In a Young's double-slit interference experiment using a yellow light of wavelength \( \lambda \), with the slits labelled \( S_{1} \)
and \( S_{2} . \) If \( P \) is the centre of a dark
fringe on the screen on which the resulting diffraction pattern is
projected, Find out the equations
relating \( S_{1} P \) and \( S_{2} P \) which could be
true?
A \( \cdot S_{1} P-S_{2} P=\frac{1}{2 \lambda} \)
B . \( S_{1} P-S_{2} P=\lambda \)
c. \( S_{1} P-S_{2} P=2 \lambda \)
D. \( S_{1} P-S_{2} P=3 \lambda \)
E . \( S_{1} P=S_{2} P \)


The pressure exerted by an electromagnetic wave of intensity
\( I\left(w a t t / m^{2}\right) \) on a non-
reflecting surface is : \( [\mathrm{c} \) is the velocity of light
\( \mathbf{A} \cdot I c \)
B . \( I c^{2} \)
\( c \cdot I / c \)
D. \( I / c^{2} \)


Give two practical applications of simple harmonic motion.


In a potentiometer experiment for measuring the emf of a cell, the null point is at \( 240 \mathrm{cm} \) when we have a \( 500 \Omega \$ \) resistor in series with the cell and galvanometer. If the series resistance reduced to half, then the null
point will be at:
A. \( 480 \mathrm{cm} \)
в. 240 ст
\( \mathrm{c} .120 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


When Astronauts fly at higher altitude, the sky appears dark because
A. Scattering of light does not take place.
B. Scattering of light takes place
c. Refraction of light takes place.
D. Dispersion of light takes place


The first fullerene was discovered in :
A. 1970
в. 1967
\( \mathrm{c} .1997 \)
D. 1985


Evaluate the following:
\( \cos ^{-1}(\cos 5) \)


Write equation for the reaction which take place when limestone reacts with
dilute HCI.


Suppose a person wears convex glasses for proper vision. Where do you think the image of the object will be formed in his
eyes when he is not using the glasses?
A. on the yellow spot
B. Behind the retina
c. In front of the retina
D. on the blind spot


The two curves \( x=y^{2}, x y=a^{3} \) cut
orthogonally at a point. Then \( a^{2} \) is equal
to
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot 2 \)
D.


Why do transition elements show variable oxidation state?

Explain their catalytic properties in details.


a) i) Name the water insoluble
component of starch.
ii) Mention one water soluble vitamin.
iii) Is Lysine an essential or nonessential amino acid?
b) Write the structure of Maltose.


If the \( p^{t h} \) term is \( q \) and \( q^{t h} \) term is \( p \) of
an A.P., then find the first term and
common difference.


Which of the following species have
shortest \( N-O \) bond length?
A . \( N O \)
B. \( N O^{+} \)
\( \mathrm{c} \cdot \mathrm{N} \mathrm{O}_{2}^{2+} \)
D. \( N O^{-} \)


According to Bohr's atomic theory, which of the following relations is/are incorrect?
This question has multiple correct options
A . kinetic energy of electron \( \propto \frac{z^{2}}{n^{2}} \)
B. The product of velocity of electron and the principal quantum number \( \propto z^{2} \)
C. Frequency of revolution of the electron in an orbit \( \alpha \) \( \frac{z^{2}}{n^{3}} \)
D. coulombic force of attraction on the electron \( \propto \frac{z^{2}}{n^{4}} \)


A light spring balance hangs from the hook of the other light spring balance and a block of mass \( M \) kg hangs from the former one. Then the true statement
about scale reading is
A. both the scales read \( M \) kg each
B. the scale of the lower one reads \( M \) kg and of upper on zero
c. the reading of the two scales can be anything but summ of the reading will be \( M \) kg
D. both the scales read \( M / 2 \mathrm{kg} \)


The value of machine depreciates every year at the rate of \( 10 \% \) of its value at the beginning of that year.If the present value of the machine is Rs.729, its worth
three years ago was:
A. Rs 1000
B. Rs 750.87
\( c . \) Rs 800
D. Rs 947.70


Obtain \( \int_{2}^{3}(3 x+8) d x \) as limit of sum.


Epinephrine is
A. Secreted from pancreas and decreases heart beat
B. Secreted from adrenal medulla and increases heart
beat
C. Secreted from adrenal medulla and decreases heart
beat
D. Secreted from pancreas and increases heart beat


A force of \( 98 \mathrm{N} \) is just able to move a block of mass \( 20 \mathrm{kg} \) on a rough horizontal surface. Calculate the
coefficient of friction and angle of friction. \( g=9.8 \mathrm{m} / \mathrm{s}^{-2} \)


An early model for an atom considered
it to have a positively charged point
nucleus of charge \( Z e \), surrounded by a
uniform density of negative charge upto a radius \( R \). The atom as a whole is
neutral. The electric field at a distance \( r \)
from the nucleus is \( (r<R) \)
A \( \cdot \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{r}{R^{3}}\right] \)
В \( \cdot \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{r}{R^{2}}\right] \)
c. \( \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{R^{3}}-\frac{r}{r^{2}}\right] \)
D. \( \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{R^{3}}+\frac{r}{r^{2}}\right] \)


A solid compound \( X \) on heating give
\( C O_{2} \) gas and a residue. The residue
mixed with water forms \( Y . \) On passing
an excess of \( C O_{2} \) through \( Y \) in water a
clear solution \( Z \) is obtained. On boiling
\( Z, \) compound \( X \) is reformed. The
compound \( \boldsymbol{X} \) is:
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( C a C O_{3} \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( K_{2} C O_{3} \)


Some of the major contaminants of
water are:
A. sewage
B. agricultural chemicals
c. industrial waste
D. all of the above


Two adjacent layers in graphite are bonded by comparatively forces.
A. strong
B. weak
c. both A and B
D. none of these


Which of the following has the smallest
size ?
\( \mathbf{A} \cdot I^{-} \)
B. \( S^{-2} \)
c. \( O^{-2} \)
D. \( C l \)


The nitride salt of \( C a \) when treated with
\( H_{2} O \) gives:
A \( . N_{2} \)
в. \( C a O \)
\( \mathbf{c} \cdot C a H_{2} \)
D. \( N H_{3} \)


Two point charges \( \boldsymbol{q}_{1}=-\boldsymbol{4} \boldsymbol{\mu} \boldsymbol{C} \) and
\( q_{2}=8 \mu C \) are lying on the \( y \) -axis. They
are equidistant from the point \( \boldsymbol{P} \), which
lies on the \( x \) -axis. A small object of
charge \( \boldsymbol{q}_{0}=8 \mu C \) and mass \( \boldsymbol{m}=12 \boldsymbol{g} \) is
placed at \( P . \) When it is released, what is
its acceleration in \( m s^{-2} ? \)
(Neglect the effect of gravity)
B. \( 9 \hat{i}+3 \sqrt{3} \hat{j} \)
c. \( 3 \hat{i}+3 \sqrt{3} \hat{j} \)
D. \( 3 \sqrt{3 i}+3 \hat{j} \)


The densities of graphite and diamond at \( 298 K \) are 2.25 and \( 3.31 g c m^{-3} \)
respectively. If the standard free energy difference is \( 1895 J m o l^{-1}, \) the
pressure at which graphite will be transformed into diamond is:
A. \( 9.92 \times 10^{8} P a \)
\( a \)
В. \( 9.92 \times 10^{7} P a \)
\( \mathbf{c} .9 .92 \times 10^{6} \mathrm{Pa} \)
D. None of these


Increase in the pressure on the following gaseous equilibrium will:
\( \mathbf{2} \boldsymbol{A}+\mathbf{3} \boldsymbol{B} \leftrightharpoons \mathbf{3} \boldsymbol{C}+\mathbf{2} \boldsymbol{D} \)
A. favour forward reaction
B. favour backward reaction
c. have no effect
D. favour forward and backward reaction


Lightning was discovered by the
A. onm
B. Thomson
c. Franklin
D. Faraday


The biggest atom is:
A. radium
B. francium
c. caesium
D. rhodium


Evaporation of water is:
\( A \cdot \) an exothermic change
B. an endothermic change
C . a process where no heat changes occur
D. a process accompanied by chemical reaction


A particle is projected at an angle of \( 30^{\circ} \) with the horizontal with a momentum \( \boldsymbol{P} \)
At the highest point its momentum is
A \( \cdot \frac{\sqrt{3}}{2} P \)
в. \( \frac{2}{\sqrt{3}} P \)
\( c . P \)
D. \( \frac{1}{2} P \)


In Earthworm, gizzard occurs in segment
A. 5
B. 6
\( c \cdot 8 \)
D. 10


The product \( B \) is:
A. 3 -nitrobenzoic acid
B. 3 -nitrotoluene
C. 4 -nitrotoluene
D. 4 -nitrobenzoic acid


An organic compound gave \( \boldsymbol{C}= \) \( 92.31 \% \) and \( H=7.69 \% . \) If molecular
weight of the compound is \( 78, \) its molecular formula is:
\( \mathbf{A} \cdot C_{6} H_{6} \)
в. \( C_{7} H_{7} \)
\( \mathbf{c} \cdot C_{6} H_{18} \)
D. \( C_{8} H_{20} \)


A potentiometer is an accurate and versatile device to make electrical
measurements of E.M.F. because the
method involves:
A. A combination of cells, galvanometer and resistances
B. Cells
c. Potential gradients
D. A condition of no current flow through the galvanometer


In primordial atmosphere when the living organism evolved the respiration
process was
A. Anaerobic as it released more energy
B. Aerobic as it was more complex.
c. Aerobic as it released more energy
D. Anaerobic because early atmosphere contained litttle or no oxygen.


Which of the following is relatively more accurate method of determining the age of fossils?
A. Uranium-lead method
B. Radio-carbon mathod
c. Study of carbohydrates/proteins in rocks
D. Electron-Spin resonance method


The vapour pressure of a liquid
decreases by 10 tor \( r \) when a nonvolatile solute is dissolved. The mole
fraction of the solute in solution is 0.1
What would be the mole fraction of the
liquid if the decrease in vapour pressure is 20 tor \( r, \) the same solute
being dissolved?
A . 0.2
B. 0.9
\( c .0 .8 \)
D. 0.6


Two Polaroids \( P_{1} \) and \( P_{2} \) are placed with their axis perpendicular to each other.
Unpolarized light \( l_{0} \) is incident on \( P_{1} . A \)
third polaroid \( P_{3} \) is kept in between \( P_{1} \)
and \( P_{2} \) such that its axis makes an
angle \( 45^{\circ} \) with that of \( P_{1} . \) The intensity
of transmitted light through \( P_{2} \) is
A \( \cdot \frac{I_{0}}{2} \)
B. \( \frac{I_{0}}{4} \)
\( c \cdot \frac{I_{0}}{8} \)
D. \( \frac{1}{16} \)


Which of the following exhibit/s \( \mathrm{H} \) bonding?
A \( . C H_{4} \)
в. \( H_{2} S e \)
\( \mathbf{c} \cdot N_{2} H_{4} \)
D. \( H_{2} S_{S} \)


The contrapositive of : "If two triangles
are congruent then they are similar" is
A. If two triangles are similar then they are congruent
B. If two triangles are not congruent then they are not similar
C. If two triangles are not similar then they are not congruent
D. None


The nature of anode rays depends upon:
A. nature of gas filled in the discharge tube
B. nature of electrode
c. nature of metal
D. none of these


Assuming all volumes measured at the same temperature and pressure, state the volume ratio of the reactants and
products when acetylene (ethyne) burning in oxygen to give carbon dioxide and steam.
A .1: 5: 4: 2
B. 2: 5: 2: 2
\( c \cdot 2: 5: 4: 1 \)
D. 2: 5: 4: 2


Trapezoid \( A B C D \) is graphed as shown
above.
Find the slope of \( \overline{C D} \)
A. -3
B. -1
\( c \)
D. \( \frac{5}{21} \)
\( E \cdot \frac{3}{2} \)


A piece of land is 100 metres \( \times 21 \) metres. A semi-circular plot has been
added on one side of its breadth. How
long will it take a man to walk round it
at the rate of 3.6 kilometres per hour?


Vitamin B \( _{1} \) is known as:
A. ascorbic acid
B. carotenoids
c. thiamine
D. pyridoxine


Arrange the ellipses in ascending order of their eccentricities when \( \angle S B S^{1} \) is
given, where \( S \& S^{1} \) are foci and \( B \) is
one end of the minor axis. For the four
ellipses \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \angle \mathbf{S B S}^{1}= \)
\( \mathbf{2 0}^{\mathbf{0}}, \mathbf{6 0}^{\mathbf{0}}, \mathbf{3 0}^{\mathbf{0}}, \mathbf{9 0}^{\mathbf{0}} \)
\( A \cdot A, C, B, D \)
B. D, B, C, A
c. \( B, D, C, A \)
D. \( A, C, D, B \)


Which one of the following represents the correct dimensions of the quantity \( x=\frac{\eta}{\rho}, \) where \( \eta= \) coefficient of
viscosity and \( \rho= \) the density of a
liquid?
A \( \cdot\left[M L^{-2} T^{-1}\right] \)
B \( \cdot\left[M L^{-4} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-5} T^{-2}\right] \)
D. \( \left[M^{0} L^{2} T^{-1}\right] \)


In \( _{-}-\ldots_{-}-_{-}- \) pathway, water crosses at least two membranes for
each cell in its path (i.e., plasma membrane on entering and exiting)
A. Apoplast
B. Symplast
c. Transmembrane
D. Both (a) and (c)


For the given diagram, a single
chromosome is represented by part
\( O \)
\( A \cdot A \)
\( B . B \)
\( c \cdot c \)
\( D \cdot D \)
\( E . E \)


A particle is projected up with an initial velocity of 80 the ball will be at a height of 96 from the ground after


Find the inclination of a line
whose slope is
(i) 1
(ii) -1
(iii) \( \sqrt{\mathbf{3}} \)
(iv) \( -\sqrt{\mathbf{3}} \)
\( (v) \frac{1}{\sqrt{3}} \)


Describe the process of translation in
Protein synthesis


The product of any number with 0 will
be
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
c. number itself
D. none of these


The \( p H \) of acid rains is:
A. more than 5.6
B. less than 5.6
c. equal to 5.6
D. none of the above


Add all of them \( x-8 y, 3 x y-y \) and
\( \boldsymbol{y}+\mathbf{1} \)


\( 3- \) Methyl-pent-2-ene on reaction
with \( H B r \) in presence of peroxide forms an addition product.
The number of possible stereoisomers
for the products:
A. \( Z \) ero
в. \( T w o \)
c. Four
D. \( \operatorname{six} \)


mass m carrying charge \( q . \) The bead
freely move on the smooth fixed ring
placed on a smooth horizontal plane. In
the same plane a charge \( +Q \) has also
been fixed as shown. The potential at
the point \( \boldsymbol{P} \) due to \( +\boldsymbol{Q} \) is \( \boldsymbol{V} \). The velocity
with which the bead should projected
from the point \( P \) so that is can complete
a circle should be greater than
A \( \cdot \sqrt{\frac{6 q V}{m}} \)
B. \( 4 \sqrt{\frac{q V}{m}} \)
c. \( \sqrt{\frac{3 q V}{m}} \)
D. \( \sqrt{\frac{7 q V}{2 m}} \)


Which of the following is determined by the oxidation of acidified potassium dichromate?
A. DO
B. BOD
\( c \cdot \cos \)
D. TLV


Select the correct statement(s).
This question has multiple correct options
A. Physical adsorption is weak, multilayer, nondirectional and non-specific.
B. Chemical adsorption is strong, unilayer, directional and strong.
C. Adsorption decreases with temperature
D. Chemical adsorption is more stronger than physical adsorption.


The correct order of boiling points of the
following amines
\( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{9}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}},\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}}\right)_{\mathbf{2}} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}(\boldsymbol{C} \boldsymbol{I} \)
is :
\( \mathbf{A} \cdot c_{2} H_{5} N\left(C H_{3}\right)_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2} \)
B \( \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2}>C_{4} H_{9} N H_{2} \)
\( \mathrm{c} \cdot_{C_{4} H_{9} N H_{2}>}\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
\( \mathbf{D} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2}>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)


Which of the following orbitals will have zero probability of finding the electron in the yz plane?
\( A \cdot P x \)
B. Py
\( c \cdot P z \)
D. \( d_{y} \)


Blocking of active site of an enzyme is a
kind of
A. Non-competitive inhibition
B. Competitive inhibition
c. Allosteric inhibition
D. Feed back inhibition


Arrange in order of increasing acidic
strength:
A \( . X>Z>Y \)
в. \( Z<X>Y \)
c. \( X>Y>Z \)
D. \( Z>X>Y \)


Differentiate between
Water potential and diffusion pressure deficit.


Write two main functions of
carbohydrates in plants.


Which of the following product predominates(Major) ine following raction?
A. 3 -chlorotoluene
B. 2-chlorotoluene
c. 4 -chlorotoluene
D. Both A and


Using Gauss's law derive an expression for the electric field intensity due to a uniform charged thin spherical shell at a point.
(i) Outside the shell
(ii) Inside the shell


Charle's law is kept constant only if
mass and pressure are kept
A. increasing
B. decreasing
c. consant
D. none of these


The equation \( 9 x^{3}+9 x^{2} y-45 x^{2}= \)
\( 4 y^{3}+4 x y^{2}-20 y^{2} \) represents 3
straight lines, two of which passes through origin. Then find the area of the triangle formed by these lines.


Give one chemical test each to
distinguish between the following pairs of compounds:
(1) Ethanol and acetic acid
(2) Acetaldehyde and benzaldehyde


IF \( z_{1}=1+i, z_{2}=1-i \) find \( z_{1} z_{2} \)
A. \( z_{1}+z_{2} \)
В. \( z_{1}-z_{2} \)
c. \( z_{1} / z_{2} \)
in
D. None


A car moves at a constant speed on a road as sown in figure. The normal force
by the road on the car is NA and NB
when it is at the points \( A \) and \( B \)
respectively.
\( \mathbf{A} \cdot N_{A}=N_{B} \)
B. \( N_{A}>N_{B} \)
\( \mathbf{c} \cdot N_{A}<N_{B} \)
D. Insufficient information to decide the relation of \( N_{A} \)
and \( N_{B} \)


The following table shows ages of 300 patients getting medical treatment in a
hospital on a particular day.
Find the median age of patients
Age (in 1 20
30
years)
\[
\text { 20 } \quad 30
\]
40
50
No. of \( \quad \) 60 \( \quad 42 \) Patients \( \begin{array}{llll}60 & 42 & 55 & 70\end{array} \)
\( \mathbf{A} \cdot 33.73 \) years
B. 38.73 years
C. 42.37 years
D. 44.73 years


If \( u \) and \( v \) are differentiable functions of
\( x \) and if \( y=u+v \) then \( \frac{d y}{d x}=\frac{d u}{d x}+\frac{d v}{d x} \)


In an estimation of sulphur by Carius method, 0.234 g of an organic sulphur compound afforded 0.334 g of \( B a S O_{4} \) Find the percentage of Sulphur in the compound.
A . \( 12.28 \% \)
B. 19.60\%
c. \( 15.96 \% \)
D . 23.67\%


A wooden box is placed on a table. The normal force on the box from the table
is \( N_{1} . \) Now another identical box is kept
on first box and the normal force on
lower block due to upper block is \( N_{2} \)
and normal force on lower block by the
table is \( N_{3} . \) For this situation, mark out
the correct statement(s)
A. \( N_{1}=N_{2}=N_{3} \)
в. \( N_{1}<N_{2}=N_{3} \)
c. \( N_{1}=N_{2}<N_{3} \)
D. \( N_{1}=N_{2}>N_{3} \)


The number of electrons in a neutral
atom is equal to its:
A. atomic mass number
B. neutron
c. valency
D. proton


An \( M B M \) applies for a job in two firms
\( X \) and \( Y . \) The probability of his being selected in firm \( X \) is 0.7 and being
rejected at \( Y \) is \( 0.5 . \) The probability of at least one of his applications being
rejected is \( 0.6 . \) The probability that he will be selected in one of the firms, is
A . 0.6
B. 0.4
\( c .0 .8 \)
D. None of these


From a semi-circular disc of mass \( M \)
and radius \( R_{2} . \) A semi-circular disc of
radius \( R_{1} \) is removed as shown in the
figure. If the mass of original uncut disc
is \( M, \) find the momentum of inertia of
residual disc about an axis passing
through centre \( O \) and perpendicular to
the plane of the disc.
\( ^{\mathbf{A}} \cdot \frac{M}{2 R_{2}^{2}}\left(R_{2}^{4}-R_{1}^{4}\right) \)
В \( \cdot \frac{M}{R_{2}^{2}}\left(R_{2}^{4}-R_{1}^{4}\right) \)
\( ^{\mathbf{c}} \cdot \frac{M}{R_{2}^{2}}\left(\frac{R_{2}^{4}}{4}-R_{1}^{4}\right) \)
D \( \frac{M}{2 R_{2}^{2}}\left(R_{2}^{4}-\frac{R_{1}^{4}}{4}\right) \)


Match the column


Which of the following is an electrica insulator:
A. Aluminium
B. Gold
c. Rubber
D. None of these


Plants that produce sexually do not produce flower.
A. True
B. False


Dobereiner grouped the elements into triads and Newland gave the:
A. law of Octaves
B. mass number
c. atomic number
D. valency


The number of real solutions of the
equation \( 1-x=[\cos x] \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


How many 6 digits odd numbers greater than 60,0000 can be formed from the
digits 5,6,7,8,9,0 if Repetitions are allowed:
\( \mathbf{A} \cdot 15552 \)
B. 31104
\( c \cdot 6^{5} \)
D. none of these


Select the correct statements:
This question has multiple correct options
A. The +1 oxidation state compared to the +3 oxidation state gets gradually more stabilized as we move from top to bottom in III group.
B. TI (III) being unstable, acts as a good oxidizing agent to get reduced to TI (II).
\( \mathrm{C} \cdot \operatorname{Sn} \mathrm{Cl}_{2} \) is good oxidizing agent.
D. All are incorrect.


If volume and surface area of a sphere
are numerically equal then it's radius is
A . 2 units
B. 3 units
c. 5 units
D. 8 units


Three fair dice are thrown. The
probability of getting a sum 6 or less on the three dice is
\( ^{A} \cdot \frac{7}{12} \)
в. \( \frac{5}{54} \)
c. \( \frac{19}{216} \)
D. \( \frac{11}{108} \)


What is ionization potential of an atom?


There are two urns. There are \( m \) white \( \& \)
\( \boldsymbol{n} \) black balls in the first urn and \( \boldsymbol{p} \) white
\& \( q \) black balls in the second urn. One
ball is taken from the first urn \& placed
into the second. Now, the probability of drawing a white ball from the second
urn is
A \( \cdot \frac{p m+(p+1) n}{(m+n)(p+q+1)} \)
B. \( \frac{(p+1) m+p n}{(m+n)(p+q+1)} \)
c. \( \frac{q m+(q+1) n}{(m+n)(p+q+1)} \)
D. \( \frac{(q+1) m+q n}{(m+n)(p+q+1)} \)


In the following circuit potential at
point 'A' is zero.Which resistance
consumes maximum power?


When a force retards the motion of a
body, the work done is :
A. zero
B. Negative
c. Positive
D. Positive or negative depending upon the magnitude of force and displacement


The density of a rod gradually decreases from one end to the other. It is pivoted at
an end so that it can move about a
vertical axis through the pivot. A horizontal force \( \boldsymbol{F} \) is applied on the free end in a direction perpendiclar to the
rod. The quantities, that do not depend on which end of the rod is pivoted, are :
A . angular acceleration
B. angular velocity when the rod completes one rotation
c. angular momentum when the rod completes one rotation
D. torque of the applied force.


Unit of magnetic induction \( B \) is :
A \( \frac{N}{A m} \)
в. \( \frac{N A}{m} \)
c. \( \frac{N m}{A} \)
D. \( \frac{N}{A} \)


Which of the following is not the standard from of a sine wave? (Here,
symbols have their usual meaning)
A \( \cdot y=A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right) \)
B. \( y=A \sin (v t-k x) \)
c. \( y=A \sin \omega\left(t-\frac{x}{v}\right) \)
D. \( y=A \sin k(v t-x) \)


toppr
Q Type your question_
\( A \)
\( B \)
\( c \)
D.


\( f(x)=x^{3}+a x^{2}+b x+c \) has a max.
at \( x=-1 \) and \( \min . \) at \( x=3 . \) Determine
the constants \( a, b, c \)
\( \mathbf{A} \ldots a=-3, b=-3, c=0 \)
В \( \ldots a=-3, b=-9, c=3 \)
\( \mathbf{c} \ldots a=-3, b=9, c=9 \)
D \( \ldots a=3, b=9, c=-3 \)


The ground state energy of Hydrogen
atom is \( -13.6 e V . \) The potential energy of the electron in this state is:
A . \( 0 e V \)
B . \( -27.2 e V \)
c. \( 1 e V \)
D. \( 2 e V \)


\( N_{2} O_{4} \rightleftharpoons 2 N O_{3}, K_{C}=4 . \) This reversible
reaction is studied graphically as shown in figure. Select the correct statements out of I, II and III
I: Reaction quotient has maximum
value at point \( \boldsymbol{A} \)

II: Reaction proceeds left to right at a
point when \( \left[\boldsymbol{N}_{2} \boldsymbol{O}_{4}\right]=\left[\boldsymbol{N} \boldsymbol{O}_{2}\right]=\mathbf{0 . 1} \boldsymbol{M} \)
Ill: \( K_{c}=Q \) when a point \( D \) or \( F \) is
reached.
\( A \cdot 1,1 \)
в. ॥, III
\( c \cdot \) ।, ॥
D. I. II. II


The isotopes \( U^{238} \) and \( U^{235} \) occur in nature in the ratio \( 140: 1 . \) Assuming that at the time of earth formation, they were present in equal ratio, the estimated age of the age of earth will be :
(The half-life period of \( U^{238} \) and \( U^{235} \) are \( 4.5 \times 10^{9} \) and \( 7.13 \times 10^{8} \) years
respectively.)
A. \( 6.04 \times 10^{9} \) years
B. \( 6.25 \times 10^{9} \) years
c. \( 6.59 \times 10^{9} \) years
D. non of these


The formula of Dolomite is :
A. \( M g C O_{3} . C a C l_{2} \)
в. \( M g C O_{3} . C a C O_{3} \)
c. \( M g C O_{3} . \) CaS \( O_{4} \)
D. \( M g C l_{2} . C a C O_{3} \)


Two trains \( A \) and \( B \) of length \( 400 m \)
each are moving on two parallel tracks with a uniform speed of \( 72 \mathrm{km} / \mathrm{h} \) in the same direction, with \( A \) ahead of \( B \)
decides to overtake \( A \) and accelerates
by \( 1 m / s^{2} . \) If after \( 50 s \) the guard of \( B \)
just brushes past the driver of \( A \), what
was the original distance between the
guard of \( \boldsymbol{B} \& \) driver of \( \boldsymbol{A} \) ?


Assume that each atom of copper
contributes one free electron. The
density of copper is 9 g \( c m^{-3} \) and atomic weight of copper is \( 63 . \) If the current flowing is 1.1 amperes, the drift velocity electrons will be :-
A . \( 0.01 \mathrm{mm} s^{-1} \)
B . 0.02 \( \mathrm{mm} \mathrm{s}^{-1} \)
c. \( 0.3 s^{-1} \)
D. 8 mm \( s^{-1} \)


Which would be larger : an atomic mass unit based on the current standard or
one based on the mass of a Be- 9 atom
\( \operatorname{set} \) at exactly 9 amu?


Name the type of joint between carpal/metacarpal of a thumb.


Define a relation \( \mathrm{R} \) on the set \( \mathrm{N} \) of
natural numbers by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{y}= \)
\( x+5, x \) is a natural number less than
\( \mathbf{4}, \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{N}\} \)
Depict this relationship using
(i) roster
form (ii) an arrow diagram. Write down the domain and range or \( \mathrm{R} \)


Which choice shows the answer to the
following mathematical operation with the correct number of significant figures?
\( \mathbf{1 4 . 5}-\mathbf{3 . 4 6}= \)
A . 11
B. 10
c. 11.04
D. 11.0
E . 11.4


In the given figure each capacitor is
equal to \( 45 \mu F \) then the equivalent
capacity between \( A \) and \( B \) in the given circuit is:
\( \mathbf{A} \cdot 15 \mu F \)
в. \( 10 \mu F \)
c. \( 40 \mu F \)
D. \( 135 \mu F \)


Suppose the potential energy between
electron and proton at a distance r is given by \( -\frac{k e^{2}}{r} . \) The value of \( -\left(V_{n} / K_{n}\right) \) is (Use Bohr's theory)


The most commonly used thermometric substance is
A. water
B. alcohol
c. mercury
D. none of these


Major role of minor elements inside
living organisms is to act as
A. cofactors of enzymes
B. Binder of cell structure
c. constitutent of hormones
D. Building blocks of amino acids


\( \ln \Delta \mathrm{ABC} \angle A=40^{\circ} \) and \( \angle B=60^{\circ} . \) The
longest side of triangle \( A B C \) is \( A B \)
A. True
B. False


Find the ratio of \( \sin x, \cos x, \tan x, \) where
\( \mathbf{x}=\mathbf{4 5}^{\mathbf{0}} ? \)


Which of the following solutions has the more capacity dissolve the solute in the
solvent?
A. Saturated solution
B. Unsaturated solution
c. super saturated solution
D. None of the above


Which of the following is correct for oxygen transport?
A. Nearly 20-25 percent of \( C O_{2} \) is transported by RBCs
B. 3 percent of \( O_{2} \) is carried in a dissolved state through the plasma
C. Maximum \( C O_{2} \) transport in the form of bicarbonate
D. Both B and C


Which pressure is responsible for
ascent of sap?
A. Negative hydrostatic pressure
B. Positive hydrostatic pressure
c. Root pressure
D. All of the above


The heat of combustion of glycogen is about \( 476 k J / m o l \) of carbon. Assume
that average rate of heat loss by an
adult male is 150 watt. If we were to
assume that all the heat comes from
oxidation of glycogen, how many units of glycogen (1 mole carbon per unit) must be oxidised per day to provide for this heat loss?


After the supernova explosion, the mass of remaining star should be greater than \( _{--}- \) times solar mass, only
then it turns into a black hole.
A.
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Non-metals are brittle while metals are
ductile. Why?
A. Because of lesser extent of bonding in non-metals
B. Because of greater extent of bonding in non-metals
C. Because of smaller size of non-metallic atoms
D. Because of lower conductivity of non-metals


\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} O(g)+800 k J . \) If a mole of \( O_{2}(g) \) is
consumed in the reaction, what energy
is produced?
A \( .200 k J \)
\( J \)
в. \( 400 k J \)
c. \( 800 k J \)
D. 1200 k \( J \)
E. \( 1600 k J \)


Which of the following exist as dimer:
A. NO
в. \( N O_{2} \)
\( \mathrm{c} \cdot P_{2} \mathrm{O}_{3} \)
D. All


Read a to d and tell the correct order of
components from outer side to inner
side in a woody dicot stem
(a) Secondary cortex
(b) Wood
(c) Secondary phloem
(d) Phellem.
A \( \cdot(\mathrm{c}),(\mathrm{d}),(\mathrm{b}), \) (a)
B. \( (a),(b),(d),(c) \)
\( D \cdot(d),(c),(a),(b) \)


In a permanent magnet at room
temperature
A. magnetic moment of each molecule is zero
B. the individual molecules have non-zero magnetic moment which are all perfectly aligned
C . domains are partially aligned
D. domains are all perfectly aligned


A body of mass \( 3 k g \) is under a constant force which causes a displacement s in metres in it given by the relation \( s= \) \( \frac{1}{3} t^{2}, \) where \( t \) is in a workdone by the
force in \( 2 s \) is


Identify chiral molecule among the following.
A. Isopropyl alcohol
B. Isobutyl alcohol
c. 2 -pentanol
D. 1-bromo-3-butene


\( 5 g \) of an unknown solute is dissolved in 295 g solvent. If molarity and density of solution are \( 0.05 \mathrm{M} \) and \( 1.5 \mathrm{g} / \mathrm{cc} \) respectively. The molecular weight of unknown solute is:
A . 375
в. 425
\( c .400 \)
D. 500


The sum of all real values of \( x \) satisfying the equation \( \left(x^{2}-5 x+5\right)^{x^{2}+4 x-60}=1 \)
is?


Assertion
Internal resistance of a battery is drawn
parallel to a battery in electricity circuit.
Reason
Heat generated in a battery is due to internal resistance.
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


The number of factors (excluding 1 and the expression itself) of the product of \( \boldsymbol{a}^{7} \boldsymbol{b}^{4} \boldsymbol{c}^{3} \) def where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f} \) are all
prime numbers is
A. 1278
B. 1360
c. 1100
D. 1005


Construct a \( \triangle P Q R, \) such that \( \angle Q=70^{\circ} \)
\( \angle R=70^{\circ} \) and \( P Q+Q R+R P=10 \)
\( \mathrm{cm} \)


The mass of a substance is 50 g and its specific heat is \( 0.09 \mathrm{cal} \mathrm{g}^{-1}^{o} \mathrm{C}^{-1}, \) then
its water equivalent is 45 g. State whether given statement is True/False
A. True
B. False


\( \boldsymbol{C H}_{3}-\boldsymbol{I}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}+\boldsymbol{I}-\boldsymbol{C} \boldsymbol{H}_{3} \stackrel{\text {dryether}}{\longrightarrow} \)
A \( \cdot C_{2} H_{5}-C_{2} H_{5} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C H_{3}-C H_{3} \)


The harmful substance to the plants is
A. Urea
в. \( H N O_{3} \)
\( c \cdot C O_{2} \)
D. \( N_{2} \)


Isobars have same number of atomic
mass.
A . True
B. False


In the following reaction \( 2 H_{2} O_{2}(a q) \rightarrow \)
\( 2 H_{2} O(l)+O_{2}(g) \) rate of formation of
\( O_{2} \) is \( 36 g . m i n^{-1} \)
(a) What is rate of formation of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
(b) What is rate of disappearance of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)


Which of the following is secant to the circle given above?
\( A \cdot A B \)
B. CD
\( c \cdot c \)
\( D . P O \)


\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { I) } \Psi^{2} \text { depends only upon distance } & \begin{array}{l}\text { a) } p- \\ \text { orbitals }\end{array} \\ \begin{array}{l}\text { 11) } \Psi^{2} \text { depends upon distance and on } \\ \text { one direction }\end{array} & \begin{array}{l}\text { b) } \mathrm{d}- \\ \text { orbital }\end{array} \\ \begin{array}{l}\text { III) } \Psi^{2} \text { depends upon distance and on } \\ \text { two directions }\end{array} & \begin{array}{l}\text { c) } \mathrm{f} \text { - } \\ \text { orbital }\end{array} \\ \begin{array}{l}\text { IV) } \Psi^{2} \text { depends upon distance and on } \\ \text { three directions }\end{array} & \begin{array}{l}\text { d) } \mathrm{s} \text { - } \\ \text { orbitals }\end{array}\end{array} \)
\( A \cdot|-d,| I-c,|I|-b, \mid V-a \)
B. \( |-c,||-b,|||-a, \mid V-d \)
C. \( |-d,| I-a,|I|-b, \mid V-c \)
D. I-d, II-a, III-c, IV-b


A cell of constant emf first connect to a
resistance \( R_{1} \) and then to connected to
the resistance \( R_{2} . \) If power delivered in
both cases in the same then internal
resistance of the cell
A. \( \frac{R_{1}-R_{2}}{2} \)
B \( . R_{1}+R_{2} \)
c. \( \sqrt{R_{1} R_{2}} \)
D. \( \sqrt{R_{1}+R_{2} / 2} \)


A choke coil and capacitor are connected in series and the current through the combination is maximum for \( A C \) of frequency \( n \). If they are connected in parallel, at what frequency is the current through the combination minimum?
\( A \)
в. \( n / 2 \)
\( c \cdot 2 n \)
D. None of these


BOD is related to
A. organic pollutants
B. Detergents
c. Putrescibility
D. Inorganic pollutants


If \( (3,2),\left(x, \frac{22}{5}\right),(8,8) \) lie on a line, then \( x \) is equal to
A . -5
B. 2
\( c \cdot 4 \)
D. 5


helps in burning.
A. Nitrogen
B. Carbon dioxide
c. oxygen
D. Ammonia


\( \boldsymbol{P}_{4}+\boldsymbol{6} \boldsymbol{C l}_{2} \rightarrow \)
A \( \cdot 2 P_{2} C l_{2} \)
B. \( 4 P C l_{3} \)
c. \( P C l_{6} \)
D. \( P_{2} C l_{5} \)


\( \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15} \)
A . \( 1 / 4 \)
в. \( 1 / 8 \)
c. \( 1 / 16 \)
D. \( 1 / 32 \)


The perimeter of a rectangle is \( 13 \mathrm{cm} \) and its width is \( 2 \frac{3}{4} \mathrm{cm} . \) Find its length.


For the equilibrium \( N H_{4} C l(s) \rightleftharpoons \)
\( N H_{3}(g)+H C l(g), K_{p}=16 a t m^{2} \)
The equilibrium pressure of the mixture is :
\( A \cdot 8 \)
B. 4
\( c \cdot 16 \)
D. 32


Mark the correct statement.
A. Metals are good conductor of heat and electricity.
B. Mercury is a poor conductor of heat.
c. Both \( A \) and \( B \)
D. None of the above


The most malleable metal is:
A. Silver
B. copper
c. Gold
D. Platinum


Last week Raul worked 11 more hours
than Angelica. If they worked a combined total of 59 hours, how many hours did Angelica work last week?
A .24
B. 35
c. 40
D. 48


Assertion
Formation of \( \boldsymbol{H} \boldsymbol{I} \) is a bimolecular
reaction
Reason
Two molecules of reactants are involved
in this reaction.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
C. Assertion is correct, but Reason is incorrect
D. Assertion is incorrect, but Reason is correct


An electrical charge of \( 2 \mu C \) is placed at the point \( (1,2,3) . \) At the point (2,3,4) the electric field and potential will be :
A \( \cdot 6 \times 10^{3} N C^{-1} \) and \( 6 \times 10^{3} J C^{-1} \)
B . \( 6000 N C^{-1} \) and \( 6000 \sqrt{3} J C^{-1} \)
c. \( 6 \times 10^{3} N C^{-1} \) and \( 3 \sqrt{3} J C^{-1} \)
D. none of the above


Find the values of \( x \) and \( y \) in the given
triangles, where \( \angle A=70^{\circ}, \angle B= \)
\( \mathbf{3 6}^{\circ}, \angle \boldsymbol{D}=\mathbf{6 8}^{\circ} \) and \( \angle \boldsymbol{F}=\mathbf{5 6}^{\circ} \)
A \( . x=103, y=80 \)
B . \( x=105, y=75 \)
C \( . x=105, y=87 \)


Give the names and atomic numbers of
the first and last members of the
actinide series


Milk of sulphur finds its application in:
A . Medicines
B. Photography
C. Head of match stick
D. Vulcanization


An echo is heard on a day when
temperature is about \( 22^{0} \) C. The echo
will be heard sooner when the
temperature is \( 40^{0} \mathrm{C} \) becuase
A. at higher temperature sound travels faster
B. at higher temperature sound reflects
c. at higher temperature sound travels slower
D. none of these


If \( Z \) is the atomic number of a one-
electron species and \( n \) is the orbit in which the electron is revolving, show that the number of revolutions made by
the electron in that orbit in 1 second
times is directly proportional to \( \frac{Z^{2}}{n^{3}} \)


Which among the following is a nonductile metal?
A. Tungsten
B. Leadd
c. Argentum
D. Mercury


The electric flux through the curve
surface of a cone. Due to a charge \( Q \)
placed at its mouth,
A. \( \phi=0 \)
в. \( \phi>\frac{Q}{2_{\varepsilon}} \)
c. \( _{\phi>\frac{Q}{\varepsilon_{0}}} \)
D. \( \phi=\frac{Q}{z_{0}} \)


If \( m \) th term of an AP is \( \frac{1}{n} \) and \( n \) th is \( \frac{1}{m} \) then show that \( (m n)^{t h} \) term of an AP is
1


The highest occupied energy band is called and lowest
unoccupied energy band is called the
A. Band Gap, conduction band
B. Valence band, Band Gap
c. conduction band, valence band
D. valence band, Conduction band


Read the following statements and mark them as True (T) or False (F)
(a) Plants can assimilate ammonium
ions only
(c) Rhizobium is an obligation anaerobe
(c) In legumes, the nodule is formed by the inner cortex and pericycle cells.


If \( \operatorname{cosec} \theta-\cot \theta=p, \) then \( \operatorname{cosec} \theta+ \)
\( \cot \theta= \)
\( A \cdot 1 / p \)
B. -1/p
\( c \cdot-p \)
D \( \cdot p^{2} \)


Nuisance growth of aquatic plants and bloom - forming algae in natural waters is generally due to high concentrations
of
A. Carbon
B. Sulphur
c. calcium
D. Phosphorus


The compound having least covalent
nature is:
A. \( A l C l_{3} \)
в. \( M g C l_{2} \)
c. \( N a C l \)
D. KCl


Two infinite parallel metal planes, contain electric charges with charge densities \( +\sigma \) and \( -\sigma \) respectively and
they are separated by a small distance
in air. If the permittivity of air is \( \epsilon_{0}, \) then
the magnitude of the field between the two planes with its direction will be:
A \( \cdot \sigma / \epsilon_{0} \) towards the positively charge plane
B . \( \sigma / \epsilon_{0} \) towards the negatively charged plane
C \( \cdot \sigma /\left(2 \epsilon_{0}\right) \) towards the positively charged plane
D. 0 and towards any direction


For inert monatomic gases, \( \frac{C_{P}}{C_{V}}=\frac{5}{x} \)
The value of \( x \) is


Four metallic plates each with a surface area of one side \( A \) are placed at a
distance \( d \) from each other as shown in
figure. Then the capacitance of the
system between \( X \) and \( Y \) is
A.
B. \( \frac{2 \epsilon_{0} A}{3 d} \)
c. \( \frac{3 \epsilon_{0} A}{d} \)
D.


What is the focal length of a convex lens of focal length \( 30 \mathrm{cm} \) in contact with a concave lens of focal length 20cm? Is
the system a converging or a diverging lens? Ignore thickness of the lenses.


What is the relation between restoring force \( (\boldsymbol{F}) \) and displacement \( (\boldsymbol{x}) \) of \( \mathbf{a} \) particle to perform SHM.
A \( . F \propto x^{2} \)
B. \( F \propto x^{-2} \)
c. \( F \propto x^{1 / 2} \)
D. \( F \propto x \)


In bessemer converter, oxides of
manganese and silicon are removed as:
A. manganese silicate
B. silica
c. magnesium oxide
D. none of these


A transition for \( H \) -atom from \( I I \) to \( I \)
orbit has same wavelength as from \( n^{t h} \)
orbit to \( 2^{n d} \) orbit for \( H e^{+} \) ion. The value
of \( ^{\prime} n^{\prime} \) is :
\( A \cdot 7 \)
B. 2
\( c .5 \)
D. 4


How many \( \alpha \) -hydrogen does this
carbocation has?
\( \boldsymbol{C H}_{3}-\begin{array}{c}C H_{3} \\ I \\ I \\ C H_{3}\end{array} \)


Find the derivative of \( e^{x} x^{n} \log _{a} x \)
A \( \cdot 2 e^{x} x^{n-1}\left\{n \log _{a} x+\frac{1}{\log _{e} a}+x \log _{a} x\right\} \)
В \( \cdot 3 e^{x} x^{n-1}\left\{n \log _{a} x+x \log _{a} x\right\} \)
c. \( e^{x} x^{n-1}\left\{n \log _{a} x+\frac{1}{\log _{e} a}+x \log _{a} x\right\} \)
D. \( e^{x} x^{n-1} \)


Air contains \( 79 \% N_{2} \) and \( 21 \% O_{2} \) by
volume. If the pressure is 750 of \( H g \), the
partial pressure of \( \boldsymbol{O}_{2} \) is:
A. 157.5 of \( H g \)
B. 175.5 of \( H g \)
c. 315.0 of \( H g \)
D. 257.5 of \( H g \)


(a) An iron ring of relative permeability
\( \mu_{r} \) has windings of insulated copper
wire of \( n \) turns per metre. When the
current in the windings is \( I \), find the expression for the magnetic field in the
ring.
(b) The susceptibility of a magnetic material is \( 0.9853 . \) Identify the type of magnetic material. Draw the modification of the field pattern on
keeping a piece of this material in a uniform magnetic field.


A circular arc \( (A B) \) of thin wire frame of radius \( R=\sqrt{2} \pi \mathrm{cm} \) and mass \( M \)
makes an angle of \( 90^{\circ} \) at the origin.Find the y co-ordinate of the CM. Taking 0 as the origin in \( \mathrm{cm} \)


Modern periodic table contains vertical columns.
A . 17
B. 19
c. 18
D. 20


If the force acting on a particle is zero then the quantities which are conserved
are :
A. momentum and angular momentum.
B. momentum and mechanical energy
c. momentum and charge
D. angular momentum and mechanical energy


Let \( A, B, C \) be three events such that \( A \) and \( \mathrm{B} \) are independent and \( \boldsymbol{P}(\boldsymbol{C})=\mathbf{0} \)
then events \( A, B, C \) are
A. independent
B. pairwise independent but not totally independent
C. \( P(A)=P(B)=P(C) \)
D. none of these


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


toppr
Q Type your question
the velocity of man with respect to
ground any how remains constant)
Plank is placed on smooth horizontal
surface. The man, while running
whistles with frequency \( f_{0} . \) A detector
(D) placed on plank detects frequency.
The man jumps off with same velocity (w.r.t. to ground) from point \( \mathrm{D} \) and slides on the smooth horizontal surface
[Assume coefficient of friction between
man and horizontal is zero]. The speed
of sound in still medium is \( 330 \mathrm{m} / \mathrm{s} \)
Answer following questions on the basis of above situations. Choose the correct
plot between the frequency detected by detector versus position of the man relative to detector:
\( A \)
B.
\( c \)
\( D \)


Splitting pf centromere and hence separation of chromatids occurs during
A. prophase-II
B. anaphase- -
c. anaphase -II
D. metaphase-I


toppr
Q Type your question
4
\( B \)
\( c \)
\( D \)


A potential difference v exists between
the ends of a metal wire of length I. The
drift velocity will be doubled if
A. v is doubled
B. I is doubled
c. The diameter of the wire is doubled
D. The temperature of the wire is doubled


Three types of tissue systems namely epidermal, fundamental and vascular, were proposed by
A. Hanstein
B. Buvat
c. sachs
D. Nageli


What is the energy band gap of silicon and germanium respectively in \( e V \) ?
A . 1.1,0.7
в. 0.7,1.1
c. -0.7,-1.1
D. -1.1,-0.7


Calculate the pressure exerted (in Pa) by \( 0.8 m \) vertical length of alcohol of density \( 0.8 g \mathrm{cm}^{-3} . \) (Acceleration due to
\( \left.\operatorname{gravity}(\boldsymbol{g})=10 m s^{-2}\right) \)


The maximum vertical distance
through which a fully dressed astronaut canjump on the earth is \( 0.5 \mathrm{m} \). If mean density of the moon is two thirds that of the earth and radius is one quarter that of the earth, the maximum vertical
distance through which he can jump on the moon and the ratio of time of
duration of the jump on the moon to
that on the earth are.
A. \( 3 \mathrm{m}, 6: \)
в. 6 m, 3:
\( c \cdot 3 m, 1: 6 \)
D. \( 6 \mathrm{m}, 1: 6 \)


Check whether \( 24 x^{3} y^{2} \) is a perfect cube or not. If not, find the smallest number
by which it should be divided to make it a perfect cube. Also, find the cube root of the perfect cube number so obtained.


Why does not all the now all the snow on
the mountains melt to water after
winter is over?


\( S_{N} 1 \) reaction feasible in
\( A \)
B.
c.
D.


If two lines intersect such that four
vertical angles are equal, then each angle is:
A . 45
B. 100
c. \( 180^{\circ} \)
D. \( 90^{\circ} \)


Vascular cambium forms
A. Secondary xylem and secondary phloem
B. Primary xylem and primary phloem
C. Only secondary phloem
D. Only primary xylem


f \( \triangle_{1}= \)
\( \mid \begin{array}{ccc}a_{1}^{2}+b_{1}+c_{1} & a_{1} a_{2}+b_{2}+c_{2} & a_{1} a_{3}+c \\ b_{1} b_{2}+c_{1} & b_{2}^{2}+c_{2} & b_{2} b_{3} \\ c_{3} c_{1} & c_{3} c_{2} & c_{3}^{2}\end{array} \)
and \( \triangle_{2}=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|, \) then \( \frac{\triangle_{1}}{\triangle_{2}} \) is
equal to
A \( \cdot a_{1} b_{2} c_{3} \)
B. \( a_{1} a_{2} a_{3} \)
\( c \cdot a_{3} b_{2} c \)
D. \( a_{1} b_{1} c_{1}+a_{2} b_{2} c_{2}+a_{3} b_{3} c_{3} \)


Three coins are tossed once. Let \( \boldsymbol{A} \)
denote the event 'three heads show", \( \boldsymbol{B} \)
denote the event "two heads and one tail
show" \( C \) denote the event "three tails
show" and \( D \) denote the event 'a head
shows on the first coin" Which events
are
(i) mutually exclusive?
(ii) simple?
(iii) compound?


Choose the correct reagent required to
carry out the transformation:
\( \mathbf{A} \cdot Z n+ \) conc. \( H C l \)
B. conc. \( H_{2} S O_{4} \)
\( \mathbf{c} \cdot L i, \) then \( H_{2} O \)
\( \mathbf{D} \cdot H_{2} / P t \)


Two guys in a room are feeling abnormalities. One of them wearing black suit and the other one wearing white suit are feeling different temperature on their body. Which of the following statements is correct :
A. Black suit guy will feel more heat due to its black colo
B. White suit guy will feel more heat due to its white color
c. Both will feel same heat
D. Neither A nor B


Molecules with multiple bonds between dissimilar atoms e.g., \( \boldsymbol{O}=\boldsymbol{C}= \)
\( \boldsymbol{O}, \boldsymbol{O}=\boldsymbol{S}=\boldsymbol{O} . \) How many \( \mathbf{S} \mathbf{0} \boldsymbol{\pi} \) bonds
are present in \( S O_{3} \), etc.


Which ones of the following animals are
invertebrates?
Housefly, silverfish, trout, jellyfish, whale, penguin, lizard and sponge.


Oxide, peroxide and superoxide - all the three can be formed by:
A. \( L i, K \)
в. \( N a, K \)
c. \( K, R b \)
D. \( N a, C s \)


In Cycas, the ovules are attached to
megasporophyll
A. Laterally
B. Dorsally
c. ventrally
D. Apically


The boiling point of a solution containing \( 68.4 \mathrm{g} \) of sucrose (molar
\( \left.\operatorname{mass}=342 g \operatorname{mol}^{-1}\right) \operatorname{in} 100 \) g of water
is:
\( \left[K_{b} \text { for water }=0.512 \mathrm{K} \mathrm{kg} \text { mol}^{-1}\right] \)
A \( \cdot 101.02^{\circ} \mathrm{C} \)
B . \( 100.512^{\circ} \mathrm{C} \)
c. \( 100.02^{\circ} \mathrm{c} \)
D. \( 98.98^{\circ} \mathrm{C} \)


In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
Number of winners
Prize for
each
\[
\begin{array}{rr}
50,000 \\
, 00,000
\end{array}
\]
winner (in Rs.)


Write the chemical reaction showing the bleaching action of chlorine.


A solution contains 200 g ppm \( C a C O_{3} \) If there is \( \frac{\boldsymbol{x} \times \boldsymbol{N}_{\boldsymbol{A}}}{\mathbf{1 0}^{\boldsymbol{6}}} \boldsymbol{C a C} \boldsymbol{O}_{3} \) molecules
per gram, what is the value of \( x ? \)


The stopping potential for the photo electrons emitted from a metal surface
of work function \( 1.7 e V \) is \( 10.4 V \)

Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of
wavelength equal to that of incident radiation for the above photoelectric effect.
A. \( n=3 \) to 1
B. \( n=3 \) to 2
\( c \cdot n=2 \) to 1
\( D \cdot n=4 \) to 1


The IUPAC name of is :
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{NH}-\mathrm{CH}_{3}
\]
A. Methyl ethyl amine
B. 1-methyl amino ethane
c. N-methyl ethanamine
D. N-ethyl ethanamine


Solve:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{(\boldsymbol{x}-\boldsymbol{y})+\boldsymbol{3}}{\boldsymbol{2}(\boldsymbol{x}-\boldsymbol{y})+\boldsymbol{5}} \)


Red algae is red due to the presence of
A. R-Phycocyanin
B. R-Phycoerythrin
c. c-Phycocyanin
D. c-Phycoerythrin


A straight line graph is obtained by plotting sine of angle of incidence versus sine of angle of refraction. The slope of this graph represents:
A. Velocity of light
B. Refractive index
c. Gravitational
D. None of these


An astronaut orbiting the earth in a circular orbit \( 120 k m \) above the surface
of earth, gently drops a ball from the spaceship. The ball will:
A. move randomly in space
B. move along with the spaceship
c. fall vertically down to earth
D. move away from the earth


Which of the following is an extensive
property?
A. mass
B. temperature
c. pressure
D. density


Find the \( Q \) value of the reaction
\( N^{14}+\alpha \rightarrow O^{17}+p \)
The masses of \( N^{14}, H e^{4}, p, \) and \( O^{17} \) are
respectively, 14.00307 u, \( 4.00260 u \) \( 1.00783 \mathrm{u}, \) and \( 16.99913 \mathrm{u} . \) Find the total
kinetic energy of the products if the striking \( \alpha- \) particle has the minimum kinetic energy required to initiate the
reaction:


Which of the following is the chemical formula of halothane?
A \( \cdot C F_{3} C H C l B r \)
в. \( C H_{3} \)СНСl Вт
c. \( C F_{3} C H_{2} \) br
D. None of the above


Find the total number of subsets of
each of the following set:
\( \boldsymbol{C}=\{\boldsymbol{x} \mid \boldsymbol{x} \in \boldsymbol{W}, \boldsymbol{x} \leq 2\} \)


According to 2011 census, the male literacy is highest in
A. Kerala
B. Maharashtra
c. Mizoram
D. west Bengal.


The force of gravity cannot act at a distance.
A . True
B. False


If \( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the G.M between \( a \) and \( b \)
then the value of \( n \) is
A. 0
B.
\( c \cdot \frac{1}{2} \)
D.


The critical volume of a gas is 0.036 lit.mol \( ^{-1} \). The radius of the molecule
will be (in \( \mathrm{cm} \) ):
(Avogadro Number \( =\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{)} \)
\( \left(\frac{9}{4 \pi} \times 10^{-23}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{B}}\left(\frac{8 \pi}{3} \times 10^{-23}\right)^{\frac{1}{3}} \)
\( \left(\frac{3}{8 \pi} \times 10^{-23}\right)^{\frac{1}{3}} \)
D. none of these


Which of the following halides doesn't hydrolyse?
A. \( P b C l_{4} \)
в. \( \operatorname{Si} C l_{4} \)
c. \( C C l_{4} \)
D. \( \operatorname{SnCl}_{4} \)


The double helix model of Watson and
Crick is known as
A. C-DNA
B. B-DNA
c. z-DNA
D. D-DNA


What is the principle of the method of a mixture? Name the law on which this
principle is based.
A. Newtons law of cooling
B. none
c. principle of calorimetry
D. principle of heat transfer


A mass \( M \) is split into two parts \( m \) and
\( (M-m) \) which are then separated by a
certain distance. The ratio \( \boldsymbol{m} / \boldsymbol{M} \) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1


\( \mathrm{If} \mathrm{A}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{l} & \boldsymbol{m} & \boldsymbol{n}\end{array}\right| \) is a skew-symmetric
matrix then which of the following is
equal to \( x+y+z ? \)
A. \( a+b+c \)
B. \( l+m+n \)
\( \mathrm{c} \cdot-b-m \)
D. \( c-l-n \)


The Sl unit of volume charge density is
\( \mathbf{A} \cdot C m^{-1} \)
в. \( C m^{-2} \)
\( \mathrm{c} \cdot \mathrm{Cm}^{-3} \)
\( \mathbf{D} \cdot C m^{-4} \)


What is the mass of photon of sodium light having a wavelength of 5890 , i? \( \left(\text { Given } h=6.6 \times 10^{-27} \text {erg }-\text { sec }\right) \)
\( \mathbf{A} \cdot 3.735 \times 10^{-29} g \)
В. \( 3.735 \times 10^{-33} g \)
c. \( 1.57 \times 10^{-33} g \)
D. \( 3.735 \times 10^{-31} g \)


The strongest base among the following
is:
A. \( C_{6} H_{5} N H_{2} \)
B . \( p-N H_{2} C_{6} H_{4} N H_{2} \)
\( \mathrm{c} \cdot m-N O_{2} C_{6} H_{4} N H_{2} \)
D. \( C_{6} H_{5} C H_{2} N H_{2} \)


The value of \( \sqrt[3]{-a^{3}} \times \sqrt[3]{-b^{3}} \) is
\( A \cdot a \)
B.
\( c \cdot a b \)
D. none of these


Which of the following factors affect pressure? This question has multiple correct options
A. Area
B. Accleration
c. Force
D. None


In a diagram of \( \Delta A B C \) and \( \Delta D E F \)
below, \( \boldsymbol{B C} \cong \boldsymbol{E} \boldsymbol{F}, \angle \boldsymbol{B} \cong \angle \boldsymbol{E} \) and \( \angle \boldsymbol{A} \cong \)
\( \angle D . \) Which method can be used to prove
\( \Delta A B C \cong \Delta D E F ? \)
A. AAA congruence
B. SAS congruence
C. AAS congruence
D. SSS congruence


Consider the table given below
Marks \( \begin{array}{llll}0- & 10- & 20- & 30- \\ 10 & 20 & 30 & 40\end{array} \)
Number
of
Students
\[
\begin{array}{lll}
18 & 27 & 20
\end{array}
\]
12
The arithmetic mean of the marks given above is
A . 18
B. 28
\( c \cdot 27 \)
D. 6


Complex conjugate of \( 3 \mathrm{i}-4 \) is
\( A \cdot 3 i+4 \)
B. - 3i- 4
\( c \cdot-3 i+4 \)
D. None of these


Convert \( \pi / 6 \) rad to degrees.


Find the area of the shaded portion in
the given figure, where \( A B C D \) is a
square of side \( 14 \mathrm{cm} \) and semicircles
are drawn with each side of square as
diameter.


Which of the following is paramagnetic?
A \( \cdot V(C O)_{6} \)
в. \( F e(C O)_{5} \)
c. \( F e_{2}(C O)_{9} \)
D. \( \operatorname{Cr}(\text {CO})_{6} \)


If \( \bar{a}, \bar{b}, \bar{c} \) are the vertices of a triangle \( A B C, \) then \( |\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|= \)
A. Area of the triangle \( \Delta A B C \)
B. Two times area of the triangle \( \Delta A B C \)
C. Three times area of the triangle \( \Delta A B C \)
D. Four times area of the triangle \( \Delta A B C \)


When the reaction of \( B r_{2} \) with acetone
is catalysed by hydroxide ion, which of the following are the likely products?
A \( . C H B r_{3} \) and acetate ion
B. Bromoacentic acid
C. Tribromoacetic acid
D. Acetyl bromide


Why are some covalent molecules
polar?
\( A \cdot O \)


Assertion
Froth floatation process is based on the
different wetting nature of ore and gangue particles.
Reason
Mustard oil is used as brother in froth
floation process.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Select the correct order of polarity of the
bond for the following molecules:
\( \mathbf{A} \cdot N H_{3}<S b H_{3}<A s H_{3}<P H_{3} \)
B. \( N H_{3}<P H_{3}<S b H_{3}<A s H_{3} \)
\( \mathbf{c} \cdot N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \)
\( \mathbf{D} \cdot N H_{3}>S b H_{3}>A s H_{3}>P H_{3} \)


Match the compounds in column I with
their
characteristic(s)/test(s)/reaction(s)/re agent(s)/stereochemistry/isomer(s) given in column II. Matching can be one or more than one.


Which of the following is not a type of lightning?
A. Intracloud (IC)
B. Cloud to Cloud (CC)
c. Cloud to Ground (CG)
D. Ground to Cloud (GC)


Find the standard deviation of the
numbers 62,58,53,50,63,52,55


Among the following compounds, the most acidic is :
A. p-nitrophenol
B. p-hydroxybenzoic acid
c. o-hydroxybenzene acid
D. p-toluic acid


There is desorption of physical adsorption when :
A. temperature is increased
B. temperature is decreased
c. pressure is increased
D. concentration is increased


Which is the nitrogenous base present only in RNA, but not in DNA?


Lichens multiply by
A. Soredia formation
B. Bud formation
c. Conidia formation
D. Oidia formation


Phenol is more acidic than:
A . acetic acid
B. p-methoxyphenol
c. p-nitropheno
D. 2, 4 dinitropheno


Prove:
\( \sin ^{-1}\left(\frac{1}{x}\right)=\operatorname{cosec}^{-1} x, \forall x \geq 1 \) or \( x \leq \)
-1
\( \cos ^{-1}\left(\frac{1}{x}\right)=\sec ^{-1} x, \forall x \geq 1 \) or \( x \leq \)
-1
\( \tan ^{-1}\left(\frac{1}{x}\right)=\cot ^{-1} x, \quad \forall x>0 \)


If the line \( y-m x+m-1=0 \) cuts the
\( \operatorname{circle} x^{2}+y^{2}-4 x-4 y+4=0 \) at two
real points, then \( m \) belongs to
A . [1,1]
B . [-2,2]
\( c \cdot(-\infty, \infty) \)
D. [-4,4]


Which molecule electrolysis
temperature is maximum?
\( \mathbf{A} \cdot A s H_{3} \)
B . \( N H_{3} \)
\( \mathbf{c} \cdot P H_{3} \)
\( \mathbf{D} \cdot S b H_{3} \)


The displacement-time graph being a straight line inclined to the time axis implies
A. that the body is at rest
B. that the body is moving with uniform velocity
c. that the body is moving with increasing velocity
D. that the body is moving with decreasing velocity


Two long and parallel straight wires \( A \) and B carrying currents of \( 8.0 \mathrm{A} \) and 5.0 A in the same direction are separated by a distance of \( 4.0 \mathrm{cm} . \) Estimate the force on a \( 10 \mathrm{cm} \) section of wire \( \mathrm{A} \)


The individual plates composing the
earth's crust are called


A steel bolt is inserted into a copper
tube as shown in figure. Find the forces induced in the bolt and in the tube when
the nut is turned through one revolution. Assume that the length of the tube is \( l \), the pitch of the bolt thread
is \( h \) and the cross-sectional areas of the
steel bolt and the copper tube are \( \boldsymbol{A}_{s} \)
and \( A_{c}, \) respectively


The hydrogen ion concentration of a 10
-8 M \( H C l \) aqueous solution at \( 298 \mathrm{K} \) is:
\( \left[\text { Given that: } \boldsymbol{K}_{\boldsymbol{w}}=10^{-14}\right] \)
A . \( 1.0 \times 10^{-6} \) М
В. \( 1.0525 \times 10^{-7} \) М
c. \( 9.525 \times 10^{-8} \) М
D. \( 1.0 \times 10^{-8} \) М


Atomic orbitals involved in
hybridization of \( S F_{6} \) molecule:
B . \( 3 s, 3 p_{x}, 3 p_{y}, 3 p_{z}, 3 d_{z} \)
\( \mathbf{c} \cdot 4 s, 4 p_{x}, 4 p_{y}, 4 p_{z}, 3 d_{x^{2}-y^{2}}, d_{x y} \)
D. \( 3 s, 3 p_{x}, 3 p_{y}, 3 d_{x y}, 3 d_{d z}, 3 d_{x z} \)


Set up an equation of a tangent to the graph of the following function. A cone is circumscribed about a sphere
of radius R. The vertex angle in the
axial section of the cone is \( 2 \alpha \). Find the
area of the axial section of the cone.
At what value of \( \alpha \) is the area of the
cone the least?


For real number \( x \) and \( y, \) define \( x R y \) iff \( x-y+\sqrt{2} \) is an irrational number
Then the relation \( R \) is
A. reflexive
B. symmetric
c. transitive
D. none of these


Solve the equation \( : \cot x-2 \sin 2 x=1 \)
A \( \cdot x=\frac{\pi}{8}+\frac{K \pi}{2} \)
в. \( x=\frac{\pi}{4}+\frac{K \pi}{4} \)
c. \( _{x}=\frac{\pi}{6}+\frac{K \pi}{3} \)
D. \( x=\frac{2 \pi}{3}+\frac{K \pi}{3} \)


State whether true or false:
A bulb is used in place of LED to detect
weak currents.
A. True
B. False


An elevator is going up vertically with a
constant acceleration of \( 2 \mathrm{m} / \mathrm{s}^{2} \). at the
instant when its velocity is \( 4 \mathrm{m} / \mathrm{s} \) a ball is projected from the floor of the elevator with a speed of \( 4 \mathrm{m} / \mathrm{s} \) relative to the floor with an angular elevation of
\( 30^{\circ} . \) the time taken by te ball to return
to the floor is : (take \( g=10 m / s^{2} \) )
A \( \cdot \frac{1}{3} \mathrm{sec} \)
B. \( \frac{1}{\sqrt{3}} \sec \)
c. \( \frac{2}{\sqrt{3}} \sec \)
D. \( \sqrt{3} \mathrm{sec} \)


Simplify the following using laws of
exponents. \( \left(\frac{3}{5}\right)^{4} \times\left(\frac{3}{5}\right)^{3} \times\left(\frac{3}{5}\right)^{8} \)


When a bus starts suddenly, the passengers are pushed backwards. Which of the following laws is illustrated in this example?
A. Newton's first law
B. Newton's second law
c. Newton's third law
D. None of Newton's laws


Number of atoms in 12 gm of \( _{6}^{12} C \) are:
A. 6
B. 12
c. \( 6.02 \times 10^{23} \)
D. \( 6 \times 6.02 \times 10^{23} \)


If \( A=1 \) and \( B=0, \) then in terms of
Boolean algebra the value of \( A . A+B \) is
A . \( A \)
B. \( B^{2} \)
\( c . B \)
D . \( A \cdot B \)


During the extraction of \( \mathrm{Ag} \) and \( \mathrm{Au} \) using a KCN solution,cyanide ions react with metal ions as:
This question has multiple correct options
A. a reducing agent
B. a complexing agent
c. a oxidizing agent
D. a Lewis base


Evaluate the integral \( \int_{0}^{\pi} x \sin ^{5} x \cos ^{6} x d x=? \)
A \( \cdot \frac{5 \pi}{16} \)
в. \( \frac{35 \pi}{128} \)
c. \( \frac{5 \pi}{8} \)
D. \( \frac{8 \pi}{693} \)


The number of primary and secondary hydroxyl groups in ribose are:
A . 1,3
в. 2,3
c. \( 3, \)
D. 3,2


Which one of the following element is present in the eyes of certain animals?
A. zinc
B. Copper
c. Gold
D. Potassium


In the P-V diagram shown, the gas does
\( 5 J \) of work in isothermal process ab and
\( 4 J \) in adiabatic process \( b c . \) What will be
the change in internal energy of the gas in straight path \( c \) to \( a \) ?
\( A \cdot 9 J \)
B. \( 1 . \)
c. \( 4 . \)
D. 5 .


Which lists elements in order of
increasing ionization energy?
A \( . S<S^{+}<S^{-} \)
B . \( S^{+}<S^{-}<S \)
c. \( S^{-}<S<S^{+} \)
D. \( S^{+}<S<S^{-} \)


Calculate the mean using step deviation method.
\begin{tabular}{|l|l|l|l|l|}
\hline Number of pages & 20 & 40 & 60 & 80 \\
\hline Number of articles & 3 & 6 & 9 & 12 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 62 \)
B. 63
\( \mathbf{c} \cdot 64 \)
D. 65


\( A \) nail has \( 2 m^{2} \) at one end and \( \frac{1}{100} m^{2} \) at other end. A force of \( 10 N \) is applied
on the first end. Calculate the pressure
acting on the wall? The answer is \( \boldsymbol{p} \times \)
\( 10^{3} P a \) then \( p= \)


Identify the correct order of phases for
the cell cycle?
I. \( G_{2} \) phase- growth and preparation for mitosis
II. Mitosis
III. \( G_{1} \) phase-cell growth
IV.S phase - DNA copied
V. Cytokinesis
в. ॥॥, ।, IV, v, II
c. ॥, ॥॥, ।, IV, v
D. IV, III, 1, , I, v
E. \( \mathrm{V}, \) ॥I, IV, ।, ।


For the system shown in figure, the
pulleys are light and frictionless. The tension in the string will be:
A \( \cdot(2 / 3) m g \sin \theta \)
B. \( (3 / 2) m g \sin \theta \)
\( c .(1 / 2) m g \sin \theta \)
D. \( 2 m g \sin \theta \)


A buffer of \( p H=9.26 \) is made by
dissolving \( x \) moles of ammonium sulphate and 0.1 mole of ammonia into
\( 100 \mathrm{mL} \) solution. If \( p K_{b} \) of ammonia is
4.74, calculate value of \( x \)


Bring about the following conversion
1-pentene \( \rightarrow 1- \) pentyne


two neighboring coils. A and B have mutual inductance of \( 20 \mathrm{mH} \). The
current flowing through A is given by \( i=3 t^{2}-4 t+6 . \) The induced emf at \( t= \)
2s is:
A . \( 100 m V \)
В. \( 160 m V \)
c. 260 \( \mathrm{mv} \)
D. 300 mv


The proper burial of dead for the first time started with which of the
following prehistoric man?
A. Peking man
B. Neanderthal man
c. Java man
D. Cro-Magnon man


A closed system receives \( 200 k J \) of
constant volume. It then rejects \( 100 k J \) of heat while it has \( 50 k J \) of work done
on it at constant pressure. If an adiabatic process can be found which can be found which will restore the
system to its initial state, the work done by the system during this process is
A. \( 100 k J \)
J \( J \)
B. \( 50 k J \)
c. \( 150 k J \)
D. 200 k


Select the correct match:
A. T. H. Morgan - Transduction
B. Ribozyme - Nucleic acid
C. G. Mendel - Transformation
D. \( F_{2} \times \) Recessive parent - Dihybrid cross


The difference between the supplement
of an angle and the angle is \( 36^{\circ} . \) The
supplement is:
A .72
B. \( 108^{\circ} \)
\( c \cdot 63 \)
D. 27


Angle of dip at a place is \( 60^{0} \) and earth's magnetic field is \( 8 \mu T . \) Its horizontal
component \( \boldsymbol{B}_{\boldsymbol{H}} \) is :
A \( .4 \sqrt{3 \mu} T \)
в. \( 4 \mu T \)
c. \( \frac{8}{\sqrt{3}} \mu T \)
D. \( 8 \sqrt{3 \mu} T \)


In the figure, measure of \( \angle x \) is
\( \mathbf{A} \cdot 65^{\circ} \)
B \( .85^{\circ} \)
\( c \cdot 75 \)
D. 55


Distinguish between the term overloading and short circuiting as
used in domestic circuits


What is a buffer?
A. A solution that contains equal amounts of a weak acid and its conjugate base, or a weak base and its conjugate acid.
B. A solution that contains both a strong acid and a base.
C. A solution that contains an acid
D. A solution that contains equal amounts of a strong acid and its conjugate base, or a strong base and its conjugate acid.
E. A solution that contains a base.


Each of the resistance in the network
shown in figure is equal to R. The
resistance between the terminals \( A \) and
B is
\( A \cdot R \)
B. 5R
\( c . \) 3R
\( D \cdot 6 r \)


For the gas-phase decomposition,
\( \boldsymbol{P C I}_{5}(\boldsymbol{g}) \triangle \rightleftharpoons \boldsymbol{P C I}_{3}(\boldsymbol{g})+\boldsymbol{C I}_{2}(\boldsymbol{g}) \)
A. \( \triangle H<0, \Delta S<0 \)
B. \( \triangle H>0, \Delta S>0 \)
c. \( \triangle H>0, \Delta S<0 \)
D. \( \triangle H<0, \Delta S>0 \)


Which of the following options shows the correct measurements of an adult
human kidney?
A. \( 10-12 \mathrm{cm} 5-7 \mathrm{cm} 2-3 \mathrm{cm} \)
\( 120-170 \mathrm{g} \)
B. \( 10-20 \mathrm{cm} 10-12 \mathrm{cm} 6-12 \mathrm{cm} \)
\( 40-50 \mathrm{g} \)
c. \( 2-6 \mathrm{cm} 8-10 \mathrm{cm} 5-10 \mathrm{cm} \)
\( 60-70 \mathrm{g} \)
D. \( 10-12 \mathrm{mm} 5-7 \mathrm{mm} 2-3 \mathrm{mm} \)
\( 120-170 \mathrm{mg} \)


In a region where intensity of electric field is \( 5 N C^{-1}, 40 \) lines of electric force are
crossing per square metre. The number of lines crossing per square metre where
intensity of electric field is \( 10 N C^{-1} \) will
be:
A . 20
B. 80
c. 100
D. 200


The histogram shows the age groups of
working women in a city. Find the
number of working women in the age
group of \( 29-34 \) years
\( A \cdot 300 \)
3. 230
\( c .320 \)
D. 41


Coralloid roots are found in
A. Pea
B. Fern
c. cycas
D. Pinus


Which is the strongest oxidizing agent?
A. \( \mathrm{F}_{2} \)
в. \( \mathrm{Cl}_{2} \)
\( c \cdot \) Вг \( _{2} \)
D. \( I_{2} \)


For the pulley system shown in
Fig.6.317, each of the cables at \( A \) and \( B \)
is given a velocity of \( 2 m s^{-1} \) in the
direction of the arrow. Determine the
upward velocity v of the load \( m \)
A \( \cdot 1.5 m s^{-} \)
\( \mathbf{B} \cdot 3 m s^{-1} \)
\( c \cdot 63 s^{-1} \)
D. \( 4.5 m s^{-} \)


Show that: \( \cos ^{-1} \frac{4}{5}+\cos ^{-1} \frac{12}{13}= \)
\( \cos ^{-1} \frac{33}{65} \)


A uniform rod of length one meter is
bent at its midpoint to make \( 90^{0} \). The
distance of centre of mass from the
centre of rod is(in cm)?
A . 20.2
в. 13.4
c. 15
D. 35.36


Evaluate: \( \int_{0}^{\pi / 8} \cos ^{3} 4 x d x \)
A . \( 1 / 6 \)
в. \( 1 / 5 \)
c. \( -1 / 3 \)
D. 1/


Prove that external angle is sum of the
opposite interior angle.


Which of the following pairs consist of non-ionic compounds?
A. \( K C l \) and \( H C l \)
B. \( H C l \) and \( C C l_{4} \)
c. \( N a C l \) and \( C a O \)
D. \( N a C l \) and \( H_{2} O \)


Distinguish between conductor and semiconductor on the basis of band
theory of solids.


Arid soil is formed in western
Rajasthan. Its main features are:
I. Arid soils range from red to yellow in colour.
II. They are generally sandy and saline.
III. Humus and moisture content is very low due to dry climate and faster evaporation.
IV. Thorny bushes are found in this region
B. Only II and III
c. only I, II and i v
D. Only II, III and IV


A ray of light is incident on a
rectangular plate at an angle of
incidence \( 60^{\circ} . \) The light ray suffers a
deviation which is \( 25 \% \) of the angle of incidence. The refractive index of the
glass will be
A \( \cdot \sqrt{3} \)
B. \( \sqrt{2} \)
c. \( \sqrt{\frac{3}{2}} \)
D. 1.5


Dictyostelium is
A. Cellular slime mould
B. Plasmodial slime mould
C. Water mould
D. None of the above


A bi-convex lens is formed with two thin
plano-convex lenses as shown in the figure. The refractive index n of the first
lens is 1.5 and that of the second lens is
1.2 Both the curved surfaces are of the
same radius of curvature \( \boldsymbol{R}=\mathbf{1 4 c m} \)
For this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance
will be
\( \mathbf{A} \cdot-280.0 \mathrm{cm} \)
в. \( 40.0 \mathrm{cm} \)
c. \( 21.5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)


A letter is known to have come either
from \( L O N D O N \) or \( C L I F T O N ; \) on the
postmark only the two consecutive letters \( \boldsymbol{O} \boldsymbol{N} \) are ellegible. The probability that it came from \( L O N D O N \) is
A \( \cdot \frac{5}{17} \)
в. \( \frac{12}{17} \)
c. \( \frac{17}{30} \)
D. \( \frac{3}{5} \)


Bony fishes can stay at any particular depth in water without spending energy
due to presence of
A. Operculum
B. Tympanum
c. Pneumatic bones
D. Swim bladder


If \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) are in A.P., then \( \boldsymbol{2} \boldsymbol{y}= \)
\( \mathbf{A} \cdot x+z \)
B. \( x-z \)
c. \( \sqrt{x y} \)
D. \( x z \)


Choose the wrong statement of the following:
A. The peak voltage across the inductor can be less than the peak voltage of the source in an LCR circuit
B. In a circuit containing and a capacitor and an ac source the current is zero at the instant source voltage is maximum
C. When an AC source is connected to a capacitor, then the rms current in the circuit gets increased if a dielectric slab is inserted into the capacitor
D. In a pure inductive circuit emf will be in phase with the current


Pyruvate dehydrogenase is used in converting
A. Glucose to Pyruvate
B. Pyruvic acid to Lactic acid
c. Pyruvate to Acetyl CoA
D. Pyruvate to Glucose


Which one of the following is not correct
\( ? \)
A \( \cdot \frac{(\sin A+\sin B)}{(\sin A-\sin B)}=\frac{\tan \frac{1+\beta}{2}}{\tan \frac{1-B}{2}} \)
\( \mathbf{B} \cdot \sin ^{2} A-\cos ^{2} B=\sin (A+B) \sin (A-B) \)
C \( \cdot \cos A-\cos B=2 \cos \frac{A+B}{2} \cos \frac{B-A}{2} \)
\( \mathbf{D} \cdot \cos ^{2} A-\cos ^{2} B=\sin (A+B) \sin (B-A) \)


The velocity of light in air is \( 3 \times \)
\( 10^{8} m s^{-1} \) and that in water is \( 2.2 \times \)
\( 10^{8} m s^{-1} . \) The polarising angle of
incidence is:
A . 45
B. \( 50^{\circ} \)
c. \( 53.74^{\circ} \)
D. \( 63^{\circ} \)


Which of the following acids are unsaturated one:

This question has multiple correct options
A. Stearic acid
B. Acrylic acid
c. Oleic acid
D. crotonic acid


If the extremities of a diagonal of a
square are (1,-2,3) and (2,-3,5)
then area of the square is
\( A \cdot 6 \)
B. 3
\( c \cdot \frac{3}{2} \)
D. \( \sqrt{3} \)


Define one coulomb charge.


toppr
Q Type your question_
across the resistor wire AB. A
standard cell which maintains a
constant emf of \( 1.02 \mathrm{V} \) (for very
moderate currents up to a few mA)
gives a balance point at \( 67.3 \mathrm{cm} \) length of the wire. To ensure very low currents drawn from the standard cell, a
very high resistance of 600 \( \mathrm{k} \Omega \) is put in series with it, which is shorted close to
the balance point. The standard cell is
then replaced by a cell of unknown emf
and the balance point found similarly, turns out to be at \( 82.3 \mathrm{cm} \) length of the
wire.(a) What is the value \( \varepsilon ?(b) \) What
purpose does the high resistance of 600
k \( \Omega \) have?(c) Is the balance point
affected by this high resistance?
(d) Is
the balance point affected by the internal resistance of the driver cell?
(e) Would the method work in the above
situation if the driver cell of the
potentiometer had an emf of \( 1.0 \mathrm{V} \) instead of 2.0 V?(f) Would the circuit
work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of a thermocouple)? If not, how will you modify the
circuit?


The water potential of pure water changes when solute is added to it


Weightlessness in the satellite is due to
A. zero gravitational acceleration
B. zero acceleration
c. zero mass
D. None of these


\( \frac{\boldsymbol{d}^{2} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}^{2}} \) equals
\( \mathbf{A} \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{-1} \)
B \( \cdot-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3} \)
C \( \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-2} \)
D \( \cdot\left(-\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-2} \)


Draw a circle. Let AB be diameter. Let P
is point on circle. Construct angle bisector of \( \angle P . \) The bisector
A. cuts diameter between B and centre
B. cuts diameter between A and centre
c. cuts diameter A and B at centre
D. none


The bond dissociation energies of
\( X_{2}, Y_{2} \) and \( X Y \) are in the ratio of 1
\( 0.5: 1 . \Delta H \) for the formation of \( X Y \) is
\( -200 k J m o l^{-1} . \) The bond dissociation
energy of \( \boldsymbol{X}_{2} \) will be:
В. 200 kJ mol-
c. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 100 k J mol\( ^{-} \)


Human eye lens is
A. Spherical and can be moved forward
B. Biconvex and cannot be moved forward.
C. Spherical and cannot be moved forward.
D. Biconvex and can be moved forward


In addition reactions of aldehydes, the carbonyl carbon atom changes from:
A \( \cdot s p^{3} \) to \( s p^{2} \)
B \( \cdot s p^{2} \) to \( s p^{3} \)
c. \( s p \) to \( s p^{3} \)
D. \( s p^{3} \) to sp


located as shown in the diagram. What
is the direction of the net force on the
charge at location \( P \), from the other two?
\( A \)
B.
\( c \)
D.


A liquid thermometer uses the property of expansion of liquids.
A. True
B. False


Consider the following two statements A and B and identify the correct choice
A) The torques produced by two forces of couple are opposite to each other
B) The direction of torque is always perpendicular to plane of rotation of body
A. A is true but B is false
B. A is false but B is true
c. Both A and B are true
D. Both A and B are false


Magnetic field which keeps the
particles in circular path must
A. remain a constant everywhere
B. increase gradually with a rate proportional to kinetic energy of the particle
C. increase gradually with a rate proportional to speed of the particle
D. none of these


A force of \( 10 \mathrm{N} \) is resolved into the
perpendicular components. If the first
component makes \( 30^{0} \) with the force
the magnitudes of the components are:
A . 5N, 5N
B . \( 5 \sqrt{2} \mathrm{N}, \) 5N
\( \mathbf{c} \cdot 5 \sqrt{3} \mathbf{N}, 5 \mathrm{N} \)
D. \( 10 \mathrm{N}, 1 \sqrt{3} \mathrm{N} \)


The output of a step down transformer
is measured to be \( 48 V \) when connected
to a \( 12 W \) bulb. The value of peak
current is
A \( \cdot \sqrt{2} A \)
в. \( \frac{1}{2 \sqrt{2}} A \)
c. \( \frac{1}{4} A \)
D. \( \frac{1}{\sqrt{2}} A \)


Polaroid glasses protect our eyes from:
A. ultraviolet rays
B. cold
c. heat
D. dryness


If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right], \) then show that \( |3 A|= \)
\( \mathbf{9}|\boldsymbol{A}| \)


Coefficient of deviation is calculated by the formula:
A \( \cdot \frac{\bar{X}}{\sigma} \times 100 \)
в. \( \frac{\bar{X}}{\sigma} \)
\( ^{\mathrm{c}} \cdot \frac{\sigma}{\bar{X}} \times 100 \)
D. \( \frac{\sigma}{\bar{X}} \)


What is the effect of temperature on
chemisorption?


What is the necessary for combustion?
A. Fuel
B. Supply of oxygen
c. source of ignition
D. All of the above


Assertion
In chemisorption, adsorption keeps on increasing with temperature.
Reason
Heat keeps on providing more and more
activation energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \ln \) an oscillating \( L-C \) circuit in which
\( C=4.00 \mu F, \) the maximum potential
across the capacitor during the oscillations is \( 1.50 V \) and the maximum
current through the inductor is \( 50.0 m A \)
What is the frequency of the oscillations?


Which of following is the incorrect
match?
A. Insulin - zinc
B. Haemoglobin - Iron
c. Vitamin \( B_{12} \) - cobalt
D. chlorophyll - chromium


Find out which of the following equations have \( x=2, y=1 \) as a
solution:
\( 2 x+3 y=1 \)


Let \( A_{1}, G_{1} \) and \( H_{1} \) denote the
arithmetic, geometric and harmonic
means respectively of two distinct
positive numbers. For \( n \geq 2, \) let \( A_{n-1} \)
and \( H_{n-1} \) have arithmetic, geometric
and harmonic means as \( \boldsymbol{A}_{n}, \boldsymbol{G}_{n}, \boldsymbol{H}_{n} \)
respectively. Which of the following statements is
correct?
\( \mathbf{A} \cdot A_{1}>A_{2}>A_{3}>\dots \)
B . \( A_{1}<A_{2}<A_{3}<\dots . . . \)
C \( \cdot A_{1}>A_{3}>A_{5} \ldots \) and \( A_{2}<A_{4}<A_{6}<\ldots \)
D. \( A_{1}<A_{3}<A_{5}<\ldots . . \) and \( A_{2}>A_{4}>A_{6}>\ldots . \)


Examine the continuity of the function:
\( f(x)=\frac{\log 100+\log (0.01+x)}{3 x}, \) for
\( \boldsymbol{x} \neq \mathbf{0} \)
\( =\frac{\mathbf{1 0 0}}{\mathbf{3}} \quad \) for \( \boldsymbol{x}= \)
\( \mathbf{0} ; \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}=\mathbf{0} \)


The statement that is not correct is :
\( \mathbf{A} \cdot \) in solid state \( P C l_{5} \) exists as \( \left[P C l_{4}\right]^{+}\left[P C l_{6}\right]^{-} \)
B. phosphorous acid on heating disproportionates to give metaphosphoric acid and phosphine
C. hypophosphorous acid reduces silver nitrate to silver
D. pure phosphine is non-inflammable


In genetic coding, triplet codons make
possible 64 types of codons. If the genetic code was a doublet instead of a triplet codon, the number of types of codons possible would be
A. 64 types of codons
B. 4 types of codons
c. 24 types of codons
D. 16 types of codons


What is the expression for the electrical power spent in flow of current through a conductor in terms of
resistance and potential difference?
A. \( V^{2} / R \)
в. \( V / R^{2} \)
c. \( V R \)
D \( \cdot V^{2} R \)


LASER is an acronym for light amplification by
A. Stimulated energetic radiation
B. Spontaneous emission of radiation
c. Stimulated emission of radiation
D. Spontaneous emission of radio waves


What is the out put of the given logic gate?
\( \mathbf{A} \cdot A \cdot B \)
в. \( \bar{A} \cdot \bar{B} \)
c. \( \bar{A}+\bar{B} \)
D. \( A+B \)


What kind of a colloidal solution is an
emulsion?
A. Solid dispersed in solid
B. Liquid dispersed in liquid
c. Gas dispersed in liquid
D. Liquid dispersed in solid


In adsorption, the substance which accumulates on the surface of the other
substance is termed as
A. adsorbate
B. adsorbent
c. accumulator
D. none


Given the species \( N_{2}, C O, N O^{+} \) and
\( C N^{-} \) which of the following statements
are true for this :
(I) All the species are diamagnetic
(II) All the species are isostructural
(III) All the species have identical bond order
(IV) More than one species have zero dipole moment
A. I, II and III
B. ।, ॥, III and IV
c. III and IV
D. I and II


Three vertical poles of heights \( h_{1}, h_{2} \)
and \( h_{3} \) at the vertices \( A, B \) and \( C \) of \( a \)
\( \triangle A B C \) subtend angles \( \alpha, \beta, \gamma \)
respectively at the circumcentre of the triangle. If \( \cot \alpha, \cot \beta, \cot \gamma \) are in \( A P \)
then \( h_{1}, h_{2}, h_{3} \) are in
\( A \cdot A P \)
в. GР
c. нр
D. None of these


If the thickness of a pile of 12 cardboards is \( 35 \mathrm{mm} \), find the thickness of a pile of 294 cardboards.


In which of the following autfnau principle is violated?
\( A \)
\( \frac{\uparrow}{2 s} \) \begin{tabular}{c|c|c}
\hline\( \uparrow \downarrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline \( \mathbf{2 p} \) & & \\
\hline
\end{tabular}
B. \( \frac{\sqrt{1} \downarrow}{2 s} \)
\( c \)
\( \uparrow \downarrow \) \begin{tabular}{c|c|c|}
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline \( 2 p \) & & \\
\hline
\end{tabular} \( 2 \mathrm{s} \)
\( D \)
\( \frac{\sqrt{1} \mid}{2 s} \) \begin{tabular}{c|c|c|c|c|}
\hline\( \uparrow \downarrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline \( 2 p \) & & & \\
\hline
\end{tabular}


If \( \left(\frac{1+i}{1-i}\right)^{m}=1, \) the least positive
integral value of \( m \) is \( \ldots \)


The middle term in the expansion of \( (x / 2+2)^{8} \) is \( 1120, \) then \( x \varepsilon R \) is equal to This question has multiple correct options
A . -2
B. 3
\( c .-3 \)
D. 2


In the circuit shown in fig. the heat
produced in \( 5 \Omega \) resistor due to a current
flowing in it is 10 cal /s. The heat
produced in \( 4 \Omega \) resistor is -
A. 4 cal 1 s
B. 1 cal /s
c. 2 cal / s
D. 3 cal /s


Let \( X \) denote the number of time tail
appear in \( n \) tosses of a fair coin. If
\( \boldsymbol{P}(\boldsymbol{X}=\mathbf{1}), \boldsymbol{P}(\boldsymbol{X}=\mathbf{2}) \) and
\( \boldsymbol{P}(\boldsymbol{X}=\mathbf{3}) \) are in A.P., then value of \( \boldsymbol{n} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B . 2
\( c \cdot 7 \)
D. None of these


Concentrated strong acid is added to a
solid mixture of 0.015 mole samples of
\( F e(O H)_{2} \) and \( C a(O H)_{2} \) placed in one litre of water. At what value of \( \mathrm{pH} \) will the dissolution of each hydroxide be
complete? (Assume negligible volume change) \( \boldsymbol{K}_{s p}\left[\boldsymbol{F e}(\boldsymbol{O H})_{2}\right]=\mathbf{7 . 9} \times \mathbf{1 0}^{-15} \) and
\( \boldsymbol{K}_{s p}\left[\boldsymbol{C u}(\boldsymbol{O} \boldsymbol{H})_{2}\right]=\mathbf{1 . 6} \times \mathbf{1 0}^{-19} \)
A . 6.67
в. 7.86
\( c .8 .86 \)
D. 7.26


Which of the following are dilution dependent but temperature independent? This question has multiple correct options
A. Formality
B. Molality
c. Mole fraction
D. Molarity


The fungus associated with discovery and source of gibberellins is
A. Fusarium oxysporum
B. Fusarium solanii
c. Fusarium moniliforms
D. Fusarium longipes


The refractive index of glass is \( 1.5 . \) From a point \( P \) inside a glass block, draw rays \( P A, P B \) and \( P C \) incident on the
glass-air surface at an angle of incidence \( 30^{\circ}, 42^{\circ} \) and \( 60^{\circ} \)
respectively. What is the angle of
refraction for the ray \( \boldsymbol{P} \boldsymbol{B} \) ? (Take
\( \sin 42^{\circ}=\frac{2}{3} \)
A \( \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Which of the following is an example of vic-dihalide?
A. Dichloromethane
B. 1, 2-Dichloroethane
c. Ethylidene chloride
D. Allyl chloride


The figure shows the variation of internal energy (U) with the pressure (P)
of 2.0 mole gas in cyclic process abcda.
The temperature of the gas at \( c \) and \( d \) are \( 300 \mathrm{K} \) and \( 500 \mathrm{K} \). Calculate the heat
absorbed by the gas during the process.
\( A \cdot 400 \mathrm{R} \ln 2 \)
B. 200 R \( \ln 2 \)
\( c \cdot 100 \mathrm{R} \ln 2 \)
D. 300 R In 2


A vessel of volume 5 litre contains \( 1.4 g \) of nitrogen at a temperature \( 1800 K \)
The pressure of the gas if \( 30 \% \) of its molecules are dissociated into atoms
at this temperature is :
A. 4.05 atm
B. 2.025 atm
c. 3.84 atm
D. 1.92 atm


\( E^{0} \) for the cell, \( Z n\left|Z n^{2+}_{(a q)}\right|\left|C u^{2+}_{(a q)}\right| C u \) is
\( 1.10 V \) at \( 25^{0} C . \) The equilibrium constant
for \( Z n+C u^{2+}_{(a q)} \rightarrow Z n^{2+}_{(a q)}+C u \) the cell
reaction is of the order of :
A \( \cdot 10^{-37} \)
B. \( 10^{37} \)
D. \( 10^{17} \)


If the system of inequalities \( y \geq 2 x+1 \)
and \( y>\frac{1}{2} x-1 \) is graphed in the \( x y \)
plane above, which quadrant contains
no solutions to the system?
B. Quadrant III
c. Quadrant IV
D. There are solutions in all four quadrants


The phenomenon by which the incident light falling on a surface is sent back into the same medium is known as
A. Refraction
B. reflection
c. Total internal reflection
D. Both B and C


\( \begin{array}{ll}\begin{array}{l}\text { List - I } \\ \text { (Compound) }\end{array} & \begin{array}{l}\text { List - II } \\ \text { (Oxidation no of sulphur) }\end{array} \\ \text { A) } H_{2} S_{2} O_{8} & \text { 1) }+1 \\ \text { B) } H_{2} S & \text { 2) }+2 \\ \text { C) } N a_{2} S O_{3} & \text { 3) }+6 \\ \text { D) } S_{2} C l_{2} & \text { 4) }+4 \\ \text { 5) }-2\end{array} \)
\( \mathbf{A} \)
\( A-3 . B-5 . C-4 . D-2 \)
\( \mathrm{B} \cdot \mathrm{A}-3, \mathrm{B}-5, \mathrm{C}-4, \mathrm{D}-1 \)
\( \mathrm{C} \cdot \mathrm{A}-6, \mathrm{B}-5, \mathrm{C}-4, \mathrm{D}-2 \)
\( D \cdot A-6, B-4, C-5, D-1 \)


Statement 1: Bakelite is hard and has
high melting point.

Statement 2: Intermolecular forces of
attraction in it are H-bonding.
A. Statement 1 is true; statement 2 is true; statement 2 is the correct explanation of statement
B. Statement 1 is true; statement 2 is true; statement 2 is not the correct explanation of statement 1
c. Statement 1 is true; statement 2 is false
D. Statement 1 is false; statement 2 is true


Write general term of this:-
\( 2 x\left(3+2 x^{2}\right)^{20} \)


The mean and variance of eight
observation are 9 and \( 9.25, \) respectively.
If six of the observation are
6,7,10,12,12 and \( 13, \) find the remaining two observations.


\( 0.29 g \) of an organic compound containing phosphorous gave 0.887 g of \( M g_{2} P_{2} O_{7} \) by the usual analysis. Calculate the percentage of phosphorous in the compound.
A . 45.8\%
B. 85.48\%
c. \( 83.7 \% \)
D. 72.2\%


What is scattering of light?


\( A \) and \( B \) alternately cut a pack of cards
which is shuffled after each cut. The
game is started by \( A \) and continuous until one of the players cuts a club. The probability that \( B \) win the game is \( k / 7 \) Find \( k \)


Two angles measure \( (30-a)^{\circ} \) and
\( (125+2 a)^{\circ} . \) If each one is the
supplement of the other, then the value
of a is:
A . 45
B. 35
\( c \cdot 25 \)
D. \( 65^{\circ} \)


Which of the following statements is/are true regarding anti conformation of 1-chloropropane? This question has multiple correct options
A. It is the most polar form.
B. It has the maximum torsional strain
c. It has the minimum steric strain.
D. It has the minimum torsional strain


Consider the three long,straight,parallel wires as shown in figure.Find the force experienced by a \( 25 \mathrm{cm} \) length of wire \( \mathrm{C} \)
A \( \cdot 2 \times 10^{-4} N \)
B. \( 3 \times 10^{-4} N \)
c. \( 5 \times 10^{-4} N \)
D. \( 6 \times 10^{-4} N \)


Which of the following compounds has the highest melting point??
A. o-dibromobenzene
B. m-dibromobenzene
c. p-dibromobenzene
D. bromobenzene


Garlic is
A. Allium cepa
B. Allium sativum
C . Hyacinthus orientalis
D. Convallaria majalis


A sphere of radius 3 ems is dropped into a cylindrical vessel of radius \( 4 \mathrm{cms} \). If the sphere is submerged completely, then the height (in \( \mathrm{cm} \) ) to which the water rises, is
A . 2.35
B. 2.30
c. 2.25
D. 2.15


The equation normal to the curve \( \boldsymbol{x}^{2 / 3}+\boldsymbol{y}^{2 / 3}=\boldsymbol{a}^{2 / 3} \) at the point \( (\boldsymbol{a}, \boldsymbol{0}) \) is
\( \mathbf{A} \cdot x=a \)
B. \( x=-a \)
\( \mathbf{c} \cdot y=a \)
D. \( y=-a \)


A car covers a distance of \( 160 \mathrm{km} \)
between two cities in \( 4 h . \) What is the
average speed of the car?


The headquarters of IUCN are at
A. North America
B. Rome
c. South America
D. Switzerland


Which of the following is not true for \( \mathbf{7}^{\mathbf{1 4}} ? \)
A. 14 is the mass number
B. 7 is the atomic number
C. \( \mathrm{N} \) is the symbol for nitrogen
D. 14 is the atomic number


Which one of the following bonds has the highest bond energy?
A \( . C-C \)
в. \( s i-s i \)
c. \( G e-G e \)
\( \mathbf{D} \cdot S n-S n \)


If \( A \) be a skew symmetric matrix of
order \( m \) than \( A+A^{\prime} \) is a
A. Nilpotent matrix
B. Orthogonal matrix
c. Null matrix
D. Skew symmetric


Stomata of CAM plants
A. Never open
B. Are always open
C . Open during the day and close at night
D. Open during the night and close during the day


Chile salt petre is the nitrate mineral of
A. potassium
B. sodium
c. calcium
D. lithium


Calculate pH of a solution whose \( 100 \mathrm{m} \)
contains \( 0.2 \mathrm{g} \) NaOH dissolved in it?
A . 10.699
в. 11.699
c. 12.699
D. 13.699


In which of the following properties does an animal and a plant differ?
A. Presence of organs
B. Growth
c. Reproduction
D. synthesis of food


In the electrical network, at \( t<0 \) (as
given in the figure), key is placed on (1)
till the capacitor got fully charged. Key
is placed on (2) at \( t=0 . \) Time when the
energy in both the capacitor and the
inductor will be same for the first time
is
A \( \cdot \frac{\pi}{4} \sqrt{L C} \)
B. \( \frac{3 \pi}{4} \sqrt{L C} \)
C \( \cdot \frac{\pi}{3} \sqrt{L C} \)
D. \( \frac{2 \pi}{3} \sqrt{L C} \)


Which of the following is/are true?
This question has multiple correct options
A. Two unit vectors may not be equal unless they have the same direction.
B. A unit vector is self reciprocal.
C. Two unit vectors may be equal irrespective of their direction.
D. All of the above are correct.


A carnot engine having an efficiency of \( \frac{1}{10} \) as heat engine, is used as a refrigerator. If the work done on the system is \( 10 J \), the amount of energy
absorbed from the reservoir at lower
temperature is :
\begin{tabular}{l}
A. \( 100 J \) \\
\hline
\end{tabular}
в. \( 1 . \)
c. \( 90 J \)
D. \( 99 . J \)


Identify \( (\boldsymbol{E}): \)
\( (a) S i \frac{H N O_{3} / H F}{c o n c, \Delta} \quad(A) \quad \stackrel{H F}{\rightarrow}(B) \)
\( \downarrow \)
\( (B)+(C) \)
(b)Graphite \( ^{h o t \operatorname{conc} H N O_{3}}(D) \)
\( (\mathrm{c}) N a_{2} C O_{3}+S i \rightarrow(E) \)
fused
A \( \cdot(E):\left(N a_{2} C O_{2}+S i O\right) \)
B . \( (E):\left(N a_{2} C O+S i O_{2}\right) \)
C \( \cdot(E):\left(N a_{2} \operatorname{Si} O_{3}+C\right) \)
D. None of these


Which out of the following statements
is false?
A. Avogadro's number \( =6.02 \times 10^{21} \)
B. The relationship between average velocity \( (\bar{v}) \) and the root mean square velocity \( (u) \) is \( \bar{v}=0.9213 u \)
C. The mean kinetic energy of an ideal gas is independent of the pressure of the gas
D. The root mean square velocity of the gas can be
calculated by the formula \( \left(\frac{3 R T}{M_{W}}\right)^{\frac{1}{2}} \)


Ship \( A \) is travelling with a velocity of
\( 5 k m h^{-1} \) due east. A second ship is
heading \( 30^{\circ} \) east of north. What should be the speed of second ship if it is to remain always due north with respect to the first ship?
A \( \cdot 10 \mathrm{kmh}^{-1} \)
B. \( 9 \mathrm{kmh}^{-1} \)
\( \mathbf{c} \cdot 8 k m h^{-1} \)
D. \( 7 \mathrm{kmh}^{-1} \)


A \( 2 p \) -orbital is -1 .
A. spherically
B. cylindrically
\( c \cdot \) not
D. none of these


Find the equation of the straight line
equally inclined to the lines, \( 3 x=4 y+ \)
7 and \( 5 y=12 x+6 \)


Which of the following is a microbial pesticide?
A. Rotenone
B. Thurioside
c. Baygon
D. Temik


\( \cos \left(\cot ^{-1}\left(\operatorname{cosec}\left(\cos ^{-1} a\right)\right)\right)=\dots \)
(where \( 0<a<1) \)
A \( \cdot \frac{1}{\sqrt{2-a^{2}}} \)
B. \( \sqrt{3-a^{2}} \)
c. \( \sqrt{2-a^{2}} \)
D. \( \frac{1}{\sqrt{2+a^{2}}} \)


Two morphologically similar populations are intersterile. They belong
to
A. One species
B. Two biospecies
c. Two sibling species
D. None of the above


If \( \boldsymbol{A}(\boldsymbol{y}, \mathbf{2}), \boldsymbol{B}(\mathbf{1}, \boldsymbol{y}) \) and \( \boldsymbol{A} \boldsymbol{B}=\mathbf{5}, \) then the
possible values are
A .6,2
B. 5,-2
c. -2,-6
D. 2,0


Find the degree of each algebraic
expression
\( 2 y^{2} z+10 y z \)


The compound from which formic acid
cannot be prepared is.
A. Methyl alcohol
B. Carbon monoxide + NaOH
c. Glycerol
D. Methyl magneisum bromide


An alternating emf given by equation \( \boldsymbol{E}=\mathbf{3 0 0} \sin [(\mathbf{1 0 0} \boldsymbol{\pi}) \boldsymbol{t}] \) volt is applied to
a resistance 100 ohms. The rms current
through the circuit is (in amperes):
\( ^{A} \cdot \frac{3}{\sqrt{2}} \)
в. \( \frac{9}{\sqrt{2}} \)
\( c \cdot 3 \)
D. \( \frac{6}{\sqrt{2}} \)


Name the plant having reticulate venation.
A. Musa
B. Mangifera
c. oryza
D. canna


When 96500 coulombs of electricity are passed through nickel sulphate solution, the amount of nicke
deposited will be:
A . 1 mol
\( c .0 .1 \mathrm{mol} \)
D. 2 mol


Find out the unit and dimentions of the the vander waal's equation pressure P,V is volume and \( R \) is gas constant:


The common area between the curve
\( x^{2}+y^{2}=8 \) and \( y^{2}=2 x \) is
A \( \cdot \frac{4}{3}+2 \pi \)
B. \( (2 \sqrt{2}+\pi-1) \)
c. \( (\sqrt{2}+\pi-1) \)
D. None of these


An electron moves with velocity \( \vec{v}=a \hat{k} \) in a magnetic field, \( \vec{B}=b \hat{i}+c \hat{j} \). Find the magnetic force on the electron.


The curve \( y^{2}=(x-1)(x-2)^{2} \) is not
defined for
\( \mathbf{A} \cdot x \geq 1 \)
B. \( x \geq 2 \)
c. \( x<2 \)
D. \( x<1 \)


An alternating current can be produced
by:
A. transformer
B. generator
c. turbine
D. electric motor


If a diffraction peak is observed when
electrons are incident at an angle \( ^{\prime} \boldsymbol{i}^{\prime} \)
from the normal to the crystal planes
with distance ' \( d^{\prime} \) between them (see
figure), de-Broglie wavelength \( \lambda_{d B} \) of
electrons can be calculated by the
relationship \( (n \text { is an integer }) \)
\( \mathbf{A} \cdot d \sin i=n \lambda_{d B} \)
B . \( 2 d \cos i=n \lambda_{d B} \)
\( \mathbf{c} \cdot 2 d \sin i=n \lambda_{d B} \)
\( \mathbf{D} \cdot d \cos i=n \lambda_{d B} \)


Lightning generally strikes on high rise buildings. Give reason


Which nitrogen is maximum basic:
\( A \)
B.
\( c \)
D. All are equally basic


Which one of the following statements
is not correct?
A. The pH of \( 1.0 \times 10^{-8} \mathrm{M} \mathrm{HCl} \) is less than 7
B. The ionic product of water at \( 25^{0} C \) is \( 1.0 \times \) \( 10^{-14} \mathrm{mol}^{2} L^{-2} \)
C \( \cdot C l^{-} \) is a Lewis acid
D. Bronsted-Lowry theory cannot explain the acidic character of \( A l C l_{3} \)


The area of the triangle formed by the points (2,6),(10,0) and \( (0, k) \) is zero square units. Find the value of \( k \)
A \( \cdot \frac{15}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{7}{2} \)
D. \( \frac{13}{2} \)


To draw a maximum current from a
combination of cells,how should the
cells be grouped?
A. Parallel
B. Series
c. Mixed grouping
D. Depends upon the relative values of internal and external resistances


A total of 324 coins of 20 paise and 25 paise make a sum of \( R s .71 \), the number
of 25 paise coins is
A . 124
в. 140
c. 200
D. 210


Two equal point charges \( Q=\sqrt{2} \mu C \) are
placed at each of the two opposite
corners of a square and equal point -
charges \( q \) at each of the other two
corner.What must be the value of \( \boldsymbol{q} \) so
that the resultant force on \( Q \) is zero?


In single slit diffraction pattern
A. Centre fringe has negligible width than others.
B. All fringes are of same width
C . Central fringe does not exist
D. None of the above


Which of the following is the product of phosphorylation?
A . PGA
B. Fructose 1,6-diphosphate
c. DPGA
D. Pyruvic acid


A narrow tube is bent in the form of a
circle of radius \( R, \) as shown in the
figure. Two small holes \( S \) and \( D \) are made in the tube at the positions right
angle to each other. A source placed at
S generated a wave of intensity \( l_{0} \) which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point \( D \) where a detector is placed. If the minima is formed at the detector then,
the magnitude of wavelength \( \lambda \) of the wave produced is given by :
This question has multiple correct options
A. \( 2 \pi R \)
R
R. \( 2 \pi \)
в. \( \frac{3 \pi R}{2} \)
c. \( \frac{2 \pi R}{3} \)
D. \( \frac{2 \pi R}{5} \)


The ratio of wavelength corresponding
to maximum emission of radiation 1:
195. The ratio of their temperature will
be
\( \mathbf{A} \cdot(195)^{2}: 1 \)
B. 1: 195
\( \mathbf{c} \cdot(195)^{4}: 1 \)
D. 195: 1


Find the remainder when \( p(x)=x^{3}- \)
\( 4 x^{2}+3 x+1 \) is divided by \( (x-1) \)


\( \boldsymbol{p}(\boldsymbol{y})=\mathbf{5} \boldsymbol{y}^{3}-\boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1 0} \) is a
polynomial in \( y \) of degree
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


The area of the plane region bounded by
the curve \( x+2 y^{2}=0 \) and \( x+3 y^{2}=1 \)
is equal to:
A \( \cdot-\frac{4}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. None of these


A gas is compressed at a constant
pressure of \( 50 N / m^{2} \) from a volume of
\( 10 m^{3} \) to a volume of \( 4 m^{3} . \) Energy of 100
Jis then added to the gas by heating. Its internal energy is
A. increased by 400
B. increased by 200 J
c. increased by 100 J
D. decreased by 200


Select the correct statement regarding the specific disorder of muscular or
skeletal system.
A. osteoporosis - decrease in bone mass and higher chances of fractures with advancing age
B. Myasthenia gravis- auto immune disorder which inhibits sliding of myosin filaments
c. Gout-inflammation of joints due to extra deposition of calcium
D. Muscular dystrophy - age related shortening of muslces


In physical adsorption Zeolite(A/B)'s applications are seperation of \( n \) paraffins and i paraffins etc.
A. True
B. False


Arboretum is a botanical garden where
A. Bonsai are made
B. Beautification is done
C. Palms are grown
D. Big trees are cultivated in the form of forests


In plants, food is transported through
the
A. Companion cell
B. Sieve tubes
c. Tracheids
D. vessels


Two hydrogen atoms collide head-on
and end up with zero kinetic energy. Each then emits a photon with a wavelength \( 121.6 n m . \) Which transition
leads to this wavelength? How fast were
the hydrogen atoms travelling before
the collision?
(Given, \( \boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 . 0 9 7} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}} \) and
\( \boldsymbol{m}_{\boldsymbol{H}}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k g} \boldsymbol{\jmath} \)


The no. of cells which may be
constructed with different \( E_{c e l l}^{o} \) values
for the reaction
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \rightarrow \boldsymbol{3} \boldsymbol{F} \boldsymbol{e}^{2+} \boldsymbol{i} \boldsymbol{s} \)


Use of pesticides decreases water
pollution
A. True
B. False


A heating coil is dipped in a bucket filled with water. Explain the significant mechanisms in heat flow.
A. Heat from coil is transferred by conduction to both water and bucket
B. Heat from coil is transferred by convection to both water and bucket
c. Heat from coil is transferred by conduction to water. In water, heat flow occurs by convection and bucket gains heat from water by conduction
D. None of the above