For the reaction
\( \boldsymbol{S O C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{S O}_{2}+2 \boldsymbol{H C l} \)
the enthalpy of reaction is \( 49.4 k J \) and
the entropy of reaction is \( 336 J K^{-1} \)
Calculate \( \Delta G \) at \( 300 K \) and predict the
nature of the reaction.


Calculate the weight of the block at a distance of four times of Earth radii
from the center of the Earth. It is given that \( g \) is the acceleration due to gravity at the surface of Earth and mass of the
block is \( \mathrm{m} \)
A. \( 16 \mathrm{mg} \)
B. \( 4 \mathrm{mg} \)
c. \( 2 \mathrm{mg} \)
D. \( \frac{1}{4} \mathrm{mg} \)
E \( \cdot \frac{1}{16} \mathrm{mg} \)


Which of the following coordination compounds would exhibit optica isomerism?
A. Pentamminenitrocobalt (III) iodide
B. Tris-(ethylenediamine) cobalt (III) bromide
c. Trans- dicyanobis (ethylenediamine)
D. Diamminedinitroplatinum (II)


Which of the following compounds is/are expected to
be colored?

This question has multiple correct options
A \( \cdot T i\left(N O_{3}\right)_{4} \)
\( \mathbf{B} \cdot\left[C u\left(N C C H_{3}\right)_{4}\right] B F_{4}^{-} \)
c. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3}+3 C l \)
D \( \cdot K_{3}\left[V F_{6}\right] \)


Which of the following compounds are
involved in the formation of sulfur
trioxide?

This question has multiple correct options
A \( \cdot H_{2} S_{2} O_{5} \)
в. \( N a H S O_{4} \)
c. \( N a_{2} S_{2} O_{7} \)
D. \( H_{2} S_{2} O_{7} \)


When a satellite falls to an orbit of
smaller radius its kinetic energy:
A . Decrease
B. Increase
c. Remains same
D. Nothing can be predicted


Lichens have an actual relationship of
A. Parasitism
B. Mutualism
C. Helotism
D. Epiphytism


"Aqua regia" is a combination of :
A. \( H C l \) and \( H_{2} S O_{4} \)
B. \( H C l \) and \( H N O_{3} \)
c. \( H C l \) and \( H B r \)
D. HCl and \( H F \)


The IUPAC name of succinic acid
is Butane-1,4-dioic acid.
If true enter \( 1, \) if false enter 0


A box of weight \( 150 k g f \) has
gravitational potential energy stored in it equal to \( 14700 J \). Find the height of the box above the ground. (Take \( g= \)
\( 9.8 N k g^{-1} \)
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 10 k m \)
\( c .1 m \)
D. \( 10 m \)


If \( \sin \alpha \sin \beta-\cos \alpha \cos \beta+1=0 \), then
show that \( 1+\cot \alpha \tan \beta=0 \)


If \( a^{2}+b^{2}+c^{2}=14, \) then \( a b+b c+c a \)
is always greater than or equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 14
c. -1
D. -


P' wave of ECG occurs before the
A. Onset of ventricular contraction.
B. End of arterial contraction.
C. Beginning of atrial contraction.
D. None of the above


Determine the shear stress at the pipe
wall
A. \( 8 \times 10^{-6} N / m^{2} \)
B. \( 3.9 \times 10^{-6} N / m^{2} \)
c. \( 2.3 \times 10^{-6} N / m^{2} \)
D. \( 10.6 \times 10^{-6} N / m^{2} \)


Solve :
\( \boldsymbol{I}=\int \frac{\boldsymbol{x}+\mathbf{9}}{\boldsymbol{x}^{2}+\mathbf{5}} \boldsymbol{d} \boldsymbol{x} \)


Which of the following gives a precipitate with moist silver oxide?
A \( \cdot C H_{2}=C H-C l \)
В \( \cdot C_{6} H_{5} C l \)
\( c \)
(c)
\( D \)
\( (d) \)


Which of the following is regulated by autonomic nervous system?
A. Heart
B. Internal organs
c. Brain
D. External organs


State and derive work energy theorem.


A body of mass m falls freely through a height h from the top of a tower. The velocityjust before touching the ground is \( \sqrt{\frac{3}{2} g h} . \) The air drag is:
A \( . m g \)
в. \( \frac{m g}{2} \)
\( c \cdot \frac{m g}{3} \)
D. \( \frac{m g}{4} \)


A thin iron ring with mean diameter
\( d=50 \mathrm{cm} \) supports a winding
consisting of \( N=800 \) turns carrying
current \( \boldsymbol{I}=\mathbf{3 . 0} \boldsymbol{A} . \) The ring has a cross
cut of width \( b=2.0 \) mm. Neglecting the
scattering of the magnetic flux at the gap edges, and using the plot shown in figure above, find the permeability of
iron under these conditions.


Draw Lewis structure for the following molecules.
¡) \( \boldsymbol{S F}_{\mathbf{6}} \)
ii) \( C_{2} H_{4} \)
iii \( N O_{2} \)


Let \( \boldsymbol{A}=\{-\mathbf{7}, \mathbf{5}, \mathbf{2}\} \) and \( \boldsymbol{B}= \)
\( \{\sqrt[3]{125}, \sqrt{4}, \sqrt{49}\} \)
Are the sets \( A \) and \( B \) equal? Choose the correct option for the above. Justify
your answer.
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Refraction of light is caused due to the change in the \( _{\text {一一一一一一 }} \) of light in different media.
A . speedd
B. frequency
c. acceleration
D. none of the above


The oxide of metal \( R \) can be reduced by
the metal \( P \) and metal \( R \) can reduce the
oxide of metal \( Q . \) Then the decreasing
order of the reactivity of metal \( P, Q \) and
\( R \) with oxygen is:
A. \( P>Q>R \)
в. \( P>R>Q \)
c. \( R>P>Q \)
D. \( Q>P>R \)


Which of the following is not a final product obtained by cross aldol condensation of ethanal and propanal?
A. 3-Methyl-but-2-enal
B. 2-Methyl-pent-2-enal
c. But-2-enal
D. Pent-2-enal


When ammonium vanadate is heated
with oxalic acid solution, a substance \( \mathbf{Z} \)
is formed. A sample of Z was treated
with \( K M n O_{4} \) solution in hot acidic
solution. The resulting liquid was
reduced with \( S O_{2}, \) the excess \( S O_{2} \)
boiled off and the liquid again titrated
with same \( K M n O_{4} . \) The ratio of
volumes of \( K M n O_{4} \) used in the two
titrations was \( 5: 1 . \) What is the
oxidation state of vanadium in
substance Z? Given than \( K M n O_{4} \)
oxidize all oxidation state of vanadium
to vanadium (+5) and \( S O_{2} \) reduces
\( V(+5) \) to \( V(+4) \)


The least value of \( 9 \sec ^{2} x+16 \operatorname{cosec}^{2} x \)
is:
A . 25
B. 49
c. 81
D. 64


The distance of geostationary orbit from the Earth is \( 15,000 \mathrm{km} \). This statement
is
A. True
B. False


Which of the following statements does not show correct difference between
adsorption and absorption?
A. In adsorption, the substance is concentrated only at the surface while in absorption it is uniformly distributed in the bulk
B. Adsorption is instantaneous while absorption is a slow process
c. A substance can be adsorbed as well as absorbed simultaneously and the process is called sorption.
D. Only gases are adsorbed while solids and liquids are absorbed


Point \( D \) has coordinates as (3,4,5)
Find the coordinates of the point \( \boldsymbol{F} \)
\( \mathbf{A} \cdot(0,4,0) \)
B. (0,0,4)
\( \mathbf{C} \cdot(0,0,5) \)
\( \mathbf{D} \cdot(0,5,0) \)


The net heat absorbed by the gas in the
path BC


If \( \sin \alpha+\sin \beta=\frac{1}{2} \) and \( \cos \alpha+ \)
\( \cos \beta=\frac{\sqrt{3}}{2}, \) then value of \( 3 \alpha+\beta \) is
A \( .90^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 60^{\circ} \)


Find the mean deviation from the mean
of the following data, using the step
deviation method:
\begin{tabular}{|l|l|}
\hline Marks & No. of students \\
\hline \( 0-10 \) & 6 \\
\hline \( 10-20 \) & 5 \\
\hline \( 20-30 \) & 8 \\
\hline \( 30-40 \) & 15 \\
\hline \( 40-50 \) & 7 \\
\hline \( 60-70 \) & 3 \\
\hline
\end{tabular}


If \( W_{1}, W_{2} \) and \( W_{3} \) represent the work
done in moving a particle from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
along three different paths 1,2 and 3
respectively (as shown) in a
gravitational field of point mass \( \boldsymbol{m} \)
then find the correct relation between
\( W_{1}, W_{2} \) and \( W_{3} \)
A \( . W_{1}=W_{2}=W_{3} \)
B. \( W_{1}>W_{2}>W_{3} \)
\( \mathbf{c} \cdot W_{1}<W_{2}<W_{3} \)
D. \( W_{2}>W_{1}>W_{3} \)


A long horizontal metallic rod with length along the east-west direction is falling under gravity. The potentiol difference between its two ends will :
A. be zero
B. be constant
c. increase with time
D. decrease with time


toppr
Q Type your question
densities \( d \) and \( 2 d \) each of height \( H / 2 \)
as shown in the figure. The lower density liquid is open to the
atmosphere having pressure \( \boldsymbol{P}_{0} \cdot \boldsymbol{A} \)
homogeneous solid cylinder of length
\( \boldsymbol{L}(\boldsymbol{L}<\boldsymbol{H} / 2), \) cross-sectional area \( \boldsymbol{A} / \mathbf{5} \)
is immersed such that it floats with its
axis vertical at the liquid-liquid
interface with length \( L / 4 \) in the denser
liquid.
The cylinder is then removed and the original arrangement is restored. A tiny hole of area \( s(s<<A) \) is punched on
the vertical side of the container at a
height \( h(h<H / 2) . \) As a result of this,
liquid starts flowing out of the hole with
a range \( x \) on the horizontal surface.
The horizontal distance traveled by the liquid, initially, is :
\( \mathbf{A} \cdot \sqrt{(3 H+4 h) h} \)
B \( \cdot \sqrt{(3 h+4 H) h} \)
\( \mathbf{c} \cdot \sqrt{(3 H-4 h) h} \)
D. \( \sqrt{(3 H-3 h) h} \)


Diamond is :
A. transparent
B. translucent
c. opaque
D. semi-absorbent


Which of the material can be used as a
dielectric?
This question has multiple correct options
A. Ceramics
B. Woodd
c. copper
D. Aluminium


In the above circuit, find out the
unknown resistance \( \mathrm{R} \)
\( A \cdot 6 \Omega \)
B. 8 ?
\( c .2 \Omega \)
D. \( 4 \Omega \)


Sugar taken in a watch glass was found
to be charred by adding a substance ' \( X \) '
(a) What is the substance 'X'?
(b) What is the reason for charring of
sugar?
(c) Which catalyst is used in the industrial preparation of the substance \( X^{\prime} ? \)


\( B r O_{3}^{-} \) is oxidised to \( B r O_{4}^{-} \) by \( X e F_{2} \)
\( \underset{\boldsymbol{m}_{1}}{\boldsymbol{X} \boldsymbol{F}_{2}}+\underset{\boldsymbol{m}_{2}}{\boldsymbol{B} \boldsymbol{r}} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{4}^{-}+ \)
\( \boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F} \)
where,
\( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) are the molar masses of
\( X e F_{2} \) and \( B r O_{3}^{-}, \) respectively.

Ratio of equivalent mass of \( X e F_{2} \) and
\( B r O_{3}^{-} \) is
A \( \cdot \frac{m_{1}}{m_{2}} \)
в. \( \frac{2 m_{1}}{m_{2}} \)
c. \( \frac{m_{1}}{2 m_{2}} \)
D. \( \frac{m_{1}}{3 m_{2}} \)


What will be the emf for the given cell :
\( P t\left|H_{2}\left(P_{1}\right)\right| H^{+}(a q)\left|H_{2}\left(P_{2}\right)\right| P t \)
\( ^{\text {A } \cdot} \frac{R T}{F} \log \frac{P_{1}}{P_{2}} \)
в. \( \frac{R T}{2 F} \log \frac{P_{1}}{P_{2}} \)
c. \( \frac{R T}{F} \log \frac{P_{2}}{P_{1}} \)
D. noneofthese


\( 5 k g \) block rests on horizontal surface.
Which of the following option is
incorrect? \( \left(\boldsymbol{g}=\mathbf{1} \mathbf{0} \mathbf{m} / \mathbf{s}^{\mathbf{2}}\right) \)
This question has multiple correct options
A. The normal force on the block equals its weight because of Newton's second law
B. The normal force on the block is equal to the weight not because of Newton's third law
C. The normal force on the block equals its weight because of Newton's third law
D. The normal force on the block is 50 N.


Factorise \( : 12 k y^{2}+8 k y-20 k \)


A temperature difference of \( 27^{\circ} \mathrm{C} \) on the Kelvin scale is equal to a difference of :
\( \mathbf{A} \cdot 27 K \)
B . \( 300 K \)
c. -246K-246K
D. zero


Greenhouse effect is a major cause of:
A . global warming
B. reduction of temperature
c. acid rain
D. all of above


A particle moves along a straight line such that its displacement \( s \) at any
time \( t \) is given by \( s=t^{3}-6 t^{2}+3 t+ \)
\( 4 m, t \) being is seconds. Find the velocity
of the particle when the acceleration is
zero.


In plant relations, \( \Psi \) indicates
A. DPD
B. Solute potential
c. water potential
D. Suction pressure


Examples of antipyretics are:
This question has multiple correct options
A. paracetamo
B. morphine
C. Barbituric acid
D. para-amino phenol


Graph between \( \log \left(\frac{x}{m}\right) \) and \( \log p \) is a
straight line at an angle \( 45^{\circ} \) with
intercept on y-axis \( 0,3010 . \) Calculate the amount of gas adsorbed in gram per gram of the adsorbent when pressure is
0.2 atm.
A . 0.4
B. 0.6
c. 0.8
D. 0.2


Here are some words translated from an
artificial language mie pie is blue light
mie tie is blue berry
aie tie is raspberry
Which words could possibly mean "light fly"?
A. pie zie
B. pie mie
c. aie zie
D. aie mie


Resistance of conductor is doubled
keeping the potential difference across it constant. The rate of generation of
heat will:
A. become one fourth
B. be halved
c. be doubled
D. become four times


The density of a gass is 3.80 g \( L^{-1} \) at
S.T.P calculate is density at \( 27^{0} C \) and
700 torr pressure.


The cells surrounding the stomatal pore
are
A. Gurad cells
B. Subsidiary cell
c. chromophil cells
D. None of the above


Evaluate \( \int_{0}^{\pi / 2} \frac{\cos x}{\left(1+\sin ^{2} x\right)} d x \)
A \( \cdot \frac{\pi}{2} \)
B. \( \frac{\pi}{4} \)
c. \( \pi \)
D. None of these


In n-type semiconductor, the Fermi
level is present:
A. just below the valence band
B. just below the conduction band
C. just above the valence band
D. in the middle of valence and conduction bands


If the angles of a triangle \( A B C \) are in
\( \boldsymbol{A} \cdot \boldsymbol{P} \)
\( \boldsymbol{a}=\mathbf{2}, \boldsymbol{c}=\mathbf{4}, \) then \( \boldsymbol{b}= \)
A \( \cdot 2 \sqrt{3} \)
3
B. \( \sqrt{21} \)
c. 8
D. 14


How does a Sonar work? Explain. Mention its uses


Let \( f(x)=\tan 2 x \cdot \tan 3 x \cdot \tan 5 x, \) then
\( \boldsymbol{f}^{\prime}(\boldsymbol{\pi}) \) equals
A . 10
B. -10
\( c .0 \)
D.


Rapid deep breathing is
A. Dyspnoea
B. Hypopnoea
c. Hyperpnoea
D. None of the above


Find modulus of following
\( (\mathrm{i}) \pm(4+3 i) \)
\( (\mathrm{ii}) \pm \sqrt{2}+0 i \)
(iii) \( \mathbf{0} \pm \sqrt{\mathbf{2}} \boldsymbol{i} \)


The resultant of two forces, one double
the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:
A \( \cdot 120^{\circ} \)
B . 135
\( c .90^{\circ} \)
D. \( 150^{\circ} \)


\( \boldsymbol{n} / \boldsymbol{m} \) means that \( \boldsymbol{n} \) is factor of \( \boldsymbol{m}, \) then
the relation ' \( \boldsymbol{f}^{\prime} \) is.
B. Transitive and symmetricc
C. reflexive, transitive and symmetric
D. Reflexive,transitive and not symmetric


Check the continuity of \( f \) given by
\[
f(x)=\left\{\begin{array}{ccc}
4-x^{2} & \text { if } & x \leq 0 \\
x-5 & \text { if } & 0<x \leq 1 \\
4 x^{2}-9 & \text { if } & 1<x<2 \\
3 x+4 & \text { if } & x \geq 2
\end{array}\right.
\]
the points 0,1 and 2


A concave mirror forms an erect image of an object placed at a distance of 10 \( \mathrm{cm} \) from it. The size of the image is double that of the object. Where is the image formed?
A. 20 cm behind the mirror
B. 20 cm in front of the mirror
c. \( 40 \mathrm{cm} \) behind the mirror
D. \( 40 \mathrm{cm} \) in front of the mirror


Catalytic decomposition of nitrous
oxide by gold at \( 900^{\circ} \mathrm{C} \) at an initia
pressure of \( 200 m m \) was \( 50 \% \) in 53
minutes and \( 73 \% \) in 100 minutes.
(a) What is the order of reaction?
(b) How much it will decompose in 100
minutes at the same temperature but at an initial pressure of 600 mm?


The process of glycolysis can be
represented as
A. \( C_{6} H_{12} O_{6} \rightarrow 2 C_{3} H_{4} O_{3}+4 H \)
B. \( C_{6} H_{12} O_{6}+6 C O_{2} \rightarrow 6 C O_{2}+6 H_{2} O \)
\( \mathrm{c} \cdot 6 H_{2} O+6 C O_{2} \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
D. None of the above


Which orbital is represented by wave
function \( \Psi_{310} ? \)
A \( \cdot 3 d_{x y} \)
B . \( 3 p_{z} \)
\( c \cdot 4 s \)
D. \( 4 d_{z} \)


A long wire carrying current \( i \) is placed
close to a U-shaped conductor (of negligible resistance). A wire of length \( l \)
as shown in figure slides with a velocity
v. Find the current induced in the loop
as a function of distance \( x \) from the
current carrying wire to slider.
A \( \cdot \frac{\mu_{0} i l u}{R x} \)
в. \( \frac{\mu_{0} i l u}{2 \pi R x} \)
c. \( \frac{\mu_{0} i l u}{2 R x} \)
D. \( \frac{\mu_{0} i l u}{4 \pi R x} \)


Cell-tissue organisation occurs in
A. Fasciola
B. Sycon
c. Hydra
D. Asterias


Which of the following can be expressed as the sum of square of two positive integers, as well as three positive integers?
A . 75
в. 192
\( c \cdot 250 \)
D. 100


Four students were given colourless liquids \( A, B, C \) of water, lemon juice and a mixture of water and lemon juice
respectively. After testing these liquids
with pH paper, following sequence
in colour change of pH paper were
reported:
I. Blue, Red and Green
Il. Orange,
Green and Green
III. Purple, Red and Green IV.Green, Red
and Red
The correct sequence of colours
observed is
\( A \)
B. II
c. ॥॥
D. IV


The landthanide contraction is
responsible for the fact that:
A. \( Z r \) and \( Y \) have almost the same radius.
B. \( Z r \) and \( N b \) have similar oxidation state
c. \( Z r \) and \( H f \) have almost the same radius
D. \( Z r \) and \( Z n \) have the same oxidation state.


A radioactive element has rate of
disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500
disintegrations per minute. The decay constant per minute is
A \( \cdot 0.2 \log _{e}^{2} \)
B . \( 0.5 \log _{e}^{2} \)
c. \( 0.6 \log _{e}^{2} \)
D. \( 0.8 \log _{e}^{2} \)


A galvanometer of resistance \( 50 \Omega \) giving full scale deflection for a current
of 10 milliampere is to be changed into a voltmeter of range \( 100 \mathrm{V} \)

A resistance of \( _{-1}-\ldots_{\text {has to be }} \)
connected in series with the
galvanometer.
A . 9950
B. 10025
c. 10000
D. 9975


Give two characteristics of magnetic field lines.


What are dimensional variables?


Atmospheric electricity is generated
due to
A. the accumulation of static charges
B. the accumulation of moving charges
C. the destruction of static charges
D. destruction of moving charges


When a flute is blown, the air inside it
gets compressed and produces sound but does not vibrate. True or false.
A. True
B. False


In the adjoining figure, parallel lines are
shown with similar markings. Find \( \angle x \)
if \( \angle x=5 \angle y \)
\( \mathbf{A} \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
c. \( 150^{\circ} \)
D. \( 170^{\circ} \)


Which is the condition, unrelated
to quantities, that indicates that the rate going into solution is equal to the rate coming out of solution?
A . Dilute
B. concentrated
c. Unsaturated
D. Saturated
E. Supersaturated


Is 0.3 the multiplicative inverse of \( 3 \frac{1}{3} ? \) Why or why not?


A dynamo developed \( 0.5 A \) at \( 6 V \). Find
the energy it generates in 1 s.


Differentiate between:
Haemoglobin and leghaemoglobin


The elements with atomic numbers
10,18 belong to the same group.
A. True
B. False


A train moving with a velocity of
\( 20 m s^{-1} \) is brought to rest by applying the brakes in 5 s. Calculate the
retardation
\( \mathbf{A} \cdot 4 m s^{-2} \)
B \( \cdot 2 m s^{-2} \)
\( \mathrm{c} \cdot 1 \mathrm{ms}^{-2} \)
D. \( 8 m s^{-2} \)


Explain:
A: Combustion is an exothermic
process.
B: Combustion is a spontaneous
process


Find the area of the region enclosed by the curves;
\( \boldsymbol{y}=\cos \boldsymbol{x}, \boldsymbol{y}=1-\frac{2 x}{\pi} \)
A \( \cdot 2-\frac{\pi}{2} \)
в. \( \pi \)
c. \( \frac{\pi}{2} \)
D.


In a Young's double slit experiment, the
fringes are displaced by a distance \( x \) when a glass plate of refractive index 1.5 is introduced in the path of one of the beams. Then this plate is replaced by another plate of the same thickness, the shift of fringes is \( \frac{3}{2} x . \) The refractive index of the second plate is :
A . 2.25
в. 2.0
c. 1.75
D. 1.25


If the radius of the Earth were increased
by a factor of 2 and its mass remained
the same, then the acceleration due to
gravity on the Earth would
A. reduce by factor 4
B. reduce by factor 2
c. not change
D. none of the above


\( \lim _{x \rightarrow 0} \tan \left(\frac{\pi}{4}+x\right) \)


The area of triangle formed by the lines
\( 18 x^{2}-9 x y+y^{2}=0 \) and the line \( y=9 \)
is
A. \( \frac{27}{4} \)
в. \( \frac{27}{2} \)
c. \( \frac{27}{8} \)
D. 27


In the figure shown, coefficient or restitution between \( A \) and \( B \) is \( e=\frac{1}{2} \)
then
This question has multiple correct options
A \cdot velocity of B after collision is \( \frac{v}{2} \)
B. Impulse between two during collision is \( \frac{3}{4} m v \)
c. Loss of kinetic energy during the collision is \( \frac{3}{16} m v^{2} \)
D. Loss of kinetic energy during the collision is \( \frac{1}{4} m v^{2} \)


The growth of tendril in pea plant is due to
A. Effect of light
B. Effect of gravity
c. Rapid cell divisions in tendrillar cells that are away from the support
D. Rapid cell divisions in tendrillar cells in contact with the support


For a first order reversible reaction \( A_{K_{b}}^{K_{f}} B, \) the initial concentration of \( A \)
and \( B \) are \( [A]_{0} \) and zero respectively. If
concentrations at equilibrium are \( [\boldsymbol{A}]_{e q} \)
and \( [\boldsymbol{B}]_{e q} ., \) derive an expression for the time taken by \( B \) to attain concentration
equal to \( [\boldsymbol{B}]_{e q / 2} \)


Find the value of \( y, \) if \( x=5^{\circ} \)
\( A \cdot 50 \)
3.45
\( c \cdot 32^{2} \)
.38
\( ^{2} \)


In which of the following pairs is there the greatest difference in the oxidation numbers of the underlined elements?
A. \( \underline{N} O_{2} \) and \( N_{2} O_{4} \)
B. \( P_{2} O_{5} \) and \( P_{4} O_{00} \)
c. \( \underline{N}_{2} \mathrm{O} \) and \( \underline{\mathrm{N}} \mathrm{O} \)
\( \mathrm{D} \cdot \underline{S} \mathrm{O}_{2} \) and \( \underline{S} \mathrm{O}_{3} \)


Extremely dangerous and deadly cardiac glycosides are carried from the milkweed plant by the?
A. Night cockroaches
B. Bumble bee
c. Larvae of the monarch butterfly
D. Green grasshopper


Choose the correct combination of
labeling of the lenticel
A . a-pore, b-complementary cells, c-cork, d-cork cambium, e-secondary cortex
B. a-pore, b-secondary cortex, c-cork, d-cork cambium, e complementary cells
c. a-pore, b-cork cambium, c-secondary cortex, d-cork. complementary cells
D. a-pore, b-cork, c-complementary cells, d-cork cambium, e-secondary cortex
E. a-pore, b-cork, c-cork cambium, d-secondary cortex, ecomplementary cells


If \( n=10, \bar{x}=12 \) and \( \sum x^{2}=1530 \)
then calculate the coefficient of
variation.
A . 20
B . 25
c. 30
D. 35


There are three boxes, each containing a different number of light bulbs. The first box has 10 bulbs, of which four are dead, the second has six bulbs, of which one is dead, and the third box has eight bulbs of which three are dead. What is
the probability of a dead bulb being selected when a bulb is chosen at
random from one of the three boxes?
A. \( \frac{115}{330} \)
В. \( \frac{113}{360} \)
c. \( \frac{113}{330} \)
D. None of these


Component of \( \vec{a}=\hat{i}-\hat{j}-\hat{k} \)
perpendicular to the vector \( \overrightarrow{\boldsymbol{b}}=2 \hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) is?
A \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
B \( \cdot \frac{1}{3}(\hat{i}-4 \hat{j}-2 \hat{k}) \)
c \( \cdot \frac{1}{3}(\hat{i}+4 \hat{j}+2 \hat{k}) \)
D \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+\hat{k}) \)


Rain is falling vertically and a man is
moving with velocity \( 6 m s^{-1} \). Find the
angle at which the man should hold his umbrella avoid getting wet.


Assertion
Human ancestors never used their tails
and so the tail expressing gene has disappeared in them.
Reason
Lamarck's theory of evolution is popularly called theory of continuity of germplasm.
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


Fill in the blanks
The distance between the eye lens and
retina is about


Graph between log \( \mathrm{K} \) and \( \frac{1}{T}[\text { Where } \mathrm{K} \) is
rate constant \( \left(S^{-1}\right) \) and \( T \) is
temperature (K)] is a straight line with
\( \boldsymbol{O} \boldsymbol{X}=\mathbf{5}, \boldsymbol{\theta}=\boldsymbol{t a n}^{-1}\left[-\frac{\mathbf{1}}{\mathbf{2 . 3 0 3}}\right] \)
Hence \( E_{a} \) and log A respectively will be:
A \( .2 .303 \times 2 c a l, 5 \)
B . \( \frac{2}{3.303} \) cal \( , e^{5} \)
c. 2 cal, 5
D. None of these


Nucleic acids are polymer of
A. Nucleotides
B. Nucleosides
C. Amino acids
D. Nitrogen bases


find the sum : tan \( x \) tan \( 2 x+ \)
\( \tan 2 x \tan 3 x+\dots \dots \dots+\dots \)
\( \tan n x \tan (n+1) x \)


\( \lim _{x \rightarrow 0} \frac{x}{\sqrt{x+4}-2} \) is equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B. \( \sqrt{2} \)
c. \( 2 \sqrt{2} \)
D.


suppose 0
\[
\text { 135 } \quad 342
\]
\[
t(\min )
\]
and
[Cone]
1.91 mol \( L^{-1} \quad \) 2.08 1.67
Find out the order of reaction and
calculate its rate constants


What is the ratio of the shortest
wavelength of the Balmer series to the shortest wavelength of the Lyman series
\( ? \)
\( A \cdot 4: \)
B. 4: 9
\( c \cdot 4: 3 \)
D. 5 : 9


The wavelength of monochromatic light is \( 5000 A \) in air what will be its wave
number in a medium of refractive index
\( \mathbf{1 . 5} ? \)
A \( \cdot 3 \times 10^{6} m^{-1} \)
В. \( 5 \times 10^{6} m^{-1} \)
c. \( 2 \times 10^{6} m^{-1} \)
D. \( 9 \times 10^{6} m^{-1} \)


Which is not an example of cytoplasmic inheritance?
A. Female sterility in maize
B. Sigma particle inheritance
c. Kappa particle inheritance
D. Plastid inheritance


In the shown arrangement of the experiment of the meter bridge if \( \mathrm{AC} \)
corresponding to null deflection of
galvanometer is \( x, \) what would be its value if the radius of the wire \( \mathrm{AB} \) is
doubled :-
\( A \)
в. \( \frac{x}{4} \)
\( c \cdot 4 x \)
\( D \cdot 2 \)


The value of \( \int e^{2 x}\left(\frac{1}{x}-\frac{1}{2 x^{2}}\right) d x \) is
\( ^{A} \cdot \frac{e^{2 x}}{2}+c \)
B. \( \frac{e^{2 x}}{2 x}+c \)
c. \( \frac{e^{2 x}}{3 x}+c \)
D. \( \frac{e^{2 x}}{x}+c \)


The octet rule is not obeyed by which of the following molecule:
A. \( C O_{2} \)
в. \( H_{2} \) о
\( c \cdot O_{2} \)
D. \( C O \)


In Freundlich isotherm, \( \frac{x}{m} \propto P^{a} \). Find the value of \( a \) from the following graph.
\( A \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{3}{2} \)
\( D \)


Two particles \( A \) and \( B \) initially at rest move towards each other under a
mutual force of attraction. The speed of
center of mass at the instant when the
speed of \( A \) is \( v \) and the speed of \( B \) is \( 2 v \) is
\( A \)
B. Zero
c. \( 2 v \)
D. \( \frac{3 v}{2} \)


Differentiate the following function w.r.t. \( x: \cos ^{-1}\left(1-2 \sin ^{2} x\right) \)


Plant cells are rigid due to the presence of
A. Cell membrane
B. Cell wall
c. cytoskeleton
D. chloroplasts
E. Centrioles


Odd one out among the following is:
A. Tartaric acid
B. Oxalic acid
c. Citric acid
D. Prussic acid


If \( A \) and \( B \) are two events in a sample
space \( S \) such that \( P(A) \neq 0 \) and
\( \boldsymbol{P}(\boldsymbol{B}) \neq \boldsymbol{0}, \) then \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
A \( \cdot P(A) \cdot P(B) \)
в. \( P(A) . P\left(\frac{B}{A}\right) \)
\( \mathbf{c} \cdot P(B) \)
D \cdot \( P(A) \)


\( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{2} \\ \mathbf{- 1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{- 1} & \mathbf{3}\end{array}\right], \) then
order of \( A B \) is
A. \( 2 \times 2 \)
в. \( 3 \times 3 \)
\( c \cdot 1 \times 3 \)
D. \( 3 \times 2 \)


Figure shows three points \( A, B \) and \( C \) in a region of uniform electric field \( \vec{E} \). The
line \( A B \) is perpendicular and \( B C \) is parallel to the field lines. Then which of
the following holds good. Here \( \boldsymbol{V}_{\boldsymbol{A}}, \boldsymbol{V}_{\boldsymbol{B}} \)
and \( V_{C} \) represents the electric potential
at point \( A, B \) and \( C \) respectively.
\( \mathbf{A} \cdot V_{A}=V_{B}=V_{C} \)
B \( \cdot V_{A}=V_{B}>V_{C} \)
\( \mathbf{c} \cdot V_{A}=V_{B}<V_{C} \)
\( \mathbf{D} \cdot V_{A}>V_{B}=V_{C} \)


If 1 lies between the roots of the
equation \( y^{2}-m y+1=0 \) and \( [x] \) is
the GIF function,
then the value of \( \left[\left(\frac{4|x|}{|x|^{2}+16}\right)^{m}\right], \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of the above


Who will spend more electrical energy
\( \mathbf{5 0 0} \) w tv set in 30 mins as 600 heater in
20 minutes?


For a given voltage \( V \), if resistance is
changed from \( R \) to \( \left(\frac{R}{n}\right), \) power
consumed changes from \( P \) to:
\( A \cdot n P \)
B. \( \frac{p}{n} \)
\( c \cdot n^{2} p \)
D. \( \frac{P}{n^{2}} \)


In astronomical observations signals observed from the distant stars are
generally weak. If the photon detector
receives a total of \( 3.15 \times 10^{-18} \) J from
the radiations of 600 nm. Calculate the
number of photons received by the detector.
A . 20
B. 10
\( c \cdot 8 \)
D.


A cell supplies a current of \( 0.9 \mathrm{A} \) through a \( 2 \Omega \) resistor and a current of
\( 0.3 \mathrm{A} \) through a \( 7 \Omega \) resistor. The internal resistance of the cell is :-
A . \( 1.0 \Omega \)
в. \( 0.5 \Omega \)
c. \( 2.0 \Omega \)
D. \( 1.2 \Omega \)


The nature of the bond in diamond is:
A. ionic
B. covalent
c. matallic
D. coordinates covelent


The IUPAC name of the following
compound \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
is:


What is the correct dimension of
Newton?
\( \mathbf{A} \cdot\left[M L T^{-2}\right] \)
В \( \cdot\left[M L T^{-1}\right] \)
c. \( \left[M L^{2} T^{-2}\right] \)
D. \( [M L T] \)


Holotype is
A. Specimen used by author as nomenclature type.
B. Specimen referred alog with original description.
C. Duplicate of nomenclature type.
D. Specimen selected from original, when nomeclature type is missing.


According to Susruta Samhita, Virudha consisted of
A. Flowering plants.
B. Shrubs
c. osadhi
D. Jangama.


Calculate the wavelength of the
radiation which would cause the
photodissocitaion of chlorine molecule
if the \( C l-C l \) bond energy is \( 243 k J \)
\( m o l^{-1} \)


When sodium peroxide is treated with water, the product obtained contains:
This question has multiple correct options
\( A \cdot O_{2} \)
в. \( N a \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( N a^{+} \)


Find the angle, if its complement is one-
fourth of its supplement.


Ascending imbricate corolla is found in
A. Pisum or Papilionadae
B. Tamarindus or Caesalpinioideae
c. Mimosa or Mimosoideae
D. Datura or Solanaceae


Statement: The product formed when
\( \boldsymbol{P H}_{3} \) reacts with aqueous \( \boldsymbol{C u}^{2+} \) is
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
State true or false.


Answer the following questions with
respect to the compound \( N O\left[B F_{4}\right] \)
(P) Bond order of the part underline.
(Q) Total number of \( \sigma \) bonds in the
compound.
(R) Total number of \( \pi \) bonds in the
compound.
(S) Number of hybrid orbitals involved in the hybridisation of boron.


State whether the given statement is true or false:
\( K O_{2}, B a O_{2}, N a_{2} O_{2} \) are superoxides.
A. True
B. False


Fill in the blanks with appropriate
words.
Digestion of \( \ldots \ldots \) begins in the mouth.


The structure of \( X e O F_{4} \) is:
A. trigonal bipyramidal
B. square planar
c. square pyramidal
D. pyramidal


(i) Why is a cathode ray tube
evacuated to a low pressure?
(ii) What happens if the negative potential is changed on a grid?


Subtract the following:
\( \boldsymbol{p}(\boldsymbol{y})=\boldsymbol{3} \boldsymbol{y}^{7}-\boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{3} \) and \( \boldsymbol{q}(\boldsymbol{y})=\boldsymbol{y}^{7}+ \)
\( \boldsymbol{y}^{2}+\boldsymbol{y} \)


If \( \bar{a} \) and \( \bar{b} \) are any two non-zero and non-
collinear vectors, then prove that any vector \( \bar{r} \) coplanar with \( \bar{a} \) and \( \bar{b} \) can be
uniquely expressed as \( \overline{\boldsymbol{r}}=\boldsymbol{t}_{1} \boldsymbol{a}+\boldsymbol{t}_{2} \boldsymbol{b} \)
where \( t_{1} \) and \( t_{2} \) are scalars.


\( 2 C+O_{2}=2 C O . \) The rate of
disappearance of \( \boldsymbol{C} \) is \( 2 \times \)
\( 10^{-3} \) mol \( L^{-1} \) sec \( ^{-1} \). What is the
instantaneous rate of the reaction?
A. \( 2 \times 10^{-3} \)
В. \( 1 \times 10^{-3} \)
c. \( 4 \times 10^{-3} \)
D. None of these


A perfectly reflecting solid sphere of radius \( r \) is kept in the path of a parallel beam of light of large aperture. If the beam carries an intensity I, find the force exerted by the beam on the sphere.


Find the absolute maximum and
minimum values of a function \( f \) given
by \( f(x)=2 x^{3}-15 x^{2}+36 x+1 \) on the
interval \( [\mathbf{1}, \mathbf{5}] \)


Solve graphically: \( 2 x+y-7=0, x+ \)
\( 3 y-11=0 \)


Write the name of device \( ^{\prime} X^{\prime} \) in the
following given diagram. Explain its working making its circuit diagram.


Two soap bubbles of radius \( r_{1}=r \) and
\( r_{2}=2 r \) coalesce to form a double as
shown, then angle \( p j i, \) is equal to
\( A \cdot 60^{\circ} \)
В \( \cdot 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. It depends on surface tension of soap solution


Striated muscle fibres possess
A. Longitudinal strips
B. Oblique strips
c. Transverse strips
D. No strips


In the hydrolysis of organic chloride in
the presence of a large excess of water,
\( \boldsymbol{R C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{R O H}+\boldsymbol{H} \boldsymbol{C l} \)
A. Molecularity and order of reaction both are 2
B. Molecularity is 2 but order of reaction is 1
c. Molecularity is 1 but order of reaction is also 1
D. Molecularity is 1 and order of reaction is also 1


1 \( g \) of hydrogen is converted into \( 0.993 g \) of helium in a thermonuclear reaction.
Then energy released is
\( \mathbf{A} \cdot 63 \times 10^{7} J \)
В. \( 63 \times 10^{10} \mathrm{J} \)
\( \mathbf{D} \cdot 63 \times 10^{20} J \)


Assertion
Each of the plates of a parallel-plate capacitor is given equal positive charge
Q. The charges on the facing surfaces will be same.
Reason
A negative charge (-Q) will be induced on each of the facing surfaces.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


Factorize \( 3 x^{2}+14 x+15 \)


The vector \( \vec{a}=\alpha \hat{i}+2 \widehat{j}+\beta \widehat{k} \) lies in the
plane of the vectors \( \overrightarrow{\boldsymbol{b}}=\widehat{\boldsymbol{i}}+\widehat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{c}}= \)
\( \widehat{j}+\widehat{k} \) and bisects the angle between \( \overrightarrow{\boldsymbol{b}} \) and \( \vec{c} . \) Then, which one of the following
gives possible values of \( \alpha \) and \( \beta ? \)
A \( \cdot \alpha=2, \beta=2 \)
в. \( \alpha=1, \beta=2 \)
c. \( \alpha=2, \beta=1 \)
D. \( \alpha=1, \beta=1 \)


Which one of the following quantities is negative?
A \( \cdot \cos \left(\tan ^{-1}(\tan 4)\right) \)
B. \( \sin \left(\cot ^{-1}(\cot 4)\right) \)
c. \( \tan \left(\cos ^{-1}(\cos 5)\right) \)
D・cot \( \left(\sin ^{-1}(\sin 4)\right) \)


Which complex compound possesses \( s p^{3} d^{2} \) hybridisation?
A \( \cdot\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
B . \( \left[F e(C N)_{6}\right]^{4-} \)
c. \( \left[F e(C N)_{6}\right]^{3} \)
D \cdot \( \left[F e(C l)_{6}\right]^{3-} \)


A derived dimension is something
which has some physical sense or is the combination of many fundamental
dimensions.
If true enter 1 , else enter 0


During interference of waves, the
amplitude of the resulting wave can be found at any position using the principle of:
A. superposition
B. interference
c. diffraction
D. none of these


Find the extreme value of Quadratic
expression \( 2 x-7-5 x^{2} \). Also state
whether it is maximum or minimum
with reason


In one average-life,
A. half the active nuclei decay
B. less than half the active nuclei decay.
C. more than half the active nuclei decay.
D. all the nuclei decay.


With out expanding show that \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \)


The advantage of RBCs being biconcave
is that
A. They increase the surface area
B. They can be packed up like coins.
c. They can fit into capillaries.
D. None of the above


\( N a_{2} O, M g O, A l_{2} O_{3} \) and \( S i O_{2} \) have
heat of formation equal to -416,-602,-1676 and -911
\( k J m o l^{-1} \) respectively. The most stable oxide is:
A. \( N a_{2} O \)
в. \( M g O \)
c. \( A l_{2} O_{3} \)
D. \( \operatorname{si} O_{2} \)


If the tangents of the angles \( A \) and \( B \) of \( a \) triangle \( A B C \) satisfy the equation
\( a b x^{2}-c^{2} x+a b=0, \) then
This question has multiple correct options
\( \mathbf{A} \cdot \tan A=\frac{a}{b} \)
B. \( \tan B=\frac{b}{a} \)
\( \mathbf{c} \cdot \cos C=0 \)
D. \( \sin ^{2} A+\sin ^{2} B+\sin ^{2} C=2 \)


If \( n-1 C_{6}+^{n-1} C_{7}>^{n} C_{6}, \) then?
\( \mathbf{A} \cdot n>4 \)
B \( . n>12 \)
\( \mathbf{C} \cdot n \geq 13 \)
D. \( n>13 \)


Which among the following is a nonmetal?
A. Bromine
B. zinç
c. sodium
D. Iron


Which compound is unstable at room
temperature?
\( A \)
B.
\( c \)
\( D \)


The nucleus of helium atom contains
two protons that are separated by distance \( 3.0 \times 10^{-15} \) m. The magnitude
of the electrostatic force that each
proton exerts on the other is:
A . \( 20.6 N \)
B. 25.6 N
c. \( 15.6 N \)
D. \( 12.6 N \)


\( \sqrt{3}+2 \sqrt{2}+\sqrt{3-2 \sqrt{2}}=\dots ? \)
A \( \cdot 2+2 \sqrt{2} \)
B. \( 2 \sqrt{2} \)
c. 1
D.


During respiration \( C O_{2} \) is transported in the form of
A. Dissolved plasma
B. Sodium carbonate
\( \mathrm{c} \cdot \mathrm{KHCO}_{3} \)
D. Partly dissolved in plasma and partly in the form of sodium and potassium bicarbonate


A wire has a resistance of \( 10 \Omega \). It is
stretched by \( 10 \% \) of its original length, what will be the new resistance?
A . \( 10 \Omega \)
в. \( 11 \Omega \)
\( c .9 \Omega \)
D. 12.12


"Gulal" a coloured powdery thing, used in Holi festival is obtained from
A. Caesalpinioideae family
B. Mimosoideae family
c. Papilionatae family
D. Liliaceae


The energy stored in one molecule of
NADPH and one molecule of ATP are
and \( \ldots \ldots . \) respectively.
A. 52 kcal, 7 kcal
B. 520 kcal, 70 kcal
c. 150 kcal, 22 kcal
D. 650 kcal, 90 kcal


Find the square root of each of the
following by prime factorization:
\( \mathbf{1 1 6 6 4} \)


Check whether the probabilities \( \boldsymbol{P}(\boldsymbol{A}) \)
and \( P(B) \) are consistently defined \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \mathbf{0 . 6} \)


The coefficient of \( x^{160} \) in the expansion
of \( \left(x^{8}+\right. \)
1) \( ^{60}\left(x^{12}+3 x^{4}+\frac{3}{x^{4}}+\frac{1}{x^{12}}\right)^{-10} \)
A. \( ^{30} C_{6} \)
B. \( ^{30} C_{5} \)
c. divisible by 189
D. divisible by 203


If the distance between two object in increase two times, they by how many times will the mass of one of the object
be change to maintain the same gravitational force?


What amount of work is done in moving a charge of 4 coulombs from a point 220 volts to a point at 230 volts?


\( \operatorname{Det}\left\{\begin{array}{ccc}-2 a & a+b & c+a \\ b+a & -2 b & b+c \\ c+a & c+b & -2 c\end{array}\right\}= \)
\( A \cdot(a+b)(b+c)(c+a) \)
В . \( (a-b)(b-c)(c-a) \)
\( c \cdot 4(a+b)(b+c)(c+a) \)
D. \( 4(a-b)(b-c)(c-a) \)


In the adjoining figure, name the
following pairs of angles.

Obstuse vertically opposite angles


Combination of
\( \boldsymbol{P t}(\boldsymbol{I} \boldsymbol{V}), \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{C l}^{-}, \boldsymbol{K}^{+} \) result in the
formation of \( x \) complexes and one such
complex is \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{4} . \boldsymbol{x} \) is :


A particle moves along the curve \( y= \)
\( x^{3 / 2} \) in the first quadrant in such a way
that its distance from the origin increases at the rate of 11 units per
second. The value of when \( x=3 \) is
A . 4
B. \( \frac{9}{2} \)
c. \( \frac{3 \sqrt{3}}{2} \)
D. none of these


Which among the following does not
react with a dilute solution of sulfuric
acid?
A \( \cdot \) NaNO \( _{3} \)
В. \( N a_{2} S \)
c. \( N a_{3} P O_{4} \)
D. \( N a_{2} C O_{3} \)
E . NaOH


The coefficient of the middle term in the
expansion of \( (1+x)^{2 n} \) is
This question has multiple correct options
A \( \cdot 2^{n} C_{n} \)
в. \( \frac{1.3 .5 \ldots \ldots(2 n-1)}{n !} 2^{\text {। }} \)
c. \( 2.6 \ldots(4 n-2) \)
D \( \cdot 2.4 \ldots \ldots . .2 n \)


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( (401)^{\frac{1}{2}} \)


Find the matrix \( X \), given that \( X+ \) \( \mathbf{2} \boldsymbol{I}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{2}\end{array}\right] \)


If the work done in stretching a wire by
1 \( m m \) is \( 2 J, \) the work necessary for
stretching another wire of same
material but with double radius of
cross-section and half the length by
1 mm is:
\( \mathbf{A} \cdot 16 J \)
B. \( 8 J \)
c. \( 4 J \)
D \( \frac{1}{4} J \)


A bidentate ligand has 3 coordination sites.
A . True
B. False


In the reaction; \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightarrow \mathbf{3} \boldsymbol{C}+\boldsymbol{D} \)
which of the following expression does not describe changes in the concentration of various species as a function of time?
A \( \cdot\{d[C] / d t\}=-\{3 d[A] / d t\} \)
B . \( \{3 d[D] / d t\}=\{d[C] / d t\} \)
c. \( \{3 d[B] / d t\}=-\{2 d[C] / d t\} \)
D . \( \{2 d[B] / d t\}=-\{d[A] / d t\} \)


From a piece of cardbord, in the shape
of a trapezium \( A B C D, \) and \( A B \| C D \)
and \( \angle B C D=90^{\circ}, \) quarter circle is
removed. Given \( A B=B C=3.5 \mathrm{cm} \) and
\( D E=2 c m . \) Calculate the area of the
remaining piece of the cardboard (Take
to be \( \left.\frac{22}{7}\right) \)


Glycinato ligand is:
\( \mathbf{A} \)
B. bidentate ligand
C \( . \) two donar sites \( N \) and \( O^{-} \)
D. all of the above


A prime number is squared and then added to a different prime number. The number thus obtained is:
I. An even number
II. An odd number
III. A positive number
A. I only
B. II only
c. ॥ only
D. I and III only
E . ।, ॥।, and III


The most active nonmetal has:
A. a high electronegativity
B. a low electronegativity
C. a medium electronegativity
D. large atomic radii
E . a deliquescent property


Find DF, if \( \mathrm{CG}=11 \mathrm{cm} \)
A. \( 5.6 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
\( c \cdot 0.55 \mathrm{cm} \)
D. \( 55 \mathrm{cm} \)


A rod of length \( l \) carrying current \( i \) is
kept in uniform magnetic field of
magnitude \( B \) is shown in figure. Then
the force on rod due to magnetic field is:
A. zero
B. ilBsin\theta
\( \mathbf{c} \cdot i l B \cos \theta \)
D. \( i l B \)


The given distribution shows the
number of runs scored by some top
batsmen of the world in one-day
international cricket matches.
find the mode of the data.


Find the angle marked \( a \)
4.77
8. 36
\( c \cdot 41^{\circ} \)
\( \mathbf{D} \cdot 13^{\circ} \)


For a reaction, \( \boldsymbol{A}(s)+\mathbf{2} \boldsymbol{B}^{+} \leftrightharpoons \boldsymbol{A}^{2+}+ \)
\( 2 B, K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A . \( 0.354 V \)
в. \( 0.708 V \)
c. \( 0.0098 V \)
D. \( 1.36 V \)


If \( 2 x=t+\sqrt{t^{2}+4} \) and \( 3 y=t- \)
\( \sqrt{t^{2}+4} \) then the value of \( y \) when \( x=\frac{2}{3} \)
is
A . -2
B. 1
\( c \cdot-1 \)
D.


The equilibrium constant for the
reaction: \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \) at
\( \mathbf{7} 15 K, \) is \( 6.0 \times 10^{-2} . \) If, in a particular
reaction, there are 0.25 mol \( L^{-1} \) of \( H_{2} \)
and \( 0.06 m o l L^{-1} \) of \( N H_{3} \) present
calculate the concentration of \( N_{2} \) at
equilibrium.


Assertion
If \( \boldsymbol{x}^{2}-\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0} \) where \( \boldsymbol{p} \) is twice the
tangent of the arithmetic mean of
\( \sin ^{-1} x \) and \( \cos ^{-1} x ; \) q is the geometric
mean of \( \tan ^{-1} x \) and \( \cot ^{-1} x \) then \( x=1 \)
Reason
\( \tan \left(\sin ^{-1} x+\cos ^{-1} x\right)=1 \)
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


What is the substrate for lipase enzyme?
A. Protein
B. Lipid
c. carbohydrate
D. Nucleic acid


The number of ciritical points of \( \mathbf{f}(\mathbf{x})= \) \( \frac{|\boldsymbol{x}-\mathbf{1}|}{\boldsymbol{x}^{2}} \) is
A . 1
B . 2
\( c \cdot 3 \)
D.


Find the product(s) when methane,
\( C H_{4}, \) burns in excess of oxygen?
A \( \cdot C H_{4} O_{2} \)
в. \( C O+H_{2} O \)
c. \( C O+C H_{2} O H \)
D. \( C O_{2}+H_{2} O \)
E \( \cdot C O_{2}+2 H_{2} \)


0.01 mol of \( A g N O_{3} \) is added to 1 L of a
solution which is \( 0.1 M N a_{2} C r O_{4} \) and
\( 0.005 M \) in \( N a I O_{3} . \) Calculate
\( \left[\boldsymbol{A} \boldsymbol{g}^{\oplus}\right],\left[\boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}\right] \) and \( \left[\boldsymbol{C r} \boldsymbol{O}_{4}^{2-}\right] \)
\( K_{s p} A g_{2} C r O_{4} \) and \( A g I O_{3} \) are \( 10^{-8} \) and \( 10^{-13} \) respectively
\( \mathbf{A} \cdot\left[A g^{\oplus}\right]=0.316 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=0.31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.0975 M \)
B \( \cdot\left[A g^{\oplus}\right]=3.16 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=3.1 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.975 M \)
C \( \cdot\left[A g^{\oplus}\right]=31.6 \times 10^{-4} M,\left[I O_{3}^{\odot}\right]=31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=9.75 M \)
D. None of these


Which part of the atmosphere is called
homosphere?
A. Atmosphere up to \( 70 \mathrm{km} \) from the surface of the earth
B. Atmosphere up to \( 80 \mathrm{km} \) from the surface of the earth
C. Atmosphere up to \( 90 \mathrm{km} \) from the surface of the earth
D. Atmosphere up to \( 110 \mathrm{km} \) from the surface of the earth


The condition that the roots of the
equation \( l x^{2}+m x+n=0 \) may be in
the ratio 3: 4 is
A \( \cdot 14 n^{2}=49 m l \)
B . \( m^{2}=9 n l \)
\( \mathbf{c} \cdot 12 m^{2}=49 n l \)
\( \mathbf{D} \cdot 4 l^{2}=49 m l \)


Write the equation of reaction of chlrobenzene :
Halogenation


Which of the following reactions is not
correctly matched?
A \( \cdot 2 C_{2} H_{5} B r+2 N a \stackrel{\text {dry ether}}{\longrightarrow} C_{4} H_{1} 0+2 N a B r \)
Wurtz reaction
B . \( C H_{3} B r+A g F \stackrel{C}{\longrightarrow} H_{3} F+A g B r \)
Etards reaction
\( \mathbf{c} \cdot C_{5} H_{6} B r+2 N a+B r C_{2} H_{5} \stackrel{\text {dry ether}}{\longrightarrow} C_{6} H_{5} C_{2} H_{5}+ \)
\( N a B r \)
Wurtz fitting reaction
D \( \cdot 2 C_{6} H_{5} B r+2 N a \stackrel{\text {dryether}}{\longrightarrow} C_{6} H_{5} C_{6} H_{5}+2 N a B r \)
Fitting reaction


When the light rays converge at a point in front of the retina and then divert to
form a blurred image on it, the defect is
known as
A. Myopia
B. Hypermetropia
c. Astigmatism
D. Presbiopia


The ratio of the diameters of wires of
circular and straight parts is
\( ^{A} \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{2 \sqrt{3}}{\pi} \)
\( c \cdot \frac{3 \sqrt{3}}{2 \pi} \)
\( D \cdot \sqrt{2} \)


A tunnel is dug along a chord of the
\( \boldsymbol{R} \)
earth at a perpendicular distance
from the earth's centre. Assume wall of
the tunnel is frictionless. Find the force
exerted by the wall on mass m at a
distance \( x \) from the centre of the tunnel
\( \mathbf{A} \)
B. \( \frac{m g x}{\sqrt{R^{2} / a+x^{2}}} \)
\( c \cdot \frac{m g}{3} \)
D. \( \frac{m g x}{R} \)


The substance that will be flattened on
beating with a hammer is :
A. crystal of iodine
B. lump of sulphur
c. piece of coal
D. zinc granule


\( 45 g \) of water at \( 50^{\circ} C \) in a beaker is cooled when \( 50 g \) of copper at \( 18^{\circ} C \) is added to it. The contents are stirred till
final constant temperature is reached. Calculate the final temperature. The specific heat capacity of copper is \( 0.39 J g^{-1} K^{-1} \) and that of water is
\( 4.2 J g^{-1} K^{-1} . \) State the assumption used.


In Nepenthes, the pitcher is modified
A. Whole leaf
B. Leaf apex
c. Lamina
D. Petiole
E. Leaf base


Bohr's atomic model couldn't explain
A. the fine spectrum of hydrogen
B. the spectra of single electron species
c. the stability of atom
D. Both \( A \) and \( C \)


The magnetic flux linked with a coil
satisfies the relation \( \phi=4 t^{2}+6 t+9 \)
Wh, where t is the time in second. The emf induced in the coil at \( t=2 s \) is
A 22 V V \( V \) ) 22
в. \( 18 V \)
\( \mathrm{c} .16 \mathrm{V} \)
D. \( 40 V \)


Let \( f \) and \( g \) be real-valued functions
such that
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=2 \boldsymbol{f}(\boldsymbol{x}) \)
\( \boldsymbol{g}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
if \( f \) is not identically zero and \( f|(x)| \leq \)
\( \mathbf{1}, \forall \boldsymbol{x} \epsilon \boldsymbol{R}, \) then \( |\boldsymbol{g}(\boldsymbol{y})| \leq \mathbf{1}, \forall \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
If true enter 1 else enter 0
A. True
B. False


The temperature of a substance
increases by \( 27^{\circ} \mathrm{C} \). On the Kelvin scale
this increase is equal to
\( \mathbf{A} \cdot 300 K \)
в. \( 2.46 K \)
c. \( 27 K \)
D. \( 7 K \)


The volume of an air bubble is doubled
as it rises from the bottom of a lake to
its surface. The atmospheric pressure is \( 75 \mathrm{cm} \) of mercury and the ratio of the density of mercury to that of lake water is \( 40 / 3, \) the depth of the lake is


The volume of the \( y= \) tethradron formed by the coterminous edges \( \bar{a}, \bar{b}, \bar{c} \) is 3 Then the volume of the parallelepiped
formed by the coterminous edges \( \overline{\boldsymbol{a}}+ \) \( \bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a} \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 18
\( c .36 \)
D.


What will be the ratio of \( C l^{35} \) and \( C l^{37} \)
respectively in chlorine if the average atomic mass of chlorine is \( 35.5 ? \)
A . 1:
B. 2:1
c. 3: 1
D. 3:2


During the meiotic division, the
A. Homologous chromosomes are separated
B. Linkage is disturbed
C. Homologous chromosomes do not segregate
D. All of the above


The current through the \( 8 \Omega \) resistor is
\( A \cdot 4 A \)
B. 2 A
c. zero
D. 2.5 A


A small object of linear dimension \( x \) lies on the axis of an optical mirror of local length \( f \) at a distance \( a \) from mirror
The linear dimension of image:
\( ^{A} \cdot_{x}\left(\frac{f}{f-a}\right)^{2} \)
B. \( x\left(\frac{f}{f-a}\right) \)
c. \( x\left(\frac{f}{a-f}\right)^{1 / 2} \)
D. \( x\left(\frac{a-f}{f}\right)^{1 / 2} \)


Find the mode for the following table.
Temperature
in \( ^{o} \boldsymbol{C} \)
\[
\begin{array}{ll}
\text { 3) } 3.4 & \text { 34.6 }
\end{array}
\]
\( \mathbf{2 9} \)
Number of
days 7 6


To get an output \( Y=1 \) in given circuit
which of the following input will be
correct.
\( \mathbf{A} \cdot A=1 ; B=0 ; C=1 \)
В. \( A=1 ; B=1 ; C=0 \)
c. \( A=0 ; B=1 ; C=0 \)
D. \( A=1 ; B=0 ; C=0 \)


Make an outline of the classification.
What are the advantages and disadvantage of this classification?


A ball strikes a smooth horizontal
ground at an angle of \( 45^{\circ} \) with the vertical. What cannot be the possible angle of its velocity with vertical after the collision? (Assume \( e \leq 1 \) )
A . \( 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 53^{\circ} \)
D. \( 60^{\circ} \)


The area of \( \square O A P B \) is:
A \( .24 \mathrm{cm}^{2} \)
B. \( 36 \mathrm{cm}^{2} \)
c. \( 48 \mathrm{cm}^{2} \)
D. \( 60 \mathrm{cm}^{2} \)


(i) Why does a current carrying, freely suspended solenoid rest along a particular direction?
(ii) State the direction in which it rests.


If a conductor has \( 10^{8} \) number of
electrons, then the total charge of the conductor is:
A. \( +1.6 \times 10^{-19} \mathrm{C} \)
В. \( -1.6 \times 10^{-19} \mathrm{c} \)
c. \( +1.6 \times 10^{-11} \mathrm{c} \)
D. \( -1.6 \times 10^{-11} \mathrm{C} \)


Which was not proposed by Darwin?
A. Struggle for existence
B. Natural selection
C . Genetic drift
D. Survival of the fittest


The ground state energy of hydrogen atom is \( -13.6 e V . \) What is the potential
energy of the electron in this state?
A \( .0 \mathrm{eV} \)
B . -27.2 eV
\( \mathrm{c} \cdot 1 \mathrm{eV} \)
D. 2 eV


Find the cube root of
\( 99-70 \sqrt{2} \)


\( N a C l \) is less soluble in \( D_{2} O \) than \( H_{2} O \)
why?


A satellite is launched into a circular
orbit of radius r around the earth. \( \mathbf{A} \)
second satellite is launched into an
orbit of radius \( 1.01 \mathrm{r} \). The period of the second satellite is larger than that of
first one by approximately.
\( A \cdot 0.5 \% \)
B . 1.0 \%
c. \( 1.5 \% \)
D. 3.0 \%


What is the value of \( \int_{0}^{a} \frac{x-a}{x+a} d x ? \)
A. \( a+2 a \log 2 \)
в. \( a-2 a \log 2 \)
c. \( 2 a \log 2-a \)
D. \( 2 a \log 2 \)


A \( 2 M e V \) neutron is emitted in a fission
reactor. If it looses half of its kinetic
energy in each collision with a
moderator atom, how many collisions must it undergo to achieve thermal energy of \( 0.039 e V ? \)
A . 20
B. 26
c. 30
D. 42
E . 48


If the standard deviation of the numbers
\( 2,3, a \) and 11 is \( 3.5, \) then which of the
following is true?
A \( \cdot 3 a^{2}-32 a+84=0 \)
B . \( 3 a^{2}-34 a+91=0 \)
c. \( 3 a^{2}-23 a+44=0 \)
D. \( 3 a^{2}-26 a+55=0 \)


If \( A \) and \( B \) are two matrices of same
order, then \( A+B \) is equal to
\( \mathbf{A} \cdot B+A \)
в. \( B A \)
c. \( (A+B) T \)
D. \( A-B \)


If \( \left.A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \text { (where } b \neq c\right) \) and satisfies the equation \( A^{2}+k I=0, \) then
\( \mathbf{A} \cdot a+d=0 \)
B . \( k=-|A| \)
c. \( k=|A| \)
D. None of the above


The adjoining curve represents the
velocity-time graph of a particle, its
acceleration values along \( \mathrm{O} \mathrm{A}, \mathrm{AB} \) and \( \mathrm{BC} \)
in \( m \cdot / \sec ^{2} \) are respectively:
A. 1,0,-0.5
В. 1,0,0.5
c. 1,1,0.5
D. \( 1,0.5 . \)


The earth has volume 'V' and surface
area 'A'; then its capacitance would be:
A \( \cdot_{4 \pi \in_{0}} \frac{A}{V} \)
в. \( _{4 \pi \in_{0}} \frac{V}{A} \)
c. \( _{12 \pi \in_{0} \frac{V}{A}} \)
D. \( _{12 \pi \in_{0}} \frac{A}{V} \)


Let \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{- 2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] . \) Find:
\( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \)


The net charge inside an atom is zero
because:
A. the magnitude of positive charge is more than negative charge inside atom
B. the magnitude of positive and negative charge is same inside atom
C. the magnitude of positive and negative charge is same outside atom
D. the magnitude of positive charge is less than negative charge inside atom


Assertion
Colloidal silver iodide is prepared by adding silver nitrate in slight excess to potassium iodide solution. When
subjected to an electric field, the
colloidal particles migrate to the anode.
Reason

Colloidal particles adsorb ions and thus become electrically charged.
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


Assertion
Alcohols are dehydrated to hydrocarbons in the presence of acidic
zeolites
Reason
Zeolites are porous catalysts.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In an election, a candidate secured \( 47 \% \) of votes polled and lost the election by 12,366 votes. Find the total votes polled and the votes secured by winning candidate.
A. 2,06,133 and 1,09,266
B. 2,16,100 and 1,19,233
c. 2,06,100 and 1,09,233
D. 2,06,233 and 1,09,200


Write balanced chemical equations to
show how \( S O_{3} \) is converted to Sulphuric
acid at the contact process.


If \( f(x)=3 x^{2}+15 x+5, \) then the
approximate value of \( \boldsymbol{f}(\mathbf{3} . \mathbf{0 2}) \) is.
A . 47.66
B. 57.66
c. 67.66
D. 77.66


State which of the following solutions contain both molecules and ions?
A. \( C H_{3} \) СООН
в. \( N a_{2} C O_{3} \)
c. oxalic acid
D. All of these


- Q. A B


Perform the following divisions and give the remainders.
\( \left(x^{2}+15 x+56\right) \div(x+8) \)


If a small angled prism, made of glass is immersed in a liquid of refractive
index '1' and a ray of light is made to incident on it, then :
A. its deviation will be zero
B. it will suffer total reflection
c. the emergent ray is bent towards the edge of the prism
D. the emergent ray is bent towards the base of prism


Solve the following inequalities graphically in two-dimensional plane:
\( y+8 \geq 2 x \)


Bag \( I \) contains 3 red and 4 black balls
and Bag \( I I \) contains 4 red and 5 black
balls. One ball is transferred from Bag \( \boldsymbol{I} \) and Bag \( I I \) and then a ball is drawn
from Bag \( I I . \) The ball so drawn is found
to be red in colour. Find 310 times the
probability that the transferred ball is
black.


Distinguish between elastic and plastic
materials.


A nuclide \( A \) undergoes \( \alpha \) decay and
another nuclide \( B \) undergoes \( \beta \) decay.
Then
This question has multiple correct options
A. all the \( \alpha \) -particles emitted by \( A \) will have almost the same speed
B. the \( \alpha \) -particles emitted by \( A \) may have widely different speeds
C . all the \( \beta \) -particles emitted b \( B \) will have almost the same speed
D. the \( \beta \) -particles emitted by \( B \) may have widely different speeds.


A particle is acted simultaneously by mutually perpendicular simple harmonic motions \( x=a c o s \omega t \) and \( y= \)
asinwt. The trajectory of motion of the
particle will be
A. an ellipse
B. a parabola
c. a circle
D. a straight line


In an experiment, 1.35 mol of oxygen (O2) are heated at constant pressure starting at \( 11.0^{\circ} \mathrm{C} \). How much heat must be added
to the gas to double its volume?
A \( \cdot 1.12 \times 10^{4} J \)
В. \( 1.40 \times 10^{4} \)
c. \( \$ \$ 2.12 \) ltimes \( 10^{\wedge} 4 \$ \$ \) J
D. \$\$3.12x10^4 J\$\$


In germanium, the energy gap is about
\( 0.75 e V . \) The wavelength of light which germanium starts absorbing is
A \( \cdot 5000 \),
B . 1650 ,
c. 16500 ,
D. 165000 ,


For the cell \( \boldsymbol{M} / \boldsymbol{M}^{+} \| \boldsymbol{X}^{-} / \boldsymbol{X}, \boldsymbol{E}_{M^{+} / M}^{\circ}= \)
0.44 and \( E_{X / X^{-}}^{\circ}=0.33 V . \) From the data it can be deduced that \( M+X \rightarrow \)
\( M^{+}+X^{-} \) is spontaneous.
A. \( M+X \rightarrow M^{+}+X^{-} \) is spontaneous
В. \( E_{\text {Сец}}=0.77 V \)
c. \( E_{\text {Cell }}=-0.77 V \)
D. None


\( A l+M n O_{4}^{-} \rightarrow A l(O H)_{4}^{-}+M n O_{2} \)
For this reaction the oxidation state of
\( A l \) and \( M n \) in the product are respectively:
\( \mathbf{A} \cdot+3 a n d+4 \)
B. +4 and +4
c. +3 and +7
D. +2 and +4


In Bryophytes, what is absent?
A. Embryo formation
B. Fertilization
c. Motile gametes
D. True roots and vascular tissue


topp
\( Q \)
the atoms are almost lacking in mobility, their kinetic energy is negligibly small. It is this lack of mobility which makes a solid rigid. This rigidity is the cause of elasticity in solids. In some solids such as steel, the atoms are bound together by larger nter-atomic forces than in solids such as aluminum. Thus, the elastic behavio
varies from solid to solid. Even fluids
exhibit elasticity. All material bodies get deformed when subjected to a suitable force. The ability of a body to regain its original shape and size is called elasticity. The deforming force per unit area is called stress. The
change in the dimension (length, shape or volume) divided by the original dimension is called strain. The three kinds of stress are tensile stress
shearing stress, and volumetric stress. The corresponding strains are called tensile strain, shearing strain and volume strain. According to Hooke's law, within the elastic limit, stress is proportional to strain. The ratio stress/strain is called the modulus of
elasticity. The figure shows the strain-stress graphs for materials A and B. From the graph it follows that:
A. material A has a higher Young's mod
B. material B has a higher Young's modulus than
\( c \)
es
for


Two moles of a gas \( A \) at \( 27^{\circ} \mathrm{C} \) mixed
with a 3 moles of \( \operatorname{gas} \) at \( 37^{\circ} \mathrm{C} \). If both are monatomic ideal gases, what will be the temperature of the mixture?
\( \mathbf{A} \cdot 66^{\circ} C \)
В. \( 11^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 22^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)


A beam of alpha-particles is fires at a
piece of gold foil as shown below. After
striking the gold foil, in which direction
do most of the alpha-particles travel?
\( A \cdot P \)
в. \( Q \)
\( c . R \)
D.


If 6,10,14 are the sides of a triangle, then its obtuse angle is
A \( \cdot 110^{\circ} \)
B . \( 120^{\circ} \)
\( \mathrm{c} \cdot 135^{\circ} \)
D. \( 115^{\circ} \)


is known as incomplete because, in this subclass, sepals and petals are not distinct. Flowers usually possess only one whorl of perianth which is sepaloid.
A. Polypetalae
B. Gamopetalae
c. Monochlamydeae
D. Both A and B


What is the ratio of the enthalpy yield on combustion of hydrogen atoms to steam to the yield on combustion of an equal mass of hydrogen molecules to steam? Given \( : \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{2} \mathbf{4} 2 \) kJ,Bond energy
\( (\boldsymbol{H}-\boldsymbol{H})=\mathbf{4 3 6} \mathbf{k J} \)
A . 0.80:
B. 1: 0.80
c. 1.80: 1
D. 2.80:


Assertion \( f: R \rightarrow\left[0, \frac{\pi}{2}\right) \) defined by \( f(x)= \)
\( \tan ^{-1}\left(x^{2}+x+a\right) \) is onto for all \( a \in \)
\( \left(-\infty, \frac{1}{4}\right) \)
Reason
For onto function codomain of \( \boldsymbol{f}= \)
Range of \( \boldsymbol{f} \)
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


Hydrogen peroxide acts both as an oxidising and as a reducing agent, depending upon the nature of the reacting species. In which of the
following cases \( H_{2} O_{2} \) acts as a reducing agent in acid medium?
A. \( M n O_{4} \)
B. \( C r_{2} O_{7}^{2} \)
\( \mathbf{c} \cdot S O_{3}^{2} \)
D. \( K I \)


The order not in accordance with the
property mentioned is ?
\( \mathbf{A} \cdot L i<N a<K<R b- \) atomic radius
B \( . F>N>O>C \) - ionisation enthalpy
c. \( S i<P<S<C l \) - electronegativity
D. \( F<C l<B r<I \) - electronegativity


An electric dipole consist of two opposite charges each of magnitude \( 1 \mu C \) separated by a distance of \( 2 \mathrm{cm} \) The dipole is placed in an external field of \( 10^{5} \mathrm{N} / \) C.The maximum torque on the
dipole is:
A. \( 2 \times 10^{-4} J \)
B . \( 2 \times 10^{-3} J \)
c. \( 4 \times 10^{-3} J \)
D. \( 10^{-3} N m \)


Two charged particles moving with
velocities \( v_{1} \) and \( v_{2} \) have some
separation between them. The ratio of magnetic force to the Colombian force between them is (c is speed of light)
A. \( \frac{v_{1} v_{2}}{c^{2}} \)
в. \( \frac{c^{2}}{v_{i} v_{2}} \)
c. \( \frac{c}{v_{1}} \)
D. \( \frac{c}{v_{2}} \)


What is a 'soap'? How is it prepared?


The area of the part of the square filed in which a horse tied to a fixed pole at
one comer by means of a 10 m rope, can
graze is
A . \( 25 \pi s q . m \).
в. \( 100 \pi s q . m \)
c. \( 50 \pi s q . m \)
D. \( 5 \pi s q . m . \)


What do we call this number which is
characteristic of a particular element?


The current density across a cylindrical
conductor of radius \( R \) varies in
magnitude according to the equation \( J=J_{0}\left(1-\frac{r}{R}\right) \) where \( r \) is the distance from the central axis. Thus, the
current density is a maximum \( J_{0} \) at
that axis \( (r=0) \) and decreases linearly
to zero at the surface \( (r=R) \). Find the
value of current in terms of \( J_{0} \) and
conductor's cross-sectional area


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


The R.I of glass and water w.r.t air are
1.5 and \( 4 / 3 \) respectively. What is the R. of glass w.r.t water.
\( ^{\mathrm{A}} \cdot \frac{1}{3 \pi}\left(\frac{\left[R_{2}-R_{1}\right]\left[2 R_{1}+R_{2}\right]}{R_{1}+R_{2}}\right) \)
В. \( \frac{1}{3 \pi}\left(\frac{\left[R_{2}-R_{1}\right]\left[2 R_{1}+R_{2}\right]}{R_{1}-R_{2}}\right) \) above
c. \( \frac{1}{3 \pi}\left(\frac{\left[R_{2}+R_{1}\right]\left[2 R_{1}+R_{2}\right]}{R_{1} \times R_{2}}\right) \) above
D \( \cdot \frac{1}{3 \pi}\left(\frac{\left[R_{2} \times R_{1}\right]\left[2 R_{1}+R_{2}\right]}{R_{1}-R_{2}}\right) \) above


According to the quantum theory of light, the energy of light is carried in discrete units called
A. alpha particles
B. photoelectrons
c. protons
D. photons


Cisplatin compound is used in the treatment of:
A. malaria
B. cancer
c. AlDS
D. yellow fever


Assertion
If a and b are positive and [x] denotes
the greatest integer \( \leq x \), then \( \lim _{x \rightarrow 0^{+}} \frac{x}{a}\left[\frac{b}{x}\right]=\frac{b}{a} \)
Reason
\( \lim _{x \rightarrow \infty} \frac{\{x\}}{x}=0, \) where denotes fractional
part of \( \mathbf{x} \)
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


Name the chronic respiratory disorder caused mainly by cigarette smoking.
A. Emphysema
B. Asthma
c. Respiratory acidosis
D. cough


The number of neutrons in the element
Lin the following nuclear changes is
\( \boldsymbol{Y}^{\boldsymbol{X}} \boldsymbol{N} \rightarrow_{\boldsymbol{B}}^{\boldsymbol{A}} \boldsymbol{L}+\mathbf{2} \boldsymbol{\beta}^{+} \)
A. 146
в. 144
\( c .140 \)
D. 142


If \( 0<x<1000 \) and \( \left[\frac{x}{2}\right]+\left[\frac{x}{3}\right]+ \)
\( \left[\frac{x}{5}\right]=\frac{31}{30} x \) where \( [x] \) is the greatest
integer less than or equal to \( x \), the number of possible values of \( x \) is
A . 34
B. 32
\( c .33 \)
D. 30


A cube has a side of length \( 1.2 \times 10^{-2} . \) Its volume upto correct significant figures is
A . \( 1.7 \times 10^{-6} m^{3} \)
В . \( 1.73 \times 10^{-6} m^{3} \)
\( \mathbf{c} \cdot 1.78 \times 10^{-6} m^{3} \)
D. \( 1.732 \times 10^{-6} \mathrm{m}^{3} \)


A solution containing 3.3 g of a substance in 125 g of benzene (b.pt. \( = \) \( 80^{\circ} \mathrm{C} \) ) boils at \( 80.66^{\circ} \mathrm{C} \). If \( \mathrm{K}_{b} \) for
benzene is \( 3.28 \mathrm{K} \mathrm{kg} \) mol\( ^{-1} \) the
molecular mass of the substance will
be:
A . 130.20
B. 129.20
c. 132.20
D. 131.20


toppr
Q Type your question
materıdı, then oy onens law, \( \overline{\sin \theta_{2}}= \)
\( \frac{n_{2}}{n}, \) it is understood that the refracted
\( \boldsymbol{n}_{\mathbf{1}} \)
ray bends towards the normal. But it
never emerges on the same side of the
normal as the incident ray. According to
electromagnetism, the refractive index
of the medium is given by the relation, \( \boldsymbol{n}=\left(\frac{\boldsymbol{c}}{\boldsymbol{v}}\right)=\pm \sqrt{\boldsymbol{\epsilon}_{\boldsymbol{r}} \boldsymbol{\mu}_{\boldsymbol{r}}}, \) where \( \boldsymbol{c} \) is the
speed of electromagnetic waves in
vacuum, \( \boldsymbol{v} \) its speed in the medium, \( \boldsymbol{\epsilon}_{\boldsymbol{r}} \)
and \( \mu_{r} \) are the relative permittivity and
permeability of the medium respectively. In normal materials, both
\( \epsilon_{r} \) and \( \mu_{r} \) are positive, implying positive
\( n \) for the medium. When both \( \epsilon_{r} \) and \( \mu_{r} \)
are negative, one must choose the
negative root of \( n . \) Such negative
refractive index materials can now be
artificially prepared and are called
meta-materials. They exhibit significantly different optical behavior, without violating any physical laws.
since \( n \) is negative, it results in a
change in the direction of propagation
of the refracted light. However, similar
to normal materials, the frequency of
light remains unchanged upon
refraction even in meta-materials.
Choose the correct statement.
A. The speed of light in the meta-material is \( v=c|n| \)
B. The speed of light in the meta-material is \( v=\frac{c}{|n|} \)
C. The speed of light in the meta-material is \( v=c \)
D. The wavelength of the light in the meta-material \( \left(\lambda_{m}\right) \) is given by \( \lambda_{m}=\lambda_{a i r}|n| \), where \( \lambda_{\text {air}} \) is the wavelength of
the light in air


Which of the following solutions when
added to \( 1 L \) of a \( 0.1 M C H_{3} C O O H \)
solution will cause no change in either the degree of dissociation of
\( C H_{3} C O O H \) or the \( p H \) of the solution.
\( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{\mathbf{4}} \) for \( \boldsymbol{C H}_{\mathbf{3}} \) COOH?
A \( .3 \mathrm{mM} \) НСООН \( \left(K_{a}=6 \times 10^{4}\right. \)
в. 0.1 М \( C H_{3} \) СОО Na .
c. 1.34 m \( M \) НС\( l \)
D. 0.1 М \( C \) Сз СОООН


A body of mass 5 kg is raised vertically to a height of \( 10 \mathrm{m} \) by a force of \( 170 \mathrm{N} \) the velocity of the body at this height will be
\( \mathbf{A} \cdot 15 m / s \)
в. \( 37 m / s \)
c. \( 9.8 m / s \)
D. \( 21.9 \mathrm{m} / \mathrm{s} \)


A long solenoid is fabricated to closely winding wire of radius \( 0.5 \mathrm{mm} \) over a cylinderical frame, so that the
successive turns nearly touch each other. The magnetic field at the centre of solenoid, if it carries a current of 5 A
is?
\( \mathbf{A} \cdot 2 \pi \times 10^{-2} \mathbf{T} \)
В . \( 2 \pi \times 10^{-3} \mathrm{T} \)
с. \( 2 \pi \times 10^{-4} \mathrm{T} \)
D. \( 2 \pi \times 10^{-5} \mathrm{T} \)


Hydrogen is a good reducing agent What do you understand by the above statement?


If \( f(x)=[x \sin \pi x], \) then which of the
following is incorrect?
A. \( f(x) \) is continuous at \( x=0 \)
B. \( f(x) \) is continuous in (-1,0)
c. \( f(x) \) is differentiable at \( x=1 \)
D. \( f(x) \) is differentiable in (-1,1)


Expression the following as the product of expression through prime factorization
\( \mathbf{2 8 8} \)


Find the values of \( x, \) if \( \left|\begin{array}{cc}\mathbf{2 x} & \mathbf{5} \\ \mathbf{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{ll}\mathbf{6} & \mathbf{5} \\ \mathbf{8} & \mathbf{3}\end{array}\right| \)


Which of the following statements regarding molecularity of the reaction
is wrong?
A. It may be either whole number or fractional.
B. It is calculated from the reaction mechanism.
c. It depends on the rate determining step.
D. It is number of molecules of reactants taking part in a single step chemical reaction


Meiosis not occurs in
A . Ovule
B. Anther
c. Microsporangia
D. shoot tip


\( N=2.5 \times 10^{3} \) wire turns are uniformly
wound on a wooden toroidal core of very
small cross-section. A current \( I \) flows
through the wire. If the ratio \( \eta \) of the magnetic induction inside the core to that at the centre of the toroid is \( x \times \)
\( 10^{2} . \) Find \( x \)


Evaluate
\( \cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2} \)


An empty bottle is closed tightly with a
cork and then heated. After some time
the cork shoots out from the mouth of
the bottle. Give reason.


The Tunica-Corpus theory was proposed by
A. Haberlandt
B. Schmidt
c. Hanstein
D. Nageli


When \( H_{2} O_{2} \) is added to an acidified
solution of \( K_{2} C r_{2} O_{7}, \) the solution:
A. turns green due to the formation of \( C r_{2} O_{3} \)
B. turns yellow due to the formation of \( K_{2} C r O_{4} \)
c. turns deep blue-violet due to the formation of \( \operatorname{Cr} O\left(O_{2}\right)_{2} \)
D. gives green precipitate due to the formation of \( C r(O H)_{3} \)


The standard reduction potentials of
\( Z n^{2+} \mid Z n \) and \( C u^{2+} \mid C u \) are \( -0.76 V \) and
\( +0.34 \mathrm{V} \) respectively. What is the cell EMF of the following cell?
\( Z n\left|Z n^{2+}(0.05 M)\right|\left|C u^{2+}(0.005 M)\right| C u \)
\( \left[\frac{R T}{F}=0.059\right] \)
A . 1.1295
в. 1.0705 V
c. 1.1000
D. 1.0412 v


Hydrogen gas is not liberated when the
following metal is added to dil. \( \boldsymbol{H} \boldsymbol{C l} \)
\( \mathbf{A} \cdot A g \)
в. \( Z n \)
\( \mathrm{c} . M g \)
D. \( S n \)


In an ellipse the length of minor axis is equal to the distance between the foci,
the length of latus rectum is 10 and \( e=\frac{1}{\sqrt{2}} . \) Then the length of semi major
axis is:
A . 16
B . 18
c. 10
D. 22


find the acute angle between \( y=5 x+ \)
6 and \( y=x \)


The value of \( \int_{0}^{1} \frac{\log x}{1+x} d x \) equals This question has multiple correct options
A \( \cdot \frac{\alpha^{2}}{12} \)
\( ^{\mathbf{B}}-\int_{0}^{1} \frac{\log (1+x)}{x} \)
\( \mathbf{C} \cdot-\frac{\pi^{2}}{12} \)
D. None of these


Two towns \( T_{1} \) and \( T_{2} \) are connected by
a regular bus service. A
scooterist moving from \( \boldsymbol{T}_{1} \) to \( \boldsymbol{T}_{2} \) with
speed of \( 20 k m h^{-1} \) notices that a bus
goes past it every 21 minutes in the
direction of his motion and every 7
minutes in the opposite direction. If a
bus leaves in either direction every \( t \)
minutes, the period \( t \) is
A . 1.5 minute
B. 9.5 minute
c. 6 minute
D. 10.5 minute


Field lines are shown close together
where the
A. magnetic field is far apart
B. magnetic fields is zero
c. magnetic fields is greater
D. all


Find the total surface area of a closed
box of wood whose dimensions are \( 2 \mathrm{m} \)
\( 1.5 \mathrm{m} \) and \( 80 \mathrm{cm}, \) cost of wood used to
make it at the rate of Rs.120.55 per \( m^{2} \)


Hierarchical level below the category of family is
A. Phylum
B. Kingdom
c. Genus
D. class


Mercury is transported in the container's made up of
\( A \cdot A l \)
B. Fe
c. \( A g \)
D. Pb


There are two long co-axial solenoids of
same length \( l \). the inner and outer coils
have radii \( r_{1} \) and \( r_{2} \) and number of
turns per unit length \( n_{1} \) and \( n_{2} \)
respectively. The rate of mutual
inductance to the self-inductance of the
inner-coil is :
\( \mathbf{A} \cdot \frac{n_{2}}{n_{1}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}} \)
B. \( \frac{n_{2}}{n_{1}} \cdot \frac{r_{1}}{r_{2}} \)
c. \( \frac{n_{1}}{n_{2}} \)
D. \( \frac{n_{2}}{n_{1}} \)


Fruits are not formed in gymnosperms,
because
A. Fertilization is absent
B. Pollination is absent
c. Seeds are not formed
D. Ovary is absent


\( \ln \operatorname{lab} H_{2} \mathrm{O}_{2} \) is prepared by
A \( \cdot \) cold \( H_{2} S O_{4}+B a O_{2} \)
в. \( H C l+B a O_{2} \)
c. \( \operatorname{conc.H}_{2} \mathrm{SO}_{4}+\mathrm{Na}_{2} \mathrm{O}_{2} \)
D. \( H_{2}+O_{2} \)


Deep sea divers use mixture of


Which of the following statements is
incorrect?
A. Earthworms and leeches are hermaphrodite animals.
B. Young ones of animals showing external fertilisation receive little or no parental care.
C. If the egg is not fertilised, it is thrown out of the body along with the lining of the uterus as menstrual flow.
D. Sex organs in human beings are formed at puberty.


The displacement x of a particle varies with time \( t \) as \( x=a e^{-\alpha t}+b e^{\beta t}, \) Where \( a \)
b, \( \alpha \) and \( \beta \) are positive constants. The
velocity of the particle will:
A. Be independent of \( \alpha \) and \( \beta \)
B. Go on increasing with time
c. Drop to zero when \( \alpha=\beta \)
D. Go on decreasing with time


Is it true to say that area of a segment of a circle is less than the area of its
corresponding sector? Why?
A. yes, it is true for minor segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment.
B. Yes, it is only true for major segment since ar.minor segment = - ar.sector-triangle made by the radii and the chord of the segment
C. No, it is only true for major segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
D. No, it is only true for minor segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.


\( (1+x)^{21}+(1+x)^{22}+\ldots+(1+x)^{30} \)
coefficient of \( \boldsymbol{x}^{5} \)


If \( f^{n}(x) \) be continuous at \( x=0, f(0) \neq \)
\( \mathbf{0}, \boldsymbol{f}^{\prime}(\mathbf{0}) \neq \mathbf{0} \) and
\( \lim _{x \rightarrow 0} \frac{2 f(x)-3 a f(2 x)+b f(8 x)}{\sin ^{2} x} \) exists
Then the values of \( a \) and \( b \) are
A \( \cdot b=\frac{1}{3}, a=\frac{7}{9} \)
В. \( a=1, b=1 \)
c. \( a=b=-1 \)
D. \( a=-1, b=1 \)


The refracting angle of a prism is \( A, \) and refractive index of the material of the
prism is cot (A/2). The angle of minimum deviation is :
A \( \cdot 90^{\circ}-A \)
\( A \)
В. \( 180^{\circ}+2 A \)
D. \( 180^{\circ}-2 A \)


The number of isomeric amines
possible for the formula \( \boldsymbol{C}_{3} \boldsymbol{H}_{\mathbf{9}} \boldsymbol{N} \)
A . 4
B. 3
\( c .5 \)
D. 6


From the following which is not an emulsifer?
A. Agar
B. Milk
c. Gum
D. Soap


Which one of the following is the correct set with respect to molecule,
hybridization and shape?
A. \( B e C l_{2}, s p^{2} \), linear
B . \( B e C l_{2}, s p^{2}, \) triangular planar
c. \( B C l_{3}, s p^{2} \), triangular planar
D. \( B C l_{3}, s p^{3} \), tetrahedral


Find the roots of each of the
following quadratic equations by the method of completing the squares
\( 2 x^{2}-5 x+3=0 \)
A. \( x=2, x=-7 \)
В. \( x=-1, x=3 \)
c. \( x=1, x=\frac{3}{2} \)
D. \( x=1, x=\frac{1}{2} \)


During the formation of hydronium ion,
water molecule acts as acceptor.
Enter 1 if the statement is True, else 0


Assertion: Chloroform gives chloropicrin
with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) vapour
Reason: Chloropicrin is used as an
insecticide
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Two plane mirrors \( M_{1} \) and \( M_{2} \) are
inclined at angle \( \theta \) as shown in the
figure. A ray of light I, which is parallel
to \( M_{1} \) strikes \( M_{2} \) and after two
reflections, the ray 2 becomes parallel
to \( M_{2} . \) The angle \( \theta \) is
A. 0
B. 30
\( c \cdot 45 \)
D. 60


A charge \( Q \) is placed on to two opposite corner of a square. A charge q is placed at each of other two corners. Given that
resultant electric force on \( Q \) is zero,
then \( Q \) is equal to :
A \( \cdot(2 \sqrt{2}) / q \)
B . \( -q /(2 \sqrt{2}) \)
c. \( (2 \sqrt{2}) q \)
D. \( (-2 \sqrt{2}) q \)


Describe double circulation in human
beings schematically. Why is it
necessary?


In metals, the conduction bands are
incompletely filled orbitals that allow electrons to flow.
A. true
B. false
c. orbit
D. none of these


A train \( 110 m \) long is travelling at \( 60 k m / h r, \) In what time it will cross a
cyclist moving at \( 6 k m / h r, \) in the same direction?


Assertion: Input of energy is required by electrolytic cells. Reason: Electrolytic cells have just one container, while voltaic cells have two
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


A conic \( C \) passing through \( P(1,2) \) is
such that the slope of its tangent at any point on the conic is inversely proportional to the ordinate of that point and conic \( C \) passes through origin. If a circle touches the conic \( C \) at the
point \( \boldsymbol{P}(1,2) \) and passes through the focus of the conic then its radius is-
A.
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \sqrt{3} \)
E. \( \sqrt{5} \)


Two identical spheres, one positively charged and the other negatively charged are held d cm apart. If the magnitude of the charges on the two spheres is equal, find the electric potential at a point midway on the line joining the centres of the two spheres.
A. zero
B. \( 10 \mathrm{v} \)
\( c .5 v \)
D. \( 1.6 \times 10^{-19} \mathrm{V} \)


a) A manufacturing company makes two models \( A \) and \( B \) of a product. Each
piece of model \( A \) requires 9 labor hours
for fabricating and 1 labor hour for finishing. Each piece of model \( \boldsymbol{B} \) requires 12 labor hours for finishing
and 3 labor hours for finishing. For fabricating and finishing, the maximum labor hours available are:
180 and 30 respectively. The company
makes a profit of Rs. 8000 on each piece of model \( A \) and Rs. 12000 on each piece
of model \( B \). How many pieces of model
\( A \) and model \( B \) should be
manufactured per week to realize a
maximum profit? What is the maximum profit per week?
b) Find the value of \( K \) so that the function \( f(x)=\left\{\begin{array}{ll}K x+1, & \text { if } x \leq 5 \\ 3 x-5, & \text { if } x \leq 5\end{array} \) at \right.
\( x=5 \) is a continuous function.


An object is placed at a distance of 1.5 \( \mathrm{m} \) from a screen and a convex lens is interposed between them. The
magnification produced is 4. The focal length of the lens is then
\( A \cdot 1 m \)
B. 0.5 \( m \)
c. \( 0.24 \mathrm{m} \)
D. \( 2 \mathrm{m} \)


When the free ends of a tester are
dipped into a solution, the magnetic needle shows deflection due to:
A . electrical effect
B. mechanical effect
c. magnetic effect
D. lighting effect


Which one of the following is called maidenhair fern?
A. Dryopteris
B. Pteris
c. Adiantum
D. Lycopodium
E. Selaginella


The metal whose hydroxide does not decompose on heating but its nitrate decomposes is:
A. \( C a \)
в. \( A l \)
c. \( N a \)
D. \( F e \)


If the lines \( 3 x-4 y+4=0 \) and \( 6 x- \)
\( 8 y-7=0 \) are tangents to a circle,
then find the radius of the circle.
\( A \cdot 3 / 4 \)
в. \( 4 / 3 \)
\( c \cdot 1 / 4 \)
D. \( 7 / 4 \)


Evaluate:
\( \lim _{x \rightarrow \infty}\left(\frac{2 x-3}{\sqrt{x^{2}-1}}\right) \)


What is the maximum number of
emission lines when the excited
electron of a \( \boldsymbol{H}-\boldsymbol{a} \boldsymbol{t o m} \) in \( \boldsymbol{n}=\boldsymbol{6} \) drops
to the ground state?


U is the PE of an oscillating particle and Fis the force acting on it at a given instant. Which of the following is true?
A \( \cdot \frac{U}{F}+x=0 \)
B. \( \frac{2 U}{F}+x=0 \)
c. \( \frac{F}{U}+x=0 \)
D. \( \frac{F}{2 U}+x=0 \)


The radius of the sphere is \( 1.41 \mathrm{cm} . \) The volume of sphere to an appropriate number of significant figures will be:
A \( \cdot 11.7 c m^{3} \)
B. \( 11.74 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 12 c m^{3} \)
D. \( 11.736 \mathrm{cm}^{3} \)


In the sulphar estimation, 0.157 g of an organic compound gave 0.4813 g of barium sulphate. What is the percentage of Sulphur in the compound?
A . \( 42.10 \% \)
B. 36.45\%
c. \( 51.95 \% \)
D. \( 48.33 \% \)


Male part of a flower is called
A. Stamen
B. stigma
\( c . \) Egg
D. Pollen tube


The work function for a certain metal is
4.2 eV. Will this metal give photoelectric emission for incident radiation of
wavelength 330 nm?


If distance between the directrices be
thrice the distance between the foci
then eccentricity of ellipse is
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{4}{5} \)


The magnitude of the force (in Newton)
acting on a body varies with time \( t \) (in
microseconds) as shown in the figure. \( A B, B C \) and \( C D \) are straight line
segments. The magnitude of the total
impulse of the force in the body from
\( \boldsymbol{t}=\mathbf{4} \boldsymbol{\mu} \boldsymbol{s} \) to \( \boldsymbol{t}=\mathbf{1 6} \boldsymbol{\mu} \boldsymbol{s} \) is
Ns.
\( \mathbf{A} \cdot 1.005 \)
B. 0.005
c. 2.005
D. 4.005


Define coelom. Explain the two types of coelom formation in animals.


A particle is constrained to move along
a straight line. The graph in the
adjoining figure shows the distance \( s \)
moved by the particle in time \( t \)
measured from the starting time. The
shape of the curve indicates that
A. Acceleration of the particle is increasing at \( X \)
B. The speed of the particle is maximum at the point \( Z \)
C. The speed of the particle \( X \) is greater than that \( Z \)
D. The particle is at rest at the point \( Y \)


Explain Haber's process and
manufacture of ammonium


If a molecule \( M X_{3} \) has zero dipole
moment, the \( \sigma \) - bonding orbitals used by M (atomic number \( <21 \) ) is:
A . pure \( p \)
B. \( s p \) - hybridized
c. \( s p^{2} \) - hybridized
D. \( s p^{3} \) - hybridized


\( \mathbf{F}_{2} \) is a stronger oxidizing agent than
\( \mathrm{Cl}_{2} \) in aqueous solution. This is
attributed to many factors except:
A. heat of dissociation
B. electron affinity
c. ionisation potential
D. heat of hydration


Find the mode of the following
frequency table:
\( \begin{array}{ll}\text { Class Interval } & \text { Frequency } \\ 140-150 & 4 \\ 150-160 & 6 \\ 160-170 & 10 \\ 170-180 & 12 \\ 180-190 & 9 \\ 190-200 & 3\end{array} \)


Combustion of a fuel produces heat
because:
A. of breaking of bonds of hydrocarbons
B. of formation of bonds of byproducts \( \left(C O_{2}, H_{2} O\right) \)
C. of formation of bonds of hydrocarbons.
D. of nuclear fission in hydrocarbons.


To get output 1 for the following circuit, the correct choice for the input is.
A . \( A=0, B=1, C=0 \)
B. \( A=1, B=0, C=0 \)
C. \( A=1, B=1, C=0 \)
D. \( A=1, B=0, C=1 \)


Two lines intersecting each other, prove that vertically opposite angles are equal.


The energy released due to loss in mass
during the process of nuclear fission and fusion is called:
A. hydro energy
B. electrical energy
c. nuclear energy
D. geothermal energy


Two electric lamps \( A \) and \( B \) radiate the
same power. Their filaments have the
same dimensions, and have
emissivities \( e_{A} \) and \( e_{B} . \) Their surface
temperatures are \( \boldsymbol{T}_{\boldsymbol{A}} \) and \( \boldsymbol{T}_{\boldsymbol{B}} \). The ratio \( \frac{\boldsymbol{T}_{\boldsymbol{A}}}{\boldsymbol{T}_{\boldsymbol{B}}} \) will be equal to
\( ^{\mathbf{A}} \cdot\left(\frac{e_{B}}{e_{A}}\right)^{1 / 4} \)
\( ^{\mathrm{B}} \cdot\left(\frac{e_{B}}{e_{A}}\right)^{1 / 2} \)
\( ^{\mathbf{c}}\left(\frac{e_{A}}{e_{B}}\right)^{1 / 2} \)
\( ^{\mathrm{D}} \cdot\left(\frac{e_{A}}{e_{B}}\right)^{1 / 4} \)


A conducting circular loop made of a thin wire, has area \( 3.5 \times 10^{-3} m^{2} \) and
resistance \( 10 \Omega \). It is placed perpendicular to a time dependent magnetic field \( B(t)=(0.4 T) \sin (50 \pi t) \)
The field is uniform in space. Then the net charge flowing through the loop during \( t=0 s \) and \( t=10 m s \) is close to:
A. \( 0.14 m C \)
В. \( 0.21 \mathrm{mC} \)
\( c \cdot 6 m C \)
D. \( 7 m C \)


Let \( A \) be the set of all \( 3 \times 3 \) skew
symmetric matrices whose entries are
either \( -1,0, \) or \( 1 . \) If there are exactly
three 0 s, three 1 s, and three (-1) s, then the number of such matrices is


Duct of Bellini is connected with
A . Collecting duct
в. DcT
c. Ureter
D. Papilla


Assertion
The solubility of salts of weak acids like phosphates decreases at lower pH.
Reason
This is because at lower \( \mathrm{pH} \), the
concentration of cations increases.
A. If both the assertion and reason are true and reason is the correct explanation of assertion.
B. If both the assertion and reason are true but 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


Divide
\( 4 \sqrt{2} y^{3} \) by \( 3 \sqrt{2} y^{2} \) The answer is \( \frac{m y}{3} \)
Then \( m= \)


Carbon-carbon bond length in ethene is
to that in \( \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H O C H}_{3} \)
A. shorter
B. longer
c. equal
D. none of the above


The height of water in a capillary tube of
radius \( 2 c m \) is \( 4 c m . \) What should be the
radius of capillary, if the water rises to \( 8 c m \) in tube?
A \( .1 \mathrm{cm} \)
в. \( 0.1 \mathrm{cm} \)
\( c .2 c m \)
D. \( 4 c m \)


Solve:
\( \int 3^{3^{x^{x}}} 3^{3^{x}} 3^{x} d x= \)


The gas estimated in Duma's method is nitrogen.
A . True
B. False


\( 10 \mathrm{mL} \) of gaseous organic compound
containing \( C, H \) and \( O \) only was mixed
with \( 100 \mathrm{mL} \) of \( \mathrm{O}_{2} \) and exploded under
identical conditions and then cooled.
The volume left after cooling was \( 90 \mathrm{mL} \)
On treatment with \( K O H, \) a contraction
of \( 20 \mathrm{mL} \) was observed. If vapour density of the compound is \( 23, \) derive molecular formula of the compound.
This question has multiple correct options
A \( \cdot C_{2} H_{6} O \)
B \( . C_{2} H_{6} O H \)
\( \mathbf{c} \cdot C_{2} H_{5} O \)
\( \mathbf{D} \cdot C_{2} H_{5} O H \)


\( \operatorname{Let} \vec{a}=\vec{i}+2 \vec{j}+\vec{k}, \vec{b}=\vec{i}-\vec{j}+\vec{k} \) and
\( \vec{c}=\vec{i}+\vec{j}-\vec{k} . A \) vector in the plane of \( \vec{a} \)
and \( \vec{b} \) has projection \( \frac{1}{\sqrt{3}} \) on \( \vec{c} \). Then, one
such vector is
A \( \cdot 4 \vec{i}+\vec{j}-4 \vec{k} \)
B. \( 3 \vec{i}+\vec{j}-3 \vec{k} \)
c. \( 4 \vec{i}-\vec{j}+4 \vec{k} \)
D. \( 2 \vec{i}+\vec{j}-2 \vec{k} \)


Rutherford's atomic model does not
obey:
A. faraday's law of electrodynamics
B. maxwell theory of electrodynamics
c. newton's law
D. none of these


S.I unit of Heat Capacity is


All reactions involving chemical decomposition:
A. are reversible
B. are reversible and endothermic
c. are exothermic
D. may be reversible or irreversible and endothermic or exothermic.


In the field of electromagnetism, the term 'EMI' stands for:
A. Electromotive Impact
B. Electromagnetic Induction
c. Electromotive inertia
D. none of these


The food is kept at low temperatures in a
refrigerator because it:
A. saves money
B. makes food more tastier
C. kills bacteria present in the food
D. is fashionable to keep the food in the refrigerator


Why is plastic a poor conductor?
A. They are non-reactive
B. They can melt
C. They have high number of free electrons
D. They do not have free electrons


Given that \( \boldsymbol{E}=\left(\left(\mathbf{3} \boldsymbol{x}^{2}+\boldsymbol{y}\right) \hat{\boldsymbol{i}}+\right. \)
\( \boldsymbol{x} \hat{\boldsymbol{y}}) \boldsymbol{k} \boldsymbol{V} / \boldsymbol{m}, \) find the work done in
moving a \( -2 \mu C \) charge from (0,5,0) to (2,-1,0) by taking the path:
\( \boldsymbol{y}=\mathbf{5}-\mathbf{3} \boldsymbol{x} \)
A . \( 12 J \)
в. \( 12 m J \)
\( \mathbf{c} \cdot 12 k J \)
D. \( 12 \mu J \)


Shape of \( C O_{2} \) is:
A. pyramidal
B. triangular
c. linear
D. spherical


In cyanide method, silver metal is
obtained as given in the following
reaction:
\( \mathbf{2} \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g} \)
In this :
A. \( A g \) has been oxidised and \( Z n \) has been reduced
B. \( A g^{+} \) has been reduced and \( Z n \) has been oxidised
c. both the metals have been oxidised
D. both the metals have been reduced


\( \tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right) \)


\( \boldsymbol{x}^{2}-(\boldsymbol{m}-\mathbf{3}) \boldsymbol{x}+\boldsymbol{m}=\mathbf{0}(\boldsymbol{m} \in \boldsymbol{R}) \) be a
quadratic equation. Find the value of \( \boldsymbol{m} \)
for which, both the roots lie in the
interval of (1,2)
A. \( (10, \infty) \)
)
в. \( (-\infty, 0) \)
\( c \cdot(-\infty, \infty) \)
D. None of the above


The aqueous solution of the salt will
colored in the case of:
This question has multiple correct options
\( \mathbf{A} \cdot Z n\left(N O_{3}\right)_{2} \)
в. \( \operatorname{LiNO}_{3} \)
\( \mathrm{c} \cdot \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2} \)
D. \( C r C l_{3} \)


A plane area of \( 100 \mathrm{cm}^{2} \) is placed in uniform electric field of \( 100 N / C \) such that the angle between area vector and
electric field is \( 60^{\circ} . \) The electric flux
over the surface is
A . \( 0.5 \mathrm{wb} \)
B. \( 5 \mathrm{Wb} \)
\( c \cdot 1 w b \)
D.


2-iodo cyclohexyl acrylate undergoes
acetolysis.Which of the following
statement(s) is/are true?

This question has multiple correct options
A. Trans-isomer of the substrate undergoes acetolysis 670 times faster than that of its cis-isomer.
B. Cis-isomer of the substrate undergoes cytolysis 670 times faster than that of its trans-isomer.
C. Both isomers undergo cytolysis with the same rate.
D. The enhanced rate of this nucleophilic substitution is due to neighbouring group participation.


Indicate the following compound as
\( 1^{\circ}, 2^{\circ} \) and \( 3^{\circ} \)
\( \boldsymbol{E} \boldsymbol{t}_{3} \boldsymbol{N} \)
\( \mathbf{A} \cdot 1^{\circ} \)
B. \( 2^{\circ} \)
\( c \cdot 3^{\circ} \)
D. Non of the above


n the given figure, \( \angle \boldsymbol{A}+\angle \boldsymbol{B}+\angle \boldsymbol{C}+ \)
\( \angle D+\angle E \) is equal to
2
\( c \cdot \frac{3 \pi}{\pi} \)
2
22


What is the effect on self inductance of
a solenoid, if a core of soft iron is placed in it?


If \( y=\cot ^{-1}(\sqrt{\cos x})- \)
\( \tan ^{-1}(\sqrt{\cos x}) P . T \sin y=\tan ^{2} x / 2 \)


The equivalent weights of a metal are
18.66 and \( 28, \) then atomic weight of
metal may be?
\( \mathbf{A} \cdot 18.66 \)
B. 28
c. 56
D. 25


Which of the following is the CORRECT
electron configuration for the
potassium ion \( \left(\boldsymbol{K}^{+1}\right) \) ?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} \)


Prove that:
\[
\begin{array}{l}
{\left[\begin{array}{lll}
\mathbf{x} \mathbf{y} & \mathbf{z}
\end{array}\right]\left[\begin{array}{lll}
\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\
\boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\
\boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}
\end{array}\right]\left[\begin{array}{l}
\boldsymbol{x} \\
\boldsymbol{y} \\
\boldsymbol{z}
\end{array}\right]} \\
= & {\left[\boldsymbol{a x}^{2}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{c} \boldsymbol{z}^{2}+\boldsymbol{c f} \boldsymbol{z}+\boldsymbol{2 g} \boldsymbol{z} \boldsymbol{x}+\boldsymbol{t}\right.}
\end{array}
\]
\( 2 h x y \)


Mark the correct option
A. Force can be seen
B. When an inflated balloon is pressed between the two hands,only its shape changes
C. Force is a push,pull or squeeze
D. All


A long solenoid has 200 turns per cm
and carries a current i.The magnetic field at its centre is \( 6.28 \times \) \( 10^{-2} W b / m^{2} . \) Another long solenoid
has 100 turns per \( \mathrm{cm} \) and it carries a
current i/3.The value of magnetic field
at its centre is:
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
в. \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)


The heat capacity at constant volume of a sample of a monoatomic gas is \( \mathbf{3 1 . 8 6 7} J / K . \) Find the internal energy at
\( 300^{\circ} \mathrm{C} \)
A. \( 8.88 k J \)
J
в. \( 9.56 k J \)
\( c .3 .56 k J \)
D. \( 8.96 k J \)


In which of the following equilibrium, equilibrium can not be identified by observing variation in pressure?
A. Decomposition of \( H I \)
B. Decomposition of \( C a C O_{3} \)
c. Decomposition of \( N H_{4} H S \)
D. None of the above


Find the volume of a cube of side \( 9 \mathrm{cm} \)
in cubic metres


The initial mass of a radioactive
isotope was 128 g. Find the mass of a material if 4 half lives occured.
\( A \cdot 8 g \)
в. 7.5
\( c .7 g \)
D. \( 6.5 \mathrm{g} \)


Integrate \( \int \frac{d x}{(x+1)(x+5)} \)


Refractive indices of water and glass
are \( 4 / 3 \) and \( 3 / 2 \) respectively. A ray of light travelling in water is incident on
the water-glass interface at \( 30^{\circ} \) Calculate the angle of refraction.


The internal resistance of a primary cell
depends on
A. the concentration of solution
B. the current drawn from the cell
c. the distance between the electrodes of the cell
D. all of the above


The following reaction is used for the
preparation of oxygen gas in the laboratory \( 2 K C l O_{3}(s) \frac{\text {Heat}}{\text {Catalyst}} 2 K C l(s)+3 O_{2}(g) \)
Which of the following statement is correct about the reaction?
A. It is a decomposition reaction and endothermic in nature
B. It is a combination reaction
c. It is a decomposition reaction and accompanied by release of heat
D. It is a photochemical decomposition reaction and exothermic in nature


The values of colligative properties of colloidal solution are of small order in
comparison to those shown by true solutions of same concentration
because of colloidal particles:
A. exhibit enormous surface area
B. remain suspended in the dispersion medium
c. form lyophilic colloids
D. are comparatively less in number


Evaluate \( (-6) \times(-2) \)
A . -8
B. +8
c. -12
D. +12