The Figure represents a part of a closed circuit. The p.d. In volts between the
points \( A \) and \( B \) i.e. \( V_{A}-V_{B} \) is


Tell whether the following is certain to happen, impossible can happen but not certain.
A tossed coin will land heads up.


Assertion(A): If the tangent at any point
\( P \) on the curve \( x y=a^{2} \) meets the axes
at \( A \) and \( B \) then \( A P: P B=1: 1 \)
Reason(R): The tangent at \( P(x, y) \) on
the curve \( \boldsymbol{X}^{\boldsymbol{m}} \cdot \boldsymbol{Y}^{\boldsymbol{n}}=\boldsymbol{a}^{\boldsymbol{m}+\boldsymbol{n}} \) meets the
axes at \( A \) and \( B \). Then the ratio of \( P \)
divides \( \overline{A B} \) is \( n: m \)
A. Both A and R are true R is the correct explanation of
B. Both A and R are true but R is not correct explanation of A
c. A is true but R is false
D. A is false but R is true


Electrical power can be calculated by
A . current \( ^{2} \times \) resistance
B. current x potential difference \( ^{2} \)
C . resistance \( ^{2} \times \) voltage
D. resistance \( \times \) charge \( ^{2} \)


Which of the following reactions of
Xenon compounds are not feasible?
\( \mathbf{A} \cdot 3 X e F_{4}+6 H_{2} O \longrightarrow 2 X e+X e O_{3}+12 H F+1.5 O_{2} \)
B \( \cdot 2 X e F_{2}+2 H_{2} O \longrightarrow 2 X e+4 H F+O_{2} \)
\( \mathbf{c} \cdot X e F_{6}+R b F \longrightarrow R b\left[X e F_{7}\right] \)
\( \mathbf{D} \cdot X e O_{3}+6 H F \longrightarrow X e F_{6}+3 H_{2} O \)


Which of the following are best suited to make the core of a transformer?
A. soft iron
B. steel
c. alnico
D. none of these


Find the distance between the following
pairs of points
(-5,7) and (-1,3)


Two conducting concentric, hollow spheres \( A \) and \( B \) have radii a and \( b \) respectively, with A inside B.Their common potentials is \( V \). A is now given some charge such that its potential becomes zero. The potential of B will
now be :
A. 0
B. \( V(1-a / b) \)
c. \( v \) a/b
D. v b/a


Statement I : The reaction of BaCl
and \( N a_{2} S O_{4} \) doesnt go to completion.
Because

Statement II : The compound barium sulfate is formed
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both the 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


Value of a when the distance between
the points \( (3, a) \) and (4,1) is \( \sqrt{10} \) is
A. 4 or -2
B . -2 or 4
c. 6 or 2
D. None


Mention against each of the following whether regular or diffused reflection win take place when a beam of light strikes. Justify your answer in each
case.
(a) Polished wooden table
(b) Chalk powder
(c) Cardboard surface
(d) Marble floor with water spread over
it
(e) Mirror
(f) Piece of paper


If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1-\sqrt{3}}{2} \)
B. 0
c. \( \frac{1}{2}(\sqrt{3}-1) \)
D. None of these


\( \operatorname{In} \) any triangle \( \prod\left(\frac{\sin ^{2} B+\sin B+1}{\sin B}\right) \)
is always greater than
\( A \cdot 9 \)
B. 3
c. 27
D. None of these


Deep sea divers use \( \left(O_{2}+H e\right) \) mixture
as preference to \( \left(O_{2}+N_{2}\right) \) mixture.
This is because:
A. helium is lighter than nitrogen
B. helium is less soluble in blood than nitrogen
c. helium is more soluble in blood.
D. helium provides a better inert atmosphere than nitrogen.


The length of an elastic string is \( L_{1} \)
when the tension is \( 4 N, \) and \( L_{2} \) when
the tension is 5 N. What is the length of
the string when the tension is \( 7 N ? \)


Arrange the following in increasing
order of radii:
a) \( \boldsymbol{I}, \boldsymbol{I}^{+}, \boldsymbol{I}^{-} \)
\( \mathbf{b}) C, N, \boldsymbol{S} \boldsymbol{i}, \boldsymbol{P} \)


Sublimation is a technique that helps chemists to:
A. break
B. purify
c. melt
D. freeze


The seventh term of a G.P. is 8 times the
fourth term and 5th term is \( 48 . \) Find the
second term of G.P.


How would you distinguish Archaea
from Eubacteria?


Find distance of a point (3,4) from the origin.


Which phenomenon is observed due to the change in speed of wave when it strikes the another medium's boundary
\( ? \)
A. Reflection
B. Refraction
c. Polarization
D. Diffraction
E. Interference


Assume an imaginary world where angular momentum is quantized to even multiple. The longest possible wave length emitted by hydrogen in the visible spectrum is
A \( .484 n m \)
B. 300nm
c. 400 n \( m \)
D. 350 nm


Four samples of water \( A, B, C \) and \( D \) have the DO values 1 mg/litre, 3 mg / litre, 5 mg/litre and \( 8 \mathrm{mg} / \) litre respectively Which one is more polluted sample of
water?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


An iron-containing protein myoglobin is present in the
A. Spleen
B. Lungs
c. Muscles
D. None of the above


The length of the longest rod that can be fitted in a cubical vessel of edge \( 10 \mathrm{cm} \)
long, is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
В. \( 10 \sqrt{2} \mathrm{cm} \)
c. \( 10 \sqrt{3} \mathrm{cm} \)
D. \( 20 c m \)


The perimeter of a rhombus is \( 146 \mathrm{cm} \)
One of its diagonals is 55 cm. Then the length of the other diagonal and the area of the rhombus is
A. \( 48 \mathrm{cm}, 1320 \mathrm{cm}^{2} \)
B . \( 45 \mathrm{cm}, 660 \mathrm{cm}^{2} \)
c. \( 27.5 \mathrm{cm}, 660 \mathrm{cm}^{2} \)
D. None of these


Fill in the blanks:
The volume of a cube \( =-----x \)
\( x \)
A. side \( \times \) length \( \times \) width
B. side \( \times \) height \( \times \) side
\( c \cdot \) side \( x \) side \( x \) side
D. side \( \times \) length \( \times \) breadth


In a meter-bridge, the balancing length from the left end when standard
resistance of 1 is in right gap is found
to be \( 20 \mathrm{cm} \). The value of unknown
resistance is
A \( .0 .25 \Omega \)
B. \( 0.5 \Omega \)
\( c .0 .4 \Omega \)
D. 4\Omega


Four hydrogenation reactions maximum catalytic activity is shown
by:
A. Group \( 5-11 \) elements
B. Group \( 5-9 \) elements
c. Group \( 7-9 \) elements
D. Group \( 9-11 \) elements


How to make a rational number line


A bullet of mass \( m \) and charge \( q \) is fired
towards a solid uniformly charged
sphere of radius \( R \) and total charge \( +q \) If it strikes the surface of the sphere
with speed \( u \), find the minimum speed
\( u \) so that it can penetrate through the sphere. (Neglect all resistance forces or
friction acting on bullet except electrostatic forces)
\( A \)
в.
\[
\frac{q}{\sqrt{4 \pi \varepsilon_{0} m R}}
\]
c. \( \frac{q}{\sqrt{8 \pi \varepsilon_{0} m R}} \)
D.


Find the area of the triangle formed by
the lines
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2} \) and \( \boldsymbol{l} \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}= \)
0


What is the degree of hardness of a
sample of water containing 24 mg of
\( M g S O_{4}(\text { mol. mass } 120) \) per kg of water?
A . 10 pp
в. 15 ррт
c. 20 ppm
D. 25 ppm


\( \mathbf{f} \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}+\boldsymbol{\gamma}^{2}=\mathbf{1}, \) then highest
integral value of \( \boldsymbol{\alpha} \boldsymbol{\beta}+\boldsymbol{\beta} \boldsymbol{\gamma}+\boldsymbol{\alpha} \boldsymbol{\gamma} \) is


Two magnetic poles of the same length
attract each other with a force of \( 2 \mathrm{N} \)
when placed on the two corners of an equilateral triangle. If a south pole of the same strength is placed at the third vertex, it experiences a force of magnitude
A . 4 N
B. 3N
c. 2 N
D. 1N


Hortorium is associated with
A. Herbarium of wood
B. Herbarium of fungal origin
C. Herbarium of horticulture origin
D. None of the above


Which of the following bond is nonpolar
covalent?
A. \( S i \) Si bond in \( C l_{3} \) sisicla
B. \( S i C l \) bond in \( C l_{3} \) sisiCla
c. \( C a F \) bond in \( C a F_{3} \)
D. \( N H \) bond in \( N H_{3} \)


The standard free energies of formation
of \( \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}, \boldsymbol{C} \boldsymbol{O}_{2}(g) \) an n-pentane are
\( -237.2 k J,-394.4 k J,-8.2 k J . \) Then
the value of \( E^{0} \) for pentane-oxygen fuel
cell is:
A . \( 1.1 V \)
в. \( 0.1 V \)
\( c .2 .0 V \)
D. 2.3V


are proteins that are crucial to body's communication process. These are present in cell membranes but a
small active part of it projects out of the
membrane.
A. Lipids
B. Enzymes
c. synapses
D. Receptors


\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{2} \boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{x}^{2}+\boldsymbol{x}-\mathbf{1} \) and
\( \boldsymbol{q}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{3} \)
Then \( p(x) \) is divisible by \( q(x), \) if we
A. Add \( (x-2) \)
B. Add \( (x-3) \)
c. Add \( (2-x) \)
D. Add \( (3-x) \)


Attention-deficit behaviour is
A. More common in boys
B. Difficulty in remaining seated
C. Inability to follow instructions
D. All of the above


The diagram in Fig. shows the displacement- time graph of a vibrating
body. Give one example of such
vibrations.


A substance having rate constant \( k \) and
initial concentration \( a \) reacts according
to zero order kinetics. What will be the
time for the reaction to go to
completion?
A \( \cdot \frac{a}{k} \)
в. \( \frac{k}{a} \)
c. \( \frac{a}{2 k} \)
D. \( \frac{2 k}{a} \)


The thermal motion means
A. motion due to heat engine
B. disorderly motion of the body as a whole
C. motion of the body that generates heat
D. random motion of molecules


The metal used for making radiation
shield is:
A . \( A l \)
в. \( F e \)
\( c \cdot Z n \)
D. \( P b \)


The derivative of \( \sin ^{-1} \frac{2 x}{1+x^{2}} \) with respect to \( \cos ^{-1} \frac{1-x^{2}}{1+x^{2}} \) is
A . -1
B.
\( c \cdot 2 \)
D. 4


The ovary of a flower grows into a fruit.
A. True
B. False


An airplane is heading north east at a speed of \( 141 m s^{-1} \). The northward
component of its velocity is:
A. \( 141.4 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
c. zero
D. \( 50 m s^{-1} \)


The charge required for reduction of
1 mol of \( C r_{2} O_{7}^{2-} \) ions to \( C r^{3+} \) is:
A . \( 9650 C \)
в. \( 2 \times 96500 C \)
c. \( 3 \times 96500 C \)
D. \( 6 \times 96500 C \)


Chlorine was discovered by:
A. Priestley
B. Davy
c. scheele
D. Cavendish


In the given figure, \( A B \| \) DC Prove that(i) \( \triangle D M U \sim \triangle B M V(\text { ii) } D M \times B V= \)
\( \boldsymbol{B} \boldsymbol{M} \times \boldsymbol{D} \boldsymbol{U} \)


We cannot see anything in a dark room because:
A. everything is black in colour
B. our eyes do not work in darkness
c. light from the room does not reach our eyes
D. all the light gets scattered


Blue-baby syndrome is caused by
A. Cadmium pollution
B. Mercury poisoning
C. Chronic exposure to arsenic
D. Excess nitrate in drinking water
E. Excess fluoride in drinking water


If \( X \) and \( Y \) are two sets, then \( X \cap(Y \cup \)
\( X)^{\prime} \) equals
\( \mathbf{A} \cdot X \)
в. \( Y \)
\( c \cdot \phi \)
D. None of these


"The structures of various phosphate and silicate anions have many similarities as both \( S i \) and \( P \) are
surrounded by tetrahedra of 0-atoms." Answer whether the above statement is
true or false.
If true enter 1 , else 0


Choose the correct answer from the
alternatives given :
An organism uses 20 amino acids while its DNA is made up of 6 types of nitrogenous bases. What would be the minimum size of a codon?
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. 2


Rashmi has a road map with a scale of
1 cm representing 18 km. She drives on a road for \( 72 \mathrm{km} \). What would be her
distance covered in the map?


What is the structure of carbonyl
group?
A. Tetrahedral
B. Trigonal planar
c. Pyramidal
D. Linear


Which one is/ are correct among the
following?

Given, the half cell emf's \( E_{C u^{+2} / C u}^{0}= \)
\( \mathbf{0 . 3 3 7}, \boldsymbol{E}_{\boldsymbol{C u}^{+1} / \boldsymbol{C u}}^{\mathbf{0}}=\mathbf{0 . 5 2 1} \)
A . \( C u^{+1} \) disproporationates
B. \( C u \) and \( C u^{2+} \) comproportionates (reverse of disproportionation into \( C u^{+} \) )
C. \( E_{C u / C u^{+2}}^{0}+E_{C u^{2} / C u}^{0} \) is positive
D. All of these


The difference between the radii of the
smaller circle and the bigger circle is \( 7 \mathrm{cm} \) and the difference between the
areas of the two circles is 1078 sq \( \mathrm{cm} \) What is the radius of the smaller circle
in cm?
A . 28
B . 21
c. 17.5
D. 35


Spoilage of food material is prevented
in cold storage due to
A. Reduced respiration at low temperature
B. Reduced enzyme activity in food articles
c. Reduced enzyme activity in microbes as well as food articles
D. Purified nature of air


Decreasing order of size of various hybrid orbitals is :
A \( \cdot s p>s p^{2}>s p^{3} \)
B \( \cdot s p^{3}>s p^{2}>s p \)
C \( \cdot s p^{2}>s p>s p^{3} \)
\( \mathbf{D} \cdot s p>s p^{3}>s p^{2} \)


Which of the following is a non metal that remains liquid at room temperature ?


The resistance of the wire in the
platinum resistance thermometer at
ice point is \( 5 \Omega \) and at steam point is
5.25 \( \Omega \). When the thermometer is
inserted in an unknown hot bath its
resistance is found to be \( 5.5 \Omega \). The
temperature of the hot bath is?
A \( \cdot 100^{\circ} \mathrm{C} \)
B . \( 200^{\circ} \mathrm{C} \)
c. \( 300^{\circ} \mathrm{C} \)
D. \( 350^{\circ} \mathrm{C} \)


A square wire frame of side \( a \) is placed
a distance \( b \) away from a long straight
conductor carrying current \( I \). The frame
has resistance \( R \) and self inductance \( L \)
The frame is rotated by \( 180^{\circ} \) about \( 00^{\prime} \)
as shown in figure. Find the electric charge flown through the frame.
\( ^{A} \cdot \frac{2 \mu_{0} i a^{2}}{2 \pi R b} \)
В. \( \frac{\mu_{0} i}{2 \pi R} \log _{e} \frac{b+a}{b-a} \)
c. \( \frac{\mu_{0} i a}{2 \pi R} \log _{e} \frac{b+a}{b-a} \)
D. none of thes


If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}=\{\mathbf{7}, \mathbf{8}, \mathbf{9}\} \) then
\( \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B}) \) is equal to
\( A \cdot 6 \)
B. 9
\( c .3 \)
\( D \)


Find the accelerations of the point \( \boldsymbol{B} \)
A \( \cdot 6.5 \mathrm{cm} / \mathrm{s}^{2} \)
в. \( 2.5 \mathrm{cm} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 5 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 2 \mathrm{cm} / \mathrm{s}^{2} \)


\( \boldsymbol{A}(\mathbf{5}, \mathbf{4}), \boldsymbol{B}(-\mathbf{3},-\mathbf{2}) \) and \( \boldsymbol{C}(\mathbf{1},-\mathbf{8}) \) are
the vertices of a triangle ABC. Find the equation of median AD.


If the straight line, \( 2 x-3 y+17=0 \)
is perpendicular to the line passing through the points (7,17) and \( (15, \beta) \)
then \( \beta \) equals:-
A . -5
B. \( -\frac{35}{3} \)
c. \( \frac{35}{3} \)
D. 5


In double slit experiment, when interference pattern due to whitelight is observed by an observer through a transparent glass of green colour, he finds black and green bright fringes. If green glass is replaced by violet colour glass, then:
A. No interference pattern will appear
B. Bright violet fringes will appear to be of smaller width than green fringes
C. Bright violet fringes will appear to be of more width than green fringes
D. Bright fringes will be produced of the same width as that of green fringes


From the given figure, find \( x \)


Select the correct statement:
This question has multiple correct options
A. Elastomers have the weakest intermolecular forces
B. Buna-N is an elastomer with crosslinks
C. Some fibres have crystalline nature
D. Thermoplastic polymers have stronger intermolecular forces than fibres


Three coplanar forces keep a body in equilibrium. The angles between adjacent forces are in the ratio of 3: 4:
5. The ratio of maximum force to the
minimum force is
A
в.
\( c \cdot \frac{4}{3} \)
D. 2


Which component of starch is a branched polymer of \( \alpha \) -glucose and insoluble in water?


Find the value of
\( \left(\tan 2^{\circ} \tan 4^{\circ} \tan 6^{\circ}------\tan 8\right. \)


The volume of a cubic is \( 1000 \mathrm{cm}^{3} \). Find
its total surface area- -
A. \( 400 \mathrm{cm}^{2} \)
B. \( 600 \mathrm{cm}^{2} \)
c. \( 200 \mathrm{cm}^{2} \)
D. None of these


Reduction in weight of an organism due to nutrition is genetically controlled.
A. True
B. False


For what value of 'a' the function
\( f(x)=x+\cos x-a \) increases
\( A \cdot 0 \)
B.
\( c .-1 \)
D. Any value


Calculate the \( p H \) at which the potential
of hydrogen electrode will be \( 0.059 V \)


Draw the graph for the equation given below. Hence find the co-ordinates of
the points where the graph drawn meets the co-ordinate axes:
\( \frac{1}{3} x+\frac{1}{5} y=1 \)
\( \mathbf{A} \cdot(6,3) \) and (5,0)
B \( \cdot(3,5) \) and (2,0)
c. (3,0) and (0,5)
\( \mathbf{D} \cdot(2,0) \) and (0,7)


In respiration, the energy not captured
by ATP is
A. Transferred to organic compounds
B. Converted into heat
C . Liberated along with \( C O_{2} \)
D. Transferred to water


A sample of calcium carbonate \( \left(C a C O_{3}\right) \) has the following percentage composition:
\( \mathrm{Ca}=40 \% ; \mathrm{C}=12 \% ; \mathrm{O}=48 \% \)
If the law of constant proportions is
true, then the weight of calcium in 4 g of a sample of calcium carbonate from another source will be:
A. \( 0.016 \mathrm{g} \)
B. \( 0.16 \mathrm{g} \)
\( c \cdot 1.6 g \)
D. \( 16 g \)


Evaluate each of the following in the
simplest form:
\( \cos 60^{\circ} \cos 30^{\circ}-\sin 60^{\circ} \sin 30^{\circ} \)


"In moist air, copper corrodes to
produce a green layer on the surface". For this, the reaction is :
\( \boldsymbol{C u}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C O}_{2}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C u} \boldsymbol{C O}_{3} \)
\( \boldsymbol{C u}(\boldsymbol{O} \boldsymbol{H})_{2} \)
If the statement is true enter 1 else
enter 0


Let \( \omega \neq 1 \) be a cube root of unity and \( S \)
be the set of all non-singular matrices of the form \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{\omega} & \boldsymbol{1} & \boldsymbol{c} \\ \boldsymbol{\omega}^{2} & \boldsymbol{\omega} & \boldsymbol{1}\end{array}\right] \) Where each of
\( a, b \) and \( c \) is either \( \omega \) or \( \omega^{2} \). Then the
number of distinct matrices in the set
\( \boldsymbol{S} \) is
\( A \cdot 2 \)
B. 6
\( c \cdot 4 \)
D. 8


A mass of \( 2 k g \) rests on an inclined
planes of gradient 1 in 8 as shown. The work done in sliding it from the lowest point of the inclined to the highest
point, if the coefficient of friction is 0.2
is -
A. \( 192 J \)
B. \( 19.2 \mathrm{J} \)
c. \( 48 J \)
D . \( 52 J \)


A ball coated with lamp black put in a glass tank containing water appears silvery white due to :
A. Refraction
B. Diffraction
c. Interference
D. Total internal reflection


Calcium lactate is a salt of weal organic acid and strong base represented as \( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{C})_{2} \cdot \boldsymbol{A} \) saturated solution of
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{C})_{2} \) contains \( \boldsymbol{0} . \boldsymbol{6} \) mole in \( \boldsymbol{2} \) litre
solution. \( p O H \) of solution is \( 5.60 . \) If \( 90 \% \) dissociation of the salt takes place then
what is \( p K_{a} \) of lactic acid?
A. \( 2.8-\log (0.54) \)
B. \( 2.8+\log (0.54) \)
c. \( 2.8+\log (0.27) \)
D. None of these


Let \( x_{1}, x_{2}, \dots \dots \dots, x_{n} \) be n observations such that \( \sum x_{i}^{2}=400 \) and \( \sum x_{i}=80 \) Then a possible value of \( n \) among the following is
A . 15
B. 18
\( c \cdot 9 \)
D. 12


Calculate variance for the following
data: 2,4,6,8 and 10


The inverse of \( \left[\begin{array}{lll}1 & a & b \\ 0 & x & 0 \\ 0 & 0 & 1\end{array}\right] \) is
\( \left[\begin{array}{ccc}1 & -a & -b \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \) then \( x= \)
\( A \)
в.
\( c .0 \)
\( D \)


Diastase enzyme converts
to
A. glucose to ethyl alcohol
B. starch to maltose
c. maltose to glucose
D. sucrose to glucose


\( \widehat{O}^{m}= \)
0
0
0
\( \widehat{Q} \)


Number of atoms in 4.25 g of \( N H_{3} \) is:
B. \( 4 \times 6.023 \times 10^{23} \)
C \( .1 .7 \times 10^{24} \)
D. \( 4.5 \times 6.023 \times 10^{23} \)


If \( \boldsymbol{A} \times \boldsymbol{B}=\boldsymbol{B} \times \boldsymbol{A}, \) then the angle
between \( A \) and \( B \) is
A. \( \pi \)
в. \( \pi / 3 \)
c. \( \pi / 2 \)
D. \( \pi / 4 \)


Fill in the blanks:
The name of the compound with the
given structural formula is


Active and passive absorption terms
were coined by
A. Kramer
B. Deutrochet
c. Priestley
D. Renner


Name of the tissue that connects two
bones.


The battery of a trunk has an emf of \( 24 \mathrm{V} \) If the internal resistance of the battery
is \( 0.8 \Omega . \) What is the maximum current
that can be drawn from the battery?
A . 30 A
B. 32 A
c. 33 A
D. 34A


A card is drawn at a random from a
pack of 52 cards. What is the probability of drawing a king or a jack?
A . \( 1 / 52 \)
в. 2/26
\( c \cdot 1 / 13 \)
D. 2/13


Potential energy of a string depends on
A. Wave velocity
B. Amplitude of the wave
c. Extent of stretching of the string
D. None of the above


Many fungi contain in their cell walls a substance which is not present in
higher plants. Name it.
A. Chitin
B. Glycogen
c. Latex
D. Ribose sugars


Given two independence events \( A \) and
\( B, \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Two circular plates of radii in the ratio 1: 2 are cut and removed from a metal
sheet of uniform thickness. The ratio of
moments of inertia of those smaller to
larger circular plates about axes perpendicular to the planes of
plates and passing through their
centers is:
A .1: 4
B. 1: 8
c. 1: 16
D. 1: 32


Heavy water is not used for drinking
because:
A. it is poisonous
B. it is costly
c. its physiological action is different from ordinary water
D. its chemical properties different from ordinary water


Identify the decimal and whole number
from the following.
\( \mathbf{9 8 1 0 1 . 2 9 1} \)


Which of the following animal respires but there is no respiratory organ in them?
\( A \cdot F \operatorname{rog} \)
B. Cockroach
c. Fish
D. Earthworm


A solution contains \( 10 \mathrm{mL} \) of \( 0.1 \mathrm{N} \) NaOH
and \( 10 \mathrm{mL} \) of \( 0.05 \mathrm{Na}_{2} \mathrm{SO}_{4} . \) pH of this
solution is
A. equal to 7
B. less than 7
c. greater than 7
D. zero


Consider the circuit, the current
through the Zener diode is
\( A \cdot 20 m A \)
в. \( 10 \mathrm{mA} \)
\( c .15 \mathrm{mA} \)
D. \( 40 \mathrm{mA} \)


Decreasing order of acidic strength of
different (-OH) group is:
\( \mathbf{A} \cdot w>x>y>z \)
в. \( w>z>x>y \)
\( \mathbf{c} . z>w>x>y \)
D. \( z>x>w>y \)


Half of the rectangular plate shown in figure is made of a material of density
\( p_{1} \) and other half of density \( p_{2} . \) The
length of the plate is \( L \). The distance of
centre of mass of the plate from origin
is:-


A car moving with a speed of 25 ms \( ^{-1} \) takes a U-turn in 5 seconds, without
changing its speed. The average acceleration during these 5 seconds is
\( \mathbf{A} \cdot 5 m s^{-2} \)
B. \( 10 m s^{-2} \)
c. \( 2.5 m s^{-2} \)
D. \( 7.5 \mathrm{ms}^{-2} \)


Which of the following is not regarded as antibiotic in true sense?
A. Tetracycline
B. Penicillin
c. Sulpha drugs
D. chloramphenicol


If the lines \( \frac{x-0}{1}=\frac{y+1}{2}=\frac{z-1}{-1} \) and \( \frac{x+1}{k}= \)
\( \frac{y-3}{-2}=\frac{z-2}{1} \) are at right angles, then the
value of k is
\( \mathbf{A} \cdot \mathbf{5} \)
B.
\( c \cdot 3 \)
D. -


Newton's third law of motion can be
used to explain:
A. Why the passengers in a bus tend to fall backward when its starts suddenly
B. Swimming of a man
c. Motion of a rocket
D. Both (B) and (C)


Which of the following substances turn blue litmus paper to red?
A. Lemonjuice
B. Carbonated soft drink
c. curd
D. All of the above


Which of the following is not correctly matched?
A \( \cdot P C l_{5}-s p^{3} d \) hybridisation
B . \( P C l_{3}-s p^{3} \) hybridisation
c. \( P C l_{5} \) (solid) \( -\left[P t C l_{4}\right]^{+}+\left[P t C l_{6}\right]^{-} \)
D. \( P C l_{5} \) - brownish powder


Write the negation of the following
statements:
(i) Chennai is the capital of Tamil Nadu
(ii) \( \sqrt{2} \) is not a complex number
(iii) All triangles are not equilateral triangle
(iv) The number 2 is greater than 7
(v) Every natural number is an integer


Find the square root of 0.1764
A . 0.42
B. 0.46
c. 0.48
D. 0.49


Bleaching powder reacts with excess di
acids to liberate chlorine which is
called:
A. nascent chlorine
B. available chlorine
c. active chlorine
D. atomic chlorine


If \( a^{2}, b^{2}, c^{2} \) are in A.P. then the following
are also in A.P. True or False? If true
write 1 otherwise write 0 \( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \)


If the H.C.F. of \( A \) and \( B \) is 24 and that of
\( C \) and \( D \) is \( 56, \) then the H.C.F. of \( A, B, C \)
and \( D \) is
A .4
B. 12
\( c \cdot 8 \)
D. 3


The S.I unit of specific heat capacity is


What \( \left(H_{3} O^{+}\right) \) must be maintained in a
saturated \( H_{2} S \) solution to precipitate
\( P b^{2+}, \) but not \( Z n^{2+} \) from a solution in
which each ion is present at a concentration of \( 0.01 M ? \)
\( \left(K_{s p} H_{2} S=1.1 \times 10^{-22} \) and \right.
\( \boldsymbol{K}_{s p} Z \boldsymbol{n} \boldsymbol{S}=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{2 1}} \mathbf{)} \)


Which of the following compounds are formed by the reaction of ammonia with
acids?
This question has multiple correct options
A. Calcium ammonium nitrate
B. Ammonium chloride
c. Ammonium phosphate
D. Ammonium sulphate


Which of the following represents the electronic configuration of a transition
elements?
A \( \cdot 1 s^{2}, 2 s^{2} p^{6} \dots . . n s^{2} p^{3} \)
B . \( 1 s^{2}, 2 s^{2} p^{6} \ldots . . n s^{2} p^{6} d^{3},(n+1) s^{2} \)
C \( \cdot 1 s^{2}, 2 s^{2} p^{6} \ldots n s^{2} p^{6} d^{10},(n+1) s^{2} p^{1} \)
D. \( 1 s^{2}, 2 s^{2} p^{6} \ldots . n s^{2} p^{6} \)


The chemical added to LPG to help detect its leakages is:
\( A \). isobutene
B. ethylamine
c. methyl mercaptan
D. ethyl mercaptan


\( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2} \)
In molecule (allene)
A \( \cdot \) All three \( C \) -atoms are \( s p^{2} \) hybridized
B. Both terminal C-atoms are \( s p^{2} \) hybridized while central C-atom is sp-hybridized
c. Both terminal C-atoms are sp-hybridized whilecentral C-atom is \( s p^{2} \) -hybridized
D. None of these


The coefficient of friction between the
tyres and the road is \( 0.1 . \) The maximum speed with which a cyclist can take a circular turn of radius \( 3 \mathrm{m} \) without
skidding is then (Take \( \left.g=10 m s^{-2}\right) \)
B. \( \sqrt{3} \mathrm{ms}^{-1} \)
D. \( \sqrt{10} \mathrm{ms}^{-1} \)


All mineral salts absorbed in cells are
A. Ions
B. Atoms
c. Molecule
D. All of the above


An object with a mass \( \mathrm{M} \) is suspended from an elastic spring with a spring constant k. The object oscillates with period T. If the mass of oscillations is quadrupled, how it will change the period of oscillations?
A. The period is increased by factor two
B. The period is increased by factor four
c. The period is decreased by factor two
D. The period remains the same


Simplify:
\( (7 m-8 n)^{2}+(7 m+8 n)^{2} \)
A \( \cdot 198 m^{2}+28 n^{2} \)
B. \( 98 m^{2}+128 n^{2} \)
\( \mathbf{c} .98 m+128 n \)
D. \( 98 m^{2}-128 n^{2} \)


The ratio in which the surface \( x^{2}+ \)
\( y^{2}+z^{2}=25 \) divides the line joining
(0,1,2) and (3,4,5) is \( \frac{a \pm \sqrt{b}}{c} \) then \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}= \)


The foundations of high-rise buildings are kept wide so that they may exert more pressure on the ground.
A. True
B. False


Two stones are thrown vertically upwards simultaneously with their initial velocities \( u_{1} \) and \( u_{2} \) respectively.
The heights reached by them would be in the ratio of
A \( \cdot u_{1}^{2}: u_{2}^{2} \)
в. \( u_{1}: u_{2} \)
c. \( u_{2}^{2}: u_{2}^{2} \)
D . \( u_{2}: u_{1} \)


Find the first three terms of an infinitely decreasing geometric progression whose sum is 1.6 and the second term
is \( -\mathbf{0 . 5} \)


A ball moving the velocity \( \hat{i} \) collides with a stationary wall and returns with a velocity \( \hat{j} / 2 . \) The coefficient of restitution for this collision is \( \frac{1}{K} . \) Find the value of \( \boldsymbol{K} \)


A block of sided \( 0.5 m \) is \( 30 \% \)
submerged in a liquid of density 1 gm / cc. Then find mass of an object
placed on block for complete submergence.
A . \( 87.3 k g \)
B. \( 85.3 k g \)
c. \( 82.3 k g \)
D. \( 80.3 k g \)


Bacteria and other monerans do not
possess
A. Ribosomes
B. Mitochondria
c. Plasma membrane
D. Nucleoid


Find the mean of the probability distribution.


Which one of the following has the highest fugacity?
A ' tosylate \( (\stackrel{\circ}{O T s}) \)
B. Mesylate
C. Triflate \( \left(F_{3} C-S O_{3}^{\odot}\right) \)
D. All are equal


Function of glomerulus in mammalian kidney is
A. Reabsorption of salts from the blood
B. Urine formation through blood filtration
c. Urine collection
D. All of the above


Assertion
Charge on all the condensers connected in series is the same
Reason
Capacitance of capacitor is directly proportional to charge on it
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


Empirical formula of a compound is
\( C H_{2} O . \) If its molecular weight is 180
then the molecular formula of the
compound is?
A. \( C_{6} H_{12} O_{6} \)
B. \( C_{5} H_{10} O_{5} \)
\( \mathbf{c} \cdot C_{3} H_{6} O_{3} \)
D. \( C_{4} H_{8} O_{4} \)


Find the square root of the following number by Division method.
\( \mathbf{1 3 6 9} \)


Predict the geometrical shapes of the following molecules and then predict which molecules you would expect to have resultant dipole moments (also refer to sec-dipole moments):
(a) \( \boldsymbol{S O}_{2} \)
(b) \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
(c) \( \boldsymbol{H}_{2} \boldsymbol{S} \)
\( (d) C_{2} H_{4} \)
\( (e) S F_{6} \)
(f) \( C H_{2} C l_{2} \)


Chlorine gas is passed in a medium which has \( p H=12 . \) Two products \( A \)
and \( B \) are formed with water. Now \( p H \) of
medium is changed to 1 by acidifying it Again a product \( C \) is formed with water
It is found that \( A \) is strong oxidising
agent Answer the following questions carefully: Oxidation of \( C l \) in compound \( \boldsymbol{B} \) is:
A. -1
в. +3
\( c .+5 \)
D. +7


Which is the correct assignment of
chirality at \( C 1 \) and \( C 4 \) of the following
molecule?
A \( .1 S, 4 R \)
в. \( 1 R, 4 R \)
c. \( 1 R, 4 S \)
D. \( 1 S, 4 S \)


A positive point charge q is carried from a point B to a point A in the electric field of a point charge \( +\mathrm{Q} \) held at \( 0 . \) If the
permittivity of free space is \( \epsilon_{0} \) and \( 0 A=a \) and \( 0 \mathrm{B}=\mathrm{b}, \) the work done in the process is given by :
A. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{1}{a}+\frac{1}{b}\right) \)
в. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{1}{a}-\frac{1}{b}\right) \)
c. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{1}{a^{2}}-\frac{1}{b^{2}}\right) \)
D. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{1}{a^{2}}+\frac{1}{b^{2}}\right) \)


If \( \bar{a} \) and \( \bar{b} \) are position vectors of \( A \) and
\( B \) respectively, then the position vector of a point \( C \) in \( A B \) produced such that \( \boldsymbol{A C}=\mathbf{3} \overline{\boldsymbol{A} \boldsymbol{B}} \) is
A \( .3 \bar{a}-\bar{b} \)
в. \( 3 \bar{b}-\bar{a} \)
c. \( 3 \bar{a}-2 \bar{b} \bar{b} \)
D. \( 3 \bar{b}-2 \bar{a} \bar{a} \)


Cuticle is secreted by
A. Epidermis
B. Endodermis
c. Both A and B
D. Hypodermis


State whether true or false:
A sheet of paper falls slower than one that is crumpled into a ball.
A. True
B. False


\( \boldsymbol{P b}(s)\left|\boldsymbol{P b S O}_{4}(\boldsymbol{s})\right| \boldsymbol{N a H S O}_{4}(\mathbf{0 . 6 0 0} \boldsymbol{M}) \mid \)
The voltage of the cell in \( V \) is \( E= \)
\( +0.061 V . \) Calculates \( K_{2}= \)
\( \left[\boldsymbol{H}^{+}\right]\left[\boldsymbol{S O}_{4}^{2-}\right] /\left[\boldsymbol{H} \boldsymbol{S O}_{4}^{-}\right], \) the
dissociation constant for \( \boldsymbol{H} \boldsymbol{S O}_{\mathbf{4}}^{-} \)
\( \operatorname{Given} \boldsymbol{P b}(\boldsymbol{s})+\boldsymbol{S O}_{4}^{2-} \rightarrow \boldsymbol{P b S O}_{4}+ \)
\( \mathbf{2} e^{-}\left(\boldsymbol{E}^{\circ}=\mathbf{0 . 3 5 6} \boldsymbol{V}\right), \boldsymbol{E}^{\circ}\left(\boldsymbol{P b}^{2+} / \boldsymbol{P b}\right)= \)
\( -0.126 V \)
Multiply the answer by 100 and fill in the blank. (write the value to the nearest
integer)


Different calenders for the month of
February are made so as to serve for all the coming years. The number of such calenders is
\( A \cdot 7 \)
B. 2
c. 14
D. None of these


The measurement of a compass-boxis
\( 16 c m \times 4 c m \times 2 c m, \) find the volume of
a compass-box.


Calculate the mass of \( C^{14} \) (half life \( = \)
\( 5720 \text { years }) \) atoms which give \( 3.7 \times 10^{7} \)
disintegrations per second.


What happens when
i) White phosphorous is heated with concentrated \( N a O H \) solution in an
inert atmosphere of \( \boldsymbol{C O}_{2} \)
ii) \( X e F_{6} \) undergoes partial hydrolysis.


The inherent property of all materials is
A. Diamagnetism
B. Paramagnetism
C. Ferromagnetism
D. Both a and


A closed circuit consists of a resistor \( \boldsymbol{R} \) inductor of inductance \( L \) and a source
of emf \( \boldsymbol{E} \) are connected in series. If the
inductance of the coil is abruptly
decreased to \( L / 4 \) (by removing its magnetic core), the new current immediately after this moment is :
(before decreasing the inductance the circuit is in steady state)
A. Zero
B. \( \frac{E}{R} \)
\( c \cdot 4 \frac{E}{R} \)
D. \( \frac{E}{4 B} \)


Which among these can exhibit
tautomerism?
\( \mathbf{a} \)
\( \mathbf{b} \)
\( \mathbf{c} \)
A. \( a \) only
B. \( b \) only
c. \( c \) only
D. \( a \) and \( c \)


The diameter of a solid metallic sphere
is equal to the inner diameter of a hollow metallic sphere. If inner diameter
of hollow sphere is two thirds of its outer diameter. Both the spheres are
made of same metal. If an equal
amount of heat is supplied the both the spheres. Find the ratio of increase in
temperature of the solid sphere to that of the hollow one?


Which of the following statement is
false?
A. Ethanoic acid is also called glacial acetic acid
B. In comparison of mineral acids carboxylic acids are weak acids
C. In comparison of mineral acids carboxylic acids are strong acids
D. Pure ethanoic acid often freeze in cold climates


Which law of thermodynamics states that energy can neither be created nor be destroyed, it can change from one to another?
A. First law
B. Second law
c. zero law
D. None of these


How many NAND gates are required to form an AND gate?
A . 1
B. 2
\( c \cdot 3 \)
\( D \)


The probability of an impossible event
is
A .
B. 0
c. less than 0
D. greater than 1


Mac Arthur process is used for the extraction of
\( A \cdot A l \)
B. Agg
\( c \cdot c u \)
D. zn


Madan purchases a compact computer system for Rs. 47,700 which includes
\( 10 \% \) rebate on the marked price and then \( 6 \% \) Sales Tax on the remaining price. Find the marked price of the
computer.


A step-down transformer with an efficiency of \( 80 \% \) is used on a 1000 v line to deliver \( 10 \mathrm{A} \) at \( 100 \mathrm{V} \) at the
secondary coil. The Current drawn from the line is
A . \( 1.5 \mathrm{A} \)
B. 2 A
\( c \cdot 3 A \)
D. 1.25 A
E. 1 A


If all the three altitudes of a triangle are equal, the triangle is equilateral. State whether the above statement is
true or false.
A. True
B. False


An acid base indicator has \( \boldsymbol{K} \boldsymbol{a}= \)
\( 3 x 10^{-5} \) The acid form of indicator is red
and the basic form of indicator is blue.
By how much must the pH change in order to change the indicator from \( 75 \% \) red to 75\% blue?
A \( \cdot 7.91 \times 10^{-5} \)
B. 0.95
c. \( 5 x 10^{23} \)
D.


Define linear charge density. Mention its \( S I \) unit.


The magnetic flux through the cross-
section of the toroidal solenoid is
A \( \cdot \frac{\mu_{0} N i h}{2 \pi} \)
В. \( \frac{\mu_{0} N i h(b-a)}{2 \pi r} \)
c. \( \frac{\mu_{0} N i h}{2 \pi} \log _{e} \frac{b}{a} \)
D. \( \frac{\mu_{0} N^{2} i h}{2 \pi} \log _{e} \frac{a}{b} \)


Select the incorrect match.
A. Morels and truffles - Phycomycetes
B. Puffballs and toad stools - Basidiomycetes
C. Early blight of potato - Alternaria solani
D. Late blight of potato - Phytophthora infestans


Which of the following chemical can be added for sweetening of food items at cooking temperature and does not provide calories?
A. sucrose
B. Glucose
c. Aspartame
D. sucralose


(t)-Sucrose has a specific rotation of \( +66.5, \) while \( D-(+) \) -glucose and \( D-(-) \) fructose have specific rotations of +52.5 and -92.4 respectively. After complete hydrolysis of (+)-sucrose by dilute acid, the specific rotation of the hydrolysis
product, called invert sugar [a 1: 1 mixture of \( \mathrm{D}-(+)-\mathrm{g} \) lucose and \( \mathrm{D}-(-) \) fructose] is \( -x \)
the nearest integer value of \( x \) is:


Find 9 th term of the \( A . P \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{9}{4} \)


Find the value of \( \tan \left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right) \)


in the magnetic meridian of a place, the horizontal component of the earth's magnetic field is 0.26 and the dip angle
is 60 and the dip angle is 60 What is the magnetic field of the earth at this location?


What will happen if the pH of the
solution of \( 0.001 \mathrm{M} M g\left(N O_{3}\right)_{2} \) solution
is adjusted to \( \boldsymbol{p} \boldsymbol{H}=\mathbf{9} ? \)
\( \left[\text { Given that }: \boldsymbol{K}_{s p} \text { of } M g(\boldsymbol{O} \boldsymbol{H})_{2}=\mathbf{8 . 9} \times\right. \)
\( \mathbf{1 0}^{-12} \) )
A. ppt will take place
B. ppt will not take place
c. solution will be saturated
D. none of the above


During blood transfusion the needle is inserted in a vein where the gauge
pressure is 2000 Pa. At what height must the blood container be placed so that blood mayjust enter the vein? [Density of whole blood \( =1.06 \times \) \( \left.10^{3} k g m^{-3}\right] \)


A body moves a distance of \( 10 \mathrm{m} \) long a straight line under the action of force of
5N. If the work done is 25 joules, the angle which the force makes with the
direction of motion of the body is:
A . \( 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A cell \( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+} \| \boldsymbol{A} \boldsymbol{g}^{\oplus}\right| \boldsymbol{A} \boldsymbol{g} \) initially
contains \( 2 \mathrm{M} A g^{\oplus} \) and \( 2 \mathrm{M} C u^{2+} \) ions in
1 L solution each. The change in cell
potential after it has supplied 1 1 current for 96500 s is :
\( \mathbf{A} \cdot-0.003 V \)
в. \( -0.02 V \)
c. \( -0.04 V \)
D. None of these


A rope ladder of length L is attached to a balloon of mass \( \mathrm{M} \). As the man of mass
m climbs the ladder into the balloon
basket, the balloon comes down by a
vertical distance s. Then the increase in
potential energy of man divided by the increase in potential energy of balloon
is
A \( \cdot \frac{L-s}{s} \)
B. \( \underline{L} \)
c. \( \frac{s}{L-s} \)
D. L- s


A coin is tossed and a single 6 -sided die is rolled. Find the probability of landing on the tail side of the coin and rolling 4
on the die.
A \( \cdot \frac{1}{12} \)
в. \( \frac{6}{5} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{4} \)


Allyl bromide is:
\( \mathbf{A} \cdot C H_{2}=C H-C H_{2}-B r \)
B \( \cdot C H_{2}=C H_{2}-B r \)
\( \mathbf{c} \cdot C H_{3}-C H=C H-B r \)
\( \mathbf{D} \cdot C H_{3}-C H_{2}-C H_{2}-B r \)


What do you mean by degenerate orbitals? Give examples.


What is the nature of the 2 strands of a
DNA duplex?
A. Identical \& Complimentary
B. Antiparallel \& complimentary
c. Dissimilar \& non complimentary
D. Antiparallel \& non complimentary


Multiple of fine structure of spectral
lines is due to:
A. presence of main energy levels
B. presence of sub-level
c. presence of electronic configuration
D. is not a characteristics of the atom.


Angles \( Q \) and \( R \) of a \( \Delta P Q R \) are \( 25^{\circ} \) and
\( 65^{\circ} . \) Write which of the following is true:
1. \( \boldsymbol{P Q}^{2}+\boldsymbol{Q} \boldsymbol{R}^{2}=\boldsymbol{R} \boldsymbol{P}^{2} \)
2. \( \boldsymbol{P Q}^{\mathbf{2}}+\boldsymbol{R} \boldsymbol{P}^{2}=\boldsymbol{Q} \boldsymbol{R}^{2} \)
3. \( \boldsymbol{R} \boldsymbol{P}^{2}+\boldsymbol{Q} \boldsymbol{R}^{2}=\boldsymbol{P} \boldsymbol{Q}^{2} \)


Which site of a tRNA molecule forms
hydrogen bonds with mRNA molecule?
A. codon
B. Anticodon
c. \( 5^{\prime} \) end of the t-RNA molecule
D. \( 3^{\prime} \) end of the t-RNA molecul


Any oscillation in which the amplitude of the oscillating quantity decreases with time is termed as
A. Damped oscillation
B. Free oscillation
c. Depletion oscillation
D. None of these


The placentation in a multilocular ovary
with ovules borne over the entire inner
surface is called as
A . Basal
B. Marginal
c. superficial
D. Free central


Which of the following metals were used as money in ancient times?
A. Gold
B. Copper
c. Iron
D. All of the above


What do \( A, B, C \) and D represent in the
following figure?
A. A : Carrier protein, B : symport, C : uniport, D : antiport
B. A : Carrier protein, B : uniport C : antiport, D : symport
C. A : Carrier protein, B : antiport, C : symport, D : uniport
D. A : Carrier protein, B : uniport, C : symport, D : antiport


Formula of calcium hypochlorite is:
A \( \cdot C O C l_{2} \)
в. \( C a(C l O)_{2} \)
c. \( c a\left(C l O_{3}\right)_{2} \)
D \( \cdot \operatorname{ca}\left(C l O_{4}\right)_{2} \)


Heat produced in a resistor when current is passed through it depends
upon-
A. Current only
B. Time only
c. Current and time
D. None of these


Lanthanoid contraction occurs because:
A. the \( 4 f \) electrons, which are gradually added, create a strong shielding effect
B. the \( 4 f \) orbitals are greater in size than the \( 3 d \) and \( 3 f \) orbitals
C. the \( 5 f \) orbitals strongly penetrate into the \( 4 f \) orbitals
D. the poor shielding effect of \( 4 f \) electrons is coupled with the increased attraction between the nucleus and
the added electrons


Fill in the blank.
When a sound wave, travelling in a medium bounces back to the same
medium after striking the same second medium then
A. reflection
B. refraction
c. diffraction
D. scattering


Let the equation of the plane through the intersection of the planes \( x+2 y+ \)
\( \mathbf{3} \boldsymbol{z}-\mathbf{4}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{z}+\mathbf{5}=\mathbf{0} \) and
perpendicular to the plane \( 5 x+3 y+ \)
\( \mathbf{6} z+\mathbf{8}=\mathbf{0} \) be \( \boldsymbol{k} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{y}+\boldsymbol{m} \boldsymbol{z}+\mathbf{1 7 3}= \)
0. Find \( k+m \)


Find the ratio in which \( 2 x+3 y+5 z= \)
1 divides the line joining the points
(1,0,-3) and (1,-5,7)
A .1: 2
B . 2: 1
c. 3: 2
D. 2: 3


The vessel shown in the figure has two
sections of area of cross section \( \boldsymbol{A}_{1} \) and
\( A_{2} \cdot A \) liquid of density \( \rho \) fills both the
section upto a height \( h \) in each.
Consider atmospheric pressure \( P_{0} \) also.
Find
(a) the pressure at the base of vessel
(b) the force exerted by the liquid on the
base of the vessel
(c) the downward force exerted by the
walls of the vessel at the level \( B \)


The refractive idea of glass is \( 3 / 2 \) velocity of light in glass would
be


If \( 10^{-17} \) J of light energy is needed by the interior of the human eye to see an
object. The photons of green light needed to see the object are:
\( [\boldsymbol{\lambda}=\mathbf{5 5 0 n m}] \)
A .27
B . 28
c. 29
D. 30


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{x}+\boldsymbol{y}^{2}=\log \boldsymbol{y}+\boldsymbol{x}^{2} \)


Name the important ore of silver. Write
all the steps and reactions involved in the Cyanide process for the extraction of silver from its ore.


For a particle performing linear S.H.M. Its average speed over one oscillation is \( (a=a m p l i t u d e \text { of } S . H . M, n= \) frequency of oscillation)
A . \( 2 a n \)
B. 4an
c. \( 6 a n \)
D. \( 8 a n \)


Albuminous cells occur in
A. Xylem
B. Phloem
c. cortex
D. conjunctive parenchyma


Which of the given metal oxides is
having minimum thermal
decomposition temperature?
A. Cao
B. FeO
\( c . \) Pbo
D. MgO


Progesterone is secreted by:
A. Thyroid
B. ovaries
c. Adrenal
D. Testes


The tangent to the circle \( x^{2}+y^{2}=9 \)
which is parallel to y-axis and does not lie in third quadrant, touches the circle
at the point
A. (-3,0)
B. (3,0)
D. (0,-3)


Two objects rest on a seesaw. The first
object has a mass of \( 3 \mathrm{kg} \) and rests 10
\( m \) from the pivot. The other rests \( 1 \mathrm{m} \)
from the pivot. What is the mass of the
second object if the seesaw is in equilibrium?
\( A \cdot 0.3 \mathrm{kg} \)
B. 3 kg
\( c \cdot 10 \mathrm{kg} \)
D. 30 kg
E. \( 50 \mathrm{kg} \)


The aviation fuel used in the engines of jet airplanes is:
A. cNG
B. Petrol
c. Kerosene
D. Diesel


The minimum value of the sum of real
numbers \( a^{-5}, a^{-4}, 3 a^{-3}, 1, a^{8} \) and \( a^{10} \)
with \( a>0 \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 8
D.


The deflection in a moving coil galvanometer falls from 50 divisions to
10 divisions when a shunt of \( 20 \Omega \) is
connected with it. The resistance of
galvanometer coil is?
A . \( 48 \Omega \)
B . \( 50 \Omega \)
\( \mathbf{c} .52 \Omega \)
D. \( 30 \Omega \)


Which one of the following oxides dissolves in sulphuric acid as well as in sodium hydroxide?
A. \( C a O \)
в. \( C O_{2} \)
\( c . Z n O \)
D. \( B a O_{2} \)


Fast neutrons can easily be slowed down by:
A. The use of lead shield
B. Passing them through heavy water
c. Elastic collision with heavy nucleus
D. Applying a strong electric field


Find the lengths of the arcs cut off from
a circle of radius \( 12 \mathrm{cm} \) by a chord 12 cm long. Also, find the area of the minor
segment. \( [\text {Take } \pi=\mathbf{3 . 1 4} \text { and } \sqrt{\mathbf{3}}=\mathbf{1 . 7 3} \)


n fig, chord \( A B \| C D \) of a circle
with centre \( O \) and radius 5 cm such
that \( A B=6 \mathrm{cm} \) and \( C D=8 \mathrm{cm} . \) if \( O P \)
\( \perp A B, O Q . \perp C D, \) then \( P Q \) in cm is
\( \mathbf{A} \cdot 4 \mathrm{cm} \)
\( \mathbf{B} \cdot 7 \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
D. \( 3 \mathrm{cm} \)


Observe the given adsorption isotherm carefully and choose the correct option.
(i) These curves indicate that at a fixed
temperature, there is a decrease in physical adsorption with increase in
pressure.
(ii) These curves always seem to approach saturation at high pressure.
(iii) \( \frac{x}{m}=k p^{1 / n}(n>1) \) is generally represented by this isotherm.
(iv) These curves indicate that at a fixed pressure, there is a decrease in physcial adsorption with increase in temperature
A. (i) and (iii) only
B. (ii) and (iv) only
\( c \)
D. All of these


Clinostat is connected with
A. Thigmotropism
B. Turgor changes
c. Measurement of stomatal pores
D. Geotropism


The maximum emf induced in the coil
will be
\( A \)
\( ^{\text {В } \cdot} \frac{\pi^{2} N B_{0}\left(a^{2}+a b+b^{2}\right)}{T} \)
\( c \)
\( D \)


Assertion
STATEMENT-1: If the mass of the
colliding particles remains constant, then the linear velocity of the individual particles change during collision along common normal direction.
Reason
STATEMENT-2: A pair of equal and
opposite impulses act along common normal direction.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
B. Both statements 1 and 2 are true but statement 2 is not correct explanation of statement 1
c. Statement 1 is true but statement 2 is false
D. Statement-1 is False, Statement-2 is True


If the area of a material is \( 4 m^{2} \) and
Iength \( 20 m . \) What will be the resistivity of that material when its resistance is
\( \mathbf{1 0 \Omega} ? \)
A. 12 mho
B. 20 mho
c. 4 mho
D. 2 mho


The difference(s) between mRNA and
tRNA is/are that:
(i) mRNA has more elaborate 3
dimensional structure due to extensive
base - pairing
(ii) tRNA has more elaborate \( 3- \)
dimensional structure due to extensive
pairing
(iii) tRNA is usually smaller than mRNA
(iv) mRNA bears anticodon but tRNA
has codons
A. (i) and (iii)
B. All of these
c. (ii) and (iii)
D. (i), (ii) and (iii)


Two spherical balls of the same radius but of different masses, are dropped at the same time from the top of a tower
19.6m high. When they are \( 1.6 \mathrm{m} \) above the ground, the balls will possess the
same
A. K.E.
B. P.E.
c. momentum
D. total energy


Draw the circuit diagram of full-wave rectifier using two p-njunction diodes and explain its working. Show the input
and output waveforms.


In Hydra, asexual reproduction takes
place by
A. Fragmentation
B. Budding
c. Binary fission
D. Spore-formation


Which of the following electromagnetic wave is used in high precision application like LASIK eye surgery?
A. Microwave
B. Ultraviolet rays
c. Gamma rays
D. X-rays


Trachea is lined with incomplete rings
of
A. Fibrous cartilage
B. Calcified cartilage
c. Elastic cartilage
D. Hyaline cartilage


Conifers are related to
A. Match industry
B. Paper industry
C. Timber industry
D. All of the above


What is the far point of a person suffering from myopia (or short sightedness)?


For a new scale of temperature called
\( P \) scale (which is linear and total
division of the new scale is 200 ) the
freezing and boiling points of water are
\( 25^{\circ} P \) and \( 225^{\circ} P \) respectively. Then the
temperature on new scale
corresponding to \( 25^{\circ} \mathrm{C} \) on the celsius
scale is :
в. \( 75^{\circ} P \)
c. \( 50^{\circ} P \)
D \( .275^{\circ} \mathrm{P} \)


For what value of \( k \) will \( x^{2}- \)
\( (3 k-1) x+2 k^{2}+2 k=11 \) have equal
roots?
\( \mathbf{A} \cdot 9,-5 \)
В. -9,5
\( c .9,5 \)
D. -9,-5


While doing any experiment, there will be a possible outcome which is called
A. An impossible event
B. A sure event
c. An exhaustive event
D. A complementary event


Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3} \) sol is :
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)


A block of mass 5 kg is lying on a rough horizontal surface. The coefficient of
static and kinetic friction are 0.3 and
0.1 and \( g=10 m s^{-2} . \) The frictional force
on the block is?
A . \( 25 \mathrm{N} \)
B. 15N
c. 10 N
D. zero


If \( \left(1+x^{2}\right) \frac{d y}{d x}=x(1-y), y(0)=\frac{4}{3} \)
then the value of \( y(\sqrt{8})+\frac{8}{9} i s \)
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D.


Identify the intensive quantities from the following. This question has multiple correct options
A. enthalpy
B. temperature
c. volume
D. refractive index


The circumference of a circular garden
is \( 572 m . \) Outside the garden a road,
\( 3.5 m \) wide, runs around it.Calculate the
\( \operatorname{cost} \) of repairing the road at the rate of Rs.375per 100.sq.m?


What amount of sodium propanoate should be added to one litre of an
aqueous solution containing 0.02 mole
of propanoic acid \( \left[\boldsymbol{K} \boldsymbol{a}=\mathbf{1 . 3 4} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{a t}\right. \)
\( \left.25^{\circ} \mathrm{C}\right] \) to obtain a buffer solution of \( \mathrm{pH} \)
4.75
A \( \cdot 4.52 \times 10^{-2} \) м
В. \( 3.52 \times 10^{-2} \) м
c. \( 2.52 \times 10^{-2} \) м
D. \( 1.52 \times 10^{-2} \) м


fan electron is moving with velocity
\( \mathbf{5 0 0 m s}^{-1}, \) which is accurate up to 0.005
\( \% \) then calculate uncertainty in its position.
\( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J}-\boldsymbol{s}, \quad \boldsymbol{m a s s}\right. \)


To avoid slipping while walking on ice, one should take smaller steps because:
A. frictional force of ice is large
B. of larger normal reaction
c. frictional force of ice is small
D. of smaller normal reaction


\( N \) similar slabs of cubical shape of
edge \( b \) are lying on ground. Density of material of slab is \( \rho . \) Work done to arrange them one over the other is
A \( \cdot\left(N^{2}-1\right) b^{3} \rho g \)
B. \( (N-1) b^{4} \rho g \)
c. \( \frac{1}{2}\left(N^{2}-N\right) b^{4} \rho g \)
D. \( \left(N^{2}-N\right) b^{4} \rho g \)


Let \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{x} \\ \boldsymbol{x}^{2} & \boldsymbol{x} & \boldsymbol{6} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{6}\end{array}\right|=\boldsymbol{a} \boldsymbol{x}^{4}+\boldsymbol{b} \boldsymbol{x}^{3}+\boldsymbol{c} \boldsymbol{x}^{2}+ \)
\( d x+e, \) then the value of \( 5 a+4 b+3 c+ \)
\( 2 d+e \) is
equal to
A.
B. 16
\( c .-16 \)
D. - -


Anti-nodal curves represent the points joining:
A. destructive interference
B. constructive interference
c. equal phase curves
D. equal pressure curves
E. zero pressure curves


The value of \( \sum_{k=0}^{n}\left(i^{k}+i^{k+1}\right), \) where
\( i^{2}=-1, \) is equal to :
\( \mathbf{A} \cdot i-i^{n} \)
B. \( -i+i^{n+1} \)
c. \( i-i^{n+1} \)
D. \( i-i^{n+2} \)
E \( .-i-i^{n} \)


Let \( \ell, r, c \) and \( v \) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \( \frac{\ell}{r c v} \) is
SI units will be:
A. \( [L T A] \)
B . \( \left[L A^{-2}\right] \)
\( \mathbf{c} \cdot\left[A^{-1}\right] \)
D \cdot \( \left[L T^{2}\right] \)


If \( f(x)=\frac{x-1}{x+2}, \) then \( \frac{d f^{-1}(x)}{d x} \) is equal
to
A \( \cdot \frac{1}{(1-x)^{2}} \)
B. \( \frac{-3}{(1-x)^{2}} \)
c. \( \frac{3}{(1-x)^{2}} \)
D. \( \frac{-1}{(1-x)^{2}} \)


Vegetative propagation through budding occurs in
A. Rose
B. Agave
c. Yeast.
D. Ginger.


Sita practiced piano for 2 hrs everyday during the month of January. How many hrs did she practice in January? (Use bar model for solving the sum)


Mercury boils at \( 356^{\circ} \mathrm{C} \). However mercury thermometers are made such
that they can measure temperatures up to \( 500^{\circ} \mathrm{C} \). This is done by :
A. maintaining vacuum above the mercury column in the steam of the thermometer
B. filling nitrogen gas at high pressure above the mercury column
C. filling nitrogen gas at low pressure above the mercury column
D. filling oxygen gas at high pressure above the mercury column


How much heat energy is gained when 5
kg of water at \( 20^{\circ} \mathrm{C} \) is brought to its boiling point?
A . 1680 K
в. 1700 кл
c. 1720 KJ
D. 1740 KJ


Which of the following is correct IUPAC
name for \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{C r}(\boldsymbol{C} \boldsymbol{N})_{2} \boldsymbol{O}_{2}(\boldsymbol{O})_{2} \boldsymbol{N} \boldsymbol{H}_{3}\right] ? \)
A. Potassium amminecyanoperoxodioxochromatic(IV)
B. Potassium amminecyanoperoxodioxochromium(V)
c. Potassium amminecyanoperoxodioxochromium(VI)
D. Potassium amminedicyanodioxoperoxochromate(VI)


What do you understand by cell cycle?


Convert \( [1 \quad-12 \)
3] into an identity
matrix by suitable row transformations.


How will you represent a resistance of \( 4500 \pm 10 \% \) using color code?


Say true or false.
\( x^{2}+6=5 x, \) then \( x=3 \) or \( x=2 \)
A. True
B. False


\( \int_{0}^{\pi} x f(\sin x) d x \) is equal to
\( \mathbf{A} \cdot \pi \int_{0}^{x} f(\cos x) d x \)
\( \mathbf{B} \cdot \pi \int_{0}^{x} f(\sin x) d x \)
\( ^{\mathbf{C}} \cdot \frac{\pi}{2} \int_{0}^{x / 2} f(\sin x) d x \)
D \( \cdot \pi \int_{0}^{\pi / 2} f(\cos x) d x \)


Different proportions of oxygen in the various oxides of nitrogen prove the law of:
A. equivalent proportions
B. multiple proportions
c. constant proportions
D. conservation of matter


Metals often react with non-metals to
form:
A. covalent bond
B. ionic bond
C. they do not react with each other at all
D. Both \( A \) and \( B \)


In a circular coil (1) of radius \( \boldsymbol{R} \), current
\( I \) is flowing and in another coil (2) of
radius \( 2 R \) a current \( 2 I \) is flowing, then the ratio of the magnetic fields produced by the two coils is
A . 1:
B. 2:
c. 1: 2
D. 3:


Hydrogen atom emits blue light when it jumps from \( n=4 \) energy level to the \( n= \) 2 level. Which colour of light would the atom emit when it changes from the \( n= \) 5 level to the \( n=2 \) level?
A . Red
B. Yellow
c. Green
D. Violet


From which of the following part of the turmeric plant (Curcuma longa), turmeric powder is obtained?
A. seed
B. Dried rhizome
c. Dried root
D. Dried fruit


Read the given statements and select
the correct option.
Statement 1: Glycolysis occurs in mitochondrial matrix.
Statement 2: Kerbs' cycle occurs on
cristae of mitochondria.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 incorrect
c. statement 1 is incorrect but statement 2 correct
D. Both statements 1 and 2 are incorrect


The compund \( X \) is :
A. chlorobenzene
B. m-dichloro benzene
C. benzene hexachloride
D. p- dichlorobenzene


Very short answer type. Mention the most significant role of neutrophils.


What is a commutator?
A. A device that reverses the direction of flow of current through a circuit is called a commutator.
B. A device that flows in the direction of flow of current through a circuit is called a commutator
C. A device that reverses the direction of flow of voltage through a circuit is called a commutator.
D. All


For detecting the
light
A. The photodiode has to be forward biased
B. The photodiode has to be reversed biased
C. The LED has to connected in forward bias mode
D. The LED has to be connected in reverse bias mode


Draw a neat and labelled diagram of
lead storage battery.


The impression of an image on the brain for one-sixteenth of a second is
called


Calculate the compound interest on Rs. 18,000 in 2 years at \( 15 \% \) per annum.


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}-\boldsymbol{3}, \quad \boldsymbol{x}<\mathbf{0} \\ \boldsymbol{x}^{2}-\mathbf{3} \boldsymbol{x}+\mathbf{2}, \quad \boldsymbol{x} \geq \mathbf{0}\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})|, \) then \( \boldsymbol{g}(\boldsymbol{x}) \) is
This question has multiple correct options
A . continuous is \( R-\{0\} \)
B. Continuous in \( R \)
C . Differentiable in \( R-\{0,1,2\} \)
D. Differentiable in \( R-\{1,2\} \)


If \( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x=A x+b \ln \left(9 e^{2 x}-\right. \)
4) \( +C ; \) then; value of \( A, B, \& C \) are
A \( \cdot A=-\frac{3}{2}, B=\frac{35}{36}, C \varepsilon R \)
в. \( A=\frac{3}{2}, B=\frac{-35}{36}, C \varepsilon R \)
c. \( A=-\frac{3}{2}, B=\frac{35}{36}, C>0 \)
D. None of these


The atoms in a molecule do not remain
stationary. They vibrate around their mean position, by stretching or bending out of plane. We gain useful knowledge about these vibrations and the energy
they carry by studying:
A. \( X \) -ray spectra
B. ultraviolet spectra
c. infrared spectra
D. visible spectra


\( \boldsymbol{O} \) is the centre of the circle having
radius \( 5 \mathrm{cm} . A B \) and \( A C \) are two chords
such that \( A B=A C=6 \mathrm{cm} . \) If \( 0 \mathrm{A} \)
meets \( B C \) at \( M, \) then \( O M \) is equal to
A . \( 3.6 \mathrm{cm} \)
B. \( 1.4 \mathrm{cm} \)
\( c \cdot 2 c m \)
\( 0.3 \mathrm{cm} \)


A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor. It's capacitance will:
A. Increase
B. Decrease
c. Remains the same
D. Becomes infinite


A solid ball of mass \( \mathrm{m} \) is made to fall
form a height \( \mathrm{H} \) on a pan suspended through a spring of spring constant \( \mathrm{K} \) as shown in figure. if the ball does not rebound and the pan is mass less, then
amplitude of oscillation is
\( A \cdot \frac{m g}{K} \)
\( ^{\mathrm{B}} \cdot \frac{m g}{K}\left(1+\frac{2 H K}{m g}\right)^{1 / 2} \)
\( ^{\mathrm{c}} \frac{m g}{K}+\left(\frac{2 H K}{m g}\right)^{1 / 2} \)
\( ^{\mathrm{D}} \cdot \frac{m g}{K}\left[1+\left(1+\frac{2 H K}{m g}\right)^{1 / 2}\right] \)


The diagram below shows an aquarium with four typical optical devices submerged in some liquid that has a higher index of refraction than glass.
Each optical device is labeled.
Which of the optical devices will converge light when submerged in this liquid?
A. The concave mirror and the convex lens
B. The convex mirror and the concave lens
c. The concave mirror and the concave lens
D. The convex mirror and the convex lens
E. All of the pictured optical devices converge light under water


To obtain \( 3 \mu F \) capacity from three
capacitors of \( 2 \mu F \) each, they will be
arranged as follows:
A. all the three in series
B. all the three in parallel
C. two capacitors in series and the third in parallel with the combination of first two
D. two capacitors in parallel and the third in series with the combination of first two


Solve the following inequation, write the
solution set and represent it on the
number line. \( -3(x-7) \geq 15-7 x>\frac{x+1}{3}, x \in R \)


If \( \int \frac{\boldsymbol{d x}}{\boldsymbol{a} e^{m x}+\boldsymbol{b} e^{-\boldsymbol{m} \boldsymbol{x}}}= \)
\( K \tan ^{-1}\left(P e^{m x}\right)+C, \) then \( K, P= \)
\( ^{\mathbf{A}} \cdot_{K}=\frac{1}{\sqrt{a b}}, P=\sqrt{\frac{a}{b}} \)
B. \( K=\frac{1}{m \sqrt{a b}}, P=\sqrt{\frac{a}{b}} \)
\( ^{\mathbf{c}} \cdot_{K}=m \sqrt{a b}, P=\sqrt{\frac{b}{a}} \)
D. \( \quad K=\frac{1}{m \sqrt{a b}}, P=\sqrt{\frac{b}{a}} \)


Write five rational numbers which are
smaller than 2


Why antihistamines do not affect the
secretion of acid in stomach?


Solve \( \left[\left(\frac{-2}{3}\right)^{4} \times\left(\frac{-2}{3}\right)^{2} \div\left(\frac{4}{9}\right)^{3}\right] \)


In cold water, bleaching powder ionises to form :
A. \( \mathrm{Ca}^{2+}, \mathrm{Cl}^{-} \) and \( \mathrm{OCl}^{-} \)
в. \( \mathrm{CaO}, \mathrm{Cl}^{-} \)
c. \( \mathrm{Ca}^{2+}, \mathrm{Cl}^{-} \) and \( \mathrm{ClO}_{3} \)
D. \( \mathrm{Ca}^{2+}, \mathrm{Cl}^{-} \) and \( \mathrm{ClO}_{2}^{-} \)


Mark the incorrect statement regarding
mirror formula
A. Values of known and unknown parameters can be used with their proper signs
B. Sign of unknown parameter comes of its own after calculation
c. Mirror formula is applicable for both concave and convex mirrors
D. All


Each of the two platinum electrodes having area 64 mm of a conductivity
cell are separated by 8 mm. The resistance of the cell containing \( 7.5 \times \) \( \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \boldsymbol{K} \boldsymbol{C l} \) solution at \( \mathbf{2 9 8} \boldsymbol{K} \) is
1250 ohm. Calculate :
(i) Cell constant
(ii) Conductivity and
(iii) Molar conductivity


For the hypothetical reactions, the equilibrium constant (K) values are given:
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{K}_{1}=\mathbf{2} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{2}=\mathbf{4} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D} ; \boldsymbol{K}_{3}=\boldsymbol{3} \)
The equilibrium constant (K) for the
reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A. 48
B. 6
\( c \cdot 24 \)
D. 12


Silicon has 4 electrons in the outermost
orbit. In forming the bonds:
A . it gains electrons
B. it loses electrons
c. it shares electrons
D. it donates electron pair


A rod of mass \( M \) and length \( L \) is placed
on a horizontal plane with one end hinged about the vertical axis. horizontal force of \( \boldsymbol{F}=\frac{\boldsymbol{m} \boldsymbol{g}}{\mathbf{3}} \) is applied
\( \boldsymbol{L} \)
at a distance \( \frac{-}{3} \) from the hinged end.
The angular acceleration of the rod will
be:-


Chlorine is in +1 oxidation state in:
A. нс
B. \( \mathrm{HClO}_{4} \)
c. \( A \& B \) both
D. none of these


Explain the term with example:
Alkane


A car acquires a velocity of \( 72 \mathrm{kmh}^{-1} \) in 10 s starting from rest. Calculate the
acceleration.
A. \( 7.2 m s^{-2} \)
B. \( 20 m s^{-2} \)
c. \( 200 m s^{-2} \)
D. \( 2 m s^{-2} \)


\( \frac{d\left(x^{n}\right)}{d x}=? \)
A \( \cdot n x^{n-1} \)
В . \( n x^{n} \)
c. \( (n-1) x^{n-1} \)
D. \( (n-1) x^{n} \)


The molar conductance at infinite
dilution of \( A g N O_{3}, A g C l \) and \( N a C l \)
are 116.5,121.6 and 110.3 respectively.
The molar conductance of \( N a N O_{3} \) is:
\( \mathbf{A} \cdot 111.4 \)
B. 105.2
c. 130.6
D. 150.2


To aqueous solution of Nal, increasing
amounts of solid \( H g I_{2} \) is added. The
vapor pressure of the solution-
A. Decreases to a constant value.
B. Increases to a constant value
c. Increases first and then decreases.
D. Remains constant because \( H g I_{2} \) is sparingly soluble in water.


According to Le-Chatelier's principle, adding heat to a solid and liquid in equilibrium
A. temperature to increase
B. temperature to decrease
c. amount of liquid to decrease
D. amount of solid to decrease


The correct rate of reaction of given
compounds towards electrophilic
aromatic substitution reaction is:
A \( \cdot(b)>(d)>(a)>(c) \)
B. \( (b)>(a)>(d)>(c) \)
C. \( (c)>(a)>(d)>(b) \)
D. \( (a)>(b)>(d)>(c) \)


Write the equations involved in the
manufacture of nitric acid by Ostwald's
process by maintaining reaction conditions


Name one unit of time bigger than a
second.
A. plank time
B. zeptosecond
c. picosecond
D. kilosecond


When excited electrons cascade to
lower energy levels in an atom then:
A. visible light is always emitted
B. the potential energy of the atom increases
C. the electrons always fall back to the first energy level
D. the electron fall indiscriminately to all levels
E. the electrons fall back to a lower unfilled energy level


Saloni took a piece of burning charcoal
and collected the gas evolved in a test
tube
(a) How will she find the nature of the
gas?
(b) Write down word equation of all the reactions taking place in this process.


If \( L_{1} L_{2} \) is the latusrectum of \( y^{2}=12 x \)
\( P \) is any point on the directrix then the
\( \operatorname{area~of} \Delta P L_{1} L_{2}= \)
\( A \cdot 32 \)
B . 18
\( c .36 \)
D. 16


Two identical beakers with negligible thermal expansion are filled with water
to the same level at \( 4^{\circ} \mathrm{C} \). If one say A is
heated while the other one is cooled, then:
This question has multiple correct options
A. water level in A must rise
B. water level in B must rise
c. water level in A must fall
D. water level in Bmust fall


What is the Sl unit of heat capacity of body?
A. \( J / K \)
в. \( J K \)
\( c . J \)
D. \( ^{\circ} C \)


If one of the diagonals of a square is along the line \( 4 x=2 y \) and one of its
vertices is \( (3,0), \) then its side through this vertex nearer to the origin is given by the equation.
A. \( y-3 x+9=0 \)
В. \( 3 y+x-3=0 \)
c. \( x-3 y-3=0 \)
D. \( 3 x+y-9=0 \)


A yellow curry stain on a white shirt turns red when it is washed with soap.
Explain why?


Find the cube root of 27000 by prime factorisation method.


To overcome the effect weightlessness
in an artificial satellite
A. the satellite is rotated around its axis with
compartment of astronaut at the centre of the satellite.
B. the satellite is shaped like wheel.
C. the satellite is rotated around and around till weightlessness disappears.
D. the compartment of astronaut is kept on the periphery of rotating wheel like satellite.


For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g) \) The equilibrium constant \( K_{p} \)
changes with:
A. Total pressure
B. Catalyst
C. The amounts of \( H_{2} \) and \( I_{2} \) present
D. Temperature


Assertion
Semiconductors are solids with
conductivities in the intermediate
range from \( 10^{-6}-10^{4} \) ohm \( ^{-1} m^{-1} \)
Reason
Intermediate conductivity in
semiconductor is due to partially filled
valence band.
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


Refractive indices of water and glass
are \( 4 / 3 \) and \( 3 / 2 \) respectively. A ray of light travelling in water is incident on
the water-glass interface at \( 30^{0} \) Calculate the sine of angle of refraction.
A . 0.460
B. 0.585
c. 0.444
D. 0.623


A mixture of minerals in the earth's
crust from which it is profitable to extract a metal is called:
A . ore
B. allotrophe
c. alloy
D. all of these


The glancing angle of incidence is \( 10^{\circ} \) What will be the glancing angle of reflection?
A \( .10^{\circ} \)
B. \( 80^{\circ} \)
c. \( 170^{\circ} \)
D. \( 60^{\circ} \)


Charges are placed on the vertices of a square as shown. Let \( \vec{E} \) be the electric
field and V the potential at the centre. If the charges on \( A \) and \( B \) are interchanged with those on D and
respectively, then
A. \( \bar{E} \) changes, v remains unchanged
B. \( \bar{E} \) remains unchanged, v changed
c. both \( \vec{E} \) and \( v \) change
D. \( \vec{E} \) and v remain unchange


Assertion
Thermonuclear fusion reactions may
become the source of unlimited power
for the mankind.
Reason
A single fusion event involving isotopes
of hydrogen produces more energy than energy from nuclear fission of \( \frac{235}{93} U \)
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


How will you convert Toluene to Benzaldehyde?


Doctors recommend sunflower oil as it
is
A. Rich source of vitamins
B. Rich in energy and reduces weight
c. Rich in saturated fatty acids
D. Rich in unsaturated fatty acids


A nucleus \( _{Z}^{A} X \) has mass represented by \( \boldsymbol{m}(\boldsymbol{A}, \boldsymbol{Z}) . \) If \( \boldsymbol{m}_{\boldsymbol{p}} \) and \( \boldsymbol{m}_{\boldsymbol{n}} \) denote the mass
of proton and neutron respectively and BE the binding energy(in MeV) then.
A \( \cdot B E=\left[m\left(A_{1} Z\right)-Z m_{p}-(A-Z) m_{n}\right] C^{2} \)
B . \( B E=\left[Z m_{p}+(A-Z) m_{n}-m(A, Z)\right] C^{2} \)
C \( . B E=\left[Z m_{p}+A m_{n}-m(A, Z)\right] C^{2} \)
D. \( B E=m\left(A_{1} Z\right)-Z m_{p}-(A-Z) m_{N} \)


What kind of solution is drinking soda?
A. Gas is liquid
B. Liquid in gas
c. Gas in gas
D. solid in liquid


Polystyrene and PVC are thermoplastics
A. True
B. False


Define radian measure of an angle.


A particle is moving eastwards with a velocity of \( 5 m s^{-1} . \) In \( 10 s, \) the velocity changes to 5 ms \( ^{-1} \) northwards. The
average acceleration in time is:
A. Zero
B. \( 1 / \sqrt{2} \mathrm{ms}^{-2} \) towards north-west
C \( \cdot 1 / 2 m s^{-2} \) towards north-west
D. \( 1 / 2 m s^{-2} \) towards north


Explain the importance of carbohydrates


The correct statement among the following is:
A. boiling point of amine is more than that of alcohol of nearly same molecular mass
B. the solubility of amines in water increases with increase in molecular mass
C. the order of boiling point of isomeric amines is primary \( > \) secondary \( > \) tertiary
D. none of these


Express \( \frac{\mathbf{5}+i \sqrt{2}}{2 i} \) in the form of \( x+i y \)


toppr
Q Type your question
dilu wattı, , Itsptulvely. Inte un anu water are immiscible. If the above ball
is in equilibrium in a mixture of this oil
and water, which of the following
pictures represents its equilibrium position?
\( A \)
B.
\( c \)
D.


Fill in the blanks:
When a ray of light travels from an optically less denser medium to an optically more denser medium, the angle of incidence is always than angle of refraction.
A. more
B. less
c. same as
D. cant say


The current \( i \) in the network is
0.6
3. 0.34
A
\( c, 0 \)
D. \( 0.2 A \)


Dissolving 120 gm of a compound of (mol.wt. 60 ) in 1000 g of water gave a solution of density \( 1.5 \mathrm{g} / \mathrm{mL} \). The molarity of the solution is:
A \( .1 .00 M \)
в. \( 1.78 M \)
\( c .2 .50 M \)
D. \( 4.00 M \)


Find the solution of \( \frac{d y}{d x}=\frac{2 y-x-4}{y-3 x+3} \)
\( \mathbf{A} \cdot\left(\log \left(v^{2}-3 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( ^{\mathrm{B}} \cdot\left(\log \left(v^{2}+3 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{3 v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( \left(\log \left(v^{2}-5 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{3 v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( \left(\log \left(v^{2}-5 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)


Answer the question based on the given
figure.
\( A B \) is ?
A. Greater than \( A C \)
B. Equal to \( A C \)
c. Less than \( A C \)
D. None of these


What do you understand by special types of inflorescence? Describe them
with diagrams and examples.


If the radius of a sphere is measured as
\( 9 \mathrm{cm} \) with an error of \( 0.03 \mathrm{cm} \) then, find
the approximate error in calculating its volume
A. \( 9.72 \pi \mathrm{cm}^{3} \)
B . \( 7.92 \pi \mathrm{cm}^{3} \)
c. \( 8.72 \pi \mathrm{cm}^{3} \)
D. None of these


Two
friends \( A \) and \( B \) are standing a distance \( x \) apart in an open field and wind is blowing from \( A \) to \( B \). A beats a drum and
B hears the sound \( t_{1} \) time
after he sees the event. A and B
interchange their positions and the experiment is repeated. This time B hears the drum
\( t_{2} \) time after he sees
the event. Calculate the velocity of sound in still air v and the velocity of
wind
u. Neglect the time light takes in travelling between the friends.
A \( \cdot \frac{1}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
B. \( \frac{x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
\( ^{\mathbf{c}} \cdot \frac{x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{3 x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)
D. \( \frac{3 x}{2}\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right), \frac{x}{2}\left(\frac{1}{t_{1}}-\frac{1}{t_{2}}\right) \)


In pteridophytes, main plant body is a
(i) which is
(ii)
into true roots, stem and leaves.
Fill the blanks in above statement and
select the correct option.
A. (i) - sporophyte, (ii) - differentiated
B. (i) - sporophyte, (ii) - not differentiated
c. (i) - gametophyte,
(ii) - differentiated
D. (i) - gametophyte, (ii) - not differentiated


Which one of the following statements is false?
This question has multiple correct options
A. Enzymes arc highly specific
B. Enzymes increase activation energy
c. Enzymes require optimum temperature
D. None of the above


A rope ladder with a length \( l \) metres
carrying a man with a mass \( m \) at its
end is attached to the basket of
a balloon with a mass \( M \). The entire
system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. In this case, the potential energy of the balloon:
A. decreases by \( m g h \)
B. increases by \( m g h \)
c. increases by \( m g(l-h) \)
D. increases by \( m g l \)


Type of redox reaction that occur in
volcanic eruptions is:
A. disproportionation
B. comproportionation
c. reduction
D. both \( A \) and \( B \)


Why does a current carrying freely suspended solenoid rest along a
particular direction?
A. It points towards the geometric poles of the earth
B. A current carrying solenoid behaves like a bar magnet
C. It points in the direction of the flow of current
D. None of the above


100 J of heat is produced each second in a \( 4 \Omega \) resistor. Find the potential
difference across the resistor.


Figure is a graph of which of the
following?
A \( \cdot x^{2}+y^{2}=9 \)
в. \( |x|=3 \) and \( |y|=3 \)
c. \( |x+y|=3 \)
D. \( |x|+|y|=3 \)
E . \( x-y=3 \)


Solve the equation \( 3^{x+1} C_{2}+P_{2}^{1} . x= \)
\( 4^{x} P_{2}, x \in N . \) Find \( x ? \)


Comproportionation is a type of:
A. displacement reaction
B. decomposition reaction
C. redox reaction
D. double displacement reaction


Name the element which is a living cell.
A. xylem fibres
B. xylem parenchyma
c. Tracheids
D. vesselss


The number of radial nodes for \( 4 p \)
orbital is:
A . 4
B. 3
\( c \cdot 2 \)
D.


Identify the correctly matched pair:
A. Material - Diamagnetic Example - Gadolinium
B. Material - Soft ferromagneti Example - Alnico
C. Material - Hard ferromagneti Example - Copper
D. Material - Paramagnetic Example -Sodium
E. Material - Permanent magnet Example - Aluminium


What is the value of a for which the
system of linear equations \( a x+3 y=a \) \( 3 ; 12 x+a y=a \) has no solution
\( \mathbf{A} \cdot a=6 \)
B . \( a=-3 \)
\( \mathbf{c} \cdot a=3 \)
D. \( a=-6 \)


The radius of a hypothetical nucleus (atomic number \( =\mathbf{7} 9 \) ) is about \( \mathbf{7} \times \)
\( 10^{-15} \mathrm{m} . \) Assuming that charge
distribution is uniform, the electric
field at distance of \( 3.5 \times 10^{-15} \) of the
nucleus is :
A \( \cdot 3 \times 10^{20} \)
В. \( 1.7 \times 10^{21} \)
c. \( 3.5 \times 10^{20} \)
D. \( 3.5 \times 10^{21} \)


No charge will flow when two conductors having the same charge are connected to each other
Given statement is:
A. True
B. False


Magnetic field in a plane electromagnetic wave is given by \( \vec{B}=B_{0} \sin (k x+\omega t) \hat{j} T \)
Expression for corresponding electric field will be :
Where \( c \) is speed of light.
A \( \cdot \vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} V / m \)
B・ \( \vec{E}=\frac{B_{0}}{c} \sin (k x+\omega t) \hat{k} V / m \)
c. \( \vec{E}=-B_{0} \operatorname{csin}(k x+\omega t) \hat{k} V / m \)
D . \( \vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} V / m \)


Sulphur is required in plants, as a nutrient element for:
A. making hormones
B. absorption of water
c. making vitamins
D. absorption of fat


Why it is easy to cut with a sharp knife
than a blunt?


A suitcase with measures \( 80 \mathrm{cm}, 48 \mathrm{cm} \)
and \( 24 \mathrm{cm} \) is to be covered with a
tarpaulin cloth. How many metres of
tarpaulin of width \( 96 \mathrm{cm} \) is required to cover 100 such suitcases?


Recall that two circles are congruent if they have the same radii. Prove that
equal chords of congruent circles subtend equal angles at their centres.


On what date will Rs.1,950 lent on \( 5^{t h} \)
January, 1991 amount to Rs.2,125.50 at 5
per cent per annum simple interest?
A \( \cdot 23^{r d} \) Oct. 1992
B. \( 20^{\text {th }} \) Oct. 1992
\( \mathrm{c} \cdot 27^{t h} \) Oct. 1992
D. \( 26^{t h} \) Oct. 1992


The final product \( (Y) \) in the following sequence of chemical reaction is:
\( \boldsymbol{C H}_{3} \boldsymbol{O H} \frac{\boldsymbol{C u}}{\mathbf{3 0 0}^{\circ} \boldsymbol{C}} \boldsymbol{X} \stackrel{\boldsymbol{N a O H}}{\longrightarrow} \boldsymbol{Y}+ \)
\( \boldsymbol{C H}_{3} \boldsymbol{O} \boldsymbol{H} \)
\( A \). an alkene
B. a carboxylic acid
c. an aldehyde
D. sodium salt of carboxylic acid


The resistivity of a semiconductor
A. Increases as the temperature increases
B. Decreases as the temperature increases
C. Remains constant even when temperature varies
D. None of the above


Antiseptic Chloroxylenol is:
A. 4 -chloro-3, 5-dimethyl phenol
B. 3-chloro-4, 5-dimethyl phenol
C. 4 -chloro-2, 5-dimethyl phenol
D. 5-chloro-3, 4-dimethyl phenol


Write a short note on P-type semiconductor


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{x}^{2} & \boldsymbol{x}=\mathbf{2} \\ \frac{\boldsymbol{k}\left(\boldsymbol{x}^{2}-\boldsymbol{4}\right)}{\mathbf{2}-\boldsymbol{x}} & \boldsymbol{x} \in \boldsymbol{Z}-\mathbf{2}\end{array}\right. \)
then \( \lim _{x \rightarrow 2} f(x) \)
A. exists only when \( k=-1 \)
B. exits for every real \( k \)
C. Exits for every real k except \( k-1 \)
D. does not exits


When gas \( Y \) react with the black solid
\( Q, \) then \( Y: \)
A. oxidises \( Q \)
B. decolourises \( Q \)
c. dissociates \( Q \)
D. reduces \( Q \)


Of the following acids:
I. Hypophosphorus acid
II. Oxalic acid
III. Glycine
A . I, Il are monobasic; III dibasic and amphoteric
B. II monobasic; I dibasic acid; III amphotericc
c. I monobasic; II dibasic; II amphoteric
D. I, Il are dibasic; III amphoteric


Which is the correct increasing order of
bond dissociation enthalpy of \( \boldsymbol{C}-\boldsymbol{X} \)
bond?
A. \( C-F, C-C l, C-B r, C-I \)
в. \( C-I, C-F, C-C l, C-B r \)
c. \( C-C l, C-F, C-B r, C-I \)
D. \( C-I, C-B r, C-C l, C-F \)


If a solid metallic sphere of radius \( 8 \mathrm{cm} \) is melted and recasted into \( n \) spherical
solid balls of radius \( 1 \mathrm{cm}, \) then \( n \) is:
A . 500
в. 510
c. 512
D. 516


\( I_{2} \) dissolve in \( K I \) solution due to
formation of:
\( \mathbf{A} \cdot K I_{2} \) and \( I^{-} \)
B. \( K^{+} ; I^{-} \) and \( I \)
\( c \cdot I_{3}^{-} \)
D. None of the above


The field \( B \) at the centre of a circular coil
of radius \( r \) is \( \pi \) times that due to a long
straight wire at a distance \( r \) from it for
equal currents. The figure shows three cases. In all cases the circular part has
radius \( r \) and straight ones are infinitely
long. For same current, the field \( B \) at the centre \( P \) in cases 1,2,3 has the ratio:
\( ^{\mathbf{A}} \cdot\left(-\frac{\pi}{2}\right): \frac{\pi}{2}:\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
\( \mathbf{C} \cdot-\frac{\pi}{2}: \frac{\pi}{2}: \frac{3 \pi}{4} \)
D \( \cdot\left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{4}+\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)


All of the given nitrogenous bases are found in DNA except
A. Adenine
B. Guanine
c. Thymine
D. Cytosine
E. Uraci


Name the species which is
isoelectronic with \( N^{3-} \)


When an object absorb waves and energy their temperature increases.
A. True
B. False


Write the difference between soap and
detergent.


From the rate expression for the following reactions, determine their order of reaction and the dimensions of
the rate constants.
(i) \( 2 N O(g) \rightarrow N_{2} O(g) ; \quad \) Rate \( = \)
\( \boldsymbol{k}[\boldsymbol{N} \boldsymbol{O}]^{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \)
\( 2 H 2 O(I)+3 I ; \quad R a t e=k\left[H_{2} O_{2}\right]\left[I^{-}\right] \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H O}(\boldsymbol{g}) \rightarrow \boldsymbol{C H}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) ; \quad \boldsymbol{R} \boldsymbol{a} \boldsymbol{t e}=\boldsymbol{k}\left[\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H O}\right]^{3 / 2} \)
(iv) \( C_{2} H_{5} C l(g) \rightarrow C_{2} H_{4}(g)+ \)
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \quad \boldsymbol{R} \boldsymbol{a} \boldsymbol{t} e=\boldsymbol{k}\left[\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}\right] \)


In the figure, \( \boldsymbol{O} \) is the center, if
\( \angle B A C=x \) and \( \angle B C O=y, \) then
A . \( x+y=180 \)
B. \( x+y=90 \)
c. \( x+y=120 \)
D. \( x+y=150 \)


Dry ice is an example of
process.
A. Evaporation
B. Crystallization
c. Sublimation
D. Purification


The form of energy used in the process of respiration is
A. Chemical energy
B. Electrical energy
c. Mechanical energy
D. Radiant energy


Which of the following statements are
true?
A. During electrolysis, charge flows through electrolytic solution via electrons.
B. The randomly moving electrons in a metal wire will start moving in a particular direction when a potential difference is applied across it.
C. A negatively charged particle has higher electric potential than a positively charged particle.
D. Charge flows only through negative charge carriers like electrons.


If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{3}}{\cos ^{2} \boldsymbol{x}}=\frac{1}{\cos ^{2} \boldsymbol{x}}, \boldsymbol{x} \boldsymbol{\epsilon}\left(\frac{-\boldsymbol{\pi}}{\boldsymbol{3}}, \frac{\boldsymbol{\pi}}{\boldsymbol{3}}\right) \)
and \( y\left(\frac{\pi}{4}\right)=\frac{4}{3}, \) then \( y\left(-\frac{\pi}{4}\right) \) equals:
A \( \cdot \frac{16}{3} \)
B. \( \frac{1}{3} \)
c. \( \frac{-4}{3} \)
D. \( \frac{1}{3}+e^{3} \)


Two supplementary angles are in the ratio 4:5. Find the angles.


Name the high energetic invisible electromagnetic wave which helps in the study of structure of crystals.
A. \( X \) -rays
B. Cathod rays
c. Gamma rays
D. All of the above


Electromagnetic radiation having \( \lambda= \) \( 310 \dot{A} \) is subjected to a metal sheet having work function \( =12.8 \mathrm{eV} . \) What will be the velocity of photo electrons having maximum kinetic energy?
A \( \cdot 1.23 \times 10^{6} m / s \)
B . \( 2.28 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 3.1 \times 10^{6} m / s \)
D. None of these


Prove the following:
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\boldsymbol{b}^{2} & \boldsymbol{c} & \boldsymbol{c} \\ \boldsymbol{c} & \frac{\boldsymbol{b}^{2}+\boldsymbol{c}^{2}}{\boldsymbol{a}} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{b} & \frac{\boldsymbol{c}^{2}+\boldsymbol{a}^{2}}{\boldsymbol{b}}\end{array}\right|=\boldsymbol{4 a b c} \)


Derive an expression for the force on current carrying in a magnetic field.


On what factors does the inertia of
motion depend?
A. Mass
B. Velocity
c. Acceleration
D. Displacement


Polymeric organic substance is commonly known as


Among the carbonates of alkali metals which one has highest stability:
A. \( C s_{2} C O_{3} \)
в. \( R b_{2} C O_{3} \)
\( \mathrm{c} \cdot K_{2} \mathrm{CO}_{3} \)
D. \( N a_{2} C O_{3} \)


A person is looking at the image of his face in a mirror by holding it close to his face. The image formed is virtual. When he moves the mirror away from his face, the image is inverted. What type of mirror is he using?
A. Plane mirror
B. Concave mirror
c. convex mirror
D. Combination of mirror and lenses


The value of
\( \sin ^{-1}\left[\cos \left[\sin ^{-1}\left(\frac{1}{2} \tan \frac{\pi}{3}\right)\right]\right] \) is
\( \mathbf{A} \cdot 2 \tan ^{-1}(2-\sqrt{3}) \)
B \( \cdot 2 \tan ^{-1}(\sqrt{2}-1) \)
\( \mathbf{c} \cdot 2 \tan ^{-1}(\sqrt{2}+1) \)
D.


Identify the most notable difference between a ultraviolet wave and a light wave?
A. Speed
B. Refractive index
c. Reflectivity
D. Amplitude
E. Frequency


Benzaldehyde is used:
A. as a flavouring agent for food
B. in the manufacture of triphenylmethane dyes like malachite green
C. as a starting material for the preparation of cinnamic acid
D. all of these


The compressibility of water \( 4 \times 10^{-5} \)
per unit atmospheric pressure. The decrease in volume of 100 cubic
centimeter of water under a pressure of
100 atmosphere will be:
A \( .0 .4 c c \)
в. \( 4 \times 10^{-5} c c \)
c. \( 0.025 c c \)
D. \( 0.004 c c \)


The change in enthalpy, \( \Delta \boldsymbol{H} \) accompanying a process depends on the path followed
A. True
B. False


A steel wire of \( 2 m m \) in diameter is
stretched by applying a force of \( 72 N \)
Stress in the wire is
A \( \cdot 2.29 \times 10^{7} N / m^{2} \)
B. \( 1.17 \times 10^{7} N / m^{2} \)
\( c \)
\( 3.6 \times 10^{7} N / m^{2} \)
D. \( 0.8 \times 10^{7} N / m^{2} \)


Which of the following laws represents the qualitative measure of force?
A. Newton's first law of motion
B. Fleming's right hand rule
c. Fleming's left hand rule
D. zeroth law of thermodynamics


Figure shows some of the electric field
lines corresponding to an electric field.
The figure suggests that:
A \( \cdot E_{A}>E_{B}>E_{C} \)
B . \( E_{A}=E_{B}=E_{O} \)
\( \mathbf{c} \cdot E_{A}=E_{C}>E_{B} \)
D. \( E_{A}=E_{C}<E_{B} \)


If \( \int \sqrt{\boldsymbol{x}}\left(1-\boldsymbol{x}^{3}\right)^{-1 / 2} \boldsymbol{d} \boldsymbol{x}=\frac{\boldsymbol{2}}{\boldsymbol{3}} \boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x}))+\boldsymbol{c} \)
then
A \( \cdot f(x)=\sqrt{x}, g(x)=\sin ^{-1} x \)
B . \( f(x)=x^{3 / 2}, g(x)=\sin ^{-1} x \)
C \( \cdot f(x)=x^{2 / 3}, g(x)=\cos ^{-1} x \)
D. \( f(x)=\sqrt{x}, g(x)=\cos ^{-1} x \)


Use the relationship between radius of a nucleus and its mass number.

Example: Find the radius of the nucleus of an atom of mass number \( 216\left(R_{0}=\right. \)
1.2 fermi).
A. \( =11.2 \times 10^{-15} \mathrm{m} \)
В. \( =7.2 \times 10^{-15} \mathrm{m} \)
\( \mathbf{c} .=8.2 \times 10^{-15} \mathrm{m} \)
D. \( =9.2 \times 10^{-15} \mathrm{m} \)


The volume of thoracic cavity increases during
A . Never
B. Expiration
c. Both A and B
D. Inspiration


Explain with example, branched and
linear polymers.


The \( (M) \) is :
A \( . S i \)
B. \( C a \)
c. \( M g \)
D. \( M g- \) Ca alloy


\( \boldsymbol{v}=\frac{\mathbf{2} \boldsymbol{\pi} \boldsymbol{r}}{\boldsymbol{T}} \)
In Physics, Uniform Circular Motion is used to describe the motion of an object traveling at a constant speed in a circle. The speed of the object, also called tangential velocity, can be calculated using the formula above. Here, \( r \)
represents the radius of the circle, \( \boldsymbol{T} \) the
time it takes for the object to make one complete revolution, called a period. Determine which of the following formulae could be used to find the
length of one period if one knows the tangential velocity and the radius of the circle?
A \( \cdot T=\frac{v}{2 \pi r} \)
B・ \( T=\frac{2 \pi r}{v} \)
c. \( T=2 \pi r v \)
D. \( T=\frac{1}{2 \pi r v} \)


The value of \( \lim _{x \rightarrow 0}\left[\frac{\tan x}{x}+\frac{\sin x}{x}\right] \) is


\( A B \) is parallel to \( Q R, \) such that \( \frac{P A}{A Q}= \) \( \frac{P B}{B R} \cdot P B=2 \mathrm{cm}, E C=4 \mathrm{cm} \) and
\( Q R=9 \mathrm{cm}, \) then find the length of \( A B \)


If coefficients \( a, b, c \) of quadratic equation \( a x^{2}+b x+c=0 \) are chosen
at random with replacement from the \( \operatorname{set} S=1,2,3,4,5,6, \) find out the
probability that roots of quadratic are real and distinct.
A \( \frac{20}{108} \)
в. \( \frac{19}{108} \)
c. \( \frac{21}{108} \)
D. \( \frac{22}{108} \)


\( P C l_{2} \rightleftharpoons P C l_{3}+C l_{2} \) in the reversible
reaction the moles of \( \boldsymbol{P C l}_{2}, \boldsymbol{P C l}_{3} \) and
\( C l_{2} \) are \( a, b \) and \( c \) respectively and total
pressure is \( \boldsymbol{P} \) then value of \( \boldsymbol{K}_{\boldsymbol{p}} \)
is
A \( \cdot \frac{b c}{a} R T \)
в. \( \frac{b}{(a+b+c)} P \)
c. \( \frac{b c P}{a(a+b+c)} \)
D. \( \frac{c}{(a+b+c)} P \)


In a gaseous reaction, \( 2 A \leftrightharpoons 3 B \) on
doubling the volume of container, the equilibrium amount of the product:
A . increases
B. decreases
c. remains same
D. data insufficient


\( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\boldsymbol{n}}{\boldsymbol{n}+\mathbf{1}} \)


Using properties of determinant, prove
\[
\text { that }\left|\begin{array}{lll}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{a} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{c}
\end{array}\right|=\mathbf{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a}^{3}-
\]
\( b^{3}-c^{3} \)


Circular motion is a example of
A. \( 1- \) D motion
B. 2-D motion
c. 3-D motion
D. None


Based on M.O.T, explain the electronic
configuration of the Hydrogen molecule
and \( B e_{2} \)


\( A B C D \) is a quadrilateral in which
\( P, Q, R \) and \( S \) are mid-points of the \( \operatorname{sides} A B, B C, C D \) and \( D A \)
respectively. Show that \( P Q R S \) is a
parallelogram.


Poisson' ratio is defined as the ratio of
A. longitudinal stress and longitudinal strain
B. Iongitudinal stress and lateral stress
C. lateral stress and longitudinal stress
D. lateral stress and lateral strain


Which of the following elements has the
same molecular mass as its atomic
mass?
A. Nitrogen
B. Neon
c. oxygen
D. Chlorine


State whether true or false.
One canjudge the approaching of a train by laying an ear on the railway track before hearing it.
A. True
B. False


A satellite is to be placed in equatorial geostationary orbit around earth for communication. The height of such a satellite is
\( \left[M_{E}=6 \times 10^{24} k g, R_{E}=6400 k m, T=\right. \)
A \( .3 .57 \times 10^{5} m \)
В. \( 3.57 \times 10^{6} m \)
c. \( 3.57 \times 10^{7} m \)
D. \( 3.57 \times 10^{8} m \)


Assertion
Space rockets are usually launched in the equatorial line from west to east
Reason
The acceleration due to gravity is minimum at the equator.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


A 20 g ball is fired horizontally toward a 100 g ball that is hanging motionless from a 1.0 -m-long string. The balls undergo a head-on, elastic collision, after which the 100 g ball swings out to a maximum angle of 50
degrees. Determine the initial speed of the 20 g ball.
A. \( 8.4 \mathrm{m} / \mathrm{s} \)
B. \( 4.2 \mathrm{m} / \mathrm{s} \)
c. \( 2.1 \mathrm{m} / \mathrm{s} \)
D. \( 16.8 \mathrm{m} / \mathrm{s} \)


Which is a two dimensional graph?
\( A \cdot \) pie
B. bar
c. histogram
D. frequency curve


A simple harmonic oscillator is of mass \( 0.100 \mathrm{kg} . \) It is oscillating with a frequency of \( \frac{5}{\pi} \mathrm{Hz} \). If its amplitude of
vibration is \( 5 \mathrm{cm}, \) the force acting on the particle at its extreme position is
A. 2 N
B. 1.5 N
\( c \cdot 1 \mathrm{N} \)
D. 0.5 N


It is easier to roll a barrel full of coal tar
than to pull it because
A. the full weight of the barrel comes into play when it is pulledd
B. the rolling friction is much less than the sliding friction
c. more surface area of the barrel is in contact with the road when it is pulled
D. coal tar is a liquid and it flows in the barrel when it is rolled


An example of chain-growth polymer is:
A. Nylon - 6,6
B. Bakelite
c. Terylene
D. Teflon


The law which indicates the
relationship between solubility of a gas in liquid and pressures is:
A. Raoult's law
B. Henry's law
C. Lowering of vapour pressure
D. van't Hoff law


Papilionaceous flower with large vexillum covering two wings and the wings covering the keel has corolla
aestivation of
A. Descending imbricate
B. Ascending imbricate
c. Twisted
D. valvate


Leading is \( \frac{x}{1000} H \)


A straight magnetised wire of magnetic
moment ' \( M^{\prime} \) is bent as shown. Find
resultant magnetic moment in each
case.


What do you mean by the sensitivity of potentiometer?


Hexaamminenickel(II)
hexanitrocobaltate(III) can be written
as?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{6}\right]_{2}\left[C o\left(N O_{2}\right)_{6}\right]_{3} \)
\( \mathbf{B} \cdot\left[N i\left(N H_{3}\right)_{6}\right]_{3}\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{6}\right]\left[C o\left(N O_{2}\right)_{6}\right] \)
D. \( \left[N i\left(N H_{3}\right)_{6}\left(N O_{2}\right)_{6}\right] C o \)


Assuming ideal behaviour, the enthalpy and volume of mixing of two liquids, respectively, are:
A. zero and zero
B. +ve and zero
c. -ve and zero
D. -ve and -ve


A particle performing SHM has time period \( \frac{2 \pi}{\sqrt{3}} \) and path length \( 4 \mathrm{cm} . \) The
displacement from mean position at which acceleration is equal to velocity is
\( A \cdot 0 c m \)
B. \( 0.5 \mathrm{cm} \)
\( c \cdot 1 c m \)
D. \( 1.5 \mathrm{cm} \)


Find the value of
\( (b-c)(c-a)(a-b)+ \)
\( (b-\omega c)(c-\omega a)(a-\omega b)+ \)
\( \left(b-\omega^{2} c\right)\left(c-\omega^{2} a\right)\left(a-\omega^{2} b\right) \)


fibres are made
from cellulose.
A. Vegetable
B. Animal
c. Both vegetable and animal
D. None of them


Which of the following oxidation numbers is not correctly matched?
A \( \cdot P \) in \( N a H_{2} P O_{4}=+5 \)
B. \( N i \) in \( \left[N i(C N)_{6}\right]^{4-}=+2 \)
\( \mathbf{c} \cdot P \) in \( M g_{2} P_{2} O_{7}=+6 \)
D. \( C r \) in \( \left(N H_{4}\right)_{2} C r_{2} O_{7}=+6 \)


If \( 75.2 \% \) of a compound is carbon and the rest of its weight is hydrogen, the formula of the compound is:
A. \( C_{3} H_{6} \)
в. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C H_{4} \)


Cyanohydrin of which of the following compound on hydrolysis gives optically active product?
A . HCHO
в. \( C H_{3} C H O \)
c. \( C H_{3} \) COCH\( _{3} \)
D. All the above


Write an expression (derivation not required) for intensity of electric field of an electric dipole, in terms of its length
(2a), dipole moment ( \( p \) ) and distance
\( (r) \) for:
(1) Axial position.
(2) Broad side position.


What should be the minimum force \( \boldsymbol{P} \)
to be applied to the string so that block
of mass \( m \) just begins to move up the
frictionless plane.
\( \mathbf{A} \cdot M g \tan \theta / 2 \)
в. \( M g \cot \theta / 2 \)
c. \( \frac{M g \cot \theta / 2}{1+\sin \theta} \)
D. \( M g \cos \theta / 2 \)


Arrange the following acids in increasing order of their acid strength:
I. \( \boldsymbol{H} \boldsymbol{C l O}_{\mathbf{4}} \)
II. \( \quad H_{2} S O_{4} \)
III \( . \)
A. \( I I I<I I<I \)
B. \( I<I I<I I I \)
c. \( I I<I I I<I \)
D. III \( <I<I I \)


Which of the following pair of compounds which will react faster in
\( S_{N} 2 \) reaction with \( \left(C H_{3}\right)_{3} C-B r \) or
\( \boldsymbol{C H}_{3} \boldsymbol{B r} ? \)


Copper is a preferred material for making wire for electrical use because of its low
A. Resistivity
B. Conductivity
c. Density
D. charge