{C} \cdot m_{1} \) will rise the more height as risen by \( m_{2} \)
D. \( m_{1} \) and \( m_{2} \) will more in opposite directons


Which one of the following statements
is false?
A. Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction
B. The osmotic pressure ( \( \pi \) ) of a solution is given by the equation \( \pi=M R T \), where, \( M \) is the molarity of the
solution
C. The correct order of osmotic pressure for \( 0.01 \mathrm{M} \)
aqueous solution of each compound is \( B a C l_{2}> \) \( K C l>C H_{3} C O O H> \)sucrose
D. Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression


The sum of angles of a triangle is
\( \mathbf{A} \cdot 180^{\circ} \)
B. 135
\( c .90^{\circ} \)
D. 45


Three rings, each of mass \( m \) and radius
\( r, \) are so placed that they touch each
other. Find the moment of inertia about
the axis as shown in the figure:
\( A \cdot 5 m r^{2} \)
B. \( \frac{5}{7} m r^{2} \)
\( c \cdot 7 m r^{2} \)


What is meant by 'shape selective
catalysis'?


Find the value of \( k \) if \( f(x)= \) \( \left\{\begin{array}{ll}\frac{1-\cos 2 x}{1+\cos 2 x}, & x \neq 0 \\ k, & x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)


One mole of ideal gas whose adiabatic exponent \( \gamma=\frac{4}{3} \) undergoes process \( P= \) \( 200+\frac{1}{V} \) then change in internal energy
of gas when volume changes from \( 2 m^{3} \)
\( \operatorname{to} 4 m^{3} \) is?
A . 400
B. 800
c. 1200 J
D. 600


Nucleophilic addition of Grignard
reagent cannot occur in:

This question has multiple correct options
\( \mathbf{A} \)
B.
\( c \)
D.


A square has lines of
symmetry.
A. one
B. Two
c. Three
D. Four


Which represents correct comparison of
the stability of ions?
A. \( M n O_{4}^{-}<M n^{2+} \)
B. \( C r^{2+}<C r^{3} \)
c. \( C r O_{4}^{2-}<C r^{3+} \)
D. All of these


What transition in the hydrogen spectrum have the same wavelength as Balmer transition \( n=4 \) to \( n=2 \) of
\( H e^{+} \) spectrum?


Choose the correct answer from the
alternatives given :
From the details, find out the number of
rural people who are not educated
\( A \cdot 28 \)
3. 16
\( c \cdot 44 \)
25


Match the list - I (enzymes) with List - II (metals) and select the correct answer
using the codes given below the lists:
List List - II
A. Nitrogenase
1. \( c \)
B. Cytochrome oxidase 2. Mo
c. cytochrome- \( c \)
3. zn
D. carboxypeptidase 4. Fe
A. A-1 B-2 C-4 D-3
B. A-2 B-1 C-3 D-4
c. \( A-2 B-1 C-4 D-3 \)
D. A-1 B-2 C-3 D-4


Find the mean of 2 and 8


If \( \sin A+\cos A=\sqrt{2} \) then \( \sin A \)
\( \cos A \) is equal to:


The formula of pertitanic acid is:
A \( . H_{2} T i O_{5} \)
в. \( H_{2} T i O_{2} \)
\( \mathrm{c} . H_{2} T i O_{4} \)
D. \( H_{2} T i O_{3} \)


A voltage of peak value \( 283 \mathrm{V} \) and varying frequency is applied to series LCR combination in which \( R=3 \Omega, L=25 \)
\( \mathrm{mH} \) and \( \mathrm{C}=400 \mu \mathrm{F} \). Then the frequency (in \( \mathrm{Hz} \) ) of the source at which maximum power is dissipated in the above is
A . 51.5
B. 50.7
\( c . \) 51.
D. 50.3


One end of a spring of natural length
\( \ell_{0}=0.1 \mathrm{m} \) and spring constant \( \mathrm{k}=80 \)
N/m is fixed to the ground and other
end is fitted with a smooth ring of mass \( \mathbf{m}=2 \mathrm{gm}, \) which is allowed to slide on a
horizontal rod fixed at a height \( h= \) \( 0.1 \mathrm{m} . \) Initially, the spring makes an
angle of \( 37^{\circ} \) with vertical when the
system is released from rest.

When the spring becomes vertical,
speed of ring is ' \( v^{\prime} \mathrm{m} / \mathrm{s}, \) find ' \( v \) '. \( \left(\cos 37^{\circ}=\frac{4}{5}\right) \)


The angle between polariser and
analyser is \( 30^{\circ} \) The ratio of intensity of incident light and transmitted by the analyser is
A. 3: 4
B. 4: 3
c. \( \sqrt{3}: 2 \)
D. \( 2: \sqrt{3} \)


A bottle of liquor ammonia should be
cooled before opening.
A. True
B. false
c. sometimes true sometimes false
D. none


Esterification of \( (-)- \) lactic acid with
methanol yields \( (+)- \) methyl lactate.
Assuming that there are no side reactions, what is true about this
reaction?
A \( \cdot \) An \( S N_{2} \) reaction has occurred, inverting the absolute configuration of the chiral centre.
B. \( A n S N_{1} \) reaction at the chiral centre has inverted the optical rotation.
C. A diastereomer has been produced; diastereomers have different physical properties, including optical rotation
D. optical rotation is not directly related to absolute configuration, so the change in sign of rotation is merely a coincidence.


Which of the following reactions are
possible?
This question has multiple correct options
\( \mathbf{A} \cdot 3 M g+2 A l^{3+} \rightarrow 2 A l+3 M g^{2+} \)
B \( \cdot C l_{2}+2 I^{-} \rightarrow I_{2}+2 C l^{-} \)
\( \mathbf{c} \cdot K^{+}+N a \rightarrow K+N a^{+} \)
\( \mathbf{D} \cdot K+N \rightarrow K^{-}+N^{+} \)


A negatively charged solution will require minimum amount of which
electrolyte for its coagulation?
A. \( N a N O_{3} \)
B. \( M g\left(N O_{3}\right)_{2} \)
\( \mathbf{c} \cdot A l\left(N O_{3}\right)_{3} \)
D. \( \operatorname{Th}\left(N O_{3}\right)_{4} \)


How is sex determined in humans??


In epsom salt, the number of molecules
of water directly coordinated with
\( M g^{2+} \) ion are :
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


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


Gravitational force
of the medium between the charges.
A. depends
B. does not depend
c. sometimes depends
D. None of these


Find out the incorrect reaction involved
in Contact process
A. \( H_{2} S_{2} O_{7}+H_{2} O \rightarrow 2 H_{2} S O_{4} \)
B. \( H_{2} S O_{4}+2 N a O H \rightarrow 2 H_{2} O+N a_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{SO}_{3} \rightarrow \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D \( \cdot 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)


The Henry's law constant for the
solubility of \( \mathbf{N}_{2} \) gas in water at \( \mathbf{2 9 8 K} \) is
\( 1.0 \times 10^{5} \) atm. The mole fraction of \( \mathbf{N}_{2} \)
in air is \( 0.8 . \) The number of moles of \( \mathbf{N}_{2} \)
from air dissolved in 10 moles of water
at \( 298 \mathrm{K} \) and 5 atm pressure is:
A \( \cdot 4.0 \times 10^{-4} \)
В. \( 4.0 \times 10^{-5} \)
c. \( 5.0 \times 10^{-4} \)
D. \( 4.0 \times 10^{-6} \)


The equivalent inductance between \( A \)
and B is:
\( A \cdot 14 \)
B. 4 .
\( c .0 .84 \)
0.16


Defined \( \boldsymbol{f}:\left[-\frac{1}{2}, \infty\right) \rightarrow \boldsymbol{R} \) by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{\mathbf{1}+\mathbf{2} \boldsymbol{x}}, \boldsymbol{x} \in\left[-\frac{\mathbf{1}}{\mathbf{2}}, \infty\right) . \) Then compute
\( \lim _{\boldsymbol{x} \rightarrow\left(\frac{\mathbf{1}}{\mathbf{2}}\right)} \boldsymbol{f}(\boldsymbol{x}) \). and also find \( \lim _{\boldsymbol{x} \rightarrow \frac{-\mathbf{1}}{\mathbf{2}}} \boldsymbol{f}(\boldsymbol{x}) \)


If \( \boldsymbol{y}=\tan ^{-1}\left(\cot \left(\frac{\pi}{2}-x\right)\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \)
B. -1
c. 0
D.


Starting from rest, when a body moves with uniform acceleration, then distances covered after 1 st, 2 nd, \( 3 r d, \)
seconds are in the ratio
A . 1: 2: 3: 4
B . 1:4: ::16.
\( c \cdot 1: 3: 5: 7 \)
D. 2:3: 5:7.


s is the sum to infinite terms of a
G.P. whose first term is 1. Then the sum
of \( n \) term is
A \( \cdot s\left(1-\left(1-\frac{1}{s}\right)^{n}\right) \)
B \( \cdot \frac{1}{s}\left(1-\left(1-\frac{1}{s}\right)^{n}\right) \)
c. \( _{1-}\left(1-\frac{1}{s}\right)^{n} \)
D. \( 1+\left(1-\frac{1}{s}\right)^{n} \)


Choose best possible option. \( \left(x+\frac{1}{2}\right)\left(\frac{3 x}{2}+1\right)= \)
\( \frac{6}{2}(x-1)(x-2) \) is quadratic.
A. Yes
B. No
c. Complex equation
D. None


and converted to steam at \( 100^{\circ} \mathrm{C} \). Which
of the following curves represent the
phenomenon qualitatively?
\( A \)
B.
\( c \)
D. None of these


Calculate the radius of first orbit in
\( H e^{+} \) ion.
A \( \cdot 0.2645 A^{\circ} \)
B . 26.45 A \( ^{\text {о }} \)
c. \( 0.2465 \times 10^{-12} \)
D. none of these


Find \( \operatorname{Var}(2 X+3) \)
A \( .5 \operatorname{Var}(X)+3 \)
в. \( 4 \operatorname{Var}(X)+3 \)
c. \( 4 \operatorname{Var}(X) \)
D. None of these


Chemosynthesis and photosynthesis
are alike as they both
A. Are associated with heterotroph
B. Require sunlight as an energy source
c. Use method of autotrophic nutrition
D. Occurin tracheophytes


ff \( \left[\begin{array}{cc}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\gamma} & -\boldsymbol{\alpha}\end{array}\right] \) is to be the square root of \( \mathbf{a} \)
two -rowed unit matrix, then \( \alpha, \beta \) and \( \gamma \)
should satisfy the relation.
A. \( 1+\alpha^{2}+\beta \gamma=0 \)
B . \( 1-\alpha^{2}-\beta \gamma=0 \)
C \( \cdot 1-\alpha^{2}+\beta \gamma=0 \)
D. \( 1+\alpha^{2}-\beta \gamma=0 \)


Maximum prescribed limit of \( C u \) in
drinking water is:
\( A \cdot 2 p p m \)
B. 1 ppm
c. 3 ppm
D. 5ppm


The activity of a nuclide is 15 millicurie.
If its decay constant is \( 0.005 \mathrm{sec}^{-1} \), the
number of atoms present in it is
A. \( 11.1 \times 10^{10} \)
B . \( 1 \times 10^{9} \)
c. \( 111 \times 10^{10} \)
D. \( 1.1 \times 10^{10} \)


the wavelength


Number of atoms (as multiples of \( \boldsymbol{N}_{\boldsymbol{o}} \)
of hydrogen present in 18 g of water is:


A particle moves rectilinearly. its displacement \( x \) at time \( t \) is given by
\( x^{2}=t^{2}+1 . \) Its acceleration at time \( t \) is
proportional to
A \( \cdot \frac{1}{x^{3}} \)
B. \( \frac{1}{x}-\frac{1}{x^{2}} \)
\( c \cdot-\frac{t}{x^{2}} \)
D. \( \frac{1}{x}-\frac{t^{2}}{x^{3}} \)


A car moving on a straight road is in
A . curvilinear motion
B. rectilinear motion
c. periodic motion
D. rotational motion


Shown below is a graph of current versus applied voltage for a diode.
Approximately what is the resistance of
the diode for an applied voltage of
\( -15 V ? \)
A . \( 2 \Omega \)
B. \( \infty \)
c. zero
D. \( 1 \Omega \)


Superhalogen is:
\( \mathbf{A} \cdot F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


A magnet is allowed to fall through a copper circular wire. Then during fall:
A. the electric current flows through the wire
B. the acceleration of magnet is less than gravitational acceleration
c. the acceleration of magnet is equal to gravitational acceleration
D. the acceleration of magnet is greater than gravitational acceleration


A gas in a \( 1 \mathrm{m}^{3} \) container has a
molecular diameter of \( 0.1 \mathrm{m} . \) There are 10 molecules. What is its mean free
path?
A . \( 2.25 \mathrm{m} \)
B. 2m
\( c .3 m \)
\( D \cdot 1 m \)


In the given (V-T) diagram, what is the
relation between pressures \( P_{1} \) and \( P_{2} ? \)
A \( \cdot P_{2}=P_{1} \)
в. \( P_{2}>P \)
\( c \cdot P_{2}<P \)
D. cannot be predicted


Evaluate: \( \int e^{x} \sin \left(e^{x}\right) d x \)
A \( \cdot \cos e^{x}+C \)
B. - \( \cos e^{x}+C \)
c. \( \left(\cos e^{x}\right)^{-1}+C \)
\( \mathbf{D} \cdot \sin e^{x}+C \)


A solenoid of length \( 1.5 \mathrm{m} \) and \( 4 \mathrm{cm} \)
diameter possesses 10 turns per \( \mathrm{cm} . \) A current of \( 5 \mathrm{A} \) is flowing through it, the magnetic induction at axis inside the
solenoid is \( \left(\mu_{0}=4 \pi \times\right. \)
\( \left.10^{-7} w e b e r a m p^{-1} m^{-1}\right) \)
A \( \cdot 4 \pi \times 10^{-5} \) gauss
В . \( 2 \pi \times 10^{-5} \) gauss
c. \( 4 \pi \times 10^{-5} \) tesla
D. \( 2 \pi \times 10^{-5} \) tesla


Amino acid binding site of tRNA has
\( A \cdot C C A-O H \)
B. CGA - OH
c. UCA - OH
D. UCG - OH


Two vectors \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{a} \hat{\boldsymbol{i}}- \)
\( 2 \hat{j} \) are perpendicular to each other. The value of a is
A.
B. 2
\( c \cdot 3 \)
D. 4


If the equation \( x^{2}+4+3 \cos (a x+ \)
\( b)=2 x \) has at least one solution where
\( \boldsymbol{a}, \boldsymbol{b} \in[\mathbf{0}, \mathbf{5}], \) then the value of \( (\boldsymbol{a}+\boldsymbol{b}) \)
equal to
This question has multiple correct options
A \( .5 \pi \)
в. \( 3 \pi \)
c. \( 2 \pi \)
D.


The side of an equilateral triangle is \( 4 \sqrt{3} \mathrm{cm} . \) The length of a perpendicular drawn from any vertex to the opposite
side will be
A. \( 4 \mathrm{cm} \)
B. 6 ст
\( c .8 c m \)
D. \( 9 \mathrm{cm} \)


Read the following features and choose the correct option about anatomy of dicot and monocot stem
(i) Collenchymatous hypodermis.
(ii) Vascular bundles are scattered.
(iii) Eustele.
(iv) Ground tissue is not differentiated.
(v) Pericycle absent
A. Dicot stem i, ii, iii ; Monocot stem iv,
B. Dicot stem i, ii, v; Monocot stem iii, iv
c. Dicot stem iii, v; Monocot stem i, ii, iv
D. Dicot stem i, iii ; Monocot stem ii, iv, \( v \)


\( f(a, b, c)=\left[\begin{array}{ccc}a & 0 & 0 \\ {[0.3 e m] 0} & b & 0 \\ {[0.3 e m] 0} & 0 & c\end{array}\right] \)
such that \( a b c \neq 0 \)
\( \operatorname{then} A^{-1}=\operatorname{diag}\left(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\right)= \)
\( \left[\begin{array}{ccc}\frac{1}{a} & 0 & 0 \\ {[0.3 e m] 0} & \frac{1}{b} & 0 \\ {[0.3 e m] 0} & 0 & \frac{1}{c}\end{array}\right] \)


A man of height \( 180 \mathrm{cm} \) is standing in front of a plane mirror. His eyes are at a height of \( 170 \mathrm{cm} \) from the floor. Find the minimum height of the mirror?


A filled shopping cart (30.0kg) is being pushed rapidly toward the back of a store so that its velocity is \( 2.0 \mathrm{m} / \mathrm{s} \)
What is the momentum of the cart. and
what is the kinetic energy of the cart?
A. \( 90 k g m / s \) and \( 60 J \)
B. \( 60 k g m / s \) and \( 90 J \)
c. \( 60 k g m / s \) and \( 60 J \)
D. \( 90 k g m / s \) and \( 90 J \)


The speed of a car as a function of time
is shown in the figure. Find the distance
traveled by car in 8 seconds and its acceleration.


The values of \( \Delta H \) and \( \Delta U \) for the
reversible isothermal evaporation of
\( 90.0 \mathrm{g} \) of water at \( 100^{\circ} \mathrm{C} \) are \( x \) cal \( \& y \) cal. Assume that water vapour behaves
as an ideal gas and heat of evaporation of water is 540 cal \( g^{-1} .(R= \)
\( \left.2 c a l \operatorname{mol}^{-1} K^{-1}\right) . \) The value of \( x+y \) is:


A car is moving in a circular track of radius \( 10 \mathrm{m} \) with a constant speed of 10 \( \mathrm{m} / \mathrm{s} . \mathrm{A} \) plumb bob is suspended from the roof of the car by a light weight rigid rod of \( 1 \mathrm{m} \) long.The angle made by the rod with track is:
A. 0
B. 30
\( c \cdot 45 \)
D. 60


Which of the following structure
produces aggregate fruit?
A. VII
B. I and \( \vee \) I
c. ॥, ॥ा, ।V, and v
D. II, V, and VI
E. III and VI


The ratio in which \( y z \) -plane divides the line segment joining (-3,4,2),(2,1,3) is
A . -4: 1
B. 3: 2
c. -2: 3
D. 1: 4


Pepsin is produced by
A. Salivary glands
B. Stomach
c. Duodenum
D. Small intestine


What does a neuron look like?


Assertion
Two charges \( -q \) each are fixed at points
\( A \) and \( B . \) When a third charge \( -q \) is
moved from \( \boldsymbol{A} \) to \( \boldsymbol{B} \), electrical potential
energy first decreases, then increases.
Reason

Along the line joining \( A \) and \( B \), the third charge is in stable equilibrium position
at centre.
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


Select the correct option:
Cell membrane is selective permeable. This means that is
A. Allows all materials to pass through
B. Allows only water to pass through
C. Allows only certain materials to pass through
D. Allows only ions to pass through


The marks of 15 students in an
examination are:
25,19,17,24,23,29,31,40,19,20,22,26
\( 17,35,21 . \) Find the median score.


Find the maximum power in the form of \( (10+x) \) which can be transmitted
by means of a steel shaft rotating about
its axis with an angular velocity \( \omega= \)
\( 120 r a d / s, \) if its length \( l=200 c m \)
radius \( r=1.50 \mathrm{cm}, \) and the
permissible torsion angle \( \varphi=2.5^{\circ} \)
Round off to the nearest integer of \( x \)


(Diet problem) A dietician has to develop a special diet using two foods \( \boldsymbol{P} \) and \( Q . \) Each packet (containing \( 30 g \) ) of
food \( P \) contains 12 units of calcium, 4
units of iron, 6 units of cholesterol and 6
units of vitamin A. Each packet of the same quantity of food \( Q \) contains 3
units of calcium, 20 units of iron, 4
units of cholesterol and 3 units of
vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of
iron and at most 300 units of
cholesterol. How many packets of each food should be used to minimise the
amount of vitamin A in the diet? What
is the minimum amount of vitamin A?


Which of the following is not a postulate of Dalton's atomic theory?
A. Different elements have atoms of different masses
B. Atoms combine in simple whole number ratios to form compounds..
c. Atoms are not created or destroyed in chemical change
D. Atoms of a single element can have different masses


Which of the following behaviour is true for an ideal binary solution?
A. Plot of \( P_{\text {total}} \) versus \( y_{B} \) (mole fraction of B in vapour phase) is linear
B. Plot of \( P_{\text {total}} \) versus \( y_{A} \) is linear
c. plot of \( \frac{1}{P_{\text {total }}} \) versus \( y_{A} \) (or \( y_{B} \) ) is non-linear
D. plot of \( \frac{1}{P_{\text {total }}} \) versus \( y_{A} \) (or \( y_{B} \) ) is linear


Taxon is
A. Species
B. Unit of classification
C. Highest rank in classification
D. None of these


(a) What happens when Phenol is treated with benzene diazonium
chloride? Give balance chemical
equation.


The graph of \( |\boldsymbol{x}|+|\boldsymbol{y}| \) consists of
A. one straight line
B. a pair of straight lines
c. the sides of a square
D. a circle
E. a point


Eight oranges can be bought for Rs
10.40, then how many more oranges can be bought for Rs \( 16.90 ? \)
A. 5 oranges
B. 3 oranges
c. 7 oranges
D. 2 oranges


Non-ionogenic surfactants are:
\( \mathbf{A} \)
\( \mathbf{B} \cdot C_{17} H_{35} C O O N a \)
\( \mathbf{c} \cdot C_{n} H_{2 n+1}\left(O C H_{2} C H_{2}\right)_{x} \)
D. all the above


Which of the following elements belongs to actinide series?
A . Lu
B. Gd
c. Th
D. La


Two cells of emf \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2}\left(\boldsymbol{E}_{1}>\boldsymbol{E}_{2}\right) \)
are connected shown in figure. When a potentiometer is connected between \( \mathbf{A} \) and \( \mathrm{B} \), the balancing length of the
potentiometer wire is \( 300 \mathrm{cm} . \) On connecting the same potentiometer between \( A \) and \( C, \) the balancing length
is \( 100 \mathrm{cm} . \) The ratio \( E_{1} / E_{2} \) is
A . 3: 1
B. 1: 3
\( c \cdot 2: 3 \)
D. 3: 2


How many 2 - digit numbers can be formed from the digits \( \{1,2,3,4, \)
5\} without repetition and with repetition?


Several octahedral complexes are
possible from combinations of
\( C o^{3+}, C l^{-} \) and \( N H_{3} . \) The correct
statement(s) regarding the octahedral coordination entities having the formula \( \cdot\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{\boldsymbol{n}} \boldsymbol{C l}_{\boldsymbol{6}-\boldsymbol{n}}\right]^{(\boldsymbol{n}-\boldsymbol{3})+} \) with
\( \boldsymbol{n} \geq \mathbf{3}, \) is \( / \) are
This question has multiple correct options
A. At most six octahedral complexes are possible
B. One of the complexes is homoleptic
C. All the complexes are paramagnetic
D. Some of the complexes dissociate in water to give \( C o^{3+} \) and \( C l^{-} \) ions


A fluid is said to be ideal, if it is
A. incompressible
B. inviscous
c. viscous and incompressible
D. inviscous and incompressible


Assertion
The equation \( 3 x^{2}-2 y^{2}+4 x-6 y=0 \)
represents a hyperbola.
Reason
The second degree equation \( a x^{2}+ \) \( 2 h x y+b y^{2}+2 g x+2 f y+c=0 \)
represents a hyperbola if \( a b c+2 f g h- \)
\( \boldsymbol{a} \boldsymbol{f}^{2}-\boldsymbol{b} \boldsymbol{g}^{2}-\boldsymbol{c h}^{2} \neq \boldsymbol{0} \& \boldsymbol{h}^{2}>\boldsymbol{a b} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Addition of silver nitrate to sodium
chloride solution causes preciptation of silve chloride. This is an example reaction


The compound used in the treatment of lead poisoning is :
A. EDTA
B. Cis-platin
c. D-penicillamine
D. desferrioxime B


Given the following molar conductivity
at infinite dilution and \( 25^{\circ} \mathrm{C} \)
\( \mathrm{HCl}: \wedge_{m}^{\infty}=426.2 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \mathrm{KCl}: \wedge_{m}^{\infty}= \)
\( 114.42 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \mathrm{CH}_{3} \mathrm{COOK}: \wedge_{m}^{\infty}= \)
\( 149.86 \mathrm{s} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
The molar conductance at infinite
dilution and \( 25^{\circ} \mathrm{C}, \) for acetic acid
solution is:
A. \( 390.76 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
B . \( 461.86 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
c. \( 289.63 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. \( 172.94 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)


Gravitational acceleration on the
surface of a planet is \( \frac{\sqrt{\mathbf{6}}}{11} \) g, where \( g \) is the gravitational acceleration on the surface of the earth. The average mass density of the planet is \( \frac{2}{3} \) times that of
the Earth. If the escape speed on the surface of the earth is taken to be 11
\( k m s^{-1}, \) the escape speed on the surface
of the planet is \( k m s^{-1} \) will be?


Assuming \( z- \) axis inter nuclear axis. In
which orbitals overlap to form \( \sigma \) bond
\( \boldsymbol{P}_{\boldsymbol{X}}+\boldsymbol{P}_{\boldsymbol{Y}} \)


A certain radioactive material is known
to decay at a rate proportional to the amount present. Initially there is \( 50 \mathrm{kg} \) of thematerial present and after two hours it is observed that themateria
has lost \( 10 \% \) of its original mass, then
the
A \( \cdot \) mass of the material after four hours is \( 50\left(\frac{9}{10}\right)^{2} \)
B. mass of the material after four hours is \( 50 . e^{-0.51 n 9} \)
c. time at which the material has decayed to half of its initial mass (in hours) is \( \frac{\left(\ell n \frac{1}{2}\right)}{\left(-\frac{1}{2} \ell n 0.9\right)} \)
D. time at which the material has decayed to half of its initial mass (in hours) is \( \frac{2 \ln \frac{1}{2}}{\ln 0.99} \)


Petroleum is
resource.
A. Inexhaustible
B. Exhaustible
c. Both \( A \& B \)
D. None of these


Which of the following reactions is called saponification?
A \( \cdot C H_{3} C O O C H_{3}+O H^{-} \rightarrow C H_{3} C O O^{-}+C H_{3} O H \)
в. \( C H_{3} C O O^{-} N a^{+} \stackrel{H C l}{\longrightarrow} C H_{3} C O O H+N a C l \)
c.
D. \( C H_{3} C O O H+C H_{3} C H_{2} O H \rightarrow C H_{3} C O O H_{2} C H_{3} \)


Assertion
Red algae contribute in producing coral reef
Reason
Some red algae secrete and deposit calcium carbonate our their walls
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


A 100 watt bulb emits monochromatic
light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb
A. \( 3 \times 10^{20} s^{-1} \)
B. \( 2 \times 10^{-20} s^{-1} \)
c. \( 2 \times 10^{20} s^{-1} \)
D. \( 1 \times 10^{-20} s^{-1} \)


Matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{m \times n} \) is a square matrix
if
\( A \cdot m<n \)
\( B \cdot m>n \)
\( c \cdot m=1 \)
\( D \cdot m=n \)


The argument of the complex number
\( \sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right) \) is
A \( \cdot \frac{6 \pi}{5} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{9 \pi}{10} \)
D. \( \frac{2 \pi}{5} \)


The lonisation potential of Hydrogen is \( 2.17 \times 10^{-11} \) erg/atom. The energy of
the electron in the second orbit of the
hydrogen atom is?
A. \( -\frac{2.17 \times 10^{-11}}{2} \)
В. \( -\frac{2.17 \times 10^{-11}}{2^{2}} \)
c. \( -\frac{2.17 \times 10^{-7}}{2^{2}} \)
D. \( -\frac{2.17 \times 10^{11}}{2^{2}} \)


faraday \( = \)
A \( .10000 C \)
B. \( 95000 C \)
c. \( 96.5 C \)
D. 96500 \( C \)


What will be the ratio of the radii of two
nuclei of mass numbers \( A_{1} \) and \( A_{2} \) ?


Agaricus is :
A. Bread Mould
B. Button Mushroom
c. Paddy Straw Mushroom
D. oyster Mushroom


According to Dalton's atomic theory, atoms combine in a small number ratio
to form :
A. big atoms
B. compounds
c. elements
D. ions


Solve: \( \int \frac{\boldsymbol{d x}}{13+3 \cos x+4 \sin x} \)


Which among the following is correctly
categorized?
A. Troponin and Myosin \( \rightarrow \) Complex proteins in striated muscles
B. Calcitonin and Thymosin \( \rightarrow \) Thyroid hormones
C. Pepsin and Prolactin \( \rightarrow \) Digestive enzymes secreted in stomach
D. Secretin and Rhodopsin \( \rightarrow \) Polypeptide hormones


Show that the points \( A, B, C \) with position vectors \( \vec{a}=\left(3 i^{-} 4 j^{-} 4 \hat{k}\right), \vec{b}= \)
\( (2 i-j+\hat{k}) \) and \( \vec{c}=(i-3 j-5 \hat{k}) \)
respectively,form the vertices of a rightangled triangle.


A hydrogen atom has mass \( 1.68 \times \) \( 10^{-27} \mathrm{kg} . \) When attached to a certain
massive molecule it oscillates with a
frequency \( 10^{14} \mathrm{Hz} \) and with an
amplitude \( 10^{-9} \mathrm{cm} . \) Find the force
acting on the hydrogen atom.
B . \( 3.31 \times 10^{-9} \) N
c. \( 4.42 \times 10^{-9} \) N
D. \( 6.63 \times 10^{-9} \) N


The function \( \frac{\sin (x+\alpha)}{\sin (x+\beta)} \) has no
maximum or minimum if (k an integer)
A. \( \beta-\alpha=k \pi \)
B. \( \beta-\alpha \neq k \pi \)
c. \( \beta-\alpha=2 k \pi \)
D. none of the above


How is carbolic acid prepared from the following compound?
(i) Aniline
(ii) Chlorobenzene and steam at \( 698 \mathrm{K} \) ?
Draw structure of DDT. Write its
environmental effects.
Mention two physical properties of carbolic acid.


The pressure \( P \) of an ideal diatomic gas
varies with its absolute temperature \( \boldsymbol{T} \)
as shown in figure. The molar heat
capacity of gas during this process is \( R \text { is gas constant }] \)
A \( .1 .7 R \)
B. \( 3.25 R \)
c. 2.5
D. \( 4.2 . R \)


What should be the angular velocity of rotation of the earth about its own axis
so that the weight of a body at the equator reduces to \( 3 / 5 \) or its present value?(Take R as the radius of the
earth)
A \( \cdot \sqrt{\frac{g}{3 R}} \)
в. \( \sqrt{\frac{2 g}{3 R}} \)
c. \( \sqrt{\frac{2 g}{5 R}} \)
D. \( \sqrt{\frac{2 g}{7 R}} \)


Show that \( f(x)=\frac{\cos 3 x-\cos 4 x}{x \sin 2 x} \) for
\( x \neq 0, f(0)=\frac{7}{4} \) is continuous at \( x= \)
0


Which of the reagents listed below
could be added to water to make \( 0.1 \mathrm{M} \)
solution of \( \boldsymbol{N} \boldsymbol{H}_{4} \) ions?
¡. \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
ii. \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
A. \( N H_{3} \) because it is a strong electrolyte
B. \( N H_{4} C l \) because it is a strong electrolyte
C. \( N H_{3} \) because it is a weak electrolyte
D. \( N H_{4} C l \) because it is a weak electrolyte


A truck and a car are moving with equal velocity, on applying brakes, both will stop after certain distance and then :
A. Truck will cover less distance before stopping
B. Car will cover less distance before stopping
c. Both will cover equal distance
D. None


Biogas contains
\( \mathbf{A} \cdot 50-70 \% \) methane
B. \( 30-40 \% \) methane
c. Traces of methane
D. \( 80-95 \% \) ethane


There are four concentric shells \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
and \( D \) of radii \( a, 2 a, 3 a \) and \( 4 a \)
respectively. Shells \( B \) and \( D \) are given
charges \( +q \) and \( -q \) respectively. Shell \( C \) is now earthed. The potential difference \( V_{A}-V_{C} \) is \( \left(k=\frac{1}{4 \pi \varepsilon_{0}}\right) \)
\( \mathbf{A} \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( \mathbf{c} \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)


A car of mass \( 600 k g \) is moving with a
speed of \( 10 m s^{-1} \) while a scooter of
mass \( 80 k g \) is moving with a speed of
\( 50 m s^{-1} . \) Compare their momentum.
A .2: 3
B. 1: 2
c. 3: 1
D. 3: 2


Calculate \( \boldsymbol{E}_{\text {cell}} \)
\( \boldsymbol{P t}(\boldsymbol{s})\left|\boldsymbol{H}_{2}(\boldsymbol{g})_{1 a t m}\right| \boldsymbol{H} \boldsymbol{A}_{\left(\boldsymbol{K}_{a}=10^{-7}\right)} \mathbf{1} \boldsymbol{M} \| \boldsymbol{H} \boldsymbol{B}_{(\boldsymbol{k}} \)
A .0 .06
B. 0.03 V
c. \( 0.04 v \)
D. \( 0.05 \mathrm{v} \)


A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 \( \mathrm{m} / \mathrm{s} . \) The total kinetic energy of rolling sphere would be (in J)
A \( .1 .4 \times 10^{-4} J \)
B. \( 0.75 \times 10^{-3} J \)
c. \( 5.75 \times 10^{-3} J \)
D. \( 4.9 \times 10^{-5} J \)


The violet flame shown by potassium in Bunsen flame is due to jumping of the electron from :
\( A \cdot 1 s \operatorname{to} 4 p \)
B. 1s to 5p
\( c \cdot 4 p \operatorname{tos} 4 s \)
D. \( 5 p \) to 4 s


A plot of \( \ln K \) against \( \frac{1}{T}(\text { abscissa }) \) is expected to be a straight line with intercept on ordinate axis equal to:
A \( \cdot \frac{\Delta S^{o}}{2.303 R^{n}} \)
в. \( \frac{\Delta S^{\circ}}{R} \)
c. \( -\frac{\Delta S^{\circ}}{R} \)
D. \( R \times \Delta S^{o} \)


(a) Draw a ray diagram to show image
formation when the concave mirror
produces a real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write
the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a refracting telescope


An atom of an element contains 29
electrons and 35 neutrons.
Deduce
(i) the number of protons and
(ii) the electronic configuration of the element.