A conductivity cell has been calibrated
with a \( 0.01 M 1: 1 \) electrolyte solution
(specific conductance \( \kappa=1.25 \times \)
\( 10^{-3} \mathrm{Scm}^{-1} \) ) in the cell and the
measure resistance was \( 800 \Omega \) at \( 25^{\circ} C \)
The cell constant will be:
A \( \cdot 1.02 \mathrm{cm}^{-1} \)
В. \( 0.102 c m^{-1} \)
c. \( 1.00 \mathrm{cm}^{-1} \)
D. \( 0.5 \mathrm{cm}^{-1} \)


A particle moves in \( x \) -y plane and at
time \( t \) is at the point \( \left(t^{2}, t^{3}-2 t\right), \) then
which of the following is/are correct? This question has multiple correct options
A. At \( t=0, \) particle is moving parallel to \( y \) -axis
B. At t= 0, direction of velocity and acceleration are perpendicular
c. \( \quad \) At \( t=\sqrt{\frac{2}{3}} \), particle is moving parallel to \( x \) -axis
D. At t = 0, particle is at rest


Assertion (A) : Silica is less harder than
diamond
Reason (R) : Silica has only two dimensional network
A. Both A and R are true and R is correct
explanation of
B. Both A and R are true and R is not correct
explanation of A
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Which of the following statements is incorrect?
A \( \cdot O_{3} \) is used as disinfectant.
B. \( N O_{2} \) is oxidised to \( N_{2} O_{5} \) by \( O_{3} \)
C. \( O_{3}^{-} \) is paramagnetic in nature
D. Dry iodine reacts with ozone and form \( I_{2} O_{5} \)


If the temperature of the Sun were to increase from \( T \) to \( 2 T \) and its radius
from \( R \) to \( 2 R \). The ratio of power
radiated by it would become:
A. 64 times
B. 16 times
c. 32 times
D. 4 times


The correct relationship between the
bond lengths \( a \) and \( b \) is:
\( \boldsymbol{O} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{3} \)
\( \mathbf{A} \cdot a=b \)
В. \( b>a \)
\( c \cdot b<a \)
D. impossible to predict


Match the animals listed below with
their nature of blood. Choose the answer
which gives the correct combination of
alphabets of the two columns.
Animals \( \quad \) Nature of blood
A. Man
(p) Plasma and cells are colourless
B.
(q) Plasms is colourless and Earthworm nucleated
\( \mathrm{C} \)
(r) Plasma is colourless and cockroach enucleated RBC
(s) Plasma is red and nucleated,
D. Frog \( \quad \) colourless RBC
(t) Plasma and RBC have haemoglobin
\( A \cdot A-p, B-s, C-q, D-r \)
B. A-t, B- r, C- p, D-s
C. \( A-r, B-s, C-p, D-q \)
D. \( A-s, B-t, C-r, D-q \)


The sum of first \( n \) terms of the \( A . P . \) \( \sqrt{\mathbf{2}}+\sqrt{\mathbf{8}}+\sqrt{\mathbf{1 8}}+\sqrt{\mathbf{3 2}}+\ldots \ldots . . \) is
A \( \cdot \frac{n(n+1)}{2} \)
B. \( 2 n(n+1) \)
c. \( \frac{n(n+1)}{\sqrt{2}} \)
D.


What are the colours of the Sun
observed most during sunrise/sunset and noon?
A. white and red
B. reddish and orange
c. yellow and reddish
D. orange and blue


If heat is supplied to the system it:
A. Does work only
B. Increase the internal energy
C. Either does work or increase the internal energy or both
D. Docs nothing


If \( f(x)=\frac{1}{2} x-1, \) then on the interval
\( [\mathbf{0}, \boldsymbol{\pi}] \)
A \( \cdot \tan (f(x)) \) and \( \frac{1}{f(x)} \) are continuous
в.
\( \tan (f(x)) \) and \( \frac{1}{f(x)} \) are discontinuous
c. \( \tan (f(x)) \) is continuous but \( \frac{1}{f(x)} \) is discontinuous
D \( \cdot \tan (f(x)) \) is discontinuous but \( \frac{1}{f(x)} \) is continuous


The equation of tangent to the curve \( y=e^{-|x|} \) at the point where the curve
cuts the line \( x=1 \) is
A. \( x+y=e \)
В. \( e(x+y)=1 \)
c. \( y+e x=1 \)
D. none of these


The variance is the
standard deviation.
A. Square
B. Cube
c. square root
D. cube root


\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=2 \hat{\boldsymbol{i}}-\boldsymbol{4} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+ \)
\( \lambda \hat{j}+3 \hat{k} \) are coplanar, then the value of
\( \lambda \) is
\( A \cdot \frac{5}{2} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{5}{3} \)
D. None of these


A negative charged object reples another charged object kept close to it. What is the nature of the charge on the other object?
A. positive
B. negative
c. both
D. none


Phyllotaxy is the arrangement of
A. Leaflets
B. Leaves
c. stipules
D. Branches


The area of a circle whose radius is 6
\( \mathrm{cm} \) is trisected by two concentric circles. The radius of the smallest circle
is
A \( \cdot 2 \sqrt{3} \mathrm{cm} \)
B . \( 2 \sqrt{6} \mathrm{cm} \)
\( c \cdot 2 \mathrm{cm} \)
D. \( 3 \mathrm{cm} \)


A small metal sphere falls from a
height \( h \) onto a plane surface strikes it with velocity \( v \) and rebounds. If \( e \) is the coefficient of restitution:
a) the height to which it rebounds after
\( n \) collisions is \( e^{n} h \)
b) the height to which it rebound after 3
collisions is \( e^{6} h \)
c) the velocity with which it rebounds after 4 collisions is \( e^{4} v \)
d) the velocity with which it strikes the surface for the second collision is \( e v \)
A. Only a and b are correct
B. Only b and c are correct
c. \( b, c \) and \( d \) are correct
D. a, b and c are correct


To which portion of the heating curve for
water does \( \Delta H_{f u s} \) apply?
\( A \cdot A-B \)
B. \( B-C \)
\( c \cdot C-D \)
D. \( D-E \)


In a semiconductor, the energy gap
between valence band and conduction
band is of the order of
A . Mev
B. kev
\( c \cdot e v \)
D. Gev


Which of the following type of radiations are radiated by on oscillating electric charge?
A. Electric
B. Magnetic
c. Thermoelectric
D. Electromagnetic


Assertion
The gases \( H e \) and \( H_{2} \) are very different
in their behaviour at any temperature and pressure but their compressibility
factors are nearly the same at the
critical point.
Reason
They have nearly the same critical
constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The ideal gas law is applicable at:
A. high \( T \), high \( P \)
B. low \( T \), high \( P \)
c. low \( T, \) low \( P \)
D. high \( T, \) low \( P \)


The term smog was coined by
A. Fourier
B. Des Voeux
c. schouw
D. Ashbel


Write the formula of the following compounds.
(i) Triamminetriaquachromium (III) chloride.
(ii) Potassiumhexacyanoferrate(III).


Find the sum up to 30 terms of an \( A P \) whose second term is \( \frac{1}{2} \) and \( 29^{t h} \) term is \( 49 \frac{1}{2} \)


Unsymmetrical ethers on hydrolysis
gives:
A. single product
B. double product
c. depends on reaction condition
D. single product only with heavy water


Estimate the increase in wavelength in
an average compton scattering process.
\( \mathbf{A} \cdot 5 \times 10^{-33} \mathrm{m} \)
B \( .5 \times 10^{-31} \mathrm{m} \)
D. \( 2 \times 10^{-31} \mathrm{m} \)


Which of the following statements are true (T) and which are false (F)?

If all the angles of a quadrilateral are equal, it is a parallelogram.
A . True
B. False


A point charge \( 50 \mu C \) is located in the
\( x-y \) plane at the position vector \( \vec{r}_{0}= \) \( (2 \hat{i}+3 \hat{j}) m . \) The electric field at the
point of position vector \( \vec{r}= \) \( (8 \hat{i}-5 \hat{j}) m, \) in vector from is equal to:
A \( \cdot 900(-3 \hat{i}+4 \hat{j}) V / m \)
B \( \cdot 90(3 \hat{i}-4 \hat{j}) V / m \)
c. \( 9(-3 \hat{i}+4 \hat{j}) V / m \)
D. \( 900(3 \hat{i}-4 \hat{j}) V / m \)


The hybridisation of the orbitals of
oxygen in \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
\( A \cdot s p^{3} d \)
B . \( s p \)
\( c \cdot s p^{2} \)
D. \( s p^{3} \)


Give four reasons why burning of a magnesium ribbon in air is considered a chemical change.


Based on cellular mechanisms there
are two major types of regeneration found in the animals. Which one of the
following is the correct example of the type mentioned?
A. Morphallaxis- Regeneration of two transversely cut equal pieces of a Hydra into two small Hydra
B. Epimorphosis- Replacement of old and dead erythrocytes by the new ones
c. Morphallaxis- Healing up of a wound in the skin
D. Epimorphosis- Regeneration of crushed and filtered out pieces of a Planaria into as many new Planarians.


8
\( 3= \)
\( \Delta x \)
\( 4 \times 0 \)
8


\( P Q R S \) is a square and \( \Delta T S R \) is ar
isosceles triangle with \( T S=T R \) Prove
that \( \boldsymbol{P T}=\boldsymbol{Q} \boldsymbol{T} \)


An isolated box, equally partitioned
contains two ideal gases \( A \) and \( B \) as
shown

When the partition is removed, the gases mix. The changes in enthalpy \( (\Delta H) \) and entropy \( (\Delta S) \) in the process, respectively, are:ositive, zero
A. Zero, positive
B. zero, negative
c. Positive, zero
D. Negative, zero


Bruners gland are characteristic feature of
A. Jejunum of small intestine
B. Ileum
c. Duodenum
D. Fundic region stomach


Which of the following compounds can be called as non-electrolytes?
A. \( C_{6} H_{12} O_{6} \)
в. \( C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. All of the above


The current in the given circuit is
A. 0.3 amp
B. 0.4 amp
\( \mathbf{c} \cdot 0.1 \mathrm{amp} \)
D. 0.2 amp


The insecticide Gammexane is:
A . DDT
B. benzene hexachloride
c. parathion
D. chloral


Soaps are formed by saponification of?
A. alcohols
B. glycosides
c. simple esters
D. carboxylic acids


A symmetric die is thrown \( (2 n+1) \) times. The probability of getting a prime score on the upturned face at most \( n \)
times is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.


\( \boldsymbol{m} \angle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R}= \)
A \( .65^{\circ} \)
B. \( 79^{\circ} \)
\( c \cdot 72 \)
D. \( 89^{\circ} \)


The structure of spiro [3,3] heptane is:
\( A \)
\( B \)
\( c \)
D.


of molasses takes place in the
presence of enzymes.
A. Fermentation
B. Reduction
c. Polymerization
D. Oxidation


Two infinitely long current carrying
conductors \( X \) and \( Y \) are kept parallel to
each other, \( 24 \mathrm{cm} \) apart in vacuum
They carry currents of \( 5 \mathrm{A} \) and \( 7 \mathrm{A} \) respectively, in the same direction, as shown in Figure above. Find the position
of a neutral point, i.e. a point where
resultant magnetic flux density is zero.
(Ignore earth's magnetic field)


Explain the structures of \( X e F_{2} \) and
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}} \)


For \( \boldsymbol{x} \in \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=|\log 2-\sin \boldsymbol{x}| \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x})), \) then:
A. g is not differential at \( X=0 \)
B \( \cdot g^{\prime}(0)=\cos (\log 2) \)
C・ \( g^{\prime}(0)=-\cos (\log 2) \)
D. g is differentiable at \( x=0 \) and \( g^{\prime}(0)=-\sin (\log 2) \)


Compound \( B \) is:
A.
в.
(B)
\( c \)
D.


Out of the following metals, which will
give \( H_{2} \) on reaction with \( N a O H ? \)
\( \boldsymbol{I}: \boldsymbol{Z} \boldsymbol{n} \)
\( \boldsymbol{I} \boldsymbol{I}: \boldsymbol{M} \boldsymbol{g} \)
\( \boldsymbol{I I I}: \boldsymbol{A l} \)
\( \boldsymbol{I} \boldsymbol{V}: \boldsymbol{B} \boldsymbol{e} \)
A. \( I, I I, I I I, I V \)
в. \( I, I I I, I V \)
c. \( I I, I V \)
D. \( I, I I I \)


Give the essential conditions (any two)
for the source to be Coherent.
(b) In
Young's double slit experiment, using
monochromatic light of wavelength \( \lambda \)
the intensity of light at a point on the screen where path difference is I, is \( 2 K \) units. Find out the intensity of light at a point where path difference is \( \lambda / 6 \)


Biosynthesis of gibberellin is inhibited
by
A. AMO-1618 and cyocel
B. Cytokinin
c. Auxin
D. All of the above


Two spheres of radius \( r=0.5 \mathrm{m} \) and mass
1 kg are placed in contact with each other, what will be the gravitational force between them:
A. \( 0 N \),since the spheres are touching each other and \( r=0 \)
В. \( 6.67 \times 10^{-11} N \)
\( \mathbf{c} \cdot 6.67 \times 10^{-4} N \)
D. \( 6.67 \times 10^{-6} N \)


Which of the following best describe the electromagnetic induction?
A. the ability of a changing magnetic field to induce a voltage in a conductor
B. the ability of a conductor to generate a magnetic field
C. the ability of a static magnetic field to induce a voltage in a conductor
D. the ability of a permanent magnet to induce a voltage in a coil
E. the ability of a conductor to induce a magnetic field


topp
\( Q \) Type your question
\( A \)
B.
\( c \)
\( D \)


Percolation tank is
A. Earthen dam
B. Concrete dam
C. Woody dam
D. None of the above


The angular diameter of the sun is 1920". If the distance of the sun from the
earth is \( 1.5 \times 10^{11} \mathrm{m}, \) then the linear
diameter of the sun is:
A \( \cdot 2.6 \times 10^{9} \mathrm{m} \)
В. \( 0.7 \times 10^{9} \mathrm{m} \)
c. \( 5.2 \times 10^{9} \mathrm{m} \)
D. \( 1.4 \times 10^{9} \mathrm{m} \)


In the reaction sequence:
\( \boldsymbol{A} \frac{\boldsymbol{S n C l}_{2} / \boldsymbol{H C l}}{\longrightarrow} \boldsymbol{B} \frac{N \boldsymbol{a} N \boldsymbol{O}_{2} / \boldsymbol{H} C l}{\boldsymbol{0}^{o}} \boldsymbol{C} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{\Delta}}{\longrightarrow} \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are:
A. benzene, nitrobenzene, aniline
B. nitrobenzene, aniline, and azo-compound
c. nitrobenzene, benzene, aniline
D. benzene, amino compound, aniline


Which of the following curve shows, how oxygen is loaded and unloaded due to
partial pressure?
A. \( O_{2} \) curve
B. \( C O_{2} \) curve
c. Bohr's curve
D. \( O_{2} \) dissociation curve


What does hydraulic jacks use to move oil through two cylinders?
A. Pipe
B. Wheel
c. Pump Plunger
D. Tube


During an adiabatic compression, \( 830 J \) of work is done on 2 moles of a
diatomic ideal gas to reduce its volume
by \( 50 \% \). The change in its temperature is nearly:
\( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A . \( 20 K \)
в. \( 14 k \)
c. \( 40 K \)
D. \( 33 K \)


Graphite differs from diamond because graphite is:
This question has multiple correct options
A. greyish black in colour and bad conductor of electricity
B. slippery to touch and good conductor of electricity
c. greyish black in colour and bad conductor of heat
D. slippery to touch and good conductor of heat


Factorise \( 4 a^{2}-8 a b \)
A. \( 4 a(a+2 b) \)
В. \( 4 a(a-b) \)
c. \( 4 a(a-2 b) \)
D. \( a(a-2 b) \)


The figure shows the input waveforms \( A \)
and B for 'AND' gate.

Draw the output waveform and write the
truth table for this logic gate.


Which of the following compounds is the reactant in Rosenmund's reaction?
A. \( C H_{3} C O O C H_{3} \)
в. \( C H_{3} C H O \)
c. \( C H_{3} C H_{2} C l \)
D. \( C H_{3} C O C l \)


The maximum value of \( F \) so that the
cylinder may not slip is :
\( \mathbf{A} \cdot 2 \mu M g \)
B. \( 3 \mu M g \)
c. \( \frac{3}{2} \mu M g \)
D. \( \frac{5}{2} \mu M g \)


Assertion
Coenzymes can be vitamins or
minerals.
Reason
NAD is an example of a coenzyme.
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.


Calculate the standard free energy
change for the reaction,
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \longrightarrow 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
\( \Delta \boldsymbol{H}^{\ominus}=+\mathbf{5 1 . 9 k J} \)
Given that the standard entropies
\( \left(\Delta S^{\ominus}\right) \) of \( H_{2}, I_{2} \) and \( H I \) are 130.6
116.7 and \( 206.3 J K^{-1} m o l^{-1} \)
respectively.
Predict whether the reaction is feasible
at the standard state or not?
A. Reaction is not feasible
B. Reaction is feasible.
c. can't predict
D. None of these


Write all the subsets of the sets
\( (i)\{a\} \)
\( (i i) \phi \)


The graph below represents the velocity of some subatomic particle in an
electric field. The graph represents the
particle' s velocity at its moves in a
straight line in positive and negative
directions.
During which of the labeled time intervals is the particles slowing down
during the entire interval?
A . 1 only
B. 4 only
c. 6 only
D. 1 and 4 only
E. 1 and 6 only


Assertion: The product of magnetic susceptibility and absolute temperature for a paramagnetic substance is constant.
Reason: Susceptibility is positive but
very small for paramagnetic substance
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


Flowers which have only stamens are
called as
A. Male flowers
B. Staminate flowers
c. Both of (A) and (B)
D. Pistillate flowers


Plane of polarisation is:
This question has multiple correct options
A. the plane in which vibrations of the electric vector takes place
B. a plane perpendicular to the plane in which vibrations of the electric vector takes place
C . perpendicular to the plane of vibration
D. horizontal plane


A cone and a hemisphere have equal bases and equal volumes. The ratio of
their height is
A .2: 1
В. \( \sqrt{2}: 1 \)
c. \( \sqrt{3}: 2 \)
D. 3: 1


The IUPAC name of :
A. 3-methyl cyclobuten-2-0
B. 4-Methyl cyclobut-2-en-1-o
c. 4-methyl cyclobuten-3-ol
D. 2-methyl cyclobut-3-en-1-ol


A bicycle travels \( 3.2 k m \) due east in \( 0.1 h \)
the \( 3.2 k m \) at 15.0 degrees east of
north in \( 0.21 h \), and finally another
\( 3.2 k m \) due east in \( 0.1 h \) to reach its
destination. The time lost in turning is negligible. What is the average velocity for the entire trip? (in \( \mathrm{km} / \mathrm{h}) \)
A . 20
B . 21
c. 19
D. 30


When the switch of an electric bell is on
then electric current in it :
A. Flows and stops in succession
B. Flows continuously
c. First flows in one direction and after sometime in other direction
D. Flows in beginning and then stops forever


The dimensions of a cuboid tin are
\( 30 \mathrm{cm} \times 40 \mathrm{cm} \times 50 \mathrm{cm} . \) Find the cost
of tin required for making 20 such tins,
If the cost of tin sheet is \( R s .20 \) per \( s q . m \)


\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{B} \boldsymbol{r} \)
The reaction obeys the following mechanism:
\( N O+B r_{2} \stackrel{F a s t}{\rightleftharpoons} N O B r_{2} \)
\( N O B r_{2}+N O \stackrel{S l o w}{\longrightarrow} 2 N O B r \)
The rate expression of the above reaction can be written as:
A \( \cdot r=k[N O]^{2}\left[B r_{2}\right] \)
B \( \cdot r=k[N O]\left[B r_{2}\right] \)
C \( \cdot r=k[N O]\left[B r_{2}\right]^{2} \)
D . \( r=k\left[N O B r_{2}\right. \)


Molar solubility of \( \mathbf{C a}(\mathbf{O} \mathbf{H})_{2} \) in a
solution that has a pH of 12.
\( \left[\boldsymbol{K}_{\boldsymbol{S P}}\left[\mathbf{C a}(\mathbf{O H})_{2}\right]=\mathbf{5 . 6} \times \mathbf{1 0}^{-12}\right] \)
в. \( 5.6 \times 10^{-8} M \)
c. \( 4 \times 10^{-4} M \)
D. None


You have two solutions A and B. The pH
of solution \( A \) is 6 and \( p H \) of solution \( B \) is
8. Which solution has more hydrogen ion concentration? Which of this is
acidic and which one is basic?


A convex lens of focal length \( 30 \mathrm{cm} \) is placed in front of a luminous point object. The separation between the object and the lens is \( 90 \mathrm{cm} . \) A glass slab of thickness \( t \) is placed between the object and the lens. A real image of the object is formed at the shortest
possible distance from the object. The refractive index of the slab is \( \frac{t}{t-k} \) Find \( k \)


An experiment was conducted by a
student and he obtained 3 values viz.
1.65,1.68 and \( 1.71, \) during three repetitive trials, respectively. After sometime, the student got the true value, which was 2.37 So, in the contrast to the real value, the
experiments' results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate, precise, but unreliable


Radius of tenth Bohr orbit of the
hydrogen atom is \( A^{0} \)
A . 0.53
B. 5.3
\( c \cdot 53 \)
D. 0.053


The pH of the solution obtained by mixing \( 100 \mathrm{ml} \) of a solution of \( \mathrm{pH}=3 \) with \( 400 \mathrm{ml} \) of a solution of \( \mathrm{pH}=4 \) is :
A. \( 3-\log 2.8 \)
B. \( 7-\log 2.8 \)
c. \( 4-\log 2.8 \)
D. \( 5-\log 2.8 \)


Calculate the wavelength of a wave if its frequency is \( 256 \mathrm{Hz} \) and and speed of the wave is \( 350 \mathrm{m} / \mathrm{s} \)
\( A \cdot 89,600 m \)
B. 350 \( m \)
\( c \cdot 94 m \)
D. \( 1.4 \mathrm{m} \)
E. \( 0.73 \mathrm{m} \)


The distance between the parallel lines \( 8 x+6 y+5=0 \) and \( 4 x+3 y-25=0 \) is
\( A \cdot \frac{7}{2} \)
B. \( \frac{9}{2} \)
c. \( \frac{11}{2} \)
D.


Find the next term of the A.P. \( \sqrt{8}, \sqrt{18}, \sqrt{32} \dots \dots \)


State true or false:
The number of persons that can be accommodated in a big hall of dimensions \( 40 m, 25 m, 15 m, \) assuming
that each person requires \( 5 m^{3} \) of air
are 3000
A. True
B. False


Calculate the current through the circuit and the potential difference across the diode shown in figure. The
drift current for the diode is \( 20 \mu A \)


The ration of the linear velocities of
point at distance \( r \) and \( \frac{r}{4} \) from the axis
rotation of a rigid body is
A . 0.25
B. 2
\( c \cdot 4 \)
D. 0.5


The factor which governs the absorption of digested food by intestinal villi is
A . Peristalsis
B. Osmosis
c. Emulsification
D. Differential absorption


The pituitary gland by virtue of itstropic hormones controls the secretory activity of other endocrine glands. Which one of the following endocrine glands can function independent of a pituitary gland?
A. Thyroid
B. Gonads
c. Adrenal glands
D. Parathyroid


A mixture of two miscible liquids \( A \) and B is distilled under equilibrium
conditions at 1 atm pressure. The mole fraction of \( A \) in solution and vapour
phase are 0.30 and 0.60 respectively. Assuming ideal behaviour of the
solution and the vapour. Calculate the
ratio of the vapour pressure of pure \( A \) to that of pure \( B \)


Foliar transpiration
A. Includes stomata and cuticular transpiration
B. Does not occur
C. Includes all type of transpiration
D. Shows stomatal transpiration


If \( a+2 b=9 \) and \( a b=7 . \) Find the value
of \( a^{2}+4 b^{2} \)


Which of the following fabrics is preferred for winter garments?
A. Nylon
B. cotton
c. wool
D. silk


Give product in following reactions


Formulate the reactions between but-I-
ene in presence of small amount of
benzoyl peroxide and \( (i) C C l_{4} \)
\( (i i) C B r C l_{3} . \) Give your reasons.


Two conductors are of same shape and
size. One of copper and the other of aluminium (less conducting) are placed in an uniform electric field. The charge induced in alumintum
A. Will be less than that in copper
B. will be more than that in copper
c. will be equal to that in copper
D. cannot be compared with that of copper


If \( D \) and \( E \) are the mi-points of the
sides \( A B \) and \( A C, \) respectively of the
\( \triangle A B C \) what percent of the whole triangular region is the area of the trapezium \( \boldsymbol{B C E D} \) ?
A . \( 50 \% \)
B . 25\%
c. \( 75 \% \)
D. 60\%


Monochromatic light of wavelength \( \mathbf{5 8 9} \) nm is incident from air on a water
surface. What are the wavelength,
frequency and speed of
(a) Reflected, and
(b) Refracted light?
Refractive index of water is 1.33


The vectors \( \overline{A B}=\overline{3 i}-\overline{2 j}+\overline{2 k} \) and
\( B C=-\bar{i}-\overline{2 k} \) are the adjacent sides
of a parallelogram. The angle between its diagonals is
A \( \cdot \frac{\pi}{2} \)
В \( \cdot \frac{\pi}{3} \) or \( \frac{2 \pi}{3} \)
c. \( \frac{3 \pi}{4} \) or \( \frac{\pi}{4} \)
D. \( \frac{5 \pi}{6} \) or \( \frac{\pi}{6} \)


\( \Delta H^{\ominus} \) for the cell reaction assuming
that these quantities remain
unchanged in the range \( 15^{\circ} C \) to \( 35^{\circ} \mathrm{C} \) is:
A. \( -99.97 k J \mathrm{mol}^{-1} \)
B. \( 99.97 k J \) mol \( ^{-1} \)
\( \mathbf{c} .-9.99 k J \mathrm{mol}^{-1} \)
D. \( 9.99 \mathrm{kJ} \mathrm{mol}^{-1} \)


In chapter 1 you read that snakes do not
have external ears. Can the snake hear
the been or does it dance when the
moves? What do you think?


\( = \)
\( k \)


Place value chart is extended on
side to provide place for fractions.
A. Right
B. Left
c. No
D. None


Dissolution of all gases in water is accompanied by evolution of heat.
A. True
B. False


Which symbol replaces the unit of atomic mass, amu?
\( A \)
B. A
\( c . \) м
\( D \)


Add \( 8 x y+4 y z-7 z x, 6 y z+11 z x- \)
\( 6 y \) and \( -5 x z+6 x-2 y x \)


In diamond crystal, each carbon atom is linked with carbon atoms? The number
of carbon atoms linked is:
A .2
B. 4
\( c .3 \)
D.


\( A \) speak the truth 8 times out of 10
times. A dice is tossed. He reports that
it was \( 5 . \) What is the probability that it was actually 5


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Primary amines show intermolecular hydrogen bonding
B. Secondary amines intermolecular hydrogen bonding.
C. Tertiary amines show intermolecular hydrogen bonding
D. Amines have lower boiling points as compared to those of alcohols and carboxylic acid of comparable molar masses.


1 \( g \) force is the force due to gravity on a mass of
\( \mathbf{A} \cdot 1 k g \)
в. \( 0.1 k g \)
c. \( 0.01 k g \)
D. \( 0.001 k g \)


Rectangle bars touching each other in which graph
A. histogram
B. bar
c. pie
D. line


The property of a material due to which shape is changed permanently is known
as:
A. Elasticity
B. Plasticity
c. Ductility
D. None of the above


With what terminal velocity will an air
bubble of diameter 0.8 mm rise in a
liquid of density \( 900 \mathrm{kg} \mathrm{m}^{-3} \) and
viscosity \( 0.15 N s m^{-2} ? \) What will be
the terminal velocity of the same bubble in water? Ignore density of air.


The largest alga is
A. Microcystic
B. Macrocystis
c. Red alga
D. Blue-green alga


Two bodies are changed by rubbing one
against the other. During the process,
one becomes positively charged while
the other becomes negatively charged.
Then,
A. mass of each body remains unchanged.
B. mass of each body changes marginally.
C. mass of each body changes slightly and hence the total mass.
D. mass of each body changes slightly but the total mass remains the same.


The product of two zeroes of the polynomial \( p(x)=x^{3}-3 x^{2}-6 x+8 \) is
\( (-2) . \) Find all the zeroes of the polynomial


The correct decreasing order of basic
strength is :
\( \mathbf{A} \cdot A s H_{3}>S b H_{3}>P H_{3}>N H_{3} \)
B \( \cdot S b H_{3}>A s H_{3}>P H_{3}>N H_{3} \)
\( \mathbf{C} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
\( \mathbf{D} \cdot P H_{3}>A s H_{3}>S b H_{3}>N H_{3} \)


Caulifiory is?
A. Production of new plants from cauline buds
B. Formation of flowers from old stem
C. Development of flowers on young branches
D. Clustering of flowers


Calculate the value of \( g \) on the surface
of planet if the planet has \( 1 / 500 \) the mass and \( 1 / 15 \) the radius of the Earth
в. \( 1.6 m / s_{2} \)
\( \mathrm{c} \cdot 2.4 \mathrm{m} / \mathrm{s}_{2} \)
D. \( 4.5 m / s_{2} \)
E \( .7 .1 \mathrm{m} / \mathrm{s}_{2} \)


The process of charging a conductor from a charged body without touching them together is called induction
A. True
B. False
c. Ambiguous
D. Data insufficient


Among the xylenes, which is thermodynamically most stable?
\( A \)
B.
\( \mathbf{c} \)
D. All are equally stable


Choose the correct statement:
A. The potential difference between the terminals of a cell in closed circuit is called EMF of the cell.
B. Electromotive force and accelerating force have the same dimensions.
C. The internal resistance of an ideal cell is infinity.
D. The difference between the emf of a cell and potential difference across the ends of the cell is called lost
volts.


Find the Arithmetic mean between 24
and 36
A . 26
B. 28
\( c .30 \)
D. 32


A parallel plate air capacitor has a
initial capacitance \( C . \) If plate
separation is slowly increased from \( \boldsymbol{d}_{1} \)
to \( d_{2} \), then mark the correct
statement(s). (Take potential of the
capacitor to be constant, i.e. throughout the process it remains connected to battery.) This question has multiple correct options
A. Work done by electric force= negative of work done by the external agent.
B. Work done by external force \( -\int \vec{F} . \overrightarrow{d x} \), where \( \vec{F} \) is the electric force of attraction between the plates at plate separation \( x \)
c. work done by electric force \( \neq \) negative of work done by external agent
D. work done by battery = two times the change in electric potential energy stored in capacitor.


Find out the correct statement from the
following.
A. In the muscles, the anaerobic respiration produces lactic acid.
B. In the muscles, the anaerobic respiration produces carbon dioxide, water and oxygen
C. Aerobic respiration produces lactic acid.
D. None of the above


What other name can you give to the
line symmetry of:
an isosceles triangle


A 'breath test' used by traffic police to check drunken driving uses \( _{--}--? \)


A fuse is used in an electrical appliance
A. To earth the appliance
B. To protect the appliance and its cable
C. To change the efficiency of the applicance
D. To change the current rating of the applicance


select the correct statement \( (s): \)
This question has multiple correct options
\( \mathbf{A} \cdot \) When \( d_{x^{2}-y^{2}} \) or \( d_{x y} \) orbitals combine in parallel planes, then \( \delta \) or \( \delta \) molecular orbitals are formed.
B. When \( d_{x^{2}-y^{2}} \) or \( d_{x y} \) orbitals combine in parallel planes, then N.B.M.O. are formed.
C. When \( d_{y z} \) or \( d_{x z} \) orbitals combine in along the y-axis, then N.B.M.O. are formed.
D. No interaction is possible when \( p_{z} \) and \( d_{x z} \) orbitals overlap with collinear z-axis


If \( f(x)=(a x+b) \cos x+(c x+d) \sin x \)
and \( f^{\prime}(x)=x \cos x, \) for all values of \( x \in \)
\( R, \) then \( a, b, c, d \) are given by
A \( a=b=c=d \)
\( d \)
в. 0,1,-1,0
c. 1,0,-1,0
D. 0,1,1,0


The middle term in the expansion of \( (1+x)^{2 n} \) is
This question has multiple correct options
A. \( \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{n !} 2^{n} \cdot x^{n} \)
в. \( \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{n !} 2^{n} \cdot x^{n} x^{n} \)
c. \( ^{2 n} C_{n} \)
D. \( 2 n C_{n}-1 x^{n-1} \)


If \( z \) is a complex number such that \( |z|=1, \) prove that \( \frac{z-1}{z+1} \) is purely imaginary. What will be your conclusion, if \( z=1 ? \)


The energy of the electron in the first orbit of \( \boldsymbol{H} \boldsymbol{e}^{-} \) is \( -\mathbf{8 7 1 . 6} \times \mathbf{1 0}^{-\mathbf{2 0}} \quad \boldsymbol{J} . \) The
energy of the electron in the first orbit of hydrogen would be:
\( \begin{array}{ll}\text { A } . & -871.6 \times 10^{-20}\end{array} \)
B . \( -435 \times 10^{-20} J \)
c. \( -217.9 \times 10^{-20} \mathrm{J} \)
D. - \( 108.9 \times 10^{-20} \mathrm{J} \)


Let \( A \) and \( B \) be matrices of orders \( 3 \times 2 \)
and \( 2 \times 4 \) respectively. Write the order
of matrix \( \boldsymbol{A} \boldsymbol{B} \)


Radioactive elements emit \( \alpha, \beta \) and \( \gamma \)
rays are characterized by their halflives. The radioactive isotope of
hydrogen is:
A. protium
B. deuterium
c. tritium
D. hydronium


Write the IUPAC name of the following
compound. \( C H \)
\( \mathbf{5} \)
\( \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3} \)


We can see an object from every direction due to of
the incident light ray on the object.
A . regular refraction
B. regular reflection
c. irregular reflection
D. none of these


Describe Watson and Crick's model of
DNA.


\( y=2 x+3 \) intersecting lines


Find the cube root of the following numbers by prime fractorisaiton method.
\( \mathbf{3 4 3} \)
\( \mathbf{4 0 9 6} \)
\( \mathbf{5 8 3 2} \)
\( \mathbf{1 2 5 0 0 0} \)


Fill in the blank:
The Indian name of the Orion
constellation is
A. Krittika
B. Mriga
c. Bichchhu
D. None of the above


Add: \( 87-35 \) and \( 35-87 \)
A .
B . - -65
\( c .-35 \)
D. 87


The mass of residue left after strongly heating 1.38 g of silver carbonate will be:
A \( .1 .16 \mathrm{g} \)
B. \( 1.33 \mathrm{g} \)
c. \( 2.66 g \)
D. 1.08 g


Provide the IUPAC name for the organic
compound shown above.
A. 3-chloro-5-methylhexanoic acid
B. 4-chloro-5-methylhexanoic acid
C. 4 -chloro-5,5-dimethylpentanoic acid
D. None of the above


The solubility product of \( A g_{2} C r O_{4} \) is \( 32 \times 10^{-12} . \) What is the concentration
of \( C r O_{4}^{-} \) ions in that solution?
A \( \cdot 2 \times 10^{-4} m / s \)
В . \( 16 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 8 \times 10^{-4} m / s \)
D. \( 8 \times 10^{-8} \mathrm{m} / \mathrm{s} \)


LH and FSH are called as
A. Anti stress hormones
B. Gonadotropic hormones
c. Emergency hormone
D. Neurohormones


If average molecular wt. of air is 29
then assuming \( N_{2} \) and \( O_{2} \) gases are
there which options are correct regarding composition of air:
i) \( 75 \% \) by mass of \( N_{2} \)
ii) \( 75 \% \) by moles \( N_{2} \)
iii) \( 72.41 \% \) by mass of \( N_{2} \)
A. only (i) is correct
B. only (ii) is correct
c. both (ii) and (iii) are correct
D. both (i) and (ii) are correct


toppr \( = \)
Q Type your question.
\( B \)
\( c \)
\( D \)


\( \int_{0}^{2 t} \frac{f(x)}{f(x)+f(2 t-x)} d x \)
A .2
B. 3t
\( c \cdot t \)
D. t/2


\( \mathbf{A}=\left[\begin{array}{lll}b^{2} c^{2} & b c & b+c \\ c^{2} a^{2} & c a & c+a \\ a^{2} b^{2} & a b & a+b\end{array}\right] \) then \( |A|=? \)
A \( \cdot a b c \)
B . \( a b c-1 \)
\( c \cdot a b c+1 \)
D.


\( (x+y+1) \frac{d y}{d x}=1 \)


There are \( m \) persons sitting in a row. two of them are selected at random. The
probability that the two selected persons are not together is \( 1-\frac{2}{m} . \) If
true enter 1 else 0


Which of the following statements
regarding metabolic pathways is incorrect?
A. Many of the steps of glycolysis can run in reverse
B. Starch, sucrose or glycogen must be hydrolysed before it can enter the glycolysis.
C. After fats are digested, glycerol enters glycolysis by forming DHAP.
D. After fat digestion, fatty acids can no longer participate in cellular respiration.


The D. E of the family of all circles in the first quadrant touching the coordinate
axes
\( \mathbf{A} \cdot\left[1+y_{1}^{2}\right]^{3}=r^{2} y_{2}^{2} \)
B \( \cdot\left[1+y_{2}\right]^{3}=r^{2} y_{1}^{2} \)
C \( \cdot\left[1+y_{1}^{2}\right]^{2}=r^{2} y_{2}^{3} \)
D. \( \left[1+y_{1}\right]^{3}=r^{2} y_{2}^{2} \)


A glass sphere, refractive index 1.5 and
radius \( 10 \mathrm{cm}, \) has a spherical cavity of
radius 5 cm concentric with it. A narrow
beam of parallel light is directed into the sphere. Find the final image and its
nature.
A \( .25 \mathrm{cm} \) left of \( S_{4} \), virtual
B. \( 25 \mathrm{cm} \) right of \( S_{4} \), virtual
C . \( 15 \mathrm{cm} \) left of \( S_{4} \), virtual
D. \( 20 \mathrm{cm} \) right of \( S_{4} \), virtual


Comment on the above reaction
\[
\mathrm{NH}_{3}+\frac{\mathrm{HgCl}_{2}}{\text { Mercuric }}>\begin{array}{c}
\mathrm{HgNH}_{2} \mathrm{Cl} \\
\text { Salts }
\end{array}
\]


A charged particle moves with a speed in a circular path of radius \( r \) around a long uniformly charged conductor then :
\( \mathbf{A} \cdot v \propto r \)
в. \( v \propto \frac{1}{r} \)
c. \( _{v \propto} \frac{1}{\sqrt{2}} r \)
D. \( v \) is independent of \( r \)


The co-ordinates of the vertices \( P, Q, R \)
\( \& S \) of square \( P Q R S \) inscribed in the \( \triangle A B C \) with vertices \( A \equiv(0,0), B \equiv \)
(3,0)\( \& C \equiv(2,1) \) given that two of its vertices \( P, Q \) are on the side \( A B \) are
respectively
\( ^{\mathbf{A}} \cdot\left(\frac{1}{4}, 0\right),\left(\frac{3}{8}, 0\right),\left(\frac{3}{8}, \frac{1}{8}\right) \&\left(\frac{1}{4}, \frac{1}{8}\right) \)
в. \( \left(\frac{1}{2}, 0\right),\left(\frac{3}{4}, 0\right),\left(\frac{3}{4}, \frac{1}{4}\right) \&\left(\frac{1}{2}, \frac{1}{4}\right) \)
c. \( (1,0),\left(\frac{3}{2}, 0\right),\left(\frac{3}{2}, \frac{1}{2}\right) \&\left(1, \frac{1}{2}\right) \)
D. \( \left(\frac{3}{2}, 0\right),\left(\frac{9}{4}, 0\right),\left(\frac{9}{4}, \frac{3}{4}\right) \&\left(\frac{3}{2}, \frac{3}{4}\right) \)


Acetamide is treated with the following
reagents separately. Which one of these
would yield methylamine?
A. \( N a O H-B r_{2} \)
B. Sodalime
c. Hot conc. \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( P C l \)


Which of the following halides of calcium is insoluble in water?
A. \( C a C l_{2} \)
в. \( C a I_{2} \)
c. \( C a F_{2} \)
D. \( C a B r_{2} \)


All the systems are closed system and at equilibrium. A decrease in the total volume of each container will increase
the number of moles of product(s) for which system?
A \( \cdot 2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
B . \( H_{2}(g)+C l_{2}(g) \rightleftharpoons 2 H C l(g) \)
c. \( 2 N O(g)+O_{2}(g) \rightleftharpoons 2 N O_{2}(g) \)
D. \( \operatorname{CO}(g)+H_{2} O(g) \rightleftharpoons C O_{2}(g)+H_{2}(g) \)
E \( \cdot F e_{3} O_{4}(s)+4 H_{2}(g) \rightleftharpoons 3 F e(s)+4 H_{2} O(g) \)


For \( \boldsymbol{X} \boldsymbol{Y}_{\mathbf{2}(\boldsymbol{g})} \rightleftharpoons \boldsymbol{X} \boldsymbol{Y}_{(\boldsymbol{g})}+\boldsymbol{Y}_{(\boldsymbol{g})}, \) intially 1
mole each of \( X Y_{2} \) and \( y \) are present in
10L flask at 500mm.lf the equilibrium
pressure of \( \mathrm{XY} \) is \( 150 \mathrm{mm}, K_{p} \) is?
A. \( 500 \mathrm{mm} \mathrm{mg} \)
B. \( \sqrt{500} \mathrm{mm} \) нв
c. \( 300 \mathrm{mm} \) Hg
D. 600mm Hg


The image of an object placed on the principal axis of a concave mirror of focal length \( 12 \mathrm{cm} \) is formed at a point which is \( 10 \mathrm{cm} \) more distance from the mirror than the object. The magnification of the image is
\( \mathbf{A} \cdot \underline{\mathbf{s}} \)
B. 2.5
\( c \cdot 2 \)
D. -1.5.


Find the equation of the plane which contains the line \( \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) and
is perpendicular to the plane \( \boldsymbol{x}+\boldsymbol{z}=\mathbf{3} \)
Find the point where this plane meets the line \( \frac{x}{2} \equiv \frac{y}{3}=\frac{z}{1} \)


\( \left(\frac{2}{5} a b+c\right)\left(\frac{2}{5} a b-c\right) \) is equal to
A \( \cdot \frac{4}{25} a^{2} b^{2}-\frac{4}{5} a b c+c^{2} \)
B \( \cdot \frac{4}{25} a^{2} b^{2}+\frac{4}{5} a b c+c^{2} \)
C \( \frac{4}{25} a^{2} b^{2}-c^{2} \)
D \( \cdot \frac{4}{25} a^{2} b^{2}+c^{2} \)


When, on large scale, negative and positive charges meet in clouds, we experience:
A. streak of bright light and sound
B. thunderstorm
c. lighting
D. all of the above


The value of \( \cos \left(\sin ^{-1} \frac{1}{2}+\sec ^{-1} 2\right) \)


Anomalous growth can be traced in
A. Dracaena
B. Yucca
c. Agave
D. All of the above


\( \mathbf{A}=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & \mathbf{1} & -\mathbf{1}\end{array}\right| \)
the minimum of \( \Delta \) is \( m_{1} \) and
maximum of \( \Delta \) is \( m_{2} \) then \( \left[m_{1}, m_{2}\right] \) are
related to
A. [4, 2]
B. [2,4]
\( c \cdot[4,0] \)
D. [0,2]


How many integers with at least one eight and at least one nine as digits are
there between 1 and 10000
A. 800
в. 974
\( c .900 \)
D. 875


An electromagnetic wave passing
through vacuum is described by the
equations. \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin (\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) \) and
\( B=B_{0} \sin (k x-\omega t) . \) Then
A \( \cdot E_{0} k=B_{0} \omega \)
в. \( E_{0} \omega=B_{0} k \)
c. \( E_{0} B_{0}=\omega k \)
D. \( E_{0}=B_{0} \)


The addition of two numbers is \( -120 . \) If
one number is four times the another
number. Find the greater number
A . -24
B. 96
\( c \cdot 24 \)
D. - 96


If maximum and minimum values of
the resultant of two forces acting at a point are \( 7 \mathrm{N} \) and \( 3 \mathrm{N} \) respectively, The smaller force is equal to


Two bodies are thrown vertically upward, with the same initial velocity of \( 98 m / s \) but 4 sec apart. How long after the first one is thrown when they meet?
A \( .10 \mathrm{sec} \)
B. 11 sec
c. 12 sec
D. 13 sec


Out of (ref. image), which one is
optically active and why?
and


Write different levels of organisations.


A man is moving with a velocity \( 3 \hat{i} \) with respect to the ground. The Rain is with a velocity \( -4 \hat{j} \) with respect to the ground. The relative velocity of rain with respect to the man is
B.
c. \( -3 \hat{i} \)
D. \( 4 \hat{j} \)


An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are 2: 1 and the odds in favor of the
price remaining the same are \( 1: 3 . \) The probability that the price of the stock will go down during the next week, is
A \( \cdot \frac{4}{12} \)
в. \( \frac{5}{12} \)
\( c \cdot \frac{7}{12} \)
D. none of these


The diagram in Fig. shows the
displacement- time graph of a vibrating
body. Name the kind of vibrations.


Write the formula of coordination
compound mercury tetrathiocyanatocobaltate (III):


State whether the following statements are true or false :
(i) The general formula of alkanes is
\( C_{n} H_{2 n+2} \)
(ii) Carbohydrates are body building nutrients.


The first stable product of fixation of atmospheric nitrogen in leguminous
plants is
\( \mathbf{A} \cdot N O_{2}^{-} \)
B. Ammonia
\( \mathbf{c} \cdot N O_{3}^{-} \)
D. Glutamate


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1}, \) equals
\( A \)
B. i-
\( c .- \)
D.


Bulb does not glow when the probs are hanged in air. The reason is:
A. air absorbs the electricity
B. air is a bad conductor of electricity
c. electricity is discharged into air
D. air disperses the electricity


\( \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \sqrt{\boldsymbol{1}+\boldsymbol{y}}+\boldsymbol{y} \sqrt{\boldsymbol{1}+\boldsymbol{x}}= \)
\( 0, \) then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{1}{(1+x)^{2}} \)
B. \( -\frac{1}{(1+x)^{2}} \)
c. \( \frac{1}{\left(1+x^{2}\right)} \)
D. \( \frac{1}{(1+x)} \)


Bleaching action of chlorine occurs in
the presence of :
A. oxygen
B. moisture
c. dry air
D. sunlight


If \( a+b=5 \) and \( a b=6 \) then find the
value of \( a^{3}+b^{3} \)


A radioactive nucleus of mass \( M \) emits
a photon of frequency \( v \) and the nucleus
recoils. The recoil energy will be
A . \( h v \)
B. \( M c^{2}-h v \)
c. \( \frac{h^{2} v^{2}}{2 M c^{2}} \)
D. zero


Which of the following is permissible during a thunderstorm?
A. Using a telephone having cord
B. Using a mobile phone
c. Taking a bath under running water
D. standing under a tree


A mixture of an organic liquid \( A \) and water distilled under one atmospheric
pressure at \( 99.2^{\circ} \mathrm{C} \). How many grams of steam will be condensed to obtained
1.0 \( g \) of liquid \( A \) in the distillate?
(Vapour pressure of water at \( 99.2^{\circ} \mathrm{C} \) is
739 mm Hg. Molecular weight of \( A= \)
\( \mathbf{1 2 3}) \)


What is the ratio of volumes of spheres and hemisphere?
A .2: 1
B. 4: 3
c. 2: 3
D. 1: 2


Find intervals in which the function \( \operatorname{given} \operatorname{by} f(x)=\sin 3 x, x \in\left[0, \frac{\pi}{2}\right] \) is
decreasing.


A certain mass of gas is expanded from \( (1 \mathrm{L} .10 \mathrm{atm}) \) to \( (4 \mathrm{L} .5 \mathrm{atm}) \) against a
constant external pressure of 1 atm. If
initial temperature of gas is \( 300 \mathrm{K} \) and
the heat capacity of process is \( 50 \mathrm{J} /^{\circ} \mathrm{C} \)
Then the enthalpy change during the process is: \( (-1 \mathrm{L} \text { atm } 100 \mathrm{J}) \)
A \( . \Delta H=15 \mathrm{kJ} \)
в. \( \Delta H=15.7 \mathrm{k} \)
c. \( \Delta H=14.4 \mathrm{kJ} \)
D. \( \Delta H=14.7 \mathrm{kJ} \)


The number of partial fraction of \( \frac{x^{2}+3 x+1}{(x-1)^{5}} \) is
A. 5
B. 4
\( c \cdot 3 \)
D.


Polymeric organic materials are called:
A . elastics
B. plastics
c. polythenes
D. None of these


Three force \( \overrightarrow{\boldsymbol{p}}, \overrightarrow{\boldsymbol{Q}} \) and \( \quad \overrightarrow{\boldsymbol{R}} \) acting
with TA,IB,IC where I is the incentance of
\( \triangle A B C \) are in equim \( \vec{P}_{Q}, \quad_{R} \)
is


Find the last term of the following sequence \( 4,4^{2}, 4^{3} \dots \dots \dots \)


Unlike \( P b C l_{4}, P I_{4} \) and \( P B r_{4} \) are not
found because:
A. bromine and iodine are more electronegative than chlorine
B. iodine and bromine are smaller in size.
c. larger iodine and bromine are able to reduce \( P b^{4+} \)to \( P b^{2+} \) or \( P b \)
D. the statement is incorrect.


A source of sound \( A \) emit waves of
frequency \( 1800 \mathrm{Hz} \) is falling towards ground with a terminal speed \( v . \) The observer \( B \) on the ground directly beneath the source receives waves of
frequency \( 2150 H z \). The source \( A \) receives waves, reflected from ground,
of frequency nearly:
(Speed of sound \( =343 \mathrm{m} / \mathrm{s} \) )
A. \( 2150 H z \)
в. \( 2500 H z \)
с. \( 1800 H z \)
D. 2400H \( z \)


Mention the essential material
(chemicals) to prepare soap in the laboratory. Describe in brief the test of determining the nature (acidic/ alkaline) of the reaction mixture of
saponification reaction


A source of sound vibrates according to the equation \( y=0.03 \sin \pi t . \) The
velocity of the wave is \( 1.5 \mathrm{m} / \mathrm{s} \). What is the wavelength of the wave?
\( A \cdot 3 m \)
B. 6 m
c. \( 4.5 \mathrm{m} \)
D. \( 1.5 \mathrm{m} \)


A substance reacts with initial concentration of \( a \) mol \( d m^{-3} \) according
to zero order kinetics. The time it takes
for the completion of the reaction is:
\( k= \) rate constant
A \( \cdot \frac{k}{a} \)
в. \( \frac{a}{2 k} \)
c. \( \frac{a}{k} \)
D. \( \frac{2 k}{a} \)


Marsh gas is produced by
A. Mycoplasma
B. Myxobacteria
c. Methanogens
D. Halophiles


The heat liberated per kilogram of a fuel
is called its:
A. calorific value
B. mass value
c. weight value
D. money value


Maximum iron filings stick to the middle of a bar magnet when it is brought near them.
A. True
B. False


\( X, Y \) and \( Z \) in the given graph are?
\( \mathbf{x}_{2}=(\mathbf{Y}) \quad \) Mole fraction \( \longrightarrow \quad \mathbf{y}_{2}=(\mathbf{Z}) \)
A. \( X=p_{1}+p_{2}, Y=1, Z=0 \)
B . \( X=p_{1}+p_{2}, Y=0, Z=0 \)
C \( \cdot X=p_{1} \times p_{2}, Y=0, Z=0 \)
D. \( X=p_{1}-p_{2}, Y=1, Z=0 \)


Which of the following oxidants is used in the determination of COD of a water
sample in the laboratory?
A \( . K N O_{3} \)
в. \( K M n O_{4} \)
c. Oxalic acid
D. \( K_{2} C r_{2} O_{7}+50 \% H_{2} S O_{4} \)


\( H_{2} O_{2} \) restores the colour of old lead
paintings, blackened by the action of
\( H_{2} S \) gas by:
A . converting \( P b O_{2} \) to \( P b \)
B. by oxidising \( P b S \) to \( P b S O_{4} \)
C. converting \( P b C O_{3} \) to \( P b \)
D. oxidising \( P b S O_{3} \) to \( P b S O_{4} \)


Which of the following acids is capable of dissolving gold?
A. Hydrochloric acid
B. Nitric acid
c. Sulfuric acid
D. A combination of A and B
E. A combination of A and C


Electric conduction in a semiconductor
takes place due to
A. electrons only
B. holes only
c. both electrons and holes
D. neither electrons nor holes


Podocytes are the cells present in
A. Cortex of nephron
B. Inner wall of Bowman's capsule
C. Proximal convoluted tubule
D. Wall of glomerular capillaries


The vapour pressure of water depends
upon:
A. surface area of container
B. volume of container
c. temperature
D. all of the above


At \( 675 K, H_{2}(g) \) and \( C O_{2}(g) \) react to
form \( C O(g) \) and \( H_{2} O(g), K_{p} \) for the reaction is \( 0.16 . \) If a mixture of 0.25
mole of \( H_{2}(g) \) and 0.25 mole of \( C O_{2} \) is
heated at \( 675 \mathrm{K} \), mole percentage of
\( \boldsymbol{C O}(\boldsymbol{g}) \) in equilibrium mixture is:
A . 7.14
B. 14.28
c. 28.57
D. 33.33


Suppose Shiva deposits Rs.1,000 in a
bank for 5 years for simple interest at
the rate of \( 8 \% \) per annum. Calculate
what he earns as interest over the years and tabulate it.


Based on this information answer the
questions given below. A string of three English letters is formed as per the following rules:
(a) The first letter is any vowel.
(b) The second letter is \( \boldsymbol{m}, \boldsymbol{n} \) or \( \boldsymbol{p} \)
(c) If the second letter is \( m \) then the
third letter is any vowel which is different from the first letter.
(d) If the second letter is \( n \) then the
third letter is \( e \) or \( u \)
(e) If the second letter is \( p \) then the third
letter is the same as the first letter.
How many strings of letters can possibly be formed using the above
rules?
\( \mathbf{A} \cdot 40 \)
B . 45
c. 30
D. 35


Two bars of same length and same cross -sectional area but of different
thermal conductivities \( K_{1} \) and \( K_{2} \) are
joined end to end as shown in the figure One end of the compound bar is at
temperature \( T_{1} \) and the opposite end at
temperature \( T_{2}\left(w h e r e T_{1}>T_{2}\right) \)
The temperature of the junction is
\( \mathbf{A} \)
\[
\frac{K_{1} T_{1}+K_{2} T_{2}}{K_{1}+K_{2}}
\]
B.
\[
\frac{K_{1} T_{2}+K_{2} T_{1}}{K_{1}+K_{2}}
\]
c. \( \frac{K_{1}\left(T_{1}+T_{2}\right)}{K_{2}} \)
D.
\[
\frac{K_{2}\left(T_{1}+T_{2}\right)}{K_{1}}
\]


Derive an expression for the velocity of
the two masses \( m_{1} \) and \( m_{2} \) with speeds
\( u_{1} \) and \( u_{2} \) undergoing elastic collision in one direction.


A ray of light enters from air to a
medium \( X . \) The speed of light in the
medium is \( 1.5 \times 10^{8} m / s \) and the speed
of light in air is \( 3 \times 10^{8} m / s \). Find the
Refractive index of the medium \( \boldsymbol{X} \)


The angle of deviation produced by the glass slab is
A . 0
B. 20
\( c .90^{\circ} \)
D. Depends on the angle formed by the light ray and normal to the slab


In simple harmonic motion, the acceleration is inversely proportional to the displacement of the body from its mean position.
A. True
B. False
c. Nither
D. Either


It is given that at \( x=1 \), the function
\( x^{4}-62 x^{2}+a x+9 \) attains its
maximum value, on the interval [0,2].
Find the value of a.


For \( x>1, \) the least value of the
expression \( 2 \log _{10} x-\log _{x}(0 \cdot 01) \) is :
A . 10
B. -0.01
\( c \cdot 2 \)
D. None of these


A magnetic moment of 1.73 BM will be
shown by which one among the following compounds?
A \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2} \)
B \( \cdot\left[N i(C N)_{4}\right]^{2-} \)
c. \( T i C l_{4} \)
D. \( \left[C o C l_{6}\right]^{4} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right] \) and
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=\boldsymbol{k}\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) then the value of
\( k \) is
\( \mathbf{A} \cdot \sin x \cos x \)
B.
c.
D.


When two bodies move uniformly towards each other, the distance
decreases by \( 6 m / s . \) If both bodies
move in the same directions with the
same speeds (as above), the distance
between them increases by \( 4 m / s \). Then
the speeds of the two bodies are
A. \( 3 m / s \) and \( 3 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \) and \( 2 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} .5 \mathrm{m} / \mathrm{s} \) and \( 1 \mathrm{m} / \mathrm{s} \)
D. \( 7 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \)


Newton's first law of motion gives the
concept of inertia.
A . True
B. False


The shape of Ammonium ion is:
A. tetrahedron
B. pyramid
c. square planar
D. square pyramid


Construct \( \triangle M N O \) where base \( N O= \)
\( 6.7 \mathrm{cm}, \angle M N O=45^{\circ} \) and \( M O \)
\( M N=2.8 \mathrm{cm} \)


The given table shows the possible food choices for lunch. How many different
types of lunch can be made each including 1 type of soup, 1 type of sandwich and 1 type of salad?
Lunch Choices
Soup Sandwich \( \quad \) Salad
Chicken Cheese Cheese \( \quad \) Vegetable
\( A \cdot 2 \)
B. 3
\( c .6 \)
D.


Which has maximum number of H-
atoms per gram of the substance?
A \( \cdot C H_{4} \)
в. \( C u S O_{4}: 5 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \)
D. \( H_{2} O \)


Oxidation of \( 1^{0} \) alcohols to aldehydes is very successful for the alcohols like:
A. Pent-2-yn-1-이
B. 1-hexanol
c. n-propyl alcohol
D. 1-pentanol
E . 1-octanol


Which of the following molecule acts as a bleaching agent?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
\( c \cdot N O_{2} \)
D. \( S O_{3} \)


\( \lim _{x \rightarrow 0} \frac{\sqrt{1+\tan x}-\sqrt{1-\tan x}}{\sin x}= \)
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D.


What is the potential of a half cell consisting of zinc electrode in \( 0.01 \mathrm{M} \)
\( Z n S O_{4} \) solution of
\( \mathbf{2 5}^{\circ} \boldsymbol{C} ?\left[\boldsymbol{E}^{\boldsymbol{o}}=\mathbf{0 . 7 6 3} \boldsymbol{V}\right] \)


Match the mixture given in column with the corresponding type of solutions given in column II


Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\left(\boldsymbol{H}_{2} \boldsymbol{O}\right) \boldsymbol{C l}_{2}\right] \)


Barium ions, \( C N^{-} \) and \( C o^{2+} \) form an
ionic complex. If that complex is supposed to be \( 75 \% \) ionised in water with vant Hoff factor 'i' equal to four
then the coordination number of \( C o^{2+} \)
in the complex can be.
A. Six
B. Five
c. Four
D. six and Four both


A hydrocarbon contains \( 10.5 g \) C-per
gram atom of hydrogen, 1 litre
hydrocarbon at \( 127^{\circ} \mathrm{C} \) and 1 atm
pressure weight \( 2.8 g . \) Find out the empirical formula and the molecular formula.


Which of the following is non-metric unit of length?
A . feet
B. yards
c. miles
D. all of the above


In the given figure, the line segment
\( X Y \) is parallel in \( A C \) of \( \Delta A B C \) and is
divided the triangle into two parts of equal areas then \( \frac{A X}{A B}=\frac{\sqrt{2}-1}{\sqrt{2}} \)
A . True
B. False


Match the following
Set- Set - II
A) \( F_{2} \)
1) pale yellow colour gas
B) \( C l_{2} \)
2) violet colour solid
C) \( B r_{2} \)
3) orange liquid
D) \( \boldsymbol{I}_{2} \)
4) greenish colour gas
Correct the matching is
A . A-1, B-3, C-2, D-4
B. A-1, B-4, C-3, D-2
c. \( A-2, B-3, C-4, D-1 \)
D. A-3, B-2, C-1, D-4


\( A=(2,4,5) \) and \( B=(3,5,-4) \) are two
points. If the \( x y \) -plane, \( y z \) -plane divide \( A B \) in the ratios \( a: b, p: q \) respectively then \( \frac{a}{b}+\frac{p}{q}= \)
A. \( \frac{7}{15} \)
в. \( \frac{-7}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{22}{25} \)


A physical quantity x depends on
quantities \( y \) and \( z \) as follows \( : x= \)
\( \boldsymbol{A} \boldsymbol{y}+\boldsymbol{B} \boldsymbol{t a n}\left(\boldsymbol{C}_{z}\right), \) where \( \boldsymbol{A}, \mathbf{B} \) and \( \boldsymbol{C} \) are
constants. Which of the followings do not have the same dimensions?
A. \( x \) and \( B \)
B. \( c \) and \( z^{-} \)
c. y and B/A
D. x and A


Which one of the following hydroxide
is insoluble in water?
\( \mathbf{A} \cdot C a(O H)_{2} \)
B. \( B a(O H)_{2} \)
\( \mathbf{c} \cdot B e(O H)_{2} \)
D. \( M g(O H)_{2} \)


State whether the following statements
are true or false.
Members of Zygomycotina and
Oomycotina are called the algal fungi because they have many common features with algae especially in the thallus structure and reproduction.
A. True
B. False


Diazonium salt used in the preparation
of phenol is obtained by treating with nitrous acid (obtained from sodium nitrite).
A. Aromatic primary amine
B. Aromatic secondary amine
c. Nitro benzene
D. None of the above


toppr 5
Q Type your question
the greatest?
\( A \)
B.
\( c \)
\( D \)
\( E \)


Draw a circle with centre \( O \) and radius
\( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( 0 . \) Draw
tangents to the circle from point \( P . \) Let
the tangents intersect the circle in points \( A \) and \( B . \) Find \( B P \)
A \( .6 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
c. \( 8.5 \mathrm{cm} \)
D. None of these


Sulphuric acid is formed when reacts with water.
\( A \cdot S O_{2} \)
B. \( S \)
\( \mathrm{c} \cdot \mathrm{SO}_{3} \)
D. \( O_{2} \)


\( \sec ^{2}\left(\tan ^{-1} 2\right)+\operatorname{cosec}^{2}\left(\cot ^{-1} 3\right) \) is equal
to
\( \mathbf{A} \cdot \mathbf{5} \)
B. 13
c. 15
D. 6


When sulphur monochloride is saturated with chlorine, the compound formed is
A \( . S C l_{6} \)
в. \( S C l \)
\( c \cdot S C l \)
D. \( S_{2} C l_{2} \)


Q Type your question_
two charges is represented by the field
lines also shown in the diagram.
What signs do the two charges have,
and which charge is stronger?
A. Charge 1 is positive, Charge 2 is negative and the stronger charge is Charge 1
B. Charge 1 is positive, Charge 2 is negative, and both charges have the same strength.
C. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 1
D. Charge 1 is negative, Charge 2 is positive, and both charges have the same strength.
E. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 2


Length of side of cube is \( 2 a \), then the
length of diagonal is


A curve \( C \) has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at \( A \) and \( B \)
and \( P \) is midpoint of \( A B . \) If the curve passes through the point (1,1) then the equation of the curve is?
A \( . x y=2 \)
в. \( x y=3 \)
c. \( x y=1 \)
D. \( x y=4 \)


Suppose \( S=\{1,2\} \) and \( T=\{a, b\} \)
\( \operatorname{then} \boldsymbol{T} \times \boldsymbol{S} \)
A \( \cdot(a, 1),(a, 2),(b, 1),(b, 2) \)
\( \mathrm{B} \times \mathrm{A}=\{(\mathrm{a}, 1),(\mathrm{a}, 2),(\mathrm{b}, 1),(\mathrm{b}, 2)\} \)
B. \( (1, a),(2, b),(b, 1),(b, 2) \)
D. None of the above


Define an ecosystem. Explain it with a suitable example.


Subtraction of \( \frac{11}{35} \) from \( \frac{12}{15} \) gives
A \( \cdot \frac{84}{35} \)
в. \( \frac{33}{35} \)
c. \( \frac{11}{15} \)
D. \( \frac{17}{35} \)


A \( . \quad R s .2100 .00 \)
B . \( R s .155 .00 \)
c. \( R s .150 .00 \)
D. \( R s .30 .00 \)


The electric field \( \mathrm{E} \), current density and conductivity \( \sigma \) of a conductor are
related as
A \( . \sigma=E / J \)
В . \( \sigma=J / E \)
\( \mathrm{c} \cdot \sigma=J E \)
D. \( \sigma=1 / E \)


Pollen, bacteria, fungal spores are also pollutants.
A. True
B. False


Justify the following with suitable reasons: Size of the atom increases as
we move down the group.


A cubical block of side \( 10 \mathrm{cm} \) floats at
the interface of an oil and water as
shown in the figure. The density of oil is
\( 0.6 g c m^{-3} \) and the lower face of ice cube
is \( 2 c m \) below the interface. The
pressure above that of the atmosphere at the lower face of the block is
A. \( 200 P a \)
с. 900 Ра
D. \( 800 P a \)


Electron was discovery by J.J. Thomson
A. True
B. False


A movie ticket costs \( R s .400 \). The tax on
it is \( 287 . \) Find the amount a customer
has to pay to buy the ticket.


Dorji has a few bottles of soft drink in his restaurant. But, unfortunately, these are not labelled. He has to serve the
drinks on the demand of customers.
One customer wants acidic drink,
another wants basic and third one
wants neutral drink. How will Dorji decide which drink is to be served to
whom?


If two intersecting lines are intersected by a transversal, then corresponding angles are equal.
A. True
B. False
c. Ambiguous
D. Data Insufficient


Express \( 90 \mathrm{cm} \) as a percent of \( 4.5 \mathrm{m} \)


If the mass of the body is doubled what'll happen to its acceleration if the same force applied.


3 years ago, the sum of the ages of a father and his son was 40 yeas. After 2 years, the sum of their ages will be
A. 46 years
B. 40 years
c. 50 years
D. 60 years


When a die is thrown, list the number of
outcomes of an event of getting
a number greater than 5


Study the given figure and label \( X, Y \)
and Z.
A. \( x \) - Backward reaction; Y - Forward reaction; \( z \)
Products
B. \( x \) - Forward reaction; \( Y \) - Backward reaction; \( z \) Equilibrium
C. \( x \) - Reversible reaction; Y - - Irreversible reaction; \( z \) -
Equilibrium
D. \( x \) - Forward reaction; Y - Forward reaction; \( z \) -
Backward reaction


Forces \( \vec{F} \) experienced by a particle having charge \( q \) and velocity \( \vec{v} \) in a magnetic field B is given by \( \overrightarrow{\boldsymbol{F}}=\mathrm{q}(\overrightarrow{\boldsymbol{v}} \times \)
\( \vec{B} \) ). What is the direction of force acting on electrons (negatively charged particles) falling vertically, at a place where the Earths magnetic field is
horizontal pointing towards North?
A. East
B. west
c. vertically up
D. Vertically down


If \( \vec{x} \& \vec{y} \) are two non collinear vectors
and \( a, b, c \) represent the sides of a
\( \Delta A B C \) satisfying \( (a-b) \vec{x}+ \)
\( (b-c) \vec{y}+(c-a)(\vec{x} \times \vec{y})=0 \) then
\( \Delta A B C \) is
A. an acute angle triangle
B. an obtuse angle triangle
c. a right angle triangle
D. a scalene triangle


The wavelength of \( H_{\alpha} \) line in hydrogen
spectrum was found to be \( 6563 A \) in the laboratory. If the wavelength of same line in the spectrum of a milky way is \( \boldsymbol{O} \)
observed to be \( 6568 A \), then recession velocity of milky way will be
A. \( 105 \mathrm{m} / \mathrm{s} \)
В. \( 1.05 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 10.5 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 0.105 \times 10^{6} \mathrm{m} / \mathrm{s} \)


When a gas is bubbled through water at \( 298 K, \) a very dilute solution of gas is
obtained. Henry's law constant for the
gas is \( 100 k \) bar. If gas exerts a pressure
of 1 bar, number of moles of gas
dissolved in 1 litre of water is :
A. 0.555
В. \( 55.55 \times 10^{-5} \)
c. \( 55.55 \times 10^{-3} \)
D. \( 5.55 \times 10^{-5} \)


State whether the following statement is true or false:

The salt which is used in medicine as a
contrast medium for stomach and
intestinal \( X \) -rays is \( B a S O_{4} \)


Write the structures of the following
compounds.
(i) \( 2- \) chloro, \( 3- \) methyl pentane
(ii) \( p- \) bromo chloro benzene


Cnidarians exhibit two basic body forms. What are they? How do they differ
from each other? Give one examples in each.


The function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}]+\cos \boldsymbol{x} \)
where \( [x] \) is the greatest integer \( \leq n \), is
A. a periodic function of period \( 2 \pi \)
B. a periodic function of period 1
c. a periodic function of indeterminate period
D. a non-periodic function


Which of the following means of birth control is most effective in preventing
AIDS?
A. Condom
в. Pill
c. Diaphragm
D. Spermicidal jelly


A plant is exposed to an optimum amount of light intensity, with a limited
supply of \( \mathrm{CO}_{2} \). As the carbon dioxide concentration increases
A. The rate of photosynthesis increases
B. The rate of photosynthesis decreases
c. The rate of photosynthesis remains constant
D. None of the above


The solubility of \( C a C O_{3} \) is \( 7 m g / \)litre. Calculate the solubility product of
\( B a C O_{3} \) from this information and from
the fact that when \( N a_{2} C O_{3} \) is added
slowly to a sloution containing equimolar concentration of \( C a^{2+} \) and
\( B a^{2+}, \) no precipitate is formed until 90
\( \% \) of \( B a^{2+} \) has been precipitated as
\( B a C O_{3} . \) The solubility product of \( B a C O_{3} \) is \( X \times 10^{-10} \) mol \( ^{2} l i t r e^{-2}, \) the
value of integer nearest to \( \boldsymbol{X} \) is:


\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{7} \\ \mathbf{9} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) find \( \boldsymbol{A}-\boldsymbol{B} \)


Assertion
Though air is a bad conductor yet a
body kept in air loses heat quickly.
Reason
The heat loss is mainly due to radiation.
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


Nucleosome contains
A. Only histone protein
B. Both DNA and histone protein
c. Only DNA
D. Both DNA and RNA


An electric dipole will experience a net force when it is placed in
A . a uniform electric field
B. a non-uniform electric field
\( c . \) both a and \( b \)
D. None of these


Write the names of the monomers for
each of the following polymers:
(a) Bakelite
(b) Nylon-2-nylon-6


How many no. of metals among the following obtained from molten salt
Electrolysis of their chlorides, oxides or hydroxides \( \mathrm{Cu}, \mathrm{Ag}, \mathrm{Ba}, \mathrm{Na}, \mathrm{Zn}, \mathrm{Fe}, \mathrm{Cs} \)


A cord is used to raise a block of mass
\( m \) vertically through a distance \( d \) at a
constant downward acceleration \( \boldsymbol{g} / \mathbf{4} \) The work done by the cord is:
\( \mathbf{A} \cdot m g d / 4 \)
в. \( 3 M g d / 4 \)
c. \( -3 M g d / 4 \)
D. \( M g d \)


Draw the intensity pattern for single slit diffraction and double slit interference.
Hence state two differences between
interference and diffraction patterns.


Assertion
Vapor in its natural state is a solid or
liquid at room temperature.
Reason
Gas in its natural state at room
temperature would still be a gas.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The different six digit numbers whose 3 digits are even and 3 digits are odd is
A . 281250
B. 281200
\( c \cdot \) 156250
D. none of these


Evaluate: \( \lim _{x \rightarrow 0} \frac{\sqrt[3]{1+\sin x}-\sqrt[3]{1-\sin x}}{x} \)
A . 0
B.
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{2} \)


Which term of the \( G P \sqrt{3}, 3,3 \sqrt{3}, \ldots . . \)
is \( 729 ? \)


The mirror formula is given by \( \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \) where the symbols have
their usual meanings. Then the lens formula is given by
A \( \cdot \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \)
в. \( \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \)
c. \( \frac{1}{v}+\frac{1}{u}=-\frac{1}{f} \)
D. \( \frac{1}{u}-\frac{1}{v}=\frac{1}{f} \)


Supination means turning plan
B. Forward
D. Bending
E. Straightening


A hexagon of side \( 8 \mathrm{cm} \) has a charge 4
\( \mu C \) at each of its vertices. The potentia
at the centre of the hexagon is
A \( \cdot 2.7 \times 10^{6} \mathrm{v} \)
B \( .7 .2 \times 10^{11} \mathrm{v} \)
C \( .2 .5 \times 10^{12} \mathrm{v} \)
D. \( 3.4 \times 10^{4} \mathrm{v} \)


The substances which vapourise during
burning, give flame.
A. True
B. False


In the neighbourhood of your school hard water required for an experiment is not available. Select from the
following grous of salts available in your school, a group each member of which, if dissolved in distilled water, will make
it hard :
A. sodium chloride, calcium chloride
B. potassium chloride, sodium chloride
c. sodium chloride, magnesium chloride
D. calcium chloride, magnesium chloride


Write the extracts of \( G_{1} \) and \( G_{2} \) phase?


In uniform circular motion the velocity
is
A. Constant
B. Variable
\( c \cdot>1 \)
D. None


Mention any two uses of a simple microscope.


Which one of the following is a driving force for the process of passive absorption of water in roots?
A. The increase in imbibitional pressure in root cells
B. Root pressure
c. Activity of aquaporins
D. Transpiration in leaves


All of the following are ways to write 25 percent of \( \boldsymbol{N} \)
EXCEPT for:
A . \( 0.25 N \)
в. \( \frac{25 N}{100} \)
c. \( \frac{1}{4} N \)
D. 25N


Match the column I with column II and
mark the appropriate choice.
" Column I
An element which
\( (A) \)
\( 1+8 \) can show
(i) oxidation state
An element with \( 7+ \)
(B) as the most stable
(ii) \( P m \) oxidation state in
its oxides
Radioactive
(iii) 0
\( \mathcal{D}_{\mathcal{S}} \)
(C) Ianthanoid
Lanthanoid which
(D) shows shows +4 oxidation state 4
(iv) \( M n \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B \( \cdot(A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i v),(D) \rightarrow(i) \)
C \( \cdot(A) \rightarrow(i v),(B) \rightarrow(i),(C) \rightarrow(i i),(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i i),(D) \rightarrow(i) \)


The relationship illustrated by the given
Venn diagram is :
\( \mathbf{A} \cdot(A \cup B) \cap C \)
\( \mathbf{B} \cdot(A \cap B) \cap C \)
\( \mathbf{c} \cdot(A \cap C) \cup B \)
\( \mathbf{D} \cdot(A \cup B)^{\prime} \cap C \)


Clear nights are colder than cloudy nights because of
A. conduction
B. condensation
c. radiation
D. insolation


Which one of the following will give optically active product with Bromine?
A. \( C H_{3}-C H=C H_{2} \)
в. \( C H_{2}=C H_{2} \)
c. Trans but-2-enc
D. 1 and 3


For an ideal binary liquid mixture:
A \( \cdot \Delta H_{(m i x)}=0 ; \quad \Delta S_{(\operatorname{mix})}<0 \)
B. \( \Delta S_{(\operatorname{mix})}>0 ; \quad \Delta G_{(\operatorname{mix})}<0 \)
\( \mathbf{c} \cdot \Delta S_{(m i x)}=0 ; \quad \Delta G_{(m i x)}=0 \)
D. \( \Delta V_{(\operatorname{mix})}=0 ; \quad \Delta G_{(\operatorname{mix})}>0 \)


The escape velocity for a planet is \( \boldsymbol{v}_{e} \cdot \mathbf{A} \) tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
A \( \cdot v_{c} \)
в. \( \frac{v_{e}}{\sqrt{2}} \)
c. \( \frac{v_{e}}{2} \)
D. zero


standard reduction potential of oxidant standard reduction potential of
reductant is more than \( 1.7 V \) then their
combination lead to explosion though it may be prevented by kinetic factors.
Now go through the following data and
answer the questions.
\( \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{\boldsymbol{0}}=\boldsymbol{0 . 8 0} \boldsymbol{V} \)
\( E_{C l O_{4}^{-} / C l O_{3}^{-}}^{0}=1.23 V \)
\( \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}^{\boldsymbol{0}}=\boldsymbol{0 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{E}_{\boldsymbol{M n O}_{\mathbf{4}}^{-} / \boldsymbol{M n}^{3+}}=\mathbf{1 . 5 4} \boldsymbol{V} \)
\( \boldsymbol{E}_{N_{2} / N_{3}^{-}}^{0}=-\mathbf{3 . 0 9} \boldsymbol{V} \)
\( \boldsymbol{E}_{N a^{+} / N a}^{0}=-2.17 V \)
\( \boldsymbol{E}_{O_{2} / \boldsymbol{H}_{2} \boldsymbol{O}_{2}}^{0}=-\mathbf{1 . 0 3} \boldsymbol{V} \)
Which of the following ionic
combinations may lead to the formation
of explosive substance?
A. Sodium ion and azide ion
B. Silver ion and perchlorate ion
c. Silver ion and azide ion
D. All the above


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


Xenia and metaxenia effects are shown
by
A. Gymnosperms
B. Angiosperms
c. Bryophytes and pteridophytes
D. All of the above


A curve drawn at constant temperature
is called an isotherm. This shows the
relationship between:
A \( \cdot P \) and \( \frac{1}{V} \)
B. \( P V \) and \( V \)
c. \( v \) and \( \frac{1}{P} \)
D. \( P \) and \( V \)


Diamond Ring is a phenomenon
observed:
A. at the start of a total solar eclipse
B. at the end of a total solar eclipse
C. only along the peripheral regions of the totality trail
D. only in the central regions of the totality trail


If we place a solid hot metal in a cool liquid the metal and the liquid come to
some final temperature together. The specific heat of the liquid is five times as great as the specific heat of the
metal. The temperature change for the metal is twenty times as much as that for the liquid.
How does the mass of the liquid
compare to the mass of the solid metal?
Assume no heat is lost from the system.
A. The mass of the liquid is 100 times as much as the mass of the metal.
B. The mass of the liquid is 5 times as much as the mass of the metal.
c. The mass of the liquid is 20 times as much as the mass of the metal.
D. The mass of the liquid is \( 1 / 4 \) times as much as the mass of the metal.
E. The mass of the liquid is 4 times as much as the mass of the metal.


Calculate N and a


Which one of the following is not a category of states of matter?
A. Solid
B. Liquid
c. Gas
D. Semi-liquid


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}x^{3}-x^{2}+10 x-5 \quad, x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-2\right), x>1\end{array} \) the set of \right.
values of \( b \) for which \( f(x) \) has greatest
value at \( x=1 \) is given by:
A. \( 1 \leq b \leq 2 \)
В . \( b=\{1,2\} \)
c. \( b \in(-\infty,-1) \)
D \( \cdot b \in[-\sqrt{130},-\sqrt{2}] \cup[\sqrt{2}, \sqrt{130}] \)


Water stored in a dam possesses:
A. no energy
B. electrical energy
c. kinetic energy
D. potential energy


Find the coordinates of the points of trisection of the line segment joining the points \( A(-4,3) \) and \( B(2,-1) \)


Which reagent will lengthen the carbon chain by two carbon in one step on reaction with an
oragnolithium reagent?
A. Acetic acid
B. Formaldehyde
c. lodo methane
D. Ethylene oxide


Two particle A and B are initially at a
distance x. Initial velocity of particles \( \mathbf{A} \) and \( \mathrm{B} \) are \( 10 \mathrm{m} / \mathrm{s} \) and 25
\( \mathrm{m} / \mathrm{s} \) respectively in the direction shown in figure and their constant
accelerations are \( 1 m / s^{2} \) and \( 2 m / s^{2} \) respectively in the direction shown in figure.What should be the minimum
value of \( x, \) so that these particle can just avoid collision:
\( ^{\mathbf{A}} \cdot \frac{125}{2} m \)
в. \( \frac{75}{2} \) г
c. \( \frac{75}{4} \) m
D. \( \frac{125}{4} m \)


IUPAC name of \( \left[\boldsymbol{F e}\left(\boldsymbol{O}_{2}\right)(\boldsymbol{C} \boldsymbol{N})_{4} \boldsymbol{C l}\right]^{4-} \) is :
A. chlorotetracyano dioxoferrate (II) ion
B. Chlorotetracyano peroxoferrate (II) ion
c. chlorotetracyano superoxoferrate (II) ion
D. Tetracyanochloro superoxoferrate (II) ion


If \( f(x)=\frac{e^{1 / x}-1}{e^{1 / x}+1}, x \neq 0 \) and \( f(0)=0 \)
then \( f(x) \) is
A. Continuous at 0
B. Right continuous at 0
c. Discontinuous at 0
D. Left continuous at 0


Draw a ray diagram of compound microscope, when final image is formed at the minimum distance of distinct
vision.


Assertion
Equation of tangent to the curve \( \boldsymbol{y}= \)
\( x^{2}+1 \) at the point where slope of
tangent is equal the function value of
the curve is \( y=2 x \)
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x}) \)
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


Figure shows three circular arcs, each
of radius \( \mathrm{R} \) and total charge as
indicated. The net electric potential at
the centre of curvature is?
A \( \cdot \frac{Q}{2 \pi \varepsilon_{R}} \)
B・ \( \frac{Q}{3 \pi \varepsilon_{R}} \)
c. \( \frac{2 Q}{\pi_{c e R} R_{R}} \)
D. \( \frac{Q}{\pi \varepsilon R} \)


Ammonia act as a Lewis base. Explain.


Following reaction takes place by mechanism
\( N O_{2}+C O \rightarrow N O+C O_{2} \)
\( \boldsymbol{\operatorname { S t e p }} \boldsymbol{I} \quad \boldsymbol{N} \boldsymbol{O}_{2}+\boldsymbol{N} \boldsymbol{O}_{2} \quad \stackrel{\boldsymbol{k}_{1}, s l o \boldsymbol{w}}{\longrightarrow} \)
\( N O_{3}+N O \)
\( \operatorname{Step} I I \quad N O_{3}+C O \quad \stackrel{k_{2}, f a s t}{\longrightarrow} \)
\( N O_{2}+C O_{2} \)
Hence, \( \left(\frac{d x}{d t}\right) \) for the given reaction is:
\( \mathbf{A} \cdot k_{1}\left[N O_{2}\right]^{2}-k_{2}\left[N O_{3}\right][C O] \)
B \( \cdot k_{1}\left[N O_{2}\right]^{2}+k_{2}\left[N O_{3}\right][C O] \)
\( \mathbf{c} \cdot k_{1}\left[N O_{2}\right]^{2} \)
D. \( k_{1}\left[N O_{2}\right]+k_{2}[C O] \)


Integrate the function \( x \log 2 x \)


A point \( P \) moves in counter-clockwise
direction on a circular path as shown in
the figure. The movement of \( \boldsymbol{P} \) is such
that it sweeps out a length \( s=t^{2}+5 \)
where \( s \) is in metres and \( t \) is in seconds.
The radius of the path is \( 20 m \). The
acceleration of \( \boldsymbol{P} \) when \( \boldsymbol{t}=\boldsymbol{2} \boldsymbol{s} \) is
approximately :
A \( \cdot 13 m / s^{2} \)
В. \( 2.15 m / s^{2} \)
\( c \cdot 7 \cdot 2 m / s^{2} \)


Matter is neither ............ nor , ............. in a
chemical reaction.


A uniform string of length / is fixed at both ends such that tension T is
produced in it. The string is excited to vibrate with maximum displacement
amplitude \( a_{o} . \) The kinetic energy of the
string for its \( f \) irst overtone is given as \( \frac{a_{0}^{2} \pi^{2} T}{x l} . \) Find \( x \)


When an electric dipole \( \vec{p} \) is kept in a uniform electric field \( \vec{E} \) then for what of a value of the angle between \( \vec{p} \) and \( \vec{E} \),
torque will be maximum:
A \( .90^{\circ} \)
B. \( 0^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 45^{\circ} \)


The volume of a sphere of radius \( r \) is:
A \( \cdot \frac{4}{3} \pi r^{3} \)
В. \( 2 \pi r^{2} \)
c. \( \frac{2}{3} \pi r^{3} \)
D. \( 4 \pi r^{2} \)


A student made the following
observations in the laboratory.
I. Clean copper metal did not react with
1 molar \( P b\left(N O_{3}\right)_{2} \) solution
II. Clean lead metal dissolved in a 1
molar \( A g N O_{3} \) solution and crystals of \( A g \) metal appeared
III. Clean silver metal did not react with
1 metal \( C u\left(N O_{3}\right)_{2} \) solution
The order of decrease in reducing
character of three metals is:
A. \( P b, C u, A g \)
в. \( P b, \) А \( g, C u \)
c. \( C u, A g, P b \)
D. \( C u, P b, A g \)


A vessel less piece of stem possessing prominent sieve tubes would belong to
A. Pinus
B. Eucalyptus
c. Grass
D. Trochodendron


Area common to the curves \( y^{2}=a x \) and
\( x^{2}+y^{2}=4 a x \) is equal to
A \( \cdot(9 \sqrt{3}+4 \pi) \frac{a^{2}}{3} \)
B . \( (9 \sqrt{3}+4 \pi) a^{2} \)
c. \( (9 \sqrt{3}-4 \pi) \frac{a^{2}}{3} \)
D. none of the above


The longest chord of a circle is a \( \ldots \). Of the circle.
A. Diameter
B. Lies on upper part of centre
c. Lies on lower part of centre
D. None of these


Write the difference between terylene
fibers and Buna-s rubber (clastomers)


Which of the following has correct direction of Inductive effect?
A \( \cdot C H_{3}-C H_{2} \rightarrow L i \)
B. \( H_{2} N \rightarrow C H=C H^{-} \)
c. \( H_{2} N \rightarrow C H_{2}-C H=C H^{-} \)
D.


A multimeter reads a voltage of a certain A.C. source as \( 100 \mathrm{V} \). What is the peak value of voltage of A.C. source?
A . 200
B. 100 V
c. \( 141.4 \mathrm{v} \)
D. 400


A toy train rotates about a circle of
radius \( 50 \mathrm{cms}, 10 \) times in 2 minutes.
What is the frequency of the train
A. 5 per second
B. 12 per second
c. \( 1 / 12 \) per second
D. \( 1 / 5 \) per second


The following are the equilibria
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} K_{1} \dots(\mathrm{i}) \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O K_{2} \)
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{K}_{3} \)
Then the equilibrium constant \( \boldsymbol{K}_{4} \) for
the reaction
\( \mathbf{2} N \boldsymbol{H}_{3}+\frac{5}{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A \( \cdot \frac{K_{2} \times K_{3}}{K_{1}} \)
B. \( \frac{K_{2} \times K_{3}^{3}}{K_{3}} \)
c. \( \frac{K_{2} \times K_{3}^{3}}{K_{1}} \)
D. \( \frac{K_{2} \times K_{1}}{K_{3}} \)


Control rods in a nuclear power plant is
to
A. Slow the neutrons thereby controlling the fission reaction
B. Shut down the reactor.
c. Both (1) and (2)
D. None of these


Shape of \( \boldsymbol{S} \boldsymbol{F}_{4} \) is:
A . tetrahedral
B. square planar
c. square pyramidal
D. see - saw


The solvent used in Wurtz reaction is:
A. \( C_{2} H_{5} O H \)
в. \( C H_{3} \) СООН
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C_{2} H_{5} O C_{2} H_{5} \) (dry)


Which of the following aqueous solution will show maximum vapour pressure at
300K?
\( \mathbf{A} \cdot 1 M N a C l \)
в. \( 1 \mathrm{M} \mathrm{CaCl}_{2} \)
c. \( 1 M A l C l_{3} \)
D. \( 1 M C_{12} H_{22} O_{11} \)


Write the products of hydrolysis of
lactose.


Which one among the following is not
correct as per indicated property?
\( \mathbf{A} \cdot B r_{2}<C l_{2}<F_{2}(\text { Oxidising power }) \)
B. \( B r_{2}<F_{2}<C l_{2} \) (Electron gain enthalpy)
\( \mathbf{c} \cdot B r_{2}<C l_{2}<F_{2}(\text { Electronegativity }) \)
\( \mathbf{D} \cdot B r_{2}<C l_{2}<F_{2}(\text { Bond energy }) \)


A hydrocarbon which on catalytic hydrogenation gives a saturated
hydrocarbon is :
A. ethanol
B. acetic acid
c. ethene
D. methane


Calculate the energy released when an electron annihilates a positron.


The biological amplification of DDT in the various trophic levels is known as.
A. Green house effect
B. Biomagnification
c. Eutrophication
D. Pollution


Which of the following sets of side lengths will not form a triangle?
A. \( 11 \mathrm{cm}, 10 \mathrm{cm}, 11 \mathrm{cm} \)
в. \( 3 \mathrm{m}, 3 \mathrm{m}, 3 \mathrm{m} \)
\( \mathbf{c} .9 \mathrm{mm}, 9 \mathrm{mm}, 12 \mathrm{mm} \)
D. \( 3 \mathrm{cm}, 4 \mathrm{cm}, 7 \mathrm{cm} \)


The vitamin which maintain the redox
potentials of cells is:
A. folic acid
B. ascorbic acid
c. pyridoxine
D. calciferol


Assertion
The equivalent thermal conductivity of two plates of same thickness in contact
is less than the smaller value of thermal
conductivity
Reason
For two plates of equal thickness in contact the equivalent thermal conductivity is given by:
\( \frac{1}{K}=\frac{1}{K}_{1}+\frac{1}{K} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A man is known to speak the truth 3 out of 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these


Find the digit at unit's place of \( 128^{3} \)
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
D. 2


The open chain aliphatic hydrocarbon
with molecular formula \( C_{9} H_{16} \) is :
\( A \). an alkane
B. an alkene
c. an alkyne
D. a cyclic


Monochromatic light of wavelength
\( 4500 A \) falls on slit of width 'a'. In
diffraction pattern second maxima
deviates through \( 30^{\circ} . \) The slit width is
\( \mathbf{A} \cdot 900 \stackrel{\circ}{A} \)
в. 18000 А
\( \mathrm{c} \cdot_{13500 \AA} \)
D \( \cdot 22500 \) 台


\( A 5 N \) force acts on a \( 2.5 \mathrm{kg} \) mass at
rest, making it accelerate in a straight line.
i) What is the acceleration of the mass?
ii) How long will it take to move the mass through \( 20 m ? \)
iii) Find its velocity after 3 seconds


A parallel plate capacitor is charged
and then isolated. What is the effect of
increasing the plate separation on charge, potential, capacitance, respectively?
A. constant, decreases, decreases
B. Increases, decreases, decreases
c. constant, decreases, increases
D. constant, increases, decreases


Find the shortest distance between the
\( x^{2}+y^{2}=9 \) and (6,8) is


\[
\begin{array}{l}
\boldsymbol{C H}_{3}-\underset{\Gamma H_{2} C H_{3}}{C H}-\stackrel{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}- \\
\frac{C H_{2} C H_{3}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3}
\end{array}
\]
What will be the IUPAC name of given
compount?
A. 2, 5-diethyl-4-methylhexane
B. 3, 4, 5-trimethyloctane
c. \( 2,5, \) 6-trimethyloctane
D. 3, 5-dimethyl-6-ethylheptane


What is binomial nomenclature?
Explain it with a suitable example. Give
its advantages.


In which experiment outcomes are not predictable?
A. sample
B. event
c. random
D. essential


What is the height of mercury which
exerts the same pressure as \( 20 \mathrm{cm} \) of water column? Take density of mercury
as \( 13.6 g / c c \)


kept in two identical vessels, which are
placed in a freezer that extracts heat
from them at the same rate causing
each liquid to transform into a solid.
The schematic figure shows the
temperature T vs time t plot for the two
materials. We denote the specific heat
in the liquid states to be \( C_{L 1} \) and \( C_{L 2} \)
for materials 1 and 2 respectively, and
latent heats of fusion \( U_{1} \) and \( U_{2} \)
respectively. Choose the correct option.
A. \( C_{L 1}>C_{L 2} \) and \( U_{1}<U_{2} \)
B. \( C_{L 1}>C_{L 2} \) and \( U_{1}>U_{2} \)
\( \mathbf{c} \cdot C_{L 1}<C_{L 2} \) and \( U_{1}>U_{2} \)
D. \( C_{L 1}<C_{L 2} \) and \( U_{1}<U_{2} \)


If a body is sent with a velocity of \( \mathrm{km} \mathrm{sec}^{-1} \), it would leave the earth
forever.
A . 11.9
в. 11.6
c. 11.4
D. 11.2


Which of the following is a redox
reaction:
\( \mathbf{A} \cdot 2 C r_{4}^{2-}+2 H^{+} \rightarrow C r_{2} O_{7}^{2-}+H_{2} O \)
B \( \cdot C u S O_{4}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
\( \mathbf{c} \cdot 2 N a_{2} S_{2} O_{3}+I_{2} \rightarrow N a_{2} S_{4} O_{6}+2 N a I \)
\( \mathbf{D} \cdot C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)


Calculate the sum of angles of a
polygon having 10 sides.
A \( .960^{\circ} \)
B. \( 1440^{\circ} \)
c. \( 900^{\circ} \)
D. 720


Q Type your question
(see figure I).The other ends are
attached to identical supports M1 and
M2 not attached to the walls. The
springs and supports have negligible mass. There is no friction anywhere. The
block B is displaced towards wall 1 by a small distance \( x \) (figure II) and released
The block returns and moves a
maximum distance y towards wall 2.
Displacements x and y are measured with respect to the
equilibrium position of the block B. The ratio \( \frac{\boldsymbol{y}}{\boldsymbol{x}} \) is
A . 4
B. 2
\( c \cdot \frac{1}{2} \)


Assume that a factory has two
machines \( A \) and \( B \). Past records shows
that machine \( A \) produces \( 60 \% \) of the
items of output and machine \( \boldsymbol{B} \) produces \( 40 \% \) of the items. Further, \( 2 \% \) of the items produced by machine \( \boldsymbol{A} \)
were defective and only \( 1 \% \) produced by
machine \( B \) were defective. If a detective
item is drawn at random, what is the
probability that it was produced by machine \( \boldsymbol{A} \) ?


What are the characteristic features of
an artery?
A. Have thick elastic, muscular walls
B. Have thin, non-elastic walls
c. Carry blood from heart to all body parts
D. Both A and C


In plant glycolipids, the sugar is normally.
A . oil
B. wax
c. glycolipid
D. phospholipid


Arrange the following compounds in the increasing order of their reactivity
towards HCN.
I. Acetaldehyde
II. Acetone
III. Methyl-tert-butyl ketone
IV. Di-tert-butyl ketone
A. III <II<IV <
B. II \( |<|<\mid V<\| \)
c. \( \mid V<\|<\|<1 \)
D. II<IV <I<III


Assertion
Kidneys maintain the osmotic
concentration of the blood.
Reason
Kidneys eliminate either hypotonic or hypertonic urine according to the need of the body.
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


\( \ln \) a closed flask of \( 511.0 g H_{2} \) is heated from 300 to 600 K. Which statement is
not correct?
A. Pressure of the gas increases
B. The rate of collisions increases
c. The number of moles of gas increases
D. The energy of gas molecules increases


A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfies \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\boldsymbol{2} \boldsymbol{a}-\boldsymbol{x}) . \) Suppose \( \boldsymbol{f}(\boldsymbol{x}) \) is
differentiable at \( x=a \) then
This question has multiple correct options
A \( \cdot f^{\prime}(a)=0 \)
B . \( f^{\prime}\left(a^{+}\right)=-f^{\prime}\left(a^{-}\right) \)
c. \( f^{\prime}\left(a^{+}\right)=f^{\prime}\left(a^{-}\right)=0 \)
D. None of these


Which of the following numbers are rational?
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 6
\( c \cdot_{3} \frac{1}{2} \)
D. All above are rationa


Lattice energy of an ionic compound depends upon:
A. charge on the ion and size of the ion
B. packing of ions only
c. size of the ion only
D. charge on the ion only


Which of the following options is not
correct?
B. 126,000 has 3 significant figures
c. \( 15.15 \mu s=1.515 \times 10^{-5} s \)
D. \( 0.0048=48 \times 10^{-3} \)


\( \boldsymbol{\alpha}=\mathbf{0 . 9 9} \) for a CE transistor amplified
circuit. The input resistance is equal to \( 1 \mathrm{K} \Omega \) and load resistance is equal to 10
K \( \Omega . \) The voltage gain of the circuit is
A . 99
в. 990
c. 9900
D. 99000


How many unbonded pairs of electrons are found in a neutral atom of sulfur?
A. Three
B. Two
c. one
D. None


If three different liquid of different
masses specific heats and temperature are mixed with each other then what is
the temperature of the mixture at
thermal equilibrium. If, \( m_{1}, s_{1}, T_{1} \rightarrow \) specification for liquid
\( \boldsymbol{m}_{2}, \boldsymbol{s}_{2}, \boldsymbol{T}_{2} \rightarrow \) specification for liquid
\( \boldsymbol{m}_{3}, \boldsymbol{s}_{3}, \boldsymbol{T}_{3} \rightarrow \) specification for liquid
A \( \cdot \frac{m_{1} T_{1}+m_{2} T_{2}+m_{3} T_{3}}{m_{1} s_{1}+m_{2} s_{2}+m_{3} s_{3}} \)
В \( \cdot\left(m_{1} s_{1} T_{1}+m_{2} s_{2} T_{2}+m_{3} s_{3} T_{3}\right) \)
c. \( \frac{m_{1} s_{1} T_{1}+m_{2} s_{2} T_{2}+m_{3} s_{3} T_{3}}{m_{1} s_{1}+m_{2} s_{2}+m_{3} s_{3}} \)
D. \( \frac{s_{1} T_{1}+s_{2} T_{2}+s_{3} T_{3}}{m_{1} s_{1}+m_{2} s_{2}+m_{3} s_{3}} \)


Which of the following is a volatile covalent liquid at \( 25^{\circ} \mathrm{C} \) and 1 atm?
A . \( N_{2} \)
в. \( K I \)
c. \( C C l_{4} \)
D. \( A g N O_{3} \)
ह. \( C a C O_{3} \)


An object looks red when seen through a piece of red glass. What is the actual colour of the object?
A. Red only
B. White only
c. Either A or B
D. Neither A nor B


Find the multiplicative inverse of \( \sqrt{5}+ \)
\( \mathbf{3} i \)
A \( . \sqrt{5}-3 i \)
B. \( \frac{\sqrt{5}-3 i}{14} \)
c. \( -\sqrt{5}+3 i \)
D. \( \frac{-\sqrt{5}+3 i}{14} \)


What are the limitations of the energy
obtained from oceans(any two)?


The \( 8^{t h} \) term of an AP is 37 and its \( 12^{t h} \)
term is \( 57 . \) Find the AP.


Probability of an impossible event is


In a square garden of \( 3.5 \mathrm{m}, \) four flower beds were laid out as shown. The
remaining area of the garden is \( 7.25 m^{2} \) If all flower beds are of same size find
length of each if the breadth of each
flower bed is \( 50 \mathrm{cm} \)


\( \lim _{x \rightarrow 0} \sin ^{-1}(\sin x) \) is equal to
A \( \cdot \frac{\pi}{2} \)
B. 1
c. zero
D. None of the above


Explain, with the help of a circuit diagram, the working to a photo-diode. Write briefly how it is used to detect the
optical signals. OR
Mention the important considerations required while fabricating a \( \boldsymbol{p}-\boldsymbol{n} \)
junction diode to be used as a Light Emitting Diode (LED). What should be
the order of band gap of an LED if it is required to emit light in the visible
range?


State the Kohlrausch law of
independent migration of ions. Why
does the conductivity of a solution decrease with dilution?


Using binomial theorem, expand \( \{(x+ \) \( \left.y)^{5}+(x-y)^{5}\right\} \) and hence find the
value of \( \left\{(\sqrt{\mathbf{2}}+\mathbf{1})^{\mathbf{5}}+(\sqrt{\mathbf{2}}-\mathbf{1})^{\mathbf{5}}\right\} \)


A ray traveling from glass into air:
A. bends away from the normal
B. bends towards the normal
c. passes undeviated
D. emerges along the normal


Choose the correct statement.
A. White or yellow phosphorus is stored under water
B. Ignition temperature of red phosphorus is low
C. Black phosphorus is non crystalline in nature
D. Phosphorus does not form hydrides


Which of the following reactions will not get affected on increasing the pressure?
\( \mathbf{A} \cdot 2 H_{2(g)}+C O_{(g)} \rightleftharpoons C H_{3} O H_{(g)} \)
B. \( 4 N H_{3(g)}+5 O_{2(g)} \rightleftharpoons 4 N O_{(g)}+6 H_{2} O_{(g)} \)
C. \( C H_{4(g)}+2 S_{2(g)} \rightleftharpoons C S_{2(g)}+2 H_{2} S_{(g)} \)
D. \( P C l_{5(g)} \rightleftharpoons P C l_{3(g)}+C l_{2 g} \)


A gaseous mixture enclosed in a vessel
of volume \( V \) consists of one mole of gas
\( \mathbf{A} \) with \( \gamma\left(=C_{P} / C_{V}\right)=5 / 3 \) and another
gas \( \mathrm{B} \) with \( \gamma=7 / 5 \) at a certain
temperature T. The relative molar
masses of the gas \( A \) and \( B \) are 4 and 32 respectively. The gases \( A \) and \( B \) do not react with each other and are assumed
to be ideal. The gaseous mixture follows the equation \( P V^{19 / 13}= \) constant, in
adiabatic processes. Compute the speed of sound in the
gaseous mixture at \( \boldsymbol{T}=\mathbf{3 0 0 K} \)
A. \( v=501 \mathrm{m} / \mathrm{s} \)
в. \( v=401 \mathrm{m} / \mathrm{s} \)
c. \( v=701 \mathrm{m} / \mathrm{s} \)
D. \( v=801 \mathrm{m} / \mathrm{s} \)


The IUPAC name of the given compound
is :
A. 3-cyclopropane-1-propene
B. 3-cyclopropyl-1-propene
C. 3-cyclopropyl-2-propene
D. 3-cyclopropane-2-propene


The distance moved by a particle travelling in a straight line in \( t \) seconds is given by \( s=45 t+11 t^{2}-t^{3} . \) The
time taken by the particle to come to
rest is
\( A \)
\( \frac{5}{3} \sec \)
B. 0 sec
\( c .9 \mathrm{sec} \)
D. \( _{\frac{3}{5}} \) sec


If the roots of \( a x^{3}+b x^{2}+c x+d=0 \)
are in A.P., then the roots of \( a(x+ \)
\( k)^{3}+b(x+k)^{2}+c(x+k)+d=0 \) are
in
A. A.P
в. G.
c. н.
D. A.G.P.


The freezing point \( \left(\text { in }^{\circ} C\right) \) of a solution
containing 0.1 g of \( K_{3}\left[F e(C N)_{6}\right] \) (molar \( \operatorname{mass} 329) \) in 100 g of water \( \left(\boldsymbol{K}_{\boldsymbol{f}}=\right. \)
1.86 \( K . k g . m o l^{-1} \) ) is :
A. \( -2.3 \times 10^{-2} \) о \( C \)
В. \( -5.7 \times 10^{-2} \) о \( C \)
c. \( -5.7 \times 10^{-3} \) о \( C \)
D. \( -1.2 \times 10^{-2} \) о \( C \)


toppr
Q Type your question
piston can enter a cylınaer tıgntıy ana
without friction, and initially it is at the
bottom of the cylinder. \( 750 g m \) of water
is now poured into the pipe so that the
piston and pipe are lifted up as show.
Then
This question has multiple correct options
\( A \)
the height \( H \) of water in the cylinder is \( -n \)
B. the height \( H \) of water in the cylinder is \( \frac{11}{32 \pi} m \)
c. the height \( h \) of water in the pipe is \( \frac{2}{\pi} \)
the height \( h \) of water in the pipe is \( \frac{11}{32 \pi} m \)


Red on first draw and red on second
draw


\( \boldsymbol{x}=\{4,5,6\} \) is the solution set for
A. \( x \geq 4 \) and \( x \leq 7 \)
B. \( x \geq 4 \) and \( x<7 \)
c. \( x>4 \) and \( x<7 \)
D. \( x>4 \) and \( x \leq 7 \)


Ferrimagnetic those expected to have large magnetism but actually have small net magnetic moment e.g. magnetic \( \left(\boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}\right), \) ferrites \( \left(\boldsymbol{M}^{2}+\right. \)
\( F e_{2} O_{4} \) ). This is because of unequal
number of domains in opposite direction.


Which one of the following statements pertaining to plant structure is correct?
A. cork lacks stomata but lenticels carry out transpiration.
B. Passage cells help in transfer of food from cortex to phloem
c. Sieve tube elements possess cytoplasm but no nuclei
D. The shoot apical meristem has a quiescent centre.


Fill in the blanks.
Current flowing through the resistor is known as while the
current flowing through the capacitor is
commonly known as
A. eddy current, displacement current
B. displacement current, conduction current
c. conduction current, eddy current
D. conduction current, displacement current


Observe the given situation and answer
the following questions. Rahul and Ravi
are playing in a ground. They start running from the same point \( x \) simultaneously in the ground and reach
point \( Y \) at the same time by following
paths marked 1 and 2 respectively, as shown in the figure.

Which of the following path does show the displacement?
A. \( x y \)
в. хоу
c. xorx
D. xyo


Why is a normal eye not able to see
clearly the objects placed closer than 25
\( \mathrm{cm} \)


Find the equation of the line passing
through the point (-4,-3) and perpendicular to the straight line joining (1,3) and (2,7)


QRS is related to
A. Ventricular contraction
B. Auricular contraction
C. Cardiac cycle
D. Auricular relaxation


Assertion
The oxidation state of \( S \) in \( H_{2} S_{2} O_{8} \) is 6
Reason
Maximum oxidation state of \( S \) is 6
because the maximum oxidation state
of an element is its number of valence
electron.
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


According to Joule's law of heating, heat produced \( \boldsymbol{H}=\boldsymbol{l}^{2} \boldsymbol{R} \boldsymbol{t}, \) where I is current
\( \mathrm{R} \) is resistance, and \( \mathrm{t} \) is time. If the
errors in the measurement of I,R and t
are \( 3 \%, 4 \% \) and \( 6 \%, \) respectively, find
error in the measurement of H.


An object falls from \( 100 \mathrm{m} \) high. Find final velocity of the object.


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